Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [448,4,Mod(1,448)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(448, 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("448.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 448 = 2^{6} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 448.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: | \(26.4328556826\) |
Analytic rank: | \(1\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 28) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 448.1 |
$q$-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 | ||||||||
\(3\) | −4.00000 | −0.769800 | −0.384900 | − | 0.922958i | \(-0.625764\pi\) | ||||
−0.384900 | + | 0.922958i | \(0.625764\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −6.00000 | −0.536656 | −0.268328 | − | 0.963328i | \(-0.586471\pi\) | ||||
−0.268328 | + | 0.963328i | \(0.586471\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 7.00000 | 0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −11.0000 | −0.407407 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 12.0000 | 0.328921 | 0.164461 | − | 0.986384i | \(-0.447412\pi\) | ||||
0.164461 | + | 0.986384i | \(0.447412\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 82.0000 | 1.74944 | 0.874720 | − | 0.484629i | \(-0.161046\pi\) | ||||
0.874720 | + | 0.484629i | \(0.161046\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 24.0000 | 0.413118 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −30.0000 | −0.428004 | −0.214002 | − | 0.976833i | \(-0.568650\pi\) | ||||
−0.214002 | + | 0.976833i | \(0.568650\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −68.0000 | −0.821067 | −0.410533 | − | 0.911846i | \(-0.634657\pi\) | ||||
−0.410533 | + | 0.911846i | \(0.634657\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −28.0000 | −0.290957 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 216.000 | 1.95822 | 0.979111 | − | 0.203326i | \(-0.0651750\pi\) | ||||
0.979111 | + | 0.203326i | \(0.0651750\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −89.0000 | −0.712000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 152.000 | 1.08342 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −246.000 | −1.57521 | −0.787604 | − | 0.616181i | \(-0.788679\pi\) | ||||
−0.787604 | + | 0.616181i | \(0.788679\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −112.000 | −0.648897 | −0.324448 | − | 0.945903i | \(-0.605179\pi\) | ||||
−0.324448 | + | 0.945903i | \(0.605179\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −48.0000 | −0.253204 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −42.0000 | −0.202837 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −110.000 | −0.488754 | −0.244377 | − | 0.969680i | \(-0.578583\pi\) | ||||
−0.244377 | + | 0.969680i | \(0.578583\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −328.000 | −1.34672 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −246.000 | −0.937043 | −0.468521 | − | 0.883452i | \(-0.655213\pi\) | ||||
−0.468521 | + | 0.883452i | \(0.655213\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 172.000 | 0.609994 | 0.304997 | − | 0.952353i | \(-0.401344\pi\) | ||||
0.304997 | + | 0.952353i | \(0.401344\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 66.0000 | 0.218638 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 192.000 | 0.595874 | 0.297937 | − | 0.954586i | \(-0.403701\pi\) | ||||
0.297937 | + | 0.954586i | \(0.403701\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 49.0000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 120.000 | 0.329478 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −558.000 | −1.44617 | −0.723087 | − | 0.690757i | \(-0.757277\pi\) | ||||
−0.723087 | + | 0.690757i | \(0.757277\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −72.0000 | −0.176518 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 272.000 | 0.632058 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −540.000 | −1.19156 | −0.595780 | − | 0.803148i | \(-0.703157\pi\) | ||||
−0.595780 | + | 0.803148i | \(0.703157\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −110.000 | −0.230886 | −0.115443 | − | 0.993314i | \(-0.536829\pi\) | ||||
−0.115443 | + | 0.993314i | \(0.536829\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −77.0000 | −0.153986 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −492.000 | −0.938848 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −140.000 | −0.255279 | −0.127640 | − | 0.991821i | \(-0.540740\pi\) | ||||
−0.127640 | + | 0.991821i | \(0.540740\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −864.000 | −1.50744 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −840.000 | −1.40408 | −0.702040 | − | 0.712138i | \(-0.747727\pi\) | ||||
−0.702040 | + | 0.712138i | \(0.747727\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −550.000 | −0.881817 | −0.440908 | − | 0.897552i | \(-0.645344\pi\) | ||||
−0.440908 | + | 0.897552i | \(0.645344\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 356.000 | 0.548098 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 84.0000 | 0.124321 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −208.000 | −0.296226 | −0.148113 | − | 0.988970i | \(-0.547320\pi\) | ||||
−0.148113 | + | 0.988970i | \(0.547320\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −311.000 | −0.426612 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −516.000 | −0.682390 | −0.341195 | − | 0.939993i | \(-0.610832\pi\) | ||||
−0.341195 | + | 0.939993i | \(0.610832\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 180.000 | 0.229691 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 984.000 | 1.21260 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −1398.00 | −1.66503 | −0.832515 | − | 0.554002i | \(-0.813100\pi\) | ||||
−0.832515 | + | 0.554002i | \(0.813100\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 574.000 | 0.661226 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 448.000 | 0.499521 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 408.000 | 0.440631 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1586.00 | 1.66014 | 0.830072 | − | 0.557657i | \(-0.188299\pi\) | ||||
0.830072 | + | 0.557657i | \(0.188299\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −132.000 | −0.134005 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1242.00 | 1.22360 | 0.611800 | − | 0.791012i | \(-0.290446\pi\) | ||||
0.611800 | + | 0.791012i | \(0.290446\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 680.000 | 0.650509 | 0.325254 | − | 0.945627i | \(-0.394550\pi\) | ||||
0.325254 | + | 0.945627i | \(0.394550\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 168.000 | 0.156144 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −996.000 | −0.899878 | −0.449939 | − | 0.893059i | \(-0.648554\pi\) | ||||
−0.449939 | + | 0.893059i | \(0.648554\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1382.00 | −1.21442 | −0.607209 | − | 0.794542i | \(-0.707711\pi\) | ||||
−0.607209 | + | 0.794542i | \(0.707711\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 440.000 | 0.376243 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −750.000 | −0.624372 | −0.312186 | − | 0.950021i | \(-0.601061\pi\) | ||||
−0.312186 | + | 0.950021i | \(0.601061\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1296.00 | −1.05089 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −902.000 | −0.712734 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −210.000 | −0.161770 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1187.00 | −0.891811 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 984.000 | 0.721336 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1284.00 | 0.918756 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 176.000 | 0.122972 | 0.0614861 | − | 0.998108i | \(-0.480416\pi\) | ||||
0.0614861 | + | 0.998108i | \(0.480416\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −688.000 | −0.469574 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1548.00 | 1.03244 | 0.516219 | − | 0.856457i | \(-0.327339\pi\) | ||||
0.516219 | + | 0.856457i | \(0.327339\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −476.000 | −0.310334 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −912.000 | −0.581426 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 378.000 | 0.235728 | 0.117864 | − | 0.993030i | \(-0.462395\pi\) | ||||
0.117864 | + | 0.993030i | \(0.462395\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2500.00 | 1.52552 | 0.762760 | − | 0.646682i | \(-0.223844\pi\) | ||||
0.762760 | + | 0.646682i | \(0.223844\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −768.000 | −0.458704 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 984.000 | 0.575428 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1476.00 | 0.845346 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −196.000 | −0.109971 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −846.000 | −0.465148 | −0.232574 | − | 0.972579i | \(-0.574715\pi\) | ||||
−0.232574 | + | 0.972579i | \(0.574715\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2536.00 | −1.36673 | −0.683367 | − | 0.730075i | \(-0.739485\pi\) | ||||
−0.683367 | + | 0.730075i | \(0.739485\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 330.000 | 0.174372 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 672.000 | 0.348234 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1186.00 | 0.602886 | 0.301443 | − | 0.953484i | \(-0.402532\pi\) | ||||
0.301443 | + | 0.953484i | \(0.402532\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 2232.00 | 1.11326 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1512.00 | 0.740138 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −2108.00 | −1.01295 | −0.506476 | − | 0.862254i | \(-0.669052\pi\) | ||||
−0.506476 | + | 0.862254i | \(0.669052\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 288.000 | 0.135883 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −1944.00 | −0.900786 | −0.450393 | − | 0.892830i | \(-0.648716\pi\) | ||||
−0.450393 | + | 0.892830i | \(0.648716\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 4527.00 | 2.06054 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 748.000 | 0.334509 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 1362.00 | 0.598560 | 0.299280 | − | 0.954165i | \(-0.403253\pi\) | ||||
0.299280 | + | 0.954165i | \(0.403253\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −623.000 | −0.269111 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 2160.00 | 0.917263 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −1596.00 | −0.666428 | −0.333214 | − | 0.942851i | \(-0.608133\pi\) | ||||
−0.333214 | + | 0.942851i | \(0.608133\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1690.00 | 0.694015 | 0.347007 | − | 0.937862i | \(-0.387198\pi\) | ||||
0.347007 | + | 0.937862i | \(0.387198\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 440.000 | 0.177736 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 660.000 | 0.262293 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −360.000 | −0.140780 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 1064.00 | 0.409495 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 3552.00 | 1.34562 | 0.672811 | − | 0.739815i | \(-0.265087\pi\) | ||||
0.672811 | + | 0.739815i | \(0.265087\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −2686.00 | −1.00177 | −0.500887 | − | 0.865512i | \(-0.666993\pi\) | ||||
−0.500887 | + | 0.865512i | \(0.666993\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 1968.00 | 0.722725 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 1410.00 | 0.509941 | 0.254970 | − | 0.966949i | \(-0.417934\pi\) | ||||
0.254970 | + | 0.966949i | \(0.417934\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −2968.00 | −1.05727 | −0.528633 | − | 0.848850i | \(-0.677295\pi\) | ||||
−0.528633 | + | 0.848850i | \(0.677295\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 560.000 | 0.196514 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −1722.00 | −0.595373 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1476.00 | 0.502870 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −2376.00 | −0.797794 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −816.000 | −0.270067 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1348.00 | 0.439811 | 0.219906 | − | 0.975521i | \(-0.429425\pi\) | ||||
0.219906 | + | 0.975521i | \(0.429425\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 3360.00 | 1.08086 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −1032.00 | −0.327357 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −784.000 | −0.245260 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 2200.00 | 0.678823 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −2460.00 | −0.748767 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 3872.00 | 1.16273 | 0.581364 | − | 0.813644i | \(-0.302519\pi\) | ||||
0.581364 | + | 0.813644i | \(0.302519\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 979.000 | 0.290074 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −5364.00 | −1.56838 | −0.784188 | − | 0.620524i | \(-0.786920\pi\) | ||||
−0.784188 | + | 0.620524i | \(0.786920\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 874.000 | 0.252208 | 0.126104 | − | 0.992017i | \(-0.459753\pi\) | ||||
0.126104 | + | 0.992017i | \(0.459753\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −336.000 | −0.0957021 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 378.000 | 0.106282 | 0.0531408 | − | 0.998587i | \(-0.483077\pi\) | ||||
0.0531408 | + | 0.998587i | \(0.483077\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1152.00 | −0.319780 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 832.000 | 0.228035 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 1920.00 | 0.519642 | 0.259821 | − | 0.965657i | \(-0.416336\pi\) | ||||
0.259821 | + | 0.965657i | \(0.416336\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 4322.00 | 1.15521 | 0.577603 | − | 0.816318i | \(-0.303988\pi\) | ||||
0.577603 | + | 0.816318i | \(0.303988\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −2860.00 | −0.755017 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −294.000 | −0.0766652 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −5576.00 | −1.43641 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 2064.00 | 0.525304 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −5292.00 | −1.33079 | −0.665395 | − | 0.746492i | \(-0.731737\pi\) | ||||
−0.665395 | + | 0.746492i | \(0.731737\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2592.00 | 0.644101 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −720.000 | −0.176816 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −5118.00 | −1.24223 | −0.621113 | − | 0.783721i | \(-0.713319\pi\) | ||||
−0.621113 | + | 0.783721i | \(0.713319\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −770.000 | −0.184732 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 2706.00 | 0.641752 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 3768.00 | 0.883440 | 0.441720 | − | 0.897153i | \(-0.354368\pi\) | ||||
0.441720 | + | 0.897153i | \(0.354368\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 3348.00 | 0.776098 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 5592.00 | 1.28174 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −3918.00 | −0.888047 | −0.444024 | − | 0.896015i | \(-0.646449\pi\) | ||||
−0.444024 | + | 0.896015i | \(0.646449\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 4880.00 | 1.09387 | 0.546935 | − | 0.837175i | \(-0.315794\pi\) | ||||
0.546935 | + | 0.837175i | \(0.315794\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −2296.00 | −0.509012 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −1068.00 | −0.234192 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 3538.00 | 0.767429 | 0.383714 | − | 0.923452i | \(-0.374645\pi\) | ||||
0.383714 | + | 0.923452i | \(0.374645\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 1232.00 | 0.264365 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −5430.00 | −1.15276 | −0.576382 | − | 0.817180i | \(-0.695536\pi\) | ||||
−0.576382 | + | 0.817180i | \(0.695536\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 6436.00 | 1.35187 | 0.675937 | − | 0.736959i | \(-0.263739\pi\) | ||||
0.675937 | + | 0.736959i | \(0.263739\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −1632.00 | −0.339198 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −1722.00 | −0.354169 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −4013.00 | −0.816813 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −6344.00 | −1.27798 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −1350.00 | −0.269174 | −0.134587 | − | 0.990902i | \(-0.542971\pi\) | ||||
−0.134587 | + | 0.990902i | \(0.542971\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 3240.00 | 0.639458 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 1824.00 | 0.356361 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 17712.0 | 3.42579 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1204.00 | 0.230556 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −4968.00 | −0.941928 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 660.000 | 0.123907 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −3332.00 | −0.619437 | −0.309719 | − | 0.950828i | \(-0.600235\pi\) | ||||
−0.309719 | + | 0.950828i | \(0.600235\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −2720.00 | −0.500762 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −4728.00 | −0.862059 | −0.431029 | − | 0.902338i | \(-0.641849\pi\) | ||||
−0.431029 | + | 0.902338i | \(0.641849\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 5114.00 | 0.923516 | 0.461758 | − | 0.887006i | \(-0.347219\pi\) | ||||
0.461758 | + | 0.887006i | \(0.347219\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 462.000 | 0.0826373 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −7206.00 | −1.27675 | −0.638374 | − | 0.769726i | \(-0.720393\pi\) | ||||
−0.638374 | + | 0.769726i | \(0.720393\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −2952.00 | −0.518120 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 3984.00 | 0.692726 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 2040.00 | 0.351420 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −7298.00 | −1.24560 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 5528.00 | 0.934860 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 1344.00 | 0.225219 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −6260.00 | −1.03952 | −0.519759 | − | 0.854313i | \(-0.673978\pi\) | ||||
−0.519759 | + | 0.854313i | \(0.673978\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 1210.00 | 0.199122 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 840.000 | 0.136997 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −5326.00 | −0.860907 | −0.430454 | − | 0.902613i | \(-0.641646\pi\) | ||||
−0.430454 | + | 0.902613i | \(0.641646\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 3000.00 | 0.480642 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −1344.00 | −0.213436 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 343.000 | 0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 5184.00 | 0.808977 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −36.0000 | −0.00556940 | −0.00278470 | − | 0.999996i | \(-0.500886\pi\) | ||||
−0.00278470 | + | 0.999996i | \(0.500886\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −3134.00 | −0.480685 | −0.240343 | − | 0.970688i | \(-0.577260\pi\) | ||||
−0.240343 | + | 0.970688i | \(0.577260\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 12464.0 | 1.89538 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 1218.00 | 0.183648 | 0.0918238 | − | 0.995775i | \(-0.470730\pi\) | ||||
0.0918238 | + | 0.995775i | \(0.470730\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 5040.00 | 0.753508 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 840.000 | 0.124531 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −10008.0 | −1.47131 | −0.735657 | − | 0.677354i | \(-0.763127\pi\) | ||||
−0.735657 | + | 0.677354i | \(0.763127\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −2235.00 | −0.325849 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 4748.00 | 0.686516 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 3300.00 | 0.473233 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −1072.00 | −0.152474 | −0.0762370 | − | 0.997090i | \(-0.524291\pi\) | ||||
−0.0762370 | + | 0.997090i | \(0.524291\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 2706.00 | 0.381758 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −3906.00 | −0.546602 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 274.000 | 0.0380353 | 0.0190177 | − | 0.999819i | \(-0.493946\pi\) | ||||
0.0190177 | + | 0.999819i | \(0.493946\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −5136.00 | −0.707258 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −20172.0 | −2.75573 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −7652.00 | −1.03709 | −0.518545 | − | 0.855051i | \(-0.673526\pi\) | ||||
−0.518545 | + | 0.855051i | \(0.673526\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −704.000 | −0.0946641 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 2160.00 | 0.288175 | 0.144087 | − | 0.989565i | \(-0.453975\pi\) | ||||
0.144087 | + | 0.989565i | \(0.453975\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −504.000 | −0.0667175 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −1892.00 | −0.248516 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 1074.00 | 0.139984 | 0.0699922 | − | 0.997548i | \(-0.477703\pi\) | ||||
0.0699922 | + | 0.997548i | \(0.477703\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −6480.00 | −0.838127 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −6192.00 | −0.794771 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 1248.00 | 0.158971 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −6926.00 | −0.875582 | −0.437791 | − | 0.899077i | \(-0.644239\pi\) | ||||
−0.437791 | + | 0.899077i | \(0.644239\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 1904.00 | 0.238895 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 1938.00 | 0.241344 | 0.120672 | − | 0.992692i | \(-0.461495\pi\) | ||||
0.120672 | + | 0.992692i | \(0.461495\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −9184.00 | −1.13521 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 1866.00 | 0.228944 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −1320.00 | −0.160762 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −9574.00 | −1.15747 | −0.578733 | − | 0.815517i | \(-0.696453\pi\) | ||||
−0.578733 | + | 0.815517i | \(0.696453\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −1512.00 | −0.181463 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −3780.00 | −0.450367 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 3096.00 | 0.366209 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −10000.0 | −1.17435 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 5052.00 | 0.589037 | 0.294518 | − | 0.955646i | \(-0.404841\pi\) | ||||
0.294518 | + | 0.955646i | \(0.404841\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −3422.00 | −0.396147 | −0.198074 | − | 0.980187i | \(-0.563469\pi\) | ||||
−0.198074 | + | 0.980187i | \(0.563469\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −2112.00 | −0.242763 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 2670.00 | 0.304739 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −770.000 | −0.0872668 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −3936.00 | −0.442965 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 2208.00 | 0.246765 | 0.123382 | − | 0.992359i | \(-0.460626\pi\) | ||||
0.123382 | + | 0.992359i | \(0.460626\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −6814.00 | −0.756259 | −0.378129 | − | 0.925753i | \(-0.623433\pi\) | ||||
−0.378129 | + | 0.925753i | \(0.623433\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −5904.00 | −0.650747 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −14688.0 | −1.60783 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 12584.0 | 1.36811 | 0.684056 | − | 0.729429i | \(-0.260214\pi\) | ||||
0.684056 | + | 0.729429i | \(0.260214\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −539.000 | −0.0582011 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −6996.00 | −0.750316 | −0.375158 | − | 0.926961i | \(-0.622412\pi\) | ||||
−0.375158 | + | 0.926961i | \(0.622412\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 8388.00 | 0.893549 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 3384.00 | 0.358071 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 9474.00 | 0.995781 | 0.497891 | − | 0.867240i | \(-0.334108\pi\) | ||||
0.497891 | + | 0.867240i | \(0.334108\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −2952.00 | −0.308213 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 10144.0 | 1.05211 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −3444.00 | −0.354851 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 5786.00 | 0.592249 | 0.296124 | − | 0.955149i | \(-0.404306\pi\) | ||||
0.296124 | + | 0.955149i | \(0.404306\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −4560.00 | −0.463709 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −3438.00 | −0.347340 | −0.173670 | − | 0.984804i | \(-0.555563\pi\) | ||||
−0.173670 | + | 0.984804i | \(0.555563\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 9392.00 | 0.942728 | 0.471364 | − | 0.881939i | \(-0.343762\pi\) | ||||
0.471364 | + | 0.881939i | \(0.343762\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −2688.00 | −0.268071 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 4956.00 | 0.491084 | 0.245542 | − | 0.969386i | \(-0.421034\pi\) | ||||
0.245542 | + | 0.969386i | \(0.421034\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −980.000 | −0.0964866 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −4744.00 | −0.464102 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 2064.00 | 0.200640 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 6052.00 | 0.584600 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 6138.00 | 0.589182 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −20592.0 | −1.96424 | −0.982122 | − | 0.188248i | \(-0.939719\pi\) | ||||
−0.982122 | + | 0.188248i | \(0.939719\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −9020.00 | −0.855045 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −6048.00 | −0.569759 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −9516.00 | −0.890926 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −13432.0 | −1.24982 | −0.624910 | − | 0.780697i | \(-0.714864\pi\) | ||||
−0.624910 | + | 0.780697i | \(0.714864\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 8432.00 | 0.779771 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 14172.0 | 1.30259 | 0.651297 | − | 0.758823i | \(-0.274225\pi\) | ||||
0.651297 | + | 0.758823i | \(0.274225\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 7380.00 | 0.674196 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 792.000 | 0.0719147 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −5880.00 | −0.530692 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 5956.00 | 0.534323 | 0.267162 | − | 0.963652i | \(-0.413914\pi\) | ||||
0.267162 | + | 0.963652i | \(0.413914\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 7776.00 | 0.693425 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 16968.0 | 1.50411 | 0.752053 | − | 0.659102i | \(-0.229064\pi\) | ||||
0.752053 | + | 0.659102i | \(0.229064\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −7452.00 | −0.656653 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −18108.0 | −1.58620 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −5214.00 | −0.454040 | −0.227020 | − | 0.973890i | \(-0.572898\pi\) | ||||
−0.227020 | + | 0.973890i | \(0.572898\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −3850.00 | −0.333295 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −10336.0 | −0.889562 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −4080.00 | −0.349100 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 2304.00 | 0.195996 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −5448.00 | −0.460772 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −1398.00 | −0.117558 | −0.0587788 | − | 0.998271i | \(-0.518721\pi\) | ||||
−0.0587788 | + | 0.998271i | \(0.518721\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 18580.0 | 1.55344 | 0.776718 | − | 0.629849i | \(-0.216883\pi\) | ||||
0.776718 | + | 0.629849i | \(0.216883\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 2492.00 | 0.207162 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 3360.00 | 0.277730 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 34489.0 | 2.83463 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 5940.00 | 0.485450 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −20172.0 | −1.63930 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 5976.00 | 0.482925 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 6384.00 | 0.513017 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 588.000 | 0.0469888 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 18970.0 | 1.50755 | 0.753774 | − | 0.657133i | \(-0.228231\pi\) | ||||
0.753774 | + | 0.657133i | \(0.228231\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −6760.00 | −0.534253 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 8292.00 | 0.651725 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 16036.0 | 1.25347 | 0.626737 | − | 0.779231i | \(-0.284390\pi\) | ||||
0.626737 | + | 0.779231i | \(0.284390\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 1210.00 | 0.0940647 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 16728.0 | 1.29335 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −1456.00 | −0.111963 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −2640.00 | −0.201913 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −8310.00 | −0.632147 | −0.316074 | − | 0.948735i | \(-0.602365\pi\) | ||||
−0.316074 | + | 0.948735i | \(0.602365\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 14104.0 | 1.06715 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 1440.00 | 0.108372 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −7092.00 | −0.530892 | −0.265446 | − | 0.964126i | \(-0.585519\pi\) | ||||
−0.265446 | + | 0.964126i | \(0.585519\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 4500.00 | 0.335073 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −2177.00 | −0.161244 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −7158.00 | −0.527380 | −0.263690 | − | 0.964608i | \(-0.584940\pi\) | ||||
−0.263690 | + | 0.964608i | \(0.584940\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −6500.00 | −0.476386 | −0.238193 | − | 0.971218i | \(-0.576555\pi\) | ||||
−0.238193 | + | 0.971218i | \(0.576555\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −14208.0 | −1.03586 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −19224.0 | −1.39425 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 21794.0 | 1.57244 | 0.786218 | − | 0.617949i | \(-0.212036\pi\) | ||||
0.786218 | + | 0.617949i | \(0.212036\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 10744.0 | 0.771166 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −3612.00 | −0.257919 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −6696.00 | −0.475678 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 5412.00 | 0.382493 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −9756.00 | −0.685985 | −0.342993 | − | 0.939338i | \(-0.611441\pi\) | ||||
−0.342993 | + | 0.939338i | \(0.611441\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 7616.00 | 0.532787 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −5640.00 | −0.392553 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 5586.00 | 0.386829 | 0.193414 | − | 0.981117i | \(-0.438044\pi\) | ||||
0.193414 | + | 0.981117i | \(0.438044\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1260.00 | 0.0868151 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 11872.0 | 0.813884 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −24.0000 | −0.00163708 | −0.000818542 | − | 1.00000i | \(-0.500261\pi\) | ||||
−0.000818542 | 1.00000i | \(0.500261\pi\) | ||||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 4298.00 | 0.291712 | 0.145856 | − | 0.989306i | \(-0.453406\pi\) | ||||
0.145856 | + | 0.989306i | \(0.453406\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 1540.00 | 0.104003 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 7122.00 | 0.478596 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 8480.00 | 0.567039 | 0.283519 | − | 0.958966i | \(-0.408498\pi\) | ||||
0.283519 | + | 0.958966i | \(0.408498\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 6888.00 | 0.458318 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 15744.0 | 1.04245 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 1906.00 | 0.125583 | 0.0627917 | − | 0.998027i | \(-0.480000\pi\) | ||||
0.0627917 | + | 0.998027i | \(0.480000\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −5904.00 | −0.387109 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 7482.00 | 0.488191 | 0.244096 | − | 0.969751i | \(-0.421509\pi\) | ||||
0.244096 | + | 0.969751i | \(0.421509\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 7348.00 | 0.477126 | 0.238563 | − | 0.971127i | \(-0.423324\pi\) | ||||
0.238563 | + | 0.971127i | \(0.423324\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 32832.0 | 2.12158 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −9786.00 | −0.629322 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 3421.00 | 0.218944 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 3264.00 | 0.207897 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 3300.00 | 0.209189 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 4520.00 | 0.285164 | 0.142582 | − | 0.989783i | \(-0.454460\pi\) | ||||
0.142582 | + | 0.989783i | \(0.454460\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −5392.00 | −0.338567 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −1056.00 | −0.0659938 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 4018.00 | 0.249920 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 9240.00 | 0.572032 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −19806.0 | −1.22042 | −0.610211 | − | 0.792239i | \(-0.708915\pi\) | ||||
−0.610211 | + | 0.792239i | \(0.708915\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 5020.00 | 0.307884 | 0.153942 | − | 0.988080i | \(-0.450803\pi\) | ||||
0.153942 | + | 0.988080i | \(0.450803\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 4128.00 | 0.252000 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 28392.0 | 1.72520 | 0.862600 | − | 0.505886i | \(-0.168834\pi\) | ||||
0.862600 | + | 0.505886i | \(0.168834\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −6480.00 | −0.391930 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 3136.00 | 0.188801 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 17562.0 | 1.05246 | 0.526228 | − | 0.850343i | \(-0.323606\pi\) | ||||
0.526228 | + | 0.850343i | \(0.323606\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −9288.00 | −0.554064 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 6050.00 | 0.359259 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −4716.00 | −0.278770 | −0.139385 | − | 0.990238i | \(-0.544513\pi\) | ||||
−0.139385 | + | 0.990238i | \(0.544513\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 22762.0 | 1.33939 | 0.669697 | − | 0.742635i | \(-0.266424\pi\) | ||||
0.669697 | + | 0.742635i | \(0.266424\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 9840.00 | 0.576401 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 2856.00 | 0.166543 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −53136.0 | −3.08461 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −15488.0 | −0.895068 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −1320.00 | −0.0759434 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 4802.00 | 0.275042 | 0.137521 | − | 0.990499i | \(-0.456086\pi\) | ||||
0.137521 | + | 0.990499i | \(0.456086\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −13528.0 | −0.771397 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −21558.0 | −1.22384 | −0.611921 | − | 0.790919i | \(-0.709603\pi\) | ||||
−0.611921 | + | 0.790919i | \(0.709603\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 11102.0 | 0.627475 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 21456.0 | 1.20734 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −3780.00 | −0.211768 | −0.105884 | − | 0.994378i | \(-0.533767\pi\) | ||||
−0.105884 | + | 0.994378i | \(0.533767\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −2268.00 | −0.126505 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −3496.00 | −0.194150 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −45756.0 | −2.52999 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 5500.00 | 0.302793 | 0.151396 | − | 0.988473i | \(-0.451623\pi\) | ||||
0.151396 | + | 0.988473i | \(0.451623\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −924.000 | −0.0506491 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −15000.0 | −0.818680 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 7380.00 | 0.401058 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −1512.00 | −0.0818156 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −10230.0 | −0.551187 | −0.275593 | − | 0.961274i | \(-0.588874\pi\) | ||||
−0.275593 | + | 0.961274i | \(0.588874\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 7480.00 | 0.401299 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 4608.00 | 0.246166 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 8694.00 | 0.462477 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −10190.0 | −0.539765 | −0.269883 | − | 0.962893i | \(-0.586985\pi\) | ||||
−0.269883 | + | 0.962893i | \(0.586985\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 2288.00 | 0.120685 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −24192.0 | −1.27068 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −5904.00 | −0.308807 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −7680.00 | −0.400021 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 9408.00 | 0.487982 | 0.243991 | − | 0.969777i | \(-0.421543\pi\) | ||||
0.243991 | + | 0.969777i | \(0.421543\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 4760.00 | 0.245869 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −17288.0 | −0.889278 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 21894.0 | 1.12155 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −33064.0 | −1.68676 | −0.843381 | − | 0.537316i | \(-0.819438\pi\) | ||||
−0.843381 | + | 0.537316i | \(0.819438\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 19837.0 | 1.00782 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −5160.00 | −0.261080 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 6322.00 | 0.318565 | 0.159283 | − | 0.987233i | \(-0.449082\pi\) | ||||
0.159283 | + | 0.987233i | \(0.449082\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 1176.00 | 0.0590169 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −1680.00 | −0.0839669 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 20740.0 | 1.03239 | 0.516193 | − | 0.856472i | \(-0.327349\pi\) | ||||
0.516193 | + | 0.856472i | \(0.327349\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 22304.0 | 1.10575 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 32040.0 | 1.58201 | 0.791005 | − | 0.611810i | \(-0.209558\pi\) | ||||
0.791005 | + | 0.611810i | \(0.209558\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 5076.00 | 0.249624 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 5676.00 | 0.278011 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −6972.00 | −0.340122 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −12832.0 | −0.623497 | −0.311749 | − | 0.950165i | \(-0.600915\pi\) | ||||
−0.311749 | + | 0.950165i | \(0.600915\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 21168.0 | 1.02444 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 15216.0 | 0.733466 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 19906.0 | 0.955741 | 0.477870 | − | 0.878430i | \(-0.341409\pi\) | ||||
0.477870 | + | 0.878430i | \(0.341409\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −10368.0 | −0.495829 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 10842.0 | 0.516455 | 0.258227 | − | 0.966084i | \(-0.416862\pi\) | ||||
0.258227 | + | 0.966084i | \(0.416862\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −9674.00 | −0.459007 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −1980.00 | −0.0935778 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −44280.0 | −2.08456 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 28274.0 | 1.32586 | 0.662930 | − | 0.748681i | \(-0.269313\pi\) | ||||
0.662930 | + | 0.748681i | \(0.269313\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 20472.0 | 0.956266 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 32346.0 | 1.50505 | 0.752526 | − | 0.658563i | \(-0.228835\pi\) | ||||
0.752526 | + | 0.658563i | \(0.228835\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 9968.00 | 0.462014 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 3080.00 | 0.142206 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 16728.0 | 0.769375 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −10080.0 | −0.461832 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −37392.0 | −1.70662 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −7116.00 | −0.323543 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −30116.0 | −1.36407 | −0.682033 | − | 0.731322i | \(-0.738904\pi\) | ||||
−0.682033 | + | 0.731322i | \(0.738904\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −15072.0 | −0.680073 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −5250.00 | −0.235991 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −9020.00 | −0.403921 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −13392.0 | −0.597441 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 6594.00 | 0.293063 | 0.146532 | − | 0.989206i | \(-0.453189\pi\) | ||||
0.146532 | + | 0.989206i | \(0.453189\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −5760.00 | −0.255036 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 15378.0 | 0.678346 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −6600.00 | −0.290048 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −9072.00 | −0.397200 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 15672.0 | 0.683619 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −43014.0 | −1.86933 | −0.934667 | − | 0.355524i | \(-0.884303\pi\) | ||||
−0.934667 | + | 0.355524i | \(0.884303\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 14164.0 | 0.613274 | 0.306637 | − | 0.951827i | \(-0.400796\pi\) | ||||
0.306637 | + | 0.951827i | \(0.400796\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −19520.0 | −0.842062 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 12648.0 | 0.543608 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −11696.0 | −0.500846 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −6314.00 | −0.269388 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −34830.0 | −1.48060 | −0.740302 | − | 0.672275i | \(-0.765317\pi\) | ||||
−0.740302 | + | 0.672275i | \(0.765317\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 31016.0 | 1.31367 | 0.656835 | − | 0.754035i | \(-0.271895\pi\) | ||||
0.656835 | + | 0.754035i | \(0.271895\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 4272.00 | 0.180281 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −9876.00 | −0.415263 | −0.207631 | − | 0.978207i | \(-0.566575\pi\) | ||||
−0.207631 | + | 0.978207i | \(0.566575\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 3154.00 | 0.132139 | 0.0660693 | − | 0.997815i | \(-0.478954\pi\) | ||||
0.0660693 | + | 0.997815i | \(0.478954\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −14152.0 | −0.590767 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −1470.00 | −0.0611434 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 11664.0 | 0.483412 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −17024.0 | −0.703029 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 36936.0 | 1.51987 | 0.759936 | − | 0.649998i | \(-0.225230\pi\) | ||||
0.759936 | + | 0.649998i | \(0.225230\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 36127.0 | 1.48128 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 21720.0 | 0.887398 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −27162.0 | −1.10580 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −8309.00 | −0.337073 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −25744.0 | −1.04067 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −23760.0 | −0.957088 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −9638.00 | −0.386869 | −0.193434 | − | 0.981113i | \(-0.561963\pi\) | ||||
−0.193434 | + | 0.981113i | \(0.561963\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −4488.00 | −0.179516 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 10266.0 | 0.409195 | 0.204597 | − | 0.978846i | \(-0.434411\pi\) | ||||
0.204597 | + | 0.978846i | \(0.434411\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 4084.00 | 0.162217 | 0.0811084 | − | 0.996705i | \(-0.474154\pi\) | ||||
0.0811084 | + | 0.996705i | \(0.474154\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 6888.00 | 0.272639 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −192.000 | −0.00757330 | −0.00378665 | − | 0.999993i | \(-0.501205\pi\) | ||||
−0.00378665 | + | 0.999993i | \(0.501205\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −8172.00 | −0.321221 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 16052.0 | 0.628783 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −2496.00 | −0.0974350 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −11480.0 | −0.446596 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −17446.0 | −0.676355 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 8988.00 | 0.347257 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −19910.0 | −0.766605 | −0.383303 | − | 0.923623i | \(-0.625213\pi\) | ||||
−0.383303 | + | 0.923623i | \(0.625213\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 5400.00 | 0.207210 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 14802.0 | 0.566052 | 0.283026 | − | 0.959112i | \(-0.408662\pi\) | ||||
0.283026 | + | 0.959112i | \(0.408662\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 32548.0 | 1.24046 | 0.620231 | − | 0.784419i | \(-0.287039\pi\) | ||||
0.620231 | + | 0.784419i | \(0.287039\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −12960.0 | −0.492255 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 1464.00 | 0.0554186 | 0.0277093 | − | 0.999616i | \(-0.491179\pi\) | ||||
0.0277093 | + | 0.999616i | \(0.491179\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1232.00 | 0.0464791 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −3732.00 | −0.140322 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −13056.0 | −0.489252 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 9576.00 | 0.357643 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −70848.0 | −2.63717 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 27552.0 | 1.02215 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 16740.0 | 0.618968 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −4816.00 | −0.177482 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −10140.0 | −0.372448 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 49564.0 | 1.81449 | 0.907247 | − | 0.420599i | \(-0.138180\pi\) | ||||
0.907247 | + | 0.420599i | \(0.138180\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −13662.0 | −0.498504 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 8448.00 | 0.307239 | 0.153619 | − | 0.988130i | \(-0.450907\pi\) | ||||
0.153619 | + | 0.988130i | \(0.450907\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −6192.00 | −0.224453 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −2640.00 | −0.0953833 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 10836.0 | 0.390225 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 14600.0 | 0.524058 | 0.262029 | − | 0.965060i | \(-0.415608\pi\) | ||||
0.262029 | + | 0.965060i | \(0.415608\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 13328.0 | 0.476843 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −68880.0 | −2.45635 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 9790.00 | 0.347993 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −7480.00 | −0.265022 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −21102.0 | −0.745247 | −0.372623 | − | 0.927983i | \(-0.621542\pi\) | ||||
−0.372623 | + | 0.927983i | \(0.621542\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −3332.00 | −0.117295 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 18912.0 | 0.663613 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 2160.00 | 0.0755503 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −20806.0 | −0.725403 | −0.362701 | − | 0.931905i | \(-0.618146\pi\) | ||||
−0.362701 | + | 0.931905i | \(0.618146\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −20456.0 | −0.710923 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −24510.0 | −0.849100 | −0.424550 | − | 0.905404i | \(-0.639568\pi\) | ||||
−0.424550 | + | 0.905404i | \(0.639568\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −53136.0 | −1.83494 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −6384.00 | −0.219758 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 44148.0 | 1.51491 | 0.757454 | − | 0.652889i | \(-0.226443\pi\) | ||||
0.757454 | + | 0.652889i | \(0.226443\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −45100.0 | −1.54268 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 28824.0 | 0.982841 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 27114.0 | 0.921625 | 0.460812 | − | 0.887498i | \(-0.347558\pi\) | ||||
0.460812 | + | 0.887498i | \(0.347558\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −21312.0 | −0.722136 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 11808.0 | 0.398849 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 2646.00 | 0.0890968 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −17247.0 | −0.578933 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 10956.0 | 0.366617 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 16116.0 | 0.537609 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −10264.0 | −0.341332 | −0.170666 | − | 0.985329i | \(-0.554592\pi\) | ||||
−0.170666 | + | 0.985329i | \(0.554592\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −8160.00 | −0.270523 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −51468.0 | −1.70102 | −0.850508 | − | 0.525962i | \(-0.823705\pi\) | ||||
−0.850508 | + | 0.525962i | \(0.823705\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 17500.0 | 0.576592 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 29192.0 | 0.958864 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −23790.0 | −0.779027 | −0.389514 | − | 0.921021i | \(-0.627357\pi\) | ||||
−0.389514 | + | 0.921021i | \(0.627357\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −16776.0 | −0.547664 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 15202.0 | 0.494763 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 26424.0 | 0.857370 | 0.428685 | − | 0.903454i | \(-0.358977\pi\) | ||||
0.428685 | + | 0.903454i | \(0.358977\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −8460.00 | −0.273663 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −5376.00 | −0.173374 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 37152.0 | 1.19450 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 39488.0 | 1.26577 | 0.632885 | − | 0.774246i | \(-0.281871\pi\) | ||||
0.632885 | + | 0.774246i | \(0.281871\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 25040.0 | 0.800222 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 17808.0 | 0.567388 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −30854.0 | −0.980096 | −0.490048 | − | 0.871695i | \(-0.663021\pi\) | ||||
−0.490048 | + | 0.871695i | \(0.663021\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −16720.0 | −0.529527 |
(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 | 448.4.a.d.1.1 | 1 | ||
4.3 | odd | 2 | 448.4.a.m.1.1 | 1 | |||
8.3 | odd | 2 | 112.4.a.c.1.1 | 1 | |||
8.5 | even | 2 | 28.4.a.b.1.1 | ✓ | 1 | ||
24.5 | odd | 2 | 252.4.a.c.1.1 | 1 | |||
24.11 | even | 2 | 1008.4.a.f.1.1 | 1 | |||
40.13 | odd | 4 | 700.4.e.f.449.2 | 2 | |||
40.29 | even | 2 | 700.4.a.e.1.1 | 1 | |||
40.37 | odd | 4 | 700.4.e.f.449.1 | 2 | |||
56.5 | odd | 6 | 196.4.e.d.165.1 | 2 | |||
56.13 | odd | 2 | 196.4.a.b.1.1 | 1 | |||
56.27 | even | 2 | 784.4.a.n.1.1 | 1 | |||
56.37 | even | 6 | 196.4.e.c.165.1 | 2 | |||
56.45 | odd | 6 | 196.4.e.d.177.1 | 2 | |||
56.53 | even | 6 | 196.4.e.c.177.1 | 2 | |||
168.5 | even | 6 | 1764.4.k.e.361.1 | 2 | |||
168.53 | odd | 6 | 1764.4.k.k.1549.1 | 2 | |||
168.101 | even | 6 | 1764.4.k.e.1549.1 | 2 | |||
168.125 | even | 2 | 1764.4.a.k.1.1 | 1 | |||
168.149 | odd | 6 | 1764.4.k.k.361.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
28.4.a.b.1.1 | ✓ | 1 | 8.5 | even | 2 | ||
112.4.a.c.1.1 | 1 | 8.3 | odd | 2 | |||
196.4.a.b.1.1 | 1 | 56.13 | odd | 2 | |||
196.4.e.c.165.1 | 2 | 56.37 | even | 6 | |||
196.4.e.c.177.1 | 2 | 56.53 | even | 6 | |||
196.4.e.d.165.1 | 2 | 56.5 | odd | 6 | |||
196.4.e.d.177.1 | 2 | 56.45 | odd | 6 | |||
252.4.a.c.1.1 | 1 | 24.5 | odd | 2 | |||
448.4.a.d.1.1 | 1 | 1.1 | even | 1 | trivial | ||
448.4.a.m.1.1 | 1 | 4.3 | odd | 2 | |||
700.4.a.e.1.1 | 1 | 40.29 | even | 2 | |||
700.4.e.f.449.1 | 2 | 40.37 | odd | 4 | |||
700.4.e.f.449.2 | 2 | 40.13 | odd | 4 | |||
784.4.a.n.1.1 | 1 | 56.27 | even | 2 | |||
1008.4.a.f.1.1 | 1 | 24.11 | even | 2 | |||
1764.4.a.k.1.1 | 1 | 168.125 | even | 2 | |||
1764.4.k.e.361.1 | 2 | 168.5 | even | 6 | |||
1764.4.k.e.1549.1 | 2 | 168.101 | even | 6 | |||
1764.4.k.k.361.1 | 2 | 168.149 | odd | 6 | |||
1764.4.k.k.1549.1 | 2 | 168.53 | odd | 6 |