LMFDB - Embedded newform 162.2.g.a.157.3

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:	$72$
Relative dimension:	$4$ over $\Q(\zeta_{27})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{27}]$

Embedding invariants

Embedding label			157.3
Character	$\chi$	$=$	162.157
Dual form			162.2.g.a.97.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.973045 + 0.230616i) q^{2} +(0.877898 - 1.49308i) q^{3} +(0.893633 - 0.448799i) q^{4} +(2.62112 + 3.52077i) q^{5} +(-0.509905 + 1.65529i) q^{6} +(-1.50529 + 0.990045i) q^{7} +(-0.766044 + 0.642788i) q^{8} +(-1.45859 - 2.62155i) q^{9} +O(q^{10})$	\(q+(-0.973045 + 0.230616i) q^{2} +(0.877898 - 1.49308i) q^{3} +(0.893633 - 0.448799i) q^{4} +(2.62112 + 3.52077i) q^{5} +(-0.509905 + 1.65529i) q^{6} +(-1.50529 + 0.990045i) q^{7} +(-0.766044 + 0.642788i) q^{8} +(-1.45859 - 2.62155i) q^{9} +(-3.36241 - 2.82140i) q^{10} +(3.24055 + 0.378766i) q^{11} +(0.114424 - 1.72827i) q^{12} +(0.00477752 + 0.0159580i) q^{13} +(1.23640 - 1.31050i) q^{14} +(7.55787 - 0.822666i) q^{15} +(0.597159 - 0.802123i) q^{16} +(-0.143186 + 0.812048i) q^{17} +(2.02384 + 2.21451i) q^{18} +(-1.34727 - 7.64077i) q^{19} +(3.92243 + 1.96992i) q^{20} +(0.156728 + 3.11668i) q^{21} +(-3.24055 + 0.378766i) q^{22} +(0.461994 + 0.303858i) q^{23} +(0.287226 + 1.70807i) q^{24} +(-4.09155 + 13.6667i) q^{25} +(-0.00832891 - 0.0144261i) q^{26} +(-5.19468 - 0.123655i) q^{27} +(-0.900845 + 1.56031i) q^{28} +(-2.21818 - 2.35113i) q^{29} +(-7.16443 + 2.54346i) q^{30} +(0.266376 - 4.57350i) q^{31} +(-0.396080 + 0.918216i) q^{32} +(3.41040 - 4.50589i) q^{33} +(-0.0479448 - 0.823180i) q^{34} +(-7.43126 - 2.70476i) q^{35} +(-2.47999 - 1.68809i) q^{36} +(3.29981 - 1.20103i) q^{37} +(3.07304 + 7.12411i) q^{38} +(0.0280208 + 0.00687629i) q^{39} +(-4.27100 - 1.01225i) q^{40} +(-10.4740 - 2.48239i) q^{41} +(-0.871259 - 2.99653i) q^{42} +(-2.30508 - 5.34378i) q^{43} +(3.06585 - 1.11588i) q^{44} +(5.40673 - 12.0067i) q^{45} +(-0.519616 - 0.189125i) q^{46} +(0.636051 + 10.9206i) q^{47} +(-0.673392 - 1.59579i) q^{48} +(-1.48685 + 3.44690i) q^{49} +(0.829498 - 14.2419i) q^{50} +(1.08675 + 0.926683i) q^{51} +(0.0114313 + 0.0121165i) q^{52} +(-2.34748 + 4.06596i) q^{53} +(5.08317 - 1.07765i) q^{54} +(7.16031 + 12.4020i) q^{55} +(0.516731 - 1.72600i) q^{56} +(-12.5911 - 4.69623i) q^{57} +(2.70059 + 1.77621i) q^{58} +(-3.16212 + 0.369599i) q^{59} +(6.38475 - 4.12713i) q^{60} +(1.76186 + 0.884840i) q^{61} +(0.795526 + 4.51165i) q^{62} +(4.79105 + 2.50212i) q^{63} +(0.173648 - 0.984808i) q^{64} +(-0.0436621 + 0.0586484i) q^{65} +(-2.27934 + 5.17092i) q^{66} +(-1.44772 + 1.53450i) q^{67} +(0.236491 + 0.789934i) q^{68} +(0.859269 - 0.423039i) q^{69} +(7.85471 + 0.918084i) q^{70} +(-7.37631 - 6.18946i) q^{71} +(2.80244 + 1.07066i) q^{72} +(4.83291 - 4.05529i) q^{73} +(-2.93389 + 1.92965i) q^{74} +(16.8136 + 18.1070i) q^{75} +(-4.63314 - 6.22339i) q^{76} +(-5.25296 + 2.63814i) q^{77} +(-0.0288513 - 0.000228888i) q^{78} +(4.63409 - 1.09830i) q^{79} +4.38931 q^{80} +(-4.74503 + 7.64753i) q^{81} +10.7642 q^{82} +(6.63975 - 1.57365i) q^{83} +(1.53882 + 2.71483i) q^{84} +(-3.23434 + 1.62435i) q^{85} +(3.47531 + 4.66815i) q^{86} +(-5.45777 + 1.24787i) q^{87} +(-2.72587 + 1.79283i) q^{88} +(9.83956 - 8.25637i) q^{89} +(-2.49205 + 12.9300i) q^{90} +(-0.0229907 - 0.0192915i) q^{91} +(0.549224 + 0.0641951i) q^{92} +(-6.59476 - 4.41279i) q^{93} +(-3.13736 - 10.4795i) q^{94} +(23.3700 - 24.7708i) q^{95} +(1.02325 + 1.39748i) q^{96} +(-5.09273 + 6.84073i) q^{97} +(0.651860 - 3.69688i) q^{98} +(-3.73368 - 9.04772i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q + 9 q^{6}+O(q^{10}) $ 72 * q + 9 * q^6	$ 72 q + 9 q^{6} + 18 q^{13} - 9 q^{20} - 81 q^{23} + 18 q^{25} - 27 q^{26} - 27 q^{27} + 18 q^{28} - 27 q^{29} - 63 q^{30} - 54 q^{31} + 9 q^{33} - 27 q^{35} - 9 q^{36} + 9 q^{38} - 9 q^{41} + 9 q^{42} + 36 q^{43} - 117 q^{45} - 18 q^{46} - 27 q^{47} + 9 q^{48} - 27 q^{51} - 36 q^{52} - 27 q^{53} + 54 q^{55} + 27 q^{57} + 9 q^{58} - 18 q^{59} + 9 q^{63} + 9 q^{65} + 36 q^{66} - 135 q^{67} - 18 q^{68} + 108 q^{69} + 18 q^{70} + 72 q^{71} + 54 q^{72} + 36 q^{73} + 99 q^{74} - 36 q^{75} - 9 q^{76} + 144 q^{77} + 90 q^{78} - 9 q^{79} + 18 q^{80} - 72 q^{82} + 99 q^{83} + 18 q^{84} + 9 q^{85} + 72 q^{86} + 207 q^{87} - 9 q^{88} + 126 q^{89} - 18 q^{90} + 63 q^{91} + 36 q^{92} + 81 q^{93} + 18 q^{94} + 45 q^{95} - 171 q^{97} + 36 q^{98} + 99 q^{99}+O(q^{100}) $ 72 * q + 9 * q^6 + 18 * q^13 - 9 * q^20 - 81 * q^23 + 18 * q^25 - 27 * q^26 - 27 * q^27 + 18 * q^28 - 27 * q^29 - 63 * q^30 - 54 * q^31 + 9 * q^33 - 27 * q^35 - 9 * q^36 + 9 * q^38 - 9 * q^41 + 9 * q^42 + 36 * q^43 - 117 * q^45 - 18 * q^46 - 27 * q^47 + 9 * q^48 - 27 * q^51 - 36 * q^52 - 27 * q^53 + 54 * q^55 + 27 * q^57 + 9 * q^58 - 18 * q^59 + 9 * q^63 + 9 * q^65 + 36 * q^66 - 135 * q^67 - 18 * q^68 + 108 * q^69 + 18 * q^70 + 72 * q^71 + 54 * q^72 + 36 * q^73 + 99 * q^74 - 36 * q^75 - 9 * q^76 + 144 * q^77 + 90 * q^78 - 9 * q^79 + 18 * q^80 - 72 * q^82 + 99 * q^83 + 18 * q^84 + 9 * q^85 + 72 * q^86 + 207 * q^87 - 9 * q^88 + 126 * q^89 - 18 * q^90 + 63 * q^91 + 36 * q^92 + 81 * q^93 + 18 * q^94 + 45 * q^95 - 171 * q^97 + 36 * q^98 + 99 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$83$
$\chi(n)$	$e\left(\frac{25}{27}\right)$

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 $

$2$	−0.973045	+	0.230616i	−0.688047	+	0.163070i
$2$	−0.973045	+	0.230616i	−0.688047	+	0.163070i
$3$	0.877898	−	1.49308i	0.506855	−	0.862032i
$3$	0.877898	−	1.49308i	0.506855	−	0.862032i
$4$	0.893633	−	0.448799i	0.446816	−	0.224400i
$5$	2.62112	+	3.52077i	1.17220	+	1.57454i	0.739758	+	0.672873i	$0.234940\pi$
$5$	2.62112	+	3.52077i	1.17220	+	1.57454i	0.432441	+	0.901662i	$0.357652\pi$
$6$	−0.509905	+	1.65529i	−0.208168	+	0.675771i
$7$	−1.50529	+	0.990045i	−0.568946	+	0.374202i	−0.801148	−	0.598466i	$-0.795777\pi$
$7$	−1.50529	+	0.990045i	−0.568946	+	0.374202i	0.232202	+	0.972668i	$0.425407\pi$
$8$	−0.766044	+	0.642788i	−0.270838	+	0.227260i
$9$	−1.45859	−	2.62155i	−0.486197	−	0.873849i
$10$	−3.36241	−	2.82140i	−1.06329	−	0.892204i
$11$	3.24055	+	0.378766i	0.977062	+	0.114202i	0.589610	−	0.807688i	$-0.299281\pi$
$11$	3.24055	+	0.378766i	0.977062	+	0.114202i	0.387452	+	0.921890i	$0.373355\pi$
$12$	0.114424	−	1.72827i	0.0330314	−	0.498908i
$13$	0.00477752	+	0.0159580i	0.00132505	+	0.00442596i	0.958649	−	0.284589i	$-0.0918573\pi$
$13$	0.00477752	+	0.0159580i	0.00132505	+	0.00442596i	−0.957324	+	0.289015i	$0.906672\pi$
$14$	1.23640	−	1.31050i	0.330440	−	0.350246i
$15$	7.55787	−	0.822666i	1.95143	−	0.212411i
$16$	0.597159	−	0.802123i	0.149290	−	0.200531i
$17$	−0.143186	+	0.812048i	−0.0347277	+	0.196950i	−0.997236	−	0.0743026i	$-0.976327\pi$
$17$	−0.143186	+	0.812048i	−0.0347277	+	0.196950i	0.962508	+	0.271253i	$0.0874380\pi$
$18$	2.02384	+	2.21451i	0.477025	+	0.521965i
$19$	−1.34727	−	7.64077i	−0.309086	−	1.75291i	−0.603619	−	0.797273i	$-0.706275\pi$
$19$	−1.34727	−	7.64077i	−0.309086	−	1.75291i	0.294533	−	0.955641i	$-0.404836\pi$
$20$	3.92243	+	1.96992i	0.877083	+	0.440487i
$21$	0.156728	+	3.11668i	0.0342008	+	0.680116i
$22$	−3.24055	+	0.378766i	−0.690887	+	0.0807531i
$23$	0.461994	+	0.303858i	0.0963324	+	0.0633588i	0.596761	−	0.802419i	$-0.296454\pi$
$23$	0.461994	+	0.303858i	0.0963324	+	0.0633588i	−0.500429	+	0.865778i	$0.666824\pi$
$24$	0.287226	+	1.70807i	0.0586298	+	0.348658i
$25$	−4.09155	+	13.6667i	−0.818310	+	2.73335i
$26$	−0.00832891	−	0.0144261i	−0.00163343	−	0.00282919i
$27$	−5.19468	−	0.123655i	−0.999717	−	0.0237974i
$28$	−0.900845	+	1.56031i	−0.170244	+	0.294871i
$29$	−2.21818	−	2.35113i	−0.411905	−	0.436594i	0.487891	−	0.872905i	$-0.337766\pi$
$29$	−2.21818	−	2.35113i	−0.411905	−	0.436594i	−0.899796	+	0.436311i	$0.856285\pi$
$30$	−7.16443	+	2.54346i	−1.30804	+	0.464369i
$31$	0.266376	−	4.57350i	0.0478426	−	0.821425i	−0.885988	−	0.463709i	$-0.846518\pi$
$31$	0.266376	−	4.57350i	0.0478426	−	0.821425i	0.933830	−	0.357716i	$-0.116445\pi$
$32$	−0.396080	+	0.918216i	−0.0700177	+	0.162319i
$33$	3.41040	−	4.50589i	0.593674	−	0.784375i
$34$	−0.0479448	−	0.823180i	−0.00822246	−	0.141174i
$35$	−7.43126	−	2.70476i	−1.25611	−	0.457187i
$36$	−2.47999	−	1.68809i	−0.413332	−	0.281348i
$37$	3.29981	−	1.20103i	0.542486	−	0.197449i	−0.0562191	−	0.998418i	$-0.517905\pi$
$37$	3.29981	−	1.20103i	0.542486	−	0.197449i	0.598705	+	0.800970i	$0.295682\pi$
$38$	3.07304	+	7.12411i	0.498513	+	1.15568i
$39$	0.0280208	+	0.00687629i	0.00448692	+	0.00110109i
$40$	−4.27100	−	1.01225i	−0.675304	−	0.160050i
$41$	−10.4740	−	2.48239i	−1.63577	−	0.387684i	−0.692948	−	0.720987i	$-0.743689\pi$
$41$	−10.4740	−	2.48239i	−1.63577	−	0.387684i	−0.942820	+	0.333303i	$0.891837\pi$
$42$	−0.871259	−	2.99653i	−0.134438	−	0.462374i
$43$	−2.30508	−	5.34378i	−0.351522	−	0.814919i	−0.998620	−	0.0525123i	$-0.983277\pi$
$43$	−2.30508	−	5.34378i	−0.351522	−	0.814919i	0.647099	−	0.762406i	$-0.275982\pi$
$44$	3.06585	−	1.11588i	0.462194	−	0.168225i
$45$	5.40673	−	12.0067i	0.805988	−	1.78986i
$46$	−0.519616	−	0.189125i	−0.0766131	−	0.0278849i
$47$	0.636051	+	10.9206i	0.0927775	+	1.59293i	0.648272	+	0.761409i	$0.275492\pi$
$47$	0.636051	+	10.9206i	0.0927775	+	1.59293i	−0.555495	+	0.831520i	$0.687471\pi$
$48$	−0.673392	−	1.59579i	−0.0971957	−	0.230332i
$49$	−1.48685	+	3.44690i	−0.212407	+	0.492415i
$50$	0.829498	−	14.2419i	0.117309	−	2.01411i
$51$	1.08675	+	0.926683i	0.152176	+	0.129762i
$52$	0.0114313	+	0.0121165i	0.00158524	+	0.00168025i
$53$	−2.34748	+	4.06596i	−0.322451	+	0.558502i	−0.980993	−	0.194042i	$-0.937840\pi$
$53$	−2.34748	+	4.06596i	−0.322451	+	0.558502i	0.658542	+	0.752544i	$0.271174\pi$
$54$	5.08317	−	1.07765i	0.691732	−	0.146650i
$55$	7.16031	+	12.4020i	0.965495	+	1.67229i
$56$	0.516731	−	1.72600i	0.0690510	−	0.230647i
$57$	−12.5911	−	4.69623i	−1.66773	−	0.622030i
$58$	2.70059	+	1.77621i	0.354605	+	0.233228i
$59$	−3.16212	+	0.369599i	−0.411673	+	0.0481177i	−0.319409	−	0.947617i	$-0.603484\pi$
$59$	−3.16212	+	0.369599i	−0.411673	+	0.0481177i	−0.0922639	+	0.995735i	$0.529410\pi$
$60$	6.38475	−	4.12713i	0.824267	−	0.532810i
$61$	1.76186	+	0.884840i	0.225583	+	0.113292i	0.558002	−	0.829840i	$-0.311568\pi$
$61$	1.76186	+	0.884840i	0.225583	+	0.113292i	−0.332418	+	0.943132i	$0.607865\pi$
$62$	0.795526	+	4.51165i	0.101032	+	0.572980i
$63$	4.79105	+	2.50212i	0.603616	+	0.315238i
$64$	0.173648	−	0.984808i	0.0217060	−	0.123101i
$65$	−0.0436621	+	0.0586484i	−0.00541562	+	0.00727443i
$66$	−2.27934	+	5.17092i	−0.280568	+	0.636497i
$67$	−1.44772	+	1.53450i	−0.176867	+	0.187469i	−0.809742	−	0.586785i	$-0.800393\pi$
$67$	−1.44772	+	1.53450i	−0.176867	+	0.187469i	0.632875	+	0.774254i	$0.281875\pi$
$68$	0.236491	+	0.789934i	0.0286787	+	0.0957936i
$69$	0.859269	−	0.423039i	0.103444	−	0.0509279i
$70$	7.85471	+	0.918084i	0.938817	+	0.109732i
$71$	−7.37631	−	6.18946i	−0.875407	−	0.734554i	0.0898221	−	0.995958i	$-0.471370\pi$
$71$	−7.37631	−	6.18946i	−0.875407	−	0.734554i	−0.965230	+	0.261404i	$0.915815\pi$
$72$	2.80244	+	1.07066i	0.330271	+	0.126178i
$73$	4.83291	−	4.05529i	0.565649	−	0.474636i	−0.314550	−	0.949241i	$-0.601854\pi$
$73$	4.83291	−	4.05529i	0.565649	−	0.474636i	0.880199	+	0.474605i	$0.157409\pi$
$74$	−2.93389	+	1.92965i	−0.341057	+	0.224317i
$75$	16.8136	+	18.1070i	1.94147	+	2.09082i
$76$	−4.63314	−	6.22339i	−0.531458	−	0.713872i
$77$	−5.25296	+	2.63814i	−0.598631	+	0.300644i
$78$	−0.0288513		0.000228888i	−0.00326677		2.59165e-5i
$79$	4.63409	−	1.09830i	0.521376	−	0.123568i	0.0385026	−	0.999258i	$-0.487741\pi$
$79$	4.63409	−	1.09830i	0.521376	−	0.123568i	0.482874	+	0.875690i	$0.339593\pi$
$80$	4.38931			0.490740
$81$	−4.74503	+	7.64753i	−0.527225	+	0.849726i
$82$	10.7642			1.18870
$83$	6.63975	−	1.57365i	0.728807	−	0.172731i	0.150570	−	0.988599i	$-0.451889\pi$
$83$	6.63975	−	1.57365i	0.728807	−	0.172731i	0.578237	+	0.815869i	$0.303741\pi$
$84$	1.53882	+	2.71483i	0.167899	+	0.296212i
$85$	−3.23434	+	1.62435i	−0.350813	+	0.176185i
$86$	3.47531	+	4.66815i	0.374752	+	0.503379i
$87$	−5.45777	+	1.24787i	−0.585134	+	0.133786i
$88$	−2.72587	+	1.79283i	−0.290579	+	0.191117i
$89$	9.83956	−	8.25637i	1.04299	−	0.875173i	0.0506516	−	0.998716i	$-0.483870\pi$
$89$	9.83956	−	8.25637i	1.04299	−	0.875173i	0.992339	+	0.123543i	$0.0394258\pi$
$90$	−2.49205	+	12.9300i	−0.262685	+	1.36294i
$91$	−0.0229907	−	0.0192915i	−0.00241008	−	0.00202230i
$92$	0.549224	+	0.0641951i	0.0572606	+	0.00669280i
$93$	−6.59476	−	4.41279i	−0.683845	−	0.457585i
$94$	−3.13736	−	10.4795i	−0.323594	−	1.08088i
$95$	23.3700	−	24.7708i	2.39772	−	2.54143i
$96$	1.02325	+	1.39748i	0.104436	+	0.142630i
$97$	−5.09273	+	6.84073i	−0.517089	+	0.694571i	−0.981590	−	0.191002i	$-0.938826\pi$
$97$	−5.09273	+	6.84073i	−0.517089	+	0.694571i	0.464501	+	0.885573i	$0.346234\pi$
$98$	0.651860	−	3.69688i	0.0658478	−	0.373441i
$99$	−3.73368	−	9.04772i	−0.375249	−	0.909330i
$100$	2.47728	+	14.0493i	0.247728	+	1.40493i
$101$	6.77246	+	3.40126i	0.673885	+	0.338438i	0.752617	−	0.658458i	$-0.228791\pi$
$101$	6.77246	+	3.40126i	0.673885	+	0.338438i	−0.0787324	+	0.996896i	$0.525087\pi$
$102$	−1.27117	−	0.651082i	−0.125864	−	0.0644667i
$103$	5.44617	−	0.636566i	0.536627	−	0.0627227i	0.156537	−	0.987672i	$-0.449967\pi$
$103$	5.44617	−	0.636566i	0.536627	−	0.0627227i	0.380090	+	0.924949i	$0.375893\pi$
$104$	−0.0139174	−	0.00915363i	−0.00136471	−	0.000897587i
$105$	−10.5623	+	8.72098i	−1.03078	+	0.851081i
$106$	1.34653	−	4.49772i	0.130787	−	0.436858i
$107$	0.492832	+	0.853611i	0.0476439	+	0.0825217i	0.888864	−	0.458171i	$-0.151495\pi$
$107$	0.492832	+	0.853611i	0.0476439	+	0.0825217i	−0.841220	+	0.540693i	$0.818162\pi$
$108$	−4.69763	+	2.22087i	−0.452030	+	0.213703i
$109$	6.84961	−	11.8639i	0.656073	−	1.13635i	−0.325550	−	0.945525i	$-0.605550\pi$
$109$	6.84961	−	11.8639i	0.656073	−	1.13635i	0.981624	−	0.190828i	$-0.0611172\pi$
$110$	−9.82740	−	10.4164i	−0.937006	−	0.993168i
$111$	1.10366	−	5.98127i	0.104754	−	0.567717i
$112$	−0.104759	+	1.79864i	−0.00989879	+	0.169956i
$113$	0.205582	−	0.476593i	0.0193395	−	0.0448341i	−0.908273	−	0.418379i	$-0.862598\pi$
$113$	0.205582	−	0.476593i	0.0193395	−	0.0448341i	0.927612	+	0.373545i	$0.121858\pi$
$114$	13.3347	+	1.66594i	1.24891	+	0.156029i
$115$	0.141125	+	2.42302i	0.0131600	+	0.225948i
$116$	−3.03742	−	1.10553i	−0.282018	−	0.102646i
$117$	0.0348663	−	0.0358007i	0.00322339	−	0.00330978i
$118$	2.99165	−	1.08887i	0.275404	−	0.100239i
$119$	−0.588427	−	1.36413i	−0.0539410	−	0.125049i
$120$	−5.26086	+	5.48830i	−0.480249	+	0.501011i
$121$	−0.345801	−	0.0819562i	−0.0314364	−	0.00745057i
$122$	−1.91843	−	0.454676i	−0.173686	−	0.0411644i
$123$	−12.9015	+	13.4593i	−1.16329	+	1.21358i
$124$	−1.81454	−	4.20658i	−0.162951	−	0.377762i
$125$	−38.2188	+	13.9105i	−3.41840	+	1.24419i
$126$	−5.23894	−	1.32978i	−0.466722	−	0.118466i
$127$	−11.8293	−	4.30552i	−1.04968	−	0.382053i	−0.241139	−	0.970490i	$-0.577521\pi$
$127$	−11.8293	−	4.30552i	−1.04968	−	0.382053i	−0.808543	+	0.588437i	$0.799743\pi$
$128$	0.0581448	+	0.998308i	0.00513933	+	0.0882388i
$129$	−10.0023	−	1.24962i	−0.880656	−	0.110022i
$130$	0.0289599	−	0.0671367i	0.00253995	−	0.00588827i
$131$	−0.0606198	+	1.04080i	−0.00529638	+	0.0909353i	−0.999920	−	0.0126169i	$-0.995984\pi$
$131$	−0.0606198	+	1.04080i	−0.00529638	+	0.0909353i	0.994624	+	0.103552i	$0.0330209\pi$
$132$	1.02540	−	5.55719i	0.0892500	−	0.483692i
$133$	9.59275	+	10.1677i	0.831797	+	0.881653i
$134$	1.05482	−	1.82700i	0.0911226	−	0.157829i
$135$	−13.1805	−	18.6134i	−1.13440	−	1.60199i
$136$	−0.412287	−	0.714103i	−0.0353533	−	0.0612338i
$137$	3.16925	−	10.5860i	0.270767	−	0.904426i	−0.709156	−	0.705052i	$-0.750924\pi$
$137$	3.16925	−	10.5860i	0.270767	−	0.904426i	0.979923	−	0.199375i	$-0.0638910\pi$
$138$	−0.738548	+	0.609797i	−0.0628694	+	0.0519094i
$139$	6.88911	+	4.53104i	0.584327	+	0.384318i	0.806979	−	0.590580i	$-0.201101\pi$
$139$	6.88911	+	4.53104i	0.584327	+	0.384318i	−0.222652	+	0.974898i	$0.571471\pi$
$140$	−7.85471	+	0.918084i	−0.663844	+	0.0775922i
$141$	16.8637	+	8.63747i	1.42018	+	0.727406i
$142$	8.60487	+	4.32153i	0.722105	+	0.362655i
$143$	0.00943743	+	0.0535223i	0.000789197	+	0.00447576i
$144$	−2.97381	−	0.395510i	−0.247818	−	0.0329592i
$145$	2.46369	−	13.9723i	0.204598	−	1.16033i
$146$	−3.76742	+	5.06053i	−0.311794	+	0.418812i
$147$	3.84121	+	5.24602i	0.316818	+	0.432684i
$148$	2.40980	−	2.55423i	0.198084	−	0.209957i
$149$	4.15611	+	13.8824i	0.340482	+	1.13729i	0.941206	+	0.337833i	$0.109694\pi$
$149$	4.15611	+	13.8824i	0.340482	+	1.13729i	−0.600724	+	0.799457i	$0.705121\pi$
$150$	−20.5362	−	13.7415i	−1.67677	−	1.12199i
$151$	−4.40676	−	0.515076i	−0.358617	−	0.0419163i	−0.0651230	−	0.997877i	$-0.520744\pi$
$151$	−4.40676	−	0.515076i	−0.358617	−	0.0419163i	−0.293494	+	0.955961i	$0.594818\pi$
$152$	5.94347	+	4.98716i	0.482079	+	0.404512i
$153$	2.33767	−	0.809076i	0.188990	−	0.0654099i
$154$	4.50297	−	3.77844i	0.362860	−	0.304476i
$155$	16.8004	−	11.0498i	1.34944	−	0.887543i
$156$	0.0281264	−	0.00643085i	0.00225191	−	0.000514880i
$157$	7.49599	+	10.0689i	0.598245	+	0.803583i	0.993360	−	0.115049i	$-0.0367025\pi$
$157$	7.49599	+	10.0689i	0.598245	+	0.803583i	−0.395115	+	0.918632i	$0.629295\pi$
$158$	−4.25590	+	2.13739i	−0.338581	+	0.170042i
$159$	4.00996	+	7.07448i	0.318011	+	0.561043i
$160$	−4.27100	+	1.01225i	−0.337652	+	0.0800250i
$161$	−0.996269			−0.0785170
$162$	2.85348	−	8.53567i	0.224191	−	0.670625i
$163$	−11.7216			−0.918108			−0.459054	−	0.888408i	$-0.651812\pi$
$163$	−11.7216			−0.918108			−0.459054	+	0.888408i	$0.651812\pi$
$164$	−10.4740	+	2.48239i	−0.817884	+	0.193842i
$165$	24.8032	+	0.196774i	1.93093	+	0.0153188i
$166$	−6.09787	+	3.06246i	−0.473286	+	0.237693i
$167$	2.68576	+	3.60760i	0.207830	+	0.279164i	0.893800	−	0.448465i	$-0.148029\pi$
$167$	2.68576	+	3.60760i	0.207830	+	0.279164i	−0.685970	+	0.727630i	$0.740622\pi$
$168$	−2.12342	−	2.28677i	−0.163826	−	0.176428i
$169$	10.8611	−	7.14346i	0.835470	−	0.549497i
$170$	2.77256	−	2.32645i	0.212645	−	0.178431i
$171$	−18.0655	+	14.6767i	−1.38151	+	1.12236i
$172$	−4.45818	−	3.74086i	−0.339933	−	0.285238i
$173$	−20.0494	−	2.34344i	−1.52433	−	0.178169i	−0.687723	−	0.725973i	$-0.741390\pi$
$173$	−20.0494	−	2.34344i	−1.52433	−	0.178169i	−0.836607	+	0.547804i	$0.815464\pi$
$174$	5.02287	−	2.47288i	0.380783	−	0.187469i
$175$	−7.37171	−	24.6232i	−0.557249	−	1.86134i
$176$	2.23894	−	2.37314i	0.168766	−	0.178882i
$177$	−2.22418	+	5.04578i	−0.167179	+	0.379264i
$178$	−7.67028	+	10.3030i	−0.574912	+	0.772240i
$179$	−2.17526	+	12.3365i	−0.162587	+	0.922075i	0.788931	+	0.614482i	$0.210635\pi$
$179$	−2.17526	+	12.3365i	−0.162587	+	0.922075i	−0.951518	+	0.307594i	$0.900476\pi$
$180$	−0.556985	−	13.1562i	−0.0415152	−	0.980602i
$181$	−0.443951	−	2.51777i	−0.0329986	−	0.187145i	0.963853	−	0.266435i	$-0.0858457\pi$
$181$	−0.443951	−	2.51777i	−0.0329986	−	0.187145i	−0.996852	+	0.0792902i	$0.974735\pi$
$182$	0.0268199	+	0.0134695i	0.00198803	+	0.000998424i
$183$	2.86787	−	1.85381i	0.211999	−	0.137037i
$184$	−0.549224	+	0.0641951i	−0.0404894	+	0.00473253i
$185$	12.8777	+	8.46983i	0.946791	+	0.622714i
$186$	7.43466	+	2.77298i	0.545136	+	0.203325i
$187$	−0.771577	+	2.57725i	−0.0564233	+	0.188467i
$188$	5.46954	+	9.47352i	0.398907	+	0.690927i
$189$	7.94193	−	4.95683i	0.577690	−	0.360556i
$190$	−17.0276	+	29.4926i	−1.23531	+	2.13962i
$191$	6.91167	+	7.32594i	0.500111	+	0.530087i	0.927421	−	0.374018i	$-0.122020\pi$
$191$	6.91167	+	7.32594i	0.500111	+	0.530087i	−0.427310	+	0.904105i	$0.640539\pi$
$192$	−1.31795	−	1.12383i	−0.0951151	−	0.0811056i
$193$	−0.882894	+	15.1587i	−0.0635521	+	1.09115i	0.804267	+	0.594267i	$0.202558\pi$
$193$	−0.882894	+	15.1587i	−0.0635521	+	1.09115i	−0.867820	+	0.496879i	$0.834479\pi$
$194$	3.37788	−	7.83080i	0.242517	−	0.562219i
$195$	0.0492360	+	0.116678i	0.00352586	+	0.00835551i
$196$	0.218271	+	3.74756i	0.0155908	+	0.267683i
$197$	15.1904	+	5.52884i	1.08227	+	0.393914i	0.820752	−	0.571285i	$-0.193555\pi$
$197$	15.1904	+	5.52884i	1.08227	+	0.393914i	0.261518	+	0.965199i	$0.415777\pi$
$198$	5.71959	+	7.94279i	0.406473	+	0.564469i
$199$	13.4805	−	4.90652i	0.955611	−	0.347814i	0.183299	−	0.983057i	$-0.441322\pi$
$199$	13.4805	−	4.90652i	0.955611	−	0.347814i	0.772312	+	0.635243i	$0.219100\pi$
$200$	−5.65050	−	13.0993i	−0.399551	−	0.926262i
$201$	1.02018	+	3.50870i	0.0719577	+	0.247485i
$202$	−7.37429	−	1.74774i	−0.518853	−	0.122971i
$203$	5.66673	+	1.34304i	0.397726	+	0.0942629i
$204$	1.38705	+	0.340381i	0.0971130	+	0.0238314i
$205$	−18.7137	−	43.3833i	−1.30702	−	3.03002i
$206$	−5.15257	+	1.87538i	−0.358996	+	0.130664i
$207$	0.122719	−	1.65434i	0.00852954	−	0.114985i
$208$	0.0156532	+	0.00569731i	0.00108536	+	0.000395038i
$209$	−1.47185	−	25.2706i	−0.101810	−	1.74800i
$210$	8.26641	−	10.9217i	0.570436	−	0.753672i
$211$	−8.67422	+	20.1091i	−0.597158	+	1.38437i	0.304747	+	0.952433i	$0.401428\pi$
$211$	−8.67422	+	20.1091i	−0.597158	+	1.38437i	−0.901905	+	0.431934i	$0.857831\pi$
$212$	−0.272988	+	4.68702i	−0.0187489	+	0.321906i
$213$	−15.7170	+	5.57973i	−1.07691	+	0.382317i
$214$	−0.676404	−	0.716947i	−0.0462381	−	0.0490095i
$215$	12.7723	−	22.1223i	0.871065	−	1.50873i
$216$	4.05884	−	3.24435i	0.276169	−	0.220750i
$217$	4.12700	+	7.14817i	0.280159	+	0.485250i
$218$	−3.92898	+	13.1237i	−0.266104	+	0.888849i
$219$	−1.81208	−	10.7761i	−0.122449	−	0.728179i
$220$	11.9647	+	7.86930i	0.806660	+	0.530548i
$221$	−0.0136427	+	0.00159461i	−0.000917710	+	0.000107265i
$222$	0.305470	+	6.07457i	0.0205018	+	0.407698i
$223$	−16.3216	−	8.19703i	−1.09298	−	0.548914i	−0.191392	−	0.981514i	$-0.561300\pi$
$223$	−16.3216	−	8.19703i	−1.09298	−	0.548914i	−0.901586	+	0.432600i	$0.857596\pi$
$224$	−0.312860	−	1.77432i	−0.0209039	−	0.118552i
$225$	41.7959	−	9.20797i	2.78639	−	0.613865i
$226$	−0.0901308	+	0.511157i	−0.00599541	+	0.0340017i
$227$	−5.09759	+	6.84725i	−0.338339	+	0.454468i	−0.938433	−	0.345461i	$-0.887722\pi$
$227$	−5.09759	+	6.84725i	−0.338339	+	0.454468i	0.600094	+	0.799929i	$0.295130\pi$
$228$	−13.3595	+	1.45416i	−0.884752	+	0.0963043i
$229$	17.6961	−	18.7567i	1.16939	−	1.23948i	0.203911	−	0.978989i	$-0.434635\pi$
$229$	17.6961	−	18.7567i	1.16939	−	1.23948i	0.965477	−	0.260490i	$-0.0838840\pi$
$230$	−0.696108	−	2.32516i	−0.0459000	−	0.153317i
$231$	−0.672608	+	10.1591i	−0.0442544	+	0.668421i
$232$	3.21050	+	0.375254i	0.210780	+	0.0246366i
$233$	6.04962	+	5.07623i	0.396324	+	0.332555i	0.819071	−	0.573693i	$-0.194490\pi$
$233$	6.04962	+	5.07623i	0.396324	+	0.332555i	−0.422747	+	0.906248i	$0.638934\pi$
$234$	−0.0256702	+	0.0428764i	−0.00167812	+	0.00280292i
$235$	−36.7816	+	30.8635i	−2.39937	+	2.01331i
$236$	−2.65990	+	1.74944i	−0.173145	+	0.113879i
$237$	2.42841	−	7.88328i	0.157742	−	0.512074i
$238$	0.887156	+	1.19166i	0.0575058	+	0.0772436i
$239$	−17.5486	+	8.81325i	−1.13513	+	0.570082i	−0.914222	−	0.405214i	$-0.867197\pi$
$239$	−17.5486	+	8.81325i	−1.13513	+	0.570082i	−0.220904	+	0.975296i	$0.570901\pi$
$240$	3.85337	−	6.55360i	0.248734	−	0.423033i
$241$	6.69826	−	1.58752i	0.431473	−	0.102261i	−0.00913991	−	0.999958i	$-0.502909\pi$
$241$	6.69826	−	1.58752i	0.431473	−	0.102261i	0.440613	+	0.897697i	$0.354761\pi$
$242$	0.355380			0.0228447
$243$	7.25275	+	13.7985i	0.465264	+	0.885172i
$244$	1.97157			0.126217
$245$	−16.0329	+	3.79988i	−1.02431	+	0.242765i
$246$	9.44985	−	16.0718i	0.602500	−	1.02470i
$247$	0.115495	−	0.0580038i	0.00734877	−	0.00369069i
$248$	2.73573	+	3.67473i	0.173719	+	0.233346i
$249$	3.47943	−	11.2952i	0.220500	−	0.715804i
$250$	33.9806	−	22.3494i	2.14912	−	1.41350i
$251$	19.2433	−	16.1470i	1.21463	−	1.01919i	0.215538	−	0.976495i	$-0.430849\pi$
$251$	19.2433	−	16.1470i	1.21463	−	1.01919i	0.999088	−	0.0426973i	$-0.0135951\pi$
$252$	5.40439	+	0.0857556i	0.340445	+	0.00540209i
$253$	1.38202	+	1.15966i	0.0868871	+	0.0729069i
$254$	12.5034	+	1.46144i	0.784532	+	0.0916986i
$255$	−0.414136	+	6.25514i	−0.0259342	+	0.391712i
$256$	−0.286803	−	0.957990i	−0.0179252	−	0.0598743i
$257$	4.78736	−	5.07430i	0.298627	−	0.316526i	−0.560634	−	0.828064i	$-0.689442\pi$
$257$	4.78736	−	5.07430i	0.298627	−	0.316526i	0.859261	+	0.511538i	$0.170924\pi$
$258$	10.0209	−	1.09076i	0.623874	−	0.0679080i
$259$	−3.77810	+	5.07486i	−0.234760	+	0.315337i
$260$	−0.0126965	+	0.0720056i	−0.000787405	+	0.00446560i
$261$	−2.92819	+	9.24440i	−0.181250	+	0.572214i
$262$	−0.181040	−	1.02673i	−0.0111847	−	0.0634314i
$263$	0.757507	+	0.380434i	0.0467099	+	0.0234586i	0.472001	−	0.881598i	$-0.343532\pi$
$263$	0.757507	+	0.380434i	0.0467099	+	0.0234586i	−0.425291	+	0.905057i	$0.639828\pi$
$264$	0.283812	+	5.64387i	0.0174674	+	0.347356i
$265$	−20.4683	+	2.39240i	−1.25736	+	0.146964i
$266$	−11.6790	−	7.68141i	−0.716086	−	0.470977i
$267$	−3.68931	−	21.9395i	−0.225782	−	1.34268i
$268$	−0.605052	+	2.02101i	−0.0369594	+	0.123453i
$269$	7.58705	+	13.1412i	0.462591	+	0.801231i	0.999089	−	0.0426706i	$-0.0135866\pi$
$269$	7.58705	+	13.1412i	0.462591	+	0.801231i	−0.536498	+	0.843901i	$0.680253\pi$
$270$	17.1178	+	15.0720i	1.04175	+	0.917254i
$271$	1.79260	−	3.10487i	0.108892	−	0.188607i	−0.806429	−	0.591330i	$-0.798603\pi$
$271$	1.79260	−	3.10487i	0.108892	−	0.188607i	0.915322	+	0.402723i	$0.131936\pi$
$272$	0.565857	+	0.599774i	0.0343101	+	0.0363666i
$273$	−0.0489873	+	0.0173911i	−0.00296485	+	0.00105256i
$274$	−0.642516	+	11.0316i	−0.0388158	+	0.666441i
$275$	−18.4354	+	42.7380i	−1.11169	+	2.57720i
$276$	0.578011	−	0.763681i	0.0347922	−	0.0459682i
$277$	1.29447	+	22.2252i	0.0777772	+	1.33538i	0.781053	+	0.624465i	$0.214683\pi$
$277$	1.29447	+	22.2252i	0.0777772	+	1.33538i	−0.703275	+	0.710918i	$0.748280\pi$
$278$	−7.74834	−	2.82017i	−0.464715	−	0.169142i
$279$	−12.3782	+	5.97255i	−0.741063	+	0.357567i
$280$	7.43126	−	2.70476i	0.444103	−	0.161640i
$281$	9.94371	+	23.0521i	0.593192	+	1.37517i	0.905156	+	0.425080i	$0.139754\pi$
$281$	9.94371	+	23.0521i	0.593192	+	1.37517i	−0.311964	+	0.950094i	$0.600987\pi$
$282$	−18.4011	−	4.51561i	−1.09577	−	0.268900i
$283$	−1.55242	−	0.367930i	−0.0922817	−	0.0218712i	0.184216	−	0.982886i	$-0.441026\pi$
$283$	−1.55242	−	0.367930i	−0.0922817	−	0.0218712i	−0.276497	+	0.961015i	$0.589174\pi$
$284$	−9.36954	−	2.22062i	−0.555980	−	0.131770i
$285$	−16.4683	−	56.6396i	−0.975500	−	3.35504i
$286$	−0.0215261	−	0.0499032i	−0.00127287	−	0.00295084i
$287$	18.2241	−	6.63304i	1.07574	−	0.391536i
$288$	2.98487	−	0.300959i	0.175885	−	0.0177342i
$289$	15.3359	+	5.58179i	0.902109	+	0.328341i
$290$	0.824949	+	14.1638i	0.0484426	+	0.831728i
$291$	5.74287	+	13.6093i	0.336653	+	0.797793i
$292$	2.49883	−	5.79295i	0.146233	−	0.339006i
$293$	−0.322116	+	5.53052i	−0.0188182	+	0.323097i	0.975741	+	0.218927i	$0.0702556\pi$
$293$	−0.322116	+	5.53052i	−0.0188182	+	0.323097i	−0.994560	+	0.104170i	$0.966781\pi$
$294$	−4.94748	−	4.21876i	−0.288543	−	0.246043i
$295$	−9.58955	−	10.1643i	−0.558325	−	0.591790i
$296$	−1.75579	+	3.04112i	−0.102053	+	0.176762i
$297$	−16.7868	−	2.36828i	−0.974068	−	0.137421i
$298$	−7.24558	−	12.5497i	−0.419725	−	0.726986i
$299$	−0.00264179	+	0.00882420i	−0.000152779	+	0.000510317i
$300$	23.1516	+	8.63510i	1.33666	+	0.498548i
$301$	8.76040	+	5.76180i	0.504941	+	0.332105i
$302$	4.40676	−	0.515076i	0.253581	−	0.0296393i
$303$	11.0239	−	7.12589i	0.633306	−	0.409371i
$304$	−6.93338	−	3.48207i	−0.397657	−	0.199711i
$305$	1.50272	+	8.52237i	0.0860457	+	0.487990i
$306$	−2.08807	+	1.32637i	−0.119367	+	0.0758236i
$307$	−0.126011	+	0.714642i	−0.00719181	+	0.0407868i	−0.988192	−	0.153218i	$-0.951036\pi$
$307$	−0.126011	+	0.714642i	−0.00719181	+	0.0407868i	0.981001	+	0.194004i	$0.0621476\pi$
$308$	−3.51022	+	4.71505i	−0.200014	+	0.268665i
$309$	3.83074	−	8.69043i	0.217923	−	0.494381i
$310$	−13.7993	+	14.6264i	−0.783749	+	0.830725i
$311$	1.82685	+	6.10212i	0.103591	+	0.346020i	0.994033	−	0.109078i	$-0.0347897\pi$
$311$	1.82685	+	6.10212i	0.103591	+	0.346020i	−0.890442	+	0.455097i	$0.849605\pi$
$312$	−0.0258852	+	0.0127439i	−0.00146546	+	0.000721481i
$313$	−8.10252	−	0.947048i	−0.457981	−	0.0535303i	−0.116025	−	0.993246i	$-0.537015\pi$
$313$	−8.10252	−	0.947048i	−0.457981	−	0.0535303i	−0.341956	+	0.939716i	$0.611089\pi$
$314$	−9.61597	−	8.06876i	−0.542661	−	0.455346i
$315$	3.74852	+	23.4265i	0.211205	+	1.31994i
$316$	3.64826	−	3.06125i	0.205231	−	0.172209i
$317$	12.1183	−	7.97032i	0.680631	−	0.447658i	−0.161542	−	0.986866i	$-0.551647\pi$
$317$	12.1183	−	7.97032i	0.680631	−	0.447658i	0.842173	+	0.539208i	$0.181276\pi$
$318$	−5.53336	−	5.95902i	−0.310295	−	0.334165i
$319$	−6.29759	−	8.45913i	−0.352597	−	0.473620i
$320$	3.92243	−	1.96992i	0.219271	−	0.110122i
$321$	1.70717	+	0.0135436i	0.0952848	+	0.000755931i
$322$	0.969414	−	0.229755i	0.0540233	−	0.0128038i
$323$	6.39758			0.355971
$324$	−0.808105	+	8.96365i	−0.0448947	+	0.497980i
$325$	−0.237642			−0.0131820
$326$	11.4057	−	2.70319i	0.631701	−	0.149716i
$327$	−11.7005	−	20.6423i	−0.647038	−	1.14152i
$328$	9.61922	−	4.83095i	0.531133	−	0.266745i
$329$	−11.7693	−	15.8089i	−0.648862	−	0.871573i
$330$	−24.1800	+	5.52855i	−1.33107	+	0.304337i
$331$	13.4994	−	8.87870i	0.741994	−	0.488017i	−0.121364	−	0.992608i	$-0.538727\pi$
$331$	13.4994	−	8.87870i	0.741994	−	0.488017i	0.863359	+	0.504591i	$0.168357\pi$
$332$	5.22725	−	4.38618i	0.286882	−	0.240723i
$333$	−7.96164	−	6.89880i	−0.436295	−	0.378052i
$334$	−3.44533	−	2.89098i	−0.188520	−	0.158187i
$335$	−9.19726	−	1.07501i	−0.502500	−	0.0587338i
$336$	2.59355	+	1.73544i	0.141490	+	0.0946759i
$337$	7.28010	+	24.3172i	0.396573	+	1.32464i	0.890437	+	0.455106i	$0.150399\pi$
$337$	7.28010	+	24.3172i	0.396573	+	1.32464i	−0.493865	+	0.869539i	$0.664416\pi$
$338$	−8.92095	+	9.45566i	−0.485236	+	0.514320i
$339$	−0.531113	−	0.725351i	−0.0288461	−	0.0393957i
$340$	−2.16131	+	2.90314i	−0.117213	+	0.157445i
$341$	2.59549	−	14.7198i	0.140554	−	0.797120i
$342$	14.1939	−	18.4473i	0.767518	−	0.997515i
$343$	−3.36447	−	19.0809i	−0.181664	−	1.03027i
$344$	5.20071	+	2.61189i	0.280403	+	0.140824i
$345$	3.74167	+	1.91645i	0.201444	+	0.103178i
$346$	20.0494	−	2.34344i	1.07786	−	0.125984i
$347$	−23.2584	−	15.2973i	−1.24858	−	0.821202i	−0.259094	−	0.965852i	$-0.583424\pi$
$347$	−23.2584	−	15.2973i	−1.24858	−	0.821202i	−0.989483	+	0.144650i	$0.953794\pi$
$348$	−4.31720	+	3.56458i	−0.231426	+	0.191081i
$349$	−1.88101	+	6.28302i	−0.100688	+	0.336322i	−0.993459	−	0.114189i	$-0.963573\pi$
$349$	−1.88101	+	6.28302i	−0.100688	+	0.336322i	0.892771	+	0.450511i	$0.148758\pi$
$350$	12.8515	+	22.2595i	0.686942	+	1.18982i
$351$	−0.0228444	−	0.0834876i	−0.00121934	−	0.00445624i
$352$	−1.63130	+	2.82550i	−0.0869488	+	0.150600i
$353$	−16.4990	−	17.4879i	−0.878152	−	0.930787i	0.119924	−	0.992783i	$-0.461735\pi$
$353$	−16.4990	−	17.4879i	−0.878152	−	0.930787i	−0.998076	+	0.0619961i	$0.980253\pi$
$354$	1.00059	−	5.42270i	0.0531806	−	0.288213i
$355$	2.45750	−	42.1936i	0.130430	−	2.23940i
$356$	5.08750	−	11.7941i	0.269637	−	0.625088i
$357$	−2.55333	−	0.318994i	−0.135137	−	0.0168830i
$358$	−0.728371	−	12.5056i	−0.0384956	−	0.660944i
$359$	−24.5313	−	8.92866i	−1.29471	−	0.471237i	−0.399442	−	0.916759i	$-0.630796\pi$
$359$	−24.5313	−	8.92866i	−1.29471	−	0.471237i	−0.895271	+	0.445522i	$0.853018\pi$
$360$	3.57599	+	12.6731i	0.188471	+	0.667930i
$361$	−38.7121	+	14.0901i	−2.03748	+	0.741582i
$362$	1.01262	+	2.34752i	0.0532223	+	0.123383i
$363$	−0.425945	+	0.444360i	−0.0223563	+	0.0233228i
$364$	−0.0292033	−	0.00692130i	−0.00153067	−	0.000362775i
$365$	26.9454	+	6.38617i	1.41038	+	0.334267i
$366$	−2.36305	+	2.46521i	−0.123519	+	0.128859i
$367$	1.62324	+	3.76309i	0.0847323	+	0.196432i	0.955314	−	0.295592i	$-0.0955168\pi$
$367$	1.62324	+	3.76309i	0.0847323	+	0.196432i	−0.870582	+	0.492023i	$0.836257\pi$
$368$	0.519616	−	0.189125i	0.0270868	−	0.00985880i
$369$	8.76961	+	31.0790i	0.456528	+	1.61791i
$370$	−14.4839	−	5.27171i	−0.752982	−	0.274063i
$371$	−0.491840	−	8.44456i	−0.0255350	−	0.438420i
$372$	−7.87375	−	0.983687i	−0.408235	−	0.0510018i
$373$	−2.38312	+	5.52468i	−0.123393	+	0.286057i	−0.968705	−	0.248216i	$-0.920156\pi$
$373$	−2.38312	+	5.52468i	−0.123393	+	0.286057i	0.845312	+	0.534274i	$0.179415\pi$
$374$	0.156425	−	2.68571i	0.00808854	−	0.138875i
$375$	−12.7827	+	69.2759i	−0.660095	+	3.57739i
$376$	−7.50685	−	7.95679i	−0.387136	−	0.410340i
$377$	0.0269220	−	0.0466303i	0.00138655	−	0.00240158i
$378$	−6.58473	+	6.65475i	−0.338682	+	0.342284i
$379$	−2.89808	−	5.01961i	−0.148864	−	0.257840i	0.781944	−	0.623349i	$-0.214228\pi$
$379$	−2.89808	−	5.01961i	−0.148864	−	0.257840i	−0.930808	+	0.365509i	$0.880895\pi$
$380$	9.76712	−	32.6244i	0.501043	−	1.67360i
$381$	−16.8134	+	13.8823i	−0.861378	+	0.711214i
$382$	−8.41484	−	5.53453i	−0.430541	−	0.283171i
$383$	−8.59376	+	1.00447i	−0.439121	+	0.0513259i	−0.332781	−	0.943004i	$-0.607987\pi$
$383$	−8.59376	+	1.00447i	−0.439121	+	0.0513259i	−0.106339	+	0.994330i	$0.533913\pi$
$384$	1.54160	+	0.789598i	0.0786695	+	0.0402940i
$385$	−23.0569	−	11.5796i	−1.17509	−	0.590151i
$386$	−2.63674	−	14.9537i	−0.134207	−	0.761123i
$387$	−10.6468	+	13.8373i	−0.541207	+	0.703388i
$388$	−1.48092	+	8.39871i	−0.0751823	+	0.426380i
$389$	−12.3418	+	16.5779i	−0.625753	+	0.840532i	−0.996088	−	0.0883664i	$-0.971835\pi$
$389$	−12.3418	+	16.5779i	−0.625753	+	0.840532i	0.370335	+	0.928898i	$0.379243\pi$
$390$	−0.0748167	−	0.102179i	−0.00378849	−	0.00517402i
$391$	−0.312898	+	0.331653i	−0.0158240	+	0.0167724i
$392$	−1.07663	−	3.59621i	−0.0543782	−	0.181636i
$393$	1.50078	+	1.00423i	0.0757046	+	0.0506566i
$394$	−16.0560	−	1.87667i	−0.808887	−	0.0945454i
$395$	16.0134	+	13.4368i	0.805719	+	0.676079i
$396$	−7.39715	−	6.40966i	−0.371721	−	0.322098i
$397$	3.28218	−	2.75408i	0.164728	−	0.138223i	−0.556697	−	0.830715i	$-0.687932\pi$
$397$	3.28218	−	2.75408i	0.164728	−	0.138223i	0.721425	+	0.692492i	$0.243487\pi$
$398$	−11.9857	+	7.88309i	−0.600787	+	0.395144i
$399$	23.6027	−	5.39655i	1.18161	−	0.270165i
$400$	8.51910	+	11.4431i	0.425955	+	0.572157i
$401$	16.1272	−	8.09940i	0.805355	−	0.404465i	0.00202470	−	0.999998i	$-0.499356\pi$
$401$	16.1272	−	8.09940i	0.805355	−	0.404465i	0.803331	+	0.595533i	$0.203059\pi$
$402$	−1.80184	−	3.17885i	−0.0898676	−	0.158547i
$403$	0.0742567	−	0.0175992i	0.00369899	−	0.000876676i
$404$	7.57857			0.377048
$405$	−39.3624	+	3.33892i	−1.95594	+	0.165912i
$406$	−5.82371			−0.289026
$407$	11.1481	−	2.64215i	0.552591	−	0.130967i
$408$	−1.42816	−	0.0113301i	−0.0707045	−	0.000560925i
$409$	34.5050	−	17.3291i	1.70616	−	0.856868i	0.719421	−	0.694574i	$-0.244407\pi$
$409$	34.5050	−	17.3291i	1.70616	−	0.856868i	0.986743	−	0.162294i	$-0.0518892\pi$
$410$	28.2141	+	37.8982i	1.39340	+	1.87166i
$411$	−13.0235	−	14.0254i	−0.642404	−	0.691823i
$412$	4.58119	−	3.01309i	0.225699	−	0.148445i
$413$	4.39399	−	3.68700i	0.216214	−	0.181425i
$414$	0.262107	+	1.63805i	0.0128819	+	0.0805059i
$415$	22.9440	+	19.2523i	1.12628	+	0.945059i
$416$	−0.0165452	−	0.00193386i	−0.000811195	−	9.48151e-5i
$417$	12.8131	−	6.30822i	0.627463	−	0.308915i
$418$	7.25997	+	24.2500i	0.355097	+	1.18611i
$419$	−24.4434	+	25.9085i	−1.19414	+	1.26571i	−0.238507	+	0.971141i	$0.576658\pi$
$419$	−24.4434	+	25.9085i	−1.19414	+	1.26571i	−0.955630	+	0.294570i	$0.904824\pi$
$420$	−5.52486	+	12.5337i	−0.269585	+	0.611583i
$421$	−5.20367	+	6.98975i	−0.253612	+	0.340659i	−0.910636	−	0.413210i	$-0.864408\pi$
$421$	−5.20367	+	6.98975i	−0.253612	+	0.340659i	0.657024	+	0.753869i	$0.271815\pi$
$422$	3.80293	−	21.5675i	0.185124	−	1.04989i
$423$	27.7011	−	17.5961i	1.34687	−	0.855551i
$424$	−0.815272	−	4.62364i	−0.0395931	−	0.224544i
$425$	−10.5122	−	5.27942i	−0.509916	−	0.256089i
$426$	14.0066	−	9.05392i	0.678622	−	0.438664i
$427$	−3.52814	+	0.412381i	−0.170739	+	0.0199565i
$428$	0.823511	+	0.541632i	0.0398059	+	0.0261808i
$429$	0.0881983	+	0.0328963i	0.00425826	+	0.00158825i
$430$	−7.32629	+	24.4715i	−0.353305	+	1.18012i
$431$	−3.84915	−	6.66692i	−0.185407	−	0.321134i	0.758307	−	0.651898i	$-0.226027\pi$
$431$	−3.84915	−	6.66692i	−0.185407	−	0.321134i	−0.943714	+	0.330764i	$0.892694\pi$
$432$	−3.20123	+	4.09293i	−0.154019	+	0.196921i
$433$	11.0881	−	19.2051i	0.532859	−	0.922939i	−0.466404	−	0.884572i	$-0.654451\pi$
$433$	11.0881	−	19.2051i	0.532859	−	0.922939i	0.999264	−	0.0383677i	$-0.0122158\pi$
$434$	−5.66424	−	6.00374i	−0.271892	−	0.288189i
$435$	−18.6989	−	15.9447i	−0.896543	−	0.764491i
$436$	0.796538	−	13.6760i	0.0381473	−	0.654963i
$437$	1.69928	−	3.93937i	0.0812876	−	0.188446i
$438$	4.24837	+	10.0677i	0.202995	+	0.481053i
$439$	0.890525	+	15.2897i	0.0425024	+	0.729738i	0.950493	+	0.310747i	$0.100579\pi$
$439$	0.890525	+	15.2897i	0.0425024	+	0.729738i	−0.907990	+	0.418991i	$0.862384\pi$
$440$	−13.4570	−	4.89794i	−0.641536	−	0.233500i
$441$	11.2049	−	1.12978i	0.533568	−	0.0537988i
$442$	0.0129073	−	0.00469786i	0.000613936	−	0.000223454i
$443$	−10.2131	−	23.6767i	−0.485241	−	1.12491i	−0.968404	−	0.249385i	$-0.919772\pi$
$443$	−10.2131	−	23.6767i	−0.485241	−	1.12491i	0.483164	−	0.875530i	$-0.339488\pi$
$444$	−1.69813	−	5.84038i	−0.0805896	−	0.277172i
$445$	54.8594	+	13.0019i	2.60058	+	0.616350i
$446$	17.7721	+	4.21205i	0.841531	+	0.199447i
$447$	24.3762	+	5.98190i	1.15295	+	0.282934i
$448$	0.713613	+	1.65434i	0.0337151	+	0.0781603i
$449$	7.67119	−	2.79209i	0.362026	−	0.131767i	−0.154602	−	0.987977i	$-0.549409\pi$
$449$	7.67119	−	2.79209i	0.362026	−	0.131767i	0.516628	+	0.856210i	$0.327187\pi$
$450$	−38.5458	+	18.5986i	−1.81707	+	0.876745i
$451$	−33.0013	−	12.0115i	−1.55397	−	0.565600i
$452$	−0.0301796	−	0.518164i	−0.00141953	−	0.0243724i
$453$	−4.63774	+	6.12747i	−0.217900	+	0.287894i
$454$	3.38110	−	7.83827i	0.158683	−	0.367868i
$455$	0.00765960	−	0.131510i	0.000359088	−	0.00616530i
$456$	12.6640	−	4.49587i	0.593046	−	0.210538i
$457$	−6.04102	−	6.40310i	−0.282587	−	0.299525i	0.570496	−	0.821301i	$-0.306751\pi$
$457$	−6.04102	−	6.40310i	−0.282587	−	0.299525i	−0.853082	+	0.521776i	$0.825270\pi$
$458$	−12.8935	+	22.3321i	−0.602472	+	1.04351i
$459$	0.844219	−	4.20062i	0.0394048	−	0.196068i
$460$	1.21356	+	2.10195i	0.0565827	+	0.0980042i
$461$	1.30515	−	4.35951i	0.0607870	−	0.203043i	−0.922202	−	0.386710i	$-0.873612\pi$
$461$	1.30515	−	4.35951i	0.0607870	−	0.203043i	0.982989	+	0.183667i	$0.0587968\pi$
$462$	−1.68838	−	10.0404i	−0.0785504	−	0.467121i
$463$	20.7820	+	13.6685i	0.965822	+	0.635231i	0.931331	−	0.364174i	$-0.118649\pi$
$463$	20.7820	+	13.6685i	0.965822	+	0.635231i	0.0344911	+	0.999405i	$0.489019\pi$
$464$	−3.21050	+	0.375254i	−0.149044	+	0.0174207i
$465$	−1.74923	−	34.7851i	−0.0811185	−	1.61312i
$466$	−7.05721	−	3.54426i	−0.326919	−	0.164185i
$467$	2.10873	+	11.9592i	0.0975806	+	0.553407i	0.993926	+	0.110051i	$0.0351013\pi$
$467$	2.10873	+	11.9592i	0.0975806	+	0.553407i	−0.896345	+	0.443356i	$0.853788\pi$
$468$	0.0150903	−	0.0476406i	0.000697550	−	0.00220219i
$469$	0.660023	−	3.74317i	0.0304770	−	0.172844i
$470$	28.6726	−	38.5140i	1.32257	−	1.77652i
$471$	21.6144	−	2.35270i	0.995937	−	0.108407i
$472$	2.18475	−	2.31570i	0.100561	−	0.106589i
$473$	−5.44569	−	18.1899i	−0.250393	−	0.836371i
$474$	−0.544940	+	8.23081i	−0.0250299	+	0.378054i
$475$	109.937	+	12.8498i	5.04425	+	0.589588i
$476$	−1.13806	−	0.954943i	−0.0521628	−	0.0437698i
$477$	14.0831	+	0.223467i	0.644822	+	0.0102319i
$478$	15.0431	−	12.6227i	0.688056	−	0.577348i
$479$	−8.35315	+	5.49395i	−0.381665	+	0.251025i	−0.725816	−	0.687889i	$-0.758537\pi$
$479$	−8.35315	+	5.49395i	−0.381665	+	0.251025i	0.344150	+	0.938915i	$0.388167\pi$
$480$	−2.23813	+	7.26560i	−0.102156	+	0.331628i
$481$	0.0349310	+	0.0469205i	0.00159272	+	0.00213939i
$482$	−6.15160	+	3.08945i	−0.280198	+	0.140721i
$483$	−0.874622	+	1.48751i	−0.0397967	+	0.0676841i
$484$	−0.345801	+	0.0819562i	−0.0157182	+	0.00372528i
$485$	−37.4333			−1.69976
$486$	−10.2394	−	11.7539i	−0.464468	−	0.533169i
$487$	25.5282			1.15679			0.578396	−	0.815756i	$-0.303679\pi$
$487$	25.5282			1.15679			0.578396	+	0.815756i	$0.303679\pi$
$488$	−1.91843	+	0.454676i	−0.0868432	+	0.0205822i
$489$	−10.2904	+	17.5013i	−0.465347	+	0.791438i
$490$	14.7245	−	7.39490i	0.665183	−	0.334068i
$491$	−16.8671	−	22.6565i	−0.761203	−	1.02247i	−0.998694	−	0.0510831i	$-0.983733\pi$
$491$	−16.8671	−	22.6565i	−0.761203	−	1.02247i	0.237492	−	0.971390i	$-0.423675\pi$
$492$	−5.48871	+	17.8179i	−0.247450	+	0.803292i
$493$	2.22684	−	1.46462i	0.100292	−	0.0659630i
$494$	−0.0990052	+	0.0830753i	−0.00445446	+	0.00373773i
$495$	22.0685	−	36.8605i	0.991906	−	1.65676i
$496$	−3.50944	−	2.94477i	−0.157579	−	0.132224i
$497$	17.2313	+	2.01406i	0.772931	+	0.0903427i
$498$	−0.780793	+	11.7931i	−0.0349882	+	0.528464i
$499$	1.32547	+	4.42739i	0.0593364	+	0.198197i	0.982518	−	0.186166i	$-0.0596062\pi$
$499$	1.32547	+	4.42739i	0.0593364	+	0.198197i	−0.923182	+	0.384363i	$0.874421\pi$
$500$	−27.9106	+	29.5835i	−1.24820	+	1.32301i
$501$	7.74426	−	0.842955i	0.345988	−	0.0376604i
$502$	−15.0008	+	20.1496i	−0.669520	+	0.899321i
$503$	3.85232	−	21.8476i	0.171767	−	0.974137i	−0.770044	−	0.637991i	$-0.779766\pi$
$503$	3.85232	−	21.8476i	0.171767	−	0.974137i	0.941810	−	0.336145i	$-0.109123\pi$
$504$	−5.27849	+	1.16289i	−0.235123	+	0.0517994i
$505$	5.77636	+	32.7594i	0.257045	+	1.45777i
$506$	−1.61221	−	0.809680i	−0.0716713	−	0.0359947i
$507$	−1.13084	−	22.4878i	−0.0502222	−	0.998717i
$508$	−12.5034	+	1.46144i	−0.554748	+	0.0648407i
$509$	−26.1564	−	17.2034i	−1.15936	−	0.762526i	−0.183956	−	0.982934i	$-0.558891\pi$
$509$	−26.1564	−	17.2034i	−1.15936	−	0.762526i	−0.975408	+	0.220409i	$0.929261\pi$
$510$	−1.03956	−	6.18204i	−0.0460326	−	0.273745i
$511$	−3.26001	+	10.8892i	−0.144214	+	0.481709i
$512$	0.500000	+	0.866025i	0.0220971	+	0.0382733i
$513$	6.05384	+	39.8580i	0.267284	+	1.75977i
$514$	−3.48810	+	6.04156i	−0.153853	+	0.266482i
$515$	16.5163	+	17.5062i	0.727793	+	0.771415i
$516$	−9.49923	+	3.37234i	−0.418180	+	0.148459i
$517$	−2.07518	+	35.6295i	−0.0912665	+	1.56699i
$518$	2.50591	−	5.80936i	0.110104	−	0.255249i
$519$	−21.1003	+	27.8782i	−0.926201	+	1.22372i
$520$	−0.00425134	−	0.0729927i	−0.000186434	−	0.00320094i
$521$	−4.14031	−	1.50695i	−0.181390	−	0.0660207i	0.249728	−	0.968316i	$-0.419659\pi$
$521$	−4.14031	−	1.50695i	−0.181390	−	0.0660207i	−0.431119	+	0.902295i	$0.641881\pi$
$522$	0.717355	−	9.67050i	0.0313978	−	0.423266i
$523$	−6.87231	+	2.50132i	−0.300505	+	0.109375i	−0.487872	−	0.872915i	$-0.662227\pi$
$523$	−6.87231	+	2.50132i	−0.300505	+	0.109375i	0.187367	+	0.982290i	$0.440005\pi$
$524$	0.412939	+	0.957300i	0.0180393	+	0.0418199i
$525$	−43.2361	−	10.6101i	−1.88698	−	0.463063i
$526$	−0.824822	−	0.195486i	−0.0359640	−	0.00852361i
$527$	3.67576	+	0.871171i	0.160119	+	0.0379488i
$528$	−1.57773	−	5.42629i	−0.0686618	−	0.236149i
$529$	−8.98873	−	20.8382i	−0.390814	−	0.906009i
$530$	19.3649	−	7.04823i	0.841156	−	0.306156i
$531$	5.58116	+	7.75056i	0.242202	+	0.336346i
$532$	13.1357	+	4.78099i	0.569503	+	0.207282i
$533$	−0.0104258	−	0.179004i	−0.000451592	−	0.00775354i
$534$	8.64947	+	20.4973i	0.374299	+	0.887006i
$535$	−1.71360	+	3.97256i	−0.0740852	+	0.171749i
$536$	0.122665	−	2.10607i	0.00529831	−	0.0909684i
$537$	16.5098	+	14.0781i	0.712450	+	0.607513i
$538$	−10.4131	−	11.0372i	−0.448941	−	0.475849i
$539$	−6.12377	+	10.6067i	−0.263770	+	0.456862i
$540$	−20.1322	−	10.7181i	−0.866352	−	0.461235i
$541$	13.3656	+	23.1498i	0.574630	+	0.995289i	0.996082	+	0.0884379i	$0.0281875\pi$
$541$	13.3656	+	23.1498i	0.574630	+	0.995289i	−0.421451	+	0.906851i	$0.638479\pi$
$542$	−1.02824	+	3.43458i	−0.0441669	+	0.147528i
$543$	−4.14899	−	1.54749i	−0.178050	−	0.0664092i
$544$	−0.688922	−	0.453111i	−0.0295373	−	0.0194270i
$545$	59.7235	−	6.98068i	2.55828	−	0.299020i
$546$	0.0436562	−	0.0282195i	0.00186831	−	0.00120768i
$547$	10.1347	+	5.08983i	0.433328	+	0.217626i	0.652073	−	0.758157i	$-0.273900\pi$
$547$	10.1347	+	5.08983i	0.433328	+	0.217626i	−0.218744	+	0.975782i	$0.570196\pi$
$548$	−1.91886	−	10.8824i	−0.0819696	−	0.464873i
$549$	−0.250184	−	5.90942i	−0.0106776	−	0.252208i
$550$	8.08238	−	45.8375i	0.344634	−	1.95452i
$551$	−14.9760	+	20.1162i	−0.637998	+	0.856980i
$552$	−0.386314	+	0.876394i	−0.0164426	+	0.0373018i
$553$	−5.88829	+	6.24122i	−0.250396	+	0.265404i
$554$	−6.38506	−	21.3276i	−0.271275	−	0.906122i
$555$	23.9515	−	11.7919i	1.01668	−	0.500538i
$556$	8.18986	+	0.957257i	0.347327	+	0.0405968i
$557$	4.24124	+	3.55882i	0.179707	+	0.150792i	0.728204	−	0.685360i	$-0.240355\pi$
$557$	4.24124	+	3.55882i	0.179707	+	0.150792i	−0.548497	+	0.836153i	$0.684800\pi$
$558$	10.6672	−	8.66616i	0.451577	−	0.366868i
$559$	0.0742636	−	0.0623145i	0.00314101	−	0.00263562i
$560$	−6.60719	+	4.34562i	−0.279205	+	0.183636i
$561$	3.17068	+	3.41459i	0.133866	+	0.144164i
$562$	−14.9919	−	20.1376i	−0.632393	−	0.849452i
$563$	10.4356	−	5.24097i	0.439809	−	0.220880i	−0.215094	−	0.976593i	$-0.569006\pi$
$563$	10.4356	−	5.24097i	0.439809	−	0.220880i	0.654903	+	0.755713i	$0.272709\pi$
$564$	18.9464	+	0.150309i	0.797789	+	0.00632916i
$565$	2.21683	−	0.525398i	0.0932627	−	0.0221037i
$566$	1.59542			0.0670607
$567$	−0.428758	−	16.2095i	−0.0180061	−	0.680737i
$568$	9.62909			0.404028
$569$	−3.87835	+	0.919185i	−0.162589	+	0.0385343i	−0.311104	−	0.950376i	$-0.600699\pi$
$569$	−3.87835	+	0.919185i	−0.162589	+	0.0385343i	0.148515	+	0.988910i	$0.452551\pi$
$570$	29.0864	+	51.3150i	1.21830	+	2.14935i
$571$	−33.0032	+	16.5748i	−1.38114	+	0.693635i	−0.975418	−	0.220361i	$-0.929276\pi$
$571$	−33.0032	+	16.5748i	−1.38114	+	0.693635i	−0.405723	+	0.913996i	$0.632980\pi$
$572$	0.0324544	+	0.0435938i	0.00135699	+	0.00182275i
$573$	17.0060	−	3.88826i	0.710435	−	0.162435i
$574$	−16.2032	+	10.6570i	−0.676309	+	0.444815i
$575$	−6.04302	+	5.07070i	−0.252012	+	0.211463i
$576$	−2.83500	+	0.981204i	−0.118125	+	0.0408835i
$577$	−2.52833	−	2.12152i	−0.105256	−	0.0883201i	0.588641	−	0.808395i	$-0.299663\pi$
$577$	−2.52833	−	2.12152i	−0.105256	−	0.0883201i	−0.693897	+	0.720074i	$0.744108\pi$
$578$	−16.2097	−	1.89465i	−0.674236	−	0.0788069i
$579$	21.8581	+	14.6260i	0.908391	+	0.607837i
$580$	−4.06911	−	13.5918i	−0.168961	−	0.564368i
$581$	−8.43677	+	8.94245i	−0.350016	+	0.370995i
$582$	−8.72660	−	11.9181i	−0.361729	−	0.494021i
$583$	−9.14717	+	12.2868i	−0.378837	+	0.508867i
$584$	−1.09553	+	6.21307i	−0.0453334	+	0.257099i
$585$	0.217435	+	0.0289183i	0.00898981	+	0.00119562i
$586$	−0.961992	−	5.45573i	−0.0397395	−	0.225374i
$587$	−1.27650	−	0.641081i	−0.0526867	−	0.0264602i	0.422261	−	0.906474i	$-0.361237\pi$
$587$	−1.27650	−	0.641081i	−0.0526867	−	0.0264602i	−0.474947	+	0.880014i	$0.657533\pi$
$588$	5.78704	+	2.96408i	0.238653	+	0.122237i
$589$	−35.3040	+	4.12644i	−1.45467	+	0.170027i
$590$	11.6751	+	7.67885i	0.480657	+	0.316133i
$591$	21.5906	−	17.8267i	0.888119	−	0.733293i
$592$	1.00713	−	3.36406i	0.0413930	−	0.138262i
$593$	−9.18341	−	15.9061i	−0.377117	−	0.653186i	0.613524	−	0.789676i	$-0.289751\pi$
$593$	−9.18341	−	15.9061i	−0.377117	−	0.653186i	−0.990641	+	0.136490i	$0.956418\pi$
$594$	16.8805	−	1.56686i	0.692613	−	0.0642890i
$595$	3.26044	−	5.64725i	0.133665	−	0.231515i
$596$	9.94444	+	10.5405i	0.407340	+	0.431755i
$597$	4.50871	−	24.4350i	0.184529	−	1.00006i
$598$	0.000535582	−	0.00919558i	2.19016e−5	−	0.000376035i
$599$	2.48144	−	5.75263i	0.101389	−	0.235046i	−0.859970	−	0.510345i	$-0.829518\pi$
$599$	2.48144	−	5.75263i	0.101389	−	0.235046i	0.961359	+	0.275299i	$0.0887769\pi$
$600$	−24.5189	−	3.06321i	−1.00098	−	0.125055i
$601$	−1.48192	−	25.4436i	−0.0604487	−	1.03786i	−0.883060	−	0.469260i	$-0.844521\pi$
$601$	−1.48192	−	25.4436i	−0.0604487	−	1.03786i	0.822611	−	0.568604i	$-0.192516\pi$
$602$	−9.85302	−	3.58621i	−0.401579	−	0.146163i
$603$	6.13439	+	1.55707i	0.249812	+	0.0634089i
$604$	−4.16919	+	1.51746i	−0.169642	+	0.0617446i
$605$	−0.617834	−	1.43230i	−0.0251185	−	0.0582313i
$606$	−9.08339	+	9.47609i	−0.368988	+	0.384940i
$607$	−46.6297	−	11.0514i	−1.89264	−	0.448564i	−0.892644	−	0.450762i	$-0.851152\pi$
$607$	−46.6297	−	11.0514i	−1.89264	−	0.448564i	−0.999998	+	0.00219801i	$0.999300\pi$
$608$	7.54951	+	1.78927i	0.306173	+	0.0725643i
$609$	6.98008	−	7.28184i	0.282847	−	0.295075i
$610$	−3.42761	−	7.94610i	−0.138780	−	0.321728i
$611$	−0.171232	+	0.0623233i	−0.00692730	+	0.00252133i
$612$	1.72591	−	1.77216i	0.0697656	−	0.0716354i
$613$	−6.28262	−	2.28669i	−0.253753	−	0.0923584i	0.212012	−	0.977267i	$-0.431998\pi$
$613$	−6.28262	−	2.28669i	−0.253753	−	0.0923584i	−0.465765	+	0.884909i	$0.654221\pi$
$614$	−0.0421938	−	0.724439i	−0.00170280	−	0.0292360i
$615$	−81.2035	−	10.1450i	−3.27444	−	0.409084i
$616$	2.32824	−	5.39747i	0.0938075	−	0.217470i
$617$	−1.00771	+	17.3018i	−0.0405690	+	0.696543i	0.915304	+	0.402763i	$0.131950\pi$
$617$	−1.00771	+	17.3018i	−0.0405690	+	0.696543i	−0.955873	+	0.293779i	$0.905087\pi$
$618$	−1.72333	+	9.33960i	−0.0693225	+	0.375694i
$619$	13.3203	+	14.1187i	0.535388	+	0.567478i	0.937444	−	0.348137i	$-0.113186\pi$
$619$	13.3203	+	14.1187i	0.535388	+	0.567478i	−0.402056	+	0.915615i	$0.631704\pi$
$620$	10.0543	−	17.4145i	0.403789	−	0.699384i
$621$	−2.36234	−	1.63557i	−0.0947974	−	0.0656334i
$622$	−3.18486	−	5.51634i	−0.127701	−	0.221185i
$623$	−6.63721	+	22.1698i	−0.265914	+	0.888216i
$624$	0.0222485	−	0.0183699i	0.000890653	−	0.000735385i
$625$	−89.5561	−	58.9020i	−3.58224	−	2.35608i
$626$	8.10252	−	0.947048i	0.323842	−	0.0378517i
$627$	−39.0232	−	19.9874i	−1.55844	−	0.798221i
$628$	11.2176	+	5.63367i	0.447629	+	0.224808i
$629$	0.502809	+	2.85157i	0.0200483	+	0.113700i
$630$	−9.05001	−	21.9306i	−0.360561	−	0.873736i
$631$	−7.16349	+	40.6262i	−0.285174	+	1.61730i	0.419489	+	0.907760i	$0.362209\pi$
$631$	−7.16349	+	40.6262i	−0.285174	+	1.61730i	−0.704663	+	0.709542i	$0.748902\pi$
$632$	−2.84395	+	3.82008i	−0.113126	+	0.151955i
$633$	22.4095	+	30.6051i	0.890696	+	1.21644i
$634$	−9.95356	+	10.5502i	−0.395306	+	0.419000i
$635$	−15.8473	−	52.9336i	−0.628880	−	2.10060i
$636$	6.75845	+	4.52232i	0.267990	+	0.179322i
$637$	−0.0621092	−	0.00725952i	−0.00246086	−	0.000287633i
$638$	8.07864	+	6.77879i	0.319836	+	0.268375i
$639$	−5.46695	+	28.3653i	−0.216269	+	1.12211i
$640$	−3.36241	+	2.82140i	−0.132911	+	0.111525i
$641$	−19.1569	+	12.5997i	−0.756651	+	0.497657i	−0.868269	−	0.496094i	$-0.834767\pi$
$641$	−19.1569	+	12.5997i	−0.756651	+	0.497657i	0.111618	+	0.993751i	$0.464397\pi$
$642$	−1.66427	+	0.380522i	−0.0656837	+	0.0150180i
$643$	3.09065	+	4.15147i	0.121883	+	0.163718i	0.858877	−	0.512182i	$-0.171163\pi$
$643$	3.09065	+	4.15147i	0.121883	+	0.163718i	−0.736994	+	0.675900i	$0.763755\pi$
$644$	−0.890298	+	0.447125i	−0.0350827	+	0.0176192i
$645$	−21.8176	−	38.4913i	−0.859069	−	1.51559i
$646$	−6.22513	+	1.47538i	−0.244925	+	0.0580482i
$647$	36.9426			1.45236			0.726182	−	0.687502i	$-0.241293\pi$
$647$	36.9426			1.45236			0.726182	+	0.687502i	$0.241293\pi$
$648$	−1.28084	−	8.90839i	−0.0503160	−	0.349955i
$649$	−10.3870			−0.407725
$650$	0.231236	−	0.0548039i	0.00906982	−	0.00214959i
$651$	14.2959	+	0.113415i	0.560300	+	0.00444507i
$652$	−10.4748	+	5.26065i	−0.410226	+	0.206023i
$653$	−15.6564	−	21.0302i	−0.612682	−	0.822975i	0.382194	−	0.924082i	$-0.375169\pi$
$653$	−15.6564	−	21.0302i	−0.612682	−	0.822975i	−0.994875	+	0.101108i	$0.967761\pi$
$654$	16.1455	+	17.3876i	0.631340	+	0.679907i
$655$	−3.82331	+	2.51463i	−0.149389	+	0.0982548i
$656$	−8.24584	+	6.91908i	−0.321946	+	0.270145i
$657$	−17.6804	−	6.75469i	−0.689777	−	0.263526i
$658$	15.0978	+	12.6686i	0.588575	+	0.493873i
$659$	−4.43944	−	0.518897i	−0.172936	−	0.0202133i	0.0291841	−	0.999574i	$-0.490709\pi$
$659$	−4.43944	−	0.518897i	−0.172936	−	0.0202133i	−0.202120	+	0.979361i	$0.564783\pi$
$660$	22.2533	−	10.9558i	0.866209	−	0.426455i
$661$	1.98525	+	6.63118i	0.0772171	+	0.257923i	0.987878	−	0.155231i	$-0.0496122\pi$
$661$	1.98525	+	6.63118i	0.0772171	+	0.257923i	−0.910661	+	0.413154i	$0.864427\pi$
$662$	−11.0880	+	11.7525i	−0.430946	+	0.456776i
$663$	−0.00959606	+	0.0217697i	−0.000372680	+	0.000845463i
$664$	−4.07482	+	5.47344i	−0.158134	+	0.212410i
$665$	−10.6545	+	60.4246i	−0.413163	+	2.34317i
$666$	9.33800	+	4.87676i	0.361840	+	0.188971i
$667$	−0.310374	−	1.76022i	−0.0120177	−	0.0681560i
$668$	4.01917	+	2.01850i	0.155506	+	0.0780982i
$669$	−26.5676	+	17.1734i	−1.02716	+	0.663962i
$670$	9.19726	−	1.07501i	0.355321	−	0.0415311i
$671$	5.37425	+	3.53470i	0.207471	+	0.136456i
$672$	−2.92386	−	1.09054i	−0.112790	−	0.0420687i
$673$	12.3944	−	41.4002i	0.477769	−	1.59586i	−0.291257	−	0.956645i	$-0.594074\pi$
$673$	12.3944	−	41.4002i	0.477769	−	1.59586i	0.769027	−	0.639216i	$-0.220741\pi$
$674$	−12.6918	−	21.9829i	−0.488870	−	0.846748i
$675$	22.9443	−	70.4884i	0.883125	−	2.71310i
$676$	6.49986	−	11.2581i	0.249995	−	0.433003i
$677$	11.0411	+	11.7029i	0.424345	+	0.449779i	0.903907	−	0.427729i	$-0.140686\pi$
$677$	11.0411	+	11.7029i	0.424345	+	0.449779i	−0.479563	+	0.877508i	$0.659205\pi$
$678$	0.684074	+	0.583316i	0.0262717	+	0.0224021i
$679$	0.893414	−	15.3393i	0.0342861	−	0.588669i
$680$	1.43354	−	3.32331i	0.0549737	−	0.127443i
$681$	5.74835	+	13.6223i	0.220277	+	0.522008i
$682$	0.869081	+	14.9215i	0.0332788	+	0.571376i
$683$	−7.00064	−	2.54803i	−0.267872	−	0.0974975i	0.204592	−	0.978847i	$-0.434413\pi$
$683$	−7.00064	−	2.54803i	−0.267872	−	0.0974975i	−0.472464	+	0.881350i	$0.656635\pi$
$684$	−9.55706	+	21.2234i	−0.365423	+	0.811496i
$685$	45.5780	−	16.5890i	1.74144	−	0.633834i
$686$	7.67413	+	17.7906i	0.293000	+	0.679250i
$687$	−12.4700	−	42.8881i	−0.475760	−	1.63628i
$688$	−5.66287	−	1.34212i	−0.215895	−	0.0511680i
$689$	−0.0760998	−	0.0180360i	−0.00289917	−	0.000687116i
$690$	−4.08277	−	1.00191i	−0.155429	−	0.0381420i
$691$	−15.6506	−	36.2821i	−0.595376	−	1.38024i	−0.903376	−	0.428850i	$-0.858919\pi$
$691$	−15.6506	−	36.2821i	−0.595376	−	1.38024i	0.308000	−	0.951386i	$-0.400340\pi$
$692$	−18.9686	+	6.90399i	−0.721076	+	0.262450i
$693$	14.5779	+	9.92293i	0.553770	+	0.376941i
$694$	26.1593	+	9.52120i	0.992992	+	0.361420i
$695$	2.10441	+	36.1313i	0.0798248	+	1.37054i
$696$	3.37878	−	4.46411i	0.128072	−	0.169212i
$697$	3.51555	−	8.14996i	0.133161	−	0.308702i
$698$	0.381346	−	6.54745i	0.0144341	−	0.247825i
$699$	12.8902	−	4.57616i	0.487551	−	0.173086i
$700$	−17.6385	−	18.6957i	−0.666672	−	0.706631i
$701$	−10.1734	+	17.6209i	−0.384246	+	0.665533i	−0.991664	−	0.128849i	$-0.958872\pi$
$701$	−10.1734	+	17.6209i	−0.384246	+	0.665533i	0.607419	+	0.794382i	$0.292205\pi$
$702$	0.0414822	+	0.0759689i	0.00156564	+	0.00286726i
$703$	−13.6226	−	23.5950i	−0.513785	−	0.889902i
$704$	0.935727	−	3.12555i	0.0352665	−	0.117798i
$705$	13.7912	+	82.0130i	0.519405	+	3.08879i
$706$	20.0872	+	13.2116i	0.755993	+	0.497225i
$707$	−13.5619	+	1.58516i	−0.510048	+	0.0596161i
$708$	0.276943	+	5.50728i	0.0104082	+	0.206976i
$709$	13.8876	+	6.97464i	0.521561	+	0.261938i	0.690045	−	0.723766i	$-0.257591\pi$
$709$	13.8876	+	6.97464i	0.521561	+	0.261938i	−0.168484	+	0.985704i	$0.553887\pi$
$710$	7.33926	+	41.6230i	0.275437	+	1.56208i
$711$	−9.63849	−	10.5465i	−0.361472	−	0.395526i
$712$	−2.23045	+	12.6495i	−0.0835895	+	0.474060i
$713$	1.51276	−	2.03199i	0.0566533	−	0.0760986i
$714$	2.55807	−	0.278444i	0.0957335	−	0.0104205i
$715$	−0.163703	+	0.173515i	−0.00612215	+	0.00648910i
$716$	3.59274	+	12.0006i	0.134267	+	0.448483i
$717$	−2.24699	+	33.9387i	−0.0839153	+	1.26746i
$718$	25.9292	+	3.03068i	0.967667	+	0.113104i
$719$	18.8117	+	15.7849i	0.701557	+	0.588677i	0.922216	−	0.386674i	$-0.126376\pi$
$719$	18.8117	+	15.7849i	0.701557	+	0.588677i	−0.220659	+	0.975351i	$0.570821\pi$
$720$	−6.40221	−	11.5068i	−0.238596	−	0.428833i
$721$	−7.56784	+	6.35017i	−0.281841	+	0.236493i
$722$	34.4192	−	22.6379i	1.28095	−	0.842495i
$723$	3.51009	−	11.3947i	0.130542	−	0.423775i
$724$	−1.52670	−	2.05072i	−0.0567395	−	0.0762144i
$725$	41.2081	−	20.6955i	1.53043	−	0.768611i
$726$	0.311987	−	0.530611i	0.0115789	−	0.0196928i
$727$	30.8141	−	7.30308i	1.14283	−	0.270856i	0.384754	−	0.923019i	$-0.374286\pi$
$727$	30.8141	−	7.30308i	1.14283	−	0.270856i	0.758079	+	0.652163i	$0.226138\pi$
$728$	0.0300122			0.00111233
$729$	26.9694	+	1.28470i	0.998867	+	0.0475813i
$730$	−27.6918			−1.02492
$731$	4.66946	−	1.10668i	0.172706	−	0.0409321i
$732$	1.73084	−	2.94372i	0.0639736	−	0.108803i
$733$	12.9741	−	6.51586i	0.479211	−	0.240669i	−0.192761	−	0.981246i	$-0.561744\pi$
$733$	12.9741	−	6.51586i	0.479211	−	0.240669i	0.671971	+	0.740577i	$0.265448\pi$
$734$	−2.44731	−	3.28731i	−0.0903319	−	0.121337i
$735$	−8.40176	+	27.2744i	−0.309904	+	1.00603i
$736$	−0.461994	+	0.303858i	−0.0170293	+	0.0112004i
$737$	−5.27263	+	4.42426i	−0.194220	+	0.162970i
$738$	−15.7005	−	28.2188i	−0.577944	−	1.03875i
$739$	4.03135	+	3.38270i	0.148296	+	0.124435i	0.713917	−	0.700230i	$-0.246919\pi$
$739$	4.03135	+	3.38270i	0.148296	+	0.124435i	−0.565622	+	0.824665i	$0.691364\pi$
$740$	15.3092	+	1.78939i	0.562778	+	0.0657793i
$741$	0.0147884	−	0.223365i	0.000543266	−	0.00820552i
$742$	2.42603	+	8.10351i	0.0890624	+	0.297489i
$743$	27.0896	−	28.7133i	0.993822	−	1.05339i	−0.00475161	−	0.999989i	$-0.501512\pi$
$743$	27.0896	−	28.7133i	0.993822	−	1.05339i	0.998573	−	0.0534006i	$-0.0170060\pi$
$744$	7.88837	−	0.858640i	0.289202	−	0.0314793i
$745$	−37.9830	+	51.0201i	−1.39159	+	1.86923i
$746$	1.04480	−	5.92535i	0.0382528	−	0.216942i
$747$	−13.8101	−	15.1111i	−0.505284	−	0.552887i
$748$	0.467160	+	2.64939i	0.0170810	+	0.0968714i
$749$	−1.58697	−	0.797006i	−0.0579866	−	0.0291220i
$750$	−3.53800	−	70.3564i	−0.129189	−	2.56905i
$751$	31.4823	−	3.67975i	1.14880	−	0.134276i	0.479692	−	0.877437i	$-0.340748\pi$
$751$	31.4823	−	3.67975i	1.14880	−	0.134276i	0.669113	+	0.743161i	$0.266674\pi$
$752$	9.13946	+	6.01112i	0.333282	+	0.219203i
$753$	−7.21522	−	42.9073i	−0.262937	−	1.56363i
$754$	−0.0154426	+	0.0515820i	−0.000562388	+	0.00187851i
$755$	−9.73716	−	16.8653i	−0.354372	−	0.613790i
$756$	4.87254	−	7.99392i	0.177213	−	0.290736i
$757$	−11.7156	+	20.2921i	−0.425812	+	0.737527i	−0.996496	−	0.0836424i	$-0.973345\pi$
$757$	−11.7156	+	20.2921i	−0.425812	+	0.737527i	0.570684	+	0.821170i	$0.306678\pi$
$758$	3.97756	+	4.21597i	0.144471	+	0.153131i
$759$	2.94474	−	1.04542i	0.106887	−	0.0379462i
$760$	−1.98013	+	33.9975i	−0.0718268	+	1.23322i
$761$	7.56317	−	17.5334i	0.274165	−	0.635586i	−0.724386	−	0.689394i	$-0.757877\pi$
$761$	7.56317	−	17.5334i	0.274165	−	0.635586i	0.998551	+	0.0538086i	$0.0171361\pi$
$762$	13.1587	−	17.3856i	0.476691	−	0.629813i
$763$	1.43512	+	24.6400i	0.0519547	+	0.892027i
$764$	9.46437	+	3.44475i	0.342409	+	0.124627i
$765$	8.97588	+	6.10972i	0.324523	+	0.220897i
$766$	8.13047	−	2.95925i	0.293766	−	0.106922i
$767$	−0.0210052	−	0.0486954i	−0.000758452	−	0.00175829i
$768$	−1.68214	&m

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)

\(f(q)\)	\(=\)	\(q+(-0.973045 + 0.230616i) q^{2} +(0.877898 - 1.49308i) q^{3} +(0.893633 - 0.448799i) q^{4} +(2.62112 + 3.52077i) q^{5} +(-0.509905 + 1.65529i) q^{6} +(-1.50529 + 0.990045i) q^{7} +(-0.766044 + 0.642788i) q^{8} +(-1.45859 - 2.62155i) q^{9} +O(q^{10})\)	\(q+(-0.973045 + 0.230616i) q^{2} +(0.877898 - 1.49308i) q^{3} +(0.893633 - 0.448799i) q^{4} +(2.62112 + 3.52077i) q^{5} +(-0.509905 + 1.65529i) q^{6} +(-1.50529 + 0.990045i) q^{7} +(-0.766044 + 0.642788i) q^{8} +(-1.45859 - 2.62155i) q^{9} +(-3.36241 - 2.82140i) q^{10} +(3.24055 + 0.378766i) q^{11} +(0.114424 - 1.72827i) q^{12} +(0.00477752 + 0.0159580i) q^{13} +(1.23640 - 1.31050i) q^{14} +(7.55787 - 0.822666i) q^{15} +(0.597159 - 0.802123i) q^{16} +(-0.143186 + 0.812048i) q^{17} +(2.02384 + 2.21451i) q^{18} +(-1.34727 - 7.64077i) q^{19} +(3.92243 + 1.96992i) q^{20} +(0.156728 + 3.11668i) q^{21} +(-3.24055 + 0.378766i) q^{22} +(0.461994 + 0.303858i) q^{23} +(0.287226 + 1.70807i) q^{24} +(-4.09155 + 13.6667i) q^{25} +(-0.00832891 - 0.0144261i) q^{26} +(-5.19468 - 0.123655i) q^{27} +(-0.900845 + 1.56031i) q^{28} +(-2.21818 - 2.35113i) q^{29} +(-7.16443 + 2.54346i) q^{30} +(0.266376 - 4.57350i) q^{31} +(-0.396080 + 0.918216i) q^{32} +(3.41040 - 4.50589i) q^{33} +(-0.0479448 - 0.823180i) q^{34} +(-7.43126 - 2.70476i) q^{35} +(-2.47999 - 1.68809i) q^{36} +(3.29981 - 1.20103i) q^{37} +(3.07304 + 7.12411i) q^{38} +(0.0280208 + 0.00687629i) q^{39} +(-4.27100 - 1.01225i) q^{40} +(-10.4740 - 2.48239i) q^{41} +(-0.871259 - 2.99653i) q^{42} +(-2.30508 - 5.34378i) q^{43} +(3.06585 - 1.11588i) q^{44} +(5.40673 - 12.0067i) q^{45} +(-0.519616 - 0.189125i) q^{46} +(0.636051 + 10.9206i) q^{47} +(-0.673392 - 1.59579i) q^{48} +(-1.48685 + 3.44690i) q^{49} +(0.829498 - 14.2419i) q^{50} +(1.08675 + 0.926683i) q^{51} +(0.0114313 + 0.0121165i) q^{52} +(-2.34748 + 4.06596i) q^{53} +(5.08317 - 1.07765i) q^{54} +(7.16031 + 12.4020i) q^{55} +(0.516731 - 1.72600i) q^{56} +(-12.5911 - 4.69623i) q^{57} +(2.70059 + 1.77621i) q^{58} +(-3.16212 + 0.369599i) q^{59} +(6.38475 - 4.12713i) q^{60} +(1.76186 + 0.884840i) q^{61} +(0.795526 + 4.51165i) q^{62} +(4.79105 + 2.50212i) q^{63} +(0.173648 - 0.984808i) q^{64} +(-0.0436621 + 0.0586484i) q^{65} +(-2.27934 + 5.17092i) q^{66} +(-1.44772 + 1.53450i) q^{67} +(0.236491 + 0.789934i) q^{68} +(0.859269 - 0.423039i) q^{69} +(7.85471 + 0.918084i) q^{70} +(-7.37631 - 6.18946i) q^{71} +(2.80244 + 1.07066i) q^{72} +(4.83291 - 4.05529i) q^{73} +(-2.93389 + 1.92965i) q^{74} +(16.8136 + 18.1070i) q^{75} +(-4.63314 - 6.22339i) q^{76} +(-5.25296 + 2.63814i) q^{77} +(-0.0288513 - 0.000228888i) q^{78} +(4.63409 - 1.09830i) q^{79} +4.38931 q^{80} +(-4.74503 + 7.64753i) q^{81} +10.7642 q^{82} +(6.63975 - 1.57365i) q^{83} +(1.53882 + 2.71483i) q^{84} +(-3.23434 + 1.62435i) q^{85} +(3.47531 + 4.66815i) q^{86} +(-5.45777 + 1.24787i) q^{87} +(-2.72587 + 1.79283i) q^{88} +(9.83956 - 8.25637i) q^{89} +(-2.49205 + 12.9300i) q^{90} +(-0.0229907 - 0.0192915i) q^{91} +(0.549224 + 0.0641951i) q^{92} +(-6.59476 - 4.41279i) q^{93} +(-3.13736 - 10.4795i) q^{94} +(23.3700 - 24.7708i) q^{95} +(1.02325 + 1.39748i) q^{96} +(-5.09273 + 6.84073i) q^{97} +(0.651860 - 3.69688i) q^{98} +(-3.73368 - 9.04772i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q + 9 q^{6}+O(q^{10}) \) 72 * q + 9 * q^6	\( 72 q + 9 q^{6} + 18 q^{13} - 9 q^{20} - 81 q^{23} + 18 q^{25} - 27 q^{26} - 27 q^{27} + 18 q^{28} - 27 q^{29} - 63 q^{30} - 54 q^{31} + 9 q^{33} - 27 q^{35} - 9 q^{36} + 9 q^{38} - 9 q^{41} + 9 q^{42} + 36 q^{43} - 117 q^{45} - 18 q^{46} - 27 q^{47} + 9 q^{48} - 27 q^{51} - 36 q^{52} - 27 q^{53} + 54 q^{55} + 27 q^{57} + 9 q^{58} - 18 q^{59} + 9 q^{63} + 9 q^{65} + 36 q^{66} - 135 q^{67} - 18 q^{68} + 108 q^{69} + 18 q^{70} + 72 q^{71} + 54 q^{72} + 36 q^{73} + 99 q^{74} - 36 q^{75} - 9 q^{76} + 144 q^{77} + 90 q^{78} - 9 q^{79} + 18 q^{80} - 72 q^{82} + 99 q^{83} + 18 q^{84} + 9 q^{85} + 72 q^{86} + 207 q^{87} - 9 q^{88} + 126 q^{89} - 18 q^{90} + 63 q^{91} + 36 q^{92} + 81 q^{93} + 18 q^{94} + 45 q^{95} - 171 q^{97} + 36 q^{98} + 99 q^{99}+O(q^{100}) \) 72 * q + 9 * q^6 + 18 * q^13 - 9 * q^20 - 81 * q^23 + 18 * q^25 - 27 * q^26 - 27 * q^27 + 18 * q^28 - 27 * q^29 - 63 * q^30 - 54 * q^31 + 9 * q^33 - 27 * q^35 - 9 * q^36 + 9 * q^38 - 9 * q^41 + 9 * q^42 + 36 * q^43 - 117 * q^45 - 18 * q^46 - 27 * q^47 + 9 * q^48 - 27 * q^51 - 36 * q^52 - 27 * q^53 + 54 * q^55 + 27 * q^57 + 9 * q^58 - 18 * q^59 + 9 * q^63 + 9 * q^65 + 36 * q^66 - 135 * q^67 - 18 * q^68 + 108 * q^69 + 18 * q^70 + 72 * q^71 + 54 * q^72 + 36 * q^73 + 99 * q^74 - 36 * q^75 - 9 * q^76 + 144 * q^77 + 90 * q^78 - 9 * q^79 + 18 * q^80 - 72 * q^82 + 99 * q^83 + 18 * q^84 + 9 * q^85 + 72 * q^86 + 207 * q^87 - 9 * q^88 + 126 * q^89 - 18 * q^90 + 63 * q^91 + 36 * q^92 + 81 * q^93 + 18 * q^94 + 45 * q^95 - 171 * q^97 + 36 * q^98 + 99 * q^99

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