Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1470,4,Mod(1,1470)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1470, 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("1470.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1470 = 2 \cdot 3 \cdot 5 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1470.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: | \(86.7328077084\) |
Analytic rank: | \(1\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 1470.1 |
$q$-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 | ||||||||
\(3\) | −3.00000 | −0.577350 | ||||||||
\(4\) | 4.00000 | 0.500000 | ||||||||
\(5\) | 5.00000 | 0.447214 | ||||||||
\(6\) | −6.00000 | −0.408248 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 8.00000 | 0.353553 | ||||||||
\(9\) | 9.00000 | 0.333333 | ||||||||
\(10\) | 10.0000 | 0.316228 | ||||||||
\(11\) | −20.0000 | −0.548202 | −0.274101 | − | 0.961701i | \(-0.588380\pi\) | ||||
−0.274101 | + | 0.961701i | \(0.588380\pi\) | |||||||
\(12\) | −12.0000 | −0.288675 | ||||||||
\(13\) | 26.0000 | 0.554700 | 0.277350 | − | 0.960769i | \(-0.410544\pi\) | ||||
0.277350 | + | 0.960769i | \(0.410544\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −15.0000 | −0.258199 | ||||||||
\(16\) | 16.0000 | 0.250000 | ||||||||
\(17\) | −26.0000 | −0.370937 | −0.185468 | − | 0.982650i | \(-0.559380\pi\) | ||||
−0.185468 | + | 0.982650i | \(0.559380\pi\) | |||||||
\(18\) | 18.0000 | 0.235702 | ||||||||
\(19\) | −42.0000 | −0.507130 | −0.253565 | − | 0.967318i | \(-0.581603\pi\) | ||||
−0.253565 | + | 0.967318i | \(0.581603\pi\) | |||||||
\(20\) | 20.0000 | 0.223607 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −40.0000 | −0.387638 | ||||||||
\(23\) | −194.000 | −1.75877 | −0.879387 | − | 0.476108i | \(-0.842047\pi\) | ||||
−0.879387 | + | 0.476108i | \(0.842047\pi\) | |||||||
\(24\) | −24.0000 | −0.204124 | ||||||||
\(25\) | 25.0000 | 0.200000 | ||||||||
\(26\) | 52.0000 | 0.392232 | ||||||||
\(27\) | −27.0000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −42.0000 | −0.268938 | −0.134469 | − | 0.990918i | \(-0.542933\pi\) | ||||
−0.134469 | + | 0.990918i | \(0.542933\pi\) | |||||||
\(30\) | −30.0000 | −0.182574 | ||||||||
\(31\) | 274.000 | 1.58748 | 0.793740 | − | 0.608258i | \(-0.208131\pi\) | ||||
0.793740 | + | 0.608258i | \(0.208131\pi\) | |||||||
\(32\) | 32.0000 | 0.176777 | ||||||||
\(33\) | 60.0000 | 0.316505 | ||||||||
\(34\) | −52.0000 | −0.262292 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 36.0000 | 0.166667 | ||||||||
\(37\) | 2.00000 | 0.00888643 | 0.00444322 | − | 0.999990i | \(-0.498586\pi\) | ||||
0.00444322 | + | 0.999990i | \(0.498586\pi\) | |||||||
\(38\) | −84.0000 | −0.358595 | ||||||||
\(39\) | −78.0000 | −0.320256 | ||||||||
\(40\) | 40.0000 | 0.158114 | ||||||||
\(41\) | −250.000 | −0.952279 | −0.476140 | − | 0.879370i | \(-0.657964\pi\) | ||||
−0.476140 | + | 0.879370i | \(0.657964\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −296.000 | −1.04976 | −0.524879 | − | 0.851177i | \(-0.675889\pi\) | ||||
−0.524879 | + | 0.851177i | \(0.675889\pi\) | |||||||
\(44\) | −80.0000 | −0.274101 | ||||||||
\(45\) | 45.0000 | 0.149071 | ||||||||
\(46\) | −388.000 | −1.24364 | ||||||||
\(47\) | −328.000 | −1.01795 | −0.508976 | − | 0.860781i | \(-0.669976\pi\) | ||||
−0.508976 | + | 0.860781i | \(0.669976\pi\) | |||||||
\(48\) | −48.0000 | −0.144338 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 50.0000 | 0.141421 | ||||||||
\(51\) | 78.0000 | 0.214160 | ||||||||
\(52\) | 104.000 | 0.277350 | ||||||||
\(53\) | −148.000 | −0.383573 | −0.191786 | − | 0.981437i | \(-0.561428\pi\) | ||||
−0.191786 | + | 0.981437i | \(0.561428\pi\) | |||||||
\(54\) | −54.0000 | −0.136083 | ||||||||
\(55\) | −100.000 | −0.245164 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 126.000 | 0.292791 | ||||||||
\(58\) | −84.0000 | −0.190168 | ||||||||
\(59\) | 488.000 | 1.07682 | 0.538408 | − | 0.842684i | \(-0.319026\pi\) | ||||
0.538408 | + | 0.842684i | \(0.319026\pi\) | |||||||
\(60\) | −60.0000 | −0.129099 | ||||||||
\(61\) | 272.000 | 0.570919 | 0.285459 | − | 0.958391i | \(-0.407854\pi\) | ||||
0.285459 | + | 0.958391i | \(0.407854\pi\) | |||||||
\(62\) | 548.000 | 1.12252 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 64.0000 | 0.125000 | ||||||||
\(65\) | 130.000 | 0.248069 | ||||||||
\(66\) | 120.000 | 0.223803 | ||||||||
\(67\) | 8.00000 | 0.0145874 | 0.00729370 | − | 0.999973i | \(-0.497678\pi\) | ||||
0.00729370 | + | 0.999973i | \(0.497678\pi\) | |||||||
\(68\) | −104.000 | −0.185468 | ||||||||
\(69\) | 582.000 | 1.01543 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −684.000 | −1.14332 | −0.571661 | − | 0.820490i | \(-0.693701\pi\) | ||||
−0.571661 | + | 0.820490i | \(0.693701\pi\) | |||||||
\(72\) | 72.0000 | 0.117851 | ||||||||
\(73\) | 310.000 | 0.497024 | 0.248512 | − | 0.968629i | \(-0.420058\pi\) | ||||
0.248512 | + | 0.968629i | \(0.420058\pi\) | |||||||
\(74\) | 4.00000 | 0.00628366 | ||||||||
\(75\) | −75.0000 | −0.115470 | ||||||||
\(76\) | −168.000 | −0.253565 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −156.000 | −0.226455 | ||||||||
\(79\) | −584.000 | −0.831711 | −0.415855 | − | 0.909431i | \(-0.636518\pi\) | ||||
−0.415855 | + | 0.909431i | \(0.636518\pi\) | |||||||
\(80\) | 80.0000 | 0.111803 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | −500.000 | −0.673363 | ||||||||
\(83\) | 404.000 | 0.534274 | 0.267137 | − | 0.963659i | \(-0.413922\pi\) | ||||
0.267137 | + | 0.963659i | \(0.413922\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −130.000 | −0.165888 | ||||||||
\(86\) | −592.000 | −0.742291 | ||||||||
\(87\) | 126.000 | 0.155271 | ||||||||
\(88\) | −160.000 | −0.193819 | ||||||||
\(89\) | −266.000 | −0.316808 | −0.158404 | − | 0.987374i | \(-0.550635\pi\) | ||||
−0.158404 | + | 0.987374i | \(0.550635\pi\) | |||||||
\(90\) | 90.0000 | 0.105409 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −776.000 | −0.879387 | ||||||||
\(93\) | −822.000 | −0.916531 | ||||||||
\(94\) | −656.000 | −0.719800 | ||||||||
\(95\) | −210.000 | −0.226795 | ||||||||
\(96\) | −96.0000 | −0.102062 | ||||||||
\(97\) | −678.000 | −0.709696 | −0.354848 | − | 0.934924i | \(-0.615467\pi\) | ||||
−0.354848 | + | 0.934924i | \(0.615467\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −180.000 | −0.182734 | ||||||||
\(100\) | 100.000 | 0.100000 | ||||||||
\(101\) | −406.000 | −0.399985 | −0.199993 | − | 0.979797i | \(-0.564092\pi\) | ||||
−0.199993 | + | 0.979797i | \(0.564092\pi\) | |||||||
\(102\) | 156.000 | 0.151434 | ||||||||
\(103\) | 292.000 | 0.279336 | 0.139668 | − | 0.990198i | \(-0.455396\pi\) | ||||
0.139668 | + | 0.990198i | \(0.455396\pi\) | |||||||
\(104\) | 208.000 | 0.196116 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −296.000 | −0.271227 | ||||||||
\(107\) | −1950.00 | −1.76181 | −0.880905 | − | 0.473294i | \(-0.843065\pi\) | ||||
−0.880905 | + | 0.473294i | \(0.843065\pi\) | |||||||
\(108\) | −108.000 | −0.0962250 | ||||||||
\(109\) | −218.000 | −0.191565 | −0.0957826 | − | 0.995402i | \(-0.530535\pi\) | ||||
−0.0957826 | + | 0.995402i | \(0.530535\pi\) | |||||||
\(110\) | −200.000 | −0.173357 | ||||||||
\(111\) | −6.00000 | −0.00513058 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1820.00 | 1.51514 | 0.757572 | − | 0.652752i | \(-0.226386\pi\) | ||||
0.757572 | + | 0.652752i | \(0.226386\pi\) | |||||||
\(114\) | 252.000 | 0.207035 | ||||||||
\(115\) | −970.000 | −0.786548 | ||||||||
\(116\) | −168.000 | −0.134469 | ||||||||
\(117\) | 234.000 | 0.184900 | ||||||||
\(118\) | 976.000 | 0.761424 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −120.000 | −0.0912871 | ||||||||
\(121\) | −931.000 | −0.699474 | ||||||||
\(122\) | 544.000 | 0.403700 | ||||||||
\(123\) | 750.000 | 0.549799 | ||||||||
\(124\) | 1096.00 | 0.793740 | ||||||||
\(125\) | 125.000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −96.0000 | −0.0670758 | −0.0335379 | − | 0.999437i | \(-0.510677\pi\) | ||||
−0.0335379 | + | 0.999437i | \(0.510677\pi\) | |||||||
\(128\) | 128.000 | 0.0883883 | ||||||||
\(129\) | 888.000 | 0.606078 | ||||||||
\(130\) | 260.000 | 0.175412 | ||||||||
\(131\) | −1872.00 | −1.24853 | −0.624265 | − | 0.781213i | \(-0.714601\pi\) | ||||
−0.624265 | + | 0.781213i | \(0.714601\pi\) | |||||||
\(132\) | 240.000 | 0.158252 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 16.0000 | 0.0103148 | ||||||||
\(135\) | −135.000 | −0.0860663 | ||||||||
\(136\) | −208.000 | −0.131146 | ||||||||
\(137\) | −316.000 | −0.197064 | −0.0985318 | − | 0.995134i | \(-0.531415\pi\) | ||||
−0.0985318 | + | 0.995134i | \(0.531415\pi\) | |||||||
\(138\) | 1164.00 | 0.718016 | ||||||||
\(139\) | −262.000 | −0.159874 | −0.0799372 | − | 0.996800i | \(-0.525472\pi\) | ||||
−0.0799372 | + | 0.996800i | \(0.525472\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 984.000 | 0.587715 | ||||||||
\(142\) | −1368.00 | −0.808451 | ||||||||
\(143\) | −520.000 | −0.304088 | ||||||||
\(144\) | 144.000 | 0.0833333 | ||||||||
\(145\) | −210.000 | −0.120273 | ||||||||
\(146\) | 620.000 | 0.351449 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 8.00000 | 0.00444322 | ||||||||
\(149\) | −2090.00 | −1.14912 | −0.574562 | − | 0.818461i | \(-0.694828\pi\) | ||||
−0.574562 | + | 0.818461i | \(0.694828\pi\) | |||||||
\(150\) | −150.000 | −0.0816497 | ||||||||
\(151\) | −2520.00 | −1.35811 | −0.679055 | − | 0.734087i | \(-0.737610\pi\) | ||||
−0.679055 | + | 0.734087i | \(0.737610\pi\) | |||||||
\(152\) | −336.000 | −0.179297 | ||||||||
\(153\) | −234.000 | −0.123646 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1370.00 | 0.709942 | ||||||||
\(156\) | −312.000 | −0.160128 | ||||||||
\(157\) | 866.000 | 0.440219 | 0.220109 | − | 0.975475i | \(-0.429359\pi\) | ||||
0.220109 | + | 0.975475i | \(0.429359\pi\) | |||||||
\(158\) | −1168.00 | −0.588108 | ||||||||
\(159\) | 444.000 | 0.221456 | ||||||||
\(160\) | 160.000 | 0.0790569 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 162.000 | 0.0785674 | ||||||||
\(163\) | −3436.00 | −1.65109 | −0.825547 | − | 0.564334i | \(-0.809133\pi\) | ||||
−0.825547 | + | 0.564334i | \(0.809133\pi\) | |||||||
\(164\) | −1000.00 | −0.476140 | ||||||||
\(165\) | 300.000 | 0.141545 | ||||||||
\(166\) | 808.000 | 0.377789 | ||||||||
\(167\) | −1656.00 | −0.767336 | −0.383668 | − | 0.923471i | \(-0.625339\pi\) | ||||
−0.383668 | + | 0.923471i | \(0.625339\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1521.00 | −0.692308 | ||||||||
\(170\) | −260.000 | −0.117301 | ||||||||
\(171\) | −378.000 | −0.169043 | ||||||||
\(172\) | −1184.00 | −0.524879 | ||||||||
\(173\) | 2154.00 | 0.946622 | 0.473311 | − | 0.880895i | \(-0.343059\pi\) | ||||
0.473311 | + | 0.880895i | \(0.343059\pi\) | |||||||
\(174\) | 252.000 | 0.109794 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −320.000 | −0.137051 | ||||||||
\(177\) | −1464.00 | −0.621700 | ||||||||
\(178\) | −532.000 | −0.224017 | ||||||||
\(179\) | 1112.00 | 0.464328 | 0.232164 | − | 0.972677i | \(-0.425419\pi\) | ||||
0.232164 | + | 0.972677i | \(0.425419\pi\) | |||||||
\(180\) | 180.000 | 0.0745356 | ||||||||
\(181\) | 512.000 | 0.210258 | 0.105129 | − | 0.994459i | \(-0.466474\pi\) | ||||
0.105129 | + | 0.994459i | \(0.466474\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −816.000 | −0.329620 | ||||||||
\(184\) | −1552.00 | −0.621820 | ||||||||
\(185\) | 10.0000 | 0.00397413 | ||||||||
\(186\) | −1644.00 | −0.648086 | ||||||||
\(187\) | 520.000 | 0.203348 | ||||||||
\(188\) | −1312.00 | −0.508976 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −420.000 | −0.160368 | ||||||||
\(191\) | −1008.00 | −0.381866 | −0.190933 | − | 0.981603i | \(-0.561151\pi\) | ||||
−0.190933 | + | 0.981603i | \(0.561151\pi\) | |||||||
\(192\) | −192.000 | −0.0721688 | ||||||||
\(193\) | 1650.00 | 0.615387 | 0.307693 | − | 0.951486i | \(-0.400443\pi\) | ||||
0.307693 | + | 0.951486i | \(0.400443\pi\) | |||||||
\(194\) | −1356.00 | −0.501831 | ||||||||
\(195\) | −390.000 | −0.143223 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 312.000 | 0.112838 | 0.0564190 | − | 0.998407i | \(-0.482032\pi\) | ||||
0.0564190 | + | 0.998407i | \(0.482032\pi\) | |||||||
\(198\) | −360.000 | −0.129213 | ||||||||
\(199\) | −1706.00 | −0.607714 | −0.303857 | − | 0.952718i | \(-0.598275\pi\) | ||||
−0.303857 | + | 0.952718i | \(0.598275\pi\) | |||||||
\(200\) | 200.000 | 0.0707107 | ||||||||
\(201\) | −24.0000 | −0.00842204 | ||||||||
\(202\) | −812.000 | −0.282832 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 312.000 | 0.107080 | ||||||||
\(205\) | −1250.00 | −0.425872 | ||||||||
\(206\) | 584.000 | 0.197520 | ||||||||
\(207\) | −1746.00 | −0.586258 | ||||||||
\(208\) | 416.000 | 0.138675 | ||||||||
\(209\) | 840.000 | 0.278010 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 5036.00 | 1.64309 | 0.821546 | − | 0.570142i | \(-0.193112\pi\) | ||||
0.821546 | + | 0.570142i | \(0.193112\pi\) | |||||||
\(212\) | −592.000 | −0.191786 | ||||||||
\(213\) | 2052.00 | 0.660097 | ||||||||
\(214\) | −3900.00 | −1.24579 | ||||||||
\(215\) | −1480.00 | −0.469466 | ||||||||
\(216\) | −216.000 | −0.0680414 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −436.000 | −0.135457 | ||||||||
\(219\) | −930.000 | −0.286957 | ||||||||
\(220\) | −400.000 | −0.122582 | ||||||||
\(221\) | −676.000 | −0.205759 | ||||||||
\(222\) | −12.0000 | −0.00362787 | ||||||||
\(223\) | −3740.00 | −1.12309 | −0.561545 | − | 0.827446i | \(-0.689793\pi\) | ||||
−0.561545 | + | 0.827446i | \(0.689793\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 225.000 | 0.0666667 | ||||||||
\(226\) | 3640.00 | 1.07137 | ||||||||
\(227\) | 2652.00 | 0.775416 | 0.387708 | − | 0.921782i | \(-0.373267\pi\) | ||||
0.387708 | + | 0.921782i | \(0.373267\pi\) | |||||||
\(228\) | 504.000 | 0.146396 | ||||||||
\(229\) | −20.0000 | −0.00577134 | −0.00288567 | − | 0.999996i | \(-0.500919\pi\) | ||||
−0.00288567 | + | 0.999996i | \(0.500919\pi\) | |||||||
\(230\) | −1940.00 | −0.556173 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −336.000 | −0.0950840 | ||||||||
\(233\) | −1288.00 | −0.362145 | −0.181072 | − | 0.983470i | \(-0.557957\pi\) | ||||
−0.181072 | + | 0.983470i | \(0.557957\pi\) | |||||||
\(234\) | 468.000 | 0.130744 | ||||||||
\(235\) | −1640.00 | −0.455242 | ||||||||
\(236\) | 1952.00 | 0.538408 | ||||||||
\(237\) | 1752.00 | 0.480188 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 3632.00 | 0.982990 | 0.491495 | − | 0.870880i | \(-0.336451\pi\) | ||||
0.491495 | + | 0.870880i | \(0.336451\pi\) | |||||||
\(240\) | −240.000 | −0.0645497 | ||||||||
\(241\) | −2216.00 | −0.592303 | −0.296152 | − | 0.955141i | \(-0.595703\pi\) | ||||
−0.296152 | + | 0.955141i | \(0.595703\pi\) | |||||||
\(242\) | −1862.00 | −0.494603 | ||||||||
\(243\) | −243.000 | −0.0641500 | ||||||||
\(244\) | 1088.00 | 0.285459 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 1500.00 | 0.388766 | ||||||||
\(247\) | −1092.00 | −0.281305 | ||||||||
\(248\) | 2192.00 | 0.561259 | ||||||||
\(249\) | −1212.00 | −0.308463 | ||||||||
\(250\) | 250.000 | 0.0632456 | ||||||||
\(251\) | −1576.00 | −0.396320 | −0.198160 | − | 0.980170i | \(-0.563497\pi\) | ||||
−0.198160 | + | 0.980170i | \(0.563497\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 3880.00 | 0.964164 | ||||||||
\(254\) | −192.000 | −0.0474297 | ||||||||
\(255\) | 390.000 | 0.0957755 | ||||||||
\(256\) | 256.000 | 0.0625000 | ||||||||
\(257\) | −7710.00 | −1.87135 | −0.935674 | − | 0.352865i | \(-0.885208\pi\) | ||||
−0.935674 | + | 0.352865i | \(0.885208\pi\) | |||||||
\(258\) | 1776.00 | 0.428562 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 520.000 | 0.124035 | ||||||||
\(261\) | −378.000 | −0.0896460 | ||||||||
\(262\) | −3744.00 | −0.882844 | ||||||||
\(263\) | −3990.00 | −0.935490 | −0.467745 | − | 0.883863i | \(-0.654933\pi\) | ||||
−0.467745 | + | 0.883863i | \(0.654933\pi\) | |||||||
\(264\) | 480.000 | 0.111901 | ||||||||
\(265\) | −740.000 | −0.171539 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 798.000 | 0.182909 | ||||||||
\(268\) | 32.0000 | 0.00729370 | ||||||||
\(269\) | −4370.00 | −0.990497 | −0.495248 | − | 0.868751i | \(-0.664923\pi\) | ||||
−0.495248 | + | 0.868751i | \(0.664923\pi\) | |||||||
\(270\) | −270.000 | −0.0608581 | ||||||||
\(271\) | 7630.00 | 1.71029 | 0.855147 | − | 0.518386i | \(-0.173467\pi\) | ||||
0.855147 | + | 0.518386i | \(0.173467\pi\) | |||||||
\(272\) | −416.000 | −0.0927342 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −632.000 | −0.139345 | ||||||||
\(275\) | −500.000 | −0.109640 | ||||||||
\(276\) | 2328.00 | 0.507714 | ||||||||
\(277\) | 434.000 | 0.0941391 | 0.0470696 | − | 0.998892i | \(-0.485012\pi\) | ||||
0.0470696 | + | 0.998892i | \(0.485012\pi\) | |||||||
\(278\) | −524.000 | −0.113048 | ||||||||
\(279\) | 2466.00 | 0.529160 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 4858.00 | 1.03133 | 0.515665 | − | 0.856790i | \(-0.327545\pi\) | ||||
0.515665 | + | 0.856790i | \(0.327545\pi\) | |||||||
\(282\) | 1968.00 | 0.415577 | ||||||||
\(283\) | −9200.00 | −1.93245 | −0.966225 | − | 0.257701i | \(-0.917035\pi\) | ||||
−0.966225 | + | 0.257701i | \(0.917035\pi\) | |||||||
\(284\) | −2736.00 | −0.571661 | ||||||||
\(285\) | 630.000 | 0.130940 | ||||||||
\(286\) | −1040.00 | −0.215023 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 288.000 | 0.0589256 | ||||||||
\(289\) | −4237.00 | −0.862406 | ||||||||
\(290\) | −420.000 | −0.0850457 | ||||||||
\(291\) | 2034.00 | 0.409743 | ||||||||
\(292\) | 1240.00 | 0.248512 | ||||||||
\(293\) | −6162.00 | −1.22863 | −0.614314 | − | 0.789062i | \(-0.710567\pi\) | ||||
−0.614314 | + | 0.789062i | \(0.710567\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 2440.00 | 0.481567 | ||||||||
\(296\) | 16.0000 | 0.00314183 | ||||||||
\(297\) | 540.000 | 0.105502 | ||||||||
\(298\) | −4180.00 | −0.812553 | ||||||||
\(299\) | −5044.00 | −0.975592 | ||||||||
\(300\) | −300.000 | −0.0577350 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −5040.00 | −0.960329 | ||||||||
\(303\) | 1218.00 | 0.230932 | ||||||||
\(304\) | −672.000 | −0.126782 | ||||||||
\(305\) | 1360.00 | 0.255323 | ||||||||
\(306\) | −468.000 | −0.0874307 | ||||||||
\(307\) | −3956.00 | −0.735442 | −0.367721 | − | 0.929936i | \(-0.619862\pi\) | ||||
−0.367721 | + | 0.929936i | \(0.619862\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −876.000 | −0.161275 | ||||||||
\(310\) | 2740.00 | 0.502005 | ||||||||
\(311\) | 9068.00 | 1.65337 | 0.826687 | − | 0.562663i | \(-0.190223\pi\) | ||||
0.826687 | + | 0.562663i | \(0.190223\pi\) | |||||||
\(312\) | −624.000 | −0.113228 | ||||||||
\(313\) | 7318.00 | 1.32153 | 0.660763 | − | 0.750594i | \(-0.270233\pi\) | ||||
0.660763 | + | 0.750594i | \(0.270233\pi\) | |||||||
\(314\) | 1732.00 | 0.311282 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −2336.00 | −0.415855 | ||||||||
\(317\) | −4188.00 | −0.742024 | −0.371012 | − | 0.928628i | \(-0.620989\pi\) | ||||
−0.371012 | + | 0.928628i | \(0.620989\pi\) | |||||||
\(318\) | 888.000 | 0.156593 | ||||||||
\(319\) | 840.000 | 0.147433 | ||||||||
\(320\) | 320.000 | 0.0559017 | ||||||||
\(321\) | 5850.00 | 1.01718 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1092.00 | 0.188113 | ||||||||
\(324\) | 324.000 | 0.0555556 | ||||||||
\(325\) | 650.000 | 0.110940 | ||||||||
\(326\) | −6872.00 | −1.16750 | ||||||||
\(327\) | 654.000 | 0.110600 | ||||||||
\(328\) | −2000.00 | −0.336681 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 600.000 | 0.100088 | ||||||||
\(331\) | −3172.00 | −0.526734 | −0.263367 | − | 0.964696i | \(-0.584833\pi\) | ||||
−0.263367 | + | 0.964696i | \(0.584833\pi\) | |||||||
\(332\) | 1616.00 | 0.267137 | ||||||||
\(333\) | 18.0000 | 0.00296214 | ||||||||
\(334\) | −3312.00 | −0.542589 | ||||||||
\(335\) | 40.0000 | 0.00652368 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 2434.00 | 0.393437 | 0.196719 | − | 0.980460i | \(-0.436971\pi\) | ||||
0.196719 | + | 0.980460i | \(0.436971\pi\) | |||||||
\(338\) | −3042.00 | −0.489535 | ||||||||
\(339\) | −5460.00 | −0.874768 | ||||||||
\(340\) | −520.000 | −0.0829440 | ||||||||
\(341\) | −5480.00 | −0.870260 | ||||||||
\(342\) | −756.000 | −0.119532 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −2368.00 | −0.371145 | ||||||||
\(345\) | 2910.00 | 0.454113 | ||||||||
\(346\) | 4308.00 | 0.669363 | ||||||||
\(347\) | −1766.00 | −0.273210 | −0.136605 | − | 0.990626i | \(-0.543619\pi\) | ||||
−0.136605 | + | 0.990626i | \(0.543619\pi\) | |||||||
\(348\) | 504.000 | 0.0776357 | ||||||||
\(349\) | 8320.00 | 1.27610 | 0.638051 | − | 0.769994i | \(-0.279741\pi\) | ||||
0.638051 | + | 0.769994i | \(0.279741\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −702.000 | −0.106752 | ||||||||
\(352\) | −640.000 | −0.0969094 | ||||||||
\(353\) | 4818.00 | 0.726448 | 0.363224 | − | 0.931702i | \(-0.381676\pi\) | ||||
0.363224 | + | 0.931702i | \(0.381676\pi\) | |||||||
\(354\) | −2928.00 | −0.439609 | ||||||||
\(355\) | −3420.00 | −0.511309 | ||||||||
\(356\) | −1064.00 | −0.158404 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 2224.00 | 0.328330 | ||||||||
\(359\) | 464.000 | 0.0682144 | 0.0341072 | − | 0.999418i | \(-0.489141\pi\) | ||||
0.0341072 | + | 0.999418i | \(0.489141\pi\) | |||||||
\(360\) | 360.000 | 0.0527046 | ||||||||
\(361\) | −5095.00 | −0.742820 | ||||||||
\(362\) | 1024.00 | 0.148675 | ||||||||
\(363\) | 2793.00 | 0.403842 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 1550.00 | 0.222276 | ||||||||
\(366\) | −1632.00 | −0.233077 | ||||||||
\(367\) | 2492.00 | 0.354445 | 0.177223 | − | 0.984171i | \(-0.443289\pi\) | ||||
0.177223 | + | 0.984171i | \(0.443289\pi\) | |||||||
\(368\) | −3104.00 | −0.439693 | ||||||||
\(369\) | −2250.00 | −0.317426 | ||||||||
\(370\) | 20.0000 | 0.00281014 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −3288.00 | −0.458266 | ||||||||
\(373\) | 5766.00 | 0.800408 | 0.400204 | − | 0.916426i | \(-0.368939\pi\) | ||||
0.400204 | + | 0.916426i | \(0.368939\pi\) | |||||||
\(374\) | 1040.00 | 0.143789 | ||||||||
\(375\) | −375.000 | −0.0516398 | ||||||||
\(376\) | −2624.00 | −0.359900 | ||||||||
\(377\) | −1092.00 | −0.149180 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 7148.00 | 0.968781 | 0.484391 | − | 0.874852i | \(-0.339041\pi\) | ||||
0.484391 | + | 0.874852i | \(0.339041\pi\) | |||||||
\(380\) | −840.000 | −0.113398 | ||||||||
\(381\) | 288.000 | 0.0387262 | ||||||||
\(382\) | −2016.00 | −0.270020 | ||||||||
\(383\) | −728.000 | −0.0971255 | −0.0485627 | − | 0.998820i | \(-0.515464\pi\) | ||||
−0.0485627 | + | 0.998820i | \(0.515464\pi\) | |||||||
\(384\) | −384.000 | −0.0510310 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 3300.00 | 0.435144 | ||||||||
\(387\) | −2664.00 | −0.349919 | ||||||||
\(388\) | −2712.00 | −0.354848 | ||||||||
\(389\) | 114.000 | 0.0148587 | 0.00742934 | − | 0.999972i | \(-0.497635\pi\) | ||||
0.00742934 | + | 0.999972i | \(0.497635\pi\) | |||||||
\(390\) | −780.000 | −0.101274 | ||||||||
\(391\) | 5044.00 | 0.652394 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 5616.00 | 0.720839 | ||||||||
\(394\) | 624.000 | 0.0797885 | ||||||||
\(395\) | −2920.00 | −0.371952 | ||||||||
\(396\) | −720.000 | −0.0913671 | ||||||||
\(397\) | 7574.00 | 0.957502 | 0.478751 | − | 0.877951i | \(-0.341090\pi\) | ||||
0.478751 | + | 0.877951i | \(0.341090\pi\) | |||||||
\(398\) | −3412.00 | −0.429719 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 400.000 | 0.0500000 | ||||||||
\(401\) | 13790.0 | 1.71731 | 0.858653 | − | 0.512557i | \(-0.171302\pi\) | ||||
0.858653 | + | 0.512557i | \(0.171302\pi\) | |||||||
\(402\) | −48.0000 | −0.00595528 | ||||||||
\(403\) | 7124.00 | 0.880575 | ||||||||
\(404\) | −1624.00 | −0.199993 | ||||||||
\(405\) | 405.000 | 0.0496904 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −40.0000 | −0.00487156 | ||||||||
\(408\) | 624.000 | 0.0757172 | ||||||||
\(409\) | −5444.00 | −0.658163 | −0.329081 | − | 0.944302i | \(-0.606739\pi\) | ||||
−0.329081 | + | 0.944302i | \(0.606739\pi\) | |||||||
\(410\) | −2500.00 | −0.301137 | ||||||||
\(411\) | 948.000 | 0.113775 | ||||||||
\(412\) | 1168.00 | 0.139668 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −3492.00 | −0.414547 | ||||||||
\(415\) | 2020.00 | 0.238935 | ||||||||
\(416\) | 832.000 | 0.0980581 | ||||||||
\(417\) | 786.000 | 0.0923036 | ||||||||
\(418\) | 1680.00 | 0.196583 | ||||||||
\(419\) | −2052.00 | −0.239252 | −0.119626 | − | 0.992819i | \(-0.538170\pi\) | ||||
−0.119626 | + | 0.992819i | \(0.538170\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 4322.00 | 0.500336 | 0.250168 | − | 0.968202i | \(-0.419514\pi\) | ||||
0.250168 | + | 0.968202i | \(0.419514\pi\) | |||||||
\(422\) | 10072.0 | 1.16184 | ||||||||
\(423\) | −2952.00 | −0.339317 | ||||||||
\(424\) | −1184.00 | −0.135613 | ||||||||
\(425\) | −650.000 | −0.0741874 | ||||||||
\(426\) | 4104.00 | 0.466759 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −7800.00 | −0.880905 | ||||||||
\(429\) | 1560.00 | 0.175565 | ||||||||
\(430\) | −2960.00 | −0.331963 | ||||||||
\(431\) | 3660.00 | 0.409039 | 0.204520 | − | 0.978862i | \(-0.434437\pi\) | ||||
0.204520 | + | 0.978862i | \(0.434437\pi\) | |||||||
\(432\) | −432.000 | −0.0481125 | ||||||||
\(433\) | −682.000 | −0.0756924 | −0.0378462 | − | 0.999284i | \(-0.512050\pi\) | ||||
−0.0378462 | + | 0.999284i | \(0.512050\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 630.000 | 0.0694395 | ||||||||
\(436\) | −872.000 | −0.0957826 | ||||||||
\(437\) | 8148.00 | 0.891926 | ||||||||
\(438\) | −1860.00 | −0.202909 | ||||||||
\(439\) | −914.000 | −0.0993687 | −0.0496843 | − | 0.998765i | \(-0.515822\pi\) | ||||
−0.0496843 | + | 0.998765i | \(0.515822\pi\) | |||||||
\(440\) | −800.000 | −0.0866784 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −1352.00 | −0.145493 | ||||||||
\(443\) | −6958.00 | −0.746241 | −0.373120 | − | 0.927783i | \(-0.621712\pi\) | ||||
−0.373120 | + | 0.927783i | \(0.621712\pi\) | |||||||
\(444\) | −24.0000 | −0.00256529 | ||||||||
\(445\) | −1330.00 | −0.141681 | ||||||||
\(446\) | −7480.00 | −0.794144 | ||||||||
\(447\) | 6270.00 | 0.663447 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 5466.00 | 0.574513 | 0.287257 | − | 0.957854i | \(-0.407257\pi\) | ||||
0.287257 | + | 0.957854i | \(0.407257\pi\) | |||||||
\(450\) | 450.000 | 0.0471405 | ||||||||
\(451\) | 5000.00 | 0.522042 | ||||||||
\(452\) | 7280.00 | 0.757572 | ||||||||
\(453\) | 7560.00 | 0.784105 | ||||||||
\(454\) | 5304.00 | 0.548302 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 1008.00 | 0.103517 | ||||||||
\(457\) | −13986.0 | −1.43159 | −0.715796 | − | 0.698310i | \(-0.753936\pi\) | ||||
−0.715796 | + | 0.698310i | \(0.753936\pi\) | |||||||
\(458\) | −40.0000 | −0.00408095 | ||||||||
\(459\) | 702.000 | 0.0713868 | ||||||||
\(460\) | −3880.00 | −0.393274 | ||||||||
\(461\) | 11946.0 | 1.20690 | 0.603450 | − | 0.797401i | \(-0.293792\pi\) | ||||
0.603450 | + | 0.797401i | \(0.293792\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −7208.00 | −0.723508 | −0.361754 | − | 0.932274i | \(-0.617822\pi\) | ||||
−0.361754 | + | 0.932274i | \(0.617822\pi\) | |||||||
\(464\) | −672.000 | −0.0672345 | ||||||||
\(465\) | −4110.00 | −0.409885 | ||||||||
\(466\) | −2576.00 | −0.256075 | ||||||||
\(467\) | 3988.00 | 0.395166 | 0.197583 | − | 0.980286i | \(-0.436691\pi\) | ||||
0.197583 | + | 0.980286i | \(0.436691\pi\) | |||||||
\(468\) | 936.000 | 0.0924500 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −3280.00 | −0.321905 | ||||||||
\(471\) | −2598.00 | −0.254160 | ||||||||
\(472\) | 3904.00 | 0.380712 | ||||||||
\(473\) | 5920.00 | 0.575480 | ||||||||
\(474\) | 3504.00 | 0.339544 | ||||||||
\(475\) | −1050.00 | −0.101426 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −1332.00 | −0.127858 | ||||||||
\(478\) | 7264.00 | 0.695079 | ||||||||
\(479\) | 7796.00 | 0.743650 | 0.371825 | − | 0.928303i | \(-0.378732\pi\) | ||||
0.371825 | + | 0.928303i | \(0.378732\pi\) | |||||||
\(480\) | −480.000 | −0.0456435 | ||||||||
\(481\) | 52.0000 | 0.00492931 | ||||||||
\(482\) | −4432.00 | −0.418822 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −3724.00 | −0.349737 | ||||||||
\(485\) | −3390.00 | −0.317386 | ||||||||
\(486\) | −486.000 | −0.0453609 | ||||||||
\(487\) | 16324.0 | 1.51891 | 0.759457 | − | 0.650558i | \(-0.225465\pi\) | ||||
0.759457 | + | 0.650558i | \(0.225465\pi\) | |||||||
\(488\) | 2176.00 | 0.201850 | ||||||||
\(489\) | 10308.0 | 0.953259 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 17856.0 | 1.64120 | 0.820601 | − | 0.571502i | \(-0.193639\pi\) | ||||
0.820601 | + | 0.571502i | \(0.193639\pi\) | |||||||
\(492\) | 3000.00 | 0.274899 | ||||||||
\(493\) | 1092.00 | 0.0997590 | ||||||||
\(494\) | −2184.00 | −0.198913 | ||||||||
\(495\) | −900.000 | −0.0817212 | ||||||||
\(496\) | 4384.00 | 0.396870 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −2424.00 | −0.218117 | ||||||||
\(499\) | 3412.00 | 0.306096 | 0.153048 | − | 0.988219i | \(-0.451091\pi\) | ||||
0.153048 | + | 0.988219i | \(0.451091\pi\) | |||||||
\(500\) | 500.000 | 0.0447214 | ||||||||
\(501\) | 4968.00 | 0.443022 | ||||||||
\(502\) | −3152.00 | −0.280240 | ||||||||
\(503\) | −15912.0 | −1.41050 | −0.705250 | − | 0.708959i | \(-0.749165\pi\) | ||||
−0.705250 | + | 0.708959i | \(0.749165\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −2030.00 | −0.178879 | ||||||||
\(506\) | 7760.00 | 0.681767 | ||||||||
\(507\) | 4563.00 | 0.399704 | ||||||||
\(508\) | −384.000 | −0.0335379 | ||||||||
\(509\) | −13434.0 | −1.16985 | −0.584923 | − | 0.811089i | \(-0.698875\pi\) | ||||
−0.584923 | + | 0.811089i | \(0.698875\pi\) | |||||||
\(510\) | 780.000 | 0.0677235 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 512.000 | 0.0441942 | ||||||||
\(513\) | 1134.00 | 0.0975971 | ||||||||
\(514\) | −15420.0 | −1.32324 | ||||||||
\(515\) | 1460.00 | 0.124923 | ||||||||
\(516\) | 3552.00 | 0.303039 | ||||||||
\(517\) | 6560.00 | 0.558043 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −6462.00 | −0.546532 | ||||||||
\(520\) | 1040.00 | 0.0877058 | ||||||||
\(521\) | 19578.0 | 1.64631 | 0.823155 | − | 0.567816i | \(-0.192212\pi\) | ||||
0.823155 | + | 0.567816i | \(0.192212\pi\) | |||||||
\(522\) | −756.000 | −0.0633893 | ||||||||
\(523\) | 20288.0 | 1.69624 | 0.848119 | − | 0.529806i | \(-0.177735\pi\) | ||||
0.848119 | + | 0.529806i | \(0.177735\pi\) | |||||||
\(524\) | −7488.00 | −0.624265 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −7980.00 | −0.661492 | ||||||||
\(527\) | −7124.00 | −0.588854 | ||||||||
\(528\) | 960.000 | 0.0791262 | ||||||||
\(529\) | 25469.0 | 2.09329 | ||||||||
\(530\) | −1480.00 | −0.121296 | ||||||||
\(531\) | 4392.00 | 0.358939 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −6500.00 | −0.528229 | ||||||||
\(534\) | 1596.00 | 0.129336 | ||||||||
\(535\) | −9750.00 | −0.787905 | ||||||||
\(536\) | 64.0000 | 0.00515742 | ||||||||
\(537\) | −3336.00 | −0.268080 | ||||||||
\(538\) | −8740.00 | −0.700387 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −540.000 | −0.0430331 | ||||||||
\(541\) | 12170.0 | 0.967152 | 0.483576 | − | 0.875302i | \(-0.339338\pi\) | ||||
0.483576 | + | 0.875302i | \(0.339338\pi\) | |||||||
\(542\) | 15260.0 | 1.20936 | ||||||||
\(543\) | −1536.00 | −0.121392 | ||||||||
\(544\) | −832.000 | −0.0655730 | ||||||||
\(545\) | −1090.00 | −0.0856706 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 11368.0 | 0.888593 | 0.444297 | − | 0.895880i | \(-0.353454\pi\) | ||||
0.444297 | + | 0.895880i | \(0.353454\pi\) | |||||||
\(548\) | −1264.00 | −0.0985318 | ||||||||
\(549\) | 2448.00 | 0.190306 | ||||||||
\(550\) | −1000.00 | −0.0775275 | ||||||||
\(551\) | 1764.00 | 0.136386 | ||||||||
\(552\) | 4656.00 | 0.359008 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 868.000 | 0.0665664 | ||||||||
\(555\) | −30.0000 | −0.00229447 | ||||||||
\(556\) | −1048.00 | −0.0799372 | ||||||||
\(557\) | 9444.00 | 0.718411 | 0.359206 | − | 0.933258i | \(-0.383048\pi\) | ||||
0.359206 | + | 0.933258i | \(0.383048\pi\) | |||||||
\(558\) | 4932.00 | 0.374172 | ||||||||
\(559\) | −7696.00 | −0.582301 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −1560.00 | −0.117403 | ||||||||
\(562\) | 9716.00 | 0.729261 | ||||||||
\(563\) | −3708.00 | −0.277573 | −0.138786 | − | 0.990322i | \(-0.544320\pi\) | ||||
−0.138786 | + | 0.990322i | \(0.544320\pi\) | |||||||
\(564\) | 3936.00 | 0.293857 | ||||||||
\(565\) | 9100.00 | 0.677593 | ||||||||
\(566\) | −18400.0 | −1.36645 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −5472.00 | −0.404225 | ||||||||
\(569\) | 17270.0 | 1.27240 | 0.636200 | − | 0.771524i | \(-0.280505\pi\) | ||||
0.636200 | + | 0.771524i | \(0.280505\pi\) | |||||||
\(570\) | 1260.00 | 0.0925888 | ||||||||
\(571\) | 8364.00 | 0.612999 | 0.306500 | − | 0.951871i | \(-0.400842\pi\) | ||||
0.306500 | + | 0.951871i | \(0.400842\pi\) | |||||||
\(572\) | −2080.00 | −0.152044 | ||||||||
\(573\) | 3024.00 | 0.220470 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −4850.00 | −0.351755 | ||||||||
\(576\) | 576.000 | 0.0416667 | ||||||||
\(577\) | −4682.00 | −0.337806 | −0.168903 | − | 0.985633i | \(-0.554023\pi\) | ||||
−0.168903 | + | 0.985633i | \(0.554023\pi\) | |||||||
\(578\) | −8474.00 | −0.609813 | ||||||||
\(579\) | −4950.00 | −0.355294 | ||||||||
\(580\) | −840.000 | −0.0601364 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 4068.00 | 0.289732 | ||||||||
\(583\) | 2960.00 | 0.210276 | ||||||||
\(584\) | 2480.00 | 0.175725 | ||||||||
\(585\) | 1170.00 | 0.0826898 | ||||||||
\(586\) | −12324.0 | −0.868771 | ||||||||
\(587\) | −27620.0 | −1.94208 | −0.971039 | − | 0.238922i | \(-0.923206\pi\) | ||||
−0.971039 | + | 0.238922i | \(0.923206\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −11508.0 | −0.805058 | ||||||||
\(590\) | 4880.00 | 0.340519 | ||||||||
\(591\) | −936.000 | −0.0651470 | ||||||||
\(592\) | 32.0000 | 0.00222161 | ||||||||
\(593\) | 6578.00 | 0.455525 | 0.227762 | − | 0.973717i | \(-0.426859\pi\) | ||||
0.227762 | + | 0.973717i | \(0.426859\pi\) | |||||||
\(594\) | 1080.00 | 0.0746009 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −8360.00 | −0.574562 | ||||||||
\(597\) | 5118.00 | 0.350864 | ||||||||
\(598\) | −10088.0 | −0.689848 | ||||||||
\(599\) | 23704.0 | 1.61689 | 0.808447 | − | 0.588569i | \(-0.200309\pi\) | ||||
0.808447 | + | 0.588569i | \(0.200309\pi\) | |||||||
\(600\) | −600.000 | −0.0408248 | ||||||||
\(601\) | 388.000 | 0.0263342 | 0.0131671 | − | 0.999913i | \(-0.495809\pi\) | ||||
0.0131671 | + | 0.999913i | \(0.495809\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 72.0000 | 0.00486247 | ||||||||
\(604\) | −10080.0 | −0.679055 | ||||||||
\(605\) | −4655.00 | −0.312814 | ||||||||
\(606\) | 2436.00 | 0.163293 | ||||||||
\(607\) | −5644.00 | −0.377402 | −0.188701 | − | 0.982035i | \(-0.560428\pi\) | ||||
−0.188701 | + | 0.982035i | \(0.560428\pi\) | |||||||
\(608\) | −1344.00 | −0.0896487 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 2720.00 | 0.180540 | ||||||||
\(611\) | −8528.00 | −0.564658 | ||||||||
\(612\) | −936.000 | −0.0618228 | ||||||||
\(613\) | 14290.0 | 0.941546 | 0.470773 | − | 0.882254i | \(-0.343975\pi\) | ||||
0.470773 | + | 0.882254i | \(0.343975\pi\) | |||||||
\(614\) | −7912.00 | −0.520036 | ||||||||
\(615\) | 3750.00 | 0.245877 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −23808.0 | −1.55344 | −0.776721 | − | 0.629845i | \(-0.783119\pi\) | ||||
−0.776721 | + | 0.629845i | \(0.783119\pi\) | |||||||
\(618\) | −1752.00 | −0.114038 | ||||||||
\(619\) | −12798.0 | −0.831010 | −0.415505 | − | 0.909591i | \(-0.636395\pi\) | ||||
−0.415505 | + | 0.909591i | \(0.636395\pi\) | |||||||
\(620\) | 5480.00 | 0.354971 | ||||||||
\(621\) | 5238.00 | 0.338476 | ||||||||
\(622\) | 18136.0 | 1.16911 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −1248.00 | −0.0800641 | ||||||||
\(625\) | 625.000 | 0.0400000 | ||||||||
\(626\) | 14636.0 | 0.934460 | ||||||||
\(627\) | −2520.00 | −0.160509 | ||||||||
\(628\) | 3464.00 | 0.220109 | ||||||||
\(629\) | −52.0000 | −0.00329630 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −8744.00 | −0.551653 | −0.275827 | − | 0.961207i | \(-0.588952\pi\) | ||||
−0.275827 | + | 0.961207i | \(0.588952\pi\) | |||||||
\(632\) | −4672.00 | −0.294054 | ||||||||
\(633\) | −15108.0 | −0.948640 | ||||||||
\(634\) | −8376.00 | −0.524690 | ||||||||
\(635\) | −480.000 | −0.0299972 | ||||||||
\(636\) | 1776.00 | 0.110728 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 1680.00 | 0.104251 | ||||||||
\(639\) | −6156.00 | −0.381107 | ||||||||
\(640\) | 640.000 | 0.0395285 | ||||||||
\(641\) | 24738.0 | 1.52432 | 0.762162 | − | 0.647386i | \(-0.224138\pi\) | ||||
0.762162 | + | 0.647386i | \(0.224138\pi\) | |||||||
\(642\) | 11700.0 | 0.719256 | ||||||||
\(643\) | −3828.00 | −0.234777 | −0.117388 | − | 0.993086i | \(-0.537452\pi\) | ||||
−0.117388 | + | 0.993086i | \(0.537452\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 4440.00 | 0.271046 | ||||||||
\(646\) | 2184.00 | 0.133016 | ||||||||
\(647\) | −14272.0 | −0.867218 | −0.433609 | − | 0.901101i | \(-0.642760\pi\) | ||||
−0.433609 | + | 0.901101i | \(0.642760\pi\) | |||||||
\(648\) | 648.000 | 0.0392837 | ||||||||
\(649\) | −9760.00 | −0.590314 | ||||||||
\(650\) | 1300.00 | 0.0784465 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −13744.0 | −0.825547 | ||||||||
\(653\) | 16468.0 | 0.986895 | 0.493448 | − | 0.869775i | \(-0.335736\pi\) | ||||
0.493448 | + | 0.869775i | \(0.335736\pi\) | |||||||
\(654\) | 1308.00 | 0.0782062 | ||||||||
\(655\) | −9360.00 | −0.558359 | ||||||||
\(656\) | −4000.00 | −0.238070 | ||||||||
\(657\) | 2790.00 | 0.165675 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −18416.0 | −1.08860 | −0.544299 | − | 0.838892i | \(-0.683204\pi\) | ||||
−0.544299 | + | 0.838892i | \(0.683204\pi\) | |||||||
\(660\) | 1200.00 | 0.0707726 | ||||||||
\(661\) | 30568.0 | 1.79873 | 0.899363 | − | 0.437203i | \(-0.144031\pi\) | ||||
0.899363 | + | 0.437203i | \(0.144031\pi\) | |||||||
\(662\) | −6344.00 | −0.372457 | ||||||||
\(663\) | 2028.00 | 0.118795 | ||||||||
\(664\) | 3232.00 | 0.188894 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 36.0000 | 0.00209455 | ||||||||
\(667\) | 8148.00 | 0.473001 | ||||||||
\(668\) | −6624.00 | −0.383668 | ||||||||
\(669\) | 11220.0 | 0.648416 | ||||||||
\(670\) | 80.0000 | 0.00461294 | ||||||||
\(671\) | −5440.00 | −0.312979 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −7970.00 | −0.456495 | −0.228247 | − | 0.973603i | \(-0.573299\pi\) | ||||
−0.228247 | + | 0.973603i | \(0.573299\pi\) | |||||||
\(674\) | 4868.00 | 0.278202 | ||||||||
\(675\) | −675.000 | −0.0384900 | ||||||||
\(676\) | −6084.00 | −0.346154 | ||||||||
\(677\) | −34394.0 | −1.95254 | −0.976269 | − | 0.216559i | \(-0.930516\pi\) | ||||
−0.976269 | + | 0.216559i | \(0.930516\pi\) | |||||||
\(678\) | −10920.0 | −0.618555 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −1040.00 | −0.0586503 | ||||||||
\(681\) | −7956.00 | −0.447687 | ||||||||
\(682\) | −10960.0 | −0.615367 | ||||||||
\(683\) | 1818.00 | 0.101850 | 0.0509252 | − | 0.998702i | \(-0.483783\pi\) | ||||
0.0509252 | + | 0.998702i | \(0.483783\pi\) | |||||||
\(684\) | −1512.00 | −0.0845216 | ||||||||
\(685\) | −1580.00 | −0.0881295 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 60.0000 | 0.00333209 | ||||||||
\(688\) | −4736.00 | −0.262439 | ||||||||
\(689\) | −3848.00 | −0.212768 | ||||||||
\(690\) | 5820.00 | 0.321107 | ||||||||
\(691\) | 11774.0 | 0.648197 | 0.324098 | − | 0.946023i | \(-0.394939\pi\) | ||||
0.324098 | + | 0.946023i | \(0.394939\pi\) | |||||||
\(692\) | 8616.00 | 0.473311 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −3532.00 | −0.193189 | ||||||||
\(695\) | −1310.00 | −0.0714980 | ||||||||
\(696\) | 1008.00 | 0.0548968 | ||||||||
\(697\) | 6500.00 | 0.353235 | ||||||||
\(698\) | 16640.0 | 0.902340 | ||||||||
\(699\) | 3864.00 | 0.209084 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −28138.0 | −1.51606 | −0.758030 | − | 0.652220i | \(-0.773838\pi\) | ||||
−0.758030 | + | 0.652220i | \(0.773838\pi\) | |||||||
\(702\) | −1404.00 | −0.0754851 | ||||||||
\(703\) | −84.0000 | −0.00450657 | ||||||||
\(704\) | −1280.00 | −0.0685253 | ||||||||
\(705\) | 4920.00 | 0.262834 | ||||||||
\(706\) | 9636.00 | 0.513677 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −5856.00 | −0.310850 | ||||||||
\(709\) | 5754.00 | 0.304790 | 0.152395 | − | 0.988320i | \(-0.451301\pi\) | ||||
0.152395 | + | 0.988320i | \(0.451301\pi\) | |||||||
\(710\) | −6840.00 | −0.361550 | ||||||||
\(711\) | −5256.00 | −0.277237 | ||||||||
\(712\) | −2128.00 | −0.112009 | ||||||||
\(713\) | −53156.0 | −2.79202 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −2600.00 | −0.135992 | ||||||||
\(716\) | 4448.00 | 0.232164 | ||||||||
\(717\) | −10896.0 | −0.567529 | ||||||||
\(718\) | 928.000 | 0.0482349 | ||||||||
\(719\) | −34428.0 | −1.78574 | −0.892870 | − | 0.450314i | \(-0.851312\pi\) | ||||
−0.892870 | + | 0.450314i | \(0.851312\pi\) | |||||||
\(720\) | 720.000 | 0.0372678 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −10190.0 | −0.525253 | ||||||||
\(723\) | 6648.00 | 0.341967 | ||||||||
\(724\) | 2048.00 | 0.105129 | ||||||||
\(725\) | −1050.00 | −0.0537876 | ||||||||
\(726\) | 5586.00 | 0.285559 | ||||||||
\(727\) | 28472.0 | 1.45250 | 0.726250 | − | 0.687430i | \(-0.241261\pi\) | ||||
0.726250 | + | 0.687430i | \(0.241261\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | 3100.00 | 0.157173 | ||||||||
\(731\) | 7696.00 | 0.389394 | ||||||||
\(732\) | −3264.00 | −0.164810 | ||||||||
\(733\) | 23586.0 | 1.18850 | 0.594249 | − | 0.804281i | \(-0.297449\pi\) | ||||
0.594249 | + | 0.804281i | \(0.297449\pi\) | |||||||
\(734\) | 4984.00 | 0.250631 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −6208.00 | −0.310910 | ||||||||
\(737\) | −160.000 | −0.00799685 | ||||||||
\(738\) | −4500.00 | −0.224454 | ||||||||
\(739\) | −28116.0 | −1.39955 | −0.699773 | − | 0.714366i | \(-0.746715\pi\) | ||||
−0.699773 | + | 0.714366i | \(0.746715\pi\) | |||||||
\(740\) | 40.0000 | 0.00198707 | ||||||||
\(741\) | 3276.00 | 0.162411 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 25446.0 | 1.25642 | 0.628212 | − | 0.778042i | \(-0.283787\pi\) | ||||
0.628212 | + | 0.778042i | \(0.283787\pi\) | |||||||
\(744\) | −6576.00 | −0.324043 | ||||||||
\(745\) | −10450.0 | −0.513904 | ||||||||
\(746\) | 11532.0 | 0.565974 | ||||||||
\(747\) | 3636.00 | 0.178091 | ||||||||
\(748\) | 2080.00 | 0.101674 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −750.000 | −0.0365148 | ||||||||
\(751\) | 18856.0 | 0.916199 | 0.458099 | − | 0.888901i | \(-0.348530\pi\) | ||||
0.458099 | + | 0.888901i | \(0.348530\pi\) | |||||||
\(752\) | −5248.00 | −0.254488 | ||||||||
\(753\) | 4728.00 | 0.228815 | ||||||||
\(754\) | −2184.00 | −0.105486 | ||||||||
\(755\) | −12600.0 | −0.607365 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 3382.00 | 0.162379 | 0.0811895 | − | 0.996699i | \(-0.474128\pi\) | ||||
0.0811895 | + | 0.996699i | \(0.474128\pi\) | |||||||
\(758\) | 14296.0 | 0.685032 | ||||||||
\(759\) | −11640.0 | −0.556660 | ||||||||
\(760\) | −1680.00 | −0.0801842 | ||||||||
\(761\) | −4434.00 | −0.211212 | −0.105606 | − | 0.994408i | \(-0.533678\pi\) | ||||
−0.105606 | + | 0.994408i | \(0.533678\pi\) | |||||||
\(762\) | 576.000 | 0.0273836 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −4032.00 | −0.190933 | ||||||||
\(765\) | −1170.00 | −0.0552960 | ||||||||
\(766\) | −1456.00 | −0.0686781 | ||||||||
\(767\) | 12688.0 | 0.597310 | ||||||||
\(768\) | −768.000 | −0.0360844 | ||||||||
\(769\) | 10540.0 | 0.494255 | 0.247128 | − | 0.968983i | \(-0.420513\pi\) | ||||
0.247128 | + | 0.968983i | \(0.420513\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 23130.0 | 1.08042 | ||||||||
\(772\) | 6600.00 | 0.307693 | ||||||||
\(773\) | −19902.0 | −0.926035 | −0.463018 | − | 0.886349i | \(-0.653233\pi\) | ||||
−0.463018 | + | 0.886349i | \(0.653233\pi\) | |||||||
\(774\) | −5328.00 | −0.247430 | ||||||||
\(775\) | 6850.00 | 0.317496 | ||||||||
\(776\) | −5424.00 | −0.250915 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 228.000 | 0.0105067 | ||||||||
\(779\) | 10500.0 | 0.482929 | ||||||||
\(780\) | −1560.00 | −0.0716115 | ||||||||
\(781\) | 13680.0 | 0.626772 | ||||||||
\(782\) | 10088.0 | 0.461312 | ||||||||
\(783\) | 1134.00 | 0.0517572 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 4330.00 | 0.196872 | ||||||||
\(786\) | 11232.0 | 0.509710 | ||||||||
\(787\) | 32304.0 | 1.46317 | 0.731584 | − | 0.681751i | \(-0.238781\pi\) | ||||
0.731584 | + | 0.681751i | \(0.238781\pi\) | |||||||
\(788\) | 1248.00 | 0.0564190 | ||||||||
\(789\) | 11970.0 | 0.540106 | ||||||||
\(790\) | −5840.00 | −0.263010 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −1440.00 | −0.0646063 | ||||||||
\(793\) | 7072.00 | 0.316689 | ||||||||
\(794\) | 15148.0 | 0.677056 | ||||||||
\(795\) | 2220.00 | 0.0990381 | ||||||||
\(796\) | −6824.00 | −0.303857 | ||||||||
\(797\) | 20410.0 | 0.907101 | 0.453550 | − | 0.891231i | \(-0.350157\pi\) | ||||
0.453550 | + | 0.891231i | \(0.350157\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 8528.00 | 0.377596 | ||||||||
\(800\) | 800.000 | 0.0353553 | ||||||||
\(801\) | −2394.00 | −0.105603 | ||||||||
\(802\) | 27580.0 | 1.21432 | ||||||||
\(803\) | −6200.00 | −0.272470 | ||||||||
\(804\) | −96.0000 | −0.00421102 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 14248.0 | 0.622661 | ||||||||
\(807\) | 13110.0 | 0.571864 | ||||||||
\(808\) | −3248.00 | −0.141416 | ||||||||
\(809\) | −14138.0 | −0.614420 | −0.307210 | − | 0.951642i | \(-0.599395\pi\) | ||||
−0.307210 | + | 0.951642i | \(0.599395\pi\) | |||||||
\(810\) | 810.000 | 0.0351364 | ||||||||
\(811\) | 43442.0 | 1.88096 | 0.940478 | − | 0.339855i | \(-0.110378\pi\) | ||||
0.940478 | + | 0.339855i | \(0.110378\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −22890.0 | −0.987438 | ||||||||
\(814\) | −80.0000 | −0.00344472 | ||||||||
\(815\) | −17180.0 | −0.738392 | ||||||||
\(816\) | 1248.00 | 0.0535401 | ||||||||
\(817\) | 12432.0 | 0.532363 | ||||||||
\(818\) | −10888.0 | −0.465391 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −5000.00 | −0.212936 | ||||||||
\(821\) | −21750.0 | −0.924580 | −0.462290 | − | 0.886729i | \(-0.652972\pi\) | ||||
−0.462290 | + | 0.886729i | \(0.652972\pi\) | |||||||
\(822\) | 1896.00 | 0.0804508 | ||||||||
\(823\) | 3632.00 | 0.153832 | 0.0769159 | − | 0.997038i | \(-0.475493\pi\) | ||||
0.0769159 | + | 0.997038i | \(0.475493\pi\) | |||||||
\(824\) | 2336.00 | 0.0987602 | ||||||||
\(825\) | 1500.00 | 0.0633010 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −9806.00 | −0.412319 | −0.206160 | − | 0.978518i | \(-0.566097\pi\) | ||||
−0.206160 | + | 0.978518i | \(0.566097\pi\) | |||||||
\(828\) | −6984.00 | −0.293129 | ||||||||
\(829\) | 18128.0 | 0.759483 | 0.379742 | − | 0.925093i | \(-0.376013\pi\) | ||||
0.379742 | + | 0.925093i | \(0.376013\pi\) | |||||||
\(830\) | 4040.00 | 0.168952 | ||||||||
\(831\) | −1302.00 | −0.0543512 | ||||||||
\(832\) | 1664.00 | 0.0693375 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 1572.00 | 0.0652685 | ||||||||
\(835\) | −8280.00 | −0.343163 | ||||||||
\(836\) | 3360.00 | 0.139005 | ||||||||
\(837\) | −7398.00 | −0.305510 | ||||||||
\(838\) | −4104.00 | −0.169177 | ||||||||
\(839\) | −35544.0 | −1.46259 | −0.731296 | − | 0.682060i | \(-0.761084\pi\) | ||||
−0.731296 | + | 0.682060i | \(0.761084\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −22625.0 | −0.927672 | ||||||||
\(842\) | 8644.00 | 0.353791 | ||||||||
\(843\) | −14574.0 | −0.595439 | ||||||||
\(844\) | 20144.0 | 0.821546 | ||||||||
\(845\) | −7605.00 | −0.309609 | ||||||||
\(846\) | −5904.00 | −0.239933 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −2368.00 | −0.0958932 | ||||||||
\(849\) | 27600.0 | 1.11570 | ||||||||
\(850\) | −1300.00 | −0.0524584 | ||||||||
\(851\) | −388.000 | −0.0156292 | ||||||||
\(852\) | 8208.00 | 0.330049 | ||||||||
\(853\) | −39490.0 | −1.58513 | −0.792563 | − | 0.609791i | \(-0.791254\pi\) | ||||
−0.792563 | + | 0.609791i | \(0.791254\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −1890.00 | −0.0755984 | ||||||||
\(856\) | −15600.0 | −0.622894 | ||||||||
\(857\) | 39990.0 | 1.59397 | 0.796985 | − | 0.603999i | \(-0.206427\pi\) | ||||
0.796985 | + | 0.603999i | \(0.206427\pi\) | |||||||
\(858\) | 3120.00 | 0.124143 | ||||||||
\(859\) | 6098.00 | 0.242213 | 0.121107 | − | 0.992640i | \(-0.461356\pi\) | ||||
0.121107 | + | 0.992640i | \(0.461356\pi\) | |||||||
\(860\) | −5920.00 | −0.234733 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 7320.00 | 0.289235 | ||||||||
\(863\) | 13614.0 | 0.536994 | 0.268497 | − | 0.963280i | \(-0.413473\pi\) | ||||
0.268497 | + | 0.963280i | \(0.413473\pi\) | |||||||
\(864\) | −864.000 | −0.0340207 | ||||||||
\(865\) | 10770.0 | 0.423342 | ||||||||
\(866\) | −1364.00 | −0.0535226 | ||||||||
\(867\) | 12711.0 | 0.497910 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 11680.0 | 0.455946 | ||||||||
\(870\) | 1260.00 | 0.0491012 | ||||||||
\(871\) | 208.000 | 0.00809163 | ||||||||
\(872\) | −1744.00 | −0.0677285 | ||||||||
\(873\) | −6102.00 | −0.236565 | ||||||||
\(874\) | 16296.0 | 0.630687 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −3720.00 | −0.143478 | ||||||||
\(877\) | 32994.0 | 1.27039 | 0.635193 | − | 0.772354i | \(-0.280921\pi\) | ||||
0.635193 | + | 0.772354i | \(0.280921\pi\) | |||||||
\(878\) | −1828.00 | −0.0702643 | ||||||||
\(879\) | 18486.0 | 0.709348 | ||||||||
\(880\) | −1600.00 | −0.0612909 | ||||||||
\(881\) | 9202.00 | 0.351899 | 0.175950 | − | 0.984399i | \(-0.443700\pi\) | ||||
0.175950 | + | 0.984399i | \(0.443700\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −41420.0 | −1.57859 | −0.789294 | − | 0.614015i | \(-0.789553\pi\) | ||||
−0.789294 | + | 0.614015i | \(0.789553\pi\) | |||||||
\(884\) | −2704.00 | −0.102879 | ||||||||
\(885\) | −7320.00 | −0.278033 | ||||||||
\(886\) | −13916.0 | −0.527672 | ||||||||
\(887\) | −2320.00 | −0.0878218 | −0.0439109 | − | 0.999035i | \(-0.513982\pi\) | ||||
−0.0439109 | + | 0.999035i | \(0.513982\pi\) | |||||||
\(888\) | −48.0000 | −0.00181394 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −2660.00 | −0.100184 | ||||||||
\(891\) | −1620.00 | −0.0609114 | ||||||||
\(892\) | −14960.0 | −0.561545 | ||||||||
\(893\) | 13776.0 | 0.516233 | ||||||||
\(894\) | 12540.0 | 0.469128 | ||||||||
\(895\) | 5560.00 | 0.207654 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 15132.0 | 0.563258 | ||||||||
\(898\) | 10932.0 | 0.406242 | ||||||||
\(899\) | −11508.0 | −0.426934 | ||||||||
\(900\) | 900.000 | 0.0333333 | ||||||||
\(901\) | 3848.00 | 0.142281 | ||||||||
\(902\) | 10000.0 | 0.369139 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 14560.0 | 0.535684 | ||||||||
\(905\) | 2560.00 | 0.0940301 | ||||||||
\(906\) | 15120.0 | 0.554446 | ||||||||
\(907\) | −46244.0 | −1.69295 | −0.846476 | − | 0.532427i | \(-0.821280\pi\) | ||||
−0.846476 | + | 0.532427i | \(0.821280\pi\) | |||||||
\(908\) | 10608.0 | 0.387708 | ||||||||
\(909\) | −3654.00 | −0.133328 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 3992.00 | 0.145182 | 0.0725910 | − | 0.997362i | \(-0.476873\pi\) | ||||
0.0725910 | + | 0.997362i | \(0.476873\pi\) | |||||||
\(912\) | 2016.00 | 0.0731978 | ||||||||
\(913\) | −8080.00 | −0.292890 | ||||||||
\(914\) | −27972.0 | −1.01229 | ||||||||
\(915\) | −4080.00 | −0.147411 | ||||||||
\(916\) | −80.0000 | −0.00288567 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 1404.00 | 0.0504781 | ||||||||
\(919\) | −31864.0 | −1.14374 | −0.571870 | − | 0.820345i | \(-0.693782\pi\) | ||||
−0.571870 | + | 0.820345i | \(0.693782\pi\) | |||||||
\(920\) | −7760.00 | −0.278087 | ||||||||
\(921\) | 11868.0 | 0.424608 | ||||||||
\(922\) | 23892.0 | 0.853407 | ||||||||
\(923\) | −17784.0 | −0.634201 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 50.0000 | 0.00177729 | ||||||||
\(926\) | −14416.0 | −0.511597 | ||||||||
\(927\) | 2628.00 | 0.0931120 | ||||||||
\(928\) | −1344.00 | −0.0475420 | ||||||||
\(929\) | −24762.0 | −0.874505 | −0.437252 | − | 0.899339i | \(-0.644048\pi\) | ||||
−0.437252 | + | 0.899339i | \(0.644048\pi\) | |||||||
\(930\) | −8220.00 | −0.289833 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −5152.00 | −0.181072 | ||||||||
\(933\) | −27204.0 | −0.954576 | ||||||||
\(934\) | 7976.00 | 0.279425 | ||||||||
\(935\) | 2600.00 | 0.0909402 | ||||||||
\(936\) | 1872.00 | 0.0653720 | ||||||||
\(937\) | −5334.00 | −0.185970 | −0.0929852 | − | 0.995667i | \(-0.529641\pi\) | ||||
−0.0929852 | + | 0.995667i | \(0.529641\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −21954.0 | −0.762984 | ||||||||
\(940\) | −6560.00 | −0.227621 | ||||||||
\(941\) | 16894.0 | 0.585259 | 0.292629 | − | 0.956226i | \(-0.405470\pi\) | ||||
0.292629 | + | 0.956226i | \(0.405470\pi\) | |||||||
\(942\) | −5196.00 | −0.179719 | ||||||||
\(943\) | 48500.0 | 1.67484 | ||||||||
\(944\) | 7808.00 | 0.269204 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 11840.0 | 0.406926 | ||||||||
\(947\) | −21378.0 | −0.733571 | −0.366785 | − | 0.930306i | \(-0.619542\pi\) | ||||
−0.366785 | + | 0.930306i | \(0.619542\pi\) | |||||||
\(948\) | 7008.00 | 0.240094 | ||||||||
\(949\) | 8060.00 | 0.275699 | ||||||||
\(950\) | −2100.00 | −0.0717189 | ||||||||
\(951\) | 12564.0 | 0.428408 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 29188.0 | 0.992122 | 0.496061 | − | 0.868288i | \(-0.334779\pi\) | ||||
0.496061 | + | 0.868288i | \(0.334779\pi\) | |||||||
\(954\) | −2664.00 | −0.0904090 | ||||||||
\(955\) | −5040.00 | −0.170775 | ||||||||
\(956\) | 14528.0 | 0.491495 | ||||||||
\(957\) | −2520.00 | −0.0851202 | ||||||||
\(958\) | 15592.0 | 0.525840 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −960.000 | −0.0322749 | ||||||||
\(961\) | 45285.0 | 1.52009 | ||||||||
\(962\) | 104.000 | 0.00348555 | ||||||||
\(963\) | −17550.0 | −0.587270 | ||||||||
\(964\) | −8864.00 | −0.296152 | ||||||||
\(965\) | 8250.00 | 0.275209 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 49676.0 | 1.65199 | 0.825994 | − | 0.563679i | \(-0.190614\pi\) | ||||
0.825994 | + | 0.563679i | \(0.190614\pi\) | |||||||
\(968\) | −7448.00 | −0.247301 | ||||||||
\(969\) | −3276.00 | −0.108607 | ||||||||
\(970\) | −6780.00 | −0.224425 | ||||||||
\(971\) | −49660.0 | −1.64126 | −0.820631 | − | 0.571459i | \(-0.806378\pi\) | ||||
−0.820631 | + | 0.571459i | \(0.806378\pi\) | |||||||
\(972\) | −972.000 | −0.0320750 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 32648.0 | 1.07403 | ||||||||
\(975\) | −1950.00 | −0.0640513 | ||||||||
\(976\) | 4352.00 | 0.142730 | ||||||||
\(977\) | −15408.0 | −0.504550 | −0.252275 | − | 0.967656i | \(-0.581179\pi\) | ||||
−0.252275 | + | 0.967656i | \(0.581179\pi\) | |||||||
\(978\) | 20616.0 | 0.674056 | ||||||||
\(979\) | 5320.00 | 0.173675 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −1962.00 | −0.0638551 | ||||||||
\(982\) | 35712.0 | 1.16050 | ||||||||
\(983\) | −37784.0 | −1.22596 | −0.612982 | − | 0.790097i | \(-0.710030\pi\) | ||||
−0.612982 | + | 0.790097i | \(0.710030\pi\) | |||||||
\(984\) | 6000.00 | 0.194383 | ||||||||
\(985\) | 1560.00 | 0.0504627 | ||||||||
\(986\) | 2184.00 | 0.0705403 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −4368.00 | −0.140652 | ||||||||
\(989\) | 57424.0 | 1.84629 | ||||||||
\(990\) | −1800.00 | −0.0577856 | ||||||||
\(991\) | −23784.0 | −0.762385 | −0.381193 | − | 0.924496i | \(-0.624487\pi\) | ||||
−0.381193 | + | 0.924496i | \(0.624487\pi\) | |||||||
\(992\) | 8768.00 | 0.280629 | ||||||||
\(993\) | 9516.00 | 0.304110 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −8530.00 | −0.271778 | ||||||||
\(996\) | −4848.00 | −0.154232 | ||||||||
\(997\) | 49998.0 | 1.58822 | 0.794109 | − | 0.607776i | \(-0.207938\pi\) | ||||
0.794109 | + | 0.607776i | \(0.207938\pi\) | |||||||
\(998\) | 6824.00 | 0.216443 | ||||||||
\(999\) | −54.0000 | −0.00171019 |
(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 | 1470.4.a.s.1.1 | ✓ | 1 | |
7.6 | odd | 2 | 1470.4.a.w.1.1 | yes | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1470.4.a.s.1.1 | ✓ | 1 | 1.1 | even | 1 | trivial | |
1470.4.a.w.1.1 | yes | 1 | 7.6 | odd | 2 |