Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1075,2,Mod(1,1075)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1075, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("1075.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1075 = 5^{2} \cdot 43 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1075.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: | \(8.58391821729\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.321.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 4x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 215) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(0.239123\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1075.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.760877 | 0.538021 | 0.269011 | − | 0.963137i | \(-0.413303\pi\) | ||||
0.269011 | + | 0.963137i | \(0.413303\pi\) | |||||||
\(3\) | −0.239123 | −0.138058 | −0.0690289 | − | 0.997615i | \(-0.521990\pi\) | ||||
−0.0690289 | + | 0.997615i | \(0.521990\pi\) | |||||||
\(4\) | −1.42107 | −0.710533 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −0.181943 | −0.0742781 | ||||||||
\(7\) | −1.94282 | −0.734317 | −0.367158 | − | 0.930158i | \(-0.619669\pi\) | ||||
−0.367158 | + | 0.930158i | \(0.619669\pi\) | |||||||
\(8\) | −2.60301 | −0.920303 | ||||||||
\(9\) | −2.94282 | −0.980940 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 5.66019 | 1.70661 | 0.853306 | − | 0.521411i | \(-0.174594\pi\) | ||||
0.853306 | + | 0.521411i | \(0.174594\pi\) | |||||||
\(12\) | 0.339810 | 0.0980947 | ||||||||
\(13\) | 0.478247 | 0.132642 | 0.0663209 | − | 0.997798i | \(-0.478874\pi\) | ||||
0.0663209 | + | 0.997798i | \(0.478874\pi\) | |||||||
\(14\) | −1.47825 | −0.395078 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0.861564 | 0.215391 | ||||||||
\(17\) | −3.52175 | −0.854151 | −0.427075 | − | 0.904216i | \(-0.640456\pi\) | ||||
−0.427075 | + | 0.904216i | \(0.640456\pi\) | |||||||
\(18\) | −2.23912 | −0.527766 | ||||||||
\(19\) | 7.88564 | 1.80909 | 0.904545 | − | 0.426378i | \(-0.140211\pi\) | ||||
0.904545 | + | 0.426378i | \(0.140211\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.464574 | 0.101378 | ||||||||
\(22\) | 4.30671 | 0.918193 | ||||||||
\(23\) | 7.88564 | 1.64427 | 0.822135 | − | 0.569293i | \(-0.192783\pi\) | ||||
0.822135 | + | 0.569293i | \(0.192783\pi\) | |||||||
\(24\) | 0.622440 | 0.127055 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0.363887 | 0.0713640 | ||||||||
\(27\) | 1.42107 | 0.273484 | ||||||||
\(28\) | 2.76088 | 0.521757 | ||||||||
\(29\) | 0.478247 | 0.0888082 | 0.0444041 | − | 0.999014i | \(-0.485861\pi\) | ||||
0.0444041 | + | 0.999014i | \(0.485861\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.57893 | 0.283585 | 0.141792 | − | 0.989896i | \(-0.454713\pi\) | ||||
0.141792 | + | 0.989896i | \(0.454713\pi\) | |||||||
\(32\) | 5.86156 | 1.03619 | ||||||||
\(33\) | −1.35348 | −0.235611 | ||||||||
\(34\) | −2.67962 | −0.459551 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 4.18194 | 0.696991 | ||||||||
\(37\) | −0.339810 | −0.0558644 | −0.0279322 | − | 0.999610i | \(-0.508892\pi\) | ||||
−0.0279322 | + | 0.999610i | \(0.508892\pi\) | |||||||
\(38\) | 6.00000 | 0.973329 | ||||||||
\(39\) | −0.114360 | −0.0183122 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −0.603010 | −0.0941743 | −0.0470872 | − | 0.998891i | \(-0.514994\pi\) | ||||
−0.0470872 | + | 0.998891i | \(0.514994\pi\) | |||||||
\(42\) | 0.353483 | 0.0545436 | ||||||||
\(43\) | 1.00000 | 0.152499 | ||||||||
\(44\) | −8.04351 | −1.21260 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 6.00000 | 0.884652 | ||||||||
\(47\) | 12.8421 | 1.87322 | 0.936609 | − | 0.350377i | \(-0.113946\pi\) | ||||
0.936609 | + | 0.350377i | \(0.113946\pi\) | |||||||
\(48\) | −0.206020 | −0.0297364 | ||||||||
\(49\) | −3.22545 | −0.460779 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0.842133 | 0.117922 | ||||||||
\(52\) | −0.679620 | −0.0942464 | ||||||||
\(53\) | −2.47825 | −0.340413 | −0.170207 | − | 0.985408i | \(-0.554444\pi\) | ||||
−0.170207 | + | 0.985408i | \(0.554444\pi\) | |||||||
\(54\) | 1.08126 | 0.147140 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 5.05718 | 0.675794 | ||||||||
\(57\) | −1.88564 | −0.249759 | ||||||||
\(58\) | 0.363887 | 0.0477807 | ||||||||
\(59\) | −6.96690 | −0.907013 | −0.453506 | − | 0.891253i | \(-0.649827\pi\) | ||||
−0.453506 | + | 0.891253i | \(0.649827\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 8.24953 | 1.05624 | 0.528122 | − | 0.849169i | \(-0.322896\pi\) | ||||
0.528122 | + | 0.849169i | \(0.322896\pi\) | |||||||
\(62\) | 1.20137 | 0.152575 | ||||||||
\(63\) | 5.71737 | 0.720321 | ||||||||
\(64\) | 2.73680 | 0.342100 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −1.02983 | −0.126764 | ||||||||
\(67\) | 7.88564 | 0.963384 | 0.481692 | − | 0.876341i | \(-0.340022\pi\) | ||||
0.481692 | + | 0.876341i | \(0.340022\pi\) | |||||||
\(68\) | 5.00465 | 0.606903 | ||||||||
\(69\) | −1.88564 | −0.227004 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −13.2060 | −1.56727 | −0.783633 | − | 0.621224i | \(-0.786636\pi\) | ||||
−0.783633 | + | 0.621224i | \(0.786636\pi\) | |||||||
\(72\) | 7.66019 | 0.902762 | ||||||||
\(73\) | −6.60301 | −0.772824 | −0.386412 | − | 0.922326i | \(-0.626286\pi\) | ||||
−0.386412 | + | 0.922326i | \(0.626286\pi\) | |||||||
\(74\) | −0.258554 | −0.0300562 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −11.2060 | −1.28542 | ||||||||
\(77\) | −10.9967 | −1.25319 | ||||||||
\(78\) | −0.0870138 | −0.00985237 | ||||||||
\(79\) | 3.06758 | 0.345130 | 0.172565 | − | 0.984998i | \(-0.444794\pi\) | ||||
0.172565 | + | 0.984998i | \(0.444794\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 8.48865 | 0.943183 | ||||||||
\(82\) | −0.458816 | −0.0506678 | ||||||||
\(83\) | 4.56526 | 0.501102 | 0.250551 | − | 0.968103i | \(-0.419388\pi\) | ||||
0.250551 | + | 0.968103i | \(0.419388\pi\) | |||||||
\(84\) | −0.660190 | −0.0720326 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0.760877 | 0.0820474 | ||||||||
\(87\) | −0.114360 | −0.0122607 | ||||||||
\(88\) | −14.7335 | −1.57060 | ||||||||
\(89\) | 14.2495 | 1.51045 | 0.755223 | − | 0.655467i | \(-0.227528\pi\) | ||||
0.755223 | + | 0.655467i | \(0.227528\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −0.929147 | −0.0974011 | ||||||||
\(92\) | −11.2060 | −1.16831 | ||||||||
\(93\) | −0.377560 | −0.0391511 | ||||||||
\(94\) | 9.77128 | 1.00783 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −1.40164 | −0.143054 | ||||||||
\(97\) | 9.77128 | 0.992123 | 0.496062 | − | 0.868287i | \(-0.334779\pi\) | ||||
0.496062 | + | 0.868287i | \(0.334779\pi\) | |||||||
\(98\) | −2.45417 | −0.247909 | ||||||||
\(99\) | −16.6569 | −1.67408 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −6.67059 | −0.663749 | −0.331874 | − | 0.943324i | \(-0.607681\pi\) | ||||
−0.331874 | + | 0.943324i | \(0.607681\pi\) | |||||||
\(102\) | 0.640760 | 0.0634447 | ||||||||
\(103\) | −13.7713 | −1.35692 | −0.678462 | − | 0.734635i | \(-0.737353\pi\) | ||||
−0.678462 | + | 0.734635i | \(0.737353\pi\) | |||||||
\(104\) | −1.24488 | −0.122071 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −1.88564 | −0.183150 | ||||||||
\(107\) | −19.5699 | −1.89189 | −0.945947 | − | 0.324321i | \(-0.894864\pi\) | ||||
−0.945947 | + | 0.324321i | \(0.894864\pi\) | |||||||
\(108\) | −2.01943 | −0.194320 | ||||||||
\(109\) | 6.05718 | 0.580173 | 0.290086 | − | 0.957000i | \(-0.406316\pi\) | ||||
0.290086 | + | 0.957000i | \(0.406316\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0.0812565 | 0.00771253 | ||||||||
\(112\) | −1.67386 | −0.158165 | ||||||||
\(113\) | 11.3776 | 1.07031 | 0.535155 | − | 0.844754i | \(-0.320253\pi\) | ||||
0.535155 | + | 0.844754i | \(0.320253\pi\) | |||||||
\(114\) | −1.43474 | −0.134376 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −0.679620 | −0.0631012 | ||||||||
\(117\) | −1.40739 | −0.130114 | ||||||||
\(118\) | −5.30095 | −0.487992 | ||||||||
\(119\) | 6.84213 | 0.627217 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 21.0377 | 1.91252 | ||||||||
\(122\) | 6.27687 | 0.568281 | ||||||||
\(123\) | 0.144194 | 0.0130015 | ||||||||
\(124\) | −2.24377 | −0.201496 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 4.35021 | 0.387548 | ||||||||
\(127\) | 16.2495 | 1.44191 | 0.720956 | − | 0.692981i | \(-0.243703\pi\) | ||||
0.720956 | + | 0.692981i | \(0.243703\pi\) | |||||||
\(128\) | −9.64076 | −0.852131 | ||||||||
\(129\) | −0.239123 | −0.0210536 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −7.52175 | −0.657179 | −0.328589 | − | 0.944473i | \(-0.606573\pi\) | ||||
−0.328589 | + | 0.944473i | \(0.606573\pi\) | |||||||
\(132\) | 1.92339 | 0.167410 | ||||||||
\(133\) | −15.3204 | −1.32845 | ||||||||
\(134\) | 6.00000 | 0.518321 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 9.16716 | 0.786077 | ||||||||
\(137\) | 11.8090 | 1.00891 | 0.504457 | − | 0.863437i | \(-0.331693\pi\) | ||||
0.504457 | + | 0.863437i | \(0.331693\pi\) | |||||||
\(138\) | −1.43474 | −0.122133 | ||||||||
\(139\) | 9.53216 | 0.808507 | 0.404254 | − | 0.914647i | \(-0.367531\pi\) | ||||
0.404254 | + | 0.914647i | \(0.367531\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −3.07085 | −0.258612 | ||||||||
\(142\) | −10.0482 | −0.843222 | ||||||||
\(143\) | 2.70697 | 0.226368 | ||||||||
\(144\) | −2.53543 | −0.211286 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −5.02408 | −0.415796 | ||||||||
\(147\) | 0.771280 | 0.0636141 | ||||||||
\(148\) | 0.482893 | 0.0396935 | ||||||||
\(149\) | −6.92915 | −0.567658 | −0.283829 | − | 0.958875i | \(-0.591605\pi\) | ||||
−0.283829 | + | 0.958875i | \(0.591605\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 12.6134 | 1.02647 | 0.513233 | − | 0.858250i | \(-0.328448\pi\) | ||||
0.513233 | + | 0.858250i | \(0.328448\pi\) | |||||||
\(152\) | −20.5264 | −1.66491 | ||||||||
\(153\) | 10.3639 | 0.837871 | ||||||||
\(154\) | −8.36716 | −0.674245 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0.162513 | 0.0130115 | ||||||||
\(157\) | 2.12476 | 0.169575 | 0.0847873 | − | 0.996399i | \(-0.472979\pi\) | ||||
0.0847873 | + | 0.996399i | \(0.472979\pi\) | |||||||
\(158\) | 2.33405 | 0.185687 | ||||||||
\(159\) | 0.592606 | 0.0469967 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −15.3204 | −1.20742 | ||||||||
\(162\) | 6.45882 | 0.507453 | ||||||||
\(163\) | 17.9097 | 1.40280 | 0.701399 | − | 0.712769i | \(-0.252559\pi\) | ||||
0.701399 | + | 0.712769i | \(0.252559\pi\) | |||||||
\(164\) | 0.856917 | 0.0669140 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 3.47360 | 0.269604 | ||||||||
\(167\) | 5.20602 | 0.402854 | 0.201427 | − | 0.979504i | \(-0.435442\pi\) | ||||
0.201427 | + | 0.979504i | \(0.435442\pi\) | |||||||
\(168\) | −1.20929 | −0.0932987 | ||||||||
\(169\) | −12.7713 | −0.982406 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −23.2060 | −1.77461 | ||||||||
\(172\) | −1.42107 | −0.108355 | ||||||||
\(173\) | 16.4782 | 1.25282 | 0.626409 | − | 0.779495i | \(-0.284524\pi\) | ||||
0.626409 | + | 0.779495i | \(0.284524\pi\) | |||||||
\(174\) | −0.0870138 | −0.00659650 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 4.87661 | 0.367589 | ||||||||
\(177\) | 1.66595 | 0.125220 | ||||||||
\(178\) | 10.8421 | 0.812652 | ||||||||
\(179\) | −8.24953 | −0.616599 | −0.308299 | − | 0.951289i | \(-0.599760\pi\) | ||||
−0.308299 | + | 0.951289i | \(0.599760\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −15.1683 | −1.12745 | −0.563724 | − | 0.825963i | \(-0.690632\pi\) | ||||
−0.563724 | + | 0.825963i | \(0.690632\pi\) | |||||||
\(182\) | −0.706966 | −0.0524038 | ||||||||
\(183\) | −1.97265 | −0.145823 | ||||||||
\(184\) | −20.5264 | −1.51323 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −0.287276 | −0.0210641 | ||||||||
\(187\) | −19.9338 | −1.45770 | ||||||||
\(188\) | −18.2495 | −1.33098 | ||||||||
\(189\) | −2.76088 | −0.200824 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −17.6843 | −1.27959 | −0.639794 | − | 0.768546i | \(-0.720980\pi\) | ||||
−0.639794 | + | 0.768546i | \(0.720980\pi\) | |||||||
\(192\) | −0.654433 | −0.0472296 | ||||||||
\(193\) | −18.1352 | −1.30540 | −0.652699 | − | 0.757617i | \(-0.726363\pi\) | ||||
−0.652699 | + | 0.757617i | \(0.726363\pi\) | |||||||
\(194\) | 7.43474 | 0.533783 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 4.58358 | 0.327399 | ||||||||
\(197\) | −4.72777 | −0.336840 | −0.168420 | − | 0.985715i | \(-0.553866\pi\) | ||||
−0.168420 | + | 0.985715i | \(0.553866\pi\) | |||||||
\(198\) | −12.6739 | −0.900692 | ||||||||
\(199\) | 2.56526 | 0.181846 | 0.0909232 | − | 0.995858i | \(-0.471018\pi\) | ||||
0.0909232 | + | 0.995858i | \(0.471018\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −1.88564 | −0.133003 | ||||||||
\(202\) | −5.07550 | −0.357111 | ||||||||
\(203\) | −0.929147 | −0.0652133 | ||||||||
\(204\) | −1.19673 | −0.0837877 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −10.4782 | −0.730054 | ||||||||
\(207\) | −23.2060 | −1.61293 | ||||||||
\(208\) | 0.412040 | 0.0285698 | ||||||||
\(209\) | 44.6342 | 3.08741 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −25.4074 | −1.74912 | −0.874559 | − | 0.484920i | \(-0.838849\pi\) | ||||
−0.874559 | + | 0.484920i | \(0.838849\pi\) | |||||||
\(212\) | 3.52175 | 0.241875 | ||||||||
\(213\) | 3.15787 | 0.216373 | ||||||||
\(214\) | −14.8903 | −1.01788 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −3.69905 | −0.251689 | ||||||||
\(217\) | −3.06758 | −0.208241 | ||||||||
\(218\) | 4.60877 | 0.312145 | ||||||||
\(219\) | 1.57893 | 0.106694 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1.68427 | −0.113296 | ||||||||
\(222\) | 0.0618262 | 0.00414950 | ||||||||
\(223\) | −4.00000 | −0.267860 | −0.133930 | − | 0.990991i | \(-0.542760\pi\) | ||||
−0.133930 | + | 0.990991i | \(0.542760\pi\) | |||||||
\(224\) | −11.3880 | −0.760890 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 8.65692 | 0.575850 | ||||||||
\(227\) | −4.87197 | −0.323364 | −0.161682 | − | 0.986843i | \(-0.551692\pi\) | ||||
−0.161682 | + | 0.986843i | \(0.551692\pi\) | |||||||
\(228\) | 2.67962 | 0.177462 | ||||||||
\(229\) | 13.5458 | 0.895134 | 0.447567 | − | 0.894250i | \(-0.352291\pi\) | ||||
0.447567 | + | 0.894250i | \(0.352291\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 2.62957 | 0.173013 | ||||||||
\(232\) | −1.24488 | −0.0817304 | ||||||||
\(233\) | 11.3308 | 0.742304 | 0.371152 | − | 0.928572i | \(-0.378963\pi\) | ||||
0.371152 | + | 0.928572i | \(0.378963\pi\) | |||||||
\(234\) | −1.07085 | −0.0700039 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 9.90042 | 0.644463 | ||||||||
\(237\) | −0.733531 | −0.0476479 | ||||||||
\(238\) | 5.20602 | 0.337456 | ||||||||
\(239\) | 9.35021 | 0.604815 | 0.302408 | − | 0.953179i | \(-0.402210\pi\) | ||||
0.302408 | + | 0.953179i | \(0.402210\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 2.22872 | 0.143564 | 0.0717822 | − | 0.997420i | \(-0.477131\pi\) | ||||
0.0717822 | + | 0.997420i | \(0.477131\pi\) | |||||||
\(242\) | 16.0071 | 1.02898 | ||||||||
\(243\) | −6.29303 | −0.403698 | ||||||||
\(244\) | −11.7231 | −0.750496 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0.109714 | 0.00699509 | ||||||||
\(247\) | 3.77128 | 0.239961 | ||||||||
\(248\) | −4.10998 | −0.260984 | ||||||||
\(249\) | −1.09166 | −0.0691811 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −1.68427 | −0.106310 | −0.0531550 | − | 0.998586i | \(-0.516928\pi\) | ||||
−0.0531550 | + | 0.998586i | \(0.516928\pi\) | |||||||
\(252\) | −8.12476 | −0.511812 | ||||||||
\(253\) | 44.6342 | 2.80613 | ||||||||
\(254\) | 12.3639 | 0.775779 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −12.8090 | −0.800564 | ||||||||
\(257\) | −2.70370 | −0.168652 | −0.0843260 | − | 0.996438i | \(-0.526874\pi\) | ||||
−0.0843260 | + | 0.996438i | \(0.526874\pi\) | |||||||
\(258\) | −0.181943 | −0.0113273 | ||||||||
\(259\) | 0.660190 | 0.0410222 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1.40739 | −0.0871155 | ||||||||
\(262\) | −5.72313 | −0.353576 | ||||||||
\(263\) | 3.54583 | 0.218645 | 0.109323 | − | 0.994006i | \(-0.465132\pi\) | ||||
0.109323 | + | 0.994006i | \(0.465132\pi\) | |||||||
\(264\) | 3.52313 | 0.216834 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −11.6569 | −0.714732 | ||||||||
\(267\) | −3.40739 | −0.208529 | ||||||||
\(268\) | −11.2060 | −0.684517 | ||||||||
\(269\) | 28.1866 | 1.71857 | 0.859283 | − | 0.511500i | \(-0.170910\pi\) | ||||
0.859283 | + | 0.511500i | \(0.170910\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −22.4887 | −1.36609 | −0.683044 | − | 0.730377i | \(-0.739344\pi\) | ||||
−0.683044 | + | 0.730377i | \(0.739344\pi\) | |||||||
\(272\) | −3.03421 | −0.183976 | ||||||||
\(273\) | 0.222181 | 0.0134470 | ||||||||
\(274\) | 8.98522 | 0.542817 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 2.67962 | 0.161294 | ||||||||
\(277\) | −5.57893 | −0.335206 | −0.167603 | − | 0.985855i | \(-0.553603\pi\) | ||||
−0.167603 | + | 0.985855i | \(0.553603\pi\) | |||||||
\(278\) | 7.25280 | 0.434994 | ||||||||
\(279\) | −4.64652 | −0.278180 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 28.6375 | 1.70837 | 0.854185 | − | 0.519970i | \(-0.174057\pi\) | ||||
0.854185 | + | 0.519970i | \(0.174057\pi\) | |||||||
\(282\) | −2.33654 | −0.139139 | ||||||||
\(283\) | 13.1190 | 0.779844 | 0.389922 | − | 0.920848i | \(-0.372502\pi\) | ||||
0.389922 | + | 0.920848i | \(0.372502\pi\) | |||||||
\(284\) | 18.7666 | 1.11359 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 2.05967 | 0.121791 | ||||||||
\(287\) | 1.17154 | 0.0691538 | ||||||||
\(288\) | −17.2495 | −1.01644 | ||||||||
\(289\) | −4.59725 | −0.270427 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −2.33654 | −0.136970 | ||||||||
\(292\) | 9.38332 | 0.549117 | ||||||||
\(293\) | 11.6361 | 0.679789 | 0.339894 | − | 0.940464i | \(-0.389609\pi\) | ||||
0.339894 | + | 0.940464i | \(0.389609\pi\) | |||||||
\(294\) | 0.586849 | 0.0342257 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0.884529 | 0.0514122 | ||||||||
\(297\) | 8.04351 | 0.466732 | ||||||||
\(298\) | −5.27223 | −0.305412 | ||||||||
\(299\) | 3.77128 | 0.218099 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1.94282 | −0.111982 | ||||||||
\(302\) | 9.59725 | 0.552260 | ||||||||
\(303\) | 1.59509 | 0.0916358 | ||||||||
\(304\) | 6.79398 | 0.389661 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 7.88564 | 0.450792 | ||||||||
\(307\) | −7.09166 | −0.404742 | −0.202371 | − | 0.979309i | \(-0.564865\pi\) | ||||
−0.202371 | + | 0.979309i | \(0.564865\pi\) | |||||||
\(308\) | 15.6271 | 0.890436 | ||||||||
\(309\) | 3.29303 | 0.187334 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 5.53216 | 0.313700 | 0.156850 | − | 0.987622i | \(-0.449866\pi\) | ||||
0.156850 | + | 0.987622i | \(0.449866\pi\) | |||||||
\(312\) | 0.297680 | 0.0168528 | ||||||||
\(313\) | −19.1488 | −1.08236 | −0.541178 | − | 0.840908i | \(-0.682022\pi\) | ||||
−0.541178 | + | 0.840908i | \(0.682022\pi\) | |||||||
\(314\) | 1.61668 | 0.0912347 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −4.35924 | −0.245226 | ||||||||
\(317\) | 12.7004 | 0.713327 | 0.356664 | − | 0.934233i | \(-0.383914\pi\) | ||||
0.356664 | + | 0.934233i | \(0.383914\pi\) | |||||||
\(318\) | 0.450900 | 0.0252852 | ||||||||
\(319\) | 2.70697 | 0.151561 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 4.67962 | 0.261191 | ||||||||
\(322\) | −11.6569 | −0.649615 | ||||||||
\(323\) | −27.7713 | −1.54524 | ||||||||
\(324\) | −12.0629 | −0.670163 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 13.6271 | 0.754735 | ||||||||
\(327\) | −1.44841 | −0.0800974 | ||||||||
\(328\) | 1.56964 | 0.0866689 | ||||||||
\(329\) | −24.9500 | −1.37554 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 5.49441 | 0.302000 | 0.151000 | − | 0.988534i | \(-0.451751\pi\) | ||||
0.151000 | + | 0.988534i | \(0.451751\pi\) | |||||||
\(332\) | −6.48754 | −0.356050 | ||||||||
\(333\) | 1.00000 | 0.0547997 | ||||||||
\(334\) | 3.96114 | 0.216744 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0.400260 | 0.0218360 | ||||||||
\(337\) | −22.4782 | −1.22447 | −0.612234 | − | 0.790677i | \(-0.709729\pi\) | ||||
−0.612234 | + | 0.790677i | \(0.709729\pi\) | |||||||
\(338\) | −9.71737 | −0.528555 | ||||||||
\(339\) | −2.72064 | −0.147765 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 8.93706 | 0.483969 | ||||||||
\(342\) | −17.6569 | −0.954777 | ||||||||
\(343\) | 19.8662 | 1.07267 | ||||||||
\(344\) | −2.60301 | −0.140345 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 12.5379 | 0.674042 | ||||||||
\(347\) | −15.8227 | −0.849407 | −0.424704 | − | 0.905332i | \(-0.639622\pi\) | ||||
−0.424704 | + | 0.905332i | \(0.639622\pi\) | |||||||
\(348\) | 0.162513 | 0.00871161 | ||||||||
\(349\) | −21.7713 | −1.16539 | −0.582695 | − | 0.812691i | \(-0.698002\pi\) | ||||
−0.582695 | + | 0.812691i | \(0.698002\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0.679620 | 0.0362754 | ||||||||
\(352\) | 33.1776 | 1.76837 | ||||||||
\(353\) | −24.1352 | −1.28459 | −0.642293 | − | 0.766459i | \(-0.722017\pi\) | ||||
−0.642293 | + | 0.766459i | \(0.722017\pi\) | |||||||
\(354\) | 1.26758 | 0.0673711 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −20.2495 | −1.07322 | ||||||||
\(357\) | −1.63611 | −0.0865923 | ||||||||
\(358\) | −6.27687 | −0.331743 | ||||||||
\(359\) | 27.7713 | 1.46571 | 0.732856 | − | 0.680384i | \(-0.238187\pi\) | ||||
0.732856 | + | 0.680384i | \(0.238187\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 43.1833 | 2.27281 | ||||||||
\(362\) | −11.5412 | −0.606591 | ||||||||
\(363\) | −5.03062 | −0.264039 | ||||||||
\(364\) | 1.32038 | 0.0692067 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −1.50095 | −0.0784557 | ||||||||
\(367\) | 8.36389 | 0.436591 | 0.218296 | − | 0.975883i | \(-0.429950\pi\) | ||||
0.218296 | + | 0.975883i | \(0.429950\pi\) | |||||||
\(368\) | 6.79398 | 0.354161 | ||||||||
\(369\) | 1.77455 | 0.0923794 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 4.81479 | 0.249971 | ||||||||
\(372\) | 0.536538 | 0.0278182 | ||||||||
\(373\) | −18.3067 | −0.947885 | −0.473943 | − | 0.880556i | \(-0.657170\pi\) | ||||
−0.473943 | + | 0.880556i | \(0.657170\pi\) | |||||||
\(374\) | −15.1672 | −0.784275 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −33.4282 | −1.72393 | ||||||||
\(377\) | 0.228720 | 0.0117797 | ||||||||
\(378\) | −2.10069 | −0.108048 | ||||||||
\(379\) | 1.88891 | 0.0970268 | 0.0485134 | − | 0.998823i | \(-0.484552\pi\) | ||||
0.0485134 | + | 0.998823i | \(0.484552\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −3.88564 | −0.199067 | ||||||||
\(382\) | −13.4555 | −0.688446 | ||||||||
\(383\) | 33.8687 | 1.73061 | 0.865305 | − | 0.501246i | \(-0.167125\pi\) | ||||
0.865305 | + | 0.501246i | \(0.167125\pi\) | |||||||
\(384\) | 2.30533 | 0.117643 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −13.7986 | −0.702332 | ||||||||
\(387\) | −2.94282 | −0.149592 | ||||||||
\(388\) | −13.8856 | −0.704937 | ||||||||
\(389\) | −7.13052 | −0.361532 | −0.180766 | − | 0.983526i | \(-0.557858\pi\) | ||||
−0.180766 | + | 0.983526i | \(0.557858\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −27.7713 | −1.40445 | ||||||||
\(392\) | 8.39588 | 0.424056 | ||||||||
\(393\) | 1.79863 | 0.0907287 | ||||||||
\(394\) | −3.59725 | −0.181227 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 23.6706 | 1.18949 | ||||||||
\(397\) | −1.56991 | −0.0787914 | −0.0393957 | − | 0.999224i | \(-0.512543\pi\) | ||||
−0.0393957 | + | 0.999224i | \(0.512543\pi\) | |||||||
\(398\) | 1.95185 | 0.0978372 | ||||||||
\(399\) | 3.66346 | 0.183402 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 6.89931 | 0.344535 | 0.172268 | − | 0.985050i | \(-0.444891\pi\) | ||||
0.172268 | + | 0.985050i | \(0.444891\pi\) | |||||||
\(402\) | −1.43474 | −0.0715583 | ||||||||
\(403\) | 0.755119 | 0.0376152 | ||||||||
\(404\) | 9.47936 | 0.471616 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −0.706966 | −0.0350861 | ||||||||
\(407\) | −1.92339 | −0.0953389 | ||||||||
\(408\) | −2.19208 | −0.108524 | ||||||||
\(409\) | −24.8421 | −1.22836 | −0.614182 | − | 0.789164i | \(-0.710514\pi\) | ||||
−0.614182 | + | 0.789164i | \(0.710514\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −2.82381 | −0.139288 | ||||||||
\(412\) | 19.5699 | 0.964140 | ||||||||
\(413\) | 13.5354 | 0.666035 | ||||||||
\(414\) | −17.6569 | −0.867790 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 2.80327 | 0.137442 | ||||||||
\(417\) | −2.27936 | −0.111621 | ||||||||
\(418\) | 33.9611 | 1.66109 | ||||||||
\(419\) | −34.6134 | −1.69098 | −0.845488 | − | 0.533994i | \(-0.820690\pi\) | ||||
−0.845488 | + | 0.533994i | \(0.820690\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 14.4509 | 0.704294 | 0.352147 | − | 0.935945i | \(-0.385452\pi\) | ||||
0.352147 | + | 0.935945i | \(0.385452\pi\) | |||||||
\(422\) | −19.3319 | −0.941062 | ||||||||
\(423\) | −37.7921 | −1.83751 | ||||||||
\(424\) | 6.45090 | 0.313283 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 2.40275 | 0.116413 | ||||||||
\(427\) | −16.0273 | −0.775618 | ||||||||
\(428\) | 27.8101 | 1.34425 | ||||||||
\(429\) | −0.647299 | −0.0312519 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −14.2599 | −0.686877 | −0.343438 | − | 0.939175i | \(-0.611592\pi\) | ||||
−0.343438 | + | 0.939175i | \(0.611592\pi\) | |||||||
\(432\) | 1.22434 | 0.0589060 | ||||||||
\(433\) | −22.4750 | −1.08008 | −0.540039 | − | 0.841640i | \(-0.681591\pi\) | ||||
−0.540039 | + | 0.841640i | \(0.681591\pi\) | |||||||
\(434\) | −2.33405 | −0.112038 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −8.60766 | −0.412232 | ||||||||
\(437\) | 62.1833 | 2.97463 | ||||||||
\(438\) | 1.20137 | 0.0574039 | ||||||||
\(439\) | 30.8389 | 1.47186 | 0.735929 | − | 0.677058i | \(-0.236746\pi\) | ||||
0.735929 | + | 0.677058i | \(0.236746\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 9.49192 | 0.451996 | ||||||||
\(442\) | −1.28152 | −0.0609556 | ||||||||
\(443\) | −27.9338 | −1.32717 | −0.663587 | − | 0.748099i | \(-0.730967\pi\) | ||||
−0.663587 | + | 0.748099i | \(0.730967\pi\) | |||||||
\(444\) | −0.115471 | −0.00548001 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −3.04351 | −0.144114 | ||||||||
\(447\) | 1.65692 | 0.0783696 | ||||||||
\(448\) | −5.31711 | −0.251210 | ||||||||
\(449\) | 8.20137 | 0.387047 | 0.193523 | − | 0.981096i | \(-0.438008\pi\) | ||||
0.193523 | + | 0.981096i | \(0.438008\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −3.41315 | −0.160719 | ||||||||
\(452\) | −16.1683 | −0.760491 | ||||||||
\(453\) | −3.01616 | −0.141712 | ||||||||
\(454\) | −3.70697 | −0.173977 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 4.90834 | 0.229854 | ||||||||
\(457\) | 10.1248 | 0.473616 | 0.236808 | − | 0.971556i | \(-0.423899\pi\) | ||||
0.236808 | + | 0.971556i | \(0.423899\pi\) | |||||||
\(458\) | 10.3067 | 0.481601 | ||||||||
\(459\) | −5.00465 | −0.233597 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −16.3606 | −0.761990 | −0.380995 | − | 0.924577i | \(-0.624418\pi\) | ||||
−0.380995 | + | 0.924577i | \(0.624418\pi\) | |||||||
\(462\) | 2.00078 | 0.0930848 | ||||||||
\(463\) | −0.738177 | −0.0343060 | −0.0171530 | − | 0.999853i | \(-0.505460\pi\) | ||||
−0.0171530 | + | 0.999853i | \(0.505460\pi\) | |||||||
\(464\) | 0.412040 | 0.0191285 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 8.62133 | 0.399375 | ||||||||
\(467\) | 11.5426 | 0.534126 | 0.267063 | − | 0.963679i | \(-0.413947\pi\) | ||||
0.267063 | + | 0.963679i | \(0.413947\pi\) | |||||||
\(468\) | 2.00000 | 0.0924500 | ||||||||
\(469\) | −15.3204 | −0.707429 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −0.508080 | −0.0234111 | ||||||||
\(472\) | 18.1349 | 0.834726 | ||||||||
\(473\) | 5.66019 | 0.260256 | ||||||||
\(474\) | −0.558126 | −0.0256356 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −9.72313 | −0.445659 | ||||||||
\(477\) | 7.29303 | 0.333925 | ||||||||
\(478\) | 7.11436 | 0.325403 | ||||||||
\(479\) | 11.3776 | 0.519854 | 0.259927 | − | 0.965628i | \(-0.416302\pi\) | ||||
0.259927 | + | 0.965628i | \(0.416302\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −0.162513 | −0.00740996 | ||||||||
\(482\) | 1.69578 | 0.0772407 | ||||||||
\(483\) | 3.66346 | 0.166693 | ||||||||
\(484\) | −29.8960 | −1.35891 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −4.78822 | −0.217198 | ||||||||
\(487\) | 25.0917 | 1.13701 | 0.568506 | − | 0.822679i | \(-0.307522\pi\) | ||||
0.568506 | + | 0.822679i | \(0.307522\pi\) | |||||||
\(488\) | −21.4736 | −0.972064 | ||||||||
\(489\) | −4.28263 | −0.193667 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 31.3685 | 1.41564 | 0.707821 | − | 0.706392i | \(-0.249678\pi\) | ||||
0.707821 | + | 0.706392i | \(0.249678\pi\) | |||||||
\(492\) | −0.204909 | −0.00923801 | ||||||||
\(493\) | −1.68427 | −0.0758555 | ||||||||
\(494\) | 2.86948 | 0.129104 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 1.36035 | 0.0610816 | ||||||||
\(497\) | 25.6569 | 1.15087 | ||||||||
\(498\) | −0.830619 | −0.0372209 | ||||||||
\(499\) | 18.4991 | 0.828131 | 0.414066 | − | 0.910247i | \(-0.364108\pi\) | ||||
0.414066 | + | 0.910247i | \(0.364108\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −1.24488 | −0.0556172 | ||||||||
\(502\) | −1.28152 | −0.0571970 | ||||||||
\(503\) | 36.8539 | 1.64323 | 0.821617 | − | 0.570039i | \(-0.193072\pi\) | ||||
0.821617 | + | 0.570039i | \(0.193072\pi\) | |||||||
\(504\) | −14.8824 | −0.662913 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 33.9611 | 1.50976 | ||||||||
\(507\) | 3.05391 | 0.135629 | ||||||||
\(508\) | −23.0917 | −1.02453 | ||||||||
\(509\) | −4.98633 | −0.221015 | −0.110508 | − | 0.993875i | \(-0.535248\pi\) | ||||
−0.110508 | + | 0.993875i | \(0.535248\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 12.8285 | 0.567498 | ||||||||
\(512\) | 9.53543 | 0.421410 | ||||||||
\(513\) | 11.2060 | 0.494758 | ||||||||
\(514\) | −2.05718 | −0.0907383 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0.339810 | 0.0149593 | ||||||||
\(517\) | 72.6889 | 3.19685 | ||||||||
\(518\) | 0.502323 | 0.0220708 | ||||||||
\(519\) | −3.94033 | −0.172961 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 6.11436 | 0.267875 | 0.133937 | − | 0.990990i | \(-0.457238\pi\) | ||||
0.133937 | + | 0.990990i | \(0.457238\pi\) | |||||||
\(522\) | −1.07085 | −0.0468700 | ||||||||
\(523\) | −16.9532 | −0.741313 | −0.370656 | − | 0.928770i | \(-0.620867\pi\) | ||||
−0.370656 | + | 0.928770i | \(0.620867\pi\) | |||||||
\(524\) | 10.6889 | 0.466947 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 2.69794 | 0.117636 | ||||||||
\(527\) | −5.56061 | −0.242224 | ||||||||
\(528\) | −1.16611 | −0.0507485 | ||||||||
\(529\) | 39.1833 | 1.70362 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 20.5023 | 0.889725 | ||||||||
\(532\) | 21.7713 | 0.943905 | ||||||||
\(533\) | −0.288387 | −0.0124914 | ||||||||
\(534\) | −2.59261 | −0.112193 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −20.5264 | −0.886605 | ||||||||
\(537\) | 1.97265 | 0.0851263 | ||||||||
\(538\) | 21.4465 | 0.924625 | ||||||||
\(539\) | −18.2567 | −0.786370 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −29.0884 | −1.25061 | −0.625304 | − | 0.780381i | \(-0.715025\pi\) | ||||
−0.625304 | + | 0.780381i | \(0.715025\pi\) | |||||||
\(542\) | −17.1111 | −0.734984 | ||||||||
\(543\) | 3.62709 | 0.155653 | ||||||||
\(544\) | −20.6430 | −0.885061 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0.169052 | 0.00723476 | ||||||||
\(547\) | −20.0000 | −0.855138 | −0.427569 | − | 0.903983i | \(-0.640630\pi\) | ||||
−0.427569 | + | 0.903983i | \(0.640630\pi\) | |||||||
\(548\) | −16.7814 | −0.716867 | ||||||||
\(549\) | −24.2769 | −1.03611 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 3.77128 | 0.160662 | ||||||||
\(552\) | 4.90834 | 0.208913 | ||||||||
\(553\) | −5.95976 | −0.253435 | ||||||||
\(554\) | −4.24488 | −0.180348 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −13.5458 | −0.574471 | ||||||||
\(557\) | −36.0963 | −1.52945 | −0.764725 | − | 0.644357i | \(-0.777125\pi\) | ||||
−0.764725 | + | 0.644357i | \(0.777125\pi\) | |||||||
\(558\) | −3.53543 | −0.149667 | ||||||||
\(559\) | 0.478247 | 0.0202277 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 4.76663 | 0.201247 | ||||||||
\(562\) | 21.7896 | 0.919139 | ||||||||
\(563\) | 7.43474 | 0.313337 | 0.156668 | − | 0.987651i | \(-0.449925\pi\) | ||||
0.156668 | + | 0.987651i | \(0.449925\pi\) | |||||||
\(564\) | 4.36389 | 0.183753 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 9.98195 | 0.419573 | ||||||||
\(567\) | −16.4919 | −0.692596 | ||||||||
\(568\) | 34.3754 | 1.44236 | ||||||||
\(569\) | −5.16035 | −0.216333 | −0.108167 | − | 0.994133i | \(-0.534498\pi\) | ||||
−0.108167 | + | 0.994133i | \(0.534498\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 17.5426 | 0.734133 | 0.367067 | − | 0.930195i | \(-0.380362\pi\) | ||||
0.367067 | + | 0.930195i | \(0.380362\pi\) | |||||||
\(572\) | −3.84678 | −0.160842 | ||||||||
\(573\) | 4.22872 | 0.176657 | ||||||||
\(574\) | 0.891397 | 0.0372062 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −8.05391 | −0.335580 | ||||||||
\(577\) | −19.9130 | −0.828988 | −0.414494 | − | 0.910052i | \(-0.636041\pi\) | ||||
−0.414494 | + | 0.910052i | \(0.636041\pi\) | |||||||
\(578\) | −3.49794 | −0.145495 | ||||||||
\(579\) | 4.33654 | 0.180220 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −8.86948 | −0.367968 | ||||||||
\(582\) | −1.77782 | −0.0736930 | ||||||||
\(583\) | −14.0273 | −0.580953 | ||||||||
\(584\) | 17.1877 | 0.711232 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 8.85365 | 0.365741 | ||||||||
\(587\) | 6.89931 | 0.284765 | 0.142383 | − | 0.989812i | \(-0.454524\pi\) | ||||
0.142383 | + | 0.989812i | \(0.454524\pi\) | |||||||
\(588\) | −1.09604 | −0.0452000 | ||||||||
\(589\) | 12.4509 | 0.513030 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 1.13052 | 0.0465034 | ||||||||
\(592\) | −0.292768 | −0.0120327 | ||||||||
\(593\) | −1.74720 | −0.0717491 | −0.0358745 | − | 0.999356i | \(-0.511422\pi\) | ||||
−0.0358745 | + | 0.999356i | \(0.511422\pi\) | |||||||
\(594\) | 6.12012 | 0.251111 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 9.84678 | 0.403340 | ||||||||
\(597\) | −0.613413 | −0.0251053 | ||||||||
\(598\) | 2.86948 | 0.117342 | ||||||||
\(599\) | 23.2085 | 0.948274 | 0.474137 | − | 0.880451i | \(-0.342760\pi\) | ||||
0.474137 | + | 0.880451i | \(0.342760\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −8.41204 | −0.343134 | −0.171567 | − | 0.985172i | \(-0.554883\pi\) | ||||
−0.171567 | + | 0.985172i | \(0.554883\pi\) | |||||||
\(602\) | −1.47825 | −0.0602488 | ||||||||
\(603\) | −23.2060 | −0.945022 | ||||||||
\(604\) | −17.9245 | −0.729338 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 1.21367 | 0.0493020 | ||||||||
\(607\) | −24.9877 | −1.01422 | −0.507110 | − | 0.861881i | \(-0.669286\pi\) | ||||
−0.507110 | + | 0.861881i | \(0.669286\pi\) | |||||||
\(608\) | 46.2222 | 1.87456 | ||||||||
\(609\) | 0.222181 | 0.00900322 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 6.14171 | 0.248467 | ||||||||
\(612\) | −14.7278 | −0.595335 | ||||||||
\(613\) | −16.0755 | −0.649283 | −0.324642 | − | 0.945837i | \(-0.605244\pi\) | ||||
−0.324642 | + | 0.945837i | \(0.605244\pi\) | |||||||
\(614\) | −5.39588 | −0.217760 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 28.6246 | 1.15332 | ||||||||
\(617\) | 15.2722 | 0.614837 | 0.307418 | − | 0.951574i | \(-0.400535\pi\) | ||||
0.307418 | + | 0.951574i | \(0.400535\pi\) | |||||||
\(618\) | 2.50559 | 0.100790 | ||||||||
\(619\) | 12.8512 | 0.516532 | 0.258266 | − | 0.966074i | \(-0.416849\pi\) | ||||
0.258266 | + | 0.966074i | \(0.416849\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 11.2060 | 0.449682 | ||||||||
\(622\) | 4.20929 | 0.168777 | ||||||||
\(623\) | −27.6843 | −1.10915 | ||||||||
\(624\) | −0.0985283 | −0.00394429 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −14.5699 | −0.582331 | ||||||||
\(627\) | −10.6731 | −0.426242 | ||||||||
\(628\) | −3.01943 | −0.120488 | ||||||||
\(629\) | 1.19673 | 0.0477166 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −0.842133 | −0.0335248 | −0.0167624 | − | 0.999860i | \(-0.505336\pi\) | ||||
−0.0167624 | + | 0.999860i | \(0.505336\pi\) | |||||||
\(632\) | −7.98495 | −0.317624 | ||||||||
\(633\) | 6.07550 | 0.241479 | ||||||||
\(634\) | 9.66346 | 0.383785 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −0.842133 | −0.0333928 | ||||||||
\(637\) | −1.54256 | −0.0611185 | ||||||||
\(638\) | 2.05967 | 0.0815430 | ||||||||
\(639\) | 38.8629 | 1.53739 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 18.1833 | 0.718198 | 0.359099 | − | 0.933299i | \(-0.383084\pi\) | ||||
0.359099 | + | 0.933299i | \(0.383084\pi\) | |||||||
\(642\) | 3.56061 | 0.140526 | ||||||||
\(643\) | 49.3893 | 1.94773 | 0.973863 | − | 0.227137i | \(-0.0729367\pi\) | ||||
0.973863 | + | 0.227137i | \(0.0729367\pi\) | |||||||
\(644\) | 21.7713 | 0.857909 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −21.1305 | −0.831369 | ||||||||
\(647\) | 7.07334 | 0.278082 | 0.139041 | − | 0.990287i | \(-0.455598\pi\) | ||||
0.139041 | + | 0.990287i | \(0.455598\pi\) | |||||||
\(648\) | −22.0960 | −0.868014 | ||||||||
\(649\) | −39.4340 | −1.54792 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0.733531 | 0.0287493 | ||||||||
\(652\) | −25.4509 | −0.996734 | ||||||||
\(653\) | −6.01832 | −0.235515 | −0.117758 | − | 0.993042i | \(-0.537571\pi\) | ||||
−0.117758 | + | 0.993042i | \(0.537571\pi\) | |||||||
\(654\) | −1.10206 | −0.0430941 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −0.519531 | −0.0202843 | ||||||||
\(657\) | 19.4315 | 0.758094 | ||||||||
\(658\) | −18.9838 | −0.740067 | ||||||||
\(659\) | 0.401636 | 0.0156455 | 0.00782276 | − | 0.999969i | \(-0.497510\pi\) | ||||
0.00782276 | + | 0.999969i | \(0.497510\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 36.8662 | 1.43393 | 0.716965 | − | 0.697109i | \(-0.245531\pi\) | ||||
0.716965 | + | 0.697109i | \(0.245531\pi\) | |||||||
\(662\) | 4.18057 | 0.162482 | ||||||||
\(663\) | 0.402747 | 0.0156414 | ||||||||
\(664\) | −11.8834 | −0.461166 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0.760877 | 0.0294834 | ||||||||
\(667\) | 3.77128 | 0.146025 | ||||||||
\(668\) | −7.39810 | −0.286241 | ||||||||
\(669\) | 0.956493 | 0.0369802 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 46.6939 | 1.80260 | ||||||||
\(672\) | 2.72313 | 0.105047 | ||||||||
\(673\) | −48.3333 | −1.86311 | −0.931555 | − | 0.363600i | \(-0.881548\pi\) | ||||
−0.931555 | + | 0.363600i | \(0.881548\pi\) | |||||||
\(674\) | −17.1032 | −0.658790 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 18.1488 | 0.698032 | ||||||||
\(677\) | 31.4796 | 1.20986 | 0.604930 | − | 0.796279i | \(-0.293201\pi\) | ||||
0.604930 | + | 0.796279i | \(0.293201\pi\) | |||||||
\(678\) | −2.07007 | −0.0795006 | ||||||||
\(679\) | −18.9838 | −0.728533 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 1.16500 | 0.0446429 | ||||||||
\(682\) | 6.80000 | 0.260386 | ||||||||
\(683\) | 7.88564 | 0.301736 | 0.150868 | − | 0.988554i | \(-0.451793\pi\) | ||||
0.150868 | + | 0.988554i | \(0.451793\pi\) | |||||||
\(684\) | 32.9773 | 1.26092 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 15.1157 | 0.577122 | ||||||||
\(687\) | −3.23912 | −0.123580 | ||||||||
\(688\) | 0.861564 | 0.0328468 | ||||||||
\(689\) | −1.18521 | −0.0451530 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −30.7759 | −1.17077 | −0.585386 | − | 0.810755i | \(-0.699057\pi\) | ||||
−0.585386 | + | 0.810755i | \(0.699057\pi\) | |||||||
\(692\) | −23.4167 | −0.890169 | ||||||||
\(693\) | 32.3614 | 1.22931 | ||||||||
\(694\) | −12.0391 | −0.456999 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0.297680 | 0.0112835 | ||||||||
\(697\) | 2.12365 | 0.0804391 | ||||||||
\(698\) | −16.5653 | −0.627004 | ||||||||
\(699\) | −2.70945 | −0.102481 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −14.7310 | −0.556384 | −0.278192 | − | 0.960526i | \(-0.589735\pi\) | ||||
−0.278192 | + | 0.960526i | \(0.589735\pi\) | |||||||
\(702\) | 0.517107 | 0.0195170 | ||||||||
\(703\) | −2.67962 | −0.101064 | ||||||||
\(704\) | 15.4908 | 0.583832 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −18.3639 | −0.691134 | ||||||||
\(707\) | 12.9598 | 0.487402 | ||||||||
\(708\) | −2.36742 | −0.0889732 | ||||||||
\(709\) | −24.6238 | −0.924767 | −0.462383 | − | 0.886680i | \(-0.653006\pi\) | ||||
−0.462383 | + | 0.886680i | \(0.653006\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −9.02735 | −0.338552 | ||||||||
\(712\) | −37.0917 | −1.39007 | ||||||||
\(713\) | 12.4509 | 0.466290 | ||||||||
\(714\) | −1.24488 | −0.0465885 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 11.7231 | 0.438114 | ||||||||
\(717\) | −2.23585 | −0.0834995 | ||||||||
\(718\) | 21.1305 | 0.788584 | ||||||||
\(719\) | −41.4315 | −1.54513 | −0.772567 | − | 0.634934i | \(-0.781027\pi\) | ||||
−0.772567 | + | 0.634934i | \(0.781027\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 26.7551 | 0.996413 | ||||||||
\(722\) | 32.8572 | 1.22282 | ||||||||
\(723\) | −0.532939 | −0.0198202 | ||||||||
\(724\) | 21.5551 | 0.801090 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −3.82768 | −0.142058 | ||||||||
\(727\) | −41.4588 | −1.53762 | −0.768811 | − | 0.639476i | \(-0.779151\pi\) | ||||
−0.768811 | + | 0.639476i | \(0.779151\pi\) | |||||||
\(728\) | 2.41858 | 0.0896385 | ||||||||
\(729\) | −23.9611 | −0.887450 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −3.52175 | −0.130257 | ||||||||
\(732\) | 2.80327 | 0.103612 | ||||||||
\(733\) | −24.4120 | −0.901679 | −0.450840 | − | 0.892605i | \(-0.648875\pi\) | ||||
−0.450840 | + | 0.892605i | \(0.648875\pi\) | |||||||
\(734\) | 6.36389 | 0.234895 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 46.2222 | 1.70377 | ||||||||
\(737\) | 44.6342 | 1.64412 | ||||||||
\(738\) | 1.35021 | 0.0497021 | ||||||||
\(739\) | −0.613413 | −0.0225648 | −0.0112824 | − | 0.999936i | \(-0.503591\pi\) | ||||
−0.0112824 | + | 0.999936i | \(0.503591\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −0.901801 | −0.0331285 | ||||||||
\(742\) | 3.66346 | 0.134490 | ||||||||
\(743\) | 38.1182 | 1.39842 | 0.699211 | − | 0.714915i | \(-0.253535\pi\) | ||||
0.699211 | + | 0.714915i | \(0.253535\pi\) | |||||||
\(744\) | 0.982792 | 0.0360309 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −13.9291 | −0.509982 | ||||||||
\(747\) | −13.4347 | −0.491551 | ||||||||
\(748\) | 28.3272 | 1.03575 | ||||||||
\(749\) | 38.0208 | 1.38925 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −8.11436 | −0.296097 | −0.148049 | − | 0.988980i | \(-0.547299\pi\) | ||||
−0.148049 | + | 0.988980i | \(0.547299\pi\) | |||||||
\(752\) | 11.0643 | 0.403474 | ||||||||
\(753\) | 0.402747 | 0.0146769 | ||||||||
\(754\) | 0.174028 | 0.00633771 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 3.92339 | 0.142692 | ||||||||
\(757\) | −32.6044 | −1.18503 | −0.592513 | − | 0.805561i | \(-0.701864\pi\) | ||||
−0.592513 | + | 0.805561i | \(0.701864\pi\) | |||||||
\(758\) | 1.43723 | 0.0522024 | ||||||||
\(759\) | −10.6731 | −0.387408 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 36.0000 | 1.30500 | 0.652499 | − | 0.757789i | \(-0.273720\pi\) | ||||
0.652499 | + | 0.757789i | \(0.273720\pi\) | |||||||
\(762\) | −2.95649 | −0.107102 | ||||||||
\(763\) | −11.7680 | −0.426031 | ||||||||
\(764\) | 25.1305 | 0.909190 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 25.7699 | 0.931104 | ||||||||
\(767\) | −3.33189 | −0.120308 | ||||||||
\(768\) | 3.06294 | 0.110524 | ||||||||
\(769\) | 13.7141 | 0.494543 | 0.247272 | − | 0.968946i | \(-0.420466\pi\) | ||||
0.247272 | + | 0.968946i | \(0.420466\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0.646517 | 0.0232837 | ||||||||
\(772\) | 25.7713 | 0.927529 | ||||||||
\(773\) | 32.2794 | 1.16101 | 0.580504 | − | 0.814257i | \(-0.302856\pi\) | ||||
0.580504 | + | 0.814257i | \(0.302856\pi\) | |||||||
\(774\) | −2.23912 | −0.0804836 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −25.4347 | −0.913054 | ||||||||
\(777\) | −0.157867 | −0.00566344 | ||||||||
\(778\) | −5.42545 | −0.194512 | ||||||||
\(779\) | −4.75512 | −0.170370 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −74.7486 | −2.67471 | ||||||||
\(782\) | −21.1305 | −0.755626 | ||||||||
\(783\) | 0.679620 | 0.0242876 | ||||||||
\(784\) | −2.77893 | −0.0992475 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 1.36853 | 0.0488140 | ||||||||
\(787\) | 43.6777 | 1.55694 | 0.778471 | − | 0.627680i | \(-0.215995\pi\) | ||||
0.778471 | + | 0.627680i | \(0.215995\pi\) | |||||||
\(788\) | 6.71848 | 0.239336 | ||||||||
\(789\) | −0.847890 | −0.0301857 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −22.1046 | −0.785947 | ||||||||
\(792\) | 43.3581 | 1.54066 | ||||||||
\(793\) | 3.94531 | 0.140102 | ||||||||
\(794\) | −1.19451 | −0.0423914 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −3.64541 | −0.129208 | ||||||||
\(797\) | 4.18057 | 0.148083 | 0.0740416 | − | 0.997255i | \(-0.476410\pi\) | ||||
0.0740416 | + | 0.997255i | \(0.476410\pi\) | |||||||
\(798\) | 2.78744 | 0.0986743 | ||||||||
\(799\) | −45.2268 | −1.60001 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −41.9338 | −1.48166 | ||||||||
\(802\) | 5.24953 | 0.185367 | ||||||||
\(803\) | −37.3743 | −1.31891 | ||||||||
\(804\) | 2.67962 | 0.0945029 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0.574553 | 0.0202378 | ||||||||
\(807\) | −6.74007 | −0.237262 | ||||||||
\(808\) | 17.3636 | 0.610850 | ||||||||
\(809\) | −21.0058 | −0.738523 | −0.369262 | − | 0.929326i | \(-0.620389\pi\) | ||||
−0.369262 | + | 0.929326i | \(0.620389\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −3.69578 | −0.129776 | −0.0648882 | − | 0.997893i | \(-0.520669\pi\) | ||||
−0.0648882 | + | 0.997893i | \(0.520669\pi\) | |||||||
\(812\) | 1.32038 | 0.0463362 | ||||||||
\(813\) | 5.37756 | 0.188599 | ||||||||
\(814\) | −1.46346 | −0.0512943 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0.725551 | 0.0253994 | ||||||||
\(817\) | 7.88564 | 0.275884 | ||||||||
\(818\) | −18.9018 | −0.660886 | ||||||||
\(819\) | 2.73431 | 0.0955446 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 31.6673 | 1.10520 | 0.552599 | − | 0.833448i | \(-0.313636\pi\) | ||||
0.552599 | + | 0.833448i | \(0.313636\pi\) | |||||||
\(822\) | −2.14857 | −0.0749401 | ||||||||
\(823\) | −40.8903 | −1.42535 | −0.712673 | − | 0.701497i | \(-0.752516\pi\) | ||||
−0.712673 | + | 0.701497i | \(0.752516\pi\) | |||||||
\(824\) | 35.8468 | 1.24878 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 10.2988 | 0.358341 | ||||||||
\(827\) | 4.07550 | 0.141719 | 0.0708595 | − | 0.997486i | \(-0.477426\pi\) | ||||
0.0708595 | + | 0.997486i | \(0.477426\pi\) | |||||||
\(828\) | 32.9773 | 1.14604 | ||||||||
\(829\) | −23.4074 | −0.812972 | −0.406486 | − | 0.913657i | \(-0.633246\pi\) | ||||
−0.406486 | + | 0.913657i | \(0.633246\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 1.33405 | 0.0462778 | ||||||||
\(832\) | 1.30887 | 0.0453767 | ||||||||
\(833\) | 11.3592 | 0.393574 | ||||||||
\(834\) | −1.73431 | −0.0600543 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −63.4282 | −2.19371 | ||||||||
\(837\) | 2.24377 | 0.0775560 | ||||||||
\(838\) | −26.3365 | −0.909781 | ||||||||
\(839\) | −6.45090 | −0.222710 | −0.111355 | − | 0.993781i | \(-0.535519\pi\) | ||||
−0.111355 | + | 0.993781i | \(0.535519\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.7713 | −0.992113 | ||||||||
\(842\) | 10.9954 | 0.378925 | ||||||||
\(843\) | −6.84789 | −0.235854 | ||||||||
\(844\) | 36.1056 | 1.24281 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −28.7551 | −0.988621 | ||||||||
\(847\) | −40.8726 | −1.40440 | ||||||||
\(848\) | −2.13517 | −0.0733219 | ||||||||
\(849\) | −3.13706 | −0.107664 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −2.67962 | −0.0918562 | ||||||||
\(852\) | −4.48754 | −0.153741 | ||||||||
\(853\) | 9.82597 | 0.336435 | 0.168217 | − | 0.985750i | \(-0.446199\pi\) | ||||
0.168217 | + | 0.985750i | \(0.446199\pi\) | |||||||
\(854\) | −12.1948 | −0.417299 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 50.9407 | 1.74112 | ||||||||
\(857\) | −42.0093 | −1.43501 | −0.717505 | − | 0.696553i | \(-0.754716\pi\) | ||||
−0.717505 | + | 0.696553i | \(0.754716\pi\) | |||||||
\(858\) | −0.492514 | −0.0168142 | ||||||||
\(859\) | −23.0643 | −0.786944 | −0.393472 | − | 0.919337i | \(-0.628726\pi\) | ||||
−0.393472 | + | 0.919337i | \(0.628726\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −0.280142 | −0.00954723 | ||||||||
\(862\) | −10.8500 | −0.369554 | ||||||||
\(863\) | −42.3822 | −1.44271 | −0.721354 | − | 0.692567i | \(-0.756480\pi\) | ||||
−0.721354 | + | 0.692567i | \(0.756480\pi\) | |||||||
\(864\) | 8.32967 | 0.283381 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −17.1007 | −0.581105 | ||||||||
\(867\) | 1.09931 | 0.0373345 | ||||||||
\(868\) | 4.35924 | 0.147962 | ||||||||
\(869\) | 17.3631 | 0.589003 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 3.77128 | 0.127785 | ||||||||
\(872\) | −15.7669 | −0.533935 | ||||||||
\(873\) | −28.7551 | −0.973213 | ||||||||
\(874\) | 47.3138 | 1.60041 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −2.24377 | −0.0758099 | ||||||||
\(877\) | −16.0755 | −0.542831 | −0.271416 | − | 0.962462i | \(-0.587492\pi\) | ||||
−0.271416 | + | 0.962462i | \(0.587492\pi\) | |||||||
\(878\) | 23.4646 | 0.791891 | ||||||||
\(879\) | −2.78247 | −0.0938502 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 2.23121 | 0.0751713 | 0.0375856 | − | 0.999293i | \(-0.488033\pi\) | ||||
0.0375856 | + | 0.999293i | \(0.488033\pi\) | |||||||
\(882\) | 7.22218 | 0.243183 | ||||||||
\(883\) | −52.2977 | −1.75996 | −0.879979 | − | 0.475013i | \(-0.842443\pi\) | ||||
−0.879979 | + | 0.475013i | \(0.842443\pi\) | |||||||
\(884\) | 2.39345 | 0.0805006 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −21.2542 | −0.714048 | ||||||||
\(887\) | −32.4991 | −1.09121 | −0.545606 | − | 0.838042i | \(-0.683700\pi\) | ||||
−0.545606 | + | 0.838042i | \(0.683700\pi\) | |||||||
\(888\) | −0.211511 | −0.00709786 | ||||||||
\(889\) | −31.5699 | −1.05882 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 48.0474 | 1.60965 | ||||||||
\(892\) | 5.68427 | 0.190323 | ||||||||
\(893\) | 101.268 | 3.38882 | ||||||||
\(894\) | 1.26071 | 0.0421645 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 18.7303 | 0.625734 | ||||||||
\(897\) | −0.901801 | −0.0301103 | ||||||||
\(898\) | 6.24023 | 0.208239 | ||||||||
\(899\) | 0.755119 | 0.0251846 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 8.72777 | 0.290764 | ||||||||
\(902\) | −2.59699 | −0.0864702 | ||||||||
\(903\) | 0.464574 | 0.0154600 | ||||||||
\(904\) | −29.6159 | −0.985010 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −2.29493 | −0.0762438 | ||||||||
\(907\) | −7.69578 | −0.255534 | −0.127767 | − | 0.991804i | \(-0.540781\pi\) | ||||
−0.127767 | + | 0.991804i | \(0.540781\pi\) | |||||||
\(908\) | 6.92339 | 0.229761 | ||||||||
\(909\) | 19.6304 | 0.651098 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −31.3412 | −1.03838 | −0.519190 | − | 0.854659i | \(-0.673766\pi\) | ||||
−0.519190 | + | 0.854659i | \(0.673766\pi\) | |||||||
\(912\) | −1.62460 | −0.0537958 | ||||||||
\(913\) | 25.8402 | 0.855187 | ||||||||
\(914\) | 7.70370 | 0.254816 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −19.2495 | −0.636022 | ||||||||
\(917\) | 14.6134 | 0.482577 | ||||||||
\(918\) | −3.80792 | −0.125680 | ||||||||
\(919\) | −16.9784 | −0.560066 | −0.280033 | − | 0.959990i | \(-0.590345\pi\) | ||||
−0.280033 | + | 0.959990i | \(0.590345\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 1.69578 | 0.0558779 | ||||||||
\(922\) | −12.4484 | −0.409967 | ||||||||
\(923\) | −6.31573 | −0.207885 | ||||||||
\(924\) | −3.73680 | −0.122932 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −0.561662 | −0.0184573 | ||||||||
\(927\) | 40.5264 | 1.33106 | ||||||||
\(928\) | 2.80327 | 0.0920219 | ||||||||
\(929\) | −50.3847 | −1.65307 | −0.826534 | − | 0.562887i | \(-0.809691\pi\) | ||||
−0.826534 | + | 0.562887i | \(0.809691\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −25.4347 | −0.833590 | ||||||||
\(932\) | −16.1018 | −0.527432 | ||||||||
\(933\) | −1.32287 | −0.0433087 | ||||||||
\(934\) | 8.78247 | 0.287371 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 3.66346 | 0.119744 | ||||||||
\(937\) | −27.1488 | −0.886914 | −0.443457 | − | 0.896296i | \(-0.646248\pi\) | ||||
−0.443457 | + | 0.896296i | \(0.646248\pi\) | |||||||
\(938\) | −11.6569 | −0.380612 | ||||||||
\(939\) | 4.57893 | 0.149428 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −0.640760 | −0.0208882 | −0.0104441 | − | 0.999945i | \(-0.503325\pi\) | ||||
−0.0104441 | + | 0.999945i | \(0.503325\pi\) | |||||||
\(942\) | −0.386587 | −0.0125957 | ||||||||
\(943\) | −4.75512 | −0.154848 | ||||||||
\(944\) | −6.00242 | −0.195362 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 4.30671 | 0.140023 | ||||||||
\(947\) | −30.5587 | −0.993025 | −0.496513 | − | 0.868030i | \(-0.665386\pi\) | ||||
−0.496513 | + | 0.868030i | \(0.665386\pi\) | |||||||
\(948\) | 1.04240 | 0.0338554 | ||||||||
\(949\) | −3.15787 | −0.102509 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −3.03697 | −0.0984804 | ||||||||
\(952\) | −17.8101 | −0.577230 | ||||||||
\(953\) | −20.4484 | −0.662389 | −0.331195 | − | 0.943562i | \(-0.607452\pi\) | ||||
−0.331195 | + | 0.943562i | \(0.607452\pi\) | |||||||
\(954\) | 5.54910 | 0.179659 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −13.2873 | −0.429741 | ||||||||
\(957\) | −0.647299 | −0.0209242 | ||||||||
\(958\) | 8.65692 | 0.279692 | ||||||||
\(959\) | −22.9428 | −0.740862 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −28.5070 | −0.919580 | ||||||||
\(962\) | −0.123652 | −0.00398671 | ||||||||
\(963\) | 57.5907 | 1.85583 | ||||||||
\(964\) | −3.16716 | −0.102007 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 2.78744 | 0.0896844 | ||||||||
\(967\) | −13.6181 | −0.437927 | −0.218964 | − | 0.975733i | \(-0.570268\pi\) | ||||
−0.218964 | + | 0.975733i | \(0.570268\pi\) | |||||||
\(968\) | −54.7615 | −1.76010 | ||||||||
\(969\) | 6.64076 | 0.213332 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 17.5789 | 0.564135 | 0.282067 | − | 0.959395i | \(-0.408980\pi\) | ||||
0.282067 | + | 0.959395i | \(0.408980\pi\) | |||||||
\(972\) | 8.94282 | 0.286841 | ||||||||
\(973\) | −18.5193 | −0.593700 | ||||||||
\(974\) | 19.0917 | 0.611736 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 7.10749 | 0.227505 | ||||||||
\(977\) | −32.7004 | −1.04618 | −0.523090 | − | 0.852278i | \(-0.675221\pi\) | ||||
−0.523090 | + | 0.852278i | \(0.675221\pi\) | |||||||
\(978\) | −3.25855 | −0.104197 | ||||||||
\(979\) | 80.6550 | 2.57775 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −17.8252 | −0.569115 | ||||||||
\(982\) | 23.8676 | 0.761645 | ||||||||
\(983\) | 29.1819 | 0.930759 | 0.465380 | − | 0.885111i | \(-0.345918\pi\) | ||||
0.465380 | + | 0.885111i | \(0.345918\pi\) | |||||||
\(984\) | −0.375338 | −0.0119653 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −1.28152 | −0.0408119 | ||||||||
\(987\) | 5.96611 | 0.189904 | ||||||||
\(988\) | −5.35924 | −0.170500 | ||||||||
\(989\) | 7.88564 | 0.250749 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −3.58796 | −0.113975 | −0.0569877 | − | 0.998375i | \(-0.518150\pi\) | ||||
−0.0569877 | + | 0.998375i | \(0.518150\pi\) | |||||||
\(992\) | 9.25502 | 0.293847 | ||||||||
\(993\) | −1.31384 | −0.0416935 | ||||||||
\(994\) | 19.5218 | 0.619192 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 1.55132 | 0.0491555 | ||||||||
\(997\) | 31.8889 | 1.00993 | 0.504966 | − | 0.863139i | \(-0.331505\pi\) | ||||
0.504966 | + | 0.863139i | \(0.331505\pi\) | |||||||
\(998\) | 14.0755 | 0.445552 | ||||||||
\(999\) | −0.482893 | −0.0152781 |
(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 | 1075.2.a.l.1.2 | 3 | ||
3.2 | odd | 2 | 9675.2.a.bp.1.2 | 3 | |||
5.2 | odd | 4 | 1075.2.b.g.474.4 | 6 | |||
5.3 | odd | 4 | 1075.2.b.g.474.3 | 6 | |||
5.4 | even | 2 | 215.2.a.b.1.2 | ✓ | 3 | ||
15.14 | odd | 2 | 1935.2.a.r.1.2 | 3 | |||
20.19 | odd | 2 | 3440.2.a.l.1.2 | 3 | |||
215.214 | odd | 2 | 9245.2.a.h.1.2 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
215.2.a.b.1.2 | ✓ | 3 | 5.4 | even | 2 | ||
1075.2.a.l.1.2 | 3 | 1.1 | even | 1 | trivial | ||
1075.2.b.g.474.3 | 6 | 5.3 | odd | 4 | |||
1075.2.b.g.474.4 | 6 | 5.2 | odd | 4 | |||
1935.2.a.r.1.2 | 3 | 15.14 | odd | 2 | |||
3440.2.a.l.1.2 | 3 | 20.19 | odd | 2 | |||
9245.2.a.h.1.2 | 3 | 215.214 | odd | 2 | |||
9675.2.a.bp.1.2 | 3 | 3.2 | odd | 2 |