Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2160,4,Mod(1,2160)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2160, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2160.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2160 = 2^{4} \cdot 3^{3} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 2160.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(127.444125612\) |
Analytic rank: | \(1\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 135) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 2160.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(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 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −5.00000 | −0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 10.0000 | 0.274101 | 0.137051 | − | 0.990564i | \(-0.456238\pi\) | ||||
0.137051 | + | 0.990564i | \(0.456238\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −80.0000 | −1.70677 | −0.853385 | − | 0.521281i | \(-0.825454\pi\) | ||||
−0.853385 | + | 0.521281i | \(0.825454\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −7.00000 | −0.0998676 | −0.0499338 | − | 0.998753i | \(-0.515901\pi\) | ||||
−0.0499338 | + | 0.998753i | \(0.515901\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 113.000 | 1.36442 | 0.682210 | − | 0.731156i | \(-0.261019\pi\) | ||||
0.682210 | + | 0.731156i | \(0.261019\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −81.0000 | −0.734333 | −0.367167 | − | 0.930155i | \(-0.619672\pi\) | ||||
−0.367167 | + | 0.930155i | \(0.619672\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 25.0000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 220.000 | 1.40872 | 0.704362 | − | 0.709841i | \(-0.251233\pi\) | ||||
0.704362 | + | 0.709841i | \(0.251233\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 189.000 | 1.09501 | 0.547506 | − | 0.836801i | \(-0.315577\pi\) | ||||
0.547506 | + | 0.836801i | \(0.315577\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 170.000 | 0.755347 | 0.377673 | − | 0.925939i | \(-0.376724\pi\) | ||||
0.377673 | + | 0.925939i | \(0.376724\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 130.000 | 0.495185 | 0.247593 | − | 0.968864i | \(-0.420361\pi\) | ||||
0.247593 | + | 0.968864i | \(0.420361\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −10.0000 | −0.0354648 | −0.0177324 | − | 0.999843i | \(-0.505645\pi\) | ||||
−0.0177324 | + | 0.999843i | \(0.505645\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 160.000 | 0.496562 | 0.248281 | − | 0.968688i | \(-0.420134\pi\) | ||||
0.248281 | + | 0.968688i | \(0.420134\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −343.000 | −1.00000 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −631.000 | −1.63537 | −0.817684 | − | 0.575667i | \(-0.804742\pi\) | ||||
−0.817684 | + | 0.575667i | \(0.804742\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −50.0000 | −0.122582 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −560.000 | −1.23569 | −0.617846 | − | 0.786299i | \(-0.711994\pi\) | ||||
−0.617846 | + | 0.786299i | \(0.711994\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 229.000 | 0.480663 | 0.240332 | − | 0.970691i | \(-0.422744\pi\) | ||||
0.240332 | + | 0.970691i | \(0.422744\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 400.000 | 0.763291 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −750.000 | −1.36757 | −0.683784 | − | 0.729684i | \(-0.739667\pi\) | ||||
−0.683784 | + | 0.729684i | \(0.739667\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 890.000 | 1.48766 | 0.743828 | − | 0.668371i | \(-0.233008\pi\) | ||||
0.743828 | + | 0.668371i | \(0.233008\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −890.000 | −1.42694 | −0.713470 | − | 0.700686i | \(-0.752878\pi\) | ||||
−0.713470 | + | 0.700686i | \(0.752878\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 27.0000 | 0.0384524 | 0.0192262 | − | 0.999815i | \(-0.493880\pi\) | ||||
0.0192262 | + | 0.999815i | \(0.493880\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 429.000 | 0.567336 | 0.283668 | − | 0.958923i | \(-0.408449\pi\) | ||||
0.283668 | + | 0.958923i | \(0.408449\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 35.0000 | 0.0446622 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 750.000 | 0.893257 | 0.446628 | − | 0.894720i | \(-0.352625\pi\) | ||||
0.446628 | + | 0.894720i | \(0.352625\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −565.000 | −0.610187 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1480.00 | −1.54919 | −0.774594 | − | 0.632459i | \(-0.782046\pi\) | ||||
−0.774594 | + | 0.632459i | \(0.782046\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1500.00 | 1.47778 | 0.738889 | − | 0.673827i | \(-0.235351\pi\) | ||||
0.738889 | + | 0.673827i | \(0.235351\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 460.000 | 0.440050 | 0.220025 | − | 0.975494i | \(-0.429386\pi\) | ||||
0.220025 | + | 0.975494i | \(0.429386\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −420.000 | −0.379467 | −0.189733 | − | 0.981836i | \(-0.560762\pi\) | ||||
−0.189733 | + | 0.981836i | \(0.560762\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −607.000 | −0.533395 | −0.266698 | − | 0.963780i | \(-0.585932\pi\) | ||||
−0.266698 | + | 0.963780i | \(0.585932\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −2170.00 | −1.80652 | −0.903259 | − | 0.429097i | \(-0.858832\pi\) | ||||
−0.903259 | + | 0.429097i | \(0.858832\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 405.000 | 0.328404 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1231.00 | −0.924869 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −125.000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1610.00 | 1.12492 | 0.562458 | − | 0.826826i | \(-0.309856\pi\) | ||||
0.562458 | + | 0.826826i | \(0.309856\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 2370.00 | 1.58067 | 0.790335 | − | 0.612674i | \(-0.209906\pi\) | ||||
0.790335 | + | 0.612674i | \(0.209906\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −1797.00 | −1.12064 | −0.560321 | − | 0.828275i | \(-0.689322\pi\) | ||||
−0.560321 | + | 0.828275i | \(0.689322\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 124.000 | 0.0756658 | 0.0378329 | − | 0.999284i | \(-0.487955\pi\) | ||||
0.0378329 | + | 0.999284i | \(0.487955\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −800.000 | −0.467828 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1100.00 | −0.630000 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 70.0000 | 0.0384874 | 0.0192437 | − | 0.999815i | \(-0.493874\pi\) | ||||
0.0192437 | + | 0.999815i | \(0.493874\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2248.00 | −1.21152 | −0.605760 | − | 0.795647i | \(-0.707131\pi\) | ||||
−0.605760 | + | 0.795647i | \(0.707131\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −945.000 | −0.489705 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1010.00 | 0.513419 | 0.256709 | − | 0.966489i | \(-0.417362\pi\) | ||||
0.256709 | + | 0.966489i | \(0.417362\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −590.000 | −0.283511 | −0.141756 | − | 0.989902i | \(-0.545275\pi\) | ||||
−0.141756 | + | 0.989902i | \(0.545275\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 2403.00 | 1.11347 | 0.556736 | − | 0.830690i | \(-0.312054\pi\) | ||||
0.556736 | + | 0.830690i | \(0.312054\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 4203.00 | 1.91306 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −801.000 | −0.352017 | −0.176008 | − | 0.984389i | \(-0.556319\pi\) | ||||
−0.176008 | + | 0.984389i | \(0.556319\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −2360.00 | −0.985445 | −0.492723 | − | 0.870186i | \(-0.663998\pi\) | ||||
−0.492723 | + | 0.870186i | \(0.663998\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1241.00 | 0.509629 | 0.254814 | − | 0.966990i | \(-0.417986\pi\) | ||||
0.254814 | + | 0.966990i | \(0.417986\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −850.000 | −0.337801 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −70.0000 | −0.0273738 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −4990.00 | −1.89039 | −0.945193 | − | 0.326512i | \(-0.894127\pi\) | ||||
−0.945193 | + | 0.326512i | \(0.894127\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −2260.00 | −0.842893 | −0.421447 | − | 0.906853i | \(-0.638477\pi\) | ||||
−0.421447 | + | 0.906853i | \(0.638477\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 2247.00 | 0.812650 | 0.406325 | − | 0.913729i | \(-0.366810\pi\) | ||||
0.406325 | + | 0.913729i | \(0.366810\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −4564.00 | −1.62580 | −0.812898 | − | 0.582406i | \(-0.802111\pi\) | ||||
−0.812898 | + | 0.582406i | \(0.802111\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −650.000 | −0.221454 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 1130.00 | 0.373989 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −4949.00 | −1.61471 | −0.807354 | − | 0.590068i | \(-0.799101\pi\) | ||||
−0.807354 | + | 0.590068i | \(0.799101\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 50.0000 | 0.0158603 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 560.000 | 0.170451 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −3890.00 | −1.16813 | −0.584067 | − | 0.811706i | \(-0.698539\pi\) | ||||
−0.584067 | + | 0.811706i | \(0.698539\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 2453.00 | 0.717231 | 0.358615 | − | 0.933485i | \(-0.383249\pi\) | ||||
0.358615 | + | 0.933485i | \(0.383249\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −6213.00 | −1.79287 | −0.896434 | − | 0.443178i | \(-0.853851\pi\) | ||||
−0.896434 | + | 0.443178i | \(0.853851\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 3450.00 | 0.970030 | 0.485015 | − | 0.874506i | \(-0.338814\pi\) | ||||
0.485015 | + | 0.874506i | \(0.338814\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −800.000 | −0.222069 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 6490.00 | 1.75650 | 0.878249 | − | 0.478203i | \(-0.158712\pi\) | ||||
0.878249 | + | 0.478203i | \(0.158712\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −3401.00 | −0.909036 | −0.454518 | − | 0.890738i | \(-0.650188\pi\) | ||||
−0.454518 | + | 0.890738i | \(0.650188\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 1715.00 | 0.447214 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −9040.00 | −2.32875 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −4980.00 | −1.25233 | −0.626165 | − | 0.779691i | \(-0.715376\pi\) | ||||
−0.626165 | + | 0.779691i | \(0.715376\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −810.000 | −0.201282 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −3357.00 | −0.814801 | −0.407401 | − | 0.913250i | \(-0.633565\pi\) | ||||
−0.407401 | + | 0.913250i | \(0.633565\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −4540.00 | −1.06444 | −0.532221 | − | 0.846605i | \(-0.678643\pi\) | ||||
−0.532221 | + | 0.846605i | \(0.678643\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 3155.00 | 0.731359 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −8410.00 | −1.90620 | −0.953098 | − | 0.302662i | \(-0.902125\pi\) | ||||
−0.953098 | + | 0.302662i | \(0.902125\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −259.000 | −0.0580558 | −0.0290279 | − | 0.999579i | \(-0.509241\pi\) | ||||
−0.0290279 | + | 0.999579i | \(0.509241\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 250.000 | 0.0548202 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −4170.00 | −0.904516 | −0.452258 | − | 0.891887i | \(-0.649381\pi\) | ||||
−0.452258 | + | 0.891887i | \(0.649381\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1740.00 | 0.369394 | 0.184697 | − | 0.982796i | \(-0.440870\pi\) | ||||
0.184697 | + | 0.982796i | \(0.440870\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 5070.00 | 1.06495 | 0.532474 | − | 0.846446i | \(-0.321262\pi\) | ||||
0.532474 | + | 0.846446i | \(0.321262\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −4864.00 | −0.990026 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 159.000 | 0.0317027 | 0.0158513 | − | 0.999874i | \(-0.494954\pi\) | ||||
0.0158513 | + | 0.999874i | \(0.494954\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 2800.00 | 0.552618 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 6480.00 | 1.25334 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −1145.00 | −0.214959 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −6490.00 | −1.20653 | −0.603264 | − | 0.797542i | \(-0.706133\pi\) | ||||
−0.603264 | + | 0.797542i | \(0.706133\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −8220.00 | −1.49876 | −0.749379 | − | 0.662142i | \(-0.769648\pi\) | ||||
−0.749379 | + | 0.662142i | \(0.769648\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −4660.00 | −0.841530 | −0.420765 | − | 0.907170i | \(-0.638238\pi\) | ||||
−0.420765 | + | 0.907170i | \(0.638238\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 6817.00 | 1.20783 | 0.603913 | − | 0.797050i | \(-0.293607\pi\) | ||||
0.603913 | + | 0.797050i | \(0.293607\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 2200.00 | 0.386133 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −791.000 | −0.136261 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −2000.00 | −0.341354 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −192.000 | −0.0318830 | −0.0159415 | − | 0.999873i | \(-0.505075\pi\) | ||||
−0.0159415 | + | 0.999873i | \(0.505075\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 3750.00 | 0.611595 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 4840.00 | 0.782349 | 0.391174 | − | 0.920317i | \(-0.372069\pi\) | ||||
0.391174 | + | 0.920317i | \(0.372069\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1890.00 | 0.300144 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −860.000 | −0.133047 | −0.0665234 | − | 0.997785i | \(-0.521191\pi\) | ||||
−0.0665234 | + | 0.997785i | \(0.521191\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 5377.00 | 0.824711 | 0.412356 | − | 0.911023i | \(-0.364706\pi\) | ||||
0.412356 | + | 0.911023i | \(0.364706\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 8010.00 | 1.20773 | 0.603866 | − | 0.797086i | \(-0.293626\pi\) | ||||
0.603866 | + | 0.797086i | \(0.293626\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −4450.00 | −0.665300 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 12930.0 | 1.90089 | 0.950445 | − | 0.310894i | \(-0.100628\pi\) | ||||
0.950445 | + | 0.310894i | \(0.100628\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 5910.00 | 0.861642 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 4450.00 | 0.638147 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 6000.00 | 0.853399 | 0.426700 | − | 0.904393i | \(-0.359676\pi\) | ||||
0.426700 | + | 0.904393i | \(0.359676\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −140.000 | −0.0194341 | −0.00971706 | − | 0.999953i | \(-0.503093\pi\) | ||||
−0.00971706 | + | 0.999953i | \(0.503093\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −17600.0 | −2.40437 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −6217.00 | −0.842601 | −0.421301 | − | 0.906921i | \(-0.638426\pi\) | ||||
−0.421301 | + | 0.906921i | \(0.638426\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 4551.00 | 0.607168 | 0.303584 | − | 0.952805i | \(-0.401817\pi\) | ||||
0.303584 | + | 0.952805i | \(0.401817\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 2310.00 | 0.301084 | 0.150542 | − | 0.988604i | \(-0.451898\pi\) | ||||
0.150542 | + | 0.988604i | \(0.451898\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 567.000 | 0.0733361 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −135.000 | −0.0171964 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −2900.00 | −0.366617 | −0.183308 | − | 0.983055i | \(-0.558681\pi\) | ||||
−0.183308 | + | 0.983055i | \(0.558681\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −2250.00 | −0.280199 | −0.140099 | − | 0.990137i | \(-0.544742\pi\) | ||||
−0.140099 | + | 0.990137i | \(0.544742\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −15120.0 | −1.86894 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 1700.00 | 0.207041 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −11263.0 | −1.36166 | −0.680831 | − | 0.732441i | \(-0.738381\pi\) | ||||
−0.680831 | + | 0.732441i | \(0.738381\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −2145.00 | −0.253720 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −6910.00 | −0.805670 | −0.402835 | − | 0.915273i | \(-0.631975\pi\) | ||||
−0.402835 | + | 0.915273i | \(0.631975\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −5249.00 | −0.607650 | −0.303825 | − | 0.952728i | \(-0.598264\pi\) | ||||
−0.303825 | + | 0.952728i | \(0.598264\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −175.000 | −0.0199735 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −11880.0 | −1.32770 | −0.663851 | − | 0.747865i | \(-0.731079\pi\) | ||||
−0.663851 | + | 0.747865i | \(0.731079\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −4280.00 | −0.475020 | −0.237510 | − | 0.971385i | \(-0.576331\pi\) | ||||
−0.237510 | + | 0.971385i | \(0.576331\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −9153.00 | −1.00194 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −6463.00 | −0.702647 | −0.351324 | − | 0.936254i | \(-0.614268\pi\) | ||||
−0.351324 | + | 0.936254i | \(0.614268\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 11721.0 | 1.25707 | 0.628534 | − | 0.777782i | \(-0.283655\pi\) | ||||
0.628534 | + | 0.777782i | \(0.283655\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −3750.00 | −0.399477 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 2180.00 | 0.229133 | 0.114566 | − | 0.993416i | \(-0.463452\pi\) | ||||
0.114566 | + | 0.993416i | \(0.463452\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1300.00 | 0.135731 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −17840.0 | −1.82608 | −0.913042 | − | 0.407866i | \(-0.866273\pi\) | ||||
−0.913042 | + | 0.407866i | \(0.866273\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 2250.00 | 0.227317 | 0.113658 | − | 0.993520i | \(-0.463743\pi\) | ||||
0.113658 | + | 0.993520i | \(0.463743\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −1230.00 | −0.123462 | −0.0617310 | − | 0.998093i | \(-0.519662\pi\) | ||||
−0.0617310 | + | 0.998093i | \(0.519662\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 5813.00 | 0.576003 | 0.288002 | − | 0.957630i | \(-0.407009\pi\) | ||||
0.288002 | + | 0.957630i | \(0.407009\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −100.000 | −0.00972094 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 2825.00 | 0.272884 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −6750.00 | −0.643873 | −0.321937 | − | 0.946761i | \(-0.604334\pi\) | ||||
−0.321937 | + | 0.946761i | \(0.604334\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −13600.0 | −1.28920 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 7400.00 | 0.692818 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 6610.00 | 0.615047 | 0.307523 | − | 0.951541i | \(-0.400500\pi\) | ||||
0.307523 | + | 0.951541i | \(0.400500\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −4990.00 | −0.458647 | −0.229323 | − | 0.973350i | \(-0.573651\pi\) | ||||
−0.229323 | + | 0.973350i | \(0.573651\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −1540.00 | −0.140686 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −1483.00 | −0.133042 | −0.0665212 | − | 0.997785i | \(-0.521190\pi\) | ||||
−0.0665212 | + | 0.997785i | \(0.521190\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −11641.0 | −1.03190 | −0.515951 | − | 0.856618i | \(-0.672561\pi\) | ||||
−0.515951 | + | 0.856618i | \(0.672561\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −7500.00 | −0.660882 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −2620.00 | −0.228152 | −0.114076 | − | 0.993472i | \(-0.536391\pi\) | ||||
−0.114076 | + | 0.993472i | \(0.536391\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −2300.00 | −0.196796 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1600.00 | 0.136108 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 13690.0 | 1.15119 | 0.575595 | − | 0.817735i | \(-0.304771\pi\) | ||||
0.575595 | + | 0.817735i | \(0.304771\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 10220.0 | 0.854473 | 0.427237 | − | 0.904140i | \(-0.359487\pi\) | ||||
0.427237 | + | 0.904140i | \(0.359487\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −1323.00 | −0.109356 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −5606.00 | −0.460754 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −10400.0 | −0.845167 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 2100.00 | 0.169703 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −3430.00 | −0.274101 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −2778.00 | −0.220768 | −0.110384 | − | 0.993889i | \(-0.535208\pi\) | ||||
−0.110384 | + | 0.993889i | \(0.535208\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 3035.00 | 0.238541 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 12830.0 | 1.00287 | 0.501436 | − | 0.865195i | \(-0.332805\pi\) | ||||
0.501436 | + | 0.865195i | \(0.332805\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 24860.0 | 1.92209 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 4950.00 | 0.376550 | 0.188275 | − | 0.982116i | \(-0.439710\pi\) | ||||
0.188275 | + | 0.982116i | \(0.439710\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 800.000 | 0.0605302 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 6540.00 | 0.489570 | 0.244785 | − | 0.969577i | \(-0.421283\pi\) | ||||
0.244785 | + | 0.969577i | \(0.421283\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 10850.0 | 0.807899 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 15240.0 | 1.12284 | 0.561418 | − | 0.827532i | \(-0.310256\pi\) | ||||
0.561418 | + | 0.827532i | \(0.310256\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 5281.00 | 0.387045 | 0.193523 | − | 0.981096i | \(-0.438009\pi\) | ||||
0.193523 | + | 0.981096i | \(0.438009\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −2025.00 | −0.146867 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −10510.0 | −0.758296 | −0.379148 | − | 0.925336i | \(-0.623783\pi\) | ||||
−0.379148 | + | 0.925336i | \(0.623783\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −6310.00 | −0.448256 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 4107.00 | 0.288780 | 0.144390 | − | 0.989521i | \(-0.453878\pi\) | ||||
0.144390 | + | 0.989521i | \(0.453878\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 21357.0 | 1.49406 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −26129.0 | −1.80943 | −0.904713 | − | 0.426022i | \(-0.859915\pi\) | ||||
−0.904713 | + | 0.426022i | \(0.859915\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −4360.00 | −0.297404 | −0.148702 | − | 0.988882i | \(-0.547509\pi\) | ||||
−0.148702 | + | 0.988882i | \(0.547509\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −16639.0 | −1.12932 | −0.564658 | − | 0.825325i | \(-0.690992\pi\) | ||||
−0.564658 | + | 0.825325i | \(0.690992\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 6155.00 | 0.413614 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −490.000 | −0.0327652 | −0.0163826 | − | 0.999866i | \(-0.505215\pi\) | ||||
−0.0163826 | + | 0.999866i | \(0.505215\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −12800.0 | −0.847516 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 18400.0 | 1.21235 | 0.606174 | − | 0.795332i | \(-0.292704\pi\) | ||||
0.606174 | + | 0.795332i | \(0.292704\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −7827.00 | −0.510702 | −0.255351 | − | 0.966848i | \(-0.582191\pi\) | ||||
−0.255351 | + | 0.966848i | \(0.582191\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 19756.0 | 1.28281 | 0.641406 | − | 0.767202i | \(-0.278351\pi\) | ||||
0.641406 | + | 0.767202i | \(0.278351\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 625.000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −1190.00 | −0.0754347 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −9829.00 | −0.620105 | −0.310053 | − | 0.950719i | \(-0.600347\pi\) | ||||
−0.310053 | + | 0.950719i | \(0.600347\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −8050.00 | −0.503078 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 27440.0 | 1.70677 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 6000.00 | 0.369713 | 0.184856 | − | 0.982766i | \(-0.440818\pi\) | ||||
0.184856 | + | 0.982766i | \(0.440818\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −8280.00 | −0.507825 | −0.253912 | − | 0.967227i | \(-0.581717\pi\) | ||||
−0.253912 | + | 0.967227i | \(0.581717\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −16637.0 | −1.01092 | −0.505462 | − | 0.862849i | \(-0.668678\pi\) | ||||
−0.505462 | + | 0.862849i | \(0.668678\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −5600.00 | −0.338705 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −19751.0 | −1.18364 | −0.591820 | − | 0.806070i | \(-0.701590\pi\) | ||||
−0.591820 | + | 0.806070i | \(0.701590\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −11850.0 | −0.706897 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 14260.0 | 0.842930 | 0.421465 | − | 0.906845i | \(-0.361516\pi\) | ||||
0.421465 | + | 0.906845i | \(0.361516\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 22318.0 | 1.31327 | 0.656634 | − | 0.754210i | \(-0.271980\pi\) | ||||
0.656634 | + | 0.754210i | \(0.271980\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −17820.0 | −1.03447 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 2290.00 | 0.131750 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 20040.0 | 1.14782 | 0.573912 | − | 0.818917i | \(-0.305425\pi\) | ||||
0.573912 | + | 0.818917i | \(0.305425\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 2310.00 | 0.131138 | 0.0655691 | − | 0.997848i | \(-0.479114\pi\) | ||||
0.0655691 | + | 0.997848i | \(0.479114\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −26739.0 | −1.49801 | −0.749004 | − | 0.662566i | \(-0.769468\pi\) | ||||
−0.749004 | + | 0.662566i | \(0.769468\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 8985.00 | 0.501167 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 50480.0 | 2.79120 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −5101.00 | −0.280827 | −0.140413 | − | 0.990093i | \(-0.544843\pi\) | ||||
−0.140413 | + | 0.990093i | \(0.544843\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −620.000 | −0.0338388 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −910.000 | −0.0494530 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −26030.0 | −1.40248 | −0.701241 | − | 0.712925i | \(-0.747370\pi\) | ||||
−0.701241 | + | 0.712925i | \(0.747370\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 19210.0 | 1.03061 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −3854.00 | −0.204147 | −0.102073 | − | 0.994777i | \(-0.532548\pi\) | ||||
−0.102073 | + | 0.994777i | \(0.532548\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −15309.0 | −0.804105 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 4000.00 | 0.209219 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −870.000 | −0.0451259 | −0.0225630 | − | 0.999745i | \(-0.507183\pi\) | ||||
−0.0225630 | + | 0.999745i | \(0.507183\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 5500.00 | 0.281745 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −35780.0 | −1.82532 | −0.912659 | − | 0.408721i | \(-0.865975\pi\) | ||||
−0.912659 | + | 0.408721i | \(0.865975\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 70.0000 | 0.00354178 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −3400.00 | −0.171326 | −0.0856629 | − | 0.996324i | \(-0.527301\pi\) | ||||
−0.0856629 | + | 0.996324i | \(0.527301\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −7500.00 | −0.374852 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 683.000 | 0.0339981 | 0.0169990 | − | 0.999856i | \(-0.494589\pi\) | ||||
0.0169990 | + | 0.999856i | \(0.494589\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −13400.0 | −0.661640 | −0.330820 | − | 0.943694i | \(-0.607325\pi\) | ||||
−0.330820 | + | 0.943694i | \(0.607325\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −350.000 | −0.0172121 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 23219.0 | 1.12819 | 0.564097 | − | 0.825709i | \(-0.309224\pi\) | ||||
0.564097 | + | 0.825709i | \(0.309224\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 11240.0 | 0.541809 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 19630.0 | 0.942489 | 0.471245 | − | 0.882003i | \(-0.343805\pi\) | ||||
0.471245 | + | 0.882003i | \(0.343805\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −2940.00 | −0.140046 | −0.0700229 | − | 0.997545i | \(-0.522307\pi\) | ||||
−0.0700229 | + | 0.997545i | \(0.522307\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 44800.0 | 2.10904 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −13987.0 | −0.655896 | −0.327948 | − | 0.944696i | \(-0.606357\pi\) | ||||
−0.327948 | + | 0.944696i | \(0.606357\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −19839.0 | −0.923104 | −0.461552 | − | 0.887113i | \(-0.652707\pi\) | ||||
−0.461552 | + | 0.887113i | \(0.652707\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 4725.00 | 0.219003 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 14690.0 | 0.675640 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 8900.00 | 0.407768 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −5050.00 | −0.229608 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 38390.0 | 1.73883 | 0.869413 | − | 0.494086i | \(-0.164497\pi\) | ||||
0.869413 | + | 0.494086i | \(0.164497\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −18320.0 | −0.820381 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 28027.0 | 1.24563 | 0.622815 | − | 0.782369i | \(-0.285989\pi\) | ||||
0.622815 | + | 0.782369i | \(0.285989\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −1120.00 | −0.0495904 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −8900.00 | −0.391126 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −8630.00 | −0.375049 | −0.187525 | − | 0.982260i | \(-0.560046\pi\) | ||||
−0.187525 | + | 0.982260i | \(0.560046\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1932.00 | 0.0836519 | 0.0418260 | − | 0.999125i | \(-0.486683\pi\) | ||||
0.0418260 | + | 0.999125i | \(0.486683\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 2950.00 | 0.126790 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −1130.00 | −0.0483889 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 18090.0 | 0.768996 | 0.384498 | − | 0.923126i | \(-0.374375\pi\) | ||||
0.384498 | + | 0.923126i | \(0.374375\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −12890.0 | −0.545950 | −0.272975 | − | 0.962021i | \(-0.588008\pi\) | ||||
−0.272975 | + | 0.962021i | \(0.588008\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 14887.0 | 0.625963 | 0.312982 | − | 0.949759i | \(-0.398672\pi\) | ||||
0.312982 | + | 0.949759i | \(0.398672\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 12666.0 | 0.530649 | 0.265325 | − | 0.964159i | \(-0.414521\pi\) | ||||
0.265325 | + | 0.964159i | \(0.414521\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 2401.00 | 0.0998676 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −12015.0 | −0.497960 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 43820.0 | 1.80314 | 0.901570 | − | 0.432633i | \(-0.142416\pi\) | ||||
0.901570 | + | 0.432633i | \(0.142416\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 24011.0 | 0.984501 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −21015.0 | −0.855548 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −13770.0 | −0.554676 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 19320.0 | 0.775503 | 0.387752 | − | 0.921764i | \(-0.373252\pi\) | ||||
0.387752 | + | 0.921764i | \(0.373252\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 3653.00 | 0.145606 | 0.0728029 | − | 0.997346i | \(-0.476806\pi\) | ||||
0.0728029 | + | 0.997346i | \(0.476806\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −24373.0 | −0.968098 | −0.484049 | − | 0.875041i | \(-0.660834\pi\) | ||||
−0.484049 | + | 0.875041i | \(0.660834\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −17629.0 | −0.695363 | −0.347681 | − | 0.937613i | \(-0.613031\pi\) | ||||
−0.347681 | + | 0.937613i | \(0.613031\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 4005.00 | 0.157427 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 270.000 | 0.0105398 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 60000.0 | 2.33412 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −21210.0 | −0.816660 | −0.408330 | − | 0.912834i | \(-0.633889\pi\) | ||||
−0.408330 | + | 0.912834i | \(0.633889\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −39340.0 | −1.50442 | −0.752212 | − | 0.658921i | \(-0.771013\pi\) | ||||
−0.752212 | + | 0.658921i | \(0.771013\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 4240.00 | 0.161594 | 0.0807969 | − | 0.996731i | \(-0.474253\pi\) | ||||
0.0807969 | + | 0.996731i | \(0.474253\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −15933.0 | −0.603132 | −0.301566 | − | 0.953445i | \(-0.597509\pi\) | ||||
−0.301566 | + | 0.953445i | \(0.597509\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 18080.0 | 0.677519 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 11800.0 | 0.440704 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 41580.0 | 1.54257 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 4417.00 | 0.163320 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −6205.00 | −0.227913 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 6780.00 | 0.248210 | 0.124105 | − | 0.992269i | \(-0.460394\pi\) | ||||
0.124105 | + | 0.992269i | \(0.460394\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −24740.0 | −0.899751 | −0.449875 | − | 0.893091i | \(-0.648532\pi\) | ||||
−0.449875 | + | 0.893091i | \(0.648532\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 4290.00 | 0.155507 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 48344.0 | 1.73528 | 0.867640 | − | 0.497194i | \(-0.165636\pi\) | ||||
0.867640 | + | 0.497194i | \(0.165636\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −71200.0 | −2.53909 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 4250.00 | 0.151069 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 29650.0 | 1.04713 | 0.523566 | − | 0.851985i | \(-0.324601\pi\) | ||||
0.523566 | + | 0.851985i | \(0.324601\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −38759.0 | −1.36442 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 350.000 | 0.0122420 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 10260.0 | 0.357716 | 0.178858 | − | 0.983875i | \(-0.442760\pi\) | ||||
0.178858 | + | 0.983875i | \(0.442760\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 16270.0 | 0.563642 | 0.281821 | − | 0.959467i | \(-0.409062\pi\) | ||||
0.281821 | + | 0.959467i | \(0.409062\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −10530.0 | −0.363631 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −23103.0 | −0.792763 | −0.396382 | − | 0.918086i | \(-0.629734\pi\) | ||||
−0.396382 | + | 0.918086i | \(0.629734\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 71200.0 | 2.43546 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 32090.0 | 1.09076 | 0.545381 | − | 0.838188i | \(-0.316385\pi\) | ||||
0.545381 | + | 0.838188i | \(0.316385\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 24950.0 | 0.845406 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 5930.00 | 0.199053 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 11300.0 | 0.376953 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 42010.0 | 1.39705 | 0.698527 | − | 0.715584i | \(-0.253839\pi\) | ||||
0.698527 | + | 0.715584i | \(0.253839\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 17490.0 | 0.578044 | 0.289022 | − | 0.957322i | \(-0.406670\pi\) | ||||
0.289022 | + | 0.957322i | \(0.406670\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 22130.0 | 0.724669 | 0.362334 | − | 0.932048i | \(-0.381980\pi\) | ||||
0.362334 | + | 0.932048i | \(0.381980\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 7500.00 | 0.244843 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 40959.0 | 1.32898 | 0.664491 | − | 0.747296i | \(-0.268648\pi\) | ||||
0.664491 | + | 0.747296i | \(0.268648\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −11235.0 | −0.363428 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 810.000 | 0.0260430 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −61169.0 | −1.96074 | −0.980372 | − | 0.197157i | \(-0.936829\pi\) | ||||
−0.980372 | + | 0.197157i | \(0.936829\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 22820.0 | 0.727078 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 26190.0 | 0.831941 | 0.415971 | − | 0.909378i | \(-0.363442\pi\) | ||||
0.415971 | + | 0.909378i | \(0.363442\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 2160.4.a.d.1.1 | 1 | ||
3.2 | odd | 2 | 2160.4.a.n.1.1 | 1 | |||
4.3 | odd | 2 | 135.4.a.d.1.1 | yes | 1 | ||
12.11 | even | 2 | 135.4.a.a.1.1 | ✓ | 1 | ||
20.3 | even | 4 | 675.4.b.c.649.1 | 2 | |||
20.7 | even | 4 | 675.4.b.c.649.2 | 2 | |||
20.19 | odd | 2 | 675.4.a.b.1.1 | 1 | |||
36.7 | odd | 6 | 405.4.e.e.271.1 | 2 | |||
36.11 | even | 6 | 405.4.e.j.271.1 | 2 | |||
36.23 | even | 6 | 405.4.e.j.136.1 | 2 | |||
36.31 | odd | 6 | 405.4.e.e.136.1 | 2 | |||
60.23 | odd | 4 | 675.4.b.d.649.2 | 2 | |||
60.47 | odd | 4 | 675.4.b.d.649.1 | 2 | |||
60.59 | even | 2 | 675.4.a.i.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
135.4.a.a.1.1 | ✓ | 1 | 12.11 | even | 2 | ||
135.4.a.d.1.1 | yes | 1 | 4.3 | odd | 2 | ||
405.4.e.e.136.1 | 2 | 36.31 | odd | 6 | |||
405.4.e.e.271.1 | 2 | 36.7 | odd | 6 | |||
405.4.e.j.136.1 | 2 | 36.23 | even | 6 | |||
405.4.e.j.271.1 | 2 | 36.11 | even | 6 | |||
675.4.a.b.1.1 | 1 | 20.19 | odd | 2 | |||
675.4.a.i.1.1 | 1 | 60.59 | even | 2 | |||
675.4.b.c.649.1 | 2 | 20.3 | even | 4 | |||
675.4.b.c.649.2 | 2 | 20.7 | even | 4 | |||
675.4.b.d.649.1 | 2 | 60.47 | odd | 4 | |||
675.4.b.d.649.2 | 2 | 60.23 | odd | 4 | |||
2160.4.a.d.1.1 | 1 | 1.1 | even | 1 | trivial | ||
2160.4.a.n.1.1 | 1 | 3.2 | odd | 2 |