Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1849,4,Mod(1,1849)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1849, 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("1849.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1849 = 43^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1849.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: | \(109.094531601\) |
Analytic rank: | \(1\) |
Dimension: | \(50\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.21 | ||
Character | \(\chi\) | \(=\) | 1849.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.06456 | −0.376378 | −0.188189 | − | 0.982133i | \(-0.560262\pi\) | ||||
−0.188189 | + | 0.982133i | \(0.560262\pi\) | |||||||
\(3\) | −7.81960 | −1.50488 | −0.752442 | − | 0.658659i | \(-0.771124\pi\) | ||||
−0.752442 | + | 0.658659i | \(0.771124\pi\) | |||||||
\(4\) | −6.86672 | −0.858340 | ||||||||
\(5\) | −6.14081 | −0.549251 | −0.274626 | − | 0.961551i | \(-0.588554\pi\) | ||||
−0.274626 | + | 0.961551i | \(0.588554\pi\) | |||||||
\(6\) | 8.32441 | 0.566404 | ||||||||
\(7\) | 5.24909 | 0.283424 | 0.141712 | − | 0.989908i | \(-0.454739\pi\) | ||||
0.141712 | + | 0.989908i | \(0.454739\pi\) | |||||||
\(8\) | 15.8265 | 0.699438 | ||||||||
\(9\) | 34.1462 | 1.26467 | ||||||||
\(10\) | 6.53724 | 0.206726 | ||||||||
\(11\) | −14.5177 | −0.397932 | −0.198966 | − | 0.980006i | \(-0.563758\pi\) | ||||
−0.198966 | + | 0.980006i | \(0.563758\pi\) | |||||||
\(12\) | 53.6950 | 1.29170 | ||||||||
\(13\) | −49.9353 | −1.06535 | −0.532675 | − | 0.846320i | \(-0.678813\pi\) | ||||
−0.532675 | + | 0.846320i | \(0.678813\pi\) | |||||||
\(14\) | −5.58795 | −0.106675 | ||||||||
\(15\) | 48.0187 | 0.826559 | ||||||||
\(16\) | 38.0856 | 0.595087 | ||||||||
\(17\) | 75.6572 | 1.07939 | 0.539693 | − | 0.841862i | \(-0.318540\pi\) | ||||
0.539693 | + | 0.841862i | \(0.318540\pi\) | |||||||
\(18\) | −36.3506 | −0.475995 | ||||||||
\(19\) | −128.126 | −1.54706 | −0.773528 | − | 0.633762i | \(-0.781510\pi\) | ||||
−0.773528 | + | 0.633762i | \(0.781510\pi\) | |||||||
\(20\) | 42.1672 | 0.471444 | ||||||||
\(21\) | −41.0458 | −0.426520 | ||||||||
\(22\) | 15.4549 | 0.149773 | ||||||||
\(23\) | −131.825 | −1.19510 | −0.597552 | − | 0.801830i | \(-0.703860\pi\) | ||||
−0.597552 | + | 0.801830i | \(0.703860\pi\) | |||||||
\(24\) | −123.757 | −1.05257 | ||||||||
\(25\) | −87.2904 | −0.698323 | ||||||||
\(26\) | 53.1589 | 0.400974 | ||||||||
\(27\) | −55.8805 | −0.398304 | ||||||||
\(28\) | −36.0440 | −0.243274 | ||||||||
\(29\) | 36.6667 | 0.234788 | 0.117394 | − | 0.993085i | \(-0.462546\pi\) | ||||
0.117394 | + | 0.993085i | \(0.462546\pi\) | |||||||
\(30\) | −51.1187 | −0.311098 | ||||||||
\(31\) | −251.659 | −1.45804 | −0.729022 | − | 0.684491i | \(-0.760025\pi\) | ||||
−0.729022 | + | 0.684491i | \(0.760025\pi\) | |||||||
\(32\) | −167.156 | −0.923415 | ||||||||
\(33\) | 113.523 | 0.598841 | ||||||||
\(34\) | −80.5414 | −0.406257 | ||||||||
\(35\) | −32.2337 | −0.155671 | ||||||||
\(36\) | −234.472 | −1.08552 | ||||||||
\(37\) | 264.673 | 1.17600 | 0.588000 | − | 0.808861i | \(-0.299916\pi\) | ||||
0.588000 | + | 0.808861i | \(0.299916\pi\) | |||||||
\(38\) | 136.397 | 0.582277 | ||||||||
\(39\) | 390.474 | 1.60323 | ||||||||
\(40\) | −97.1874 | −0.384167 | ||||||||
\(41\) | −0.0646232 | −0.000246157 0 | −0.000123079 | − | 1.00000i | \(-0.500039\pi\) | ||||
−0.000123079 | 1.00000i | \(0.500039\pi\) | ||||||||
\(42\) | 43.6956 | 0.160533 | ||||||||
\(43\) | 0 | 0 | ||||||||
\(44\) | 99.6890 | 0.341561 | ||||||||
\(45\) | −209.685 | −0.694624 | ||||||||
\(46\) | 140.335 | 0.449810 | ||||||||
\(47\) | 346.105 | 1.07414 | 0.537070 | − | 0.843538i | \(-0.319531\pi\) | ||||
0.537070 | + | 0.843538i | \(0.319531\pi\) | |||||||
\(48\) | −297.814 | −0.895537 | ||||||||
\(49\) | −315.447 | −0.919671 | ||||||||
\(50\) | 92.9256 | 0.262833 | ||||||||
\(51\) | −591.610 | −1.62435 | ||||||||
\(52\) | 342.892 | 0.914433 | ||||||||
\(53\) | 468.928 | 1.21532 | 0.607662 | − | 0.794196i | \(-0.292107\pi\) | ||||
0.607662 | + | 0.794196i | \(0.292107\pi\) | |||||||
\(54\) | 59.4880 | 0.149913 | ||||||||
\(55\) | 89.1505 | 0.218565 | ||||||||
\(56\) | 83.0745 | 0.198237 | ||||||||
\(57\) | 1001.89 | 2.32814 | ||||||||
\(58\) | −39.0338 | −0.0883688 | ||||||||
\(59\) | 586.702 | 1.29461 | 0.647306 | − | 0.762230i | \(-0.275895\pi\) | ||||
0.647306 | + | 0.762230i | \(0.275895\pi\) | |||||||
\(60\) | −329.731 | −0.709468 | ||||||||
\(61\) | 592.038 | 1.24267 | 0.621333 | − | 0.783546i | \(-0.286591\pi\) | ||||
0.621333 | + | 0.783546i | \(0.286591\pi\) | |||||||
\(62\) | 267.906 | 0.548775 | ||||||||
\(63\) | 179.236 | 0.358439 | ||||||||
\(64\) | −126.738 | −0.247534 | ||||||||
\(65\) | 306.643 | 0.585145 | ||||||||
\(66\) | −120.851 | −0.225390 | ||||||||
\(67\) | −472.805 | −0.862125 | −0.431062 | − | 0.902322i | \(-0.641861\pi\) | ||||
−0.431062 | + | 0.902322i | \(0.641861\pi\) | |||||||
\(68\) | −519.517 | −0.926481 | ||||||||
\(69\) | 1030.82 | 1.79849 | ||||||||
\(70\) | 34.3146 | 0.0585911 | ||||||||
\(71\) | 548.204 | 0.916336 | 0.458168 | − | 0.888866i | \(-0.348506\pi\) | ||||
0.458168 | + | 0.888866i | \(0.348506\pi\) | |||||||
\(72\) | 540.414 | 0.884561 | ||||||||
\(73\) | 328.014 | 0.525905 | 0.262953 | − | 0.964809i | \(-0.415304\pi\) | ||||
0.262953 | + | 0.964809i | \(0.415304\pi\) | |||||||
\(74\) | −281.759 | −0.442620 | ||||||||
\(75\) | 682.576 | 1.05090 | ||||||||
\(76\) | 879.804 | 1.32790 | ||||||||
\(77\) | −76.2047 | −0.112784 | ||||||||
\(78\) | −415.682 | −0.603419 | ||||||||
\(79\) | 801.655 | 1.14169 | 0.570843 | − | 0.821059i | \(-0.306616\pi\) | ||||
0.570843 | + | 0.821059i | \(0.306616\pi\) | |||||||
\(80\) | −233.876 | −0.326852 | ||||||||
\(81\) | −484.984 | −0.665273 | ||||||||
\(82\) | 0.0687950 | 9.26480e−5 0 | ||||||||
\(83\) | −1348.75 | −1.78368 | −0.891838 | − | 0.452356i | \(-0.850584\pi\) | ||||
−0.891838 | + | 0.452356i | \(0.850584\pi\) | |||||||
\(84\) | 281.850 | 0.366099 | ||||||||
\(85\) | −464.597 | −0.592854 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −286.719 | −0.353328 | ||||||||
\(88\) | −229.764 | −0.278329 | ||||||||
\(89\) | 1491.49 | 1.77638 | 0.888189 | − | 0.459478i | \(-0.151964\pi\) | ||||
0.888189 | + | 0.459478i | \(0.151964\pi\) | |||||||
\(90\) | 223.222 | 0.261441 | ||||||||
\(91\) | −262.115 | −0.301946 | ||||||||
\(92\) | 905.205 | 1.02581 | ||||||||
\(93\) | 1967.88 | 2.19419 | ||||||||
\(94\) | −368.448 | −0.404282 | ||||||||
\(95\) | 786.796 | 0.849722 | ||||||||
\(96\) | 1307.09 | 1.38963 | ||||||||
\(97\) | −281.945 | −0.295125 | −0.147563 | − | 0.989053i | \(-0.547143\pi\) | ||||
−0.147563 | + | 0.989053i | \(0.547143\pi\) | |||||||
\(98\) | 335.811 | 0.346143 | ||||||||
\(99\) | −495.724 | −0.503254 | ||||||||
\(100\) | 599.399 | 0.599399 | ||||||||
\(101\) | 1102.45 | 1.08612 | 0.543060 | − | 0.839694i | \(-0.317266\pi\) | ||||
0.543060 | + | 0.839694i | \(0.317266\pi\) | |||||||
\(102\) | 629.802 | 0.611370 | ||||||||
\(103\) | −1857.59 | −1.77703 | −0.888514 | − | 0.458849i | \(-0.848262\pi\) | ||||
−0.888514 | + | 0.458849i | \(0.848262\pi\) | |||||||
\(104\) | −790.299 | −0.745146 | ||||||||
\(105\) | 252.055 | 0.234267 | ||||||||
\(106\) | −499.200 | −0.457421 | ||||||||
\(107\) | 187.602 | 0.169497 | 0.0847487 | − | 0.996402i | \(-0.472991\pi\) | ||||
0.0847487 | + | 0.996402i | \(0.472991\pi\) | |||||||
\(108\) | 383.716 | 0.341880 | ||||||||
\(109\) | 116.470 | 0.102347 | 0.0511733 | − | 0.998690i | \(-0.483704\pi\) | ||||
0.0511733 | + | 0.998690i | \(0.483704\pi\) | |||||||
\(110\) | −94.9058 | −0.0822628 | ||||||||
\(111\) | −2069.64 | −1.76974 | ||||||||
\(112\) | 199.915 | 0.168662 | ||||||||
\(113\) | −1240.45 | −1.03267 | −0.516334 | − | 0.856387i | \(-0.672704\pi\) | ||||
−0.516334 | + | 0.856387i | \(0.672704\pi\) | |||||||
\(114\) | −1066.57 | −0.876260 | ||||||||
\(115\) | 809.512 | 0.656412 | ||||||||
\(116\) | −251.780 | −0.201528 | ||||||||
\(117\) | −1705.10 | −1.34732 | ||||||||
\(118\) | −624.578 | −0.487263 | ||||||||
\(119\) | 397.132 | 0.305924 | ||||||||
\(120\) | 759.967 | 0.578126 | ||||||||
\(121\) | −1120.24 | −0.841650 | ||||||||
\(122\) | −630.258 | −0.467712 | ||||||||
\(123\) | 0.505328 | 0.000370438 0 | ||||||||
\(124\) | 1728.07 | 1.25150 | ||||||||
\(125\) | 1303.64 | 0.932806 | ||||||||
\(126\) | −190.807 | −0.134909 | ||||||||
\(127\) | 92.3145 | 0.0645007 | 0.0322503 | − | 0.999480i | \(-0.489733\pi\) | ||||
0.0322503 | + | 0.999480i | \(0.489733\pi\) | |||||||
\(128\) | 1472.17 | 1.01658 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −326.439 | −0.220235 | ||||||||
\(131\) | 1721.43 | 1.14811 | 0.574055 | − | 0.818817i | \(-0.305370\pi\) | ||||
0.574055 | + | 0.818817i | \(0.305370\pi\) | |||||||
\(132\) | −779.528 | −0.514009 | ||||||||
\(133\) | −672.544 | −0.438473 | ||||||||
\(134\) | 503.328 | 0.324485 | ||||||||
\(135\) | 343.152 | 0.218769 | ||||||||
\(136\) | 1197.39 | 0.754964 | ||||||||
\(137\) | 1677.68 | 1.04624 | 0.523118 | − | 0.852261i | \(-0.324769\pi\) | ||||
0.523118 | + | 0.852261i | \(0.324769\pi\) | |||||||
\(138\) | −1097.36 | −0.676912 | ||||||||
\(139\) | 2819.71 | 1.72061 | 0.860306 | − | 0.509778i | \(-0.170272\pi\) | ||||
0.860306 | + | 0.509778i | \(0.170272\pi\) | |||||||
\(140\) | 221.340 | 0.133619 | ||||||||
\(141\) | −2706.40 | −1.61646 | ||||||||
\(142\) | −583.594 | −0.344888 | ||||||||
\(143\) | 724.946 | 0.423937 | ||||||||
\(144\) | 1300.48 | 0.752592 | ||||||||
\(145\) | −225.163 | −0.128957 | ||||||||
\(146\) | −349.189 | −0.197939 | ||||||||
\(147\) | 2466.67 | 1.38400 | ||||||||
\(148\) | −1817.43 | −1.00941 | ||||||||
\(149\) | 971.666 | 0.534241 | 0.267121 | − | 0.963663i | \(-0.413928\pi\) | ||||
0.267121 | + | 0.963663i | \(0.413928\pi\) | |||||||
\(150\) | −726.641 | −0.395533 | ||||||||
\(151\) | −876.678 | −0.472470 | −0.236235 | − | 0.971696i | \(-0.575914\pi\) | ||||
−0.236235 | + | 0.971696i | \(0.575914\pi\) | |||||||
\(152\) | −2027.78 | −1.08207 | ||||||||
\(153\) | 2583.41 | 1.36507 | ||||||||
\(154\) | 81.1242 | 0.0424492 | ||||||||
\(155\) | 1545.39 | 0.800832 | ||||||||
\(156\) | −2681.28 | −1.37611 | ||||||||
\(157\) | 2191.29 | 1.11391 | 0.556955 | − | 0.830543i | \(-0.311970\pi\) | ||||
0.556955 | + | 0.830543i | \(0.311970\pi\) | |||||||
\(158\) | −853.407 | −0.429705 | ||||||||
\(159\) | −3666.83 | −1.82892 | ||||||||
\(160\) | 1026.47 | 0.507187 | ||||||||
\(161\) | −691.961 | −0.338721 | ||||||||
\(162\) | 516.293 | 0.250394 | ||||||||
\(163\) | 212.798 | 0.102255 | 0.0511276 | − | 0.998692i | \(-0.483718\pi\) | ||||
0.0511276 | + | 0.998692i | \(0.483718\pi\) | |||||||
\(164\) | 0.443749 | 0.000211287 0 | ||||||||
\(165\) | −697.122 | −0.328914 | ||||||||
\(166\) | 1435.83 | 0.671335 | ||||||||
\(167\) | 268.336 | 0.124338 | 0.0621691 | − | 0.998066i | \(-0.480198\pi\) | ||||
0.0621691 | + | 0.998066i | \(0.480198\pi\) | |||||||
\(168\) | −649.610 | −0.298324 | ||||||||
\(169\) | 296.533 | 0.134972 | ||||||||
\(170\) | 494.590 | 0.223137 | ||||||||
\(171\) | −4375.01 | −1.95652 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −310.456 | −0.136437 | −0.0682183 | − | 0.997670i | \(-0.521731\pi\) | ||||
−0.0682183 | + | 0.997670i | \(0.521731\pi\) | |||||||
\(174\) | 305.229 | 0.132985 | ||||||||
\(175\) | −458.195 | −0.197922 | ||||||||
\(176\) | −552.915 | −0.236804 | ||||||||
\(177\) | −4587.78 | −1.94824 | ||||||||
\(178\) | −1587.78 | −0.668589 | ||||||||
\(179\) | −3308.82 | −1.38163 | −0.690817 | − | 0.723030i | \(-0.742749\pi\) | ||||
−0.690817 | + | 0.723030i | \(0.742749\pi\) | |||||||
\(180\) | 1439.85 | 0.596223 | ||||||||
\(181\) | 1215.01 | 0.498957 | 0.249479 | − | 0.968380i | \(-0.419741\pi\) | ||||
0.249479 | + | 0.968380i | \(0.419741\pi\) | |||||||
\(182\) | 279.036 | 0.113646 | ||||||||
\(183\) | −4629.50 | −1.87007 | ||||||||
\(184\) | −2086.32 | −0.835901 | ||||||||
\(185\) | −1625.31 | −0.645919 | ||||||||
\(186\) | −2094.92 | −0.825842 | ||||||||
\(187\) | −1098.37 | −0.429523 | ||||||||
\(188\) | −2376.61 | −0.921977 | ||||||||
\(189\) | −293.322 | −0.112889 | ||||||||
\(190\) | −837.589 | −0.319816 | ||||||||
\(191\) | 3262.00 | 1.23576 | 0.617880 | − | 0.786273i | \(-0.287992\pi\) | ||||
0.617880 | + | 0.786273i | \(0.287992\pi\) | |||||||
\(192\) | 991.038 | 0.372511 | ||||||||
\(193\) | −596.437 | −0.222448 | −0.111224 | − | 0.993795i | \(-0.535477\pi\) | ||||
−0.111224 | + | 0.993795i | \(0.535477\pi\) | |||||||
\(194\) | 300.146 | 0.111079 | ||||||||
\(195\) | −2397.83 | −0.880575 | ||||||||
\(196\) | 2166.09 | 0.789390 | ||||||||
\(197\) | 3156.54 | 1.14160 | 0.570798 | − | 0.821091i | \(-0.306634\pi\) | ||||
0.570798 | + | 0.821091i | \(0.306634\pi\) | |||||||
\(198\) | 527.727 | 0.189414 | ||||||||
\(199\) | 1617.31 | 0.576120 | 0.288060 | − | 0.957612i | \(-0.406990\pi\) | ||||
0.288060 | + | 0.957612i | \(0.406990\pi\) | |||||||
\(200\) | −1381.50 | −0.488434 | ||||||||
\(201\) | 3697.15 | 1.29740 | ||||||||
\(202\) | −1173.62 | −0.408791 | ||||||||
\(203\) | 192.467 | 0.0665445 | ||||||||
\(204\) | 4062.42 | 1.39425 | ||||||||
\(205\) | 0.396839 | 0.000135202 0 | ||||||||
\(206\) | 1977.51 | 0.668834 | ||||||||
\(207\) | −4501.32 | −1.51142 | ||||||||
\(208\) | −1901.81 | −0.633977 | ||||||||
\(209\) | 1860.09 | 0.615623 | ||||||||
\(210\) | −268.326 | −0.0881728 | ||||||||
\(211\) | −3160.29 | −1.03110 | −0.515552 | − | 0.856858i | \(-0.672413\pi\) | ||||
−0.515552 | + | 0.856858i | \(0.672413\pi\) | |||||||
\(212\) | −3220.00 | −1.04316 | ||||||||
\(213\) | −4286.74 | −1.37898 | ||||||||
\(214\) | −199.713 | −0.0637950 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −884.391 | −0.278589 | ||||||||
\(217\) | −1320.98 | −0.413245 | ||||||||
\(218\) | −123.989 | −0.0385209 | ||||||||
\(219\) | −2564.94 | −0.791426 | ||||||||
\(220\) | −612.171 | −0.187603 | ||||||||
\(221\) | −3777.97 | −1.14993 | ||||||||
\(222\) | 2203.25 | 0.666091 | ||||||||
\(223\) | 3030.41 | 0.910006 | 0.455003 | − | 0.890490i | \(-0.349638\pi\) | ||||
0.455003 | + | 0.890490i | \(0.349638\pi\) | |||||||
\(224\) | −877.417 | −0.261718 | ||||||||
\(225\) | −2980.64 | −0.883152 | ||||||||
\(226\) | 1320.53 | 0.388673 | ||||||||
\(227\) | −4911.55 | −1.43608 | −0.718041 | − | 0.696000i | \(-0.754961\pi\) | ||||
−0.718041 | + | 0.696000i | \(0.754961\pi\) | |||||||
\(228\) | −6879.72 | −1.99833 | ||||||||
\(229\) | −5122.08 | −1.47806 | −0.739031 | − | 0.673671i | \(-0.764716\pi\) | ||||
−0.739031 | + | 0.673671i | \(0.764716\pi\) | |||||||
\(230\) | −861.771 | −0.247059 | ||||||||
\(231\) | 595.891 | 0.169726 | ||||||||
\(232\) | 580.305 | 0.164219 | ||||||||
\(233\) | −1455.82 | −0.409332 | −0.204666 | − | 0.978832i | \(-0.565611\pi\) | ||||
−0.204666 | + | 0.978832i | \(0.565611\pi\) | |||||||
\(234\) | 1815.18 | 0.507102 | ||||||||
\(235\) | −2125.37 | −0.589973 | ||||||||
\(236\) | −4028.72 | −1.11122 | ||||||||
\(237\) | −6268.62 | −1.71810 | ||||||||
\(238\) | −422.769 | −0.115143 | ||||||||
\(239\) | 5646.52 | 1.52821 | 0.764107 | − | 0.645089i | \(-0.223180\pi\) | ||||
0.764107 | + | 0.645089i | \(0.223180\pi\) | |||||||
\(240\) | 1828.82 | 0.491875 | ||||||||
\(241\) | −2920.77 | −0.780677 | −0.390339 | − | 0.920671i | \(-0.627642\pi\) | ||||
−0.390339 | + | 0.920671i | \(0.627642\pi\) | |||||||
\(242\) | 1192.56 | 0.316778 | ||||||||
\(243\) | 5301.16 | 1.39946 | ||||||||
\(244\) | −4065.36 | −1.06663 | ||||||||
\(245\) | 1937.10 | 0.505130 | ||||||||
\(246\) | −0.537950 | −0.000139425 0 | ||||||||
\(247\) | 6398.00 | 1.64816 | ||||||||
\(248\) | −3982.88 | −1.01981 | ||||||||
\(249\) | 10546.7 | 2.68422 | ||||||||
\(250\) | −1387.79 | −0.351087 | ||||||||
\(251\) | −2486.12 | −0.625189 | −0.312594 | − | 0.949887i | \(-0.601198\pi\) | ||||
−0.312594 | + | 0.949887i | \(0.601198\pi\) | |||||||
\(252\) | −1230.77 | −0.307663 | ||||||||
\(253\) | 1913.79 | 0.475570 | ||||||||
\(254\) | −98.2740 | −0.0242766 | ||||||||
\(255\) | 3632.96 | 0.892177 | ||||||||
\(256\) | −553.304 | −0.135084 | ||||||||
\(257\) | −7326.49 | −1.77826 | −0.889132 | − | 0.457650i | \(-0.848691\pi\) | ||||
−0.889132 | + | 0.457650i | \(0.848691\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1389.29 | 0.333307 | ||||||||
\(260\) | −2105.63 | −0.502253 | ||||||||
\(261\) | 1252.03 | 0.296930 | ||||||||
\(262\) | −1832.56 | −0.432123 | ||||||||
\(263\) | −251.220 | −0.0589008 | −0.0294504 | − | 0.999566i | \(-0.509376\pi\) | ||||
−0.0294504 | + | 0.999566i | \(0.509376\pi\) | |||||||
\(264\) | 1796.66 | 0.418852 | ||||||||
\(265\) | −2879.60 | −0.667518 | ||||||||
\(266\) | 715.961 | 0.165031 | ||||||||
\(267\) | −11662.9 | −2.67324 | ||||||||
\(268\) | 3246.62 | 0.739996 | ||||||||
\(269\) | −4741.17 | −1.07463 | −0.537313 | − | 0.843383i | \(-0.680560\pi\) | ||||
−0.537313 | + | 0.843383i | \(0.680560\pi\) | |||||||
\(270\) | −365.304 | −0.0823397 | ||||||||
\(271\) | 3799.34 | 0.851637 | 0.425819 | − | 0.904809i | \(-0.359986\pi\) | ||||
0.425819 | + | 0.904809i | \(0.359986\pi\) | |||||||
\(272\) | 2881.45 | 0.642329 | ||||||||
\(273\) | 2049.63 | 0.454394 | ||||||||
\(274\) | −1785.99 | −0.393779 | ||||||||
\(275\) | 1267.26 | 0.277885 | ||||||||
\(276\) | −7078.34 | −1.54372 | ||||||||
\(277\) | 4768.63 | 1.03437 | 0.517183 | − | 0.855875i | \(-0.326981\pi\) | ||||
0.517183 | + | 0.855875i | \(0.326981\pi\) | |||||||
\(278\) | −3001.75 | −0.647600 | ||||||||
\(279\) | −8593.21 | −1.84395 | ||||||||
\(280\) | −510.145 | −0.108882 | ||||||||
\(281\) | 2410.33 | 0.511703 | 0.255851 | − | 0.966716i | \(-0.417644\pi\) | ||||
0.255851 | + | 0.966716i | \(0.417644\pi\) | |||||||
\(282\) | 2881.12 | 0.608398 | ||||||||
\(283\) | −8196.95 | −1.72176 | −0.860880 | − | 0.508808i | \(-0.830086\pi\) | ||||
−0.860880 | + | 0.508808i | \(0.830086\pi\) | |||||||
\(284\) | −3764.36 | −0.786528 | ||||||||
\(285\) | −6152.44 | −1.27873 | ||||||||
\(286\) | −771.746 | −0.159560 | ||||||||
\(287\) | −0.339213 | −6.97669e−5 0 | ||||||||
\(288\) | −5707.74 | −1.16782 | ||||||||
\(289\) | 811.018 | 0.165076 | ||||||||
\(290\) | 239.699 | 0.0485366 | ||||||||
\(291\) | 2204.70 | 0.444129 | ||||||||
\(292\) | −2252.38 | −0.451405 | ||||||||
\(293\) | 4556.22 | 0.908455 | 0.454227 | − | 0.890886i | \(-0.349915\pi\) | ||||
0.454227 | + | 0.890886i | \(0.349915\pi\) | |||||||
\(294\) | −2625.91 | −0.520906 | ||||||||
\(295\) | −3602.83 | −0.711067 | ||||||||
\(296\) | 4188.84 | 0.822538 | ||||||||
\(297\) | 811.257 | 0.158498 | ||||||||
\(298\) | −1034.39 | −0.201076 | ||||||||
\(299\) | 6582.71 | 1.27320 | ||||||||
\(300\) | −4687.06 | −0.902025 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 933.273 | 0.177827 | ||||||||
\(303\) | −8620.74 | −1.63448 | ||||||||
\(304\) | −4879.74 | −0.920633 | ||||||||
\(305\) | −3635.59 | −0.682536 | ||||||||
\(306\) | −2750.18 | −0.513783 | ||||||||
\(307\) | 592.948 | 0.110232 | 0.0551162 | − | 0.998480i | \(-0.482447\pi\) | ||||
0.0551162 | + | 0.998480i | \(0.482447\pi\) | |||||||
\(308\) | 523.276 | 0.0968066 | ||||||||
\(309\) | 14525.6 | 2.67422 | ||||||||
\(310\) | −1645.16 | −0.301415 | ||||||||
\(311\) | 462.957 | 0.0844113 | 0.0422056 | − | 0.999109i | \(-0.486562\pi\) | ||||
0.0422056 | + | 0.999109i | \(0.486562\pi\) | |||||||
\(312\) | 6179.83 | 1.12136 | ||||||||
\(313\) | −2003.19 | −0.361748 | −0.180874 | − | 0.983506i | \(-0.557893\pi\) | ||||
−0.180874 | + | 0.983506i | \(0.557893\pi\) | |||||||
\(314\) | −2332.75 | −0.419251 | ||||||||
\(315\) | −1100.66 | −0.196873 | ||||||||
\(316\) | −5504.74 | −0.979955 | ||||||||
\(317\) | 7514.15 | 1.33135 | 0.665673 | − | 0.746244i | \(-0.268145\pi\) | ||||
0.665673 | + | 0.746244i | \(0.268145\pi\) | |||||||
\(318\) | 3903.55 | 0.688365 | ||||||||
\(319\) | −532.317 | −0.0934295 | ||||||||
\(320\) | 778.272 | 0.135959 | ||||||||
\(321\) | −1466.98 | −0.255074 | ||||||||
\(322\) | 736.631 | 0.127487 | ||||||||
\(323\) | −9693.64 | −1.66987 | ||||||||
\(324\) | 3330.25 | 0.571031 | ||||||||
\(325\) | 4358.87 | 0.743959 | ||||||||
\(326\) | −226.535 | −0.0384866 | ||||||||
\(327\) | −910.747 | −0.154020 | ||||||||
\(328\) | −1.02276 | −0.000172172 0 | ||||||||
\(329\) | 1816.74 | 0.304437 | ||||||||
\(330\) | 742.125 | 0.123796 | ||||||||
\(331\) | 45.1750 | 0.00750164 | 0.00375082 | − | 0.999993i | \(-0.498806\pi\) | ||||
0.00375082 | + | 0.999993i | \(0.498806\pi\) | |||||||
\(332\) | 9261.52 | 1.53100 | ||||||||
\(333\) | 9037.58 | 1.48726 | ||||||||
\(334\) | −285.659 | −0.0467981 | ||||||||
\(335\) | 2903.41 | 0.473523 | ||||||||
\(336\) | −1563.25 | −0.253817 | ||||||||
\(337\) | −3243.02 | −0.524209 | −0.262105 | − | 0.965039i | \(-0.584417\pi\) | ||||
−0.262105 | + | 0.965039i | \(0.584417\pi\) | |||||||
\(338\) | −315.676 | −0.0508003 | ||||||||
\(339\) | 9699.82 | 1.55405 | ||||||||
\(340\) | 3190.26 | 0.508870 | ||||||||
\(341\) | 3653.51 | 0.580202 | ||||||||
\(342\) | 4657.45 | 0.736391 | ||||||||
\(343\) | −3456.25 | −0.544081 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −6330.06 | −0.987824 | ||||||||
\(346\) | 330.498 | 0.0513517 | ||||||||
\(347\) | 3928.20 | 0.607715 | 0.303857 | − | 0.952718i | \(-0.401725\pi\) | ||||
0.303857 | + | 0.952718i | \(0.401725\pi\) | |||||||
\(348\) | 1968.82 | 0.303275 | ||||||||
\(349\) | 9860.04 | 1.51231 | 0.756154 | − | 0.654393i | \(-0.227076\pi\) | ||||
0.756154 | + | 0.654393i | \(0.227076\pi\) | |||||||
\(350\) | 487.775 | 0.0744933 | ||||||||
\(351\) | 2790.41 | 0.424333 | ||||||||
\(352\) | 2426.72 | 0.367456 | ||||||||
\(353\) | 3705.00 | 0.558633 | 0.279316 | − | 0.960199i | \(-0.409892\pi\) | ||||
0.279316 | + | 0.960199i | \(0.409892\pi\) | |||||||
\(354\) | 4883.95 | 0.733274 | ||||||||
\(355\) | −3366.42 | −0.503299 | ||||||||
\(356\) | −10241.6 | −1.52474 | ||||||||
\(357\) | −3105.41 | −0.460380 | ||||||||
\(358\) | 3522.42 | 0.520016 | ||||||||
\(359\) | 3869.65 | 0.568892 | 0.284446 | − | 0.958692i | \(-0.408190\pi\) | ||||
0.284446 | + | 0.958692i | \(0.408190\pi\) | |||||||
\(360\) | −3318.58 | −0.485846 | ||||||||
\(361\) | 9557.21 | 1.39338 | ||||||||
\(362\) | −1293.45 | −0.187796 | ||||||||
\(363\) | 8759.80 | 1.26659 | ||||||||
\(364\) | 1799.87 | 0.259172 | ||||||||
\(365\) | −2014.27 | −0.288854 | ||||||||
\(366\) | 4928.36 | 0.703852 | ||||||||
\(367\) | −10876.6 | −1.54702 | −0.773508 | − | 0.633786i | \(-0.781500\pi\) | ||||
−0.773508 | + | 0.633786i | \(0.781500\pi\) | |||||||
\(368\) | −5020.63 | −0.711191 | ||||||||
\(369\) | −2.20664 | −0.000311309 0 | ||||||||
\(370\) | 1730.23 | 0.243109 | ||||||||
\(371\) | 2461.44 | 0.344452 | ||||||||
\(372\) | −13512.9 | −1.88336 | ||||||||
\(373\) | 10131.1 | 1.40634 | 0.703172 | − | 0.711020i | \(-0.251766\pi\) | ||||
0.703172 | + | 0.711020i | \(0.251766\pi\) | |||||||
\(374\) | 1169.28 | 0.161663 | ||||||||
\(375\) | −10193.9 | −1.40376 | ||||||||
\(376\) | 5477.62 | 0.751294 | ||||||||
\(377\) | −1830.96 | −0.250131 | ||||||||
\(378\) | 312.258 | 0.0424889 | ||||||||
\(379\) | −8606.22 | −1.16642 | −0.583208 | − | 0.812323i | \(-0.698203\pi\) | ||||
−0.583208 | + | 0.812323i | \(0.698203\pi\) | |||||||
\(380\) | −5402.71 | −0.729350 | ||||||||
\(381\) | −721.862 | −0.0970660 | ||||||||
\(382\) | −3472.58 | −0.465112 | ||||||||
\(383\) | −3345.75 | −0.446370 | −0.223185 | − | 0.974776i | \(-0.571645\pi\) | ||||
−0.223185 | + | 0.974776i | \(0.571645\pi\) | |||||||
\(384\) | −11511.8 | −1.52984 | ||||||||
\(385\) | 467.959 | 0.0619465 | ||||||||
\(386\) | 634.941 | 0.0837245 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 1936.03 | 0.253318 | ||||||||
\(389\) | −3603.72 | −0.469706 | −0.234853 | − | 0.972031i | \(-0.575461\pi\) | ||||
−0.234853 | + | 0.972031i | \(0.575461\pi\) | |||||||
\(390\) | 2552.62 | 0.331429 | ||||||||
\(391\) | −9973.51 | −1.28998 | ||||||||
\(392\) | −4992.41 | −0.643252 | ||||||||
\(393\) | −13460.9 | −1.72777 | ||||||||
\(394\) | −3360.32 | −0.429671 | ||||||||
\(395\) | −4922.81 | −0.627072 | ||||||||
\(396\) | 3404.00 | 0.431963 | ||||||||
\(397\) | 4178.70 | 0.528270 | 0.264135 | − | 0.964486i | \(-0.414914\pi\) | ||||
0.264135 | + | 0.964486i | \(0.414914\pi\) | |||||||
\(398\) | −1721.71 | −0.216839 | ||||||||
\(399\) | 5259.02 | 0.659851 | ||||||||
\(400\) | −3324.51 | −0.415563 | ||||||||
\(401\) | −6248.54 | −0.778147 | −0.389074 | − | 0.921207i | \(-0.627205\pi\) | ||||
−0.389074 | + | 0.921207i | \(0.627205\pi\) | |||||||
\(402\) | −3935.83 | −0.488311 | ||||||||
\(403\) | 12566.7 | 1.55333 | ||||||||
\(404\) | −7570.23 | −0.932260 | ||||||||
\(405\) | 2978.20 | 0.365402 | ||||||||
\(406\) | −204.892 | −0.0250458 | ||||||||
\(407\) | −3842.44 | −0.467968 | ||||||||
\(408\) | −9363.09 | −1.13613 | ||||||||
\(409\) | −2173.77 | −0.262802 | −0.131401 | − | 0.991329i | \(-0.541948\pi\) | ||||
−0.131401 | + | 0.991329i | \(0.541948\pi\) | |||||||
\(410\) | −0.422457 | −5.08870e−5 0 | ||||||||
\(411\) | −13118.8 | −1.57446 | ||||||||
\(412\) | 12755.6 | 1.52529 | ||||||||
\(413\) | 3079.65 | 0.366925 | ||||||||
\(414\) | 4791.91 | 0.568864 | ||||||||
\(415\) | 8282.45 | 0.979685 | ||||||||
\(416\) | 8346.98 | 0.983761 | ||||||||
\(417\) | −22049.1 | −2.58932 | ||||||||
\(418\) | −1980.17 | −0.231707 | ||||||||
\(419\) | −9987.39 | −1.16448 | −0.582238 | − | 0.813018i | \(-0.697823\pi\) | ||||
−0.582238 | + | 0.813018i | \(0.697823\pi\) | |||||||
\(420\) | −1730.79 | −0.201080 | ||||||||
\(421\) | −6981.99 | −0.808269 | −0.404134 | − | 0.914700i | \(-0.632427\pi\) | ||||
−0.404134 | + | 0.914700i | \(0.632427\pi\) | |||||||
\(422\) | 3364.30 | 0.388085 | ||||||||
\(423\) | 11818.2 | 1.35844 | ||||||||
\(424\) | 7421.47 | 0.850043 | ||||||||
\(425\) | −6604.15 | −0.753761 | ||||||||
\(426\) | 4563.48 | 0.519017 | ||||||||
\(427\) | 3107.66 | 0.352202 | ||||||||
\(428\) | −1288.21 | −0.145486 | ||||||||
\(429\) | −5668.79 | −0.637976 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 222.271 | 0.0248408 | 0.0124204 | − | 0.999923i | \(-0.496046\pi\) | ||||
0.0124204 | + | 0.999923i | \(0.496046\pi\) | |||||||
\(432\) | −2128.24 | −0.237026 | ||||||||
\(433\) | 5956.90 | 0.661132 | 0.330566 | − | 0.943783i | \(-0.392760\pi\) | ||||
0.330566 | + | 0.943783i | \(0.392760\pi\) | |||||||
\(434\) | 1406.26 | 0.155536 | ||||||||
\(435\) | 1760.69 | 0.194066 | ||||||||
\(436\) | −799.765 | −0.0878481 | ||||||||
\(437\) | 16890.2 | 1.84889 | ||||||||
\(438\) | 2730.52 | 0.297875 | ||||||||
\(439\) | 6259.09 | 0.680478 | 0.340239 | − | 0.940339i | \(-0.389492\pi\) | ||||
0.340239 | + | 0.940339i | \(0.389492\pi\) | |||||||
\(440\) | 1410.94 | 0.152872 | ||||||||
\(441\) | −10771.3 | −1.16308 | ||||||||
\(442\) | 4021.86 | 0.432806 | ||||||||
\(443\) | 10832.7 | 1.16180 | 0.580902 | − | 0.813974i | \(-0.302700\pi\) | ||||
0.580902 | + | 0.813974i | \(0.302700\pi\) | |||||||
\(444\) | 14211.6 | 1.51904 | ||||||||
\(445\) | −9158.96 | −0.975677 | ||||||||
\(446\) | −3226.04 | −0.342506 | ||||||||
\(447\) | −7598.04 | −0.803971 | ||||||||
\(448\) | −665.257 | −0.0701573 | ||||||||
\(449\) | −10794.8 | −1.13461 | −0.567305 | − | 0.823508i | \(-0.692014\pi\) | ||||
−0.567305 | + | 0.823508i | \(0.692014\pi\) | |||||||
\(450\) | 3173.06 | 0.332398 | ||||||||
\(451\) | 0.938180 | 9.79538e−5 0 | ||||||||
\(452\) | 8517.81 | 0.886381 | ||||||||
\(453\) | 6855.27 | 0.711013 | ||||||||
\(454\) | 5228.62 | 0.540509 | ||||||||
\(455\) | 1609.60 | 0.165844 | ||||||||
\(456\) | 15856.4 | 1.62839 | ||||||||
\(457\) | −12577.4 | −1.28741 | −0.643706 | − | 0.765273i | \(-0.722604\pi\) | ||||
−0.643706 | + | 0.765273i | \(0.722604\pi\) | |||||||
\(458\) | 5452.74 | 0.556310 | ||||||||
\(459\) | −4227.76 | −0.429924 | ||||||||
\(460\) | −5558.69 | −0.563425 | ||||||||
\(461\) | −14738.5 | −1.48902 | −0.744510 | − | 0.667611i | \(-0.767317\pi\) | ||||
−0.744510 | + | 0.667611i | \(0.767317\pi\) | |||||||
\(462\) | −634.359 | −0.0638811 | ||||||||
\(463\) | −877.733 | −0.0881030 | −0.0440515 | − | 0.999029i | \(-0.514027\pi\) | ||||
−0.0440515 | + | 0.999029i | \(0.514027\pi\) | |||||||
\(464\) | 1396.47 | 0.139719 | ||||||||
\(465\) | −12084.4 | −1.20516 | ||||||||
\(466\) | 1549.81 | 0.154063 | ||||||||
\(467\) | −3211.66 | −0.318239 | −0.159120 | − | 0.987259i | \(-0.550866\pi\) | ||||
−0.159120 | + | 0.987259i | \(0.550866\pi\) | |||||||
\(468\) | 11708.4 | 1.15646 | ||||||||
\(469\) | −2481.80 | −0.244347 | ||||||||
\(470\) | 2262.57 | 0.222052 | ||||||||
\(471\) | −17135.0 | −1.67630 | ||||||||
\(472\) | 9285.43 | 0.905501 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 6673.30 | 0.646656 | ||||||||
\(475\) | 11184.2 | 1.08035 | ||||||||
\(476\) | −2726.99 | −0.262587 | ||||||||
\(477\) | 16012.1 | 1.53699 | ||||||||
\(478\) | −6011.04 | −0.575186 | ||||||||
\(479\) | −6177.44 | −0.589258 | −0.294629 | − | 0.955612i | \(-0.595196\pi\) | ||||
−0.294629 | + | 0.955612i | \(0.595196\pi\) | |||||||
\(480\) | −8026.62 | −0.763257 | ||||||||
\(481\) | −13216.5 | −1.25285 | ||||||||
\(482\) | 3109.32 | 0.293829 | ||||||||
\(483\) | 5410.86 | 0.509736 | ||||||||
\(484\) | 7692.35 | 0.722422 | ||||||||
\(485\) | 1731.37 | 0.162098 | ||||||||
\(486\) | −5643.38 | −0.526726 | ||||||||
\(487\) | 15600.7 | 1.45161 | 0.725807 | − | 0.687899i | \(-0.241467\pi\) | ||||
0.725807 | + | 0.687899i | \(0.241467\pi\) | |||||||
\(488\) | 9369.86 | 0.869168 | ||||||||
\(489\) | −1663.99 | −0.153882 | ||||||||
\(490\) | −2062.15 | −0.190120 | ||||||||
\(491\) | −108.625 | −0.00998406 | −0.00499203 | − | 0.999988i | \(-0.501589\pi\) | ||||
−0.00499203 | + | 0.999988i | \(0.501589\pi\) | |||||||
\(492\) | −3.46994 | −0.000317962 0 | ||||||||
\(493\) | 2774.10 | 0.253427 | ||||||||
\(494\) | −6811.03 | −0.620329 | ||||||||
\(495\) | 3044.15 | 0.276413 | ||||||||
\(496\) | −9584.59 | −0.867663 | ||||||||
\(497\) | 2877.57 | 0.259712 | ||||||||
\(498\) | −11227.6 | −1.01028 | ||||||||
\(499\) | 1133.22 | 0.101663 | 0.0508317 | − | 0.998707i | \(-0.483813\pi\) | ||||
0.0508317 | + | 0.998707i | \(0.483813\pi\) | |||||||
\(500\) | −8951.70 | −0.800664 | ||||||||
\(501\) | −2098.28 | −0.187115 | ||||||||
\(502\) | 2646.61 | 0.235307 | ||||||||
\(503\) | 12385.7 | 1.09791 | 0.548956 | − | 0.835852i | \(-0.315026\pi\) | ||||
0.548956 | + | 0.835852i | \(0.315026\pi\) | |||||||
\(504\) | 2836.68 | 0.250706 | ||||||||
\(505\) | −6769.95 | −0.596552 | ||||||||
\(506\) | −2037.34 | −0.178994 | ||||||||
\(507\) | −2318.77 | −0.203117 | ||||||||
\(508\) | −633.897 | −0.0553635 | ||||||||
\(509\) | −5798.36 | −0.504927 | −0.252464 | − | 0.967606i | \(-0.581241\pi\) | ||||
−0.252464 | + | 0.967606i | \(0.581241\pi\) | |||||||
\(510\) | −3867.50 | −0.335795 | ||||||||
\(511\) | 1721.77 | 0.149054 | ||||||||
\(512\) | −11188.3 | −0.965739 | ||||||||
\(513\) | 7159.73 | 0.616199 | ||||||||
\(514\) | 7799.46 | 0.669299 | ||||||||
\(515\) | 11407.1 | 0.976035 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −5024.65 | −0.427435 | ||||||||
\(518\) | −1478.98 | −0.125449 | ||||||||
\(519\) | 2427.64 | 0.205321 | ||||||||
\(520\) | 4853.08 | 0.409272 | ||||||||
\(521\) | −1523.74 | −0.128131 | −0.0640653 | − | 0.997946i | \(-0.520407\pi\) | ||||
−0.0640653 | + | 0.997946i | \(0.520407\pi\) | |||||||
\(522\) | −1332.86 | −0.111758 | ||||||||
\(523\) | 7712.81 | 0.644852 | 0.322426 | − | 0.946595i | \(-0.395502\pi\) | ||||
0.322426 | + | 0.946595i | \(0.395502\pi\) | |||||||
\(524\) | −11820.6 | −0.985468 | ||||||||
\(525\) | 3582.90 | 0.297849 | ||||||||
\(526\) | 267.438 | 0.0221690 | ||||||||
\(527\) | −19039.8 | −1.57379 | ||||||||
\(528\) | 4323.58 | 0.356363 | ||||||||
\(529\) | 5210.81 | 0.428274 | ||||||||
\(530\) | 3065.50 | 0.251239 | ||||||||
\(531\) | 20033.7 | 1.63726 | ||||||||
\(532\) | 4618.17 | 0.376359 | ||||||||
\(533\) | 3.22698 | 0.000262244 0 | ||||||||
\(534\) | 12415.8 | 1.00615 | ||||||||
\(535\) | −1152.03 | −0.0930966 | ||||||||
\(536\) | −7482.84 | −0.603003 | ||||||||
\(537\) | 25873.6 | 2.07920 | ||||||||
\(538\) | 5047.24 | 0.404465 | ||||||||
\(539\) | 4579.57 | 0.365966 | ||||||||
\(540\) | −2356.33 | −0.187778 | ||||||||
\(541\) | −17909.6 | −1.42328 | −0.711640 | − | 0.702544i | \(-0.752047\pi\) | ||||
−0.711640 | + | 0.702544i | \(0.752047\pi\) | |||||||
\(542\) | −4044.62 | −0.320537 | ||||||||
\(543\) | −9500.92 | −0.750872 | ||||||||
\(544\) | −12646.6 | −0.996722 | ||||||||
\(545\) | −715.219 | −0.0562139 | ||||||||
\(546\) | −2181.95 | −0.171024 | ||||||||
\(547\) | 6691.92 | 0.523082 | 0.261541 | − | 0.965192i | \(-0.415769\pi\) | ||||
0.261541 | + | 0.965192i | \(0.415769\pi\) | |||||||
\(548\) | −11520.2 | −0.898025 | ||||||||
\(549\) | 20215.8 | 1.57157 | ||||||||
\(550\) | −1349.07 | −0.104590 | ||||||||
\(551\) | −4697.95 | −0.363230 | ||||||||
\(552\) | 16314.2 | 1.25793 | ||||||||
\(553\) | 4207.96 | 0.323581 | ||||||||
\(554\) | −5076.48 | −0.389312 | ||||||||
\(555\) | 12709.3 | 0.972032 | ||||||||
\(556\) | −19362.2 | −1.47687 | ||||||||
\(557\) | 9117.59 | 0.693581 | 0.346790 | − | 0.937943i | \(-0.387271\pi\) | ||||
0.346790 | + | 0.937943i | \(0.387271\pi\) | |||||||
\(558\) | 9147.96 | 0.694021 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | −1227.64 | −0.0926378 | ||||||||
\(561\) | 8588.81 | 0.646381 | ||||||||
\(562\) | −2565.94 | −0.192593 | ||||||||
\(563\) | 16518.8 | 1.23656 | 0.618282 | − | 0.785956i | \(-0.287829\pi\) | ||||
0.618282 | + | 0.785956i | \(0.287829\pi\) | |||||||
\(564\) | 18584.1 | 1.38747 | ||||||||
\(565\) | 7617.36 | 0.567194 | ||||||||
\(566\) | 8726.12 | 0.648032 | ||||||||
\(567\) | −2545.72 | −0.188554 | ||||||||
\(568\) | 8676.13 | 0.640920 | ||||||||
\(569\) | 25394.8 | 1.87101 | 0.935505 | − | 0.353313i | \(-0.114945\pi\) | ||||
0.935505 | + | 0.353313i | \(0.114945\pi\) | |||||||
\(570\) | 6549.62 | 0.481286 | ||||||||
\(571\) | 13697.9 | 1.00392 | 0.501960 | − | 0.864891i | \(-0.332613\pi\) | ||||
0.501960 | + | 0.864891i | \(0.332613\pi\) | |||||||
\(572\) | −4978.00 | −0.363882 | ||||||||
\(573\) | −25507.6 | −1.85967 | ||||||||
\(574\) | 0.361111 | 2.62587e−5 0 | ||||||||
\(575\) | 11507.1 | 0.834569 | ||||||||
\(576\) | −4327.61 | −0.313051 | ||||||||
\(577\) | −763.733 | −0.0551033 | −0.0275517 | − | 0.999620i | \(-0.508771\pi\) | ||||
−0.0275517 | + | 0.999620i | \(0.508771\pi\) | |||||||
\(578\) | −863.375 | −0.0621309 | ||||||||
\(579\) | 4663.90 | 0.334759 | ||||||||
\(580\) | 1546.13 | 0.110689 | ||||||||
\(581\) | −7079.73 | −0.505537 | ||||||||
\(582\) | −2347.02 | −0.167160 | ||||||||
\(583\) | −6807.75 | −0.483616 | ||||||||
\(584\) | 5191.29 | 0.367838 | ||||||||
\(585\) | 10470.7 | 0.740018 | ||||||||
\(586\) | −4850.36 | −0.341922 | ||||||||
\(587\) | −7553.03 | −0.531085 | −0.265543 | − | 0.964099i | \(-0.585551\pi\) | ||||
−0.265543 | + | 0.964099i | \(0.585551\pi\) | |||||||
\(588\) | −16937.9 | −1.18794 | ||||||||
\(589\) | 32244.0 | 2.25567 | ||||||||
\(590\) | 3835.42 | 0.267630 | ||||||||
\(591\) | −24682.9 | −1.71797 | ||||||||
\(592\) | 10080.2 | 0.699822 | ||||||||
\(593\) | −23780.6 | −1.64680 | −0.823401 | − | 0.567460i | \(-0.807926\pi\) | ||||
−0.823401 | + | 0.567460i | \(0.807926\pi\) | |||||||
\(594\) | −863.629 | −0.0596551 | ||||||||
\(595\) | −2438.71 | −0.168029 | ||||||||
\(596\) | −6672.16 | −0.458561 | ||||||||
\(597\) | −12646.7 | −0.866993 | ||||||||
\(598\) | −7007.67 | −0.479206 | ||||||||
\(599\) | −5509.20 | −0.375792 | −0.187896 | − | 0.982189i | \(-0.560167\pi\) | ||||
−0.187896 | + | 0.982189i | \(0.560167\pi\) | |||||||
\(600\) | 10802.8 | 0.735036 | ||||||||
\(601\) | −19229.4 | −1.30513 | −0.652565 | − | 0.757733i | \(-0.726307\pi\) | ||||
−0.652565 | + | 0.757733i | \(0.726307\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −16144.5 | −1.09031 | ||||||||
\(604\) | 6019.90 | 0.405540 | ||||||||
\(605\) | 6879.16 | 0.462277 | ||||||||
\(606\) | 9177.26 | 0.615183 | ||||||||
\(607\) | −16273.8 | −1.08820 | −0.544098 | − | 0.839022i | \(-0.683128\pi\) | ||||
−0.544098 | + | 0.839022i | \(0.683128\pi\) | |||||||
\(608\) | 21417.0 | 1.42858 | ||||||||
\(609\) | −1505.01 | −0.100142 | ||||||||
\(610\) | 3870.29 | 0.256891 | ||||||||
\(611\) | −17282.8 | −1.14434 | ||||||||
\(612\) | −17739.5 | −1.17170 | ||||||||
\(613\) | 22778.0 | 1.50081 | 0.750404 | − | 0.660979i | \(-0.229859\pi\) | ||||
0.750404 | + | 0.660979i | \(0.229859\pi\) | |||||||
\(614\) | −631.227 | −0.0414890 | ||||||||
\(615\) | −3.10312 | −0.000203463 0 | ||||||||
\(616\) | −1206.05 | −0.0788850 | ||||||||
\(617\) | −2928.42 | −0.191076 | −0.0955379 | − | 0.995426i | \(-0.530457\pi\) | ||||
−0.0955379 | + | 0.995426i | \(0.530457\pi\) | |||||||
\(618\) | −15463.4 | −1.00652 | ||||||||
\(619\) | −21693.7 | −1.40863 | −0.704316 | − | 0.709886i | \(-0.748746\pi\) | ||||
−0.704316 | + | 0.709886i | \(0.748746\pi\) | |||||||
\(620\) | −10611.8 | −0.687386 | ||||||||
\(621\) | 7366.44 | 0.476015 | ||||||||
\(622\) | −492.844 | −0.0317705 | ||||||||
\(623\) | 7828.96 | 0.503468 | ||||||||
\(624\) | 14871.4 | 0.954061 | ||||||||
\(625\) | 2905.92 | 0.185979 | ||||||||
\(626\) | 2132.51 | 0.136154 | ||||||||
\(627\) | −14545.2 | −0.926441 | ||||||||
\(628\) | −15047.0 | −0.956113 | ||||||||
\(629\) | 20024.4 | 1.26936 | ||||||||
\(630\) | 1171.71 | 0.0740986 | ||||||||
\(631\) | 6428.64 | 0.405579 | 0.202789 | − | 0.979222i | \(-0.434999\pi\) | ||||
0.202789 | + | 0.979222i | \(0.434999\pi\) | |||||||
\(632\) | 12687.4 | 0.798538 | ||||||||
\(633\) | 24712.2 | 1.55169 | ||||||||
\(634\) | −7999.23 | −0.501089 | ||||||||
\(635\) | −566.886 | −0.0354271 | ||||||||
\(636\) | 25179.1 | 1.56984 | ||||||||
\(637\) | 15751.9 | 0.979772 | ||||||||
\(638\) | 566.681 | 0.0351648 | ||||||||
\(639\) | 18719.1 | 1.15887 | ||||||||
\(640\) | −9040.30 | −0.558358 | ||||||||
\(641\) | −16640.2 | −1.02535 | −0.512675 | − | 0.858583i | \(-0.671345\pi\) | ||||
−0.512675 | + | 0.858583i | \(0.671345\pi\) | |||||||
\(642\) | 1561.68 | 0.0960041 | ||||||||
\(643\) | −22067.1 | −1.35341 | −0.676705 | − | 0.736254i | \(-0.736593\pi\) | ||||
−0.676705 | + | 0.736254i | \(0.736593\pi\) | |||||||
\(644\) | 4751.50 | 0.290738 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 10319.4 | 0.628502 | ||||||||
\(647\) | 21490.3 | 1.30583 | 0.652914 | − | 0.757432i | \(-0.273546\pi\) | ||||
0.652914 | + | 0.757432i | \(0.273546\pi\) | |||||||
\(648\) | −7675.58 | −0.465317 | ||||||||
\(649\) | −8517.57 | −0.515168 | ||||||||
\(650\) | −4640.27 | −0.280010 | ||||||||
\(651\) | 10329.6 | 0.621885 | ||||||||
\(652\) | −1461.22 | −0.0877698 | ||||||||
\(653\) | −6820.47 | −0.408738 | −0.204369 | − | 0.978894i | \(-0.565514\pi\) | ||||
−0.204369 | + | 0.978894i | \(0.565514\pi\) | |||||||
\(654\) | 969.542 | 0.0579695 | ||||||||
\(655\) | −10571.0 | −0.630600 | ||||||||
\(656\) | −2.46121 | −0.000146485 0 | ||||||||
\(657\) | 11200.4 | 0.665099 | ||||||||
\(658\) | −1934.02 | −0.114583 | ||||||||
\(659\) | 22489.9 | 1.32941 | 0.664705 | − | 0.747106i | \(-0.268557\pi\) | ||||
0.664705 | + | 0.747106i | \(0.268557\pi\) | |||||||
\(660\) | 4786.94 | 0.282320 | ||||||||
\(661\) | 4415.60 | 0.259829 | 0.129915 | − | 0.991525i | \(-0.458530\pi\) | ||||
0.129915 | + | 0.991525i | \(0.458530\pi\) | |||||||
\(662\) | −48.0913 | −0.00282345 | ||||||||
\(663\) | 29542.2 | 1.73050 | ||||||||
\(664\) | −21346.0 | −1.24757 | ||||||||
\(665\) | 4129.96 | 0.240832 | ||||||||
\(666\) | −9621.01 | −0.559770 | ||||||||
\(667\) | −4833.59 | −0.280596 | ||||||||
\(668\) | −1842.59 | −0.106724 | ||||||||
\(669\) | −23696.6 | −1.36945 | ||||||||
\(670\) | −3090.84 | −0.178223 | ||||||||
\(671\) | −8595.03 | −0.494497 | ||||||||
\(672\) | 6861.05 | 0.393855 | ||||||||
\(673\) | 12380.3 | 0.709099 | 0.354550 | − | 0.935037i | \(-0.384634\pi\) | ||||
0.354550 | + | 0.935037i | \(0.384634\pi\) | |||||||
\(674\) | 3452.38 | 0.197301 | ||||||||
\(675\) | 4877.83 | 0.278145 | ||||||||
\(676\) | −2036.21 | −0.115852 | ||||||||
\(677\) | 13581.0 | 0.770988 | 0.385494 | − | 0.922710i | \(-0.374031\pi\) | ||||
0.385494 | + | 0.922710i | \(0.374031\pi\) | |||||||
\(678\) | −10326.0 | −0.584908 | ||||||||
\(679\) | −1479.95 | −0.0836456 | ||||||||
\(680\) | −7352.93 | −0.414665 | ||||||||
\(681\) | 38406.4 | 2.16114 | ||||||||
\(682\) | −3889.37 | −0.218375 | ||||||||
\(683\) | −11883.8 | −0.665772 | −0.332886 | − | 0.942967i | \(-0.608022\pi\) | ||||
−0.332886 | + | 0.942967i | \(0.608022\pi\) | |||||||
\(684\) | 30042.0 | 1.67936 | ||||||||
\(685\) | −10302.3 | −0.574646 | ||||||||
\(686\) | 3679.37 | 0.204780 | ||||||||
\(687\) | 40052.6 | 2.22431 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −23416.0 | −1.29475 | ||||||||
\(690\) | 6738.71 | 0.371795 | ||||||||
\(691\) | −29404.3 | −1.61880 | −0.809401 | − | 0.587256i | \(-0.800208\pi\) | ||||
−0.809401 | + | 0.587256i | \(0.800208\pi\) | |||||||
\(692\) | 2131.81 | 0.117109 | ||||||||
\(693\) | −2602.10 | −0.142634 | ||||||||
\(694\) | −4181.80 | −0.228730 | ||||||||
\(695\) | −17315.3 | −0.945048 | ||||||||
\(696\) | −4537.75 | −0.247131 | ||||||||
\(697\) | −4.88921 | −0.000265699 0 | ||||||||
\(698\) | −10496.6 | −0.569199 | ||||||||
\(699\) | 11384.0 | 0.615996 | ||||||||
\(700\) | 3146.30 | 0.169884 | ||||||||
\(701\) | −3434.39 | −0.185043 | −0.0925214 | − | 0.995711i | \(-0.529493\pi\) | ||||
−0.0925214 | + | 0.995711i | \(0.529493\pi\) | |||||||
\(702\) | −2970.55 | −0.159710 | ||||||||
\(703\) | −33911.4 | −1.81934 | ||||||||
\(704\) | 1839.94 | 0.0985019 | ||||||||
\(705\) | 16619.5 | 0.887840 | ||||||||
\(706\) | −3944.18 | −0.210257 | ||||||||
\(707\) | 5786.87 | 0.307832 | ||||||||
\(708\) | 31503.0 | 1.67225 | ||||||||
\(709\) | 9505.59 | 0.503512 | 0.251756 | − | 0.967791i | \(-0.418992\pi\) | ||||
0.251756 | + | 0.967791i | \(0.418992\pi\) | |||||||
\(710\) | 3583.74 | 0.189430 | ||||||||
\(711\) | 27373.5 | 1.44386 | ||||||||
\(712\) | 23605.0 | 1.24247 | ||||||||
\(713\) | 33175.0 | 1.74251 | ||||||||
\(714\) | 3305.89 | 0.173277 | ||||||||
\(715\) | −4451.76 | −0.232848 | ||||||||
\(716\) | 22720.7 | 1.18591 | ||||||||
\(717\) | −44153.6 | −2.29978 | ||||||||
\(718\) | −4119.46 | −0.214118 | ||||||||
\(719\) | −30161.2 | −1.56443 | −0.782214 | − | 0.623010i | \(-0.785909\pi\) | ||||
−0.782214 | + | 0.623010i | \(0.785909\pi\) | |||||||
\(720\) | −7985.99 | −0.413362 | ||||||||
\(721\) | −9750.66 | −0.503653 | ||||||||
\(722\) | −10174.2 | −0.524438 | ||||||||
\(723\) | 22839.3 | 1.17483 | ||||||||
\(724\) | −8343.16 | −0.428275 | ||||||||
\(725\) | −3200.65 | −0.163958 | ||||||||
\(726\) | −9325.31 | −0.476714 | ||||||||
\(727\) | 13578.6 | 0.692713 | 0.346356 | − | 0.938103i | \(-0.387419\pi\) | ||||
0.346356 | + | 0.938103i | \(0.387419\pi\) | |||||||
\(728\) | −4148.35 | −0.211192 | ||||||||
\(729\) | −28358.4 | −1.44076 | ||||||||
\(730\) | 2144.30 | 0.108718 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 31789.5 | 1.60515 | ||||||||
\(733\) | −30598.7 | −1.54187 | −0.770934 | − | 0.636915i | \(-0.780210\pi\) | ||||
−0.770934 | + | 0.636915i | \(0.780210\pi\) | |||||||
\(734\) | 11578.8 | 0.582263 | ||||||||
\(735\) | −15147.4 | −0.760162 | ||||||||
\(736\) | 22035.3 | 1.10358 | ||||||||
\(737\) | 6864.05 | 0.343067 | ||||||||
\(738\) | 2.34909 | 0.000117170 0 | ||||||||
\(739\) | −6419.22 | −0.319533 | −0.159766 | − | 0.987155i | \(-0.551074\pi\) | ||||
−0.159766 | + | 0.987155i | \(0.551074\pi\) | |||||||
\(740\) | 11160.5 | 0.554418 | ||||||||
\(741\) | −50029.8 | −2.48028 | ||||||||
\(742\) | −2620.35 | −0.129644 | ||||||||
\(743\) | −30806.9 | −1.52113 | −0.760563 | − | 0.649264i | \(-0.775077\pi\) | ||||
−0.760563 | + | 0.649264i | \(0.775077\pi\) | |||||||
\(744\) | 31144.5 | 1.53470 | ||||||||
\(745\) | −5966.82 | −0.293433 | ||||||||
\(746\) | −10785.1 | −0.529317 | ||||||||
\(747\) | −46054.8 | −2.25577 | ||||||||
\(748\) | 7542.19 | 0.368676 | ||||||||
\(749\) | 984.742 | 0.0480396 | ||||||||
\(750\) | 10852.0 | 0.528345 | ||||||||
\(751\) | −19700.5 | −0.957233 | −0.478616 | − | 0.878024i | \(-0.658862\pi\) | ||||
−0.478616 | + | 0.878024i | \(0.658862\pi\) | |||||||
\(752\) | 13181.6 | 0.639207 | ||||||||
\(753\) | 19440.5 | 0.940836 | ||||||||
\(754\) | 1949.16 | 0.0941437 | ||||||||
\(755\) | 5383.51 | 0.259505 | ||||||||
\(756\) | 2014.16 | 0.0968971 | ||||||||
\(757\) | −11597.2 | −0.556813 | −0.278406 | − | 0.960463i | \(-0.589806\pi\) | ||||
−0.278406 | + | 0.960463i | \(0.589806\pi\) | |||||||
\(758\) | 9161.81 | 0.439013 | ||||||||
\(759\) | −14965.1 | −0.715678 | ||||||||
\(760\) | 12452.2 | 0.594328 | ||||||||
\(761\) | 35405.7 | 1.68654 | 0.843269 | − | 0.537492i | \(-0.180628\pi\) | ||||
0.843269 | + | 0.537492i | \(0.180628\pi\) | |||||||
\(762\) | 768.464 | 0.0365335 | ||||||||
\(763\) | 611.360 | 0.0290075 | ||||||||
\(764\) | −22399.2 | −1.06070 | ||||||||
\(765\) | −15864.2 | −0.749768 | ||||||||
\(766\) | 3561.74 | 0.168004 | ||||||||
\(767\) | −29297.2 | −1.37922 | ||||||||
\(768\) | 4326.62 | 0.203286 | ||||||||
\(769\) | −22021.1 | −1.03264 | −0.516321 | − | 0.856395i | \(-0.672699\pi\) | ||||
−0.516321 | + | 0.856395i | \(0.672699\pi\) | |||||||
\(770\) | −498.169 | −0.0233153 | ||||||||
\(771\) | 57290.3 | 2.67608 | ||||||||
\(772\) | 4095.57 | 0.190936 | ||||||||
\(773\) | 4710.78 | 0.219191 | 0.109596 | − | 0.993976i | \(-0.465044\pi\) | ||||
0.109596 | + | 0.993976i | \(0.465044\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 21967.4 | 1.01819 | ||||||||
\(776\) | −4462.19 | −0.206422 | ||||||||
\(777\) | −10863.7 | −0.501588 | ||||||||
\(778\) | 3836.36 | 0.176787 | ||||||||
\(779\) | 8.27989 | 0.000380819 0 | ||||||||
\(780\) | 16465.2 | 0.755832 | ||||||||
\(781\) | −7958.67 | −0.364639 | ||||||||
\(782\) | 10617.4 | 0.485519 | ||||||||
\(783\) | −2048.95 | −0.0935168 | ||||||||
\(784\) | −12014.0 | −0.547284 | ||||||||
\(785\) | −13456.3 | −0.611816 | ||||||||
\(786\) | 14329.9 | 0.650294 | ||||||||
\(787\) | 23336.9 | 1.05701 | 0.528506 | − | 0.848929i | \(-0.322752\pi\) | ||||
0.528506 | + | 0.848929i | \(0.322752\pi\) | |||||||
\(788\) | −21675.1 | −0.979877 | ||||||||
\(789\) | 1964.44 | 0.0886389 | ||||||||
\(790\) | 5240.61 | 0.236016 | ||||||||
\(791\) | −6511.23 | −0.292683 | ||||||||
\(792\) | −7845.57 | −0.351995 | ||||||||
\(793\) | −29563.6 | −1.32388 | ||||||||
\(794\) | −4448.47 | −0.198829 | ||||||||
\(795\) | 22517.3 | 1.00454 | ||||||||
\(796\) | −11105.6 | −0.494506 | ||||||||
\(797\) | −35188.8 | −1.56393 | −0.781964 | − | 0.623324i | \(-0.785782\pi\) | ||||
−0.781964 | + | 0.623324i | \(0.785782\pi\) | |||||||
\(798\) | −5598.53 | −0.248353 | ||||||||
\(799\) | 26185.3 | 1.15941 | ||||||||
\(800\) | 14591.1 | 0.644842 | ||||||||
\(801\) | 50928.7 | 2.24654 | ||||||||
\(802\) | 6651.92 | 0.292877 | ||||||||
\(803\) | −4762.00 | −0.209275 | ||||||||
\(804\) | −25387.3 | −1.11361 | ||||||||
\(805\) | 4249.20 | 0.186043 | ||||||||
\(806\) | −13377.9 | −0.584638 | ||||||||
\(807\) | 37074.1 | 1.61719 | ||||||||
\(808\) | 17447.9 | 0.759673 | ||||||||
\(809\) | 34912.8 | 1.51727 | 0.758634 | − | 0.651517i | \(-0.225867\pi\) | ||||
0.758634 | + | 0.651517i | \(0.225867\pi\) | |||||||
\(810\) | −3170.46 | −0.137529 | ||||||||
\(811\) | 12039.2 | 0.521274 | 0.260637 | − | 0.965437i | \(-0.416067\pi\) | ||||
0.260637 | + | 0.965437i | \(0.416067\pi\) | |||||||
\(812\) | −1321.62 | −0.0571178 | ||||||||
\(813\) | −29709.4 | −1.28161 | ||||||||
\(814\) | 4090.50 | 0.176133 | ||||||||
\(815\) | −1306.75 | −0.0561638 | ||||||||
\(816\) | −22531.8 | −0.966631 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 2314.10 | 0.0989128 | ||||||||
\(819\) | −8950.22 | −0.381863 | ||||||||
\(820\) | −2.72498 | −0.000116049 0 | ||||||||
\(821\) | −15367.9 | −0.653282 | −0.326641 | − | 0.945148i | \(-0.605917\pi\) | ||||
−0.326641 | + | 0.945148i | \(0.605917\pi\) | |||||||
\(822\) | 13965.7 | 0.592592 | ||||||||
\(823\) | −13492.2 | −0.571458 | −0.285729 | − | 0.958311i | \(-0.592236\pi\) | ||||
−0.285729 | + | 0.958311i | \(0.592236\pi\) | |||||||
\(824\) | −29399.1 | −1.24292 | ||||||||
\(825\) | −9909.44 | −0.418185 | ||||||||
\(826\) | −3278.47 | −0.138102 | ||||||||
\(827\) | −20247.3 | −0.851351 | −0.425675 | − | 0.904876i | \(-0.639963\pi\) | ||||
−0.425675 | + | 0.904876i | \(0.639963\pi\) | |||||||
\(828\) | 30909.3 | 1.29731 | ||||||||
\(829\) | 19359.2 | 0.811063 | 0.405531 | − | 0.914081i | \(-0.367086\pi\) | ||||
0.405531 | + | 0.914081i | \(0.367086\pi\) | |||||||
\(830\) | −8817.14 | −0.368732 | ||||||||
\(831\) | −37288.8 | −1.55660 | ||||||||
\(832\) | 6328.68 | 0.263711 | ||||||||
\(833\) | −23865.9 | −0.992680 | ||||||||
\(834\) | 23472.5 | 0.974562 | ||||||||
\(835\) | −1647.80 | −0.0682929 | ||||||||
\(836\) | −12772.7 | −0.528414 | ||||||||
\(837\) | 14062.8 | 0.580744 | ||||||||
\(838\) | 10632.1 | 0.438283 | ||||||||
\(839\) | −8186.73 | −0.336874 | −0.168437 | − | 0.985712i | \(-0.553872\pi\) | ||||
−0.168437 | + | 0.985712i | \(0.553872\pi\) | |||||||
\(840\) | 3989.13 | 0.163855 | ||||||||
\(841\) | −23044.6 | −0.944875 | ||||||||
\(842\) | 7432.72 | 0.304214 | ||||||||
\(843\) | −18847.9 | −0.770053 | ||||||||
\(844\) | 21700.8 | 0.885038 | ||||||||
\(845\) | −1820.95 | −0.0741334 | ||||||||
\(846\) | −12581.1 | −0.511286 | ||||||||
\(847\) | −5880.22 | −0.238544 | ||||||||
\(848\) | 17859.4 | 0.723224 | ||||||||
\(849\) | 64096.9 | 2.59105 | ||||||||
\(850\) | 7030.49 | 0.283699 | ||||||||
\(851\) | −34890.5 | −1.40544 | ||||||||
\(852\) | 29435.8 | 1.18363 | ||||||||
\(853\) | −35270.2 | −1.41574 | −0.707871 | − | 0.706342i | \(-0.750344\pi\) | ||||
−0.707871 | + | 0.706342i | \(0.750344\pi\) | |||||||
\(854\) | −3308.28 | −0.132561 | ||||||||
\(855\) | 26866.1 | 1.07462 | ||||||||
\(856\) | 2969.08 | 0.118553 | ||||||||
\(857\) | 24977.7 | 0.995593 | 0.497797 | − | 0.867294i | \(-0.334143\pi\) | ||||
0.497797 | + | 0.867294i | \(0.334143\pi\) | |||||||
\(858\) | 6034.75 | 0.240120 | ||||||||
\(859\) | 31619.8 | 1.25594 | 0.627972 | − | 0.778236i | \(-0.283885\pi\) | ||||
0.627972 | + | 0.778236i | \(0.283885\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 2.65251 | 0.000104991 0 | ||||||||
\(862\) | −236.620 | −0.00934953 | ||||||||
\(863\) | 18436.6 | 0.727220 | 0.363610 | − | 0.931551i | \(-0.381544\pi\) | ||||
0.363610 | + | 0.931551i | \(0.381544\pi\) | |||||||
\(864\) | 9340.76 | 0.367800 | ||||||||
\(865\) | 1906.45 | 0.0749379 | ||||||||
\(866\) | −6341.46 | −0.248835 | ||||||||
\(867\) | −6341.84 | −0.248420 | ||||||||
\(868\) | 9070.81 | 0.354704 | ||||||||
\(869\) | −11638.2 | −0.454313 | ||||||||
\(870\) | −1874.35 | −0.0730420 | ||||||||
\(871\) | 23609.7 | 0.918465 | ||||||||
\(872\) | 1843.30 | 0.0715850 | ||||||||
\(873\) | −9627.34 | −0.373237 | ||||||||
\(874\) | −17980.5 | −0.695882 | ||||||||
\(875\) | 6842.90 | 0.264380 | ||||||||
\(876\) | 17612.7 | 0.679313 | ||||||||
\(877\) | 48236.4 | 1.85727 | 0.928635 | − | 0.370994i | \(-0.120983\pi\) | ||||
0.928635 | + | 0.370994i | \(0.120983\pi\) | |||||||
\(878\) | −6663.15 | −0.256117 | ||||||||
\(879\) | −35627.8 | −1.36712 | ||||||||
\(880\) | 3395.35 | 0.130065 | ||||||||
\(881\) | 33308.7 | 1.27378 | 0.636888 | − | 0.770956i | \(-0.280221\pi\) | ||||
0.636888 | + | 0.770956i | \(0.280221\pi\) | |||||||
\(882\) | 11466.7 | 0.437759 | ||||||||
\(883\) | 31091.7 | 1.18496 | 0.592479 | − | 0.805586i | \(-0.298149\pi\) | ||||
0.592479 | + | 0.805586i | \(0.298149\pi\) | |||||||
\(884\) | 25942.2 | 0.987027 | ||||||||
\(885\) | 28172.7 | 1.07007 | ||||||||
\(886\) | −11532.1 | −0.437277 | ||||||||
\(887\) | 6550.91 | 0.247980 | 0.123990 | − | 0.992283i | \(-0.460431\pi\) | ||||
0.123990 | + | 0.992283i | \(0.460431\pi\) | |||||||
\(888\) | −32755.0 | −1.23782 | ||||||||
\(889\) | 484.567 | 0.0182810 | ||||||||
\(890\) | 9750.23 | 0.367223 | ||||||||
\(891\) | 7040.86 | 0.264734 | ||||||||
\(892\) | −20809.0 | −0.781094 | ||||||||
\(893\) | −44345.0 | −1.66176 | ||||||||
\(894\) | 8088.55 | 0.302597 | ||||||||
\(895\) | 20318.8 | 0.758864 | ||||||||
\(896\) | 7727.54 | 0.288124 | ||||||||
\(897\) | −51474.2 | −1.91602 | ||||||||
\(898\) | 11491.7 | 0.427042 | ||||||||
\(899\) | −9227.52 | −0.342330 | ||||||||
\(900\) | 20467.2 | 0.758044 | ||||||||
\(901\) | 35477.8 | 1.31181 | ||||||||
\(902\) | −0.998746 | −3.68676e−5 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −19631.9 | −0.722287 | ||||||||
\(905\) | −7461.17 | −0.274053 | ||||||||
\(906\) | −7297.83 | −0.267609 | ||||||||
\(907\) | −46718.5 | −1.71032 | −0.855160 | − | 0.518364i | \(-0.826541\pi\) | ||||
−0.855160 | + | 0.518364i | \(0.826541\pi\) | |||||||
\(908\) | 33726.2 | 1.23265 | ||||||||
\(909\) | 37644.5 | 1.37359 | ||||||||
\(910\) | −1713.51 | −0.0624200 | ||||||||
\(911\) | −18054.8 | −0.656620 | −0.328310 | − | 0.944570i | \(-0.606479\pi\) | ||||
−0.328310 | + | 0.944570i | \(0.606479\pi\) | |||||||
\(912\) | 38157.7 | 1.38545 | ||||||||
\(913\) | 19580.8 | 0.709781 | ||||||||
\(914\) | 13389.4 | 0.484553 | ||||||||
\(915\) | 28428.9 | 1.02714 | ||||||||
\(916\) | 35171.9 | 1.26868 | ||||||||
\(917\) | 9035.96 | 0.325402 | ||||||||
\(918\) | 4500.70 | 0.161814 | ||||||||
\(919\) | −42321.3 | −1.51910 | −0.759548 | − | 0.650451i | \(-0.774580\pi\) | ||||
−0.759548 | + | 0.650451i | \(0.774580\pi\) | |||||||
\(920\) | 12811.7 | 0.459119 | ||||||||
\(921\) | −4636.62 | −0.165887 | ||||||||
\(922\) | 15689.9 | 0.560434 | ||||||||
\(923\) | −27374.7 | −0.976219 | ||||||||
\(924\) | −4091.81 | −0.145683 | ||||||||
\(925\) | −23103.4 | −0.821228 | ||||||||
\(926\) | 934.396 | 0.0331600 | ||||||||
\(927\) | −63429.7 | −2.24736 | ||||||||
\(928\) | −6129.06 | −0.216806 | ||||||||
\(929\) | −32859.5 | −1.16048 | −0.580240 | − | 0.814446i | \(-0.697041\pi\) | ||||
−0.580240 | + | 0.814446i | \(0.697041\pi\) | |||||||
\(930\) | 12864.5 | 0.453595 | ||||||||
\(931\) | 40416.9 | 1.42278 | ||||||||
\(932\) | 9996.74 | 0.351346 | ||||||||
\(933\) | −3620.14 | −0.127029 | ||||||||
\(934\) | 3418.99 | 0.119778 | ||||||||
\(935\) | 6744.88 | 0.235916 | ||||||||
\(936\) | −26985.7 | −0.942367 | ||||||||
\(937\) | −14.5879 | −0.000508608 0 | −0.000254304 | − | 1.00000i | \(-0.500081\pi\) | ||||
−0.000254304 | 1.00000i | \(0.500081\pi\) | ||||||||
\(938\) | 2642.01 | 0.0919668 | ||||||||
\(939\) | 15664.2 | 0.544389 | ||||||||
\(940\) | 14594.3 | 0.506397 | ||||||||
\(941\) | 9884.04 | 0.342413 | 0.171206 | − | 0.985235i | \(-0.445233\pi\) | ||||
0.171206 | + | 0.985235i | \(0.445233\pi\) | |||||||
\(942\) | 18241.2 | 0.630924 | ||||||||
\(943\) | 8.51894 | 0.000294183 0 | ||||||||
\(944\) | 22344.9 | 0.770408 | ||||||||
\(945\) | 1801.23 | 0.0620044 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 43165.9 | 1.48121 | 0.740603 | − | 0.671943i | \(-0.234540\pi\) | ||||
0.740603 | + | 0.671943i | \(0.234540\pi\) | |||||||
\(948\) | 43044.9 | 1.47472 | ||||||||
\(949\) | −16379.4 | −0.560273 | ||||||||
\(950\) | −11906.2 | −0.406618 | ||||||||
\(951\) | −58757.6 | −2.00352 | ||||||||
\(952\) | 6285.19 | 0.213975 | ||||||||
\(953\) | −11414.8 | −0.387998 | −0.193999 | − | 0.981002i | \(-0.562146\pi\) | ||||
−0.193999 | + | 0.981002i | \(0.562146\pi\) | |||||||
\(954\) | −17045.8 | −0.578488 | ||||||||
\(955\) | −20031.3 | −0.678742 | ||||||||
\(956\) | −38773.1 | −1.31173 | ||||||||
\(957\) | 4162.50 | 0.140600 | ||||||||
\(958\) | 6576.23 | 0.221783 | ||||||||
\(959\) | 8806.31 | 0.296528 | ||||||||
\(960\) | −6085.78 | −0.204602 | ||||||||
\(961\) | 33541.4 | 1.12589 | ||||||||
\(962\) | 14069.7 | 0.471545 | ||||||||
\(963\) | 6405.91 | 0.214359 | ||||||||
\(964\) | 20056.1 | 0.670086 | ||||||||
\(965\) | 3662.61 | 0.122180 | ||||||||
\(966\) | −5760.17 | −0.191853 | ||||||||
\(967\) | −21094.6 | −0.701508 | −0.350754 | − | 0.936468i | \(-0.614075\pi\) | ||||
−0.350754 | + | 0.936468i | \(0.614075\pi\) | |||||||
\(968\) | −17729.4 | −0.588682 | ||||||||
\(969\) | 75800.4 | 2.51296 | ||||||||
\(970\) | −1843.14 | −0.0610100 | ||||||||
\(971\) | −17622.1 | −0.582409 | −0.291205 | − | 0.956661i | \(-0.594056\pi\) | ||||
−0.291205 | + | 0.956661i | \(0.594056\pi\) | |||||||
\(972\) | −36401.6 | −1.20121 | ||||||||
\(973\) | 14800.9 | 0.487663 | ||||||||
\(974\) | −16607.8 | −0.546355 | ||||||||
\(975\) | −34084.7 | −1.11957 | ||||||||
\(976\) | 22548.1 | 0.739495 | ||||||||
\(977\) | 29292.7 | 0.959218 | 0.479609 | − | 0.877482i | \(-0.340778\pi\) | ||||
0.479609 | + | 0.877482i | \(0.340778\pi\) | |||||||
\(978\) | 1771.42 | 0.0579178 | ||||||||
\(979\) | −21653.0 | −0.706878 | ||||||||
\(980\) | −13301.5 | −0.433573 | ||||||||
\(981\) | 3977.00 | 0.129435 | ||||||||
\(982\) | 115.637 | 0.00375778 | ||||||||
\(983\) | −36585.0 | −1.18706 | −0.593531 | − | 0.804811i | \(-0.702266\pi\) | ||||
−0.593531 | + | 0.804811i | \(0.702266\pi\) | |||||||
\(984\) | 7.99755 | 0.000259098 0 | ||||||||
\(985\) | −19383.7 | −0.627023 | ||||||||
\(986\) | −2953.19 | −0.0953841 | ||||||||
\(987\) | −14206.2 | −0.458143 | ||||||||
\(988\) | −43933.2 | −1.41468 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | −3240.67 | −0.104036 | ||||||||
\(991\) | 8841.74 | 0.283418 | 0.141709 | − | 0.989908i | \(-0.454740\pi\) | ||||
0.141709 | + | 0.989908i | \(0.454740\pi\) | |||||||
\(992\) | 42066.4 | 1.34638 | ||||||||
\(993\) | −353.251 | −0.0112891 | ||||||||
\(994\) | −3063.34 | −0.0977497 | ||||||||
\(995\) | −9931.58 | −0.316434 | ||||||||
\(996\) | −72421.4 | −2.30398 | ||||||||
\(997\) | 6013.86 | 0.191034 | 0.0955169 | − | 0.995428i | \(-0.469550\pi\) | ||||
0.0955169 | + | 0.995428i | \(0.469550\pi\) | |||||||
\(998\) | −1206.38 | −0.0382638 | ||||||||
\(999\) | −14790.1 | −0.468405 |
(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 | 1849.4.a.i.1.21 | ✓ | 50 | |
43.42 | odd | 2 | 1849.4.a.j.1.30 | yes | 50 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1849.4.a.i.1.21 | ✓ | 50 | 1.1 | even | 1 | trivial | |
1849.4.a.j.1.30 | yes | 50 | 43.42 | odd | 2 |