LMFDB - Embedded newform 486.2.g.a.199.4

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			199.4
Character	$\chi$	$=$	486.199
Dual form			486.2.g.a.127.4

$q$-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 $\left(\mathbb{Z}/486\mathbb{Z}\right)^\times$.

$n$	$245$
$\chi(n)$	$e\left(\frac{7}{27}\right)$

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	0.767815	−	0.640671i	$-0.221344\pi$
$5$	3.71787	−	0.434557i	1.66268	−	0.194340i	0.894868	+	0.446331i	$0.147270\pi$
$6$		0			0
$7$	−3.25050	−	1.63246i	−1.22858	−	0.617014i	−0.288336	−	0.957529i	$-0.593102\pi$
$7$	−3.25050	−	1.63246i	−1.22858	−	0.617014i	−0.940239	+	0.340515i	$0.889398\pi$
$8$	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	−0.872979	−	0.487758i	$-0.837815\pi$
$11$	−2.08512	−	4.83385i	−0.628687	−	1.45746i	0.244292	−	0.969702i	$-0.421444\pi$
$12$		0			0
$13$	−0.202747	−	0.0480518i	−0.0562318	−	0.0133272i	0.202404	−	0.979302i	$-0.435125\pi$
$13$	−0.202747	−	0.0480518i	−0.0562318	−	0.0133272i	−0.258635	+	0.965975i	$0.583273\pi$
$14$	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	−0.929175	−	0.369639i	$-0.879481\pi$
$17$	0.290217	−	1.64590i	0.0703879	−	0.399189i	0.999563	−	0.0295503i	$-0.00940753\pi$
$18$		0			0
$19$	0.286765	+	1.62633i	0.0657885	+	0.373105i	0.999871	+	0.0160484i	$0.00510858\pi$
$19$	0.286765	+	1.62633i	0.0657885	+	0.373105i	−0.934083	+	0.357057i	$0.883780\pi$
$20$	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	0.630648	−	0.776069i	$-0.282789\pi$
$23$	7.81600	−	3.92534i	1.62975	−	0.818490i	0.999100	−	0.0424209i	$-0.0135070\pi$
$24$		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	−0.975707	−	0.219079i	$-0.929695\pi$
$29$	−0.216107	+	0.721848i	−0.0401301	+	0.134044i	0.935577	+	0.353122i	$0.114880\pi$
$30$		0			0
$31$	−4.77184	−	3.13849i	−0.857047	−	0.563689i	0.0432006	−	0.999066i	$-0.486245\pi$
$31$	−4.77184	−	3.13849i	−0.857047	−	0.563689i	−0.900248	+	0.435377i	$0.856615\pi$
$32$	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	0.118434	−	0.992962i	$-0.462213\pi$
$37$	5.15467	−	1.87615i	0.847423	−	0.308437i	0.728989	+	0.684525i	$0.239990\pi$
$38$	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	−0.937615	−	0.347675i	$-0.886971\pi$
$41$	−3.43214	+	3.63786i	−0.536010	+	0.568138i	0.401605	+	0.915813i	$0.368453\pi$
$42$		0			0
$43$	−0.625285	+	0.839904i	−0.0953551	+	0.128084i	−0.847240	−	0.531210i	$-0.821737\pi$
$43$	−0.625285	+	0.839904i	−0.0953551	+	0.128084i	0.751885	+	0.659294i	$0.229145\pi$
$44$	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	−0.835854	−	0.548952i	$-0.815027\pi$
$47$	−4.54436	+	2.98887i	−0.662863	+	0.435972i	0.172991	+	0.984923i	$0.444657\pi$
$48$		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	−0.649042	−	0.760753i	$-0.724830\pi$
$53$	2.43382	−	4.21549i	0.334310	−	0.579042i	0.983352	+	0.181710i	$0.0581633\pi$
$54$		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	−0.267542	−	0.963546i	$-0.586211\pi$
$59$	4.73861	−	10.9853i	0.616914	−	1.43017i	0.884457	−	0.466622i	$-0.154529\pi$
$60$		0			0
$61$	0.123728	+	2.12434i	0.0158418	+	0.271993i	0.996922	+	0.0783938i	$0.0249792\pi$
$61$	0.123728	+	2.12434i	0.0158418	+	0.271993i	−0.981081	+	0.193599i	$0.937984\pi$
$62$	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	0.994932	+	0.100546i	$0.0320590\pi$
$67$	1.79201	+	5.98575i	0.218929	+	0.731275i	−0.776003	+	0.630729i	$0.782756\pi$
$68$	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	0.752490	−	0.658604i	$-0.228853\pi$
$71$	1.97644	+	1.65843i	0.234560	+	0.196820i	−0.517930	+	0.855423i	$0.673297\pi$
$72$		0			0
$73$	−4.28632	+	3.59665i	−0.501676	+	0.420956i	−0.858189	−	0.513334i	$-0.828410\pi$
$73$	−4.28632	+	3.59665i	−0.501676	+	0.420956i	0.356513	+	0.934291i	$0.383966\pi$
$74$	−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	0.872558	−	0.488511i	$-0.162460\pi$
$79$	2.96988	+	3.14789i	0.334138	+	0.354166i	−0.538420	+	0.842677i	$0.680978\pi$
$80$	−3.74318			−0.418501
$81$		0			0
$82$	5.00136			0.552308
$83$	9.81132	+	10.3994i	1.07693	+	1.14148i	0.989385	+	0.145321i	$0.0464215\pi$
$83$	9.81132	+	10.3994i	1.07693	+	1.14148i	0.0875474	+	0.996160i	$0.472097\pi$
$84$		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	−0.663584	−	0.748102i	$-0.730965\pi$
$89$	−0.396952	+	0.333082i	−0.0420768	+	0.0353067i	0.621507	+	0.783409i	$0.286521\pi$
$90$		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	0.209401	−	0.977830i	$-0.432849\pi$
$97$	1.84818	+	0.216021i	0.187654	+	0.0219337i	−0.0217465	+	0.999764i	$0.506923\pi$
$98$	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	−0.851958	−	0.523610i	$-0.824585\pi$
$101$	−0.668800	−	11.4829i	−0.0665481	−	1.14259i	0.785410	−	0.618976i	$-0.212452\pi$
$102$		0			0
$103$	−5.88743	+	13.6486i	−0.580105	+	1.34484i	0.335228	+	0.942137i	$0.391187\pi$
$103$	−5.88743	+	13.6486i	−0.580105	+	1.34484i	−0.915333	+	0.402698i	$0.868073\pi$
$104$	−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	0.797535	−	0.603272i	$-0.206137\pi$
$107$	−1.27937	−	2.21593i	−0.123681	−	0.214222i	−0.921217	+	0.389050i	$0.872803\pi$
$108$		0			0
$109$	−5.38593	+	9.32871i	−0.515879	+	0.893528i	0.483951	+	0.875095i	$0.339201\pi$
$109$	−5.38593	+	9.32871i	−0.515879	+	0.893528i	−0.999830	+	0.0184331i	$0.994132\pi$
$110$	−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	0.999787	−	0.0206167i	$-0.00656295\pi$
$113$	7.36982	+	9.89939i	0.693295	+	0.931256i	−0.306493	+	0.951873i	$0.599156\pi$
$114$		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	0.963605	−	0.267331i	$-0.0861417\pi$
$127$	17.2415	+	6.27538i	1.52993	+	0.556850i	0.566327	+	0.824181i	$0.308364\pi$
$128$	−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	0.556728	−	0.830695i	$-0.312056\pi$
$131$	0.165733	+	0.109005i	0.0144802	+	0.00952378i	−0.542248	+	0.840218i	$0.682427\pi$
$132$		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	−0.0428037	−	0.999084i	$-0.513629\pi$
$137$	4.29953	−	1.01901i	0.367333	−	0.0870596i	0.410137	+	0.912024i	$0.365481\pi$
$138$		0			0
$139$	−1.10445	+	0.554676i	−0.0936783	+	0.0470470i	−0.495021	−	0.868881i	$-0.664840\pi$
$139$	−1.10445	+	0.554676i	−0.0936783	+	0.0470470i	0.401343	+	0.915928i	$0.368543\pi$
$140$	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	−0.103507	−	0.994629i	$-0.533007\pi$
$149$	−7.84141	−	1.85845i	−0.642394	−	0.152250i	−0.538886	+	0.842379i	$0.681155\pi$
$150$		0			0
$151$	2.94676	+	6.83136i	0.239804	+	0.555928i	0.995034	−	0.0995312i	$-0.0317343\pi$
$151$	2.94676	+	6.83136i	0.239804	+	0.555928i	−0.755230	+	0.655459i	$0.772475\pi$
$152$	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	0.709843	−	0.704360i	$-0.248766\pi$
$157$	19.5842	−	2.28906i	1.56299	−	0.182687i	0.853145	+	0.521673i	$0.174692\pi$
$158$	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	−0.803320	−	0.595547i	$-0.796935\pi$
$167$	−18.7077	+	2.18662i	−1.44764	+	0.169205i	−0.644324	+	0.764753i	$0.722861\pi$
$168$		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	0.834500	−	0.551007i	$-0.185756\pi$
$173$	−1.82769	−	4.23707i	−0.138957	−	0.322138i	−0.973457	+	0.228869i	$0.926497\pi$
$174$		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	0.185320	+	0.982678i	$0.440668\pi$
$179$	−4.34713	+	24.6538i	−0.324920	+	1.84271i	−0.510240	+	0.860032i	$0.670443\pi$
$180$		0			0
$181$	2.73733	+	15.5241i	0.203464	+	1.15390i	0.899839	+	0.436223i	$0.143684\pi$
$181$	2.73733	+	15.5241i	0.203464	+	1.15390i	−0.696375	+	0.717678i	$0.745205\pi$
$182$	−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	−0.943046	−	0.332662i	$-0.892053\pi$
$191$	0.382243	−	1.27678i	0.0276581	−	0.0923845i	0.970704	+	0.240277i	$0.0772384\pi$
$192$		0			0
$193$	−11.1785	−	7.35219i	−0.804644	−	0.529222i	0.0792808	−	0.996852i	$-0.474738\pi$
$193$	−11.1785	−	7.35219i	−0.804644	−	0.529222i	−0.883924	+	0.467630i	$0.845108\pi$
$194$	−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	0.999961	−	0.00885463i	$-0.00281855\pi$
$197$	24.7068	+	8.99252i	1.76028	+	0.640691i	0.760323	+	0.649545i	$0.225041\pi$
$198$		0			0
$199$	−2.18009	+	0.793488i	−0.154542	+	0.0562489i	−0.418133	−	0.908386i	$-0.637315\pi$
$199$	−2.18009	+	0.793488i	−0.154542	+	0.0562489i	0.263591	+	0.964635i	$0.415093\pi$
$200$	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	0.554566	−	0.832140i	$-0.312884\pi$
$211$	−5.83455	−	7.83716i	−0.401667	−	0.539532i	−0.956233	+	0.292608i	$0.905477\pi$
$212$	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	−0.990335	−	0.138694i	$-0.955710\pi$
$223$	−0.340442	−	5.84516i	−0.0227977	−	0.391421i	0.967538	−	0.252727i	$-0.0813274\pi$
$224$	−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	0.360642	−	0.932705i	$-0.382558\pi$
$227$	7.48001	+	0.874287i	0.496465	+	0.0580285i	0.135824	+	0.990733i	$0.456632\pi$
$228$		0			0
$229$	−3.23898	−	10.8190i	−0.214038	−	0.714937i	−0.995816	−	0.0913799i	$-0.970872\pi$
$229$	−3.23898	−	10.8190i	−0.214038	−	0.714937i	0.781778	−	0.623557i	$-0.214313\pi$
$230$	−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	0.431694	−	0.902020i	$-0.357916\pi$
$233$	−5.82577	−	4.88840i	−0.381659	−	0.320250i	−0.813353	+	0.581770i	$0.802360\pi$
$234$		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	0.749008	+	0.662561i	$0.230530\pi$
$239$	−1.11084	+	19.0723i	−0.0718541	+	1.23369i	−0.820862	+	0.571126i	$0.806507\pi$
$240$		0			0
$241$	4.44457	+	4.71097i	0.286300	+	0.303460i	0.854522	−	0.519415i	$-0.173850\pi$
$241$	4.44457	+	4.71097i	0.286300	+	0.303460i	−0.568222	+	0.822875i	$0.692369\pi$
$242$	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	−0.433078	−	0.901356i	$-0.642573\pi$
$251$	6.01053	−	5.04343i	0.379381	−	0.318339i	0.812459	+	0.583018i	$0.198128\pi$
$252$		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	−0.996960	−	0.0779088i	$-0.975176\pi$
$257$	−3.31564	−	11.0750i	−0.206824	−	0.690839i	0.790137	−	0.612931i	$-0.210009\pi$
$258$		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	−0.986271	−	0.165136i	$-0.947194\pi$
$263$	−0.419053	−	7.19487i	−0.0258399	−	0.443655i	0.960431	−	0.278519i	$-0.0898434\pi$
$264$		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	−0.980426	−	0.196888i	$-0.936917\pi$
$269$	−10.8367	−	18.7696i	−0.660723	−	1.14441i	0.319703	−	0.947518i	$-0.396417\pi$
$270$		0			0
$271$	10.7244	−	18.5753i	0.651463	−	1.12837i	−0.331305	−	0.943524i	$-0.607489\pi$
$271$	10.7244	−	18.5753i	0.651463	−	1.12837i	0.982768	−	0.184844i	$-0.0591779\pi$
$272$	−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	−0.814164	−	0.580635i	$-0.802804\pi$
$277$	−10.0441	+	6.60609i	−0.603490	+	0.396922i	0.210674	+	0.977556i	$0.432434\pi$
$278$	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	−0.605622	−	0.795753i	$-0.707075\pi$
$281$	5.53844	−	7.43941i	0.330395	−	0.443798i	0.936017	+	0.351955i	$0.114483\pi$
$282$		0			0
$283$	16.3804	−	17.3622i	0.973714	−	1.03208i	−0.0257605	−	0.999668i	$-0.508201\pi$
$283$	16.3804	−	17.3622i	0.973714	−	1.03208i	0.999475	−	0.0324087i	$-0.0103178\pi$
$284$	−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	0.837330	−	0.546697i	$-0.184115\pi$
$293$	11.4171	+	7.50914i	0.666994	+	0.438689i	−0.170337	+	0.985386i	$0.554485\pi$
$294$		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	0.842071	+	0.539367i	$0.181336\pi$
$307$	−2.34246	+	13.2847i	−0.133691	+	0.758201i	−0.975762	+	0.218834i	$0.929775\pi$
$308$	−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	0.390314	−	0.920682i	$-0.372367\pi$
$311$	5.74747	+	1.36218i	0.325909	+	0.0772419i	−0.0644043	+	0.997924i	$0.520515\pi$
$312$		0			0
$313$	3.49181	+	8.09493i	0.197369	+	0.457552i	0.987944	−	0.154813i	$-0.0494775\pi$
$313$	3.49181	+	8.09493i	0.197369	+	0.457552i	−0.790575	+	0.612365i	$0.790218\pi$
$314$	−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	0.622580	−	0.782556i	$-0.286085\pi$
$317$	6.52805	+	3.27851i	0.366652	+	0.184139i	−0.255928	+	0.966696i	$0.582381\pi$
$318$		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	−0.573374	−	0.819294i	$-0.694366\pi$
$331$	−28.6172	−	14.3721i	−1.57294	−	0.789962i	−0.999570	+	0.0293318i	$0.990662\pi$
$332$	−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	0.851538	−	0.524293i	$-0.175670\pi$
$337$	25.2820	+	5.99194i	1.37720	+	0.326402i	0.525660	+	0.850695i	$0.323819\pi$
$338$	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	−0.734007	−	0.679142i	$-0.762352\pi$
$347$	−11.6904	+	5.87112i	−0.627571	+	0.315178i	0.106436	+	0.994320i	$0.466056\pi$
$348$		0			0
$349$	−19.4854	+	4.61812i	−1.04303	+	0.247202i	−0.716210	−	0.697885i	$-0.754125\pi$
$349$	−19.4854	+	4.61812i	−1.04303	+	0.247202i	−0.326819	+	0.945087i	$0.605977\pi$
$350$	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	−0.383173	−	0.923676i	$-0.625169\pi$
$353$	8.35199	−	27.8976i	0.444532	−	1.48484i	0.827705	−	0.561163i	$-0.189646\pi$
$354$		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	−0.0736220	−	0.997286i	$-0.523456\pi$
$359$	−14.6096	−	5.31744i	−0.771063	−	0.280644i	−0.697441	+	0.716642i	$0.745678\pi$
$360$		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	−0.922468	−	0.386073i	$-0.873831\pi$
$367$	−5.51820	+	7.41223i	−0.288048	+	0.386915i	0.634421	+	0.772988i	$0.281239\pi$
$368$	−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	0.913555	+	0.406716i	$0.133326\pi$
$373$	20.1084	+	27.0103i	1.04117	+	1.39854i	0.127619	+	0.991823i	$0.459266\pi$
$374$	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	0.869029	−	0.494761i	$-0.164744\pi$
$379$	0.117576	+	0.203648i	0.00603950	+	0.0104607i	−0.862990	+	0.505221i	$0.831411\pi$
$380$	−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	−0.999756	−	0.0220908i	$-0.992968\pi$
$383$	−5.82441	+	13.5025i	−0.297614	+	0.689946i	0.702142	+	0.712037i	$0.252227\pi$
$384$		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	0.635654	−	0.771974i	$-0.280731\pi$
$389$	21.2249	+	2.48083i	1.07614	+	0.125783i	0.440490	+	0.897757i	$0.354805\pi$
$390$		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	−0.968809	−	0.247811i	$-0.920289\pi$
$397$	−17.7928	+	14.9299i	−0.892995	+	0.749311i	0.0758139	+	0.997122i	$0.475845\pi$
$398$	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	−0.891368	−	0.453280i	$-0.850254\pi$
$401$	0.933075	−	16.0203i	0.0465955	−	0.800014i	0.937964	−	0.346734i	$-0.112709\pi$
$402$		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	0.989396	+	0.145242i	$0.0463959\pi$
$409$	−0.205707	+	3.53186i	−0.0101716	+	0.174639i	−0.999568	+	0.0293976i	$0.990641\pi$
$410$	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	−0.837221	−	0.546865i	$-0.815821\pi$
$419$	−8.97055	−	29.9637i	−0.438240	−	1.46382i	0.398981	−	0.916959i	$-0.369364\pi$
$420$		0			0
$421$	−17.7199	−	2.07115i	−0.863613	−	0.100942i	−0.327259	−	0.944935i	$-0.606125\pi$
$421$	−17.7199	−	2.07115i	−0.863613	−	0.100942i	−0.536354	+	0.843993i	$0.680199\pi$
$422$	−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	0.997694	−	0.0678655i	$-0.0216189\pi$
$431$	9.13617	+	15.8243i	0.440074	+	0.762230i	−0.557621	+	0.830096i	$0.688286\pi$
$432$		0			0
$433$	14.1667	−	24.5374i	0.680806	−	1.17919i	−0.293929	−	0.955827i	$-0.594963\pi$
$433$	14.1667	−	24.5374i	0.680806	−	1.17919i	0.974735	−	0.223363i	$-0.0717037\pi$
$434$	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	−0.611081	−	0.791568i	$-0.709265\pi$
$439$	−2.64602	+	1.74031i	−0.126287	+	0.0830605i	0.484794	+	0.874629i	$0.338895\pi$
$440$	−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	−0.0680955	−	0.997679i	$-0.521692\pi$
$443$	19.0944	−	25.6482i	0.907200	−	1.21858i	0.975296	−	0.220903i	$-0.0709003\pi$
$444$		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	−0.287022	−	0.957924i	$-0.592665\pi$
$449$	2.30646	−	0.839483i	0.108849	−	0.0396177i	0.395870	+	0.918306i	$0.370443\pi$
$450$		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	−0.670884	−	0.741562i	$-0.734085\pi$
$457$	6.35184	−	21.2166i	0.297126	−	0.992471i	0.968011	−	0.250909i	$-0.0807295\pi$
$458$	−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	−0.415439	−	0.909621i	$-0.636372\pi$
$461$	−8.12571	+	1.92583i	−0.378452	+	0.0896948i	0.0369870	+	0.999316i	$0.488224\pi$
$462$		0			0
$463$	−21.8558	+	10.9764i	−1.01572	+	0.510116i	−0.877140	−	0.480235i	$-0.840552\pi$
$463$	−21.8558	+	10.9764i	−1.01572	+	0.510116i	−0.138585	+	0.990351i	$0.544255\pi$
$464$	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	0.855982	+	0.517006i	$0.172954\pi$
$467$	4.93682	+	27.9981i	0.228449	+	1.29560i	−0.627533	+	0.778590i	$0.715935\pi$
$468$		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	0.0955017	−	0.995429i	$-0.469554\pi$
$479$	−14.1368	−	7.09975i	−0.645926	−	0.324396i	−0.741427	+	0.671033i	$0.765851\pi$
$480$		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	−0.249801	−	0.968297i	$-0.580365\pi$
$491$	−5.97315	+	0.698161i	−0.269565	+	0.0315076i	−0.0197632	+	0.999805i	$0.506291\pi$
$492$		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	0.436216	−	0.899842i	$-0.356318\pi$
$499$	9.43087	+	2.23516i	0.422184	+	0.100059i	−0.0140319	+	0.999902i	$0.504467\pi$
$500$	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	−0.474116	−	0.880463i	$-0.657232\pi$
$503$	6.11251	−	34.6658i	0.272543	−	1.54567i	0.746659	−	0.665207i	$-0.231657\pi$
$504$		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	−0.768045	−	0.640396i	$-0.778770\pi$
$509$	−16.0863	+	8.07886i	−0.713014	+	0.358089i	0.0550313	+	0.998485i	$0.482474\pi$
$510$		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	0.431231	−	0.902242i	$-0.358079\pi$
$521$	4.14562	+	1.50888i	0.181623	+	0.0661054i	−0.249608	+	0.968347i	$0.580302\pi$
$522$		0			0
$523$	−33.2656	+	12.1077i	−1.45460	+	0.529432i	−0.943873	−	0.330309i	$-0.892847\pi$
$523$	−33.2656	+	12.1077i	−1.45460	+	0.529432i	−0.510730	+	0.859741i	$0.670625\pi$
$524$	−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	−0.998906	−	0.0467676i	$-0.985108\pi$
$541$	−12.5590	−	21.7529i	−0.539955	−	0.935229i	0.458951	−	0.888462i	$-0.348225\pi$
$542$	−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	0.998166	−	0.0605416i	$-0.0192828\pi$
$547$	−0.00653029	−	0.112121i	−0.000279215	−	0.00479394i	−0.998445	+	0.0557477i	$0.982246\pi$
$548$	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	−0.0912573	−	0.995827i	$-0.529089\pi$
$557$	−25.6731	−	21.5423i	−1.08780	−	0.912775i	−0.996545	+	0.0830527i	$0.973533\pi$
$558$		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	−0.218549	−	0.975826i	$-0.570132\pi$
$563$	2.65296	−	45.5495i	0.111809	−	1.91968i	0.330357	−	0.943856i	$-0.392831\pi$
$564$		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	0.661091	−	0.750306i	$-0.270094\pi$
$569$	−3.01473	−	3.19543i	−0.126384	−	0.133959i	−0.787475	+	0.616346i	$0.788612\pi$
$570$		0			0
$571$	−2.32506	+	39.9197i	−0.0973006	+	1.67059i	0.498071	+	0.867136i	$0.334042\pi$
$571$	−2.32506	+	39.9197i	−0.0973006	+	1.67059i	−0.595371	+	0.803451i	$0.702995\pi$
$572$	−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	0.558901	−	0.829234i	$-0.311223\pi$
$577$	−3.85975	−	3.23872i	−0.160684	−	0.134830i	−0.719584	+	0.694405i	$0.755668\pi$
$578$	−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	0.916469	+	0.400106i	$0.131027\pi$
$587$	1.27552	+	21.8998i	0.0526463	+	0.903902i	−0.863823	+	0.503796i	$0.831936\pi$
$588$		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	0.768614	−	0.639713i	$-0.220947\pi$
$593$	−4.13250	−	7.15770i	−0.169701	−	0.293931i	−0.938315	+	0.345782i	$0.887614\pi$
$594$		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	0.937218	−	0.348743i	$-0.113391\pi$
$599$	8.18252	+	10.9910i	0.334329	+	0.449081i	−0.602890	+	0.797825i	$0.705984\pi$
$600$		0			0
$601$	26.4263	−	17.3809i	1.07795	−	0.708980i	0.119098	−	0.992882i	$-0.462000\pi$
$601$	26.4263	−	17.3809i	1.07795	−	0.708980i	0.958853	+	0.283902i	$0.0916292\pi$
$602$	−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	−0.744428	−	0.667703i	$-0.767278\pi$
$607$	−0.851718	+	0.902768i	−0.0345702	+	0.0366422i	0.709858	+	0.704345i	$0.248759\pi$
$608$	−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	−0.347221	−	0.937783i	$-0.612875\pi$
$613$	−30.1068	−	10.9580i	−1.21600	−	0.442589i	−0.868782	+	0.495195i	$0.835097\pi$
$614$	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	0.682138	−	0.731224i	$-0.261050\pi$
$617$	6.97735	+	4.58907i	0.280897	+	0.184749i	−0.401240	+	0.915973i	$0.631421\pi$
$618$		0			0
$619$	−7.76825	+	25.9478i	−0.312232	+	1.04293i	0.647512	+	0.762055i	$0.275809\pi$
$619$	−7.76825	+	25.9478i	−0.312232	+	1.04293i	−0.959745	+	0.280874i	$0.909376\pi$
$620$	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	−0.816607	−	0.577194i	$-0.804147\pi$
$631$	3.72186	−	21.1077i	0.148165	−	0.840284i	0.964771	−	0.263089i	$-0.0847414\pi$
$632$	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	0.704511	−	0.709693i	$-0.251166\pi$
$641$	14.0757	+	7.06906i	0.555955	+	0.279211i	−0.148556	+	0.988904i	$0.547463\pi$
$642$		0			0
$643$	44.1265	−	5.15764i	1.74018	−	0.203398i	0.814099	−	0.580726i	$-0.197231\pi$
$643$	44.1265	−	5.15764i	1.74018	−	0.203398i	0.926079	+	0.377329i	$0.123157\pi$
$644$	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	−0.480051	−	0.877241i	$-0.659382\pi$
$653$	−19.0339	+	2.22475i	−0.744856	+	0.0870611i	−0.264805	+	0.964302i	$0.585308\pi$
$654$		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	0.904993	−	0.425427i	$-0.139876\pi$
$659$	−0.654481	−	1.51726i	−0.0254950	−	0.0591040i	−0.930488	+	0.366323i	$0.880617\pi$
$660$		0			0
$661$	−41.3076	−	9.79007i	−1.60668	−	0.380790i	−0.673211	−	0.739451i	$-0.735085\pi$
$661$	−41.3076	−	9.79007i	−1.60668	−	0.380790i	−0.933468	+	0.358661i	$0.883233\pi$
$662$	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	0.0144998	−	0.999895i	$-0.495384\pi$
$673$	12.3539	−	2.92794i	0.476209	−	0.112864i	0.461710	+	0.887031i	$0.347236\pi$
$674$	−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	−0.874646	−	0.484762i	$-0.838906\pi$
$677$	3.18713	−	10.6457i	0.122491	−	0.409149i	0.997137	+	0.0756130i	$0.0240914\pi$
$678$		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	0.679207	−	0.733947i	$-0.262324\pi$
$683$	19.0189	+	6.92231i	0.727737	+	0.264875i	0.0485305	+	0.998822i	$0.484546\pi$
$684$		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	−0.391269	−	0.920277i	$-0.627964\pi$
$691$	15.8395	−	21.2762i	0.602564	−	0.809384i	0.993832	+	0.110893i	$0.0353711\pi$
$692$	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	−0.755178	−	0.655520i	$-0.772450\pi$
$701$	5.03336	−	8.71804i	0.190107	−	0.329276i	0.945286	+	0.326244i	$0.105783\pi$
$702$		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	0.534962	+	0.844876i	$0.320326\pi$
$709$	2.70801	+	46.4947i	0.101701	+	1.74614i	−0.433261	+	0.901269i	$0.642637\pi$
$710$	−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	0.988180	−	0.153298i	$-0.0489893\pi$
$719$	27.0503	+	22.6979i	1.00881	+	0.846490i	0.0206270	+	0.999787i	$0.493434\pi$
$720$		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	0.646937	−	0.762544i	$-0.276050\pi$
$727$	−4.09655	−	4.34209i	−0.151933	−	0.161039i	−0.798870	+	0.601504i	$0.794568\pi$
$728$	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	−0.441447	−	0.897287i	$-0.645535\pi$
$733$	2.73945	−	47.0345i	0.101184	−	1.73726i	0.542631	−	0.839971i	$-0.317428\pi$
$734$	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	0.457748	−	0.889082i	$-0.348656\pi$
$739$	−9.19760	−	7.71770i	−0.338339	−	0.283900i	−0.796088	+	0.605182i	$0.793101\pi$
$740$	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	−0.934664	−	0.355532i	$-0.884300\pi$
$743$	−9.51664	−	31.7878i	−0.349132	−	1.16618i	0.585533	−	0.810649i	$-0.300885\pi$
$744$		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	0.431003	+	0.902351i	$0.358160\pi$
$751$	−14.2808	+	33.1067i	−0.521115	+	1.20808i	−0.952118	+	0.305731i	$0.901099\pi$
$752$	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	0.457990	+	0.888957i	$0.348569\pi$
$757$	−14.8811	+	25.7749i	−0.540864	+	0.936804i	−0.998855	+	0.0478471i	$0.984764\pi$
$758$	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	−0.755281	−	0.655401i	$-0.772500\pi$
$761$	−32.1802	−	43.2255i	−1.16653	−	1.56692i	−0.411250	−	0.911522i	$-0.634908\pi$
$762$		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	−0.824211	−	0.566283i	$-0.808381\pi$
$769$	−5.85019	+	6.20084i	−0.210963	+	0.223608i	0.613248	+	0.789890i	$0.289863\pi$
$770$	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	−0.900318	−	0.435234i	$-0.856666\pi$
$773$	−36.4284	+	13.2589i	−1.31024	+	0.476888i	−0.409921	+	0.912121i	$0.634444\pi$
$774$		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	−0.337857	−	0.941198i	$-0.609702\pi$
$787$	6.04121	−	3.03401i	0.215346	−	0.108151i	0.553202	+	0.833047i	$0.313406\pi$
$788$	−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	0.204008	−	0.978969i	$-0.434603\pi$
$797$	−1.49748	−	0.354909i	−0.0530434	−	0.0125715i	−0.257052	+	0.966398i	$0.582751\pi$
$798$		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	0.671340	+	0.741150i	$0.265719\pi$
$821$	21.4821	+	49.8012i	0.749731	+	1.73807i	0.0783916	+	0.996923i	$0.475022\pi$
$822$		0			0
$823$	7.83046	+	1.85585i	0.272953	+	0.0646910i	0.364813	−	0.931081i	$-0.381133\pi$
$823$	7.83046	+	1.85585i	0.272953	+	0.0646910i	−0.0918599	+	0.995772i	$0.529281\pi$
$824$	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	0.426950	+	0.904275i	$0.359588\pi$
$827$	−8.15370	+	46.2420i	−0.283532	+	1.60799i	−0.710482	+	0.703715i	$0.751523\pi$
$828$		0			0
$829$	4.57598	+	25.9517i	0.158930	+	0.901339i	0.955104	+	0.296271i	$0.0957430\pi$
$829$	4.57598	+	25.9517i	0.158930	+	0.901339i	−0.796174	+	0.605068i	$0.793146\pi$
$830$	−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	−0.927030	−	0.374988i	$-0.877647\pi$
$839$	1.55115	−	5.18120i	0.0535516	−	0.178875i	0.980581	+	0.196113i	$0.0628320\pi$
$840$		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	−0.965569	−	0.260149i	$-0.916228\pi$
$853$	−12.8338	+	17.2388i	−0.439421	+	0.590244i	0.526148	+	0.850393i	$0.323636\pi$
$854$	−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	−0.317336	−	0.948313i	$-0.602788\pi$
$857$	12.5216	−	8.23558i	0.427729	−	0.281322i	0.745066	+	0.666991i	$0.232418\pi$
$858$		0			0
$859$	−30.0492	−	40.3630i	−1.02526	−	1.37717i	−0.924036	−	0.382306i	$-0.875130\pi$
$859$	−30.0492	−	40.3630i	−1.02526	−	1.37717i	−0.101229	−	0.994863i	$-0.532277\pi$
$860$	−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	−0.995766	−	0.0919267i	$-0.970697\pi$
$863$	−12.2875	+	21.2826i	−0.418272	+	0.724468i	0.577494	+	0.816395i	$0.304031\pi$
$864$		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	0.884048	+	0.467397i	$0.154808\pi$
$877$	11.9131	+	39.7924i	0.402275	+	1.34369i	−0.481772	+	0.876296i	$0.660007\pi$
$878$	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	−0.984616	−	0.174731i	$-0.944095\pi$
$881$	−39.4074	−	33.0667i	−1.32767	−	1.11405i	−0.343053	−	0.939316i	$-0.611461\pi$
$882$		0			0
$883$	11.6864	−	9.80605i	0.393279	−	0.330000i	−0.424610	−	0.905376i	$-0.639589\pi$
$883$	11.6864	−	9.80605i	0.393279	−	0.330000i	0.817889	+	0.575376i	$0.195144\pi$
$884$	−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	0.489238	+	0.872150i	$0.337275\pi$
$887$	−2.91698	+	50.0825i	−0.0979424	+	1.68161i	−0.587180	+	0.809456i	$0.699762\pi$
$888$		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	0.958411	−	0.285390i	$-0.0921232\pi$
$907$	54.9677	+	6.42481i	1.82517	+	0.213332i	0.866762	+	0.498722i	$0.166197\pi$
$908$	−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	0.777615	+	0.628741i	$0.216429\pi$
$911$	2.36181	+	40.5508i	0.0782503	+	1.34351i	−0.699364	+	0.714765i	$0.746534\pi$
$912$		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	0.460573	+	0.887622i	$0.347644\pi$
$919$	−16.3221	+	28.2707i	−0.538417	+	0.932565i	−0.998990	+	0.0449430i	$0.985689\pi$
$920$	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	0.00931285	+	0.999957i	$0.497036\pi$
$929$	−28.9953	+	38.9475i	−0.951306	+	1.27783i	−0.960619	+	0.277869i	$0.910372\pi$
$930$		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	0.417983	−	0.908455i	$-0.362737\pi$
$937$	4.72115	+	1.71836i	0.154233	+	0.0561363i	−0.263750	+	0.964591i	$0.584959\pi$
$938$	−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	0.828862	−	0.559453i	$-0.188989\pi$
$941$	19.7386	+	12.9823i	0.643459	+	0.423210i	−0.185403	+	0.982663i	$0.559359\pi$
$942$		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	−0.498268	−	0.867023i	$-0.666030\pi$
$947$	−17.0613	+	4.04359i	−0.554416	+	0.131399i	−0.0561488	+	0.998422i	$0.517882\pi$
$948$		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	−0.755229	−	0.655462i	$-0.772474\pi$
$953$	−8.32666	−	47.2228i	−0.269727	−	1.52970i	0.485502	−	0.874236i	$-0.338637\pi$
$954$		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	0.582770	−	0.812637i	$-0.301969\pi$
$967$	41.5836	−	4.86042i	1.33724	−	0.156301i	0.754468	+	0.656337i	$0.227895\pi$
$968$	−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	0.0439914	−	0.999032i	$-0.485993\pi$
$977$	9.91440	−	1.15883i	0.317190	−	0.0370741i	0.273198	+	0.961958i	$0.411919\pi$
$978$		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	0.869273	−	0.494332i	$-0.164587\pi$
$983$	−2.72214	−	6.31062i	−0.0868227	−	0.201278i	−0.956096	+	0.293055i	$0.905328\pi$
$984$		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	−0.968241	−	0.250019i	$-0.919563\pi$
$991$	−4.53010	−	25.6915i	−0.143903	−	0.816117i	0.824338	−	0.566099i	$-0.191548\pi$
$992$	−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	−0.926527	−	0.376228i	$-0.877221\pi$
$997$	−50.0674	+	11.8662i	−1.58565	+	0.375806i	−0.659124	+	0.752035i	$0.729073\pi$
$998$	−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.199.4		72
3.2	odd	2		162.2.g.a.103.1	✓	72
81.11	odd	54		162.2.g.a.151.1	yes	72
81.70	even	27	inner	486.2.g.a.127.4		72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
162.2.g.a.103.1	✓	72	3.2	odd	2
162.2.g.a.151.1	yes	72	81.11	odd	54
486.2.g.a.127.4		72	81.70	even	27	inner
486.2.g.a.199.4		72	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)

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