Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6010,2,Mod(1,6010)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6010, 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("6010.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6010 = 2 \cdot 5 \cdot 601 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6010.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: | \(47.9900916148\) |
Analytic rank: | \(1\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 8 x^{15} + 9 x^{14} + 75 x^{13} - 178 x^{12} - 232 x^{11} + 872 x^{10} + 228 x^{9} - 1986 x^{8} + \cdots - 10 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.10 | ||
Root | \(1.27770\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6010.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | 0.277700 | 0.160330 | 0.0801651 | − | 0.996782i | \(-0.474455\pi\) | ||||
0.0801651 | + | 0.996782i | \(0.474455\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 0.277700 | 0.113371 | ||||||||
\(7\) | 2.55233 | 0.964689 | 0.482344 | − | 0.875982i | \(-0.339785\pi\) | ||||
0.482344 | + | 0.875982i | \(0.339785\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | −2.92288 | −0.974294 | ||||||||
\(10\) | 1.00000 | 0.316228 | ||||||||
\(11\) | −4.94159 | −1.48995 | −0.744973 | − | 0.667094i | \(-0.767538\pi\) | ||||
−0.744973 | + | 0.667094i | \(0.767538\pi\) | |||||||
\(12\) | 0.277700 | 0.0801651 | ||||||||
\(13\) | 4.28763 | 1.18918 | 0.594588 | − | 0.804031i | \(-0.297315\pi\) | ||||
0.594588 | + | 0.804031i | \(0.297315\pi\) | |||||||
\(14\) | 2.55233 | 0.682138 | ||||||||
\(15\) | 0.277700 | 0.0717019 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −3.28799 | −0.797455 | −0.398727 | − | 0.917070i | \(-0.630548\pi\) | ||||
−0.398727 | + | 0.917070i | \(0.630548\pi\) | |||||||
\(18\) | −2.92288 | −0.688930 | ||||||||
\(19\) | −3.94209 | −0.904377 | −0.452189 | − | 0.891922i | \(-0.649357\pi\) | ||||
−0.452189 | + | 0.891922i | \(0.649357\pi\) | |||||||
\(20\) | 1.00000 | 0.223607 | ||||||||
\(21\) | 0.708781 | 0.154669 | ||||||||
\(22\) | −4.94159 | −1.05355 | ||||||||
\(23\) | −6.03884 | −1.25918 | −0.629592 | − | 0.776926i | \(-0.716778\pi\) | ||||
−0.629592 | + | 0.776926i | \(0.716778\pi\) | |||||||
\(24\) | 0.277700 | 0.0566853 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 4.28763 | 0.840874 | ||||||||
\(27\) | −1.64479 | −0.316539 | ||||||||
\(28\) | 2.55233 | 0.482344 | ||||||||
\(29\) | −7.47038 | −1.38721 | −0.693607 | − | 0.720353i | \(-0.743980\pi\) | ||||
−0.693607 | + | 0.720353i | \(0.743980\pi\) | |||||||
\(30\) | 0.277700 | 0.0507009 | ||||||||
\(31\) | −4.60144 | −0.826443 | −0.413222 | − | 0.910630i | \(-0.635597\pi\) | ||||
−0.413222 | + | 0.910630i | \(0.635597\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | −1.37228 | −0.238884 | ||||||||
\(34\) | −3.28799 | −0.563886 | ||||||||
\(35\) | 2.55233 | 0.431422 | ||||||||
\(36\) | −2.92288 | −0.487147 | ||||||||
\(37\) | −1.65521 | −0.272115 | −0.136058 | − | 0.990701i | \(-0.543443\pi\) | ||||
−0.136058 | + | 0.990701i | \(0.543443\pi\) | |||||||
\(38\) | −3.94209 | −0.639491 | ||||||||
\(39\) | 1.19068 | 0.190661 | ||||||||
\(40\) | 1.00000 | 0.158114 | ||||||||
\(41\) | −8.01358 | −1.25151 | −0.625755 | − | 0.780019i | \(-0.715209\pi\) | ||||
−0.625755 | + | 0.780019i | \(0.715209\pi\) | |||||||
\(42\) | 0.708781 | 0.109367 | ||||||||
\(43\) | 1.78175 | 0.271715 | 0.135857 | − | 0.990728i | \(-0.456621\pi\) | ||||
0.135857 | + | 0.990728i | \(0.456621\pi\) | |||||||
\(44\) | −4.94159 | −0.744973 | ||||||||
\(45\) | −2.92288 | −0.435718 | ||||||||
\(46\) | −6.03884 | −0.890378 | ||||||||
\(47\) | −3.33231 | −0.486068 | −0.243034 | − | 0.970018i | \(-0.578143\pi\) | ||||
−0.243034 | + | 0.970018i | \(0.578143\pi\) | |||||||
\(48\) | 0.277700 | 0.0400826 | ||||||||
\(49\) | −0.485632 | −0.0693761 | ||||||||
\(50\) | 1.00000 | 0.141421 | ||||||||
\(51\) | −0.913075 | −0.127856 | ||||||||
\(52\) | 4.28763 | 0.594588 | ||||||||
\(53\) | −8.76375 | −1.20379 | −0.601896 | − | 0.798574i | \(-0.705588\pi\) | ||||
−0.601896 | + | 0.798574i | \(0.705588\pi\) | |||||||
\(54\) | −1.64479 | −0.223827 | ||||||||
\(55\) | −4.94159 | −0.666324 | ||||||||
\(56\) | 2.55233 | 0.341069 | ||||||||
\(57\) | −1.09472 | −0.144999 | ||||||||
\(58\) | −7.47038 | −0.980909 | ||||||||
\(59\) | 6.61220 | 0.860836 | 0.430418 | − | 0.902630i | \(-0.358366\pi\) | ||||
0.430418 | + | 0.902630i | \(0.358366\pi\) | |||||||
\(60\) | 0.277700 | 0.0358509 | ||||||||
\(61\) | 10.0369 | 1.28509 | 0.642547 | − | 0.766246i | \(-0.277878\pi\) | ||||
0.642547 | + | 0.766246i | \(0.277878\pi\) | |||||||
\(62\) | −4.60144 | −0.584384 | ||||||||
\(63\) | −7.46015 | −0.939890 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 4.28763 | 0.531816 | ||||||||
\(66\) | −1.37228 | −0.168916 | ||||||||
\(67\) | −5.12837 | −0.626530 | −0.313265 | − | 0.949666i | \(-0.601423\pi\) | ||||
−0.313265 | + | 0.949666i | \(0.601423\pi\) | |||||||
\(68\) | −3.28799 | −0.398727 | ||||||||
\(69\) | −1.67699 | −0.201885 | ||||||||
\(70\) | 2.55233 | 0.305061 | ||||||||
\(71\) | 2.50077 | 0.296787 | 0.148394 | − | 0.988928i | \(-0.452590\pi\) | ||||
0.148394 | + | 0.988928i | \(0.452590\pi\) | |||||||
\(72\) | −2.92288 | −0.344465 | ||||||||
\(73\) | 2.44565 | 0.286241 | 0.143121 | − | 0.989705i | \(-0.454286\pi\) | ||||
0.143121 | + | 0.989705i | \(0.454286\pi\) | |||||||
\(74\) | −1.65521 | −0.192415 | ||||||||
\(75\) | 0.277700 | 0.0320661 | ||||||||
\(76\) | −3.94209 | −0.452189 | ||||||||
\(77\) | −12.6126 | −1.43733 | ||||||||
\(78\) | 1.19068 | 0.134818 | ||||||||
\(79\) | 10.1143 | 1.13795 | 0.568975 | − | 0.822355i | \(-0.307340\pi\) | ||||
0.568975 | + | 0.822355i | \(0.307340\pi\) | |||||||
\(80\) | 1.00000 | 0.111803 | ||||||||
\(81\) | 8.31189 | 0.923543 | ||||||||
\(82\) | −8.01358 | −0.884952 | ||||||||
\(83\) | 1.46001 | 0.160257 | 0.0801287 | − | 0.996785i | \(-0.474467\pi\) | ||||
0.0801287 | + | 0.996785i | \(0.474467\pi\) | |||||||
\(84\) | 0.708781 | 0.0773344 | ||||||||
\(85\) | −3.28799 | −0.356633 | ||||||||
\(86\) | 1.78175 | 0.192131 | ||||||||
\(87\) | −2.07453 | −0.222412 | ||||||||
\(88\) | −4.94159 | −0.526776 | ||||||||
\(89\) | −7.59665 | −0.805243 | −0.402622 | − | 0.915367i | \(-0.631901\pi\) | ||||
−0.402622 | + | 0.915367i | \(0.631901\pi\) | |||||||
\(90\) | −2.92288 | −0.308099 | ||||||||
\(91\) | 10.9434 | 1.14718 | ||||||||
\(92\) | −6.03884 | −0.629592 | ||||||||
\(93\) | −1.27782 | −0.132504 | ||||||||
\(94\) | −3.33231 | −0.343702 | ||||||||
\(95\) | −3.94209 | −0.404450 | ||||||||
\(96\) | 0.277700 | 0.0283427 | ||||||||
\(97\) | −0.655528 | −0.0665588 | −0.0332794 | − | 0.999446i | \(-0.510595\pi\) | ||||
−0.0332794 | + | 0.999446i | \(0.510595\pi\) | |||||||
\(98\) | −0.485632 | −0.0490563 | ||||||||
\(99\) | 14.4437 | 1.45165 | ||||||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | −6.14651 | −0.611601 | −0.305800 | − | 0.952096i | \(-0.598924\pi\) | ||||
−0.305800 | + | 0.952096i | \(0.598924\pi\) | |||||||
\(102\) | −0.913075 | −0.0904079 | ||||||||
\(103\) | −2.00406 | −0.197465 | −0.0987327 | − | 0.995114i | \(-0.531479\pi\) | ||||
−0.0987327 | + | 0.995114i | \(0.531479\pi\) | |||||||
\(104\) | 4.28763 | 0.420437 | ||||||||
\(105\) | 0.708781 | 0.0691700 | ||||||||
\(106\) | −8.76375 | −0.851210 | ||||||||
\(107\) | −5.83270 | −0.563869 | −0.281934 | − | 0.959434i | \(-0.590976\pi\) | ||||
−0.281934 | + | 0.959434i | \(0.590976\pi\) | |||||||
\(108\) | −1.64479 | −0.158270 | ||||||||
\(109\) | 2.38596 | 0.228534 | 0.114267 | − | 0.993450i | \(-0.463548\pi\) | ||||
0.114267 | + | 0.993450i | \(0.463548\pi\) | |||||||
\(110\) | −4.94159 | −0.471162 | ||||||||
\(111\) | −0.459653 | −0.0436283 | ||||||||
\(112\) | 2.55233 | 0.241172 | ||||||||
\(113\) | 2.53256 | 0.238243 | 0.119121 | − | 0.992880i | \(-0.461992\pi\) | ||||
0.119121 | + | 0.992880i | \(0.461992\pi\) | |||||||
\(114\) | −1.09472 | −0.102530 | ||||||||
\(115\) | −6.03884 | −0.563125 | ||||||||
\(116\) | −7.47038 | −0.693607 | ||||||||
\(117\) | −12.5323 | −1.15861 | ||||||||
\(118\) | 6.61220 | 0.608703 | ||||||||
\(119\) | −8.39202 | −0.769295 | ||||||||
\(120\) | 0.277700 | 0.0253504 | ||||||||
\(121\) | 13.4193 | 1.21994 | ||||||||
\(122\) | 10.0369 | 0.908699 | ||||||||
\(123\) | −2.22537 | −0.200655 | ||||||||
\(124\) | −4.60144 | −0.413222 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | −7.46015 | −0.664603 | ||||||||
\(127\) | 4.39330 | 0.389842 | 0.194921 | − | 0.980819i | \(-0.437555\pi\) | ||||
0.194921 | + | 0.980819i | \(0.437555\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 0.494793 | 0.0435641 | ||||||||
\(130\) | 4.28763 | 0.376050 | ||||||||
\(131\) | 12.5579 | 1.09719 | 0.548596 | − | 0.836087i | \(-0.315162\pi\) | ||||
0.548596 | + | 0.836087i | \(0.315162\pi\) | |||||||
\(132\) | −1.37228 | −0.119442 | ||||||||
\(133\) | −10.0615 | −0.872442 | ||||||||
\(134\) | −5.12837 | −0.443024 | ||||||||
\(135\) | −1.64479 | −0.141561 | ||||||||
\(136\) | −3.28799 | −0.281943 | ||||||||
\(137\) | 6.12044 | 0.522905 | 0.261452 | − | 0.965216i | \(-0.415799\pi\) | ||||
0.261452 | + | 0.965216i | \(0.415799\pi\) | |||||||
\(138\) | −1.67699 | −0.142755 | ||||||||
\(139\) | 8.54580 | 0.724846 | 0.362423 | − | 0.932014i | \(-0.381950\pi\) | ||||
0.362423 | + | 0.932014i | \(0.381950\pi\) | |||||||
\(140\) | 2.55233 | 0.215711 | ||||||||
\(141\) | −0.925383 | −0.0779313 | ||||||||
\(142\) | 2.50077 | 0.209860 | ||||||||
\(143\) | −21.1877 | −1.77181 | ||||||||
\(144\) | −2.92288 | −0.243574 | ||||||||
\(145\) | −7.47038 | −0.620381 | ||||||||
\(146\) | 2.44565 | 0.202403 | ||||||||
\(147\) | −0.134860 | −0.0111231 | ||||||||
\(148\) | −1.65521 | −0.136058 | ||||||||
\(149\) | 4.25428 | 0.348524 | 0.174262 | − | 0.984699i | \(-0.444246\pi\) | ||||
0.174262 | + | 0.984699i | \(0.444246\pi\) | |||||||
\(150\) | 0.277700 | 0.0226741 | ||||||||
\(151\) | −1.20287 | −0.0978879 | −0.0489440 | − | 0.998802i | \(-0.515586\pi\) | ||||
−0.0489440 | + | 0.998802i | \(0.515586\pi\) | |||||||
\(152\) | −3.94209 | −0.319746 | ||||||||
\(153\) | 9.61041 | 0.776955 | ||||||||
\(154\) | −12.6126 | −1.01635 | ||||||||
\(155\) | −4.60144 | −0.369597 | ||||||||
\(156\) | 1.19068 | 0.0953304 | ||||||||
\(157\) | −10.1536 | −0.810349 | −0.405175 | − | 0.914239i | \(-0.632789\pi\) | ||||
−0.405175 | + | 0.914239i | \(0.632789\pi\) | |||||||
\(158\) | 10.1143 | 0.804652 | ||||||||
\(159\) | −2.43369 | −0.193004 | ||||||||
\(160\) | 1.00000 | 0.0790569 | ||||||||
\(161\) | −15.4131 | −1.21472 | ||||||||
\(162\) | 8.31189 | 0.653044 | ||||||||
\(163\) | −7.04820 | −0.552058 | −0.276029 | − | 0.961149i | \(-0.589019\pi\) | ||||
−0.276029 | + | 0.961149i | \(0.589019\pi\) | |||||||
\(164\) | −8.01358 | −0.625755 | ||||||||
\(165\) | −1.37228 | −0.106832 | ||||||||
\(166\) | 1.46001 | 0.113319 | ||||||||
\(167\) | 13.1292 | 1.01597 | 0.507984 | − | 0.861367i | \(-0.330391\pi\) | ||||
0.507984 | + | 0.861367i | \(0.330391\pi\) | |||||||
\(168\) | 0.708781 | 0.0546837 | ||||||||
\(169\) | 5.38380 | 0.414139 | ||||||||
\(170\) | −3.28799 | −0.252177 | ||||||||
\(171\) | 11.5223 | 0.881129 | ||||||||
\(172\) | 1.78175 | 0.135857 | ||||||||
\(173\) | 9.66095 | 0.734508 | 0.367254 | − | 0.930121i | \(-0.380298\pi\) | ||||
0.367254 | + | 0.930121i | \(0.380298\pi\) | |||||||
\(174\) | −2.07453 | −0.157269 | ||||||||
\(175\) | 2.55233 | 0.192938 | ||||||||
\(176\) | −4.94159 | −0.372487 | ||||||||
\(177\) | 1.83621 | 0.138018 | ||||||||
\(178\) | −7.59665 | −0.569393 | ||||||||
\(179\) | −12.4660 | −0.931756 | −0.465878 | − | 0.884849i | \(-0.654261\pi\) | ||||
−0.465878 | + | 0.884849i | \(0.654261\pi\) | |||||||
\(180\) | −2.92288 | −0.217859 | ||||||||
\(181\) | −5.60337 | −0.416495 | −0.208248 | − | 0.978076i | \(-0.566776\pi\) | ||||
−0.208248 | + | 0.978076i | \(0.566776\pi\) | |||||||
\(182\) | 10.9434 | 0.811182 | ||||||||
\(183\) | 2.78725 | 0.206039 | ||||||||
\(184\) | −6.03884 | −0.445189 | ||||||||
\(185\) | −1.65521 | −0.121694 | ||||||||
\(186\) | −1.27782 | −0.0936944 | ||||||||
\(187\) | 16.2479 | 1.18816 | ||||||||
\(188\) | −3.33231 | −0.243034 | ||||||||
\(189\) | −4.19803 | −0.305362 | ||||||||
\(190\) | −3.94209 | −0.285989 | ||||||||
\(191\) | 13.5010 | 0.976895 | 0.488448 | − | 0.872593i | \(-0.337563\pi\) | ||||
0.488448 | + | 0.872593i | \(0.337563\pi\) | |||||||
\(192\) | 0.277700 | 0.0200413 | ||||||||
\(193\) | 0.481989 | 0.0346943 | 0.0173472 | − | 0.999850i | \(-0.494478\pi\) | ||||
0.0173472 | + | 0.999850i | \(0.494478\pi\) | |||||||
\(194\) | −0.655528 | −0.0470642 | ||||||||
\(195\) | 1.19068 | 0.0852661 | ||||||||
\(196\) | −0.485632 | −0.0346880 | ||||||||
\(197\) | −9.40948 | −0.670397 | −0.335199 | − | 0.942147i | \(-0.608803\pi\) | ||||
−0.335199 | + | 0.942147i | \(0.608803\pi\) | |||||||
\(198\) | 14.4437 | 1.02647 | ||||||||
\(199\) | 18.8322 | 1.33498 | 0.667490 | − | 0.744619i | \(-0.267369\pi\) | ||||
0.667490 | + | 0.744619i | \(0.267369\pi\) | |||||||
\(200\) | 1.00000 | 0.0707107 | ||||||||
\(201\) | −1.42415 | −0.100452 | ||||||||
\(202\) | −6.14651 | −0.432467 | ||||||||
\(203\) | −19.0668 | −1.33823 | ||||||||
\(204\) | −0.913075 | −0.0639281 | ||||||||
\(205\) | −8.01358 | −0.559693 | ||||||||
\(206\) | −2.00406 | −0.139629 | ||||||||
\(207\) | 17.6508 | 1.22682 | ||||||||
\(208\) | 4.28763 | 0.297294 | ||||||||
\(209\) | 19.4802 | 1.34747 | ||||||||
\(210\) | 0.708781 | 0.0489106 | ||||||||
\(211\) | −0.421081 | −0.0289884 | −0.0144942 | − | 0.999895i | \(-0.504614\pi\) | ||||
−0.0144942 | + | 0.999895i | \(0.504614\pi\) | |||||||
\(212\) | −8.76375 | −0.601896 | ||||||||
\(213\) | 0.694465 | 0.0475840 | ||||||||
\(214\) | −5.83270 | −0.398715 | ||||||||
\(215\) | 1.78175 | 0.121514 | ||||||||
\(216\) | −1.64479 | −0.111913 | ||||||||
\(217\) | −11.7444 | −0.797260 | ||||||||
\(218\) | 2.38596 | 0.161598 | ||||||||
\(219\) | 0.679157 | 0.0458932 | ||||||||
\(220\) | −4.94159 | −0.333162 | ||||||||
\(221\) | −14.0977 | −0.948314 | ||||||||
\(222\) | −0.459653 | −0.0308499 | ||||||||
\(223\) | 7.75783 | 0.519503 | 0.259751 | − | 0.965676i | \(-0.416359\pi\) | ||||
0.259751 | + | 0.965676i | \(0.416359\pi\) | |||||||
\(224\) | 2.55233 | 0.170534 | ||||||||
\(225\) | −2.92288 | −0.194859 | ||||||||
\(226\) | 2.53256 | 0.168463 | ||||||||
\(227\) | −1.26402 | −0.0838958 | −0.0419479 | − | 0.999120i | \(-0.513356\pi\) | ||||
−0.0419479 | + | 0.999120i | \(0.513356\pi\) | |||||||
\(228\) | −1.09472 | −0.0724995 | ||||||||
\(229\) | 17.1590 | 1.13390 | 0.566950 | − | 0.823752i | \(-0.308123\pi\) | ||||
0.566950 | + | 0.823752i | \(0.308123\pi\) | |||||||
\(230\) | −6.03884 | −0.398189 | ||||||||
\(231\) | −3.50251 | −0.230448 | ||||||||
\(232\) | −7.47038 | −0.490454 | ||||||||
\(233\) | −11.0937 | −0.726769 | −0.363385 | − | 0.931639i | \(-0.618379\pi\) | ||||
−0.363385 | + | 0.931639i | \(0.618379\pi\) | |||||||
\(234\) | −12.5323 | −0.819259 | ||||||||
\(235\) | −3.33231 | −0.217376 | ||||||||
\(236\) | 6.61220 | 0.430418 | ||||||||
\(237\) | 2.80875 | 0.182448 | ||||||||
\(238\) | −8.39202 | −0.543974 | ||||||||
\(239\) | −12.0870 | −0.781845 | −0.390922 | − | 0.920424i | \(-0.627844\pi\) | ||||
−0.390922 | + | 0.920424i | \(0.627844\pi\) | |||||||
\(240\) | 0.277700 | 0.0179255 | ||||||||
\(241\) | −25.6218 | −1.65044 | −0.825222 | − | 0.564809i | \(-0.808950\pi\) | ||||
−0.825222 | + | 0.564809i | \(0.808950\pi\) | |||||||
\(242\) | 13.4193 | 0.862628 | ||||||||
\(243\) | 7.24257 | 0.464611 | ||||||||
\(244\) | 10.0369 | 0.642547 | ||||||||
\(245\) | −0.485632 | −0.0310259 | ||||||||
\(246\) | −2.22537 | −0.141885 | ||||||||
\(247\) | −16.9022 | −1.07546 | ||||||||
\(248\) | −4.60144 | −0.292192 | ||||||||
\(249\) | 0.405446 | 0.0256941 | ||||||||
\(250\) | 1.00000 | 0.0632456 | ||||||||
\(251\) | −18.7449 | −1.18317 | −0.591583 | − | 0.806244i | \(-0.701497\pi\) | ||||
−0.591583 | + | 0.806244i | \(0.701497\pi\) | |||||||
\(252\) | −7.46015 | −0.469945 | ||||||||
\(253\) | 29.8415 | 1.87612 | ||||||||
\(254\) | 4.39330 | 0.275660 | ||||||||
\(255\) | −0.913075 | −0.0571790 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −11.5427 | −0.720015 | −0.360008 | − | 0.932949i | \(-0.617226\pi\) | ||||
−0.360008 | + | 0.932949i | \(0.617226\pi\) | |||||||
\(258\) | 0.494793 | 0.0308045 | ||||||||
\(259\) | −4.22464 | −0.262506 | ||||||||
\(260\) | 4.28763 | 0.265908 | ||||||||
\(261\) | 21.8350 | 1.35156 | ||||||||
\(262\) | 12.5579 | 0.775832 | ||||||||
\(263\) | −1.04321 | −0.0643271 | −0.0321635 | − | 0.999483i | \(-0.510240\pi\) | ||||
−0.0321635 | + | 0.999483i | \(0.510240\pi\) | |||||||
\(264\) | −1.37228 | −0.0844581 | ||||||||
\(265\) | −8.76375 | −0.538353 | ||||||||
\(266\) | −10.0615 | −0.616910 | ||||||||
\(267\) | −2.10959 | −0.129105 | ||||||||
\(268\) | −5.12837 | −0.313265 | ||||||||
\(269\) | 2.08721 | 0.127260 | 0.0636299 | − | 0.997974i | \(-0.479732\pi\) | ||||
0.0636299 | + | 0.997974i | \(0.479732\pi\) | |||||||
\(270\) | −1.64479 | −0.100098 | ||||||||
\(271\) | 32.6766 | 1.98496 | 0.992480 | − | 0.122405i | \(-0.0390607\pi\) | ||||
0.992480 | + | 0.122405i | \(0.0390607\pi\) | |||||||
\(272\) | −3.28799 | −0.199364 | ||||||||
\(273\) | 3.03900 | 0.183928 | ||||||||
\(274\) | 6.12044 | 0.369749 | ||||||||
\(275\) | −4.94159 | −0.297989 | ||||||||
\(276\) | −1.67699 | −0.100943 | ||||||||
\(277\) | −22.1396 | −1.33024 | −0.665120 | − | 0.746737i | \(-0.731620\pi\) | ||||
−0.665120 | + | 0.746737i | \(0.731620\pi\) | |||||||
\(278\) | 8.54580 | 0.512543 | ||||||||
\(279\) | 13.4495 | 0.805199 | ||||||||
\(280\) | 2.55233 | 0.152531 | ||||||||
\(281\) | 8.01321 | 0.478028 | 0.239014 | − | 0.971016i | \(-0.423176\pi\) | ||||
0.239014 | + | 0.971016i | \(0.423176\pi\) | |||||||
\(282\) | −0.925383 | −0.0551058 | ||||||||
\(283\) | 23.1815 | 1.37799 | 0.688997 | − | 0.724764i | \(-0.258051\pi\) | ||||
0.688997 | + | 0.724764i | \(0.258051\pi\) | |||||||
\(284\) | 2.50077 | 0.148394 | ||||||||
\(285\) | −1.09472 | −0.0648455 | ||||||||
\(286\) | −21.1877 | −1.25286 | ||||||||
\(287\) | −20.4533 | −1.20732 | ||||||||
\(288\) | −2.92288 | −0.172233 | ||||||||
\(289\) | −6.18912 | −0.364066 | ||||||||
\(290\) | −7.47038 | −0.438676 | ||||||||
\(291\) | −0.182040 | −0.0106714 | ||||||||
\(292\) | 2.44565 | 0.143121 | ||||||||
\(293\) | 2.75354 | 0.160864 | 0.0804319 | − | 0.996760i | \(-0.474370\pi\) | ||||
0.0804319 | + | 0.996760i | \(0.474370\pi\) | |||||||
\(294\) | −0.134860 | −0.00786521 | ||||||||
\(295\) | 6.61220 | 0.384977 | ||||||||
\(296\) | −1.65521 | −0.0962073 | ||||||||
\(297\) | 8.12786 | 0.471626 | ||||||||
\(298\) | 4.25428 | 0.246444 | ||||||||
\(299\) | −25.8923 | −1.49739 | ||||||||
\(300\) | 0.277700 | 0.0160330 | ||||||||
\(301\) | 4.54761 | 0.262120 | ||||||||
\(302\) | −1.20287 | −0.0692172 | ||||||||
\(303\) | −1.70689 | −0.0980581 | ||||||||
\(304\) | −3.94209 | −0.226094 | ||||||||
\(305\) | 10.0369 | 0.574712 | ||||||||
\(306\) | 9.61041 | 0.549390 | ||||||||
\(307\) | −10.2302 | −0.583866 | −0.291933 | − | 0.956439i | \(-0.594298\pi\) | ||||
−0.291933 | + | 0.956439i | \(0.594298\pi\) | |||||||
\(308\) | −12.6126 | −0.718667 | ||||||||
\(309\) | −0.556527 | −0.0316597 | ||||||||
\(310\) | −4.60144 | −0.261344 | ||||||||
\(311\) | −2.39920 | −0.136046 | −0.0680231 | − | 0.997684i | \(-0.521669\pi\) | ||||
−0.0680231 | + | 0.997684i | \(0.521669\pi\) | |||||||
\(312\) | 1.19068 | 0.0674088 | ||||||||
\(313\) | −15.1268 | −0.855015 | −0.427508 | − | 0.904012i | \(-0.640608\pi\) | ||||
−0.427508 | + | 0.904012i | \(0.640608\pi\) | |||||||
\(314\) | −10.1536 | −0.573003 | ||||||||
\(315\) | −7.46015 | −0.420332 | ||||||||
\(316\) | 10.1143 | 0.568975 | ||||||||
\(317\) | −20.8116 | −1.16890 | −0.584448 | − | 0.811431i | \(-0.698689\pi\) | ||||
−0.584448 | + | 0.811431i | \(0.698689\pi\) | |||||||
\(318\) | −2.43369 | −0.136475 | ||||||||
\(319\) | 36.9156 | 2.06688 | ||||||||
\(320\) | 1.00000 | 0.0559017 | ||||||||
\(321\) | −1.61974 | −0.0904052 | ||||||||
\(322\) | −15.4131 | −0.858938 | ||||||||
\(323\) | 12.9615 | 0.721200 | ||||||||
\(324\) | 8.31189 | 0.461772 | ||||||||
\(325\) | 4.28763 | 0.237835 | ||||||||
\(326\) | −7.04820 | −0.390364 | ||||||||
\(327\) | 0.662583 | 0.0366409 | ||||||||
\(328\) | −8.01358 | −0.442476 | ||||||||
\(329\) | −8.50514 | −0.468904 | ||||||||
\(330\) | −1.37228 | −0.0755416 | ||||||||
\(331\) | −8.14597 | −0.447743 | −0.223872 | − | 0.974619i | \(-0.571870\pi\) | ||||
−0.223872 | + | 0.974619i | \(0.571870\pi\) | |||||||
\(332\) | 1.46001 | 0.0801287 | ||||||||
\(333\) | 4.83799 | 0.265120 | ||||||||
\(334\) | 13.1292 | 0.718398 | ||||||||
\(335\) | −5.12837 | −0.280193 | ||||||||
\(336\) | 0.708781 | 0.0386672 | ||||||||
\(337\) | −9.14403 | −0.498107 | −0.249053 | − | 0.968490i | \(-0.580119\pi\) | ||||
−0.249053 | + | 0.968490i | \(0.580119\pi\) | |||||||
\(338\) | 5.38380 | 0.292840 | ||||||||
\(339\) | 0.703291 | 0.0381975 | ||||||||
\(340\) | −3.28799 | −0.178316 | ||||||||
\(341\) | 22.7385 | 1.23136 | ||||||||
\(342\) | 11.5223 | 0.623053 | ||||||||
\(343\) | −19.1058 | −1.03161 | ||||||||
\(344\) | 1.78175 | 0.0960656 | ||||||||
\(345\) | −1.67699 | −0.0902859 | ||||||||
\(346\) | 9.66095 | 0.519376 | ||||||||
\(347\) | −5.88331 | −0.315833 | −0.157916 | − | 0.987452i | \(-0.550478\pi\) | ||||
−0.157916 | + | 0.987452i | \(0.550478\pi\) | |||||||
\(348\) | −2.07453 | −0.111206 | ||||||||
\(349\) | 3.32250 | 0.177850 | 0.0889248 | − | 0.996038i | \(-0.471657\pi\) | ||||
0.0889248 | + | 0.996038i | \(0.471657\pi\) | |||||||
\(350\) | 2.55233 | 0.136428 | ||||||||
\(351\) | −7.05224 | −0.376421 | ||||||||
\(352\) | −4.94159 | −0.263388 | ||||||||
\(353\) | 22.7150 | 1.20900 | 0.604499 | − | 0.796606i | \(-0.293373\pi\) | ||||
0.604499 | + | 0.796606i | \(0.293373\pi\) | |||||||
\(354\) | 1.83621 | 0.0975935 | ||||||||
\(355\) | 2.50077 | 0.132727 | ||||||||
\(356\) | −7.59665 | −0.402622 | ||||||||
\(357\) | −2.33047 | −0.123341 | ||||||||
\(358\) | −12.4660 | −0.658851 | ||||||||
\(359\) | 15.2694 | 0.805888 | 0.402944 | − | 0.915225i | \(-0.367987\pi\) | ||||
0.402944 | + | 0.915225i | \(0.367987\pi\) | |||||||
\(360\) | −2.92288 | −0.154049 | ||||||||
\(361\) | −3.45994 | −0.182102 | ||||||||
\(362\) | −5.60337 | −0.294507 | ||||||||
\(363\) | 3.72656 | 0.195593 | ||||||||
\(364\) | 10.9434 | 0.573592 | ||||||||
\(365\) | 2.44565 | 0.128011 | ||||||||
\(366\) | 2.78725 | 0.145692 | ||||||||
\(367\) | 26.3432 | 1.37511 | 0.687553 | − | 0.726134i | \(-0.258685\pi\) | ||||
0.687553 | + | 0.726134i | \(0.258685\pi\) | |||||||
\(368\) | −6.03884 | −0.314796 | ||||||||
\(369\) | 23.4227 | 1.21934 | ||||||||
\(370\) | −1.65521 | −0.0860504 | ||||||||
\(371\) | −22.3679 | −1.16129 | ||||||||
\(372\) | −1.27782 | −0.0662519 | ||||||||
\(373\) | 25.4950 | 1.32008 | 0.660040 | − | 0.751230i | \(-0.270539\pi\) | ||||
0.660040 | + | 0.751230i | \(0.270539\pi\) | |||||||
\(374\) | 16.2479 | 0.840159 | ||||||||
\(375\) | 0.277700 | 0.0143404 | ||||||||
\(376\) | −3.33231 | −0.171851 | ||||||||
\(377\) | −32.0302 | −1.64964 | ||||||||
\(378\) | −4.19803 | −0.215923 | ||||||||
\(379\) | −19.8048 | −1.01730 | −0.508652 | − | 0.860972i | \(-0.669856\pi\) | ||||
−0.508652 | + | 0.860972i | \(0.669856\pi\) | |||||||
\(380\) | −3.94209 | −0.202225 | ||||||||
\(381\) | 1.22002 | 0.0625035 | ||||||||
\(382\) | 13.5010 | 0.690769 | ||||||||
\(383\) | −12.7968 | −0.653884 | −0.326942 | − | 0.945044i | \(-0.606018\pi\) | ||||
−0.326942 | + | 0.945044i | \(0.606018\pi\) | |||||||
\(384\) | 0.277700 | 0.0141713 | ||||||||
\(385\) | −12.6126 | −0.642795 | ||||||||
\(386\) | 0.481989 | 0.0245326 | ||||||||
\(387\) | −5.20785 | −0.264730 | ||||||||
\(388\) | −0.655528 | −0.0332794 | ||||||||
\(389\) | 1.10510 | 0.0560307 | 0.0280154 | − | 0.999607i | \(-0.491081\pi\) | ||||
0.0280154 | + | 0.999607i | \(0.491081\pi\) | |||||||
\(390\) | 1.19068 | 0.0602923 | ||||||||
\(391\) | 19.8556 | 1.00414 | ||||||||
\(392\) | −0.485632 | −0.0245281 | ||||||||
\(393\) | 3.48734 | 0.175913 | ||||||||
\(394\) | −9.40948 | −0.474043 | ||||||||
\(395\) | 10.1143 | 0.508906 | ||||||||
\(396\) | 14.4437 | 0.725823 | ||||||||
\(397\) | −10.7718 | −0.540619 | −0.270310 | − | 0.962773i | \(-0.587126\pi\) | ||||
−0.270310 | + | 0.962773i | \(0.587126\pi\) | |||||||
\(398\) | 18.8322 | 0.943973 | ||||||||
\(399\) | −2.79408 | −0.139879 | ||||||||
\(400\) | 1.00000 | 0.0500000 | ||||||||
\(401\) | −4.30494 | −0.214978 | −0.107489 | − | 0.994206i | \(-0.534281\pi\) | ||||
−0.107489 | + | 0.994206i | \(0.534281\pi\) | |||||||
\(402\) | −1.42415 | −0.0710301 | ||||||||
\(403\) | −19.7293 | −0.982786 | ||||||||
\(404\) | −6.14651 | −0.305800 | ||||||||
\(405\) | 8.31189 | 0.413021 | ||||||||
\(406\) | −19.0668 | −0.946271 | ||||||||
\(407\) | 8.17939 | 0.405437 | ||||||||
\(408\) | −0.913075 | −0.0452040 | ||||||||
\(409\) | 28.0375 | 1.38636 | 0.693182 | − | 0.720763i | \(-0.256208\pi\) | ||||
0.693182 | + | 0.720763i | \(0.256208\pi\) | |||||||
\(410\) | −8.01358 | −0.395762 | ||||||||
\(411\) | 1.69965 | 0.0838374 | ||||||||
\(412\) | −2.00406 | −0.0987327 | ||||||||
\(413\) | 16.8765 | 0.830438 | ||||||||
\(414\) | 17.6508 | 0.867490 | ||||||||
\(415\) | 1.46001 | 0.0716693 | ||||||||
\(416\) | 4.28763 | 0.210219 | ||||||||
\(417\) | 2.37317 | 0.116215 | ||||||||
\(418\) | 19.4802 | 0.952808 | ||||||||
\(419\) | 9.83699 | 0.480569 | 0.240284 | − | 0.970703i | \(-0.422759\pi\) | ||||
0.240284 | + | 0.970703i | \(0.422759\pi\) | |||||||
\(420\) | 0.708781 | 0.0345850 | ||||||||
\(421\) | −11.3117 | −0.551296 | −0.275648 | − | 0.961259i | \(-0.588892\pi\) | ||||
−0.275648 | + | 0.961259i | \(0.588892\pi\) | |||||||
\(422\) | −0.421081 | −0.0204979 | ||||||||
\(423\) | 9.73995 | 0.473573 | ||||||||
\(424\) | −8.76375 | −0.425605 | ||||||||
\(425\) | −3.28799 | −0.159491 | ||||||||
\(426\) | 0.694465 | 0.0336469 | ||||||||
\(427\) | 25.6175 | 1.23972 | ||||||||
\(428\) | −5.83270 | −0.281934 | ||||||||
\(429\) | −5.88384 | −0.284074 | ||||||||
\(430\) | 1.78175 | 0.0859237 | ||||||||
\(431\) | −20.3784 | −0.981594 | −0.490797 | − | 0.871274i | \(-0.663294\pi\) | ||||
−0.490797 | + | 0.871274i | \(0.663294\pi\) | |||||||
\(432\) | −1.64479 | −0.0791348 | ||||||||
\(433\) | −16.2983 | −0.783246 | −0.391623 | − | 0.920126i | \(-0.628086\pi\) | ||||
−0.391623 | + | 0.920126i | \(0.628086\pi\) | |||||||
\(434\) | −11.7444 | −0.563748 | ||||||||
\(435\) | −2.07453 | −0.0994659 | ||||||||
\(436\) | 2.38596 | 0.114267 | ||||||||
\(437\) | 23.8056 | 1.13878 | ||||||||
\(438\) | 0.679157 | 0.0324514 | ||||||||
\(439\) | 16.3355 | 0.779650 | 0.389825 | − | 0.920889i | \(-0.372535\pi\) | ||||
0.389825 | + | 0.920889i | \(0.372535\pi\) | |||||||
\(440\) | −4.94159 | −0.235581 | ||||||||
\(441\) | 1.41945 | 0.0675927 | ||||||||
\(442\) | −14.0977 | −0.670559 | ||||||||
\(443\) | −30.3955 | −1.44413 | −0.722066 | − | 0.691824i | \(-0.756807\pi\) | ||||
−0.722066 | + | 0.691824i | \(0.756807\pi\) | |||||||
\(444\) | −0.459653 | −0.0218142 | ||||||||
\(445\) | −7.59665 | −0.360116 | ||||||||
\(446\) | 7.75783 | 0.367344 | ||||||||
\(447\) | 1.18141 | 0.0558789 | ||||||||
\(448\) | 2.55233 | 0.120586 | ||||||||
\(449\) | 11.9134 | 0.562230 | 0.281115 | − | 0.959674i | \(-0.409296\pi\) | ||||
0.281115 | + | 0.959674i | \(0.409296\pi\) | |||||||
\(450\) | −2.92288 | −0.137786 | ||||||||
\(451\) | 39.5998 | 1.86468 | ||||||||
\(452\) | 2.53256 | 0.119121 | ||||||||
\(453\) | −0.334036 | −0.0156944 | ||||||||
\(454\) | −1.26402 | −0.0593233 | ||||||||
\(455\) | 10.9434 | 0.513036 | ||||||||
\(456\) | −1.09472 | −0.0512649 | ||||||||
\(457\) | −35.3128 | −1.65186 | −0.825931 | − | 0.563771i | \(-0.809350\pi\) | ||||
−0.825931 | + | 0.563771i | \(0.809350\pi\) | |||||||
\(458\) | 17.1590 | 0.801788 | ||||||||
\(459\) | 5.40804 | 0.252426 | ||||||||
\(460\) | −6.03884 | −0.281562 | ||||||||
\(461\) | 37.5505 | 1.74890 | 0.874450 | − | 0.485116i | \(-0.161223\pi\) | ||||
0.874450 | + | 0.485116i | \(0.161223\pi\) | |||||||
\(462\) | −3.50251 | −0.162951 | ||||||||
\(463\) | 29.2633 | 1.35998 | 0.679992 | − | 0.733220i | \(-0.261983\pi\) | ||||
0.679992 | + | 0.733220i | \(0.261983\pi\) | |||||||
\(464\) | −7.47038 | −0.346804 | ||||||||
\(465\) | −1.27782 | −0.0592575 | ||||||||
\(466\) | −11.0937 | −0.513904 | ||||||||
\(467\) | −2.05376 | −0.0950366 | −0.0475183 | − | 0.998870i | \(-0.515131\pi\) | ||||
−0.0475183 | + | 0.998870i | \(0.515131\pi\) | |||||||
\(468\) | −12.5323 | −0.579303 | ||||||||
\(469\) | −13.0893 | −0.604406 | ||||||||
\(470\) | −3.33231 | −0.153708 | ||||||||
\(471\) | −2.81967 | −0.129924 | ||||||||
\(472\) | 6.61220 | 0.304351 | ||||||||
\(473\) | −8.80469 | −0.404840 | ||||||||
\(474\) | 2.80875 | 0.129010 | ||||||||
\(475\) | −3.94209 | −0.180875 | ||||||||
\(476\) | −8.39202 | −0.384648 | ||||||||
\(477\) | 25.6154 | 1.17285 | ||||||||
\(478\) | −12.0870 | −0.552848 | ||||||||
\(479\) | −22.3022 | −1.01901 | −0.509506 | − | 0.860467i | \(-0.670172\pi\) | ||||
−0.509506 | + | 0.860467i | \(0.670172\pi\) | |||||||
\(480\) | 0.277700 | 0.0126752 | ||||||||
\(481\) | −7.09695 | −0.323593 | ||||||||
\(482\) | −25.6218 | −1.16704 | ||||||||
\(483\) | −4.28022 | −0.194757 | ||||||||
\(484\) | 13.4193 | 0.609970 | ||||||||
\(485\) | −0.655528 | −0.0297660 | ||||||||
\(486\) | 7.24257 | 0.328530 | ||||||||
\(487\) | −22.7781 | −1.03218 | −0.516088 | − | 0.856536i | \(-0.672612\pi\) | ||||
−0.516088 | + | 0.856536i | \(0.672612\pi\) | |||||||
\(488\) | 10.0369 | 0.454349 | ||||||||
\(489\) | −1.95729 | −0.0885116 | ||||||||
\(490\) | −0.485632 | −0.0219386 | ||||||||
\(491\) | −18.0674 | −0.815372 | −0.407686 | − | 0.913122i | \(-0.633664\pi\) | ||||
−0.407686 | + | 0.913122i | \(0.633664\pi\) | |||||||
\(492\) | −2.22537 | −0.100328 | ||||||||
\(493\) | 24.5625 | 1.10624 | ||||||||
\(494\) | −16.9022 | −0.760467 | ||||||||
\(495\) | 14.4437 | 0.649196 | ||||||||
\(496\) | −4.60144 | −0.206611 | ||||||||
\(497\) | 6.38279 | 0.286307 | ||||||||
\(498\) | 0.405446 | 0.0181685 | ||||||||
\(499\) | −37.4965 | −1.67857 | −0.839286 | − | 0.543690i | \(-0.817027\pi\) | ||||
−0.839286 | + | 0.543690i | \(0.817027\pi\) | |||||||
\(500\) | 1.00000 | 0.0447214 | ||||||||
\(501\) | 3.64598 | 0.162890 | ||||||||
\(502\) | −18.7449 | −0.836624 | ||||||||
\(503\) | 19.0805 | 0.850757 | 0.425378 | − | 0.905016i | \(-0.360141\pi\) | ||||
0.425378 | + | 0.905016i | \(0.360141\pi\) | |||||||
\(504\) | −7.46015 | −0.332301 | ||||||||
\(505\) | −6.14651 | −0.273516 | ||||||||
\(506\) | 29.8415 | 1.32662 | ||||||||
\(507\) | 1.49508 | 0.0663990 | ||||||||
\(508\) | 4.39330 | 0.194921 | ||||||||
\(509\) | −32.0076 | −1.41871 | −0.709356 | − | 0.704851i | \(-0.751014\pi\) | ||||
−0.709356 | + | 0.704851i | \(0.751014\pi\) | |||||||
\(510\) | −0.913075 | −0.0404317 | ||||||||
\(511\) | 6.24209 | 0.276134 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 6.48389 | 0.286271 | ||||||||
\(514\) | −11.5427 | −0.509128 | ||||||||
\(515\) | −2.00406 | −0.0883092 | ||||||||
\(516\) | 0.494793 | 0.0217820 | ||||||||
\(517\) | 16.4669 | 0.724215 | ||||||||
\(518\) | −4.22464 | −0.185620 | ||||||||
\(519\) | 2.68285 | 0.117764 | ||||||||
\(520\) | 4.28763 | 0.188025 | ||||||||
\(521\) | −18.1180 | −0.793765 | −0.396882 | − | 0.917870i | \(-0.629908\pi\) | ||||
−0.396882 | + | 0.917870i | \(0.629908\pi\) | |||||||
\(522\) | 21.8350 | 0.955694 | ||||||||
\(523\) | −10.0446 | −0.439219 | −0.219610 | − | 0.975588i | \(-0.570478\pi\) | ||||
−0.219610 | + | 0.975588i | \(0.570478\pi\) | |||||||
\(524\) | 12.5579 | 0.548596 | ||||||||
\(525\) | 0.708781 | 0.0309338 | ||||||||
\(526\) | −1.04321 | −0.0454861 | ||||||||
\(527\) | 15.1295 | 0.659051 | ||||||||
\(528\) | −1.37228 | −0.0597209 | ||||||||
\(529\) | 13.4676 | 0.585546 | ||||||||
\(530\) | −8.76375 | −0.380673 | ||||||||
\(531\) | −19.3267 | −0.838707 | ||||||||
\(532\) | −10.0615 | −0.436221 | ||||||||
\(533\) | −34.3593 | −1.48827 | ||||||||
\(534\) | −2.10959 | −0.0912909 | ||||||||
\(535\) | −5.83270 | −0.252170 | ||||||||
\(536\) | −5.12837 | −0.221512 | ||||||||
\(537\) | −3.46182 | −0.149389 | ||||||||
\(538\) | 2.08721 | 0.0899862 | ||||||||
\(539\) | 2.39980 | 0.103367 | ||||||||
\(540\) | −1.64479 | −0.0707803 | ||||||||
\(541\) | 13.4911 | 0.580028 | 0.290014 | − | 0.957022i | \(-0.406340\pi\) | ||||
0.290014 | + | 0.957022i | \(0.406340\pi\) | |||||||
\(542\) | 32.6766 | 1.40358 | ||||||||
\(543\) | −1.55606 | −0.0667768 | ||||||||
\(544\) | −3.28799 | −0.140971 | ||||||||
\(545\) | 2.38596 | 0.102203 | ||||||||
\(546\) | 3.03900 | 0.130057 | ||||||||
\(547\) | −12.1566 | −0.519777 | −0.259889 | − | 0.965639i | \(-0.583686\pi\) | ||||
−0.259889 | + | 0.965639i | \(0.583686\pi\) | |||||||
\(548\) | 6.12044 | 0.261452 | ||||||||
\(549\) | −29.3367 | −1.25206 | ||||||||
\(550\) | −4.94159 | −0.210710 | ||||||||
\(551\) | 29.4489 | 1.25456 | ||||||||
\(552\) | −1.67699 | −0.0713773 | ||||||||
\(553\) | 25.8150 | 1.09777 | ||||||||
\(554\) | −22.1396 | −0.940621 | ||||||||
\(555\) | −0.459653 | −0.0195112 | ||||||||
\(556\) | 8.54580 | 0.362423 | ||||||||
\(557\) | −15.8398 | −0.671152 | −0.335576 | − | 0.942013i | \(-0.608931\pi\) | ||||
−0.335576 | + | 0.942013i | \(0.608931\pi\) | |||||||
\(558\) | 13.4495 | 0.569362 | ||||||||
\(559\) | 7.63950 | 0.323116 | ||||||||
\(560\) | 2.55233 | 0.107855 | ||||||||
\(561\) | 4.51205 | 0.190499 | ||||||||
\(562\) | 8.01321 | 0.338017 | ||||||||
\(563\) | 10.3672 | 0.436927 | 0.218464 | − | 0.975845i | \(-0.429895\pi\) | ||||
0.218464 | + | 0.975845i | \(0.429895\pi\) | |||||||
\(564\) | −0.925383 | −0.0389657 | ||||||||
\(565\) | 2.53256 | 0.106545 | ||||||||
\(566\) | 23.1815 | 0.974389 | ||||||||
\(567\) | 21.2147 | 0.890932 | ||||||||
\(568\) | 2.50077 | 0.104930 | ||||||||
\(569\) | −30.1146 | −1.26247 | −0.631235 | − | 0.775592i | \(-0.717452\pi\) | ||||
−0.631235 | + | 0.775592i | \(0.717452\pi\) | |||||||
\(570\) | −1.09472 | −0.0458527 | ||||||||
\(571\) | −30.8585 | −1.29139 | −0.645695 | − | 0.763596i | \(-0.723432\pi\) | ||||
−0.645695 | + | 0.763596i | \(0.723432\pi\) | |||||||
\(572\) | −21.1877 | −0.885904 | ||||||||
\(573\) | 3.74922 | 0.156626 | ||||||||
\(574\) | −20.4533 | −0.853703 | ||||||||
\(575\) | −6.03884 | −0.251837 | ||||||||
\(576\) | −2.92288 | −0.121787 | ||||||||
\(577\) | −25.0135 | −1.04132 | −0.520662 | − | 0.853763i | \(-0.674315\pi\) | ||||
−0.520662 | + | 0.853763i | \(0.674315\pi\) | |||||||
\(578\) | −6.18912 | −0.257434 | ||||||||
\(579\) | 0.133848 | 0.00556255 | ||||||||
\(580\) | −7.47038 | −0.310191 | ||||||||
\(581\) | 3.72643 | 0.154598 | ||||||||
\(582\) | −0.182040 | −0.00754581 | ||||||||
\(583\) | 43.3069 | 1.79359 | ||||||||
\(584\) | 2.44565 | 0.101202 | ||||||||
\(585\) | −12.5323 | −0.518145 | ||||||||
\(586\) | 2.75354 | 0.113748 | ||||||||
\(587\) | 11.1035 | 0.458291 | 0.229145 | − | 0.973392i | \(-0.426407\pi\) | ||||
0.229145 | + | 0.973392i | \(0.426407\pi\) | |||||||
\(588\) | −0.134860 | −0.00556154 | ||||||||
\(589\) | 18.1393 | 0.747416 | ||||||||
\(590\) | 6.61220 | 0.272220 | ||||||||
\(591\) | −2.61301 | −0.107485 | ||||||||
\(592\) | −1.65521 | −0.0680288 | ||||||||
\(593\) | −12.1577 | −0.499256 | −0.249628 | − | 0.968342i | \(-0.580308\pi\) | ||||
−0.249628 | + | 0.968342i | \(0.580308\pi\) | |||||||
\(594\) | 8.12786 | 0.333490 | ||||||||
\(595\) | −8.39202 | −0.344039 | ||||||||
\(596\) | 4.25428 | 0.174262 | ||||||||
\(597\) | 5.22971 | 0.214038 | ||||||||
\(598\) | −25.8923 | −1.05882 | ||||||||
\(599\) | −44.2078 | −1.80628 | −0.903141 | − | 0.429345i | \(-0.858744\pi\) | ||||
−0.903141 | + | 0.429345i | \(0.858744\pi\) | |||||||
\(600\) | 0.277700 | 0.0113371 | ||||||||
\(601\) | −1.00000 | −0.0407909 | ||||||||
\(602\) | 4.54761 | 0.185347 | ||||||||
\(603\) | 14.9896 | 0.610425 | ||||||||
\(604\) | −1.20287 | −0.0489440 | ||||||||
\(605\) | 13.4193 | 0.545574 | ||||||||
\(606\) | −1.70689 | −0.0693376 | ||||||||
\(607\) | −28.9368 | −1.17451 | −0.587255 | − | 0.809402i | \(-0.699791\pi\) | ||||
−0.587255 | + | 0.809402i | \(0.699791\pi\) | |||||||
\(608\) | −3.94209 | −0.159873 | ||||||||
\(609\) | −5.29487 | −0.214559 | ||||||||
\(610\) | 10.0369 | 0.406382 | ||||||||
\(611\) | −14.2877 | −0.578020 | ||||||||
\(612\) | 9.61041 | 0.388478 | ||||||||
\(613\) | 3.16304 | 0.127754 | 0.0638770 | − | 0.997958i | \(-0.479653\pi\) | ||||
0.0638770 | + | 0.997958i | \(0.479653\pi\) | |||||||
\(614\) | −10.2302 | −0.412856 | ||||||||
\(615\) | −2.22537 | −0.0897357 | ||||||||
\(616\) | −12.6126 | −0.508174 | ||||||||
\(617\) | 18.2934 | 0.736465 | 0.368232 | − | 0.929734i | \(-0.379963\pi\) | ||||
0.368232 | + | 0.929734i | \(0.379963\pi\) | |||||||
\(618\) | −0.556527 | −0.0223868 | ||||||||
\(619\) | 0.884234 | 0.0355404 | 0.0177702 | − | 0.999842i | \(-0.494343\pi\) | ||||
0.0177702 | + | 0.999842i | \(0.494343\pi\) | |||||||
\(620\) | −4.60144 | −0.184798 | ||||||||
\(621\) | 9.93259 | 0.398581 | ||||||||
\(622\) | −2.39920 | −0.0961992 | ||||||||
\(623\) | −19.3891 | −0.776809 | ||||||||
\(624\) | 1.19068 | 0.0476652 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −15.1268 | −0.604587 | ||||||||
\(627\) | 5.40965 | 0.216041 | ||||||||
\(628\) | −10.1536 | −0.405175 | ||||||||
\(629\) | 5.44232 | 0.217000 | ||||||||
\(630\) | −7.46015 | −0.297219 | ||||||||
\(631\) | −12.5644 | −0.500183 | −0.250091 | − | 0.968222i | \(-0.580461\pi\) | ||||
−0.250091 | + | 0.968222i | \(0.580461\pi\) | |||||||
\(632\) | 10.1143 | 0.402326 | ||||||||
\(633\) | −0.116934 | −0.00464772 | ||||||||
\(634\) | −20.8116 | −0.826534 | ||||||||
\(635\) | 4.39330 | 0.174343 | ||||||||
\(636\) | −2.43369 | −0.0965022 | ||||||||
\(637\) | −2.08221 | −0.0825003 | ||||||||
\(638\) | 36.9156 | 1.46150 | ||||||||
\(639\) | −7.30947 | −0.289158 | ||||||||
\(640\) | 1.00000 | 0.0395285 | ||||||||
\(641\) | 4.36246 | 0.172307 | 0.0861535 | − | 0.996282i | \(-0.472542\pi\) | ||||
0.0861535 | + | 0.996282i | \(0.472542\pi\) | |||||||
\(642\) | −1.61974 | −0.0639262 | ||||||||
\(643\) | 29.1984 | 1.15147 | 0.575736 | − | 0.817636i | \(-0.304716\pi\) | ||||
0.575736 | + | 0.817636i | \(0.304716\pi\) | |||||||
\(644\) | −15.4131 | −0.607361 | ||||||||
\(645\) | 0.494793 | 0.0194824 | ||||||||
\(646\) | 12.9615 | 0.509965 | ||||||||
\(647\) | −32.3343 | −1.27119 | −0.635595 | − | 0.772022i | \(-0.719245\pi\) | ||||
−0.635595 | + | 0.772022i | \(0.719245\pi\) | |||||||
\(648\) | 8.31189 | 0.326522 | ||||||||
\(649\) | −32.6748 | −1.28260 | ||||||||
\(650\) | 4.28763 | 0.168175 | ||||||||
\(651\) | −3.26142 | −0.127825 | ||||||||
\(652\) | −7.04820 | −0.276029 | ||||||||
\(653\) | 24.9559 | 0.976598 | 0.488299 | − | 0.872676i | \(-0.337617\pi\) | ||||
0.488299 | + | 0.872676i | \(0.337617\pi\) | |||||||
\(654\) | 0.662583 | 0.0259090 | ||||||||
\(655\) | 12.5579 | 0.490680 | ||||||||
\(656\) | −8.01358 | −0.312878 | ||||||||
\(657\) | −7.14834 | −0.278883 | ||||||||
\(658\) | −8.50514 | −0.331565 | ||||||||
\(659\) | −44.1975 | −1.72169 | −0.860844 | − | 0.508868i | \(-0.830064\pi\) | ||||
−0.860844 | + | 0.508868i | \(0.830064\pi\) | |||||||
\(660\) | −1.37228 | −0.0534160 | ||||||||
\(661\) | −25.1576 | −0.978516 | −0.489258 | − | 0.872139i | \(-0.662732\pi\) | ||||
−0.489258 | + | 0.872139i | \(0.662732\pi\) | |||||||
\(662\) | −8.14597 | −0.316602 | ||||||||
\(663\) | −3.91493 | −0.152043 | ||||||||
\(664\) | 1.46001 | 0.0566595 | ||||||||
\(665\) | −10.0615 | −0.390168 | ||||||||
\(666\) | 4.83799 | 0.187468 | ||||||||
\(667\) | 45.1124 | 1.74676 | ||||||||
\(668\) | 13.1292 | 0.507984 | ||||||||
\(669\) | 2.15435 | 0.0832920 | ||||||||
\(670\) | −5.12837 | −0.198126 | ||||||||
\(671\) | −49.5983 | −1.91472 | ||||||||
\(672\) | 0.708781 | 0.0273418 | ||||||||
\(673\) | −13.0385 | −0.502598 | −0.251299 | − | 0.967910i | \(-0.580858\pi\) | ||||
−0.251299 | + | 0.967910i | \(0.580858\pi\) | |||||||
\(674\) | −9.14403 | −0.352215 | ||||||||
\(675\) | −1.64479 | −0.0633078 | ||||||||
\(676\) | 5.38380 | 0.207069 | ||||||||
\(677\) | 14.6706 | 0.563835 | 0.281918 | − | 0.959439i | \(-0.409030\pi\) | ||||
0.281918 | + | 0.959439i | \(0.409030\pi\) | |||||||
\(678\) | 0.703291 | 0.0270097 | ||||||||
\(679\) | −1.67312 | −0.0642085 | ||||||||
\(680\) | −3.28799 | −0.126089 | ||||||||
\(681\) | −0.351018 | −0.0134510 | ||||||||
\(682\) | 22.7385 | 0.870701 | ||||||||
\(683\) | 23.0514 | 0.882039 | 0.441019 | − | 0.897498i | \(-0.354617\pi\) | ||||
0.441019 | + | 0.897498i | \(0.354617\pi\) | |||||||
\(684\) | 11.5223 | 0.440565 | ||||||||
\(685\) | 6.12044 | 0.233850 | ||||||||
\(686\) | −19.1058 | −0.729462 | ||||||||
\(687\) | 4.76506 | 0.181798 | ||||||||
\(688\) | 1.78175 | 0.0679286 | ||||||||
\(689\) | −37.5757 | −1.43152 | ||||||||
\(690\) | −1.67699 | −0.0638418 | ||||||||
\(691\) | −12.3973 | −0.471614 | −0.235807 | − | 0.971800i | \(-0.575773\pi\) | ||||
−0.235807 | + | 0.971800i | \(0.575773\pi\) | |||||||
\(692\) | 9.66095 | 0.367254 | ||||||||
\(693\) | 36.8650 | 1.40039 | ||||||||
\(694\) | −5.88331 | −0.223328 | ||||||||
\(695\) | 8.54580 | 0.324161 | ||||||||
\(696\) | −2.07453 | −0.0786347 | ||||||||
\(697\) | 26.3486 | 0.998023 | ||||||||
\(698\) | 3.32250 | 0.125759 | ||||||||
\(699\) | −3.08071 | −0.116523 | ||||||||
\(700\) | 2.55233 | 0.0964689 | ||||||||
\(701\) | 44.9218 | 1.69667 | 0.848337 | − | 0.529456i | \(-0.177604\pi\) | ||||
0.848337 | + | 0.529456i | \(0.177604\pi\) | |||||||
\(702\) | −7.05224 | −0.266170 | ||||||||
\(703\) | 6.52499 | 0.246095 | ||||||||
\(704\) | −4.94159 | −0.186243 | ||||||||
\(705\) | −0.925383 | −0.0348520 | ||||||||
\(706\) | 22.7150 | 0.854891 | ||||||||
\(707\) | −15.6879 | −0.590004 | ||||||||
\(708\) | 1.83621 | 0.0690090 | ||||||||
\(709\) | −10.9410 | −0.410899 | −0.205449 | − | 0.978668i | \(-0.565866\pi\) | ||||
−0.205449 | + | 0.978668i | \(0.565866\pi\) | |||||||
\(710\) | 2.50077 | 0.0938523 | ||||||||
\(711\) | −29.5630 | −1.10870 | ||||||||
\(712\) | −7.59665 | −0.284696 | ||||||||
\(713\) | 27.7874 | 1.04064 | ||||||||
\(714\) | −2.33047 | −0.0872155 | ||||||||
\(715\) | −21.1877 | −0.792377 | ||||||||
\(716\) | −12.4660 | −0.465878 | ||||||||
\(717\) | −3.35657 | −0.125353 | ||||||||
\(718\) | 15.2694 | 0.569849 | ||||||||
\(719\) | 15.7049 | 0.585693 | 0.292847 | − | 0.956159i | \(-0.405397\pi\) | ||||
0.292847 | + | 0.956159i | \(0.405397\pi\) | |||||||
\(720\) | −2.92288 | −0.108929 | ||||||||
\(721\) | −5.11500 | −0.190493 | ||||||||
\(722\) | −3.45994 | −0.128766 | ||||||||
\(723\) | −7.11517 | −0.264616 | ||||||||
\(724\) | −5.60337 | −0.208248 | ||||||||
\(725\) | −7.47038 | −0.277443 | ||||||||
\(726\) | 3.72656 | 0.138305 | ||||||||
\(727\) | −11.8864 | −0.440841 | −0.220421 | − | 0.975405i | \(-0.570743\pi\) | ||||
−0.220421 | + | 0.975405i | \(0.570743\pi\) | |||||||
\(728\) | 10.9434 | 0.405591 | ||||||||
\(729\) | −22.9244 | −0.849052 | ||||||||
\(730\) | 2.44565 | 0.0905175 | ||||||||
\(731\) | −5.85838 | −0.216680 | ||||||||
\(732\) | 2.78725 | 0.103020 | ||||||||
\(733\) | 45.6422 | 1.68583 | 0.842916 | − | 0.538045i | \(-0.180837\pi\) | ||||
0.842916 | + | 0.538045i | \(0.180837\pi\) | |||||||
\(734\) | 26.3432 | 0.972347 | ||||||||
\(735\) | −0.134860 | −0.00497439 | ||||||||
\(736\) | −6.03884 | −0.222595 | ||||||||
\(737\) | 25.3423 | 0.933497 | ||||||||
\(738\) | 23.4227 | 0.862203 | ||||||||
\(739\) | −11.0877 | −0.407869 | −0.203934 | − | 0.978985i | \(-0.565373\pi\) | ||||
−0.203934 | + | 0.978985i | \(0.565373\pi\) | |||||||
\(740\) | −1.65521 | −0.0608468 | ||||||||
\(741\) | −4.69375 | −0.172429 | ||||||||
\(742\) | −22.3679 | −0.821153 | ||||||||
\(743\) | 11.3725 | 0.417217 | 0.208609 | − | 0.977999i | \(-0.433107\pi\) | ||||
0.208609 | + | 0.977999i | \(0.433107\pi\) | |||||||
\(744\) | −1.27782 | −0.0468472 | ||||||||
\(745\) | 4.25428 | 0.155865 | ||||||||
\(746\) | 25.4950 | 0.933438 | ||||||||
\(747\) | −4.26745 | −0.156138 | ||||||||
\(748\) | 16.2479 | 0.594082 | ||||||||
\(749\) | −14.8870 | −0.543958 | ||||||||
\(750\) | 0.277700 | 0.0101402 | ||||||||
\(751\) | −3.67148 | −0.133974 | −0.0669870 | − | 0.997754i | \(-0.521339\pi\) | ||||
−0.0669870 | + | 0.997754i | \(0.521339\pi\) | |||||||
\(752\) | −3.33231 | −0.121517 | ||||||||
\(753\) | −5.20545 | −0.189697 | ||||||||
\(754\) | −32.0302 | −1.16647 | ||||||||
\(755\) | −1.20287 | −0.0437768 | ||||||||
\(756\) | −4.19803 | −0.152681 | ||||||||
\(757\) | −11.4260 | −0.415286 | −0.207643 | − | 0.978205i | \(-0.566579\pi\) | ||||
−0.207643 | + | 0.978205i | \(0.566579\pi\) | |||||||
\(758\) | −19.8048 | −0.719343 | ||||||||
\(759\) | 8.28699 | 0.300799 | ||||||||
\(760\) | −3.94209 | −0.142995 | ||||||||
\(761\) | 22.6045 | 0.819414 | 0.409707 | − | 0.912217i | \(-0.365631\pi\) | ||||
0.409707 | + | 0.912217i | \(0.365631\pi\) | |||||||
\(762\) | 1.22002 | 0.0441967 | ||||||||
\(763\) | 6.08976 | 0.220464 | ||||||||
\(764\) | 13.5010 | 0.488448 | ||||||||
\(765\) | 9.61041 | 0.347465 | ||||||||
\(766\) | −12.7968 | −0.462366 | ||||||||
\(767\) | 28.3507 | 1.02368 | ||||||||
\(768\) | 0.277700 | 0.0100206 | ||||||||
\(769\) | 0.658801 | 0.0237570 | 0.0118785 | − | 0.999929i | \(-0.496219\pi\) | ||||
0.0118785 | + | 0.999929i | \(0.496219\pi\) | |||||||
\(770\) | −12.6126 | −0.454525 | ||||||||
\(771\) | −3.20542 | −0.115440 | ||||||||
\(772\) | 0.481989 | 0.0173472 | ||||||||
\(773\) | −35.8459 | −1.28929 | −0.644644 | − | 0.764483i | \(-0.722994\pi\) | ||||
−0.644644 | + | 0.764483i | \(0.722994\pi\) | |||||||
\(774\) | −5.20785 | −0.187192 | ||||||||
\(775\) | −4.60144 | −0.165289 | ||||||||
\(776\) | −0.655528 | −0.0235321 | ||||||||
\(777\) | −1.17318 | −0.0420877 | ||||||||
\(778\) | 1.10510 | 0.0396197 | ||||||||
\(779\) | 31.5902 | 1.13184 | ||||||||
\(780\) | 1.19068 | 0.0426331 | ||||||||
\(781\) | −12.3578 | −0.442197 | ||||||||
\(782\) | 19.8556 | 0.710036 | ||||||||
\(783\) | 12.2872 | 0.439108 | ||||||||
\(784\) | −0.485632 | −0.0173440 | ||||||||
\(785\) | −10.1536 | −0.362399 | ||||||||
\(786\) | 3.48734 | 0.124389 | ||||||||
\(787\) | 14.7576 | 0.526053 | 0.263026 | − | 0.964789i | \(-0.415279\pi\) | ||||
0.263026 | + | 0.964789i | \(0.415279\pi\) | |||||||
\(788\) | −9.40948 | −0.335199 | ||||||||
\(789\) | −0.289700 | −0.0103136 | ||||||||
\(790\) | 10.1143 | 0.359851 | ||||||||
\(791\) | 6.46391 | 0.229830 | ||||||||
\(792\) | 14.4437 | 0.513234 | ||||||||
\(793\) | 43.0346 | 1.52820 | ||||||||
\(794\) | −10.7718 | −0.382275 | ||||||||
\(795\) | −2.43369 | −0.0863142 | ||||||||
\(796\) | 18.8322 | 0.667490 | ||||||||
\(797\) | −3.04398 | −0.107823 | −0.0539116 | − | 0.998546i | \(-0.517169\pi\) | ||||
−0.0539116 | + | 0.998546i | \(0.517169\pi\) | |||||||
\(798\) | −2.79408 | −0.0989093 | ||||||||
\(799\) | 10.9566 | 0.387617 | ||||||||
\(800\) | 1.00000 | 0.0353553 | ||||||||
\(801\) | 22.2041 | 0.784544 | ||||||||
\(802\) | −4.30494 | −0.152013 | ||||||||
\(803\) | −12.0854 | −0.426484 | ||||||||
\(804\) | −1.42415 | −0.0502259 | ||||||||
\(805\) | −15.4131 | −0.543240 | ||||||||
\(806\) | −19.7293 | −0.694935 | ||||||||
\(807\) | 0.579620 | 0.0204036 | ||||||||
\(808\) | −6.14651 | −0.216234 | ||||||||
\(809\) | 0.954037 | 0.0335422 | 0.0167711 | − | 0.999859i | \(-0.494661\pi\) | ||||
0.0167711 | + | 0.999859i | \(0.494661\pi\) | |||||||
\(810\) | 8.31189 | 0.292050 | ||||||||
\(811\) | −3.29009 | −0.115531 | −0.0577654 | − | 0.998330i | \(-0.518398\pi\) | ||||
−0.0577654 | + | 0.998330i | \(0.518398\pi\) | |||||||
\(812\) | −19.0668 | −0.669115 | ||||||||
\(813\) | 9.07429 | 0.318249 | ||||||||
\(814\) | 8.17939 | 0.286687 | ||||||||
\(815\) | −7.04820 | −0.246888 | ||||||||
\(816\) | −0.913075 | −0.0319640 | ||||||||
\(817\) | −7.02382 | −0.245732 | ||||||||
\(818\) | 28.0375 | 0.980307 | ||||||||
\(819\) | −31.9864 | −1.11769 | ||||||||
\(820\) | −8.01358 | −0.279846 | ||||||||
\(821\) | 23.2855 | 0.812670 | 0.406335 | − | 0.913724i | \(-0.366807\pi\) | ||||
0.406335 | + | 0.913724i | \(0.366807\pi\) | |||||||
\(822\) | 1.69965 | 0.0592820 | ||||||||
\(823\) | −40.0869 | −1.39734 | −0.698670 | − | 0.715444i | \(-0.746225\pi\) | ||||
−0.698670 | + | 0.715444i | \(0.746225\pi\) | |||||||
\(824\) | −2.00406 | −0.0698146 | ||||||||
\(825\) | −1.37228 | −0.0477767 | ||||||||
\(826\) | 16.8765 | 0.587208 | ||||||||
\(827\) | −17.1194 | −0.595301 | −0.297651 | − | 0.954675i | \(-0.596203\pi\) | ||||
−0.297651 | + | 0.954675i | \(0.596203\pi\) | |||||||
\(828\) | 17.6508 | 0.613408 | ||||||||
\(829\) | 6.44906 | 0.223985 | 0.111993 | − | 0.993709i | \(-0.464277\pi\) | ||||
0.111993 | + | 0.993709i | \(0.464277\pi\) | |||||||
\(830\) | 1.46001 | 0.0506778 | ||||||||
\(831\) | −6.14817 | −0.213278 | ||||||||
\(832\) | 4.28763 | 0.148647 | ||||||||
\(833\) | 1.59675 | 0.0553243 | ||||||||
\(834\) | 2.37317 | 0.0821762 | ||||||||
\(835\) | 13.1292 | 0.454355 | ||||||||
\(836\) | 19.4802 | 0.673737 | ||||||||
\(837\) | 7.56839 | 0.261602 | ||||||||
\(838\) | 9.83699 | 0.339813 | ||||||||
\(839\) | −8.16787 | −0.281986 | −0.140993 | − | 0.990011i | \(-0.545030\pi\) | ||||
−0.140993 | + | 0.990011i | \(0.545030\pi\) | |||||||
\(840\) | 0.708781 | 0.0244553 | ||||||||
\(841\) | 26.8066 | 0.924364 | ||||||||
\(842\) | −11.3117 | −0.389825 | ||||||||
\(843\) | 2.22527 | 0.0766424 | ||||||||
\(844\) | −0.421081 | −0.0144942 | ||||||||
\(845\) | 5.38380 | 0.185209 | ||||||||
\(846\) | 9.73995 | 0.334867 | ||||||||
\(847\) | 34.2505 | 1.17686 | ||||||||
\(848\) | −8.76375 | −0.300948 | ||||||||
\(849\) | 6.43749 | 0.220934 | ||||||||
\(850\) | −3.28799 | −0.112777 | ||||||||
\(851\) | 9.99556 | 0.342643 | ||||||||
\(852\) | 0.694465 | 0.0237920 | ||||||||
\(853\) | 46.9574 | 1.60779 | 0.803895 | − | 0.594772i | \(-0.202757\pi\) | ||||
0.803895 | + | 0.594772i | \(0.202757\pi\) | |||||||
\(854\) | 25.6175 | 0.876611 | ||||||||
\(855\) | 11.5223 | 0.394053 | ||||||||
\(856\) | −5.83270 | −0.199358 | ||||||||
\(857\) | 33.5470 | 1.14594 | 0.572971 | − | 0.819576i | \(-0.305791\pi\) | ||||
0.572971 | + | 0.819576i | \(0.305791\pi\) | |||||||
\(858\) | −5.88384 | −0.200871 | ||||||||
\(859\) | 37.2655 | 1.27148 | 0.635741 | − | 0.771902i | \(-0.280695\pi\) | ||||
0.635741 | + | 0.771902i | \(0.280695\pi\) | |||||||
\(860\) | 1.78175 | 0.0607572 | ||||||||
\(861\) | −5.67987 | −0.193570 | ||||||||
\(862\) | −20.3784 | −0.694092 | ||||||||
\(863\) | 24.6009 | 0.837425 | 0.418712 | − | 0.908119i | \(-0.362482\pi\) | ||||
0.418712 | + | 0.908119i | \(0.362482\pi\) | |||||||
\(864\) | −1.64479 | −0.0559567 | ||||||||
\(865\) | 9.66095 | 0.328482 | ||||||||
\(866\) | −16.2983 | −0.553839 | ||||||||
\(867\) | −1.71872 | −0.0583708 | ||||||||
\(868\) | −11.7444 | −0.398630 | ||||||||
\(869\) | −49.9808 | −1.69548 | ||||||||
\(870\) | −2.07453 | −0.0703330 | ||||||||
\(871\) | −21.9886 | −0.745054 | ||||||||
\(872\) | 2.38596 | 0.0807989 | ||||||||
\(873\) | 1.91603 | 0.0648478 | ||||||||
\(874\) | 23.8056 | 0.805238 | ||||||||
\(875\) | 2.55233 | 0.0862844 | ||||||||
\(876\) | 0.679157 | 0.0229466 | ||||||||
\(877\) | −15.4347 | −0.521194 | −0.260597 | − | 0.965448i | \(-0.583919\pi\) | ||||
−0.260597 | + | 0.965448i | \(0.583919\pi\) | |||||||
\(878\) | 16.3355 | 0.551296 | ||||||||
\(879\) | 0.764660 | 0.0257913 | ||||||||
\(880\) | −4.94159 | −0.166581 | ||||||||
\(881\) | 21.1992 | 0.714218 | 0.357109 | − | 0.934063i | \(-0.383762\pi\) | ||||
0.357109 | + | 0.934063i | \(0.383762\pi\) | |||||||
\(882\) | 1.41945 | 0.0477952 | ||||||||
\(883\) | −0.952077 | −0.0320400 | −0.0160200 | − | 0.999872i | \(-0.505100\pi\) | ||||
−0.0160200 | + | 0.999872i | \(0.505100\pi\) | |||||||
\(884\) | −14.0977 | −0.474157 | ||||||||
\(885\) | 1.83621 | 0.0617235 | ||||||||
\(886\) | −30.3955 | −1.02116 | ||||||||
\(887\) | 38.0504 | 1.27761 | 0.638804 | − | 0.769370i | \(-0.279430\pi\) | ||||
0.638804 | + | 0.769370i | \(0.279430\pi\) | |||||||
\(888\) | −0.459653 | −0.0154249 | ||||||||
\(889\) | 11.2131 | 0.376076 | ||||||||
\(890\) | −7.59665 | −0.254640 | ||||||||
\(891\) | −41.0740 | −1.37603 | ||||||||
\(892\) | 7.75783 | 0.259751 | ||||||||
\(893\) | 13.1363 | 0.439588 | ||||||||
\(894\) | 1.18141 | 0.0395124 | ||||||||
\(895\) | −12.4660 | −0.416694 | ||||||||
\(896\) | 2.55233 | 0.0852672 | ||||||||
\(897\) | −7.19030 | −0.240077 | ||||||||
\(898\) | 11.9134 | 0.397556 | ||||||||
\(899\) | 34.3745 | 1.14645 | ||||||||
\(900\) | −2.92288 | −0.0974294 | ||||||||
\(901\) | 28.8151 | 0.959970 | ||||||||
\(902\) | 39.5998 | 1.31853 | ||||||||
\(903\) | 1.26287 | 0.0420258 | ||||||||
\(904\) | 2.53256 | 0.0842316 | ||||||||
\(905\) | −5.60337 | −0.186262 | ||||||||
\(906\) | −0.334036 | −0.0110976 | ||||||||
\(907\) | −1.49117 | −0.0495136 | −0.0247568 | − | 0.999694i | \(-0.507881\pi\) | ||||
−0.0247568 | + | 0.999694i | \(0.507881\pi\) | |||||||
\(908\) | −1.26402 | −0.0419479 | ||||||||
\(909\) | 17.9655 | 0.595879 | ||||||||
\(910\) | 10.9434 | 0.362771 | ||||||||
\(911\) | 40.7106 | 1.34880 | 0.674401 | − | 0.738365i | \(-0.264402\pi\) | ||||
0.674401 | + | 0.738365i | \(0.264402\pi\) | |||||||
\(912\) | −1.09472 | −0.0362498 | ||||||||
\(913\) | −7.21480 | −0.238775 | ||||||||
\(914\) | −35.3128 | −1.16804 | ||||||||
\(915\) | 2.78725 | 0.0921437 | ||||||||
\(916\) | 17.1590 | 0.566950 | ||||||||
\(917\) | 32.0520 | 1.05845 | ||||||||
\(918\) | 5.40804 | 0.178492 | ||||||||
\(919\) | 35.6676 | 1.17656 | 0.588282 | − | 0.808655i | \(-0.299804\pi\) | ||||
0.588282 | + | 0.808655i | \(0.299804\pi\) | |||||||
\(920\) | −6.03884 | −0.199095 | ||||||||
\(921\) | −2.84092 | −0.0936114 | ||||||||
\(922\) | 37.5505 | 1.23666 | ||||||||
\(923\) | 10.7224 | 0.352932 | ||||||||
\(924\) | −3.50251 | −0.115224 | ||||||||
\(925\) | −1.65521 | −0.0544231 | ||||||||
\(926\) | 29.2633 | 0.961653 | ||||||||
\(927\) | 5.85762 | 0.192389 | ||||||||
\(928\) | −7.47038 | −0.245227 | ||||||||
\(929\) | 35.6442 | 1.16945 | 0.584724 | − | 0.811232i | \(-0.301203\pi\) | ||||
0.584724 | + | 0.811232i | \(0.301203\pi\) | |||||||
\(930\) | −1.27782 | −0.0419014 | ||||||||
\(931\) | 1.91441 | 0.0627421 | ||||||||
\(932\) | −11.0937 | −0.363385 | ||||||||
\(933\) | −0.666259 | −0.0218123 | ||||||||
\(934\) | −2.05376 | −0.0672010 | ||||||||
\(935\) | 16.2479 | 0.531363 | ||||||||
\(936\) | −12.5323 | −0.409629 | ||||||||
\(937\) | 4.74195 | 0.154913 | 0.0774564 | − | 0.996996i | \(-0.475320\pi\) | ||||
0.0774564 | + | 0.996996i | \(0.475320\pi\) | |||||||
\(938\) | −13.0893 | −0.427380 | ||||||||
\(939\) | −4.20070 | −0.137085 | ||||||||
\(940\) | −3.33231 | −0.108688 | ||||||||
\(941\) | 17.7737 | 0.579407 | 0.289703 | − | 0.957116i | \(-0.406443\pi\) | ||||
0.289703 | + | 0.957116i | \(0.406443\pi\) | |||||||
\(942\) | −2.81967 | −0.0918698 | ||||||||
\(943\) | 48.3927 | 1.57588 | ||||||||
\(944\) | 6.61220 | 0.215209 | ||||||||
\(945\) | −4.19803 | −0.136562 | ||||||||
\(946\) | −8.80469 | −0.286265 | ||||||||
\(947\) | 37.4217 | 1.21604 | 0.608020 | − | 0.793921i | \(-0.291964\pi\) | ||||
0.608020 | + | 0.793921i | \(0.291964\pi\) | |||||||
\(948\) | 2.80875 | 0.0912239 | ||||||||
\(949\) | 10.4860 | 0.340391 | ||||||||
\(950\) | −3.94209 | −0.127898 | ||||||||
\(951\) | −5.77939 | −0.187409 | ||||||||
\(952\) | −8.39202 | −0.271987 | ||||||||
\(953\) | −9.13396 | −0.295878 | −0.147939 | − | 0.988997i | \(-0.547264\pi\) | ||||
−0.147939 | + | 0.988997i | \(0.547264\pi\) | |||||||
\(954\) | 25.6154 | 0.829329 | ||||||||
\(955\) | 13.5010 | 0.436881 | ||||||||
\(956\) | −12.0870 | −0.390922 | ||||||||
\(957\) | 10.2515 | 0.331383 | ||||||||
\(958\) | −22.3022 | −0.720550 | ||||||||
\(959\) | 15.6214 | 0.504440 | ||||||||
\(960\) | 0.277700 | 0.00896273 | ||||||||
\(961\) | −9.82673 | −0.316991 | ||||||||
\(962\) | −7.09695 | −0.228815 | ||||||||
\(963\) | 17.0483 | 0.549374 | ||||||||
\(964\) | −25.6218 | −0.825222 | ||||||||
\(965\) | 0.481989 | 0.0155158 | ||||||||
\(966\) | −4.28022 | −0.137714 | ||||||||
\(967\) | 43.0359 | 1.38394 | 0.691970 | − | 0.721926i | \(-0.256743\pi\) | ||||
0.691970 | + | 0.721926i | \(0.256743\pi\) | |||||||
\(968\) | 13.4193 | 0.431314 | ||||||||
\(969\) | 3.59942 | 0.115630 | ||||||||
\(970\) | −0.655528 | −0.0210477 | ||||||||
\(971\) | 23.5469 | 0.755657 | 0.377829 | − | 0.925876i | \(-0.376671\pi\) | ||||
0.377829 | + | 0.925876i | \(0.376671\pi\) | |||||||
\(972\) | 7.24257 | 0.232306 | ||||||||
\(973\) | 21.8117 | 0.699250 | ||||||||
\(974\) | −22.7781 | −0.729859 | ||||||||
\(975\) | 1.19068 | 0.0381322 | ||||||||
\(976\) | 10.0369 | 0.321274 | ||||||||
\(977\) | −43.6340 | −1.39597 | −0.697987 | − | 0.716110i | \(-0.745921\pi\) | ||||
−0.697987 | + | 0.716110i | \(0.745921\pi\) | |||||||
\(978\) | −1.95729 | −0.0625872 | ||||||||
\(979\) | 37.5395 | 1.19977 | ||||||||
\(980\) | −0.485632 | −0.0155130 | ||||||||
\(981\) | −6.97389 | −0.222659 | ||||||||
\(982\) | −18.0674 | −0.576555 | ||||||||
\(983\) | 17.4569 | 0.556790 | 0.278395 | − | 0.960467i | \(-0.410198\pi\) | ||||
0.278395 | + | 0.960467i | \(0.410198\pi\) | |||||||
\(984\) | −2.22537 | −0.0709423 | ||||||||
\(985\) | −9.40948 | −0.299811 | ||||||||
\(986\) | 24.5625 | 0.782230 | ||||||||
\(987\) | −2.36188 | −0.0751795 | ||||||||
\(988\) | −16.9022 | −0.537732 | ||||||||
\(989\) | −10.7597 | −0.342139 | ||||||||
\(990\) | 14.4437 | 0.459051 | ||||||||
\(991\) | 23.6777 | 0.752146 | 0.376073 | − | 0.926590i | \(-0.377274\pi\) | ||||
0.376073 | + | 0.926590i | \(0.377274\pi\) | |||||||
\(992\) | −4.60144 | −0.146096 | ||||||||
\(993\) | −2.26214 | −0.0717868 | ||||||||
\(994\) | 6.38279 | 0.202450 | ||||||||
\(995\) | 18.8322 | 0.597021 | ||||||||
\(996\) | 0.405446 | 0.0128471 | ||||||||
\(997\) | −33.3445 | −1.05603 | −0.528015 | − | 0.849235i | \(-0.677064\pi\) | ||||
−0.528015 | + | 0.849235i | \(0.677064\pi\) | |||||||
\(998\) | −37.4965 | −1.18693 | ||||||||
\(999\) | 2.72247 | 0.0861351 |
(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 | 6010.2.a.c.1.10 | ✓ | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6010.2.a.c.1.10 | ✓ | 16 | 1.1 | even | 1 | trivial |