LMFDB - Embedded newform 162.2.g.a.157.2

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			157.2
Character	$\chi$	$=$	162.157
Dual form			162.2.g.a.97.2

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

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

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.973045	+	0.230616i	−0.688047	+	0.163070i
$2$	−0.973045	+	0.230616i	−0.688047	+	0.163070i
$3$	−0.598238	−	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	0.429291	−	0.903166i	$-0.358763\pi$
$5$	−1.25008	−	1.67915i	−0.559055	−	0.750941i	−0.988346	+	0.152226i	$0.951356\pi$
$6$	0.956969	+	1.44368i	0.390681	+	0.589380i
$7$	−0.725742	+	0.477328i	−0.274305	+	0.180413i	−0.679207	−	0.733947i	$-0.737676\pi$
$7$	−0.725742	+	0.477328i	−0.274305	+	0.180413i	0.404902	+	0.914360i	$0.367306\pi$
$8$	−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	−0.536933	−	0.843625i	$-0.680417\pi$
$11$	−4.15887	−	0.486102i	−1.25395	−	0.146565i	−0.717013	+	0.697059i	$0.754491\pi$
$12$	−1.26411	−	1.18407i	−0.364917	−	0.341812i
$13$	−0.644916	−	2.15417i	−0.178867	−	0.597459i	−0.999656	−	0.0262267i	$-0.991651\pi$
$13$	−0.644916	−	2.15417i	−0.178867	−	0.597459i	0.820789	−	0.571232i	$-0.193534\pi$
$14$	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	−0.738811	−	0.673912i	$-0.764613\pi$
$17$	0.766633	−	4.34779i	0.185936	−	1.05449i	0.924747	−	0.380582i	$-0.124276\pi$
$18$	1.77414	−	2.41918i	0.418170	−	0.570205i
$19$	0.162474	+	0.921436i	0.0372741	+	0.211392i	0.997756	−	0.0669492i	$-0.0213265\pi$
$19$	0.162474	+	0.921436i	0.0372741	+	0.211392i	−0.960482	+	0.278341i	$0.910215\pi$
$20$	−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	0.402864	−	0.915260i	$-0.368015\pi$
$23$	−1.33313	−	0.876812i	−0.277976	−	0.182828i	−0.680840	+	0.732432i	$0.738385\pi$
$24$	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	0.627756	−	0.778410i	$-0.283973\pi$
$29$	−1.00076	−	1.06075i	−0.185837	−	0.196976i	−0.813594	+	0.581434i	$0.802492\pi$
$30$	1.22787	−	3.41162i	0.224177	−	0.622874i
$31$	0.0259757	−	0.445985i	0.00466536	−	0.0801012i	−0.995172	−	0.0981486i	$-0.968708\pi$
$31$	0.0259757	−	0.445985i	0.00466536	−	0.0801012i	0.999837	+	0.0180474i	$0.00574498\pi$
$32$	−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	0.246552	−	0.969130i	$-0.420702\pi$
$37$	6.43779	−	2.34316i	1.05837	−	0.385214i	0.811814	+	0.583916i	$0.198480\pi$
$38$	−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	0.999841	+	0.0178481i	$0.00568154\pi$
$41$	12.1745	+	2.88542i	1.90134	+	0.450626i	0.901501	+	0.432778i	$0.142467\pi$
$42$	−1.38362	−	0.590951i	−0.213497	−	0.0911856i
$43$	−4.10222	−	9.51002i	−0.625583	−	1.45026i	−0.876089	−	0.482150i	$-0.839856\pi$
$43$	−4.10222	−	9.51002i	−0.625583	−	1.45026i	0.250506	−	0.968115i	$-0.419403\pi$
$44$	−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	0.696134	+	0.717912i	$0.254902\pi$
$47$	0.603651	+	10.3643i	0.0880515	+	1.51179i	−0.608082	+	0.793874i	$0.708061\pi$
$48$	−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	0.129520	−	0.991577i	$-0.458656\pi$
$53$	6.72311	−	11.6448i	0.923491	−	1.59953i	0.793971	−	0.607956i	$-0.208010\pi$
$54$	−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	−0.339637	−	0.940557i	$-0.610304\pi$
$59$	−3.48119	+	0.406893i	−0.453212	+	0.0529729i	−0.113575	+	0.993529i	$0.536230\pi$
$60$	−0.407998	+	3.60282i	−0.0526723	+	0.465123i
$61$	−9.52931	−	4.78580i	−1.22010	−	0.612759i	−0.282099	−	0.959385i	$-0.591031\pi$
$61$	−9.52931	−	4.78580i	−1.22010	−	0.612759i	−0.938003	+	0.346627i	$0.887327\pi$
$62$	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	0.110189	−	0.993911i	$-0.464855\pi$
$67$	8.97123	−	9.50895i	1.09601	−	1.16170i	0.985822	−	0.167793i	$-0.0536640\pi$
$68$	−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	0.236703	−	0.971582i	$-0.423933\pi$
$71$	−5.72149	−	4.80090i	−0.679015	−	0.569762i	−0.915718	+	0.401820i	$0.868378\pi$
$72$	0.499708	−	2.95809i	0.0588911	−	0.348614i
$73$	0.298511	−	0.250480i	0.0349381	−	0.0293165i	−0.625151	−	0.780503i	$-0.714963\pi$
$73$	0.298511	−	0.250480i	0.0349381	−	0.0293165i	0.660089	+	0.751187i	$0.270518\pi$
$74$	−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	−0.866330	−	0.499472i	$-0.833527\pi$
$79$	−12.5888	+	2.98359i	−1.41635	+	0.335681i	−0.550018	+	0.835153i	$0.685379\pi$
$80$	−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	−0.143873	−	0.989596i	$-0.545956\pi$
$83$	1.56415	−	0.370711i	0.171688	−	0.0406908i	0.315561	+	0.948905i	$0.397807\pi$
$84$	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	−0.0704828	−	0.997513i	$-0.522454\pi$
$89$	8.48715	−	7.12157i	0.899637	−	0.754885i	0.970119	+	0.242628i	$0.0780095\pi$
$90$	−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	−0.684318	−	0.729184i	$-0.739900\pi$
$97$	2.07315	−	2.78473i	0.210497	−	0.282746i	0.894815	+	0.446437i	$0.147307\pi$
$98$	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	0.786468	−	0.617631i	$-0.211908\pi$
$101$	7.64492	+	3.83942i	0.760698	+	0.382037i	−0.0257703	+	0.999668i	$0.508204\pi$
$102$	7.01046	−	3.05393i	0.694139	−	0.302384i
$103$	−6.27863	+	0.733867i	−0.618652	+	0.0723100i	−0.419645	−	0.907688i	$-0.637846\pi$
$103$	−6.27863	+	0.733867i	−0.618652	+	0.0723100i	−0.199007	+	0.979998i	$0.563772\pi$
$104$	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	0.986065	−	0.166361i	$-0.0532019\pi$
$107$	3.60966	+	6.25212i	0.348959	+	0.604415i	−0.637106	+	0.770776i	$0.719869\pi$
$108$	5.19032	+	0.246217i	0.499438	+	0.0236923i
$109$	−10.1284	+	17.5429i	−0.970125	+	1.68031i	−0.274962	+	0.961455i	$0.588665\pi$
$109$	−10.1284	+	17.5429i	−0.970125	+	1.68031i	−0.695164	+	0.718851i	$0.744668\pi$
$110$	−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	0.227165	+	0.973856i	$0.427054\pi$
$113$	−6.77228	+	15.6999i	−0.637083	+	1.47692i	−0.864247	+	0.503067i	$0.832205\pi$
$114$	−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	−0.0622403	−	0.998061i	$-0.519825\pi$
$127$	−8.46853	−	3.08229i	−0.751460	−	0.273509i	−0.689220	+	0.724552i	$0.742047\pi$
$128$	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	0.928420	+	0.371533i	$0.121168\pi$
$131$	−0.421822	+	7.24240i	−0.0368548	+	0.632772i	−0.965274	+	0.261238i	$0.915869\pi$
$132$	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	−0.798016	−	0.602636i	$-0.794117\pi$
$137$	2.33943	−	7.81423i	0.199871	−	0.667615i	0.997887	−	0.0649784i	$-0.0206979\pi$
$138$	−0.00992662	−	2.76369i	−0.000845010	−	0.235261i
$139$	9.76300	+	6.42123i	0.828087	+	0.544642i	0.891329	−	0.453357i	$-0.149774\pi$
$139$	9.76300	+	6.42123i	0.828087	+	0.544642i	−0.0632419	+	0.997998i	$0.520144\pi$
$140$	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	0.977718	−	0.209922i	$-0.0673209\pi$
$149$	0.555309	+	1.85486i	0.0454927	+	0.151956i	−0.932225	+	0.361878i	$0.882136\pi$
$150$	1.02388	−	0.310543i	0.0835999	−	0.0253557i
$151$	22.0040	+	2.57189i	1.79066	+	0.209298i	0.945590	−	0.325362i	$-0.105486\pi$
$151$	22.0040	+	2.57189i	1.79066	+	0.209298i	0.845068	+	0.534659i	$0.179560\pi$
$152$	−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	0.301158	−	0.953574i	$-0.402627\pi$
$157$	−8.75505	−	11.7601i	−0.698729	−	0.938556i	−0.999887	+	0.0150183i	$0.995219\pi$
$158$	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	−0.999754	−	0.0221698i	$-0.992943\pi$
$167$	−9.48873	−	12.7456i	−0.734260	−	0.986282i	0.265494	−	0.964112i	$-0.414465\pi$
$168$	−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	0.0667971	−	0.997767i	$-0.478722\pi$
$173$	−1.29303	−	0.151133i	−0.0983072	−	0.0114905i	−0.165104	+	0.986276i	$0.552796\pi$
$174$	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	−0.875744	−	0.482776i	$-0.839629\pi$
$179$	1.50254	−	8.52134i	0.112305	−	0.636915i	0.988049	−	0.154139i	$-0.0492604\pi$
$180$	6.10032	−	1.49216i	0.454691	−	0.111219i
$181$	−1.76679	−	10.0200i	−0.131324	−	0.744777i	−0.977349	−	0.211634i	$-0.932122\pi$
$181$	−1.76679	−	10.0200i	−0.131324	−	0.744777i	0.846025	−	0.533144i	$-0.178989\pi$
$182$	−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	0.645395	−	0.763849i	$-0.276693\pi$
$191$	−2.13784	−	2.26598i	−0.154689	−	0.163960i	−0.800083	+	0.599889i	$0.795211\pi$
$192$	−1.70465	+	0.306892i	−0.123022	+	0.0221480i
$193$	−0.0668182	+	1.14722i	−0.00480968	+	0.0825790i	−0.999859	−	0.0168056i	$-0.994650\pi$
$193$	−0.0668182	+	1.14722i	−0.00480968	+	0.0825790i	0.995049	+	0.0993846i	$0.0316874\pi$
$194$	−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	0.0563027	−	0.998414i	$-0.482069\pi$
$197$	−7.61203	−	2.77055i	−0.542335	−	0.197394i	−0.598638	+	0.801020i	$0.704291\pi$
$198$	−8.55440	+	9.19863i	−0.607935	+	0.653718i
$199$	−0.654014	+	0.238042i	−0.0463618	+	0.0168743i	−0.365097	−	0.930969i	$-0.618964\pi$
$199$	−0.654014	+	0.238042i	−0.0463618	+	0.0168743i	0.318735	+	0.947844i	$0.396742\pi$
$200$	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	−0.888547	−	0.458785i	$-0.848285\pi$
$211$	0.797744	−	1.84938i	0.0549190	−	0.127316i	0.943466	+	0.331469i	$0.107544\pi$
$212$	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	0.787181	−	0.616722i	$-0.211540\pi$
$223$	11.3875	+	5.71904i	0.762566	+	0.382975i	−0.0246149	+	0.999697i	$0.507836\pi$
$224$	−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	−0.951899	−	0.306411i	$-0.900872\pi$
$227$	−5.80593	+	7.79872i	−0.385353	+	0.517619i	0.566546	+	0.824030i	$0.308279\pi$
$228$	0.885662	−	1.35718i	0.0586544	−	0.0898812i
$229$	−8.49357	+	9.00266i	−0.561271	+	0.594913i	−0.944407	−	0.328779i	$-0.893363\pi$
$229$	−8.49357	+	9.00266i	−0.561271	+	0.594913i	0.383136	+	0.923692i	$0.374844\pi$
$230$	−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	0.134216	−	0.990952i	$-0.457148\pi$
$233$	−12.4919	−	10.4820i	−0.818375	−	0.686698i	−0.952591	+	0.304254i	$0.901593\pi$
$234$	−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	−0.682366	−	0.731011i	$-0.739049\pi$
$239$	−7.78369	+	3.90912i	−0.503485	+	0.252860i	0.178880	+	0.983871i	$0.442752\pi$
$240$	1.25234	+	3.40271i	0.0808385	+	0.219644i
$241$	13.1012	−	3.10504i	0.843923	−	0.200013i	0.214158	−	0.976799i	$-0.431299\pi$
$241$	13.1012	−	3.10504i	0.843923	−	0.200013i	0.629765	+	0.776786i	$0.283151\pi$
$242$	−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	0.253927	−	0.967223i	$-0.418278\pi$
$251$	19.8124	−	16.6246i	1.25055	−	1.04934i	0.996623	−	0.0821128i	$-0.0261668\pi$
$252$	−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	−0.784193	−	0.620517i	$-0.786923\pi$
$257$	−1.90977	+	2.02424i	−0.119128	+	0.126269i	0.665064	+	0.746786i	$0.268404\pi$
$258$	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	0.776748	−	0.629811i	$-0.216868\pi$
$263$	11.9262	+	5.98959i	0.735404	+	0.369334i	−0.0413444	+	0.999145i	$0.513164\pi$
$264$	−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	0.797431	−	0.603410i	$-0.206192\pi$
$269$	−2.03133	−	3.51837i	−0.123853	−	0.214519i	−0.921284	+	0.388891i	$0.872858\pi$
$270$	3.83027	+	10.1809i	0.233103	+	0.619589i
$271$	6.13785	−	10.6311i	0.372848	−	0.645791i	−0.617155	−	0.786842i	$-0.711715\pi$
$271$	6.13785	−	10.6311i	0.372848	−	0.645791i	0.990002	+	0.141051i	$0.0450480\pi$
$272$	−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	0.997753	−	0.0669946i	$-0.0213410\pi$
$277$	−0.0171617	−	0.294655i	−0.00103115	−	0.0177041i	−0.998784	+	0.0492905i	$0.984304\pi$
$278$	−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	0.727956	−	0.685624i	$-0.240471\pi$
$281$	−4.53110	−	10.5043i	−0.270302	−	0.626632i	−0.998258	+	0.0589923i	$0.981211\pi$
$282$	−14.3850	+	10.7898i	−0.856616	+	0.642522i
$283$	21.7276	+	5.14954i	1.29157	+	0.306108i	0.818291	−	0.574804i	$-0.194922\pi$
$283$	21.7276	+	5.14954i	1.29157	+	0.306108i	0.473281	+	0.880912i	$0.343070\pi$
$284$	−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	−0.932569	−	0.360991i	$-0.882439\pi$
$293$	0.609421	−	10.4634i	0.0356027	−	0.611276i	0.968172	−	0.250285i	$-0.0805243\pi$
$294$	−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	−0.990265	−	0.139192i	$-0.955549\pi$
$307$	−0.212251	+	1.20374i	−0.0121138	+	0.0687009i	0.978152	+	0.207893i	$0.0666606\pi$
$308$	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	0.963523	−	0.267625i	$-0.0862388\pi$
$311$	0.201906	+	0.674413i	0.0114490	+	0.0382425i	−0.952074	+	0.305867i	$0.901054\pi$
$312$	0.884573	−	3.79297i	0.0500791	−	0.214734i
$313$	24.4482	+	2.85758i	1.38189	+	0.161520i	0.774345	−	0.632763i	$-0.218079\pi$
$313$	24.4482	+	2.85758i	1.38189	+	0.161520i	0.607547	+	0.794284i	$0.292154\pi$
$314$	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	0.110560	−	0.993869i	$-0.464736\pi$
$317$	18.9963	−	12.4940i	1.06694	−	0.701736i	0.956377	+	0.292134i	$0.0943653\pi$
$318$	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	0.0783803	−	0.996924i	$-0.475025\pi$
$331$	18.6449	−	12.2629i	1.02482	−	0.674032i	0.946436	+	0.322891i	$0.104655\pi$
$332$	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	0.942590	−	0.333952i	$-0.108382\pi$
$337$	−0.522125	−	1.74402i	−0.0284420	−	0.0950028i	−0.971032	+	0.238949i	$0.923197\pi$
$338$	−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	0.160602	−	0.987019i	$-0.448656\pi$
$347$	−12.7058	−	8.35675i	−0.682084	−	0.448614i	−0.842686	+	0.538406i	$0.819027\pi$
$348$	0.00907244	+	2.52588i	0.000486334	+	0.135401i
$349$	−8.19252	+	27.3649i	−0.438536	+	1.46481i	0.398248	+	0.917278i	$0.369618\pi$
$349$	−8.19252	+	27.3649i	−0.438536	+	1.46481i	−0.836784	+	0.547534i	$0.815567\pi$
$350$	−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	0.994661	−	0.103193i	$-0.0329058\pi$
$353$	15.6658	+	16.6048i	0.833809	+	0.883786i	−0.160853	+	0.986978i	$0.551424\pi$
$354$	−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	0.617644	−	0.786458i	$-0.288087\pi$
$359$	11.0891	+	4.03610i	0.585261	+	0.213017i	−0.0323831	+	0.999476i	$0.510310\pi$
$360$	−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	−0.940380	−	0.340125i	$-0.889531\pi$
$367$	−10.3919	−	24.0910i	−0.542450	−	1.25754i	0.397930	−	0.917416i	$-0.369729\pi$
$368$	−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	−0.0592644	+	0.998242i	$0.518875\pi$
$373$	−14.3823	+	33.3420i	−0.744690	+	1.72639i	−0.685425	+	0.728143i	$0.740384\pi$
$374$	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	−0.998704	−	0.0508940i	$-0.983793\pi$
$379$	−10.5794	−	18.3241i	−0.543428	−	0.941244i	0.455277	−	0.890350i	$-0.349540\pi$
$380$	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	0.291140	−	0.956681i	$-0.405966\pi$
$383$	15.5596	−	1.81865i	0.795057	−	0.0929289i	0.503918	+	0.863752i	$0.331891\pi$
$384$	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	−0.518384	−	0.855148i	$-0.673466\pi$
$389$	8.86577	−	11.9088i	0.449512	−	0.603800i	0.967897	+	0.251348i	$0.0808738\pi$
$390$	−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	−0.884224	−	0.467064i	$-0.845312\pi$
$397$	−11.5126	+	9.66019i	−0.577799	+	0.484831i	0.306424	+	0.951895i	$0.400867\pi$
$398$	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	−0.435889	−	0.900000i	$-0.643566\pi$
$401$	0.515172	−	0.258729i	0.0257264	−	0.0129203i	0.461616	+	0.887080i	$0.347270\pi$
$402$	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	−0.224238	−	0.974534i	$-0.571989\pi$
$409$	8.56582	−	4.30192i	0.423553	−	0.212716i	0.647791	+	0.761818i	$0.275693\pi$
$410$	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	0.396775	−	0.917916i	$-0.370129\pi$
$419$	26.4070	−	27.9898i	1.29007	−	1.36739i	0.893292	−	0.449476i	$-0.148389\pi$
$420$	−1.42363	−	2.80947i	−0.0694659	−	0.137088i
$421$	−5.19429	+	6.97715i	−0.253154	+	0.340045i	−0.910474	−	0.413567i	$-0.864283\pi$
$421$	−5.19429	+	6.97715i	−0.253154	+	0.340045i	0.657319	+	0.753612i	$0.271690\pi$
$422$	−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	0.999039	−	0.0438243i	$-0.0139542\pi$
$431$	9.58237	+	16.5972i	0.461567	+	0.799457i	−0.537473	+	0.843281i	$0.680621\pi$
$432$	4.74874	−	2.10938i	0.228474	−	0.101488i
$433$	−1.63588	+	2.83343i	−0.0786154	+	0.136166i	−0.902653	−	0.430370i	$-0.858383\pi$
$433$	−1.63588	+	2.83343i	−0.0786154	+	0.136166i	0.824037	+	0.566535i	$0.191717\pi$
$434$	−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	0.727316	+	0.686303i	$0.240767\pi$
$439$	1.77241	+	30.4312i	0.0845927	+	1.45240i	−0.642723	+	0.766098i	$0.722196\pi$
$440$	−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	−0.983721	−	0.179701i	$-0.942487\pi$
$443$	−9.24747	−	21.4381i	−0.439361	−	1.01855i	0.544360	−	0.838851i	$-0.316772\pi$
$444$	−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	−0.934440	−	0.356121i	$-0.884099\pi$
$449$	−30.1179	+	10.9620i	−1.42135	+	0.517330i	−0.486912	+	0.873451i	$0.661877\pi$
$450$	−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	0.219068	−	0.975710i	$-0.429698\pi$
$457$	−16.4122	−	17.3959i	−0.767729	−	0.813745i	−0.986797	+	0.161965i	$0.948217\pi$
$458$	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	−0.997647	−	0.0685589i	$-0.978160\pi$
$461$	−2.71503	+	9.06882i	−0.126451	+	0.422377i	0.871196	+	0.490936i	$0.163345\pi$
$462$	5.46704	+	3.13027i	0.254350	+	0.145633i
$463$	−31.5131	−	20.7265i	−1.46454	−	0.963241i	−0.996847	−	0.0793481i	$-0.974716\pi$
$463$	−31.5131	−	20.7265i	−1.46454	−	0.963241i	−0.467690	−	0.883893i	$-0.654913\pi$
$464$	−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	0.956074	+	0.293126i	$0.0946954\pi$
$467$	3.41253	+	19.3534i	0.157913	+	0.895570i	−0.798161	+	0.602445i	$0.794193\pi$
$468$	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	0.0450061	−	0.998987i	$-0.485669\pi$
$479$	21.4509	−	14.1085i	0.980118	−	0.644634i	0.935112	+	0.354353i	$0.115299\pi$
$480$	−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	0.484175	−	0.874971i	$-0.339120\pi$
$491$	−10.9220	−	14.6707i	−0.492901	−	0.662081i	−0.977076	+	0.212890i	$0.931712\pi$
$492$	−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	0.998425	+	0.0561014i	$0.0178670\pi$
$499$	4.35779	+	14.5560i	0.195081	+	0.651617i	−0.803344	+	0.595516i	$0.796948\pi$
$500$	−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	−0.988644	−	0.150275i	$-0.951984\pi$
$503$	−0.184478	+	1.04623i	−0.00822547	+	0.0466490i	0.980419	+	0.196924i	$0.0630952\pi$
$504$	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	0.365041	−	0.930992i	$-0.381055\pi$
$509$	−7.78865	−	5.12267i	−0.345226	−	0.227059i	−0.710266	+	0.703933i	$0.751425\pi$
$510$	−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	0.613597	−	0.789619i	$-0.289722\pi$
$521$	13.1493	+	4.78597i	0.576083	+	0.209677i	−0.0375146	+	0.999296i	$0.511944\pi$
$522$	−4.34163	+	0.539106i	−0.190028	+	0.0235960i
$523$	−38.9824	+	14.1884i	−1.70458	+	0.620416i	−0.996334	−	0.0855490i	$-0.972736\pi$
$523$	−38.9824	+	14.1884i	−1.70458	+	0.620416i	−0.708246	+	0.705965i	$0.750513\pi$
$524$	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	0.923749	−	0.382999i	$-0.125109\pi$
$541$	3.02808	+	5.24480i	0.130188	+	0.225491i	−0.793561	+	0.608490i	$0.791775\pi$
$542$	−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	−0.308655	−	0.951174i	$-0.599879\pi$
$547$	−29.3737	−	14.7520i	−1.25593	−	0.630752i	−0.947275	+	0.320423i	$0.896175\pi$
$548$	−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	0.586161	−	0.810195i	$-0.300639\pi$
$557$	−2.59467	−	2.17719i	−0.109940	−	0.0922503i	−0.696100	+	0.717944i	$0.745083\pi$
$558$	−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	−0.757504	−	0.652830i	$-0.773581\pi$
$563$	−16.2820	+	8.17712i	−0.686204	+	0.344625i	0.0713003	+	0.997455i	$0.477285\pi$
$564$	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	0.589315	−	0.807903i	$-0.299398\pi$
$569$	35.2685	−	8.35879i	1.47853	−	0.350419i	0.889218	+	0.457485i	$0.151249\pi$
$570$	3.34308	+	0.577103i	0.140026	+	0.0241722i
$571$	29.6253	−	14.8784i	1.23978	−	0.622640i	0.296624	−	0.954994i	$-0.404139\pi$
$571$	29.6253	−	14.8784i	1.23978	−	0.622640i	0.943155	+	0.332354i	$0.107843\pi$
$572$	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	0.913586	−	0.406646i	$-0.133302\pi$
$577$	16.1362	+	13.5399i	0.671760	+	0.563674i	−0.241826	+	0.970320i	$0.577746\pi$
$578$	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	0.443366	−	0.896341i	$-0.353784\pi$
$587$	−0.262882	−	0.132025i	−0.0108503	−	0.00544923i	−0.454216	+	0.890892i	$0.650081\pi$
$588$	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	0.815198	−	0.579183i	$-0.196628\pi$
$593$	−2.28876	−	3.96425i	−0.0939881	−	0.162792i	−0.909186	+	0.416391i	$0.863295\pi$
$594$	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	−0.576319	−	0.817225i	$-0.695511\pi$
$599$	10.1227	−	23.4671i	0.413603	−	0.958839i	0.989922	−	0.141614i	$-0.0452293\pi$
$600$	0.775606	−	0.737030i	0.0316640	−	0.0300891i
$601$	1.87619	+	32.2129i	0.0765313	+	1.31399i	0.789914	+	0.613217i	$0.210125\pi$
$601$	1.87619	+	32.2129i	0.0765313	+	1.31399i	−0.713383	+	0.700774i	$0.752838\pi$
$602$	−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	0.163241	−	0.986586i	$-0.447805\pi$
$607$	−3.29304	−	0.780465i	−0.133660	−	0.0316781i	−0.296902	+	0.954908i	$0.595953\pi$
$608$	−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	0.942938	−	0.332970i	$-0.108051\pi$
$613$	35.9310	+	13.0778i	1.45124	+	0.528208i	0.508303	+	0.861178i	$0.330273\pi$
$614$	−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	0.867905	+	0.496730i	$0.165466\pi$
$617$	−1.28664	+	22.0908i	−0.0517984	+	0.889344i	−0.919703	+	0.392614i	$0.871571\pi$
$618$	−7.06792	−	8.36204i	−0.284314	−	0.336371i
$619$	−13.2276	−	14.0205i	−0.531664	−	0.563530i	0.404751	−	0.914427i	$-0.367358\pi$
$619$	−13.2276	−	14.0205i	−0.531664	−	0.563530i	−0.936414	+	0.350897i	$0.885877\pi$
$620$	−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	−0.996233	−	0.0867207i	$-0.972361\pi$
$631$	−0.764140	+	4.33366i	−0.0304200	+	0.172520i	0.965813	+	0.259241i	$0.0834723\pi$
$632$	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	−0.470470	+	0.882416i	$0.655915\pi$
$641$	−37.1430	+	24.4294i	−1.46706	+	0.964902i	−0.996592	+	0.0824856i	$0.973714\pi$
$642$	−5.57172	+	11.1943i	−0.219898	+	0.441803i
$643$	11.3318	+	15.2213i	0.446883	+	0.600268i	0.967297	−	0.253646i	$-0.0816297\pi$
$643$	11.3318	+	15.2213i	0.446883	+	0.600268i	−0.520414	+	0.853914i	$0.674222\pi$
$644$	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	0.999965	−	0.00840991i	$-0.00267699\pi$
$653$	18.0184	+	24.2029i	0.705115	+	0.947134i	−0.294850	+	0.955544i	$0.595270\pi$
$654$	−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	0.136248	−	0.990675i	$-0.456495\pi$
$659$	1.03605	+	0.121097i	0.0403589	+	0.00471728i	−0.0958895	+	0.995392i	$0.530570\pi$
$660$	3.44815	−	14.7854i	0.134219	−	0.575519i
$661$	7.06217	+	23.5893i	0.274687	+	0.917517i	0.978345	+	0.206979i	$0.0663633\pi$
$661$	7.06217	+	23.5893i	0.274687	+	0.917517i	−0.703659	+	0.710538i	$0.748452\pi$
$662$	−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	−0.825802	−	0.563960i	$-0.809277\pi$
$673$	4.51516	−	15.0817i	0.174047	−	0.581356i	0.999849	−	0.0173963i	$-0.00553769\pi$
$674$	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	0.593148	−	0.805093i	$-0.297885\pi$
$677$	−6.37657	−	6.75877i	−0.245071	−	0.259760i	−0.838220	+	0.545333i	$0.816403\pi$
$678$	−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	−0.407337	−	0.913278i	$-0.633543\pi$
$683$	−34.1423	−	12.4268i	−1.30642	−	0.475498i	−0.899082	+	0.437780i	$0.855765\pi$
$684$	−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	0.896413	+	0.443220i	$0.146164\pi$
$691$	15.8679	+	36.7859i	0.603644	+	1.39940i	−0.292769	+	0.956183i	$0.594577\pi$
$692$	−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	−0.316744	−	0.948511i	$-0.602590\pi$
$701$	17.5555	−	30.4070i	0.663063	−	1.14846i	0.979807	−	0.199947i	$-0.0640771\pi$
$702$	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	−0.239551	−	0.970884i	$-0.577000\pi$
$709$	−30.9238	−	15.5305i	−1.16137	−	0.583261i	−0.921818	+	0.387623i	$0.873296\pi$
$710$	−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	0.855178	−	0.518334i	$-0.173447\pi$
$719$	13.2253	+	11.0973i	0.493220	+	0.413860i	−0.361959	+	0.932194i	$0.617892\pi$
$720$	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	−0.198136	−	0.980175i	$-0.563489\pi$
$727$	1.74465	−	0.413490i	0.0647055	−	0.0153355i	0.262841	+	0.964839i	$0.415340\pi$
$728$	−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	−0.0223008	−	0.999751i	$-0.507099\pi$
$733$	20.7469	−	10.4195i	0.766306	−	0.384853i	0.788607	+	0.614898i	$0.210803\pi$
$734$	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	0.417497	−	0.908678i	$-0.362907\pi$
$739$	−11.0065	−	9.23551i	−0.404879	−	0.339734i	−0.822376	+	0.568945i	$0.807352\pi$
$740$	−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	−0.154999	−	0.987915i	$-0.549537\pi$
$743$	22.9038	−	24.2766i	0.840257	−	0.890621i	0.995256	+	0.0972942i	$0.0310188\pi$
$744$	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	0.402786	−	0.915294i	$-0.368042\pi$
$751$	27.5632	−	3.22168i	1.00580	−	0.117561i	0.603010	+	0.797734i	$0.293968\pi$
$752$	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	−0.628959	−	0.777438i	$-0.716519\pi$
$757$	9.87193	−	17.0987i	0.358802	−	0.621462i	0.987761	+	0.155976i	$0.0498522\pi$
$758$	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	0.592989	+	0.805210i	$0.297948\pi$
$761$	−11.0244	+	25.5574i	−0.399633	+	0.926454i	−0.992623	+	0.121244i	$0.961312\pi$
$762$	−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	+	0.0375022i
$769$	27.8700	+	6.60531i	1.00502	+	0.238193i	0.699992	−	0.714151i	$-0.253187\pi$
$769$	27.8700	+	6.60531i	1.00502	+	0.238193i	0.305025	+	0.952344i	$0.401335\pi$
$770$	7.40877	+	1.75591i	0.266994	+	0.0632787i
$771$	4.43282	+	1.89327i	0.159644	+	0.0681846i
$772$	0.455162	+	1.05518i	0.0163816	+	0.0379769i
$773$	−3.23884	+	1.17884i	−0.116493	+	0.0424000i	−0.399609	−	0.916686i	$-0.630854\pi$
$773$	−3.23884	+	1.17884i	−0.116493	+	0.0424000i	0.283116	+	0.959086i	$0.408632\pi$
$774$	−30.2844	−	6.94814i	−1.08855	−	0.249746i
$775$	−0.259323	−	0.0943858i	−0.00931516	−	0.00339044i
$776$	0.201861	+	3.46582i	0.00724640	+	0.124416i
$777$	9.88504	+	2.92074i	0.354624	+	0.104781i
$778$	−5.88043	+	13.6324i	−0.210824	+	0.488744i
$779$	−0.680681	+	11.6868i	−0.0243879	+	0.418725i
$780$	8.02421	−	1.44462i	0.287313	−	0.0517258i
$781$	21.4612	+	22.7475i	0.767942	+	0.813971i
$782$	3.52224	−	6.10070i	0.125955	−	0.218160i
$783$	−1.82688	−	7.35417i	−0.0652874	−	0.262816i
$784$	3.12273	+	5.40872i	0.111526	+	0.193169i
$785$	−8.80243	+	29.4022i	−0.314172	+	1.04941i
$786$	−10.8594	+	6.32178i	−0.387341	+	0.225490i
$787$	−21.5844	−	14.1963i	−0.769400	−	0.506042i	0.103091	−	0.994672i	$-0.467127\pi$
$787$	−21.5844	−	14.1963i	−0.769400	−	0.506042i	−0.872491	+	0.488630i	$0.837497\pi$
$788$	−8.04578	+	0.940417i	−0.286619	+	0.0335010i
$789$	2.60108	−	22.9688i	0.0926008	−	0.817711i
$790$	−24.2024	−	12.1549i	−0.861084	−	0.432453i
$791$	−2.57908	−	14.6267i	−0.0917015	−	0.520065i
$792$	−3.51615	+	12.0594i	−0.124941	+	0.428512i
$793$	−4.16381	+	23.6142i	−0.147861	+	0.838564i
$794$	8.97445	−	12.0548i	0.318491	−	0.427808i
$795$	22.0371	+	43.4893i	0.781576	+	1.54241i
$796$	−0.477615	+	0.506242i	−0.0169286	+	0.0179433i
$797$	−4.04684	−	13.5174i	−0.143346	−	0.478810i	0.855920	−	0.517108i	$-0.172992\pi$
$797$	−4.04684	−	13.5174i	−0.143346	−	0.478810i	−0.999266	+	0.0382981i	$0.987806\pi$
$798$	0.319721	−	1.37093i	0.0113180	−	0.0485305i
$799$	45.5245	+	5.32105i	1.61054	+	0.188245i
$800$	0.473210	+	0.397070i	0.0167305	+	0.0140386i
$801$	−5.53636	+	32.7732i	−0.195618	+	1.15799i
$802$	−0.441618	+	0.370562i	−0.0155941	+	0.0130850i
$803$	−1.36323	+	0.896609i	−0.0481072	+	0.0316406i
$804$	−22.5999	+	1.39776i	−0.797037	+	0.0492953i
$805$	−1.73266	−	2.32736i	−0.0610682	−	0.0820288i
$806$	0.897704	−	0.450844i	0.0316203	−	0.0158803i
$807$	−4.50375	+	5.40667i	−0.158539	+	0.190324i
$808$	−8.32428	+	1.97289i	−0.292847	+	0.0694060i
$809$	−3.45367			−0.121425			−0.0607123	−	0.998155i	$-0.519337\pi$
$809$	−3.45367			−0.121425			−0.0607123	+	0.998155i	$0.519337\pi$
$810$	14.2572	−	12.3165i	0.500946	−	0.432759i
$811$	−25.0153			−0.878407			−0.439204	−	0.898387i	$-0.644739\pi$
$811$	−25.0153			−0.878407			−0.439204	+	0.898387i	$0.644739\pi$
$812$	1.23262	−	0.292136i	0.0432565	−	0.0102520i
$813$	−20.9522	−	3.61690i	−0.734827	−	0.126850i
$814$	25.6349	−	12.8743i	0.898504	−	0.451245i
$815$	−17.1007	−	22.9703i	−0.599013	−	0.804614i
$816$	−3.40730	+	6.84568i	−0.119279	+	0.239647i
$817$	8.09637	−	5.32507i	0.283256	−	0.186301i
$818$	−7.34284	+	6.16137i	−0.256736	+	0.215427i
$819$	−5.85964	+	0.0420938i	−0.204752	+	0.00147088i
$820$	−20.0642	−	16.8359i	−0.700673	−	0.587935i
$821$	−4.83735	−	0.565405i	−0.168825	−	0.0197328i	0.0312606	−	0.999511i	$-0.490048\pi$
$821$	−4.83735	−	0.565405i	−0.168825	−	0.0197328i	−0.200085	+	0.979779i	$0.564122\pi$
$822$	13.5200	−	4.10059i	0.471564	−	0.143025i
$823$	−4.65639	−	15.5534i	−0.162312	−	0.542159i	0.837680	−	0.546161i	$-0.183911\pi$
$823$	−4.65639	−	15.5534i	−0.162312	−	0.542159i	−0.999992	+	0.00400211i	$0.998726\pi$
$824$	4.33799	−	4.59800i	0.151121	−	0.160179i
$825$	4.47337	+	0.244426i	0.155743	+	0.00850981i
$826$	−1.81805	+	2.44207i	−0.0632581	+	0.0849703i
$827$	−2.56963	+	14.5731i	−0.0893548	+	0.506756i	0.906977	+	0.421180i	$0.138384\pi$
$827$	−2.56963	+	14.5731i	−0.0893548	+	0.506756i	−0.996332	+	0.0855759i	$0.972727\pi$
$828$	3.98039	−	2.65910i	0.138328	−	0.0924100i
$829$	9.85633	+	55.8980i	0.342324	+	1.94142i	0.337205	+	0.941431i	$0.390518\pi$
$829$	9.85633	+	55.8980i	0.342324	+	1.94142i	0.00511907	+	0.999987i	$0.498371\pi$
$830$	3.00714	+	1.51024i	0.104379	+	0.0524214i
$831$	−0.468683	+	0.204170i	−0.0162584	+	0.00708257i
$832$	−2.23343	+	0.261051i	−0.0774302	+	0.00905030i
$833$	23.0368	+	15.1515i	0.798177	+	0.524969i
$834$	0.0726964	+	20.2396i	0.00251727	+	0.700839i
$835$	−9.54008	+	31.8661i	−0.330148	+	1.10277i
$836$	−1.95887	−	3.39286i	−0.0677489	−	0.117345i
$837$	1.25462	−	1.95308i	0.0433660	−	0.0675082i
$838$	−19.2403	+	33.3252i	−0.664646	+	1.15120i
$839$	−34.9460	−	37.0406i	−1.20647	−	1.27878i	−0.950007	−	0.312228i	$-0.898925\pi$
$839$	−34.9460	−	37.0406i	−1.20647	−	1.27878i	−0.256462	−	0.966554i	$-0.582557\pi$
$840$	2.03316	+	2.40543i	0.0701507	+	0.0829952i
$841$	1.56254	−	26.8278i	0.0538808	−	0.925097i
$842$	3.44524	−	7.98696i	0.118731	−	0.275249i
$843$	−14.3635	+	13.6492i	−0.494707	+	0.470102i
$844$	−0.117109	−	2.01069i	−0.00403107	−	0.0692109i
$845$	−15.6263	−	5.68749i	−0.537560	−	0.195656i
$846$	26.1440	+	16.9274i	0.898849	+	0.581976i
$847$	−5.33221	+	1.94077i	−0.183217	+	0.0666855i
$848$	−5.32578	−	12.3465i	−0.182888	−	0.423982i
$849$	−4.62794	−	38.3979i	−0.158830	−	1.31781i
$850$	2.65369	+	0.628936i	0.0910207	+	0.0215723i
$851$	−10.6369	−	2.52100i	−0.364629	−	0.0864186i
$852$	1.54797	+	12.8435i	0.0530327	+	0.440011i
$853$	−7.18688	−	16.6611i	−0.246074	−	0.570464i	0.749754	−	0.661717i	$-0.230172\pi$
$853$	−7.18688	−	16.6611i	−0.246074	−	0.570464i	−0.995828	+	0.0912533i	$0.970913\pi$
$854$	−8.70423	+	3.16808i	−0.297852	+	0.108409i
$855$	−0.299513	+	5.86840i	−0.0102431	+	0.200695i
$856$	−6.78394	−	2.46915i	−0.231870	−	0.0843939i
$857$	−0.701124	−	12.0378i	−0.0239499	−	0.411205i	−0.988882	−	0.148704i	$-0.952490\pi$
$857$	−0.701124	−	12.0378i	−0.0239499	−	0.411205i	0.964932	−	0.262501i	$-0.0845472\pi$
$858$	−11.8218	+	11.2338i	−0.403588	+	0.383515i
$859$	6.17056	−	14.3050i	0.210537	−	0.488079i	−0.779924	−	0.625874i	$-0.784742\pi$
$859$	6.17056	−	14.3050i	0.210537	−	0.488079i	0.990461	+	0.137795i	$0.0440016\pi$
$860$	−1.26066	+	21.6447i	−0.0429881	+	0.738077i
$861$	12.1518	+	14.3768i	0.414133	+	0.489960i
$862$	−13.1516	−	13.9399i	−0.447947	−	0.474796i
$863$	−4.43659	+	7.68440i	−0.151023	+	0.261580i	−0.931604	−	0.363475i	$-0.881590\pi$
$863$	−4.43659	+	7.68440i	−0.151023	+	0.261580i	0.780581	+	0.625055i	$0.214924\pi$
$864$	−4.13428	+	3.14766i	−0.140651	+	0.107085i
$865$	1.36262	+	2.36012i	0.0463304	+	0.0802466i
$866$	0.938352	−	3.13431i	0.0318865	−	0.106508i
$867$	0.0154969	+	4.31452i	0.000526302	+	0.146529i
$868$	0.324218	+	0.213242i	0.0110047	+	0.00723790i
$869$	53.8054	−	6.28895i	1.82522	−	0.213338i
$870$	−4.84767	+	2.11177i	−0.164351	+	0.0715956i
$871$	−26.2696	−	13.1931i	−0.890111	−	0.447030i
$872$	−3.51756	−	19.9491i	−0.119120	−	0.675561i
$873$	0.680259	+	10.3929i	0.0230233	+	0.351745i
$874$	−0.259248	+	1.47027i	−0.00876920	+	0.0497326i
$875$	6.10017	−	8.19396i	0.206224	−	0.277006i
$876$	−0.673937	−	0.0368240i	−0.0227702	−	0.00124417i
$877$	−19.8111	+	20.9985i	−0.668972	+	0.709069i	−0.969606	−	0.244670i	$-0.921320\pi$
$877$	−19.8111	+	20.9985i	−0.668972	+	0.709069i	0.300634	+	0.953740i	$0.402802\pi$
$878$	−8.74255	−	29.2022i	−0.295047	−	0.985525i
$879$	−17.3723	+	5.26899i	−0.585953	+	0.177719i
$880$	8.70612	+	1.01760i	0.293483	+	0.0343033i
$881$	2.19196	+	1.83927i	0.0738490	+	0.0619667i	0.678965	−	0.734171i	$-0.262429\pi$
$881$	2.19196	+	1.83927i	0.0738490	+	0.0619667i	−0.605116	+	0.796137i	$0.706873\pi$
$882$	9.48450	+	16.1585i	0.319360	+	0.544084i
$883$	21.7527	−	18.2527i	0.732038	−	0.614253i	−0.198649	−	0.980071i	$-0.563655\pi$
$883$	21.7527	−	18.2527i	0.732038	−	0.614253i	0.930686	+	0.365818i	$0.119211\pi$
$884$	−8.29423	+	5.45520i	−0.278965	+	0.183478i
$885$	5.66261	−	11.3769i	0.190346	−	0.382430i
$886$	13.9422	+	18.7276i	0.468396	+	0.629165i
$887$	45.5674	−	22.8848i	1.53000	−	0.768396i	0.533025	−	0.846099i	$-0.321055\pi$
$887$	45.5674	−	22.8848i	1.53000	−	0.768396i	0.996977	+	0.0777034i	$0.0247587\pi$
$888$	11.6933	+	2.01856i	0.392400	+	0.0677384i
$889$	7.61723	−	1.80532i	0.255474	−	0.0605484i
$890$	23.1930			0.777432
$891$	−10.2883	+	36.2530i	−0.344671	+	1.21452i
$892$	12.7430			0.426666
$893$	−9.45195	+	2.24015i	−0.316297	+	0.0749638i
$894$	−2.14641	+	2.57673i	−0.0717868	+	0.0861789i
$895$	−16.1869	+	8.12939i	−0.541070	+	0.271736i
$896$	−0.518718	−	0.696760i	−0.0173292	−	0.0232771i
$897$	6.20272	−	0.383626i	0.207103	−	0.0128089i
$898$	26.7781	−	17.6122i	0.893595	−	0.587727i
$899$	−0.499073	+	0.418772i	−0.0166450	+	0.0139668i
$900$	1.42815	+	1.18098i	0.0476050	+	0.0393661i
$901$	−45.4749	−	38.1579i	−1.51499	−	1.27123i
$902$	52.0349	+	6.08200i	1.73257	+	0.202509i
$903$	3.53911	−	15.1754i	0.117774	−	0.505004i
$904$	−4.90384	−	16.3800i	−0.163099	−	0.544790i
$905$	−14.6164	+	15.4925i	−0.485866	+	0.514988i
$906$	17.3441	+	34.2279i	0.576220	+	1.13715i
$907$	−24.6638	+	33.1292i	−0.818948	+	1.10004i	0.174376	+	0.984679i	$0.444209\pi$
$907$	−24.6638	+	33.1292i	−0.818948	+	1.10004i	−0.993324	+	0.115359i	$0.963198\pi$
$908$	−1.68831	+	9.57489i	−0.0560286	+	0.317754i
$909$	−24.9297	+	6.09791i	−0.826865	+	0.202255i
$910$	0.710036	+	4.02682i	0.0235375	+	0.133488i
$911$	−34.6879	−	17.4209i	−1.14926	−	0.577180i	−0.230920	−	0.972973i	$-0.574174\pi$
$911$	−34.6879	−	17.4209i	−1.14926	−	0.577180i	−0.918340	+	0.395792i	$0.870470\pi$
$912$	0.182357	−	1.61030i	0.00603844	−	0.0533224i
$913$	−6.68530	+	0.781400i	−0.221251	+	0.0258606i
$914$	19.9815	+	13.1421i	0.660931	+	0.434701i
$915$	33.4148	−	19.4524i	1.10466	−	0.643076i
$916$	−3.54975	+	11.8570i	−0.117287	+	0.391766i
$917$	−3.15087	−	5.45746i	−0.104051	−	0.180221i
$918$	−10.0741	+	20.6099i	−0.332495	+	0.680229i
$919$	0.558348	−	0.967087i	0.0184182	−	0.0319012i	−0.856669	−	0.515866i	$-0.827470\pi$
$919$	0.558348	−	0.967087i	0.0184182	−	0.0319012i	0.875088	+	0.483965i	$0.160804\pi$
$920$	−2.29223	−	2.42962i	−0.0755726	−	0.0801023i
$921$	2.08360	−	0.375116i	0.0686569	−	0.0123605i
$922$	0.550429	−	9.45050i	0.0181274	−	0.311236i
$923$	−6.65206	+	15.4212i	−0.218955	+	0.507595i
$924$	−6.04156	−	1.78511i	−0.198753	−	0.0587257i
$925$	−0.246072	−	4.22489i	−0.00809079	−	0.138914i
$926$	35.4435	+	12.9004i	1.16475	+	0.423933i
$927$	12.9145	−	13.8871i	0.424169	−	0.456113i
$928$	1.37038	−	0.498777i	0.0449849	−	0.0163731i
$929$	19.9507	+	46.2510i	0.654563	+	1.51745i	0.844446	+	0.535640i	$0.179930\pi$
$929$	19.9507	+	46.2510i	0.654563	+	1.51745i	−0.189884	+	0.981807i	$0.560811\pi$
$930$	−1.48964	−	0.636230i	−0.0488471	−	0.0208628i
$931$	−5.68605	−	1.34762i	−0.186353	−	0.0441664i
$932$	−15.8675	−	3.76067i	−0.519758	−	0.123185i
$933$	0.975442	−	0.731650i	0.0319345	−	0.0239531i
$934$	−7.78376	−	18.0448i	−0.254692	−	0.590443i
$935$	36.3642	−	13.2355i	1.18924	−	0.432847i
$936$	−6.69449	+	0.831263i	−0.218816	+	0.0271707i
$937$	50.7128	+	18.4579i	1.65671	+	0.602995i	0.989841	−	0.142177i	$-0.0454103\pi$
$937$	50.7128	+	18.4579i	1.65671	+	0.602995i	0.666873	+	0.745172i	$0.267633\pi$
$938$	−0.660280	−	11.3366i	−0.0215589	−	0.370152i
$939$	−9.98096	−	41.4490i	−0.325716	−	1.35264i
$940$	8.60809	−	19.9558i	0.280765	−	0.650886i
$941$	−1.47319	+	25.2937i	−0.0480247	+	0.824552i	0.885189	+	0.465231i	$0.154029\pi$
$941$	−1.47319	+	25.2937i	−0.0480247	+	0.824552i	−0.933214	+	0.359321i	$0.883008\pi$
$942$	8.59946	−	23.8935i	0.280186	−	0.778493i
$943$	−13.7002	−	14.5214i	−0.446141	−	0.472882i
$944$	−1.75244	+	3.03532i	−0.0570372	+	0.0987913i
$945$	6.15117	+	7.17228i	0.200097	+	0.233314i
$946$	−21.6835	−	37.5568i	−0.704990	−	1.22108i
$947$	−2.66808	+	8.91200i	−0.0867009	+	0.289601i	−0.990333	−	0.138707i	$-0.955705\pi$
$947$	−2.66808	+	8.91200i	−0.0867009	+	0.289601i	0.903632	+	0.428309i	$0.140890\pi$
$948$	19.4464	+	11.1344i	0.631589	+	0.361630i
$949$	−0.732091	−	0.481504i	−0.0237647	−	0.0156303i
$950$	−0.574073	+	0.0670995i	−0.0186254	+	0.00217699i
$951$	−31.6728	−	23.4032i	−1.02706	−	0.758901i
$952$	−3.42703	−	1.72112i	−0.111071	−	0.0557818i
$953$	6.11150	+	34.6600i	0.197971	+	1.12275i	0.908124	+	0.418701i	$0.137514\pi$
$953$	6.11150	+	34.6600i	0.197971	+	1.12275i	−0.710153	+	0.704047i	$0.751374\pi$
$954$	−16.2430	−	36.9239i	−0.525886	−	1.19546i
$955$	−1.13245	+	6.42242i	−0.0366451	+	0.207825i
$956$	−5.20135	+	6.98663i	−0.168224	+	0.225964i
$957$	5.78004	−	8.85725i	0.186842	−	0.286314i
$958$	−17.6191	+	18.6751i	−0.569246	+	0.603366i
$959$	2.03213	+	6.78779i	0.0656209	+	0.219189i
$960$	2.64627	+	2.47872i	0.0854080	+	0.0800004i
$961$	30.5922	+	3.57571i	0.986844	+	0.115346i
$962$	11.8011	+	9.90233i	0.380484	+	0.319264i
$963$	−20.4045	−	7.26107i	−0.657526	−	0.233985i
$964$	10.3141	−	8.65458i	0.332195	−	0.278745i
$965$	2.00989	−	1.32193i	0.0647008	−	0.0425544i
$966$	1.32639	+	2.00099i	0.0426759	+	0.0643807i
$967$	14.7394	+	19.7985i	0.473987	+	0.636676i	0.973243	−	0.229779i	$-0.0738004\pi$
$967$	14.7394	+	19.7985i	0.473987	+	0.636676i	−0.499255	+	0.866455i	$0.666393\pi$
$968$	−5.83765	+	2.93178i	−0.187629	+	0.0942310i
$969$	−2.47118	−	6.71439i	−0.0793859	−	0.215697i
$970$	7.07171	−	1.67603i	0.227059	−	0.0538139i
$971$	49.4872			1.58812			0.794060	−	0.607840i	$-0.207964\pi$
$971$	49.4872			1.58812			0.794060	+	0.607840i	$0.207964\pi$
$972$	−12.3347	+	9.53182i	−0.395635	+	0.305733i
$973$	−10.1505			−0.325409
$974$	−9.94503	+	2.35701i	−0.318659	+	0.0755236i
$975$	0.830985	+	2.25785i	0.0266128	+	0.0723089i
$976$	−9.52931	+	4.78580i	−0.305026	+	0.153190i
$977$	−19.7270	−	26.4980i	−0.631123	−	0.847746i	0.365418	−	0.930844i	$-0.380926\pi$
$977$	−19.7270	−	26.4980i	−0.631123	−	0.847746i	−0.996541	+	0.0830977i	$0.973519\pi$
$978$	13.0910	+	19.7491i	0.418605	+	0.631505i
$979$	−38.7588	+	25.4921i	−1.23874	+	0.814730i
$980$	10.0154	−	8.40391i	0.319930	−	0.268453i
$981$	−10.9823	−	59.7699i	−0.350638	−	1.90830i
$982$	14.0109	+	11.7565i	0.447104	+	0.375165i
$983$	32.2468	+	3.76911i	1.02851	+	0.120216i	0.613577	−	0.789635i	$-0.289730\pi$
$983$	32.2468	+	3.76911i	1.02851	+	0.120216i	0.414936	+	0.909851i	$0.363804\pi$
$984$	15.8163	+	14.8149i	0.504204	+	0.472280i
$985$	4.86349	+	16.2452i	0.154964	+	0.517615i
$986$	4.41823	−	4.68305i	0.140705	−	0.149139i
$987$	−8.53633	+	13.0810i	−0.271714	+	0.416371i
$988$	1.25638	−	1.68762i	0.0399709	−	0.0536902i
$989$	−2.86971	+	16.2750i	−0.0912516	+	0.517513i
$990$	26.1396	+	2.86510i	0.830772	+	0.0910588i
$991$	−2.48861	−	14.1136i	−0.0790532	−	0.448333i	−0.998482	−	0.0550768i	$-0.982460\pi$
$991$	−2.48861	−	14.1136i	−0.0790532	−	0.448333i	0.919429	−	0.393256i	$-0.128651\pi$
$992$	0.399222	+	0.200497i	0.0126753	+	0.00636578i
$993$	−31.0870	−	22.9703i	−0.986516	−	0.728941i
$994$	−6.44392	+	0.753187i	−0.204389	+	0.0238896i
$995$	1.21728	+	0.800618i	0.0385904	+	0.0253813i
$996$	−2.41621	−	1.38345i	−0.0765604	−	0.0438363i
$997$	6.57658	−	21.9673i	0.208282	−	0.695712i	−0.788462	−	0.615084i	$-0.789122\pi$
$997$	6.57658	−	21.9673i	0.208282	−	0.695712i	0.996744	−	0.0806279i	$-0.0256926\pi$
$998$	−7.59717	−	13.1587i	−0.240484	−	0.416531i
$999$	35.1224	+	5.80352i	1.11122	+	0.183615i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	162.2.g.a.157.2	yes	72
3.2	odd	2		486.2.g.a.361.3		72
81.16	even	27	inner	162.2.g.a.97.2	✓	72
81.65	odd	54		486.2.g.a.451.3		72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
162.2.g.a.97.2	✓	72	81.16	even	27	inner
162.2.g.a.157.2	yes	72	1.1	even	1	trivial
486.2.g.a.361.3		72	3.2	odd	2
486.2.g.a.451.3		72	81.65	odd	54

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

Introduction

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