LMFDB - Embedded newform 162.2.g.b.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:	$90$
Relative dimension:	$5$ 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.b.157.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.973045 + 0.230616i) q^{2} +(-1.60214 - 0.658149i) q^{3} +(0.893633 + 0.448799i) q^{4} +(2.07319 - 2.78478i) q^{5} +(-1.40717 - 1.00989i) q^{6} +(-1.72864 - 1.13695i) q^{7} +(0.766044 + 0.642788i) q^{8} +(2.13368 + 2.10889i) q^{9} +O(q^{10})$	\(q+(0.973045 + 0.230616i) q^{2} +(-1.60214 - 0.658149i) q^{3} +(0.893633 + 0.448799i) q^{4} +(2.07319 - 2.78478i) q^{5} +(-1.40717 - 1.00989i) q^{6} +(-1.72864 - 1.13695i) q^{7} +(0.766044 + 0.642788i) q^{8} +(2.13368 + 2.10889i) q^{9} +(2.65952 - 2.23160i) q^{10} +(1.29350 - 0.151189i) q^{11} +(-1.13634 - 1.30718i) q^{12} +(0.585568 - 1.95593i) q^{13} +(-1.41985 - 1.50495i) q^{14} +(-5.15433 + 3.09712i) q^{15} +(0.597159 + 0.802123i) q^{16} +(1.17515 + 6.66463i) q^{17} +(1.58982 + 2.54410i) q^{18} +(0.360368 - 2.04375i) q^{19} +(3.10247 - 1.55812i) q^{20} +(2.02124 + 2.95925i) q^{21} +(1.29350 + 0.151189i) q^{22} +(-4.39975 + 2.89376i) q^{23} +(-0.804257 - 1.53400i) q^{24} +(-2.02285 - 6.75679i) q^{25} +(1.02085 - 1.76817i) q^{26} +(-2.03048 - 4.78301i) q^{27} +(-1.03451 - 1.79183i) q^{28} +(-5.65986 + 5.99910i) q^{29} +(-5.72964 + 1.82497i) q^{30} +(0.391315 + 6.71861i) q^{31} +(0.396080 + 0.918216i) q^{32} +(-2.17187 - 0.609092i) q^{33} +(-0.393492 + 6.75599i) q^{34} +(-6.74995 + 2.45678i) q^{35} +(0.960258 + 2.84217i) q^{36} +(-5.04246 - 1.83530i) q^{37} +(0.821975 - 1.90555i) q^{38} +(-2.22545 + 2.74828i) q^{39} +(3.37817 - 0.800642i) q^{40} +(11.5101 - 2.72795i) q^{41} +(1.28431 + 3.34561i) q^{42} +(0.530760 - 1.23044i) q^{43} +(1.22377 + 0.445415i) q^{44} +(10.2963 - 1.56969i) q^{45} +(-4.94851 + 1.80111i) q^{46} +(-0.169635 + 2.91252i) q^{47} +(-0.428812 - 1.67813i) q^{48} +(-1.07700 - 2.49676i) q^{49} +(-0.410101 - 7.04116i) q^{50} +(2.50356 - 11.4511i) q^{51} +(1.40110 - 1.48508i) q^{52} +(1.23166 + 2.13330i) q^{53} +(-0.872711 - 5.12234i) q^{54} +(2.26064 - 3.91555i) q^{55} +(-0.593403 - 1.98210i) q^{56} +(-1.92245 + 3.03719i) q^{57} +(-6.89078 + 4.53214i) q^{58} +(14.3938 + 1.68240i) q^{59} +(-5.99606 + 0.454431i) q^{60} +(3.25606 - 1.63525i) q^{61} +(-1.16865 + 6.62775i) q^{62} +(-1.29068 - 6.07140i) q^{63} +(0.173648 + 0.984808i) q^{64} +(-4.23284 - 5.68569i) q^{65} +(-1.97286 - 1.09354i) q^{66} +(6.78857 + 7.19547i) q^{67} +(-1.94092 + 6.48314i) q^{68} +(8.95353 - 1.74051i) q^{69} +(-7.13458 + 0.833912i) q^{70} +(-0.218742 + 0.183547i) q^{71} +(0.278925 + 2.98701i) q^{72} +(-12.7160 - 10.6700i) q^{73} +(-4.48329 - 2.94870i) q^{74} +(-1.20609 + 12.1566i) q^{75} +(1.23927 - 1.66463i) q^{76} +(-2.40790 - 1.20929i) q^{77} +(-2.79926 + 2.16097i) q^{78} +(-7.68164 - 1.82058i) q^{79} +3.47176 q^{80} +(0.105173 + 8.99939i) q^{81} +11.8290 q^{82} +(-9.75035 - 2.31088i) q^{83} +(0.478139 + 3.55161i) q^{84} +(20.9958 + 10.5445i) q^{85} +(0.800212 - 1.07487i) q^{86} +(13.0162 - 5.88634i) q^{87} +(1.08806 + 0.715629i) q^{88} +(-2.63775 - 2.21333i) q^{89} +(10.3808 + 0.847109i) q^{90} +(-3.23603 + 2.71535i) q^{91} +(-5.23048 + 0.611356i) q^{92} +(3.79491 - 11.0217i) q^{93} +(-0.836736 + 2.79489i) q^{94} +(-4.94427 - 5.24062i) q^{95} +(-0.0302504 - 1.73179i) q^{96} +(-0.0866270 - 0.116360i) q^{97} +(-0.472174 - 2.67783i) q^{98} +(3.07876 + 2.40526i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 90 q - 9 q^{6}+O(q^{10}) $ 90 * q - 9 * q^6	$ 90 q - 9 q^{6} - 18 q^{13} - 9 q^{18} - 9 q^{20} - 54 q^{21} + 27 q^{23} - 18 q^{25} - 27 q^{26} - 27 q^{27} - 18 q^{28} - 27 q^{29} + 9 q^{30} + 54 q^{31} - 63 q^{33} - 27 q^{35} - 9 q^{36} - 18 q^{38} - 9 q^{41} - 9 q^{42} - 36 q^{43} + 63 q^{45} + 18 q^{46} - 27 q^{47} - 9 q^{48} - 36 q^{51} + 36 q^{52} - 27 q^{53} - 54 q^{55} - 81 q^{57} - 9 q^{58} - 45 q^{59} - 63 q^{63} + 9 q^{65} + 36 q^{66} + 81 q^{67} + 36 q^{68} + 18 q^{69} - 72 q^{70} + 72 q^{71} + 18 q^{72} - 36 q^{73} + 45 q^{74} + 216 q^{75} - 18 q^{76} + 144 q^{77} + 54 q^{78} - 99 q^{79} + 18 q^{80} + 144 q^{81} + 72 q^{82} + 45 q^{83} + 18 q^{84} - 117 q^{85} + 72 q^{86} + 81 q^{87} - 18 q^{88} + 45 q^{89} + 162 q^{90} - 63 q^{91} + 36 q^{92} + 45 q^{93} - 72 q^{94} + 45 q^{95} + 18 q^{96} + 117 q^{97} + 36 q^{98} - 81 q^{99}+O(q^{100}) $ 90 * q - 9 * q^6 - 18 * q^13 - 9 * q^18 - 9 * q^20 - 54 * q^21 + 27 * q^23 - 18 * q^25 - 27 * q^26 - 27 * q^27 - 18 * q^28 - 27 * q^29 + 9 * q^30 + 54 * q^31 - 63 * q^33 - 27 * q^35 - 9 * q^36 - 18 * q^38 - 9 * q^41 - 9 * q^42 - 36 * q^43 + 63 * q^45 + 18 * q^46 - 27 * q^47 - 9 * q^48 - 36 * q^51 + 36 * q^52 - 27 * q^53 - 54 * q^55 - 81 * q^57 - 9 * q^58 - 45 * q^59 - 63 * q^63 + 9 * q^65 + 36 * q^66 + 81 * q^67 + 36 * q^68 + 18 * q^69 - 72 * q^70 + 72 * q^71 + 18 * q^72 - 36 * q^73 + 45 * q^74 + 216 * q^75 - 18 * q^76 + 144 * q^77 + 54 * q^78 - 99 * q^79 + 18 * q^80 + 144 * q^81 + 72 * q^82 + 45 * q^83 + 18 * q^84 - 117 * q^85 + 72 * q^86 + 81 * q^87 - 18 * q^88 + 45 * q^89 + 162 * q^90 - 63 * q^91 + 36 * q^92 + 45 * q^93 - 72 * q^94 + 45 * q^95 + 18 * q^96 + 117 * q^97 + 36 * q^98 - 81 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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
$3$	−1.60214	−	0.658149i	−0.924994	−	0.379983i
$3$	−1.60214	−	0.658149i	−0.924994	−	0.379983i
$4$	0.893633	+	0.448799i	0.446816	+	0.224400i
$5$	2.07319	−	2.78478i	0.927158	−	1.24539i	−0.0420420	−	0.999116i	$-0.513386\pi$
$5$	2.07319	−	2.78478i	0.927158	−	1.24539i	0.969200	−	0.246274i	$-0.0792063\pi$
$6$	−1.40717	−	1.00989i	−0.574475	−	0.412285i
$7$	−1.72864	−	1.13695i	−0.653366	−	0.429726i	0.179078	−	0.983835i	$-0.442689\pi$
$7$	−1.72864	−	1.13695i	−0.653366	−	0.429726i	−0.832444	+	0.554109i	$0.813059\pi$
$8$	0.766044	+	0.642788i	0.270838	+	0.227260i
$9$	2.13368	+	2.10889i	0.711226	+	0.702963i
$10$	2.65952	−	2.23160i	0.841014	−	0.705694i
$11$	1.29350	−	0.151189i	0.390005	−	0.0455851i	0.0811691	−	0.996700i	$-0.474135\pi$
$11$	1.29350	−	0.151189i	0.390005	−	0.0455851i	0.308836	+	0.951115i	$0.400061\pi$
$12$	−1.13634	−	1.30718i	−0.328034	−	0.377351i
$13$	0.585568	−	1.95593i	0.162407	−	0.542478i	−0.837585	−	0.546306i	$-0.816033\pi$
$13$	0.585568	−	1.95593i	0.162407	−	0.542478i	0.999993	+	0.00382838i	$0.00121861\pi$
$14$	−1.41985	−	1.50495i	−0.379471	−	0.402216i
$15$	−5.15433	+	3.09712i	−1.33084	+	0.799673i
$16$	0.597159	+	0.802123i	0.149290	+	0.200531i
$17$	1.17515	+	6.66463i	0.285017	+	1.61641i	0.705226	+	0.708983i	$0.250846\pi$
$17$	1.17515	+	6.66463i	0.285017	+	1.61641i	−0.420209	+	0.907427i	$0.638043\pi$
$18$	1.58982	+	2.54410i	0.374725	+	0.599651i
$19$	0.360368	−	2.04375i	0.0826741	−	0.468868i	−0.915160	−	0.403090i	$-0.867936\pi$
$19$	0.360368	−	2.04375i	0.0826741	−	0.468868i	0.997834	−	0.0657777i	$-0.0209528\pi$
$20$	3.10247	−	1.55812i	0.693734	−	0.348407i
$21$	2.02124	+	2.95925i	0.441071	+	0.645761i
$22$	1.29350	+	0.151189i	0.275775	+	0.0322335i
$23$	−4.39975	+	2.89376i	−0.917412	+	0.603391i	−0.917988	−	0.396608i	$-0.870187\pi$
$23$	−4.39975	+	2.89376i	−0.917412	+	0.603391i	0.000575831		1.00000i	$0.499817\pi$
$24$	−0.804257	−	1.53400i	−0.164168	−	0.313127i
$25$	−2.02285	−	6.75679i	−0.404570	−	1.35136i
$26$	1.02085	−	1.76817i	0.200206	−	0.346766i
$27$	−2.03048	−	4.78301i	−0.390766	−	0.920490i
$28$	−1.03451	−	1.79183i	−0.195504	−	0.338624i
$29$	−5.65986	+	5.99910i	−1.05101	+	1.11400i	−0.0577215	+	0.998333i	$0.518384\pi$
$29$	−5.65986	+	5.99910i	−1.05101	+	1.11400i	−0.993288	+	0.115672i	$0.963098\pi$
$30$	−5.72964	+	1.82497i	−1.04608	+	0.333192i
$31$	0.391315	+	6.71861i	0.0702822	+	1.20670i	0.830496	+	0.557025i	$0.188057\pi$
$31$	0.391315	+	6.71861i	0.0702822	+	1.20670i	−0.760214	+	0.649673i	$0.774906\pi$
$32$	0.396080	+	0.918216i	0.0700177	+	0.162319i
$33$	−2.17187	−	0.609092i	−0.378074	−	0.106029i
$34$	−0.393492	+	6.75599i	−0.0674833	+	1.15864i
$35$	−6.74995	+	2.45678i	−1.14095	+	0.415272i
$36$	0.960258	+	2.84217i	0.160043	+	0.473694i
$37$	−5.04246	−	1.83530i	−0.828975	−	0.301722i	−0.107537	−	0.994201i	$-0.534296\pi$
$37$	−5.04246	−	1.83530i	−0.828975	−	0.301722i	−0.721438	+	0.692479i	$0.756519\pi$
$38$	0.821975	−	1.90555i	0.133342	−	0.309121i
$39$	−2.22545	+	2.74828i	−0.356358	+	0.440077i
$40$	3.37817	−	0.800642i	0.534136	−	0.126593i
$41$	11.5101	−	2.72795i	1.79758	−	0.426034i	0.810431	−	0.585835i	$-0.199233\pi$
$41$	11.5101	−	2.72795i	1.79758	−	0.426034i	0.987149	+	0.159800i	$0.0510850\pi$
$42$	1.28431	+	3.34561i	0.198173	+	0.516239i
$43$	0.530760	−	1.23044i	0.0809401	−	0.187640i	−0.872940	−	0.487827i	$-0.837790\pi$
$43$	0.530760	−	1.23044i	0.0809401	−	0.187640i	0.953880	+	0.300187i	$0.0970490\pi$
$44$	1.22377	+	0.445415i	0.184490	+	0.0671488i
$45$	10.2963	−	1.56969i	1.53488	−	0.233996i
$46$	−4.94851	+	1.80111i	−0.729617	+	0.265559i
$47$	−0.169635	+	2.91252i	−0.0247438	+	0.424835i	0.963076	+	0.269231i	$0.0867694\pi$
$47$	−0.169635	+	2.91252i	−0.0247438	+	0.424835i	−0.987820	+	0.155604i	$0.950268\pi$
$48$	−0.428812	−	1.67813i	−0.0618937	−	0.242217i
$49$	−1.07700	−	2.49676i	−0.153857	−	0.356680i
$50$	−0.410101	−	7.04116i	−0.0579970	−	0.995770i
$51$	2.50356	−	11.4511i	0.350569	−	1.60347i
$52$	1.40110	−	1.48508i	0.194298	−	0.205944i
$53$	1.23166	+	2.13330i	0.169182	+	0.293031i	0.938132	−	0.346277i	$-0.112554\pi$
$53$	1.23166	+	2.13330i	0.169182	+	0.293031i	−0.768951	+	0.639308i	$0.779221\pi$
$54$	−0.872711	−	5.12234i	−0.118761	−	0.697062i
$55$	2.26064	−	3.91555i	0.304825	−	0.527973i
$56$	−0.593403	−	1.98210i	−0.0792968	−	0.264870i
$57$	−1.92245	+	3.03719i	−0.254635	+	0.402285i
$58$	−6.89078	+	4.53214i	−0.904804	+	0.595099i
$59$	14.3938	+	1.68240i	1.87392	+	0.219029i	0.975482	−	0.220078i	$-0.0706313\pi$
$59$	14.3938	+	1.68240i	1.87392	+	0.219029i	0.898434	+	0.439108i	$0.144705\pi$
$60$	−5.99606	+	0.454431i	−0.774088	+	0.0586668i
$61$	3.25606	−	1.63525i	0.416896	−	0.209373i	−0.227971	−	0.973668i	$-0.573209\pi$
$61$	3.25606	−	1.63525i	0.416896	−	0.209373i	0.644867	+	0.764295i	$0.276913\pi$
$62$	−1.16865	+	6.62775i	−0.148419	+	0.841726i
$63$	−1.29068	−	6.07140i	−0.162610	−	0.764925i
$64$	0.173648	+	0.984808i	0.0217060	+	0.123101i
$65$	−4.23284	−	5.68569i	−0.525019	−	0.705223i
$66$	−1.97286	−	1.09354i	−0.242842	−	0.134606i
$67$	6.78857	+	7.19547i	0.829356	+	0.879066i	0.994232	−	0.107248i	$-0.0342039\pi$
$67$	6.78857	+	7.19547i	0.829356	+	0.879066i	−0.164876	+	0.986314i	$0.552722\pi$
$68$	−1.94092	+	6.48314i	−0.235372	+	0.786196i
$69$	8.95353	−	1.74051i	1.07788	−	0.209533i
$70$	−7.13458	+	0.833912i	−0.852745	+	0.0996716i
$71$	−0.218742	+	0.183547i	−0.0259599	+	0.0217830i	−0.655675	−	0.755043i	$-0.727616\pi$
$71$	−0.218742	+	0.183547i	−0.0259599	+	0.0217830i	0.629715	+	0.776826i	$0.283172\pi$
$72$	0.278925	+	2.98701i	0.0328717	+	0.352022i
$73$	−12.7160	−	10.6700i	−1.48830	−	1.24883i	−0.896729	−	0.442580i	$-0.854063\pi$
$73$	−12.7160	−	10.6700i	−1.48830	−	1.24883i	−0.591571	−	0.806253i	$-0.701492\pi$
$74$	−4.48329	−	2.94870i	−0.521171	−	0.342780i
$75$	−1.20609	+	12.1566i	−0.139268	+	1.40373i
$76$	1.23927	−	1.66463i	0.142154	−	0.190946i
$77$	−2.40790	−	1.20929i	−0.274405	−	0.137811i
$78$	−2.79926	+	2.16097i	−0.316954	+	0.244682i
$79$	−7.68164	−	1.82058i	−0.864252	−	0.204832i	−0.225499	−	0.974243i	$-0.572401\pi$
$79$	−7.68164	−	1.82058i	−0.864252	−	0.204832i	−0.638753	+	0.769412i	$0.720549\pi$
$80$	3.47176			0.388154
$81$	0.105173	+	8.99939i	0.0116859	+	0.999932i
$82$	11.8290			1.30629
$83$	−9.75035	−	2.31088i	−1.07024	−	0.253652i	−0.342509	−	0.939514i	$-0.611277\pi$
$83$	−9.75035	−	2.31088i	−1.07024	−	0.253652i	−0.727731	+	0.685863i	$0.759425\pi$
$84$	0.478139	+	3.55161i	0.0521693	+	0.387513i
$85$	20.9958	+	10.5445i	2.27732	+	1.14371i
$86$	0.800212	−	1.07487i	0.0862891	−	0.115906i
$87$	13.0162	−	5.88634i	1.39548	−	0.631082i
$88$	1.08806	+	0.715629i	0.115988	+	0.0762863i
$89$	−2.63775	−	2.21333i	−0.279601	−	0.234613i	0.492193	−	0.870486i	$-0.336196\pi$
$89$	−2.63775	−	2.21333i	−0.279601	−	0.234613i	−0.771793	+	0.635873i	$0.780640\pi$
$90$	10.3808	+	0.847109i	1.09423	+	0.0892932i
$91$	−3.23603	+	2.71535i	−0.339228	+	0.284646i
$92$	−5.23048	+	0.611356i	−0.545315	+	0.0637382i
$93$	3.79491	−	11.0217i	0.393514	−	1.14289i
$94$	−0.836736	+	2.79489i	−0.0863027	+	0.288271i
$95$	−4.94427	−	5.24062i	−0.507271	−	0.537676i
$96$	−0.0302504	−	1.73179i	−0.00308742	−	0.176750i
$97$	−0.0866270	−	0.116360i	−0.00879564	−	0.0118146i	0.797704	−	0.603050i	$-0.206048\pi$
$97$	−0.0866270	−	0.116360i	−0.00879564	−	0.0118146i	−0.806499	+	0.591235i	$0.798641\pi$
$98$	−0.472174	−	2.67783i	−0.0476967	−	0.270502i
$99$	3.07876	+	2.40526i	0.309427	+	0.241738i
$100$	1.22476	−	6.94594i	0.122476	−	0.694594i
$101$	−7.89340	+	3.96422i	−0.785423	+	0.394454i	−0.795852	−	0.605491i	$-0.792977\pi$
$101$	−7.89340	+	3.96422i	−0.785423	+	0.394454i	0.0104289	+	0.999946i	$0.496680\pi$
$102$	5.07688	−	10.5650i	0.502686	−	1.04610i
$103$	−9.51929	−	1.11265i	−0.937964	−	0.109632i	−0.366645	−	0.930361i	$-0.619494\pi$
$103$	−9.51929	−	1.11265i	−0.937964	−	0.109632i	−0.571318	+	0.820729i	$0.693568\pi$
$104$	1.70582	−	1.12194i	0.167269	−	0.110015i
$105$	12.4313	+	0.506378i	1.21317	+	0.0494174i
$106$	0.706489	+	2.35984i	0.0686203	+	0.229208i
$107$	5.10948	−	8.84988i	0.493952	−	0.855550i	−0.506024	−	0.862520i	$-0.668885\pi$
$107$	5.10948	−	8.84988i	0.493952	−	0.855550i	0.999976	+	0.00696974i	$0.00221855\pi$
$108$	0.332106	−	5.18553i	0.0319569	−	0.498978i
$109$	1.31791	+	2.28269i	0.126233	+	0.218642i	0.922214	−	0.386679i	$-0.126378\pi$
$109$	1.31791	+	2.28269i	0.126233	+	0.218642i	−0.795981	+	0.605322i	$0.793045\pi$
$110$	3.10270	−	3.28867i	0.295831	−	0.313562i
$111$	6.87080	+	6.25909i	0.652147	+	0.594087i
$112$	−0.120303	−	2.06552i	−0.0113676	−	0.195174i
$113$	−2.96110	−	6.86461i	−0.278557	−	0.645768i	0.720295	−	0.693668i	$-0.244006\pi$
$113$	−2.96110	−	6.86461i	−0.278557	−	0.645768i	−0.998852	+	0.0478997i	$0.984747\pi$
$114$	−2.57105	+	2.51197i	−0.240801	+	0.235268i
$115$	−1.06304	+	18.2516i	−0.0991287	+	1.70197i
$116$	−7.75022	+	2.82085i	−0.719590	+	0.261909i
$117$	5.37426	−	2.93843i	0.496850	−	0.271658i
$118$	13.6179	+	4.95649i	1.25362	+	0.456282i
$119$	5.54591	−	12.8569i	0.508393	−	1.17859i
$120$	−5.93924	−	0.940606i	−0.542176	−	0.0858651i
$121$	−9.05321	+	2.14565i	−0.823019	+	0.195059i
$122$	3.54541	−	0.840277i	0.320986	−	0.0760751i
$123$	−20.2362	−	3.20483i	−1.82464	−	0.288970i
$124$	−2.66562	+	6.17959i	−0.239379	+	0.554944i
$125$	−6.69797	−	2.43786i	−0.599084	−	0.218049i
$126$	0.144275	−	6.20540i	0.0128530	−	0.552821i
$127$	12.6347	−	4.59865i	1.12115	−	0.408064i	0.286076	−	0.958207i	$-0.407649\pi$
$127$	12.6347	−	4.59865i	1.12115	−	0.408064i	0.835071	+	0.550143i	$0.185427\pi$
$128$	−0.0581448	+	0.998308i	−0.00513933	+	0.0882388i
$129$	−1.66016	+	1.62201i	−0.146169	+	0.142810i
$130$	−2.80753	−	6.50859i	−0.246237	−	0.570841i
$131$	−0.621679	−	10.6738i	−0.0543164	−	0.932576i	−0.909878	−	0.414875i	$-0.863825\pi$
$131$	−0.621679	−	10.6738i	−0.0543164	−	0.932576i	0.855562	−	0.517701i	$-0.173212\pi$
$132$	−1.66749	−	1.51904i	−0.145137	−	0.132215i
$133$	−2.94658	+	3.12319i	−0.255501	+	0.270815i
$134$	4.94620	+	8.56707i	0.427286	+	0.740082i
$135$	−17.5292	−	4.26164i	−1.50867	−	0.366784i
$136$	−3.38372	+	5.86078i	−0.290152	+	0.502558i
$137$	0.853366	+	2.85044i	0.0729080	+	0.243530i	0.986674	−	0.162712i	$-0.0520242\pi$
$137$	0.853366	+	2.85044i	0.0729080	+	0.243530i	−0.913766	+	0.406242i	$0.866839\pi$
$138$	9.11358	+	0.371234i	0.775799	+	0.0316016i
$139$	9.37730	−	6.16755i	0.795372	−	0.523125i	−0.0855790	−	0.996331i	$-0.527274\pi$
$139$	9.37730	−	6.16755i	0.795372	−	0.523125i	0.880951	+	0.473207i	$0.156904\pi$
$140$	−7.13458	−	0.833912i	−0.602982	−	0.0704785i
$141$	2.18865	−	4.55461i	0.184318	−	0.383567i
$142$	−0.255175	+	0.128154i	−0.0214138	+	0.0107544i
$143$	0.461718	−	2.61853i	0.0386108	−	0.218973i
$144$	−0.417444	+	2.97081i	−0.0347870	+	0.247568i
$145$	4.97219	+	28.1987i	0.412918	+	2.34177i
$146$	−9.91260	−	13.3149i	−0.820373	−	1.10195i
$147$	0.0822550	+	4.70897i	0.00678428	+	0.388389i
$148$	−3.68242	−	3.90314i	−0.302693	−	0.320836i
$149$	−5.05693	+	16.8913i	−0.414280	+	1.38379i	0.455448	+	0.890262i	$0.349479\pi$
$149$	−5.05693	+	16.8913i	−0.414280	+	1.38379i	−0.869729	+	0.493530i	$0.835706\pi$
$150$	−3.97710	+	11.5508i	−0.324728	+	0.943119i
$151$	−20.9120	+	2.44426i	−1.70179	+	0.198911i	−0.910781	−	0.412889i	$-0.864520\pi$
$151$	−20.9120	+	2.44426i	−1.70179	+	0.198911i	−0.791012	+	0.611800i	$0.790446\pi$
$152$	1.58975	−	1.33396i	0.128946	−	0.108199i
$153$	−11.5476	+	16.6985i	−0.933565	+	1.34999i
$154$	−2.06411	−	1.73199i	−0.166331	−	0.139568i
$155$	19.5211	+	12.8392i	1.56797	+	1.03127i
$156$	−3.22216	+	1.45717i	−0.257980	+	0.116667i
$157$	6.59546	−	8.85924i	0.526375	−	0.707044i	−0.456829	−	0.889554i	$-0.651015\pi$
$157$	6.59546	−	8.85924i	0.526375	−	0.707044i	0.983204	+	0.182510i	$0.0584223\pi$
$158$	−7.05473	−	3.54302i	−0.561244	−	0.281867i
$159$	−0.569259	−	4.22845i	−0.0451452	−	0.335338i
$160$	3.37817	+	0.800642i	0.267068	+	0.0632963i
$161$	10.8957			0.858699
$162$	−1.97306	+	8.78106i	−0.155018	+	0.689905i
$163$	−6.59384			−0.516470			−0.258235	−	0.966082i	$-0.583141\pi$
$163$	−6.59384			−0.516470			−0.258235	+	0.966082i	$0.583141\pi$
$164$	11.5101	+	2.72795i	0.898790	+	0.213017i
$165$	−6.19888	+	4.78540i	−0.482582	+	0.372543i
$166$	−8.95460	−	4.49717i	−0.695012	−	0.349048i
$167$	−3.65008	+	4.90291i	−0.282452	+	0.379399i	−0.920595	−	0.390519i	$-0.872295\pi$
$167$	−3.65008	+	4.90291i	−0.282452	+	0.379399i	0.638143	+	0.769918i	$0.279703\pi$
$168$	−0.353808	+	3.56615i	−0.0272969	+	0.275134i
$169$	7.37856	+	4.85296i	0.567582	+	0.373304i
$170$	17.9981	+	15.1022i	1.38039	+	1.15829i
$171$	5.07895	−	3.60073i	0.388397	−	0.275354i
$172$	1.02652	−	0.861357i	0.0782718	−	0.0656778i
$173$	−12.3744	+	1.44636i	−0.940811	+	0.109965i	−0.572653	−	0.819798i	$-0.694086\pi$
$173$	−12.3744	+	1.44636i	−0.940811	+	0.109965i	−0.368158	+	0.929763i	$0.620012\pi$
$174$	14.0228	−	2.72594i	1.06307	−	0.206653i
$175$	−4.18532	+	13.9800i	−0.316381	+	1.05679i
$176$	0.893697	+	0.947263i	0.0673649	+	0.0714027i
$177$	−21.9536	−	12.1687i	−1.65013	−	0.914657i
$178$	−2.05622	−	2.76198i	−0.154120	−	0.207019i
$179$	−2.46930	−	14.0041i	−0.184564	−	1.04672i	−0.926514	−	0.376260i	$-0.877210\pi$
$179$	−2.46930	−	14.0041i	−0.184564	−	1.04672i	0.741950	−	0.670455i	$-0.233901\pi$
$180$	9.90559	+	3.21824i	0.738319	+	0.239874i
$181$	0.334484	−	1.89695i	0.0248620	−	0.140999i	−0.969850	−	0.243702i	$-0.921638\pi$
$181$	0.334484	−	1.89695i	0.0248620	−	0.140999i	0.994712	+	0.102703i	$0.0327491\pi$
$182$	−3.77501	+	1.89588i	−0.279822	+	0.140532i
$183$	−6.29289	+	0.476927i	−0.465184	+	0.0352555i
$184$	−5.23048	−	0.611356i	−0.385596	−	0.0450697i
$185$	−15.5649	+	10.2372i	−1.14435	+	0.752652i
$186$	6.23439	−	9.84941i	0.457128	−	0.722194i
$187$	2.52768	+	8.44303i	0.184842	+	0.617416i
$188$	−1.45873	+	2.52659i	−0.106389	+	0.184271i
$189$	−1.92805	+	10.5767i	−0.140245	+	0.769339i
$190$	−3.60243	−	6.23959i	−0.261347	−	0.452667i
$191$	0.0137183	−	0.0145405i	0.000992618	−	0.00105211i	−0.726877	−	0.686768i	$-0.759029\pi$
$191$	0.0137183	−	0.0145405i	0.000992618	−	0.00105211i	0.727870	+	0.685715i	$0.240511\pi$
$192$	0.369942	−	1.69208i	0.0266983	−	0.122116i
$193$	−0.739021	−	12.6885i	−0.0531959	−	0.913338i	−0.914332	−	0.404964i	$-0.867284\pi$
$193$	−0.739021	−	12.6885i	−0.0531959	−	0.913338i	0.861137	−	0.508374i	$-0.169753\pi$
$194$	−0.0574574	−	0.133201i	−0.00412520	−	0.00956330i
$195$	3.03955	+	11.8951i	0.217667	+	0.851825i
$196$	0.158104	−	2.71454i	0.0112931	−	0.193896i
$197$	−17.1982	+	6.25962i	−1.22532	+	0.445979i	−0.871992	−	0.489521i	$-0.837172\pi$
$197$	−17.1982	+	6.25962i	−1.22532	+	0.445979i	−0.353327	+	0.935500i	$0.614950\pi$
$198$	2.44108	+	3.05044i	0.173480	+	0.216785i
$199$	−4.11318	−	1.49707i	−0.291575	−	0.106125i	0.192091	−	0.981377i	$-0.438473\pi$
$199$	−4.11318	−	1.49707i	−0.291575	−	0.106125i	−0.483667	+	0.875252i	$0.660695\pi$
$200$	2.79359	−	6.47626i	0.197536	−	0.457941i
$201$	−6.14053	−	15.9960i	−0.433119	−	1.12827i
$202$	−8.59485	+	2.03702i	−0.604731	+	0.143324i
$203$	16.6045	−	3.93535i	1.16541	−	0.276207i
$204$	7.37650	−	9.10945i	0.516458	−	0.637789i
$205$	16.2659	−	37.7087i	1.13606	−	2.63369i
$206$	−9.00610	−	3.27795i	−0.627485	−	0.228386i
$207$	−15.4903	−	3.10423i	−1.07665	−	0.215759i
$208$	1.91858	−	0.698304i	0.133029	−	0.0484187i
$209$	0.157145	−	2.69807i	0.0108699	−	0.186630i
$210$	11.9794	+	3.35958i	0.826657	+	0.231833i
$211$	0.972388	+	2.25425i	0.0669420	+	0.155189i	0.948403	−	0.317069i	$-0.102699\pi$
$211$	0.972388	+	2.25425i	0.0669420	+	0.155189i	−0.881461	+	0.472257i	$0.843439\pi$
$212$	0.143230	+	2.45916i	0.00983704	+	0.168896i
$213$	0.471256	−	0.150102i	0.0322899	−	0.0102848i
$214$	7.01267	−	7.43300i	0.479376	−	0.508109i
$215$	−2.32613	−	4.02898i	−0.158641	−	0.274774i
$216$	1.51902	−	4.96916i	0.103356	−	0.338109i
$217$	6.96226	−	12.0590i	0.472629	−	0.818618i
$218$	0.755964	+	2.52510i	0.0512003	+	0.171021i
$219$	13.3504	+	25.4639i	0.902134	+	1.72069i
$220$	3.77748	−	2.48449i	0.254678	−	0.167504i
$221$	13.7237	+	1.60407i	0.923156	+	0.107901i
$222$	5.24215	+	7.67489i	0.351830	+	0.515105i
$223$	14.5615	−	7.31304i	0.975107	−	0.489717i	0.111435	−	0.993772i	$-0.464455\pi$
$223$	14.5615	−	7.31304i	0.975107	−	0.489717i	0.863672	+	0.504054i	$0.168159\pi$
$224$	0.359282	−	2.03759i	0.0240056	−	0.136142i
$225$	9.93320	−	18.6828i	0.662214	−	1.24552i
$226$	−1.29820	−	7.36245i	−0.0863549	−	0.489743i
$227$	7.33999	+	9.85932i	0.487172	+	0.654386i	0.975943	−	0.218026i	$-0.0699618\pi$
$227$	7.33999	+	9.85932i	0.487172	+	0.654386i	−0.488770	+	0.872412i	$0.662554\pi$
$228$	−3.08105	+	1.85134i	−0.204048	+	0.122608i
$229$	−10.5563	−	11.1890i	−0.697580	−	0.739392i	0.277626	−	0.960689i	$-0.410452\pi$
$229$	−10.5563	−	11.1890i	−0.697580	−	0.739392i	−0.975206	+	0.221297i	$0.928971\pi$
$230$	−5.24350	+	17.5145i	−0.345746	+	1.15487i
$231$	3.06188	+	3.52220i	0.201457	+	0.231744i
$232$	−8.19185	+	0.957490i	−0.537821	+	0.0628623i
$233$	13.2173	−	11.0906i	0.865895	−	0.726572i	−0.0973344	−	0.995252i	$-0.531032\pi$
$233$	13.2173	−	11.0906i	0.865895	−	0.726572i	0.963230	+	0.268679i	$0.0865872\pi$
$234$	5.90704	−	1.61984i	0.386156	−	0.105892i
$235$	7.75903	+	6.51060i	0.506144	+	0.424705i
$236$	12.1077	+	7.96338i	0.788146	+	0.518372i
$237$	11.1088	+	7.97249i	0.721596	+	0.517869i
$238$	8.36142	−	11.2313i	0.541990	−	0.728019i
$239$	4.32912	+	2.17417i	0.280028	+	0.140635i	0.583270	−	0.812278i	$-0.301773\pi$
$239$	4.32912	+	2.17417i	0.280028	+	0.140635i	−0.303243	+	0.952913i	$0.598069\pi$
$240$	−5.56223	−	2.28493i	−0.359040	−	0.147492i
$241$	−9.87724	−	2.34095i	−0.636249	−	0.150794i	−0.100182	−	0.994969i	$-0.531942\pi$
$241$	−9.87724	−	2.34095i	−0.636249	−	0.150794i	−0.536067	+	0.844175i	$0.680091\pi$
$242$	−9.30400			−0.598084
$243$	5.75444	−	14.4875i	0.369147	−	0.929371i
$244$	3.64362			0.233259
$245$	−9.18573	−	2.17706i	−0.586854	−	0.139087i
$246$	−18.9516	−	7.78523i	−1.20831	−	0.496368i
$247$	−3.78641	−	1.90161i	−0.240924	−	0.120996i
$248$	−4.01888	+	5.39829i	−0.255199	+	0.342792i
$249$	14.1005	+	10.1195i	0.893582	+	0.641299i
$250$	−5.95521	−	3.91681i	−0.376641	−	0.247721i
$251$	18.7631	+	15.7441i	1.18432	+	0.993761i	0.999941	+	0.0109054i	$0.00347135\pi$
$251$	18.7631	+	15.7441i	1.18432	+	0.993761i	0.184378	+	0.982855i	$0.440973\pi$
$252$	1.57145	−	6.00486i	0.0989920	−	0.378270i
$253$	−5.25358	+	4.40828i	−0.330290	+	0.277146i
$254$	13.3546	−	1.56093i	0.837944	−	0.0979416i
$255$	−26.6983	−	30.7121i	−1.67191	−	1.92327i
$256$	−0.286803	+	0.957990i	−0.0179252	+	0.0598743i
$257$	18.6301	+	19.7467i	1.16211	+	1.23177i	0.968044	+	0.250779i	$0.0806868\pi$
$257$	18.6301	+	19.7467i	1.16211	+	1.23177i	0.194068	+	0.980988i	$0.437832\pi$
$258$	−1.98947	+	1.19543i	−0.123859	+	0.0744243i
$259$	6.62997	+	8.90559i	0.411966	+	0.553367i
$260$	−1.23087	−	6.98062i	−0.0763354	−	0.432919i
$261$	−24.7277	+	0.864139i	−1.53061	+	0.0534889i
$262$	1.85663	−	10.5295i	0.114703	−	0.650513i
$263$	11.3976	−	5.72409i	0.702807	−	0.352963i	−0.0612406	−	0.998123i	$-0.519506\pi$
$263$	11.3976	−	5.72409i	0.702807	−	0.352963i	0.764047	+	0.645160i	$0.223209\pi$
$264$	−1.27223	−	1.86264i	−0.0783004	−	0.114638i
$265$	8.49423	+	0.992833i	0.521796	+	0.0609893i
$266$	−3.58741	+	2.35948i	−0.219959	+	0.144669i
$267$	2.76933	+	5.28209i	0.169480	+	0.323259i
$268$	2.83717	+	9.47681i	0.173308	+	0.578888i
$269$	11.1399	−	19.2949i	0.679214	−	1.17643i	−0.296004	−	0.955187i	$-0.595654\pi$
$269$	11.1399	−	19.2949i	0.679214	−	1.17643i	0.975218	−	0.221246i	$-0.0710125\pi$
$270$	−16.0739	−	8.18928i	−0.978224	−	0.498383i
$271$	6.95209	+	12.0414i	0.422309	+	0.731461i	0.996165	−	0.0874955i	$-0.0278863\pi$
$271$	6.95209	+	12.0414i	0.422309	+	0.731461i	−0.573856	+	0.818956i	$0.694553\pi$
$272$	−4.64410	+	4.92246i	−0.281590	+	0.298468i
$273$	6.97167	−	2.22057i	0.421945	−	0.134395i
$274$	0.173007	+	2.97041i	0.0104517	+	0.179449i
$275$	−3.63811	−	8.43408i	−0.219386	−	0.508594i
$276$	8.78231	+	2.46296i	0.528633	+	0.148253i
$277$	−0.315400	+	5.41521i	−0.0189506	+	0.325369i	0.975488	+	0.220052i	$0.0706227\pi$
$277$	−0.315400	+	5.41521i	−0.0189506	+	0.325369i	−0.994439	+	0.105317i	$0.966414\pi$
$278$	10.5469	−	3.83875i	0.632559	−	0.230233i
$279$	−13.3339	+	15.1606i	−0.798278	+	0.907641i
$280$	−6.74995	−	2.45678i	−0.403387	−	0.146821i
$281$	−3.94606	+	9.14799i	−0.235402	+	0.545723i	−0.994438	−	0.105326i	$-0.966412\pi$
$281$	−3.94606	+	9.14799i	−0.235402	+	0.545723i	0.759036	+	0.651049i	$0.225671\pi$
$282$	3.18002	−	3.92710i	0.189368	−	0.233855i
$283$	−7.20262	+	1.70705i	−0.428151	+	0.101474i	−0.439041	−	0.898467i	$-0.644682\pi$
$283$	−7.20262	+	1.70705i	−0.428151	+	0.101474i	0.0108897	+	0.999941i	$0.496534\pi$
$284$	−0.277851	+	0.0658519i	−0.0164874	+	0.00390759i
$285$	4.47228	+	11.6503i	0.264915	+	0.690101i
$286$	1.05315	−	2.44147i	0.0622739	−	0.144367i
$287$	−22.9985	−	8.37075i	−1.35756	−	0.494110i
$288$	−1.09131	+	2.79447i	−0.0643060	+	0.164666i
$289$	−27.0615	+	9.84959i	−1.59186	+	0.579388i
$290$	−1.66490	+	28.5853i	−0.0977664	+	1.67858i
$291$	0.0622058	+	0.243438i	0.00364657	+	0.0142706i
$292$	−6.57477	−	15.2420i	−0.384759	−	0.891973i
$293$	0.0145683	+	0.250129i	0.000851092	+	0.0146127i	0.998707	−	0.0508369i	$-0.0161889\pi$
$293$	0.0145683	+	0.250129i	0.000851092	+	0.0146127i	−0.997856	+	0.0654496i	$0.979152\pi$
$294$	−1.00593	+	4.60101i	−0.0586667	+	0.268336i
$295$	34.5262	−	36.5957i	2.01019	−	2.13068i
$296$	−2.68303	−	4.64715i	−0.155948	−	0.270110i
$297$	−3.34956	−	5.87984i	−0.194361	−	0.341183i
$298$	−8.81604	+	15.2698i	−0.510699	+	0.884557i
$299$	3.08365	+	10.3001i	0.178332	+	0.595671i
$300$	−6.53369	+	10.3223i	−0.377223	+	0.595956i
$301$	−2.31644	+	1.52355i	−0.133517	+	0.0878158i
$302$	−20.9120	−	2.44426i	−1.20335	−	0.140651i
$303$	15.2554	−	1.15618i	0.876397	−	0.0664206i
$304$	1.85453	−	0.931382i	0.106365	−	0.0534184i
$305$	2.19661	−	12.4576i	0.125777	−	0.713320i
$306$	−15.0872	+	13.5853i	−0.862479	+	0.776619i
$307$	−0.710614	−	4.03009i	−0.0405569	−	0.230010i	0.957791	−	0.287465i	$-0.0928125\pi$
$307$	−0.710614	−	4.03009i	−0.0405569	−	0.230010i	−0.998348	+	0.0574552i	$0.981701\pi$
$308$	−1.60905	−	2.16132i	−0.0916839	−	0.123153i
$309$	14.5189	+	8.04772i	0.825952	+	0.457819i
$310$	16.0340	+	16.9950i	0.910668	+	0.965252i
$311$	7.01563	−	23.4338i	0.397820	−	1.32881i	−0.491242	−	0.871023i	$-0.663457\pi$
$311$	7.01563	−	23.4338i	0.397820	−	1.32881i	0.889062	−	0.457788i	$-0.151358\pi$
$312$	−3.47136	+	0.674809i	−0.196527	+	0.0382035i
$313$	−17.8803	+	2.08991i	−1.01066	+	0.118129i	−0.605273	−	0.796018i	$-0.706936\pi$
$313$	−17.8803	+	2.08991i	−1.01066	+	0.118129i	−0.405383	+	0.914147i	$0.632862\pi$
$314$	8.46076	−	7.09942i	0.477468	−	0.400643i
$315$	−19.5833	−	8.99291i	−1.10339	−	0.506693i
$316$	−6.04749	−	5.07445i	−0.340198	−	0.285460i
$317$	−6.86494	−	4.51514i	−0.385573	−	0.253596i	0.341893	−	0.939739i	$-0.388932\pi$
$317$	−6.86494	−	4.51514i	−0.385573	−	0.253596i	−0.727466	+	0.686143i	$0.759302\pi$
$318$	0.421234	−	4.24576i	0.0236216	−	0.238090i
$319$	−6.41403	+	8.61554i	−0.359117	+	0.482378i
$320$	3.10247	+	1.55812i	0.173434	+	0.0871016i
$321$	−14.0106	+	10.8159i	−0.781996	+	0.603685i
$322$	10.6020	+	2.51271i	0.590825	+	0.140028i
$323$	14.0443			0.781446
$324$	−3.94493	+	8.08935i	−0.219163	+	0.449408i
$325$	−14.4003			−0.798787
$326$	−6.41611	−	1.52064i	−0.355355	−	0.0842207i
$327$	−0.609124	−	4.52457i	−0.0336846	−	0.250209i
$328$	10.5708	+	5.30884i	0.583673	+	0.293131i
$329$	3.60462	−	4.84185i	0.198729	−	0.266940i
$330$	−7.13538	+	3.22685i	−0.392790	+	0.177632i
$331$	25.1073	+	16.5133i	1.38002	+	0.907653i	0.999851	−	0.0172635i	$-0.00549542\pi$
$331$	25.1073	+	16.5133i	1.38002	+	0.907653i	0.380169	+	0.924917i	$0.375866\pi$
$332$	−7.67611	−	6.44102i	−0.421281	−	0.353497i
$333$	−6.88853	−	14.5499i	−0.377489	−	0.797331i
$334$	−4.68238	+	3.92898i	−0.256208	+	0.214984i
$335$	34.1118	−	3.98709i	1.86372	−	0.217838i
$336$	−1.16668	+	3.38843i	−0.0636477	+	0.184854i
$337$	1.91644	−	6.40135i	0.104395	−	0.348704i	−0.889793	−	0.456365i	$-0.849151\pi$
$337$	1.91644	−	6.40135i	0.104395	−	0.348704i	0.994188	+	0.107662i	$0.0343363\pi$
$338$	6.06050	+	6.42376i	0.329648	+	0.349406i
$339$	0.226153	+	12.9469i	0.0122829	+	0.703178i
$340$	14.0302	+	18.8458i	0.760894	+	1.02206i
$341$	1.52194	+	8.63137i	0.0824178	+	0.467415i
$342$	5.77243	−	2.33238i	0.312137	−	0.126121i
$343$	−3.49191	+	19.8036i	−0.188546	+	1.06930i
$344$	1.19750	−	0.601406i	0.0645647	−	0.0324256i
$345$	13.7154	−	28.5420i	0.738414	−	1.53665i
$346$	−12.3744	−	1.44636i	−0.665254	−	0.0777570i
$347$	−6.50327	+	4.27727i	−0.349114	+	0.229616i	−0.711939	−	0.702242i	$-0.752183\pi$
$347$	−6.50327	+	4.27727i	−0.349114	+	0.229616i	0.362825	+	0.931857i	$0.381812\pi$
$348$	14.2735	+	0.581417i	0.765137	+	0.0311672i
$349$	−5.83721	−	19.4976i	−0.312459	−	1.04369i	−0.959612	−	0.281326i	$-0.909226\pi$
$349$	−5.83721	−	19.4976i	−0.312459	−	1.04369i	0.647154	−	0.762360i	$-0.275959\pi$
$350$	−7.29651	+	12.6379i	−0.390015	+	0.675525i
$351$	−10.5442	+	1.17071i	−0.562809	+	0.0624878i
$352$	0.651153	+	1.12783i	0.0347066	+	0.0601136i
$353$	−4.25333	+	4.50827i	−0.226382	+	0.239951i	−0.830602	−	0.556867i	$-0.812003\pi$
$353$	−4.25333	+	4.50827i	−0.226382	+	0.239951i	0.604220	+	0.796818i	$0.293485\pi$
$354$	−18.5555	−	16.9036i	−0.986216	−	0.898414i
$355$	0.0576420	+	0.989676i	0.00305932	+	0.0525265i
$356$	−1.36384	−	3.16173i	−0.0722831	−	0.167571i
$357$	−17.3470	+	16.9484i	−0.918103	+	0.897005i
$358$	0.826828	−	14.1961i	0.0436992	−	0.750286i
$359$	−22.6211	+	8.23340i	−1.19389	+	0.434542i	−0.861089	−	0.508454i	$-0.830217\pi$
$359$	−22.6211	+	8.23340i	−1.19389	+	0.434542i	−0.332805	+	0.942996i	$0.607995\pi$
$360$	8.89641	+	5.41588i	0.468882	+	0.285442i
$361$	13.8071	+	5.02538i	0.726690	+	0.264494i
$362$	0.762936	−	1.76868i	0.0400990	−	0.0929600i
$363$	15.9166	+	2.52074i	0.835406	+	0.132305i
$364$	−4.11047	+	0.974199i	−0.215447	+	0.0510619i
$365$	−56.0764	+	13.2904i	−2.93517	+	0.695649i
$366$	−6.23325	−	0.987169i	−0.325817	−	0.0516002i
$367$	2.73441	−	6.33908i	0.142735	−	0.330897i	−0.831820	−	0.555046i	$-0.812701\pi$
$367$	2.73441	−	6.33908i	0.142735	−	0.330897i	0.974555	+	0.224148i	$0.0719600\pi$
$368$	−4.94851	−	1.80111i	−0.257959	−	0.0938893i
$369$	30.3119	+	18.4530i	1.57797	+	0.960626i
$370$	−17.5062	+	6.37173i	−0.910103	+	0.331250i
$371$	0.296345	−	5.08805i	0.0153855	−	0.264159i
$372$	8.33777	−	8.14617i	0.432293	−	0.422359i
$373$	2.88512	+	6.68847i	0.149386	+	0.346316i	0.976434	−	0.215815i	$-0.0692409\pi$
$373$	2.88512	+	6.68847i	0.149386	+	0.346316i	−0.827048	+	0.562131i	$0.809982\pi$
$374$	0.512447	+	8.79837i	0.0264980	+	0.454953i
$375$	9.12658	+	8.31405i	0.471294	+	0.429336i
$376$	−2.00208	+	2.12208i	−0.103249	+	0.109438i
$377$	8.41960	+	14.5832i	0.433631	+	0.751072i
$378$	−4.31522	+	9.84693i	−0.221951	+	0.506472i
$379$	17.9590	−	31.1059i	0.922491	−	1.59780i	0.126945	−	0.991910i	$-0.459483\pi$
$379$	17.9590	−	31.1059i	0.922491	−	1.59780i	0.795547	−	0.605892i	$-0.207184\pi$
$380$	−2.06638	−	6.90217i	−0.106003	−	0.354074i
$381$	−23.2691	−	0.947847i	−1.19211	−	0.0485597i
$382$	0.0167017	−	0.0109849i	0.000854536	−	0.000562037i
$383$	6.75668	+	0.789743i	0.345250	+	0.0403540i	0.286951	−	0.957945i	$-0.407358\pi$
$383$	6.75668	+	0.789743i	0.345250	+	0.0403540i	0.0582990	+	0.998299i	$0.481432\pi$
$384$	0.750192	−	1.56116i	0.0382831	−	0.0796675i
$385$	−8.35963	+	4.19836i	−0.426046	+	0.213968i
$386$	2.20707	−	12.5169i	0.112337	−	0.637094i
$387$	3.72733	−	1.50605i	0.189471	−	0.0765568i
$388$	−0.0251903	−	0.142861i	−0.00127885	−	0.00725269i
$389$	5.31095	+	7.13384i	0.269276	+	0.361700i	0.916108	−	0.400933i	$-0.131314\pi$
$389$	5.31095	+	7.13384i	0.269276	+	0.361700i	−0.646832	+	0.762633i	$0.723906\pi$
$390$	0.214424	+	12.2754i	0.0108578	+	0.621590i
$391$	−24.4563	−	25.9221i	−1.23681	−	1.31094i
$392$	0.779858	−	2.60491i	0.0393888	−	0.131568i
$393$	−6.02895	+	17.5101i	−0.304120	+	0.883266i
$394$	−18.1782	+	2.12472i	−0.915802	+	0.107042i
$395$	−20.9954	+	17.6172i	−1.05639	+	0.886420i
$396$	1.67180	+	3.53116i	0.0840109	+	0.177448i
$397$	6.14266	+	5.15431i	0.308292	+	0.258687i	0.783785	−	0.621032i	$-0.213286\pi$
$397$	6.14266	+	5.15431i	0.308292	+	0.258687i	−0.475494	+	0.879719i	$0.657731\pi$
$398$	−3.65706	−	2.40528i	−0.183312	−	0.120566i
$399$	6.77635	−	3.06449i	0.339242	−	0.153416i
$400$	4.21181	−	5.65745i	0.210591	−	0.282872i
$401$	−16.4209	−	8.24686i	−0.820018	−	0.411829i	−0.0112360	−	0.999937i	$-0.503577\pi$
$401$	−16.4209	−	8.24686i	−0.820018	−	0.411829i	−0.808782	+	0.588108i	$0.799873\pi$
$402$	−2.28607	−	16.9809i	−0.114019	−	0.846932i
$403$	13.3703	+	3.16882i	0.666022	+	0.157850i
$404$	−8.83294			−0.439455
$405$	25.2793	+	18.3645i	1.25614	+	0.912541i
$406$	17.0645			0.846898
$407$	−6.79990	−	1.61161i	−0.337058	−	0.0798843i
$408$	9.27845	−	7.16277i	0.459352	−	0.354610i
$409$	12.6874	+	6.37186i	0.627352	+	0.315068i	0.733919	−	0.679237i	$-0.237689\pi$
$409$	12.6874	+	6.37186i	0.627352	+	0.315068i	−0.106566	+	0.994306i	$0.533986\pi$
$410$	24.5237	−	32.9411i	1.21114	−	1.62684i
$411$	0.508807	−	5.12844i	0.0250976	−	0.252967i
$412$	−8.00740	−	5.26655i	−0.394496	−	0.259464i
$413$	−22.9690	−	19.2733i	−1.13023	−	0.948377i
$414$	−14.3569	−	6.59286i	−0.705601	−	0.324021i
$415$	−26.6496	+	22.3617i	−1.30818	+	1.09769i
$416$	2.02790	−	0.237028i	0.0994260	−	0.0116212i
$417$	−19.0829	+	3.70959i	−0.934493	+	0.181659i
$418$	0.775127	−	2.58911i	0.0379127	−	0.126637i
$419$	−19.1542	−	20.3023i	−0.935743	−	0.991830i	0.0642379	−	0.997935i	$-0.479538\pi$
$419$	−19.1542	−	20.3023i	−0.935743	−	0.991830i	−0.999981	+	0.00610446i	$0.998057\pi$
$420$	10.8817	+	6.03166i	0.530974	+	0.294315i
$421$	17.6515	+	23.7101i	0.860281	+	1.15556i	0.986533	+	0.163559i	$0.0522975\pi$
$421$	17.6515	+	23.7101i	0.860281	+	1.15556i	−0.126253	+	0.991998i	$0.540295\pi$
$422$	0.426312	+	2.41773i	0.0207525	+	0.117693i
$423$	−6.50413	+	5.85664i	−0.316242	+	0.284760i
$424$	−0.427752	+	2.42590i	−0.0207735	+	0.117812i
$425$	42.6543	−	21.4218i	2.06904	−	1.03911i
$426$	0.493169	−	0.0373764i	0.0238941	−	0.00181089i
$427$	−7.48777	−	0.875195i	−0.362359	−	0.0423536i
$428$	8.53781	−	5.61541i	0.412691	−	0.271431i
$429$	−2.46312	+	3.89136i	−0.118920	+	0.187877i
$430$	−1.33429	−	4.45682i	−0.0643450	−	0.214927i
$431$	−2.57859	+	4.46626i	−0.124207	+	0.215132i	−0.921423	−	0.388562i	$-0.872972\pi$
$431$	−2.57859	+	4.46626i	−0.124207	+	0.215132i	0.797216	+	0.603694i	$0.206305\pi$
$432$	2.62404	−	4.48491i	0.126249	−	0.215780i
$433$	1.08815	+	1.88473i	0.0522930	+	0.0905742i	0.890987	−	0.454029i	$-0.150014\pi$
$433$	1.08815	+	1.88473i	0.0522930	+	0.0905742i	−0.838694	+	0.544603i	$0.816680\pi$
$434$	9.55559	−	10.1283i	0.458683	−	0.486176i
$435$	10.5928	−	48.4506i	0.507887	−	2.32303i
$436$	0.153260	+	2.63137i	0.00733981	+	0.126020i
$437$	4.32859	+	10.0348i	0.207065	+	0.480030i
$438$	7.11812	+	27.8563i	0.340117	+	1.33103i
$439$	−1.87778	+	32.2402i	−0.0896215	+	1.53874i	0.591340	+	0.806423i	$0.298599\pi$
$439$	−1.87778	+	32.2402i	−0.0896215	+	1.53874i	−0.680961	+	0.732320i	$0.738438\pi$
$440$	4.24862	−	1.54637i	0.202545	−	0.0737204i
$441$	2.96742	−	7.59854i	0.141306	−	0.361835i
$442$	12.9838	+	4.72573i	0.617579	+	0.224780i
$443$	−2.91436	+	6.75625i	−0.138465	+	0.320999i	−0.973313	−	0.229483i	$-0.926297\pi$
$443$	−2.91436	+	6.75625i	−0.138465	+	0.320999i	0.834847	+	0.550482i	$0.185556\pi$
$444$	3.33089	+	8.67694i	0.158077	+	0.411789i
$445$	−11.6322	+	2.75688i	−0.551418	+	0.130689i
$446$	15.8555	−	3.75781i	0.750777	−	0.177938i
$447$	19.2189	−	23.7340i	0.909024	−	1.12258i
$448$	0.819499	−	1.89981i	0.0387177	−	0.0897576i
$449$	6.98792	+	2.54340i	0.329780	+	0.120030i	0.501604	−	0.865098i	$-0.332744\pi$
$449$	6.98792	+	2.54340i	0.329780	+	0.120030i	−0.171823	+	0.985128i	$0.554966\pi$
$450$	13.9740	−	15.8884i	0.658741	−	0.748988i
$451$	14.4759	−	5.26881i	0.681645	−	0.248098i
$452$	0.434692	−	7.46338i	0.0204462	−	0.351048i
$453$	35.1125	+	9.84717i	1.64973	+	0.462660i
$454$	4.86843	+	11.2863i	0.228487	+	0.529691i
$455$	0.852745	+	14.6411i	0.0399773	+	0.686383i
$456$	−3.42495	+	1.09089i	−0.160388	+	0.0510857i
$457$	−0.798851	+	0.846733i	−0.0373687	+	0.0396085i	−0.745788	−	0.666183i	$-0.767927\pi$
$457$	−0.798851	+	0.846733i	−0.0373687	+	0.0396085i	0.708420	+	0.705791i	$0.249408\pi$
$458$	−7.69139	−	13.3219i	−0.359395	−	0.622491i
$459$	29.4908	−	19.1532i	1.37651	−	0.893993i
$460$	−9.14129	+	15.8332i	−0.426215	+	0.738226i
$461$	−3.88861	−	12.9889i	−0.181110	−	0.604951i	−0.999540	−	0.0303436i	$-0.990340\pi$
$461$	−3.88861	−	12.9889i	−0.181110	−	0.604951i	0.818429	−	0.574608i	$-0.194845\pi$
$462$	2.16707	+	4.13338i	0.100821	+	0.192302i
$463$	1.96903	−	1.29505i	0.0915086	−	0.0601862i	−0.502930	−	0.864327i	$-0.667745\pi$
$463$	1.96903	−	1.29505i	0.0915086	−	0.0601862i	0.594439	+	0.804141i	$0.297374\pi$
$464$	−8.19185	−	0.957490i	−0.380297	−	0.0444503i
$465$	−22.8253	−	33.4180i	−1.05850	−	1.54972i
$466$	15.4187	−	7.74357i	0.714259	−	0.358714i
$467$	−0.906829	+	5.14288i	−0.0419630	+	0.237984i	−0.998574	−	0.0533839i	$-0.982999\pi$
$467$	−0.906829	+	5.14288i	−0.0419630	+	0.237984i	0.956611	+	0.291368i	$0.0941104\pi$
$468$	6.12138	−	0.213919i	0.282961	−	0.00988839i
$469$	−3.55416	−	20.1567i	−0.164116	−	0.930748i
$470$	6.04844	+	8.12446i	0.278994	+	0.374754i
$471$	−16.3975	+	9.85291i	−0.755558	+	0.453998i
$472$	9.94489	+	10.5410i	0.457750	+	0.485187i
$473$	0.500510	−	1.67182i	0.0230135	−	0.0768704i
$474$	8.97080	+	10.3195i	0.412042	+	0.473989i
$475$	−14.5381	+	1.69926i	−0.667056	+	0.0779676i
$476$	10.7262	−	9.00031i	0.491633	−	0.412529i
$477$	−1.87092	+	7.14922i	−0.0856637	+	0.327340i
$478$	3.71103	+	3.11393i	0.169739	+	0.142428i
$479$	−10.6399	−	6.99798i	−0.486150	−	0.319746i	0.282663	−	0.959219i	$-0.408782\pi$
$479$	−10.6399	−	6.99798i	−0.486150	−	0.319746i	−0.768813	+	0.639473i	$0.779152\pi$
$480$	−4.88535	−	3.50608i	−0.222985	−	0.160030i
$481$	−6.54243	+	8.78801i	−0.298309	+	0.400699i
$482$	−9.07114	−	4.55570i	−0.413179	−	0.207506i
$483$	−17.4563	−	7.17097i	−0.794291	−	0.326291i
$484$	−9.05321	−	2.14565i	−0.411509	−	0.0975295i
$485$	−0.503631			−0.0228687
$486$	8.94036	−	12.7699i	0.405543	−	0.579254i
$487$	20.3549			0.922370			0.461185	−	0.887304i	$-0.347424\pi$
$487$	20.3549			0.922370			0.461185	+	0.887304i	$0.347424\pi$
$488$	3.54541	+	0.840277i	0.160493	+	0.0380376i
$489$	10.5642	+	4.33973i	0.477731	+	0.196250i
$490$	−8.43606	−	4.23675i	−0.381102	−	0.191397i
$491$	2.55111	−	3.42673i	0.115130	−	0.154646i	−0.740823	−	0.671701i	$-0.765564\pi$
$491$	2.55111	−	3.42673i	0.115130	−	0.154646i	0.855952	+	0.517054i	$0.172972\pi$
$492$	−16.6454	−	11.9459i	−0.750432	−	0.538564i
$493$	−46.6330	−	30.6710i	−2.10024	−	1.38135i
$494$	−3.24581	−	2.72356i	−0.146036	−	0.122539i
$495$	13.0810	−	3.58708i	0.587945	−	0.161227i
$496$	−5.15548	+	4.32596i	−0.231488	+	0.194241i
$497$	0.586811	−	0.0685883i	0.0263221	−	0.00307661i
$498$	11.3867	+	13.0985i	0.510249	+	0.586960i
$499$	0.311253	−	1.03966i	0.0139336	−	0.0465415i	−0.950740	−	0.309989i	$-0.899675\pi$
$499$	0.311253	−	1.03966i	0.0139336	−	0.0465415i	0.964674	+	0.263448i	$0.0848597\pi$
$500$	−4.89141	−	5.18459i	−0.218751	−	0.231862i
$501$	9.07477	−	5.45283i	0.405431	−	0.243614i
$502$	14.6265	+	19.6468i	0.652813	+	0.876881i
$503$	2.39027	+	13.5559i	0.106577	+	0.604428i	0.990579	+	0.136945i	$0.0437282\pi$
$503$	2.39027	+	13.5559i	0.106577	+	0.604428i	−0.884002	+	0.467484i	$0.845161\pi$
$504$	2.91391	−	5.48059i	0.129796	−	0.244125i
$505$	−5.32506	+	30.1999i	−0.236962	+	1.34388i
$506$	−6.12859	+	3.07789i	−0.272449	+	0.136829i
$507$	−8.62749	−	12.6313i	−0.383160	−	0.560975i
$508$	13.3546	+	1.56093i	0.592516	+	0.0692552i
$509$	8.02873	−	5.28058i	0.355867	−	0.234058i	−0.358969	−	0.933350i	$-0.616872\pi$
$509$	8.02873	−	5.28058i	0.355867	−	0.234058i	0.714836	+	0.699292i	$0.246501\pi$
$510$	−18.8960	−	36.0413i	−0.836727	−	1.59594i
$511$	9.85026	+	32.9022i	0.435750	+	1.45551i
$512$	−0.500000	+	0.866025i	−0.0220971	+	0.0382733i
$513$	−10.5070	+	2.42615i	−0.463895	+	0.107117i
$514$	13.5740	+	23.5108i	0.598723	+	1.03702i
$515$	−22.8338	+	24.2024i	−1.00618	+	1.06648i
$516$	−2.21153	+	0.704404i	−0.0973574	+	0.0310097i
$517$	0.220917	+	3.79299i	0.00971591	+	0.166816i
$518$	4.39749	+	10.1945i	0.193214	+	0.447921i
$519$	20.7775	+	5.82695i	0.912029	+	0.255775i
$520$	0.412148	−	7.07631i	0.0180739	−	0.310317i
$521$	0.322424	−	0.117353i	0.0141257	−	0.00514132i	−0.334948	−	0.942237i	$-0.608719\pi$
$521$	0.322424	−	0.117353i	0.0141257	−	0.00514132i	0.349073	+	0.937095i	$0.386496\pi$
$522$	−24.2605	−	4.86177i	−1.06185	−	0.212794i
$523$	−27.8175	−	10.1248i	−1.21638	−	0.442725i	−0.347465	−	0.937693i	$-0.612958\pi$
$523$	−27.8175	−	10.1248i	−1.21638	−	0.442725i	−0.868911	+	0.494968i	$0.835180\pi$
$524$	4.23485	−	9.81748i	0.185000	−	0.428879i
$525$	15.9064	−	19.6432i	0.694210	−	0.857300i
$526$	12.4105	−	2.94133i	0.541121	−	0.128248i
$527$	−44.3172	+	10.5034i	−1.93049	+	0.457534i
$528$	−0.808383	−	2.10583i	−0.0351804	−	0.0916445i
$529$	1.87413	−	4.34472i	0.0814839	−	0.188901i
$530$	8.03631	+	2.92498i	0.349075	+	0.127053i
$531$	27.1638	+	33.9447i	1.17881	+	1.47307i
$532$	−4.03485	+	1.46856i	−0.174933	+	0.0636704i
$533$	1.40427	−	24.1104i	0.0608258	−	1.04434i
$534$	1.47654	+	5.77836i	0.0638963	+	0.250054i
$535$	−14.0520	−	32.5762i	−0.607521	−	1.40839i
$536$	0.575192	+	9.87566i	0.0248445	+	0.426564i
$537$	−5.26063	+	24.0616i	−0.227013	+	1.03834i
$538$	15.2894	−	16.2058i	0.659172	−	0.698681i
$539$	−1.77058	−	3.06673i	−0.0762641	−	0.132093i
$540$	−13.7520	−	11.6754i	−0.591793	−	0.502430i
$541$	1.46072	−	2.53004i	0.0628013	−	0.108775i	−0.832915	−	0.553401i	$-0.813330\pi$
$541$	1.46072	−	2.53004i	0.0628013	−	0.108775i	0.895717	+	0.444625i	$0.146663\pi$
$542$	3.98776	+	13.3200i	0.171289	+	0.572145i
$543$	−1.78437	+	2.81904i	−0.0765746	+	0.120976i
$544$	−5.65412	+	3.71877i	−0.242418	+	0.159441i
$545$	9.08908	+	1.06236i	0.389333	+	0.0455065i
$546$	7.29584	−	0.552939i	0.312233	−	0.0236636i
$547$	8.26501	−	4.15085i	0.353386	−	0.177477i	−0.263246	−	0.964729i	$-0.584793\pi$
$547$	8.26501	−	4.15085i	0.353386	−	0.177477i	0.616632	+	0.787252i	$0.288497\pi$
$548$	−0.516680	+	2.93024i	−0.0220715	+	0.125174i
$549$	10.3960	+	3.37756i	0.443689	+	0.144151i
$550$	−1.59501	−	9.04574i	−0.0680114	−	0.385712i
$551$	10.2210	+	13.7292i	0.435430	+	0.584884i
$552$	7.97758	+	4.42191i	0.339548	+	0.188209i
$553$	11.2089	+	11.8808i	0.476652	+	0.505222i
$554$	−1.55573	+	5.19651i	−0.0660967	+	0.220778i
$555$	31.6746	−	6.15734i	1.34451	−	0.261365i
$556$	11.1479	−	1.30300i	0.472774	−	0.0552594i
$557$	4.51453	−	3.78814i	0.191287	−	0.160509i	−0.542114	−	0.840305i	$-0.682376\pi$
$557$	4.51453	−	3.78814i	0.191287	−	0.160509i	0.733401	+	0.679796i	$0.237932\pi$
$558$	−16.4707	+	11.6769i	−0.697261	+	0.494324i
$559$	−2.09586	−	1.75864i	−0.0886455	−	0.0743824i
$560$	−6.00143	−	3.94720i	−0.253607	−	0.166800i
$561$	1.50709	−	15.1905i	0.0636295	−	0.641342i
$562$	−5.94936	+	7.99138i	−0.250959	+	0.337096i
$563$	−12.2120	−	6.13309i	−0.514673	−	0.258479i	0.172451	−	0.985018i	$-0.444831\pi$
$563$	−12.2120	−	6.13309i	−0.514673	−	0.258479i	−0.687125	+	0.726539i	$0.741127\pi$
$564$	3.99996	−	3.08788i	0.168429	−	0.130023i
$565$	−25.2553	−	5.98562i	−1.06250	−	0.251817i
$566$	−7.40215			−0.311135
$567$	10.0500	−	15.6763i	0.422061	−	0.658343i
$568$	−0.285548			−0.0119813
$569$	1.17908	+	0.279447i	0.0494295	+	0.0117150i	0.255256	−	0.966873i	$-0.417840\pi$
$569$	1.17908	+	0.279447i	0.0494295	+	0.0117150i	−0.205827	+	0.978588i	$0.565988\pi$
$570$	1.66500	+	12.3676i	0.0697391	+	0.518022i
$571$	−32.7769	−	16.4612i	−1.37167	−	0.688879i	−0.398117	−	0.917335i	$-0.630336\pi$
$571$	−32.7769	−	16.4612i	−1.37167	−	0.688879i	−0.973554	+	0.228456i	$0.926632\pi$
$572$	1.58780	−	2.13279i	0.0663893	−	0.0891763i
$573$	−0.0315483	+	0.0142672i	−0.00131795	+	0.000596021i
$574$	−20.4481	−	13.4489i	−0.853487	−	0.561347i
$575$	28.4526	+	23.8745i	1.18655	+	0.995638i
$576$	−1.70634	+	2.46747i	−0.0710975	+	0.102811i
$577$	15.9774	−	13.4066i	0.665149	−	0.558126i	−0.246476	−	0.969149i	$-0.579273\pi$
$577$	15.9774	−	13.4066i	0.665149	−	0.558126i	0.911625	+	0.411023i	$0.134828\pi$
$578$	−28.6036	+	3.34328i	−1.18975	+	0.139062i
$579$	−7.16691	+	20.8151i	−0.297847	+	0.865045i
$580$	−8.21224	+	27.4308i	−0.340995	+	1.13900i
$581$	14.2275	+	15.0803i	0.590258	+	0.625637i
$582$	0.00438828	+	0.251222i	0.000181900	+	0.0104135i
$583$	1.91569	+	2.57321i	0.0793396	+	0.106572i
$584$	−2.88249	−	16.3474i	−0.119278	−	0.676462i
$585$	2.95897	−	21.0580i	0.122338	−	0.870643i
$586$	−0.0435080	+	0.246746i	−0.00179730	+	0.0101930i
$587$	−18.4027	+	9.24219i	−0.759561	+	0.381466i	−0.786034	−	0.618183i	$-0.787869\pi$
$587$	−18.4027	+	9.24219i	−0.759561	+	0.381466i	0.0264724	+	0.999650i	$0.491573\pi$
$588$	−2.03988	+	4.24500i	−0.0841230	+	0.175061i
$589$	13.8722	+	1.62142i	0.571593	+	0.0668096i
$590$	42.0351	−	27.6469i	1.73056	−	1.13821i
$591$	31.6736	+	1.29020i	1.30288	+	0.0530716i
$592$	−1.53901	−	5.14064i	−0.0632528	−	0.211279i
$593$	13.6473	−	23.6379i	0.560428	−	0.970691i	−0.437030	−	0.899447i	$-0.643970\pi$
$593$	13.6473	−	23.6379i	0.560428	−	0.970691i	0.997459	−	0.0712439i	$-0.0226969\pi$
$594$	−1.90329	−	6.49381i	−0.0780930	−	0.266444i
$595$	−24.3058	−	42.0988i	−0.996439	−	1.72588i
$596$	−12.0999	+	12.8251i	−0.495630	+	0.525337i
$597$	5.60457	+	5.10560i	0.229380	+	0.208958i
$598$	0.625162	+	10.7336i	0.0255648	+	0.438930i
$599$	−0.106741	−	0.247454i	−0.00436132	−	0.0101107i	0.916022	−	0.401129i	$-0.131382\pi$
$599$	−0.106741	−	0.247454i	−0.00436132	−	0.0101107i	−0.920383	+	0.391018i	$0.872123\pi$
$600$	−8.73805	+	8.53725i	−0.356729	+	0.348532i
$601$	−0.343647	+	5.90018i	−0.0140176	+	0.240674i	0.984020	+	0.178058i	$0.0569813\pi$
$601$	−0.343647	+	5.90018i	−0.0140176	+	0.240674i	−0.998038	+	0.0626159i	$0.980056\pi$
$602$	−2.60536	+	0.948272i	−0.106186	+	0.0386487i
$603$	−0.689806	+	29.6692i	−0.0280911	+	1.20822i
$604$	−19.7846	−	7.20101i	−0.805025	−	0.293005i
$605$	−12.7939	+	29.6595i	−0.520144	+	1.20583i
$606$	15.1108	+	2.39312i	0.613833	+	0.0972137i
$607$	34.6957	−	8.22304i	1.40826	−	0.333763i	0.544961	−	0.838462i	$-0.316545\pi$
$607$	34.6957	−	8.22304i	1.40826	−	0.333763i	0.863296	+	0.504699i	$0.168396\pi$
$608$	2.01934	−	0.478592i	0.0818949	−	0.0194095i
$609$	−29.1928	−	4.62330i	−1.18295	−	0.187346i
$610$	5.01032	−	11.6152i	0.202862	−	0.470287i
$611$	5.59736	+	2.03727i	0.226445	+	0.0824192i
$612$	−17.8135	+	9.73974i	−0.720069	+	0.393706i
$613$	19.0997	−	6.95172i	0.771429	−	0.280777i	0.0738351	−	0.997270i	$-0.476476\pi$
$613$	19.0997	−	6.95172i	0.771429	−	0.280777i	0.697594	+	0.716493i	$0.254254\pi$
$614$	0.237944	−	4.08534i	0.00960264	−	0.164871i
$615$	−50.8782	+	49.7090i	−2.05161	+	2.00446i
$616$	−1.06724	−	2.47414i	−0.0430003	−	0.0996858i
$617$	2.40095	+	41.2228i	0.0966588	+	1.65957i	0.603377	+	0.797456i	$0.293821\pi$
$617$	2.40095	+	41.2228i	0.0966588	+	1.65957i	−0.506719	+	0.862112i	$0.669142\pi$
$618$	12.2716	+	11.1791i	0.493637	+	0.449689i
$619$	−30.0497	+	31.8508i	−1.20780	+	1.28019i	−0.258431	+	0.966030i	$0.583205\pi$
$619$	−30.0497	+	31.8508i	−1.20780	+	1.28019i	−0.949369	+	0.314163i	$0.898276\pi$
$620$	11.6825	+	20.2346i	0.469179	+	0.812641i
$621$	22.7745	+	15.1683i	0.913909	+	0.608684i
$622$	12.2307	−	21.1843i	0.490408	−	0.849411i
$623$	2.04328	+	6.82505i	0.0818625	+	0.273440i
$624$	−3.53341	−	0.143930i	−0.141449	−	0.00576183i
$625$	8.78881	−	5.78049i	0.351552	−	0.231220i
$626$	−17.8803	−	2.08991i	−0.714642	−	0.0835296i
$627$	−2.02750	+	4.21925i	−0.0809706	+	0.168501i
$628$	9.86993	−	4.95687i	0.393853	−	0.197801i
$629$	6.30596	−	35.7629i	0.251435	−	1.42596i
$630$	−16.9815	−	13.2667i	−0.676560	−	0.528559i
$631$	−0.416899	−	2.36435i	−0.0165965	−	0.0941233i	0.975384	−	0.220511i	$-0.0707726\pi$
$631$	−0.416899	−	2.36435i	−0.0165965	−	0.0941233i	−0.991981	+	0.126388i	$0.959662\pi$
$632$	−4.71423	−	6.33231i	−0.187522	−	0.251886i
$633$	−0.0742657	−	4.25159i	−0.00295179	−	0.168986i
$634$	−5.63863	−	5.97660i	−0.223939	−	0.237361i
$635$	13.3879	−	44.7186i	0.531282	−	1.77460i
$636$	1.38902	−	4.03417i	0.0550782	−	0.159965i
$637$	−5.51414	+	0.644511i	−0.218478	+	0.0255364i
$638$	−8.22802	+	6.90413i	−0.325751	+	0.273337i
$639$	−0.853806	−	0.0696738i	−0.0337760	−	0.00275625i
$640$	2.65952	+	2.23160i	0.105127	+	0.0882118i
$641$	−1.02294	−	0.672796i	−0.0404036	−	0.0265739i	0.529147	−	0.848530i	$-0.322512\pi$
$641$	−1.02294	−	0.672796i	−0.0404036	−	0.0265739i	−0.569550	+	0.821957i	$0.692883\pi$
$642$	−16.1273	+	7.29329i	−0.636493	+	0.287843i
$643$	−22.2659	+	29.9084i	−0.878083	+	1.17947i	0.104662	+	0.994508i	$0.466624\pi$
$643$	−22.2659	+	29.9084i	−0.878083	+	1.17947i	−0.982746	+	0.184963i	$0.940784\pi$
$644$	9.73672	+	4.88997i	0.383681	+	0.192692i
$645$	1.07511	+	7.98592i	0.0423325	+	0.314445i
$646$	13.6657	+	3.23884i	0.537672	+	0.127431i
$647$	−26.3510			−1.03597			−0.517983	−	0.855391i	$-0.673317\pi$
$647$	−26.3510			−1.03597			−0.517983	+	0.855391i	$0.673317\pi$
$648$	−5.70413	+	6.96153i	−0.224079	+	0.273475i
$649$	18.8728			0.740821
$650$	−14.0122	−	3.32095i	−0.549602	−	0.130258i
$651$	−19.0911	+	14.7379i	−0.748240	+	0.577625i
$652$	−5.89247	−	2.95931i	−0.230767	−	0.115896i
$653$	−17.0372	+	22.8849i	−0.666717	+	0.895556i	−0.998863	−	0.0476717i	$-0.984820\pi$
$653$	−17.0372	+	22.8849i	−0.666717	+	0.895556i	0.332146	+	0.943228i	$0.392227\pi$
$654$	0.450733	−	4.54308i	0.0176250	−	0.177649i
$655$	−31.0131	−	20.3976i	−1.21178	−	0.797000i
$656$	9.06152	+	7.60352i	0.353793	+	0.296868i
$657$	−4.63005	−	49.5831i	−0.180636	−	1.93442i
$658$	4.62407	−	3.88005i	0.180265	−	0.151260i
$659$	−27.5329	+	3.21814i	−1.07253	+	0.125361i	−0.633983	−	0.773347i	$-0.718581\pi$
$659$	−27.5329	+	3.21814i	−1.07253	+	0.125361i	−0.438547	+	0.898708i	$0.644507\pi$
$660$	−7.68721	+	1.49434i	−0.299224	+	0.0581672i
$661$	10.1414	−	33.8746i	0.394455	−	1.31757i	−0.498291	−	0.867010i	$-0.666039\pi$
$661$	10.1414	−	33.8746i	0.394455	−	1.31757i	0.892746	−	0.450561i	$-0.148776\pi$
$662$	20.6223	+	21.8583i	0.801507	+	0.849548i
$663$	−20.9315	−	11.6022i	−0.812913	−	0.450591i
$664$	−5.98380	−	8.03764i	−0.232216	−	0.311921i
$665$	2.58858	+	14.6805i	0.100381	+	0.569287i
$666$	−3.34740	−	15.7463i	−0.129709	−	0.610158i
$667$	7.54201	−	42.7728i	0.292028	−	1.65617i
$668$	−5.46225	+	2.74325i	−0.211341	+	0.106139i
$669$	−28.1425	+	2.13287i	−1.08805	+	0.0824615i
$670$	34.1118	+	3.98709i	1.31785	+	0.154035i
$671$	3.96448	−	2.60748i	0.153047	−	0.100661i
$672$	−1.91666	+	3.02804i	−0.0739367	+	0.116809i
$673$	3.13564	+	10.4738i	0.120870	+	0.403734i	0.996914	−	0.0784967i	$-0.0250120\pi$
$673$	3.13564	+	10.4738i	0.120870	+	0.403734i	−0.876044	+	0.482230i	$0.839827\pi$
$674$	3.34103	−	5.78684i	0.128692	−	0.222901i
$675$	−28.2104	+	23.3948i	−1.08582	+	0.900467i
$676$	4.41572	+	7.64825i	0.169835	+	0.294163i
$677$	21.5218	−	22.8118i	0.827152	−	0.876729i	−0.166863	−	0.985980i	$-0.553364\pi$
$677$	21.5218	−	22.8118i	0.827152	−	0.876729i	0.994014	+	0.109251i	$0.0348451\pi$
$678$	−2.76570	+	12.6501i	−0.106216	+	0.485823i
$679$	0.0174518	+	0.299636i	0.000669739	+	0.0114990i
$680$	9.30586	+	21.5734i	0.356863	+	0.827302i
$681$	−5.27076	−	20.6268i	−0.201976	−	0.790420i
$682$	−0.509611	+	8.74969i	−0.0195140	+	0.335043i
$683$	31.3970	−	11.4276i	1.20137	−	0.437264i	0.337670	−	0.941265i	$-0.390361\pi$
$683$	31.3970	−	11.4276i	1.20137	−	0.437264i	0.863703	+	0.504001i	$0.168139\pi$
$684$	6.15472	−	0.938299i	0.235331	−	0.0358768i
$685$	9.70703	+	3.53307i	0.370887	+	0.134992i
$686$	−7.96482	+	18.4645i	−0.304098	+	0.704979i
$687$	9.54859	+	24.8740i	0.364301	+	0.949001i
$688$	1.30391	−	0.309033i	0.0497112	−	0.0117818i
$689$	4.89381	−	1.15985i	0.186439	−	0.0441870i
$690$	19.9280	−	24.6096i	0.758645	−	0.936873i
$691$	4.86530	−	11.2790i	0.185085	−	0.429074i	−0.800259	−	0.599654i	$-0.795305\pi$
$691$	4.86530	−	11.2790i	0.185085	−	0.429074i	0.985344	+	0.170580i	$0.0545641\pi$
$692$	−11.7073	−	4.26112i	−0.445046	−	0.161983i
$693$	−2.58742	−	7.65822i	−0.0982879	−	0.290912i
$694$	−7.31437	+	2.66221i	−0.277650	+	0.101056i
$695$	2.26568	−	38.9002i	0.0859421	−	1.47557i
$696$	13.7546	+	3.85743i	0.521368	+	0.146215i
$697$	31.7070	+	73.5050i	1.20099	+	2.78420i
$698$	−1.18340	−	20.3182i	−0.0447925	−	0.769057i
$699$	−28.4752	+	9.06976i	−1.07703	+	0.343050i
$700$	−10.0143	+	10.6146i	−0.378506	+	0.401193i
$701$	20.4899	+	35.4896i	0.773895	+	1.34042i	0.935414	+	0.353555i	$0.115027\pi$
$701$	20.4899	+	35.4896i	0.773895	+	1.34042i	−0.161519	+	0.986870i	$0.551639\pi$
$702$	−10.5300	−	1.29251i	−0.397429	−	0.0487828i
$703$	−5.56804	+	9.64412i	−0.210003	+	0.363735i
$704$	0.373506	+	1.24760i	0.0140770	+	0.0470205i
$705$	−8.14608	−	15.5375i	−0.306799	−	0.585175i
$706$	−5.17836	+	3.40586i	−0.194890	+	0.128181i
$707$	18.1520	+	2.12166i	0.682676	+	0.0797934i
$708$	−14.1571	−	20.7271i	−0.532058	−	0.778973i
$709$	29.6797	−	14.9057i	1.11464	−	0.559795i	0.206497	−	0.978447i	$-0.433794\pi$
$709$	29.6797	−	14.9057i	1.11464	−	0.559795i	0.908147	+	0.418652i	$0.137497\pi$
$710$	−0.172147	+	0.976292i	−0.00646055	+	0.0366396i
$711$	−12.5508	−	20.0843i	−0.470690	−	0.753219i
$712$	−0.597929	−	3.39102i	−0.0224083	−	0.127084i
$713$	−21.1638	−	28.4279i	−0.792589	−	1.06463i
$714$	−20.7880	+	12.4911i	−0.777972	+	0.467466i
$715$	−6.33479	−	6.71449i	−0.236908	−	0.251108i
$716$	4.07838	−	13.6227i	0.152416	−	0.509106i
$717$	−5.50491	−	6.33252i	−0.205585	−	0.236492i
$718$	−23.9101	+	2.79469i	−0.892316	+	0.104297i
$719$	0.809269	−	0.679057i	0.0301806	−	0.0253246i	−0.627573	−	0.778558i	$-0.715951\pi$
$719$	0.809269	−	0.679057i	0.0301806	−	0.0253246i	0.657753	+	0.753234i	$0.271507\pi$
$720$	7.40761	+	7.32155i	0.276065	+	0.272858i
$721$	15.1905	+	12.7463i	0.565722	+	0.474697i
$722$	12.2760	+	8.07406i	0.456866	+	0.300485i
$723$	14.2840	+	10.2512i	0.531227	+	0.381247i
$724$	1.15026	−	1.54506i	0.0427490	−	0.0574218i
$725$	51.9837	+	26.1072i	1.93062	+	0.969596i
$726$	14.9063	+	6.12342i	0.553224	+	0.227261i
$727$	−24.5162	−	5.81044i	−0.909255	−	0.215497i	−0.250730	−	0.968057i	$-0.580671\pi$
$727$	−24.5162	−	5.81044i	−0.909255	−	0.215497i	−0.658524	+	0.752560i	$0.728819\pi$
$728$	−4.22434			−0.156564
$729$	−18.7543	+	19.4236i	−0.694604	+	0.719393i
$730$	−57.6298			−2.13298
$731$	8.82415	+	2.09136i	0.326373	+	0.0773518i
$732$	−5.83758	−	2.39805i	−0.215763	−	0.0886344i
$733$	4.18257	+	2.10056i	0.154487	+	0.0775861i	0.524363	−	0.851495i	$-0.324304\pi$
$733$	4.18257	+	2.10056i	0.154487	+	0.0775861i	−0.369876	+	0.929081i	$0.620600\pi$
$734$	4.12260	−	5.53761i	0.152168	−	0.204397i
$735$	13.2840	+	9.53352i	0.489986	+	0.351649i
$736$	−4.39975	−	2.89376i	−0.162177	−	0.106666i
$737$	9.86890	+	8.28099i	0.363525	+	0.305034i
$738$	25.2392	+	24.9460i	0.929070	+	0.918275i
$739$	26.1188	−	21.9163i	0.960795	−	0.806203i	−0.0202869	−	0.999794i	$-0.506458\pi$
$739$	26.1188	−	21.9163i	0.960795	−	0.806203i	0.981082	+	0.193591i	$0.0620135\pi$
$740$	−18.5037	+	2.16277i	−0.680210	+	0.0795052i
$741$	4.81481	+	5.53866i	0.176876	+	0.203468i
$742$	1.46174	−	4.88256i	0.0536623	−	0.179244i
$743$	18.5809	+	19.6946i	0.681668	+	0.722526i	0.972151	−	0.234354i	$-0.0752975\pi$
$743$	18.5809	+	19.6946i	0.681668	+	0.722526i	−0.290483	+	0.956880i	$0.593816\pi$
$744$	9.99166	−	6.00377i	0.366312	−	0.220109i
$745$	36.5546	+	49.1014i	1.33926	+	1.79893i
$746$	1.26489	+	7.17354i	0.0463108	+	0.262642i
$747$	−15.9307	−	25.4931i	−0.582875	−	0.932743i
$748$	−1.53041	+	8.67939i	−0.0559574	+	0.317350i
$749$	−18.8943	+	9.48908i	−0.690383	+	0.346723i
$750$	6.96322	+	10.1947i	0.254261	+	0.372257i
$751$	9.31361	+	1.08860i	0.339858	+	0.0397237i	0.284310	−	0.958732i	$-0.408235\pi$
$751$	9.31361	+	1.08860i	0.339858	+	0.0397237i	0.0555479	+	0.998456i	$0.482309\pi$
$752$	−2.43750	+	1.60317i	−0.0888865	+	0.0584616i
$753$	−19.6991	−	37.5732i	−0.717875	−	1.36924i
$754$	4.82954	+	16.1318i	0.175881	+	0.587485i
$755$	−36.5478	+	63.3026i	−1.33011	+	2.30382i
$756$	−6.46977	+	8.58635i	−0.235303	+	0.312282i
$757$	11.2315	+	19.4536i	0.408217	+	0.707053i	0.994690	−	0.102916i	$-0.0328174\pi$
$757$	11.2315	+	19.4536i	0.408217	+	0.707053i	−0.586473	+	0.809969i	$0.699484\pi$
$758$	24.6484	−	26.1258i	0.895271	−	0.948932i
$759$	11.3183	−	3.60502i	0.410827	−	0.130854i
$760$	−0.418925	−	7.19266i	−0.0151960	−	0.260905i
$761$	−14.6480	−	33.9578i	−0.530989	−	1.23097i	−0.946889	−	0.321560i	$-0.895793\pi$
$761$	−14.6480	−	33.9578i	−0.530989	−	1.23097i	0.415900	−	0.909410i	$-0.363467\pi$
$762$	−22.4233	−	6.28851i	−0.812309	−	0.227809i
$763$	0.317098	−	5.44437i	0.0114797	−	0.197099i
$764$	0.0187848	−	0.00683712i	0.000679612	−	0.000247358i
$765$	22.5612	+	66.7764i	0.815701	+	2.41431i
$766$	6.39243	+	2.32665i	0.230968	+	0.0840654i
$767$	11.7192	−	27.1682i	0.423156	−	0.980987i

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)

\(f(q)\)	\(=\)	\(q+(0.973045 + 0.230616i) q^{2} +(-1.60214 - 0.658149i) q^{3} +(0.893633 + 0.448799i) q^{4} +(2.07319 - 2.78478i) q^{5} +(-1.40717 - 1.00989i) q^{6} +(-1.72864 - 1.13695i) q^{7} +(0.766044 + 0.642788i) q^{8} +(2.13368 + 2.10889i) q^{9} +O(q^{10})\)	\(q+(0.973045 + 0.230616i) q^{2} +(-1.60214 - 0.658149i) q^{3} +(0.893633 + 0.448799i) q^{4} +(2.07319 - 2.78478i) q^{5} +(-1.40717 - 1.00989i) q^{6} +(-1.72864 - 1.13695i) q^{7} +(0.766044 + 0.642788i) q^{8} +(2.13368 + 2.10889i) q^{9} +(2.65952 - 2.23160i) q^{10} +(1.29350 - 0.151189i) q^{11} +(-1.13634 - 1.30718i) q^{12} +(0.585568 - 1.95593i) q^{13} +(-1.41985 - 1.50495i) q^{14} +(-5.15433 + 3.09712i) q^{15} +(0.597159 + 0.802123i) q^{16} +(1.17515 + 6.66463i) q^{17} +(1.58982 + 2.54410i) q^{18} +(0.360368 - 2.04375i) q^{19} +(3.10247 - 1.55812i) q^{20} +(2.02124 + 2.95925i) q^{21} +(1.29350 + 0.151189i) q^{22} +(-4.39975 + 2.89376i) q^{23} +(-0.804257 - 1.53400i) q^{24} +(-2.02285 - 6.75679i) q^{25} +(1.02085 - 1.76817i) q^{26} +(-2.03048 - 4.78301i) q^{27} +(-1.03451 - 1.79183i) q^{28} +(-5.65986 + 5.99910i) q^{29} +(-5.72964 + 1.82497i) q^{30} +(0.391315 + 6.71861i) q^{31} +(0.396080 + 0.918216i) q^{32} +(-2.17187 - 0.609092i) q^{33} +(-0.393492 + 6.75599i) q^{34} +(-6.74995 + 2.45678i) q^{35} +(0.960258 + 2.84217i) q^{36} +(-5.04246 - 1.83530i) q^{37} +(0.821975 - 1.90555i) q^{38} +(-2.22545 + 2.74828i) q^{39} +(3.37817 - 0.800642i) q^{40} +(11.5101 - 2.72795i) q^{41} +(1.28431 + 3.34561i) q^{42} +(0.530760 - 1.23044i) q^{43} +(1.22377 + 0.445415i) q^{44} +(10.2963 - 1.56969i) q^{45} +(-4.94851 + 1.80111i) q^{46} +(-0.169635 + 2.91252i) q^{47} +(-0.428812 - 1.67813i) q^{48} +(-1.07700 - 2.49676i) q^{49} +(-0.410101 - 7.04116i) q^{50} +(2.50356 - 11.4511i) q^{51} +(1.40110 - 1.48508i) q^{52} +(1.23166 + 2.13330i) q^{53} +(-0.872711 - 5.12234i) q^{54} +(2.26064 - 3.91555i) q^{55} +(-0.593403 - 1.98210i) q^{56} +(-1.92245 + 3.03719i) q^{57} +(-6.89078 + 4.53214i) q^{58} +(14.3938 + 1.68240i) q^{59} +(-5.99606 + 0.454431i) q^{60} +(3.25606 - 1.63525i) q^{61} +(-1.16865 + 6.62775i) q^{62} +(-1.29068 - 6.07140i) q^{63} +(0.173648 + 0.984808i) q^{64} +(-4.23284 - 5.68569i) q^{65} +(-1.97286 - 1.09354i) q^{66} +(6.78857 + 7.19547i) q^{67} +(-1.94092 + 6.48314i) q^{68} +(8.95353 - 1.74051i) q^{69} +(-7.13458 + 0.833912i) q^{70} +(-0.218742 + 0.183547i) q^{71} +(0.278925 + 2.98701i) q^{72} +(-12.7160 - 10.6700i) q^{73} +(-4.48329 - 2.94870i) q^{74} +(-1.20609 + 12.1566i) q^{75} +(1.23927 - 1.66463i) q^{76} +(-2.40790 - 1.20929i) q^{77} +(-2.79926 + 2.16097i) q^{78} +(-7.68164 - 1.82058i) q^{79} +3.47176 q^{80} +(0.105173 + 8.99939i) q^{81} +11.8290 q^{82} +(-9.75035 - 2.31088i) q^{83} +(0.478139 + 3.55161i) q^{84} +(20.9958 + 10.5445i) q^{85} +(0.800212 - 1.07487i) q^{86} +(13.0162 - 5.88634i) q^{87} +(1.08806 + 0.715629i) q^{88} +(-2.63775 - 2.21333i) q^{89} +(10.3808 + 0.847109i) q^{90} +(-3.23603 + 2.71535i) q^{91} +(-5.23048 + 0.611356i) q^{92} +(3.79491 - 11.0217i) q^{93} +(-0.836736 + 2.79489i) q^{94} +(-4.94427 - 5.24062i) q^{95} +(-0.0302504 - 1.73179i) q^{96} +(-0.0866270 - 0.116360i) q^{97} +(-0.472174 - 2.67783i) q^{98} +(3.07876 + 2.40526i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 90 q - 9 q^{6}+O(q^{10}) \) 90 * q - 9 * q^6	\( 90 q - 9 q^{6} - 18 q^{13} - 9 q^{18} - 9 q^{20} - 54 q^{21} + 27 q^{23} - 18 q^{25} - 27 q^{26} - 27 q^{27} - 18 q^{28} - 27 q^{29} + 9 q^{30} + 54 q^{31} - 63 q^{33} - 27 q^{35} - 9 q^{36} - 18 q^{38} - 9 q^{41} - 9 q^{42} - 36 q^{43} + 63 q^{45} + 18 q^{46} - 27 q^{47} - 9 q^{48} - 36 q^{51} + 36 q^{52} - 27 q^{53} - 54 q^{55} - 81 q^{57} - 9 q^{58} - 45 q^{59} - 63 q^{63} + 9 q^{65} + 36 q^{66} + 81 q^{67} + 36 q^{68} + 18 q^{69} - 72 q^{70} + 72 q^{71} + 18 q^{72} - 36 q^{73} + 45 q^{74} + 216 q^{75} - 18 q^{76} + 144 q^{77} + 54 q^{78} - 99 q^{79} + 18 q^{80} + 144 q^{81} + 72 q^{82} + 45 q^{83} + 18 q^{84} - 117 q^{85} + 72 q^{86} + 81 q^{87} - 18 q^{88} + 45 q^{89} + 162 q^{90} - 63 q^{91} + 36 q^{92} + 45 q^{93} - 72 q^{94} + 45 q^{95} + 18 q^{96} + 117 q^{97} + 36 q^{98} - 81 q^{99}+O(q^{100}) \) 90 * q - 9 * q^6 - 18 * q^13 - 9 * q^18 - 9 * q^20 - 54 * q^21 + 27 * q^23 - 18 * q^25 - 27 * q^26 - 27 * q^27 - 18 * q^28 - 27 * q^29 + 9 * q^30 + 54 * q^31 - 63 * q^33 - 27 * q^35 - 9 * q^36 - 18 * q^38 - 9 * q^41 - 9 * q^42 - 36 * q^43 + 63 * q^45 + 18 * q^46 - 27 * q^47 - 9 * q^48 - 36 * q^51 + 36 * q^52 - 27 * q^53 - 54 * q^55 - 81 * q^57 - 9 * q^58 - 45 * q^59 - 63 * q^63 + 9 * q^65 + 36 * q^66 + 81 * q^67 + 36 * q^68 + 18 * q^69 - 72 * q^70 + 72 * q^71 + 18 * q^72 - 36 * q^73 + 45 * q^74 + 216 * q^75 - 18 * q^76 + 144 * q^77 + 54 * q^78 - 99 * q^79 + 18 * q^80 + 144 * q^81 + 72 * q^82 + 45 * q^83 + 18 * q^84 - 117 * q^85 + 72 * q^86 + 81 * q^87 - 18 * q^88 + 45 * q^89 + 162 * q^90 - 63 * q^91 + 36 * q^92 + 45 * q^93 - 72 * q^94 + 45 * q^95 + 18 * q^96 + 117 * q^97 + 36 * q^98 - 81 * q^99

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