Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [289,4,Mod(1,289)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(289, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("289.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 289 = 17^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 289.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: | \(17.0515519917\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 72 x^{10} - 17 x^{9} + 1872 x^{8} + 627 x^{7} - 20922 x^{6} - 5163 x^{5} + 93255 x^{4} - 4607 x^{3} - 117822 x^{2} + 21960 x + 29352 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{3}\cdot 17^{2} \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(3.73276\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 289.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −3.73276 | −1.31973 | −0.659865 | − | 0.751384i | \(-0.729387\pi\) | ||||
−0.659865 | + | 0.751384i | \(0.729387\pi\) | |||||||
\(3\) | −3.65511 | −0.703426 | −0.351713 | − | 0.936108i | \(-0.614401\pi\) | ||||
−0.351713 | + | 0.936108i | \(0.614401\pi\) | |||||||
\(4\) | 5.93351 | 0.741689 | ||||||||
\(5\) | −14.5154 | −1.29829 | −0.649146 | − | 0.760664i | \(-0.724874\pi\) | ||||
−0.649146 | + | 0.760664i | \(0.724874\pi\) | |||||||
\(6\) | 13.6437 | 0.928333 | ||||||||
\(7\) | 12.9694 | 0.700284 | 0.350142 | − | 0.936697i | \(-0.386133\pi\) | ||||
0.350142 | + | 0.936697i | \(0.386133\pi\) | |||||||
\(8\) | 7.71372 | 0.340901 | ||||||||
\(9\) | −13.6402 | −0.505191 | ||||||||
\(10\) | 54.1823 | 1.71340 | ||||||||
\(11\) | −20.2490 | −0.555028 | −0.277514 | − | 0.960722i | \(-0.589511\pi\) | ||||
−0.277514 | + | 0.960722i | \(0.589511\pi\) | |||||||
\(12\) | −21.6876 | −0.521723 | ||||||||
\(13\) | −90.7856 | −1.93688 | −0.968438 | − | 0.249253i | \(-0.919815\pi\) | ||||
−0.968438 | + | 0.249253i | \(0.919815\pi\) | |||||||
\(14\) | −48.4118 | −0.924186 | ||||||||
\(15\) | 53.0552 | 0.913253 | ||||||||
\(16\) | −76.2615 | −1.19159 | ||||||||
\(17\) | 0 | 0 | ||||||||
\(18\) | 50.9155 | 0.666716 | ||||||||
\(19\) | −127.359 | −1.53779 | −0.768897 | − | 0.639373i | \(-0.779194\pi\) | ||||
−0.768897 | + | 0.639373i | \(0.779194\pi\) | |||||||
\(20\) | −86.1270 | −0.962929 | ||||||||
\(21\) | −47.4047 | −0.492598 | ||||||||
\(22\) | 75.5848 | 0.732488 | ||||||||
\(23\) | −69.5078 | −0.630147 | −0.315073 | − | 0.949067i | \(-0.602029\pi\) | ||||
−0.315073 | + | 0.949067i | \(0.602029\pi\) | |||||||
\(24\) | −28.1945 | −0.239799 | ||||||||
\(25\) | 85.6954 | 0.685563 | ||||||||
\(26\) | 338.881 | 2.55616 | ||||||||
\(27\) | 148.544 | 1.05879 | ||||||||
\(28\) | 76.9542 | 0.519392 | ||||||||
\(29\) | −43.9568 | −0.281468 | −0.140734 | − | 0.990047i | \(-0.544946\pi\) | ||||
−0.140734 | + | 0.990047i | \(0.544946\pi\) | |||||||
\(30\) | −198.042 | −1.20525 | ||||||||
\(31\) | −218.817 | −1.26776 | −0.633882 | − | 0.773430i | \(-0.718540\pi\) | ||||
−0.633882 | + | 0.773430i | \(0.718540\pi\) | |||||||
\(32\) | 222.956 | 1.23167 | ||||||||
\(33\) | 74.0124 | 0.390422 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −188.256 | −0.909173 | ||||||||
\(36\) | −80.9340 | −0.374695 | ||||||||
\(37\) | −41.5125 | −0.184449 | −0.0922245 | − | 0.995738i | \(-0.529398\pi\) | ||||
−0.0922245 | + | 0.995738i | \(0.529398\pi\) | |||||||
\(38\) | 475.399 | 2.02947 | ||||||||
\(39\) | 331.832 | 1.36245 | ||||||||
\(40\) | −111.967 | −0.442590 | ||||||||
\(41\) | 440.141 | 1.67655 | 0.838274 | − | 0.545249i | \(-0.183565\pi\) | ||||
0.838274 | + | 0.545249i | \(0.183565\pi\) | |||||||
\(42\) | 176.951 | 0.650097 | ||||||||
\(43\) | −310.790 | −1.10221 | −0.551106 | − | 0.834435i | \(-0.685794\pi\) | ||||
−0.551106 | + | 0.834435i | \(0.685794\pi\) | |||||||
\(44\) | −120.148 | −0.411658 | ||||||||
\(45\) | 197.992 | 0.655886 | ||||||||
\(46\) | 259.456 | 0.831624 | ||||||||
\(47\) | 84.3763 | 0.261863 | 0.130931 | − | 0.991391i | \(-0.458203\pi\) | ||||
0.130931 | + | 0.991391i | \(0.458203\pi\) | |||||||
\(48\) | 278.744 | 0.838194 | ||||||||
\(49\) | −174.794 | −0.509603 | ||||||||
\(50\) | −319.880 | −0.904759 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −538.677 | −1.43656 | ||||||||
\(53\) | 47.6186 | 0.123414 | 0.0617068 | − | 0.998094i | \(-0.480346\pi\) | ||||
0.0617068 | + | 0.998094i | \(0.480346\pi\) | |||||||
\(54\) | −554.480 | −1.39732 | ||||||||
\(55\) | 293.922 | 0.720589 | ||||||||
\(56\) | 100.043 | 0.238728 | ||||||||
\(57\) | 465.510 | 1.08172 | ||||||||
\(58\) | 164.080 | 0.371462 | ||||||||
\(59\) | −1.73428 | −0.00382685 | −0.00191342 | − | 0.999998i | \(-0.500609\pi\) | ||||
−0.00191342 | + | 0.999998i | \(0.500609\pi\) | |||||||
\(60\) | 314.804 | 0.677350 | ||||||||
\(61\) | 159.400 | 0.334575 | 0.167287 | − | 0.985908i | \(-0.446499\pi\) | ||||
0.167287 | + | 0.985908i | \(0.446499\pi\) | |||||||
\(62\) | 816.792 | 1.67311 | ||||||||
\(63\) | −176.905 | −0.353777 | ||||||||
\(64\) | −222.151 | −0.433888 | ||||||||
\(65\) | 1317.78 | 2.51463 | ||||||||
\(66\) | −276.271 | −0.515251 | ||||||||
\(67\) | 141.756 | 0.258482 | 0.129241 | − | 0.991613i | \(-0.458746\pi\) | ||||
0.129241 | + | 0.991613i | \(0.458746\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 254.059 | 0.443262 | ||||||||
\(70\) | 702.714 | 1.19986 | ||||||||
\(71\) | 447.302 | 0.747675 | 0.373838 | − | 0.927494i | \(-0.378042\pi\) | ||||
0.373838 | + | 0.927494i | \(0.378042\pi\) | |||||||
\(72\) | −105.216 | −0.172220 | ||||||||
\(73\) | 757.081 | 1.21383 | 0.606916 | − | 0.794766i | \(-0.292407\pi\) | ||||
0.606916 | + | 0.794766i | \(0.292407\pi\) | |||||||
\(74\) | 154.956 | 0.243423 | ||||||||
\(75\) | −313.226 | −0.482243 | ||||||||
\(76\) | −755.684 | −1.14056 | ||||||||
\(77\) | −262.618 | −0.388677 | ||||||||
\(78\) | −1238.65 | −1.79807 | ||||||||
\(79\) | 529.801 | 0.754523 | 0.377261 | − | 0.926107i | \(-0.376866\pi\) | ||||
0.377261 | + | 0.926107i | \(0.376866\pi\) | |||||||
\(80\) | 1106.96 | 1.54703 | ||||||||
\(81\) | −174.662 | −0.239591 | ||||||||
\(82\) | −1642.94 | −2.21259 | ||||||||
\(83\) | −762.097 | −1.00784 | −0.503922 | − | 0.863749i | \(-0.668110\pi\) | ||||
−0.503922 | + | 0.863749i | \(0.668110\pi\) | |||||||
\(84\) | −281.276 | −0.365354 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 1160.11 | 1.45462 | ||||||||
\(87\) | 160.667 | 0.197992 | ||||||||
\(88\) | −156.195 | −0.189210 | ||||||||
\(89\) | −397.434 | −0.473348 | −0.236674 | − | 0.971589i | \(-0.576057\pi\) | ||||
−0.236674 | + | 0.971589i | \(0.576057\pi\) | |||||||
\(90\) | −739.056 | −0.865593 | ||||||||
\(91\) | −1177.44 | −1.35636 | ||||||||
\(92\) | −412.425 | −0.467373 | ||||||||
\(93\) | 799.801 | 0.891779 | ||||||||
\(94\) | −314.957 | −0.345588 | ||||||||
\(95\) | 1848.66 | 1.99651 | ||||||||
\(96\) | −814.930 | −0.866391 | ||||||||
\(97\) | −427.919 | −0.447924 | −0.223962 | − | 0.974598i | \(-0.571899\pi\) | ||||
−0.223962 | + | 0.974598i | \(0.571899\pi\) | |||||||
\(98\) | 652.464 | 0.672538 | ||||||||
\(99\) | 276.200 | 0.280395 | ||||||||
\(100\) | 508.474 | 0.508474 | ||||||||
\(101\) | 1591.35 | 1.56778 | 0.783889 | − | 0.620901i | \(-0.213233\pi\) | ||||
0.783889 | + | 0.620901i | \(0.213233\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1094.59 | −1.04712 | −0.523558 | − | 0.851990i | \(-0.675396\pi\) | ||||
−0.523558 | + | 0.851990i | \(0.675396\pi\) | |||||||
\(104\) | −700.295 | −0.660284 | ||||||||
\(105\) | 688.096 | 0.639536 | ||||||||
\(106\) | −177.749 | −0.162873 | ||||||||
\(107\) | −1321.45 | −1.19392 | −0.596960 | − | 0.802271i | \(-0.703625\pi\) | ||||
−0.596960 | + | 0.802271i | \(0.703625\pi\) | |||||||
\(108\) | 881.389 | 0.785293 | ||||||||
\(109\) | −1324.25 | −1.16367 | −0.581835 | − | 0.813307i | \(-0.697665\pi\) | ||||
−0.581835 | + | 0.813307i | \(0.697665\pi\) | |||||||
\(110\) | −1097.14 | −0.950983 | ||||||||
\(111\) | 151.733 | 0.129746 | ||||||||
\(112\) | −989.069 | −0.834449 | ||||||||
\(113\) | −1621.26 | −1.34969 | −0.674847 | − | 0.737958i | \(-0.735790\pi\) | ||||
−0.674847 | + | 0.737958i | \(0.735790\pi\) | |||||||
\(114\) | −1737.64 | −1.42758 | ||||||||
\(115\) | 1008.93 | 0.818115 | ||||||||
\(116\) | −260.818 | −0.208762 | ||||||||
\(117\) | 1238.33 | 0.978493 | ||||||||
\(118\) | 6.47365 | 0.00505041 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 409.253 | 0.311329 | ||||||||
\(121\) | −920.977 | −0.691944 | ||||||||
\(122\) | −595.001 | −0.441548 | ||||||||
\(123\) | −1608.76 | −1.17933 | ||||||||
\(124\) | −1298.35 | −0.940287 | ||||||||
\(125\) | 570.520 | 0.408231 | ||||||||
\(126\) | 660.345 | 0.466890 | ||||||||
\(127\) | 423.287 | 0.295753 | 0.147876 | − | 0.989006i | \(-0.452756\pi\) | ||||
0.147876 | + | 0.989006i | \(0.452756\pi\) | |||||||
\(128\) | −954.415 | −0.659056 | ||||||||
\(129\) | 1135.97 | 0.775325 | ||||||||
\(130\) | −4918.98 | −3.31864 | ||||||||
\(131\) | −792.977 | −0.528876 | −0.264438 | − | 0.964403i | \(-0.585186\pi\) | ||||
−0.264438 | + | 0.964403i | \(0.585186\pi\) | |||||||
\(132\) | 439.153 | 0.289571 | ||||||||
\(133\) | −1651.77 | −1.07689 | ||||||||
\(134\) | −529.143 | −0.341127 | ||||||||
\(135\) | −2156.17 | −1.37462 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 809.512 | 0.504827 | 0.252414 | − | 0.967619i | \(-0.418776\pi\) | ||||
0.252414 | + | 0.967619i | \(0.418776\pi\) | |||||||
\(138\) | −948.341 | −0.584986 | ||||||||
\(139\) | 2842.04 | 1.73424 | 0.867119 | − | 0.498102i | \(-0.165969\pi\) | ||||
0.867119 | + | 0.498102i | \(0.165969\pi\) | |||||||
\(140\) | −1117.02 | −0.674323 | ||||||||
\(141\) | −308.405 | −0.184201 | ||||||||
\(142\) | −1669.67 | −0.986730 | ||||||||
\(143\) | 1838.32 | 1.07502 | ||||||||
\(144\) | 1040.22 | 0.601979 | ||||||||
\(145\) | 638.048 | 0.365428 | ||||||||
\(146\) | −2826.00 | −1.60193 | ||||||||
\(147\) | 638.891 | 0.358468 | ||||||||
\(148\) | −246.315 | −0.136804 | ||||||||
\(149\) | −1010.84 | −0.555782 | −0.277891 | − | 0.960613i | \(-0.589635\pi\) | ||||
−0.277891 | + | 0.960613i | \(0.589635\pi\) | |||||||
\(150\) | 1169.20 | 0.636431 | ||||||||
\(151\) | 1340.29 | 0.722327 | 0.361163 | − | 0.932503i | \(-0.382380\pi\) | ||||
0.361163 | + | 0.932503i | \(0.382380\pi\) | |||||||
\(152\) | −982.409 | −0.524236 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 980.292 | 0.512949 | ||||||||
\(155\) | 3176.21 | 1.64593 | ||||||||
\(156\) | 1968.93 | 1.01051 | ||||||||
\(157\) | −947.372 | −0.481583 | −0.240792 | − | 0.970577i | \(-0.577407\pi\) | ||||
−0.240792 | + | 0.970577i | \(0.577407\pi\) | |||||||
\(158\) | −1977.62 | −0.995766 | ||||||||
\(159\) | −174.051 | −0.0868123 | ||||||||
\(160\) | −3236.29 | −1.59907 | ||||||||
\(161\) | −901.477 | −0.441282 | ||||||||
\(162\) | 651.970 | 0.316195 | ||||||||
\(163\) | 966.144 | 0.464259 | 0.232129 | − | 0.972685i | \(-0.425431\pi\) | ||||
0.232129 | + | 0.972685i | \(0.425431\pi\) | |||||||
\(164\) | 2611.58 | 1.24348 | ||||||||
\(165\) | −1074.32 | −0.506881 | ||||||||
\(166\) | 2844.73 | 1.33008 | ||||||||
\(167\) | 1193.13 | 0.552857 | 0.276429 | − | 0.961034i | \(-0.410849\pi\) | ||||
0.276429 | + | 0.961034i | \(0.410849\pi\) | |||||||
\(168\) | −365.667 | −0.167927 | ||||||||
\(169\) | 6045.03 | 2.75149 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1737.19 | 0.776880 | ||||||||
\(172\) | −1844.08 | −0.817498 | ||||||||
\(173\) | −8.50924 | −0.00373957 | −0.00186978 | − | 0.999998i | \(-0.500595\pi\) | ||||
−0.00186978 | + | 0.999998i | \(0.500595\pi\) | |||||||
\(174\) | −599.731 | −0.261296 | ||||||||
\(175\) | 1111.42 | 0.480089 | ||||||||
\(176\) | 1544.22 | 0.661364 | ||||||||
\(177\) | 6.33899 | 0.00269191 | ||||||||
\(178\) | 1483.53 | 0.624691 | ||||||||
\(179\) | −909.300 | −0.379689 | −0.189844 | − | 0.981814i | \(-0.560798\pi\) | ||||
−0.189844 | + | 0.981814i | \(0.560798\pi\) | |||||||
\(180\) | 1174.79 | 0.486463 | ||||||||
\(181\) | 2448.71 | 1.00559 | 0.502793 | − | 0.864407i | \(-0.332306\pi\) | ||||
0.502793 | + | 0.864407i | \(0.332306\pi\) | |||||||
\(182\) | 4395.10 | 1.79003 | ||||||||
\(183\) | −582.624 | −0.235349 | ||||||||
\(184\) | −536.164 | −0.214818 | ||||||||
\(185\) | 602.568 | 0.239469 | ||||||||
\(186\) | −2985.47 | −1.17691 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 500.648 | 0.194221 | ||||||||
\(189\) | 1926.54 | 0.741454 | ||||||||
\(190\) | −6900.59 | −2.63485 | ||||||||
\(191\) | 845.418 | 0.320274 | 0.160137 | − | 0.987095i | \(-0.448806\pi\) | ||||
0.160137 | + | 0.987095i | \(0.448806\pi\) | |||||||
\(192\) | 811.986 | 0.305208 | ||||||||
\(193\) | −7.70682 | −0.00287435 | −0.00143717 | − | 0.999999i | \(-0.500457\pi\) | ||||
−0.00143717 | + | 0.999999i | \(0.500457\pi\) | |||||||
\(194\) | 1597.32 | 0.591139 | ||||||||
\(195\) | −4816.65 | −1.76886 | ||||||||
\(196\) | −1037.14 | −0.377967 | ||||||||
\(197\) | −5024.07 | −1.81701 | −0.908503 | − | 0.417879i | \(-0.862773\pi\) | ||||
−0.908503 | + | 0.417879i | \(0.862773\pi\) | |||||||
\(198\) | −1030.99 | −0.370046 | ||||||||
\(199\) | 1210.87 | 0.431339 | 0.215669 | − | 0.976466i | \(-0.430807\pi\) | ||||
0.215669 | + | 0.976466i | \(0.430807\pi\) | |||||||
\(200\) | 661.030 | 0.233709 | ||||||||
\(201\) | −518.135 | −0.181823 | ||||||||
\(202\) | −5940.15 | −2.06905 | ||||||||
\(203\) | −570.095 | −0.197107 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −6388.80 | −2.17665 | ||||||||
\(206\) | 4085.84 | 1.38191 | ||||||||
\(207\) | 948.098 | 0.318345 | ||||||||
\(208\) | 6923.45 | 2.30796 | ||||||||
\(209\) | 2578.89 | 0.853519 | ||||||||
\(210\) | −2568.50 | −0.844016 | ||||||||
\(211\) | −3047.09 | −0.994172 | −0.497086 | − | 0.867701i | \(-0.665597\pi\) | ||||
−0.497086 | + | 0.867701i | \(0.665597\pi\) | |||||||
\(212\) | 282.545 | 0.0915344 | ||||||||
\(213\) | −1634.94 | −0.525934 | ||||||||
\(214\) | 4932.66 | 1.57565 | ||||||||
\(215\) | 4511.23 | 1.43099 | ||||||||
\(216\) | 1145.83 | 0.360943 | ||||||||
\(217\) | −2837.93 | −0.887795 | ||||||||
\(218\) | 4943.10 | 1.53573 | ||||||||
\(219\) | −2767.22 | −0.853841 | ||||||||
\(220\) | 1743.99 | 0.534453 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | −566.382 | −0.171230 | ||||||||
\(223\) | −2883.35 | −0.865846 | −0.432923 | − | 0.901431i | \(-0.642518\pi\) | ||||
−0.432923 | + | 0.901431i | \(0.642518\pi\) | |||||||
\(224\) | 2891.62 | 0.862520 | ||||||||
\(225\) | −1168.90 | −0.346340 | ||||||||
\(226\) | 6051.78 | 1.78123 | ||||||||
\(227\) | 5402.18 | 1.57954 | 0.789770 | − | 0.613403i | \(-0.210200\pi\) | ||||
0.789770 | + | 0.613403i | \(0.210200\pi\) | |||||||
\(228\) | 2762.11 | 0.802303 | ||||||||
\(229\) | −1524.25 | −0.439849 | −0.219925 | − | 0.975517i | \(-0.570581\pi\) | ||||
−0.219925 | + | 0.975517i | \(0.570581\pi\) | |||||||
\(230\) | −3766.10 | −1.07969 | ||||||||
\(231\) | 959.899 | 0.273406 | ||||||||
\(232\) | −339.070 | −0.0959528 | ||||||||
\(233\) | −1685.79 | −0.473989 | −0.236995 | − | 0.971511i | \(-0.576162\pi\) | ||||
−0.236995 | + | 0.971511i | \(0.576162\pi\) | |||||||
\(234\) | −4622.39 | −1.29135 | ||||||||
\(235\) | −1224.75 | −0.339975 | ||||||||
\(236\) | −10.2904 | −0.00283833 | ||||||||
\(237\) | −1936.48 | −0.530751 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −4887.91 | −1.32290 | −0.661449 | − | 0.749990i | \(-0.730058\pi\) | ||||
−0.661449 | + | 0.749990i | \(0.730058\pi\) | |||||||
\(240\) | −4046.07 | −1.08822 | ||||||||
\(241\) | −3416.56 | −0.913195 | −0.456597 | − | 0.889673i | \(-0.650932\pi\) | ||||
−0.456597 | + | 0.889673i | \(0.650932\pi\) | |||||||
\(242\) | 3437.79 | 0.913179 | ||||||||
\(243\) | −3372.29 | −0.890257 | ||||||||
\(244\) | 945.800 | 0.248150 | ||||||||
\(245\) | 2537.19 | 0.661614 | ||||||||
\(246\) | 6005.13 | 1.55640 | ||||||||
\(247\) | 11562.3 | 2.97852 | ||||||||
\(248\) | −1687.89 | −0.432183 | ||||||||
\(249\) | 2785.55 | 0.708944 | ||||||||
\(250\) | −2129.62 | −0.538755 | ||||||||
\(251\) | 2357.42 | 0.592825 | 0.296413 | − | 0.955060i | \(-0.404210\pi\) | ||||
0.296413 | + | 0.955060i | \(0.404210\pi\) | |||||||
\(252\) | −1049.67 | −0.262392 | ||||||||
\(253\) | 1407.47 | 0.349749 | ||||||||
\(254\) | −1580.03 | −0.390314 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 5339.81 | 1.30366 | ||||||||
\(257\) | 2033.64 | 0.493598 | 0.246799 | − | 0.969067i | \(-0.420621\pi\) | ||||
0.246799 | + | 0.969067i | \(0.420621\pi\) | |||||||
\(258\) | −4240.32 | −1.02322 | ||||||||
\(259\) | −538.393 | −0.129167 | ||||||||
\(260\) | 7819.09 | 1.86507 | ||||||||
\(261\) | 599.578 | 0.142195 | ||||||||
\(262\) | 2960.00 | 0.697974 | ||||||||
\(263\) | 5377.07 | 1.26070 | 0.630351 | − | 0.776310i | \(-0.282911\pi\) | ||||
0.630351 | + | 0.776310i | \(0.282911\pi\) | |||||||
\(264\) | 570.911 | 0.133095 | ||||||||
\(265\) | −691.200 | −0.160227 | ||||||||
\(266\) | 6165.66 | 1.42121 | ||||||||
\(267\) | 1452.67 | 0.332965 | ||||||||
\(268\) | 841.113 | 0.191713 | ||||||||
\(269\) | 3012.15 | 0.682728 | 0.341364 | − | 0.939931i | \(-0.389111\pi\) | ||||
0.341364 | + | 0.939931i | \(0.389111\pi\) | |||||||
\(270\) | 8048.48 | 1.81413 | ||||||||
\(271\) | −1340.23 | −0.300417 | −0.150209 | − | 0.988654i | \(-0.547995\pi\) | ||||
−0.150209 | + | 0.988654i | \(0.547995\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 4303.67 | 0.954102 | ||||||||
\(274\) | −3021.72 | −0.666236 | ||||||||
\(275\) | −1735.25 | −0.380507 | ||||||||
\(276\) | 1507.46 | 0.328762 | ||||||||
\(277\) | −4917.83 | −1.06673 | −0.533365 | − | 0.845885i | \(-0.679073\pi\) | ||||
−0.533365 | + | 0.845885i | \(0.679073\pi\) | |||||||
\(278\) | −10608.7 | −2.28873 | ||||||||
\(279\) | 2984.70 | 0.640463 | ||||||||
\(280\) | −1452.15 | −0.309938 | ||||||||
\(281\) | −697.896 | −0.148160 | −0.0740801 | − | 0.997252i | \(-0.523602\pi\) | ||||
−0.0740801 | + | 0.997252i | \(0.523602\pi\) | |||||||
\(282\) | 1151.20 | 0.243096 | ||||||||
\(283\) | −5379.29 | −1.12991 | −0.564957 | − | 0.825121i | \(-0.691107\pi\) | ||||
−0.564957 | + | 0.825121i | \(0.691107\pi\) | |||||||
\(284\) | 2654.07 | 0.554542 | ||||||||
\(285\) | −6757.04 | −1.40439 | ||||||||
\(286\) | −6862.01 | −1.41874 | ||||||||
\(287\) | 5708.38 | 1.17406 | ||||||||
\(288\) | −3041.16 | −0.622230 | ||||||||
\(289\) | 0 | 0 | ||||||||
\(290\) | −2381.68 | −0.482266 | ||||||||
\(291\) | 1564.09 | 0.315081 | ||||||||
\(292\) | 4492.15 | 0.900285 | ||||||||
\(293\) | 2876.89 | 0.573616 | 0.286808 | − | 0.957988i | \(-0.407406\pi\) | ||||
0.286808 | + | 0.957988i | \(0.407406\pi\) | |||||||
\(294\) | −2384.83 | −0.473081 | ||||||||
\(295\) | 25.1737 | 0.00496837 | ||||||||
\(296\) | −320.216 | −0.0628789 | ||||||||
\(297\) | −3007.88 | −0.587659 | ||||||||
\(298\) | 3773.24 | 0.733482 | ||||||||
\(299\) | 6310.31 | 1.22052 | ||||||||
\(300\) | −1858.53 | −0.357674 | ||||||||
\(301\) | −4030.78 | −0.771861 | ||||||||
\(302\) | −5002.99 | −0.953276 | ||||||||
\(303\) | −5816.58 | −1.10282 | ||||||||
\(304\) | 9712.57 | 1.83241 | ||||||||
\(305\) | −2313.74 | −0.434376 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −3765.61 | −0.700048 | −0.350024 | − | 0.936741i | \(-0.613827\pi\) | ||||
−0.350024 | + | 0.936741i | \(0.613827\pi\) | |||||||
\(308\) | −1558.25 | −0.288277 | ||||||||
\(309\) | 4000.84 | 0.736570 | ||||||||
\(310\) | −11856.0 | −2.17218 | ||||||||
\(311\) | 1043.69 | 0.190297 | 0.0951483 | − | 0.995463i | \(-0.469667\pi\) | ||||
0.0951483 | + | 0.995463i | \(0.469667\pi\) | |||||||
\(312\) | 2559.66 | 0.464461 | ||||||||
\(313\) | 801.837 | 0.144800 | 0.0724002 | − | 0.997376i | \(-0.476934\pi\) | ||||
0.0724002 | + | 0.997376i | \(0.476934\pi\) | |||||||
\(314\) | 3536.31 | 0.635560 | ||||||||
\(315\) | 2567.84 | 0.459306 | ||||||||
\(316\) | 3143.58 | 0.559621 | ||||||||
\(317\) | −806.122 | −0.142827 | −0.0714137 | − | 0.997447i | \(-0.522751\pi\) | ||||
−0.0714137 | + | 0.997447i | \(0.522751\pi\) | |||||||
\(318\) | 649.692 | 0.114569 | ||||||||
\(319\) | 890.082 | 0.156223 | ||||||||
\(320\) | 3224.60 | 0.563314 | ||||||||
\(321\) | 4830.05 | 0.839836 | ||||||||
\(322\) | 3365.00 | 0.582373 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | −1036.36 | −0.177702 | ||||||||
\(325\) | −7779.91 | −1.32785 | ||||||||
\(326\) | −3606.38 | −0.612697 | ||||||||
\(327\) | 4840.27 | 0.818556 | ||||||||
\(328\) | 3395.12 | 0.571538 | ||||||||
\(329\) | 1094.31 | 0.183378 | ||||||||
\(330\) | 4010.17 | 0.668947 | ||||||||
\(331\) | 2607.01 | 0.432913 | 0.216457 | − | 0.976292i | \(-0.430550\pi\) | ||||
0.216457 | + | 0.976292i | \(0.430550\pi\) | |||||||
\(332\) | −4521.91 | −0.747506 | ||||||||
\(333\) | 566.237 | 0.0931820 | ||||||||
\(334\) | −4453.67 | −0.729623 | ||||||||
\(335\) | −2057.64 | −0.335585 | ||||||||
\(336\) | 3615.16 | 0.586973 | ||||||||
\(337\) | −1067.31 | −0.172523 | −0.0862614 | − | 0.996273i | \(-0.527492\pi\) | ||||
−0.0862614 | + | 0.996273i | \(0.527492\pi\) | |||||||
\(338\) | −22564.6 | −3.63123 | ||||||||
\(339\) | 5925.89 | 0.949410 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 4430.83 | 0.703645 | ||||||||
\(342\) | −6484.53 | −1.02527 | ||||||||
\(343\) | −6715.49 | −1.05715 | ||||||||
\(344\) | −2397.35 | −0.375745 | ||||||||
\(345\) | −3687.75 | −0.575484 | ||||||||
\(346\) | 31.7630 | 0.00493522 | ||||||||
\(347\) | −11380.2 | −1.76058 | −0.880288 | − | 0.474439i | \(-0.842651\pi\) | ||||
−0.880288 | + | 0.474439i | \(0.842651\pi\) | |||||||
\(348\) | 953.319 | 0.146848 | ||||||||
\(349\) | −2447.03 | −0.375320 | −0.187660 | − | 0.982234i | \(-0.560090\pi\) | ||||
−0.187660 | + | 0.982234i | \(0.560090\pi\) | |||||||
\(350\) | −4148.67 | −0.633588 | ||||||||
\(351\) | −13485.7 | −2.05075 | ||||||||
\(352\) | −4514.65 | −0.683613 | ||||||||
\(353\) | 5229.05 | 0.788426 | 0.394213 | − | 0.919019i | \(-0.371017\pi\) | ||||
0.394213 | + | 0.919019i | \(0.371017\pi\) | |||||||
\(354\) | −23.6619 | −0.00355259 | ||||||||
\(355\) | −6492.74 | −0.970701 | ||||||||
\(356\) | −2358.18 | −0.351077 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 3394.20 | 0.501087 | ||||||||
\(359\) | 9108.24 | 1.33904 | 0.669519 | − | 0.742795i | \(-0.266500\pi\) | ||||
0.669519 | + | 0.742795i | \(0.266500\pi\) | |||||||
\(360\) | 1527.25 | 0.223592 | ||||||||
\(361\) | 9361.22 | 1.36481 | ||||||||
\(362\) | −9140.44 | −1.32710 | ||||||||
\(363\) | 3366.27 | 0.486731 | ||||||||
\(364\) | −6986.34 | −1.00600 | ||||||||
\(365\) | −10989.3 | −1.57591 | ||||||||
\(366\) | 2174.80 | 0.310597 | ||||||||
\(367\) | −1155.57 | −0.164360 | −0.0821801 | − | 0.996617i | \(-0.526188\pi\) | ||||
−0.0821801 | + | 0.996617i | \(0.526188\pi\) | |||||||
\(368\) | 5300.77 | 0.750875 | ||||||||
\(369\) | −6003.59 | −0.846977 | ||||||||
\(370\) | −2249.24 | −0.316034 | ||||||||
\(371\) | 617.586 | 0.0864245 | ||||||||
\(372\) | 4745.62 | 0.661422 | ||||||||
\(373\) | −9949.97 | −1.38121 | −0.690603 | − | 0.723234i | \(-0.742655\pi\) | ||||
−0.690603 | + | 0.723234i | \(0.742655\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −2085.31 | −0.287160 | ||||||||
\(376\) | 650.855 | 0.0892694 | ||||||||
\(377\) | 3990.64 | 0.545169 | ||||||||
\(378\) | −7191.30 | −0.978520 | ||||||||
\(379\) | 1443.78 | 0.195678 | 0.0978388 | − | 0.995202i | \(-0.468807\pi\) | ||||
0.0978388 | + | 0.995202i | \(0.468807\pi\) | |||||||
\(380\) | 10969.0 | 1.48079 | ||||||||
\(381\) | −1547.16 | −0.208040 | ||||||||
\(382\) | −3155.74 | −0.422675 | ||||||||
\(383\) | −8249.59 | −1.10061 | −0.550306 | − | 0.834963i | \(-0.685489\pi\) | ||||
−0.550306 | + | 0.834963i | \(0.685489\pi\) | |||||||
\(384\) | 3488.49 | 0.463598 | ||||||||
\(385\) | 3812.00 | 0.504617 | ||||||||
\(386\) | 28.7677 | 0.00379336 | ||||||||
\(387\) | 4239.23 | 0.556827 | ||||||||
\(388\) | −2539.06 | −0.332220 | ||||||||
\(389\) | −9396.96 | −1.22479 | −0.612397 | − | 0.790551i | \(-0.709794\pi\) | ||||
−0.612397 | + | 0.790551i | \(0.709794\pi\) | |||||||
\(390\) | 17979.4 | 2.33442 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | −1348.31 | −0.173724 | ||||||||
\(393\) | 2898.42 | 0.372025 | ||||||||
\(394\) | 18753.6 | 2.39796 | ||||||||
\(395\) | −7690.25 | −0.979591 | ||||||||
\(396\) | 1638.83 | 0.207966 | ||||||||
\(397\) | −11970.7 | −1.51333 | −0.756667 | − | 0.653800i | \(-0.773174\pi\) | ||||
−0.756667 | + | 0.653800i | \(0.773174\pi\) | |||||||
\(398\) | −4519.90 | −0.569251 | ||||||||
\(399\) | 6037.40 | 0.757514 | ||||||||
\(400\) | −6535.26 | −0.816908 | ||||||||
\(401\) | −10710.9 | −1.33386 | −0.666928 | − | 0.745122i | \(-0.732391\pi\) | ||||
−0.666928 | + | 0.745122i | \(0.732391\pi\) | |||||||
\(402\) | 1934.08 | 0.239958 | ||||||||
\(403\) | 19865.4 | 2.45550 | ||||||||
\(404\) | 9442.31 | 1.16280 | ||||||||
\(405\) | 2535.27 | 0.311059 | ||||||||
\(406\) | 2128.03 | 0.260129 | ||||||||
\(407\) | 840.587 | 0.102374 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −1220.58 | −0.147565 | −0.0737824 | − | 0.997274i | \(-0.523507\pi\) | ||||
−0.0737824 | + | 0.997274i | \(0.523507\pi\) | |||||||
\(410\) | 23847.9 | 2.87259 | ||||||||
\(411\) | −2958.86 | −0.355109 | ||||||||
\(412\) | −6494.75 | −0.776634 | ||||||||
\(413\) | −22.4926 | −0.00267988 | ||||||||
\(414\) | −3539.02 | −0.420129 | ||||||||
\(415\) | 11062.1 | 1.30848 | ||||||||
\(416\) | −20241.2 | −2.38560 | ||||||||
\(417\) | −10388.0 | −1.21991 | ||||||||
\(418\) | −9626.37 | −1.12641 | ||||||||
\(419\) | 10940.2 | 1.27557 | 0.637784 | − | 0.770215i | \(-0.279851\pi\) | ||||
0.637784 | + | 0.770215i | \(0.279851\pi\) | |||||||
\(420\) | 4082.82 | 0.474337 | ||||||||
\(421\) | −2304.87 | −0.266823 | −0.133411 | − | 0.991061i | \(-0.542593\pi\) | ||||
−0.133411 | + | 0.991061i | \(0.542593\pi\) | |||||||
\(422\) | 11374.1 | 1.31204 | ||||||||
\(423\) | −1150.91 | −0.132291 | ||||||||
\(424\) | 367.316 | 0.0420718 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 6102.83 | 0.694092 | ||||||||
\(427\) | 2067.32 | 0.234297 | ||||||||
\(428\) | −7840.84 | −0.885518 | ||||||||
\(429\) | −6719.26 | −0.756198 | ||||||||
\(430\) | −16839.4 | −1.88852 | ||||||||
\(431\) | 5741.54 | 0.641671 | 0.320835 | − | 0.947135i | \(-0.396036\pi\) | ||||
0.320835 | + | 0.947135i | \(0.396036\pi\) | |||||||
\(432\) | −11328.2 | −1.26164 | ||||||||
\(433\) | 4553.54 | 0.505379 | 0.252690 | − | 0.967547i | \(-0.418685\pi\) | ||||
0.252690 | + | 0.967547i | \(0.418685\pi\) | |||||||
\(434\) | 10593.3 | 1.17165 | ||||||||
\(435\) | −2332.14 | −0.257051 | ||||||||
\(436\) | −7857.44 | −0.863080 | ||||||||
\(437\) | 8852.42 | 0.969036 | ||||||||
\(438\) | 10329.4 | 1.12684 | ||||||||
\(439\) | 10786.4 | 1.17268 | 0.586340 | − | 0.810065i | \(-0.300568\pi\) | ||||
0.586340 | + | 0.810065i | \(0.300568\pi\) | |||||||
\(440\) | 2267.23 | 0.245650 | ||||||||
\(441\) | 2384.22 | 0.257447 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 13133.5 | 1.40856 | 0.704280 | − | 0.709922i | \(-0.251270\pi\) | ||||
0.704280 | + | 0.709922i | \(0.251270\pi\) | |||||||
\(444\) | 900.307 | 0.0962313 | ||||||||
\(445\) | 5768.90 | 0.614544 | ||||||||
\(446\) | 10762.9 | 1.14268 | ||||||||
\(447\) | 3694.74 | 0.390952 | ||||||||
\(448\) | −2881.17 | −0.303845 | ||||||||
\(449\) | −714.661 | −0.0751157 | −0.0375578 | − | 0.999294i | \(-0.511958\pi\) | ||||
−0.0375578 | + | 0.999294i | \(0.511958\pi\) | |||||||
\(450\) | 4363.22 | 0.457076 | ||||||||
\(451\) | −8912.42 | −0.930531 | ||||||||
\(452\) | −9619.77 | −1.00105 | ||||||||
\(453\) | −4898.91 | −0.508104 | ||||||||
\(454\) | −20165.1 | −2.08457 | ||||||||
\(455\) | 17090.9 | 1.76096 | ||||||||
\(456\) | 3590.81 | 0.368761 | ||||||||
\(457\) | −976.357 | −0.0999388 | −0.0499694 | − | 0.998751i | \(-0.515912\pi\) | ||||
−0.0499694 | + | 0.998751i | \(0.515912\pi\) | |||||||
\(458\) | 5689.67 | 0.580482 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 5986.50 | 0.606787 | ||||||||
\(461\) | −17713.0 | −1.78953 | −0.894767 | − | 0.446533i | \(-0.852659\pi\) | ||||
−0.894767 | + | 0.446533i | \(0.852659\pi\) | |||||||
\(462\) | −3583.08 | −0.360822 | ||||||||
\(463\) | −13597.7 | −1.36488 | −0.682441 | − | 0.730941i | \(-0.739082\pi\) | ||||
−0.682441 | + | 0.730941i | \(0.739082\pi\) | |||||||
\(464\) | 3352.21 | 0.335393 | ||||||||
\(465\) | −11609.4 | −1.15779 | ||||||||
\(466\) | 6292.63 | 0.625538 | ||||||||
\(467\) | 9115.78 | 0.903272 | 0.451636 | − | 0.892202i | \(-0.350841\pi\) | ||||
0.451636 | + | 0.892202i | \(0.350841\pi\) | |||||||
\(468\) | 7347.64 | 0.725737 | ||||||||
\(469\) | 1838.50 | 0.181011 | ||||||||
\(470\) | 4571.71 | 0.448675 | ||||||||
\(471\) | 3462.75 | 0.338758 | ||||||||
\(472\) | −13.3777 | −0.00130458 | ||||||||
\(473\) | 6293.20 | 0.611758 | ||||||||
\(474\) | 7228.43 | 0.700448 | ||||||||
\(475\) | −10914.0 | −1.05425 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −649.525 | −0.0623474 | ||||||||
\(478\) | 18245.4 | 1.74587 | ||||||||
\(479\) | 11483.2 | 1.09537 | 0.547683 | − | 0.836686i | \(-0.315510\pi\) | ||||
0.547683 | + | 0.836686i | \(0.315510\pi\) | |||||||
\(480\) | 11829.0 | 1.12483 | ||||||||
\(481\) | 3768.74 | 0.357255 | ||||||||
\(482\) | 12753.2 | 1.20517 | ||||||||
\(483\) | 3295.00 | 0.310409 | ||||||||
\(484\) | −5464.63 | −0.513207 | ||||||||
\(485\) | 6211.40 | 0.581536 | ||||||||
\(486\) | 12588.0 | 1.17490 | ||||||||
\(487\) | −4117.57 | −0.383131 | −0.191565 | − | 0.981480i | \(-0.561356\pi\) | ||||
−0.191565 | + | 0.981480i | \(0.561356\pi\) | |||||||
\(488\) | 1229.57 | 0.114057 | ||||||||
\(489\) | −3531.36 | −0.326572 | ||||||||
\(490\) | −9470.74 | −0.873152 | ||||||||
\(491\) | −11870.1 | −1.09102 | −0.545509 | − | 0.838105i | \(-0.683664\pi\) | ||||
−0.545509 | + | 0.838105i | \(0.683664\pi\) | |||||||
\(492\) | −9545.61 | −0.874694 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | −43159.4 | −3.93084 | ||||||||
\(495\) | −4009.14 | −0.364035 | ||||||||
\(496\) | 16687.3 | 1.51065 | ||||||||
\(497\) | 5801.25 | 0.523585 | ||||||||
\(498\) | −10397.8 | −0.935615 | ||||||||
\(499\) | 16770.4 | 1.50450 | 0.752252 | − | 0.658875i | \(-0.228967\pi\) | ||||
0.752252 | + | 0.658875i | \(0.228967\pi\) | |||||||
\(500\) | 3385.19 | 0.302780 | ||||||||
\(501\) | −4361.02 | −0.388895 | ||||||||
\(502\) | −8799.69 | −0.782369 | ||||||||
\(503\) | −14451.7 | −1.28105 | −0.640525 | − | 0.767938i | \(-0.721283\pi\) | ||||
−0.640525 | + | 0.767938i | \(0.721283\pi\) | |||||||
\(504\) | −1364.60 | −0.120603 | ||||||||
\(505\) | −23099.1 | −2.03544 | ||||||||
\(506\) | −5253.73 | −0.461575 | ||||||||
\(507\) | −22095.2 | −1.93547 | ||||||||
\(508\) | 2511.57 | 0.219357 | ||||||||
\(509\) | 22279.2 | 1.94010 | 0.970049 | − | 0.242910i | \(-0.0781019\pi\) | ||||
0.970049 | + | 0.242910i | \(0.0781019\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 9818.92 | 0.850026 | ||||||||
\(512\) | −12296.9 | −1.06143 | ||||||||
\(513\) | −18918.4 | −1.62820 | ||||||||
\(514\) | −7591.08 | −0.651417 | ||||||||
\(515\) | 15888.3 | 1.35946 | ||||||||
\(516\) | 6740.31 | 0.575049 | ||||||||
\(517\) | −1708.54 | −0.145341 | ||||||||
\(518\) | 2009.69 | 0.170465 | ||||||||
\(519\) | 31.1022 | 0.00263051 | ||||||||
\(520\) | 10165.0 | 0.857242 | ||||||||
\(521\) | −16004.3 | −1.34580 | −0.672898 | − | 0.739735i | \(-0.734951\pi\) | ||||
−0.672898 | + | 0.739735i | \(0.734951\pi\) | |||||||
\(522\) | −2238.08 | −0.187659 | ||||||||
\(523\) | −22158.6 | −1.85264 | −0.926319 | − | 0.376739i | \(-0.877045\pi\) | ||||
−0.926319 | + | 0.376739i | \(0.877045\pi\) | |||||||
\(524\) | −4705.14 | −0.392261 | ||||||||
\(525\) | −4062.37 | −0.337707 | ||||||||
\(526\) | −20071.3 | −1.66379 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | −5644.30 | −0.465221 | ||||||||
\(529\) | −7335.66 | −0.602915 | ||||||||
\(530\) | 2580.09 | 0.211456 | ||||||||
\(531\) | 23.6559 | 0.00193329 | ||||||||
\(532\) | −9800.79 | −0.798718 | ||||||||
\(533\) | −39958.5 | −3.24727 | ||||||||
\(534\) | −5422.46 | −0.439424 | ||||||||
\(535\) | 19181.3 | 1.55006 | ||||||||
\(536\) | 1093.47 | 0.0881169 | ||||||||
\(537\) | 3323.59 | 0.267083 | ||||||||
\(538\) | −11243.6 | −0.901017 | ||||||||
\(539\) | 3539.40 | 0.282844 | ||||||||
\(540\) | −12793.7 | −1.01954 | ||||||||
\(541\) | 3099.41 | 0.246310 | 0.123155 | − | 0.992387i | \(-0.460699\pi\) | ||||
0.123155 | + | 0.992387i | \(0.460699\pi\) | |||||||
\(542\) | 5002.75 | 0.396470 | ||||||||
\(543\) | −8950.30 | −0.707355 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 19221.9 | 1.51078 | ||||||||
\(546\) | −16064.6 | −1.25916 | ||||||||
\(547\) | −21795.9 | −1.70370 | −0.851852 | − | 0.523783i | \(-0.824520\pi\) | ||||
−0.851852 | + | 0.523783i | \(0.824520\pi\) | |||||||
\(548\) | 4803.25 | 0.374424 | ||||||||
\(549\) | −2174.24 | −0.169024 | ||||||||
\(550\) | 6477.27 | 0.502167 | ||||||||
\(551\) | 5598.28 | 0.432839 | ||||||||
\(552\) | 1959.74 | 0.151109 | ||||||||
\(553\) | 6871.22 | 0.528380 | ||||||||
\(554\) | 18357.1 | 1.40780 | ||||||||
\(555\) | −2202.45 | −0.168449 | ||||||||
\(556\) | 16863.3 | 1.28626 | ||||||||
\(557\) | 12689.7 | 0.965315 | 0.482658 | − | 0.875809i | \(-0.339672\pi\) | ||||
0.482658 | + | 0.875809i | \(0.339672\pi\) | |||||||
\(558\) | −11141.2 | −0.845239 | ||||||||
\(559\) | 28215.3 | 2.13485 | ||||||||
\(560\) | 14356.7 | 1.08336 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 2605.08 | 0.195532 | ||||||||
\(563\) | −10849.0 | −0.812129 | −0.406065 | − | 0.913844i | \(-0.633099\pi\) | ||||
−0.406065 | + | 0.913844i | \(0.633099\pi\) | |||||||
\(564\) | −1829.92 | −0.136620 | ||||||||
\(565\) | 23533.2 | 1.75230 | ||||||||
\(566\) | 20079.6 | 1.49118 | ||||||||
\(567\) | −2265.26 | −0.167781 | ||||||||
\(568\) | 3450.36 | 0.254884 | ||||||||
\(569\) | −5582.88 | −0.411329 | −0.205665 | − | 0.978623i | \(-0.565936\pi\) | ||||
−0.205665 | + | 0.978623i | \(0.565936\pi\) | |||||||
\(570\) | 25222.4 | 1.85342 | ||||||||
\(571\) | 20899.4 | 1.53172 | 0.765859 | − | 0.643008i | \(-0.222314\pi\) | ||||
0.765859 | + | 0.643008i | \(0.222314\pi\) | |||||||
\(572\) | 10907.7 | 0.797331 | ||||||||
\(573\) | −3090.10 | −0.225289 | ||||||||
\(574\) | −21308.0 | −1.54944 | ||||||||
\(575\) | −5956.50 | −0.432006 | ||||||||
\(576\) | 3030.17 | 0.219196 | ||||||||
\(577\) | −7924.36 | −0.571742 | −0.285871 | − | 0.958268i | \(-0.592283\pi\) | ||||
−0.285871 | + | 0.958268i | \(0.592283\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 28.1693 | 0.00202189 | ||||||||
\(580\) | 3785.86 | 0.271034 | ||||||||
\(581\) | −9883.97 | −0.705776 | ||||||||
\(582\) | −5838.38 | −0.415823 | ||||||||
\(583\) | −964.230 | −0.0684980 | ||||||||
\(584\) | 5839.91 | 0.413797 | ||||||||
\(585\) | −17974.8 | −1.27037 | ||||||||
\(586\) | −10738.7 | −0.757019 | ||||||||
\(587\) | 1139.92 | 0.0801529 | 0.0400764 | − | 0.999197i | \(-0.487240\pi\) | ||||
0.0400764 | + | 0.999197i | \(0.487240\pi\) | |||||||
\(588\) | 3790.86 | 0.265872 | ||||||||
\(589\) | 27868.2 | 1.94956 | ||||||||
\(590\) | −93.9673 | −0.00655690 | ||||||||
\(591\) | 18363.5 | 1.27813 | ||||||||
\(592\) | 3165.81 | 0.219787 | ||||||||
\(593\) | 2645.81 | 0.183222 | 0.0916109 | − | 0.995795i | \(-0.470798\pi\) | ||||
0.0916109 | + | 0.995795i | \(0.470798\pi\) | |||||||
\(594\) | 11227.7 | 0.775552 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −5997.84 | −0.412217 | ||||||||
\(597\) | −4425.87 | −0.303415 | ||||||||
\(598\) | −23554.9 | −1.61075 | ||||||||
\(599\) | −21822.7 | −1.48856 | −0.744282 | − | 0.667865i | \(-0.767208\pi\) | ||||
−0.744282 | + | 0.667865i | \(0.767208\pi\) | |||||||
\(600\) | −2416.14 | −0.164397 | ||||||||
\(601\) | 10909.3 | 0.740434 | 0.370217 | − | 0.928945i | \(-0.379283\pi\) | ||||
0.370217 | + | 0.928945i | \(0.379283\pi\) | |||||||
\(602\) | 15045.9 | 1.01865 | ||||||||
\(603\) | −1933.58 | −0.130583 | ||||||||
\(604\) | 7952.63 | 0.535741 | ||||||||
\(605\) | 13368.3 | 0.898345 | ||||||||
\(606\) | 21711.9 | 1.45542 | ||||||||
\(607\) | 15308.1 | 1.02362 | 0.511808 | − | 0.859100i | \(-0.328976\pi\) | ||||
0.511808 | + | 0.859100i | \(0.328976\pi\) | |||||||
\(608\) | −28395.4 | −1.89406 | ||||||||
\(609\) | 2083.76 | 0.138651 | ||||||||
\(610\) | 8636.65 | 0.573259 | ||||||||
\(611\) | −7660.16 | −0.507196 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 24096.7 | 1.58769 | 0.793847 | − | 0.608118i | \(-0.208075\pi\) | ||||
0.793847 | + | 0.608118i | \(0.208075\pi\) | |||||||
\(614\) | 14056.1 | 0.923875 | ||||||||
\(615\) | 23351.8 | 1.53111 | ||||||||
\(616\) | −2025.76 | −0.132501 | ||||||||
\(617\) | 7030.91 | 0.458758 | 0.229379 | − | 0.973337i | \(-0.426330\pi\) | ||||
0.229379 | + | 0.973337i | \(0.426330\pi\) | |||||||
\(618\) | −14934.2 | −0.972073 | ||||||||
\(619\) | 19270.2 | 1.25127 | 0.625635 | − | 0.780116i | \(-0.284840\pi\) | ||||
0.625635 | + | 0.780116i | \(0.284840\pi\) | |||||||
\(620\) | 18846.0 | 1.22077 | ||||||||
\(621\) | −10325.0 | −0.667194 | ||||||||
\(622\) | −3895.85 | −0.251140 | ||||||||
\(623\) | −5154.50 | −0.331478 | ||||||||
\(624\) | −25306.0 | −1.62348 | ||||||||
\(625\) | −18993.2 | −1.21557 | ||||||||
\(626\) | −2993.07 | −0.191097 | ||||||||
\(627\) | −9426.12 | −0.600388 | ||||||||
\(628\) | −5621.24 | −0.357185 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | −9585.14 | −0.606160 | ||||||||
\(631\) | −1474.23 | −0.0930079 | −0.0465040 | − | 0.998918i | \(-0.514808\pi\) | ||||
−0.0465040 | + | 0.998918i | \(0.514808\pi\) | |||||||
\(632\) | 4086.74 | 0.257218 | ||||||||
\(633\) | 11137.5 | 0.699327 | ||||||||
\(634\) | 3009.06 | 0.188494 | ||||||||
\(635\) | −6144.15 | −0.383974 | ||||||||
\(636\) | −1032.73 | −0.0643877 | ||||||||
\(637\) | 15868.8 | 0.987038 | ||||||||
\(638\) | −3322.46 | −0.206172 | ||||||||
\(639\) | −6101.27 | −0.377719 | ||||||||
\(640\) | 13853.7 | 0.855648 | ||||||||
\(641\) | 18747.7 | 1.15521 | 0.577604 | − | 0.816317i | \(-0.303988\pi\) | ||||
0.577604 | + | 0.816317i | \(0.303988\pi\) | |||||||
\(642\) | −18029.4 | −1.10836 | ||||||||
\(643\) | −2324.44 | −0.142561 | −0.0712807 | − | 0.997456i | \(-0.522709\pi\) | ||||
−0.0712807 | + | 0.997456i | \(0.522709\pi\) | |||||||
\(644\) | −5348.92 | −0.327294 | ||||||||
\(645\) | −16489.1 | −1.00660 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −11883.3 | −0.722071 | −0.361036 | − | 0.932552i | \(-0.617577\pi\) | ||||
−0.361036 | + | 0.932552i | \(0.617577\pi\) | |||||||
\(648\) | −1347.29 | −0.0816768 | ||||||||
\(649\) | 35.1175 | 0.00212401 | ||||||||
\(650\) | 29040.5 | 1.75241 | ||||||||
\(651\) | 10373.0 | 0.624498 | ||||||||
\(652\) | 5732.62 | 0.344336 | ||||||||
\(653\) | −873.094 | −0.0523228 | −0.0261614 | − | 0.999658i | \(-0.508328\pi\) | ||||
−0.0261614 | + | 0.999658i | \(0.508328\pi\) | |||||||
\(654\) | −18067.6 | −1.08027 | ||||||||
\(655\) | 11510.3 | 0.686636 | ||||||||
\(656\) | −33565.8 | −1.99775 | ||||||||
\(657\) | −10326.7 | −0.613217 | ||||||||
\(658\) | −4084.81 | −0.242010 | ||||||||
\(659\) | −965.182 | −0.0570534 | −0.0285267 | − | 0.999593i | \(-0.509082\pi\) | ||||
−0.0285267 | + | 0.999593i | \(0.509082\pi\) | |||||||
\(660\) | −6374.47 | −0.375948 | ||||||||
\(661\) | 10564.2 | 0.621631 | 0.310815 | − | 0.950470i | \(-0.399398\pi\) | ||||
0.310815 | + | 0.950470i | \(0.399398\pi\) | |||||||
\(662\) | −9731.35 | −0.571329 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −5878.60 | −0.343575 | ||||||||
\(665\) | 23976.0 | 1.39812 | ||||||||
\(666\) | −2113.63 | −0.122975 | ||||||||
\(667\) | 3055.34 | 0.177366 | ||||||||
\(668\) | 7079.45 | 0.410048 | ||||||||
\(669\) | 10539.0 | 0.609059 | ||||||||
\(670\) | 7680.69 | 0.442882 | ||||||||
\(671\) | −3227.69 | −0.185698 | ||||||||
\(672\) | −10569.2 | −0.606719 | ||||||||
\(673\) | −24755.2 | −1.41789 | −0.708947 | − | 0.705262i | \(-0.750829\pi\) | ||||
−0.708947 | + | 0.705262i | \(0.750829\pi\) | |||||||
\(674\) | 3984.02 | 0.227684 | ||||||||
\(675\) | 12729.6 | 0.725868 | ||||||||
\(676\) | 35868.2 | 2.04075 | ||||||||
\(677\) | 34038.8 | 1.93238 | 0.966188 | − | 0.257840i | \(-0.0830107\pi\) | ||||
0.966188 | + | 0.257840i | \(0.0830107\pi\) | |||||||
\(678\) | −22119.9 | −1.25297 | ||||||||
\(679\) | −5549.87 | −0.313674 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −19745.6 | −1.11109 | ||||||||
\(682\) | −16539.2 | −0.928622 | ||||||||
\(683\) | −23062.1 | −1.29202 | −0.646008 | − | 0.763330i | \(-0.723563\pi\) | ||||
−0.646008 | + | 0.763330i | \(0.723563\pi\) | |||||||
\(684\) | 10307.6 | 0.576203 | ||||||||
\(685\) | −11750.4 | −0.655413 | ||||||||
\(686\) | 25067.3 | 1.39515 | ||||||||
\(687\) | 5571.31 | 0.309401 | ||||||||
\(688\) | 23701.4 | 1.31338 | ||||||||
\(689\) | −4323.08 | −0.239037 | ||||||||
\(690\) | 13765.5 | 0.759484 | ||||||||
\(691\) | 14331.9 | 0.789018 | 0.394509 | − | 0.918892i | \(-0.370915\pi\) | ||||
0.394509 | + | 0.918892i | \(0.370915\pi\) | |||||||
\(692\) | −50.4896 | −0.00277360 | ||||||||
\(693\) | 3582.16 | 0.196356 | ||||||||
\(694\) | 42479.5 | 2.32349 | ||||||||
\(695\) | −41253.3 | −2.25155 | ||||||||
\(696\) | 1239.34 | 0.0674958 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 9134.19 | 0.495321 | ||||||||
\(699\) | 6161.73 | 0.333417 | ||||||||
\(700\) | 6594.62 | 0.356076 | ||||||||
\(701\) | 28211.9 | 1.52004 | 0.760020 | − | 0.649900i | \(-0.225189\pi\) | ||||
0.760020 | + | 0.649900i | \(0.225189\pi\) | |||||||
\(702\) | 50338.9 | 2.70644 | ||||||||
\(703\) | 5286.97 | 0.283644 | ||||||||
\(704\) | 4498.34 | 0.240820 | ||||||||
\(705\) | 4476.61 | 0.239147 | ||||||||
\(706\) | −19518.8 | −1.04051 | ||||||||
\(707\) | 20639.0 | 1.09789 | ||||||||
\(708\) | 37.6124 | 0.00199656 | ||||||||
\(709\) | −5397.14 | −0.285887 | −0.142943 | − | 0.989731i | \(-0.545657\pi\) | ||||
−0.142943 | + | 0.989731i | \(0.545657\pi\) | |||||||
\(710\) | 24235.8 | 1.28106 | ||||||||
\(711\) | −7226.57 | −0.381178 | ||||||||
\(712\) | −3065.70 | −0.161365 | ||||||||
\(713\) | 15209.5 | 0.798878 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −26683.9 | −1.39569 | ||||||||
\(716\) | −5395.34 | −0.281611 | ||||||||
\(717\) | 17865.9 | 0.930562 | ||||||||
\(718\) | −33998.9 | −1.76717 | ||||||||
\(719\) | −17858.0 | −0.926276 | −0.463138 | − | 0.886286i | \(-0.653277\pi\) | ||||
−0.463138 | + | 0.886286i | \(0.653277\pi\) | |||||||
\(720\) | −15099.2 | −0.781545 | ||||||||
\(721\) | −14196.2 | −0.733279 | ||||||||
\(722\) | −34943.2 | −1.80118 | ||||||||
\(723\) | 12487.9 | 0.642366 | ||||||||
\(724\) | 14529.4 | 0.745831 | ||||||||
\(725\) | −3766.89 | −0.192964 | ||||||||
\(726\) | −12565.5 | −0.642354 | ||||||||
\(727\) | 27634.4 | 1.40977 | 0.704885 | − | 0.709322i | \(-0.250999\pi\) | ||||
0.704885 | + | 0.709322i | \(0.250999\pi\) | |||||||
\(728\) | −9082.43 | −0.462386 | ||||||||
\(729\) | 17042.0 | 0.865821 | ||||||||
\(730\) | 41020.4 | 2.07977 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | −3457.00 | −0.174555 | ||||||||
\(733\) | 16773.4 | 0.845209 | 0.422605 | − | 0.906314i | \(-0.361116\pi\) | ||||
0.422605 | + | 0.906314i | \(0.361116\pi\) | |||||||
\(734\) | 4313.46 | 0.216911 | ||||||||
\(735\) | −9273.72 | −0.465396 | ||||||||
\(736\) | −15497.2 | −0.776134 | ||||||||
\(737\) | −2870.43 | −0.143465 | ||||||||
\(738\) | 22410.0 | 1.11778 | ||||||||
\(739\) | −26618.2 | −1.32499 | −0.662495 | − | 0.749067i | \(-0.730502\pi\) | ||||
−0.662495 | + | 0.749067i | \(0.730502\pi\) | |||||||
\(740\) | 3575.34 | 0.177611 | ||||||||
\(741\) | −42261.6 | −2.09517 | ||||||||
\(742\) | −2305.30 | −0.114057 | ||||||||
\(743\) | 3231.55 | 0.159561 | 0.0797806 | − | 0.996812i | \(-0.474578\pi\) | ||||
0.0797806 | + | 0.996812i | \(0.474578\pi\) | |||||||
\(744\) | 6169.44 | 0.304009 | ||||||||
\(745\) | 14672.7 | 0.721567 | ||||||||
\(746\) | 37140.9 | 1.82282 | ||||||||
\(747\) | 10395.1 | 0.509154 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −17138.5 | −0.836083 | ||||||||
\(750\) | 7783.98 | 0.378974 | ||||||||
\(751\) | −6094.29 | −0.296117 | −0.148058 | − | 0.988979i | \(-0.547302\pi\) | ||||
−0.148058 | + | 0.988979i | \(0.547302\pi\) | |||||||
\(752\) | −6434.67 | −0.312032 | ||||||||
\(753\) | −8616.63 | −0.417009 | ||||||||
\(754\) | −14896.1 | −0.719476 | ||||||||
\(755\) | −19454.8 | −0.937791 | ||||||||
\(756\) | 11431.1 | 0.549928 | ||||||||
\(757\) | −4282.74 | −0.205626 | −0.102813 | − | 0.994701i | \(-0.532784\pi\) | ||||
−0.102813 | + | 0.994701i | \(0.532784\pi\) | |||||||
\(758\) | −5389.27 | −0.258242 | ||||||||
\(759\) | −5144.44 | −0.246023 | ||||||||
\(760\) | 14260.0 | 0.680612 | ||||||||
\(761\) | −35191.9 | −1.67636 | −0.838178 | − | 0.545397i | \(-0.816379\pi\) | ||||
−0.838178 | + | 0.545397i | \(0.816379\pi\) | |||||||
\(762\) | 5775.18 | 0.274557 | ||||||||
\(763\) | −17174.7 | −0.814899 | ||||||||
\(764\) | 5016.29 | 0.237543 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 30793.8 | 1.45251 | ||||||||
\(767\) | 157.448 | 0.00741213 | ||||||||
\(768\) | −19517.6 | −0.917032 | ||||||||
\(769\) | 23142.5 | 1.08523 | 0.542614 | − | 0.839982i | \(-0.317434\pi\) | ||||
0.542614 | + | 0.839982i | \(0.317434\pi\) | |||||||
\(770\) | −14229.3 | −0.665958 | ||||||||
\(771\) | −7433.17 | −0.347210 | ||||||||
\(772\) | −45.7285 | −0.00213187 | ||||||||
\(773\) | −4345.19 | −0.202181 | −0.101090 | − | 0.994877i | \(-0.532233\pi\) | ||||
−0.101090 | + | 0.994877i | \(0.532233\pi\) | |||||||
\(774\) | −15824.0 | −0.734862 | ||||||||
\(775\) | −18751.6 | −0.869133 | ||||||||
\(776\) | −3300.85 | −0.152698 | ||||||||
\(777\) | 1967.89 | 0.0908592 | ||||||||
\(778\) | 35076.6 | 1.61640 | ||||||||
\(779\) | −56055.7 | −2.57818 | ||||||||
\(780\) | −28579.6 | −1.31194 | ||||||||
\(781\) | −9057.42 | −0.414981 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −6529.53 | −0.298016 | ||||||||
\(784\) | 13330.0 | 0.607236 | ||||||||
\(785\) | 13751.4 | 0.625236 | ||||||||
\(786\) | −10819.1 | −0.490973 | ||||||||
\(787\) | 15543.2 | 0.704010 | 0.352005 | − | 0.935998i | \(-0.385500\pi\) | ||||
0.352005 | + | 0.935998i | \(0.385500\pi\) | |||||||
\(788\) | −29810.3 | −1.34765 | ||||||||
\(789\) | −19653.8 | −0.886811 | ||||||||
\(790\) | 28705.9 | 1.29280 | ||||||||
\(791\) | −21026.8 | −0.945169 | ||||||||
\(792\) | 2130.53 | 0.0955872 | ||||||||
\(793\) | −14471.2 | −0.648030 | ||||||||
\(794\) | 44683.9 | 1.99719 | ||||||||
\(795\) | 2526.41 | 0.112708 | ||||||||
\(796\) | 7184.72 | 0.319919 | ||||||||
\(797\) | 15559.4 | 0.691519 | 0.345759 | − | 0.938323i | \(-0.387621\pi\) | ||||
0.345759 | + | 0.938323i | \(0.387621\pi\) | |||||||
\(798\) | −22536.2 | −0.999714 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 19106.3 | 0.844389 | ||||||||
\(801\) | 5421.07 | 0.239131 | ||||||||
\(802\) | 39981.2 | 1.76033 | ||||||||
\(803\) | −15330.2 | −0.673711 | ||||||||
\(804\) | −3074.36 | −0.134856 | ||||||||
\(805\) | 13085.3 | 0.572913 | ||||||||
\(806\) | −74153.0 | −3.24060 | ||||||||
\(807\) | −11009.7 | −0.480249 | ||||||||
\(808\) | 12275.3 | 0.534458 | ||||||||
\(809\) | 9433.22 | 0.409956 | 0.204978 | − | 0.978767i | \(-0.434288\pi\) | ||||
0.204978 | + | 0.978767i | \(0.434288\pi\) | |||||||
\(810\) | −9463.57 | −0.410514 | ||||||||
\(811\) | −12596.0 | −0.545381 | −0.272691 | − | 0.962102i | \(-0.587914\pi\) | ||||
−0.272691 | + | 0.962102i | \(0.587914\pi\) | |||||||
\(812\) | −3382.66 | −0.146192 | ||||||||
\(813\) | 4898.68 | 0.211321 | ||||||||
\(814\) | −3137.71 | −0.135107 | ||||||||
\(815\) | −14023.9 | −0.602744 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 39581.8 | 1.69497 | ||||||||
\(818\) | 4556.15 | 0.194746 | ||||||||
\(819\) | 16060.4 | 0.685223 | ||||||||
\(820\) | −37908.0 | −1.61440 | ||||||||
\(821\) | −24332.2 | −1.03435 | −0.517175 | − | 0.855880i | \(-0.673016\pi\) | ||||
−0.517175 | + | 0.855880i | \(0.673016\pi\) | |||||||
\(822\) | 11044.7 | 0.468648 | ||||||||
\(823\) | 40516.8 | 1.71607 | 0.858035 | − | 0.513591i | \(-0.171685\pi\) | ||||
0.858035 | + | 0.513591i | \(0.171685\pi\) | |||||||
\(824\) | −8443.35 | −0.356964 | ||||||||
\(825\) | 6342.53 | 0.267659 | ||||||||
\(826\) | 83.9596 | 0.00353672 | ||||||||
\(827\) | 3544.77 | 0.149049 | 0.0745247 | − | 0.997219i | \(-0.476256\pi\) | ||||
0.0745247 | + | 0.997219i | \(0.476256\pi\) | |||||||
\(828\) | 5625.55 | 0.236113 | ||||||||
\(829\) | −25265.7 | −1.05852 | −0.529260 | − | 0.848460i | \(-0.677530\pi\) | ||||
−0.529260 | + | 0.848460i | \(0.677530\pi\) | |||||||
\(830\) | −41292.2 | −1.72684 | ||||||||
\(831\) | 17975.2 | 0.750366 | ||||||||
\(832\) | 20168.1 | 0.840388 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 38775.9 | 1.60995 | ||||||||
\(835\) | −17318.7 | −0.717771 | ||||||||
\(836\) | 15301.9 | 0.633045 | ||||||||
\(837\) | −32504.0 | −1.34230 | ||||||||
\(838\) | −40837.1 | −1.68341 | ||||||||
\(839\) | 32421.0 | 1.33408 | 0.667042 | − | 0.745021i | \(-0.267560\pi\) | ||||
0.667042 | + | 0.745021i | \(0.267560\pi\) | |||||||
\(840\) | 5307.78 | 0.218019 | ||||||||
\(841\) | −22456.8 | −0.920776 | ||||||||
\(842\) | 8603.51 | 0.352134 | ||||||||
\(843\) | 2550.89 | 0.104220 | ||||||||
\(844\) | −18079.9 | −0.737366 | ||||||||
\(845\) | −87745.7 | −3.57224 | ||||||||
\(846\) | 4296.06 | 0.174588 | ||||||||
\(847\) | −11944.6 | −0.484557 | ||||||||
\(848\) | −3631.47 | −0.147058 | ||||||||
\(849\) | 19661.9 | 0.794811 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 2885.44 | 0.116230 | ||||||||
\(852\) | −9700.91 | −0.390080 | ||||||||
\(853\) | −31041.4 | −1.24600 | −0.623000 | − | 0.782222i | \(-0.714087\pi\) | ||||
−0.623000 | + | 0.782222i | \(0.714087\pi\) | |||||||
\(854\) | −7716.83 | −0.309209 | ||||||||
\(855\) | −25216.0 | −1.00862 | ||||||||
\(856\) | −10193.3 | −0.407009 | ||||||||
\(857\) | 6852.25 | 0.273125 | 0.136563 | − | 0.990631i | \(-0.456394\pi\) | ||||
0.136563 | + | 0.990631i | \(0.456394\pi\) | |||||||
\(858\) | 25081.4 | 0.997978 | ||||||||
\(859\) | 31049.1 | 1.23327 | 0.616636 | − | 0.787248i | \(-0.288495\pi\) | ||||
0.616636 | + | 0.787248i | \(0.288495\pi\) | |||||||
\(860\) | 26767.4 | 1.06135 | ||||||||
\(861\) | −20864.8 | −0.825864 | ||||||||
\(862\) | −21431.8 | −0.846833 | ||||||||
\(863\) | 31789.3 | 1.25391 | 0.626953 | − | 0.779057i | \(-0.284302\pi\) | ||||
0.626953 | + | 0.779057i | \(0.284302\pi\) | |||||||
\(864\) | 33118.9 | 1.30408 | ||||||||
\(865\) | 123.515 | 0.00485505 | ||||||||
\(866\) | −16997.3 | −0.666964 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −16838.9 | −0.658467 | ||||||||
\(869\) | −10728.0 | −0.418781 | ||||||||
\(870\) | 8705.31 | 0.339239 | ||||||||
\(871\) | −12869.4 | −0.500648 | ||||||||
\(872\) | −10214.9 | −0.396697 | ||||||||
\(873\) | 5836.89 | 0.226287 | ||||||||
\(874\) | −33044.0 | −1.27887 | ||||||||
\(875\) | 7399.32 | 0.285877 | ||||||||
\(876\) | −16419.3 | −0.633284 | ||||||||
\(877\) | 34579.2 | 1.33142 | 0.665711 | − | 0.746210i | \(-0.268128\pi\) | ||||
0.665711 | + | 0.746210i | \(0.268128\pi\) | |||||||
\(878\) | −40263.0 | −1.54762 | ||||||||
\(879\) | −10515.3 | −0.403497 | ||||||||
\(880\) | −22414.9 | −0.858644 | ||||||||
\(881\) | 14088.5 | 0.538765 | 0.269383 | − | 0.963033i | \(-0.413180\pi\) | ||||
0.269383 | + | 0.963033i | \(0.413180\pi\) | |||||||
\(882\) | −8899.71 | −0.339761 | ||||||||
\(883\) | 4779.77 | 0.182165 | 0.0910827 | − | 0.995843i | \(-0.470967\pi\) | ||||
0.0910827 | + | 0.995843i | \(0.470967\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −92.0126 | −0.00349488 | ||||||||
\(886\) | −49024.3 | −1.85892 | ||||||||
\(887\) | 14254.5 | 0.539594 | 0.269797 | − | 0.962917i | \(-0.413043\pi\) | ||||
0.269797 | + | 0.962917i | \(0.413043\pi\) | |||||||
\(888\) | 1170.42 | 0.0442307 | ||||||||
\(889\) | 5489.79 | 0.207111 | ||||||||
\(890\) | −21533.9 | −0.811032 | ||||||||
\(891\) | 3536.73 | 0.132980 | ||||||||
\(892\) | −17108.4 | −0.642188 | ||||||||
\(893\) | −10746.1 | −0.402691 | ||||||||
\(894\) | −13791.6 | −0.515951 | ||||||||
\(895\) | 13198.8 | 0.492947 | ||||||||
\(896\) | −12378.2 | −0.461526 | ||||||||
\(897\) | −23064.9 | −0.858544 | ||||||||
\(898\) | 2667.66 | 0.0991325 | ||||||||
\(899\) | 9618.49 | 0.356835 | ||||||||
\(900\) | −6935.67 | −0.256877 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 33268.0 | 1.22805 | ||||||||
\(903\) | 14732.9 | 0.542947 | ||||||||
\(904\) | −12506.0 | −0.460113 | ||||||||
\(905\) | −35543.8 | −1.30554 | ||||||||
\(906\) | 18286.5 | 0.670560 | ||||||||
\(907\) | 36585.5 | 1.33936 | 0.669680 | − | 0.742650i | \(-0.266431\pi\) | ||||
0.669680 | + | 0.742650i | \(0.266431\pi\) | |||||||
\(908\) | 32053.9 | 1.17153 | ||||||||
\(909\) | −21706.3 | −0.792028 | ||||||||
\(910\) | −63796.3 | −2.32399 | ||||||||
\(911\) | 19721.3 | 0.717230 | 0.358615 | − | 0.933486i | \(-0.383249\pi\) | ||||
0.358615 | + | 0.933486i | \(0.383249\pi\) | |||||||
\(912\) | −35500.5 | −1.28897 | ||||||||
\(913\) | 15431.7 | 0.559382 | ||||||||
\(914\) | 3644.51 | 0.131892 | ||||||||
\(915\) | 8456.99 | 0.305551 | ||||||||
\(916\) | −9044.16 | −0.326231 | ||||||||
\(917\) | −10284.5 | −0.370363 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −28189.0 | −1.01183 | −0.505913 | − | 0.862585i | \(-0.668844\pi\) | ||||
−0.505913 | + | 0.862585i | \(0.668844\pi\) | |||||||
\(920\) | 7782.60 | 0.278897 | ||||||||
\(921\) | 13763.7 | 0.492432 | ||||||||
\(922\) | 66118.3 | 2.36170 | ||||||||
\(923\) | −40608.5 | −1.44815 | ||||||||
\(924\) | 5695.57 | 0.202782 | ||||||||
\(925\) | −3557.43 | −0.126451 | ||||||||
\(926\) | 50757.1 | 1.80128 | ||||||||
\(927\) | 14930.4 | 0.528994 | ||||||||
\(928\) | −9800.45 | −0.346676 | ||||||||
\(929\) | −30866.1 | −1.09008 | −0.545040 | − | 0.838410i | \(-0.683485\pi\) | ||||
−0.545040 | + | 0.838410i | \(0.683485\pi\) | |||||||
\(930\) | 43335.1 | 1.52797 | ||||||||
\(931\) | 22261.5 | 0.783664 | ||||||||
\(932\) | −10002.6 | −0.351552 | ||||||||
\(933\) | −3814.80 | −0.133860 | ||||||||
\(934\) | −34027.0 | −1.19208 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 9552.13 | 0.333570 | ||||||||
\(937\) | 13990.7 | 0.487785 | 0.243893 | − | 0.969802i | \(-0.421576\pi\) | ||||
0.243893 | + | 0.969802i | \(0.421576\pi\) | |||||||
\(938\) | −6862.68 | −0.238885 | ||||||||
\(939\) | −2930.80 | −0.101856 | ||||||||
\(940\) | −7267.08 | −0.252155 | ||||||||
\(941\) | −4495.60 | −0.155741 | −0.0778706 | − | 0.996963i | \(-0.524812\pi\) | ||||
−0.0778706 | + | 0.996963i | \(0.524812\pi\) | |||||||
\(942\) | −12925.6 | −0.447070 | ||||||||
\(943\) | −30593.2 | −1.05647 | ||||||||
\(944\) | 132.259 | 0.00456002 | ||||||||
\(945\) | −27964.3 | −0.962624 | ||||||||
\(946\) | −23491.0 | −0.807356 | ||||||||
\(947\) | 29959.5 | 1.02804 | 0.514019 | − | 0.857779i | \(-0.328156\pi\) | ||||
0.514019 | + | 0.857779i | \(0.328156\pi\) | |||||||
\(948\) | −11490.1 | −0.393652 | ||||||||
\(949\) | −68732.1 | −2.35104 | ||||||||
\(950\) | 40739.5 | 1.39133 | ||||||||
\(951\) | 2946.47 | 0.100469 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −44526.8 | −1.51350 | −0.756750 | − | 0.653704i | \(-0.773214\pi\) | ||||
−0.756750 | + | 0.653704i | \(0.773214\pi\) | |||||||
\(954\) | 2424.52 | 0.0822818 | ||||||||
\(955\) | −12271.5 | −0.415809 | ||||||||
\(956\) | −29002.5 | −0.981178 | ||||||||
\(957\) | −3253.35 | −0.109891 | ||||||||
\(958\) | −42864.0 | −1.44559 | ||||||||
\(959\) | 10498.9 | 0.353522 | ||||||||
\(960\) | −11786.3 | −0.396250 | ||||||||
\(961\) | 18089.9 | 0.607227 | ||||||||
\(962\) | −14067.8 | −0.471480 | ||||||||
\(963\) | 18024.8 | 0.603158 | ||||||||
\(964\) | −20272.2 | −0.677306 | ||||||||
\(965\) | 111.867 | 0.00373174 | ||||||||
\(966\) | −12299.4 | −0.409656 | ||||||||
\(967\) | 31696.1 | 1.05406 | 0.527031 | − | 0.849846i | \(-0.323305\pi\) | ||||
0.527031 | + | 0.849846i | \(0.323305\pi\) | |||||||
\(968\) | −7104.16 | −0.235885 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −23185.7 | −0.767471 | ||||||||
\(971\) | −47645.1 | −1.57467 | −0.787335 | − | 0.616525i | \(-0.788540\pi\) | ||||
−0.787335 | + | 0.616525i | \(0.788540\pi\) | |||||||
\(972\) | −20009.5 | −0.660293 | ||||||||
\(973\) | 36859.7 | 1.21446 | ||||||||
\(974\) | 15369.9 | 0.505629 | ||||||||
\(975\) | 28436.4 | 0.934046 | ||||||||
\(976\) | −12156.1 | −0.398675 | ||||||||
\(977\) | 47682.5 | 1.56141 | 0.780706 | − | 0.624898i | \(-0.214860\pi\) | ||||
0.780706 | + | 0.624898i | \(0.214860\pi\) | |||||||
\(978\) | 13181.7 | 0.430987 | ||||||||
\(979\) | 8047.66 | 0.262721 | ||||||||
\(980\) | 15054.5 | 0.490711 | ||||||||
\(981\) | 18063.0 | 0.587875 | ||||||||
\(982\) | 44308.2 | 1.43985 | ||||||||
\(983\) | 42569.9 | 1.38125 | 0.690626 | − | 0.723212i | \(-0.257335\pi\) | ||||
0.690626 | + | 0.723212i | \(0.257335\pi\) | |||||||
\(984\) | −12409.6 | −0.402035 | ||||||||
\(985\) | 72926.1 | 2.35900 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −3999.84 | −0.128993 | ||||||||
\(988\) | 68605.2 | 2.20913 | ||||||||
\(989\) | 21602.4 | 0.694555 | ||||||||
\(990\) | 14965.2 | 0.480428 | ||||||||
\(991\) | 36264.9 | 1.16245 | 0.581227 | − | 0.813742i | \(-0.302573\pi\) | ||||
0.581227 | + | 0.813742i | \(0.302573\pi\) | |||||||
\(992\) | −48786.7 | −1.56147 | ||||||||
\(993\) | −9528.92 | −0.304523 | ||||||||
\(994\) | −21654.7 | −0.690991 | ||||||||
\(995\) | −17576.2 | −0.560004 | ||||||||
\(996\) | 16528.1 | 0.525816 | ||||||||
\(997\) | 37027.1 | 1.17619 | 0.588094 | − | 0.808792i | \(-0.299878\pi\) | ||||
0.588094 | + | 0.808792i | \(0.299878\pi\) | |||||||
\(998\) | −62600.0 | −1.98554 | ||||||||
\(999\) | −6166.44 | −0.195293 |
(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 | 289.4.a.i.1.3 | yes | 12 | |
17.4 | even | 4 | 289.4.b.f.288.20 | 24 | |||
17.13 | even | 4 | 289.4.b.f.288.19 | 24 | |||
17.16 | even | 2 | 289.4.a.h.1.3 | ✓ | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
289.4.a.h.1.3 | ✓ | 12 | 17.16 | even | 2 | ||
289.4.a.i.1.3 | yes | 12 | 1.1 | even | 1 | trivial | |
289.4.b.f.288.19 | 24 | 17.13 | even | 4 | |||
289.4.b.f.288.20 | 24 | 17.4 | even | 4 |