LMFDB - Embedded newform 162.2.g.b.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:	$90$
Relative dimension:	$5$ 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.b.97.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.973045 - 0.230616i) q^{2} +(-1.60214 + 0.658149i) q^{3} +(0.893633 - 0.448799i) q^{4} +(2.07319 + 2.78478i) q^{5} +(-1.40717 + 1.00989i) q^{6} +(-1.72864 + 1.13695i) q^{7} +(0.766044 - 0.642788i) q^{8} +(2.13368 - 2.10889i) q^{9} +O(q^{10})$	\(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 $\left(\mathbb{Z}/162\mathbb{Z}\right)^\times$.

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

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
$3$	−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	0.969200	+	0.246274i	$0.0792063\pi$
$5$	2.07319	+	2.78478i	0.927158	+	1.24539i	−0.0420420	+	0.999116i	$0.513386\pi$
$6$	−1.40717	+	1.00989i	−0.574475	+	0.412285i
$7$	−1.72864	+	1.13695i	−0.653366	+	0.429726i	−0.832444	−	0.554109i	$-0.813059\pi$
$7$	−1.72864	+	1.13695i	−0.653366	+	0.429726i	0.179078	+	0.983835i	$0.442689\pi$
$8$	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	0.308836	−	0.951115i	$-0.400061\pi$
$11$	1.29350	+	0.151189i	0.390005	+	0.0455851i	0.0811691	+	0.996700i	$0.474135\pi$
$12$	−1.13634	+	1.30718i	−0.328034	+	0.377351i
$13$	0.585568	+	1.95593i	0.162407	+	0.542478i	0.999993	−	0.00382838i	$-0.00121861\pi$
$13$	0.585568	+	1.95593i	0.162407	+	0.542478i	−0.837585	+	0.546306i	$0.816033\pi$
$14$	−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	−0.420209	−	0.907427i	$-0.638043\pi$
$17$	1.17515	−	6.66463i	0.285017	−	1.61641i	0.705226	−	0.708983i	$-0.250846\pi$
$18$	1.58982	−	2.54410i	0.374725	−	0.599651i
$19$	0.360368	+	2.04375i	0.0826741	+	0.468868i	0.997834	+	0.0657777i	$0.0209528\pi$
$19$	0.360368	+	2.04375i	0.0826741	+	0.468868i	−0.915160	+	0.403090i	$0.867936\pi$
$20$	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	0.000575831	−	1.00000i	$-0.499817\pi$
$23$	−4.39975	−	2.89376i	−0.917412	−	0.603391i	−0.917988	+	0.396608i	$0.870187\pi$
$24$	−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	−0.993288	−	0.115672i	$-0.963098\pi$
$29$	−5.65986	−	5.99910i	−1.05101	−	1.11400i	−0.0577215	−	0.998333i	$-0.518384\pi$
$30$	−5.72964	−	1.82497i	−1.04608	−	0.333192i
$31$	0.391315	−	6.71861i	0.0702822	−	1.20670i	−0.760214	−	0.649673i	$-0.774906\pi$
$31$	0.391315	−	6.71861i	0.0702822	−	1.20670i	0.830496	−	0.557025i	$-0.188057\pi$
$32$	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	−0.721438	−	0.692479i	$-0.756519\pi$
$37$	−5.04246	+	1.83530i	−0.828975	+	0.301722i	−0.107537	+	0.994201i	$0.534296\pi$
$38$	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	0.987149	−	0.159800i	$-0.0510850\pi$
$41$	11.5101	+	2.72795i	1.79758	+	0.426034i	0.810431	+	0.585835i	$0.199233\pi$
$42$	1.28431	−	3.34561i	0.198173	−	0.516239i
$43$	0.530760	+	1.23044i	0.0809401	+	0.187640i	0.953880	−	0.300187i	$-0.0970490\pi$
$43$	0.530760	+	1.23044i	0.0809401	+	0.187640i	−0.872940	+	0.487827i	$0.837790\pi$
$44$	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	−0.987820	−	0.155604i	$-0.950268\pi$
$47$	−0.169635	−	2.91252i	−0.0247438	−	0.424835i	0.963076	−	0.269231i	$-0.0867694\pi$
$48$	−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	−0.768951	−	0.639308i	$-0.779221\pi$
$53$	1.23166	−	2.13330i	0.169182	−	0.293031i	0.938132	+	0.346277i	$0.112554\pi$
$54$	−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	0.898434	−	0.439108i	$-0.144705\pi$
$59$	14.3938	−	1.68240i	1.87392	−	0.219029i	0.975482	+	0.220078i	$0.0706313\pi$
$60$	−5.99606	−	0.454431i	−0.774088	−	0.0586668i
$61$	3.25606	+	1.63525i	0.416896	+	0.209373i	0.644867	−	0.764295i	$-0.276913\pi$
$61$	3.25606	+	1.63525i	0.416896	+	0.209373i	−0.227971	+	0.973668i	$0.573209\pi$
$62$	−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	−0.164876	−	0.986314i	$-0.552722\pi$
$67$	6.78857	−	7.19547i	0.829356	−	0.879066i	0.994232	+	0.107248i	$0.0342039\pi$
$68$	−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	0.629715	−	0.776826i	$-0.283172\pi$
$71$	−0.218742	−	0.183547i	−0.0259599	−	0.0217830i	−0.655675	+	0.755043i	$0.727616\pi$
$72$	0.278925	−	2.98701i	0.0328717	−	0.352022i
$73$	−12.7160	+	10.6700i	−1.48830	+	1.24883i	−0.591571	+	0.806253i	$0.701492\pi$
$73$	−12.7160	+	10.6700i	−1.48830	+	1.24883i	−0.896729	+	0.442580i	$0.854063\pi$
$74$	−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	−0.638753	−	0.769412i	$-0.720549\pi$
$79$	−7.68164	+	1.82058i	−0.864252	+	0.204832i	−0.225499	+	0.974243i	$0.572401\pi$
$80$	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	−0.727731	−	0.685863i	$-0.759425\pi$
$83$	−9.75035	+	2.31088i	−1.07024	+	0.253652i	−0.342509	+	0.939514i	$0.611277\pi$
$84$	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	−0.771793	−	0.635873i	$-0.780640\pi$
$89$	−2.63775	+	2.21333i	−0.279601	+	0.234613i	0.492193	+	0.870486i	$0.336196\pi$
$90$	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	−0.806499	−	0.591235i	$-0.798641\pi$
$97$	−0.0866270	+	0.116360i	−0.00879564	+	0.0118146i	0.797704	+	0.603050i	$0.206048\pi$
$98$	−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	0.0104289	−	0.999946i	$-0.496680\pi$
$101$	−7.89340	−	3.96422i	−0.785423	−	0.394454i	−0.795852	+	0.605491i	$0.792977\pi$
$102$	5.07688	+	10.5650i	0.502686	+	1.04610i
$103$	−9.51929	+	1.11265i	−0.937964	+	0.109632i	−0.571318	−	0.820729i	$-0.693568\pi$
$103$	−9.51929	+	1.11265i	−0.937964	+	0.109632i	−0.366645	+	0.930361i	$0.619494\pi$
$104$	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	0.999976	−	0.00696974i	$-0.00221855\pi$
$107$	5.10948	+	8.84988i	0.493952	+	0.855550i	−0.506024	+	0.862520i	$0.668885\pi$
$108$	0.332106	+	5.18553i	0.0319569	+	0.498978i
$109$	1.31791	−	2.28269i	0.126233	−	0.218642i	−0.795981	−	0.605322i	$-0.793045\pi$
$109$	1.31791	−	2.28269i	0.126233	−	0.218642i	0.922214	+	0.386679i	$0.126378\pi$
$110$	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	−0.998852	−	0.0478997i	$-0.984747\pi$
$113$	−2.96110	+	6.86461i	−0.278557	+	0.645768i	0.720295	+	0.693668i	$0.244006\pi$
$114$	−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	0.835071	−	0.550143i	$-0.185427\pi$
$127$	12.6347	+	4.59865i	1.12115	+	0.408064i	0.286076	+	0.958207i	$0.407649\pi$
$128$	−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	0.855562	+	0.517701i	$0.173212\pi$
$131$	−0.621679	+	10.6738i	−0.0543164	+	0.932576i	−0.909878	+	0.414875i	$0.863825\pi$
$132$	−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	−0.913766	−	0.406242i	$-0.866839\pi$
$137$	0.853366	−	2.85044i	0.0729080	−	0.243530i	0.986674	+	0.162712i	$0.0520242\pi$
$138$	9.11358	−	0.371234i	0.775799	−	0.0316016i
$139$	9.37730	+	6.16755i	0.795372	+	0.523125i	0.880951	−	0.473207i	$-0.156904\pi$
$139$	9.37730	+	6.16755i	0.795372	+	0.523125i	−0.0855790	+	0.996331i	$0.527274\pi$
$140$	−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	−0.869729	−	0.493530i	$-0.835706\pi$
$149$	−5.05693	−	16.8913i	−0.414280	−	1.38379i	0.455448	−	0.890262i	$-0.349479\pi$
$150$	−3.97710	−	11.5508i	−0.324728	−	0.943119i
$151$	−20.9120	−	2.44426i	−1.70179	−	0.198911i	−0.791012	−	0.611800i	$-0.790446\pi$
$151$	−20.9120	−	2.44426i	−1.70179	−	0.198911i	−0.910781	+	0.412889i	$0.864520\pi$
$152$	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	0.983204	−	0.182510i	$-0.0584223\pi$
$157$	6.59546	+	8.85924i	0.526375	+	0.707044i	−0.456829	+	0.889554i	$0.651015\pi$
$158$	−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	0.638143	−	0.769918i	$-0.279703\pi$
$167$	−3.65008	−	4.90291i	−0.282452	−	0.379399i	−0.920595	+	0.390519i	$0.872295\pi$
$168$	−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	−0.368158	−	0.929763i	$-0.620012\pi$
$173$	−12.3744	−	1.44636i	−0.940811	−	0.109965i	−0.572653	+	0.819798i	$0.694086\pi$
$174$	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	0.741950	+	0.670455i	$0.233901\pi$
$179$	−2.46930	+	14.0041i	−0.184564	+	1.04672i	−0.926514	+	0.376260i	$0.877210\pi$
$180$	9.90559	−	3.21824i	0.738319	−	0.239874i
$181$	0.334484	+	1.89695i	0.0248620	+	0.140999i	0.994712	−	0.102703i	$-0.0327491\pi$
$181$	0.334484	+	1.89695i	0.0248620	+	0.140999i	−0.969850	+	0.243702i	$0.921638\pi$
$182$	−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	0.727870	−	0.685715i	$-0.240511\pi$
$191$	0.0137183	+	0.0145405i	0.000992618	+	0.00105211i	−0.726877	+	0.686768i	$0.759029\pi$
$192$	0.369942	+	1.69208i	0.0266983	+	0.122116i
$193$	−0.739021	+	12.6885i	−0.0531959	+	0.913338i	0.861137	+	0.508374i	$0.169753\pi$
$193$	−0.739021	+	12.6885i	−0.0531959	+	0.913338i	−0.914332	+	0.404964i	$0.867284\pi$
$194$	−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	−0.353327	−	0.935500i	$-0.614950\pi$
$197$	−17.1982	−	6.25962i	−1.22532	−	0.445979i	−0.871992	+	0.489521i	$0.837172\pi$
$198$	2.44108	−	3.05044i	0.173480	−	0.216785i
$199$	−4.11318	+	1.49707i	−0.291575	+	0.106125i	−0.483667	−	0.875252i	$-0.660695\pi$
$199$	−4.11318	+	1.49707i	−0.291575	+	0.106125i	0.192091	+	0.981377i	$0.438473\pi$
$200$	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	−0.881461	−	0.472257i	$-0.843439\pi$
$211$	0.972388	−	2.25425i	0.0669420	−	0.155189i	0.948403	+	0.317069i	$0.102699\pi$
$212$	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	0.863672	−	0.504054i	$-0.168159\pi$
$223$	14.5615	+	7.31304i	0.975107	+	0.489717i	0.111435	+	0.993772i	$0.464455\pi$
$224$	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	−0.488770	−	0.872412i	$-0.662554\pi$
$227$	7.33999	−	9.85932i	0.487172	−	0.654386i	0.975943	+	0.218026i	$0.0699618\pi$
$228$	−3.08105	−	1.85134i	−0.204048	−	0.122608i
$229$	−10.5563	+	11.1890i	−0.697580	+	0.739392i	−0.975206	−	0.221297i	$-0.928971\pi$
$229$	−10.5563	+	11.1890i	−0.697580	+	0.739392i	0.277626	+	0.960689i	$0.410452\pi$
$230$	−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	0.963230	−	0.268679i	$-0.0865872\pi$
$233$	13.2173	+	11.0906i	0.865895	+	0.726572i	−0.0973344	+	0.995252i	$0.531032\pi$
$234$	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	−0.303243	−	0.952913i	$-0.598069\pi$
$239$	4.32912	−	2.17417i	0.280028	−	0.140635i	0.583270	+	0.812278i	$0.301773\pi$
$240$	−5.56223	+	2.28493i	−0.359040	+	0.147492i
$241$	−9.87724	+	2.34095i	−0.636249	+	0.150794i	−0.536067	−	0.844175i	$-0.680091\pi$
$241$	−9.87724	+	2.34095i	−0.636249	+	0.150794i	−0.100182	+	0.994969i	$0.531942\pi$
$242$	−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	0.184378	−	0.982855i	$-0.440973\pi$
$251$	18.7631	−	15.7441i	1.18432	−	0.993761i	0.999941	−	0.0109054i	$-0.00347135\pi$
$252$	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	0.194068	−	0.980988i	$-0.437832\pi$
$257$	18.6301	−	19.7467i	1.16211	−	1.23177i	0.968044	−	0.250779i	$-0.0806868\pi$
$258$	−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	0.764047	−	0.645160i	$-0.223209\pi$
$263$	11.3976	+	5.72409i	0.702807	+	0.352963i	−0.0612406	+	0.998123i	$0.519506\pi$
$264$	−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	0.975218	+	0.221246i	$0.0710125\pi$
$269$	11.1399	+	19.2949i	0.679214	+	1.17643i	−0.296004	+	0.955187i	$0.595654\pi$
$270$	−16.0739	+	8.18928i	−0.978224	+	0.498383i
$271$	6.95209	−	12.0414i	0.422309	−	0.731461i	−0.573856	−	0.818956i	$-0.694553\pi$
$271$	6.95209	−	12.0414i	0.422309	−	0.731461i	0.996165	+	0.0874955i	$0.0278863\pi$
$272$	−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	−0.994439	−	0.105317i	$-0.966414\pi$
$277$	−0.315400	−	5.41521i	−0.0189506	−	0.325369i	0.975488	−	0.220052i	$-0.0706227\pi$
$278$	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	0.759036	−	0.651049i	$-0.225671\pi$
$281$	−3.94606	−	9.14799i	−0.235402	−	0.545723i	−0.994438	+	0.105326i	$0.966412\pi$
$282$	3.18002	+	3.92710i	0.189368	+	0.233855i
$283$	−7.20262	−	1.70705i	−0.428151	−	0.101474i	0.0108897	−	0.999941i	$-0.496534\pi$
$283$	−7.20262	−	1.70705i	−0.428151	−	0.101474i	−0.439041	+	0.898467i	$0.644682\pi$
$284$	−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	−0.997856	−	0.0654496i	$-0.979152\pi$
$293$	0.0145683	−	0.250129i	0.000851092	−	0.0146127i	0.998707	+	0.0508369i	$0.0161889\pi$
$294$	−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	−0.998348	−	0.0574552i	$-0.981701\pi$
$307$	−0.710614	+	4.03009i	−0.0405569	+	0.230010i	0.957791	+	0.287465i	$0.0928125\pi$
$308$	−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	0.889062	+	0.457788i	$0.151358\pi$
$311$	7.01563	+	23.4338i	0.397820	+	1.32881i	−0.491242	+	0.871023i	$0.663457\pi$
$312$	−3.47136	−	0.674809i	−0.196527	−	0.0382035i
$313$	−17.8803	−	2.08991i	−1.01066	−	0.118129i	−0.405383	−	0.914147i	$-0.632862\pi$
$313$	−17.8803	−	2.08991i	−1.01066	−	0.118129i	−0.605273	+	0.796018i	$0.706936\pi$
$314$	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	−0.727466	−	0.686143i	$-0.759302\pi$
$317$	−6.86494	+	4.51514i	−0.385573	+	0.253596i	0.341893	+	0.939739i	$0.388932\pi$
$318$	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	0.380169	−	0.924917i	$-0.375866\pi$
$331$	25.1073	−	16.5133i	1.38002	−	0.907653i	0.999851	+	0.0172635i	$0.00549542\pi$
$332$	−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	0.994188	−	0.107662i	$-0.0343363\pi$
$337$	1.91644	+	6.40135i	0.104395	+	0.348704i	−0.889793	+	0.456365i	$0.849151\pi$
$338$	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	0.362825	−	0.931857i	$-0.381812\pi$
$347$	−6.50327	−	4.27727i	−0.349114	−	0.229616i	−0.711939	+	0.702242i	$0.752183\pi$
$348$	14.2735	−	0.581417i	0.765137	−	0.0311672i
$349$	−5.83721	+	19.4976i	−0.312459	+	1.04369i	0.647154	+	0.762360i	$0.275959\pi$
$349$	−5.83721	+	19.4976i	−0.312459	+	1.04369i	−0.959612	+	0.281326i	$0.909226\pi$
$350$	−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	0.604220	−	0.796818i	$-0.293485\pi$
$353$	−4.25333	−	4.50827i	−0.226382	−	0.239951i	−0.830602	+	0.556867i	$0.812003\pi$
$354$	−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	−0.332805	−	0.942996i	$-0.607995\pi$
$359$	−22.6211	−	8.23340i	−1.19389	−	0.434542i	−0.861089	+	0.508454i	$0.830217\pi$
$360$	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	0.974555	−	0.224148i	$-0.0719600\pi$
$367$	2.73441	+	6.33908i	0.142735	+	0.330897i	−0.831820	+	0.555046i	$0.812701\pi$
$368$	−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	−0.827048	−	0.562131i	$-0.809982\pi$
$373$	2.88512	−	6.68847i	0.149386	−	0.346316i	0.976434	+	0.215815i	$0.0692409\pi$
$374$	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	0.795547	+	0.605892i	$0.207184\pi$
$379$	17.9590	+	31.1059i	0.922491	+	1.59780i	0.126945	+	0.991910i	$0.459483\pi$
$380$	−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	0.0582990	−	0.998299i	$-0.481432\pi$
$383$	6.75668	−	0.789743i	0.345250	−	0.0403540i	0.286951	+	0.957945i	$0.407358\pi$
$384$	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	−0.646832	−	0.762633i	$-0.723906\pi$
$389$	5.31095	−	7.13384i	0.269276	−	0.361700i	0.916108	+	0.400933i	$0.131314\pi$
$390$	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	−0.475494	−	0.879719i	$-0.657731\pi$
$397$	6.14266	−	5.15431i	0.308292	−	0.258687i	0.783785	+	0.621032i	$0.213286\pi$
$398$	−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	−0.808782	−	0.588108i	$-0.799873\pi$
$401$	−16.4209	+	8.24686i	−0.820018	+	0.411829i	−0.0112360	+	0.999937i	$0.503577\pi$
$402$	−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	−0.106566	−	0.994306i	$-0.533986\pi$
$409$	12.6874	−	6.37186i	0.627352	−	0.315068i	0.733919	+	0.679237i	$0.237689\pi$
$410$	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	−0.999981	−	0.00610446i	$-0.998057\pi$
$419$	−19.1542	+	20.3023i	−0.935743	+	0.991830i	0.0642379	+	0.997935i	$0.479538\pi$
$420$	10.8817	−	6.03166i	0.530974	−	0.294315i
$421$	17.6515	−	23.7101i	0.860281	−	1.15556i	−0.126253	−	0.991998i	$-0.540295\pi$
$421$	17.6515	−	23.7101i	0.860281	−	1.15556i	0.986533	−	0.163559i	$-0.0522975\pi$
$422$	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	0.797216	−	0.603694i	$-0.206305\pi$
$431$	−2.57859	−	4.46626i	−0.124207	−	0.215132i	−0.921423	+	0.388562i	$0.872972\pi$
$432$	2.62404	+	4.48491i	0.126249	+	0.215780i
$433$	1.08815	−	1.88473i	0.0522930	−	0.0905742i	−0.838694	−	0.544603i	$-0.816680\pi$
$433$	1.08815	−	1.88473i	0.0522930	−	0.0905742i	0.890987	+	0.454029i	$0.150014\pi$
$434$	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	−0.680961	−	0.732320i	$-0.738438\pi$
$439$	−1.87778	−	32.2402i	−0.0896215	−	1.53874i	0.591340	−	0.806423i	$-0.298599\pi$
$440$	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	0.834847	−	0.550482i	$-0.185556\pi$
$443$	−2.91436	−	6.75625i	−0.138465	−	0.320999i	−0.973313	+	0.229483i	$0.926297\pi$
$444$	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	−0.171823	−	0.985128i	$-0.554966\pi$
$449$	6.98792	−	2.54340i	0.329780	−	0.120030i	0.501604	+	0.865098i	$0.332744\pi$
$450$	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	0.708420	−	0.705791i	$-0.249408\pi$
$457$	−0.798851	−	0.846733i	−0.0373687	−	0.0396085i	−0.745788	+	0.666183i	$0.767927\pi$
$458$	−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	0.818429	+	0.574608i	$0.194845\pi$
$461$	−3.88861	+	12.9889i	−0.181110	+	0.604951i	−0.999540	+	0.0303436i	$0.990340\pi$
$462$	2.16707	−	4.13338i	0.100821	−	0.192302i
$463$	1.96903	+	1.29505i	0.0915086	+	0.0601862i	0.594439	−	0.804141i	$-0.297374\pi$
$463$	1.96903	+	1.29505i	0.0915086	+	0.0601862i	−0.502930	+	0.864327i	$0.667745\pi$
$464$	−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	0.956611	−	0.291368i	$-0.0941104\pi$
$467$	−0.906829	−	5.14288i	−0.0419630	−	0.237984i	−0.998574	+	0.0533839i	$0.982999\pi$
$468$	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	−0.768813	−	0.639473i	$-0.779152\pi$
$479$	−10.6399	+	6.99798i	−0.486150	+	0.319746i	0.282663	+	0.959219i	$0.408782\pi$
$480$	−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	0.855952	−	0.517054i	$-0.172972\pi$
$491$	2.55111	+	3.42673i	0.115130	+	0.154646i	−0.740823	+	0.671701i	$0.765564\pi$
$492$	−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	0.964674	−	0.263448i	$-0.0848597\pi$
$499$	0.311253	+	1.03966i	0.0139336	+	0.0465415i	−0.950740	+	0.309989i	$0.899675\pi$
$500$	−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	−0.884002	−	0.467484i	$-0.845161\pi$
$503$	2.39027	−	13.5559i	0.106577	−	0.604428i	0.990579	−	0.136945i	$-0.0437282\pi$
$504$	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	0.714836	−	0.699292i	$-0.246501\pi$
$509$	8.02873	+	5.28058i	0.355867	+	0.234058i	−0.358969	+	0.933350i	$0.616872\pi$
$510$	−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	0.349073	−	0.937095i	$-0.386496\pi$
$521$	0.322424	+	0.117353i	0.0141257	+	0.00514132i	−0.334948	+	0.942237i	$0.608719\pi$
$522$	−24.2605	+	4.86177i	−1.06185	+	0.212794i
$523$	−27.8175	+	10.1248i	−1.21638	+	0.442725i	−0.868911	−	0.494968i	$-0.835180\pi$
$523$	−27.8175	+	10.1248i	−1.21638	+	0.442725i	−0.347465	+	0.937693i	$0.612958\pi$
$524$	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	0.895717	−	0.444625i	$-0.146663\pi$
$541$	1.46072	+	2.53004i	0.0628013	+	0.108775i	−0.832915	+	0.553401i	$0.813330\pi$
$542$	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	0.616632	−	0.787252i	$-0.288497\pi$
$547$	8.26501	+	4.15085i	0.353386	+	0.177477i	−0.263246	+	0.964729i	$0.584793\pi$
$548$	−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	0.733401	−	0.679796i	$-0.237932\pi$
$557$	4.51453	+	3.78814i	0.191287	+	0.160509i	−0.542114	+	0.840305i	$0.682376\pi$
$558$	−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	−0.687125	−	0.726539i	$-0.741127\pi$
$563$	−12.2120	+	6.13309i	−0.514673	+	0.258479i	0.172451	+	0.985018i	$0.444831\pi$
$564$	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	−0.205827	−	0.978588i	$-0.565988\pi$
$569$	1.17908	−	0.279447i	0.0494295	−	0.0117150i	0.255256	+	0.966873i	$0.417840\pi$
$570$	1.66500	−	12.3676i	0.0697391	−	0.518022i
$571$	−32.7769	+	16.4612i	−1.37167	+	0.688879i	−0.973554	−	0.228456i	$-0.926632\pi$
$571$	−32.7769	+	16.4612i	−1.37167	+	0.688879i	−0.398117	+	0.917335i	$0.630336\pi$
$572$	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	0.911625	−	0.411023i	$-0.134828\pi$
$577$	15.9774	+	13.4066i	0.665149	+	0.558126i	−0.246476	+	0.969149i	$0.579273\pi$
$578$	−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	0.0264724	−	0.999650i	$-0.491573\pi$
$587$	−18.4027	−	9.24219i	−0.759561	−	0.381466i	−0.786034	+	0.618183i	$0.787869\pi$
$588$	−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	0.997459	+	0.0712439i	$0.0226969\pi$
$593$	13.6473	+	23.6379i	0.560428	+	0.970691i	−0.437030	+	0.899447i	$0.643970\pi$
$594$	−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	−0.920383	−	0.391018i	$-0.872123\pi$
$599$	−0.106741	+	0.247454i	−0.00436132	+	0.0101107i	0.916022	+	0.401129i	$0.131382\pi$
$600$	−8.73805	−	8.53725i	−0.356729	−	0.348532i
$601$	−0.343647	−	5.90018i	−0.0140176	−	0.240674i	−0.998038	−	0.0626159i	$-0.980056\pi$
$601$	−0.343647	−	5.90018i	−0.0140176	−	0.240674i	0.984020	−	0.178058i	$-0.0569813\pi$
$602$	−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	0.863296	−	0.504699i	$-0.168396\pi$
$607$	34.6957	+	8.22304i	1.40826	+	0.333763i	0.544961	+	0.838462i	$0.316545\pi$
$608$	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	0.697594	−	0.716493i	$-0.254254\pi$
$613$	19.0997	+	6.95172i	0.771429	+	0.280777i	0.0738351	+	0.997270i	$0.476476\pi$
$614$	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	−0.506719	−	0.862112i	$-0.669142\pi$
$617$	2.40095	−	41.2228i	0.0966588	−	1.65957i	0.603377	−	0.797456i	$-0.293821\pi$
$618$	12.2716	−	11.1791i	0.493637	−	0.449689i
$619$	−30.0497	−	31.8508i	−1.20780	−	1.28019i	−0.949369	−	0.314163i	$-0.898276\pi$
$619$	−30.0497	−	31.8508i	−1.20780	−	1.28019i	−0.258431	−	0.966030i	$-0.583205\pi$
$620$	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	−0.991981	−	0.126388i	$-0.959662\pi$
$631$	−0.416899	+	2.36435i	−0.0165965	+	0.0941233i	0.975384	+	0.220511i	$0.0707726\pi$
$632$	−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	−0.569550	−	0.821957i	$-0.692883\pi$
$641$	−1.02294	+	0.672796i	−0.0404036	+	0.0265739i	0.529147	+	0.848530i	$0.322512\pi$
$642$	−16.1273	−	7.29329i	−0.636493	−	0.287843i
$643$	−22.2659	−	29.9084i	−0.878083	−	1.17947i	−0.982746	−	0.184963i	$-0.940784\pi$
$643$	−22.2659	−	29.9084i	−0.878083	−	1.17947i	0.104662	−	0.994508i	$-0.466624\pi$
$644$	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	0.332146	−	0.943228i	$-0.392227\pi$
$653$	−17.0372	−	22.8849i	−0.666717	−	0.895556i	−0.998863	+	0.0476717i	$0.984820\pi$
$654$	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	−0.438547	−	0.898708i	$-0.644507\pi$
$659$	−27.5329	−	3.21814i	−1.07253	−	0.125361i	−0.633983	+	0.773347i	$0.718581\pi$
$660$	−7.68721	−	1.49434i	−0.299224	−	0.0581672i
$661$	10.1414	+	33.8746i	0.394455	+	1.31757i	0.892746	+	0.450561i	$0.148776\pi$
$661$	10.1414	+	33.8746i	0.394455	+	1.31757i	−0.498291	+	0.867010i	$0.666039\pi$
$662$	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	−0.876044	−	0.482230i	$-0.839827\pi$
$673$	3.13564	−	10.4738i	0.120870	−	0.403734i	0.996914	+	0.0784967i	$0.0250120\pi$
$674$	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	0.994014	−	0.109251i	$-0.0348451\pi$
$677$	21.5218	+	22.8118i	0.827152	+	0.876729i	−0.166863	+	0.985980i	$0.553364\pi$
$678$	−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	0.863703	−	0.504001i	$-0.168139\pi$
$683$	31.3970	+	11.4276i	1.20137	+	0.437264i	0.337670	+	0.941265i	$0.390361\pi$
$684$	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	0.985344	−	0.170580i	$-0.0545641\pi$
$691$	4.86530	+	11.2790i	0.185085	+	0.429074i	−0.800259	+	0.599654i	$0.795305\pi$
$692$	−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	−0.161519	−	0.986870i	$-0.551639\pi$
$701$	20.4899	−	35.4896i	0.773895	−	1.34042i	0.935414	−	0.353555i	$-0.115027\pi$
$702$	−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	0.908147	−	0.418652i	$-0.137497\pi$
$709$	29.6797	+	14.9057i	1.11464	+	0.559795i	0.206497	+	0.978447i	$0.433794\pi$
$710$	−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	0.657753	−	0.753234i	$-0.271507\pi$
$719$	0.809269	+	0.679057i	0.0301806	+	0.0253246i	−0.627573	+	0.778558i	$0.715951\pi$
$720$	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	−0.658524	−	0.752560i	$-0.728819\pi$
$727$	−24.5162	+	5.81044i	−0.909255	+	0.215497i	−0.250730	+	0.968057i	$0.580671\pi$
$728$	−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	−0.369876	−	0.929081i	$-0.620600\pi$
$733$	4.18257	−	2.10056i	0.154487	−	0.0775861i	0.524363	+	0.851495i	$0.324304\pi$
$734$	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	0.981082	−	0.193591i	$-0.0620135\pi$
$739$	26.1188	+	21.9163i	0.960795	+	0.806203i	−0.0202869	+	0.999794i	$0.506458\pi$
$740$	−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	−0.290483	−	0.956880i	$-0.593816\pi$
$743$	18.5809	−	19.6946i	0.681668	−	0.722526i	0.972151	+	0.234354i	$0.0752975\pi$
$744$	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	0.0555479	−	0.998456i	$-0.482309\pi$
$751$	9.31361	−	1.08860i	0.339858	−	0.0397237i	0.284310	+	0.958732i	$0.408235\pi$
$752$	−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	−0.586473	−	0.809969i	$-0.699484\pi$
$757$	11.2315	−	19.4536i	0.408217	−	0.707053i	0.994690	+	0.102916i	$0.0328174\pi$
$758$	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	0.415900	+	0.909410i	$0.363467\pi$
$761$	−14.6480	+	33.9578i	−0.530989	+	1.23097i	−0.946889	+	0.321560i	$0.895793\pi$
$762$	−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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