LMFDB - Embedded newform 540.2.q.a.251.24

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [540,2,Mod(71,540)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(540, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([3, 5, 0])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("540.71"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 540 = 2^{2} \cdot 3^{3} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	540.q (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$4.31192170915$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 180)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			251.24
Character	$\chi$	$=$	540.251
Dual form			540.2.q.a.71.24

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.39556 + 0.228922i) q^{2} +(1.89519 + 0.638951i) q^{4} +(0.866025 - 0.500000i) q^{5} +(-1.04714 - 0.604565i) q^{7} +(2.49858 + 1.32555i) q^{8} +(1.32305 - 0.499529i) q^{10} +(1.52161 - 2.63550i) q^{11} +(2.53958 + 4.39869i) q^{13} +(-1.32295 - 1.08342i) q^{14} +(3.18348 + 2.42186i) q^{16} -2.23944i q^{17} +2.53835i q^{19} +(1.96076 - 0.394247i) q^{20} +(2.72682 - 3.32968i) q^{22} +(-3.48067 - 6.02870i) q^{23} +(0.500000 - 0.866025i) q^{25} +(2.53719 + 6.72001i) q^{26} +(-1.59824 - 1.81484i) q^{28} +(4.84407 + 2.79673i) q^{29} +(-2.83759 + 1.63828i) q^{31} +(3.88833 + 4.10863i) q^{32} +(0.512657 - 3.12527i) q^{34} -1.20913 q^{35} -10.3514 q^{37} +(-0.581085 + 3.54243i) q^{38} +(2.82661 - 0.101336i) q^{40} +(-3.70208 + 2.13740i) q^{41} +(3.74108 + 2.15991i) q^{43} +(4.56769 - 4.02254i) q^{44} +(-3.47739 - 9.21023i) q^{46} +(-5.15071 + 8.92129i) q^{47} +(-2.76900 - 4.79605i) q^{49} +(0.896034 - 1.09413i) q^{50} +(2.00245 + 9.95902i) q^{52} -9.42683i q^{53} -3.04322i q^{55} +(-1.81498 - 2.89859i) q^{56} +(6.11997 + 5.01192i) q^{58} +(-4.46335 - 7.73074i) q^{59} +(1.32896 - 2.30183i) q^{61} +(-4.33508 + 1.63674i) q^{62} +(4.48585 + 6.62398i) q^{64} +(4.39869 + 2.53958i) q^{65} +(-12.4858 + 7.20867i) q^{67} +(1.43089 - 4.24416i) q^{68} +(-1.68742 - 0.276797i) q^{70} +3.49303 q^{71} +5.10052 q^{73} +(-14.4461 - 2.36967i) q^{74} +(-1.62188 + 4.81065i) q^{76} +(-3.18667 + 1.83982i) q^{77} +(3.26472 + 1.88488i) q^{79} +(3.96791 + 0.505654i) q^{80} +(-5.65579 + 2.13538i) q^{82} +(-0.286172 + 0.495665i) q^{83} +(-1.11972 - 1.93941i) q^{85} +(4.72646 + 3.87071i) q^{86} +(7.29535 - 4.56806i) q^{88} -2.40129i q^{89} -6.14138i q^{91} +(-2.74449 - 13.6495i) q^{92} +(-9.23042 + 11.2711i) q^{94} +(1.26918 + 2.19828i) q^{95} +(5.82556 - 10.0902i) q^{97} +(-2.76639 - 7.32708i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 30 q^{14} + 24 q^{25} + 12 q^{29} - 6 q^{34} - 60 q^{38} - 6 q^{40} + 60 q^{41} - 12 q^{46} + 24 q^{49} - 18 q^{52} + 42 q^{56} - 18 q^{58} - 48 q^{64} - 48 q^{68} - 24 q^{73} - 84 q^{74} + 6 q^{76}+ \cdots - 12 q^{97}+O(q^{100}) $ 48 * q + 30 * q^14 + 24 * q^25 + 12 * q^29 - 6 * q^34 - 60 * q^38 - 6 * q^40 + 60 * q^41 - 12 * q^46 + 24 * q^49 - 18 * q^52 + 42 * q^56 - 18 * q^58 - 48 * q^64 - 48 * q^68 - 24 * q^73 - 84 * q^74 + 6 * q^76 - 48 * q^77 - 36 * q^82 + 54 * q^86 - 60 * q^92 + 18 * q^94 - 12 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/540\mathbb{Z}\right)^\times$.

$n$	$217$	$271$	$461$
$\chi(n)$	$1$	$-1$	$e\left(\frac{1}{6}\right)$

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 $

$2$	1.39556	+	0.228922i	0.986812	+	0.161872i
$2$	1.39556	+	0.228922i	0.986812	+	0.161872i
$3$		0			0
$3$		0			0
$4$	1.89519	+	0.638951i	0.947595	+	0.319475i
$5$	0.866025	−	0.500000i	0.387298	−	0.223607i
$5$	0.866025	−	0.500000i	0.387298	−	0.223607i
$6$		0			0
$7$	−1.04714	−	0.604565i	−0.395781	−	0.228504i	0.288881	−	0.957365i	$-0.406717\pi$
$7$	−1.04714	−	0.604565i	−0.395781	−	0.228504i	−0.684662	+	0.728861i	$0.740050\pi$
$8$	2.49858	+	1.32555i	0.883383	+	0.468651i
$9$		0			0
$10$	1.32305	−	0.499529i	0.418386	−	0.157965i
$11$	1.52161	−	2.63550i	0.458782	−	0.794634i	−0.540115	−	0.841591i	$-0.681619\pi$
$11$	1.52161	−	2.63550i	0.458782	−	0.794634i	0.998897	+	0.0469575i	$0.0149525\pi$
$12$		0			0
$13$	2.53958	+	4.39869i	0.704354	+	1.21998i	0.966924	+	0.255064i	$0.0820965\pi$
$13$	2.53958	+	4.39869i	0.704354	+	1.21998i	−0.262570	+	0.964913i	$0.584570\pi$
$14$	−1.32295	−	1.08342i	−0.353573	−	0.289557i
$15$		0			0
$16$	3.18348	+	2.42186i	0.795871	+	0.605466i
$17$		−	2.23944i		−	0.543143i	−0.962418	−	0.271572i	$-0.912457\pi$
$17$		−	2.23944i		−	0.543143i	0.962418	−	0.271572i	$-0.0875434\pi$
$18$		0			0
$19$			2.53835i			0.582337i	0.956672	+	0.291169i	$0.0940441\pi$
$19$			2.53835i			0.582337i	−0.956672	+	0.291169i	$0.905956\pi$
$20$	1.96076	−	0.394247i	0.438439	−	0.0881564i
$21$		0			0
$22$	2.72682	−	3.32968i	0.581361	−	0.709890i
$23$	−3.48067	−	6.02870i	−0.725770	−	1.25707i	−0.958656	−	0.284567i	$-0.908150\pi$
$23$	−3.48067	−	6.02870i	−0.725770	−	1.25707i	0.232886	−	0.972504i	$-0.425183\pi$
$24$		0			0
$25$	0.500000	−	0.866025i	0.100000	−	0.173205i
$26$	2.53719	+	6.72001i	0.497584	+	1.31790i
$27$		0			0
$28$	−1.59824	−	1.81484i	−0.302038	−	0.342972i
$29$	4.84407	+	2.79673i	0.899521	+	0.519339i	0.877045	−	0.480408i	$-0.159512\pi$
$29$	4.84407	+	2.79673i	0.899521	+	0.519339i	0.0224766	+	0.999747i	$0.492845\pi$
$30$		0			0
$31$	−2.83759	+	1.63828i	−0.509647	+	0.294245i	−0.732688	−	0.680564i	$-0.761735\pi$
$31$	−2.83759	+	1.63828i	−0.509647	+	0.294245i	0.223042	+	0.974809i	$0.428401\pi$
$32$	3.88833	+	4.10863i	0.687367	+	0.726311i
$33$		0			0
$34$	0.512657	−	3.12527i	0.0879199	−	0.535980i
$35$	−1.20913			−0.204380
$36$		0			0
$37$	−10.3514			−1.70176			−0.850882	−	0.525356i	$-0.823932\pi$
$37$	−10.3514			−1.70176			−0.850882	+	0.525356i	$0.823932\pi$
$38$	−0.581085	+	3.54243i	−0.0942644	+	0.574657i
$39$		0			0
$40$	2.82661	−	0.101336i	0.446926	−	0.0160226i
$41$	−3.70208	+	2.13740i	−0.578168	+	0.333806i	−0.760405	−	0.649449i	$-0.775000\pi$
$41$	−3.70208	+	2.13740i	−0.578168	+	0.333806i	0.182237	+	0.983255i	$0.441666\pi$
$42$		0			0
$43$	3.74108	+	2.15991i	0.570509	+	0.329384i	0.757353	−	0.653006i	$-0.226492\pi$
$43$	3.74108	+	2.15991i	0.570509	+	0.329384i	−0.186844	+	0.982390i	$0.559826\pi$
$44$	4.56769	−	4.02254i	0.688605	−	0.606421i
$45$		0			0
$46$	−3.47739	−	9.21023i	−0.512713	−	1.35797i
$47$	−5.15071	+	8.92129i	−0.751308	+	1.30130i	0.195880	+	0.980628i	$0.437244\pi$
$47$	−5.15071	+	8.92129i	−0.751308	+	1.30130i	−0.947189	+	0.320677i	$0.896090\pi$
$48$		0			0
$49$	−2.76900	−	4.79605i	−0.395572	−	0.685150i
$50$	0.896034	−	1.09413i	0.126718	−	0.154734i
$51$		0			0
$52$	2.00245	+	9.95902i	0.277690	+	1.38107i
$53$		−	9.42683i		−	1.29487i	−0.762119	−	0.647437i	$-0.775841\pi$
$53$		−	9.42683i		−	1.29487i	0.762119	−	0.647437i	$-0.224159\pi$
$54$		0			0
$55$		−	3.04322i		−	0.410347i
$56$	−1.81498	−	2.89859i	−0.242537	−	0.387340i
$57$		0			0
$58$	6.11997	+	5.01192i	0.803592	+	0.658098i
$59$	−4.46335	−	7.73074i	−0.581078	−	1.00646i	−0.995352	−	0.0963045i	$-0.969298\pi$
$59$	−4.46335	−	7.73074i	−0.581078	−	1.00646i	0.414274	−	0.910152i	$-0.364036\pi$
$60$		0			0
$61$	1.32896	−	2.30183i	0.170156	−	0.294720i	−0.768318	−	0.640068i	$-0.778906\pi$
$61$	1.32896	−	2.30183i	0.170156	−	0.294720i	0.938474	+	0.345349i	$0.112239\pi$
$62$	−4.33508	+	1.63674i	−0.550555	+	0.207866i
$63$		0			0
$64$	4.48585	+	6.62398i	0.560732	+	0.827998i
$65$	4.39869	+	2.53958i	0.545590	+	0.314997i
$66$		0			0
$67$	−12.4858	+	7.20867i	−1.52538	+	0.880679i	−0.525833	+	0.850588i	$0.676246\pi$
$67$	−12.4858	+	7.20867i	−1.52538	+	0.880679i	−0.999547	+	0.0300911i	$0.990420\pi$
$68$	1.43089	−	4.24416i	0.173521	−	0.514679i
$69$		0			0
$70$	−1.68742	−	0.276797i	−0.201685	−	0.0330836i
$71$	3.49303			0.414546			0.207273	−	0.978283i	$-0.433541\pi$
$71$	3.49303			0.414546			0.207273	+	0.978283i	$0.433541\pi$
$72$		0			0
$73$	5.10052			0.596970			0.298485	−	0.954414i	$-0.403519\pi$
$73$	5.10052			0.596970			0.298485	+	0.954414i	$0.403519\pi$
$74$	−14.4461	−	2.36967i	−1.67932	−	0.275469i
$75$		0			0
$76$	−1.62188	+	4.81065i	−0.186042	+	0.551820i
$77$	−3.18667	+	1.83982i	−0.363154	+	0.209667i
$78$		0			0
$79$	3.26472	+	1.88488i	0.367309	+	0.212066i	0.672282	−	0.740295i	$-0.265314\pi$
$79$	3.26472	+	1.88488i	0.367309	+	0.212066i	−0.304973	+	0.952361i	$0.598647\pi$
$80$	3.96791	+	0.505654i	0.443626	+	0.0565338i
$81$		0			0
$82$	−5.65579	+	2.13538i	−0.624577	+	0.235814i
$83$	−0.286172	+	0.495665i	−0.0314115	+	0.0544063i	−0.881304	−	0.472550i	$-0.843334\pi$
$83$	−0.286172	+	0.495665i	−0.0314115	+	0.0544063i	0.849892	+	0.526956i	$0.176667\pi$
$84$		0			0
$85$	−1.11972	−	1.93941i	−0.121450	−	0.210358i
$86$	4.72646	+	3.87071i	0.509667	+	0.417389i
$87$		0			0
$88$	7.29535	−	4.56806i	0.777687	−	0.486957i
$89$		−	2.40129i		−	0.254536i	−0.991868	−	0.127268i	$-0.959379\pi$
$89$		−	2.40129i		−	0.254536i	0.991868	−	0.127268i	$-0.0406208\pi$
$90$		0			0
$91$		−	6.14138i		−	0.643791i
$92$	−2.74449	−	13.6495i	−0.286133	−	1.42306i
$93$		0			0
$94$	−9.23042	+	11.2711i	−0.952045	+	1.16253i
$95$	1.26918	+	2.19828i	0.130215	+	0.225538i
$96$		0			0
$97$	5.82556	−	10.0902i	0.591496	−	1.02450i	−0.402535	−	0.915404i	$-0.631871\pi$
$97$	5.82556	−	10.0902i	0.591496	−	1.02450i	0.994031	−	0.109096i	$-0.0347957\pi$
$98$	−2.76639	−	7.32708i	−0.279448	−	0.740146i
$99$		0			0
$100$	1.50094	−	1.32181i	0.150094	−	0.132181i
$101$	4.13758	+	2.38883i	0.411704	+	0.237698i	0.691522	−	0.722356i	$-0.256941\pi$
$101$	4.13758	+	2.38883i	0.411704	+	0.237698i	−0.279818	+	0.960053i	$0.590274\pi$
$102$		0			0
$103$	−8.19166	+	4.72945i	−0.807148	+	0.466007i	−0.845964	−	0.533239i	$-0.820975\pi$
$103$	−8.19166	+	4.72945i	−0.807148	+	0.466007i	0.0388166	+	0.999246i	$0.487641\pi$
$104$	0.514701	+	14.3568i	0.0504706	+	1.40780i
$105$		0			0
$106$	2.15801	−	13.1557i	0.209605	−	1.27780i
$107$	−18.3014			−1.76926			−0.884630	−	0.466294i	$-0.845589\pi$
$107$	−18.3014			−1.76926			−0.884630	+	0.466294i	$0.845589\pi$
$108$		0			0
$109$	−10.2589			−0.982625			−0.491312	−	0.870983i	$-0.663483\pi$
$109$	−10.2589			−0.982625			−0.491312	+	0.870983i	$0.663483\pi$
$110$	0.696660	−	4.24700i	0.0664239	−	0.404935i
$111$		0			0
$112$	−1.86937	−	4.46065i	−0.176639	−	0.421492i
$113$	−5.31273	+	3.06731i	−0.499780	+	0.288548i	−0.728623	−	0.684915i	$-0.759839\pi$
$113$	−5.31273	+	3.06731i	−0.499780	+	0.288548i	0.228843	+	0.973463i	$0.426506\pi$
$114$		0			0
$115$	−6.02870	−	3.48067i	−0.562179	−	0.324574i
$116$	7.39346	+	8.39545i	0.686466	+	0.779498i
$117$		0			0
$118$	−4.45914	−	11.8105i	−0.410497	−	1.08724i
$119$	−1.35389	+	2.34500i	−0.124110	+	0.214966i
$120$		0			0
$121$	0.869419	+	1.50588i	0.0790381	+	0.136898i
$122$	2.38159	−	2.90812i	0.215619	−	0.263289i
$123$		0			0
$124$	−6.42456	+	1.29178i	−0.576942	+	0.116005i
$125$		−	1.00000i		−	0.0894427i
$126$		0			0
$127$			9.41213i			0.835192i	0.908633	+	0.417596i	$0.137127\pi$
$127$			9.41213i			0.835192i	−0.908633	+	0.417596i	$0.862873\pi$
$128$	4.74391	+	10.2711i	0.419307	+	0.907845i
$129$		0			0
$130$	5.55728	+	4.55111i	0.487405	+	0.399158i
$131$	1.06630	+	1.84689i	0.0931633	+	0.161364i	0.908841	−	0.417144i	$-0.136969\pi$
$131$	1.06630	+	1.84689i	0.0931633	+	0.161364i	−0.815677	+	0.578507i	$0.803635\pi$
$132$		0			0
$133$	1.53460	−	2.65800i	0.133067	−	0.230478i
$134$	−19.0749	+	7.20187i	−1.64782	+	0.622147i
$135$		0			0
$136$	2.96848	−	5.59542i	0.254545	−	0.479803i
$137$	−14.2781	−	8.24344i	−1.21986	−	0.704285i	−0.254969	−	0.966949i	$-0.582065\pi$
$137$	−14.2781	−	8.24344i	−1.21986	−	0.704285i	−0.964887	+	0.262665i	$0.915399\pi$
$138$		0			0
$139$	17.4077	−	10.0504i	1.47650	−	0.852460i	0.476856	−	0.878981i	$-0.341776\pi$
$139$	17.4077	−	10.0504i	1.47650	−	0.852460i	0.999648	+	0.0265213i	$0.00844298\pi$
$140$	−2.29153	−	0.772575i	−0.193670	−	0.0652945i
$141$		0			0
$142$	4.87474	+	0.799631i	0.409079	+	0.0671036i
$143$	15.4570			1.29258
$144$		0			0
$145$	5.59345			0.464511
$146$	7.11809	+	1.16762i	0.589097	+	0.0966331i
$147$		0			0
$148$	−19.6179	−	6.61405i	−1.61258	−	0.543672i
$149$	−1.63133	+	0.941851i	−0.133644	+	0.0771594i	−0.565331	−	0.824864i	$-0.691252\pi$
$149$	−1.63133	+	0.941851i	−0.133644	+	0.0771594i	0.431687	+	0.902023i	$0.357918\pi$
$150$		0			0
$151$	−5.35919	−	3.09413i	−0.436124	−	0.251796i	0.265828	−	0.964020i	$-0.414355\pi$
$151$	−5.35919	−	3.09413i	−0.436124	−	0.251796i	−0.701952	+	0.712224i	$0.747688\pi$
$152$	−3.36470	+	6.34228i	−0.272913	+	0.514427i
$153$		0			0
$154$	−4.86837	+	1.83809i	−0.392304	+	0.148117i
$155$	−1.63828	+	2.83759i	−0.131590	+	0.227921i
$156$		0			0
$157$	1.10012	+	1.90546i	0.0877991	+	0.152073i	0.906581	−	0.422033i	$-0.138683\pi$
$157$	1.10012	+	1.90546i	0.0877991	+	0.152073i	−0.818781	+	0.574105i	$0.805350\pi$
$158$	4.12462	+	3.37784i	0.328137	+	0.268726i
$159$		0			0
$160$	5.42171	+	1.61401i	0.428624	+	0.127599i
$161$			8.41717i			0.663366i
$162$		0			0
$163$		−	15.3649i		−	1.20347i	−0.798694	−	0.601737i	$-0.794475\pi$
$163$		−	15.3649i		−	1.20347i	0.798694	−	0.601737i	$-0.205525\pi$
$164$	−8.38184	+	1.68533i	−0.654512	+	0.131602i
$165$		0			0
$166$	−0.512840	+	0.626220i	−0.0398041	+	0.0486041i
$167$	11.1124	+	19.2472i	0.859901	+	1.48939i	0.872023	+	0.489465i	$0.162808\pi$
$167$	11.1124	+	19.2472i	0.859901	+	1.48939i	−0.0121218	+	0.999927i	$0.503859\pi$
$168$		0			0
$169$	−6.39897	+	11.0833i	−0.492229	+	0.852565i
$170$	−1.11866	−	2.96289i	−0.0857975	−	0.227244i
$171$		0			0
$172$	5.70997	+	6.48381i	0.435381	+	0.494386i
$173$	13.3460	+	7.70532i	1.01468	+	0.585825i	0.912558	−	0.408947i	$-0.134104\pi$
$173$	13.3460	+	7.70532i	1.01468	+	0.585825i	0.102120	+	0.994772i	$0.467437\pi$
$174$		0			0
$175$	−1.04714	+	0.604565i	−0.0791562	+	0.0457008i
$176$	11.2268	−	4.70495i	0.846255	−	0.354649i
$177$		0			0
$178$	0.549708	−	3.35115i	0.0412024	−	0.251179i
$179$	12.8229			0.958425			0.479212	−	0.877699i	$-0.340922\pi$
$179$	12.8229			0.958425			0.479212	+	0.877699i	$0.340922\pi$
$180$		0			0
$181$	17.3649			1.29072			0.645360	−	0.763879i	$-0.276707\pi$
$181$	17.3649			1.29072			0.645360	+	0.763879i	$0.276707\pi$
$182$	1.40590	−	8.57068i	0.104212	−	0.635301i
$183$		0			0
$184$	−0.705432	−	19.6770i	−0.0520052	−	1.45061i
$185$	−8.96460	+	5.17572i	−0.659091	+	0.380526i
$186$		0			0
$187$	−5.90204	−	3.40754i	−0.431600	−	0.249184i
$188$	−15.4618	+	13.6165i	−1.12767	+	0.993085i
$189$		0			0
$190$	1.26798	+	3.35837i	0.0919889	+	0.243642i
$191$	8.91431	−	15.4400i	0.645017	−	1.11720i	−0.339281	−	0.940685i	$-0.610184\pi$
$191$	8.91431	−	15.4400i	0.645017	−	1.11720i	0.984298	−	0.176516i	$-0.0564829\pi$
$192$		0			0
$193$	2.44181	+	4.22934i	0.175765	+	0.304434i	0.940426	−	0.339999i	$-0.110427\pi$
$193$	2.44181	+	4.22934i	0.175765	+	0.304434i	−0.764661	+	0.644433i	$0.777093\pi$
$194$	10.4398	−	12.7479i	0.749533	−	0.915242i
$195$		0			0
$196$	−2.18334	−	10.8587i	−0.155953	−	0.775620i
$197$		−	16.8173i		−	1.19818i	−0.800682	−	0.599090i	$-0.795529\pi$
$197$		−	16.8173i		−	1.19818i	0.800682	−	0.599090i	$-0.204471\pi$
$198$		0			0
$199$			5.91492i			0.419297i	0.977777	+	0.209649i	$0.0672320\pi$
$199$			5.91492i			0.419297i	−0.977777	+	0.209649i	$0.932768\pi$
$200$	2.39725	−	1.50106i	0.169511	−	0.106141i
$201$		0			0
$202$	5.22739	+	4.28095i	0.367798	+	0.301206i
$203$	−3.38161	−	5.85712i	−0.237342	−	0.411089i
$204$		0			0
$205$	−2.13740	+	3.70208i	−0.149282	+	0.258565i
$206$	−12.5146	+	4.72500i	−0.871937	+	0.329206i
$207$		0			0
$208$	−2.56830	+	20.1537i	−0.178080	+	1.39741i
$209$	6.68983	+	3.86237i	0.462745	+	0.267166i
$210$		0			0
$211$	23.9485	−	13.8267i	1.64868	−	0.951868i	0.671089	−	0.741377i	$-0.265827\pi$
$211$	23.9485	−	13.8267i	1.64868	−	0.951868i	0.977596	−	0.210491i	$-0.0675063\pi$
$212$	6.02328	−	17.8656i	0.413681	−	1.22702i
$213$		0			0
$214$	−25.5407	−	4.18959i	−1.74593	−	0.286394i
$215$	4.31983			0.294610
$216$		0			0
$217$	3.96180			0.268945
$218$	−14.3169	−	2.34849i	−0.969665	−	0.159060i
$219$		0			0
$220$	1.94446	−	5.76747i	0.131096	−	0.388843i
$221$	9.85058	−	5.68724i	0.662622	−	0.382565i
$222$		0			0
$223$	20.7390	+	11.9737i	1.38878	+	0.801815i	0.993178	−	0.116605i	$-0.0372013\pi$
$223$	20.7390	+	11.9737i	1.38878	+	0.801815i	0.395606	+	0.918420i	$0.370535\pi$
$224$	−1.58768	−	6.65306i	−0.106082	−	0.444526i
$225$		0			0
$226$	−8.11643	+	3.06442i	−0.539897	+	0.203842i
$227$	−3.45979	+	5.99253i	−0.229634	+	0.397739i	−0.957700	−	0.287769i	$-0.907086\pi$
$227$	−3.45979	+	5.99253i	−0.229634	+	0.397739i	0.728065	+	0.685508i	$0.240420\pi$
$228$		0			0
$229$	7.65837	+	13.2647i	0.506080	+	0.876556i	0.999975	+	0.00703439i	$0.00223914\pi$
$229$	7.65837	+	13.2647i	0.506080	+	0.876556i	−0.493896	+	0.869521i	$0.664428\pi$
$230$	−7.61662	−	6.23760i	−0.502225	−	0.411295i
$231$		0			0
$232$	8.39613	+	13.4089i	0.551233	+	0.880337i
$233$		−	6.61050i		−	0.433068i	−0.976275	−	0.216534i	$-0.930525\pi$
$233$		−	6.61050i		−	0.433068i	0.976275	−	0.216534i	$-0.0694753\pi$
$234$		0			0
$235$			10.3014i			0.671991i
$236$	−3.51932	−	17.5031i	−0.229088	−	1.13935i
$237$		0			0
$238$	−2.42625	+	2.96266i	−0.157271	+	0.192041i
$239$	4.11060	+	7.11976i	0.265892	+	0.460539i	0.967797	−	0.251732i	$-0.0810001\pi$
$239$	4.11060	+	7.11976i	0.265892	+	0.460539i	−0.701905	+	0.712271i	$0.747667\pi$
$240$		0			0
$241$	−7.30777	+	12.6574i	−0.470735	+	0.815337i	−0.999440	−	0.0334691i	$-0.989344\pi$
$241$	−7.30777	+	12.6574i	−0.470735	+	0.815337i	0.528705	+	0.848806i	$0.322678\pi$
$242$	0.868600	+	2.30058i	0.0558357	+	0.147887i
$243$		0			0
$244$	3.98940	−	3.51327i	0.255395	−	0.224914i
$245$	−4.79605	−	2.76900i	−0.306408	−	0.176905i
$246$		0			0
$247$	−11.1654	+	6.44635i	−0.710438	+	0.410172i
$248$	−9.26159	+	0.332033i	−0.588111	+	0.0210841i
$249$		0			0
$250$	0.228922	−	1.39556i	0.0144783	−	0.0882631i
$251$	2.39191			0.150976			0.0754880	−	0.997147i	$-0.475949\pi$
$251$	2.39191			0.150976			0.0754880	+	0.997147i	$0.475949\pi$
$252$		0			0
$253$	−21.1849			−1.33188
$254$	−2.15465	+	13.1352i	−0.135195	+	0.824177i
$255$		0			0
$256$	4.26915	+	15.4199i	0.266822	+	0.963746i
$257$	−7.31747	+	4.22474i	−0.456451	+	0.263532i	−0.710551	−	0.703646i	$-0.751554\pi$
$257$	−7.31747	+	4.22474i	−0.456451	+	0.263532i	0.254100	+	0.967178i	$0.418221\pi$
$258$		0			0
$259$	10.8394	+	6.25812i	0.673526	+	0.388860i
$260$	6.71368	+	7.62354i	0.416365	+	0.472792i
$261$		0			0
$262$	1.06530	+	2.82155i	0.0658143	+	0.174316i
$263$	−3.23162	+	5.59733i	−0.199270	+	0.345146i	−0.948292	−	0.317399i	$-0.897190\pi$
$263$	−3.23162	+	5.59733i	−0.199270	+	0.345146i	0.749022	+	0.662545i	$0.230524\pi$
$264$		0			0
$265$	−4.71342	−	8.16388i	−0.289543	−	0.501503i
$266$	2.75010	−	3.35810i	0.168620	−	0.205899i
$267$		0			0
$268$	−28.2689	+	5.68399i	−1.72680	+	0.347205i
$269$			6.14888i			0.374904i	0.982274	+	0.187452i	$0.0600229\pi$
$269$			6.14888i			0.374904i	−0.982274	+	0.187452i	$0.939977\pi$
$270$		0			0
$271$			0.446839i			0.0271436i	0.999908	+	0.0135718i	$0.00432016\pi$
$271$			0.446839i			0.0271436i	−0.999908	+	0.0135718i	$0.995680\pi$
$272$	5.42361	−	7.12921i	0.328855	−	0.432272i
$273$		0			0
$274$	−18.0388	−	14.7728i	−1.08976	−	0.892457i
$275$	−1.52161	−	2.63550i	−0.0917564	−	0.158927i
$276$		0			0
$277$	−3.41624	+	5.91710i	−0.205262	+	0.355524i	−0.950216	−	0.311592i	$-0.899138\pi$
$277$	−3.41624	+	5.91710i	−0.205262	+	0.355524i	0.744954	+	0.667115i	$0.232471\pi$
$278$	26.5943	−	10.0409i	1.59502	−	0.602212i
$279$		0			0
$280$	−3.02112	−	1.60276i	−0.180546	−	0.0957832i
$281$	2.85059	+	1.64579i	0.170052	+	0.0981794i	0.582610	−	0.812752i	$-0.302031\pi$
$281$	2.85059	+	1.64579i	0.170052	+	0.0981794i	−0.412559	+	0.910931i	$0.635365\pi$
$282$		0			0
$283$	20.2974	−	11.7187i	1.20655	−	0.696603i	0.244548	−	0.969637i	$-0.421360\pi$
$283$	20.2974	−	11.7187i	1.20655	−	0.696603i	0.962004	+	0.273034i	$0.0880271\pi$
$284$	6.61994	+	2.23187i	0.392821	+	0.132437i
$285$		0			0
$286$	21.5712	+	3.53845i	1.27553	+	0.209233i
$287$	5.16879			0.305104
$288$		0			0
$289$	11.9849			0.704996
$290$	7.80601	+	1.28047i	0.458385	+	0.0751915i
$291$		0			0
$292$	9.66644	+	3.25898i	0.565686	+	0.190717i
$293$	−24.1734	+	13.9565i	−1.41223	+	0.815349i	−0.995598	−	0.0937278i	$-0.970122\pi$
$293$	−24.1734	+	13.9565i	−1.41223	+	0.815349i	−0.416628	+	0.909077i	$0.636788\pi$
$294$		0			0
$295$	−7.73074	−	4.46335i	−0.450101	−	0.259866i
$296$	−25.8639	−	13.7213i	−1.50331	−	0.797535i
$297$		0			0
$298$	−2.49224	+	0.940963i	−0.144371	+	0.0545085i
$299$	17.6789	−	30.6208i	1.02240	−	1.77085i
$300$		0			0
$301$	−2.61162	−	4.52345i	−0.150531	−	0.260727i
$302$	−6.77076	−	5.54488i	−0.389614	−	0.319072i
$303$		0			0
$304$	−6.14754	+	8.08080i	−0.352586	+	0.463466i
$305$		−	2.65793i		−	0.152193i
$306$		0			0
$307$		−	22.5939i		−	1.28950i	−0.764393	−	0.644750i	$-0.776961\pi$
$307$		−	22.5939i		−	1.28950i	0.764393	−	0.644750i	$-0.223039\pi$
$308$	−7.21489	+	1.45069i	−0.411107	+	0.0826607i
$309$		0			0
$310$	−2.93592	+	3.58500i	−0.166749	+	0.203614i
$311$	2.94543	+	5.10164i	0.167020	+	0.289287i	0.937371	−	0.348333i	$-0.113252\pi$
$311$	2.94543	+	5.10164i	0.167020	+	0.289287i	−0.770351	+	0.637620i	$0.779919\pi$
$312$		0			0
$313$	−3.88369	+	6.72675i	−0.219519	+	0.380218i	−0.954661	−	0.297695i	$-0.903782\pi$
$313$	−3.88369	+	6.72675i	−0.219519	+	0.380218i	0.735142	+	0.677913i	$0.237115\pi$
$314$	1.09908	+	2.91104i	0.0620249	+	0.164279i
$315$		0			0
$316$	4.98291	+	5.65820i	0.280310	+	0.318299i
$317$	10.1939	+	5.88545i	0.572547	+	0.330560i	0.758166	−	0.652062i	$-0.226096\pi$
$317$	10.1939	+	5.88545i	0.572547	+	0.330560i	−0.185619	+	0.982622i	$0.559429\pi$
$318$		0			0
$319$	14.7416	−	8.51104i	0.825369	−	0.476527i
$320$	7.19685	+	3.49361i	0.402316	+	0.195299i
$321$		0			0
$322$	−1.92688	+	11.7467i	−0.107381	+	0.654618i
$323$	5.68447			0.316293
$324$		0			0
$325$	5.07917			0.281742
$326$	3.51737	−	21.4427i	0.194809	−	1.18760i
$327$		0			0
$328$	−12.0832	+	0.433190i	−0.667183	+	0.0239189i
$329$	10.7870	−	6.22788i	0.594707	−	0.343354i
$330$		0			0
$331$	3.74464	+	2.16197i	0.205824	+	0.118833i	0.599369	−	0.800473i	$-0.295418\pi$
$331$	3.74464	+	2.16197i	0.205824	+	0.118833i	−0.393545	+	0.919305i	$0.628751\pi$
$332$	−0.859056	+	0.756529i	−0.0471468	+	0.0415199i
$333$		0			0
$334$	11.1019	+	29.4045i	0.607469	+	1.60894i
$335$	−7.20867	+	12.4858i	−0.393852	+	0.682171i
$336$		0			0
$337$	−3.88505	−	6.72910i	−0.211632	−	0.366558i	0.740593	−	0.671953i	$-0.234545\pi$
$337$	−3.88505	−	6.72910i	−0.211632	−	0.366558i	−0.952225	+	0.305396i	$0.901211\pi$
$338$	−11.4674	+	14.0026i	−0.623744	+	0.761643i
$339$		0			0
$340$	−0.882891	−	4.39099i	−0.0478815	−	0.238135i
$341$			9.97131i			0.539977i
$342$		0			0
$343$			15.1601i			0.818568i
$344$	6.48434	+	10.3557i	0.349612	+	0.558342i
$345$		0			0
$346$	16.8613	+	13.8085i	0.906468	+	0.742347i
$347$	−5.63307	−	9.75677i	−0.302399	−	0.523771i	0.674280	−	0.738476i	$-0.264454\pi$
$347$	−5.63307	−	9.75677i	−0.302399	−	0.523771i	−0.976679	+	0.214705i	$0.931121\pi$
$348$		0			0
$349$	11.1403	−	19.2956i	0.596326	−	1.03287i	−0.397032	−	0.917805i	$-0.629960\pi$
$349$	11.1403	−	19.2956i	0.596326	−	1.03287i	0.993358	−	0.115063i	$-0.0367069\pi$
$350$	−1.59974	+	0.603996i	−0.0855100	+	0.0322849i
$351$		0			0
$352$	16.7448	−	3.99598i	0.892502	−	0.212986i
$353$	19.1084	+	11.0323i	1.01704	+	0.587188i	0.913245	−	0.407411i	$-0.133568\pi$
$353$	19.1084	+	11.0323i	1.01704	+	0.587188i	0.103794	+	0.994599i	$0.466902\pi$
$354$		0			0
$355$	3.02505	−	1.74651i	0.160553	−	0.0926953i
$356$	1.53431	−	4.55090i	0.0813180	−	0.241197i
$357$		0			0
$358$	17.8951	+	2.93544i	0.945785	+	0.155143i
$359$	−1.70332			−0.0898978			−0.0449489	−	0.998989i	$-0.514313\pi$
$359$	−1.70332			−0.0898978			−0.0449489	+	0.998989i	$0.514313\pi$
$360$		0			0
$361$	12.5568			0.660883
$362$	24.2337	+	3.97520i	1.27370	+	0.208932i
$363$		0			0
$364$	3.92404	−	11.6391i	0.205675	−	0.610053i
$365$	4.41718	−	2.55026i	0.231206	−	0.133487i
$366$		0			0
$367$	−8.15927	−	4.71076i	−0.425910	−	0.245900i	0.271692	−	0.962384i	$-0.412417\pi$
$367$	−8.15927	−	4.71076i	−0.425910	−	0.245900i	−0.697603	+	0.716485i	$0.745750\pi$
$368$	3.52003	−	27.6220i	0.183494	−	1.43990i
$369$		0			0
$370$	−13.6955	+	5.17084i	−0.711995	+	0.268819i
$371$	−5.69914	+	9.87119i	−0.295884	+	0.512487i
$372$		0			0
$373$	−7.29277	−	12.6314i	−0.377605	−	0.654031i	0.613108	−	0.789999i	$-0.289919\pi$
$373$	−7.29277	−	12.6314i	−0.377605	−	0.654031i	−0.990713	+	0.135968i	$0.956586\pi$
$374$	−7.45660	−	6.10655i	−0.385572	−	0.315762i
$375$		0			0
$376$	−24.6951	+	15.4631i	−1.27355	+	0.797449i
$377$			28.4101i			1.46319i
$378$		0			0
$379$		−	9.46065i		−	0.485961i	−0.970031	−	0.242980i	$-0.921875\pi$
$379$		−	9.46065i		−	0.485961i	0.970031	−	0.242980i	$-0.0781251\pi$
$380$	1.00074	+	4.97709i	0.0513367	+	0.255319i
$381$		0			0
$382$	15.9750	−	19.5068i	0.817354	−	0.998057i
$383$	3.43007	+	5.94105i	0.175268	+	0.303573i	0.940254	−	0.340474i	$-0.110587\pi$
$383$	3.43007	+	5.94105i	0.175268	+	0.303573i	−0.764986	+	0.644047i	$0.777254\pi$
$384$		0			0
$385$	−1.83982	+	3.18667i	−0.0937661	+	0.162408i
$386$	2.43951	+	6.46129i	0.124168	+	0.328871i
$387$		0			0
$388$	17.4876	−	15.4005i	0.887801	−	0.781843i
$389$	−7.11643	−	4.10868i	−0.360818	−	0.208318i	0.308622	−	0.951185i	$-0.400132\pi$
$389$	−7.11643	−	4.10868i	−0.360818	−	0.208318i	−0.669439	+	0.742867i	$0.733466\pi$
$390$		0			0
$391$	−13.5009	+	7.79474i	−0.682769	+	0.394197i
$392$	−0.561197	−	15.6538i	−0.0283447	−	0.790635i
$393$		0			0
$394$	3.84984	−	23.4695i	0.193952	−	1.18238i
$395$	3.76977			0.189678
$396$		0			0
$397$	−7.07936			−0.355303			−0.177651	−	0.984093i	$-0.556850\pi$
$397$	−7.07936			−0.355303			−0.177651	+	0.984093i	$0.556850\pi$
$398$	−1.35406	+	8.25463i	−0.0678727	+	0.413767i
$399$		0			0
$400$	3.68914	−	1.54605i	0.184457	−	0.0773023i
$401$	15.3220	−	8.84615i	0.765143	−	0.441755i	−0.0659963	−	0.997820i	$-0.521023\pi$
$401$	15.3220	−	8.84615i	0.765143	−	0.441755i	0.831139	+	0.556064i	$0.187689\pi$
$402$		0			0
$403$	−14.4126	−	8.32112i	−0.717943	−	0.414505i
$404$	6.31514	+	7.17099i	0.314190	+	0.356770i
$405$		0			0
$406$	−3.37842	−	8.94810i	−0.167668	−	0.444087i
$407$	−15.7508	+	27.2812i	−0.780739	+	1.35228i
$408$		0			0
$409$	11.3542	+	19.6660i	0.561428	+	0.972422i	0.997372	+	0.0724482i	$0.0230812\pi$
$409$	11.3542	+	19.6660i	0.561428	+	0.972422i	−0.435944	+	0.899974i	$0.643585\pi$
$410$	−3.83036	+	4.67719i	−0.189168	+	0.230990i
$411$		0			0
$412$	−18.5466	+	3.72915i	−0.913727	+	0.183722i
$413$			10.7935i			0.531115i
$414$		0			0
$415$			0.572344i			0.0280953i
$416$	−8.19785	+	27.5378i	−0.401933	+	1.35015i
$417$		0			0
$418$	8.45189	+	6.92163i	0.413395	+	0.338548i
$419$	−13.1805	−	22.8292i	−0.643908	−	1.11528i	−0.984553	−	0.175089i	$-0.943979\pi$
$419$	−13.1805	−	22.8292i	−0.643908	−	1.11528i	0.340645	−	0.940192i	$-0.389355\pi$
$420$		0			0
$421$	−8.57768	+	14.8570i	−0.418050	+	0.724084i	−0.995743	−	0.0921697i	$-0.970620\pi$
$421$	−8.57768	+	14.8570i	−0.418050	+	0.724084i	0.577693	+	0.816254i	$0.303953\pi$
$422$	36.5869	−	13.8137i	1.78102	−	0.672438i
$423$		0			0
$424$	12.4957	−	23.5537i	0.606845	−	1.14387i
$425$	−1.93941	−	1.11972i	−0.0940751	−	0.0543143i
$426$		0			0
$427$	−2.78322	+	1.60689i	−0.134689	+	0.0777629i
$428$	−34.6846	−	11.6937i	−1.67654	−	0.565235i
$429$		0			0
$430$	6.02859	+	0.988904i	0.290724	+	0.0476892i
$431$	−12.5816			−0.606037			−0.303018	−	0.952985i	$-0.597994\pi$
$431$	−12.5816			−0.606037			−0.303018	+	0.952985i	$0.597994\pi$
$432$		0			0
$433$	−11.7433			−0.564346			−0.282173	−	0.959364i	$-0.591055\pi$
$433$	−11.7433			−0.564346			−0.282173	+	0.959364i	$0.591055\pi$
$434$	5.52894	+	0.906944i	0.265398	+	0.0435347i
$435$		0			0
$436$	−19.4426	−	6.55493i	−0.931130	−	0.313924i
$437$	15.3030	−	8.83516i	0.732039	−	0.422643i
$438$		0			0
$439$	1.45738	+	0.841421i	0.0695571	+	0.0401588i	0.534375	−	0.845247i	$-0.320547\pi$
$439$	1.45738	+	0.841421i	0.0695571	+	0.0401588i	−0.464818	+	0.885406i	$0.653880\pi$
$440$	4.03392	−	7.60373i	0.192310	−	0.362494i
$441$		0			0
$442$	15.0490	−	5.68188i	0.715810	−	0.270259i
$443$	0.379510	−	0.657331i	0.0180311	−	0.0312307i	−0.856869	−	0.515534i	$-0.827594\pi$
$443$	0.379510	−	0.657331i	0.0180311	−	0.0312307i	0.874900	+	0.484303i	$0.160927\pi$
$444$		0			0
$445$	−1.20064	−	2.07958i	−0.0569160	−	0.0985814i
$446$	26.2015	+	21.4576i	1.24068	+	1.01605i
$447$		0			0
$448$	−0.692678	−	9.64821i	−0.0327260	−	0.455835i
$449$		−	17.4579i		−	0.823887i	−0.911209	−	0.411943i	$-0.864850\pi$
$449$		−	17.4579i		−	0.823887i	0.911209	−	0.411943i	$-0.135150\pi$
$450$		0			0
$451$			13.0091i			0.612576i
$452$	−12.0285	+	2.41856i	−0.565773	+	0.113759i
$453$		0			0
$454$	−6.20018	+	7.57093i	−0.290989	+	0.355322i
$455$	−3.07069	−	5.31859i	−0.143956	−	0.249339i
$456$		0			0
$457$	17.4319	−	30.1929i	0.815430	−	1.41237i	−0.0935884	−	0.995611i	$-0.529834\pi$
$457$	17.4319	−	30.1929i	0.815430	−	1.41237i	0.909019	−	0.416756i	$-0.136833\pi$
$458$	7.65116	+	20.2649i	0.357515	+	0.946916i
$459$		0			0
$460$	−9.20155	−	10.4486i	−0.429025	−	0.487167i
$461$	−27.0906	−	15.6407i	−1.26173	−	0.728462i	−0.288324	−	0.957533i	$-0.593098\pi$
$461$	−27.0906	−	15.6407i	−1.26173	−	0.728462i	−0.973410	+	0.229071i	$0.926431\pi$
$462$		0			0
$463$	−8.90511	+	5.14137i	−0.413856	+	0.238940i	−0.692445	−	0.721471i	$-0.743466\pi$
$463$	−8.90511	+	5.14137i	−0.413856	+	0.238940i	0.278589	+	0.960410i	$0.410133\pi$
$464$	8.64773	+	20.6350i	0.401461	+	0.957957i
$465$		0			0
$466$	1.51329	−	9.22537i	0.0701018	−	0.427357i
$467$	2.90585			0.134467			0.0672333	−	0.997737i	$-0.478583\pi$
$467$	2.90585			0.134467			0.0672333	+	0.997737i	$0.478583\pi$
$468$		0			0
$469$	17.4324			0.804955
$470$	−2.35822	+	14.3763i	−0.108777	+	0.663128i
$471$		0			0
$472$	−0.904592	−	25.2323i	−0.0416372	−	1.16141i
$473$	11.3849	−	6.57308i	0.523479	−	0.302231i
$474$		0			0
$475$	2.19828	+	1.26918i	0.100864	+	0.0582337i
$476$	−4.06421	+	3.57915i	−0.186283	+	0.164050i
$477$		0			0
$478$	4.10672	+	10.8771i	0.187837	+	0.497506i
$479$	9.42773	−	16.3293i	0.430764	−	0.746105i	−0.566175	−	0.824285i	$-0.691578\pi$
$479$	9.42773	−	16.3293i	0.430764	−	0.746105i	0.996939	+	0.0781799i	$0.0249109\pi$
$480$		0			0
$481$	−26.2883	−	45.5327i	−1.19864	−	2.07611i
$482$	−13.0960	+	15.9913i	−0.596507	+	0.728385i
$483$		0			0
$484$	0.685532	+	3.40944i	0.0311605	+	0.154975i
$485$		−	11.6511i		−	0.529050i
$486$		0			0
$487$			11.5696i			0.524268i	0.965031	+	0.262134i	$0.0844263\pi$
$487$			11.5696i			0.524268i	−0.965031	+	0.262134i	$0.915574\pi$
$488$	6.37172	−	3.98972i	0.288434	−	0.180606i
$489$		0			0
$490$	−6.05930	−	4.96224i	−0.273731	−	0.224171i
$491$	−0.747617	−	1.29491i	−0.0337395	−	0.0584385i	0.848663	−	0.528935i	$-0.177408\pi$
$491$	−0.747617	−	1.29491i	−0.0337395	−	0.0584385i	−0.882402	+	0.470496i	$0.844075\pi$
$492$		0			0
$493$	6.26309	−	10.8480i	0.282075	−	0.488569i
$494$	−17.0577	+	6.44028i	−0.767464	+	0.289762i
$495$		0			0
$496$	−13.0011	−	1.65681i	−0.583768	−	0.0743930i
$497$	−3.65768	−	2.11176i	−0.164069	−	0.0947255i
$498$		0			0
$499$	−27.2612	+	15.7393i	−1.22038	+	0.704586i	−0.964999	−	0.262254i	$-0.915534\pi$
$499$	−27.2612	+	15.7393i	−1.22038	+	0.704586i	−0.255380	+	0.966841i	$0.582201\pi$
$500$	0.638951	−	1.89519i	0.0285747	−	0.0847554i
$501$		0			0
$502$	3.33806	+	0.547562i	0.148985	+	0.0244389i
$503$	−1.90449			−0.0849171			−0.0424585	−	0.999098i	$-0.513519\pi$
$503$	−1.90449			−0.0849171			−0.0424585	+	0.999098i	$0.513519\pi$
$504$		0			0
$505$	4.77766			0.212603
$506$	−29.5648	−	4.84969i	−1.31432	−	0.215595i
$507$		0			0
$508$	−6.01389	+	17.8378i	−0.266823	+	0.791423i
$509$	−27.2228	+	15.7171i	−1.20663	+	0.696647i	−0.962021	−	0.272975i	$-0.911992\pi$
$509$	−27.2228	+	15.7171i	−1.20663	+	0.696647i	−0.244607	+	0.969622i	$0.578659\pi$
$510$		0			0
$511$	−5.34094	−	3.08360i	−0.236269	−	0.136410i
$512$	2.42789	+	22.4968i	0.107299	+	0.994227i
$513$		0			0
$514$	−11.1791	+	4.22076i	−0.493090	+	0.186170i
$515$	−4.72945	+	8.19166i	−0.208405	+	0.360967i
$516$		0			0
$517$	15.6747	+	27.1494i	0.689374	+	1.19403i
$518$	13.6944	+	11.2150i	0.601698	+	0.492757i
$519$		0			0
$520$	7.62416	+	12.1760i	0.334342	+	0.533954i
$521$		−	23.2742i		−	1.01966i	−0.860275	−	0.509831i	$-0.829708\pi$
$521$		−	23.2742i		−	1.01966i	0.860275	−	0.509831i	$-0.170292\pi$
$522$		0			0
$523$			10.8804i			0.475769i	0.971293	+	0.237884i	$0.0764539\pi$
$523$			10.8804i			0.475769i	−0.971293	+	0.237884i	$0.923546\pi$
$524$	0.840774	+	4.18152i	0.0367294	+	0.182671i
$525$		0			0
$526$	−5.79128	+	7.07163i	−0.252512	+	0.308338i
$527$	3.66883	+	6.35461i	0.159817	+	0.276811i
$528$		0			0
$529$	−12.7302	+	22.0493i	−0.553485	+	0.958664i
$530$	−4.70897	−	12.4722i	−0.204545	−	0.541758i
$531$		0			0
$532$	4.60669	−	4.05689i	0.199725	−	0.175888i
$533$	−18.8035	−	10.8562i	−0.814470	−	0.470235i
$534$		0			0
$535$	−15.8495	+	9.15068i	−0.685231	+	0.395619i
$536$	−40.7522	+	1.46099i	−1.76023	+	0.0631052i
$537$		0			0
$538$	−1.40762	+	8.58115i	−0.0606867	+	0.369960i
$539$	−16.8533			−0.725925
$540$		0			0
$541$	−6.53795			−0.281088			−0.140544	−	0.990074i	$-0.544885\pi$
$541$	−6.53795			−0.281088			−0.140544	+	0.990074i	$0.544885\pi$
$542$	−0.102291	+	0.623592i	−0.00439379	+	0.0267856i
$543$		0			0
$544$	9.20102	−	8.70767i	0.394491	−	0.373338i
$545$	−8.88447	+	5.12945i	−0.380569	+	0.219722i
$546$		0			0
$547$	−23.0165	−	13.2886i	−0.984113	−	0.568178i	−0.0806034	−	0.996746i	$-0.525685\pi$
$547$	−23.0165	−	13.2886i	−0.984113	−	0.568178i	−0.903509	+	0.428569i	$0.859018\pi$
$548$	−21.7925	−	24.7458i	−0.930928	−	1.05709i
$549$		0			0
$550$	−1.52017	−	4.02634i	−0.0648204	−	0.171684i
$551$	−7.09907	+	12.2959i	−0.302431	+	0.523825i
$552$		0			0
$553$	−2.27907	−	3.94747i	−0.0969160	−	0.167863i
$554$	−6.12213	+	7.47562i	−0.260104	+	0.317609i
$555$		0			0
$556$	39.4126	−	7.92465i	1.67147	−	0.336080i
$557$		−	8.68248i		−	0.367889i	−0.982937	−	0.183944i	$-0.941113\pi$
$557$		−	8.68248i		−	0.367889i	0.982937	−	0.183944i	$-0.0588866\pi$
$558$		0			0
$559$			21.9411i			0.928010i
$560$	−3.84925	−	2.92835i	−0.162660	−	0.123745i
$561$		0			0
$562$	3.60141	+	2.94936i	0.151916	+	0.124411i
$563$	−15.8324	−	27.4226i	−0.667257	−	1.15572i	−0.978668	−	0.205448i	$-0.934135\pi$
$563$	−15.8324	−	27.4226i	−0.667257	−	1.15572i	0.311411	−	0.950275i	$-0.399199\pi$
$564$		0			0
$565$	−3.06731	+	5.31273i	−0.129043	+	0.223508i
$566$	31.0089	−	11.7076i	1.30340	−	0.492109i
$567$		0			0
$568$	8.72762	+	4.63017i	0.366203	+	0.194278i
$569$	−27.9697	−	16.1483i	−1.17255	−	0.676973i	−0.218272	−	0.975888i	$-0.570042\pi$
$569$	−27.9697	−	16.1483i	−1.17255	−	0.676973i	−0.954280	+	0.298915i	$0.903375\pi$
$570$		0			0
$571$	−12.7245	+	7.34651i	−0.532505	+	0.307442i	−0.742036	−	0.670360i	$-0.766140\pi$
$571$	−12.7245	+	7.34651i	−0.532505	+	0.307442i	0.209531	+	0.977802i	$0.432806\pi$
$572$	29.2939	+	9.87626i	1.22484	+	0.412947i
$573$		0			0
$574$	7.21337	+	1.18325i	0.301080	+	0.0493879i
$575$	−6.96134			−0.290308
$576$		0			0
$577$	−22.4886			−0.936214			−0.468107	−	0.883672i	$-0.655064\pi$
$577$	−22.4886			−0.936214			−0.468107	+	0.883672i	$0.655064\pi$
$578$	16.7257	+	2.74362i	0.695698	+	0.114119i
$579$		0			0
$580$	10.6006	+	3.57394i	0.440168	+	0.148400i
$581$	0.599324	−	0.346020i	0.0248641	−	0.0143553i
$582$		0			0
$583$	−24.8444	−	14.3439i	−1.02895	−	0.594065i
$584$	12.7441	+	6.76097i	0.527354	+	0.279771i
$585$		0			0
$586$	−36.9305	+	13.9434i	−1.52558	+	0.575996i
$587$	17.2484	−	29.8752i	0.711919	−	1.23308i	−0.252217	−	0.967671i	$-0.581160\pi$
$587$	17.2484	−	29.8752i	0.711919	−	1.23308i	0.964136	−	0.265409i	$-0.0855069\pi$
$588$		0			0
$589$	−4.15854	−	7.20280i	−0.171350	−	0.296786i
$590$	−9.76697	−	7.99862i	−0.402100	−	0.329298i
$591$		0			0
$592$	−32.9536	−	25.0698i	−1.35439	−	1.03036i
$593$		−	11.5133i		−	0.472794i	−0.971656	−	0.236397i	$-0.924033\pi$
$593$		−	11.5133i		−	0.472794i	0.971656	−	0.236397i	$-0.0759667\pi$
$594$		0			0
$595$			2.70777i			0.111008i
$596$	−3.69348	+	0.742644i	−0.151291	+	0.0304199i
$597$		0			0
$598$	31.6818	−	38.6861i	1.29557	−	1.58199i
$599$	17.8060	+	30.8410i	0.727535	+	1.26013i	0.957922	+	0.287028i	$0.0926674\pi$
$599$	17.8060	+	30.8410i	0.727535	+	1.26013i	−0.230387	+	0.973099i	$0.573999\pi$
$600$		0			0
$601$	−20.4137	+	35.3576i	−0.832693	+	1.44227i	0.0632021	+	0.998001i	$0.479869\pi$
$601$	−20.4137	+	35.3576i	−0.832693	+	1.44227i	−0.895895	+	0.444266i	$0.853465\pi$
$602$	−2.60916	−	6.91062i	−0.106341	−	0.281656i
$603$		0			0
$604$	−8.17968	−	9.28821i	−0.332826	−	0.377932i
$605$	1.50588	+	0.869419i	0.0612226	+	0.0353469i
$606$		0			0
$607$	−1.90026	+	1.09711i	−0.0771290	+	0.0445304i	−0.538069	−	0.842901i	$-0.680846\pi$
$607$	−1.90026	+	1.09711i	−0.0771290	+	0.0445304i	0.460940	+	0.887432i	$0.347513\pi$
$608$	−10.4292	+	9.86995i	−0.422958	+	0.400279i
$609$		0			0
$610$	0.608459	−	3.70930i	0.0246358	−	0.150185i
$611$	−52.3227			−2.11675
$612$		0			0
$613$	38.7673			1.56580			0.782899	−	0.622149i	$-0.213740\pi$
$613$	38.7673			1.56580			0.782899	+	0.622149i	$0.213740\pi$
$614$	5.17224	−	31.5312i	0.208735	−	1.27249i
$615$		0			0
$616$	−10.4009	+	0.372879i	−0.419065	+	0.0150237i
$617$	12.8653	−	7.42778i	0.517937	−	0.299031i	−0.218153	−	0.975915i	$-0.570003\pi$
$617$	12.8653	−	7.42778i	0.517937	−	0.299031i	0.736090	+	0.676884i	$0.236670\pi$
$618$		0			0
$619$	−12.3383	−	7.12352i	−0.495918	−	0.286318i	0.231108	−	0.972928i	$-0.425765\pi$
$619$	−12.3383	−	7.12352i	−0.495918	−	0.286318i	−0.727026	+	0.686610i	$0.759098\pi$
$620$	−4.91794	+	4.33099i	−0.197509	+	0.173937i
$621$		0			0
$622$	2.94266	+	7.79393i	0.117990	+	0.312508i
$623$	−1.45174	+	2.51448i	−0.0581626	+	0.100741i
$624$		0			0
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	−6.95983	+	8.49853i	−0.278171	+	0.339670i
$627$		0			0
$628$	0.867439	+	4.31414i	0.0346146	+	0.172153i
$629$			23.1814i			0.924302i
$630$		0			0
$631$			38.8200i			1.54540i	0.634772	+	0.772700i	$0.281094\pi$
$631$			38.8200i			1.54540i	−0.634772	+	0.772700i	$0.718906\pi$
$632$	5.65867	+	9.03707i	0.225090	+	0.359476i
$633$		0			0
$634$	12.8789	+	10.5471i	0.511487	+	0.418880i
$635$	4.70607	+	8.15115i	0.186755	+	0.323468i
$636$		0			0
$637$	14.0642	−	24.3599i	0.557245	−	0.965176i
$638$	22.5211	−	8.50302i	0.891620	−	0.336638i
$639$		0			0
$640$	9.24389	+	6.52307i	0.365397	+	0.257847i
$641$	−16.5595	−	9.56061i	−0.654060	−	0.377621i	0.135950	−	0.990716i	$-0.456591\pi$
$641$	−16.5595	−	9.56061i	−0.654060	−	0.377621i	−0.790010	+	0.613094i	$0.789925\pi$
$642$		0			0
$643$	5.69143	−	3.28595i	0.224448	−	0.129585i	−0.383560	−	0.923516i	$-0.625302\pi$
$643$	5.69143	−	3.28595i	0.224448	−	0.129585i	0.608008	+	0.793931i	$0.291969\pi$
$644$	−5.37816	+	15.9521i	−0.211929	+	0.628602i
$645$		0			0
$646$	7.93304	+	1.30130i	0.312121	+	0.0511991i
$647$	−12.7191			−0.500040			−0.250020	−	0.968241i	$-0.580437\pi$
$647$	−12.7191			−0.500040			−0.250020	+	0.968241i	$0.580437\pi$
$648$		0			0
$649$	−27.1658			−1.06635
$650$	7.08830	+	1.16273i	0.278026	+	0.0456062i
$651$		0			0
$652$	9.81743	−	29.1195i	0.384480	−	1.14041i
$653$	38.1762	−	22.0410i	1.49395	−	0.862532i	0.493974	−	0.869477i	$-0.335544\pi$
$653$	38.1762	−	22.0410i	1.49395	−	0.862532i	0.999976	+	0.00694441i	$0.00221049\pi$
$654$		0			0
$655$	1.84689	+	1.06630i	0.0721640	+	0.0416639i
$656$	−16.9620	−	2.16157i	−0.662256	−	0.0843951i
$657$		0			0
$658$	16.4796	−	6.22201i	0.642444	−	0.242559i
$659$	−10.8929	+	18.8671i	−0.424328	+	0.734957i	−0.996357	−	0.0852757i	$-0.972823\pi$
$659$	−10.8929	+	18.8671i	−0.424328	+	0.734957i	0.572030	+	0.820233i	$0.306156\pi$
$660$		0			0
$661$	−10.2756	−	17.7979i	−0.399676	−	0.692260i	0.594009	−	0.804458i	$-0.297544\pi$
$661$	−10.2756	−	17.7979i	−0.399676	−	0.692260i	−0.993686	+	0.112198i	$0.964211\pi$
$662$	4.73096	+	3.87439i	0.183874	+	0.150583i
$663$		0			0
$664$	−1.37205	+	0.859126i	−0.0532460	+	0.0333406i
$665$		−	3.06920i		−	0.119018i
$666$		0			0
$667$		−	38.9379i		−	1.50768i
$668$	8.76204	+	43.5773i	0.339014	+	1.68606i
$669$		0			0
$670$	−12.9184	+	15.7745i	−0.499082	+	0.609420i
$671$	−4.04432	−	7.00497i	−0.156129	−	0.270424i
$672$		0			0
$673$	1.08874	−	1.88576i	0.0419680	−	0.0726906i	−0.844278	−	0.535905i	$-0.819971\pi$
$673$	1.08874	−	1.88576i	0.0419680	−	0.0726906i	0.886246	+	0.463214i	$0.153304\pi$
$674$	−3.88139	−	10.2803i	−0.149505	−	0.395981i
$675$		0			0
$676$	−19.2090	+	16.9164i	−0.738807	+	0.650631i
$677$	−1.92840	−	1.11336i	−0.0741143	−	0.0427899i	0.462485	−	0.886627i	$-0.346958\pi$
$677$	−1.92840	−	1.11336i	−0.0741143	−	0.0427899i	−0.536599	+	0.843837i	$0.680291\pi$
$678$		0			0
$679$	−12.2003	+	7.04386i	−0.468205	+	0.270319i
$680$	−0.226935	−	6.33002i	−0.00870255	−	0.242745i
$681$		0			0
$682$	−2.28265	+	13.9156i	−0.0874073	+	0.532855i
$683$	−12.9800			−0.496665			−0.248333	−	0.968675i	$-0.579883\pi$
$683$	−12.9800			−0.496665			−0.248333	+	0.968675i	$0.579883\pi$
$684$		0			0
$685$	−16.4869			−0.629931
$686$	−3.47048	+	21.1568i	−0.132504	+	0.807772i
$687$		0			0
$688$	6.67865	+	15.9364i	0.254621	+	0.607571i
$689$	41.4657	−	23.9402i	1.57972	−	0.912050i
$690$		0			0
$691$	24.1859	+	13.9637i	0.920074	+	0.531205i	0.883659	−	0.468132i	$-0.155073\pi$
$691$	24.1859	+	13.9637i	0.920074	+	0.531205i	0.0364156	+	0.999337i	$0.488406\pi$
$692$	20.3699	+	23.1305i	0.774347	+	0.879289i
$693$		0			0
$694$	−5.62776	−	14.9057i	−0.213627	−	0.565813i
$695$	10.0504	−	17.4077i	0.381232	−	0.660313i
$696$		0			0
$697$	4.78657	+	8.29058i	0.181304	+	0.314028i
$698$	19.9642	−	24.3779i	0.755655	−	0.922717i
$699$		0			0
$700$	−2.37081	+	0.476696i	−0.0896083	+	0.0180174i
$701$			31.0643i			1.17328i	0.809847	+	0.586641i	$0.199550\pi$
$701$			31.0643i			1.17328i	−0.809847	+	0.586641i	$0.800450\pi$
$702$		0			0
$703$		−	26.2756i		−	0.991001i
$704$	24.2832	−	1.74338i	0.915208	−	0.0657060i
$705$		0			0
$706$	24.1415	+	19.7705i	0.908576	+	0.744074i
$707$	−2.88841	−	5.00287i	−0.108630	−	0.188152i
$708$		0			0
$709$	21.7239	−	37.6269i	0.815859	−	1.41311i	−0.0928511	−	0.995680i	$-0.529598\pi$
$709$	21.7239	−	37.6269i	0.815859	−	1.41311i	0.908710	−	0.417429i	$-0.137069\pi$
$710$	4.62146	−	1.74487i	0.173440	−	0.0654837i
$711$		0			0
$712$	3.18302	−	5.99982i	0.119289	−	0.224853i
$713$	19.7535	+	11.4047i	0.739773	+	0.427108i
$714$		0			0
$715$	13.3862	−	7.72850i	0.500614	−	0.289030i
$716$	24.3017	+	8.19317i	0.908198	+	0.306193i
$717$		0			0
$718$	−2.37709	−	0.389928i	−0.0887122	−	0.0145520i
$719$	12.6495			0.471747			0.235874	−	0.971784i	$-0.424205\pi$
$719$	12.6495			0.471747			0.235874	+	0.971784i	$0.424205\pi$
$720$		0			0
$721$	11.4371			0.425938
$722$	17.5238	+	2.87453i	0.652167	+	0.106979i
$723$		0			0
$724$	32.9097	+	11.0953i	1.22308	+	0.412353i
$725$	4.84407	−	2.79673i	0.179904	−	0.103868i
$726$		0			0
$727$	43.4035	+	25.0590i	1.60975	+	0.929389i	0.989425	+	0.145042i	$0.0463318\pi$
$727$	43.4035	+	25.0590i	1.60975	+	0.929389i	0.620323	+	0.784347i	$0.287002\pi$
$728$	8.14068	−	15.3448i	0.301714	−	0.568714i
$729$		0			0
$730$	6.74826	−	2.54785i	0.249764	−	0.0943003i
$731$	4.83699	−	8.37791i	0.178902	−	0.309868i
$732$		0			0
$733$	14.7327	+	25.5178i	0.544166	+	0.942523i	0.998659	+	0.0517728i	$0.0164872\pi$
$733$	14.7327	+	25.5178i	0.544166	+	0.942523i	−0.454493	+	0.890750i	$0.650179\pi$
$734$	−10.3084	−	8.44199i	−0.380489	−	0.311600i
$735$		0			0
$736$	11.2357	−	37.7424i	0.414154	−	1.39120i
$737$			43.8751i			1.61616i
$738$		0			0
$739$		−	45.3131i		−	1.66687i	−0.552618	−	0.833435i	$-0.686371\pi$
$739$		−	45.3131i		−	1.66687i	0.552618	−	0.833435i	$-0.313629\pi$
$740$	−20.2966	+	4.08102i	−0.746120	+	0.150021i
$741$		0			0
$742$	−10.2132	+	12.4712i	−0.374940	+	0.457832i
$743$	4.03779	+	6.99366i	0.148132	+	0.256573i	0.930537	−	0.366197i	$-0.119341\pi$
$743$	4.03779	+	6.99366i	0.148132	+	0.256573i	−0.782405	+	0.622770i	$0.786007\pi$
$744$		0			0
$745$	−0.941851	+	1.63133i	−0.0345067	+	0.0597674i
$746$	−7.28589	−	19.2974i	−0.266756	−	0.706530i
$747$		0			0
$748$	−9.00823	−	10.2291i	−0.329373	−	0.374011i
$749$	19.1641	+	11.0644i	0.700239	+	0.404283i
$750$		0			0
$751$	9.71367	−	5.60819i	0.354457	−	0.204646i	−0.312190	−	0.950020i	$-0.601062\pi$
$751$	9.71367	−	5.60819i	0.354457	−	0.204646i	0.666646	+	0.745374i	$0.267729\pi$
$752$	−38.0034	+	15.9265i	−1.38584	+	0.580779i
$753$		0			0
$754$	−6.50370	+	39.6480i	−0.236851	+	1.44390i
$755$	−6.18825			−0.225214
$756$		0			0
$757$	−26.9148			−0.978236			−0.489118	−	0.872218i	$-0.662681\pi$
$757$	−26.9148			−0.978236			−0.489118	+	0.872218i	$0.662681\pi$
$758$	2.16575	−	13.2029i	0.0786637	−	0.479552i
$759$		0			0
$760$	0.257225	+	7.17493i	0.00933055	+	0.260262i
$761$	−6.74550	+	3.89451i	−0.244524	+	0.141176i	−0.617254	−	0.786764i	$-0.711755\pi$
$761$	−6.74550	+	3.89451i	−0.244524	+	0.141176i	0.372730	+	0.927940i	$0.378422\pi$
$762$		0			0
$763$	10.7425	+	6.20218i	0.388904	+	0.224534i
$764$	26.7597	−	23.5660i	0.968132	−	0.852587i
$765$		0			0
$766$	3.42683	+	9.07632i	0.123816	+	0.327941i
$767$	22.6701	−	39.2657i	0.818569	−	1.41780i
$768$		0			0
$769$	−3.36491	−	5.82819i	−0.121342	−	0.210170i	0.798955	−	0.601390i	$-0.205386\pi$
$769$	−3.36491	−	5.82819i	−0.121342	−	0.210170i	−0.920297	+	0.391220i	$0.872053\pi$
$770$	−3.29709	+	4.02602i	−0.118819	+	0.145088i
$771$		0			0
$772$	1.92535	+	9.57559i	0.0692950	+	0.344633i
$773$			16.5270i			0.594435i	0.954810	+	0.297217i	$0.0960586\pi$
$773$			16.5270i			0.594435i	−0.954810	+	0.297217i	$0.903941\pi$
$774$		0			0
$775$			3.27657i			0.117698i
$776$	27.9306	−	17.4891i	1.00265	−	0.627821i
$777$		0			0
$778$	−8.99086	−	7.36302i	−0.322338	−	0.263977i
$779$	−5.42547	−	9.39719i	−0.194388	−	0.336689i
$780$		0			0
$781$	5.31502	−	9.20588i	0.190186	−	0.329412i
$782$	−20.6257	+	7.78740i	−0.737574	+	0.278477i
$783$		0			0
$784$	2.80031	−	21.9743i	0.100011	−	0.784796i
$785$	1.90546	+	1.10012i	0.0680089	+	0.0392650i
$786$		0			0
$787$	2.38973	−	1.37971i	0.0851847	−	0.0491814i	−0.456803	−	0.889568i	$-0.651005\pi$
$787$	2.38973	−	1.37971i	0.0851847	−	0.0491814i	0.541987	+	0.840387i	$0.317672\pi$
$788$	10.7454	−	31.8719i	0.382789	−	1.13539i
$789$		0			0
$790$	5.26095	+	0.862984i	0.187176	+	0.0307036i
$791$	7.41755			0.263738
$792$		0			0
$793$	13.5001			0.479401
$794$	−9.87968	−	1.62062i	−0.350617	−	0.0575137i
$795$		0			0
$796$	−3.77934	+	11.2099i	−0.133955	+	0.397324i
$797$	−4.54011	+	2.62123i	−0.160819	+	0.0928488i	−0.578250	−	0.815860i	$-0.696264\pi$
$797$	−4.54011	+	2.62123i	−0.160819	+	0.0928488i	0.417431	+	0.908709i	$0.362931\pi$
$798$		0			0
$799$	19.9787	+	11.5347i	0.706794	+	0.408068i
$800$	5.50235	−	1.31308i	0.194537	−	0.0464243i
$801$		0			0
$802$	23.4079	−	8.83781i	0.826560	−	0.312074i
$803$	7.76099	−	13.4424i	0.273879	−	0.474373i
$804$		0			0
$805$	4.20859	+	7.28949i	0.148333	+	0.256921i
$806$	−18.2088	−	14.9120i	−0.641378	−	0.525253i
$807$		0			0
$808$	7.17158	+	11.4532i	0.252295	+	0.402924i
$809$			47.1813i			1.65881i	0.558650	+	0.829403i	$0.311319\pi$
$809$			47.1813i			1.65881i	−0.558650	+	0.829403i	$0.688681\pi$
$810$		0			0
$811$			18.8666i			0.662495i	0.943544	+	0.331247i	$0.107469\pi$
$811$			18.8666i			0.662495i	−0.943544	+	0.331247i	$0.892531\pi$
$812$	−2.66638	−	13.2610i	−0.0935715	−	0.465371i
$813$		0			0
$814$	−28.2265	+	34.4669i	−0.989339	+	1.20807i
$815$	−7.68247	−	13.3064i	−0.269105	−	0.466104i
$816$		0			0
$817$	−5.48261	+	9.49617i	−0.191812	+	0.332229i
$818$	11.3435	+	30.0444i	0.396615	+	1.05048i
$819$		0			0
$820$	−6.41622	+	5.65046i	−0.224064	+	0.197323i
$821$	−1.12399	−	0.648938i	−0.0392277	−	0.0226481i	0.480258	−	0.877127i	$-0.340543\pi$
$821$	−1.12399	−	0.648938i	−0.0392277	−	0.0226481i	−0.519486	+	0.854479i	$0.673876\pi$
$822$		0			0
$823$	5.77693	−	3.33531i	0.201371	−	0.116262i	−0.395924	−	0.918283i	$-0.629576\pi$
$823$	5.77693	−	3.33531i	0.201371	−	0.116262i	0.597295	+	0.802022i	$0.296242\pi$
$824$	−26.7367	+	0.958525i	−0.931416	+	0.0333918i
$825$		0			0
$826$	−2.47088	+	15.0631i	−0.0859729	+	0.524111i
$827$	37.4924			1.30374			0.651869	−	0.758331i	$-0.273985\pi$
$827$	37.4924			1.30374			0.651869	+	0.758331i	$0.273985\pi$
$828$		0			0
$829$	−22.9261			−0.796255			−0.398127	−	0.917330i	$-0.630340\pi$
$829$	−22.9261			−0.796255			−0.398127	+	0.917330i	$0.630340\pi$
$830$	−0.131022	+	0.798742i	−0.00454785	+	0.0277248i
$831$		0			0
$832$	−17.7446	+	36.5540i	−0.615184	+	1.26728i
$833$	−10.7405	+	6.20100i	−0.372135	+	0.214852i
$834$		0			0
$835$	19.2472	+	11.1124i	0.666076	+	0.384559i
$836$	10.2106	+	11.5944i	0.353142	+	0.401001i
$837$		0			0
$838$	−13.1680	−	34.8769i	−0.454882	−	1.20480i
$839$	−9.11048	+	15.7798i	−0.314529	+	0.544780i	−0.979337	−	0.202234i	$-0.935180\pi$
$839$	−9.11048	+	15.7798i	−0.314529	+	0.544780i	0.664808	+	0.747014i	$0.268513\pi$
$840$		0			0
$841$	1.14335	+	1.98034i	0.0394259	+	0.0682877i
$842$	−15.3718	+	18.7702i	−0.529746	+	0.646864i
$843$		0			0
$844$	54.2216	−	10.9023i	1.86638	−	0.375271i
$845$			12.7979i			0.440263i
$846$		0			0
$847$		−	2.10248i		−	0.0722422i
$848$	22.8305	−	30.0102i	0.784003	−	1.03055i
$849$		0			0
$850$	−2.45024	−	2.00661i	−0.0840425	−	0.0688262i
$851$	36.0299	+	62.4057i	1.23509	+	2.13924i
$852$		0			0
$853$	0.975478	−	1.68958i	0.0333997	−	0.0578500i	−0.848842	−	0.528646i	$-0.822700\pi$
$853$	0.975478	−	1.68958i	0.0333997	−	0.0578500i	0.882242	+	0.470796i	$0.156033\pi$
$854$	−4.25201	+	1.60538i	−0.145501	+	0.0549349i
$855$		0			0
$856$	−45.7275	−	24.2593i	−1.56293	−	0.829166i
$857$	−11.2785	−	6.51166i	−0.385267	−	0.222434i	0.294840	−	0.955546i	$-0.404733\pi$
$857$	−11.2785	−	6.51166i	−0.385267	−	0.222434i	−0.680107	+	0.733113i	$0.738067\pi$
$858$		0			0
$859$	3.50034	−	2.02092i	0.119430	−	0.0689530i	−0.439095	−	0.898441i	$-0.644701\pi$
$859$	3.50034	−	2.02092i	0.119430	−	0.0689530i	0.558525	+	0.829488i	$0.311367\pi$
$860$	8.18689	+	2.76015i	0.279171	+	0.0941205i
$861$		0			0
$862$	−17.5585	−	2.88022i	−0.598044	−	0.0981006i
$863$	10.6258			0.361705			0.180853	−	0.983510i	$-0.442114\pi$
$863$	10.6258			0.361705			0.180853	+	0.983510i	$0.442114\pi$
$864$		0			0
$865$	15.4106			0.523978
$866$	−16.3885	−	2.68830i	−0.556903	−	0.0913521i
$867$		0			0
$868$	7.50836	+	2.53139i	0.254850	+	0.0859211i
$869$	9.93523	−	5.73611i	0.337030	−	0.194584i
$870$		0			0
$871$	−63.4174	−	36.6140i	−2.14882	−	1.24062i
$872$	−25.6327	−	13.5986i	−0.868034	−	0.460508i
$873$		0			0
$874$	23.3788	−	8.82684i	0.790799	−	0.298572i
$875$	−0.604565	+	1.04714i	−0.0204380	+	0.0353997i
$876$		0			0
$877$	26.5530	+	45.9911i	0.896631	+	1.55301i	0.831774	+	0.555115i	$0.187326\pi$
$877$	26.5530	+	45.9911i	0.896631	+	1.55301i	0.0648570	+	0.997895i	$0.479341\pi$
$878$	1.84125	+	1.50788i	0.0621392	+	0.0508886i
$879$		0			0
$880$	7.37026	−	9.68803i	0.248451	−	0.326583i
$881$			10.8244i			0.364685i	0.983235	+	0.182342i	$0.0583679\pi$
$881$			10.8244i			0.364685i	−0.983235	+	0.182342i	$0.941632\pi$
$882$		0			0
$883$			21.6083i			0.727178i	0.931559	+	0.363589i	$0.118449\pi$
$883$			21.6083i			0.727178i	−0.931559	+	0.363589i	$0.881551\pi$
$884$	22.3026	−	4.48435i	0.750117	−	0.150825i
$885$		0			0
$886$	0.680108	−	0.830468i	0.0228487	−	0.0279001i
$887$	−0.264026	−	0.457306i	−0.00886511	−	0.0153548i	0.861559	−	0.507658i	$-0.169489\pi$
$887$	−0.264026	−	0.457306i	−0.00886511	−	0.0153548i	−0.870424	+	0.492303i	$0.836155\pi$
$888$		0			0
$889$	5.69025	−	9.85580i	0.190845	−	0.330553i
$890$	−1.19951	−	3.17703i	−0.0402078	−	0.106494i
$891$		0			0
$892$	31.6537	+	35.9435i	1.05984	+	1.20348i
$893$	−22.6454	−	13.0743i	−0.757798	−	0.437515i
$894$		0			0
$895$	11.1049	−	6.41143i	0.371196	−	0.214310i
$896$	1.24201	−	13.6233i	0.0414928	−	0.455121i
$897$		0			0
$898$	3.99649	−	24.3635i	0.133365	−	0.813021i
$899$	−18.3273			−0.611251
$900$		0			0
$901$	−21.1108			−0.703302
$902$	−2.97808	+	18.1551i	−0.0991592	+	0.604497i
$903$		0			0
$904$	−17.3402	+	0.621656i	−0.576726	+	0.0206760i
$905$	15.0384	−	8.68243i	0.499894	−	0.288614i
$906$		0			0
$907$	40.9884	+	23.6647i	1.36100	+	0.785773i	0.989757	−	0.142763i	$-0.0455988\pi$
$907$	40.9884	+	23.6647i	1.36100	+	0.785773i	0.371242	+	0.928536i	$0.378932\pi$
$908$	−10.3859	+	9.14635i	−0.344668	+	0.303532i
$909$		0			0
$910$	−3.06779	−	8.12537i	−0.101696	−	0.269353i
$911$	18.8160	−	32.5902i	0.623401	−	1.07976i	−0.365447	−	0.930832i	$-0.619084\pi$
$911$	18.8160	−	32.5902i	0.623401	−	1.07976i	0.988848	−	0.148930i	$-0.0475829\pi$
$912$		0			0
$913$	0.870884	+	1.50841i	0.0288220	+	0.0499213i
$914$	31.2392	−	38.1456i	1.03330	−	1.26174i
$915$		0			0
$916$	6.03859	+	30.0324i	0.199520	+	0.992299i
$917$		−	2.57860i		−	0.0851528i
$918$		0			0
$919$		−	42.9157i		−	1.41566i	−0.706383	−	0.707830i	$-0.749674\pi$
$919$		−	42.9157i		−	1.41566i	0.706383	−	0.707830i	$-0.250326\pi$
$920$	−10.4494	−	16.6881i	−0.344507	−	0.550190i
$921$		0			0
$922$	−34.2261	−	28.0293i	−1.12718	−	0.923095i
$923$	8.87083	+	15.3647i	0.291987	+	0.505736i
$924$		0			0
$925$	−5.17572	+	8.96460i	−0.170176	+	0.294754i
$926$	−13.6046	+	5.13652i	−0.447075	+	0.168797i
$927$		0			0
$928$	7.34464	+	30.7771i	0.241100	+	1.01031i
$929$	25.1609	+	14.5267i	0.825503	+	0.476605i	0.852311	−	0.523036i	$-0.175201\pi$
$929$	25.1609	+	14.5267i	0.825503	+	0.476605i	−0.0268072	+	0.999641i	$0.508534\pi$
$930$		0			0
$931$	12.1741	−	7.02870i	0.398989	−	0.230356i
$932$	4.22378	−	12.5282i	0.138355	−	0.410373i
$933$		0			0
$934$	4.05529	+	0.665213i	0.132693	+	0.0217665i
$935$	−6.81509			−0.222877
$936$		0			0
$937$	51.0143			1.66656			0.833282	−	0.552848i	$-0.186459\pi$
$937$	51.0143			1.66656			0.833282	+	0.552848i	$0.186459\pi$
$938$	24.3281	+	3.99067i	0.794339	+	0.130300i
$939$		0			0
$940$	−6.58210	+	19.5231i	−0.214684	+	0.636775i
$941$	−7.54730	+	4.35743i	−0.246035	+	0.142048i	−0.617947	−	0.786220i	$-0.712036\pi$
$941$	−7.54730	+	4.35743i	−0.246035	+	0.142048i	0.371912	+	0.928268i	$0.378702\pi$
$942$		0			0
$943$	25.7715	+	14.8792i	0.839235	+	0.484532i
$944$	4.51382	−	35.4203i	0.146912	−	1.15283i
$945$		0			0
$946$	17.3931	−	6.56689i	0.565498	−	0.213508i
$947$	19.0803	−	33.0481i	0.620028	−	1.07392i	−0.369452	−	0.929250i	$-0.620455\pi$
$947$	19.0803	−	33.0481i	0.620028	−	1.07392i	0.989480	−	0.144670i	$-0.0462120\pi$
$948$		0			0
$949$	12.9532	+	22.4356i	0.420478	+	0.728290i
$950$	2.77729	+	2.27445i	0.0901071	+	0.0737928i
$951$		0			0
$952$	−6.49120	+	4.06454i	−0.210381	+	0.131732i
$953$		−	40.4395i		−	1.30996i	−0.755645	−	0.654982i	$-0.772676\pi$
$953$		−	40.4395i		−	1.30996i	0.755645	−	0.654982i	$-0.227324\pi$
$954$		0			0
$955$		−	17.8286i		−	0.576920i
$956$	3.24118	+	16.1198i	0.104827	+	0.521350i
$957$		0			0
$958$	16.8951	−	20.6303i	0.545857	−	0.666536i
$959$	9.96739	+	17.2640i	0.321864	+	0.557485i
$960$		0			0
$961$	−10.1320	+	17.5492i	−0.326840	+	0.566104i
$962$	−26.2636	−	69.5617i	−0.846771	−	2.24276i
$963$		0			0
$964$	−21.9371	+	19.3189i	−0.706546	+	0.622220i
$965$	4.22934	+	2.44181i	0.136147	+	0.0786046i
$966$		0			0
$967$	14.5754	−	8.41511i	0.468713	−	0.270612i	−0.246988	−	0.969019i	$-0.579441\pi$
$967$	14.5754	−	8.41511i	0.468713	−	0.270612i	0.715701	+	0.698407i	$0.246107\pi$
$968$	0.176206	+	4.91502i	0.00566349	+	0.157975i
$969$		0			0
$970$	2.66720	−	16.2599i	0.0856386	−	0.522073i
$971$	34.0951			1.09416			0.547082	−	0.837079i	$-0.315738\pi$
$971$	34.0951			1.09416			0.547082	+	0.837079i	$0.315738\pi$
$972$		0			0
$973$	−24.3044			−0.779163
$974$	−2.64854	+	16.1461i	−0.0848646	+	0.517354i
$975$		0			0
$976$	9.80546	−	4.10928i	0.313865	−	0.131535i
$977$	−0.748148	+	0.431943i	−0.0239354	+	0.0138191i	−0.511920	−	0.859033i	$-0.671066\pi$
$977$	−0.748148	+	0.431943i	−0.0239354	+	0.0138191i	0.487985	+	0.872852i	$0.337732\pi$
$978$		0			0
$979$	−6.32860	−	3.65382i	−0.202263	−	0.116777i
$980$	−7.32017	−	8.31222i	−0.233834	−	0.265524i
$981$		0			0
$982$	−0.746913	−	1.97828i	−0.0238349	−	0.0631293i
$983$	−18.4107	+	31.8882i	−0.587209	+	1.01708i	0.407387	+	0.913256i	$0.366440\pi$
$983$	−18.4107	+	31.8882i	−0.587209	+	1.01708i	−0.994596	+	0.103821i	$0.966893\pi$
$984$		0			0
$985$	−8.40863	−	14.5642i	−0.267921	−	0.464053i
$986$	11.2239	−	13.7053i	0.357441	−	0.436465i
$987$		0			0
$988$	−25.2795	+	5.08291i	−0.804247	+	0.161709i
$989$		−	30.0718i		−	0.956227i
$990$		0			0
$991$		−	35.9773i		−	1.14286i	−0.820652	−	0.571428i	$-0.806390\pi$
$991$		−	35.9773i		−	1.14286i	0.820652	−	0.571428i	$-0.193610\pi$
$992$	−17.7646	−	5.28843i	−0.564027	−	0.167908i
$993$		0			0
$994$	−4.62109	−	3.78442i	−0.146572	−	0.120035i
$995$	2.95746	+	5.12247i	0.0937577	+	0.162393i
$996$		0			0
$997$	16.7322	−	28.9811i	0.529915	−	0.917840i	−0.469476	−	0.882945i	$-0.655557\pi$
$997$	16.7322	−	28.9811i	0.529915	−	0.917840i	0.999391	−	0.0348944i	$-0.0111095\pi$
$998$	−41.6478	+	15.7244i	−1.31834	+	0.497748i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	540.2.q.a.251.24		48
3.2	odd	2		180.2.q.a.11.1	✓	48
4.3	odd	2	inner	540.2.q.a.251.17		48
9.2	odd	6		1620.2.e.b.971.32		48
9.4	even	3		180.2.q.a.131.8	yes	48
9.5	odd	6	inner	540.2.q.a.71.17		48
9.7	even	3		1620.2.e.b.971.17		48
12.11	even	2		180.2.q.a.11.8	yes	48
15.2	even	4		900.2.o.c.299.14		48
15.8	even	4		900.2.o.b.299.11		48
15.14	odd	2		900.2.r.f.551.24		48
36.7	odd	6		1620.2.e.b.971.31		48
36.11	even	6		1620.2.e.b.971.18		48
36.23	even	6	inner	540.2.q.a.71.24		48
36.31	odd	6		180.2.q.a.131.1	yes	48
45.4	even	6		900.2.r.f.851.17		48
45.13	odd	12		900.2.o.c.599.19		48
45.22	odd	12		900.2.o.b.599.6		48
60.23	odd	4		900.2.o.b.299.6		48
60.47	odd	4		900.2.o.c.299.19		48
60.59	even	2		900.2.r.f.551.17		48
180.67	even	12		900.2.o.b.599.11		48
180.103	even	12		900.2.o.c.599.14		48
180.139	odd	6		900.2.r.f.851.24		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
180.2.q.a.11.1	✓	48	3.2	odd	2
180.2.q.a.11.8	yes	48	12.11	even	2
180.2.q.a.131.1	yes	48	36.31	odd	6
180.2.q.a.131.8	yes	48	9.4	even	3
540.2.q.a.71.17		48	9.5	odd	6	inner
540.2.q.a.71.24		48	36.23	even	6	inner
540.2.q.a.251.17		48	4.3	odd	2	inner
540.2.q.a.251.24		48	1.1	even	1	trivial
900.2.o.b.299.6		48	60.23	odd	4
900.2.o.b.299.11		48	15.8	even	4
900.2.o.b.599.6		48	45.22	odd	12
900.2.o.b.599.11		48	180.67	even	12
900.2.o.c.299.14		48	15.2	even	4
900.2.o.c.299.19		48	60.47	odd	4
900.2.o.c.599.14		48	180.103	even	12
900.2.o.c.599.19		48	45.13	odd	12
900.2.r.f.551.17		48	60.59	even	2
900.2.r.f.551.24		48	15.14	odd	2
900.2.r.f.851.17		48	45.4	even	6
900.2.r.f.851.24		48	180.139	odd	6
1620.2.e.b.971.17		48	9.7	even	3
1620.2.e.b.971.18		48	36.11	even	6
1620.2.e.b.971.31		48	36.7	odd	6
1620.2.e.b.971.32		48	9.2	odd	6

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:	\( N \)	\(=\)	\( 540 = 2^{2} \cdot 3^{3} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	540.q (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.39556 + 0.228922i) q^{2} +(1.89519 + 0.638951i) q^{4} +(0.866025 - 0.500000i) q^{5} +(-1.04714 - 0.604565i) q^{7} +(2.49858 + 1.32555i) q^{8} +(1.32305 - 0.499529i) q^{10} +(1.52161 - 2.63550i) q^{11} +(2.53958 + 4.39869i) q^{13} +(-1.32295 - 1.08342i) q^{14} +(3.18348 + 2.42186i) q^{16} -2.23944i q^{17} +2.53835i q^{19} +(1.96076 - 0.394247i) q^{20} +(2.72682 - 3.32968i) q^{22} +(-3.48067 - 6.02870i) q^{23} +(0.500000 - 0.866025i) q^{25} +(2.53719 + 6.72001i) q^{26} +(-1.59824 - 1.81484i) q^{28} +(4.84407 + 2.79673i) q^{29} +(-2.83759 + 1.63828i) q^{31} +(3.88833 + 4.10863i) q^{32} +(0.512657 - 3.12527i) q^{34} -1.20913 q^{35} -10.3514 q^{37} +(-0.581085 + 3.54243i) q^{38} +(2.82661 - 0.101336i) q^{40} +(-3.70208 + 2.13740i) q^{41} +(3.74108 + 2.15991i) q^{43} +(4.56769 - 4.02254i) q^{44} +(-3.47739 - 9.21023i) q^{46} +(-5.15071 + 8.92129i) q^{47} +(-2.76900 - 4.79605i) q^{49} +(0.896034 - 1.09413i) q^{50} +(2.00245 + 9.95902i) q^{52} -9.42683i q^{53} -3.04322i q^{55} +(-1.81498 - 2.89859i) q^{56} +(6.11997 + 5.01192i) q^{58} +(-4.46335 - 7.73074i) q^{59} +(1.32896 - 2.30183i) q^{61} +(-4.33508 + 1.63674i) q^{62} +(4.48585 + 6.62398i) q^{64} +(4.39869 + 2.53958i) q^{65} +(-12.4858 + 7.20867i) q^{67} +(1.43089 - 4.24416i) q^{68} +(-1.68742 - 0.276797i) q^{70} +3.49303 q^{71} +5.10052 q^{73} +(-14.4461 - 2.36967i) q^{74} +(-1.62188 + 4.81065i) q^{76} +(-3.18667 + 1.83982i) q^{77} +(3.26472 + 1.88488i) q^{79} +(3.96791 + 0.505654i) q^{80} +(-5.65579 + 2.13538i) q^{82} +(-0.286172 + 0.495665i) q^{83} +(-1.11972 - 1.93941i) q^{85} +(4.72646 + 3.87071i) q^{86} +(7.29535 - 4.56806i) q^{88} -2.40129i q^{89} -6.14138i q^{91} +(-2.74449 - 13.6495i) q^{92} +(-9.23042 + 11.2711i) q^{94} +(1.26918 + 2.19828i) q^{95} +(5.82556 - 10.0902i) q^{97} +(-2.76639 - 7.32708i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 30 q^{14} + 24 q^{25} + 12 q^{29} - 6 q^{34} - 60 q^{38} - 6 q^{40} + 60 q^{41} - 12 q^{46} + 24 q^{49} - 18 q^{52} + 42 q^{56} - 18 q^{58} - 48 q^{64} - 48 q^{68} - 24 q^{73} - 84 q^{74} + 6 q^{76}+ \cdots - 12 q^{97}+O(q^{100}) \) 48 * q + 30 * q^14 + 24 * q^25 + 12 * q^29 - 6 * q^34 - 60 * q^38 - 6 * q^40 + 60 * q^41 - 12 * q^46 + 24 * q^49 - 18 * q^52 + 42 * q^56 - 18 * q^58 - 48 * q^64 - 48 * q^68 - 24 * q^73 - 84 * q^74 + 6 * q^76 - 48 * q^77 - 36 * q^82 + 54 * q^86 - 60 * q^92 + 18 * q^94 - 12 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more