Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1638,4,Mod(1,1638)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1638, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1638.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1638 = 2 \cdot 3^{2} \cdot 7 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1638.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: | \(96.6451285894\) |
Analytic rank: | \(0\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 546) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 1638.1 |
$q$-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 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 4.00000 | 0.500000 | ||||||||
\(5\) | 14.0000 | 1.25220 | 0.626099 | − | 0.779744i | \(-0.284651\pi\) | ||||
0.626099 | + | 0.779744i | \(0.284651\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −7.00000 | −0.377964 | ||||||||
\(8\) | −8.00000 | −0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −28.0000 | −0.885438 | ||||||||
\(11\) | −8.00000 | −0.219281 | −0.109640 | − | 0.993971i | \(-0.534970\pi\) | ||||
−0.109640 | + | 0.993971i | \(0.534970\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 13.0000 | 0.277350 | ||||||||
\(14\) | 14.0000 | 0.267261 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 16.0000 | 0.250000 | ||||||||
\(17\) | 98.0000 | 1.39815 | 0.699073 | − | 0.715050i | \(-0.253596\pi\) | ||||
0.699073 | + | 0.715050i | \(0.253596\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −28.0000 | −0.338086 | −0.169043 | − | 0.985609i | \(-0.554068\pi\) | ||||
−0.169043 | + | 0.985609i | \(0.554068\pi\) | |||||||
\(20\) | 56.0000 | 0.626099 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 16.0000 | 0.155055 | ||||||||
\(23\) | 52.0000 | 0.471424 | 0.235712 | − | 0.971823i | \(-0.424258\pi\) | ||||
0.235712 | + | 0.971823i | \(0.424258\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 71.0000 | 0.568000 | ||||||||
\(26\) | −26.0000 | −0.196116 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −28.0000 | −0.188982 | ||||||||
\(29\) | 2.00000 | 0.0128066 | 0.00640329 | − | 0.999979i | \(-0.497962\pi\) | ||||
0.00640329 | + | 0.999979i | \(0.497962\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −168.000 | −0.973345 | −0.486672 | − | 0.873585i | \(-0.661789\pi\) | ||||
−0.486672 | + | 0.873585i | \(0.661789\pi\) | |||||||
\(32\) | −32.0000 | −0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −196.000 | −0.988639 | ||||||||
\(35\) | −98.0000 | −0.473286 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −146.000 | −0.648710 | −0.324355 | − | 0.945936i | \(-0.605147\pi\) | ||||
−0.324355 | + | 0.945936i | \(0.605147\pi\) | |||||||
\(38\) | 56.0000 | 0.239063 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −112.000 | −0.442719 | ||||||||
\(41\) | 514.000 | 1.95789 | 0.978943 | − | 0.204135i | \(-0.0654380\pi\) | ||||
0.978943 | + | 0.204135i | \(0.0654380\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −236.000 | −0.836969 | −0.418484 | − | 0.908224i | \(-0.637439\pi\) | ||||
−0.418484 | + | 0.908224i | \(0.637439\pi\) | |||||||
\(44\) | −32.0000 | −0.109640 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −104.000 | −0.333347 | ||||||||
\(47\) | 216.000 | 0.670358 | 0.335179 | − | 0.942154i | \(-0.391203\pi\) | ||||
0.335179 | + | 0.942154i | \(0.391203\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 49.0000 | 0.142857 | ||||||||
\(50\) | −142.000 | −0.401637 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 52.0000 | 0.138675 | ||||||||
\(53\) | 66.0000 | 0.171053 | 0.0855264 | − | 0.996336i | \(-0.472743\pi\) | ||||
0.0855264 | + | 0.996336i | \(0.472743\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −112.000 | −0.274583 | ||||||||
\(56\) | 56.0000 | 0.133631 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −4.00000 | −0.00905562 | ||||||||
\(59\) | 84.0000 | 0.185354 | 0.0926769 | − | 0.995696i | \(-0.470458\pi\) | ||||
0.0926769 | + | 0.995696i | \(0.470458\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 446.000 | 0.936138 | 0.468069 | − | 0.883692i | \(-0.344950\pi\) | ||||
0.468069 | + | 0.883692i | \(0.344950\pi\) | |||||||
\(62\) | 336.000 | 0.688259 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 64.0000 | 0.125000 | ||||||||
\(65\) | 182.000 | 0.347297 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 292.000 | 0.532440 | 0.266220 | − | 0.963912i | \(-0.414225\pi\) | ||||
0.266220 | + | 0.963912i | \(0.414225\pi\) | |||||||
\(68\) | 392.000 | 0.699073 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 196.000 | 0.334664 | ||||||||
\(71\) | −100.000 | −0.167152 | −0.0835762 | − | 0.996501i | \(-0.526634\pi\) | ||||
−0.0835762 | + | 0.996501i | \(0.526634\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 450.000 | 0.721487 | 0.360743 | − | 0.932665i | \(-0.382523\pi\) | ||||
0.360743 | + | 0.932665i | \(0.382523\pi\) | |||||||
\(74\) | 292.000 | 0.458707 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −112.000 | −0.169043 | ||||||||
\(77\) | 56.0000 | 0.0828804 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 392.000 | 0.558271 | 0.279136 | − | 0.960252i | \(-0.409952\pi\) | ||||
0.279136 | + | 0.960252i | \(0.409952\pi\) | |||||||
\(80\) | 224.000 | 0.313050 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −1028.00 | −1.38443 | ||||||||
\(83\) | 292.000 | 0.386159 | 0.193079 | − | 0.981183i | \(-0.438153\pi\) | ||||
0.193079 | + | 0.981183i | \(0.438153\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1372.00 | 1.75076 | ||||||||
\(86\) | 472.000 | 0.591826 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 64.0000 | 0.0775275 | ||||||||
\(89\) | 402.000 | 0.478786 | 0.239393 | − | 0.970923i | \(-0.423052\pi\) | ||||
0.239393 | + | 0.970923i | \(0.423052\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −91.0000 | −0.104828 | ||||||||
\(92\) | 208.000 | 0.235712 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −432.000 | −0.474015 | ||||||||
\(95\) | −392.000 | −0.423351 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 314.000 | 0.328679 | 0.164340 | − | 0.986404i | \(-0.447451\pi\) | ||||
0.164340 | + | 0.986404i | \(0.447451\pi\) | |||||||
\(98\) | −98.0000 | −0.101015 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 284.000 | 0.284000 | ||||||||
\(101\) | −858.000 | −0.845289 | −0.422645 | − | 0.906296i | \(-0.638898\pi\) | ||||
−0.422645 | + | 0.906296i | \(0.638898\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −944.000 | −0.903059 | −0.451530 | − | 0.892256i | \(-0.649121\pi\) | ||||
−0.451530 | + | 0.892256i | \(0.649121\pi\) | |||||||
\(104\) | −104.000 | −0.0980581 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −132.000 | −0.120953 | ||||||||
\(107\) | −840.000 | −0.758933 | −0.379467 | − | 0.925205i | \(-0.623893\pi\) | ||||
−0.379467 | + | 0.925205i | \(0.623893\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1334.00 | 1.17224 | 0.586119 | − | 0.810225i | \(-0.300655\pi\) | ||||
0.586119 | + | 0.810225i | \(0.300655\pi\) | |||||||
\(110\) | 224.000 | 0.194160 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −112.000 | −0.0944911 | ||||||||
\(113\) | −946.000 | −0.787542 | −0.393771 | − | 0.919209i | \(-0.628830\pi\) | ||||
−0.393771 | + | 0.919209i | \(0.628830\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 728.000 | 0.590316 | ||||||||
\(116\) | 8.00000 | 0.00640329 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −168.000 | −0.131065 | ||||||||
\(119\) | −686.000 | −0.528450 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1267.00 | −0.951916 | ||||||||
\(122\) | −892.000 | −0.661950 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −672.000 | −0.486672 | ||||||||
\(125\) | −756.000 | −0.540950 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 904.000 | 0.631630 | 0.315815 | − | 0.948821i | \(-0.397722\pi\) | ||||
0.315815 | + | 0.948821i | \(0.397722\pi\) | |||||||
\(128\) | −128.000 | −0.0883883 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −364.000 | −0.245576 | ||||||||
\(131\) | 1476.00 | 0.984418 | 0.492209 | − | 0.870477i | \(-0.336190\pi\) | ||||
0.492209 | + | 0.870477i | \(0.336190\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 196.000 | 0.127785 | ||||||||
\(134\) | −584.000 | −0.376492 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −784.000 | −0.494319 | ||||||||
\(137\) | 62.0000 | 0.0386644 | 0.0193322 | − | 0.999813i | \(-0.493846\pi\) | ||||
0.0193322 | + | 0.999813i | \(0.493846\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −908.000 | −0.554069 | −0.277034 | − | 0.960860i | \(-0.589352\pi\) | ||||
−0.277034 | + | 0.960860i | \(0.589352\pi\) | |||||||
\(140\) | −392.000 | −0.236643 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 200.000 | 0.118195 | ||||||||
\(143\) | −104.000 | −0.0608176 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 28.0000 | 0.0160364 | ||||||||
\(146\) | −900.000 | −0.510168 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −584.000 | −0.324355 | ||||||||
\(149\) | 2514.00 | 1.38225 | 0.691124 | − | 0.722736i | \(-0.257116\pi\) | ||||
0.691124 | + | 0.722736i | \(0.257116\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1048.00 | −0.564802 | −0.282401 | − | 0.959297i | \(-0.591131\pi\) | ||||
−0.282401 | + | 0.959297i | \(0.591131\pi\) | |||||||
\(152\) | 224.000 | 0.119532 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −112.000 | −0.0586053 | ||||||||
\(155\) | −2352.00 | −1.21882 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 3166.00 | 1.60939 | 0.804695 | − | 0.593688i | \(-0.202329\pi\) | ||||
0.804695 | + | 0.593688i | \(0.202329\pi\) | |||||||
\(158\) | −784.000 | −0.394758 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −448.000 | −0.221359 | ||||||||
\(161\) | −364.000 | −0.178181 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −492.000 | −0.236420 | −0.118210 | − | 0.992989i | \(-0.537716\pi\) | ||||
−0.118210 | + | 0.992989i | \(0.537716\pi\) | |||||||
\(164\) | 2056.00 | 0.978943 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −584.000 | −0.273055 | ||||||||
\(167\) | 1104.00 | 0.511557 | 0.255779 | − | 0.966735i | \(-0.417668\pi\) | ||||
0.255779 | + | 0.966735i | \(0.417668\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 169.000 | 0.0769231 | ||||||||
\(170\) | −2744.00 | −1.23797 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −944.000 | −0.418484 | ||||||||
\(173\) | 2686.00 | 1.18042 | 0.590210 | − | 0.807249i | \(-0.299045\pi\) | ||||
0.590210 | + | 0.807249i | \(0.299045\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −497.000 | −0.214684 | ||||||||
\(176\) | −128.000 | −0.0548202 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −804.000 | −0.338553 | ||||||||
\(179\) | −2088.00 | −0.871868 | −0.435934 | − | 0.899979i | \(-0.643582\pi\) | ||||
−0.435934 | + | 0.899979i | \(0.643582\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −242.000 | −0.0993797 | −0.0496898 | − | 0.998765i | \(-0.515823\pi\) | ||||
−0.0496898 | + | 0.998765i | \(0.515823\pi\) | |||||||
\(182\) | 182.000 | 0.0741249 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −416.000 | −0.166674 | ||||||||
\(185\) | −2044.00 | −0.812313 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −784.000 | −0.306587 | ||||||||
\(188\) | 864.000 | 0.335179 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 784.000 | 0.299354 | ||||||||
\(191\) | 1284.00 | 0.486424 | 0.243212 | − | 0.969973i | \(-0.421799\pi\) | ||||
0.243212 | + | 0.969973i | \(0.421799\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −2734.00 | −1.01968 | −0.509838 | − | 0.860270i | \(-0.670295\pi\) | ||||
−0.509838 | + | 0.860270i | \(0.670295\pi\) | |||||||
\(194\) | −628.000 | −0.232411 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 196.000 | 0.0714286 | ||||||||
\(197\) | −5118.00 | −1.85098 | −0.925488 | − | 0.378776i | \(-0.876345\pi\) | ||||
−0.925488 | + | 0.378776i | \(0.876345\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1528.00 | 0.544307 | 0.272153 | − | 0.962254i | \(-0.412264\pi\) | ||||
0.272153 | + | 0.962254i | \(0.412264\pi\) | |||||||
\(200\) | −568.000 | −0.200818 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 1716.00 | 0.597710 | ||||||||
\(203\) | −14.0000 | −0.00484043 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 7196.00 | 2.45166 | ||||||||
\(206\) | 1888.00 | 0.638559 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 208.000 | 0.0693375 | ||||||||
\(209\) | 224.000 | 0.0741359 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 268.000 | 0.0874402 | 0.0437201 | − | 0.999044i | \(-0.486079\pi\) | ||||
0.0437201 | + | 0.999044i | \(0.486079\pi\) | |||||||
\(212\) | 264.000 | 0.0855264 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 1680.00 | 0.536647 | ||||||||
\(215\) | −3304.00 | −1.04805 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1176.00 | 0.367890 | ||||||||
\(218\) | −2668.00 | −0.828898 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −448.000 | −0.137292 | ||||||||
\(221\) | 1274.00 | 0.387776 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1392.00 | 0.418005 | 0.209003 | − | 0.977915i | \(-0.432978\pi\) | ||||
0.209003 | + | 0.977915i | \(0.432978\pi\) | |||||||
\(224\) | 224.000 | 0.0668153 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 1892.00 | 0.556876 | ||||||||
\(227\) | 6140.00 | 1.79527 | 0.897635 | − | 0.440740i | \(-0.145284\pi\) | ||||
0.897635 | + | 0.440740i | \(0.145284\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1870.00 | 0.539620 | 0.269810 | − | 0.962914i | \(-0.413039\pi\) | ||||
0.269810 | + | 0.962914i | \(0.413039\pi\) | |||||||
\(230\) | −1456.00 | −0.417417 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −16.0000 | −0.00452781 | ||||||||
\(233\) | −50.0000 | −0.0140584 | −0.00702920 | − | 0.999975i | \(-0.502237\pi\) | ||||
−0.00702920 | + | 0.999975i | \(0.502237\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 3024.00 | 0.839421 | ||||||||
\(236\) | 336.000 | 0.0926769 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 1372.00 | 0.373670 | ||||||||
\(239\) | 3228.00 | 0.873648 | 0.436824 | − | 0.899547i | \(-0.356103\pi\) | ||||
0.436824 | + | 0.899547i | \(0.356103\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 5978.00 | 1.59783 | 0.798915 | − | 0.601444i | \(-0.205408\pi\) | ||||
0.798915 | + | 0.601444i | \(0.205408\pi\) | |||||||
\(242\) | 2534.00 | 0.673106 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 1784.00 | 0.468069 | ||||||||
\(245\) | 686.000 | 0.178885 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −364.000 | −0.0937683 | ||||||||
\(248\) | 1344.00 | 0.344129 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 1512.00 | 0.382509 | ||||||||
\(251\) | 4084.00 | 1.02701 | 0.513506 | − | 0.858086i | \(-0.328347\pi\) | ||||
0.513506 | + | 0.858086i | \(0.328347\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −416.000 | −0.103374 | ||||||||
\(254\) | −1808.00 | −0.446630 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 256.000 | 0.0625000 | ||||||||
\(257\) | −2646.00 | −0.642229 | −0.321115 | − | 0.947040i | \(-0.604057\pi\) | ||||
−0.321115 | + | 0.947040i | \(0.604057\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1022.00 | 0.245189 | ||||||||
\(260\) | 728.000 | 0.173649 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −2952.00 | −0.696088 | ||||||||
\(263\) | −5164.00 | −1.21074 | −0.605372 | − | 0.795942i | \(-0.706976\pi\) | ||||
−0.605372 | + | 0.795942i | \(0.706976\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 924.000 | 0.214192 | ||||||||
\(266\) | −392.000 | −0.0903574 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 1168.00 | 0.266220 | ||||||||
\(269\) | 4710.00 | 1.06756 | 0.533780 | − | 0.845623i | \(-0.320771\pi\) | ||||
0.533780 | + | 0.845623i | \(0.320771\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −3144.00 | −0.704739 | −0.352370 | − | 0.935861i | \(-0.614624\pi\) | ||||
−0.352370 | + | 0.935861i | \(0.614624\pi\) | |||||||
\(272\) | 1568.00 | 0.349537 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −124.000 | −0.0273398 | ||||||||
\(275\) | −568.000 | −0.124552 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 3310.00 | 0.717973 | 0.358987 | − | 0.933343i | \(-0.383122\pi\) | ||||
0.358987 | + | 0.933343i | \(0.383122\pi\) | |||||||
\(278\) | 1816.00 | 0.391786 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 784.000 | 0.167332 | ||||||||
\(281\) | 4910.00 | 1.04237 | 0.521185 | − | 0.853444i | \(-0.325490\pi\) | ||||
0.521185 | + | 0.853444i | \(0.325490\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 7436.00 | 1.56192 | 0.780962 | − | 0.624579i | \(-0.214729\pi\) | ||||
0.780962 | + | 0.624579i | \(0.214729\pi\) | |||||||
\(284\) | −400.000 | −0.0835762 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 208.000 | 0.0430045 | ||||||||
\(287\) | −3598.00 | −0.740011 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 4691.00 | 0.954814 | ||||||||
\(290\) | −56.0000 | −0.0113394 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 1800.00 | 0.360743 | ||||||||
\(293\) | 310.000 | 0.0618102 | 0.0309051 | − | 0.999522i | \(-0.490161\pi\) | ||||
0.0309051 | + | 0.999522i | \(0.490161\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1176.00 | 0.232100 | ||||||||
\(296\) | 1168.00 | 0.229353 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −5028.00 | −0.977397 | ||||||||
\(299\) | 676.000 | 0.130749 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1652.00 | 0.316345 | ||||||||
\(302\) | 2096.00 | 0.399375 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −448.000 | −0.0845216 | ||||||||
\(305\) | 6244.00 | 1.17223 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −3516.00 | −0.653644 | −0.326822 | − | 0.945086i | \(-0.605978\pi\) | ||||
−0.326822 | + | 0.945086i | \(0.605978\pi\) | |||||||
\(308\) | 224.000 | 0.0414402 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 4704.00 | 0.861836 | ||||||||
\(311\) | −3216.00 | −0.586375 | −0.293188 | − | 0.956055i | \(-0.594716\pi\) | ||||
−0.293188 | + | 0.956055i | \(0.594716\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −1398.00 | −0.252459 | −0.126229 | − | 0.992001i | \(-0.540288\pi\) | ||||
−0.126229 | + | 0.992001i | \(0.540288\pi\) | |||||||
\(314\) | −6332.00 | −1.13801 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 1568.00 | 0.279136 | ||||||||
\(317\) | 9034.00 | 1.60063 | 0.800315 | − | 0.599579i | \(-0.204665\pi\) | ||||
0.800315 | + | 0.599579i | \(0.204665\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −16.0000 | −0.00280824 | ||||||||
\(320\) | 896.000 | 0.156525 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 728.000 | 0.125993 | ||||||||
\(323\) | −2744.00 | −0.472694 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 923.000 | 0.157535 | ||||||||
\(326\) | 984.000 | 0.167174 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −4112.00 | −0.692217 | ||||||||
\(329\) | −1512.00 | −0.253372 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 9108.00 | 1.51245 | 0.756225 | − | 0.654312i | \(-0.227042\pi\) | ||||
0.756225 | + | 0.654312i | \(0.227042\pi\) | |||||||
\(332\) | 1168.00 | 0.193079 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −2208.00 | −0.361726 | ||||||||
\(335\) | 4088.00 | 0.666720 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −1566.00 | −0.253132 | −0.126566 | − | 0.991958i | \(-0.540396\pi\) | ||||
−0.126566 | + | 0.991958i | \(0.540396\pi\) | |||||||
\(338\) | −338.000 | −0.0543928 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 5488.00 | 0.875378 | ||||||||
\(341\) | 1344.00 | 0.213436 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −343.000 | −0.0539949 | ||||||||
\(344\) | 1888.00 | 0.295913 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −5372.00 | −0.834684 | ||||||||
\(347\) | −4528.00 | −0.700507 | −0.350253 | − | 0.936655i | \(-0.613904\pi\) | ||||
−0.350253 | + | 0.936655i | \(0.613904\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −1090.00 | −0.167182 | −0.0835908 | − | 0.996500i | \(-0.526639\pi\) | ||||
−0.0835908 | + | 0.996500i | \(0.526639\pi\) | |||||||
\(350\) | 994.000 | 0.151804 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 256.000 | 0.0387638 | ||||||||
\(353\) | 11234.0 | 1.69384 | 0.846920 | − | 0.531720i | \(-0.178454\pi\) | ||||
0.846920 | + | 0.531720i | \(0.178454\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −1400.00 | −0.209308 | ||||||||
\(356\) | 1608.00 | 0.239393 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 4176.00 | 0.616504 | ||||||||
\(359\) | −3444.00 | −0.506316 | −0.253158 | − | 0.967425i | \(-0.581469\pi\) | ||||
−0.253158 | + | 0.967425i | \(0.581469\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −6075.00 | −0.885698 | ||||||||
\(362\) | 484.000 | 0.0702720 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −364.000 | −0.0524142 | ||||||||
\(365\) | 6300.00 | 0.903444 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 11712.0 | 1.66583 | 0.832917 | − | 0.553397i | \(-0.186669\pi\) | ||||
0.832917 | + | 0.553397i | \(0.186669\pi\) | |||||||
\(368\) | 832.000 | 0.117856 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 4088.00 | 0.574392 | ||||||||
\(371\) | −462.000 | −0.0646519 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 10990.0 | 1.52558 | 0.762789 | − | 0.646647i | \(-0.223829\pi\) | ||||
0.762789 | + | 0.646647i | \(0.223829\pi\) | |||||||
\(374\) | 1568.00 | 0.216790 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −1728.00 | −0.237007 | ||||||||
\(377\) | 26.0000 | 0.00355190 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −7004.00 | −0.949265 | −0.474632 | − | 0.880184i | \(-0.657419\pi\) | ||||
−0.474632 | + | 0.880184i | \(0.657419\pi\) | |||||||
\(380\) | −1568.00 | −0.211676 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −2568.00 | −0.343954 | ||||||||
\(383\) | 5472.00 | 0.730042 | 0.365021 | − | 0.930999i | \(-0.381062\pi\) | ||||
0.365021 | + | 0.930999i | \(0.381062\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 784.000 | 0.103783 | ||||||||
\(386\) | 5468.00 | 0.721020 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 1256.00 | 0.164340 | ||||||||
\(389\) | −1910.00 | −0.248948 | −0.124474 | − | 0.992223i | \(-0.539724\pi\) | ||||
−0.124474 | + | 0.992223i | \(0.539724\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 5096.00 | 0.659120 | ||||||||
\(392\) | −392.000 | −0.0505076 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 10236.0 | 1.30884 | ||||||||
\(395\) | 5488.00 | 0.699066 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −13234.0 | −1.67304 | −0.836518 | − | 0.547939i | \(-0.815413\pi\) | ||||
−0.836518 | + | 0.547939i | \(0.815413\pi\) | |||||||
\(398\) | −3056.00 | −0.384883 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 1136.00 | 0.142000 | ||||||||
\(401\) | −4586.00 | −0.571107 | −0.285554 | − | 0.958363i | \(-0.592177\pi\) | ||||
−0.285554 | + | 0.958363i | \(0.592177\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −2184.00 | −0.269957 | ||||||||
\(404\) | −3432.00 | −0.422645 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 28.0000 | 0.00342270 | ||||||||
\(407\) | 1168.00 | 0.142250 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −4174.00 | −0.504624 | −0.252312 | − | 0.967646i | \(-0.581191\pi\) | ||||
−0.252312 | + | 0.967646i | \(0.581191\pi\) | |||||||
\(410\) | −14392.0 | −1.73359 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −3776.00 | −0.451530 | ||||||||
\(413\) | −588.000 | −0.0700571 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 4088.00 | 0.483547 | ||||||||
\(416\) | −416.000 | −0.0490290 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −448.000 | −0.0524220 | ||||||||
\(419\) | 10012.0 | 1.16735 | 0.583673 | − | 0.811989i | \(-0.301615\pi\) | ||||
0.583673 | + | 0.811989i | \(0.301615\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −1250.00 | −0.144706 | −0.0723531 | − | 0.997379i | \(-0.523051\pi\) | ||||
−0.0723531 | + | 0.997379i | \(0.523051\pi\) | |||||||
\(422\) | −536.000 | −0.0618296 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −528.000 | −0.0604763 | ||||||||
\(425\) | 6958.00 | 0.794147 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −3122.00 | −0.353827 | ||||||||
\(428\) | −3360.00 | −0.379467 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 6608.00 | 0.741084 | ||||||||
\(431\) | −6236.00 | −0.696932 | −0.348466 | − | 0.937321i | \(-0.613297\pi\) | ||||
−0.348466 | + | 0.937321i | \(0.613297\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −3966.00 | −0.440170 | −0.220085 | − | 0.975481i | \(-0.570634\pi\) | ||||
−0.220085 | + | 0.975481i | \(0.570634\pi\) | |||||||
\(434\) | −2352.00 | −0.260137 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 5336.00 | 0.586119 | ||||||||
\(437\) | −1456.00 | −0.159382 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 8776.00 | 0.954113 | 0.477057 | − | 0.878873i | \(-0.341704\pi\) | ||||
0.477057 | + | 0.878873i | \(0.341704\pi\) | |||||||
\(440\) | 896.000 | 0.0970798 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −2548.00 | −0.274199 | ||||||||
\(443\) | −6096.00 | −0.653792 | −0.326896 | − | 0.945060i | \(-0.606003\pi\) | ||||
−0.326896 | + | 0.945060i | \(0.606003\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 5628.00 | 0.599534 | ||||||||
\(446\) | −2784.00 | −0.295574 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −448.000 | −0.0472456 | ||||||||
\(449\) | 9390.00 | 0.986952 | 0.493476 | − | 0.869759i | \(-0.335726\pi\) | ||||
0.493476 | + | 0.869759i | \(0.335726\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −4112.00 | −0.429327 | ||||||||
\(452\) | −3784.00 | −0.393771 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −12280.0 | −1.26945 | ||||||||
\(455\) | −1274.00 | −0.131266 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −6.00000 | −0.000614154 0 | −0.000307077 | − | 1.00000i | \(-0.500098\pi\) | ||||
−0.000307077 | 1.00000i | \(0.500098\pi\) | ||||||||
\(458\) | −3740.00 | −0.381569 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 2912.00 | 0.295158 | ||||||||
\(461\) | 9374.00 | 0.947051 | 0.473526 | − | 0.880780i | \(-0.342981\pi\) | ||||
0.473526 | + | 0.880780i | \(0.342981\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 4008.00 | 0.402306 | 0.201153 | − | 0.979560i | \(-0.435531\pi\) | ||||
0.201153 | + | 0.979560i | \(0.435531\pi\) | |||||||
\(464\) | 32.0000 | 0.00320164 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 100.000 | 0.00994080 | ||||||||
\(467\) | 3260.00 | 0.323030 | 0.161515 | − | 0.986870i | \(-0.448362\pi\) | ||||
0.161515 | + | 0.986870i | \(0.448362\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −2044.00 | −0.201243 | ||||||||
\(470\) | −6048.00 | −0.593561 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −672.000 | −0.0655324 | ||||||||
\(473\) | 1888.00 | 0.183531 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1988.00 | −0.192033 | ||||||||
\(476\) | −2744.00 | −0.264225 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −6456.00 | −0.617763 | ||||||||
\(479\) | −12696.0 | −1.21105 | −0.605527 | − | 0.795825i | \(-0.707038\pi\) | ||||
−0.605527 | + | 0.795825i | \(0.707038\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1898.00 | −0.179920 | ||||||||
\(482\) | −11956.0 | −1.12984 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −5068.00 | −0.475958 | ||||||||
\(485\) | 4396.00 | 0.411571 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 10760.0 | 1.00120 | 0.500598 | − | 0.865680i | \(-0.333114\pi\) | ||||
0.500598 | + | 0.865680i | \(0.333114\pi\) | |||||||
\(488\) | −3568.00 | −0.330975 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −1372.00 | −0.126491 | ||||||||
\(491\) | 11600.0 | 1.06619 | 0.533096 | − | 0.846055i | \(-0.321028\pi\) | ||||
0.533096 | + | 0.846055i | \(0.321028\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 196.000 | 0.0179055 | ||||||||
\(494\) | 728.000 | 0.0663042 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −2688.00 | −0.243336 | ||||||||
\(497\) | 700.000 | 0.0631776 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −15908.0 | −1.42713 | −0.713567 | − | 0.700587i | \(-0.752922\pi\) | ||||
−0.713567 | + | 0.700587i | \(0.752922\pi\) | |||||||
\(500\) | −3024.00 | −0.270475 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −8168.00 | −0.726207 | ||||||||
\(503\) | 12232.0 | 1.08429 | 0.542145 | − | 0.840285i | \(-0.317612\pi\) | ||||
0.542145 | + | 0.840285i | \(0.317612\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −12012.0 | −1.05847 | ||||||||
\(506\) | 832.000 | 0.0730967 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 3616.00 | 0.315815 | ||||||||
\(509\) | 13350.0 | 1.16253 | 0.581266 | − | 0.813714i | \(-0.302558\pi\) | ||||
0.581266 | + | 0.813714i | \(0.302558\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −3150.00 | −0.272696 | ||||||||
\(512\) | −512.000 | −0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 5292.00 | 0.454125 | ||||||||
\(515\) | −13216.0 | −1.13081 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −1728.00 | −0.146997 | ||||||||
\(518\) | −2044.00 | −0.173375 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −1456.00 | −0.122788 | ||||||||
\(521\) | 18282.0 | 1.53733 | 0.768665 | − | 0.639652i | \(-0.220921\pi\) | ||||
0.768665 | + | 0.639652i | \(0.220921\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −6108.00 | −0.510677 | −0.255339 | − | 0.966852i | \(-0.582187\pi\) | ||||
−0.255339 | + | 0.966852i | \(0.582187\pi\) | |||||||
\(524\) | 5904.00 | 0.492209 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 10328.0 | 0.856126 | ||||||||
\(527\) | −16464.0 | −1.36088 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −9463.00 | −0.777760 | ||||||||
\(530\) | −1848.00 | −0.151457 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 784.000 | 0.0638923 | ||||||||
\(533\) | 6682.00 | 0.543020 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −11760.0 | −0.950335 | ||||||||
\(536\) | −2336.00 | −0.188246 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −9420.00 | −0.754879 | ||||||||
\(539\) | −392.000 | −0.0313259 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −14906.0 | −1.18458 | −0.592291 | − | 0.805724i | \(-0.701776\pi\) | ||||
−0.592291 | + | 0.805724i | \(0.701776\pi\) | |||||||
\(542\) | 6288.00 | 0.498326 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −3136.00 | −0.247160 | ||||||||
\(545\) | 18676.0 | 1.46788 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 5492.00 | 0.429289 | 0.214644 | − | 0.976692i | \(-0.431141\pi\) | ||||
0.214644 | + | 0.976692i | \(0.431141\pi\) | |||||||
\(548\) | 248.000 | 0.0193322 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 1136.00 | 0.0880713 | ||||||||
\(551\) | −56.0000 | −0.00432973 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −2744.00 | −0.211007 | ||||||||
\(554\) | −6620.00 | −0.507684 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −3632.00 | −0.277034 | ||||||||
\(557\) | 6746.00 | 0.513173 | 0.256586 | − | 0.966521i | \(-0.417402\pi\) | ||||
0.256586 | + | 0.966521i | \(0.417402\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −3068.00 | −0.232133 | ||||||||
\(560\) | −1568.00 | −0.118322 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −9820.00 | −0.737067 | ||||||||
\(563\) | −596.000 | −0.0446153 | −0.0223076 | − | 0.999751i | \(-0.507101\pi\) | ||||
−0.0223076 | + | 0.999751i | \(0.507101\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −13244.0 | −0.986158 | ||||||||
\(566\) | −14872.0 | −1.10445 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 800.000 | 0.0590973 | ||||||||
\(569\) | 2638.00 | 0.194360 | 0.0971799 | − | 0.995267i | \(-0.469018\pi\) | ||||
0.0971799 | + | 0.995267i | \(0.469018\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −22612.0 | −1.65724 | −0.828619 | − | 0.559813i | \(-0.810873\pi\) | ||||
−0.828619 | + | 0.559813i | \(0.810873\pi\) | |||||||
\(572\) | −416.000 | −0.0304088 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 7196.00 | 0.523267 | ||||||||
\(575\) | 3692.00 | 0.267769 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −1806.00 | −0.130303 | −0.0651514 | − | 0.997875i | \(-0.520753\pi\) | ||||
−0.0651514 | + | 0.997875i | \(0.520753\pi\) | |||||||
\(578\) | −9382.00 | −0.675155 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 112.000 | 0.00801818 | ||||||||
\(581\) | −2044.00 | −0.145954 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −528.000 | −0.0375086 | ||||||||
\(584\) | −3600.00 | −0.255084 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −620.000 | −0.0437064 | ||||||||
\(587\) | 27156.0 | 1.90945 | 0.954726 | − | 0.297487i | \(-0.0961486\pi\) | ||||
0.954726 | + | 0.297487i | \(0.0961486\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 4704.00 | 0.329075 | ||||||||
\(590\) | −2352.00 | −0.164119 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −2336.00 | −0.162177 | ||||||||
\(593\) | 6034.00 | 0.417853 | 0.208926 | − | 0.977931i | \(-0.433003\pi\) | ||||
0.208926 | + | 0.977931i | \(0.433003\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −9604.00 | −0.661724 | ||||||||
\(596\) | 10056.0 | 0.691124 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −1352.00 | −0.0924538 | ||||||||
\(599\) | −19284.0 | −1.31540 | −0.657699 | − | 0.753281i | \(-0.728470\pi\) | ||||
−0.657699 | + | 0.753281i | \(0.728470\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 10490.0 | 0.711973 | 0.355987 | − | 0.934491i | \(-0.384145\pi\) | ||||
0.355987 | + | 0.934491i | \(0.384145\pi\) | |||||||
\(602\) | −3304.00 | −0.223689 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −4192.00 | −0.282401 | ||||||||
\(605\) | −17738.0 | −1.19199 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −13216.0 | −0.883725 | −0.441862 | − | 0.897083i | \(-0.645682\pi\) | ||||
−0.441862 | + | 0.897083i | \(0.645682\pi\) | |||||||
\(608\) | 896.000 | 0.0597658 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −12488.0 | −0.828892 | ||||||||
\(611\) | 2808.00 | 0.185924 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −8242.00 | −0.543053 | −0.271526 | − | 0.962431i | \(-0.587528\pi\) | ||||
−0.271526 | + | 0.962431i | \(0.587528\pi\) | |||||||
\(614\) | 7032.00 | 0.462196 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −448.000 | −0.0293027 | ||||||||
\(617\) | 18206.0 | 1.18792 | 0.593959 | − | 0.804495i | \(-0.297564\pi\) | ||||
0.593959 | + | 0.804495i | \(0.297564\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 16580.0 | 1.07659 | 0.538293 | − | 0.842758i | \(-0.319069\pi\) | ||||
0.538293 | + | 0.842758i | \(0.319069\pi\) | |||||||
\(620\) | −9408.00 | −0.609410 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 6432.00 | 0.414630 | ||||||||
\(623\) | −2814.00 | −0.180964 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −19459.0 | −1.24538 | ||||||||
\(626\) | 2796.00 | 0.178515 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 12664.0 | 0.804695 | ||||||||
\(629\) | −14308.0 | −0.906991 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 21040.0 | 1.32740 | 0.663700 | − | 0.747999i | \(-0.268985\pi\) | ||||
0.663700 | + | 0.747999i | \(0.268985\pi\) | |||||||
\(632\) | −3136.00 | −0.197379 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −18068.0 | −1.13182 | ||||||||
\(635\) | 12656.0 | 0.790926 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 637.000 | 0.0396214 | ||||||||
\(638\) | 32.0000 | 0.00198572 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −1792.00 | −0.110680 | ||||||||
\(641\) | −170.000 | −0.0104752 | −0.00523759 | − | 0.999986i | \(-0.501667\pi\) | ||||
−0.00523759 | + | 0.999986i | \(0.501667\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 23924.0 | 1.46729 | 0.733647 | − | 0.679530i | \(-0.237816\pi\) | ||||
0.733647 | + | 0.679530i | \(0.237816\pi\) | |||||||
\(644\) | −1456.00 | −0.0890907 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 5488.00 | 0.334245 | ||||||||
\(647\) | −22992.0 | −1.39708 | −0.698538 | − | 0.715572i | \(-0.746166\pi\) | ||||
−0.698538 | + | 0.715572i | \(0.746166\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −672.000 | −0.0406445 | ||||||||
\(650\) | −1846.00 | −0.111394 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −1968.00 | −0.118210 | ||||||||
\(653\) | −12990.0 | −0.778466 | −0.389233 | − | 0.921139i | \(-0.627260\pi\) | ||||
−0.389233 | + | 0.921139i | \(0.627260\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 20664.0 | 1.23269 | ||||||||
\(656\) | 8224.00 | 0.489471 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 3024.00 | 0.179161 | ||||||||
\(659\) | −11088.0 | −0.655428 | −0.327714 | − | 0.944777i | \(-0.606278\pi\) | ||||
−0.327714 | + | 0.944777i | \(0.606278\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 6886.00 | 0.405196 | 0.202598 | − | 0.979262i | \(-0.435062\pi\) | ||||
0.202598 | + | 0.979262i | \(0.435062\pi\) | |||||||
\(662\) | −18216.0 | −1.06946 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −2336.00 | −0.136528 | ||||||||
\(665\) | 2744.00 | 0.160012 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 104.000 | 0.00603733 | ||||||||
\(668\) | 4416.00 | 0.255779 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −8176.00 | −0.471442 | ||||||||
\(671\) | −3568.00 | −0.205277 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −8238.00 | −0.471845 | −0.235922 | − | 0.971772i | \(-0.575811\pi\) | ||||
−0.235922 | + | 0.971772i | \(0.575811\pi\) | |||||||
\(674\) | 3132.00 | 0.178991 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 676.000 | 0.0384615 | ||||||||
\(677\) | −778.000 | −0.0441669 | −0.0220834 | − | 0.999756i | \(-0.507030\pi\) | ||||
−0.0220834 | + | 0.999756i | \(0.507030\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −2198.00 | −0.124229 | ||||||||
\(680\) | −10976.0 | −0.618986 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −2688.00 | −0.150922 | ||||||||
\(683\) | −19552.0 | −1.09537 | −0.547684 | − | 0.836685i | \(-0.684490\pi\) | ||||
−0.547684 | + | 0.836685i | \(0.684490\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 868.000 | 0.0484154 | ||||||||
\(686\) | 686.000 | 0.0381802 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −3776.00 | −0.209242 | ||||||||
\(689\) | 858.000 | 0.0474415 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −31700.0 | −1.74519 | −0.872594 | − | 0.488446i | \(-0.837564\pi\) | ||||
−0.872594 | + | 0.488446i | \(0.837564\pi\) | |||||||
\(692\) | 10744.0 | 0.590210 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 9056.00 | 0.495333 | ||||||||
\(695\) | −12712.0 | −0.693804 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 50372.0 | 2.73741 | ||||||||
\(698\) | 2180.00 | 0.118215 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −1988.00 | −0.107342 | ||||||||
\(701\) | −1470.00 | −0.0792028 | −0.0396014 | − | 0.999216i | \(-0.512609\pi\) | ||||
−0.0396014 | + | 0.999216i | \(0.512609\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 4088.00 | 0.219320 | ||||||||
\(704\) | −512.000 | −0.0274101 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −22468.0 | −1.19773 | ||||||||
\(707\) | 6006.00 | 0.319489 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 26718.0 | 1.41525 | 0.707627 | − | 0.706586i | \(-0.249766\pi\) | ||||
0.707627 | + | 0.706586i | \(0.249766\pi\) | |||||||
\(710\) | 2800.00 | 0.148003 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −3216.00 | −0.169276 | ||||||||
\(713\) | −8736.00 | −0.458858 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1456.00 | −0.0761557 | ||||||||
\(716\) | −8352.00 | −0.435934 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 6888.00 | 0.358019 | ||||||||
\(719\) | 7408.00 | 0.384244 | 0.192122 | − | 0.981371i | \(-0.438463\pi\) | ||||
0.192122 | + | 0.981371i | \(0.438463\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 6608.00 | 0.341324 | ||||||||
\(722\) | 12150.0 | 0.626283 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −968.000 | −0.0496898 | ||||||||
\(725\) | 142.000 | 0.00727413 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −21120.0 | −1.07744 | −0.538719 | − | 0.842486i | \(-0.681092\pi\) | ||||
−0.538719 | + | 0.842486i | \(0.681092\pi\) | |||||||
\(728\) | 728.000 | 0.0370625 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −12600.0 | −0.638831 | ||||||||
\(731\) | −23128.0 | −1.17021 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −39354.0 | −1.98305 | −0.991523 | − | 0.129929i | \(-0.958525\pi\) | ||||
−0.991523 | + | 0.129929i | \(0.958525\pi\) | |||||||
\(734\) | −23424.0 | −1.17792 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −1664.00 | −0.0833368 | ||||||||
\(737\) | −2336.00 | −0.116754 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −15596.0 | −0.776330 | −0.388165 | − | 0.921590i | \(-0.626891\pi\) | ||||
−0.388165 | + | 0.921590i | \(0.626891\pi\) | |||||||
\(740\) | −8176.00 | −0.406156 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 924.000 | 0.0457158 | ||||||||
\(743\) | −4468.00 | −0.220612 | −0.110306 | − | 0.993898i | \(-0.535183\pi\) | ||||
−0.110306 | + | 0.993898i | \(0.535183\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 35196.0 | 1.73085 | ||||||||
\(746\) | −21980.0 | −1.07875 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −3136.00 | −0.153293 | ||||||||
\(749\) | 5880.00 | 0.286850 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 5440.00 | 0.264325 | 0.132163 | − | 0.991228i | \(-0.457808\pi\) | ||||
0.132163 | + | 0.991228i | \(0.457808\pi\) | |||||||
\(752\) | 3456.00 | 0.167590 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −52.0000 | −0.00251158 | ||||||||
\(755\) | −14672.0 | −0.707243 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 14638.0 | 0.702810 | 0.351405 | − | 0.936224i | \(-0.385704\pi\) | ||||
0.351405 | + | 0.936224i | \(0.385704\pi\) | |||||||
\(758\) | 14008.0 | 0.671231 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 3136.00 | 0.149677 | ||||||||
\(761\) | −35950.0 | −1.71247 | −0.856233 | − | 0.516590i | \(-0.827201\pi\) | ||||
−0.856233 | + | 0.516590i | \(0.827201\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −9338.00 | −0.443065 | ||||||||
\(764\) | 5136.00 | 0.243212 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −10944.0 | −0.516218 | ||||||||
\(767\) | 1092.00 | 0.0514079 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −24974.0 | −1.17111 | −0.585556 | − | 0.810632i | \(-0.699124\pi\) | ||||
−0.585556 | + | 0.810632i | \(0.699124\pi\) | |||||||
\(770\) | −1568.00 | −0.0733855 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −10936.0 | −0.509838 | ||||||||
\(773\) | 41254.0 | 1.91954 | 0.959769 | − | 0.280790i | \(-0.0905964\pi\) | ||||
0.959769 | + | 0.280790i | \(0.0905964\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −11928.0 | −0.552860 | ||||||||
\(776\) | −2512.00 | −0.116206 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 3820.00 | 0.176033 | ||||||||
\(779\) | −14392.0 | −0.661934 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 800.000 | 0.0366533 | ||||||||
\(782\) | −10192.0 | −0.466068 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 784.000 | 0.0357143 | ||||||||
\(785\) | 44324.0 | 2.01528 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 26780.0 | 1.21297 | 0.606483 | − | 0.795097i | \(-0.292580\pi\) | ||||
0.606483 | + | 0.795097i | \(0.292580\pi\) | |||||||
\(788\) | −20472.0 | −0.925488 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −10976.0 | −0.494315 | ||||||||
\(791\) | 6622.00 | 0.297663 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 5798.00 | 0.259638 | ||||||||
\(794\) | 26468.0 | 1.18302 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 6112.00 | 0.272153 | ||||||||
\(797\) | 18222.0 | 0.809857 | 0.404929 | − | 0.914348i | \(-0.367296\pi\) | ||||
0.404929 | + | 0.914348i | \(0.367296\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 21168.0 | 0.937259 | ||||||||
\(800\) | −2272.00 | −0.100409 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 9172.00 | 0.403834 | ||||||||
\(803\) | −3600.00 | −0.158208 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −5096.00 | −0.223119 | ||||||||
\(806\) | 4368.00 | 0.190889 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 6864.00 | 0.298855 | ||||||||
\(809\) | −7338.00 | −0.318900 | −0.159450 | − | 0.987206i | \(-0.550972\pi\) | ||||
−0.159450 | + | 0.987206i | \(0.550972\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 12500.0 | 0.541226 | 0.270613 | − | 0.962688i | \(-0.412774\pi\) | ||||
0.270613 | + | 0.962688i | \(0.412774\pi\) | |||||||
\(812\) | −56.0000 | −0.00242022 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −2336.00 | −0.100586 | ||||||||
\(815\) | −6888.00 | −0.296044 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 6608.00 | 0.282968 | ||||||||
\(818\) | 8348.00 | 0.356823 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 28784.0 | 1.22583 | ||||||||
\(821\) | −44830.0 | −1.90570 | −0.952849 | − | 0.303445i | \(-0.901863\pi\) | ||||
−0.952849 | + | 0.303445i | \(0.901863\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 11152.0 | 0.472338 | 0.236169 | − | 0.971712i | \(-0.424108\pi\) | ||||
0.236169 | + | 0.971712i | \(0.424108\pi\) | |||||||
\(824\) | 7552.00 | 0.319280 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 1176.00 | 0.0495379 | ||||||||
\(827\) | 2408.00 | 0.101251 | 0.0506254 | − | 0.998718i | \(-0.483879\pi\) | ||||
0.0506254 | + | 0.998718i | \(0.483879\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −44922.0 | −1.88203 | −0.941017 | − | 0.338360i | \(-0.890128\pi\) | ||||
−0.941017 | + | 0.338360i | \(0.890128\pi\) | |||||||
\(830\) | −8176.00 | −0.341919 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 832.000 | 0.0346688 | ||||||||
\(833\) | 4802.00 | 0.199735 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 15456.0 | 0.640571 | ||||||||
\(836\) | 896.000 | 0.0370680 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −20024.0 | −0.825439 | ||||||||
\(839\) | −36720.0 | −1.51098 | −0.755492 | − | 0.655158i | \(-0.772602\pi\) | ||||
−0.755492 | + | 0.655158i | \(0.772602\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −24385.0 | −0.999836 | ||||||||
\(842\) | 2500.00 | 0.102323 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 1072.00 | 0.0437201 | ||||||||
\(845\) | 2366.00 | 0.0963229 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 8869.00 | 0.359790 | ||||||||
\(848\) | 1056.00 | 0.0427632 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −13916.0 | −0.561547 | ||||||||
\(851\) | −7592.00 | −0.305817 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 16006.0 | 0.642479 | 0.321240 | − | 0.946998i | \(-0.395900\pi\) | ||||
0.321240 | + | 0.946998i | \(0.395900\pi\) | |||||||
\(854\) | 6244.00 | 0.250194 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 6720.00 | 0.268323 | ||||||||
\(857\) | −37278.0 | −1.48587 | −0.742936 | − | 0.669363i | \(-0.766567\pi\) | ||||
−0.742936 | + | 0.669363i | \(0.766567\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −45236.0 | −1.79678 | −0.898389 | − | 0.439201i | \(-0.855262\pi\) | ||||
−0.898389 | + | 0.439201i | \(0.855262\pi\) | |||||||
\(860\) | −13216.0 | −0.524025 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 12472.0 | 0.492805 | ||||||||
\(863\) | 23916.0 | 0.943349 | 0.471674 | − | 0.881773i | \(-0.343650\pi\) | ||||
0.471674 | + | 0.881773i | \(0.343650\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 37604.0 | 1.47812 | ||||||||
\(866\) | 7932.00 | 0.311247 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 4704.00 | 0.183945 | ||||||||
\(869\) | −3136.00 | −0.122418 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 3796.00 | 0.147672 | ||||||||
\(872\) | −10672.0 | −0.414449 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 2912.00 | 0.112700 | ||||||||
\(875\) | 5292.00 | 0.204460 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −24538.0 | −0.944800 | −0.472400 | − | 0.881384i | \(-0.656612\pi\) | ||||
−0.472400 | + | 0.881384i | \(0.656612\pi\) | |||||||
\(878\) | −17552.0 | −0.674660 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −1792.00 | −0.0686458 | ||||||||
\(881\) | −910.000 | −0.0347999 | −0.0173999 | − | 0.999849i | \(-0.505539\pi\) | ||||
−0.0173999 | + | 0.999849i | \(0.505539\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 10460.0 | 0.398649 | 0.199324 | − | 0.979934i | \(-0.436125\pi\) | ||||
0.199324 | + | 0.979934i | \(0.436125\pi\) | |||||||
\(884\) | 5096.00 | 0.193888 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 12192.0 | 0.462301 | ||||||||
\(887\) | −20048.0 | −0.758902 | −0.379451 | − | 0.925212i | \(-0.623887\pi\) | ||||
−0.379451 | + | 0.925212i | \(0.623887\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −6328.00 | −0.238734 | ||||||||
\(890\) | −11256.0 | −0.423935 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 5568.00 | 0.209003 | ||||||||
\(893\) | −6048.00 | −0.226639 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −29232.0 | −1.09175 | ||||||||
\(896\) | 896.000 | 0.0334077 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −18780.0 | −0.697881 | ||||||||
\(899\) | −336.000 | −0.0124652 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 6468.00 | 0.239157 | ||||||||
\(902\) | 8224.00 | 0.303580 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 7568.00 | 0.278438 | ||||||||
\(905\) | −3388.00 | −0.124443 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −876.000 | −0.0320696 | −0.0160348 | − | 0.999871i | \(-0.505104\pi\) | ||||
−0.0160348 | + | 0.999871i | \(0.505104\pi\) | |||||||
\(908\) | 24560.0 | 0.897635 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 2548.00 | 0.0928191 | ||||||||
\(911\) | −14796.0 | −0.538105 | −0.269052 | − | 0.963126i | \(-0.586710\pi\) | ||||
−0.269052 | + | 0.963126i | \(0.586710\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −2336.00 | −0.0846772 | ||||||||
\(914\) | 12.0000 | 0.000434272 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 7480.00 | 0.269810 | ||||||||
\(917\) | −10332.0 | −0.372075 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 728.000 | 0.0261311 | 0.0130656 | − | 0.999915i | \(-0.495841\pi\) | ||||
0.0130656 | + | 0.999915i | \(0.495841\pi\) | |||||||
\(920\) | −5824.00 | −0.208708 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −18748.0 | −0.669666 | ||||||||
\(923\) | −1300.00 | −0.0463597 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −10366.0 | −0.368467 | ||||||||
\(926\) | −8016.00 | −0.284473 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −64.0000 | −0.00226390 | ||||||||
\(929\) | −39894.0 | −1.40891 | −0.704456 | − | 0.709747i | \(-0.748809\pi\) | ||||
−0.704456 | + | 0.709747i | \(0.748809\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1372.00 | −0.0482980 | ||||||||
\(932\) | −200.000 | −0.00702920 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −6520.00 | −0.228416 | ||||||||
\(935\) | −10976.0 | −0.383908 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 18906.0 | 0.659159 | 0.329580 | − | 0.944128i | \(-0.393093\pi\) | ||||
0.329580 | + | 0.944128i | \(0.393093\pi\) | |||||||
\(938\) | 4088.00 | 0.142301 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 12096.0 | 0.419711 | ||||||||
\(941\) | −49514.0 | −1.71531 | −0.857657 | − | 0.514222i | \(-0.828081\pi\) | ||||
−0.857657 | + | 0.514222i | \(0.828081\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 26728.0 | 0.922994 | ||||||||
\(944\) | 1344.00 | 0.0463384 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −3776.00 | −0.129776 | ||||||||
\(947\) | −16384.0 | −0.562205 | −0.281103 | − | 0.959678i | \(-0.590700\pi\) | ||||
−0.281103 | + | 0.959678i | \(0.590700\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 5850.00 | 0.200104 | ||||||||
\(950\) | 3976.00 | 0.135788 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 5488.00 | 0.186835 | ||||||||
\(953\) | 30742.0 | 1.04494 | 0.522472 | − | 0.852657i | \(-0.325010\pi\) | ||||
0.522472 | + | 0.852657i | \(0.325010\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 17976.0 | 0.609099 | ||||||||
\(956\) | 12912.0 | 0.436824 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 25392.0 | 0.856345 | ||||||||
\(959\) | −434.000 | −0.0146138 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −1567.00 | −0.0525998 | ||||||||
\(962\) | 3796.00 | 0.127222 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 23912.0 | 0.798915 | ||||||||
\(965\) | −38276.0 | −1.27684 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −41376.0 | −1.37597 | −0.687985 | − | 0.725725i | \(-0.741504\pi\) | ||||
−0.687985 | + | 0.725725i | \(0.741504\pi\) | |||||||
\(968\) | 10136.0 | 0.336553 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −8792.00 | −0.291025 | ||||||||
\(971\) | −57300.0 | −1.89376 | −0.946882 | − | 0.321582i | \(-0.895786\pi\) | ||||
−0.946882 | + | 0.321582i | \(0.895786\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 6356.00 | 0.209418 | ||||||||
\(974\) | −21520.0 | −0.707952 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 7136.00 | 0.234035 | ||||||||
\(977\) | 7734.00 | 0.253258 | 0.126629 | − | 0.991950i | \(-0.459584\pi\) | ||||
0.126629 | + | 0.991950i | \(0.459584\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −3216.00 | −0.104989 | ||||||||
\(980\) | 2744.00 | 0.0894427 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −23200.0 | −0.753912 | ||||||||
\(983\) | 31432.0 | 1.01986 | 0.509931 | − | 0.860215i | \(-0.329671\pi\) | ||||
0.509931 | + | 0.860215i | \(0.329671\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −71652.0 | −2.31779 | ||||||||
\(986\) | −392.000 | −0.0126611 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −1456.00 | −0.0468841 | ||||||||
\(989\) | −12272.0 | −0.394567 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −24432.0 | −0.783156 | −0.391578 | − | 0.920145i | \(-0.628071\pi\) | ||||
−0.391578 | + | 0.920145i | \(0.628071\pi\) | |||||||
\(992\) | 5376.00 | 0.172065 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −1400.00 | −0.0446733 | ||||||||
\(995\) | 21392.0 | 0.681580 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 3094.00 | 0.0982828 | 0.0491414 | − | 0.998792i | \(-0.484352\pi\) | ||||
0.0491414 | + | 0.998792i | \(0.484352\pi\) | |||||||
\(998\) | 31816.0 | 1.00914 | ||||||||
\(999\) | 0 | 0 |
(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 | 1638.4.a.h.1.1 | 1 | ||
3.2 | odd | 2 | 546.4.a.c.1.1 | ✓ | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
546.4.a.c.1.1 | ✓ | 1 | 3.2 | odd | 2 | ||
1638.4.a.h.1.1 | 1 | 1.1 | even | 1 | trivial |