Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2023,4,Mod(1,2023)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2023, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2023.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2023 = 7 \cdot 17^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 2023.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: | \(119.360863942\) |
Analytic rank: | \(1\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 7) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 2023.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.353553 | −0.176777 | − | 0.984251i | \(-0.556567\pi\) | ||||
−0.176777 | + | 0.984251i | \(0.556567\pi\) | |||||||
\(3\) | 2.00000 | 0.384900 | 0.192450 | − | 0.981307i | \(-0.438357\pi\) | ||||
0.192450 | + | 0.981307i | \(0.438357\pi\) | |||||||
\(4\) | −7.00000 | −0.875000 | ||||||||
\(5\) | −16.0000 | −1.43108 | −0.715542 | − | 0.698570i | \(-0.753820\pi\) | ||||
−0.715542 | + | 0.698570i | \(0.753820\pi\) | |||||||
\(6\) | −2.00000 | −0.136083 | ||||||||
\(7\) | 7.00000 | 0.377964 | ||||||||
\(8\) | 15.0000 | 0.662913 | ||||||||
\(9\) | −23.0000 | −0.851852 | ||||||||
\(10\) | 16.0000 | 0.505964 | ||||||||
\(11\) | 8.00000 | 0.219281 | 0.109640 | − | 0.993971i | \(-0.465030\pi\) | ||||
0.109640 | + | 0.993971i | \(0.465030\pi\) | |||||||
\(12\) | −14.0000 | −0.336788 | ||||||||
\(13\) | 28.0000 | 0.597369 | 0.298685 | − | 0.954352i | \(-0.403452\pi\) | ||||
0.298685 | + | 0.954352i | \(0.403452\pi\) | |||||||
\(14\) | −7.00000 | −0.133631 | ||||||||
\(15\) | −32.0000 | −0.550824 | ||||||||
\(16\) | 41.0000 | 0.640625 | ||||||||
\(17\) | 0 | 0 | ||||||||
\(18\) | 23.0000 | 0.301175 | ||||||||
\(19\) | −110.000 | −1.32820 | −0.664098 | − | 0.747645i | \(-0.731184\pi\) | ||||
−0.664098 | + | 0.747645i | \(0.731184\pi\) | |||||||
\(20\) | 112.000 | 1.25220 | ||||||||
\(21\) | 14.0000 | 0.145479 | ||||||||
\(22\) | −8.00000 | −0.0775275 | ||||||||
\(23\) | −48.0000 | −0.435161 | −0.217580 | − | 0.976042i | \(-0.569816\pi\) | ||||
−0.217580 | + | 0.976042i | \(0.569816\pi\) | |||||||
\(24\) | 30.0000 | 0.255155 | ||||||||
\(25\) | 131.000 | 1.04800 | ||||||||
\(26\) | −28.0000 | −0.211202 | ||||||||
\(27\) | −100.000 | −0.712778 | ||||||||
\(28\) | −49.0000 | −0.330719 | ||||||||
\(29\) | 110.000 | 0.704362 | 0.352181 | − | 0.935932i | \(-0.385440\pi\) | ||||
0.352181 | + | 0.935932i | \(0.385440\pi\) | |||||||
\(30\) | 32.0000 | 0.194746 | ||||||||
\(31\) | −12.0000 | −0.0695246 | −0.0347623 | − | 0.999396i | \(-0.511067\pi\) | ||||
−0.0347623 | + | 0.999396i | \(0.511067\pi\) | |||||||
\(32\) | −161.000 | −0.889408 | ||||||||
\(33\) | 16.0000 | 0.0844013 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −112.000 | −0.540899 | ||||||||
\(36\) | 161.000 | 0.745370 | ||||||||
\(37\) | 246.000 | 1.09303 | 0.546516 | − | 0.837449i | \(-0.315954\pi\) | ||||
0.546516 | + | 0.837449i | \(0.315954\pi\) | |||||||
\(38\) | 110.000 | 0.469588 | ||||||||
\(39\) | 56.0000 | 0.229928 | ||||||||
\(40\) | −240.000 | −0.948683 | ||||||||
\(41\) | −182.000 | −0.693259 | −0.346630 | − | 0.938002i | \(-0.612674\pi\) | ||||
−0.346630 | + | 0.938002i | \(0.612674\pi\) | |||||||
\(42\) | −14.0000 | −0.0514344 | ||||||||
\(43\) | 128.000 | 0.453949 | 0.226975 | − | 0.973901i | \(-0.427117\pi\) | ||||
0.226975 | + | 0.973901i | \(0.427117\pi\) | |||||||
\(44\) | −56.0000 | −0.191871 | ||||||||
\(45\) | 368.000 | 1.21907 | ||||||||
\(46\) | 48.0000 | 0.153852 | ||||||||
\(47\) | 324.000 | 1.00554 | 0.502769 | − | 0.864421i | \(-0.332315\pi\) | ||||
0.502769 | + | 0.864421i | \(0.332315\pi\) | |||||||
\(48\) | 82.0000 | 0.246577 | ||||||||
\(49\) | 49.0000 | 0.142857 | ||||||||
\(50\) | −131.000 | −0.370524 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −196.000 | −0.522698 | ||||||||
\(53\) | −162.000 | −0.419857 | −0.209928 | − | 0.977717i | \(-0.567323\pi\) | ||||
−0.209928 | + | 0.977717i | \(0.567323\pi\) | |||||||
\(54\) | 100.000 | 0.252005 | ||||||||
\(55\) | −128.000 | −0.313809 | ||||||||
\(56\) | 105.000 | 0.250557 | ||||||||
\(57\) | −220.000 | −0.511223 | ||||||||
\(58\) | −110.000 | −0.249029 | ||||||||
\(59\) | 810.000 | 1.78734 | 0.893670 | − | 0.448725i | \(-0.148122\pi\) | ||||
0.893670 | + | 0.448725i | \(0.148122\pi\) | |||||||
\(60\) | 224.000 | 0.481971 | ||||||||
\(61\) | 488.000 | 1.02430 | 0.512148 | − | 0.858898i | \(-0.328850\pi\) | ||||
0.512148 | + | 0.858898i | \(0.328850\pi\) | |||||||
\(62\) | 12.0000 | 0.0245807 | ||||||||
\(63\) | −161.000 | −0.321970 | ||||||||
\(64\) | −167.000 | −0.326172 | ||||||||
\(65\) | −448.000 | −0.854886 | ||||||||
\(66\) | −16.0000 | −0.0298404 | ||||||||
\(67\) | 244.000 | 0.444916 | 0.222458 | − | 0.974942i | \(-0.428592\pi\) | ||||
0.222458 | + | 0.974942i | \(0.428592\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −96.0000 | −0.167493 | ||||||||
\(70\) | 112.000 | 0.191237 | ||||||||
\(71\) | 768.000 | 1.28373 | 0.641865 | − | 0.766818i | \(-0.278161\pi\) | ||||
0.641865 | + | 0.766818i | \(0.278161\pi\) | |||||||
\(72\) | −345.000 | −0.564703 | ||||||||
\(73\) | 702.000 | 1.12552 | 0.562759 | − | 0.826621i | \(-0.309740\pi\) | ||||
0.562759 | + | 0.826621i | \(0.309740\pi\) | |||||||
\(74\) | −246.000 | −0.386445 | ||||||||
\(75\) | 262.000 | 0.403375 | ||||||||
\(76\) | 770.000 | 1.16217 | ||||||||
\(77\) | 56.0000 | 0.0828804 | ||||||||
\(78\) | −56.0000 | −0.0812917 | ||||||||
\(79\) | −440.000 | −0.626631 | −0.313316 | − | 0.949649i | \(-0.601440\pi\) | ||||
−0.313316 | + | 0.949649i | \(0.601440\pi\) | |||||||
\(80\) | −656.000 | −0.916788 | ||||||||
\(81\) | 421.000 | 0.577503 | ||||||||
\(82\) | 182.000 | 0.245104 | ||||||||
\(83\) | −1302.00 | −1.72184 | −0.860922 | − | 0.508737i | \(-0.830113\pi\) | ||||
−0.860922 | + | 0.508737i | \(0.830113\pi\) | |||||||
\(84\) | −98.0000 | −0.127294 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −128.000 | −0.160495 | ||||||||
\(87\) | 220.000 | 0.271109 | ||||||||
\(88\) | 120.000 | 0.145364 | ||||||||
\(89\) | 730.000 | 0.869436 | 0.434718 | − | 0.900567i | \(-0.356848\pi\) | ||||
0.434718 | + | 0.900567i | \(0.356848\pi\) | |||||||
\(90\) | −368.000 | −0.431007 | ||||||||
\(91\) | 196.000 | 0.225784 | ||||||||
\(92\) | 336.000 | 0.380765 | ||||||||
\(93\) | −24.0000 | −0.0267600 | ||||||||
\(94\) | −324.000 | −0.355511 | ||||||||
\(95\) | 1760.00 | 1.90076 | ||||||||
\(96\) | −322.000 | −0.342333 | ||||||||
\(97\) | −294.000 | −0.307744 | −0.153872 | − | 0.988091i | \(-0.549174\pi\) | ||||
−0.153872 | + | 0.988091i | \(0.549174\pi\) | |||||||
\(98\) | −49.0000 | −0.0505076 | ||||||||
\(99\) | −184.000 | −0.186795 | ||||||||
\(100\) | −917.000 | −0.917000 | ||||||||
\(101\) | −688.000 | −0.677808 | −0.338904 | − | 0.940821i | \(-0.610056\pi\) | ||||
−0.338904 | + | 0.940821i | \(0.610056\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1388.00 | 1.32780 | 0.663901 | − | 0.747820i | \(-0.268899\pi\) | ||||
0.663901 | + | 0.747820i | \(0.268899\pi\) | |||||||
\(104\) | 420.000 | 0.396004 | ||||||||
\(105\) | −224.000 | −0.208192 | ||||||||
\(106\) | 162.000 | 0.148442 | ||||||||
\(107\) | −244.000 | −0.220452 | −0.110226 | − | 0.993907i | \(-0.535157\pi\) | ||||
−0.110226 | + | 0.993907i | \(0.535157\pi\) | |||||||
\(108\) | 700.000 | 0.623681 | ||||||||
\(109\) | −90.0000 | −0.0790866 | −0.0395433 | − | 0.999218i | \(-0.512590\pi\) | ||||
−0.0395433 | + | 0.999218i | \(0.512590\pi\) | |||||||
\(110\) | 128.000 | 0.110948 | ||||||||
\(111\) | 492.000 | 0.420708 | ||||||||
\(112\) | 287.000 | 0.242133 | ||||||||
\(113\) | −1318.00 | −1.09723 | −0.548615 | − | 0.836075i | \(-0.684845\pi\) | ||||
−0.548615 | + | 0.836075i | \(0.684845\pi\) | |||||||
\(114\) | 220.000 | 0.180745 | ||||||||
\(115\) | 768.000 | 0.622751 | ||||||||
\(116\) | −770.000 | −0.616316 | ||||||||
\(117\) | −644.000 | −0.508870 | ||||||||
\(118\) | −810.000 | −0.631920 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −480.000 | −0.365148 | ||||||||
\(121\) | −1267.00 | −0.951916 | ||||||||
\(122\) | −488.000 | −0.362143 | ||||||||
\(123\) | −364.000 | −0.266836 | ||||||||
\(124\) | 84.0000 | 0.0608341 | ||||||||
\(125\) | −96.0000 | −0.0686920 | ||||||||
\(126\) | 161.000 | 0.113833 | ||||||||
\(127\) | −1776.00 | −1.24090 | −0.620451 | − | 0.784245i | \(-0.713050\pi\) | ||||
−0.620451 | + | 0.784245i | \(0.713050\pi\) | |||||||
\(128\) | 1455.00 | 1.00473 | ||||||||
\(129\) | 256.000 | 0.174725 | ||||||||
\(130\) | 448.000 | 0.302248 | ||||||||
\(131\) | 1118.00 | 0.745650 | 0.372825 | − | 0.927902i | \(-0.378389\pi\) | ||||
0.372825 | + | 0.927902i | \(0.378389\pi\) | |||||||
\(132\) | −112.000 | −0.0738511 | ||||||||
\(133\) | −770.000 | −0.502011 | ||||||||
\(134\) | −244.000 | −0.157301 | ||||||||
\(135\) | 1600.00 | 1.02004 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 2274.00 | 1.41811 | 0.709054 | − | 0.705154i | \(-0.249122\pi\) | ||||
0.709054 | + | 0.705154i | \(0.249122\pi\) | |||||||
\(138\) | 96.0000 | 0.0592178 | ||||||||
\(139\) | 210.000 | 0.128144 | 0.0640718 | − | 0.997945i | \(-0.479591\pi\) | ||||
0.0640718 | + | 0.997945i | \(0.479591\pi\) | |||||||
\(140\) | 784.000 | 0.473286 | ||||||||
\(141\) | 648.000 | 0.387032 | ||||||||
\(142\) | −768.000 | −0.453867 | ||||||||
\(143\) | 224.000 | 0.130992 | ||||||||
\(144\) | −943.000 | −0.545718 | ||||||||
\(145\) | −1760.00 | −1.00800 | ||||||||
\(146\) | −702.000 | −0.397931 | ||||||||
\(147\) | 98.0000 | 0.0549857 | ||||||||
\(148\) | −1722.00 | −0.956402 | ||||||||
\(149\) | −2010.00 | −1.10514 | −0.552569 | − | 0.833467i | \(-0.686352\pi\) | ||||
−0.552569 | + | 0.833467i | \(0.686352\pi\) | |||||||
\(150\) | −262.000 | −0.142615 | ||||||||
\(151\) | 1112.00 | 0.599293 | 0.299647 | − | 0.954050i | \(-0.403131\pi\) | ||||
0.299647 | + | 0.954050i | \(0.403131\pi\) | |||||||
\(152\) | −1650.00 | −0.880478 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −56.0000 | −0.0293027 | ||||||||
\(155\) | 192.000 | 0.0994956 | ||||||||
\(156\) | −392.000 | −0.201187 | ||||||||
\(157\) | 124.000 | 0.0630336 | 0.0315168 | − | 0.999503i | \(-0.489966\pi\) | ||||
0.0315168 | + | 0.999503i | \(0.489966\pi\) | |||||||
\(158\) | 440.000 | 0.221548 | ||||||||
\(159\) | −324.000 | −0.161603 | ||||||||
\(160\) | 2576.00 | 1.27282 | ||||||||
\(161\) | −336.000 | −0.164475 | ||||||||
\(162\) | −421.000 | −0.204178 | ||||||||
\(163\) | −2008.00 | −0.964900 | −0.482450 | − | 0.875924i | \(-0.660253\pi\) | ||||
−0.482450 | + | 0.875924i | \(0.660253\pi\) | |||||||
\(164\) | 1274.00 | 0.606602 | ||||||||
\(165\) | −256.000 | −0.120785 | ||||||||
\(166\) | 1302.00 | 0.608764 | ||||||||
\(167\) | −2884.00 | −1.33635 | −0.668176 | − | 0.744004i | \(-0.732924\pi\) | ||||
−0.668176 | + | 0.744004i | \(0.732924\pi\) | |||||||
\(168\) | 210.000 | 0.0964396 | ||||||||
\(169\) | −1413.00 | −0.643150 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 2530.00 | 1.13143 | ||||||||
\(172\) | −896.000 | −0.397206 | ||||||||
\(173\) | −2228.00 | −0.979143 | −0.489571 | − | 0.871963i | \(-0.662847\pi\) | ||||
−0.489571 | + | 0.871963i | \(0.662847\pi\) | |||||||
\(174\) | −220.000 | −0.0958515 | ||||||||
\(175\) | 917.000 | 0.396107 | ||||||||
\(176\) | 328.000 | 0.140477 | ||||||||
\(177\) | 1620.00 | 0.687947 | ||||||||
\(178\) | −730.000 | −0.307392 | ||||||||
\(179\) | −820.000 | −0.342400 | −0.171200 | − | 0.985236i | \(-0.554764\pi\) | ||||
−0.171200 | + | 0.985236i | \(0.554764\pi\) | |||||||
\(180\) | −2576.00 | −1.06669 | ||||||||
\(181\) | −3892.00 | −1.59829 | −0.799144 | − | 0.601140i | \(-0.794713\pi\) | ||||
−0.799144 | + | 0.601140i | \(0.794713\pi\) | |||||||
\(182\) | −196.000 | −0.0798268 | ||||||||
\(183\) | 976.000 | 0.394251 | ||||||||
\(184\) | −720.000 | −0.288473 | ||||||||
\(185\) | −3936.00 | −1.56422 | ||||||||
\(186\) | 24.0000 | 0.00946110 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | −2268.00 | −0.879845 | ||||||||
\(189\) | −700.000 | −0.269405 | ||||||||
\(190\) | −1760.00 | −0.672020 | ||||||||
\(191\) | −5048.00 | −1.91236 | −0.956179 | − | 0.292782i | \(-0.905419\pi\) | ||||
−0.956179 | + | 0.292782i | \(0.905419\pi\) | |||||||
\(192\) | −334.000 | −0.125544 | ||||||||
\(193\) | 2962.00 | 1.10471 | 0.552356 | − | 0.833608i | \(-0.313729\pi\) | ||||
0.552356 | + | 0.833608i | \(0.313729\pi\) | |||||||
\(194\) | 294.000 | 0.108804 | ||||||||
\(195\) | −896.000 | −0.329046 | ||||||||
\(196\) | −343.000 | −0.125000 | ||||||||
\(197\) | −3334.00 | −1.20577 | −0.602887 | − | 0.797826i | \(-0.705983\pi\) | ||||
−0.602887 | + | 0.797826i | \(0.705983\pi\) | |||||||
\(198\) | 184.000 | 0.0660420 | ||||||||
\(199\) | −1860.00 | −0.662572 | −0.331286 | − | 0.943530i | \(-0.607483\pi\) | ||||
−0.331286 | + | 0.943530i | \(0.607483\pi\) | |||||||
\(200\) | 1965.00 | 0.694732 | ||||||||
\(201\) | 488.000 | 0.171248 | ||||||||
\(202\) | 688.000 | 0.239641 | ||||||||
\(203\) | 770.000 | 0.266224 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 2912.00 | 0.992112 | ||||||||
\(206\) | −1388.00 | −0.469449 | ||||||||
\(207\) | 1104.00 | 0.370692 | ||||||||
\(208\) | 1148.00 | 0.382690 | ||||||||
\(209\) | −880.000 | −0.291248 | ||||||||
\(210\) | 224.000 | 0.0736070 | ||||||||
\(211\) | 4268.00 | 1.39252 | 0.696259 | − | 0.717791i | \(-0.254847\pi\) | ||||
0.696259 | + | 0.717791i | \(0.254847\pi\) | |||||||
\(212\) | 1134.00 | 0.367375 | ||||||||
\(213\) | 1536.00 | 0.494108 | ||||||||
\(214\) | 244.000 | 0.0779416 | ||||||||
\(215\) | −2048.00 | −0.649639 | ||||||||
\(216\) | −1500.00 | −0.472510 | ||||||||
\(217\) | −84.0000 | −0.0262778 | ||||||||
\(218\) | 90.0000 | 0.0279613 | ||||||||
\(219\) | 1404.00 | 0.433212 | ||||||||
\(220\) | 896.000 | 0.274583 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | −492.000 | −0.148743 | ||||||||
\(223\) | −5432.00 | −1.63118 | −0.815591 | − | 0.578629i | \(-0.803588\pi\) | ||||
−0.815591 | + | 0.578629i | \(0.803588\pi\) | |||||||
\(224\) | −1127.00 | −0.336165 | ||||||||
\(225\) | −3013.00 | −0.892741 | ||||||||
\(226\) | 1318.00 | 0.387929 | ||||||||
\(227\) | 2046.00 | 0.598228 | 0.299114 | − | 0.954217i | \(-0.403309\pi\) | ||||
0.299114 | + | 0.954217i | \(0.403309\pi\) | |||||||
\(228\) | 1540.00 | 0.447320 | ||||||||
\(229\) | −2980.00 | −0.859930 | −0.429965 | − | 0.902846i | \(-0.641474\pi\) | ||||
−0.429965 | + | 0.902846i | \(0.641474\pi\) | |||||||
\(230\) | −768.000 | −0.220176 | ||||||||
\(231\) | 112.000 | 0.0319007 | ||||||||
\(232\) | 1650.00 | 0.466930 | ||||||||
\(233\) | −4458.00 | −1.25345 | −0.626724 | − | 0.779241i | \(-0.715605\pi\) | ||||
−0.626724 | + | 0.779241i | \(0.715605\pi\) | |||||||
\(234\) | 644.000 | 0.179913 | ||||||||
\(235\) | −5184.00 | −1.43901 | ||||||||
\(236\) | −5670.00 | −1.56392 | ||||||||
\(237\) | −880.000 | −0.241190 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 4440.00 | 1.20167 | 0.600836 | − | 0.799372i | \(-0.294834\pi\) | ||||
0.600836 | + | 0.799372i | \(0.294834\pi\) | |||||||
\(240\) | −1312.00 | −0.352872 | ||||||||
\(241\) | −3302.00 | −0.882575 | −0.441287 | − | 0.897366i | \(-0.645478\pi\) | ||||
−0.441287 | + | 0.897366i | \(0.645478\pi\) | |||||||
\(242\) | 1267.00 | 0.336553 | ||||||||
\(243\) | 3542.00 | 0.935059 | ||||||||
\(244\) | −3416.00 | −0.896258 | ||||||||
\(245\) | −784.000 | −0.204441 | ||||||||
\(246\) | 364.000 | 0.0943406 | ||||||||
\(247\) | −3080.00 | −0.793424 | ||||||||
\(248\) | −180.000 | −0.0460888 | ||||||||
\(249\) | −2604.00 | −0.662738 | ||||||||
\(250\) | 96.0000 | 0.0242863 | ||||||||
\(251\) | 1582.00 | 0.397829 | 0.198914 | − | 0.980017i | \(-0.436258\pi\) | ||||
0.198914 | + | 0.980017i | \(0.436258\pi\) | |||||||
\(252\) | 1127.00 | 0.281724 | ||||||||
\(253\) | −384.000 | −0.0954224 | ||||||||
\(254\) | 1776.00 | 0.438725 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −119.000 | −0.0290527 | ||||||||
\(257\) | 2354.00 | 0.571356 | 0.285678 | − | 0.958326i | \(-0.407781\pi\) | ||||
0.285678 | + | 0.958326i | \(0.407781\pi\) | |||||||
\(258\) | −256.000 | −0.0617747 | ||||||||
\(259\) | 1722.00 | 0.413127 | ||||||||
\(260\) | 3136.00 | 0.748025 | ||||||||
\(261\) | −2530.00 | −0.600012 | ||||||||
\(262\) | −1118.00 | −0.263627 | ||||||||
\(263\) | −3872.00 | −0.907824 | −0.453912 | − | 0.891046i | \(-0.649972\pi\) | ||||
−0.453912 | + | 0.891046i | \(0.649972\pi\) | |||||||
\(264\) | 240.000 | 0.0559507 | ||||||||
\(265\) | 2592.00 | 0.600850 | ||||||||
\(266\) | 770.000 | 0.177488 | ||||||||
\(267\) | 1460.00 | 0.334646 | ||||||||
\(268\) | −1708.00 | −0.389301 | ||||||||
\(269\) | −180.000 | −0.0407985 | −0.0203992 | − | 0.999792i | \(-0.506494\pi\) | ||||
−0.0203992 | + | 0.999792i | \(0.506494\pi\) | |||||||
\(270\) | −1600.00 | −0.360640 | ||||||||
\(271\) | 2032.00 | 0.455480 | 0.227740 | − | 0.973722i | \(-0.426866\pi\) | ||||
0.227740 | + | 0.973722i | \(0.426866\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 392.000 | 0.0869045 | ||||||||
\(274\) | −2274.00 | −0.501377 | ||||||||
\(275\) | 1048.00 | 0.229806 | ||||||||
\(276\) | 672.000 | 0.146557 | ||||||||
\(277\) | 5426.00 | 1.17696 | 0.588478 | − | 0.808513i | \(-0.299727\pi\) | ||||
0.588478 | + | 0.808513i | \(0.299727\pi\) | |||||||
\(278\) | −210.000 | −0.0453056 | ||||||||
\(279\) | 276.000 | 0.0592247 | ||||||||
\(280\) | −1680.00 | −0.358569 | ||||||||
\(281\) | 842.000 | 0.178753 | 0.0893764 | − | 0.995998i | \(-0.471513\pi\) | ||||
0.0893764 | + | 0.995998i | \(0.471513\pi\) | |||||||
\(282\) | −648.000 | −0.136836 | ||||||||
\(283\) | 3782.00 | 0.794405 | 0.397202 | − | 0.917731i | \(-0.369981\pi\) | ||||
0.397202 | + | 0.917731i | \(0.369981\pi\) | |||||||
\(284\) | −5376.00 | −1.12326 | ||||||||
\(285\) | 3520.00 | 0.731603 | ||||||||
\(286\) | −224.000 | −0.0463126 | ||||||||
\(287\) | −1274.00 | −0.262027 | ||||||||
\(288\) | 3703.00 | 0.757644 | ||||||||
\(289\) | 0 | 0 | ||||||||
\(290\) | 1760.00 | 0.356382 | ||||||||
\(291\) | −588.000 | −0.118451 | ||||||||
\(292\) | −4914.00 | −0.984829 | ||||||||
\(293\) | −4312.00 | −0.859760 | −0.429880 | − | 0.902886i | \(-0.641444\pi\) | ||||
−0.429880 | + | 0.902886i | \(0.641444\pi\) | |||||||
\(294\) | −98.0000 | −0.0194404 | ||||||||
\(295\) | −12960.0 | −2.55783 | ||||||||
\(296\) | 3690.00 | 0.724584 | ||||||||
\(297\) | −800.000 | −0.156299 | ||||||||
\(298\) | 2010.00 | 0.390725 | ||||||||
\(299\) | −1344.00 | −0.259952 | ||||||||
\(300\) | −1834.00 | −0.352953 | ||||||||
\(301\) | 896.000 | 0.171577 | ||||||||
\(302\) | −1112.00 | −0.211882 | ||||||||
\(303\) | −1376.00 | −0.260888 | ||||||||
\(304\) | −4510.00 | −0.850876 | ||||||||
\(305\) | −7808.00 | −1.46585 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 2674.00 | 0.497112 | 0.248556 | − | 0.968618i | \(-0.420044\pi\) | ||||
0.248556 | + | 0.968618i | \(0.420044\pi\) | |||||||
\(308\) | −392.000 | −0.0725204 | ||||||||
\(309\) | 2776.00 | 0.511072 | ||||||||
\(310\) | −192.000 | −0.0351770 | ||||||||
\(311\) | 3768.00 | 0.687021 | 0.343511 | − | 0.939149i | \(-0.388384\pi\) | ||||
0.343511 | + | 0.939149i | \(0.388384\pi\) | |||||||
\(312\) | 840.000 | 0.152422 | ||||||||
\(313\) | −2438.00 | −0.440268 | −0.220134 | − | 0.975470i | \(-0.570649\pi\) | ||||
−0.220134 | + | 0.975470i | \(0.570649\pi\) | |||||||
\(314\) | −124.000 | −0.0222857 | ||||||||
\(315\) | 2576.00 | 0.460766 | ||||||||
\(316\) | 3080.00 | 0.548302 | ||||||||
\(317\) | 3186.00 | 0.564491 | 0.282245 | − | 0.959342i | \(-0.408921\pi\) | ||||
0.282245 | + | 0.959342i | \(0.408921\pi\) | |||||||
\(318\) | 324.000 | 0.0571353 | ||||||||
\(319\) | 880.000 | 0.154453 | ||||||||
\(320\) | 2672.00 | 0.466779 | ||||||||
\(321\) | −488.000 | −0.0848520 | ||||||||
\(322\) | 336.000 | 0.0581508 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | −2947.00 | −0.505316 | ||||||||
\(325\) | 3668.00 | 0.626043 | ||||||||
\(326\) | 2008.00 | 0.341144 | ||||||||
\(327\) | −180.000 | −0.0304404 | ||||||||
\(328\) | −2730.00 | −0.459570 | ||||||||
\(329\) | 2268.00 | 0.380057 | ||||||||
\(330\) | 256.000 | 0.0427040 | ||||||||
\(331\) | 8672.00 | 1.44005 | 0.720025 | − | 0.693949i | \(-0.244131\pi\) | ||||
0.720025 | + | 0.693949i | \(0.244131\pi\) | |||||||
\(332\) | 9114.00 | 1.50661 | ||||||||
\(333\) | −5658.00 | −0.931101 | ||||||||
\(334\) | 2884.00 | 0.472471 | ||||||||
\(335\) | −3904.00 | −0.636711 | ||||||||
\(336\) | 574.000 | 0.0931972 | ||||||||
\(337\) | −814.000 | −0.131577 | −0.0657884 | − | 0.997834i | \(-0.520956\pi\) | ||||
−0.0657884 | + | 0.997834i | \(0.520956\pi\) | |||||||
\(338\) | 1413.00 | 0.227388 | ||||||||
\(339\) | −2636.00 | −0.422324 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −96.0000 | −0.0152454 | ||||||||
\(342\) | −2530.00 | −0.400020 | ||||||||
\(343\) | 343.000 | 0.0539949 | ||||||||
\(344\) | 1920.00 | 0.300929 | ||||||||
\(345\) | 1536.00 | 0.239697 | ||||||||
\(346\) | 2228.00 | 0.346179 | ||||||||
\(347\) | −9344.00 | −1.44557 | −0.722784 | − | 0.691074i | \(-0.757138\pi\) | ||||
−0.722784 | + | 0.691074i | \(0.757138\pi\) | |||||||
\(348\) | −1540.00 | −0.237220 | ||||||||
\(349\) | −5180.00 | −0.794496 | −0.397248 | − | 0.917711i | \(-0.630035\pi\) | ||||
−0.397248 | + | 0.917711i | \(0.630035\pi\) | |||||||
\(350\) | −917.000 | −0.140045 | ||||||||
\(351\) | −2800.00 | −0.425792 | ||||||||
\(352\) | −1288.00 | −0.195030 | ||||||||
\(353\) | 12178.0 | 1.83617 | 0.918087 | − | 0.396379i | \(-0.129733\pi\) | ||||
0.918087 | + | 0.396379i | \(0.129733\pi\) | |||||||
\(354\) | −1620.00 | −0.243226 | ||||||||
\(355\) | −12288.0 | −1.83712 | ||||||||
\(356\) | −5110.00 | −0.760757 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 820.000 | 0.121057 | ||||||||
\(359\) | 440.000 | 0.0646861 | 0.0323431 | − | 0.999477i | \(-0.489703\pi\) | ||||
0.0323431 | + | 0.999477i | \(0.489703\pi\) | |||||||
\(360\) | 5520.00 | 0.808138 | ||||||||
\(361\) | 5241.00 | 0.764106 | ||||||||
\(362\) | 3892.00 | 0.565080 | ||||||||
\(363\) | −2534.00 | −0.366393 | ||||||||
\(364\) | −1372.00 | −0.197561 | ||||||||
\(365\) | −11232.0 | −1.61071 | ||||||||
\(366\) | −976.000 | −0.139389 | ||||||||
\(367\) | 9816.00 | 1.39616 | 0.698080 | − | 0.716019i | \(-0.254038\pi\) | ||||
0.698080 | + | 0.716019i | \(0.254038\pi\) | |||||||
\(368\) | −1968.00 | −0.278775 | ||||||||
\(369\) | 4186.00 | 0.590554 | ||||||||
\(370\) | 3936.00 | 0.553035 | ||||||||
\(371\) | −1134.00 | −0.158691 | ||||||||
\(372\) | 168.000 | 0.0234150 | ||||||||
\(373\) | −442.000 | −0.0613563 | −0.0306781 | − | 0.999529i | \(-0.509767\pi\) | ||||
−0.0306781 | + | 0.999529i | \(0.509767\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −192.000 | −0.0264396 | ||||||||
\(376\) | 4860.00 | 0.666583 | ||||||||
\(377\) | 3080.00 | 0.420764 | ||||||||
\(378\) | 700.000 | 0.0952490 | ||||||||
\(379\) | 3960.00 | 0.536706 | 0.268353 | − | 0.963321i | \(-0.413521\pi\) | ||||
0.268353 | + | 0.963321i | \(0.413521\pi\) | |||||||
\(380\) | −12320.0 | −1.66316 | ||||||||
\(381\) | −3552.00 | −0.477623 | ||||||||
\(382\) | 5048.00 | 0.676121 | ||||||||
\(383\) | 6708.00 | 0.894942 | 0.447471 | − | 0.894298i | \(-0.352325\pi\) | ||||
0.447471 | + | 0.894298i | \(0.352325\pi\) | |||||||
\(384\) | 2910.00 | 0.386720 | ||||||||
\(385\) | −896.000 | −0.118609 | ||||||||
\(386\) | −2962.00 | −0.390575 | ||||||||
\(387\) | −2944.00 | −0.386697 | ||||||||
\(388\) | 2058.00 | 0.269276 | ||||||||
\(389\) | −13350.0 | −1.74003 | −0.870015 | − | 0.493025i | \(-0.835891\pi\) | ||||
−0.870015 | + | 0.493025i | \(0.835891\pi\) | |||||||
\(390\) | 896.000 | 0.116335 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 735.000 | 0.0947018 | ||||||||
\(393\) | 2236.00 | 0.287001 | ||||||||
\(394\) | 3334.00 | 0.426306 | ||||||||
\(395\) | 7040.00 | 0.896762 | ||||||||
\(396\) | 1288.00 | 0.163446 | ||||||||
\(397\) | 1356.00 | 0.171425 | 0.0857125 | − | 0.996320i | \(-0.472683\pi\) | ||||
0.0857125 | + | 0.996320i | \(0.472683\pi\) | |||||||
\(398\) | 1860.00 | 0.234255 | ||||||||
\(399\) | −1540.00 | −0.193224 | ||||||||
\(400\) | 5371.00 | 0.671375 | ||||||||
\(401\) | −6222.00 | −0.774843 | −0.387421 | − | 0.921903i | \(-0.626634\pi\) | ||||
−0.387421 | + | 0.921903i | \(0.626634\pi\) | |||||||
\(402\) | −488.000 | −0.0605453 | ||||||||
\(403\) | −336.000 | −0.0415319 | ||||||||
\(404\) | 4816.00 | 0.593082 | ||||||||
\(405\) | −6736.00 | −0.826456 | ||||||||
\(406\) | −770.000 | −0.0941243 | ||||||||
\(407\) | 1968.00 | 0.239681 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 5150.00 | 0.622619 | 0.311309 | − | 0.950309i | \(-0.399232\pi\) | ||||
0.311309 | + | 0.950309i | \(0.399232\pi\) | |||||||
\(410\) | −2912.00 | −0.350764 | ||||||||
\(411\) | 4548.00 | 0.545830 | ||||||||
\(412\) | −9716.00 | −1.16183 | ||||||||
\(413\) | 5670.00 | 0.675551 | ||||||||
\(414\) | −1104.00 | −0.131060 | ||||||||
\(415\) | 20832.0 | 2.46410 | ||||||||
\(416\) | −4508.00 | −0.531305 | ||||||||
\(417\) | 420.000 | 0.0493225 | ||||||||
\(418\) | 880.000 | 0.102972 | ||||||||
\(419\) | −2310.00 | −0.269334 | −0.134667 | − | 0.990891i | \(-0.542996\pi\) | ||||
−0.134667 | + | 0.990891i | \(0.542996\pi\) | |||||||
\(420\) | 1568.00 | 0.182168 | ||||||||
\(421\) | 1262.00 | 0.146095 | 0.0730476 | − | 0.997328i | \(-0.476727\pi\) | ||||
0.0730476 | + | 0.997328i | \(0.476727\pi\) | |||||||
\(422\) | −4268.00 | −0.492329 | ||||||||
\(423\) | −7452.00 | −0.856569 | ||||||||
\(424\) | −2430.00 | −0.278328 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −1536.00 | −0.174694 | ||||||||
\(427\) | 3416.00 | 0.387147 | ||||||||
\(428\) | 1708.00 | 0.192896 | ||||||||
\(429\) | 448.000 | 0.0504188 | ||||||||
\(430\) | 2048.00 | 0.229682 | ||||||||
\(431\) | 4488.00 | 0.501576 | 0.250788 | − | 0.968042i | \(-0.419310\pi\) | ||||
0.250788 | + | 0.968042i | \(0.419310\pi\) | |||||||
\(432\) | −4100.00 | −0.456623 | ||||||||
\(433\) | 17038.0 | 1.89098 | 0.945490 | − | 0.325652i | \(-0.105584\pi\) | ||||
0.945490 | + | 0.325652i | \(0.105584\pi\) | |||||||
\(434\) | 84.0000 | 0.00929062 | ||||||||
\(435\) | −3520.00 | −0.387979 | ||||||||
\(436\) | 630.000 | 0.0692008 | ||||||||
\(437\) | 5280.00 | 0.577979 | ||||||||
\(438\) | −1404.00 | −0.153164 | ||||||||
\(439\) | −16200.0 | −1.76124 | −0.880619 | − | 0.473824i | \(-0.842873\pi\) | ||||
−0.880619 | + | 0.473824i | \(0.842873\pi\) | |||||||
\(440\) | −1920.00 | −0.208028 | ||||||||
\(441\) | −1127.00 | −0.121693 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −8772.00 | −0.940791 | −0.470395 | − | 0.882456i | \(-0.655889\pi\) | ||||
−0.470395 | + | 0.882456i | \(0.655889\pi\) | |||||||
\(444\) | −3444.00 | −0.368119 | ||||||||
\(445\) | −11680.0 | −1.24424 | ||||||||
\(446\) | 5432.00 | 0.576710 | ||||||||
\(447\) | −4020.00 | −0.425368 | ||||||||
\(448\) | −1169.00 | −0.123281 | ||||||||
\(449\) | −2130.00 | −0.223877 | −0.111939 | − | 0.993715i | \(-0.535706\pi\) | ||||
−0.111939 | + | 0.993715i | \(0.535706\pi\) | |||||||
\(450\) | 3013.00 | 0.315632 | ||||||||
\(451\) | −1456.00 | −0.152019 | ||||||||
\(452\) | 9226.00 | 0.960076 | ||||||||
\(453\) | 2224.00 | 0.230668 | ||||||||
\(454\) | −2046.00 | −0.211506 | ||||||||
\(455\) | −3136.00 | −0.323116 | ||||||||
\(456\) | −3300.00 | −0.338896 | ||||||||
\(457\) | 10534.0 | 1.07825 | 0.539124 | − | 0.842226i | \(-0.318755\pi\) | ||||
0.539124 | + | 0.842226i | \(0.318755\pi\) | |||||||
\(458\) | 2980.00 | 0.304031 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −5376.00 | −0.544907 | ||||||||
\(461\) | −9268.00 | −0.936342 | −0.468171 | − | 0.883638i | \(-0.655087\pi\) | ||||
−0.468171 | + | 0.883638i | \(0.655087\pi\) | |||||||
\(462\) | −112.000 | −0.0112786 | ||||||||
\(463\) | −9392.00 | −0.942728 | −0.471364 | − | 0.881939i | \(-0.656238\pi\) | ||||
−0.471364 | + | 0.881939i | \(0.656238\pi\) | |||||||
\(464\) | 4510.00 | 0.451232 | ||||||||
\(465\) | 384.000 | 0.0382959 | ||||||||
\(466\) | 4458.00 | 0.443161 | ||||||||
\(467\) | −10806.0 | −1.07075 | −0.535377 | − | 0.844613i | \(-0.679830\pi\) | ||||
−0.535377 | + | 0.844613i | \(0.679830\pi\) | |||||||
\(468\) | 4508.00 | 0.445261 | ||||||||
\(469\) | 1708.00 | 0.168162 | ||||||||
\(470\) | 5184.00 | 0.508766 | ||||||||
\(471\) | 248.000 | 0.0242616 | ||||||||
\(472\) | 12150.0 | 1.18485 | ||||||||
\(473\) | 1024.00 | 0.0995424 | ||||||||
\(474\) | 880.000 | 0.0852737 | ||||||||
\(475\) | −14410.0 | −1.39195 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 3726.00 | 0.357656 | ||||||||
\(478\) | −4440.00 | −0.424855 | ||||||||
\(479\) | −4940.00 | −0.471220 | −0.235610 | − | 0.971848i | \(-0.575709\pi\) | ||||
−0.235610 | + | 0.971848i | \(0.575709\pi\) | |||||||
\(480\) | 5152.00 | 0.489907 | ||||||||
\(481\) | 6888.00 | 0.652943 | ||||||||
\(482\) | 3302.00 | 0.312037 | ||||||||
\(483\) | −672.000 | −0.0633065 | ||||||||
\(484\) | 8869.00 | 0.832926 | ||||||||
\(485\) | 4704.00 | 0.440407 | ||||||||
\(486\) | −3542.00 | −0.330593 | ||||||||
\(487\) | 5216.00 | 0.485338 | 0.242669 | − | 0.970109i | \(-0.421977\pi\) | ||||
0.242669 | + | 0.970109i | \(0.421977\pi\) | |||||||
\(488\) | 7320.00 | 0.679018 | ||||||||
\(489\) | −4016.00 | −0.371390 | ||||||||
\(490\) | 784.000 | 0.0722806 | ||||||||
\(491\) | 4412.00 | 0.405521 | 0.202760 | − | 0.979228i | \(-0.435009\pi\) | ||||
0.202760 | + | 0.979228i | \(0.435009\pi\) | |||||||
\(492\) | 2548.00 | 0.233481 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 3080.00 | 0.280518 | ||||||||
\(495\) | 2944.00 | 0.267319 | ||||||||
\(496\) | −492.000 | −0.0445392 | ||||||||
\(497\) | 5376.00 | 0.485204 | ||||||||
\(498\) | 2604.00 | 0.234313 | ||||||||
\(499\) | −19060.0 | −1.70991 | −0.854953 | − | 0.518706i | \(-0.826414\pi\) | ||||
−0.854953 | + | 0.518706i | \(0.826414\pi\) | |||||||
\(500\) | 672.000 | 0.0601055 | ||||||||
\(501\) | −5768.00 | −0.514362 | ||||||||
\(502\) | −1582.00 | −0.140654 | ||||||||
\(503\) | −12768.0 | −1.13180 | −0.565902 | − | 0.824473i | \(-0.691472\pi\) | ||||
−0.565902 | + | 0.824473i | \(0.691472\pi\) | |||||||
\(504\) | −2415.00 | −0.213438 | ||||||||
\(505\) | 11008.0 | 0.969999 | ||||||||
\(506\) | 384.000 | 0.0337369 | ||||||||
\(507\) | −2826.00 | −0.247548 | ||||||||
\(508\) | 12432.0 | 1.08579 | ||||||||
\(509\) | −5500.00 | −0.478945 | −0.239473 | − | 0.970903i | \(-0.576975\pi\) | ||||
−0.239473 | + | 0.970903i | \(0.576975\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 4914.00 | 0.425406 | ||||||||
\(512\) | −11521.0 | −0.994455 | ||||||||
\(513\) | 11000.0 | 0.946709 | ||||||||
\(514\) | −2354.00 | −0.202005 | ||||||||
\(515\) | −22208.0 | −1.90020 | ||||||||
\(516\) | −1792.00 | −0.152884 | ||||||||
\(517\) | 2592.00 | 0.220495 | ||||||||
\(518\) | −1722.00 | −0.146062 | ||||||||
\(519\) | −4456.00 | −0.376872 | ||||||||
\(520\) | −6720.00 | −0.566714 | ||||||||
\(521\) | 7338.00 | 0.617051 | 0.308526 | − | 0.951216i | \(-0.400164\pi\) | ||||
0.308526 | + | 0.951216i | \(0.400164\pi\) | |||||||
\(522\) | 2530.00 | 0.212136 | ||||||||
\(523\) | −17582.0 | −1.46999 | −0.734997 | − | 0.678070i | \(-0.762817\pi\) | ||||
−0.734997 | + | 0.678070i | \(0.762817\pi\) | |||||||
\(524\) | −7826.00 | −0.652444 | ||||||||
\(525\) | 1834.00 | 0.152462 | ||||||||
\(526\) | 3872.00 | 0.320964 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 656.000 | 0.0540696 | ||||||||
\(529\) | −9863.00 | −0.810635 | ||||||||
\(530\) | −2592.00 | −0.212433 | ||||||||
\(531\) | −18630.0 | −1.52255 | ||||||||
\(532\) | 5390.00 | 0.439260 | ||||||||
\(533\) | −5096.00 | −0.414132 | ||||||||
\(534\) | −1460.00 | −0.118315 | ||||||||
\(535\) | 3904.00 | 0.315485 | ||||||||
\(536\) | 3660.00 | 0.294940 | ||||||||
\(537\) | −1640.00 | −0.131790 | ||||||||
\(538\) | 180.000 | 0.0144244 | ||||||||
\(539\) | 392.000 | 0.0313259 | ||||||||
\(540\) | −11200.0 | −0.892539 | ||||||||
\(541\) | 1618.00 | 0.128583 | 0.0642914 | − | 0.997931i | \(-0.479521\pi\) | ||||
0.0642914 | + | 0.997931i | \(0.479521\pi\) | |||||||
\(542\) | −2032.00 | −0.161037 | ||||||||
\(543\) | −7784.00 | −0.615181 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 1440.00 | 0.113179 | ||||||||
\(546\) | −392.000 | −0.0307254 | ||||||||
\(547\) | −16144.0 | −1.26192 | −0.630958 | − | 0.775817i | \(-0.717338\pi\) | ||||
−0.630958 | + | 0.775817i | \(0.717338\pi\) | |||||||
\(548\) | −15918.0 | −1.24085 | ||||||||
\(549\) | −11224.0 | −0.872548 | ||||||||
\(550\) | −1048.00 | −0.0812489 | ||||||||
\(551\) | −12100.0 | −0.935531 | ||||||||
\(552\) | −1440.00 | −0.111033 | ||||||||
\(553\) | −3080.00 | −0.236844 | ||||||||
\(554\) | −5426.00 | −0.416117 | ||||||||
\(555\) | −7872.00 | −0.602068 | ||||||||
\(556\) | −1470.00 | −0.112126 | ||||||||
\(557\) | 4654.00 | 0.354033 | 0.177016 | − | 0.984208i | \(-0.443355\pi\) | ||||
0.177016 | + | 0.984208i | \(0.443355\pi\) | |||||||
\(558\) | −276.000 | −0.0209391 | ||||||||
\(559\) | 3584.00 | 0.271175 | ||||||||
\(560\) | −4592.00 | −0.346513 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −842.000 | −0.0631986 | ||||||||
\(563\) | 10078.0 | 0.754418 | 0.377209 | − | 0.926128i | \(-0.376884\pi\) | ||||
0.377209 | + | 0.926128i | \(0.376884\pi\) | |||||||
\(564\) | −4536.00 | −0.338653 | ||||||||
\(565\) | 21088.0 | 1.57023 | ||||||||
\(566\) | −3782.00 | −0.280865 | ||||||||
\(567\) | 2947.00 | 0.218276 | ||||||||
\(568\) | 11520.0 | 0.851001 | ||||||||
\(569\) | −5930.00 | −0.436904 | −0.218452 | − | 0.975848i | \(-0.570101\pi\) | ||||
−0.218452 | + | 0.975848i | \(0.570101\pi\) | |||||||
\(570\) | −3520.00 | −0.258661 | ||||||||
\(571\) | 19048.0 | 1.39603 | 0.698016 | − | 0.716082i | \(-0.254067\pi\) | ||||
0.698016 | + | 0.716082i | \(0.254067\pi\) | |||||||
\(572\) | −1568.00 | −0.114618 | ||||||||
\(573\) | −10096.0 | −0.736067 | ||||||||
\(574\) | 1274.00 | 0.0926406 | ||||||||
\(575\) | −6288.00 | −0.456048 | ||||||||
\(576\) | 3841.00 | 0.277850 | ||||||||
\(577\) | −14366.0 | −1.03651 | −0.518253 | − | 0.855227i | \(-0.673418\pi\) | ||||
−0.518253 | + | 0.855227i | \(0.673418\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 5924.00 | 0.425204 | ||||||||
\(580\) | 12320.0 | 0.882000 | ||||||||
\(581\) | −9114.00 | −0.650796 | ||||||||
\(582\) | 588.000 | 0.0418787 | ||||||||
\(583\) | −1296.00 | −0.0920666 | ||||||||
\(584\) | 10530.0 | 0.746121 | ||||||||
\(585\) | 10304.0 | 0.728236 | ||||||||
\(586\) | 4312.00 | 0.303971 | ||||||||
\(587\) | −3626.00 | −0.254959 | −0.127480 | − | 0.991841i | \(-0.540689\pi\) | ||||
−0.127480 | + | 0.991841i | \(0.540689\pi\) | |||||||
\(588\) | −686.000 | −0.0481125 | ||||||||
\(589\) | 1320.00 | 0.0923424 | ||||||||
\(590\) | 12960.0 | 0.904330 | ||||||||
\(591\) | −6668.00 | −0.464103 | ||||||||
\(592\) | 10086.0 | 0.700223 | ||||||||
\(593\) | −1062.00 | −0.0735432 | −0.0367716 | − | 0.999324i | \(-0.511707\pi\) | ||||
−0.0367716 | + | 0.999324i | \(0.511707\pi\) | |||||||
\(594\) | 800.000 | 0.0552599 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 14070.0 | 0.966996 | ||||||||
\(597\) | −3720.00 | −0.255024 | ||||||||
\(598\) | 1344.00 | 0.0919068 | ||||||||
\(599\) | −10200.0 | −0.695761 | −0.347880 | − | 0.937539i | \(-0.613098\pi\) | ||||
−0.347880 | + | 0.937539i | \(0.613098\pi\) | |||||||
\(600\) | 3930.00 | 0.267403 | ||||||||
\(601\) | 25158.0 | 1.70751 | 0.853757 | − | 0.520671i | \(-0.174318\pi\) | ||||
0.853757 | + | 0.520671i | \(0.174318\pi\) | |||||||
\(602\) | −896.000 | −0.0606615 | ||||||||
\(603\) | −5612.00 | −0.379002 | ||||||||
\(604\) | −7784.00 | −0.524382 | ||||||||
\(605\) | 20272.0 | 1.36227 | ||||||||
\(606\) | 1376.00 | 0.0922379 | ||||||||
\(607\) | −25664.0 | −1.71609 | −0.858047 | − | 0.513570i | \(-0.828323\pi\) | ||||
−0.858047 | + | 0.513570i | \(0.828323\pi\) | |||||||
\(608\) | 17710.0 | 1.18131 | ||||||||
\(609\) | 1540.00 | 0.102470 | ||||||||
\(610\) | 7808.00 | 0.518257 | ||||||||
\(611\) | 9072.00 | 0.600677 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 19018.0 | 1.25307 | 0.626533 | − | 0.779395i | \(-0.284473\pi\) | ||||
0.626533 | + | 0.779395i | \(0.284473\pi\) | |||||||
\(614\) | −2674.00 | −0.175755 | ||||||||
\(615\) | 5824.00 | 0.381864 | ||||||||
\(616\) | 840.000 | 0.0549425 | ||||||||
\(617\) | −17334.0 | −1.13102 | −0.565511 | − | 0.824741i | \(-0.691321\pi\) | ||||
−0.565511 | + | 0.824741i | \(0.691321\pi\) | |||||||
\(618\) | −2776.00 | −0.180691 | ||||||||
\(619\) | −18730.0 | −1.21619 | −0.608096 | − | 0.793864i | \(-0.708066\pi\) | ||||
−0.608096 | + | 0.793864i | \(0.708066\pi\) | |||||||
\(620\) | −1344.00 | −0.0870586 | ||||||||
\(621\) | 4800.00 | 0.310173 | ||||||||
\(622\) | −3768.00 | −0.242899 | ||||||||
\(623\) | 5110.00 | 0.328616 | ||||||||
\(624\) | 2296.00 | 0.147297 | ||||||||
\(625\) | −14839.0 | −0.949696 | ||||||||
\(626\) | 2438.00 | 0.155658 | ||||||||
\(627\) | −1760.00 | −0.112101 | ||||||||
\(628\) | −868.000 | −0.0551544 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | −2576.00 | −0.162905 | ||||||||
\(631\) | −6928.00 | −0.437083 | −0.218541 | − | 0.975828i | \(-0.570130\pi\) | ||||
−0.218541 | + | 0.975828i | \(0.570130\pi\) | |||||||
\(632\) | −6600.00 | −0.415402 | ||||||||
\(633\) | 8536.00 | 0.535980 | ||||||||
\(634\) | −3186.00 | −0.199578 | ||||||||
\(635\) | 28416.0 | 1.77583 | ||||||||
\(636\) | 2268.00 | 0.141403 | ||||||||
\(637\) | 1372.00 | 0.0853385 | ||||||||
\(638\) | −880.000 | −0.0546074 | ||||||||
\(639\) | −17664.0 | −1.09355 | ||||||||
\(640\) | −23280.0 | −1.43785 | ||||||||
\(641\) | −16302.0 | −1.00451 | −0.502255 | − | 0.864720i | \(-0.667496\pi\) | ||||
−0.502255 | + | 0.864720i | \(0.667496\pi\) | |||||||
\(642\) | 488.000 | 0.0299997 | ||||||||
\(643\) | −4718.00 | −0.289362 | −0.144681 | − | 0.989478i | \(-0.546216\pi\) | ||||
−0.144681 | + | 0.989478i | \(0.546216\pi\) | |||||||
\(644\) | 2352.00 | 0.143916 | ||||||||
\(645\) | −4096.00 | −0.250046 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −21436.0 | −1.30253 | −0.651264 | − | 0.758851i | \(-0.725761\pi\) | ||||
−0.651264 | + | 0.758851i | \(0.725761\pi\) | |||||||
\(648\) | 6315.00 | 0.382834 | ||||||||
\(649\) | 6480.00 | 0.391930 | ||||||||
\(650\) | −3668.00 | −0.221340 | ||||||||
\(651\) | −168.000 | −0.0101143 | ||||||||
\(652\) | 14056.0 | 0.844287 | ||||||||
\(653\) | −4458.00 | −0.267159 | −0.133580 | − | 0.991038i | \(-0.542647\pi\) | ||||
−0.133580 | + | 0.991038i | \(0.542647\pi\) | |||||||
\(654\) | 180.000 | 0.0107623 | ||||||||
\(655\) | −17888.0 | −1.06709 | ||||||||
\(656\) | −7462.00 | −0.444119 | ||||||||
\(657\) | −16146.0 | −0.958775 | ||||||||
\(658\) | −2268.00 | −0.134371 | ||||||||
\(659\) | −26640.0 | −1.57473 | −0.787365 | − | 0.616487i | \(-0.788555\pi\) | ||||
−0.787365 | + | 0.616487i | \(0.788555\pi\) | |||||||
\(660\) | 1792.00 | 0.105687 | ||||||||
\(661\) | 7432.00 | 0.437324 | 0.218662 | − | 0.975801i | \(-0.429831\pi\) | ||||
0.218662 | + | 0.975801i | \(0.429831\pi\) | |||||||
\(662\) | −8672.00 | −0.509134 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −19530.0 | −1.14143 | ||||||||
\(665\) | 12320.0 | 0.718420 | ||||||||
\(666\) | 5658.00 | 0.329194 | ||||||||
\(667\) | −5280.00 | −0.306510 | ||||||||
\(668\) | 20188.0 | 1.16931 | ||||||||
\(669\) | −10864.0 | −0.627842 | ||||||||
\(670\) | 3904.00 | 0.225111 | ||||||||
\(671\) | 3904.00 | 0.224608 | ||||||||
\(672\) | −2254.00 | −0.129390 | ||||||||
\(673\) | −58.0000 | −0.00332204 | −0.00166102 | − | 0.999999i | \(-0.500529\pi\) | ||||
−0.00166102 | + | 0.999999i | \(0.500529\pi\) | |||||||
\(674\) | 814.000 | 0.0465194 | ||||||||
\(675\) | −13100.0 | −0.746991 | ||||||||
\(676\) | 9891.00 | 0.562756 | ||||||||
\(677\) | 21516.0 | 1.22146 | 0.610729 | − | 0.791840i | \(-0.290876\pi\) | ||||
0.610729 | + | 0.791840i | \(0.290876\pi\) | |||||||
\(678\) | 2636.00 | 0.149314 | ||||||||
\(679\) | −2058.00 | −0.116316 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 4092.00 | 0.230258 | ||||||||
\(682\) | 96.0000 | 0.00539007 | ||||||||
\(683\) | −18108.0 | −1.01447 | −0.507235 | − | 0.861808i | \(-0.669332\pi\) | ||||
−0.507235 | + | 0.861808i | \(0.669332\pi\) | |||||||
\(684\) | −17710.0 | −0.989998 | ||||||||
\(685\) | −36384.0 | −2.02943 | ||||||||
\(686\) | −343.000 | −0.0190901 | ||||||||
\(687\) | −5960.00 | −0.330987 | ||||||||
\(688\) | 5248.00 | 0.290811 | ||||||||
\(689\) | −4536.00 | −0.250810 | ||||||||
\(690\) | −1536.00 | −0.0847457 | ||||||||
\(691\) | 10078.0 | 0.554827 | 0.277413 | − | 0.960751i | \(-0.410523\pi\) | ||||
0.277413 | + | 0.960751i | \(0.410523\pi\) | |||||||
\(692\) | 15596.0 | 0.856750 | ||||||||
\(693\) | −1288.00 | −0.0706018 | ||||||||
\(694\) | 9344.00 | 0.511086 | ||||||||
\(695\) | −3360.00 | −0.183384 | ||||||||
\(696\) | 3300.00 | 0.179722 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 5180.00 | 0.280897 | ||||||||
\(699\) | −8916.00 | −0.482452 | ||||||||
\(700\) | −6419.00 | −0.346593 | ||||||||
\(701\) | 18762.0 | 1.01089 | 0.505443 | − | 0.862860i | \(-0.331329\pi\) | ||||
0.505443 | + | 0.862860i | \(0.331329\pi\) | |||||||
\(702\) | 2800.00 | 0.150540 | ||||||||
\(703\) | −27060.0 | −1.45176 | ||||||||
\(704\) | −1336.00 | −0.0715233 | ||||||||
\(705\) | −10368.0 | −0.553874 | ||||||||
\(706\) | −12178.0 | −0.649186 | ||||||||
\(707\) | −4816.00 | −0.256187 | ||||||||
\(708\) | −11340.0 | −0.601954 | ||||||||
\(709\) | −6810.00 | −0.360726 | −0.180363 | − | 0.983600i | \(-0.557727\pi\) | ||||
−0.180363 | + | 0.983600i | \(0.557727\pi\) | |||||||
\(710\) | 12288.0 | 0.649522 | ||||||||
\(711\) | 10120.0 | 0.533797 | ||||||||
\(712\) | 10950.0 | 0.576360 | ||||||||
\(713\) | 576.000 | 0.0302544 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −3584.00 | −0.187460 | ||||||||
\(716\) | 5740.00 | 0.299600 | ||||||||
\(717\) | 8880.00 | 0.462524 | ||||||||
\(718\) | −440.000 | −0.0228700 | ||||||||
\(719\) | −4860.00 | −0.252083 | −0.126041 | − | 0.992025i | \(-0.540227\pi\) | ||||
−0.126041 | + | 0.992025i | \(0.540227\pi\) | |||||||
\(720\) | 15088.0 | 0.780967 | ||||||||
\(721\) | 9716.00 | 0.501862 | ||||||||
\(722\) | −5241.00 | −0.270152 | ||||||||
\(723\) | −6604.00 | −0.339703 | ||||||||
\(724\) | 27244.0 | 1.39850 | ||||||||
\(725\) | 14410.0 | 0.738171 | ||||||||
\(726\) | 2534.00 | 0.129539 | ||||||||
\(727\) | −13636.0 | −0.695641 | −0.347821 | − | 0.937561i | \(-0.613078\pi\) | ||||
−0.347821 | + | 0.937561i | \(0.613078\pi\) | |||||||
\(728\) | 2940.00 | 0.149675 | ||||||||
\(729\) | −4283.00 | −0.217599 | ||||||||
\(730\) | 11232.0 | 0.569473 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | −6832.00 | −0.344970 | ||||||||
\(733\) | 2088.00 | 0.105214 | 0.0526071 | − | 0.998615i | \(-0.483247\pi\) | ||||
0.0526071 | + | 0.998615i | \(0.483247\pi\) | |||||||
\(734\) | −9816.00 | −0.493617 | ||||||||
\(735\) | −1568.00 | −0.0786892 | ||||||||
\(736\) | 7728.00 | 0.387035 | ||||||||
\(737\) | 1952.00 | 0.0975615 | ||||||||
\(738\) | −4186.00 | −0.208792 | ||||||||
\(739\) | −5160.00 | −0.256852 | −0.128426 | − | 0.991719i | \(-0.540992\pi\) | ||||
−0.128426 | + | 0.991719i | \(0.540992\pi\) | |||||||
\(740\) | 27552.0 | 1.36869 | ||||||||
\(741\) | −6160.00 | −0.305389 | ||||||||
\(742\) | 1134.00 | 0.0561057 | ||||||||
\(743\) | 28152.0 | 1.39004 | 0.695018 | − | 0.718992i | \(-0.255396\pi\) | ||||
0.695018 | + | 0.718992i | \(0.255396\pi\) | |||||||
\(744\) | −360.000 | −0.0177396 | ||||||||
\(745\) | 32160.0 | 1.58155 | ||||||||
\(746\) | 442.000 | 0.0216927 | ||||||||
\(747\) | 29946.0 | 1.46676 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −1708.00 | −0.0833230 | ||||||||
\(750\) | 192.000 | 0.00934780 | ||||||||
\(751\) | 16808.0 | 0.816688 | 0.408344 | − | 0.912828i | \(-0.366106\pi\) | ||||
0.408344 | + | 0.912828i | \(0.366106\pi\) | |||||||
\(752\) | 13284.0 | 0.644172 | ||||||||
\(753\) | 3164.00 | 0.153124 | ||||||||
\(754\) | −3080.00 | −0.148763 | ||||||||
\(755\) | −17792.0 | −0.857639 | ||||||||
\(756\) | 4900.00 | 0.235729 | ||||||||
\(757\) | 21674.0 | 1.04063 | 0.520314 | − | 0.853975i | \(-0.325815\pi\) | ||||
0.520314 | + | 0.853975i | \(0.325815\pi\) | |||||||
\(758\) | −3960.00 | −0.189754 | ||||||||
\(759\) | −768.000 | −0.0367281 | ||||||||
\(760\) | 26400.0 | 1.26004 | ||||||||
\(761\) | 7422.00 | 0.353544 | 0.176772 | − | 0.984252i | \(-0.443434\pi\) | ||||
0.176772 | + | 0.984252i | \(0.443434\pi\) | |||||||
\(762\) | 3552.00 | 0.168865 | ||||||||
\(763\) | −630.000 | −0.0298919 | ||||||||
\(764\) | 35336.0 | 1.67331 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −6708.00 | −0.316410 | ||||||||
\(767\) | 22680.0 | 1.06770 | ||||||||
\(768\) | −238.000 | −0.0111824 | ||||||||
\(769\) | 13790.0 | 0.646658 | 0.323329 | − | 0.946287i | \(-0.395198\pi\) | ||||
0.323329 | + | 0.946287i | \(0.395198\pi\) | |||||||
\(770\) | 896.000 | 0.0419345 | ||||||||
\(771\) | 4708.00 | 0.219915 | ||||||||
\(772\) | −20734.0 | −0.966623 | ||||||||
\(773\) | −6232.00 | −0.289973 | −0.144987 | − | 0.989434i | \(-0.546314\pi\) | ||||
−0.144987 | + | 0.989434i | \(0.546314\pi\) | |||||||
\(774\) | 2944.00 | 0.136718 | ||||||||
\(775\) | −1572.00 | −0.0728618 | ||||||||
\(776\) | −4410.00 | −0.204007 | ||||||||
\(777\) | 3444.00 | 0.159013 | ||||||||
\(778\) | 13350.0 | 0.615194 | ||||||||
\(779\) | 20020.0 | 0.920784 | ||||||||
\(780\) | 6272.00 | 0.287915 | ||||||||
\(781\) | 6144.00 | 0.281498 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −11000.0 | −0.502054 | ||||||||
\(784\) | 2009.00 | 0.0915179 | ||||||||
\(785\) | −1984.00 | −0.0902064 | ||||||||
\(786\) | −2236.00 | −0.101470 | ||||||||
\(787\) | 1766.00 | 0.0799887 | 0.0399943 | − | 0.999200i | \(-0.487266\pi\) | ||||
0.0399943 | + | 0.999200i | \(0.487266\pi\) | |||||||
\(788\) | 23338.0 | 1.05505 | ||||||||
\(789\) | −7744.00 | −0.349422 | ||||||||
\(790\) | −7040.00 | −0.317053 | ||||||||
\(791\) | −9226.00 | −0.414714 | ||||||||
\(792\) | −2760.00 | −0.123829 | ||||||||
\(793\) | 13664.0 | 0.611883 | ||||||||
\(794\) | −1356.00 | −0.0606079 | ||||||||
\(795\) | 5184.00 | 0.231267 | ||||||||
\(796\) | 13020.0 | 0.579751 | ||||||||
\(797\) | 1204.00 | 0.0535105 | 0.0267552 | − | 0.999642i | \(-0.491483\pi\) | ||||
0.0267552 | + | 0.999642i | \(0.491483\pi\) | |||||||
\(798\) | 1540.00 | 0.0683150 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | −21091.0 | −0.932099 | ||||||||
\(801\) | −16790.0 | −0.740631 | ||||||||
\(802\) | 6222.00 | 0.273948 | ||||||||
\(803\) | 5616.00 | 0.246805 | ||||||||
\(804\) | −3416.00 | −0.149842 | ||||||||
\(805\) | 5376.00 | 0.235378 | ||||||||
\(806\) | 336.000 | 0.0146837 | ||||||||
\(807\) | −360.000 | −0.0157033 | ||||||||
\(808\) | −10320.0 | −0.449327 | ||||||||
\(809\) | 7050.00 | 0.306384 | 0.153192 | − | 0.988196i | \(-0.451045\pi\) | ||||
0.153192 | + | 0.988196i | \(0.451045\pi\) | |||||||
\(810\) | 6736.00 | 0.292196 | ||||||||
\(811\) | −23282.0 | −1.00807 | −0.504033 | − | 0.863684i | \(-0.668151\pi\) | ||||
−0.504033 | + | 0.863684i | \(0.668151\pi\) | |||||||
\(812\) | −5390.00 | −0.232946 | ||||||||
\(813\) | 4064.00 | 0.175315 | ||||||||
\(814\) | −1968.00 | −0.0847400 | ||||||||
\(815\) | 32128.0 | 1.38085 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −14080.0 | −0.602934 | ||||||||
\(818\) | −5150.00 | −0.220129 | ||||||||
\(819\) | −4508.00 | −0.192335 | ||||||||
\(820\) | −20384.0 | −0.868098 | ||||||||
\(821\) | −10142.0 | −0.431131 | −0.215565 | − | 0.976489i | \(-0.569159\pi\) | ||||
−0.215565 | + | 0.976489i | \(0.569159\pi\) | |||||||
\(822\) | −4548.00 | −0.192980 | ||||||||
\(823\) | 9192.00 | 0.389323 | 0.194662 | − | 0.980870i | \(-0.437639\pi\) | ||||
0.194662 | + | 0.980870i | \(0.437639\pi\) | |||||||
\(824\) | 20820.0 | 0.880217 | ||||||||
\(825\) | 2096.00 | 0.0884525 | ||||||||
\(826\) | −5670.00 | −0.238843 | ||||||||
\(827\) | 46716.0 | 1.96430 | 0.982149 | − | 0.188104i | \(-0.0602344\pi\) | ||||
0.982149 | + | 0.188104i | \(0.0602344\pi\) | |||||||
\(828\) | −7728.00 | −0.324356 | ||||||||
\(829\) | 11240.0 | 0.470906 | 0.235453 | − | 0.971886i | \(-0.424343\pi\) | ||||
0.235453 | + | 0.971886i | \(0.424343\pi\) | |||||||
\(830\) | −20832.0 | −0.871192 | ||||||||
\(831\) | 10852.0 | 0.453010 | ||||||||
\(832\) | −4676.00 | −0.194845 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −420.000 | −0.0174381 | ||||||||
\(835\) | 46144.0 | 1.91243 | ||||||||
\(836\) | 6160.00 | 0.254842 | ||||||||
\(837\) | 1200.00 | 0.0495556 | ||||||||
\(838\) | 2310.00 | 0.0952239 | ||||||||
\(839\) | −700.000 | −0.0288042 | −0.0144021 | − | 0.999896i | \(-0.504584\pi\) | ||||
−0.0144021 | + | 0.999896i | \(0.504584\pi\) | |||||||
\(840\) | −3360.00 | −0.138013 | ||||||||
\(841\) | −12289.0 | −0.503875 | ||||||||
\(842\) | −1262.00 | −0.0516525 | ||||||||
\(843\) | 1684.00 | 0.0688019 | ||||||||
\(844\) | −29876.0 | −1.21845 | ||||||||
\(845\) | 22608.0 | 0.920401 | ||||||||
\(846\) | 7452.00 | 0.302843 | ||||||||
\(847\) | −8869.00 | −0.359790 | ||||||||
\(848\) | −6642.00 | −0.268971 | ||||||||
\(849\) | 7564.00 | 0.305767 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −11808.0 | −0.475644 | ||||||||
\(852\) | −10752.0 | −0.432344 | ||||||||
\(853\) | 37492.0 | 1.50493 | 0.752463 | − | 0.658635i | \(-0.228866\pi\) | ||||
0.752463 | + | 0.658635i | \(0.228866\pi\) | |||||||
\(854\) | −3416.00 | −0.136877 | ||||||||
\(855\) | −40480.0 | −1.61917 | ||||||||
\(856\) | −3660.00 | −0.146140 | ||||||||
\(857\) | −28894.0 | −1.15169 | −0.575846 | − | 0.817558i | \(-0.695327\pi\) | ||||
−0.575846 | + | 0.817558i | \(0.695327\pi\) | |||||||
\(858\) | −448.000 | −0.0178257 | ||||||||
\(859\) | −2770.00 | −0.110025 | −0.0550123 | − | 0.998486i | \(-0.517520\pi\) | ||||
−0.0550123 | + | 0.998486i | \(0.517520\pi\) | |||||||
\(860\) | 14336.0 | 0.568434 | ||||||||
\(861\) | −2548.00 | −0.100854 | ||||||||
\(862\) | −4488.00 | −0.177334 | ||||||||
\(863\) | 17688.0 | 0.697690 | 0.348845 | − | 0.937180i | \(-0.386574\pi\) | ||||
0.348845 | + | 0.937180i | \(0.386574\pi\) | |||||||
\(864\) | 16100.0 | 0.633950 | ||||||||
\(865\) | 35648.0 | 1.40124 | ||||||||
\(866\) | −17038.0 | −0.668562 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 588.000 | 0.0229931 | ||||||||
\(869\) | −3520.00 | −0.137408 | ||||||||
\(870\) | 3520.00 | 0.137171 | ||||||||
\(871\) | 6832.00 | 0.265779 | ||||||||
\(872\) | −1350.00 | −0.0524275 | ||||||||
\(873\) | 6762.00 | 0.262152 | ||||||||
\(874\) | −5280.00 | −0.204346 | ||||||||
\(875\) | −672.000 | −0.0259631 | ||||||||
\(876\) | −9828.00 | −0.379061 | ||||||||
\(877\) | 33566.0 | 1.29241 | 0.646205 | − | 0.763164i | \(-0.276355\pi\) | ||||
0.646205 | + | 0.763164i | \(0.276355\pi\) | |||||||
\(878\) | 16200.0 | 0.622692 | ||||||||
\(879\) | −8624.00 | −0.330922 | ||||||||
\(880\) | −5248.00 | −0.201034 | ||||||||
\(881\) | 16758.0 | 0.640853 | 0.320426 | − | 0.947273i | \(-0.396174\pi\) | ||||
0.320426 | + | 0.947273i | \(0.396174\pi\) | |||||||
\(882\) | 1127.00 | 0.0430250 | ||||||||
\(883\) | 11468.0 | 0.437066 | 0.218533 | − | 0.975830i | \(-0.429873\pi\) | ||||
0.218533 | + | 0.975830i | \(0.429873\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −25920.0 | −0.984510 | ||||||||
\(886\) | 8772.00 | 0.332620 | ||||||||
\(887\) | 50356.0 | 1.90619 | 0.953094 | − | 0.302674i | \(-0.0978793\pi\) | ||||
0.953094 | + | 0.302674i | \(0.0978793\pi\) | |||||||
\(888\) | 7380.00 | 0.278893 | ||||||||
\(889\) | −12432.0 | −0.469017 | ||||||||
\(890\) | 11680.0 | 0.439904 | ||||||||
\(891\) | 3368.00 | 0.126636 | ||||||||
\(892\) | 38024.0 | 1.42728 | ||||||||
\(893\) | −35640.0 | −1.33555 | ||||||||
\(894\) | 4020.00 | 0.150390 | ||||||||
\(895\) | 13120.0 | 0.490004 | ||||||||
\(896\) | 10185.0 | 0.379751 | ||||||||
\(897\) | −2688.00 | −0.100055 | ||||||||
\(898\) | 2130.00 | 0.0791526 | ||||||||
\(899\) | −1320.00 | −0.0489705 | ||||||||
\(900\) | 21091.0 | 0.781148 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 1456.00 | 0.0537467 | ||||||||
\(903\) | 1792.00 | 0.0660399 | ||||||||
\(904\) | −19770.0 | −0.727368 | ||||||||
\(905\) | 62272.0 | 2.28728 | ||||||||
\(906\) | −2224.00 | −0.0815535 | ||||||||
\(907\) | 8716.00 | 0.319085 | 0.159542 | − | 0.987191i | \(-0.448998\pi\) | ||||
0.159542 | + | 0.987191i | \(0.448998\pi\) | |||||||
\(908\) | −14322.0 | −0.523450 | ||||||||
\(909\) | 15824.0 | 0.577392 | ||||||||
\(910\) | 3136.00 | 0.114239 | ||||||||
\(911\) | −7632.00 | −0.277563 | −0.138781 | − | 0.990323i | \(-0.544318\pi\) | ||||
−0.138781 | + | 0.990323i | \(0.544318\pi\) | |||||||
\(912\) | −9020.00 | −0.327502 | ||||||||
\(913\) | −10416.0 | −0.377568 | ||||||||
\(914\) | −10534.0 | −0.381219 | ||||||||
\(915\) | −15616.0 | −0.564207 | ||||||||
\(916\) | 20860.0 | 0.752439 | ||||||||
\(917\) | 7826.00 | 0.281829 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −23080.0 | −0.828443 | −0.414221 | − | 0.910176i | \(-0.635946\pi\) | ||||
−0.414221 | + | 0.910176i | \(0.635946\pi\) | |||||||
\(920\) | 11520.0 | 0.412830 | ||||||||
\(921\) | 5348.00 | 0.191338 | ||||||||
\(922\) | 9268.00 | 0.331047 | ||||||||
\(923\) | 21504.0 | 0.766861 | ||||||||
\(924\) | −784.000 | −0.0279131 | ||||||||
\(925\) | 32226.0 | 1.14550 | ||||||||
\(926\) | 9392.00 | 0.333305 | ||||||||
\(927\) | −31924.0 | −1.13109 | ||||||||
\(928\) | −17710.0 | −0.626465 | ||||||||
\(929\) | −45110.0 | −1.59312 | −0.796561 | − | 0.604558i | \(-0.793350\pi\) | ||||
−0.796561 | + | 0.604558i | \(0.793350\pi\) | |||||||
\(930\) | −384.000 | −0.0135396 | ||||||||
\(931\) | −5390.00 | −0.189742 | ||||||||
\(932\) | 31206.0 | 1.09677 | ||||||||
\(933\) | 7536.00 | 0.264435 | ||||||||
\(934\) | 10806.0 | 0.378569 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −9660.00 | −0.337337 | ||||||||
\(937\) | 16674.0 | 0.581340 | 0.290670 | − | 0.956823i | \(-0.406122\pi\) | ||||
0.290670 | + | 0.956823i | \(0.406122\pi\) | |||||||
\(938\) | −1708.00 | −0.0594543 | ||||||||
\(939\) | −4876.00 | −0.169459 | ||||||||
\(940\) | 36288.0 | 1.25913 | ||||||||
\(941\) | −43832.0 | −1.51847 | −0.759236 | − | 0.650815i | \(-0.774427\pi\) | ||||
−0.759236 | + | 0.650815i | \(0.774427\pi\) | |||||||
\(942\) | −248.000 | −0.00857779 | ||||||||
\(943\) | 8736.00 | 0.301679 | ||||||||
\(944\) | 33210.0 | 1.14501 | ||||||||
\(945\) | 11200.0 | 0.385541 | ||||||||
\(946\) | −1024.00 | −0.0351936 | ||||||||
\(947\) | 736.000 | 0.0252553 | 0.0126277 | − | 0.999920i | \(-0.495980\pi\) | ||||
0.0126277 | + | 0.999920i | \(0.495980\pi\) | |||||||
\(948\) | 6160.00 | 0.211042 | ||||||||
\(949\) | 19656.0 | 0.672351 | ||||||||
\(950\) | 14410.0 | 0.492129 | ||||||||
\(951\) | 6372.00 | 0.217273 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 38138.0 | 1.29634 | 0.648169 | − | 0.761496i | \(-0.275535\pi\) | ||||
0.648169 | + | 0.761496i | \(0.275535\pi\) | |||||||
\(954\) | −3726.00 | −0.126450 | ||||||||
\(955\) | 80768.0 | 2.73674 | ||||||||
\(956\) | −31080.0 | −1.05146 | ||||||||
\(957\) | 1760.00 | 0.0594490 | ||||||||
\(958\) | 4940.00 | 0.166601 | ||||||||
\(959\) | 15918.0 | 0.535995 | ||||||||
\(960\) | 5344.00 | 0.179663 | ||||||||
\(961\) | −29647.0 | −0.995166 | ||||||||
\(962\) | −6888.00 | −0.230850 | ||||||||
\(963\) | 5612.00 | 0.187792 | ||||||||
\(964\) | 23114.0 | 0.772253 | ||||||||
\(965\) | −47392.0 | −1.58094 | ||||||||
\(966\) | 672.000 | 0.0223822 | ||||||||
\(967\) | 26224.0 | 0.872086 | 0.436043 | − | 0.899926i | \(-0.356380\pi\) | ||||
0.436043 | + | 0.899926i | \(0.356380\pi\) | |||||||
\(968\) | −19005.0 | −0.631037 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −4704.00 | −0.155708 | ||||||||
\(971\) | 18762.0 | 0.620084 | 0.310042 | − | 0.950723i | \(-0.399657\pi\) | ||||
0.310042 | + | 0.950723i | \(0.399657\pi\) | |||||||
\(972\) | −24794.0 | −0.818177 | ||||||||
\(973\) | 1470.00 | 0.0484337 | ||||||||
\(974\) | −5216.00 | −0.171593 | ||||||||
\(975\) | 7336.00 | 0.240964 | ||||||||
\(976\) | 20008.0 | 0.656189 | ||||||||
\(977\) | 38394.0 | 1.25725 | 0.628625 | − | 0.777709i | \(-0.283618\pi\) | ||||
0.628625 | + | 0.777709i | \(0.283618\pi\) | |||||||
\(978\) | 4016.00 | 0.131306 | ||||||||
\(979\) | 5840.00 | 0.190651 | ||||||||
\(980\) | 5488.00 | 0.178885 | ||||||||
\(981\) | 2070.00 | 0.0673700 | ||||||||
\(982\) | −4412.00 | −0.143373 | ||||||||
\(983\) | −5388.00 | −0.174822 | −0.0874112 | − | 0.996172i | \(-0.527859\pi\) | ||||
−0.0874112 | + | 0.996172i | \(0.527859\pi\) | |||||||
\(984\) | −5460.00 | −0.176889 | ||||||||
\(985\) | 53344.0 | 1.72556 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 4536.00 | 0.146284 | ||||||||
\(988\) | 21560.0 | 0.694246 | ||||||||
\(989\) | −6144.00 | −0.197541 | ||||||||
\(990\) | −2944.00 | −0.0945116 | ||||||||
\(991\) | −25472.0 | −0.816493 | −0.408247 | − | 0.912872i | \(-0.633860\pi\) | ||||
−0.408247 | + | 0.912872i | \(0.633860\pi\) | |||||||
\(992\) | 1932.00 | 0.0618357 | ||||||||
\(993\) | 17344.0 | 0.554275 | ||||||||
\(994\) | −5376.00 | −0.171546 | ||||||||
\(995\) | 29760.0 | 0.948196 | ||||||||
\(996\) | 18228.0 | 0.579896 | ||||||||
\(997\) | 17096.0 | 0.543065 | 0.271532 | − | 0.962429i | \(-0.412470\pi\) | ||||
0.271532 | + | 0.962429i | \(0.412470\pi\) | |||||||
\(998\) | 19060.0 | 0.604543 | ||||||||
\(999\) | −24600.0 | −0.779089 |
(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 | 2023.4.a.a.1.1 | 1 | ||
17.16 | even | 2 | 7.4.a.a.1.1 | ✓ | 1 | ||
51.50 | odd | 2 | 63.4.a.b.1.1 | 1 | |||
68.67 | odd | 2 | 112.4.a.f.1.1 | 1 | |||
85.33 | odd | 4 | 175.4.b.b.99.2 | 2 | |||
85.67 | odd | 4 | 175.4.b.b.99.1 | 2 | |||
85.84 | even | 2 | 175.4.a.b.1.1 | 1 | |||
119.16 | even | 6 | 49.4.c.c.18.1 | 2 | |||
119.33 | odd | 6 | 49.4.c.b.18.1 | 2 | |||
119.67 | even | 6 | 49.4.c.c.30.1 | 2 | |||
119.101 | odd | 6 | 49.4.c.b.30.1 | 2 | |||
119.118 | odd | 2 | 49.4.a.b.1.1 | 1 | |||
136.67 | odd | 2 | 448.4.a.e.1.1 | 1 | |||
136.101 | even | 2 | 448.4.a.i.1.1 | 1 | |||
187.186 | odd | 2 | 847.4.a.b.1.1 | 1 | |||
204.203 | even | 2 | 1008.4.a.c.1.1 | 1 | |||
221.220 | even | 2 | 1183.4.a.b.1.1 | 1 | |||
255.254 | odd | 2 | 1575.4.a.e.1.1 | 1 | |||
357.101 | even | 6 | 441.4.e.e.226.1 | 2 | |||
357.152 | even | 6 | 441.4.e.e.361.1 | 2 | |||
357.254 | odd | 6 | 441.4.e.h.361.1 | 2 | |||
357.305 | odd | 6 | 441.4.e.h.226.1 | 2 | |||
357.356 | even | 2 | 441.4.a.i.1.1 | 1 | |||
476.475 | even | 2 | 784.4.a.g.1.1 | 1 | |||
595.594 | odd | 2 | 1225.4.a.j.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
7.4.a.a.1.1 | ✓ | 1 | 17.16 | even | 2 | ||
49.4.a.b.1.1 | 1 | 119.118 | odd | 2 | |||
49.4.c.b.18.1 | 2 | 119.33 | odd | 6 | |||
49.4.c.b.30.1 | 2 | 119.101 | odd | 6 | |||
49.4.c.c.18.1 | 2 | 119.16 | even | 6 | |||
49.4.c.c.30.1 | 2 | 119.67 | even | 6 | |||
63.4.a.b.1.1 | 1 | 51.50 | odd | 2 | |||
112.4.a.f.1.1 | 1 | 68.67 | odd | 2 | |||
175.4.a.b.1.1 | 1 | 85.84 | even | 2 | |||
175.4.b.b.99.1 | 2 | 85.67 | odd | 4 | |||
175.4.b.b.99.2 | 2 | 85.33 | odd | 4 | |||
441.4.a.i.1.1 | 1 | 357.356 | even | 2 | |||
441.4.e.e.226.1 | 2 | 357.101 | even | 6 | |||
441.4.e.e.361.1 | 2 | 357.152 | even | 6 | |||
441.4.e.h.226.1 | 2 | 357.305 | odd | 6 | |||
441.4.e.h.361.1 | 2 | 357.254 | odd | 6 | |||
448.4.a.e.1.1 | 1 | 136.67 | odd | 2 | |||
448.4.a.i.1.1 | 1 | 136.101 | even | 2 | |||
784.4.a.g.1.1 | 1 | 476.475 | even | 2 | |||
847.4.a.b.1.1 | 1 | 187.186 | odd | 2 | |||
1008.4.a.c.1.1 | 1 | 204.203 | even | 2 | |||
1183.4.a.b.1.1 | 1 | 221.220 | even | 2 | |||
1225.4.a.j.1.1 | 1 | 595.594 | odd | 2 | |||
1575.4.a.e.1.1 | 1 | 255.254 | odd | 2 | |||
2023.4.a.a.1.1 | 1 | 1.1 | even | 1 | trivial |