Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3640,2,Mod(1,3640)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3640, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3640.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3640 = 2^{3} \cdot 5 \cdot 7 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3640.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: | \(29.0655463357\) |
Analytic rank: | \(1\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.229.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - 4x - 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-1.86081\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3640.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −1.46260 | −0.844432 | −0.422216 | − | 0.906495i | \(-0.638748\pi\) | ||||
−0.422216 | + | 0.906495i | \(0.638748\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −0.860806 | −0.286935 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.39821 | −0.421575 | −0.210788 | − | 0.977532i | \(-0.567603\pi\) | ||||
−0.210788 | + | 0.977532i | \(0.567603\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.00000 | 0.277350 | ||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.46260 | 0.377641 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.25901 | 0.305356 | 0.152678 | − | 0.988276i | \(-0.451210\pi\) | ||||
0.152678 | + | 0.988276i | \(0.451210\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −0.462598 | −0.106127 | −0.0530637 | − | 0.998591i | \(-0.516899\pi\) | ||||
−0.0530637 | + | 0.998591i | \(0.516899\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.46260 | 0.319165 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 8.04502 | 1.67750 | 0.838751 | − | 0.544515i | \(-0.183286\pi\) | ||||
0.838751 | + | 0.544515i | \(0.183286\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 5.64681 | 1.08673 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −5.65722 | −1.05052 | −0.525260 | − | 0.850942i | \(-0.676032\pi\) | ||||
−0.525260 | + | 0.850942i | \(0.676032\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 5.46260 | 0.981112 | 0.490556 | − | 0.871410i | \(-0.336794\pi\) | ||||
0.490556 | + | 0.871410i | \(0.336794\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 2.04502 | 0.355992 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1.00000 | 0.169031 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −0.815790 | −0.134115 | −0.0670575 | − | 0.997749i | \(-0.521361\pi\) | ||||
−0.0670575 | + | 0.997749i | \(0.521361\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −1.46260 | −0.234203 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 7.58242 | 1.18417 | 0.592087 | − | 0.805874i | \(-0.298304\pi\) | ||||
0.592087 | + | 0.805874i | \(0.298304\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.07480 | −0.163906 | −0.0819530 | − | 0.996636i | \(-0.526116\pi\) | ||||
−0.0819530 | + | 0.996636i | \(0.526116\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0.860806 | 0.128321 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −8.69182 | −1.26783 | −0.633916 | − | 0.773402i | \(-0.718554\pi\) | ||||
−0.633916 | + | 0.773402i | \(0.718554\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −1.84143 | −0.257852 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −4.79641 | −0.658838 | −0.329419 | − | 0.944184i | \(-0.606853\pi\) | ||||
−0.329419 | + | 0.944184i | \(0.606853\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.39821 | 0.188534 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0.676596 | 0.0896173 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 6.43281 | 0.837481 | 0.418740 | − | 0.908106i | \(-0.362472\pi\) | ||||
0.418740 | + | 0.908106i | \(0.362472\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −4.60179 | −0.589199 | −0.294600 | − | 0.955621i | \(-0.595186\pi\) | ||||
−0.294600 | + | 0.955621i | \(0.595186\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0.860806 | 0.108451 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −1.00000 | −0.124035 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2.13919 | 0.261344 | 0.130672 | − | 0.991426i | \(-0.458286\pi\) | ||||
0.130672 | + | 0.991426i | \(0.458286\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −11.7666 | −1.41654 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0.128782 | 0.0152836 | 0.00764180 | − | 0.999971i | \(-0.497568\pi\) | ||||
0.00764180 | + | 0.999971i | \(0.497568\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −13.4882 | −1.57868 | −0.789340 | − | 0.613957i | \(-0.789577\pi\) | ||||
−0.789340 | + | 0.613957i | \(0.789577\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −1.46260 | −0.168886 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1.39821 | 0.159341 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 3.06439 | 0.344771 | 0.172385 | − | 0.985030i | \(-0.444853\pi\) | ||||
0.172385 | + | 0.985030i | \(0.444853\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −5.67660 | −0.630733 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 1.44322 | 0.158414 | 0.0792072 | − | 0.996858i | \(-0.474761\pi\) | ||||
0.0792072 | + | 0.996858i | \(0.474761\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.25901 | −0.136559 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 8.27424 | 0.887092 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −11.5076 | −1.21980 | −0.609902 | − | 0.792477i | \(-0.708791\pi\) | ||||
−0.609902 | + | 0.792477i | \(0.708791\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.00000 | −0.104828 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −7.98959 | −0.828482 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0.462598 | 0.0474616 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −8.17380 | −0.829923 | −0.414962 | − | 0.909839i | \(-0.636205\pi\) | ||||
−0.414962 | + | 0.909839i | \(0.636205\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1.20359 | 0.120965 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −13.4882 | −1.34213 | −0.671065 | − | 0.741399i | \(-0.734163\pi\) | ||||
−0.671065 | + | 0.741399i | \(0.734163\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 9.75622 | 0.961308 | 0.480654 | − | 0.876910i | \(-0.340399\pi\) | ||||
0.480654 | + | 0.876910i | \(0.340399\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −1.46260 | −0.142735 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −13.5720 | −1.31206 | −0.656028 | − | 0.754737i | \(-0.727765\pi\) | ||||
−0.656028 | + | 0.754737i | \(0.727765\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 14.7368 | 1.41153 | 0.705767 | − | 0.708444i | \(-0.250603\pi\) | ||||
0.705767 | + | 0.708444i | \(0.250603\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 1.19317 | 0.113251 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 16.2638 | 1.52997 | 0.764986 | − | 0.644047i | \(-0.222746\pi\) | ||||
0.764986 | + | 0.644047i | \(0.222746\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −8.04502 | −0.750202 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −0.860806 | −0.0795815 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −1.25901 | −0.115414 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −9.04502 | −0.822274 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −11.0900 | −0.999955 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −4.99104 | −0.442883 | −0.221441 | − | 0.975174i | \(-0.571076\pi\) | ||||
−0.221441 | + | 0.975174i | \(0.571076\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 1.57201 | 0.138407 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −9.35319 | −0.817192 | −0.408596 | − | 0.912715i | \(-0.633982\pi\) | ||||
−0.408596 | + | 0.912715i | \(0.633982\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.462598 | 0.0401124 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −5.64681 | −0.486000 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −3.63640 | −0.310678 | −0.155339 | − | 0.987861i | \(-0.549647\pi\) | ||||
−0.155339 | + | 0.987861i | \(0.549647\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −6.21881 | −0.527473 | −0.263736 | − | 0.964595i | \(-0.584955\pi\) | ||||
−0.263736 | + | 0.964595i | \(0.584955\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 12.7126 | 1.07060 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −1.39821 | −0.116924 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 5.65722 | 0.469807 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −1.46260 | −0.120633 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 16.7819 | 1.37482 | 0.687412 | − | 0.726268i | \(-0.258747\pi\) | ||||
0.687412 | + | 0.726268i | \(0.258747\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 21.8116 | 1.77501 | 0.887503 | − | 0.460802i | \(-0.152438\pi\) | ||||
0.887503 | + | 0.460802i | \(0.152438\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −1.08377 | −0.0876173 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −5.46260 | −0.438766 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −22.7562 | −1.81614 | −0.908072 | − | 0.418814i | \(-0.862446\pi\) | ||||
−0.908072 | + | 0.418814i | \(0.862446\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 7.01523 | 0.556344 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −8.04502 | −0.634036 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −9.87603 | −0.773551 | −0.386775 | − | 0.922174i | \(-0.626411\pi\) | ||||
−0.386775 | + | 0.922174i | \(0.626411\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −2.04502 | −0.159204 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −17.4224 | −1.34819 | −0.674093 | − | 0.738647i | \(-0.735465\pi\) | ||||
−0.674093 | + | 0.738647i | \(0.735465\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0.398207 | 0.0304517 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −23.0796 | −1.75471 | −0.877356 | − | 0.479841i | \(-0.840694\pi\) | ||||
−0.877356 | + | 0.479841i | \(0.840694\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1.00000 | −0.0755929 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −9.40862 | −0.707195 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 12.1842 | 0.910691 | 0.455345 | − | 0.890315i | \(-0.349516\pi\) | ||||
0.455345 | + | 0.890315i | \(0.349516\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 15.3595 | 1.14166 | 0.570830 | − | 0.821068i | \(-0.306622\pi\) | ||||
0.570830 | + | 0.821068i | \(0.306622\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 6.73057 | 0.497538 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0.815790 | 0.0599781 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1.76036 | −0.128730 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −5.64681 | −0.410745 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −3.41758 | −0.247288 | −0.123644 | − | 0.992327i | \(-0.539458\pi\) | ||||
−0.123644 | + | 0.992327i | \(0.539458\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −14.5526 | −1.04752 | −0.523761 | − | 0.851865i | \(-0.675471\pi\) | ||||
−0.523761 | + | 0.851865i | \(0.675471\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 1.46260 | 0.104739 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −3.09418 | −0.220451 | −0.110226 | − | 0.993907i | \(-0.535157\pi\) | ||||
−0.110226 | + | 0.993907i | \(0.535157\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −18.3684 | −1.30210 | −0.651051 | − | 0.759034i | \(-0.725672\pi\) | ||||
−0.651051 | + | 0.759034i | \(0.725672\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −3.12878 | −0.220687 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 5.65722 | 0.397059 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −7.58242 | −0.529579 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −6.92520 | −0.481334 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0.646809 | 0.0447407 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 22.0554 | 1.51836 | 0.759179 | − | 0.650882i | \(-0.225601\pi\) | ||||
0.759179 | + | 0.650882i | \(0.225601\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −0.188356 | −0.0129060 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 1.07480 | 0.0733010 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −5.46260 | −0.370825 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 19.7279 | 1.33309 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1.25901 | 0.0846904 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 9.11982 | 0.610708 | 0.305354 | − | 0.952239i | \(-0.401225\pi\) | ||||
0.305354 | + | 0.952239i | \(0.401225\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −0.860806 | −0.0573871 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −6.00000 | −0.398234 | −0.199117 | − | 0.979976i | \(-0.563807\pi\) | ||||
−0.199117 | + | 0.979976i | \(0.563807\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −11.6662 | −0.770923 | −0.385462 | − | 0.922724i | \(-0.625958\pi\) | ||||
−0.385462 | + | 0.922724i | \(0.625958\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −2.04502 | −0.134552 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −18.7819 | −1.23044 | −0.615220 | − | 0.788355i | \(-0.710933\pi\) | ||||
−0.615220 | + | 0.788355i | \(0.710933\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 8.69182 | 0.566992 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −4.48197 | −0.291135 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −0.407170 | −0.0263377 | −0.0131688 | − | 0.999913i | \(-0.504192\pi\) | ||||
−0.0131688 | + | 0.999913i | \(0.504192\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −7.77704 | −0.500963 | −0.250482 | − | 0.968121i | \(-0.580589\pi\) | ||||
−0.250482 | + | 0.968121i | \(0.580589\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −8.63785 | −0.554118 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −1.00000 | −0.0638877 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −0.462598 | −0.0294344 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −2.11086 | −0.133770 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −14.8206 | −0.935468 | −0.467734 | − | 0.883869i | \(-0.654930\pi\) | ||||
−0.467734 | + | 0.883869i | \(0.654930\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −11.2486 | −0.707193 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 1.84143 | 0.115315 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 2.09003 | 0.130373 | 0.0651863 | − | 0.997873i | \(-0.479236\pi\) | ||||
0.0651863 | + | 0.997873i | \(0.479236\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0.815790 | 0.0506907 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 4.86977 | 0.301431 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 0.497202 | 0.0306588 | 0.0153294 | − | 0.999882i | \(-0.495120\pi\) | ||||
0.0153294 | + | 0.999882i | \(0.495120\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 4.79641 | 0.294641 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 16.8310 | 1.03004 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −23.7279 | −1.44671 | −0.723357 | − | 0.690474i | \(-0.757402\pi\) | ||||
−0.723357 | + | 0.690474i | \(0.757402\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 11.5478 | 0.701480 | 0.350740 | − | 0.936473i | \(-0.385930\pi\) | ||||
0.350740 | + | 0.936473i | \(0.385930\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 1.46260 | 0.0885205 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −1.39821 | −0.0843151 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −25.8504 | −1.55320 | −0.776600 | − | 0.629994i | \(-0.783057\pi\) | ||||
−0.776600 | + | 0.629994i | \(0.783057\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −4.70224 | −0.281516 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 14.3684 | 0.857148 | 0.428574 | − | 0.903507i | \(-0.359016\pi\) | ||||
0.428574 | + | 0.903507i | \(0.359016\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 15.1336 | 0.899599 | 0.449800 | − | 0.893130i | \(-0.351495\pi\) | ||||
0.449800 | + | 0.893130i | \(0.351495\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −0.676596 | −0.0400781 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −7.58242 | −0.447576 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −15.4149 | −0.906758 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 11.9550 | 0.700814 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −3.31444 | −0.193632 | −0.0968159 | − | 0.995302i | \(-0.530866\pi\) | ||||
−0.0968159 | + | 0.995302i | \(0.530866\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −6.43281 | −0.374533 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −7.89541 | −0.458138 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 8.04502 | 0.465255 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.07480 | 0.0619506 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 19.7279 | 1.13334 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 4.60179 | 0.263498 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −8.49720 | −0.484961 | −0.242480 | − | 0.970156i | \(-0.577961\pi\) | ||||
−0.242480 | + | 0.970156i | \(0.577961\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −14.2694 | −0.811759 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 15.0748 | 0.854814 | 0.427407 | − | 0.904059i | \(-0.359427\pi\) | ||||
0.427407 | + | 0.904059i | \(0.359427\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −1.91478 | −0.108230 | −0.0541150 | − | 0.998535i | \(-0.517234\pi\) | ||||
−0.0541150 | + | 0.998535i | \(0.517234\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −0.860806 | −0.0485009 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −27.1890 | −1.52709 | −0.763544 | − | 0.645756i | \(-0.776542\pi\) | ||||
−0.763544 | + | 0.645756i | \(0.776542\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 7.90997 | 0.442873 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 19.8504 | 1.10794 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −0.582418 | −0.0324066 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1.00000 | 0.0554700 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −21.5541 | −1.19194 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 8.69182 | 0.479196 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −18.9494 | −1.04155 | −0.520776 | − | 0.853693i | \(-0.674357\pi\) | ||||
−0.520776 | + | 0.853693i | \(0.674357\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0.702237 | 0.0384823 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −2.13919 | −0.116877 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 25.2486 | 1.37538 | 0.687689 | − | 0.726005i | \(-0.258625\pi\) | ||||
0.687689 | + | 0.726005i | \(0.258625\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −23.7875 | −1.29196 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −7.63785 | −0.413613 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 11.7666 | 0.633494 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −18.3476 | −0.984951 | −0.492475 | − | 0.870326i | \(-0.663908\pi\) | ||||
−0.492475 | + | 0.870326i | \(0.663908\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 17.2292 | 0.922259 | 0.461130 | − | 0.887333i | \(-0.347444\pi\) | ||||
0.461130 | + | 0.887333i | \(0.347444\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 5.64681 | 0.301404 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 2.19462 | 0.116808 | 0.0584040 | − | 0.998293i | \(-0.481399\pi\) | ||||
0.0584040 | + | 0.998293i | \(0.481399\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −0.128782 | −0.00683504 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 1.84143 | 0.0974589 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −30.5664 | −1.61323 | −0.806617 | − | 0.591075i | \(-0.798704\pi\) | ||||
−0.806617 | + | 0.591075i | \(0.798704\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.7860 | −0.988737 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 13.2292 | 0.694354 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 13.4882 | 0.706007 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −10.4072 | −0.543250 | −0.271625 | − | 0.962403i | \(-0.587561\pi\) | ||||
−0.271625 | + | 0.962403i | \(0.587561\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −6.52699 | −0.339781 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 4.79641 | 0.249017 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 16.4585 | 0.852186 | 0.426093 | − | 0.904679i | \(-0.359890\pi\) | ||||
0.426093 | + | 0.904679i | \(0.359890\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 1.46260 | 0.0755283 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −5.65722 | −0.291362 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 31.3836 | 1.61207 | 0.806035 | − | 0.591868i | \(-0.201609\pi\) | ||||
0.806035 | + | 0.591868i | \(0.201609\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 7.29988 | 0.373984 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 27.5270 | 1.40656 | 0.703282 | − | 0.710911i | \(-0.251717\pi\) | ||||
0.703282 | + | 0.710911i | \(0.251717\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1.39821 | −0.0712592 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0.925197 | 0.0470304 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −8.07625 | −0.409482 | −0.204741 | − | 0.978816i | \(-0.565635\pi\) | ||||
−0.204741 | + | 0.978816i | \(0.565635\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 10.1288 | 0.512235 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 13.6800 | 0.690063 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −3.06439 | −0.154186 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −9.33237 | −0.468378 | −0.234189 | − | 0.972191i | \(-0.575243\pi\) | ||||
−0.234189 | + | 0.972191i | \(0.575243\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −0.676596 | −0.0338722 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 20.9073 | 1.04406 | 0.522030 | − | 0.852927i | \(-0.325175\pi\) | ||||
0.522030 | + | 0.852927i | \(0.325175\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 5.46260 | 0.272111 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 5.67660 | 0.282072 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 1.14064 | 0.0565396 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 34.9169 | 1.72653 | 0.863265 | − | 0.504751i | \(-0.168416\pi\) | ||||
0.863265 | + | 0.504751i | \(0.168416\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 5.31859 | 0.262347 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −6.43281 | −0.316538 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −1.44322 | −0.0708451 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 9.09563 | 0.445415 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −29.4674 | −1.43958 | −0.719789 | − | 0.694193i | \(-0.755761\pi\) | ||||
−0.719789 | + | 0.694193i | \(0.755761\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −19.4882 | −0.949799 | −0.474899 | − | 0.880040i | \(-0.657516\pi\) | ||||
−0.474899 | + | 0.880040i | \(0.657516\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 7.48197 | 0.363786 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 1.25901 | 0.0610711 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 4.60179 | 0.222696 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 2.04502 | 0.0987343 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −10.2605 | −0.494229 | −0.247115 | − | 0.968986i | \(-0.579482\pi\) | ||||
−0.247115 | + | 0.968986i | \(0.579482\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −10.9211 | −0.524832 | −0.262416 | − | 0.964955i | \(-0.584519\pi\) | ||||
−0.262416 | + | 0.964955i | \(0.584519\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −8.27424 | −0.396720 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −3.72161 | −0.178029 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −9.38365 | −0.447857 | −0.223929 | − | 0.974606i | \(-0.571888\pi\) | ||||
−0.223929 | + | 0.974606i | \(0.571888\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −0.860806 | −0.0409908 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −20.5872 | −0.978129 | −0.489065 | − | 0.872248i | \(-0.662662\pi\) | ||||
−0.489065 | + | 0.872248i | \(0.662662\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 11.5076 | 0.545513 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −24.5451 | −1.16094 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −25.9612 | −1.22519 | −0.612594 | − | 0.790398i | \(-0.709874\pi\) | ||||
−0.612594 | + | 0.790398i | \(0.709874\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −10.6018 | −0.499219 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −31.9017 | −1.49887 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 1.00000 | 0.0468807 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −13.5284 | −0.632834 | −0.316417 | − | 0.948620i | \(-0.602480\pi\) | ||||
−0.316417 | + | 0.948620i | \(0.602480\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 7.10941 | 0.331839 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −34.6129 | −1.61208 | −0.806041 | − | 0.591859i | \(-0.798394\pi\) | ||||
−0.806041 | + | 0.591859i | \(0.798394\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −8.55263 | −0.397474 | −0.198737 | − | 0.980053i | \(-0.563684\pi\) | ||||
−0.198737 | + | 0.980053i | \(0.563684\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 7.98959 | 0.370508 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 15.6274 | 0.723151 | 0.361576 | − | 0.932343i | \(-0.382239\pi\) | ||||
0.361576 | + | 0.932343i | \(0.382239\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −2.13919 | −0.0987788 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 33.2832 | 1.53361 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 1.50280 | 0.0690987 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −0.462598 | −0.0212255 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 4.12878 | 0.189044 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −12.5824 | −0.574905 | −0.287453 | − | 0.957795i | \(-0.592808\pi\) | ||||
−0.287453 | + | 0.957795i | \(0.592808\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −0.815790 | −0.0371968 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 11.7666 | 0.535400 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 8.17380 | 0.371153 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 34.1849 | 1.54906 | 0.774532 | − | 0.632534i | \(-0.217985\pi\) | ||||
0.774532 | + | 0.632534i | \(0.217985\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 14.4447 | 0.653211 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 10.1496 | 0.458045 | 0.229023 | − | 0.973421i | \(-0.426447\pi\) | ||||
0.229023 | + | 0.973421i | \(0.426447\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −7.12252 | −0.320782 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −1.20359 | −0.0540971 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −0.128782 | −0.00577666 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 18.9910 | 0.850156 | 0.425078 | − | 0.905157i | \(-0.360247\pi\) | ||||
0.425078 | + | 0.905157i | \(0.360247\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 25.4820 | 1.13845 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 21.7729 | 0.970805 | 0.485403 | − | 0.874291i | \(-0.338673\pi\) | ||||
0.485403 | + | 0.874291i | \(0.338673\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 13.4882 | 0.600219 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −1.46260 | −0.0649563 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −16.0554 | −0.711644 | −0.355822 | − | 0.934554i | \(-0.615799\pi\) | ||||
−0.355822 | + | 0.934554i | \(0.615799\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 13.4882 | 0.596685 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −2.61220 | −0.115332 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −9.75622 | −0.429910 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 12.1530 | 0.534487 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 33.7562 | 1.48173 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 27.4916 | 1.20443 | 0.602215 | − | 0.798334i | \(-0.294285\pi\) | ||||
0.602215 | + | 0.798334i | \(0.294285\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −2.34423 | −0.102506 | −0.0512530 | − | 0.998686i | \(-0.516321\pi\) | ||||
−0.0512530 | + | 0.998686i | \(0.516321\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 1.46260 | 0.0638330 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 6.87748 | 0.299588 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 41.7223 | 1.81401 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −5.53740 | −0.240303 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 7.58242 | 0.328431 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 13.5720 | 0.586769 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −17.8206 | −0.769016 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −1.39821 | −0.0602251 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −21.8116 | −0.937756 | −0.468878 | − | 0.883263i | \(-0.655342\pi\) | ||||
−0.468878 | + | 0.883263i | \(0.655342\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −22.4647 | −0.964053 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −14.7368 | −0.631257 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 0.796415 | 0.0340522 | 0.0170261 | − | 0.999855i | \(-0.494580\pi\) | ||||
0.0170261 | + | 0.999855i | \(0.494580\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 3.96125 | 0.169062 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 2.61702 | 0.111489 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −3.06439 | −0.130311 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −1.19317 | −0.0506474 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 15.7625 | 0.667878 | 0.333939 | − | 0.942595i | \(-0.391622\pi\) | ||||
0.333939 | + | 0.942595i | \(0.391622\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −1.07480 | −0.0454593 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 2.57470 | 0.108704 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −9.49239 | −0.400056 | −0.200028 | − | 0.979790i | \(-0.564103\pi\) | ||||
−0.200028 | + | 0.979790i | \(0.564103\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −16.2638 | −0.684224 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 5.67660 | 0.238395 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 29.7327 | 1.24646 | 0.623230 | − | 0.782039i | \(-0.285820\pi\) | ||||
0.623230 | + | 0.782039i | \(0.285820\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 26.6032 | 1.11331 | 0.556656 | − | 0.830743i | \(-0.312084\pi\) | ||||
0.556656 | + | 0.830743i | \(0.312084\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 4.99855 | 0.208817 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 8.04502 | 0.335500 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 3.05398 | 0.127139 | 0.0635694 | − | 0.997977i | \(-0.479752\pi\) | ||||
0.0635694 | + | 0.997977i | \(0.479752\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 21.2847 | 0.884560 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −1.44322 | −0.0598750 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 6.70638 | 0.277750 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0.860806 | 0.0355899 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −21.3144 | −0.879741 | −0.439871 | − | 0.898061i | \(-0.644976\pi\) | ||||
−0.439871 | + | 0.898061i | \(0.644976\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −2.52699 | −0.104123 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 4.52554 | 0.186156 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 4.64681 | 0.190822 | 0.0954108 | − | 0.995438i | \(-0.469584\pi\) | ||||
0.0954108 | + | 0.995438i | \(0.469584\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1.25901 | 0.0516145 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 26.8656 | 1.09954 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 21.0215 | 0.858915 | 0.429457 | − | 0.903087i | \(-0.358705\pi\) | ||||
0.429457 | + | 0.903087i | \(0.358705\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 34.2188 | 1.39581 | 0.697907 | − | 0.716188i | \(-0.254115\pi\) | ||||
0.697907 | + | 0.716188i | \(0.254115\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −1.84143 | −0.0749889 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 9.04502 | 0.367732 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −42.4841 | −1.72438 | −0.862188 | − | 0.506588i | \(-0.830906\pi\) | ||||
−0.862188 | + | 0.506588i | \(0.830906\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −8.27424 | −0.335289 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −8.69182 | −0.351634 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 12.6018 | 0.508982 | 0.254491 | − | 0.967075i | \(-0.418092\pi\) | ||||
0.254491 | + | 0.967075i | \(0.418092\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 11.0900 | 0.447193 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −9.71747 | −0.391210 | −0.195605 | − | 0.980683i | \(-0.562667\pi\) | ||||
−0.195605 | + | 0.980683i | \(0.562667\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −13.7473 | −0.552549 | −0.276274 | − | 0.961079i | \(-0.589100\pi\) | ||||
−0.276274 | + | 0.961079i | \(0.589100\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 45.4287 | 1.82299 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 11.5076 | 0.461043 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −0.946021 | −0.0377804 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −1.02709 | −0.0409528 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 42.5664 | 1.69454 | 0.847271 | − | 0.531161i | \(-0.178244\pi\) | ||||
0.847271 | + | 0.531161i | \(0.178244\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −32.2582 | −1.28215 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 4.99104 | 0.198063 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1.00000 | 0.0396214 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −0.110856 | −0.00438541 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −2.49575 | −0.0985763 | −0.0492882 | − | 0.998785i | \(-0.515695\pi\) | ||||
−0.0492882 | + | 0.998785i | \(0.515695\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −0.963947 | −0.0380144 | −0.0190072 | − | 0.999819i | \(-0.506051\pi\) | ||||
−0.0190072 | + | 0.999819i | \(0.506051\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −1.57201 | −0.0618977 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −7.32755 | −0.288076 | −0.144038 | − | 0.989572i | \(-0.546009\pi\) | ||||
−0.144038 | + | 0.989572i | \(0.546009\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −8.99440 | −0.353061 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 7.98959 | 0.313137 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −11.7812 | −0.461033 | −0.230517 | − | 0.973068i | \(-0.574042\pi\) | ||||
−0.230517 | + | 0.973068i | \(0.574042\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 9.35319 | 0.365459 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 11.6108 | 0.452979 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −38.2147 | −1.48863 | −0.744316 | − | 0.667828i | \(-0.767224\pi\) | ||||
−0.744316 | + | 0.667828i | \(0.767224\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −23.5679 | −0.916683 | −0.458342 | − | 0.888776i | \(-0.651556\pi\) | ||||
−0.458342 | + | 0.888776i | \(0.651556\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −1.84143 | −0.0715152 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −0.462598 | −0.0179388 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −45.5124 | −1.76225 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −13.3386 | −0.515701 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 6.43426 | 0.248392 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 43.3870 | 1.67245 | 0.836223 | − | 0.548389i | \(-0.184759\pi\) | ||||
0.836223 | + | 0.548389i | \(0.184759\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 5.64681 | 0.217346 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 0.691825 | 0.0265890 | 0.0132945 | − | 0.999912i | \(-0.495768\pi\) | ||||
0.0132945 | + | 0.999912i | \(0.495768\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 8.17380 | 0.313682 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 8.77559 | 0.336281 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 35.8704 | 1.37254 | 0.686272 | − | 0.727345i | \(-0.259246\pi\) | ||||
0.686272 | + | 0.727345i | \(0.259246\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 3.63640 | 0.138940 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 17.0629 | 0.650992 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −4.79641 | −0.182729 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 32.6337 | 1.24144 | 0.620722 | − | 0.784031i | \(-0.286839\pi\) | ||||
0.620722 | + | 0.784031i | \(0.286839\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −1.20359 | −0.0457204 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 6.21881 | 0.235893 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 9.54636 | 0.361594 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 27.4703 | 1.03902 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 6.83102 | 0.258004 | 0.129002 | − | 0.991644i | \(-0.458823\pi\) | ||||
0.129002 | + | 0.991644i | \(0.458823\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0.377383 | 0.0142333 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −12.7126 | −0.478786 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 13.4882 | 0.507277 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −22.1350 | −0.831299 | −0.415650 | − | 0.909525i | \(-0.636446\pi\) | ||||
−0.415650 | + | 0.909525i | \(0.636446\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −2.63785 | −0.0989269 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 43.9467 | 1.64582 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1.39821 | 0.0522900 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0.595527 | 0.0222403 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −43.2549 | −1.61313 | −0.806567 | − | 0.591142i | \(-0.798677\pi\) | ||||
−0.806567 | + | 0.591142i | \(0.798677\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −9.75622 | −0.363340 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 11.3747 | 0.423029 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −5.65722 | −0.210104 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −48.8109 | −1.81029 | −0.905147 | − | 0.425098i | \(-0.860240\pi\) | ||||
−0.905147 | + | 0.425098i | \(0.860240\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 29.6635 | 1.09865 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −1.35319 | −0.0500496 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 3.20359 | 0.118327 | 0.0591636 | − | 0.998248i | \(-0.481157\pi\) | ||||
0.0591636 | + | 0.998248i | \(0.481157\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 1.46260 | 0.0539488 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −2.99104 | −0.110176 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 8.18836 | 0.301214 | 0.150607 | − | 0.988594i | \(-0.451877\pi\) | ||||
0.150607 | + | 0.988594i | \(0.451877\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0.676596 | 0.0248554 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 35.7175 | 1.31035 | 0.655173 | − | 0.755479i | \(-0.272596\pi\) | ||||
0.655173 | + | 0.755479i | \(0.272596\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −16.7819 | −0.614840 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −1.24234 | −0.0454547 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 13.5720 | 0.495910 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −14.5374 | −0.530477 | −0.265239 | − | 0.964183i | \(-0.585451\pi\) | ||||
−0.265239 | + | 0.964183i | \(0.585451\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 21.6766 | 0.789939 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −21.8116 | −0.793807 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 19.2036 | 0.697966 | 0.348983 | − | 0.937129i | \(-0.386527\pi\) | ||||
0.348983 | + | 0.937129i | \(0.386527\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 16.4522 | 0.597177 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 0.0401993 | 0.00145722 | 0.000728612 | − | 1.00000i | \(-0.499768\pi\) | ||||
0.000728612 | 1.00000i | \(0.499768\pi\) | ||||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −14.7368 | −0.533509 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 1.08377 | 0.0391836 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 6.43281 | 0.232275 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 39.5783 | 1.42723 | 0.713614 | − | 0.700539i | \(-0.247057\pi\) | ||||
0.713614 | + | 0.700539i | \(0.247057\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −3.05688 | −0.110091 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −39.8504 | −1.43332 | −0.716660 | − | 0.697423i | \(-0.754330\pi\) | ||||
−0.716660 | + | 0.697423i | \(0.754330\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 5.46260 | 0.196222 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −1.19317 | −0.0428048 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −3.50761 | −0.125673 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −0.180064 | −0.00644319 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −31.9452 | −1.14163 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 22.7562 | 0.812204 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −39.4141 | −1.40496 | −0.702481 | − | 0.711703i | \(-0.747924\pi\) | ||||
−0.702481 | + | 0.711703i | \(0.747924\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −0.727207 | −0.0258893 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −16.2638 | −0.578275 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −4.60179 | −0.163414 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −7.01523 | −0.248805 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −22.1094 | −0.783155 | −0.391578 | − | 0.920145i | \(-0.628071\pi\) | ||||
−0.391578 | + | 0.920145i | \(0.628071\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −10.9431 | −0.387140 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 9.90582 | 0.350005 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 18.8594 | 0.665532 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 8.04502 | 0.283550 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 34.7044 | 1.22165 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −26.2951 | −0.924485 | −0.462243 | − | 0.886753i | \(-0.652955\pi\) | ||||
−0.462243 | + | 0.886753i | \(0.652955\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 2.70638 | 0.0950340 | 0.0475170 | − | 0.998870i | \(-0.484869\pi\) | ||||
0.0475170 | + | 0.998870i | \(0.484869\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −16.8898 | −0.592352 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 9.87603 | 0.345942 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0.497202 | 0.0173949 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0.860806 | 0.0300790 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 47.5845 | 1.66071 | 0.830356 | − | 0.557233i | \(-0.188137\pi\) | ||||
0.830356 | + | 0.557233i | \(0.188137\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −24.6323 | −0.858626 | −0.429313 | − | 0.903156i | \(-0.641244\pi\) | ||||
−0.429313 | + | 0.903156i | \(0.641244\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 2.04502 | 0.0711983 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −16.7785 | −0.583445 | −0.291723 | − | 0.956503i | \(-0.594228\pi\) | ||||
−0.291723 | + | 0.956503i | \(0.594228\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −21.9821 | −0.763469 | −0.381734 | − | 0.924272i | \(-0.624673\pi\) | ||||
−0.381734 | + | 0.924272i | \(0.624673\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 37.8087 | 1.31157 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 1.25901 | 0.0436222 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 17.4224 | 0.602927 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 30.8462 | 1.06620 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 50.6143 | 1.74740 | 0.873700 | − | 0.486465i | \(-0.161714\pi\) | ||||
0.873700 | + | 0.486465i | \(0.161714\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 3.00415 | 0.103591 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −21.0152 | −0.723803 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −1.00000 | −0.0344010 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 9.04502 | 0.310790 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −22.1344 | −0.759650 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −6.56304 | −0.224978 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 9.55118 | 0.327026 | 0.163513 | − | 0.986541i | \(-0.447717\pi\) | ||||
0.163513 | + | 0.986541i | \(0.447717\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −0.398207 | −0.0136184 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 41.3193 | 1.41144 | 0.705719 | − | 0.708491i | \(-0.250624\pi\) | ||||
0.705719 | + | 0.708491i | \(0.250624\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −40.7015 | −1.38872 | −0.694358 | − | 0.719630i | \(-0.744312\pi\) | ||||
−0.694358 | + | 0.719630i | \(0.744312\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 11.0900 | 0.377947 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −38.6039 | −1.31409 | −0.657046 | − | 0.753850i | \(-0.728194\pi\) | ||||
−0.657046 | + | 0.753850i | \(0.728194\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 23.0796 | 0.784731 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 22.5458 | 0.765695 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −4.28465 | −0.145347 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 2.13919 | 0.0724838 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 7.03605 | 0.238134 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 1.00000 | 0.0338062 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −35.0256 | −1.18273 | −0.591366 | − | 0.806403i | \(-0.701411\pi\) | ||||
−0.591366 | + | 0.806403i | \(0.701411\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 4.84770 | 0.163509 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −7.60246 | −0.256133 | −0.128067 | − | 0.991766i | \(-0.540877\pi\) | ||||
−0.128067 | + | 0.991766i | \(0.540877\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 38.2396 | 1.28687 | 0.643433 | − | 0.765502i | \(-0.277509\pi\) | ||||
0.643433 | + | 0.765502i | \(0.277509\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 9.40862 | 0.316267 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −15.2084 | −0.510648 | −0.255324 | − | 0.966856i | \(-0.582182\pi\) | ||||
−0.255324 | + | 0.966856i | \(0.582182\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 4.99104 | 0.167394 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 7.93706 | 0.265901 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 4.02082 | 0.134552 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −12.1842 | −0.407273 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −11.7666 | −0.392876 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −30.9031 | −1.03068 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −6.03875 | −0.201180 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −1.57201 | −0.0523131 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −15.3595 | −0.510566 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 43.1440 | 1.43257 | 0.716287 | − | 0.697806i | \(-0.245840\pi\) | ||||
0.716287 | + | 0.697806i | \(0.245840\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 11.6108 | 0.385104 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1.59698 | 0.0529102 | 0.0264551 | − | 0.999650i | \(-0.491578\pi\) | ||||
0.0264551 | + | 0.999650i | \(0.491578\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −2.01793 | −0.0667836 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −6.73057 | −0.222506 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 9.35319 | 0.308870 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 19.8310 | 0.654165 | 0.327082 | − | 0.944996i | \(-0.393935\pi\) | ||||
0.327082 | + | 0.944996i | \(0.393935\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 12.4280 | 0.409516 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0.128782 | 0.00423891 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −0.815790 | −0.0268230 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −8.39821 | −0.275833 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −41.4335 | −1.35939 | −0.679694 | − | 0.733496i | \(-0.737888\pi\) | ||||
−0.679694 | + | 0.733496i | \(0.737888\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −0.462598 | −0.0151611 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −22.0484 | −0.721832 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 1.76036 | 0.0575700 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 36.7923 | 1.20195 | 0.600976 | − | 0.799267i | \(-0.294779\pi\) | ||||
0.600976 | + | 0.799267i | \(0.294779\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 2.80056 | 0.0913929 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −13.2174 | −0.430874 | −0.215437 | − | 0.976518i | \(-0.569118\pi\) | ||||
−0.215437 | + | 0.976518i | \(0.569118\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 61.0007 | 1.98646 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 5.64681 | 0.183691 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −32.4834 | −1.05557 | −0.527785 | − | 0.849378i | \(-0.676977\pi\) | ||||
−0.527785 | + | 0.849378i | \(0.676977\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −13.4882 | −0.437847 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 39.7666 | 1.28952 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 23.8325 | 0.772009 | 0.386005 | − | 0.922497i | \(-0.373855\pi\) | ||||
0.386005 | + | 0.922497i | \(0.373855\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 3.41758 | 0.110590 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −11.5691 | −0.373976 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 3.63640 | 0.117425 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −1.16002 | −0.0374200 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 11.6829 | 0.376475 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 14.5526 | 0.468466 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 12.0256 | 0.386719 | 0.193359 | − | 0.981128i | \(-0.438062\pi\) | ||||
0.193359 | + | 0.981128i | \(0.438062\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0.851843 | 0.0273651 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −4.75140 | −0.152480 | −0.0762398 | − | 0.997090i | \(-0.524291\pi\) | ||||
−0.0762398 | + | 0.997090i | \(0.524291\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 6.21881 | 0.199366 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −1.46260 | −0.0468406 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 20.5139 | 0.656297 | 0.328149 | − | 0.944626i | \(-0.393575\pi\) | ||||
0.328149 | + | 0.944626i | \(0.393575\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 16.0900 | 0.514240 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −12.6856 | −0.405019 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −5.35319 | −0.170740 | −0.0853701 | − | 0.996349i | \(-0.527207\pi\) | ||||
−0.0853701 | + | 0.996349i | \(0.527207\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 3.09418 | 0.0985887 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −12.7126 | −0.404648 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −8.64681 | −0.274953 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 13.9508 | 0.443163 | 0.221581 | − | 0.975142i | \(-0.428878\pi\) | ||||
0.221581 | + | 0.975142i | \(0.428878\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 27.7153 | 0.879520 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 18.3684 | 0.582318 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 29.4120 | 0.931487 | 0.465743 | − | 0.884920i | \(-0.345787\pi\) | ||||
0.465743 | + | 0.884920i | \(0.345787\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −4.60661 | −0.145747 |
(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 | 3640.2.a.o.1.2 | ✓ | 3 | |
4.3 | odd | 2 | 7280.2.a.bp.1.2 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3640.2.a.o.1.2 | ✓ | 3 | 1.1 | even | 1 | trivial | |
7280.2.a.bp.1.2 | 3 | 4.3 | odd | 2 |