Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1421,4,Mod(1,1421)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1421, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1421.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1421 = 7^{2} \cdot 29 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1421.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: | \(83.8417141182\) |
Analytic rank: | \(1\) |
Dimension: | \(5\) |
Coefficient field: | 5.5.13458092.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{5} - x^{4} - 14x^{3} + 18x^{2} + 20x - 8 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 29) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-0.957567\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1421.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.84972 | −1.00753 | −0.503765 | − | 0.863841i | \(-0.668052\pi\) | ||||
−0.503765 | + | 0.863841i | \(0.668052\pi\) | |||||||
\(3\) | −4.64574 | −0.894072 | −0.447036 | − | 0.894516i | \(-0.647520\pi\) | ||||
−0.447036 | + | 0.894516i | \(0.647520\pi\) | |||||||
\(4\) | 0.120922 | 0.0151152 | ||||||||
\(5\) | −12.8729 | −1.15138 | −0.575692 | − | 0.817667i | \(-0.695267\pi\) | ||||
−0.575692 | + | 0.817667i | \(0.695267\pi\) | |||||||
\(6\) | 13.2391 | 0.900804 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 22.4532 | 0.992300 | ||||||||
\(9\) | −5.41713 | −0.200635 | ||||||||
\(10\) | 36.6841 | 1.16005 | ||||||||
\(11\) | −62.8274 | −1.72211 | −0.861053 | − | 0.508515i | \(-0.830195\pi\) | ||||
−0.861053 | + | 0.508515i | \(0.830195\pi\) | |||||||
\(12\) | −0.561770 | −0.0135141 | ||||||||
\(13\) | −22.3936 | −0.477759 | −0.238879 | − | 0.971049i | \(-0.576780\pi\) | ||||
−0.238879 | + | 0.971049i | \(0.576780\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 59.8039 | 1.02942 | ||||||||
\(16\) | −64.9528 | −1.01489 | ||||||||
\(17\) | 57.9808 | 0.827201 | 0.413601 | − | 0.910458i | \(-0.364271\pi\) | ||||
0.413601 | + | 0.910458i | \(0.364271\pi\) | |||||||
\(18\) | 15.4373 | 0.202145 | ||||||||
\(19\) | −71.3143 | −0.861086 | −0.430543 | − | 0.902570i | \(-0.641678\pi\) | ||||
−0.430543 | + | 0.902570i | \(0.641678\pi\) | |||||||
\(20\) | −1.55661 | −0.0174034 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 179.041 | 1.73507 | ||||||||
\(23\) | −49.5307 | −0.449037 | −0.224519 | − | 0.974470i | \(-0.572081\pi\) | ||||
−0.224519 | + | 0.974470i | \(0.572081\pi\) | |||||||
\(24\) | −104.312 | −0.887188 | ||||||||
\(25\) | 40.7104 | 0.325683 | ||||||||
\(26\) | 63.8155 | 0.481356 | ||||||||
\(27\) | 150.601 | 1.07345 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −29.0000 | −0.185695 | ||||||||
\(30\) | −170.425 | −1.03717 | ||||||||
\(31\) | −62.9198 | −0.364540 | −0.182270 | − | 0.983249i | \(-0.558344\pi\) | ||||
−0.182270 | + | 0.983249i | \(0.558344\pi\) | |||||||
\(32\) | 5.47182 | 0.0302278 | ||||||||
\(33\) | 291.880 | 1.53969 | ||||||||
\(34\) | −165.229 | −0.833429 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −0.655048 | −0.00303263 | ||||||||
\(37\) | 119.123 | 0.529288 | 0.264644 | − | 0.964346i | \(-0.414746\pi\) | ||||
0.264644 | + | 0.964346i | \(0.414746\pi\) | |||||||
\(38\) | 203.226 | 0.867569 | ||||||||
\(39\) | 104.035 | 0.427151 | ||||||||
\(40\) | −289.037 | −1.14252 | ||||||||
\(41\) | 414.916 | 1.58046 | 0.790231 | − | 0.612810i | \(-0.209961\pi\) | ||||
0.790231 | + | 0.612810i | \(0.209961\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −348.009 | −1.23421 | −0.617103 | − | 0.786882i | \(-0.711694\pi\) | ||||
−0.617103 | + | 0.786882i | \(0.711694\pi\) | |||||||
\(44\) | −7.59719 | −0.0260300 | ||||||||
\(45\) | 69.7340 | 0.231007 | ||||||||
\(46\) | 141.149 | 0.452418 | ||||||||
\(47\) | −553.259 | −1.71705 | −0.858523 | − | 0.512775i | \(-0.828618\pi\) | ||||
−0.858523 | + | 0.512775i | \(0.828618\pi\) | |||||||
\(48\) | 301.753 | 0.907382 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −116.013 | −0.328136 | ||||||||
\(51\) | −269.364 | −0.739578 | ||||||||
\(52\) | −2.70787 | −0.00722142 | ||||||||
\(53\) | −107.308 | −0.278111 | −0.139055 | − | 0.990285i | \(-0.544407\pi\) | ||||
−0.139055 | + | 0.990285i | \(0.544407\pi\) | |||||||
\(54\) | −429.172 | −1.08154 | ||||||||
\(55\) | 808.768 | 1.98280 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 331.308 | 0.769873 | ||||||||
\(58\) | 82.6420 | 0.187093 | ||||||||
\(59\) | −136.881 | −0.302041 | −0.151020 | − | 0.988531i | \(-0.548256\pi\) | ||||
−0.151020 | + | 0.988531i | \(0.548256\pi\) | |||||||
\(60\) | 7.23158 | 0.0155599 | ||||||||
\(61\) | 579.408 | 1.21616 | 0.608078 | − | 0.793877i | \(-0.291941\pi\) | ||||
0.608078 | + | 0.793877i | \(0.291941\pi\) | |||||||
\(62\) | 179.304 | 0.367285 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 504.029 | 0.984431 | ||||||||
\(65\) | 288.269 | 0.550084 | ||||||||
\(66\) | −831.776 | −1.55128 | ||||||||
\(67\) | 919.959 | 1.67748 | 0.838738 | − | 0.544535i | \(-0.183294\pi\) | ||||
0.838738 | + | 0.544535i | \(0.183294\pi\) | |||||||
\(68\) | 7.01113 | 0.0125033 | ||||||||
\(69\) | 230.106 | 0.401472 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 781.802 | 1.30680 | 0.653400 | − | 0.757013i | \(-0.273342\pi\) | ||||
0.653400 | + | 0.757013i | \(0.273342\pi\) | |||||||
\(72\) | −121.632 | −0.199090 | ||||||||
\(73\) | 133.237 | 0.213619 | 0.106810 | − | 0.994279i | \(-0.465936\pi\) | ||||
0.106810 | + | 0.994279i | \(0.465936\pi\) | |||||||
\(74\) | −339.467 | −0.533273 | ||||||||
\(75\) | −189.130 | −0.291185 | ||||||||
\(76\) | −8.62344 | −0.0130155 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −296.470 | −0.430367 | ||||||||
\(79\) | 868.196 | 1.23645 | 0.618225 | − | 0.786001i | \(-0.287852\pi\) | ||||
0.618225 | + | 0.786001i | \(0.287852\pi\) | |||||||
\(80\) | 836.127 | 1.16852 | ||||||||
\(81\) | −553.392 | −0.759111 | ||||||||
\(82\) | −1182.39 | −1.59236 | ||||||||
\(83\) | 83.3560 | 0.110235 | 0.0551175 | − | 0.998480i | \(-0.482447\pi\) | ||||
0.0551175 | + | 0.998480i | \(0.482447\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −746.379 | −0.952425 | ||||||||
\(86\) | 991.730 | 1.24350 | ||||||||
\(87\) | 134.726 | 0.166025 | ||||||||
\(88\) | −1410.68 | −1.70885 | ||||||||
\(89\) | 357.919 | 0.426284 | 0.213142 | − | 0.977021i | \(-0.431630\pi\) | ||||
0.213142 | + | 0.977021i | \(0.431630\pi\) | |||||||
\(90\) | −198.722 | −0.232747 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −5.98933 | −0.00678729 | ||||||||
\(93\) | 292.309 | 0.325925 | ||||||||
\(94\) | 1576.64 | 1.72997 | ||||||||
\(95\) | 918.019 | 0.991440 | ||||||||
\(96\) | −25.4206 | −0.0270259 | ||||||||
\(97\) | 187.105 | 0.195852 | 0.0979260 | − | 0.995194i | \(-0.468779\pi\) | ||||
0.0979260 | + | 0.995194i | \(0.468779\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 340.344 | 0.345514 | ||||||||
\(100\) | 4.92277 | 0.00492277 | ||||||||
\(101\) | 959.423 | 0.945209 | 0.472605 | − | 0.881275i | \(-0.343314\pi\) | ||||
0.472605 | + | 0.881275i | \(0.343314\pi\) | |||||||
\(102\) | 767.612 | 0.745146 | ||||||||
\(103\) | −78.8738 | −0.0754531 | −0.0377265 | − | 0.999288i | \(-0.512012\pi\) | ||||
−0.0377265 | + | 0.999288i | \(0.512012\pi\) | |||||||
\(104\) | −502.808 | −0.474080 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 305.797 | 0.280205 | ||||||||
\(107\) | 713.851 | 0.644959 | 0.322479 | − | 0.946577i | \(-0.395484\pi\) | ||||
0.322479 | + | 0.946577i | \(0.395484\pi\) | |||||||
\(108\) | 18.2110 | 0.0162255 | ||||||||
\(109\) | 536.561 | 0.471497 | 0.235749 | − | 0.971814i | \(-0.424246\pi\) | ||||
0.235749 | + | 0.971814i | \(0.424246\pi\) | |||||||
\(110\) | −2304.76 | −1.99773 | ||||||||
\(111\) | −553.412 | −0.473222 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1946.36 | 1.62034 | 0.810170 | − | 0.586195i | \(-0.199375\pi\) | ||||
0.810170 | + | 0.586195i | \(0.199375\pi\) | |||||||
\(114\) | −944.135 | −0.775670 | ||||||||
\(115\) | 637.601 | 0.517014 | ||||||||
\(116\) | −3.50673 | −0.00280682 | ||||||||
\(117\) | 121.309 | 0.0958549 | ||||||||
\(118\) | 390.073 | 0.304315 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 1342.79 | 1.02149 | ||||||||
\(121\) | 2616.28 | 1.96565 | ||||||||
\(122\) | −1651.15 | −1.22531 | ||||||||
\(123\) | −1927.59 | −1.41305 | ||||||||
\(124\) | −7.60837 | −0.00551009 | ||||||||
\(125\) | 1085.05 | 0.776397 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1995.14 | −1.39402 | −0.697009 | − | 0.717062i | \(-0.745486\pi\) | ||||
−0.697009 | + | 0.717062i | \(0.745486\pi\) | |||||||
\(128\) | −1480.12 | −1.02207 | ||||||||
\(129\) | 1616.76 | 1.10347 | ||||||||
\(130\) | −821.488 | −0.554225 | ||||||||
\(131\) | −1544.84 | −1.03033 | −0.515164 | − | 0.857092i | \(-0.672269\pi\) | ||||
−0.515164 | + | 0.857092i | \(0.672269\pi\) | |||||||
\(132\) | 35.2945 | 0.0232727 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −2621.63 | −1.69011 | ||||||||
\(135\) | −1938.67 | −1.23596 | ||||||||
\(136\) | 1301.85 | 0.820832 | ||||||||
\(137\) | −1294.93 | −0.807543 | −0.403771 | − | 0.914860i | \(-0.632301\pi\) | ||||
−0.403771 | + | 0.914860i | \(0.632301\pi\) | |||||||
\(138\) | −655.740 | −0.404495 | ||||||||
\(139\) | −1999.66 | −1.22021 | −0.610105 | − | 0.792320i | \(-0.708873\pi\) | ||||
−0.610105 | + | 0.792320i | \(0.708873\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 2570.30 | 1.53516 | ||||||||
\(142\) | −2227.92 | −1.31664 | ||||||||
\(143\) | 1406.93 | 0.822752 | ||||||||
\(144\) | 351.858 | 0.203621 | ||||||||
\(145\) | 373.313 | 0.213807 | ||||||||
\(146\) | −379.688 | −0.215228 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 14.4045 | 0.00800029 | ||||||||
\(149\) | 1187.63 | 0.652984 | 0.326492 | − | 0.945200i | \(-0.394133\pi\) | ||||
0.326492 | + | 0.945200i | \(0.394133\pi\) | |||||||
\(150\) | 538.968 | 0.293377 | ||||||||
\(151\) | −2257.61 | −1.21670 | −0.608350 | − | 0.793669i | \(-0.708168\pi\) | ||||
−0.608350 | + | 0.793669i | \(0.708168\pi\) | |||||||
\(152\) | −1601.23 | −0.854456 | ||||||||
\(153\) | −314.090 | −0.165965 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 809.958 | 0.419725 | ||||||||
\(156\) | 12.5800 | 0.00645647 | ||||||||
\(157\) | −1188.18 | −0.603995 | −0.301997 | − | 0.953309i | \(-0.597653\pi\) | ||||
−0.301997 | + | 0.953309i | \(0.597653\pi\) | |||||||
\(158\) | −2474.12 | −1.24576 | ||||||||
\(159\) | 498.524 | 0.248651 | ||||||||
\(160\) | −70.4379 | −0.0348038 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 1577.01 | 0.764827 | ||||||||
\(163\) | −2452.33 | −1.17841 | −0.589207 | − | 0.807982i | \(-0.700560\pi\) | ||||
−0.589207 | + | 0.807982i | \(0.700560\pi\) | |||||||
\(164\) | 50.1722 | 0.0238890 | ||||||||
\(165\) | −3757.32 | −1.77277 | ||||||||
\(166\) | −237.541 | −0.111065 | ||||||||
\(167\) | 2020.14 | 0.936067 | 0.468034 | − | 0.883711i | \(-0.344963\pi\) | ||||
0.468034 | + | 0.883711i | \(0.344963\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1695.53 | −0.771746 | ||||||||
\(170\) | 2126.97 | 0.959597 | ||||||||
\(171\) | 386.319 | 0.172764 | ||||||||
\(172\) | −42.0818 | −0.0186553 | ||||||||
\(173\) | −2862.12 | −1.25782 | −0.628910 | − | 0.777478i | \(-0.716499\pi\) | ||||
−0.628910 | + | 0.777478i | \(0.716499\pi\) | |||||||
\(174\) | −383.933 | −0.167275 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 4080.81 | 1.74774 | ||||||||
\(177\) | 635.914 | 0.270046 | ||||||||
\(178\) | −1019.97 | −0.429494 | ||||||||
\(179\) | −232.651 | −0.0971460 | −0.0485730 | − | 0.998820i | \(-0.515467\pi\) | ||||
−0.0485730 | + | 0.998820i | \(0.515467\pi\) | |||||||
\(180\) | 8.43234 | 0.00349172 | ||||||||
\(181\) | 2607.67 | 1.07086 | 0.535432 | − | 0.844578i | \(-0.320149\pi\) | ||||
0.535432 | + | 0.844578i | \(0.320149\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −2691.78 | −1.08733 | ||||||||
\(184\) | −1112.12 | −0.445580 | ||||||||
\(185\) | −1533.45 | −0.609413 | ||||||||
\(186\) | −833.000 | −0.328379 | ||||||||
\(187\) | −3642.78 | −1.42453 | ||||||||
\(188\) | −66.9010 | −0.0259535 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −2616.10 | −0.998905 | ||||||||
\(191\) | 1528.90 | 0.579202 | 0.289601 | − | 0.957147i | \(-0.406477\pi\) | ||||
0.289601 | + | 0.957147i | \(0.406477\pi\) | |||||||
\(192\) | −2341.59 | −0.880153 | ||||||||
\(193\) | 1017.58 | 0.379518 | 0.189759 | − | 0.981831i | \(-0.439229\pi\) | ||||
0.189759 | + | 0.981831i | \(0.439229\pi\) | |||||||
\(194\) | −533.197 | −0.197327 | ||||||||
\(195\) | −1339.22 | −0.491815 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 3290.20 | 1.18994 | 0.594968 | − | 0.803749i | \(-0.297165\pi\) | ||||
0.594968 | + | 0.803749i | \(0.297165\pi\) | |||||||
\(198\) | −969.887 | −0.348115 | ||||||||
\(199\) | 29.9190 | 0.0106578 | 0.00532891 | − | 0.999986i | \(-0.498304\pi\) | ||||
0.00532891 | + | 0.999986i | \(0.498304\pi\) | |||||||
\(200\) | 914.079 | 0.323176 | ||||||||
\(201\) | −4273.89 | −1.49979 | ||||||||
\(202\) | −2734.09 | −0.952326 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −32.5719 | −0.0111789 | ||||||||
\(205\) | −5341.15 | −1.81972 | ||||||||
\(206\) | 224.769 | 0.0760212 | ||||||||
\(207\) | 268.314 | 0.0900924 | ||||||||
\(208\) | 1454.53 | 0.484871 | ||||||||
\(209\) | 4480.49 | 1.48288 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2267.20 | 0.739717 | 0.369859 | − | 0.929088i | \(-0.379406\pi\) | ||||
0.369859 | + | 0.929088i | \(0.379406\pi\) | |||||||
\(212\) | −12.9758 | −0.00420370 | ||||||||
\(213\) | −3632.05 | −1.16837 | ||||||||
\(214\) | −2034.28 | −0.649815 | ||||||||
\(215\) | 4479.87 | 1.42105 | ||||||||
\(216\) | 3381.48 | 1.06519 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −1529.05 | −0.475047 | ||||||||
\(219\) | −618.984 | −0.190991 | ||||||||
\(220\) | 97.7975 | 0.0299705 | ||||||||
\(221\) | −1298.40 | −0.395203 | ||||||||
\(222\) | 1577.07 | 0.476785 | ||||||||
\(223\) | −4945.03 | −1.48495 | −0.742474 | − | 0.669875i | \(-0.766348\pi\) | ||||
−0.742474 | + | 0.669875i | \(0.766348\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −220.534 | −0.0653433 | ||||||||
\(226\) | −5546.59 | −1.63254 | ||||||||
\(227\) | 3559.46 | 1.04075 | 0.520374 | − | 0.853938i | \(-0.325792\pi\) | ||||
0.520374 | + | 0.853938i | \(0.325792\pi\) | |||||||
\(228\) | 40.0622 | 0.0116368 | ||||||||
\(229\) | −6143.40 | −1.77278 | −0.886391 | − | 0.462937i | \(-0.846796\pi\) | ||||
−0.886391 | + | 0.462937i | \(0.846796\pi\) | |||||||
\(230\) | −1816.99 | −0.520907 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −651.143 | −0.184266 | ||||||||
\(233\) | −1087.06 | −0.305648 | −0.152824 | − | 0.988253i | \(-0.548837\pi\) | ||||
−0.152824 | + | 0.988253i | \(0.548837\pi\) | |||||||
\(234\) | −345.697 | −0.0965766 | ||||||||
\(235\) | 7122.03 | 1.97698 | ||||||||
\(236\) | −16.5519 | −0.00456540 | ||||||||
\(237\) | −4033.41 | −1.10548 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 1079.00 | 0.292027 | 0.146013 | − | 0.989283i | \(-0.453356\pi\) | ||||
0.146013 | + | 0.989283i | \(0.453356\pi\) | |||||||
\(240\) | −3884.43 | −1.04474 | ||||||||
\(241\) | 989.224 | 0.264405 | 0.132202 | − | 0.991223i | \(-0.457795\pi\) | ||||
0.132202 | + | 0.991223i | \(0.457795\pi\) | |||||||
\(242\) | −7455.68 | −1.98045 | ||||||||
\(243\) | −1495.33 | −0.394754 | ||||||||
\(244\) | 70.0629 | 0.0183824 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 5493.09 | 1.42369 | ||||||||
\(247\) | 1596.98 | 0.411391 | ||||||||
\(248\) | −1412.75 | −0.361733 | ||||||||
\(249\) | −387.250 | −0.0985581 | ||||||||
\(250\) | −3092.09 | −0.782243 | ||||||||
\(251\) | −900.246 | −0.226386 | −0.113193 | − | 0.993573i | \(-0.536108\pi\) | ||||
−0.113193 | + | 0.993573i | \(0.536108\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 3111.88 | 0.773290 | ||||||||
\(254\) | 5685.61 | 1.40451 | ||||||||
\(255\) | 3467.48 | 0.851537 | ||||||||
\(256\) | 185.693 | 0.0453353 | ||||||||
\(257\) | 3125.18 | 0.758534 | 0.379267 | − | 0.925287i | \(-0.376176\pi\) | ||||
0.379267 | + | 0.925287i | \(0.376176\pi\) | |||||||
\(258\) | −4607.31 | −1.11178 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 34.8580 | 0.00831462 | ||||||||
\(261\) | 157.097 | 0.0372569 | ||||||||
\(262\) | 4402.35 | 1.03808 | ||||||||
\(263\) | 2814.89 | 0.659976 | 0.329988 | − | 0.943985i | \(-0.392955\pi\) | ||||
0.329988 | + | 0.943985i | \(0.392955\pi\) | |||||||
\(264\) | 6553.63 | 1.52783 | ||||||||
\(265\) | 1381.36 | 0.320212 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −1662.80 | −0.381129 | ||||||||
\(268\) | 111.243 | 0.0253554 | ||||||||
\(269\) | −4409.28 | −0.999400 | −0.499700 | − | 0.866199i | \(-0.666556\pi\) | ||||
−0.499700 | + | 0.866199i | \(0.666556\pi\) | |||||||
\(270\) | 5524.68 | 1.24526 | ||||||||
\(271\) | 4417.97 | 0.990304 | 0.495152 | − | 0.868806i | \(-0.335112\pi\) | ||||
0.495152 | + | 0.868806i | \(0.335112\pi\) | |||||||
\(272\) | −3766.01 | −0.839515 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 3690.19 | 0.813623 | ||||||||
\(275\) | −2557.73 | −0.560862 | ||||||||
\(276\) | 27.8248 | 0.00606833 | ||||||||
\(277\) | −887.577 | −0.192525 | −0.0962624 | − | 0.995356i | \(-0.530689\pi\) | ||||
−0.0962624 | + | 0.995356i | \(0.530689\pi\) | |||||||
\(278\) | 5698.49 | 1.22940 | ||||||||
\(279\) | 340.845 | 0.0731393 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −4286.58 | −0.910021 | −0.455010 | − | 0.890486i | \(-0.650364\pi\) | ||||
−0.455010 | + | 0.890486i | \(0.650364\pi\) | |||||||
\(282\) | −7324.64 | −1.54672 | ||||||||
\(283\) | 1709.59 | 0.359097 | 0.179549 | − | 0.983749i | \(-0.442536\pi\) | ||||
0.179549 | + | 0.983749i | \(0.442536\pi\) | |||||||
\(284\) | 94.5367 | 0.0197525 | ||||||||
\(285\) | −4264.88 | −0.886419 | ||||||||
\(286\) | −4009.36 | −0.828946 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −29.6416 | −0.00606474 | ||||||||
\(289\) | −1551.22 | −0.315738 | ||||||||
\(290\) | −1063.84 | −0.215416 | ||||||||
\(291\) | −869.241 | −0.175106 | ||||||||
\(292\) | 16.1112 | 0.00322890 | ||||||||
\(293\) | −1145.01 | −0.228301 | −0.114151 | − | 0.993463i | \(-0.536415\pi\) | ||||
−0.114151 | + | 0.993463i | \(0.536415\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1762.05 | 0.347765 | ||||||||
\(296\) | 2674.68 | 0.525212 | ||||||||
\(297\) | −9461.90 | −1.84860 | ||||||||
\(298\) | −3384.42 | −0.657900 | ||||||||
\(299\) | 1109.17 | 0.214532 | ||||||||
\(300\) | −22.8699 | −0.00440131 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 6433.56 | 1.22586 | ||||||||
\(303\) | −4457.23 | −0.845086 | ||||||||
\(304\) | 4632.06 | 0.873905 | ||||||||
\(305\) | −7458.63 | −1.40026 | ||||||||
\(306\) | 895.069 | 0.167215 | ||||||||
\(307\) | −1079.39 | −0.200665 | −0.100333 | − | 0.994954i | \(-0.531991\pi\) | ||||
−0.100333 | + | 0.994954i | \(0.531991\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 366.427 | 0.0674605 | ||||||||
\(310\) | −2308.16 | −0.422885 | ||||||||
\(311\) | −2313.90 | −0.421895 | −0.210947 | − | 0.977497i | \(-0.567655\pi\) | ||||
−0.210947 | + | 0.977497i | \(0.567655\pi\) | |||||||
\(312\) | 2335.91 | 0.423862 | ||||||||
\(313\) | 7653.19 | 1.38206 | 0.691029 | − | 0.722827i | \(-0.257158\pi\) | ||||
0.691029 | + | 0.722827i | \(0.257158\pi\) | |||||||
\(314\) | 3385.99 | 0.608542 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 104.984 | 0.0186892 | ||||||||
\(317\) | −3657.23 | −0.647982 | −0.323991 | − | 0.946060i | \(-0.605025\pi\) | ||||
−0.323991 | + | 0.946060i | \(0.605025\pi\) | |||||||
\(318\) | −1420.65 | −0.250523 | ||||||||
\(319\) | 1821.99 | 0.319787 | ||||||||
\(320\) | −6488.29 | −1.13346 | ||||||||
\(321\) | −3316.36 | −0.576640 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −4134.86 | −0.712291 | ||||||||
\(324\) | −66.9170 | −0.0114741 | ||||||||
\(325\) | −911.653 | −0.155598 | ||||||||
\(326\) | 6988.47 | 1.18729 | ||||||||
\(327\) | −2492.72 | −0.421553 | ||||||||
\(328\) | 9316.18 | 1.56829 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 10707.3 | 1.78612 | ||||||||
\(331\) | 3237.92 | 0.537681 | 0.268841 | − | 0.963185i | \(-0.413360\pi\) | ||||
0.268841 | + | 0.963185i | \(0.413360\pi\) | |||||||
\(332\) | 10.0795 | 0.00166622 | ||||||||
\(333\) | −645.303 | −0.106193 | ||||||||
\(334\) | −5756.84 | −0.943115 | ||||||||
\(335\) | −11842.5 | −1.93142 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −7976.89 | −1.28940 | −0.644702 | − | 0.764434i | \(-0.723018\pi\) | ||||
−0.644702 | + | 0.764434i | \(0.723018\pi\) | |||||||
\(338\) | 4831.78 | 0.777557 | ||||||||
\(339\) | −9042.29 | −1.44870 | ||||||||
\(340\) | −90.2533 | −0.0143961 | ||||||||
\(341\) | 3953.09 | 0.627777 | ||||||||
\(342\) | −1100.90 | −0.174064 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −7813.92 | −1.22470 | ||||||||
\(345\) | −2962.13 | −0.462248 | ||||||||
\(346\) | 8156.25 | 1.26729 | ||||||||
\(347\) | −8355.93 | −1.29271 | −0.646354 | − | 0.763037i | \(-0.723707\pi\) | ||||
−0.646354 | + | 0.763037i | \(0.723707\pi\) | |||||||
\(348\) | 16.2913 | 0.00250950 | ||||||||
\(349\) | −5544.56 | −0.850411 | −0.425205 | − | 0.905097i | \(-0.639798\pi\) | ||||
−0.425205 | + | 0.905097i | \(0.639798\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −3372.51 | −0.512852 | ||||||||
\(352\) | −343.780 | −0.0520555 | ||||||||
\(353\) | 1682.79 | 0.253727 | 0.126864 | − | 0.991920i | \(-0.459509\pi\) | ||||
0.126864 | + | 0.991920i | \(0.459509\pi\) | |||||||
\(354\) | −1812.18 | −0.272080 | ||||||||
\(355\) | −10064.0 | −1.50463 | ||||||||
\(356\) | 43.2801 | 0.00644337 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 662.990 | 0.0978774 | ||||||||
\(359\) | 7143.13 | 1.05014 | 0.525069 | − | 0.851059i | \(-0.324039\pi\) | ||||
0.525069 | + | 0.851059i | \(0.324039\pi\) | |||||||
\(360\) | 1565.75 | 0.229229 | ||||||||
\(361\) | −1773.27 | −0.258531 | ||||||||
\(362\) | −7431.13 | −1.07893 | ||||||||
\(363\) | −12154.6 | −1.75743 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −1715.14 | −0.245958 | ||||||||
\(366\) | 7670.81 | 1.09552 | ||||||||
\(367\) | 4456.16 | 0.633814 | 0.316907 | − | 0.948457i | \(-0.397356\pi\) | ||||
0.316907 | + | 0.948457i | \(0.397356\pi\) | |||||||
\(368\) | 3217.15 | 0.455722 | ||||||||
\(369\) | −2247.65 | −0.317095 | ||||||||
\(370\) | 4369.90 | 0.614001 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 35.3465 | 0.00492642 | ||||||||
\(373\) | 2508.28 | 0.348187 | 0.174094 | − | 0.984729i | \(-0.444300\pi\) | ||||
0.174094 | + | 0.984729i | \(0.444300\pi\) | |||||||
\(374\) | 10380.9 | 1.43525 | ||||||||
\(375\) | −5040.85 | −0.694155 | ||||||||
\(376\) | −12422.4 | −1.70383 | ||||||||
\(377\) | 649.414 | 0.0887176 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −12733.9 | −1.72585 | −0.862926 | − | 0.505331i | \(-0.831371\pi\) | ||||
−0.862926 | + | 0.505331i | \(0.831371\pi\) | |||||||
\(380\) | 111.008 | 0.0149858 | ||||||||
\(381\) | 9268.91 | 1.24635 | ||||||||
\(382\) | −4356.95 | −0.583563 | ||||||||
\(383\) | 1027.19 | 0.137042 | 0.0685209 | − | 0.997650i | \(-0.478172\pi\) | ||||
0.0685209 | + | 0.997650i | \(0.478172\pi\) | |||||||
\(384\) | 6876.23 | 0.913806 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −2899.82 | −0.382376 | ||||||||
\(387\) | 1885.21 | 0.247624 | ||||||||
\(388\) | 22.6250 | 0.00296034 | ||||||||
\(389\) | 5153.35 | 0.671684 | 0.335842 | − | 0.941918i | \(-0.390979\pi\) | ||||
0.335842 | + | 0.941918i | \(0.390979\pi\) | |||||||
\(390\) | 3816.42 | 0.495518 | ||||||||
\(391\) | −2871.83 | −0.371444 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 7176.90 | 0.921187 | ||||||||
\(394\) | −9376.17 | −1.19890 | ||||||||
\(395\) | −11176.2 | −1.42363 | ||||||||
\(396\) | 41.1550 | 0.00522251 | ||||||||
\(397\) | −6250.95 | −0.790242 | −0.395121 | − | 0.918629i | \(-0.629297\pi\) | ||||
−0.395121 | + | 0.918629i | \(0.629297\pi\) | |||||||
\(398\) | −85.2610 | −0.0107381 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −2644.25 | −0.330532 | ||||||||
\(401\) | 11083.8 | 1.38029 | 0.690145 | − | 0.723671i | \(-0.257547\pi\) | ||||
0.690145 | + | 0.723671i | \(0.257547\pi\) | |||||||
\(402\) | 12179.4 | 1.51108 | ||||||||
\(403\) | 1409.00 | 0.174162 | ||||||||
\(404\) | 116.015 | 0.0142870 | ||||||||
\(405\) | 7123.74 | 0.874028 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −7484.17 | −0.911490 | ||||||||
\(408\) | −6048.07 | −0.733883 | ||||||||
\(409\) | 3375.43 | 0.408079 | 0.204039 | − | 0.978963i | \(-0.434593\pi\) | ||||
0.204039 | + | 0.978963i | \(0.434593\pi\) | |||||||
\(410\) | 15220.8 | 1.83342 | ||||||||
\(411\) | 6015.91 | 0.722002 | ||||||||
\(412\) | −9.53754 | −0.00114049 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −764.621 | −0.0907707 | ||||||||
\(415\) | −1073.03 | −0.126923 | ||||||||
\(416\) | −122.534 | −0.0144416 | ||||||||
\(417\) | 9289.91 | 1.09096 | ||||||||
\(418\) | −12768.2 | −1.49405 | ||||||||
\(419\) | −6486.50 | −0.756292 | −0.378146 | − | 0.925746i | \(-0.623438\pi\) | ||||
−0.378146 | + | 0.925746i | \(0.623438\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −10938.6 | −1.26631 | −0.633153 | − | 0.774026i | \(-0.718240\pi\) | ||||
−0.633153 | + | 0.774026i | \(0.718240\pi\) | |||||||
\(422\) | −6460.89 | −0.745287 | ||||||||
\(423\) | 2997.08 | 0.344499 | ||||||||
\(424\) | −2409.40 | −0.275969 | ||||||||
\(425\) | 2360.42 | 0.269406 | ||||||||
\(426\) | 10350.3 | 1.17717 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 86.3200 | 0.00974867 | ||||||||
\(429\) | −6536.23 | −0.735600 | ||||||||
\(430\) | −12766.4 | −1.43174 | ||||||||
\(431\) | 4124.34 | 0.460934 | 0.230467 | − | 0.973080i | \(-0.425975\pi\) | ||||
0.230467 | + | 0.973080i | \(0.425975\pi\) | |||||||
\(432\) | −9781.98 | −1.08943 | ||||||||
\(433\) | 1561.41 | 0.173295 | 0.0866473 | − | 0.996239i | \(-0.472385\pi\) | ||||
0.0866473 | + | 0.996239i | \(0.472385\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −1734.31 | −0.191158 | ||||||||
\(436\) | 64.8818 | 0.00712677 | ||||||||
\(437\) | 3532.25 | 0.386660 | ||||||||
\(438\) | 1763.93 | 0.192429 | ||||||||
\(439\) | 15712.7 | 1.70826 | 0.854130 | − | 0.520060i | \(-0.174091\pi\) | ||||
0.854130 | + | 0.520060i | \(0.174091\pi\) | |||||||
\(440\) | 18159.4 | 1.96754 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 3700.08 | 0.398178 | ||||||||
\(443\) | 12763.5 | 1.36888 | 0.684439 | − | 0.729070i | \(-0.260047\pi\) | ||||
0.684439 | + | 0.729070i | \(0.260047\pi\) | |||||||
\(444\) | −66.9195 | −0.00715284 | ||||||||
\(445\) | −4607.44 | −0.490817 | ||||||||
\(446\) | 14092.0 | 1.49613 | ||||||||
\(447\) | −5517.42 | −0.583815 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 3117.88 | 0.327710 | 0.163855 | − | 0.986484i | \(-0.447607\pi\) | ||||
0.163855 | + | 0.986484i | \(0.447607\pi\) | |||||||
\(450\) | 628.460 | 0.0658353 | ||||||||
\(451\) | −26068.1 | −2.72172 | ||||||||
\(452\) | 235.357 | 0.0244918 | ||||||||
\(453\) | 10488.3 | 1.08782 | ||||||||
\(454\) | −10143.5 | −1.04858 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 7438.91 | 0.763945 | ||||||||
\(457\) | −8479.41 | −0.867943 | −0.433972 | − | 0.900927i | \(-0.642888\pi\) | ||||
−0.433972 | + | 0.900927i | \(0.642888\pi\) | |||||||
\(458\) | 17507.0 | 1.78613 | ||||||||
\(459\) | 8732.00 | 0.887962 | ||||||||
\(460\) | 77.0997 | 0.00781477 | ||||||||
\(461\) | −9253.32 | −0.934859 | −0.467430 | − | 0.884030i | \(-0.654820\pi\) | ||||
−0.467430 | + | 0.884030i | \(0.654820\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 521.395 | 0.0523354 | 0.0261677 | − | 0.999658i | \(-0.491670\pi\) | ||||
0.0261677 | + | 0.999658i | \(0.491670\pi\) | |||||||
\(464\) | 1883.63 | 0.188460 | ||||||||
\(465\) | −3762.85 | −0.375265 | ||||||||
\(466\) | 3097.83 | 0.307949 | ||||||||
\(467\) | −4337.35 | −0.429783 | −0.214891 | − | 0.976638i | \(-0.568940\pi\) | ||||
−0.214891 | + | 0.976638i | \(0.568940\pi\) | |||||||
\(468\) | 14.6689 | 0.00144887 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −20295.8 | −1.99186 | ||||||||
\(471\) | 5519.98 | 0.540015 | ||||||||
\(472\) | −3073.42 | −0.299715 | ||||||||
\(473\) | 21864.5 | 2.12544 | ||||||||
\(474\) | 11494.1 | 1.11380 | ||||||||
\(475\) | −2903.24 | −0.280441 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 581.300 | 0.0557986 | ||||||||
\(478\) | −3074.84 | −0.294226 | ||||||||
\(479\) | 11258.1 | 1.07390 | 0.536949 | − | 0.843615i | \(-0.319577\pi\) | ||||
0.536949 | + | 0.843615i | \(0.319577\pi\) | |||||||
\(480\) | 327.236 | 0.0311171 | ||||||||
\(481\) | −2667.58 | −0.252872 | ||||||||
\(482\) | −2819.02 | −0.266395 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 316.365 | 0.0297112 | ||||||||
\(485\) | −2408.58 | −0.225501 | ||||||||
\(486\) | 4261.26 | 0.397726 | ||||||||
\(487\) | 4353.54 | 0.405088 | 0.202544 | − | 0.979273i | \(-0.435079\pi\) | ||||
0.202544 | + | 0.979273i | \(0.435079\pi\) | |||||||
\(488\) | 13009.6 | 1.20679 | ||||||||
\(489\) | 11392.9 | 1.05359 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −8458.77 | −0.777472 | −0.388736 | − | 0.921349i | \(-0.627088\pi\) | ||||
−0.388736 | + | 0.921349i | \(0.627088\pi\) | |||||||
\(492\) | −233.087 | −0.0213585 | ||||||||
\(493\) | −1681.44 | −0.153607 | ||||||||
\(494\) | −4550.96 | −0.414489 | ||||||||
\(495\) | −4381.20 | −0.397819 | ||||||||
\(496\) | 4086.82 | 0.369967 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 1103.56 | 0.0993002 | ||||||||
\(499\) | 14850.9 | 1.33230 | 0.666149 | − | 0.745819i | \(-0.267942\pi\) | ||||
0.666149 | + | 0.745819i | \(0.267942\pi\) | |||||||
\(500\) | 131.206 | 0.0117354 | ||||||||
\(501\) | −9385.04 | −0.836912 | ||||||||
\(502\) | 2565.45 | 0.228091 | ||||||||
\(503\) | 1686.45 | 0.149493 | 0.0747464 | − | 0.997203i | \(-0.476185\pi\) | ||||
0.0747464 | + | 0.997203i | \(0.476185\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −12350.5 | −1.08830 | ||||||||
\(506\) | −8868.00 | −0.779112 | ||||||||
\(507\) | 7876.97 | 0.689997 | ||||||||
\(508\) | −241.256 | −0.0210709 | ||||||||
\(509\) | 11113.5 | 0.967773 | 0.483887 | − | 0.875131i | \(-0.339225\pi\) | ||||
0.483887 | + | 0.875131i | \(0.339225\pi\) | |||||||
\(510\) | −9881.36 | −0.857949 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 11311.8 | 0.976395 | ||||||||
\(513\) | −10740.0 | −0.924336 | ||||||||
\(514\) | −8905.90 | −0.764246 | ||||||||
\(515\) | 1015.33 | 0.0868754 | ||||||||
\(516\) | 195.501 | 0.0166792 | ||||||||
\(517\) | 34759.8 | 2.95694 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 13296.7 | 1.12458 | ||||||||
\(520\) | 6472.57 | 0.545848 | ||||||||
\(521\) | 15931.1 | 1.33964 | 0.669820 | − | 0.742523i | \(-0.266371\pi\) | ||||
0.669820 | + | 0.742523i | \(0.266371\pi\) | |||||||
\(522\) | −447.682 | −0.0375374 | ||||||||
\(523\) | 7960.43 | 0.665555 | 0.332778 | − | 0.943005i | \(-0.392014\pi\) | ||||
0.332778 | + | 0.943005i | \(0.392014\pi\) | |||||||
\(524\) | −186.804 | −0.0155736 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −8021.67 | −0.664945 | ||||||||
\(527\) | −3648.14 | −0.301548 | ||||||||
\(528\) | −18958.4 | −1.56261 | ||||||||
\(529\) | −9713.71 | −0.798366 | ||||||||
\(530\) | −3936.49 | −0.322623 | ||||||||
\(531\) | 741.503 | 0.0605998 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −9291.45 | −0.755079 | ||||||||
\(534\) | 4738.51 | 0.383999 | ||||||||
\(535\) | −9189.30 | −0.742594 | ||||||||
\(536\) | 20656.0 | 1.66456 | ||||||||
\(537\) | 1080.83 | 0.0868555 | ||||||||
\(538\) | 12565.2 | 1.00692 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −234.427 | −0.0186817 | ||||||||
\(541\) | 13818.9 | 1.09819 | 0.549096 | − | 0.835760i | \(-0.314972\pi\) | ||||
0.549096 | + | 0.835760i | \(0.314972\pi\) | |||||||
\(542\) | −12590.0 | −0.997760 | ||||||||
\(543\) | −12114.5 | −0.957430 | ||||||||
\(544\) | 317.261 | 0.0250045 | ||||||||
\(545\) | −6907.07 | −0.542874 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 22093.3 | 1.72695 | 0.863474 | − | 0.504393i | \(-0.168284\pi\) | ||||
0.863474 | + | 0.504393i | \(0.168284\pi\) | |||||||
\(548\) | −156.585 | −0.0122062 | ||||||||
\(549\) | −3138.73 | −0.244003 | ||||||||
\(550\) | 7288.82 | 0.565084 | ||||||||
\(551\) | 2068.12 | 0.159900 | ||||||||
\(552\) | 5166.62 | 0.398381 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 2529.35 | 0.193974 | ||||||||
\(555\) | 7124.00 | 0.544859 | ||||||||
\(556\) | −241.802 | −0.0184437 | ||||||||
\(557\) | −3110.34 | −0.236606 | −0.118303 | − | 0.992978i | \(-0.537745\pi\) | ||||
−0.118303 | + | 0.992978i | \(0.537745\pi\) | |||||||
\(558\) | −971.314 | −0.0736900 | ||||||||
\(559\) | 7793.17 | 0.589653 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 16923.4 | 1.27363 | ||||||||
\(562\) | 12215.6 | 0.916873 | ||||||||
\(563\) | 13284.6 | 0.994455 | 0.497227 | − | 0.867620i | \(-0.334351\pi\) | ||||
0.497227 | + | 0.867620i | \(0.334351\pi\) | |||||||
\(564\) | 310.804 | 0.0232043 | ||||||||
\(565\) | −25055.2 | −1.86563 | ||||||||
\(566\) | −4871.86 | −0.361801 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 17553.9 | 1.29674 | ||||||||
\(569\) | −6809.18 | −0.501680 | −0.250840 | − | 0.968029i | \(-0.580707\pi\) | ||||
−0.250840 | + | 0.968029i | \(0.580707\pi\) | |||||||
\(570\) | 12153.7 | 0.893093 | ||||||||
\(571\) | −13471.8 | −0.987352 | −0.493676 | − | 0.869646i | \(-0.664347\pi\) | ||||
−0.493676 | + | 0.869646i | \(0.664347\pi\) | |||||||
\(572\) | 170.128 | 0.0124361 | ||||||||
\(573\) | −7102.88 | −0.517849 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −2016.41 | −0.146244 | ||||||||
\(576\) | −2730.39 | −0.197511 | ||||||||
\(577\) | −5331.06 | −0.384636 | −0.192318 | − | 0.981333i | \(-0.561601\pi\) | ||||
−0.192318 | + | 0.981333i | \(0.561601\pi\) | |||||||
\(578\) | 4420.56 | 0.318116 | ||||||||
\(579\) | −4727.41 | −0.339317 | ||||||||
\(580\) | 45.1416 | 0.00323173 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 2477.10 | 0.176424 | ||||||||
\(583\) | 6741.87 | 0.478936 | ||||||||
\(584\) | 2991.59 | 0.211974 | ||||||||
\(585\) | −1561.59 | −0.110366 | ||||||||
\(586\) | 3262.96 | 0.230020 | ||||||||
\(587\) | −3333.96 | −0.234425 | −0.117212 | − | 0.993107i | \(-0.537396\pi\) | ||||
−0.117212 | + | 0.993107i | \(0.537396\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 4487.09 | 0.313900 | ||||||||
\(590\) | −5021.36 | −0.350383 | ||||||||
\(591\) | −15285.4 | −1.06389 | ||||||||
\(592\) | −7737.34 | −0.537167 | ||||||||
\(593\) | 23405.3 | 1.62081 | 0.810404 | − | 0.585872i | \(-0.199248\pi\) | ||||
0.810404 | + | 0.585872i | \(0.199248\pi\) | |||||||
\(594\) | 26963.8 | 1.86252 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 143.610 | 0.00986998 | ||||||||
\(597\) | −138.996 | −0.00952886 | ||||||||
\(598\) | −3160.83 | −0.216147 | ||||||||
\(599\) | −10352.1 | −0.706133 | −0.353067 | − | 0.935598i | \(-0.614861\pi\) | ||||
−0.353067 | + | 0.935598i | \(0.614861\pi\) | |||||||
\(600\) | −4246.57 | −0.288943 | ||||||||
\(601\) | −15171.1 | −1.02969 | −0.514843 | − | 0.857285i | \(-0.672150\pi\) | ||||
−0.514843 | + | 0.857285i | \(0.672150\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −4983.54 | −0.336560 | ||||||||
\(604\) | −272.994 | −0.0183907 | ||||||||
\(605\) | −33679.0 | −2.26322 | ||||||||
\(606\) | 12701.9 | 0.851449 | ||||||||
\(607\) | 20823.0 | 1.39239 | 0.696193 | − | 0.717854i | \(-0.254876\pi\) | ||||
0.696193 | + | 0.717854i | \(0.254876\pi\) | |||||||
\(608\) | −390.219 | −0.0260287 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 21255.0 | 1.41081 | ||||||||
\(611\) | 12389.5 | 0.820334 | ||||||||
\(612\) | −37.9802 | −0.00250859 | ||||||||
\(613\) | −19071.6 | −1.25660 | −0.628299 | − | 0.777972i | \(-0.716249\pi\) | ||||
−0.628299 | + | 0.777972i | \(0.716249\pi\) | |||||||
\(614\) | 3075.97 | 0.202176 | ||||||||
\(615\) | 24813.6 | 1.62696 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 15200.4 | 0.991806 | 0.495903 | − | 0.868378i | \(-0.334837\pi\) | ||||
0.495903 | + | 0.868378i | \(0.334837\pi\) | |||||||
\(618\) | −1044.22 | −0.0679684 | ||||||||
\(619\) | −4358.76 | −0.283026 | −0.141513 | − | 0.989936i | \(-0.545197\pi\) | ||||
−0.141513 | + | 0.989936i | \(0.545197\pi\) | |||||||
\(620\) | 97.9414 | 0.00634423 | ||||||||
\(621\) | −7459.39 | −0.482021 | ||||||||
\(622\) | 6593.98 | 0.425071 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −6757.34 | −0.433510 | ||||||||
\(625\) | −19056.5 | −1.21961 | ||||||||
\(626\) | −21809.5 | −1.39246 | ||||||||
\(627\) | −20815.2 | −1.32580 | ||||||||
\(628\) | −143.677 | −0.00912950 | ||||||||
\(629\) | 6906.83 | 0.437827 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −2580.66 | −0.162812 | −0.0814062 | − | 0.996681i | \(-0.525941\pi\) | ||||
−0.0814062 | + | 0.996681i | \(0.525941\pi\) | |||||||
\(632\) | 19493.8 | 1.22693 | ||||||||
\(633\) | −10532.8 | −0.661361 | ||||||||
\(634\) | 10422.1 | 0.652861 | ||||||||
\(635\) | 25683.2 | 1.60505 | ||||||||
\(636\) | 60.2823 | 0.00375841 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −5192.18 | −0.322195 | ||||||||
\(639\) | −4235.12 | −0.262189 | ||||||||
\(640\) | 19053.3 | 1.17680 | ||||||||
\(641\) | 19858.9 | 1.22368 | 0.611840 | − | 0.790982i | \(-0.290430\pi\) | ||||
0.611840 | + | 0.790982i | \(0.290430\pi\) | |||||||
\(642\) | 9450.72 | 0.580981 | ||||||||
\(643\) | −17371.9 | −1.06545 | −0.532723 | − | 0.846290i | \(-0.678831\pi\) | ||||
−0.532723 | + | 0.846290i | \(0.678831\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −20812.3 | −1.27052 | ||||||||
\(646\) | 11783.2 | 0.717654 | ||||||||
\(647\) | −3275.07 | −0.199005 | −0.0995024 | − | 0.995037i | \(-0.531725\pi\) | ||||
−0.0995024 | + | 0.995037i | \(0.531725\pi\) | |||||||
\(648\) | −12425.4 | −0.753266 | ||||||||
\(649\) | 8599.88 | 0.520146 | ||||||||
\(650\) | 2597.96 | 0.156770 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −296.540 | −0.0178120 | ||||||||
\(653\) | 20726.5 | 1.24210 | 0.621049 | − | 0.783772i | \(-0.286707\pi\) | ||||
0.621049 | + | 0.783772i | \(0.286707\pi\) | |||||||
\(654\) | 7103.56 | 0.424727 | ||||||||
\(655\) | 19886.4 | 1.18630 | ||||||||
\(656\) | −26949.9 | −1.60399 | ||||||||
\(657\) | −721.762 | −0.0428594 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −18404.6 | −1.08792 | −0.543960 | − | 0.839111i | \(-0.683076\pi\) | ||||
−0.543960 | + | 0.839111i | \(0.683076\pi\) | |||||||
\(660\) | −454.341 | −0.0267958 | ||||||||
\(661\) | 7146.10 | 0.420501 | 0.210250 | − | 0.977648i | \(-0.432572\pi\) | ||||
0.210250 | + | 0.977648i | \(0.432572\pi\) | |||||||
\(662\) | −9227.19 | −0.541729 | ||||||||
\(663\) | 6032.02 | 0.353340 | ||||||||
\(664\) | 1871.61 | 0.109386 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 1838.94 | 0.106993 | ||||||||
\(667\) | 1436.39 | 0.0833841 | ||||||||
\(668\) | 244.279 | 0.0141488 | ||||||||
\(669\) | 22973.3 | 1.32765 | ||||||||
\(670\) | 33747.9 | 1.94596 | ||||||||
\(671\) | −36402.7 | −2.09435 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −26819.0 | −1.53610 | −0.768051 | − | 0.640389i | \(-0.778773\pi\) | ||||
−0.768051 | + | 0.640389i | \(0.778773\pi\) | |||||||
\(674\) | 22731.9 | 1.29911 | ||||||||
\(675\) | 6131.05 | 0.349606 | ||||||||
\(676\) | −205.026 | −0.0116651 | ||||||||
\(677\) | 20093.1 | 1.14068 | 0.570340 | − | 0.821408i | \(-0.306811\pi\) | ||||
0.570340 | + | 0.821408i | \(0.306811\pi\) | |||||||
\(678\) | 25768.0 | 1.45961 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −16758.6 | −0.945092 | ||||||||
\(681\) | −16536.3 | −0.930505 | ||||||||
\(682\) | −11265.2 | −0.632503 | ||||||||
\(683\) | −6876.22 | −0.385229 | −0.192614 | − | 0.981275i | \(-0.561697\pi\) | ||||
−0.192614 | + | 0.981275i | \(0.561697\pi\) | |||||||
\(684\) | 46.7143 | 0.00261135 | ||||||||
\(685\) | 16669.5 | 0.929791 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 28540.6 | 1.58500 | ||||||||
\(688\) | 22604.1 | 1.25258 | ||||||||
\(689\) | 2403.01 | 0.132870 | ||||||||
\(690\) | 8441.24 | 0.465728 | ||||||||
\(691\) | −17332.7 | −0.954224 | −0.477112 | − | 0.878842i | \(-0.658316\pi\) | ||||
−0.477112 | + | 0.878842i | \(0.658316\pi\) | |||||||
\(692\) | −346.092 | −0.0190122 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 23812.1 | 1.30244 | ||||||||
\(695\) | 25741.4 | 1.40493 | ||||||||
\(696\) | 3025.04 | 0.164747 | ||||||||
\(697\) | 24057.1 | 1.30736 | ||||||||
\(698\) | 15800.5 | 0.856814 | ||||||||
\(699\) | 5050.21 | 0.273271 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 11127.5 | 0.599545 | 0.299772 | − | 0.954011i | \(-0.403089\pi\) | ||||
0.299772 | + | 0.954011i | \(0.403089\pi\) | |||||||
\(702\) | 9610.71 | 0.516714 | ||||||||
\(703\) | −8495.15 | −0.455762 | ||||||||
\(704\) | −31666.8 | −1.69530 | ||||||||
\(705\) | −33087.1 | −1.76756 | ||||||||
\(706\) | −4795.48 | −0.255638 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 76.8957 | 0.00408180 | ||||||||
\(709\) | 17432.0 | 0.923374 | 0.461687 | − | 0.887043i | \(-0.347244\pi\) | ||||
0.461687 | + | 0.887043i | \(0.347244\pi\) | |||||||
\(710\) | 28679.7 | 1.51596 | ||||||||
\(711\) | −4703.13 | −0.248075 | ||||||||
\(712\) | 8036.42 | 0.423002 | ||||||||
\(713\) | 3116.46 | 0.163692 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −18111.2 | −0.947302 | ||||||||
\(716\) | −28.1325 | −0.00146838 | ||||||||
\(717\) | −5012.73 | −0.261093 | ||||||||
\(718\) | −20355.9 | −1.05805 | ||||||||
\(719\) | −21082.7 | −1.09353 | −0.546767 | − | 0.837285i | \(-0.684142\pi\) | ||||
−0.546767 | + | 0.837285i | \(0.684142\pi\) | |||||||
\(720\) | −4529.41 | −0.234446 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 5053.32 | 0.260478 | ||||||||
\(723\) | −4595.68 | −0.236397 | ||||||||
\(724\) | 315.323 | 0.0161863 | ||||||||
\(725\) | −1180.60 | −0.0604779 | ||||||||
\(726\) | 34637.1 | 1.77067 | ||||||||
\(727\) | 25839.1 | 1.31818 | 0.659091 | − | 0.752063i | \(-0.270941\pi\) | ||||
0.659091 | + | 0.752063i | \(0.270941\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 21888.5 | 1.11205 | ||||||||
\(730\) | 4887.67 | 0.247810 | ||||||||
\(731\) | −20177.9 | −1.02094 | ||||||||
\(732\) | −325.494 | −0.0164352 | ||||||||
\(733\) | −1278.54 | −0.0644256 | −0.0322128 | − | 0.999481i | \(-0.510255\pi\) | ||||
−0.0322128 | + | 0.999481i | \(0.510255\pi\) | |||||||
\(734\) | −12698.8 | −0.638586 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −271.023 | −0.0135734 | ||||||||
\(737\) | −57798.6 | −2.88879 | ||||||||
\(738\) | 6405.19 | 0.319483 | ||||||||
\(739\) | 4224.54 | 0.210287 | 0.105144 | − | 0.994457i | \(-0.466470\pi\) | ||||
0.105144 | + | 0.994457i | \(0.466470\pi\) | |||||||
\(740\) | −185.427 | −0.00921140 | ||||||||
\(741\) | −7419.17 | −0.367814 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −17992.3 | −0.888390 | −0.444195 | − | 0.895930i | \(-0.646510\pi\) | ||||
−0.444195 | + | 0.895930i | \(0.646510\pi\) | |||||||
\(744\) | 6563.27 | 0.323416 | ||||||||
\(745\) | −15288.2 | −0.751835 | ||||||||
\(746\) | −7147.91 | −0.350809 | ||||||||
\(747\) | −451.550 | −0.0221170 | ||||||||
\(748\) | −440.491 | −0.0215320 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 14365.0 | 0.699381 | ||||||||
\(751\) | −10082.4 | −0.489895 | −0.244948 | − | 0.969536i | \(-0.578771\pi\) | ||||
−0.244948 | + | 0.969536i | \(0.578771\pi\) | |||||||
\(752\) | 35935.7 | 1.74261 | ||||||||
\(753\) | 4182.30 | 0.202406 | ||||||||
\(754\) | −1850.65 | −0.0893856 | ||||||||
\(755\) | 29061.9 | 1.40089 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 10806.5 | 0.518851 | 0.259425 | − | 0.965763i | \(-0.416467\pi\) | ||||
0.259425 | + | 0.965763i | \(0.416467\pi\) | |||||||
\(758\) | 36288.2 | 1.73885 | ||||||||
\(759\) | −14457.0 | −0.691377 | ||||||||
\(760\) | 20612.5 | 0.983806 | ||||||||
\(761\) | 30710.4 | 1.46288 | 0.731439 | − | 0.681907i | \(-0.238849\pi\) | ||||
0.731439 | + | 0.681907i | \(0.238849\pi\) | |||||||
\(762\) | −26413.8 | −1.25574 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 184.877 | 0.00875475 | ||||||||
\(765\) | 4043.23 | 0.191089 | ||||||||
\(766\) | −2927.21 | −0.138074 | ||||||||
\(767\) | 3065.26 | 0.144303 | ||||||||
\(768\) | −862.682 | −0.0405330 | ||||||||
\(769\) | −10757.1 | −0.504436 | −0.252218 | − | 0.967670i | \(-0.581160\pi\) | ||||
−0.252218 | + | 0.967670i | \(0.581160\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −14518.8 | −0.678185 | ||||||||
\(772\) | 123.047 | 0.00573649 | ||||||||
\(773\) | 18077.2 | 0.841125 | 0.420563 | − | 0.907263i | \(-0.361833\pi\) | ||||
0.420563 | + | 0.907263i | \(0.361833\pi\) | |||||||
\(774\) | −5372.33 | −0.249489 | ||||||||
\(775\) | −2561.49 | −0.118725 | ||||||||
\(776\) | 4201.10 | 0.194344 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −14685.6 | −0.676742 | ||||||||
\(779\) | −29589.4 | −1.36091 | ||||||||
\(780\) | −161.941 | −0.00743387 | ||||||||
\(781\) | −49118.6 | −2.25045 | ||||||||
\(782\) | 8183.92 | 0.374241 | ||||||||
\(783\) | −4367.44 | −0.199335 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 15295.3 | 0.695430 | ||||||||
\(786\) | −20452.2 | −0.928123 | ||||||||
\(787\) | 31543.7 | 1.42873 | 0.714366 | − | 0.699773i | \(-0.246715\pi\) | ||||
0.714366 | + | 0.699773i | \(0.246715\pi\) | |||||||
\(788\) | 397.857 | 0.0179861 | ||||||||
\(789\) | −13077.3 | −0.590066 | ||||||||
\(790\) | 31848.9 | 1.43435 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 7641.81 | 0.342854 | ||||||||
\(793\) | −12975.0 | −0.581030 | ||||||||
\(794\) | 17813.5 | 0.796192 | ||||||||
\(795\) | −6417.42 | −0.286293 | ||||||||
\(796\) | 3.61786 | 0.000161095 0 | ||||||||
\(797\) | −18280.9 | −0.812477 | −0.406239 | − | 0.913767i | \(-0.633160\pi\) | ||||
−0.406239 | + | 0.913767i | \(0.633160\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −32078.4 | −1.42034 | ||||||||
\(800\) | 222.760 | 0.00984470 | ||||||||
\(801\) | −1938.89 | −0.0855273 | ||||||||
\(802\) | −31585.6 | −1.39068 | ||||||||
\(803\) | −8370.93 | −0.367875 | ||||||||
\(804\) | −516.805 | −0.0226695 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −4015.26 | −0.175473 | ||||||||
\(807\) | 20484.4 | 0.893536 | ||||||||
\(808\) | 21542.1 | 0.937932 | ||||||||
\(809\) | 21776.3 | 0.946372 | 0.473186 | − | 0.880963i | \(-0.343104\pi\) | ||||
0.473186 | + | 0.880963i | \(0.343104\pi\) | |||||||
\(810\) | −20300.7 | −0.880609 | ||||||||
\(811\) | −17035.7 | −0.737612 | −0.368806 | − | 0.929506i | \(-0.620233\pi\) | ||||
−0.368806 | + | 0.929506i | \(0.620233\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −20524.7 | −0.885404 | ||||||||
\(814\) | 21327.8 | 0.918353 | ||||||||
\(815\) | 31568.5 | 1.35681 | ||||||||
\(816\) | 17495.9 | 0.750588 | ||||||||
\(817\) | 24818.0 | 1.06276 | ||||||||
\(818\) | −9619.03 | −0.411151 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −645.860 | −0.0275054 | ||||||||
\(821\) | −45120.7 | −1.91805 | −0.959027 | − | 0.283314i | \(-0.908566\pi\) | ||||
−0.959027 | + | 0.283314i | \(0.908566\pi\) | |||||||
\(822\) | −17143.7 | −0.727438 | ||||||||
\(823\) | 22261.7 | 0.942883 | 0.471442 | − | 0.881897i | \(-0.343734\pi\) | ||||
0.471442 | + | 0.881897i | \(0.343734\pi\) | |||||||
\(824\) | −1770.97 | −0.0748721 | ||||||||
\(825\) | 11882.5 | 0.501451 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 10280.4 | 0.432266 | 0.216133 | − | 0.976364i | \(-0.430655\pi\) | ||||
0.216133 | + | 0.976364i | \(0.430655\pi\) | |||||||
\(828\) | 32.4450 | 0.00136176 | ||||||||
\(829\) | −28509.2 | −1.19441 | −0.597206 | − | 0.802088i | \(-0.703722\pi\) | ||||
−0.597206 | + | 0.802088i | \(0.703722\pi\) | |||||||
\(830\) | 3057.84 | 0.127878 | ||||||||
\(831\) | 4123.45 | 0.172131 | ||||||||
\(832\) | −11287.0 | −0.470321 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −26473.7 | −1.09917 | ||||||||
\(835\) | −26005.0 | −1.07777 | ||||||||
\(836\) | 541.788 | 0.0224140 | ||||||||
\(837\) | −9475.82 | −0.391317 | ||||||||
\(838\) | 18484.7 | 0.761986 | ||||||||
\(839\) | −4746.97 | −0.195332 | −0.0976661 | − | 0.995219i | \(-0.531138\pi\) | ||||
−0.0976661 | + | 0.995219i | \(0.531138\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 841.000 | 0.0344828 | ||||||||
\(842\) | 31172.0 | 1.27584 | ||||||||
\(843\) | 19914.3 | 0.813625 | ||||||||
\(844\) | 274.153 | 0.0111810 | ||||||||
\(845\) | 21826.3 | 0.888576 | ||||||||
\(846\) | −8540.85 | −0.347093 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 6969.94 | 0.282251 | ||||||||
\(849\) | −7942.30 | −0.321059 | ||||||||
\(850\) | −6726.56 | −0.271434 | ||||||||
\(851\) | −5900.22 | −0.237670 | ||||||||
\(852\) | −439.193 | −0.0176602 | ||||||||
\(853\) | −35313.3 | −1.41747 | −0.708736 | − | 0.705473i | \(-0.750734\pi\) | ||||
−0.708736 | + | 0.705473i | \(0.750734\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −4973.03 | −0.198917 | ||||||||
\(856\) | 16028.2 | 0.639993 | ||||||||
\(857\) | −32142.8 | −1.28119 | −0.640594 | − | 0.767880i | \(-0.721312\pi\) | ||||
−0.640594 | + | 0.767880i | \(0.721312\pi\) | |||||||
\(858\) | 18626.4 | 0.741138 | ||||||||
\(859\) | −37568.2 | −1.49221 | −0.746107 | − | 0.665826i | \(-0.768079\pi\) | ||||
−0.746107 | + | 0.665826i | \(0.768079\pi\) | |||||||
\(860\) | 541.713 | 0.0214794 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −11753.2 | −0.464404 | ||||||||
\(863\) | 3416.95 | 0.134779 | 0.0673896 | − | 0.997727i | \(-0.478533\pi\) | ||||
0.0673896 | + | 0.997727i | \(0.478533\pi\) | |||||||
\(864\) | 824.064 | 0.0324482 | ||||||||
\(865\) | 36843.6 | 1.44823 | ||||||||
\(866\) | −4449.59 | −0.174599 | ||||||||
\(867\) | 7206.57 | 0.282293 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −54546.5 | −2.12930 | ||||||||
\(870\) | 4942.31 | 0.192598 | ||||||||
\(871\) | −20601.2 | −0.801429 | ||||||||
\(872\) | 12047.5 | 0.467867 | ||||||||
\(873\) | −1013.57 | −0.0392947 | ||||||||
\(874\) | −10065.9 | −0.389571 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −74.8485 | −0.00288687 | ||||||||
\(877\) | −11891.0 | −0.457847 | −0.228923 | − | 0.973444i | \(-0.573521\pi\) | ||||
−0.228923 | + | 0.973444i | \(0.573521\pi\) | |||||||
\(878\) | −44776.8 | −1.72112 | ||||||||
\(879\) | 5319.42 | 0.204118 | ||||||||
\(880\) | −52531.7 | −2.01232 | ||||||||
\(881\) | −20042.7 | −0.766464 | −0.383232 | − | 0.923652i | \(-0.625189\pi\) | ||||
−0.383232 | + | 0.923652i | \(0.625189\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −18042.8 | −0.687641 | −0.343821 | − | 0.939035i | \(-0.611721\pi\) | ||||
−0.343821 | + | 0.939035i | \(0.611721\pi\) | |||||||
\(884\) | −157.004 | −0.00597356 | ||||||||
\(885\) | −8186.02 | −0.310927 | ||||||||
\(886\) | −36372.5 | −1.37919 | ||||||||
\(887\) | −2247.91 | −0.0850929 | −0.0425464 | − | 0.999094i | \(-0.513547\pi\) | ||||
−0.0425464 | + | 0.999094i | \(0.513547\pi\) | |||||||
\(888\) | −12425.9 | −0.469578 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 13129.9 | 0.494512 | ||||||||
\(891\) | 34768.2 | 1.30727 | ||||||||
\(892\) | −597.960 | −0.0224453 | ||||||||
\(893\) | 39455.3 | 1.47852 | ||||||||
\(894\) | 15723.1 | 0.588211 | ||||||||
\(895\) | 2994.88 | 0.111852 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −5152.91 | −0.191807 | ||||||||
\(898\) | −8885.09 | −0.330177 | ||||||||
\(899\) | 1824.68 | 0.0676934 | ||||||||
\(900\) | −26.6673 | −0.000987677 0 | ||||||||
\(901\) | −6221.80 | −0.230053 | ||||||||
\(902\) | 74286.7 | 2.74222 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 43702.1 | 1.60786 | ||||||||
\(905\) | −33568.1 | −1.23298 | ||||||||
\(906\) | −29888.6 | −1.09601 | ||||||||
\(907\) | −1798.34 | −0.0658354 | −0.0329177 | − | 0.999458i | \(-0.510480\pi\) | ||||
−0.0329177 | + | 0.999458i | \(0.510480\pi\) | |||||||
\(908\) | 430.416 | 0.0157311 | ||||||||
\(909\) | −5197.32 | −0.189642 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 4602.02 | 0.167367 | 0.0836837 | − | 0.996492i | \(-0.473331\pi\) | ||||
0.0836837 | + | 0.996492i | \(0.473331\pi\) | |||||||
\(912\) | −21519.3 | −0.781334 | ||||||||
\(913\) | −5237.04 | −0.189836 | ||||||||
\(914\) | 24164.0 | 0.874478 | ||||||||
\(915\) | 34650.8 | 1.25194 | ||||||||
\(916\) | −742.869 | −0.0267960 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −24883.8 | −0.894648 | ||||||||
\(919\) | 20622.0 | 0.740215 | 0.370107 | − | 0.928989i | \(-0.379321\pi\) | ||||
0.370107 | + | 0.928989i | \(0.379321\pi\) | |||||||
\(920\) | 14316.2 | 0.513033 | ||||||||
\(921\) | 5014.58 | 0.179409 | ||||||||
\(922\) | 26369.4 | 0.941898 | ||||||||
\(923\) | −17507.4 | −0.624335 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 4849.53 | 0.172380 | ||||||||
\(926\) | −1485.83 | −0.0527294 | ||||||||
\(927\) | 427.270 | 0.0151385 | ||||||||
\(928\) | −158.683 | −0.00561316 | ||||||||
\(929\) | 24061.8 | 0.849777 | 0.424889 | − | 0.905246i | \(-0.360313\pi\) | ||||
0.424889 | + | 0.905246i | \(0.360313\pi\) | |||||||
\(930\) | 10723.1 | 0.378090 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −131.449 | −0.00461992 | ||||||||
\(933\) | 10749.8 | 0.377204 | ||||||||
\(934\) | 12360.2 | 0.433019 | ||||||||
\(935\) | 46893.0 | 1.64018 | ||||||||
\(936\) | 2723.78 | 0.0951169 | ||||||||
\(937\) | 6581.96 | 0.229481 | 0.114740 | − | 0.993396i | \(-0.463396\pi\) | ||||
0.114740 | + | 0.993396i | \(0.463396\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −35554.7 | −1.23566 | ||||||||
\(940\) | 861.207 | 0.0298824 | ||||||||
\(941\) | −23579.7 | −0.816873 | −0.408436 | − | 0.912787i | \(-0.633926\pi\) | ||||
−0.408436 | + | 0.912787i | \(0.633926\pi\) | |||||||
\(942\) | −15730.4 | −0.544081 | ||||||||
\(943\) | −20551.0 | −0.709686 | ||||||||
\(944\) | 8890.80 | 0.306537 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −62307.8 | −2.14144 | ||||||||
\(947\) | −36368.6 | −1.24796 | −0.623982 | − | 0.781439i | \(-0.714486\pi\) | ||||
−0.623982 | + | 0.781439i | \(0.714486\pi\) | |||||||
\(948\) | −487.726 | −0.0167095 | ||||||||
\(949\) | −2983.65 | −0.102058 | ||||||||
\(950\) | 8273.42 | 0.282553 | ||||||||
\(951\) | 16990.5 | 0.579343 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 44404.3 | 1.50933 | 0.754667 | − | 0.656108i | \(-0.227798\pi\) | ||||
0.754667 | + | 0.656108i | \(0.227798\pi\) | |||||||
\(954\) | −1656.55 | −0.0562187 | ||||||||
\(955\) | −19681.4 | −0.666884 | ||||||||
\(956\) | 130.474 | 0.00441404 | ||||||||
\(957\) | −8464.51 | −0.285913 | ||||||||
\(958\) | −32082.5 | −1.08198 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 30142.9 | 1.01339 | ||||||||
\(961\) | −25832.1 | −0.867111 | ||||||||
\(962\) | 7601.88 | 0.254776 | ||||||||
\(963\) | −3867.02 | −0.129401 | ||||||||
\(964\) | 119.619 | 0.00399653 | ||||||||
\(965\) | −13099.2 | −0.436971 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 21928.3 | 0.729230 | 0.364615 | − | 0.931158i | \(-0.381201\pi\) | ||||
0.364615 | + | 0.931158i | \(0.381201\pi\) | |||||||
\(968\) | 58743.9 | 1.95052 | ||||||||
\(969\) | 19209.5 | 0.636840 | ||||||||
\(970\) | 6863.77 | 0.227198 | ||||||||
\(971\) | 6352.95 | 0.209965 | 0.104982 | − | 0.994474i | \(-0.466521\pi\) | ||||
0.104982 | + | 0.994474i | \(0.466521\pi\) | |||||||
\(972\) | −180.817 | −0.00596678 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −12406.4 | −0.408138 | ||||||||
\(975\) | 4235.30 | 0.139116 | ||||||||
\(976\) | −37634.1 | −1.23426 | ||||||||
\(977\) | 12792.8 | 0.418913 | 0.209456 | − | 0.977818i | \(-0.432831\pi\) | ||||
0.209456 | + | 0.977818i | \(0.432831\pi\) | |||||||
\(978\) | −32466.6 | −1.06152 | ||||||||
\(979\) | −22487.1 | −0.734107 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −2906.62 | −0.0945986 | ||||||||
\(982\) | 24105.1 | 0.783326 | ||||||||
\(983\) | −7536.73 | −0.244542 | −0.122271 | − | 0.992497i | \(-0.539018\pi\) | ||||
−0.122271 | + | 0.992497i | \(0.539018\pi\) | |||||||
\(984\) | −43280.5 | −1.40217 | ||||||||
\(985\) | −42354.3 | −1.37007 | ||||||||
\(986\) | 4791.65 | 0.154764 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 193.110 | 0.00621826 | ||||||||
\(989\) | 17237.1 | 0.554205 | ||||||||
\(990\) | 12485.2 | 0.400814 | ||||||||
\(991\) | −28088.3 | −0.900357 | −0.450179 | − | 0.892938i | \(-0.648640\pi\) | ||||
−0.450179 | + | 0.892938i | \(0.648640\pi\) | |||||||
\(992\) | −344.286 | −0.0110192 | ||||||||
\(993\) | −15042.5 | −0.480726 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −385.144 | −0.0122712 | ||||||||
\(996\) | −46.8269 | −0.00148973 | ||||||||
\(997\) | 44951.9 | 1.42793 | 0.713963 | − | 0.700184i | \(-0.246899\pi\) | ||||
0.713963 | + | 0.700184i | \(0.246899\pi\) | |||||||
\(998\) | −42320.9 | −1.34233 | ||||||||
\(999\) | 17940.0 | 0.568166 |
(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 | 1421.4.a.e.1.2 | 5 | ||
7.6 | odd | 2 | 29.4.a.b.1.2 | ✓ | 5 | ||
21.20 | even | 2 | 261.4.a.f.1.4 | 5 | |||
28.27 | even | 2 | 464.4.a.l.1.2 | 5 | |||
35.34 | odd | 2 | 725.4.a.c.1.4 | 5 | |||
56.13 | odd | 2 | 1856.4.a.y.1.2 | 5 | |||
56.27 | even | 2 | 1856.4.a.bb.1.4 | 5 | |||
203.202 | odd | 2 | 841.4.a.b.1.4 | 5 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
29.4.a.b.1.2 | ✓ | 5 | 7.6 | odd | 2 | ||
261.4.a.f.1.4 | 5 | 21.20 | even | 2 | |||
464.4.a.l.1.2 | 5 | 28.27 | even | 2 | |||
725.4.a.c.1.4 | 5 | 35.34 | odd | 2 | |||
841.4.a.b.1.4 | 5 | 203.202 | odd | 2 | |||
1421.4.a.e.1.2 | 5 | 1.1 | even | 1 | trivial | ||
1856.4.a.y.1.2 | 5 | 56.13 | odd | 2 | |||
1856.4.a.bb.1.4 | 5 | 56.27 | even | 2 |