LMFDB - Embedded newform 216.4.l.b.35.32

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [216,4,Mod(35,216)] 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("216.35"); S:= CuspForms(chi, 4); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(216, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([3, 3, 1])) N = Newforms(chi, 4, names="a")

Level:	$ N $	$=$	$ 216 = 2^{3} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	216.l (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:	$12.7444125612$
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			35.32
Character	$\chi$	$=$	216.35
Dual form			216.4.l.b.179.32

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(2.81730 + 0.250612i) q^{2} +(7.87439 + 1.41210i) q^{4} +(-3.52304 - 6.10209i) q^{5} +(16.9049 + 9.76005i) q^{7} +(21.8306 + 5.95172i) q^{8} +(-8.39622 - 18.0744i) q^{10} +(-11.8232 - 6.82610i) q^{11} +(55.8938 - 32.2703i) q^{13} +(45.1802 + 31.7336i) q^{14} +(60.0120 + 22.2388i) q^{16} +47.8376i q^{17} +14.9265 q^{19} +(-19.1251 - 53.0251i) q^{20} +(-31.5987 - 22.1942i) q^{22} +(25.1060 + 43.4848i) q^{23} +(37.6763 - 65.2573i) q^{25} +(165.557 - 76.9075i) q^{26} +(119.334 + 100.726i) q^{28} +(129.302 - 223.957i) q^{29} +(-108.559 + 62.6768i) q^{31} +(163.499 + 77.6932i) q^{32} +(-11.9887 + 134.773i) q^{34} -137.540i q^{35} +208.987i q^{37} +(42.0526 + 3.74077i) q^{38} +(-40.5924 - 154.181i) q^{40} +(-411.520 + 237.591i) q^{41} +(-178.732 + 309.573i) q^{43} +(-83.4610 - 70.4468i) q^{44} +(59.8333 + 128.802i) q^{46} +(156.128 - 270.422i) q^{47} +(19.0170 + 32.9384i) q^{49} +(122.500 - 174.407i) q^{50} +(485.698 - 175.181i) q^{52} -476.697 q^{53} +96.1946i q^{55} +(310.956 + 313.681i) q^{56} +(420.409 - 598.551i) q^{58} +(425.920 - 245.905i) q^{59} +(-661.465 - 381.897i) q^{61} +(-321.552 + 149.373i) q^{62} +(441.154 + 259.860i) q^{64} +(-393.832 - 227.379i) q^{65} +(277.112 + 479.972i) q^{67} +(-67.5514 + 376.692i) q^{68} +(34.4692 - 387.493i) q^{70} +87.1038 q^{71} -818.083 q^{73} +(-52.3747 + 588.780i) q^{74} +(117.537 + 21.0778i) q^{76} +(-133.246 - 230.789i) q^{77} +(-1030.34 - 594.866i) q^{79} +(-75.7214 - 444.547i) q^{80} +(-1218.92 + 566.235i) q^{82} +(-400.564 - 231.266i) q^{83} +(291.910 - 168.534i) q^{85} +(-581.125 + 827.369i) q^{86} +(-217.480 - 219.386i) q^{88} +1047.78i q^{89} +1259.84 q^{91} +(136.289 + 377.868i) q^{92} +(507.631 - 722.732i) q^{94} +(-52.5869 - 91.0831i) q^{95} +(-562.907 + 974.983i) q^{97} +(45.3219 + 97.5633i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q + 3 q^{2} - 17 q^{4} + 12 q^{10} - 48 q^{11} - 72 q^{14} + 127 q^{16} - 220 q^{19} + 234 q^{20} - 217 q^{22} - 902 q^{25} - 132 q^{28} + 693 q^{32} + 509 q^{34} + 1977 q^{38} - 36 q^{40} - 1620 q^{41}+ \cdots - 1912 q^{97}+O(q^{100}) $ 64 * q + 3 * q^2 - 17 * q^4 + 12 * q^10 - 48 * q^11 - 72 * q^14 + 127 * q^16 - 220 * q^19 + 234 * q^20 - 217 * q^22 - 902 * q^25 - 132 * q^28 + 693 * q^32 + 509 * q^34 + 1977 * q^38 - 36 * q^40 - 1620 * q^41 - 292 * q^43 + 48 * q^46 + 1762 * q^49 + 1227 * q^50 + 330 * q^52 - 942 * q^56 - 282 * q^58 - 5592 * q^59 + 1090 * q^64 + 6 * q^65 + 68 * q^67 + 2025 * q^68 + 600 * q^70 - 868 * q^73 + 420 * q^74 - 1471 * q^76 + 362 * q^82 - 3654 * q^83 + 4119 * q^86 + 3155 * q^88 - 1380 * q^91 + 744 * q^92 - 138 * q^94 - 1912 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/216\mathbb{Z}\right)^\times$.

$n$	$55$	$109$	$137$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{1}{6}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	2.81730	+	0.250612i	0.996067	+	0.0886047i
$2$	2.81730	+	0.250612i	0.996067	+	0.0886047i
$3$		0			0
$3$		0			0
$4$	7.87439	+	1.41210i	0.984298	+	0.176512i
$5$	−3.52304	−	6.10209i	−0.315111	−	0.545788i	0.664350	−	0.747421i	$-0.268708\pi$
$5$	−3.52304	−	6.10209i	−0.315111	−	0.545788i	−0.979461	+	0.201634i	$0.935375\pi$
$6$		0			0
$7$	16.9049	+	9.76005i	0.912779	+	0.526993i	0.881324	−	0.472512i	$-0.156653\pi$
$7$	16.9049	+	9.76005i	0.912779	+	0.526993i	0.0314545	+	0.999505i	$0.489986\pi$
$8$	21.8306	+	5.95172i	0.964787	+	0.263031i
$9$		0			0
$10$	−8.39622	−	18.0744i	−0.265512	−	0.571561i
$11$	−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	$0.0916141\pi$
$14$	45.1802	+	31.7336i	0.862494	+	0.605797i
$15$		0			0
$16$	60.0120	+	22.2388i	0.937687	+	0.347482i
$17$			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	$-0.471276\pi$
$19$	14.9265			0.180231			0.0901154	+	0.995931i	$0.471276\pi$
$20$	−19.1251	−	53.0251i	−0.213825	−	0.592839i
$21$		0			0
$22$	−31.5987	−	22.1942i	−0.306221	−	0.215083i
$23$	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
$26$	165.557	−	76.9075i	1.24878	−	0.580108i
$27$		0			0
$28$	119.334	+	100.726i	0.805426	+	0.679835i
$29$	129.302	−	223.957i	0.827956	−	1.43406i	−0.0716823	−	0.997428i	$-0.522837\pi$
$29$	129.302	−	223.957i	0.827956	−	1.43406i	0.899639	−	0.436635i	$-0.143830\pi$
$30$		0			0
$31$	−108.559	+	62.6768i	−0.628962	+	0.363132i	−0.780350	−	0.625343i	$-0.784959\pi$
$31$	−108.559	+	62.6768i	−0.628962	+	0.363132i	0.151388	+	0.988474i	$0.451626\pi$
$32$	163.499	+	77.6932i	0.903210	+	0.429198i
$33$		0			0
$34$	−11.9887	+	134.773i	−0.0604718	+	0.679806i
$35$		−	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	$0.846310\pi$
$38$	42.0526	+	3.74077i	0.179522	+	0.0159693i
$39$		0			0
$40$	−40.5924	−	154.181i	−0.160455	−	0.609453i
$41$	−411.520	+	237.591i	−1.56753	+	0.905013i	−0.571073	+	0.820900i	$0.693473\pi$
$41$	−411.520	+	237.591i	−1.56753	+	0.905013i	−0.996456	+	0.0841137i	$0.973194\pi$
$42$		0			0
$43$	−178.732	+	309.573i	−0.633870	+	1.09789i	0.352884	+	0.935667i	$0.385201\pi$
$43$	−178.732	+	309.573i	−0.633870	+	1.09789i	−0.986753	+	0.162228i	$0.948132\pi$
$44$	−83.4610	−	70.4468i	−0.285959	−	0.241369i
$45$		0			0
$46$	59.8333	+	128.802i	0.191781	+	0.412843i
$47$	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
$50$	122.500	−	174.407i	0.346482	−	0.493299i
$51$		0			0
$52$	485.698	−	175.181i	1.29527	−	0.467178i
$53$	−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
$56$	310.956	+	313.681i	0.742021	+	0.748526i
$57$		0			0
$58$	420.409	−	598.551i	0.951765	−	1.35506i
$59$	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	$0.962678\pi$
$62$	−321.552	+	149.373i	−0.658664	+	0.305974i
$63$		0			0
$64$	441.154	+	259.860i	0.861629	+	0.507539i
$65$	−393.832	−	227.379i	−0.751521	−	0.433891i
$66$		0			0
$67$	277.112	+	479.972i	0.505293	+	0.875193i	0.999981	+	0.00612269i	$0.00194893\pi$
$67$	277.112	+	479.972i	0.505293	+	0.875193i	−0.494688	+	0.869071i	$0.664718\pi$
$68$	−67.5514	+	376.692i	−0.120468	+	0.671774i
$69$		0			0
$70$	34.4692	−	387.493i	0.0588551	−	0.661632i
$71$	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	$0.727676\pi$
$74$	−52.3747	+	588.780i	−0.0822761	+	0.924923i
$75$		0			0
$76$	117.537	+	21.0778i	0.177401	+	0.0318129i
$77$	−133.246	−	230.789i	−0.197205	−	0.341569i
$78$		0			0
$79$	−1030.34	−	594.866i	−1.46737	−	0.847186i	−0.468036	−	0.883710i	$-0.655038\pi$
$79$	−1030.34	−	594.866i	−1.46737	−	0.847186i	−0.999333	+	0.0365241i	$0.988371\pi$
$80$	−75.7214	−	444.547i	−0.105824	−	0.621273i
$81$		0			0
$82$	−1218.92	+	566.235i	−1.64155	+	0.762563i
$83$	−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
$86$	−581.125	+	827.369i	−0.728655	+	1.03741i
$87$		0			0
$88$	−217.480	−	219.386i	−0.263448	−	0.265757i
$89$			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
$92$	136.289	+	377.868i	0.154447	+	0.428212i
$93$		0			0
$94$	507.631	−	722.732i	0.557001	−	0.793022i
$95$	−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	$0.966101\pi$
$98$	45.3219	+	97.5633i	0.0467163	+	0.100565i
$99$		0			0
$100$	388.828	−	460.659i	0.388828	−	0.460659i
$101$	312.444	−	541.170i	0.307816	−	0.533152i	−0.670069	−	0.742299i	$-0.733735\pi$
$101$	312.444	−	541.170i	0.307816	−	0.533152i	0.977884	+	0.209147i	$0.0670687\pi$
$102$		0			0
$103$	135.960	−	78.4965i	0.130063	−	0.0750922i	−0.433557	−	0.901126i	$-0.642742\pi$
$103$	135.960	−	78.4965i	0.130063	−	0.0750922i	0.563620	+	0.826034i	$0.309408\pi$
$104$	1412.26	−	371.817i	1.33157	−	0.350573i
$105$		0			0
$106$	−1343.00	−	119.466i	−1.23060	−	0.109467i
$107$			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	$-0.179619\pi$
$110$	−24.1075	+	271.009i	−0.0208960	+	0.234907i
$111$		0			0
$112$	797.444	+	961.664i	0.672780	+	0.811328i
$113$	−303.893	+	175.453i	−0.252990	+	0.146064i	−0.621132	−	0.783706i	$-0.713327\pi$
$113$	−303.893	+	175.453i	−0.252990	+	0.146064i	0.368143	+	0.929769i	$0.379994\pi$
$114$		0			0
$115$	176.899	−	306.398i	0.143443	−	0.248450i
$116$	1334.42	−	1580.94i	1.06809	−	1.26540i
$117$		0			0
$118$	1261.57	−	586.048i	0.984212	−	0.457204i
$119$	−466.897	+	808.690i	−0.359667	+	0.622962i
$120$		0			0
$121$	−572.309	−	991.268i	−0.429984	−	0.744754i
$122$	−1767.84	−	1241.69i	−1.31191	−	0.921454i
$123$		0			0
$124$	−943.344	+	340.245i	−0.683184	+	0.246410i
$125$	−1411.70			−1.01013
$126$		0			0
$127$			2003.55i			1.39989i	0.714195	+	0.699947i	$0.246793\pi$
$127$			2003.55i			1.39989i	−0.714195	+	0.699947i	$0.753207\pi$
$128$	1177.74	+	842.662i	0.813270	+	0.581887i
$129$		0			0
$130$	−1052.56	−	739.295i	−0.710121	−	0.498773i
$131$	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
$134$	660.422	+	1421.67i	0.425759	+	0.916522i
$135$		0			0
$136$	−284.716	+	1044.33i	−0.179516	+	0.658458i
$137$	−562.186	−	324.578i	−0.350590	−	0.202413i	0.314355	−	0.949305i	$-0.398212\pi$
$137$	−562.186	−	324.578i	−0.350590	−	0.202413i	−0.664945	+	0.746892i	$0.731545\pi$
$138$		0			0
$139$	−535.022	−	926.685i	−0.326475	−	0.565471i	0.655335	−	0.755338i	$-0.272527\pi$
$139$	−535.022	−	926.685i	−0.326475	−	0.565471i	−0.981810	+	0.189868i	$0.939194\pi$
$140$	194.220	−	1083.05i	0.117247	−	0.653815i
$141$		0			0
$142$	245.398	+	21.8292i	0.145023	+	0.0129005i
$143$	−881.121			−0.515266
$144$		0			0
$145$	−1822.14			−1.04359
$146$	−2304.79	−	205.021i	−1.30648	−	0.116217i
$147$		0			0
$148$	−295.111	+	1645.65i	−0.163905	+	0.913995i
$149$	296.044	+	512.764i	0.162771	+	0.281928i	0.935862	−	0.352368i	$-0.114623\pi$
$149$	296.044	+	512.764i	0.162771	+	0.281928i	−0.773090	+	0.634296i	$0.781290\pi$
$150$		0			0
$151$	1813.60	+	1047.08i	0.977411	+	0.564308i	0.901487	−	0.432805i	$-0.142476\pi$
$151$	1813.60	+	1047.08i	0.977411	+	0.564308i	0.0759232	+	0.997114i	$0.475810\pi$
$152$	325.856	+	88.8387i	0.173884	+	0.0474064i
$153$		0			0
$154$	−317.556	−	683.596i	−0.166165	−	0.357699i
$155$	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	$0.321845\pi$
$158$	−2753.69	−	1934.13i	−1.38653	−	0.973869i
$159$		0			0
$160$	−101.922	−	1271.40i	−0.0503600	−	0.628206i
$161$			980.141i			0.479789i
$162$		0			0
$163$	3642.04			1.75010			0.875051	−	0.484031i	$-0.160828\pi$
$163$	3642.04			1.75010			0.875051	+	0.484031i	$0.160828\pi$
$164$	−3575.97	+	1289.78i	−1.70266	+	0.614115i
$165$		0			0
$166$	−1070.55	−	751.931i	−0.500548	−	0.351573i
$167$	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
$170$	864.634	−	401.655i	0.390085	−	0.181209i
$171$		0			0
$172$	−1844.55	+	2185.31i	−0.817709	+	0.968770i
$173$	−11.9219	+	20.6493i	−0.00523934	+	0.00907480i	−0.868633	−	0.495456i	$-0.835001\pi$
$173$	−11.9219	+	20.6493i	−0.00523934	+	0.00907480i	0.863394	+	0.504531i	$0.168334\pi$
$174$		0			0
$175$	1273.83	−	735.445i	0.550242	−	0.317683i
$176$	−557.726	−	672.581i	−0.238865	−	0.288055i
$177$		0			0
$178$	−262.585	+	2951.91i	−0.110571	+	1.24300i
$179$		−	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	$-0.00180813\pi$
$182$	3549.34	+	315.730i	1.44558	+	0.128591i
$183$		0			0
$184$	289.270	+	1098.72i	0.115898	+	0.440212i
$185$	1275.26	−	736.271i	0.506805	−	0.292604i
$186$		0			0
$187$	326.544	−	565.592i	0.127697	−	0.221177i
$188$	1611.27	−	1908.94i	0.625076	−	0.740551i
$189$		0			0
$190$	−125.327	−	269.788i	−0.0478534	−	0.103013i
$191$	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	$0.807062\pi$
$194$	−1830.22	+	2605.75i	−0.677331	+	0.964341i
$195$		0			0
$196$	103.235	+	286.224i	0.0376221	+	0.104309i
$197$	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	$0.102936\pi$
$199$			1784.15i			0.635555i	−0.948165	+	0.317777i	$0.897064\pi$
$200$	1210.89	−	1200.37i	0.428115	−	0.424395i
$201$		0			0
$202$	1015.87	−	1446.34i	0.353845	−	0.503781i
$203$	4371.67	−	2523.98i	1.51148	−	0.872654i
$204$		0			0
$205$	2899.61	+	1674.09i	0.987890	+	0.570359i
$206$	402.712	−	187.075i	0.136205	−	0.0632726i
$207$		0			0
$208$	4071.95	−	693.591i	1.35740	−	0.231211i
$209$	−176.479	−	101.890i	−0.0584081	−	0.0337219i
$210$		0			0
$211$	734.854	+	1272.80i	0.239760	+	0.415277i	0.960645	−	0.277777i	$-0.0895978\pi$
$211$	734.854	+	1272.80i	0.239760	+	0.415277i	−0.720885	+	0.693055i	$0.756264\pi$
$212$	−3753.69	−	673.143i	−1.21606	−	0.218074i
$213$		0			0
$214$	−105.369	+	1184.53i	−0.0336584	+	0.378378i
$215$	2518.73			0.798956
$216$		0			0
$217$	−2446.91			−0.765471
$218$	305.053	−	3429.31i	0.0947743	−	1.06542i
$219$		0			0
$220$	−135.836	+	757.474i	−0.0416276	+	0.232131i
$221$	1543.73	+	2673.83i	0.469877	+	0.813850i
$222$		0			0
$223$	−1047.05	−	604.513i	−0.314419	−	0.181530i	0.334483	−	0.942402i	$-0.391438\pi$
$223$	−1047.05	−	604.513i	−0.314419	−	0.181530i	−0.648902	+	0.760872i	$0.724772\pi$
$224$	2005.64	+	2909.15i	0.598246	+	0.867748i
$225$		0			0
$226$	−900.128	+	418.144i	−0.264937	+	0.123073i
$227$	−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	$0.298066\pi$
$230$	575.164	−	818.882i	0.164892	−	0.234763i
$231$		0			0
$232$	4155.67	−	4119.56i	1.17601	−	1.16579i
$233$			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
$236$	3701.10	−	1334.91i	1.02085	−	0.368200i
$237$		0			0
$238$	−1518.06	+	2161.31i	−0.413450	+	0.588644i
$239$	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	$-0.0814560\pi$
$242$	−1363.94	−	2936.13i	−0.362304	−	0.779924i
$243$		0			0
$244$	−4669.36	−	3941.26i	−1.22510	−	1.03407i
$245$	133.995	−	232.087i	0.0349414	−	0.0605203i
$246$		0			0
$247$	834.301	−	481.684i	0.214920	−	0.124084i
$248$	−2742.95	+	722.159i	−0.702330	+	0.184908i
$249$		0			0
$250$	−3977.19	−	353.789i	−1.00616	−	0.0895024i
$251$			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
$254$	−502.114	+	5644.61i	−0.124037	+	1.39439i
$255$		0			0
$256$	3106.87	+	2669.19i	0.758513	+	0.651658i
$257$	−586.357	+	338.534i	−0.142319	+	0.0821679i	−0.569469	−	0.822013i	$-0.692851\pi$
$257$	−586.357	+	338.534i	−0.142319	+	0.0821679i	0.427150	+	0.904181i	$0.359518\pi$
$258$		0			0
$259$	−2039.73	+	3532.91i	−0.489353	+	0.847584i
$260$	−2780.11	−	2346.60i	−0.663134	−	0.559731i
$261$		0			0
$262$	2864.32	−	1330.58i	0.675412	−	0.313755i
$263$	−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
$266$	674.385	+	473.673i	0.155448	+	0.109183i
$267$		0			0
$268$	1504.32	+	4170.80i	0.342877	+	0.950642i
$269$	−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	$-0.869044\pi$
$271$		−	3568.10i		−	0.799804i	0.916558	−	0.399902i	$-0.130956\pi$
$272$	−1063.85	+	2870.83i	−0.237153	+	0.639962i
$273$		0			0
$274$	−1502.51	−	1055.33i	−0.331276	−	0.232681i
$275$	−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	$0.499312\pi$
$278$	−1275.08	−	2744.84i	−0.275087	−	0.592174i
$279$		0			0
$280$	818.602	−	3002.59i	0.174717	−	0.640854i
$281$	−2505.78	−	1446.71i	−0.531966	−	0.307131i	0.209851	−	0.977733i	$-0.432702\pi$
$281$	−2505.78	−	1446.71i	−0.531966	−	0.307131i	−0.741817	+	0.670603i	$0.766036\pi$
$282$		0			0
$283$	−4140.78	−	7172.04i	−0.869766	−	1.50648i	−0.862235	−	0.506508i	$-0.830936\pi$
$283$	−4140.78	−	7172.04i	−0.869766	−	1.50648i	−0.00753096	−	0.999972i	$-0.502397\pi$
$284$	685.889	+	122.999i	0.143310	+	0.0256995i
$285$		0			0
$286$	−2482.38	−	220.819i	−0.513239	−	0.0456550i
$287$	−9275.61			−1.90774
$288$		0			0
$289$	2624.56			0.534207
$290$	−5133.53	−	456.651i	−1.03949	−	0.0924671i
$291$		0			0
$292$	−6441.91	−	1155.21i	−1.29104	−	0.231520i
$293$	−1863.44	−	3227.58i	−0.371548	−	0.643540i	0.618256	−	0.785977i	$-0.287840\pi$
$293$	−1863.44	−	3227.58i	−0.371548	−	0.643540i	−0.989804	+	0.142437i	$0.954506\pi$
$294$		0			0
$295$	−3001.07	−	1732.67i	−0.592301	−	0.341965i
$296$	−1243.83	+	4562.33i	−0.244245	+	0.895878i
$297$		0			0
$298$	705.542	+	1518.80i	0.137151	+	0.295241i
$299$	2806.53	+	1620.35i	0.542830	+	0.313403i
$300$		0			0
$301$	−6042.90	+	3488.87i	−1.15717	+	0.668090i
$302$	4847.06	+	3404.46i	0.923566	+	0.648692i
$303$		0			0
$304$	895.771	+	331.949i	0.169000	+	0.0626269i
$305$			5381.76i			1.01036i
$306$		0			0
$307$	1481.74			0.275464			0.137732	−	0.990470i	$-0.456019\pi$
$307$	1481.74			0.275464			0.137732	+	0.990470i	$0.456019\pi$
$308$	−723.335	−	2005.48i	−0.133818	−	0.371015i
$309$		0			0
$310$	2044.33	+	1435.89i	0.374549	+	0.263075i
$311$	−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	$0.0751170\pi$
$314$	364.175	−	169.173i	0.0654509	−	0.0304044i
$315$		0			0
$316$	−7273.27	−	6139.14i	−1.29479	−	1.09289i
$317$	954.296	−	1652.89i	0.169081	−	0.292856i	−0.769016	−	0.639229i	$-0.779253\pi$
$317$	954.296	−	1652.89i	0.169081	−	0.292856i	0.938097	+	0.346373i	$0.112587\pi$
$318$		0			0
$319$	−3057.51	+	1765.25i	−0.536638	+	0.309828i
$320$	31.4839	−	3607.46i	0.00550001	−	0.630197i
$321$		0			0
$322$	−245.635	+	2761.35i	−0.0425115	+	0.477902i
$323$			714.050i			0.123006i
$324$		0			0
$325$		−	4863.30i		−	0.830054i
$326$	10260.7	+	912.738i	1.74322	+	0.155067i
$327$		0			0
$328$	−10397.8	+	2737.52i	−1.75038	+	0.460836i
$329$	5278.65	−	3047.63i	0.884564	−	0.510703i
$330$		0			0
$331$	−3378.13	+	5851.10i	−0.560964	+	0.971618i	0.436449	+	0.899729i	$0.356236\pi$
$331$	−3378.13	+	5851.10i	−0.560964	+	0.971618i	−0.997413	+	0.0718887i	$0.977097\pi$
$332$	−2827.63	−	2386.71i	−0.467428	−	0.394542i
$333$		0			0
$334$	3394.40	+	7307.04i	0.556087	+	1.19708i
$335$	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	$0.542219\pi$
$338$	3200.14	−	4556.15i	0.514984	−	0.733202i
$339$		0			0
$340$	2536.60	−	914.897i	0.404607	−	0.145933i
$341$	1711.35			0.271774
$342$		0			0
$343$		−	5952.96i		−	0.937113i
$344$	−5744.33	+	5694.42i	−0.900330	+	0.892507i
$345$		0			0
$346$	−38.7626	+	55.1877i	−0.00602280	+	0.00857488i
$347$	−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	$0.852719\pi$
$350$	3773.07	−	1752.74i	0.576226	−	0.267679i
$351$		0			0
$352$	−1402.73	−	2034.64i	−0.212402	−	0.308087i
$353$	2455.03	+	1417.41i	0.370164	+	0.213714i	0.673530	−	0.739160i	$-0.264777\pi$
$353$	2455.03	+	1417.41i	0.370164	+	0.213714i	−0.303366	+	0.952874i	$0.598111\pi$
$354$		0			0
$355$	−306.870	−	531.515i	−0.0458789	−	0.0794645i
$356$	−1479.57	+	8250.61i	−0.220272	+	1.22832i
$357$		0			0
$358$	487.351	−	5478.65i	0.0719478	−	0.808815i
$359$	−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
$362$	6.93310	−	77.9398i	0.00100662	−	0.0113161i
$363$		0			0
$364$	9920.45	+	1779.02i	1.42850	+	0.256170i
$365$	2882.14	+	4992.02i	0.413310	+	0.715875i
$366$		0			0
$367$	4576.87	+	2642.46i	0.650983	+	0.375845i	0.788833	−	0.614608i	$-0.210686\pi$
$367$	4576.87	+	2642.46i	0.650983	+	0.375845i	−0.137850	+	0.990453i	$0.544019\pi$
$368$	539.607	+	3167.93i	0.0764374	+	0.448750i
$369$		0			0
$370$	3777.31	−	1754.70i	0.530738	−	0.246548i
$371$	−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	$0.551667\pi$
$374$	1061.72	−	1511.61i	0.146792	−	0.208993i
$375$		0			0
$376$	5017.85	−	4974.25i	0.688234	−	0.682253i
$377$		−	16690.4i		−	2.28011i
$378$		0			0
$379$	−1196.44			−0.162156			−0.0810778	−	0.996708i	$-0.525836\pi$
$379$	−1196.44			−0.162156			−0.0810778	+	0.996708i	$0.525836\pi$
$380$	−285.471	−	791.482i	−0.0385378	−	0.106848i
$381$		0			0
$382$	5156.75	−	7341.85i	0.690686	−	0.983355i
$383$	−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
$386$	526.792	+	1134.01i	0.0694637	+	0.149533i
$387$		0			0
$388$	−5809.32	+	6882.52i	−0.760112	+	0.900533i
$389$	−797.621	+	1381.52i	−0.103961	+	0.180067i	−0.913313	−	0.407257i	$-0.866485\pi$
$389$	−797.621	+	1381.52i	−0.103961	+	0.180067i	0.809352	+	0.587324i	$0.199819\pi$
$390$		0			0
$391$	−2080.21	+	1201.01i	−0.269056	+	0.155339i
$392$	219.113	+	832.250i	0.0282318	+	0.107232i
$393$		0			0
$394$	8688.77	+	772.905i	1.11100	+	0.0988284i
$395$			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	$-0.0154222\pi$
$398$	−447.130	+	5026.50i	−0.0563131	+	0.633055i
$399$		0			0
$400$	3712.28	−	3078.34i	0.464034	−	0.384793i
$401$	170.330	−	98.3398i	0.0212116	−	0.0122465i	−0.489357	−	0.872084i	$-0.662768\pi$
$401$	170.330	−	98.3398i	0.0212116	−	0.0122465i	0.510568	+	0.859837i	$0.329435\pi$
$402$		0			0
$403$	−4045.19	+	7006.48i	−0.500013	+	0.866049i
$404$	3224.49	−	3820.18i	0.397090	−	0.470448i
$405$		0			0
$406$	12948.8	−	6015.23i	1.58286	−	0.735298i
$407$	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	$0.640078\pi$
$410$	7749.53	+	5443.09i	0.933468	+	0.655647i
$411$		0			0
$412$	1181.45	−	426.123i	0.141276	−	0.0509553i
$413$	9600.17			1.14381
$414$		0			0
$415$			3259.04i			0.385494i
$416$	11645.7	−	933.578i	1.37255	−	0.110030i
$417$		0			0
$418$	−471.659	−	331.283i	−0.0551905	−	0.0387645i
$419$	−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	$0.686593\pi$
$422$	1751.33	+	3770.04i	0.202022	+	0.434888i
$423$		0			0
$424$	−10406.6	−	2837.17i	−1.19195	−	0.324965i
$425$	3121.75	+	1802.35i	0.356300	+	0.205710i
$426$		0			0
$427$	−7454.67	−	12911.9i	−0.844864	−	1.46335i
$428$	−593.715	+	3310.78i	−0.0670521	+	0.373907i
$429$		0			0
$430$	7096.01	+	631.222i	0.795814	+	0.0707913i
$431$	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	$0.415688\pi$
$434$	−6893.69	−	613.225i	−0.762460	−	0.0678243i
$435$		0			0
$436$	1718.85	−	9584.96i	0.188803	−	1.05284i
$437$	374.745	+	649.078i	0.0410217	+	0.0710517i
$438$		0			0
$439$	−5611.44	−	3239.77i	−0.610068	−	0.352223i	0.162924	−	0.986639i	$-0.447907\pi$
$439$	−5611.44	−	3239.77i	−0.610068	−	0.352223i	−0.772992	+	0.634416i	$0.781241\pi$
$440$	−572.524	+	2099.99i	−0.0620318	+	0.227530i
$441$		0			0
$442$	3679.07	+	7919.85i	0.395918	+	0.852283i
$443$	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
$446$	−2798.35	−	1965.50i	−0.297098	−	0.208675i
$447$		0			0
$448$	4921.42	+	8698.59i	0.519007	+	0.917343i
$449$		−	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
$452$	−2640.73	+	952.455i	−0.274799	+	0.0991144i
$453$		0			0
$454$	−5201.98	−	3653.75i	−0.537756	−	0.377707i
$455$	−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	$0.142518\pi$
$458$	1965.78	−	913.180i	0.200557	−	0.0931662i
$459$		0			0
$460$	1825.63	−	2162.90i	0.185045	−	0.219229i
$461$	6037.19	−	10456.7i	0.609935	−	1.05644i	−0.381316	−	0.924445i	$-0.624529\pi$
$461$	6037.19	−	10456.7i	0.609935	−	1.05644i	0.991251	−	0.131993i	$-0.0421378\pi$
$462$		0			0
$463$	13152.8	−	7593.77i	1.32022	−	0.762230i	0.336457	−	0.941699i	$-0.390771\pi$
$463$	13152.8	−	7593.77i	1.32022	−	0.762230i	0.983764	+	0.179469i	$0.0574379\pi$
$464$	12740.2	−	10564.6i	1.27467	−	1.05700i
$465$		0			0
$466$	−200.786	+	2257.18i	−0.0199597	+	0.224381i
$467$			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
$470$	−6198.58	−	551.392i	−0.608339	−	0.0541145i
$471$		0			0
$472$	10761.7	−	2833.31i	1.04946	−	0.276300i
$473$	4226.36	−	2440.09i	0.410842	−	0.237199i
$474$		0			0
$475$	562.377	−	974.066i	0.0543235	−	0.0940910i
$476$	−4818.48	+	5708.63i	−0.463981	+	0.549695i
$477$		0			0
$478$	7227.57	+	15558.6i	0.691593	+	1.48878i
$479$	−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
$482$	8550.69	−	12173.9i	0.808036	−	1.15043i
$483$		0			0
$484$	−3106.81	−	8613.78i	−0.291774	−	0.808958i
$485$	7932.58			0.742680
$486$		0			0
$487$			5556.22i			0.516994i	0.966012	+	0.258497i	$0.0832273\pi$
$487$			5556.22i			0.516994i	−0.966012	+	0.258497i	$0.916773\pi$
$488$	−12167.3	−	12273.9i	−1.12866	−	1.13855i
$489$		0			0
$490$	435.669	−	620.278i	0.0401664	−	0.0571863i
$491$	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
$494$	2471.19	−	1147.96i	0.225069	−	0.104553i
$495$		0			0
$496$	−7908.71	+	1347.12i	−0.715951	+	0.121951i
$497$	1472.48	+	850.137i	0.132897	+	0.0767281i
$498$		0			0
$499$	−1626.32	−	2816.87i	−0.145900	−	0.252707i	0.783808	−	0.621003i	$-0.213274\pi$
$499$	−1626.32	−	2816.87i	−0.145900	−	0.252707i	−0.929708	+	0.368296i	$0.879941\pi$
$500$	−11116.3	−	1993.46i	−0.994271	−	0.178301i
$501$		0			0
$502$	−716.889	+	8059.06i	−0.0637377	+	0.716520i
$503$	−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
$506$	171.795	−	1931.27i	0.0150933	−	0.169675i
$507$		0			0
$508$	−2829.21	+	15776.8i	−0.247099	+	1.37791i
$509$	−4599.12	−	7965.92i	−0.400496	−	0.693680i	0.593290	−	0.804989i	$-0.297829\pi$
$509$	−4599.12	−	7965.92i	−0.400496	−	0.693680i	−0.993786	+	0.111309i	$0.964496\pi$
$510$		0			0
$511$	−13829.6	−	7984.53i	−1.19723	−	0.691223i
$512$	8084.06	+	8298.54i	0.697790	+	0.716303i
$513$		0			0
$514$	−1736.79	+	806.804i	−0.149040	+	0.0692346i
$515$	−957.986	−	553.093i	−0.0819687	−	0.0473247i
$516$		0			0
$517$	−3691.85	+	2131.49i	−0.314057	+	0.181321i
$518$	−6631.91	+	9442.09i	−0.562528	+	0.800891i
$519$		0			0
$520$	−7244.32	−	7307.82i	−0.610931	−	0.616286i
$521$		−	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	$-0.582801\pi$
$523$	−6152.61			−0.514407			−0.257203	+	0.966357i	$0.582801\pi$
$524$	8403.10	−	3030.83i	0.700556	−	0.252676i
$525$		0			0
$526$	−1884.13	+	2682.51i	−0.156183	+	0.222363i
$527$	−2998.31	−	5193.22i	−0.247834	−	0.429260i
$528$		0			0
$529$	4822.88	−	8353.48i	0.396390	−	0.686568i
$530$	4002.45	+	8615.98i	0.328029	+	0.706140i
$531$		0			0
$532$	1781.24	+	1503.49i	0.145162	+	0.122527i
$533$	−15334.3	+	26559.8i	−1.24616	+	2.15841i
$534$		0			0
$535$	2565.62	−	1481.26i	0.207329	−	0.119702i
$536$	3192.87	+	12127.4i	0.257297	+	0.977283i
$537$		0			0
$538$	−21744.9	−	1934.31i	−1.74255	−	0.155007i
$539$		−	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	$0.991374\pi$
$542$	894.209	−	10052.4i	0.0708664	−	0.796658i
$543$		0			0
$544$	−3716.66	+	7821.38i	−0.292924	+	0.616432i
$545$	−7427.67	+	4288.36i	−0.583791	+	0.337052i
$546$		0			0
$547$	2410.39	−	4174.92i	0.188411	−	0.326337i	−0.756310	−	0.654214i	$-0.773000\pi$
$547$	2410.39	−	4174.92i	0.188411	−	0.326337i	0.944721	+	0.327876i	$0.106333\pi$
$548$	−3968.54	−	3349.72i	−0.309357	−	0.261118i
$549$		0			0
$550$	−2638.86	+	1225.85i	−0.204584	+	0.0950371i
$551$	1930.03	−	3342.91i	0.149223	−	0.258462i
$552$		0			0
$553$	−11611.8	−	20112.3i	−0.892922	−	1.54659i
$554$	10710.4	+	7522.78i	0.821378	+	0.576917i
$555$		0			0
$556$	−2904.40	−	8052.58i	−0.221536	−	0.614219i
$557$	−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
$560$	3058.73	−	8254.06i	0.230813	−	0.622853i
$561$		0			0
$562$	−6696.98	−	4703.81i	−0.502661	−	0.353057i
$563$	−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
$566$	−9868.43	−	21243.5i	−0.732864	−	1.57762i
$567$		0			0
$568$	1901.53	+	518.418i	0.140469	+	0.0382963i
$569$	2663.36	+	1537.69i	0.196229	+	0.113293i	0.594895	−	0.803803i	$-0.297194\pi$
$569$	2663.36	+	1537.69i	0.196229	+	0.113293i	−0.398667	+	0.917096i	$0.630527\pi$
$570$		0			0
$571$	4651.48	+	8056.60i	0.340908	+	0.590470i	0.984602	−	0.174813i	$-0.0559322\pi$
$571$	4651.48	+	8056.60i	0.340908	+	0.590470i	−0.643694	+	0.765283i	$0.722599\pi$
$572$	−6938.29	−	1244.23i	−0.507175	−	0.0909508i
$573$		0			0
$574$	−26132.2	−	2324.58i	−1.90024	−	0.169035i
$575$	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	$0.470166\pi$
$578$	7394.18	+	657.746i	0.532106	+	0.0473333i
$579$		0			0
$580$	−14348.3	−	2573.05i	−1.02721	−	0.184207i
$581$	−4514.33	−	7819.04i	−0.322351	−	0.558328i
$582$		0			0
$583$	5636.06	+	3253.98i	0.400380	+	0.231160i
$584$	−17859.3	−	4869.01i	−1.26545	−	0.345002i
$585$		0			0
$586$	−4441.02	−	9560.07i	−0.313066	−	0.673930i
$587$	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
$590$	−8020.69	−	5633.55i	−0.559672	−	0.393101i
$591$		0			0
$592$	−4647.63	+	12541.7i	−0.322663	+	0.870713i
$593$			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
$596$	1607.10	+	4455.75i	0.110452	+	0.306232i
$597$		0			0
$598$	7500.77	+	5268.37i	0.512926	+	0.360267i
$599$	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	$-0.0742227\pi$
$602$	−17899.0	+	8314.78i	−1.21181	+	0.562932i
$603$		0			0
$604$	12802.4	+	10806.1i	0.862456	+	0.727973i
$605$	−4032.54	+	6984.56i	−0.270985	+	0.469360i
$606$		0			0
$607$	24259.0	−	14005.9i	1.62214	−	0.936545i	0.635798	−	0.771856i	$-0.280671\pi$
$607$	24259.0	−	14005.9i	1.62214	−	0.936545i	0.986346	−	0.164689i	$-0.0526621\pi$
$608$	2440.47	+	1159.69i	0.162786	+	0.0773547i
$609$		0			0
$610$	−1348.73	+	15162.1i	−0.0895223	+	1.00638i
$611$		−	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	$-0.209639\pi$
$614$	4174.52	+	371.342i	0.274381	+	0.0244074i
$615$		0			0
$616$	−1535.26	−	5831.32i	−0.100418	−	0.381413i
$617$	−1871.75	+	1080.65i	−0.122129	+	0.0705114i	−0.559820	−	0.828614i	$-0.689130\pi$
$617$	−1871.75	+	1080.65i	−0.122129	+	0.0705114i	0.437691	+	0.899126i	$0.355796\pi$
$618$		0			0
$619$	−3435.93	+	5951.20i	−0.223104	+	0.386428i	−0.955749	−	0.294183i	$-0.904952\pi$
$619$	−3435.93	+	5951.20i	−0.223104	+	0.386428i	0.732645	+	0.680611i	$0.238286\pi$
$620$	5399.65	+	4557.67i	0.349766	+	0.295227i
$621$		0			0
$622$	−9472.34	−	20390.9i	−0.610621	−	1.31447i
$623$	−10226.4	+	17712.6i	−0.657641	+	1.13907i
$624$		0			0
$625$	263.949	+	457.172i	0.0168927	+	0.0292590i
$626$	5107.24	−	7271.36i	0.326080	−	0.464252i
$627$		0			0
$628$	1068.39	−	385.345i	0.0678874	−	0.0244856i
$629$	−9997.45			−0.633743
$630$		0			0
$631$		−	14045.7i		−	0.886134i	−0.896488	−	0.443067i	$-0.853890\pi$
$631$		−	14045.7i		−	0.886134i	0.896488	−	0.443067i	$-0.146110\pi$
$632$	−18952.5	−	19118.6i	−1.19286	−	1.20332i
$633$		0			0
$634$	3102.77	−	4417.53i	0.194364	−	0.276723i
$635$	12225.9	−	7058.60i	0.764045	−	0.441122i
$636$		0			0
$637$	2125.86	+	1227.37i	0.132229	+	0.0763423i
$638$	−9056.32	+	4207.01i	−0.561980	+	0.261061i
$639$		0			0
$640$	992.772	−	10155.4i	0.0613168	−	0.627231i
$641$	9674.91	+	5585.81i	0.596156	+	0.344191i	0.767528	−	0.641016i	$-0.221487\pi$
$641$	9674.91	+	5585.81i	0.596156	+	0.344191i	−0.171372	+	0.985206i	$0.554820\pi$
$642$		0			0
$643$	−3853.78	−	6674.94i	−0.236358	−	0.409384i	0.723309	−	0.690525i	$-0.242620\pi$
$643$	−3853.78	−	6674.94i	−0.236358	−	0.409384i	−0.959666	+	0.281141i	$0.909287\pi$
$644$	−1384.06	+	7718.01i	−0.0846886	+	0.472255i
$645$		0			0
$646$	−178.949	+	2011.70i	−0.0108989	+	0.122522i
$647$	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
$650$	1218.80	−	13701.4i	0.0735466	−	0.826789i
$651$		0			0
$652$	28678.8	+	5142.92i	1.72262	+	0.308915i
$653$	11606.7	+	20103.4i	0.695567	+	1.20476i	0.969989	+	0.243148i	$0.0781802\pi$
$653$	11606.7	+	20103.4i	0.695567	+	1.20476i	−0.274422	+	0.961609i	$0.588487\pi$
$654$		0			0
$655$	−6813.73	−	3933.91i	−0.406465	−	0.234673i
$656$	−29979.9	+	5106.60i	−1.78433	+	0.303932i
$657$		0			0
$658$	15635.3	−	7263.21i	0.926336	−	0.430318i
$659$	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	$0.0897475\pi$
$662$	−10983.6	+	15637.7i	−0.644847	+	0.918092i
$663$		0			0
$664$	−7368.14	−	7432.72i	−0.430631	−	0.434406i
$665$		−	2053.00i		−	0.119717i
$666$		0			0
$667$	12985.0			0.753794
$668$	7731.81	+	21436.8i	0.447834	+	1.24164i
$669$		0			0
$670$	6348.49	−	9038.58i	0.366065	−	0.521180i
$671$	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	$0.933965\pi$
$674$	11681.5	+	25146.5i	0.667588	+	1.43710i
$675$		0			0
$676$	10157.6	−	12034.1i	0.577924	−	0.684688i
$677$	12028.2	−	20833.5i	0.682840	−	1.18271i	−0.291271	−	0.956641i	$-0.594078\pi$
$677$	12028.2	−	20833.5i	0.682840	−	1.18271i	0.974110	−	0.226072i	$-0.0725886\pi$
$678$		0			0
$679$	−19031.8	+	10988.0i	−1.07566	+	0.621032i
$680$	7375.64	−	1941.84i	0.415945	−	0.109509i
$681$		0			0
$682$	4821.39	+	428.885i	0.270705	+	0.0240804i
$683$		−	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
$686$	1491.88	−	16771.3i	0.0830326	−	0.933428i
$687$		0			0
$688$	−17610.6	+	14603.3i	−0.975870	+	0.809223i
$689$	−26644.4	+	15383.1i	−1.47325	+	0.850582i
$690$		0			0
$691$	−7125.35	+	12341.5i	−0.392274	+	0.679438i	−0.992749	−	0.120205i	$-0.961645\pi$
$691$	−7125.35	+	12341.5i	−0.392274	+	0.679438i	0.600475	+	0.799643i	$0.294978\pi$
$692$	−123.037	+	145.766i	−0.00675889	+	0.00800750i
$693$		0			0
$694$	−31542.8	+	14652.9i	−1.72529	+	0.801462i
$695$	−3769.81	+	6529.51i	−0.205751	+	0.356372i
$696$		0			0
$697$	−11365.8	−	19686.2i	−0.617662	−	1.06982i
$698$	−16653.4	−	11697.0i	−0.903067	−	0.634294i
$699$		0			0
$700$	11069.1	−	3992.41i	0.597677	−	0.215570i
$701$	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
$704$	−3442.00	−	6083.72i	−0.184269	−	0.325695i
$705$		0			0
$706$	6561.33	+	4608.53i	0.349772	+	0.245672i
$707$	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	$0.828053\pi$
$710$	−731.343	−	1574.34i	−0.0386575	−	0.0832170i
$711$		0			0
$712$	−6236.08	+	22873.7i	−0.328240	+	1.20397i
$713$	−5450.97	−	3147.12i	−0.286312	−	0.165302i
$714$		0			0
$715$	3104.23	+	5376.68i	0.162366	+	0.281226i
$716$	2746.03	−	15312.9i	0.143330	−	0.799259i
$717$		0			0
$718$	−9713.14	−	864.027i	−0.504862	−	0.0449098i
$719$	−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
$722$	−18696.2	−	1663.11i	−0.963712	−	0.0857265i
$723$		0			0
$724$	39.0653	−	217.842i	0.00200532	−	0.0111824i
$725$	−9743.23	−	16875.8i	−0.499110	−	0.864483i
$726$		0			0
$727$	12935.1	+	7468.08i	0.659884	+	0.380984i	0.792233	−	0.610219i	$-0.208918\pi$
$727$	12935.1	+	7468.08i	0.659884	+	0.380984i	−0.132348	+	0.991203i	$0.542252\pi$
$728$	27503.1	+	7498.21i	1.40018	+	0.381733i
$729$		0			0
$730$	6868.81	+	14786.3i	0.348255	+	0.749680i
$731$	−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	$0.337353\pi$
$734$	12232.2	+	8591.63i	0.615121	+	0.432047i
$735$		0			0
$736$	726.315	+	9060.26i	0.0363754	+	0.453758i
$737$		−	7566.38i		−	0.378170i
$738$		0			0
$739$	11047.6			0.549922			0.274961	−	0.961455i	$-0.411335\pi$
$739$	11047.6			0.549922			0.274961	+	0.961455i	$0.411335\pi$
$740$	11081.6	−	3996.89i	0.550496	−	0.198552i
$741$		0			0
$742$	−21537.3	−	15127.3i	−1.06558	−	0.748437i
$743$	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
$746$	−23408.5	+	10874.1i	−1.14885	+	0.533687i
$747$		0			0
$748$	3370.01	−	3992.57i	0.164732	−	0.195164i
$749$	−4103.60	+	7107.64i	−0.200190	+	0.346739i
$750$		0			0
$751$	−32163.5	+	18569.6i	−1.56280	+	0.902282i	−0.565827	+	0.824524i	$0.691443\pi$
$751$	−32163.5	+	18569.6i	−1.56280	+	0.902282i	−0.996972	+	0.0777583i	$0.975224\pi$
$752$	15383.4	−	12756.4i	0.745977	−	0.618589i
$753$		0			0
$754$	4182.82	−	47022.0i	0.202028	−	2.27114i
$755$		−	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	$0.944263\pi$
$758$	−3370.73	−	299.842i	−0.161518	−	0.0143677i
$759$		0			0
$760$	−605.904	−	2301.39i	−0.0289190	−	0.109842i
$761$	7953.62	−	4592.02i	0.378868	−	0.218739i	−0.298458	−	0.954423i	$-0.596472\pi$
$761$	7953.62	−	4592.02i	0.378868	−	0.218739i	0.677326	+	0.735683i	$0.263139\pi$
$762$		0			0
$763$	11880.2	−	20577.2i	0.563688	−	0.976336i
$764$	16368.1	−	19391.9i	0.775100	−	0.918289i
$765$		0			0
$766$	−6248.99	−	13452.0i	−0.294758	−	0.634520i
$767$	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	$0.526300\pi$
$770$	−3052.60	+	4346.09i	−0.142868	+	0.203406i
$771$		0			0
$772$	1199.93	+	3326.87i	0.0559412	+	0.155100i
$773$	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
$776$	−18091.4	+	17934.2i	−0.836914	+	0.829642i
$777$		0			0
$778$	−2593.37	+	3692.27i	−0.119507	+	0.170147i
$779$	−6142.58	+	3546.42i	−0.282517	+	0.163111i
$780$		0			0
$781$	−1029.84	−	594.579i	−0.0471839	−	0.0272416i
$782$	−6161.57	+	2862.28i	−0.281761	+	0.130889i
$783$		0			0
$784$	408.736	+	2399.61i	0.0186195	+	0.109312i
$785$	−866.311	−	500.165i	−0.0393885	−	0.0227410i
$786$		0			0
$787$	2740.75	+	4747.12i	0.124139	+	0.215015i	0.921396	−	0.388625i	$-0.127050\pi$
$787$	2740.75	+	4747.12i	0.124139	+	0.215015i	−0.797257	+	0.603640i	$0.793717\pi$
$788$	24285.2	+	4355.02i	1.09787	+	0.196879i
$789$		0			0
$790$	−2100.87	+	23617.3i	−0.0946146	+	1.06363i
$791$	−6849.70			−0.307898
$792$		0			0
$793$	−49295.7			−2.20749
$794$	192.018	−	2158.61i	0.00858247	−	0.0964815i
$795$		0			0
$796$	−2519.40	+	14049.1i	−0.112183	+	0.625575i
$797$	−15906.0	−	27550.0i	−0.706926	−	1.22443i	−0.965992	−	0.258573i	$-0.916748\pi$
$797$	−15906.0	−	27550.0i	−0.706926	−	1.22443i	0.259065	−	0.965860i	$-0.416585\pi$
$798$		0			0
$799$	12936.3	+	7468.79i	0.572784	+	0.330697i
$800$	11230.1	−	7742.28i	0.496304	−	0.342164i
$801$		0			0
$802$	504.515	−	234.366i	0.0222133	−	0.0103189i
$803$	9672.33	+	5584.32i	0.425067	+	0.245413i
$804$		0			0
$805$	5980.91	−	3453.08i	0.261863	−	0.151186i
$806$	−13152.4	+	18725.6i	−0.574783	+	0.818339i
$807$		0			0
$808$	10041.8	−	9954.50i	0.437212	−	0.433413i
$809$		−	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	$-0.326346\pi$
$811$	23968.2			1.03778			0.518889	+	0.854841i	$0.326346\pi$
$812$	37988.3	−	13701.6i	1.64178	−	0.592157i
$813$		0			0
$814$	4638.31	−	6603.73i	0.199721	−	0.284349i
$815$	−12831.1	−	22224.1i	−0.551476	−	0.955184i
$816$		0			0
$817$	−2667.85	+	4620.86i	−0.114243	+	0.197874i
$818$	11246.5	+	24210.0i	0.480714	+	1.03482i
$819$		0			0
$820$	20468.7	+	17277.0i	0.871703	+	0.735778i
$821$	−2750.46	+	4763.94i	−0.116921	+	0.202512i	−0.918546	−	0.395314i	$-0.870636\pi$
$821$	−2750.46	+	4763.94i	−0.116921	+	0.202512i	0.801625	+	0.597827i	$0.203969\pi$
$822$		0			0
$823$	4259.38	−	2459.15i	0.180404	−	0.104156i	−0.407078	−	0.913393i	$-0.633452\pi$
$823$	4259.38	−	2459.15i	0.180404	−	0.104156i	0.587483	+	0.809237i	$0.300119\pi$
$824$	3435.28	−	904.433i	0.145235	−	0.0382372i
$825$		0			0
$826$	27046.6	+	2405.92i	1.13931	+	0.101347i
$827$			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	$0.937692\pi$
$830$	−816.753	+	9181.69i	−0.0341565	+	0.383977i
$831$		0			0
$832$	33043.5	+	288.386i	1.37690	+	0.0120168i
$833$	−1575.69	+	909.728i	−0.0655397	+	0.0378394i
$834$		0			0
$835$	10035.6	−	17382.2i	0.415925	−	0.720403i
$836$	−1245.78	−	1051.53i	−0.0515387	−	0.0435022i
$837$		0			0
$838$	−30456.5	+	14148.2i	−1.25549	+	0.583223i
$839$	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
$842$	−2501.63	−	1757.09i	−0.102389	−	0.0719160i
$843$		0			0
$844$	3989.20	+	11060.2i	0.162694	+	0.451077i
$845$	−13870.1			−0.564670
$846$		0			0
$847$		−	22343.0i		−	0.906394i
$848$	−28607.5	−	10601.2i	−1.15847	−	0.429299i
$849$		0			0
$850$	8343.24	+	5860.10i	0.336671	+	0.236470i
$851$	−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	$0.712688\pi$
$854$	−17766.2	−	38244.9i	−0.711881	−	1.53245i
$855$		0			0
$856$	−2502.39	+	9178.66i	−0.0999183	+	0.366496i
$857$	−13290.3	−	7673.16i	−0.529741	−	0.305846i	0.211170	−	0.977449i	$-0.432273\pi$
$857$	−13290.3	−	7673.16i	−0.529741	−	0.305846i	−0.740911	+	0.671603i	$0.765606\pi$
$858$		0			0
$859$	18277.1	+	31656.9i	0.725969	+	1.25742i	0.958574	+	0.284844i	$0.0919419\pi$
$859$	18277.1	+	31656.9i	0.725969	+	1.25742i	−0.232604	+	0.972571i	$0.574725\pi$
$860$	19833.4	+	3556.69i	0.786412	+	0.141026i
$861$		0			0
$862$	47508.2	+	4226.07i	1.87719	+	0.166984i
$863$	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
$866$	13290.6	+	1182.26i	0.521518	+	0.0463914i
$867$		0			0
$868$	−19267.9	−	3455.28i	−0.753452	−	0.135115i
$869$	8121.23	+	14066.4i	0.317024	+	0.549102i
$870$		0			0
$871$	30977.7	+	17885.0i	1.20510	+	0.695763i
$872$	7244.63	−	26573.0i	0.281347	−	1.03197i
$873$		0			0
$874$	893.104	+	1922.56i	0.0345649	+	0.0744070i
$875$	−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	$0.298733\pi$
$878$	−14997.2	−	10533.7i	−0.576459	−	0.404892i
$879$		0			0
$880$	−2139.25	+	5772.83i	−0.0819480	+	0.221139i
$881$			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	$-0.542680\pi$
$883$	−7015.23			−0.267363			−0.133681	+	0.991024i	$0.542680\pi$
$884$	8380.25	+	23234.6i	0.318844	+	0.884011i
$885$		0			0
$886$	4535.21	+	3185.43i	0.171968	+	0.120786i
$887$	−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
$890$	18937.9	−	8797.38i	0.713258	−	0.331336i
$891$		0			0
$892$	−7391.22	−	6238.70i	−0.277440	−	0.234178i
$893$	2330.45	−	4036.46i	0.0873299	−	0.151260i
$894$		0			0
$895$	−11866.4	+	6851.07i	−0.443184	+	0.255873i
$896$	11685.2	+	25739.9i	0.435685	+	0.959721i
$897$		0			0
$898$	643.230	−	7230.99i	0.0239030	−	0.268710i
$899$			32416.9i			1.20263i
$900$		0			0
$901$		−	22804.0i		−	0.843188i
$902$	18276.7	+	1625.79i	0.674663	+	0.0600143i
$903$		0			0
$904$	−7678.42	+	2021.56i	−0.282501	+	0.0743761i
$905$	−168.812	+	97.4639i	−0.00620057	+	0.00357990i
$906$		0			0
$907$	3011.58	−	5216.21i	0.110251	−	0.190961i	−0.805620	−	0.592432i	$-0.798168\pi$
$907$	3011.58	−	5216.21i	0.110251	−	0.190961i	0.915872	+	0.401472i	$0.131501\pi$
$908$	−13739.9	−	11597.4i	−0.502174	−	0.423869i
$909$		0			0
$910$	−10577.9	−	22770.8i	−0.385333	−	0.829498i
$911$	−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
$914$	2407.51	−	3427.66i	0.0871263	−	0.124045i
$915$		0			0
$916$	5767.05	−	2080.06i	0.208023	−	0.0750295i
$917$	21796.6			0.784936
$918$		0			0
$919$			88.2115i			0.00316630i	0.999999	+	0.00158315i	$0.000503932\pi$
$919$			88.2115i			0.00316630i	−0.999999	+	0.00158315i	$0.999496\pi$
$920$	5685.41	−	5636.01i	0.203742	−	0.201971i
$921$		0			0
$922$	19629.2	−	27946.8i	0.701141	−	0.998240i
$923$	4868.56	−	2810.86i	0.173619	−	0.100239i
$924$		0			0
$925$	13637.9	+	7873.87i	0.484771	+	0.279883i
$926$	38958.5	−	18097.7i	1.38257	−	0.642254i
$927$		0			0
$928$	38540.6	−	26570.8i	1.36332	−	0.939903i
$929$	−18113.2	−	10457.7i	−0.639695	−	0.369328i	0.144802	−	0.989461i	$-0.453745\pi$
$929$	−18113.2	−	10457.7i	−0.639695	−	0.369328i	−0.784497	+	0.620133i	$0.787079\pi$
$930$		0			0
$931$	283.858	+	491.657i	0.00999256	+	0.0173076i
$932$	−1131.35	+	6308.84i	−0.0397625	+	0.221730i
$933$		0			0
$934$	−11.5948	+	130.345i	−0.000406203	+	0.00456642i
$935$	−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	$0.386313\pi$
$938$	−2711.25	+	30479.0i	−0.0943767	+	1.06095i
$939$		0			0
$940$	−17325.1	−	3106.88i	−0.601151	−	0.107803i
$941$	−1432.61	−	2481.36i	−0.0496300	−	0.0859616i	0.840143	−	0.542365i	$-0.182471\pi$
$941$	−1432.61	−	2481.36i	−0.0496300	−	0.0859616i	−0.889773	+	0.456403i	$0.849138\pi$
$942$		0			0
$943$	−20663.2	−	11929.9i	−0.713560	−	0.411974i
$944$	31028.9	−	5285.28i	1.06981	−	0.182226i
$945$		0			0
$946$	12518.4	−	5815.29i	0.430243	−	0.199864i
$947$	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
$950$	1828.50	−	2603.30i	0.0624467	−	0.0889076i
$951$		0			0
$952$	−15005.8	+	14875.4i	−0.510861	+	0.506422i
$953$		−	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
$956$	16463.1	+	45644.7i	0.556960	+	1.54420i
$957$		0			0
$958$	−23869.3	+	33983.6i	−0.804993	+	1.14610i
$959$	−6335.80	−	10973.9i	−0.213341	−	0.369517i
$960$		0			0
$961$	−7038.75	+	12191.5i	−0.236271	+	0.409233i
$962$	16072.7	+	34599.3i	0.538674	+	1.15959i
$963$		0			0
$964$	27140.8	−	32154.7i	0.906791	−	1.07431i
$965$	1557.47	−	2697.62i	0.0519553	−	0.0899892i
$966$		0			0
$967$	9529.32	−	5501.75i	0.316900	−	0.182962i	−0.333110	−	0.942888i	$-0.608098\pi$
$967$	9529.32	−	5501.75i	0.316900	−	0.182962i	0.650010	+	0.759926i	$0.274765\pi$
$968$	−6594.12	−	25046.2i	−0.218949	−	0.831629i
$969$		0			0
$970$	22348.5	+	1988.00i	0.739759	+	0.0658049i
$971$		−	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
$974$	−1392.45	+	15653.5i	−0.0458081	+	0.514961i
$975$		0			0
$976$	−31202.9	−	37628.6i	−1.02334	−	1.23408i
$977$	−32261.5	+	18626.2i	−1.05643	+	0.609932i	−0.924444	−	0.381319i	$-0.875470\pi$
$977$	−32261.5	+	18626.2i	−1.05643	+	0.609932i	−0.131990	+	0.991251i	$0.542137\pi$
$978$		0			0
$979$	7152.24	−	12388.0i	0.233490	−	0.404416i
$980$	1382.86	−	1638.33i	0.0450754	−	0.0534025i
$981$		0			0
$982$	22213.9	−	10319.2i	0.721868	−	0.335335i
$983$	−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
$986$	28633.2	+	20111.3i	0.924816	+	0.649570i
$987$		0			0
$988$	7249.79	−	2614.85i	0.233448	−	0.0841999i
$989$	−17949.0			−0.577092
$990$		0			0
$991$		−	12374.8i		−	0.396669i	−0.980134	−	0.198334i	$-0.936447\pi$
$991$		−	12374.8i		−	0.396669i	0.980134	−	0.198334i	$-0.0635532\pi$
$992$	−22618.8	+	1813.24i	−0.723941	+	0.0580346i
$993$		0			0
$994$	3935.37	+	2764.11i	0.125576	+	0.0882016i
$995$	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	$0.693258\pi$
$998$	−3875.90	−	8343.56i	−0.122935	−	0.264640i
$999$		0			0

Twists

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

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 216 = 2^{3} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	216.l (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(2.81730 + 0.250612i) q^{2} +(7.87439 + 1.41210i) q^{4} +(-3.52304 - 6.10209i) q^{5} +(16.9049 + 9.76005i) q^{7} +(21.8306 + 5.95172i) q^{8} +(-8.39622 - 18.0744i) q^{10} +(-11.8232 - 6.82610i) q^{11} +(55.8938 - 32.2703i) q^{13} +(45.1802 + 31.7336i) q^{14} +(60.0120 + 22.2388i) q^{16} +47.8376i q^{17} +14.9265 q^{19} +(-19.1251 - 53.0251i) q^{20} +(-31.5987 - 22.1942i) q^{22} +(25.1060 + 43.4848i) q^{23} +(37.6763 - 65.2573i) q^{25} +(165.557 - 76.9075i) q^{26} +(119.334 + 100.726i) q^{28} +(129.302 - 223.957i) q^{29} +(-108.559 + 62.6768i) q^{31} +(163.499 + 77.6932i) q^{32} +(-11.9887 + 134.773i) q^{34} -137.540i q^{35} +208.987i q^{37} +(42.0526 + 3.74077i) q^{38} +(-40.5924 - 154.181i) q^{40} +(-411.520 + 237.591i) q^{41} +(-178.732 + 309.573i) q^{43} +(-83.4610 - 70.4468i) q^{44} +(59.8333 + 128.802i) q^{46} +(156.128 - 270.422i) q^{47} +(19.0170 + 32.9384i) q^{49} +(122.500 - 174.407i) q^{50} +(485.698 - 175.181i) q^{52} -476.697 q^{53} +96.1946i q^{55} +(310.956 + 313.681i) q^{56} +(420.409 - 598.551i) q^{58} +(425.920 - 245.905i) q^{59} +(-661.465 - 381.897i) q^{61} +(-321.552 + 149.373i) q^{62} +(441.154 + 259.860i) q^{64} +(-393.832 - 227.379i) q^{65} +(277.112 + 479.972i) q^{67} +(-67.5514 + 376.692i) q^{68} +(34.4692 - 387.493i) q^{70} +87.1038 q^{71} -818.083 q^{73} +(-52.3747 + 588.780i) q^{74} +(117.537 + 21.0778i) q^{76} +(-133.246 - 230.789i) q^{77} +(-1030.34 - 594.866i) q^{79} +(-75.7214 - 444.547i) q^{80} +(-1218.92 + 566.235i) q^{82} +(-400.564 - 231.266i) q^{83} +(291.910 - 168.534i) q^{85} +(-581.125 + 827.369i) q^{86} +(-217.480 - 219.386i) q^{88} +1047.78i q^{89} +1259.84 q^{91} +(136.289 + 377.868i) q^{92} +(507.631 - 722.732i) q^{94} +(-52.5869 - 91.0831i) q^{95} +(-562.907 + 974.983i) q^{97} +(45.3219 + 97.5633i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q + 3 q^{2} - 17 q^{4} + 12 q^{10} - 48 q^{11} - 72 q^{14} + 127 q^{16} - 220 q^{19} + 234 q^{20} - 217 q^{22} - 902 q^{25} - 132 q^{28} + 693 q^{32} + 509 q^{34} + 1977 q^{38} - 36 q^{40} - 1620 q^{41}+ \cdots - 1912 q^{97}+O(q^{100}) \) 64 * q + 3 * q^2 - 17 * q^4 + 12 * q^10 - 48 * q^11 - 72 * q^14 + 127 * q^16 - 220 * q^19 + 234 * q^20 - 217 * q^22 - 902 * q^25 - 132 * q^28 + 693 * q^32 + 509 * q^34 + 1977 * q^38 - 36 * q^40 - 1620 * q^41 - 292 * q^43 + 48 * q^46 + 1762 * q^49 + 1227 * q^50 + 330 * q^52 - 942 * q^56 - 282 * q^58 - 5592 * q^59 + 1090 * q^64 + 6 * q^65 + 68 * q^67 + 2025 * q^68 + 600 * q^70 - 868 * q^73 + 420 * q^74 - 1471 * q^76 + 362 * q^82 - 3654 * q^83 + 4119 * q^86 + 3155 * q^88 - 1380 * q^91 + 744 * q^92 - 138 * q^94 - 1912 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more