Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1225,4,Mod(1,1225)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1225, 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("1225.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1225 = 5^{2} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1225.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: | \(72.2773397570\) |
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 | \(\chi\) | \(=\) | 1225.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.00000 | −0.707107 | −0.353553 | − | 0.935414i | \(-0.615027\pi\) | ||||
−0.353553 | + | 0.935414i | \(0.615027\pi\) | |||||||
\(3\) | 7.00000 | 1.34715 | 0.673575 | − | 0.739119i | \(-0.264758\pi\) | ||||
0.673575 | + | 0.739119i | \(0.264758\pi\) | |||||||
\(4\) | −4.00000 | −0.500000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −14.0000 | −0.952579 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 24.0000 | 1.06066 | ||||||||
\(9\) | 22.0000 | 0.814815 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −5.00000 | −0.137051 | −0.0685253 | − | 0.997649i | \(-0.521829\pi\) | ||||
−0.0685253 | + | 0.997649i | \(0.521829\pi\) | |||||||
\(12\) | −28.0000 | −0.673575 | ||||||||
\(13\) | −14.0000 | −0.298685 | −0.149342 | − | 0.988786i | \(-0.547716\pi\) | ||||
−0.149342 | + | 0.988786i | \(0.547716\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −16.0000 | −0.250000 | ||||||||
\(17\) | −21.0000 | −0.299603 | −0.149801 | − | 0.988716i | \(-0.547863\pi\) | ||||
−0.149801 | + | 0.988716i | \(0.547863\pi\) | |||||||
\(18\) | −44.0000 | −0.576161 | ||||||||
\(19\) | −49.0000 | −0.591651 | −0.295826 | − | 0.955242i | \(-0.595595\pi\) | ||||
−0.295826 | + | 0.955242i | \(0.595595\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 10.0000 | 0.0969094 | ||||||||
\(23\) | 159.000 | 1.44147 | 0.720735 | − | 0.693211i | \(-0.243805\pi\) | ||||
0.720735 | + | 0.693211i | \(0.243805\pi\) | |||||||
\(24\) | 168.000 | 1.42887 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 28.0000 | 0.211202 | ||||||||
\(27\) | −35.0000 | −0.249472 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 58.0000 | 0.371391 | 0.185695 | − | 0.982607i | \(-0.440546\pi\) | ||||
0.185695 | + | 0.982607i | \(0.440546\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −147.000 | −0.851677 | −0.425838 | − | 0.904799i | \(-0.640021\pi\) | ||||
−0.425838 | + | 0.904799i | \(0.640021\pi\) | |||||||
\(32\) | −160.000 | −0.883883 | ||||||||
\(33\) | −35.0000 | −0.184628 | ||||||||
\(34\) | 42.0000 | 0.211851 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −88.0000 | −0.407407 | ||||||||
\(37\) | −219.000 | −0.973064 | −0.486532 | − | 0.873663i | \(-0.661738\pi\) | ||||
−0.486532 | + | 0.873663i | \(0.661738\pi\) | |||||||
\(38\) | 98.0000 | 0.418361 | ||||||||
\(39\) | −98.0000 | −0.402373 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −350.000 | −1.33319 | −0.666595 | − | 0.745420i | \(-0.732249\pi\) | ||||
−0.666595 | + | 0.745420i | \(0.732249\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 124.000 | 0.439763 | 0.219882 | − | 0.975527i | \(-0.429433\pi\) | ||||
0.219882 | + | 0.975527i | \(0.429433\pi\) | |||||||
\(44\) | 20.0000 | 0.0685253 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −318.000 | −1.01927 | ||||||||
\(47\) | 525.000 | 1.62934 | 0.814671 | − | 0.579923i | \(-0.196917\pi\) | ||||
0.814671 | + | 0.579923i | \(0.196917\pi\) | |||||||
\(48\) | −112.000 | −0.336788 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −147.000 | −0.403610 | ||||||||
\(52\) | 56.0000 | 0.149342 | ||||||||
\(53\) | −303.000 | −0.785288 | −0.392644 | − | 0.919691i | \(-0.628439\pi\) | ||||
−0.392644 | + | 0.919691i | \(0.628439\pi\) | |||||||
\(54\) | 70.0000 | 0.176404 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −343.000 | −0.797043 | ||||||||
\(58\) | −116.000 | −0.262613 | ||||||||
\(59\) | 105.000 | 0.231692 | 0.115846 | − | 0.993267i | \(-0.463042\pi\) | ||||
0.115846 | + | 0.993267i | \(0.463042\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 413.000 | 0.866873 | 0.433436 | − | 0.901184i | \(-0.357301\pi\) | ||||
0.433436 | + | 0.901184i | \(0.357301\pi\) | |||||||
\(62\) | 294.000 | 0.602226 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 448.000 | 0.875000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 70.0000 | 0.130552 | ||||||||
\(67\) | −415.000 | −0.756721 | −0.378361 | − | 0.925658i | \(-0.623512\pi\) | ||||
−0.378361 | + | 0.925658i | \(0.623512\pi\) | |||||||
\(68\) | 84.0000 | 0.149801 | ||||||||
\(69\) | 1113.00 | 1.94188 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −432.000 | −0.722098 | −0.361049 | − | 0.932547i | \(-0.617581\pi\) | ||||
−0.361049 | + | 0.932547i | \(0.617581\pi\) | |||||||
\(72\) | 528.000 | 0.864242 | ||||||||
\(73\) | −1113.00 | −1.78448 | −0.892238 | − | 0.451565i | \(-0.850866\pi\) | ||||
−0.892238 | + | 0.451565i | \(0.850866\pi\) | |||||||
\(74\) | 438.000 | 0.688060 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 196.000 | 0.295826 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 196.000 | 0.284521 | ||||||||
\(79\) | −103.000 | −0.146689 | −0.0733443 | − | 0.997307i | \(-0.523367\pi\) | ||||
−0.0733443 | + | 0.997307i | \(0.523367\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −839.000 | −1.15089 | ||||||||
\(82\) | 700.000 | 0.942708 | ||||||||
\(83\) | 1092.00 | 1.44413 | 0.722064 | − | 0.691827i | \(-0.243194\pi\) | ||||
0.722064 | + | 0.691827i | \(0.243194\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −248.000 | −0.310960 | ||||||||
\(87\) | 406.000 | 0.500319 | ||||||||
\(88\) | −120.000 | −0.145364 | ||||||||
\(89\) | 329.000 | 0.391842 | 0.195921 | − | 0.980620i | \(-0.437230\pi\) | ||||
0.195921 | + | 0.980620i | \(0.437230\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −636.000 | −0.720735 | ||||||||
\(93\) | −1029.00 | −1.14734 | ||||||||
\(94\) | −1050.00 | −1.15212 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −1120.00 | −1.19072 | ||||||||
\(97\) | −882.000 | −0.923232 | −0.461616 | − | 0.887080i | \(-0.652730\pi\) | ||||
−0.461616 | + | 0.887080i | \(0.652730\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −110.000 | −0.111671 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1379.00 | −1.35857 | −0.679285 | − | 0.733874i | \(-0.737710\pi\) | ||||
−0.679285 | + | 0.733874i | \(0.737710\pi\) | |||||||
\(102\) | 294.000 | 0.285395 | ||||||||
\(103\) | −679.000 | −0.649552 | −0.324776 | − | 0.945791i | \(-0.605289\pi\) | ||||
−0.324776 | + | 0.945791i | \(0.605289\pi\) | |||||||
\(104\) | −336.000 | −0.316803 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 606.000 | 0.555282 | ||||||||
\(107\) | −457.000 | −0.412896 | −0.206448 | − | 0.978458i | \(-0.566190\pi\) | ||||
−0.206448 | + | 0.978458i | \(0.566190\pi\) | |||||||
\(108\) | 140.000 | 0.124736 | ||||||||
\(109\) | −1125.00 | −0.988582 | −0.494291 | − | 0.869296i | \(-0.664572\pi\) | ||||
−0.494291 | + | 0.869296i | \(0.664572\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −1533.00 | −1.31086 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1538.00 | 1.28038 | 0.640190 | − | 0.768217i | \(-0.278856\pi\) | ||||
0.640190 | + | 0.768217i | \(0.278856\pi\) | |||||||
\(114\) | 686.000 | 0.563595 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −232.000 | −0.185695 | ||||||||
\(117\) | −308.000 | −0.243373 | ||||||||
\(118\) | −210.000 | −0.163831 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1306.00 | −0.981217 | ||||||||
\(122\) | −826.000 | −0.612972 | ||||||||
\(123\) | −2450.00 | −1.79601 | ||||||||
\(124\) | 588.000 | 0.425838 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −72.0000 | −0.0503068 | −0.0251534 | − | 0.999684i | \(-0.508007\pi\) | ||||
−0.0251534 | + | 0.999684i | \(0.508007\pi\) | |||||||
\(128\) | 384.000 | 0.265165 | ||||||||
\(129\) | 868.000 | 0.592427 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −2149.00 | −1.43327 | −0.716637 | − | 0.697446i | \(-0.754320\pi\) | ||||
−0.716637 | + | 0.697446i | \(0.754320\pi\) | |||||||
\(132\) | 140.000 | 0.0923139 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 830.000 | 0.535083 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −504.000 | −0.317777 | ||||||||
\(137\) | 1125.00 | 0.701571 | 0.350786 | − | 0.936456i | \(-0.385915\pi\) | ||||
0.350786 | + | 0.936456i | \(0.385915\pi\) | |||||||
\(138\) | −2226.00 | −1.37311 | ||||||||
\(139\) | −252.000 | −0.153772 | −0.0768862 | − | 0.997040i | \(-0.524498\pi\) | ||||
−0.0768862 | + | 0.997040i | \(0.524498\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 3675.00 | 2.19497 | ||||||||
\(142\) | 864.000 | 0.510600 | ||||||||
\(143\) | 70.0000 | 0.0409349 | ||||||||
\(144\) | −352.000 | −0.203704 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 2226.00 | 1.26182 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 876.000 | 0.486532 | ||||||||
\(149\) | −201.000 | −0.110514 | −0.0552569 | − | 0.998472i | \(-0.517598\pi\) | ||||
−0.0552569 | + | 0.998472i | \(0.517598\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1619.00 | 0.872532 | 0.436266 | − | 0.899818i | \(-0.356301\pi\) | ||||
0.436266 | + | 0.899818i | \(0.356301\pi\) | |||||||
\(152\) | −1176.00 | −0.627541 | ||||||||
\(153\) | −462.000 | −0.244121 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 392.000 | 0.201187 | ||||||||
\(157\) | 679.000 | 0.345160 | 0.172580 | − | 0.984996i | \(-0.444790\pi\) | ||||
0.172580 | + | 0.984996i | \(0.444790\pi\) | |||||||
\(158\) | 206.000 | 0.103725 | ||||||||
\(159\) | −2121.00 | −1.05790 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 1678.00 | 0.813803 | ||||||||
\(163\) | 467.000 | 0.224407 | 0.112203 | − | 0.993685i | \(-0.464209\pi\) | ||||
0.112203 | + | 0.993685i | \(0.464209\pi\) | |||||||
\(164\) | 1400.00 | 0.666595 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −2184.00 | −1.02115 | ||||||||
\(167\) | 1204.00 | 0.557894 | 0.278947 | − | 0.960306i | \(-0.410015\pi\) | ||||
0.278947 | + | 0.960306i | \(0.410015\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −2001.00 | −0.910787 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1078.00 | −0.482086 | ||||||||
\(172\) | −496.000 | −0.219882 | ||||||||
\(173\) | −2821.00 | −1.23975 | −0.619875 | − | 0.784701i | \(-0.712817\pi\) | ||||
−0.619875 | + | 0.784701i | \(0.712817\pi\) | |||||||
\(174\) | −812.000 | −0.353779 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 80.0000 | 0.0342627 | ||||||||
\(177\) | 735.000 | 0.312124 | ||||||||
\(178\) | −658.000 | −0.277074 | ||||||||
\(179\) | −3253.00 | −1.35833 | −0.679164 | − | 0.733987i | \(-0.737657\pi\) | ||||
−0.679164 | + | 0.733987i | \(0.737657\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1582.00 | −0.649664 | −0.324832 | − | 0.945772i | \(-0.605308\pi\) | ||||
−0.324832 | + | 0.945772i | \(0.605308\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 2891.00 | 1.16781 | ||||||||
\(184\) | 3816.00 | 1.52891 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 2058.00 | 0.811290 | ||||||||
\(187\) | 105.000 | 0.0410608 | ||||||||
\(188\) | −2100.00 | −0.814671 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 2557.00 | 0.968681 | 0.484340 | − | 0.874880i | \(-0.339060\pi\) | ||||
0.484340 | + | 0.874880i | \(0.339060\pi\) | |||||||
\(192\) | 3136.00 | 1.17876 | ||||||||
\(193\) | 397.000 | 0.148066 | 0.0740329 | − | 0.997256i | \(-0.476413\pi\) | ||||
0.0740329 | + | 0.997256i | \(0.476413\pi\) | |||||||
\(194\) | 1764.00 | 0.652824 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −2914.00 | −1.05388 | −0.526939 | − | 0.849903i | \(-0.676660\pi\) | ||||
−0.526939 | + | 0.849903i | \(0.676660\pi\) | |||||||
\(198\) | 220.000 | 0.0789632 | ||||||||
\(199\) | −3339.00 | −1.18942 | −0.594712 | − | 0.803939i | \(-0.702734\pi\) | ||||
−0.594712 | + | 0.803939i | \(0.702734\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −2905.00 | −1.01942 | ||||||||
\(202\) | 2758.00 | 0.960654 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 588.000 | 0.201805 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 1358.00 | 0.459303 | ||||||||
\(207\) | 3498.00 | 1.17453 | ||||||||
\(208\) | 224.000 | 0.0746712 | ||||||||
\(209\) | 245.000 | 0.0810861 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1780.00 | 0.580759 | 0.290380 | − | 0.956911i | \(-0.406218\pi\) | ||||
0.290380 | + | 0.956911i | \(0.406218\pi\) | |||||||
\(212\) | 1212.00 | 0.392644 | ||||||||
\(213\) | −3024.00 | −0.972775 | ||||||||
\(214\) | 914.000 | 0.291961 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −840.000 | −0.264605 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 2250.00 | 0.699033 | ||||||||
\(219\) | −7791.00 | −2.40396 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 294.000 | 0.0894868 | ||||||||
\(222\) | 3066.00 | 0.926921 | ||||||||
\(223\) | −1400.00 | −0.420408 | −0.210204 | − | 0.977658i | \(-0.567413\pi\) | ||||
−0.210204 | + | 0.977658i | \(0.567413\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −3076.00 | −0.905365 | ||||||||
\(227\) | −2205.00 | −0.644718 | −0.322359 | − | 0.946617i | \(-0.604476\pi\) | ||||
−0.322359 | + | 0.946617i | \(0.604476\pi\) | |||||||
\(228\) | 1372.00 | 0.398522 | ||||||||
\(229\) | −287.000 | −0.0828188 | −0.0414094 | − | 0.999142i | \(-0.513185\pi\) | ||||
−0.0414094 | + | 0.999142i | \(0.513185\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 1392.00 | 0.393919 | ||||||||
\(233\) | −4587.00 | −1.28972 | −0.644859 | − | 0.764301i | \(-0.723084\pi\) | ||||
−0.644859 | + | 0.764301i | \(0.723084\pi\) | |||||||
\(234\) | 616.000 | 0.172091 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −420.000 | −0.115846 | ||||||||
\(237\) | −721.000 | −0.197612 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 1668.00 | 0.451439 | 0.225720 | − | 0.974192i | \(-0.427527\pi\) | ||||
0.225720 | + | 0.974192i | \(0.427527\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 3409.00 | 0.911174 | 0.455587 | − | 0.890191i | \(-0.349429\pi\) | ||||
0.455587 | + | 0.890191i | \(0.349429\pi\) | |||||||
\(242\) | 2612.00 | 0.693825 | ||||||||
\(243\) | −4928.00 | −1.30095 | ||||||||
\(244\) | −1652.00 | −0.433436 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 4900.00 | 1.26997 | ||||||||
\(247\) | 686.000 | 0.176717 | ||||||||
\(248\) | −3528.00 | −0.903340 | ||||||||
\(249\) | 7644.00 | 1.94546 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 4760.00 | 1.19701 | 0.598503 | − | 0.801121i | \(-0.295762\pi\) | ||||
0.598503 | + | 0.801121i | \(0.295762\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −795.000 | −0.197554 | ||||||||
\(254\) | 144.000 | 0.0355723 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −4352.00 | −1.06250 | ||||||||
\(257\) | −805.000 | −0.195387 | −0.0976936 | − | 0.995217i | \(-0.531147\pi\) | ||||
−0.0976936 | + | 0.995217i | \(0.531147\pi\) | |||||||
\(258\) | −1736.00 | −0.418909 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1276.00 | 0.302615 | ||||||||
\(262\) | 4298.00 | 1.01348 | ||||||||
\(263\) | 257.000 | 0.0602559 | 0.0301279 | − | 0.999546i | \(-0.490409\pi\) | ||||
0.0301279 | + | 0.999546i | \(0.490409\pi\) | |||||||
\(264\) | −840.000 | −0.195827 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 2303.00 | 0.527870 | ||||||||
\(268\) | 1660.00 | 0.378361 | ||||||||
\(269\) | −3591.00 | −0.813930 | −0.406965 | − | 0.913444i | \(-0.633413\pi\) | ||||
−0.406965 | + | 0.913444i | \(0.633413\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1393.00 | −0.312246 | −0.156123 | − | 0.987738i | \(-0.549900\pi\) | ||||
−0.156123 | + | 0.987738i | \(0.549900\pi\) | |||||||
\(272\) | 336.000 | 0.0749007 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −2250.00 | −0.496086 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −4452.00 | −0.970938 | ||||||||
\(277\) | −415.000 | −0.0900178 | −0.0450089 | − | 0.998987i | \(-0.514332\pi\) | ||||
−0.0450089 | + | 0.998987i | \(0.514332\pi\) | |||||||
\(278\) | 504.000 | 0.108733 | ||||||||
\(279\) | −3234.00 | −0.693959 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −4954.00 | −1.05171 | −0.525856 | − | 0.850574i | \(-0.676255\pi\) | ||||
−0.525856 | + | 0.850574i | \(0.676255\pi\) | |||||||
\(282\) | −7350.00 | −1.55208 | ||||||||
\(283\) | −4277.00 | −0.898379 | −0.449190 | − | 0.893437i | \(-0.648287\pi\) | ||||
−0.449190 | + | 0.893437i | \(0.648287\pi\) | |||||||
\(284\) | 1728.00 | 0.361049 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −140.000 | −0.0289454 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −3520.00 | −0.720201 | ||||||||
\(289\) | −4472.00 | −0.910238 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −6174.00 | −1.24373 | ||||||||
\(292\) | 4452.00 | 0.892238 | ||||||||
\(293\) | 7742.00 | 1.54366 | 0.771830 | − | 0.635829i | \(-0.219342\pi\) | ||||
0.771830 | + | 0.635829i | \(0.219342\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −5256.00 | −1.03209 | ||||||||
\(297\) | 175.000 | 0.0341903 | ||||||||
\(298\) | 402.000 | 0.0781451 | ||||||||
\(299\) | −2226.00 | −0.430545 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −3238.00 | −0.616973 | ||||||||
\(303\) | −9653.00 | −1.83020 | ||||||||
\(304\) | 784.000 | 0.147913 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 924.000 | 0.172619 | ||||||||
\(307\) | −7364.00 | −1.36901 | −0.684504 | − | 0.729009i | \(-0.739981\pi\) | ||||
−0.684504 | + | 0.729009i | \(0.739981\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −4753.00 | −0.875044 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −9975.00 | −1.81875 | −0.909374 | − | 0.415980i | \(-0.863438\pi\) | ||||
−0.909374 | + | 0.415980i | \(0.863438\pi\) | |||||||
\(312\) | −2352.00 | −0.426781 | ||||||||
\(313\) | −4753.00 | −0.858324 | −0.429162 | − | 0.903228i | \(-0.641191\pi\) | ||||
−0.429162 | + | 0.903228i | \(0.641191\pi\) | |||||||
\(314\) | −1358.00 | −0.244065 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 412.000 | 0.0733443 | ||||||||
\(317\) | 3477.00 | 0.616050 | 0.308025 | − | 0.951378i | \(-0.400332\pi\) | ||||
0.308025 | + | 0.951378i | \(0.400332\pi\) | |||||||
\(318\) | 4242.00 | 0.748049 | ||||||||
\(319\) | −290.000 | −0.0508993 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −3199.00 | −0.556233 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1029.00 | 0.177260 | ||||||||
\(324\) | 3356.00 | 0.575446 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −934.000 | −0.158679 | ||||||||
\(327\) | −7875.00 | −1.33177 | ||||||||
\(328\) | −8400.00 | −1.41406 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 3341.00 | 0.554797 | 0.277399 | − | 0.960755i | \(-0.410528\pi\) | ||||
0.277399 | + | 0.960755i | \(0.410528\pi\) | |||||||
\(332\) | −4368.00 | −0.722064 | ||||||||
\(333\) | −4818.00 | −0.792867 | ||||||||
\(334\) | −2408.00 | −0.394491 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −7366.00 | −1.19066 | −0.595329 | − | 0.803482i | \(-0.702978\pi\) | ||||
−0.595329 | + | 0.803482i | \(0.702978\pi\) | |||||||
\(338\) | 4002.00 | 0.644024 | ||||||||
\(339\) | 10766.0 | 1.72486 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 735.000 | 0.116723 | ||||||||
\(342\) | 2156.00 | 0.340886 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 2976.00 | 0.466439 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 5642.00 | 0.876635 | ||||||||
\(347\) | −7415.00 | −1.14714 | −0.573571 | − | 0.819156i | \(-0.694442\pi\) | ||||
−0.573571 | + | 0.819156i | \(0.694442\pi\) | |||||||
\(348\) | −1624.00 | −0.250160 | ||||||||
\(349\) | 3878.00 | 0.594798 | 0.297399 | − | 0.954753i | \(-0.403881\pi\) | ||||
0.297399 | + | 0.954753i | \(0.403881\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 490.000 | 0.0745136 | ||||||||
\(352\) | 800.000 | 0.121137 | ||||||||
\(353\) | 1267.00 | 0.191036 | 0.0955179 | − | 0.995428i | \(-0.469549\pi\) | ||||
0.0955179 | + | 0.995428i | \(0.469549\pi\) | |||||||
\(354\) | −1470.00 | −0.220705 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −1316.00 | −0.195921 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 6506.00 | 0.960483 | ||||||||
\(359\) | 4685.00 | 0.688760 | 0.344380 | − | 0.938830i | \(-0.388089\pi\) | ||||
0.344380 | + | 0.938830i | \(0.388089\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −4458.00 | −0.649949 | ||||||||
\(362\) | 3164.00 | 0.459382 | ||||||||
\(363\) | −9142.00 | −1.32185 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −5782.00 | −0.825765 | ||||||||
\(367\) | −4641.00 | −0.660104 | −0.330052 | − | 0.943963i | \(-0.607066\pi\) | ||||
−0.330052 | + | 0.943963i | \(0.607066\pi\) | |||||||
\(368\) | −2544.00 | −0.360367 | ||||||||
\(369\) | −7700.00 | −1.08630 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 4116.00 | 0.573668 | ||||||||
\(373\) | 8797.00 | 1.22116 | 0.610578 | − | 0.791956i | \(-0.290937\pi\) | ||||
0.610578 | + | 0.791956i | \(0.290937\pi\) | |||||||
\(374\) | −210.000 | −0.0290343 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 12600.0 | 1.72818 | ||||||||
\(377\) | −812.000 | −0.110929 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 13680.0 | 1.85407 | 0.927037 | − | 0.374969i | \(-0.122347\pi\) | ||||
0.927037 | + | 0.374969i | \(0.122347\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −504.000 | −0.0677709 | ||||||||
\(382\) | −5114.00 | −0.684961 | ||||||||
\(383\) | 9765.00 | 1.30279 | 0.651395 | − | 0.758739i | \(-0.274184\pi\) | ||||
0.651395 | + | 0.758739i | \(0.274184\pi\) | |||||||
\(384\) | 2688.00 | 0.357217 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −794.000 | −0.104698 | ||||||||
\(387\) | 2728.00 | 0.358326 | ||||||||
\(388\) | 3528.00 | 0.461616 | ||||||||
\(389\) | 1731.00 | 0.225617 | 0.112809 | − | 0.993617i | \(-0.464015\pi\) | ||||
0.112809 | + | 0.993617i | \(0.464015\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −3339.00 | −0.431868 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −15043.0 | −1.93084 | ||||||||
\(394\) | 5828.00 | 0.745204 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 440.000 | 0.0558354 | ||||||||
\(397\) | 10983.0 | 1.38847 | 0.694233 | − | 0.719750i | \(-0.255744\pi\) | ||||
0.694233 | + | 0.719750i | \(0.255744\pi\) | |||||||
\(398\) | 6678.00 | 0.841050 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 6603.00 | 0.822289 | 0.411145 | − | 0.911570i | \(-0.365129\pi\) | ||||
0.411145 | + | 0.911570i | \(0.365129\pi\) | |||||||
\(402\) | 5810.00 | 0.720837 | ||||||||
\(403\) | 2058.00 | 0.254383 | ||||||||
\(404\) | 5516.00 | 0.679285 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 1095.00 | 0.133359 | ||||||||
\(408\) | −3528.00 | −0.428093 | ||||||||
\(409\) | −10955.0 | −1.32443 | −0.662213 | − | 0.749316i | \(-0.730382\pi\) | ||||
−0.662213 | + | 0.749316i | \(0.730382\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 7875.00 | 0.945122 | ||||||||
\(412\) | 2716.00 | 0.324776 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −6996.00 | −0.830518 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 2240.00 | 0.264002 | ||||||||
\(417\) | −1764.00 | −0.207155 | ||||||||
\(418\) | −490.000 | −0.0573366 | ||||||||
\(419\) | −6636.00 | −0.773723 | −0.386861 | − | 0.922138i | \(-0.626441\pi\) | ||||
−0.386861 | + | 0.922138i | \(0.626441\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −16630.0 | −1.92517 | −0.962585 | − | 0.270980i | \(-0.912652\pi\) | ||||
−0.962585 | + | 0.270980i | \(0.912652\pi\) | |||||||
\(422\) | −3560.00 | −0.410659 | ||||||||
\(423\) | 11550.0 | 1.32761 | ||||||||
\(424\) | −7272.00 | −0.832923 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 6048.00 | 0.687856 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 1828.00 | 0.206448 | ||||||||
\(429\) | 490.000 | 0.0551455 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 4923.00 | 0.550192 | 0.275096 | − | 0.961417i | \(-0.411290\pi\) | ||||
0.275096 | + | 0.961417i | \(0.411290\pi\) | |||||||
\(432\) | 560.000 | 0.0623681 | ||||||||
\(433\) | 8974.00 | 0.995988 | 0.497994 | − | 0.867180i | \(-0.334070\pi\) | ||||
0.497994 | + | 0.867180i | \(0.334070\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 4500.00 | 0.494291 | ||||||||
\(437\) | −7791.00 | −0.852847 | ||||||||
\(438\) | 15582.0 | 1.69986 | ||||||||
\(439\) | 4179.00 | 0.454334 | 0.227167 | − | 0.973856i | \(-0.427054\pi\) | ||||
0.227167 | + | 0.973856i | \(0.427054\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −588.000 | −0.0632767 | ||||||||
\(443\) | 12927.0 | 1.38641 | 0.693206 | − | 0.720740i | \(-0.256198\pi\) | ||||
0.693206 | + | 0.720740i | \(0.256198\pi\) | |||||||
\(444\) | 6132.00 | 0.655432 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 2800.00 | 0.297273 | ||||||||
\(447\) | −1407.00 | −0.148879 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −2826.00 | −0.297032 | −0.148516 | − | 0.988910i | \(-0.547450\pi\) | ||||
−0.148516 | + | 0.988910i | \(0.547450\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1750.00 | 0.182715 | ||||||||
\(452\) | −6152.00 | −0.640190 | ||||||||
\(453\) | 11333.0 | 1.17543 | ||||||||
\(454\) | 4410.00 | 0.455884 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −8232.00 | −0.845392 | ||||||||
\(457\) | −8479.00 | −0.867901 | −0.433951 | − | 0.900937i | \(-0.642881\pi\) | ||||
−0.433951 | + | 0.900937i | \(0.642881\pi\) | |||||||
\(458\) | 574.000 | 0.0585617 | ||||||||
\(459\) | 735.000 | 0.0747426 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −9338.00 | −0.943414 | −0.471707 | − | 0.881755i | \(-0.656362\pi\) | ||||
−0.471707 | + | 0.881755i | \(0.656362\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 4016.00 | 0.403109 | 0.201554 | − | 0.979477i | \(-0.435401\pi\) | ||||
0.201554 | + | 0.979477i | \(0.435401\pi\) | |||||||
\(464\) | −928.000 | −0.0928477 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 9174.00 | 0.911969 | ||||||||
\(467\) | −5859.00 | −0.580561 | −0.290281 | − | 0.956942i | \(-0.593749\pi\) | ||||
−0.290281 | + | 0.956942i | \(0.593749\pi\) | |||||||
\(468\) | 1232.00 | 0.121686 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 4753.00 | 0.464982 | ||||||||
\(472\) | 2520.00 | 0.245747 | ||||||||
\(473\) | −620.000 | −0.0602698 | ||||||||
\(474\) | 1442.00 | 0.139733 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −6666.00 | −0.639864 | ||||||||
\(478\) | −3336.00 | −0.319216 | ||||||||
\(479\) | −6503.00 | −0.620312 | −0.310156 | − | 0.950686i | \(-0.600381\pi\) | ||||
−0.310156 | + | 0.950686i | \(0.600381\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 3066.00 | 0.290639 | ||||||||
\(482\) | −6818.00 | −0.644297 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 5224.00 | 0.490609 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 9856.00 | 0.919912 | ||||||||
\(487\) | 16049.0 | 1.49333 | 0.746663 | − | 0.665203i | \(-0.231655\pi\) | ||||
0.746663 | + | 0.665203i | \(0.231655\pi\) | |||||||
\(488\) | 9912.00 | 0.919457 | ||||||||
\(489\) | 3269.00 | 0.302309 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 8864.00 | 0.814718 | 0.407359 | − | 0.913268i | \(-0.366450\pi\) | ||||
0.407359 | + | 0.913268i | \(0.366450\pi\) | |||||||
\(492\) | 9800.00 | 0.898004 | ||||||||
\(493\) | −1218.00 | −0.111270 | ||||||||
\(494\) | −1372.00 | −0.124958 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 2352.00 | 0.212919 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −15288.0 | −1.37565 | ||||||||
\(499\) | −10211.0 | −0.916046 | −0.458023 | − | 0.888940i | \(-0.651442\pi\) | ||||
−0.458023 | + | 0.888940i | \(0.651442\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 8428.00 | 0.751567 | ||||||||
\(502\) | −9520.00 | −0.846411 | ||||||||
\(503\) | −1680.00 | −0.148921 | −0.0744607 | − | 0.997224i | \(-0.523724\pi\) | ||||
−0.0744607 | + | 0.997224i | \(0.523724\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 1590.00 | 0.139692 | ||||||||
\(507\) | −14007.0 | −1.22697 | ||||||||
\(508\) | 288.000 | 0.0251534 | ||||||||
\(509\) | 9457.00 | 0.823525 | 0.411762 | − | 0.911291i | \(-0.364913\pi\) | ||||
0.411762 | + | 0.911291i | \(0.364913\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 5632.00 | 0.486136 | ||||||||
\(513\) | 1715.00 | 0.147601 | ||||||||
\(514\) | 1610.00 | 0.138160 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −3472.00 | −0.296214 | ||||||||
\(517\) | −2625.00 | −0.223302 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −19747.0 | −1.67013 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 18081.0 | 1.52043 | 0.760214 | − | 0.649673i | \(-0.225094\pi\) | ||||
0.760214 | + | 0.649673i | \(0.225094\pi\) | |||||||
\(522\) | −2552.00 | −0.213981 | ||||||||
\(523\) | 20377.0 | 1.70368 | 0.851839 | − | 0.523803i | \(-0.175487\pi\) | ||||
0.851839 | + | 0.523803i | \(0.175487\pi\) | |||||||
\(524\) | 8596.00 | 0.716637 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −514.000 | −0.0426073 | ||||||||
\(527\) | 3087.00 | 0.255165 | ||||||||
\(528\) | 560.000 | 0.0461570 | ||||||||
\(529\) | 13114.0 | 1.07783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 2310.00 | 0.188786 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 4900.00 | 0.398204 | ||||||||
\(534\) | −4606.00 | −0.373261 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −9960.00 | −0.802624 | ||||||||
\(537\) | −22771.0 | −1.82987 | ||||||||
\(538\) | 7182.00 | 0.575535 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −6193.00 | −0.492159 | −0.246079 | − | 0.969250i | \(-0.579142\pi\) | ||||
−0.246079 | + | 0.969250i | \(0.579142\pi\) | |||||||
\(542\) | 2786.00 | 0.220791 | ||||||||
\(543\) | −11074.0 | −0.875195 | ||||||||
\(544\) | 3360.00 | 0.264814 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 18464.0 | 1.44326 | 0.721630 | − | 0.692279i | \(-0.243393\pi\) | ||||
0.721630 | + | 0.692279i | \(0.243393\pi\) | |||||||
\(548\) | −4500.00 | −0.350786 | ||||||||
\(549\) | 9086.00 | 0.706341 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −2842.00 | −0.219734 | ||||||||
\(552\) | 26712.0 | 2.05967 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 830.000 | 0.0636522 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 1008.00 | 0.0768862 | ||||||||
\(557\) | 9413.00 | 0.716053 | 0.358027 | − | 0.933711i | \(-0.383450\pi\) | ||||
0.358027 | + | 0.933711i | \(0.383450\pi\) | |||||||
\(558\) | 6468.00 | 0.490703 | ||||||||
\(559\) | −1736.00 | −0.131351 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 735.000 | 0.0553150 | ||||||||
\(562\) | 9908.00 | 0.743672 | ||||||||
\(563\) | 3199.00 | 0.239470 | 0.119735 | − | 0.992806i | \(-0.461795\pi\) | ||||
0.119735 | + | 0.992806i | \(0.461795\pi\) | |||||||
\(564\) | −14700.0 | −1.09749 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 8554.00 | 0.635250 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −10368.0 | −0.765901 | ||||||||
\(569\) | 21583.0 | 1.59017 | 0.795085 | − | 0.606498i | \(-0.207426\pi\) | ||||
0.795085 | + | 0.606498i | \(0.207426\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 20267.0 | 1.48537 | 0.742686 | − | 0.669640i | \(-0.233551\pi\) | ||||
0.742686 | + | 0.669640i | \(0.233551\pi\) | |||||||
\(572\) | −280.000 | −0.0204675 | ||||||||
\(573\) | 17899.0 | 1.30496 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 9856.00 | 0.712963 | ||||||||
\(577\) | 13951.0 | 1.00656 | 0.503282 | − | 0.864122i | \(-0.332126\pi\) | ||||
0.503282 | + | 0.864122i | \(0.332126\pi\) | |||||||
\(578\) | 8944.00 | 0.643636 | ||||||||
\(579\) | 2779.00 | 0.199467 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 12348.0 | 0.879452 | ||||||||
\(583\) | 1515.00 | 0.107624 | ||||||||
\(584\) | −26712.0 | −1.89272 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −15484.0 | −1.09153 | ||||||||
\(587\) | −20972.0 | −1.47463 | −0.737314 | − | 0.675550i | \(-0.763906\pi\) | ||||
−0.737314 | + | 0.675550i | \(0.763906\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 7203.00 | 0.503895 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −20398.0 | −1.41973 | ||||||||
\(592\) | 3504.00 | 0.243266 | ||||||||
\(593\) | −189.000 | −0.0130882 | −0.00654410 | − | 0.999979i | \(-0.502083\pi\) | ||||
−0.00654410 | + | 0.999979i | \(0.502083\pi\) | |||||||
\(594\) | −350.000 | −0.0241762 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 804.000 | 0.0552569 | ||||||||
\(597\) | −23373.0 | −1.60233 | ||||||||
\(598\) | 4452.00 | 0.304441 | ||||||||
\(599\) | −10281.0 | −0.701286 | −0.350643 | − | 0.936509i | \(-0.614037\pi\) | ||||
−0.350643 | + | 0.936509i | \(0.614037\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 6090.00 | 0.413338 | 0.206669 | − | 0.978411i | \(-0.433738\pi\) | ||||
0.206669 | + | 0.978411i | \(0.433738\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −9130.00 | −0.616588 | ||||||||
\(604\) | −6476.00 | −0.436266 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 19306.0 | 1.29415 | ||||||||
\(607\) | 4949.00 | 0.330929 | 0.165464 | − | 0.986216i | \(-0.447088\pi\) | ||||
0.165464 | + | 0.986216i | \(0.447088\pi\) | |||||||
\(608\) | 7840.00 | 0.522951 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −7350.00 | −0.486660 | ||||||||
\(612\) | 1848.00 | 0.122060 | ||||||||
\(613\) | 15797.0 | 1.04084 | 0.520420 | − | 0.853910i | \(-0.325775\pi\) | ||||
0.520420 | + | 0.853910i | \(0.325775\pi\) | |||||||
\(614\) | 14728.0 | 0.968035 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 9378.00 | 0.611903 | 0.305951 | − | 0.952047i | \(-0.401025\pi\) | ||||
0.305951 | + | 0.952047i | \(0.401025\pi\) | |||||||
\(618\) | 9506.00 | 0.618750 | ||||||||
\(619\) | 24353.0 | 1.58131 | 0.790654 | − | 0.612263i | \(-0.209741\pi\) | ||||
0.790654 | + | 0.612263i | \(0.209741\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −5565.00 | −0.359607 | ||||||||
\(622\) | 19950.0 | 1.28605 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 1568.00 | 0.100593 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 9506.00 | 0.606927 | ||||||||
\(627\) | 1715.00 | 0.109235 | ||||||||
\(628\) | −2716.00 | −0.172580 | ||||||||
\(629\) | 4599.00 | 0.291533 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −12640.0 | −0.797449 | −0.398725 | − | 0.917071i | \(-0.630547\pi\) | ||||
−0.398725 | + | 0.917071i | \(0.630547\pi\) | |||||||
\(632\) | −2472.00 | −0.155587 | ||||||||
\(633\) | 12460.0 | 0.782371 | ||||||||
\(634\) | −6954.00 | −0.435613 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 8484.00 | 0.528950 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 580.000 | 0.0359913 | ||||||||
\(639\) | −9504.00 | −0.588376 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −1041.00 | −0.0641451 | −0.0320726 | − | 0.999486i | \(-0.510211\pi\) | ||||
−0.0320726 | + | 0.999486i | \(0.510211\pi\) | |||||||
\(642\) | 6398.00 | 0.393316 | ||||||||
\(643\) | 9548.00 | 0.585593 | 0.292797 | − | 0.956175i | \(-0.405414\pi\) | ||||
0.292797 | + | 0.956175i | \(0.405414\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −2058.00 | −0.125342 | ||||||||
\(647\) | −3241.00 | −0.196935 | −0.0984674 | − | 0.995140i | \(-0.531394\pi\) | ||||
−0.0984674 | + | 0.995140i | \(0.531394\pi\) | |||||||
\(648\) | −20136.0 | −1.22070 | ||||||||
\(649\) | −525.000 | −0.0317535 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −1868.00 | −0.112203 | ||||||||
\(653\) | 8853.00 | 0.530543 | 0.265272 | − | 0.964174i | \(-0.414538\pi\) | ||||
0.265272 | + | 0.964174i | \(0.414538\pi\) | |||||||
\(654\) | 15750.0 | 0.941703 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 5600.00 | 0.333298 | ||||||||
\(657\) | −24486.0 | −1.45402 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 7044.00 | 0.416381 | 0.208191 | − | 0.978088i | \(-0.433243\pi\) | ||||
0.208191 | + | 0.978088i | \(0.433243\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 12089.0 | 0.711358 | 0.355679 | − | 0.934608i | \(-0.384250\pi\) | ||||
0.355679 | + | 0.934608i | \(0.384250\pi\) | |||||||
\(662\) | −6682.00 | −0.392301 | ||||||||
\(663\) | 2058.00 | 0.120552 | ||||||||
\(664\) | 26208.0 | 1.53173 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 9636.00 | 0.560642 | ||||||||
\(667\) | 9222.00 | 0.535348 | ||||||||
\(668\) | −4816.00 | −0.278947 | ||||||||
\(669\) | −9800.00 | −0.566353 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −2065.00 | −0.118805 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −982.000 | −0.0562456 | −0.0281228 | − | 0.999604i | \(-0.508953\pi\) | ||||
−0.0281228 | + | 0.999604i | \(0.508953\pi\) | |||||||
\(674\) | 14732.0 | 0.841922 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 8004.00 | 0.455394 | ||||||||
\(677\) | −30513.0 | −1.73222 | −0.866108 | − | 0.499857i | \(-0.833386\pi\) | ||||
−0.866108 | + | 0.499857i | \(0.833386\pi\) | |||||||
\(678\) | −21532.0 | −1.21966 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −15435.0 | −0.868532 | ||||||||
\(682\) | −1470.00 | −0.0825355 | ||||||||
\(683\) | −11475.0 | −0.642868 | −0.321434 | − | 0.946932i | \(-0.604165\pi\) | ||||
−0.321434 | + | 0.946932i | \(0.604165\pi\) | |||||||
\(684\) | 4312.00 | 0.241043 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −2009.00 | −0.111569 | ||||||||
\(688\) | −1984.00 | −0.109941 | ||||||||
\(689\) | 4242.00 | 0.234553 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 28315.0 | 1.55883 | 0.779416 | − | 0.626506i | \(-0.215516\pi\) | ||||
0.779416 | + | 0.626506i | \(0.215516\pi\) | |||||||
\(692\) | 11284.0 | 0.619875 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 14830.0 | 0.811151 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 9744.00 | 0.530669 | ||||||||
\(697\) | 7350.00 | 0.399428 | ||||||||
\(698\) | −7756.00 | −0.420586 | ||||||||
\(699\) | −32109.0 | −1.73744 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 10614.0 | 0.571876 | 0.285938 | − | 0.958248i | \(-0.407695\pi\) | ||||
0.285938 | + | 0.958248i | \(0.407695\pi\) | |||||||
\(702\) | −980.000 | −0.0526891 | ||||||||
\(703\) | 10731.0 | 0.575715 | ||||||||
\(704\) | −2240.00 | −0.119919 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −2534.00 | −0.135083 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −2940.00 | −0.156062 | ||||||||
\(709\) | 10299.0 | 0.545539 | 0.272769 | − | 0.962079i | \(-0.412060\pi\) | ||||
0.272769 | + | 0.962079i | \(0.412060\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −2266.00 | −0.119524 | ||||||||
\(712\) | 7896.00 | 0.415611 | ||||||||
\(713\) | −23373.0 | −1.22767 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 13012.0 | 0.679164 | ||||||||
\(717\) | 11676.0 | 0.608156 | ||||||||
\(718\) | −9370.00 | −0.487027 | ||||||||
\(719\) | −32529.0 | −1.68724 | −0.843621 | − | 0.536939i | \(-0.819580\pi\) | ||||
−0.843621 | + | 0.536939i | \(0.819580\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 8916.00 | 0.459583 | ||||||||
\(723\) | 23863.0 | 1.22749 | ||||||||
\(724\) | 6328.00 | 0.324832 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 18284.0 | 0.934687 | ||||||||
\(727\) | 29456.0 | 1.50270 | 0.751350 | − | 0.659904i | \(-0.229403\pi\) | ||||
0.751350 | + | 0.659904i | \(0.229403\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −11843.0 | −0.601687 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −2604.00 | −0.131754 | ||||||||
\(732\) | −11564.0 | −0.583904 | ||||||||
\(733\) | 27867.0 | 1.40422 | 0.702109 | − | 0.712070i | \(-0.252242\pi\) | ||||
0.702109 | + | 0.712070i | \(0.252242\pi\) | |||||||
\(734\) | 9282.00 | 0.466764 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −25440.0 | −1.27409 | ||||||||
\(737\) | 2075.00 | 0.103709 | ||||||||
\(738\) | 15400.0 | 0.768133 | ||||||||
\(739\) | 19539.0 | 0.972603 | 0.486302 | − | 0.873791i | \(-0.338346\pi\) | ||||
0.486302 | + | 0.873791i | \(0.338346\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 4802.00 | 0.238065 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −1248.00 | −0.0616214 | −0.0308107 | − | 0.999525i | \(-0.509809\pi\) | ||||
−0.0308107 | + | 0.999525i | \(0.509809\pi\) | |||||||
\(744\) | −24696.0 | −1.21693 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −17594.0 | −0.863488 | ||||||||
\(747\) | 24024.0 | 1.17670 | ||||||||
\(748\) | −420.000 | −0.0205304 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 28093.0 | 1.36502 | 0.682509 | − | 0.730877i | \(-0.260889\pi\) | ||||
0.682509 | + | 0.730877i | \(0.260889\pi\) | |||||||
\(752\) | −8400.00 | −0.407336 | ||||||||
\(753\) | 33320.0 | 1.61255 | ||||||||
\(754\) | 1624.00 | 0.0784385 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −35954.0 | −1.72625 | −0.863124 | − | 0.504991i | \(-0.831496\pi\) | ||||
−0.863124 | + | 0.504991i | \(0.831496\pi\) | |||||||
\(758\) | −27360.0 | −1.31103 | ||||||||
\(759\) | −5565.00 | −0.266135 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 861.000 | 0.0410134 | 0.0205067 | − | 0.999790i | \(-0.493472\pi\) | ||||
0.0205067 | + | 0.999790i | \(0.493472\pi\) | |||||||
\(762\) | 1008.00 | 0.0479212 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −10228.0 | −0.484340 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −19530.0 | −0.921211 | ||||||||
\(767\) | −1470.00 | −0.0692029 | ||||||||
\(768\) | −30464.0 | −1.43135 | ||||||||
\(769\) | −24710.0 | −1.15873 | −0.579366 | − | 0.815067i | \(-0.696700\pi\) | ||||
−0.579366 | + | 0.815067i | \(0.696700\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −5635.00 | −0.263216 | ||||||||
\(772\) | −1588.00 | −0.0740329 | ||||||||
\(773\) | 16499.0 | 0.767694 | 0.383847 | − | 0.923397i | \(-0.374599\pi\) | ||||
0.383847 | + | 0.923397i | \(0.374599\pi\) | |||||||
\(774\) | −5456.00 | −0.253375 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −21168.0 | −0.979236 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −3462.00 | −0.159536 | ||||||||
\(779\) | 17150.0 | 0.788784 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 2160.00 | 0.0989640 | ||||||||
\(782\) | 6678.00 | 0.305377 | ||||||||
\(783\) | −2030.00 | −0.0926517 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 30086.0 | 1.36531 | ||||||||
\(787\) | 16471.0 | 0.746033 | 0.373016 | − | 0.927825i | \(-0.378324\pi\) | ||||
0.373016 | + | 0.927825i | \(0.378324\pi\) | |||||||
\(788\) | 11656.0 | 0.526939 | ||||||||
\(789\) | 1799.00 | 0.0811738 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −2640.00 | −0.118445 | ||||||||
\(793\) | −5782.00 | −0.258922 | ||||||||
\(794\) | −21966.0 | −0.981794 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 13356.0 | 0.594712 | ||||||||
\(797\) | −36470.0 | −1.62087 | −0.810435 | − | 0.585828i | \(-0.800769\pi\) | ||||
−0.810435 | + | 0.585828i | \(0.800769\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −11025.0 | −0.488156 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 7238.00 | 0.319279 | ||||||||
\(802\) | −13206.0 | −0.581446 | ||||||||
\(803\) | 5565.00 | 0.244564 | ||||||||
\(804\) | 11620.0 | 0.509709 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −4116.00 | −0.179876 | ||||||||
\(807\) | −25137.0 | −1.09649 | ||||||||
\(808\) | −33096.0 | −1.44098 | ||||||||
\(809\) | 35751.0 | 1.55369 | 0.776847 | − | 0.629690i | \(-0.216818\pi\) | ||||
0.776847 | + | 0.629690i | \(0.216818\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 16492.0 | 0.714072 | 0.357036 | − | 0.934091i | \(-0.383787\pi\) | ||||
0.357036 | + | 0.934091i | \(0.383787\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −9751.00 | −0.420643 | ||||||||
\(814\) | −2190.00 | −0.0942991 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 2352.00 | 0.100903 | ||||||||
\(817\) | −6076.00 | −0.260186 | ||||||||
\(818\) | 21910.0 | 0.936510 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −41473.0 | −1.76299 | −0.881497 | − | 0.472190i | \(-0.843464\pi\) | ||||
−0.881497 | + | 0.472190i | \(0.843464\pi\) | |||||||
\(822\) | −15750.0 | −0.668302 | ||||||||
\(823\) | 25065.0 | 1.06162 | 0.530809 | − | 0.847492i | \(-0.321888\pi\) | ||||
0.530809 | + | 0.847492i | \(0.321888\pi\) | |||||||
\(824\) | −16296.0 | −0.688954 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −9732.00 | −0.409208 | −0.204604 | − | 0.978845i | \(-0.565591\pi\) | ||||
−0.204604 | + | 0.978845i | \(0.565591\pi\) | |||||||
\(828\) | −13992.0 | −0.587265 | ||||||||
\(829\) | −27755.0 | −1.16281 | −0.581406 | − | 0.813614i | \(-0.697497\pi\) | ||||
−0.581406 | + | 0.813614i | \(0.697497\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −2905.00 | −0.121268 | ||||||||
\(832\) | −6272.00 | −0.261349 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 3528.00 | 0.146480 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −980.000 | −0.0405431 | ||||||||
\(837\) | 5145.00 | 0.212470 | ||||||||
\(838\) | 13272.0 | 0.547105 | ||||||||
\(839\) | −21112.0 | −0.868733 | −0.434367 | − | 0.900736i | \(-0.643028\pi\) | ||||
−0.434367 | + | 0.900736i | \(0.643028\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −21025.0 | −0.862069 | ||||||||
\(842\) | 33260.0 | 1.36130 | ||||||||
\(843\) | −34678.0 | −1.41681 | ||||||||
\(844\) | −7120.00 | −0.290380 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −23100.0 | −0.938764 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 4848.00 | 0.196322 | ||||||||
\(849\) | −29939.0 | −1.21025 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −34821.0 | −1.40264 | ||||||||
\(852\) | 12096.0 | 0.486387 | ||||||||
\(853\) | −21238.0 | −0.852492 | −0.426246 | − | 0.904607i | \(-0.640164\pi\) | ||||
−0.426246 | + | 0.904607i | \(0.640164\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −10968.0 | −0.437942 | ||||||||
\(857\) | −35609.0 | −1.41935 | −0.709673 | − | 0.704531i | \(-0.751158\pi\) | ||||
−0.709673 | + | 0.704531i | \(0.751158\pi\) | |||||||
\(858\) | −980.000 | −0.0389938 | ||||||||
\(859\) | −2177.00 | −0.0864706 | −0.0432353 | − | 0.999065i | \(-0.513767\pi\) | ||||
−0.0432353 | + | 0.999065i | \(0.513767\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −9846.00 | −0.389044 | ||||||||
\(863\) | 32247.0 | 1.27196 | 0.635980 | − | 0.771706i | \(-0.280596\pi\) | ||||
0.635980 | + | 0.771706i | \(0.280596\pi\) | |||||||
\(864\) | 5600.00 | 0.220504 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −17948.0 | −0.704270 | ||||||||
\(867\) | −31304.0 | −1.22623 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 515.000 | 0.0201038 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 5810.00 | 0.226021 | ||||||||
\(872\) | −27000.0 | −1.04855 | ||||||||
\(873\) | −19404.0 | −0.752263 | ||||||||
\(874\) | 15582.0 | 0.603054 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 31164.0 | 1.20198 | ||||||||
\(877\) | −27631.0 | −1.06389 | −0.531946 | − | 0.846779i | \(-0.678539\pi\) | ||||
−0.531946 | + | 0.846779i | \(0.678539\pi\) | |||||||
\(878\) | −8358.00 | −0.321263 | ||||||||
\(879\) | 54194.0 | 2.07954 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −24402.0 | −0.933172 | −0.466586 | − | 0.884476i | \(-0.654516\pi\) | ||||
−0.466586 | + | 0.884476i | \(0.654516\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 19612.0 | 0.747448 | 0.373724 | − | 0.927540i | \(-0.378081\pi\) | ||||
0.373724 | + | 0.927540i | \(0.378081\pi\) | |||||||
\(884\) | −1176.00 | −0.0447434 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −25854.0 | −0.980341 | ||||||||
\(887\) | 2261.00 | 0.0855884 | 0.0427942 | − | 0.999084i | \(-0.486374\pi\) | ||||
0.0427942 | + | 0.999084i | \(0.486374\pi\) | |||||||
\(888\) | −36792.0 | −1.39038 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 4195.00 | 0.157730 | ||||||||
\(892\) | 5600.00 | 0.210204 | ||||||||
\(893\) | −25725.0 | −0.964003 | ||||||||
\(894\) | 2814.00 | 0.105273 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −15582.0 | −0.580009 | ||||||||
\(898\) | 5652.00 | 0.210033 | ||||||||
\(899\) | −8526.00 | −0.316305 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 6363.00 | 0.235274 | ||||||||
\(902\) | −3500.00 | −0.129199 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 36912.0 | 1.35805 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −22666.0 | −0.831156 | ||||||||
\(907\) | 23833.0 | 0.872505 | 0.436252 | − | 0.899824i | \(-0.356305\pi\) | ||||
0.436252 | + | 0.899824i | \(0.356305\pi\) | |||||||
\(908\) | 8820.00 | 0.322359 | ||||||||
\(909\) | −30338.0 | −1.10698 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 31824.0 | 1.15738 | 0.578692 | − | 0.815546i | \(-0.303563\pi\) | ||||
0.578692 | + | 0.815546i | \(0.303563\pi\) | |||||||
\(912\) | 5488.00 | 0.199261 | ||||||||
\(913\) | −5460.00 | −0.197919 | ||||||||
\(914\) | 16958.0 | 0.613699 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 1148.00 | 0.0414094 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −1470.00 | −0.0528510 | ||||||||
\(919\) | −16819.0 | −0.603708 | −0.301854 | − | 0.953354i | \(-0.597606\pi\) | ||||
−0.301854 | + | 0.953354i | \(0.597606\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −51548.0 | −1.84426 | ||||||||
\(922\) | 18676.0 | 0.667095 | ||||||||
\(923\) | 6048.00 | 0.215680 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −8032.00 | −0.285041 | ||||||||
\(927\) | −14938.0 | −0.529265 | ||||||||
\(928\) | −9280.00 | −0.328266 | ||||||||
\(929\) | −1799.00 | −0.0635342 | −0.0317671 | − | 0.999495i | \(-0.510113\pi\) | ||||
−0.0317671 | + | 0.999495i | \(0.510113\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 18348.0 | 0.644859 | ||||||||
\(933\) | −69825.0 | −2.45013 | ||||||||
\(934\) | 11718.0 | 0.410519 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −7392.00 | −0.258136 | ||||||||
\(937\) | 14154.0 | 0.493480 | 0.246740 | − | 0.969082i | \(-0.420641\pi\) | ||||
0.246740 | + | 0.969082i | \(0.420641\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −33271.0 | −1.15629 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −12047.0 | −0.417344 | −0.208672 | − | 0.977986i | \(-0.566914\pi\) | ||||
−0.208672 | + | 0.977986i | \(0.566914\pi\) | |||||||
\(942\) | −9506.00 | −0.328792 | ||||||||
\(943\) | −55650.0 | −1.92175 | ||||||||
\(944\) | −1680.00 | −0.0579230 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 1240.00 | 0.0426172 | ||||||||
\(947\) | 24379.0 | 0.836548 | 0.418274 | − | 0.908321i | \(-0.362635\pi\) | ||||
0.418274 | + | 0.908321i | \(0.362635\pi\) | |||||||
\(948\) | 2884.00 | 0.0988059 | ||||||||
\(949\) | 15582.0 | 0.532996 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 24339.0 | 0.829912 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 52330.0 | 1.77874 | 0.889368 | − | 0.457192i | \(-0.151145\pi\) | ||||
0.889368 | + | 0.457192i | \(0.151145\pi\) | |||||||
\(954\) | 13332.0 | 0.452452 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −6672.00 | −0.225720 | ||||||||
\(957\) | −2030.00 | −0.0685690 | ||||||||
\(958\) | 13006.0 | 0.438627 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −8182.00 | −0.274647 | ||||||||
\(962\) | −6132.00 | −0.205513 | ||||||||
\(963\) | −10054.0 | −0.336434 | ||||||||
\(964\) | −13636.0 | −0.455587 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 12416.0 | 0.412897 | 0.206449 | − | 0.978457i | \(-0.433809\pi\) | ||||
0.206449 | + | 0.978457i | \(0.433809\pi\) | |||||||
\(968\) | −31344.0 | −1.04074 | ||||||||
\(969\) | 7203.00 | 0.238796 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −36813.0 | −1.21667 | −0.608334 | − | 0.793681i | \(-0.708162\pi\) | ||||
−0.608334 | + | 0.793681i | \(0.708162\pi\) | |||||||
\(972\) | 19712.0 | 0.650476 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −32098.0 | −1.05594 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −6608.00 | −0.216718 | ||||||||
\(977\) | −34995.0 | −1.14595 | −0.572973 | − | 0.819574i | \(-0.694210\pi\) | ||||
−0.572973 | + | 0.819574i | \(0.694210\pi\) | |||||||
\(978\) | −6538.00 | −0.213765 | ||||||||
\(979\) | −1645.00 | −0.0537022 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −24750.0 | −0.805511 | ||||||||
\(982\) | −17728.0 | −0.576093 | ||||||||
\(983\) | −14301.0 | −0.464019 | −0.232010 | − | 0.972713i | \(-0.574530\pi\) | ||||
−0.232010 | + | 0.972713i | \(0.574530\pi\) | |||||||
\(984\) | −58800.0 | −1.90495 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 2436.00 | 0.0786796 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −2744.00 | −0.0883586 | ||||||||
\(989\) | 19716.0 | 0.633905 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −2665.00 | −0.0854253 | −0.0427127 | − | 0.999087i | \(-0.513600\pi\) | ||||
−0.0427127 | + | 0.999087i | \(0.513600\pi\) | |||||||
\(992\) | 23520.0 | 0.752783 | ||||||||
\(993\) | 23387.0 | 0.747396 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −30576.0 | −0.972729 | ||||||||
\(997\) | 24871.0 | 0.790043 | 0.395021 | − | 0.918672i | \(-0.370737\pi\) | ||||
0.395021 | + | 0.918672i | \(0.370737\pi\) | |||||||
\(998\) | 20422.0 | 0.647743 | ||||||||
\(999\) | 7665.00 | 0.242753 |
(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 | 1225.4.a.d.1.1 | 1 | ||
5.4 | even | 2 | 49.4.a.c.1.1 | 1 | |||
7.3 | odd | 6 | 175.4.e.a.51.1 | 2 | |||
7.5 | odd | 6 | 175.4.e.a.151.1 | 2 | |||
7.6 | odd | 2 | 1225.4.a.c.1.1 | 1 | |||
15.14 | odd | 2 | 441.4.a.e.1.1 | 1 | |||
20.19 | odd | 2 | 784.4.a.r.1.1 | 1 | |||
35.3 | even | 12 | 175.4.k.a.149.1 | 4 | |||
35.4 | even | 6 | 49.4.c.a.30.1 | 2 | |||
35.9 | even | 6 | 49.4.c.a.18.1 | 2 | |||
35.12 | even | 12 | 175.4.k.a.74.1 | 4 | |||
35.17 | even | 12 | 175.4.k.a.149.2 | 4 | |||
35.19 | odd | 6 | 7.4.c.a.4.1 | yes | 2 | ||
35.24 | odd | 6 | 7.4.c.a.2.1 | ✓ | 2 | ||
35.33 | even | 12 | 175.4.k.a.74.2 | 4 | |||
35.34 | odd | 2 | 49.4.a.d.1.1 | 1 | |||
105.44 | odd | 6 | 441.4.e.k.361.1 | 2 | |||
105.59 | even | 6 | 63.4.e.b.37.1 | 2 | |||
105.74 | odd | 6 | 441.4.e.k.226.1 | 2 | |||
105.89 | even | 6 | 63.4.e.b.46.1 | 2 | |||
105.104 | even | 2 | 441.4.a.d.1.1 | 1 | |||
140.19 | even | 6 | 112.4.i.c.81.1 | 2 | |||
140.59 | even | 6 | 112.4.i.c.65.1 | 2 | |||
140.139 | even | 2 | 784.4.a.b.1.1 | 1 | |||
280.19 | even | 6 | 448.4.i.a.193.1 | 2 | |||
280.59 | even | 6 | 448.4.i.a.65.1 | 2 | |||
280.229 | odd | 6 | 448.4.i.f.193.1 | 2 | |||
280.269 | odd | 6 | 448.4.i.f.65.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
7.4.c.a.2.1 | ✓ | 2 | 35.24 | odd | 6 | ||
7.4.c.a.4.1 | yes | 2 | 35.19 | odd | 6 | ||
49.4.a.c.1.1 | 1 | 5.4 | even | 2 | |||
49.4.a.d.1.1 | 1 | 35.34 | odd | 2 | |||
49.4.c.a.18.1 | 2 | 35.9 | even | 6 | |||
49.4.c.a.30.1 | 2 | 35.4 | even | 6 | |||
63.4.e.b.37.1 | 2 | 105.59 | even | 6 | |||
63.4.e.b.46.1 | 2 | 105.89 | even | 6 | |||
112.4.i.c.65.1 | 2 | 140.59 | even | 6 | |||
112.4.i.c.81.1 | 2 | 140.19 | even | 6 | |||
175.4.e.a.51.1 | 2 | 7.3 | odd | 6 | |||
175.4.e.a.151.1 | 2 | 7.5 | odd | 6 | |||
175.4.k.a.74.1 | 4 | 35.12 | even | 12 | |||
175.4.k.a.74.2 | 4 | 35.33 | even | 12 | |||
175.4.k.a.149.1 | 4 | 35.3 | even | 12 | |||
175.4.k.a.149.2 | 4 | 35.17 | even | 12 | |||
441.4.a.d.1.1 | 1 | 105.104 | even | 2 | |||
441.4.a.e.1.1 | 1 | 15.14 | odd | 2 | |||
441.4.e.k.226.1 | 2 | 105.74 | odd | 6 | |||
441.4.e.k.361.1 | 2 | 105.44 | odd | 6 | |||
448.4.i.a.65.1 | 2 | 280.59 | even | 6 | |||
448.4.i.a.193.1 | 2 | 280.19 | even | 6 | |||
448.4.i.f.65.1 | 2 | 280.269 | odd | 6 | |||
448.4.i.f.193.1 | 2 | 280.229 | odd | 6 | |||
784.4.a.b.1.1 | 1 | 140.139 | even | 2 | |||
784.4.a.r.1.1 | 1 | 20.19 | odd | 2 | |||
1225.4.a.c.1.1 | 1 | 7.6 | odd | 2 | |||
1225.4.a.d.1.1 | 1 | 1.1 | even | 1 | trivial |