Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1440,4,Mod(1,1440)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1440, 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("1440.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1440 = 2^{5} \cdot 3^{2} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1440.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: | \(84.9627504083\) |
Analytic rank: | \(0\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 160) |
Fricke sign: | \(+1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 1440.1 |
$q$-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 | ||||||||
\(7\) | −6.00000 | −0.323970 | −0.161985 | − | 0.986793i | \(-0.551790\pi\) | ||||
−0.161985 | + | 0.986793i | \(0.551790\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 60.0000 | 1.64461 | 0.822304 | − | 0.569049i | \(-0.192689\pi\) | ||||
0.822304 | + | 0.569049i | \(0.192689\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 50.0000 | 1.06673 | 0.533366 | − | 0.845885i | \(-0.320927\pi\) | ||||
0.533366 | + | 0.845885i | \(0.320927\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 30.0000 | 0.428004 | 0.214002 | − | 0.976833i | \(-0.431350\pi\) | ||||
0.214002 | + | 0.976833i | \(0.431350\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −40.0000 | −0.482980 | −0.241490 | − | 0.970403i | \(-0.577636\pi\) | ||||
−0.241490 | + | 0.970403i | \(0.577636\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 178.000 | 1.61372 | 0.806860 | − | 0.590743i | \(-0.201165\pi\) | ||||
0.806860 | + | 0.590743i | \(0.201165\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 25.0000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −166.000 | −1.06295 | −0.531473 | − | 0.847075i | \(-0.678361\pi\) | ||||
−0.531473 | + | 0.847075i | \(0.678361\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −20.0000 | −0.115874 | −0.0579372 | − | 0.998320i | \(-0.518452\pi\) | ||||
−0.0579372 | + | 0.998320i | \(0.518452\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −30.0000 | −0.144884 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 10.0000 | 0.0444322 | 0.0222161 | − | 0.999753i | \(-0.492928\pi\) | ||||
0.0222161 | + | 0.999753i | \(0.492928\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 250.000 | 0.952279 | 0.476140 | − | 0.879370i | \(-0.342036\pi\) | ||||
0.476140 | + | 0.879370i | \(0.342036\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −142.000 | −0.503600 | −0.251800 | − | 0.967779i | \(-0.581023\pi\) | ||||
−0.251800 | + | 0.967779i | \(0.581023\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 214.000 | 0.664151 | 0.332076 | − | 0.943253i | \(-0.392251\pi\) | ||||
0.332076 | + | 0.943253i | \(0.392251\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −307.000 | −0.895044 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −490.000 | −1.26994 | −0.634969 | − | 0.772538i | \(-0.718987\pi\) | ||||
−0.634969 | + | 0.772538i | \(0.718987\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 300.000 | 0.735491 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −800.000 | −1.76527 | −0.882637 | − | 0.470056i | \(-0.844234\pi\) | ||||
−0.882637 | + | 0.470056i | \(0.844234\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 250.000 | 0.524741 | 0.262371 | − | 0.964967i | \(-0.415496\pi\) | ||||
0.262371 | + | 0.964967i | \(0.415496\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 250.000 | 0.477057 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 774.000 | 1.41133 | 0.705665 | − | 0.708545i | \(-0.250648\pi\) | ||||
0.705665 | + | 0.708545i | \(0.250648\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 100.000 | 0.167152 | 0.0835762 | − | 0.996501i | \(-0.473366\pi\) | ||||
0.0835762 | + | 0.996501i | \(0.473366\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −230.000 | −0.368760 | −0.184380 | − | 0.982855i | \(-0.559028\pi\) | ||||
−0.184380 | + | 0.982855i | \(0.559028\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −360.000 | −0.532803 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1320.00 | 1.87989 | 0.939947 | − | 0.341321i | \(-0.110874\pi\) | ||||
0.939947 | + | 0.341321i | \(0.110874\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 982.000 | 1.29866 | 0.649328 | − | 0.760508i | \(-0.275050\pi\) | ||||
0.649328 | + | 0.760508i | \(0.275050\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 150.000 | 0.191409 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −874.000 | −1.04094 | −0.520471 | − | 0.853879i | \(-0.674244\pi\) | ||||
−0.520471 | + | 0.853879i | \(0.674244\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −300.000 | −0.345588 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −200.000 | −0.215995 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −310.000 | −0.324492 | −0.162246 | − | 0.986750i | \(-0.551874\pi\) | ||||
−0.162246 | + | 0.986750i | \(0.551874\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1498.00 | 1.47581 | 0.737904 | − | 0.674906i | \(-0.235816\pi\) | ||||
0.737904 | + | 0.674906i | \(0.235816\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1402.00 | −1.34120 | −0.670598 | − | 0.741821i | \(-0.733962\pi\) | ||||
−0.670598 | + | 0.741821i | \(0.733962\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 1194.00 | 1.07877 | 0.539385 | − | 0.842059i | \(-0.318657\pi\) | ||||
0.539385 | + | 0.842059i | \(0.318657\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 650.000 | 0.571181 | 0.285590 | − | 0.958352i | \(-0.407810\pi\) | ||||
0.285590 | + | 0.958352i | \(0.407810\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1510.00 | 1.25707 | 0.628535 | − | 0.777782i | \(-0.283655\pi\) | ||||
0.628535 | + | 0.777782i | \(0.283655\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 890.000 | 0.721678 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −180.000 | −0.138660 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 2269.00 | 1.70473 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 125.000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1246.00 | −0.870588 | −0.435294 | − | 0.900288i | \(-0.643355\pi\) | ||||
−0.435294 | + | 0.900288i | \(0.643355\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 2660.00 | 1.77409 | 0.887043 | − | 0.461687i | \(-0.152756\pi\) | ||||
0.887043 | + | 0.461687i | \(0.152756\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 240.000 | 0.156471 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −2770.00 | −1.72742 | −0.863712 | − | 0.503986i | \(-0.831866\pi\) | ||||
−0.863712 | + | 0.503986i | \(0.831866\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 560.000 | 0.341716 | 0.170858 | − | 0.985296i | \(-0.445346\pi\) | ||||
0.170858 | + | 0.985296i | \(0.445346\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 3000.00 | 1.75435 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −830.000 | −0.475364 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 2350.00 | 1.29208 | 0.646039 | − | 0.763305i | \(-0.276424\pi\) | ||||
0.646039 | + | 0.763305i | \(0.276424\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −580.000 | −0.312581 | −0.156290 | − | 0.987711i | \(-0.549954\pi\) | ||||
−0.156290 | + | 0.987711i | \(0.549954\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −100.000 | −0.0518206 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1310.00 | −0.665920 | −0.332960 | − | 0.942941i | \(-0.608047\pi\) | ||||
−0.332960 | + | 0.942941i | \(0.608047\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1068.00 | −0.522796 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1862.00 | −0.894743 | −0.447371 | − | 0.894348i | \(-0.647640\pi\) | ||||
−0.447371 | + | 0.894348i | \(0.647640\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 726.000 | 0.336405 | 0.168202 | − | 0.985752i | \(-0.446204\pi\) | ||||
0.168202 | + | 0.985752i | \(0.446204\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 303.000 | 0.137915 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −3250.00 | −1.42828 | −0.714141 | − | 0.700001i | \(-0.753183\pi\) | ||||
−0.714141 | + | 0.700001i | \(0.753183\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −150.000 | −0.0647939 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −1120.00 | −0.467669 | −0.233834 | − | 0.972276i | \(-0.575127\pi\) | ||||
−0.233834 | + | 0.972276i | \(0.575127\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −2842.00 | −1.16710 | −0.583548 | − | 0.812079i | \(-0.698336\pi\) | ||||
−0.583548 | + | 0.812079i | \(0.698336\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 50.0000 | 0.0198707 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1800.00 | 0.703899 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 3180.00 | 1.20469 | 0.602347 | − | 0.798234i | \(-0.294232\pi\) | ||||
0.602347 | + | 0.798234i | \(0.294232\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −4670.00 | −1.74173 | −0.870865 | − | 0.491522i | \(-0.836441\pi\) | ||||
−0.870865 | + | 0.491522i | \(0.836441\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 2990.00 | 1.08136 | 0.540682 | − | 0.841227i | \(-0.318166\pi\) | ||||
0.540682 | + | 0.841227i | \(0.318166\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 4240.00 | 1.51038 | 0.755190 | − | 0.655506i | \(-0.227545\pi\) | ||||
0.755190 | + | 0.655506i | \(0.227545\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 996.000 | 0.344362 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1250.00 | 0.425872 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −2400.00 | −0.794313 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 4060.00 | 1.32465 | 0.662327 | − | 0.749215i | \(-0.269569\pi\) | ||||
0.662327 | + | 0.749215i | \(0.269569\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −710.000 | −0.225217 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 120.000 | 0.0375398 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1500.00 | 0.456565 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 5622.00 | 1.68824 | 0.844119 | − | 0.536156i | \(-0.180124\pi\) | ||||
0.844119 | + | 0.536156i | \(0.180124\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 1554.00 | 0.454373 | 0.227186 | − | 0.973851i | \(-0.427047\pi\) | ||||
0.227186 | + | 0.973851i | \(0.427047\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1134.00 | 0.327235 | 0.163618 | − | 0.986524i | \(-0.447684\pi\) | ||||
0.163618 | + | 0.986524i | \(0.447684\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 1710.00 | 0.480798 | 0.240399 | − | 0.970674i | \(-0.422722\pi\) | ||||
0.240399 | + | 0.970674i | \(0.422722\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1070.00 | 0.297017 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 4440.00 | 1.20167 | 0.600836 | − | 0.799372i | \(-0.294834\pi\) | ||||
0.600836 | + | 0.799372i | \(0.294834\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −850.000 | −0.227192 | −0.113596 | − | 0.993527i | \(-0.536237\pi\) | ||||
−0.113596 | + | 0.993527i | \(0.536237\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −1535.00 | −0.400276 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −2000.00 | −0.515210 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −660.000 | −0.165971 | −0.0829857 | − | 0.996551i | \(-0.526446\pi\) | ||||
−0.0829857 | + | 0.996551i | \(0.526446\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 10680.0 | 2.65394 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 7590.00 | 1.84222 | 0.921111 | − | 0.389299i | \(-0.127283\pi\) | ||||
0.921111 | + | 0.389299i | \(0.127283\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −60.0000 | −0.0143947 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 762.000 | 0.178658 | 0.0893288 | − | 0.996002i | \(-0.471528\pi\) | ||||
0.0893288 | + | 0.996002i | \(0.471528\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −2450.00 | −0.567933 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 150.000 | 0.0339987 | 0.0169994 | − | 0.999856i | \(-0.494589\pi\) | ||||
0.0169994 | + | 0.999856i | \(0.494589\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 6580.00 | 1.47493 | 0.737466 | − | 0.675384i | \(-0.236022\pi\) | ||||
0.737466 | + | 0.675384i | \(0.236022\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 1500.00 | 0.328921 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 4530.00 | 0.982604 | 0.491302 | − | 0.870989i | \(-0.336521\pi\) | ||||
0.491302 | + | 0.870989i | \(0.336521\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −6950.00 | −1.47545 | −0.737726 | − | 0.675100i | \(-0.764101\pi\) | ||||
−0.737726 | + | 0.675100i | \(0.764101\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 3882.00 | 0.815410 | 0.407705 | − | 0.913114i | \(-0.366329\pi\) | ||||
0.407705 | + | 0.913114i | \(0.366329\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −1500.00 | −0.308509 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −4013.00 | −0.816813 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −1370.00 | −0.273161 | −0.136581 | − | 0.990629i | \(-0.543611\pi\) | ||||
−0.136581 | + | 0.990629i | \(0.543611\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −4000.00 | −0.789454 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 8900.00 | 1.72141 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 852.000 | 0.163151 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 1250.00 | 0.234671 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −4106.00 | −0.763328 | −0.381664 | − | 0.924301i | \(-0.624649\pi\) | ||||
−0.381664 | + | 0.924301i | \(0.624649\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 2220.00 | 0.404774 | 0.202387 | − | 0.979306i | \(-0.435130\pi\) | ||||
0.202387 | + | 0.979306i | \(0.435130\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −9430.00 | −1.70292 | −0.851462 | − | 0.524417i | \(-0.824283\pi\) | ||||
−0.851462 | + | 0.524417i | \(0.824283\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 6470.00 | 1.14635 | 0.573173 | − | 0.819435i | \(-0.305712\pi\) | ||||
0.573173 | + | 0.819435i | \(0.305712\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −9960.00 | −1.74813 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −1200.00 | −0.206718 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1250.00 | 0.213346 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −1284.00 | −0.215165 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −900.000 | −0.149452 | −0.0747258 | − | 0.997204i | \(-0.523808\pi\) | ||||
−0.0747258 | + | 0.997204i | \(0.523808\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 3870.00 | 0.631166 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 530.000 | 0.0856704 | 0.0428352 | − | 0.999082i | \(-0.486361\pi\) | ||||
0.0428352 | + | 0.999082i | \(0.486361\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −1200.00 | −0.190568 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 3900.00 | 0.613936 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −414.000 | −0.0640481 | −0.0320240 | − | 0.999487i | \(-0.510195\pi\) | ||||
−0.0320240 | + | 0.999487i | \(0.510195\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 8614.00 | 1.32119 | 0.660597 | − | 0.750741i | \(-0.270303\pi\) | ||||
0.660597 | + | 0.750741i | \(0.270303\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 2270.00 | 0.342266 | 0.171133 | − | 0.985248i | \(-0.445257\pi\) | ||||
0.171133 | + | 0.985248i | \(0.445257\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 500.000 | 0.0747528 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 8080.00 | 1.18787 | 0.593936 | − | 0.804512i | \(-0.297573\pi\) | ||||
0.593936 | + | 0.804512i | \(0.297573\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −5259.00 | −0.766730 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −1150.00 | −0.164914 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −2374.00 | −0.337662 | −0.168831 | − | 0.985645i | \(-0.553999\pi\) | ||||
−0.168831 | + | 0.985645i | \(0.553999\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 2940.00 | 0.411421 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 1810.00 | 0.251255 | 0.125628 | − | 0.992077i | \(-0.459906\pi\) | ||||
0.125628 | + | 0.992077i | \(0.459906\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −8300.00 | −1.13388 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −8120.00 | −1.10052 | −0.550259 | − | 0.834994i | \(-0.685471\pi\) | ||||
−0.550259 | + | 0.834994i | \(0.685471\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −11782.0 | −1.57189 | −0.785943 | − | 0.618299i | \(-0.787822\pi\) | ||||
−0.785943 | + | 0.618299i | \(0.787822\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1800.00 | −0.238277 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 4350.00 | 0.566976 | 0.283488 | − | 0.958976i | \(-0.408508\pi\) | ||||
0.283488 | + | 0.958976i | \(0.408508\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 5340.00 | 0.690679 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 6600.00 | 0.840714 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −7470.00 | −0.944354 | −0.472177 | − | 0.881504i | \(-0.656532\pi\) | ||||
−0.472177 | + | 0.881504i | \(0.656532\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −11698.0 | −1.45678 | −0.728392 | − | 0.685161i | \(-0.759732\pi\) | ||||
−0.728392 | + | 0.685161i | \(0.759732\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1000.00 | −0.123607 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 600.000 | 0.0730735 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −3650.00 | −0.441274 | −0.220637 | − | 0.975356i | \(-0.570814\pi\) | ||||
−0.220637 | + | 0.975356i | \(0.570814\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 4800.00 | 0.571895 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 4910.00 | 0.580777 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −1120.00 | −0.130586 | −0.0652931 | − | 0.997866i | \(-0.520798\pi\) | ||||
−0.0652931 | + | 0.997866i | \(0.520798\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 4850.00 | 0.561460 | 0.280730 | − | 0.959787i | \(-0.409424\pi\) | ||||
0.280730 | + | 0.959787i | \(0.409424\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 750.000 | 0.0856008 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −1500.00 | −0.170000 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −12580.0 | −1.40593 | −0.702967 | − | 0.711223i | \(-0.748142\pi\) | ||||
−0.702967 | + | 0.711223i | \(0.748142\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 13130.0 | 1.45725 | 0.728623 | − | 0.684915i | \(-0.240161\pi\) | ||||
0.728623 | + | 0.684915i | \(0.240161\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −7120.00 | −0.779395 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −8560.00 | −0.930630 | −0.465315 | − | 0.885145i | \(-0.654059\pi\) | ||||
−0.465315 | + | 0.885145i | \(0.654059\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −4258.00 | −0.456667 | −0.228334 | − | 0.973583i | \(-0.573328\pi\) | ||||
−0.228334 | + | 0.973583i | \(0.573328\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −4370.00 | −0.465523 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −2550.00 | −0.268022 | −0.134011 | − | 0.990980i | \(-0.542786\pi\) | ||||
−0.134011 | + | 0.990980i | \(0.542786\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 15000.0 | 1.56613 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −1500.00 | −0.154552 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −6710.00 | −0.686828 | −0.343414 | − | 0.939184i | \(-0.611583\pi\) | ||||
−0.343414 | + | 0.939184i | \(0.611583\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 14482.0 | 1.46311 | 0.731555 | − | 0.681782i | \(-0.238795\pi\) | ||||
0.731555 | + | 0.681782i | \(0.238795\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −162.000 | −0.0162609 | −0.00813043 | − | 0.999967i | \(-0.502588\pi\) | ||||
−0.00813043 | + | 0.999967i | \(0.502588\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −15974.0 | −1.58284 | −0.791422 | − | 0.611270i | \(-0.790659\pi\) | ||||
−0.791422 | + | 0.611270i | \(0.790659\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −4644.00 | −0.457228 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −8520.00 | −0.828224 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1000.00 | −0.0965961 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −10760.0 | −1.02638 | −0.513191 | − | 0.858274i | \(-0.671537\pi\) | ||||
−0.513191 | + | 0.858274i | \(0.671537\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 500.000 | 0.0473972 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −1550.00 | −0.145117 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 9266.00 | 0.862182 | 0.431091 | − | 0.902309i | \(-0.358129\pi\) | ||||
0.431091 | + | 0.902309i | \(0.358129\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 2860.00 | 0.262872 | 0.131436 | − | 0.991325i | \(-0.458041\pi\) | ||||
0.131436 | + | 0.991325i | \(0.458041\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −4980.00 | −0.454945 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −600.000 | −0.0541523 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −7160.00 | −0.642336 | −0.321168 | − | 0.947022i | \(-0.604075\pi\) | ||||
−0.321168 | + | 0.947022i | \(0.604075\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −1398.00 | −0.123924 | −0.0619620 | − | 0.998079i | \(-0.519736\pi\) | ||||
−0.0619620 | + | 0.998079i | \(0.519736\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 7490.00 | 0.660001 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −7446.00 | −0.648405 | −0.324203 | − | 0.945988i | \(-0.605096\pi\) | ||||
−0.324203 | + | 0.945988i | \(0.605096\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1380.00 | 0.119467 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −7010.00 | −0.599801 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 12840.0 | 1.09227 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 16438.0 | 1.38227 | 0.691134 | − | 0.722726i | \(-0.257111\pi\) | ||||
0.691134 | + | 0.722726i | \(0.257111\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 7322.00 | 0.612177 | 0.306089 | − | 0.952003i | \(-0.400980\pi\) | ||||
0.306089 | + | 0.952003i | \(0.400980\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −600.000 | −0.0495947 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 19517.0 | 1.60409 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 12500.0 | 1.01583 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 5970.00 | 0.482440 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −18420.0 | −1.47200 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 10878.0 | 0.864476 | 0.432238 | − | 0.901759i | \(-0.357724\pi\) | ||||
0.432238 | + | 0.901759i | \(0.357724\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 3250.00 | 0.255440 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −16114.0 | −1.25957 | −0.629785 | − | 0.776769i | \(-0.716857\pi\) | ||||
−0.629785 | + | 0.776769i | \(0.716857\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 6640.00 | 0.513382 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −7920.00 | −0.609028 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −3690.00 | −0.280701 | −0.140350 | − | 0.990102i | \(-0.544823\pi\) | ||||
−0.140350 | + | 0.990102i | \(0.544823\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −7100.00 | −0.537206 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −2562.00 | −0.191786 | −0.0958929 | − | 0.995392i | \(-0.530571\pi\) | ||||
−0.0958929 | + | 0.995392i | \(0.530571\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 7550.00 | 0.562179 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 6050.00 | 0.445746 | 0.222873 | − | 0.974848i | \(-0.428457\pi\) | ||||
0.222873 | + | 0.974848i | \(0.428457\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −8260.00 | −0.605377 | −0.302688 | − | 0.953090i | \(-0.597884\pi\) | ||||
−0.302688 | + | 0.953090i | \(0.597884\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 4450.00 | 0.322744 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −16870.0 | −1.21717 | −0.608585 | − | 0.793489i | \(-0.708263\pi\) | ||||
−0.608585 | + | 0.793489i | \(0.708263\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −5892.00 | −0.420725 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −29400.0 | −2.08855 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −966.000 | −0.0679235 | −0.0339617 | − | 0.999423i | \(-0.510812\pi\) | ||||
−0.0339617 | + | 0.999423i | \(0.510812\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 800.000 | 0.0559651 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −26290.0 | −1.82057 | −0.910287 | − | 0.413977i | \(-0.864139\pi\) | ||||
−0.910287 | + | 0.413977i | \(0.864139\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −900.000 | −0.0620108 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −11640.0 | −0.793986 | −0.396993 | − | 0.917822i | \(-0.629946\pi\) | ||||
−0.396993 | + | 0.917822i | \(0.629946\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −25450.0 | −1.72733 | −0.863667 | − | 0.504064i | \(-0.831838\pi\) | ||||
−0.863667 | + | 0.504064i | \(0.831838\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 11345.0 | 0.762380 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −16694.0 | −1.11629 | −0.558145 | − | 0.829743i | \(-0.688487\pi\) | ||||
−0.558145 | + | 0.829743i | \(0.688487\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 10700.0 | 0.708471 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 15890.0 | 1.04697 | 0.523484 | − | 0.852036i | \(-0.324632\pi\) | ||||
0.523484 | + | 0.852036i | \(0.324632\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 1230.00 | 0.0802560 | 0.0401280 | − | 0.999195i | \(-0.487223\pi\) | ||||
0.0401280 | + | 0.999195i | \(0.487223\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 10840.0 | 0.703871 | 0.351936 | − | 0.936024i | \(-0.385524\pi\) | ||||
0.351936 | + | 0.936024i | \(0.385524\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 5244.00 | 0.337233 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 625.000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 300.000 | 0.0190171 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 14060.0 | 0.887036 | 0.443518 | − | 0.896265i | \(-0.353730\pi\) | ||||
0.443518 | + | 0.896265i | \(0.353730\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −6230.00 | −0.389339 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −15350.0 | −0.954771 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 17650.0 | 1.08757 | 0.543786 | − | 0.839224i | \(-0.316990\pi\) | ||||
0.543786 | + | 0.839224i | \(0.316990\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −27358.0 | −1.67791 | −0.838953 | − | 0.544203i | \(-0.816832\pi\) | ||||
−0.838953 | + | 0.544203i | \(0.816832\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −6786.00 | −0.412342 | −0.206171 | − | 0.978516i | \(-0.566100\pi\) | ||||
−0.206171 | + | 0.978516i | \(0.566100\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −48000.0 | −2.90318 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 9030.00 | 0.541150 | 0.270575 | − | 0.962699i | \(-0.412786\pi\) | ||||
0.270575 | + | 0.962699i | \(0.412786\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 13300.0 | 0.793395 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −15600.0 | −0.922139 | −0.461070 | − | 0.887364i | \(-0.652534\pi\) | ||||
−0.461070 | + | 0.887364i | \(0.652534\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 16850.0 | 0.991511 | 0.495756 | − | 0.868462i | \(-0.334891\pi\) | ||||
0.495756 | + | 0.868462i | \(0.334891\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 1200.00 | 0.0699759 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −29548.0 | −1.71530 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 15000.0 | 0.862993 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −7990.00 | −0.457640 | −0.228820 | − | 0.973469i | \(-0.573487\pi\) | ||||
−0.228820 | + | 0.973469i | \(0.573487\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −18690.0 | −1.06103 | −0.530513 | − | 0.847677i | \(-0.678001\pi\) | ||||
−0.530513 | + | 0.847677i | \(0.678001\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1860.00 | 0.105126 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 19182.0 | 1.07464 | 0.537320 | − | 0.843379i | \(-0.319437\pi\) | ||||
0.537320 | + | 0.843379i | \(0.319437\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −13850.0 | −0.772527 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −24500.0 | −1.35468 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 23380.0 | 1.28714 | 0.643572 | − | 0.765385i | \(-0.277452\pi\) | ||||
0.643572 | + | 0.765385i | \(0.277452\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 2800.00 | 0.152820 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 7500.00 | 0.407579 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −11850.0 | −0.638471 | −0.319236 | − | 0.947675i | \(-0.603426\pi\) | ||||
−0.319236 | + | 0.947675i | \(0.603426\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −400.000 | −0.0214599 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −8988.00 | −0.478117 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 25646.0 | 1.35847 | 0.679235 | − | 0.733921i | \(-0.262312\pi\) | ||||
0.679235 | + | 0.733921i | \(0.262312\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −3560.00 | −0.186989 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 15000.0 | 0.784571 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −30280.0 | −1.57059 | −0.785294 | − | 0.619122i | \(-0.787488\pi\) | ||||
−0.785294 | + | 0.619122i | \(0.787488\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 8412.00 | 0.434507 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −4150.00 | −0.212589 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −17446.0 | −0.890009 | −0.445004 | − | 0.895528i | \(-0.646798\pi\) | ||||
−0.445004 | + | 0.895528i | \(0.646798\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −4260.00 | −0.215543 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −16750.0 | −0.844032 | −0.422016 | − | 0.906588i | \(-0.638677\pi\) | ||||
−0.422016 | + | 0.906588i | \(0.638677\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 46440.0 | 2.32108 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 36560.0 | 1.81987 | 0.909933 | − | 0.414755i | \(-0.136133\pi\) | ||||
0.909933 | + | 0.414755i | \(0.136133\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −30142.0 | −1.48829 | −0.744147 | − | 0.668016i | \(-0.767144\pi\) | ||||
−0.744147 | + | 0.668016i | \(0.767144\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 11750.0 | 0.577834 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −7164.00 | −0.349488 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −11860.0 | −0.576268 | −0.288134 | − | 0.957590i | \(-0.593035\pi\) | ||||
−0.288134 | + | 0.957590i | \(0.593035\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −2900.00 | −0.139790 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 37010.0 | 1.77695 | 0.888475 | − | 0.458925i | \(-0.151765\pi\) | ||||
0.888475 | + | 0.458925i | \(0.151765\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 11718.0 | 0.558183 | 0.279091 | − | 0.960265i | \(-0.409967\pi\) | ||||
0.279091 | + | 0.960265i | \(0.409967\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −3900.00 | −0.185045 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −40000.0 | −1.88307 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 4706.00 | 0.220680 | 0.110340 | − | 0.993894i | \(-0.464806\pi\) | ||||
0.110340 | + | 0.993894i | \(0.464806\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 28670.0 | 1.33401 | 0.667004 | − | 0.745054i | \(-0.267576\pi\) | ||||
0.667004 | + | 0.745054i | \(0.267576\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −500.000 | −0.0231749 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −10000.0 | −0.459932 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 6000.00 | 0.274900 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −6550.00 | −0.297808 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −20434.0 | −0.925532 | −0.462766 | − | 0.886481i | \(-0.653143\pi\) | ||||
−0.462766 | + | 0.886481i | \(0.653143\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −9060.00 | −0.407252 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 12500.0 | 0.559758 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −3930.00 | −0.174665 | −0.0873323 | − | 0.996179i | \(-0.527834\pi\) | ||||
−0.0873323 | + | 0.996179i | \(0.527834\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 6420.00 | 0.284259 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −13800.0 | −0.606465 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −5340.00 | −0.233802 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 4854.00 | 0.210949 | 0.105474 | − | 0.994422i | \(-0.466364\pi\) | ||||
0.105474 | + | 0.994422i | \(0.466364\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 13140.0 | 0.568937 | 0.284468 | − | 0.958685i | \(-0.408183\pi\) | ||||
0.284468 | + | 0.958685i | \(0.408183\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −9310.00 | −0.400141 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 5680.00 | 0.243229 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −22050.0 | −0.937333 | −0.468666 | − | 0.883375i | \(-0.655265\pi\) | ||||
−0.468666 | + | 0.883375i | \(0.655265\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −14578.0 | −0.617445 | −0.308722 | − | 0.951152i | \(-0.599901\pi\) | ||||
−0.308722 | + | 0.951152i | \(0.599901\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −37054.0 | −1.55803 | −0.779017 | − | 0.627003i | \(-0.784281\pi\) | ||||
−0.779017 | + | 0.627003i | \(0.784281\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −6150.00 | −0.257658 | −0.128829 | − | 0.991667i | \(-0.541122\pi\) | ||||
−0.128829 | + | 0.991667i | \(0.541122\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −9210.00 | −0.383082 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 3630.00 | 0.150445 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −8200.00 | −0.337420 | −0.168710 | − | 0.985666i | \(-0.553960\pi\) | ||||
−0.168710 | + | 0.985666i | \(0.553960\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 3167.00 | 0.129854 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 1515.00 | 0.0616776 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −13614.0 | −0.552282 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1780.00 | 0.0717011 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −42990.0 | −1.72561 | −0.862807 | − | 0.505533i | \(-0.831296\pi\) | ||||
−0.862807 | + | 0.505533i | \(0.831296\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −32130.0 | −1.28068 | −0.640338 | − | 0.768093i | \(-0.721206\pi\) | ||||
−0.640338 | + | 0.768093i | \(0.721206\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −15440.0 | −0.613278 | −0.306639 | − | 0.951826i | \(-0.599204\pi\) | ||||
−0.306639 | + | 0.951826i | \(0.599204\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 46938.0 | 1.85143 | 0.925717 | − | 0.378216i | \(-0.123462\pi\) | ||||
0.925717 | + | 0.378216i | \(0.123462\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −16250.0 | −0.638747 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 79200.0 | 3.09169 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 38700.0 | 1.50551 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −750.000 | −0.0289767 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −31230.0 | −1.20247 | −0.601233 | − | 0.799074i | \(-0.705324\pi\) | ||||
−0.601233 | + | 0.799074i | \(0.705324\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −25550.0 | −0.977073 | −0.488537 | − | 0.872543i | \(-0.662469\pi\) | ||||
−0.488537 | + | 0.872543i | \(0.662469\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −4318.00 | −0.164567 | −0.0822833 | − | 0.996609i | \(-0.526221\pi\) | ||||
−0.0822833 | + | 0.996609i | \(0.526221\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 1766.00 | 0.0668506 | 0.0334253 | − | 0.999441i | \(-0.489358\pi\) | ||||
0.0334253 | + | 0.999441i | \(0.489358\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 7476.00 | 0.282044 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −8560.00 | −0.320772 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −5600.00 | −0.209148 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 3320.00 | 0.123168 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −14700.0 | −0.543538 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −14210.0 | −0.521941 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −41906.0 | −1.53414 | −0.767071 | − | 0.641563i | \(-0.778286\pi\) | ||||
−0.767071 | + | 0.641563i | \(0.778286\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 25140.0 | 0.914298 | 0.457149 | − | 0.889390i | \(-0.348871\pi\) | ||||
0.457149 | + | 0.889390i | \(0.348871\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 58920.0 | 2.13578 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −15960.0 | −0.574750 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −32920.0 | −1.18164 | −0.590822 | − | 0.806802i | \(-0.701196\pi\) | ||||
−0.590822 | + | 0.806802i | \(0.701196\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 5000.00 | 0.178307 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 250.000 | 0.00888643 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −10150.0 | −0.358461 | −0.179231 | − | 0.983807i | \(-0.557361\pi\) | ||||
−0.179231 | + | 0.983807i | \(0.557361\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 12280.0 | 0.432289 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 9000.00 | 0.314793 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 28530.0 | 0.994701 | 0.497350 | − | 0.867550i | \(-0.334306\pi\) | ||||
0.497350 | + | 0.867550i | \(0.334306\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −9678.00 | −0.335275 | −0.167638 | − | 0.985849i | \(-0.553614\pi\) | ||||
−0.167638 | + | 0.985849i | \(0.553614\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 44500.0 | 1.53671 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 36986.0 | 1.26915 | 0.634574 | − | 0.772862i | \(-0.281176\pi\) | ||||
0.634574 | + | 0.772862i | \(0.281176\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −11500.0 | −0.393368 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 3350.00 | 0.113869 | 0.0569345 | − | 0.998378i | \(-0.481867\pi\) | ||||
0.0569345 | + | 0.998378i | \(0.481867\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 15900.0 | 0.538756 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 16620.0 | 0.559633 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −29391.0 | −0.986573 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −23350.0 | −0.778925 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −43774.0 | −1.45572 | −0.727858 | − | 0.685728i | \(-0.759484\pi\) | ||||
−0.727858 | + | 0.685728i | \(0.759484\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 8740.00 | 0.288857 | 0.144428 | − | 0.989515i | \(-0.453866\pi\) | ||||
0.144428 | + | 0.989515i | \(0.453866\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −3360.00 | −0.110706 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 48310.0 | 1.58196 | 0.790979 | − | 0.611843i | \(-0.209571\pi\) | ||||
0.790979 | + | 0.611843i | \(0.209571\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −52440.0 | −1.71194 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 2282.00 | 0.0740432 | 0.0370216 | − | 0.999314i | \(-0.488213\pi\) | ||||
0.0370216 | + | 0.999314i | \(0.488213\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 14950.0 | 0.483601 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −25276.0 | −0.812669 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 31580.0 | 1.01228 | 0.506141 | − | 0.862451i | \(-0.331071\pi\) | ||||
0.506141 | + | 0.862451i | \(0.331071\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 21200.0 | 0.675462 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −2790.00 | −0.0886261 | −0.0443130 | − | 0.999018i | \(-0.514110\pi\) | ||||
−0.0443130 | + | 0.999018i | \(0.514110\pi\) | |||||||
\(998\) | 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 | 1440.4.a.n.1.1 | 1 | ||
3.2 | odd | 2 | 160.4.a.b.1.1 | yes | 1 | ||
4.3 | odd | 2 | 1440.4.a.o.1.1 | 1 | |||
12.11 | even | 2 | 160.4.a.a.1.1 | ✓ | 1 | ||
15.2 | even | 4 | 800.4.c.e.449.1 | 2 | |||
15.8 | even | 4 | 800.4.c.e.449.2 | 2 | |||
15.14 | odd | 2 | 800.4.a.d.1.1 | 1 | |||
24.5 | odd | 2 | 320.4.a.f.1.1 | 1 | |||
24.11 | even | 2 | 320.4.a.i.1.1 | 1 | |||
48.5 | odd | 4 | 1280.4.d.k.641.1 | 2 | |||
48.11 | even | 4 | 1280.4.d.f.641.2 | 2 | |||
48.29 | odd | 4 | 1280.4.d.k.641.2 | 2 | |||
48.35 | even | 4 | 1280.4.d.f.641.1 | 2 | |||
60.23 | odd | 4 | 800.4.c.f.449.1 | 2 | |||
60.47 | odd | 4 | 800.4.c.f.449.2 | 2 | |||
60.59 | even | 2 | 800.4.a.h.1.1 | 1 | |||
120.29 | odd | 2 | 1600.4.a.bj.1.1 | 1 | |||
120.59 | even | 2 | 1600.4.a.r.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
160.4.a.a.1.1 | ✓ | 1 | 12.11 | even | 2 | ||
160.4.a.b.1.1 | yes | 1 | 3.2 | odd | 2 | ||
320.4.a.f.1.1 | 1 | 24.5 | odd | 2 | |||
320.4.a.i.1.1 | 1 | 24.11 | even | 2 | |||
800.4.a.d.1.1 | 1 | 15.14 | odd | 2 | |||
800.4.a.h.1.1 | 1 | 60.59 | even | 2 | |||
800.4.c.e.449.1 | 2 | 15.2 | even | 4 | |||
800.4.c.e.449.2 | 2 | 15.8 | even | 4 | |||
800.4.c.f.449.1 | 2 | 60.23 | odd | 4 | |||
800.4.c.f.449.2 | 2 | 60.47 | odd | 4 | |||
1280.4.d.f.641.1 | 2 | 48.35 | even | 4 | |||
1280.4.d.f.641.2 | 2 | 48.11 | even | 4 | |||
1280.4.d.k.641.1 | 2 | 48.5 | odd | 4 | |||
1280.4.d.k.641.2 | 2 | 48.29 | odd | 4 | |||
1440.4.a.n.1.1 | 1 | 1.1 | even | 1 | trivial | ||
1440.4.a.o.1.1 | 1 | 4.3 | odd | 2 | |||
1600.4.a.r.1.1 | 1 | 120.59 | even | 2 | |||
1600.4.a.bj.1.1 | 1 | 120.29 | odd | 2 |