Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [240,4,Mod(1,240)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(240, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("240.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 240 = 2^{4} \cdot 3 \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 240.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: | \(14.1604584014\) |
Analytic rank: | \(0\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 120) |
Fricke sign: | \(+1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 240.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 3.00000 | 0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 5.00000 | 0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 16.0000 | 0.863919 | 0.431959 | − | 0.901893i | \(-0.357822\pi\) | ||||
0.431959 | + | 0.901893i | \(0.357822\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 9.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 28.0000 | 0.767483 | 0.383742 | − | 0.923440i | \(-0.374635\pi\) | ||||
0.383742 | + | 0.923440i | \(0.374635\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −26.0000 | −0.554700 | −0.277350 | − | 0.960769i | \(-0.589456\pi\) | ||||
−0.277350 | + | 0.960769i | \(0.589456\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 15.0000 | 0.258199 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −62.0000 | −0.884542 | −0.442271 | − | 0.896882i | \(-0.645827\pi\) | ||||
−0.442271 | + | 0.896882i | \(0.645827\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 68.0000 | 0.821067 | 0.410533 | − | 0.911846i | \(-0.365343\pi\) | ||||
0.410533 | + | 0.911846i | \(0.365343\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 48.0000 | 0.498784 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 208.000 | 1.88570 | 0.942848 | − | 0.333224i | \(-0.108136\pi\) | ||||
0.942848 | + | 0.333224i | \(0.108136\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 25.0000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 27.0000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −58.0000 | −0.371391 | −0.185695 | − | 0.982607i | \(-0.559454\pi\) | ||||
−0.185695 | + | 0.982607i | \(0.559454\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −160.000 | −0.926995 | −0.463498 | − | 0.886098i | \(-0.653406\pi\) | ||||
−0.463498 | + | 0.886098i | \(0.653406\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 84.0000 | 0.443107 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 80.0000 | 0.386356 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 270.000 | 1.19967 | 0.599834 | − | 0.800124i | \(-0.295233\pi\) | ||||
0.599834 | + | 0.800124i | \(0.295233\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −78.0000 | −0.320256 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 282.000 | 1.07417 | 0.537085 | − | 0.843528i | \(-0.319525\pi\) | ||||
0.537085 | + | 0.843528i | \(0.319525\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −76.0000 | −0.269532 | −0.134766 | − | 0.990877i | \(-0.543028\pi\) | ||||
−0.134766 | + | 0.990877i | \(0.543028\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 45.0000 | 0.149071 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 280.000 | 0.868983 | 0.434491 | − | 0.900676i | \(-0.356928\pi\) | ||||
0.434491 | + | 0.900676i | \(0.356928\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −87.0000 | −0.253644 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −186.000 | −0.510690 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −210.000 | −0.544259 | −0.272129 | − | 0.962261i | \(-0.587728\pi\) | ||||
−0.272129 | + | 0.962261i | \(0.587728\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 140.000 | 0.343229 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 204.000 | 0.474043 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −196.000 | −0.432492 | −0.216246 | − | 0.976339i | \(-0.569381\pi\) | ||||
−0.216246 | + | 0.976339i | \(0.569381\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 742.000 | 1.55743 | 0.778716 | − | 0.627376i | \(-0.215871\pi\) | ||||
0.778716 | + | 0.627376i | \(0.215871\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 144.000 | 0.287973 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −130.000 | −0.248069 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −836.000 | −1.52438 | −0.762191 | − | 0.647352i | \(-0.775877\pi\) | ||||
−0.762191 | + | 0.647352i | \(0.775877\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 624.000 | 1.08871 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 504.000 | 0.842448 | 0.421224 | − | 0.906957i | \(-0.361601\pi\) | ||||
0.421224 | + | 0.906957i | \(0.361601\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −1062.00 | −1.70271 | −0.851354 | − | 0.524591i | \(-0.824218\pi\) | ||||
−0.851354 | + | 0.524591i | \(0.824218\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 75.0000 | 0.115470 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 448.000 | 0.663043 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −768.000 | −1.09376 | −0.546878 | − | 0.837212i | \(-0.684184\pi\) | ||||
−0.546878 | + | 0.837212i | \(0.684184\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 1052.00 | 1.39123 | 0.695614 | − | 0.718415i | \(-0.255132\pi\) | ||||
0.695614 | + | 0.718415i | \(0.255132\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −310.000 | −0.395579 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −174.000 | −0.214423 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −726.000 | −0.864672 | −0.432336 | − | 0.901712i | \(-0.642311\pi\) | ||||
−0.432336 | + | 0.901712i | \(0.642311\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −416.000 | −0.479216 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −480.000 | −0.535201 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 340.000 | 0.367192 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1406.00 | −1.47173 | −0.735864 | − | 0.677129i | \(-0.763224\pi\) | ||||
−0.735864 | + | 0.677129i | \(0.763224\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 252.000 | 0.255828 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 990.000 | 0.975333 | 0.487667 | − | 0.873030i | \(-0.337848\pi\) | ||||
0.487667 | + | 0.873030i | \(0.337848\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −736.000 | −0.704080 | −0.352040 | − | 0.935985i | \(-0.614512\pi\) | ||||
−0.352040 | + | 0.935985i | \(0.614512\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 240.000 | 0.223063 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −1212.00 | −1.09503 | −0.547516 | − | 0.836795i | \(-0.684427\pi\) | ||||
−0.547516 | + | 0.836795i | \(0.684427\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1834.00 | −1.61161 | −0.805804 | − | 0.592182i | \(-0.798267\pi\) | ||||
−0.805804 | + | 0.592182i | \(0.798267\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 810.000 | 0.692629 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −2046.00 | −1.70329 | −0.851644 | − | 0.524121i | \(-0.824394\pi\) | ||||
−0.851644 | + | 0.524121i | \(0.824394\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1040.00 | 0.843309 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −234.000 | −0.184900 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −992.000 | −0.764172 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −547.000 | −0.410969 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 846.000 | 0.620173 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 125.000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1176.00 | −0.821678 | −0.410839 | − | 0.911708i | \(-0.634764\pi\) | ||||
−0.410839 | + | 0.911708i | \(0.634764\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −228.000 | −0.155615 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −12.0000 | −0.00800340 | −0.00400170 | − | 0.999992i | \(-0.501274\pi\) | ||||
−0.00400170 | + | 0.999992i | \(0.501274\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1088.00 | 0.709335 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 135.000 | 0.0860663 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −790.000 | −0.492659 | −0.246329 | − | 0.969186i | \(-0.579225\pi\) | ||||
−0.246329 | + | 0.969186i | \(0.579225\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 924.000 | 0.563832 | 0.281916 | − | 0.959439i | \(-0.409030\pi\) | ||||
0.281916 | + | 0.959439i | \(0.409030\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 840.000 | 0.501708 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −728.000 | −0.425723 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −290.000 | −0.166091 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −261.000 | −0.146442 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 3022.00 | 1.66156 | 0.830778 | − | 0.556604i | \(-0.187896\pi\) | ||||
0.830778 | + | 0.556604i | \(0.187896\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1736.00 | −0.935587 | −0.467794 | − | 0.883838i | \(-0.654951\pi\) | ||||
−0.467794 | + | 0.883838i | \(0.654951\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −558.000 | −0.294847 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −800.000 | −0.414565 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1322.00 | −0.672020 | −0.336010 | − | 0.941858i | \(-0.609078\pi\) | ||||
−0.336010 | + | 0.941858i | \(0.609078\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −630.000 | −0.314228 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 3328.00 | 1.62909 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 908.000 | 0.436319 | 0.218160 | − | 0.975913i | \(-0.429995\pi\) | ||||
0.218160 | + | 0.975913i | \(0.429995\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 420.000 | 0.198163 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −1296.00 | −0.600524 | −0.300262 | − | 0.953857i | \(-0.597074\pi\) | ||||
−0.300262 | + | 0.953857i | \(0.597074\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1521.00 | −0.692308 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 612.000 | 0.273689 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 2134.00 | 0.937832 | 0.468916 | − | 0.883243i | \(-0.344645\pi\) | ||||
0.468916 | + | 0.883243i | \(0.344645\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 400.000 | 0.172784 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −588.000 | −0.249699 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −1612.00 | −0.673109 | −0.336555 | − | 0.941664i | \(-0.609262\pi\) | ||||
−0.336555 | + | 0.941664i | \(0.609262\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 3086.00 | 1.26730 | 0.633648 | − | 0.773621i | \(-0.281557\pi\) | ||||
0.633648 | + | 0.773621i | \(0.281557\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 2226.00 | 0.899184 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 1350.00 | 0.536508 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1736.00 | −0.678871 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 432.000 | 0.166261 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 4208.00 | 1.59414 | 0.797069 | − | 0.603889i | \(-0.206383\pi\) | ||||
0.797069 | + | 0.603889i | \(0.206383\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 2818.00 | 1.05101 | 0.525503 | − | 0.850792i | \(-0.323877\pi\) | ||||
0.525503 | + | 0.850792i | \(0.323877\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −390.000 | −0.143223 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −418.000 | −0.151174 | −0.0755870 | − | 0.997139i | \(-0.524083\pi\) | ||||
−0.0755870 | + | 0.997139i | \(0.524083\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 3352.00 | 1.19406 | 0.597028 | − | 0.802221i | \(-0.296348\pi\) | ||||
0.597028 | + | 0.802221i | \(0.296348\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −2508.00 | −0.880103 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −928.000 | −0.320851 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1410.00 | 0.480384 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 1872.00 | 0.628565 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 1904.00 | 0.630155 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 4276.00 | 1.39513 | 0.697564 | − | 0.716523i | \(-0.254267\pi\) | ||||
0.697564 | + | 0.716523i | \(0.254267\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 1512.00 | 0.486387 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −380.000 | −0.120539 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −2560.00 | −0.800848 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −3186.00 | −0.983059 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1612.00 | 0.490655 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −4712.00 | −1.41497 | −0.707486 | − | 0.706727i | \(-0.750171\pi\) | ||||
−0.707486 | + | 0.706727i | \(0.750171\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 225.000 | 0.0666667 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 732.000 | 0.214029 | 0.107014 | − | 0.994257i | \(-0.465871\pi\) | ||||
0.107014 | + | 0.994257i | \(0.465871\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −5186.00 | −1.49651 | −0.748254 | − | 0.663412i | \(-0.769108\pi\) | ||||
−0.748254 | + | 0.663412i | \(0.769108\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1344.00 | 0.382808 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −3798.00 | −1.06788 | −0.533938 | − | 0.845523i | \(-0.679289\pi\) | ||||
−0.533938 | + | 0.845523i | \(0.679289\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1400.00 | 0.388621 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −2304.00 | −0.631481 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 3120.00 | 0.844419 | 0.422209 | − | 0.906498i | \(-0.361255\pi\) | ||||
0.422209 | + | 0.906498i | \(0.361255\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1490.00 | 0.398255 | 0.199127 | − | 0.979974i | \(-0.436189\pi\) | ||||
0.199127 | + | 0.979974i | \(0.436189\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 243.000 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −435.000 | −0.113433 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1768.00 | −0.455446 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 3156.00 | 0.803226 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 5292.00 | 1.33079 | 0.665395 | − | 0.746492i | \(-0.268263\pi\) | ||||
0.665395 | + | 0.746492i | \(0.268263\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 5824.00 | 1.44724 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −930.000 | −0.228388 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −3918.00 | −0.950965 | −0.475483 | − | 0.879725i | \(-0.657727\pi\) | ||||
−0.475483 | + | 0.879725i | \(0.657727\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 4320.00 | 1.03642 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −522.000 | −0.123797 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −6624.00 | −1.55305 | −0.776527 | − | 0.630084i | \(-0.783021\pi\) | ||||
−0.776527 | + | 0.630084i | \(0.783021\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1050.00 | −0.243400 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −2178.00 | −0.499219 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −2954.00 | −0.669549 | −0.334774 | − | 0.942298i | \(-0.608660\pi\) | ||||
−0.334774 | + | 0.942298i | \(0.608660\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 6576.00 | 1.47404 | 0.737018 | − | 0.675874i | \(-0.236233\pi\) | ||||
0.737018 | + | 0.675874i | \(0.236233\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −1248.00 | −0.276675 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 700.000 | 0.153497 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 4478.00 | 0.971325 | 0.485662 | − | 0.874146i | \(-0.338578\pi\) | ||||
0.485662 | + | 0.874146i | \(0.338578\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −1440.00 | −0.308998 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −6358.00 | −1.34977 | −0.674887 | − | 0.737921i | \(-0.735808\pi\) | ||||
−0.674887 | + | 0.737921i | \(0.735808\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −860.000 | −0.180642 | −0.0903210 | − | 0.995913i | \(-0.528789\pi\) | ||||
−0.0903210 | + | 0.995913i | \(0.528789\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 1020.00 | 0.211999 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 4512.00 | 0.927996 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1069.00 | −0.217586 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −4218.00 | −0.849703 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −5794.00 | −1.15525 | −0.577626 | − | 0.816301i | \(-0.696021\pi\) | ||||
−0.577626 | + | 0.816301i | \(0.696021\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −980.000 | −0.193416 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 756.000 | 0.147702 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −5408.00 | −1.04600 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1216.00 | −0.232854 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 2970.00 | 0.563109 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 3710.00 | 0.696505 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 6860.00 | 1.27531 | 0.637656 | − | 0.770321i | \(-0.279904\pi\) | ||||
0.637656 | + | 0.770321i | \(0.279904\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −2208.00 | −0.406501 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 6248.00 | 1.13920 | 0.569601 | − | 0.821922i | \(-0.307098\pi\) | ||||
0.569601 | + | 0.821922i | \(0.307098\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 11018.0 | 1.98969 | 0.994847 | − | 0.101388i | \(-0.0323284\pi\) | ||||
0.994847 | + | 0.101388i | \(0.0323284\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 720.000 | 0.128785 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −954.000 | −0.169028 | −0.0845142 | − | 0.996422i | \(-0.526934\pi\) | ||||
−0.0845142 | + | 0.996422i | \(0.526934\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1624.00 | −0.285036 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −3636.00 | −0.632217 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −4216.00 | −0.726268 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −650.000 | −0.110940 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −5502.00 | −0.930463 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 4480.00 | 0.750731 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −9396.00 | −1.56027 | −0.780137 | − | 0.625608i | \(-0.784851\pi\) | ||||
−0.780137 | + | 0.625608i | \(0.784851\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 2430.00 | 0.399889 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −4180.00 | −0.681725 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 5074.00 | 0.820173 | 0.410087 | − | 0.912047i | \(-0.365498\pi\) | ||||
0.410087 | + | 0.912047i | \(0.365498\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −6138.00 | −0.983394 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −4480.00 | −0.711453 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −6880.00 | −1.08305 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 3120.00 | 0.486885 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −3916.00 | −0.605827 | −0.302913 | − | 0.953018i | \(-0.597959\pi\) | ||||
−0.302913 | + | 0.953018i | \(0.597959\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −1818.00 | −0.278840 | −0.139420 | − | 0.990233i | \(-0.544524\pi\) | ||||
−0.139420 | + | 0.990233i | \(0.544524\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −702.000 | −0.106752 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −7118.00 | −1.07324 | −0.536619 | − | 0.843825i | \(-0.680299\pi\) | ||||
−0.536619 | + | 0.843825i | \(0.680299\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 2520.00 | 0.376754 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −2976.00 | −0.441195 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −5304.00 | −0.779762 | −0.389881 | − | 0.920865i | \(-0.627484\pi\) | ||||
−0.389881 | + | 0.920865i | \(0.627484\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −2235.00 | −0.325849 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −1641.00 | −0.237273 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −5310.00 | −0.761474 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −5672.00 | −0.806747 | −0.403373 | − | 0.915036i | \(-0.632162\pi\) | ||||
−0.403373 | + | 0.915036i | \(0.632162\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 2538.00 | 0.358057 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −3360.00 | −0.470195 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 7774.00 | 1.07915 | 0.539574 | − | 0.841938i | \(-0.318585\pi\) | ||||
0.539574 | + | 0.841938i | \(0.318585\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 375.000 | 0.0516398 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 1508.00 | 0.206010 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 5516.00 | 0.747593 | 0.373797 | − | 0.927511i | \(-0.378056\pi\) | ||||
0.373797 | + | 0.927511i | \(0.378056\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −3528.00 | −0.474396 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 7128.00 | 0.950976 | 0.475488 | − | 0.879722i | \(-0.342272\pi\) | ||||
0.475488 | + | 0.879722i | \(0.342272\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 2240.00 | 0.296522 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −684.000 | −0.0898441 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −10722.0 | −1.39750 | −0.698749 | − | 0.715367i | \(-0.746260\pi\) | ||||
−0.698749 | + | 0.715367i | \(0.746260\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −12896.0 | −1.66798 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −36.0000 | −0.00462076 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −3840.00 | −0.489143 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −12122.0 | −1.53246 | −0.766229 | − | 0.642568i | \(-0.777869\pi\) | ||||
−0.766229 | + | 0.642568i | \(0.777869\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 3264.00 | 0.409535 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 10482.0 | 1.30535 | 0.652676 | − | 0.757637i | \(-0.273646\pi\) | ||||
0.652676 | + | 0.757637i | \(0.273646\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 4160.00 | 0.514204 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 405.000 | 0.0496904 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 7560.00 | 0.920726 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 3850.00 | 0.465453 | 0.232726 | − | 0.972542i | \(-0.425235\pi\) | ||||
0.232726 | + | 0.972542i | \(0.425235\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −2370.00 | −0.284437 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −3136.00 | −0.373638 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 5260.00 | 0.622176 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 2772.00 | 0.325529 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 5796.00 | 0.675783 | 0.337892 | − | 0.941185i | \(-0.390286\pi\) | ||||
0.337892 | + | 0.941185i | \(0.390286\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 3294.00 | 0.381330 | 0.190665 | − | 0.981655i | \(-0.438936\pi\) | ||||
0.190665 | + | 0.981655i | \(0.438936\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 2520.00 | 0.289661 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −1550.00 | −0.176908 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 11872.0 | 1.34549 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −2184.00 | −0.245791 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −1696.00 | −0.189544 | −0.0947720 | − | 0.995499i | \(-0.530212\pi\) | ||||
−0.0947720 | + | 0.995499i | \(0.530212\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −12334.0 | −1.36890 | −0.684451 | − | 0.729059i | \(-0.739958\pi\) | ||||
−0.684451 | + | 0.729059i | \(0.739958\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −870.000 | −0.0958927 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 14144.0 | 1.54828 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −376.000 | −0.0408781 | −0.0204391 | − | 0.999791i | \(-0.506506\pi\) | ||||
−0.0204391 | + | 0.999791i | \(0.506506\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −783.000 | −0.0845481 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −8028.00 | −0.860997 | −0.430499 | − | 0.902591i | \(-0.641662\pi\) | ||||
−0.430499 | + | 0.902591i | \(0.641662\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −3630.00 | −0.386693 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 9066.00 | 0.959300 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 8898.00 | 0.935240 | 0.467620 | − | 0.883930i | \(-0.345112\pi\) | ||||
0.467620 | + | 0.883930i | \(0.345112\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 7896.00 | 0.824408 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −5208.00 | −0.540162 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −2080.00 | −0.214312 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 10330.0 | 1.05737 | 0.528684 | − | 0.848819i | \(-0.322686\pi\) | ||||
0.528684 | + | 0.848819i | \(0.322686\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −1674.00 | −0.170230 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 1878.00 | 0.189734 | 0.0948668 | − | 0.995490i | \(-0.469757\pi\) | ||||
0.0948668 | + | 0.995490i | \(0.469757\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 13224.0 | 1.32737 | 0.663684 | − | 0.748013i | \(-0.268992\pi\) | ||||
0.663684 | + | 0.748013i | \(0.268992\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −2400.00 | −0.239349 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 8012.00 | 0.793900 | 0.396950 | − | 0.917840i | \(-0.370069\pi\) | ||||
0.396950 | + | 0.917840i | \(0.370069\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −13376.0 | −1.31694 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −3966.00 | −0.387991 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −2128.00 | −0.206862 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1700.00 | 0.164213 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −1890.00 | −0.181420 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 1792.00 | 0.170936 | 0.0854682 | − | 0.996341i | \(-0.472761\pi\) | ||||
0.0854682 | + | 0.996341i | \(0.472761\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −7020.00 | −0.665456 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 9984.00 | 0.940554 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −7030.00 | −0.658177 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −8272.00 | −0.769692 | −0.384846 | − | 0.922981i | \(-0.625745\pi\) | ||||
−0.384846 | + | 0.922981i | \(0.625745\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 2724.00 | 0.251909 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −516.000 | −0.0474272 | −0.0237136 | − | 0.999719i | \(-0.507549\pi\) | ||||
−0.0237136 | + | 0.999719i | \(0.507549\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 3596.00 | 0.328511 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 1260.00 | 0.114410 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 8064.00 | 0.727807 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 14020.0 | 1.25776 | 0.628879 | − | 0.777503i | \(-0.283514\pi\) | ||||
0.628879 | + | 0.777503i | \(0.283514\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −3888.00 | −0.346713 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −1872.00 | −0.165941 | −0.0829705 | − | 0.996552i | \(-0.526441\pi\) | ||||
−0.0829705 | + | 0.996552i | \(0.526441\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 4950.00 | 0.436182 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −4563.00 | −0.399704 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 8678.00 | 0.755689 | 0.377844 | − | 0.925869i | \(-0.376665\pi\) | ||||
0.377844 | + | 0.925869i | \(0.376665\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −16992.0 | −1.47100 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 1836.00 | 0.158014 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −3680.00 | −0.314874 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 7840.00 | 0.666930 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 6402.00 | 0.541458 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 18074.0 | 1.51984 | 0.759920 | − | 0.650017i | \(-0.225238\pi\) | ||||
0.759920 | + | 0.650017i | \(0.225238\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 20852.0 | 1.74339 | 0.871696 | − | 0.490047i | \(-0.163020\pi\) | ||||
0.871696 | + | 0.490047i | \(0.163020\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 1200.00 | 0.0997567 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 9920.00 | 0.819966 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 31097.0 | 2.55585 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −1764.00 | −0.144164 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −7332.00 | −0.595843 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −6060.00 | −0.489713 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −4836.00 | −0.388620 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −2436.00 | −0.194668 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −12410.0 | −0.986225 | −0.493112 | − | 0.869966i | \(-0.664141\pi\) | ||||
−0.493112 | + | 0.869966i | \(0.664141\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 9258.00 | 0.731674 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −9170.00 | −0.720733 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −3620.00 | −0.282962 | −0.141481 | − | 0.989941i | \(-0.545186\pi\) | ||||
−0.141481 | + | 0.989941i | \(0.545186\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 6678.00 | 0.519144 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −3944.00 | −0.304937 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −12288.0 | −0.944917 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 4050.00 | 0.309753 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 11734.0 | 0.892613 | 0.446307 | − | 0.894880i | \(-0.352739\pi\) | ||||
0.446307 | + | 0.894880i | \(0.352739\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1976.00 | 0.149510 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −5208.00 | −0.391946 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 1372.00 | 0.102705 | 0.0513525 | − | 0.998681i | \(-0.483647\pi\) | ||||
0.0513525 | + | 0.998681i | \(0.483647\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −10230.0 | −0.761733 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 1296.00 | 0.0959910 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 18922.0 | 1.39412 | 0.697058 | − | 0.717015i | \(-0.254492\pi\) | ||||
0.697058 | + | 0.717015i | \(0.254492\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −14596.0 | −1.06974 | −0.534872 | − | 0.844933i | \(-0.679640\pi\) | ||||
−0.534872 | + | 0.844933i | \(0.679640\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 12624.0 | 0.920376 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 5200.00 | 0.377139 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −2302.00 | −0.166089 | −0.0830446 | − | 0.996546i | \(-0.526464\pi\) | ||||
−0.0830446 | + | 0.996546i | \(0.526464\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 8454.00 | 0.606798 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 16832.0 | 1.20191 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −5880.00 | −0.417710 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −1170.00 | −0.0826898 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −23292.0 | −1.63776 | −0.818879 | − | 0.573966i | \(-0.805404\pi\) | ||||
−0.818879 | + | 0.573966i | \(0.805404\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −10880.0 | −0.761125 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −1254.00 | −0.0872803 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −16542.0 | −1.14553 | −0.572764 | − | 0.819720i | \(-0.694129\pi\) | ||||
−0.572764 | + | 0.819720i | \(0.694129\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −4960.00 | −0.341748 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 10056.0 | 0.689388 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −7464.00 | −0.509133 | −0.254567 | − | 0.967055i | \(-0.581933\pi\) | ||||
−0.254567 | + | 0.967055i | \(0.581933\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −17270.0 | −1.17214 | −0.586072 | − | 0.810259i | \(-0.699326\pi\) | ||||
−0.586072 | + | 0.810259i | \(0.699326\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −7524.00 | −0.508128 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −2735.00 | −0.183791 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −984.000 | −0.0657979 | −0.0328990 | − | 0.999459i | \(-0.510474\pi\) | ||||
−0.0328990 | + | 0.999459i | \(0.510474\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −2784.00 | −0.185244 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −7280.00 | −0.482025 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 7278.00 | 0.479536 | 0.239768 | − | 0.970830i | \(-0.422929\pi\) | ||||
0.239768 | + | 0.970830i | \(0.422929\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 4230.00 | 0.277350 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 18090.0 | 1.18035 | 0.590175 | − | 0.807275i | \(-0.299059\pi\) | ||||
0.590175 | + | 0.807275i | \(0.299059\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −24740.0 | −1.60644 | −0.803219 | − | 0.595684i | \(-0.796881\pi\) | ||||
−0.803219 | + | 0.595684i | \(0.796881\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 5616.00 | 0.362902 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −11616.0 | −0.747007 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 625.000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 5712.00 | 0.363820 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −16740.0 | −1.06116 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −19720.0 | −1.24412 | −0.622061 | − | 0.782969i | \(-0.713704\pi\) | ||||
−0.622061 | + | 0.782969i | \(0.713704\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 12828.0 | 0.805477 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −5880.00 | −0.367466 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 2262.00 | 0.140697 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 4536.00 | 0.280816 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −16542.0 | −1.01930 | −0.509649 | − | 0.860383i | \(-0.670225\pi\) | ||||
−0.509649 | + | 0.860383i | \(0.670225\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 10092.0 | 0.618957 | 0.309479 | − | 0.950906i | \(-0.399845\pi\) | ||||
0.309479 | + | 0.950906i | \(0.399845\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −1140.00 | −0.0695930 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 14544.0 | 0.883746 | 0.441873 | − | 0.897078i | \(-0.354314\pi\) | ||||
0.441873 | + | 0.897078i | \(0.354314\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −5488.00 | −0.331930 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −7680.00 | −0.462370 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 23062.0 | 1.38206 | 0.691030 | − | 0.722826i | \(-0.257157\pi\) | ||||
0.691030 | + | 0.722826i | \(0.257157\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −60.0000 | −0.00357923 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −9558.00 | −0.567569 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 28020.0 | 1.65630 | 0.828152 | − | 0.560504i | \(-0.189392\pi\) | ||||
0.828152 | + | 0.560504i | \(0.189392\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −6738.00 | −0.396487 | −0.198243 | − | 0.980153i | \(-0.563524\pi\) | ||||
−0.198243 | + | 0.980153i | \(0.563524\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 4836.00 | 0.283280 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 5440.00 | 0.317224 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −12064.0 | −0.700330 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −14136.0 | −0.816935 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 20776.0 | 1.19530 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −14430.0 | −0.826502 | −0.413251 | − | 0.910617i | \(-0.635607\pi\) | ||||
−0.413251 | + | 0.910617i | \(0.635607\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 675.000 | 0.0384900 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −17890.0 | −1.01561 | −0.507805 | − | 0.861472i | \(-0.669543\pi\) | ||||
−0.507805 | + | 0.861472i | \(0.669543\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −22496.0 | −1.27145 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 2196.00 | 0.123570 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −10860.0 | −0.608413 | −0.304207 | − | 0.952606i | \(-0.598391\pi\) | ||||
−0.304207 | + | 0.952606i | \(0.598391\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −3950.00 | −0.220324 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −15558.0 | −0.864010 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 5460.00 | 0.301900 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 8692.00 | 0.478523 | 0.239261 | − | 0.970955i | \(-0.423095\pi\) | ||||
0.239261 | + | 0.970955i | \(0.423095\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 4032.00 | 0.221014 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 4620.00 | 0.252153 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −17484.0 | −0.950149 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −11394.0 | −0.616539 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −698.000 | −0.0376078 | −0.0188039 | − | 0.999823i | \(-0.505986\pi\) | ||||
−0.0188039 | + | 0.999823i | \(0.505986\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 18360.0 | 0.985008 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 4200.00 | 0.224370 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 15840.0 | 0.842609 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 2654.00 | 0.140583 | 0.0702913 | − | 0.997527i | \(-0.477607\pi\) | ||||
0.0702913 | + | 0.997527i | \(0.477607\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −6912.00 | −0.364585 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −33280.0 | −1.74803 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −3640.00 | −0.190389 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 9360.00 | 0.487525 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 28240.0 | 1.46478 | 0.732388 | − | 0.680887i | \(-0.238406\pi\) | ||||
0.732388 | + | 0.680887i | \(0.238406\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −11776.0 | −0.608268 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 4470.00 | 0.229932 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −1450.00 | −0.0742781 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 8320.00 | 0.424445 | 0.212223 | − | 0.977221i | \(-0.431930\pi\) | ||||
0.212223 | + | 0.977221i | \(0.431930\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 4712.00 | 0.238413 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −2154.00 | −0.108540 | −0.0542700 | − | 0.998526i | \(-0.517283\pi\) | ||||
−0.0542700 | + | 0.998526i | \(0.517283\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −1305.00 | −0.0654907 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −23408.0 | −1.16994 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −22380.0 | −1.11402 | −0.557011 | − | 0.830505i | \(-0.688052\pi\) | ||||
−0.557011 | + | 0.830505i | \(0.688052\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −5304.00 | −0.262952 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 5760.00 | 0.284406 | 0.142203 | − | 0.989837i | \(-0.454581\pi\) | ||||
0.142203 | + | 0.989837i | \(0.454581\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 15110.0 | 0.743071 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 9468.00 | 0.463743 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −19392.0 | −0.946019 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 6192.00 | 0.300865 | 0.150432 | − | 0.988620i | \(-0.451933\pi\) | ||||
0.150432 | + | 0.988620i | \(0.451933\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 15876.0 | 0.768331 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −8680.00 | −0.418407 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −13666.0 | −0.656142 | −0.328071 | − | 0.944653i | \(-0.606398\pi\) | ||||
−0.328071 | + | 0.944653i | \(0.606398\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 17472.0 | 0.835564 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −32022.0 | −1.52536 | −0.762678 | − | 0.646778i | \(-0.776116\pi\) | ||||
−0.762678 | + | 0.646778i | \(0.776116\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −29344.0 | −1.39230 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −2790.00 | −0.131860 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 5096.00 | 0.239903 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 22786.0 | 1.06851 | 0.534255 | − | 0.845323i | \(-0.320592\pi\) | ||||
0.534255 | + | 0.845323i | \(0.320592\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −11754.0 | −0.549040 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 8286.00 | 0.385546 | 0.192773 | − | 0.981243i | \(-0.438252\pi\) | ||||
0.192773 | + | 0.981243i | \(0.438252\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −4000.00 | −0.185399 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 12960.0 | 0.598375 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 19176.0 | 0.881966 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 14112.0 | 0.646565 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −1566.00 | −0.0714742 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −6610.00 | −0.300536 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 25804.0 | 1.16876 | 0.584379 | − | 0.811481i | \(-0.301338\pi\) | ||||
0.584379 | + | 0.811481i | \(0.301338\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −19872.0 | −0.896656 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −32736.0 | −1.47150 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −19292.0 | −0.863908 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −3150.00 | −0.140527 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 17670.0 | 0.785324 | 0.392662 | − | 0.919683i | \(-0.371554\pi\) | ||||
0.392662 | + | 0.919683i | \(0.371554\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −17360.0 | −0.768652 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −6534.00 | −0.288224 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −29736.0 | −1.30680 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 16640.0 | 0.728550 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −8862.00 | −0.386564 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −7398.00 | −0.321508 | −0.160754 | − | 0.986995i | \(-0.551393\pi\) | ||||
−0.160754 | + | 0.986995i | \(0.551393\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 28108.0 | 1.21702 | 0.608511 | − | 0.793545i | \(-0.291767\pi\) | ||||
0.608511 | + | 0.793545i | \(0.291767\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 19728.0 | 0.851035 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 4540.00 | 0.195128 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −5168.00 | −0.221304 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −3744.00 | −0.159739 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 30830.0 | 1.31057 | 0.655283 | − | 0.755384i | \(-0.272549\pi\) | ||||
0.655283 | + | 0.755384i | \(0.272549\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −5872.00 | −0.248706 | −0.124353 | − | 0.992238i | \(-0.539686\pi\) | ||||
−0.124353 | + | 0.992238i | \(0.539686\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 2100.00 | 0.0886214 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 16308.0 | 0.685713 | 0.342857 | − | 0.939388i | \(-0.388606\pi\) | ||||
0.342857 | + | 0.939388i | \(0.388606\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 28294.0 | 1.18539 | 0.592697 | − | 0.805426i | \(-0.298063\pi\) | ||||
0.592697 | + | 0.805426i | \(0.298063\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 13434.0 | 0.560795 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 5394.00 | 0.224359 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −6480.00 | −0.268562 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −4320.00 | −0.178400 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −20536.0 | −0.845032 | −0.422516 | − | 0.906356i | \(-0.638853\pi\) | ||||
−0.422516 | + | 0.906356i | \(0.638853\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −21025.0 | −0.862069 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −19074.0 | −0.779292 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −7605.00 | −0.309609 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −8752.00 | −0.355044 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −2580.00 | −0.104294 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 56160.0 | 2.26221 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 27710.0 | 1.11228 | 0.556139 | − | 0.831090i | \(-0.312282\pi\) | ||||
0.556139 | + | 0.831090i | \(0.312282\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 3060.00 | 0.122397 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 12858.0 | 0.512510 | 0.256255 | − | 0.966609i | \(-0.417511\pi\) | ||||
0.256255 | + | 0.966609i | \(0.417511\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 3148.00 | 0.125039 | 0.0625194 | − | 0.998044i | \(-0.480086\pi\) | ||||
0.0625194 | + | 0.998044i | \(0.480086\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 13536.0 | 0.535779 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −48456.0 | −1.91131 | −0.955656 | − | 0.294487i | \(-0.904851\pi\) | ||||
−0.955656 | + | 0.294487i | \(0.904851\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 10670.0 | 0.419411 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −3207.00 | −0.125623 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −21504.0 | −0.839440 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 21736.0 | 0.845576 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −12654.0 | −0.490576 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 2000.00 | 0.0772712 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 9478.00 | 0.364937 | 0.182468 | − | 0.983212i | \(-0.441591\pi\) | ||||
0.182468 | + | 0.983212i | \(0.441591\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −17382.0 | −0.666986 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 8178.00 | 0.312740 | 0.156370 | − | 0.987699i | \(-0.450021\pi\) | ||||
0.156370 | + | 0.987699i | \(0.450021\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 316.000 | 0.0120433 | 0.00602166 | − | 0.999982i | \(-0.498083\pi\) | ||||
0.00602166 | + | 0.999982i | \(0.498083\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −2940.00 | −0.111669 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 6304.00 | 0.238633 | 0.119317 | − | 0.992856i | \(-0.461930\pi\) | ||||
0.119317 | + | 0.992856i | \(0.461930\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −18816.0 | −0.709863 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 2268.00 | 0.0852759 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 19040.0 | 0.713493 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −8060.00 | −0.301024 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −16224.0 | −0.603906 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 9280.00 | 0.344277 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 13020.0 | 0.481420 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −3648.00 | −0.134438 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 15430.0 | 0.566752 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −1596.00 | −0.0584281 | −0.0292141 | − | 0.999573i | \(-0.509300\pi\) | ||||
−0.0292141 | + | 0.999573i | \(0.509300\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 8910.00 | 0.325111 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 25792.0 | 0.938010 | 0.469005 | − | 0.883196i | \(-0.344613\pi\) | ||||
0.469005 | + | 0.883196i | \(0.344613\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 29456.0 | 1.06775 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 11130.0 | 0.402127 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −192.000 | −0.00691428 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 9736.00 | 0.349468 | 0.174734 | − | 0.984616i | \(-0.444093\pi\) | ||||
0.174734 | + | 0.984616i | \(0.444093\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 20580.0 | 0.736302 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −13104.0 | −0.467306 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 6750.00 | 0.239934 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −6624.00 | −0.234693 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −94.0000 | −0.00331974 | −0.00165987 | − | 0.999999i | \(-0.500528\pi\) | ||||
−0.00165987 | + | 0.999999i | \(0.500528\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −5916.00 | −0.208259 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 18744.0 | 0.657718 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −8680.00 | −0.303600 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −8678.00 | −0.302559 | −0.151280 | − | 0.988491i | \(-0.548339\pi\) | ||||
−0.151280 | + | 0.988491i | \(0.548339\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 33054.0 | 1.14875 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 28406.0 | 0.984069 | 0.492035 | − | 0.870576i | \(-0.336253\pi\) | ||||
0.492035 | + | 0.870576i | \(0.336253\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 58656.0 | 2.02556 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 2160.00 | 0.0743543 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −31988.0 | −1.09765 | −0.548823 | − | 0.835939i | \(-0.684924\pi\) | ||||
−0.548823 | + | 0.835939i | \(0.684924\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 27612.0 | 0.944493 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −2862.00 | −0.0975885 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 6714.00 | 0.228214 | 0.114107 | − | 0.993468i | \(-0.463599\pi\) | ||||
0.114107 | + | 0.993468i | \(0.463599\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 21040.0 | 0.712920 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −4872.00 | −0.164566 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −12640.0 | −0.425617 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −4191.00 | −0.140680 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −10908.0 | −0.365011 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 14090.0 | 0.470024 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −15312.0 | −0.509204 | −0.254602 | − | 0.967046i | \(-0.581945\pi\) | ||||
−0.254602 | + | 0.967046i | \(0.581945\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −12648.0 | −0.419311 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 8540.00 | 0.282247 | 0.141123 | − | 0.989992i | \(-0.454929\pi\) | ||||
0.141123 | + | 0.989992i | \(0.454929\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 14784.0 | 0.487105 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −1950.00 | −0.0640513 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −8126.00 | −0.266094 | −0.133047 | − | 0.991110i | \(-0.542476\pi\) | ||||
−0.133047 | + | 0.991110i | \(0.542476\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −20328.0 | −0.663622 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −16506.0 | −0.537203 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −1392.00 | −0.0451657 | −0.0225829 | − | 0.999745i | \(-0.507189\pi\) | ||||
−0.0225829 | + | 0.999745i | \(0.507189\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −2090.00 | −0.0676070 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 13440.0 | 0.433435 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −15808.0 | −0.508256 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 48832.0 | 1.56529 | 0.782644 | − | 0.622470i | \(-0.213871\pi\) | ||||
0.782644 | + | 0.622470i | \(0.213871\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −28188.0 | −0.900825 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 16760.0 | 0.533998 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 46926.0 | 1.49063 | 0.745317 | − | 0.666711i | \(-0.232298\pi\) | ||||
0.745317 | + | 0.666711i | \(0.232298\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 7290.00 | 0.230876 |
(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 | 240.4.a.l.1.1 | 1 | ||
3.2 | odd | 2 | 720.4.a.l.1.1 | 1 | |||
4.3 | odd | 2 | 120.4.a.c.1.1 | ✓ | 1 | ||
5.2 | odd | 4 | 1200.4.f.o.49.1 | 2 | |||
5.3 | odd | 4 | 1200.4.f.o.49.2 | 2 | |||
5.4 | even | 2 | 1200.4.a.c.1.1 | 1 | |||
8.3 | odd | 2 | 960.4.a.u.1.1 | 1 | |||
8.5 | even | 2 | 960.4.a.h.1.1 | 1 | |||
12.11 | even | 2 | 360.4.a.b.1.1 | 1 | |||
20.3 | even | 4 | 600.4.f.c.49.1 | 2 | |||
20.7 | even | 4 | 600.4.f.c.49.2 | 2 | |||
20.19 | odd | 2 | 600.4.a.q.1.1 | 1 | |||
60.23 | odd | 4 | 1800.4.f.r.649.2 | 2 | |||
60.47 | odd | 4 | 1800.4.f.r.649.1 | 2 | |||
60.59 | even | 2 | 1800.4.a.bb.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
120.4.a.c.1.1 | ✓ | 1 | 4.3 | odd | 2 | ||
240.4.a.l.1.1 | 1 | 1.1 | even | 1 | trivial | ||
360.4.a.b.1.1 | 1 | 12.11 | even | 2 | |||
600.4.a.q.1.1 | 1 | 20.19 | odd | 2 | |||
600.4.f.c.49.1 | 2 | 20.3 | even | 4 | |||
600.4.f.c.49.2 | 2 | 20.7 | even | 4 | |||
720.4.a.l.1.1 | 1 | 3.2 | odd | 2 | |||
960.4.a.h.1.1 | 1 | 8.5 | even | 2 | |||
960.4.a.u.1.1 | 1 | 8.3 | odd | 2 | |||
1200.4.a.c.1.1 | 1 | 5.4 | even | 2 | |||
1200.4.f.o.49.1 | 2 | 5.2 | odd | 4 | |||
1200.4.f.o.49.2 | 2 | 5.3 | odd | 4 | |||
1800.4.a.bb.1.1 | 1 | 60.59 | even | 2 | |||
1800.4.f.r.649.1 | 2 | 60.47 | odd | 4 | |||
1800.4.f.r.649.2 | 2 | 60.23 | odd | 4 |