LMFDB - Embedded newform 162.2.g.a.97.2

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			97.2
Character	$\chi$	$=$	162.97
Dual form			162.2.g.a.157.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.973045 - 0.230616i) q^{2} +(-0.598238 + 1.62546i) q^{3} +(0.893633 + 0.448799i) q^{4} +(-1.25008 + 1.67915i) q^{5} +(0.956969 - 1.44368i) q^{6} +(-0.725742 - 0.477328i) q^{7} +(-0.766044 - 0.642788i) q^{8} +(-2.28422 - 1.94482i) q^{9} +O(q^{10})$	\(q+(-0.973045 - 0.230616i) q^{2} +(-0.598238 + 1.62546i) q^{3} +(0.893633 + 0.448799i) q^{4} +(-1.25008 + 1.67915i) q^{5} +(0.956969 - 1.44368i) q^{6} +(-0.725742 - 0.477328i) q^{7} +(-0.766044 - 0.642788i) q^{8} +(-2.28422 - 1.94482i) q^{9} +(1.60363 - 1.34560i) q^{10} +(-4.15887 + 0.486102i) q^{11} +(-1.26411 + 1.18407i) q^{12} +(-0.644916 + 2.15417i) q^{13} +(0.596100 + 0.631829i) q^{14} +(-1.98154 - 3.03649i) q^{15} +(0.597159 + 0.802123i) q^{16} +(0.766633 + 4.34779i) q^{17} +(1.77414 + 2.41918i) q^{18} +(0.162474 - 0.921436i) q^{19} +(-1.87072 + 0.939510i) q^{20} +(1.21004 - 0.894106i) q^{21} +(4.15887 + 0.486102i) q^{22} +(-1.33313 + 0.876812i) q^{23} +(1.50310 - 0.860632i) q^{24} +(0.177167 + 0.591780i) q^{25} +(1.12432 - 1.94737i) q^{26} +(4.52773 - 2.54944i) q^{27} +(-0.434322 - 0.752268i) q^{28} +(-1.00076 + 1.06075i) q^{29} +(1.22787 + 3.41162i) q^{30} +(0.0259757 + 0.445985i) q^{31} +(-0.396080 - 0.918216i) q^{32} +(1.69786 - 7.05087i) q^{33} +(0.256701 - 4.40739i) q^{34} +(1.70875 - 0.621932i) q^{35} +(-1.16842 - 2.76311i) q^{36} +(6.43779 + 2.34316i) q^{37} +(-0.370592 + 0.859129i) q^{38} +(-3.11569 - 2.33699i) q^{39} +(2.03696 - 0.482768i) q^{40} +(12.1745 - 2.88542i) q^{41} +(-1.38362 + 0.590951i) q^{42} +(-4.10222 + 9.51002i) q^{43} +(-3.93466 - 1.43210i) q^{44} +(6.12112 - 1.40437i) q^{45} +(1.49940 - 0.545737i) q^{46} +(0.603651 - 10.3643i) q^{47} +(-1.66106 + 0.490795i) q^{48} +(-2.47370 - 5.73468i) q^{49} +(-0.0359179 - 0.616686i) q^{50} +(-7.52578 - 1.35489i) q^{51} +(-1.54311 + 1.63560i) q^{52} +(6.72311 + 11.6448i) q^{53} +(-4.99363 + 1.43655i) q^{54} +(4.38270 - 7.59105i) q^{55} +(0.249130 + 0.832152i) q^{56} +(1.40056 + 0.815333i) q^{57} +(1.21841 - 0.801363i) q^{58} +(-3.48119 - 0.406893i) q^{59} +(-0.407998 - 3.60282i) q^{60} +(-9.52931 + 4.78580i) q^{61} +(0.0775757 - 0.439954i) q^{62} +(0.729438 + 2.50176i) q^{63} +(0.173648 + 0.984808i) q^{64} +(-2.81098 - 3.77580i) q^{65} +(-3.27813 + 6.46926i) q^{66} +(8.97123 + 9.50895i) q^{67} +(-1.26620 + 4.22939i) q^{68} +(-0.627692 - 2.69149i) q^{69} +(-1.80611 + 0.211104i) q^{70} +(-5.72149 + 4.80090i) q^{71} +(0.499708 + 2.95809i) q^{72} +(0.298511 + 0.250480i) q^{73} +(-5.72389 - 3.76466i) q^{74} +(-1.06790 - 0.0660477i) q^{75} +(0.558732 - 0.750507i) q^{76} +(3.25030 + 1.63236i) q^{77} +(2.49276 + 2.99252i) q^{78} +(-12.5888 - 2.98359i) q^{79} -2.09339 q^{80} +(1.43534 + 8.88481i) q^{81} -12.5118 q^{82} +(1.56415 + 0.370711i) q^{83} +(1.48261 - 0.255936i) q^{84} +(-8.25897 - 4.14781i) q^{85} +(6.18481 - 8.30764i) q^{86} +(-1.12550 - 2.26128i) q^{87} +(3.49834 + 2.30089i) q^{88} +(8.48715 + 7.12157i) q^{89} +(-6.28000 - 0.0451136i) q^{90} +(1.49629 - 1.25553i) q^{91} +(-1.58484 + 0.185241i) q^{92} +(-0.740469 - 0.224583i) q^{93} +(-2.97755 + 9.94570i) q^{94} +(1.34413 + 1.42469i) q^{95} +(1.72947 - 0.0944985i) q^{96} +(2.07315 + 2.78473i) q^{97} +(1.08451 + 6.15057i) q^{98} +(10.4452 + 6.97790i) 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
$3$	−0.598238	+	1.62546i	−0.345393	+	0.938458i
$3$	−0.598238	+	1.62546i	−0.345393	+	0.938458i
$4$	0.893633	+	0.448799i	0.446816	+	0.224400i
$5$	−1.25008	+	1.67915i	−0.559055	+	0.750941i	−0.988346	−	0.152226i	$-0.951356\pi$
$5$	−1.25008	+	1.67915i	−0.559055	+	0.750941i	0.429291	+	0.903166i	$0.358763\pi$
$6$	0.956969	−	1.44368i	0.390681	−	0.589380i
$7$	−0.725742	−	0.477328i	−0.274305	−	0.180413i	0.404902	−	0.914360i	$-0.367306\pi$
$7$	−0.725742	−	0.477328i	−0.274305	−	0.180413i	−0.679207	+	0.733947i	$0.737676\pi$
$8$	−0.766044	−	0.642788i	−0.270838	−	0.227260i
$9$	−2.28422	−	1.94482i	−0.761407	−	0.648274i
$10$	1.60363	−	1.34560i	0.507111	−	0.425517i
$11$	−4.15887	+	0.486102i	−1.25395	+	0.146565i	−0.717013	−	0.697059i	$-0.754491\pi$
$11$	−4.15887	+	0.486102i	−1.25395	+	0.146565i	−0.536933	+	0.843625i	$0.680417\pi$
$12$	−1.26411	+	1.18407i	−0.364917	+	0.341812i
$13$	−0.644916	+	2.15417i	−0.178867	+	0.597459i	0.820789	+	0.571232i	$0.193534\pi$
$13$	−0.644916	+	2.15417i	−0.178867	+	0.597459i	−0.999656	+	0.0262267i	$0.991651\pi$
$14$	0.596100	+	0.631829i	0.159314	+	0.168863i
$15$	−1.98154	−	3.03649i	−0.511633	−	0.784019i
$16$	0.597159	+	0.802123i	0.149290	+	0.200531i
$17$	0.766633	+	4.34779i	0.185936	+	1.05449i	0.924747	+	0.380582i	$0.124276\pi$
$17$	0.766633	+	4.34779i	0.185936	+	1.05449i	−0.738811	+	0.673912i	$0.764613\pi$
$18$	1.77414	+	2.41918i	0.418170	+	0.570205i
$19$	0.162474	−	0.921436i	0.0372741	−	0.211392i	−0.960482	−	0.278341i	$-0.910215\pi$
$19$	0.162474	−	0.921436i	0.0372741	−	0.211392i	0.997756	+	0.0669492i	$0.0213265\pi$
$20$	−1.87072	+	0.939510i	−0.418305	+	0.210081i
$21$	1.21004	−	0.894106i	0.264053	−	0.195110i
$22$	4.15887	+	0.486102i	0.886674	+	0.103637i
$23$	−1.33313	+	0.876812i	−0.277976	+	0.182828i	−0.680840	−	0.732432i	$-0.738385\pi$
$23$	−1.33313	+	0.876812i	−0.277976	+	0.182828i	0.402864	+	0.915260i	$0.368015\pi$
$24$	1.50310	−	0.860632i	0.306819	−	0.175676i
$25$	0.177167	+	0.591780i	0.0354335	+	0.118356i
$26$	1.12432	−	1.94737i	0.220497	−	0.381912i
$27$	4.52773	−	2.54944i	0.871363	−	0.490639i
$28$	−0.434322	−	0.752268i	−0.0820792	−	0.142165i
$29$	−1.00076	+	1.06075i	−0.185837	+	0.196976i	−0.813594	−	0.581434i	$-0.802492\pi$
$29$	−1.00076	+	1.06075i	−0.185837	+	0.196976i	0.627756	+	0.778410i	$0.283973\pi$
$30$	1.22787	+	3.41162i	0.224177	+	0.622874i
$31$	0.0259757	+	0.445985i	0.00466536	+	0.0801012i	0.999837	−	0.0180474i	$-0.00574498\pi$
$31$	0.0259757	+	0.445985i	0.00466536	+	0.0801012i	−0.995172	+	0.0981486i	$0.968708\pi$
$32$	−0.396080	−	0.918216i	−0.0700177	−	0.162319i
$33$	1.69786	−	7.05087i	0.295559	−	1.22740i
$34$	0.256701	−	4.40739i	0.0440239	−	0.755862i
$35$	1.70875	−	0.621932i	0.288831	−	0.105126i
$36$	−1.16842	−	2.76311i	−0.194737	−	0.460519i
$37$	6.43779	+	2.34316i	1.05837	+	0.385214i	0.811814	−	0.583916i	$-0.198480\pi$
$37$	6.43779	+	2.34316i	1.05837	+	0.385214i	0.246552	+	0.969130i	$0.420702\pi$
$38$	−0.370592	+	0.859129i	−0.0601180	+	0.139369i
$39$	−3.11569	−	2.33699i	−0.498910	−	0.374218i
$40$	2.03696	−	0.482768i	0.322072	−	0.0763324i
$41$	12.1745	−	2.88542i	1.90134	−	0.450626i	0.901501	−	0.432778i	$-0.142467\pi$
$41$	12.1745	−	2.88542i	1.90134	−	0.450626i	0.999841	−	0.0178481i	$-0.00568154\pi$
$42$	−1.38362	+	0.590951i	−0.213497	+	0.0911856i
$43$	−4.10222	+	9.51002i	−0.625583	+	1.45026i	0.250506	+	0.968115i	$0.419403\pi$
$43$	−4.10222	+	9.51002i	−0.625583	+	1.45026i	−0.876089	+	0.482150i	$0.839856\pi$
$44$	−3.93466	−	1.43210i	−0.593173	−	0.215897i
$45$	6.12112	−	1.40437i	0.912483	−	0.209351i
$46$	1.49940	−	0.545737i	0.221074	−	0.0804645i
$47$	0.603651	−	10.3643i	0.0880515	−	1.51179i	−0.608082	−	0.793874i	$-0.708061\pi$
$47$	0.603651	−	10.3643i	0.0880515	−	1.51179i	0.696134	−	0.717912i	$-0.254902\pi$
$48$	−1.66106	+	0.490795i	−0.239753	+	0.0708401i
$49$	−2.47370	−	5.73468i	−0.353386	−	0.819240i
$50$	−0.0359179	−	0.616686i	−0.00507956	−	0.0872126i
$51$	−7.52578	−	1.35489i	−1.05382	−	0.189722i
$52$	−1.54311	+	1.63560i	−0.213990	+	0.226817i
$53$	6.72311	+	11.6448i	0.923491	+	1.59953i	0.793971	+	0.607956i	$0.208010\pi$
$53$	6.72311	+	11.6448i	0.923491	+	1.59953i	0.129520	+	0.991577i	$0.458656\pi$
$54$	−4.99363	+	1.43655i	−0.679547	+	0.195490i
$55$	4.38270	−	7.59105i	0.590963	−	1.02358i
$56$	0.249130	+	0.832152i	0.0332914	+	0.111201i
$57$	1.40056	+	0.815333i	0.185508	+	0.107993i
$58$	1.21841	−	0.801363i	0.159985	−	0.105224i
$59$	−3.48119	−	0.406893i	−0.453212	−	0.0529729i	−0.113575	−	0.993529i	$-0.536230\pi$
$59$	−3.48119	−	0.406893i	−0.453212	−	0.0529729i	−0.339637	+	0.940557i	$0.610304\pi$
$60$	−0.407998	−	3.60282i	−0.0526723	−	0.465123i
$61$	−9.52931	+	4.78580i	−1.22010	+	0.612759i	−0.938003	−	0.346627i	$-0.887327\pi$
$61$	−9.52931	+	4.78580i	−1.22010	+	0.612759i	−0.282099	+	0.959385i	$0.591031\pi$
$62$	0.0775757	−	0.439954i	0.00985212	−	0.0558742i
$63$	0.729438	+	2.50176i	0.0919005	+	0.315192i
$64$	0.173648	+	0.984808i	0.0217060	+	0.123101i
$65$	−2.81098	−	3.77580i	−0.348659	−	0.468331i
$66$	−3.27813	+	6.46926i	−0.403510	+	0.796311i
$67$	8.97123	+	9.50895i	1.09601	+	1.16170i	0.985822	+	0.167793i	$0.0536640\pi$
$67$	8.97123	+	9.50895i	1.09601	+	1.16170i	0.110189	+	0.993911i	$0.464855\pi$
$68$	−1.26620	+	4.22939i	−0.153549	+	0.512889i
$69$	−0.627692	−	2.69149i	−0.0755652	−	0.324017i
$70$	−1.80611	+	0.211104i	−0.215872	+	0.0252318i
$71$	−5.72149	+	4.80090i	−0.679015	+	0.569762i	−0.915718	−	0.401820i	$-0.868378\pi$
$71$	−5.72149	+	4.80090i	−0.679015	+	0.569762i	0.236703	+	0.971582i	$0.423933\pi$
$72$	0.499708	+	2.95809i	0.0588911	+	0.348614i
$73$	0.298511	+	0.250480i	0.0349381	+	0.0293165i	0.660089	−	0.751187i	$-0.270518\pi$
$73$	0.298511	+	0.250480i	0.0349381	+	0.0293165i	−0.625151	+	0.780503i	$0.714963\pi$
$74$	−5.72389	−	3.76466i	−0.665389	−	0.437633i
$75$	−1.06790	−	0.0660477i	−0.123311	−	0.00762653i
$76$	0.558732	−	0.750507i	0.0640909	−	0.0860891i
$77$	3.25030	+	1.63236i	0.370406	+	0.186025i
$78$	2.49276	+	2.99252i	0.282250	+	0.338837i
$79$	−12.5888	−	2.98359i	−1.41635	−	0.335681i	−0.550018	−	0.835153i	$-0.685379\pi$
$79$	−12.5888	−	2.98359i	−1.41635	−	0.335681i	−0.866330	+	0.499472i	$0.833527\pi$
$80$	−2.09339			−0.234048
$81$	1.43534	+	8.88481i	0.159482	+	0.987201i
$82$	−12.5118			−1.38170
$83$	1.56415	+	0.370711i	0.171688	+	0.0406908i	0.315561	−	0.948905i	$-0.397807\pi$
$83$	1.56415	+	0.370711i	0.171688	+	0.0406908i	−0.143873	+	0.989596i	$0.545956\pi$
$84$	1.48261	−	0.255936i	0.161766	−	0.0279250i
$85$	−8.25897	−	4.14781i	−0.895811	−	0.449893i
$86$	6.18481	−	8.30764i	0.666925	−	0.895836i
$87$	−1.12550	−	2.26128i	−0.120667	−	0.242434i
$88$	3.49834	+	2.30089i	0.372924	+	0.245276i
$89$	8.48715	+	7.12157i	0.899637	+	0.754885i	0.970119	−	0.242628i	$-0.0780095\pi$
$89$	8.48715	+	7.12157i	0.899637	+	0.754885i	−0.0704828	+	0.997513i	$0.522454\pi$
$90$	−6.28000	−	0.0451136i	−0.661970	−	0.00475539i
$91$	1.49629	−	1.25553i	0.156853	−	0.131616i
$92$	−1.58484	+	0.185241i	−0.165231	+	0.0193127i
$93$	−0.740469	−	0.224583i	−0.0767830	−	0.0232882i
$94$	−2.97755	+	9.94570i	−0.307111	+	1.02582i
$95$	1.34413	+	1.42469i	0.137904	+	0.146170i
$96$	1.72947	−	0.0944985i	0.176513	−	0.00964472i
$97$	2.07315	+	2.78473i	0.210497	+	0.282746i	0.894815	−	0.446437i	$-0.147307\pi$
$97$	2.07315	+	2.78473i	0.210497	+	0.282746i	−0.684318	+	0.729184i	$0.739900\pi$
$98$	1.08451	+	6.15057i	0.109552	+	0.621302i
$99$	10.4452	+	6.97790i	1.04978	+	0.701305i
$100$	−0.107268	+	0.608347i	−0.0107268	+	0.0608347i
$101$	7.64492	−	3.83942i	0.760698	−	0.382037i	−0.0257703	−	0.999668i	$-0.508204\pi$
$101$	7.64492	−	3.83942i	0.760698	−	0.382037i	0.786468	+	0.617631i	$0.211908\pi$
$102$	7.01046	+	3.05393i	0.694139	+	0.302384i
$103$	−6.27863	−	0.733867i	−0.618652	−	0.0723100i	−0.199007	−	0.979998i	$-0.563772\pi$
$103$	−6.27863	−	0.733867i	−0.618652	−	0.0723100i	−0.419645	+	0.907688i	$0.637846\pi$
$104$	1.87871	−	1.23564i	0.184222	−	0.121165i
$105$	−0.0113126	+	3.14956i	−0.00110399	+	0.307365i
$106$	−3.85642	−	12.8813i	−0.374569	−	1.25115i
$107$	3.60966	−	6.25212i	0.348959	−	0.604415i	−0.637106	−	0.770776i	$-0.719869\pi$
$107$	3.60966	−	6.25212i	0.348959	−	0.604415i	0.986065	+	0.166361i	$0.0532019\pi$
$108$	5.19032	−	0.246217i	0.499438	−	0.0236923i
$109$	−10.1284	−	17.5429i	−0.970125	−	1.68031i	−0.695164	−	0.718851i	$-0.744668\pi$
$109$	−10.1284	−	17.5429i	−0.970125	−	1.68031i	−0.274962	−	0.961455i	$-0.588665\pi$
$110$	−6.01518	+	6.37572i	−0.573525	+	0.607901i
$111$	−7.66005	+	9.06258i	−0.727060	+	0.860182i
$112$	−0.0505072	−	0.867175i	−0.00477248	−	0.0819403i
$113$	−6.77228	−	15.6999i	−0.637083	−	1.47692i	−0.864247	−	0.503067i	$-0.832205\pi$
$113$	−6.77228	−	15.6999i	−0.637083	−	1.47692i	0.227165	−	0.973856i	$-0.427054\pi$
$114$	−1.17478	−	1.11635i	−0.110028	−	0.104555i
$115$	0.194219	−	3.33462i	0.0181110	−	0.310955i
$116$	−1.37038	+	0.498777i	−0.127236	+	0.0463103i
$117$	5.66260	−	3.66635i	0.523508	−	0.338954i
$118$	3.29352	+	1.19874i	0.303193	+	0.110353i
$119$	1.51894	−	3.52131i	0.139241	−	0.322798i
$120$	−0.433868	+	3.59980i	−0.0396066	+	0.328615i
$121$	6.35641	−	1.50650i	0.577856	−	0.136954i
$122$	10.3761	−	2.45919i	0.939410	−	0.222644i
$123$	−2.59315	+	21.5153i	−0.233816	+	1.93997i
$124$	−0.176945	+	0.410204i	−0.0158901	+	0.0368374i
$125$	−11.0509	−	4.02219i	−0.988419	−	0.359755i
$126$	−0.132830	−	2.60255i	−0.0118334	−	0.231853i
$127$	−8.46853	+	3.08229i	−0.751460	+	0.273509i	−0.689220	−	0.724552i	$-0.742047\pi$
$127$	−8.46853	+	3.08229i	−0.751460	+	0.273509i	−0.0622403	+	0.998061i	$0.519825\pi$
$128$	0.0581448	−	0.998308i	0.00513933	−	0.0882388i
$129$	−13.0040	−	12.3572i	−1.14494	−	1.08799i
$130$	1.86445	+	4.32228i	0.163523	+	0.379089i
$131$	−0.421822	−	7.24240i	−0.0368548	−	0.632772i	−0.965274	−	0.261238i	$-0.915869\pi$
$131$	−0.421822	−	7.24240i	−0.0368548	−	0.632772i	0.928420	−	0.371533i	$-0.121168\pi$
$132$	4.68169	−	5.53889i	0.407488	−	0.482099i
$133$	−0.557741	+	0.591171i	−0.0483623	+	0.0512610i
$134$	−6.53650	−	11.3215i	−0.564667	−	0.978033i
$135$	−1.37915	+	10.7898i	−0.118698	+	0.928636i
$136$	2.20743	−	3.82338i	0.189286	−	0.327852i
$137$	2.33943	+	7.81423i	0.199871	+	0.667615i	0.997887	+	0.0649784i	$0.0206979\pi$
$137$	2.33943	+	7.81423i	0.199871	+	0.667615i	−0.798016	+	0.602636i	$0.794117\pi$
$138$	−0.00992662	+	2.76369i	−0.000845010	+	0.235261i
$139$	9.76300	−	6.42123i	0.828087	−	0.544642i	−0.0632419	−	0.997998i	$-0.520144\pi$
$139$	9.76300	−	6.42123i	0.828087	−	0.544642i	0.891329	+	0.453357i	$0.149774\pi$
$140$	1.80611	+	0.211104i	0.152644	+	0.0178416i
$141$	16.4856	+	7.18152i	1.38834	+	0.604793i
$142$	6.67443	−	3.35202i	0.560105	−	0.281295i
$143$	1.63497	−	9.27240i	0.136723	−	0.775397i
$144$	0.195944	−	2.99359i	0.0163287	−	0.249466i
$145$	−0.530120	−	3.00646i	−0.0440241	−	0.249673i
$146$	−0.232700	−	0.312570i	−0.0192584	−	0.0258685i
$147$	10.8013	−	0.590187i	0.890879	−	0.0486778i
$148$	4.70141	+	4.98320i	0.386454	+	0.409617i
$149$	0.555309	−	1.85486i	0.0454927	−	0.151956i	−0.932225	−	0.361878i	$-0.882136\pi$
$149$	0.555309	−	1.85486i	0.0454927	−	0.151956i	0.977718	+	0.209922i	$0.0673209\pi$
$150$	1.02388	+	0.310543i	0.0835999	+	0.0253557i
$151$	22.0040	−	2.57189i	1.79066	−	0.209298i	0.845068	−	0.534659i	$-0.179560\pi$
$151$	22.0040	−	2.57189i	1.79066	−	0.209298i	0.945590	+	0.325362i	$0.105486\pi$
$152$	−0.716750	+	0.601425i	−0.0581361	+	0.0487820i
$153$	6.70452	−	11.4223i	0.542028	−	0.923437i
$154$	−2.78624	−	2.33793i	−0.224521	−	0.188396i
$155$	−0.781349	−	0.513901i	−0.0627594	−	0.0412775i
$156$	−1.73545	−	3.48673i	−0.138947	−	0.279162i
$157$	−8.75505	+	11.7601i	−0.698729	+	0.938556i	−0.999887	−	0.0150183i	$-0.995219\pi$
$157$	−8.75505	+	11.7601i	−0.698729	+	0.938556i	0.301158	+	0.953574i	$0.402627\pi$
$158$	11.5614	+	5.80634i	0.919774	+	0.461928i
$159$	−22.9501	+	3.96178i	−1.82006	+	0.314190i
$160$	2.03696	+	0.482768i	0.161036	+	0.0381662i
$161$	1.38603			0.109235
$162$	0.652330	−	8.97633i	0.0512519	−	0.705247i
$163$	13.6797			1.07147			0.535737	−	0.844385i	$-0.320034\pi$
$163$	13.6797			1.07147			0.535737	+	0.844385i	$0.320034\pi$
$164$	12.1745	+	2.88542i	0.950671	+	0.225313i
$165$	9.71703	+	11.6651i	0.756470	+	0.908130i
$166$	−1.43650	−	0.721436i	−0.111494	−	0.0559943i
$167$	−9.48873	+	12.7456i	−0.734260	+	0.986282i	0.265494	+	0.964112i	$0.414465\pi$
$167$	−9.48873	+	12.7456i	−0.734260	+	0.986282i	−0.999754	+	0.0221698i	$0.992943\pi$
$168$	−1.50167	−	0.0928753i	−0.115856	−	0.00716548i
$169$	6.63682	+	4.36510i	0.510524	+	0.335777i
$170$	7.07979	+	5.94065i	0.542995	+	0.455627i
$171$	−2.16316	+	1.78878i	−0.165421	+	0.136791i
$172$	−7.93397	+	6.65739i	−0.604960	+	0.507621i
$173$	−1.29303	+	0.151133i	−0.0983072	+	0.0114905i	−0.165104	−	0.986276i	$-0.552796\pi$
$173$	−1.29303	+	0.151133i	−0.0983072	+	0.0114905i	0.0667971	+	0.997767i	$0.478722\pi$
$174$	0.573680	+	2.45988i	0.0434905	+	0.186483i
$175$	0.153895	−	0.514047i	0.0116334	−	0.0388583i
$176$	−2.87342	−	3.04565i	−0.216592	−	0.229574i
$177$	2.74397	−	5.41511i	0.206249	−	0.407024i
$178$	−6.61604	−	8.88688i	−0.495893	−	0.666100i
$179$	1.50254	+	8.52134i	0.112305	+	0.636915i	0.988049	+	0.154139i	$0.0492604\pi$
$179$	1.50254	+	8.52134i	0.112305	+	0.636915i	−0.875744	+	0.482776i	$0.839629\pi$
$180$	6.10032	+	1.49216i	0.454691	+	0.111219i
$181$	−1.76679	+	10.0200i	−0.131324	+	0.744777i	0.846025	+	0.533144i	$0.178989\pi$
$181$	−1.76679	+	10.0200i	−0.131324	+	0.744777i	−0.977349	+	0.211634i	$0.932122\pi$
$182$	−1.74550	+	0.876623i	−0.129385	+	0.0649796i
$183$	−2.07831	−	18.3525i	−0.153633	−	1.35666i
$184$	1.58484	+	0.185241i	0.116836	+	0.0136562i
$185$	−11.9823	+	7.88089i	−0.880957	+	0.579415i
$186$	0.668717	+	0.389293i	0.0490327	+	0.0285443i
$187$	−5.30180	−	17.7092i	−0.387706	−	1.29503i
$188$	5.19092	−	8.99095i	0.378587	−	0.655732i
$189$	−4.50288	−	0.310980i	−0.327537	−	0.0226205i
$190$	−0.979339	−	1.69627i	−0.0710487	−	0.123060i
$191$	−2.13784	+	2.26598i	−0.154689	+	0.163960i	−0.800083	−	0.599889i	$-0.795211\pi$
$191$	−2.13784	+	2.26598i	−0.154689	+	0.163960i	0.645395	+	0.763849i	$0.276693\pi$
$192$	−1.70465	−	0.306892i	−0.123022	−	0.0221480i
$193$	−0.0668182	−	1.14722i	−0.00480968	−	0.0825790i	0.995049	−	0.0993846i	$-0.0316874\pi$
$193$	−0.0668182	−	1.14722i	−0.00480968	−	0.0825790i	−0.999859	+	0.0168056i	$0.994650\pi$
$194$	−1.37507	−	3.18777i	−0.0987242	−	0.228869i
$195$	7.81904	−	2.31030i	0.559933	−	0.165444i
$196$	0.363141	−	6.23489i	0.0259386	−	0.445349i
$197$	−7.61203	+	2.77055i	−0.542335	+	0.197394i	−0.598638	−	0.801020i	$-0.704291\pi$
$197$	−7.61203	+	2.77055i	−0.542335	+	0.197394i	0.0563027	+	0.998414i	$0.482069\pi$
$198$	−8.55440	−	9.19863i	−0.607935	−	0.653718i
$199$	−0.654014	−	0.238042i	−0.0463618	−	0.0168743i	0.318735	−	0.947844i	$-0.396742\pi$
$199$	−0.654014	−	0.238042i	−0.0463618	−	0.0168743i	−0.365097	+	0.930969i	$0.618964\pi$
$200$	0.244671	−	0.567211i	0.0173009	−	0.0401079i
$201$	−20.8233	+	8.89374i	−1.46876	+	0.627316i
$202$	−8.32428	+	1.97289i	−0.585694	+	0.138812i
$203$	1.23262	−	0.292136i	0.0865130	−	0.0205040i
$204$	−6.11721	−	4.58833i	−0.428290	−	0.321248i
$205$	−10.3741	+	24.0499i	−0.724560	+	1.67972i
$206$	5.94015	+	2.16204i	0.413870	+	0.150636i
$207$	4.75040	+	0.589863i	0.330176	+	0.0409983i
$208$	−2.11303	+	0.769078i	−0.146512	+	0.0533260i
$209$	−0.227796	+	3.91111i	−0.0157570	+	0.270537i
$210$	0.737345	−	3.06205i	0.0508817	−	0.211302i
$211$	0.797744	+	1.84938i	0.0549190	+	0.127316i	0.943466	−	0.331469i	$-0.107544\pi$
$211$	0.797744	+	1.84938i	0.0549190	+	0.127316i	−0.888547	+	0.458785i	$0.848285\pi$
$212$	0.781828	+	13.4235i	0.0536962	+	0.921928i
$213$	−4.38084	−	12.1721i	−0.300170	−	0.834019i
$214$	−4.95420	+	5.25115i	−0.338662	+	0.358961i
$215$	−10.8407	−	18.7766i	−0.739327	−	1.28055i
$216$	−5.10719	−	0.957389i	−0.347500	−	0.0651420i
$217$	0.194029	−	0.336069i	0.0131716	−	0.0228138i
$218$	5.80972	+	19.4058i	0.393484	+	1.31433i
$219$	−0.585726	+	0.335370i	−0.0395797	+	0.0226622i
$220$	7.32338	−	4.81666i	0.493742	−	0.324739i
$221$	−9.86028	−	1.15250i	−0.663274	−	0.0775257i
$222$	9.54355	−	7.05177i	0.640521	−	0.473284i
$223$	11.3875	−	5.71904i	0.762566	−	0.382975i	−0.0246149	−	0.999697i	$-0.507836\pi$
$223$	11.3875	−	5.71904i	0.762566	−	0.382975i	0.787181	+	0.616722i	$0.211540\pi$
$224$	−0.150839	+	0.855448i	−0.0100783	+	0.0571570i
$225$	0.746218	−	1.69632i	0.0497478	−	0.113088i
$226$	2.96908	+	16.8385i	0.197501	+	1.12008i
$227$	−5.80593	−	7.79872i	−0.385353	−	0.517619i	0.566546	−	0.824030i	$-0.308279\pi$
$227$	−5.80593	−	7.79872i	−0.385353	−	0.517619i	−0.951899	+	0.306411i	$0.900872\pi$
$228$	0.885662	+	1.35718i	0.0586544	+	0.0898812i
$229$	−8.49357	−	9.00266i	−0.561271	−	0.594913i	0.383136	−	0.923692i	$-0.374844\pi$
$229$	−8.49357	−	9.00266i	−0.561271	−	0.594913i	−0.944407	+	0.328779i	$0.893363\pi$
$230$	−0.957999	+	3.19994i	−0.0631686	+	0.210998i
$231$	−4.59778	+	4.30668i	−0.302512	+	0.283359i
$232$	1.44846	−	0.169301i	0.0950964	−	0.0111152i
$233$	−12.4919	+	10.4820i	−0.818375	+	0.686698i	−0.952591	−	0.304254i	$-0.901593\pi$
$233$	−12.4919	+	10.4820i	−0.818375	+	0.686698i	0.134216	+	0.990952i	$0.457148\pi$
$234$	−6.35549	+	2.26164i	−0.415471	+	0.147848i
$235$	16.6486	+	13.9698i	1.08604	+	0.911292i
$236$	−2.92829	−	1.92597i	−0.190616	−	0.125370i
$237$	12.3808	−	18.6776i	0.804219	−	1.21324i
$238$	−2.29007	+	3.07610i	−0.148443	+	0.199394i
$239$	−7.78369	−	3.90912i	−0.503485	−	0.252860i	0.178880	−	0.983871i	$-0.442752\pi$
$239$	−7.78369	−	3.90912i	−0.503485	−	0.252860i	−0.682366	+	0.731011i	$0.739049\pi$
$240$	1.25234	−	3.40271i	0.0808385	−	0.219644i
$241$	13.1012	+	3.10504i	0.843923	+	0.200013i	0.629765	−	0.776786i	$-0.283151\pi$
$241$	13.1012	+	3.10504i	0.843923	+	0.200013i	0.214158	+	0.976799i	$0.431299\pi$
$242$	−6.53250			−0.419925
$243$	−15.3005	−	2.98215i	−0.981531	−	0.191305i
$244$	−10.6636			−0.682665
$245$	12.7217	+	3.01511i	0.812762	+	0.192628i
$246$	7.48503	−	20.3374i	0.477228	−	1.29666i
$247$	1.88015	+	0.944245i	0.119631	+	0.0600809i
$248$	0.266775	−	0.358341i	0.0169402	−	0.0227547i
$249$	−1.53831	+	2.32069i	−0.0974864	+	0.147068i
$250$	9.82541	+	6.46227i	0.621413	+	0.408710i
$251$	19.8124	+	16.6246i	1.25055	+	1.04934i	0.996623	+	0.0821128i	$0.0261668\pi$
$251$	19.8124	+	16.6246i	1.25055	+	1.04934i	0.253927	+	0.967223i	$0.418278\pi$
$252$	−0.470939	+	2.56303i	−0.0296664	+	0.161455i
$253$	5.11809	−	4.29458i	0.321771	−	0.269998i
$254$	8.95108	−	1.04623i	0.561641	−	0.0656464i
$255$	11.6829	−	10.9432i	0.731612	−	0.685291i
$256$	−0.286803	+	0.957990i	−0.0179252	+	0.0598743i
$257$	−1.90977	−	2.02424i	−0.119128	−	0.126269i	0.665064	−	0.746786i	$-0.268404\pi$
$257$	−1.90977	−	2.02424i	−0.119128	−	0.126269i	−0.784193	+	0.620517i	$0.786923\pi$
$258$	9.80372	+	15.0231i	0.610353	+	0.935297i
$259$	−3.55372	−	4.77347i	−0.220817	−	0.296609i
$260$	−0.817407	−	4.63575i	−0.0506935	−	0.287497i
$261$	4.34893	−	0.476676i	0.269192	−	0.0295055i
$262$	−1.25976	+	7.14446i	−0.0778283	+	0.441386i
$263$	11.9262	−	5.98959i	0.735404	−	0.369334i	−0.0413444	−	0.999145i	$-0.513164\pi$
$263$	11.9262	−	5.98959i	0.735404	−	0.369334i	0.776748	+	0.629811i	$0.216868\pi$
$264$	−5.83285	+	4.30992i	−0.358987	+	0.265257i
$265$	−27.9578	−	3.26780i	−1.71744	−	0.200739i
$266$	0.679041	−	0.446612i	0.0416347	−	0.0273835i
$267$	−16.6531	+	9.53511i	−1.01916	+	0.583539i
$268$	3.74938	+	12.5238i	0.229030	+	0.765012i
$269$	−2.03133	+	3.51837i	−0.123853	+	0.214519i	−0.921284	−	0.388891i	$-0.872858\pi$
$269$	−2.03133	+	3.51837i	−0.123853	+	0.214519i	0.797431	+	0.603410i	$0.206192\pi$
$270$	3.83027	−	10.1809i	0.233103	−	0.619589i
$271$	6.13785	+	10.6311i	0.372848	+	0.645791i	0.990002	−	0.141051i	$-0.0450480\pi$
$271$	6.13785	+	10.6311i	0.372848	+	0.645791i	−0.617155	+	0.786842i	$0.711715\pi$
$272$	−3.02966	+	3.21125i	−0.183700	+	0.194711i
$273$	1.14568	+	3.18326i	0.0693397	+	0.192660i
$274$	−0.474282	−	8.14311i	−0.0286524	−	0.491943i
$275$	−1.02448	−	2.37502i	−0.0617786	−	0.143219i
$276$	0.647010	−	2.68691i	0.0389454	−	0.161733i
$277$	−0.0171617	+	0.294655i	−0.00103115	+	0.0177041i	−0.998784	−	0.0492905i	$-0.984304\pi$
$277$	−0.0171617	+	0.294655i	−0.00103115	+	0.0177041i	0.997753	+	0.0669946i	$0.0213410\pi$
$278$	−10.9807	+	3.99664i	−0.658577	+	0.239703i
$279$	0.808027	−	1.06925i	0.0483753	−	0.0640141i
$280$	−1.70875	−	0.621932i	−0.102117	−	0.0371676i
$281$	−4.53110	+	10.5043i	−0.270302	+	0.626632i	−0.998258	−	0.0589923i	$-0.981211\pi$
$281$	−4.53110	+	10.5043i	−0.270302	+	0.626632i	0.727956	+	0.685624i	$0.240471\pi$
$282$	−14.3850	−	10.7898i	−0.856616	−	0.642522i
$283$	21.7276	−	5.14954i	1.29157	−	0.306108i	0.473281	−	0.880912i	$-0.343070\pi$
$283$	21.7276	−	5.14954i	1.29157	−	0.306108i	0.818291	+	0.574804i	$0.194922\pi$
$284$	−7.26754	+	1.72244i	−0.431249	+	0.102208i
$285$	−3.11988	+	1.33252i	−0.184806	+	0.0789314i
$286$	−3.72927	+	8.64541i	−0.220516	+	0.511214i
$287$	−10.2129	−	3.71717i	−0.602846	−	0.219418i
$288$	−0.881033	+	2.86771i	−0.0519153	+	0.168982i
$289$	−2.34078	+	0.851974i	−0.137693	+	0.0501161i
$290$	−0.177507	+	3.04767i	−0.0104236	+	0.178966i
$291$	−5.76670	+	1.70389i	−0.338050	+	0.0998839i
$292$	0.154344	+	0.357809i	0.00903228	+	0.0209392i
$293$	0.609421	+	10.4634i	0.0356027	+	0.611276i	0.968172	+	0.250285i	$0.0805243\pi$
$293$	0.609421	+	10.4634i	0.0356027	+	0.611276i	−0.932569	+	0.360991i	$0.882439\pi$
$294$	−10.6463	−	1.91668i	−0.620904	−	0.111783i
$295$	5.03501	−	5.33680i	0.293150	−	0.310721i
$296$	−3.42548	−	5.93310i	−0.199102	−	0.344854i
$297$	−17.5910	+	12.8037i	−1.02073	+	0.742947i
$298$	−0.968102	+	1.67680i	−0.0560806	+	0.0971345i
$299$	−1.02905	−	3.43725i	−0.0595112	−	0.198781i
$300$	−0.924670	−	0.538296i	−0.0533858	−	0.0310785i
$301$	7.51655	−	4.94372i	0.433247	−	0.284951i
$302$	−22.0040	−	2.57189i	−1.26619	−	0.147996i
$303$	1.66733	+	14.7234i	0.0957857	+	0.845836i
$304$	0.836128	−	0.419919i	0.0479552	−	0.0240840i
$305$	3.87634	−	21.9838i	0.221959	−	1.25879i
$306$	−9.15796	+	9.56822i	−0.523525	+	0.546979i
$307$	−0.212251	−	1.20374i	−0.0121138	−	0.0687009i	0.978152	−	0.207893i	$-0.0666606\pi$
$307$	−0.212251	−	1.20374i	−0.0121138	−	0.0687009i	−0.990265	+	0.139192i	$0.955549\pi$
$308$	2.17197	+	2.91746i	0.123759	+	0.166238i
$309$	4.94899	−	9.76662i	0.281538	−	0.555604i
$310$	0.641774	+	0.680240i	0.0364503	+	0.0386351i
$311$	0.201906	−	0.674413i	0.0114490	−	0.0382425i	−0.952074	−	0.305867i	$-0.901054\pi$
$311$	0.201906	−	0.674413i	0.0114490	−	0.0382425i	0.963523	+	0.267625i	$0.0862388\pi$
$312$	0.884573	+	3.79297i	0.0500791	+	0.214734i
$313$	24.4482	−	2.85758i	1.38189	−	0.161520i	0.607547	−	0.794284i	$-0.292154\pi$
$313$	24.4482	−	2.85758i	1.38189	−	0.161520i	0.774345	+	0.632763i	$0.218079\pi$
$314$	11.2311	−	9.42402i	0.633808	−	0.531828i
$315$	−5.11270	−	1.90257i	−0.288068	−	0.107198i
$316$	−9.91070	−	8.31607i	−0.557521	−	0.467815i
$317$	18.9963	+	12.4940i	1.06694	+	0.701736i	0.956377	−	0.292134i	$-0.0943653\pi$
$317$	18.9963	+	12.4940i	1.06694	+	0.701736i	0.110560	+	0.993869i	$0.464736\pi$
$318$	23.2451	+	1.43767i	1.30352	+	0.0806204i
$319$	3.64641	−	4.89798i	0.204160	−	0.274235i
$320$	−1.87072	−	0.939510i	−0.104576	−	0.0525202i
$321$	8.00311	+	9.60761i	0.446690	+	0.536244i
$322$	−1.34867	−	0.319641i	−0.0751586	−	0.0178129i
$323$	4.13077			0.229842
$324$	−2.70483	+	8.58393i	−0.150268	+	0.476885i
$325$	−1.38905			−0.0770508
$326$	−13.3109	−	3.15475i	−0.737224	−	0.174725i
$327$	34.5745	−	5.96845i	1.91197	−	0.330056i
$328$	−11.1809	−	5.61528i	−0.617364	−	0.310052i
$329$	−5.38526	+	7.23366i	−0.296899	+	0.398804i
$330$	−6.76494	−	13.5916i	−0.372398	−	0.748194i
$331$	18.6449	+	12.2629i	1.02482	+	0.674032i	0.946436	−	0.322891i	$-0.104655\pi$
$331$	18.6449	+	12.2629i	1.02482	+	0.674032i	0.0783803	+	0.996924i	$0.475025\pi$
$332$	1.23140	+	1.03327i	0.0675819	+	0.0567080i
$333$	−10.1483	−	17.8727i	−0.556124	−	0.979416i
$334$	12.1723	−	10.2138i	0.666038	−	0.558872i
$335$	−27.1818	+	3.17710i	−1.48510	+	0.173583i
$336$	1.43977	+	0.436680i	0.0785459	+	0.0238228i
$337$	−0.522125	+	1.74402i	−0.0284420	+	0.0950028i	−0.971032	−	0.238949i	$-0.923197\pi$
$337$	−0.522125	+	1.74402i	−0.0284420	+	0.0950028i	0.942590	+	0.333952i	$0.108382\pi$
$338$	−5.45126	−	5.77800i	−0.296509	−	0.314282i
$339$	29.5710	−	1.61576i	1.60607	−	0.0877561i
$340$	−5.51895	−	7.41323i	−0.299307	−	0.402039i
$341$	−0.324824	−	1.84217i	−0.0175902	−	0.0997589i
$342$	2.51737	−	1.24171i	0.136124	−	0.0671438i
$343$	−1.99793	+	11.3308i	−0.107878	+	0.611806i
$344$	9.25541	−	4.64824i	0.499018	−	0.250616i
$345$	5.30409	+	2.31059i	0.285562	+	0.124398i
$346$	1.29303	+	0.151133i	0.0695137	+	0.00812498i
$347$	−12.7058	+	8.35675i	−0.682084	+	0.448614i	−0.842686	−	0.538406i	$-0.819027\pi$
$347$	−12.7058	+	8.35675i	−0.682084	+	0.448614i	0.160602	+	0.987019i	$0.448656\pi$
$348$	0.00907244	−	2.52588i	0.000486334	−	0.135401i
$349$	−8.19252	−	27.3649i	−0.438536	−	1.46481i	−0.836784	−	0.547534i	$-0.815567\pi$
$349$	−8.19252	−	27.3649i	−0.438536	−	1.46481i	0.398248	−	0.917278i	$-0.369618\pi$
$350$	−0.268295	+	0.464700i	−0.0143409	+	0.0248392i
$351$	2.57191	+	11.3977i	0.137278	+	0.608363i
$352$	2.09359	+	3.62621i	0.111589	+	0.193277i
$353$	15.6658	−	16.6048i	0.833809	−	0.883786i	−0.160853	−	0.986978i	$-0.551424\pi$
$353$	15.6658	−	16.6048i	0.833809	−	0.883786i	0.994661	+	0.103193i	$0.0329058\pi$
$354$	−3.91881	+	4.63634i	−0.208283	+	0.246419i
$355$	−0.909108	−	15.6088i	−0.0482504	−	0.828428i
$356$	4.38824	+	10.1731i	0.232576	+	0.539173i
$357$	4.81505	+	4.57556i	0.254839	+	0.242164i
$358$	0.503115	−	8.63816i	0.0265905	−	0.456541i
$359$	11.0891	−	4.03610i	0.585261	−	0.213017i	−0.0323831	−	0.999476i	$-0.510310\pi$
$359$	11.0891	−	4.03610i	0.585261	−	0.213017i	0.617644	+	0.786458i	$0.288087\pi$
$360$	−5.59176	−	2.85877i	−0.294712	−	0.150671i
$361$	17.0315	+	6.19896i	0.896395	+	0.326261i
$362$	4.02992	−	9.34242i	0.211808	−	0.491026i
$363$	−1.35390	+	11.2333i	−0.0710615	+	0.589597i
$364$	1.90061	−	0.450454i	0.0996192	−	0.0236102i
$365$	−0.793759	+	0.188124i	−0.0415472	+	0.00984688i
$366$	−2.21009	+	18.3371i	−0.115523	+	0.958497i
$367$	−10.3919	+	24.0910i	−0.542450	+	1.25754i	0.397930	+	0.917416i	$0.369729\pi$
$367$	−10.3919	+	24.0910i	−0.542450	+	1.25754i	−0.940380	+	0.340125i	$0.889531\pi$
$368$	−1.49940	−	0.545737i	−0.0781616	−	0.0284485i
$369$	−33.4209	−	17.0864i	−1.73982	−	0.889480i
$370$	13.4768	−	4.90515i	0.700625	−	0.255007i
$371$	0.679131	−	11.6602i	0.0352587	−	0.605369i
$372$	−0.560914	−	0.533016i	−0.0290821	−	0.0276356i
$373$	−14.3823	−	33.3420i	−0.744690	−	1.72639i	−0.685425	−	0.728143i	$-0.740384\pi$
$373$	−14.3823	−	33.3420i	−0.744690	−	1.72639i	−0.0592644	−	0.998242i	$-0.518875\pi$
$374$	1.07486	+	18.4546i	0.0555795	+	0.954262i
$375$	13.1489	−	15.5565i	0.679008	−	0.803333i
$376$	−7.12446	+	7.55148i	−0.367416	+	0.389438i
$377$	−1.63962	−	2.83991i	−0.0844447	−	0.146263i
$378$	4.30979	+	1.34103i	0.221672	+	0.0689754i
$379$	−10.5794	+	18.3241i	−0.543428	+	0.941244i	0.455277	+	0.890350i	$0.349540\pi$
$379$	−10.5794	+	18.3241i	−0.543428	+	0.941244i	−0.998704	+	0.0508940i	$0.983793\pi$
$380$	0.561755	+	1.87639i	0.0288174	+	0.0962570i
$381$	0.0560650	−	15.6092i	0.00287230	−	0.799682i
$382$	2.60278	−	1.71188i	0.133170	−	0.0875872i
$383$	15.5596	+	1.81865i	0.795057	+	0.0929289i	0.503918	−	0.863752i	$-0.331891\pi$
$383$	15.5596	+	1.81865i	0.795057	+	0.0929289i	0.291140	+	0.956681i	$0.405966\pi$
$384$	1.58792	+	0.691738i	0.0810333	+	0.0353001i
$385$	−6.80413	+	3.41716i	−0.346770	+	0.174155i
$386$	−0.199551	+	1.13171i	−0.0101569	+	0.0576025i
$387$	27.8657	−	13.7449i	1.41649	−	0.698693i
$388$	0.602854	+	3.41896i	0.0306053	+	0.173571i
$389$	8.86577	+	11.9088i	0.449512	+	0.603800i	0.967897	−	0.251348i	$-0.0808738\pi$
$389$	8.86577	+	11.9088i	0.449512	+	0.603800i	−0.518384	+	0.855148i	$0.673466\pi$
$390$	−8.14107	+	0.444829i	−0.412239	+	0.0225248i
$391$	−4.83421	−	5.12397i	−0.244477	−	0.259130i
$392$	−1.79122	+	5.98308i	−0.0904701	+	0.302191i
$393$	12.0246	+	3.64703i	0.606559	+	0.183968i
$394$	8.04578	−	0.940417i	0.405341	−	0.0473775i
$395$	20.7469	−	17.4087i	1.04389	−	0.875929i
$396$	6.20247	+	10.9235i	0.311686	+	0.548924i
$397$	−11.5126	−	9.66019i	−0.577799	−	0.484831i	0.306424	−	0.951895i	$-0.400867\pi$
$397$	−11.5126	−	9.66019i	−0.577799	−	0.484831i	−0.884224	+	0.467064i	$0.845312\pi$
$398$	0.581488	+	0.382451i	0.0291474	+	0.0191705i
$399$	−0.627261	−	1.26025i	−0.0314023	−	0.0630912i
$400$	−0.368884	+	0.495497i	−0.0184442	+	0.0247748i
$401$	0.515172	+	0.258729i	0.0257264	+	0.0129203i	0.461616	−	0.887080i	$-0.347270\pi$
$401$	0.515172	+	0.258729i	0.0257264	+	0.0129203i	−0.435889	+	0.900000i	$0.643566\pi$
$402$	22.3131	−	3.85181i	1.11288	−	0.192111i
$403$	−0.977478	−	0.231667i	−0.0486917	−	0.0115401i
$404$	8.55488			0.425621
$405$	−16.7133	−	8.69660i	−0.830488	−	0.432138i
$406$	−1.26677			−0.0628686
$407$	−27.9130	−	6.61549i	−1.38359	−	0.327918i
$408$	4.89417	+	5.87538i	0.242298	+	0.290875i
$409$	8.56582	+	4.30192i	0.423553	+	0.212716i	0.647791	−	0.761818i	$-0.275693\pi$
$409$	8.56582	+	4.30192i	0.423553	+	0.212716i	−0.224238	+	0.974534i	$0.571989\pi$
$410$	15.6408	−	21.0092i	0.772443	−	1.03757i
$411$	−14.1012	−	0.872134i	−0.695562	−	0.0430192i
$412$	−5.28143	−	3.47365i	−0.260197	−	0.171135i
$413$	2.33222	+	1.95697i	0.114761	+	0.0962961i
$414$	−4.48632	−	1.66948i	−0.220491	−	0.0820505i
$415$	−2.57780	+	2.16303i	−0.126539	+	0.106179i
$416$	2.23343	−	0.261051i	0.109503	−	0.0127991i
$417$	4.59683	+	19.7108i	0.225108	+	0.965241i
$418$	1.12362	−	3.75315i	0.0549581	−	0.183573i
$419$	26.4070	+	27.9898i	1.29007	+	1.36739i	0.893292	+	0.449476i	$0.148389\pi$
$419$	26.4070	+	27.9898i	1.29007	+	1.36739i	0.396775	+	0.917916i	$0.370129\pi$
$420$	−1.42363	+	2.80947i	−0.0694659	+	0.137088i
$421$	−5.19429	−	6.97715i	−0.253154	−	0.340045i	0.657319	−	0.753612i	$-0.271690\pi$
$421$	−5.19429	−	6.97715i	−0.253154	−	0.340045i	−0.910474	+	0.413567i	$0.864283\pi$
$422$	−0.349745	−	1.98350i	−0.0170253	−	0.0965553i
$423$	−21.5356	+	22.5003i	−1.04709	+	1.09400i
$424$	2.33491	−	13.2419i	0.113393	−	0.643086i
$425$	−2.43711	+	1.22396i	−0.118217	+	0.0593710i
$426$	1.45567	+	12.8543i	0.0705275	+	0.622793i
$427$	9.20021	+	1.07535i	0.445229	+	0.0520399i
$428$	6.03166	−	3.96708i	0.291551	−	0.191756i
$429$	14.0938	+	8.20469i	0.680454	+	0.396126i
$430$	6.21828	+	20.7705i	0.299872	+	1.00164i
$431$	9.58237	−	16.5972i	0.461567	−	0.799457i	−0.537473	−	0.843281i	$-0.680621\pi$
$431$	9.58237	−	16.5972i	0.461567	−	0.799457i	0.999039	+	0.0438243i	$0.0139542\pi$
$432$	4.74874	+	2.10938i	0.228474	+	0.101488i
$433$	−1.63588	−	2.83343i	−0.0786154	−	0.136166i	0.824037	−	0.566535i	$-0.191717\pi$
$433$	−1.63588	−	2.83343i	−0.0786154	−	0.136166i	−0.902653	+	0.430370i	$0.858383\pi$
$434$	−0.266302	+	0.282264i	−0.0127829	+	0.0135491i
$435$	5.20401	+	0.936892i	0.249513	+	0.0449206i
$436$	−1.17783	−	20.2225i	−0.0564078	−	0.968484i
$437$	0.591327	+	1.37085i	0.0282870	+	0.0655767i
$438$	0.647279	−	0.191252i	0.0309282	−	0.00913838i
$439$	1.77241	−	30.4312i	0.0845927	−	1.45240i	−0.642723	−	0.766098i	$-0.722196\pi$
$439$	1.77241	−	30.4312i	0.0845927	−	1.45240i	0.727316	−	0.686303i	$-0.240767\pi$
$440$	−8.23678	+	2.99794i	−0.392673	+	0.142921i
$441$	−5.50245	+	17.9102i	−0.262021	+	0.852866i
$442$	9.32871	+	3.39537i	0.443722	+	0.161501i
$443$	−9.24747	+	21.4381i	−0.439361	+	1.01855i	0.544360	+	0.838851i	$0.316772\pi$
$443$	−9.24747	+	21.4381i	−0.439361	+	1.01855i	−0.983721	+	0.179701i	$0.942487\pi$
$444$	−10.9125	+	4.66080i	−0.517887	+	0.221192i
$445$	−22.5679	+	5.34868i	−1.06982	+	0.253552i
$446$	−12.3995	+	2.93873i	−0.587133	+	0.139153i
$447$	2.68279	+	2.01228i	0.126892	+	0.0951776i
$448$	0.344052	−	0.797603i	0.0162550	−	0.0376832i
$449$	−30.1179	−	10.9620i	−1.42135	−	0.517330i	−0.486912	−	0.873451i	$-0.661877\pi$
$449$	−30.1179	−	10.9620i	−1.42135	−	0.517330i	−0.934440	+	0.356121i	$0.884099\pi$
$450$	−1.11730	+	1.47850i	−0.0526701	+	0.0696973i
$451$	−49.2297	+	17.9181i	−2.31813	+	0.843732i
$452$	0.994176	−	17.0693i	0.0467621	−	0.802875i
$453$	−8.98311	+	37.3051i	−0.422063	+	1.75275i
$454$	3.85092	+	8.92745i	0.180733	+	0.418986i
$455$	0.237751	+	4.08202i	0.0111459	+	0.191368i
$456$	−0.548803	−	1.52484i	−0.0257000	−	0.0714072i
$457$	−16.4122	+	17.3959i	−0.767729	+	0.813745i	−0.986797	−	0.161965i	$-0.948217\pi$
$457$	−16.4122	+	17.3959i	−0.767729	+	0.813745i	0.219068	+	0.975710i	$0.429698\pi$
$458$	6.18847	+	10.7187i	0.289168	+	0.500854i
$459$	14.5555	+	17.7312i	0.679394	+	0.827619i
$460$	1.67013	−	2.89276i	0.0778704	−	0.134875i
$461$	−2.71503	−	9.06882i	−0.126451	−	0.422377i	0.871196	−	0.490936i	$-0.163345\pi$
$461$	−2.71503	−	9.06882i	−0.126451	−	0.422377i	−0.997647	+	0.0685589i	$0.978160\pi$
$462$	5.46704	−	3.13027i	0.254350	−	0.145633i
$463$	−31.5131	+	20.7265i	−1.46454	+	0.963241i	−0.467690	+	0.883893i	$0.654913\pi$
$463$	−31.5131	+	20.7265i	−1.46454	+	0.963241i	−0.996847	+	0.0793481i	$0.974716\pi$
$464$	−1.44846	−	0.169301i	−0.0672433	−	0.00785961i
$465$	1.30276	−	0.962614i	0.0604139	−	0.0446401i
$466$	14.5725	−	7.31860i	0.675060	−	0.339028i
$467$	3.41253	−	19.3534i	0.157913	−	0.895570i	−0.798161	−	0.602445i	$-0.794193\pi$
$467$	3.41253	−	19.3534i	0.157913	−	0.895570i	0.956074	−	0.293126i	$-0.0946954\pi$
$468$	6.70574	−	0.735000i	0.309973	−	0.0339754i
$469$	−1.97191	−	11.1833i	−0.0910544	−	0.516395i
$470$	−12.9782	−	17.4327i	−0.598639	−	0.804112i
$471$	−13.8779	−	21.2663i	−0.639459	−	0.979899i
$472$	2.40520	+	2.54936i	0.110708	+	0.117344i
$473$	12.4378	−	41.5450i	0.571889	−	1.91024i
$474$	−16.3544	+	15.3189i	−0.751183	+	0.703622i
$475$	0.574073	−	0.0670995i	0.0263403	−	0.00307874i
$476$	2.93774	−	2.46506i	0.134651	−	0.112986i
$477$	7.28993	−	39.6745i	0.333783	−	1.81657i
$478$	6.67238	+	5.59879i	0.305187	+	0.256083i
$479$	21.4509	+	14.1085i	0.980118	+	0.644634i	0.935112	−	0.354353i	$-0.115299\pi$
$479$	21.4509	+	14.1085i	0.980118	+	0.644634i	0.0450061	+	0.998987i	$0.485669\pi$
$480$	−2.00331	+	3.02218i	−0.0914380	+	0.137943i
$481$	−9.19940	+	12.3569i	−0.419457	+	0.563428i
$482$	−12.0320	−	6.04269i	−0.548042	−	0.275237i
$483$	−0.829179	+	2.25294i	−0.0377289	+	0.102512i
$484$	6.35641	+	1.50650i	0.288928	+	0.0684772i
$485$	−7.26761			−0.330005
$486$	14.2004	+	6.43032i	0.644143	+	0.291685i
$487$	10.2205			0.463136			0.231568	−	0.972819i	$-0.425614\pi$
$487$	10.2205			0.463136			0.231568	+	0.972819i	$0.425614\pi$
$488$	10.3761	+	2.45919i	0.469705	+	0.111322i
$489$	−8.18370	+	22.2357i	−0.370080	+	1.00553i
$490$	−11.6835	−	5.86767i	−0.527806	−	0.265074i
$491$	−10.9220	+	14.6707i	−0.492901	+	0.662081i	−0.977076	−	0.212890i	$-0.931712\pi$
$491$	−10.9220	+	14.6707i	−0.492901	+	0.662081i	0.484175	+	0.874971i	$0.339120\pi$
$492$	−11.9734	+	18.0630i	−0.539802	+	0.814343i
$493$	−5.37913	−	3.53791i	−0.242264	−	0.159339i
$494$	−1.61171	−	1.35238i	−0.0725142	−	0.0608466i
$495$	−24.7743	+	8.81608i	−1.11352	+	0.396254i
$496$	−0.342223	+	0.287159i	−0.0153663	+	0.0128938i
$497$	6.44392	−	0.753187i	0.289049	−	0.0337850i
$498$	2.03203	−	1.90337i	0.0910575	−	0.0852922i
$499$	4.35779	−	14.5560i	0.195081	−	0.651617i	−0.803344	−	0.595516i	$-0.796948\pi$
$499$	4.35779	−	14.5560i	0.195081	−	0.651617i	0.998425	−	0.0561014i	$-0.0178670\pi$
$500$	−8.07026	−	8.55398i	−0.360913	−	0.382545i
$501$	−15.0409	−	23.0484i	−0.671976	−	1.02973i
$502$	−15.4445	−	20.7456i	−0.689322	−	0.925919i
$503$	−0.184478	−	1.04623i	−0.00822547	−	0.0466490i	0.980419	−	0.196924i	$-0.0630952\pi$
$503$	−0.184478	−	1.04623i	−0.00822547	−	0.0466490i	−0.988644	+	0.150275i	$0.951984\pi$
$504$	1.04932	−	2.38533i	0.0467404	−	0.106251i
$505$	−3.10981	+	17.6366i	−0.138385	+	0.784818i
$506$	−5.97053	+	2.99851i	−0.265422	+	0.133300i
$507$	−11.0657	+	8.17649i	−0.491444	+	0.363131i
$508$	−8.95108	−	1.04623i	−0.397140	−	0.0464190i
$509$	−7.78865	+	5.12267i	−0.345226	+	0.227059i	−0.710266	−	0.703933i	$-0.751425\pi$
$509$	−7.78865	+	5.12267i	−0.345226	+	0.227059i	0.365041	+	0.930992i	$0.381055\pi$
$510$	−13.8917	+	7.95397i	−0.615134	+	0.352208i
$511$	−0.0970806	−	0.324272i	−0.00429459	−	0.0143449i
$512$	0.500000	−	0.866025i	0.0220971	−	0.0382733i
$513$	−1.61350	−	4.58623i	−0.0712379	−	0.202487i
$514$	1.39147	+	2.41010i	0.0613752	+	0.106305i
$515$	9.08109	−	9.62540i	0.400161	−	0.424146i
$516$	−6.07490	−	16.8790i	−0.267433	−	0.743058i
$517$	2.52760	+	43.3972i	0.111164	+	1.90860i
$518$	2.35709	+	5.46434i	0.103564	+	0.240089i
$519$	0.527879	−	2.19218i	0.0231713	−	0.0962259i
$520$	−0.273703	+	4.69930i	−0.0120027	+	0.206078i
$521$	13.1493	−	4.78597i	0.576083	−	0.209677i	−0.0375146	−	0.999296i	$-0.511944\pi$
$521$	13.1493	−	4.78597i	0.576083	−	0.209677i	0.613597	+	0.789619i	$0.289722\pi$
$522$	−4.34163	−	0.539106i	−0.190028	−	0.0235960i
$523$	−38.9824	−	14.1884i	−1.70458	−	0.620416i	−0.708246	−	0.705965i	$-0.750513\pi$
$523$	−38.9824	−	14.1884i	−1.70458	−	0.620416i	−0.996334	+	0.0855490i	$0.972736\pi$
$524$	2.87343	−	6.66136i	0.125526	−	0.291003i
$525$	0.743495	+	0.557673i	0.0324488	+	0.0243388i
$526$	−12.9861	+	3.07775i	−0.566219	+	0.134196i
$527$	−1.91913	+	0.454843i	−0.0835988	+	0.0198133i
$528$	6.66956	−	2.84860i	0.290255	−	0.123969i
$529$	−8.10140	+	18.7812i	−0.352235	+	0.816572i
$530$	26.4506	+	9.62723i	1.14894	+	0.418180i
$531$	7.16048	+	7.69973i	0.310738	+	0.334140i
$532$	−0.763733	+	0.277976i	−0.0331120	+	0.0120518i
$533$	−1.63587	+	28.0868i	−0.0708574	+	1.21658i
$534$	18.4032	−	5.43761i	0.796385	−	0.235308i
$535$	5.98589	+	13.8768i	0.258793	+	0.599949i
$536$	−0.760127	−	13.0509i	−0.0328325	−	0.563712i
$537$	−14.7500	−	2.65548i	−0.636507	−	0.114592i
$538$	2.78797	−	2.95508i	0.120198	−	0.127402i
$539$	13.0754	+	22.6473i	0.563199	+	0.975489i
$540$	−6.07489	+	9.02313i	−0.261422	+	0.388294i
$541$	3.02808	−	5.24480i	0.130188	−	0.225491i	−0.793561	−	0.608490i	$-0.791775\pi$
$541$	3.02808	−	5.24480i	0.130188	−	0.225491i	0.923749	+	0.382999i	$0.125109\pi$
$542$	−3.52071	−	11.7600i	−0.151227	−	0.505135i
$543$	−15.2300	−	8.86616i	−0.653584	−	0.380483i
$544$	3.68856	−	2.42601i	0.158146	−	0.104014i
$545$	42.1186	+	4.92296i	1.80416	+	0.210876i
$546$	−0.380688	−	3.36167i	−0.0162919	−	0.143866i
$547$	−29.3737	+	14.7520i	−1.25593	+	0.630752i	−0.947275	−	0.320423i	$-0.896175\pi$
$547$	−29.3737	+	14.7520i	−1.25593	+	0.630752i	−0.308655	+	0.951174i	$0.599879\pi$
$548$	−1.41643	+	8.03298i	−0.0605070	+	0.343152i
$549$	31.0746	+	7.60098i	1.32623	+	0.324402i
$550$	0.449151	+	2.54726i	0.0191518	+	0.108616i
$551$	0.814813	+	1.09448i	0.0347122	+	0.0466266i
$552$	−1.24921	+	2.46527i	−0.0531700	+	0.104929i
$553$	7.71205	+	8.17429i	0.327950	+	0.347606i
$554$	0.0846513	−	0.282755i	0.00359649	−	0.0120131i
$555$	−5.64177	−	24.1914i	−0.239480	−	1.02687i
$556$	11.6064	−	1.35659i	0.492220	−	0.0575323i
$557$	−2.59467	+	2.17719i	−0.109940	+	0.0922503i	−0.696100	−	0.717944i	$-0.745083\pi$
$557$	−2.59467	+	2.17719i	−0.109940	+	0.0922503i	0.586161	+	0.810195i	$0.300639\pi$
$558$	−1.03283	+	0.854080i	−0.0437232	+	0.0361561i
$559$	−17.8406	−	14.9700i	−0.754577	−	0.633165i
$560$	1.51926	+	0.999232i	0.0642004	+	0.0422253i
$561$	31.9573	+	1.97650i	1.34924	+	0.0834479i
$562$	6.83141	−	9.17617i	0.288166	−	0.387074i
$563$	−16.2820	−	8.17712i	−0.686204	−	0.344625i	0.0713003	−	0.997455i	$-0.477285\pi$
$563$	−16.2820	−	8.17712i	−0.686204	−	0.344625i	−0.757504	+	0.652830i	$0.773581\pi$
$564$	11.5090	+	13.8164i	0.484616	+	0.581773i
$565$	34.8285	+	8.25450i	1.46525	+	0.347270i
$566$	−22.3295			−0.938579
$567$	3.19928	−	7.13320i	0.134357	−	0.299566i
$568$	7.46887			0.313387
$569$	35.2685	+	8.35879i	1.47853	+	0.350419i	0.889218	−	0.457485i	$-0.151249\pi$
$569$	35.2685	+	8.35879i	1.47853	+	0.350419i	0.589315	+	0.807903i	$0.299398\pi$
$570$	3.34308	−	0.577103i	0.140026	−	0.0241722i
$571$	29.6253	+	14.8784i	1.23978	+	0.622640i	0.943155	−	0.332354i	$-0.107843\pi$
$571$	29.6253	+	14.8784i	1.23978	+	0.622640i	0.296624	+	0.954994i	$0.404139\pi$
$572$	5.62251	−	7.55234i	0.235089	−	0.315779i
$573$	−2.40431	−	4.83056i	−0.100441	−	0.201799i
$574$	9.08032	+	5.97222i	0.379005	+	0.249276i
$575$	−0.755067	−	0.633576i	−0.0314885	−	0.0264220i
$576$	1.51862	−	2.58723i	0.0632760	−	0.107801i
$577$	16.1362	−	13.5399i	0.671760	−	0.563674i	−0.241826	−	0.970320i	$-0.577746\pi$
$577$	16.1362	−	13.5399i	0.671760	−	0.563674i	0.913586	+	0.406646i	$0.133302\pi$
$578$	2.47416	−	0.289188i	0.102912	−	0.0120286i
$579$	1.90474	+	0.577703i	0.0791581	+	0.0240085i
$580$	0.875564	−	2.92459i	0.0363558	−	0.121437i
$581$	−0.958219	−	1.01565i	−0.0397536	−	0.0421364i
$582$	6.00420	−	0.328070i	0.248882	−	0.0135990i
$583$	−33.6211	−	45.1610i	−1.39244	−	1.87038i
$584$	−0.0676669	−	0.383758i	−0.00280008	−	0.0158800i
$585$	−0.922360	+	14.0916i	−0.0381349	+	0.582617i
$586$	1.82002	−	10.3219i	0.0751844	−	0.426392i
$587$	−0.262882	+	0.132025i	−0.0108503	+	0.00544923i	−0.454216	−	0.890892i	$-0.650081\pi$
$587$	−0.262882	+	0.132025i	−0.0108503	+	0.00544923i	0.443366	+	0.896341i	$0.353784\pi$
$588$	9.91730	+	4.32022i	0.408983	+	0.178163i
$589$	0.415167	+	0.0485260i	0.0171066	+	0.00199948i
$590$	−6.13005	+	4.03180i	−0.252370	+	0.165986i
$591$	0.0503947	−	14.0305i	0.00207296	−	0.577137i
$592$	1.96488	+	6.56314i	0.0807559	+	0.269743i
$593$	−2.28876	+	3.96425i	−0.0939881	+	0.162792i	−0.909186	−	0.416391i	$-0.863295\pi$
$593$	−2.28876	+	3.96425i	−0.0939881	+	0.162792i	0.815198	+	0.579183i	$0.196628\pi$
$594$	20.0695	−	8.40184i	0.823463	−	0.344732i
$595$	4.01401	+	6.95247i	0.164558	+	0.285024i
$596$	1.32870	−	1.40834i	0.0544258	−	0.0576880i
$597$	0.778182	−	0.920666i	0.0318489	−	0.0376803i
$598$	0.208623	+	3.58191i	0.00853122	+	0.146475i
$599$	10.1227	+	23.4671i	0.413603	+	0.958839i	0.989922	+	0.141614i	$0.0452293\pi$
$599$	10.1227	+	23.4671i	0.413603	+	0.958839i	−0.576319	+	0.817225i	$0.695511\pi$
$600$	0.775606	+	0.737030i	0.0316640	+	0.0300891i
$601$	1.87619	−	32.2129i	0.0765313	−	1.31399i	−0.713383	−	0.700774i	$-0.752838\pi$
$601$	1.87619	−	32.2129i	0.0765313	−	1.31399i	0.789914	−	0.613217i	$-0.210125\pi$
$602$	−8.45404	+	3.07702i	−0.344561	+	0.125410i
$603$	−1.99907	−	39.1680i	−0.0814084	−	1.59504i
$604$	20.8177	+	7.57703i	0.847061	+	0.308305i
$605$	−5.41641	+	12.5566i	−0.220208	+	0.510500i
$606$	1.77305	−	14.7110i	0.0720254	−	0.597594i
$607$	−3.29304	+	0.780465i	−0.133660	+	0.0316781i	−0.296902	−	0.954908i	$-0.595953\pi$
$607$	−3.29304	+	0.780465i	−0.133660	+	0.0316781i	0.163241	+	0.986586i	$0.447805\pi$
$608$	−0.910430	+	0.215776i	−0.0369228	+	0.00875087i
$609$	−0.262546	+	2.17834i	−0.0106389	+	0.0882707i
$610$	−8.84167	+	20.4973i	−0.357989	+	0.829911i
$611$	21.9371	+	7.98445i	0.887480	+	0.323016i
$612$	11.1177	−	7.19834i	0.449406	−	0.290976i
$613$	35.9310	−	13.0778i	1.45124	−	0.528208i	0.508303	−	0.861178i	$-0.330273\pi$
$613$	35.9310	−	13.0778i	1.45124	−	0.528208i	0.942938	+	0.332970i	$0.108051\pi$
$614$	−0.0710708	+	1.22024i	−0.00286818	+	0.0492448i
$615$	−32.8859	−	31.2503i	−1.32609	−	1.26013i
$616$	−1.44061	−	3.33971i	−0.0580439	−	0.134561i
$617$	−1.28664	−	22.0908i	−0.0517984	−	0.889344i	−0.919703	−	0.392614i	$-0.871571\pi$
$617$	−1.28664	−	22.0908i	−0.0517984	−	0.889344i	0.867905	−	0.496730i	$-0.165466\pi$
$618$	−7.06792	+	8.36204i	−0.284314	+	0.336371i
$619$	−13.2276	+	14.0205i	−0.531664	+	0.563530i	−0.936414	−	0.350897i	$-0.885877\pi$
$619$	−13.2276	+	14.0205i	−0.531664	+	0.563530i	0.404751	+	0.914427i	$0.367358\pi$
$620$	−0.467600	−	0.809908i	−0.0187793	−	0.0325267i
$621$	−3.80067	+	7.36870i	−0.152516	+	0.295696i
$622$	−0.351994	+	0.609672i	−0.0141137	+	0.0244456i
$623$	−2.76016	−	9.21958i	−0.110583	−	0.369374i
$624$	0.0139891	−	3.89472i	0.000560011	−	0.155914i
$625$	17.9878	−	11.8308i	0.719514	−	0.473232i
$626$	−24.4482	−	2.85758i	−0.977146	−	0.114212i
$627$	−6.22107	−	2.71005i	−0.248446	−	0.108229i
$628$	−13.1017	+	6.57992i	−0.522815	+	0.262568i
$629$	−5.25217	+	29.7865i	−0.209418	+	1.18767i
$630$	4.53612	+	3.03036i	0.180723	+	0.120732i
$631$	−0.764140	−	4.33366i	−0.0304200	−	0.172520i	0.965813	−	0.259241i	$-0.0834723\pi$
$631$	−0.764140	−	4.33366i	−0.0304200	−	0.172520i	−0.996233	+	0.0867207i	$0.972361\pi$
$632$	7.72574	+	10.3775i	0.307313	+	0.412794i
$633$	−3.48333	+	0.190329i	−0.138450	+	0.00756492i
$634$	−15.6029	−	16.5381i	−0.619671	−	0.656812i
$635$	5.41073	−	18.0731i	0.214718	−	0.717209i
$636$	−22.2870	−	6.75961i	−0.883737	−	0.268036i
$637$	13.9488	−	1.63038i	0.552671	−	0.0645980i
$638$	−4.67768	+	3.92504i	−0.185191	+	0.155394i
$639$	22.4060	+	0.160958i	0.886369	+	0.00636740i
$640$	1.60363	+	1.34560i	0.0633889	+	0.0531896i
$641$	−37.1430	−	24.4294i	−1.46706	−	0.964902i	−0.996592	−	0.0824856i	$-0.973714\pi$
$641$	−37.1430	−	24.4294i	−1.46706	−	0.964902i	−0.470470	−	0.882416i	$-0.655915\pi$
$642$	−5.57172	−	11.1943i	−0.219898	−	0.441803i
$643$	11.3318	−	15.2213i	0.446883	−	0.600268i	−0.520414	−	0.853914i	$-0.674222\pi$
$643$	11.3318	−	15.2213i	0.446883	−	0.600268i	0.967297	+	0.253646i	$0.0816297\pi$
$644$	1.23860	+	0.622051i	0.0488079	+	0.0245122i
$645$	37.0058	−	6.38817i	1.45710	−	0.251534i
$646$	−4.01942	−	0.952621i	−0.158142	−	0.0374804i
$647$	−28.0313			−1.10202			−0.551012	−	0.834497i	$-0.685758\pi$
$647$	−28.0313			−1.10202			−0.551012	+	0.834497i	$0.685758\pi$
$648$	4.61151	−	7.72877i	0.181157	−	0.303615i
$649$	14.6756			0.576068
$650$	1.35161	+	0.320338i	0.0530145	+	0.0125647i
$651$	0.430189	+	0.516436i	0.0168605	+	0.0202407i
$652$	12.2246	+	6.13942i	0.478752	+	0.240438i
$653$	18.0184	−	24.2029i	0.705115	−	0.947134i	−0.294850	−	0.955544i	$-0.595270\pi$
$653$	18.0184	−	24.2029i	0.705115	−	0.947134i	0.999965	+	0.00840991i	$0.00267699\pi$
$654$	−35.0189	−	2.16585i	−1.36935	−	0.0846916i
$655$	12.6884	+	8.34531i	0.495778	+	0.326078i
$656$	9.58458	+	8.04242i	0.374215	+	0.314004i
$657$	−0.194725	−	1.15270i	−0.00759696	−	0.0449712i
$658$	6.90829	−	5.79675i	0.269313	−	0.225981i
$659$	1.03605	−	0.121097i	0.0403589	−	0.00471728i	−0.0958895	−	0.995392i	$-0.530570\pi$
$659$	1.03605	−	0.121097i	0.0403589	−	0.00471728i	0.136248	+	0.990675i	$0.456495\pi$
$660$	3.44815	+	14.7854i	0.134219	+	0.575519i
$661$	7.06217	−	23.5893i	0.274687	−	0.917517i	−0.703659	−	0.710538i	$-0.748452\pi$
$661$	7.06217	−	23.5893i	0.274687	−	0.917517i	0.978345	−	0.206979i	$-0.0663633\pi$
$662$	−15.3143	−	16.2322i	−0.595207	−	0.630883i
$663$	7.77214	−	15.3380i	0.301845	−	0.595678i
$664$	−0.959921	−	1.28940i	−0.0372522	−	0.0500383i
$665$	−0.295444	−	1.67555i	−0.0114568	−	0.0649749i
$666$	5.75304	+	19.7313i	0.222926	+	0.764571i
$667$	0.404070	−	2.29159i	0.0156456	−	0.0887309i
$668$	−14.1996	+	7.13133i	−0.549401	+	0.275919i
$669$	2.48359	+	21.9313i	0.0960210	+	0.847913i
$670$	27.1818	+	3.17710i	1.05012	+	0.122742i
$671$	37.3048	−	24.5357i	1.44013	−	0.947191i
$672$	−1.30026	−	0.756943i	−0.0501585	−	0.0291997i
$673$	4.51516	+	15.0817i	0.174047	+	0.581356i	0.999849	+	0.0173963i	$0.00553769\pi$
$673$	4.51516	+	15.0817i	0.174047	+	0.581356i	−0.825802	+	0.563960i	$0.809277\pi$
$674$	0.910250	−	1.57660i	0.0350615	−	0.0607283i
$675$	2.31087	+	2.22775i	0.0889456	+	0.0857460i
$676$	3.97182	+	6.87940i	0.152762	+	0.264592i
$677$	−6.37657	+	6.75877i	−0.245071	+	0.259760i	−0.838220	−	0.545333i	$-0.816403\pi$
$677$	−6.37657	+	6.75877i	−0.245071	+	0.259760i	0.593148	+	0.805093i	$0.297885\pi$
$678$	−29.1465	−	5.24733i	−1.11936	−	0.201522i
$679$	−0.175346	−	3.01057i	−0.00672915	−	0.115535i
$680$	3.66057	+	8.48617i	0.140377	+	0.325430i
$681$	16.1498	−	4.77180i	0.618862	−	0.182856i
$682$	−0.108765	+	1.86742i	−0.00416482	+	0.0715072i
$683$	−34.1423	+	12.4268i	−1.30642	+	0.475498i	−0.899082	−	0.437780i	$-0.855765\pi$
$683$	−34.1423	+	12.4268i	−1.30642	+	0.475498i	−0.407337	+	0.913278i	$0.633543\pi$
$684$	−2.73587	+	0.627691i	−0.104609	+	0.0240004i
$685$	−16.0458	−	5.84019i	−0.613078	−	0.223142i
$686$	4.55713	−	10.5646i	0.173992	−	0.403359i
$687$	19.7146	−	8.42020i	0.752160	−	0.321251i
$688$	−10.0779	+	2.38850i	−0.384216	+	0.0910608i
$689$	−29.4206	+	6.97282i	−1.12084	+	0.265643i
$690$	−4.62825	−	3.47151i	−0.176195	−	0.132158i
$691$	15.8679	−	36.7859i	0.603644	−	1.39940i	−0.292769	−	0.956183i	$-0.594577\pi$
$691$	15.8679	−	36.7859i	0.603644	−	1.39940i	0.896413	−	0.443220i	$-0.146164\pi$
$692$	−1.22332	−	0.445253i	−0.0465037	−	0.0169260i
$693$	−4.24975	−	10.0499i	−0.161435	−	0.381765i
$694$	14.2905	−	5.20133i	0.542461	−	0.197440i
$695$	−1.42234	+	24.4207i	−0.0539525	+	0.926329i
$696$	−0.591335	+	2.45570i	−0.0224145	+	0.0930831i
$697$	21.8786	+	50.7202i	0.828710	+	1.92117i
$698$	1.66090	+	28.5166i	0.0628662	+	1.07937i
$699$	−9.56486	−	26.5759i	−0.361776	−	1.00519i
$700$	0.368230	−	0.390301i	0.0139178	−	0.0147520i
$701$	17.5555	+	30.4070i	0.663063	+	1.14846i	0.979807	+	0.199947i	$0.0640771\pi$
$701$	17.5555	+	30.4070i	0.663063	+	1.14846i	−0.316744	+	0.948511i	$0.602590\pi$
$702$	0.125899	−	11.6836i	0.00475177	−	0.440968i
$703$	3.20505	−	5.55131i	0.120881	−	0.209372i
$704$	−1.20090	−	4.01128i	−0.0452605	−	0.151181i
$705$	−32.6672	+	18.7043i	−1.23032	+	0.704445i
$706$	−19.0729	+	12.5444i	−0.717818	+	0.472117i
$707$	−7.38090	−	0.862703i	−0.277587	−	0.0324453i
$708$	4.88239	−	3.60762i	0.183492	−	0.135583i
$709$	−30.9238	+	15.5305i	−1.16137	+	0.583261i	−0.921818	−	0.387623i	$-0.873296\pi$
$709$	−30.9238	+	15.5305i	−1.16137	+	0.583261i	−0.239551	+	0.970884i	$0.577000\pi$
$710$	−2.71503	+	15.3977i	−0.101893	+	0.577865i
$711$	22.9530	+	31.2981i	0.860804	+	1.17377i
$712$	−1.92388	−	10.9109i	−0.0721005	−	0.408902i
$713$	−0.425674	−	0.571779i	−0.0159416	−	0.0214133i
$714$	−3.63006	−	5.56265i	−0.135852	−	0.208177i
$715$	13.5259	+	14.3367i	0.505841	+	0.536160i
$716$	−2.48165	+	8.28929i	−0.0927436	+	0.309785i
$717$	11.0106	−	10.3135i	0.411199	−	0.385164i
$718$	−11.7210	+	1.36999i	−0.437423	+	0.0511275i
$719$	13.2253	−	11.0973i	0.493220	−	0.413860i	−0.361959	−	0.932194i	$-0.617892\pi$
$719$	13.2253	−	11.0973i	0.493220	−	0.413860i	0.855178	+	0.518334i	$0.173447\pi$
$720$	4.78176	+	4.07126i	0.178206	+	0.151727i
$721$	4.20637	+	3.52956i	0.156653	+	0.131448i
$722$	−15.1428	−	9.95961i	−0.563558	−	0.370658i
$723$	−12.8848	+	19.4379i	−0.479189	+	0.722903i
$724$	−6.07581	+	8.16122i	−0.225806	+	0.303310i
$725$	−0.805032	−	0.404302i	−0.0298981	−	0.0150154i
$726$	3.90799	−	10.6183i	0.145039	−	0.394082i
$727$	1.74465	+	0.413490i	0.0647055	+	0.0153355i	0.262841	−	0.964839i	$-0.415340\pi$
$727$	1.74465	+	0.413490i	0.0647055	+	0.0153355i	−0.198136	+	0.980175i	$0.563489\pi$
$728$	−1.95326			−0.0723928
$729$	14.0007	−	23.0863i	0.518546	−	0.855050i
$730$	0.815747			0.0301922
$731$	−44.4925	−	10.5449i	−1.64561	−	0.390018i
$732$	6.37935	−	17.3332i	0.235788	−	0.640652i
$733$	20.7469	+	10.4195i	0.766306	+	0.384853i	0.788607	−	0.614898i	$-0.210803\pi$
$733$	20.7469	+	10.4195i	0.766306	+	0.384853i	−0.0223008	+	0.999751i	$0.507099\pi$
$734$	15.6675	−	21.0451i	0.578298	−	0.776790i
$735$	−12.5116	+	18.8749i	−0.461496	+	0.696211i
$736$	1.33313	+	0.876812i	0.0491397	+	0.0323197i
$737$	−41.9325	−	35.1856i	−1.54460	−	1.29608i
$738$	28.5797	+	24.3332i	1.05203	+	0.895717i
$739$	−11.0065	+	9.23551i	−0.404879	+	0.339734i	−0.822376	−	0.568945i	$-0.807352\pi$
$739$	−11.0065	+	9.23551i	−0.404879	+	0.339734i	0.417497	+	0.908678i	$0.362907\pi$
$740$	−14.2447	+	1.66497i	−0.523646	+	0.0612055i
$741$	−2.65960	+	2.49121i	−0.0977030	+	0.0915170i
$742$	−3.34986	+	11.1893i	−0.122977	+	0.410772i
$743$	22.9038	+	24.2766i	0.840257	+	0.890621i	0.995256	−	0.0972942i	$-0.0310188\pi$
$743$	22.9038	+	24.2766i	0.840257	+	0.890621i	−0.154999	+	0.987915i	$0.549537\pi$
$744$	0.422873	+	0.648005i	0.0155033	+	0.0237570i
$745$	2.42042	+	3.25118i	0.0886772	+	0.119114i
$746$	6.30547	+	35.7601i	0.230860	+	1.30927i
$747$	−2.85190	−	3.88878i	−0.104346	−	0.142283i
$748$	3.21003	−	18.2050i	0.117370	−	0.665640i
$749$	−5.60399	+	2.81443i	−0.204765	+	0.102837i
$750$	−16.3821	+	12.1048i	−0.598189	+	0.442005i
$751$	27.5632	+	3.22168i	1.00580	+	0.117561i	0.603010	−	0.797734i	$-0.293968\pi$
$751$	27.5632	+	3.22168i	1.00580	+	0.117561i	0.402786	+	0.915294i	$0.368042\pi$
$752$	8.67391	−	5.70492i	0.316305	−	0.208037i
$753$	−38.8752	+	22.2588i	−1.41669	+	0.811155i
$754$	0.940497	+	3.14148i	0.0342509	+	0.114406i
$755$	−23.1882	+	40.1631i	−0.843905	+	1.46169i
$756$	−3.88436	−	2.29879i	−0.141273	−	0.0836063i
$757$	9.87193	+	17.0987i	0.358802	+	0.621462i	0.987761	−	0.155976i	$-0.0498522\pi$
$757$	9.87193	+	17.0987i	0.358802	+	0.621462i	−0.628959	+	0.777438i	$0.716519\pi$
$758$	14.5201	−	15.3904i	0.527392	−	0.559003i
$759$	3.91883	+	10.8884i	0.142244	+	0.395224i
$760$	−0.113887	−	1.95536i	−0.00413112	−	0.0709285i
$761$	−11.0244	−	25.5574i	−0.399633	−	0.926454i	−0.992623	−	0.121244i	$-0.961312\pi$
$761$	−11.0244	−	25.5574i	−0.399633	−	0.926454i	0.592989	−	0.805210i	$-0.297948\pi$
$762$	−3.65428	+	15.1755i	−0.132381	+	0.549750i
$763$	−1.02311	+	17.5662i	−0.0370392	+	0.635939i
$764$	−2.92741	+	1.06549i	−0.105910	+	0.0385481i
$765$	10.7986	+	25.5367i	0.390423	+	0.923282i
$766$	−14.7208	−	5.35792i	−0.531883	−	0.193589i
$767$	3.12159	−	7.23666i	0.112714	−	0.261301i
$768$	−1.38559	−	1.03929i	−0.0499983	−

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)

\(f(q)\)	\(=\)	\(q+(-0.973045 - 0.230616i) q^{2} +(-0.598238 + 1.62546i) q^{3} +(0.893633 + 0.448799i) q^{4} +(-1.25008 + 1.67915i) q^{5} +(0.956969 - 1.44368i) q^{6} +(-0.725742 - 0.477328i) q^{7} +(-0.766044 - 0.642788i) q^{8} +(-2.28422 - 1.94482i) q^{9} +O(q^{10})\)	\(q+(-0.973045 - 0.230616i) q^{2} +(-0.598238 + 1.62546i) q^{3} +(0.893633 + 0.448799i) q^{4} +(-1.25008 + 1.67915i) q^{5} +(0.956969 - 1.44368i) q^{6} +(-0.725742 - 0.477328i) q^{7} +(-0.766044 - 0.642788i) q^{8} +(-2.28422 - 1.94482i) q^{9} +(1.60363 - 1.34560i) q^{10} +(-4.15887 + 0.486102i) q^{11} +(-1.26411 + 1.18407i) q^{12} +(-0.644916 + 2.15417i) q^{13} +(0.596100 + 0.631829i) q^{14} +(-1.98154 - 3.03649i) q^{15} +(0.597159 + 0.802123i) q^{16} +(0.766633 + 4.34779i) q^{17} +(1.77414 + 2.41918i) q^{18} +(0.162474 - 0.921436i) q^{19} +(-1.87072 + 0.939510i) q^{20} +(1.21004 - 0.894106i) q^{21} +(4.15887 + 0.486102i) q^{22} +(-1.33313 + 0.876812i) q^{23} +(1.50310 - 0.860632i) q^{24} +(0.177167 + 0.591780i) q^{25} +(1.12432 - 1.94737i) q^{26} +(4.52773 - 2.54944i) q^{27} +(-0.434322 - 0.752268i) q^{28} +(-1.00076 + 1.06075i) q^{29} +(1.22787 + 3.41162i) q^{30} +(0.0259757 + 0.445985i) q^{31} +(-0.396080 - 0.918216i) q^{32} +(1.69786 - 7.05087i) q^{33} +(0.256701 - 4.40739i) q^{34} +(1.70875 - 0.621932i) q^{35} +(-1.16842 - 2.76311i) q^{36} +(6.43779 + 2.34316i) q^{37} +(-0.370592 + 0.859129i) q^{38} +(-3.11569 - 2.33699i) q^{39} +(2.03696 - 0.482768i) q^{40} +(12.1745 - 2.88542i) q^{41} +(-1.38362 + 0.590951i) q^{42} +(-4.10222 + 9.51002i) q^{43} +(-3.93466 - 1.43210i) q^{44} +(6.12112 - 1.40437i) q^{45} +(1.49940 - 0.545737i) q^{46} +(0.603651 - 10.3643i) q^{47} +(-1.66106 + 0.490795i) q^{48} +(-2.47370 - 5.73468i) q^{49} +(-0.0359179 - 0.616686i) q^{50} +(-7.52578 - 1.35489i) q^{51} +(-1.54311 + 1.63560i) q^{52} +(6.72311 + 11.6448i) q^{53} +(-4.99363 + 1.43655i) q^{54} +(4.38270 - 7.59105i) q^{55} +(0.249130 + 0.832152i) q^{56} +(1.40056 + 0.815333i) q^{57} +(1.21841 - 0.801363i) q^{58} +(-3.48119 - 0.406893i) q^{59} +(-0.407998 - 3.60282i) q^{60} +(-9.52931 + 4.78580i) q^{61} +(0.0775757 - 0.439954i) q^{62} +(0.729438 + 2.50176i) q^{63} +(0.173648 + 0.984808i) q^{64} +(-2.81098 - 3.77580i) q^{65} +(-3.27813 + 6.46926i) q^{66} +(8.97123 + 9.50895i) q^{67} +(-1.26620 + 4.22939i) q^{68} +(-0.627692 - 2.69149i) q^{69} +(-1.80611 + 0.211104i) q^{70} +(-5.72149 + 4.80090i) q^{71} +(0.499708 + 2.95809i) q^{72} +(0.298511 + 0.250480i) q^{73} +(-5.72389 - 3.76466i) q^{74} +(-1.06790 - 0.0660477i) q^{75} +(0.558732 - 0.750507i) q^{76} +(3.25030 + 1.63236i) q^{77} +(2.49276 + 2.99252i) q^{78} +(-12.5888 - 2.98359i) q^{79} -2.09339 q^{80} +(1.43534 + 8.88481i) q^{81} -12.5118 q^{82} +(1.56415 + 0.370711i) q^{83} +(1.48261 - 0.255936i) q^{84} +(-8.25897 - 4.14781i) q^{85} +(6.18481 - 8.30764i) q^{86} +(-1.12550 - 2.26128i) q^{87} +(3.49834 + 2.30089i) q^{88} +(8.48715 + 7.12157i) q^{89} +(-6.28000 - 0.0451136i) q^{90} +(1.49629 - 1.25553i) q^{91} +(-1.58484 + 0.185241i) q^{92} +(-0.740469 - 0.224583i) q^{93} +(-2.97755 + 9.94570i) q^{94} +(1.34413 + 1.42469i) q^{95} +(1.72947 - 0.0944985i) q^{96} +(2.07315 + 2.78473i) q^{97} +(1.08451 + 6.15057i) q^{98} +(10.4452 + 6.97790i) 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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