LMFDB - Embedded newform 486.2.g.b.451.2

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			451.2
Character	$\chi$	$=$	486.451
Dual form			486.2.g.b.361.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.973045 - 0.230616i) q^{2} +(0.893633 + 0.448799i) q^{4} +(-0.537372 + 0.721815i) q^{5} +(-3.95679 - 2.60242i) q^{7} +(-0.766044 - 0.642788i) q^{8} +(0.689349 - 0.578432i) q^{10} +(4.21098 - 0.492194i) q^{11} +(-1.75605 + 5.86562i) q^{13} +(3.24997 + 3.44477i) q^{14} +(0.597159 + 0.802123i) q^{16} +(0.432180 + 2.45101i) q^{17} +(-0.284021 + 1.61076i) q^{19} +(-0.804163 + 0.403866i) q^{20} +(-4.21098 - 0.492194i) q^{22} +(-6.35325 + 4.17860i) q^{23} +(1.20177 + 4.01418i) q^{25} +(3.06142 - 5.30254i) q^{26} +(-2.36795 - 4.10141i) q^{28} +(-2.09368 + 2.21918i) q^{29} +(-0.107618 - 1.84773i) q^{31} +(-0.396080 - 0.918216i) q^{32} +(0.144712 - 2.48461i) q^{34} +(4.00473 - 1.45760i) q^{35} +(-8.42259 - 3.06557i) q^{37} +(0.647833 - 1.50184i) q^{38} +(0.875624 - 0.207527i) q^{40} +(-5.04755 + 1.19629i) q^{41} +(1.06337 - 2.46516i) q^{43} +(3.98397 + 1.45005i) q^{44} +(7.14564 - 2.60080i) q^{46} +(-0.486795 + 8.35794i) q^{47} +(6.11101 + 14.1669i) q^{49} +(-0.243639 - 4.18313i) q^{50} +(-4.20175 + 4.45360i) q^{52} +(1.11544 + 1.93201i) q^{53} +(-1.90759 + 3.30404i) q^{55} +(1.35827 + 4.53694i) q^{56} +(2.54903 - 1.67652i) q^{58} +(3.71218 + 0.433892i) q^{59} +(2.81018 - 1.41133i) q^{61} +(-0.321399 + 1.82275i) q^{62} +(0.173648 + 0.984808i) q^{64} +(-3.29024 - 4.41957i) q^{65} +(3.28793 + 3.48500i) q^{67} +(-0.713803 + 2.38427i) q^{68} +(-4.23293 + 0.494758i) q^{70} +(3.18551 - 2.67296i) q^{71} +(1.09995 + 0.922965i) q^{73} +(7.48859 + 4.92532i) q^{74} +(-0.976720 + 1.31196i) q^{76} +(-17.9429 - 9.01124i) q^{77} +(-5.03759 - 1.19393i) q^{79} -0.899881 q^{80} +5.18737 q^{82} +(2.63513 + 0.624537i) q^{83} +(-2.00142 - 1.00515i) q^{85} +(-1.60321 + 2.15349i) q^{86} +(-3.54218 - 2.32973i) q^{88} +(-12.5970 - 10.5701i) q^{89} +(22.2131 - 18.6390i) q^{91} +(-7.55282 + 0.882798i) q^{92} +(2.40115 - 8.02039i) q^{94} +(-1.01005 - 1.07059i) q^{95} +(2.79423 + 3.75330i) q^{97} +(-2.67917 - 15.1943i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/486\mathbb{Z}\right)^\times$.

$n$	$245$
$\chi(n)$	$e\left(\frac{2}{27}\right)$

Coefficient data

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

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

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

$2$	−0.973045	−	0.230616i	−0.688047	−	0.163070i
$2$	−0.973045	−	0.230616i	−0.688047	−	0.163070i
$3$		0			0
$3$		0			0
$4$	0.893633	+	0.448799i	0.446816	+	0.224400i
$5$	−0.537372	+	0.721815i	−0.240320	+	0.322806i	−0.905877	−	0.423542i	$-0.860787\pi$
$5$	−0.537372	+	0.721815i	−0.240320	+	0.322806i	0.665557	+	0.746347i	$0.268194\pi$
$6$		0			0
$7$	−3.95679	−	2.60242i	−1.49552	−	0.983622i	−0.992879	−	0.119129i	$-0.961990\pi$
$7$	−3.95679	−	2.60242i	−1.49552	−	0.983622i	−0.502646	−	0.864493i	$-0.667640\pi$
$8$	−0.766044	−	0.642788i	−0.270838	−	0.227260i
$9$		0			0
$10$	0.689349	−	0.578432i	0.217991	−	0.182916i
$11$	4.21098	−	0.492194i	1.26966	−	0.148402i	0.545545	−	0.838082i	$-0.316323\pi$
$11$	4.21098	−	0.492194i	1.26966	−	0.148402i	0.724115	+	0.689680i	$0.242249\pi$
$12$		0			0
$13$	−1.75605	+	5.86562i	−0.487041	+	1.62683i	0.262541	+	0.964921i	$0.415439\pi$
$13$	−1.75605	+	5.86562i	−0.487041	+	1.62683i	−0.749583	+	0.661911i	$0.769746\pi$
$14$	3.24997	+	3.44477i	0.868591	+	0.920653i
$15$		0			0
$16$	0.597159	+	0.802123i	0.149290	+	0.200531i
$17$	0.432180	+	2.45101i	0.104819	+	0.594458i	0.991292	+	0.131679i	$0.0420367\pi$
$17$	0.432180	+	2.45101i	0.104819	+	0.594458i	−0.886473	+	0.462780i	$0.846852\pi$
$18$		0			0
$19$	−0.284021	+	1.61076i	−0.0651589	+	0.369534i	0.934740	+	0.355332i	$0.115632\pi$
$19$	−0.284021	+	1.61076i	−0.0651589	+	0.369534i	−0.999899	+	0.0142026i	$0.995479\pi$
$20$	−0.804163	+	0.403866i	−0.179816	+	0.0903071i
$21$		0			0
$22$	−4.21098	−	0.492194i	−0.897785	−	0.104936i
$23$	−6.35325	+	4.17860i	−1.32474	+	0.871297i	−0.997290	−	0.0735700i	$-0.976561\pi$
$23$	−6.35325	+	4.17860i	−1.32474	+	0.871297i	−0.327453	+	0.944867i	$0.606190\pi$
$24$		0			0
$25$	1.20177	+	4.01418i	0.240353	+	0.802836i
$26$	3.06142	−	5.30254i	0.600395	−	1.03991i
$27$		0			0
$28$	−2.36795	−	4.10141i	−0.447500	−	0.775093i
$29$	−2.09368	+	2.21918i	−0.388787	+	0.412091i	−0.891974	−	0.452087i	$-0.850679\pi$
$29$	−2.09368	+	2.21918i	−0.388787	+	0.412091i	0.503186	+	0.864178i	$0.332161\pi$
$30$		0			0
$31$	−0.107618	−	1.84773i	−0.0193288	−	0.331863i	−0.994086	−	0.108595i	$-0.965365\pi$
$31$	−0.107618	−	1.84773i	−0.0193288	−	0.331863i	0.974757	−	0.223267i	$-0.0716723\pi$
$32$	−0.396080	−	0.918216i	−0.0700177	−	0.162319i
$33$		0			0
$34$	0.144712	−	2.48461i	0.0248180	−	0.426108i
$35$	4.00473	−	1.45760i	0.676923	−	0.246380i
$36$		0			0
$37$	−8.42259	−	3.06557i	−1.38467	−	0.503977i	−0.461076	−	0.887361i	$-0.652537\pi$
$37$	−8.42259	−	3.06557i	−1.38467	−	0.503977i	−0.923589	+	0.383384i	$0.874759\pi$
$38$	0.647833	−	1.50184i	0.105092	−	0.243631i
$39$		0			0
$40$	0.875624	−	0.207527i	0.138448	−	0.0328129i
$41$	−5.04755	+	1.19629i	−0.788295	+	0.186829i	−0.604996	−	0.796228i	$-0.706825\pi$
$41$	−5.04755	+	1.19629i	−0.788295	+	0.186829i	−0.183298	+	0.983057i	$0.558677\pi$
$42$		0			0
$43$	1.06337	−	2.46516i	0.162162	−	0.375934i	−0.817690	−	0.575659i	$-0.804746\pi$
$43$	1.06337	−	2.46516i	0.162162	−	0.375934i	0.979852	+	0.199725i	$0.0640049\pi$
$44$	3.98397	+	1.45005i	0.600606	+	0.218603i
$45$		0			0
$46$	7.14564	−	2.60080i	1.05357	−	0.383467i
$47$	−0.486795	+	8.35794i	−0.0710063	+	1.21913i	0.755097	+	0.655613i	$0.227590\pi$
$47$	−0.486795	+	8.35794i	−0.0710063	+	1.21913i	−0.826103	+	0.563519i	$0.809447\pi$
$48$		0			0
$49$	6.11101	+	14.1669i	0.873002	+	2.02384i
$50$	−0.243639	−	4.18313i	−0.0344558	−	0.591583i
$51$		0			0
$52$	−4.20175	+	4.45360i	−0.582678	+	0.617603i
$53$	1.11544	+	1.93201i	0.153218	+	0.265381i	0.932409	−	0.361406i	$-0.117703\pi$
$53$	1.11544	+	1.93201i	0.153218	+	0.265381i	−0.779191	+	0.626787i	$0.784370\pi$
$54$		0			0
$55$	−1.90759	+	3.30404i	−0.257219	+	0.445517i
$56$	1.35827	+	4.53694i	0.181507	+	0.606274i
$57$		0			0
$58$	2.54903	−	1.67652i	0.334703	−	0.220138i
$59$	3.71218	+	0.433892i	0.483285	+	0.0564879i	0.354247	−	0.935152i	$-0.384737\pi$
$59$	3.71218	+	0.433892i	0.483285	+	0.0564879i	0.129038	+	0.991640i	$0.458811\pi$
$60$		0			0
$61$	2.81018	−	1.41133i	0.359807	−	0.180702i	−0.259707	−	0.965687i	$-0.583626\pi$
$61$	2.81018	−	1.41133i	0.359807	−	0.180702i	0.619514	+	0.784986i	$0.287330\pi$
$62$	−0.321399	+	1.82275i	−0.0408178	+	0.231489i
$63$		0			0
$64$	0.173648	+	0.984808i	0.0217060	+	0.123101i
$65$	−3.29024	−	4.41957i	−0.408105	−	0.548180i
$66$		0			0
$67$	3.28793	+	3.48500i	0.401685	+	0.425761i	0.896367	−	0.443313i	$-0.146197\pi$
$67$	3.28793	+	3.48500i	0.401685	+	0.425761i	−0.494682	+	0.869074i	$0.664716\pi$
$68$	−0.713803	+	2.38427i	−0.0865614	+	0.289135i
$69$		0			0
$70$	−4.23293	+	0.494758i	−0.505932	+	0.0591349i
$71$	3.18551	−	2.67296i	0.378051	−	0.317222i	−0.433886	−	0.900968i	$-0.642858\pi$
$71$	3.18551	−	2.67296i	0.378051	−	0.317222i	0.811937	+	0.583746i	$0.198413\pi$
$72$		0			0
$73$	1.09995	+	0.922965i	0.128739	+	0.108025i	0.704884	−	0.709323i	$-0.250999\pi$
$73$	1.09995	+	0.922965i	0.128739	+	0.108025i	−0.576145	+	0.817348i	$0.695444\pi$
$74$	7.48859	+	4.92532i	0.870531	+	0.572557i
$75$		0			0
$76$	−0.976720	+	1.31196i	−0.112037	+	0.150492i
$77$	−17.9429	−	9.01124i	−2.04478	−	1.02693i
$78$		0			0
$79$	−5.03759	−	1.19393i	−0.566773	−	0.134328i	−0.0627675	−	0.998028i	$-0.519993\pi$
$79$	−5.03759	−	1.19393i	−0.566773	−	0.134328i	−0.504005	+	0.863701i	$0.668141\pi$
$80$	−0.899881			−0.100610
$81$		0			0
$82$	5.18737			0.572850
$83$	2.63513	+	0.624537i	0.289243	+	0.0685519i	0.372676	−	0.927962i	$-0.378440\pi$
$83$	2.63513	+	0.624537i	0.289243	+	0.0685519i	−0.0834329	+	0.996513i	$0.526588\pi$
$84$		0			0
$85$	−2.00142	−	1.00515i	−0.217085	−	0.109024i
$86$	−1.60321	+	2.15349i	−0.172879	+	0.232216i
$87$		0			0
$88$	−3.54218	−	2.32973i	−0.377597	−	0.248350i
$89$	−12.5970	−	10.5701i	−1.33528	−	1.12043i	−0.982813	−	0.184604i	$-0.940900\pi$
$89$	−12.5970	−	10.5701i	−1.33528	−	1.12043i	−0.352463	−	0.935826i	$-0.614656\pi$
$90$		0			0
$91$	22.2131	−	18.6390i	2.32857	−	1.95390i
$92$	−7.55282	+	0.882798i	−0.787436	+	0.0920380i
$93$		0			0
$94$	2.40115	−	8.02039i	0.247659	−	0.827240i
$95$	−1.01005	−	1.07059i	−0.103629	−	0.109840i
$96$		0			0
$97$	2.79423	+	3.75330i	0.283711	+	0.381090i	0.921018	−	0.389520i	$-0.127359\pi$
$97$	2.79423	+	3.75330i	0.283711	+	0.381090i	−0.637307	+	0.770610i	$0.719952\pi$
$98$	−2.67917	−	15.1943i	−0.270637	−	1.53486i
$99$		0			0
$100$	−0.727623	+	4.12656i	−0.0727623	+	0.412656i
$101$	10.7240	−	5.38577i	1.06707	−	0.535904i	0.173506	−	0.984833i	$-0.444490\pi$
$101$	10.7240	−	5.38577i	1.06707	−	0.535904i	0.893568	+	0.448928i	$0.148194\pi$
$102$		0			0
$103$	7.07350	+	0.826773i	0.696972	+	0.0814644i	0.457199	−	0.889364i	$-0.348853\pi$
$103$	7.07350	+	0.826773i	0.696972	+	0.0814644i	0.239774	+	0.970829i	$0.422927\pi$
$104$	5.11557	−	3.36456i	0.501622	−	0.329922i
$105$		0			0
$106$	−0.639826	−	2.13717i	−0.0621454	−	0.207580i
$107$	4.54371	−	7.86994i	0.439257	−	0.760816i	−0.558375	−	0.829589i	$-0.688575\pi$
$107$	4.54371	−	7.86994i	0.439257	−	0.760816i	0.997632	+	0.0687727i	$0.0219083\pi$
$108$		0			0
$109$	−4.27740	−	7.40867i	−0.409700	−	0.709622i	0.585156	−	0.810921i	$-0.301033\pi$
$109$	−4.27740	−	7.40867i	−0.409700	−	0.709622i	−0.994856	+	0.101299i	$0.967700\pi$
$110$	2.61814	−	2.77506i	0.249629	−	0.264592i
$111$		0			0
$112$	−0.275368	−	4.72789i	−0.0260198	−	0.446743i
$113$	2.11058	+	4.89288i	0.198547	+	0.460284i	0.988180	−	0.153295i	$-0.0489886\pi$
$113$	2.11058	+	4.89288i	0.198547	+	0.460284i	−0.789633	+	0.613579i	$0.789729\pi$
$114$		0			0
$115$	0.397880	−	6.83133i	0.0371025	−	0.637025i
$116$	−2.86695	+	1.04348i	−0.266189	+	0.0968850i
$117$		0			0
$118$	−3.51206	−	1.27828i	−0.323311	−	0.117676i
$119$	4.66852	−	10.8229i	0.427963	−	0.992129i
$120$		0			0
$121$	6.78664	−	1.60846i	0.616968	−	0.146224i
$122$	−3.05991	+	0.725211i	−0.277031	+	0.0656576i
$123$		0			0
$124$	0.733090	−	1.69949i	0.0658334	−	0.152619i
$125$	−7.77135	−	2.82854i	−0.695091	−	0.252992i
$126$		0			0
$127$	−2.08699	+	0.759602i	−0.185190	+	0.0674038i	−0.432951	−	0.901418i	$-0.642528\pi$
$127$	−2.08699	+	0.759602i	−0.185190	+	0.0674038i	0.247760	+	0.968821i	$0.420305\pi$
$128$	0.0581448	−	0.998308i	0.00513933	−	0.0882388i
$129$		0			0
$130$	2.18233	+	5.05922i	0.191403	+	0.443723i
$131$	−0.0633149	−	1.08707i	−0.00553185	−	0.0949781i	0.994412	−	0.105568i	$-0.0336661\pi$
$131$	−0.0633149	−	1.08707i	−0.00553185	−	0.0949781i	−0.999944	+	0.0105899i	$0.996629\pi$
$132$		0			0
$133$	5.31569	−	5.63430i	0.460929	−	0.488556i
$134$	−2.39561	−	4.14931i	−0.206949	−	0.358446i
$135$		0			0
$136$	1.24441	−	2.15539i	0.106708	−	0.184823i
$137$	1.73952	+	5.81040i	0.148617	+	0.496416i	0.999585	−	0.0288015i	$-0.00916906\pi$
$137$	1.73952	+	5.81040i	0.148617	+	0.496416i	−0.850968	+	0.525218i	$0.823984\pi$
$138$		0			0
$139$	−11.7886	+	7.75350i	−0.999898	+	0.657644i	−0.940218	−	0.340574i	$-0.889379\pi$
$139$	−11.7886	+	7.75350i	−0.999898	+	0.657644i	−0.0596807	+	0.998218i	$0.519008\pi$
$140$	4.23293	+	0.494758i	0.357748	+	0.0418147i
$141$		0			0
$142$	−3.71607	+	1.86628i	−0.311846	+	0.156615i
$143$	−4.50769	+	25.5644i	−0.376952	+	2.13780i
$144$		0			0
$145$	−0.476748	−	2.70377i	−0.0395918	−	0.224536i
$146$	−0.857447	−	1.15175i	−0.0709628	−	0.0953196i
$147$		0			0
$148$	−6.15088	−	6.51955i	−0.505599	−	0.535903i
$149$	0.589967	−	1.97063i	0.0483319	−	0.161440i	−0.930417	−	0.366503i	$-0.880555\pi$
$149$	0.589967	−	1.97063i	0.0483319	−	0.161440i	0.978749	+	0.205063i	$0.0657400\pi$
$150$		0			0
$151$	−8.84148	+	1.03342i	−0.719509	+	0.0840986i	−0.467965	−	0.883747i	$-0.655013\pi$
$151$	−8.84148	+	1.03342i	−0.719509	+	0.0840986i	−0.251545	+	0.967846i	$0.580939\pi$
$152$	1.25295	−	1.05135i	0.101628	−	0.0852758i
$153$		0			0
$154$	15.3811	+	12.9063i	1.23944	+	1.04002i
$155$	1.39155	+	0.915239i	0.111772	+	0.0735138i
$156$		0			0
$157$	−2.34792	+	3.15381i	−0.187385	+	0.251701i	−0.885881	−	0.463912i	$-0.846445\pi$
$157$	−2.34792	+	3.15381i	−0.187385	+	0.251701i	0.698496	+	0.715613i	$0.253853\pi$
$158$	4.62646	+	2.32349i	0.368061	+	0.184847i
$159$		0			0
$160$	0.875624	+	0.207527i	0.0692242	+	0.0164064i
$161$	36.0129			2.83821
$162$		0			0
$163$	−10.9972			−0.861367			−0.430683	−	0.902503i	$-0.641727\pi$
$163$	−10.9972			−0.861367			−0.430683	+	0.902503i	$0.641727\pi$
$164$	−5.04755	−	1.19629i	−0.394147	−	0.0934146i
$165$		0			0
$166$	−2.42007	−	1.21541i	−0.187834	−	0.0943338i
$167$	9.59118	−	12.8832i	0.742188	−	0.996931i	−0.257343	−	0.966320i	$-0.582847\pi$
$167$	9.59118	−	12.8832i	0.742188	−	0.996931i	0.999531	−	0.0306113i	$-0.00974542\pi$
$168$		0			0
$169$	−20.4605	−	13.4571i	−1.57388	−	1.03516i
$170$	1.71567	+	1.43962i	0.131586	+	0.110414i
$171$		0			0
$172$	2.05662	−	1.72571i	0.156816	−	0.131584i
$173$	11.5069	−	1.34497i	0.874855	−	0.102256i	0.333199	−	0.942856i	$-0.391872\pi$
$173$	11.5069	−	1.34497i	0.874855	−	0.102256i	0.541655	+	0.840601i	$0.317798\pi$
$174$		0			0
$175$	5.69145	−	19.0108i	0.430233	−	1.43708i
$176$	2.90943	+	3.08381i	0.219306	+	0.232451i
$177$		0			0
$178$	9.81978	+	13.1903i	0.736024	+	0.988651i
$179$	−1.19249	−	6.76294i	−0.0891308	−	0.505486i	−0.996389	−	0.0849109i	$-0.972939\pi$
$179$	−1.19249	−	6.76294i	−0.0891308	−	0.505486i	0.907258	−	0.420575i	$-0.138172\pi$
$180$		0			0
$181$	−4.15485	+	23.5633i	−0.308827	+	1.75145i	0.296092	+	0.955159i	$0.404316\pi$
$181$	−4.15485	+	23.5633i	−0.308827	+	1.75145i	−0.604919	+	0.796287i	$0.706795\pi$
$182$	−25.9128	+	13.0139i	−1.92079	+	0.964656i
$183$		0			0
$184$	7.55282	+	0.882798i	0.556801	+	0.0650807i
$185$	6.73884	−	4.43220i	0.495449	−	0.325862i
$186$		0			0
$187$	3.02628	+	10.1085i	0.221303	+	0.739204i
$188$	−4.18605	+	7.25046i	−0.305299	+	0.528794i
$189$		0			0
$190$	0.735928	+	1.27466i	0.0533898	+	0.0924739i
$191$	−6.80578	+	7.21370i	−0.492449	+	0.521965i	−0.925165	−	0.379565i	$-0.876074\pi$
$191$	−6.80578	+	7.21370i	−0.492449	+	0.521965i	0.432716	+	0.901530i	$0.357555\pi$
$192$		0			0
$193$	−1.01279	−	17.3890i	−0.0729023	−	1.25168i	−0.814231	−	0.580542i	$-0.802841\pi$
$193$	−1.01279	−	17.3890i	−0.0729023	−	1.25168i	0.741328	−	0.671143i	$-0.234196\pi$
$194$	−1.85334	−	4.29653i	−0.133062	−	0.308473i
$195$		0			0
$196$	−0.897101	+	15.4026i	−0.0640787	+	1.10019i
$197$	−19.0553	+	6.93558i	−1.35764	+	0.494140i	−0.915323	−	0.402720i	$-0.868065\pi$
$197$	−19.0553	+	6.93558i	−1.35764	+	0.494140i	−0.442314	+	0.896860i	$0.645842\pi$
$198$		0			0
$199$	4.91031	+	1.78721i	0.348083	+	0.126692i	0.510144	−	0.860089i	$-0.329592\pi$
$199$	4.91031	+	1.78721i	0.348083	+	0.126692i	−0.162062	+	0.986781i	$0.551814\pi$
$200$	1.65966	−	3.84752i	0.117356	−	0.272061i
$201$		0			0
$202$	−11.6769	+	2.76748i	−0.821586	+	0.194720i
$203$	14.0595	−	3.33216i	0.986782	−	0.233872i
$204$		0			0
$205$	1.84891	−	4.28625i	0.129133	−	0.299365i
$206$	−6.69216	−	2.43575i	−0.466265	−	0.169707i
$207$		0			0
$208$	−5.75360	+	2.09414i	−0.398940	+	0.145202i
$209$	−0.403201	+	6.92269i	−0.0278900	+	0.478853i
$210$		0			0
$211$	−3.96517	−	9.19229i	−0.272973	−	0.632823i	0.725490	−	0.688232i	$-0.241613\pi$
$211$	−3.96517	−	9.19229i	−0.272973	−	0.632823i	−0.998464	+	0.0554089i	$0.982354\pi$
$212$	0.129715	+	2.22711i	0.00890884	+	0.152959i
$213$		0			0
$214$	−6.23617	+	6.60995i	−0.426296	+	0.451847i
$215$	1.20797	+	2.09226i	0.0823828	+	0.142691i
$216$		0			0
$217$	−4.38275	+	7.59115i	−0.297521	+	0.515321i
$218$	2.45354	+	8.19540i	0.166175	+	0.555063i
$219$		0			0
$220$	−3.18754	+	2.09648i	−0.214904	+	0.141344i
$221$	−15.1357	−	1.76911i	−1.01813	−	0.119003i
$222$		0			0
$223$	20.2555	−	10.1727i	1.35641	−	0.681215i	0.385961	−	0.922515i	$-0.373870\pi$
$223$	20.2555	−	10.1727i	1.35641	−	0.681215i	0.970451	+	0.241300i	$0.0775738\pi$
$224$	−0.822380	+	4.66395i	−0.0549476	+	0.311623i
$225$		0			0
$226$	−0.925316	−	5.24773i	−0.0615511	−	0.349074i
$227$	−1.72373	−	2.31537i	−0.114408	−	0.153677i	0.741230	−	0.671251i	$-0.234243\pi$
$227$	−1.72373	−	2.31537i	−0.114408	−	0.153677i	−0.855638	+	0.517574i	$0.826835\pi$
$228$		0			0
$229$	13.2406	+	14.0343i	0.874967	+	0.927410i	0.997885	−	0.0650064i	$-0.0207068\pi$
$229$	13.2406	+	14.0343i	0.874967	+	0.927410i	−0.122918	+	0.992417i	$0.539225\pi$
$230$	−1.96257	+	6.55543i	−0.129408	+	0.432252i
$231$		0			0
$232$	3.03031	−	0.354193i	0.198950	−	0.0232539i
$233$	−20.8609	+	17.5044i	−1.36664	+	1.14675i	−0.392777	+	0.919634i	$0.628485\pi$
$233$	−20.8609	+	17.5044i	−1.36664	+	1.14675i	−0.973868	+	0.227117i	$0.927070\pi$
$234$		0			0
$235$	−5.77130	−	4.84270i	−0.376478	−	0.315903i
$236$	3.12260	+	2.05376i	0.203264	+	0.133689i
$237$		0			0
$238$	−7.03860	+	9.45449i	−0.456245	+	0.612843i
$239$	−7.06865	−	3.55001i	−0.457233	−	0.229631i	0.205248	−	0.978710i	$-0.434200\pi$
$239$	−7.06865	−	3.55001i	−0.457233	−	0.229631i	−0.662481	+	0.749079i	$0.730496\pi$
$240$		0			0
$241$	−0.421799	−	0.0999681i	−0.0271704	−	0.00643951i	0.217008	−	0.976170i	$-0.430370\pi$
$241$	−0.421799	−	0.0999681i	−0.0271704	−	0.00643951i	−0.244179	+	0.969730i	$0.578518\pi$
$242$	−6.97465			−0.448347
$243$		0			0
$244$	3.14467			0.201317
$245$	−13.5098	−	3.20188i	−0.863108	−	0.204560i
$246$		0			0
$247$	−8.94938	−	4.49455i	−0.569435	−	0.285981i
$248$	−1.10526	+	1.48462i	−0.0701841	+	0.0942736i
$249$		0			0
$250$	6.90957	+	4.54449i	0.436999	+	0.287419i
$251$	4.62180	+	3.87815i	0.291725	+	0.244787i	0.776890	−	0.629636i	$-0.216796\pi$
$251$	4.62180	+	3.87815i	0.291725	+	0.244787i	−0.485165	+	0.874423i	$0.661240\pi$
$252$		0			0
$253$	−24.6967	+	20.7230i	−1.55267	+	1.30285i
$254$	2.20591	−	0.257834i	0.138411	−	0.0161780i
$255$		0			0
$256$	−0.286803	+	0.957990i	−0.0179252	+	0.0598743i
$257$	11.6285	+	12.3254i	0.725363	+	0.768840i	0.980171	−	0.198152i	$-0.0634938\pi$
$257$	11.6285	+	12.3254i	0.725363	+	0.768840i	−0.254808	+	0.966992i	$0.582012\pi$
$258$		0			0
$259$	25.3485	+	34.0489i	1.57508	+	2.11570i
$260$	−0.956773	−	5.42613i	−0.0593365	−	0.336514i
$261$		0			0
$262$	−0.189088	+	1.07237i	−0.0116819	+	0.0662515i
$263$	20.4228	−	10.2567i	1.25933	−	0.632458i	0.311198	−	0.950345i	$-0.399270\pi$
$263$	20.4228	−	10.2567i	1.25933	−	0.632458i	0.948128	+	0.317887i	$0.102973\pi$
$264$		0			0
$265$	−1.99396	−	0.233060i	−0.122488	−	0.0143168i
$266$	−6.47176	+	4.25655i	−0.396809	+	0.260986i
$267$		0			0
$268$	1.37414	+	4.58993i	0.0839387	+	0.280375i
$269$	−11.0727	+	19.1784i	−0.675113	+	1.16933i	0.301323	+	0.953522i	$0.402572\pi$
$269$	−11.0727	+	19.1784i	−0.675113	+	1.16933i	−0.976436	+	0.215808i	$0.930761\pi$
$270$		0			0
$271$	8.46422	+	14.6605i	0.514165	+	0.890559i	0.999865	+	0.0164339i	$0.00523130\pi$
$271$	8.46422	+	14.6605i	0.514165	+	0.890559i	−0.485700	+	0.874125i	$0.661435\pi$
$272$	−1.70794	+	1.81031i	−0.103559	+	0.109766i
$273$		0			0
$274$	−0.352660	−	6.05494i	−0.0213050	−	0.365793i
$275$	7.03638	+	16.3122i	0.424309	+	0.983660i
$276$		0			0
$277$	1.38639	−	23.8035i	0.0833004	−	1.43021i	−0.654943	−	0.755678i	$-0.727307\pi$
$277$	1.38639	−	23.8035i	0.0833004	−	1.43021i	0.738244	−	0.674534i	$-0.235655\pi$
$278$	13.2589	−	4.82586i	0.795219	−	0.289436i
$279$		0			0
$280$	−4.00473	−	1.45760i	−0.239328	−	0.0871084i
$281$	−2.40187	+	5.56816i	−0.143284	+	0.332169i	−0.974713	−	0.223462i	$-0.928264\pi$
$281$	−2.40187	+	5.56816i	−0.143284	+	0.332169i	0.831429	+	0.555631i	$0.187523\pi$
$282$		0			0
$283$	6.35030	−	1.50505i	0.377486	−	0.0894659i	−0.0374926	−	0.999297i	$-0.511937\pi$
$283$	6.35030	−	1.50505i	0.377486	−	0.0894659i	0.414979	+	0.909831i	$0.363789\pi$
$284$	4.04630	−	0.958991i	0.240104	−	0.0569056i
$285$		0			0
$286$	10.2817	−	23.8357i	0.607972	−	1.40944i
$287$	23.0853	+	8.40237i	1.36268	+	0.495976i
$288$		0			0
$289$	10.1541	−	3.69578i	0.597299	−	0.217399i
$290$	−0.159636	+	2.74084i	−0.00937413	+	0.160948i
$291$		0			0
$292$	0.568723	+	1.31845i	0.0332820	+	0.0771563i
$293$	−0.343009	−	5.88924i	−0.0200388	−	0.344053i	−0.993394	−	0.114751i	$-0.963393\pi$
$293$	−0.343009	−	5.88924i	−0.0200388	−	0.344053i	0.973355	−	0.229302i	$-0.0736442\pi$
$294$		0			0
$295$	−2.30801	+	2.44635i	−0.134378	+	0.142432i
$296$	4.48157	+	7.76230i	0.260486	+	0.451175i
$297$		0			0
$298$	−1.02852	+	1.78145i	−0.0595806	+	0.103197i
$299$	−13.3534	−	44.6036i	−0.772249	−	2.57949i
$300$		0			0
$301$	−10.6229	+	6.98680i	−0.612294	+	0.402712i
$302$	8.84148	+	1.03342i	0.508770	+	0.0594667i
$303$		0			0
$304$	−1.46164	+	0.734061i	−0.0838306	+	0.0421013i
$305$	−0.491395	+	2.78684i	−0.0281372	+	0.159574i
$306$		0			0
$307$	−2.40217	−	13.6234i	−0.137099	−	0.777527i	−0.973375	−	0.229219i	$-0.926383\pi$
$307$	−2.40217	−	13.6234i	−0.137099	−	0.777527i	0.836276	−	0.548309i	$-0.184728\pi$
$308$	−11.9901	−	16.1055i	−0.683199	−	0.917695i
$309$		0			0
$310$	−1.14297	−	1.21148i	−0.0649166	−	0.0688076i
$311$	−6.10565	+	20.3943i	−0.346220	+	1.15645i	0.590695	+	0.806895i	$0.298854\pi$
$311$	−6.10565	+	20.3943i	−0.346220	+	1.15645i	−0.936914	+	0.349559i	$0.886331\pi$
$312$		0			0
$313$	−13.4077	+	1.56714i	−0.757849	+	0.0885799i	−0.486237	−	0.873827i	$-0.661631\pi$
$313$	−13.4077	+	1.56714i	−0.757849	+	0.0885799i	−0.271612	+	0.962407i	$0.587557\pi$
$314$	3.01195	−	2.52733i	0.169974	−	0.142625i
$315$		0			0
$316$	−3.96592	−	3.32780i	−0.223100	−	0.187203i
$317$	7.36594	+	4.84465i	0.413712	+	0.272103i	0.739256	−	0.673424i	$-0.235177\pi$
$317$	7.36594	+	4.84465i	0.413712	+	0.272103i	−0.325544	+	0.945527i	$0.605548\pi$
$318$		0			0
$319$	−7.72421	+	10.3754i	−0.432473	+	0.580912i
$320$	−0.804163	−	0.403866i	−0.0449541	−	0.0225768i
$321$		0			0
$322$	−35.0422	−	8.30514i	−1.95282	−	0.462828i
$323$	−4.07075			−0.226503
$324$		0			0
$325$	−25.6560			−1.42314
$326$	10.7008	+	2.53613i	0.592660	+	0.140463i
$327$		0			0
$328$	4.63561	+	2.32809i	0.255959	+	0.128547i
$329$	23.6770	−	31.8038i	1.30536	−	1.75340i
$330$		0			0
$331$	−2.52570	−	1.66118i	−0.138825	−	0.0913066i	0.478197	−	0.878253i	$-0.341291\pi$
$331$	−2.52570	−	1.66118i	−0.138825	−	0.0913066i	−0.617022	+	0.786946i	$0.711661\pi$
$332$	2.07455	+	1.74075i	0.113856	+	0.0955361i
$333$		0			0
$334$	−12.3037	+	10.3240i	−0.673230	+	0.564907i
$335$	−4.28237	+	0.500537i	−0.233971	+	0.0273473i
$336$		0			0
$337$	−0.618666	+	2.06649i	−0.0337009	+	0.112569i	−0.973185	−	0.230023i	$-0.926120\pi$
$337$	−0.618666	+	2.06649i	−0.0337009	+	0.112569i	0.939484	+	0.342592i	$0.111305\pi$
$338$	16.8056	+	17.8129i	0.914102	+	0.968891i
$339$		0			0
$340$	−1.33742	−	1.79647i	−0.0725320	−	0.0974274i
$341$	−1.36262	−	7.72781i	−0.0737901	−	0.418484i
$342$		0			0
$343$	6.93163	−	39.3112i	0.374273	−	2.12261i
$344$	−2.39916	+	1.20491i	−0.129354	+	0.0649641i
$345$		0			0
$346$	−11.5069	−	1.34497i	−0.618616	−	0.0723058i
$347$	−24.2348	+	15.9395i	−1.30099	+	0.855677i	−0.995336	−	0.0964641i	$-0.969247\pi$
$347$	−24.2348	+	15.9395i	−1.30099	+	0.855677i	−0.305658	+	0.952141i	$0.598876\pi$
$348$		0			0
$349$	7.51624	+	25.1060i	0.402335	+	1.34389i	0.883980	+	0.467525i	$0.154854\pi$
$349$	7.51624	+	25.1060i	0.402335	+	1.34389i	−0.481645	+	0.876367i	$0.659960\pi$
$350$	−9.92222	+	17.1858i	−0.530365	+	0.918619i
$351$		0			0
$352$	−2.11983	−	3.67165i	−0.112987	−	0.195699i
$353$	−10.1452	+	10.7533i	−0.539974	+	0.572339i	−0.938702	−	0.344731i	$-0.887970\pi$
$353$	−10.1452	+	10.7533i	−0.539974	+	0.572339i	0.398728	+	0.917069i	$0.369452\pi$
$354$		0			0
$355$	0.217581	+	3.73572i	0.0115480	+	0.198272i
$356$	−6.51321	−	15.0993i	−0.345199	−	0.800262i
$357$		0			0
$358$	−0.399296	+	6.85565i	−0.0211035	+	0.362332i
$359$	22.1228	−	8.05203i	1.16760	−	0.424970i	0.315790	−	0.948829i	$-0.397730\pi$
$359$	22.1228	−	8.05203i	1.16760	−	0.424970i	0.851805	+	0.523859i	$0.175508\pi$
$360$		0			0
$361$	15.3403	+	5.58340i	0.807383	+	0.293863i
$362$	9.47692	−	21.9700i	0.498096	−	1.15472i
$363$		0			0
$364$	28.2156	−	6.68721i	1.47890	−	0.350505i
$365$	−1.25729	+	0.297983i	−0.0658096	+	0.0155972i
$366$		0			0
$367$	11.0697	−	25.6624i	0.577833	−	1.33957i	−0.339184	−	0.940720i	$-0.610151\pi$
$367$	11.0697	−	25.6624i	0.577833	−	1.33957i	0.917017	−	0.398848i	$-0.130590\pi$
$368$	−7.14564	−	2.60080i	−0.372492	−	0.135576i
$369$		0			0
$370$	−7.57933	+	2.75865i	−0.394030	+	0.143415i
$371$	0.614315	−	10.5474i	0.0318937	−	0.547593i
$372$		0			0
$373$	−5.01904	−	11.6354i	−0.259876	−	0.602460i	0.737461	−	0.675389i	$-0.236024\pi$
$373$	−5.01904	−	11.6354i	−0.259876	−	0.602460i	−0.997337	+	0.0729295i	$0.976765\pi$
$374$	−0.613530	−	10.5339i	−0.0317249	−	0.544695i
$375$		0			0
$376$	5.74529	−	6.08965i	0.296291	−	0.314050i
$377$	−9.34023	−	16.1778i	−0.481046	−	0.833197i
$378$		0			0
$379$	−4.98552	+	8.63517i	−0.256089	+	0.443559i	−0.965191	−	0.261547i	$-0.915767\pi$
$379$	−4.98552	+	8.63517i	−0.256089	+	0.443559i	0.709102	+	0.705106i	$0.249101\pi$
$380$	−0.422133	−	1.41002i	−0.0216550	−	0.0723326i
$381$		0			0
$382$	8.28592	−	5.44974i	0.423945	−	0.278833i
$383$	31.6256	+	3.69650i	1.61599	+	0.188882i	0.875512	−	0.483197i	$-0.160524\pi$
$383$	31.6256	+	3.69650i	1.61599	+	0.188882i	0.740479	+	0.672079i	$0.234599\pi$
$384$		0			0
$385$	16.1464	−	8.10904i	0.822898	−	0.413275i
$386$	−3.02468	+	17.1538i	−0.153952	+	0.873105i
$387$		0			0
$388$	0.812536	+	4.60812i	0.0412503	+	0.233942i
$389$	12.8269	+	17.2296i	0.650351	+	0.873573i	0.997945	−	0.0640717i	$-0.0204086\pi$
$389$	12.8269	+	17.2296i	0.650351	+	0.873573i	−0.347594	+	0.937645i	$0.613001\pi$
$390$		0			0
$391$	−12.9875	−	13.7660i	−0.656808	−	0.696176i
$392$	4.42501	−	14.7806i	0.223497	−	0.746531i
$393$		0			0
$394$	20.1412	−	2.35416i	1.01470	−	0.118601i
$395$	3.56885	−	2.99462i	0.179568	−	0.150676i
$396$		0			0
$397$	3.00463	+	2.52118i	0.150798	+	0.126535i	0.715065	−	0.699058i	$-0.246397\pi$
$397$	3.00463	+	2.52118i	0.150798	+	0.126535i	−0.564267	+	0.825592i	$0.690841\pi$
$398$	−4.36579	−	2.87143i	−0.218837	−	0.143932i
$399$		0			0
$400$	−2.50222	+	3.36107i	−0.125111	+	0.168053i
$401$	22.9043	+	11.5030i	1.14378	+	0.574430i	0.916752	−	0.399457i	$-0.130801\pi$
$401$	22.9043	+	11.5030i	1.14378	+	0.574430i	0.227032	+	0.973887i	$0.427098\pi$
$402$		0			0
$403$	11.0271	+	2.61347i	0.549299	+	0.130186i
$404$	12.0004			0.597043
$405$		0			0
$406$	−14.4490			−0.717090
$407$	−36.9763	−	8.76353i	−1.83284	−	0.434392i
$408$		0			0
$409$	−12.5591	−	6.30740i	−0.621006	−	0.311881i	0.110333	−	0.993895i	$-0.464808\pi$
$409$	−12.5591	−	6.30740i	−0.621006	−	0.311881i	−0.731339	+	0.682014i	$0.761104\pi$
$410$	−2.78755	+	3.74433i	−0.137667	+	0.184919i
$411$		0			0
$412$	5.95005	+	3.91341i	0.293138	+	0.192800i
$413$	−13.5591	−	11.3775i	−0.667202	−	0.559849i
$414$		0			0
$415$	−1.86684	+	1.56647i	−0.0916398	+	0.0768949i
$416$	6.08145	−	0.710819i	0.298168	−	0.0348508i
$417$		0			0
$418$	1.98882	−	6.64310i	0.0972761	−	0.324925i
$419$	−27.6612	−	29.3192i	−1.35134	−	1.43234i	−0.802854	−	0.596176i	$-0.796686\pi$
$419$	−27.6612	−	29.3192i	−1.35134	−	1.43234i	−0.548485	−	0.836160i	$-0.684795\pi$
$420$		0			0
$421$	10.5011	+	14.1054i	0.511791	+	0.687455i	0.980639	−	0.195824i	$-0.0627382\pi$
$421$	10.5011	+	14.1054i	0.511791	+	0.687455i	−0.468848	+	0.883279i	$0.655331\pi$
$422$	1.73840	+	9.85894i	0.0846239	+	0.479926i
$423$		0			0
$424$	0.387390	−	2.19700i	0.0188133	−	0.106696i
$425$	−9.31944	+	4.68040i	−0.452059	+	0.227033i
$426$		0			0
$427$	−14.7922	−	1.72895i	−0.715842	−	0.0836700i
$428$	7.59243	−	4.99362i	0.366994	−	0.241376i
$429$		0			0
$430$	−0.692899	−	2.31444i	−0.0334146	−	0.111612i
$431$	12.3193	−	21.3377i	0.593402	−	1.02780i	−0.400368	−	0.916354i	$-0.631118\pi$
$431$	12.3193	−	21.3377i	0.593402	−	1.02780i	0.993770	−	0.111448i	$-0.0355489\pi$
$432$		0			0
$433$	7.80606	+	13.5205i	0.375135	+	0.649754i	0.990347	−	0.138608i	$-0.0442629\pi$
$433$	7.80606	+	13.5205i	0.375135	+	0.649754i	−0.615212	+	0.788362i	$0.710930\pi$
$434$	6.01526	−	6.37580i	0.288742	−	0.306048i
$435$		0			0
$436$	−0.497417	−	8.54032i	−0.0238220	−	0.409007i
$437$	−4.92627	−	11.4204i	−0.235656	−	0.546311i
$438$		0			0
$439$	−1.84393	+	31.6591i	−0.0880062	+	1.51101i	0.608556	+	0.793511i	$0.291749\pi$
$439$	−1.84393	+	31.6591i	−0.0880062	+	1.51101i	−0.696562	+	0.717497i	$0.745288\pi$
$440$	3.58510	−	1.30487i	0.170913	−	0.0622072i
$441$		0			0
$442$	14.3197	+	5.21194i	0.681118	+	0.247907i
$443$	−6.05206	+	14.0302i	−0.287542	+	0.666597i	−0.999360	−	0.0357667i	$-0.988613\pi$
$443$	−6.05206	+	14.0302i	−0.287542	+	0.666597i	0.711818	+	0.702364i	$0.247872\pi$
$444$		0			0
$445$	14.3989	−	3.41261i	0.682574	−	0.161773i
$446$	−22.0555	+	5.22726i	−1.04436	+	0.247518i
$447$		0			0
$448$	1.87579	−	4.34858i	0.0886229	−	0.205451i
$449$	6.40822	+	2.33240i	0.302423	+	0.110073i	0.488774	−	0.872410i	$-0.337444\pi$
$449$	6.40822	+	2.33240i	0.302423	+	0.110073i	−0.186352	+	0.982483i	$0.559666\pi$
$450$		0			0
$451$	−20.6663	+	7.52193i	−0.973140	+	0.354194i
$452$	−0.309835	+	5.31967i	−0.0145734	+	0.250216i
$453$		0			0
$454$	1.14331	+	2.65048i	0.0536580	+	0.124393i
$455$	1.51723	+	26.0499i	0.0711289	+	1.22124i
$456$		0			0
$457$	4.39074	−	4.65391i	0.205390	−	0.217701i	−0.616488	−	0.787364i	$-0.711445\pi$
$457$	4.39074	−	4.65391i	0.205390	−	0.217701i	0.821878	+	0.569664i	$0.192927\pi$
$458$	−9.64722	−	16.7095i	−0.450785	−	0.780782i
$459$		0			0
$460$	3.42145	−	5.92613i	0.159526	−	0.276307i
$461$	0.513842	+	1.71635i	0.0239320	+	0.0799385i	0.969121	−	0.246584i	$-0.0793082\pi$
$461$	0.513842	+	1.71635i	0.0239320	+	0.0799385i	−0.945189	+	0.326523i	$0.894123\pi$
$462$		0			0
$463$	15.9861	−	10.5142i	0.742936	−	0.488637i	−0.120740	−	0.992684i	$-0.538527\pi$
$463$	15.9861	−	10.5142i	0.742936	−	0.488637i	0.863676	+	0.504047i	$0.168156\pi$
$464$	−3.03031	−	0.354193i	−0.140679	−	0.0164430i
$465$		0			0
$466$	24.3354	−	12.2217i	1.12732	−	0.566159i
$467$	0.191366	−	1.08529i	0.00885536	−	0.0502212i	−0.980060	−	0.198702i	$-0.936327\pi$
$467$	0.191366	−	1.08529i	0.00885536	−	0.0502212i	0.988915	+	0.148481i	$0.0474384\pi$
$468$		0			0
$469$	−3.94020	−	22.3460i	−0.181941	−	1.03184i
$470$	4.49893	+	6.04312i	0.207520	+	0.278748i
$471$		0			0
$472$	−2.56480	−	2.71852i	−0.118054	−	0.125130i
$473$	3.26449	−	10.9041i	0.150101	−	0.501373i
$474$		0			0
$475$	−6.80722	+	0.795650i	−0.312337	+	0.0365069i
$476$	9.02923	−	7.57643i	0.413854	−	0.347265i
$477$		0			0
$478$	6.05943	+	5.08446i	0.277152	+	0.232558i
$479$	−28.4725	−	18.7266i	−1.30094	−	0.855642i	−0.305608	−	0.952157i	$-0.598860\pi$
$479$	−28.4725	−	18.7266i	−1.30094	−	0.855642i	−0.995331	+	0.0965158i	$0.969230\pi$
$480$		0			0
$481$	32.7720	−	44.0204i	1.49428	−	2.00716i
$482$	0.387375	+	0.194547i	0.0176444	+	0.00886137i
$483$		0			0
$484$	6.78664	+	1.60846i	0.308484	+	0.0731120i
$485$	−4.21073			−0.191199
$486$		0			0
$487$	−6.28526			−0.284812			−0.142406	−	0.989808i	$-0.545484\pi$
$487$	−6.28526			−0.284812			−0.142406	+	0.989808i	$0.545484\pi$
$488$	−3.05991	−	0.725211i	−0.138515	−	0.0328288i
$489$		0			0
$490$	12.4072	+	6.23114i	0.560501	+	0.281494i
$491$	−24.0769	+	32.3409i	−1.08658	+	1.45952i	−0.210348	+	0.977627i	$0.567460\pi$
$491$	−24.0769	+	32.3409i	−1.08658	+	1.45952i	−0.876227	+	0.481898i	$0.839948\pi$
$492$		0			0
$493$	−6.34408	−	4.17257i	−0.285723	−	0.187923i
$494$	7.67163	+	6.43726i	0.345163	+	0.289626i
$495$		0			0
$496$	1.41784	−	1.18971i	0.0636631	−	0.0534197i
$497$	−19.5605	+	2.28630i	−0.877411	+	0.102555i
$498$		0			0
$499$	−6.22942	+	20.8077i	−0.278867	+	0.931481i	0.697722	+	0.716368i	$0.254197\pi$
$499$	−6.22942	+	20.8077i	−0.278867	+	0.931481i	−0.976589	+	0.215112i	$0.930988\pi$
$500$	−5.67529	−	6.01545i	−0.253806	−	0.269019i
$501$		0			0
$502$	−3.60285	−	4.83947i	−0.160803	−	0.215996i
$503$	−2.83726	−	16.0909i	−0.126507	−	0.717457i	−0.980401	−	0.197011i	$-0.936877\pi$
$503$	−2.83726	−	16.0909i	−0.126507	−	0.717457i	0.853894	−	0.520447i	$-0.174234\pi$
$504$		0			0
$505$	−1.87522	+	10.6349i	−0.0834460	+	0.473246i
$506$	28.8101	−	14.4690i	1.28077	−	0.643224i
$507$		0			0
$508$	−2.20591	−	0.257834i	−0.0978715	−	0.0114395i
$509$	23.8891	−	15.7121i	1.05887	−	0.696428i	0.104337	−	0.994542i	$-0.466728\pi$
$509$	23.8891	−	15.7121i	1.05887	−	0.696428i	0.954530	+	0.298115i	$0.0963577\pi$
$510$		0			0
$511$	−1.95031	−	6.51450i	−0.0862768	−	0.288184i
$512$	0.500000	−	0.866025i	0.0220971	−	0.0382733i
$513$		0			0
$514$	−8.47257	−	14.6749i	−0.373709	−	0.647283i
$515$	−4.39787	+	4.66147i	−0.193793	+	0.205409i
$516$		0			0
$517$	2.06384	+	35.4348i	0.0907676	+	1.55842i
$518$	−16.8130	−	38.9769i	−0.738720	−	1.71255i
$519$		0			0
$520$	−0.320368	+	5.50051i	−0.0140491	+	0.241213i
$521$	−6.35056	+	2.31141i	−0.278223	+	0.101265i	−0.477363	−	0.878706i	$-0.658407\pi$
$521$	−6.35056	+	2.31141i	−0.278223	+	0.101265i	0.199140	+	0.979971i	$0.436185\pi$
$522$		0			0
$523$	41.5732	+	15.1314i	1.81787	+	0.661650i	0.995725	+	0.0923727i	$0.0294451\pi$
$523$	41.5732	+	15.1314i	1.81787	+	0.661650i	0.822145	+	0.569278i	$0.192777\pi$
$524$	0.431298	−	0.999861i	0.0188413	−	0.0436791i
$525$		0			0
$526$	−22.2377	+	5.27044i	−0.969610	+	0.229802i
$527$	4.48231	−	1.06233i	0.195253	−	0.0462757i
$528$		0			0
$529$	13.7932	−	31.9763i	0.599706	−	1.39027i
$530$	1.88646	+	0.686617i	0.0819428	+	0.0298247i
$531$		0			0
$532$	7.27894	−	2.64932i	0.315582	−	0.114863i
$533$	1.84677	−	31.7078i	0.0799924	−	1.37342i
$534$		0			0
$535$	3.23898	+	7.50880i	0.140033	+	0.324634i
$536$	−0.278584	−	4.78311i	−0.0120330	−	0.206599i
$537$		0			0
$538$	15.1971	−	16.1079i	0.655192	−	0.694463i
$539$	32.7062	+	56.6489i	1.40876	+	2.44004i
$540$		0			0
$541$	2.15840	−	3.73845i	0.0927967	−	0.160729i	−0.815890	−	0.578207i	$-0.803753\pi$
$541$	2.15840	−	3.73845i	0.0927967	−	0.160729i	0.908687	+	0.417478i	$0.137086\pi$
$542$	−4.85513	−	16.2173i	−0.208546	−	0.696591i
$543$		0			0
$544$	2.07938	−	1.36763i	0.0891528	−	0.0586367i
$545$	7.64624	+	0.893718i	0.327529	+	0.0382827i
$546$		0			0
$547$	−29.0025	+	14.5656i	−1.24006	+	0.622779i	−0.943226	−	0.332151i	$-0.892226\pi$
$547$	−29.0025	+	14.5656i	−1.24006	+	0.622779i	−0.296829	+	0.954931i	$0.595929\pi$
$548$	−1.05321	+	5.97306i	−0.0449910	+	0.255157i
$549$		0			0
$550$	−3.08487	−	17.4952i	−0.131539	−	0.745996i
$551$	−2.97992	−	4.00272i	−0.126949	−	0.170522i
$552$		0			0
$553$	16.8255	+	17.8340i	0.715495	+	0.758380i
$554$	−6.83848	+	22.8421i	−0.290539	+	0.970469i
$555$		0			0
$556$	−14.0145	+	1.63806i	−0.594346	+	0.0694691i
$557$	−27.5704	+	23.1343i	−1.16820	+	0.980233i	−0.999985	−	0.00551749i	$-0.998244\pi$
$557$	−27.5704	+	23.1343i	−1.16820	+	0.980233i	−0.168212	+	0.985751i	$0.553799\pi$
$558$		0			0
$559$	12.5924	+	10.5663i	0.532602	+	0.446906i
$560$	3.56064	+	2.34187i	0.150464	+	0.0989619i
$561$		0			0
$562$	3.62123	−	4.86416i	0.152753	−	0.205182i
$563$	−10.7328	−	5.39023i	−0.452335	−	0.227171i	0.208020	−	0.978125i	$-0.433298\pi$
$563$	−10.7328	−	5.39023i	−0.452335	−	0.227171i	−0.660355	+	0.750953i	$0.729594\pi$
$564$		0			0
$565$	−4.66592	−	1.10584i	−0.196297	−	0.0465232i
$566$	−6.52622			−0.274317
$567$		0			0
$568$	−4.15839			−0.174482
$569$	29.2471	+	6.93169i	1.22610	+	0.290592i	0.792140	−	0.610339i	$-0.208967\pi$
$569$	29.2471	+	6.93169i	1.22610	+	0.290592i	0.433963	+	0.900931i	$0.357115\pi$
$570$		0			0
$571$	−18.7127	−	9.39786i	−0.783101	−	0.393288i	0.0118744	−	0.999929i	$-0.496220\pi$
$571$	−18.7127	−	9.39786i	−0.783101	−	0.393288i	−0.794976	+	0.606641i	$0.792516\pi$
$572$	−15.5015	+	20.8221i	−0.648150	+	0.870616i
$573$		0			0
$574$	−20.5253	−	13.4997i	−0.856711	−	0.563467i
$575$	−24.4088	−	20.4814i	−1.01792	−	0.854133i
$576$		0			0
$577$	25.8767	−	21.7131i	1.07726	−	0.903928i	0.0815689	−	0.996668i	$-0.474007\pi$
$577$	25.8767	−	21.7131i	1.07726	−	0.903928i	0.995690	+	0.0927399i	$0.0295625\pi$
$578$	−10.7327	+	1.25447i	−0.446421	+	0.0521791i
$579$		0			0
$580$	0.787414	−	2.63015i	0.0326956	−	0.109211i
$581$	−8.80134	−	9.32887i	−0.365141	−	0.387027i
$582$		0			0
$583$	5.64804	+	7.58663i	0.233918	+	0.314206i
$584$	−0.249338	−	1.41406i	−0.0103177	−	0.0585144i
$585$		0			0
$586$	−1.02439	+	5.80960i	−0.0423171	+	0.239992i
$587$	5.91286	−	2.96955i	0.244050	−	0.122567i	−0.322570	−	0.946545i	$-0.604547\pi$
$587$	5.91286	−	2.96955i	0.244050	−	0.122567i	0.566620	+	0.823979i	$0.308251\pi$
$588$		0			0
$589$	3.00683	+	0.351448i	0.123894	+	0.0144811i
$590$	2.80996	−	1.84814i	0.115684	−	0.0760868i
$591$		0			0
$592$	−2.57066	−	8.58659i	−0.105653	−	0.352907i
$593$	0.624047	−	1.08088i	0.0256266	−	0.0443865i	−0.852928	−	0.522029i	$-0.825175\pi$
$593$	0.624047	−	1.08088i	0.0256266	−	0.0443865i	0.878554	+	0.477643i	$0.158509\pi$
$594$		0			0
$595$	5.30337	+	9.18570i	0.217417	+	0.376577i
$596$	1.41163	−	1.49624i	0.0578226	−	0.0612883i
$597$		0			0
$598$	2.70720	+	46.4808i	0.110706	+	1.90074i
$599$	16.0453	+	37.1971i	0.655592	+	1.51983i	0.843207	+	0.537590i	$0.180665\pi$
$599$	16.0453	+	37.1971i	0.655592	+	1.51983i	−0.187615	+	0.982243i	$0.560076\pi$
$600$		0			0
$601$	−2.24413	+	38.5302i	−0.0915399	+	1.57168i	0.569921	+	0.821700i	$0.306974\pi$
$601$	−2.24413	+	38.5302i	−0.0915399	+	1.57168i	−0.661461	+	0.749980i	$0.730063\pi$
$602$	11.9478	−	4.34866i	0.486957	−	0.177238i
$603$		0			0
$604$	−8.36483	−	3.04455i	−0.340360	−	0.123881i
$605$	−2.48594	+	5.76305i	−0.101068	+	0.234301i
$606$		0			0
$607$	−27.8613	+	6.60324i	−1.13085	+	0.268017i	−0.753111	−	0.657893i	$-0.771448\pi$
$607$	−27.8613	+	6.60324i	−1.13085	+	0.268017i	−0.377743	+	0.925910i	$0.623300\pi$
$608$	1.59152	−	0.377198i	0.0645448	−	0.0152974i
$609$		0			0
$610$	1.12084	−	2.59840i	0.0453814	−	0.105206i
$611$	−48.1697	−	17.5323i	−1.94874	−	0.709283i
$612$		0			0
$613$	−3.45856	+	1.25881i	−0.139690	+	0.0508429i	−0.410919	−	0.911672i	$-0.634792\pi$
$613$	−3.45856	+	1.25881i	−0.139690	+	0.0508429i	0.271229	+	0.962515i	$0.412570\pi$
$614$	−0.804349	+	13.8101i	−0.0324609	+	0.557332i
$615$		0			0
$616$	7.95271	+	18.4365i	0.320424	+	0.742826i
$617$	0.480387	+	8.24792i	0.0193396	+	0.332049i	0.994076	+	0.108689i	$0.0346653\pi$
$617$	0.480387	+	8.24792i	0.0193396	+	0.332049i	−0.974736	+	0.223359i	$0.928298\pi$
$618$		0			0
$619$	−10.8014	+	11.4488i	−0.434143	+	0.460165i	−0.907097	−	0.420923i	$-0.861706\pi$
$619$	−10.8014	+	11.4488i	−0.434143	+	0.460165i	0.472953	+	0.881087i	$0.343188\pi$
$620$	0.832779	+	1.44242i	0.0334452	+	0.0579288i
$621$		0			0
$622$	10.6443	−	18.4365i	0.426798	−	0.739236i
$623$	22.3356	+	74.6063i	0.894859	+	2.98904i
$624$		0			0
$625$	−11.2866	+	7.42330i	−0.451463	+	0.296932i
$626$	13.4077	+	1.56714i	0.535880	+	0.0626354i
$627$		0			0
$628$	−3.51361	+	1.76460i	−0.140208	+	0.0704152i
$629$	3.87369	−	21.9688i	0.154454	−	0.875952i
$630$		0			0
$631$	6.42930	+	36.4624i	0.255947	+	1.45155i	0.793631	+	0.608399i	$0.208188\pi$
$631$	6.42930	+	36.4624i	0.255947	+	1.45155i	−0.537685	+	0.843146i	$0.680701\pi$
$632$	3.09157	+	4.15270i	0.122976	+	0.165186i
$633$		0			0
$634$	−6.05013	−	6.41277i	−0.240281	−	0.254683i
$635$	0.573197	−	1.91461i	0.0227466	−	0.0759790i
$636$		0			0
$637$	−93.8291	+	10.9670i	−3.71764	+	0.434530i
$638$	9.90873	−	8.31442i	0.392291	−	0.329171i
$639$		0			0
$640$	0.689349	+	0.578432i	0.0272489	+	0.0228645i
$641$	39.3612	+	25.8883i	1.55467	+	1.02253i	0.978758	+	0.205017i	$0.0657250\pi$
$641$	39.3612	+	25.8883i	1.55467	+	1.02253i	0.575916	+	0.817509i	$0.304645\pi$
$642$		0			0
$643$	3.24751	−	4.36216i	0.128069	−	0.172027i	−0.733464	−	0.679729i	$-0.762097\pi$
$643$	3.24751	−	4.36216i	0.128069	−	0.172027i	0.861533	+	0.507702i	$0.169505\pi$
$644$	32.1823	+	16.1626i	1.26816	+	0.636894i
$645$		0			0
$646$	3.96102	+	0.938780i	0.155844	+	0.0369358i
$647$	−25.2978			−0.994557			−0.497279	−	0.867591i	$-0.665667\pi$
$647$	−25.2978			−0.994557			−0.497279	+	0.867591i	$0.665667\pi$
$648$		0			0
$649$	15.8455			0.621990
$650$	24.9645	+	5.91669i	0.979188	+	0.232072i
$651$		0			0
$652$	−9.82745	−	4.93553i	−0.384873	−	0.193290i
$653$	18.2201	−	24.4739i	0.713008	−	0.957736i	−0.286992	−	0.957933i	$-0.592655\pi$
$653$	18.2201	−	24.4739i	0.713008	−	0.957736i	1.00000		0.000197051i	$6.27231e-5\pi$
$654$		0			0
$655$	0.818691	+	0.538461i	0.0319889	+	0.0210394i
$656$	−3.97376	−	3.33438i	−0.155149	−	0.130186i
$657$		0			0
$658$	−30.3732	+	25.4862i	−1.18407	+	0.993555i
$659$	18.6840	−	2.18385i	0.727826	−	0.0850706i	0.255893	−	0.966705i	$-0.417631\pi$
$659$	18.6840	−	2.18385i	0.727826	−	0.0850706i	0.471933	+	0.881635i	$0.343557\pi$
$660$		0			0
$661$	−0.384072	+	1.28289i	−0.0149387	+	0.0498987i	−0.965134	−	0.261757i	$-0.915698\pi$
$661$	−0.384072	+	1.28289i	−0.0149387	+	0.0498987i	0.950195	+	0.311655i	$0.100883\pi$
$662$	2.07452	+	2.19887i	0.0806286	+	0.0854613i
$663$		0			0
$664$	−1.61718	−	2.17225i	−0.0627588	−	0.0842997i
$665$	1.21042	+	6.86466i	0.0469383	+	0.266200i
$666$		0			0
$667$	4.02865	−	22.8476i	0.155990	−	0.884664i
$668$	14.3530	−	7.20833i	0.555333	−	0.278899i
$669$		0			0
$670$	4.28237	+	0.500537i	0.165442	+	0.0193374i
$671$	11.1390	−	7.32623i	0.430016	−	0.282826i
$672$		0			0
$673$	−8.59506	−	28.7095i	−0.331315	−	1.10667i	−0.947683	−	0.319212i	$-0.896582\pi$
$673$	−8.59506	−	28.7095i	−0.331315	−	1.10667i	0.616368	−	0.787458i	$-0.288603\pi$
$674$	1.07856	−	1.86811i	0.0415444	−	0.0719570i
$675$		0			0
$676$	−12.2446	−	21.2083i	−0.470948	−	0.815705i
$677$	10.4366	−	11.0621i	0.401110	−	0.425152i	−0.495062	−	0.868857i	$-0.664855\pi$
$677$	10.4366	−	11.0621i	0.401110	−	0.425152i	0.896173	+	0.443705i	$0.146336\pi$
$678$		0			0
$679$	−1.28850	−	22.1228i	−0.0494483	−	0.848994i
$680$	0.887079	+	2.05648i	0.0340179	+	0.0788624i
$681$		0			0
$682$	−0.456264	+	7.83375i	−0.0174712	+	0.299970i
$683$	32.1031	−	11.6846i	1.22839	−	0.447098i	0.355346	−	0.934735i	$-0.384363\pi$
$683$	32.1031	−	11.6846i	1.22839	−	0.447098i	0.873047	+	0.487637i	$0.162141\pi$
$684$		0			0
$685$	−5.12881	−	1.86673i	−0.195962	−	0.0713242i
$686$	−15.8106	+	36.6530i	−0.603650	+	1.39942i
$687$		0			0
$688$	2.61236	−	0.619142i	0.0995955	−	0.0236046i
$689$	−13.2912	+	3.15007i	−0.506354	+	0.120008i
$690$		0			0
$691$	−3.28549	+	7.61662i	−0.124986	+	0.289750i	−0.969208	−	0.246244i	$-0.920804\pi$
$691$	−3.28549	+	7.61662i	−0.124986	+	0.289750i	0.844222	+	0.535994i	$0.180063\pi$
$692$	10.8866	+	3.96239i	0.413845	+	0.150627i
$693$		0			0
$694$	27.2575	−	9.92091i	1.03468	−	0.376593i
$695$	0.738277	−	12.6757i	0.0280044	−	0.480818i
$696$		0			0
$697$	−5.11358	−	11.8546i	−0.193690	−	0.449025i
$698$	−1.52380	−	26.1626i	−0.0576766	−	0.990269i
$699$		0			0
$700$	13.6181	−	14.4343i	0.514715	−	0.545566i
$701$	−20.0087	−	34.6561i	−0.755718	−	1.30894i	−0.945016	−	0.327023i	$-0.893955\pi$
$701$	−20.0087	−	34.6561i	−0.755718	−	1.30894i	0.189298	−	0.981920i	$-0.439379\pi$
$702$		0			0
$703$	7.33010	−	12.6961i	0.276460	−	0.478843i
$704$	1.21595	+	4.06154i	0.0458277	+	0.153075i
$705$		0			0
$706$	12.3516	−	8.12377i	0.464858	−	0.305742i
$707$	−56.4484	−	6.59788i	−2.12296	−	0.248139i
$708$		0			0
$709$	26.9452	−	13.5324i	1.01195	−	0.508219i	0.136043	−	0.990703i	$-0.456561\pi$
$709$	26.9452	−	13.5324i	1.01195	−	0.508219i	0.875905	+	0.482483i	$0.160265\pi$
$710$	0.649801	−	3.68520i	0.0243866	−	0.138303i
$711$		0			0
$712$	2.85550	+	16.1944i	0.107014	+	0.606909i
$713$	8.40466	+	11.2894i	0.314757	+	0.422792i
$714$		0			0
$715$	−16.0305	−	16.9913i	−0.599505	−	0.635438i
$716$	1.96956	−	6.57877i	0.0736057	−	0.245860i
$717$		0			0
$718$	−23.3834	+	2.73313i	−0.872660	+	0.101999i
$719$	20.1751	−	16.9289i	0.752404	−	0.631342i	−0.183733	−	0.982976i	$-0.558818\pi$
$719$	20.1751	−	16.9289i	0.752404	−	0.631342i	0.936138	+	0.351634i	$0.114374\pi$
$720$		0			0
$721$	−25.8367	−	21.6796i	−0.962209	−	0.807389i
$722$	−13.6392	−	8.97061i	−0.507597	−	0.333852i
$723$		0			0
$724$	−14.2881	+	19.1922i	−0.531013	+	0.713274i
$725$	−11.4243	−	5.73750i	−0.424288	−	0.213085i
$726$		0			0
$727$	−37.7796	−	8.95394i	−1.40117	−	0.332083i	−0.540542	−	0.841317i	$-0.681781\pi$
$727$	−37.7796	−	8.95394i	−1.40117	−	0.332083i	−0.860628	+	0.509234i	$0.829929\pi$
$728$	−28.9972			−1.07471
$729$		0			0
$730$	1.29212			0.0478235
$731$	6.50172	+	1.54094i	0.240475	+	0.0569936i
$732$		0			0
$733$	23.1712	+	11.6370i	0.855849	+	0.429823i	0.821921	−	0.569601i	$-0.192902\pi$
$733$	23.1712	+	11.6370i	0.855849	+	0.429823i	0.0339274	+	0.999424i	$0.489198\pi$
$734$	−16.6895	+	22.4178i	−0.616019	+	0.827458i
$735$		0			0
$736$	6.35325	+	4.17860i	0.234184	+	0.154025i
$737$	15.5607	+	13.0570i	0.573186	+	0.480960i
$738$		0			0
$739$	15.3874	−	12.9116i	0.566034	−	0.474959i	−0.314293	−	0.949326i	$-0.601767\pi$
$739$	15.3874	−	12.9116i	0.566034	−	0.474959i	0.880327	+	0.474367i	$0.157323\pi$
$740$	8.01121	−	0.936377i	0.294498	−	0.0344219i
$741$		0			0
$742$	−3.03015	+	10.1214i	−0.111240	+	0.371569i
$743$	−10.1530	−	10.7616i	−0.372478	−	0.394804i	0.513836	−	0.857889i	$-0.328224\pi$
$743$	−10.1530	−	10.7616i	−0.372478	−	0.394804i	−0.886314	+	0.463085i	$0.846743\pi$
$744$		0			0
$745$	1.10540	+	1.48480i	0.0404986	+	0.0543990i
$746$	2.20043	+	12.4793i	0.0805635	+	0.456899i
$747$		0			0
$748$	−1.83229	+	10.3914i	−0.0669953	+	0.379949i
$749$	−38.4594	+	19.3150i	−1.40528	+	0.705756i
$750$		0			0
$751$	16.2830	+	1.90321i	0.594176	+	0.0694492i	0.407866	−	0.913042i	$-0.366273\pi$
$751$	16.2830	+	1.90321i	0.594176	+	0.0694492i	0.186310	+	0.982491i	$0.440347\pi$
$752$	−6.99479	+	4.60055i	−0.255074	+	0.167765i
$753$		0			0
$754$	5.35762	+	17.8957i	0.195113	+	0.651722i
$755$	4.00522	−	6.93725i	0.145765	−	0.252472i
$756$		0			0
$757$	−0.252679	−	0.437653i	−0.00918377	−	0.0159068i	0.861397	−	0.507932i	$-0.169590\pi$
$757$	−0.252679	−	0.437653i	−0.00918377	−	0.0159068i	−0.870581	+	0.492026i	$0.836257\pi$
$758$	6.84254	−	7.25267i	0.248532	−	0.263429i
$759$		0			0
$760$	0.0855808	+	1.46937i	0.00310434	+	0.0532995i
$761$	7.50717	+	17.4036i	0.272135	+	0.630879i	0.998401	−	0.0565345i	$-0.0180051\pi$
$761$	7.50717	+	17.4036i	0.272135	+	0.630879i	−0.726266	+	0.687414i	$0.758746\pi$
$762$		0			0
$763$	−2.35572	+	40.4461i	−0.0852827	+	1.46425i
$764$	−9.31937	+	3.39197i	−0.337163	+	0.122717i
$765$		0			0
$766$	−29.9206	−	10.8902i	−1.08108	−	0.393480i
$767$	−9.06383	+	21.0123i	−0.327276	+	0.758711i
$768$		0			0
$769$	25.7141	−	6.09434i	0.927273	−	0.219768i	0.260882	−	0.965371i	$-0.415987\pi$
$769$	25.7141	−	6.09434i	0.927273	−	0.219768i	0.666390	+	0.745603i	$0.267838\pi$
$770$	−17.5813	+	4.16684i	−0.633585	+	0.150162i
$771$		0			0
$772$	6.89908	−	15.9939i	0.248303	−	0.575632i
$773$	43.8623	+	15.9646i	1.57762	+	0.574205i	0.974684	−	0.223587i	$-0.0717768\pi$
$773$	43.8623	+	15.9646i	1.57762	+	0.574205i	0.602932	+	0.797793i	$0.293999\pi$
$774$		0			0
$775$	7.28781	−	2.65254i	0.261786	−	0.0952822i
$776$	0.272072	−	4.67129i	0.00976681	−	0.167690i
$777$		0			0
$778$	−8.50777	−	19.7232i	−0.305018	−	0.707112i
$779$	−0.493332	−	8.47018i	−0.0176754	−	0.303476i
$780$		0			0
$781$	12.0985	−	12.8237i	0.432919	−	0.458868i
$782$	9.46281	+	16.3901i	0.338389	+	0.586107i
$783$		0			0
$784$	−7.71437	+	13.3617i	−0.275513	+	0.477203i
$785$	−1.01476	−	3.38954i	−0.0362183	−	0.120978i
$786$		0			0
$787$	15.5522	−	10.2289i	0.554377	−	0.364619i	−0.241197	−	0.970476i	$-0.577540\pi$
$787$	15.5522	−	10.2289i	0.554377	−	0.364619i	0.795574	+	0.605857i	$0.207170\pi$
$788$	−20.1412	−	2.35416i	−0.717499	−	0.0838636i
$789$		0			0
$790$	−4.16326	+	2.09087i	−0.148122	+	0.0743898i
$791$	4.38220	−	24.8527i	0.155813	−	0.883660i
$792$		0			0
$793$	3.34348	+	18.9618i	0.118731	+	0.673355i
$794$	−2.34221	−	3.14614i	−0.0831221	−	0.111652i
$795$		0			0
$796$	3.58592	+	3.80085i	0.127099	+	0.134717i
$797$	−5.36478	+	17.9196i	−0.190030	+	0.634746i	0.808876	+	0.587980i	$0.200077\pi$
$797$	−5.36478	+	17.9196i	−0.190030	+	0.634746i	−0.998906	+	0.0467657i	$0.985109\pi$
$798$		0			0
$799$	−20.6958	+	2.41900i	−0.732166	+	0.0855779i
$800$	3.20989	−	2.69342i	0.113487	−	0.0952267i
$801$		0			0
$802$	−19.6341	−	16.4750i	−0.693305	−	0.581752i
$803$	5.08614	+	3.34521i	0.179486	+	0.118050i
$804$		0			0
$805$	−19.3523	+	25.9946i	−0.682079	+	0.916191i
$806$	−10.1271	−	5.08605i	−0.356714	−	0.179148i
$807$		0			0
$808$	−11.6769	−	2.76748i	−0.410793	−	0.0973598i
$809$	−0.742090			−0.0260905			−0.0130452	−	0.999915i	$-0.504153\pi$
$809$	−0.742090			−0.0260905			−0.0130452	+	0.999915i	$0.504153\pi$
$810$		0			0
$811$	54.1951			1.90305			0.951524	−	0.307575i	$-0.0995176\pi$
$811$	54.1951			1.90305			0.951524	+	0.307575i	$0.0995176\pi$
$812$	14.0595	+	3.33216i	0.493391	+	0.116936i
$813$		0			0
$814$	33.9585	+	17.0546i	1.19025	+	0.597764i
$815$	5.90958	−	7.93794i	0.207003	−	0.278054i
$816$		0			0
$817$	3.66878	+	2.41299i	0.128354	+	0.0844199i
$818$	10.7659	+	9.03370i	0.376423	+	0.315856i
$819$		0			0
$820$	3.57591	−	3.00054i	0.124876	−	0.104784i
$821$	−22.7451	+	2.65852i	−0.793809	+	0.0927830i	−0.503326	−	0.864097i	$-0.667890\pi$
$821$	−22.7451	+	2.65852i	−0.793809	+	0.0927830i	−0.290484	+	0.956880i	$0.593816\pi$
$822$		0			0
$823$	−10.4292	+	34.8359i	−0.363539	+	1.21430i	0.559250	+	0.828999i	$0.311089\pi$
$823$	−10.4292	+	34.8359i	−0.363539	+	1.21430i	−0.922789	+	0.385306i	$0.874096\pi$
$824$	−4.88717	−	5.18010i	−0.170253	−	0.180457i
$825$		0			0
$826$	10.5698	+	14.1977i	0.367771	+	0.494002i
$827$	5.01639	+	28.4493i	0.174437	+	0.989281i	0.938792	+	0.344485i	$0.111946\pi$
$827$	5.01639	+	28.4493i	0.174437	+	0.989281i	−0.764355	+	0.644796i	$0.776942\pi$
$828$		0			0
$829$	1.94646	−	11.0389i	0.0676032	−	0.383397i	−0.932168	−	0.362025i	$-0.882086\pi$
$829$	1.94646	−	11.0389i	0.0676032	−	0.383397i	0.999772	−	0.0213718i	$-0.00680336\pi$
$830$	2.17778	−	1.09372i	0.0755917	−	0.0379636i
$831$		0			0
$832$	−6.08145	−	0.710819i	−0.210836	−	0.0246432i
$833$	−32.0823	+	21.1008i	−1.11158	+	0.731101i
$834$		0			0
$835$	4.14526	+	13.8461i	0.143453	+	0.479165i
$836$	−3.46721	+	6.00539i	−0.119916	+	0.207701i
$837$		0			0
$838$	20.1541	+	34.9080i	0.696213	+	1.20588i
$839$	−9.69596	+	10.2771i	−0.334742	+	0.354806i	−0.872779	−	0.488116i	$-0.837684\pi$
$839$	−9.69596	+	10.2771i	−0.334742	+	0.354806i	0.538037	+	0.842921i	$0.319166\pi$
$840$		0			0
$841$	1.14497	+	19.6584i	0.0394818	+	0.677877i
$842$	−6.96509	−	16.1469i	−0.240033	−	0.556459i
$843$		0			0
$844$	0.582090	−	9.99410i	0.0200364	−	0.344011i
$845$	20.7084	−	7.53724i	0.712391	−	0.259289i
$846$		0			0
$847$	−31.0392	−	11.2973i	−1.06652	−	0.388181i
$848$	−0.883610	+	2.04844i	−0.0303433	+	0.0703436i
$849$		0			0
$850$	10.1476	−	2.40503i	0.348060	−	0.0824917i
$851$	66.3206	−	15.7183i	2.27344	−	0.538815i
$852$		0			0
$853$	1.24036	−	2.87547i	0.0424690	−	0.0984543i	−0.895661	−	0.444737i	$-0.853297\pi$
$853$	1.24036	−	2.87547i	0.0424690	−	0.0984543i	0.938130	+	0.346283i	$0.112556\pi$
$854$	13.9947	+	5.09365i	0.478889	+	0.174301i
$855$		0			0
$856$	−8.53939	+	3.10808i	−0.291870	+	0.106232i
$857$	−1.40729	+	24.1622i	−0.0480721	+	0.825365i	0.884981	+	0.465627i	$0.154171\pi$
$857$	−1.40729	+	24.1622i	−0.0480721	+	0.825365i	−0.933053	+	0.359738i	$0.882866\pi$
$858$		0			0
$859$	−16.7443	−	38.8176i	−0.571308	−	1.32444i	−0.921724	−	0.387846i	$-0.873219\pi$
$859$	−16.7443	−	38.8176i	−0.571308	−	1.32444i	0.350416	−	0.936594i	$-0.386040\pi$
$860$	0.140474	+	2.41185i	0.00479013	+	0.0822434i
$861$		0			0
$862$	−16.9081	+	17.9215i	−0.575892	+	0.610410i
$863$	−26.7136	−	46.2693i	−0.909341	−	1.57502i	−0.814982	−	0.579486i	$-0.803253\pi$
$863$	−26.7136	−	46.2693i	−0.909341	−	1.57502i	−0.0943581	−	0.995538i	$-0.530080\pi$
$864$		0			0
$865$	−5.21267	+	9.02861i	−0.177236	+	0.306982i
$866$	−4.47761	−	14.9563i	−0.152155	−	0.508234i
$867$		0			0
$868$	−7.32348	+	4.81673i	−0.248575	+	0.163490i
$869$	−21.8008	−	2.54815i	−0.739543	−	0.0864402i
$870$		0			0
$871$	−26.2155	+	13.1659i	−0.888278	+	0.446110i
$872$	−1.48552	+	8.42483i	−0.0503062	+	0.285301i
$873$		0			0
$874$	2.15976	+	12.2486i	0.0730550	+	0.414316i
$875$	23.3885	+	31.4162i	0.790676	+	1.06206i
$876$		0			0
$877$	4.64672	+	4.92524i	0.156909	+	0.166314i	0.801059	−	0.598585i	$-0.204270\pi$
$877$	4.64672	+	4.92524i	0.156909	+	0.166314i	−0.644150	+	0.764899i	$0.722789\pi$
$878$	9.09533	−	30.3805i	0.306952	−	1.02529i
$879$		0			0
$880$	−3.78938	+	0.442915i	−0.127740	+	0.0149307i
$881$	30.0377	−	25.2046i	1.01199	−	0.849164i	0.0233941	−	0.999726i	$-0.492553\pi$
$881$	30.0377	−	25.2046i	1.01199	−	0.849164i	0.988601	+	0.150562i	$0.0481083\pi$
$882$		0			0
$883$	−28.9431	−	24.2861i	−0.974012	−	0.817293i	0.00916322	−	0.999958i	$-0.497083\pi$
$883$	−28.9431	−	24.2861i	−0.974012	−	0.817293i	−0.983175	+	0.182665i	$0.941528\pi$
$884$	−12.7317	−	8.37380i	−0.428215	−	0.281641i
$885$		0			0
$886$	9.12452	−	12.2564i	0.306544	−	0.411760i
$887$	19.6726	+	9.87993i	0.660540	+	0.331736i	0.747293	−	0.664494i	$-0.231353\pi$
$887$	19.6726	+	9.87993i	0.660540	+	0.331736i	−0.0867535	+	0.996230i	$0.527649\pi$
$888$		0			0
$889$	10.2346	+	2.42564i	0.343257	+	0.0813533i
$890$	−14.7978			−0.496023
$891$		0			0
$892$	22.6665			0.758931
$893$	−13.3244	−	3.15794i	−0.445884	−	0.105677i
$894$		0			0
$895$	5.52240	+	2.77346i	0.184594	+	0.0927064i
$896$	−2.82808	+	3.79877i	−0.0944796	+	0.126908i
$897$		0			0
$898$	−5.69760	−	3.74737i	−0.190131	−	0.125051i
$899$	4.32576	+	3.62975i	0.144272	+	0.121059i
$900$		0			0
$901$	−4.25330	+	3.56894i	−0.141698	+	0.118899i
$902$	21.8440	−	2.55319i	0.727324	−	0.0850120i
$903$		0			0
$904$	1.52828	−	5.10482i	0.0508299	−	0.169784i
$905$	−14.7757	−	15.6613i	−0.491159	−	0.520598i
$906$		0			0
$907$	12.6817	+	17.0345i	0.421089	+	0.565620i	0.961157	−	0.276001i	$-0.0890092\pi$
$907$	12.6817	+	17.0345i	0.421089	+	0.565620i	−0.540069	+	0.841621i	$0.681602\pi$
$908$	−0.501245	−	2.84270i	−0.0166344	−	0.0943384i
$909$		0			0
$910$	4.53118	−	25.6976i	0.150207	−	0.851867i
$911$	−38.1183	+	19.1437i	−1.26292	+	0.634260i	−0.949025	−	0.315199i	$-0.897929\pi$
$911$	−38.1183	+	19.1437i	−1.26292	+	0.634260i	−0.313890	+	0.949459i	$0.601632\pi$
$912$		0			0
$913$	11.4039	+	1.33292i	0.377414	+	0.0441133i
$914$	−5.34565	+	3.51589i	−0.176818	+	0.116295i
$915$		0			0
$916$	5.53371	+	18.4839i	0.182839	+	0.610724i
$917$	−2.57850	+	4.46609i	−0.0851496	+	0.147483i
$918$		0			0
$919$	−3.54171	−	6.13441i	−0.116830	−	0.202356i	0.801680	−	0.597754i	$-0.203940\pi$
$919$	−3.54171	−	6.13441i	−0.116830	−	0.202356i	−0.918510	+	0.395398i	$0.870607\pi$
$920$	−4.69589	+	4.97735i	−0.154819	+	0.164098i
$921$		0			0
$922$	−0.104173	−	1.78859i	−0.00343077	−	0.0589040i
$923$	10.0847	+	23.3789i	0.331941	+	0.769525i
$924$		0			0
$925$	2.18377	−	37.4939i	0.0718020	−	1.23279i
$926$	−17.9799	+	6.54416i	−0.590857	+	0.215054i
$927$		0			0
$928$	2.86695	+	1.04348i	0.0941122	+	0.0342540i
$929$	0.339206	−	0.786369i	0.0111290	−	0.0257999i	−0.912561	−	0.408941i	$-0.865898\pi$
$929$	0.339206	−	0.786369i	0.0111290	−	0.0257999i	0.923690	+	0.383141i	$0.125158\pi$
$930$		0			0
$931$	−24.5552	+	5.81969i	−0.804764	+	0.190733i
$932$	−26.4980	+	6.28013i	−0.867969	+	0.205713i
$933$		0			0
$934$	−0.436493	+	1.01190i	−0.0142825	+	0.0331105i
$935$	−8.92268	−	3.24759i	−0.291803	−	0.106208i
$936$		0			0
$937$	15.4751	−	5.63247i	0.505549	−	0.184005i	−0.0766392	−	0.997059i	$-0.524419\pi$
$937$	15.4751	−	5.63247i	0.505549	−	0.184005i	0.582188	+	0.813054i	$0.302197\pi$
$938$	−1.31935	+	22.6523i	−0.0430782	+	0.739624i
$939$		0			0
$940$	−2.98403	−	6.91775i	−0.0973282	−	0.225632i
$941$	3.32253	+	57.0457i	0.108312	+	1.85964i	0.417551	+	0.908653i	$0.362888\pi$
$941$	3.32253	+	57.0457i	0.108312	+	1.85964i	−0.309240	+	0.950984i	$0.600075\pi$
$942$		0			0
$943$	27.0695	−	28.6920i	0.881504	−	0.934340i
$944$	1.86873	+	3.23673i	0.0608219	+	0.105347i
$945$		0			0
$946$	−5.69116	+	9.85738i	−0.185036	+	0.320491i
$947$	−8.19001	−	27.3565i	−0.266139	−	0.888968i	−0.981703	−	0.190420i	$-0.939015\pi$
$947$	−8.19001	−	27.3565i	−0.266139	−	0.888968i	0.715563	−	0.698548i	$-0.246170\pi$
$948$		0			0
$949$	−7.34533	+	4.83110i	−0.238440	+	0.156824i
$950$	6.80722	+	0.795650i	0.220855	+	0.0258143i
$951$		0			0
$952$	−10.5331	+	5.28992i	−0.341379	+	0.171447i
$953$	8.34796	−	47.3436i	0.270417	−	1.53361i	−0.482737	−	0.875766i	$-0.660357\pi$
$953$	8.34796	−	47.3436i	0.270417	−	1.53361i	0.753154	−	0.657845i	$-0.228532\pi$
$954$		0			0
$955$	−1.54973	−	8.78895i	−0.0501481	−	0.284404i
$956$	−4.72354	−	6.34481i	−0.152770	−	0.205206i
$957$		0			0
$958$	23.3863	+	24.7881i	0.755578	+	0.800866i
$959$	8.23819	−	27.5175i	0.266025	−	0.888586i
$960$		0			0
$961$	27.3879	−	3.20118i	0.883479	−	0.103264i
$962$	−42.0404	+	35.2761i	−1.35544	+	1.13735i
$963$		0			0
$964$	−0.332067	−	0.278638i	−0.0106952	−	0.00897432i
$965$	13.0959	+	8.61328i	0.421570	+	0.277271i
$966$		0			0
$967$	−3.37172	+	4.52900i	−0.108427	+	0.145643i	−0.853024	−	0.521871i	$-0.825234\pi$
$967$	−3.37172	+	4.52900i	−0.108427	+	0.145643i	0.744597	+	0.667514i	$0.232642\pi$
$968$	−6.23277	−	3.13022i	−0.200329	−	0.100609i
$969$		0			0
$970$	4.09723	+	0.971061i	0.131554	+	0.0311789i
$971$	−11.5616			−0.371028			−0.185514	−	0.982642i	$-0.559395\pi$
$971$	−11.5616			−0.371028			−0.185514	+	0.982642i	$0.559395\pi$
$972$		0			0
$973$	66.8229			2.14225
$974$	6.11584	+	1.44948i	0.195964	+	0.0464443i
$975$		0			0
$976$	2.81018	+	1.41133i	0.0899517	+	0.0451755i
$977$	8.12127	−	10.9088i	0.259822	−	0.349002i	−0.653001	−	0.757357i	$-0.726490\pi$
$977$	8.12127	−	10.9088i	0.259822	−	0.349002i	0.912823	+	0.408355i	$0.133898\pi$
$978$		0			0
$979$	−58.2482	−	38.3104i	−1.86162	−	1.22441i
$980$	−10.6358	−	8.92448i	−0.339747	−	0.285082i
$981$		0			0
$982$	30.8862	−	25.9166i	0.985619	−	0.827033i
$983$	16.7654	−	1.95959i	0.534732	−	0.0625012i	0.155558	−	0.987827i	$-0.450282\pi$
$983$	16.7654	−	1.95959i	0.534732	−	0.0625012i	0.379174	+	0.925325i	$0.376208\pi$
$984$		0			0
$985$	5.23359	−	17.4814i	0.166756	−	0.557004i
$986$	5.21081	+	5.52314i	0.165946	+	0.175893i
$987$		0			0
$988$	−5.98031	−	8.03294i	−0.190259	−	0.255562i
$989$	3.54508	+	20.1052i	0.112727	+	0.639307i
$990$		0			0
$991$	−5.98687	+	33.9532i	−0.190179	+	1.07856i	0.728939	+	0.684579i	$0.240014\pi$
$991$	−5.98687	+	33.9532i	−0.190179	+	1.07856i	−0.919118	+	0.393982i	$0.871097\pi$
$992$	−1.65399	+	0.830667i	−0.0525143	+	0.0263737i
$993$		0			0
$994$	19.5605	+	2.28630i	0.620423	+	0.0725170i
$995$	−3.92869	+	2.58394i	−0.124548	+	0.0819165i
$996$		0			0
$997$	4.82965	+	16.1322i	0.152957	+	0.510910i	0.999780	−	0.0209632i	$-0.00667330\pi$
$997$	4.82965	+	16.1322i	0.152957	+	0.510910i	−0.846824	+	0.531874i	$0.821488\pi$
$998$	10.8601	−	18.8102i	0.343770	−	0.595427i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	486.2.g.b.451.2		90
3.2	odd	2		162.2.g.b.97.5	✓	90
81.5	odd	54		162.2.g.b.157.5	yes	90
81.76	even	27	inner	486.2.g.b.361.2		90

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
162.2.g.b.97.5	✓	90	3.2	odd	2
162.2.g.b.157.5	yes	90	81.5	odd	54
486.2.g.b.361.2		90	81.76	even	27	inner
486.2.g.b.451.2		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)

\(f(q)\)	\(=\)	\(q+(-0.973045 - 0.230616i) q^{2} +(0.893633 + 0.448799i) q^{4} +(-0.537372 + 0.721815i) q^{5} +(-3.95679 - 2.60242i) q^{7} +(-0.766044 - 0.642788i) q^{8} +(0.689349 - 0.578432i) q^{10} +(4.21098 - 0.492194i) q^{11} +(-1.75605 + 5.86562i) q^{13} +(3.24997 + 3.44477i) q^{14} +(0.597159 + 0.802123i) q^{16} +(0.432180 + 2.45101i) q^{17} +(-0.284021 + 1.61076i) q^{19} +(-0.804163 + 0.403866i) q^{20} +(-4.21098 - 0.492194i) q^{22} +(-6.35325 + 4.17860i) q^{23} +(1.20177 + 4.01418i) q^{25} +(3.06142 - 5.30254i) q^{26} +(-2.36795 - 4.10141i) q^{28} +(-2.09368 + 2.21918i) q^{29} +(-0.107618 - 1.84773i) q^{31} +(-0.396080 - 0.918216i) q^{32} +(0.144712 - 2.48461i) q^{34} +(4.00473 - 1.45760i) q^{35} +(-8.42259 - 3.06557i) q^{37} +(0.647833 - 1.50184i) q^{38} +(0.875624 - 0.207527i) q^{40} +(-5.04755 + 1.19629i) q^{41} +(1.06337 - 2.46516i) q^{43} +(3.98397 + 1.45005i) q^{44} +(7.14564 - 2.60080i) q^{46} +(-0.486795 + 8.35794i) q^{47} +(6.11101 + 14.1669i) q^{49} +(-0.243639 - 4.18313i) q^{50} +(-4.20175 + 4.45360i) q^{52} +(1.11544 + 1.93201i) q^{53} +(-1.90759 + 3.30404i) q^{55} +(1.35827 + 4.53694i) q^{56} +(2.54903 - 1.67652i) q^{58} +(3.71218 + 0.433892i) q^{59} +(2.81018 - 1.41133i) q^{61} +(-0.321399 + 1.82275i) q^{62} +(0.173648 + 0.984808i) q^{64} +(-3.29024 - 4.41957i) q^{65} +(3.28793 + 3.48500i) q^{67} +(-0.713803 + 2.38427i) q^{68} +(-4.23293 + 0.494758i) q^{70} +(3.18551 - 2.67296i) q^{71} +(1.09995 + 0.922965i) q^{73} +(7.48859 + 4.92532i) q^{74} +(-0.976720 + 1.31196i) q^{76} +(-17.9429 - 9.01124i) q^{77} +(-5.03759 - 1.19393i) q^{79} -0.899881 q^{80} +5.18737 q^{82} +(2.63513 + 0.624537i) q^{83} +(-2.00142 - 1.00515i) q^{85} +(-1.60321 + 2.15349i) q^{86} +(-3.54218 - 2.32973i) q^{88} +(-12.5970 - 10.5701i) q^{89} +(22.2131 - 18.6390i) q^{91} +(-7.55282 + 0.882798i) q^{92} +(2.40115 - 8.02039i) q^{94} +(-1.01005 - 1.07059i) q^{95} +(2.79423 + 3.75330i) q^{97} +(-2.67917 - 15.1943i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 90 q - 18 q^{13} + 9 q^{20} - 27 q^{23} - 18 q^{25} + 27 q^{26} - 18 q^{28} + 27 q^{29} + 54 q^{31} + 27 q^{35} + 18 q^{38} + 9 q^{41} - 36 q^{43} + 18 q^{46} + 27 q^{47} + 36 q^{52} + 27 q^{53} - 54 q^{55}+ \cdots - 36 q^{98}+O(q^{100}) \) 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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