Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1575,4,Mod(1,1575)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1575, 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("1575.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1575 = 3^{2} \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1575.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: | \(92.9280082590\) |
Analytic rank: | \(0\) |
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 | \(\chi\) | \(=\) | 1575.1 |
$q$-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 | \(0.556567\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −7.00000 | −0.875000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 7.00000 | 0.377964 | ||||||||
\(8\) | 15.0000 | 0.662913 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 8.00000 | 0.219281 | 0.109640 | − | 0.993971i | \(-0.465030\pi\) | ||||
0.109640 | + | 0.993971i | \(0.465030\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −28.0000 | −0.597369 | −0.298685 | − | 0.954352i | \(-0.596548\pi\) | ||||
−0.298685 | + | 0.954352i | \(0.596548\pi\) | |||||||
\(14\) | −7.00000 | −0.133631 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 41.0000 | 0.640625 | ||||||||
\(17\) | 54.0000 | 0.770407 | 0.385204 | − | 0.922832i | \(-0.374131\pi\) | ||||
0.385204 | + | 0.922832i | \(0.374131\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −110.000 | −1.32820 | −0.664098 | − | 0.747645i | \(-0.731184\pi\) | ||||
−0.664098 | + | 0.747645i | \(0.731184\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −8.00000 | −0.0775275 | ||||||||
\(23\) | 48.0000 | 0.435161 | 0.217580 | − | 0.976042i | \(-0.430184\pi\) | ||||
0.217580 | + | 0.976042i | \(0.430184\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 28.0000 | 0.211202 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −49.0000 | −0.330719 | ||||||||
\(29\) | 110.000 | 0.704362 | 0.352181 | − | 0.935932i | \(-0.385440\pi\) | ||||
0.352181 | + | 0.935932i | \(0.385440\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 12.0000 | 0.0695246 | 0.0347623 | − | 0.999396i | \(-0.488933\pi\) | ||||
0.0347623 | + | 0.999396i | \(0.488933\pi\) | |||||||
\(32\) | −161.000 | −0.889408 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −54.0000 | −0.272380 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 246.000 | 1.09303 | 0.546516 | − | 0.837449i | \(-0.315954\pi\) | ||||
0.546516 | + | 0.837449i | \(0.315954\pi\) | |||||||
\(38\) | 110.000 | 0.469588 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −182.000 | −0.693259 | −0.346630 | − | 0.938002i | \(-0.612674\pi\) | ||||
−0.346630 | + | 0.938002i | \(0.612674\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −128.000 | −0.453949 | −0.226975 | − | 0.973901i | \(-0.572883\pi\) | ||||
−0.226975 | + | 0.973901i | \(0.572883\pi\) | |||||||
\(44\) | −56.0000 | −0.191871 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −48.0000 | −0.153852 | ||||||||
\(47\) | 324.000 | 1.00554 | 0.502769 | − | 0.864421i | \(-0.332315\pi\) | ||||
0.502769 | + | 0.864421i | \(0.332315\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 49.0000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 196.000 | 0.522698 | ||||||||
\(53\) | −162.000 | −0.419857 | −0.209928 | − | 0.977717i | \(-0.567323\pi\) | ||||
−0.209928 | + | 0.977717i | \(0.567323\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 105.000 | 0.250557 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −110.000 | −0.249029 | ||||||||
\(59\) | −810.000 | −1.78734 | −0.893670 | − | 0.448725i | \(-0.851878\pi\) | ||||
−0.893670 | + | 0.448725i | \(0.851878\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −488.000 | −1.02430 | −0.512148 | − | 0.858898i | \(-0.671150\pi\) | ||||
−0.512148 | + | 0.858898i | \(0.671150\pi\) | |||||||
\(62\) | −12.0000 | −0.0245807 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −167.000 | −0.326172 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −244.000 | −0.444916 | −0.222458 | − | 0.974942i | \(-0.571408\pi\) | ||||
−0.222458 | + | 0.974942i | \(0.571408\pi\) | |||||||
\(68\) | −378.000 | −0.674106 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 768.000 | 1.28373 | 0.641865 | − | 0.766818i | \(-0.278161\pi\) | ||||
0.641865 | + | 0.766818i | \(0.278161\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 702.000 | 1.12552 | 0.562759 | − | 0.826621i | \(-0.309740\pi\) | ||||
0.562759 | + | 0.826621i | \(0.309740\pi\) | |||||||
\(74\) | −246.000 | −0.386445 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 770.000 | 1.16217 | ||||||||
\(77\) | 56.0000 | 0.0828804 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 440.000 | 0.626631 | 0.313316 | − | 0.949649i | \(-0.398560\pi\) | ||||
0.313316 | + | 0.949649i | \(0.398560\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 182.000 | 0.245104 | ||||||||
\(83\) | −1302.00 | −1.72184 | −0.860922 | − | 0.508737i | \(-0.830113\pi\) | ||||
−0.860922 | + | 0.508737i | \(0.830113\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 128.000 | 0.160495 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 120.000 | 0.145364 | ||||||||
\(89\) | −730.000 | −0.869436 | −0.434718 | − | 0.900567i | \(-0.643152\pi\) | ||||
−0.434718 | + | 0.900567i | \(0.643152\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −196.000 | −0.225784 | ||||||||
\(92\) | −336.000 | −0.380765 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −324.000 | −0.355511 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −294.000 | −0.307744 | −0.153872 | − | 0.988091i | \(-0.549174\pi\) | ||||
−0.153872 | + | 0.988091i | \(0.549174\pi\) | |||||||
\(98\) | −49.0000 | −0.0505076 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 688.000 | 0.677808 | 0.338904 | − | 0.940821i | \(-0.389944\pi\) | ||||
0.338904 | + | 0.940821i | \(0.389944\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1388.00 | −1.32780 | −0.663901 | − | 0.747820i | \(-0.731101\pi\) | ||||
−0.663901 | + | 0.747820i | \(0.731101\pi\) | |||||||
\(104\) | −420.000 | −0.396004 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 162.000 | 0.148442 | ||||||||
\(107\) | 244.000 | 0.220452 | 0.110226 | − | 0.993907i | \(-0.464843\pi\) | ||||
0.110226 | + | 0.993907i | \(0.464843\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 90.0000 | 0.0790866 | 0.0395433 | − | 0.999218i | \(-0.487410\pi\) | ||||
0.0395433 | + | 0.999218i | \(0.487410\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 287.000 | 0.242133 | ||||||||
\(113\) | 1318.00 | 1.09723 | 0.548615 | − | 0.836075i | \(-0.315155\pi\) | ||||
0.548615 | + | 0.836075i | \(0.315155\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −770.000 | −0.616316 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 810.000 | 0.631920 | ||||||||
\(119\) | 378.000 | 0.291187 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1267.00 | −0.951916 | ||||||||
\(122\) | 488.000 | 0.362143 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −84.0000 | −0.0608341 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1776.00 | 1.24090 | 0.620451 | − | 0.784245i | \(-0.286950\pi\) | ||||
0.620451 | + | 0.784245i | \(0.286950\pi\) | |||||||
\(128\) | 1455.00 | 1.00473 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1118.00 | 0.745650 | 0.372825 | − | 0.927902i | \(-0.378389\pi\) | ||||
0.372825 | + | 0.927902i | \(0.378389\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −770.000 | −0.502011 | ||||||||
\(134\) | 244.000 | 0.157301 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 810.000 | 0.510713 | ||||||||
\(137\) | 2274.00 | 1.41811 | 0.709054 | − | 0.705154i | \(-0.249122\pi\) | ||||
0.709054 | + | 0.705154i | \(0.249122\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −210.000 | −0.128144 | −0.0640718 | − | 0.997945i | \(-0.520409\pi\) | ||||
−0.0640718 | + | 0.997945i | \(0.520409\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −768.000 | −0.453867 | ||||||||
\(143\) | −224.000 | −0.130992 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −702.000 | −0.397931 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −1722.00 | −0.956402 | ||||||||
\(149\) | 2010.00 | 1.10514 | 0.552569 | − | 0.833467i | \(-0.313648\pi\) | ||||
0.552569 | + | 0.833467i | \(0.313648\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 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 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −124.000 | −0.0630336 | −0.0315168 | − | 0.999503i | \(-0.510034\pi\) | ||||
−0.0315168 | + | 0.999503i | \(0.510034\pi\) | |||||||
\(158\) | −440.000 | −0.221548 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 336.000 | 0.164475 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −2008.00 | −0.964900 | −0.482450 | − | 0.875924i | \(-0.660253\pi\) | ||||
−0.482450 | + | 0.875924i | \(0.660253\pi\) | |||||||
\(164\) | 1274.00 | 0.606602 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 1302.00 | 0.608764 | ||||||||
\(167\) | 2884.00 | 1.33635 | 0.668176 | − | 0.744004i | \(-0.267076\pi\) | ||||
0.668176 | + | 0.744004i | \(0.267076\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1413.00 | −0.643150 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 896.000 | 0.397206 | ||||||||
\(173\) | 2228.00 | 0.979143 | 0.489571 | − | 0.871963i | \(-0.337153\pi\) | ||||
0.489571 | + | 0.871963i | \(0.337153\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 328.000 | 0.140477 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 730.000 | 0.307392 | ||||||||
\(179\) | 820.000 | 0.342400 | 0.171200 | − | 0.985236i | \(-0.445236\pi\) | ||||
0.171200 | + | 0.985236i | \(0.445236\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 3892.00 | 1.59829 | 0.799144 | − | 0.601140i | \(-0.205287\pi\) | ||||
0.799144 | + | 0.601140i | \(0.205287\pi\) | |||||||
\(182\) | 196.000 | 0.0798268 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 720.000 | 0.288473 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 432.000 | 0.168936 | ||||||||
\(188\) | −2268.00 | −0.879845 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 5048.00 | 1.91236 | 0.956179 | − | 0.292782i | \(-0.0945810\pi\) | ||||
0.956179 | + | 0.292782i | \(0.0945810\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 2962.00 | 1.10471 | 0.552356 | − | 0.833608i | \(-0.313729\pi\) | ||||
0.552356 | + | 0.833608i | \(0.313729\pi\) | |||||||
\(194\) | 294.000 | 0.108804 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −343.000 | −0.125000 | ||||||||
\(197\) | 3334.00 | 1.20577 | 0.602887 | − | 0.797826i | \(-0.294017\pi\) | ||||
0.602887 | + | 0.797826i | \(0.294017\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1860.00 | 0.662572 | 0.331286 | − | 0.943530i | \(-0.392517\pi\) | ||||
0.331286 | + | 0.943530i | \(0.392517\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −688.000 | −0.239641 | ||||||||
\(203\) | 770.000 | 0.266224 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 1388.00 | 0.469449 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −1148.00 | −0.382690 | ||||||||
\(209\) | −880.000 | −0.291248 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −4268.00 | −1.39252 | −0.696259 | − | 0.717791i | \(-0.745153\pi\) | ||||
−0.696259 | + | 0.717791i | \(0.745153\pi\) | |||||||
\(212\) | 1134.00 | 0.367375 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −244.000 | −0.0779416 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 84.0000 | 0.0262778 | ||||||||
\(218\) | −90.0000 | −0.0279613 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1512.00 | −0.460218 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 5432.00 | 1.63118 | 0.815591 | − | 0.578629i | \(-0.196412\pi\) | ||||
0.815591 | + | 0.578629i | \(0.196412\pi\) | |||||||
\(224\) | −1127.00 | −0.336165 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −1318.00 | −0.387929 | ||||||||
\(227\) | −2046.00 | −0.598228 | −0.299114 | − | 0.954217i | \(-0.596691\pi\) | ||||
−0.299114 | + | 0.954217i | \(0.596691\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −2980.00 | −0.859930 | −0.429965 | − | 0.902846i | \(-0.641474\pi\) | ||||
−0.429965 | + | 0.902846i | \(0.641474\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 1650.00 | 0.466930 | ||||||||
\(233\) | 4458.00 | 1.25345 | 0.626724 | − | 0.779241i | \(-0.284395\pi\) | ||||
0.626724 | + | 0.779241i | \(0.284395\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 5670.00 | 1.56392 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −378.000 | −0.102950 | ||||||||
\(239\) | −4440.00 | −1.20167 | −0.600836 | − | 0.799372i | \(-0.705166\pi\) | ||||
−0.600836 | + | 0.799372i | \(0.705166\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 3302.00 | 0.882575 | 0.441287 | − | 0.897366i | \(-0.354522\pi\) | ||||
0.441287 | + | 0.897366i | \(0.354522\pi\) | |||||||
\(242\) | 1267.00 | 0.336553 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 3416.00 | 0.896258 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 3080.00 | 0.793424 | ||||||||
\(248\) | 180.000 | 0.0460888 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −1582.00 | −0.397829 | −0.198914 | − | 0.980017i | \(-0.563742\pi\) | ||||
−0.198914 | + | 0.980017i | \(0.563742\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 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 | \(0.407781\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1722.00 | 0.413127 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −1118.00 | −0.263627 | ||||||||
\(263\) | −3872.00 | −0.907824 | −0.453912 | − | 0.891046i | \(-0.649972\pi\) | ||||
−0.453912 | + | 0.891046i | \(0.649972\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 770.000 | 0.177488 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 1708.00 | 0.389301 | ||||||||
\(269\) | −180.000 | −0.0407985 | −0.0203992 | − | 0.999792i | \(-0.506494\pi\) | ||||
−0.0203992 | + | 0.999792i | \(0.506494\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2032.00 | 0.455480 | 0.227740 | − | 0.973722i | \(-0.426866\pi\) | ||||
0.227740 | + | 0.973722i | \(0.426866\pi\) | |||||||
\(272\) | 2214.00 | 0.493542 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −2274.00 | −0.501377 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 5426.00 | 1.17696 | 0.588478 | − | 0.808513i | \(-0.299727\pi\) | ||||
0.588478 | + | 0.808513i | \(0.299727\pi\) | |||||||
\(278\) | 210.000 | 0.0453056 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −842.000 | −0.178753 | −0.0893764 | − | 0.995998i | \(-0.528487\pi\) | ||||
−0.0893764 | + | 0.995998i | \(0.528487\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 3782.00 | 0.794405 | 0.397202 | − | 0.917731i | \(-0.369981\pi\) | ||||
0.397202 | + | 0.917731i | \(0.369981\pi\) | |||||||
\(284\) | −5376.00 | −1.12326 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 224.000 | 0.0463126 | ||||||||
\(287\) | −1274.00 | −0.262027 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1997.00 | −0.406473 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −4914.00 | −0.984829 | ||||||||
\(293\) | −4312.00 | −0.859760 | −0.429880 | − | 0.902886i | \(-0.641444\pi\) | ||||
−0.429880 | + | 0.902886i | \(0.641444\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 3690.00 | 0.724584 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −2010.00 | −0.390725 | ||||||||
\(299\) | −1344.00 | −0.259952 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −896.000 | −0.171577 | ||||||||
\(302\) | −1112.00 | −0.211882 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −4510.00 | −0.850876 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −2674.00 | −0.497112 | −0.248556 | − | 0.968618i | \(-0.579956\pi\) | ||||
−0.248556 | + | 0.968618i | \(0.579956\pi\) | |||||||
\(308\) | −392.000 | −0.0725204 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 3768.00 | 0.687021 | 0.343511 | − | 0.939149i | \(-0.388384\pi\) | ||||
0.343511 | + | 0.939149i | \(0.388384\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −2438.00 | −0.440268 | −0.220134 | − | 0.975470i | \(-0.570649\pi\) | ||||
−0.220134 | + | 0.975470i | \(0.570649\pi\) | |||||||
\(314\) | 124.000 | 0.0222857 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −3080.00 | −0.548302 | ||||||||
\(317\) | −3186.00 | −0.564491 | −0.282245 | − | 0.959342i | \(-0.591079\pi\) | ||||
−0.282245 | + | 0.959342i | \(0.591079\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 880.000 | 0.154453 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −336.000 | −0.0581508 | ||||||||
\(323\) | −5940.00 | −1.02325 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 2008.00 | 0.341144 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −2730.00 | −0.459570 | ||||||||
\(329\) | 2268.00 | 0.380057 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 8672.00 | 1.44005 | 0.720025 | − | 0.693949i | \(-0.244131\pi\) | ||||
0.720025 | + | 0.693949i | \(0.244131\pi\) | |||||||
\(332\) | 9114.00 | 1.50661 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −2884.00 | −0.472471 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −814.000 | −0.131577 | −0.0657884 | − | 0.997834i | \(-0.520956\pi\) | ||||
−0.0657884 | + | 0.997834i | \(0.520956\pi\) | |||||||
\(338\) | 1413.00 | 0.227388 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 96.0000 | 0.0152454 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 343.000 | 0.0539949 | ||||||||
\(344\) | −1920.00 | −0.300929 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −2228.00 | −0.346179 | ||||||||
\(347\) | 9344.00 | 1.44557 | 0.722784 | − | 0.691074i | \(-0.242862\pi\) | ||||
0.722784 | + | 0.691074i | \(0.242862\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −5180.00 | −0.794496 | −0.397248 | − | 0.917711i | \(-0.630035\pi\) | ||||
−0.397248 | + | 0.917711i | \(0.630035\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −1288.00 | −0.195030 | ||||||||
\(353\) | 12178.0 | 1.83617 | 0.918087 | − | 0.396379i | \(-0.129733\pi\) | ||||
0.918087 | + | 0.396379i | \(0.129733\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 5110.00 | 0.760757 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −820.000 | −0.121057 | ||||||||
\(359\) | −440.000 | −0.0646861 | −0.0323431 | − | 0.999477i | \(-0.510297\pi\) | ||||
−0.0323431 | + | 0.999477i | \(0.510297\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 5241.00 | 0.764106 | ||||||||
\(362\) | −3892.00 | −0.565080 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 1372.00 | 0.197561 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 9816.00 | 1.39616 | 0.698080 | − | 0.716019i | \(-0.254038\pi\) | ||||
0.698080 | + | 0.716019i | \(0.254038\pi\) | |||||||
\(368\) | 1968.00 | 0.278775 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −1134.00 | −0.158691 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 442.000 | 0.0613563 | 0.0306781 | − | 0.999529i | \(-0.490233\pi\) | ||||
0.0306781 | + | 0.999529i | \(0.490233\pi\) | |||||||
\(374\) | −432.000 | −0.0597278 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 4860.00 | 0.666583 | ||||||||
\(377\) | −3080.00 | −0.420764 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −3960.00 | −0.536706 | −0.268353 | − | 0.963321i | \(-0.586479\pi\) | ||||
−0.268353 | + | 0.963321i | \(0.586479\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −5048.00 | −0.676121 | ||||||||
\(383\) | 6708.00 | 0.894942 | 0.447471 | − | 0.894298i | \(-0.352325\pi\) | ||||
0.447471 | + | 0.894298i | \(0.352325\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −2962.00 | −0.390575 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 2058.00 | 0.269276 | ||||||||
\(389\) | 13350.0 | 1.74003 | 0.870015 | − | 0.493025i | \(-0.164109\pi\) | ||||
0.870015 | + | 0.493025i | \(0.164109\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2592.00 | 0.335251 | ||||||||
\(392\) | 735.000 | 0.0947018 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −3334.00 | −0.426306 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 1356.00 | 0.171425 | 0.0857125 | − | 0.996320i | \(-0.472683\pi\) | ||||
0.0857125 | + | 0.996320i | \(0.472683\pi\) | |||||||
\(398\) | −1860.00 | −0.234255 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −6222.00 | −0.774843 | −0.387421 | − | 0.921903i | \(-0.626634\pi\) | ||||
−0.387421 | + | 0.921903i | \(0.626634\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −336.000 | −0.0415319 | ||||||||
\(404\) | −4816.00 | −0.593082 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −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 | \(0.399232\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 9716.00 | 1.16183 | ||||||||
\(413\) | −5670.00 | −0.675551 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 4508.00 | 0.531305 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 880.000 | 0.102972 | ||||||||
\(419\) | −2310.00 | −0.269334 | −0.134667 | − | 0.990891i | \(-0.542996\pi\) | ||||
−0.134667 | + | 0.990891i | \(0.542996\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 1262.00 | 0.146095 | 0.0730476 | − | 0.997328i | \(-0.476727\pi\) | ||||
0.0730476 | + | 0.997328i | \(0.476727\pi\) | |||||||
\(422\) | 4268.00 | 0.492329 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −2430.00 | −0.278328 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −3416.00 | −0.387147 | ||||||||
\(428\) | −1708.00 | −0.192896 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 4488.00 | 0.501576 | 0.250788 | − | 0.968042i | \(-0.419310\pi\) | ||||
0.250788 | + | 0.968042i | \(0.419310\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −17038.0 | −1.89098 | −0.945490 | − | 0.325652i | \(-0.894416\pi\) | ||||
−0.945490 | + | 0.325652i | \(0.894416\pi\) | |||||||
\(434\) | −84.0000 | −0.00929062 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −630.000 | −0.0692008 | ||||||||
\(437\) | −5280.00 | −0.577979 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 16200.0 | 1.76124 | 0.880619 | − | 0.473824i | \(-0.157127\pi\) | ||||
0.880619 | + | 0.473824i | \(0.157127\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 1512.00 | 0.162712 | ||||||||
\(443\) | −8772.00 | −0.940791 | −0.470395 | − | 0.882456i | \(-0.655889\pi\) | ||||
−0.470395 | + | 0.882456i | \(0.655889\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −5432.00 | −0.576710 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −1169.00 | −0.123281 | ||||||||
\(449\) | −2130.00 | −0.223877 | −0.111939 | − | 0.993715i | \(-0.535706\pi\) | ||||
−0.111939 | + | 0.993715i | \(0.535706\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1456.00 | −0.152019 | ||||||||
\(452\) | −9226.00 | −0.960076 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 2046.00 | 0.211506 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −10534.0 | −1.07825 | −0.539124 | − | 0.842226i | \(-0.681245\pi\) | ||||
−0.539124 | + | 0.842226i | \(0.681245\pi\) | |||||||
\(458\) | 2980.00 | 0.304031 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 9268.00 | 0.936342 | 0.468171 | − | 0.883638i | \(-0.344913\pi\) | ||||
0.468171 | + | 0.883638i | \(0.344913\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 9392.00 | 0.942728 | 0.471364 | − | 0.881939i | \(-0.343762\pi\) | ||||
0.471364 | + | 0.881939i | \(0.343762\pi\) | |||||||
\(464\) | 4510.00 | 0.451232 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −4458.00 | −0.443161 | ||||||||
\(467\) | −10806.0 | −1.07075 | −0.535377 | − | 0.844613i | \(-0.679830\pi\) | ||||
−0.535377 | + | 0.844613i | \(0.679830\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −1708.00 | −0.168162 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −12150.0 | −1.18485 | ||||||||
\(473\) | −1024.00 | −0.0995424 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −2646.00 | −0.254788 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 4440.00 | 0.424855 | ||||||||
\(479\) | −4940.00 | −0.471220 | −0.235610 | − | 0.971848i | \(-0.575709\pi\) | ||||
−0.235610 | + | 0.971848i | \(0.575709\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −6888.00 | −0.652943 | ||||||||
\(482\) | −3302.00 | −0.312037 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 8869.00 | 0.832926 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 5216.00 | 0.485338 | 0.242669 | − | 0.970109i | \(-0.421977\pi\) | ||||
0.242669 | + | 0.970109i | \(0.421977\pi\) | |||||||
\(488\) | −7320.00 | −0.679018 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −4412.00 | −0.405521 | −0.202760 | − | 0.979228i | \(-0.564991\pi\) | ||||
−0.202760 | + | 0.979228i | \(0.564991\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 5940.00 | 0.542645 | ||||||||
\(494\) | −3080.00 | −0.280518 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 492.000 | 0.0445392 | ||||||||
\(497\) | 5376.00 | 0.485204 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 19060.0 | 1.70991 | 0.854953 | − | 0.518706i | \(-0.173586\pi\) | ||||
0.854953 | + | 0.518706i | \(0.173586\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 1582.00 | 0.140654 | ||||||||
\(503\) | 12768.0 | 1.13180 | 0.565902 | − | 0.824473i | \(-0.308528\pi\) | ||||
0.565902 | + | 0.824473i | \(0.308528\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −384.000 | −0.0337369 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −12432.0 | −1.08579 | ||||||||
\(509\) | 5500.00 | 0.478945 | 0.239473 | − | 0.970903i | \(-0.423025\pi\) | ||||
0.239473 | + | 0.970903i | \(0.423025\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 4914.00 | 0.425406 | ||||||||
\(512\) | −11521.0 | −0.994455 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −2354.00 | −0.202005 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 2592.00 | 0.220495 | ||||||||
\(518\) | −1722.00 | −0.146062 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 7338.00 | 0.617051 | 0.308526 | − | 0.951216i | \(-0.400164\pi\) | ||||
0.308526 | + | 0.951216i | \(0.400164\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 17582.0 | 1.46999 | 0.734997 | − | 0.678070i | \(-0.237183\pi\) | ||||
0.734997 | + | 0.678070i | \(0.237183\pi\) | |||||||
\(524\) | −7826.00 | −0.652444 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 3872.00 | 0.320964 | ||||||||
\(527\) | 648.000 | 0.0535623 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −9863.00 | −0.810635 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 5390.00 | 0.439260 | ||||||||
\(533\) | 5096.00 | 0.414132 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −3660.00 | −0.294940 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 180.000 | 0.0144244 | ||||||||
\(539\) | 392.000 | 0.0313259 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −1618.00 | −0.128583 | −0.0642914 | − | 0.997931i | \(-0.520479\pi\) | ||||
−0.0642914 | + | 0.997931i | \(0.520479\pi\) | |||||||
\(542\) | −2032.00 | −0.161037 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −8694.00 | −0.685206 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −16144.0 | −1.26192 | −0.630958 | − | 0.775817i | \(-0.717338\pi\) | ||||
−0.630958 | + | 0.775817i | \(0.717338\pi\) | |||||||
\(548\) | −15918.0 | −1.24085 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −12100.0 | −0.935531 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 3080.00 | 0.236844 | ||||||||
\(554\) | −5426.00 | −0.416117 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 1470.00 | 0.112126 | ||||||||
\(557\) | 4654.00 | 0.354033 | 0.177016 | − | 0.984208i | \(-0.443355\pi\) | ||||
0.177016 | + | 0.984208i | \(0.443355\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 3584.00 | 0.271175 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 842.000 | 0.0631986 | ||||||||
\(563\) | 10078.0 | 0.754418 | 0.377209 | − | 0.926128i | \(-0.376884\pi\) | ||||
0.377209 | + | 0.926128i | \(0.376884\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −3782.00 | −0.280865 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 11520.0 | 0.851001 | ||||||||
\(569\) | 5930.00 | 0.436904 | 0.218452 | − | 0.975848i | \(-0.429899\pi\) | ||||
0.218452 | + | 0.975848i | \(0.429899\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −19048.0 | −1.39603 | −0.698016 | − | 0.716082i | \(-0.745933\pi\) | ||||
−0.698016 | + | 0.716082i | \(0.745933\pi\) | |||||||
\(572\) | 1568.00 | 0.114618 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 1274.00 | 0.0926406 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 14366.0 | 1.03651 | 0.518253 | − | 0.855227i | \(-0.326582\pi\) | ||||
0.518253 | + | 0.855227i | \(0.326582\pi\) | |||||||
\(578\) | 1997.00 | 0.143710 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −9114.00 | −0.650796 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1296.00 | −0.0920666 | ||||||||
\(584\) | 10530.0 | 0.746121 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 4312.00 | 0.303971 | ||||||||
\(587\) | −3626.00 | −0.254959 | −0.127480 | − | 0.991841i | \(-0.540689\pi\) | ||||
−0.127480 | + | 0.991841i | \(0.540689\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1320.00 | −0.0923424 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 10086.0 | 0.700223 | ||||||||
\(593\) | −1062.00 | −0.0735432 | −0.0367716 | − | 0.999324i | \(-0.511707\pi\) | ||||
−0.0367716 | + | 0.999324i | \(0.511707\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −14070.0 | −0.966996 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 1344.00 | 0.0919068 | ||||||||
\(599\) | 10200.0 | 0.695761 | 0.347880 | − | 0.937539i | \(-0.386902\pi\) | ||||
0.347880 | + | 0.937539i | \(0.386902\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −25158.0 | −1.70751 | −0.853757 | − | 0.520671i | \(-0.825682\pi\) | ||||
−0.853757 | + | 0.520671i | \(0.825682\pi\) | |||||||
\(602\) | 896.000 | 0.0606615 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −7784.00 | −0.524382 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −25664.0 | −1.71609 | −0.858047 | − | 0.513570i | \(-0.828323\pi\) | ||||
−0.858047 | + | 0.513570i | \(0.828323\pi\) | |||||||
\(608\) | 17710.0 | 1.18131 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −9072.00 | −0.600677 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −19018.0 | −1.25307 | −0.626533 | − | 0.779395i | \(-0.715527\pi\) | ||||
−0.626533 | + | 0.779395i | \(0.715527\pi\) | |||||||
\(614\) | 2674.00 | 0.175755 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 840.000 | 0.0549425 | ||||||||
\(617\) | 17334.0 | 1.13102 | 0.565511 | − | 0.824741i | \(-0.308679\pi\) | ||||
0.565511 | + | 0.824741i | \(0.308679\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 18730.0 | 1.21619 | 0.608096 | − | 0.793864i | \(-0.291934\pi\) | ||||
0.608096 | + | 0.793864i | \(0.291934\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −3768.00 | −0.242899 | ||||||||
\(623\) | −5110.00 | −0.328616 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 2438.00 | 0.155658 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 868.000 | 0.0551544 | ||||||||
\(629\) | 13284.0 | 0.842079 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −6928.00 | −0.437083 | −0.218541 | − | 0.975828i | \(-0.570130\pi\) | ||||
−0.218541 | + | 0.975828i | \(0.570130\pi\) | |||||||
\(632\) | 6600.00 | 0.415402 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 3186.00 | 0.199578 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1372.00 | −0.0853385 | ||||||||
\(638\) | −880.000 | −0.0546074 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −16302.0 | −1.00451 | −0.502255 | − | 0.864720i | \(-0.667496\pi\) | ||||
−0.502255 | + | 0.864720i | \(0.667496\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −4718.00 | −0.289362 | −0.144681 | − | 0.989478i | \(-0.546216\pi\) | ||||
−0.144681 | + | 0.989478i | \(0.546216\pi\) | |||||||
\(644\) | −2352.00 | −0.143916 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 5940.00 | 0.361774 | ||||||||
\(647\) | −21436.0 | −1.30253 | −0.651264 | − | 0.758851i | \(-0.725761\pi\) | ||||
−0.651264 | + | 0.758851i | \(0.725761\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −6480.00 | −0.391930 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 14056.0 | 0.844287 | ||||||||
\(653\) | 4458.00 | 0.267159 | 0.133580 | − | 0.991038i | \(-0.457353\pi\) | ||||
0.133580 | + | 0.991038i | \(0.457353\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −7462.00 | −0.444119 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −2268.00 | −0.134371 | ||||||||
\(659\) | 26640.0 | 1.57473 | 0.787365 | − | 0.616487i | \(-0.211445\pi\) | ||||
0.787365 | + | 0.616487i | \(0.211445\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 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 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 5280.00 | 0.306510 | ||||||||
\(668\) | −20188.0 | −1.16931 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −3904.00 | −0.224608 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −58.0000 | −0.00332204 | −0.00166102 | − | 0.999999i | \(-0.500529\pi\) | ||||
−0.00166102 | + | 0.999999i | \(0.500529\pi\) | |||||||
\(674\) | 814.000 | 0.0465194 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 9891.00 | 0.562756 | ||||||||
\(677\) | −21516.0 | −1.22146 | −0.610729 | − | 0.791840i | \(-0.709124\pi\) | ||||
−0.610729 | + | 0.791840i | \(0.709124\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −2058.00 | −0.116316 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −96.0000 | −0.00539007 | ||||||||
\(683\) | 18108.0 | 1.01447 | 0.507235 | − | 0.861808i | \(-0.330668\pi\) | ||||
0.507235 | + | 0.861808i | \(0.330668\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −343.000 | −0.0190901 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −5248.00 | −0.290811 | ||||||||
\(689\) | 4536.00 | 0.250810 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −10078.0 | −0.554827 | −0.277413 | − | 0.960751i | \(-0.589477\pi\) | ||||
−0.277413 | + | 0.960751i | \(0.589477\pi\) | |||||||
\(692\) | −15596.0 | −0.856750 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −9344.00 | −0.511086 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −9828.00 | −0.534092 | ||||||||
\(698\) | 5180.00 | 0.280897 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −18762.0 | −1.01089 | −0.505443 | − | 0.862860i | \(-0.668671\pi\) | ||||
−0.505443 | + | 0.862860i | \(0.668671\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −27060.0 | −1.45176 | ||||||||
\(704\) | −1336.00 | −0.0715233 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −12178.0 | −0.649186 | ||||||||
\(707\) | 4816.00 | 0.256187 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 6810.00 | 0.360726 | 0.180363 | − | 0.983600i | \(-0.442273\pi\) | ||||
0.180363 | + | 0.983600i | \(0.442273\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −10950.0 | −0.576360 | ||||||||
\(713\) | 576.000 | 0.0302544 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −5740.00 | −0.299600 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 440.000 | 0.0228700 | ||||||||
\(719\) | −4860.00 | −0.252083 | −0.126041 | − | 0.992025i | \(-0.540227\pi\) | ||||
−0.126041 | + | 0.992025i | \(0.540227\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −9716.00 | −0.501862 | ||||||||
\(722\) | −5241.00 | −0.270152 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −27244.0 | −1.39850 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 13636.0 | 0.695641 | 0.347821 | − | 0.937561i | \(-0.386922\pi\) | ||||
0.347821 | + | 0.937561i | \(0.386922\pi\) | |||||||
\(728\) | −2940.00 | −0.149675 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −6912.00 | −0.349726 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −2088.00 | −0.105214 | −0.0526071 | − | 0.998615i | \(-0.516753\pi\) | ||||
−0.0526071 | + | 0.998615i | \(0.516753\pi\) | |||||||
\(734\) | −9816.00 | −0.493617 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −7728.00 | −0.387035 | ||||||||
\(737\) | −1952.00 | −0.0975615 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −5160.00 | −0.256852 | −0.128426 | − | 0.991719i | \(-0.540992\pi\) | ||||
−0.128426 | + | 0.991719i | \(0.540992\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 1134.00 | 0.0561057 | ||||||||
\(743\) | −28152.0 | −1.39004 | −0.695018 | − | 0.718992i | \(-0.744604\pi\) | ||||
−0.695018 | + | 0.718992i | \(0.744604\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −442.000 | −0.0216927 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −3024.00 | −0.147819 | ||||||||
\(749\) | 1708.00 | 0.0833230 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −16808.0 | −0.816688 | −0.408344 | − | 0.912828i | \(-0.633894\pi\) | ||||
−0.408344 | + | 0.912828i | \(0.633894\pi\) | |||||||
\(752\) | 13284.0 | 0.644172 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 3080.00 | 0.148763 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −21674.0 | −1.04063 | −0.520314 | − | 0.853975i | \(-0.674185\pi\) | ||||
−0.520314 | + | 0.853975i | \(0.674185\pi\) | |||||||
\(758\) | 3960.00 | 0.189754 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −7422.00 | −0.353544 | −0.176772 | − | 0.984252i | \(-0.556566\pi\) | ||||
−0.176772 | + | 0.984252i | \(0.556566\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 630.000 | 0.0298919 | ||||||||
\(764\) | −35336.0 | −1.67331 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −6708.00 | −0.316410 | ||||||||
\(767\) | 22680.0 | 1.06770 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 13790.0 | 0.646658 | 0.323329 | − | 0.946287i | \(-0.395198\pi\) | ||||
0.323329 | + | 0.946287i | \(0.395198\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −20734.0 | −0.966623 | ||||||||
\(773\) | −6232.00 | −0.289973 | −0.144987 | − | 0.989434i | \(-0.546314\pi\) | ||||
−0.144987 | + | 0.989434i | \(0.546314\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −4410.00 | −0.204007 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −13350.0 | −0.615194 | ||||||||
\(779\) | 20020.0 | 0.920784 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 6144.00 | 0.281498 | ||||||||
\(782\) | −2592.00 | −0.118529 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 2009.00 | 0.0915179 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 1766.00 | 0.0799887 | 0.0399943 | − | 0.999200i | \(-0.487266\pi\) | ||||
0.0399943 | + | 0.999200i | \(0.487266\pi\) | |||||||
\(788\) | −23338.0 | −1.05505 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 9226.00 | 0.414714 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 13664.0 | 0.611883 | ||||||||
\(794\) | −1356.00 | −0.0606079 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −13020.0 | −0.579751 | ||||||||
\(797\) | 1204.00 | 0.0535105 | 0.0267552 | − | 0.999642i | \(-0.491483\pi\) | ||||
0.0267552 | + | 0.999642i | \(0.491483\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 17496.0 | 0.774673 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 6222.00 | 0.273948 | ||||||||
\(803\) | 5616.00 | 0.246805 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 336.000 | 0.0146837 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 10320.0 | 0.449327 | ||||||||
\(809\) | 7050.00 | 0.306384 | 0.153192 | − | 0.988196i | \(-0.451045\pi\) | ||||
0.153192 | + | 0.988196i | \(0.451045\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 23282.0 | 1.00807 | 0.504033 | − | 0.863684i | \(-0.331849\pi\) | ||||
0.504033 | + | 0.863684i | \(0.331849\pi\) | |||||||
\(812\) | −5390.00 | −0.232946 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −1968.00 | −0.0847400 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 14080.0 | 0.602934 | ||||||||
\(818\) | −5150.00 | −0.220129 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −10142.0 | −0.431131 | −0.215565 | − | 0.976489i | \(-0.569159\pi\) | ||||
−0.215565 | + | 0.976489i | \(0.569159\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 9192.00 | 0.389323 | 0.194662 | − | 0.980870i | \(-0.437639\pi\) | ||||
0.194662 | + | 0.980870i | \(0.437639\pi\) | |||||||
\(824\) | −20820.0 | −0.880217 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 5670.00 | 0.238843 | ||||||||
\(827\) | −46716.0 | −1.96430 | −0.982149 | − | 0.188104i | \(-0.939766\pi\) | ||||
−0.982149 | + | 0.188104i | \(0.939766\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 11240.0 | 0.470906 | 0.235453 | − | 0.971886i | \(-0.424343\pi\) | ||||
0.235453 | + | 0.971886i | \(0.424343\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 4676.00 | 0.194845 | ||||||||
\(833\) | 2646.00 | 0.110058 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 6160.00 | 0.254842 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 2310.00 | 0.0952239 | ||||||||
\(839\) | −700.000 | −0.0288042 | −0.0144021 | − | 0.999896i | \(-0.504584\pi\) | ||||
−0.0144021 | + | 0.999896i | \(0.504584\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −12289.0 | −0.503875 | ||||||||
\(842\) | −1262.00 | −0.0516525 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 29876.0 | 1.21845 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −8869.00 | −0.359790 | ||||||||
\(848\) | −6642.00 | −0.268971 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 11808.0 | 0.475644 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 37492.0 | 1.50493 | 0.752463 | − | 0.658635i | \(-0.228866\pi\) | ||||
0.752463 | + | 0.658635i | \(0.228866\pi\) | |||||||
\(854\) | 3416.00 | 0.136877 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 3660.00 | 0.146140 | ||||||||
\(857\) | 28894.0 | 1.15169 | 0.575846 | − | 0.817558i | \(-0.304673\pi\) | ||||
0.575846 | + | 0.817558i | \(0.304673\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −2770.00 | −0.110025 | −0.0550123 | − | 0.998486i | \(-0.517520\pi\) | ||||
−0.0550123 | + | 0.998486i | \(0.517520\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −4488.00 | −0.177334 | ||||||||
\(863\) | 17688.0 | 0.697690 | 0.348845 | − | 0.937180i | \(-0.386574\pi\) | ||||
0.348845 | + | 0.937180i | \(0.386574\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 17038.0 | 0.668562 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −588.000 | −0.0229931 | ||||||||
\(869\) | 3520.00 | 0.137408 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 6832.00 | 0.265779 | ||||||||
\(872\) | 1350.00 | 0.0524275 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 5280.00 | 0.204346 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 33566.0 | 1.29241 | 0.646205 | − | 0.763164i | \(-0.276355\pi\) | ||||
0.646205 | + | 0.763164i | \(0.276355\pi\) | |||||||
\(878\) | −16200.0 | −0.622692 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 16758.0 | 0.640853 | 0.320426 | − | 0.947273i | \(-0.396174\pi\) | ||||
0.320426 | + | 0.947273i | \(0.396174\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −11468.0 | −0.437066 | −0.218533 | − | 0.975830i | \(-0.570127\pi\) | ||||
−0.218533 | + | 0.975830i | \(0.570127\pi\) | |||||||
\(884\) | 10584.0 | 0.402691 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 8772.00 | 0.332620 | ||||||||
\(887\) | −50356.0 | −1.90619 | −0.953094 | − | 0.302674i | \(-0.902121\pi\) | ||||
−0.953094 | + | 0.302674i | \(0.902121\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 12432.0 | 0.469017 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −38024.0 | −1.42728 | ||||||||
\(893\) | −35640.0 | −1.33555 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 10185.0 | 0.379751 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 2130.00 | 0.0791526 | ||||||||
\(899\) | 1320.00 | 0.0489705 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −8748.00 | −0.323461 | ||||||||
\(902\) | 1456.00 | 0.0537467 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 19770.0 | 0.727368 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 8716.00 | 0.319085 | 0.159542 | − | 0.987191i | \(-0.448998\pi\) | ||||
0.159542 | + | 0.987191i | \(0.448998\pi\) | |||||||
\(908\) | 14322.0 | 0.523450 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −7632.00 | −0.277563 | −0.138781 | − | 0.990323i | \(-0.544318\pi\) | ||||
−0.138781 | + | 0.990323i | \(0.544318\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −10416.0 | −0.377568 | ||||||||
\(914\) | 10534.0 | 0.381219 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 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 | \(0.635946\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −9268.00 | −0.331047 | ||||||||
\(923\) | −21504.0 | −0.766861 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −9392.00 | −0.333305 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −17710.0 | −0.626465 | ||||||||
\(929\) | −45110.0 | −1.59312 | −0.796561 | − | 0.604558i | \(-0.793350\pi\) | ||||
−0.796561 | + | 0.604558i | \(0.793350\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −5390.00 | −0.189742 | ||||||||
\(932\) | −31206.0 | −1.09677 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 10806.0 | 0.378569 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −16674.0 | −0.581340 | −0.290670 | − | 0.956823i | \(-0.593878\pi\) | ||||
−0.290670 | + | 0.956823i | \(0.593878\pi\) | |||||||
\(938\) | 1708.00 | 0.0594543 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −43832.0 | −1.51847 | −0.759236 | − | 0.650815i | \(-0.774427\pi\) | ||||
−0.759236 | + | 0.650815i | \(0.774427\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −8736.00 | −0.301679 | ||||||||
\(944\) | −33210.0 | −1.14501 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 1024.00 | 0.0351936 | ||||||||
\(947\) | −736.000 | −0.0252553 | −0.0126277 | − | 0.999920i | \(-0.504020\pi\) | ||||
−0.0126277 | + | 0.999920i | \(0.504020\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −19656.0 | −0.672351 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 5670.00 | 0.193031 | ||||||||
\(953\) | 38138.0 | 1.29634 | 0.648169 | − | 0.761496i | \(-0.275535\pi\) | ||||
0.648169 | + | 0.761496i | \(0.275535\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 31080.0 | 1.05146 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 4940.00 | 0.166601 | ||||||||
\(959\) | 15918.0 | 0.535995 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −29647.0 | −0.995166 | ||||||||
\(962\) | 6888.00 | 0.230850 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −23114.0 | −0.772253 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −26224.0 | −0.872086 | −0.436043 | − | 0.899926i | \(-0.643620\pi\) | ||||
−0.436043 | + | 0.899926i | \(0.643620\pi\) | |||||||
\(968\) | −19005.0 | −0.631037 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −18762.0 | −0.620084 | −0.310042 | − | 0.950723i | \(-0.600343\pi\) | ||||
−0.310042 | + | 0.950723i | \(0.600343\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −1470.00 | −0.0484337 | ||||||||
\(974\) | −5216.00 | −0.171593 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −20008.0 | −0.656189 | ||||||||
\(977\) | 38394.0 | 1.25725 | 0.628625 | − | 0.777709i | \(-0.283618\pi\) | ||||
0.628625 | + | 0.777709i | \(0.283618\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −5840.00 | −0.190651 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 4412.00 | 0.143373 | ||||||||
\(983\) | 5388.00 | 0.174822 | 0.0874112 | − | 0.996172i | \(-0.472141\pi\) | ||||
0.0874112 | + | 0.996172i | \(0.472141\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −5940.00 | −0.191854 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −21560.0 | −0.694246 | ||||||||
\(989\) | −6144.00 | −0.197541 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 25472.0 | 0.816493 | 0.408247 | − | 0.912872i | \(-0.366140\pi\) | ||||
0.408247 | + | 0.912872i | \(0.366140\pi\) | |||||||
\(992\) | −1932.00 | −0.0618357 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −5376.00 | −0.171546 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 17096.0 | 0.543065 | 0.271532 | − | 0.962429i | \(-0.412470\pi\) | ||||
0.271532 | + | 0.962429i | \(0.412470\pi\) | |||||||
\(998\) | −19060.0 | −0.604543 | ||||||||
\(999\) | 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 | 1575.4.a.e.1.1 | 1 | ||
3.2 | odd | 2 | 175.4.a.b.1.1 | 1 | |||
5.4 | even | 2 | 63.4.a.b.1.1 | 1 | |||
15.2 | even | 4 | 175.4.b.b.99.2 | 2 | |||
15.8 | even | 4 | 175.4.b.b.99.1 | 2 | |||
15.14 | odd | 2 | 7.4.a.a.1.1 | ✓ | 1 | ||
20.19 | odd | 2 | 1008.4.a.c.1.1 | 1 | |||
21.20 | even | 2 | 1225.4.a.j.1.1 | 1 | |||
35.4 | even | 6 | 441.4.e.h.226.1 | 2 | |||
35.9 | even | 6 | 441.4.e.h.361.1 | 2 | |||
35.19 | odd | 6 | 441.4.e.e.361.1 | 2 | |||
35.24 | odd | 6 | 441.4.e.e.226.1 | 2 | |||
35.34 | odd | 2 | 441.4.a.i.1.1 | 1 | |||
60.59 | even | 2 | 112.4.a.f.1.1 | 1 | |||
105.44 | odd | 6 | 49.4.c.c.18.1 | 2 | |||
105.59 | even | 6 | 49.4.c.b.30.1 | 2 | |||
105.74 | odd | 6 | 49.4.c.c.30.1 | 2 | |||
105.89 | even | 6 | 49.4.c.b.18.1 | 2 | |||
105.104 | even | 2 | 49.4.a.b.1.1 | 1 | |||
120.29 | odd | 2 | 448.4.a.i.1.1 | 1 | |||
120.59 | even | 2 | 448.4.a.e.1.1 | 1 | |||
165.164 | even | 2 | 847.4.a.b.1.1 | 1 | |||
195.194 | odd | 2 | 1183.4.a.b.1.1 | 1 | |||
255.254 | odd | 2 | 2023.4.a.a.1.1 | 1 | |||
420.419 | odd | 2 | 784.4.a.g.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
7.4.a.a.1.1 | ✓ | 1 | 15.14 | odd | 2 | ||
49.4.a.b.1.1 | 1 | 105.104 | even | 2 | |||
49.4.c.b.18.1 | 2 | 105.89 | even | 6 | |||
49.4.c.b.30.1 | 2 | 105.59 | even | 6 | |||
49.4.c.c.18.1 | 2 | 105.44 | odd | 6 | |||
49.4.c.c.30.1 | 2 | 105.74 | odd | 6 | |||
63.4.a.b.1.1 | 1 | 5.4 | even | 2 | |||
112.4.a.f.1.1 | 1 | 60.59 | even | 2 | |||
175.4.a.b.1.1 | 1 | 3.2 | odd | 2 | |||
175.4.b.b.99.1 | 2 | 15.8 | even | 4 | |||
175.4.b.b.99.2 | 2 | 15.2 | even | 4 | |||
441.4.a.i.1.1 | 1 | 35.34 | odd | 2 | |||
441.4.e.e.226.1 | 2 | 35.24 | odd | 6 | |||
441.4.e.e.361.1 | 2 | 35.19 | odd | 6 | |||
441.4.e.h.226.1 | 2 | 35.4 | even | 6 | |||
441.4.e.h.361.1 | 2 | 35.9 | even | 6 | |||
448.4.a.e.1.1 | 1 | 120.59 | even | 2 | |||
448.4.a.i.1.1 | 1 | 120.29 | odd | 2 | |||
784.4.a.g.1.1 | 1 | 420.419 | odd | 2 | |||
847.4.a.b.1.1 | 1 | 165.164 | even | 2 | |||
1008.4.a.c.1.1 | 1 | 20.19 | odd | 2 | |||
1183.4.a.b.1.1 | 1 | 195.194 | odd | 2 | |||
1225.4.a.j.1.1 | 1 | 21.20 | even | 2 | |||
1575.4.a.e.1.1 | 1 | 1.1 | even | 1 | trivial | ||
2023.4.a.a.1.1 | 1 | 255.254 | odd | 2 |