Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1638,4,Mod(1,1638)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1638, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1638.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1638 = 2 \cdot 3^{2} \cdot 7 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1638.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(96.6451285894\) |
Analytic rank: | \(1\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 546) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 1638.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.00000 | −0.707107 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 4.00000 | 0.500000 | ||||||||
\(5\) | −9.00000 | −0.804984 | −0.402492 | − | 0.915423i | \(-0.631856\pi\) | ||||
−0.402492 | + | 0.915423i | \(0.631856\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −7.00000 | −0.377964 | ||||||||
\(8\) | −8.00000 | −0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 18.0000 | 0.569210 | ||||||||
\(11\) | −62.0000 | −1.69943 | −0.849714 | − | 0.527244i | \(-0.823225\pi\) | ||||
−0.849714 | + | 0.527244i | \(0.823225\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −13.0000 | −0.277350 | ||||||||
\(14\) | 14.0000 | 0.267261 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 16.0000 | 0.250000 | ||||||||
\(17\) | 16.0000 | 0.228269 | 0.114134 | − | 0.993465i | \(-0.463591\pi\) | ||||
0.114134 | + | 0.993465i | \(0.463591\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 79.0000 | 0.953886 | 0.476943 | − | 0.878934i | \(-0.341745\pi\) | ||||
0.476943 | + | 0.878934i | \(0.341745\pi\) | |||||||
\(20\) | −36.0000 | −0.402492 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 124.000 | 1.20168 | ||||||||
\(23\) | 155.000 | 1.40521 | 0.702603 | − | 0.711582i | \(-0.252021\pi\) | ||||
0.702603 | + | 0.711582i | \(0.252021\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −44.0000 | −0.352000 | ||||||||
\(26\) | 26.0000 | 0.196116 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −28.0000 | −0.188982 | ||||||||
\(29\) | −51.0000 | −0.326568 | −0.163284 | − | 0.986579i | \(-0.552209\pi\) | ||||
−0.163284 | + | 0.986579i | \(0.552209\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 243.000 | 1.40787 | 0.703937 | − | 0.710263i | \(-0.251424\pi\) | ||||
0.703937 | + | 0.710263i | \(0.251424\pi\) | |||||||
\(32\) | −32.0000 | −0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −32.0000 | −0.161410 | ||||||||
\(35\) | 63.0000 | 0.304256 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 412.000 | 1.83060 | 0.915302 | − | 0.402767i | \(-0.131952\pi\) | ||||
0.915302 | + | 0.402767i | \(0.131952\pi\) | |||||||
\(38\) | −158.000 | −0.674500 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 72.0000 | 0.284605 | ||||||||
\(41\) | 406.000 | 1.54650 | 0.773251 | − | 0.634101i | \(-0.218629\pi\) | ||||
0.773251 | + | 0.634101i | \(0.218629\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −103.000 | −0.365287 | −0.182644 | − | 0.983179i | \(-0.558465\pi\) | ||||
−0.182644 | + | 0.983179i | \(0.558465\pi\) | |||||||
\(44\) | −248.000 | −0.849714 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −310.000 | −0.993631 | ||||||||
\(47\) | −429.000 | −1.33141 | −0.665703 | − | 0.746217i | \(-0.731868\pi\) | ||||
−0.665703 | + | 0.746217i | \(0.731868\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 49.0000 | 0.142857 | ||||||||
\(50\) | 88.0000 | 0.248902 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −52.0000 | −0.138675 | ||||||||
\(53\) | 169.000 | 0.437999 | 0.218999 | − | 0.975725i | \(-0.429721\pi\) | ||||
0.218999 | + | 0.975725i | \(0.429721\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 558.000 | 1.36801 | ||||||||
\(56\) | 56.0000 | 0.133631 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 102.000 | 0.230918 | ||||||||
\(59\) | −320.000 | −0.706109 | −0.353055 | − | 0.935603i | \(-0.614857\pi\) | ||||
−0.353055 | + | 0.935603i | \(0.614857\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −614.000 | −1.28876 | −0.644382 | − | 0.764703i | \(-0.722885\pi\) | ||||
−0.644382 | + | 0.764703i | \(0.722885\pi\) | |||||||
\(62\) | −486.000 | −0.995517 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 64.0000 | 0.125000 | ||||||||
\(65\) | 117.000 | 0.223263 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 258.000 | 0.470444 | 0.235222 | − | 0.971942i | \(-0.424418\pi\) | ||||
0.235222 | + | 0.971942i | \(0.424418\pi\) | |||||||
\(68\) | 64.0000 | 0.114134 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −126.000 | −0.215141 | ||||||||
\(71\) | 264.000 | 0.441282 | 0.220641 | − | 0.975355i | \(-0.429185\pi\) | ||||
0.220641 | + | 0.975355i | \(0.429185\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −121.000 | −0.194000 | −0.0969999 | − | 0.995284i | \(-0.530925\pi\) | ||||
−0.0969999 | + | 0.995284i | \(0.530925\pi\) | |||||||
\(74\) | −824.000 | −1.29443 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 316.000 | 0.476943 | ||||||||
\(77\) | 434.000 | 0.642323 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −967.000 | −1.37716 | −0.688582 | − | 0.725158i | \(-0.741767\pi\) | ||||
−0.688582 | + | 0.725158i | \(0.741767\pi\) | |||||||
\(80\) | −144.000 | −0.201246 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −812.000 | −1.09354 | ||||||||
\(83\) | 679.000 | 0.897951 | 0.448975 | − | 0.893544i | \(-0.351789\pi\) | ||||
0.448975 | + | 0.893544i | \(0.351789\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −144.000 | −0.183753 | ||||||||
\(86\) | 206.000 | 0.258297 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 496.000 | 0.600838 | ||||||||
\(89\) | −1059.00 | −1.26128 | −0.630639 | − | 0.776076i | \(-0.717207\pi\) | ||||
−0.630639 | + | 0.776076i | \(0.717207\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 91.0000 | 0.104828 | ||||||||
\(92\) | 620.000 | 0.702603 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 858.000 | 0.941446 | ||||||||
\(95\) | −711.000 | −0.767864 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −21.0000 | −0.0219817 | −0.0109909 | − | 0.999940i | \(-0.503499\pi\) | ||||
−0.0109909 | + | 0.999940i | \(0.503499\pi\) | |||||||
\(98\) | −98.0000 | −0.101015 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −176.000 | −0.176000 | ||||||||
\(101\) | −894.000 | −0.880756 | −0.440378 | − | 0.897813i | \(-0.645156\pi\) | ||||
−0.440378 | + | 0.897813i | \(0.645156\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 128.000 | 0.122449 | 0.0612243 | − | 0.998124i | \(-0.480499\pi\) | ||||
0.0612243 | + | 0.998124i | \(0.480499\pi\) | |||||||
\(104\) | 104.000 | 0.0980581 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −338.000 | −0.309712 | ||||||||
\(107\) | 708.000 | 0.639672 | 0.319836 | − | 0.947473i | \(-0.396372\pi\) | ||||
0.319836 | + | 0.947473i | \(0.396372\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1238.00 | 1.08788 | 0.543940 | − | 0.839124i | \(-0.316932\pi\) | ||||
0.543940 | + | 0.839124i | \(0.316932\pi\) | |||||||
\(110\) | −1116.00 | −0.967331 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −112.000 | −0.0944911 | ||||||||
\(113\) | −1073.00 | −0.893269 | −0.446634 | − | 0.894717i | \(-0.647377\pi\) | ||||
−0.446634 | + | 0.894717i | \(0.647377\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1395.00 | −1.13117 | ||||||||
\(116\) | −204.000 | −0.163284 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 640.000 | 0.499295 | ||||||||
\(119\) | −112.000 | −0.0862775 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 2513.00 | 1.88805 | ||||||||
\(122\) | 1228.00 | 0.911294 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 972.000 | 0.703937 | ||||||||
\(125\) | 1521.00 | 1.08834 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1748.00 | −1.22134 | −0.610669 | − | 0.791886i | \(-0.709099\pi\) | ||||
−0.610669 | + | 0.791886i | \(0.709099\pi\) | |||||||
\(128\) | −128.000 | −0.0883883 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −234.000 | −0.157870 | ||||||||
\(131\) | 936.000 | 0.624265 | 0.312132 | − | 0.950039i | \(-0.398957\pi\) | ||||
0.312132 | + | 0.950039i | \(0.398957\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −553.000 | −0.360535 | ||||||||
\(134\) | −516.000 | −0.332654 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −128.000 | −0.0807052 | ||||||||
\(137\) | 1128.00 | 0.703442 | 0.351721 | − | 0.936105i | \(-0.385597\pi\) | ||||
0.351721 | + | 0.936105i | \(0.385597\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −854.000 | −0.521118 | −0.260559 | − | 0.965458i | \(-0.583907\pi\) | ||||
−0.260559 | + | 0.965458i | \(0.583907\pi\) | |||||||
\(140\) | 252.000 | 0.152128 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −528.000 | −0.312034 | ||||||||
\(143\) | 806.000 | 0.471336 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 459.000 | 0.262882 | ||||||||
\(146\) | 242.000 | 0.137179 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 1648.00 | 0.915302 | ||||||||
\(149\) | 442.000 | 0.243020 | 0.121510 | − | 0.992590i | \(-0.461226\pi\) | ||||
0.121510 | + | 0.992590i | \(0.461226\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1016.00 | −0.547556 | −0.273778 | − | 0.961793i | \(-0.588273\pi\) | ||||
−0.273778 | + | 0.961793i | \(0.588273\pi\) | |||||||
\(152\) | −632.000 | −0.337250 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −868.000 | −0.454191 | ||||||||
\(155\) | −2187.00 | −1.13332 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −3880.00 | −1.97234 | −0.986171 | − | 0.165731i | \(-0.947002\pi\) | ||||
−0.986171 | + | 0.165731i | \(0.947002\pi\) | |||||||
\(158\) | 1934.00 | 0.973802 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 288.000 | 0.142302 | ||||||||
\(161\) | −1085.00 | −0.531118 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1604.00 | −0.770767 | −0.385383 | − | 0.922757i | \(-0.625931\pi\) | ||||
−0.385383 | + | 0.922757i | \(0.625931\pi\) | |||||||
\(164\) | 1624.00 | 0.773251 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −1358.00 | −0.634947 | ||||||||
\(167\) | −959.000 | −0.444369 | −0.222185 | − | 0.975005i | \(-0.571319\pi\) | ||||
−0.222185 | + | 0.975005i | \(0.571319\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 169.000 | 0.0769231 | ||||||||
\(170\) | 288.000 | 0.129933 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −412.000 | −0.182644 | ||||||||
\(173\) | 488.000 | 0.214462 | 0.107231 | − | 0.994234i | \(-0.465802\pi\) | ||||
0.107231 | + | 0.994234i | \(0.465802\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 308.000 | 0.133043 | ||||||||
\(176\) | −992.000 | −0.424857 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 2118.00 | 0.891858 | ||||||||
\(179\) | −2533.00 | −1.05768 | −0.528842 | − | 0.848721i | \(-0.677373\pi\) | ||||
−0.528842 | + | 0.848721i | \(0.677373\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −3626.00 | −1.48905 | −0.744526 | − | 0.667593i | \(-0.767325\pi\) | ||||
−0.744526 | + | 0.667593i | \(0.767325\pi\) | |||||||
\(182\) | −182.000 | −0.0741249 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −1240.00 | −0.496815 | ||||||||
\(185\) | −3708.00 | −1.47361 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −992.000 | −0.387926 | ||||||||
\(188\) | −1716.00 | −0.665703 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 1422.00 | 0.542962 | ||||||||
\(191\) | 4992.00 | 1.89114 | 0.945572 | − | 0.325413i | \(-0.105503\pi\) | ||||
0.945572 | + | 0.325413i | \(0.105503\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −470.000 | −0.175292 | −0.0876460 | − | 0.996152i | \(-0.527934\pi\) | ||||
−0.0876460 | + | 0.996152i | \(0.527934\pi\) | |||||||
\(194\) | 42.0000 | 0.0155434 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 196.000 | 0.0714286 | ||||||||
\(197\) | 3190.00 | 1.15370 | 0.576848 | − | 0.816852i | \(-0.304283\pi\) | ||||
0.576848 | + | 0.816852i | \(0.304283\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1944.00 | 0.692495 | 0.346248 | − | 0.938143i | \(-0.387456\pi\) | ||||
0.346248 | + | 0.938143i | \(0.387456\pi\) | |||||||
\(200\) | 352.000 | 0.124451 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 1788.00 | 0.622788 | ||||||||
\(203\) | 357.000 | 0.123431 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −3654.00 | −1.24491 | ||||||||
\(206\) | −256.000 | −0.0865843 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −208.000 | −0.0693375 | ||||||||
\(209\) | −4898.00 | −1.62106 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1139.00 | −0.371621 | −0.185810 | − | 0.982586i | \(-0.559491\pi\) | ||||
−0.185810 | + | 0.982586i | \(0.559491\pi\) | |||||||
\(212\) | 676.000 | 0.218999 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −1416.00 | −0.452317 | ||||||||
\(215\) | 927.000 | 0.294051 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1701.00 | −0.532126 | ||||||||
\(218\) | −2476.00 | −0.769247 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 2232.00 | 0.684006 | ||||||||
\(221\) | −208.000 | −0.0633104 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 833.000 | 0.250143 | 0.125071 | − | 0.992148i | \(-0.460084\pi\) | ||||
0.125071 | + | 0.992148i | \(0.460084\pi\) | |||||||
\(224\) | 224.000 | 0.0668153 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 2146.00 | 0.631636 | ||||||||
\(227\) | 3516.00 | 1.02804 | 0.514020 | − | 0.857778i | \(-0.328156\pi\) | ||||
0.514020 | + | 0.857778i | \(0.328156\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 3222.00 | 0.929763 | 0.464882 | − | 0.885373i | \(-0.346097\pi\) | ||||
0.464882 | + | 0.885373i | \(0.346097\pi\) | |||||||
\(230\) | 2790.00 | 0.799857 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 408.000 | 0.115459 | ||||||||
\(233\) | 477.000 | 0.134117 | 0.0670586 | − | 0.997749i | \(-0.478639\pi\) | ||||
0.0670586 | + | 0.997749i | \(0.478639\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 3861.00 | 1.07176 | ||||||||
\(236\) | −1280.00 | −0.353055 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 224.000 | 0.0610074 | ||||||||
\(239\) | 6368.00 | 1.72348 | 0.861740 | − | 0.507350i | \(-0.169375\pi\) | ||||
0.861740 | + | 0.507350i | \(0.169375\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 747.000 | 0.199662 | 0.0998309 | − | 0.995004i | \(-0.468170\pi\) | ||||
0.0998309 | + | 0.995004i | \(0.468170\pi\) | |||||||
\(242\) | −5026.00 | −1.33506 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −2456.00 | −0.644382 | ||||||||
\(245\) | −441.000 | −0.114998 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1027.00 | −0.264561 | ||||||||
\(248\) | −1944.00 | −0.497759 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −3042.00 | −0.769572 | ||||||||
\(251\) | −7518.00 | −1.89057 | −0.945283 | − | 0.326252i | \(-0.894214\pi\) | ||||
−0.945283 | + | 0.326252i | \(0.894214\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −9610.00 | −2.38805 | ||||||||
\(254\) | 3496.00 | 0.863616 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 256.000 | 0.0625000 | ||||||||
\(257\) | −1094.00 | −0.265532 | −0.132766 | − | 0.991147i | \(-0.542386\pi\) | ||||
−0.132766 | + | 0.991147i | \(0.542386\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −2884.00 | −0.691904 | ||||||||
\(260\) | 468.000 | 0.111631 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −1872.00 | −0.441422 | ||||||||
\(263\) | 1289.00 | 0.302217 | 0.151109 | − | 0.988517i | \(-0.451716\pi\) | ||||
0.151109 | + | 0.988517i | \(0.451716\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1521.00 | −0.352582 | ||||||||
\(266\) | 1106.00 | 0.254937 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 1032.00 | 0.235222 | ||||||||
\(269\) | 2060.00 | 0.466916 | 0.233458 | − | 0.972367i | \(-0.424996\pi\) | ||||
0.233458 | + | 0.972367i | \(0.424996\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 576.000 | 0.129113 | 0.0645563 | − | 0.997914i | \(-0.479437\pi\) | ||||
0.0645563 | + | 0.997914i | \(0.479437\pi\) | |||||||
\(272\) | 256.000 | 0.0570672 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −2256.00 | −0.497409 | ||||||||
\(275\) | 2728.00 | 0.598199 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −5699.00 | −1.23617 | −0.618086 | − | 0.786110i | \(-0.712092\pi\) | ||||
−0.618086 | + | 0.786110i | \(0.712092\pi\) | |||||||
\(278\) | 1708.00 | 0.368486 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −504.000 | −0.107571 | ||||||||
\(281\) | −4062.00 | −0.862344 | −0.431172 | − | 0.902270i | \(-0.641900\pi\) | ||||
−0.431172 | + | 0.902270i | \(0.641900\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −772.000 | −0.162158 | −0.0810789 | − | 0.996708i | \(-0.525837\pi\) | ||||
−0.0810789 | + | 0.996708i | \(0.525837\pi\) | |||||||
\(284\) | 1056.00 | 0.220641 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −1612.00 | −0.333285 | ||||||||
\(287\) | −2842.00 | −0.584522 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −4657.00 | −0.947893 | ||||||||
\(290\) | −918.000 | −0.185886 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −484.000 | −0.0969999 | ||||||||
\(293\) | −7833.00 | −1.56180 | −0.780902 | − | 0.624653i | \(-0.785240\pi\) | ||||
−0.780902 | + | 0.624653i | \(0.785240\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 2880.00 | 0.568407 | ||||||||
\(296\) | −3296.00 | −0.647217 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −884.000 | −0.171841 | ||||||||
\(299\) | −2015.00 | −0.389734 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 721.000 | 0.138066 | ||||||||
\(302\) | 2032.00 | 0.387180 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 1264.00 | 0.238472 | ||||||||
\(305\) | 5526.00 | 1.03744 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −2891.00 | −0.537453 | −0.268727 | − | 0.963217i | \(-0.586603\pi\) | ||||
−0.268727 | + | 0.963217i | \(0.586603\pi\) | |||||||
\(308\) | 1736.00 | 0.321162 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 4374.00 | 0.801376 | ||||||||
\(311\) | 3530.00 | 0.643627 | 0.321813 | − | 0.946803i | \(-0.395708\pi\) | ||||
0.321813 | + | 0.946803i | \(0.395708\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 5490.00 | 0.991416 | 0.495708 | − | 0.868489i | \(-0.334909\pi\) | ||||
0.495708 | + | 0.868489i | \(0.334909\pi\) | |||||||
\(314\) | 7760.00 | 1.39466 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −3868.00 | −0.688582 | ||||||||
\(317\) | 5636.00 | 0.998578 | 0.499289 | − | 0.866435i | \(-0.333595\pi\) | ||||
0.499289 | + | 0.866435i | \(0.333595\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 3162.00 | 0.554978 | ||||||||
\(320\) | −576.000 | −0.100623 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 2170.00 | 0.375557 | ||||||||
\(323\) | 1264.00 | 0.217743 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 572.000 | 0.0976272 | ||||||||
\(326\) | 3208.00 | 0.545014 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −3248.00 | −0.546771 | ||||||||
\(329\) | 3003.00 | 0.503224 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −9962.00 | −1.65426 | −0.827131 | − | 0.562008i | \(-0.810029\pi\) | ||||
−0.827131 | + | 0.562008i | \(0.810029\pi\) | |||||||
\(332\) | 2716.00 | 0.448975 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 1918.00 | 0.314216 | ||||||||
\(335\) | −2322.00 | −0.378700 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −11415.0 | −1.84515 | −0.922574 | − | 0.385821i | \(-0.873918\pi\) | ||||
−0.922574 | + | 0.385821i | \(0.873918\pi\) | |||||||
\(338\) | −338.000 | −0.0543928 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −576.000 | −0.0918764 | ||||||||
\(341\) | −15066.0 | −2.39258 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −343.000 | −0.0539949 | ||||||||
\(344\) | 824.000 | 0.129149 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −976.000 | −0.151648 | ||||||||
\(347\) | −4864.00 | −0.752488 | −0.376244 | − | 0.926521i | \(-0.622784\pi\) | ||||
−0.376244 | + | 0.926521i | \(0.622784\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −469.000 | −0.0719341 | −0.0359670 | − | 0.999353i | \(-0.511451\pi\) | ||||
−0.0359670 | + | 0.999353i | \(0.511451\pi\) | |||||||
\(350\) | −616.000 | −0.0940760 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 1984.00 | 0.300419 | ||||||||
\(353\) | −4198.00 | −0.632966 | −0.316483 | − | 0.948598i | \(-0.602502\pi\) | ||||
−0.316483 | + | 0.948598i | \(0.602502\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −2376.00 | −0.355225 | ||||||||
\(356\) | −4236.00 | −0.630639 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 5066.00 | 0.747895 | ||||||||
\(359\) | −3408.00 | −0.501023 | −0.250512 | − | 0.968114i | \(-0.580599\pi\) | ||||
−0.250512 | + | 0.968114i | \(0.580599\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −618.000 | −0.0901006 | ||||||||
\(362\) | 7252.00 | 1.05292 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 364.000 | 0.0524142 | ||||||||
\(365\) | 1089.00 | 0.156167 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −8290.00 | −1.17911 | −0.589557 | − | 0.807727i | \(-0.700697\pi\) | ||||
−0.589557 | + | 0.807727i | \(0.700697\pi\) | |||||||
\(368\) | 2480.00 | 0.351301 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 7416.00 | 1.04200 | ||||||||
\(371\) | −1183.00 | −0.165548 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −9906.00 | −1.37510 | −0.687551 | − | 0.726136i | \(-0.741314\pi\) | ||||
−0.687551 | + | 0.726136i | \(0.741314\pi\) | |||||||
\(374\) | 1984.00 | 0.274305 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 3432.00 | 0.470723 | ||||||||
\(377\) | 663.000 | 0.0905736 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −9238.00 | −1.25204 | −0.626021 | − | 0.779806i | \(-0.715318\pi\) | ||||
−0.626021 | + | 0.779806i | \(0.715318\pi\) | |||||||
\(380\) | −2844.00 | −0.383932 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −9984.00 | −1.33724 | ||||||||
\(383\) | −4972.00 | −0.663335 | −0.331668 | − | 0.943396i | \(-0.607611\pi\) | ||||
−0.331668 | + | 0.943396i | \(0.607611\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −3906.00 | −0.517060 | ||||||||
\(386\) | 940.000 | 0.123950 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −84.0000 | −0.0109909 | ||||||||
\(389\) | −7454.00 | −0.971550 | −0.485775 | − | 0.874084i | \(-0.661462\pi\) | ||||
−0.485775 | + | 0.874084i | \(0.661462\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2480.00 | 0.320765 | ||||||||
\(392\) | −392.000 | −0.0505076 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −6380.00 | −0.815786 | ||||||||
\(395\) | 8703.00 | 1.10860 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 7219.00 | 0.912623 | 0.456311 | − | 0.889820i | \(-0.349170\pi\) | ||||
0.456311 | + | 0.889820i | \(0.349170\pi\) | |||||||
\(398\) | −3888.00 | −0.489668 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −704.000 | −0.0880000 | ||||||||
\(401\) | −10772.0 | −1.34147 | −0.670733 | − | 0.741699i | \(-0.734020\pi\) | ||||
−0.670733 | + | 0.741699i | \(0.734020\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −3159.00 | −0.390474 | ||||||||
\(404\) | −3576.00 | −0.440378 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −714.000 | −0.0872789 | ||||||||
\(407\) | −25544.0 | −3.11098 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 13151.0 | 1.58991 | 0.794957 | − | 0.606665i | \(-0.207493\pi\) | ||||
0.794957 | + | 0.606665i | \(0.207493\pi\) | |||||||
\(410\) | 7308.00 | 0.880284 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 512.000 | 0.0612243 | ||||||||
\(413\) | 2240.00 | 0.266884 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −6111.00 | −0.722837 | ||||||||
\(416\) | 416.000 | 0.0490290 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 9796.00 | 1.14626 | ||||||||
\(419\) | −6034.00 | −0.703533 | −0.351766 | − | 0.936088i | \(-0.614419\pi\) | ||||
−0.351766 | + | 0.936088i | \(0.614419\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 8864.00 | 1.02614 | 0.513070 | − | 0.858347i | \(-0.328508\pi\) | ||||
0.513070 | + | 0.858347i | \(0.328508\pi\) | |||||||
\(422\) | 2278.00 | 0.262776 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −1352.00 | −0.154856 | ||||||||
\(425\) | −704.000 | −0.0803506 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 4298.00 | 0.487107 | ||||||||
\(428\) | 2832.00 | 0.319836 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −1854.00 | −0.207925 | ||||||||
\(431\) | 134.000 | 0.0149758 | 0.00748788 | − | 0.999972i | \(-0.497617\pi\) | ||||
0.00748788 | + | 0.999972i | \(0.497617\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 12376.0 | 1.37356 | 0.686781 | − | 0.726864i | \(-0.259023\pi\) | ||||
0.686781 | + | 0.726864i | \(0.259023\pi\) | |||||||
\(434\) | 3402.00 | 0.376270 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 4952.00 | 0.543940 | ||||||||
\(437\) | 12245.0 | 1.34041 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 14198.0 | 1.54358 | 0.771792 | − | 0.635875i | \(-0.219361\pi\) | ||||
0.771792 | + | 0.635875i | \(0.219361\pi\) | |||||||
\(440\) | −4464.00 | −0.483666 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 416.000 | 0.0447672 | ||||||||
\(443\) | −7657.00 | −0.821208 | −0.410604 | − | 0.911814i | \(-0.634682\pi\) | ||||
−0.410604 | + | 0.911814i | \(0.634682\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 9531.00 | 1.01531 | ||||||||
\(446\) | −1666.00 | −0.176878 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −448.000 | −0.0472456 | ||||||||
\(449\) | −15500.0 | −1.62915 | −0.814577 | − | 0.580055i | \(-0.803031\pi\) | ||||
−0.814577 | + | 0.580055i | \(0.803031\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −25172.0 | −2.62817 | ||||||||
\(452\) | −4292.00 | −0.446634 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −7032.00 | −0.726934 | ||||||||
\(455\) | −819.000 | −0.0843853 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 10184.0 | 1.04242 | 0.521212 | − | 0.853427i | \(-0.325480\pi\) | ||||
0.521212 | + | 0.853427i | \(0.325480\pi\) | |||||||
\(458\) | −6444.00 | −0.657442 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −5580.00 | −0.565584 | ||||||||
\(461\) | −19250.0 | −1.94482 | −0.972410 | − | 0.233279i | \(-0.925054\pi\) | ||||
−0.972410 | + | 0.233279i | \(0.925054\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −15622.0 | −1.56807 | −0.784034 | − | 0.620717i | \(-0.786841\pi\) | ||||
−0.784034 | + | 0.620717i | \(0.786841\pi\) | |||||||
\(464\) | −816.000 | −0.0816419 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −954.000 | −0.0948352 | ||||||||
\(467\) | 15594.0 | 1.54519 | 0.772596 | − | 0.634898i | \(-0.218958\pi\) | ||||
0.772596 | + | 0.634898i | \(0.218958\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −1806.00 | −0.177811 | ||||||||
\(470\) | −7722.00 | −0.757850 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 2560.00 | 0.249647 | ||||||||
\(473\) | 6386.00 | 0.620779 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −3476.00 | −0.335768 | ||||||||
\(476\) | −448.000 | −0.0431388 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −12736.0 | −1.21868 | ||||||||
\(479\) | −3239.00 | −0.308964 | −0.154482 | − | 0.987996i | \(-0.549371\pi\) | ||||
−0.154482 | + | 0.987996i | \(0.549371\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −5356.00 | −0.507718 | ||||||||
\(482\) | −1494.00 | −0.141182 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 10052.0 | 0.944027 | ||||||||
\(485\) | 189.000 | 0.0176949 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 1798.00 | 0.167300 | 0.0836501 | − | 0.996495i | \(-0.473342\pi\) | ||||
0.0836501 | + | 0.996495i | \(0.473342\pi\) | |||||||
\(488\) | 4912.00 | 0.455647 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 882.000 | 0.0813157 | ||||||||
\(491\) | −13708.0 | −1.25995 | −0.629973 | − | 0.776617i | \(-0.716934\pi\) | ||||
−0.629973 | + | 0.776617i | \(0.716934\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −816.000 | −0.0745452 | ||||||||
\(494\) | 2054.00 | 0.187073 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 3888.00 | 0.351968 | ||||||||
\(497\) | −1848.00 | −0.166789 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −11936.0 | −1.07080 | −0.535400 | − | 0.844599i | \(-0.679839\pi\) | ||||
−0.535400 | + | 0.844599i | \(0.679839\pi\) | |||||||
\(500\) | 6084.00 | 0.544170 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 15036.0 | 1.33683 | ||||||||
\(503\) | −2562.00 | −0.227105 | −0.113553 | − | 0.993532i | \(-0.536223\pi\) | ||||
−0.113553 | + | 0.993532i | \(0.536223\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 8046.00 | 0.708995 | ||||||||
\(506\) | 19220.0 | 1.68860 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −6992.00 | −0.610669 | ||||||||
\(509\) | 8055.00 | 0.701437 | 0.350719 | − | 0.936481i | \(-0.385937\pi\) | ||||
0.350719 | + | 0.936481i | \(0.385937\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 847.000 | 0.0733250 | ||||||||
\(512\) | −512.000 | −0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 2188.00 | 0.187760 | ||||||||
\(515\) | −1152.00 | −0.0985693 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 26598.0 | 2.26263 | ||||||||
\(518\) | 5768.00 | 0.489250 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −936.000 | −0.0789352 | ||||||||
\(521\) | 5980.00 | 0.502857 | 0.251429 | − | 0.967876i | \(-0.419100\pi\) | ||||
0.251429 | + | 0.967876i | \(0.419100\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 19238.0 | 1.60845 | 0.804225 | − | 0.594325i | \(-0.202581\pi\) | ||||
0.804225 | + | 0.594325i | \(0.202581\pi\) | |||||||
\(524\) | 3744.00 | 0.312132 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −2578.00 | −0.213700 | ||||||||
\(527\) | 3888.00 | 0.321374 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 11858.0 | 0.974603 | ||||||||
\(530\) | 3042.00 | 0.249313 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −2212.00 | −0.180268 | ||||||||
\(533\) | −5278.00 | −0.428922 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −6372.00 | −0.514926 | ||||||||
\(536\) | −2064.00 | −0.166327 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −4120.00 | −0.330160 | ||||||||
\(539\) | −3038.00 | −0.242775 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 13012.0 | 1.03407 | 0.517033 | − | 0.855966i | \(-0.327036\pi\) | ||||
0.517033 | + | 0.855966i | \(0.327036\pi\) | |||||||
\(542\) | −1152.00 | −0.0912964 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −512.000 | −0.0403526 | ||||||||
\(545\) | −11142.0 | −0.875726 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 18055.0 | 1.41129 | 0.705645 | − | 0.708565i | \(-0.250657\pi\) | ||||
0.705645 | + | 0.708565i | \(0.250657\pi\) | |||||||
\(548\) | 4512.00 | 0.351721 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −5456.00 | −0.422990 | ||||||||
\(551\) | −4029.00 | −0.311508 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 6769.00 | 0.520519 | ||||||||
\(554\) | 11398.0 | 0.874106 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −3416.00 | −0.260559 | ||||||||
\(557\) | 19608.0 | 1.49159 | 0.745797 | − | 0.666174i | \(-0.232069\pi\) | ||||
0.745797 | + | 0.666174i | \(0.232069\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1339.00 | 0.101312 | ||||||||
\(560\) | 1008.00 | 0.0760639 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 8124.00 | 0.609769 | ||||||||
\(563\) | 13512.0 | 1.01148 | 0.505740 | − | 0.862686i | \(-0.331220\pi\) | ||||
0.505740 | + | 0.862686i | \(0.331220\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 9657.00 | 0.719067 | ||||||||
\(566\) | 1544.00 | 0.114663 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −2112.00 | −0.156017 | ||||||||
\(569\) | 4061.00 | 0.299202 | 0.149601 | − | 0.988746i | \(-0.452201\pi\) | ||||
0.149601 | + | 0.988746i | \(0.452201\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −2255.00 | −0.165269 | −0.0826347 | − | 0.996580i | \(-0.526333\pi\) | ||||
−0.0826347 | + | 0.996580i | \(0.526333\pi\) | |||||||
\(572\) | 3224.00 | 0.235668 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 5684.00 | 0.413320 | ||||||||
\(575\) | −6820.00 | −0.494632 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −254.000 | −0.0183261 | −0.00916305 | − | 0.999958i | \(-0.502917\pi\) | ||||
−0.00916305 | + | 0.999958i | \(0.502917\pi\) | |||||||
\(578\) | 9314.00 | 0.670262 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 1836.00 | 0.131441 | ||||||||
\(581\) | −4753.00 | −0.339394 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −10478.0 | −0.744347 | ||||||||
\(584\) | 968.000 | 0.0685893 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 15666.0 | 1.10436 | ||||||||
\(587\) | −15057.0 | −1.05872 | −0.529360 | − | 0.848397i | \(-0.677568\pi\) | ||||
−0.529360 | + | 0.848397i | \(0.677568\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 19197.0 | 1.34295 | ||||||||
\(590\) | −5760.00 | −0.401924 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 6592.00 | 0.457651 | ||||||||
\(593\) | −19917.0 | −1.37925 | −0.689623 | − | 0.724168i | \(-0.742224\pi\) | ||||
−0.689623 | + | 0.724168i | \(0.742224\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1008.00 | 0.0694521 | ||||||||
\(596\) | 1768.00 | 0.121510 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 4030.00 | 0.275584 | ||||||||
\(599\) | 15107.0 | 1.03048 | 0.515238 | − | 0.857047i | \(-0.327703\pi\) | ||||
0.515238 | + | 0.857047i | \(0.327703\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 23674.0 | 1.60679 | 0.803397 | − | 0.595444i | \(-0.203024\pi\) | ||||
0.803397 | + | 0.595444i | \(0.203024\pi\) | |||||||
\(602\) | −1442.00 | −0.0976271 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −4064.00 | −0.273778 | ||||||||
\(605\) | −22617.0 | −1.51985 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 23746.0 | 1.58784 | 0.793921 | − | 0.608021i | \(-0.208036\pi\) | ||||
0.793921 | + | 0.608021i | \(0.208036\pi\) | |||||||
\(608\) | −2528.00 | −0.168625 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −11052.0 | −0.733578 | ||||||||
\(611\) | 5577.00 | 0.369266 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −19216.0 | −1.26611 | −0.633056 | − | 0.774106i | \(-0.718200\pi\) | ||||
−0.633056 | + | 0.774106i | \(0.718200\pi\) | |||||||
\(614\) | 5782.00 | 0.380037 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −3472.00 | −0.227096 | ||||||||
\(617\) | −20862.0 | −1.36122 | −0.680610 | − | 0.732646i | \(-0.738285\pi\) | ||||
−0.680610 | + | 0.732646i | \(0.738285\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 124.000 | 0.00805167 | 0.00402583 | − | 0.999992i | \(-0.498719\pi\) | ||||
0.00402583 | + | 0.999992i | \(0.498719\pi\) | |||||||
\(620\) | −8748.00 | −0.566658 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −7060.00 | −0.455113 | ||||||||
\(623\) | 7413.00 | 0.476718 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −8189.00 | −0.524096 | ||||||||
\(626\) | −10980.0 | −0.701037 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −15520.0 | −0.986171 | ||||||||
\(629\) | 6592.00 | 0.417870 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 23942.0 | 1.51048 | 0.755242 | − | 0.655446i | \(-0.227519\pi\) | ||||
0.755242 | + | 0.655446i | \(0.227519\pi\) | |||||||
\(632\) | 7736.00 | 0.486901 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −11272.0 | −0.706101 | ||||||||
\(635\) | 15732.0 | 0.983158 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −637.000 | −0.0396214 | ||||||||
\(638\) | −6324.00 | −0.392429 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 1152.00 | 0.0711512 | ||||||||
\(641\) | 15723.0 | 0.968832 | 0.484416 | − | 0.874838i | \(-0.339032\pi\) | ||||
0.484416 | + | 0.874838i | \(0.339032\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −5544.00 | −0.340022 | −0.170011 | − | 0.985442i | \(-0.554380\pi\) | ||||
−0.170011 | + | 0.985442i | \(0.554380\pi\) | |||||||
\(644\) | −4340.00 | −0.265559 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −2528.00 | −0.153967 | ||||||||
\(647\) | 6078.00 | 0.369321 | 0.184661 | − | 0.982802i | \(-0.440881\pi\) | ||||
0.184661 | + | 0.982802i | \(0.440881\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 19840.0 | 1.19998 | ||||||||
\(650\) | −1144.00 | −0.0690329 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −6416.00 | −0.385383 | ||||||||
\(653\) | −30778.0 | −1.84447 | −0.922233 | − | 0.386635i | \(-0.873637\pi\) | ||||
−0.922233 | + | 0.386635i | \(0.873637\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −8424.00 | −0.502524 | ||||||||
\(656\) | 6496.00 | 0.386625 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −6006.00 | −0.355833 | ||||||||
\(659\) | 11205.0 | 0.662344 | 0.331172 | − | 0.943570i | \(-0.392556\pi\) | ||||
0.331172 | + | 0.943570i | \(0.392556\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −20785.0 | −1.22306 | −0.611530 | − | 0.791221i | \(-0.709446\pi\) | ||||
−0.611530 | + | 0.791221i | \(0.709446\pi\) | |||||||
\(662\) | 19924.0 | 1.16974 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −5432.00 | −0.317474 | ||||||||
\(665\) | 4977.00 | 0.290225 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −7905.00 | −0.458895 | ||||||||
\(668\) | −3836.00 | −0.222185 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 4644.00 | 0.267781 | ||||||||
\(671\) | 38068.0 | 2.19016 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 1297.00 | 0.0742878 | 0.0371439 | − | 0.999310i | \(-0.488174\pi\) | ||||
0.0371439 | + | 0.999310i | \(0.488174\pi\) | |||||||
\(674\) | 22830.0 | 1.30472 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 676.000 | 0.0384615 | ||||||||
\(677\) | −7310.00 | −0.414987 | −0.207493 | − | 0.978236i | \(-0.566531\pi\) | ||||
−0.207493 | + | 0.978236i | \(0.566531\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 147.000 | 0.00830831 | ||||||||
\(680\) | 1152.00 | 0.0649664 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 30132.0 | 1.69181 | ||||||||
\(683\) | 26384.0 | 1.47812 | 0.739060 | − | 0.673640i | \(-0.235270\pi\) | ||||
0.739060 | + | 0.673640i | \(0.235270\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −10152.0 | −0.566260 | ||||||||
\(686\) | 686.000 | 0.0381802 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −1648.00 | −0.0913218 | ||||||||
\(689\) | −2197.00 | −0.121479 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −27823.0 | −1.53175 | −0.765873 | − | 0.642992i | \(-0.777693\pi\) | ||||
−0.765873 | + | 0.642992i | \(0.777693\pi\) | |||||||
\(692\) | 1952.00 | 0.107231 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 9728.00 | 0.532089 | ||||||||
\(695\) | 7686.00 | 0.419492 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 6496.00 | 0.353018 | ||||||||
\(698\) | 938.000 | 0.0508651 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 1232.00 | 0.0665217 | ||||||||
\(701\) | −24117.0 | −1.29941 | −0.649705 | − | 0.760186i | \(-0.725108\pi\) | ||||
−0.649705 | + | 0.760186i | \(0.725108\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 32548.0 | 1.74619 | ||||||||
\(704\) | −3968.00 | −0.212428 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 8396.00 | 0.447575 | ||||||||
\(707\) | 6258.00 | 0.332894 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 28286.0 | 1.49831 | 0.749156 | − | 0.662394i | \(-0.230459\pi\) | ||||
0.749156 | + | 0.662394i | \(0.230459\pi\) | |||||||
\(710\) | 4752.00 | 0.251182 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 8472.00 | 0.445929 | ||||||||
\(713\) | 37665.0 | 1.97835 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −7254.00 | −0.379418 | ||||||||
\(716\) | −10132.0 | −0.528842 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 6816.00 | 0.354277 | ||||||||
\(719\) | 26346.0 | 1.36654 | 0.683268 | − | 0.730167i | \(-0.260558\pi\) | ||||
0.683268 | + | 0.730167i | \(0.260558\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −896.000 | −0.0462813 | ||||||||
\(722\) | 1236.00 | 0.0637107 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −14504.0 | −0.744526 | ||||||||
\(725\) | 2244.00 | 0.114952 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −22862.0 | −1.16631 | −0.583153 | − | 0.812362i | \(-0.698181\pi\) | ||||
−0.583153 | + | 0.812362i | \(0.698181\pi\) | |||||||
\(728\) | −728.000 | −0.0370625 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −2178.00 | −0.110427 | ||||||||
\(731\) | −1648.00 | −0.0833837 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 18587.0 | 0.936598 | 0.468299 | − | 0.883570i | \(-0.344867\pi\) | ||||
0.468299 | + | 0.883570i | \(0.344867\pi\) | |||||||
\(734\) | 16580.0 | 0.833759 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −4960.00 | −0.248408 | ||||||||
\(737\) | −15996.0 | −0.799485 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 5102.00 | 0.253965 | 0.126982 | − | 0.991905i | \(-0.459471\pi\) | ||||
0.126982 | + | 0.991905i | \(0.459471\pi\) | |||||||
\(740\) | −14832.0 | −0.736804 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 2366.00 | 0.117060 | ||||||||
\(743\) | −27428.0 | −1.35429 | −0.677144 | − | 0.735851i | \(-0.736783\pi\) | ||||
−0.677144 | + | 0.735851i | \(0.736783\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −3978.00 | −0.195628 | ||||||||
\(746\) | 19812.0 | 0.972344 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −3968.00 | −0.193963 | ||||||||
\(749\) | −4956.00 | −0.241773 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 125.000 | 0.00607365 | 0.00303683 | − | 0.999995i | \(-0.499033\pi\) | ||||
0.00303683 | + | 0.999995i | \(0.499033\pi\) | |||||||
\(752\) | −6864.00 | −0.332851 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −1326.00 | −0.0640452 | ||||||||
\(755\) | 9144.00 | 0.440774 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −27907.0 | −1.33989 | −0.669945 | − | 0.742410i | \(-0.733682\pi\) | ||||
−0.669945 | + | 0.742410i | \(0.733682\pi\) | |||||||
\(758\) | 18476.0 | 0.885328 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 5688.00 | 0.271481 | ||||||||
\(761\) | −7793.00 | −0.371217 | −0.185608 | − | 0.982624i | \(-0.559426\pi\) | ||||
−0.185608 | + | 0.982624i | \(0.559426\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −8666.00 | −0.411180 | ||||||||
\(764\) | 19968.0 | 0.945572 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 9944.00 | 0.469049 | ||||||||
\(767\) | 4160.00 | 0.195839 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 29393.0 | 1.37833 | 0.689167 | − | 0.724603i | \(-0.257977\pi\) | ||||
0.689167 | + | 0.724603i | \(0.257977\pi\) | |||||||
\(770\) | 7812.00 | 0.365617 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −1880.00 | −0.0876460 | ||||||||
\(773\) | −20326.0 | −0.945764 | −0.472882 | − | 0.881126i | \(-0.656786\pi\) | ||||
−0.472882 | + | 0.881126i | \(0.656786\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −10692.0 | −0.495572 | ||||||||
\(776\) | 168.000 | 0.00777171 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 14908.0 | 0.686989 | ||||||||
\(779\) | 32074.0 | 1.47519 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −16368.0 | −0.749927 | ||||||||
\(782\) | −4960.00 | −0.226815 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 784.000 | 0.0357143 | ||||||||
\(785\) | 34920.0 | 1.58770 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 16679.0 | 0.755454 | 0.377727 | − | 0.925917i | \(-0.376706\pi\) | ||||
0.377727 | + | 0.925917i | \(0.376706\pi\) | |||||||
\(788\) | 12760.0 | 0.576848 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −17406.0 | −0.783896 | ||||||||
\(791\) | 7511.00 | 0.337624 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 7982.00 | 0.357439 | ||||||||
\(794\) | −14438.0 | −0.645322 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 7776.00 | 0.346248 | ||||||||
\(797\) | 9282.00 | 0.412529 | 0.206264 | − | 0.978496i | \(-0.433869\pi\) | ||||
0.206264 | + | 0.978496i | \(0.433869\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −6864.00 | −0.303918 | ||||||||
\(800\) | 1408.00 | 0.0622254 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 21544.0 | 0.948560 | ||||||||
\(803\) | 7502.00 | 0.329688 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 9765.00 | 0.427542 | ||||||||
\(806\) | 6318.00 | 0.276107 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 7152.00 | 0.311394 | ||||||||
\(809\) | 883.000 | 0.0383741 | 0.0191870 | − | 0.999816i | \(-0.493892\pi\) | ||||
0.0191870 | + | 0.999816i | \(0.493892\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −12684.0 | −0.549193 | −0.274596 | − | 0.961560i | \(-0.588544\pi\) | ||||
−0.274596 | + | 0.961560i | \(0.588544\pi\) | |||||||
\(812\) | 1428.00 | 0.0617155 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 51088.0 | 2.19980 | ||||||||
\(815\) | 14436.0 | 0.620455 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −8137.00 | −0.348443 | ||||||||
\(818\) | −26302.0 | −1.12424 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −14616.0 | −0.622455 | ||||||||
\(821\) | 34126.0 | 1.45068 | 0.725338 | − | 0.688393i | \(-0.241683\pi\) | ||||
0.725338 | + | 0.688393i | \(0.241683\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −7568.00 | −0.320539 | −0.160270 | − | 0.987073i | \(-0.551236\pi\) | ||||
−0.160270 | + | 0.987073i | \(0.551236\pi\) | |||||||
\(824\) | −1024.00 | −0.0432921 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −4480.00 | −0.188716 | ||||||||
\(827\) | −32076.0 | −1.34872 | −0.674360 | − | 0.738403i | \(-0.735580\pi\) | ||||
−0.674360 | + | 0.738403i | \(0.735580\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −22598.0 | −0.946756 | −0.473378 | − | 0.880859i | \(-0.656966\pi\) | ||||
−0.473378 | + | 0.880859i | \(0.656966\pi\) | |||||||
\(830\) | 12222.0 | 0.511123 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −832.000 | −0.0346688 | ||||||||
\(833\) | 784.000 | 0.0326098 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 8631.00 | 0.357710 | ||||||||
\(836\) | −19592.0 | −0.810530 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 12068.0 | 0.497473 | ||||||||
\(839\) | −25480.0 | −1.04847 | −0.524236 | − | 0.851573i | \(-0.675649\pi\) | ||||
−0.524236 | + | 0.851573i | \(0.675649\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −21788.0 | −0.893354 | ||||||||
\(842\) | −17728.0 | −0.725591 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −4556.00 | −0.185810 | ||||||||
\(845\) | −1521.00 | −0.0619219 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −17591.0 | −0.713617 | ||||||||
\(848\) | 2704.00 | 0.109500 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 1408.00 | 0.0568165 | ||||||||
\(851\) | 63860.0 | 2.57238 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −22939.0 | −0.920770 | −0.460385 | − | 0.887719i | \(-0.652289\pi\) | ||||
−0.460385 | + | 0.887719i | \(0.652289\pi\) | |||||||
\(854\) | −8596.00 | −0.344437 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −5664.00 | −0.226158 | ||||||||
\(857\) | 38782.0 | 1.54582 | 0.772910 | − | 0.634516i | \(-0.218800\pi\) | ||||
0.772910 | + | 0.634516i | \(0.218800\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −13970.0 | −0.554890 | −0.277445 | − | 0.960742i | \(-0.589488\pi\) | ||||
−0.277445 | + | 0.960742i | \(0.589488\pi\) | |||||||
\(860\) | 3708.00 | 0.147025 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −268.000 | −0.0105895 | ||||||||
\(863\) | 22212.0 | 0.876136 | 0.438068 | − | 0.898942i | \(-0.355663\pi\) | ||||
0.438068 | + | 0.898942i | \(0.355663\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −4392.00 | −0.172639 | ||||||||
\(866\) | −24752.0 | −0.971255 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −6804.00 | −0.266063 | ||||||||
\(869\) | 59954.0 | 2.34039 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −3354.00 | −0.130478 | ||||||||
\(872\) | −9904.00 | −0.384624 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −24490.0 | −0.947811 | ||||||||
\(875\) | −10647.0 | −0.411353 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −24816.0 | −0.955504 | −0.477752 | − | 0.878495i | \(-0.658548\pi\) | ||||
−0.477752 | + | 0.878495i | \(0.658548\pi\) | |||||||
\(878\) | −28396.0 | −1.09148 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 8928.00 | 0.342003 | ||||||||
\(881\) | −7490.00 | −0.286430 | −0.143215 | − | 0.989692i | \(-0.545744\pi\) | ||||
−0.143215 | + | 0.989692i | \(0.545744\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 6092.00 | 0.232177 | 0.116088 | − | 0.993239i | \(-0.462964\pi\) | ||||
0.116088 | + | 0.993239i | \(0.462964\pi\) | |||||||
\(884\) | −832.000 | −0.0316552 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 15314.0 | 0.580682 | ||||||||
\(887\) | 6480.00 | 0.245295 | 0.122648 | − | 0.992450i | \(-0.460861\pi\) | ||||
0.122648 | + | 0.992450i | \(0.460861\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 12236.0 | 0.461622 | ||||||||
\(890\) | −19062.0 | −0.717932 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 3332.00 | 0.125071 | ||||||||
\(893\) | −33891.0 | −1.27001 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 22797.0 | 0.851419 | ||||||||
\(896\) | 896.000 | 0.0334077 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 31000.0 | 1.15199 | ||||||||
\(899\) | −12393.0 | −0.459766 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 2704.00 | 0.0999815 | ||||||||
\(902\) | 50344.0 | 1.85839 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 8584.00 | 0.315818 | ||||||||
\(905\) | 32634.0 | 1.19866 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −12111.0 | −0.443373 | −0.221686 | − | 0.975118i | \(-0.571156\pi\) | ||||
−0.221686 | + | 0.975118i | \(0.571156\pi\) | |||||||
\(908\) | 14064.0 | 0.514020 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 1638.00 | 0.0596694 | ||||||||
\(911\) | −7191.00 | −0.261524 | −0.130762 | − | 0.991414i | \(-0.541742\pi\) | ||||
−0.130762 | + | 0.991414i | \(0.541742\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −42098.0 | −1.52600 | ||||||||
\(914\) | −20368.0 | −0.737105 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 12888.0 | 0.464882 | ||||||||
\(917\) | −6552.00 | −0.235950 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −12272.0 | −0.440496 | −0.220248 | − | 0.975444i | \(-0.570687\pi\) | ||||
−0.220248 | + | 0.975444i | \(0.570687\pi\) | |||||||
\(920\) | 11160.0 | 0.399929 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 38500.0 | 1.37520 | ||||||||
\(923\) | −3432.00 | −0.122390 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −18128.0 | −0.644373 | ||||||||
\(926\) | 31244.0 | 1.10879 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 1632.00 | 0.0577296 | ||||||||
\(929\) | −3285.00 | −0.116014 | −0.0580072 | − | 0.998316i | \(-0.518475\pi\) | ||||
−0.0580072 | + | 0.998316i | \(0.518475\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 3871.00 | 0.136269 | ||||||||
\(932\) | 1908.00 | 0.0670586 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −31188.0 | −1.09262 | ||||||||
\(935\) | 8928.00 | 0.312275 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −5068.00 | −0.176696 | −0.0883481 | − | 0.996090i | \(-0.528159\pi\) | ||||
−0.0883481 | + | 0.996090i | \(0.528159\pi\) | |||||||
\(938\) | 3612.00 | 0.125731 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 15444.0 | 0.535881 | ||||||||
\(941\) | −13571.0 | −0.470140 | −0.235070 | − | 0.971978i | \(-0.575532\pi\) | ||||
−0.235070 | + | 0.971978i | \(0.575532\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 62930.0 | 2.17315 | ||||||||
\(944\) | −5120.00 | −0.176527 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −12772.0 | −0.438957 | ||||||||
\(947\) | 17662.0 | 0.606059 | 0.303030 | − | 0.952981i | \(-0.402002\pi\) | ||||
0.303030 | + | 0.952981i | \(0.402002\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1573.00 | 0.0538058 | ||||||||
\(950\) | 6952.00 | 0.237424 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 896.000 | 0.0305037 | ||||||||
\(953\) | −37893.0 | −1.28801 | −0.644006 | − | 0.765021i | \(-0.722729\pi\) | ||||
−0.644006 | + | 0.765021i | \(0.722729\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −44928.0 | −1.52234 | ||||||||
\(956\) | 25472.0 | 0.861740 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 6478.00 | 0.218470 | ||||||||
\(959\) | −7896.00 | −0.265876 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 29258.0 | 0.982109 | ||||||||
\(962\) | 10712.0 | 0.359011 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 2988.00 | 0.0998309 | ||||||||
\(965\) | 4230.00 | 0.141107 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −48914.0 | −1.62665 | −0.813324 | − | 0.581811i | \(-0.802344\pi\) | ||||
−0.813324 | + | 0.581811i | \(0.802344\pi\) | |||||||
\(968\) | −20104.0 | −0.667528 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −378.000 | −0.0125122 | ||||||||
\(971\) | −31110.0 | −1.02818 | −0.514092 | − | 0.857735i | \(-0.671871\pi\) | ||||
−0.514092 | + | 0.857735i | \(0.671871\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 5978.00 | 0.196964 | ||||||||
\(974\) | −3596.00 | −0.118299 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −9824.00 | −0.322191 | ||||||||
\(977\) | −22294.0 | −0.730039 | −0.365020 | − | 0.931000i | \(-0.618938\pi\) | ||||
−0.365020 | + | 0.931000i | \(0.618938\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 65658.0 | 2.14345 | ||||||||
\(980\) | −1764.00 | −0.0574989 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 27416.0 | 0.890916 | ||||||||
\(983\) | 317.000 | 0.0102856 | 0.00514279 | − | 0.999987i | \(-0.498363\pi\) | ||||
0.00514279 | + | 0.999987i | \(0.498363\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −28710.0 | −0.928707 | ||||||||
\(986\) | 1632.00 | 0.0527114 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −4108.00 | −0.132280 | ||||||||
\(989\) | −15965.0 | −0.513304 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 40564.0 | 1.30026 | 0.650130 | − | 0.759823i | \(-0.274714\pi\) | ||||
0.650130 | + | 0.759823i | \(0.274714\pi\) | |||||||
\(992\) | −7776.00 | −0.248879 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 3696.00 | 0.117938 | ||||||||
\(995\) | −17496.0 | −0.557448 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −57528.0 | −1.82741 | −0.913706 | − | 0.406376i | \(-0.866792\pi\) | ||||
−0.913706 | + | 0.406376i | \(0.866792\pi\) | |||||||
\(998\) | 23872.0 | 0.757169 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 1638.4.a.b.1.1 | 1 | ||
3.2 | odd | 2 | 546.4.a.e.1.1 | ✓ | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
546.4.a.e.1.1 | ✓ | 1 | 3.2 | odd | 2 | ||
1638.4.a.b.1.1 | 1 | 1.1 | even | 1 | trivial |