Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [378,4,Mod(1,378)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(378, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("378.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 378 = 2 \cdot 3^{3} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 378.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: | \(22.3027219822\) |
Analytic rank: | \(0\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 378.1 |
$q$-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 | ||||||||
\(5\) | 9.00000 | 0.804984 | 0.402492 | − | 0.915423i | \(-0.368144\pi\) | ||||
0.402492 | + | 0.915423i | \(0.368144\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 7.00000 | 0.377964 | ||||||||
\(8\) | −8.00000 | −0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −18.0000 | −0.569210 | ||||||||
\(11\) | 45.0000 | 1.23346 | 0.616728 | − | 0.787177i | \(-0.288458\pi\) | ||||
0.616728 | + | 0.787177i | \(0.288458\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −16.0000 | −0.341354 | −0.170677 | − | 0.985327i | \(-0.554595\pi\) | ||||
−0.170677 | + | 0.985327i | \(0.554595\pi\) | |||||||
\(14\) | −14.0000 | −0.267261 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 16.0000 | 0.250000 | ||||||||
\(17\) | 66.0000 | 0.941609 | 0.470804 | − | 0.882238i | \(-0.343964\pi\) | ||||
0.470804 | + | 0.882238i | \(0.343964\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 11.0000 | 0.132820 | 0.0664098 | − | 0.997792i | \(-0.478846\pi\) | ||||
0.0664098 | + | 0.997792i | \(0.478846\pi\) | |||||||
\(20\) | 36.0000 | 0.402492 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −90.0000 | −0.872185 | ||||||||
\(23\) | 27.0000 | 0.244778 | 0.122389 | − | 0.992482i | \(-0.460944\pi\) | ||||
0.122389 | + | 0.992482i | \(0.460944\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −44.0000 | −0.352000 | ||||||||
\(26\) | 32.0000 | 0.241374 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 28.0000 | 0.188982 | ||||||||
\(29\) | −12.0000 | −0.0768395 | −0.0384197 | − | 0.999262i | \(-0.512232\pi\) | ||||
−0.0384197 | + | 0.999262i | \(0.512232\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −169.000 | −0.979139 | −0.489569 | − | 0.871964i | \(-0.662846\pi\) | ||||
−0.489569 | + | 0.871964i | \(0.662846\pi\) | |||||||
\(32\) | −32.0000 | −0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −132.000 | −0.665818 | ||||||||
\(35\) | 63.0000 | 0.304256 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 209.000 | 0.928632 | 0.464316 | − | 0.885670i | \(-0.346300\pi\) | ||||
0.464316 | + | 0.885670i | \(0.346300\pi\) | |||||||
\(38\) | −22.0000 | −0.0939177 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −72.0000 | −0.284605 | ||||||||
\(41\) | 291.000 | 1.10845 | 0.554226 | − | 0.832366i | \(-0.313014\pi\) | ||||
0.554226 | + | 0.832366i | \(0.313014\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −394.000 | −1.39731 | −0.698656 | − | 0.715458i | \(-0.746218\pi\) | ||||
−0.698656 | + | 0.715458i | \(0.746218\pi\) | |||||||
\(44\) | 180.000 | 0.616728 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −54.0000 | −0.173084 | ||||||||
\(47\) | 174.000 | 0.540011 | 0.270005 | − | 0.962859i | \(-0.412975\pi\) | ||||
0.270005 | + | 0.962859i | \(0.412975\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 49.0000 | 0.142857 | ||||||||
\(50\) | 88.0000 | 0.248902 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −64.0000 | −0.170677 | ||||||||
\(53\) | 228.000 | 0.590910 | 0.295455 | − | 0.955357i | \(-0.404529\pi\) | ||||
0.295455 | + | 0.955357i | \(0.404529\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 405.000 | 0.992913 | ||||||||
\(56\) | −56.0000 | −0.133631 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 24.0000 | 0.0543337 | ||||||||
\(59\) | 474.000 | 1.04592 | 0.522962 | − | 0.852356i | \(-0.324827\pi\) | ||||
0.522962 | + | 0.852356i | \(0.324827\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −232.000 | −0.486960 | −0.243480 | − | 0.969906i | \(-0.578289\pi\) | ||||
−0.243480 | + | 0.969906i | \(0.578289\pi\) | |||||||
\(62\) | 338.000 | 0.692356 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 64.0000 | 0.125000 | ||||||||
\(65\) | −144.000 | −0.274785 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 992.000 | 1.80884 | 0.904419 | − | 0.426646i | \(-0.140305\pi\) | ||||
0.904419 | + | 0.426646i | \(0.140305\pi\) | |||||||
\(68\) | 264.000 | 0.470804 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −126.000 | −0.215141 | ||||||||
\(71\) | −153.000 | −0.255743 | −0.127872 | − | 0.991791i | \(-0.540815\pi\) | ||||
−0.127872 | + | 0.991791i | \(0.540815\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 686.000 | 1.09987 | 0.549933 | − | 0.835209i | \(-0.314653\pi\) | ||||
0.549933 | + | 0.835209i | \(0.314653\pi\) | |||||||
\(74\) | −418.000 | −0.656642 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 44.0000 | 0.0664098 | ||||||||
\(77\) | 315.000 | 0.466202 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1046.00 | 1.48967 | 0.744837 | − | 0.667247i | \(-0.232527\pi\) | ||||
0.744837 | + | 0.667247i | \(0.232527\pi\) | |||||||
\(80\) | 144.000 | 0.201246 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −582.000 | −0.783794 | ||||||||
\(83\) | 708.000 | 0.936302 | 0.468151 | − | 0.883648i | \(-0.344920\pi\) | ||||
0.468151 | + | 0.883648i | \(0.344920\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 594.000 | 0.757981 | ||||||||
\(86\) | 788.000 | 0.988049 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −360.000 | −0.436092 | ||||||||
\(89\) | 195.000 | 0.232247 | 0.116123 | − | 0.993235i | \(-0.462953\pi\) | ||||
0.116123 | + | 0.993235i | \(0.462953\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −112.000 | −0.129020 | ||||||||
\(92\) | 108.000 | 0.122389 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −348.000 | −0.381845 | ||||||||
\(95\) | 99.0000 | 0.106918 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −88.0000 | −0.0921139 | −0.0460569 | − | 0.998939i | \(-0.514666\pi\) | ||||
−0.0460569 | + | 0.998939i | \(0.514666\pi\) | |||||||
\(98\) | −98.0000 | −0.101015 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −176.000 | −0.176000 | ||||||||
\(101\) | −1206.00 | −1.18813 | −0.594067 | − | 0.804416i | \(-0.702479\pi\) | ||||
−0.594067 | + | 0.804416i | \(0.702479\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1177.00 | −1.12595 | −0.562977 | − | 0.826473i | \(-0.690344\pi\) | ||||
−0.562977 | + | 0.826473i | \(0.690344\pi\) | |||||||
\(104\) | 128.000 | 0.120687 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −456.000 | −0.417836 | ||||||||
\(107\) | −156.000 | −0.140945 | −0.0704724 | − | 0.997514i | \(-0.522451\pi\) | ||||
−0.0704724 | + | 0.997514i | \(0.522451\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 11.0000 | 0.00966614 | 0.00483307 | − | 0.999988i | \(-0.498462\pi\) | ||||
0.00483307 | + | 0.999988i | \(0.498462\pi\) | |||||||
\(110\) | −810.000 | −0.702095 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 112.000 | 0.0944911 | ||||||||
\(113\) | 1038.00 | 0.864131 | 0.432066 | − | 0.901842i | \(-0.357785\pi\) | ||||
0.432066 | + | 0.901842i | \(0.357785\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 243.000 | 0.197042 | ||||||||
\(116\) | −48.0000 | −0.0384197 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −948.000 | −0.739580 | ||||||||
\(119\) | 462.000 | 0.355895 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 694.000 | 0.521412 | ||||||||
\(122\) | 464.000 | 0.344333 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −676.000 | −0.489569 | ||||||||
\(125\) | −1521.00 | −1.08834 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 2216.00 | 1.54833 | 0.774166 | − | 0.632982i | \(-0.218169\pi\) | ||||
0.774166 | + | 0.632982i | \(0.218169\pi\) | |||||||
\(128\) | −128.000 | −0.0883883 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 288.000 | 0.194302 | ||||||||
\(131\) | 918.000 | 0.612260 | 0.306130 | − | 0.951990i | \(-0.400966\pi\) | ||||
0.306130 | + | 0.951990i | \(0.400966\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 77.0000 | 0.0502011 | ||||||||
\(134\) | −1984.00 | −1.27904 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −528.000 | −0.332909 | ||||||||
\(137\) | −2448.00 | −1.52662 | −0.763309 | − | 0.646033i | \(-0.776427\pi\) | ||||
−0.763309 | + | 0.646033i | \(0.776427\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1244.00 | 0.759099 | 0.379549 | − | 0.925172i | \(-0.376079\pi\) | ||||
0.379549 | + | 0.925172i | \(0.376079\pi\) | |||||||
\(140\) | 252.000 | 0.152128 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 306.000 | 0.180838 | ||||||||
\(143\) | −720.000 | −0.421045 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −108.000 | −0.0618546 | ||||||||
\(146\) | −1372.00 | −0.777723 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 836.000 | 0.464316 | ||||||||
\(149\) | −954.000 | −0.524528 | −0.262264 | − | 0.964996i | \(-0.584469\pi\) | ||||
−0.262264 | + | 0.964996i | \(0.584469\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1942.00 | −1.04661 | −0.523304 | − | 0.852146i | \(-0.675301\pi\) | ||||
−0.523304 | + | 0.852146i | \(0.675301\pi\) | |||||||
\(152\) | −88.0000 | −0.0469588 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −630.000 | −0.329655 | ||||||||
\(155\) | −1521.00 | −0.788191 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −2032.00 | −1.03294 | −0.516469 | − | 0.856306i | \(-0.672754\pi\) | ||||
−0.516469 | + | 0.856306i | \(0.672754\pi\) | |||||||
\(158\) | −2092.00 | −1.05336 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −288.000 | −0.142302 | ||||||||
\(161\) | 189.000 | 0.0925173 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 2252.00 | 1.08215 | 0.541074 | − | 0.840975i | \(-0.318018\pi\) | ||||
0.541074 | + | 0.840975i | \(0.318018\pi\) | |||||||
\(164\) | 1164.00 | 0.554226 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −1416.00 | −0.662066 | ||||||||
\(167\) | 4170.00 | 1.93224 | 0.966121 | − | 0.258091i | \(-0.0830934\pi\) | ||||
0.966121 | + | 0.258091i | \(0.0830934\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1941.00 | −0.883477 | ||||||||
\(170\) | −1188.00 | −0.535973 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −1576.00 | −0.698656 | ||||||||
\(173\) | −4353.00 | −1.91302 | −0.956510 | − | 0.291700i | \(-0.905779\pi\) | ||||
−0.956510 | + | 0.291700i | \(0.905779\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −308.000 | −0.133043 | ||||||||
\(176\) | 720.000 | 0.308364 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −390.000 | −0.164223 | ||||||||
\(179\) | −3984.00 | −1.66357 | −0.831783 | − | 0.555102i | \(-0.812679\pi\) | ||||
−0.831783 | + | 0.555102i | \(0.812679\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 650.000 | 0.266929 | 0.133464 | − | 0.991054i | \(-0.457390\pi\) | ||||
0.133464 | + | 0.991054i | \(0.457390\pi\) | |||||||
\(182\) | 224.000 | 0.0912307 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −216.000 | −0.0865420 | ||||||||
\(185\) | 1881.00 | 0.747534 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 2970.00 | 1.16143 | ||||||||
\(188\) | 696.000 | 0.270005 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −198.000 | −0.0756023 | ||||||||
\(191\) | −2967.00 | −1.12400 | −0.562002 | − | 0.827136i | \(-0.689969\pi\) | ||||
−0.562002 | + | 0.827136i | \(0.689969\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −2842.00 | −1.05996 | −0.529978 | − | 0.848011i | \(-0.677800\pi\) | ||||
−0.529978 | + | 0.848011i | \(0.677800\pi\) | |||||||
\(194\) | 176.000 | 0.0651343 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 196.000 | 0.0714286 | ||||||||
\(197\) | 2286.00 | 0.826755 | 0.413378 | − | 0.910560i | \(-0.364349\pi\) | ||||
0.413378 | + | 0.910560i | \(0.364349\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1645.00 | −0.585985 | −0.292992 | − | 0.956115i | \(-0.594651\pi\) | ||||
−0.292992 | + | 0.956115i | \(0.594651\pi\) | |||||||
\(200\) | 352.000 | 0.124451 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 2412.00 | 0.840137 | ||||||||
\(203\) | −84.0000 | −0.0290426 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 2619.00 | 0.892287 | ||||||||
\(206\) | 2354.00 | 0.796170 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −256.000 | −0.0853385 | ||||||||
\(209\) | 495.000 | 0.163827 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −2878.00 | −0.939003 | −0.469502 | − | 0.882932i | \(-0.655566\pi\) | ||||
−0.469502 | + | 0.882932i | \(0.655566\pi\) | |||||||
\(212\) | 912.000 | 0.295455 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 312.000 | 0.0996630 | ||||||||
\(215\) | −3546.00 | −1.12481 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1183.00 | −0.370080 | ||||||||
\(218\) | −22.0000 | −0.00683499 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 1620.00 | 0.496456 | ||||||||
\(221\) | −1056.00 | −0.321422 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 4349.00 | 1.30597 | 0.652983 | − | 0.757372i | \(-0.273517\pi\) | ||||
0.652983 | + | 0.757372i | \(0.273517\pi\) | |||||||
\(224\) | −224.000 | −0.0668153 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −2076.00 | −0.611033 | ||||||||
\(227\) | −4266.00 | −1.24733 | −0.623666 | − | 0.781691i | \(-0.714357\pi\) | ||||
−0.623666 | + | 0.781691i | \(0.714357\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −1060.00 | −0.305881 | −0.152941 | − | 0.988235i | \(-0.548874\pi\) | ||||
−0.152941 | + | 0.988235i | \(0.548874\pi\) | |||||||
\(230\) | −486.000 | −0.139330 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 96.0000 | 0.0271668 | ||||||||
\(233\) | 2814.00 | 0.791207 | 0.395604 | − | 0.918421i | \(-0.370535\pi\) | ||||
0.395604 | + | 0.918421i | \(0.370535\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1566.00 | 0.434700 | ||||||||
\(236\) | 1896.00 | 0.522962 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −924.000 | −0.251656 | ||||||||
\(239\) | 1200.00 | 0.324776 | 0.162388 | − | 0.986727i | \(-0.448080\pi\) | ||||
0.162388 | + | 0.986727i | \(0.448080\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −5650.00 | −1.51016 | −0.755080 | − | 0.655633i | \(-0.772402\pi\) | ||||
−0.755080 | + | 0.655633i | \(0.772402\pi\) | |||||||
\(242\) | −1388.00 | −0.368694 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −928.000 | −0.243480 | ||||||||
\(245\) | 441.000 | 0.114998 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −176.000 | −0.0453385 | ||||||||
\(248\) | 1352.00 | 0.346178 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 3042.00 | 0.769572 | ||||||||
\(251\) | 2160.00 | 0.543179 | 0.271590 | − | 0.962413i | \(-0.412451\pi\) | ||||
0.271590 | + | 0.962413i | \(0.412451\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1215.00 | 0.301923 | ||||||||
\(254\) | −4432.00 | −1.09484 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 256.000 | 0.0625000 | ||||||||
\(257\) | −2457.00 | −0.596356 | −0.298178 | − | 0.954510i | \(-0.596379\pi\) | ||||
−0.298178 | + | 0.954510i | \(0.596379\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1463.00 | 0.350990 | ||||||||
\(260\) | −576.000 | −0.137392 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −1836.00 | −0.432933 | ||||||||
\(263\) | −2889.00 | −0.677351 | −0.338676 | − | 0.940903i | \(-0.609979\pi\) | ||||
−0.338676 | + | 0.940903i | \(0.609979\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 2052.00 | 0.475673 | ||||||||
\(266\) | −154.000 | −0.0354975 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 3968.00 | 0.904419 | ||||||||
\(269\) | 7221.00 | 1.63670 | 0.818350 | − | 0.574721i | \(-0.194889\pi\) | ||||
0.818350 | + | 0.574721i | \(0.194889\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2504.00 | 0.561281 | 0.280641 | − | 0.959813i | \(-0.409453\pi\) | ||||
0.280641 | + | 0.959813i | \(0.409453\pi\) | |||||||
\(272\) | 1056.00 | 0.235402 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 4896.00 | 1.07948 | ||||||||
\(275\) | −1980.00 | −0.434176 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −2455.00 | −0.532515 | −0.266257 | − | 0.963902i | \(-0.585787\pi\) | ||||
−0.266257 | + | 0.963902i | \(0.585787\pi\) | |||||||
\(278\) | −2488.00 | −0.536764 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −504.000 | −0.107571 | ||||||||
\(281\) | 8070.00 | 1.71322 | 0.856612 | − | 0.515961i | \(-0.172565\pi\) | ||||
0.856612 | + | 0.515961i | \(0.172565\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1244.00 | 0.261301 | 0.130650 | − | 0.991429i | \(-0.458293\pi\) | ||||
0.130650 | + | 0.991429i | \(0.458293\pi\) | |||||||
\(284\) | −612.000 | −0.127872 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 1440.00 | 0.297724 | ||||||||
\(287\) | 2037.00 | 0.418956 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −557.000 | −0.113373 | ||||||||
\(290\) | 216.000 | 0.0437378 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 2744.00 | 0.549933 | ||||||||
\(293\) | 3450.00 | 0.687888 | 0.343944 | − | 0.938990i | \(-0.388237\pi\) | ||||
0.343944 | + | 0.938990i | \(0.388237\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 4266.00 | 0.841953 | ||||||||
\(296\) | −1672.00 | −0.328321 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 1908.00 | 0.370898 | ||||||||
\(299\) | −432.000 | −0.0835559 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2758.00 | −0.528134 | ||||||||
\(302\) | 3884.00 | 0.740063 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 176.000 | 0.0332049 | ||||||||
\(305\) | −2088.00 | −0.391995 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −2761.00 | −0.513285 | −0.256643 | − | 0.966506i | \(-0.582616\pi\) | ||||
−0.256643 | + | 0.966506i | \(0.582616\pi\) | |||||||
\(308\) | 1260.00 | 0.233101 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 3042.00 | 0.557335 | ||||||||
\(311\) | 7008.00 | 1.27777 | 0.638886 | − | 0.769301i | \(-0.279395\pi\) | ||||
0.638886 | + | 0.769301i | \(0.279395\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −160.000 | −0.0288937 | −0.0144469 | − | 0.999896i | \(-0.504599\pi\) | ||||
−0.0144469 | + | 0.999896i | \(0.504599\pi\) | |||||||
\(314\) | 4064.00 | 0.730397 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 4184.00 | 0.744837 | ||||||||
\(317\) | 750.000 | 0.132884 | 0.0664420 | − | 0.997790i | \(-0.478835\pi\) | ||||
0.0664420 | + | 0.997790i | \(0.478835\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −540.000 | −0.0947780 | ||||||||
\(320\) | 576.000 | 0.100623 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −378.000 | −0.0654196 | ||||||||
\(323\) | 726.000 | 0.125064 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 704.000 | 0.120157 | ||||||||
\(326\) | −4504.00 | −0.765195 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −2328.00 | −0.391897 | ||||||||
\(329\) | 1218.00 | 0.204105 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 3188.00 | 0.529391 | 0.264695 | − | 0.964332i | \(-0.414729\pi\) | ||||
0.264695 | + | 0.964332i | \(0.414729\pi\) | |||||||
\(332\) | 2832.00 | 0.468151 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −8340.00 | −1.36630 | ||||||||
\(335\) | 8928.00 | 1.45609 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −8917.00 | −1.44136 | −0.720682 | − | 0.693265i | \(-0.756171\pi\) | ||||
−0.720682 | + | 0.693265i | \(0.756171\pi\) | |||||||
\(338\) | 3882.00 | 0.624713 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 2376.00 | 0.378990 | ||||||||
\(341\) | −7605.00 | −1.20772 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 343.000 | 0.0539949 | ||||||||
\(344\) | 3152.00 | 0.494025 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 8706.00 | 1.35271 | ||||||||
\(347\) | −7491.00 | −1.15890 | −0.579449 | − | 0.815008i | \(-0.696732\pi\) | ||||
−0.579449 | + | 0.815008i | \(0.696732\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −7450.00 | −1.14266 | −0.571331 | − | 0.820719i | \(-0.693573\pi\) | ||||
−0.571331 | + | 0.820719i | \(0.693573\pi\) | |||||||
\(350\) | 616.000 | 0.0940760 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −1440.00 | −0.218046 | ||||||||
\(353\) | 9225.00 | 1.39093 | 0.695463 | − | 0.718561i | \(-0.255199\pi\) | ||||
0.695463 | + | 0.718561i | \(0.255199\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −1377.00 | −0.205869 | ||||||||
\(356\) | 780.000 | 0.116123 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 7968.00 | 1.17632 | ||||||||
\(359\) | 3660.00 | 0.538071 | 0.269035 | − | 0.963130i | \(-0.413295\pi\) | ||||
0.269035 | + | 0.963130i | \(0.413295\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −6738.00 | −0.982359 | ||||||||
\(362\) | −1300.00 | −0.188747 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −448.000 | −0.0645098 | ||||||||
\(365\) | 6174.00 | 0.885375 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −10213.0 | −1.45263 | −0.726314 | − | 0.687363i | \(-0.758768\pi\) | ||||
−0.726314 | + | 0.687363i | \(0.758768\pi\) | |||||||
\(368\) | 432.000 | 0.0611944 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −3762.00 | −0.528587 | ||||||||
\(371\) | 1596.00 | 0.223343 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −8629.00 | −1.19784 | −0.598918 | − | 0.800811i | \(-0.704402\pi\) | ||||
−0.598918 | + | 0.800811i | \(0.704402\pi\) | |||||||
\(374\) | −5940.00 | −0.821257 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −1392.00 | −0.190923 | ||||||||
\(377\) | 192.000 | 0.0262295 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 1226.00 | 0.166162 | 0.0830810 | − | 0.996543i | \(-0.473524\pi\) | ||||
0.0830810 | + | 0.996543i | \(0.473524\pi\) | |||||||
\(380\) | 396.000 | 0.0534589 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 5934.00 | 0.794790 | ||||||||
\(383\) | 10998.0 | 1.46729 | 0.733644 | − | 0.679534i | \(-0.237818\pi\) | ||||
0.733644 | + | 0.679534i | \(0.237818\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 2835.00 | 0.375286 | ||||||||
\(386\) | 5684.00 | 0.749503 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −352.000 | −0.0460569 | ||||||||
\(389\) | −2772.00 | −0.361301 | −0.180650 | − | 0.983547i | \(-0.557820\pi\) | ||||
−0.180650 | + | 0.983547i | \(0.557820\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1782.00 | 0.230485 | ||||||||
\(392\) | −392.000 | −0.0505076 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −4572.00 | −0.584604 | ||||||||
\(395\) | 9414.00 | 1.19916 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −6118.00 | −0.773435 | −0.386717 | − | 0.922198i | \(-0.626391\pi\) | ||||
−0.386717 | + | 0.922198i | \(0.626391\pi\) | |||||||
\(398\) | 3290.00 | 0.414354 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −704.000 | −0.0880000 | ||||||||
\(401\) | −14076.0 | −1.75292 | −0.876461 | − | 0.481472i | \(-0.840102\pi\) | ||||
−0.876461 | + | 0.481472i | \(0.840102\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 2704.00 | 0.334233 | ||||||||
\(404\) | −4824.00 | −0.594067 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 168.000 | 0.0205362 | ||||||||
\(407\) | 9405.00 | 1.14543 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 542.000 | 0.0655261 | 0.0327631 | − | 0.999463i | \(-0.489569\pi\) | ||||
0.0327631 | + | 0.999463i | \(0.489569\pi\) | |||||||
\(410\) | −5238.00 | −0.630942 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −4708.00 | −0.562977 | ||||||||
\(413\) | 3318.00 | 0.395322 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 6372.00 | 0.753709 | ||||||||
\(416\) | 512.000 | 0.0603434 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −990.000 | −0.115843 | ||||||||
\(419\) | −6090.00 | −0.710062 | −0.355031 | − | 0.934855i | \(-0.615530\pi\) | ||||
−0.355031 | + | 0.934855i | \(0.615530\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −14335.0 | −1.65949 | −0.829745 | − | 0.558143i | \(-0.811514\pi\) | ||||
−0.829745 | + | 0.558143i | \(0.811514\pi\) | |||||||
\(422\) | 5756.00 | 0.663976 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −1824.00 | −0.208918 | ||||||||
\(425\) | −2904.00 | −0.331446 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −1624.00 | −0.184054 | ||||||||
\(428\) | −624.000 | −0.0704724 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 7092.00 | 0.795364 | ||||||||
\(431\) | −16755.0 | −1.87253 | −0.936264 | − | 0.351296i | \(-0.885741\pi\) | ||||
−0.936264 | + | 0.351296i | \(0.885741\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 7436.00 | 0.825292 | 0.412646 | − | 0.910892i | \(-0.364605\pi\) | ||||
0.412646 | + | 0.910892i | \(0.364605\pi\) | |||||||
\(434\) | 2366.00 | 0.261686 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 44.0000 | 0.00483307 | ||||||||
\(437\) | 297.000 | 0.0325113 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 1352.00 | 0.146987 | 0.0734937 | − | 0.997296i | \(-0.476585\pi\) | ||||
0.0734937 | + | 0.997296i | \(0.476585\pi\) | |||||||
\(440\) | −3240.00 | −0.351048 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 2112.00 | 0.227280 | ||||||||
\(443\) | 147.000 | 0.0157656 | 0.00788282 | − | 0.999969i | \(-0.497491\pi\) | ||||
0.00788282 | + | 0.999969i | \(0.497491\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1755.00 | 0.186955 | ||||||||
\(446\) | −8698.00 | −0.923458 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 448.000 | 0.0472456 | ||||||||
\(449\) | −10638.0 | −1.11813 | −0.559063 | − | 0.829125i | \(-0.688839\pi\) | ||||
−0.559063 | + | 0.829125i | \(0.688839\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 13095.0 | 1.36723 | ||||||||
\(452\) | 4152.00 | 0.432066 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 8532.00 | 0.881997 | ||||||||
\(455\) | −1008.00 | −0.103859 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −3499.00 | −0.358154 | −0.179077 | − | 0.983835i | \(-0.557311\pi\) | ||||
−0.179077 | + | 0.983835i | \(0.557311\pi\) | |||||||
\(458\) | 2120.00 | 0.216291 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 972.000 | 0.0985212 | ||||||||
\(461\) | 4119.00 | 0.416141 | 0.208070 | − | 0.978114i | \(-0.433282\pi\) | ||||
0.208070 | + | 0.978114i | \(0.433282\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −13318.0 | −1.33680 | −0.668402 | − | 0.743801i | \(-0.733021\pi\) | ||||
−0.668402 | + | 0.743801i | \(0.733021\pi\) | |||||||
\(464\) | −192.000 | −0.0192099 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −5628.00 | −0.559468 | ||||||||
\(467\) | −3306.00 | −0.327588 | −0.163794 | − | 0.986495i | \(-0.552373\pi\) | ||||
−0.163794 | + | 0.986495i | \(0.552373\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 6944.00 | 0.683676 | ||||||||
\(470\) | −3132.00 | −0.307380 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −3792.00 | −0.369790 | ||||||||
\(473\) | −17730.0 | −1.72352 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −484.000 | −0.0467525 | ||||||||
\(476\) | 1848.00 | 0.177947 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −2400.00 | −0.229652 | ||||||||
\(479\) | 2376.00 | 0.226643 | 0.113322 | − | 0.993558i | \(-0.463851\pi\) | ||||
0.113322 | + | 0.993558i | \(0.463851\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −3344.00 | −0.316992 | ||||||||
\(482\) | 11300.0 | 1.06784 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 2776.00 | 0.260706 | ||||||||
\(485\) | −792.000 | −0.0741502 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 14186.0 | 1.31998 | 0.659989 | − | 0.751276i | \(-0.270561\pi\) | ||||
0.659989 | + | 0.751276i | \(0.270561\pi\) | |||||||
\(488\) | 1856.00 | 0.172166 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −882.000 | −0.0813157 | ||||||||
\(491\) | −10599.0 | −0.974188 | −0.487094 | − | 0.873350i | \(-0.661943\pi\) | ||||
−0.487094 | + | 0.873350i | \(0.661943\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −792.000 | −0.0723527 | ||||||||
\(494\) | 352.000 | 0.0320592 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −2704.00 | −0.244785 | ||||||||
\(497\) | −1071.00 | −0.0966618 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −3022.00 | −0.271109 | −0.135554 | − | 0.990770i | \(-0.543282\pi\) | ||||
−0.135554 | + | 0.990770i | \(0.543282\pi\) | |||||||
\(500\) | −6084.00 | −0.544170 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −4320.00 | −0.384086 | ||||||||
\(503\) | 8244.00 | 0.730779 | 0.365389 | − | 0.930855i | \(-0.380936\pi\) | ||||
0.365389 | + | 0.930855i | \(0.380936\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −10854.0 | −0.956429 | ||||||||
\(506\) | −2430.00 | −0.213491 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 8864.00 | 0.774166 | ||||||||
\(509\) | −8406.00 | −0.732003 | −0.366001 | − | 0.930614i | \(-0.619273\pi\) | ||||
−0.366001 | + | 0.930614i | \(0.619273\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 4802.00 | 0.415710 | ||||||||
\(512\) | −512.000 | −0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 4914.00 | 0.421687 | ||||||||
\(515\) | −10593.0 | −0.906375 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 7830.00 | 0.666079 | ||||||||
\(518\) | −2926.00 | −0.248187 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 1152.00 | 0.0971510 | ||||||||
\(521\) | 7005.00 | 0.589049 | 0.294525 | − | 0.955644i | \(-0.404839\pi\) | ||||
0.294525 | + | 0.955644i | \(0.404839\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 18695.0 | 1.56305 | 0.781525 | − | 0.623874i | \(-0.214442\pi\) | ||||
0.781525 | + | 0.623874i | \(0.214442\pi\) | |||||||
\(524\) | 3672.00 | 0.306130 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 5778.00 | 0.478960 | ||||||||
\(527\) | −11154.0 | −0.921966 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −11438.0 | −0.940084 | ||||||||
\(530\) | −4104.00 | −0.336352 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 308.000 | 0.0251006 | ||||||||
\(533\) | −4656.00 | −0.378375 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −1404.00 | −0.113458 | ||||||||
\(536\) | −7936.00 | −0.639521 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −14442.0 | −1.15732 | ||||||||
\(539\) | 2205.00 | 0.176208 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 6113.00 | 0.485801 | 0.242901 | − | 0.970051i | \(-0.421901\pi\) | ||||
0.242901 | + | 0.970051i | \(0.421901\pi\) | |||||||
\(542\) | −5008.00 | −0.396886 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −2112.00 | −0.166455 | ||||||||
\(545\) | 99.0000 | 0.00778109 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 2036.00 | 0.159146 | 0.0795732 | − | 0.996829i | \(-0.474644\pi\) | ||||
0.0795732 | + | 0.996829i | \(0.474644\pi\) | |||||||
\(548\) | −9792.00 | −0.763309 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 3960.00 | 0.307009 | ||||||||
\(551\) | −132.000 | −0.0102058 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 7322.00 | 0.563044 | ||||||||
\(554\) | 4910.00 | 0.376545 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 4976.00 | 0.379549 | ||||||||
\(557\) | 11262.0 | 0.856708 | 0.428354 | − | 0.903611i | \(-0.359094\pi\) | ||||
0.428354 | + | 0.903611i | \(0.359094\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 6304.00 | 0.476978 | ||||||||
\(560\) | 1008.00 | 0.0760639 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −16140.0 | −1.21143 | ||||||||
\(563\) | −11028.0 | −0.825532 | −0.412766 | − | 0.910837i | \(-0.635437\pi\) | ||||
−0.412766 | + | 0.910837i | \(0.635437\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 9342.00 | 0.695612 | ||||||||
\(566\) | −2488.00 | −0.184768 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 1224.00 | 0.0904188 | ||||||||
\(569\) | 10686.0 | 0.787312 | 0.393656 | − | 0.919258i | \(-0.371210\pi\) | ||||
0.393656 | + | 0.919258i | \(0.371210\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 2018.00 | 0.147900 | 0.0739498 | − | 0.997262i | \(-0.476440\pi\) | ||||
0.0739498 | + | 0.997262i | \(0.476440\pi\) | |||||||
\(572\) | −2880.00 | −0.210522 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −4074.00 | −0.296246 | ||||||||
\(575\) | −1188.00 | −0.0861618 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −10006.0 | −0.721933 | −0.360966 | − | 0.932579i | \(-0.617553\pi\) | ||||
−0.360966 | + | 0.932579i | \(0.617553\pi\) | |||||||
\(578\) | 1114.00 | 0.0801666 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −432.000 | −0.0309273 | ||||||||
\(581\) | 4956.00 | 0.353889 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 10260.0 | 0.728861 | ||||||||
\(584\) | −5488.00 | −0.388861 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −6900.00 | −0.486410 | ||||||||
\(587\) | 13254.0 | 0.931944 | 0.465972 | − | 0.884799i | \(-0.345705\pi\) | ||||
0.465972 | + | 0.884799i | \(0.345705\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1859.00 | −0.130049 | ||||||||
\(590\) | −8532.00 | −0.595351 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 3344.00 | 0.232158 | ||||||||
\(593\) | −23187.0 | −1.60569 | −0.802847 | − | 0.596186i | \(-0.796682\pi\) | ||||
−0.802847 | + | 0.596186i | \(0.796682\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 4158.00 | 0.286490 | ||||||||
\(596\) | −3816.00 | −0.262264 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 864.000 | 0.0590829 | ||||||||
\(599\) | −27255.0 | −1.85911 | −0.929557 | − | 0.368679i | \(-0.879810\pi\) | ||||
−0.929557 | + | 0.368679i | \(0.879810\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −21976.0 | −1.49155 | −0.745773 | − | 0.666200i | \(-0.767920\pi\) | ||||
−0.745773 | + | 0.666200i | \(0.767920\pi\) | |||||||
\(602\) | 5516.00 | 0.373447 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −7768.00 | −0.523304 | ||||||||
\(605\) | 6246.00 | 0.419729 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 13052.0 | 0.872758 | 0.436379 | − | 0.899763i | \(-0.356261\pi\) | ||||
0.436379 | + | 0.899763i | \(0.356261\pi\) | |||||||
\(608\) | −352.000 | −0.0234794 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 4176.00 | 0.277182 | ||||||||
\(611\) | −2784.00 | −0.184335 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −2923.00 | −0.192592 | −0.0962960 | − | 0.995353i | \(-0.530700\pi\) | ||||
−0.0962960 | + | 0.995353i | \(0.530700\pi\) | |||||||
\(614\) | 5522.00 | 0.362948 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −2520.00 | −0.164827 | ||||||||
\(617\) | −3714.00 | −0.242334 | −0.121167 | − | 0.992632i | \(-0.538664\pi\) | ||||
−0.121167 | + | 0.992632i | \(0.538664\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 17705.0 | 1.14963 | 0.574817 | − | 0.818282i | \(-0.305073\pi\) | ||||
0.574817 | + | 0.818282i | \(0.305073\pi\) | |||||||
\(620\) | −6084.00 | −0.394096 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −14016.0 | −0.903522 | ||||||||
\(623\) | 1365.00 | 0.0877810 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −8189.00 | −0.524096 | ||||||||
\(626\) | 320.000 | 0.0204309 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −8128.00 | −0.516469 | ||||||||
\(629\) | 13794.0 | 0.874408 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −19978.0 | −1.26040 | −0.630199 | − | 0.776433i | \(-0.717027\pi\) | ||||
−0.630199 | + | 0.776433i | \(0.717027\pi\) | |||||||
\(632\) | −8368.00 | −0.526679 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −1500.00 | −0.0939631 | ||||||||
\(635\) | 19944.0 | 1.24638 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −784.000 | −0.0487649 | ||||||||
\(638\) | 1080.00 | 0.0670182 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −1152.00 | −0.0711512 | ||||||||
\(641\) | −11502.0 | −0.708739 | −0.354369 | − | 0.935105i | \(-0.615304\pi\) | ||||
−0.354369 | + | 0.935105i | \(0.615304\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 31439.0 | 1.92820 | 0.964100 | − | 0.265538i | \(-0.0855496\pi\) | ||||
0.964100 | + | 0.265538i | \(0.0855496\pi\) | |||||||
\(644\) | 756.000 | 0.0462587 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −1452.00 | −0.0884337 | ||||||||
\(647\) | 10650.0 | 0.647132 | 0.323566 | − | 0.946206i | \(-0.395118\pi\) | ||||
0.323566 | + | 0.946206i | \(0.395118\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 21330.0 | 1.29010 | ||||||||
\(650\) | −1408.00 | −0.0849635 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 9008.00 | 0.541074 | ||||||||
\(653\) | −9774.00 | −0.585737 | −0.292868 | − | 0.956153i | \(-0.594610\pi\) | ||||
−0.292868 | + | 0.956153i | \(0.594610\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 8262.00 | 0.492860 | ||||||||
\(656\) | 4656.00 | 0.277113 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −2436.00 | −0.144324 | ||||||||
\(659\) | 13857.0 | 0.819108 | 0.409554 | − | 0.912286i | \(-0.365684\pi\) | ||||
0.409554 | + | 0.912286i | \(0.365684\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 3908.00 | 0.229960 | 0.114980 | − | 0.993368i | \(-0.463320\pi\) | ||||
0.114980 | + | 0.993368i | \(0.463320\pi\) | |||||||
\(662\) | −6376.00 | −0.374336 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −5664.00 | −0.331033 | ||||||||
\(665\) | 693.000 | 0.0404111 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −324.000 | −0.0188086 | ||||||||
\(668\) | 16680.0 | 0.966121 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −17856.0 | −1.02961 | ||||||||
\(671\) | −10440.0 | −0.600643 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 26570.0 | 1.52184 | 0.760920 | − | 0.648846i | \(-0.224748\pi\) | ||||
0.760920 | + | 0.648846i | \(0.224748\pi\) | |||||||
\(674\) | 17834.0 | 1.01920 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −7764.00 | −0.441739 | ||||||||
\(677\) | −1725.00 | −0.0979278 | −0.0489639 | − | 0.998801i | \(-0.515592\pi\) | ||||
−0.0489639 | + | 0.998801i | \(0.515592\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −616.000 | −0.0348158 | ||||||||
\(680\) | −4752.00 | −0.267987 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 15210.0 | 0.853990 | ||||||||
\(683\) | 31071.0 | 1.74070 | 0.870350 | − | 0.492433i | \(-0.163892\pi\) | ||||
0.870350 | + | 0.492433i | \(0.163892\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −22032.0 | −1.22890 | ||||||||
\(686\) | −686.000 | −0.0381802 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −6304.00 | −0.349328 | ||||||||
\(689\) | −3648.00 | −0.201709 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 19964.0 | 1.09908 | 0.549541 | − | 0.835466i | \(-0.314802\pi\) | ||||
0.549541 | + | 0.835466i | \(0.314802\pi\) | |||||||
\(692\) | −17412.0 | −0.956510 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 14982.0 | 0.819465 | ||||||||
\(695\) | 11196.0 | 0.611063 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 19206.0 | 1.04373 | ||||||||
\(698\) | 14900.0 | 0.807985 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −1232.00 | −0.0665217 | ||||||||
\(701\) | −25884.0 | −1.39462 | −0.697308 | − | 0.716772i | \(-0.745619\pi\) | ||||
−0.697308 | + | 0.716772i | \(0.745619\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 2299.00 | 0.123341 | ||||||||
\(704\) | 2880.00 | 0.154182 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −18450.0 | −0.983534 | ||||||||
\(707\) | −8442.00 | −0.449072 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −23821.0 | −1.26180 | −0.630900 | − | 0.775864i | \(-0.717314\pi\) | ||||
−0.630900 | + | 0.775864i | \(0.717314\pi\) | |||||||
\(710\) | 2754.00 | 0.145572 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −1560.00 | −0.0821116 | ||||||||
\(713\) | −4563.00 | −0.239671 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −6480.00 | −0.338935 | ||||||||
\(716\) | −15936.0 | −0.831783 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −7320.00 | −0.380474 | ||||||||
\(719\) | −28254.0 | −1.46550 | −0.732751 | − | 0.680497i | \(-0.761764\pi\) | ||||
−0.732751 | + | 0.680497i | \(0.761764\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −8239.00 | −0.425571 | ||||||||
\(722\) | 13476.0 | 0.694633 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 2600.00 | 0.133464 | ||||||||
\(725\) | 528.000 | 0.0270475 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −17152.0 | −0.875010 | −0.437505 | − | 0.899216i | \(-0.644138\pi\) | ||||
−0.437505 | + | 0.899216i | \(0.644138\pi\) | |||||||
\(728\) | 896.000 | 0.0456153 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −12348.0 | −0.626055 | ||||||||
\(731\) | −26004.0 | −1.31572 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 254.000 | 0.0127991 | 0.00639953 | − | 0.999980i | \(-0.497963\pi\) | ||||
0.00639953 | + | 0.999980i | \(0.497963\pi\) | |||||||
\(734\) | 20426.0 | 1.02716 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −864.000 | −0.0432710 | ||||||||
\(737\) | 44640.0 | 2.23112 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −12382.0 | −0.616345 | −0.308173 | − | 0.951330i | \(-0.599717\pi\) | ||||
−0.308173 | + | 0.951330i | \(0.599717\pi\) | |||||||
\(740\) | 7524.00 | 0.373767 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −3192.00 | −0.157927 | ||||||||
\(743\) | 34671.0 | 1.71192 | 0.855959 | − | 0.517043i | \(-0.172967\pi\) | ||||
0.855959 | + | 0.517043i | \(0.172967\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −8586.00 | −0.422237 | ||||||||
\(746\) | 17258.0 | 0.846998 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 11880.0 | 0.580716 | ||||||||
\(749\) | −1092.00 | −0.0532721 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −28150.0 | −1.36779 | −0.683894 | − | 0.729582i | \(-0.739715\pi\) | ||||
−0.683894 | + | 0.729582i | \(0.739715\pi\) | |||||||
\(752\) | 2784.00 | 0.135003 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −384.000 | −0.0185470 | ||||||||
\(755\) | −17478.0 | −0.842503 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −26638.0 | −1.27896 | −0.639481 | − | 0.768807i | \(-0.720851\pi\) | ||||
−0.639481 | + | 0.768807i | \(0.720851\pi\) | |||||||
\(758\) | −2452.00 | −0.117494 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −792.000 | −0.0378011 | ||||||||
\(761\) | 26154.0 | 1.24584 | 0.622918 | − | 0.782287i | \(-0.285947\pi\) | ||||
0.622918 | + | 0.782287i | \(0.285947\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 77.0000 | 0.00365346 | ||||||||
\(764\) | −11868.0 | −0.562002 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −21996.0 | −1.03753 | ||||||||
\(767\) | −7584.00 | −0.357030 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 36416.0 | 1.70767 | 0.853833 | − | 0.520548i | \(-0.174272\pi\) | ||||
0.853833 | + | 0.520548i | \(0.174272\pi\) | |||||||
\(770\) | −5670.00 | −0.265367 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −11368.0 | −0.529978 | ||||||||
\(773\) | −16917.0 | −0.787144 | −0.393572 | − | 0.919294i | \(-0.628761\pi\) | ||||
−0.393572 | + | 0.919294i | \(0.628761\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 7436.00 | 0.344657 | ||||||||
\(776\) | 704.000 | 0.0325672 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 5544.00 | 0.255478 | ||||||||
\(779\) | 3201.00 | 0.147224 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −6885.00 | −0.315448 | ||||||||
\(782\) | −3564.00 | −0.162977 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 784.000 | 0.0357143 | ||||||||
\(785\) | −18288.0 | −0.831499 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −20032.0 | −0.907324 | −0.453662 | − | 0.891174i | \(-0.649883\pi\) | ||||
−0.453662 | + | 0.891174i | \(0.649883\pi\) | |||||||
\(788\) | 9144.00 | 0.413378 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −18828.0 | −0.847937 | ||||||||
\(791\) | 7266.00 | 0.326611 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 3712.00 | 0.166226 | ||||||||
\(794\) | 12236.0 | 0.546901 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −6580.00 | −0.292992 | ||||||||
\(797\) | 34095.0 | 1.51532 | 0.757658 | − | 0.652652i | \(-0.226344\pi\) | ||||
0.757658 | + | 0.652652i | \(0.226344\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 11484.0 | 0.508479 | ||||||||
\(800\) | 1408.00 | 0.0622254 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 28152.0 | 1.23950 | ||||||||
\(803\) | 30870.0 | 1.35664 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1701.00 | 0.0744750 | ||||||||
\(806\) | −5408.00 | −0.236338 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 9648.00 | 0.420069 | ||||||||
\(809\) | 37164.0 | 1.61510 | 0.807550 | − | 0.589798i | \(-0.200793\pi\) | ||||
0.807550 | + | 0.589798i | \(0.200793\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 17525.0 | 0.758799 | 0.379399 | − | 0.925233i | \(-0.376131\pi\) | ||||
0.379399 | + | 0.925233i | \(0.376131\pi\) | |||||||
\(812\) | −336.000 | −0.0145213 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −18810.0 | −0.809939 | ||||||||
\(815\) | 20268.0 | 0.871113 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −4334.00 | −0.185591 | ||||||||
\(818\) | −1084.00 | −0.0463340 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 10476.0 | 0.446144 | ||||||||
\(821\) | −2778.00 | −0.118091 | −0.0590456 | − | 0.998255i | \(-0.518806\pi\) | ||||
−0.0590456 | + | 0.998255i | \(0.518806\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −5470.00 | −0.231679 | −0.115840 | − | 0.993268i | \(-0.536956\pi\) | ||||
−0.115840 | + | 0.993268i | \(0.536956\pi\) | |||||||
\(824\) | 9416.00 | 0.398085 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −6636.00 | −0.279535 | ||||||||
\(827\) | 27711.0 | 1.16518 | 0.582591 | − | 0.812765i | \(-0.302039\pi\) | ||||
0.582591 | + | 0.812765i | \(0.302039\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −6550.00 | −0.274416 | −0.137208 | − | 0.990542i | \(-0.543813\pi\) | ||||
−0.137208 | + | 0.990542i | \(0.543813\pi\) | |||||||
\(830\) | −12744.0 | −0.532953 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −1024.00 | −0.0426692 | ||||||||
\(833\) | 3234.00 | 0.134516 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 37530.0 | 1.55542 | ||||||||
\(836\) | 1980.00 | 0.0819136 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 12180.0 | 0.502090 | ||||||||
\(839\) | −7068.00 | −0.290840 | −0.145420 | − | 0.989370i | \(-0.546453\pi\) | ||||
−0.145420 | + | 0.989370i | \(0.546453\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −24245.0 | −0.994096 | ||||||||
\(842\) | 28670.0 | 1.17344 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −11512.0 | −0.469502 | ||||||||
\(845\) | −17469.0 | −0.711186 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 4858.00 | 0.197075 | ||||||||
\(848\) | 3648.00 | 0.147727 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 5808.00 | 0.234368 | ||||||||
\(851\) | 5643.00 | 0.227309 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 41528.0 | 1.66693 | 0.833465 | − | 0.552572i | \(-0.186354\pi\) | ||||
0.833465 | + | 0.552572i | \(0.186354\pi\) | |||||||
\(854\) | 3248.00 | 0.130146 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 1248.00 | 0.0498315 | ||||||||
\(857\) | 32751.0 | 1.30543 | 0.652715 | − | 0.757604i | \(-0.273630\pi\) | ||||
0.652715 | + | 0.757604i | \(0.273630\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 15995.0 | 0.635323 | 0.317661 | − | 0.948204i | \(-0.397102\pi\) | ||||
0.317661 | + | 0.948204i | \(0.397102\pi\) | |||||||
\(860\) | −14184.0 | −0.562407 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 33510.0 | 1.32408 | ||||||||
\(863\) | −15528.0 | −0.612490 | −0.306245 | − | 0.951953i | \(-0.599073\pi\) | ||||
−0.306245 | + | 0.951953i | \(0.599073\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −39177.0 | −1.53995 | ||||||||
\(866\) | −14872.0 | −0.583569 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −4732.00 | −0.185040 | ||||||||
\(869\) | 47070.0 | 1.83745 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −15872.0 | −0.617454 | ||||||||
\(872\) | −88.0000 | −0.00341750 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −594.000 | −0.0229890 | ||||||||
\(875\) | −10647.0 | −0.411353 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 40214.0 | 1.54838 | 0.774191 | − | 0.632953i | \(-0.218157\pi\) | ||||
0.774191 | + | 0.632953i | \(0.218157\pi\) | |||||||
\(878\) | −2704.00 | −0.103936 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 6480.00 | 0.248228 | ||||||||
\(881\) | −24435.0 | −0.934434 | −0.467217 | − | 0.884143i | \(-0.654743\pi\) | ||||
−0.467217 | + | 0.884143i | \(0.654743\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −18736.0 | −0.714062 | −0.357031 | − | 0.934093i | \(-0.616211\pi\) | ||||
−0.357031 | + | 0.934093i | \(0.616211\pi\) | |||||||
\(884\) | −4224.00 | −0.160711 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −294.000 | −0.0111480 | ||||||||
\(887\) | 23940.0 | 0.906231 | 0.453115 | − | 0.891452i | \(-0.350313\pi\) | ||||
0.453115 | + | 0.891452i | \(0.350313\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 15512.0 | 0.585215 | ||||||||
\(890\) | −3510.00 | −0.132197 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 17396.0 | 0.652983 | ||||||||
\(893\) | 1914.00 | 0.0717240 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −35856.0 | −1.33914 | ||||||||
\(896\) | −896.000 | −0.0334077 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 21276.0 | 0.790634 | ||||||||
\(899\) | 2028.00 | 0.0752365 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 15048.0 | 0.556406 | ||||||||
\(902\) | −26190.0 | −0.966776 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −8304.00 | −0.305517 | ||||||||
\(905\) | 5850.00 | 0.214874 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 31358.0 | 1.14799 | 0.573994 | − | 0.818859i | \(-0.305393\pi\) | ||||
0.573994 | + | 0.818859i | \(0.305393\pi\) | |||||||
\(908\) | −17064.0 | −0.623666 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 2016.00 | 0.0734393 | ||||||||
\(911\) | −9408.00 | −0.342153 | −0.171076 | − | 0.985258i | \(-0.554724\pi\) | ||||
−0.171076 | + | 0.985258i | \(0.554724\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 31860.0 | 1.15489 | ||||||||
\(914\) | 6998.00 | 0.253253 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −4240.00 | −0.152941 | ||||||||
\(917\) | 6426.00 | 0.231412 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −6748.00 | −0.242215 | −0.121108 | − | 0.992639i | \(-0.538645\pi\) | ||||
−0.121108 | + | 0.992639i | \(0.538645\pi\) | |||||||
\(920\) | −1944.00 | −0.0696650 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −8238.00 | −0.294256 | ||||||||
\(923\) | 2448.00 | 0.0872989 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −9196.00 | −0.326879 | ||||||||
\(926\) | 26636.0 | 0.945263 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 384.000 | 0.0135834 | ||||||||
\(929\) | 18246.0 | 0.644383 | 0.322192 | − | 0.946675i | \(-0.395580\pi\) | ||||
0.322192 | + | 0.946675i | \(0.395580\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 539.000 | 0.0189742 | ||||||||
\(932\) | 11256.0 | 0.395604 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 6612.00 | 0.231639 | ||||||||
\(935\) | 26730.0 | 0.934935 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 19748.0 | 0.688516 | 0.344258 | − | 0.938875i | \(-0.388131\pi\) | ||||
0.344258 | + | 0.938875i | \(0.388131\pi\) | |||||||
\(938\) | −13888.0 | −0.483432 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 6264.00 | 0.217350 | ||||||||
\(941\) | −55875.0 | −1.93568 | −0.967839 | − | 0.251571i | \(-0.919053\pi\) | ||||
−0.967839 | + | 0.251571i | \(0.919053\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 7857.00 | 0.271325 | ||||||||
\(944\) | 7584.00 | 0.261481 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 35460.0 | 1.21871 | ||||||||
\(947\) | −37977.0 | −1.30315 | −0.651577 | − | 0.758583i | \(-0.725892\pi\) | ||||
−0.651577 | + | 0.758583i | \(0.725892\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −10976.0 | −0.375444 | ||||||||
\(950\) | 968.000 | 0.0330590 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −3696.00 | −0.125828 | ||||||||
\(953\) | −28332.0 | −0.963026 | −0.481513 | − | 0.876439i | \(-0.659913\pi\) | ||||
−0.481513 | + | 0.876439i | \(0.659913\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −26703.0 | −0.904805 | ||||||||
\(956\) | 4800.00 | 0.162388 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −4752.00 | −0.160261 | ||||||||
\(959\) | −17136.0 | −0.577008 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −1230.00 | −0.0412876 | ||||||||
\(962\) | 6688.00 | 0.224147 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −22600.0 | −0.755080 | ||||||||
\(965\) | −25578.0 | −0.853249 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −50902.0 | −1.69276 | −0.846380 | − | 0.532580i | \(-0.821222\pi\) | ||||
−0.846380 | + | 0.532580i | \(0.821222\pi\) | |||||||
\(968\) | −5552.00 | −0.184347 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 1584.00 | 0.0524321 | ||||||||
\(971\) | −54444.0 | −1.79937 | −0.899686 | − | 0.436537i | \(-0.856205\pi\) | ||||
−0.899686 | + | 0.436537i | \(0.856205\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 8708.00 | 0.286912 | ||||||||
\(974\) | −28372.0 | −0.933365 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −3712.00 | −0.121740 | ||||||||
\(977\) | 34836.0 | 1.14074 | 0.570370 | − | 0.821388i | \(-0.306800\pi\) | ||||
0.570370 | + | 0.821388i | \(0.306800\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 8775.00 | 0.286466 | ||||||||
\(980\) | 1764.00 | 0.0574989 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 21198.0 | 0.688855 | ||||||||
\(983\) | −34974.0 | −1.13479 | −0.567394 | − | 0.823446i | \(-0.692048\pi\) | ||||
−0.567394 | + | 0.823446i | \(0.692048\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 20574.0 | 0.665525 | ||||||||
\(986\) | 1584.00 | 0.0511611 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −704.000 | −0.0226693 | ||||||||
\(989\) | −10638.0 | −0.342031 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −36844.0 | −1.18102 | −0.590509 | − | 0.807031i | \(-0.701073\pi\) | ||||
−0.590509 | + | 0.807031i | \(0.701073\pi\) | |||||||
\(992\) | 5408.00 | 0.173089 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 2142.00 | 0.0683502 | ||||||||
\(995\) | −14805.0 | −0.471709 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −45970.0 | −1.46027 | −0.730133 | − | 0.683305i | \(-0.760542\pi\) | ||||
−0.730133 | + | 0.683305i | \(0.760542\pi\) | |||||||
\(998\) | 6044.00 | 0.191703 | ||||||||
\(999\) | 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 | 378.4.a.e.1.1 | ✓ | 1 | |
3.2 | odd | 2 | 378.4.a.h.1.1 | yes | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
378.4.a.e.1.1 | ✓ | 1 | 1.1 | even | 1 | trivial | |
378.4.a.h.1.1 | yes | 1 | 3.2 | odd | 2 |