Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2312,4,Mod(1,2312)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2312, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2312.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2312 = 2^{3} \cdot 17^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 2312.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: | \(136.412415933\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 95x^{6} + 756x^{4} - 1780x^{2} + 1152 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{13} \) |
Twist minimal: | no (minimal twist has level 136) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(-9.30031\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2312.1 |
$q$-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 | ||||||||
\(3\) | −2.62097 | −0.504407 | −0.252203 | − | 0.967674i | \(-0.581155\pi\) | ||||
−0.252203 | + | 0.967674i | \(0.581155\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 11.5318 | 1.03143 | 0.515716 | − | 0.856759i | \(-0.327526\pi\) | ||||
0.515716 | + | 0.856759i | \(0.327526\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 23.0485 | 1.24450 | 0.622251 | − | 0.782817i | \(-0.286218\pi\) | ||||
0.622251 | + | 0.782817i | \(0.286218\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −20.1305 | −0.745574 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.19452 | 0.0327419 | 0.0163710 | − | 0.999866i | \(-0.494789\pi\) | ||||
0.0163710 | + | 0.999866i | \(0.494789\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 58.3731 | 1.24537 | 0.622684 | − | 0.782474i | \(-0.286042\pi\) | ||||
0.622684 | + | 0.782474i | \(0.286042\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −30.2245 | −0.520262 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0 | 0 | ||||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −138.971 | −1.67800 | −0.839001 | − | 0.544130i | \(-0.816860\pi\) | ||||
−0.839001 | + | 0.544130i | \(0.816860\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −60.4096 | −0.627736 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 180.911 | 1.64011 | 0.820055 | − | 0.572284i | \(-0.193943\pi\) | ||||
0.820055 | + | 0.572284i | \(0.193943\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 7.98158 | 0.0638527 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 123.528 | 0.880479 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −115.027 | −0.736551 | −0.368275 | − | 0.929717i | \(-0.620052\pi\) | ||||
−0.368275 | + | 0.929717i | \(0.620052\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 210.726 | 1.22088 | 0.610442 | − | 0.792061i | \(-0.290992\pi\) | ||||
0.610442 | + | 0.792061i | \(0.290992\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −3.13080 | −0.0165152 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 265.790 | 1.28362 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 210.661 | 0.936010 | 0.468005 | − | 0.883726i | \(-0.344973\pi\) | ||||
0.468005 | + | 0.883726i | \(0.344973\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −152.994 | −0.628172 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −297.500 | −1.13321 | −0.566605 | − | 0.823989i | \(-0.691743\pi\) | ||||
−0.566605 | + | 0.823989i | \(0.691743\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −174.746 | −0.619734 | −0.309867 | − | 0.950780i | \(-0.600285\pi\) | ||||
−0.309867 | + | 0.950780i | \(0.600285\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −232.140 | −0.769009 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −199.717 | −0.619823 | −0.309911 | − | 0.950765i | \(-0.600299\pi\) | ||||
−0.309911 | + | 0.950765i | \(0.600299\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 188.234 | 0.548787 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 706.217 | 1.83031 | 0.915154 | − | 0.403105i | \(-0.132069\pi\) | ||||
0.915154 | + | 0.403105i | \(0.132069\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 13.7749 | 0.0337711 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 364.238 | 0.846396 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 182.746 | 0.403247 | 0.201623 | − | 0.979463i | \(-0.435378\pi\) | ||||
0.201623 | + | 0.979463i | \(0.435378\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 489.499 | 1.02744 | 0.513720 | − | 0.857958i | \(-0.328267\pi\) | ||||
0.513720 | + | 0.857958i | \(0.328267\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −463.978 | −0.927869 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 673.144 | 1.28451 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −167.043 | −0.304590 | −0.152295 | − | 0.988335i | \(-0.548666\pi\) | ||||
−0.152295 | + | 0.988335i | \(0.548666\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −474.163 | −0.827283 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 818.157 | 1.36757 | 0.683784 | − | 0.729684i | \(-0.260333\pi\) | ||||
0.683784 | + | 0.729684i | \(0.260333\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 1090.15 | 1.74784 | 0.873919 | − | 0.486071i | \(-0.161570\pi\) | ||||
0.873919 | + | 0.486071i | \(0.161570\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −20.9195 | −0.0322077 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 27.5319 | 0.0407474 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −110.196 | −0.156937 | −0.0784685 | − | 0.996917i | \(-0.525003\pi\) | ||||
−0.0784685 | + | 0.996917i | \(0.525003\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 219.760 | 0.301454 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −118.672 | −0.156939 | −0.0784696 | − | 0.996917i | \(-0.525003\pi\) | ||||
−0.0784696 | + | 0.996917i | \(0.525003\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 301.483 | 0.371521 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 400.332 | 0.476799 | 0.238399 | − | 0.971167i | \(-0.423377\pi\) | ||||
0.238399 | + | 0.971167i | \(0.423377\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1345.41 | 1.54986 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −552.306 | −0.615823 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −1602.58 | −1.73075 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −924.543 | −0.967764 | −0.483882 | − | 0.875133i | \(-0.660774\pi\) | ||||
−0.483882 | + | 0.875133i | \(0.660774\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −24.0463 | −0.0244115 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 223.816 | 0.220500 | 0.110250 | − | 0.993904i | \(-0.464835\pi\) | ||||
0.110250 | + | 0.993904i | \(0.464835\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1280.06 | −1.22454 | −0.612271 | − | 0.790648i | \(-0.709744\pi\) | ||||
−0.612271 | + | 0.790648i | \(0.709744\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −696.629 | −0.647467 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −1099.03 | −0.992969 | −0.496485 | − | 0.868046i | \(-0.665376\pi\) | ||||
−0.496485 | + | 0.868046i | \(0.665376\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −733.360 | −0.644433 | −0.322216 | − | 0.946666i | \(-0.604428\pi\) | ||||
−0.322216 | + | 0.946666i | \(0.604428\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −552.136 | −0.472130 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1637.39 | 1.36312 | 0.681561 | − | 0.731761i | \(-0.261301\pi\) | ||||
0.681561 | + | 0.731761i | \(0.261301\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 2086.22 | 1.69166 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −1175.08 | −0.928513 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1329.57 | −0.998928 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 779.739 | 0.571599 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1349.43 | −0.965573 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1502.71 | 1.04995 | 0.524977 | − | 0.851117i | \(-0.324074\pi\) | ||||
0.524977 | + | 0.851117i | \(0.324074\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 458.006 | 0.312598 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −702.381 | −0.468453 | −0.234226 | − | 0.972182i | \(-0.575256\pi\) | ||||
−0.234226 | + | 0.972182i | \(0.575256\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −3203.07 | −2.08828 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 1424.49 | 0.908155 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 18.9889 | 0.0118418 | 0.00592092 | − | 0.999982i | \(-0.498115\pi\) | ||||
0.00592092 | + | 0.999982i | \(0.498115\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −276.969 | −0.169009 | −0.0845043 | − | 0.996423i | \(-0.526931\pi\) | ||||
−0.0845043 | + | 0.996423i | \(0.526931\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 523.452 | 0.312643 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 69.7277 | 0.0407757 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1326.46 | −0.759702 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −493.357 | −0.276812 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 128.491 | 0.0706468 | 0.0353234 | − | 0.999376i | \(-0.488754\pi\) | ||||
0.0353234 | + | 0.999376i | \(0.488754\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2097.44 | 1.13038 | 0.565190 | − | 0.824961i | \(-0.308803\pi\) | ||||
0.565190 | + | 0.824961i | \(0.308803\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 2430.04 | 1.25926 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2911.59 | 1.48007 | 0.740033 | − | 0.672571i | \(-0.234810\pi\) | ||||
0.740033 | + | 0.672571i | \(0.234810\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −1850.98 | −0.923220 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 4169.73 | 2.04112 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1574.26 | −0.756478 | −0.378239 | − | 0.925708i | \(-0.623470\pi\) | ||||
−0.378239 | + | 0.925708i | \(0.623470\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −36.1037 | −0.0170344 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −1290.10 | −0.597788 | −0.298894 | − | 0.954286i | \(-0.596618\pi\) | ||||
−0.298894 | + | 0.954286i | \(0.596618\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1210.41 | 0.550939 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 2797.55 | 1.25107 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 2370.19 | 1.04163 | 0.520816 | − | 0.853669i | \(-0.325628\pi\) | ||||
0.520816 | + | 0.853669i | \(0.325628\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 183.964 | 0.0794648 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −478.974 | −0.203400 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −1719.87 | −0.718153 | −0.359077 | − | 0.933308i | \(-0.616908\pi\) | ||||
−0.359077 | + | 0.933308i | \(0.616908\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −61.7101 | −0.0253418 | −0.0126709 | − | 0.999920i | \(-0.504033\pi\) | ||||
−0.0126709 | + | 0.999920i | \(0.504033\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −1282.96 | −0.518248 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 2429.29 | 0.965431 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 2847.13 | 1.09576 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −2565.34 | −0.971839 | −0.485919 | − | 0.874004i | \(-0.661515\pi\) | ||||
−0.485919 | + | 0.874004i | \(0.661515\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1991.65 | −0.742810 | −0.371405 | − | 0.928471i | \(-0.621124\pi\) | ||||
−0.371405 | + | 0.928471i | \(0.621124\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −1764.29 | −0.647917 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −3831.76 | −1.38579 | −0.692897 | − | 0.721036i | \(-0.743666\pi\) | ||||
−0.692897 | + | 0.721036i | \(0.743666\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 2171.38 | 0.773492 | 0.386746 | − | 0.922186i | \(-0.373599\pi\) | ||||
0.386746 | + | 0.922186i | \(0.373599\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 437.815 | 0.153637 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −2651.20 | −0.916639 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −3430.69 | −1.16883 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −3641.83 | −1.22282 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −166.003 | −0.0549410 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2069.97 | 0.675369 | 0.337685 | − | 0.941259i | \(-0.390356\pi\) | ||||
0.337685 | + | 0.941259i | \(0.390356\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −2144.37 | −0.689811 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −2015.13 | −0.639214 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 4856.91 | 1.51939 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −2857.25 | −0.881622 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 4297.20 | 1.29041 | 0.645206 | − | 0.764008i | \(-0.276771\pi\) | ||||
0.645206 | + | 0.764008i | \(0.276771\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −160.673 | −0.0476069 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 336.979 | 0.0985291 | 0.0492646 | − | 0.998786i | \(-0.484312\pi\) | ||||
0.0492646 | + | 0.998786i | \(0.484312\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 3076.57 | 0.887798 | 0.443899 | − | 0.896077i | \(-0.353595\pi\) | ||||
0.443899 | + | 0.896077i | \(0.353595\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −72.1604 | −0.0205533 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 6537.86 | 1.83824 | 0.919119 | − | 0.393980i | \(-0.128902\pi\) | ||||
0.919119 | + | 0.393980i | \(0.128902\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −2303.09 | −0.639305 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 288.821 | 0.0791601 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −3432.31 | −0.928943 | −0.464472 | − | 0.885588i | \(-0.653756\pi\) | ||||
−0.464472 | + | 0.885588i | \(0.653756\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1312.48 | 0.350807 | 0.175404 | − | 0.984497i | \(-0.443877\pi\) | ||||
0.175404 | + | 0.984497i | \(0.443877\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −3911.24 | −1.03253 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 2170.67 | 0.566037 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −8112.14 | −2.08973 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 311.037 | 0.0791612 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 6498.55 | 1.63420 | 0.817101 | − | 0.576494i | \(-0.195580\pi\) | ||||
0.817101 | + | 0.576494i | \(0.195580\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 216.102 | 0.0537004 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 4874.66 | 1.18316 | 0.591582 | − | 0.806245i | \(-0.298504\pi\) | ||||
0.591582 | + | 0.806245i | \(0.298504\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 4855.41 | 1.16487 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 2315.55 | 0.549153 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −1482.50 | −0.347584 | −0.173792 | − | 0.984782i | \(-0.555602\pi\) | ||||
−0.173792 | + | 0.984782i | \(0.555602\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 8143.92 | 1.88784 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −1049.26 | −0.240501 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 5058.75 | 1.14661 | 0.573304 | − | 0.819343i | \(-0.305662\pi\) | ||||
0.573304 | + | 0.819343i | \(0.305662\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1133.70 | 0.254122 | 0.127061 | − | 0.991895i | \(-0.459446\pi\) | ||||
0.127061 | + | 0.991895i | \(0.459446\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −3526.29 | −0.781761 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 9.53415 | 0.00209066 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −3698.34 | −0.802208 | −0.401104 | − | 0.916033i | \(-0.631373\pi\) | ||||
−0.401104 | + | 0.916033i | \(0.631373\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −4242.01 | −0.910260 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −2190.08 | −0.464945 | −0.232472 | − | 0.972603i | \(-0.574682\pi\) | ||||
−0.232472 | + | 0.972603i | \(0.574682\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −8159.66 | −1.71393 | −0.856963 | − | 0.515378i | \(-0.827652\pi\) | ||||
−0.856963 | + | 0.515378i | \(0.827652\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 4200.31 | 0.873000 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −6856.92 | −1.41028 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 0 | 0 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 2423.20 | 0.488147 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 4777.49 | 0.952574 | 0.476287 | − | 0.879290i | \(-0.341982\pi\) | ||||
0.476287 | + | 0.879290i | \(0.341982\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 2107.39 | 0.415922 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 147.556 | 0.0288286 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 10560.3 | 2.04254 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −4027.65 | −0.771261 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −586.615 | −0.111222 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 5644.78 | 1.05974 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 531.103 | 0.0987351 | 0.0493675 | − | 0.998781i | \(-0.484279\pi\) | ||||
0.0493675 | + | 0.998781i | \(0.484279\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 3355.00 | 0.617667 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 4767.26 | 0.869217 | 0.434609 | − | 0.900619i | \(-0.356887\pi\) | ||||
0.434609 | + | 0.900619i | \(0.356887\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 8613.47 | 1.55547 | 0.777735 | − | 0.628593i | \(-0.216369\pi\) | ||||
0.777735 | + | 0.628593i | \(0.216369\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −5350.48 | −0.957034 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 2453.20 | 0.434654 | 0.217327 | − | 0.976099i | \(-0.430266\pi\) | ||||
0.217327 | + | 0.976099i | \(0.430266\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −137.402 | −0.0241161 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 2880.54 | 0.500860 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 465.909 | 0.0795200 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 1922.12 | 0.325056 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −4603.17 | −0.771371 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 11003.5 | 1.82721 | 0.913605 | − | 0.406604i | \(-0.133287\pi\) | ||||
0.913605 | + | 0.406604i | \(0.133287\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −4240.70 | −0.697865 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −1926.30 | −0.314164 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 3664.37 | 0.592318 | 0.296159 | − | 0.955139i | \(-0.404294\pi\) | ||||
0.296159 | + | 0.955139i | \(0.404294\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −4291.56 | −0.687568 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 251.716 | 0.0399741 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −3567.12 | −0.561535 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −5467.94 | −0.853286 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −3173.37 | −0.490938 | −0.245469 | − | 0.969404i | \(-0.578942\pi\) | ||||
−0.245469 | + | 0.969404i | \(0.578942\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 2185.47 | 0.335202 | 0.167601 | − | 0.985855i | \(-0.446398\pi\) | ||||
0.167601 | + | 0.985855i | \(0.446398\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 7210.70 | 1.09652 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 1216.36 | 0.183400 | 0.0917002 | − | 0.995787i | \(-0.470770\pi\) | ||||
0.0917002 | + | 0.995787i | \(0.470770\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 9434.80 | 1.41055 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 7448.93 | 1.09510 | 0.547548 | − | 0.836774i | \(-0.315561\pi\) | ||||
0.547548 | + | 0.836774i | \(0.315561\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 12453.8 | 1.81569 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 3484.78 | 0.503866 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 12571.3 | 1.80278 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −2374.59 | −0.337746 | −0.168873 | − | 0.985638i | \(-0.554013\pi\) | ||||
−0.168873 | + | 0.985638i | \(0.554013\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 5988.81 | 0.844892 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 16277.2 | 2.27782 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 12231.7 | 1.69795 | 0.848974 | − | 0.528435i | \(-0.177221\pi\) | ||||
0.848974 | + | 0.528435i | \(0.177221\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 3536.82 | 0.487041 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −6714.48 | −0.917276 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 14129.9 | 1.91505 | 0.957523 | − | 0.288358i | \(-0.0931094\pi\) | ||||
0.957523 | + | 0.288358i | \(0.0931094\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −3938.57 | −0.529604 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −13306.4 | −1.77526 | −0.887631 | − | 0.460556i | \(-0.847650\pi\) | ||||
−0.887631 | + | 0.460556i | \(0.847650\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 317.491 | 0.0420282 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 3517.73 | 0.462058 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 8007.84 | 1.04374 | 0.521868 | − | 0.853026i | \(-0.325235\pi\) | ||||
0.521868 | + | 0.853026i | \(0.325235\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 1840.92 | 0.236291 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −1270.76 | −0.161870 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 13185.2 | 1.66687 | 0.833434 | − | 0.552619i | \(-0.186372\pi\) | ||||
0.833434 | + | 0.552619i | \(0.186372\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 8395.15 | 1.05334 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −3205.81 | −0.399228 | −0.199614 | − | 0.979875i | \(-0.563969\pi\) | ||||
−0.199614 | + | 0.979875i | \(0.563969\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 12300.7 | 1.52045 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 2534.22 | 0.310929 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 251.638 | 0.0306468 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −15693.3 | −1.89727 | −0.948636 | − | 0.316369i | \(-0.897536\pi\) | ||||
−0.948636 | + | 0.316369i | \(0.897536\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −49.7695 | −0.00597311 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 4212.03 | 0.501842 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −1368.50 | −0.161872 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 725.929 | 0.0852491 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 6910.65 | 0.805745 | 0.402873 | − | 0.915256i | \(-0.368012\pi\) | ||||
0.402873 | + | 0.915256i | \(0.368012\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 9225.05 | 1.06794 | 0.533968 | − | 0.845505i | \(-0.320700\pi\) | ||||
0.533968 | + | 0.845505i | \(0.320700\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 4020.40 | 0.462124 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 11282.2 | 1.27865 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −182.755 | −0.0205675 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −8822.74 | −0.986024 | −0.493012 | − | 0.870022i | \(-0.664104\pi\) | ||||
−0.493012 | + | 0.870022i | \(0.664104\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 3190.95 | 0.354151 | 0.177075 | − | 0.984197i | \(-0.443336\pi\) | ||||
0.177075 | + | 0.984197i | \(0.443336\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 3476.63 | 0.383199 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −25141.3 | −2.75211 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −15069.5 | −1.63834 | −0.819168 | − | 0.573553i | \(-0.805565\pi\) | ||||
−0.819168 | + | 0.573553i | \(0.805565\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −3789.24 | −0.409161 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −3026.24 | −0.324562 | −0.162281 | − | 0.986745i | \(-0.551885\pi\) | ||||
−0.162281 | + | 0.986745i | \(0.551885\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 4616.53 | 0.491786 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −336.771 | −0.0356347 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 4641.02 | 0.487802 | 0.243901 | − | 0.969800i | \(-0.421573\pi\) | ||||
0.243901 | + | 0.969800i | \(0.421573\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −355.369 | −0.0371035 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −5497.34 | −0.570171 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 15515.0 | 1.59858 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −17393.2 | −1.78035 | −0.890174 | − | 0.455620i | \(-0.849418\pi\) | ||||
−0.890174 | + | 0.455620i | \(0.849418\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −2451.93 | −0.247718 | −0.123859 | − | 0.992300i | \(-0.539527\pi\) | ||||
−0.123859 | + | 0.992300i | \(0.539527\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −14586.3 | −1.46411 | −0.732054 | − | 0.681246i | \(-0.761438\pi\) | ||||
−0.732054 | + | 0.681246i | \(0.761438\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −6369.07 | −0.635179 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −15195.6 | −1.50572 | −0.752859 | − | 0.658182i | \(-0.771326\pi\) | ||||
−0.752859 | + | 0.658182i | \(0.771326\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −3850.09 | −0.379063 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −7631.21 | −0.746555 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −208.738 | −0.0202913 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1109.21 | −0.107145 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −14216.5 | −1.36463 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −4422.10 | −0.421819 | −0.210909 | − | 0.977506i | \(-0.567642\pi\) | ||||
−0.210909 | + | 0.977506i | \(0.567642\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 12296.9 | 1.16568 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −10928.8 | −1.02956 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −10661.6 | −0.998183 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 17772.7 | 1.65371 | 0.826856 | − | 0.562414i | \(-0.190127\pi\) | ||||
0.826856 | + | 0.562414i | \(0.190127\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 4126.11 | 0.381573 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −4845.34 | −0.445350 | −0.222675 | − | 0.974893i | \(-0.571479\pi\) | ||||
−0.222675 | + | 0.974893i | \(0.571479\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −277.296 | −0.0251788 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 18857.3 | 1.70194 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 1060.23 | 0.0951153 | 0.0475576 | − | 0.998868i | \(-0.484856\pi\) | ||||
0.0475576 | + | 0.998868i | \(0.484856\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 3381.31 | 0.301528 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −2803.19 | −0.248485 | −0.124243 | − | 0.992252i | \(-0.539650\pi\) | ||||
−0.124243 | + | 0.992252i | \(0.539650\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 2580.99 | 0.227431 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −3172.46 | −0.277898 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 1658.97 | 0.144465 | 0.0722323 | − | 0.997388i | \(-0.476988\pi\) | ||||
0.0722323 | + | 0.997388i | \(0.476988\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 25126.3 | 2.17519 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −17166.7 | −1.47745 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −14761.3 | −1.26303 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −238.565 | −0.0202942 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −6212.21 | −0.525406 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 12553.6 | 1.05563 | 0.527815 | − | 0.849359i | \(-0.323011\pi\) | ||||
0.527815 | + | 0.849359i | \(0.323011\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −12031.6 | −1.00593 | −0.502967 | − | 0.864306i | \(-0.667758\pi\) | ||||
−0.502967 | + | 0.864306i | \(0.667758\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −482.164 | −0.0400826 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 20561.8 | 1.68996 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −3678.78 | −0.300650 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −17366.0 | −1.41126 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −12673.8 | −1.02418 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 4507.75 | 0.362241 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 224.849 | 0.0179683 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −10632.7 | −0.844984 | −0.422492 | − | 0.906367i | \(-0.638845\pi\) | ||||
−0.422492 | + | 0.906367i | \(0.638845\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 161.741 | 0.0127826 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −8456.94 | −0.664689 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 17370.0 | 1.35774 | 0.678872 | − | 0.734257i | \(-0.262469\pi\) | ||||
0.678872 | + | 0.734257i | \(0.262469\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −9853.85 | −0.766033 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 15985.4 | 1.23593 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −2539.86 | −0.195309 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −6367.10 | −0.486970 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 1084.77 | 0.0825190 | 0.0412595 | − | 0.999148i | \(-0.486863\pi\) | ||||
0.0412595 | + | 0.999148i | \(0.486863\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −10200.5 | −0.771797 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 5494.27 | 0.411289 | 0.205645 | − | 0.978627i | \(-0.434071\pi\) | ||||
0.205645 | + | 0.978627i | \(0.434071\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 18882.0 | 1.40597 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 5065.14 | 0.375160 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 11612.4 | 0.855569 | 0.427784 | − | 0.903881i | \(-0.359294\pi\) | ||||
0.427784 | + | 0.903881i | \(0.359294\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −3413.97 | −0.250210 | −0.125105 | − | 0.992143i | \(-0.539927\pi\) | ||||
−0.125105 | + | 0.992143i | \(0.539927\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 6723.68 | 0.490202 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1443.96 | 0.104725 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 1355.70 | 0.0978141 | 0.0489070 | − | 0.998803i | \(-0.484426\pi\) | ||||
0.0489070 | + | 0.998803i | \(0.484426\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 5220.07 | 0.374678 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −2735.22 | −0.195311 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 843.589 | 0.0599278 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −13550.7 | −0.957698 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −25232.2 | −1.77418 | −0.887092 | − | 0.461593i | \(-0.847278\pi\) | ||||
−0.887092 | + | 0.461593i | \(0.847278\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −29284.7 | −2.04865 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 10042.9 | 0.699004 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 14327.4 | 0.992171 | 0.496086 | − | 0.868274i | \(-0.334770\pi\) | ||||
0.496086 | + | 0.868274i | \(0.334770\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −5691.13 | −0.390155 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −2523.52 | −0.172134 | −0.0860671 | − | 0.996289i | \(-0.527430\pi\) | ||||
−0.0860671 | + | 0.996289i | \(0.527430\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 17286.6 | 1.17327 | 0.586634 | − | 0.809853i | \(-0.300453\pi\) | ||||
0.586634 | + | 0.809853i | \(0.300453\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 3362.66 | 0.227095 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −15332.3 | −1.03033 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 6413.65 | 0.428867 | 0.214433 | − | 0.976739i | \(-0.431210\pi\) | ||||
0.214433 | + | 0.976739i | \(0.431210\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 6948.73 | 0.462359 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −11658.1 | −0.771907 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 485.788 | 0.0320078 | 0.0160039 | − | 0.999872i | \(-0.494906\pi\) | ||||
0.0160039 | + | 0.999872i | \(0.494906\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 8991.76 | 0.589566 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 6830.32 | 0.445670 | 0.222835 | − | 0.974856i | \(-0.428469\pi\) | ||||
0.222835 | + | 0.974856i | \(0.428469\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 10667.8 | 0.692689 | 0.346344 | − | 0.938107i | \(-0.387423\pi\) | ||||
0.346344 | + | 0.938107i | \(0.387423\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 22347.5 | 1.44408 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 9227.05 | 0.593377 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −16559.0 | −1.05978 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 435.090 | 0.0277126 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 15251.2 | 0.962188 | 0.481094 | − | 0.876669i | \(-0.340240\pi\) | ||||
0.481094 | + | 0.876669i | \(0.340240\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −5425.35 | −0.340661 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 17328.9 | 1.08296 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 10987.8 | 0.683442 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −16469.9 | −1.01962 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 12000.9 | 0.739480 | 0.369740 | − | 0.929135i | \(-0.379447\pi\) | ||||
0.369740 | + | 0.929135i | \(0.379447\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −5642.30 | −0.346051 | −0.173025 | − | 0.984917i | \(-0.555354\pi\) | ||||
−0.173025 | + | 0.984917i | \(0.555354\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 5281.62 | 0.322424 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 7790.69 | 0.473391 | 0.236695 | − | 0.971584i | \(-0.423936\pi\) | ||||
0.236695 | + | 0.971584i | \(0.423936\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 218.294 | 0.0132031 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −12729.8 | −0.766393 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 6755.02 | 0.404815 | 0.202408 | − | 0.979301i | \(-0.435123\pi\) | ||||
0.202408 | + | 0.979301i | \(0.435123\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −8099.69 | −0.483177 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −21945.2 | −1.30314 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −14303.3 | −0.845492 | −0.422746 | − | 0.906248i | \(-0.638934\pi\) | ||||
−0.422746 | + | 0.906248i | \(0.638934\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 26136.0 | 1.53793 | 0.768966 | − | 0.639289i | \(-0.220771\pi\) | ||||
0.768966 | + | 0.639289i | \(0.220771\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −36937.0 | −2.15392 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −20809.6 | −1.20802 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −11262.9 | −0.650893 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 584.715 | 0.0336404 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 19026.5 | 1.08977 | 0.544887 | − | 0.838509i | \(-0.316572\pi\) | ||||
0.544887 | + | 0.838509i | \(0.316572\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 985.948 | 0.0562210 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −25683.6 | −1.45805 | −0.729026 | − | 0.684486i | \(-0.760026\pi\) | ||||
−0.729026 | + | 0.684486i | \(0.760026\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −21309.3 | −1.20439 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −883.214 | −0.0496988 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 28196.4 | 1.57966 | 0.789829 | − | 0.613327i | \(-0.210169\pi\) | ||||
0.789829 | + | 0.613327i | \(0.210169\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 218.976 | 0.0122141 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −8063.62 | −0.447811 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 41224.0 | 2.27941 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −35037.4 | −1.92892 | −0.964462 | − | 0.264221i | \(-0.914885\pi\) | ||||
−0.964462 | + | 0.264221i | \(0.914885\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −554.230 | −0.0303802 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −3193.94 | −0.174321 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −17135.6 | −0.927220 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −3539.51 | −0.190707 | −0.0953535 | − | 0.995443i | \(-0.530398\pi\) | ||||
−0.0953535 | + | 0.995443i | \(0.530398\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −29275.6 | −1.57063 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 6036.33 | 0.322470 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 5158.62 | 0.274413 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 7264.39 | 0.384795 | 0.192398 | − | 0.981317i | \(-0.438374\pi\) | ||||
0.192398 | + | 0.981317i | \(0.438374\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 2218.30 | 0.117008 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 38122.6 | 2.00239 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 804.084 | 0.0420574 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 8995.99 | 0.468565 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −9704.92 | −0.503383 | −0.251692 | − | 0.967807i | \(-0.580987\pi\) | ||||
−0.251692 | + | 0.967807i | \(0.580987\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −29503.4 | −1.52395 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −3439.99 | −0.176949 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −918.097 | −0.0470307 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 10937.3 | 0.557967 | 0.278983 | − | 0.960296i | \(-0.410003\pi\) | ||||
0.278983 | + | 0.960296i | \(0.410003\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 4317.73 | 0.219364 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −14196.3 | −0.715351 | −0.357675 | − | 0.933846i | \(-0.616431\pi\) | ||||
−0.357675 | + | 0.933846i | \(0.616431\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −5689.27 | −0.285513 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −199.536 | −0.00997287 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −8477.05 | −0.421966 | −0.210983 | − | 0.977490i | \(-0.567667\pi\) | ||||
−0.210983 | + | 0.977490i | \(0.567667\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 21261.7 | 1.05407 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −5251.86 | −0.259316 | −0.129658 | − | 0.991559i | \(-0.541388\pi\) | ||||
−0.129658 | + | 0.991559i | \(0.541388\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 1481.72 | 0.0728674 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 2388.93 | 0.117010 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −25331.1 | −1.23575 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −16018.0 | −0.778302 | −0.389151 | − | 0.921174i | \(-0.627232\pi\) | ||||
−0.389151 | + | 0.921174i | \(0.627232\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −17032.5 | −0.824303 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 24187.2 | 1.16591 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 9344.23 | 0.448642 | 0.224321 | − | 0.974515i | \(-0.427984\pi\) | ||||
0.224321 | + | 0.974515i | \(0.427984\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −566.397 | −0.0270868 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 35043.1 | 1.66927 | 0.834633 | − | 0.550807i | \(-0.185680\pi\) | ||||
0.834633 | + | 0.550807i | \(0.185680\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −16902.9 | −0.801998 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 10667.5 | 0.502190 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −6719.33 | −0.315091 | −0.157546 | − | 0.987512i | \(-0.550358\pi\) | ||||
−0.157546 | + | 0.987512i | \(0.550358\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −12776.4 | −0.596796 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −18716.9 | −0.870892 | −0.435446 | − | 0.900215i | \(-0.643409\pi\) | ||||
−0.435446 | + | 0.900215i | \(0.643409\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1681.92 | 0.0779568 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −12725.9 | −0.587567 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 41343.7 | 1.90153 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 977.304 | 0.0447768 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −14209.0 | −0.648518 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 33575.8 | 1.52659 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −15916.1 | −0.720898 | −0.360449 | − | 0.932779i | \(-0.617377\pi\) | ||||
−0.360449 | + | 0.932779i | \(0.617377\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 3885.59 | 0.175324 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 37739.4 | 1.69641 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 28573.5 | 1.27954 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −21345.0 | −0.952239 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −39802.4 | −1.76898 | −0.884489 | − | 0.466562i | \(-0.845492\pi\) | ||||
−0.884489 | + | 0.466562i | \(0.845492\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −8058.88 | −0.355489 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 1302.20 | 0.0572276 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 48084.3 | 2.10528 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −13258.9 | −0.578357 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −12250.3 | −0.532384 | −0.266192 | − | 0.963920i | \(-0.585766\pi\) | ||||
−0.266192 | + | 0.963920i | \(0.585766\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −15936.1 | −0.690002 | −0.345001 | − | 0.938602i | \(-0.612121\pi\) | ||||
−0.345001 | + | 0.938602i | \(0.612121\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −2971.39 | −0.128181 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −18154.0 | −0.780256 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 24284.6 | 1.03992 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −27083.8 | −1.15554 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −10389.6 | −0.441656 | −0.220828 | − | 0.975313i | \(-0.570876\pi\) | ||||
−0.220828 | + | 0.975313i | \(0.570876\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 1915.45 | 0.0811281 | 0.0405640 | − | 0.999177i | \(-0.487085\pi\) | ||||
0.0405640 | + | 0.999177i | \(0.487085\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −24.9888 | −0.00105454 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 1406.72 | 0.0591492 | 0.0295746 | − | 0.999563i | \(-0.490585\pi\) | ||||
0.0295746 | + | 0.999563i | \(0.490585\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −22131.8 | −0.927226 | −0.463613 | − | 0.886038i | \(-0.653447\pi\) | ||||
−0.463613 | + | 0.886038i | \(0.653447\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 9693.25 | 0.404639 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −14877.1 | −0.616578 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 26030.5 | 1.07496 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 5716.82 | 0.235240 | 0.117620 | − | 0.993059i | \(-0.462473\pi\) | ||||
0.117620 | + | 0.993059i | \(0.462473\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −11157.8 | −0.457493 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 5740.16 | 0.234521 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 13958.2 | 0.568257 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −30644.7 | −1.24317 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 21386.3 | 0.864516 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 38110.8 | 1.53516 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −26801.3 | −1.07580 | −0.537900 | − | 0.843008i | \(-0.680782\pi\) | ||||
−0.537900 | + | 0.843008i | \(0.680782\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 32260.6 | 1.29040 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −6701.95 | −0.267135 | −0.133567 | − | 0.991040i | \(-0.542643\pi\) | ||||
−0.133567 | + | 0.991040i | \(0.542643\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −33950.5 | −1.34852 | −0.674259 | − | 0.738495i | \(-0.735537\pi\) | ||||
−0.674259 | + | 0.738495i | \(0.735537\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 17971.8 | 0.711357 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −43090.0 | −1.69965 | −0.849827 | − | 0.527062i | \(-0.823294\pi\) | ||||
−0.849827 | + | 0.527062i | \(0.823294\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 27332.5 | 1.07437 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −131.631 | −0.00513842 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −9750.81 | −0.379327 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 18611.5 | 0.721540 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −31102.3 | −1.20166 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −38515.6 | −1.48299 | −0.741493 | − | 0.670960i | \(-0.765882\pi\) | ||||
−0.741493 | + | 0.670960i | \(0.765882\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −12521.7 | −0.480485 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −32178.8 | −1.23057 | −0.615284 | − | 0.788305i | \(-0.710959\pi\) | ||||
−0.615284 | + | 0.788305i | \(0.710959\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −33578.7 | −1.27974 | −0.639871 | − | 0.768482i | \(-0.721012\pi\) | ||||
−0.639871 | + | 0.768482i | \(0.721012\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −5523.41 | −0.209794 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 17336.8 | 0.656273 | 0.328137 | − | 0.944630i | \(-0.393579\pi\) | ||||
0.328137 | + | 0.944630i | \(0.393579\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 34635.3 | 1.30667 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 262.507 | 0.00987018 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 27754.7 | 1.04006 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −19833.2 | −0.740726 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −27678.4 | −1.03027 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −24239.1 | −0.899244 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 10556.4 | 0.389029 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −711.626 | −0.0261384 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −2865.79 | −0.104914 | −0.0524570 | − | 0.998623i | \(-0.516705\pi\) | ||||
−0.0524570 | + | 0.998623i | \(0.516705\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −4505.52 | −0.164399 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −23972.0 | −0.871819 | −0.435910 | − | 0.899990i | \(-0.643573\pi\) | ||||
−0.435910 | + | 0.899990i | \(0.643573\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −141.756 | −0.00513849 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −14794.8 | −0.534538 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −16188.8 | −0.582991 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 49371.5 | 1.77216 | 0.886081 | − | 0.463530i | \(-0.153418\pi\) | ||||
0.886081 | + | 0.463530i | \(0.153418\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −1392.01 | −0.0498026 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 47758.3 | 1.70313 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1681.40 | 0.0597668 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 25768.2 | 0.912986 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 47434.7 | 1.67522 | 0.837612 | − | 0.546266i | \(-0.183951\pi\) | ||||
0.837612 | + | 0.546266i | \(0.183951\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −26159.0 | −0.920866 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −12494.9 | −0.438439 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −37330.2 | −1.30152 | −0.650760 | − | 0.759283i | \(-0.725550\pi\) | ||||
−0.650760 | + | 0.759283i | \(0.725550\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −22575.7 | −0.784589 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −32070.6 | −1.11102 | −0.555511 | − | 0.831509i | \(-0.687477\pi\) | ||||
−0.555511 | + | 0.831509i | \(0.687477\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −53820.9 | −1.85859 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 32832.5 | 1.13020 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −23171.6 | −0.795118 | −0.397559 | − | 0.917577i | \(-0.630143\pi\) | ||||
−0.397559 | + | 0.917577i | \(0.630143\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 63635.3 | 2.17670 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −6429.77 | −0.219242 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −39914.2 | −1.35671 | −0.678357 | − | 0.734733i | \(-0.737307\pi\) | ||||
−0.678357 | + | 0.734733i | \(0.737307\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −29582.8 | −1.00239 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 360.127 | 0.0121643 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 437.666 | 0.0147372 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 14614.3 | 0.490560 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 22124.1 | 0.740332 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −22967.3 | −0.766158 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 40591.6 | 1.34988 | 0.674941 | − | 0.737871i | \(-0.264169\pi\) | ||||
0.674941 | + | 0.737871i | \(0.264169\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −29860.5 | −0.986890 | −0.493445 | − | 0.869777i | \(-0.664263\pi\) | ||||
−0.493445 | + | 0.869777i | \(0.664263\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −6383.73 | −0.210332 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −1221.14 | −0.0401104 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 35041.0 | 1.14745 | 0.573726 | − | 0.819048i | \(-0.305498\pi\) | ||||
0.573726 | + | 0.819048i | \(0.305498\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 478.204 | 0.0156113 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 14762.9 | 0.480472 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 54091.0 | 1.75507 | 0.877535 | − | 0.479513i | \(-0.159187\pi\) | ||||
0.877535 | + | 0.479513i | \(0.159187\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −44187.0 | −1.42935 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 12064.8 | 0.389085 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −31613.5 | −1.01643 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −15918.2 | −0.510251 | −0.255126 | − | 0.966908i | \(-0.582117\pi\) | ||||
−0.255126 | + | 0.966908i | \(0.582117\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −28839.9 | −0.921657 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 25039.8 | 0.797805 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 15294.7 | 0.485845 | 0.242923 | − | 0.970046i | \(-0.421894\pi\) | ||||
0.242923 | + | 0.970046i | \(0.421894\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 26022.4 | 0.824138 |
(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 | 2312.4.a.k.1.4 | 8 | ||
17.4 | even | 4 | 136.4.b.b.33.5 | yes | 8 | ||
17.13 | even | 4 | 136.4.b.b.33.4 | ✓ | 8 | ||
17.16 | even | 2 | inner | 2312.4.a.k.1.5 | 8 | ||
51.38 | odd | 4 | 1224.4.c.e.577.6 | 8 | |||
51.47 | odd | 4 | 1224.4.c.e.577.3 | 8 | |||
68.47 | odd | 4 | 272.4.b.f.33.5 | 8 | |||
68.55 | odd | 4 | 272.4.b.f.33.4 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
136.4.b.b.33.4 | ✓ | 8 | 17.13 | even | 4 | ||
136.4.b.b.33.5 | yes | 8 | 17.4 | even | 4 | ||
272.4.b.f.33.4 | 8 | 68.55 | odd | 4 | |||
272.4.b.f.33.5 | 8 | 68.47 | odd | 4 | |||
1224.4.c.e.577.3 | 8 | 51.47 | odd | 4 | |||
1224.4.c.e.577.6 | 8 | 51.38 | odd | 4 | |||
2312.4.a.k.1.4 | 8 | 1.1 | even | 1 | trivial | ||
2312.4.a.k.1.5 | 8 | 17.16 | even | 2 | inner |