LMFDB - Embedded newform 288.4.p.b.239.11

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [288,4,Mod(47,288)] 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("288.47"); S:= CuspForms(chi, 4); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(288, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([3, 3, 1])) N = Newforms(chi, 4, names="a")

Level:	$ N $	$=$	$ 288 = 2^{5} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	288.p (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [64] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$16.9925500817$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$32$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 72)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			239.11
Character	$\chi$	$=$	288.239
Dual form			288.4.p.b.47.11

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.93713 - 4.28640i) q^{3} +(-3.52304 + 6.10209i) q^{5} +(16.9049 - 9.76005i) q^{7} +(-9.74649 + 25.1795i) q^{9} +(-11.8232 + 6.82610i) q^{11} +(-55.8938 - 32.2703i) q^{13} +(36.5037 - 2.82147i) q^{15} +47.8376i q^{17} -14.9265 q^{19} +(-91.4874 - 43.7946i) q^{21} +(-25.1060 + 43.4848i) q^{23} +(37.6763 + 65.2573i) q^{25} +(136.556 - 32.1781i) q^{27} +(129.302 + 223.957i) q^{29} +(-108.559 - 62.6768i) q^{31} +(63.9856 + 30.6296i) q^{33} +137.540i q^{35} +208.987i q^{37} +(25.8441 + 334.365i) q^{39} +(411.520 + 237.591i) q^{41} +(178.732 + 309.573i) q^{43} +(-119.310 - 148.182i) q^{45} +(-156.128 - 270.422i) q^{47} +(19.0170 - 32.9384i) q^{49} +(205.051 - 140.506i) q^{51} -476.697 q^{53} -96.1946i q^{55} +(43.8413 + 63.9812i) q^{57} +(425.920 + 245.905i) q^{59} +(661.465 - 381.897i) q^{61} +(80.9894 + 520.783i) q^{63} +(393.832 - 227.379i) q^{65} +(-277.112 + 479.972i) q^{67} +(260.133 - 20.1064i) q^{69} -87.1038 q^{71} -818.083 q^{73} +(169.059 - 353.165i) q^{75} +(-133.246 + 230.789i) q^{77} +(-1030.34 + 594.866i) q^{79} +(-539.012 - 490.823i) q^{81} +(-400.564 + 231.266i) q^{83} +(-291.910 - 168.534i) q^{85} +(580.194 - 1212.03i) q^{87} +1047.78i q^{89} -1259.84 q^{91} +(50.1955 + 649.419i) q^{93} +(52.5869 - 91.0831i) q^{95} +(-562.907 - 974.983i) q^{97} +(-56.6434 - 364.231i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q - 6 q^{3} + 42 q^{9} - 48 q^{11} + 220 q^{19} - 902 q^{25} + 252 q^{27} - 660 q^{33} + 1620 q^{41} + 292 q^{43} + 1762 q^{49} + 1794 q^{51} - 294 q^{57} - 5592 q^{59} - 6 q^{65} - 68 q^{67} - 868 q^{73}+ \cdots + 2118 q^{99}+O(q^{100}) $ 64 * q - 6 * q^3 + 42 * q^9 - 48 * q^11 + 220 * q^19 - 902 * q^25 + 252 * q^27 - 660 * q^33 + 1620 * q^41 + 292 * q^43 + 1762 * q^49 + 1794 * q^51 - 294 * q^57 - 5592 * q^59 - 6 * q^65 - 68 * q^67 - 868 * q^73 + 4254 * q^75 + 498 * q^81 - 3654 * q^83 + 1380 * q^91 - 1912 * q^97 + 2118 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/288\mathbb{Z}\right)^\times$.

$n$	$37$	$65$	$127$
$\chi(n)$	$-1$	$e\left(\frac{5}{6}\right)$	$-1$

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			0
$2$		0			0
$3$	−2.93713	−	4.28640i	−0.565252	−	0.824919i
$3$	−2.93713	−	4.28640i	−0.565252	−	0.824919i
$4$		0			0
$5$	−3.52304	+	6.10209i	−0.315111	+	0.545788i	−0.979461	−	0.201634i	$-0.935375\pi$
$5$	−3.52304	+	6.10209i	−0.315111	+	0.545788i	0.664350	+	0.747421i	$0.268708\pi$
$6$		0			0
$7$	16.9049	−	9.76005i	0.912779	−	0.526993i	0.0314545	−	0.999505i	$-0.489986\pi$
$7$	16.9049	−	9.76005i	0.912779	−	0.526993i	0.881324	+	0.472512i	$0.156653\pi$
$8$		0			0
$9$	−9.74649	+	25.1795i	−0.360981	+	0.932573i
$10$		0			0
$11$	−11.8232	+	6.82610i	−0.324074	+	0.187104i	−0.653207	−	0.757179i	$-0.726577\pi$
$11$	−11.8232	+	6.82610i	−0.324074	+	0.187104i	0.329133	+	0.944284i	$0.393244\pi$
$12$		0			0
$13$	−55.8938	−	32.2703i	−1.19247	−	0.688474i	−0.233606	−	0.972331i	$-0.575053\pi$
$13$	−55.8938	−	32.2703i	−1.19247	−	0.688474i	−0.958867	+	0.283857i	$0.908386\pi$
$14$		0			0
$15$	36.5037	−	2.82147i	0.628347	−	0.0485668i
$16$		0			0
$17$			47.8376i			0.682490i	0.939974	+	0.341245i	$0.110849\pi$
$17$			47.8376i			0.682490i	−0.939974	+	0.341245i	$0.889151\pi$
$18$		0			0
$19$	−14.9265			−0.180231			−0.0901154	−	0.995931i	$-0.528724\pi$
$19$	−14.9265			−0.180231			−0.0901154	+	0.995931i	$0.528724\pi$
$20$		0			0
$21$	−91.4874	−	43.7946i	−0.950676	−	0.455084i
$22$		0			0
$23$	−25.1060	+	43.4848i	−0.227607	+	0.394226i	−0.957098	−	0.289763i	$-0.906423\pi$
$23$	−25.1060	+	43.4848i	−0.227607	+	0.394226i	0.729492	+	0.683990i	$0.239757\pi$
$24$		0			0
$25$	37.6763	+	65.2573i	0.301411	+	0.522058i
$26$		0			0
$27$	136.556	−	32.1781i	0.973342	−	0.229359i
$28$		0			0
$29$	129.302	+	223.957i	0.827956	+	1.43406i	0.899639	+	0.436635i	$0.143830\pi$
$29$	129.302	+	223.957i	0.827956	+	1.43406i	−0.0716823	+	0.997428i	$0.522837\pi$
$30$		0			0
$31$	−108.559	−	62.6768i	−0.628962	−	0.363132i	0.151388	−	0.988474i	$-0.451626\pi$
$31$	−108.559	−	62.6768i	−0.628962	−	0.363132i	−0.780350	+	0.625343i	$0.784959\pi$
$32$		0			0
$33$	63.9856	+	30.6296i	0.337529	+	0.161574i
$34$		0			0
$35$			137.540i			0.664244i
$36$		0			0
$37$			208.987i			0.928576i	0.885684	+	0.464288i	$0.153690\pi$
$37$			208.987i			0.928576i	−0.885684	+	0.464288i	$0.846310\pi$
$38$		0			0
$39$	25.8441	+	334.365i	0.106112	+	1.37285i
$40$		0			0
$41$	411.520	+	237.591i	1.56753	+	0.905013i	0.996456	+	0.0841137i	$0.0268059\pi$
$41$	411.520	+	237.591i	1.56753	+	0.905013i	0.571073	+	0.820900i	$0.306527\pi$
$42$		0			0
$43$	178.732	+	309.573i	0.633870	+	1.09789i	0.986753	+	0.162228i	$0.0518679\pi$
$43$	178.732	+	309.573i	0.633870	+	1.09789i	−0.352884	+	0.935667i	$0.614799\pi$
$44$		0			0
$45$	−119.310	−	148.182i	−0.395238	−	0.490883i
$46$		0			0
$47$	−156.128	−	270.422i	−0.484545	−	0.839256i	0.515297	−	0.857011i	$-0.327681\pi$
$47$	−156.128	−	270.422i	−0.484545	−	0.839256i	−0.999842	+	0.0177550i	$0.994348\pi$
$48$		0			0
$49$	19.0170	−	32.9384i	0.0554431	−	0.0960303i
$50$		0			0
$51$	205.051	−	140.506i	0.562999	−	0.385779i
$52$		0			0
$53$	−476.697			−1.23546			−0.617729	−	0.786391i	$-0.711947\pi$
$53$	−476.697			−1.23546			−0.617729	+	0.786391i	$0.711947\pi$
$54$		0			0
$55$		−	96.1946i		−	0.235834i
$56$		0			0
$57$	43.8413	+	63.9812i	0.101876	+	0.148676i
$58$		0			0
$59$	425.920	+	245.905i	0.939831	+	0.542612i	0.889907	−	0.456141i	$-0.150769\pi$
$59$	425.920	+	245.905i	0.939831	+	0.542612i	0.0499237	+	0.998753i	$0.484102\pi$
$60$		0			0
$61$	661.465	−	381.897i	1.38839	−	0.801589i	0.395259	−	0.918570i	$-0.370655\pi$
$61$	661.465	−	381.897i	1.38839	−	0.801589i	0.993134	+	0.116981i	$0.0373216\pi$
$62$		0			0
$63$	80.9894	+	520.783i	0.161964	+	1.04147i
$64$		0			0
$65$	393.832	−	227.379i	0.751521	−	0.433891i
$66$		0			0
$67$	−277.112	+	479.972i	−0.505293	+	0.875193i	0.494688	+	0.869071i	$0.335282\pi$
$67$	−277.112	+	479.972i	−0.505293	+	0.875193i	−0.999981	+	0.00612269i	$0.998051\pi$
$68$		0			0
$69$	260.133	−	20.1064i	0.453860	−	0.0350801i
$70$		0			0
$71$	−87.1038			−0.145596			−0.0727980	−	0.997347i	$-0.523193\pi$
$71$	−87.1038			−0.145596			−0.0727980	+	0.997347i	$0.523193\pi$
$72$		0			0
$73$	−818.083			−1.31164			−0.655818	−	0.754919i	$-0.727676\pi$
$73$	−818.083			−1.31164			−0.655818	+	0.754919i	$0.727676\pi$
$74$		0			0
$75$	169.059	−	353.165i	0.260283	−	0.543734i
$76$		0			0
$77$	−133.246	+	230.789i	−0.197205	+	0.341569i
$78$		0			0
$79$	−1030.34	+	594.866i	−1.46737	+	0.847186i	−0.999333	−	0.0365241i	$-0.988371\pi$
$79$	−1030.34	+	594.866i	−1.46737	+	0.847186i	−0.468036	+	0.883710i	$0.655038\pi$
$80$		0			0
$81$	−539.012	−	490.823i	−0.739385	−	0.673283i
$82$		0			0
$83$	−400.564	+	231.266i	−0.529730	+	0.305840i	−0.740907	−	0.671608i	$-0.765604\pi$
$83$	−400.564	+	231.266i	−0.529730	+	0.305840i	0.211176	+	0.977448i	$0.432271\pi$
$84$		0			0
$85$	−291.910	−	168.534i	−0.372495	−	0.215060i
$86$		0			0
$87$	580.194	−	1212.03i	0.714981	−	1.49360i
$88$		0			0
$89$			1047.78i			1.24791i	0.781459	+	0.623956i	$0.214476\pi$
$89$			1047.78i			1.24791i	−0.781459	+	0.623956i	$0.785524\pi$
$90$		0			0
$91$	−1259.84			−1.45128
$92$		0			0
$93$	50.1955	+	649.419i	0.0559680	+	0.724103i
$94$		0			0
$95$	52.5869	−	91.0831i	0.0567926	−	0.0983677i
$96$		0			0
$97$	−562.907	−	974.983i	−0.589222	−	1.02056i	−0.994335	−	0.106296i	$-0.966101\pi$
$97$	−562.907	−	974.983i	−0.589222	−	1.02056i	0.405113	−	0.914267i	$-0.367232\pi$
$98$		0			0
$99$	−56.6434	−	364.231i	−0.0575038	−	0.369764i
$100$		0			0
$101$	312.444	+	541.170i	0.307816	+	0.533152i	0.977884	−	0.209147i	$-0.0670687\pi$
$101$	312.444	+	541.170i	0.307816	+	0.533152i	−0.670069	+	0.742299i	$0.733735\pi$
$102$		0			0
$103$	135.960	+	78.4965i	0.130063	+	0.0750922i	0.563620	−	0.826034i	$-0.309408\pi$
$103$	135.960	+	78.4965i	0.130063	+	0.0750922i	−0.433557	+	0.901126i	$0.642742\pi$
$104$		0			0
$105$	589.553	−	403.974i	0.547947	−	0.375465i
$106$		0			0
$107$		−	420.449i		−	0.379872i	−0.981796	−	0.189936i	$-0.939172\pi$
$107$		−	420.449i		−	0.379872i	0.981796	−	0.189936i	$-0.0608280\pi$
$108$		0			0
$109$		−	1217.23i		−	1.06963i	−0.844969	−	0.534815i	$-0.820381\pi$
$109$		−	1217.23i		−	1.06963i	0.844969	−	0.534815i	$-0.179619\pi$
$110$		0			0
$111$	895.803	−	613.824i	0.765999	−	0.524879i
$112$		0			0
$113$	303.893	+	175.453i	0.252990	+	0.146064i	0.621132	−	0.783706i	$-0.286673\pi$
$113$	303.893	+	175.453i	0.252990	+	0.146064i	−0.368143	+	0.929769i	$0.620006\pi$
$114$		0			0
$115$	−176.899	−	306.398i	−0.143443	−	0.248450i
$116$		0			0
$117$	1357.32	−	1092.85i	1.07251	−	0.863542i
$118$		0			0
$119$	466.897	+	808.690i	0.359667	+	0.622962i
$120$		0			0
$121$	−572.309	+	991.268i	−0.429984	+	0.744754i
$122$		0			0
$123$	−190.278	−	2461.78i	−0.139486	−	1.80464i
$124$		0			0
$125$	−1411.70			−1.01013
$126$		0			0
$127$		−	2003.55i		−	1.39989i	−0.714195	−	0.699947i	$-0.753207\pi$
$127$		−	2003.55i		−	1.39989i	0.714195	−	0.699947i	$-0.246793\pi$
$128$		0			0
$129$	801.995	−	1675.38i	0.547378	−	1.14348i
$130$		0			0
$131$	967.023	+	558.311i	0.644956	+	0.372365i	0.786521	−	0.617564i	$-0.211880\pi$
$131$	967.023	+	558.311i	0.644956	+	0.372365i	−0.141565	+	0.989929i	$0.545214\pi$
$132$		0			0
$133$	−252.332	+	145.684i	−0.164511	+	0.0949803i
$134$		0			0
$135$	−284.739	+	946.643i	−0.181529	+	0.603511i
$136$		0			0
$137$	562.186	−	324.578i	0.350590	−	0.202413i	−0.314355	−	0.949305i	$-0.601788\pi$
$137$	562.186	−	324.578i	0.350590	−	0.202413i	0.664945	+	0.746892i	$0.268455\pi$
$138$		0			0
$139$	535.022	−	926.685i	0.326475	−	0.565471i	−0.655335	−	0.755338i	$-0.727473\pi$
$139$	535.022	−	926.685i	0.326475	−	0.565471i	0.981810	+	0.189868i	$0.0608059\pi$
$140$		0			0
$141$	−700.567	+	1463.49i	−0.418428	+	0.874101i
$142$		0			0
$143$	881.121			0.515266
$144$		0			0
$145$	−1822.14			−1.04359
$146$		0			0
$147$	−197.043	+	15.2300i	−0.110557	+	0.00854523i
$148$		0			0
$149$	296.044	−	512.764i	0.162771	−	0.281928i	−0.773090	−	0.634296i	$-0.781290\pi$
$149$	296.044	−	512.764i	0.162771	−	0.281928i	0.935862	+	0.352368i	$0.114623\pi$
$150$		0			0
$151$	1813.60	−	1047.08i	0.977411	−	0.564308i	0.0759232	−	0.997114i	$-0.475810\pi$
$151$	1813.60	−	1047.08i	0.977411	−	0.564308i	0.901487	+	0.432805i	$0.142476\pi$
$152$		0			0
$153$	−1204.53	−	466.249i	−0.636472	−	0.246366i
$154$		0			0
$155$	764.918	−	441.626i	0.396385	−	0.228853i
$156$		0			0
$157$	−122.949	−	70.9848i	−0.0624995	−	0.0360841i	0.468425	−	0.883503i	$-0.344822\pi$
$157$	−122.949	−	70.9848i	−0.0624995	−	0.0360841i	−0.530924	+	0.847419i	$0.678155\pi$
$158$		0			0
$159$	1400.12	+	2043.31i	0.698345	+	1.01915i
$160$		0			0
$161$			980.141i			0.479789i
$162$		0			0
$163$	−3642.04			−1.75010			−0.875051	−	0.484031i	$-0.839172\pi$
$163$	−3642.04			−1.75010			−0.875051	+	0.484031i	$0.839172\pi$
$164$		0			0
$165$	−412.329	+	282.536i	−0.194544	+	0.133306i
$166$		0			0
$167$	−1424.28	+	2466.93i	−0.659966	+	1.14310i	0.320657	+	0.947195i	$0.396096\pi$
$167$	−1424.28	+	2466.93i	−0.659966	+	1.14310i	−0.980624	+	0.195900i	$0.937237\pi$
$168$		0			0
$169$	984.242	+	1704.76i	0.447994	+	0.775948i
$170$		0			0
$171$	145.481	−	375.843i	0.0650599	−	0.168078i
$172$		0			0
$173$	−11.9219	−	20.6493i	−0.00523934	−	0.00907480i	0.863394	−	0.504531i	$-0.168334\pi$
$173$	−11.9219	−	20.6493i	−0.00523934	−	0.00907480i	−0.868633	+	0.495456i	$0.835001\pi$
$174$		0			0
$175$	1273.83	+	735.445i	0.550242	+	0.317683i
$176$		0			0
$177$	−196.936	−	2547.92i	−0.0836306	−	1.08200i
$178$		0			0
$179$			1944.64i			0.812009i	0.913871	+	0.406004i	$0.133078\pi$
$179$			1944.64i			0.812009i	−0.913871	+	0.406004i	$0.866922\pi$
$180$		0			0
$181$		−	27.6647i		−	0.0113608i	−0.999984	−	0.00568039i	$-0.998192\pi$
$181$		−	27.6647i		−	0.0113608i	0.999984	−	0.00568039i	$-0.00180813\pi$
$182$		0			0
$183$	−3579.78	−	1713.62i	−1.44604	−	0.692211i
$184$		0			0
$185$	−1275.26	−	736.271i	−0.506805	−	0.292604i
$186$		0			0
$187$	−326.544	−	565.592i	−0.127697	−	0.221177i
$188$		0			0
$189$	1994.41	−	1876.76i	0.767575	−	0.722298i
$190$		0			0
$191$	−1586.02	−	2747.07i	−0.600840	−	1.04069i	−0.992694	−	0.120658i	$-0.961500\pi$
$191$	−1586.02	−	2747.07i	−0.600840	−	1.04069i	0.391854	−	0.920027i	$-0.371834\pi$
$192$		0			0
$193$	221.041	−	382.854i	0.0824398	−	0.142790i	−0.821858	−	0.569693i	$-0.807062\pi$
$193$	221.041	−	382.854i	0.0824398	−	0.142790i	0.904297	+	0.426903i	$0.140395\pi$
$194$		0			0
$195$	−2131.38	−	1020.28i	−0.782724	−	0.374686i
$196$		0			0
$197$	3084.07			1.11539			0.557693	−	0.830047i	$-0.311687\pi$
$197$	3084.07			1.11539			0.557693	+	0.830047i	$0.311687\pi$
$198$		0			0
$199$		−	1784.15i		−	0.635555i	−0.948165	−	0.317777i	$-0.897064\pi$
$199$		−	1784.15i		−	0.635555i	0.948165	−	0.317777i	$-0.102936\pi$
$200$		0			0
$201$	2871.27	−	221.929i	1.00758	−	0.0778788i
$202$		0			0
$203$	4371.67	+	2523.98i	1.51148	+	0.872654i
$204$		0			0
$205$	−2899.61	+	1674.09i	−0.987890	+	0.570359i
$206$		0			0
$207$	−850.229	−	1055.98i	−0.285483	−	0.354568i
$208$		0			0
$209$	176.479	−	101.890i	0.0584081	−	0.0337219i
$210$		0			0
$211$	−734.854	+	1272.80i	−0.239760	+	0.415277i	−0.960645	−	0.277777i	$-0.910402\pi$
$211$	−734.854	+	1272.80i	−0.239760	+	0.415277i	0.720885	+	0.693055i	$0.243736\pi$
$212$		0			0
$213$	255.835	+	373.362i	0.0822984	+	0.120105i
$214$		0			0
$215$	−2518.73			−0.798956
$216$		0			0
$217$	−2446.91			−0.765471
$218$		0			0
$219$	2402.82	+	3506.63i	0.741404	+	1.08199i
$220$		0			0
$221$	1543.73	−	2673.83i	0.469877	−	0.813850i
$222$		0			0
$223$	−1047.05	+	604.513i	−0.314419	+	0.181530i	−0.648902	−	0.760872i	$-0.724772\pi$
$223$	−1047.05	+	604.513i	−0.314419	+	0.181530i	0.334483	+	0.942402i	$0.391438\pi$
$224$		0			0
$225$	−2010.36	+	312.640i	−0.595661	+	0.0926342i
$226$		0			0
$227$	−1946.40	+	1123.76i	−0.569107	+	0.328574i	−0.756793	−	0.653655i	$-0.773235\pi$
$227$	−1946.40	+	1123.76i	−0.569107	+	0.328574i	0.187686	+	0.982229i	$0.439901\pi$
$228$		0			0
$229$	−663.668	−	383.169i	−0.191513	−	0.110570i	0.401178	−	0.916000i	$-0.368601\pi$
$229$	−663.668	−	383.169i	−0.191513	−	0.110570i	−0.592691	+	0.805430i	$0.701934\pi$
$230$		0			0
$231$	1380.62	−	106.712i	0.393238	−	0.0303945i
$232$		0			0
$233$			801.184i			0.225267i	0.993637	+	0.112634i	$0.0359287\pi$
$233$			801.184i			0.225267i	−0.993637	+	0.112634i	$0.964071\pi$
$234$		0			0
$235$	2200.18			0.610741
$236$		0			0
$237$	5576.08	+	2669.24i	1.52829	+	0.731586i
$238$		0			0
$239$	−3032.68	+	5252.75i	−0.820785	+	1.42164i	0.0843128	+	0.996439i	$0.473130\pi$
$239$	−3032.68	+	5252.75i	−0.820785	+	1.42164i	−0.905098	+	0.425203i	$0.860203\pi$
$240$		0			0
$241$	2629.87	+	4555.07i	0.702924	+	1.21750i	0.967435	+	0.253118i	$0.0814560\pi$
$241$	2629.87	+	4555.07i	0.702924	+	1.21750i	−0.264511	+	0.964383i	$0.585211\pi$
$242$		0			0
$243$	−520.715	+	3752.03i	−0.137464	+	0.990507i
$244$		0			0
$245$	133.995	+	232.087i	0.0349414	+	0.0605203i
$246$		0			0
$247$	834.301	+	481.684i	0.214920	+	0.124084i
$248$		0			0
$249$	2167.81	+	1037.72i	0.551724	+	0.264108i
$250$		0			0
$251$		−	2860.56i		−	0.719350i	−0.933078	−	0.359675i	$-0.882888\pi$
$251$		−	2860.56i		−	0.719350i	0.933078	−	0.359675i	$-0.117112\pi$
$252$		0			0
$253$		−	685.503i		−	0.170345i
$254$		0			0
$255$	134.973	+	1746.25i	0.0331463	+	0.428841i
$256$		0			0
$257$	586.357	+	338.534i	0.142319	+	0.0821679i	0.569469	−	0.822013i	$-0.307149\pi$
$257$	586.357	+	338.534i	0.142319	+	0.0821679i	−0.427150	+	0.904181i	$0.640482\pi$
$258$		0			0
$259$	2039.73	+	3532.91i	0.489353	+	0.847584i
$260$		0			0
$261$	−6899.36	+	1072.95i	−1.63624	+	0.254460i
$262$		0			0
$263$	579.488	+	1003.70i	0.135866	+	0.235327i	0.925928	−	0.377700i	$-0.123285\pi$
$263$	579.488	+	1003.70i	0.135866	+	0.235327i	−0.790062	+	0.613027i	$0.789952\pi$
$264$		0			0
$265$	1679.42	−	2908.85i	0.389306	−	0.674298i
$266$		0			0
$267$	4491.20	−	3077.46i	1.02943	−	0.705385i
$268$		0			0
$269$	−7718.35			−1.74943			−0.874714	−	0.484640i	$-0.838951\pi$
$269$	−7718.35			−1.74943			−0.874714	+	0.484640i	$0.838951\pi$
$270$		0			0
$271$			3568.10i			0.799804i	0.916558	+	0.399902i	$0.130956\pi$
$271$			3568.10i			0.799804i	−0.916558	+	0.399902i	$0.869044\pi$
$272$		0			0
$273$	3700.31	+	5400.17i	0.820341	+	1.19719i
$274$		0			0
$275$	−890.906	−	514.365i	−0.195359	−	0.112790i
$276$		0			0
$277$	−4007.48	+	2313.72i	−0.869265	+	0.501870i	−0.867104	−	0.498128i	$-0.834021\pi$
$277$	−4007.48	+	2313.72i	−0.869265	+	0.501870i	−0.00216082	+	0.999998i	$0.500688\pi$
$278$		0			0
$279$	2636.24	−	2122.59i	0.565690	−	0.455470i
$280$		0			0
$281$	2505.78	−	1446.71i	0.531966	−	0.307131i	−0.209851	−	0.977733i	$-0.567298\pi$
$281$	2505.78	−	1446.71i	0.531966	−	0.307131i	0.741817	+	0.670603i	$0.233964\pi$
$282$		0			0
$283$	4140.78	−	7172.04i	0.869766	−	1.50648i	0.00753096	−	0.999972i	$-0.497603\pi$
$283$	4140.78	−	7172.04i	0.869766	−	1.50648i	0.862235	−	0.506508i	$-0.169064\pi$
$284$		0			0
$285$	−544.874	+	42.1149i	−0.113247	+	0.00875323i
$286$		0			0
$287$	9275.61			1.90774
$288$		0			0
$289$	2624.56			0.534207
$290$		0			0
$291$	−2525.84	+	5276.50i	−0.508822	+	1.06293i
$292$		0			0
$293$	−1863.44	+	3227.58i	−0.371548	+	0.643540i	−0.989804	−	0.142437i	$-0.954506\pi$
$293$	−1863.44	+	3227.58i	−0.371548	+	0.643540i	0.618256	+	0.785977i	$0.287840\pi$
$294$		0			0
$295$	−3001.07	+	1732.67i	−0.592301	+	0.341965i
$296$		0			0
$297$	−1394.87	+	1312.59i	−0.272521	+	0.256446i
$298$		0			0
$299$	2806.53	−	1620.35i	0.542830	−	0.313403i
$300$		0			0
$301$	6042.90	+	3488.87i	1.15717	+	0.668090i
$302$		0			0
$303$	1401.98	−	2928.75i	0.265814	−	0.555288i
$304$		0			0
$305$			5381.76i			1.01036i
$306$		0			0
$307$	−1481.74			−0.275464			−0.137732	−	0.990470i	$-0.543981\pi$
$307$	−1481.74			−0.275464			−0.137732	+	0.990470i	$0.543981\pi$
$308$		0			0
$309$	−62.8649	−	813.334i	−0.0115737	−	0.149738i
$310$		0			0
$311$	3974.58	−	6884.18i	0.724688	−	1.25520i	−0.234415	−	0.972137i	$-0.575317\pi$
$311$	3974.58	−	6884.18i	0.724688	−	1.25520i	0.959102	−	0.283059i	$-0.0913492\pi$
$312$		0			0
$313$	1570.79	+	2720.69i	0.283663	+	0.491318i	0.972284	−	0.233803i	$-0.0751170\pi$
$313$	1570.79	+	2720.69i	0.283663	+	0.491318i	−0.688621	+	0.725121i	$0.741784\pi$
$314$		0			0
$315$	−3463.19	−	1340.53i	−0.619456	−	0.239780i
$316$		0			0
$317$	954.296	+	1652.89i	0.169081	+	0.292856i	0.938097	−	0.346373i	$-0.112587\pi$
$317$	954.296	+	1652.89i	0.169081	+	0.292856i	−0.769016	+	0.639229i	$0.779253\pi$
$318$		0			0
$319$	−3057.51	−	1765.25i	−0.536638	−	0.309828i
$320$		0			0
$321$	−1802.21	+	1234.91i	−0.313363	+	0.214723i
$322$		0			0
$323$		−	714.050i		−	0.123006i
$324$		0			0
$325$		−	4863.30i		−	0.830054i
$326$		0			0
$327$	−5217.55	+	3575.18i	−0.882358	+	0.604611i
$328$		0			0
$329$	−5278.65	−	3047.63i	−0.884564	−	0.510703i
$330$		0			0
$331$	3378.13	+	5851.10i	0.560964	+	0.971618i	0.997413	+	0.0718887i	$0.0229026\pi$
$331$	3378.13	+	5851.10i	0.560964	+	0.971618i	−0.436449	+	0.899729i	$0.643764\pi$
$332$		0			0
$333$	−5262.19	−	2036.89i	−0.865965	−	0.335198i
$334$		0			0
$335$	−1952.56	−	3381.93i	−0.318446	−	0.551565i
$336$		0			0
$337$	4901.54	−	8489.71i	0.792296	−	1.37230i	−0.132246	−	0.991217i	$-0.542219\pi$
$337$	4901.54	−	8489.71i	0.792296	−	1.37230i	0.924542	−	0.381080i	$-0.124448\pi$
$338$		0			0
$339$	−140.513	−	1817.93i	−0.0225122	−	0.291259i
$340$		0			0
$341$	1711.35			0.271774
$342$		0			0
$343$			5952.96i			0.937113i
$344$		0			0
$345$	−793.768	+	1658.19i	−0.123870	+	0.258765i
$346$		0			0
$347$	−10649.2	−	6148.32i	−1.64749	−	0.951178i	−0.978066	−	0.208297i	$-0.933208\pi$
$347$	−10649.2	−	6148.32i	−1.64749	−	0.951178i	−0.669424	−	0.742881i	$-0.733459\pi$
$348$		0			0
$349$	6231.13	−	3597.55i	0.955716	−	0.551783i	0.0608642	−	0.998146i	$-0.480614\pi$
$349$	6231.13	−	3597.55i	0.955716	−	0.551783i	0.894852	+	0.446363i	$0.147281\pi$
$350$		0			0
$351$	−8671.03	−	2608.15i	−1.31859	−	0.396617i
$352$		0			0
$353$	−2455.03	+	1417.41i	−0.370164	+	0.213714i	−0.673530	−	0.739160i	$-0.735223\pi$
$353$	−2455.03	+	1417.41i	−0.370164	+	0.213714i	0.303366	+	0.952874i	$0.401889\pi$
$354$		0			0
$355$	306.870	−	531.515i	0.0458789	−	0.0794645i
$356$		0			0
$357$	2095.03	−	4376.54i	0.310590	−	0.648827i
$358$		0			0
$359$	3447.67			0.506856			0.253428	−	0.967354i	$-0.418442\pi$
$359$	3447.67			0.506856			0.253428	+	0.967354i	$0.418442\pi$
$360$		0			0
$361$	−6636.20			−0.967517
$362$		0			0
$363$	5929.92	−	458.341i	0.857411	−	0.0662718i
$364$		0			0
$365$	2882.14	−	4992.02i	0.413310	−	0.715875i
$366$		0			0
$367$	4576.87	−	2642.46i	0.650983	−	0.375845i	−0.137850	−	0.990453i	$-0.544019\pi$
$367$	4576.87	−	2642.46i	0.650983	−	0.375845i	0.788833	+	0.614608i	$0.210686\pi$
$368$		0			0
$369$	−9993.31	+	8046.18i	−1.40984	+	1.13514i
$370$		0			0
$371$	−8058.51	+	4652.58i	−1.12770	+	0.651078i
$372$		0			0
$373$	7902.95	+	4562.77i	1.09705	+	0.633381i	0.935444	−	0.353474i	$-0.115000\pi$
$373$	7902.95	+	4562.77i	1.09705	+	0.633381i	0.161604	+	0.986856i	$0.448333\pi$
$374$		0			0
$375$	4146.36	+	6051.12i	0.570979	+	0.833277i
$376$		0			0
$377$		−	16690.4i		−	2.28011i
$378$		0			0
$379$	1196.44			0.162156			0.0810778	−	0.996708i	$-0.474164\pi$
$379$	1196.44			0.162156			0.0810778	+	0.996708i	$0.474164\pi$
$380$		0			0
$381$	−8588.03	+	5884.70i	−1.15480	+	0.791293i
$382$		0			0
$383$	2622.07	−	4541.55i	0.349821	−	0.605907i	−0.636397	−	0.771362i	$-0.719576\pi$
$383$	2622.07	−	4541.55i	0.349821	−	0.605907i	0.986217	+	0.165455i	$0.0529092\pi$
$384$		0			0
$385$	−938.864	−	1626.16i	−0.124283	−	0.215264i
$386$		0			0
$387$	−9536.90	+	1483.13i	−1.25268	+	0.194811i
$388$		0			0
$389$	−797.621	−	1381.52i	−0.103961	−	0.180067i	0.809352	−	0.587324i	$-0.199819\pi$
$389$	−797.621	−	1381.52i	−0.103961	−	0.180067i	−0.913313	+	0.407257i	$0.866485\pi$
$390$		0			0
$391$	−2080.21	−	1201.01i	−0.269056	−	0.155339i
$392$		0			0
$393$	−447.130	−	5784.88i	−0.0573912	−	0.742516i
$394$		0			0
$395$		−	8382.96i		−	1.06783i
$396$		0			0
$397$		−	766.199i		−	0.0968625i	−0.998827	−	0.0484313i	$-0.984578\pi$
$397$		−	766.199i		−	0.0968625i	0.998827	−	0.0484313i	$-0.0154222\pi$
$398$		0			0
$399$	1365.59	+	653.702i	0.171341	+	0.0820202i
$400$		0			0
$401$	−170.330	−	98.3398i	−0.0212116	−	0.0122465i	0.489357	−	0.872084i	$-0.337232\pi$
$401$	−170.330	−	98.3398i	−0.0212116	−	0.0122465i	−0.510568	+	0.859837i	$0.670565\pi$
$402$		0			0
$403$	4045.19	+	7006.48i	0.500013	+	0.866049i
$404$		0			0
$405$	4894.01	−	1559.91i	0.600457	−	0.191389i
$406$		0			0
$407$	−1426.57	−	2470.89i	−0.173740	−	0.300927i
$408$		0			0
$409$	4719.01	−	8173.56i	0.570513	−	0.988158i	−0.426000	−	0.904723i	$-0.640078\pi$
$409$	4719.01	−	8173.56i	0.570513	−	0.988158i	0.996513	−	0.0834349i	$-0.0265891\pi$
$410$		0			0
$411$	−3042.49	−	1456.43i	−0.365146	−	0.174794i
$412$		0			0
$413$	9600.17			1.14381
$414$		0			0
$415$		−	3259.04i		−	0.385494i
$416$		0			0
$417$	−5543.58	+	428.479i	−0.651007	+	0.0503183i
$418$		0			0
$419$	−10282.4	−	5936.56i	−1.19888	−	0.692171i	−0.238571	−	0.971125i	$-0.576679\pi$
$419$	−10282.4	−	5936.56i	−1.19888	−	0.692171i	−0.960305	+	0.278954i	$0.910012\pi$
$420$		0			0
$421$	936.025	−	540.414i	0.108359	−	0.0625610i	−0.444841	−	0.895609i	$-0.646740\pi$
$421$	936.025	−	540.414i	0.108359	−	0.0625610i	0.553200	+	0.833048i	$0.313407\pi$
$422$		0			0
$423$	8330.77	−	1295.56i	0.957579	−	0.148918i
$424$		0			0
$425$	−3121.75	+	1802.35i	−0.356300	+	0.205710i
$426$		0			0
$427$	7454.67	−	12911.9i	0.844864	−	1.46335i
$428$		0			0
$429$	−2587.97	−	3776.84i	−0.291255	−	0.425052i
$430$		0			0
$431$	−16863.0			−1.88460			−0.942299	−	0.334772i	$-0.891341\pi$
$431$	−16863.0			−1.88460			−0.942299	+	0.334772i	$0.891341\pi$
$432$		0			0
$433$	4717.51			0.523577			0.261789	−	0.965125i	$-0.415688\pi$
$433$	4717.51			0.523577			0.261789	+	0.965125i	$0.415688\pi$
$434$		0			0
$435$	5351.88	+	7810.44i	0.589892	+	0.860878i
$436$		0			0
$437$	374.745	−	649.078i	0.0410217	−	0.0710517i
$438$		0			0
$439$	−5611.44	+	3239.77i	−0.610068	+	0.352223i	−0.772992	−	0.634416i	$-0.781241\pi$
$439$	−5611.44	+	3239.77i	−0.610068	+	0.352223i	0.162924	+	0.986639i	$0.447907\pi$
$440$		0			0
$441$	644.023	+	799.872i	0.0695414	+	0.0863699i
$442$		0			0
$443$	1696.92	−	979.717i	0.181993	−	0.105074i	−0.406236	−	0.913768i	$-0.633159\pi$
$443$	1696.92	−	979.717i	0.181993	−	0.105074i	0.588229	+	0.808694i	$0.299825\pi$
$444$		0			0
$445$	−6393.63	−	3691.37i	−0.681095	−	0.393230i
$446$		0			0
$447$	−3067.43	+	237.091i	−0.324574	+	0.0250873i
$448$		0			0
$449$		−	2566.64i		−	0.269771i	−0.990861	−	0.134885i	$-0.956933\pi$
$449$		−	2566.64i		−	0.269771i	0.990861	−	0.134885i	$-0.0430666\pi$
$450$		0			0
$451$	−6487.29			−0.677327
$452$		0			0
$453$	−9815.02	−	4698.41i	−1.01799	−	0.487308i
$454$		0			0
$455$	4438.46	−	7687.64i	0.457315	−	0.792093i
$456$		0			0
$457$	740.460	+	1282.51i	0.0757927	+	0.131277i	0.901431	−	0.432923i	$-0.142518\pi$
$457$	740.460	+	1282.51i	0.0757927	+	0.131277i	−0.825638	+	0.564200i	$0.809185\pi$
$458$		0			0
$459$	1539.32	+	6532.52i	0.156535	+	0.664296i
$460$		0			0
$461$	6037.19	+	10456.7i	0.609935	+	1.05644i	0.991251	+	0.131993i	$0.0421378\pi$
$461$	6037.19	+	10456.7i	0.609935	+	1.05644i	−0.381316	+	0.924445i	$0.624529\pi$
$462$		0			0
$463$	13152.8	+	7593.77i	1.32022	+	0.762230i	0.983764	−	0.179469i	$-0.0574379\pi$
$463$	13152.8	+	7593.77i	1.32022	+	0.762230i	0.336457	+	0.941699i	$0.390771\pi$
$464$		0			0
$465$	−4139.65	−	1981.63i	−0.412843	−	0.197626i
$466$		0			0
$467$		−	46.2660i		−	0.00458445i	−0.999997	−	0.00229222i	$-0.999270\pi$
$467$		−	46.2660i		−	0.00458445i	0.999997	−	0.00229222i	$-0.000729638\pi$
$468$		0			0
$469$			10818.5i			1.06514i
$470$		0			0
$471$	56.8490	+	735.501i	0.00556150	+	0.0719535i
$472$		0			0
$473$	−4226.36	−	2440.09i	−0.410842	−	0.237199i
$474$		0			0
$475$	−562.377	−	974.066i	−0.0543235	−	0.0940910i
$476$		0			0
$477$	4646.12	−	12003.0i	0.445977	−	1.15216i
$478$		0			0
$479$	7341.31	+	12715.5i	0.700278	+	1.21292i	0.968369	+	0.249523i	$0.0802738\pi$
$479$	7341.31	+	12715.5i	0.700278	+	1.21292i	−0.268091	+	0.963393i	$0.586393\pi$
$480$		0			0
$481$	6744.08	−	11681.1i	0.639300	−	1.10730i
$482$		0			0
$483$	4201.28	−	2878.81i	0.395786	−	0.271201i
$484$		0			0
$485$	7932.58			0.742680
$486$		0			0
$487$		−	5556.22i		−	0.516994i	−0.966012	−	0.258497i	$-0.916773\pi$
$487$		−	5556.22i		−	0.516994i	0.966012	−	0.258497i	$-0.0832273\pi$
$488$		0			0
$489$	10697.2	+	15611.2i	0.989248	+	1.44369i
$490$		0			0
$491$	7499.65	+	4329.93i	0.689317	+	0.397977i	0.803356	−	0.595499i	$-0.203046\pi$
$491$	7499.65	+	4329.93i	0.689317	+	0.397977i	−0.114039	+	0.993476i	$0.536379\pi$
$492$		0			0
$493$	−10713.6	+	6185.49i	−0.978733	+	0.565072i
$494$		0			0
$495$	2422.13	+	937.560i	0.219933	+	0.0851317i
$496$		0			0
$497$	−1472.48	+	850.137i	−0.132897	+	0.0767281i
$498$		0			0
$499$	1626.32	−	2816.87i	0.145900	−	0.252707i	−0.783808	−	0.621003i	$-0.786726\pi$
$499$	1626.32	−	2816.87i	0.145900	−	0.252707i	0.929708	+	0.368296i	$0.120059\pi$
$500$		0			0
$501$	14757.6	−	1140.66i	1.31601	−	0.101718i
$502$		0			0
$503$	2500.59			0.221662			0.110831	−	0.993839i	$-0.464649\pi$
$503$	2500.59			0.221662			0.110831	+	0.993839i	$0.464649\pi$
$504$		0			0
$505$	−4403.02			−0.387984
$506$		0			0
$507$	4416.42	−	9225.96i	0.386865	−	0.808164i
$508$		0			0
$509$	−4599.12	+	7965.92i	−0.400496	+	0.693680i	−0.993786	−	0.111309i	$-0.964496\pi$
$509$	−4599.12	+	7965.92i	−0.400496	+	0.693680i	0.593290	+	0.804989i	$0.297829\pi$
$510$		0			0
$511$	−13829.6	+	7984.53i	−1.19723	+	0.691223i
$512$		0			0
$513$	−2038.31	+	480.308i	−0.175426	+	0.0413375i
$514$		0			0
$515$	−957.986	+	553.093i	−0.0819687	+	0.0473247i
$516$		0			0
$517$	3691.85	+	2131.49i	0.314057	+	0.181321i
$518$		0			0
$519$	−53.4952	+	111.752i	−0.00452443	+	0.00945157i
$520$		0			0
$521$		−	7635.67i		−	0.642082i	−0.947065	−	0.321041i	$-0.895967\pi$
$521$		−	7635.67i		−	0.642082i	0.947065	−	0.321041i	$-0.104033\pi$
$522$		0			0
$523$	6152.61			0.514407			0.257203	−	0.966357i	$-0.417199\pi$
$523$	6152.61			0.514407			0.257203	+	0.966357i	$0.417199\pi$
$524$		0			0
$525$	−588.991	−	7620.24i	−0.0489632	−	0.633476i
$526$		0			0
$527$	2998.31	−	5193.22i	0.247834	−	0.429260i
$528$		0			0
$529$	4822.88	+	8353.48i	0.396390	+	0.686568i
$530$		0			0
$531$	−10343.0	+	8327.73i	−0.845286	+	0.680589i
$532$		0			0
$533$	−15334.3	−	26559.8i	−1.24616	−	2.15841i
$534$		0			0
$535$	2565.62	+	1481.26i	0.207329	+	0.119702i
$536$		0			0
$537$	8335.53	−	5711.68i	0.669841	−	0.458989i
$538$		0			0
$539$			519.248i			0.0414946i
$540$		0			0
$541$			681.956i			0.0541952i	0.999633	+	0.0270976i	$0.00862649\pi$
$541$			681.956i			0.0541952i	−0.999633	+	0.0270976i	$0.991374\pi$
$542$		0			0
$543$	−118.582	+	81.2549i	−0.00937171	+	0.00642170i
$544$		0			0
$545$	7427.67	+	4288.36i	0.583791	+	0.337052i
$546$		0			0
$547$	−2410.39	−	4174.92i	−0.188411	−	0.326337i	0.756310	−	0.654214i	$-0.227000\pi$
$547$	−2410.39	−	4174.92i	−0.188411	−	0.326337i	−0.944721	+	0.327876i	$0.893667\pi$
$548$		0			0
$549$	3169.01	+	20377.5i	0.246357	+	1.58414i
$550$		0			0
$551$	−1930.03	−	3342.91i	−0.149223	−	0.258462i
$552$		0			0
$553$	−11611.8	+	20112.3i	−0.892922	+	1.54659i
$554$		0			0
$555$	589.652	+	7628.80i	0.0450979	+	0.583468i
$556$		0			0
$557$	−5948.96			−0.452541			−0.226271	−	0.974064i	$-0.572653\pi$
$557$	−5948.96			−0.452541			−0.226271	+	0.974064i	$0.572653\pi$
$558$		0			0
$559$		−	23071.0i		−	1.74561i
$560$		0			0
$561$	−1465.25	+	3060.92i	−0.110272	+	0.230360i
$562$		0			0
$563$	−1046.18	−	604.012i	−0.0783148	−	0.0452151i	0.460331	−	0.887747i	$-0.347731\pi$
$563$	−1046.18	−	604.012i	−0.0783148	−	0.0452151i	−0.538646	+	0.842532i	$0.681064\pi$
$564$		0			0
$565$	−2141.26	+	1236.25i	−0.159439	+	0.0920524i
$566$		0			0
$567$	−13902.4	−	3036.53i	−1.02971	−	0.224907i
$568$		0			0
$569$	−2663.36	+	1537.69i	−0.196229	+	0.113293i	−0.594895	−	0.803803i	$-0.702806\pi$
$569$	−2663.36	+	1537.69i	−0.196229	+	0.113293i	0.398667	+	0.917096i	$0.369473\pi$
$570$		0			0
$571$	−4651.48	+	8056.60i	−0.340908	+	0.590470i	−0.984602	−	0.174813i	$-0.944068\pi$
$571$	−4651.48	+	8056.60i	−0.340908	+	0.590470i	0.643694	+	0.765283i	$0.277401\pi$
$572$		0			0
$573$	−7116.69	+	14866.8i	−0.518855	+	1.08389i
$574$		0			0
$575$	−3783.60			−0.274412
$576$		0			0
$577$	2594.28			0.187178			0.0935888	−	0.995611i	$-0.470166\pi$
$577$	2594.28			0.187178			0.0935888	+	0.995611i	$0.470166\pi$
$578$		0			0
$579$	−2290.29	+	177.023i	−0.164389	+	0.0127061i
$580$		0			0
$581$	−4514.33	+	7819.04i	−0.322351	+	0.558328i
$582$		0			0
$583$	5636.06	−	3253.98i	0.400380	−	0.231160i
$584$		0			0
$585$	1886.81	+	12132.6i	0.133350	+	0.857475i
$586$		0			0
$587$	11408.0	−	6586.41i	0.802144	−	0.463118i	−0.0420762	−	0.999114i	$-0.513397\pi$
$587$	11408.0	−	6586.41i	0.802144	−	0.463118i	0.844220	+	0.535996i	$0.180064\pi$
$588$		0			0
$589$	1620.42	+	935.547i	0.113358	+	0.0654475i
$590$		0			0
$591$	−9058.34	−	13219.6i	−0.630474	−	0.920103i
$592$		0			0
$593$			20600.6i			1.42659i	0.700865	+	0.713294i	$0.252798\pi$
$593$			20600.6i			1.42659i	−0.700865	+	0.713294i	$0.747202\pi$
$594$		0			0
$595$	−6579.60			−0.453340
$596$		0			0
$597$	−7647.61	+	5240.30i	−0.524281	+	0.359248i
$598$		0			0
$599$	−5529.60	+	9577.55i	−0.377184	+	0.653302i	−0.990651	−	0.136418i	$-0.956441\pi$
$599$	−5529.60	+	9577.55i	−0.377184	+	0.653302i	0.613467	+	0.789720i	$0.289774\pi$
$600$		0			0
$601$	10115.9	+	17521.2i	0.686581	+	1.18919i	0.972937	+	0.231070i	$0.0742227\pi$
$601$	10115.9	+	17521.2i	0.686581	+	1.18919i	−0.286356	+	0.958123i	$0.592444\pi$
$602$		0			0
$603$	−9384.58	−	11655.6i	−0.633780	−	0.787151i
$604$		0			0
$605$	−4032.54	−	6984.56i	−0.270985	−	0.469360i
$606$		0			0
$607$	24259.0	+	14005.9i	1.62214	+	0.936545i	0.986346	+	0.164689i	$0.0526621\pi$
$607$	24259.0	+	14005.9i	1.62214	+	0.936545i	0.635798	+	0.771856i	$0.280671\pi$
$608$		0			0
$609$	−2021.36	−	26152.0i	−0.134499	−	1.74012i
$610$		0			0
$611$			20153.2i			1.33439i
$612$		0			0
$613$		−	18577.2i		−	1.22402i	−0.790849	−	0.612012i	$-0.790361\pi$
$613$		−	18577.2i		−	1.22402i	0.790849	−	0.612012i	$-0.209639\pi$
$614$		0			0
$615$	15692.4	+	7511.86i	1.02891	+	0.492533i
$616$		0			0
$617$	1871.75	+	1080.65i	0.122129	+	0.0705114i	0.559820	−	0.828614i	$-0.310870\pi$
$617$	1871.75	+	1080.65i	0.122129	+	0.0705114i	−0.437691	+	0.899126i	$0.644204\pi$
$618$		0			0
$619$	3435.93	+	5951.20i	0.223104	+	0.386428i	0.955749	−	0.294183i	$-0.0950476\pi$
$619$	3435.93	+	5951.20i	0.223104	+	0.386428i	−0.732645	+	0.680611i	$0.761714\pi$
$620$		0			0
$621$	−2029.11	+	6745.98i	−0.131120	+	0.435921i
$622$		0			0
$623$	10226.4	+	17712.6i	0.657641	+	1.13907i
$624$		0			0
$625$	263.949	−	457.172i	0.0168927	−	0.0292590i
$626$		0			0
$627$	−955.084	−	457.194i	−0.0608331	−	0.0291206i
$628$		0			0
$629$	−9997.45			−0.633743
$630$		0			0
$631$			14045.7i			0.886134i	0.896488	+	0.443067i	$0.146110\pi$
$631$			14045.7i			0.886134i	−0.896488	+	0.443067i	$0.853890\pi$
$632$		0			0
$633$	7614.12	−	588.517i	0.478095	−	0.0369533i
$634$		0			0
$635$	12225.9	+	7058.60i	0.764045	+	0.441122i
$636$		0			0
$637$	−2125.86	+	1227.37i	−0.132229	+	0.0763423i
$638$		0			0
$639$	848.956	−	2193.23i	0.0525574	−	0.135779i
$640$		0			0
$641$	−9674.91	+	5585.81i	−0.596156	+	0.344191i	−0.767528	−	0.641016i	$-0.778513\pi$
$641$	−9674.91	+	5585.81i	−0.596156	+	0.344191i	0.171372	+	0.985206i	$0.445180\pi$
$642$		0			0
$643$	3853.78	−	6674.94i	0.236358	−	0.409384i	−0.723309	−	0.690525i	$-0.757380\pi$
$643$	3853.78	−	6674.94i	0.236358	−	0.409384i	0.959666	+	0.281141i	$0.0907129\pi$
$644$		0			0
$645$	7397.83	+	10796.3i	0.451611	+	0.659074i
$646$		0			0
$647$	−10087.3			−0.612943			−0.306472	−	0.951880i	$-0.599148\pi$
$647$	−10087.3			−0.612943			−0.306472	+	0.951880i	$0.599148\pi$
$648$		0			0
$649$	−6714.29			−0.406100
$650$		0			0
$651$	7186.91	+	10488.4i	0.432684	+	0.631451i
$652$		0			0
$653$	11606.7	−	20103.4i	0.695567	−	1.20476i	−0.274422	−	0.961609i	$-0.588487\pi$
$653$	11606.7	−	20103.4i	0.695567	−	1.20476i	0.969989	−	0.243148i	$-0.0781802\pi$
$654$		0			0
$655$	−6813.73	+	3933.91i	−0.406465	+	0.234673i
$656$		0			0
$657$	7973.44	−	20598.9i	0.473476	−	1.22320i
$658$		0			0
$659$	23327.3	−	13468.0i	1.37891	−	0.796115i	0.386883	−	0.922129i	$-0.373552\pi$
$659$	23327.3	−	13468.0i	1.37891	−	0.796115i	0.992029	+	0.126014i	$0.0402183\pi$
$660$		0			0
$661$	−20390.0	−	11772.2i	−1.19982	−	0.692715i	−0.239304	−	0.970945i	$-0.576919\pi$
$661$	−20390.0	−	11772.2i	−1.19982	−	0.692715i	−0.960515	+	0.278229i	$0.910252\pi$
$662$		0			0
$663$	−15995.2	+	1236.32i	−0.936959	+	0.0724203i
$664$		0			0
$665$		−	2053.00i		−	0.119717i
$666$		0			0
$667$	−12985.0			−0.753794
$668$		0			0
$669$	5666.50	+	2712.53i	0.327473	+	0.156760i
$670$		0			0
$671$	−5213.74	+	9030.46i	−0.299961	+	0.519548i
$672$		0			0
$673$	−11656.7	−	20189.9i	−0.667654	−	1.15641i	−0.978559	−	0.205969i	$-0.933965\pi$
$673$	−11656.7	−	20189.9i	−0.667654	−	1.15641i	0.310905	−	0.950441i	$-0.399368\pi$
$674$		0			0
$675$	7244.79	+	7698.93i	0.413114	+	0.439010i
$676$		0			0
$677$	12028.2	+	20833.5i	0.682840	+	1.18271i	0.974110	+	0.226072i	$0.0725886\pi$
$677$	12028.2	+	20833.5i	0.682840	+	1.18271i	−0.291271	+	0.956641i	$0.594078\pi$
$678$		0			0
$679$	−19031.8	−	10988.0i	−1.07566	−	0.621032i
$680$		0			0
$681$	10533.7	+	5042.44i	0.592736	+	0.283740i
$682$		0			0
$683$			18439.7i			1.03305i	0.856272	+	0.516525i	$0.172775\pi$
$683$			18439.7i			1.03305i	−0.856272	+	0.516525i	$0.827225\pi$
$684$		0			0
$685$			4574.02i			0.255130i
$686$		0			0
$687$	306.866	+	3970.17i	0.0170417	+	0.220482i
$688$		0			0
$689$	26644.4	+	15383.1i	1.47325	+	0.850582i
$690$		0			0
$691$	7125.35	+	12341.5i	0.392274	+	0.679438i	0.992749	−	0.120205i	$-0.0383553\pi$
$691$	7125.35	+	12341.5i	0.392274	+	0.679438i	−0.600475	+	0.799643i	$0.705022\pi$
$692$		0			0
$693$	−4512.46	−	5604.45i	−0.247351	−	0.307208i
$694$		0			0
$695$	3769.81	+	6529.51i	0.205751	+	0.356372i
$696$		0			0
$697$	−11365.8	+	19686.2i	−0.617662	+	1.06982i
$698$		0			0
$699$	3434.20	−	2353.19i	0.185827	−	0.127333i
$700$		0			0
$701$	15415.0			0.830549			0.415274	−	0.909696i	$-0.363686\pi$
$701$	15415.0			0.830549			0.415274	+	0.909696i	$0.363686\pi$
$702$		0			0
$703$		−	3119.46i		−	0.167358i
$704$		0			0
$705$	−6462.23	−	9430.87i	−0.345222	−	0.503811i
$706$		0			0
$707$	10563.7	+	6098.94i	0.561935	+	0.324433i
$708$		0			0
$709$	15877.4	−	9166.80i	0.841025	−	0.485566i	−0.0165875	−	0.999862i	$-0.505280\pi$
$709$	15877.4	−	9166.80i	0.841025	−	0.485566i	0.857613	+	0.514296i	$0.171947\pi$
$710$		0			0
$711$	−4936.23	−	31741.2i	−0.260370	−	1.67425i
$712$		0			0
$713$	5450.97	−	3147.12i	0.286312	−	0.165302i
$714$		0			0
$715$	−3104.23	+	5376.68i	−0.162366	+	0.281226i
$716$		0			0
$717$	31422.8	−	2428.76i	1.63669	−	0.126504i
$718$		0			0
$719$	10428.9			0.540936			0.270468	−	0.962729i	$-0.412822\pi$
$719$	10428.9			0.540936			0.270468	+	0.962729i	$0.412822\pi$
$720$		0			0
$721$	3064.52			0.158292
$722$		0			0
$723$	11800.6	−	24651.5i	0.607009	−	1.26805i
$724$		0			0
$725$	−9743.23	+	16875.8i	−0.499110	+	0.864483i
$726$		0			0
$727$	12935.1	−	7468.08i	0.659884	−	0.380984i	−0.132348	−	0.991203i	$-0.542252\pi$
$727$	12935.1	−	7468.08i	0.659884	−	0.380984i	0.792233	+	0.610219i	$0.208918\pi$
$728$		0			0
$729$	17612.1	−	8788.23i	0.894789	−	0.446489i
$730$		0			0
$731$	−14809.2	+	8550.12i	−0.749302	+	0.432610i
$732$		0			0
$733$	434.025	+	250.584i	0.0218705	+	0.0126269i	0.510895	−	0.859643i	$-0.329314\pi$
$733$	434.025	+	250.584i	0.0218705	+	0.0126269i	−0.489025	+	0.872270i	$0.662647\pi$
$734$		0			0
$735$	601.255	−	1256.03i	0.0301736	−	0.0630331i
$736$		0			0
$737$		−	7566.38i		−	0.378170i
$738$		0			0
$739$	−11047.6			−0.549922			−0.274961	−	0.961455i	$-0.588665\pi$
$739$	−11047.6			−0.549922			−0.274961	+	0.961455i	$0.588665\pi$
$740$		0			0
$741$	−385.763	−	4990.92i	−0.0191246	−	0.247430i
$742$		0			0
$743$	−16450.7	+	28493.5i	−0.812272	+	1.40690i	0.0989987	+	0.995088i	$0.468436\pi$
$743$	−16450.7	+	28493.5i	−0.812272	+	1.40690i	−0.911270	+	0.411808i	$0.864897\pi$
$744$		0			0
$745$	2085.95	+	3612.98i	0.102582	+	0.177677i
$746$		0			0
$747$	−1919.06	−	12340.0i	−0.0939954	−	0.604414i
$748$		0			0
$749$	−4103.60	−	7107.64i	−0.200190	−	0.346739i
$750$		0			0
$751$	−32163.5	−	18569.6i	−1.56280	−	0.902282i	−0.996972	−	0.0777583i	$-0.975224\pi$
$751$	−32163.5	−	18569.6i	−1.56280	−	0.902282i	−0.565827	−	0.824524i	$-0.691443\pi$
$752$		0			0
$753$	−12261.5	+	8401.84i	−0.593405	+	0.406614i
$754$		0			0
$755$			14755.7i			0.711278i
$756$		0			0
$757$			7256.87i			0.348422i	0.984708	+	0.174211i	$0.0557375\pi$
$757$			7256.87i			0.348422i	−0.984708	+	0.174211i	$0.944263\pi$
$758$		0			0
$759$	−2938.34	+	2013.41i	−0.140521	+	0.0962877i
$760$		0			0
$761$	−7953.62	−	4592.02i	−0.378868	−	0.218739i	0.298458	−	0.954423i	$-0.403528\pi$
$761$	−7953.62	−	4592.02i	−0.378868	−	0.218739i	−0.677326	+	0.735683i	$0.736861\pi$
$762$		0			0
$763$	−11880.2	−	20577.2i	−0.563688	−	0.976336i
$764$		0			0
$765$	7088.69	−	5707.51i	0.335023	−	0.269746i
$766$		0			0
$767$	−15870.8	−	27489.1i	−0.747148	−	1.29410i
$768$		0			0
$769$	17525.0	−	30354.2i	0.821806	−	1.42341i	−0.0825304	−	0.996589i	$-0.526300\pi$
$769$	17525.0	−	30354.2i	0.821806	−	1.42341i	0.904336	−	0.426821i	$-0.140366\pi$
$770$		0			0
$771$	−271.119	−	3507.68i	−0.0126642	−	0.163847i
$772$		0			0
$773$	1390.01			0.0646768			0.0323384	−	0.999477i	$-0.489705\pi$
$773$	1390.01			0.0646768			0.0323384	+	0.999477i	$0.489705\pi$
$774$		0			0
$775$		−	9445.72i		−	0.437807i
$776$		0			0
$777$	9152.52	−	19119.7i	0.422580	−	0.882774i
$778$		0			0
$779$	−6142.58	−	3546.42i	−0.282517	−	0.163111i
$780$		0			0
$781$	1029.84	−	594.579i	0.0471839	−	0.0272416i
$782$		0			0
$783$	24863.5	+	26422.0i	1.13480	+	1.20593i
$784$		0			0
$785$	866.311	−	500.165i	0.0393885	−	0.0227410i
$786$		0			0
$787$	−2740.75	+	4747.12i	−0.124139	+	0.215015i	−0.921396	−	0.388625i	$-0.872950\pi$
$787$	−2740.75	+	4747.12i	−0.124139	+	0.215015i	0.797257	+	0.603640i	$0.206283\pi$
$788$		0			0
$789$	2600.24	−	5431.93i	0.117327	−	0.245097i
$790$		0			0
$791$	6849.70			0.307898
$792$		0			0
$793$	−49295.7			−2.20749
$794$		0			0
$795$	−17401.2	+	1344.99i	−0.776297	+	0.0600022i
$796$		0			0
$797$	−15906.0	+	27550.0i	−0.706926	+	1.22443i	0.259065	+	0.965860i	$0.416585\pi$
$797$	−15906.0	+	27550.0i	−0.706926	+	1.22443i	−0.965992	+	0.258573i	$0.916748\pi$
$798$		0			0
$799$	12936.3	−	7468.79i	0.572784	−	0.330697i
$800$		0			0
$801$	−26382.5	−	10212.2i	−1.16377	−	0.450473i
$802$		0			0
$803$	9672.33	−	5584.32i	0.425067	−	0.245413i
$804$		0			0
$805$	−5980.91	−	3453.08i	−0.261863	−	0.151186i
$806$		0			0
$807$	22669.8	+	33084.0i	0.988867	+	1.44314i
$808$		0			0
$809$		−	2788.69i		−	0.121193i	−0.998162	−	0.0605966i	$-0.980700\pi$
$809$		−	2788.69i		−	0.121193i	0.998162	−	0.0605966i	$-0.0193003\pi$
$810$		0			0
$811$	−23968.2			−1.03778			−0.518889	−	0.854841i	$-0.673654\pi$
$811$	−23968.2			−1.03778			−0.518889	+	0.854841i	$0.673654\pi$
$812$		0			0
$813$	15294.3	−	10480.0i	0.659773	−	0.452091i
$814$		0			0
$815$	12831.1	−	22224.1i	0.551476	−	0.955184i
$816$		0			0
$817$	−2667.85	−	4620.86i	−0.114243	−	0.197874i
$818$		0			0
$819$	12279.0	−	31722.1i	0.523886	−	1.35343i
$820$		0			0
$821$	−2750.46	−	4763.94i	−0.116921	−	0.202512i	0.801625	−	0.597827i	$-0.203969\pi$
$821$	−2750.46	−	4763.94i	−0.116921	−	0.202512i	−0.918546	+	0.395314i	$0.870636\pi$
$822$		0			0
$823$	4259.38	+	2459.15i	0.180404	+	0.104156i	0.587483	−	0.809237i	$-0.300119\pi$
$823$	4259.38	+	2459.15i	0.180404	+	0.104156i	−0.407078	+	0.913393i	$0.633452\pi$
$824$		0			0
$825$	411.936	+	5329.54i	0.0173839	+	0.224910i
$826$		0			0
$827$		−	17035.6i		−	0.716307i	−0.933663	−	0.358153i	$-0.883407\pi$
$827$		−	17035.6i		−	0.716307i	0.933663	−	0.358153i	$-0.116593\pi$
$828$		0			0
$829$			9284.88i			0.388995i	0.980903	+	0.194498i	$0.0623077\pi$
$829$			9284.88i			0.388995i	−0.980903	+	0.194498i	$0.937692\pi$
$830$		0			0
$831$	21688.1	+	10382.0i	0.905355	+	0.433390i
$832$		0			0
$833$	1575.69	+	909.728i	0.0655397	+	0.0378394i
$834$		0			0
$835$	−10035.6	−	17382.2i	−0.415925	−	0.720403i
$836$		0			0
$837$	−16841.3	−	5065.66i	−0.695483	−	0.209193i
$838$		0			0
$839$	−4605.12	−	7976.30i	−0.189495	−	0.328215i	0.755587	−	0.655048i	$-0.227352\pi$
$839$	−4605.12	−	7976.30i	−0.189495	−	0.328215i	−0.945082	+	0.326833i	$0.894018\pi$
$840$		0			0
$841$	−21243.4	+	36794.6i	−0.871024	+	1.50866i
$842$		0			0
$843$	−13561.0	−	6491.60i	−0.554053	−	0.265222i
$844$		0			0
$845$	−13870.1			−0.564670
$846$		0			0
$847$			22343.0i			0.906394i
$848$		0			0
$849$	−42904.3	+	3316.20i	−1.73436	+	0.134054i
$850$		0			0
$851$	−9087.77	−	5246.83i	−0.366069	−	0.211350i
$852$		0			0
$853$	6216.93	−	3589.35i	0.249547	−	0.144076i	−0.370010	−	0.929028i	$-0.620646\pi$
$853$	6216.93	−	3589.35i	0.249547	−	0.144076i	0.619557	+	0.784952i	$0.287312\pi$
$854$		0			0
$855$	1780.89	+	2211.85i	0.0712340	+	0.0884722i
$856$		0			0
$857$	13290.3	−	7673.16i	0.529741	−	0.305846i	−0.211170	−	0.977449i	$-0.567727\pi$
$857$	13290.3	−	7673.16i	0.529741	−	0.305846i	0.740911	+	0.671603i	$0.234394\pi$
$858$		0			0
$859$	−18277.1	+	31656.9i	−0.725969	+	1.25742i	0.232604	+	0.972571i	$0.425275\pi$
$859$	−18277.1	+	31656.9i	−0.725969	+	1.25742i	−0.958574	+	0.284844i	$0.908058\pi$
$860$		0			0
$861$	−27243.7	−	39759.0i	−1.07835	−	1.57373i
$862$		0			0
$863$	−27501.0			−1.08476			−0.542378	−	0.840135i	$-0.682476\pi$
$863$	−27501.0			−1.08476			−0.542378	+	0.840135i	$0.682476\pi$
$864$		0			0
$865$	168.006			0.00660388
$866$		0			0
$867$	−7708.69	−	11249.9i	−0.301962	−	0.440678i
$868$		0			0
$869$	8121.23	−	14066.4i	0.317024	−	0.549102i
$870$		0			0
$871$	30977.7	−	17885.0i	1.20510	−	0.695763i
$872$		0			0
$873$	30035.9	−	4671.03i	1.16445	−	0.181089i
$874$		0			0
$875$	−23864.7	+	13778.3i	−0.922027	+	0.532332i
$876$		0			0
$877$	−4880.15	−	2817.56i	−0.187903	−	0.108486i	0.403098	−	0.915157i	$-0.367934\pi$
$877$	−4880.15	−	2817.56i	−0.187903	−	0.108486i	−0.591000	+	0.806671i	$0.701267\pi$
$878$		0			0
$879$	19307.9	−	1492.36i	0.740887	−	0.0572653i
$880$		0			0
$881$			51429.9i			1.96676i	0.181554	+	0.983381i	$0.441887\pi$
$881$			51429.9i			1.96676i	−0.181554	+	0.983381i	$0.558113\pi$
$882$		0			0
$883$	7015.23			0.267363			0.133681	−	0.991024i	$-0.457320\pi$
$883$	7015.23			0.267363			0.133681	+	0.991024i	$0.457320\pi$
$884$		0			0
$885$	16241.4	+	7774.71i	0.616893	+	0.295304i
$886$		0			0
$887$	18173.6	−	31477.6i	0.687948	−	1.19156i	−0.284553	−	0.958660i	$-0.591845\pi$
$887$	18173.6	−	31477.6i	0.687948	−	1.19156i	0.972501	−	0.232900i	$-0.0748214\pi$
$888$		0			0
$889$	−19554.8	−	33869.9i	−0.737734	−	1.27779i
$890$		0			0
$891$	9723.23	+	2123.73i	0.365590	+	0.0798513i
$892$		0			0
$893$	2330.45	+	4036.46i	0.0873299	+	0.151260i
$894$		0			0
$895$	−11866.4	−	6851.07i	−0.443184	−	0.255873i
$896$		0			0
$897$	−15188.6	−	7270.74i	−0.565367	−	0.270639i
$898$		0			0
$899$		−	32416.9i		−	1.20263i
$900$		0			0
$901$		−	22804.0i		−	0.843188i
$902$		0			0
$903$	−2794.10	−	36149.6i	−0.102970	−	1.33221i
$904$		0			0
$905$	168.812	+	97.4639i	0.00620057	+	0.00357990i
$906$		0			0
$907$	−3011.58	−	5216.21i	−0.110251	−	0.190961i	0.805620	−	0.592432i	$-0.201832\pi$
$907$	−3011.58	−	5216.21i	−0.110251	−	0.190961i	−0.915872	+	0.401472i	$0.868499\pi$
$908$		0			0
$909$	−16671.6	+	2592.68i	−0.608319	+	0.0946027i
$910$		0			0
$911$	2996.17	+	5189.52i	0.108965	+	0.188734i	0.915351	−	0.402656i	$-0.131913\pi$
$911$	2996.17	+	5189.52i	0.108965	+	0.188734i	−0.806386	+	0.591390i	$0.798580\pi$
$912$		0			0
$913$	3157.29	−	5468.58i	0.114448	−	0.198230i
$914$		0			0
$915$	23068.4	−	15807.0i	0.833462	−	0.571106i
$916$		0			0
$917$	21796.6			0.784936
$918$		0			0
$919$		−	88.2115i		−	0.00316630i	−0.999999	−	0.00158315i	$-0.999496\pi$
$919$		−	88.2115i		−	0.00316630i	0.999999	−	0.00158315i	$-0.000503932\pi$
$920$		0			0
$921$	4352.08	+	6351.35i	0.155707	+	0.227236i
$922$		0			0
$923$	4868.56	+	2810.86i	0.173619	+	0.100239i
$924$		0			0
$925$	−13637.9	+	7873.87i	−0.484771	+	0.279883i
$926$		0			0
$927$	−3301.63	+	2658.33i	−0.116979	+	0.0941868i
$928$		0			0
$929$	18113.2	−	10457.7i	0.639695	−	0.369328i	−0.144802	−	0.989461i	$-0.546255\pi$
$929$	18113.2	−	10457.7i	0.639695	−	0.369328i	0.784497	+	0.620133i	$0.212921\pi$
$930$		0			0
$931$	−283.858	+	491.657i	−0.00999256	+	0.0173076i
$932$		0			0
$933$	−41182.2	+	3183.09i	−1.44507	+	0.111693i
$934$		0			0
$935$	4601.72			0.160954
$936$		0			0
$937$	20055.2			0.699227			0.349614	−	0.936894i	$-0.386313\pi$
$937$	20055.2			0.699227			0.349614	+	0.936894i	$0.386313\pi$
$938$		0			0
$939$	7048.36	−	14724.1i	0.244957	−	0.511717i
$940$		0			0
$941$	−1432.61	+	2481.36i	−0.0496300	+	0.0859616i	−0.889773	−	0.456403i	$-0.849138\pi$
$941$	−1432.61	+	2481.36i	−0.0496300	+	0.0859616i	0.840143	+	0.542365i	$0.182471\pi$
$942$		0			0
$943$	−20663.2	+	11929.9i	−0.713560	+	0.411974i
$944$		0			0
$945$	4425.79	+	18782.0i	0.152350	+	0.646537i
$946$		0			0
$947$	7218.72	−	4167.73i	0.247705	−	0.143013i	−0.371008	−	0.928630i	$-0.620988\pi$
$947$	7218.72	−	4167.73i	0.247705	−	0.143013i	0.618713	+	0.785617i	$0.287654\pi$
$948$		0			0
$949$	45725.8	+	26399.8i	1.56409	+	0.903028i
$950$		0			0
$951$	4282.05	−	8945.25i	0.146010	−	0.305015i
$952$		0			0
$953$		−	39658.3i		−	1.34802i	−0.738724	−	0.674008i	$-0.764571\pi$
$953$		−	39658.3i		−	1.34802i	0.738724	−	0.674008i	$-0.235429\pi$
$954$		0			0
$955$	22350.5			0.757324
$956$		0			0
$957$	1413.73	+	18290.5i	0.0477526	+	0.617814i
$958$		0			0
$959$	6335.80	−	10973.9i	0.213341	−	0.369517i
$960$		0			0
$961$	−7038.75	−	12191.5i	−0.236271	−	0.409233i
$962$		0			0
$963$	10586.7	+	4097.90i	0.354258	+	0.137127i
$964$		0			0
$965$	1557.47	+	2697.62i	0.0519553	+	0.0899892i
$966$		0			0
$967$	9529.32	+	5501.75i	0.316900	+	0.182962i	0.650010	−	0.759926i	$-0.274765\pi$
$967$	9529.32	+	5501.75i	0.316900	+	0.182962i	−0.333110	+	0.942888i	$0.608098\pi$
$968$		0			0
$969$	−3060.71	+	2097.26i	−0.101470	+	0.0695292i
$970$		0			0
$971$			18334.6i			0.605958i	0.952997	+	0.302979i	$0.0979813\pi$
$971$			18334.6i			0.605958i	−0.952997	+	0.302979i	$0.902019\pi$
$972$		0			0
$973$		−	20887.4i		−	0.688199i
$974$		0			0
$975$	−20846.1	+	14284.2i	−0.684727	+	0.469189i
$976$		0			0
$977$	32261.5	+	18626.2i	1.05643	+	0.609932i	0.924444	−	0.381319i	$-0.124530\pi$
$977$	32261.5	+	18626.2i	1.05643	+	0.609932i	0.131990	+	0.991251i	$0.457863\pi$
$978$		0			0
$979$	−7152.24	−	12388.0i	−0.233490	−	0.404416i
$980$		0			0
$981$	30649.3	+	11863.7i	0.997509	+	0.386117i
$982$		0			0
$983$	5395.60	+	9345.46i	0.175069	+	0.303229i	0.940185	−	0.340664i	$-0.110652\pi$
$983$	5395.60	+	9345.46i	0.175069	+	0.303229i	−0.765116	+	0.643892i	$0.777318\pi$
$984$		0			0
$985$	−10865.3	+	18819.3i	−0.351470	+	0.608764i
$986$		0			0
$987$	2440.74	+	31577.7i	0.0787127	+	1.01837i
$988$		0			0
$989$	−17949.0			−0.577092
$990$		0			0
$991$			12374.8i			0.396669i	0.980134	+	0.198334i	$0.0635532\pi$
$991$			12374.8i			0.396669i	−0.980134	+	0.198334i	$0.936447\pi$
$992$		0			0
$993$	15158.1	−	31665.5i	0.484420	−	1.01196i
$994$		0			0
$995$	10887.1	+	6285.66i	0.346878	+	0.200270i
$996$		0			0
$997$	4549.81	−	2626.84i	0.144528	−	0.0834431i	−0.425992	−	0.904727i	$-0.640075\pi$
$997$	4549.81	−	2626.84i	0.144528	−	0.0834431i	0.570520	+	0.821284i	$0.306742\pi$
$998$		0			0
$999$	6724.82	+	28538.5i	0.212977	+	0.903822i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	288.4.p.b.239.11		64
3.2	odd	2		864.4.p.b.719.21		64
4.3	odd	2		72.4.l.b.59.10	yes	64
8.3	odd	2	inner	288.4.p.b.239.12		64
8.5	even	2		72.4.l.b.59.1	yes	64
9.2	odd	6	inner	288.4.p.b.47.12		64
9.7	even	3		864.4.p.b.143.12		64
12.11	even	2		216.4.l.b.179.23		64
24.5	odd	2		216.4.l.b.179.32		64
24.11	even	2		864.4.p.b.719.12		64
36.7	odd	6		216.4.l.b.35.32		64
36.11	even	6		72.4.l.b.11.1	✓	64
72.11	even	6	inner	288.4.p.b.47.11		64
72.29	odd	6		72.4.l.b.11.10	yes	64
72.43	odd	6		864.4.p.b.143.21		64
72.61	even	6		216.4.l.b.35.23		64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
72.4.l.b.11.1	✓	64	36.11	even	6
72.4.l.b.11.10	yes	64	72.29	odd	6
72.4.l.b.59.1	yes	64	8.5	even	2
72.4.l.b.59.10	yes	64	4.3	odd	2
216.4.l.b.35.23		64	72.61	even	6
216.4.l.b.35.32		64	36.7	odd	6
216.4.l.b.179.23		64	12.11	even	2
216.4.l.b.179.32		64	24.5	odd	2
288.4.p.b.47.11		64	72.11	even	6	inner
288.4.p.b.47.12		64	9.2	odd	6	inner
288.4.p.b.239.11		64	1.1	even	1	trivial
288.4.p.b.239.12		64	8.3	odd	2	inner
864.4.p.b.143.12		64	9.7	even	3
864.4.p.b.143.21		64	72.43	odd	6
864.4.p.b.719.12		64	24.11	even	2
864.4.p.b.719.21		64	3.2	odd	2

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:	\( N \)	\(=\)	\( 288 = 2^{5} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	288.p (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-2.93713 - 4.28640i) q^{3} +(-3.52304 + 6.10209i) q^{5} +(16.9049 - 9.76005i) q^{7} +(-9.74649 + 25.1795i) q^{9} +(-11.8232 + 6.82610i) q^{11} +(-55.8938 - 32.2703i) q^{13} +(36.5037 - 2.82147i) q^{15} +47.8376i q^{17} -14.9265 q^{19} +(-91.4874 - 43.7946i) q^{21} +(-25.1060 + 43.4848i) q^{23} +(37.6763 + 65.2573i) q^{25} +(136.556 - 32.1781i) q^{27} +(129.302 + 223.957i) q^{29} +(-108.559 - 62.6768i) q^{31} +(63.9856 + 30.6296i) q^{33} +137.540i q^{35} +208.987i q^{37} +(25.8441 + 334.365i) q^{39} +(411.520 + 237.591i) q^{41} +(178.732 + 309.573i) q^{43} +(-119.310 - 148.182i) q^{45} +(-156.128 - 270.422i) q^{47} +(19.0170 - 32.9384i) q^{49} +(205.051 - 140.506i) q^{51} -476.697 q^{53} -96.1946i q^{55} +(43.8413 + 63.9812i) q^{57} +(425.920 + 245.905i) q^{59} +(661.465 - 381.897i) q^{61} +(80.9894 + 520.783i) q^{63} +(393.832 - 227.379i) q^{65} +(-277.112 + 479.972i) q^{67} +(260.133 - 20.1064i) q^{69} -87.1038 q^{71} -818.083 q^{73} +(169.059 - 353.165i) q^{75} +(-133.246 + 230.789i) q^{77} +(-1030.34 + 594.866i) q^{79} +(-539.012 - 490.823i) q^{81} +(-400.564 + 231.266i) q^{83} +(-291.910 - 168.534i) q^{85} +(580.194 - 1212.03i) q^{87} +1047.78i q^{89} -1259.84 q^{91} +(50.1955 + 649.419i) q^{93} +(52.5869 - 91.0831i) q^{95} +(-562.907 - 974.983i) q^{97} +(-56.6434 - 364.231i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q - 6 q^{3} + 42 q^{9} - 48 q^{11} + 220 q^{19} - 902 q^{25} + 252 q^{27} - 660 q^{33} + 1620 q^{41} + 292 q^{43} + 1762 q^{49} + 1794 q^{51} - 294 q^{57} - 5592 q^{59} - 6 q^{65} - 68 q^{67} - 868 q^{73}+ \cdots + 2118 q^{99}+O(q^{100}) \) 64 * q - 6 * q^3 + 42 * q^9 - 48 * q^11 + 220 * q^19 - 902 * q^25 + 252 * q^27 - 660 * q^33 + 1620 * q^41 + 292 * q^43 + 1762 * q^49 + 1794 * q^51 - 294 * q^57 - 5592 * q^59 - 6 * q^65 - 68 * q^67 - 868 * q^73 + 4254 * q^75 + 498 * q^81 - 3654 * q^83 + 1380 * q^91 - 1912 * q^97 + 2118 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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