Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [432,4,Mod(1,432)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(432, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("432.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 432 = 2^{4} \cdot 3^{3} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 432.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: | \(25.4888251225\) |
Analytic rank: | \(1\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 216) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 432.1 |
$q$-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 | ||||||||
\(5\) | −1.00000 | −0.0894427 | −0.0447214 | − | 0.998999i | \(-0.514240\pi\) | ||||
−0.0447214 | + | 0.998999i | \(0.514240\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 9.00000 | 0.485954 | 0.242977 | − | 0.970032i | \(-0.421876\pi\) | ||||
0.242977 | + | 0.970032i | \(0.421876\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −17.0000 | −0.465972 | −0.232986 | − | 0.972480i | \(-0.574850\pi\) | ||||
−0.232986 | + | 0.972480i | \(0.574850\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −44.0000 | −0.938723 | −0.469362 | − | 0.883006i | \(-0.655516\pi\) | ||||
−0.469362 | + | 0.883006i | \(0.655516\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −56.0000 | −0.798941 | −0.399470 | − | 0.916746i | \(-0.630806\pi\) | ||||
−0.399470 | + | 0.916746i | \(0.630806\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 94.0000 | 1.13500 | 0.567502 | − | 0.823372i | \(-0.307910\pi\) | ||||
0.567502 | + | 0.823372i | \(0.307910\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −50.0000 | −0.453292 | −0.226646 | − | 0.973977i | \(-0.572776\pi\) | ||||
−0.226646 | + | 0.973977i | \(0.572776\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −124.000 | −0.992000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 30.0000 | 0.192099 | 0.0960493 | − | 0.995377i | \(-0.469379\pi\) | ||||
0.0960493 | + | 0.995377i | \(0.469379\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 139.000 | 0.805327 | 0.402663 | − | 0.915348i | \(-0.368084\pi\) | ||||
0.402663 | + | 0.915348i | \(0.368084\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −9.00000 | −0.0434651 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −174.000 | −0.773120 | −0.386560 | − | 0.922264i | \(-0.626337\pi\) | ||||
−0.386560 | + | 0.922264i | \(0.626337\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −318.000 | −1.21130 | −0.605649 | − | 0.795732i | \(-0.707087\pi\) | ||||
−0.605649 | + | 0.795732i | \(0.707087\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 242.000 | 0.858248 | 0.429124 | − | 0.903246i | \(-0.358822\pi\) | ||||
0.429124 | + | 0.903246i | \(0.358822\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −630.000 | −1.95521 | −0.977606 | − | 0.210445i | \(-0.932509\pi\) | ||||
−0.977606 | + | 0.210445i | \(0.932509\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −262.000 | −0.763848 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −547.000 | −1.41766 | −0.708832 | − | 0.705377i | \(-0.750778\pi\) | ||||
−0.708832 | + | 0.705377i | \(0.750778\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 17.0000 | 0.0416778 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −236.000 | −0.520756 | −0.260378 | − | 0.965507i | \(-0.583847\pi\) | ||||
−0.260378 | + | 0.965507i | \(0.583847\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 328.000 | 0.688461 | 0.344230 | − | 0.938885i | \(-0.388140\pi\) | ||||
0.344230 | + | 0.938885i | \(0.388140\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 44.0000 | 0.0839620 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −614.000 | −1.11958 | −0.559791 | − | 0.828634i | \(-0.689119\pi\) | ||||
−0.559791 | + | 0.828634i | \(0.689119\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 296.000 | 0.494771 | 0.247385 | − | 0.968917i | \(-0.420429\pi\) | ||||
0.247385 | + | 0.968917i | \(0.420429\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 433.000 | 0.694230 | 0.347115 | − | 0.937823i | \(-0.387161\pi\) | ||||
0.347115 | + | 0.937823i | \(0.387161\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −153.000 | −0.226441 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 56.0000 | 0.0797531 | 0.0398765 | − | 0.999205i | \(-0.487304\pi\) | ||||
0.0398765 | + | 0.999205i | \(0.487304\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −1225.00 | −1.62001 | −0.810007 | − | 0.586420i | \(-0.800537\pi\) | ||||
−0.810007 | + | 0.586420i | \(0.800537\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 56.0000 | 0.0714594 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −1506.00 | −1.79366 | −0.896830 | − | 0.442376i | \(-0.854136\pi\) | ||||
−0.896830 | + | 0.442376i | \(0.854136\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −396.000 | −0.456177 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −94.0000 | −0.101518 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1391.00 | 1.45603 | 0.728014 | − | 0.685563i | \(-0.240444\pi\) | ||||
0.728014 | + | 0.685563i | \(0.240444\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1665.00 | 1.64033 | 0.820167 | − | 0.572124i | \(-0.193881\pi\) | ||||
0.820167 | + | 0.572124i | \(0.193881\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1468.00 | −1.40433 | −0.702167 | − | 0.712013i | \(-0.747784\pi\) | ||||
−0.702167 | + | 0.712013i | \(0.747784\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 627.000 | 0.566490 | 0.283245 | − | 0.959048i | \(-0.408589\pi\) | ||||
0.283245 | + | 0.959048i | \(0.408589\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 610.000 | 0.536031 | 0.268016 | − | 0.963415i | \(-0.413632\pi\) | ||||
0.268016 | + | 0.963415i | \(0.413632\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −1134.00 | −0.944051 | −0.472025 | − | 0.881585i | \(-0.656477\pi\) | ||||
−0.472025 | + | 0.881585i | \(0.656477\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 50.0000 | 0.0405437 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −504.000 | −0.388249 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1042.00 | −0.782870 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 249.000 | 0.178170 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −505.000 | −0.352846 | −0.176423 | − | 0.984314i | \(-0.556453\pi\) | ||||
−0.176423 | + | 0.984314i | \(0.556453\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 515.000 | 0.343479 | 0.171740 | − | 0.985142i | \(-0.445061\pi\) | ||||
0.171740 | + | 0.985142i | \(0.445061\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 846.000 | 0.551560 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 6.00000 | 0.00374171 | 0.00187086 | − | 0.999998i | \(-0.499404\pi\) | ||||
0.00187086 | + | 0.999998i | \(0.499404\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −636.000 | −0.388092 | −0.194046 | − | 0.980992i | \(-0.562161\pi\) | ||||
−0.194046 | + | 0.980992i | \(0.562161\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 748.000 | 0.437419 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −30.0000 | −0.0171818 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 2239.00 | 1.23105 | 0.615524 | − | 0.788118i | \(-0.288945\pi\) | ||||
0.615524 | + | 0.788118i | \(0.288945\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2695.00 | 1.45242 | 0.726212 | − | 0.687471i | \(-0.241279\pi\) | ||||
0.726212 | + | 0.687471i | \(0.241279\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −139.000 | −0.0720306 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1988.00 | −1.01057 | −0.505286 | − | 0.862952i | \(-0.668613\pi\) | ||||
−0.505286 | + | 0.862952i | \(0.668613\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −450.000 | −0.220279 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 2580.00 | 1.23976 | 0.619881 | − | 0.784696i | \(-0.287181\pi\) | ||||
0.619881 | + | 0.784696i | \(0.287181\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 1878.00 | 0.870204 | 0.435102 | − | 0.900381i | \(-0.356712\pi\) | ||||
0.435102 | + | 0.900381i | \(0.356712\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −261.000 | −0.118798 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 2163.00 | 0.950577 | 0.475289 | − | 0.879830i | \(-0.342344\pi\) | ||||
0.475289 | + | 0.879830i | \(0.342344\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1116.00 | −0.482067 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 2181.00 | 0.910702 | 0.455351 | − | 0.890312i | \(-0.349514\pi\) | ||||
0.455351 | + | 0.890312i | \(0.349514\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1488.00 | −0.611062 | −0.305531 | − | 0.952182i | \(-0.598834\pi\) | ||||
−0.305531 | + | 0.952182i | \(0.598834\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 174.000 | 0.0691499 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 952.000 | 0.372284 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1764.00 | 0.668265 | 0.334132 | − | 0.942526i | \(-0.391557\pi\) | ||||
0.334132 | + | 0.942526i | \(0.391557\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −3547.00 | −1.32289 | −0.661447 | − | 0.749992i | \(-0.730057\pi\) | ||||
−0.661447 | + | 0.749992i | \(0.730057\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 4941.00 | 1.78696 | 0.893481 | − | 0.449100i | \(-0.148255\pi\) | ||||
0.893481 | + | 0.449100i | \(0.148255\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1487.00 | 0.529702 | 0.264851 | − | 0.964289i | \(-0.414677\pi\) | ||||
0.264851 | + | 0.964289i | \(0.414677\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 270.000 | 0.0933512 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 318.000 | 0.108342 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −1598.00 | −0.528880 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −442.000 | −0.144211 | −0.0721055 | − | 0.997397i | \(-0.522972\pi\) | ||||
−0.0721055 | + | 0.997397i | \(0.522972\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −242.000 | −0.0767640 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1251.00 | 0.391352 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 2464.00 | 0.749985 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 5096.00 | 1.53028 | 0.765142 | − | 0.643861i | \(-0.222669\pi\) | ||||
0.765142 | + | 0.643861i | \(0.222669\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 5484.00 | 1.60346 | 0.801731 | − | 0.597685i | \(-0.203913\pi\) | ||||
0.801731 | + | 0.597685i | \(0.203913\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −3530.00 | −1.01864 | −0.509321 | − | 0.860577i | \(-0.670103\pi\) | ||||
−0.509321 | + | 0.860577i | \(0.670103\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −1630.00 | −0.458304 | −0.229152 | − | 0.973391i | \(-0.573595\pi\) | ||||
−0.229152 | + | 0.973391i | \(0.573595\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 630.000 | 0.174879 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −1990.00 | −0.538587 | −0.269294 | − | 0.963058i | \(-0.586790\pi\) | ||||
−0.269294 | + | 0.963058i | \(0.586790\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 2214.00 | 0.591769 | 0.295884 | − | 0.955224i | \(-0.404386\pi\) | ||||
0.295884 | + | 0.955224i | \(0.404386\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 262.000 | 0.0683207 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −4136.00 | −1.06545 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −4480.00 | −1.12659 | −0.563297 | − | 0.826254i | \(-0.690467\pi\) | ||||
−0.563297 | + | 0.826254i | \(0.690467\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 850.000 | 0.211222 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −2204.00 | −0.534948 | −0.267474 | − | 0.963565i | \(-0.586189\pi\) | ||||
−0.267474 | + | 0.963565i | \(0.586189\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1566.00 | −0.375701 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 1942.00 | 0.455319 | 0.227659 | − | 0.973741i | \(-0.426893\pi\) | ||||
0.227659 | + | 0.973741i | \(0.426893\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 547.000 | 0.126800 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 7606.00 | 1.72396 | 0.861981 | − | 0.506940i | \(-0.169223\pi\) | ||||
0.861981 | + | 0.506940i | \(0.169223\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −4391.00 | −0.984259 | −0.492130 | − | 0.870522i | \(-0.663781\pi\) | ||||
−0.492130 | + | 0.870522i | \(0.663781\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 2108.00 | 0.462244 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 7000.00 | 1.51837 | 0.759186 | − | 0.650873i | \(-0.225597\pi\) | ||||
0.759186 | + | 0.650873i | \(0.225597\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −8912.00 | −1.89198 | −0.945988 | − | 0.324201i | \(-0.894905\pi\) | ||||
−0.945988 | + | 0.324201i | \(0.894905\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −3614.00 | −0.759117 | −0.379558 | − | 0.925168i | \(-0.623924\pi\) | ||||
−0.379558 | + | 0.925168i | \(0.623924\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −2862.00 | −0.588636 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1777.00 | −0.361693 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 4194.00 | 0.836232 | 0.418116 | − | 0.908394i | \(-0.362690\pi\) | ||||
0.418116 | + | 0.908394i | \(0.362690\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 236.000 | 0.0465778 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 2200.00 | 0.425516 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2178.00 | 0.417069 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −328.000 | −0.0615778 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −840.000 | −0.156161 | −0.0780803 | − | 0.996947i | \(-0.524879\pi\) | ||||
−0.0780803 | + | 0.996947i | \(0.524879\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 606.000 | 0.110492 | 0.0552462 | − | 0.998473i | \(-0.482406\pi\) | ||||
0.0552462 | + | 0.998473i | \(0.482406\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 2037.00 | 0.367853 | 0.183927 | − | 0.982940i | \(-0.441119\pi\) | ||||
0.183927 | + | 0.982940i | \(0.441119\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −519.000 | −0.0919557 | −0.0459778 | − | 0.998942i | \(-0.514640\pi\) | ||||
−0.0459778 | + | 0.998942i | \(0.514640\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −510.000 | −0.0895126 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −5264.00 | −0.906801 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 5456.00 | 0.931214 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −5670.00 | −0.950144 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −2750.00 | −0.456658 | −0.228329 | − | 0.973584i | \(-0.573326\pi\) | ||||
−0.228329 | + | 0.973584i | \(0.573326\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 614.000 | 0.100139 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 4410.00 | 0.712843 | 0.356421 | − | 0.934325i | \(-0.383997\pi\) | ||||
0.356421 | + | 0.934325i | \(0.383997\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −2363.00 | −0.375260 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −5445.00 | −0.857150 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −10911.0 | −1.68799 | −0.843996 | − | 0.536350i | \(-0.819803\pi\) | ||||
−0.843996 | + | 0.536350i | \(0.819803\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −4650.00 | −0.713206 | −0.356603 | − | 0.934256i | \(-0.616065\pi\) | ||||
−0.356603 | + | 0.934256i | \(0.616065\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −9410.00 | −1.41882 | −0.709410 | − | 0.704796i | \(-0.751039\pi\) | ||||
−0.709410 | + | 0.704796i | \(0.751039\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −296.000 | −0.0442537 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −2130.00 | −0.313140 | −0.156570 | − | 0.987667i | \(-0.550044\pi\) | ||||
−0.156570 | + | 0.987667i | \(0.550044\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1977.00 | 0.288234 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −433.000 | −0.0620939 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −1393.00 | −0.198131 | −0.0990654 | − | 0.995081i | \(-0.531585\pi\) | ||||
−0.0990654 | + | 0.995081i | \(0.531585\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −4923.00 | −0.688920 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −2920.00 | −0.405340 | −0.202670 | − | 0.979247i | \(-0.564962\pi\) | ||||
−0.202670 | + | 0.979247i | \(0.564962\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −1320.00 | −0.180327 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 10780.0 | 1.46103 | 0.730516 | − | 0.682895i | \(-0.239279\pi\) | ||||
0.730516 | + | 0.682895i | \(0.239279\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −3888.00 | −0.518714 | −0.259357 | − | 0.965782i | \(-0.583511\pi\) | ||||
−0.259357 | + | 0.965782i | \(0.583511\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 153.000 | 0.0202535 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −4009.00 | −0.522531 | −0.261265 | − | 0.965267i | \(-0.584140\pi\) | ||||
−0.261265 | + | 0.965267i | \(0.584140\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2800.00 | 0.362154 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −56.0000 | −0.00713333 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 860.000 | 0.108721 | 0.0543604 | − | 0.998521i | \(-0.482688\pi\) | ||||
0.0543604 | + | 0.998521i | \(0.482688\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −1716.00 | −0.213698 | −0.106849 | − | 0.994275i | \(-0.534076\pi\) | ||||
−0.106849 | + | 0.994275i | \(0.534076\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −6116.00 | −0.755979 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 2958.00 | 0.360252 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −3201.00 | −0.386991 | −0.193495 | − | 0.981101i | \(-0.561982\pi\) | ||||
−0.193495 | + | 0.981101i | \(0.561982\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −2124.00 | −0.253063 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 1225.00 | 0.144899 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 5700.00 | 0.664590 | 0.332295 | − | 0.943175i | \(-0.392177\pi\) | ||||
0.332295 | + | 0.943175i | \(0.392177\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −10312.0 | −1.19377 | −0.596884 | − | 0.802328i | \(-0.703595\pi\) | ||||
−0.596884 | + | 0.802328i | \(0.703595\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 6944.00 | 0.792549 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 2952.00 | 0.334560 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −10354.0 | −1.15716 | −0.578578 | − | 0.815627i | \(-0.696392\pi\) | ||||
−0.578578 | + | 0.815627i | \(0.696392\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −10787.0 | −1.19721 | −0.598603 | − | 0.801046i | \(-0.704277\pi\) | ||||
−0.598603 | + | 0.801046i | \(0.704277\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −4700.00 | −0.514489 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 14715.0 | 1.59979 | 0.799896 | − | 0.600139i | \(-0.204888\pi\) | ||||
0.799896 | + | 0.600139i | \(0.204888\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −6628.00 | −0.710848 | −0.355424 | − | 0.934705i | \(-0.615664\pi\) | ||||
−0.355424 | + | 0.934705i | \(0.615664\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1506.00 | 0.160430 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −8122.00 | −0.853677 | −0.426838 | − | 0.904328i | \(-0.640373\pi\) | ||||
−0.426838 | + | 0.904328i | \(0.640373\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 5406.00 | 0.564431 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 396.000 | 0.0408017 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −6553.00 | −0.670758 | −0.335379 | − | 0.942083i | \(-0.608864\pi\) | ||||
−0.335379 | + | 0.942083i | \(0.608864\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 4079.00 | 0.412100 | 0.206050 | − | 0.978541i | \(-0.433939\pi\) | ||||
0.206050 | + | 0.978541i | \(0.433939\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 12685.0 | 1.27327 | 0.636633 | − | 0.771167i | \(-0.280327\pi\) | ||||
0.636633 | + | 0.771167i | \(0.280327\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 6111.00 | 0.605532 | 0.302766 | − | 0.953065i | \(-0.402090\pi\) | ||||
0.302766 | + | 0.953065i | \(0.402090\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −5526.00 | −0.544066 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −4114.00 | −0.399919 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −11656.0 | −1.12592 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −11254.0 | −1.07350 | −0.536752 | − | 0.843740i | \(-0.680349\pi\) | ||||
−0.536752 | + | 0.843740i | \(0.680349\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 7656.00 | 0.725745 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −1391.00 | −0.130231 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −13936.0 | −1.29672 | −0.648358 | − | 0.761336i | \(-0.724544\pi\) | ||||
−0.648358 | + | 0.761336i | \(0.724544\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 6045.00 | 0.555615 | 0.277808 | − | 0.960637i | \(-0.410392\pi\) | ||||
0.277808 | + | 0.960637i | \(0.410392\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −1680.00 | −0.153475 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 2664.00 | 0.240436 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 19482.0 | 1.74776 | 0.873882 | − | 0.486138i | \(-0.161595\pi\) | ||||
0.873882 | + | 0.486138i | \(0.161595\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 19770.0 | 1.75249 | 0.876243 | − | 0.481869i | \(-0.160042\pi\) | ||||
0.876243 | + | 0.481869i | \(0.160042\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −1665.00 | −0.146716 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 11613.0 | 1.01127 | 0.505636 | − | 0.862747i | \(-0.331258\pi\) | ||||
0.505636 | + | 0.862747i | \(0.331258\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 3897.00 | 0.337364 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 1468.00 | 0.125607 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 10710.0 | 0.911074 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 5500.00 | 0.462494 | 0.231247 | − | 0.972895i | \(-0.425719\pi\) | ||||
0.231247 | + | 0.972895i | \(0.425719\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 8024.00 | 0.670870 | 0.335435 | − | 0.942063i | \(-0.391117\pi\) | ||||
0.335435 | + | 0.942063i | \(0.391117\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −7784.00 | −0.643409 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −9667.00 | −0.794526 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 13992.0 | 1.13707 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −627.000 | −0.0506684 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 4454.00 | 0.355932 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −9036.00 | −0.718092 | −0.359046 | − | 0.933320i | \(-0.616898\pi\) | ||||
−0.359046 | + | 0.933320i | \(0.616898\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −610.000 | −0.0479441 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −23456.0 | −1.83347 | −0.916733 | − | 0.399500i | \(-0.869184\pi\) | ||||
−0.916733 | + | 0.399500i | \(0.869184\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 2820.00 | 0.218033 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 504.000 | 0.0387563 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −18721.0 | −1.42412 | −0.712059 | − | 0.702119i | \(-0.752237\pi\) | ||||
−0.712059 | + | 0.702119i | \(0.752237\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −10648.0 | −0.805657 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 1417.00 | 0.106074 | 0.0530368 | − | 0.998593i | \(-0.483110\pi\) | ||||
0.0530368 | + | 0.998593i | \(0.483110\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 1134.00 | 0.0844385 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 18596.0 | 1.37010 | 0.685048 | − | 0.728498i | \(-0.259781\pi\) | ||||
0.685048 | + | 0.728498i | \(0.259781\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 3708.00 | 0.271760 | 0.135880 | − | 0.990725i | \(-0.456614\pi\) | ||||
0.135880 | + | 0.990725i | \(0.456614\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 6200.00 | 0.449666 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 21494.0 | 1.55079 | 0.775396 | − | 0.631475i | \(-0.217550\pi\) | ||||
0.775396 | + | 0.631475i | \(0.217550\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −11025.0 | −0.787253 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 9299.00 | 0.660592 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −16049.0 | −1.12847 | −0.564236 | − | 0.825614i | \(-0.690829\pi\) | ||||
−0.564236 | + | 0.825614i | \(0.690829\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 13066.0 | 0.914049 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 4658.00 | 0.322565 | 0.161283 | − | 0.986908i | \(-0.448437\pi\) | ||||
0.161283 | + | 0.986908i | \(0.448437\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 504.000 | 0.0347260 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 26538.0 | 1.81021 | 0.905103 | − | 0.425193i | \(-0.139794\pi\) | ||||
0.905103 | + | 0.425193i | \(0.139794\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1147.00 | 0.0778488 | 0.0389244 | − | 0.999242i | \(-0.487607\pi\) | ||||
0.0389244 | + | 0.999242i | \(0.487607\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 1042.00 | 0.0700220 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −26048.0 | −1.74177 | −0.870886 | − | 0.491485i | \(-0.836454\pi\) | ||||
−0.870886 | + | 0.491485i | \(0.836454\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 27720.0 | 1.83540 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −394.000 | −0.0259600 | −0.0129800 | − | 0.999916i | \(-0.504132\pi\) | ||||
−0.0129800 | + | 0.999916i | \(0.504132\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 27822.0 | 1.81535 | 0.907675 | − | 0.419673i | \(-0.137855\pi\) | ||||
0.907675 | + | 0.419673i | \(0.137855\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −21580.0 | −1.40125 | −0.700625 | − | 0.713530i | \(-0.747095\pi\) | ||||
−0.700625 | + | 0.713530i | \(0.747095\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −13554.0 | −0.871637 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 15251.0 | 0.976064 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 9744.00 | 0.617677 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −7855.00 | −0.495567 | −0.247783 | − | 0.968815i | \(-0.579702\pi\) | ||||
−0.247783 | + | 0.968815i | \(0.579702\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 505.000 | 0.0315595 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 11528.0 | 0.717042 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 30770.0 | 1.89601 | 0.948005 | − | 0.318257i | \(-0.103097\pi\) | ||||
0.948005 | + | 0.318257i | \(0.103097\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 18420.0 | 1.12973 | 0.564863 | − | 0.825185i | \(-0.308929\pi\) | ||||
0.564863 | + | 0.825185i | \(0.308929\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 10448.0 | 0.634858 | 0.317429 | − | 0.948282i | \(-0.397180\pi\) | ||||
0.317429 | + | 0.948282i | \(0.397180\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 4012.00 | 0.242658 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −19221.0 | −1.15188 | −0.575939 | − | 0.817493i | \(-0.695363\pi\) | ||||
−0.575939 | + | 0.817493i | \(0.695363\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −515.000 | −0.0307217 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 29649.0 | 1.75260 | 0.876298 | − | 0.481769i | \(-0.160006\pi\) | ||||
0.876298 | + | 0.481769i | \(0.160006\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 4478.00 | 0.263501 | 0.131750 | − | 0.991283i | \(-0.457940\pi\) | ||||
0.131750 | + | 0.991283i | \(0.457940\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −846.000 | −0.0493330 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1500.00 | −0.0870768 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −5576.00 | −0.320803 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −14099.0 | −0.807543 | −0.403772 | − | 0.914860i | \(-0.632301\pi\) | ||||
−0.403772 | + | 0.914860i | \(0.632301\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −14782.0 | −0.839170 | −0.419585 | − | 0.907716i | \(-0.637824\pi\) | ||||
−0.419585 | + | 0.907716i | \(0.637824\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 12519.0 | 0.707563 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −24620.0 | −1.37929 | −0.689647 | − | 0.724145i | \(-0.742234\pi\) | ||||
−0.689647 | + | 0.724145i | \(0.742234\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −6.00000 | −0.000334669 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 24068.0 | 1.33080 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −30716.0 | −1.69102 | −0.845508 | − | 0.533963i | \(-0.820702\pi\) | ||||
−0.845508 | + | 0.533963i | \(0.820702\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 636.000 | 0.0347120 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 17808.0 | 0.967756 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −3147.00 | −0.169559 | −0.0847793 | − | 0.996400i | \(-0.527019\pi\) | ||||
−0.0847793 | + | 0.996400i | \(0.527019\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −16356.0 | −0.877494 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 14985.0 | 0.797127 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −22660.0 | −1.20030 | −0.600151 | − | 0.799887i | \(-0.704893\pi\) | ||||
−0.600151 | + | 0.799887i | \(0.704893\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −6950.00 | −0.365048 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −748.000 | −0.0391239 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 4828.00 | 0.250423 | 0.125211 | − | 0.992130i | \(-0.460039\pi\) | ||||
0.125211 | + | 0.992130i | \(0.460039\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −13212.0 | −0.682442 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −3720.00 | −0.190562 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 3849.00 | 0.196357 | 0.0981785 | − | 0.995169i | \(-0.468698\pi\) | ||||
0.0981785 | + | 0.995169i | \(0.468698\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −13552.0 | −0.685689 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 11738.0 | 0.591477 | 0.295739 | − | 0.955269i | \(-0.404434\pi\) | ||||
0.295739 | + | 0.955269i | \(0.404434\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 10438.0 | 0.521694 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 26824.0 | 1.33523 | 0.667616 | − | 0.744506i | \(-0.267315\pi\) | ||||
0.667616 | + | 0.744506i | \(0.267315\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −68.0000 | −0.00335757 | −0.00167879 | − | 0.999999i | \(-0.500534\pi\) | ||||
−0.00167879 | + | 0.999999i | \(0.500534\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −2239.00 | −0.110108 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 5643.00 | 0.275288 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 36039.0 | 1.75111 | 0.875554 | − | 0.483121i | \(-0.160497\pi\) | ||||
0.875554 | + | 0.483121i | \(0.160497\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −2695.00 | −0.129909 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 18650.0 | 0.895437 | 0.447718 | − | 0.894175i | \(-0.352237\pi\) | ||||
0.447718 | + | 0.894175i | \(0.352237\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −18848.0 | −0.897818 | −0.448909 | − | 0.893577i | \(-0.648187\pi\) | ||||
−0.448909 | + | 0.893577i | \(0.648187\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 5490.00 | 0.260487 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 10384.0 | 0.488846 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −29215.0 | −1.36999 | −0.684993 | − | 0.728549i | \(-0.740195\pi\) | ||||
−0.684993 | + | 0.728549i | \(0.740195\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −26586.0 | −1.23704 | −0.618520 | − | 0.785769i | \(-0.712267\pi\) | ||||
−0.618520 | + | 0.785769i | \(0.712267\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −17236.0 | −0.798884 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −29892.0 | −1.37483 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −5032.00 | −0.230549 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 1988.00 | 0.0903882 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −15520.0 | −0.702958 | −0.351479 | − | 0.936196i | \(-0.614321\pi\) | ||||
−0.351479 | + | 0.936196i | \(0.614321\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −10206.0 | −0.458766 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −14432.0 | −0.646274 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −7477.00 | −0.332307 | −0.166154 | − | 0.986100i | \(-0.553135\pi\) | ||||
−0.166154 | + | 0.986100i | \(0.553135\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 35280.0 | 1.56210 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −7361.00 | −0.323492 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 450.000 | 0.0197024 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 25282.0 | 1.09872 | 0.549362 | − | 0.835584i | \(-0.314871\pi\) | ||||
0.549362 | + | 0.835584i | \(0.314871\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 35582.0 | 1.54063 | 0.770316 | − | 0.637662i | \(-0.220098\pi\) | ||||
0.770316 | + | 0.637662i | \(0.220098\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −2580.00 | −0.110888 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 22748.0 | 0.974115 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −37506.0 | −1.59436 | −0.797179 | − | 0.603743i | \(-0.793675\pi\) | ||||
−0.797179 | + | 0.603743i | \(0.793675\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −12185.0 | −0.516090 | −0.258045 | − | 0.966133i | \(-0.583078\pi\) | ||||
−0.258045 | + | 0.966133i | \(0.583078\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −8128.00 | −0.341763 | −0.170882 | − | 0.985292i | \(-0.554662\pi\) | ||||
−0.170882 | + | 0.985292i | \(0.554662\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −39542.0 | −1.65664 | −0.828318 | − | 0.560259i | \(-0.810702\pi\) | ||||
−0.828318 | + | 0.560259i | \(0.810702\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 14672.0 | 0.610270 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −1878.00 | −0.0778334 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 40368.0 | 1.66109 | 0.830547 | − | 0.556948i | \(-0.188028\pi\) | ||||
0.830547 | + | 0.556948i | \(0.188028\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −23489.0 | −0.963098 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 261.000 | 0.0106256 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −9378.00 | −0.380439 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 8700.00 | 0.350449 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −20194.0 | −0.810585 | −0.405293 | − | 0.914187i | \(-0.632830\pi\) | ||||
−0.405293 | + | 0.914187i | \(0.632830\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −8664.00 | −0.345340 | −0.172670 | − | 0.984980i | \(-0.555239\pi\) | ||||
−0.172670 | + | 0.984980i | \(0.555239\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 15672.0 | 0.622493 | 0.311247 | − | 0.950329i | \(-0.399253\pi\) | ||||
0.311247 | + | 0.950329i | \(0.399253\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −46076.0 | −1.81743 | −0.908717 | − | 0.417413i | \(-0.862937\pi\) | ||||
−0.908717 | + | 0.417413i | \(0.862937\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −2163.00 | −0.0850222 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −952.000 | −0.0371627 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 27016.0 | 1.05098 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 2241.00 | 0.0865824 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −28926.0 | −1.11375 | −0.556877 | − | 0.830595i | \(-0.688000\pi\) | ||||
−0.556877 | + | 0.830595i | \(0.688000\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 10372.0 | 0.396642 | 0.198321 | − | 0.980137i | \(-0.436451\pi\) | ||||
0.198321 | + | 0.980137i | \(0.436451\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 15502.0 | 0.590808 | 0.295404 | − | 0.955372i | \(-0.404546\pi\) | ||||
0.295404 | + | 0.955372i | \(0.404546\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −29524.0 | −1.11761 | −0.558804 | − | 0.829300i | \(-0.688740\pi\) | ||||
−0.558804 | + | 0.829300i | \(0.688740\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −4545.00 | −0.171467 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −59220.0 | −2.21917 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −2181.00 | −0.0814556 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 4170.00 | 0.154702 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 30632.0 | 1.13263 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 1488.00 | 0.0546550 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −27226.0 | −0.996719 | −0.498360 | − | 0.866970i | \(-0.666064\pi\) | ||||
−0.498360 | + | 0.866970i | \(0.666064\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −53510.0 | −1.94607 | −0.973033 | − | 0.230668i | \(-0.925909\pi\) | ||||
−0.973033 | + | 0.230668i | \(0.925909\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 20825.0 | 0.754882 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 4635.00 | 0.166915 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 443.000 | 0.0159012 | 0.00795061 | − | 0.999968i | \(-0.497469\pi\) | ||||
0.00795061 | + | 0.999968i | \(0.497469\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −13024.0 | −0.464453 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 21576.0 | 0.766935 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −27260.0 | −0.962725 | −0.481363 | − | 0.876522i | \(-0.659858\pi\) | ||||
−0.481363 | + | 0.876522i | \(0.659858\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −24628.0 | −0.866971 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −952.000 | −0.0332981 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 21075.0 | 0.734781 | 0.367391 | − | 0.930067i | \(-0.380251\pi\) | ||||
0.367391 | + | 0.930067i | \(0.380251\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −22749.0 | −0.788094 | −0.394047 | − | 0.919090i | \(-0.628925\pi\) | ||||
−0.394047 | + | 0.919090i | \(0.628925\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 15900.0 | 0.549072 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 36201.0 | 1.24221 | 0.621106 | − | 0.783727i | \(-0.286684\pi\) | ||||
0.621106 | + | 0.783727i | \(0.286684\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −19052.0 | −0.651690 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 4428.00 | 0.150511 | 0.0752555 | − | 0.997164i | \(-0.476023\pi\) | ||||
0.0752555 | + | 0.997164i | \(0.476023\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −1764.00 | −0.0597714 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 54.0000 | 0.00181830 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −10470.0 | −0.351448 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 3547.00 | 0.118323 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −26927.0 | −0.895464 | −0.447732 | − | 0.894168i | \(-0.647768\pi\) | ||||
−0.447732 | + | 0.894168i | \(0.647768\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −47961.0 | −1.58511 | −0.792555 | − | 0.609800i | \(-0.791250\pi\) | ||||
−0.792555 | + | 0.609800i | \(0.791250\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −5724.00 | −0.188595 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −16746.0 | −0.548364 | −0.274182 | − | 0.961678i | \(-0.588407\pi\) | ||||
−0.274182 | + | 0.961678i | \(0.588407\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 25602.0 | 0.835795 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 37146.0 | 1.20526 | 0.602631 | − | 0.798020i | \(-0.294119\pi\) | ||||
0.602631 | + | 0.798020i | \(0.294119\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −4941.00 | −0.159831 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −12100.0 | −0.389037 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −42079.0 | −1.34882 | −0.674411 | − | 0.738356i | \(-0.735603\pi\) | ||||
−0.674411 | + | 0.738356i | \(0.735603\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −1487.00 | −0.0473780 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 46492.0 | 1.47685 | 0.738423 | − | 0.674337i | \(-0.235571\pi\) | ||||
0.738423 | + | 0.674337i | \(0.235571\pi\) | |||||||
\(998\) | 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 | 432.4.a.f.1.1 | 1 | ||
3.2 | odd | 2 | 432.4.a.i.1.1 | 1 | |||
4.3 | odd | 2 | 216.4.a.b.1.1 | ✓ | 1 | ||
8.3 | odd | 2 | 1728.4.a.s.1.1 | 1 | |||
8.5 | even | 2 | 1728.4.a.t.1.1 | 1 | |||
12.11 | even | 2 | 216.4.a.c.1.1 | yes | 1 | ||
24.5 | odd | 2 | 1728.4.a.n.1.1 | 1 | |||
24.11 | even | 2 | 1728.4.a.m.1.1 | 1 | |||
36.7 | odd | 6 | 648.4.i.g.433.1 | 2 | |||
36.11 | even | 6 | 648.4.i.f.433.1 | 2 | |||
36.23 | even | 6 | 648.4.i.f.217.1 | 2 | |||
36.31 | odd | 6 | 648.4.i.g.217.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
216.4.a.b.1.1 | ✓ | 1 | 4.3 | odd | 2 | ||
216.4.a.c.1.1 | yes | 1 | 12.11 | even | 2 | ||
432.4.a.f.1.1 | 1 | 1.1 | even | 1 | trivial | ||
432.4.a.i.1.1 | 1 | 3.2 | odd | 2 | |||
648.4.i.f.217.1 | 2 | 36.23 | even | 6 | |||
648.4.i.f.433.1 | 2 | 36.11 | even | 6 | |||
648.4.i.g.217.1 | 2 | 36.31 | odd | 6 | |||
648.4.i.g.433.1 | 2 | 36.7 | odd | 6 | |||
1728.4.a.m.1.1 | 1 | 24.11 | even | 2 | |||
1728.4.a.n.1.1 | 1 | 24.5 | odd | 2 | |||
1728.4.a.s.1.1 | 1 | 8.3 | odd | 2 | |||
1728.4.a.t.1.1 | 1 | 8.5 | even | 2 |