LMFDB - Embedded newform 486.2.g.a.127.4

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:	$72$
Relative dimension:	$4$ over $\Q(\zeta_{27})$
Twist minimal:	no (minimal twist has level 162)
Sato-Tate group:	$\mathrm{SU}(2)[C_{27}]$

Embedding invariants

Embedding label			127.4
Character	$\chi$	$=$	486.127
Dual form			486.2.g.a.199.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.686242 + 0.727374i) q^{2} +(-0.0581448 - 0.998308i) q^{4} +(3.71787 + 0.434557i) q^{5} +(-3.25050 + 1.63246i) q^{7} +(0.766044 + 0.642788i) q^{8} +(-2.86744 + 2.40607i) q^{10} +(-2.08512 + 4.83385i) q^{11} +(-0.202747 + 0.0480518i) q^{13} +(1.04322 - 3.48460i) q^{14} +(-0.993238 + 0.116093i) q^{16} +(0.290217 + 1.64590i) q^{17} +(0.286765 - 1.62633i) q^{19} +(0.217647 - 3.73685i) q^{20} +(-2.08512 - 4.83385i) q^{22} +(7.81600 + 3.92534i) q^{23} +(8.76851 + 2.07818i) q^{25} +(0.104182 - 0.180448i) q^{26} +(1.81870 + 3.15009i) q^{28} +(-0.216107 - 0.721848i) q^{29} +(-4.77184 + 3.13849i) q^{31} +(0.597159 - 0.802123i) q^{32} +(-1.39634 - 0.918389i) q^{34} +(-12.7944 + 4.65677i) q^{35} +(5.15467 + 1.87615i) q^{37} +(0.986157 + 1.32464i) q^{38} +(2.56873 + 2.72269i) q^{40} +(-3.43214 - 3.63786i) q^{41} +(-0.625285 - 0.839904i) q^{43} +(4.94691 + 1.80053i) q^{44} +(-8.21885 + 2.99142i) q^{46} +(-4.54436 - 2.98887i) q^{47} +(3.72073 - 4.99781i) q^{49} +(-7.52893 + 4.95185i) q^{50} +(0.0597592 + 0.199610i) q^{52} +(2.43382 + 4.21549i) q^{53} +(-9.85278 + 17.0655i) q^{55} +(-3.53936 - 0.838844i) q^{56} +(0.673355 + 0.338172i) q^{58} +(4.73861 + 10.9853i) q^{59} +(0.123728 - 2.12434i) q^{61} +(0.991781 - 5.62467i) q^{62} +(0.173648 + 0.984808i) q^{64} +(-0.774668 + 0.0905456i) q^{65} +(1.79201 - 5.98575i) q^{67} +(1.62624 - 0.385426i) q^{68} +(5.39281 - 12.5019i) q^{70} +(1.97644 - 1.65843i) q^{71} +(-4.28632 - 3.59665i) q^{73} +(-4.90201 + 2.46188i) q^{74} +(-1.64025 - 0.191718i) q^{76} +(-1.11340 - 19.1163i) q^{77} +(2.96988 - 3.14789i) q^{79} -3.74318 q^{80} +5.00136 q^{82} +(9.81132 - 10.3994i) q^{83} +(0.363751 + 6.24536i) q^{85} +(1.04002 + 0.121561i) q^{86} +(-4.70443 + 2.36265i) q^{88} +(-0.396952 - 0.333082i) q^{89} +(0.580586 - 0.487170i) q^{91} +(3.46424 - 8.03101i) q^{92} +(5.29255 - 1.25436i) q^{94} +(1.77289 - 5.92186i) q^{95} +(1.84818 - 0.216021i) q^{97} +(1.08195 + 6.13606i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q + 18 q^{13} + 9 q^{20} + 81 q^{23} + 18 q^{25} + 27 q^{26} + 18 q^{28} + 27 q^{29} - 54 q^{31} + 27 q^{35} - 9 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}) $ 72 * q + 18 * q^13 + 9 * q^20 + 81 * q^23 + 18 * q^25 + 27 * q^26 + 18 * q^28 + 27 * q^29 - 54 * q^31 + 27 * q^35 - 9 * 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 + 18 * q^59 - 9 * q^65 - 135 * q^67 + 18 * q^68 + 18 * q^70 - 72 * q^71 + 36 * q^73 - 99 * q^74 - 9 * q^76 - 144 * q^77 - 9 * q^79 - 18 * q^80 - 72 * q^82 - 99 * q^83 + 9 * q^85 - 72 * q^86 - 9 * q^88 - 126 * q^89 + 63 * q^91 - 36 * q^92 + 18 * q^94 - 45 * q^95 - 171 * q^97 - 36 * q^98

Character values

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

$n$	$245$
$\chi(n)$	$e\left(\frac{20}{27}\right)$

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 $

$2$	−0.686242	+	0.727374i	−0.485246	+	0.514331i
$2$	−0.686242	+	0.727374i	−0.485246	+	0.514331i
$3$		0			0
$3$		0			0
$4$	−0.0581448	−	0.998308i	−0.0290724	−	0.499154i
$5$	3.71787	+	0.434557i	1.66268	+	0.194340i	0.894868	−	0.446331i	$-0.147270\pi$
$5$	3.71787	+	0.434557i	1.66268	+	0.194340i	0.767815	+	0.640671i	$0.221344\pi$
$6$		0			0
$7$	−3.25050	+	1.63246i	−1.22858	+	0.617014i	−0.940239	−	0.340515i	$-0.889398\pi$
$7$	−3.25050	+	1.63246i	−1.22858	+	0.617014i	−0.288336	+	0.957529i	$0.593102\pi$
$8$	0.766044	+	0.642788i	0.270838	+	0.227260i
$9$		0			0
$10$	−2.86744	+	2.40607i	−0.906765	+	0.760867i
$11$	−2.08512	+	4.83385i	−0.628687	+	1.45746i	0.244292	+	0.969702i	$0.421444\pi$
$11$	−2.08512	+	4.83385i	−0.628687	+	1.45746i	−0.872979	+	0.487758i	$0.837815\pi$
$12$		0			0
$13$	−0.202747	+	0.0480518i	−0.0562318	+	0.0133272i	−0.258635	−	0.965975i	$-0.583273\pi$
$13$	−0.202747	+	0.0480518i	−0.0562318	+	0.0133272i	0.202404	+	0.979302i	$0.435125\pi$
$14$	1.04322	−	3.48460i	0.278812	−	0.931298i
$15$		0			0
$16$	−0.993238	+	0.116093i	−0.248310	+	0.0290232i
$17$	0.290217	+	1.64590i	0.0703879	+	0.399189i	0.999563	+	0.0295503i	$0.00940753\pi$
$17$	0.290217	+	1.64590i	0.0703879	+	0.399189i	−0.929175	+	0.369639i	$0.879481\pi$
$18$		0			0
$19$	0.286765	−	1.62633i	0.0657885	−	0.373105i	−0.934083	−	0.357057i	$-0.883780\pi$
$19$	0.286765	−	1.62633i	0.0657885	−	0.373105i	0.999871	−	0.0160484i	$-0.00510858\pi$
$20$	0.217647	−	3.73685i	0.0486673	−	0.835585i
$21$		0			0
$22$	−2.08512	−	4.83385i	−0.444549	−	1.03058i
$23$	7.81600	+	3.92534i	1.62975	+	0.818490i	0.999100	+	0.0424209i	$0.0135070\pi$
$23$	7.81600	+	3.92534i	1.62975	+	0.818490i	0.630648	+	0.776069i	$0.282789\pi$
$24$		0			0
$25$	8.76851	+	2.07818i	1.75370	+	0.415635i
$26$	0.104182	−	0.180448i	0.0204317	−	0.0353887i
$27$		0			0
$28$	1.81870	+	3.15009i	0.343703	+	0.595310i
$29$	−0.216107	−	0.721848i	−0.0401301	−	0.134044i	0.935577	−	0.353122i	$-0.114880\pi$
$29$	−0.216107	−	0.721848i	−0.0401301	−	0.134044i	−0.975707	+	0.219079i	$0.929695\pi$
$30$		0			0
$31$	−4.77184	+	3.13849i	−0.857047	+	0.563689i	−0.900248	−	0.435377i	$-0.856615\pi$
$31$	−4.77184	+	3.13849i	−0.857047	+	0.563689i	0.0432006	+	0.999066i	$0.486245\pi$
$32$	0.597159	−	0.802123i	0.105564	−	0.141797i
$33$		0			0
$34$	−1.39634	−	0.918389i	−0.239471	−	0.157502i
$35$	−12.7944	+	4.65677i	−2.16264	+	0.787137i
$36$		0			0
$37$	5.15467	+	1.87615i	0.847423	+	0.308437i	0.728989	−	0.684525i	$-0.239990\pi$
$37$	5.15467	+	1.87615i	0.847423	+	0.308437i	0.118434	+	0.992962i	$0.462213\pi$
$38$	0.986157	+	1.32464i	0.159976	+	0.214885i
$39$		0			0
$40$	2.56873	+	2.72269i	0.406152	+	0.430495i
$41$	−3.43214	−	3.63786i	−0.536010	−	0.568138i	0.401605	−	0.915813i	$-0.368453\pi$
$41$	−3.43214	−	3.63786i	−0.536010	−	0.568138i	−0.937615	+	0.347675i	$0.886971\pi$
$42$		0			0
$43$	−0.625285	−	0.839904i	−0.0953551	−	0.128084i	0.751885	−	0.659294i	$-0.229145\pi$
$43$	−0.625285	−	0.839904i	−0.0953551	−	0.128084i	−0.847240	+	0.531210i	$0.821737\pi$
$44$	4.94691	+	1.80053i	0.745774	+	0.271440i
$45$		0			0
$46$	−8.21885	+	2.99142i	−1.21180	+	0.441060i
$47$	−4.54436	−	2.98887i	−0.662863	−	0.435972i	0.172991	−	0.984923i	$-0.444657\pi$
$47$	−4.54436	−	2.98887i	−0.662863	−	0.435972i	−0.835854	+	0.548952i	$0.815027\pi$
$48$		0			0
$49$	3.72073	−	4.99781i	0.531533	−	0.713972i
$50$	−7.52893	+	4.95185i	−1.06475	+	0.700298i
$51$		0			0
$52$	0.0597592	+	0.199610i	0.00828711	+	0.0276809i
$53$	2.43382	+	4.21549i	0.334310	+	0.579042i	0.983352	−	0.181710i	$-0.0581633\pi$
$53$	2.43382	+	4.21549i	0.334310	+	0.579042i	−0.649042	+	0.760753i	$0.724830\pi$
$54$		0			0
$55$	−9.85278	+	17.0655i	−1.32855	+	2.30111i
$56$	−3.53936	−	0.838844i	−0.472967	−	0.112095i
$57$		0			0
$58$	0.673355	+	0.338172i	0.0884159	+	0.0444041i
$59$	4.73861	+	10.9853i	0.616914	+	1.43017i	0.884457	+	0.466622i	$0.154529\pi$
$59$	4.73861	+	10.9853i	0.616914	+	1.43017i	−0.267542	+	0.963546i	$0.586211\pi$
$60$		0			0
$61$	0.123728	−	2.12434i	0.0158418	−	0.271993i	−0.981081	−	0.193599i	$-0.937984\pi$
$61$	0.123728	−	2.12434i	0.0158418	−	0.271993i	0.996922	−	0.0783938i	$-0.0249792\pi$
$62$	0.991781	−	5.62467i	0.125956	−	0.714334i
$63$		0			0
$64$	0.173648	+	0.984808i	0.0217060	+	0.123101i
$65$	−0.774668	+	0.0905456i	−0.0960857	+	0.0112308i
$66$		0			0
$67$	1.79201	−	5.98575i	0.218929	−	0.731275i	−0.776003	−	0.630729i	$-0.782756\pi$
$67$	1.79201	−	5.98575i	0.218929	−	0.731275i	0.994932	−	0.100546i	$-0.0320590\pi$
$68$	1.62624	−	0.385426i	0.197211	−	0.0467398i
$69$		0			0
$70$	5.39281	−	12.5019i	0.644565	−	1.49427i
$71$	1.97644	−	1.65843i	0.234560	−	0.196820i	−0.517930	−	0.855423i	$-0.673297\pi$
$71$	1.97644	−	1.65843i	0.234560	−	0.196820i	0.752490	+	0.658604i	$0.228853\pi$
$72$		0			0
$73$	−4.28632	−	3.59665i	−0.501676	−	0.420956i	0.356513	−	0.934291i	$-0.383966\pi$
$73$	−4.28632	−	3.59665i	−0.501676	−	0.420956i	−0.858189	+	0.513334i	$0.828410\pi$
$74$	−4.90201	+	2.46188i	−0.569847	+	0.286188i
$75$		0			0
$76$	−1.64025	−	0.191718i	−0.188150	−	0.0219915i
$77$	−1.11340	−	19.1163i	−0.126884	−	2.17851i
$78$		0			0
$79$	2.96988	−	3.14789i	0.334138	−	0.354166i	−0.538420	−	0.842677i	$-0.680978\pi$
$79$	2.96988	−	3.14789i	0.334138	−	0.354166i	0.872558	+	0.488511i	$0.162460\pi$
$80$	−3.74318			−0.418501
$81$		0			0
$82$	5.00136			0.552308
$83$	9.81132	−	10.3994i	1.07693	−	1.14148i	0.0875474	−	0.996160i	$-0.472097\pi$
$83$	9.81132	−	10.3994i	1.07693	−	1.14148i	0.989385	−	0.145321i	$-0.0464215\pi$
$84$		0			0
$85$	0.363751	+	6.24536i	0.0394543	+	0.677405i
$86$	1.04002	+	0.121561i	0.112148	+	0.0131083i
$87$		0			0
$88$	−4.70443	+	2.36265i	−0.501494	+	0.251860i
$89$	−0.396952	−	0.333082i	−0.0420768	−	0.0353067i	0.621507	−	0.783409i	$-0.286521\pi$
$89$	−0.396952	−	0.333082i	−0.0420768	−	0.0353067i	−0.663584	+	0.748102i	$0.730965\pi$
$90$		0			0
$91$	0.580586	−	0.487170i	0.0608620	−	0.0510692i
$92$	3.46424	−	8.03101i	0.361172	−	0.837291i
$93$		0			0
$94$	5.29255	−	1.25436i	0.545885	−	0.129377i
$95$	1.77289	−	5.92186i	0.181895	−	0.607570i
$96$		0			0
$97$	1.84818	−	0.216021i	0.187654	−	0.0219337i	−0.0217465	−	0.999764i	$-0.506923\pi$
$97$	1.84818	−	0.216021i	0.187654	−	0.0219337i	0.209401	+	0.977830i	$0.432849\pi$
$98$	1.08195	+	6.13606i	0.109294	+	0.619836i
$99$		0			0
$100$	1.56482	−	8.87451i	0.156482	−	0.887451i
$101$	−0.668800	+	11.4829i	−0.0665481	+	1.14259i	0.785410	+	0.618976i	$0.212452\pi$
$101$	−0.668800	+	11.4829i	−0.0665481	+	1.14259i	−0.851958	+	0.523610i	$0.824585\pi$
$102$		0			0
$103$	−5.88743	−	13.6486i	−0.580105	−	1.34484i	−0.915333	−	0.402698i	$-0.868073\pi$
$103$	−5.88743	−	13.6486i	−0.580105	−	1.34484i	0.335228	−	0.942137i	$-0.391187\pi$
$104$	−0.186200	−	0.0935132i	−0.0182584	−	0.00916972i
$105$		0			0
$106$	−4.73642	−	1.12255i	−0.460042	−	0.109032i
$107$	−1.27937	+	2.21593i	−0.123681	+	0.214222i	−0.921217	−	0.389050i	$-0.872803\pi$
$107$	−1.27937	+	2.21593i	−0.123681	+	0.214222i	0.797535	+	0.603272i	$0.206137\pi$
$108$		0			0
$109$	−5.38593	−	9.32871i	−0.515879	−	0.893528i	−0.999830	−	0.0184331i	$-0.994132\pi$
$109$	−5.38593	−	9.32871i	−0.515879	−	0.893528i	0.483951	−	0.875095i	$-0.339201\pi$
$110$	−5.65162	−	18.8777i	−0.538861	−	1.79992i
$111$		0			0
$112$	3.03901	−	1.99879i	0.287159	−	0.188868i
$113$	7.36982	−	9.89939i	0.693295	−	0.931256i	−0.306493	−	0.951873i	$-0.599156\pi$
$113$	7.36982	−	9.89939i	0.693295	−	0.931256i	0.999787	+	0.0206167i	$0.00656295\pi$
$114$		0			0
$115$	27.3531	+	17.9904i	2.55069	+	1.67761i
$116$	−0.708062	+	0.257713i	−0.0657419	+	0.0239281i
$117$		0			0
$118$	−11.2423	−	4.09185i	−1.03494	−	0.376686i
$119$	−3.63022	−	4.87624i	−0.332782	−	0.447004i
$120$		0			0
$121$	−11.4697	−	12.1572i	−1.04270	−	1.10520i
$122$	1.46028	+	1.54780i	0.132207	+	0.140132i
$123$		0			0
$124$	3.41064	+	4.58128i	0.306284	+	0.411411i
$125$	14.1099	+	5.13559i	1.26203	+	0.459341i
$126$		0			0
$127$	17.2415	−	6.27538i	1.52993	−	0.556850i	0.566327	−	0.824181i	$-0.308364\pi$
$127$	17.2415	−	6.27538i	1.52993	−	0.556850i	0.963605	+	0.267331i	$0.0861417\pi$
$128$	−0.835488	−	0.549509i	−0.0738474	−	0.0485702i
$129$		0			0
$130$	0.465749	−	0.625609i	0.0408489	−	0.0548695i
$131$	0.165733	−	0.109005i	0.0144802	−	0.00952378i	−0.542248	−	0.840218i	$-0.682427\pi$
$131$	0.165733	−	0.109005i	0.0144802	−	0.00952378i	0.556728	+	0.830695i	$0.312056\pi$
$132$		0			0
$133$	1.72279	+	5.75452i	0.149385	+	0.498980i
$134$	3.12412	+	5.41113i	0.269883	+	0.467451i
$135$		0			0
$136$	−0.835645	+	1.44738i	−0.0716560	+	0.124112i
$137$	4.29953	+	1.01901i	0.367333	+	0.0870596i	0.410137	−	0.912024i	$-0.365481\pi$
$137$	4.29953	+	1.01901i	0.367333	+	0.0870596i	−0.0428037	+	0.999084i	$0.513629\pi$
$138$		0			0
$139$	−1.10445	−	0.554676i	−0.0936783	−	0.0470470i	0.401343	−	0.915928i	$-0.368543\pi$
$139$	−1.10445	−	0.554676i	−0.0936783	−	0.0470470i	−0.495021	+	0.868881i	$0.664840\pi$
$140$	5.39281	+	12.5019i	0.455776	+	1.05661i
$141$		0			0
$142$	−0.150017	+	2.57570i	−0.0125892	+	0.216148i
$143$	0.190475	−	1.08024i	0.0159284	−	0.0903342i
$144$		0			0
$145$	−0.489775	−	2.77765i	−0.0406736	−	0.230671i
$146$	5.55756	−	0.649586i	0.459947	−	0.0537601i
$147$		0			0
$148$	1.57326	−	5.25504i	0.129321	−	0.431962i
$149$	−7.84141	+	1.85845i	−0.642394	+	0.152250i	−0.538886	−	0.842379i	$-0.681155\pi$
$149$	−7.84141	+	1.85845i	−0.642394	+	0.152250i	−0.103507	+	0.994629i	$0.533007\pi$
$150$		0			0
$151$	2.94676	−	6.83136i	0.239804	−	0.555928i	−0.755230	−	0.655459i	$-0.772475\pi$
$151$	2.94676	−	6.83136i	0.239804	−	0.555928i	0.995034	+	0.0995312i	$0.0317343\pi$
$152$	1.26506	−	1.06151i	0.102610	−	0.0860998i
$153$		0			0
$154$	14.6688	+	12.3086i	1.18204	+	0.991852i
$155$	−19.1049	+	9.59486i	−1.53455	+	0.770678i
$156$		0			0
$157$	19.5842	+	2.28906i	1.56299	+	0.182687i	0.853145	−	0.521673i	$-0.174692\pi$
$157$	19.5842	+	2.28906i	1.56299	+	0.182687i	0.709843	+	0.704360i	$0.248766\pi$
$158$	0.251636	+	4.32043i	0.0200191	+	0.343715i
$159$		0			0
$160$	2.56873	−	2.72269i	0.203076	−	0.215248i
$161$	−31.8139			−2.50729
$162$		0			0
$163$	7.25041			0.567896			0.283948	−	0.958840i	$-0.408356\pi$
$163$	7.25041			0.567896			0.283948	+	0.958840i	$0.408356\pi$
$164$	−3.43214	+	3.63786i	−0.268005	+	0.284069i
$165$		0			0
$166$	0.831307	+	14.2730i	0.0645219	+	1.10780i
$167$	−18.7077	−	2.18662i	−1.44764	−	0.169205i	−0.644324	−	0.764753i	$-0.722861\pi$
$167$	−18.7077	−	2.18662i	−1.44764	−	0.169205i	−0.803320	+	0.595547i	$0.796935\pi$
$168$		0			0
$169$	−11.5784	+	5.81490i	−0.890648	+	0.447300i
$170$	−4.79233	−	4.02124i	−0.367555	−	0.308415i
$171$		0			0
$172$	−0.802126	+	0.673063i	−0.0611615	+	0.0513206i
$173$	−1.82769	+	4.23707i	−0.138957	+	0.322138i	−0.973457	−	0.228869i	$-0.926497\pi$
$173$	−1.82769	+	4.23707i	−0.138957	+	0.322138i	0.834500	+	0.551007i	$0.185756\pi$
$174$		0			0
$175$	−31.8946	+	7.55917i	−2.41101	+	0.571419i
$176$	1.50984	−	5.04323i	0.113809	−	0.380148i
$177$		0			0
$178$	0.514681	−	0.0601575i	0.0385769	−	0.00450900i
$179$	−4.34713	−	24.6538i	−0.324920	−	1.84271i	−0.510240	−	0.860032i	$-0.670443\pi$
$179$	−4.34713	−	24.6538i	−0.324920	−	1.84271i	0.185320	−	0.982678i	$-0.440668\pi$
$180$		0			0
$181$	2.73733	−	15.5241i	0.203464	−	1.15390i	−0.696375	−	0.717678i	$-0.745205\pi$
$181$	2.73733	−	15.5241i	0.203464	−	1.15390i	0.899839	−	0.436223i	$-0.143684\pi$
$182$	−0.0440680	+	0.756619i	−0.00326654	+	0.0560843i
$183$		0			0
$184$	3.46424	+	8.03101i	0.255387	+	0.592054i
$185$	18.3491	+	9.21528i	1.34905	+	0.677521i
$186$		0			0
$187$	−8.56116	−	2.02903i	−0.626054	−	0.148378i
$188$	−2.71958	+	4.71046i	−0.198346	+	0.343545i
$189$		0			0
$190$	3.09078	+	5.35338i	0.224228	+	0.388375i
$191$	0.382243	+	1.27678i	0.0276581	+	0.0923845i	0.970704	−	0.240277i	$-0.0772384\pi$
$191$	0.382243	+	1.27678i	0.0276581	+	0.0923845i	−0.943046	+	0.332662i	$0.892053\pi$
$192$		0			0
$193$	−11.1785	+	7.35219i	−0.804644	+	0.529222i	−0.883924	−	0.467630i	$-0.845108\pi$
$193$	−11.1785	+	7.35219i	−0.804644	+	0.529222i	0.0792808	+	0.996852i	$0.474738\pi$
$194$	−1.11117	+	1.49256i	−0.0797774	+	0.107160i
$195$		0			0
$196$	−5.20569	−	3.42384i	−0.371835	−	0.244560i
$197$	24.7068	−	8.99252i	1.76028	−	0.640691i	0.760323	−	0.649545i	$-0.225041\pi$
$197$	24.7068	−	8.99252i	1.76028	−	0.640691i	0.999961	+	0.00885463i	$0.00281855\pi$
$198$		0			0
$199$	−2.18009	−	0.793488i	−0.154542	−	0.0562489i	0.263591	−	0.964635i	$-0.415093\pi$
$199$	−2.18009	−	0.793488i	−0.154542	−	0.0562489i	−0.418133	+	0.908386i	$0.637315\pi$
$200$	5.38124	+	7.22827i	0.380511	+	0.511116i
$201$		0			0
$202$	−7.89336	−	8.36648i	−0.555375	−	0.588663i
$203$	1.88085	+	1.99358i	0.132010	+	0.139922i
$204$		0			0
$205$	−11.1794	−	15.0166i	−0.780804	−	1.04880i
$206$	13.9678	+	5.08387i	0.973184	+	0.354210i
$207$		0			0
$208$	0.195797	−	0.0712644i	0.0135761	−	0.00494130i
$209$	7.26347	+	4.77726i	0.502425	+	0.330450i
$210$		0			0
$211$	−5.83455	+	7.83716i	−0.401667	+	0.539532i	−0.956233	−	0.292608i	$-0.905477\pi$
$211$	−5.83455	+	7.83716i	−0.401667	+	0.539532i	0.554566	+	0.832140i	$0.312884\pi$
$212$	4.06685	−	2.67481i	0.279312	−	0.183706i
$213$		0			0
$214$	−0.733854	−	2.45124i	−0.0501653	−	0.167564i
$215$	−1.95974	−	3.39438i	−0.133653	−	0.231495i
$216$		0			0
$217$	10.3874	−	17.9915i	0.705144	−	1.22134i
$218$	10.4815	+	2.48416i	0.709897	+	0.168249i
$219$		0			0
$220$	17.6095	+	8.84384i	1.18723	+	0.596252i
$221$	−0.137929	−	0.319755i	−0.00927811	−	0.0215091i
$222$		0			0
$223$	−0.340442	+	5.84516i	−0.0227977	+	0.391421i	0.967538	+	0.252727i	$0.0813274\pi$
$223$	−0.340442	+	5.84516i	−0.0227977	+	0.391421i	−0.990335	+	0.138694i	$0.955710\pi$
$224$	−0.631629	+	3.58215i	−0.0422025	+	0.239342i
$225$		0			0
$226$	2.14308	+	12.1540i	0.142555	+	0.808471i
$227$	7.48001	−	0.874287i	0.496465	−	0.0580285i	0.135824	−	0.990733i	$-0.456632\pi$
$227$	7.48001	−	0.874287i	0.496465	−	0.0580285i	0.360642	+	0.932705i	$0.382558\pi$
$228$		0			0
$229$	−3.23898	+	10.8190i	−0.214038	+	0.714937i	0.781778	+	0.623557i	$0.214313\pi$
$229$	−3.23898	+	10.8190i	−0.214038	+	0.714937i	−0.995816	+	0.0913799i	$0.970872\pi$
$230$	−31.8566	+	7.55015i	−2.10056	+	0.497842i
$231$		0			0
$232$	0.298448	−	0.691879i	0.0195940	−	0.0454241i
$233$	−5.82577	+	4.88840i	−0.381659	+	0.320250i	−0.813353	−	0.581770i	$-0.802360\pi$
$233$	−5.82577	+	4.88840i	−0.381659	+	0.320250i	0.431694	+	0.902020i	$0.357916\pi$
$234$		0			0
$235$	−15.5965	−	13.0870i	−1.01740	−	0.853703i
$236$	10.6912	−	5.36933i	0.695939	−	0.349514i
$237$		0			0
$238$	6.03806	+	0.705748i	0.391389	+	0.0457468i
$239$	−1.11084	−	19.0723i	−0.0718541	−	1.23369i	−0.820862	−	0.571126i	$-0.806507\pi$
$239$	−1.11084	−	19.0723i	−0.0718541	−	1.23369i	0.749008	−	0.662561i	$-0.230530\pi$
$240$		0			0
$241$	4.44457	−	4.71097i	0.286300	−	0.303460i	−0.568222	−	0.822875i	$-0.692369\pi$
$241$	4.44457	−	4.71097i	0.286300	−	0.303460i	0.854522	+	0.519415i	$0.173850\pi$
$242$	16.7138			1.07440
$243$		0			0
$244$	−2.12794			−0.136227
$245$	16.0050	−	16.9643i	1.02252	−	1.08381i
$246$		0			0
$247$	0.0200073	+	0.343512i	0.00127303	+	0.0218571i
$248$	−5.67282	−	0.663058i	−0.360224	−	0.0421042i
$249$		0			0
$250$	−13.4183	+	6.73893i	−0.848648	+	0.426207i
$251$	6.01053	+	5.04343i	0.379381	+	0.318339i	0.812459	−	0.583018i	$-0.198128\pi$
$251$	6.01053	+	5.04343i	0.379381	+	0.318339i	−0.433078	+	0.901356i	$0.642573\pi$
$252$		0			0
$253$	−35.2718	+	29.5965i	−2.21752	+	1.86072i
$254$	−7.26726	+	16.8474i	−0.455989	+	1.05710i
$255$		0			0
$256$	0.973045	−	0.230616i	0.0608153	−	0.0144135i
$257$	−3.31564	+	11.0750i	−0.206824	+	0.690839i	0.790137	+	0.612931i	$0.210009\pi$
$257$	−3.31564	+	11.0750i	−0.206824	+	0.690839i	−0.996960	+	0.0779088i	$0.975176\pi$
$258$		0			0
$259$	−19.8180	+	2.31640i	−1.23143	+	0.143934i
$260$	0.135435	+	0.768092i	0.00839935	+	0.0476351i
$261$		0			0
$262$	−0.0344461	+	0.195354i	−0.00212809	+	0.0120690i
$263$	−0.419053	+	7.19487i	−0.0258399	+	0.443655i	0.960431	+	0.278519i	$0.0898434\pi$
$263$	−0.419053	+	7.19487i	−0.0258399	+	0.443655i	−0.986271	+	0.165136i	$0.947194\pi$
$264$		0			0
$265$	7.21674	+	16.7303i	0.443321	+	1.02773i
$266$	−5.36793	−	2.69588i	−0.329129	−	0.165295i
$267$		0			0
$268$	−6.07982	−	1.44094i	−0.371384	−	0.0880196i
$269$	−10.8367	+	18.7696i	−0.660723	+	1.14441i	0.319703	+	0.947518i	$0.396417\pi$
$269$	−10.8367	+	18.7696i	−0.660723	+	1.14441i	−0.980426	+	0.196888i	$0.936917\pi$
$270$		0			0
$271$	10.7244	+	18.5753i	0.651463	+	1.12837i	0.982768	+	0.184844i	$0.0591779\pi$
$271$	10.7244	+	18.5753i	0.651463	+	1.12837i	−0.331305	+	0.943524i	$0.607489\pi$
$272$	−0.479332	−	1.60108i	−0.0290637	−	0.0970797i
$273$		0			0
$274$	−3.69171	+	2.42808i	−0.223024	+	0.146686i
$275$	−28.3290	+	38.0524i	−1.70830	+	2.29465i
$276$		0			0
$277$	−10.0441	−	6.60609i	−0.603490	−	0.396922i	0.210674	−	0.977556i	$-0.432434\pi$
$277$	−10.0441	−	6.60609i	−0.603490	−	0.396922i	−0.814164	+	0.580635i	$0.802804\pi$
$278$	1.16138	−	0.422707i	0.0696548	−	0.0253523i
$279$		0			0
$280$	−12.7944	−	4.65677i	−0.764609	−	0.278295i
$281$	5.53844	+	7.43941i	0.330395	+	0.443798i	0.936017	−	0.351955i	$-0.114483\pi$
$281$	5.53844	+	7.43941i	0.330395	+	0.443798i	−0.605622	+	0.795753i	$0.707075\pi$
$282$		0			0
$283$	16.3804	+	17.3622i	0.973714	+	1.03208i	0.999475	+	0.0324087i	$0.0103178\pi$
$283$	16.3804	+	17.3622i	0.973714	+	1.03208i	−0.0257605	+	0.999668i	$0.508201\pi$
$284$	−1.77054	−	1.87667i	−0.105063	−	0.111360i
$285$		0			0
$286$	0.655026	+	0.879852i	0.0387325	+	0.0520268i
$287$	17.0949	+	6.22202i	1.00908	+	0.367274i
$288$		0			0
$289$	13.3500	−	4.85901i	0.785295	−	0.285824i
$290$	2.35649	+	1.54989i	0.138378	+	0.0910127i
$291$		0			0
$292$	−3.34134	+	4.48820i	−0.195537	+	0.262652i
$293$	11.4171	−	7.50914i	0.666994	−	0.438689i	−0.170337	−	0.985386i	$-0.554485\pi$
$293$	11.4171	−	7.50914i	0.666994	−	0.438689i	0.837330	+	0.546697i	$0.184115\pi$
$294$		0			0
$295$	12.8438	+	42.9013i	0.747795	+	2.49781i
$296$	2.74274	+	4.75057i	0.159419	+	0.276121i
$297$		0			0
$298$	4.02932	−	6.97898i	0.233412	−	0.404282i
$299$	−1.77329	−	0.420277i	−0.102552	−	0.0243052i
$300$		0			0
$301$	3.40361	+	1.70935i	0.196181	+	0.0985256i
$302$	2.94676	+	6.83136i	0.169567	+	0.393101i
$303$		0			0
$304$	−0.0960213	+	1.64862i	−0.00550720	+	0.0945549i
$305$	1.38315	−	7.84424i	0.0791990	−	0.449160i
$306$		0			0
$307$	−2.34246	−	13.2847i	−0.133691	−	0.758201i	−0.975762	−	0.218834i	$-0.929775\pi$
$307$	−2.34246	−	13.2847i	−0.133691	−	0.758201i	0.842071	−	0.539367i	$-0.181336\pi$
$308$	−19.0192	+	2.22303i	−1.08372	+	0.126669i
$309$		0			0
$310$	6.13156	−	20.4808i	0.348249	−	1.16323i
$311$	5.74747	−	1.36218i	0.325909	−	0.0772419i	−0.0644043	−	0.997924i	$-0.520515\pi$
$311$	5.74747	−	1.36218i	0.325909	−	0.0772419i	0.390314	+	0.920682i	$0.372367\pi$
$312$		0			0
$313$	3.49181	−	8.09493i	0.197369	−	0.457552i	−0.790575	−	0.612365i	$-0.790218\pi$
$313$	3.49181	−	8.09493i	0.197369	−	0.457552i	0.987944	+	0.154813i	$0.0494775\pi$
$314$	−15.1045	+	12.6742i	−0.852395	+	0.715245i
$315$		0			0
$316$	−3.31525	−	2.78182i	−0.186497	−	0.156490i
$317$	6.52805	−	3.27851i	0.366652	−	0.184139i	−0.255928	−	0.966696i	$-0.582381\pi$
$317$	6.52805	−	3.27851i	0.366652	−	0.184139i	0.622580	+	0.782556i	$0.286085\pi$
$318$		0			0
$319$	3.93991	+	0.460510i	0.220593	+	0.0257836i
$320$	0.217647	+	3.73685i	0.0121668	+	0.208896i
$321$		0			0
$322$	21.8320	−	23.1406i	1.21665	−	1.28958i
$323$	2.76000			0.153570
$324$		0			0
$325$	−1.87765			−0.104153
$326$	−4.97554	+	5.27376i	−0.275569	+	0.292087i
$327$		0			0
$328$	−0.290803	−	4.99290i	−0.0160569	−	0.275687i
$329$	19.6507	+	2.29683i	1.08338	+	0.126629i
$330$		0			0
$331$	−28.6172	+	14.3721i	−1.57294	+	0.789962i	−0.999570	−	0.0293318i	$-0.990662\pi$
$331$	−28.6172	+	14.3721i	−1.57294	+	0.789962i	−0.573374	+	0.819294i	$0.694366\pi$
$332$	−10.9523	−	9.19005i	−0.601084	−	0.504369i
$333$		0			0
$334$	14.4285	−	12.1069i	0.789491	−	0.662462i
$335$	9.26363	−	21.4755i	0.506126	−	1.17333i
$336$		0			0
$337$	25.2820	−	5.99194i	1.37720	−	0.326402i	0.525660	−	0.850695i	$-0.323819\pi$
$337$	25.2820	−	5.99194i	1.37720	−	0.326402i	0.851538	+	0.524293i	$0.175670\pi$
$338$	3.71599	−	12.4123i	0.202123	−	0.675139i
$339$		0			0
$340$	6.21365	−	0.726271i	0.336982	−	0.0393876i
$341$	−5.22112	−	29.6104i	−0.282740	−	1.60350i
$342$		0			0
$343$	0.485898	−	2.75566i	0.0262360	−	0.148792i
$344$	0.0608835	−	1.04533i	0.00328262	−	0.0563604i
$345$		0			0
$346$	−1.82769	−	4.23707i	−0.0982573	−	0.227786i
$347$	−11.6904	−	5.87112i	−0.627571	−	0.315178i	0.106436	−	0.994320i	$-0.466056\pi$
$347$	−11.6904	−	5.87112i	−0.627571	−	0.315178i	−0.734007	+	0.679142i	$0.762352\pi$
$348$		0			0
$349$	−19.4854	−	4.61812i	−1.04303	−	0.247202i	−0.326819	−	0.945087i	$-0.605977\pi$
$349$	−19.4854	−	4.61812i	−1.04303	−	0.247202i	−0.716210	+	0.697885i	$0.754125\pi$
$350$	16.3891	−	28.3867i	0.876034	−	1.51733i
$351$		0			0
$352$	2.63219	+	4.55909i	0.140296	+	0.243001i
$353$	8.35199	+	27.8976i	0.444532	+	1.48484i	0.827705	+	0.561163i	$0.189646\pi$
$353$	8.35199	+	27.8976i	0.444532	+	1.48484i	−0.383173	+	0.923676i	$0.625169\pi$
$354$		0			0
$355$	8.06884	−	5.30696i	0.428249	−	0.281664i
$356$	−0.309438	+	0.415648i	−0.0164002	+	0.0220293i
$357$		0			0
$358$	20.9157	+	13.7565i	1.10543	+	0.727052i
$359$	−14.6096	+	5.31744i	−0.771063	+	0.280644i	−0.697441	−	0.716642i	$-0.745678\pi$
$359$	−14.6096	+	5.31744i	−0.771063	+	0.280644i	−0.0736220	+	0.997286i	$0.523456\pi$
$360$		0			0
$361$	15.2915	+	5.56563i	0.804813	+	0.292928i
$362$	9.41339	+	12.6444i	0.494757	+	0.664574i
$363$		0			0
$364$	−0.520103	−	0.551277i	−0.0272608	−	0.0288948i
$365$	−14.3731	−	15.2345i	−0.752320	−	0.797413i
$366$		0			0
$367$	−5.51820	−	7.41223i	−0.288048	−	0.386915i	0.634421	−	0.772988i	$-0.281239\pi$
$367$	−5.51820	−	7.41223i	−0.288048	−	0.386915i	−0.922468	+	0.386073i	$0.873831\pi$
$368$	−8.21885	−	2.99142i	−0.428437	−	0.155938i
$369$		0			0
$370$	−19.2949	+	7.02276i	−1.00309	+	0.365096i
$371$	−14.7928	−	9.72936i	−0.768002	−	0.505123i
$372$		0			0
$373$	20.1084	−	27.0103i	1.04117	−	1.39854i	0.127619	−	0.991823i	$-0.459266\pi$
$373$	20.1084	−	27.0103i	1.04117	−	1.39854i	0.913555	−	0.406716i	$-0.133326\pi$
$374$	7.35089	−	4.83476i	0.380106	−	0.249999i
$375$		0			0
$376$	−1.55997	−	5.21066i	−0.0804493	−	0.268719i
$377$	0.0785012	+	0.135968i	0.00404302	+	0.00700271i
$378$		0			0
$379$	0.117576	−	0.203648i	0.00603950	−	0.0104607i	−0.862990	−	0.505221i	$-0.831411\pi$
$379$	0.117576	−	0.203648i	0.00603950	−	0.0104607i	0.869029	+	0.494761i	$0.164744\pi$
$380$	−6.01493	−	1.42556i	−0.308559	−	0.0731299i
$381$		0			0
$382$	−1.19101	−	0.598146i	−0.0609372	−	0.0306038i
$383$	−5.82441	−	13.5025i	−0.297614	−	0.689946i	0.702142	−	0.712037i	$-0.252227\pi$
$383$	−5.82441	−	13.5025i	−0.297614	−	0.689946i	−0.999756	+	0.0220908i	$0.992968\pi$
$384$		0			0
$385$	4.16766	−	71.5559i	0.212403	−	3.64683i
$386$	2.32334	−	13.1763i	0.118255	−	0.670656i
$387$		0			0
$388$	−0.323118	−	1.83249i	−0.0164038	−	0.0930308i
$389$	21.2249	−	2.48083i	1.07614	−	0.125783i	0.440490	−	0.897757i	$-0.354805\pi$
$389$	21.2249	−	2.48083i	1.07614	−	0.125783i	0.635654	+	0.771974i	$0.280731\pi$
$390$		0			0
$391$	−4.19239	+	14.0035i	−0.212018	+	0.708190i
$392$	6.06277	−	1.43690i	0.306216	−	0.0725746i
$393$		0			0
$394$	−10.4139	+	24.1421i	−0.524644	+	1.21626i
$395$	12.4096	−	10.4129i	0.624394	−	0.523929i
$396$		0			0
$397$	−17.7928	−	14.9299i	−0.892995	−	0.749311i	0.0758139	−	0.997122i	$-0.475845\pi$
$397$	−17.7928	−	14.9299i	−0.892995	−	0.749311i	−0.968809	+	0.247811i	$0.920289\pi$
$398$	2.07323	−	1.04122i	0.103922	−	0.0521914i
$399$		0			0
$400$	−8.95048	−	1.04616i	−0.447524	−	0.0523081i
$401$	0.933075	+	16.0203i	0.0465955	+	0.800014i	0.937964	+	0.346734i	$0.112709\pi$
$401$	0.933075	+	16.0203i	0.0465955	+	0.800014i	−0.891368	+	0.453280i	$0.850254\pi$
$402$		0			0
$403$	0.816664	−	0.865613i	0.0406809	−	0.0431193i
$404$	11.5023			0.572261
$405$		0			0
$406$	−2.74080			−0.136024
$407$	−19.8171	+	21.0049i	−0.982298	+	1.04117i
$408$		0			0
$409$	−0.205707	−	3.53186i	−0.0101716	−	0.174639i	−0.999568	−	0.0293976i	$-0.990641\pi$
$409$	−0.205707	−	3.53186i	−0.0101716	−	0.174639i	0.989396	−	0.145242i	$-0.0463959\pi$
$410$	18.5944	+	2.17338i	0.918313	+	0.107335i
$411$		0			0
$412$	−13.2832	+	6.67106i	−0.654415	+	0.328659i
$413$	−33.3360	−	27.9723i	−1.64036	−	1.37642i
$414$		0			0
$415$	40.9964	−	34.4000i	2.01243	−	1.68863i
$416$	−0.0825284	+	0.191322i	−0.00404629	+	0.00938035i
$417$		0			0
$418$	−8.45935	+	2.00490i	−0.413761	+	0.0980630i
$419$	−8.97055	+	29.9637i	−0.438240	+	1.46382i	0.398981	+	0.916959i	$0.369364\pi$
$419$	−8.97055	+	29.9637i	−0.438240	+	1.46382i	−0.837221	+	0.546865i	$0.815821\pi$
$420$		0			0
$421$	−17.7199	+	2.07115i	−0.863613	+	0.100942i	−0.536354	−	0.843993i	$-0.680199\pi$
$421$	−17.7199	+	2.07115i	−0.863613	+	0.100942i	−0.327259	+	0.944935i	$0.606125\pi$
$422$	−1.69663	−	9.62208i	−0.0825907	−	0.468395i
$423$		0			0
$424$	−0.845255	+	4.79368i	−0.0410492	+	0.232802i
$425$	−0.875701	+	15.0352i	−0.0424778	+	0.729315i
$426$		0			0
$427$	3.06572	+	7.10714i	0.148361	+	0.343939i
$428$	2.28657	+	1.14836i	0.110526	+	0.0555081i
$429$		0			0
$430$	3.81384	+	0.903896i	0.183920	+	0.0435898i
$431$	9.13617	−	15.8243i	0.440074	−	0.762230i	−0.557621	−	0.830096i	$-0.688286\pi$
$431$	9.13617	−	15.8243i	0.440074	−	0.762230i	0.997694	+	0.0678655i	$0.0216189\pi$
$432$		0			0
$433$	14.1667	+	24.5374i	0.680806	+	1.17919i	0.974735	+	0.223363i	$0.0717037\pi$
$433$	14.1667	+	24.5374i	0.680806	+	1.17919i	−0.293929	+	0.955827i	$0.594963\pi$
$434$	5.95829	+	19.9021i	0.286007	+	0.955330i
$435$		0			0
$436$	−8.99976	+	5.91923i	−0.431010	+	0.283480i
$437$	8.62524	−	11.5857i	0.412601	−	0.554220i
$438$		0			0
$439$	−2.64602	−	1.74031i	−0.126287	−	0.0830605i	0.484794	−	0.874629i	$-0.338895\pi$
$439$	−2.64602	−	1.74031i	−0.126287	−	0.0830605i	−0.611081	+	0.791568i	$0.709265\pi$
$440$	−18.5172	+	6.73970i	−0.882772	+	0.321303i
$441$		0			0
$442$	0.327234	+	0.119103i	0.0155649	+	0.00566518i
$443$	19.0944	+	25.6482i	0.907200	+	1.21858i	0.975296	+	0.220903i	$0.0709003\pi$
$443$	19.0944	+	25.6482i	0.907200	+	1.21858i	−0.0680955	+	0.997679i	$0.521692\pi$
$444$		0			0
$445$	−1.33107	−	1.41086i	−0.0630990	−	0.0668810i
$446$	−4.01799	−	4.25882i	−0.190257	−	0.201661i
$447$		0			0
$448$	−2.17211	−	2.91765i	−0.102622	−	0.137846i
$449$	2.30646	+	0.839483i	0.108849	+	0.0396177i	0.395870	−	0.918306i	$-0.370443\pi$
$449$	2.30646	+	0.839483i	0.108849	+	0.0396177i	−0.287022	+	0.957924i	$0.592665\pi$
$450$		0			0
$451$	24.7413	−	9.00508i	1.16502	−	0.424033i
$452$	−10.3112	−	6.78176i	−0.484996	−	0.318987i
$453$		0			0
$454$	−4.49716	+	6.04073i	−0.211062	+	0.283506i
$455$	2.37025	−	1.55894i	0.111119	−	0.0730841i
$456$		0			0
$457$	6.35184	+	21.2166i	0.297126	+	0.992471i	0.968011	+	0.250909i	$0.0807295\pi$
$457$	6.35184	+	21.2166i	0.297126	+	0.992471i	−0.670884	+	0.741562i	$0.734085\pi$
$458$	−5.64670	−	9.78037i	−0.263853	−	0.457007i
$459$		0			0
$460$	16.3695	−	28.3529i	0.763233	−	1.32196i
$461$	−8.12571	−	1.92583i	−0.378452	−	0.0896948i	0.0369870	−	0.999316i	$-0.488224\pi$
$461$	−8.12571	−	1.92583i	−0.378452	−	0.0896948i	−0.415439	+	0.909621i	$0.636372\pi$
$462$		0			0
$463$	−21.8558	−	10.9764i	−1.01572	−	0.510116i	−0.138585	−	0.990351i	$-0.544255\pi$
$463$	−21.8558	−	10.9764i	−1.01572	−	0.510116i	−0.877140	+	0.480235i	$0.840552\pi$
$464$	0.298448	+	0.691879i	0.0138551	+	0.0321197i
$465$		0			0
$466$	0.442192	−	7.59214i	0.0204841	−	0.351699i
$467$	4.93682	−	27.9981i	0.228449	−	1.29560i	−0.627533	−	0.778590i	$-0.715935\pi$
$467$	4.93682	−	27.9981i	0.228449	−	1.29560i	0.855982	−	0.517006i	$-0.172954\pi$
$468$		0			0
$469$	3.94657	+	22.3821i	0.182236	+	1.03351i
$470$	20.2221	−	2.36363i	0.932777	−	0.109026i
$471$		0			0
$472$	−3.43125	+	11.4612i	−0.157936	+	0.527543i
$473$	5.36376	−	1.27123i	0.246626	−	0.0584514i
$474$		0			0
$475$	5.89430	−	13.6645i	0.270449	−	0.626971i
$476$	−4.65691	+	3.90761i	−0.213449	+	0.179105i
$477$		0			0
$478$	14.6350	+	12.2802i	0.669390	+	0.561685i
$479$	−14.1368	+	7.09975i	−0.645926	+	0.324396i	−0.741427	−	0.671033i	$-0.765851\pi$
$479$	−14.1368	+	7.09975i	−0.645926	+	0.324396i	0.0955017	+	0.995429i	$0.469554\pi$
$480$		0			0
$481$	−1.13525	−	0.132691i	−0.0517627	−	0.00605020i
$482$	0.376586	+	6.46573i	0.0171530	+	0.294506i
$483$		0			0
$484$	−11.4697	+	12.1572i	−0.521350	+	0.552598i
$485$	6.96518			0.316272
$486$		0			0
$487$	9.74171			0.441439			0.220720	−	0.975337i	$-0.429159\pi$
$487$	9.74171			0.441439			0.220720	+	0.975337i	$0.429159\pi$
$488$	1.46028	−	1.54780i	0.0661037	−	0.0700658i
$489$		0			0
$490$	1.35610	+	23.2833i	0.0612622	+	1.05183i
$491$	−5.97315	−	0.698161i	−0.269565	−	0.0315076i	−0.0197632	−	0.999805i	$-0.506291\pi$
$491$	−5.97315	−	0.698161i	−0.269565	−	0.0315076i	−0.249801	+	0.968297i	$0.580365\pi$
$492$		0			0
$493$	1.12537	−	0.565183i	0.0506842	−	0.0254546i
$494$	−0.263591	−	0.221179i	−0.0118595	−	0.00995133i
$495$		0			0
$496$	4.37522	−	3.67124i	0.196453	−	0.164844i
$497$	−3.71710	+	8.61721i	−0.166735	+	0.386535i
$498$		0			0
$499$	9.43087	−	2.23516i	0.422184	−	0.100059i	−0.0140319	−	0.999902i	$-0.504467\pi$
$499$	9.43087	−	2.23516i	0.422184	−	0.100059i	0.436216	+	0.899842i	$0.356318\pi$
$500$	4.30648	−	14.3847i	0.192592	−	0.643301i
$501$		0			0
$502$	−7.79314	+	0.910887i	−0.347825	+	0.0406549i
$503$	6.11251	+	34.6658i	0.272543	+	1.54567i	0.746659	+	0.665207i	$0.231657\pi$
$503$	6.11251	+	34.6658i	0.272543	+	1.54567i	−0.474116	+	0.880463i	$0.657232\pi$
$504$		0			0
$505$	−7.47647	+	42.4011i	−0.332698	+	1.88683i
$506$	2.67722	−	45.9661i	0.119017	−	2.04344i
$507$		0			0
$508$	−7.26726	−	16.8474i	−0.322433	−	0.747483i
$509$	−16.0863	−	8.07886i	−0.713014	−	0.358089i	0.0550313	−	0.998485i	$-0.482474\pi$
$509$	−16.0863	−	8.07886i	−0.713014	−	0.358089i	−0.768045	+	0.640396i	$0.778770\pi$
$510$		0			0
$511$	19.8041	+	4.69366i	0.876083	+	0.207635i
$512$	−0.500000	+	0.866025i	−0.0220971	+	0.0382733i
$513$		0			0
$514$	−5.78033	−	10.0118i	−0.254960	−	0.441603i
$515$	−15.9576	−	53.3021i	−0.703176	−	2.34877i
$516$		0			0
$517$	23.9233	−	15.7346i	1.05214	−	0.692006i
$518$	11.9151	−	16.0047i	0.523518	−	0.703207i
$519$		0			0
$520$	−0.651631	−	0.428585i	−0.0285759	−	0.0187947i
$521$	4.14562	−	1.50888i	0.181623	−	0.0661054i	−0.249608	−	0.968347i	$-0.580302\pi$
$521$	4.14562	−	1.50888i	0.181623	−	0.0661054i	0.431231	+	0.902242i	$0.358079\pi$
$522$		0			0
$523$	−33.2656	−	12.1077i	−1.45460	−	0.529432i	−0.510730	−	0.859741i	$-0.670625\pi$
$523$	−33.2656	−	12.1077i	−1.45460	−	0.529432i	−0.943873	+	0.330309i	$0.892847\pi$
$524$	−0.118457	−	0.159115i	−0.00517481	−	0.00695097i
$525$		0			0
$526$	−4.94579	−	5.24223i	−0.215646	−	0.228572i
$527$	−6.55050	−	6.94313i	−0.285344	−	0.302447i
$528$		0			0
$529$	31.9468	+	42.9120i	1.38899	+	1.86574i
$530$	−17.1216	−	6.23175i	−0.743715	−	0.270690i
$531$		0			0
$532$	5.64461	−	2.05447i	0.244725	−	0.0890726i
$533$	0.870661	+	0.572643i	0.0377125	+	0.0248039i
$534$		0			0
$535$	−5.71948	+	7.68260i	−0.247275	+	0.332148i
$536$	5.22033	−	3.43346i	0.225484	−	0.148303i
$537$		0			0
$538$	−6.21598	−	20.7628i	−0.267990	−	0.895148i
$539$	16.4005	+	28.4064i	0.706418	+	1.22355i
$540$		0			0
$541$	−12.5590	+	21.7529i	−0.539955	+	0.935229i	0.458951	+	0.888462i	$0.348225\pi$
$541$	−12.5590	+	21.7529i	−0.539955	+	0.935229i	−0.998906	+	0.0467676i	$0.985108\pi$
$542$	−20.8707	−	4.94645i	−0.896474	−	0.212468i
$543$		0			0
$544$	1.49352	+	0.750074i	0.0640341	+	0.0321591i
$545$	−15.9704	−	37.0234i	−0.684095	−	1.58591i
$546$		0			0
$547$	−0.00653029	+	0.112121i	−0.000279215	+	0.00479394i	−0.998445	−	0.0557477i	$-0.982246\pi$
$547$	−0.00653029	+	0.112121i	−0.000279215	+	0.00479394i	0.998166	+	0.0605416i	$0.0192828\pi$
$548$	0.767287	−	4.35150i	0.0327769	−	0.185887i
$549$		0			0
$550$	−8.23780	−	46.7189i	−0.351261	−	1.99210i
$551$	−1.23593	+	0.144460i	−0.0526526	+	0.00615420i
$552$		0			0
$553$	−4.51480	+	15.0805i	−0.191989	+	0.641287i
$554$	11.6978	−	2.77242i	0.496990	−	0.117789i
$555$		0			0
$556$	−0.489520	+	1.13483i	−0.0207603	+	0.0481277i
$557$	−25.6731	+	21.5423i	−1.08780	+	0.912775i	−0.996545	−	0.0830527i	$-0.973533\pi$
$557$	−25.6731	+	21.5423i	−1.08780	+	0.912775i	−0.0912573	+	0.995827i	$0.529089\pi$
$558$		0			0
$559$	0.167133	+	0.140242i	0.00706899	+	0.00593159i
$560$	12.1672	−	6.11061i	0.514159	−	0.258221i
$561$		0			0
$562$	−9.21194	−	1.07672i	−0.388582	−	0.0454187i
$563$	2.65296	+	45.5495i	0.111809	+	1.91968i	0.330357	+	0.943856i	$0.392831\pi$
$563$	2.65296	+	45.5495i	0.111809	+	1.91968i	−0.218549	+	0.975826i	$0.570132\pi$
$564$		0			0
$565$	31.7019	−	33.6021i	1.33371	−	1.41365i
$566$	−23.8697			−1.00332
$567$		0			0
$568$	2.58006			0.108257
$569$	−3.01473	+	3.19543i	−0.126384	+	0.133959i	−0.787475	−	0.616346i	$-0.788612\pi$
$569$	−3.01473	+	3.19543i	−0.126384	+	0.133959i	0.661091	+	0.750306i	$0.270094\pi$
$570$		0			0
$571$	−2.32506	−	39.9197i	−0.0973006	−	1.67059i	−0.595371	−	0.803451i	$-0.702995\pi$
$571$	−2.32506	−	39.9197i	−0.0973006	−	1.67059i	0.498071	−	0.867136i	$-0.334042\pi$
$572$	−1.08949	−	0.127343i	−0.0455538	−	0.00532447i
$573$		0			0
$574$	−16.2569	+	8.16455i	−0.678552	+	0.340782i
$575$	60.3771	+	50.6624i	2.51790	+	2.11277i
$576$		0			0
$577$	−3.85975	+	3.23872i	−0.160684	+	0.134830i	−0.719584	−	0.694405i	$-0.755668\pi$
$577$	−3.85975	+	3.23872i	−0.160684	+	0.134830i	0.558901	+	0.829234i	$0.311223\pi$
$578$	−5.62702	+	13.0449i	−0.234053	+	0.542596i
$579$		0			0
$580$	−2.74447	+	0.650452i	−0.113958	+	0.0270086i
$581$	−14.9151	+	49.8199i	−0.618783	+	2.06688i
$582$		0			0
$583$	−25.4518	+	2.97489i	−1.05411	+	0.123207i
$584$	−0.971631	−	5.51039i	−0.0402064	−	0.228022i
$585$		0			0
$586$	−2.37293	+	13.4576i	−0.0980250	+	0.555927i
$587$	1.27552	−	21.8998i	0.0526463	−	0.903902i	−0.863823	−	0.503796i	$-0.831936\pi$
$587$	1.27552	−	21.8998i	0.0526463	−	0.903902i	0.916469	−	0.400106i	$-0.131027\pi$
$588$		0			0
$589$	3.73581	+	8.66058i	0.153931	+	0.356853i
$590$	−40.0192	−	20.0984i	−1.64756	−	0.827438i
$591$		0			0
$592$	−5.33763	−	1.26504i	−0.219375	−	0.0519929i
$593$	−4.13250	+	7.15770i	−0.169701	+	0.293931i	−0.938315	−	0.345782i	$-0.887614\pi$
$593$	−4.13250	+	7.15770i	−0.169701	+	0.293931i	0.768614	+	0.639713i	$0.220947\pi$
$594$		0			0
$595$	−11.3777	−	19.7068i	−0.466441	−	0.807899i
$596$	2.31124	+	7.72009i	0.0946722	+	0.316227i
$597$		0			0
$598$	1.52260	−	1.00143i	0.0622638	−	0.0409515i
$599$	8.18252	−	10.9910i	0.334329	−	0.449081i	−0.602890	−	0.797825i	$-0.705984\pi$
$599$	8.18252	−	10.9910i	0.334329	−	0.449081i	0.937218	+	0.348743i	$0.113391\pi$
$600$		0			0
$601$	26.4263	+	17.3809i	1.07795	+	0.708980i	0.958853	−	0.283902i	$-0.0916292\pi$
$601$	26.4263	+	17.3809i	1.07795	+	0.708980i	0.119098	+	0.992882i	$0.462000\pi$
$602$	−3.57904	+	1.30266i	−0.145871	+	0.0530926i
$603$		0			0
$604$	−6.99114	−	2.54457i	−0.284465	−	0.103537i
$605$	−37.3599	−	50.1830i	−1.51889	−	2.04023i
$606$		0			0
$607$	−0.851718	−	0.902768i	−0.0345702	−	0.0366422i	0.709858	−	0.704345i	$-0.248759\pi$
$607$	−0.851718	−	0.902768i	−0.0345702	−	0.0366422i	−0.744428	+	0.667703i	$0.767278\pi$
$608$	−1.13327	−	1.20120i	−0.0459602	−	0.0487149i
$609$		0			0
$610$	4.75652	+	6.38911i	0.192586	+	0.258688i
$611$	1.06497	+	0.387619i	0.0430842	+	0.0156814i
$612$		0			0
$613$	−30.1068	+	10.9580i	−1.21600	+	0.442589i	−0.868782	−	0.495195i	$-0.835097\pi$
$613$	−30.1068	+	10.9580i	−1.21600	+	0.442589i	−0.347221	+	0.937783i	$0.612875\pi$
$614$	11.2705	+	7.41270i	0.454839	+	0.299152i
$615$		0			0
$616$	11.4348	−	15.3596i	0.460722	−	0.618857i
$617$	6.97735	−	4.58907i	0.280897	−	0.184749i	−0.401240	−	0.915973i	$-0.631421\pi$
$617$	6.97735	−	4.58907i	0.280897	−	0.184749i	0.682138	+	0.731224i	$0.261050\pi$
$618$		0			0
$619$	−7.76825	−	25.9478i	−0.312232	−	1.04293i	−0.959745	−	0.280874i	$-0.909376\pi$
$619$	−7.76825	−	25.9478i	−0.312232	−	1.04293i	0.647512	−	0.762055i	$-0.275809\pi$
$620$	10.6895	+	18.5147i	0.429300	+	0.743569i
$621$		0			0
$622$	−2.95334	+	5.11534i	−0.118418	+	0.205107i
$623$	1.83404	+	0.434676i	0.0734793	+	0.0174149i
$624$		0			0
$625$	9.96269	+	5.00345i	0.398508	+	0.200138i
$626$	3.49181	+	8.09493i	0.139561	+	0.323538i
$627$		0			0
$628$	1.14647	−	19.6841i	0.0457492	−	0.785483i
$629$	−1.59198	+	9.02857i	−0.0634764	+	0.359992i
$630$		0			0
$631$	3.72186	+	21.1077i	0.148165	+	0.840284i	0.964771	+	0.263089i	$0.0847414\pi$
$631$	3.72186	+	21.1077i	0.148165	+	0.840284i	−0.816607	+	0.577194i	$0.804147\pi$
$632$	4.29849	−	0.502421i	0.170985	−	0.0199852i
$633$		0			0
$634$	−2.09512	+	6.99818i	−0.0832078	+	0.277933i
$635$	66.8285	−	15.8387i	2.65201	−	0.628538i
$636$		0			0
$637$	−0.514212	+	1.19208i	−0.0203738	+	0.0472318i
$638$	−3.03870	+	2.54977i	−0.120303	+	0.100946i
$639$		0			0
$640$	−2.86744	−	2.40607i	−0.113346	−	0.0951083i
$641$	14.0757	−	7.06906i	0.555955	−	0.279211i	−0.148556	−	0.988904i	$-0.547463\pi$
$641$	14.0757	−	7.06906i	0.555955	−	0.279211i	0.704511	+	0.709693i	$0.251166\pi$
$642$		0			0
$643$	44.1265	+	5.15764i	1.74018	+	0.203398i	0.926079	−	0.377329i	$-0.123157\pi$
$643$	44.1265	+	5.15764i	1.74018	+	0.203398i	0.814099	+	0.580726i	$0.197231\pi$
$644$	1.84981	+	31.7601i	0.0728929	+	1.25152i
$645$		0			0
$646$	−1.89402	+	2.00755i	−0.0745194	+	0.0789859i
$647$	−18.9018			−0.743108			−0.371554	−	0.928411i	$-0.621175\pi$
$647$	−18.9018			−0.743108			−0.371554	+	0.928411i	$0.621175\pi$
$648$		0			0
$649$	−62.9820			−2.47226
$650$	1.28852	−	1.36575i	0.0505399	−	0.0535691i
$651$		0			0
$652$	−0.421574	−	7.23815i	−0.0165101	−	0.283468i
$653$	−19.0339	−	2.22475i	−0.744856	−	0.0870611i	−0.264805	−	0.964302i	$-0.585308\pi$
$653$	−19.0339	−	2.22475i	−0.744856	−	0.0870611i	−0.480051	+	0.877241i	$0.659382\pi$
$654$		0			0
$655$	0.663544	−	0.333245i	0.0259268	−	0.0130209i
$656$	3.83126	+	3.21481i	0.149586	+	0.125517i
$657$		0			0
$658$	−15.1558	+	12.7172i	−0.590833	+	0.495768i
$659$	−0.654481	+	1.51726i	−0.0254950	+	0.0591040i	−0.930488	−	0.366323i	$-0.880617\pi$
$659$	−0.654481	+	1.51726i	−0.0254950	+	0.0591040i	0.904993	+	0.425427i	$0.139876\pi$
$660$		0			0
$661$	−41.3076	+	9.79007i	−1.60668	+	0.380790i	−0.933468	−	0.358661i	$-0.883233\pi$
$661$	−41.3076	+	9.79007i	−1.60668	+	0.380790i	−0.673211	+	0.739451i	$0.735085\pi$
$662$	9.18443	−	30.6781i	0.356963	−	1.19234i
$663$		0			0
$664$	14.2005	−	1.65980i	0.551086	−	0.0644128i
$665$	3.90445	+	22.1432i	0.151408	+	0.858677i
$666$		0			0
$667$	1.14441	−	6.49026i	0.0443116	−	0.251304i
$668$	−1.09516	+	18.8032i	−0.0423730	+	0.727517i
$669$		0			0
$670$	9.26363	+	21.4755i	0.357885	+	0.829671i
$671$	10.0107	+	5.02757i	0.386460	+	0.194087i
$672$		0			0
$673$	12.3539	+	2.92794i	0.476209	+	0.112864i	0.461710	−	0.887031i	$-0.347236\pi$
$673$	12.3539	+	2.92794i	0.476209	+	0.112864i	0.0144998	+	0.999895i	$0.495384\pi$
$674$	−12.9912	+	22.5014i	−0.500401	+	0.866720i
$675$		0			0
$676$	6.47829	+	11.2207i	0.249165	+	0.431567i
$677$	3.18713	+	10.6457i	0.122491	+	0.409149i	0.997137	−	0.0756130i	$-0.0240914\pi$
$677$	3.18713	+	10.6457i	0.122491	+	0.409149i	−0.874646	+	0.484762i	$0.838906\pi$
$678$		0			0
$679$	−5.65488	+	3.71927i	−0.217014	+	0.142733i
$680$	−3.73579	+	5.01804i	−0.143261	+	0.192433i
$681$		0			0
$682$	25.1208	+	16.5222i	0.961925	+	0.632668i
$683$	19.0189	−	6.92231i	0.727737	−	0.264875i	0.0485305	−	0.998822i	$-0.484546\pi$
$683$	19.0189	−	6.92231i	0.727737	−	0.264875i	0.679207	+	0.733947i	$0.262324\pi$
$684$		0			0
$685$	15.5423	+	5.65692i	0.593840	+	0.216140i
$686$	1.67095	+	2.24448i	0.0637973	+	0.0856947i
$687$		0			0
$688$	0.718564	+	0.761633i	0.0273950	+	0.0290370i
$689$	−0.696010	−	0.737728i	−0.0265159	−	0.0281052i
$690$		0			0
$691$	15.8395	+	21.2762i	0.602564	+	0.809384i	0.993832	−	0.110893i	$-0.0353711\pi$
$691$	15.8395	+	21.2762i	0.602564	+	0.809384i	−0.391269	+	0.920277i	$0.627964\pi$
$692$	4.33617	+	1.57824i	0.164836	+	0.0599955i
$693$		0			0
$694$	12.2929	−	4.47425i	0.466632	−	0.169840i
$695$	−3.86517	−	2.54216i	−0.146614	−	0.0964297i
$696$		0			0
$697$	4.99149	−	6.70473i	0.189066	−	0.253960i
$698$	16.7308	−	11.0040i	0.633269	−	0.416508i
$699$		0			0
$700$	9.40089	+	31.4011i	0.355320	+	1.18685i
$701$	5.03336	+	8.71804i	0.190107	+	0.329276i	0.945286	−	0.326244i	$-0.105783\pi$
$701$	5.03336	+	8.71804i	0.190107	+	0.329276i	−0.755178	+	0.655520i	$0.772450\pi$
$702$		0			0
$703$	4.52941	−	7.84517i	0.170830	−	0.295886i
$704$	−5.12249	−	1.21405i	−0.193061	−	0.0457563i
$705$		0			0
$706$	−26.0235	−	13.0695i	−0.979406	−	0.491876i
$707$	−16.5714	−	38.4169i	−0.623232	−	1.44481i
$708$		0			0
$709$	2.70801	−	46.4947i	0.101701	−	1.74614i	−0.433261	−	0.901269i	$-0.642637\pi$
$709$	2.70801	−	46.4947i	0.101701	−	1.74614i	0.534962	−	0.844876i	$-0.320326\pi$
$710$	−1.67703	+	9.51092i	−0.0629379	+	0.356938i
$711$		0			0
$712$	−0.0899818	−	0.510312i	−0.00337221	−	0.0191247i
$713$	−49.6163	+	5.79931i	−1.85814	+	0.217186i
$714$		0			0
$715$	1.17759	−	3.93342i	0.0440393	−	0.147102i
$716$	−24.3593	+	5.77326i	−0.910350	+	0.215757i
$717$		0			0
$718$	6.15792	−	14.2757i	0.229811	−	0.532763i
$719$	27.0503	−	22.6979i	1.00881	−	0.846490i	0.0206270	−	0.999787i	$-0.493434\pi$
$719$	27.0503	−	22.6979i	1.00881	−	0.846490i	0.988180	+	0.153298i	$0.0489893\pi$
$720$		0			0
$721$	41.4179	+	34.7538i	1.54248	+	1.29430i
$722$	−14.5419	+	7.30323i	−0.541195	+	0.271798i
$723$		0			0
$724$	−15.6570	−	1.83005i	−0.581889	−	0.0680131i
$725$	−0.394811	−	6.77865i	−0.0146629	−	0.251753i
$726$		0			0
$727$	−4.09655	+	4.34209i	−0.151933	+	0.161039i	−0.798870	−	0.601504i	$-0.794568\pi$
$727$	−4.09655	+	4.34209i	−0.151933	+	0.161039i	0.646937	+	0.762544i	$0.276050\pi$
$728$	0.757901			0.0280897
$729$		0			0
$730$	20.9446			0.775194
$731$	1.20093	−	1.27291i	0.0444180	−	0.0470803i
$732$		0			0
$733$	2.73945	+	47.0345i	0.101184	+	1.73726i	0.542631	+	0.839971i	$0.317428\pi$
$733$	2.73945	+	47.0345i	0.101184	+	1.73726i	−0.441447	+	0.897287i	$0.645535\pi$
$734$	9.17828	+	1.07279i	0.338776	+	0.0395973i
$735$		0			0
$736$	7.81600	−	3.92534i	0.288101	−	0.144690i
$737$	25.1976	+	21.1433i	0.928166	+	0.778824i
$738$		0			0
$739$	−9.19760	+	7.71770i	−0.338339	+	0.283900i	−0.796088	−	0.605182i	$-0.793101\pi$
$739$	−9.19760	+	7.71770i	−0.338339	+	0.283900i	0.457748	+	0.889082i	$0.348656\pi$
$740$	8.13278	−	18.8539i	0.298967	−	0.693083i
$741$		0			0
$742$	17.2283	−	4.08318i	0.632471	−	0.149898i
$743$	−9.51664	+	31.7878i	−0.349132	+	1.16618i	0.585533	+	0.810649i	$0.300885\pi$
$743$	−9.51664	+	31.7878i	−0.349132	+	1.16618i	−0.934664	+	0.355532i	$0.884300\pi$
$744$		0			0
$745$	−29.9610	+	3.50194i	−1.09769	+	0.128301i
$746$	5.84734	+	33.1619i	0.214086	+	1.21414i
$747$		0			0
$748$	−1.52781	+	8.66466i	−0.0558624	+	0.316811i
$749$	0.541164	−	9.29142i	0.0197737	−	0.339501i
$750$		0			0
$751$	−14.2808	−	33.1067i	−0.521115	−	1.20808i	−0.952118	−	0.305731i	$-0.901099\pi$
$751$	−14.2808	−	33.1067i	−0.521115	−	1.20808i	0.431003	−	0.902351i	$-0.358160\pi$
$752$	4.86062	+	2.44109i	0.177248	+	0.0890175i
$753$		0			0
$754$	−0.152770	−	0.0362072i	−0.00556357	−	0.00131859i
$755$	13.9243	−	24.1176i	0.506757	−	0.877729i
$756$		0			0
$757$	−14.8811	−	25.7749i	−0.540864	−	0.936804i	−0.998855	−	0.0478471i	$-0.984764\pi$
$757$	−14.8811	−	25.7749i	−0.540864	−	0.936804i	0.457990	−	0.888957i	$-0.348569\pi$
$758$	0.0674426	+	0.225274i	0.00244963	+	0.00818232i
$759$		0			0
$760$	5.16461	−	3.39682i	0.187340	−	0.123216i
$761$	−32.1802	+	43.2255i	−1.16653	+	1.56692i	−0.411250	+	0.911522i	$0.634908\pi$
$761$	−32.1802	+	43.2255i	−1.16653	+	1.56692i	−0.755281	+	0.655401i	$0.772500\pi$
$762$		0			0
$763$	32.7358	+	21.5307i	1.18511	+	0.779462i
$764$	1.25239	−	0.455834i	0.0453100	−	0.0164915i
$765$		0			0
$766$	13.8183	+	5.02946i	0.499276	+	0.181722i
$767$	−1.48860	−	1.99954i	−0.0537503	−	0.0721992i
$768$		0			0
$769$	−5.85019	−	6.20084i	−0.210963	−	0.223608i	0.613248	−	0.789890i	$-0.289863\pi$
$769$	−5.85019	−	6.20084i	−0.210963	−	0.223608i	−0.824211	+	0.566283i	$0.808381\pi$
$770$	49.1878	+	52.1361i	1.77261	+	1.87885i
$771$		0			0
$772$	7.98972	+	10.7321i	0.287556	+	0.386255i
$773$	−36.4284	−	13.2589i	−1.31024	−	0.476888i	−0.409921	−	0.912121i	$-0.634444\pi$
$773$	−36.4284	−	13.2589i	−1.31024	−	0.476888i	−0.900318	+	0.435234i	$0.856666\pi$
$774$		0			0
$775$	−48.3642	+	17.6031i	−1.73730	+	0.632324i
$776$	1.55465	+	1.02251i	0.0558085	+	0.0367058i
$777$		0			0
$778$	−12.7609	+	17.1409i	−0.457501	+	0.614530i
$779$	−6.90057	+	4.53857i	−0.247238	+	0.162611i
$780$		0			0
$781$	3.89549	+	13.0118i	0.139392	+	0.465600i
$782$	−7.30882	−	12.6592i	−0.261363	−	0.452694i
$783$		0			0
$784$	−3.11536	+	5.39596i	−0.111263	+	0.192713i
$785$	71.8168	+	17.0209i	2.56325	+	0.607502i
$786$		0			0
$787$	6.04121	+	3.03401i	0.215346	+	0.108151i	0.553202	−	0.833047i	$-0.313406\pi$
$787$	6.04121	+	3.03401i	0.215346	+	0.108151i	−0.337857	+	0.941198i	$0.609702\pi$
$788$	−10.4139	−	24.1421i	−0.370979	−	0.860026i
$789$		0			0
$790$	−0.941921	+	16.1722i	−0.0335120	+	0.575379i
$791$	−7.79524	+	44.2090i	−0.277167	+	1.57189i
$792$		0			0
$793$	0.0769927	+	0.436647i	0.00273409	+	0.0155058i
$794$	23.0698	−	2.69647i	0.818716	−	0.0956942i
$795$		0			0
$796$	−0.665384	+	2.22254i	−0.0235839	+	0.0787758i
$797$	−1.49748	+	0.354909i	−0.0530434	+	0.0125715i	−0.257052	−	0.966398i	$-0.582751\pi$
$797$	−1.49748	+	0.354909i	−0.0530434	+	0.0125715i	0.204008	+	0.978969i	$0.434603\pi$
$798$		0			0
$799$	3.60053	−	8.34698i	0.127378	−	0.295295i
$800$	6.90314	−	5.79243i	0.244063	−	0.204793i
$801$		0			0
$802$	−12.2930	−	10.3151i	−0.434082	−	0.364238i
$803$	26.3232	−	13.2200i	0.928924	−	0.466523i
$804$		0			0
$805$	−118.280	−	13.8250i	−4.16882	−	0.487266i
$806$	0.0691955	+	1.18804i	0.00243731	+	0.0418469i
$807$		0			0
$808$	−7.89336	+	8.36648i	−0.277688	+	0.294332i
$809$	35.4763			1.24728			0.623639	−	0.781712i	$-0.285653\pi$
$809$	35.4763			1.24728			0.623639	+	0.781712i	$0.285653\pi$
$810$		0			0
$811$	2.83568			0.0995740			0.0497870	−	0.998760i	$-0.484146\pi$
$811$	2.83568			0.0995740			0.0497870	+	0.998760i	$0.484146\pi$
$812$	1.88085	−	1.99358i	0.0660049	−	0.0699611i
$813$		0			0
$814$	−1.67909	−	28.8289i	−0.0588521	−	1.01045i
$815$	26.9561	+	3.15072i	0.944232	+	0.110365i
$816$		0			0
$817$	−1.54527	+	0.776063i	−0.0540621	+	0.0271510i
$818$	2.71014	+	2.27408i	0.0947580	+	0.0795114i
$819$		0			0
$820$	−14.3411	+	12.0336i	−0.500814	+	0.420233i
$821$	21.4821	−	49.8012i	0.749731	−	1.73807i	0.0783916	−	0.996923i	$-0.475022\pi$
$821$	21.4821	−	49.8012i	0.749731	−	1.73807i	0.671340	−	0.741150i	$-0.265719\pi$
$822$		0			0
$823$	7.83046	−	1.85585i	0.272953	−	0.0646910i	−0.0918599	−	0.995772i	$-0.529281\pi$
$823$	7.83046	−	1.85585i	0.272953	−	0.0646910i	0.364813	+	0.931081i	$0.381133\pi$
$824$	4.26311	−	14.2398i	0.148513	−	0.496066i
$825$		0			0
$826$	43.2229	−	5.05203i	1.50392	−	0.175783i
$827$	−8.15370	−	46.2420i	−0.283532	−	1.60799i	−0.710482	−	0.703715i	$-0.751523\pi$
$827$	−8.15370	−	46.2420i	−0.283532	−	1.60799i	0.426950	−	0.904275i	$-0.359588\pi$
$828$		0			0
$829$	4.57598	−	25.9517i	0.158930	−	0.901339i	−0.796174	−	0.605068i	$-0.793146\pi$
$829$	4.57598	−	25.9517i	0.158930	−	0.901339i	0.955104	−	0.296271i	$-0.0957430\pi$
$830$	−3.11173	+	53.4264i	−0.108010	+	1.85446i
$831$		0			0
$832$	−0.0825284	−	0.191322i	−0.00286116	−	0.00663291i
$833$	9.30571	+	4.67350i	0.322424	+	0.161927i
$834$		0			0
$835$	−68.6026	−	16.2591i	−2.37409	−	0.562670i
$836$	4.34685	−	7.52896i	0.150339	−	0.260395i
$837$		0			0
$838$	−15.6389	−	27.0873i	−0.540235	−	0.935715i
$839$	1.55115	+	5.18120i	0.0535516	+	0.178875i	0.980581	−	0.196113i	$-0.0628320\pi$
$839$	1.55115	+	5.18120i	0.0535516	+	0.178875i	−0.927030	+	0.374988i	$0.877647\pi$
$840$		0			0
$841$	23.7548	−	15.6238i	0.819130	−	0.538751i
$842$	10.6536	−	14.3103i	0.367147	−	0.493165i
$843$		0			0
$844$	8.16315	+	5.36899i	0.280987	+	0.184808i
$845$	−45.5740	+	16.5876i	−1.56779	+	0.570630i
$846$		0			0
$847$	57.1284	+	20.7930i	1.96296	+	0.714458i
$848$	−2.90675	−	3.90444i	−0.0998181	−	0.134079i
$849$		0			0
$850$	−10.3353	−	10.9548i	−0.354497	−	0.375745i
$851$	32.9244	+	34.8978i	1.12863	+	1.19628i
$852$		0			0
$853$	−12.8338	−	17.2388i	−0.439421	−	0.590244i	0.526148	−	0.850393i	$-0.323636\pi$
$853$	−12.8338	−	17.2388i	−0.439421	−	0.590244i	−0.965569	+	0.260149i	$0.916228\pi$
$854$	−7.27338	−	2.64729i	−0.248890	−	0.0905885i
$855$		0			0
$856$	−2.40443	+	0.875140i	−0.0821816	+	0.0299117i
$857$	12.5216	+	8.23558i	0.427729	+	0.281322i	0.745066	−	0.666991i	$-0.232418\pi$
$857$	12.5216	+	8.23558i	0.427729	+	0.281322i	−0.317336	+	0.948313i	$0.602788\pi$
$858$		0			0
$859$	−30.0492	+	40.3630i	−1.02526	+	1.37717i	−0.101229	+	0.994863i	$0.532277\pi$
$859$	−30.0492	+	40.3630i	−1.02526	+	1.37717i	−0.924036	+	0.382306i	$0.875130\pi$
$860$	−3.27469	+	2.15379i	−0.111666	+	0.0734438i
$861$		0			0
$862$	5.24057	+	17.5047i	0.178494	+	0.596213i
$863$	−12.2875	−	21.2826i	−0.418272	−	0.724468i	0.577494	−	0.816395i	$-0.304031\pi$
$863$	−12.2875	−	21.2826i	−0.418272	−	0.724468i	−0.995766	+	0.0919267i	$0.970697\pi$
$864$		0			0
$865$	−8.63637	+	14.9586i	−0.293645	+	0.508609i
$866$	−27.5696	−	6.53411i	−0.936853	−	0.222038i
$867$		0			0
$868$	−18.5651	−	9.32372i	−0.630139	−	0.316468i
$869$	9.02387	+	20.9197i	0.306114	+	0.709652i
$870$		0			0
$871$	−0.0756989	+	1.29970i	−0.00256496	+	0.0440386i
$872$	1.87051	−	10.6082i	0.0633436	−	0.359239i
$873$		0			0
$874$	2.50814	+	14.2244i	0.0848391	+	0.481147i
$875$	−54.2480	+	6.34068i	−1.83392	+	0.214354i
$876$		0			0
$877$	11.9131	−	39.7924i	0.402275	−	1.34369i	−0.481772	−	0.876296i	$-0.660007\pi$
$877$	11.9131	−	39.7924i	0.402275	−	1.34369i	0.884048	−	0.467397i	$-0.154808\pi$
$878$	3.08166	−	0.730367i	0.104001	−	0.0246487i
$879$		0			0
$880$	7.80498	−	18.0940i	0.263106	−	0.609948i
$881$	−39.4074	+	33.0667i	−1.32767	+	1.11405i	−0.343053	+	0.939316i	$0.611461\pi$
$881$	−39.4074	+	33.0667i	−1.32767	+	1.11405i	−0.984616	+	0.174731i	$0.944095\pi$
$882$		0			0
$883$	11.6864	+	9.80605i	0.393279	+	0.330000i	0.817889	−	0.575376i	$-0.195144\pi$
$883$	11.6864	+	9.80605i	0.393279	+	0.330000i	−0.424610	+	0.905376i	$0.639589\pi$
$884$	−0.311194	+	0.156288i	−0.0104666	+	0.00525653i
$885$		0			0
$886$	−31.7592	−	3.71211i	−1.06697	−	0.124711i
$887$	−2.91698	−	50.0825i	−0.0979424	−	1.68161i	−0.587180	−	0.809456i	$-0.699762\pi$
$887$	−2.91698	−	50.0825i	−0.0979424	−	1.68161i	0.489238	−	0.872150i	$-0.337275\pi$
$888$		0			0
$889$	−45.7991	+	48.5442i	−1.53605	+	1.62812i
$890$	1.93966			0.0650175
$891$		0			0
$892$	5.85506			0.196042
$893$	−6.16404	+	6.53351i	−0.206272	+	0.218635i
$894$		0			0
$895$	−5.44859	−	93.5487i	−0.182126	−	3.12699i
$896$	3.61281	+	0.422277i	0.120696	+	0.0141073i
$897$		0			0
$898$	−2.19341	+	1.10157i	−0.0731950	+	0.0367599i
$899$	3.29674	+	2.76629i	0.109952	+	0.0922611i
$900$		0			0
$901$	−6.23194	+	5.22922i	−0.207616	+	0.174211i
$902$	−10.4284	+	24.1758i	−0.347229	+	0.804966i
$903$		0			0
$904$	12.0088	−	2.84614i	0.399407	−	0.0946613i
$905$	16.9232	−	56.5273i	0.562545	−	1.87903i
$906$		0			0
$907$	54.9677	−	6.42481i	1.82517	−	0.213332i	0.866762	−	0.498722i	$-0.166197\pi$
$907$	54.9677	−	6.42481i	1.82517	−	0.213332i	0.958411	+	0.285390i	$0.0921232\pi$
$908$	−1.30773	−	7.41652i	−0.0433986	−	0.246126i
$909$		0			0
$910$	−0.492633	+	2.79386i	−0.0163306	+	0.0926157i
$911$	2.36181	−	40.5508i	0.0782503	−	1.34351i	−0.699364	−	0.714765i	$-0.746534\pi$
$911$	2.36181	−	40.5508i	0.0782503	−	1.34351i	0.777615	−	0.628741i	$-0.216429\pi$
$912$		0			0
$913$	29.8113	+	69.1103i	0.986610	+	2.28722i
$914$	−19.7913	−	9.93956i	−0.654638	−	0.328771i
$915$		0			0
$916$	10.9890	+	2.60444i	0.363086	+	0.0860530i
$917$	−0.360771	+	0.624874i	−0.0119137	+	0.0206352i
$918$		0			0
$919$	−16.3221	−	28.2707i	−0.538417	−	0.932565i	−0.998990	−	0.0449430i	$-0.985689\pi$
$919$	−16.3221	−	28.2707i	−0.538417	−	0.932565i	0.460573	−	0.887622i	$-0.347644\pi$
$920$	9.38967	+	31.3637i	0.309568	+	1.03403i
$921$		0			0
$922$	6.97700	−	4.58885i	0.229775	−	0.151126i
$923$	−0.321026	+	0.431213i	−0.0105667	+	0.0141935i
$924$		0			0
$925$	41.2999	+	27.1633i	1.35793	+	0.893125i
$926$	22.9823	−	8.36487i	0.755245	−	0.274887i
$927$		0			0
$928$	−0.708062	−	0.257713i	−0.0232433	−	0.00845986i
$929$	−28.9953	−	38.9475i	−0.951306	−	1.27783i	−0.960619	−	0.277869i	$-0.910372\pi$
$929$	−28.9953	−	38.9475i	−0.951306	−	1.27783i	0.00931285	−	0.999957i	$-0.497036\pi$
$930$		0			0
$931$	−7.06109	−	7.48432i	−0.231418	−	0.245289i
$932$	5.21887	+	5.53168i	0.170950	+	0.181196i
$933$		0			0
$934$	16.9772	+	22.8044i	0.555511	+	0.746181i
$935$	−30.9476	−	11.2640i	−1.01209	−	0.368372i
$936$		0			0
$937$	4.72115	−	1.71836i	0.154233	−	0.0561363i	−0.263750	−	0.964591i	$-0.584959\pi$
$937$	4.72115	−	1.71836i	0.154233	−	0.0561363i	0.417983	+	0.908455i	$0.362737\pi$
$938$	−18.9884	−	12.4889i	−0.619995	−	0.407777i
$939$		0			0
$940$	−12.1580	+	16.3311i	−0.396551	+	0.532660i
$941$	19.7386	−	12.9823i	0.643459	−	0.423210i	−0.185403	−	0.982663i	$-0.559359\pi$
$941$	19.7386	−	12.9823i	0.643459	−	0.423210i	0.828862	+	0.559453i	$0.188989\pi$
$942$		0			0
$943$	−12.5458	−	41.9058i	−0.408547	−	1.36464i
$944$	−5.98189	−	10.3609i	−0.194694	−	0.337220i
$945$		0			0
$946$	−2.75617	+	4.77383i	−0.0896109	+	0.155211i
$947$	−17.0613	−	4.04359i	−0.554416	−	0.131399i	−0.0561488	−	0.998422i	$-0.517882\pi$
$947$	−17.0613	−	4.04359i	−0.554416	−	0.131399i	−0.498268	+	0.867023i	$0.666030\pi$
$948$		0			0
$949$	1.04186	+	0.523244i	0.0338203	+	0.0169852i
$950$	5.89430	+	13.6645i	0.191236	+	0.443336i
$951$		0			0
$952$	0.353472	−	6.06888i	0.0114561	−	0.196693i
$953$	−8.32666	+	47.2228i	−0.269727	+	1.52970i	0.485502	+	0.874236i	$0.338637\pi$
$953$	−8.32666	+	47.2228i	−0.269727	+	1.52970i	−0.755229	+	0.655462i	$0.772474\pi$
$954$		0			0
$955$	0.866296	+	4.91301i	0.0280327	+	0.158981i
$956$	−18.9755	+	2.21792i	−0.613711	+	0.0717325i
$957$		0			0
$958$	4.53707	−	15.1549i	0.146586	−	0.489631i
$959$	−15.6391	+	3.70654i	−0.505014	+	0.119690i
$960$		0			0
$961$	0.641865	−	1.48801i	0.0207053	−	0.0480003i
$962$	0.875569	−	0.734689i	0.0282295	−	0.0236873i
$963$		0			0
$964$	−4.96143	−	4.16313i	−0.159797	−	0.134085i
$965$	−44.7551	+	22.4768i	−1.44072	+	0.723555i
$966$		0			0
$967$	41.5836	+	4.86042i	1.33724	+	0.156301i	0.754468	−	0.656337i	$-0.227895\pi$
$967$	41.5836	+	4.86042i	1.33724	+	0.156301i	0.582770	+	0.812637i	$0.301969\pi$
$968$	−0.971820	−	16.6855i	−0.0312355	−	0.536292i
$969$		0			0
$970$	−4.77979	+	5.06629i	−0.153470	+	0.162669i
$971$	−2.57508			−0.0826384			−0.0413192	−	0.999146i	$-0.513156\pi$
$971$	−2.57508			−0.0826384			−0.0413192	+	0.999146i	$0.513156\pi$
$972$		0			0
$973$	4.49551			0.144120
$974$	−6.68517	+	7.08586i	−0.214207	+	0.227046i
$975$		0			0
$976$	0.123728	+	2.12434i	0.00396045	+	0.0679983i
$977$	9.91440	+	1.15883i	0.317190	+	0.0370741i	0.273198	−	0.961958i	$-0.411919\pi$
$977$	9.91440	+	1.15883i	0.317190	+	0.0370741i	0.0439914	+	0.999032i	$0.485993\pi$
$978$		0			0
$979$	2.43776	−	1.22429i	0.0779112	−	0.0391285i
$980$	−17.8662	−	14.9916i	−0.570716	−	0.478888i
$981$		0			0
$982$	4.60685	−	3.86561i	0.147010	−	0.123356i
$983$	−2.72214	+	6.31062i	−0.0868227	+	0.201278i	−0.956096	−	0.293055i	$-0.905328\pi$
$983$	−2.72214	+	6.31062i	−0.0868227	+	0.201278i	0.869273	+	0.494332i	$0.164587\pi$
$984$		0			0
$985$	95.7643	−	22.6966i	3.05131	−	0.723173i
$986$	−0.361178	+	1.20642i	−0.0115023	+	0.0384202i
$987$		0			0
$988$	0.341768	−	0.0399469i	0.0108731	−	0.00127088i
$989$	−1.59032	−	9.01914i	−0.0505692	−	0.286792i
$990$		0			0
$991$	−4.53010	+	25.6915i	−0.143903	+	0.816117i	0.824338	+	0.566099i	$0.191548\pi$
$991$	−4.53010	+	25.6915i	−0.143903	+	0.816117i	−0.968241	+	0.250019i	$0.919563\pi$
$992$	−0.332091	+	5.70178i	−0.0105439	+	0.181032i
$993$		0			0
$994$	−3.71710	−	8.61721i	−0.117899	−	0.273321i
$995$	−7.76048	−	3.89746i	−0.246024	−	0.123558i
$996$		0			0
$997$	−50.0674	−	11.8662i	−1.58565	−	0.375806i	−0.659124	−	0.752035i	$-0.729073\pi$
$997$	−50.0674	−	11.8662i	−1.58565	−	0.375806i	−0.926527	+	0.376228i	$0.877221\pi$
$998$	−4.84606	+	8.39362i	−0.153399	+	0.265696i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	486.2.g.a.127.4		72
3.2	odd	2		162.2.g.a.151.1	yes	72
81.22	even	27	inner	486.2.g.a.199.4		72
81.59	odd	54		162.2.g.a.103.1	✓	72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
162.2.g.a.103.1	✓	72	81.59	odd	54
162.2.g.a.151.1	yes	72	3.2	odd	2
486.2.g.a.127.4		72	1.1	even	1	trivial
486.2.g.a.199.4		72	81.22	even	27	inner

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)

\(f(q)\)	\(=\)	\(q+(-0.686242 + 0.727374i) q^{2} +(-0.0581448 - 0.998308i) q^{4} +(3.71787 + 0.434557i) q^{5} +(-3.25050 + 1.63246i) q^{7} +(0.766044 + 0.642788i) q^{8} +(-2.86744 + 2.40607i) q^{10} +(-2.08512 + 4.83385i) q^{11} +(-0.202747 + 0.0480518i) q^{13} +(1.04322 - 3.48460i) q^{14} +(-0.993238 + 0.116093i) q^{16} +(0.290217 + 1.64590i) q^{17} +(0.286765 - 1.62633i) q^{19} +(0.217647 - 3.73685i) q^{20} +(-2.08512 - 4.83385i) q^{22} +(7.81600 + 3.92534i) q^{23} +(8.76851 + 2.07818i) q^{25} +(0.104182 - 0.180448i) q^{26} +(1.81870 + 3.15009i) q^{28} +(-0.216107 - 0.721848i) q^{29} +(-4.77184 + 3.13849i) q^{31} +(0.597159 - 0.802123i) q^{32} +(-1.39634 - 0.918389i) q^{34} +(-12.7944 + 4.65677i) q^{35} +(5.15467 + 1.87615i) q^{37} +(0.986157 + 1.32464i) q^{38} +(2.56873 + 2.72269i) q^{40} +(-3.43214 - 3.63786i) q^{41} +(-0.625285 - 0.839904i) q^{43} +(4.94691 + 1.80053i) q^{44} +(-8.21885 + 2.99142i) q^{46} +(-4.54436 - 2.98887i) q^{47} +(3.72073 - 4.99781i) q^{49} +(-7.52893 + 4.95185i) q^{50} +(0.0597592 + 0.199610i) q^{52} +(2.43382 + 4.21549i) q^{53} +(-9.85278 + 17.0655i) q^{55} +(-3.53936 - 0.838844i) q^{56} +(0.673355 + 0.338172i) q^{58} +(4.73861 + 10.9853i) q^{59} +(0.123728 - 2.12434i) q^{61} +(0.991781 - 5.62467i) q^{62} +(0.173648 + 0.984808i) q^{64} +(-0.774668 + 0.0905456i) q^{65} +(1.79201 - 5.98575i) q^{67} +(1.62624 - 0.385426i) q^{68} +(5.39281 - 12.5019i) q^{70} +(1.97644 - 1.65843i) q^{71} +(-4.28632 - 3.59665i) q^{73} +(-4.90201 + 2.46188i) q^{74} +(-1.64025 - 0.191718i) q^{76} +(-1.11340 - 19.1163i) q^{77} +(2.96988 - 3.14789i) q^{79} -3.74318 q^{80} +5.00136 q^{82} +(9.81132 - 10.3994i) q^{83} +(0.363751 + 6.24536i) q^{85} +(1.04002 + 0.121561i) q^{86} +(-4.70443 + 2.36265i) q^{88} +(-0.396952 - 0.333082i) q^{89} +(0.580586 - 0.487170i) q^{91} +(3.46424 - 8.03101i) q^{92} +(5.29255 - 1.25436i) q^{94} +(1.77289 - 5.92186i) q^{95} +(1.84818 - 0.216021i) q^{97} +(1.08195 + 6.13606i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q + 18 q^{13} + 9 q^{20} + 81 q^{23} + 18 q^{25} + 27 q^{26} + 18 q^{28} + 27 q^{29} - 54 q^{31} + 27 q^{35} - 9 q^{38} + 9 q^{41} + 36 q^{43} - 18 q^{46} + 27 q^{47} - 36 q^{52} + 27 q^{53} + 54 q^{55}+ \cdots - 36 q^{98}+O(q^{100}) \) 72 * q + 18 * q^13 + 9 * q^20 + 81 * q^23 + 18 * q^25 + 27 * q^26 + 18 * q^28 + 27 * q^29 - 54 * q^31 + 27 * q^35 - 9 * 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 + 18 * q^59 - 9 * q^65 - 135 * q^67 + 18 * q^68 + 18 * q^70 - 72 * q^71 + 36 * q^73 - 99 * q^74 - 9 * q^76 - 144 * q^77 - 9 * q^79 - 18 * q^80 - 72 * q^82 - 99 * q^83 + 9 * q^85 - 72 * q^86 - 9 * q^88 - 126 * q^89 + 63 * q^91 - 36 * q^92 + 18 * q^94 - 45 * q^95 - 171 * q^97 - 36 * q^98

Introduction

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