LMFDB - Embedded newform 459.2.l.a.406.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [459,2,Mod(298,459)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("459.298"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(459, base_ring=CyclotomicField(8)) chi = DirichletCharacter(H, H._module([0, 1])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 459 = 3^{3} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	459.l (of order $8$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [48,0,0,0,0,0,0,0,0,-16,0,0,0,0,0,-48,0,0,-16] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(19)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$3.66513345278$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$12$ over $\Q(\zeta_{8})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			406.5
Character	$\chi$	$=$	459.406
Dual form			459.2.l.a.433.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.377143 - 0.377143i) q^{2} -1.71553i q^{4} +(1.86220 - 0.771351i) q^{5} +(-2.33552 - 0.967406i) q^{7} +(-1.40129 + 1.40129i) q^{8} +(-0.993228 - 0.411408i) q^{10} +(0.930989 - 2.24761i) q^{11} -3.12835i q^{13} +(0.515977 + 1.24568i) q^{14} -2.37408 q^{16} +(2.17080 + 3.50537i) q^{17} +(-3.97227 - 3.97227i) q^{19} +(-1.32327 - 3.19466i) q^{20} +(-1.19879 + 0.496554i) q^{22} +(-0.833806 + 2.01298i) q^{23} +(-0.662708 + 0.662708i) q^{25} +(-1.17984 + 1.17984i) q^{26} +(-1.65961 + 4.00665i) q^{28} +(4.38962 - 1.81824i) q^{29} +(-1.70961 - 4.12737i) q^{31} +(3.69794 + 3.69794i) q^{32} +(0.503326 - 2.14073i) q^{34} -5.09543 q^{35} +(1.79365 + 4.33025i) q^{37} +2.99623i q^{38} +(-1.52860 + 3.69036i) q^{40} +(-8.67965 - 3.59523i) q^{41} +(6.86189 - 6.86189i) q^{43} +(-3.85583 - 1.59714i) q^{44} +(1.07365 - 0.444720i) q^{46} -10.4884i q^{47} +(-0.430951 - 0.430951i) q^{49} +0.499872 q^{50} -5.36677 q^{52} +(2.00679 + 2.00679i) q^{53} -4.90362i q^{55} +(4.62835 - 1.91712i) q^{56} +(-2.34125 - 0.969779i) q^{58} +(-2.47820 + 2.47820i) q^{59} +(7.28899 + 3.01920i) q^{61} +(-0.911842 + 2.20138i) q^{62} +1.95885i q^{64} +(-2.41306 - 5.82563i) q^{65} +4.16861 q^{67} +(6.01356 - 3.72406i) q^{68} +(1.92171 + 1.92171i) q^{70} +(1.72607 + 4.16711i) q^{71} +(11.5823 - 4.79756i) q^{73} +(0.956663 - 2.30959i) q^{74} +(-6.81453 + 6.81453i) q^{76} +(-4.34870 + 4.34870i) q^{77} +(-1.73218 + 4.18185i) q^{79} +(-4.42102 + 1.83125i) q^{80} +(1.91756 + 4.62939i) q^{82} +(7.65476 + 7.65476i) q^{83} +(6.74634 + 4.85328i) q^{85} -5.17583 q^{86} +(1.84496 + 4.45412i) q^{88} +16.2213i q^{89} +(-3.02639 + 7.30634i) q^{91} +(3.45333 + 1.43042i) q^{92} +(-3.95563 + 3.95563i) q^{94} +(-10.4612 - 4.33317i) q^{95} +(-0.741725 + 0.307233i) q^{97} +0.325061i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 16 q^{10} - 48 q^{16} - 16 q^{19} - 24 q^{22} + 16 q^{25} + 24 q^{28} - 40 q^{31} + 64 q^{34} + 48 q^{37} - 48 q^{40} - 8 q^{43} + 24 q^{46} - 16 q^{49} + 32 q^{52} + 64 q^{58} - 24 q^{61} - 32 q^{67}+ \cdots - 88 q^{97}+O(q^{100}) $ 48 * q - 16 * q^10 - 48 * q^16 - 16 * q^19 - 24 * q^22 + 16 * q^25 + 24 * q^28 - 40 * q^31 + 64 * q^34 + 48 * q^37 - 48 * q^40 - 8 * q^43 + 24 * q^46 - 16 * q^49 + 32 * q^52 + 64 * q^58 - 24 * q^61 - 32 * q^67 + 96 * q^70 + 48 * q^73 + 96 * q^76 - 48 * q^79 + 112 * q^82 - 56 * q^85 - 160 * q^88 - 80 * q^91 - 40 * q^94 - 88 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/459\mathbb{Z}\right)^\times$.

$n$	$137$	$190$
$\chi(n)$	$1$	$e\left(\frac{3}{8}\right)$

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 $

$2$	−0.377143	−	0.377143i	−0.266681	−	0.266681i	0.561081	−	0.827761i	$-0.310386\pi$
$2$	−0.377143	−	0.377143i	−0.266681	−	0.266681i	−0.827761	+	0.561081i	$0.810386\pi$
$3$		0			0
$3$		0			0
$4$		−	1.71553i		−	0.857763i
$5$	1.86220	−	0.771351i	0.832803	−	0.344958i	0.0747915	−	0.997199i	$-0.476171\pi$
$5$	1.86220	−	0.771351i	0.832803	−	0.344958i	0.758012	+	0.652241i	$0.226171\pi$
$6$		0			0
$7$	−2.33552	−	0.967406i	−0.882745	−	0.365645i	−0.105184	−	0.994453i	$-0.533543\pi$
$7$	−2.33552	−	0.967406i	−0.882745	−	0.365645i	−0.777561	+	0.628808i	$0.783543\pi$
$8$	−1.40129	+	1.40129i	−0.495429	+	0.495429i
$9$		0			0
$10$	−0.993228	−	0.411408i	−0.314086	−	0.130099i
$11$	0.930989	−	2.24761i	0.280704	−	0.677679i	−0.719149	−	0.694856i	$-0.755468\pi$
$11$	0.930989	−	2.24761i	0.280704	−	0.677679i	0.999852	+	0.0171772i	$0.00546794\pi$
$12$		0			0
$13$		−	3.12835i		−	0.867649i	−0.900997	−	0.433824i	$-0.857164\pi$
$13$		−	3.12835i		−	0.867649i	0.900997	−	0.433824i	$-0.142836\pi$
$14$	0.515977	+	1.24568i	0.137901	+	0.332921i
$15$		0			0
$16$	−2.37408			−0.593520
$17$	2.17080	+	3.50537i	0.526496	+	0.850178i
$17$	2.17080	+	3.50537i	0.526496	+	0.850178i
$18$		0			0
$19$	−3.97227	−	3.97227i	−0.911301	−	0.911301i	0.0850736	−	0.996375i	$-0.472887\pi$
$19$	−3.97227	−	3.97227i	−0.911301	−	0.911301i	−0.996375	+	0.0850736i	$0.972887\pi$
$20$	−1.32327	−	3.19466i	−0.295893	−	0.714348i
$21$		0			0
$22$	−1.19879	+	0.496554i	−0.255582	+	0.105866i
$23$	−0.833806	+	2.01298i	−0.173860	+	0.419736i	−0.986657	−	0.162811i	$-0.947944\pi$
$23$	−0.833806	+	2.01298i	−0.173860	+	0.419736i	0.812797	+	0.582547i	$0.197944\pi$
$24$		0			0
$25$	−0.662708	+	0.662708i	−0.132542	+	0.132542i
$26$	−1.17984	+	1.17984i	−0.231385	+	0.231385i
$27$		0			0
$28$	−1.65961	+	4.00665i	−0.313637	+	0.757186i
$29$	4.38962	−	1.81824i	0.815132	−	0.337639i	0.0641325	−	0.997941i	$-0.479572\pi$
$29$	4.38962	−	1.81824i	0.815132	−	0.337639i	0.751000	+	0.660303i	$0.229572\pi$
$30$		0			0
$31$	−1.70961	−	4.12737i	−0.307056	−	0.741298i	−0.999798	−	0.0201125i	$-0.993598\pi$
$31$	−1.70961	−	4.12737i	−0.307056	−	0.741298i	0.692742	−	0.721185i	$-0.256402\pi$
$32$	3.69794	+	3.69794i	0.653710	+	0.653710i
$33$		0			0
$34$	0.503326	−	2.14073i	0.0863197	−	0.367132i
$35$	−5.09543			−0.861285
$36$		0			0
$37$	1.79365	+	4.33025i	0.294874	+	0.711889i	0.999996	+	0.00280322i	$0.000892293\pi$
$37$	1.79365	+	4.33025i	0.294874	+	0.711889i	−0.705122	+	0.709086i	$0.749108\pi$
$38$			2.99623i			0.486053i
$39$		0			0
$40$	−1.52860	+	3.69036i	−0.241693	+	0.583498i
$41$	−8.67965	−	3.59523i	−1.35553	−	0.561481i	−0.417707	−	0.908582i	$-0.637166\pi$
$41$	−8.67965	−	3.59523i	−1.35553	−	0.561481i	−0.937828	+	0.347101i	$0.887166\pi$
$42$		0			0
$43$	6.86189	−	6.86189i	1.04643	−	1.04643i	0.0475600	−	0.998868i	$-0.484855\pi$
$43$	6.86189	−	6.86189i	1.04643	−	1.04643i	0.998868	−	0.0475600i	$-0.0151445\pi$
$44$	−3.85583	−	1.59714i	−0.581288	−	0.240777i
$45$		0			0
$46$	1.07365	−	0.444720i	0.158301	−	0.0655703i
$47$		−	10.4884i		−	1.52989i	−0.644094	−	0.764946i	$-0.722766\pi$
$47$		−	10.4884i		−	1.52989i	0.644094	−	0.764946i	$-0.277234\pi$
$48$		0			0
$49$	−0.430951	−	0.430951i	−0.0615644	−	0.0615644i
$50$	0.499872			0.0706926
$51$		0			0
$52$	−5.36677			−0.744237
$53$	2.00679	+	2.00679i	0.275654	+	0.275654i	0.831371	−	0.555717i	$-0.187556\pi$
$53$	2.00679	+	2.00679i	0.275654	+	0.275654i	−0.555717	+	0.831371i	$0.687556\pi$
$54$		0			0
$55$		−	4.90362i		−	0.661205i
$56$	4.62835	−	1.91712i	0.618489	−	0.256187i
$57$		0			0
$58$	−2.34125	−	0.969779i	−0.307422	−	0.127338i
$59$	−2.47820	+	2.47820i	−0.322634	+	0.322634i	−0.849777	−	0.527143i	$-0.823263\pi$
$59$	−2.47820	+	2.47820i	−0.322634	+	0.322634i	0.527143	+	0.849777i	$0.323263\pi$
$60$		0			0
$61$	7.28899	+	3.01920i	0.933260	+	0.386569i	0.796914	−	0.604093i	$-0.206464\pi$
$61$	7.28899	+	3.01920i	0.933260	+	0.386569i	0.136346	+	0.990661i	$0.456464\pi$
$62$	−0.911842	+	2.20138i	−0.115804	+	0.279576i
$63$		0			0
$64$			1.95885i			0.244857i
$65$	−2.41306	−	5.82563i	−0.299303	−	0.722581i
$66$		0			0
$67$	4.16861			0.509277			0.254639	−	0.967036i	$-0.418043\pi$
$67$	4.16861			0.509277			0.254639	+	0.967036i	$0.418043\pi$
$68$	6.01356	−	3.72406i	0.729251	−	0.451609i
$69$		0			0
$70$	1.92171	+	1.92171i	0.229688	+	0.229688i
$71$	1.72607	+	4.16711i	0.204847	+	0.494544i	0.992598	−	0.121450i	$-0.0387544\pi$
$71$	1.72607	+	4.16711i	0.204847	+	0.494544i	−0.787751	+	0.615994i	$0.788754\pi$
$72$		0			0
$73$	11.5823	−	4.79756i	1.35561	−	0.561512i	0.417762	−	0.908557i	$-0.362815\pi$
$73$	11.5823	−	4.79756i	1.35561	−	0.561512i	0.937849	+	0.347044i	$0.112815\pi$
$74$	0.956663	−	2.30959i	0.111210	−	0.268484i
$75$		0			0
$76$	−6.81453	+	6.81453i	−0.781680	+	0.781680i
$77$	−4.34870	+	4.34870i	−0.495580	+	0.495580i
$78$		0			0
$79$	−1.73218	+	4.18185i	−0.194885	+	0.470495i	−0.990870	−	0.134822i	$-0.956954\pi$
$79$	−1.73218	+	4.18185i	−0.194885	+	0.470495i	0.795984	+	0.605317i	$0.206954\pi$
$80$	−4.42102	+	1.83125i	−0.494286	+	0.204740i
$81$		0			0
$82$	1.91756	+	4.62939i	0.211759	+	0.511231i
$83$	7.65476	+	7.65476i	0.840219	+	0.840219i	0.988887	−	0.148668i	$-0.0474986\pi$
$83$	7.65476	+	7.65476i	0.840219	+	0.840219i	−0.148668	+	0.988887i	$0.547499\pi$
$84$		0			0
$85$	6.74634	+	4.85328i	0.731744	+	0.526412i
$86$	−5.17583			−0.558124
$87$		0			0
$88$	1.84496	+	4.45412i	0.196673	+	0.474811i
$89$			16.2213i			1.71945i	0.510756	+	0.859726i	$0.329366\pi$
$89$			16.2213i			1.71945i	−0.510756	+	0.859726i	$0.670634\pi$
$90$		0			0
$91$	−3.02639	+	7.30634i	−0.317251	+	0.765913i
$92$	3.45333	+	1.43042i	0.360034	+	0.149131i
$93$		0			0
$94$	−3.95563	+	3.95563i	−0.407993	+	0.407993i
$95$	−10.4612	−	4.33317i	−1.07330	−	0.444574i
$96$		0			0
$97$	−0.741725	+	0.307233i	−0.0753108	+	0.0311947i	−0.420021	−	0.907514i	$-0.637977\pi$
$97$	−0.741725	+	0.307233i	−0.0753108	+	0.0311947i	0.344710	+	0.938709i	$0.387977\pi$
$98$			0.325061i			0.0328361i
$99$		0			0
$100$	1.13689	+	1.13689i	0.113689	+	0.113689i
$101$	10.7867			1.07331			0.536657	−	0.843801i	$-0.319687\pi$
$101$	10.7867			1.07331			0.536657	+	0.843801i	$0.319687\pi$
$102$		0			0
$103$	13.2358			1.30416			0.652082	−	0.758149i	$-0.273896\pi$
$103$	13.2358			1.30416			0.652082	+	0.758149i	$0.273896\pi$
$104$	4.38372	+	4.38372i	0.429859	+	0.429859i
$105$		0			0
$106$		−	1.51370i		−	0.147023i
$107$	7.58488	−	3.14176i	0.733258	−	0.303725i	0.0153679	−	0.999882i	$-0.495108\pi$
$107$	7.58488	−	3.14176i	0.733258	−	0.303725i	0.717890	+	0.696157i	$0.245108\pi$
$108$		0			0
$109$	0.211368	+	0.0875515i	0.0202454	+	0.00838592i	0.392783	−	0.919631i	$-0.371512\pi$
$109$	0.211368	+	0.0875515i	0.0202454	+	0.00838592i	−0.372538	+	0.928017i	$0.621512\pi$
$110$	−1.84937	+	1.84937i	−0.176330	+	0.176330i
$111$		0			0
$112$	5.54472	+	2.29670i	0.523927	+	0.217018i
$113$	4.59701	−	11.0982i	0.432451	−	1.04403i	−0.546044	−	0.837756i	$-0.683867\pi$
$113$	4.59701	−	11.0982i	0.432451	−	1.04403i	0.978495	−	0.206272i	$-0.0661331\pi$
$114$		0			0
$115$			4.39175i			0.409533i
$116$	−3.11924	−	7.53051i	−0.289614	−	0.699190i
$117$		0			0
$118$	1.86927			0.172081
$119$	−1.67883	−	10.2869i	−0.153898	−	0.943001i
$120$		0			0
$121$	3.59318	+	3.59318i	0.326652	+	0.326652i
$122$	−1.61032	−	3.88767i	−0.145792	−	0.351973i
$123$		0			0
$124$	−7.08061	+	2.93289i	−0.635858	+	0.263381i
$125$	−4.57967	+	11.0563i	−0.409618	+	0.988906i
$126$		0			0
$127$	−6.72812	+	6.72812i	−0.597024	+	0.597024i	−0.939519	−	0.342496i	$-0.888728\pi$
$127$	−6.72812	+	6.72812i	−0.597024	+	0.597024i	0.342496	+	0.939519i	$0.388728\pi$
$128$	8.13465	−	8.13465i	0.719008	−	0.719008i
$129$		0			0
$130$	−1.28703	+	3.10717i	−0.112880	+	0.272517i
$131$	13.7875	−	5.71095i	1.20462	−	0.498968i	0.312128	−	0.950040i	$-0.398958\pi$
$131$	13.7875	−	5.71095i	1.20462	−	0.498968i	0.892488	+	0.451072i	$0.148958\pi$
$132$		0			0
$133$	5.43453	+	13.1201i	0.471234	+	1.13766i
$134$	−1.57216	−	1.57216i	−0.135814	−	0.135814i
$135$		0			0
$136$	−7.95394	−	1.87012i	−0.682045	−	0.160361i
$137$	−14.1629			−1.21002			−0.605009	−	0.796219i	$-0.706830\pi$
$137$	−14.1629			−1.21002			−0.605009	+	0.796219i	$0.706830\pi$
$138$		0			0
$139$	−5.89525	−	14.2324i	−0.500029	−	1.20718i	−0.949468	−	0.313865i	$-0.898376\pi$
$139$	−5.89525	−	14.2324i	−0.500029	−	1.20718i	0.449439	−	0.893311i	$-0.351624\pi$
$140$			8.74135i			0.738779i
$141$		0			0
$142$	0.920620	−	2.22257i	0.0772567	−	0.186514i
$143$	−7.03131	−	2.91246i	−0.587988	−	0.243552i
$144$		0			0
$145$	6.77187	−	6.77187i	0.562373	−	0.562373i
$146$	−6.17757	−	2.55883i	−0.511260	−	0.211771i
$147$		0			0
$148$	7.42866	−	3.07705i	0.610632	−	0.252932i
$149$			6.62192i			0.542489i	0.962511	+	0.271244i	$0.0874352\pi$
$149$			6.62192i			0.542489i	−0.962511	+	0.271244i	$0.912565\pi$
$150$		0			0
$151$	−12.0584	−	12.0584i	−0.981297	−	0.981297i	0.0185313	−	0.999828i	$-0.494101\pi$
$151$	−12.0584	−	12.0584i	−0.981297	−	0.981297i	−0.999828	+	0.0185313i	$0.994101\pi$
$152$	11.1326			0.902971
$153$		0			0
$154$	3.28016			0.264323
$155$	−6.36730	−	6.36730i	−0.511434	−	0.511434i
$156$		0			0
$157$			14.5703i			1.16284i	0.813605	+	0.581418i	$0.197502\pi$
$157$			14.5703i			1.16284i	−0.813605	+	0.581418i	$0.802498\pi$
$158$	2.23044	−	0.923878i	0.177444	−	0.0734998i
$159$		0			0
$160$	9.73873	+	4.03391i	0.769914	+	0.318909i
$161$	3.89475	−	3.89475i	0.306949	−	0.306949i
$162$		0			0
$163$	−4.98486	−	2.06480i	−0.390444	−	0.161727i	0.178820	−	0.983882i	$-0.442772\pi$
$163$	−4.98486	−	2.06480i	−0.390444	−	0.161727i	−0.569265	+	0.822154i	$0.692772\pi$
$164$	−6.16771	+	14.8902i	−0.481617	+	1.16273i
$165$		0			0
$166$		−	5.77388i		−	0.448140i
$167$	4.76729	+	11.5093i	0.368904	+	0.890613i	0.993931	+	0.110010i	$0.0350881\pi$
$167$	4.76729	+	11.5093i	0.368904	+	0.890613i	−0.625027	+	0.780603i	$0.714912\pi$
$168$		0			0
$169$	3.21341			0.247185
$170$	−0.713958	−	4.37472i	−0.0547580	−	0.335526i
$171$		0			0
$172$	−11.7717	−	11.7717i	−0.897587	−	0.897587i
$173$	−1.02321	−	2.47026i	−0.0777936	−	0.187810i	0.880198	−	0.474607i	$-0.157410\pi$
$173$	−1.02321	−	2.47026i	−0.0777936	−	0.187810i	−0.957992	+	0.286796i	$0.907410\pi$
$174$		0			0
$175$	2.18888	−	0.906663i	0.165464	−	0.0685373i
$176$	−2.21024	+	5.33600i	−0.166603	+	0.402216i
$177$		0			0
$178$	6.11775	−	6.11775i	0.458544	−	0.458544i
$179$	9.90545	−	9.90545i	0.740368	−	0.740368i	−0.232281	−	0.972649i	$-0.574619\pi$
$179$	9.90545	−	9.90545i	0.740368	−	0.740368i	0.972649	+	0.232281i	$0.0746188\pi$
$180$		0			0
$181$	5.11394	−	12.3461i	0.380116	−	0.917681i	−0.611826	−	0.790992i	$-0.709565\pi$
$181$	5.11394	−	12.3461i	0.380116	−	0.917681i	0.991942	−	0.126689i	$-0.0404351\pi$
$182$	3.89692	−	1.61416i	0.288859	−	0.119649i
$183$		0			0
$184$	−1.65237	−	3.98917i	−0.121814	−	0.294085i
$185$	6.68029	+	6.68029i	0.491145	+	0.491145i
$186$		0			0
$187$	9.89969	−	1.61564i	0.723937	−	0.118147i
$188$	−17.9931			−1.31228
$189$		0			0
$190$	2.31114	+	5.57959i	0.167668	+	0.404786i
$191$			20.9983i			1.51938i	0.650285	+	0.759691i	$0.274650\pi$
$191$			20.9983i			1.51938i	−0.650285	+	0.759691i	$0.725350\pi$
$192$		0			0
$193$	1.95682	−	4.72418i	0.140855	−	0.340054i	−0.837672	−	0.546174i	$-0.816084\pi$
$193$	1.95682	−	4.72418i	0.140855	−	0.340054i	0.978527	+	0.206120i	$0.0660838\pi$
$194$	0.395607	+	0.163866i	0.0284030	+	0.0117649i
$195$		0			0
$196$	−0.739307	+	0.739307i	−0.0528077	+	0.0528077i
$197$	3.54743	+	1.46940i	0.252744	+	0.104690i	0.505459	−	0.862851i	$-0.331323\pi$
$197$	3.54743	+	1.46940i	0.252744	+	0.104690i	−0.252714	+	0.967541i	$0.581323\pi$
$198$		0			0
$199$	6.67711	−	2.76575i	0.473328	−	0.196059i	−0.133251	−	0.991082i	$-0.542542\pi$
$199$	6.67711	−	2.76575i	0.473328	−	0.196059i	0.606579	+	0.795024i	$0.292542\pi$
$200$		−	1.85729i		−	0.131330i
$201$		0			0
$202$	−4.06812	−	4.06812i	−0.286232	−	0.286232i
$203$	−12.0110			−0.843010
$204$		0			0
$205$	−18.9365			−1.32258
$206$	−4.99180	−	4.99180i	−0.347795	−	0.347795i
$207$		0			0
$208$			7.42696i			0.514967i
$209$	−12.6262	+	5.22996i	−0.873376	+	0.361764i
$210$		0			0
$211$	−11.6035	−	4.80633i	−0.798819	−	0.330882i	−0.0543357	−	0.998523i	$-0.517304\pi$
$211$	−11.6035	−	4.80633i	−0.798819	−	0.330882i	−0.744483	+	0.667641i	$0.767304\pi$
$212$	3.44270	−	3.44270i	0.236446	−	0.236446i
$213$		0			0
$214$	−4.04548	−	1.67569i	−0.276543	−	0.114548i
$215$	7.48532	−	18.0712i	0.510495	−	1.23244i
$216$		0			0
$217$			11.2935i			0.766650i
$218$	−0.0466966	−	0.112736i	−0.00316269	−	0.00763541i
$219$		0			0
$220$	−8.41230			−0.567157
$221$	10.9660	−	6.79102i	0.737656	−	0.456814i
$222$		0			0
$223$	−3.39198	−	3.39198i	−0.227144	−	0.227144i	0.584355	−	0.811498i	$-0.301348\pi$
$223$	−3.39198	−	3.39198i	−0.227144	−	0.227144i	−0.811498	+	0.584355i	$0.801348\pi$
$224$	−5.05922	−	12.2140i	−0.338033	−	0.816084i
$225$		0			0
$226$	−5.91933	+	2.45187i	−0.393748	+	0.163096i
$227$	−8.60058	+	20.7636i	−0.570840	+	1.37813i	0.330000	+	0.943981i	$0.392951\pi$
$227$	−8.60058	+	20.7636i	−0.570840	+	1.37813i	−0.900841	+	0.434150i	$0.857049\pi$
$228$		0			0
$229$	−1.61900	+	1.61900i	−0.106987	+	0.106987i	−0.758574	−	0.651587i	$-0.774103\pi$
$229$	−1.61900	+	1.61900i	−0.106987	+	0.106987i	0.651587	+	0.758574i	$0.274103\pi$
$230$	1.65632	−	1.65632i	0.109214	−	0.109214i
$231$		0			0
$232$	−3.60324	+	8.69899i	−0.236564	+	0.571117i
$233$	23.0850	−	9.56213i	1.51235	−	0.626436i	0.536309	−	0.844022i	$-0.319818\pi$
$233$	23.0850	−	9.56213i	1.51235	−	0.626436i	0.976041	+	0.217586i	$0.0698183\pi$
$234$		0			0
$235$	−8.09024	−	19.5316i	−0.527749	−	1.27410i
$236$	4.25141	+	4.25141i	0.276744	+	0.276744i
$237$		0			0
$238$	−3.24648	+	4.51281i	−0.210438	+	0.292522i
$239$	−16.8913			−1.09261			−0.546304	−	0.837587i	$-0.683966\pi$
$239$	−16.8913			−1.09261			−0.546304	+	0.837587i	$0.683966\pi$
$240$		0			0
$241$	−11.4769	−	27.7078i	−0.739295	−	1.78482i	−0.608732	−	0.793376i	$-0.708321\pi$
$241$	−11.4769	−	27.7078i	−0.739295	−	1.78482i	−0.130564	−	0.991440i	$-0.541679\pi$
$242$		−	2.71029i		−	0.174224i
$243$		0			0
$244$	5.17951	−	12.5045i	0.331584	−	0.800516i
$245$	−1.13493	−	0.470105i	−0.0725082	−	0.0300339i
$246$		0			0
$247$	−12.4267	+	12.4267i	−0.790689	+	0.790689i
$248$	8.17929	+	3.38797i	0.519385	+	0.215136i
$249$		0			0
$250$	5.89700	−	2.44262i	0.372959	−	0.154485i
$251$			24.1719i			1.52572i	0.646566	+	0.762858i	$0.276205\pi$
$251$			24.1719i			1.52572i	−0.646566	+	0.762858i	$0.723795\pi$
$252$		0			0
$253$	3.74814	+	3.74814i	0.235643	+	0.235643i
$254$	5.07493			0.318429
$255$		0			0
$256$	−2.21815			−0.138634
$257$	−18.9089	−	18.9089i	−1.17950	−	1.17950i	−0.979871	−	0.199632i	$-0.936025\pi$
$257$	−18.9089	−	18.9089i	−1.17950	−	1.17950i	−0.199632	−	0.979871i	$-0.563975\pi$
$258$		0			0
$259$		−	11.8486i		−	0.736236i
$260$	−9.99403	+	4.13966i	−0.619803	+	0.256731i
$261$		0			0
$262$	−7.35370	−	3.04600i	−0.454313	−	0.188183i
$263$	−1.65645	+	1.65645i	−0.102141	+	0.102141i	−0.756331	−	0.654190i	$-0.773010\pi$
$263$	−1.65645	+	1.65645i	−0.102141	+	0.102141i	0.654190	+	0.756331i	$0.273010\pi$
$264$		0			0
$265$	5.28500	+	2.18912i	0.324655	+	0.134476i
$266$	2.89857	−	6.99777i	0.177723	−	0.429061i
$267$		0			0
$268$		−	7.15136i		−	0.436839i
$269$	−6.59059	−	15.9111i	−0.401835	−	0.970116i	−0.987220	−	0.159361i	$-0.949057\pi$
$269$	−6.59059	−	15.9111i	−0.401835	−	0.970116i	0.585385	−	0.810755i	$-0.300943\pi$
$270$		0			0
$271$	−24.8158			−1.50745			−0.753726	−	0.657189i	$-0.771746\pi$
$271$	−24.8158			−1.50745			−0.753726	+	0.657189i	$0.771746\pi$
$272$	−5.15365	−	8.32204i	−0.312486	−	0.504597i
$273$		0			0
$274$	5.34144	+	5.34144i	0.322688	+	0.322688i
$275$	0.872534	+	2.10648i	0.0526158	+	0.127026i
$276$		0			0
$277$	−17.0987	+	7.08252i	−1.02736	+	0.425548i	−0.831760	−	0.555136i	$-0.812666\pi$
$277$	−17.0987	+	7.08252i	−1.02736	+	0.425548i	−0.195603	+	0.980683i	$0.562666\pi$
$278$	−3.14430	+	7.59101i	−0.188582	+	0.455278i
$279$		0			0
$280$	7.14016	−	7.14016i	0.426706	−	0.426706i
$281$	−12.2066	+	12.2066i	−0.728182	+	0.728182i	−0.970257	−	0.242075i	$-0.922172\pi$
$281$	−12.2066	+	12.2066i	−0.728182	+	0.728182i	0.242075	+	0.970257i	$0.422172\pi$
$282$		0			0
$283$	7.92580	−	19.1346i	0.471140	−	1.13743i	−0.492521	−	0.870301i	$-0.663924\pi$
$283$	7.92580	−	19.1346i	0.471140	−	1.13743i	0.963660	−	0.267131i	$-0.0860756\pi$
$284$	7.14878	−	2.96112i	0.424202	−	0.175710i
$285$		0			0
$286$	1.55340	+	3.75023i	0.0918542	+	0.221756i
$287$	16.7935	+	16.7935i	0.991288	+	0.991288i
$288$		0			0
$289$	−7.57527	+	15.2189i	−0.445604	+	0.895230i
$290$	−5.10793			−0.299948
$291$		0			0
$292$	−8.23034	−	19.8698i	−0.481644	−	1.16279i
$293$		−	23.8401i		−	1.39275i	−0.717678	−	0.696375i	$-0.754795\pi$
$293$		−	23.8401i		−	1.39275i	0.717678	−	0.696375i	$-0.245205\pi$
$294$		0			0
$295$	−2.70335	+	6.52648i	−0.157395	+	0.379986i
$296$	−8.58134	−	3.55451i	−0.498780	−	0.206602i
$297$		0			0
$298$	2.49741	−	2.49741i	0.144671	−	0.144671i
$299$	6.29733	+	2.60844i	0.364184	+	0.150850i
$300$		0			0
$301$	−22.6643	+	9.38787i	−1.30635	+	0.541108i
$302$			9.09548i			0.523386i
$303$		0			0
$304$	9.43049	+	9.43049i	0.540875	+	0.540875i
$305$	15.9025			0.910572
$306$		0			0
$307$	13.9729			0.797474			0.398737	−	0.917065i	$-0.369449\pi$
$307$	13.9729			0.797474			0.398737	+	0.917065i	$0.369449\pi$
$308$	7.46030	+	7.46030i	0.425090	+	0.425090i
$309$		0			0
$310$			4.80277i			0.272779i
$311$	9.01213	−	3.73295i	0.511031	−	0.211676i	−0.112241	−	0.993681i	$-0.535803\pi$
$311$	9.01213	−	3.73295i	0.511031	−	0.211676i	0.623272	+	0.782005i	$0.285803\pi$
$312$		0			0
$313$	30.7112	+	12.7210i	1.73590	+	0.719032i	0.999077	+	0.0429439i	$0.0136737\pi$
$313$	30.7112	+	12.7210i	1.73590	+	0.719032i	0.736820	+	0.676089i	$0.236326\pi$
$314$	5.49509	−	5.49509i	0.310106	−	0.310106i
$315$		0			0
$316$	7.17407	+	2.97160i	0.403573	+	0.167166i
$317$	2.80943	−	6.78257i	0.157793	−	0.380947i	−0.825135	−	0.564936i	$-0.808901\pi$
$317$	2.80943	−	6.78257i	0.157793	−	0.380947i	0.982928	+	0.183989i	$0.0589010\pi$
$318$		0			0
$319$		−	11.5589i		−	0.647175i
$320$	1.51096	+	3.64779i	0.0844654	+	0.203917i
$321$		0			0
$322$	−2.93775			−0.163715
$323$	5.30129	−	22.5473i	0.294972	−	1.25456i
$324$		0			0
$325$	2.07319	+	2.07319i	0.115000	+	0.115000i
$326$	1.10128	+	2.65873i	0.0609944	+	0.147254i
$327$		0			0
$328$	17.2006	−	7.12473i	0.949745	−	0.393397i
$329$	−10.1465	+	24.4959i	−0.559397	+	1.35050i
$330$		0			0
$331$	1.45111	−	1.45111i	0.0797602	−	0.0797602i	−0.666101	−	0.745861i	$-0.732038\pi$
$331$	1.45111	−	1.45111i	0.0797602	−	0.0797602i	0.745861	+	0.666101i	$0.232038\pi$
$332$	13.1319	−	13.1319i	0.720709	−	0.720709i
$333$		0			0
$334$	2.54269	−	6.13859i	0.139130	−	0.335889i
$335$	7.76281	−	3.21546i	0.424128	−	0.175679i
$336$		0			0
$337$	2.33424	+	5.63535i	0.127154	+	0.306977i	0.974617	−	0.223877i	$-0.0718713\pi$
$337$	2.33424	+	5.63535i	0.127154	+	0.306977i	−0.847463	+	0.530854i	$0.821871\pi$
$338$	−1.21192	−	1.21192i	−0.0659195	−	0.0659195i
$339$		0			0
$340$	8.32592	−	11.5735i	0.451536	−	0.627662i
$341$	−10.8683			−0.588554
$342$		0			0
$343$	7.36143	+	17.7721i	0.397480	+	0.959601i
$344$			19.2309i			1.03686i
$345$		0			0
$346$	−0.545743	+	1.31754i	−0.0293393	+	0.0708314i
$347$	−31.7950	−	13.1699i	−1.70684	−	0.706998i	−0.706845	−	0.707369i	$-0.749882\pi$
$347$	−31.7950	−	13.1699i	−1.70684	−	0.706998i	−1.00000		0.000370632i	$0.999882\pi$
$348$		0			0
$349$	12.3245	−	12.3245i	0.659713	−	0.659713i	−0.295599	−	0.955312i	$-0.595519\pi$
$349$	12.3245	−	12.3245i	0.659713	−	0.659713i	0.955312	+	0.295599i	$0.0955192\pi$
$350$	−1.16746	−	0.483579i	−0.0624035	−	0.0258484i
$351$		0			0
$352$	11.7543	−	4.86877i	0.626504	−	0.259507i
$353$			35.9886i			1.91548i	0.287638	+	0.957739i	$0.407130\pi$
$353$			35.9886i			1.91548i	−0.287638	+	0.957739i	$0.592870\pi$
$354$		0			0
$355$	6.42860	+	6.42860i	0.341195	+	0.341195i
$356$	27.8280			1.47488
$357$		0			0
$358$	−7.47155			−0.394884
$359$	13.2408	+	13.2408i	0.698823	+	0.698823i	0.964157	−	0.265334i	$-0.0854822\pi$
$359$	13.2408	+	13.2408i	0.698823	+	0.698823i	−0.265334	+	0.964157i	$0.585482\pi$
$360$		0			0
$361$			12.5578i			0.660939i
$362$	−6.58495	+	2.72758i	−0.346097	+	0.143358i
$363$		0			0
$364$	12.5342	+	5.19184i	0.656971	+	0.272127i
$365$	17.8681	−	17.8681i	0.935259	−	0.935259i
$366$		0			0
$367$	−22.4274	−	9.28972i	−1.17070	−	0.484919i	−0.289275	−	0.957246i	$-0.593414\pi$
$367$	−22.4274	−	9.28972i	−1.17070	−	0.484919i	−0.881424	+	0.472326i	$0.843414\pi$
$368$	1.97952	−	4.77899i	0.103190	−	0.249122i
$369$		0			0
$370$		−	5.03885i		−	0.261957i
$371$	−2.74553	−	6.62829i	−0.142541	−	0.344124i
$372$		0			0
$373$	−1.52714			−0.0790723			−0.0395361	−	0.999218i	$-0.512588\pi$
$373$	−1.52714			−0.0790723			−0.0395361	+	0.999218i	$0.512588\pi$
$374$	−4.34293	−	3.12428i	−0.224568	−	0.161552i
$375$		0			0
$376$	14.6973	+	14.6973i	0.757953	+	0.757953i
$377$	−5.68810	−	13.7323i	−0.292952	−	0.707249i
$378$		0			0
$379$	−5.34466	+	2.21383i	−0.274537	+	0.113717i	−0.515704	−	0.856767i	$-0.672470\pi$
$379$	−5.34466	+	2.21383i	−0.274537	+	0.113717i	0.241168	+	0.970483i	$0.422470\pi$
$380$	−7.43366	+	17.9464i	−0.381339	+	0.920633i
$381$		0			0
$382$	7.91936	−	7.91936i	0.405190	−	0.405190i
$383$	−19.7415	+	19.7415i	−1.00874	+	1.00874i	−0.00877965	+	0.999961i	$0.502795\pi$
$383$	−19.7415	+	19.7415i	−1.00874	+	1.00874i	−0.999961	+	0.00877965i	$0.997205\pi$
$384$		0			0
$385$	−4.74379	+	11.4525i	−0.241766	+	0.583675i
$386$	−2.51969	+	1.04369i	−0.128249	+	0.0531225i
$387$		0			0
$388$	0.527065	+	1.27245i	0.0267577	+	0.0645988i
$389$	4.09825	+	4.09825i	0.207789	+	0.207789i	0.803327	−	0.595538i	$-0.203061\pi$
$389$	4.09825	+	4.09825i	0.207789	+	0.207789i	−0.595538	+	0.803327i	$0.703061\pi$
$390$		0			0
$391$	−8.86629	+	1.44698i	−0.448387	+	0.0731772i
$392$	1.20777			0.0610016
$393$		0			0
$394$	−0.783718	−	1.89206i	−0.0394832	−	0.0953208i
$395$			9.12358i			0.459057i
$396$		0			0
$397$	−9.81920	+	23.7057i	−0.492812	+	1.18975i	0.460472	+	0.887674i	$0.347680\pi$
$397$	−9.81920	+	23.7057i	−0.492812	+	1.18975i	−0.953283	+	0.302078i	$0.902320\pi$
$398$	−3.56131	−	1.47514i	−0.178512	−	0.0739423i
$399$		0			0
$400$	1.57332	−	1.57332i	0.0786661	−	0.0786661i
$401$	−1.79781	−	0.744678i	−0.0897784	−	0.0371875i	0.337342	−	0.941382i	$-0.390472\pi$
$401$	−1.79781	−	0.744678i	−0.0897784	−	0.0371875i	−0.427121	+	0.904195i	$0.640472\pi$
$402$		0			0
$403$	−12.9119	+	5.34827i	−0.643186	+	0.266417i
$404$		−	18.5048i		−	0.920648i
$405$		0			0
$406$	4.52988	+	4.52988i	0.224814	+	0.224814i
$407$	11.4026			0.565205
$408$		0			0
$409$	9.72007			0.480627			0.240313	−	0.970695i	$-0.422750\pi$
$409$	9.72007			0.480627			0.240313	+	0.970695i	$0.422750\pi$
$410$	7.14177	+	7.14177i	0.352707	+	0.352707i
$411$		0			0
$412$		−	22.7064i		−	1.11866i
$413$	8.18532	−	3.39047i	0.402773	−	0.166834i
$414$		0			0
$415$	20.1592	+	8.35023i	0.989578	+	0.409897i
$416$	11.5685	−	11.5685i	0.567191	−	0.567191i
$417$		0			0
$418$	6.73435	+	2.78946i	0.329388	+	0.136437i
$419$	−1.88624	+	4.55378i	−0.0921486	+	0.222466i	−0.963233	−	0.268666i	$-0.913417\pi$
$419$	−1.88624	+	4.55378i	−0.0921486	+	0.222466i	0.871085	+	0.491133i	$0.163417\pi$
$420$		0			0
$421$			33.8369i			1.64911i	0.565783	+	0.824554i	$0.308574\pi$
$421$			33.8369i			1.64911i	−0.565783	+	0.824554i	$0.691426\pi$
$422$	2.56351	+	6.18887i	0.124790	+	0.301269i
$423$		0			0
$424$	−5.62418			−0.273134
$425$	−3.76165	−	0.884433i	−0.182467	−	0.0429013i
$426$		0			0
$427$	−14.1028	−	14.1028i	−0.682483	−	0.682483i
$428$	−5.38977	−	13.0121i	−0.260524	−	0.628961i
$429$		0			0
$430$	−9.63846	+	3.99238i	−0.464808	+	0.192530i
$431$	5.73801	−	13.8528i	0.276390	−	0.667265i	−0.723340	−	0.690492i	$-0.757394\pi$
$431$	5.73801	−	13.8528i	0.276390	−	0.667265i	0.999730	+	0.0232273i	$0.00739415\pi$
$432$		0			0
$433$	0.403620	−	0.403620i	0.0193967	−	0.0193967i	−0.697342	−	0.716739i	$-0.745634\pi$
$433$	0.403620	−	0.403620i	0.0193967	−	0.0193967i	0.716739	+	0.697342i	$0.245634\pi$
$434$	4.25926	−	4.25926i	0.204451	−	0.204451i
$435$		0			0
$436$	0.150197	−	0.362607i	0.00719313	−	0.0173657i
$437$	11.3082	−	4.68402i	0.540945	−	0.224067i
$438$		0			0
$439$	9.73553	+	23.5037i	0.464652	+	1.12177i	0.966466	+	0.256793i	$0.0826659\pi$
$439$	9.73553	+	23.5037i	0.464652	+	1.12177i	−0.501815	+	0.864975i	$0.667334\pi$
$440$	6.87138	+	6.87138i	0.327580	+	0.327580i
$441$		0			0
$442$	−6.69696	−	1.57458i	−0.318542	−	0.0748952i
$443$	−1.27194			−0.0604317			−0.0302158	−	0.999543i	$-0.509619\pi$
$443$	−1.27194			−0.0604317			−0.0302158	+	0.999543i	$0.509619\pi$
$444$		0			0
$445$	12.5123	+	30.2073i	0.593139	+	1.43196i
$446$			2.55852i			0.121150i
$447$		0			0
$448$	1.89501	−	4.57495i	0.0895306	−	0.216146i
$449$	−28.4228	−	11.7731i	−1.34135	−	0.555607i	−0.407482	−	0.913213i	$-0.633593\pi$
$449$	−28.4228	−	11.7731i	−1.34135	−	0.555607i	−0.933873	+	0.357606i	$0.883593\pi$
$450$		0			0
$451$	−16.1613	+	16.1613i	−0.761007	+	0.761007i
$452$	−19.0392	−	7.88629i	−0.895529	−	0.370940i
$453$		0			0
$454$	11.0745	−	4.58721i	0.519753	−	0.215289i
$455$			15.9403i			0.747293i
$456$		0			0
$457$	16.6124	+	16.6124i	0.777096	+	0.777096i	0.979336	−	0.202240i	$-0.0648221\pi$
$457$	16.6124	+	16.6124i	0.777096	+	0.777096i	−0.202240	+	0.979336i	$0.564822\pi$
$458$	1.22119			0.0570625
$459$		0			0
$460$	7.53416			0.351282
$461$	−6.02393	−	6.02393i	−0.280562	−	0.280562i	0.552771	−	0.833333i	$-0.313570\pi$
$461$	−6.02393	−	6.02393i	−0.280562	−	0.280562i	−0.833333	+	0.552771i	$0.813570\pi$
$462$		0			0
$463$			17.6689i			0.821143i	0.911828	+	0.410571i	$0.134671\pi$
$463$			17.6689i			0.821143i	−0.911828	+	0.410571i	$0.865329\pi$
$464$	−10.4213	+	4.31665i	−0.483797	+	0.200395i
$465$		0			0
$466$	−12.3127	−	5.10007i	−0.570373	−	0.236256i
$467$	−4.43871	+	4.43871i	−0.205399	+	0.205399i	−0.802309	−	0.596910i	$-0.796395\pi$
$467$	−4.43871	+	4.43871i	−0.205399	+	0.205399i	0.596910	+	0.802309i	$0.296395\pi$
$468$		0			0
$469$	−9.73589	−	4.03274i	−0.449562	−	0.186215i
$470$	−4.31502	+	10.4174i	−0.199037	+	0.480518i
$471$		0			0
$472$		−	6.94533i		−	0.319685i
$473$	−9.03449	−	21.8112i	−0.415406	−	1.00288i
$474$		0			0
$475$	5.26491			0.241571
$476$	−17.6475	+	2.88008i	−0.808871	+	0.132008i
$477$		0			0
$478$	6.37045	+	6.37045i	0.291377	+	0.291377i
$479$	−12.9498	−	31.2636i	−0.591692	−	1.42847i	−0.881867	−	0.471498i	$-0.843713\pi$
$479$	−12.9498	−	31.2636i	−0.591692	−	1.42847i	0.290174	−	0.956974i	$-0.406287\pi$
$480$		0			0
$481$	13.5466	−	5.61117i	0.617670	−	0.255847i
$482$	−6.12136	+	14.7783i	−0.278820	+	0.673132i
$483$		0			0
$484$	6.16419	−	6.16419i	0.280190	−	0.280190i
$485$	−1.14426	+	1.14426i	−0.0519582	+	0.0519582i
$486$		0			0
$487$	6.63178	−	16.0105i	0.300515	−	0.725506i	−0.699427	−	0.714704i	$-0.746561\pi$
$487$	6.63178	−	16.0105i	0.300515	−	0.725506i	0.999942	−	0.0108024i	$-0.00343859\pi$
$488$	−14.4447	+	5.98320i	−0.653882	+	0.270847i
$489$		0			0
$490$	0.250736	+	0.605329i	0.0113271	+	0.0273460i
$491$	13.3600	+	13.3600i	0.602928	+	0.602928i	0.941088	−	0.338161i	$-0.109805\pi$
$491$	13.3600	+	13.3600i	0.602928	+	0.602928i	−0.338161	+	0.941088i	$0.609805\pi$
$492$		0			0
$493$	15.9026	+	11.4402i	0.716217	+	0.515242i
$494$	9.37326			0.421723
$495$		0			0
$496$	4.05876	+	9.79871i	0.182244	+	0.439975i
$497$		−	11.4022i		−	0.511458i
$498$		0			0
$499$	−2.48005	+	5.98738i	−0.111022	+	0.268032i	−0.969619	−	0.244620i	$-0.921337\pi$
$499$	−2.48005	+	5.98738i	−0.111022	+	0.268032i	0.858597	+	0.512652i	$0.171337\pi$
$500$	18.9674	+	7.85654i	0.848247	+	0.351355i
$501$		0			0
$502$	9.11627	−	9.11627i	0.406879	−	0.406879i
$503$	15.3938	+	6.37634i	0.686378	+	0.284307i	0.698490	−	0.715620i	$-0.253856\pi$
$503$	15.3938	+	6.37634i	0.686378	+	0.284307i	−0.0121125	+	0.999927i	$0.503856\pi$
$504$		0			0
$505$	20.0870	−	8.32030i	0.893859	−	0.370248i
$506$		−	2.82717i		−	0.125683i
$507$		0			0
$508$	11.5423	+	11.5423i	0.512105	+	0.512105i
$509$	19.1265			0.847767			0.423884	−	0.905717i	$-0.360667\pi$
$509$	19.1265			0.847767			0.423884	+	0.905717i	$0.360667\pi$
$510$		0			0
$511$	−31.6920			−1.40197
$512$	−15.4327	−	15.4327i	−0.682037	−	0.682037i
$513$		0			0
$514$			14.2627i			0.629101i
$515$	24.6478	−	10.2095i	1.08611	−	0.449882i
$516$		0			0
$517$	−23.5738	−	9.76460i	−1.03678	−	0.429447i
$518$	−4.46862	+	4.46862i	−0.196340	+	0.196340i
$519$		0			0
$520$	11.5448	+	4.78200i	0.506271	+	0.209704i
$521$	−5.50543	+	13.2913i	−0.241197	+	0.582302i	−0.997402	−	0.0720330i	$-0.977051\pi$
$521$	−5.50543	+	13.2913i	−0.241197	+	0.582302i	0.756205	+	0.654335i	$0.227051\pi$
$522$		0			0
$523$			6.11004i			0.267173i	0.991037	+	0.133587i	$0.0426495\pi$
$523$			6.11004i			0.267173i	−0.991037	+	0.133587i	$0.957351\pi$
$524$	−9.79729	−	23.6527i	−0.427997	−	1.03328i
$525$		0			0
$526$	1.24944			0.0544781
$527$	10.7568	−	14.9525i	0.468571	−	0.651342i
$528$		0			0
$529$	12.9066	+	12.9066i	0.561156	+	0.561156i
$530$	−1.16759	−	2.81881i	−0.0507169	−	0.122441i
$531$		0			0
$532$	22.5079	−	9.32308i	0.975842	−	0.404207i
$533$	−11.2471	+	27.1530i	−0.487168	+	1.17613i
$534$		0			0
$535$	11.7012	−	11.7012i	0.505887	−	0.505887i
$536$	−5.84142	+	5.84142i	−0.252311	+	0.252311i
$537$		0			0
$538$	−3.51517	+	8.48636i	−0.151550	+	0.365873i
$539$	−1.36982	+	0.567398i	−0.0590023	+	0.0244395i
$540$		0			0
$541$	−10.9678	−	26.4785i	−0.471541	−	1.13840i	−0.963482	−	0.267773i	$-0.913712\pi$
$541$	−10.9678	−	26.4785i	−0.471541	−	1.13840i	0.491941	−	0.870629i	$-0.336288\pi$
$542$	9.35911	+	9.35911i	0.402008	+	0.402008i
$543$		0			0
$544$	−4.93518	+	20.9901i	−0.211594	+	0.899945i
$545$	0.461144			0.0197532
$546$		0			0
$547$	−6.49532	−	15.6811i	−0.277720	−	0.670475i	0.722052	−	0.691839i	$-0.243199\pi$
$547$	−6.49532	−	15.6811i	−0.277720	−	0.670475i	−0.999772	+	0.0213641i	$0.993199\pi$
$548$			24.2968i			1.03791i
$549$		0			0
$550$	0.465376	−	1.12352i	0.0198437	−	0.0479069i
$551$	−24.6593	−	10.2142i	−1.05052	−	0.435140i
$552$		0			0
$553$	8.09109	−	8.09109i	0.344068	−	0.344068i
$554$	9.11980	+	3.77754i	0.387463	+	0.160492i
$555$		0			0
$556$	−24.4160	+	10.1135i	−1.03547	+	0.428906i
$557$			11.2465i			0.476530i	0.971200	+	0.238265i	$0.0765787\pi$
$557$			11.2465i			0.476530i	−0.971200	+	0.238265i	$0.923421\pi$
$558$		0			0
$559$	−21.4664	−	21.4664i	−0.907932	−	0.907932i
$560$	12.0970			0.511190
$561$		0			0
$562$	9.20724			0.388384
$563$	−0.954391	−	0.954391i	−0.0402228	−	0.0402228i	0.686709	−	0.726932i	$-0.259055\pi$
$563$	−0.954391	−	0.954391i	−0.0402228	−	0.0402228i	−0.726932	+	0.686709i	$0.759055\pi$
$564$		0			0
$565$		−	24.2130i		−	1.01865i
$566$	−10.2056	+	4.22731i	−0.428975	+	0.177687i
$567$		0			0
$568$	−8.25802	−	3.42059i	−0.346499	−	0.143525i
$569$	0.349944	−	0.349944i	0.0146704	−	0.0146704i	−0.699734	−	0.714404i	$-0.746698\pi$
$569$	0.349944	−	0.349944i	0.0146704	−	0.0146704i	0.714404	+	0.699734i	$0.246698\pi$
$570$		0			0
$571$	−23.0580	−	9.55093i	−0.964946	−	0.399694i	−0.156118	−	0.987738i	$-0.549898\pi$
$571$	−23.0580	−	9.55093i	−0.964946	−	0.399694i	−0.808828	+	0.588045i	$0.799898\pi$
$572$	−4.99641	+	12.0624i	−0.208910	+	0.504354i
$573$		0			0
$574$		−	12.6671i		−	0.528715i
$575$	−0.781452	−	1.88659i	−0.0325888	−	0.0786763i
$576$		0			0
$577$	23.0850			0.961043			0.480521	−	0.876983i	$-0.340447\pi$
$577$	23.0850			0.961043			0.480521	+	0.876983i	$0.340447\pi$
$578$	8.59667	−	2.88275i	0.357575	−	0.119907i
$579$		0			0
$580$	−11.6173	−	11.6173i	−0.482383	−	0.482383i
$581$	−10.4726	−	25.2831i	−0.434477	−	1.04892i
$582$		0			0
$583$	6.37878	−	2.64218i	0.264182	−	0.109428i
$584$	−9.50742	+	22.9529i	−0.393420	+	0.949799i
$585$		0			0
$586$	−8.99112	+	8.99112i	−0.371420	+	0.371420i
$587$	14.8242	−	14.8242i	0.611862	−	0.611862i	−0.331569	−	0.943431i	$-0.607578\pi$
$587$	14.8242	−	14.8242i	0.611862	−	0.611862i	0.943431	+	0.331569i	$0.107578\pi$
$588$		0			0
$589$	−9.60399	+	23.1861i	−0.395725	+	0.955366i
$590$	3.48097	−	1.44186i	0.143309	−	0.0593606i
$591$		0			0
$592$	−4.25827	−	10.2804i	−0.175014	−	0.422521i
$593$	19.4560	+	19.4560i	0.798962	+	0.798962i	0.982932	−	0.183970i	$-0.0588950\pi$
$593$	19.4560	+	19.4560i	0.798962	+	0.798962i	−0.183970	+	0.982932i	$0.558895\pi$
$594$		0			0
$595$	−11.0612	−	17.8614i	−0.453463	−	0.732245i
$596$	11.3601			0.465327
$597$		0			0
$598$	−1.39124	−	3.35875i	−0.0568920	−	0.137350i
$599$			43.8786i			1.79283i	0.443215	+	0.896415i	$0.353838\pi$
$599$			43.8786i			1.79283i	−0.443215	+	0.896415i	$0.646162\pi$
$600$		0			0
$601$	16.5992	−	40.0741i	0.677097	−	1.63466i	−0.0921808	−	0.995742i	$-0.529384\pi$
$601$	16.5992	−	40.0741i	0.677097	−	1.63466i	0.769278	−	0.638914i	$-0.220616\pi$
$602$	12.0883	+	5.00713i	0.492681	+	0.204075i
$603$		0			0
$604$	−20.6865	+	20.6865i	−0.841720	+	0.841720i
$605$	9.46283	+	3.91963i	0.384719	+	0.159356i
$606$		0			0
$607$	−19.4229	+	8.04524i	−0.788352	+	0.326546i	−0.740281	−	0.672298i	$-0.765308\pi$
$607$	−19.4229	+	8.04524i	−0.788352	+	0.326546i	−0.0480715	+	0.998844i	$0.515308\pi$
$608$		−	29.3784i		−	1.19145i
$609$		0			0
$610$	−5.99751	−	5.99751i	−0.242832	−	0.242832i
$611$	−32.8114			−1.32741
$612$		0			0
$613$	30.5509			1.23394			0.616969	−	0.786987i	$-0.288360\pi$
$613$	30.5509			1.23394			0.616969	+	0.786987i	$0.288360\pi$
$614$	−5.26978	−	5.26978i	−0.212671	−	0.212671i
$615$		0			0
$616$		−	12.1875i		−	0.491050i
$617$	7.46839	−	3.09351i	0.300666	−	0.124540i	−0.227250	−	0.973836i	$-0.572974\pi$
$617$	7.46839	−	3.09351i	0.300666	−	0.124540i	0.527916	+	0.849296i	$0.322974\pi$
$618$		0			0
$619$	−6.78527	−	2.81055i	−0.272723	−	0.112966i	0.242131	−	0.970244i	$-0.422154\pi$
$619$	−6.78527	−	2.81055i	−0.272723	−	0.112966i	−0.514854	+	0.857278i	$0.672154\pi$
$620$	−10.9233	+	10.9233i	−0.438689	+	0.438689i
$621$		0			0
$622$	−4.80672	−	1.99101i	−0.192732	−	0.0798322i
$623$	15.6925	−	37.8852i	0.628709	−	1.51784i
$624$		0			0
$625$			19.4356i			0.777423i
$626$	−6.78488	−	16.3801i	−0.271178	−	0.654682i
$627$		0			0
$628$	24.9957			0.997438
$629$	−11.2855	+	15.6875i	−0.449982	+	0.625502i
$630$		0			0
$631$	−30.5755	−	30.5755i	−1.21719	−	1.21719i	−0.968612	−	0.248578i	$-0.920037\pi$
$631$	−30.5755	−	30.5755i	−1.21719	−	1.21719i	−0.248578	−	0.968612i	$-0.579963\pi$
$632$	−3.43269	−	8.28725i	−0.136545	−	0.329649i
$633$		0			0
$634$	−3.61756	+	1.49844i	−0.143672	+	0.0595107i
$635$	−7.33940	+	17.7189i	−0.291255	+	0.703152i
$636$		0			0
$637$	−1.34817	+	1.34817i	−0.0534163	+	0.0534163i
$638$	−4.35937	+	4.35937i	−0.172589	+	0.172589i
$639$		0			0
$640$	8.87372	−	21.4231i	0.350764	−	0.846820i
$641$	8.72402	−	3.61361i	0.344578	−	0.142729i	−0.203681	−	0.979037i	$-0.565291\pi$
$641$	8.72402	−	3.61361i	0.344578	−	0.142729i	0.548259	+	0.836308i	$0.315291\pi$
$642$		0			0
$643$	0.132474	+	0.319820i	0.00522426	+	0.0126125i	0.926470	−	0.376368i	$-0.122827\pi$
$643$	0.132474	+	0.319820i	0.00522426	+	0.0126125i	−0.921246	+	0.388981i	$0.872827\pi$
$644$	−6.68154	−	6.68154i	−0.263289	−	0.263289i
$645$		0			0
$646$	−10.5029	+	6.50421i	−0.413231	+	0.255905i
$647$	−2.21802			−0.0871996			−0.0435998	−	0.999049i	$-0.513883\pi$
$647$	−2.21802			−0.0871996			−0.0435998	+	0.999049i	$0.513883\pi$
$648$		0			0
$649$	3.26284	+	7.87720i	0.128078	+	0.309207i
$650$		−	1.56378i		−	0.0613363i
$651$		0			0
$652$	−3.54221	+	8.55166i	−0.138724	+	0.334909i
$653$	3.52400	+	1.45969i	0.137905	+	0.0571221i	0.450569	−	0.892742i	$-0.351221\pi$
$653$	3.52400	+	1.45969i	0.137905	+	0.0571221i	−0.312664	+	0.949864i	$0.601221\pi$
$654$		0			0
$655$	21.2699	−	21.2699i	0.831085	−	0.831085i
$656$	20.6062	+	8.53537i	0.804537	+	0.333250i
$657$		0			0
$658$	13.0652	−	5.41177i	0.509334	−	0.210973i
$659$		−	29.3352i		−	1.14274i	−0.820694	−	0.571368i	$-0.806413\pi$
$659$		−	29.3352i		−	1.14274i	0.820694	−	0.571368i	$-0.193587\pi$
$660$		0			0
$661$	−4.47539	−	4.47539i	−0.174072	−	0.174072i	0.614694	−	0.788766i	$-0.289280\pi$
$661$	−4.47539	−	4.47539i	−0.174072	−	0.174072i	−0.788766	+	0.614694i	$0.789280\pi$
$662$	−1.09455			−0.0425410
$663$		0			0
$664$	−21.4530			−0.832538
$665$	20.2404	+	20.2404i	0.784890	+	0.784890i
$666$		0			0
$667$			10.3523i			0.400843i
$668$	19.7444	−	8.17841i	0.763935	−	0.316432i
$669$		0			0
$670$	−4.14038	−	1.71500i	−0.159957	−	0.0662563i
$671$	13.5719	−	13.5719i	0.523939	−	0.523939i
$672$		0			0
$673$	25.5794	+	10.5953i	0.986013	+	0.408420i	0.816650	−	0.577133i	$-0.195829\pi$
$673$	25.5794	+	10.5953i	0.986013	+	0.408420i	0.169364	+	0.985554i	$0.445829\pi$
$674$	1.24499	−	3.00568i	0.0479553	−	0.115774i
$675$		0			0
$676$		−	5.51269i		−	0.212026i
$677$	14.8623	+	35.8807i	0.571204	+	1.37901i	0.900531	+	0.434792i	$0.143178\pi$
$677$	14.8623	+	35.8807i	0.571204	+	1.37901i	−0.329327	+	0.944216i	$0.606822\pi$
$678$		0			0
$679$	2.02953			0.0778864
$680$	−16.2544	+	2.65273i	−0.623327	+	0.101727i
$681$		0			0
$682$	4.09892	+	4.09892i	0.156956	+	0.156956i
$683$	−1.43187	−	3.45684i	−0.0547889	−	0.132272i	0.894115	−	0.447838i	$-0.147806\pi$
$683$	−1.43187	−	3.45684i	−0.0547889	−	0.132272i	−0.948904	+	0.315566i	$0.897806\pi$
$684$		0			0
$685$	−26.3742	+	10.9246i	−1.00771	+	0.417406i
$686$	3.92630	−	9.47893i	0.149907	−	0.361907i
$687$		0			0
$688$	−16.2907	+	16.2907i	−0.621076	+	0.621076i
$689$	6.27795	−	6.27795i	0.239171	−	0.239171i
$690$		0			0
$691$	−13.0015	+	31.3884i	−0.494600	+	1.19407i	0.457755	+	0.889078i	$0.348654\pi$
$691$	−13.0015	+	31.3884i	−0.494600	+	1.19407i	−0.952355	+	0.304992i	$0.901346\pi$
$692$	−4.23779	+	1.75535i	−0.161097	+	0.0667284i
$693$		0			0
$694$	7.02432	+	16.9582i	0.266640	+	0.643725i
$695$	−21.9563	−	21.9563i	−0.832851	−	0.832851i
$696$		0			0
$697$	−6.23916	−	38.2299i	−0.236325	−	1.44806i
$698$	−9.29618			−0.351866
$699$		0			0
$700$	−1.55540	−	3.75508i	−0.0587887	−	0.141929i
$701$		−	19.8395i		−	0.749327i	−0.927161	−	0.374663i	$-0.877758\pi$
$701$		−	19.8395i		−	0.749327i	0.927161	−	0.374663i	$-0.122242\pi$
$702$		0			0
$703$	10.0761	−	24.3258i	0.380026	−	0.917465i
$704$	4.40273	+	1.82367i	0.165934	+	0.0687322i
$705$		0			0
$706$	13.5729	−	13.5729i	0.510821	−	0.510821i
$707$	−25.1925	−	10.4351i	−0.947462	−	0.392452i
$708$		0			0
$709$	−45.1577	+	18.7049i	−1.69593	+	0.702479i	−0.999880	−	0.0155099i	$-0.995063\pi$
$709$	−45.1577	+	18.7049i	−1.69593	+	0.702479i	−0.696055	+	0.717989i	$0.745063\pi$
$710$		−	4.84901i		−	0.181980i
$711$		0			0
$712$	−22.7306	−	22.7306i	−0.851867	−	0.851867i
$713$	9.73382			0.364535
$714$		0			0
$715$	−15.3403			−0.573694
$716$	−16.9931	−	16.9931i	−0.635060	−	0.635060i
$717$		0			0
$718$		−	9.98736i		−	0.372725i
$719$	−4.30491	+	1.78315i	−0.160546	+	0.0665003i	−0.461509	−	0.887135i	$-0.652692\pi$
$719$	−4.30491	+	1.78315i	−0.160546	+	0.0665003i	0.300963	+	0.953636i	$0.402692\pi$
$720$		0			0
$721$	−30.9126	−	12.8044i	−1.15124	−	0.476861i
$722$	4.73611	−	4.73611i	0.176260	−	0.176260i
$723$		0			0
$724$	−21.1801	−	8.77309i	−0.787153	−	0.326049i
$725$	−1.70407	+	4.11400i	−0.0632878	+	0.152790i
$726$		0			0
$727$		−	34.8089i		−	1.29099i	−0.763765	−	0.645495i	$-0.776651\pi$
$727$		−	34.8089i		−	1.29099i	0.763765	−	0.645495i	$-0.223349\pi$
$728$	−5.99744	−	14.4791i	−0.222280	−	0.536631i
$729$		0			0
$730$	−13.4777			−0.498831
$731$	38.9493	+	9.15770i	1.44059	+	0.338710i
$732$		0			0
$733$	14.2982	+	14.2982i	0.528115	+	0.528115i	0.920010	−	0.391895i	$-0.128180\pi$
$733$	14.2982	+	14.2982i	0.528115	+	0.528115i	−0.391895	+	0.920010i	$0.628180\pi$
$734$	4.95478	+	11.9619i	0.182884	+	0.441521i
$735$		0			0
$736$	−10.5273	+	4.36053i	−0.388040	+	0.160731i
$737$	3.88094	−	9.36941i	0.142956	−	0.345127i
$738$		0			0
$739$	−14.6769	+	14.6769i	−0.539900	+	0.539900i	−0.923499	−	0.383600i	$-0.874684\pi$
$739$	−14.6769	+	14.6769i	−0.539900	+	0.539900i	0.383600	+	0.923499i	$0.374684\pi$
$740$	11.4602	−	11.4602i	0.421286	−	0.421286i
$741$		0			0
$742$	−1.46436	+	3.53527i	−0.0537583	+	0.129784i
$743$	−12.9540	+	5.36572i	−0.475236	+	0.196849i	−0.607428	−	0.794375i	$-0.707798\pi$
$743$	−12.9540	+	5.36572i	−0.475236	+	0.196849i	0.132192	+	0.991224i	$0.457798\pi$
$744$		0			0
$745$	5.10782	+	12.3314i	0.187136	+	0.451786i
$746$	0.575950	+	0.575950i	0.0210870	+	0.0210870i
$747$		0			0
$748$	−2.77167	−	16.9832i	−0.101342	−	0.620966i
$749$	−20.7540			−0.758335
$750$		0			0
$751$	12.9100	+	31.1675i	0.471092	+	1.13732i	0.963681	+	0.267055i	$0.0860507\pi$
$751$	12.9100	+	31.1675i	0.471092	+	1.13732i	−0.492589	+	0.870262i	$0.663949\pi$
$752$			24.9003i			0.908022i
$753$		0			0
$754$	−3.03381	+	7.32427i	−0.110485	+	0.266734i
$755$	−31.7564	−	13.1539i	−1.15573	−	0.478721i
$756$		0			0
$757$	−26.2964	+	26.2964i	−0.955760	+	0.955760i	−0.999062	−	0.0433020i	$-0.986212\pi$
$757$	−26.2964	+	26.2964i	−0.955760	+	0.955760i	0.0433020	+	0.999062i	$0.486212\pi$
$758$	2.85063	+	1.18077i	0.103540	+	0.0428875i
$759$		0			0
$760$	20.7311	−	8.58711i	0.751997	−	0.311487i
$761$		−	10.1020i		−	0.366198i	−0.983094	−	0.183099i	$-0.941387\pi$
$761$		−	10.1020i		−	0.366198i	0.983094	−	0.183099i	$-0.0586130\pi$
$762$		0			0
$763$	−0.408957	−	0.408957i	−0.0148052	−	0.0148052i
$764$	36.0231			1.30327
$765$		0			0
$766$	14.8907			0.538023
$767$	7.75268	+	7.75268i	0.279933	+	0.279933i
$768$		0			0
$769$		−	51.1798i		−	1.84559i	−0.385288	−	0.922796i	$-0.625898\pi$
$769$		−	51.1798i		−	1.84559i	0.385288	−	0.922796i	$-0.374102\pi$
$770$	6.10834	−	2.53016i	0.220129	−	0.0911805i
$771$		0			0
$772$	−8.10445	−	3.35697i	−0.291685	−	0.120820i
$773$	−14.9138	+	14.9138i	−0.536414	+	0.536414i	−0.922474	−	0.386060i	$-0.873836\pi$
$773$	−14.9138	+	14.9138i	−0.536414	+	0.536414i	0.386060	+	0.922474i	$0.373836\pi$
$774$		0			0
$775$	3.86822	+	1.60227i	0.138951	+	0.0575552i
$776$	0.608848	−	1.46989i	0.0218564	−	0.0527660i
$777$		0			0
$778$		−	3.09125i		−	0.110827i
$779$	20.1967	+	48.7591i	0.723622	+	1.74698i
$780$		0			0
$781$	10.9730			0.392644
$782$	3.88958	+	2.79814i	0.139091	+	0.100061i
$783$		0			0
$784$	1.02311	+	1.02311i	0.0365397	+	0.0365397i
$785$	11.2388	+	27.1329i	0.401130	+	0.968414i
$786$		0			0
$787$	16.4775	−	6.82521i	0.587360	−	0.243292i	−0.0691547	−	0.997606i	$-0.522030\pi$
$787$	16.4775	−	6.82521i	0.587360	−	0.243292i	0.656514	+	0.754314i	$0.272030\pi$
$788$	2.52079	−	6.08571i	0.0897993	−	0.216795i
$789$		0			0
$790$	3.44090	−	3.44090i	0.122422	−	0.122422i
$791$	−21.4729	+	21.4729i	−0.763487	+	0.763487i
$792$		0			0
$793$	9.44512	−	22.8025i	0.335406	−	0.809742i
$794$	12.6437	−	5.23718i	0.448707	−	0.185861i
$795$		0			0
$796$	−4.74472	−	11.4548i	−0.168172	−	0.406003i
$797$	13.3379	+	13.3379i	0.472453	+	0.472453i	0.902708	−	0.430254i	$-0.141576\pi$
$797$	13.3379	+	13.3379i	0.472453	+	0.472453i	−0.430254	+	0.902708i	$0.641576\pi$
$798$		0			0
$799$	36.7658	−	22.7682i	1.30068	−	0.805482i
$800$	−4.90131			−0.173288
$801$		0			0
$802$	0.397182	+	0.958883i	0.0140250	+	0.0338593i
$803$		−	30.4990i		−	1.07629i
$804$		0			0
$805$	4.24860	−	10.2570i	0.149743	−	0.361513i
$806$	6.88669	+	2.85256i	0.242573	+	0.100477i
$807$		0			0
$808$	−15.1152	+	15.1152i	−0.531751	+	0.531751i
$809$	−2.90215	−	1.20211i	−0.102034	−	0.0422639i	0.331082	−	0.943602i	$-0.392586\pi$
$809$	−2.90215	−	1.20211i	−0.102034	−	0.0422639i	−0.433117	+	0.901338i	$0.642586\pi$
$810$		0			0
$811$	43.8806	−	18.1759i	1.54086	−	0.638244i	0.559222	−	0.829018i	$-0.311100\pi$
$811$	43.8806	−	18.1759i	1.54086	−	0.638244i	0.981634	+	0.190774i	$0.0610998\pi$
$812$			20.6052i			0.723102i
$813$		0			0
$814$	−4.30041	−	4.30041i	−0.150729	−	0.150729i
$815$	−10.8755			−0.380953
$816$		0			0
$817$	−54.5145			−1.90722
$818$	−3.66586	−	3.66586i	−0.128174	−	0.128174i
$819$		0			0
$820$			32.4860i			1.13446i
$821$	−13.5930	+	5.63041i	−0.474400	+	0.196503i	−0.607056	−	0.794659i	$-0.707649\pi$
$821$	−13.5930	+	5.63041i	−0.474400	+	0.196503i	0.132656	+	0.991162i	$0.457649\pi$
$822$		0			0
$823$	26.2173	+	10.8596i	0.913877	+	0.378540i	0.789539	−	0.613700i	$-0.210319\pi$
$823$	26.2173	+	10.8596i	0.913877	+	0.378540i	0.124337	+	0.992240i	$0.460319\pi$
$824$	−18.5472	+	18.5472i	−0.646121	+	0.646121i
$825$		0			0
$826$	−4.36573	−	1.80834i	−0.151903	−	0.0629204i
$827$	−6.46551	+	15.6091i	−0.224828	+	0.542783i	−0.995534	−	0.0944088i	$-0.969904\pi$
$827$	−6.46551	+	15.6091i	−0.224828	+	0.542783i	0.770706	+	0.637191i	$0.219904\pi$
$828$		0			0
$829$		−	3.03136i		−	0.105283i	−0.998613	−	0.0526417i	$-0.983236\pi$
$829$		−	3.03136i		−	0.105283i	0.998613	−	0.0526417i	$-0.0167641\pi$
$830$	−4.45369	−	10.7522i	−0.154590	−	0.373213i
$831$		0			0
$832$	6.12798			0.212450
$833$	0.575136	−	2.44615i	0.0199273	−	0.0847541i
$834$		0			0
$835$	17.7553	+	17.7553i	0.614449	+	0.614449i
$836$	8.97213	+	21.6606i	0.310308	+	0.749149i
$837$		0			0
$838$	2.42881	−	1.00604i	0.0839018	−	0.0347532i
$839$	14.3458	−	34.6339i	0.495273	−	1.19570i	−0.456730	−	0.889606i	$-0.650979\pi$
$839$	14.3458	−	34.6339i	0.495273	−	1.19570i	0.952003	−	0.306090i	$-0.0990207\pi$
$840$		0			0
$841$	−4.54332	+	4.54332i	−0.156666	+	0.156666i
$842$	12.7613	−	12.7613i	0.439785	−	0.439785i
$843$		0			0
$844$	−8.24539	+	19.9061i	−0.283818	+	0.685197i
$845$	5.98403	−	2.47866i	0.205857	−	0.0852687i
$846$		0			0
$847$	−4.91589	−	11.8680i	−0.168912	−	0.407790i
$848$	−4.76429	−	4.76429i	−0.163606	−	0.163606i
$849$		0			0
$850$	1.08512	+	1.75224i	0.0372194	+	0.0601013i
$851$	−10.2123			−0.350073
$852$		0			0
$853$	−12.1626	−	29.3630i	−0.416438	−	1.00537i	−0.983371	−	0.181607i	$-0.941870\pi$
$853$	−12.1626	−	29.3630i	−0.416438	−	1.00537i	0.566933	−	0.823764i	$-0.308130\pi$
$854$			10.6376i			0.364010i
$855$		0			0
$856$	−6.22608	+	15.0311i	−0.212803	+	0.513752i
$857$	−20.8905	−	8.65313i	−0.713606	−	0.295585i	−0.00381018	−	0.999993i	$-0.501213\pi$
$857$	−20.8905	−	8.65313i	−0.713606	−	0.295585i	−0.709796	+	0.704407i	$0.751213\pi$
$858$		0			0
$859$	−26.1263	+	26.1263i	−0.891417	+	0.891417i	−0.994657	−	0.103239i	$-0.967079\pi$
$859$	−26.1263	+	26.1263i	−0.891417	+	0.891417i	0.103239	+	0.994657i	$0.467079\pi$
$860$	−31.0016	−	12.8413i	−1.05714	−	0.437883i
$861$		0			0
$862$	−7.38853	+	3.06043i	−0.251654	+	0.104239i
$863$			32.8262i			1.11742i	0.829364	+	0.558709i	$0.188703\pi$
$863$			32.8262i			1.11742i	−0.829364	+	0.558709i	$0.811297\pi$
$864$		0			0
$865$	−3.81087	−	3.81087i	−0.129573	−	0.129573i
$866$	−0.304445			−0.0103455
$867$		0			0
$868$	19.3742			0.657604
$869$	7.78652	+	7.78652i	0.264140	+	0.264140i
$870$		0			0
$871$		−	13.0409i		−	0.441874i
$872$	−0.418872	+	0.173502i	−0.0141848	+	0.00587553i
$873$		0			0
$874$	−6.03137	−	2.49827i	−0.204014	−	0.0845054i
$875$	21.3919	−	21.3919i	0.723177	−	0.723177i
$876$		0			0
$877$	23.3398	+	9.66766i	0.788129	+	0.326454i	0.740191	−	0.672397i	$-0.234735\pi$
$877$	23.3398	+	9.66766i	0.788129	+	0.326454i	0.0479379	+	0.998850i	$0.484735\pi$
$878$	5.19256	−	12.5359i	0.175240	−	0.423067i
$879$		0			0
$880$			11.6416i			0.392438i
$881$	4.38254	+	10.5804i	0.147651	+	0.356462i	0.980350	−	0.197264i	$-0.0632056\pi$
$881$	4.38254	+	10.5804i	0.147651	+	0.356462i	−0.832699	+	0.553726i	$0.813206\pi$
$882$		0			0
$883$	37.1590			1.25050			0.625251	−	0.780424i	$-0.284997\pi$
$883$	37.1590			1.25050			0.625251	+	0.780424i	$0.284997\pi$
$884$	−11.6502	−	18.8125i	−0.391838	−	0.632734i
$885$		0			0
$886$	0.479704	+	0.479704i	0.0161160	+	0.0161160i
$887$	7.86263	+	18.9821i	0.264001	+	0.637355i	0.999179	−	0.0405193i	$-0.0129012\pi$
$887$	7.86263	+	18.9821i	0.264001	+	0.637355i	−0.735178	+	0.677875i	$0.762901\pi$
$888$		0			0
$889$	22.2225	−	9.20486i	0.745318	−	0.308721i
$890$	6.67357	−	16.1114i	0.223699	−	0.540056i
$891$		0			0
$892$	−5.81902	+	5.81902i	−0.194835	+	0.194835i
$893$	−41.6628	+	41.6628i	−1.39419	+	1.39419i
$894$		0			0
$895$	10.8054	−	26.0866i	0.361185	−	0.871977i
$896$	−26.8682	+	11.1292i	−0.897603	+	0.371799i
$897$		0			0
$898$	6.27932	+	15.1596i	0.209544	+	0.505883i
$899$	−15.0091	−	15.0091i	−0.500582	−	0.500582i
$900$		0			0
$901$	−2.67821	+	11.3909i	−0.0892242	+	0.379486i
$902$	12.1903			0.405892
$903$		0			0
$904$	9.10998	+	21.9934i	0.302993	+	0.731491i
$905$		−	26.9357i		−	0.895372i
$906$		0			0
$907$	−12.6275	+	30.4854i	−0.419288	+	1.01225i	0.563266	+	0.826276i	$0.309545\pi$
$907$	−12.6275	+	30.4854i	−0.419288	+	1.01225i	−0.982554	+	0.185976i	$0.940455\pi$
$908$	35.6205	+	14.7545i	1.18211	+	0.489646i
$909$		0			0
$910$	6.01178	−	6.01178i	0.199289	−	0.199289i
$911$	−6.12703	−	2.53790i	−0.202998	−	0.0840843i	0.278868	−	0.960329i	$-0.410041\pi$
$911$	−6.12703	−	2.53790i	−0.202998	−	0.0840843i	−0.481866	+	0.876245i	$0.660041\pi$
$912$		0			0
$913$	24.3314	−	10.0784i	0.805252	−	0.333546i
$914$		−	12.5305i		−	0.414473i
$915$		0			0
$916$	2.77744	+	2.77744i	0.0917692	+	0.0917692i
$917$	−37.7257			−1.24581
$918$		0			0
$919$	58.7318			1.93738			0.968692	−	0.248265i	$-0.0798604\pi$
$919$	58.7318			1.93738			0.968692	+	0.248265i	$0.0798604\pi$
$920$	−6.15409	−	6.15409i	−0.202894	−	0.202894i
$921$		0			0
$922$			4.54377i			0.149641i
$923$	13.0362	−	5.39976i	0.429091	−	0.177735i
$924$		0			0
$925$	−4.05836	−	1.68103i	−0.133438	−	0.0552719i
$926$	6.66370	−	6.66370i	0.218983	−	0.218983i
$927$		0			0
$928$	22.9563	+	9.50881i	0.753577	+	0.312142i
$929$	19.0522	−	45.9962i	0.625083	−	1.50908i	−0.220580	−	0.975369i	$-0.570795\pi$
$929$	19.0522	−	45.9962i	0.625083	−	1.50908i	0.845664	−	0.533716i	$-0.179205\pi$
$930$		0			0
$931$			3.42371i			0.112207i
$932$	−16.4041	−	39.6029i	−0.537333	−	1.29724i
$933$		0			0
$934$	3.34806			0.109552
$935$	17.1890	−	10.6448i	0.562141	−	0.348122i
$936$		0			0
$937$	15.9963	+	15.9963i	0.522577	+	0.522577i	0.918349	−	0.395772i	$-0.129523\pi$
$937$	15.9963	+	15.9963i	0.522577	+	0.522577i	−0.395772	+	0.918349i	$0.629523\pi$
$938$	2.15091	+	5.19275i	0.0702296	+	0.169549i
$939$		0			0
$940$	−33.5069	+	13.8790i	−1.09287	+	0.452684i
$941$	12.9985	−	31.3812i	0.423739	−	1.02300i	−0.557496	−	0.830180i	$-0.688238\pi$
$941$	12.9985	−	31.3812i	0.423739	−	1.02300i	0.981235	−	0.192817i	$-0.0617623\pi$
$942$		0			0
$943$	14.4743	−	14.4743i	0.471348	−	0.471348i
$944$	5.88344	−	5.88344i	0.191490	−	0.191490i
$945$		0			0
$946$	−4.81865	+	11.6332i	−0.156668	+	0.378229i
$947$	10.7473	−	4.45169i	0.349241	−	0.144661i	−0.201165	−	0.979557i	$-0.564473\pi$
$947$	10.7473	−	4.45169i	0.349241	−	0.144661i	0.550406	+	0.834897i	$0.314473\pi$
$948$		0			0
$949$	−15.0085	−	36.2337i	−0.487196	−	1.17619i
$950$	−1.98563	−	1.98563i	−0.0644222	−	0.0644222i
$951$		0			0
$952$	16.7674	+	12.0624i	0.543436	+	0.390944i
$953$	−57.8467			−1.87384			−0.936919	−	0.349547i	$-0.886336\pi$
$953$	−57.8467			−1.87384			−0.936919	+	0.349547i	$0.886336\pi$
$954$		0			0
$955$	16.1970	+	39.1031i	0.524123	+	1.26535i
$956$			28.9775i			0.937199i
$957$		0			0
$958$	−6.90693	+	16.6748i	−0.223153	+	0.538739i
$959$	33.0778	+	13.7013i	1.06814	+	0.442437i
$960$		0			0
$961$	7.80789	−	7.80789i	0.251867	−	0.251867i
$962$	−7.22521	−	2.99278i	−0.232950	−	0.0964911i
$963$		0			0
$964$	−47.5334	+	19.6890i	−1.53095	+	0.634140i
$965$		−	10.3068i		−	0.331787i
$966$		0			0
$967$	19.3170	+	19.3170i	0.621194	+	0.621194i	0.945837	−	0.324643i	$-0.105244\pi$
$967$	19.3170	+	19.3170i	0.621194	+	0.621194i	−0.324643	+	0.945837i	$0.605244\pi$
$968$	−10.0701			−0.323666
$969$		0			0
$970$	0.863100			0.0277125
$971$	−7.11574	−	7.11574i	−0.228355	−	0.228355i	0.583650	−	0.812005i	$-0.301624\pi$
$971$	−7.11574	−	7.11574i	−0.228355	−	0.228355i	−0.812005	+	0.583650i	$0.801624\pi$
$972$		0			0
$973$			38.9432i			1.24846i
$974$	−8.53940	+	3.53713i	−0.273620	+	0.113337i
$975$		0			0
$976$	−17.3047	−	7.16782i	−0.553908	−	0.229436i
$977$	−18.7855	+	18.7855i	−0.601002	+	0.601002i	−0.940579	−	0.339576i	$-0.889716\pi$
$977$	−18.7855	+	18.7855i	−0.601002	+	0.601002i	0.339576	+	0.940579i	$0.389716\pi$
$978$		0			0
$979$	36.4591	+	15.1018i	1.16524	+	0.482657i
$980$	−0.806477	+	1.94701i	−0.0257620	+	0.0621949i
$981$		0			0
$982$		−	10.0773i		−	0.321578i
$983$	11.6888	+	28.2193i	0.372815	+	0.900055i	0.993271	+	0.115814i	$0.0369476\pi$
$983$	11.6888	+	28.2193i	0.372815	+	0.900055i	−0.620456	+	0.784241i	$0.713052\pi$
$984$		0			0
$985$	7.73947			0.246600
$986$	−1.68295	−	10.3122i	−0.0535961	−	0.328406i
$987$		0			0
$988$	21.3183	+	21.3183i	0.678224	+	0.678224i
$989$	8.09140	+	19.5344i	0.257291	+	0.621157i
$990$		0			0
$991$	−1.91168	+	0.791842i	−0.0607264	+	0.0251537i	−0.412840	−	0.910804i	$-0.635463\pi$
$991$	−1.91168	+	0.791842i	−0.0607264	+	0.0251537i	0.352114	+	0.935957i	$0.385463\pi$
$992$	8.94073	−	21.5848i	0.283868	−	0.685319i
$993$		0			0
$994$	−4.30026	+	4.30026i	−0.136396	+	0.136396i
$995$	10.3008	−	10.3008i	0.326557	−	0.326557i
$996$		0			0
$997$	−11.3994	+	27.5205i	−0.361022	+	0.871583i	0.634130	+	0.773227i	$0.281358\pi$
$997$	−11.3994	+	27.5205i	−0.361022	+	0.871583i	−0.995151	+	0.0983564i	$0.968642\pi$
$998$	3.19344	−	1.32276i	0.101086	−	0.0418714i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	459.2.l.a.406.5	✓	48
3.2	odd	2	inner	459.2.l.a.406.8	yes	48
17.5	odd	16		7803.2.a.cg.1.15		24
17.8	even	8	inner	459.2.l.a.433.5	yes	48
17.12	odd	16		7803.2.a.cd.1.15		24
51.5	even	16		7803.2.a.cd.1.10		24
51.8	odd	8	inner	459.2.l.a.433.8	yes	48
51.29	even	16		7803.2.a.cg.1.10		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
459.2.l.a.406.5	✓	48	1.1	even	1	trivial
459.2.l.a.406.8	yes	48	3.2	odd	2	inner
459.2.l.a.433.5	yes	48	17.8	even	8	inner
459.2.l.a.433.8	yes	48	51.8	odd	8	inner
7803.2.a.cd.1.10		24	51.5	even	16
7803.2.a.cd.1.15		24	17.12	odd	16
7803.2.a.cg.1.10		24	51.29	even	16
7803.2.a.cg.1.15		24	17.5	odd	16

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 459 = 3^{3} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	459.l (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.377143 - 0.377143i) q^{2} -1.71553i q^{4} +(1.86220 - 0.771351i) q^{5} +(-2.33552 - 0.967406i) q^{7} +(-1.40129 + 1.40129i) q^{8} +(-0.993228 - 0.411408i) q^{10} +(0.930989 - 2.24761i) q^{11} -3.12835i q^{13} +(0.515977 + 1.24568i) q^{14} -2.37408 q^{16} +(2.17080 + 3.50537i) q^{17} +(-3.97227 - 3.97227i) q^{19} +(-1.32327 - 3.19466i) q^{20} +(-1.19879 + 0.496554i) q^{22} +(-0.833806 + 2.01298i) q^{23} +(-0.662708 + 0.662708i) q^{25} +(-1.17984 + 1.17984i) q^{26} +(-1.65961 + 4.00665i) q^{28} +(4.38962 - 1.81824i) q^{29} +(-1.70961 - 4.12737i) q^{31} +(3.69794 + 3.69794i) q^{32} +(0.503326 - 2.14073i) q^{34} -5.09543 q^{35} +(1.79365 + 4.33025i) q^{37} +2.99623i q^{38} +(-1.52860 + 3.69036i) q^{40} +(-8.67965 - 3.59523i) q^{41} +(6.86189 - 6.86189i) q^{43} +(-3.85583 - 1.59714i) q^{44} +(1.07365 - 0.444720i) q^{46} -10.4884i q^{47} +(-0.430951 - 0.430951i) q^{49} +0.499872 q^{50} -5.36677 q^{52} +(2.00679 + 2.00679i) q^{53} -4.90362i q^{55} +(4.62835 - 1.91712i) q^{56} +(-2.34125 - 0.969779i) q^{58} +(-2.47820 + 2.47820i) q^{59} +(7.28899 + 3.01920i) q^{61} +(-0.911842 + 2.20138i) q^{62} +1.95885i q^{64} +(-2.41306 - 5.82563i) q^{65} +4.16861 q^{67} +(6.01356 - 3.72406i) q^{68} +(1.92171 + 1.92171i) q^{70} +(1.72607 + 4.16711i) q^{71} +(11.5823 - 4.79756i) q^{73} +(0.956663 - 2.30959i) q^{74} +(-6.81453 + 6.81453i) q^{76} +(-4.34870 + 4.34870i) q^{77} +(-1.73218 + 4.18185i) q^{79} +(-4.42102 + 1.83125i) q^{80} +(1.91756 + 4.62939i) q^{82} +(7.65476 + 7.65476i) q^{83} +(6.74634 + 4.85328i) q^{85} -5.17583 q^{86} +(1.84496 + 4.45412i) q^{88} +16.2213i q^{89} +(-3.02639 + 7.30634i) q^{91} +(3.45333 + 1.43042i) q^{92} +(-3.95563 + 3.95563i) q^{94} +(-10.4612 - 4.33317i) q^{95} +(-0.741725 + 0.307233i) q^{97} +0.325061i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 16 q^{10} - 48 q^{16} - 16 q^{19} - 24 q^{22} + 16 q^{25} + 24 q^{28} - 40 q^{31} + 64 q^{34} + 48 q^{37} - 48 q^{40} - 8 q^{43} + 24 q^{46} - 16 q^{49} + 32 q^{52} + 64 q^{58} - 24 q^{61} - 32 q^{67}+ \cdots - 88 q^{97}+O(q^{100}) \) 48 * q - 16 * q^10 - 48 * q^16 - 16 * q^19 - 24 * q^22 + 16 * q^25 + 24 * q^28 - 40 * q^31 + 64 * q^34 + 48 * q^37 - 48 * q^40 - 8 * q^43 + 24 * q^46 - 16 * q^49 + 32 * q^52 + 64 * q^58 - 24 * q^61 - 32 * q^67 + 96 * q^70 + 48 * q^73 + 96 * q^76 - 48 * q^79 + 112 * q^82 - 56 * q^85 - 160 * q^88 - 80 * q^91 - 40 * q^94 - 88 * q^97

Introduction

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