LMFDB - Embedded newform 288.4.p.b.47.12

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			47.12
Character	$\chi$	$=$	288.47
Dual form			288.4.p.b.239.12

$q$-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 $\left(\mathbb{Z}/288\mathbb{Z}\right)^\times$.

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

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	$-0.0646250\pi$
$5$	3.52304	+	6.10209i	0.315111	+	0.545788i	−0.664350	+	0.747421i	$0.731292\pi$
$6$		0			0
$7$	−16.9049	−	9.76005i	−0.912779	−	0.526993i	−0.0314545	−	0.999505i	$-0.510014\pi$
$7$	−16.9049	−	9.76005i	−0.912779	−	0.526993i	−0.881324	+	0.472512i	$0.843347\pi$
$8$		0			0
$9$	−9.74649	−	25.1795i	−0.360981	−	0.932573i
$10$		0			0
$11$	−11.8232	−	6.82610i	−0.324074	−	0.187104i	0.329133	−	0.944284i	$-0.393244\pi$
$11$	−11.8232	−	6.82610i	−0.324074	−	0.187104i	−0.653207	+	0.757179i	$0.726577\pi$
$12$		0			0
$13$	55.8938	−	32.2703i	1.19247	−	0.688474i	0.233606	−	0.972331i	$-0.424947\pi$
$13$	55.8938	−	32.2703i	1.19247	−	0.688474i	0.958867	+	0.283857i	$0.0916141\pi$
$14$		0			0
$15$	−36.5037	−	2.82147i	−0.628347	−	0.0485668i
$16$		0			0
$17$		−	47.8376i		−	0.682490i	−0.939974	−	0.341245i	$-0.889151\pi$
$17$		−	47.8376i		−	0.682490i	0.939974	−	0.341245i	$-0.110849\pi$
$18$		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	$-0.0935766\pi$
$23$	25.1060	+	43.4848i	0.227607	+	0.394226i	−0.729492	+	0.683990i	$0.760243\pi$
$24$		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	0.0716823	+	0.997428i	$0.477163\pi$
$29$	−129.302	+	223.957i	−0.827956	+	1.43406i	−0.899639	+	0.436635i	$0.856170\pi$
$30$		0			0
$31$	108.559	−	62.6768i	0.628962	−	0.363132i	−0.151388	−	0.988474i	$-0.548374\pi$
$31$	108.559	−	62.6768i	0.628962	−	0.363132i	0.780350	+	0.625343i	$0.215041\pi$
$32$		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	0.571073	−	0.820900i	$-0.306527\pi$
$41$	411.520	−	237.591i	1.56753	−	0.905013i	0.996456	−	0.0841137i	$-0.0268059\pi$
$42$		0			0
$43$	178.732	−	309.573i	0.633870	−	1.09789i	−0.352884	−	0.935667i	$-0.614799\pi$
$43$	178.732	−	309.573i	0.633870	−	1.09789i	0.986753	−	0.162228i	$-0.0518679\pi$
$44$		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	$-0.672319\pi$
$47$	156.128	−	270.422i	0.484545	−	0.839256i	0.999842	+	0.0177550i	$0.00565190\pi$
$48$		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	$-0.288053\pi$
$53$	476.697			1.23546			0.617729	+	0.786391i	$0.288053\pi$
$54$		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	0.0499237	−	0.998753i	$-0.484102\pi$
$59$	425.920	−	245.905i	0.939831	−	0.542612i	0.889907	+	0.456141i	$0.150769\pi$
$60$		0			0
$61$	−661.465	−	381.897i	−1.38839	−	0.801589i	−0.395259	−	0.918570i	$-0.629345\pi$
$61$	−661.465	−	381.897i	−1.38839	−	0.801589i	−0.993134	+	0.116981i	$0.962678\pi$
$62$		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	−0.999981	−	0.00612269i	$-0.998051\pi$
$67$	−277.112	−	479.972i	−0.505293	−	0.875193i	0.494688	−	0.869071i	$-0.335282\pi$
$68$		0			0
$69$	−260.133	−	20.1064i	−0.453860	−	0.0350801i
$70$		0			0
$71$	87.1038			0.145596			0.0727980	−	0.997347i	$-0.476807\pi$
$71$	87.1038			0.145596			0.0727980	+	0.997347i	$0.476807\pi$
$72$		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	$-0.0116286\pi$
$79$	1030.34	+	594.866i	1.46737	+	0.847186i	0.468036	+	0.883710i	$0.344962\pi$
$80$		0			0
$81$	−539.012	+	490.823i	−0.739385	+	0.673283i
$82$		0			0
$83$	−400.564	−	231.266i	−0.529730	−	0.305840i	0.211176	−	0.977448i	$-0.432271\pi$
$83$	−400.564	−	231.266i	−0.529730	−	0.305840i	−0.740907	+	0.671608i	$0.765604\pi$
$84$		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	$-0.785524\pi$
$89$		−	1047.78i		−	1.24791i	0.781459	−	0.623956i	$-0.214476\pi$
$90$		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	0.405113	+	0.914267i	$0.367232\pi$
$97$	−562.907	+	974.983i	−0.589222	+	1.02056i	−0.994335	+	0.106296i	$0.966101\pi$
$98$		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	$-0.932931\pi$
$101$	−312.444	+	541.170i	−0.307816	+	0.533152i	0.670069	+	0.742299i	$0.266265\pi$
$102$		0			0
$103$	−135.960	+	78.4965i	−0.130063	+	0.0750922i	−0.563620	−	0.826034i	$-0.690592\pi$
$103$	−135.960	+	78.4965i	−0.130063	+	0.0750922i	0.433557	+	0.901126i	$0.357258\pi$
$104$		0			0
$105$	589.553	+	403.974i	0.547947	+	0.375465i
$106$		0			0
$107$			420.449i			0.379872i	0.981796	+	0.189936i	$0.0608280\pi$
$107$			420.449i			0.379872i	−0.981796	+	0.189936i	$0.939172\pi$
$108$		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	−0.368143	−	0.929769i	$-0.620006\pi$
$113$	303.893	−	175.453i	0.252990	−	0.146064i	0.621132	+	0.783706i	$0.286673\pi$
$114$		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	−0.141565	−	0.989929i	$-0.545214\pi$
$131$	967.023	−	558.311i	0.644956	−	0.372365i	0.786521	+	0.617564i	$0.211880\pi$
$132$		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	0.664945	−	0.746892i	$-0.268455\pi$
$137$	562.186	+	324.578i	0.350590	+	0.202413i	−0.314355	+	0.949305i	$0.601788\pi$
$138$		0			0
$139$	535.022	+	926.685i	0.326475	+	0.565471i	0.981810	−	0.189868i	$-0.0608059\pi$
$139$	535.022	+	926.685i	0.326475	+	0.565471i	−0.655335	+	0.755338i	$0.727473\pi$
$140$		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	$-0.218710\pi$
$149$	−296.044	−	512.764i	−0.162771	−	0.281928i	−0.935862	+	0.352368i	$0.885377\pi$
$150$		0			0
$151$	−1813.60	−	1047.08i	−0.977411	−	0.564308i	−0.0759232	−	0.997114i	$-0.524190\pi$
$151$	−1813.60	−	1047.08i	−0.977411	−	0.564308i	−0.901487	+	0.432805i	$0.857524\pi$
$152$		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	$-0.655178\pi$
$157$	122.949	−	70.9848i	0.0624995	−	0.0360841i	0.530924	+	0.847419i	$0.321845\pi$
$158$		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	0.980624	+	0.195900i	$0.0627629\pi$
$167$	1424.28	+	2466.93i	0.659966	+	1.14310i	−0.320657	+	0.947195i	$0.603904\pi$
$168$		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	$-0.831666\pi$
$173$	11.9219	−	20.6493i	0.00523934	−	0.00907480i	0.868633	+	0.495456i	$0.164999\pi$
$174$		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	$-0.866922\pi$
$179$		−	1944.64i		−	0.812009i	0.913871	−	0.406004i	$-0.133078\pi$
$180$		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	−0.391854	−	0.920027i	$-0.628166\pi$
$191$	1586.02	−	2747.07i	0.600840	−	1.04069i	0.992694	−	0.120658i	$-0.0385005\pi$
$192$		0			0
$193$	221.041	+	382.854i	0.0824398	+	0.142790i	0.904297	−	0.426903i	$-0.140395\pi$
$193$	221.041	+	382.854i	0.0824398	+	0.142790i	−0.821858	+	0.569693i	$0.807062\pi$
$194$		0			0
$195$	−2131.38	+	1020.28i	−0.782724	+	0.374686i
$196$		0			0
$197$	−3084.07			−1.11539			−0.557693	−	0.830047i	$-0.688313\pi$
$197$	−3084.07			−1.11539			−0.557693	+	0.830047i	$0.688313\pi$
$198$		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	0.720885	−	0.693055i	$-0.243736\pi$
$211$	−734.854	−	1272.80i	−0.239760	−	0.415277i	−0.960645	+	0.277777i	$0.910402\pi$
$212$		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	$-0.275228\pi$
$223$	1047.05	+	604.513i	0.314419	+	0.181530i	−0.334483	+	0.942402i	$0.608562\pi$
$224$		0			0
$225$	−2010.36	−	312.640i	−0.595661	−	0.0926342i
$226$		0			0
$227$	−1946.40	−	1123.76i	−0.569107	−	0.328574i	0.187686	−	0.982229i	$-0.439901\pi$
$227$	−1946.40	−	1123.76i	−0.569107	−	0.328574i	−0.756793	+	0.653655i	$0.773235\pi$
$228$		0			0
$229$	663.668	−	383.169i	0.191513	−	0.110570i	−0.401178	−	0.916000i	$-0.631399\pi$
$229$	663.668	−	383.169i	0.191513	−	0.110570i	0.592691	+	0.805430i	$0.298066\pi$
$230$		0			0
$231$	−1380.62	−	106.712i	−0.393238	−	0.0303945i
$232$		0			0
$233$		−	801.184i		−	0.225267i	−0.993637	−	0.112634i	$-0.964071\pi$
$233$		−	801.184i		−	0.225267i	0.993637	−	0.112634i	$-0.0359287\pi$
$234$		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	0.905098	+	0.425203i	$0.139797\pi$
$239$	3032.68	+	5252.75i	0.820785	+	1.42164i	−0.0843128	+	0.996439i	$0.526870\pi$
$240$		0			0
$241$	2629.87	−	4555.07i	0.702924	−	1.21750i	−0.264511	−	0.964383i	$-0.585211\pi$
$241$	2629.87	−	4555.07i	0.702924	−	1.21750i	0.967435	−	0.253118i	$-0.0814560\pi$
$242$		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	$0.117112\pi$
$251$			2860.56i			0.719350i	−0.933078	+	0.359675i	$0.882888\pi$
$252$		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	−0.427150	−	0.904181i	$-0.640482\pi$
$257$	586.357	−	338.534i	0.142319	−	0.0821679i	0.569469	+	0.822013i	$0.307149\pi$
$258$		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	$-0.876715\pi$
$263$	−579.488	+	1003.70i	−0.135866	+	0.235327i	0.790062	+	0.613027i	$0.210048\pi$
$264$		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	$-0.161049\pi$
$269$	7718.35			1.74943			0.874714	+	0.484640i	$0.161049\pi$
$270$		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	$-0.165979\pi$
$277$	4007.48	+	2313.72i	0.869265	+	0.501870i	0.00216082	+	0.999998i	$0.499312\pi$
$278$		0			0
$279$	−2636.24	−	2122.59i	−0.565690	−	0.455470i
$280$		0			0
$281$	2505.78	+	1446.71i	0.531966	+	0.307131i	0.741817	−	0.670603i	$-0.233964\pi$
$281$	2505.78	+	1446.71i	0.531966	+	0.307131i	−0.209851	+	0.977733i	$0.567298\pi$
$282$		0			0
$283$	4140.78	+	7172.04i	0.869766	+	1.50648i	0.862235	+	0.506508i	$0.169064\pi$
$283$	4140.78	+	7172.04i	0.869766	+	1.50648i	0.00753096	+	0.999972i	$0.497603\pi$
$284$		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	$-0.0454937\pi$
$293$	1863.44	+	3227.58i	0.371548	+	0.643540i	−0.618256	+	0.785977i	$0.712160\pi$
$294$		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	−0.959102	−	0.283059i	$-0.908651\pi$
$311$	−3974.58	−	6884.18i	−0.724688	−	1.25520i	0.234415	−	0.972137i	$-0.424683\pi$
$312$		0			0
$313$	1570.79	−	2720.69i	0.283663	−	0.491318i	−0.688621	−	0.725121i	$-0.741784\pi$
$313$	1570.79	−	2720.69i	0.283663	−	0.491318i	0.972284	+	0.233803i	$0.0751170\pi$
$314$		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	$-0.887413\pi$
$317$	−954.296	+	1652.89i	−0.169081	+	0.292856i	0.769016	+	0.639229i	$0.220747\pi$
$318$		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	−0.436449	−	0.899729i	$-0.643764\pi$
$331$	3378.13	−	5851.10i	0.560964	−	0.971618i	0.997413	−	0.0718887i	$-0.0229026\pi$
$332$		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	0.924542	+	0.381080i	$0.124448\pi$
$337$	4901.54	+	8489.71i	0.792296	+	1.37230i	−0.132246	+	0.991217i	$0.542219\pi$
$338$		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	−0.669424	+	0.742881i	$0.733459\pi$
$347$	−10649.2	+	6148.32i	−1.64749	+	0.951178i	−0.978066	+	0.208297i	$0.933208\pi$
$348$		0			0
$349$	−6231.13	−	3597.55i	−0.955716	−	0.551783i	−0.0608642	−	0.998146i	$-0.519386\pi$
$349$	−6231.13	−	3597.55i	−0.955716	−	0.551783i	−0.894852	+	0.446363i	$0.852719\pi$
$350$		0			0
$351$	8671.03	−	2608.15i	1.31859	−	0.396617i
$352$		0			0
$353$	−2455.03	−	1417.41i	−0.370164	−	0.213714i	0.303366	−	0.952874i	$-0.401889\pi$
$353$	−2455.03	−	1417.41i	−0.370164	−	0.213714i	−0.673530	+	0.739160i	$0.735223\pi$
$354$		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	$-0.581558\pi$
$359$	−3447.67			−0.506856			−0.253428	+	0.967354i	$0.581558\pi$
$360$		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	$-0.455981\pi$
$367$	−4576.87	−	2642.46i	−0.650983	−	0.375845i	−0.788833	+	0.614608i	$0.789314\pi$
$368$		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	$-0.885000\pi$
$373$	−7902.95	+	4562.77i	−1.09705	+	0.633381i	−0.161604	+	0.986856i	$0.551667\pi$
$374$		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	$-0.280424\pi$
$383$	−2622.07	−	4541.55i	−0.349821	−	0.605907i	−0.986217	+	0.165455i	$0.947091\pi$
$384$		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	$-0.800181\pi$
$389$	797.621	−	1381.52i	0.103961	−	0.180067i	0.913313	+	0.407257i	$0.133515\pi$
$390$		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	−0.510568	−	0.859837i	$-0.670565\pi$
$401$	−170.330	+	98.3398i	−0.0212116	+	0.0122465i	0.489357	+	0.872084i	$0.337232\pi$
$402$		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	0.996513	+	0.0834349i	$0.0265891\pi$
$409$	4719.01	+	8173.56i	0.570513	+	0.988158i	−0.426000	+	0.904723i	$0.640078\pi$
$410$		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	−0.960305	−	0.278954i	$-0.910012\pi$
$419$	−10282.4	+	5936.56i	−1.19888	+	0.692171i	−0.238571	+	0.971125i	$0.576679\pi$
$420$		0			0
$421$	−936.025	−	540.414i	−0.108359	−	0.0625610i	0.444841	−	0.895609i	$-0.353260\pi$
$421$	−936.025	−	540.414i	−0.108359	−	0.0625610i	−0.553200	+	0.833048i	$0.686593\pi$
$422$		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	$-0.108659\pi$
$431$	16863.0			1.88460			0.942299	+	0.334772i	$0.108659\pi$
$432$		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	$-0.218759\pi$
$439$	5611.44	+	3239.77i	0.610068	+	0.352223i	−0.162924	+	0.986639i	$0.552093\pi$
$440$		0			0
$441$	644.023	−	799.872i	0.0695414	−	0.0863699i
$442$		0			0
$443$	1696.92	+	979.717i	0.181993	+	0.105074i	0.588229	−	0.808694i	$-0.299825\pi$
$443$	1696.92	+	979.717i	0.181993	+	0.105074i	−0.406236	+	0.913768i	$0.633159\pi$
$444$		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	$0.0430666\pi$
$449$			2566.64i			0.269771i	−0.990861	+	0.134885i	$0.956933\pi$
$450$		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	−0.825638	−	0.564200i	$-0.809185\pi$
$457$	740.460	−	1282.51i	0.0757927	−	0.131277i	0.901431	+	0.432923i	$0.142518\pi$
$458$		0			0
$459$	1539.32	−	6532.52i	0.156535	−	0.664296i
$460$		0			0
$461$	−6037.19	+	10456.7i	−0.609935	+	1.05644i	0.381316	+	0.924445i	$0.375471\pi$
$461$	−6037.19	+	10456.7i	−0.609935	+	1.05644i	−0.991251	+	0.131993i	$0.957862\pi$
$462$		0			0
$463$	−13152.8	+	7593.77i	−1.32022	+	0.762230i	−0.983764	−	0.179469i	$-0.942562\pi$
$463$	−13152.8	+	7593.77i	−1.32022	+	0.762230i	−0.336457	+	0.941699i	$0.609229\pi$
$464$		0			0
$465$	−4139.65	+	1981.63i	−0.412843	+	0.197626i
$466$		0			0
$467$			46.2660i			0.00458445i	0.999997	+	0.00229222i	$0.000729638\pi$
$467$			46.2660i			0.00458445i	−0.999997	+	0.00229222i	$0.999270\pi$
$468$		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	0.268091	+	0.963393i	$0.413607\pi$
$479$	−7341.31	+	12715.5i	−0.700278	+	1.21292i	−0.968369	+	0.249523i	$0.919726\pi$
$480$		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	−0.114039	−	0.993476i	$-0.536379\pi$
$491$	7499.65	−	4329.93i	0.689317	−	0.397977i	0.803356	+	0.595499i	$0.203046\pi$
$492$		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	0.929708	−	0.368296i	$-0.120059\pi$
$499$	1626.32	+	2816.87i	0.145900	+	0.252707i	−0.783808	+	0.621003i	$0.786726\pi$
$500$		0			0
$501$	−14757.6	−	1140.66i	−1.31601	−	0.101718i
$502$		0			0
$503$	−2500.59			−0.221662			−0.110831	−	0.993839i	$-0.535351\pi$
$503$	−2500.59			−0.221662			−0.110831	+	0.993839i	$0.535351\pi$
$504$		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	$-0.0355044\pi$
$509$	4599.12	+	7965.92i	0.400496	+	0.693680i	−0.593290	+	0.804989i	$0.702171\pi$
$510$		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	$0.104033\pi$
$521$			7635.67i			0.642082i	−0.947065	+	0.321041i	$0.895967\pi$
$522$		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	−0.944721	−	0.327876i	$-0.893667\pi$
$547$	−2410.39	+	4174.92i	−0.188411	+	0.326337i	0.756310	+	0.654214i	$0.227000\pi$
$548$		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	$-0.427347\pi$
$557$	5948.96			0.452541			0.226271	+	0.974064i	$0.427347\pi$
$558$		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	−0.538646	−	0.842532i	$-0.681064\pi$
$563$	−1046.18	+	604.012i	−0.0783148	+	0.0452151i	0.460331	+	0.887747i	$0.347731\pi$
$564$		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	0.398667	−	0.917096i	$-0.369473\pi$
$569$	−2663.36	−	1537.69i	−0.196229	−	0.113293i	−0.594895	+	0.803803i	$0.702806\pi$
$570$		0			0
$571$	−4651.48	−	8056.60i	−0.340908	−	0.590470i	0.643694	−	0.765283i	$-0.277401\pi$
$571$	−4651.48	−	8056.60i	−0.340908	−	0.590470i	−0.984602	+	0.174813i	$0.944068\pi$
$572$		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	0.844220	−	0.535996i	$-0.180064\pi$
$587$	11408.0	+	6586.41i	0.802144	+	0.463118i	−0.0420762	+	0.999114i	$0.513397\pi$
$588$		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	$-0.747202\pi$
$593$		−	20600.6i		−	1.42659i	0.700865	−	0.713294i	$-0.252798\pi$
$594$		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	$-0.0435590\pi$
$599$	5529.60	+	9577.55i	0.377184	+	0.653302i	−0.613467	+	0.789720i	$0.710226\pi$
$600$		0			0
$601$	10115.9	−	17521.2i	0.686581	−	1.18919i	−0.286356	−	0.958123i	$-0.592444\pi$
$601$	10115.9	−	17521.2i	0.686581	−	1.18919i	0.972937	−	0.231070i	$-0.0742227\pi$
$602$		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	−0.635798	+	0.771856i	$0.719329\pi$
$607$	−24259.0	+	14005.9i	−1.62214	+	0.936545i	−0.986346	+	0.164689i	$0.947338\pi$
$608$		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	−0.437691	−	0.899126i	$-0.644204\pi$
$617$	1871.75	−	1080.65i	0.122129	−	0.0705114i	0.559820	+	0.828614i	$0.310870\pi$
$618$		0			0
$619$	3435.93	−	5951.20i	0.223104	−	0.386428i	−0.732645	−	0.680611i	$-0.761714\pi$
$619$	3435.93	−	5951.20i	0.223104	−	0.386428i	0.955749	+	0.294183i	$0.0950476\pi$
$620$		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	0.171372	−	0.985206i	$-0.445180\pi$
$641$	−9674.91	−	5585.81i	−0.596156	−	0.344191i	−0.767528	+	0.641016i	$0.778513\pi$
$642$		0			0
$643$	3853.78	+	6674.94i	0.236358	+	0.409384i	0.959666	−	0.281141i	$-0.0907129\pi$
$643$	3853.78	+	6674.94i	0.236358	+	0.409384i	−0.723309	+	0.690525i	$0.757380\pi$
$644$		0			0
$645$	−7397.83	+	10796.3i	−0.451611	+	0.659074i
$646$		0			0
$647$	10087.3			0.612943			0.306472	−	0.951880i	$-0.400852\pi$
$647$	10087.3			0.612943			0.306472	+	0.951880i	$0.400852\pi$
$648$		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	−0.969989	−	0.243148i	$-0.921820\pi$
$653$	−11606.7	−	20103.4i	−0.695567	−	1.20476i	0.274422	−	0.961609i	$-0.411513\pi$
$654$		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	0.992029	−	0.126014i	$-0.0402183\pi$
$659$	23327.3	+	13468.0i	1.37891	+	0.796115i	0.386883	+	0.922129i	$0.373552\pi$
$660$		0			0
$661$	20390.0	−	11772.2i	1.19982	−	0.692715i	0.239304	−	0.970945i	$-0.423081\pi$
$661$	20390.0	−	11772.2i	1.19982	−	0.692715i	0.960515	+	0.278229i	$0.0897475\pi$
$662$		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	0.310905	+	0.950441i	$0.399368\pi$
$673$	−11656.7	+	20189.9i	−0.667654	+	1.15641i	−0.978559	+	0.205969i	$0.933965\pi$
$674$		0			0
$675$	7244.79	−	7698.93i	0.413114	−	0.439010i
$676$		0			0
$677$	−12028.2	+	20833.5i	−0.682840	+	1.18271i	0.291271	+	0.956641i	$0.405922\pi$
$677$	−12028.2	+	20833.5i	−0.682840	+	1.18271i	−0.974110	+	0.226072i	$0.927411\pi$
$678$		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	$-0.827225\pi$
$683$		−	18439.7i		−	1.03305i	0.856272	−	0.516525i	$-0.172775\pi$
$684$		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	−0.600475	−	0.799643i	$-0.705022\pi$
$691$	7125.35	−	12341.5i	0.392274	−	0.679438i	0.992749	+	0.120205i	$0.0383553\pi$
$692$		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	$-0.636314\pi$
$701$	−15415.0			−0.830549			−0.415274	+	0.909696i	$0.636314\pi$
$702$		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	$-0.494720\pi$
$709$	−15877.4	−	9166.80i	−0.841025	−	0.485566i	−0.857613	+	0.514296i	$0.828053\pi$
$710$		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	$-0.587178\pi$
$719$	−10428.9			−0.540936			−0.270468	+	0.962729i	$0.587178\pi$
$720$		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	$-0.457748\pi$
$727$	−12935.1	−	7468.08i	−0.659884	−	0.380984i	−0.792233	+	0.610219i	$0.791082\pi$
$728$		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	$-0.670686\pi$
$733$	−434.025	+	250.584i	−0.0218705	+	0.0126269i	0.489025	+	0.872270i	$0.337353\pi$
$734$		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	0.911270	+	0.411808i	$0.135103\pi$
$743$	16450.7	+	28493.5i	0.812272	+	1.40690i	−0.0989987	+	0.995088i	$0.531564\pi$
$744$		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	0.565827	−	0.824524i	$-0.308557\pi$
$751$	32163.5	−	18569.6i	1.56280	−	0.902282i	0.996972	−	0.0777583i	$-0.0247762\pi$
$752$		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	−0.677326	−	0.735683i	$-0.736861\pi$
$761$	−7953.62	+	4592.02i	−0.378868	+	0.218739i	0.298458	+	0.954423i	$0.403528\pi$
$762$		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	0.904336	+	0.426821i	$0.140366\pi$
$769$	17525.0	+	30354.2i	0.821806	+	1.42341i	−0.0825304	+	0.996589i	$0.526300\pi$
$770$		0			0
$771$	−271.119	+	3507.68i	−0.0126642	+	0.163847i
$772$		0			0
$773$	−1390.01			−0.0646768			−0.0323384	−	0.999477i	$-0.510295\pi$
$773$	−1390.01			−0.0646768			−0.0323384	+	0.999477i	$0.510295\pi$
$774$		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	0.797257	−	0.603640i	$-0.206283\pi$
$787$	−2740.75	−	4747.12i	−0.124139	−	0.215015i	−0.921396	+	0.388625i	$0.872950\pi$
$788$		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	0.965992	+	0.258573i	$0.0832521\pi$
$797$	15906.0	+	27550.0i	0.706926	+	1.22443i	−0.259065	+	0.965860i	$0.583415\pi$
$798$		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	$0.0193003\pi$
$809$			2788.69i			0.121193i	−0.998162	+	0.0605966i	$0.980700\pi$
$810$		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	$-0.796031\pi$
$821$	2750.46	−	4763.94i	0.116921	−	0.202512i	0.918546	+	0.395314i	$0.129364\pi$
$822$		0			0
$823$	−4259.38	+	2459.15i	−0.180404	+	0.104156i	−0.587483	−	0.809237i	$-0.699881\pi$
$823$	−4259.38	+	2459.15i	−0.180404	+	0.104156i	0.407078	+	0.913393i	$0.366548\pi$
$824$		0			0
$825$	411.936	−	5329.54i	0.0173839	−	0.224910i
$826$		0			0
$827$			17035.6i			0.716307i	0.933663	+	0.358153i	$0.116593\pi$
$827$			17035.6i			0.716307i	−0.933663	+	0.358153i	$0.883407\pi$
$828$		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	$-0.772648\pi$
$839$	4605.12	−	7976.30i	0.189495	−	0.328215i	0.945082	+	0.326833i	$0.105982\pi$
$840$		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	$-0.379354\pi$
$853$	−6216.93	−	3589.35i	−0.249547	−	0.144076i	−0.619557	+	0.784952i	$0.712688\pi$
$854$		0			0
$855$	−1780.89	+	2211.85i	−0.0712340	+	0.0884722i
$856$		0			0
$857$	13290.3	+	7673.16i	0.529741	+	0.305846i	0.740911	−	0.671603i	$-0.234394\pi$
$857$	13290.3	+	7673.16i	0.529741	+	0.305846i	−0.211170	+	0.977449i	$0.567727\pi$
$858$		0			0
$859$	−18277.1	−	31656.9i	−0.725969	−	1.25742i	−0.958574	−	0.284844i	$-0.908058\pi$
$859$	−18277.1	−	31656.9i	−0.725969	−	1.25742i	0.232604	−	0.972571i	$-0.425275\pi$
$860$		0			0
$861$	27243.7	−	39759.0i	1.07835	−	1.57373i
$862$		0			0
$863$	27501.0			1.08476			0.542378	−	0.840135i	$-0.317524\pi$
$863$	27501.0			1.08476			0.542378	+	0.840135i	$0.317524\pi$
$864$		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	$-0.632066\pi$
$877$	4880.15	−	2817.56i	0.187903	−	0.108486i	0.591000	+	0.806671i	$0.298733\pi$
$878$		0			0
$879$	−19307.9	−	1492.36i	−0.740887	−	0.0572653i
$880$		0			0
$881$		−	51429.9i		−	1.96676i	−0.181554	−	0.983381i	$-0.558113\pi$
$881$		−	51429.9i		−	1.96676i	0.181554	−	0.983381i	$-0.441887\pi$
$882$		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	−0.972501	−	0.232900i	$-0.925179\pi$
$887$	−18173.6	−	31477.6i	−0.687948	−	1.19156i	0.284553	−	0.958660i	$-0.408155\pi$
$888$		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	−0.915872	−	0.401472i	$-0.868499\pi$
$907$	−3011.58	+	5216.21i	−0.110251	+	0.190961i	0.805620	+	0.592432i	$0.201832\pi$
$908$		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	$-0.868087\pi$
$911$	−2996.17	+	5189.52i	−0.108965	+	0.188734i	0.806386	+	0.591390i	$0.201420\pi$
$912$		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	0.784497	−	0.620133i	$-0.212921\pi$
$929$	18113.2	+	10457.7i	0.639695	+	0.369328i	−0.144802	+	0.989461i	$0.546255\pi$
$930$		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	$-0.150862\pi$
$941$	1432.61	+	2481.36i	0.0496300	+	0.0859616i	−0.840143	+	0.542365i	$0.817529\pi$
$942$		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	0.618713	−	0.785617i	$-0.287654\pi$
$947$	7218.72	+	4167.73i	0.247705	+	0.143013i	−0.371008	+	0.928630i	$0.620988\pi$
$948$		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	$0.235429\pi$
$953$			39658.3i			1.34802i	−0.738724	+	0.674008i	$0.764571\pi$
$954$		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	$-0.725235\pi$
$967$	−9529.32	+	5501.75i	−0.316900	+	0.182962i	0.333110	+	0.942888i	$0.391902\pi$
$968$		0			0
$969$	−3060.71	−	2097.26i	−0.101470	−	0.0695292i
$970$		0			0
$971$		−	18334.6i		−	0.605958i	−0.952997	−	0.302979i	$-0.902019\pi$
$971$		−	18334.6i		−	0.605958i	0.952997	−	0.302979i	$-0.0979813\pi$
$972$		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	0.131990	−	0.991251i	$-0.457863\pi$
$977$	32261.5	−	18626.2i	1.05643	−	0.609932i	0.924444	+	0.381319i	$0.124530\pi$
$978$		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	$-0.889348\pi$
$983$	−5395.60	+	9345.46i	−0.175069	+	0.303229i	0.765116	+	0.643892i	$0.222682\pi$
$984$		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	$-0.359925\pi$
$997$	−4549.81	−	2626.84i	−0.144528	−	0.0834431i	−0.570520	+	0.821284i	$0.693258\pi$
$998$		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.47.12		64
3.2	odd	2		864.4.p.b.143.12		64
4.3	odd	2		72.4.l.b.11.1	✓	64
8.3	odd	2	inner	288.4.p.b.47.11		64
8.5	even	2		72.4.l.b.11.10	yes	64
9.4	even	3		864.4.p.b.719.21		64
9.5	odd	6	inner	288.4.p.b.239.11		64
12.11	even	2		216.4.l.b.35.32		64
24.5	odd	2		216.4.l.b.35.23		64
24.11	even	2		864.4.p.b.143.21		64
36.23	even	6		72.4.l.b.59.10	yes	64
36.31	odd	6		216.4.l.b.179.23		64
72.5	odd	6		72.4.l.b.59.1	yes	64
72.13	even	6		216.4.l.b.179.32		64
72.59	even	6	inner	288.4.p.b.239.12		64
72.67	odd	6		864.4.p.b.719.12		64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
72.4.l.b.11.1	✓	64	4.3	odd	2
72.4.l.b.11.10	yes	64	8.5	even	2
72.4.l.b.59.1	yes	64	72.5	odd	6
72.4.l.b.59.10	yes	64	36.23	even	6
216.4.l.b.35.23		64	24.5	odd	2
216.4.l.b.35.32		64	12.11	even	2
216.4.l.b.179.23		64	36.31	odd	6
216.4.l.b.179.32		64	72.13	even	6
288.4.p.b.47.11		64	8.3	odd	2	inner
288.4.p.b.47.12		64	1.1	even	1	trivial
288.4.p.b.239.11		64	9.5	odd	6	inner
288.4.p.b.239.12		64	72.59	even	6	inner
864.4.p.b.143.12		64	3.2	odd	2
864.4.p.b.143.21		64	24.11	even	2
864.4.p.b.719.12		64	72.67	odd	6
864.4.p.b.719.21		64	9.4	even	3

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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