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: | \(0\) |
Dimension: | \(110\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.14 | ||
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −4.62802 | −1.63625 | −0.818127 | − | 0.575038i | \(-0.804987\pi\) | ||||
−0.818127 | + | 0.575038i | \(0.804987\pi\) | |||||||
\(3\) | −8.10864 | −1.56051 | −0.780254 | − | 0.625462i | \(-0.784910\pi\) | ||||
−0.780254 | + | 0.625462i | \(0.784910\pi\) | |||||||
\(4\) | 13.4186 | 1.67733 | ||||||||
\(5\) | −17.9110 | −1.60201 | −0.801006 | − | 0.598656i | \(-0.795702\pi\) | ||||
−0.801006 | + | 0.598656i | \(0.795702\pi\) | |||||||
\(6\) | 37.5270 | 2.55339 | ||||||||
\(7\) | −27.1680 | −1.46694 | −0.733468 | − | 0.679724i | \(-0.762100\pi\) | ||||
−0.733468 | + | 0.679724i | \(0.762100\pi\) | |||||||
\(8\) | −25.0774 | −1.10828 | ||||||||
\(9\) | 38.7501 | 1.43519 | ||||||||
\(10\) | 82.8927 | 2.62130 | ||||||||
\(11\) | −26.9318 | −0.738203 | −0.369101 | − | 0.929389i | \(-0.620334\pi\) | ||||
−0.369101 | + | 0.929389i | \(0.620334\pi\) | |||||||
\(12\) | −108.807 | −2.61748 | ||||||||
\(13\) | −21.2445 | −0.453243 | −0.226621 | − | 0.973983i | \(-0.572768\pi\) | ||||
−0.226621 | + | 0.973983i | \(0.572768\pi\) | |||||||
\(14\) | 125.734 | 2.40028 | ||||||||
\(15\) | 145.234 | 2.49995 | ||||||||
\(16\) | 8.71017 | 0.136096 | ||||||||
\(17\) | −8.28413 | −0.118188 | −0.0590940 | − | 0.998252i | \(-0.518821\pi\) | ||||
−0.0590940 | + | 0.998252i | \(0.518821\pi\) | |||||||
\(18\) | −179.336 | −2.34833 | ||||||||
\(19\) | 131.030 | 1.58212 | 0.791061 | − | 0.611738i | \(-0.209529\pi\) | ||||
0.791061 | + | 0.611738i | \(0.209529\pi\) | |||||||
\(20\) | −240.341 | −2.68710 | ||||||||
\(21\) | 220.296 | 2.28917 | ||||||||
\(22\) | 124.641 | 1.20789 | ||||||||
\(23\) | −42.4012 | −0.384403 | −0.192201 | − | 0.981355i | \(-0.561563\pi\) | ||||
−0.192201 | + | 0.981355i | \(0.561563\pi\) | |||||||
\(24\) | 203.344 | 1.72948 | ||||||||
\(25\) | 195.805 | 1.56644 | ||||||||
\(26\) | 98.3199 | 0.741620 | ||||||||
\(27\) | −95.2771 | −0.679114 | ||||||||
\(28\) | −364.557 | −2.46053 | ||||||||
\(29\) | 103.779 | 0.664528 | 0.332264 | − | 0.943186i | \(-0.392188\pi\) | ||||
0.332264 | + | 0.943186i | \(0.392188\pi\) | |||||||
\(30\) | −672.147 | −4.09056 | ||||||||
\(31\) | −145.326 | −0.841976 | −0.420988 | − | 0.907066i | \(-0.638316\pi\) | ||||
−0.420988 | + | 0.907066i | \(0.638316\pi\) | |||||||
\(32\) | 160.309 | 0.885589 | ||||||||
\(33\) | 218.380 | 1.15197 | ||||||||
\(34\) | 38.3391 | 0.193386 | ||||||||
\(35\) | 486.608 | 2.35005 | ||||||||
\(36\) | 519.972 | 2.40728 | ||||||||
\(37\) | −370.571 | −1.64653 | −0.823263 | − | 0.567660i | \(-0.807849\pi\) | ||||
−0.823263 | + | 0.567660i | \(0.807849\pi\) | |||||||
\(38\) | −606.409 | −2.58875 | ||||||||
\(39\) | 172.264 | 0.707289 | ||||||||
\(40\) | 449.163 | 1.77547 | ||||||||
\(41\) | 275.150 | 1.04808 | 0.524038 | − | 0.851695i | \(-0.324425\pi\) | ||||
0.524038 | + | 0.851695i | \(0.324425\pi\) | |||||||
\(42\) | −1019.53 | −3.74566 | ||||||||
\(43\) | 0 | 0 | ||||||||
\(44\) | −361.387 | −1.23821 | ||||||||
\(45\) | −694.054 | −2.29919 | ||||||||
\(46\) | 196.234 | 0.628981 | ||||||||
\(47\) | 331.305 | 1.02821 | 0.514105 | − | 0.857727i | \(-0.328124\pi\) | ||||
0.514105 | + | 0.857727i | \(0.328124\pi\) | |||||||
\(48\) | −70.6277 | −0.212380 | ||||||||
\(49\) | 395.103 | 1.15190 | ||||||||
\(50\) | −906.192 | −2.56310 | ||||||||
\(51\) | 67.1730 | 0.184433 | ||||||||
\(52\) | −285.071 | −0.760235 | ||||||||
\(53\) | 223.453 | 0.579126 | 0.289563 | − | 0.957159i | \(-0.406490\pi\) | ||||
0.289563 | + | 0.957159i | \(0.406490\pi\) | |||||||
\(54\) | 440.944 | 1.11120 | ||||||||
\(55\) | 482.376 | 1.18261 | ||||||||
\(56\) | 681.305 | 1.62577 | ||||||||
\(57\) | −1062.47 | −2.46891 | ||||||||
\(58\) | −480.293 | −1.08734 | ||||||||
\(59\) | −364.823 | −0.805016 | −0.402508 | − | 0.915417i | \(-0.631861\pi\) | ||||
−0.402508 | + | 0.915417i | \(0.631861\pi\) | |||||||
\(60\) | 1948.84 | 4.19324 | ||||||||
\(61\) | 381.036 | 0.799781 | 0.399891 | − | 0.916563i | \(-0.369048\pi\) | ||||
0.399891 | + | 0.916563i | \(0.369048\pi\) | |||||||
\(62\) | 672.570 | 1.37769 | ||||||||
\(63\) | −1052.76 | −2.10533 | ||||||||
\(64\) | −811.594 | −1.58514 | ||||||||
\(65\) | 380.510 | 0.726100 | ||||||||
\(66\) | −1010.67 | −1.88492 | ||||||||
\(67\) | −348.629 | −0.635699 | −0.317849 | − | 0.948141i | \(-0.602961\pi\) | ||||
−0.317849 | + | 0.948141i | \(0.602961\pi\) | |||||||
\(68\) | −111.161 | −0.198240 | ||||||||
\(69\) | 343.816 | 0.599864 | ||||||||
\(70\) | −2252.03 | −3.84528 | ||||||||
\(71\) | 262.187 | 0.438251 | 0.219126 | − | 0.975697i | \(-0.429680\pi\) | ||||
0.219126 | + | 0.975697i | \(0.429680\pi\) | |||||||
\(72\) | −971.753 | −1.59059 | ||||||||
\(73\) | −223.890 | −0.358964 | −0.179482 | − | 0.983761i | \(-0.557442\pi\) | ||||
−0.179482 | + | 0.983761i | \(0.557442\pi\) | |||||||
\(74\) | 1715.01 | 2.69413 | ||||||||
\(75\) | −1587.71 | −2.44445 | ||||||||
\(76\) | 1758.24 | 2.65373 | ||||||||
\(77\) | 731.683 | 1.08290 | ||||||||
\(78\) | −797.241 | −1.15730 | ||||||||
\(79\) | 1165.37 | 1.65967 | 0.829835 | − | 0.558009i | \(-0.188434\pi\) | ||||
0.829835 | + | 0.558009i | \(0.188434\pi\) | |||||||
\(80\) | −156.008 | −0.218028 | ||||||||
\(81\) | −273.684 | −0.375424 | ||||||||
\(82\) | −1273.40 | −1.71492 | ||||||||
\(83\) | −819.505 | −1.08376 | −0.541882 | − | 0.840455i | \(-0.682288\pi\) | ||||
−0.541882 | + | 0.840455i | \(0.682288\pi\) | |||||||
\(84\) | 2956.06 | 3.83968 | ||||||||
\(85\) | 148.377 | 0.189339 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −841.508 | −1.03700 | ||||||||
\(88\) | 675.380 | 0.818133 | ||||||||
\(89\) | −886.496 | −1.05582 | −0.527912 | − | 0.849299i | \(-0.677025\pi\) | ||||
−0.527912 | + | 0.849299i | \(0.677025\pi\) | |||||||
\(90\) | 3212.10 | 3.76205 | ||||||||
\(91\) | 577.170 | 0.664878 | ||||||||
\(92\) | −568.966 | −0.644769 | ||||||||
\(93\) | 1178.39 | 1.31391 | ||||||||
\(94\) | −1533.29 | −1.68241 | ||||||||
\(95\) | −2346.88 | −2.53458 | ||||||||
\(96\) | −1299.89 | −1.38197 | ||||||||
\(97\) | −1463.59 | −1.53201 | −0.766007 | − | 0.642832i | \(-0.777759\pi\) | ||||
−0.766007 | + | 0.642832i | \(0.777759\pi\) | |||||||
\(98\) | −1828.54 | −1.88480 | ||||||||
\(99\) | −1043.61 | −1.05946 | ||||||||
\(100\) | 2627.43 | 2.62743 | ||||||||
\(101\) | 98.8379 | 0.0973736 | 0.0486868 | − | 0.998814i | \(-0.484496\pi\) | ||||
0.0486868 | + | 0.998814i | \(0.484496\pi\) | |||||||
\(102\) | −310.878 | −0.301780 | ||||||||
\(103\) | 102.876 | 0.0984141 | 0.0492071 | − | 0.998789i | \(-0.484331\pi\) | ||||
0.0492071 | + | 0.998789i | \(0.484331\pi\) | |||||||
\(104\) | 532.757 | 0.502318 | ||||||||
\(105\) | −3945.73 | −3.66727 | ||||||||
\(106\) | −1034.15 | −0.947597 | ||||||||
\(107\) | 963.342 | 0.870371 | 0.435186 | − | 0.900341i | \(-0.356683\pi\) | ||||
0.435186 | + | 0.900341i | \(0.356683\pi\) | |||||||
\(108\) | −1278.49 | −1.13910 | ||||||||
\(109\) | −935.346 | −0.821926 | −0.410963 | − | 0.911652i | \(-0.634807\pi\) | ||||
−0.410963 | + | 0.911652i | \(0.634807\pi\) | |||||||
\(110\) | −2232.45 | −1.93505 | ||||||||
\(111\) | 3004.83 | 2.56942 | ||||||||
\(112\) | −236.638 | −0.199645 | ||||||||
\(113\) | 317.314 | 0.264163 | 0.132082 | − | 0.991239i | \(-0.457834\pi\) | ||||
0.132082 | + | 0.991239i | \(0.457834\pi\) | |||||||
\(114\) | 4917.15 | 4.03977 | ||||||||
\(115\) | 759.450 | 0.615818 | ||||||||
\(116\) | 1392.57 | 1.11463 | ||||||||
\(117\) | −823.224 | −0.650488 | ||||||||
\(118\) | 1688.41 | 1.31721 | ||||||||
\(119\) | 225.064 | 0.173374 | ||||||||
\(120\) | −3642.10 | −2.77064 | ||||||||
\(121\) | −605.680 | −0.455057 | ||||||||
\(122\) | −1763.44 | −1.30864 | ||||||||
\(123\) | −2231.09 | −1.63553 | ||||||||
\(124\) | −1950.07 | −1.41227 | ||||||||
\(125\) | −1268.20 | −0.907448 | ||||||||
\(126\) | 4872.21 | 3.44485 | ||||||||
\(127\) | 291.872 | 0.203933 | 0.101966 | − | 0.994788i | \(-0.467487\pi\) | ||||
0.101966 | + | 0.994788i | \(0.467487\pi\) | |||||||
\(128\) | 2473.61 | 1.70811 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −1761.01 | −1.18808 | ||||||||
\(131\) | −1658.08 | −1.10585 | −0.552927 | − | 0.833230i | \(-0.686489\pi\) | ||||
−0.552927 | + | 0.833230i | \(0.686489\pi\) | |||||||
\(132\) | 2930.36 | 1.93223 | ||||||||
\(133\) | −3559.82 | −2.32087 | ||||||||
\(134\) | 1613.46 | 1.04016 | ||||||||
\(135\) | 1706.51 | 1.08795 | ||||||||
\(136\) | 207.745 | 0.130985 | ||||||||
\(137\) | −524.125 | −0.326854 | −0.163427 | − | 0.986555i | \(-0.552255\pi\) | ||||
−0.163427 | + | 0.986555i | \(0.552255\pi\) | |||||||
\(138\) | −1591.19 | −0.981530 | ||||||||
\(139\) | −251.305 | −0.153348 | −0.0766741 | − | 0.997056i | \(-0.524430\pi\) | ||||
−0.0766741 | + | 0.997056i | \(0.524430\pi\) | |||||||
\(140\) | 6529.60 | 3.94180 | ||||||||
\(141\) | −2686.44 | −1.60453 | ||||||||
\(142\) | −1213.41 | −0.717090 | ||||||||
\(143\) | 572.151 | 0.334585 | ||||||||
\(144\) | 337.520 | 0.195324 | ||||||||
\(145\) | −1858.79 | −1.06458 | ||||||||
\(146\) | 1036.17 | 0.587356 | ||||||||
\(147\) | −3203.75 | −1.79755 | ||||||||
\(148\) | −4972.54 | −2.76176 | ||||||||
\(149\) | 2652.79 | 1.45856 | 0.729279 | − | 0.684217i | \(-0.239856\pi\) | ||||
0.729279 | + | 0.684217i | \(0.239856\pi\) | |||||||
\(150\) | 7347.98 | 3.99974 | ||||||||
\(151\) | −2927.52 | −1.57774 | −0.788868 | − | 0.614562i | \(-0.789333\pi\) | ||||
−0.788868 | + | 0.614562i | \(0.789333\pi\) | |||||||
\(152\) | −3285.89 | −1.75343 | ||||||||
\(153\) | −321.010 | −0.169622 | ||||||||
\(154\) | −3386.25 | −1.77189 | ||||||||
\(155\) | 2602.93 | 1.34885 | ||||||||
\(156\) | 2311.54 | 1.18635 | ||||||||
\(157\) | −1869.65 | −0.950412 | −0.475206 | − | 0.879875i | \(-0.657626\pi\) | ||||
−0.475206 | + | 0.879875i | \(0.657626\pi\) | |||||||
\(158\) | −5393.34 | −2.71564 | ||||||||
\(159\) | −1811.90 | −0.903731 | ||||||||
\(160\) | −2871.30 | −1.41872 | ||||||||
\(161\) | 1151.96 | 0.563895 | ||||||||
\(162\) | 1266.62 | 0.614289 | ||||||||
\(163\) | −2200.87 | −1.05758 | −0.528789 | − | 0.848753i | \(-0.677354\pi\) | ||||
−0.528789 | + | 0.848753i | \(0.677354\pi\) | |||||||
\(164\) | 3692.12 | 1.75797 | ||||||||
\(165\) | −3911.41 | −1.84547 | ||||||||
\(166\) | 3792.69 | 1.77331 | ||||||||
\(167\) | −2704.67 | −1.25326 | −0.626628 | − | 0.779319i | \(-0.715565\pi\) | ||||
−0.626628 | + | 0.779319i | \(0.715565\pi\) | |||||||
\(168\) | −5524.46 | −2.53703 | ||||||||
\(169\) | −1745.67 | −0.794571 | ||||||||
\(170\) | −686.694 | −0.309806 | ||||||||
\(171\) | 5077.41 | 2.27064 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 1112.09 | 0.488733 | 0.244367 | − | 0.969683i | \(-0.421420\pi\) | ||||
0.244367 | + | 0.969683i | \(0.421420\pi\) | |||||||
\(174\) | 3894.52 | 1.69680 | ||||||||
\(175\) | −5319.65 | −2.29787 | ||||||||
\(176\) | −234.580 | −0.100467 | ||||||||
\(177\) | 2958.22 | 1.25623 | ||||||||
\(178\) | 4102.72 | 1.72760 | ||||||||
\(179\) | 3332.30 | 1.39144 | 0.695719 | − | 0.718314i | \(-0.255086\pi\) | ||||
0.695719 | + | 0.718314i | \(0.255086\pi\) | |||||||
\(180\) | −9313.24 | −3.85649 | ||||||||
\(181\) | 1439.34 | 0.591079 | 0.295539 | − | 0.955331i | \(-0.404501\pi\) | ||||
0.295539 | + | 0.955331i | \(0.404501\pi\) | |||||||
\(182\) | −2671.16 | −1.08791 | ||||||||
\(183\) | −3089.68 | −1.24807 | ||||||||
\(184\) | 1063.31 | 0.426025 | ||||||||
\(185\) | 6637.31 | 2.63775 | ||||||||
\(186\) | −5453.63 | −2.14989 | ||||||||
\(187\) | 223.106 | 0.0872467 | ||||||||
\(188\) | 4445.66 | 1.72464 | ||||||||
\(189\) | 2588.49 | 0.996217 | ||||||||
\(190\) | 10861.4 | 4.14721 | ||||||||
\(191\) | 1385.59 | 0.524908 | 0.262454 | − | 0.964944i | \(-0.415468\pi\) | ||||
0.262454 | + | 0.964944i | \(0.415468\pi\) | |||||||
\(192\) | 6580.92 | 2.47363 | ||||||||
\(193\) | 1882.56 | 0.702123 | 0.351061 | − | 0.936352i | \(-0.385821\pi\) | ||||
0.351061 | + | 0.936352i | \(0.385821\pi\) | |||||||
\(194\) | 6773.55 | 2.50676 | ||||||||
\(195\) | −3085.42 | −1.13309 | ||||||||
\(196\) | 5301.73 | 1.93212 | ||||||||
\(197\) | −5286.88 | −1.91205 | −0.956026 | − | 0.293281i | \(-0.905253\pi\) | ||||
−0.956026 | + | 0.293281i | \(0.905253\pi\) | |||||||
\(198\) | 4829.84 | 1.73354 | ||||||||
\(199\) | −4740.76 | −1.68876 | −0.844381 | − | 0.535743i | \(-0.820032\pi\) | ||||
−0.844381 | + | 0.535743i | \(0.820032\pi\) | |||||||
\(200\) | −4910.30 | −1.73605 | ||||||||
\(201\) | 2826.91 | 0.992013 | ||||||||
\(202\) | −457.424 | −0.159328 | ||||||||
\(203\) | −2819.48 | −0.974820 | ||||||||
\(204\) | 901.368 | 0.309355 | ||||||||
\(205\) | −4928.21 | −1.67903 | ||||||||
\(206\) | −476.112 | −0.161030 | ||||||||
\(207\) | −1643.05 | −0.551690 | ||||||||
\(208\) | −185.043 | −0.0616847 | ||||||||
\(209\) | −3528.86 | −1.16793 | ||||||||
\(210\) | 18260.9 | 6.00059 | ||||||||
\(211\) | −4360.95 | −1.42285 | −0.711423 | − | 0.702764i | \(-0.751949\pi\) | ||||
−0.711423 | + | 0.702764i | \(0.751949\pi\) | |||||||
\(212\) | 2998.43 | 0.971383 | ||||||||
\(213\) | −2125.98 | −0.683895 | ||||||||
\(214\) | −4458.37 | −1.42415 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 2389.31 | 0.752646 | ||||||||
\(217\) | 3948.21 | 1.23512 | ||||||||
\(218\) | 4328.80 | 1.34488 | ||||||||
\(219\) | 1815.45 | 0.560167 | ||||||||
\(220\) | 6472.81 | 1.98362 | ||||||||
\(221\) | 175.992 | 0.0535678 | ||||||||
\(222\) | −13906.4 | −4.20422 | ||||||||
\(223\) | 3349.18 | 1.00573 | 0.502864 | − | 0.864365i | \(-0.332280\pi\) | ||||
0.502864 | + | 0.864365i | \(0.332280\pi\) | |||||||
\(224\) | −4355.27 | −1.29910 | ||||||||
\(225\) | 7587.47 | 2.24814 | ||||||||
\(226\) | −1468.54 | −0.432238 | ||||||||
\(227\) | −3572.45 | −1.04455 | −0.522273 | − | 0.852778i | \(-0.674916\pi\) | ||||
−0.522273 | + | 0.852778i | \(0.674916\pi\) | |||||||
\(228\) | −14256.9 | −4.14117 | ||||||||
\(229\) | −5180.16 | −1.49482 | −0.747412 | − | 0.664361i | \(-0.768704\pi\) | ||||
−0.747412 | + | 0.664361i | \(0.768704\pi\) | |||||||
\(230\) | −3514.75 | −1.00763 | ||||||||
\(231\) | −5932.96 | −1.68987 | ||||||||
\(232\) | −2602.52 | −0.736481 | ||||||||
\(233\) | −2409.88 | −0.677582 | −0.338791 | − | 0.940862i | \(-0.610018\pi\) | ||||
−0.338791 | + | 0.940862i | \(0.610018\pi\) | |||||||
\(234\) | 3809.90 | 1.06436 | ||||||||
\(235\) | −5934.03 | −1.64720 | ||||||||
\(236\) | −4895.42 | −1.35027 | ||||||||
\(237\) | −9449.54 | −2.58993 | ||||||||
\(238\) | −1041.60 | −0.283684 | ||||||||
\(239\) | 1035.13 | 0.280154 | 0.140077 | − | 0.990141i | \(-0.455265\pi\) | ||||
0.140077 | + | 0.990141i | \(0.455265\pi\) | |||||||
\(240\) | 1265.01 | 0.340235 | ||||||||
\(241\) | 335.817 | 0.0897589 | 0.0448795 | − | 0.998992i | \(-0.485710\pi\) | ||||
0.0448795 | + | 0.998992i | \(0.485710\pi\) | |||||||
\(242\) | 2803.10 | 0.744588 | ||||||||
\(243\) | 4791.69 | 1.26497 | ||||||||
\(244\) | 5112.97 | 1.34149 | ||||||||
\(245\) | −7076.70 | −1.84536 | ||||||||
\(246\) | 10325.5 | 2.67615 | ||||||||
\(247\) | −2783.66 | −0.717085 | ||||||||
\(248\) | 3644.39 | 0.933142 | ||||||||
\(249\) | 6645.07 | 1.69122 | ||||||||
\(250\) | 5869.24 | 1.48481 | ||||||||
\(251\) | 1094.80 | 0.275312 | 0.137656 | − | 0.990480i | \(-0.456043\pi\) | ||||
0.137656 | + | 0.990480i | \(0.456043\pi\) | |||||||
\(252\) | −14126.6 | −3.53132 | ||||||||
\(253\) | 1141.94 | 0.283767 | ||||||||
\(254\) | −1350.79 | −0.333685 | ||||||||
\(255\) | −1203.14 | −0.295465 | ||||||||
\(256\) | −4955.16 | −1.20976 | ||||||||
\(257\) | −1121.45 | −0.272196 | −0.136098 | − | 0.990695i | \(-0.543456\pi\) | ||||
−0.136098 | + | 0.990695i | \(0.543456\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 10067.7 | 2.41535 | ||||||||
\(260\) | 5105.92 | 1.21791 | ||||||||
\(261\) | 4021.45 | 0.953722 | ||||||||
\(262\) | 7673.62 | 1.80946 | ||||||||
\(263\) | −2318.07 | −0.543492 | −0.271746 | − | 0.962369i | \(-0.587601\pi\) | ||||
−0.271746 | + | 0.962369i | \(0.587601\pi\) | |||||||
\(264\) | −5476.41 | −1.27670 | ||||||||
\(265\) | −4002.28 | −0.927767 | ||||||||
\(266\) | 16475.0 | 3.79753 | ||||||||
\(267\) | 7188.28 | 1.64762 | ||||||||
\(268\) | −4678.12 | −1.06627 | ||||||||
\(269\) | 4467.82 | 1.01267 | 0.506334 | − | 0.862337i | \(-0.331000\pi\) | ||||
0.506334 | + | 0.862337i | \(0.331000\pi\) | |||||||
\(270\) | −7897.77 | −1.78016 | ||||||||
\(271\) | 7459.35 | 1.67204 | 0.836020 | − | 0.548699i | \(-0.184877\pi\) | ||||
0.836020 | + | 0.548699i | \(0.184877\pi\) | |||||||
\(272\) | −72.1562 | −0.0160850 | ||||||||
\(273\) | −4680.07 | −1.03755 | ||||||||
\(274\) | 2425.66 | 0.534817 | ||||||||
\(275\) | −5273.38 | −1.15635 | ||||||||
\(276\) | 4613.54 | 1.00617 | ||||||||
\(277\) | −534.456 | −0.115929 | −0.0579645 | − | 0.998319i | \(-0.518461\pi\) | ||||
−0.0579645 | + | 0.998319i | \(0.518461\pi\) | |||||||
\(278\) | 1163.04 | 0.250916 | ||||||||
\(279\) | −5631.38 | −1.20839 | ||||||||
\(280\) | −12202.9 | −2.60451 | ||||||||
\(281\) | −3148.15 | −0.668338 | −0.334169 | − | 0.942513i | \(-0.608456\pi\) | ||||
−0.334169 | + | 0.942513i | \(0.608456\pi\) | |||||||
\(282\) | 12432.9 | 2.62542 | ||||||||
\(283\) | 7594.95 | 1.59531 | 0.797656 | − | 0.603113i | \(-0.206073\pi\) | ||||
0.797656 | + | 0.603113i | \(0.206073\pi\) | |||||||
\(284\) | 3518.18 | 0.735090 | ||||||||
\(285\) | 19030.0 | 3.95523 | ||||||||
\(286\) | −2647.93 | −0.547466 | ||||||||
\(287\) | −7475.28 | −1.53746 | ||||||||
\(288\) | 6211.97 | 1.27099 | ||||||||
\(289\) | −4844.37 | −0.986032 | ||||||||
\(290\) | 8602.54 | 1.74193 | ||||||||
\(291\) | 11867.8 | 2.39072 | ||||||||
\(292\) | −3004.30 | −0.602100 | ||||||||
\(293\) | −187.454 | −0.0373761 | −0.0186881 | − | 0.999825i | \(-0.505949\pi\) | ||||
−0.0186881 | + | 0.999825i | \(0.505949\pi\) | |||||||
\(294\) | 14827.0 | 2.94125 | ||||||||
\(295\) | 6534.36 | 1.28964 | ||||||||
\(296\) | 9292.97 | 1.82481 | ||||||||
\(297\) | 2565.98 | 0.501324 | ||||||||
\(298\) | −12277.2 | −2.38657 | ||||||||
\(299\) | 900.791 | 0.174228 | ||||||||
\(300\) | −21304.9 | −4.10013 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 13548.6 | 2.58158 | ||||||||
\(303\) | −801.441 | −0.151952 | ||||||||
\(304\) | 1141.29 | 0.215321 | ||||||||
\(305\) | −6824.75 | −1.28126 | ||||||||
\(306\) | 1485.64 | 0.277545 | ||||||||
\(307\) | −4496.18 | −0.835865 | −0.417933 | − | 0.908478i | \(-0.637245\pi\) | ||||
−0.417933 | + | 0.908478i | \(0.637245\pi\) | |||||||
\(308\) | 9818.17 | 1.81637 | ||||||||
\(309\) | −834.183 | −0.153576 | ||||||||
\(310\) | −12046.4 | −2.20707 | ||||||||
\(311\) | 4628.31 | 0.843883 | 0.421942 | − | 0.906623i | \(-0.361349\pi\) | ||||
0.421942 | + | 0.906623i | \(0.361349\pi\) | |||||||
\(312\) | −4319.93 | −0.783872 | ||||||||
\(313\) | 7309.28 | 1.31995 | 0.659976 | − | 0.751287i | \(-0.270567\pi\) | ||||
0.659976 | + | 0.751287i | \(0.270567\pi\) | |||||||
\(314\) | 8652.81 | 1.55511 | ||||||||
\(315\) | 18856.1 | 3.37276 | ||||||||
\(316\) | 15637.6 | 2.78381 | ||||||||
\(317\) | 2626.74 | 0.465402 | 0.232701 | − | 0.972548i | \(-0.425244\pi\) | ||||
0.232701 | + | 0.972548i | \(0.425244\pi\) | |||||||
\(318\) | 8385.53 | 1.47873 | ||||||||
\(319\) | −2794.96 | −0.490556 | ||||||||
\(320\) | 14536.5 | 2.53942 | ||||||||
\(321\) | −7811.39 | −1.35822 | ||||||||
\(322\) | −5331.29 | −0.922675 | ||||||||
\(323\) | −1085.47 | −0.186988 | ||||||||
\(324\) | −3672.46 | −0.629709 | ||||||||
\(325\) | −4159.78 | −0.709978 | ||||||||
\(326\) | 10185.7 | 1.73047 | ||||||||
\(327\) | 7584.39 | 1.28262 | ||||||||
\(328\) | −6900.05 | −1.16156 | ||||||||
\(329\) | −9000.92 | −1.50832 | ||||||||
\(330\) | 18102.1 | 3.01966 | ||||||||
\(331\) | 9551.68 | 1.58613 | 0.793063 | − | 0.609140i | \(-0.208485\pi\) | ||||
0.793063 | + | 0.609140i | \(0.208485\pi\) | |||||||
\(332\) | −10996.6 | −1.81782 | ||||||||
\(333\) | −14359.6 | −2.36307 | ||||||||
\(334\) | 12517.3 | 2.05064 | ||||||||
\(335\) | 6244.31 | 1.01840 | ||||||||
\(336\) | 1918.82 | 0.311547 | ||||||||
\(337\) | −6719.78 | −1.08620 | −0.543101 | − | 0.839668i | \(-0.682750\pi\) | ||||
−0.543101 | + | 0.839668i | \(0.682750\pi\) | |||||||
\(338\) | 8079.02 | 1.30012 | ||||||||
\(339\) | −2572.99 | −0.412229 | ||||||||
\(340\) | 1991.02 | 0.317583 | ||||||||
\(341\) | 3913.87 | 0.621549 | ||||||||
\(342\) | −23498.4 | −3.71534 | ||||||||
\(343\) | −1415.53 | −0.222831 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −6158.11 | −0.960990 | ||||||||
\(346\) | −5146.79 | −0.799691 | ||||||||
\(347\) | −350.904 | −0.0542868 | −0.0271434 | − | 0.999632i | \(-0.508641\pi\) | ||||
−0.0271434 | + | 0.999632i | \(0.508641\pi\) | |||||||
\(348\) | −11291.9 | −1.73939 | ||||||||
\(349\) | −1148.96 | −0.176225 | −0.0881127 | − | 0.996111i | \(-0.528084\pi\) | ||||
−0.0881127 | + | 0.996111i | \(0.528084\pi\) | |||||||
\(350\) | 24619.5 | 3.75990 | ||||||||
\(351\) | 2024.11 | 0.307803 | ||||||||
\(352\) | −4317.40 | −0.653744 | ||||||||
\(353\) | 9613.89 | 1.44956 | 0.724781 | − | 0.688979i | \(-0.241941\pi\) | ||||
0.724781 | + | 0.688979i | \(0.241941\pi\) | |||||||
\(354\) | −13690.7 | −2.05552 | ||||||||
\(355\) | −4696.03 | −0.702083 | ||||||||
\(356\) | −11895.5 | −1.77096 | ||||||||
\(357\) | −1824.96 | −0.270552 | ||||||||
\(358\) | −15421.9 | −2.27675 | ||||||||
\(359\) | 11546.8 | 1.69755 | 0.848774 | − | 0.528757i | \(-0.177342\pi\) | ||||
0.848774 | + | 0.528757i | \(0.177342\pi\) | |||||||
\(360\) | 17405.1 | 2.54814 | ||||||||
\(361\) | 10309.8 | 1.50311 | ||||||||
\(362\) | −6661.30 | −0.967155 | ||||||||
\(363\) | 4911.24 | 0.710120 | ||||||||
\(364\) | 7744.82 | 1.11522 | ||||||||
\(365\) | 4010.11 | 0.575065 | ||||||||
\(366\) | 14299.1 | 2.04215 | ||||||||
\(367\) | 2521.04 | 0.358575 | 0.179288 | − | 0.983797i | \(-0.442621\pi\) | ||||
0.179288 | + | 0.983797i | \(0.442621\pi\) | |||||||
\(368\) | −369.322 | −0.0523159 | ||||||||
\(369\) | 10662.1 | 1.50419 | ||||||||
\(370\) | −30717.6 | −4.31604 | ||||||||
\(371\) | −6070.79 | −0.849541 | ||||||||
\(372\) | 15812.4 | 2.20386 | ||||||||
\(373\) | −9791.01 | −1.35914 | −0.679570 | − | 0.733610i | \(-0.737834\pi\) | ||||
−0.679570 | + | 0.733610i | \(0.737834\pi\) | |||||||
\(374\) | −1032.54 | −0.142758 | ||||||||
\(375\) | 10283.4 | 1.41608 | ||||||||
\(376\) | −8308.30 | −1.13954 | ||||||||
\(377\) | −2204.73 | −0.301192 | ||||||||
\(378\) | −11979.6 | −1.63006 | ||||||||
\(379\) | −1072.81 | −0.145400 | −0.0726999 | − | 0.997354i | \(-0.523162\pi\) | ||||
−0.0726999 | + | 0.997354i | \(0.523162\pi\) | |||||||
\(380\) | −31491.9 | −4.25131 | ||||||||
\(381\) | −2366.68 | −0.318239 | ||||||||
\(382\) | −6412.53 | −0.858883 | ||||||||
\(383\) | 1715.35 | 0.228852 | 0.114426 | − | 0.993432i | \(-0.463497\pi\) | ||||
0.114426 | + | 0.993432i | \(0.463497\pi\) | |||||||
\(384\) | −20057.6 | −2.66552 | ||||||||
\(385\) | −13105.2 | −1.73481 | ||||||||
\(386\) | −8712.54 | −1.14885 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −19639.4 | −2.56969 | ||||||||
\(389\) | 1269.47 | 0.165463 | 0.0827313 | − | 0.996572i | \(-0.473636\pi\) | ||||
0.0827313 | + | 0.996572i | \(0.473636\pi\) | |||||||
\(390\) | 14279.4 | 1.85401 | ||||||||
\(391\) | 351.257 | 0.0454318 | ||||||||
\(392\) | −9908.16 | −1.27663 | ||||||||
\(393\) | 13444.8 | 1.72569 | ||||||||
\(394\) | 24467.8 | 3.12860 | ||||||||
\(395\) | −20872.9 | −2.65881 | ||||||||
\(396\) | −14003.8 | −1.77706 | ||||||||
\(397\) | 1029.48 | 0.130147 | 0.0650733 | − | 0.997880i | \(-0.479272\pi\) | ||||
0.0650733 | + | 0.997880i | \(0.479272\pi\) | |||||||
\(398\) | 21940.4 | 2.76324 | ||||||||
\(399\) | 28865.3 | 3.62174 | ||||||||
\(400\) | 1705.50 | 0.213187 | ||||||||
\(401\) | 7787.03 | 0.969741 | 0.484870 | − | 0.874586i | \(-0.338867\pi\) | ||||
0.484870 | + | 0.874586i | \(0.338867\pi\) | |||||||
\(402\) | −13083.0 | −1.62319 | ||||||||
\(403\) | 3087.36 | 0.381619 | ||||||||
\(404\) | 1326.27 | 0.163327 | ||||||||
\(405\) | 4901.97 | 0.601434 | ||||||||
\(406\) | 13048.6 | 1.59505 | ||||||||
\(407\) | 9980.12 | 1.21547 | ||||||||
\(408\) | −1684.53 | −0.204403 | ||||||||
\(409\) | 6662.70 | 0.805500 | 0.402750 | − | 0.915310i | \(-0.368054\pi\) | ||||
0.402750 | + | 0.915310i | \(0.368054\pi\) | |||||||
\(410\) | 22807.9 | 2.74732 | ||||||||
\(411\) | 4249.94 | 0.510059 | ||||||||
\(412\) | 1380.45 | 0.165073 | ||||||||
\(413\) | 9911.53 | 1.18091 | ||||||||
\(414\) | 7604.08 | 0.902705 | ||||||||
\(415\) | 14678.2 | 1.73620 | ||||||||
\(416\) | −3405.67 | −0.401386 | ||||||||
\(417\) | 2037.74 | 0.239301 | ||||||||
\(418\) | 16331.7 | 1.91102 | ||||||||
\(419\) | −2462.39 | −0.287101 | −0.143551 | − | 0.989643i | \(-0.545852\pi\) | ||||
−0.143551 | + | 0.989643i | \(0.545852\pi\) | |||||||
\(420\) | −52946.2 | −6.15121 | ||||||||
\(421\) | −3437.41 | −0.397931 | −0.198966 | − | 0.980006i | \(-0.563758\pi\) | ||||
−0.198966 | + | 0.980006i | \(0.563758\pi\) | |||||||
\(422\) | 20182.6 | 2.32814 | ||||||||
\(423\) | 12838.1 | 1.47567 | ||||||||
\(424\) | −5603.64 | −0.641832 | ||||||||
\(425\) | −1622.08 | −0.185135 | ||||||||
\(426\) | 9839.07 | 1.11902 | ||||||||
\(427\) | −10352.0 | −1.17323 | ||||||||
\(428\) | 12926.7 | 1.45990 | ||||||||
\(429\) | −4639.36 | −0.522123 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −13486.2 | −1.50721 | −0.753604 | − | 0.657328i | \(-0.771686\pi\) | ||||
−0.753604 | + | 0.657328i | \(0.771686\pi\) | |||||||
\(432\) | −829.879 | −0.0924250 | ||||||||
\(433\) | −3114.54 | −0.345670 | −0.172835 | − | 0.984951i | \(-0.555293\pi\) | ||||
−0.172835 | + | 0.984951i | \(0.555293\pi\) | |||||||
\(434\) | −18272.4 | −2.02098 | ||||||||
\(435\) | 15072.3 | 1.66129 | ||||||||
\(436\) | −12551.0 | −1.37864 | ||||||||
\(437\) | −5555.83 | −0.608172 | ||||||||
\(438\) | −8401.93 | −0.916575 | ||||||||
\(439\) | 695.858 | 0.0756526 | 0.0378263 | − | 0.999284i | \(-0.487957\pi\) | ||||
0.0378263 | + | 0.999284i | \(0.487957\pi\) | |||||||
\(440\) | −12096.8 | −1.31066 | ||||||||
\(441\) | 15310.3 | 1.65320 | ||||||||
\(442\) | −814.494 | −0.0876506 | ||||||||
\(443\) | 16844.9 | 1.80660 | 0.903299 | − | 0.429011i | \(-0.141138\pi\) | ||||
0.903299 | + | 0.429011i | \(0.141138\pi\) | |||||||
\(444\) | 40320.6 | 4.30975 | ||||||||
\(445\) | 15878.1 | 1.69144 | ||||||||
\(446\) | −15500.1 | −1.64563 | ||||||||
\(447\) | −21510.5 | −2.27609 | ||||||||
\(448\) | 22049.4 | 2.32531 | ||||||||
\(449\) | −109.155 | −0.0114729 | −0.00573646 | − | 0.999984i | \(-0.501826\pi\) | ||||
−0.00573646 | + | 0.999984i | \(0.501826\pi\) | |||||||
\(450\) | −35115.0 | −3.67852 | ||||||||
\(451\) | −7410.26 | −0.773693 | ||||||||
\(452\) | 4257.92 | 0.443088 | ||||||||
\(453\) | 23738.2 | 2.46207 | ||||||||
\(454\) | 16533.4 | 1.70914 | ||||||||
\(455\) | −10337.7 | −1.06514 | ||||||||
\(456\) | 26644.1 | 2.73624 | ||||||||
\(457\) | 1458.15 | 0.149254 | 0.0746271 | − | 0.997212i | \(-0.476223\pi\) | ||||
0.0746271 | + | 0.997212i | \(0.476223\pi\) | |||||||
\(458\) | 23973.9 | 2.44591 | ||||||||
\(459\) | 789.287 | 0.0802631 | ||||||||
\(460\) | 10190.8 | 1.03293 | ||||||||
\(461\) | −13360.3 | −1.34979 | −0.674893 | − | 0.737916i | \(-0.735810\pi\) | ||||
−0.674893 | + | 0.737916i | \(0.735810\pi\) | |||||||
\(462\) | 27457.9 | 2.76506 | ||||||||
\(463\) | 10181.3 | 1.02195 | 0.510976 | − | 0.859595i | \(-0.329284\pi\) | ||||
0.510976 | + | 0.859595i | \(0.329284\pi\) | |||||||
\(464\) | 903.935 | 0.0904399 | ||||||||
\(465\) | −21106.2 | −2.10490 | ||||||||
\(466\) | 11153.0 | 1.10870 | ||||||||
\(467\) | −6856.74 | −0.679426 | −0.339713 | − | 0.940529i | \(-0.610330\pi\) | ||||
−0.339713 | + | 0.940529i | \(0.610330\pi\) | |||||||
\(468\) | −11046.5 | −1.09108 | ||||||||
\(469\) | 9471.57 | 0.932529 | ||||||||
\(470\) | 27462.8 | 2.69524 | ||||||||
\(471\) | 15160.4 | 1.48313 | ||||||||
\(472\) | 9148.83 | 0.892180 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 43732.7 | 4.23778 | ||||||||
\(475\) | 25656.3 | 2.47830 | ||||||||
\(476\) | 3020.04 | 0.290805 | ||||||||
\(477\) | 8658.83 | 0.831154 | ||||||||
\(478\) | −4790.60 | −0.458403 | ||||||||
\(479\) | −13897.5 | −1.32567 | −0.662834 | − | 0.748767i | \(-0.730646\pi\) | ||||
−0.662834 | + | 0.748767i | \(0.730646\pi\) | |||||||
\(480\) | 23282.3 | 2.21393 | ||||||||
\(481\) | 7872.58 | 0.746276 | ||||||||
\(482\) | −1554.17 | −0.146868 | ||||||||
\(483\) | −9340.82 | −0.879963 | ||||||||
\(484\) | −8127.39 | −0.763278 | ||||||||
\(485\) | 26214.5 | 2.45431 | ||||||||
\(486\) | −22176.0 | −2.06981 | ||||||||
\(487\) | −6523.20 | −0.606970 | −0.303485 | − | 0.952836i | \(-0.598150\pi\) | ||||
−0.303485 | + | 0.952836i | \(0.598150\pi\) | |||||||
\(488\) | −9555.41 | −0.886379 | ||||||||
\(489\) | 17846.0 | 1.65036 | ||||||||
\(490\) | 32751.1 | 3.01948 | ||||||||
\(491\) | −17751.6 | −1.63161 | −0.815805 | − | 0.578327i | \(-0.803706\pi\) | ||||
−0.815805 | + | 0.578327i | \(0.803706\pi\) | |||||||
\(492\) | −29938.1 | −2.74332 | ||||||||
\(493\) | −859.720 | −0.0785392 | ||||||||
\(494\) | 12882.8 | 1.17333 | ||||||||
\(495\) | 18692.1 | 1.69727 | ||||||||
\(496\) | −1265.81 | −0.114590 | ||||||||
\(497\) | −7123.10 | −0.642886 | ||||||||
\(498\) | −30753.5 | −2.76727 | ||||||||
\(499\) | −13680.8 | −1.22733 | −0.613666 | − | 0.789566i | \(-0.710306\pi\) | ||||
−0.613666 | + | 0.789566i | \(0.710306\pi\) | |||||||
\(500\) | −17017.4 | −1.52209 | ||||||||
\(501\) | 21931.2 | 1.95572 | ||||||||
\(502\) | −5066.77 | −0.450480 | ||||||||
\(503\) | 12076.8 | 1.07053 | 0.535265 | − | 0.844684i | \(-0.320212\pi\) | ||||
0.535265 | + | 0.844684i | \(0.320212\pi\) | |||||||
\(504\) | 26400.6 | 2.33329 | ||||||||
\(505\) | −1770.29 | −0.155994 | ||||||||
\(506\) | −5284.93 | −0.464315 | ||||||||
\(507\) | 14155.0 | 1.23994 | ||||||||
\(508\) | 3916.51 | 0.342061 | ||||||||
\(509\) | −2357.43 | −0.205288 | −0.102644 | − | 0.994718i | \(-0.532730\pi\) | ||||
−0.102644 | + | 0.994718i | \(0.532730\pi\) | |||||||
\(510\) | 5568.15 | 0.483455 | ||||||||
\(511\) | 6082.66 | 0.526578 | ||||||||
\(512\) | 3143.75 | 0.271358 | ||||||||
\(513\) | −12484.1 | −1.07444 | ||||||||
\(514\) | 5190.12 | 0.445382 | ||||||||
\(515\) | −1842.61 | −0.157661 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −8922.64 | −0.759028 | ||||||||
\(518\) | −46593.5 | −3.95212 | ||||||||
\(519\) | −9017.56 | −0.762672 | ||||||||
\(520\) | −9542.23 | −0.804720 | ||||||||
\(521\) | 7560.92 | 0.635796 | 0.317898 | − | 0.948125i | \(-0.397023\pi\) | ||||
0.317898 | + | 0.948125i | \(0.397023\pi\) | |||||||
\(522\) | −18611.4 | −1.56053 | ||||||||
\(523\) | −13283.5 | −1.11061 | −0.555304 | − | 0.831648i | \(-0.687398\pi\) | ||||
−0.555304 | + | 0.831648i | \(0.687398\pi\) | |||||||
\(524\) | −22249.1 | −1.85488 | ||||||||
\(525\) | 43135.1 | 3.58585 | ||||||||
\(526\) | 10728.1 | 0.889291 | ||||||||
\(527\) | 1203.90 | 0.0995114 | ||||||||
\(528\) | 1902.13 | 0.156779 | ||||||||
\(529\) | −10369.1 | −0.852234 | ||||||||
\(530\) | 18522.7 | 1.51806 | ||||||||
\(531\) | −14136.9 | −1.15535 | ||||||||
\(532\) | −47767.9 | −3.89286 | ||||||||
\(533\) | −5845.40 | −0.475033 | ||||||||
\(534\) | −33267.5 | −2.69593 | ||||||||
\(535\) | −17254.4 | −1.39435 | ||||||||
\(536\) | 8742.72 | 0.704530 | ||||||||
\(537\) | −27020.4 | −2.17135 | ||||||||
\(538\) | −20677.2 | −1.65698 | ||||||||
\(539\) | −10640.8 | −0.850338 | ||||||||
\(540\) | 22899.0 | 1.82484 | ||||||||
\(541\) | −10761.0 | −0.855176 | −0.427588 | − | 0.903974i | \(-0.640637\pi\) | ||||
−0.427588 | + | 0.903974i | \(0.640637\pi\) | |||||||
\(542\) | −34522.0 | −2.73588 | ||||||||
\(543\) | −11671.1 | −0.922383 | ||||||||
\(544\) | −1328.02 | −0.104666 | ||||||||
\(545\) | 16753.0 | 1.31673 | ||||||||
\(546\) | 21659.5 | 1.69769 | ||||||||
\(547\) | −20661.6 | −1.61504 | −0.807521 | − | 0.589839i | \(-0.799191\pi\) | ||||
−0.807521 | + | 0.589839i | \(0.799191\pi\) | |||||||
\(548\) | −7033.03 | −0.548241 | ||||||||
\(549\) | 14765.2 | 1.14784 | ||||||||
\(550\) | 24405.3 | 1.89209 | ||||||||
\(551\) | 13598.2 | 1.05136 | ||||||||
\(552\) | −8622.04 | −0.664816 | ||||||||
\(553\) | −31660.7 | −2.43463 | ||||||||
\(554\) | 2473.47 | 0.189689 | ||||||||
\(555\) | −53819.6 | −4.11624 | ||||||||
\(556\) | −3372.16 | −0.257215 | ||||||||
\(557\) | −17603.1 | −1.33908 | −0.669538 | − | 0.742777i | \(-0.733508\pi\) | ||||
−0.669538 | + | 0.742777i | \(0.733508\pi\) | |||||||
\(558\) | 26062.1 | 1.97724 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 4238.44 | 0.319833 | ||||||||
\(561\) | −1809.09 | −0.136149 | ||||||||
\(562\) | 14569.7 | 1.09357 | ||||||||
\(563\) | 4080.71 | 0.305473 | 0.152737 | − | 0.988267i | \(-0.451191\pi\) | ||||
0.152737 | + | 0.988267i | \(0.451191\pi\) | |||||||
\(564\) | −36048.2 | −2.69132 | ||||||||
\(565\) | −5683.43 | −0.423192 | ||||||||
\(566\) | −35149.6 | −2.61033 | ||||||||
\(567\) | 7435.47 | 0.550724 | ||||||||
\(568\) | −6574.97 | −0.485704 | ||||||||
\(569\) | 5719.77 | 0.421415 | 0.210708 | − | 0.977549i | \(-0.432423\pi\) | ||||
0.210708 | + | 0.977549i | \(0.432423\pi\) | |||||||
\(570\) | −88071.4 | −6.47176 | ||||||||
\(571\) | −6951.99 | −0.509512 | −0.254756 | − | 0.967005i | \(-0.581995\pi\) | ||||
−0.254756 | + | 0.967005i | \(0.581995\pi\) | |||||||
\(572\) | 7677.47 | 0.561208 | ||||||||
\(573\) | −11235.2 | −0.819124 | ||||||||
\(574\) | 34595.8 | 2.51568 | ||||||||
\(575\) | −8302.39 | −0.602145 | ||||||||
\(576\) | −31449.3 | −2.27498 | ||||||||
\(577\) | 207.650 | 0.0149819 | 0.00749097 | − | 0.999972i | \(-0.497616\pi\) | ||||
0.00749097 | + | 0.999972i | \(0.497616\pi\) | |||||||
\(578\) | 22419.9 | 1.61340 | ||||||||
\(579\) | −15265.0 | −1.09567 | ||||||||
\(580\) | −24942.4 | −1.78565 | ||||||||
\(581\) | 22264.3 | 1.58981 | ||||||||
\(582\) | −54924.3 | −3.91183 | ||||||||
\(583\) | −6017.99 | −0.427512 | ||||||||
\(584\) | 5614.60 | 0.397832 | ||||||||
\(585\) | 14744.8 | 1.04209 | ||||||||
\(586\) | 867.543 | 0.0611568 | ||||||||
\(587\) | −19920.8 | −1.40071 | −0.700357 | − | 0.713793i | \(-0.746976\pi\) | ||||
−0.700357 | + | 0.713793i | \(0.746976\pi\) | |||||||
\(588\) | −42989.8 | −3.01508 | ||||||||
\(589\) | −19042.0 | −1.33211 | ||||||||
\(590\) | −30241.2 | −2.11019 | ||||||||
\(591\) | 42869.4 | 2.98377 | ||||||||
\(592\) | −3227.74 | −0.224086 | ||||||||
\(593\) | −21162.6 | −1.46550 | −0.732752 | − | 0.680495i | \(-0.761765\pi\) | ||||
−0.732752 | + | 0.680495i | \(0.761765\pi\) | |||||||
\(594\) | −11875.4 | −0.820293 | ||||||||
\(595\) | −4031.12 | −0.277748 | ||||||||
\(596\) | 35596.7 | 2.44648 | ||||||||
\(597\) | 38441.1 | 2.63533 | ||||||||
\(598\) | −4168.88 | −0.285081 | ||||||||
\(599\) | 14057.7 | 0.958901 | 0.479451 | − | 0.877569i | \(-0.340836\pi\) | ||||
0.479451 | + | 0.877569i | \(0.340836\pi\) | |||||||
\(600\) | 39815.8 | 2.70912 | ||||||||
\(601\) | −13682.7 | −0.928666 | −0.464333 | − | 0.885661i | \(-0.653706\pi\) | ||||
−0.464333 | + | 0.885661i | \(0.653706\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −13509.4 | −0.912347 | ||||||||
\(604\) | −39283.3 | −2.64638 | ||||||||
\(605\) | 10848.4 | 0.729006 | ||||||||
\(606\) | 3709.09 | 0.248633 | ||||||||
\(607\) | −21386.3 | −1.43005 | −0.715027 | − | 0.699096i | \(-0.753586\pi\) | ||||
−0.715027 | + | 0.699096i | \(0.753586\pi\) | |||||||
\(608\) | 21005.2 | 1.40111 | ||||||||
\(609\) | 22862.1 | 1.52122 | ||||||||
\(610\) | 31585.1 | 2.09646 | ||||||||
\(611\) | −7038.41 | −0.466028 | ||||||||
\(612\) | −4307.51 | −0.284511 | ||||||||
\(613\) | 6950.38 | 0.457950 | 0.228975 | − | 0.973432i | \(-0.426463\pi\) | ||||
0.228975 | + | 0.973432i | \(0.426463\pi\) | |||||||
\(614\) | 20808.4 | 1.36769 | ||||||||
\(615\) | 39961.1 | 2.62014 | ||||||||
\(616\) | −18348.7 | −1.20015 | ||||||||
\(617\) | −21710.1 | −1.41656 | −0.708278 | − | 0.705934i | \(-0.750528\pi\) | ||||
−0.708278 | + | 0.705934i | \(0.750528\pi\) | |||||||
\(618\) | 3860.62 | 0.251289 | ||||||||
\(619\) | 11841.9 | 0.768929 | 0.384465 | − | 0.923140i | \(-0.374386\pi\) | ||||
0.384465 | + | 0.923140i | \(0.374386\pi\) | |||||||
\(620\) | 34927.7 | 2.26247 | ||||||||
\(621\) | 4039.86 | 0.261053 | ||||||||
\(622\) | −21420.0 | −1.38081 | ||||||||
\(623\) | 24084.4 | 1.54883 | ||||||||
\(624\) | 1500.45 | 0.0962595 | ||||||||
\(625\) | −1760.95 | −0.112701 | ||||||||
\(626\) | −33827.5 | −2.15977 | ||||||||
\(627\) | 28614.3 | 1.82256 | ||||||||
\(628\) | −25088.2 | −1.59415 | ||||||||
\(629\) | 3069.86 | 0.194600 | ||||||||
\(630\) | −87266.4 | −5.51869 | ||||||||
\(631\) | −3519.70 | −0.222056 | −0.111028 | − | 0.993817i | \(-0.535414\pi\) | ||||
−0.111028 | + | 0.993817i | \(0.535414\pi\) | |||||||
\(632\) | −29224.4 | −1.83937 | ||||||||
\(633\) | 35361.4 | 2.22036 | ||||||||
\(634\) | −12156.6 | −0.761516 | ||||||||
\(635\) | −5227.73 | −0.326702 | ||||||||
\(636\) | −24313.2 | −1.51585 | ||||||||
\(637\) | −8393.74 | −0.522091 | ||||||||
\(638\) | 12935.1 | 0.802675 | ||||||||
\(639\) | 10159.7 | 0.628972 | ||||||||
\(640\) | −44304.9 | −2.73641 | ||||||||
\(641\) | −3923.72 | −0.241775 | −0.120887 | − | 0.992666i | \(-0.538574\pi\) | ||||
−0.120887 | + | 0.992666i | \(0.538574\pi\) | |||||||
\(642\) | 36151.3 | 2.22240 | ||||||||
\(643\) | −12134.0 | −0.744198 | −0.372099 | − | 0.928193i | \(-0.621362\pi\) | ||||
−0.372099 | + | 0.928193i | \(0.621362\pi\) | |||||||
\(644\) | 15457.7 | 0.945835 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 5023.57 | 0.305959 | ||||||||
\(647\) | 28496.2 | 1.73153 | 0.865766 | − | 0.500449i | \(-0.166832\pi\) | ||||
0.865766 | + | 0.500449i | \(0.166832\pi\) | |||||||
\(648\) | 6863.30 | 0.416074 | ||||||||
\(649\) | 9825.33 | 0.594265 | ||||||||
\(650\) | 19251.6 | 1.16170 | ||||||||
\(651\) | −32014.6 | −1.92742 | ||||||||
\(652\) | −29532.6 | −1.77390 | ||||||||
\(653\) | −8815.15 | −0.528275 | −0.264138 | − | 0.964485i | \(-0.585087\pi\) | ||||
−0.264138 | + | 0.964485i | \(0.585087\pi\) | |||||||
\(654\) | −35100.7 | −2.09870 | ||||||||
\(655\) | 29697.9 | 1.77159 | ||||||||
\(656\) | 2396.60 | 0.142640 | ||||||||
\(657\) | −8675.76 | −0.515181 | ||||||||
\(658\) | 41656.5 | 2.46799 | ||||||||
\(659\) | −2797.40 | −0.165358 | −0.0826791 | − | 0.996576i | \(-0.526348\pi\) | ||||
−0.0826791 | + | 0.996576i | \(0.526348\pi\) | |||||||
\(660\) | −52485.7 | −3.09546 | ||||||||
\(661\) | −21286.4 | −1.25257 | −0.626283 | − | 0.779596i | \(-0.715424\pi\) | ||||
−0.626283 | + | 0.779596i | \(0.715424\pi\) | |||||||
\(662\) | −44205.4 | −2.59530 | ||||||||
\(663\) | −1427.05 | −0.0835931 | ||||||||
\(664\) | 20551.1 | 1.20111 | ||||||||
\(665\) | 63760.1 | 3.71806 | ||||||||
\(666\) | 66456.8 | 3.86659 | ||||||||
\(667\) | −4400.37 | −0.255447 | ||||||||
\(668\) | −36292.9 | −2.10212 | ||||||||
\(669\) | −27157.3 | −1.56945 | ||||||||
\(670\) | −28898.8 | −1.66636 | ||||||||
\(671\) | −10262.0 | −0.590401 | ||||||||
\(672\) | 35315.4 | 2.02726 | ||||||||
\(673\) | −28413.7 | −1.62744 | −0.813721 | − | 0.581256i | \(-0.802562\pi\) | ||||
−0.813721 | + | 0.581256i | \(0.802562\pi\) | |||||||
\(674\) | 31099.3 | 1.77730 | ||||||||
\(675\) | −18655.8 | −1.06379 | ||||||||
\(676\) | −23424.5 | −1.33275 | ||||||||
\(677\) | −29392.6 | −1.66861 | −0.834305 | − | 0.551303i | \(-0.814131\pi\) | ||||
−0.834305 | + | 0.551303i | \(0.814131\pi\) | |||||||
\(678\) | 11907.9 | 0.674511 | ||||||||
\(679\) | 39763.0 | 2.24737 | ||||||||
\(680\) | −3720.92 | −0.209840 | ||||||||
\(681\) | 28967.7 | 1.63002 | ||||||||
\(682\) | −18113.5 | −1.01701 | ||||||||
\(683\) | −1108.89 | −0.0621236 | −0.0310618 | − | 0.999517i | \(-0.509889\pi\) | ||||
−0.0310618 | + | 0.999517i | \(0.509889\pi\) | |||||||
\(684\) | 68131.8 | 3.80860 | ||||||||
\(685\) | 9387.63 | 0.523625 | ||||||||
\(686\) | 6551.09 | 0.364609 | ||||||||
\(687\) | 42004.1 | 2.33269 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −4747.14 | −0.262484 | ||||||||
\(690\) | 28499.9 | 1.57242 | ||||||||
\(691\) | 16069.1 | 0.884659 | 0.442329 | − | 0.896853i | \(-0.354152\pi\) | ||||
0.442329 | + | 0.896853i | \(0.354152\pi\) | |||||||
\(692\) | 14922.7 | 0.819765 | ||||||||
\(693\) | 28352.8 | 1.55416 | ||||||||
\(694\) | 1623.99 | 0.0888270 | ||||||||
\(695\) | 4501.13 | 0.245666 | ||||||||
\(696\) | 21102.9 | 1.14929 | ||||||||
\(697\) | −2279.37 | −0.123870 | ||||||||
\(698\) | 5317.43 | 0.288349 | ||||||||
\(699\) | 19540.9 | 1.05737 | ||||||||
\(700\) | −71382.3 | −3.85428 | ||||||||
\(701\) | −20319.8 | −1.09482 | −0.547408 | − | 0.836866i | \(-0.684386\pi\) | ||||
−0.547408 | + | 0.836866i | \(0.684386\pi\) | |||||||
\(702\) | −9367.63 | −0.503644 | ||||||||
\(703\) | −48555.8 | −2.60500 | ||||||||
\(704\) | 21857.7 | 1.17016 | ||||||||
\(705\) | 48116.9 | 2.57048 | ||||||||
\(706\) | −44493.3 | −2.37185 | ||||||||
\(707\) | −2685.23 | −0.142841 | ||||||||
\(708\) | 39695.2 | 2.10711 | ||||||||
\(709\) | −30651.7 | −1.62362 | −0.811810 | − | 0.583921i | \(-0.801518\pi\) | ||||
−0.811810 | + | 0.583921i | \(0.801518\pi\) | |||||||
\(710\) | 21733.4 | 1.14879 | ||||||||
\(711\) | 45158.0 | 2.38194 | ||||||||
\(712\) | 22231.0 | 1.17015 | ||||||||
\(713\) | 6161.98 | 0.323658 | ||||||||
\(714\) | 8445.96 | 0.442692 | ||||||||
\(715\) | −10247.8 | −0.536009 | ||||||||
\(716\) | 44714.8 | 2.33390 | ||||||||
\(717\) | −8393.48 | −0.437183 | ||||||||
\(718\) | −53439.1 | −2.77762 | ||||||||
\(719\) | −10638.1 | −0.551788 | −0.275894 | − | 0.961188i | \(-0.588974\pi\) | ||||
−0.275894 | + | 0.961188i | \(0.588974\pi\) | |||||||
\(720\) | −6045.33 | −0.312911 | ||||||||
\(721\) | −2794.93 | −0.144367 | ||||||||
\(722\) | −47714.1 | −2.45947 | ||||||||
\(723\) | −2723.02 | −0.140070 | ||||||||
\(724\) | 19313.9 | 0.991432 | ||||||||
\(725\) | 20320.5 | 1.04094 | ||||||||
\(726\) | −22729.4 | −1.16194 | ||||||||
\(727\) | 24420.8 | 1.24583 | 0.622913 | − | 0.782291i | \(-0.285949\pi\) | ||||
0.622913 | + | 0.782291i | \(0.285949\pi\) | |||||||
\(728\) | −14474.0 | −0.736869 | ||||||||
\(729\) | −31464.6 | −1.59857 | ||||||||
\(730\) | −18558.9 | −0.940952 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | −41459.3 | −2.09341 | ||||||||
\(733\) | −18873.8 | −0.951049 | −0.475524 | − | 0.879703i | \(-0.657742\pi\) | ||||
−0.475524 | + | 0.879703i | \(0.657742\pi\) | |||||||
\(734\) | −11667.4 | −0.586720 | ||||||||
\(735\) | 57382.4 | 2.87970 | ||||||||
\(736\) | −6797.29 | −0.340423 | ||||||||
\(737\) | 9389.19 | 0.469275 | ||||||||
\(738\) | −49344.3 | −2.46123 | ||||||||
\(739\) | −13017.8 | −0.647994 | −0.323997 | − | 0.946058i | \(-0.605027\pi\) | ||||
−0.323997 | + | 0.946058i | \(0.605027\pi\) | |||||||
\(740\) | 89063.4 | 4.42437 | ||||||||
\(741\) | 22571.7 | 1.11902 | ||||||||
\(742\) | 28095.8 | 1.39006 | ||||||||
\(743\) | −15017.9 | −0.741525 | −0.370762 | − | 0.928728i | \(-0.620904\pi\) | ||||
−0.370762 | + | 0.928728i | \(0.620904\pi\) | |||||||
\(744\) | −29551.1 | −1.45618 | ||||||||
\(745\) | −47514.2 | −2.33663 | ||||||||
\(746\) | 45313.1 | 2.22390 | ||||||||
\(747\) | −31755.9 | −1.55540 | ||||||||
\(748\) | 2993.77 | 0.146341 | ||||||||
\(749\) | −26172.1 | −1.27678 | ||||||||
\(750\) | −47591.6 | −2.31707 | ||||||||
\(751\) | −33475.8 | −1.62656 | −0.813281 | − | 0.581871i | \(-0.802321\pi\) | ||||
−0.813281 | + | 0.581871i | \(0.802321\pi\) | |||||||
\(752\) | 2885.73 | 0.139936 | ||||||||
\(753\) | −8877.36 | −0.429627 | ||||||||
\(754\) | 10203.6 | 0.492827 | ||||||||
\(755\) | 52434.9 | 2.52755 | ||||||||
\(756\) | 34733.9 | 1.67098 | ||||||||
\(757\) | 25911.7 | 1.24409 | 0.622046 | − | 0.782981i | \(-0.286302\pi\) | ||||
0.622046 | + | 0.782981i | \(0.286302\pi\) | |||||||
\(758\) | 4964.99 | 0.237911 | ||||||||
\(759\) | −9259.58 | −0.442821 | ||||||||
\(760\) | 58853.8 | 2.80901 | ||||||||
\(761\) | 37213.7 | 1.77266 | 0.886331 | − | 0.463052i | \(-0.153246\pi\) | ||||
0.886331 | + | 0.463052i | \(0.153246\pi\) | |||||||
\(762\) | 10953.1 | 0.520719 | ||||||||
\(763\) | 25411.5 | 1.20571 | ||||||||
\(764\) | 18592.6 | 0.880442 | ||||||||
\(765\) | 5749.63 | 0.271736 | ||||||||
\(766\) | −7938.70 | −0.374461 | ||||||||
\(767\) | 7750.47 | 0.364867 | ||||||||
\(768\) | 40179.6 | 1.88783 | ||||||||
\(769\) | 34874.0 | 1.63536 | 0.817679 | − | 0.575675i | \(-0.195261\pi\) | ||||
0.817679 | + | 0.575675i | \(0.195261\pi\) | |||||||
\(770\) | 60651.2 | 2.83859 | ||||||||
\(771\) | 9093.47 | 0.424765 | ||||||||
\(772\) | 25261.3 | 1.17769 | ||||||||
\(773\) | 24556.5 | 1.14261 | 0.571304 | − | 0.820738i | \(-0.306438\pi\) | ||||
0.571304 | + | 0.820738i | \(0.306438\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −28455.5 | −1.31891 | ||||||||
\(776\) | 36703.2 | 1.69790 | ||||||||
\(777\) | −81635.2 | −3.76917 | ||||||||
\(778\) | −5875.16 | −0.270739 | ||||||||
\(779\) | 36052.8 | 1.65818 | ||||||||
\(780\) | −41402.1 | −1.90055 | ||||||||
\(781\) | −7061.15 | −0.323518 | ||||||||
\(782\) | −1625.63 | −0.0743380 | ||||||||
\(783\) | −9887.78 | −0.451290 | ||||||||
\(784\) | 3441.41 | 0.156770 | ||||||||
\(785\) | 33487.5 | 1.52257 | ||||||||
\(786\) | −62222.6 | −2.82367 | ||||||||
\(787\) | 9587.48 | 0.434252 | 0.217126 | − | 0.976144i | \(-0.430332\pi\) | ||||
0.217126 | + | 0.976144i | \(0.430332\pi\) | |||||||
\(788\) | −70942.5 | −3.20714 | ||||||||
\(789\) | 18796.4 | 0.848124 | ||||||||
\(790\) | 96600.4 | 4.35049 | ||||||||
\(791\) | −8620.81 | −0.387511 | ||||||||
\(792\) | 26171.0 | 1.17417 | ||||||||
\(793\) | −8094.90 | −0.362495 | ||||||||
\(794\) | −4764.46 | −0.212953 | ||||||||
\(795\) | 32453.1 | 1.44779 | ||||||||
\(796\) | −63614.4 | −2.83260 | ||||||||
\(797\) | 3512.54 | 0.156111 | 0.0780556 | − | 0.996949i | \(-0.475129\pi\) | ||||
0.0780556 | + | 0.996949i | \(0.475129\pi\) | |||||||
\(798\) | −133589. | −5.92609 | ||||||||
\(799\) | −2744.58 | −0.121522 | ||||||||
\(800\) | 31389.3 | 1.38722 | ||||||||
\(801\) | −34351.8 | −1.51531 | ||||||||
\(802\) | −36038.6 | −1.58674 | ||||||||
\(803\) | 6029.76 | 0.264988 | ||||||||
\(804\) | 37933.2 | 1.66393 | ||||||||
\(805\) | −20632.8 | −0.903366 | ||||||||
\(806\) | −14288.4 | −0.624426 | ||||||||
\(807\) | −36228.0 | −1.58028 | ||||||||
\(808\) | −2478.60 | −0.107917 | ||||||||
\(809\) | 5036.49 | 0.218879 | 0.109440 | − | 0.993993i | \(-0.465094\pi\) | ||||
0.109440 | + | 0.993993i | \(0.465094\pi\) | |||||||
\(810\) | −22686.4 | −0.984099 | ||||||||
\(811\) | −8272.59 | −0.358187 | −0.179094 | − | 0.983832i | \(-0.557316\pi\) | ||||
−0.179094 | + | 0.983832i | \(0.557316\pi\) | |||||||
\(812\) | −37833.5 | −1.63509 | ||||||||
\(813\) | −60485.2 | −2.60923 | ||||||||
\(814\) | −46188.3 | −1.98882 | ||||||||
\(815\) | 39419.8 | 1.69425 | ||||||||
\(816\) | 585.089 | 0.0251007 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | −30835.2 | −1.31800 | ||||||||
\(819\) | 22365.4 | 0.954225 | ||||||||
\(820\) | −66129.8 | −2.81628 | ||||||||
\(821\) | 35068.1 | 1.49073 | 0.745363 | − | 0.666659i | \(-0.232276\pi\) | ||||
0.745363 | + | 0.666659i | \(0.232276\pi\) | |||||||
\(822\) | −19668.8 | −0.834586 | ||||||||
\(823\) | 18610.5 | 0.788241 | 0.394121 | − | 0.919059i | \(-0.371049\pi\) | ||||
0.394121 | + | 0.919059i | \(0.371049\pi\) | |||||||
\(824\) | −2579.86 | −0.109070 | ||||||||
\(825\) | 42760.0 | 1.80450 | ||||||||
\(826\) | −45870.8 | −1.93226 | ||||||||
\(827\) | 23150.2 | 0.973412 | 0.486706 | − | 0.873566i | \(-0.338198\pi\) | ||||
0.486706 | + | 0.873566i | \(0.338198\pi\) | |||||||
\(828\) | −22047.5 | −0.925365 | ||||||||
\(829\) | 1109.11 | 0.0464668 | 0.0232334 | − | 0.999730i | \(-0.492604\pi\) | ||||
0.0232334 | + | 0.999730i | \(0.492604\pi\) | |||||||
\(830\) | −67931.0 | −2.84087 | ||||||||
\(831\) | 4333.71 | 0.180908 | ||||||||
\(832\) | 17241.9 | 0.718455 | ||||||||
\(833\) | −3273.08 | −0.136141 | ||||||||
\(834\) | −9430.71 | −0.391557 | ||||||||
\(835\) | 48443.4 | 2.00773 | ||||||||
\(836\) | −47352.4 | −1.95899 | ||||||||
\(837\) | 13846.2 | 0.571797 | ||||||||
\(838\) | 11396.0 | 0.469770 | ||||||||
\(839\) | 27967.9 | 1.15085 | 0.575423 | − | 0.817856i | \(-0.304838\pi\) | ||||
0.575423 | + | 0.817856i | \(0.304838\pi\) | |||||||
\(840\) | 98948.8 | 4.06435 | ||||||||
\(841\) | −13618.9 | −0.558403 | ||||||||
\(842\) | 15908.4 | 0.651117 | ||||||||
\(843\) | 25527.2 | 1.04295 | ||||||||
\(844\) | −58517.9 | −2.38658 | ||||||||
\(845\) | 31266.8 | 1.27291 | ||||||||
\(846\) | −59415.1 | −2.41458 | ||||||||
\(847\) | 16455.1 | 0.667539 | ||||||||
\(848\) | 1946.32 | 0.0788170 | ||||||||
\(849\) | −61584.7 | −2.48950 | ||||||||
\(850\) | 7507.01 | 0.302927 | ||||||||
\(851\) | 15712.7 | 0.632930 | ||||||||
\(852\) | −28527.7 | −1.14711 | ||||||||
\(853\) | −7589.83 | −0.304655 | −0.152328 | − | 0.988330i | \(-0.548677\pi\) | ||||
−0.152328 | + | 0.988330i | \(0.548677\pi\) | |||||||
\(854\) | 47909.3 | 1.91970 | ||||||||
\(855\) | −90941.8 | −3.63759 | ||||||||
\(856\) | −24158.1 | −0.964613 | ||||||||
\(857\) | −28883.4 | −1.15127 | −0.575635 | − | 0.817707i | \(-0.695245\pi\) | ||||
−0.575635 | + | 0.817707i | \(0.695245\pi\) | |||||||
\(858\) | 21471.1 | 0.854325 | ||||||||
\(859\) | 6651.57 | 0.264201 | 0.132101 | − | 0.991236i | \(-0.457828\pi\) | ||||
0.132101 | + | 0.991236i | \(0.457828\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 60614.3 | 2.39922 | ||||||||
\(862\) | 62414.4 | 2.46618 | ||||||||
\(863\) | 31395.0 | 1.23835 | 0.619175 | − | 0.785253i | \(-0.287467\pi\) | ||||
0.619175 | + | 0.785253i | \(0.287467\pi\) | |||||||
\(864\) | −15273.7 | −0.601416 | ||||||||
\(865\) | −19918.7 | −0.782956 | ||||||||
\(866\) | 14414.1 | 0.565604 | ||||||||
\(867\) | 39281.3 | 1.53871 | ||||||||
\(868\) | 52979.5 | 2.07171 | ||||||||
\(869\) | −31385.4 | −1.22517 | ||||||||
\(870\) | −69754.9 | −2.71829 | ||||||||
\(871\) | 7406.43 | 0.288126 | ||||||||
\(872\) | 23456.1 | 0.910922 | ||||||||
\(873\) | −56714.4 | −2.19873 | ||||||||
\(874\) | 25712.5 | 0.995124 | ||||||||
\(875\) | 34454.4 | 1.33117 | ||||||||
\(876\) | 24360.8 | 0.939582 | ||||||||
\(877\) | −16966.2 | −0.653259 | −0.326630 | − | 0.945152i | \(-0.605913\pi\) | ||||
−0.326630 | + | 0.945152i | \(0.605913\pi\) | |||||||
\(878\) | −3220.45 | −0.123787 | ||||||||
\(879\) | 1520.00 | 0.0583257 | ||||||||
\(880\) | 4201.58 | 0.160949 | ||||||||
\(881\) | 28409.0 | 1.08641 | 0.543204 | − | 0.839601i | \(-0.317211\pi\) | ||||
0.543204 | + | 0.839601i | \(0.317211\pi\) | |||||||
\(882\) | −70856.2 | −2.70505 | ||||||||
\(883\) | −10627.6 | −0.405036 | −0.202518 | − | 0.979278i | \(-0.564913\pi\) | ||||
−0.202518 | + | 0.979278i | \(0.564913\pi\) | |||||||
\(884\) | 2361.57 | 0.0898507 | ||||||||
\(885\) | −52984.8 | −2.01250 | ||||||||
\(886\) | −77958.4 | −2.95605 | ||||||||
\(887\) | −108.704 | −0.00411489 | −0.00205745 | − | 0.999998i | \(-0.500655\pi\) | ||||
−0.00205745 | + | 0.999998i | \(0.500655\pi\) | |||||||
\(888\) | −75353.4 | −2.84763 | ||||||||
\(889\) | −7929.59 | −0.299156 | ||||||||
\(890\) | −73484.0 | −2.76763 | ||||||||
\(891\) | 7370.80 | 0.277139 | ||||||||
\(892\) | 44941.3 | 1.68694 | ||||||||
\(893\) | 43410.9 | 1.62675 | ||||||||
\(894\) | 99551.2 | 3.72426 | ||||||||
\(895\) | −59684.9 | −2.22910 | ||||||||
\(896\) | −67203.1 | −2.50569 | ||||||||
\(897\) | −7304.19 | −0.271884 | ||||||||
\(898\) | 505.171 | 0.0187726 | ||||||||
\(899\) | −15081.8 | −0.559516 | ||||||||
\(900\) | 101813. | 3.77086 | ||||||||
\(901\) | −1851.12 | −0.0684457 | ||||||||
\(902\) | 34294.9 | 1.26596 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −7957.44 | −0.292766 | ||||||||
\(905\) | −25780.1 | −0.946915 | ||||||||
\(906\) | −109861. | −4.02857 | ||||||||
\(907\) | −13689.8 | −0.501171 | −0.250586 | − | 0.968094i | \(-0.580623\pi\) | ||||
−0.250586 | + | 0.968094i | \(0.580623\pi\) | |||||||
\(908\) | −47937.3 | −1.75204 | ||||||||
\(909\) | 3829.97 | 0.139749 | ||||||||
\(910\) | 47843.2 | 1.74284 | ||||||||
\(911\) | 13891.9 | 0.505223 | 0.252612 | − | 0.967568i | \(-0.418710\pi\) | ||||
0.252612 | + | 0.967568i | \(0.418710\pi\) | |||||||
\(912\) | −9254.33 | −0.336010 | ||||||||
\(913\) | 22070.7 | 0.800037 | ||||||||
\(914\) | −6748.33 | −0.244218 | ||||||||
\(915\) | 55339.4 | 1.99942 | ||||||||
\(916\) | −69510.5 | −2.50731 | ||||||||
\(917\) | 45046.7 | 1.62222 | ||||||||
\(918\) | −3652.84 | −0.131331 | ||||||||
\(919\) | 48072.7 | 1.72554 | 0.862770 | − | 0.505596i | \(-0.168727\pi\) | ||||
0.862770 | + | 0.505596i | \(0.168727\pi\) | |||||||
\(920\) | −19045.1 | −0.682497 | ||||||||
\(921\) | 36457.9 | 1.30437 | ||||||||
\(922\) | 61831.8 | 2.20859 | ||||||||
\(923\) | −5570.01 | −0.198634 | ||||||||
\(924\) | −79612.0 | −2.83446 | ||||||||
\(925\) | −72559.7 | −2.57919 | ||||||||
\(926\) | −47119.2 | −1.67217 | ||||||||
\(927\) | 3986.44 | 0.141243 | ||||||||
\(928\) | 16636.7 | 0.588499 | ||||||||
\(929\) | −27959.3 | −0.987423 | −0.493712 | − | 0.869626i | \(-0.664360\pi\) | ||||
−0.493712 | + | 0.869626i | \(0.664360\pi\) | |||||||
\(930\) | 97680.2 | 3.44415 | ||||||||
\(931\) | 51770.2 | 1.82245 | ||||||||
\(932\) | −32337.2 | −1.13653 | ||||||||
\(933\) | −37529.3 | −1.31689 | ||||||||
\(934\) | 31733.2 | 1.11171 | ||||||||
\(935\) | −3996.06 | −0.139770 | ||||||||
\(936\) | 20644.4 | 0.720921 | ||||||||
\(937\) | −8650.71 | −0.301608 | −0.150804 | − | 0.988564i | \(-0.548186\pi\) | ||||
−0.150804 | + | 0.988564i | \(0.548186\pi\) | |||||||
\(938\) | −43834.6 | −1.52585 | ||||||||
\(939\) | −59268.3 | −2.05980 | ||||||||
\(940\) | −79626.4 | −2.76290 | ||||||||
\(941\) | −38299.6 | −1.32681 | −0.663407 | − | 0.748258i | \(-0.730890\pi\) | ||||
−0.663407 | + | 0.748258i | \(0.730890\pi\) | |||||||
\(942\) | −70162.5 | −2.42677 | ||||||||
\(943\) | −11666.7 | −0.402884 | ||||||||
\(944\) | −3177.67 | −0.109560 | ||||||||
\(945\) | −46362.6 | −1.59595 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 9535.13 | 0.327191 | 0.163596 | − | 0.986527i | \(-0.447691\pi\) | ||||
0.163596 | + | 0.986527i | \(0.447691\pi\) | |||||||
\(948\) | −126800. | −4.34416 | ||||||||
\(949\) | 4756.43 | 0.162698 | ||||||||
\(950\) | −118738. | −4.05513 | ||||||||
\(951\) | −21299.3 | −0.726265 | ||||||||
\(952\) | −5644.02 | −0.192147 | ||||||||
\(953\) | −18679.6 | −0.634932 | −0.317466 | − | 0.948270i | \(-0.602832\pi\) | ||||
−0.317466 | + | 0.948270i | \(0.602832\pi\) | |||||||
\(954\) | −40073.3 | −1.35998 | ||||||||
\(955\) | −24817.3 | −0.840909 | ||||||||
\(956\) | 13890.0 | 0.469910 | ||||||||
\(957\) | 22663.3 | 0.765518 | ||||||||
\(958\) | 64318.1 | 2.16913 | ||||||||
\(959\) | 14239.5 | 0.479475 | ||||||||
\(960\) | −117871. | −3.96279 | ||||||||
\(961\) | −8671.48 | −0.291077 | ||||||||
\(962\) | −36434.5 | −1.22110 | ||||||||
\(963\) | 37329.5 | 1.24915 | ||||||||
\(964\) | 4506.20 | 0.150555 | ||||||||
\(965\) | −33718.6 | −1.12481 | ||||||||
\(966\) | 43229.5 | 1.43984 | ||||||||
\(967\) | −17137.5 | −0.569911 | −0.284956 | − | 0.958541i | \(-0.591979\pi\) | ||||
−0.284956 | + | 0.958541i | \(0.591979\pi\) | |||||||
\(968\) | 15188.9 | 0.504329 | ||||||||
\(969\) | 8801.67 | 0.291796 | ||||||||
\(970\) | −121321. | −4.01587 | ||||||||
\(971\) | −21152.2 | −0.699081 | −0.349540 | − | 0.936921i | \(-0.613662\pi\) | ||||
−0.349540 | + | 0.936921i | \(0.613662\pi\) | |||||||
\(972\) | 64297.8 | 2.12176 | ||||||||
\(973\) | 6827.46 | 0.224952 | ||||||||
\(974\) | 30189.5 | 0.993157 | ||||||||
\(975\) | 33730.1 | 1.10793 | ||||||||
\(976\) | 3318.89 | 0.108847 | ||||||||
\(977\) | −36352.9 | −1.19041 | −0.595205 | − | 0.803574i | \(-0.702929\pi\) | ||||
−0.595205 | + | 0.803574i | \(0.702929\pi\) | |||||||
\(978\) | −82591.9 | −2.70041 | ||||||||
\(979\) | 23874.9 | 0.779412 | ||||||||
\(980\) | −94959.4 | −3.09527 | ||||||||
\(981\) | −36244.7 | −1.17962 | ||||||||
\(982\) | 82155.0 | 2.66973 | ||||||||
\(983\) | −16139.9 | −0.523687 | −0.261844 | − | 0.965110i | \(-0.584330\pi\) | ||||
−0.261844 | + | 0.965110i | \(0.584330\pi\) | |||||||
\(984\) | 55950.0 | 1.81262 | ||||||||
\(985\) | 94693.4 | 3.06313 | ||||||||
\(986\) | 3978.81 | 0.128510 | ||||||||
\(987\) | 72985.2 | 2.35374 | ||||||||
\(988\) | −37352.8 | −1.20278 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | −86507.5 | −2.77716 | ||||||||
\(991\) | −38726.1 | −1.24135 | −0.620674 | − | 0.784069i | \(-0.713141\pi\) | ||||
−0.620674 | + | 0.784069i | \(0.713141\pi\) | |||||||
\(992\) | −23297.0 | −0.745644 | ||||||||
\(993\) | −77451.1 | −2.47516 | ||||||||
\(994\) | 32965.9 | 1.05193 | ||||||||
\(995\) | 84912.0 | 2.70542 | ||||||||
\(996\) | 89167.6 | 2.83673 | ||||||||
\(997\) | 44312.0 | 1.40760 | 0.703799 | − | 0.710399i | \(-0.251485\pi\) | ||||
0.703799 | + | 0.710399i | \(0.251485\pi\) | |||||||
\(998\) | 63315.3 | 2.00823 | ||||||||
\(999\) | 35306.9 | 1.11818 |
(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.m.1.14 | ✓ | 110 | |
43.42 | odd | 2 | inner | 1849.4.a.m.1.97 | yes | 110 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1849.4.a.m.1.14 | ✓ | 110 | 1.1 | even | 1 | trivial | |
1849.4.a.m.1.97 | yes | 110 | 43.42 | odd | 2 | inner |