Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8001,2,Mod(1,8001)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8001, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("8001.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8001 = 3^{2} \cdot 7 \cdot 127 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8001.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: | \(63.8883066572\) |
Analytic rank: | \(1\) |
Dimension: | \(11\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{11} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{11} - 2 x^{10} - 15 x^{9} + 25 x^{8} + 88 x^{7} - 112 x^{6} - 247 x^{5} + 215 x^{4} + 313 x^{3} + \cdots + 57 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 2667) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.5 | ||
Root | \(-0.910036\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8001.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.910036 | −0.643493 | −0.321746 | − | 0.946826i | \(-0.604270\pi\) | ||||
−0.321746 | + | 0.946826i | \(0.604270\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.17183 | −0.585917 | ||||||||
\(5\) | −2.84869 | −1.27397 | −0.636986 | − | 0.770875i | \(-0.719819\pi\) | ||||
−0.636986 | + | 0.770875i | \(0.719819\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | 2.88648 | 1.02053 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 2.59241 | 0.819792 | ||||||||
\(11\) | 1.86466 | 0.562217 | 0.281108 | − | 0.959676i | \(-0.409298\pi\) | ||||
0.281108 | + | 0.959676i | \(0.409298\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −6.19675 | −1.71867 | −0.859334 | − | 0.511415i | \(-0.829122\pi\) | ||||
−0.859334 | + | 0.511415i | \(0.829122\pi\) | |||||||
\(14\) | 0.910036 | 0.243217 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.283136 | −0.0707841 | ||||||||
\(17\) | −2.49732 | −0.605688 | −0.302844 | − | 0.953040i | \(-0.597936\pi\) | ||||
−0.302844 | + | 0.953040i | \(0.597936\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −6.22887 | −1.42900 | −0.714500 | − | 0.699635i | \(-0.753346\pi\) | ||||
−0.714500 | + | 0.699635i | \(0.753346\pi\) | |||||||
\(20\) | 3.33819 | 0.746442 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −1.69691 | −0.361782 | ||||||||
\(23\) | 5.12980 | 1.06964 | 0.534819 | − | 0.844967i | \(-0.320380\pi\) | ||||
0.534819 | + | 0.844967i | \(0.320380\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 3.11503 | 0.623006 | ||||||||
\(26\) | 5.63926 | 1.10595 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 1.17183 | 0.221456 | ||||||||
\(29\) | 7.68531 | 1.42713 | 0.713563 | − | 0.700591i | \(-0.247080\pi\) | ||||
0.713563 | + | 0.700591i | \(0.247080\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.32504 | 0.776800 | 0.388400 | − | 0.921491i | \(-0.373028\pi\) | ||||
0.388400 | + | 0.921491i | \(0.373028\pi\) | |||||||
\(32\) | −5.51530 | −0.974977 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 2.27265 | 0.389756 | ||||||||
\(35\) | 2.84869 | 0.481516 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.90361 | 0.477350 | 0.238675 | − | 0.971100i | \(-0.423287\pi\) | ||||
0.238675 | + | 0.971100i | \(0.423287\pi\) | |||||||
\(38\) | 5.66849 | 0.919551 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −8.22269 | −1.30012 | ||||||||
\(41\) | −4.60795 | −0.719640 | −0.359820 | − | 0.933022i | \(-0.617162\pi\) | ||||
−0.359820 | + | 0.933022i | \(0.617162\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −9.98321 | −1.52243 | −0.761213 | − | 0.648502i | \(-0.775396\pi\) | ||||
−0.761213 | + | 0.648502i | \(0.775396\pi\) | |||||||
\(44\) | −2.18507 | −0.329412 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −4.66830 | −0.688304 | ||||||||
\(47\) | 10.9278 | 1.59398 | 0.796989 | − | 0.603994i | \(-0.206425\pi\) | ||||
0.796989 | + | 0.603994i | \(0.206425\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −2.83479 | −0.400900 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 7.26156 | 1.00700 | ||||||||
\(53\) | 10.7010 | 1.46990 | 0.734948 | − | 0.678123i | \(-0.237207\pi\) | ||||
0.734948 | + | 0.678123i | \(0.237207\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −5.31184 | −0.716249 | ||||||||
\(56\) | −2.88648 | −0.385723 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −6.99391 | −0.918345 | ||||||||
\(59\) | −11.4224 | −1.48707 | −0.743533 | − | 0.668699i | \(-0.766851\pi\) | ||||
−0.743533 | + | 0.668699i | \(0.766851\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.39989 | 0.179237 | 0.0896185 | − | 0.995976i | \(-0.471435\pi\) | ||||
0.0896185 | + | 0.995976i | \(0.471435\pi\) | |||||||
\(62\) | −3.93594 | −0.499865 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 5.58540 | 0.698175 | ||||||||
\(65\) | 17.6526 | 2.18954 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 14.3600 | 1.75436 | 0.877178 | − | 0.480164i | \(-0.159423\pi\) | ||||
0.877178 | + | 0.480164i | \(0.159423\pi\) | |||||||
\(68\) | 2.92644 | 0.354883 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −2.59241 | −0.309852 | ||||||||
\(71\) | −9.49609 | −1.12698 | −0.563489 | − | 0.826123i | \(-0.690541\pi\) | ||||
−0.563489 | + | 0.826123i | \(0.690541\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −16.1291 | −1.88777 | −0.943887 | − | 0.330269i | \(-0.892861\pi\) | ||||
−0.943887 | + | 0.330269i | \(0.892861\pi\) | |||||||
\(74\) | −2.64239 | −0.307171 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 7.29920 | 0.837276 | ||||||||
\(77\) | −1.86466 | −0.212498 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 12.5570 | 1.41277 | 0.706384 | − | 0.707829i | \(-0.250325\pi\) | ||||
0.706384 | + | 0.707829i | \(0.250325\pi\) | |||||||
\(80\) | 0.806567 | 0.0901770 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 4.19340 | 0.463083 | ||||||||
\(83\) | 6.86150 | 0.753148 | 0.376574 | − | 0.926387i | \(-0.377102\pi\) | ||||
0.376574 | + | 0.926387i | \(0.377102\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 7.11407 | 0.771630 | ||||||||
\(86\) | 9.08509 | 0.979670 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 5.38232 | 0.573757 | ||||||||
\(89\) | 8.88528 | 0.941838 | 0.470919 | − | 0.882176i | \(-0.343922\pi\) | ||||
0.470919 | + | 0.882176i | \(0.343922\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 6.19675 | 0.649596 | ||||||||
\(92\) | −6.01128 | −0.626719 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −9.94466 | −1.02571 | ||||||||
\(95\) | 17.7441 | 1.82051 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1.23342 | 0.125235 | 0.0626176 | − | 0.998038i | \(-0.480055\pi\) | ||||
0.0626176 | + | 0.998038i | \(0.480055\pi\) | |||||||
\(98\) | −0.910036 | −0.0919275 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −3.65030 | −0.365030 | ||||||||
\(101\) | 4.39135 | 0.436956 | 0.218478 | − | 0.975842i | \(-0.429891\pi\) | ||||
0.218478 | + | 0.975842i | \(0.429891\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 4.10635 | 0.404610 | 0.202305 | − | 0.979323i | \(-0.435157\pi\) | ||||
0.202305 | + | 0.979323i | \(0.435157\pi\) | |||||||
\(104\) | −17.8868 | −1.75395 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −9.73830 | −0.945867 | ||||||||
\(107\) | −16.0178 | −1.54850 | −0.774250 | − | 0.632880i | \(-0.781873\pi\) | ||||
−0.774250 | + | 0.632880i | \(0.781873\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 4.60049 | 0.440647 | 0.220324 | − | 0.975427i | \(-0.429289\pi\) | ||||
0.220324 | + | 0.975427i | \(0.429289\pi\) | |||||||
\(110\) | 4.83397 | 0.460901 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0.283136 | 0.0267539 | ||||||||
\(113\) | 10.3473 | 0.973393 | 0.486697 | − | 0.873571i | \(-0.338202\pi\) | ||||
0.486697 | + | 0.873571i | \(0.338202\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −14.6132 | −1.36269 | ||||||||
\(116\) | −9.00591 | −0.836178 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 10.3948 | 0.956916 | ||||||||
\(119\) | 2.49732 | 0.228929 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −7.52304 | −0.683912 | ||||||||
\(122\) | −1.27395 | −0.115338 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −5.06823 | −0.455141 | ||||||||
\(125\) | 5.36970 | 0.480281 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1.00000 | 0.0887357 | ||||||||
\(128\) | 5.94769 | 0.525707 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −16.0645 | −1.40895 | ||||||||
\(131\) | −1.45092 | −0.126768 | −0.0633838 | − | 0.997989i | \(-0.520189\pi\) | ||||
−0.0633838 | + | 0.997989i | \(0.520189\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 6.22887 | 0.540111 | ||||||||
\(134\) | −13.0681 | −1.12892 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −7.20846 | −0.618120 | ||||||||
\(137\) | −8.15630 | −0.696840 | −0.348420 | − | 0.937339i | \(-0.613282\pi\) | ||||
−0.348420 | + | 0.937339i | \(0.613282\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 17.9807 | 1.52510 | 0.762550 | − | 0.646929i | \(-0.223947\pi\) | ||||
0.762550 | + | 0.646929i | \(0.223947\pi\) | |||||||
\(140\) | −3.33819 | −0.282129 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 8.64179 | 0.725203 | ||||||||
\(143\) | −11.5548 | −0.966264 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −21.8931 | −1.81812 | ||||||||
\(146\) | 14.6781 | 1.21477 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −3.40255 | −0.279688 | ||||||||
\(149\) | 7.83149 | 0.641580 | 0.320790 | − | 0.947150i | \(-0.396052\pi\) | ||||
0.320790 | + | 0.947150i | \(0.396052\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2.72817 | −0.222015 | −0.111008 | − | 0.993820i | \(-0.535408\pi\) | ||||
−0.111008 | + | 0.993820i | \(0.535408\pi\) | |||||||
\(152\) | −17.9795 | −1.45833 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 1.69691 | 0.136741 | ||||||||
\(155\) | −12.3207 | −0.989622 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −19.3454 | −1.54393 | −0.771964 | − | 0.635666i | \(-0.780726\pi\) | ||||
−0.771964 | + | 0.635666i | \(0.780726\pi\) | |||||||
\(158\) | −11.4273 | −0.909106 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 15.7114 | 1.24209 | ||||||||
\(161\) | −5.12980 | −0.404285 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −4.44858 | −0.348440 | −0.174220 | − | 0.984707i | \(-0.555740\pi\) | ||||
−0.174220 | + | 0.984707i | \(0.555740\pi\) | |||||||
\(164\) | 5.39975 | 0.421649 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −6.24422 | −0.484645 | ||||||||
\(167\) | 11.3915 | 0.881499 | 0.440750 | − | 0.897630i | \(-0.354713\pi\) | ||||
0.440750 | + | 0.897630i | \(0.354713\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 25.3997 | 1.95382 | ||||||||
\(170\) | −6.47406 | −0.496538 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 11.6987 | 0.892015 | ||||||||
\(173\) | 1.47427 | 0.112086 | 0.0560432 | − | 0.998428i | \(-0.482152\pi\) | ||||
0.0560432 | + | 0.998428i | \(0.482152\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −3.11503 | −0.235474 | ||||||||
\(176\) | −0.527954 | −0.0397960 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −8.08593 | −0.606066 | ||||||||
\(179\) | 1.38218 | 0.103309 | 0.0516545 | − | 0.998665i | \(-0.483551\pi\) | ||||
0.0516545 | + | 0.998665i | \(0.483551\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 12.5132 | 0.930098 | 0.465049 | − | 0.885285i | \(-0.346037\pi\) | ||||
0.465049 | + | 0.885285i | \(0.346037\pi\) | |||||||
\(182\) | −5.63926 | −0.418010 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 14.8071 | 1.09159 | ||||||||
\(185\) | −8.27147 | −0.608131 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −4.65665 | −0.340528 | ||||||||
\(188\) | −12.8055 | −0.933939 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −16.1478 | −1.17148 | ||||||||
\(191\) | −7.25363 | −0.524855 | −0.262427 | − | 0.964952i | \(-0.584523\pi\) | ||||
−0.262427 | + | 0.964952i | \(0.584523\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −3.03198 | −0.218247 | −0.109123 | − | 0.994028i | \(-0.534804\pi\) | ||||
−0.109123 | + | 0.994028i | \(0.534804\pi\) | |||||||
\(194\) | −1.12246 | −0.0805879 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −1.17183 | −0.0837024 | ||||||||
\(197\) | 25.6531 | 1.82771 | 0.913853 | − | 0.406045i | \(-0.133092\pi\) | ||||
0.913853 | + | 0.406045i | \(0.133092\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −10.3539 | −0.733971 | −0.366985 | − | 0.930227i | \(-0.619610\pi\) | ||||
−0.366985 | + | 0.930227i | \(0.619610\pi\) | |||||||
\(200\) | 8.99148 | 0.635793 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −3.99629 | −0.281178 | ||||||||
\(203\) | −7.68531 | −0.539403 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 13.1266 | 0.916802 | ||||||||
\(206\) | −3.73692 | −0.260364 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 1.75452 | 0.121654 | ||||||||
\(209\) | −11.6147 | −0.803408 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 18.9676 | 1.30578 | 0.652891 | − | 0.757452i | \(-0.273556\pi\) | ||||
0.652891 | + | 0.757452i | \(0.273556\pi\) | |||||||
\(212\) | −12.5398 | −0.861237 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 14.5768 | 0.996448 | ||||||||
\(215\) | 28.4391 | 1.93953 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −4.32504 | −0.293603 | ||||||||
\(218\) | −4.18661 | −0.283553 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 6.22460 | 0.419662 | ||||||||
\(221\) | 15.4752 | 1.04098 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 9.10091 | 0.609442 | 0.304721 | − | 0.952442i | \(-0.401437\pi\) | ||||
0.304721 | + | 0.952442i | \(0.401437\pi\) | |||||||
\(224\) | 5.51530 | 0.368507 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −9.41643 | −0.626372 | ||||||||
\(227\) | 4.71243 | 0.312775 | 0.156388 | − | 0.987696i | \(-0.450015\pi\) | ||||
0.156388 | + | 0.987696i | \(0.450015\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −11.1018 | −0.733629 | −0.366815 | − | 0.930294i | \(-0.619552\pi\) | ||||
−0.366815 | + | 0.930294i | \(0.619552\pi\) | |||||||
\(230\) | 13.2985 | 0.876880 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 22.1835 | 1.45642 | ||||||||
\(233\) | −9.44652 | −0.618862 | −0.309431 | − | 0.950922i | \(-0.600139\pi\) | ||||
−0.309431 | + | 0.950922i | \(0.600139\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −31.1298 | −2.03068 | ||||||||
\(236\) | 13.3851 | 0.871297 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −2.27265 | −0.147314 | ||||||||
\(239\) | −0.884259 | −0.0571979 | −0.0285990 | − | 0.999591i | \(-0.509105\pi\) | ||||
−0.0285990 | + | 0.999591i | \(0.509105\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −16.4107 | −1.05711 | −0.528554 | − | 0.848900i | \(-0.677266\pi\) | ||||
−0.528554 | + | 0.848900i | \(0.677266\pi\) | |||||||
\(242\) | 6.84623 | 0.440093 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −1.64043 | −0.105018 | ||||||||
\(245\) | −2.84869 | −0.181996 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 38.5987 | 2.45598 | ||||||||
\(248\) | 12.4842 | 0.792745 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −4.88662 | −0.309057 | ||||||||
\(251\) | 31.1797 | 1.96804 | 0.984022 | − | 0.178045i | \(-0.0569772\pi\) | ||||
0.984022 | + | 0.178045i | \(0.0569772\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 9.56534 | 0.601368 | ||||||||
\(254\) | −0.910036 | −0.0571007 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −16.5834 | −1.03646 | ||||||||
\(257\) | 8.99673 | 0.561201 | 0.280600 | − | 0.959825i | \(-0.409466\pi\) | ||||
0.280600 | + | 0.959825i | \(0.409466\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −2.90361 | −0.180421 | ||||||||
\(260\) | −20.6859 | −1.28289 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 1.32039 | 0.0815740 | ||||||||
\(263\) | 10.2900 | 0.634511 | 0.317256 | − | 0.948340i | \(-0.397239\pi\) | ||||
0.317256 | + | 0.948340i | \(0.397239\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −30.4838 | −1.87261 | ||||||||
\(266\) | −5.66849 | −0.347558 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −16.8276 | −1.02791 | ||||||||
\(269\) | −21.1306 | −1.28835 | −0.644177 | − | 0.764877i | \(-0.722800\pi\) | ||||
−0.644177 | + | 0.764877i | \(0.722800\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −19.6434 | −1.19325 | −0.596625 | − | 0.802520i | \(-0.703492\pi\) | ||||
−0.596625 | + | 0.802520i | \(0.703492\pi\) | |||||||
\(272\) | 0.707081 | 0.0428731 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 7.42253 | 0.448411 | ||||||||
\(275\) | 5.80847 | 0.350264 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −17.9075 | −1.07596 | −0.537979 | − | 0.842959i | \(-0.680812\pi\) | ||||
−0.537979 | + | 0.842959i | \(0.680812\pi\) | |||||||
\(278\) | −16.3631 | −0.981391 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 8.22269 | 0.491400 | ||||||||
\(281\) | −15.3397 | −0.915089 | −0.457545 | − | 0.889187i | \(-0.651271\pi\) | ||||
−0.457545 | + | 0.889187i | \(0.651271\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 3.98371 | 0.236807 | 0.118404 | − | 0.992966i | \(-0.462222\pi\) | ||||
0.118404 | + | 0.992966i | \(0.462222\pi\) | |||||||
\(284\) | 11.1278 | 0.660316 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 10.5153 | 0.621784 | ||||||||
\(287\) | 4.60795 | 0.271998 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −10.7634 | −0.633142 | ||||||||
\(290\) | 19.9235 | 1.16995 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 18.9007 | 1.10608 | ||||||||
\(293\) | −14.2180 | −0.830627 | −0.415313 | − | 0.909678i | \(-0.636328\pi\) | ||||
−0.415313 | + | 0.909678i | \(0.636328\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 32.5388 | 1.89448 | ||||||||
\(296\) | 8.38121 | 0.487148 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −7.12694 | −0.412852 | ||||||||
\(299\) | −31.7881 | −1.83835 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 9.98321 | 0.575423 | ||||||||
\(302\) | 2.48273 | 0.142865 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 1.76362 | 0.101150 | ||||||||
\(305\) | −3.98784 | −0.228343 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 25.3729 | 1.44811 | 0.724054 | − | 0.689744i | \(-0.242277\pi\) | ||||
0.724054 | + | 0.689744i | \(0.242277\pi\) | |||||||
\(308\) | 2.18507 | 0.124506 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 11.2123 | 0.636815 | ||||||||
\(311\) | −22.4753 | −1.27446 | −0.637228 | − | 0.770675i | \(-0.719919\pi\) | ||||
−0.637228 | + | 0.770675i | \(0.719919\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 28.4319 | 1.60707 | 0.803533 | − | 0.595261i | \(-0.202951\pi\) | ||||
0.803533 | + | 0.595261i | \(0.202951\pi\) | |||||||
\(314\) | 17.6050 | 0.993507 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −14.7147 | −0.827765 | ||||||||
\(317\) | 6.99427 | 0.392838 | 0.196419 | − | 0.980520i | \(-0.437069\pi\) | ||||
0.196419 | + | 0.980520i | \(0.437069\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 14.3305 | 0.802354 | ||||||||
\(320\) | −15.9111 | −0.889455 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 4.66830 | 0.260154 | ||||||||
\(323\) | 15.5554 | 0.865528 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −19.3030 | −1.07074 | ||||||||
\(326\) | 4.04837 | 0.224218 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −13.3008 | −0.734412 | ||||||||
\(329\) | −10.9278 | −0.602467 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 2.79465 | 0.153608 | 0.0768040 | − | 0.997046i | \(-0.475528\pi\) | ||||
0.0768040 | + | 0.997046i | \(0.475528\pi\) | |||||||
\(332\) | −8.04054 | −0.441282 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −10.3667 | −0.567238 | ||||||||
\(335\) | −40.9073 | −2.23500 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −9.11926 | −0.496758 | −0.248379 | − | 0.968663i | \(-0.579898\pi\) | ||||
−0.248379 | + | 0.968663i | \(0.579898\pi\) | |||||||
\(338\) | −23.1146 | −1.25727 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −8.33652 | −0.452111 | ||||||||
\(341\) | 8.06474 | 0.436730 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | −28.8164 | −1.55368 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −1.34164 | −0.0721268 | ||||||||
\(347\) | 32.7437 | 1.75778 | 0.878888 | − | 0.477029i | \(-0.158286\pi\) | ||||
0.878888 | + | 0.477029i | \(0.158286\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −20.9539 | −1.12164 | −0.560818 | − | 0.827939i | \(-0.689513\pi\) | ||||
−0.560818 | + | 0.827939i | \(0.689513\pi\) | |||||||
\(350\) | 2.83479 | 0.151526 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −10.2842 | −0.548148 | ||||||||
\(353\) | −25.5672 | −1.36080 | −0.680401 | − | 0.732840i | \(-0.738194\pi\) | ||||
−0.680401 | + | 0.732840i | \(0.738194\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 27.0514 | 1.43574 | ||||||||
\(356\) | −10.4121 | −0.551839 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −1.25783 | −0.0664786 | ||||||||
\(359\) | −0.235612 | −0.0124351 | −0.00621757 | − | 0.999981i | \(-0.501979\pi\) | ||||
−0.00621757 | + | 0.999981i | \(0.501979\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 19.7988 | 1.04204 | ||||||||
\(362\) | −11.3874 | −0.598511 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −7.26156 | −0.380609 | ||||||||
\(365\) | 45.9469 | 2.40497 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −14.6165 | −0.762977 | −0.381488 | − | 0.924374i | \(-0.624588\pi\) | ||||
−0.381488 | + | 0.924374i | \(0.624588\pi\) | |||||||
\(368\) | −1.45243 | −0.0757133 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 7.52734 | 0.391328 | ||||||||
\(371\) | −10.7010 | −0.555568 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 8.31248 | 0.430404 | 0.215202 | − | 0.976570i | \(-0.430959\pi\) | ||||
0.215202 | + | 0.976570i | \(0.430959\pi\) | |||||||
\(374\) | 4.23772 | 0.219127 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 31.5428 | 1.62670 | ||||||||
\(377\) | −47.6239 | −2.45276 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −29.3794 | −1.50912 | −0.754560 | − | 0.656231i | \(-0.772150\pi\) | ||||
−0.754560 | + | 0.656231i | \(0.772150\pi\) | |||||||
\(380\) | −20.7931 | −1.06667 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 6.60107 | 0.337740 | ||||||||
\(383\) | −32.6225 | −1.66693 | −0.833466 | − | 0.552570i | \(-0.813647\pi\) | ||||
−0.833466 | + | 0.552570i | \(0.813647\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 5.31184 | 0.270717 | ||||||||
\(386\) | 2.75921 | 0.140440 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −1.44537 | −0.0733774 | ||||||||
\(389\) | −15.2301 | −0.772198 | −0.386099 | − | 0.922457i | \(-0.626178\pi\) | ||||
−0.386099 | + | 0.922457i | \(0.626178\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −12.8107 | −0.647866 | ||||||||
\(392\) | 2.88648 | 0.145789 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −23.3452 | −1.17612 | ||||||||
\(395\) | −35.7708 | −1.79983 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −18.7221 | −0.939634 | −0.469817 | − | 0.882764i | \(-0.655680\pi\) | ||||
−0.469817 | + | 0.882764i | \(0.655680\pi\) | |||||||
\(398\) | 9.42245 | 0.472305 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −0.881977 | −0.0440989 | ||||||||
\(401\) | 5.46933 | 0.273125 | 0.136563 | − | 0.990631i | \(-0.456395\pi\) | ||||
0.136563 | + | 0.990631i | \(0.456395\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −26.8012 | −1.33506 | ||||||||
\(404\) | −5.14594 | −0.256020 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 6.99391 | 0.347102 | ||||||||
\(407\) | 5.41425 | 0.268374 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 10.4460 | 0.516522 | 0.258261 | − | 0.966075i | \(-0.416851\pi\) | ||||
0.258261 | + | 0.966075i | \(0.416851\pi\) | |||||||
\(410\) | −11.9457 | −0.589955 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −4.81196 | −0.237068 | ||||||||
\(413\) | 11.4224 | 0.562058 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −19.5463 | −0.959490 | ||||||||
\(416\) | 34.1769 | 1.67566 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 10.5698 | 0.516987 | ||||||||
\(419\) | 8.46705 | 0.413642 | 0.206821 | − | 0.978379i | \(-0.433688\pi\) | ||||
0.206821 | + | 0.978379i | \(0.433688\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 5.21912 | 0.254365 | 0.127182 | − | 0.991879i | \(-0.459407\pi\) | ||||
0.127182 | + | 0.991879i | \(0.459407\pi\) | |||||||
\(422\) | −17.2612 | −0.840261 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 30.8883 | 1.50007 | ||||||||
\(425\) | −7.77921 | −0.377347 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −1.39989 | −0.0677452 | ||||||||
\(428\) | 18.7702 | 0.907292 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −25.8806 | −1.24807 | ||||||||
\(431\) | −12.8810 | −0.620458 | −0.310229 | − | 0.950662i | \(-0.600406\pi\) | ||||
−0.310229 | + | 0.950662i | \(0.600406\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −28.9525 | −1.39137 | −0.695684 | − | 0.718348i | \(-0.744899\pi\) | ||||
−0.695684 | + | 0.718348i | \(0.744899\pi\) | |||||||
\(434\) | 3.93594 | 0.188931 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −5.39101 | −0.258183 | ||||||||
\(437\) | −31.9528 | −1.52851 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −18.4236 | −0.879311 | −0.439656 | − | 0.898166i | \(-0.644900\pi\) | ||||
−0.439656 | + | 0.898166i | \(0.644900\pi\) | |||||||
\(440\) | −15.3325 | −0.730950 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −14.0830 | −0.669861 | ||||||||
\(443\) | −17.7779 | −0.844655 | −0.422328 | − | 0.906443i | \(-0.638787\pi\) | ||||
−0.422328 | + | 0.906443i | \(0.638787\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −25.3114 | −1.19988 | ||||||||
\(446\) | −8.28216 | −0.392171 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −5.58540 | −0.263885 | ||||||||
\(449\) | −8.68627 | −0.409930 | −0.204965 | − | 0.978769i | \(-0.565708\pi\) | ||||
−0.204965 | + | 0.978769i | \(0.565708\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −8.59226 | −0.404594 | ||||||||
\(452\) | −12.1253 | −0.570328 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −4.28848 | −0.201269 | ||||||||
\(455\) | −17.6526 | −0.827567 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 5.23318 | 0.244798 | 0.122399 | − | 0.992481i | \(-0.460941\pi\) | ||||
0.122399 | + | 0.992481i | \(0.460941\pi\) | |||||||
\(458\) | 10.1031 | 0.472085 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 17.1243 | 0.798422 | ||||||||
\(461\) | −9.90168 | −0.461167 | −0.230584 | − | 0.973052i | \(-0.574064\pi\) | ||||
−0.230584 | + | 0.973052i | \(0.574064\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −25.6117 | −1.19028 | −0.595139 | − | 0.803623i | \(-0.702903\pi\) | ||||
−0.595139 | + | 0.803623i | \(0.702903\pi\) | |||||||
\(464\) | −2.17599 | −0.101018 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 8.59667 | 0.398233 | ||||||||
\(467\) | −8.39998 | −0.388705 | −0.194352 | − | 0.980932i | \(-0.562261\pi\) | ||||
−0.194352 | + | 0.980932i | \(0.562261\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −14.3600 | −0.663085 | ||||||||
\(470\) | 28.3292 | 1.30673 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −32.9705 | −1.51759 | ||||||||
\(473\) | −18.6153 | −0.855933 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −19.4031 | −0.890275 | ||||||||
\(476\) | −2.92644 | −0.134133 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0.804707 | 0.0368065 | ||||||||
\(479\) | −43.2028 | −1.97399 | −0.986993 | − | 0.160763i | \(-0.948605\pi\) | ||||
−0.986993 | + | 0.160763i | \(0.948605\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −17.9929 | −0.820406 | ||||||||
\(482\) | 14.9344 | 0.680241 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 8.81575 | 0.400716 | ||||||||
\(485\) | −3.51364 | −0.159546 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −6.80293 | −0.308270 | −0.154135 | − | 0.988050i | \(-0.549259\pi\) | ||||
−0.154135 | + | 0.988050i | \(0.549259\pi\) | |||||||
\(488\) | 4.04075 | 0.182916 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 2.59241 | 0.117113 | ||||||||
\(491\) | −29.7692 | −1.34347 | −0.671733 | − | 0.740794i | \(-0.734450\pi\) | ||||
−0.671733 | + | 0.740794i | \(0.734450\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −19.1926 | −0.864393 | ||||||||
\(494\) | −35.1262 | −1.58040 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −1.22458 | −0.0549851 | ||||||||
\(497\) | 9.49609 | 0.425958 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 30.0896 | 1.34700 | 0.673498 | − | 0.739189i | \(-0.264791\pi\) | ||||
0.673498 | + | 0.739189i | \(0.264791\pi\) | |||||||
\(500\) | −6.29240 | −0.281405 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −28.3746 | −1.26642 | ||||||||
\(503\) | −24.1598 | −1.07723 | −0.538616 | − | 0.842551i | \(-0.681053\pi\) | ||||
−0.538616 | + | 0.842551i | \(0.681053\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −12.5096 | −0.556670 | ||||||||
\(506\) | −8.70481 | −0.386976 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −1.17183 | −0.0519917 | ||||||||
\(509\) | −1.01922 | −0.0451761 | −0.0225881 | − | 0.999745i | \(-0.507191\pi\) | ||||
−0.0225881 | + | 0.999745i | \(0.507191\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 16.1291 | 0.713511 | ||||||||
\(512\) | 3.19612 | 0.141250 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −8.18735 | −0.361129 | ||||||||
\(515\) | −11.6977 | −0.515462 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 20.3766 | 0.896161 | ||||||||
\(518\) | 2.64239 | 0.116100 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 50.9539 | 2.23448 | ||||||||
\(521\) | −23.8097 | −1.04312 | −0.521561 | − | 0.853214i | \(-0.674650\pi\) | ||||
−0.521561 | + | 0.853214i | \(0.674650\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 5.03806 | 0.220299 | 0.110149 | − | 0.993915i | \(-0.464867\pi\) | ||||
0.110149 | + | 0.993915i | \(0.464867\pi\) | |||||||
\(524\) | 1.70024 | 0.0742752 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −9.36431 | −0.408304 | ||||||||
\(527\) | −10.8010 | −0.470499 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 3.31485 | 0.144124 | ||||||||
\(530\) | 27.7414 | 1.20501 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −7.29920 | −0.316460 | ||||||||
\(533\) | 28.5543 | 1.23682 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 45.6297 | 1.97275 | ||||||||
\(536\) | 41.4500 | 1.79037 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 19.2296 | 0.829046 | ||||||||
\(539\) | 1.86466 | 0.0803167 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −5.22853 | −0.224792 | −0.112396 | − | 0.993663i | \(-0.535853\pi\) | ||||
−0.112396 | + | 0.993663i | \(0.535853\pi\) | |||||||
\(542\) | 17.8762 | 0.767848 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 13.7735 | 0.590532 | ||||||||
\(545\) | −13.1054 | −0.561372 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −6.31818 | −0.270146 | −0.135073 | − | 0.990836i | \(-0.543127\pi\) | ||||
−0.135073 | + | 0.990836i | \(0.543127\pi\) | |||||||
\(548\) | 9.55783 | 0.408290 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −5.28592 | −0.225392 | ||||||||
\(551\) | −47.8708 | −2.03936 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −12.5570 | −0.533976 | ||||||||
\(554\) | 16.2965 | 0.692371 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −21.0704 | −0.893582 | ||||||||
\(557\) | 13.0444 | 0.552711 | 0.276356 | − | 0.961055i | \(-0.410873\pi\) | ||||
0.276356 | + | 0.961055i | \(0.410873\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 61.8634 | 2.61654 | ||||||||
\(560\) | −0.806567 | −0.0340837 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 13.9597 | 0.588853 | ||||||||
\(563\) | 45.5329 | 1.91898 | 0.959491 | − | 0.281738i | \(-0.0909109\pi\) | ||||
0.959491 | + | 0.281738i | \(0.0909109\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −29.4763 | −1.24008 | ||||||||
\(566\) | −3.62532 | −0.152384 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −27.4103 | −1.15011 | ||||||||
\(569\) | −2.80352 | −0.117530 | −0.0587649 | − | 0.998272i | \(-0.518716\pi\) | ||||
−0.0587649 | + | 0.998272i | \(0.518716\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −35.8981 | −1.50229 | −0.751144 | − | 0.660138i | \(-0.770498\pi\) | ||||
−0.751144 | + | 0.660138i | \(0.770498\pi\) | |||||||
\(572\) | 13.5404 | 0.566151 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −4.19340 | −0.175029 | ||||||||
\(575\) | 15.9795 | 0.666390 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 32.3851 | 1.34821 | 0.674105 | − | 0.738636i | \(-0.264530\pi\) | ||||
0.674105 | + | 0.738636i | \(0.264530\pi\) | |||||||
\(578\) | 9.79510 | 0.407422 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 25.6550 | 1.06527 | ||||||||
\(581\) | −6.86150 | −0.284663 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 19.9538 | 0.826400 | ||||||||
\(584\) | −46.5565 | −1.92652 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 12.9389 | 0.534502 | ||||||||
\(587\) | 12.0855 | 0.498824 | 0.249412 | − | 0.968397i | \(-0.419763\pi\) | ||||
0.249412 | + | 0.968397i | \(0.419763\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −26.9401 | −1.11005 | ||||||||
\(590\) | −29.6115 | −1.21908 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −0.822116 | −0.0337888 | ||||||||
\(593\) | −15.7649 | −0.647385 | −0.323693 | − | 0.946162i | \(-0.604924\pi\) | ||||
−0.323693 | + | 0.946162i | \(0.604924\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −7.11407 | −0.291649 | ||||||||
\(596\) | −9.17720 | −0.375913 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 28.9283 | 1.18297 | ||||||||
\(599\) | 28.8610 | 1.17923 | 0.589614 | − | 0.807685i | \(-0.299280\pi\) | ||||
0.589614 | + | 0.807685i | \(0.299280\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 23.7006 | 0.966766 | 0.483383 | − | 0.875409i | \(-0.339408\pi\) | ||||
0.483383 | + | 0.875409i | \(0.339408\pi\) | |||||||
\(602\) | −9.08509 | −0.370280 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 3.19696 | 0.130083 | ||||||||
\(605\) | 21.4308 | 0.871285 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −5.11336 | −0.207545 | −0.103772 | − | 0.994601i | \(-0.533091\pi\) | ||||
−0.103772 | + | 0.994601i | \(0.533091\pi\) | |||||||
\(608\) | 34.3541 | 1.39324 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 3.62908 | 0.146937 | ||||||||
\(611\) | −67.7166 | −2.73952 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −25.7355 | −1.03945 | −0.519724 | − | 0.854334i | \(-0.673965\pi\) | ||||
−0.519724 | + | 0.854334i | \(0.673965\pi\) | |||||||
\(614\) | −23.0902 | −0.931846 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −5.38232 | −0.216860 | ||||||||
\(617\) | 8.33851 | 0.335696 | 0.167848 | − | 0.985813i | \(-0.446318\pi\) | ||||
0.167848 | + | 0.985813i | \(0.446318\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 34.3577 | 1.38095 | 0.690476 | − | 0.723355i | \(-0.257401\pi\) | ||||
0.690476 | + | 0.723355i | \(0.257401\pi\) | |||||||
\(620\) | 14.4378 | 0.579837 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 20.4533 | 0.820103 | ||||||||
\(623\) | −8.88528 | −0.355981 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −30.8717 | −1.23487 | ||||||||
\(626\) | −25.8740 | −1.03413 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 22.6696 | 0.904614 | ||||||||
\(629\) | −7.25122 | −0.289125 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 12.8597 | 0.511935 | 0.255968 | − | 0.966685i | \(-0.417606\pi\) | ||||
0.255968 | + | 0.966685i | \(0.417606\pi\) | |||||||
\(632\) | 36.2454 | 1.44177 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −6.36504 | −0.252788 | ||||||||
\(635\) | −2.84869 | −0.113047 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −6.19675 | −0.245524 | ||||||||
\(638\) | −13.0413 | −0.516309 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −16.9431 | −0.669736 | ||||||||
\(641\) | −35.1723 | −1.38922 | −0.694611 | − | 0.719386i | \(-0.744423\pi\) | ||||
−0.694611 | + | 0.719386i | \(0.744423\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 40.3387 | 1.59080 | 0.795401 | − | 0.606084i | \(-0.207260\pi\) | ||||
0.795401 | + | 0.606084i | \(0.207260\pi\) | |||||||
\(644\) | 6.01128 | 0.236877 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −14.1560 | −0.556961 | ||||||||
\(647\) | 38.7448 | 1.52321 | 0.761607 | − | 0.648039i | \(-0.224411\pi\) | ||||
0.761607 | + | 0.648039i | \(0.224411\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −21.2989 | −0.836053 | ||||||||
\(650\) | 17.5665 | 0.689013 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 5.21300 | 0.204157 | ||||||||
\(653\) | −6.11456 | −0.239281 | −0.119641 | − | 0.992817i | \(-0.538174\pi\) | ||||
−0.119641 | + | 0.992817i | \(0.538174\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 4.13322 | 0.161498 | ||||||||
\(656\) | 1.30468 | 0.0509391 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 9.94466 | 0.387683 | ||||||||
\(659\) | 40.4854 | 1.57709 | 0.788543 | − | 0.614979i | \(-0.210836\pi\) | ||||
0.788543 | + | 0.614979i | \(0.210836\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −47.4100 | −1.84404 | −0.922018 | − | 0.387146i | \(-0.873461\pi\) | ||||
−0.922018 | + | 0.387146i | \(0.873461\pi\) | |||||||
\(662\) | −2.54323 | −0.0988456 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 19.8056 | 0.768607 | ||||||||
\(665\) | −17.7441 | −0.688087 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 39.4241 | 1.52651 | ||||||||
\(668\) | −13.3489 | −0.516485 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 37.2271 | 1.43821 | ||||||||
\(671\) | 2.61031 | 0.100770 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −45.1817 | −1.74163 | −0.870813 | − | 0.491615i | \(-0.836407\pi\) | ||||
−0.870813 | + | 0.491615i | \(0.836407\pi\) | |||||||
\(674\) | 8.29886 | 0.319660 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −29.7642 | −1.14478 | ||||||||
\(677\) | 39.3478 | 1.51226 | 0.756130 | − | 0.654422i | \(-0.227088\pi\) | ||||
0.756130 | + | 0.654422i | \(0.227088\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −1.23342 | −0.0473344 | ||||||||
\(680\) | 20.5347 | 0.787468 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −7.33921 | −0.281033 | ||||||||
\(683\) | −8.53221 | −0.326476 | −0.163238 | − | 0.986587i | \(-0.552194\pi\) | ||||
−0.163238 | + | 0.986587i | \(0.552194\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 23.2348 | 0.887755 | ||||||||
\(686\) | 0.910036 | 0.0347453 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 2.82661 | 0.107764 | ||||||||
\(689\) | −66.3114 | −2.52626 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 51.8607 | 1.97287 | 0.986437 | − | 0.164143i | \(-0.0524857\pi\) | ||||
0.986437 | + | 0.164143i | \(0.0524857\pi\) | |||||||
\(692\) | −1.72760 | −0.0656734 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −29.7980 | −1.13112 | ||||||||
\(695\) | −51.2213 | −1.94294 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 11.5075 | 0.435877 | ||||||||
\(698\) | 19.0688 | 0.721765 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 3.65030 | 0.137968 | ||||||||
\(701\) | −30.3697 | −1.14705 | −0.573524 | − | 0.819189i | \(-0.694424\pi\) | ||||
−0.573524 | + | 0.819189i | \(0.694424\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −18.0862 | −0.682133 | ||||||||
\(704\) | 10.4149 | 0.392526 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 23.2670 | 0.875666 | ||||||||
\(707\) | −4.39135 | −0.165154 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 7.22623 | 0.271387 | 0.135693 | − | 0.990751i | \(-0.456674\pi\) | ||||
0.135693 | + | 0.990751i | \(0.456674\pi\) | |||||||
\(710\) | −24.6178 | −0.923888 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 25.6472 | 0.961170 | ||||||||
\(713\) | 22.1866 | 0.830895 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 32.9161 | 1.23099 | ||||||||
\(716\) | −1.61969 | −0.0605305 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0.214416 | 0.00800192 | ||||||||
\(719\) | 5.93481 | 0.221331 | 0.110666 | − | 0.993858i | \(-0.464702\pi\) | ||||
0.110666 | + | 0.993858i | \(0.464702\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −4.10635 | −0.152928 | ||||||||
\(722\) | −18.0176 | −0.670546 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −14.6634 | −0.544960 | ||||||||
\(725\) | 23.9400 | 0.889107 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 11.2737 | 0.418120 | 0.209060 | − | 0.977903i | \(-0.432960\pi\) | ||||
0.209060 | + | 0.977903i | \(0.432960\pi\) | |||||||
\(728\) | 17.8868 | 0.662929 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −41.8134 | −1.54758 | ||||||||
\(731\) | 24.9312 | 0.922115 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −15.2465 | −0.563144 | −0.281572 | − | 0.959540i | \(-0.590856\pi\) | ||||
−0.281572 | + | 0.959540i | \(0.590856\pi\) | |||||||
\(734\) | 13.3016 | 0.490970 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −28.2924 | −1.04287 | ||||||||
\(737\) | 26.7766 | 0.986329 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −44.7526 | −1.64625 | −0.823126 | − | 0.567859i | \(-0.807772\pi\) | ||||
−0.823126 | + | 0.567859i | \(0.807772\pi\) | |||||||
\(740\) | 9.69279 | 0.356314 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 9.73830 | 0.357504 | ||||||||
\(743\) | −34.8351 | −1.27798 | −0.638988 | − | 0.769217i | \(-0.720647\pi\) | ||||
−0.638988 | + | 0.769217i | \(0.720647\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −22.3095 | −0.817356 | ||||||||
\(746\) | −7.56466 | −0.276962 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 5.45682 | 0.199521 | ||||||||
\(749\) | 16.0178 | 0.585278 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −51.3734 | −1.87464 | −0.937321 | − | 0.348467i | \(-0.886702\pi\) | ||||
−0.937321 | + | 0.348467i | \(0.886702\pi\) | |||||||
\(752\) | −3.09405 | −0.112828 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 43.3395 | 1.57833 | ||||||||
\(755\) | 7.77171 | 0.282841 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −0.972360 | −0.0353410 | −0.0176705 | − | 0.999844i | \(-0.505625\pi\) | ||||
−0.0176705 | + | 0.999844i | \(0.505625\pi\) | |||||||
\(758\) | 26.7363 | 0.971107 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 51.2181 | 1.85787 | ||||||||
\(761\) | 14.6105 | 0.529631 | 0.264815 | − | 0.964299i | \(-0.414689\pi\) | ||||
0.264815 | + | 0.964299i | \(0.414689\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −4.60049 | −0.166549 | ||||||||
\(764\) | 8.50006 | 0.307521 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 29.6877 | 1.07266 | ||||||||
\(767\) | 70.7815 | 2.55577 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −34.5936 | −1.24748 | −0.623738 | − | 0.781633i | \(-0.714387\pi\) | ||||
−0.623738 | + | 0.781633i | \(0.714387\pi\) | |||||||
\(770\) | −4.83397 | −0.174204 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 3.55298 | 0.127875 | ||||||||
\(773\) | 12.4898 | 0.449226 | 0.224613 | − | 0.974448i | \(-0.427888\pi\) | ||||
0.224613 | + | 0.974448i | \(0.427888\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 13.4726 | 0.483951 | ||||||||
\(776\) | 3.56026 | 0.127806 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 13.8600 | 0.496904 | ||||||||
\(779\) | 28.7023 | 1.02837 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −17.7070 | −0.633606 | ||||||||
\(782\) | 11.6582 | 0.416897 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −0.283136 | −0.0101120 | ||||||||
\(785\) | 55.1089 | 1.96692 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 2.75373 | 0.0981597 | 0.0490798 | − | 0.998795i | \(-0.484371\pi\) | ||||
0.0490798 | + | 0.998795i | \(0.484371\pi\) | |||||||
\(788\) | −30.0612 | −1.07088 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 32.5528 | 1.15818 | ||||||||
\(791\) | −10.3473 | −0.367908 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −8.67473 | −0.308049 | ||||||||
\(794\) | 17.0378 | 0.604648 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 12.1331 | 0.430046 | ||||||||
\(797\) | −21.4910 | −0.761252 | −0.380626 | − | 0.924729i | \(-0.624291\pi\) | ||||
−0.380626 | + | 0.924729i | \(0.624291\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −27.2901 | −0.965453 | ||||||||
\(800\) | −17.1803 | −0.607416 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −4.97729 | −0.175754 | ||||||||
\(803\) | −30.0754 | −1.06134 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 14.6132 | 0.515048 | ||||||||
\(806\) | 24.3900 | 0.859103 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 12.6756 | 0.445925 | ||||||||
\(809\) | 7.69502 | 0.270543 | 0.135271 | − | 0.990809i | \(-0.456809\pi\) | ||||
0.135271 | + | 0.990809i | \(0.456809\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −39.7158 | −1.39461 | −0.697306 | − | 0.716774i | \(-0.745618\pi\) | ||||
−0.697306 | + | 0.716774i | \(0.745618\pi\) | |||||||
\(812\) | 9.00591 | 0.316045 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −4.92716 | −0.172697 | ||||||||
\(815\) | 12.6726 | 0.443902 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 62.1841 | 2.17555 | ||||||||
\(818\) | −9.50624 | −0.332378 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −15.3822 | −0.537170 | ||||||||
\(821\) | 31.6422 | 1.10432 | 0.552160 | − | 0.833738i | \(-0.313804\pi\) | ||||
0.552160 | + | 0.833738i | \(0.313804\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 50.2891 | 1.75297 | 0.876484 | − | 0.481431i | \(-0.159883\pi\) | ||||
0.876484 | + | 0.481431i | \(0.159883\pi\) | |||||||
\(824\) | 11.8529 | 0.412915 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −10.3948 | −0.361680 | ||||||||
\(827\) | 27.3110 | 0.949698 | 0.474849 | − | 0.880067i | \(-0.342503\pi\) | ||||
0.474849 | + | 0.880067i | \(0.342503\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −5.34901 | −0.185779 | −0.0928894 | − | 0.995676i | \(-0.529610\pi\) | ||||
−0.0928894 | + | 0.995676i | \(0.529610\pi\) | |||||||
\(830\) | 17.7878 | 0.617425 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −34.6113 | −1.19993 | ||||||||
\(833\) | −2.49732 | −0.0865269 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −32.4508 | −1.12301 | ||||||||
\(836\) | 13.6105 | 0.470730 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −7.70532 | −0.266176 | ||||||||
\(839\) | 6.12466 | 0.211447 | 0.105723 | − | 0.994396i | \(-0.466284\pi\) | ||||
0.105723 | + | 0.994396i | \(0.466284\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 30.0640 | 1.03669 | ||||||||
\(842\) | −4.74959 | −0.163682 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −22.2269 | −0.765080 | ||||||||
\(845\) | −72.3557 | −2.48911 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 7.52304 | 0.258495 | ||||||||
\(848\) | −3.02984 | −0.104045 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 7.07936 | 0.242820 | ||||||||
\(851\) | 14.8949 | 0.510591 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −12.7046 | −0.434996 | −0.217498 | − | 0.976061i | \(-0.569789\pi\) | ||||
−0.217498 | + | 0.976061i | \(0.569789\pi\) | |||||||
\(854\) | 1.27395 | 0.0435935 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −46.2351 | −1.58028 | ||||||||
\(857\) | −11.0623 | −0.377880 | −0.188940 | − | 0.981989i | \(-0.560505\pi\) | ||||
−0.188940 | + | 0.981989i | \(0.560505\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −5.41515 | −0.184763 | −0.0923813 | − | 0.995724i | \(-0.529448\pi\) | ||||
−0.0923813 | + | 0.995724i | \(0.529448\pi\) | |||||||
\(860\) | −33.3259 | −1.13640 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 11.7222 | 0.399260 | ||||||||
\(863\) | −21.3557 | −0.726956 | −0.363478 | − | 0.931603i | \(-0.618411\pi\) | ||||
−0.363478 | + | 0.931603i | \(0.618411\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −4.19973 | −0.142795 | ||||||||
\(866\) | 26.3478 | 0.895335 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 5.06823 | 0.172027 | ||||||||
\(869\) | 23.4145 | 0.794282 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −88.9855 | −3.01516 | ||||||||
\(872\) | 13.2792 | 0.449692 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 29.0782 | 0.983586 | ||||||||
\(875\) | −5.36970 | −0.181529 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −9.00207 | −0.303978 | −0.151989 | − | 0.988382i | \(-0.548568\pi\) | ||||
−0.151989 | + | 0.988382i | \(0.548568\pi\) | |||||||
\(878\) | 16.7662 | 0.565830 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 1.50398 | 0.0506990 | ||||||||
\(881\) | 38.3952 | 1.29357 | 0.646783 | − | 0.762674i | \(-0.276114\pi\) | ||||
0.646783 | + | 0.762674i | \(0.276114\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −52.5943 | −1.76994 | −0.884969 | − | 0.465650i | \(-0.845821\pi\) | ||||
−0.884969 | + | 0.465650i | \(0.845821\pi\) | |||||||
\(884\) | −18.1344 | −0.609926 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 16.1786 | 0.543529 | ||||||||
\(887\) | −0.462980 | −0.0155453 | −0.00777267 | − | 0.999970i | \(-0.502474\pi\) | ||||
−0.00777267 | + | 0.999970i | \(0.502474\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1.00000 | −0.0335389 | ||||||||
\(890\) | 23.0343 | 0.772111 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −10.6648 | −0.357082 | ||||||||
\(893\) | −68.0676 | −2.27779 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −3.93740 | −0.131613 | ||||||||
\(896\) | −5.94769 | −0.198698 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 7.90482 | 0.263787 | ||||||||
\(899\) | 33.2393 | 1.10859 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −26.7238 | −0.890298 | ||||||||
\(902\) | 7.81927 | 0.260353 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 29.8674 | 0.993373 | ||||||||
\(905\) | −35.6462 | −1.18492 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 9.91810 | 0.329325 | 0.164663 | − | 0.986350i | \(-0.447346\pi\) | ||||
0.164663 | + | 0.986350i | \(0.447346\pi\) | |||||||
\(908\) | −5.52219 | −0.183260 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 16.0645 | 0.532533 | ||||||||
\(911\) | 8.34507 | 0.276485 | 0.138242 | − | 0.990398i | \(-0.455855\pi\) | ||||
0.138242 | + | 0.990398i | \(0.455855\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 12.7944 | 0.423432 | ||||||||
\(914\) | −4.76238 | −0.157526 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 13.0095 | 0.429846 | ||||||||
\(917\) | 1.45092 | 0.0479136 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 27.2474 | 0.898807 | 0.449404 | − | 0.893329i | \(-0.351637\pi\) | ||||
0.449404 | + | 0.893329i | \(0.351637\pi\) | |||||||
\(920\) | −42.1808 | −1.39066 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 9.01089 | 0.296758 | ||||||||
\(923\) | 58.8449 | 1.93690 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 9.04481 | 0.297392 | ||||||||
\(926\) | 23.3076 | 0.765936 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −42.3868 | −1.39142 | ||||||||
\(929\) | 22.7028 | 0.744854 | 0.372427 | − | 0.928062i | \(-0.378526\pi\) | ||||
0.372427 | + | 0.928062i | \(0.378526\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −6.22887 | −0.204143 | ||||||||
\(932\) | 11.0698 | 0.362602 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 7.64429 | 0.250129 | ||||||||
\(935\) | 13.2653 | 0.433823 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 28.1759 | 0.920468 | 0.460234 | − | 0.887798i | \(-0.347765\pi\) | ||||
0.460234 | + | 0.887798i | \(0.347765\pi\) | |||||||
\(938\) | 13.0681 | 0.426690 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 36.4789 | 1.18981 | ||||||||
\(941\) | −22.7468 | −0.741523 | −0.370762 | − | 0.928728i | \(-0.620903\pi\) | ||||
−0.370762 | + | 0.928728i | \(0.620903\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −23.6378 | −0.769754 | ||||||||
\(944\) | 3.23409 | 0.105261 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 16.9406 | 0.550787 | ||||||||
\(947\) | 18.0753 | 0.587367 | 0.293683 | − | 0.955903i | \(-0.405119\pi\) | ||||
0.293683 | + | 0.955903i | \(0.405119\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 99.9482 | 3.24446 | ||||||||
\(950\) | 17.6575 | 0.572885 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 7.20846 | 0.233628 | ||||||||
\(953\) | −37.0138 | −1.19899 | −0.599497 | − | 0.800377i | \(-0.704633\pi\) | ||||
−0.599497 | + | 0.800377i | \(0.704633\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 20.6633 | 0.668650 | ||||||||
\(956\) | 1.03620 | 0.0335132 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 39.3161 | 1.27025 | ||||||||
\(959\) | 8.15630 | 0.263381 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −12.2940 | −0.396581 | ||||||||
\(962\) | 16.3742 | 0.527925 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 19.2307 | 0.619378 | ||||||||
\(965\) | 8.63717 | 0.278040 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −1.69090 | −0.0543755 | −0.0271878 | − | 0.999630i | \(-0.508655\pi\) | ||||
−0.0271878 | + | 0.999630i | \(0.508655\pi\) | |||||||
\(968\) | −21.7151 | −0.697950 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 3.19754 | 0.102667 | ||||||||
\(971\) | −4.21235 | −0.135181 | −0.0675904 | − | 0.997713i | \(-0.521531\pi\) | ||||
−0.0675904 | + | 0.997713i | \(0.521531\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −17.9807 | −0.576434 | ||||||||
\(974\) | 6.19091 | 0.198370 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −0.396358 | −0.0126871 | ||||||||
\(977\) | −6.21411 | −0.198807 | −0.0994036 | − | 0.995047i | \(-0.531693\pi\) | ||||
−0.0994036 | + | 0.995047i | \(0.531693\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 16.5680 | 0.529517 | ||||||||
\(980\) | 3.33819 | 0.106635 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 27.0911 | 0.864510 | ||||||||
\(983\) | −25.0905 | −0.800263 | −0.400131 | − | 0.916458i | \(-0.631036\pi\) | ||||
−0.400131 | + | 0.916458i | \(0.631036\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −73.0776 | −2.32845 | ||||||||
\(986\) | 17.4660 | 0.556231 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −45.2313 | −1.43900 | ||||||||
\(989\) | −51.2119 | −1.62844 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −46.2979 | −1.47070 | −0.735351 | − | 0.677687i | \(-0.762983\pi\) | ||||
−0.735351 | + | 0.677687i | \(0.762983\pi\) | |||||||
\(992\) | −23.8539 | −0.757363 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −8.64179 | −0.274101 | ||||||||
\(995\) | 29.4951 | 0.935059 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 12.5863 | 0.398614 | 0.199307 | − | 0.979937i | \(-0.436131\pi\) | ||||
0.199307 | + | 0.979937i | \(0.436131\pi\) | |||||||
\(998\) | −27.3826 | −0.866782 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 8001.2.a.m.1.5 | 11 | ||
3.2 | odd | 2 | 2667.2.a.k.1.7 | ✓ | 11 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2667.2.a.k.1.7 | ✓ | 11 | 3.2 | odd | 2 | ||
8001.2.a.m.1.5 | 11 | 1.1 | even | 1 | trivial |