LMFDB - Embedded newform 486.2.g.b.253.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [486,2,Mod(19,486)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(486, base_ring=CyclotomicField(54))

chi = DirichletCharacter(H, H._module([52]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("486.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 486 = 2 \cdot 3^{5} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	486.g (of order $27$, degree $18$, not 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:	$3.88072953823$
Analytic rank:	$0$
Dimension:	$90$
Relative dimension:	$5$ over $\Q(\zeta_{27})$
Twist minimal:	no (minimal twist has level 162)
Sato-Tate group:	$\mathrm{SU}(2)[C_{27}]$

Embedding invariants

Embedding label			253.2
Character	$\chi$	$=$	486.253
Dual form			486.2.g.b.73.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.893633 - 0.448799i) q^{2} +(0.597159 + 0.802123i) q^{4} +(-0.664151 - 2.21842i) q^{5} +(-0.590051 - 1.36789i) q^{7} +(-0.173648 - 0.984808i) q^{8} +(-0.402118 + 2.28052i) q^{10} +(4.28069 - 1.01454i) q^{11} +(0.407438 + 0.267976i) q^{13} +(-0.0866199 + 1.48721i) q^{14} +(-0.286803 + 0.957990i) q^{16} +(-6.18123 + 2.24978i) q^{17} +(-6.76026 - 2.46053i) q^{19} +(1.38284 - 1.85748i) q^{20} +(-4.28069 - 1.01454i) q^{22} +(1.15348 - 2.67407i) q^{23} +(-0.302850 + 0.199188i) q^{25} +(-0.243833 - 0.422330i) q^{26} +(0.744864 - 1.29014i) q^{28} +(-0.382974 - 6.57542i) q^{29} +(-1.78001 + 0.208053i) q^{31} +(0.686242 - 0.727374i) q^{32} +(6.53345 + 0.763651i) q^{34} +(-2.64267 + 2.21747i) q^{35} +(-3.51174 - 2.94670i) q^{37} +(4.93690 + 5.23281i) q^{38} +(-2.06939 + 1.03929i) q^{40} +(7.03828 - 3.53476i) q^{41} +(-0.304424 - 0.322671i) q^{43} +(3.37004 + 2.82780i) q^{44} +(-2.23091 + 1.87195i) q^{46} +(-7.76840 - 0.907996i) q^{47} +(3.28072 - 3.47736i) q^{49} +(0.360032 - 0.0420817i) q^{50} +(0.0283552 + 0.486840i) q^{52} +(-0.984340 + 1.70493i) q^{53} +(-5.09371 - 8.82256i) q^{55} +(-1.24465 + 0.818618i) q^{56} +(-2.60880 + 6.04789i) q^{58} +(-12.3643 - 2.93038i) q^{59} +(4.60541 - 6.18613i) q^{61} +(1.68405 + 0.612943i) q^{62} +(-0.939693 + 0.342020i) q^{64} +(0.323883 - 1.08185i) q^{65} +(-0.221954 + 3.81081i) q^{67} +(-5.49578 - 3.61463i) q^{68} +(3.35678 - 0.795571i) q^{70} +(-1.34489 + 7.62726i) q^{71} +(1.74940 + 9.92135i) q^{73} +(1.81573 + 4.20933i) q^{74} +(-2.06330 - 6.89189i) q^{76} +(-3.91361 - 5.25689i) q^{77} +(15.0035 + 7.53506i) q^{79} +2.31570 q^{80} -7.87604 q^{82} +(4.65331 + 2.33698i) q^{83} +(9.09624 + 12.2184i) q^{85} +(0.127229 + 0.424975i) q^{86} +(-1.74246 - 4.03949i) q^{88} +(0.537926 + 3.05073i) q^{89} +(0.126153 - 0.715451i) q^{91} +(2.83374 - 0.671609i) q^{92} +(6.53459 + 4.29787i) q^{94} +(-0.968660 + 16.6313i) q^{95} +(0.403864 - 1.34900i) q^{97} +(-4.49240 + 1.63510i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 90 q - 18 q^{13} + 9 q^{20} - 27 q^{23} - 18 q^{25} + 27 q^{26} - 18 q^{28} + 27 q^{29} + 54 q^{31} + 27 q^{35} + 18 q^{38} + 9 q^{41} - 36 q^{43} + 18 q^{46} + 27 q^{47} + 36 q^{52} + 27 q^{53} - 54 q^{55}+ \cdots - 36 q^{98}+O(q^{100}) $ 90 * q - 18 * q^13 + 9 * q^20 - 27 * q^23 - 18 * q^25 + 27 * q^26 - 18 * q^28 + 27 * q^29 + 54 * q^31 + 27 * q^35 + 18 * q^38 + 9 * q^41 - 36 * q^43 + 18 * q^46 + 27 * q^47 + 36 * q^52 + 27 * q^53 - 54 * q^55 - 9 * q^58 + 45 * q^59 - 9 * q^65 + 81 * q^67 - 36 * q^68 - 72 * q^70 - 72 * q^71 - 36 * q^73 - 45 * q^74 - 18 * q^76 - 144 * q^77 - 99 * q^79 - 18 * q^80 + 72 * q^82 - 45 * q^83 - 117 * q^85 - 72 * q^86 - 18 * q^88 - 45 * q^89 - 63 * q^91 - 36 * q^92 - 72 * q^94 - 45 * q^95 + 117 * q^97 - 36 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/486\mathbb{Z}\right)^\times$.

$n$	$245$
$\chi(n)$	$e\left(\frac{4}{27}\right)$

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 $

$2$	−0.893633	−	0.448799i	−0.631894	−	0.317349i
$2$	−0.893633	−	0.448799i	−0.631894	−	0.317349i
$3$		0			0
$3$		0			0
$4$	0.597159	+	0.802123i	0.298579	+	0.401062i
$5$	−0.664151	−	2.21842i	−0.297017	−	0.992107i	−0.968066	−	0.250694i	$-0.919341\pi$
$5$	−0.664151	−	2.21842i	−0.297017	−	0.992107i	0.671049	−	0.741413i	$-0.265844\pi$
$6$		0			0
$7$	−0.590051	−	1.36789i	−0.223018	−	0.517014i	0.769567	−	0.638566i	$-0.220472\pi$
$7$	−0.590051	−	1.36789i	−0.223018	−	0.517014i	−0.992585	+	0.121552i	$0.961213\pi$
$8$	−0.173648	−	0.984808i	−0.0613939	−	0.348182i
$9$		0			0
$10$	−0.402118	+	2.28052i	−0.127161	+	0.721165i
$11$	4.28069	−	1.01454i	1.29068	−	0.305896i	0.472739	−	0.881202i	$-0.343265\pi$
$11$	4.28069	−	1.01454i	1.29068	−	0.305896i	0.817938	+	0.575306i	$0.195117\pi$
$12$		0			0
$13$	0.407438	+	0.267976i	0.113003	+	0.0743233i	0.604752	−	0.796413i	$-0.293272\pi$
$13$	0.407438	+	0.267976i	0.113003	+	0.0743233i	−0.491749	+	0.870737i	$0.663642\pi$
$14$	−0.0866199	+	1.48721i	−0.0231502	+	0.397473i
$15$		0			0
$16$	−0.286803	+	0.957990i	−0.0717008	+	0.239497i
$17$	−6.18123	+	2.24978i	−1.49917	+	0.545653i	−0.955845	−	0.293871i	$-0.905056\pi$
$17$	−6.18123	+	2.24978i	−1.49917	+	0.545653i	−0.543323	+	0.839524i	$0.682834\pi$
$18$		0			0
$19$	−6.76026	−	2.46053i	−1.55091	−	0.564485i	−0.582279	−	0.812989i	$-0.697839\pi$
$19$	−6.76026	−	2.46053i	−1.55091	−	0.564485i	−0.968631	+	0.248504i	$0.920061\pi$
$20$	1.38284	−	1.85748i	0.309213	−	0.415345i
$21$		0			0
$22$	−4.28069	−	1.01454i	−0.912647	−	0.216301i
$23$	1.15348	−	2.67407i	0.240517	−	0.557582i	−0.754611	−	0.656173i	$-0.772174\pi$
$23$	1.15348	−	2.67407i	0.240517	−	0.557582i	0.995128	+	0.0985910i	$0.0314336\pi$
$24$		0			0
$25$	−0.302850	+	0.199188i	−0.0605701	+	0.0398376i
$26$	−0.243833	−	0.422330i	−0.0478195	−	0.0828258i
$27$		0			0
$28$	0.744864	−	1.29014i	0.140766	−	0.243814i
$29$	−0.382974	−	6.57542i	−0.0711166	−	1.22102i	−0.825428	−	0.564508i	$-0.809066\pi$
$29$	−0.382974	−	6.57542i	−0.0711166	−	1.22102i	0.754311	−	0.656517i	$-0.227971\pi$
$30$		0			0
$31$	−1.78001	+	0.208053i	−0.319699	+	0.0373674i	−0.274429	−	0.961607i	$-0.588489\pi$
$31$	−1.78001	+	0.208053i	−0.319699	+	0.0373674i	−0.0452698	+	0.998975i	$0.514415\pi$
$32$	0.686242	−	0.727374i	0.121312	−	0.128583i
$33$		0			0
$34$	6.53345	+	0.763651i	1.12048	+	0.130965i
$35$	−2.64267	+	2.21747i	−0.446694	+	0.374820i
$36$		0			0
$37$	−3.51174	−	2.94670i	−0.577326	−	0.484434i	0.306742	−	0.951793i	$-0.400761\pi$
$37$	−3.51174	−	2.94670i	−0.577326	−	0.484434i	−0.884068	+	0.467359i	$0.845206\pi$
$38$	4.93690	+	5.23281i	0.800871	+	0.848874i
$39$		0			0
$40$	−2.06939	+	1.03929i	−0.327199	+	0.164326i
$41$	7.03828	−	3.53476i	1.09920	−	0.552037i	0.195713	−	0.980661i	$-0.437298\pi$
$41$	7.03828	−	3.53476i	1.09920	−	0.552037i	0.903483	+	0.428625i	$0.141002\pi$
$42$		0			0
$43$	−0.304424	−	0.322671i	−0.0464243	−	0.0492069i	0.703745	−	0.710452i	$-0.251510\pi$
$43$	−0.304424	−	0.322671i	−0.0464243	−	0.0492069i	−0.750170	+	0.661246i	$0.770028\pi$
$44$	3.37004	+	2.82780i	0.508053	+	0.426307i
$45$		0			0
$46$	−2.23091	+	1.87195i	−0.328929	+	0.276004i
$47$	−7.76840	−	0.907996i	−1.13314	−	0.132445i	−0.471216	−	0.882018i	$-0.656185\pi$
$47$	−7.76840	−	0.907996i	−1.13314	−	0.132445i	−0.661922	+	0.749573i	$0.730259\pi$
$48$		0			0
$49$	3.28072	−	3.47736i	0.468675	−	0.496766i
$50$	0.360032	−	0.0420817i	0.0509162	−	0.00595126i
$51$		0			0
$52$	0.0283552	+	0.486840i	0.00393216	+	0.0675126i
$53$	−0.984340	+	1.70493i	−0.135209	+	0.234190i	−0.925677	−	0.378314i	$-0.876504\pi$
$53$	−0.984340	+	1.70493i	−0.135209	+	0.234190i	0.790468	+	0.612503i	$0.209837\pi$
$54$		0			0
$55$	−5.09371	−	8.82256i	−0.686836	−	1.18963i
$56$	−1.24465	+	0.818618i	−0.166323	+	0.109392i
$57$		0			0
$58$	−2.60880	+	6.04789i	−0.342553	+	0.794126i
$59$	−12.3643	−	2.93038i	−1.60969	−	0.381503i	−0.675240	−	0.737598i	$-0.735960\pi$
$59$	−12.3643	−	2.93038i	−1.60969	−	0.381503i	−0.934450	+	0.356095i	$0.884108\pi$
$60$		0			0
$61$	4.60541	−	6.18613i	0.589662	−	0.792053i	−0.402711	−	0.915327i	$-0.631932\pi$
$61$	4.60541	−	6.18613i	0.589662	−	0.792053i	0.992373	+	0.123274i	$0.0393394\pi$
$62$	1.68405	+	0.612943i	0.213874	+	0.0778439i
$63$		0			0
$64$	−0.939693	+	0.342020i	−0.117462	+	0.0427525i
$65$	0.323883	−	1.08185i	0.0401728	−	0.134186i
$66$		0			0
$67$	−0.221954	+	3.81081i	−0.0271160	+	0.465564i	0.957231	+	0.289324i	$0.0934305\pi$
$67$	−0.221954	+	3.81081i	−0.0271160	+	0.465564i	−0.984347	+	0.176240i	$0.943606\pi$
$68$	−5.49578	−	3.61463i	−0.666461	−	0.438338i
$69$		0			0
$70$	3.35678	−	0.795571i	0.401212	−	0.0950889i
$71$	−1.34489	+	7.62726i	−0.159609	+	0.905189i	0.794841	+	0.606818i	$0.207554\pi$
$71$	−1.34489	+	7.62726i	−0.159609	+	0.905189i	−0.954450	+	0.298371i	$0.903557\pi$
$72$		0			0
$73$	1.74940	+	9.92135i	0.204752	+	1.16121i	0.897830	+	0.440343i	$0.145143\pi$
$73$	1.74940	+	9.92135i	0.204752	+	1.16121i	−0.693078	+	0.720863i	$0.743746\pi$
$74$	1.81573	+	4.20933i	0.211074	+	0.489325i
$75$		0			0
$76$	−2.06330	−	6.89189i	−0.236676	−	0.790554i
$77$	−3.91361	−	5.25689i	−0.445997	−	0.599078i
$78$		0			0
$79$	15.0035	+	7.53506i	1.68803	+	0.847761i	0.991481	+	0.130252i	$0.0415787\pi$
$79$	15.0035	+	7.53506i	1.68803	+	0.847761i	0.696550	+	0.717509i	$0.254718\pi$
$80$	2.31570			0.258904
$81$		0			0
$82$	−7.87604			−0.869763
$83$	4.65331	+	2.33698i	0.510767	+	0.256517i	0.685465	−	0.728105i	$-0.259599\pi$
$83$	4.65331	+	2.33698i	0.510767	+	0.256517i	−0.174698	+	0.984622i	$0.555895\pi$
$84$		0			0
$85$	9.09624	+	12.2184i	0.986625	+	1.32527i
$86$	0.127229	+	0.424975i	0.0137195	+	0.0458262i
$87$		0			0
$88$	−1.74246	−	4.03949i	−0.185747	−	0.430611i
$89$	0.537926	+	3.05073i	0.0570200	+	0.323377i	0.999954	−	0.00960343i	$-0.00305691\pi$
$89$	0.537926	+	3.05073i	0.0570200	+	0.323377i	−0.942934	+	0.332980i	$0.891946\pi$
$90$		0			0
$91$	0.126153	−	0.715451i	0.0132245	−	0.0749996i
$92$	2.83374	−	0.671609i	0.295438	−	0.0700201i
$93$		0			0
$94$	6.53459	+	4.29787i	0.673991	+	0.443291i
$95$	−0.968660	+	16.6313i	−0.0993825	+	1.70633i
$96$		0			0
$97$	0.403864	−	1.34900i	0.0410062	−	0.136970i	−0.935035	−	0.354555i	$-0.884633\pi$
$97$	0.403864	−	1.34900i	0.0410062	−	0.136970i	0.976042	+	0.217584i	$0.0698177\pi$
$98$	−4.49240	+	1.63510i	−0.453801	+	0.165170i
$99$		0			0
$100$	−0.340623	−	0.123977i	−0.0340623	−	0.0123977i
$101$	6.00167	−	8.06164i	0.597188	−	0.802163i	−0.396053	−	0.918228i	$-0.629620\pi$
$101$	6.00167	−	8.06164i	0.597188	−	0.802163i	0.993242	+	0.116064i	$0.0370279\pi$
$102$		0			0
$103$	−1.63242	−	0.386890i	−0.160847	−	0.0381214i	0.149403	−	0.988776i	$-0.452265\pi$
$103$	−1.63242	−	0.386890i	−0.160847	−	0.0381214i	−0.310250	+	0.950655i	$0.600413\pi$
$104$	0.193154	−	0.447782i	0.0189403	−	0.0439086i
$105$		0			0
$106$	1.64481	−	1.08181i	0.159758	−	0.105074i
$107$	6.16214	+	10.6731i	0.595717	+	1.03181i	0.993445	+	0.114309i	$0.0364653\pi$
$107$	6.16214	+	10.6731i	0.595717	+	1.03181i	−0.397728	+	0.917503i	$0.630201\pi$
$108$		0			0
$109$	9.54562	−	16.5335i	0.914305	−	1.58362i	0.106389	−	0.994325i	$-0.466071\pi$
$109$	9.54562	−	16.5335i	0.914305	−	1.58362i	0.807916	−	0.589298i	$-0.200595\pi$
$110$	0.592346	+	10.1702i	0.0564779	+	0.969689i
$111$		0			0
$112$	1.47965	−	0.172947i	0.139814	−	0.0163419i
$113$	5.52918	−	5.86059i	0.520142	−	0.551318i	−0.413045	−	0.910711i	$-0.635535\pi$
$113$	5.52918	−	5.86059i	0.520142	−	0.551318i	0.933186	+	0.359393i	$0.117016\pi$
$114$		0			0
$115$	−6.69829	−	0.782918i	−0.624619	−	0.0730075i
$116$	5.04560	−	4.23376i	0.468472	−	0.393095i
$117$		0			0
$118$	9.73395	+	8.16776i	0.896083	+	0.751903i
$119$	6.72470	+	7.12777i	0.616452	+	0.653401i
$120$		0			0
$121$	7.46507	−	3.74910i	0.678643	−	0.340827i
$122$	−6.89187	+	3.46123i	−0.623961	+	0.313365i
$123$		0			0
$124$	−1.22983	−	1.30355i	−0.110442	−	0.117062i
$125$	−8.22664	−	6.90297i	−0.735813	−	0.617420i
$126$		0			0
$127$	14.4311	−	12.1091i	1.28055	−	1.07451i	0.287382	−	0.957816i	$-0.407215\pi$
$127$	14.4311	−	12.1091i	1.28055	−	1.07451i	0.993168	−	0.116693i	$-0.0372293\pi$
$128$	0.993238	+	0.116093i	0.0877907	+	0.0102613i
$129$		0			0
$130$	−0.774964	+	0.821414i	−0.0679689	+	0.0720428i
$131$	13.3322	−	1.55832i	1.16484	−	0.136151i	0.488383	−	0.872629i	$-0.337587\pi$
$131$	13.3322	−	1.55832i	1.16484	−	0.136151i	0.676461	+	0.736479i	$0.263513\pi$
$132$		0			0
$133$	0.623154	+	10.6991i	0.0540343	+	0.927733i
$134$	1.90863	−	3.30585i	0.164881	−	0.285582i
$135$		0			0
$136$	3.28896	+	5.69665i	0.282026	+	0.488484i
$137$	−4.42901	+	2.91301i	−0.378396	+	0.248875i	−0.724432	−	0.689346i	$-0.757898\pi$
$137$	−4.42901	+	2.91301i	−0.378396	+	0.248875i	0.346036	+	0.938221i	$0.387528\pi$
$138$		0			0
$139$	−7.14865	+	16.5724i	−0.606340	+	1.40565i	0.287723	+	0.957714i	$0.407102\pi$
$139$	−7.14865	+	16.5724i	−0.606340	+	1.40565i	−0.894063	+	0.447941i	$0.852157\pi$
$140$	−3.35678	−	0.795571i	−0.283700	−	0.0672380i
$141$		0			0
$142$	4.62495	−	6.21238i	0.388117	−	0.521332i
$143$	2.01599	+	0.733761i	0.168586	+	0.0613601i
$144$		0			0
$145$	−14.3327	+	5.21667i	−1.19026	+	0.433221i
$146$	2.88937	−	9.65117i	0.239126	−	0.798737i
$147$		0			0
$148$	0.266550	−	4.57649i	0.0219103	−	0.376185i
$149$	14.7989	+	9.73339i	1.21237	+	0.797390i	0.984343	−	0.176264i	$-0.0564011\pi$
$149$	14.7989	+	9.73339i	1.21237	+	0.797390i	0.228030	+	0.973654i	$0.426771\pi$
$150$		0			0
$151$	−2.32779	+	0.551696i	−0.189433	+	0.0448964i	−0.324237	−	0.945976i	$-0.605108\pi$
$151$	−2.32779	+	0.551696i	−0.189433	+	0.0448964i	0.134804	+	0.990872i	$0.456959\pi$
$152$	−1.24925	+	7.08482i	−0.101327	+	0.574655i
$153$		0			0
$154$	1.13804	+	6.45415i	0.0917060	+	0.520091i
$155$	1.64374	+	3.81063i	0.132029	+	0.306077i
$156$		0			0
$157$	2.97910	+	9.95089i	0.237758	+	0.794167i	0.990698	+	0.136078i	$0.0434498\pi$
$157$	2.97910	+	9.95089i	0.237758	+	0.794167i	−0.752940	+	0.658089i	$0.771365\pi$
$158$	−10.0259	−	13.4672i	−0.797620	−	1.07139i
$159$		0			0
$160$	−2.06939	−	1.03929i	−0.163600	−	0.0821628i
$161$	−4.33845			−0.341917
$162$		0			0
$163$	−6.60659			−0.517468			−0.258734	−	0.965949i	$-0.583305\pi$
$163$	−6.60659			−0.517468			−0.258734	+	0.965949i	$0.583305\pi$
$164$	7.03828	+	3.53476i	0.549598	+	0.276018i
$165$		0			0
$166$	−3.10951	−	4.17680i	−0.241345	−	0.324183i
$167$	−1.98331	−	6.62473i	−0.153473	−	0.512637i	0.846326	−	0.532665i	$-0.178810\pi$
$167$	−1.98331	−	6.62473i	−0.153473	−	0.512637i	−0.999799	+	0.0200284i	$0.993624\pi$
$168$		0			0
$169$	−5.05484	−	11.7184i	−0.388834	−	0.901419i
$170$	−2.64510	−	15.0011i	−0.202870	−	1.15053i
$171$		0			0
$172$	0.0770323	−	0.436872i	0.00587365	−	0.0333112i
$173$	12.3276	−	2.92169i	0.937249	−	0.222132i	0.266516	−	0.963831i	$-0.414128\pi$
$173$	12.3276	−	2.92169i	0.937249	−	0.222132i	0.670734	+	0.741698i	$0.265979\pi$
$174$		0			0
$175$	0.451164	+	0.296735i	0.0341048	+	0.0224311i
$176$	−0.255795	+	4.39183i	−0.0192813	+	0.331047i
$177$		0			0
$178$	0.888457	−	2.96765i	0.0665926	−	0.222435i
$179$	0.951462	−	0.346304i	0.0711156	−	0.0258840i	−0.306217	−	0.951962i	$-0.599063\pi$
$179$	0.951462	−	0.346304i	0.0711156	−	0.0258840i	0.377333	+	0.926078i	$0.376841\pi$
$180$		0			0
$181$	14.7137	+	5.35534i	1.09366	+	0.398059i	0.824975	−	0.565169i	$-0.191189\pi$
$181$	14.7137	+	5.35534i	1.09366	+	0.398059i	0.268684	+	0.963228i	$0.413411\pi$
$182$	−0.433828	+	0.582733i	−0.0321575	+	0.0431950i
$183$		0			0
$184$	−2.83374	−	0.671609i	−0.208906	−	0.0495117i
$185$	−4.20469	+	9.74756i	−0.309135	+	0.716655i
$186$		0			0
$187$	−24.1774	+	15.9018i	−1.76803	+	1.16285i
$188$	−3.91064	−	6.77343i	−0.285213	−	0.494003i
$189$		0			0
$190$	8.32972	−	14.4275i	0.604301	−	1.04668i
$191$	0.257431	+	4.41992i	0.0186271	+	0.319814i	0.994732	+	0.102513i	$0.0326884\pi$
$191$	0.257431	+	4.41992i	0.0186271	+	0.319814i	−0.976105	+	0.217301i	$0.930275\pi$
$192$		0			0
$193$	−18.8735	+	2.20600i	−1.35855	+	0.158791i	−0.763972	−	0.645250i	$-0.776753\pi$
$193$	−18.8735	+	2.20600i	−1.35855	+	0.158791i	−0.594574	+	0.804041i	$0.702679\pi$
$194$	−0.966336	+	1.02426i	−0.0693789	+	0.0735373i
$195$		0			0
$196$	4.74839	+	0.555007i	0.339171	+	0.0396433i
$197$	17.3672	−	14.5728i	1.23736	−	1.03827i	0.239637	−	0.970863i	$-0.422972\pi$
$197$	17.3672	−	14.5728i	1.23736	−	1.03827i	0.997726	−	0.0674075i	$-0.0214728\pi$
$198$		0			0
$199$	−2.88695	−	2.42244i	−0.204650	−	0.171722i	0.534702	−	0.845041i	$-0.320424\pi$
$199$	−2.88695	−	2.42244i	−0.204650	−	0.171722i	−0.739352	+	0.673319i	$0.764868\pi$
$200$	0.248751	+	0.263661i	0.0175894	+	0.0186436i
$201$		0			0
$202$	−8.98134	+	4.51060i	−0.631925	+	0.317365i
$203$	−8.76848	+	4.40370i	−0.615427	+	0.309079i
$204$		0			0
$205$	−12.5161	−	13.2663i	−0.874160	−	0.926555i
$206$	1.28515	+	1.07837i	0.0895403	+	0.0751333i
$207$		0			0
$208$	−0.373573	+	0.313465i	−0.0259026	+	0.0217349i
$209$	−31.4349	−	3.67421i	−2.17440	−	0.254151i
$210$		0			0
$211$	9.04987	−	9.59230i	0.623019	−	0.660361i	−0.336606	−	0.941646i	$-0.609279\pi$
$211$	9.04987	−	9.59230i	0.623019	−	0.660361i	0.959624	+	0.281284i	$0.0907604\pi$
$212$	−1.95537	+	0.228550i	−0.134295	+	0.0156969i
$213$		0			0
$214$	−0.716594	−	12.3034i	−0.0489853	−	0.841046i
$215$	−0.513636	+	0.889644i	−0.0350297	+	0.0606732i
$216$		0			0
$217$	1.33489	+	2.31210i	0.0906182	+	0.156955i
$218$	−15.9505	+	10.4908i	−1.08030	+	0.710527i
$219$		0			0
$220$	4.03503	−	9.35425i	0.272042	−	0.630663i
$221$	−3.12136	−	0.739775i	−0.209965	−	0.0497627i
$222$		0			0
$223$	−4.24353	+	5.70006i	−0.284168	+	0.381704i	−0.921171	−	0.389157i	$-0.872766\pi$
$223$	−4.24353	+	5.70006i	−0.284168	+	0.381704i	0.637003	+	0.770861i	$0.280174\pi$
$224$	−1.39989	−	0.509517i	−0.0935338	−	0.0340435i
$225$		0			0
$226$	−7.57128	+	2.75572i	−0.503634	+	0.183308i
$227$	−0.642640	+	2.14657i	−0.0426535	+	0.142473i	−0.976664	−	0.214773i	$-0.931099\pi$
$227$	−0.642640	+	2.14657i	−0.0426535	+	0.142473i	0.934011	+	0.357246i	$0.116284\pi$
$228$		0			0
$229$	0.903744	−	15.5167i	0.0597211	−	1.02537i	−0.826745	−	0.562577i	$-0.809810\pi$
$229$	0.903744	−	15.5167i	0.0597211	−	1.02537i	0.886466	−	0.462794i	$-0.153153\pi$
$230$	5.63444	+	3.70583i	0.371524	+	0.244355i
$231$		0			0
$232$	−6.40902	+	1.51897i	−0.420773	+	0.0997250i
$233$	−1.36995	+	7.76937i	−0.0897483	+	0.508988i	0.906482	+	0.422244i	$0.138757\pi$
$233$	−1.36995	+	7.76937i	−0.0897483	+	0.508988i	−0.996231	+	0.0867442i	$0.972354\pi$
$234$		0			0
$235$	3.14508	+	17.8366i	0.205162	+	1.16353i
$236$	−5.03290	−	11.6676i	−0.327614	−	0.759494i
$237$		0			0
$238$	−2.81048	−	9.38764i	−0.182176	−	0.608511i
$239$	−3.07871	−	4.13542i	−0.199145	−	0.267498i	0.691321	−	0.722548i	$-0.257029\pi$
$239$	−3.07871	−	4.13542i	−0.199145	−	0.267498i	−0.890466	+	0.455049i	$0.849622\pi$
$240$		0			0
$241$	−1.85788	−	0.933061i	−0.119676	−	0.0601038i	0.387954	−	0.921679i	$-0.373182\pi$
$241$	−1.85788	−	0.933061i	−0.119676	−	0.0601038i	−0.507630	+	0.861575i	$0.669478\pi$
$242$	−8.35362			−0.536991
$243$		0			0
$244$	7.71220			0.493723
$245$	−9.89315	−	4.96853i	−0.632050	−	0.317428i
$246$		0			0
$247$	−2.09502	−	2.81410i	−0.133303	−	0.179057i
$248$	0.513987	+	1.71684i	0.0326382	+	0.109019i
$249$		0			0
$250$	4.25355	+	9.86083i	0.269018	+	0.623654i
$251$	−3.84832	−	21.8249i	−0.242904	−	1.37757i	−0.825311	−	0.564678i	$-0.809000\pi$
$251$	−3.84832	−	21.8249i	−0.242904	−	1.37757i	0.582408	−	0.812897i	$-0.302111\pi$
$252$		0			0
$253$	2.22474	−	12.6171i	0.139868	−	0.793231i
$254$	−18.3306	+	4.34444i	−1.15017	+	0.272594i
$255$		0			0
$256$	−0.835488	−	0.549509i	−0.0522180	−	0.0343443i
$257$	0.653529	−	11.2207i	0.0407660	−	0.699925i	−0.914574	−	0.404418i	$-0.867474\pi$
$257$	0.653529	−	11.2207i	0.0407660	−	0.699925i	0.955340	−	0.295507i	$-0.0954887\pi$
$258$		0			0
$259$	−1.95866	+	6.54238i	−0.121705	+	0.406524i
$260$	1.06118	−	0.386239i	0.0658118	−	0.0239535i
$261$		0			0
$262$	−12.6135	−	4.59094i	−0.779264	−	0.283629i
$263$	−0.769213	+	1.03323i	−0.0474317	+	0.0637118i	−0.825206	−	0.564832i	$-0.808941\pi$
$263$	−0.769213	+	1.03323i	−0.0474317	+	0.0637118i	0.777775	+	0.628543i	$0.216349\pi$
$264$		0			0
$265$	4.43599	+	1.05135i	0.272501	+	0.0645839i
$266$	4.24489	−	9.84077i	0.260271	−	0.603376i
$267$		0			0
$268$	−3.18928	+	2.09762i	−0.194816	+	0.128133i
$269$	8.37641	+	14.5084i	0.510719	+	0.884591i	0.999923	+	0.0124213i	$0.00395392\pi$
$269$	8.37641	+	14.5084i	0.510719	+	0.884591i	−0.489204	+	0.872169i	$0.662713\pi$
$270$		0			0
$271$	−13.9516	+	24.1649i	−0.847502	+	1.46792i	0.0359290	+	0.999354i	$0.488561\pi$
$271$	−13.9516	+	24.1649i	−0.847502	+	1.46792i	−0.883431	+	0.468562i	$0.844772\pi$
$272$	−0.382472	−	6.56680i	−0.0231908	−	0.398171i
$273$		0			0
$274$	5.26526	−	0.615421i	0.318086	−	0.0371790i
$275$	−1.09432	+	1.15992i	−0.0659902	+	0.0699456i
$276$		0			0
$277$	3.12877	+	0.365701i	0.187990	+	0.0219728i	0.209567	−	0.977794i	$-0.432795\pi$
$277$	3.12877	+	0.365701i	0.187990	+	0.0219728i	−0.0215771	+	0.999767i	$0.506869\pi$
$278$	13.8260	−	11.6014i	0.829226	−	0.695803i
$279$		0			0
$280$	2.64267	+	2.21747i	0.157930	+	0.132519i
$281$	0.756901	+	0.802268i	0.0451529	+	0.0478593i	0.749556	−	0.661941i	$-0.230267\pi$
$281$	0.756901	+	0.802268i	0.0451529	+	0.0478593i	−0.704403	+	0.709800i	$0.748785\pi$
$282$		0			0
$283$	28.2064	−	14.1658i	1.67670	−	0.842068i	0.682941	−	0.730473i	$-0.260700\pi$
$283$	28.2064	−	14.1658i	1.67670	−	0.842068i	0.993754	−	0.111595i	$-0.0355959\pi$
$284$	−6.92112	+	3.47592i	−0.410693	+	0.206258i
$285$		0			0
$286$	−1.47224	−	1.56049i	−0.0870556	−	0.0922736i
$287$	−8.98811	−	7.54192i	−0.530551	−	0.445186i
$288$		0			0
$289$	20.1233	−	16.8855i	1.18372	−	0.993263i
$290$	15.1494	+	1.77071i	0.889603	+	0.103980i
$291$		0			0
$292$	−6.91347	+	7.32785i	−0.404580	+	0.428830i
$293$	28.2115	−	3.29745i	1.64813	−	0.192639i	0.759258	−	0.650790i	$-0.225562\pi$
$293$	28.2115	−	3.29745i	1.64813	−	0.192639i	0.888874	+	0.458151i	$0.151488\pi$
$294$		0			0
$295$	1.71092	+	29.3753i	0.0996135	+	1.71030i
$296$	−2.29212	+	3.97008i	−0.133227	+	0.230756i
$297$		0			0
$298$	−8.85644	−	15.3398i	−0.513040	−	0.888611i
$299$	1.18656	−	0.780412i	0.0686204	−	0.0451324i
$300$		0			0
$301$	−0.261753	+	0.606812i	−0.0150872	+	0.0349761i
$302$	2.32779	+	0.551696i	0.133949	+	0.0317465i
$303$		0			0
$304$	4.29603	−	5.77057i	0.246394	−	0.330965i
$305$	−16.7821	−	6.10819i	−0.960942	−	0.349754i
$306$		0			0
$307$	−28.0570	+	10.2119i	−1.60130	+	0.582824i	−0.979692	−	0.200507i	$-0.935741\pi$
$307$	−28.0570	+	10.2119i	−1.60130	+	0.582824i	−0.621604	+	0.783332i	$0.713519\pi$
$308$	1.87963	−	6.27839i	0.107102	−	0.357745i
$309$		0			0
$310$	0.241303	−	4.14301i	0.0137051	−	0.235307i
$311$	−1.52200	−	1.00103i	−0.0863046	−	0.0567634i	0.505623	−	0.862754i	$-0.331263\pi$
$311$	−1.52200	−	1.00103i	−0.0863046	−	0.0567634i	−0.591928	+	0.805991i	$0.701633\pi$
$312$		0			0
$313$	−4.20142	+	0.995754i	−0.237478	+	0.0562833i	−0.347631	−	0.937631i	$-0.613014\pi$
$313$	−4.20142	+	0.995754i	−0.237478	+	0.0562833i	0.110153	+	0.993915i	$0.464866\pi$
$314$	1.80373	−	10.2295i	0.101790	−	0.577282i
$315$		0			0
$316$	2.91545	+	16.5343i	0.164007	+	0.930128i
$317$	−12.9195	−	29.9507i	−0.725630	−	1.68220i	−0.731152	−	0.682215i	$-0.761017\pi$
$317$	−12.9195	−	29.9507i	−0.725630	−	1.68220i	0.00552184	−	0.999985i	$-0.498242\pi$
$318$		0			0
$319$	−8.31044	−	27.7588i	−0.465295	−	1.55419i
$320$	1.38284	+	1.85748i	0.0773032	+	0.103836i
$321$		0			0
$322$	3.87698	+	1.94709i	0.216055	+	0.108507i
$323$	47.3224			2.63309
$324$		0			0
$325$	−0.176770			−0.00980546
$326$	5.90386	+	2.96503i	0.326985	+	0.164218i
$327$		0			0
$328$	−4.70324	−	6.31755i	−0.259693	−	0.348828i
$329$	3.34171	+	11.1621i	0.184234	+	0.615386i
$330$		0			0
$331$	−3.78788	−	8.78130i	−0.208201	−	0.482664i	0.781834	−	0.623487i	$-0.214284\pi$
$331$	−3.78788	−	8.78130i	−0.208201	−	0.482664i	−0.990035	+	0.140823i	$0.955025\pi$
$332$	0.904218	+	5.12807i	0.0496254	+	0.281440i
$333$		0			0
$334$	−1.20082	+	6.81018i	−0.0657059	+	0.372637i
$335$	8.60138	−	2.03856i	0.469944	−	0.111379i
$336$		0			0
$337$	−13.9009	−	9.14276i	−0.757230	−	0.498038i	0.111232	−	0.993794i	$-0.464520\pi$
$337$	−13.9009	−	9.14276i	−0.757230	−	0.498038i	−0.868461	+	0.495757i	$0.834891\pi$
$338$	−0.742055	+	12.7406i	−0.0403625	+	0.692997i
$339$		0			0
$340$	−4.36874	+	14.5926i	−0.236928	+	0.791395i
$341$	−7.40859	+	2.69651i	−0.401198	+	0.146024i
$342$		0			0
$343$	−16.4917	−	6.00247i	−0.890465	−	0.324103i
$344$	−0.264906	+	0.355831i	−0.0142828	+	0.0191851i
$345$		0			0
$346$	−12.3276	−	2.92169i	−0.662735	−	0.157071i
$347$	−9.89690	+	22.9436i	−0.531294	+	1.23168i	0.415429	+	0.909626i	$0.363632\pi$
$347$	−9.89690	+	22.9436i	−0.531294	+	1.23168i	−0.946722	+	0.322051i	$0.895628\pi$
$348$		0			0
$349$	17.1526	−	11.2815i	0.918160	−	0.603884i	−3.99838e−5	−	1.00000i	$-0.500013\pi$
$349$	17.1526	−	11.2815i	0.918160	−	0.603884i	0.918200	+	0.396116i	$0.129642\pi$
$350$	−0.270001	−	0.467655i	−0.0144321	−	0.0249972i
$351$		0			0
$352$	2.19964	−	3.80988i	0.117241	−	0.203067i
$353$	1.05164	+	18.0559i	0.0559731	+	0.961021i	0.903046	+	0.429544i	$0.141326\pi$
$353$	1.05164	+	18.0559i	0.0559731	+	0.961021i	−0.847073	+	0.531477i	$0.821637\pi$
$354$		0			0
$355$	17.8137	−	2.08212i	0.945452	−	0.110507i
$356$	−2.12583	+	2.25325i	−0.112669	+	0.119422i
$357$		0			0
$358$	−1.00568	−	0.117547i	−0.0531518	−	0.00621255i
$359$	−23.7236	+	19.9065i	−1.25209	+	1.05062i	−0.255607	+	0.966781i	$0.582275\pi$
$359$	−23.7236	+	19.9065i	−1.25209	+	1.05062i	−0.996479	+	0.0838438i	$0.973280\pi$
$360$		0			0
$361$	25.0920	+	21.0547i	1.32063	+	1.10814i
$362$	−10.7452	−	11.3892i	−0.564753	−	0.598603i
$363$		0			0
$364$	0.649213	−	0.326047i	0.0340280	−	0.0170895i
$365$	20.8479	−	10.4702i	1.09123	−	0.548034i
$366$		0			0
$367$	−5.49865	−	5.82823i	−0.287027	−	0.304231i	0.567776	−	0.823183i	$-0.307804\pi$
$367$	−5.49865	−	5.82823i	−0.287027	−	0.304231i	−0.854803	+	0.518952i	$0.826322\pi$
$368$	2.23091	+	1.87195i	0.116294	+	0.0975823i
$369$		0			0
$370$	8.13214	−	6.82368i	0.422770	−	0.354746i
$371$	2.91296	+	0.340477i	0.151234	+	0.0176767i
$372$		0			0
$373$	−15.3339	+	16.2530i	−0.793962	+	0.841550i	−0.990294	−	0.138987i	$-0.955615\pi$
$373$	−15.3339	+	16.2530i	−0.793962	+	0.841550i	0.196332	+	0.980537i	$0.437097\pi$
$374$	28.7424	−	3.35951i	1.48624	−	0.173716i
$375$		0			0
$376$	0.454767	+	7.80805i	0.0234528	+	0.402670i
$377$	1.60602	−	2.78170i	0.0827141	−	0.143265i
$378$		0			0
$379$	10.1868	+	17.6441i	0.523262	+	0.906317i	0.999633	+	0.0270727i	$0.00861857\pi$
$379$	10.1868	+	17.6441i	0.523262	+	0.906317i	−0.476371	+	0.879244i	$0.658048\pi$
$380$	−13.9188	+	9.15451i	−0.714017	+	0.469617i
$381$		0			0
$382$	1.75361	−	4.06532i	0.0897224	−	0.208000i
$383$	−2.46010	−	0.583054i	−0.125705	−	0.0297927i	0.167282	−	0.985909i	$-0.446501\pi$
$383$	−2.46010	−	0.583054i	−0.125705	−	0.0297927i	−0.292987	+	0.956116i	$0.594649\pi$
$384$		0			0
$385$	−9.06276	+	12.1734i	−0.461881	+	0.620414i
$386$	17.8560	+	6.49907i	0.908848	+	0.330794i
$387$		0			0
$388$	1.32323	−	0.481618i	0.0671771	−	0.0244505i
$389$	−4.54869	+	15.1937i	−0.230628	+	0.770350i	0.761832	+	0.647775i	$0.224300\pi$
$389$	−4.54869	+	15.1937i	−0.230628	+	0.770350i	−0.992459	+	0.122575i	$0.960885\pi$
$390$		0			0
$391$	−1.11385	+	19.1241i	−0.0563299	+	0.967148i
$392$	−3.99423	−	2.62704i	−0.201739	−	0.132686i
$393$		0			0
$394$	−22.0602	+	5.22836i	−1.11138	+	0.263401i
$395$	6.75131	−	38.2886i	0.339695	−	1.92651i
$396$		0			0
$397$	5.19212	+	29.4460i	0.260585	+	1.47785i	0.781319	+	0.624132i	$0.214547\pi$
$397$	5.19212	+	29.4460i	0.260585	+	1.47785i	−0.520734	+	0.853719i	$0.674341\pi$
$398$	1.49268	+	3.46043i	0.0748214	+	0.173456i
$399$		0			0
$400$	−0.103961	−	0.347255i	−0.00519807	−	0.0173628i
$401$	5.58127	+	7.49695i	0.278715	+	0.374380i	0.919333	−	0.393480i	$-0.128729\pi$
$401$	5.58127	+	7.49695i	0.278715	+	0.374380i	−0.640618	+	0.767860i	$0.721322\pi$
$402$		0			0
$403$	−0.780997	−	0.392231i	−0.0389042	−	0.0195384i
$404$	10.0504			0.500025
$405$		0			0
$406$	9.81218			0.486970
$407$	−18.0222	−	9.05110i	−0.893328	−	0.448646i
$408$		0			0
$409$	−0.379338	−	0.509540i	−0.0187571	−	0.0251951i	0.792646	−	0.609683i	$-0.208703\pi$
$409$	−0.379338	−	0.509540i	−0.0187571	−	0.0251951i	−0.811403	+	0.584487i	$0.801296\pi$
$410$	5.23088	+	17.4724i	0.258335	+	0.862898i
$411$		0			0
$412$	−0.664479	−	1.54043i	−0.0327365	−	0.0758918i
$413$	3.28709	+	18.6420i	0.161747	+	0.917315i
$414$		0			0
$415$	2.09390	−	11.8751i	0.102786	−	0.582926i
$416$	0.474520	−	0.112463i	0.0232653	−	0.00551397i
$417$		0			0
$418$	26.4423	+	17.3914i	1.29333	+	0.850639i
$419$	−0.398563	+	6.84305i	−0.0194711	+	0.334305i	0.974479	+	0.224477i	$0.0720672\pi$
$419$	−0.398563	+	6.84305i	−0.0194711	+	0.334305i	−0.993951	+	0.109829i	$0.964970\pi$
$420$		0			0
$421$	6.42595	−	21.4642i	0.313182	−	1.04610i	−0.646007	−	0.763332i	$-0.723562\pi$
$421$	6.42595	−	21.4642i	0.313182	−	1.04610i	0.959188	−	0.282768i	$-0.0912526\pi$
$422$	−12.3923	+	4.51042i	−0.603247	+	0.219564i
$423$		0			0
$424$	1.84995	+	0.673328i	0.0898417	+	0.0326997i
$425$	1.42386	−	1.91257i	0.0690673	−	0.0927734i
$426$		0			0
$427$	−11.1794	−	2.64956i	−0.541008	−	0.128221i
$428$	−4.88140	+	11.3164i	−0.235951	+	0.546997i
$429$		0			0
$430$	0.858273	−	0.564495i	0.0413896	−	0.0272224i
$431$	−7.62700	−	13.2103i	−0.367379	−	0.636320i	0.621776	−	0.783196i	$-0.286412\pi$
$431$	−7.62700	−	13.2103i	−0.367379	−	0.636320i	−0.989155	+	0.146876i	$0.953078\pi$
$432$		0			0
$433$	8.83327	−	15.2997i	0.424500	−	0.735255i	−0.571874	−	0.820342i	$-0.693783\pi$
$433$	8.83327	−	15.2997i	0.424500	−	0.735255i	0.996374	+	0.0850866i	$0.0271167\pi$
$434$	−0.155234	−	2.66526i	−0.00745146	−	0.127937i
$435$		0			0
$436$	18.9622	−	2.21636i	0.908123	−	0.106144i
$437$	−14.3775	+	15.2392i	−0.687767	+	0.728990i
$438$		0			0
$439$	23.6609	+	2.76556i	1.12927	+	0.131993i	0.660146	−	0.751137i	$-0.270494\pi$
$439$	23.6609	+	2.76556i	1.12927	+	0.131993i	0.469127	+	0.883131i	$0.344569\pi$
$440$	−7.80401	+	6.54835i	−0.372042	+	0.312180i
$441$		0			0
$442$	2.45734	+	2.06195i	0.116884	+	0.0980770i
$443$	−10.1320	−	10.7393i	−0.481385	−	0.510239i	0.440473	−	0.897766i	$-0.354811\pi$
$443$	−10.1320	−	10.7393i	−0.481385	−	0.510239i	−0.921858	+	0.387527i	$0.873329\pi$
$444$		0			0
$445$	6.41053	−	3.21949i	0.303888	−	0.152619i
$446$	6.35034	−	3.18926i	0.300697	−	0.151016i
$447$		0			0
$448$	1.02231	+	1.08359i	0.0482997	+	0.0511947i
$449$	8.26585	+	6.93587i	0.390090	+	0.327324i	0.816648	−	0.577136i	$-0.195830\pi$
$449$	8.26585	+	6.93587i	0.390090	+	0.327324i	−0.426558	+	0.904460i	$0.640274\pi$
$450$		0			0
$451$	26.5426	−	22.2719i	1.24984	−	1.04874i
$452$	8.00271	+	0.935383i	0.376416	+	0.0439967i
$453$		0			0
$454$	1.53766	−	1.62983i	0.0721660	−	0.0764915i
$455$	−1.67096	+	0.195307i	−0.0783356	+	0.00915612i
$456$		0			0
$457$	−1.75430	−	30.1202i	−0.0820627	−	1.40896i	−0.748368	−	0.663284i	$-0.769162\pi$
$457$	−1.75430	−	30.1202i	−0.0820627	−	1.40896i	0.666305	−	0.745679i	$-0.267875\pi$
$458$	−7.77149	+	13.4606i	−0.363138	+	0.628974i
$459$		0			0
$460$	−3.37194	−	5.84038i	−0.157218	−	0.272309i
$461$	16.9882	−	11.1733i	0.791219	−	0.520393i	−0.0883926	−	0.996086i	$-0.528173\pi$
$461$	16.9882	−	11.1733i	0.791219	−	0.520393i	0.879611	+	0.475693i	$0.157803\pi$
$462$		0			0
$463$	8.36162	−	19.3844i	0.388597	−	0.900870i	−0.605845	−	0.795583i	$-0.707165\pi$
$463$	8.36162	−	19.3844i	0.388597	−	0.900870i	0.994442	−	0.105287i	$-0.0335760\pi$
$464$	6.40902	+	1.51897i	0.297531	+	0.0705162i
$465$		0			0
$466$	4.71112	−	6.32813i	0.218238	−	0.293145i
$467$	−16.2329	−	5.90831i	−0.751171	−	0.273404i	−0.0620726	−	0.998072i	$-0.519771\pi$
$467$	−16.2329	−	5.90831i	−0.751171	−	0.273404i	−0.689098	+	0.724668i	$0.741993\pi$
$468$		0			0
$469$	5.34374	−	1.94496i	0.246751	−	0.0898099i
$470$	5.19452	−	17.3509i	0.239605	−	0.800337i
$471$		0			0
$472$	−0.738833	+	12.6853i	−0.0340076	+	0.583887i
$473$	−1.63051	−	1.07240i	−0.0749710	−	0.0493092i
$474$		0			0
$475$	2.53745	−	0.601388i	0.116426	−	0.0275936i
$476$	−1.70163	+	9.65044i	−0.0779943	+	0.442327i
$477$		0			0
$478$	0.895260	+	5.07727i	0.0409482	+	0.232229i
$479$	8.46394	+	19.6216i	0.386727	+	0.896534i	0.994723	+	0.102594i	$0.0327144\pi$
$479$	8.46394	+	19.6216i	0.386727	+	0.896534i	−0.607996	+	0.793940i	$0.708026\pi$
$480$		0			0
$481$	−0.641171	−	2.14166i	−0.0292349	−	0.0976513i
$482$	1.24150	+	1.66763i	0.0565489	+	0.0759584i
$483$		0			0
$484$	7.46507	+	3.74910i	0.339321	+	0.170414i
$485$	−3.26087			−0.148069
$486$		0			0
$487$	−11.1991			−0.507482			−0.253741	−	0.967272i	$-0.581661\pi$
$487$	−11.1991			−0.507482			−0.253741	+	0.967272i	$0.581661\pi$
$488$	−6.89187	−	3.46123i	−0.311980	−	0.156682i
$489$		0			0
$490$	6.61097	+	8.88008i	0.298653	+	0.401161i
$491$	2.57840	+	8.61245i	0.116361	+	0.388674i	0.996252	−	0.0865028i	$-0.0275692\pi$
$491$	2.57840	+	8.61245i	0.116361	+	0.388674i	−0.879890	+	0.475177i	$0.842384\pi$
$492$		0			0
$493$	17.1605	+	39.7826i	0.772871	+	1.79172i
$494$	0.609213	+	3.45502i	0.0274098	+	0.155449i
$495$		0			0
$496$	0.311199	−	1.76490i	0.0139733	−	0.0792463i
$497$	11.2268	−	2.66081i	0.503592	−	0.119353i
$498$		0			0
$499$	−1.29086	−	0.849012i	−0.0577868	−	0.0380070i	0.520287	−	0.853992i	$-0.325825\pi$
$499$	−1.29086	−	0.849012i	−0.0577868	−	0.0380070i	−0.578074	+	0.815985i	$0.696195\pi$
$500$	0.624424	−	10.7209i	0.0279251	−	0.479455i
$501$		0			0
$502$	−6.35601	+	21.2306i	−0.283683	+	0.947566i
$503$	8.36142	−	3.04331i	0.372817	−	0.135694i	−0.148815	−	0.988865i	$-0.547546\pi$
$503$	8.36142	−	3.04331i	0.372817	−	0.135694i	0.521632	+	0.853171i	$0.325324\pi$
$504$		0			0
$505$	−21.8701	−	7.96007i	−0.973207	−	0.354219i
$506$	−7.65065	+	10.2766i	−0.340113	+	0.456851i
$507$		0			0
$508$	18.3306	+	4.34444i	0.813290	+	0.192753i
$509$	−5.04282	+	11.6906i	−0.223519	+	0.518176i	−0.992665	−	0.120898i	$-0.961423\pi$
$509$	−5.04282	+	11.6906i	−0.223519	+	0.518176i	0.769146	+	0.639073i	$0.220682\pi$
$510$		0			0
$511$	12.5391	−	8.24709i	0.554697	−	0.364830i
$512$	0.500000	+	0.866025i	0.0220971	+	0.0382733i
$513$		0			0
$514$	−5.61983	+	9.73384i	−0.247880	+	0.429341i
$515$	0.225888	+	3.87834i	0.00995380	+	0.170900i
$516$		0			0
$517$	−34.1753	+	3.99452i	−1.50303	+	0.175679i
$518$	4.68654	−	4.96744i	0.205915	−	0.218257i
$519$		0			0
$520$	−1.12165	−	0.131102i	−0.0491877	−	0.00574922i
$521$	−13.0420	+	10.9435i	−0.571380	+	0.479445i	−0.882104	−	0.471056i	$-0.843873\pi$
$521$	−13.0420	+	10.9435i	−0.571380	+	0.479445i	0.310724	+	0.950500i	$0.399429\pi$
$522$		0			0
$523$	−12.6277	−	10.5959i	−0.552172	−	0.463327i	0.323504	−	0.946227i	$-0.395139\pi$
$523$	−12.6277	−	10.5959i	−0.552172	−	0.463327i	−0.875676	+	0.482900i	$0.839584\pi$
$524$	9.21142	+	9.76354i	0.402403	+	0.426522i
$525$		0			0
$526$	1.15111	−	0.578108i	0.0501907	−	0.0252067i
$527$	10.5346	−	5.29066i	0.458893	−	0.230465i
$528$		0			0
$529$	9.96344	+	10.5606i	0.433193	+	0.459158i
$530$	−3.49230	−	2.93039i	−0.151696	−	0.127288i
$531$		0			0
$532$	−8.20991	+	6.88893i	−0.355945	+	0.298673i
$533$	3.81490	+	0.445898i	0.165242	+	0.0193140i
$534$		0			0
$535$	19.5849	−	20.7588i	0.846730	−	0.897482i
$536$	3.79145	−	0.443157i	0.163766	−	0.0191415i
$537$		0			0
$538$	−0.974090	−	16.7245i	−0.0419960	−	0.721043i
$539$	10.5158	−	18.2140i	0.452949	−	0.784531i
$540$		0			0
$541$	22.2115	+	38.4714i	0.954947	+	1.65402i	0.734490	+	0.678620i	$0.237422\pi$
$541$	22.2115	+	38.4714i	0.954947	+	1.65402i	0.220457	+	0.975397i	$0.429245\pi$
$542$	23.3128	−	15.3331i	1.00137	−	0.658613i
$543$		0			0
$544$	−2.60538	+	6.03996i	−0.111705	+	0.258961i
$545$	−43.0180	−	10.1954i	−1.84269	−	0.436725i
$546$		0			0
$547$	7.39145	−	9.92844i	0.316036	−	0.424509i	−0.615513	−	0.788127i	$-0.711051\pi$
$547$	7.39145	−	9.92844i	0.316036	−	0.424509i	0.931548	+	0.363617i	$0.118458\pi$
$548$	−4.98141	−	1.81309i	−0.212795	−	0.0774512i
$549$		0			0
$550$	1.49849	−	0.545407i	0.0638960	−	0.0232562i
$551$	−13.5900	+	45.3938i	−0.578954	+	1.93384i
$552$		0			0
$553$	1.45430	−	24.9693i	0.0618429	−	1.06180i
$554$	−2.63185	−	1.73099i	−0.111816	−	0.0735428i
$555$		0			0
$556$	−17.5620	+	4.16227i	−0.744795	+	0.176520i
$557$	−1.00425	+	5.69536i	−0.0425512	+	0.241320i	−0.998664	−	0.0516799i	$-0.983542\pi$
$557$	−1.00425	+	5.69536i	−0.0425512	+	0.241320i	0.956112	+	0.293000i	$0.0946536\pi$
$558$		0			0
$559$	−0.0375659	−	0.213047i	−0.00158887	−	0.00901093i
$560$	−1.36638	−	3.16763i	−0.0577402	−	0.133857i
$561$		0			0
$562$	−0.316334	−	1.05663i	−0.0133438	−	0.0445712i
$563$	0.346453	+	0.465367i	0.0146013	+	0.0196129i	0.809364	−	0.587308i	$-0.199812\pi$
$563$	0.346453	+	0.465367i	0.0146013	+	0.0196129i	−0.794763	+	0.606920i	$0.792405\pi$
$564$		0			0
$565$	−16.6735	−	8.37373i	−0.701458	−	0.352285i
$566$	−31.5637			−1.32672
$567$		0			0
$568$	7.74492			0.324970
$569$	6.61617	+	3.32276i	0.277364	+	0.139298i	0.582044	−	0.813157i	$-0.302253\pi$
$569$	6.61617	+	3.32276i	0.277364	+	0.139298i	−0.304680	+	0.952455i	$0.598549\pi$
$570$		0			0
$571$	−13.5093	−	18.1461i	−0.565346	−	0.759391i	0.423891	−	0.905713i	$-0.360664\pi$
$571$	−13.5093	−	18.1461i	−0.565346	−	0.759391i	−0.989237	+	0.146322i	$0.953256\pi$
$572$	0.615300	+	2.05524i	0.0257270	+	0.0859341i
$573$		0			0
$574$	4.64726	+	10.7736i	0.193973	+	0.449680i
$575$	0.183310	+	1.03960i	0.00764455	+	0.0433544i
$576$		0			0
$577$	2.27449	−	12.8993i	0.0946884	−	0.537004i	−0.900154	−	0.435572i	$-0.856546\pi$
$577$	2.27449	−	12.8993i	0.0946884	−	0.537004i	0.994842	−	0.101433i	$-0.0323427\pi$
$578$	−25.5610	+	6.05808i	−1.06320	+	0.251983i
$579$		0			0
$580$	−12.7433	−	8.38140i	−0.529137	−	0.348019i
$581$	0.451046	−	7.74416i	0.0187125	−	0.321282i
$582$		0			0
$583$	−2.48393	+	8.29692i	−0.102874	+	0.343623i
$584$	9.46684	−	3.44565i	0.391741	−	0.142582i
$585$		0			0
$586$	−26.6906	−	9.71458i	−1.10258	−	0.401306i
$587$	−16.7999	+	22.5661i	−0.693404	+	0.931403i	−0.999790	−	0.0205040i	$-0.993473\pi$
$587$	−16.7999	+	22.5661i	−0.693404	+	0.931403i	0.306386	+	0.951907i	$0.400880\pi$
$588$		0			0
$589$	12.5452	+	2.97328i	0.516917	+	0.122512i
$590$	11.6547	−	27.0186i	0.479816	−	1.11234i
$591$		0			0
$592$	3.83008	−	2.51909i	0.157415	−	0.103534i
$593$	0.451178	+	0.781463i	0.0185276	+	0.0320908i	0.875141	−	0.483869i	$-0.160769\pi$
$593$	0.451178	+	0.781463i	0.0185276	+	0.0320908i	−0.856613	+	0.515960i	$0.827435\pi$
$594$		0			0
$595$	11.3462	−	19.6521i	0.465147	−	0.805658i
$596$	1.02991	+	17.6829i	0.0421869	+	0.724321i
$597$		0			0
$598$	−1.41060	+	0.164875i	−0.0576835	+	0.00674224i
$599$	12.4157	−	13.1599i	0.507292	−	0.537698i	−0.422218	−	0.906494i	$-0.638748\pi$
$599$	12.4157	−	13.1599i	0.507292	−	0.537698i	0.929510	+	0.368796i	$0.120230\pi$
$600$		0			0
$601$	−33.5660	−	3.92330i	−1.36918	−	0.160035i	−0.600480	−	0.799640i	$-0.705024\pi$
$601$	−33.5660	−	3.92330i	−1.36918	−	0.160035i	−0.768704	+	0.639605i	$0.779098\pi$
$602$	0.506248	−	0.424792i	0.0206331	−	0.0173132i
$603$		0			0
$604$	−1.83259	−	1.53772i	−0.0745669	−	0.0625690i
$605$	−13.2750	−	14.0707i	−0.539706	−	0.572055i
$606$		0			0
$607$	−15.0269	+	7.54680i	−0.609924	+	0.306315i	−0.726819	−	0.686829i	$-0.759002\pi$
$607$	−15.0269	+	7.54680i	−0.609924	+	0.306315i	0.116895	+	0.993144i	$0.462706\pi$
$608$	−6.42890	+	3.22871i	−0.260726	+	0.130942i
$609$		0			0
$610$	12.2557	+	12.9903i	0.496219	+	0.525961i
$611$	−2.92182	−	2.45170i	−0.118204	−	0.0991851i
$612$		0			0
$613$	9.62863	−	8.07938i	0.388897	−	0.326323i	−0.427287	−	0.904116i	$-0.640530\pi$
$613$	9.62863	−	8.07938i	0.388897	−	0.326323i	0.816183	+	0.577793i	$0.196086\pi$
$614$	29.6557	+	3.46626i	1.19681	+	0.139887i
$615$		0			0
$616$	−4.49744	+	4.76700i	−0.181207	+	0.192068i
$617$	−19.1926	+	2.24329i	−0.772663	+	0.0903114i	−0.493283	−	0.869869i	$-0.664203\pi$
$617$	−19.1926	+	2.24329i	−0.772663	+	0.0903114i	−0.279381	+	0.960180i	$0.590129\pi$
$618$		0			0
$619$	−0.922443	−	15.8377i	−0.0370761	−	0.636572i	−0.964748	−	0.263176i	$-0.915230\pi$
$619$	−0.922443	−	15.8377i	−0.0370761	−	0.636572i	0.927672	−	0.373397i	$-0.121807\pi$
$620$	−2.07502	+	3.59403i	−0.0833347	+	0.144340i
$621$		0			0
$622$	0.910844	+	1.57763i	0.0365215	+	0.0632571i
$623$	3.85566	−	2.53591i	0.154474	−	0.101599i
$624$		0			0
$625$	−10.5678	+	24.4989i	−0.422713	+	0.979958i
$626$	4.20142	+	0.995754i	0.167922	+	0.0397983i
$627$		0			0
$628$	−6.20284	+	8.33186i	−0.247520	+	0.332478i
$629$	28.3363	+	10.3136i	1.12984	+	0.411229i
$630$		0			0
$631$	−17.8744	+	6.50576i	−0.711570	+	0.258990i	−0.672343	−	0.740240i	$-0.734712\pi$
$631$	−17.8744	+	6.50576i	−0.711570	+	0.258990i	−0.0392270	+	0.999230i	$0.512490\pi$
$632$	4.81525	−	16.0841i	0.191540	−	0.639789i
$633$		0			0
$634$	−1.89659	+	32.5632i	−0.0753232	+	1.29325i
$635$	−36.4475	−	23.9719i	−1.44637	−	0.951295i
$636$		0			0
$637$	2.26854	−	0.537655i	0.0898830	−	0.0213027i
$638$	−5.03165	+	28.5359i	−0.199205	+	1.12975i
$639$		0			0
$640$	−0.402118	−	2.28052i	−0.0158951	−	0.0901456i
$641$	−3.51399	−	8.14633i	−0.138794	−	0.321761i	0.834615	−	0.550833i	$-0.185690\pi$
$641$	−3.51399	−	8.14633i	−0.138794	−	0.321761i	−0.973409	+	0.229072i	$0.926431\pi$
$642$		0			0
$643$	12.9312	+	43.1932i	0.509957	+	1.70337i	0.693582	+	0.720378i	$0.256031\pi$
$643$	12.9312	+	43.1932i	0.509957	+	1.70337i	−0.183625	+	0.982996i	$0.558783\pi$
$644$	−2.59074	−	3.47997i	−0.102089	−	0.137130i
$645$		0			0
$646$	−42.2888	−	21.2382i	−1.66383	−	0.835608i
$647$	−3.10784			−0.122182			−0.0610909	−	0.998132i	$-0.519458\pi$
$647$	−3.10784			−0.122182			−0.0610909	+	0.998132i	$0.519458\pi$
$648$		0			0
$649$	−55.9006			−2.19429
$650$	0.157968	+	0.0793344i	0.00619601	+	0.00311175i
$651$		0			0
$652$	−3.94518	−	5.29930i	−0.154505	−	0.207537i
$653$	−11.3354	−	37.8629i	−0.443588	−	1.48169i	−0.829161	−	0.559010i	$-0.811181\pi$
$653$	−11.3354	−	37.8629i	−0.443588	−	1.48169i	0.385572	−	0.922678i	$-0.374004\pi$
$654$		0			0
$655$	−12.3116	−	28.5416i	−0.481055	−	1.11521i
$656$	1.36766	+	7.75638i	0.0533981	+	0.302836i
$657$		0			0
$658$	2.02328	−	11.4746i	0.0788755	−	0.447325i
$659$	27.9731	−	6.62974i	1.08968	−	0.258258i	0.353764	−	0.935335i	$-0.384902\pi$
$659$	27.9731	−	6.62974i	1.08968	−	0.258258i	0.735913	+	0.677077i	$0.236753\pi$
$660$		0			0
$661$	11.3890	+	7.49066i	0.442981	+	0.291353i	0.751338	−	0.659918i	$-0.229409\pi$
$661$	11.3890	+	7.49066i	0.442981	+	0.291353i	−0.308357	+	0.951271i	$0.599779\pi$
$662$	−0.556064	+	9.54726i	−0.0216121	+	0.371065i
$663$		0			0
$664$	1.49344	−	4.98843i	0.0579566	−	0.193588i
$665$	23.3213	−	8.48826i	0.904362	−	0.329161i
$666$		0			0
$667$	−18.0249	−	6.56051i	−0.697926	−	0.254024i
$668$	4.12950	−	5.54687i	0.159775	−	0.214615i
$669$		0			0
$670$	−8.60138	−	2.03856i	−0.332300	−	0.0787566i
$671$	13.4382	−	31.1533i	0.518777	−	1.20266i
$672$		0			0
$673$	23.5724	−	15.5038i	0.908650	−	0.597629i	−0.00683660	−	0.999977i	$-0.502176\pi$
$673$	23.5724	−	15.5038i	0.908650	−	0.597629i	0.915487	+	0.402348i	$0.131806\pi$
$674$	8.31903	+	14.4090i	0.320437	+	0.555013i
$675$		0			0
$676$	6.38109	−	11.0524i	0.245427	−	0.425091i
$677$	0.00439596	+	0.0754757i	0.000168951	+	0.00290077i	0.998392	−	0.0566944i	$-0.0180561\pi$
$677$	0.00439596	+	0.0754757i	0.000168951	+	0.00290077i	−0.998223	+	0.0595952i	$0.981019\pi$
$678$		0			0
$679$	−2.08359	+	0.243536i	−0.0799607	+	0.00934606i
$680$	10.4532	−	11.0797i	0.400862	−	0.424889i
$681$		0			0
$682$	7.83074	+	0.915283i	0.299855	+	0.0350480i
$683$	14.4335	−	12.1112i	0.552283	−	0.463421i	−0.323430	−	0.946252i	$-0.604836\pi$
$683$	14.4335	−	12.1112i	0.552283	−	0.463421i	0.875713	+	0.482831i	$0.160392\pi$
$684$		0			0
$685$	9.40381	+	7.89073i	0.359301	+	0.301489i
$686$	12.0436	+	12.7654i	0.459826	+	0.487387i
$687$		0			0
$688$	0.396425	−	0.199092i	0.0151136	−	0.00759032i
$689$	−0.857937	+	0.430872i	−0.0326848	+	0.0164149i
$690$		0			0
$691$	16.9118	+	17.9255i	0.643357	+	0.681918i	0.964189	−	0.265218i	$-0.0854439\pi$
$691$	16.9118	+	17.9255i	0.643357	+	0.681918i	−0.320832	+	0.947136i	$0.603962\pi$
$692$	9.70508	+	8.14353i	0.368932	+	0.309571i
$693$		0			0
$694$	19.1413	−	16.0614i	0.726592	−	0.609683i
$695$	41.5124	+	4.85210i	1.57465	+	0.184051i
$696$		0			0
$697$	−35.5528	+	37.6838i	−1.34666	+	1.42737i
$698$	−20.3913	+	2.38340i	−0.771821	+	0.0902130i
$699$		0			0
$700$	0.0313983	+	0.539088i	0.00118674	+	0.0203756i
$701$	−1.67068	+	2.89370i	−0.0631007	+	0.109294i	−0.895850	−	0.444357i	$-0.853432\pi$
$701$	−1.67068	+	2.89370i	−0.0631007	+	0.109294i	0.832749	+	0.553650i	$0.186766\pi$
$702$		0			0
$703$	16.4898	+	28.5612i	0.621925	+	1.07721i
$704$	−3.67554	+	2.41744i	−0.138527	+	0.0911107i
$705$		0			0
$706$	7.16371	−	16.6074i	0.269610	−	0.625026i
$707$	−14.5687	−	3.45285i	−0.547914	−	0.129858i
$708$		0			0
$709$	6.61150	−	8.88078i	0.248300	−	0.333525i	−0.660447	−	0.750873i	$-0.729633\pi$
$709$	6.61150	−	8.88078i	0.248300	−	0.333525i	0.908747	+	0.417348i	$0.137040\pi$
$710$	−16.8533	−	6.13411i	−0.632495	−	0.230209i
$711$		0			0
$712$	2.91097	−	1.05951i	0.109093	−	0.0397067i
$713$	−1.49686	+	4.99985i	−0.0560577	+	0.187246i
$714$		0			0
$715$	0.288866	−	4.95964i	0.0108030	−	0.185480i
$716$	0.845952	+	0.556392i	0.0316147	+	0.0207933i
$717$		0			0
$718$	30.1342	−	7.14194i	1.12460	−	0.266535i
$719$	5.92011	−	33.5746i	0.220783	−	1.25212i	−0.649802	−	0.760104i	$-0.725148\pi$
$719$	5.92011	−	33.5746i	0.220783	−	1.25212i	0.870585	−	0.492019i	$-0.163741\pi$
$720$		0			0
$721$	0.433986	+	2.46125i	0.0161625	+	0.0916619i
$722$	−12.9737	−	30.0764i	−0.482832	−	1.11933i
$723$		0			0
$724$	4.49076	+	15.0002i	0.166898	+	0.557477i
$725$	1.42573	+	1.91508i	0.0529502	+	0.0711244i
$726$		0			0
$727$	40.5032	+	20.3415i	1.50218	+	0.754423i	0.994261	−	0.106981i	$-0.0341185\pi$
$727$	40.5032	+	20.3415i	1.50218	+	0.754423i	0.507919	+	0.861405i	$0.330415\pi$
$728$	−0.726488			−0.0269254
$729$		0			0
$730$	−23.3293			−0.863457
$731$	2.60766	+	1.30961i	0.0964477	+	0.0484379i
$732$		0			0
$733$	−1.17522	−	1.57859i	−0.0434077	−	0.0583067i	0.779889	−	0.625917i	$-0.215275\pi$
$733$	−1.17522	−	1.57859i	−0.0434077	−	0.0583067i	−0.823297	+	0.567611i	$0.807868\pi$
$734$	2.29807	+	7.67608i	0.0848232	+	0.283329i
$735$		0			0
$736$	−1.15348	−	2.67407i	−0.0425178	−	0.0985674i
$737$	2.91611	+	16.5381i	0.107416	+	0.609188i
$738$		0			0
$739$	5.15688	−	29.2461i	0.189699	−	1.07584i	−0.730069	−	0.683373i	$-0.760512\pi$
$739$	5.15688	−	29.2461i	0.189699	−	1.07584i	0.919768	−	0.392463i	$-0.128377\pi$
$740$	−10.3296	+	2.44816i	−0.379724	+	0.0899963i
$741$		0			0
$742$	−2.45031	−	1.61160i	−0.0899539	−	0.0591636i
$743$	0.258982	−	4.44654i	0.00950111	−	0.163128i	−0.990220	−	0.139514i	$-0.955446\pi$
$743$	0.258982	−	4.44654i	0.00950111	−	0.163128i	0.999721	−	0.0236135i	$-0.00751710\pi$
$744$		0			0
$745$	11.7640	−	39.2946i	0.431001	−	1.43964i
$746$	20.9973	−	7.64238i	0.768765	−	0.279807i
$747$		0			0
$748$	−27.1929	−	9.89742i	−0.994272	−	0.361885i
$749$	10.9637	−	14.7268i	0.400606	−	0.538107i
$750$		0			0
$751$	12.0048	+	2.84520i	0.438063	+	0.103823i	0.443729	−	0.896161i	$-0.353655\pi$
$751$	12.0048	+	2.84520i	0.438063	+	0.103823i	−0.00566597	+	0.999984i	$0.501804\pi$
$752$	3.09785	−	7.18163i	0.112967	−	0.261887i
$753$		0			0
$754$	−2.68362	+	1.76504i	−0.0977316	+	0.0642791i
$755$	2.76990	+	4.79760i	0.100807	+	0.174603i
$756$		0			0
$757$	−11.3233	+	19.6125i	−0.411551	+	0.712827i	−0.995060	−	0.0992801i	$-0.968346\pi$
$757$	−11.3233	+	19.6125i	−0.411551	+	0.712827i	0.583509	+	0.812107i	$0.301679\pi$
$758$	−1.18462	−	20.3392i	−0.0430275	−	0.738753i
$759$		0			0
$760$	16.5468	−	1.93404i	0.600215	−	0.0701551i
$761$	7.24273	−	7.67684i	0.262549	−	0.278285i	−0.582667	−	0.812711i	$-0.697991\pi$
$761$	7.24273	−	7.67684i	0.262549	−	0.278285i	0.845215	+	0.534426i	$0.179472\pi$
$762$		0			0
$763$	−28.2484	−	3.30177i	−1.02266	−	0.119532i
$764$	−3.39160	+	2.84589i	−0.122704	+	0.102961i
$765$		0			0
$766$	1.93675	+	1.62513i	0.0699776	+	0.0587182i
$767$	−4.25240	−	4.50728i	−0.153545	−	0.162748i
$768$		0			0
$769$	−36.5243	+	18.3432i	−1.31710	+	0.661473i	−0.961922	−	0.273326i	$-0.911876\pi$
$769$	−36.5243	+	18.3432i	−1.31710	+	0.661473i	−0.355179	+	0.934798i	$0.615580\pi$
$770$	13.5622	−	6.81119i	0.488747	−	0.245458i
$771$		0			0
$772$	−13.0400	−	13.8216i	−0.469319	−	0.497449i
$773$	−24.8151	−	20.8223i	−0.892537	−	0.748928i	0.0761803	−	0.997094i	$-0.475728\pi$
$773$	−24.8151	−	20.8223i	−0.892537	−	0.748928i	−0.968717	+	0.248167i	$0.920172\pi$
$774$		0			0
$775$	0.497634	−	0.417565i	0.0178756	−	0.0149994i
$776$	−1.39864	−	0.163477i	−0.0502081	−	0.00586848i
$777$		0			0
$778$	10.8838	−	11.5361i	0.390202	−	0.413590i
$779$	−56.2780	+	6.57795i	−2.01637	+	0.235680i
$780$		0			0
$781$	1.98111	+	34.0144i	0.0708898	+	1.21713i
$782$	9.57826	−	16.5900i	0.342518	−	0.593258i
$783$		0			0
$784$	2.39036	+	4.14022i	0.0853699	+	0.147865i
$785$	20.0967	−	13.2178i	0.717281	−	0.471763i
$786$		0			0
$787$	4.22566	−	9.79619i	0.150629	−	0.349196i	−0.826149	−	0.563452i	$-0.809473\pi$
$787$	4.22566	−	9.79619i	0.150629	−	0.349196i	0.976778	+	0.214255i	$0.0687324\pi$
$788$	22.0602	+	5.22836i	0.785861	+	0.186252i
$789$		0			0
$790$	−23.2171	+	31.1859i	−0.826026	+	1.10955i
$791$	−11.2791	−	4.10527i	−0.401040	−	0.145967i
$792$		0			0
$793$	3.53416	−	1.28633i	0.125502	−	0.0456788i
$794$	8.57548	−	28.6441i	0.304333	−	1.01654i
$795$		0			0
$796$	0.219127	−	3.76227i	0.00776675	−	0.133350i
$797$	−15.7578	−	10.3641i	−0.558169	−	0.367114i	0.238860	−	0.971054i	$-0.423226\pi$
$797$	−15.7578	−	10.3641i	−0.558169	−	0.367114i	−0.797030	+	0.603940i	$0.793597\pi$
$798$		0			0
$799$	50.0611	−	11.8647i	1.77103	−	0.419743i
$800$	−0.0629446	+	0.356976i	−0.00222543	+	0.0126210i
$801$		0			0
$802$	−1.62298	−	9.20438i	−0.0573095	−	0.325018i
$803$	17.5543	+	40.6954i	0.619477	+	1.43611i
$804$		0			0
$805$	2.88138	+	9.62449i	0.101555	+	0.339219i
$806$	0.521891	+	0.701021i	0.0183828	+	0.0246924i
$807$		0			0
$808$	−8.98134	−	4.51060i	−0.315963	−	0.158682i
$809$	−42.8188			−1.50543			−0.752715	−	0.658347i	$-0.771256\pi$
$809$	−42.8188			−1.50543			−0.752715	+	0.658347i	$0.771256\pi$
$810$		0			0
$811$	12.5236			0.439761			0.219881	−	0.975527i	$-0.429433\pi$
$811$	12.5236			0.439761			0.219881	+	0.975527i	$0.429433\pi$
$812$	−8.76848	−	4.40370i	−0.307713	−	0.154540i
$813$		0			0
$814$	12.0431	+	16.1767i	0.422111	+	0.566994i
$815$	4.38777	+	14.6562i	0.153697	+	0.513384i
$816$		0			0
$817$	1.26404	+	2.93039i	0.0442233	+	0.102521i
$818$	0.110308	+	0.625588i	0.00385683	+	0.0218732i
$819$		0			0
$820$	3.16709	−	17.9615i	0.110600	−	0.627242i
$821$	−21.5050	+	5.09678i	−0.750530	+	0.177879i	−0.588041	−	0.808831i	$-0.700101\pi$
$821$	−21.5050	+	5.09678i	−0.750530	+	0.177879i	−0.162490	+	0.986710i	$0.551952\pi$
$822$		0			0
$823$	−0.0154692	−	0.0101742i	−0.000539222	−	0.000354652i	0.549239	−	0.835665i	$-0.314918\pi$
$823$	−0.0154692	−	0.0101742i	−0.000539222	−	0.000354652i	−0.549779	+	0.835310i	$0.685288\pi$
$824$	−0.0975460	+	1.67480i	−0.00339818	+	0.0583444i
$825$		0			0
$826$	5.42908	−	18.1344i	0.188902	−	0.630976i
$827$	5.05612	−	1.84028i	0.175819	−	0.0639927i	−0.252611	−	0.967568i	$-0.581289\pi$
$827$	5.05612	−	1.84028i	0.175819	−	0.0639927i	0.428429	+	0.903575i	$0.359067\pi$
$828$		0			0
$829$	−21.3345	−	7.76512i	−0.740978	−	0.269694i	−0.0561737	−	0.998421i	$-0.517890\pi$
$829$	−21.3345	−	7.76512i	−0.740978	−	0.269694i	−0.684804	+	0.728727i	$0.740112\pi$
$830$	−7.20071	+	9.67224i	−0.249940	+	0.335728i
$831$		0			0
$832$	−0.474520	−	0.112463i	−0.0164510	−	0.00389896i
$833$	−12.4556	+	28.8753i	−0.431561	+	1.00047i
$834$		0			0
$835$	−13.3792	+	8.79964i	−0.463007	+	0.304524i
$836$	−15.8244	−	27.4087i	−0.547300	−	0.947951i
$837$		0			0
$838$	3.42733	−	5.93630i	0.118395	−	0.205066i
$839$	−1.28480	−	22.0592i	−0.0443564	−	0.761569i	−0.945012	−	0.327036i	$-0.893950\pi$
$839$	−1.28480	−	22.0592i	−0.0443564	−	0.761569i	0.900656	−	0.434534i	$-0.143087\pi$
$840$		0			0
$841$	−14.2855	+	1.66974i	−0.492605	+	0.0575772i
$842$	−15.3755	+	16.2971i	−0.529876	+	0.561636i
$843$		0			0
$844$	13.0984	+	1.53099i	0.450866	+	0.0526987i
$845$	−22.6392	+	18.9966i	−0.778814	+	0.653502i
$846$		0			0
$847$	−9.53313	−	7.99924i	−0.327562	−	0.274857i
$848$	−1.35099	−	1.43197i	−0.0463932	−	0.0491739i
$849$		0			0
$850$	−2.13077	+	1.07011i	−0.0730847	+	0.0367045i
$851$	−11.9304	+	5.99167i	−0.408968	+	0.205392i
$852$		0			0
$853$	−5.27828	−	5.59465i	−0.180725	−	0.191557i	0.630678	−	0.776045i	$-0.282777\pi$
$853$	−5.27828	−	5.59465i	−0.180725	−	0.191557i	−0.811403	+	0.584488i	$0.801295\pi$
$854$	8.80114	+	7.38503i	0.301169	+	0.252711i
$855$		0			0
$856$	9.44095	−	7.92190i	0.322685	−	0.270765i
$857$	17.3892	+	2.03251i	0.594004	+	0.0694291i	0.407783	−	0.913079i	$-0.366302\pi$
$857$	17.3892	+	2.03251i	0.594004	+	0.0694291i	0.186221	+	0.982508i	$0.440376\pi$
$858$		0			0
$859$	−5.20412	+	5.51605i	−0.177562	+	0.188205i	−0.810042	−	0.586372i	$-0.800556\pi$
$859$	−5.20412	+	5.51605i	−0.177562	+	0.188205i	0.632480	+	0.774577i	$0.282037\pi$
$860$	−1.02033	+	0.119259i	−0.0347928	+	0.00406670i
$861$		0			0
$862$	0.886941	+	15.2282i	0.0302093	+	0.518674i
$863$	−13.9025	+	24.0798i	−0.473245	+	0.819685i	−0.999531	−	0.0306232i	$-0.990251\pi$
$863$	−13.9025	+	24.0798i	−0.473245	+	0.819685i	0.526286	+	0.850308i	$0.323584\pi$
$864$		0			0
$865$	−14.6689	−	25.4073i	−0.498758	−	0.863875i
$866$	−14.7602	+	9.70792i	−0.501571	+	0.329888i
$867$		0			0
$868$	−1.05745	+	2.45143i	−0.0358920	+	0.0832071i
$869$	71.8702	+	17.0335i	2.43803	+	0.577824i
$870$		0			0
$871$	−1.11164	+	1.49319i	−0.0376664	+	0.0505948i
$872$	−17.9399	−	6.52959i	−0.607522	−	0.221120i
$873$		0			0
$874$	19.6875	−	7.16567i	0.665940	−	0.242382i
$875$	−4.58838	+	15.3263i	−0.155116	+	0.518122i
$876$		0			0
$877$	−2.12328	+	36.4552i	−0.0716979	+	1.23101i	0.750138	+	0.661282i	$0.229987\pi$
$877$	−2.12328	+	36.4552i	−0.0716979	+	1.23101i	−0.821836	+	0.569725i	$0.807050\pi$
$878$	−19.9030	−	13.0904i	−0.671693	−	0.441779i
$879$		0			0
$880$	9.91281	−	2.34938i	0.334161	−	0.0791976i
$881$	−6.68482	+	37.9115i	−0.225217	+	1.27727i	0.637052	+	0.770821i	$0.280154\pi$
$881$	−6.68482	+	37.9115i	−0.225217	+	1.27727i	−0.862269	+	0.506450i	$0.830957\pi$
$882$		0			0
$883$	1.47794	+	8.38181i	0.0497366	+	0.282070i	0.999525	−	0.0308231i	$-0.00981285\pi$
$883$	1.47794	+	8.38181i	0.0497366	+	0.282070i	−0.949788	+	0.312893i	$0.898702\pi$
$884$	−1.27055	−	2.94548i	−0.0427334	−	0.0990671i
$885$		0			0
$886$	4.23449	+	14.1442i	0.142261	+	0.475184i
$887$	−23.2390	−	31.2154i	−0.780289	−	1.04811i	−0.997407	−	0.0719647i	$-0.977073\pi$
$887$	−23.2390	−	31.2154i	−0.780289	−	1.04811i	0.217118	−	0.976145i	$-0.430334\pi$
$888$		0			0
$889$	−25.0790	−	12.5951i	−0.841123	−	0.422428i
$890$	−7.17357			−0.240459
$891$		0			0
$892$	−7.10621			−0.237933
$893$	50.2822	+	25.2527i	1.68263	+	0.845049i
$894$		0			0
$895$	−1.40016	−	1.88074i	−0.0468023	−	0.0628663i
$896$	−0.427259	−	1.42714i	−0.0142737	−	0.0476775i
$897$		0			0
$898$	−4.27382	−	9.90783i	−0.142619	−	0.330629i
$899$	2.04973	+	11.6246i	0.0683624	+	0.387703i
$900$		0			0
$901$	2.24871	−	12.7531i	0.0749155	−	0.424867i
$902$	−33.7149	+	7.99058i	−1.12258	+	0.266057i
$903$		0			0
$904$	−6.73169	−	4.42750i	−0.223893	−	0.147256i
$905$	2.10829	−	36.1979i	0.0700818	−	1.20326i
$906$		0			0
$907$	0.490184	−	1.63733i	0.0162763	−	0.0543666i	−0.949466	−	0.313871i	$-0.898374\pi$
$907$	0.490184	−	1.63733i	0.0162763	−	0.0543666i	0.965742	+	0.259504i	$0.0835592\pi$
$908$	−2.10557	+	0.766364i	−0.0698757	+	0.0254327i
$909$		0			0
$910$	1.58087	+	0.575391i	0.0524055	+	0.0190740i
$911$	9.37413	−	12.5916i	0.310579	−	0.417180i	−0.619238	−	0.785204i	$-0.712558\pi$
$911$	9.37413	−	12.5916i	0.310579	−	0.417180i	0.929816	+	0.368024i	$0.119966\pi$
$912$		0			0
$913$	22.2903	+	5.28291i	0.737703	+	0.174839i
$914$	−11.9502	+	27.7037i	−0.395278	+	0.916357i
$915$		0			0
$916$	12.9860	−	8.54101i	0.429069	−	0.282203i
$917$	−9.99831	−	17.3176i	−0.330173	−	0.571877i
$918$		0			0
$919$	−11.2459	+	19.4785i	−0.370969	+	0.642537i	−0.989715	−	0.143054i	$-0.954308\pi$
$919$	−11.2459	+	19.4785i	−0.370969	+	0.642537i	0.618746	+	0.785591i	$0.287641\pi$
$920$	0.392122	+	6.73248i	0.0129279	+	0.221963i
$921$		0			0
$922$	−20.1958	+	2.36055i	−0.665112	+	0.0777405i
$923$	−2.59189	+	2.74724i	−0.0853130	+	0.0904265i
$924$		0			0
$925$	1.65048	+	0.192913i	0.0542674	+	0.00634294i
$926$	−16.1719	+	13.5699i	−0.531442	+	0.445933i
$927$		0			0
$928$	−5.04560	−	4.23376i	−0.165630	−	0.138980i
$929$	−37.6794	−	39.9379i	−1.23622	−	1.31032i	−0.934084	−	0.357055i	$-0.883781\pi$
$929$	−37.6794	−	39.9379i	−1.23622	−	1.31032i	−0.302138	−	0.953264i	$-0.597700\pi$
$930$		0			0
$931$	−30.7347	+	15.4356i	−1.00729	+	0.505880i
$932$	−7.05007	+	3.54068i	−0.230933	+	0.115979i
$933$		0			0
$934$	11.8546	+	12.5652i	0.387896	+	0.411146i
$935$	51.3342	+	43.0745i	1.67881	+	1.40869i
$936$		0			0
$937$	−7.52251	+	6.31214i	−0.245750	+	0.206209i	−0.757340	−	0.653021i	$-0.773501\pi$
$937$	−7.52251	+	6.31214i	−0.245750	+	0.206209i	0.511590	+	0.859230i	$0.329057\pi$
$938$	−5.64823	−	0.660184i	−0.184421	−	0.0215558i
$939$		0			0
$940$	−12.4291	+	13.1740i	−0.405391	+	0.429689i
$941$	22.4201	−	2.62054i	0.730875	−	0.0854271i	0.257488	−	0.966281i	$-0.417105\pi$
$941$	22.4201	−	2.62054i	0.730875	−	0.0854271i	0.473387	+	0.880854i	$0.343031\pi$
$942$		0			0
$943$	−1.33366	−	22.8981i	−0.0434301	−	0.745665i
$944$	6.35339	−	11.0044i	0.206785	−	0.358162i
$945$		0			0
$946$	0.975784	+	1.69011i	0.0317255	+	0.0549501i
$947$	36.6967	−	24.1358i	1.19248	−	0.784308i	0.211305	−	0.977420i	$-0.432229\pi$
$947$	36.6967	−	24.1358i	1.19248	−	0.784308i	0.981177	+	0.193112i	$0.0618582\pi$
$948$		0			0
$949$	−1.94591	+	4.51113i	−0.0631670	+	0.146438i
$950$	−2.53745	−	0.601388i	−0.0823259	−	0.0195116i
$951$		0			0
$952$	5.85175	−	7.86026i	0.189656	−	0.254753i
$953$	26.3447	+	9.58870i	0.853389	+	0.310608i	0.731421	−	0.681926i	$-0.238857\pi$
$953$	26.3447	+	9.58870i	0.853389	+	0.310608i	0.121968	+	0.992534i	$0.461079\pi$
$954$		0			0
$955$	9.63427	−	3.50659i	0.311758	−	0.113471i
$956$	1.47864	−	4.93901i	0.0478227	−	0.159739i
$957$		0			0
$958$	1.24251	−	21.3331i	0.0401438	−	0.689242i
$959$	6.59802	+	4.33959i	0.213061	+	0.140133i
$960$		0			0
$961$	−27.0392	+	6.40842i	−0.872234	+	0.206723i
$962$	−0.388204	+	2.20161i	−0.0125162	+	0.0709829i
$963$		0			0
$964$	−0.361018	−	2.04743i	−0.0116276	−	0.0659434i
$965$	17.4287	+	40.4043i	0.561050	+	1.30066i
$966$		0			0
$967$	4.56167	+	15.2370i	0.146693	+	0.489990i	0.999479	−	0.0322708i	$-0.0102739\pi$
$967$	4.56167	+	15.2370i	0.146693	+	0.489990i	−0.852786	+	0.522261i	$0.825089\pi$
$968$	−4.98844	−	6.70063i	−0.160334	−	0.215366i
$969$		0			0
$970$	2.91402	+	1.46348i	0.0935637	+	0.0469894i
$971$	−15.4071			−0.494438			−0.247219	−	0.968960i	$-0.579517\pi$
$971$	−15.4071			−0.494438			−0.247219	+	0.968960i	$0.579517\pi$
$972$		0			0
$973$	26.8873			0.861969
$974$	10.0079	+	5.02617i	0.320674	+	0.161049i
$975$		0			0
$976$	4.60541	+	6.18613i	0.147415	+	0.198013i
$977$	8.32046	+	27.7923i	0.266195	+	0.889154i	0.981682	+	0.190527i	$0.0610198\pi$
$977$	8.32046	+	27.7923i	0.266195	+	0.889154i	−0.715487	+	0.698626i	$0.753795\pi$
$978$		0			0
$979$	5.39779	+	12.5135i	0.172514	+	0.399933i
$980$	−1.92241	−	10.9025i	−0.0614091	−	0.348268i
$981$		0			0
$982$	1.56112	−	8.85355i	0.0498173	−	0.282528i
$983$	28.8192	−	6.83027i	0.919189	−	0.217852i	0.256324	−	0.966591i	$-0.417489\pi$
$983$	28.8192	−	6.83027i	0.919189	−	0.217852i	0.662865	+	0.748739i	$0.269340\pi$
$984$		0			0
$985$	−43.8631	−	28.8492i	−1.39759	−	0.919212i
$986$	2.51918	−	43.2526i	0.0802270	−	1.37744i
$987$		0			0
$988$	1.00620	−	3.36093i	0.0320114	−	0.106926i
$989$	−1.21399	+	0.441857i	−0.0386027	+	0.0140502i
$990$		0			0
$991$	−34.5253	−	12.5662i	−1.09673	−	0.399178i	−0.270622	−	0.962686i	$-0.587229\pi$
$991$	−34.5253	−	12.5662i	−1.09673	−	0.399178i	−0.826111	+	0.563508i	$0.809452\pi$
$992$	−1.07018	+	1.43751i	−0.0339784	+	0.0456408i
$993$		0			0
$994$	−11.2268	−	2.66081i	−0.356093	−	0.0843956i
$995$	−3.45661	+	8.01332i	−0.109582	+	0.254039i
$996$		0			0
$997$	30.2226	−	19.8777i	0.957158	−	0.629533i	0.0281546	−	0.999604i	$-0.491037\pi$
$997$	30.2226	−	19.8777i	0.957158	−	0.629533i	0.929004	+	0.370071i	$0.120667\pi$
$998$	0.772519	+	1.33804i	0.0244537	+	0.0423550i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	486.2.g.b.253.2		90
3.2	odd	2		162.2.g.b.13.4	✓	90
81.25	even	27	inner	486.2.g.b.73.2		90
81.56	odd	54		162.2.g.b.25.4	yes	90

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
162.2.g.b.13.4	✓	90	3.2	odd	2
162.2.g.b.25.4	yes	90	81.56	odd	54
486.2.g.b.73.2		90	81.25	even	27	inner
486.2.g.b.253.2		90	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 486 = 2 \cdot 3^{5} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	486.g (of order \(27\), degree \(18\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.893633 - 0.448799i) q^{2} +(0.597159 + 0.802123i) q^{4} +(-0.664151 - 2.21842i) q^{5} +(-0.590051 - 1.36789i) q^{7} +(-0.173648 - 0.984808i) q^{8} +(-0.402118 + 2.28052i) q^{10} +(4.28069 - 1.01454i) q^{11} +(0.407438 + 0.267976i) q^{13} +(-0.0866199 + 1.48721i) q^{14} +(-0.286803 + 0.957990i) q^{16} +(-6.18123 + 2.24978i) q^{17} +(-6.76026 - 2.46053i) q^{19} +(1.38284 - 1.85748i) q^{20} +(-4.28069 - 1.01454i) q^{22} +(1.15348 - 2.67407i) q^{23} +(-0.302850 + 0.199188i) q^{25} +(-0.243833 - 0.422330i) q^{26} +(0.744864 - 1.29014i) q^{28} +(-0.382974 - 6.57542i) q^{29} +(-1.78001 + 0.208053i) q^{31} +(0.686242 - 0.727374i) q^{32} +(6.53345 + 0.763651i) q^{34} +(-2.64267 + 2.21747i) q^{35} +(-3.51174 - 2.94670i) q^{37} +(4.93690 + 5.23281i) q^{38} +(-2.06939 + 1.03929i) q^{40} +(7.03828 - 3.53476i) q^{41} +(-0.304424 - 0.322671i) q^{43} +(3.37004 + 2.82780i) q^{44} +(-2.23091 + 1.87195i) q^{46} +(-7.76840 - 0.907996i) q^{47} +(3.28072 - 3.47736i) q^{49} +(0.360032 - 0.0420817i) q^{50} +(0.0283552 + 0.486840i) q^{52} +(-0.984340 + 1.70493i) q^{53} +(-5.09371 - 8.82256i) q^{55} +(-1.24465 + 0.818618i) q^{56} +(-2.60880 + 6.04789i) q^{58} +(-12.3643 - 2.93038i) q^{59} +(4.60541 - 6.18613i) q^{61} +(1.68405 + 0.612943i) q^{62} +(-0.939693 + 0.342020i) q^{64} +(0.323883 - 1.08185i) q^{65} +(-0.221954 + 3.81081i) q^{67} +(-5.49578 - 3.61463i) q^{68} +(3.35678 - 0.795571i) q^{70} +(-1.34489 + 7.62726i) q^{71} +(1.74940 + 9.92135i) q^{73} +(1.81573 + 4.20933i) q^{74} +(-2.06330 - 6.89189i) q^{76} +(-3.91361 - 5.25689i) q^{77} +(15.0035 + 7.53506i) q^{79} +2.31570 q^{80} -7.87604 q^{82} +(4.65331 + 2.33698i) q^{83} +(9.09624 + 12.2184i) q^{85} +(0.127229 + 0.424975i) q^{86} +(-1.74246 - 4.03949i) q^{88} +(0.537926 + 3.05073i) q^{89} +(0.126153 - 0.715451i) q^{91} +(2.83374 - 0.671609i) q^{92} +(6.53459 + 4.29787i) q^{94} +(-0.968660 + 16.6313i) q^{95} +(0.403864 - 1.34900i) q^{97} +(-4.49240 + 1.63510i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 90 q - 18 q^{13} + 9 q^{20} - 27 q^{23} - 18 q^{25} + 27 q^{26} - 18 q^{28} + 27 q^{29} + 54 q^{31} + 27 q^{35} + 18 q^{38} + 9 q^{41} - 36 q^{43} + 18 q^{46} + 27 q^{47} + 36 q^{52} + 27 q^{53} - 54 q^{55}+ \cdots - 36 q^{98}+O(q^{100}) \) 90 * q - 18 * q^13 + 9 * q^20 - 27 * q^23 - 18 * q^25 + 27 * q^26 - 18 * q^28 + 27 * q^29 + 54 * q^31 + 27 * q^35 + 18 * q^38 + 9 * q^41 - 36 * q^43 + 18 * q^46 + 27 * q^47 + 36 * q^52 + 27 * q^53 - 54 * q^55 - 9 * q^58 + 45 * q^59 - 9 * q^65 + 81 * q^67 - 36 * q^68 - 72 * q^70 - 72 * q^71 - 36 * q^73 - 45 * q^74 - 18 * q^76 - 144 * q^77 - 99 * q^79 - 18 * q^80 + 72 * q^82 - 45 * q^83 - 117 * q^85 - 72 * q^86 - 18 * q^88 - 45 * q^89 - 63 * q^91 - 36 * q^92 - 72 * q^94 - 45 * q^95 + 117 * q^97 - 36 * q^98

Introduction

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