LMFDB - Embedded newform 162.2.g.a.97.3

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			97.3
Character	$\chi$	$=$	162.97
Dual form			162.2.g.a.157.3

$q$-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 $\left(\mathbb{Z}/162\mathbb{Z}\right)^\times$.

$n$	$83$
$\chi(n)$	$e\left(\frac{2}{27}\right)$

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	0.432441	−	0.901662i	$-0.357652\pi$
$5$	2.62112	−	3.52077i	1.17220	−	1.57454i	0.739758	−	0.672873i	$-0.234940\pi$
$6$	−0.509905	−	1.65529i	−0.208168	−	0.675771i
$7$	−1.50529	−	0.990045i	−0.568946	−	0.374202i	0.232202	−	0.972668i	$-0.425407\pi$
$7$	−1.50529	−	0.990045i	−0.568946	−	0.374202i	−0.801148	+	0.598466i	$0.795777\pi$
$8$	−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	0.387452	−	0.921890i	$-0.373355\pi$
$11$	3.24055	−	0.378766i	0.977062	−	0.114202i	0.589610	+	0.807688i	$0.299281\pi$
$12$	0.114424	+	1.72827i	0.0330314	+	0.498908i
$13$	0.00477752	−	0.0159580i	0.00132505	−	0.00442596i	−0.957324	−	0.289015i	$-0.906672\pi$
$13$	0.00477752	−	0.0159580i	0.00132505	−	0.00442596i	0.958649	+	0.284589i	$0.0918573\pi$
$14$	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	0.962508	−	0.271253i	$-0.0874380\pi$
$17$	−0.143186	−	0.812048i	−0.0347277	−	0.196950i	−0.997236	+	0.0743026i	$0.976327\pi$
$18$	2.02384	−	2.21451i	0.477025	−	0.521965i
$19$	−1.34727	+	7.64077i	−0.309086	+	1.75291i	0.294533	+	0.955641i	$0.404836\pi$
$19$	−1.34727	+	7.64077i	−0.309086	+	1.75291i	−0.603619	+	0.797273i	$0.706275\pi$
$20$	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	−0.500429	−	0.865778i	$-0.666824\pi$
$23$	0.461994	−	0.303858i	0.0963324	−	0.0633588i	0.596761	+	0.802419i	$0.296454\pi$
$24$	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	−0.899796	−	0.436311i	$-0.856285\pi$
$29$	−2.21818	+	2.35113i	−0.411905	+	0.436594i	0.487891	+	0.872905i	$0.337766\pi$
$30$	−7.16443	−	2.54346i	−1.30804	−	0.464369i
$31$	0.266376	+	4.57350i	0.0478426	+	0.821425i	0.933830	+	0.357716i	$0.116445\pi$
$31$	0.266376	+	4.57350i	0.0478426	+	0.821425i	−0.885988	+	0.463709i	$0.846518\pi$
$32$	−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	0.598705	−	0.800970i	$-0.295682\pi$
$37$	3.29981	+	1.20103i	0.542486	+	0.197449i	−0.0562191	+	0.998418i	$0.517905\pi$
$38$	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	−0.942820	−	0.333303i	$-0.891837\pi$
$41$	−10.4740	+	2.48239i	−1.63577	+	0.387684i	−0.692948	+	0.720987i	$0.743689\pi$
$42$	−0.871259	+	2.99653i	−0.134438	+	0.462374i
$43$	−2.30508	+	5.34378i	−0.351522	+	0.814919i	0.647099	+	0.762406i	$0.275982\pi$
$43$	−2.30508	+	5.34378i	−0.351522	+	0.814919i	−0.998620	+	0.0525123i	$0.983277\pi$
$44$	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	−0.555495	−	0.831520i	$-0.687471\pi$
$47$	0.636051	−	10.9206i	0.0927775	−	1.59293i	0.648272	−	0.761409i	$-0.275492\pi$
$48$	−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	0.658542	−	0.752544i	$-0.271174\pi$
$53$	−2.34748	−	4.06596i	−0.322451	−	0.558502i	−0.980993	+	0.194042i	$0.937840\pi$
$54$	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	−0.0922639	−	0.995735i	$-0.529410\pi$
$59$	−3.16212	−	0.369599i	−0.411673	−	0.0481177i	−0.319409	+	0.947617i	$0.603484\pi$
$60$	6.38475	+	4.12713i	0.824267	+	0.532810i
$61$	1.76186	−	0.884840i	0.225583	−	0.113292i	−0.332418	−	0.943132i	$-0.607865\pi$
$61$	1.76186	−	0.884840i	0.225583	−	0.113292i	0.558002	+	0.829840i	$0.311568\pi$
$62$	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	0.632875	−	0.774254i	$-0.281875\pi$
$67$	−1.44772	−	1.53450i	−0.176867	−	0.187469i	−0.809742	+	0.586785i	$0.800393\pi$
$68$	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	−0.965230	−	0.261404i	$-0.915815\pi$
$71$	−7.37631	+	6.18946i	−0.875407	+	0.734554i	0.0898221	+	0.995958i	$0.471370\pi$
$72$	2.80244	−	1.07066i	0.330271	−	0.126178i
$73$	4.83291	+	4.05529i	0.565649	+	0.474636i	0.880199	−	0.474605i	$-0.157409\pi$
$73$	4.83291	+	4.05529i	0.565649	+	0.474636i	−0.314550	+	0.949241i	$0.601854\pi$
$74$	−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	0.482874	−	0.875690i	$-0.339593\pi$
$79$	4.63409	+	1.09830i	0.521376	+	0.123568i	0.0385026	+	0.999258i	$0.487741\pi$
$80$	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	0.578237	−	0.815869i	$-0.303741\pi$
$83$	6.63975	+	1.57365i	0.728807	+	0.172731i	0.150570	+	0.988599i	$0.451889\pi$
$84$	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	0.992339	−	0.123543i	$-0.0394258\pi$
$89$	9.83956	+	8.25637i	1.04299	+	0.875173i	0.0506516	+	0.998716i	$0.483870\pi$
$90$	−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	0.464501	−	0.885573i	$-0.346234\pi$
$97$	−5.09273	−	6.84073i	−0.517089	−	0.694571i	−0.981590	+	0.191002i	$0.938826\pi$
$98$	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	−0.0787324	−	0.996896i	$-0.525087\pi$
$101$	6.77246	−	3.40126i	0.673885	−	0.338438i	0.752617	+	0.658458i	$0.228791\pi$
$102$	−1.27117	+	0.651082i	−0.125864	+	0.0644667i
$103$	5.44617	+	0.636566i	0.536627	+	0.0627227i	0.380090	−	0.924949i	$-0.375893\pi$
$103$	5.44617	+	0.636566i	0.536627	+	0.0627227i	0.156537	+	0.987672i	$0.449967\pi$
$104$	−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	−0.841220	−	0.540693i	$-0.818162\pi$
$107$	0.492832	−	0.853611i	0.0476439	−	0.0825217i	0.888864	+	0.458171i	$0.151495\pi$
$108$	−4.69763	−	2.22087i	−0.452030	−	0.213703i
$109$	6.84961	+	11.8639i	0.656073	+	1.13635i	0.981624	+	0.190828i	$0.0611172\pi$
$109$	6.84961	+	11.8639i	0.656073	+	1.13635i	−0.325550	+	0.945525i	$0.605550\pi$
$110$	−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	0.927612	−	0.373545i	$-0.121858\pi$
$113$	0.205582	+	0.476593i	0.0193395	+	0.0448341i	−0.908273	+	0.418379i	$0.862598\pi$
$114$	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	−0.808543	−	0.588437i	$-0.799743\pi$
$127$	−11.8293	+	4.30552i	−1.04968	+	0.382053i	−0.241139	+	0.970490i	$0.577521\pi$
$128$	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	0.994624	−	0.103552i	$-0.0330209\pi$
$131$	−0.0606198	−	1.04080i	−0.00529638	−	0.0909353i	−0.999920	+	0.0126169i	$0.995984\pi$
$132$	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	0.979923	+	0.199375i	$0.0638910\pi$
$137$	3.16925	+	10.5860i	0.270767	+	0.904426i	−0.709156	+	0.705052i	$0.750924\pi$
$138$	−0.738548	−	0.609797i	−0.0628694	−	0.0519094i
$139$	6.88911	−	4.53104i	0.584327	−	0.384318i	−0.222652	−	0.974898i	$-0.571471\pi$
$139$	6.88911	−	4.53104i	0.584327	−	0.384318i	0.806979	+	0.590580i	$0.201101\pi$
$140$	−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	−0.600724	−	0.799457i	$-0.705121\pi$
$149$	4.15611	−	13.8824i	0.340482	−	1.13729i	0.941206	−	0.337833i	$-0.109694\pi$
$150$	−20.5362	+	13.7415i	−1.67677	+	1.12199i
$151$	−4.40676	+	0.515076i	−0.358617	+	0.0419163i	−0.293494	−	0.955961i	$-0.594818\pi$
$151$	−4.40676	+	0.515076i	−0.358617	+	0.0419163i	−0.0651230	+	0.997877i	$0.520744\pi$
$152$	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	−0.395115	−	0.918632i	$-0.629295\pi$
$157$	7.49599	−	10.0689i	0.598245	−	0.803583i	0.993360	+	0.115049i	$0.0367025\pi$
$158$	−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	−0.685970	−	0.727630i	$-0.740622\pi$
$167$	2.68576	−	3.60760i	0.207830	−	0.279164i	0.893800	+	0.448465i	$0.148029\pi$
$168$	−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	−0.836607	−	0.547804i	$-0.815464\pi$
$173$	−20.0494	+	2.34344i	−1.52433	+	0.178169i	−0.687723	+	0.725973i	$0.741390\pi$
$174$	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	−0.951518	−	0.307594i	$-0.900476\pi$
$179$	−2.17526	−	12.3365i	−0.162587	−	0.922075i	0.788931	−	0.614482i	$-0.210635\pi$
$180$	−0.556985	+	13.1562i	−0.0415152	+	0.980602i
$181$	−0.443951	+	2.51777i	−0.0329986	+	0.187145i	−0.996852	−	0.0792902i	$-0.974735\pi$
$181$	−0.443951	+	2.51777i	−0.0329986	+	0.187145i	0.963853	+	0.266435i	$0.0858457\pi$
$182$	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	−0.427310	−	0.904105i	$-0.640539\pi$
$191$	6.91167	−	7.32594i	0.500111	−	0.530087i	0.927421	+	0.374018i	$0.122020\pi$
$192$	−1.31795	+	1.12383i	−0.0951151	+	0.0811056i
$193$	−0.882894	−	15.1587i	−0.0635521	−	1.09115i	−0.867820	−	0.496879i	$-0.834479\pi$
$193$	−0.882894	−	15.1587i	−0.0635521	−	1.09115i	0.804267	−	0.594267i	$-0.202558\pi$
$194$	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	0.261518	−	0.965199i	$-0.415777\pi$
$197$	15.1904	−	5.52884i	1.08227	−	0.393914i	0.820752	+	0.571285i	$0.193555\pi$
$198$	5.71959	−	7.94279i	0.406473	−	0.564469i
$199$	13.4805	+	4.90652i	0.955611	+	0.347814i	0.772312	−	0.635243i	$-0.219100\pi$
$199$	13.4805	+	4.90652i	0.955611	+	0.347814i	0.183299	+	0.983057i	$0.441322\pi$
$200$	−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	−0.901905	−	0.431934i	$-0.857831\pi$
$211$	−8.67422	−	20.1091i	−0.597158	−	1.38437i	0.304747	−	0.952433i	$-0.401428\pi$
$212$	−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	−0.901586	−	0.432600i	$-0.857596\pi$
$223$	−16.3216	+	8.19703i	−1.09298	+	0.548914i	−0.191392	+	0.981514i	$0.561300\pi$
$224$	−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	0.600094	−	0.799929i	$-0.295130\pi$
$227$	−5.09759	−	6.84725i	−0.338339	−	0.454468i	−0.938433	+	0.345461i	$0.887722\pi$
$228$	−13.3595	−	1.45416i	−0.884752	−	0.0963043i
$229$	17.6961	+	18.7567i	1.16939	+	1.23948i	0.965477	+	0.260490i	$0.0838840\pi$
$229$	17.6961	+	18.7567i	1.16939	+	1.23948i	0.203911	+	0.978989i	$0.434635\pi$
$230$	−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	−0.422747	−	0.906248i	$-0.638934\pi$
$233$	6.04962	−	5.07623i	0.396324	−	0.332555i	0.819071	+	0.573693i	$0.194490\pi$
$234$	−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	−0.220904	−	0.975296i	$-0.570901\pi$
$239$	−17.5486	−	8.81325i	−1.13513	−	0.570082i	−0.914222	+	0.405214i	$0.867197\pi$
$240$	3.85337	+	6.55360i	0.248734	+	0.423033i
$241$	6.69826	+	1.58752i	0.431473	+	0.102261i	0.440613	−	0.897697i	$-0.354761\pi$
$241$	6.69826	+	1.58752i	0.431473	+	0.102261i	−0.00913991	+	0.999958i	$0.502909\pi$
$242$	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	0.999088	+	0.0426973i	$0.0135951\pi$
$251$	19.2433	+	16.1470i	1.21463	+	1.01919i	0.215538	+	0.976495i	$0.430849\pi$
$252$	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	0.859261	−	0.511538i	$-0.170924\pi$
$257$	4.78736	+	5.07430i	0.298627	+	0.316526i	−0.560634	+	0.828064i	$0.689442\pi$
$258$	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	−0.425291	−	0.905057i	$-0.639828\pi$
$263$	0.757507	−	0.380434i	0.0467099	−	0.0234586i	0.472001	+	0.881598i	$0.343532\pi$
$264$	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	−0.536498	−	0.843901i	$-0.680253\pi$
$269$	7.58705	−	13.1412i	0.462591	−	0.801231i	0.999089	+	0.0426706i	$0.0135866\pi$
$270$	17.1178	−	15.0720i	1.04175	−	0.917254i
$271$	1.79260	+	3.10487i	0.108892	+	0.188607i	0.915322	−	0.402723i	$-0.131936\pi$
$271$	1.79260	+	3.10487i	0.108892	+	0.188607i	−0.806429	+	0.591330i	$0.798603\pi$
$272$	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	−0.703275	−	0.710918i	$-0.748280\pi$
$277$	1.29447	−	22.2252i	0.0777772	−	1.33538i	0.781053	−	0.624465i	$-0.214683\pi$
$278$	−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	−0.311964	−	0.950094i	$-0.600987\pi$
$281$	9.94371	−	23.0521i	0.593192	−	1.37517i	0.905156	−	0.425080i	$-0.139754\pi$
$282$	−18.4011	+	4.51561i	−1.09577	+	0.268900i
$283$	−1.55242	+	0.367930i	−0.0922817	+	0.0218712i	−0.276497	−	0.961015i	$-0.589174\pi$
$283$	−1.55242	+	0.367930i	−0.0922817	+	0.0218712i	0.184216	+	0.982886i	$0.441026\pi$
$284$	−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	−0.994560	−	0.104170i	$-0.966781\pi$
$293$	−0.322116	−	5.53052i	−0.0188182	−	0.323097i	0.975741	−	0.218927i	$-0.0702556\pi$
$294$	−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	0.981001	−	0.194004i	$-0.0621476\pi$
$307$	−0.126011	−	0.714642i	−0.00719181	−	0.0407868i	−0.988192	+	0.153218i	$0.951036\pi$
$308$	−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	−0.890442	−	0.455097i	$-0.849605\pi$
$311$	1.82685	−	6.10212i	0.103591	−	0.346020i	0.994033	+	0.109078i	$0.0347897\pi$
$312$	−0.0258852	−	0.0127439i	−0.00146546	−	0.000721481i
$313$	−8.10252	+	0.947048i	−0.457981	+	0.0535303i	−0.341956	−	0.939716i	$-0.611089\pi$
$313$	−8.10252	+	0.947048i	−0.457981	+	0.0535303i	−0.116025	+	0.993246i	$0.537015\pi$
$314$	−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	0.842173	−	0.539208i	$-0.181276\pi$
$317$	12.1183	+	7.97032i	0.680631	+	0.447658i	−0.161542	+	0.986866i	$0.551647\pi$
$318$	−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	0.863359	−	0.504591i	$-0.168357\pi$
$331$	13.4994	+	8.87870i	0.741994	+	0.488017i	−0.121364	+	0.992608i	$0.538727\pi$
$332$	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	−0.493865	−	0.869539i	$-0.664416\pi$
$337$	7.28010	−	24.3172i	0.396573	−	1.32464i	0.890437	−	0.455106i	$-0.150399\pi$
$338$	−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	−0.989483	−	0.144650i	$-0.953794\pi$
$347$	−23.2584	+	15.2973i	−1.24858	+	0.821202i	−0.259094	+	0.965852i	$0.583424\pi$
$348$	−4.31720	−	3.56458i	−0.231426	−	0.191081i
$349$	−1.88101	−	6.28302i	−0.100688	−	0.336322i	0.892771	−	0.450511i	$-0.148758\pi$
$349$	−1.88101	−	6.28302i	−0.100688	−	0.336322i	−0.993459	+	0.114189i	$0.963573\pi$
$350$	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	−0.998076	−	0.0619961i	$-0.980253\pi$
$353$	−16.4990	+	17.4879i	−0.878152	+	0.930787i	0.119924	+	0.992783i	$0.461735\pi$
$354$	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	−0.895271	−	0.445522i	$-0.853018\pi$
$359$	−24.5313	+	8.92866i	−1.29471	+	0.471237i	−0.399442	+	0.916759i	$0.630796\pi$
$360$	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	−0.870582	−	0.492023i	$-0.836257\pi$
$367$	1.62324	−	3.76309i	0.0847323	−	0.196432i	0.955314	+	0.295592i	$0.0955168\pi$
$368$	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	0.845312	−	0.534274i	$-0.179415\pi$
$373$	−2.38312	−	5.52468i	−0.123393	−	0.286057i	−0.968705	+	0.248216i	$0.920156\pi$
$374$	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	−0.930808	−	0.365509i	$-0.880895\pi$
$379$	−2.89808	+	5.01961i	−0.148864	+	0.257840i	0.781944	+	0.623349i	$0.214228\pi$
$380$	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	−0.106339	−	0.994330i	$-0.533913\pi$
$383$	−8.59376	−	1.00447i	−0.439121	−	0.0513259i	−0.332781	+	0.943004i	$0.607987\pi$
$384$	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	0.370335	−	0.928898i	$-0.379243\pi$
$389$	−12.3418	−	16.5779i	−0.625753	−	0.840532i	−0.996088	+	0.0883664i	$0.971835\pi$
$390$	−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	0.721425	−	0.692492i	$-0.243487\pi$
$397$	3.28218	+	2.75408i	0.164728	+	0.138223i	−0.556697	+	0.830715i	$0.687932\pi$
$398$	−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	0.803331	−	0.595533i	$-0.203059\pi$
$401$	16.1272	+	8.09940i	0.805355	+	0.404465i	0.00202470	+	0.999998i	$0.499356\pi$
$402$	−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	0.986743	+	0.162294i	$0.0518892\pi$
$409$	34.5050	+	17.3291i	1.70616	+	0.856868i	0.719421	+	0.694574i	$0.244407\pi$
$410$	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	−0.955630	−	0.294570i	$-0.904824\pi$
$419$	−24.4434	−	25.9085i	−1.19414	−	1.26571i	−0.238507	−	0.971141i	$-0.576658\pi$
$420$	−5.52486	−	12.5337i	−0.269585	−	0.611583i
$421$	−5.20367	−	6.98975i	−0.253612	−	0.340659i	0.657024	−	0.753869i	$-0.271815\pi$
$421$	−5.20367	−	6.98975i	−0.253612	−	0.340659i	−0.910636	+	0.413210i	$0.864408\pi$
$422$	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	−0.943714	−	0.330764i	$-0.892694\pi$
$431$	−3.84915	+	6.66692i	−0.185407	+	0.321134i	0.758307	+	0.651898i	$0.226027\pi$
$432$	−3.20123	−	4.09293i	−0.154019	−	0.196921i
$433$	11.0881	+	19.2051i	0.532859	+	0.922939i	0.999264	+	0.0383677i	$0.0122158\pi$
$433$	11.0881	+	19.2051i	0.532859	+	0.922939i	−0.466404	+	0.884572i	$0.654451\pi$
$434$	−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	−0.907990	−	0.418991i	$-0.862384\pi$
$439$	0.890525	−	15.2897i	0.0425024	−	0.729738i	0.950493	−	0.310747i	$-0.100579\pi$
$440$	−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	0.483164	+	0.875530i	$0.339488\pi$
$443$	−10.2131	+	23.6767i	−0.485241	+	1.12491i	−0.968404	+	0.249385i	$0.919772\pi$
$444$	−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	0.516628	−	0.856210i	$-0.327187\pi$
$449$	7.67119	+	2.79209i	0.362026	+	0.131767i	−0.154602	+	0.987977i	$0.549409\pi$
$450$	−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	−0.853082	−	0.521776i	$-0.825270\pi$
$457$	−6.04102	+	6.40310i	−0.282587	+	0.299525i	0.570496	+	0.821301i	$0.306751\pi$
$458$	−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	0.982989	−	0.183667i	$-0.0587968\pi$
$461$	1.30515	+	4.35951i	0.0607870	+	0.203043i	−0.922202	+	0.386710i	$0.873612\pi$
$462$	−1.68838	+	10.0404i	−0.0785504	+	0.467121i
$463$	20.7820	−	13.6685i	0.965822	−	0.635231i	0.0344911	−	0.999405i	$-0.489019\pi$
$463$	20.7820	−	13.6685i	0.965822	−	0.635231i	0.931331	+	0.364174i	$0.118649\pi$
$464$	−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	−0.896345	−	0.443356i	$-0.853788\pi$
$467$	2.10873	−	11.9592i	0.0975806	−	0.553407i	0.993926	−	0.110051i	$-0.0351013\pi$
$468$	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	0.344150	−	0.938915i	$-0.388167\pi$
$479$	−8.35315	−	5.49395i	−0.381665	−	0.251025i	−0.725816	+	0.687889i	$0.758537\pi$
$480$	−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	0.237492	+	0.971390i	$0.423675\pi$
$491$	−16.8671	+	22.6565i	−0.761203	+	1.02247i	−0.998694	+	0.0510831i	$0.983733\pi$
$492$	−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	−0.923182	−	0.384363i	$-0.874421\pi$
$499$	1.32547	−	4.42739i	0.0593364	−	0.198197i	0.982518	+	0.186166i	$0.0596062\pi$
$500$	−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	0.941810	+	0.336145i	$0.109123\pi$
$503$	3.85232	+	21.8476i	0.171767	+	0.974137i	−0.770044	+	0.637991i	$0.779766\pi$
$504$	−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	−0.975408	−	0.220409i	$-0.929261\pi$
$509$	−26.1564	+	17.2034i	−1.15936	+	0.762526i	−0.183956	+	0.982934i	$0.558891\pi$
$510$	−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	−0.431119	−	0.902295i	$-0.641881\pi$
$521$	−4.14031	+	1.50695i	−0.181390	+	0.0660207i	0.249728	+	0.968316i	$0.419659\pi$
$522$	0.717355	+	9.67050i	0.0313978	+	0.423266i
$523$	−6.87231	−	2.50132i	−0.300505	−	0.109375i	0.187367	−	0.982290i	$-0.440005\pi$
$523$	−6.87231	−	2.50132i	−0.300505	−	0.109375i	−0.487872	+	0.872915i	$0.662227\pi$
$524$	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	−0.421451	−	0.906851i	$-0.638479\pi$
$541$	13.3656	−	23.1498i	0.574630	−	0.995289i	0.996082	−	0.0884379i	$-0.0281875\pi$
$542$	−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	−0.218744	−	0.975782i	$-0.570196\pi$
$547$	10.1347	−	5.08983i	0.433328	−	0.217626i	0.652073	+	0.758157i	$0.273900\pi$
$548$	−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	−0.548497	−	0.836153i	$-0.684800\pi$
$557$	4.24124	−	3.55882i	0.179707	−	0.150792i	0.728204	+	0.685360i	$0.240355\pi$
$558$	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	0.654903	−	0.755713i	$-0.272709\pi$
$563$	10.4356	+	5.24097i	0.439809	+	0.220880i	−0.215094	+	0.976593i	$0.569006\pi$
$564$	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	0.148515	−	0.988910i	$-0.452551\pi$
$569$	−3.87835	−	0.919185i	−0.162589	−	0.0385343i	−0.311104	+	0.950376i	$0.600699\pi$
$570$	29.0864	−	51.3150i	1.21830	−	2.14935i
$571$	−33.0032	−	16.5748i	−1.38114	−	0.693635i	−0.405723	−	0.913996i	$-0.632980\pi$
$571$	−33.0032	−	16.5748i	−1.38114	−	0.693635i	−0.975418	+	0.220361i	$0.929276\pi$
$572$	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	−0.693897	−	0.720074i	$-0.744108\pi$
$577$	−2.52833	+	2.12152i	−0.105256	+	0.0883201i	0.588641	+	0.808395i	$0.299663\pi$
$578$	−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	−0.474947	−	0.880014i	$-0.657533\pi$
$587$	−1.27650	+	0.641081i	−0.0526867	+	0.0264602i	0.422261	+	0.906474i	$0.361237\pi$
$588$	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	−0.990641	−	0.136490i	$-0.956418\pi$
$593$	−9.18341	+	15.9061i	−0.377117	+	0.653186i	0.613524	+	0.789676i	$0.289751\pi$
$594$	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	0.961359	−	0.275299i	$-0.0887769\pi$
$599$	2.48144	+	5.75263i	0.101389	+	0.235046i	−0.859970	+	0.510345i	$0.829518\pi$
$600$	−24.5189	+	3.06321i	−1.00098	+	0.125055i
$601$	−1.48192	+	25.4436i	−0.0604487	+	1.03786i	0.822611	+	0.568604i	$0.192516\pi$
$601$	−1.48192	+	25.4436i	−0.0604487	+	1.03786i	−0.883060	+	0.469260i	$0.844521\pi$
$602$	−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	−0.999998	−	0.00219801i	$-0.999300\pi$
$607$	−46.6297	+	11.0514i	−1.89264	+	0.448564i	−0.892644	+	0.450762i	$0.851152\pi$
$608$	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	−0.465765	−	0.884909i	$-0.654221\pi$
$613$	−6.28262	+	2.28669i	−0.253753	+	0.0923584i	0.212012	+	0.977267i	$0.431998\pi$
$614$	−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	−0.955873	−	0.293779i	$-0.905087\pi$
$617$	−1.00771	−	17.3018i	−0.0405690	−	0.696543i	0.915304	−	0.402763i	$-0.131950\pi$
$618$	−1.72333	−	9.33960i	−0.0693225	−	0.375694i
$619$	13.3203	−	14.1187i	0.535388	−	0.567478i	−0.402056	−	0.915615i	$-0.631704\pi$
$619$	13.3203	−	14.1187i	0.535388	−	0.567478i	0.937444	+	0.348137i	$0.113186\pi$
$620$	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	−0.704663	−	0.709542i	$-0.748902\pi$
$631$	−7.16349	−	40.6262i	−0.285174	−	1.61730i	0.419489	−	0.907760i	$-0.362209\pi$
$632$	−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	0.111618	−	0.993751i	$-0.464397\pi$
$641$	−19.1569	−	12.5997i	−0.756651	−	0.497657i	−0.868269	+	0.496094i	$0.834767\pi$
$642$	−1.66427	−	0.380522i	−0.0656837	−	0.0150180i
$643$	3.09065	−	4.15147i	0.121883	−	0.163718i	−0.736994	−	0.675900i	$-0.763755\pi$
$643$	3.09065	−	4.15147i	0.121883	−	0.163718i	0.858877	+	0.512182i	$0.171163\pi$
$644$	−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	−0.994875	−	0.101108i	$-0.967761\pi$
$653$	−15.6564	+	21.0302i	−0.612682	+	0.822975i	0.382194	+	0.924082i	$0.375169\pi$
$654$	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	−0.202120	−	0.979361i	$-0.564783\pi$
$659$	−4.43944	+	0.518897i	−0.172936	+	0.0202133i	0.0291841	+	0.999574i	$0.490709\pi$
$660$	22.2533	+	10.9558i	0.866209	+	0.426455i
$661$	1.98525	−	6.63118i	0.0772171	−	0.257923i	−0.910661	−	0.413154i	$-0.864427\pi$
$661$	1.98525	−	6.63118i	0.0772171	−	0.257923i	0.987878	+	0.155231i	$0.0496122\pi$
$662$	−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	0.769027	+	0.639216i	$0.220741\pi$
$673$	12.3944	+	41.4002i	0.477769	+	1.59586i	−0.291257	+	0.956645i	$0.594074\pi$
$674$	−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	−0.479563	−	0.877508i	$-0.659205\pi$
$677$	11.0411	−	11.7029i	0.424345	−	0.449779i	0.903907	+	0.427729i	$0.140686\pi$
$678$	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	−0.472464	−	0.881350i	$-0.656635\pi$
$683$	−7.00064	+	2.54803i	−0.267872	+	0.0974975i	0.204592	+	0.978847i	$0.434413\pi$
$684$	−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	0.308000	+	0.951386i	$0.400340\pi$
$691$	−15.6506	+	36.2821i	−0.595376	+	1.38024i	−0.903376	+	0.428850i	$0.858919\pi$
$692$	−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	0.607419	−	0.794382i	$-0.292205\pi$
$701$	−10.1734	−	17.6209i	−0.384246	−	0.665533i	−0.991664	+	0.128849i	$0.958872\pi$
$702$	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	−0.168484	−	0.985704i	$-0.553887\pi$
$709$	13.8876	−	6.97464i	0.521561	−	0.261938i	0.690045	+	0.723766i	$0.257591\pi$
$710$	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	−0.220659	−	0.975351i	$-0.570821\pi$
$719$	18.8117	−	15.7849i	0.701557	−	0.588677i	0.922216	+	0.386674i	$0.126376\pi$
$720$	−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	0.758079	−	0.652163i	$-0.226138\pi$
$727$	30.8141	+	7.30308i	1.14283	+	0.270856i	0.384754	+	0.923019i	$0.374286\pi$
$728$	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	0.671971	−	0.740577i	$-0.265448\pi$
$733$	12.9741	+	6.51586i	0.479211	+	0.240669i	−0.192761	+	0.981246i	$0.561744\pi$
$734$	−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	−0.565622	−	0.824665i	$-0.691364\pi$
$739$	4.03135	−	3.38270i	0.148296	−	0.124435i	0.713917	+	0.700230i	$0.246919\pi$
$740$	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	0.998573	+	0.0534006i	$0.0170060\pi$
$743$	27.0896	+	28.7133i	0.993822	+	1.05339i	−0.00475161	+	0.999989i	$0.501512\pi$
$744$	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	0.669113	−	0.743161i	$-0.266674\pi$
$751$	31.4823	+	3.67975i	1.14880	+	0.134276i	0.479692	+	0.877437i	$0.340748\pi$
$752$	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	0.570684	−	0.821170i	$-0.306678\pi$
$757$	−11.7156	−	20.2921i	−0.425812	−	0.737527i	−0.996496	+	0.0836424i	$0.973345\pi$
$758$	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	0.998551	−	0.0538086i	$-0.0171361\pi$
$761$	7.56317	+	17.5334i	0.274165	+	0.635586i	−0.724386	+	0.689394i	$0.757877\pi$
$762$	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	+	0.412796i	−0.0606990

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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