Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2013,4,Mod(1,2013)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2013, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("2013.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2013 = 3 \cdot 11 \cdot 61 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 2013.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: | \(118.770844842\) |
Analytic rank: | \(1\) |
Dimension: | \(37\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.8 | ||
Character | \(\chi\) | \(=\) | 2013.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −3.99170 | −1.41128 | −0.705639 | − | 0.708572i | \(-0.749340\pi\) | ||||
−0.705639 | + | 0.708572i | \(0.749340\pi\) | |||||||
\(3\) | −3.00000 | −0.577350 | ||||||||
\(4\) | 7.93363 | 0.991704 | ||||||||
\(5\) | 2.24192 | 0.200523 | 0.100262 | − | 0.994961i | \(-0.468032\pi\) | ||||
0.100262 | + | 0.994961i | \(0.468032\pi\) | |||||||
\(6\) | 11.9751 | 0.814801 | ||||||||
\(7\) | 2.67076 | 0.144207 | 0.0721036 | − | 0.997397i | \(-0.477029\pi\) | ||||
0.0721036 | + | 0.997397i | \(0.477029\pi\) | |||||||
\(8\) | 0.264912 | 0.0117076 | ||||||||
\(9\) | 9.00000 | 0.333333 | ||||||||
\(10\) | −8.94905 | −0.282994 | ||||||||
\(11\) | 11.0000 | 0.301511 | ||||||||
\(12\) | −23.8009 | −0.572561 | ||||||||
\(13\) | 67.0862 | 1.43126 | 0.715630 | − | 0.698480i | \(-0.246140\pi\) | ||||
0.715630 | + | 0.698480i | \(0.246140\pi\) | |||||||
\(14\) | −10.6608 | −0.203516 | ||||||||
\(15\) | −6.72575 | −0.115772 | ||||||||
\(16\) | −64.5265 | −1.00823 | ||||||||
\(17\) | −40.8746 | −0.583150 | −0.291575 | − | 0.956548i | \(-0.594179\pi\) | ||||
−0.291575 | + | 0.956548i | \(0.594179\pi\) | |||||||
\(18\) | −35.9253 | −0.470426 | ||||||||
\(19\) | 109.209 | 1.31864 | 0.659321 | − | 0.751862i | \(-0.270844\pi\) | ||||
0.659321 | + | 0.751862i | \(0.270844\pi\) | |||||||
\(20\) | 17.7865 | 0.198860 | ||||||||
\(21\) | −8.01227 | −0.0832581 | ||||||||
\(22\) | −43.9087 | −0.425516 | ||||||||
\(23\) | 175.390 | 1.59006 | 0.795029 | − | 0.606571i | \(-0.207455\pi\) | ||||
0.795029 | + | 0.606571i | \(0.207455\pi\) | |||||||
\(24\) | −0.794737 | −0.00675938 | ||||||||
\(25\) | −119.974 | −0.959790 | ||||||||
\(26\) | −267.788 | −2.01990 | ||||||||
\(27\) | −27.0000 | −0.192450 | ||||||||
\(28\) | 21.1888 | 0.143011 | ||||||||
\(29\) | −109.835 | −0.703304 | −0.351652 | − | 0.936131i | \(-0.614380\pi\) | ||||
−0.351652 | + | 0.936131i | \(0.614380\pi\) | |||||||
\(30\) | 26.8471 | 0.163387 | ||||||||
\(31\) | −258.630 | −1.49843 | −0.749214 | − | 0.662328i | \(-0.769568\pi\) | ||||
−0.749214 | + | 0.662328i | \(0.769568\pi\) | |||||||
\(32\) | 255.451 | 1.41118 | ||||||||
\(33\) | −33.0000 | −0.174078 | ||||||||
\(34\) | 163.159 | 0.822987 | ||||||||
\(35\) | 5.98761 | 0.0289169 | ||||||||
\(36\) | 71.4027 | 0.330568 | ||||||||
\(37\) | −18.8963 | −0.0839605 | −0.0419803 | − | 0.999118i | \(-0.513367\pi\) | ||||
−0.0419803 | + | 0.999118i | \(0.513367\pi\) | |||||||
\(38\) | −435.928 | −1.86097 | ||||||||
\(39\) | −201.259 | −0.826338 | ||||||||
\(40\) | 0.593911 | 0.00234764 | ||||||||
\(41\) | −294.905 | −1.12333 | −0.561663 | − | 0.827366i | \(-0.689838\pi\) | ||||
−0.561663 | + | 0.827366i | \(0.689838\pi\) | |||||||
\(42\) | 31.9825 | 0.117500 | ||||||||
\(43\) | 120.524 | 0.427437 | 0.213719 | − | 0.976895i | \(-0.431442\pi\) | ||||
0.213719 | + | 0.976895i | \(0.431442\pi\) | |||||||
\(44\) | 87.2700 | 0.299010 | ||||||||
\(45\) | 20.1772 | 0.0668410 | ||||||||
\(46\) | −700.104 | −2.24401 | ||||||||
\(47\) | 546.321 | 1.69551 | 0.847756 | − | 0.530387i | \(-0.177953\pi\) | ||||
0.847756 | + | 0.530387i | \(0.177953\pi\) | |||||||
\(48\) | 193.580 | 0.582100 | ||||||||
\(49\) | −335.867 | −0.979204 | ||||||||
\(50\) | 478.899 | 1.35453 | ||||||||
\(51\) | 122.624 | 0.336682 | ||||||||
\(52\) | 532.237 | 1.41939 | ||||||||
\(53\) | 47.7726 | 0.123813 | 0.0619063 | − | 0.998082i | \(-0.480282\pi\) | ||||
0.0619063 | + | 0.998082i | \(0.480282\pi\) | |||||||
\(54\) | 107.776 | 0.271600 | ||||||||
\(55\) | 24.6611 | 0.0604600 | ||||||||
\(56\) | 0.707516 | 0.00168832 | ||||||||
\(57\) | −327.626 | −0.761318 | ||||||||
\(58\) | 438.427 | 0.992558 | ||||||||
\(59\) | −813.600 | −1.79528 | −0.897641 | − | 0.440727i | \(-0.854721\pi\) | ||||
−0.897641 | + | 0.440727i | \(0.854721\pi\) | |||||||
\(60\) | −53.3596 | −0.114812 | ||||||||
\(61\) | −61.0000 | −0.128037 | ||||||||
\(62\) | 1032.37 | 2.11470 | ||||||||
\(63\) | 24.0368 | 0.0480691 | ||||||||
\(64\) | −503.470 | −0.983340 | ||||||||
\(65\) | 150.402 | 0.287001 | ||||||||
\(66\) | 131.726 | 0.245672 | ||||||||
\(67\) | −441.614 | −0.805250 | −0.402625 | − | 0.915365i | \(-0.631902\pi\) | ||||
−0.402625 | + | 0.915365i | \(0.631902\pi\) | |||||||
\(68\) | −324.284 | −0.578313 | ||||||||
\(69\) | −526.170 | −0.918021 | ||||||||
\(70\) | −23.9007 | −0.0408097 | ||||||||
\(71\) | −295.111 | −0.493285 | −0.246642 | − | 0.969107i | \(-0.579327\pi\) | ||||
−0.246642 | + | 0.969107i | \(0.579327\pi\) | |||||||
\(72\) | 2.38421 | 0.00390253 | ||||||||
\(73\) | −930.124 | −1.49127 | −0.745636 | − | 0.666354i | \(-0.767854\pi\) | ||||
−0.745636 | + | 0.666354i | \(0.767854\pi\) | |||||||
\(74\) | 75.4284 | 0.118492 | ||||||||
\(75\) | 359.921 | 0.554135 | ||||||||
\(76\) | 866.422 | 1.30770 | ||||||||
\(77\) | 29.3783 | 0.0434801 | ||||||||
\(78\) | 803.363 | 1.16619 | ||||||||
\(79\) | −100.760 | −0.143498 | −0.0717489 | − | 0.997423i | \(-0.522858\pi\) | ||||
−0.0717489 | + | 0.997423i | \(0.522858\pi\) | |||||||
\(80\) | −144.663 | −0.202173 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | 1177.17 | 1.58532 | ||||||||
\(83\) | −100.458 | −0.132852 | −0.0664260 | − | 0.997791i | \(-0.521160\pi\) | ||||
−0.0664260 | + | 0.997791i | \(0.521160\pi\) | |||||||
\(84\) | −63.5664 | −0.0825674 | ||||||||
\(85\) | −91.6375 | −0.116935 | ||||||||
\(86\) | −481.097 | −0.603233 | ||||||||
\(87\) | 329.505 | 0.406053 | ||||||||
\(88\) | 2.91404 | 0.00352997 | ||||||||
\(89\) | −1429.55 | −1.70260 | −0.851302 | − | 0.524676i | \(-0.824186\pi\) | ||||
−0.851302 | + | 0.524676i | \(0.824186\pi\) | |||||||
\(90\) | −80.5414 | −0.0943312 | ||||||||
\(91\) | 179.171 | 0.206398 | ||||||||
\(92\) | 1391.48 | 1.57687 | ||||||||
\(93\) | 775.889 | 0.865117 | ||||||||
\(94\) | −2180.75 | −2.39284 | ||||||||
\(95\) | 244.837 | 0.264418 | ||||||||
\(96\) | −766.353 | −0.814745 | ||||||||
\(97\) | −1342.63 | −1.40540 | −0.702700 | − | 0.711486i | \(-0.748022\pi\) | ||||
−0.702700 | + | 0.711486i | \(0.748022\pi\) | |||||||
\(98\) | 1340.68 | 1.38193 | ||||||||
\(99\) | 99.0000 | 0.100504 | ||||||||
\(100\) | −951.828 | −0.951828 | ||||||||
\(101\) | −173.566 | −0.170995 | −0.0854973 | − | 0.996338i | \(-0.527248\pi\) | ||||
−0.0854973 | + | 0.996338i | \(0.527248\pi\) | |||||||
\(102\) | −489.477 | −0.475152 | ||||||||
\(103\) | 1017.48 | 0.973348 | 0.486674 | − | 0.873584i | \(-0.338210\pi\) | ||||
0.486674 | + | 0.873584i | \(0.338210\pi\) | |||||||
\(104\) | 17.7720 | 0.0167566 | ||||||||
\(105\) | −17.9628 | −0.0166952 | ||||||||
\(106\) | −190.694 | −0.174734 | ||||||||
\(107\) | 1555.50 | 1.40538 | 0.702690 | − | 0.711496i | \(-0.251982\pi\) | ||||
0.702690 | + | 0.711496i | \(0.251982\pi\) | |||||||
\(108\) | −214.208 | −0.190854 | ||||||||
\(109\) | 2058.04 | 1.80848 | 0.904240 | − | 0.427025i | \(-0.140439\pi\) | ||||
0.904240 | + | 0.427025i | \(0.140439\pi\) | |||||||
\(110\) | −98.4395 | −0.0853258 | ||||||||
\(111\) | 56.6890 | 0.0484746 | ||||||||
\(112\) | −172.335 | −0.145394 | ||||||||
\(113\) | 748.711 | 0.623299 | 0.311650 | − | 0.950197i | \(-0.399118\pi\) | ||||
0.311650 | + | 0.950197i | \(0.399118\pi\) | |||||||
\(114\) | 1307.78 | 1.07443 | ||||||||
\(115\) | 393.210 | 0.318844 | ||||||||
\(116\) | −871.390 | −0.697470 | ||||||||
\(117\) | 603.776 | 0.477086 | ||||||||
\(118\) | 3247.64 | 2.53364 | ||||||||
\(119\) | −109.166 | −0.0840945 | ||||||||
\(120\) | −1.78173 | −0.00135541 | ||||||||
\(121\) | 121.000 | 0.0909091 | ||||||||
\(122\) | 243.493 | 0.180696 | ||||||||
\(123\) | 884.714 | 0.648552 | ||||||||
\(124\) | −2051.87 | −1.48600 | ||||||||
\(125\) | −549.211 | −0.392983 | ||||||||
\(126\) | −95.9476 | −0.0678388 | ||||||||
\(127\) | −463.434 | −0.323804 | −0.161902 | − | 0.986807i | \(-0.551763\pi\) | ||||
−0.161902 | + | 0.986807i | \(0.551763\pi\) | |||||||
\(128\) | −33.9076 | −0.0234144 | ||||||||
\(129\) | −361.573 | −0.246781 | ||||||||
\(130\) | −600.358 | −0.405037 | ||||||||
\(131\) | −1307.14 | −0.871794 | −0.435897 | − | 0.899997i | \(-0.643569\pi\) | ||||
−0.435897 | + | 0.899997i | \(0.643569\pi\) | |||||||
\(132\) | −261.810 | −0.172634 | ||||||||
\(133\) | 291.670 | 0.190158 | ||||||||
\(134\) | 1762.79 | 1.13643 | ||||||||
\(135\) | −60.5317 | −0.0385907 | ||||||||
\(136\) | −10.8282 | −0.00682728 | ||||||||
\(137\) | −445.612 | −0.277892 | −0.138946 | − | 0.990300i | \(-0.544371\pi\) | ||||
−0.138946 | + | 0.990300i | \(0.544371\pi\) | |||||||
\(138\) | 2100.31 | 1.29558 | ||||||||
\(139\) | 1680.60 | 1.02551 | 0.512757 | − | 0.858534i | \(-0.328624\pi\) | ||||
0.512757 | + | 0.858534i | \(0.328624\pi\) | |||||||
\(140\) | 47.5035 | 0.0286770 | ||||||||
\(141\) | −1638.96 | −0.978904 | ||||||||
\(142\) | 1177.99 | 0.696162 | ||||||||
\(143\) | 737.948 | 0.431541 | ||||||||
\(144\) | −580.739 | −0.336076 | ||||||||
\(145\) | −246.241 | −0.141029 | ||||||||
\(146\) | 3712.77 | 2.10460 | ||||||||
\(147\) | 1007.60 | 0.565344 | ||||||||
\(148\) | −149.917 | −0.0832640 | ||||||||
\(149\) | 1773.96 | 0.975359 | 0.487679 | − | 0.873023i | \(-0.337844\pi\) | ||||
0.487679 | + | 0.873023i | \(0.337844\pi\) | |||||||
\(150\) | −1436.70 | −0.782039 | ||||||||
\(151\) | −2289.22 | −1.23373 | −0.616867 | − | 0.787068i | \(-0.711598\pi\) | ||||
−0.616867 | + | 0.787068i | \(0.711598\pi\) | |||||||
\(152\) | 28.9307 | 0.0154381 | ||||||||
\(153\) | −367.872 | −0.194383 | ||||||||
\(154\) | −117.269 | −0.0613625 | ||||||||
\(155\) | −579.826 | −0.300469 | ||||||||
\(156\) | −1596.71 | −0.819483 | ||||||||
\(157\) | −3759.96 | −1.91132 | −0.955662 | − | 0.294466i | \(-0.904858\pi\) | ||||
−0.955662 | + | 0.294466i | \(0.904858\pi\) | |||||||
\(158\) | 402.201 | 0.202515 | ||||||||
\(159\) | −143.318 | −0.0714833 | ||||||||
\(160\) | 572.700 | 0.282974 | ||||||||
\(161\) | 468.424 | 0.229298 | ||||||||
\(162\) | −323.327 | −0.156809 | ||||||||
\(163\) | −1024.17 | −0.492142 | −0.246071 | − | 0.969252i | \(-0.579140\pi\) | ||||
−0.246071 | + | 0.969252i | \(0.579140\pi\) | |||||||
\(164\) | −2339.66 | −1.11401 | ||||||||
\(165\) | −73.9832 | −0.0349066 | ||||||||
\(166\) | 400.998 | 0.187491 | ||||||||
\(167\) | −844.133 | −0.391144 | −0.195572 | − | 0.980689i | \(-0.562656\pi\) | ||||
−0.195572 | + | 0.980689i | \(0.562656\pi\) | |||||||
\(168\) | −2.12255 | −0.000974751 0 | ||||||||
\(169\) | 2303.56 | 1.04850 | ||||||||
\(170\) | 365.789 | 0.165028 | ||||||||
\(171\) | 982.878 | 0.439547 | ||||||||
\(172\) | 956.197 | 0.423891 | ||||||||
\(173\) | 3389.52 | 1.48960 | 0.744799 | − | 0.667289i | \(-0.232546\pi\) | ||||
0.744799 | + | 0.667289i | \(0.232546\pi\) | |||||||
\(174\) | −1315.28 | −0.573053 | ||||||||
\(175\) | −320.421 | −0.138409 | ||||||||
\(176\) | −709.792 | −0.303992 | ||||||||
\(177\) | 2440.80 | 1.03651 | ||||||||
\(178\) | 5706.32 | 2.40285 | ||||||||
\(179\) | 4365.13 | 1.82271 | 0.911355 | − | 0.411622i | \(-0.135038\pi\) | ||||
0.911355 | + | 0.411622i | \(0.135038\pi\) | |||||||
\(180\) | 160.079 | 0.0662865 | ||||||||
\(181\) | −1511.96 | −0.620902 | −0.310451 | − | 0.950589i | \(-0.600480\pi\) | ||||
−0.310451 | + | 0.950589i | \(0.600480\pi\) | |||||||
\(182\) | −715.196 | −0.291285 | ||||||||
\(183\) | 183.000 | 0.0739221 | ||||||||
\(184\) | 46.4630 | 0.0186157 | ||||||||
\(185\) | −42.3640 | −0.0168360 | ||||||||
\(186\) | −3097.11 | −1.22092 | ||||||||
\(187\) | −449.621 | −0.175826 | ||||||||
\(188\) | 4334.31 | 1.68145 | ||||||||
\(189\) | −72.1104 | −0.0277527 | ||||||||
\(190\) | −977.314 | −0.373167 | ||||||||
\(191\) | 1053.18 | 0.398979 | 0.199490 | − | 0.979900i | \(-0.436072\pi\) | ||||
0.199490 | + | 0.979900i | \(0.436072\pi\) | |||||||
\(192\) | 1510.41 | 0.567732 | ||||||||
\(193\) | 2253.70 | 0.840544 | 0.420272 | − | 0.907398i | \(-0.361935\pi\) | ||||
0.420272 | + | 0.907398i | \(0.361935\pi\) | |||||||
\(194\) | 5359.39 | 1.98341 | ||||||||
\(195\) | −451.205 | −0.165700 | ||||||||
\(196\) | −2664.65 | −0.971081 | ||||||||
\(197\) | −1848.96 | −0.668697 | −0.334348 | − | 0.942450i | \(-0.608516\pi\) | ||||
−0.334348 | + | 0.942450i | \(0.608516\pi\) | |||||||
\(198\) | −395.178 | −0.141839 | ||||||||
\(199\) | −1951.91 | −0.695313 | −0.347656 | − | 0.937622i | \(-0.613022\pi\) | ||||
−0.347656 | + | 0.937622i | \(0.613022\pi\) | |||||||
\(200\) | −31.7825 | −0.0112368 | ||||||||
\(201\) | 1324.84 | 0.464911 | ||||||||
\(202\) | 692.823 | 0.241321 | ||||||||
\(203\) | −293.342 | −0.101422 | ||||||||
\(204\) | 972.853 | 0.333889 | ||||||||
\(205\) | −661.151 | −0.225253 | ||||||||
\(206\) | −4061.45 | −1.37366 | ||||||||
\(207\) | 1578.51 | 0.530020 | ||||||||
\(208\) | −4328.84 | −1.44303 | ||||||||
\(209\) | 1201.30 | 0.397586 | ||||||||
\(210\) | 71.7022 | 0.0235615 | ||||||||
\(211\) | 5704.16 | 1.86109 | 0.930547 | − | 0.366173i | \(-0.119332\pi\) | ||||
0.930547 | + | 0.366173i | \(0.119332\pi\) | |||||||
\(212\) | 379.010 | 0.122786 | ||||||||
\(213\) | 885.333 | 0.284798 | ||||||||
\(214\) | −6209.08 | −1.98338 | ||||||||
\(215\) | 270.206 | 0.0857110 | ||||||||
\(216\) | −7.15263 | −0.00225313 | ||||||||
\(217\) | −690.736 | −0.216084 | ||||||||
\(218\) | −8215.06 | −2.55227 | ||||||||
\(219\) | 2790.37 | 0.860986 | ||||||||
\(220\) | 195.652 | 0.0599584 | ||||||||
\(221\) | −2742.13 | −0.834639 | ||||||||
\(222\) | −226.285 | −0.0684111 | ||||||||
\(223\) | −5584.71 | −1.67704 | −0.838520 | − | 0.544871i | \(-0.816578\pi\) | ||||
−0.838520 | + | 0.544871i | \(0.816578\pi\) | |||||||
\(224\) | 682.247 | 0.203502 | ||||||||
\(225\) | −1079.76 | −0.319930 | ||||||||
\(226\) | −2988.63 | −0.879648 | ||||||||
\(227\) | −2667.31 | −0.779893 | −0.389946 | − | 0.920838i | \(-0.627506\pi\) | ||||
−0.389946 | + | 0.920838i | \(0.627506\pi\) | |||||||
\(228\) | −2599.27 | −0.755003 | ||||||||
\(229\) | 1342.31 | 0.387346 | 0.193673 | − | 0.981066i | \(-0.437960\pi\) | ||||
0.193673 | + | 0.981066i | \(0.437960\pi\) | |||||||
\(230\) | −1569.57 | −0.449977 | ||||||||
\(231\) | −88.1349 | −0.0251033 | ||||||||
\(232\) | −29.0966 | −0.00823400 | ||||||||
\(233\) | 1278.88 | 0.359579 | 0.179790 | − | 0.983705i | \(-0.442458\pi\) | ||||
0.179790 | + | 0.983705i | \(0.442458\pi\) | |||||||
\(234\) | −2410.09 | −0.673301 | ||||||||
\(235\) | 1224.81 | 0.339989 | ||||||||
\(236\) | −6454.80 | −1.78039 | ||||||||
\(237\) | 302.279 | 0.0828485 | ||||||||
\(238\) | 435.758 | 0.118681 | ||||||||
\(239\) | 4266.39 | 1.15469 | 0.577343 | − | 0.816502i | \(-0.304090\pi\) | ||||
0.577343 | + | 0.816502i | \(0.304090\pi\) | |||||||
\(240\) | 433.989 | 0.116725 | ||||||||
\(241\) | −2907.71 | −0.777186 | −0.388593 | − | 0.921409i | \(-0.627039\pi\) | ||||
−0.388593 | + | 0.921409i | \(0.627039\pi\) | |||||||
\(242\) | −482.995 | −0.128298 | ||||||||
\(243\) | −243.000 | −0.0641500 | ||||||||
\(244\) | −483.952 | −0.126975 | ||||||||
\(245\) | −752.986 | −0.196353 | ||||||||
\(246\) | −3531.51 | −0.915287 | ||||||||
\(247\) | 7326.40 | 1.88732 | ||||||||
\(248\) | −68.5142 | −0.0175430 | ||||||||
\(249\) | 301.374 | 0.0767021 | ||||||||
\(250\) | 2192.28 | 0.554608 | ||||||||
\(251\) | 6253.33 | 1.57254 | 0.786268 | − | 0.617885i | \(-0.212010\pi\) | ||||
0.786268 | + | 0.617885i | \(0.212010\pi\) | |||||||
\(252\) | 190.699 | 0.0476703 | ||||||||
\(253\) | 1929.29 | 0.479421 | ||||||||
\(254\) | 1849.89 | 0.456978 | ||||||||
\(255\) | 274.913 | 0.0675125 | ||||||||
\(256\) | 4163.11 | 1.01638 | ||||||||
\(257\) | 4501.11 | 1.09250 | 0.546248 | − | 0.837623i | \(-0.316056\pi\) | ||||
0.546248 | + | 0.837623i | \(0.316056\pi\) | |||||||
\(258\) | 1443.29 | 0.348276 | ||||||||
\(259\) | −50.4675 | −0.0121077 | ||||||||
\(260\) | 1193.23 | 0.284620 | ||||||||
\(261\) | −988.514 | −0.234435 | ||||||||
\(262\) | 5217.69 | 1.23034 | ||||||||
\(263\) | −6667.74 | −1.56331 | −0.781655 | − | 0.623711i | \(-0.785624\pi\) | ||||
−0.781655 | + | 0.623711i | \(0.785624\pi\) | |||||||
\(264\) | −8.74211 | −0.00203803 | ||||||||
\(265\) | 107.102 | 0.0248273 | ||||||||
\(266\) | −1164.26 | −0.268365 | ||||||||
\(267\) | 4288.64 | 0.982999 | ||||||||
\(268\) | −3503.61 | −0.798570 | ||||||||
\(269\) | 3321.01 | 0.752735 | 0.376367 | − | 0.926471i | \(-0.377173\pi\) | ||||
0.376367 | + | 0.926471i | \(0.377173\pi\) | |||||||
\(270\) | 241.624 | 0.0544622 | ||||||||
\(271\) | −5905.76 | −1.32380 | −0.661900 | − | 0.749592i | \(-0.730250\pi\) | ||||
−0.661900 | + | 0.749592i | \(0.730250\pi\) | |||||||
\(272\) | 2637.50 | 0.587948 | ||||||||
\(273\) | −537.513 | −0.119164 | ||||||||
\(274\) | 1778.75 | 0.392183 | ||||||||
\(275\) | −1319.71 | −0.289388 | ||||||||
\(276\) | −4174.44 | −0.910405 | ||||||||
\(277\) | −5094.03 | −1.10495 | −0.552474 | − | 0.833530i | \(-0.686316\pi\) | ||||
−0.552474 | + | 0.833530i | \(0.686316\pi\) | |||||||
\(278\) | −6708.44 | −1.44728 | ||||||||
\(279\) | −2327.67 | −0.499476 | ||||||||
\(280\) | 1.58619 | 0.000338547 0 | ||||||||
\(281\) | 7481.11 | 1.58821 | 0.794103 | − | 0.607784i | \(-0.207941\pi\) | ||||
0.794103 | + | 0.607784i | \(0.207941\pi\) | |||||||
\(282\) | 6542.24 | 1.38151 | ||||||||
\(283\) | −7206.27 | −1.51367 | −0.756835 | − | 0.653606i | \(-0.773255\pi\) | ||||
−0.756835 | + | 0.653606i | \(0.773255\pi\) | |||||||
\(284\) | −2341.30 | −0.489193 | ||||||||
\(285\) | −734.510 | −0.152662 | ||||||||
\(286\) | −2945.67 | −0.609024 | ||||||||
\(287\) | −787.618 | −0.161992 | ||||||||
\(288\) | 2299.06 | 0.470393 | ||||||||
\(289\) | −3242.26 | −0.659936 | ||||||||
\(290\) | 982.918 | 0.199031 | ||||||||
\(291\) | 4027.90 | 0.811408 | ||||||||
\(292\) | −7379.27 | −1.47890 | ||||||||
\(293\) | −2913.02 | −0.580820 | −0.290410 | − | 0.956902i | \(-0.593792\pi\) | ||||
−0.290410 | + | 0.956902i | \(0.593792\pi\) | |||||||
\(294\) | −4022.04 | −0.797857 | ||||||||
\(295\) | −1824.02 | −0.359996 | ||||||||
\(296\) | −5.00587 | −0.000982975 0 | ||||||||
\(297\) | −297.000 | −0.0580259 | ||||||||
\(298\) | −7081.11 | −1.37650 | ||||||||
\(299\) | 11766.3 | 2.27579 | ||||||||
\(300\) | 2855.48 | 0.549538 | ||||||||
\(301\) | 321.891 | 0.0616395 | ||||||||
\(302\) | 9137.85 | 1.74114 | ||||||||
\(303\) | 520.698 | 0.0987238 | ||||||||
\(304\) | −7046.86 | −1.32949 | ||||||||
\(305\) | −136.757 | −0.0256744 | ||||||||
\(306\) | 1468.43 | 0.274329 | ||||||||
\(307\) | 7775.77 | 1.44556 | 0.722780 | − | 0.691078i | \(-0.242864\pi\) | ||||
0.722780 | + | 0.691078i | \(0.242864\pi\) | |||||||
\(308\) | 233.077 | 0.0431194 | ||||||||
\(309\) | −3052.43 | −0.561963 | ||||||||
\(310\) | 2314.49 | 0.424046 | ||||||||
\(311\) | −8046.28 | −1.46708 | −0.733542 | − | 0.679645i | \(-0.762134\pi\) | ||||
−0.733542 | + | 0.679645i | \(0.762134\pi\) | |||||||
\(312\) | −53.3159 | −0.00967442 | ||||||||
\(313\) | 295.432 | 0.0533508 | 0.0266754 | − | 0.999644i | \(-0.491508\pi\) | ||||
0.0266754 | + | 0.999644i | \(0.491508\pi\) | |||||||
\(314\) | 15008.6 | 2.69741 | ||||||||
\(315\) | 53.8885 | 0.00963896 | ||||||||
\(316\) | −799.389 | −0.142307 | ||||||||
\(317\) | 1289.69 | 0.228505 | 0.114253 | − | 0.993452i | \(-0.463553\pi\) | ||||
0.114253 | + | 0.993452i | \(0.463553\pi\) | |||||||
\(318\) | 572.081 | 0.100883 | ||||||||
\(319\) | −1208.18 | −0.212054 | ||||||||
\(320\) | −1128.74 | −0.197182 | ||||||||
\(321\) | −4666.50 | −0.811397 | ||||||||
\(322\) | −1869.81 | −0.323603 | ||||||||
\(323\) | −4463.87 | −0.768967 | ||||||||
\(324\) | 642.624 | 0.110189 | ||||||||
\(325\) | −8048.59 | −1.37371 | ||||||||
\(326\) | 4088.17 | 0.694548 | ||||||||
\(327\) | −6174.11 | −1.04413 | ||||||||
\(328\) | −78.1239 | −0.0131514 | ||||||||
\(329\) | 1459.09 | 0.244505 | ||||||||
\(330\) | 295.319 | 0.0492629 | ||||||||
\(331\) | −6123.95 | −1.01693 | −0.508463 | − | 0.861084i | \(-0.669786\pi\) | ||||
−0.508463 | + | 0.861084i | \(0.669786\pi\) | |||||||
\(332\) | −796.998 | −0.131750 | ||||||||
\(333\) | −170.067 | −0.0279868 | ||||||||
\(334\) | 3369.52 | 0.552012 | ||||||||
\(335\) | −990.062 | −0.161471 | ||||||||
\(336\) | 517.004 | 0.0839430 | ||||||||
\(337\) | −6824.24 | −1.10309 | −0.551543 | − | 0.834146i | \(-0.685961\pi\) | ||||
−0.551543 | + | 0.834146i | \(0.685961\pi\) | |||||||
\(338\) | −9195.11 | −1.47973 | ||||||||
\(339\) | −2246.13 | −0.359862 | ||||||||
\(340\) | −727.019 | −0.115965 | ||||||||
\(341\) | −2844.93 | −0.451793 | ||||||||
\(342\) | −3923.35 | −0.620323 | ||||||||
\(343\) | −1813.09 | −0.285416 | ||||||||
\(344\) | 31.9284 | 0.00500426 | ||||||||
\(345\) | −1179.63 | −0.184084 | ||||||||
\(346\) | −13529.9 | −2.10224 | ||||||||
\(347\) | 6039.69 | 0.934373 | 0.467187 | − | 0.884159i | \(-0.345268\pi\) | ||||
0.467187 | + | 0.884159i | \(0.345268\pi\) | |||||||
\(348\) | 2614.17 | 0.402684 | ||||||||
\(349\) | −8066.34 | −1.23720 | −0.618598 | − | 0.785708i | \(-0.712299\pi\) | ||||
−0.618598 | + | 0.785708i | \(0.712299\pi\) | |||||||
\(350\) | 1279.02 | 0.195333 | ||||||||
\(351\) | −1811.33 | −0.275446 | ||||||||
\(352\) | 2809.96 | 0.425487 | ||||||||
\(353\) | −3512.75 | −0.529645 | −0.264823 | − | 0.964297i | \(-0.585313\pi\) | ||||
−0.264823 | + | 0.964297i | \(0.585313\pi\) | |||||||
\(354\) | −9742.93 | −1.46280 | ||||||||
\(355\) | −661.614 | −0.0989150 | ||||||||
\(356\) | −11341.5 | −1.68848 | ||||||||
\(357\) | 327.499 | 0.0485520 | ||||||||
\(358\) | −17424.3 | −2.57235 | ||||||||
\(359\) | −11407.4 | −1.67705 | −0.838524 | − | 0.544864i | \(-0.816581\pi\) | ||||
−0.838524 | + | 0.544864i | \(0.816581\pi\) | |||||||
\(360\) | 5.34520 | 0.000782547 0 | ||||||||
\(361\) | 5067.54 | 0.738817 | ||||||||
\(362\) | 6035.29 | 0.876265 | ||||||||
\(363\) | −363.000 | −0.0524864 | ||||||||
\(364\) | 1421.48 | 0.204686 | ||||||||
\(365\) | −2085.26 | −0.299034 | ||||||||
\(366\) | −730.480 | −0.104325 | ||||||||
\(367\) | −900.420 | −0.128070 | −0.0640348 | − | 0.997948i | \(-0.520397\pi\) | ||||
−0.0640348 | + | 0.997948i | \(0.520397\pi\) | |||||||
\(368\) | −11317.3 | −1.60314 | ||||||||
\(369\) | −2654.14 | −0.374442 | ||||||||
\(370\) | 169.104 | 0.0237603 | ||||||||
\(371\) | 127.589 | 0.0178547 | ||||||||
\(372\) | 6155.62 | 0.857941 | ||||||||
\(373\) | 4846.74 | 0.672800 | 0.336400 | − | 0.941719i | \(-0.390791\pi\) | ||||
0.336400 | + | 0.941719i | \(0.390791\pi\) | |||||||
\(374\) | 1794.75 | 0.248140 | ||||||||
\(375\) | 1647.63 | 0.226889 | ||||||||
\(376\) | 144.727 | 0.0198503 | ||||||||
\(377\) | −7368.41 | −1.00661 | ||||||||
\(378\) | 287.843 | 0.0391668 | ||||||||
\(379\) | −14352.1 | −1.94517 | −0.972585 | − | 0.232549i | \(-0.925294\pi\) | ||||
−0.972585 | + | 0.232549i | \(0.925294\pi\) | |||||||
\(380\) | 1942.45 | 0.262225 | ||||||||
\(381\) | 1390.30 | 0.186949 | ||||||||
\(382\) | −4203.95 | −0.563071 | ||||||||
\(383\) | −5901.76 | −0.787378 | −0.393689 | − | 0.919244i | \(-0.628801\pi\) | ||||
−0.393689 | + | 0.919244i | \(0.628801\pi\) | |||||||
\(384\) | 101.723 | 0.0135183 | ||||||||
\(385\) | 65.8637 | 0.00871877 | ||||||||
\(386\) | −8996.10 | −1.18624 | ||||||||
\(387\) | 1084.72 | 0.142479 | ||||||||
\(388\) | −10652.0 | −1.39374 | ||||||||
\(389\) | 12187.1 | 1.58845 | 0.794226 | − | 0.607622i | \(-0.207876\pi\) | ||||
0.794226 | + | 0.607622i | \(0.207876\pi\) | |||||||
\(390\) | 1801.07 | 0.233848 | ||||||||
\(391\) | −7169.01 | −0.927244 | ||||||||
\(392\) | −88.9753 | −0.0114641 | ||||||||
\(393\) | 3921.41 | 0.503330 | ||||||||
\(394\) | 7380.51 | 0.943717 | ||||||||
\(395\) | −225.894 | −0.0287746 | ||||||||
\(396\) | 785.430 | 0.0996700 | ||||||||
\(397\) | −8268.63 | −1.04532 | −0.522658 | − | 0.852542i | \(-0.675060\pi\) | ||||
−0.522658 | + | 0.852542i | \(0.675060\pi\) | |||||||
\(398\) | 7791.43 | 0.981279 | ||||||||
\(399\) | −875.009 | −0.109788 | ||||||||
\(400\) | 7741.49 | 0.967687 | ||||||||
\(401\) | −7799.16 | −0.971251 | −0.485626 | − | 0.874167i | \(-0.661408\pi\) | ||||
−0.485626 | + | 0.874167i | \(0.661408\pi\) | |||||||
\(402\) | −5288.37 | −0.656119 | ||||||||
\(403\) | −17350.5 | −2.14464 | ||||||||
\(404\) | −1377.01 | −0.169576 | ||||||||
\(405\) | 181.595 | 0.0222803 | ||||||||
\(406\) | 1170.93 | 0.143134 | ||||||||
\(407\) | −207.860 | −0.0253150 | ||||||||
\(408\) | 32.4846 | 0.00394173 | ||||||||
\(409\) | −6821.09 | −0.824649 | −0.412324 | − | 0.911037i | \(-0.635283\pi\) | ||||
−0.412324 | + | 0.911037i | \(0.635283\pi\) | |||||||
\(410\) | 2639.11 | 0.317894 | ||||||||
\(411\) | 1336.84 | 0.160441 | ||||||||
\(412\) | 8072.28 | 0.965273 | ||||||||
\(413\) | −2172.93 | −0.258893 | ||||||||
\(414\) | −6300.93 | −0.748005 | ||||||||
\(415\) | −225.219 | −0.0266399 | ||||||||
\(416\) | 17137.2 | 2.01976 | ||||||||
\(417\) | −5041.79 | −0.592081 | ||||||||
\(418\) | −4795.21 | −0.561103 | ||||||||
\(419\) | 13676.3 | 1.59458 | 0.797290 | − | 0.603596i | \(-0.206266\pi\) | ||||
0.797290 | + | 0.603596i | \(0.206266\pi\) | |||||||
\(420\) | −142.511 | −0.0165567 | ||||||||
\(421\) | −8428.78 | −0.975757 | −0.487879 | − | 0.872911i | \(-0.662229\pi\) | ||||
−0.487879 | + | 0.872911i | \(0.662229\pi\) | |||||||
\(422\) | −22769.3 | −2.62652 | ||||||||
\(423\) | 4916.89 | 0.565171 | ||||||||
\(424\) | 12.6556 | 0.00144955 | ||||||||
\(425\) | 4903.89 | 0.559702 | ||||||||
\(426\) | −3533.98 | −0.401929 | ||||||||
\(427\) | −162.916 | −0.0184638 | ||||||||
\(428\) | 12340.8 | 1.39372 | ||||||||
\(429\) | −2213.85 | −0.249150 | ||||||||
\(430\) | −1078.58 | −0.120962 | ||||||||
\(431\) | −4529.29 | −0.506191 | −0.253096 | − | 0.967441i | \(-0.581449\pi\) | ||||
−0.253096 | + | 0.967441i | \(0.581449\pi\) | |||||||
\(432\) | 1742.22 | 0.194033 | ||||||||
\(433\) | −3706.69 | −0.411391 | −0.205696 | − | 0.978616i | \(-0.565946\pi\) | ||||
−0.205696 | + | 0.978616i | \(0.565946\pi\) | |||||||
\(434\) | 2757.21 | 0.304955 | ||||||||
\(435\) | 738.722 | 0.0814230 | ||||||||
\(436\) | 16327.7 | 1.79348 | ||||||||
\(437\) | 19154.1 | 2.09672 | ||||||||
\(438\) | −11138.3 | −1.21509 | ||||||||
\(439\) | −12906.1 | −1.40313 | −0.701567 | − | 0.712603i | \(-0.747516\pi\) | ||||
−0.701567 | + | 0.712603i | \(0.747516\pi\) | |||||||
\(440\) | 6.53303 | 0.000707840 0 | ||||||||
\(441\) | −3022.80 | −0.326401 | ||||||||
\(442\) | 10945.7 | 1.17791 | ||||||||
\(443\) | −9858.29 | −1.05730 | −0.528648 | − | 0.848841i | \(-0.677301\pi\) | ||||
−0.528648 | + | 0.848841i | \(0.677301\pi\) | |||||||
\(444\) | 449.750 | 0.0480725 | ||||||||
\(445\) | −3204.93 | −0.341411 | ||||||||
\(446\) | 22292.5 | 2.36677 | ||||||||
\(447\) | −5321.88 | −0.563124 | ||||||||
\(448\) | −1344.65 | −0.141805 | ||||||||
\(449\) | 12701.1 | 1.33497 | 0.667484 | − | 0.744624i | \(-0.267371\pi\) | ||||
0.667484 | + | 0.744624i | \(0.267371\pi\) | |||||||
\(450\) | 4310.09 | 0.451510 | ||||||||
\(451\) | −3243.95 | −0.338695 | ||||||||
\(452\) | 5940.00 | 0.618129 | ||||||||
\(453\) | 6867.65 | 0.712296 | ||||||||
\(454\) | 10647.1 | 1.10065 | ||||||||
\(455\) | 401.686 | 0.0413876 | ||||||||
\(456\) | −86.7922 | −0.00891320 | ||||||||
\(457\) | −5788.98 | −0.592554 | −0.296277 | − | 0.955102i | \(-0.595745\pi\) | ||||
−0.296277 | + | 0.955102i | \(0.595745\pi\) | |||||||
\(458\) | −5358.09 | −0.546653 | ||||||||
\(459\) | 1103.62 | 0.112227 | ||||||||
\(460\) | 3119.58 | 0.316199 | ||||||||
\(461\) | 2120.81 | 0.214265 | 0.107132 | − | 0.994245i | \(-0.465833\pi\) | ||||
0.107132 | + | 0.994245i | \(0.465833\pi\) | |||||||
\(462\) | 351.808 | 0.0354277 | ||||||||
\(463\) | 13567.7 | 1.36187 | 0.680933 | − | 0.732346i | \(-0.261575\pi\) | ||||
0.680933 | + | 0.732346i | \(0.261575\pi\) | |||||||
\(464\) | 7087.26 | 0.709090 | ||||||||
\(465\) | 1739.48 | 0.173476 | ||||||||
\(466\) | −5104.89 | −0.507466 | ||||||||
\(467\) | 2315.82 | 0.229472 | 0.114736 | − | 0.993396i | \(-0.463398\pi\) | ||||
0.114736 | + | 0.993396i | \(0.463398\pi\) | |||||||
\(468\) | 4790.14 | 0.473129 | ||||||||
\(469\) | −1179.44 | −0.116123 | ||||||||
\(470\) | −4889.05 | −0.479819 | ||||||||
\(471\) | 11279.9 | 1.10350 | ||||||||
\(472\) | −215.533 | −0.0210184 | ||||||||
\(473\) | 1325.77 | 0.128877 | ||||||||
\(474\) | −1206.60 | −0.116922 | ||||||||
\(475\) | −13102.2 | −1.26562 | ||||||||
\(476\) | −866.085 | −0.0833969 | ||||||||
\(477\) | 429.953 | 0.0412709 | ||||||||
\(478\) | −17030.1 | −1.62958 | ||||||||
\(479\) | −7486.16 | −0.714094 | −0.357047 | − | 0.934086i | \(-0.616216\pi\) | ||||
−0.357047 | + | 0.934086i | \(0.616216\pi\) | |||||||
\(480\) | −1718.10 | −0.163375 | ||||||||
\(481\) | −1267.68 | −0.120169 | ||||||||
\(482\) | 11606.7 | 1.09683 | ||||||||
\(483\) | −1405.27 | −0.132385 | ||||||||
\(484\) | 959.970 | 0.0901549 | ||||||||
\(485\) | −3010.07 | −0.281815 | ||||||||
\(486\) | 969.982 | 0.0905335 | ||||||||
\(487\) | 13430.0 | 1.24964 | 0.624818 | − | 0.780771i | \(-0.285173\pi\) | ||||
0.624818 | + | 0.780771i | \(0.285173\pi\) | |||||||
\(488\) | −16.1597 | −0.00149900 | ||||||||
\(489\) | 3072.51 | 0.284138 | ||||||||
\(490\) | 3005.69 | 0.277109 | ||||||||
\(491\) | −16271.7 | −1.49559 | −0.747793 | − | 0.663932i | \(-0.768886\pi\) | ||||
−0.747793 | + | 0.663932i | \(0.768886\pi\) | |||||||
\(492\) | 7018.99 | 0.643172 | ||||||||
\(493\) | 4489.46 | 0.410132 | ||||||||
\(494\) | −29244.8 | −2.66353 | ||||||||
\(495\) | 221.950 | 0.0201533 | ||||||||
\(496\) | 16688.5 | 1.51075 | ||||||||
\(497\) | −788.169 | −0.0711352 | ||||||||
\(498\) | −1203.00 | −0.108248 | ||||||||
\(499\) | 5012.15 | 0.449648 | 0.224824 | − | 0.974399i | \(-0.427819\pi\) | ||||
0.224824 | + | 0.974399i | \(0.427819\pi\) | |||||||
\(500\) | −4357.24 | −0.389723 | ||||||||
\(501\) | 2532.40 | 0.225827 | ||||||||
\(502\) | −24961.4 | −2.21929 | ||||||||
\(503\) | −5118.34 | −0.453709 | −0.226854 | − | 0.973929i | \(-0.572844\pi\) | ||||
−0.226854 | + | 0.973929i | \(0.572844\pi\) | |||||||
\(504\) | 6.36765 | 0.000562773 0 | ||||||||
\(505\) | −389.120 | −0.0342884 | ||||||||
\(506\) | −7701.14 | −0.676596 | ||||||||
\(507\) | −6910.68 | −0.605353 | ||||||||
\(508\) | −3676.72 | −0.321118 | ||||||||
\(509\) | 16458.7 | 1.43324 | 0.716619 | − | 0.697464i | \(-0.245688\pi\) | ||||
0.716619 | + | 0.697464i | \(0.245688\pi\) | |||||||
\(510\) | −1097.37 | −0.0952789 | ||||||||
\(511\) | −2484.13 | −0.215052 | ||||||||
\(512\) | −16346.6 | −1.41099 | ||||||||
\(513\) | −2948.64 | −0.253773 | ||||||||
\(514\) | −17967.1 | −1.54182 | ||||||||
\(515\) | 2281.10 | 0.195179 | ||||||||
\(516\) | −2868.59 | −0.244734 | ||||||||
\(517\) | 6009.53 | 0.511216 | ||||||||
\(518\) | 201.451 | 0.0170873 | ||||||||
\(519\) | −10168.6 | −0.860019 | ||||||||
\(520\) | 39.8433 | 0.00336008 | ||||||||
\(521\) | −3408.90 | −0.286654 | −0.143327 | − | 0.989675i | \(-0.545780\pi\) | ||||
−0.143327 | + | 0.989675i | \(0.545780\pi\) | |||||||
\(522\) | 3945.85 | 0.330853 | ||||||||
\(523\) | 2755.28 | 0.230363 | 0.115182 | − | 0.993344i | \(-0.463255\pi\) | ||||
0.115182 | + | 0.993344i | \(0.463255\pi\) | |||||||
\(524\) | −10370.3 | −0.864562 | ||||||||
\(525\) | 961.262 | 0.0799103 | ||||||||
\(526\) | 26615.6 | 2.20626 | ||||||||
\(527\) | 10571.4 | 0.873809 | ||||||||
\(528\) | 2129.38 | 0.175510 | ||||||||
\(529\) | 18594.7 | 1.52829 | ||||||||
\(530\) | −427.519 | −0.0350382 | ||||||||
\(531\) | −7322.40 | −0.598427 | ||||||||
\(532\) | 2314.00 | 0.188580 | ||||||||
\(533\) | −19784.0 | −1.60777 | ||||||||
\(534\) | −17119.0 | −1.38728 | ||||||||
\(535\) | 3487.30 | 0.281811 | ||||||||
\(536\) | −116.989 | −0.00942753 | ||||||||
\(537\) | −13095.4 | −1.05234 | ||||||||
\(538\) | −13256.5 | −1.06232 | ||||||||
\(539\) | −3694.54 | −0.295241 | ||||||||
\(540\) | −480.237 | −0.0382705 | ||||||||
\(541\) | −16902.5 | −1.34325 | −0.671624 | − | 0.740892i | \(-0.734403\pi\) | ||||
−0.671624 | + | 0.740892i | \(0.734403\pi\) | |||||||
\(542\) | 23574.0 | 1.86825 | ||||||||
\(543\) | 4535.89 | 0.358478 | ||||||||
\(544\) | −10441.5 | −0.822930 | ||||||||
\(545\) | 4613.95 | 0.362642 | ||||||||
\(546\) | 2145.59 | 0.168173 | ||||||||
\(547\) | 7298.36 | 0.570485 | 0.285243 | − | 0.958455i | \(-0.407926\pi\) | ||||
0.285243 | + | 0.958455i | \(0.407926\pi\) | |||||||
\(548\) | −3535.33 | −0.275587 | ||||||||
\(549\) | −549.000 | −0.0426790 | ||||||||
\(550\) | 5267.89 | 0.408406 | ||||||||
\(551\) | −11994.9 | −0.927407 | ||||||||
\(552\) | −139.389 | −0.0107478 | ||||||||
\(553\) | −269.104 | −0.0206934 | ||||||||
\(554\) | 20333.8 | 1.55939 | ||||||||
\(555\) | 127.092 | 0.00972028 | ||||||||
\(556\) | 13333.2 | 1.01701 | ||||||||
\(557\) | −10198.5 | −0.775807 | −0.387904 | − | 0.921700i | \(-0.626801\pi\) | ||||
−0.387904 | + | 0.921700i | \(0.626801\pi\) | |||||||
\(558\) | 9291.34 | 0.704899 | ||||||||
\(559\) | 8085.53 | 0.611773 | ||||||||
\(560\) | −386.360 | −0.0291548 | ||||||||
\(561\) | 1348.86 | 0.101513 | ||||||||
\(562\) | −29862.3 | −2.24140 | ||||||||
\(563\) | −26648.5 | −1.99485 | −0.997426 | − | 0.0717064i | \(-0.977156\pi\) | ||||
−0.997426 | + | 0.0717064i | \(0.977156\pi\) | |||||||
\(564\) | −13002.9 | −0.970783 | ||||||||
\(565\) | 1678.55 | 0.124986 | ||||||||
\(566\) | 28765.2 | 2.13621 | ||||||||
\(567\) | 216.331 | 0.0160230 | ||||||||
\(568\) | −78.1785 | −0.00577517 | ||||||||
\(569\) | 22863.4 | 1.68451 | 0.842254 | − | 0.539080i | \(-0.181228\pi\) | ||||
0.842254 | + | 0.539080i | \(0.181228\pi\) | |||||||
\(570\) | 2931.94 | 0.215448 | ||||||||
\(571\) | 6252.57 | 0.458252 | 0.229126 | − | 0.973397i | \(-0.426413\pi\) | ||||
0.229126 | + | 0.973397i | \(0.426413\pi\) | |||||||
\(572\) | 5854.61 | 0.427961 | ||||||||
\(573\) | −3159.53 | −0.230351 | ||||||||
\(574\) | 3143.93 | 0.228615 | ||||||||
\(575\) | −21042.2 | −1.52612 | ||||||||
\(576\) | −4531.23 | −0.327780 | ||||||||
\(577\) | 10199.7 | 0.735906 | 0.367953 | − | 0.929844i | \(-0.380059\pi\) | ||||
0.367953 | + | 0.929844i | \(0.380059\pi\) | |||||||
\(578\) | 12942.1 | 0.931352 | ||||||||
\(579\) | −6761.11 | −0.485289 | ||||||||
\(580\) | −1953.58 | −0.139859 | ||||||||
\(581\) | −268.299 | −0.0191582 | ||||||||
\(582\) | −16078.2 | −1.14512 | ||||||||
\(583\) | 525.499 | 0.0373309 | ||||||||
\(584\) | −246.401 | −0.0174592 | ||||||||
\(585\) | 1353.62 | 0.0956668 | ||||||||
\(586\) | 11627.9 | 0.819698 | ||||||||
\(587\) | −1668.87 | −0.117345 | −0.0586724 | − | 0.998277i | \(-0.518687\pi\) | ||||
−0.0586724 | + | 0.998277i | \(0.518687\pi\) | |||||||
\(588\) | 7993.94 | 0.560654 | ||||||||
\(589\) | −28244.6 | −1.97589 | ||||||||
\(590\) | 7280.94 | 0.508054 | ||||||||
\(591\) | 5546.89 | 0.386072 | ||||||||
\(592\) | 1219.32 | 0.0846512 | ||||||||
\(593\) | 10622.3 | 0.735594 | 0.367797 | − | 0.929906i | \(-0.380112\pi\) | ||||
0.367797 | + | 0.929906i | \(0.380112\pi\) | |||||||
\(594\) | 1185.53 | 0.0818906 | ||||||||
\(595\) | −244.741 | −0.0168629 | ||||||||
\(596\) | 14073.9 | 0.967267 | ||||||||
\(597\) | 5855.73 | 0.401439 | ||||||||
\(598\) | −46967.3 | −3.21177 | ||||||||
\(599\) | −9284.75 | −0.633330 | −0.316665 | − | 0.948538i | \(-0.602563\pi\) | ||||
−0.316665 | + | 0.948538i | \(0.602563\pi\) | |||||||
\(600\) | 95.3476 | 0.00648759 | ||||||||
\(601\) | −15104.7 | −1.02518 | −0.512589 | − | 0.858634i | \(-0.671313\pi\) | ||||
−0.512589 | + | 0.858634i | \(0.671313\pi\) | |||||||
\(602\) | −1284.89 | −0.0869905 | ||||||||
\(603\) | −3974.53 | −0.268417 | ||||||||
\(604\) | −18161.8 | −1.22350 | ||||||||
\(605\) | 271.272 | 0.0182294 | ||||||||
\(606\) | −2078.47 | −0.139327 | ||||||||
\(607\) | 2067.69 | 0.138262 | 0.0691310 | − | 0.997608i | \(-0.477977\pi\) | ||||
0.0691310 | + | 0.997608i | \(0.477977\pi\) | |||||||
\(608\) | 27897.5 | 1.86084 | ||||||||
\(609\) | 880.026 | 0.0585558 | ||||||||
\(610\) | 545.892 | 0.0362336 | ||||||||
\(611\) | 36650.6 | 2.42672 | ||||||||
\(612\) | −2918.56 | −0.192771 | ||||||||
\(613\) | 27466.8 | 1.80975 | 0.904873 | − | 0.425682i | \(-0.139966\pi\) | ||||
0.904873 | + | 0.425682i | \(0.139966\pi\) | |||||||
\(614\) | −31038.5 | −2.04009 | ||||||||
\(615\) | 1983.45 | 0.130050 | ||||||||
\(616\) | 7.78268 | 0.000509047 0 | ||||||||
\(617\) | −5072.67 | −0.330985 | −0.165493 | − | 0.986211i | \(-0.552921\pi\) | ||||
−0.165493 | + | 0.986211i | \(0.552921\pi\) | |||||||
\(618\) | 12184.4 | 0.793085 | ||||||||
\(619\) | 17665.2 | 1.14705 | 0.573525 | − | 0.819188i | \(-0.305575\pi\) | ||||
0.573525 | + | 0.819188i | \(0.305575\pi\) | |||||||
\(620\) | −4600.13 | −0.297977 | ||||||||
\(621\) | −4735.53 | −0.306007 | ||||||||
\(622\) | 32118.3 | 2.07046 | ||||||||
\(623\) | −3817.97 | −0.245528 | ||||||||
\(624\) | 12986.5 | 0.833136 | ||||||||
\(625\) | 13765.4 | 0.880988 | ||||||||
\(626\) | −1179.27 | −0.0752928 | ||||||||
\(627\) | −3603.89 | −0.229546 | ||||||||
\(628\) | −29830.2 | −1.89547 | ||||||||
\(629\) | 772.381 | 0.0489616 | ||||||||
\(630\) | −215.106 | −0.0136032 | ||||||||
\(631\) | −18056.7 | −1.13918 | −0.569592 | − | 0.821927i | \(-0.692899\pi\) | ||||
−0.569592 | + | 0.821927i | \(0.692899\pi\) | |||||||
\(632\) | −26.6924 | −0.00168001 | ||||||||
\(633\) | −17112.5 | −1.07450 | ||||||||
\(634\) | −5148.05 | −0.322484 | ||||||||
\(635\) | −1038.98 | −0.0649302 | ||||||||
\(636\) | −1137.03 | −0.0708903 | ||||||||
\(637\) | −22532.1 | −1.40150 | ||||||||
\(638\) | 4822.70 | 0.299267 | ||||||||
\(639\) | −2656.00 | −0.164428 | ||||||||
\(640\) | −76.0180 | −0.00469512 | ||||||||
\(641\) | −6459.28 | −0.398013 | −0.199006 | − | 0.979998i | \(-0.563771\pi\) | ||||
−0.199006 | + | 0.979998i | \(0.563771\pi\) | |||||||
\(642\) | 18627.2 | 1.14511 | ||||||||
\(643\) | −20371.7 | −1.24943 | −0.624713 | − | 0.780854i | \(-0.714784\pi\) | ||||
−0.624713 | + | 0.780854i | \(0.714784\pi\) | |||||||
\(644\) | 3716.30 | 0.227396 | ||||||||
\(645\) | −810.617 | −0.0494853 | ||||||||
\(646\) | 17818.4 | 1.08523 | ||||||||
\(647\) | −16697.8 | −1.01462 | −0.507309 | − | 0.861764i | \(-0.669360\pi\) | ||||
−0.507309 | + | 0.861764i | \(0.669360\pi\) | |||||||
\(648\) | 21.4579 | 0.00130084 | ||||||||
\(649\) | −8949.60 | −0.541298 | ||||||||
\(650\) | 32127.5 | 1.93868 | ||||||||
\(651\) | 2072.21 | 0.124756 | ||||||||
\(652\) | −8125.38 | −0.488059 | ||||||||
\(653\) | 5762.13 | 0.345313 | 0.172657 | − | 0.984982i | \(-0.444765\pi\) | ||||
0.172657 | + | 0.984982i | \(0.444765\pi\) | |||||||
\(654\) | 24645.2 | 1.47355 | ||||||||
\(655\) | −2930.49 | −0.174815 | ||||||||
\(656\) | 19029.2 | 1.13257 | ||||||||
\(657\) | −8371.12 | −0.497091 | ||||||||
\(658\) | −5824.24 | −0.345065 | ||||||||
\(659\) | −5279.50 | −0.312079 | −0.156040 | − | 0.987751i | \(-0.549873\pi\) | ||||
−0.156040 | + | 0.987751i | \(0.549873\pi\) | |||||||
\(660\) | −586.956 | −0.0346170 | ||||||||
\(661\) | 3845.20 | 0.226265 | 0.113132 | − | 0.993580i | \(-0.463912\pi\) | ||||
0.113132 | + | 0.993580i | \(0.463912\pi\) | |||||||
\(662\) | 24444.9 | 1.43517 | ||||||||
\(663\) | 8226.38 | 0.481879 | ||||||||
\(664\) | −26.6126 | −0.00155538 | ||||||||
\(665\) | 653.899 | 0.0381310 | ||||||||
\(666\) | 678.856 | 0.0394972 | ||||||||
\(667\) | −19263.9 | −1.11830 | ||||||||
\(668\) | −6697.05 | −0.387899 | ||||||||
\(669\) | 16754.1 | 0.968239 | ||||||||
\(670\) | 3952.03 | 0.227881 | ||||||||
\(671\) | −671.000 | −0.0386046 | ||||||||
\(672\) | −2046.74 | −0.117492 | ||||||||
\(673\) | −1717.40 | −0.0983668 | −0.0491834 | − | 0.998790i | \(-0.515662\pi\) | ||||
−0.0491834 | + | 0.998790i | \(0.515662\pi\) | |||||||
\(674\) | 27240.3 | 1.55676 | ||||||||
\(675\) | 3239.29 | 0.184712 | ||||||||
\(676\) | 18275.6 | 1.03980 | ||||||||
\(677\) | −4018.17 | −0.228110 | −0.114055 | − | 0.993474i | \(-0.536384\pi\) | ||||
−0.114055 | + | 0.993474i | \(0.536384\pi\) | |||||||
\(678\) | 8965.88 | 0.507865 | ||||||||
\(679\) | −3585.85 | −0.202669 | ||||||||
\(680\) | −24.2759 | −0.00136903 | ||||||||
\(681\) | 8001.93 | 0.450271 | ||||||||
\(682\) | 11356.1 | 0.637605 | ||||||||
\(683\) | −6488.05 | −0.363482 | −0.181741 | − | 0.983346i | \(-0.558173\pi\) | ||||
−0.181741 | + | 0.983346i | \(0.558173\pi\) | |||||||
\(684\) | 7797.80 | 0.435901 | ||||||||
\(685\) | −999.026 | −0.0557238 | ||||||||
\(686\) | 7237.30 | 0.402801 | ||||||||
\(687\) | −4026.93 | −0.223634 | ||||||||
\(688\) | −7777.02 | −0.430954 | ||||||||
\(689\) | 3204.88 | 0.177208 | ||||||||
\(690\) | 4708.72 | 0.259794 | ||||||||
\(691\) | −6253.37 | −0.344268 | −0.172134 | − | 0.985074i | \(-0.555066\pi\) | ||||
−0.172134 | + | 0.985074i | \(0.555066\pi\) | |||||||
\(692\) | 26891.2 | 1.47724 | ||||||||
\(693\) | 264.405 | 0.0144934 | ||||||||
\(694\) | −24108.6 | −1.31866 | ||||||||
\(695\) | 3767.76 | 0.205639 | ||||||||
\(696\) | 87.2899 | 0.00475390 | ||||||||
\(697\) | 12054.1 | 0.655068 | ||||||||
\(698\) | 32198.4 | 1.74603 | ||||||||
\(699\) | −3836.63 | −0.207603 | ||||||||
\(700\) | −2542.10 | −0.137261 | ||||||||
\(701\) | 14074.9 | 0.758350 | 0.379175 | − | 0.925325i | \(-0.376208\pi\) | ||||
0.379175 | + | 0.925325i | \(0.376208\pi\) | |||||||
\(702\) | 7230.27 | 0.388731 | ||||||||
\(703\) | −2063.64 | −0.110714 | ||||||||
\(704\) | −5538.17 | −0.296488 | ||||||||
\(705\) | −3674.42 | −0.196293 | ||||||||
\(706\) | 14021.8 | 0.747476 | ||||||||
\(707\) | −463.552 | −0.0246587 | ||||||||
\(708\) | 19364.4 | 1.02791 | ||||||||
\(709\) | 27959.7 | 1.48103 | 0.740513 | − | 0.672042i | \(-0.234583\pi\) | ||||
0.740513 | + | 0.672042i | \(0.234583\pi\) | |||||||
\(710\) | 2640.96 | 0.139596 | ||||||||
\(711\) | −906.836 | −0.0478326 | ||||||||
\(712\) | −378.705 | −0.0199334 | ||||||||
\(713\) | −45361.1 | −2.38259 | ||||||||
\(714\) | −1307.27 | −0.0685203 | ||||||||
\(715\) | 1654.42 | 0.0865339 | ||||||||
\(716\) | 34631.3 | 1.80759 | ||||||||
\(717\) | −12799.2 | −0.666658 | ||||||||
\(718\) | 45534.9 | 2.36678 | ||||||||
\(719\) | −7188.98 | −0.372884 | −0.186442 | − | 0.982466i | \(-0.559696\pi\) | ||||
−0.186442 | + | 0.982466i | \(0.559696\pi\) | |||||||
\(720\) | −1301.97 | −0.0673909 | ||||||||
\(721\) | 2717.43 | 0.140364 | ||||||||
\(722\) | −20228.1 | −1.04268 | ||||||||
\(723\) | 8723.12 | 0.448709 | ||||||||
\(724\) | −11995.4 | −0.615751 | ||||||||
\(725\) | 13177.3 | 0.675025 | ||||||||
\(726\) | 1448.99 | 0.0740729 | ||||||||
\(727\) | −17217.9 | −0.878375 | −0.439187 | − | 0.898396i | \(-0.644734\pi\) | ||||
−0.439187 | + | 0.898396i | \(0.644734\pi\) | |||||||
\(728\) | 47.4646 | 0.00241642 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | 8323.73 | 0.422021 | ||||||||
\(731\) | −4926.39 | −0.249260 | ||||||||
\(732\) | 1451.86 | 0.0733089 | ||||||||
\(733\) | 13280.9 | 0.669226 | 0.334613 | − | 0.942356i | \(-0.391394\pi\) | ||||
0.334613 | + | 0.942356i | \(0.391394\pi\) | |||||||
\(734\) | 3594.20 | 0.180742 | ||||||||
\(735\) | 2258.96 | 0.113364 | ||||||||
\(736\) | 44803.6 | 2.24386 | ||||||||
\(737\) | −4857.76 | −0.242792 | ||||||||
\(738\) | 10594.5 | 0.528441 | ||||||||
\(739\) | 4521.30 | 0.225059 | 0.112530 | − | 0.993648i | \(-0.464105\pi\) | ||||
0.112530 | + | 0.993648i | \(0.464105\pi\) | |||||||
\(740\) | −336.101 | −0.0166964 | ||||||||
\(741\) | −21979.2 | −1.08964 | ||||||||
\(742\) | −509.296 | −0.0251979 | ||||||||
\(743\) | −14399.9 | −0.711013 | −0.355506 | − | 0.934674i | \(-0.615692\pi\) | ||||
−0.355506 | + | 0.934674i | \(0.615692\pi\) | |||||||
\(744\) | 205.543 | 0.0101284 | ||||||||
\(745\) | 3977.07 | 0.195582 | ||||||||
\(746\) | −19346.7 | −0.949508 | ||||||||
\(747\) | −904.123 | −0.0442840 | ||||||||
\(748\) | −3567.13 | −0.174368 | ||||||||
\(749\) | 4154.36 | 0.202666 | ||||||||
\(750\) | −6576.85 | −0.320203 | ||||||||
\(751\) | 30878.8 | 1.50038 | 0.750190 | − | 0.661223i | \(-0.229962\pi\) | ||||
0.750190 | + | 0.661223i | \(0.229962\pi\) | |||||||
\(752\) | −35252.2 | −1.70946 | ||||||||
\(753\) | −18760.0 | −0.907904 | ||||||||
\(754\) | 29412.4 | 1.42061 | ||||||||
\(755\) | −5132.23 | −0.247392 | ||||||||
\(756\) | −572.098 | −0.0275225 | ||||||||
\(757\) | 26375.7 | 1.26637 | 0.633183 | − | 0.774002i | \(-0.281748\pi\) | ||||
0.633183 | + | 0.774002i | \(0.281748\pi\) | |||||||
\(758\) | 57289.3 | 2.74517 | ||||||||
\(759\) | −5787.87 | −0.276794 | ||||||||
\(760\) | 64.8603 | 0.00309570 | ||||||||
\(761\) | 9667.12 | 0.460490 | 0.230245 | − | 0.973133i | \(-0.426047\pi\) | ||||
0.230245 | + | 0.973133i | \(0.426047\pi\) | |||||||
\(762\) | −5549.67 | −0.263836 | ||||||||
\(763\) | 5496.51 | 0.260796 | ||||||||
\(764\) | 8355.51 | 0.395670 | ||||||||
\(765\) | −824.738 | −0.0389784 | ||||||||
\(766\) | 23558.0 | 1.11121 | ||||||||
\(767\) | −54581.3 | −2.56951 | ||||||||
\(768\) | −12489.3 | −0.586810 | ||||||||
\(769\) | −12188.5 | −0.571559 | −0.285780 | − | 0.958295i | \(-0.592253\pi\) | ||||
−0.285780 | + | 0.958295i | \(0.592253\pi\) | |||||||
\(770\) | −262.908 | −0.0123046 | ||||||||
\(771\) | −13503.3 | −0.630753 | ||||||||
\(772\) | 17880.1 | 0.833572 | ||||||||
\(773\) | 3407.30 | 0.158541 | 0.0792704 | − | 0.996853i | \(-0.474741\pi\) | ||||
0.0792704 | + | 0.996853i | \(0.474741\pi\) | |||||||
\(774\) | −4329.87 | −0.201078 | ||||||||
\(775\) | 31028.8 | 1.43818 | ||||||||
\(776\) | −355.680 | −0.0164538 | ||||||||
\(777\) | 151.402 | 0.00699039 | ||||||||
\(778\) | −48647.0 | −2.24175 | ||||||||
\(779\) | −32206.1 | −1.48126 | ||||||||
\(780\) | −3579.70 | −0.164325 | ||||||||
\(781\) | −3246.22 | −0.148731 | ||||||||
\(782\) | 28616.5 | 1.30860 | ||||||||
\(783\) | 2965.54 | 0.135351 | ||||||||
\(784\) | 21672.3 | 0.987260 | ||||||||
\(785\) | −8429.53 | −0.383265 | ||||||||
\(786\) | −15653.1 | −0.710339 | ||||||||
\(787\) | 7104.30 | 0.321780 | 0.160890 | − | 0.986972i | \(-0.448564\pi\) | ||||
0.160890 | + | 0.986972i | \(0.448564\pi\) | |||||||
\(788\) | −14669.0 | −0.663150 | ||||||||
\(789\) | 20003.2 | 0.902577 | ||||||||
\(790\) | 901.702 | 0.0406090 | ||||||||
\(791\) | 1999.62 | 0.0898843 | ||||||||
\(792\) | 26.2263 | 0.00117666 | ||||||||
\(793\) | −4092.26 | −0.183254 | ||||||||
\(794\) | 33005.9 | 1.47523 | ||||||||
\(795\) | −321.307 | −0.0143341 | ||||||||
\(796\) | −15485.7 | −0.689544 | ||||||||
\(797\) | −6283.40 | −0.279259 | −0.139629 | − | 0.990204i | \(-0.544591\pi\) | ||||
−0.139629 | + | 0.990204i | \(0.544591\pi\) | |||||||
\(798\) | 3492.77 | 0.154941 | ||||||||
\(799\) | −22330.7 | −0.988738 | ||||||||
\(800\) | −30647.4 | −1.35444 | ||||||||
\(801\) | −12865.9 | −0.567535 | ||||||||
\(802\) | 31131.9 | 1.37070 | ||||||||
\(803\) | −10231.4 | −0.449635 | ||||||||
\(804\) | 10510.8 | 0.461055 | ||||||||
\(805\) | 1050.17 | 0.0459795 | ||||||||
\(806\) | 69257.8 | 3.02668 | ||||||||
\(807\) | −9963.03 | −0.434591 | ||||||||
\(808\) | −45.9798 | −0.00200193 | ||||||||
\(809\) | −6692.10 | −0.290830 | −0.145415 | − | 0.989371i | \(-0.546452\pi\) | ||||
−0.145415 | + | 0.989371i | \(0.546452\pi\) | |||||||
\(810\) | −724.873 | −0.0314437 | ||||||||
\(811\) | 19507.5 | 0.844637 | 0.422318 | − | 0.906448i | \(-0.361216\pi\) | ||||
0.422318 | + | 0.906448i | \(0.361216\pi\) | |||||||
\(812\) | −2327.27 | −0.100580 | ||||||||
\(813\) | 17717.3 | 0.764296 | ||||||||
\(814\) | 829.713 | 0.0357266 | ||||||||
\(815\) | −2296.10 | −0.0986858 | ||||||||
\(816\) | −7912.50 | −0.339452 | ||||||||
\(817\) | 13162.3 | 0.563637 | ||||||||
\(818\) | 27227.7 | 1.16381 | ||||||||
\(819\) | 1612.54 | 0.0687993 | ||||||||
\(820\) | −5245.33 | −0.223384 | ||||||||
\(821\) | −23775.2 | −1.01067 | −0.505336 | − | 0.862923i | \(-0.668631\pi\) | ||||
−0.505336 | + | 0.862923i | \(0.668631\pi\) | |||||||
\(822\) | −5336.25 | −0.226427 | ||||||||
\(823\) | 35936.2 | 1.52206 | 0.761031 | − | 0.648716i | \(-0.224694\pi\) | ||||
0.761031 | + | 0.648716i | \(0.224694\pi\) | |||||||
\(824\) | 269.542 | 0.0113956 | ||||||||
\(825\) | 3959.14 | 0.167078 | ||||||||
\(826\) | 8673.66 | 0.365369 | ||||||||
\(827\) | 25096.8 | 1.05526 | 0.527631 | − | 0.849474i | \(-0.323080\pi\) | ||||
0.527631 | + | 0.849474i | \(0.323080\pi\) | |||||||
\(828\) | 12523.3 | 0.525623 | ||||||||
\(829\) | 8329.67 | 0.348976 | 0.174488 | − | 0.984659i | \(-0.444173\pi\) | ||||
0.174488 | + | 0.984659i | \(0.444173\pi\) | |||||||
\(830\) | 899.005 | 0.0375963 | ||||||||
\(831\) | 15282.1 | 0.637942 | ||||||||
\(832\) | −33775.9 | −1.40741 | ||||||||
\(833\) | 13728.4 | 0.571023 | ||||||||
\(834\) | 20125.3 | 0.835590 | ||||||||
\(835\) | −1892.48 | −0.0784334 | ||||||||
\(836\) | 9530.64 | 0.394287 | ||||||||
\(837\) | 6983.00 | 0.288372 | ||||||||
\(838\) | −54591.5 | −2.25040 | ||||||||
\(839\) | 7103.90 | 0.292317 | 0.146158 | − | 0.989261i | \(-0.453309\pi\) | ||||
0.146158 | + | 0.989261i | \(0.453309\pi\) | |||||||
\(840\) | −4.75858 | −0.000195460 0 | ||||||||
\(841\) | −12325.3 | −0.505363 | ||||||||
\(842\) | 33645.1 | 1.37706 | ||||||||
\(843\) | −22443.3 | −0.916951 | ||||||||
\(844\) | 45254.7 | 1.84565 | ||||||||
\(845\) | 5164.39 | 0.210249 | ||||||||
\(846\) | −19626.7 | −0.797613 | ||||||||
\(847\) | 323.161 | 0.0131097 | ||||||||
\(848\) | −3082.60 | −0.124831 | ||||||||
\(849\) | 21618.8 | 0.873917 | ||||||||
\(850\) | −19574.8 | −0.789895 | ||||||||
\(851\) | −3314.23 | −0.133502 | ||||||||
\(852\) | 7023.90 | 0.282435 | ||||||||
\(853\) | 12516.6 | 0.502414 | 0.251207 | − | 0.967933i | \(-0.419173\pi\) | ||||
0.251207 | + | 0.967933i | \(0.419173\pi\) | |||||||
\(854\) | 650.311 | 0.0260576 | ||||||||
\(855\) | 2203.53 | 0.0881394 | ||||||||
\(856\) | 412.071 | 0.0164536 | ||||||||
\(857\) | 3228.70 | 0.128693 | 0.0643467 | − | 0.997928i | \(-0.479504\pi\) | ||||
0.0643467 | + | 0.997928i | \(0.479504\pi\) | |||||||
\(858\) | 8837.00 | 0.351620 | ||||||||
\(859\) | 4995.43 | 0.198419 | 0.0992095 | − | 0.995067i | \(-0.468369\pi\) | ||||
0.0992095 | + | 0.995067i | \(0.468369\pi\) | |||||||
\(860\) | 2143.71 | 0.0850000 | ||||||||
\(861\) | 2362.85 | 0.0935259 | ||||||||
\(862\) | 18079.6 | 0.714376 | ||||||||
\(863\) | 34594.5 | 1.36456 | 0.682278 | − | 0.731093i | \(-0.260989\pi\) | ||||
0.682278 | + | 0.731093i | \(0.260989\pi\) | |||||||
\(864\) | −6897.18 | −0.271582 | ||||||||
\(865\) | 7599.02 | 0.298699 | ||||||||
\(866\) | 14796.0 | 0.580587 | ||||||||
\(867\) | 9726.79 | 0.381014 | ||||||||
\(868\) | −5480.05 | −0.214291 | ||||||||
\(869\) | −1108.35 | −0.0432662 | ||||||||
\(870\) | −2948.75 | −0.114910 | ||||||||
\(871\) | −29626.2 | −1.15252 | ||||||||
\(872\) | 545.200 | 0.0211729 | ||||||||
\(873\) | −12083.7 | −0.468467 | ||||||||
\(874\) | −76457.4 | −2.95905 | ||||||||
\(875\) | −1466.81 | −0.0566710 | ||||||||
\(876\) | 22137.8 | 0.853844 | ||||||||
\(877\) | −22394.1 | −0.862253 | −0.431126 | − | 0.902291i | \(-0.641884\pi\) | ||||
−0.431126 | + | 0.902291i | \(0.641884\pi\) | |||||||
\(878\) | 51517.3 | 1.98021 | ||||||||
\(879\) | 8739.05 | 0.335337 | ||||||||
\(880\) | −1591.29 | −0.0609574 | ||||||||
\(881\) | 50195.6 | 1.91956 | 0.959781 | − | 0.280750i | \(-0.0905831\pi\) | ||||
0.959781 | + | 0.280750i | \(0.0905831\pi\) | |||||||
\(882\) | 12066.1 | 0.460643 | ||||||||
\(883\) | 644.524 | 0.0245640 | 0.0122820 | − | 0.999925i | \(-0.496090\pi\) | ||||
0.0122820 | + | 0.999925i | \(0.496090\pi\) | |||||||
\(884\) | −21755.0 | −0.827715 | ||||||||
\(885\) | 5472.07 | 0.207844 | ||||||||
\(886\) | 39351.3 | 1.49214 | ||||||||
\(887\) | 34884.1 | 1.32051 | 0.660256 | − | 0.751041i | \(-0.270448\pi\) | ||||
0.660256 | + | 0.751041i | \(0.270448\pi\) | |||||||
\(888\) | 15.0176 | 0.000567521 0 | ||||||||
\(889\) | −1237.72 | −0.0466949 | ||||||||
\(890\) | 12793.1 | 0.481826 | ||||||||
\(891\) | 891.000 | 0.0335013 | ||||||||
\(892\) | −44307.0 | −1.66313 | ||||||||
\(893\) | 59663.0 | 2.23577 | ||||||||
\(894\) | 21243.3 | 0.794724 | ||||||||
\(895\) | 9786.25 | 0.365495 | ||||||||
\(896\) | −90.5590 | −0.00337652 | ||||||||
\(897\) | −35298.8 | −1.31393 | ||||||||
\(898\) | −50698.8 | −1.88401 | ||||||||
\(899\) | 28406.6 | 1.05385 | ||||||||
\(900\) | −8566.45 | −0.317276 | ||||||||
\(901\) | −1952.69 | −0.0722014 | ||||||||
\(902\) | 12948.9 | 0.477993 | ||||||||
\(903\) | −965.674 | −0.0355876 | ||||||||
\(904\) | 198.343 | 0.00729733 | ||||||||
\(905\) | −3389.69 | −0.124505 | ||||||||
\(906\) | −27413.6 | −1.00525 | ||||||||
\(907\) | 26682.9 | 0.976839 | 0.488419 | − | 0.872609i | \(-0.337574\pi\) | ||||
0.488419 | + | 0.872609i | \(0.337574\pi\) | |||||||
\(908\) | −21161.5 | −0.773423 | ||||||||
\(909\) | −1562.09 | −0.0569982 | ||||||||
\(910\) | −1603.41 | −0.0584093 | ||||||||
\(911\) | −48632.5 | −1.76868 | −0.884339 | − | 0.466846i | \(-0.845390\pi\) | ||||
−0.884339 | + | 0.466846i | \(0.845390\pi\) | |||||||
\(912\) | 21140.6 | 0.767582 | ||||||||
\(913\) | −1105.04 | −0.0400564 | ||||||||
\(914\) | 23107.8 | 0.836258 | ||||||||
\(915\) | 410.271 | 0.0148231 | ||||||||
\(916\) | 10649.4 | 0.384133 | ||||||||
\(917\) | −3491.04 | −0.125719 | ||||||||
\(918\) | −4405.30 | −0.158384 | ||||||||
\(919\) | 18165.4 | 0.652038 | 0.326019 | − | 0.945363i | \(-0.394293\pi\) | ||||
0.326019 | + | 0.945363i | \(0.394293\pi\) | |||||||
\(920\) | 104.166 | 0.00373289 | ||||||||
\(921\) | −23327.3 | −0.834594 | ||||||||
\(922\) | −8465.63 | −0.302387 | ||||||||
\(923\) | −19797.9 | −0.706018 | ||||||||
\(924\) | −699.230 | −0.0248950 | ||||||||
\(925\) | 2267.07 | 0.0805845 | ||||||||
\(926\) | −54158.1 | −1.92197 | ||||||||
\(927\) | 9157.28 | 0.324449 | ||||||||
\(928\) | −28057.4 | −0.992489 | ||||||||
\(929\) | −18526.4 | −0.654286 | −0.327143 | − | 0.944975i | \(-0.606086\pi\) | ||||
−0.327143 | + | 0.944975i | \(0.606086\pi\) | |||||||
\(930\) | −6943.47 | −0.244823 | ||||||||
\(931\) | −36679.6 | −1.29122 | ||||||||
\(932\) | 10146.1 | 0.356596 | ||||||||
\(933\) | 24138.9 | 0.847021 | ||||||||
\(934\) | −9244.06 | −0.323849 | ||||||||
\(935\) | −1008.01 | −0.0352573 | ||||||||
\(936\) | 159.948 | 0.00558553 | ||||||||
\(937\) | −32603.9 | −1.13674 | −0.568369 | − | 0.822774i | \(-0.692425\pi\) | ||||
−0.568369 | + | 0.822774i | \(0.692425\pi\) | |||||||
\(938\) | 4707.98 | 0.163882 | ||||||||
\(939\) | −886.296 | −0.0308021 | ||||||||
\(940\) | 9717.16 | 0.337169 | ||||||||
\(941\) | 10872.5 | 0.376657 | 0.188329 | − | 0.982106i | \(-0.439693\pi\) | ||||
0.188329 | + | 0.982106i | \(0.439693\pi\) | |||||||
\(942\) | −45025.9 | −1.55735 | ||||||||
\(943\) | −51723.3 | −1.78615 | ||||||||
\(944\) | 52498.8 | 1.81005 | ||||||||
\(945\) | −161.665 | −0.00556506 | ||||||||
\(946\) | −5292.06 | −0.181881 | ||||||||
\(947\) | −41316.9 | −1.41776 | −0.708881 | − | 0.705329i | \(-0.750799\pi\) | ||||
−0.708881 | + | 0.705329i | \(0.750799\pi\) | |||||||
\(948\) | 2398.17 | 0.0821613 | ||||||||
\(949\) | −62398.5 | −2.13440 | ||||||||
\(950\) | 52299.9 | 1.78614 | ||||||||
\(951\) | −3869.07 | −0.131928 | ||||||||
\(952\) | −28.9195 | −0.000984544 0 | ||||||||
\(953\) | −51658.4 | −1.75591 | −0.877953 | − | 0.478746i | \(-0.841091\pi\) | ||||
−0.877953 | + | 0.478746i | \(0.841091\pi\) | |||||||
\(954\) | −1716.24 | −0.0582447 | ||||||||
\(955\) | 2361.13 | 0.0800046 | ||||||||
\(956\) | 33848.0 | 1.14511 | ||||||||
\(957\) | 3624.55 | 0.122430 | ||||||||
\(958\) | 29882.5 | 1.00779 | ||||||||
\(959\) | −1190.12 | −0.0400741 | ||||||||
\(960\) | 3386.21 | 0.113843 | ||||||||
\(961\) | 37098.3 | 1.24528 | ||||||||
\(962\) | 5060.21 | 0.169592 | ||||||||
\(963\) | 13999.5 | 0.468460 | ||||||||
\(964\) | −23068.7 | −0.770739 | ||||||||
\(965\) | 5052.61 | 0.168549 | ||||||||
\(966\) | 5609.42 | 0.186832 | ||||||||
\(967\) | −10619.6 | −0.353156 | −0.176578 | − | 0.984287i | \(-0.556503\pi\) | ||||
−0.176578 | + | 0.984287i | \(0.556503\pi\) | |||||||
\(968\) | 32.0544 | 0.00106433 | ||||||||
\(969\) | 13391.6 | 0.443963 | ||||||||
\(970\) | 12015.3 | 0.397719 | ||||||||
\(971\) | 12318.6 | 0.407129 | 0.203564 | − | 0.979062i | \(-0.434747\pi\) | ||||
0.203564 | + | 0.979062i | \(0.434747\pi\) | |||||||
\(972\) | −1927.87 | −0.0636179 | ||||||||
\(973\) | 4488.47 | 0.147887 | ||||||||
\(974\) | −53608.6 | −1.76358 | ||||||||
\(975\) | 24145.8 | 0.793111 | ||||||||
\(976\) | 3936.12 | 0.129090 | ||||||||
\(977\) | 34480.4 | 1.12910 | 0.564548 | − | 0.825400i | \(-0.309051\pi\) | ||||
0.564548 | + | 0.825400i | \(0.309051\pi\) | |||||||
\(978\) | −12264.5 | −0.400998 | ||||||||
\(979\) | −15725.0 | −0.513354 | ||||||||
\(980\) | −5973.91 | −0.194724 | ||||||||
\(981\) | 18522.3 | 0.602826 | ||||||||
\(982\) | 64951.8 | 2.11069 | ||||||||
\(983\) | −41959.7 | −1.36145 | −0.680726 | − | 0.732538i | \(-0.738335\pi\) | ||||
−0.680726 | + | 0.732538i | \(0.738335\pi\) | |||||||
\(984\) | 234.372 | 0.00759298 | ||||||||
\(985\) | −4145.22 | −0.134089 | ||||||||
\(986\) | −17920.6 | −0.578810 | ||||||||
\(987\) | −4377.27 | −0.141165 | ||||||||
\(988\) | 58125.0 | 1.87166 | ||||||||
\(989\) | 21138.8 | 0.679650 | ||||||||
\(990\) | −885.956 | −0.0284419 | ||||||||
\(991\) | −38529.0 | −1.23503 | −0.617514 | − | 0.786560i | \(-0.711860\pi\) | ||||
−0.617514 | + | 0.786560i | \(0.711860\pi\) | |||||||
\(992\) | −66067.2 | −2.11455 | ||||||||
\(993\) | 18371.8 | 0.587123 | ||||||||
\(994\) | 3146.13 | 0.100392 | ||||||||
\(995\) | −4376.02 | −0.139426 | ||||||||
\(996\) | 2390.99 | 0.0760658 | ||||||||
\(997\) | 38875.5 | 1.23490 | 0.617452 | − | 0.786609i | \(-0.288165\pi\) | ||||
0.617452 | + | 0.786609i | \(0.288165\pi\) | |||||||
\(998\) | −20007.0 | −0.634578 | ||||||||
\(999\) | 510.201 | 0.0161582 |
(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 | 2013.4.a.d.1.8 | ✓ | 37 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2013.4.a.d.1.8 | ✓ | 37 | 1.1 | even | 1 | trivial |