Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [768,4,Mod(1,768)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(768, 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("768.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 768 = 2^{8} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 768.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: | \(45.3134668844\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{12})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - 3 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 192) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(1.73205\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 768.1 |
$q$-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 | ||||||||
\(3\) | −3.00000 | −0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 10.3923 | 0.929516 | 0.464758 | − | 0.885438i | \(-0.346141\pi\) | ||||
0.464758 | + | 0.885438i | \(0.346141\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.46410 | 0.187044 | 0.0935220 | − | 0.995617i | \(-0.470187\pi\) | ||||
0.0935220 | + | 0.995617i | \(0.470187\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 9.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −55.4256 | −1.18248 | −0.591242 | − | 0.806494i | \(-0.701362\pi\) | ||||
−0.591242 | + | 0.806494i | \(0.701362\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −31.1769 | −0.536656 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −90.0000 | −1.28401 | −0.642006 | − | 0.766700i | \(-0.721898\pi\) | ||||
−0.642006 | + | 0.766700i | \(0.721898\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 116.000 | 1.40064 | 0.700322 | − | 0.713827i | \(-0.253040\pi\) | ||||
0.700322 | + | 0.713827i | \(0.253040\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −10.3923 | −0.107990 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 103.923 | 0.942150 | 0.471075 | − | 0.882093i | \(-0.343866\pi\) | ||||
0.471075 | + | 0.882093i | \(0.343866\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −17.0000 | −0.136000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −27.0000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −259.808 | −1.66362 | −0.831811 | − | 0.555058i | \(-0.812696\pi\) | ||||
−0.831811 | + | 0.555058i | \(0.812696\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −301.377 | −1.74609 | −0.873046 | − | 0.487637i | \(-0.837859\pi\) | ||||
−0.873046 | + | 0.487637i | \(0.837859\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 36.0000 | 0.173860 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 34.6410 | 0.153918 | 0.0769588 | − | 0.997034i | \(-0.475479\pi\) | ||||
0.0769588 | + | 0.997034i | \(0.475479\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 166.277 | 0.682708 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 54.0000 | 0.205692 | 0.102846 | − | 0.994697i | \(-0.467205\pi\) | ||||
0.102846 | + | 0.994697i | \(0.467205\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 20.0000 | 0.0709296 | 0.0354648 | − | 0.999371i | \(-0.488709\pi\) | ||||
0.0354648 | + | 0.999371i | \(0.488709\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 93.5307 | 0.309839 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 394.908 | 1.22560 | 0.612800 | − | 0.790238i | \(-0.290043\pi\) | ||||
0.612800 | + | 0.790238i | \(0.290043\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −331.000 | −0.965015 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 270.000 | 0.741325 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 488.438 | 1.26589 | 0.632945 | − | 0.774197i | \(-0.281846\pi\) | ||||
0.632945 | + | 0.774197i | \(0.281846\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −348.000 | −0.808662 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 324.000 | 0.714936 | 0.357468 | − | 0.933925i | \(-0.383640\pi\) | ||||
0.357468 | + | 0.933925i | \(0.383640\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 575.041 | 1.20699 | 0.603495 | − | 0.797366i | \(-0.293774\pi\) | ||||
0.603495 | + | 0.797366i | \(0.293774\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 31.1769 | 0.0623480 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −576.000 | −1.09914 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −116.000 | −0.211517 | −0.105759 | − | 0.994392i | \(-0.533727\pi\) | ||||
−0.105759 | + | 0.994392i | \(0.533727\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −311.769 | −0.543951 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −1101.58 | −1.84132 | −0.920662 | − | 0.390361i | \(-0.872350\pi\) | ||||
−0.920662 | + | 0.390361i | \(0.872350\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −1106.00 | −1.77325 | −0.886627 | − | 0.462486i | \(-0.846958\pi\) | ||||
−0.886627 | + | 0.462486i | \(0.846958\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 51.0000 | 0.0785196 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −148.956 | −0.212138 | −0.106069 | − | 0.994359i | \(-0.533826\pi\) | ||||
−0.106069 | + | 0.994359i | \(0.533826\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −1152.00 | −1.52348 | −0.761738 | − | 0.647886i | \(-0.775653\pi\) | ||||
−0.761738 | + | 0.647886i | \(0.775653\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −935.307 | −1.19351 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 779.423 | 0.960493 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −918.000 | −1.09335 | −0.546673 | − | 0.837346i | \(-0.684106\pi\) | ||||
−0.546673 | + | 0.837346i | \(0.684106\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −192.000 | −0.221177 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 904.131 | 1.00811 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 1205.51 | 1.30192 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 190.000 | 0.198882 | 0.0994411 | − | 0.995043i | \(-0.468295\pi\) | ||||
0.0994411 | + | 0.995043i | \(0.468295\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −10.3923 | −0.0102383 | −0.00511917 | − | 0.999987i | \(-0.501629\pi\) | ||||
−0.00511917 | + | 0.999987i | \(0.501629\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −793.279 | −0.758875 | −0.379438 | − | 0.925217i | \(-0.623882\pi\) | ||||
−0.379438 | + | 0.925217i | \(0.623882\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −108.000 | −0.100378 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −252.000 | −0.227680 | −0.113840 | − | 0.993499i | \(-0.536315\pi\) | ||||
−0.113840 | + | 0.993499i | \(0.536315\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 457.261 | 0.401814 | 0.200907 | − | 0.979610i | \(-0.435611\pi\) | ||||
0.200907 | + | 0.979610i | \(0.435611\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −103.923 | −0.0888643 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −2214.00 | −1.84315 | −0.921573 | − | 0.388204i | \(-0.873096\pi\) | ||||
−0.921573 | + | 0.388204i | \(0.873096\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1080.00 | 0.875744 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −498.831 | −0.394162 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −311.769 | −0.240167 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1331.00 | −1.00000 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −162.000 | −0.118756 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1475.71 | −1.05593 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −696.284 | −0.486498 | −0.243249 | − | 0.969964i | \(-0.578213\pi\) | ||||
−0.243249 | + | 0.969964i | \(0.578213\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −60.0000 | −0.0409512 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −2268.00 | −1.51264 | −0.756321 | − | 0.654201i | \(-0.773005\pi\) | ||||
−0.756321 | + | 0.654201i | \(0.773005\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 401.836 | 0.261982 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −280.592 | −0.178885 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −522.000 | −0.325529 | −0.162764 | − | 0.986665i | \(-0.552041\pi\) | ||||
−0.162764 | + | 0.986665i | \(0.552041\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 676.000 | 0.412501 | 0.206250 | − | 0.978499i | \(-0.433874\pi\) | ||||
0.206250 | + | 0.978499i | \(0.433874\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −1184.72 | −0.707600 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −2700.00 | −1.54636 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 993.000 | 0.557151 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 1465.31 | 0.805660 | 0.402830 | − | 0.915275i | \(-0.368027\pi\) | ||||
0.402830 | + | 0.915275i | \(0.368027\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2386.77 | 1.28631 | 0.643153 | − | 0.765738i | \(-0.277626\pi\) | ||||
0.643153 | + | 0.765738i | \(0.277626\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −810.000 | −0.428004 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −3132.00 | −1.62302 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −2016.11 | −1.02486 | −0.512430 | − | 0.858729i | \(-0.671254\pi\) | ||||
−0.512430 | + | 0.858729i | \(0.671254\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −1465.31 | −0.730862 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 360.000 | 0.176223 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −388.000 | −0.186445 | −0.0932224 | − | 0.995645i | \(-0.529717\pi\) | ||||
−0.0932224 | + | 0.995645i | \(0.529717\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 2203.17 | 1.02088 | 0.510438 | − | 0.859915i | \(-0.329483\pi\) | ||||
0.510438 | + | 0.859915i | \(0.329483\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 875.000 | 0.398270 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1044.00 | 0.466881 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −197.454 | −0.0867753 | −0.0433877 | − | 0.999058i | \(-0.513815\pi\) | ||||
−0.0433877 | + | 0.999058i | \(0.513815\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −58.8897 | −0.0254380 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −972.000 | −0.412768 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 2844.00 | 1.18754 | 0.593772 | − | 0.804633i | \(-0.297638\pi\) | ||||
0.593772 | + | 0.804633i | \(0.297638\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −96.9948 | −0.0398319 | −0.0199159 | − | 0.999802i | \(-0.506340\pi\) | ||||
−0.0199159 | + | 0.999802i | \(0.506340\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −1725.12 | −0.696856 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 360.000 | 0.143069 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −93.5307 | −0.0359966 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −3200.83 | −1.21259 | −0.606293 | − | 0.795241i | \(-0.707344\pi\) | ||||
−0.606293 | + | 0.795241i | \(0.707344\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1342.00 | −0.500514 | −0.250257 | − | 0.968179i | \(-0.580515\pi\) | ||||
−0.250257 | + | 0.968179i | \(0.580515\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 1728.00 | 0.634588 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −966.484 | −0.349539 | −0.174769 | − | 0.984609i | \(-0.555918\pi\) | ||||
−0.174769 | + | 0.984609i | \(0.555918\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1784.01 | 0.635504 | 0.317752 | − | 0.948174i | \(-0.397072\pi\) | ||||
0.317752 | + | 0.948174i | \(0.397072\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 348.000 | 0.122120 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −900.000 | −0.311171 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 561.184 | 0.191194 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 935.307 | 0.314050 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2764.00 | 0.901809 | 0.450904 | − | 0.892572i | \(-0.351102\pi\) | ||||
0.450904 | + | 0.892572i | \(0.351102\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 3304.75 | 1.06309 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 207.846 | 0.0659302 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1044.00 | −0.326596 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 3318.00 | 1.02379 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 4988.31 | 1.51832 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 4292.02 | 1.28886 | 0.644428 | − | 0.764665i | \(-0.277095\pi\) | ||||
0.644428 | + | 0.764665i | \(0.277095\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −153.000 | −0.0453333 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −5688.00 | −1.66311 | −0.831555 | − | 0.555443i | \(-0.812549\pi\) | ||||
−0.831555 | + | 0.555443i | \(0.812549\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 5570.28 | 1.60740 | 0.803699 | − | 0.595036i | \(-0.202862\pi\) | ||||
0.803699 | + | 0.595036i | \(0.202862\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −2718.00 | −0.764215 | −0.382108 | − | 0.924118i | \(-0.624802\pi\) | ||||
−0.382108 | + | 0.924118i | \(0.624802\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 4104.00 | 1.13921 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 446.869 | 0.122478 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −3574.95 | −0.967550 | −0.483775 | − | 0.875192i | \(-0.660735\pi\) | ||||
−0.483775 | + | 0.875192i | \(0.660735\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 4490.00 | 1.20011 | 0.600055 | − | 0.799959i | \(-0.295146\pi\) | ||||
0.600055 | + | 0.799959i | \(0.295146\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −243.000 | −0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −3439.85 | −0.896996 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −6429.37 | −1.65624 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 3456.00 | 0.879579 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −4608.00 | −1.15878 | −0.579391 | − | 0.815050i | \(-0.696710\pi\) | ||||
−0.579391 | + | 0.815050i | \(0.696710\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 2805.92 | 0.689073 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 4626.00 | 1.12281 | 0.561405 | − | 0.827541i | \(-0.310261\pi\) | ||||
0.561405 | + | 0.827541i | \(0.310261\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 120.000 | 0.0287893 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −2338.27 | −0.554541 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −1995.32 | −0.467821 | −0.233910 | − | 0.972258i | \(-0.575152\pi\) | ||||
−0.233910 | + | 0.972258i | \(0.575152\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 5076.00 | 1.17666 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 2754.00 | 0.631244 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 3148.87 | 0.713717 | 0.356859 | − | 0.934158i | \(-0.383848\pi\) | ||||
0.356859 | + | 0.934158i | \(0.383848\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 5345.11 | 1.19813 | 0.599063 | − | 0.800702i | \(-0.295540\pi\) | ||||
0.599063 | + | 0.800702i | \(0.295540\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 576.000 | 0.127696 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −6526.37 | −1.41564 | −0.707818 | − | 0.706394i | \(-0.750321\pi\) | ||||
−0.707818 | + | 0.706394i | \(0.750321\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −2712.39 | −0.582031 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1170.00 | 0.248386 | 0.124193 | − | 0.992258i | \(-0.460366\pi\) | ||||
0.124193 | + | 0.992258i | \(0.460366\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 5740.00 | 1.20568 | 0.602840 | − | 0.797862i | \(-0.294036\pi\) | ||||
0.602840 | + | 0.797862i | \(0.294036\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −3616.52 | −0.751664 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 187.061 | 0.0384735 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 3187.00 | 0.648687 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −570.000 | −0.114825 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −7991.68 | −1.59344 | −0.796722 | − | 0.604346i | \(-0.793434\pi\) | ||||
−0.796722 | + | 0.604346i | \(0.793434\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 3367.11 | 0.664544 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −5760.00 | −1.11408 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 69.2820 | 0.0132669 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 31.1769 | 0.00591111 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 5976.00 | 1.12192 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 5452.00 | 1.01356 | 0.506779 | − | 0.862076i | \(-0.330836\pi\) | ||||
0.506779 | + | 0.862076i | \(0.330836\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 2379.84 | 0.438137 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 2203.17 | 0.401705 | 0.200852 | − | 0.979622i | \(-0.435629\pi\) | ||||
0.200852 | + | 0.979622i | \(0.435629\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 1034.00 | 0.186726 | 0.0933628 | − | 0.995632i | \(-0.470238\pi\) | ||||
0.0933628 | + | 0.995632i | \(0.470238\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 324.000 | 0.0579534 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 2650.04 | 0.469530 | 0.234765 | − | 0.972052i | \(-0.424568\pi\) | ||||
0.234765 | + | 0.972052i | \(0.424568\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 756.000 | 0.131451 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −10440.0 | −1.79844 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 942.236 | 0.160818 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −1371.78 | −0.231987 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 1368.00 | 0.229241 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 4132.00 | 0.686149 | 0.343074 | − | 0.939308i | \(-0.388532\pi\) | ||||
0.343074 | + | 0.939308i | \(0.388532\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 311.769 | 0.0513058 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −1205.51 | −0.196609 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −458.000 | −0.0740322 | −0.0370161 | − | 0.999315i | \(-0.511785\pi\) | ||||
−0.0370161 | + | 0.999315i | \(0.511785\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 6642.00 | 1.06414 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −2334.80 | −0.367544 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −3240.00 | −0.505611 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −11016.0 | −1.70424 | −0.852118 | − | 0.523350i | \(-0.824682\pi\) | ||||
−0.852118 | + | 0.523350i | \(0.824682\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −2528.79 | −0.387860 | −0.193930 | − | 0.981015i | \(-0.562124\pi\) | ||||
−0.193930 | + | 0.981015i | \(0.562124\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1496.49 | 0.227569 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 5562.00 | 0.838627 | 0.419314 | − | 0.907841i | \(-0.362271\pi\) | ||||
0.419314 | + | 0.907841i | \(0.362271\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −11448.0 | −1.71154 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 935.307 | 0.138660 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 8875.03 | 1.30475 | 0.652376 | − | 0.757895i | \(-0.273772\pi\) | ||||
0.652376 | + | 0.757895i | \(0.273772\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 6597.00 | 0.961802 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 3993.00 | 0.577350 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −11493.9 | −1.64827 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −12799.9 | −1.82056 | −0.910282 | − | 0.413989i | \(-0.864135\pi\) | ||||
−0.910282 | + | 0.413989i | \(0.864135\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 486.000 | 0.0685641 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1692.00 | 0.236777 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 4981.38 | 0.691491 | 0.345745 | − | 0.938328i | \(-0.387626\pi\) | ||||
0.345745 | + | 0.938328i | \(0.387626\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 4427.12 | 0.609642 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 14400.0 | 1.96721 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −9892.00 | −1.34068 | −0.670340 | − | 0.742054i | \(-0.733852\pi\) | ||||
−0.670340 | + | 0.742054i | \(0.733852\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 2088.85 | 0.280880 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 8771.11 | 1.17019 | 0.585095 | − | 0.810965i | \(-0.301057\pi\) | ||||
0.585095 | + | 0.810965i | \(0.301057\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 180.000 | 0.0236432 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 9903.87 | 1.29086 | 0.645432 | − | 0.763818i | \(-0.276677\pi\) | ||||
0.645432 | + | 0.763818i | \(0.276677\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −9353.07 | −1.20973 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 6804.00 | 0.873324 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −1548.00 | −0.197186 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 103.923 | 0.0131379 | 0.00656895 | − | 0.999978i | \(-0.497909\pi\) | ||||
0.00656895 | + | 0.999978i | \(0.497909\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −1205.51 | −0.151255 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 1062.00 | 0.132254 | 0.0661269 | − | 0.997811i | \(-0.478936\pi\) | ||||
0.0661269 | + | 0.997811i | \(0.478936\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 16704.0 | 2.06473 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 841.777 | 0.103280 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 8614.00 | 1.04141 | 0.520703 | − | 0.853738i | \(-0.325670\pi\) | ||||
0.520703 | + | 0.853738i | \(0.325670\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 1566.00 | 0.187944 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 1122.37 | 0.133724 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −11971.9 | −1.41609 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −2028.00 | −0.238157 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −10440.0 | −1.21725 | −0.608625 | − | 0.793458i | \(-0.708278\pi\) | ||||
−0.608625 | + | 0.793458i | \(0.708278\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −900.666 | −0.104266 | −0.0521328 | − | 0.998640i | \(-0.516602\pi\) | ||||
−0.0521328 | + | 0.998640i | \(0.516602\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 3554.17 | 0.408533 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 1530.00 | 0.174626 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1992.00 | 0.225760 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −394.908 | −0.0441346 | −0.0220673 | − | 0.999756i | \(-0.507025\pi\) | ||||
−0.0220673 | + | 0.999756i | \(0.507025\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 12958.0 | 1.43816 | 0.719078 | − | 0.694929i | \(-0.244564\pi\) | ||||
0.719078 | + | 0.694929i | \(0.244564\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 8100.00 | 0.892794 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 12055.1 | 1.31962 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 11441.9 | 1.24395 | 0.621974 | − | 0.783038i | \(-0.286331\pi\) | ||||
0.621974 | + | 0.783038i | \(0.286331\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −2979.00 | −0.321672 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −1800.00 | −0.193049 | −0.0965244 | − | 0.995331i | \(-0.530773\pi\) | ||||
−0.0965244 | + | 0.995331i | \(0.530773\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −9540.14 | −1.01628 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −4395.94 | −0.465148 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −13626.0 | −1.43218 | −0.716092 | − | 0.698006i | \(-0.754071\pi\) | ||||
−0.716092 | + | 0.698006i | \(0.754071\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −7160.30 | −0.742649 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −1995.32 | −0.205587 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −12602.0 | −1.28993 | −0.644964 | − | 0.764213i | \(-0.723127\pi\) | ||||
−0.644964 | + | 0.764213i | \(0.723127\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 2430.00 | 0.247108 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 1839.44 | 0.185838 | 0.0929188 | − | 0.995674i | \(-0.470380\pi\) | ||||
0.0929188 | + | 0.995674i | \(0.470380\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 11012.4 | 1.10538 | 0.552688 | − | 0.833389i | \(-0.313602\pi\) | ||||
0.552688 | + | 0.833389i | \(0.313602\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 9396.00 | 0.937052 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −9144.00 | −0.906068 | −0.453034 | − | 0.891493i | \(-0.649658\pi\) | ||||
−0.453034 | + | 0.891493i | \(0.649658\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −401.836 | −0.0395630 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 6048.32 | 0.591703 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1972.00 | −0.190488 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 4395.94 | 0.421963 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −6173.03 | −0.588837 | −0.294418 | − | 0.955677i | \(-0.595126\pi\) | ||||
−0.294418 | + | 0.955677i | \(0.595126\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1920.00 | −0.182005 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −1080.00 | −0.101743 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 1974.54 | 0.184864 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 3204.29 | 0.298153 | 0.149076 | − | 0.988826i | \(-0.452370\pi\) | ||||
0.149076 | + | 0.988826i | \(0.452370\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 1164.00 | 0.107644 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 396.000 | 0.0363976 | 0.0181988 | − | 0.999834i | \(-0.494207\pi\) | ||||
0.0181988 | + | 0.999834i | \(0.494207\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 23382.7 | 2.13611 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −3816.00 | −0.344408 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 12436.0 | 1.11565 | 0.557827 | − | 0.829957i | \(-0.311635\pi\) | ||||
0.557827 | + | 0.829957i | \(0.311635\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −6609.51 | −0.589403 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −16482.2 | −1.46104 | −0.730522 | − | 0.682890i | \(-0.760723\pi\) | ||||
−0.730522 | + | 0.682890i | \(0.760723\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −108.000 | −0.00951671 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −2625.00 | −0.229942 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −9155.62 | −0.797280 | −0.398640 | − | 0.917107i | \(-0.630518\pi\) | ||||
−0.398640 | + | 0.917107i | \(0.630518\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −3831.30 | −0.331676 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −3132.00 | −0.269554 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −8244.00 | −0.705386 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 592.361 | 0.0500998 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −7650.00 | −0.643287 | −0.321644 | − | 0.946861i | \(-0.604235\pi\) | ||||
−0.321644 | + | 0.946861i | \(0.604235\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 18332.0 | 1.53270 | 0.766350 | − | 0.642423i | \(-0.222071\pi\) | ||||
0.766350 | + | 0.642423i | \(0.222071\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 176.669 | 0.0146866 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 27123.9 | 2.24200 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −1367.00 | −0.112353 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 2916.00 | 0.238312 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −2992.98 | −0.243228 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −2618.86 | −0.211632 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −8532.00 | −0.685629 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 16863.2 | 1.34012 | 0.670062 | − | 0.742305i | \(-0.266267\pi\) | ||||
0.670062 | + | 0.742305i | \(0.266267\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 290.985 | 0.0229969 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 4752.00 | 0.373492 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −1684.00 | −0.131632 | −0.0658159 | − | 0.997832i | \(-0.520965\pi\) | ||||
−0.0658159 | + | 0.997832i | \(0.520965\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 5175.37 | 0.402330 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −30137.7 | −2.33014 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −516.000 | −0.0396791 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −1080.00 | −0.0826008 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −2275.91 | −0.173130 | −0.0865652 | − | 0.996246i | \(-0.527589\pi\) | ||||
−0.0865652 | + | 0.996246i | \(0.527589\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −1108.51 | −0.0838731 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 7992.00 | 0.598264 | 0.299132 | − | 0.954212i | \(-0.403303\pi\) | ||||
0.299132 | + | 0.954212i | \(0.403303\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −23008.6 | −1.71323 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 280.592 | 0.0207827 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 5526.00 | 0.407139 | 0.203569 | − | 0.979061i | \(-0.434746\pi\) | ||||
0.203569 | + | 0.979061i | \(0.434746\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 13420.0 | 0.983554 | 0.491777 | − | 0.870721i | \(-0.336347\pi\) | ||||
0.491777 | + | 0.870721i | \(0.336347\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 9602.49 | 0.700087 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −1766.69 | −0.128132 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −10178.0 | −0.734343 | −0.367171 | − | 0.930153i | \(-0.619674\pi\) | ||||
−0.367171 | + | 0.930153i | \(0.619674\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 4026.00 | 0.288972 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −3990.65 | −0.284957 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −5184.00 | −0.366380 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 18684.0 | 1.31375 | 0.656875 | − | 0.754000i | \(-0.271878\pi\) | ||||
0.656875 | + | 0.754000i | \(0.271878\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −34959.7 | −2.44565 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 2899.45 | 0.201806 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −5094.00 | −0.352758 | −0.176379 | − | 0.984322i | \(-0.556438\pi\) | ||||
−0.176379 | + | 0.984322i | \(0.556438\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −3240.00 | −0.223239 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −5352.04 | −0.366908 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 19433.6 | 1.32560 | 0.662801 | − | 0.748795i | \(-0.269367\pi\) | ||||
0.662801 | + | 0.748795i | \(0.269367\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −27722.0 | −1.88154 | −0.940769 | − | 0.339049i | \(-0.889895\pi\) | ||||
−0.940769 | + | 0.339049i | \(0.889895\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −1044.00 | −0.0705057 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −13832.2 | −0.929516 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 26684.0 | 1.78430 | 0.892149 | − | 0.451741i | \(-0.149197\pi\) | ||||
0.892149 | + | 0.451741i | \(0.149197\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 2700.00 | 0.179654 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −21888.0 | −1.44925 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −16911.7 | −1.11429 | −0.557144 | − | 0.830416i | \(-0.688103\pi\) | ||||
−0.557144 | + | 0.830416i | \(0.688103\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −1683.55 | −0.110386 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −17694.0 | −1.15451 | −0.577256 | − | 0.816563i | \(-0.695876\pi\) | ||||
−0.577256 | + | 0.816563i | \(0.695876\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −13652.0 | −0.886462 | −0.443231 | − | 0.896407i | \(-0.646168\pi\) | ||||
−0.443231 | + | 0.896407i | \(0.646168\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −2805.92 | −0.181317 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −3180.05 | −0.204504 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −13211.0 | −0.845504 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −3117.69 | −0.197632 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 9162.55 | 0.578059 | 0.289030 | − | 0.957320i | \(-0.406667\pi\) | ||||
0.289030 | + | 0.957320i | \(0.406667\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −8292.00 | −0.520659 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −7236.00 | −0.452208 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 18345.9 | 1.14112 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −9914.26 | −0.613775 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −5202.00 | −0.320541 | −0.160270 | − | 0.987073i | \(-0.551237\pi\) | ||||
−0.160270 | + | 0.987073i | \(0.551237\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −15892.0 | −0.974680 | −0.487340 | − | 0.873212i | \(-0.662033\pi\) | ||||
−0.487340 | + | 0.873212i | \(0.662033\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −623.538 | −0.0380648 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −478.046 | −0.0290478 | −0.0145239 | − | 0.999895i | \(-0.504623\pi\) | ||||
−0.0145239 | + | 0.999895i | \(0.504623\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 3132.00 | 0.188560 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 24660.9 | 1.47788 | 0.738941 | − | 0.673770i | \(-0.235326\pi\) | ||||
0.738941 | + | 0.673770i | \(0.235326\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −23569.7 | −1.40602 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −9954.00 | −0.591085 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 28260.0 | 1.67049 | 0.835245 | − | 0.549878i | \(-0.185326\pi\) | ||||
0.835245 | + | 0.549878i | \(0.185326\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 25863.0 | 1.52187 | 0.760933 | − | 0.648830i | \(-0.224742\pi\) | ||||
0.760933 | + | 0.648830i | \(0.224742\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −14964.9 | −0.876605 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 4176.00 | 0.243516 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −27000.0 | −1.56738 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −12876.1 | −0.744122 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 190.000 | 0.0108826 | 0.00544128 | − | 0.999985i | \(-0.498268\pi\) | ||||
0.00544128 | + | 0.999985i | \(0.498268\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 459.000 | 0.0261732 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 4998.70 | 0.283775 | 0.141887 | − | 0.989883i | \(-0.454683\pi\) | ||||
0.141887 | + | 0.989883i | \(0.454683\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 658.179 | 0.0371997 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 17064.0 | 0.960197 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −8064.00 | −0.451772 | −0.225886 | − | 0.974154i | \(-0.572528\pi\) | ||||
−0.225886 | + | 0.974154i | \(0.572528\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −5424.78 | −0.302584 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −16710.8 | −0.928032 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −27072.0 | −1.49690 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 19244.0 | 1.05944 | 0.529722 | − | 0.848171i | \(-0.322296\pi\) | ||||
0.529722 | + | 0.848171i | \(0.322296\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 7025.20 | 0.383426 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −4860.00 | −0.264111 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 8154.00 | 0.441220 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −6204.21 | −0.334279 | −0.167140 | − | 0.985933i | \(-0.553453\pi\) | ||||
−0.167140 | + | 0.985933i | \(0.553453\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 4018.36 | 0.215584 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −12312.0 | −0.657726 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −36.0000 | −0.00191502 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 15020.3 | 0.795629 | 0.397814 | − | 0.917466i | \(-0.369769\pi\) | ||||
0.397814 | + | 0.917466i | \(0.369769\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −1340.61 | −0.0707127 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −31320.0 | −1.64508 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 10724.9 | 0.558615 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −30740.4 | −1.59447 | −0.797236 | − | 0.603668i | \(-0.793705\pi\) | ||||
−0.797236 | + | 0.603668i | \(0.793705\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −2748.00 | −0.141943 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −13470.0 | −0.692883 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 4416.73 | 0.226253 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 12127.8 | 0.618701 | 0.309351 | − | 0.950948i | \(-0.399888\pi\) | ||||
0.309351 | + | 0.950948i | \(0.399888\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −1800.00 | −0.0910744 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −12387.6 | −0.624212 | −0.312106 | − | 0.950047i | \(-0.601034\pi\) | ||||
−0.312106 | + | 0.950047i | \(0.601034\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 10319.6 | 0.517881 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −11180.0 | −0.556513 | −0.278256 | − | 0.960507i | \(-0.589756\pi\) | ||||
−0.278256 | + | 0.960507i | \(0.589756\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 19288.1 | 0.956230 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 35500.1 | 1.75286 | 0.876429 | − | 0.481532i | \(-0.159919\pi\) | ||||
0.876429 | + | 0.481532i | \(0.159919\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 15228.0 | 0.748873 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −10368.0 | −0.507825 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −872.954 | −0.0425862 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 37970.0 | 1.84493 | 0.922467 | − | 0.386076i | \(-0.126170\pi\) | ||||
0.922467 | + | 0.386076i | \(0.126170\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 13824.0 | 0.669023 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 24804.0 | 1.19564 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 39047.4 | 1.87477 | 0.937385 | − | 0.348296i | \(-0.113240\pi\) | ||||
0.937385 | + | 0.348296i | \(0.113240\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 12222.0 | 0.582191 | 0.291095 | − | 0.956694i | \(-0.405980\pi\) | ||||
0.291095 | + | 0.956694i | \(0.405980\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1584.00 | 0.0751568 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −8417.77 | −0.397837 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −17957.9 | −0.845401 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −34030.0 | −1.59578 | −0.797889 | − | 0.602804i | \(-0.794050\pi\) | ||||
−0.797889 | + | 0.602804i | \(0.794050\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −13878.0 | −0.648254 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −4873.99 | −0.226786 | −0.113393 | − | 0.993550i | \(-0.536172\pi\) | ||||
−0.113393 | + | 0.993550i | \(0.536172\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 5123.41 | 0.237469 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −360.000 | −0.0166215 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 6264.00 | 0.288102 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 7014.81 | 0.320164 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −20952.0 | −0.952623 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −30988.0 | −1.40356 | −0.701781 | − | 0.712393i | \(-0.747611\pi\) | ||||
−0.701781 | + | 0.712393i | \(0.747611\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 5985.97 | 0.270096 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −7669.52 | −0.344749 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −31872.0 | −1.42725 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −15228.0 | −0.679348 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 7160.30 | 0.318232 | 0.159116 | − | 0.987260i | \(-0.449136\pi\) | ||||
0.159116 | + | 0.987260i | \(0.449136\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −35541.7 | −1.57369 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −8262.00 | −0.364449 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 3741.23 | 0.163803 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −9446.61 | −0.412065 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −37530.0 | −1.63101 | −0.815503 | − | 0.578752i | \(-0.803540\pi\) | ||||
−0.815503 | + | 0.578752i | \(0.803540\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −10852.0 | −0.469871 | −0.234935 | − | 0.972011i | \(-0.575488\pi\) | ||||
−0.234935 | + | 0.972011i | \(0.575488\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −16035.3 | −0.691739 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −4032.21 | −0.173303 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 2320.00 | 0.0993470 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −1728.00 | −0.0737255 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −31353.6 | −1.33282 | −0.666411 | − | 0.745584i | \(-0.732171\pi\) | ||||
−0.666411 | + | 0.745584i | \(0.732171\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −32947.1 | −1.39546 | −0.697729 | − | 0.716361i | \(-0.745806\pi\) | ||||
−0.697729 | + | 0.716361i | \(0.745806\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −10044.0 | −0.422327 | −0.211163 | − | 0.977451i | \(-0.567725\pi\) | ||||
−0.211163 | + | 0.977451i | \(0.567725\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −9796.48 | −0.410429 | −0.205215 | − | 0.978717i | \(-0.565789\pi\) | ||||
−0.205215 | + | 0.978717i | \(0.565789\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 19579.1 | 0.817318 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 29790.0 | 1.23909 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 22896.0 | 0.948921 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 8137.17 | 0.336036 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 21054.8 | 0.866380 | 0.433190 | − | 0.901303i | \(-0.357388\pi\) | ||||
0.433190 | + | 0.901303i | \(0.357388\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 43111.0 | 1.76764 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −3510.00 | −0.143405 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 9093.27 | 0.370199 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −4610.72 | −0.187044 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −17220.0 | −0.696100 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 3600.00 | 0.145013 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −40703.2 | −1.63382 | −0.816911 | − | 0.576763i | \(-0.804316\pi\) | ||||
−0.816911 | + | 0.576763i | \(0.804316\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 10849.6 | 0.433973 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 18342.0 | 0.731098 | 0.365549 | − | 0.930792i | \(-0.380881\pi\) | ||||
0.365549 | + | 0.930792i | \(0.380881\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 26324.0 | 1.04559 | 0.522796 | − | 0.852458i | \(-0.324889\pi\) | ||||
0.522796 | + | 0.852458i | \(0.324889\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −561.184 | −0.0222127 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 12761.8 | 0.503378 | 0.251689 | − | 0.967808i | \(-0.419014\pi\) | ||||
0.251689 | + | 0.967808i | \(0.419014\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −2052.00 | −0.0806591 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −9561.00 | −0.374520 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 6429.37 | 0.250116 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 1710.00 | 0.0662941 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −5112.00 | −0.197505 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 2459.51 | 0.0946999 | 0.0473500 | − | 0.998878i | \(-0.484922\pi\) | ||||
0.0473500 | + | 0.998878i | \(0.484922\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 23975.0 | 0.919975 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 37314.0 | 1.42695 | 0.713474 | − | 0.700682i | \(-0.247121\pi\) | ||||
0.713474 | + | 0.700682i | \(0.247121\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −18244.0 | −0.695311 | −0.347655 | − | 0.937622i | \(-0.613022\pi\) | ||||
−0.347655 | + | 0.937622i | \(0.613022\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −10101.3 | −0.383675 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −17957.9 | −0.679783 | −0.339891 | − | 0.940465i | \(-0.610390\pi\) | ||||
−0.339891 | + | 0.940465i | \(0.610390\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −2412.00 | −0.0909965 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 45809.3 | 1.71663 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 29555.7 | 1.10384 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 17280.0 | 0.643213 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 78300.0 | 2.90484 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −43959.4 | −1.62542 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −207.846 | −0.00765967 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −1008.00 | −0.0370244 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 16388.0 | 0.599950 | 0.299975 | − | 0.953947i | \(-0.403022\pi\) | ||||
0.299975 | + | 0.953947i | \(0.403022\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −93.5307 | −0.00341278 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −25107.8 | −0.913127 | −0.456564 | − | 0.889691i | \(-0.650920\pi\) | ||||
−0.456564 | + | 0.889691i | \(0.650920\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −17928.0 | −0.647739 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −7856.58 | −0.282930 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −27155.1 | −0.974716 | −0.487358 | − | 0.873202i | \(-0.662039\pi\) | ||||
−0.487358 | + | 0.873202i | \(0.662039\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −16356.0 | −0.585178 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 61056.0 | 2.17734 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −588.897 | −0.0209328 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −7139.51 | −0.252958 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 48006.0 | 1.69540 | 0.847700 | − | 0.530477i | \(-0.177987\pi\) | ||||
0.847700 | + | 0.530477i | \(0.177987\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −38396.0 | −1.35164 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −6609.51 | −0.231924 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −7894.00 | −0.275225 | −0.137612 | − | 0.990486i | \(-0.543943\pi\) | ||||
−0.137612 | + | 0.990486i | \(0.543943\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −3102.00 | −0.107806 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 2670.82 | 0.0925253 | 0.0462627 | − | 0.998929i | \(-0.485269\pi\) | ||||
0.0462627 | + | 0.998929i | \(0.485269\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 5611.84 | 0.193793 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −972.000 | −0.0334594 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −22356.0 | −0.767130 | −0.383565 | − | 0.923514i | \(-0.625304\pi\) | ||||
−0.383565 | + | 0.923514i | \(0.625304\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 61300.7 | 2.09685 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −7950.11 | −0.271083 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 14958.0 | 0.508434 | 0.254217 | − | 0.967147i | \(-0.418182\pi\) | ||||
0.254217 | + | 0.967147i | \(0.418182\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −33264.0 | −1.12712 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −1808.26 | −0.0608882 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 61037.0 | 2.04884 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −2268.00 | −0.0758933 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −13946.5 | −0.465236 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −17476.4 | −0.581182 | −0.290591 | − | 0.956847i | \(-0.593852\pi\) | ||||
−0.290591 | + | 0.956847i | \(0.593852\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 31320.0 | 1.03833 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 48528.0 | 1.60385 | 0.801925 | − | 0.597425i | \(-0.203810\pi\) | ||||
0.801925 | + | 0.597425i | \(0.203810\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 2341.73 | 0.0771557 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −2826.71 | −0.0928483 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −39978.0 | −1.30912 | −0.654560 | − | 0.756010i | \(-0.727146\pi\) | ||||
−0.654560 | + | 0.756010i | \(0.727146\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 4115.35 | 0.133938 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −17957.9 | −0.582674 | −0.291337 | − | 0.956621i | \(-0.594100\pi\) | ||||
−0.291337 | + | 0.956621i | \(0.594100\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −10044.0 | −0.324902 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −4104.00 | −0.132352 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 2078.46 | 0.0668263 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1666.23 | 0.0534103 | 0.0267052 | − | 0.999643i | \(-0.491498\pi\) | ||||
0.0267052 | + | 0.999643i | \(0.491498\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −12396.0 | −0.396148 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 18540.0 | 0.590711 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −41465.3 | −1.31717 | −0.658585 | − | 0.752506i | \(-0.728845\pi\) | ||||
−0.658585 | + | 0.752506i | \(0.728845\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −935.307 | −0.0296214 |
(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 | 768.4.a.g.1.2 | 2 | ||
3.2 | odd | 2 | 2304.4.a.bg.1.1 | 2 | |||
4.3 | odd | 2 | 768.4.a.n.1.2 | 2 | |||
8.3 | odd | 2 | inner | 768.4.a.g.1.1 | 2 | ||
8.5 | even | 2 | 768.4.a.n.1.1 | 2 | |||
12.11 | even | 2 | 2304.4.a.be.1.1 | 2 | |||
16.3 | odd | 4 | 192.4.d.a.97.3 | yes | 4 | ||
16.5 | even | 4 | 192.4.d.a.97.4 | yes | 4 | ||
16.11 | odd | 4 | 192.4.d.a.97.2 | yes | 4 | ||
16.13 | even | 4 | 192.4.d.a.97.1 | ✓ | 4 | ||
24.5 | odd | 2 | 2304.4.a.be.1.2 | 2 | |||
24.11 | even | 2 | 2304.4.a.bg.1.2 | 2 | |||
48.5 | odd | 4 | 576.4.d.g.289.1 | 4 | |||
48.11 | even | 4 | 576.4.d.g.289.2 | 4 | |||
48.29 | odd | 4 | 576.4.d.g.289.3 | 4 | |||
48.35 | even | 4 | 576.4.d.g.289.4 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
192.4.d.a.97.1 | ✓ | 4 | 16.13 | even | 4 | ||
192.4.d.a.97.2 | yes | 4 | 16.11 | odd | 4 | ||
192.4.d.a.97.3 | yes | 4 | 16.3 | odd | 4 | ||
192.4.d.a.97.4 | yes | 4 | 16.5 | even | 4 | ||
576.4.d.g.289.1 | 4 | 48.5 | odd | 4 | |||
576.4.d.g.289.2 | 4 | 48.11 | even | 4 | |||
576.4.d.g.289.3 | 4 | 48.29 | odd | 4 | |||
576.4.d.g.289.4 | 4 | 48.35 | even | 4 | |||
768.4.a.g.1.1 | 2 | 8.3 | odd | 2 | inner | ||
768.4.a.g.1.2 | 2 | 1.1 | even | 1 | trivial | ||
768.4.a.n.1.1 | 2 | 8.5 | even | 2 | |||
768.4.a.n.1.2 | 2 | 4.3 | odd | 2 | |||
2304.4.a.be.1.1 | 2 | 12.11 | even | 2 | |||
2304.4.a.be.1.2 | 2 | 24.5 | odd | 2 | |||
2304.4.a.bg.1.1 | 2 | 3.2 | odd | 2 | |||
2304.4.a.bg.1.2 | 2 | 24.11 | even | 2 |