Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [23,4,Mod(1,23)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(23, 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("23.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 23 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 23.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: | \(1.35704393013\) |
Analytic rank: | \(1\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 23.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.00000 | −0.707107 | −0.353553 | − | 0.935414i | \(-0.615027\pi\) | ||||
−0.353553 | + | 0.935414i | \(0.615027\pi\) | |||||||
\(3\) | −5.00000 | −0.962250 | −0.481125 | − | 0.876652i | \(-0.659772\pi\) | ||||
−0.481125 | + | 0.876652i | \(0.659772\pi\) | |||||||
\(4\) | −4.00000 | −0.500000 | ||||||||
\(5\) | −6.00000 | −0.536656 | −0.268328 | − | 0.963328i | \(-0.586471\pi\) | ||||
−0.268328 | + | 0.963328i | \(0.586471\pi\) | |||||||
\(6\) | 10.0000 | 0.680414 | ||||||||
\(7\) | −8.00000 | −0.431959 | −0.215980 | − | 0.976398i | \(-0.569295\pi\) | ||||
−0.215980 | + | 0.976398i | \(0.569295\pi\) | |||||||
\(8\) | 24.0000 | 1.06066 | ||||||||
\(9\) | −2.00000 | −0.0740741 | ||||||||
\(10\) | 12.0000 | 0.379473 | ||||||||
\(11\) | 34.0000 | 0.931944 | 0.465972 | − | 0.884799i | \(-0.345705\pi\) | ||||
0.465972 | + | 0.884799i | \(0.345705\pi\) | |||||||
\(12\) | 20.0000 | 0.481125 | ||||||||
\(13\) | −57.0000 | −1.21607 | −0.608037 | − | 0.793909i | \(-0.708043\pi\) | ||||
−0.608037 | + | 0.793909i | \(0.708043\pi\) | |||||||
\(14\) | 16.0000 | 0.305441 | ||||||||
\(15\) | 30.0000 | 0.516398 | ||||||||
\(16\) | −16.0000 | −0.250000 | ||||||||
\(17\) | −80.0000 | −1.14134 | −0.570672 | − | 0.821178i | \(-0.693317\pi\) | ||||
−0.570672 | + | 0.821178i | \(0.693317\pi\) | |||||||
\(18\) | 4.00000 | 0.0523783 | ||||||||
\(19\) | −70.0000 | −0.845216 | −0.422608 | − | 0.906313i | \(-0.638885\pi\) | ||||
−0.422608 | + | 0.906313i | \(0.638885\pi\) | |||||||
\(20\) | 24.0000 | 0.268328 | ||||||||
\(21\) | 40.0000 | 0.415653 | ||||||||
\(22\) | −68.0000 | −0.658984 | ||||||||
\(23\) | 23.0000 | 0.208514 | ||||||||
\(24\) | −120.000 | −1.02062 | ||||||||
\(25\) | −89.0000 | −0.712000 | ||||||||
\(26\) | 114.000 | 0.859894 | ||||||||
\(27\) | 145.000 | 1.03353 | ||||||||
\(28\) | 32.0000 | 0.215980 | ||||||||
\(29\) | 245.000 | 1.56881 | 0.784403 | − | 0.620252i | \(-0.212970\pi\) | ||||
0.784403 | + | 0.620252i | \(0.212970\pi\) | |||||||
\(30\) | −60.0000 | −0.365148 | ||||||||
\(31\) | 103.000 | 0.596753 | 0.298377 | − | 0.954448i | \(-0.403555\pi\) | ||||
0.298377 | + | 0.954448i | \(0.403555\pi\) | |||||||
\(32\) | −160.000 | −0.883883 | ||||||||
\(33\) | −170.000 | −0.896764 | ||||||||
\(34\) | 160.000 | 0.807052 | ||||||||
\(35\) | 48.0000 | 0.231814 | ||||||||
\(36\) | 8.00000 | 0.0370370 | ||||||||
\(37\) | −298.000 | −1.32408 | −0.662039 | − | 0.749469i | \(-0.730309\pi\) | ||||
−0.662039 | + | 0.749469i | \(0.730309\pi\) | |||||||
\(38\) | 140.000 | 0.597658 | ||||||||
\(39\) | 285.000 | 1.17017 | ||||||||
\(40\) | −144.000 | −0.569210 | ||||||||
\(41\) | 95.0000 | 0.361866 | 0.180933 | − | 0.983495i | \(-0.442088\pi\) | ||||
0.180933 | + | 0.983495i | \(0.442088\pi\) | |||||||
\(42\) | −80.0000 | −0.293911 | ||||||||
\(43\) | 88.0000 | 0.312090 | 0.156045 | − | 0.987750i | \(-0.450125\pi\) | ||||
0.156045 | + | 0.987750i | \(0.450125\pi\) | |||||||
\(44\) | −136.000 | −0.465972 | ||||||||
\(45\) | 12.0000 | 0.0397523 | ||||||||
\(46\) | −46.0000 | −0.147442 | ||||||||
\(47\) | −357.000 | −1.10795 | −0.553977 | − | 0.832532i | \(-0.686890\pi\) | ||||
−0.553977 | + | 0.832532i | \(0.686890\pi\) | |||||||
\(48\) | 80.0000 | 0.240563 | ||||||||
\(49\) | −279.000 | −0.813411 | ||||||||
\(50\) | 178.000 | 0.503460 | ||||||||
\(51\) | 400.000 | 1.09826 | ||||||||
\(52\) | 228.000 | 0.608037 | ||||||||
\(53\) | −414.000 | −1.07297 | −0.536484 | − | 0.843911i | \(-0.680248\pi\) | ||||
−0.536484 | + | 0.843911i | \(0.680248\pi\) | |||||||
\(54\) | −290.000 | −0.730815 | ||||||||
\(55\) | −204.000 | −0.500134 | ||||||||
\(56\) | −192.000 | −0.458162 | ||||||||
\(57\) | 350.000 | 0.813309 | ||||||||
\(58\) | −490.000 | −1.10931 | ||||||||
\(59\) | −408.000 | −0.900289 | −0.450145 | − | 0.892956i | \(-0.648628\pi\) | ||||
−0.450145 | + | 0.892956i | \(0.648628\pi\) | |||||||
\(60\) | −120.000 | −0.258199 | ||||||||
\(61\) | 822.000 | 1.72535 | 0.862675 | − | 0.505759i | \(-0.168788\pi\) | ||||
0.862675 | + | 0.505759i | \(0.168788\pi\) | |||||||
\(62\) | −206.000 | −0.421968 | ||||||||
\(63\) | 16.0000 | 0.0319970 | ||||||||
\(64\) | 448.000 | 0.875000 | ||||||||
\(65\) | 342.000 | 0.652614 | ||||||||
\(66\) | 340.000 | 0.634108 | ||||||||
\(67\) | 926.000 | 1.68849 | 0.844246 | − | 0.535957i | \(-0.180049\pi\) | ||||
0.844246 | + | 0.535957i | \(0.180049\pi\) | |||||||
\(68\) | 320.000 | 0.570672 | ||||||||
\(69\) | −115.000 | −0.200643 | ||||||||
\(70\) | −96.0000 | −0.163917 | ||||||||
\(71\) | 335.000 | 0.559960 | 0.279980 | − | 0.960006i | \(-0.409672\pi\) | ||||
0.279980 | + | 0.960006i | \(0.409672\pi\) | |||||||
\(72\) | −48.0000 | −0.0785674 | ||||||||
\(73\) | −899.000 | −1.44137 | −0.720685 | − | 0.693263i | \(-0.756173\pi\) | ||||
−0.720685 | + | 0.693263i | \(0.756173\pi\) | |||||||
\(74\) | 596.000 | 0.936265 | ||||||||
\(75\) | 445.000 | 0.685122 | ||||||||
\(76\) | 280.000 | 0.422608 | ||||||||
\(77\) | −272.000 | −0.402562 | ||||||||
\(78\) | −570.000 | −0.827433 | ||||||||
\(79\) | −1322.00 | −1.88274 | −0.941371 | − | 0.337373i | \(-0.890462\pi\) | ||||
−0.941371 | + | 0.337373i | \(0.890462\pi\) | |||||||
\(80\) | 96.0000 | 0.134164 | ||||||||
\(81\) | −671.000 | −0.920439 | ||||||||
\(82\) | −190.000 | −0.255878 | ||||||||
\(83\) | −36.0000 | −0.0476086 | −0.0238043 | − | 0.999717i | \(-0.507578\pi\) | ||||
−0.0238043 | + | 0.999717i | \(0.507578\pi\) | |||||||
\(84\) | −160.000 | −0.207827 | ||||||||
\(85\) | 480.000 | 0.612510 | ||||||||
\(86\) | −176.000 | −0.220681 | ||||||||
\(87\) | −1225.00 | −1.50958 | ||||||||
\(88\) | 816.000 | 0.988476 | ||||||||
\(89\) | −460.000 | −0.547864 | −0.273932 | − | 0.961749i | \(-0.588324\pi\) | ||||
−0.273932 | + | 0.961749i | \(0.588324\pi\) | |||||||
\(90\) | −24.0000 | −0.0281091 | ||||||||
\(91\) | 456.000 | 0.525294 | ||||||||
\(92\) | −92.0000 | −0.104257 | ||||||||
\(93\) | −515.000 | −0.574226 | ||||||||
\(94\) | 714.000 | 0.783441 | ||||||||
\(95\) | 420.000 | 0.453590 | ||||||||
\(96\) | 800.000 | 0.850517 | ||||||||
\(97\) | −964.000 | −1.00907 | −0.504533 | − | 0.863393i | \(-0.668335\pi\) | ||||
−0.504533 | + | 0.863393i | \(0.668335\pi\) | |||||||
\(98\) | 558.000 | 0.575168 | ||||||||
\(99\) | −68.0000 | −0.0690329 | ||||||||
\(100\) | 356.000 | 0.356000 | ||||||||
\(101\) | −310.000 | −0.305407 | −0.152704 | − | 0.988272i | \(-0.548798\pi\) | ||||
−0.152704 | + | 0.988272i | \(0.548798\pi\) | |||||||
\(102\) | −800.000 | −0.776586 | ||||||||
\(103\) | 1044.00 | 0.998722 | 0.499361 | − | 0.866394i | \(-0.333568\pi\) | ||||
0.499361 | + | 0.866394i | \(0.333568\pi\) | |||||||
\(104\) | −1368.00 | −1.28984 | ||||||||
\(105\) | −240.000 | −0.223063 | ||||||||
\(106\) | 828.000 | 0.758703 | ||||||||
\(107\) | 414.000 | 0.374046 | 0.187023 | − | 0.982356i | \(-0.440116\pi\) | ||||
0.187023 | + | 0.982356i | \(0.440116\pi\) | |||||||
\(108\) | −580.000 | −0.516764 | ||||||||
\(109\) | 704.000 | 0.618633 | 0.309316 | − | 0.950959i | \(-0.399900\pi\) | ||||
0.309316 | + | 0.950959i | \(0.399900\pi\) | |||||||
\(110\) | 408.000 | 0.353648 | ||||||||
\(111\) | 1490.00 | 1.27409 | ||||||||
\(112\) | 128.000 | 0.107990 | ||||||||
\(113\) | 952.000 | 0.792537 | 0.396268 | − | 0.918135i | \(-0.370305\pi\) | ||||
0.396268 | + | 0.918135i | \(0.370305\pi\) | |||||||
\(114\) | −700.000 | −0.575097 | ||||||||
\(115\) | −138.000 | −0.111901 | ||||||||
\(116\) | −980.000 | −0.784403 | ||||||||
\(117\) | 114.000 | 0.0900795 | ||||||||
\(118\) | 816.000 | 0.636601 | ||||||||
\(119\) | 640.000 | 0.493014 | ||||||||
\(120\) | 720.000 | 0.547723 | ||||||||
\(121\) | −175.000 | −0.131480 | ||||||||
\(122\) | −1644.00 | −1.22001 | ||||||||
\(123\) | −475.000 | −0.348206 | ||||||||
\(124\) | −412.000 | −0.298377 | ||||||||
\(125\) | 1284.00 | 0.918756 | ||||||||
\(126\) | −32.0000 | −0.0226253 | ||||||||
\(127\) | 261.000 | 0.182362 | 0.0911811 | − | 0.995834i | \(-0.470936\pi\) | ||||
0.0911811 | + | 0.995834i | \(0.470936\pi\) | |||||||
\(128\) | 384.000 | 0.265165 | ||||||||
\(129\) | −440.000 | −0.300309 | ||||||||
\(130\) | −684.000 | −0.461467 | ||||||||
\(131\) | −1441.00 | −0.961074 | −0.480537 | − | 0.876974i | \(-0.659558\pi\) | ||||
−0.480537 | + | 0.876974i | \(0.659558\pi\) | |||||||
\(132\) | 680.000 | 0.448382 | ||||||||
\(133\) | 560.000 | 0.365099 | ||||||||
\(134\) | −1852.00 | −1.19394 | ||||||||
\(135\) | −870.000 | −0.554649 | ||||||||
\(136\) | −1920.00 | −1.21058 | ||||||||
\(137\) | 1556.00 | 0.970351 | 0.485175 | − | 0.874417i | \(-0.338756\pi\) | ||||
0.485175 | + | 0.874417i | \(0.338756\pi\) | |||||||
\(138\) | 230.000 | 0.141876 | ||||||||
\(139\) | 25.0000 | 0.0152552 | 0.00762760 | − | 0.999971i | \(-0.497572\pi\) | ||||
0.00762760 | + | 0.999971i | \(0.497572\pi\) | |||||||
\(140\) | −192.000 | −0.115907 | ||||||||
\(141\) | 1785.00 | 1.06613 | ||||||||
\(142\) | −670.000 | −0.395952 | ||||||||
\(143\) | −1938.00 | −1.13331 | ||||||||
\(144\) | 32.0000 | 0.0185185 | ||||||||
\(145\) | −1470.00 | −0.841909 | ||||||||
\(146\) | 1798.00 | 1.01920 | ||||||||
\(147\) | 1395.00 | 0.782705 | ||||||||
\(148\) | 1192.00 | 0.662039 | ||||||||
\(149\) | 822.000 | 0.451952 | 0.225976 | − | 0.974133i | \(-0.427443\pi\) | ||||
0.225976 | + | 0.974133i | \(0.427443\pi\) | |||||||
\(150\) | −890.000 | −0.484455 | ||||||||
\(151\) | −1489.00 | −0.802471 | −0.401235 | − | 0.915975i | \(-0.631419\pi\) | ||||
−0.401235 | + | 0.915975i | \(0.631419\pi\) | |||||||
\(152\) | −1680.00 | −0.896487 | ||||||||
\(153\) | 160.000 | 0.0845440 | ||||||||
\(154\) | 544.000 | 0.284654 | ||||||||
\(155\) | −618.000 | −0.320251 | ||||||||
\(156\) | −1140.00 | −0.585084 | ||||||||
\(157\) | −632.000 | −0.321268 | −0.160634 | − | 0.987014i | \(-0.551354\pi\) | ||||
−0.160634 | + | 0.987014i | \(0.551354\pi\) | |||||||
\(158\) | 2644.00 | 1.33130 | ||||||||
\(159\) | 2070.00 | 1.03246 | ||||||||
\(160\) | 960.000 | 0.474342 | ||||||||
\(161\) | −184.000 | −0.0900698 | ||||||||
\(162\) | 1342.00 | 0.650849 | ||||||||
\(163\) | −3043.00 | −1.46225 | −0.731123 | − | 0.682245i | \(-0.761004\pi\) | ||||
−0.731123 | + | 0.682245i | \(0.761004\pi\) | |||||||
\(164\) | −380.000 | −0.180933 | ||||||||
\(165\) | 1020.00 | 0.481254 | ||||||||
\(166\) | 72.0000 | 0.0336644 | ||||||||
\(167\) | −2224.00 | −1.03053 | −0.515264 | − | 0.857031i | \(-0.672306\pi\) | ||||
−0.515264 | + | 0.857031i | \(0.672306\pi\) | |||||||
\(168\) | 960.000 | 0.440867 | ||||||||
\(169\) | 1052.00 | 0.478835 | ||||||||
\(170\) | −960.000 | −0.433110 | ||||||||
\(171\) | 140.000 | 0.0626086 | ||||||||
\(172\) | −352.000 | −0.156045 | ||||||||
\(173\) | 3230.00 | 1.41949 | 0.709747 | − | 0.704457i | \(-0.248809\pi\) | ||||
0.709747 | + | 0.704457i | \(0.248809\pi\) | |||||||
\(174\) | 2450.00 | 1.06744 | ||||||||
\(175\) | 712.000 | 0.307555 | ||||||||
\(176\) | −544.000 | −0.232986 | ||||||||
\(177\) | 2040.00 | 0.866304 | ||||||||
\(178\) | 920.000 | 0.387398 | ||||||||
\(179\) | 369.000 | 0.154080 | 0.0770401 | − | 0.997028i | \(-0.475453\pi\) | ||||
0.0770401 | + | 0.997028i | \(0.475453\pi\) | |||||||
\(180\) | −48.0000 | −0.0198762 | ||||||||
\(181\) | −1370.00 | −0.562604 | −0.281302 | − | 0.959619i | \(-0.590766\pi\) | ||||
−0.281302 | + | 0.959619i | \(0.590766\pi\) | |||||||
\(182\) | −912.000 | −0.371439 | ||||||||
\(183\) | −4110.00 | −1.66022 | ||||||||
\(184\) | 552.000 | 0.221163 | ||||||||
\(185\) | 1788.00 | 0.710575 | ||||||||
\(186\) | 1030.00 | 0.406039 | ||||||||
\(187\) | −2720.00 | −1.06367 | ||||||||
\(188\) | 1428.00 | 0.553977 | ||||||||
\(189\) | −1160.00 | −0.446442 | ||||||||
\(190\) | −840.000 | −0.320737 | ||||||||
\(191\) | 4410.00 | 1.67066 | 0.835331 | − | 0.549747i | \(-0.185276\pi\) | ||||
0.835331 | + | 0.549747i | \(0.185276\pi\) | |||||||
\(192\) | −2240.00 | −0.841969 | ||||||||
\(193\) | −135.000 | −0.0503498 | −0.0251749 | − | 0.999683i | \(-0.508014\pi\) | ||||
−0.0251749 | + | 0.999683i | \(0.508014\pi\) | |||||||
\(194\) | 1928.00 | 0.713517 | ||||||||
\(195\) | −1710.00 | −0.627978 | ||||||||
\(196\) | 1116.00 | 0.406706 | ||||||||
\(197\) | 1221.00 | 0.441587 | 0.220794 | − | 0.975321i | \(-0.429135\pi\) | ||||
0.220794 | + | 0.975321i | \(0.429135\pi\) | |||||||
\(198\) | 136.000 | 0.0488136 | ||||||||
\(199\) | −1098.00 | −0.391131 | −0.195566 | − | 0.980691i | \(-0.562654\pi\) | ||||
−0.195566 | + | 0.980691i | \(0.562654\pi\) | |||||||
\(200\) | −2136.00 | −0.755190 | ||||||||
\(201\) | −4630.00 | −1.62475 | ||||||||
\(202\) | 620.000 | 0.215956 | ||||||||
\(203\) | −1960.00 | −0.677660 | ||||||||
\(204\) | −1600.00 | −0.549129 | ||||||||
\(205\) | −570.000 | −0.194198 | ||||||||
\(206\) | −2088.00 | −0.706203 | ||||||||
\(207\) | −46.0000 | −0.0154455 | ||||||||
\(208\) | 912.000 | 0.304018 | ||||||||
\(209\) | −2380.00 | −0.787694 | ||||||||
\(210\) | 480.000 | 0.157729 | ||||||||
\(211\) | −3676.00 | −1.19937 | −0.599683 | − | 0.800238i | \(-0.704707\pi\) | ||||
−0.599683 | + | 0.800238i | \(0.704707\pi\) | |||||||
\(212\) | 1656.00 | 0.536484 | ||||||||
\(213\) | −1675.00 | −0.538822 | ||||||||
\(214\) | −828.000 | −0.264490 | ||||||||
\(215\) | −528.000 | −0.167485 | ||||||||
\(216\) | 3480.00 | 1.09622 | ||||||||
\(217\) | −824.000 | −0.257773 | ||||||||
\(218\) | −1408.00 | −0.437439 | ||||||||
\(219\) | 4495.00 | 1.38696 | ||||||||
\(220\) | 816.000 | 0.250067 | ||||||||
\(221\) | 4560.00 | 1.38796 | ||||||||
\(222\) | −2980.00 | −0.900921 | ||||||||
\(223\) | 1656.00 | 0.497282 | 0.248641 | − | 0.968596i | \(-0.420016\pi\) | ||||
0.248641 | + | 0.968596i | \(0.420016\pi\) | |||||||
\(224\) | 1280.00 | 0.381802 | ||||||||
\(225\) | 178.000 | 0.0527407 | ||||||||
\(226\) | −1904.00 | −0.560408 | ||||||||
\(227\) | 2940.00 | 0.859624 | 0.429812 | − | 0.902918i | \(-0.358580\pi\) | ||||
0.429812 | + | 0.902918i | \(0.358580\pi\) | |||||||
\(228\) | −1400.00 | −0.406655 | ||||||||
\(229\) | 3612.00 | 1.04230 | 0.521152 | − | 0.853464i | \(-0.325502\pi\) | ||||
0.521152 | + | 0.853464i | \(0.325502\pi\) | |||||||
\(230\) | 276.000 | 0.0791257 | ||||||||
\(231\) | 1360.00 | 0.387366 | ||||||||
\(232\) | 5880.00 | 1.66397 | ||||||||
\(233\) | −4325.00 | −1.21605 | −0.608026 | − | 0.793917i | \(-0.708038\pi\) | ||||
−0.608026 | + | 0.793917i | \(0.708038\pi\) | |||||||
\(234\) | −228.000 | −0.0636958 | ||||||||
\(235\) | 2142.00 | 0.594590 | ||||||||
\(236\) | 1632.00 | 0.450145 | ||||||||
\(237\) | 6610.00 | 1.81167 | ||||||||
\(238\) | −1280.00 | −0.348614 | ||||||||
\(239\) | 2735.00 | 0.740219 | 0.370110 | − | 0.928988i | \(-0.379320\pi\) | ||||
0.370110 | + | 0.928988i | \(0.379320\pi\) | |||||||
\(240\) | −480.000 | −0.129099 | ||||||||
\(241\) | −6710.00 | −1.79348 | −0.896741 | − | 0.442556i | \(-0.854072\pi\) | ||||
−0.896741 | + | 0.442556i | \(0.854072\pi\) | |||||||
\(242\) | 350.000 | 0.0929705 | ||||||||
\(243\) | −560.000 | −0.147835 | ||||||||
\(244\) | −3288.00 | −0.862675 | ||||||||
\(245\) | 1674.00 | 0.436522 | ||||||||
\(246\) | 950.000 | 0.246219 | ||||||||
\(247\) | 3990.00 | 1.02784 | ||||||||
\(248\) | 2472.00 | 0.632952 | ||||||||
\(249\) | 180.000 | 0.0458114 | ||||||||
\(250\) | −2568.00 | −0.649658 | ||||||||
\(251\) | −6948.00 | −1.74723 | −0.873613 | − | 0.486621i | \(-0.838229\pi\) | ||||
−0.873613 | + | 0.486621i | \(0.838229\pi\) | |||||||
\(252\) | −64.0000 | −0.0159985 | ||||||||
\(253\) | 782.000 | 0.194324 | ||||||||
\(254\) | −522.000 | −0.128950 | ||||||||
\(255\) | −2400.00 | −0.589388 | ||||||||
\(256\) | −4352.00 | −1.06250 | ||||||||
\(257\) | −4929.00 | −1.19635 | −0.598176 | − | 0.801365i | \(-0.704108\pi\) | ||||
−0.598176 | + | 0.801365i | \(0.704108\pi\) | |||||||
\(258\) | 880.000 | 0.212350 | ||||||||
\(259\) | 2384.00 | 0.571948 | ||||||||
\(260\) | −1368.00 | −0.326307 | ||||||||
\(261\) | −490.000 | −0.116208 | ||||||||
\(262\) | 2882.00 | 0.679582 | ||||||||
\(263\) | 6138.00 | 1.43911 | 0.719554 | − | 0.694437i | \(-0.244346\pi\) | ||||
0.719554 | + | 0.694437i | \(0.244346\pi\) | |||||||
\(264\) | −4080.00 | −0.951162 | ||||||||
\(265\) | 2484.00 | 0.575815 | ||||||||
\(266\) | −1120.00 | −0.258164 | ||||||||
\(267\) | 2300.00 | 0.527182 | ||||||||
\(268\) | −3704.00 | −0.844246 | ||||||||
\(269\) | −2063.00 | −0.467596 | −0.233798 | − | 0.972285i | \(-0.575115\pi\) | ||||
−0.233798 | + | 0.972285i | \(0.575115\pi\) | |||||||
\(270\) | 1740.00 | 0.392196 | ||||||||
\(271\) | −1064.00 | −0.238500 | −0.119250 | − | 0.992864i | \(-0.538049\pi\) | ||||
−0.119250 | + | 0.992864i | \(0.538049\pi\) | |||||||
\(272\) | 1280.00 | 0.285336 | ||||||||
\(273\) | −2280.00 | −0.505465 | ||||||||
\(274\) | −3112.00 | −0.686142 | ||||||||
\(275\) | −3026.00 | −0.663544 | ||||||||
\(276\) | 460.000 | 0.100322 | ||||||||
\(277\) | 5729.00 | 1.24268 | 0.621340 | − | 0.783541i | \(-0.286589\pi\) | ||||
0.621340 | + | 0.783541i | \(0.286589\pi\) | |||||||
\(278\) | −50.0000 | −0.0107871 | ||||||||
\(279\) | −206.000 | −0.0442039 | ||||||||
\(280\) | 1152.00 | 0.245876 | ||||||||
\(281\) | −960.000 | −0.203804 | −0.101902 | − | 0.994794i | \(-0.532493\pi\) | ||||
−0.101902 | + | 0.994794i | \(0.532493\pi\) | |||||||
\(282\) | −3570.00 | −0.753867 | ||||||||
\(283\) | −114.000 | −0.0239456 | −0.0119728 | − | 0.999928i | \(-0.503811\pi\) | ||||
−0.0119728 | + | 0.999928i | \(0.503811\pi\) | |||||||
\(284\) | −1340.00 | −0.279980 | ||||||||
\(285\) | −2100.00 | −0.436468 | ||||||||
\(286\) | 3876.00 | 0.801373 | ||||||||
\(287\) | −760.000 | −0.156311 | ||||||||
\(288\) | 320.000 | 0.0654729 | ||||||||
\(289\) | 1487.00 | 0.302666 | ||||||||
\(290\) | 2940.00 | 0.595320 | ||||||||
\(291\) | 4820.00 | 0.970974 | ||||||||
\(292\) | 3596.00 | 0.720685 | ||||||||
\(293\) | −7048.00 | −1.40529 | −0.702643 | − | 0.711543i | \(-0.747997\pi\) | ||||
−0.702643 | + | 0.711543i | \(0.747997\pi\) | |||||||
\(294\) | −2790.00 | −0.553456 | ||||||||
\(295\) | 2448.00 | 0.483146 | ||||||||
\(296\) | −7152.00 | −1.40440 | ||||||||
\(297\) | 4930.00 | 0.963191 | ||||||||
\(298\) | −1644.00 | −0.319578 | ||||||||
\(299\) | −1311.00 | −0.253569 | ||||||||
\(300\) | −1780.00 | −0.342561 | ||||||||
\(301\) | −704.000 | −0.134810 | ||||||||
\(302\) | 2978.00 | 0.567433 | ||||||||
\(303\) | 1550.00 | 0.293878 | ||||||||
\(304\) | 1120.00 | 0.211304 | ||||||||
\(305\) | −4932.00 | −0.925920 | ||||||||
\(306\) | −320.000 | −0.0597816 | ||||||||
\(307\) | 3872.00 | 0.719826 | 0.359913 | − | 0.932986i | \(-0.382806\pi\) | ||||
0.359913 | + | 0.932986i | \(0.382806\pi\) | |||||||
\(308\) | 1088.00 | 0.201281 | ||||||||
\(309\) | −5220.00 | −0.961021 | ||||||||
\(310\) | 1236.00 | 0.226452 | ||||||||
\(311\) | −4977.00 | −0.907459 | −0.453730 | − | 0.891139i | \(-0.649907\pi\) | ||||
−0.453730 | + | 0.891139i | \(0.649907\pi\) | |||||||
\(312\) | 6840.00 | 1.24115 | ||||||||
\(313\) | −2536.00 | −0.457965 | −0.228983 | − | 0.973430i | \(-0.573540\pi\) | ||||
−0.228983 | + | 0.973430i | \(0.573540\pi\) | |||||||
\(314\) | 1264.00 | 0.227171 | ||||||||
\(315\) | −96.0000 | −0.0171714 | ||||||||
\(316\) | 5288.00 | 0.941371 | ||||||||
\(317\) | 1434.00 | 0.254074 | 0.127037 | − | 0.991898i | \(-0.459453\pi\) | ||||
0.127037 | + | 0.991898i | \(0.459453\pi\) | |||||||
\(318\) | −4140.00 | −0.730062 | ||||||||
\(319\) | 8330.00 | 1.46204 | ||||||||
\(320\) | −2688.00 | −0.469574 | ||||||||
\(321\) | −2070.00 | −0.359926 | ||||||||
\(322\) | 368.000 | 0.0636889 | ||||||||
\(323\) | 5600.00 | 0.964682 | ||||||||
\(324\) | 2684.00 | 0.460219 | ||||||||
\(325\) | 5073.00 | 0.865844 | ||||||||
\(326\) | 6086.00 | 1.03396 | ||||||||
\(327\) | −3520.00 | −0.595280 | ||||||||
\(328\) | 2280.00 | 0.383817 | ||||||||
\(329\) | 2856.00 | 0.478591 | ||||||||
\(330\) | −2040.00 | −0.340298 | ||||||||
\(331\) | 5469.00 | 0.908167 | 0.454084 | − | 0.890959i | \(-0.349967\pi\) | ||||
0.454084 | + | 0.890959i | \(0.349967\pi\) | |||||||
\(332\) | 144.000 | 0.0238043 | ||||||||
\(333\) | 596.000 | 0.0980799 | ||||||||
\(334\) | 4448.00 | 0.728694 | ||||||||
\(335\) | −5556.00 | −0.906139 | ||||||||
\(336\) | −640.000 | −0.103913 | ||||||||
\(337\) | −7796.00 | −1.26016 | −0.630082 | − | 0.776529i | \(-0.716979\pi\) | ||||
−0.630082 | + | 0.776529i | \(0.716979\pi\) | |||||||
\(338\) | −2104.00 | −0.338587 | ||||||||
\(339\) | −4760.00 | −0.762619 | ||||||||
\(340\) | −1920.00 | −0.306255 | ||||||||
\(341\) | 3502.00 | 0.556141 | ||||||||
\(342\) | −280.000 | −0.0442710 | ||||||||
\(343\) | 4976.00 | 0.783320 | ||||||||
\(344\) | 2112.00 | 0.331022 | ||||||||
\(345\) | 690.000 | 0.107676 | ||||||||
\(346\) | −6460.00 | −1.00373 | ||||||||
\(347\) | −10068.0 | −1.55758 | −0.778788 | − | 0.627288i | \(-0.784165\pi\) | ||||
−0.778788 | + | 0.627288i | \(0.784165\pi\) | |||||||
\(348\) | 4900.00 | 0.754792 | ||||||||
\(349\) | −7495.00 | −1.14956 | −0.574782 | − | 0.818306i | \(-0.694913\pi\) | ||||
−0.574782 | + | 0.818306i | \(0.694913\pi\) | |||||||
\(350\) | −1424.00 | −0.217474 | ||||||||
\(351\) | −8265.00 | −1.25685 | ||||||||
\(352\) | −5440.00 | −0.823730 | ||||||||
\(353\) | 10617.0 | 1.60081 | 0.800405 | − | 0.599460i | \(-0.204618\pi\) | ||||
0.800405 | + | 0.599460i | \(0.204618\pi\) | |||||||
\(354\) | −4080.00 | −0.612569 | ||||||||
\(355\) | −2010.00 | −0.300506 | ||||||||
\(356\) | 1840.00 | 0.273932 | ||||||||
\(357\) | −3200.00 | −0.474403 | ||||||||
\(358\) | −738.000 | −0.108951 | ||||||||
\(359\) | 2522.00 | 0.370769 | 0.185384 | − | 0.982666i | \(-0.440647\pi\) | ||||
0.185384 | + | 0.982666i | \(0.440647\pi\) | |||||||
\(360\) | 288.000 | 0.0421637 | ||||||||
\(361\) | −1959.00 | −0.285610 | ||||||||
\(362\) | 2740.00 | 0.397821 | ||||||||
\(363\) | 875.000 | 0.126517 | ||||||||
\(364\) | −1824.00 | −0.262647 | ||||||||
\(365\) | 5394.00 | 0.773520 | ||||||||
\(366\) | 8220.00 | 1.17395 | ||||||||
\(367\) | 7204.00 | 1.02465 | 0.512324 | − | 0.858792i | \(-0.328785\pi\) | ||||
0.512324 | + | 0.858792i | \(0.328785\pi\) | |||||||
\(368\) | −368.000 | −0.0521286 | ||||||||
\(369\) | −190.000 | −0.0268049 | ||||||||
\(370\) | −3576.00 | −0.502452 | ||||||||
\(371\) | 3312.00 | 0.463478 | ||||||||
\(372\) | 2060.00 | 0.287113 | ||||||||
\(373\) | −13310.0 | −1.84763 | −0.923815 | − | 0.382840i | \(-0.874946\pi\) | ||||
−0.923815 | + | 0.382840i | \(0.874946\pi\) | |||||||
\(374\) | 5440.00 | 0.752128 | ||||||||
\(375\) | −6420.00 | −0.884073 | ||||||||
\(376\) | −8568.00 | −1.17516 | ||||||||
\(377\) | −13965.0 | −1.90778 | ||||||||
\(378\) | 2320.00 | 0.315682 | ||||||||
\(379\) | 12952.0 | 1.75541 | 0.877704 | − | 0.479203i | \(-0.159074\pi\) | ||||
0.877704 | + | 0.479203i | \(0.159074\pi\) | |||||||
\(380\) | −1680.00 | −0.226795 | ||||||||
\(381\) | −1305.00 | −0.175478 | ||||||||
\(382\) | −8820.00 | −1.18134 | ||||||||
\(383\) | −2812.00 | −0.375161 | −0.187580 | − | 0.982249i | \(-0.560064\pi\) | ||||
−0.187580 | + | 0.982249i | \(0.560064\pi\) | |||||||
\(384\) | −1920.00 | −0.255155 | ||||||||
\(385\) | 1632.00 | 0.216037 | ||||||||
\(386\) | 270.000 | 0.0356027 | ||||||||
\(387\) | −176.000 | −0.0231178 | ||||||||
\(388\) | 3856.00 | 0.504533 | ||||||||
\(389\) | 1264.00 | 0.164749 | 0.0823745 | − | 0.996601i | \(-0.473750\pi\) | ||||
0.0823745 | + | 0.996601i | \(0.473750\pi\) | |||||||
\(390\) | 3420.00 | 0.444047 | ||||||||
\(391\) | −1840.00 | −0.237987 | ||||||||
\(392\) | −6696.00 | −0.862753 | ||||||||
\(393\) | 7205.00 | 0.924794 | ||||||||
\(394\) | −2442.00 | −0.312249 | ||||||||
\(395\) | 7932.00 | 1.01039 | ||||||||
\(396\) | 272.000 | 0.0345165 | ||||||||
\(397\) | 7119.00 | 0.899981 | 0.449990 | − | 0.893033i | \(-0.351427\pi\) | ||||
0.449990 | + | 0.893033i | \(0.351427\pi\) | |||||||
\(398\) | 2196.00 | 0.276572 | ||||||||
\(399\) | −2800.00 | −0.351317 | ||||||||
\(400\) | 1424.00 | 0.178000 | ||||||||
\(401\) | 4262.00 | 0.530758 | 0.265379 | − | 0.964144i | \(-0.414503\pi\) | ||||
0.265379 | + | 0.964144i | \(0.414503\pi\) | |||||||
\(402\) | 9260.00 | 1.14887 | ||||||||
\(403\) | −5871.00 | −0.725696 | ||||||||
\(404\) | 1240.00 | 0.152704 | ||||||||
\(405\) | 4026.00 | 0.493959 | ||||||||
\(406\) | 3920.00 | 0.479178 | ||||||||
\(407\) | −10132.0 | −1.23397 | ||||||||
\(408\) | 9600.00 | 1.16488 | ||||||||
\(409\) | 229.000 | 0.0276854 | 0.0138427 | − | 0.999904i | \(-0.495594\pi\) | ||||
0.0138427 | + | 0.999904i | \(0.495594\pi\) | |||||||
\(410\) | 1140.00 | 0.137319 | ||||||||
\(411\) | −7780.00 | −0.933720 | ||||||||
\(412\) | −4176.00 | −0.499361 | ||||||||
\(413\) | 3264.00 | 0.388888 | ||||||||
\(414\) | 92.0000 | 0.0109216 | ||||||||
\(415\) | 216.000 | 0.0255495 | ||||||||
\(416\) | 9120.00 | 1.07487 | ||||||||
\(417\) | −125.000 | −0.0146793 | ||||||||
\(418\) | 4760.00 | 0.556984 | ||||||||
\(419\) | 15776.0 | 1.83940 | 0.919699 | − | 0.392623i | \(-0.128432\pi\) | ||||
0.919699 | + | 0.392623i | \(0.128432\pi\) | |||||||
\(420\) | 960.000 | 0.111531 | ||||||||
\(421\) | −8728.00 | −1.01040 | −0.505198 | − | 0.863003i | \(-0.668581\pi\) | ||||
−0.505198 | + | 0.863003i | \(0.668581\pi\) | |||||||
\(422\) | 7352.00 | 0.848080 | ||||||||
\(423\) | 714.000 | 0.0820706 | ||||||||
\(424\) | −9936.00 | −1.13805 | ||||||||
\(425\) | 7120.00 | 0.812637 | ||||||||
\(426\) | 3350.00 | 0.381005 | ||||||||
\(427\) | −6576.00 | −0.745281 | ||||||||
\(428\) | −1656.00 | −0.187023 | ||||||||
\(429\) | 9690.00 | 1.09053 | ||||||||
\(430\) | 1056.00 | 0.118430 | ||||||||
\(431\) | −2928.00 | −0.327232 | −0.163616 | − | 0.986524i | \(-0.552316\pi\) | ||||
−0.163616 | + | 0.986524i | \(0.552316\pi\) | |||||||
\(432\) | −2320.00 | −0.258382 | ||||||||
\(433\) | −5314.00 | −0.589780 | −0.294890 | − | 0.955531i | \(-0.595283\pi\) | ||||
−0.294890 | + | 0.955531i | \(0.595283\pi\) | |||||||
\(434\) | 1648.00 | 0.182273 | ||||||||
\(435\) | 7350.00 | 0.810128 | ||||||||
\(436\) | −2816.00 | −0.309316 | ||||||||
\(437\) | −1610.00 | −0.176240 | ||||||||
\(438\) | −8990.00 | −0.980728 | ||||||||
\(439\) | 2585.00 | 0.281037 | 0.140519 | − | 0.990078i | \(-0.455123\pi\) | ||||
0.140519 | + | 0.990078i | \(0.455123\pi\) | |||||||
\(440\) | −4896.00 | −0.530472 | ||||||||
\(441\) | 558.000 | 0.0602527 | ||||||||
\(442\) | −9120.00 | −0.981435 | ||||||||
\(443\) | −2997.00 | −0.321426 | −0.160713 | − | 0.987001i | \(-0.551379\pi\) | ||||
−0.160713 | + | 0.987001i | \(0.551379\pi\) | |||||||
\(444\) | −5960.00 | −0.637047 | ||||||||
\(445\) | 2760.00 | 0.294015 | ||||||||
\(446\) | −3312.00 | −0.351632 | ||||||||
\(447\) | −4110.00 | −0.434891 | ||||||||
\(448\) | −3584.00 | −0.377964 | ||||||||
\(449\) | −16562.0 | −1.74078 | −0.870389 | − | 0.492365i | \(-0.836132\pi\) | ||||
−0.870389 | + | 0.492365i | \(0.836132\pi\) | |||||||
\(450\) | −356.000 | −0.0372933 | ||||||||
\(451\) | 3230.00 | 0.337239 | ||||||||
\(452\) | −3808.00 | −0.396268 | ||||||||
\(453\) | 7445.00 | 0.772178 | ||||||||
\(454\) | −5880.00 | −0.607846 | ||||||||
\(455\) | −2736.00 | −0.281903 | ||||||||
\(456\) | 8400.00 | 0.862645 | ||||||||
\(457\) | 3924.00 | 0.401656 | 0.200828 | − | 0.979626i | \(-0.435637\pi\) | ||||
0.200828 | + | 0.979626i | \(0.435637\pi\) | |||||||
\(458\) | −7224.00 | −0.737020 | ||||||||
\(459\) | −11600.0 | −1.17961 | ||||||||
\(460\) | 552.000 | 0.0559503 | ||||||||
\(461\) | −4543.00 | −0.458977 | −0.229489 | − | 0.973311i | \(-0.573705\pi\) | ||||
−0.229489 | + | 0.973311i | \(0.573705\pi\) | |||||||
\(462\) | −2720.00 | −0.273909 | ||||||||
\(463\) | 9616.00 | 0.965213 | 0.482606 | − | 0.875837i | \(-0.339690\pi\) | ||||
0.482606 | + | 0.875837i | \(0.339690\pi\) | |||||||
\(464\) | −3920.00 | −0.392201 | ||||||||
\(465\) | 3090.00 | 0.308162 | ||||||||
\(466\) | 8650.00 | 0.859879 | ||||||||
\(467\) | 7826.00 | 0.775469 | 0.387735 | − | 0.921771i | \(-0.373258\pi\) | ||||
0.387735 | + | 0.921771i | \(0.373258\pi\) | |||||||
\(468\) | −456.000 | −0.0450398 | ||||||||
\(469\) | −7408.00 | −0.729360 | ||||||||
\(470\) | −4284.00 | −0.420439 | ||||||||
\(471\) | 3160.00 | 0.309140 | ||||||||
\(472\) | −9792.00 | −0.954901 | ||||||||
\(473\) | 2992.00 | 0.290851 | ||||||||
\(474\) | −13220.0 | −1.28104 | ||||||||
\(475\) | 6230.00 | 0.601794 | ||||||||
\(476\) | −2560.00 | −0.246507 | ||||||||
\(477\) | 828.000 | 0.0794791 | ||||||||
\(478\) | −5470.00 | −0.523414 | ||||||||
\(479\) | 11404.0 | 1.08781 | 0.543906 | − | 0.839146i | \(-0.316945\pi\) | ||||
0.543906 | + | 0.839146i | \(0.316945\pi\) | |||||||
\(480\) | −4800.00 | −0.456435 | ||||||||
\(481\) | 16986.0 | 1.61018 | ||||||||
\(482\) | 13420.0 | 1.26818 | ||||||||
\(483\) | 920.000 | 0.0866697 | ||||||||
\(484\) | 700.000 | 0.0657400 | ||||||||
\(485\) | 5784.00 | 0.541521 | ||||||||
\(486\) | 1120.00 | 0.104535 | ||||||||
\(487\) | −9267.00 | −0.862275 | −0.431137 | − | 0.902286i | \(-0.641888\pi\) | ||||
−0.431137 | + | 0.902286i | \(0.641888\pi\) | |||||||
\(488\) | 19728.0 | 1.83001 | ||||||||
\(489\) | 15215.0 | 1.40705 | ||||||||
\(490\) | −3348.00 | −0.308668 | ||||||||
\(491\) | −18191.0 | −1.67199 | −0.835996 | − | 0.548735i | \(-0.815110\pi\) | ||||
−0.835996 | + | 0.548735i | \(0.815110\pi\) | |||||||
\(492\) | 1900.00 | 0.174103 | ||||||||
\(493\) | −19600.0 | −1.79055 | ||||||||
\(494\) | −7980.00 | −0.726796 | ||||||||
\(495\) | 408.000 | 0.0370469 | ||||||||
\(496\) | −1648.00 | −0.149188 | ||||||||
\(497\) | −2680.00 | −0.241880 | ||||||||
\(498\) | −360.000 | −0.0323935 | ||||||||
\(499\) | 19315.0 | 1.73278 | 0.866391 | − | 0.499366i | \(-0.166434\pi\) | ||||
0.866391 | + | 0.499366i | \(0.166434\pi\) | |||||||
\(500\) | −5136.00 | −0.459378 | ||||||||
\(501\) | 11120.0 | 0.991627 | ||||||||
\(502\) | 13896.0 | 1.23548 | ||||||||
\(503\) | 8422.00 | 0.746557 | 0.373279 | − | 0.927719i | \(-0.378234\pi\) | ||||
0.373279 | + | 0.927719i | \(0.378234\pi\) | |||||||
\(504\) | 384.000 | 0.0339379 | ||||||||
\(505\) | 1860.00 | 0.163899 | ||||||||
\(506\) | −1564.00 | −0.137408 | ||||||||
\(507\) | −5260.00 | −0.460759 | ||||||||
\(508\) | −1044.00 | −0.0911811 | ||||||||
\(509\) | −863.000 | −0.0751509 | −0.0375754 | − | 0.999294i | \(-0.511963\pi\) | ||||
−0.0375754 | + | 0.999294i | \(0.511963\pi\) | |||||||
\(510\) | 4800.00 | 0.416760 | ||||||||
\(511\) | 7192.00 | 0.622613 | ||||||||
\(512\) | 5632.00 | 0.486136 | ||||||||
\(513\) | −10150.0 | −0.873554 | ||||||||
\(514\) | 9858.00 | 0.845949 | ||||||||
\(515\) | −6264.00 | −0.535971 | ||||||||
\(516\) | 1760.00 | 0.150154 | ||||||||
\(517\) | −12138.0 | −1.03255 | ||||||||
\(518\) | −4768.00 | −0.404428 | ||||||||
\(519\) | −16150.0 | −1.36591 | ||||||||
\(520\) | 8208.00 | 0.692201 | ||||||||
\(521\) | 19260.0 | 1.61957 | 0.809785 | − | 0.586727i | \(-0.199584\pi\) | ||||
0.809785 | + | 0.586727i | \(0.199584\pi\) | |||||||
\(522\) | 980.000 | 0.0821713 | ||||||||
\(523\) | −11740.0 | −0.981557 | −0.490779 | − | 0.871284i | \(-0.663288\pi\) | ||||
−0.490779 | + | 0.871284i | \(0.663288\pi\) | |||||||
\(524\) | 5764.00 | 0.480537 | ||||||||
\(525\) | −3560.00 | −0.295945 | ||||||||
\(526\) | −12276.0 | −1.01760 | ||||||||
\(527\) | −8240.00 | −0.681101 | ||||||||
\(528\) | 2720.00 | 0.224191 | ||||||||
\(529\) | 529.000 | 0.0434783 | ||||||||
\(530\) | −4968.00 | −0.407163 | ||||||||
\(531\) | 816.000 | 0.0666881 | ||||||||
\(532\) | −2240.00 | −0.182549 | ||||||||
\(533\) | −5415.00 | −0.440056 | ||||||||
\(534\) | −4600.00 | −0.372774 | ||||||||
\(535\) | −2484.00 | −0.200734 | ||||||||
\(536\) | 22224.0 | 1.79092 | ||||||||
\(537\) | −1845.00 | −0.148264 | ||||||||
\(538\) | 4126.00 | 0.330640 | ||||||||
\(539\) | −9486.00 | −0.758054 | ||||||||
\(540\) | 3480.00 | 0.277325 | ||||||||
\(541\) | 17741.0 | 1.40988 | 0.704940 | − | 0.709267i | \(-0.250974\pi\) | ||||
0.704940 | + | 0.709267i | \(0.250974\pi\) | |||||||
\(542\) | 2128.00 | 0.168645 | ||||||||
\(543\) | 6850.00 | 0.541366 | ||||||||
\(544\) | 12800.0 | 1.00882 | ||||||||
\(545\) | −4224.00 | −0.331993 | ||||||||
\(546\) | 4560.00 | 0.357418 | ||||||||
\(547\) | −6571.00 | −0.513630 | −0.256815 | − | 0.966461i | \(-0.582673\pi\) | ||||
−0.256815 | + | 0.966461i | \(0.582673\pi\) | |||||||
\(548\) | −6224.00 | −0.485175 | ||||||||
\(549\) | −1644.00 | −0.127804 | ||||||||
\(550\) | 6052.00 | 0.469197 | ||||||||
\(551\) | −17150.0 | −1.32598 | ||||||||
\(552\) | −2760.00 | −0.212814 | ||||||||
\(553\) | 10576.0 | 0.813268 | ||||||||
\(554\) | −11458.0 | −0.878707 | ||||||||
\(555\) | −8940.00 | −0.683751 | ||||||||
\(556\) | −100.000 | −0.00762760 | ||||||||
\(557\) | −1372.00 | −0.104369 | −0.0521845 | − | 0.998637i | \(-0.516618\pi\) | ||||
−0.0521845 | + | 0.998637i | \(0.516618\pi\) | |||||||
\(558\) | 412.000 | 0.0312569 | ||||||||
\(559\) | −5016.00 | −0.379524 | ||||||||
\(560\) | −768.000 | −0.0579534 | ||||||||
\(561\) | 13600.0 | 1.02352 | ||||||||
\(562\) | 1920.00 | 0.144111 | ||||||||
\(563\) | 4332.00 | 0.324284 | 0.162142 | − | 0.986767i | \(-0.448160\pi\) | ||||
0.162142 | + | 0.986767i | \(0.448160\pi\) | |||||||
\(564\) | −7140.00 | −0.533064 | ||||||||
\(565\) | −5712.00 | −0.425320 | ||||||||
\(566\) | 228.000 | 0.0169321 | ||||||||
\(567\) | 5368.00 | 0.397592 | ||||||||
\(568\) | 8040.00 | 0.593928 | ||||||||
\(569\) | −3546.00 | −0.261258 | −0.130629 | − | 0.991431i | \(-0.541700\pi\) | ||||
−0.130629 | + | 0.991431i | \(0.541700\pi\) | |||||||
\(570\) | 4200.00 | 0.308629 | ||||||||
\(571\) | −6160.00 | −0.451468 | −0.225734 | − | 0.974189i | \(-0.572478\pi\) | ||||
−0.225734 | + | 0.974189i | \(0.572478\pi\) | |||||||
\(572\) | 7752.00 | 0.566656 | ||||||||
\(573\) | −22050.0 | −1.60760 | ||||||||
\(574\) | 1520.00 | 0.110529 | ||||||||
\(575\) | −2047.00 | −0.148462 | ||||||||
\(576\) | −896.000 | −0.0648148 | ||||||||
\(577\) | 2953.00 | 0.213059 | 0.106529 | − | 0.994310i | \(-0.466026\pi\) | ||||
0.106529 | + | 0.994310i | \(0.466026\pi\) | |||||||
\(578\) | −2974.00 | −0.214017 | ||||||||
\(579\) | 675.000 | 0.0484491 | ||||||||
\(580\) | 5880.00 | 0.420955 | ||||||||
\(581\) | 288.000 | 0.0205650 | ||||||||
\(582\) | −9640.00 | −0.686582 | ||||||||
\(583\) | −14076.0 | −0.999946 | ||||||||
\(584\) | −21576.0 | −1.52880 | ||||||||
\(585\) | −684.000 | −0.0483417 | ||||||||
\(586\) | 14096.0 | 0.993687 | ||||||||
\(587\) | −2949.00 | −0.207356 | −0.103678 | − | 0.994611i | \(-0.533061\pi\) | ||||
−0.103678 | + | 0.994611i | \(0.533061\pi\) | |||||||
\(588\) | −5580.00 | −0.391353 | ||||||||
\(589\) | −7210.00 | −0.504385 | ||||||||
\(590\) | −4896.00 | −0.341636 | ||||||||
\(591\) | −6105.00 | −0.424917 | ||||||||
\(592\) | 4768.00 | 0.331020 | ||||||||
\(593\) | 16390.0 | 1.13500 | 0.567501 | − | 0.823372i | \(-0.307910\pi\) | ||||
0.567501 | + | 0.823372i | \(0.307910\pi\) | |||||||
\(594\) | −9860.00 | −0.681079 | ||||||||
\(595\) | −3840.00 | −0.264579 | ||||||||
\(596\) | −3288.00 | −0.225976 | ||||||||
\(597\) | 5490.00 | 0.376366 | ||||||||
\(598\) | 2622.00 | 0.179300 | ||||||||
\(599\) | −12920.0 | −0.881297 | −0.440648 | − | 0.897680i | \(-0.645251\pi\) | ||||
−0.440648 | + | 0.897680i | \(0.645251\pi\) | |||||||
\(600\) | 10680.0 | 0.726682 | ||||||||
\(601\) | −13835.0 | −0.939004 | −0.469502 | − | 0.882931i | \(-0.655567\pi\) | ||||
−0.469502 | + | 0.882931i | \(0.655567\pi\) | |||||||
\(602\) | 1408.00 | 0.0953252 | ||||||||
\(603\) | −1852.00 | −0.125073 | ||||||||
\(604\) | 5956.00 | 0.401235 | ||||||||
\(605\) | 1050.00 | 0.0705596 | ||||||||
\(606\) | −3100.00 | −0.207803 | ||||||||
\(607\) | 6004.00 | 0.401474 | 0.200737 | − | 0.979645i | \(-0.435666\pi\) | ||||
0.200737 | + | 0.979645i | \(0.435666\pi\) | |||||||
\(608\) | 11200.0 | 0.747072 | ||||||||
\(609\) | 9800.00 | 0.652079 | ||||||||
\(610\) | 9864.00 | 0.654724 | ||||||||
\(611\) | 20349.0 | 1.34735 | ||||||||
\(612\) | −640.000 | −0.0422720 | ||||||||
\(613\) | −16416.0 | −1.08162 | −0.540812 | − | 0.841143i | \(-0.681883\pi\) | ||||
−0.540812 | + | 0.841143i | \(0.681883\pi\) | |||||||
\(614\) | −7744.00 | −0.508994 | ||||||||
\(615\) | 2850.00 | 0.186867 | ||||||||
\(616\) | −6528.00 | −0.426982 | ||||||||
\(617\) | 3786.00 | 0.247032 | 0.123516 | − | 0.992343i | \(-0.460583\pi\) | ||||
0.123516 | + | 0.992343i | \(0.460583\pi\) | |||||||
\(618\) | 10440.0 | 0.679544 | ||||||||
\(619\) | 15824.0 | 1.02750 | 0.513748 | − | 0.857941i | \(-0.328257\pi\) | ||||
0.513748 | + | 0.857941i | \(0.328257\pi\) | |||||||
\(620\) | 2472.00 | 0.160126 | ||||||||
\(621\) | 3335.00 | 0.215506 | ||||||||
\(622\) | 9954.00 | 0.641670 | ||||||||
\(623\) | 3680.00 | 0.236655 | ||||||||
\(624\) | −4560.00 | −0.292542 | ||||||||
\(625\) | 3421.00 | 0.218944 | ||||||||
\(626\) | 5072.00 | 0.323830 | ||||||||
\(627\) | 11900.0 | 0.757959 | ||||||||
\(628\) | 2528.00 | 0.160634 | ||||||||
\(629\) | 23840.0 | 1.51123 | ||||||||
\(630\) | 192.000 | 0.0121420 | ||||||||
\(631\) | 17852.0 | 1.12627 | 0.563135 | − | 0.826365i | \(-0.309595\pi\) | ||||
0.563135 | + | 0.826365i | \(0.309595\pi\) | |||||||
\(632\) | −31728.0 | −1.99695 | ||||||||
\(633\) | 18380.0 | 1.15409 | ||||||||
\(634\) | −2868.00 | −0.179657 | ||||||||
\(635\) | −1566.00 | −0.0978658 | ||||||||
\(636\) | −8280.00 | −0.516232 | ||||||||
\(637\) | 15903.0 | 0.989168 | ||||||||
\(638\) | −16660.0 | −1.03382 | ||||||||
\(639\) | −670.000 | −0.0414785 | ||||||||
\(640\) | −2304.00 | −0.142302 | ||||||||
\(641\) | 10324.0 | 0.636152 | 0.318076 | − | 0.948065i | \(-0.396963\pi\) | ||||
0.318076 | + | 0.948065i | \(0.396963\pi\) | |||||||
\(642\) | 4140.00 | 0.254506 | ||||||||
\(643\) | −14702.0 | −0.901696 | −0.450848 | − | 0.892601i | \(-0.648878\pi\) | ||||
−0.450848 | + | 0.892601i | \(0.648878\pi\) | |||||||
\(644\) | 736.000 | 0.0450349 | ||||||||
\(645\) | 2640.00 | 0.161163 | ||||||||
\(646\) | −11200.0 | −0.682133 | ||||||||
\(647\) | 11939.0 | 0.725457 | 0.362728 | − | 0.931895i | \(-0.381845\pi\) | ||||
0.362728 | + | 0.931895i | \(0.381845\pi\) | |||||||
\(648\) | −16104.0 | −0.976273 | ||||||||
\(649\) | −13872.0 | −0.839019 | ||||||||
\(650\) | −10146.0 | −0.612244 | ||||||||
\(651\) | 4120.00 | 0.248042 | ||||||||
\(652\) | 12172.0 | 0.731123 | ||||||||
\(653\) | 6159.00 | 0.369097 | 0.184548 | − | 0.982823i | \(-0.440918\pi\) | ||||
0.184548 | + | 0.982823i | \(0.440918\pi\) | |||||||
\(654\) | 7040.00 | 0.420926 | ||||||||
\(655\) | 8646.00 | 0.515767 | ||||||||
\(656\) | −1520.00 | −0.0904665 | ||||||||
\(657\) | 1798.00 | 0.106768 | ||||||||
\(658\) | −5712.00 | −0.338415 | ||||||||
\(659\) | −21692.0 | −1.28225 | −0.641123 | − | 0.767438i | \(-0.721531\pi\) | ||||
−0.641123 | + | 0.767438i | \(0.721531\pi\) | |||||||
\(660\) | −4080.00 | −0.240627 | ||||||||
\(661\) | 16502.0 | 0.971034 | 0.485517 | − | 0.874227i | \(-0.338631\pi\) | ||||
0.485517 | + | 0.874227i | \(0.338631\pi\) | |||||||
\(662\) | −10938.0 | −0.642171 | ||||||||
\(663\) | −22800.0 | −1.33556 | ||||||||
\(664\) | −864.000 | −0.0504965 | ||||||||
\(665\) | −3360.00 | −0.195933 | ||||||||
\(666\) | −1192.00 | −0.0693529 | ||||||||
\(667\) | 5635.00 | 0.327119 | ||||||||
\(668\) | 8896.00 | 0.515264 | ||||||||
\(669\) | −8280.00 | −0.478510 | ||||||||
\(670\) | 11112.0 | 0.640737 | ||||||||
\(671\) | 27948.0 | 1.60793 | ||||||||
\(672\) | −6400.00 | −0.367389 | ||||||||
\(673\) | −27733.0 | −1.58845 | −0.794226 | − | 0.607622i | \(-0.792124\pi\) | ||||
−0.794226 | + | 0.607622i | \(0.792124\pi\) | |||||||
\(674\) | 15592.0 | 0.891070 | ||||||||
\(675\) | −12905.0 | −0.735872 | ||||||||
\(676\) | −4208.00 | −0.239417 | ||||||||
\(677\) | −8814.00 | −0.500369 | −0.250184 | − | 0.968198i | \(-0.580491\pi\) | ||||
−0.250184 | + | 0.968198i | \(0.580491\pi\) | |||||||
\(678\) | 9520.00 | 0.539253 | ||||||||
\(679\) | 7712.00 | 0.435875 | ||||||||
\(680\) | 11520.0 | 0.649664 | ||||||||
\(681\) | −14700.0 | −0.827174 | ||||||||
\(682\) | −7004.00 | −0.393251 | ||||||||
\(683\) | −22999.0 | −1.28848 | −0.644240 | − | 0.764823i | \(-0.722826\pi\) | ||||
−0.644240 | + | 0.764823i | \(0.722826\pi\) | |||||||
\(684\) | −560.000 | −0.0313043 | ||||||||
\(685\) | −9336.00 | −0.520745 | ||||||||
\(686\) | −9952.00 | −0.553891 | ||||||||
\(687\) | −18060.0 | −1.00296 | ||||||||
\(688\) | −1408.00 | −0.0780225 | ||||||||
\(689\) | 23598.0 | 1.30481 | ||||||||
\(690\) | −1380.00 | −0.0761387 | ||||||||
\(691\) | −12140.0 | −0.668346 | −0.334173 | − | 0.942512i | \(-0.608457\pi\) | ||||
−0.334173 | + | 0.942512i | \(0.608457\pi\) | |||||||
\(692\) | −12920.0 | −0.709747 | ||||||||
\(693\) | 544.000 | 0.0298194 | ||||||||
\(694\) | 20136.0 | 1.10137 | ||||||||
\(695\) | −150.000 | −0.00818680 | ||||||||
\(696\) | −29400.0 | −1.60116 | ||||||||
\(697\) | −7600.00 | −0.413014 | ||||||||
\(698\) | 14990.0 | 0.812865 | ||||||||
\(699\) | 21625.0 | 1.17015 | ||||||||
\(700\) | −2848.00 | −0.153778 | ||||||||
\(701\) | −20024.0 | −1.07888 | −0.539441 | − | 0.842024i | \(-0.681364\pi\) | ||||
−0.539441 | + | 0.842024i | \(0.681364\pi\) | |||||||
\(702\) | 16530.0 | 0.888725 | ||||||||
\(703\) | 20860.0 | 1.11913 | ||||||||
\(704\) | 15232.0 | 0.815451 | ||||||||
\(705\) | −10710.0 | −0.572145 | ||||||||
\(706\) | −21234.0 | −1.13194 | ||||||||
\(707\) | 2480.00 | 0.131924 | ||||||||
\(708\) | −8160.00 | −0.433152 | ||||||||
\(709\) | −4956.00 | −0.262520 | −0.131260 | − | 0.991348i | \(-0.541902\pi\) | ||||
−0.131260 | + | 0.991348i | \(0.541902\pi\) | |||||||
\(710\) | 4020.00 | 0.212490 | ||||||||
\(711\) | 2644.00 | 0.139462 | ||||||||
\(712\) | −11040.0 | −0.581098 | ||||||||
\(713\) | 2369.00 | 0.124432 | ||||||||
\(714\) | 6400.00 | 0.335454 | ||||||||
\(715\) | 11628.0 | 0.608199 | ||||||||
\(716\) | −1476.00 | −0.0770401 | ||||||||
\(717\) | −13675.0 | −0.712276 | ||||||||
\(718\) | −5044.00 | −0.262173 | ||||||||
\(719\) | 2760.00 | 0.143158 | 0.0715790 | − | 0.997435i | \(-0.477196\pi\) | ||||
0.0715790 | + | 0.997435i | \(0.477196\pi\) | |||||||
\(720\) | −192.000 | −0.00993808 | ||||||||
\(721\) | −8352.00 | −0.431407 | ||||||||
\(722\) | 3918.00 | 0.201957 | ||||||||
\(723\) | 33550.0 | 1.72578 | ||||||||
\(724\) | 5480.00 | 0.281302 | ||||||||
\(725\) | −21805.0 | −1.11699 | ||||||||
\(726\) | −1750.00 | −0.0894609 | ||||||||
\(727\) | 7746.00 | 0.395163 | 0.197581 | − | 0.980287i | \(-0.436691\pi\) | ||||
0.197581 | + | 0.980287i | \(0.436691\pi\) | |||||||
\(728\) | 10944.0 | 0.557159 | ||||||||
\(729\) | 20917.0 | 1.06269 | ||||||||
\(730\) | −10788.0 | −0.546961 | ||||||||
\(731\) | −7040.00 | −0.356202 | ||||||||
\(732\) | 16440.0 | 0.830109 | ||||||||
\(733\) | −11976.0 | −0.603470 | −0.301735 | − | 0.953392i | \(-0.597566\pi\) | ||||
−0.301735 | + | 0.953392i | \(0.597566\pi\) | |||||||
\(734\) | −14408.0 | −0.724535 | ||||||||
\(735\) | −8370.00 | −0.420044 | ||||||||
\(736\) | −3680.00 | −0.184302 | ||||||||
\(737\) | 31484.0 | 1.57358 | ||||||||
\(738\) | 380.000 | 0.0189539 | ||||||||
\(739\) | 15057.0 | 0.749500 | 0.374750 | − | 0.927126i | \(-0.377728\pi\) | ||||
0.374750 | + | 0.927126i | \(0.377728\pi\) | |||||||
\(740\) | −7152.00 | −0.355287 | ||||||||
\(741\) | −19950.0 | −0.989044 | ||||||||
\(742\) | −6624.00 | −0.327729 | ||||||||
\(743\) | 18532.0 | 0.915038 | 0.457519 | − | 0.889200i | \(-0.348738\pi\) | ||||
0.457519 | + | 0.889200i | \(0.348738\pi\) | |||||||
\(744\) | −12360.0 | −0.609059 | ||||||||
\(745\) | −4932.00 | −0.242543 | ||||||||
\(746\) | 26620.0 | 1.30647 | ||||||||
\(747\) | 72.0000 | 0.00352656 | ||||||||
\(748\) | 10880.0 | 0.531834 | ||||||||
\(749\) | −3312.00 | −0.161573 | ||||||||
\(750\) | 12840.0 | 0.625134 | ||||||||
\(751\) | −192.000 | −0.00932913 | −0.00466457 | − | 0.999989i | \(-0.501485\pi\) | ||||
−0.00466457 | + | 0.999989i | \(0.501485\pi\) | |||||||
\(752\) | 5712.00 | 0.276988 | ||||||||
\(753\) | 34740.0 | 1.68127 | ||||||||
\(754\) | 27930.0 | 1.34901 | ||||||||
\(755\) | 8934.00 | 0.430651 | ||||||||
\(756\) | 4640.00 | 0.223221 | ||||||||
\(757\) | −9830.00 | −0.471965 | −0.235982 | − | 0.971757i | \(-0.575831\pi\) | ||||
−0.235982 | + | 0.971757i | \(0.575831\pi\) | |||||||
\(758\) | −25904.0 | −1.24126 | ||||||||
\(759\) | −3910.00 | −0.186988 | ||||||||
\(760\) | 10080.0 | 0.481105 | ||||||||
\(761\) | −30219.0 | −1.43947 | −0.719736 | − | 0.694248i | \(-0.755737\pi\) | ||||
−0.719736 | + | 0.694248i | \(0.755737\pi\) | |||||||
\(762\) | 2610.00 | 0.124082 | ||||||||
\(763\) | −5632.00 | −0.267224 | ||||||||
\(764\) | −17640.0 | −0.835331 | ||||||||
\(765\) | −960.000 | −0.0453711 | ||||||||
\(766\) | 5624.00 | 0.265279 | ||||||||
\(767\) | 23256.0 | 1.09482 | ||||||||
\(768\) | 21760.0 | 1.02239 | ||||||||
\(769\) | 1122.00 | 0.0526142 | 0.0263071 | − | 0.999654i | \(-0.491625\pi\) | ||||
0.0263071 | + | 0.999654i | \(0.491625\pi\) | |||||||
\(770\) | −3264.00 | −0.152762 | ||||||||
\(771\) | 24645.0 | 1.15119 | ||||||||
\(772\) | 540.000 | 0.0251749 | ||||||||
\(773\) | 19300.0 | 0.898024 | 0.449012 | − | 0.893526i | \(-0.351776\pi\) | ||||
0.449012 | + | 0.893526i | \(0.351776\pi\) | |||||||
\(774\) | 352.000 | 0.0163467 | ||||||||
\(775\) | −9167.00 | −0.424888 | ||||||||
\(776\) | −23136.0 | −1.07028 | ||||||||
\(777\) | −11920.0 | −0.550357 | ||||||||
\(778\) | −2528.00 | −0.116495 | ||||||||
\(779\) | −6650.00 | −0.305855 | ||||||||
\(780\) | 6840.00 | 0.313989 | ||||||||
\(781\) | 11390.0 | 0.521852 | ||||||||
\(782\) | 3680.00 | 0.168282 | ||||||||
\(783\) | 35525.0 | 1.62140 | ||||||||
\(784\) | 4464.00 | 0.203353 | ||||||||
\(785\) | 3792.00 | 0.172411 | ||||||||
\(786\) | −14410.0 | −0.653928 | ||||||||
\(787\) | −19396.0 | −0.878517 | −0.439258 | − | 0.898361i | \(-0.644759\pi\) | ||||
−0.439258 | + | 0.898361i | \(0.644759\pi\) | |||||||
\(788\) | −4884.00 | −0.220794 | ||||||||
\(789\) | −30690.0 | −1.38478 | ||||||||
\(790\) | −15864.0 | −0.714450 | ||||||||
\(791\) | −7616.00 | −0.342344 | ||||||||
\(792\) | −1632.00 | −0.0732204 | ||||||||
\(793\) | −46854.0 | −2.09815 | ||||||||
\(794\) | −14238.0 | −0.636383 | ||||||||
\(795\) | −12420.0 | −0.554078 | ||||||||
\(796\) | 4392.00 | 0.195566 | ||||||||
\(797\) | −39034.0 | −1.73482 | −0.867412 | − | 0.497590i | \(-0.834218\pi\) | ||||
−0.867412 | + | 0.497590i | \(0.834218\pi\) | |||||||
\(798\) | 5600.00 | 0.248418 | ||||||||
\(799\) | 28560.0 | 1.26456 | ||||||||
\(800\) | 14240.0 | 0.629325 | ||||||||
\(801\) | 920.000 | 0.0405825 | ||||||||
\(802\) | −8524.00 | −0.375303 | ||||||||
\(803\) | −30566.0 | −1.34328 | ||||||||
\(804\) | 18520.0 | 0.812376 | ||||||||
\(805\) | 1104.00 | 0.0483365 | ||||||||
\(806\) | 11742.0 | 0.513144 | ||||||||
\(807\) | 10315.0 | 0.449944 | ||||||||
\(808\) | −7440.00 | −0.323934 | ||||||||
\(809\) | −10310.0 | −0.448060 | −0.224030 | − | 0.974582i | \(-0.571921\pi\) | ||||
−0.224030 | + | 0.974582i | \(0.571921\pi\) | |||||||
\(810\) | −8052.00 | −0.349282 | ||||||||
\(811\) | −40693.0 | −1.76193 | −0.880965 | − | 0.473182i | \(-0.843105\pi\) | ||||
−0.880965 | + | 0.473182i | \(0.843105\pi\) | |||||||
\(812\) | 7840.00 | 0.338830 | ||||||||
\(813\) | 5320.00 | 0.229496 | ||||||||
\(814\) | 20264.0 | 0.872546 | ||||||||
\(815\) | 18258.0 | 0.784724 | ||||||||
\(816\) | −6400.00 | −0.274565 | ||||||||
\(817\) | −6160.00 | −0.263784 | ||||||||
\(818\) | −458.000 | −0.0195765 | ||||||||
\(819\) | −912.000 | −0.0389107 | ||||||||
\(820\) | 2280.00 | 0.0970988 | ||||||||
\(821\) | −13934.0 | −0.592326 | −0.296163 | − | 0.955137i | \(-0.595707\pi\) | ||||
−0.296163 | + | 0.955137i | \(0.595707\pi\) | |||||||
\(822\) | 15560.0 | 0.660240 | ||||||||
\(823\) | 6175.00 | 0.261539 | 0.130770 | − | 0.991413i | \(-0.458255\pi\) | ||||
0.130770 | + | 0.991413i | \(0.458255\pi\) | |||||||
\(824\) | 25056.0 | 1.05930 | ||||||||
\(825\) | 15130.0 | 0.638496 | ||||||||
\(826\) | −6528.00 | −0.274986 | ||||||||
\(827\) | 28664.0 | 1.20525 | 0.602627 | − | 0.798023i | \(-0.294121\pi\) | ||||
0.602627 | + | 0.798023i | \(0.294121\pi\) | |||||||
\(828\) | 184.000 | 0.00772276 | ||||||||
\(829\) | −39590.0 | −1.65865 | −0.829323 | − | 0.558770i | \(-0.811274\pi\) | ||||
−0.829323 | + | 0.558770i | \(0.811274\pi\) | |||||||
\(830\) | −432.000 | −0.0180662 | ||||||||
\(831\) | −28645.0 | −1.19577 | ||||||||
\(832\) | −25536.0 | −1.06406 | ||||||||
\(833\) | 22320.0 | 0.928382 | ||||||||
\(834\) | 250.000 | 0.0103798 | ||||||||
\(835\) | 13344.0 | 0.553040 | ||||||||
\(836\) | 9520.00 | 0.393847 | ||||||||
\(837\) | 14935.0 | 0.616761 | ||||||||
\(838\) | −31552.0 | −1.30065 | ||||||||
\(839\) | −14316.0 | −0.589086 | −0.294543 | − | 0.955638i | \(-0.595167\pi\) | ||||
−0.294543 | + | 0.955638i | \(0.595167\pi\) | |||||||
\(840\) | −5760.00 | −0.236594 | ||||||||
\(841\) | 35636.0 | 1.46115 | ||||||||
\(842\) | 17456.0 | 0.714458 | ||||||||
\(843\) | 4800.00 | 0.196110 | ||||||||
\(844\) | 14704.0 | 0.599683 | ||||||||
\(845\) | −6312.00 | −0.256970 | ||||||||
\(846\) | −1428.00 | −0.0580327 | ||||||||
\(847\) | 1400.00 | 0.0567941 | ||||||||
\(848\) | 6624.00 | 0.268242 | ||||||||
\(849\) | 570.000 | 0.0230416 | ||||||||
\(850\) | −14240.0 | −0.574621 | ||||||||
\(851\) | −6854.00 | −0.276089 | ||||||||
\(852\) | 6700.00 | 0.269411 | ||||||||
\(853\) | 28366.0 | 1.13861 | 0.569304 | − | 0.822127i | \(-0.307213\pi\) | ||||
0.569304 | + | 0.822127i | \(0.307213\pi\) | |||||||
\(854\) | 13152.0 | 0.526993 | ||||||||
\(855\) | −840.000 | −0.0335993 | ||||||||
\(856\) | 9936.00 | 0.396735 | ||||||||
\(857\) | 19283.0 | 0.768605 | 0.384303 | − | 0.923207i | \(-0.374442\pi\) | ||||
0.384303 | + | 0.923207i | \(0.374442\pi\) | |||||||
\(858\) | −19380.0 | −0.771122 | ||||||||
\(859\) | −26101.0 | −1.03673 | −0.518367 | − | 0.855158i | \(-0.673460\pi\) | ||||
−0.518367 | + | 0.855158i | \(0.673460\pi\) | |||||||
\(860\) | 2112.00 | 0.0837426 | ||||||||
\(861\) | 3800.00 | 0.150411 | ||||||||
\(862\) | 5856.00 | 0.231388 | ||||||||
\(863\) | 973.000 | 0.0383793 | 0.0191896 | − | 0.999816i | \(-0.493891\pi\) | ||||
0.0191896 | + | 0.999816i | \(0.493891\pi\) | |||||||
\(864\) | −23200.0 | −0.913519 | ||||||||
\(865\) | −19380.0 | −0.761780 | ||||||||
\(866\) | 10628.0 | 0.417037 | ||||||||
\(867\) | −7435.00 | −0.291241 | ||||||||
\(868\) | 3296.00 | 0.128887 | ||||||||
\(869\) | −44948.0 | −1.75461 | ||||||||
\(870\) | −14700.0 | −0.572847 | ||||||||
\(871\) | −52782.0 | −2.05333 | ||||||||
\(872\) | 16896.0 | 0.656159 | ||||||||
\(873\) | 1928.00 | 0.0747456 | ||||||||
\(874\) | 3220.00 | 0.124620 | ||||||||
\(875\) | −10272.0 | −0.396865 | ||||||||
\(876\) | −17980.0 | −0.693479 | ||||||||
\(877\) | 5694.00 | 0.219239 | 0.109620 | − | 0.993974i | \(-0.465037\pi\) | ||||
0.109620 | + | 0.993974i | \(0.465037\pi\) | |||||||
\(878\) | −5170.00 | −0.198723 | ||||||||
\(879\) | 35240.0 | 1.35224 | ||||||||
\(880\) | 3264.00 | 0.125033 | ||||||||
\(881\) | 45960.0 | 1.75758 | 0.878792 | − | 0.477205i | \(-0.158350\pi\) | ||||
0.878792 | + | 0.477205i | \(0.158350\pi\) | |||||||
\(882\) | −1116.00 | −0.0426051 | ||||||||
\(883\) | 17188.0 | 0.655065 | 0.327532 | − | 0.944840i | \(-0.393783\pi\) | ||||
0.327532 | + | 0.944840i | \(0.393783\pi\) | |||||||
\(884\) | −18240.0 | −0.693979 | ||||||||
\(885\) | −12240.0 | −0.464907 | ||||||||
\(886\) | 5994.00 | 0.227283 | ||||||||
\(887\) | 8451.00 | 0.319906 | 0.159953 | − | 0.987125i | \(-0.448866\pi\) | ||||
0.159953 | + | 0.987125i | \(0.448866\pi\) | |||||||
\(888\) | 35760.0 | 1.35138 | ||||||||
\(889\) | −2088.00 | −0.0787731 | ||||||||
\(890\) | −5520.00 | −0.207900 | ||||||||
\(891\) | −22814.0 | −0.857798 | ||||||||
\(892\) | −6624.00 | −0.248641 | ||||||||
\(893\) | 24990.0 | 0.936460 | ||||||||
\(894\) | 8220.00 | 0.307514 | ||||||||
\(895\) | −2214.00 | −0.0826881 | ||||||||
\(896\) | −3072.00 | −0.114541 | ||||||||
\(897\) | 6555.00 | 0.243997 | ||||||||
\(898\) | 33124.0 | 1.23092 | ||||||||
\(899\) | 25235.0 | 0.936190 | ||||||||
\(900\) | −712.000 | −0.0263704 | ||||||||
\(901\) | 33120.0 | 1.22463 | ||||||||
\(902\) | −6460.00 | −0.238464 | ||||||||
\(903\) | 3520.00 | 0.129721 | ||||||||
\(904\) | 22848.0 | 0.840612 | ||||||||
\(905\) | 8220.00 | 0.301925 | ||||||||
\(906\) | −14890.0 | −0.546012 | ||||||||
\(907\) | 32774.0 | 1.19983 | 0.599913 | − | 0.800065i | \(-0.295202\pi\) | ||||
0.599913 | + | 0.800065i | \(0.295202\pi\) | |||||||
\(908\) | −11760.0 | −0.429812 | ||||||||
\(909\) | 620.000 | 0.0226228 | ||||||||
\(910\) | 5472.00 | 0.199335 | ||||||||
\(911\) | −23690.0 | −0.861564 | −0.430782 | − | 0.902456i | \(-0.641762\pi\) | ||||
−0.430782 | + | 0.902456i | \(0.641762\pi\) | |||||||
\(912\) | −5600.00 | −0.203327 | ||||||||
\(913\) | −1224.00 | −0.0443686 | ||||||||
\(914\) | −7848.00 | −0.284014 | ||||||||
\(915\) | 24660.0 | 0.890967 | ||||||||
\(916\) | −14448.0 | −0.521152 | ||||||||
\(917\) | 11528.0 | 0.415145 | ||||||||
\(918\) | 23200.0 | 0.834111 | ||||||||
\(919\) | −30044.0 | −1.07841 | −0.539206 | − | 0.842174i | \(-0.681275\pi\) | ||||
−0.539206 | + | 0.842174i | \(0.681275\pi\) | |||||||
\(920\) | −3312.00 | −0.118688 | ||||||||
\(921\) | −19360.0 | −0.692653 | ||||||||
\(922\) | 9086.00 | 0.324546 | ||||||||
\(923\) | −19095.0 | −0.680953 | ||||||||
\(924\) | −5440.00 | −0.193683 | ||||||||
\(925\) | 26522.0 | 0.942744 | ||||||||
\(926\) | −19232.0 | −0.682508 | ||||||||
\(927\) | −2088.00 | −0.0739794 | ||||||||
\(928\) | −39200.0 | −1.38664 | ||||||||
\(929\) | −39705.0 | −1.40224 | −0.701119 | − | 0.713044i | \(-0.747316\pi\) | ||||
−0.701119 | + | 0.713044i | \(0.747316\pi\) | |||||||
\(930\) | −6180.00 | −0.217903 | ||||||||
\(931\) | 19530.0 | 0.687508 | ||||||||
\(932\) | 17300.0 | 0.608026 | ||||||||
\(933\) | 24885.0 | 0.873203 | ||||||||
\(934\) | −15652.0 | −0.548339 | ||||||||
\(935\) | 16320.0 | 0.570825 | ||||||||
\(936\) | 2736.00 | 0.0955438 | ||||||||
\(937\) | 17422.0 | 0.607419 | 0.303710 | − | 0.952765i | \(-0.401775\pi\) | ||||
0.303710 | + | 0.952765i | \(0.401775\pi\) | |||||||
\(938\) | 14816.0 | 0.515735 | ||||||||
\(939\) | 12680.0 | 0.440677 | ||||||||
\(940\) | −8568.00 | −0.297295 | ||||||||
\(941\) | −25292.0 | −0.876191 | −0.438095 | − | 0.898928i | \(-0.644347\pi\) | ||||
−0.438095 | + | 0.898928i | \(0.644347\pi\) | |||||||
\(942\) | −6320.00 | −0.218595 | ||||||||
\(943\) | 2185.00 | 0.0754543 | ||||||||
\(944\) | 6528.00 | 0.225072 | ||||||||
\(945\) | 6960.00 | 0.239586 | ||||||||
\(946\) | −5984.00 | −0.205662 | ||||||||
\(947\) | 33211.0 | 1.13961 | 0.569806 | − | 0.821779i | \(-0.307018\pi\) | ||||
0.569806 | + | 0.821779i | \(0.307018\pi\) | |||||||
\(948\) | −26440.0 | −0.905835 | ||||||||
\(949\) | 51243.0 | 1.75281 | ||||||||
\(950\) | −12460.0 | −0.425532 | ||||||||
\(951\) | −7170.00 | −0.244483 | ||||||||
\(952\) | 15360.0 | 0.522921 | ||||||||
\(953\) | −14154.0 | −0.481105 | −0.240552 | − | 0.970636i | \(-0.577329\pi\) | ||||
−0.240552 | + | 0.970636i | \(0.577329\pi\) | |||||||
\(954\) | −1656.00 | −0.0562002 | ||||||||
\(955\) | −26460.0 | −0.896571 | ||||||||
\(956\) | −10940.0 | −0.370110 | ||||||||
\(957\) | −41650.0 | −1.40685 | ||||||||
\(958\) | −22808.0 | −0.769199 | ||||||||
\(959\) | −12448.0 | −0.419152 | ||||||||
\(960\) | 13440.0 | 0.451848 | ||||||||
\(961\) | −19182.0 | −0.643886 | ||||||||
\(962\) | −33972.0 | −1.13857 | ||||||||
\(963\) | −828.000 | −0.0277071 | ||||||||
\(964\) | 26840.0 | 0.896741 | ||||||||
\(965\) | 810.000 | 0.0270205 | ||||||||
\(966\) | −1840.00 | −0.0612847 | ||||||||
\(967\) | −46343.0 | −1.54115 | −0.770574 | − | 0.637350i | \(-0.780030\pi\) | ||||
−0.770574 | + | 0.637350i | \(0.780030\pi\) | |||||||
\(968\) | −4200.00 | −0.139456 | ||||||||
\(969\) | −28000.0 | −0.928266 | ||||||||
\(970\) | −11568.0 | −0.382914 | ||||||||
\(971\) | 11710.0 | 0.387015 | 0.193508 | − | 0.981099i | \(-0.438014\pi\) | ||||
0.193508 | + | 0.981099i | \(0.438014\pi\) | |||||||
\(972\) | 2240.00 | 0.0739177 | ||||||||
\(973\) | −200.000 | −0.00658963 | ||||||||
\(974\) | 18534.0 | 0.609720 | ||||||||
\(975\) | −25365.0 | −0.833159 | ||||||||
\(976\) | −13152.0 | −0.431337 | ||||||||
\(977\) | 47854.0 | 1.56703 | 0.783513 | − | 0.621375i | \(-0.213426\pi\) | ||||
0.783513 | + | 0.621375i | \(0.213426\pi\) | |||||||
\(978\) | −30430.0 | −0.994933 | ||||||||
\(979\) | −15640.0 | −0.510579 | ||||||||
\(980\) | −6696.00 | −0.218261 | ||||||||
\(981\) | −1408.00 | −0.0458246 | ||||||||
\(982\) | 36382.0 | 1.18228 | ||||||||
\(983\) | −22078.0 | −0.716357 | −0.358178 | − | 0.933653i | \(-0.616602\pi\) | ||||
−0.358178 | + | 0.933653i | \(0.616602\pi\) | |||||||
\(984\) | −11400.0 | −0.369328 | ||||||||
\(985\) | −7326.00 | −0.236980 | ||||||||
\(986\) | 39200.0 | 1.26611 | ||||||||
\(987\) | −14280.0 | −0.460524 | ||||||||
\(988\) | −15960.0 | −0.513922 | ||||||||
\(989\) | 2024.00 | 0.0650753 | ||||||||
\(990\) | −816.000 | −0.0261961 | ||||||||
\(991\) | −4288.00 | −0.137450 | −0.0687249 | − | 0.997636i | \(-0.521893\pi\) | ||||
−0.0687249 | + | 0.997636i | \(0.521893\pi\) | |||||||
\(992\) | −16480.0 | −0.527460 | ||||||||
\(993\) | −27345.0 | −0.873885 | ||||||||
\(994\) | 5360.00 | 0.171035 | ||||||||
\(995\) | 6588.00 | 0.209903 | ||||||||
\(996\) | −720.000 | −0.0229057 | ||||||||
\(997\) | 28966.0 | 0.920123 | 0.460061 | − | 0.887887i | \(-0.347827\pi\) | ||||
0.460061 | + | 0.887887i | \(0.347827\pi\) | |||||||
\(998\) | −38630.0 | −1.22526 | ||||||||
\(999\) | −43210.0 | −1.36847 |
(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 | 23.4.a.a.1.1 | ✓ | 1 | |
3.2 | odd | 2 | 207.4.a.a.1.1 | 1 | |||
4.3 | odd | 2 | 368.4.a.d.1.1 | 1 | |||
5.2 | odd | 4 | 575.4.b.b.24.1 | 2 | |||
5.3 | odd | 4 | 575.4.b.b.24.2 | 2 | |||
5.4 | even | 2 | 575.4.a.g.1.1 | 1 | |||
7.6 | odd | 2 | 1127.4.a.a.1.1 | 1 | |||
8.3 | odd | 2 | 1472.4.a.c.1.1 | 1 | |||
8.5 | even | 2 | 1472.4.a.h.1.1 | 1 | |||
23.22 | odd | 2 | 529.4.a.a.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
23.4.a.a.1.1 | ✓ | 1 | 1.1 | even | 1 | trivial | |
207.4.a.a.1.1 | 1 | 3.2 | odd | 2 | |||
368.4.a.d.1.1 | 1 | 4.3 | odd | 2 | |||
529.4.a.a.1.1 | 1 | 23.22 | odd | 2 | |||
575.4.a.g.1.1 | 1 | 5.4 | even | 2 | |||
575.4.b.b.24.1 | 2 | 5.2 | odd | 4 | |||
575.4.b.b.24.2 | 2 | 5.3 | odd | 4 | |||
1127.4.a.a.1.1 | 1 | 7.6 | odd | 2 | |||
1472.4.a.c.1.1 | 1 | 8.3 | odd | 2 | |||
1472.4.a.h.1.1 | 1 | 8.5 | even | 2 |