Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2450,4,Mod(1,2450)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2450, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("2450.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2450 = 2 \cdot 5^{2} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 2450.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: | \(144.554679514\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 146x^{6} + 4997x^{4} - 4646x^{2} + 676 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 2\cdot 7^{2}\cdot 11^{2} \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.8 | ||
Root | \(7.24569\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2450.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.00000 | −0.707107 | ||||||||
\(3\) | 8.65990 | 1.66660 | 0.833299 | − | 0.552822i | \(-0.186449\pi\) | ||||
0.833299 | + | 0.552822i | \(0.186449\pi\) | |||||||
\(4\) | 4.00000 | 0.500000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −17.3198 | −1.17846 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −8.00000 | −0.353553 | ||||||||
\(9\) | 47.9939 | 1.77755 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 22.1723 | 0.607745 | 0.303872 | − | 0.952713i | \(-0.401720\pi\) | ||||
0.303872 | + | 0.952713i | \(0.401720\pi\) | |||||||
\(12\) | 34.6396 | 0.833299 | ||||||||
\(13\) | 66.1544 | 1.41138 | 0.705689 | − | 0.708522i | \(-0.250638\pi\) | ||||
0.705689 | + | 0.708522i | \(0.250638\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 16.0000 | 0.250000 | ||||||||
\(17\) | 132.325 | 1.88785 | 0.943927 | − | 0.330155i | \(-0.107101\pi\) | ||||
0.943927 | + | 0.330155i | \(0.107101\pi\) | |||||||
\(18\) | −95.9878 | −1.25692 | ||||||||
\(19\) | 56.5761 | 0.683129 | 0.341565 | − | 0.939858i | \(-0.389043\pi\) | ||||
0.341565 | + | 0.939858i | \(0.389043\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −44.3445 | −0.429740 | ||||||||
\(23\) | −21.9085 | −0.198619 | −0.0993096 | − | 0.995057i | \(-0.531663\pi\) | ||||
−0.0993096 | + | 0.995057i | \(0.531663\pi\) | |||||||
\(24\) | −69.2792 | −0.589232 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −132.309 | −0.997995 | ||||||||
\(27\) | 181.805 | 1.29587 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −93.9344 | −0.601489 | −0.300744 | − | 0.953705i | \(-0.597235\pi\) | ||||
−0.300744 | + | 0.953705i | \(0.597235\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 299.832 | 1.73714 | 0.868570 | − | 0.495566i | \(-0.165039\pi\) | ||||
0.868570 | + | 0.495566i | \(0.165039\pi\) | |||||||
\(32\) | −32.0000 | −0.176777 | ||||||||
\(33\) | 192.010 | 1.01287 | ||||||||
\(34\) | −264.650 | −1.33491 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 191.976 | 0.888776 | ||||||||
\(37\) | 170.797 | 0.758889 | 0.379445 | − | 0.925214i | \(-0.376115\pi\) | ||||
0.379445 | + | 0.925214i | \(0.376115\pi\) | |||||||
\(38\) | −113.152 | −0.483045 | ||||||||
\(39\) | 572.890 | 2.35220 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −137.875 | −0.525182 | −0.262591 | − | 0.964907i | \(-0.584577\pi\) | ||||
−0.262591 | + | 0.964907i | \(0.584577\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −275.761 | −0.977979 | −0.488990 | − | 0.872290i | \(-0.662634\pi\) | ||||
−0.488990 | + | 0.872290i | \(0.662634\pi\) | |||||||
\(44\) | 88.6891 | 0.303872 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 43.8170 | 0.140445 | ||||||||
\(47\) | 100.717 | 0.312577 | 0.156289 | − | 0.987711i | \(-0.450047\pi\) | ||||
0.156289 | + | 0.987711i | \(0.450047\pi\) | |||||||
\(48\) | 138.558 | 0.416650 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 1145.92 | 3.14629 | ||||||||
\(52\) | 264.617 | 0.705689 | ||||||||
\(53\) | −36.2240 | −0.0938822 | −0.0469411 | − | 0.998898i | \(-0.514947\pi\) | ||||
−0.0469411 | + | 0.998898i | \(0.514947\pi\) | |||||||
\(54\) | −363.610 | −0.916316 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 489.944 | 1.13850 | ||||||||
\(58\) | 187.869 | 0.425317 | ||||||||
\(59\) | −717.346 | −1.58289 | −0.791445 | − | 0.611241i | \(-0.790671\pi\) | ||||
−0.791445 | + | 0.611241i | \(0.790671\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 722.798 | 1.51713 | 0.758564 | − | 0.651599i | \(-0.225901\pi\) | ||||
0.758564 | + | 0.651599i | \(0.225901\pi\) | |||||||
\(62\) | −599.663 | −1.22834 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 64.0000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −384.019 | −0.716205 | ||||||||
\(67\) | −123.976 | −0.226060 | −0.113030 | − | 0.993592i | \(-0.536056\pi\) | ||||
−0.113030 | + | 0.993592i | \(0.536056\pi\) | |||||||
\(68\) | 529.300 | 0.943927 | ||||||||
\(69\) | −189.726 | −0.331018 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −907.172 | −1.51636 | −0.758180 | − | 0.652046i | \(-0.773911\pi\) | ||||
−0.758180 | + | 0.652046i | \(0.773911\pi\) | |||||||
\(72\) | −383.951 | −0.628460 | ||||||||
\(73\) | −794.370 | −1.27362 | −0.636808 | − | 0.771023i | \(-0.719745\pi\) | ||||
−0.636808 | + | 0.771023i | \(0.719745\pi\) | |||||||
\(74\) | −341.594 | −0.536616 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 226.304 | 0.341565 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −1145.78 | −1.66326 | ||||||||
\(79\) | −1163.27 | −1.65669 | −0.828346 | − | 0.560217i | \(-0.810718\pi\) | ||||
−0.828346 | + | 0.560217i | \(0.810718\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 278.579 | 0.382139 | ||||||||
\(82\) | 275.750 | 0.371360 | ||||||||
\(83\) | 1130.09 | 1.49450 | 0.747249 | − | 0.664544i | \(-0.231374\pi\) | ||||
0.747249 | + | 0.664544i | \(0.231374\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 551.521 | 0.691536 | ||||||||
\(87\) | −813.463 | −1.00244 | ||||||||
\(88\) | −177.378 | −0.214870 | ||||||||
\(89\) | −897.342 | −1.06874 | −0.534371 | − | 0.845250i | \(-0.679452\pi\) | ||||
−0.534371 | + | 0.845250i | \(0.679452\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −87.6340 | −0.0993096 | ||||||||
\(93\) | 2596.51 | 2.89512 | ||||||||
\(94\) | −201.435 | −0.221026 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −277.117 | −0.294616 | ||||||||
\(97\) | 1517.68 | 1.58863 | 0.794315 | − | 0.607506i | \(-0.207830\pi\) | ||||
0.794315 | + | 0.607506i | \(0.207830\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1064.13 | 1.08030 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −45.5877 | −0.0449123 | −0.0224562 | − | 0.999748i | \(-0.507149\pi\) | ||||
−0.0224562 | + | 0.999748i | \(0.507149\pi\) | |||||||
\(102\) | −2291.84 | −2.22477 | ||||||||
\(103\) | −1063.01 | −1.01691 | −0.508456 | − | 0.861088i | \(-0.669784\pi\) | ||||
−0.508456 | + | 0.861088i | \(0.669784\pi\) | |||||||
\(104\) | −529.235 | −0.498998 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 72.4481 | 0.0663847 | ||||||||
\(107\) | 264.881 | 0.239318 | 0.119659 | − | 0.992815i | \(-0.461820\pi\) | ||||
0.119659 | + | 0.992815i | \(0.461820\pi\) | |||||||
\(108\) | 727.221 | 0.647934 | ||||||||
\(109\) | 885.061 | 0.777738 | 0.388869 | − | 0.921293i | \(-0.372866\pi\) | ||||
0.388869 | + | 0.921293i | \(0.372866\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 1479.09 | 1.26476 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −1605.55 | −1.33661 | −0.668305 | − | 0.743887i | \(-0.732980\pi\) | ||||
−0.668305 | + | 0.743887i | \(0.732980\pi\) | |||||||
\(114\) | −979.887 | −0.805043 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −375.738 | −0.300744 | ||||||||
\(117\) | 3175.01 | 2.50880 | ||||||||
\(118\) | 1434.69 | 1.11927 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −839.390 | −0.630646 | ||||||||
\(122\) | −1445.60 | −1.07277 | ||||||||
\(123\) | −1193.98 | −0.875268 | ||||||||
\(124\) | 1199.33 | 0.868570 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −2468.88 | −1.72502 | −0.862511 | − | 0.506038i | \(-0.831110\pi\) | ||||
−0.862511 | + | 0.506038i | \(0.831110\pi\) | |||||||
\(128\) | −128.000 | −0.0883883 | ||||||||
\(129\) | −2388.06 | −1.62990 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 2763.11 | 1.84285 | 0.921427 | − | 0.388551i | \(-0.127024\pi\) | ||||
0.921427 | + | 0.388551i | \(0.127024\pi\) | |||||||
\(132\) | 768.039 | 0.506433 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 247.951 | 0.159849 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −1058.60 | −0.667457 | ||||||||
\(137\) | −337.270 | −0.210328 | −0.105164 | − | 0.994455i | \(-0.533537\pi\) | ||||
−0.105164 | + | 0.994455i | \(0.533537\pi\) | |||||||
\(138\) | 379.451 | 0.234065 | ||||||||
\(139\) | 1644.19 | 1.00329 | 0.501647 | − | 0.865072i | \(-0.332728\pi\) | ||||
0.501647 | + | 0.865072i | \(0.332728\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 872.203 | 0.520941 | ||||||||
\(142\) | 1814.34 | 1.07223 | ||||||||
\(143\) | 1466.79 | 0.857758 | ||||||||
\(144\) | 767.902 | 0.444388 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 1588.74 | 0.900582 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 683.189 | 0.379445 | ||||||||
\(149\) | −1894.41 | −1.04158 | −0.520792 | − | 0.853683i | \(-0.674363\pi\) | ||||
−0.520792 | + | 0.853683i | \(0.674363\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 859.608 | 0.463271 | 0.231635 | − | 0.972803i | \(-0.425592\pi\) | ||||
0.231635 | + | 0.972803i | \(0.425592\pi\) | |||||||
\(152\) | −452.609 | −0.241523 | ||||||||
\(153\) | 6350.79 | 3.35576 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 2291.56 | 1.17610 | ||||||||
\(157\) | −1389.94 | −0.706554 | −0.353277 | − | 0.935519i | \(-0.614933\pi\) | ||||
−0.353277 | + | 0.935519i | \(0.614933\pi\) | |||||||
\(158\) | 2326.55 | 1.17146 | ||||||||
\(159\) | −313.697 | −0.156464 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −557.159 | −0.270213 | ||||||||
\(163\) | 3170.43 | 1.52348 | 0.761740 | − | 0.647883i | \(-0.224345\pi\) | ||||
0.761740 | + | 0.647883i | \(0.224345\pi\) | |||||||
\(164\) | −551.500 | −0.262591 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −2260.18 | −1.05677 | ||||||||
\(167\) | −497.526 | −0.230537 | −0.115269 | − | 0.993334i | \(-0.536773\pi\) | ||||
−0.115269 | + | 0.993334i | \(0.536773\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 2179.40 | 0.991988 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 2715.31 | 1.21430 | ||||||||
\(172\) | −1103.04 | −0.488990 | ||||||||
\(173\) | 4231.03 | 1.85942 | 0.929709 | − | 0.368294i | \(-0.120058\pi\) | ||||
0.929709 | + | 0.368294i | \(0.120058\pi\) | |||||||
\(174\) | 1626.93 | 0.708833 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 354.756 | 0.151936 | ||||||||
\(177\) | −6212.14 | −2.63804 | ||||||||
\(178\) | 1794.68 | 0.755715 | ||||||||
\(179\) | 797.157 | 0.332862 | 0.166431 | − | 0.986053i | \(-0.446776\pi\) | ||||
0.166431 | + | 0.986053i | \(0.446776\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1893.79 | 0.777703 | 0.388851 | − | 0.921301i | \(-0.372872\pi\) | ||||
0.388851 | + | 0.921301i | \(0.372872\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 6259.36 | 2.52844 | ||||||||
\(184\) | 175.268 | 0.0702225 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −5193.02 | −2.04716 | ||||||||
\(187\) | 2933.94 | 1.14733 | ||||||||
\(188\) | 402.870 | 0.156289 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 3988.00 | 1.51079 | 0.755397 | − | 0.655268i | \(-0.227444\pi\) | ||||
0.755397 | + | 0.655268i | \(0.227444\pi\) | |||||||
\(192\) | 554.234 | 0.208325 | ||||||||
\(193\) | −4051.43 | −1.51103 | −0.755513 | − | 0.655134i | \(-0.772612\pi\) | ||||
−0.755513 | + | 0.655134i | \(0.772612\pi\) | |||||||
\(194\) | −3035.36 | −1.12333 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −1749.83 | −0.632842 | −0.316421 | − | 0.948619i | \(-0.602481\pi\) | ||||
−0.316421 | + | 0.948619i | \(0.602481\pi\) | |||||||
\(198\) | −2128.27 | −0.763886 | ||||||||
\(199\) | 2317.90 | 0.825685 | 0.412843 | − | 0.910802i | \(-0.364536\pi\) | ||||
0.412843 | + | 0.910802i | \(0.364536\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −1073.62 | −0.376752 | ||||||||
\(202\) | 91.1753 | 0.0317578 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 4583.68 | 1.57315 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 2126.03 | 0.719065 | ||||||||
\(207\) | −1051.47 | −0.353056 | ||||||||
\(208\) | 1058.47 | 0.352845 | ||||||||
\(209\) | 1254.42 | 0.415168 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2196.02 | 0.716493 | 0.358246 | − | 0.933627i | \(-0.383375\pi\) | ||||
0.358246 | + | 0.933627i | \(0.383375\pi\) | |||||||
\(212\) | −144.896 | −0.0469411 | ||||||||
\(213\) | −7856.02 | −2.52716 | ||||||||
\(214\) | −529.762 | −0.169223 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −1454.44 | −0.458158 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −1770.12 | −0.549944 | ||||||||
\(219\) | −6879.16 | −2.12261 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 8753.87 | 2.66447 | ||||||||
\(222\) | −2958.17 | −0.894323 | ||||||||
\(223\) | −2111.54 | −0.634077 | −0.317038 | − | 0.948413i | \(-0.602688\pi\) | ||||
−0.317038 | + | 0.948413i | \(0.602688\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 3211.09 | 0.945127 | ||||||||
\(227\) | 3728.06 | 1.09004 | 0.545022 | − | 0.838422i | \(-0.316521\pi\) | ||||
0.545022 | + | 0.838422i | \(0.316521\pi\) | |||||||
\(228\) | 1959.77 | 0.569251 | ||||||||
\(229\) | 700.918 | 0.202262 | 0.101131 | − | 0.994873i | \(-0.467754\pi\) | ||||
0.101131 | + | 0.994873i | \(0.467754\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 751.475 | 0.212658 | ||||||||
\(233\) | −4355.40 | −1.22460 | −0.612300 | − | 0.790625i | \(-0.709756\pi\) | ||||
−0.612300 | + | 0.790625i | \(0.709756\pi\) | |||||||
\(234\) | −6350.01 | −1.77399 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −2869.38 | −0.791445 | ||||||||
\(237\) | −10073.8 | −2.76104 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 2722.45 | 0.736823 | 0.368412 | − | 0.929663i | \(-0.379902\pi\) | ||||
0.368412 | + | 0.929663i | \(0.379902\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 2477.11 | 0.662094 | 0.331047 | − | 0.943614i | \(-0.392598\pi\) | ||||
0.331047 | + | 0.943614i | \(0.392598\pi\) | |||||||
\(242\) | 1678.78 | 0.445934 | ||||||||
\(243\) | −2496.27 | −0.658995 | ||||||||
\(244\) | 2891.19 | 0.758564 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 2387.97 | 0.618908 | ||||||||
\(247\) | 3742.76 | 0.964153 | ||||||||
\(248\) | −2398.65 | −0.614172 | ||||||||
\(249\) | 9786.45 | 2.49073 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 249.512 | 0.0627453 | 0.0313727 | − | 0.999508i | \(-0.490012\pi\) | ||||
0.0313727 | + | 0.999508i | \(0.490012\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −485.761 | −0.120710 | ||||||||
\(254\) | 4937.77 | 1.21978 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 256.000 | 0.0625000 | ||||||||
\(257\) | 960.811 | 0.233205 | 0.116603 | − | 0.993179i | \(-0.462800\pi\) | ||||
0.116603 | + | 0.993179i | \(0.462800\pi\) | |||||||
\(258\) | 4776.12 | 1.15251 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −4508.28 | −1.06918 | ||||||||
\(262\) | −5526.22 | −1.30309 | ||||||||
\(263\) | 3956.63 | 0.927665 | 0.463833 | − | 0.885923i | \(-0.346474\pi\) | ||||
0.463833 | + | 0.885923i | \(0.346474\pi\) | |||||||
\(264\) | −1536.08 | −0.358102 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −7770.90 | −1.78117 | ||||||||
\(268\) | −495.902 | −0.113030 | ||||||||
\(269\) | 1832.93 | 0.415449 | 0.207725 | − | 0.978187i | \(-0.433394\pi\) | ||||
0.207725 | + | 0.978187i | \(0.433394\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1907.68 | −0.427614 | −0.213807 | − | 0.976876i | \(-0.568586\pi\) | ||||
−0.213807 | + | 0.976876i | \(0.568586\pi\) | |||||||
\(272\) | 2117.20 | 0.471963 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 674.539 | 0.148724 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −758.902 | −0.165509 | ||||||||
\(277\) | −7418.68 | −1.60919 | −0.804594 | − | 0.593825i | \(-0.797617\pi\) | ||||
−0.804594 | + | 0.593825i | \(0.797617\pi\) | |||||||
\(278\) | −3288.37 | −0.709436 | ||||||||
\(279\) | 14390.1 | 3.08786 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −7297.51 | −1.54923 | −0.774614 | − | 0.632435i | \(-0.782056\pi\) | ||||
−0.774614 | + | 0.632435i | \(0.782056\pi\) | |||||||
\(282\) | −1744.41 | −0.368361 | ||||||||
\(283\) | −4034.47 | −0.847435 | −0.423718 | − | 0.905794i | \(-0.639275\pi\) | ||||
−0.423718 | + | 0.905794i | \(0.639275\pi\) | |||||||
\(284\) | −3628.69 | −0.758180 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −2933.58 | −0.606526 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −1535.80 | −0.314230 | ||||||||
\(289\) | 12596.9 | 2.56399 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 13143.0 | 2.64761 | ||||||||
\(292\) | −3177.48 | −0.636808 | ||||||||
\(293\) | −5854.31 | −1.16728 | −0.583639 | − | 0.812013i | \(-0.698372\pi\) | ||||
−0.583639 | + | 0.812013i | \(0.698372\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −1366.38 | −0.268308 | ||||||||
\(297\) | 4031.03 | 0.787556 | ||||||||
\(298\) | 3788.82 | 0.736511 | ||||||||
\(299\) | −1449.34 | −0.280327 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −1719.22 | −0.327582 | ||||||||
\(303\) | −394.785 | −0.0748508 | ||||||||
\(304\) | 905.218 | 0.170782 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −12701.6 | −2.37288 | ||||||||
\(307\) | 2659.84 | 0.494479 | 0.247240 | − | 0.968954i | \(-0.420476\pi\) | ||||
0.247240 | + | 0.968954i | \(0.420476\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −9205.60 | −1.69478 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 4574.29 | 0.834032 | 0.417016 | − | 0.908899i | \(-0.363076\pi\) | ||||
0.417016 | + | 0.908899i | \(0.363076\pi\) | |||||||
\(312\) | −4583.12 | −0.831629 | ||||||||
\(313\) | −4987.46 | −0.900665 | −0.450332 | − | 0.892861i | \(-0.648694\pi\) | ||||
−0.450332 | + | 0.892861i | \(0.648694\pi\) | |||||||
\(314\) | 2779.87 | 0.499609 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −4653.10 | −0.828346 | ||||||||
\(317\) | −5692.82 | −1.00865 | −0.504323 | − | 0.863515i | \(-0.668258\pi\) | ||||
−0.504323 | + | 0.863515i | \(0.668258\pi\) | |||||||
\(318\) | 627.393 | 0.110637 | ||||||||
\(319\) | −2082.74 | −0.365552 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 2293.85 | 0.398847 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 7486.43 | 1.28965 | ||||||||
\(324\) | 1114.32 | 0.191069 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −6340.86 | −1.07726 | ||||||||
\(327\) | 7664.54 | 1.29618 | ||||||||
\(328\) | 1103.00 | 0.185680 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −6368.23 | −1.05749 | −0.528746 | − | 0.848780i | \(-0.677338\pi\) | ||||
−0.528746 | + | 0.848780i | \(0.677338\pi\) | |||||||
\(332\) | 4520.35 | 0.747249 | ||||||||
\(333\) | 8197.23 | 1.34896 | ||||||||
\(334\) | 995.051 | 0.163014 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 6228.66 | 1.00682 | 0.503408 | − | 0.864049i | \(-0.332079\pi\) | ||||
0.503408 | + | 0.864049i | \(0.332079\pi\) | |||||||
\(338\) | −4358.80 | −0.701442 | ||||||||
\(339\) | −13903.9 | −2.22759 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 6647.95 | 1.05574 | ||||||||
\(342\) | −5430.62 | −0.858638 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 2206.09 | 0.345768 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −8462.06 | −1.31481 | ||||||||
\(347\) | −3405.25 | −0.526812 | −0.263406 | − | 0.964685i | \(-0.584846\pi\) | ||||
−0.263406 | + | 0.964685i | \(0.584846\pi\) | |||||||
\(348\) | −3253.85 | −0.501220 | ||||||||
\(349\) | 11985.4 | 1.83829 | 0.919143 | − | 0.393925i | \(-0.128883\pi\) | ||||
0.919143 | + | 0.393925i | \(0.128883\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 12027.2 | 1.82896 | ||||||||
\(352\) | −709.513 | −0.107435 | ||||||||
\(353\) | −8400.71 | −1.26664 | −0.633321 | − | 0.773889i | \(-0.718309\pi\) | ||||
−0.633321 | + | 0.773889i | \(0.718309\pi\) | |||||||
\(354\) | 12424.3 | 1.86538 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −3589.37 | −0.534371 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −1594.31 | −0.235369 | ||||||||
\(359\) | −716.465 | −0.105330 | −0.0526652 | − | 0.998612i | \(-0.516772\pi\) | ||||
−0.0526652 | + | 0.998612i | \(0.516772\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −3658.14 | −0.533335 | ||||||||
\(362\) | −3787.58 | −0.549919 | ||||||||
\(363\) | −7269.04 | −1.05103 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −12518.7 | −1.78788 | ||||||||
\(367\) | 2509.69 | 0.356962 | 0.178481 | − | 0.983943i | \(-0.442882\pi\) | ||||
0.178481 | + | 0.983943i | \(0.442882\pi\) | |||||||
\(368\) | −350.536 | −0.0496548 | ||||||||
\(369\) | −6617.16 | −0.933539 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 10386.0 | 1.44756 | ||||||||
\(373\) | −802.750 | −0.111434 | −0.0557169 | − | 0.998447i | \(-0.517744\pi\) | ||||
−0.0557169 | + | 0.998447i | \(0.517744\pi\) | |||||||
\(374\) | −5867.89 | −0.811287 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −805.739 | −0.110513 | ||||||||
\(377\) | −6214.17 | −0.848928 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −5322.77 | −0.721404 | −0.360702 | − | 0.932681i | \(-0.617463\pi\) | ||||
−0.360702 | + | 0.932681i | \(0.617463\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −21380.3 | −2.87492 | ||||||||
\(382\) | −7976.00 | −1.06829 | ||||||||
\(383\) | −13490.7 | −1.79985 | −0.899923 | − | 0.436049i | \(-0.856377\pi\) | ||||
−0.899923 | + | 0.436049i | \(0.856377\pi\) | |||||||
\(384\) | −1108.47 | −0.147308 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 8102.85 | 1.06846 | ||||||||
\(387\) | −13234.8 | −1.73841 | ||||||||
\(388\) | 6070.72 | 0.794315 | ||||||||
\(389\) | 5129.21 | 0.668538 | 0.334269 | − | 0.942478i | \(-0.391511\pi\) | ||||
0.334269 | + | 0.942478i | \(0.391511\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −2899.04 | −0.374964 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 23928.2 | 3.07130 | ||||||||
\(394\) | 3499.65 | 0.447487 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 4256.54 | 0.540149 | ||||||||
\(397\) | 6546.69 | 0.827630 | 0.413815 | − | 0.910361i | \(-0.364196\pi\) | ||||
0.413815 | + | 0.910361i | \(0.364196\pi\) | |||||||
\(398\) | −4635.79 | −0.583848 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 26.4671 | 0.00329602 | 0.00164801 | − | 0.999999i | \(-0.499475\pi\) | ||||
0.00164801 | + | 0.999999i | \(0.499475\pi\) | |||||||
\(402\) | 2147.23 | 0.266404 | ||||||||
\(403\) | 19835.2 | 2.45176 | ||||||||
\(404\) | −182.351 | −0.0224562 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 3786.96 | 0.461211 | ||||||||
\(408\) | −9167.37 | −1.11238 | ||||||||
\(409\) | −5918.35 | −0.715510 | −0.357755 | − | 0.933816i | \(-0.616458\pi\) | ||||
−0.357755 | + | 0.933816i | \(0.616458\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −2920.72 | −0.350532 | ||||||||
\(412\) | −4252.06 | −0.508456 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 2102.95 | 0.249648 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −2116.94 | −0.249499 | ||||||||
\(417\) | 14238.5 | 1.67209 | ||||||||
\(418\) | −2508.84 | −0.293568 | ||||||||
\(419\) | 4228.31 | 0.492999 | 0.246499 | − | 0.969143i | \(-0.420720\pi\) | ||||
0.246499 | + | 0.969143i | \(0.420720\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 4466.68 | 0.517084 | 0.258542 | − | 0.966000i | \(-0.416758\pi\) | ||||
0.258542 | + | 0.966000i | \(0.416758\pi\) | |||||||
\(422\) | −4392.03 | −0.506637 | ||||||||
\(423\) | 4833.82 | 0.555623 | ||||||||
\(424\) | 289.792 | 0.0331924 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 15712.0 | 1.78697 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 1059.52 | 0.119659 | ||||||||
\(429\) | 12702.3 | 1.42954 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −1962.97 | −0.219381 | −0.109690 | − | 0.993966i | \(-0.534986\pi\) | ||||
−0.109690 | + | 0.993966i | \(0.534986\pi\) | |||||||
\(432\) | 2908.88 | 0.323967 | ||||||||
\(433\) | −2734.59 | −0.303501 | −0.151751 | − | 0.988419i | \(-0.548491\pi\) | ||||
−0.151751 | + | 0.988419i | \(0.548491\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 3540.24 | 0.388869 | ||||||||
\(437\) | −1239.50 | −0.135682 | ||||||||
\(438\) | 13758.3 | 1.50091 | ||||||||
\(439\) | −8595.68 | −0.934509 | −0.467255 | − | 0.884123i | \(-0.654757\pi\) | ||||
−0.467255 | + | 0.884123i | \(0.654757\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −17507.7 | −1.88407 | ||||||||
\(443\) | 1284.76 | 0.137790 | 0.0688951 | − | 0.997624i | \(-0.478053\pi\) | ||||
0.0688951 | + | 0.997624i | \(0.478053\pi\) | |||||||
\(444\) | 5916.35 | 0.632382 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 4223.08 | 0.448360 | ||||||||
\(447\) | −16405.4 | −1.73590 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −2633.49 | −0.276798 | −0.138399 | − | 0.990377i | \(-0.544196\pi\) | ||||
−0.138399 | + | 0.990377i | \(0.544196\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −3057.00 | −0.319177 | ||||||||
\(452\) | −6422.18 | −0.668305 | ||||||||
\(453\) | 7444.12 | 0.772087 | ||||||||
\(454\) | −7456.12 | −0.770778 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −3919.55 | −0.402521 | ||||||||
\(457\) | 687.957 | 0.0704185 | 0.0352093 | − | 0.999380i | \(-0.488790\pi\) | ||||
0.0352093 | + | 0.999380i | \(0.488790\pi\) | |||||||
\(458\) | −1401.84 | −0.143021 | ||||||||
\(459\) | 24057.3 | 2.44641 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 4355.06 | 0.439989 | 0.219995 | − | 0.975501i | \(-0.429396\pi\) | ||||
0.219995 | + | 0.975501i | \(0.429396\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 10900.6 | 1.09416 | 0.547080 | − | 0.837081i | \(-0.315740\pi\) | ||||
0.547080 | + | 0.837081i | \(0.315740\pi\) | |||||||
\(464\) | −1502.95 | −0.150372 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 8710.81 | 0.865923 | ||||||||
\(467\) | −15746.8 | −1.56033 | −0.780166 | − | 0.625572i | \(-0.784866\pi\) | ||||
−0.780166 | + | 0.625572i | \(0.784866\pi\) | |||||||
\(468\) | 12700.0 | 1.25440 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −12036.7 | −1.17754 | ||||||||
\(472\) | 5738.77 | 0.559636 | ||||||||
\(473\) | −6114.24 | −0.594362 | ||||||||
\(474\) | 20147.7 | 1.95235 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −1738.53 | −0.166880 | ||||||||
\(478\) | −5444.90 | −0.521013 | ||||||||
\(479\) | −3752.10 | −0.357907 | −0.178954 | − | 0.983857i | \(-0.557271\pi\) | ||||
−0.178954 | + | 0.983857i | \(0.557271\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 11299.0 | 1.07108 | ||||||||
\(482\) | −4954.22 | −0.468171 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −3357.56 | −0.315323 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 4992.54 | 0.465980 | ||||||||
\(487\) | 7497.49 | 0.697625 | 0.348813 | − | 0.937192i | \(-0.386585\pi\) | ||||
0.348813 | + | 0.937192i | \(0.386585\pi\) | |||||||
\(488\) | −5782.38 | −0.536386 | ||||||||
\(489\) | 27455.6 | 2.53903 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 2364.21 | 0.217302 | 0.108651 | − | 0.994080i | \(-0.465347\pi\) | ||||
0.108651 | + | 0.994080i | \(0.465347\pi\) | |||||||
\(492\) | −4775.94 | −0.437634 | ||||||||
\(493\) | −12429.9 | −1.13552 | ||||||||
\(494\) | −7485.51 | −0.681759 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 4797.31 | 0.434285 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −19572.9 | −1.76121 | ||||||||
\(499\) | −2964.11 | −0.265916 | −0.132958 | − | 0.991122i | \(-0.542448\pi\) | ||||
−0.132958 | + | 0.991122i | \(0.542448\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −4308.52 | −0.384213 | ||||||||
\(502\) | −499.025 | −0.0443677 | ||||||||
\(503\) | 2777.43 | 0.246202 | 0.123101 | − | 0.992394i | \(-0.460716\pi\) | ||||
0.123101 | + | 0.992394i | \(0.460716\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 971.523 | 0.0853547 | ||||||||
\(507\) | 18873.4 | 1.65325 | ||||||||
\(508\) | −9875.53 | −0.862511 | ||||||||
\(509\) | 6479.21 | 0.564216 | 0.282108 | − | 0.959383i | \(-0.408966\pi\) | ||||
0.282108 | + | 0.959383i | \(0.408966\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −512.000 | −0.0441942 | ||||||||
\(513\) | 10285.8 | 0.885245 | ||||||||
\(514\) | −1921.62 | −0.164901 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −9552.24 | −0.814950 | ||||||||
\(517\) | 2233.13 | 0.189967 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 36640.3 | 3.09891 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 1303.17 | 0.109584 | 0.0547919 | − | 0.998498i | \(-0.482550\pi\) | ||||
0.0547919 | + | 0.998498i | \(0.482550\pi\) | |||||||
\(522\) | 9016.56 | 0.756023 | ||||||||
\(523\) | −6088.73 | −0.509066 | −0.254533 | − | 0.967064i | \(-0.581922\pi\) | ||||
−0.254533 | + | 0.967064i | \(0.581922\pi\) | |||||||
\(524\) | 11052.4 | 0.921427 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −7913.25 | −0.655958 | ||||||||
\(527\) | 39675.2 | 3.27947 | ||||||||
\(528\) | 3072.16 | 0.253217 | ||||||||
\(529\) | −11687.0 | −0.960550 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −34428.2 | −2.81367 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −9121.04 | −0.741231 | ||||||||
\(534\) | 15541.8 | 1.25947 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 991.805 | 0.0799243 | ||||||||
\(537\) | 6903.30 | 0.554748 | ||||||||
\(538\) | −3665.86 | −0.293767 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 18411.9 | 1.46320 | 0.731598 | − | 0.681736i | \(-0.238775\pi\) | ||||
0.731598 | + | 0.681736i | \(0.238775\pi\) | |||||||
\(542\) | 3815.36 | 0.302368 | ||||||||
\(543\) | 16400.0 | 1.29612 | ||||||||
\(544\) | −4234.40 | −0.333728 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 14541.5 | 1.13666 | 0.568328 | − | 0.822802i | \(-0.307591\pi\) | ||||
0.568328 | + | 0.822802i | \(0.307591\pi\) | |||||||
\(548\) | −1349.08 | −0.105164 | ||||||||
\(549\) | 34689.9 | 2.69677 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −5314.44 | −0.410895 | ||||||||
\(552\) | 1517.80 | 0.117033 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 14837.4 | 1.13787 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 6576.74 | 0.501647 | ||||||||
\(557\) | −19433.6 | −1.47833 | −0.739164 | − | 0.673525i | \(-0.764779\pi\) | ||||
−0.739164 | + | 0.673525i | \(0.764779\pi\) | |||||||
\(558\) | −28780.2 | −2.18344 | ||||||||
\(559\) | −18242.8 | −1.38030 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 25407.7 | 1.91214 | ||||||||
\(562\) | 14595.0 | 1.09547 | ||||||||
\(563\) | −3896.11 | −0.291654 | −0.145827 | − | 0.989310i | \(-0.546584\pi\) | ||||
−0.145827 | + | 0.989310i | \(0.546584\pi\) | |||||||
\(564\) | 3488.81 | 0.260471 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 8068.93 | 0.599227 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 7257.38 | 0.536114 | ||||||||
\(569\) | 8980.15 | 0.661630 | 0.330815 | − | 0.943696i | \(-0.392676\pi\) | ||||
0.330815 | + | 0.943696i | \(0.392676\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 18716.1 | 1.37170 | 0.685851 | − | 0.727742i | \(-0.259430\pi\) | ||||
0.685851 | + | 0.727742i | \(0.259430\pi\) | |||||||
\(572\) | 5867.17 | 0.428879 | ||||||||
\(573\) | 34535.7 | 2.51789 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 3071.61 | 0.222194 | ||||||||
\(577\) | −9696.89 | −0.699631 | −0.349815 | − | 0.936819i | \(-0.613756\pi\) | ||||
−0.349815 | + | 0.936819i | \(0.613756\pi\) | |||||||
\(578\) | −25193.8 | −1.81301 | ||||||||
\(579\) | −35085.0 | −2.51827 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −26285.9 | −1.87214 | ||||||||
\(583\) | −803.169 | −0.0570564 | ||||||||
\(584\) | 6354.96 | 0.450291 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 11708.6 | 0.825390 | ||||||||
\(587\) | −73.3324 | −0.00515631 | −0.00257815 | − | 0.999997i | \(-0.500821\pi\) | ||||
−0.00257815 | + | 0.999997i | \(0.500821\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 16963.3 | 1.18669 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −15153.3 | −1.05469 | ||||||||
\(592\) | 2732.76 | 0.189722 | ||||||||
\(593\) | 27701.9 | 1.91835 | 0.959174 | − | 0.282816i | \(-0.0912685\pi\) | ||||
0.959174 | + | 0.282816i | \(0.0912685\pi\) | |||||||
\(594\) | −8062.07 | −0.556886 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −7577.64 | −0.520792 | ||||||||
\(597\) | 20072.8 | 1.37609 | ||||||||
\(598\) | 2898.69 | 0.198221 | ||||||||
\(599\) | 15982.2 | 1.09018 | 0.545088 | − | 0.838379i | \(-0.316496\pi\) | ||||
0.545088 | + | 0.838379i | \(0.316496\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 17877.9 | 1.21340 | 0.606700 | − | 0.794931i | \(-0.292493\pi\) | ||||
0.606700 | + | 0.794931i | \(0.292493\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −5950.07 | −0.401834 | ||||||||
\(604\) | 3438.43 | 0.231635 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 789.570 | 0.0529275 | ||||||||
\(607\) | −4146.93 | −0.277296 | −0.138648 | − | 0.990342i | \(-0.544276\pi\) | ||||
−0.138648 | + | 0.990342i | \(0.544276\pi\) | |||||||
\(608\) | −1810.44 | −0.120761 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 6662.89 | 0.441165 | ||||||||
\(612\) | 25403.2 | 1.67788 | ||||||||
\(613\) | −662.364 | −0.0436421 | −0.0218211 | − | 0.999762i | \(-0.506946\pi\) | ||||
−0.0218211 | + | 0.999762i | \(0.506946\pi\) | |||||||
\(614\) | −5319.68 | −0.349650 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −8693.21 | −0.567221 | −0.283611 | − | 0.958940i | \(-0.591532\pi\) | ||||
−0.283611 | + | 0.958940i | \(0.591532\pi\) | |||||||
\(618\) | 18411.2 | 1.19839 | ||||||||
\(619\) | 2914.63 | 0.189255 | 0.0946275 | − | 0.995513i | \(-0.469834\pi\) | ||||
0.0946275 | + | 0.995513i | \(0.469834\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −3983.08 | −0.257384 | ||||||||
\(622\) | −9148.58 | −0.589750 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 9166.24 | 0.588050 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 9974.92 | 0.636866 | ||||||||
\(627\) | 10863.2 | 0.691919 | ||||||||
\(628\) | −5559.75 | −0.353277 | ||||||||
\(629\) | 22600.7 | 1.43267 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −894.747 | −0.0564490 | −0.0282245 | − | 0.999602i | \(-0.508985\pi\) | ||||
−0.0282245 | + | 0.999602i | \(0.508985\pi\) | |||||||
\(632\) | 9306.20 | 0.585729 | ||||||||
\(633\) | 19017.3 | 1.19411 | ||||||||
\(634\) | 11385.6 | 0.713221 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −1254.79 | −0.0782320 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 4165.48 | 0.258484 | ||||||||
\(639\) | −43538.7 | −2.69541 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −20085.0 | −1.23762 | −0.618808 | − | 0.785542i | \(-0.712384\pi\) | ||||
−0.618808 | + | 0.785542i | \(0.712384\pi\) | |||||||
\(642\) | −4587.69 | −0.282028 | ||||||||
\(643\) | −851.943 | −0.0522510 | −0.0261255 | − | 0.999659i | \(-0.508317\pi\) | ||||
−0.0261255 | + | 0.999659i | \(0.508317\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −14972.9 | −0.911918 | ||||||||
\(647\) | −20767.9 | −1.26193 | −0.630966 | − | 0.775810i | \(-0.717341\pi\) | ||||
−0.630966 | + | 0.775810i | \(0.717341\pi\) | |||||||
\(648\) | −2228.63 | −0.135107 | ||||||||
\(649\) | −15905.2 | −0.961993 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 12681.7 | 0.761740 | ||||||||
\(653\) | 14705.7 | 0.881282 | 0.440641 | − | 0.897683i | \(-0.354751\pi\) | ||||
0.440641 | + | 0.897683i | \(0.354751\pi\) | |||||||
\(654\) | −15329.1 | −0.916536 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −2206.00 | −0.131296 | ||||||||
\(657\) | −38124.9 | −2.26392 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −27657.2 | −1.63486 | −0.817428 | − | 0.576031i | \(-0.804601\pi\) | ||||
−0.817428 | + | 0.576031i | \(0.804601\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 19683.3 | 1.15823 | 0.579117 | − | 0.815244i | \(-0.303397\pi\) | ||||
0.579117 | + | 0.815244i | \(0.303397\pi\) | |||||||
\(662\) | 12736.5 | 0.747760 | ||||||||
\(663\) | 75807.6 | 4.44061 | ||||||||
\(664\) | −9040.71 | −0.528385 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −16394.5 | −0.953862 | ||||||||
\(667\) | 2057.96 | 0.119467 | ||||||||
\(668\) | −1990.10 | −0.115269 | ||||||||
\(669\) | −18285.7 | −1.05675 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 16026.1 | 0.922026 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −3443.85 | −0.197252 | −0.0986260 | − | 0.995125i | \(-0.531445\pi\) | ||||
−0.0986260 | + | 0.995125i | \(0.531445\pi\) | |||||||
\(674\) | −12457.3 | −0.711926 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 8717.59 | 0.495994 | ||||||||
\(677\) | −28254.1 | −1.60398 | −0.801988 | − | 0.597340i | \(-0.796224\pi\) | ||||
−0.801988 | + | 0.597340i | \(0.796224\pi\) | |||||||
\(678\) | 27807.7 | 1.57515 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 32284.6 | 1.81667 | ||||||||
\(682\) | −13295.9 | −0.746519 | ||||||||
\(683\) | −23937.4 | −1.34105 | −0.670525 | − | 0.741887i | \(-0.733931\pi\) | ||||
−0.670525 | + | 0.741887i | \(0.733931\pi\) | |||||||
\(684\) | 10861.2 | 0.607149 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 6069.88 | 0.337089 | ||||||||
\(688\) | −4412.17 | −0.244495 | ||||||||
\(689\) | −2396.38 | −0.132503 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 35157.3 | 1.93552 | 0.967762 | − | 0.251867i | \(-0.0810444\pi\) | ||||
0.967762 | + | 0.251867i | \(0.0810444\pi\) | |||||||
\(692\) | 16924.1 | 0.929709 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 6810.51 | 0.372512 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 6507.70 | 0.354416 | ||||||||
\(697\) | −18244.3 | −0.991467 | ||||||||
\(698\) | −23970.7 | −1.29986 | ||||||||
\(699\) | −37717.4 | −2.04092 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −4703.07 | −0.253399 | −0.126699 | − | 0.991941i | \(-0.540438\pi\) | ||||
−0.126699 | + | 0.991941i | \(0.540438\pi\) | |||||||
\(702\) | −24054.4 | −1.29327 | ||||||||
\(703\) | 9663.04 | 0.518419 | ||||||||
\(704\) | 1419.03 | 0.0759681 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 16801.4 | 0.895651 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −24848.6 | −1.31902 | ||||||||
\(709\) | 13101.7 | 0.693997 | 0.346999 | − | 0.937866i | \(-0.387201\pi\) | ||||
0.346999 | + | 0.937866i | \(0.387201\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −55830.1 | −2.94485 | ||||||||
\(712\) | 7178.74 | 0.377858 | ||||||||
\(713\) | −6568.86 | −0.345029 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 3188.63 | 0.166431 | ||||||||
\(717\) | 23576.2 | 1.22799 | ||||||||
\(718\) | 1432.93 | 0.0744798 | ||||||||
\(719\) | −22401.9 | −1.16196 | −0.580981 | − | 0.813917i | \(-0.697331\pi\) | ||||
−0.580981 | + | 0.813917i | \(0.697331\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 7316.29 | 0.377125 | ||||||||
\(723\) | 21451.5 | 1.10344 | ||||||||
\(724\) | 7575.15 | 0.388851 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 14538.1 | 0.743194 | ||||||||
\(727\) | 13870.4 | 0.707600 | 0.353800 | − | 0.935321i | \(-0.384889\pi\) | ||||
0.353800 | + | 0.935321i | \(0.384889\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −29139.1 | −1.48042 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −36490.0 | −1.84628 | ||||||||
\(732\) | 25037.4 | 1.26422 | ||||||||
\(733\) | −10216.2 | −0.514791 | −0.257396 | − | 0.966306i | \(-0.582864\pi\) | ||||
−0.257396 | + | 0.966306i | \(0.582864\pi\) | |||||||
\(734\) | −5019.39 | −0.252410 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 701.072 | 0.0351112 | ||||||||
\(737\) | −2748.82 | −0.137387 | ||||||||
\(738\) | 13234.3 | 0.660112 | ||||||||
\(739\) | 19171.5 | 0.954310 | 0.477155 | − | 0.878819i | \(-0.341668\pi\) | ||||
0.477155 | + | 0.878819i | \(0.341668\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 32411.9 | 1.60686 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 19779.8 | 0.976650 | 0.488325 | − | 0.872662i | \(-0.337608\pi\) | ||||
0.488325 | + | 0.872662i | \(0.337608\pi\) | |||||||
\(744\) | −20772.1 | −1.02358 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 1605.50 | 0.0787956 | ||||||||
\(747\) | 54237.3 | 2.65655 | ||||||||
\(748\) | 11735.8 | 0.573666 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 20104.8 | 0.976875 | 0.488438 | − | 0.872599i | \(-0.337567\pi\) | ||||
0.488438 | + | 0.872599i | \(0.337567\pi\) | |||||||
\(752\) | 1611.48 | 0.0781444 | ||||||||
\(753\) | 2160.75 | 0.104571 | ||||||||
\(754\) | 12428.3 | 0.600283 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 10958.5 | 0.526149 | 0.263074 | − | 0.964776i | \(-0.415264\pi\) | ||||
0.263074 | + | 0.964776i | \(0.415264\pi\) | |||||||
\(758\) | 10645.5 | 0.510110 | ||||||||
\(759\) | −4206.65 | −0.201175 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 16633.4 | 0.792327 | 0.396164 | − | 0.918180i | \(-0.370341\pi\) | ||||
0.396164 | + | 0.918180i | \(0.370341\pi\) | |||||||
\(762\) | 42760.6 | 2.03288 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 15952.0 | 0.755397 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 26981.3 | 1.27268 | ||||||||
\(767\) | −47455.6 | −2.23406 | ||||||||
\(768\) | 2216.93 | 0.104162 | ||||||||
\(769\) | −24813.6 | −1.16359 | −0.581796 | − | 0.813335i | \(-0.697650\pi\) | ||||
−0.581796 | + | 0.813335i | \(0.697650\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 8320.53 | 0.388660 | ||||||||
\(772\) | −16205.7 | −0.755513 | ||||||||
\(773\) | 35576.5 | 1.65537 | 0.827683 | − | 0.561196i | \(-0.189659\pi\) | ||||
0.827683 | + | 0.561196i | \(0.189659\pi\) | |||||||
\(774\) | 26469.7 | 1.22924 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −12141.4 | −0.561666 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −10258.4 | −0.472728 | ||||||||
\(779\) | −7800.44 | −0.358767 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −20114.1 | −0.921559 | ||||||||
\(782\) | 5798.08 | 0.265139 | ||||||||
\(783\) | −17077.8 | −0.779450 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −47856.5 | −2.17174 | ||||||||
\(787\) | −3112.14 | −0.140960 | −0.0704802 | − | 0.997513i | \(-0.522453\pi\) | ||||
−0.0704802 | + | 0.997513i | \(0.522453\pi\) | |||||||
\(788\) | −6999.30 | −0.316421 | ||||||||
\(789\) | 34264.0 | 1.54605 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −8513.07 | −0.381943 | ||||||||
\(793\) | 47816.2 | 2.14124 | ||||||||
\(794\) | −13093.4 | −0.585223 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 9271.59 | 0.412843 | ||||||||
\(797\) | 4340.97 | 0.192930 | 0.0964649 | − | 0.995336i | \(-0.469246\pi\) | ||||
0.0964649 | + | 0.995336i | \(0.469246\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 13327.4 | 0.590100 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −43067.0 | −1.89975 | ||||||||
\(802\) | −52.9342 | −0.00233064 | ||||||||
\(803\) | −17613.0 | −0.774033 | ||||||||
\(804\) | −4294.47 | −0.188376 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −39670.3 | −1.73366 | ||||||||
\(807\) | 15873.0 | 0.692387 | ||||||||
\(808\) | 364.701 | 0.0158789 | ||||||||
\(809\) | −34714.6 | −1.50865 | −0.754327 | − | 0.656499i | \(-0.772037\pi\) | ||||
−0.754327 | + | 0.656499i | \(0.772037\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 8124.96 | 0.351795 | 0.175898 | − | 0.984408i | \(-0.443717\pi\) | ||||
0.175898 | + | 0.984408i | \(0.443717\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −16520.3 | −0.712660 | ||||||||
\(814\) | −7573.93 | −0.326125 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 18334.7 | 0.786574 | ||||||||
\(817\) | −15601.5 | −0.668086 | ||||||||
\(818\) | 11836.7 | 0.505942 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −4762.15 | −0.202436 | −0.101218 | − | 0.994864i | \(-0.532274\pi\) | ||||
−0.101218 | + | 0.994864i | \(0.532274\pi\) | |||||||
\(822\) | 5841.44 | 0.247863 | ||||||||
\(823\) | 13577.1 | 0.575051 | 0.287526 | − | 0.957773i | \(-0.407167\pi\) | ||||
0.287526 | + | 0.957773i | \(0.407167\pi\) | |||||||
\(824\) | 8504.12 | 0.359533 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −22576.6 | −0.949294 | −0.474647 | − | 0.880176i | \(-0.657424\pi\) | ||||
−0.474647 | + | 0.880176i | \(0.657424\pi\) | |||||||
\(828\) | −4205.90 | −0.176528 | ||||||||
\(829\) | −18235.2 | −0.763976 | −0.381988 | − | 0.924167i | \(-0.624760\pi\) | ||||
−0.381988 | + | 0.924167i | \(0.624760\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −64245.0 | −2.68187 | ||||||||
\(832\) | 4233.88 | 0.176422 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −28477.0 | −1.18235 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 5017.68 | 0.207584 | ||||||||
\(837\) | 54510.9 | 2.25110 | ||||||||
\(838\) | −8456.62 | −0.348603 | ||||||||
\(839\) | −34955.5 | −1.43838 | −0.719189 | − | 0.694815i | \(-0.755486\pi\) | ||||
−0.719189 | + | 0.694815i | \(0.755486\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −15565.3 | −0.638211 | ||||||||
\(842\) | −8933.35 | −0.365634 | ||||||||
\(843\) | −63195.7 | −2.58194 | ||||||||
\(844\) | 8784.06 | 0.358246 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −9667.64 | −0.392885 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −579.585 | −0.0234705 | ||||||||
\(849\) | −34938.1 | −1.41233 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −3741.91 | −0.150730 | ||||||||
\(852\) | −31424.1 | −1.26358 | ||||||||
\(853\) | 8243.14 | 0.330879 | 0.165439 | − | 0.986220i | \(-0.447096\pi\) | ||||
0.165439 | + | 0.986220i | \(0.447096\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −2119.05 | −0.0846117 | ||||||||
\(857\) | 6675.90 | 0.266096 | 0.133048 | − | 0.991110i | \(-0.457524\pi\) | ||||
0.133048 | + | 0.991110i | \(0.457524\pi\) | |||||||
\(858\) | −25404.6 | −1.01084 | ||||||||
\(859\) | −29038.8 | −1.15342 | −0.576712 | − | 0.816948i | \(-0.695664\pi\) | ||||
−0.576712 | + | 0.816948i | \(0.695664\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 3925.94 | 0.155125 | ||||||||
\(863\) | −9681.42 | −0.381876 | −0.190938 | − | 0.981602i | \(-0.561153\pi\) | ||||
−0.190938 | + | 0.981602i | \(0.561153\pi\) | |||||||
\(864\) | −5817.76 | −0.229079 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 5469.18 | 0.214608 | ||||||||
\(867\) | 109088. | 4.27314 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −25792.4 | −1.00685 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −8201.53 | −0.319056 | ||||||||
\(872\) | −7080.49 | −0.274972 | ||||||||
\(873\) | 72839.4 | 2.82387 | ||||||||
\(874\) | 2479.00 | 0.0959420 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −27516.7 | −1.06130 | ||||||||
\(877\) | −20310.9 | −0.782040 | −0.391020 | − | 0.920382i | \(-0.627878\pi\) | ||||
−0.391020 | + | 0.920382i | \(0.627878\pi\) | |||||||
\(878\) | 17191.4 | 0.660798 | ||||||||
\(879\) | −50697.7 | −1.94538 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −25065.3 | −0.958539 | −0.479269 | − | 0.877668i | \(-0.659098\pi\) | ||||
−0.479269 | + | 0.877668i | \(0.659098\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −13015.5 | −0.496045 | −0.248023 | − | 0.968754i | \(-0.579781\pi\) | ||||
−0.248023 | + | 0.968754i | \(0.579781\pi\) | |||||||
\(884\) | 35015.5 | 1.33224 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −2569.53 | −0.0974323 | ||||||||
\(887\) | 31630.5 | 1.19735 | 0.598674 | − | 0.800992i | \(-0.295694\pi\) | ||||
0.598674 | + | 0.800992i | \(0.295694\pi\) | |||||||
\(888\) | −11832.7 | −0.447161 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 6176.74 | 0.232243 | ||||||||
\(892\) | −8446.15 | −0.317038 | ||||||||
\(893\) | 5698.20 | 0.213531 | ||||||||
\(894\) | 32810.8 | 1.22747 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −12551.2 | −0.467192 | ||||||||
\(898\) | 5266.98 | 0.195725 | ||||||||
\(899\) | −28164.5 | −1.04487 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −4793.34 | −0.177236 | ||||||||
\(902\) | 6114.01 | 0.225692 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 12844.4 | 0.472563 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −14888.2 | −0.545948 | ||||||||
\(907\) | −48111.3 | −1.76131 | −0.880656 | − | 0.473757i | \(-0.842898\pi\) | ||||
−0.880656 | + | 0.473757i | \(0.842898\pi\) | |||||||
\(908\) | 14912.2 | 0.545022 | ||||||||
\(909\) | −2187.93 | −0.0798340 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −11465.5 | −0.416982 | −0.208491 | − | 0.978024i | \(-0.566855\pi\) | ||||
−0.208491 | + | 0.978024i | \(0.566855\pi\) | |||||||
\(912\) | 7839.10 | 0.284626 | ||||||||
\(913\) | 25056.6 | 0.908273 | ||||||||
\(914\) | −1375.91 | −0.0497934 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 2803.67 | 0.101131 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −48114.7 | −1.72987 | ||||||||
\(919\) | 26141.9 | 0.938347 | 0.469174 | − | 0.883106i | \(-0.344552\pi\) | ||||
0.469174 | + | 0.883106i | \(0.344552\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 23034.0 | 0.824099 | ||||||||
\(922\) | −8710.11 | −0.311120 | ||||||||
\(923\) | −60013.4 | −2.14016 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −21801.3 | −0.773687 | ||||||||
\(927\) | −51018.2 | −1.80761 | ||||||||
\(928\) | 3005.90 | 0.106329 | ||||||||
\(929\) | −3155.76 | −0.111450 | −0.0557251 | − | 0.998446i | \(-0.517747\pi\) | ||||
−0.0557251 | + | 0.998446i | \(0.517747\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −17421.6 | −0.612300 | ||||||||
\(933\) | 39612.9 | 1.39000 | ||||||||
\(934\) | 31493.6 | 1.10332 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −25400.0 | −0.886994 | ||||||||
\(937\) | −50554.9 | −1.76260 | −0.881301 | − | 0.472556i | \(-0.843331\pi\) | ||||
−0.881301 | + | 0.472556i | \(0.843331\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −43190.9 | −1.50105 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 53927.4 | 1.86821 | 0.934104 | − | 0.357002i | \(-0.116201\pi\) | ||||
0.934104 | + | 0.357002i | \(0.116201\pi\) | |||||||
\(942\) | 24073.4 | 0.832648 | ||||||||
\(943\) | 3020.64 | 0.104311 | ||||||||
\(944\) | −11477.5 | −0.395722 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 12228.5 | 0.420277 | ||||||||
\(947\) | 29301.0 | 1.00544 | 0.502722 | − | 0.864448i | \(-0.332332\pi\) | ||||
0.502722 | + | 0.864448i | \(0.332332\pi\) | |||||||
\(948\) | −40295.4 | −1.38052 | ||||||||
\(949\) | −52551.0 | −1.79755 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −49299.3 | −1.68101 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −35739.2 | −1.21480 | −0.607401 | − | 0.794396i | \(-0.707788\pi\) | ||||
−0.607401 | + | 0.794396i | \(0.707788\pi\) | |||||||
\(954\) | 3477.07 | 0.118002 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 10889.8 | 0.368412 | ||||||||
\(957\) | −18036.3 | −0.609228 | ||||||||
\(958\) | 7504.19 | 0.253079 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 60108.0 | 2.01766 | ||||||||
\(962\) | −22598.0 | −0.757368 | ||||||||
\(963\) | 12712.7 | 0.425400 | ||||||||
\(964\) | 9908.43 | 0.331047 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 47240.9 | 1.57101 | 0.785503 | − | 0.618857i | \(-0.212404\pi\) | ||||
0.785503 | + | 0.618857i | \(0.212404\pi\) | |||||||
\(968\) | 6715.12 | 0.222967 | ||||||||
\(969\) | 64831.7 | 2.14932 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 35861.0 | 1.18521 | 0.592603 | − | 0.805494i | \(-0.298100\pi\) | ||||
0.592603 | + | 0.805494i | \(0.298100\pi\) | |||||||
\(972\) | −9985.08 | −0.329497 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −14995.0 | −0.493296 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 11564.8 | 0.379282 | ||||||||
\(977\) | −22986.5 | −0.752714 | −0.376357 | − | 0.926475i | \(-0.622823\pi\) | ||||
−0.376357 | + | 0.926475i | \(0.622823\pi\) | |||||||
\(978\) | −54911.2 | −1.79537 | ||||||||
\(979\) | −19896.1 | −0.649523 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 42477.5 | 1.38247 | ||||||||
\(982\) | −4728.41 | −0.153656 | ||||||||
\(983\) | −45451.8 | −1.47476 | −0.737379 | − | 0.675479i | \(-0.763937\pi\) | ||||
−0.737379 | + | 0.675479i | \(0.763937\pi\) | |||||||
\(984\) | 9551.88 | 0.309454 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 24859.7 | 0.802936 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 14971.0 | 0.482077 | ||||||||
\(989\) | 6041.50 | 0.194245 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 10088.7 | 0.323389 | 0.161694 | − | 0.986841i | \(-0.448304\pi\) | ||||
0.161694 | + | 0.986841i | \(0.448304\pi\) | |||||||
\(992\) | −9594.61 | −0.307086 | ||||||||
\(993\) | −55148.3 | −1.76241 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 39145.8 | 1.24536 | ||||||||
\(997\) | −45887.2 | −1.45763 | −0.728817 | − | 0.684709i | \(-0.759929\pi\) | ||||
−0.728817 | + | 0.684709i | \(0.759929\pi\) | |||||||
\(998\) | 5928.23 | 0.188031 | ||||||||
\(999\) | 31051.8 | 0.983419 |
(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 | 2450.4.a.cz.1.8 | yes | 8 | |
5.4 | even | 2 | 2450.4.a.da.1.1 | yes | 8 | ||
7.6 | odd | 2 | inner | 2450.4.a.cz.1.1 | ✓ | 8 | |
35.34 | odd | 2 | 2450.4.a.da.1.8 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2450.4.a.cz.1.1 | ✓ | 8 | 7.6 | odd | 2 | inner | |
2450.4.a.cz.1.8 | yes | 8 | 1.1 | even | 1 | trivial | |
2450.4.a.da.1.1 | yes | 8 | 5.4 | even | 2 | ||
2450.4.a.da.1.8 | yes | 8 | 35.34 | odd | 2 |