Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2001,2,Mod(1,2001)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2001, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2001.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2001 = 3 \cdot 23 \cdot 29 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2001.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: | \(15.9780654445\) |
Analytic rank: | \(1\) |
Dimension: | \(5\) |
Coefficient field: | 5.5.312617.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{5} - 2x^{4} - 5x^{3} + 11x^{2} - x - 3 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(2.26093\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2001.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.31874 | −0.932489 | −0.466244 | − | 0.884656i | \(-0.654393\pi\) | ||||
−0.466244 | + | 0.884656i | \(0.654393\pi\) | |||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | −0.260930 | −0.130465 | ||||||||
\(5\) | 2.51371 | 1.12417 | 0.562083 | − | 0.827081i | \(-0.310000\pi\) | ||||
0.562083 | + | 0.827081i | \(0.310000\pi\) | |||||||
\(6\) | 1.31874 | 0.538373 | ||||||||
\(7\) | −2.25278 | −0.851471 | −0.425735 | − | 0.904848i | \(-0.639985\pi\) | ||||
−0.425735 | + | 0.904848i | \(0.639985\pi\) | |||||||
\(8\) | 2.98157 | 1.05415 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −3.31493 | −1.04827 | ||||||||
\(11\) | −0.206934 | −0.0623931 | −0.0311965 | − | 0.999513i | \(-0.509932\pi\) | ||||
−0.0311965 | + | 0.999513i | \(0.509932\pi\) | |||||||
\(12\) | 0.260930 | 0.0753240 | ||||||||
\(13\) | −0.720644 | −0.199871 | −0.0999354 | − | 0.994994i | \(-0.531864\pi\) | ||||
−0.0999354 | + | 0.994994i | \(0.531864\pi\) | |||||||
\(14\) | 2.97083 | 0.793987 | ||||||||
\(15\) | −2.51371 | −0.649037 | ||||||||
\(16\) | −3.41006 | −0.852514 | ||||||||
\(17\) | 2.26093 | 0.548356 | 0.274178 | − | 0.961679i | \(-0.411594\pi\) | ||||
0.274178 | + | 0.961679i | \(0.411594\pi\) | |||||||
\(18\) | −1.31874 | −0.310830 | ||||||||
\(19\) | −4.58613 | −1.05213 | −0.526065 | − | 0.850444i | \(-0.676333\pi\) | ||||
−0.526065 | + | 0.850444i | \(0.676333\pi\) | |||||||
\(20\) | −0.655902 | −0.146664 | ||||||||
\(21\) | 2.25278 | 0.491597 | ||||||||
\(22\) | 0.272892 | 0.0581808 | ||||||||
\(23\) | 1.00000 | 0.208514 | ||||||||
\(24\) | −2.98157 | −0.608611 | ||||||||
\(25\) | 1.31874 | 0.263748 | ||||||||
\(26\) | 0.950341 | 0.186377 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0.587818 | 0.111087 | ||||||||
\(29\) | 1.00000 | 0.185695 | ||||||||
\(30\) | 3.31493 | 0.605220 | ||||||||
\(31\) | −0.615304 | −0.110512 | −0.0552559 | − | 0.998472i | \(-0.517597\pi\) | ||||
−0.0552559 | + | 0.998472i | \(0.517597\pi\) | |||||||
\(32\) | −1.46618 | −0.259186 | ||||||||
\(33\) | 0.206934 | 0.0360227 | ||||||||
\(34\) | −2.98157 | −0.511336 | ||||||||
\(35\) | −5.66284 | −0.957194 | ||||||||
\(36\) | −0.260930 | −0.0434883 | ||||||||
\(37\) | 1.84272 | 0.302942 | 0.151471 | − | 0.988462i | \(-0.451599\pi\) | ||||
0.151471 | + | 0.988462i | \(0.451599\pi\) | |||||||
\(38\) | 6.04791 | 0.981100 | ||||||||
\(39\) | 0.720644 | 0.115395 | ||||||||
\(40\) | 7.49481 | 1.18503 | ||||||||
\(41\) | −3.39931 | −0.530883 | −0.265441 | − | 0.964127i | \(-0.585518\pi\) | ||||
−0.265441 | + | 0.964127i | \(0.585518\pi\) | |||||||
\(42\) | −2.97083 | −0.458409 | ||||||||
\(43\) | −8.50175 | −1.29650 | −0.648252 | − | 0.761426i | \(-0.724500\pi\) | ||||
−0.648252 | + | 0.761426i | \(0.724500\pi\) | |||||||
\(44\) | 0.0539954 | 0.00814011 | ||||||||
\(45\) | 2.51371 | 0.374722 | ||||||||
\(46\) | −1.31874 | −0.194437 | ||||||||
\(47\) | 5.89878 | 0.860425 | 0.430213 | − | 0.902728i | \(-0.358439\pi\) | ||||
0.430213 | + | 0.902728i | \(0.358439\pi\) | |||||||
\(48\) | 3.41006 | 0.492199 | ||||||||
\(49\) | −1.92498 | −0.274997 | ||||||||
\(50\) | −1.73907 | −0.245942 | ||||||||
\(51\) | −2.26093 | −0.316593 | ||||||||
\(52\) | 0.188038 | 0.0260761 | ||||||||
\(53\) | 5.61905 | 0.771836 | 0.385918 | − | 0.922533i | \(-0.373885\pi\) | ||||
0.385918 | + | 0.922533i | \(0.373885\pi\) | |||||||
\(54\) | 1.31874 | 0.179458 | ||||||||
\(55\) | −0.520173 | −0.0701401 | ||||||||
\(56\) | −6.71683 | −0.897574 | ||||||||
\(57\) | 4.58613 | 0.607448 | ||||||||
\(58\) | −1.31874 | −0.173159 | ||||||||
\(59\) | 1.23398 | 0.160651 | 0.0803253 | − | 0.996769i | \(-0.474404\pi\) | ||||
0.0803253 | + | 0.996769i | \(0.474404\pi\) | |||||||
\(60\) | 0.655902 | 0.0846766 | ||||||||
\(61\) | 9.37442 | 1.20027 | 0.600136 | − | 0.799898i | \(-0.295113\pi\) | ||||
0.600136 | + | 0.799898i | \(0.295113\pi\) | |||||||
\(62\) | 0.811425 | 0.103051 | ||||||||
\(63\) | −2.25278 | −0.283824 | ||||||||
\(64\) | 8.75362 | 1.09420 | ||||||||
\(65\) | −1.81149 | −0.224688 | ||||||||
\(66\) | −0.272892 | −0.0335907 | ||||||||
\(67\) | −9.43319 | −1.15245 | −0.576224 | − | 0.817292i | \(-0.695474\pi\) | ||||
−0.576224 | + | 0.817292i | \(0.695474\pi\) | |||||||
\(68\) | −0.589944 | −0.0715412 | ||||||||
\(69\) | −1.00000 | −0.120386 | ||||||||
\(70\) | 7.46780 | 0.892573 | ||||||||
\(71\) | 1.35812 | 0.161179 | 0.0805896 | − | 0.996747i | \(-0.474320\pi\) | ||||
0.0805896 | + | 0.996747i | \(0.474320\pi\) | |||||||
\(72\) | 2.98157 | 0.351382 | ||||||||
\(73\) | −1.27374 | −0.149080 | −0.0745398 | − | 0.997218i | \(-0.523749\pi\) | ||||
−0.0745398 | + | 0.997218i | \(0.523749\pi\) | |||||||
\(74\) | −2.43007 | −0.282490 | ||||||||
\(75\) | −1.31874 | −0.152275 | ||||||||
\(76\) | 1.19666 | 0.137266 | ||||||||
\(77\) | 0.466178 | 0.0531259 | ||||||||
\(78\) | −0.950341 | −0.107605 | ||||||||
\(79\) | 9.36077 | 1.05317 | 0.526585 | − | 0.850123i | \(-0.323472\pi\) | ||||
0.526585 | + | 0.850123i | \(0.323472\pi\) | |||||||
\(80\) | −8.57189 | −0.958367 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 4.48280 | 0.495042 | ||||||||
\(83\) | −13.4640 | −1.47786 | −0.738932 | − | 0.673780i | \(-0.764670\pi\) | ||||
−0.738932 | + | 0.673780i | \(0.764670\pi\) | |||||||
\(84\) | −0.587818 | −0.0641362 | ||||||||
\(85\) | 5.68332 | 0.616443 | ||||||||
\(86\) | 11.2116 | 1.20898 | ||||||||
\(87\) | −1.00000 | −0.107211 | ||||||||
\(88\) | −0.616990 | −0.0657714 | ||||||||
\(89\) | −3.61318 | −0.382996 | −0.191498 | − | 0.981493i | \(-0.561335\pi\) | ||||
−0.191498 | + | 0.981493i | \(0.561335\pi\) | |||||||
\(90\) | −3.31493 | −0.349424 | ||||||||
\(91\) | 1.62345 | 0.170184 | ||||||||
\(92\) | −0.260930 | −0.0272038 | ||||||||
\(93\) | 0.615304 | 0.0638041 | ||||||||
\(94\) | −7.77895 | −0.802337 | ||||||||
\(95\) | −11.5282 | −1.18277 | ||||||||
\(96\) | 1.46618 | 0.149641 | ||||||||
\(97\) | 1.72542 | 0.175190 | 0.0875950 | − | 0.996156i | \(-0.472082\pi\) | ||||
0.0875950 | + | 0.996156i | \(0.472082\pi\) | |||||||
\(98\) | 2.53855 | 0.256432 | ||||||||
\(99\) | −0.206934 | −0.0207977 | ||||||||
\(100\) | −0.344098 | −0.0344098 | ||||||||
\(101\) | −5.34150 | −0.531499 | −0.265750 | − | 0.964042i | \(-0.585619\pi\) | ||||
−0.265750 | + | 0.964042i | \(0.585619\pi\) | |||||||
\(102\) | 2.98157 | 0.295220 | ||||||||
\(103\) | −8.03732 | −0.791941 | −0.395970 | − | 0.918263i | \(-0.629592\pi\) | ||||
−0.395970 | + | 0.918263i | \(0.629592\pi\) | |||||||
\(104\) | −2.14866 | −0.210693 | ||||||||
\(105\) | 5.66284 | 0.552636 | ||||||||
\(106\) | −7.41006 | −0.719728 | ||||||||
\(107\) | −3.51280 | −0.339595 | −0.169798 | − | 0.985479i | \(-0.554311\pi\) | ||||
−0.169798 | + | 0.985479i | \(0.554311\pi\) | |||||||
\(108\) | 0.260930 | 0.0251080 | ||||||||
\(109\) | 18.5175 | 1.77366 | 0.886828 | − | 0.462100i | \(-0.152904\pi\) | ||||
0.886828 | + | 0.462100i | \(0.152904\pi\) | |||||||
\(110\) | 0.685972 | 0.0654049 | ||||||||
\(111\) | −1.84272 | −0.174904 | ||||||||
\(112\) | 7.68211 | 0.725891 | ||||||||
\(113\) | −17.2446 | −1.62224 | −0.811119 | − | 0.584882i | \(-0.801141\pi\) | ||||
−0.811119 | + | 0.584882i | \(0.801141\pi\) | |||||||
\(114\) | −6.04791 | −0.566438 | ||||||||
\(115\) | 2.51371 | 0.234405 | ||||||||
\(116\) | −0.260930 | −0.0242267 | ||||||||
\(117\) | −0.720644 | −0.0666236 | ||||||||
\(118\) | −1.62730 | −0.149805 | ||||||||
\(119\) | −5.09338 | −0.466909 | ||||||||
\(120\) | −7.49481 | −0.684180 | ||||||||
\(121\) | −10.9572 | −0.996107 | ||||||||
\(122\) | −12.3624 | −1.11924 | ||||||||
\(123\) | 3.39931 | 0.306505 | ||||||||
\(124\) | 0.160551 | 0.0144179 | ||||||||
\(125\) | −9.25362 | −0.827669 | ||||||||
\(126\) | 2.97083 | 0.264662 | ||||||||
\(127\) | 14.4331 | 1.28073 | 0.640364 | − | 0.768072i | \(-0.278783\pi\) | ||||
0.640364 | + | 0.768072i | \(0.278783\pi\) | |||||||
\(128\) | −8.61137 | −0.761145 | ||||||||
\(129\) | 8.50175 | 0.748537 | ||||||||
\(130\) | 2.38888 | 0.209519 | ||||||||
\(131\) | −9.95272 | −0.869573 | −0.434787 | − | 0.900533i | \(-0.643176\pi\) | ||||
−0.434787 | + | 0.900533i | \(0.643176\pi\) | |||||||
\(132\) | −0.0539954 | −0.00469969 | ||||||||
\(133\) | 10.3315 | 0.895859 | ||||||||
\(134\) | 12.4399 | 1.07464 | ||||||||
\(135\) | −2.51371 | −0.216346 | ||||||||
\(136\) | 6.74113 | 0.578047 | ||||||||
\(137\) | −21.7145 | −1.85519 | −0.927597 | − | 0.373582i | \(-0.878129\pi\) | ||||
−0.927597 | + | 0.373582i | \(0.878129\pi\) | |||||||
\(138\) | 1.31874 | 0.112258 | ||||||||
\(139\) | −9.64007 | −0.817660 | −0.408830 | − | 0.912610i | \(-0.634063\pi\) | ||||
−0.408830 | + | 0.912610i | \(0.634063\pi\) | |||||||
\(140\) | 1.47760 | 0.124880 | ||||||||
\(141\) | −5.89878 | −0.496767 | ||||||||
\(142\) | −1.79101 | −0.150298 | ||||||||
\(143\) | 0.149126 | 0.0124706 | ||||||||
\(144\) | −3.41006 | −0.284171 | ||||||||
\(145\) | 2.51371 | 0.208752 | ||||||||
\(146\) | 1.67973 | 0.139015 | ||||||||
\(147\) | 1.92498 | 0.158770 | ||||||||
\(148\) | −0.480822 | −0.0395233 | ||||||||
\(149\) | 3.81234 | 0.312319 | 0.156159 | − | 0.987732i | \(-0.450089\pi\) | ||||
0.156159 | + | 0.987732i | \(0.450089\pi\) | |||||||
\(150\) | 1.73907 | 0.141994 | ||||||||
\(151\) | −24.1476 | −1.96511 | −0.982553 | − | 0.185983i | \(-0.940453\pi\) | ||||
−0.982553 | + | 0.185983i | \(0.940453\pi\) | |||||||
\(152\) | −13.6739 | −1.10910 | ||||||||
\(153\) | 2.26093 | 0.182785 | ||||||||
\(154\) | −0.614766 | −0.0495393 | ||||||||
\(155\) | −1.54670 | −0.124234 | ||||||||
\(156\) | −0.188038 | −0.0150551 | ||||||||
\(157\) | 13.7130 | 1.09442 | 0.547209 | − | 0.836996i | \(-0.315690\pi\) | ||||
0.547209 | + | 0.836996i | \(0.315690\pi\) | |||||||
\(158\) | −12.3444 | −0.982068 | ||||||||
\(159\) | −5.61905 | −0.445620 | ||||||||
\(160\) | −3.68555 | −0.291368 | ||||||||
\(161\) | −2.25278 | −0.177544 | ||||||||
\(162\) | −1.31874 | −0.103610 | ||||||||
\(163\) | 1.12483 | 0.0881033 | 0.0440516 | − | 0.999029i | \(-0.485973\pi\) | ||||
0.0440516 | + | 0.999029i | \(0.485973\pi\) | |||||||
\(164\) | 0.886981 | 0.0692616 | ||||||||
\(165\) | 0.520173 | 0.0404954 | ||||||||
\(166\) | 17.7555 | 1.37809 | ||||||||
\(167\) | 7.17952 | 0.555568 | 0.277784 | − | 0.960644i | \(-0.410400\pi\) | ||||
0.277784 | + | 0.960644i | \(0.410400\pi\) | |||||||
\(168\) | 6.71683 | 0.518215 | ||||||||
\(169\) | −12.4807 | −0.960052 | ||||||||
\(170\) | −7.49481 | −0.574826 | ||||||||
\(171\) | −4.58613 | −0.350710 | ||||||||
\(172\) | 2.21836 | 0.169148 | ||||||||
\(173\) | 3.39322 | 0.257982 | 0.128991 | − | 0.991646i | \(-0.458826\pi\) | ||||
0.128991 | + | 0.991646i | \(0.458826\pi\) | |||||||
\(174\) | 1.31874 | 0.0999733 | ||||||||
\(175\) | −2.97083 | −0.224573 | ||||||||
\(176\) | 0.705658 | 0.0531910 | ||||||||
\(177\) | −1.23398 | −0.0927517 | ||||||||
\(178\) | 4.76483 | 0.357139 | ||||||||
\(179\) | −12.3767 | −0.925078 | −0.462539 | − | 0.886599i | \(-0.653061\pi\) | ||||
−0.462539 | + | 0.886599i | \(0.653061\pi\) | |||||||
\(180\) | −0.655902 | −0.0488880 | ||||||||
\(181\) | −21.5325 | −1.60050 | −0.800251 | − | 0.599666i | \(-0.795300\pi\) | ||||
−0.800251 | + | 0.599666i | \(0.795300\pi\) | |||||||
\(182\) | −2.14091 | −0.158695 | ||||||||
\(183\) | −9.37442 | −0.692977 | ||||||||
\(184\) | 2.98157 | 0.219805 | ||||||||
\(185\) | 4.63207 | 0.340557 | ||||||||
\(186\) | −0.811425 | −0.0594966 | ||||||||
\(187\) | −0.467864 | −0.0342136 | ||||||||
\(188\) | −1.53917 | −0.112255 | ||||||||
\(189\) | 2.25278 | 0.163866 | ||||||||
\(190\) | 15.2027 | 1.10292 | ||||||||
\(191\) | −18.6497 | −1.34944 | −0.674722 | − | 0.738072i | \(-0.735737\pi\) | ||||
−0.674722 | + | 0.738072i | \(0.735737\pi\) | |||||||
\(192\) | −8.75362 | −0.631738 | ||||||||
\(193\) | −8.16030 | −0.587391 | −0.293696 | − | 0.955899i | \(-0.594885\pi\) | ||||
−0.293696 | + | 0.955899i | \(0.594885\pi\) | |||||||
\(194\) | −2.27538 | −0.163363 | ||||||||
\(195\) | 1.81149 | 0.129724 | ||||||||
\(196\) | 0.502285 | 0.0358775 | ||||||||
\(197\) | 13.5299 | 0.963969 | 0.481984 | − | 0.876180i | \(-0.339916\pi\) | ||||
0.481984 | + | 0.876180i | \(0.339916\pi\) | |||||||
\(198\) | 0.272892 | 0.0193936 | ||||||||
\(199\) | −3.83619 | −0.271941 | −0.135970 | − | 0.990713i | \(-0.543415\pi\) | ||||
−0.135970 | + | 0.990713i | \(0.543415\pi\) | |||||||
\(200\) | 3.93192 | 0.278028 | ||||||||
\(201\) | 9.43319 | 0.665366 | ||||||||
\(202\) | 7.04404 | 0.495617 | ||||||||
\(203\) | −2.25278 | −0.158114 | ||||||||
\(204\) | 0.589944 | 0.0413043 | ||||||||
\(205\) | −8.54488 | −0.596800 | ||||||||
\(206\) | 10.5991 | 0.738476 | ||||||||
\(207\) | 1.00000 | 0.0695048 | ||||||||
\(208\) | 2.45744 | 0.170393 | ||||||||
\(209\) | 0.949029 | 0.0656457 | ||||||||
\(210\) | −7.46780 | −0.515327 | ||||||||
\(211\) | −18.0641 | −1.24359 | −0.621793 | − | 0.783181i | \(-0.713596\pi\) | ||||
−0.621793 | + | 0.783181i | \(0.713596\pi\) | |||||||
\(212\) | −1.46618 | −0.100698 | ||||||||
\(213\) | −1.35812 | −0.0930569 | ||||||||
\(214\) | 4.63246 | 0.316669 | ||||||||
\(215\) | −21.3709 | −1.45749 | ||||||||
\(216\) | −2.98157 | −0.202870 | ||||||||
\(217\) | 1.38614 | 0.0940976 | ||||||||
\(218\) | −24.4197 | −1.65391 | ||||||||
\(219\) | 1.27374 | 0.0860712 | ||||||||
\(220\) | 0.135729 | 0.00915083 | ||||||||
\(221\) | −1.62933 | −0.109600 | ||||||||
\(222\) | 2.43007 | 0.163096 | ||||||||
\(223\) | 5.81999 | 0.389736 | 0.194868 | − | 0.980830i | \(-0.437572\pi\) | ||||
0.194868 | + | 0.980830i | \(0.437572\pi\) | |||||||
\(224\) | 3.30298 | 0.220689 | ||||||||
\(225\) | 1.31874 | 0.0879159 | ||||||||
\(226\) | 22.7411 | 1.51272 | ||||||||
\(227\) | −15.3483 | −1.01870 | −0.509352 | − | 0.860558i | \(-0.670115\pi\) | ||||
−0.509352 | + | 0.860558i | \(0.670115\pi\) | |||||||
\(228\) | −1.19666 | −0.0792506 | ||||||||
\(229\) | −15.8178 | −1.04527 | −0.522634 | − | 0.852557i | \(-0.675050\pi\) | ||||
−0.522634 | + | 0.852557i | \(0.675050\pi\) | |||||||
\(230\) | −3.31493 | −0.218580 | ||||||||
\(231\) | −0.466178 | −0.0306722 | ||||||||
\(232\) | 2.98157 | 0.195750 | ||||||||
\(233\) | 10.8064 | 0.707951 | 0.353975 | − | 0.935255i | \(-0.384830\pi\) | ||||
0.353975 | + | 0.935255i | \(0.384830\pi\) | |||||||
\(234\) | 0.950341 | 0.0621258 | ||||||||
\(235\) | 14.8278 | 0.967260 | ||||||||
\(236\) | −0.321982 | −0.0209593 | ||||||||
\(237\) | −9.36077 | −0.608047 | ||||||||
\(238\) | 6.71683 | 0.435388 | ||||||||
\(239\) | −12.4863 | −0.807670 | −0.403835 | − | 0.914832i | \(-0.632323\pi\) | ||||
−0.403835 | + | 0.914832i | \(0.632323\pi\) | |||||||
\(240\) | 8.57189 | 0.553313 | ||||||||
\(241\) | −3.94214 | −0.253935 | −0.126968 | − | 0.991907i | \(-0.540524\pi\) | ||||
−0.126968 | + | 0.991907i | \(0.540524\pi\) | |||||||
\(242\) | 14.4496 | 0.928859 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | −2.44607 | −0.156593 | ||||||||
\(245\) | −4.83884 | −0.309142 | ||||||||
\(246\) | −4.48280 | −0.285813 | ||||||||
\(247\) | 3.30497 | 0.210290 | ||||||||
\(248\) | −1.83457 | −0.116496 | ||||||||
\(249\) | 13.4640 | 0.853245 | ||||||||
\(250\) | 12.2031 | 0.771792 | ||||||||
\(251\) | 6.79990 | 0.429206 | 0.214603 | − | 0.976701i | \(-0.431154\pi\) | ||||
0.214603 | + | 0.976701i | \(0.431154\pi\) | |||||||
\(252\) | 0.587818 | 0.0370290 | ||||||||
\(253\) | −0.206934 | −0.0130099 | ||||||||
\(254\) | −19.0334 | −1.19426 | ||||||||
\(255\) | −5.68332 | −0.355903 | ||||||||
\(256\) | −6.15109 | −0.384443 | ||||||||
\(257\) | −25.4934 | −1.59023 | −0.795116 | − | 0.606457i | \(-0.792590\pi\) | ||||
−0.795116 | + | 0.606457i | \(0.792590\pi\) | |||||||
\(258\) | −11.2116 | −0.698002 | ||||||||
\(259\) | −4.15125 | −0.257946 | ||||||||
\(260\) | 0.472672 | 0.0293139 | ||||||||
\(261\) | 1.00000 | 0.0618984 | ||||||||
\(262\) | 13.1250 | 0.810867 | ||||||||
\(263\) | 5.87654 | 0.362363 | 0.181181 | − | 0.983450i | \(-0.442008\pi\) | ||||
0.181181 | + | 0.983450i | \(0.442008\pi\) | |||||||
\(264\) | 0.616990 | 0.0379731 | ||||||||
\(265\) | 14.1247 | 0.867671 | ||||||||
\(266\) | −13.6246 | −0.835378 | ||||||||
\(267\) | 3.61318 | 0.221123 | ||||||||
\(268\) | 2.46140 | 0.150354 | ||||||||
\(269\) | −3.61181 | −0.220216 | −0.110108 | − | 0.993920i | \(-0.535120\pi\) | ||||
−0.110108 | + | 0.993920i | \(0.535120\pi\) | |||||||
\(270\) | 3.31493 | 0.201740 | ||||||||
\(271\) | −23.1450 | −1.40596 | −0.702980 | − | 0.711209i | \(-0.748148\pi\) | ||||
−0.702980 | + | 0.711209i | \(0.748148\pi\) | |||||||
\(272\) | −7.70990 | −0.467481 | ||||||||
\(273\) | −1.62345 | −0.0982559 | ||||||||
\(274\) | 28.6357 | 1.72995 | ||||||||
\(275\) | −0.272892 | −0.0164560 | ||||||||
\(276\) | 0.260930 | 0.0157061 | ||||||||
\(277\) | 15.9558 | 0.958693 | 0.479346 | − | 0.877626i | \(-0.340874\pi\) | ||||
0.479346 | + | 0.877626i | \(0.340874\pi\) | |||||||
\(278\) | 12.7127 | 0.762459 | ||||||||
\(279\) | −0.615304 | −0.0368373 | ||||||||
\(280\) | −16.8842 | −1.00902 | ||||||||
\(281\) | −3.25850 | −0.194386 | −0.0971928 | − | 0.995266i | \(-0.530986\pi\) | ||||
−0.0971928 | + | 0.995266i | \(0.530986\pi\) | |||||||
\(282\) | 7.77895 | 0.463229 | ||||||||
\(283\) | 7.75465 | 0.460966 | 0.230483 | − | 0.973076i | \(-0.425969\pi\) | ||||
0.230483 | + | 0.973076i | \(0.425969\pi\) | |||||||
\(284\) | −0.354374 | −0.0210282 | ||||||||
\(285\) | 11.5282 | 0.682872 | ||||||||
\(286\) | −0.196658 | −0.0116287 | ||||||||
\(287\) | 7.65790 | 0.452031 | ||||||||
\(288\) | −1.46618 | −0.0863954 | ||||||||
\(289\) | −11.8882 | −0.699306 | ||||||||
\(290\) | −3.31493 | −0.194659 | ||||||||
\(291\) | −1.72542 | −0.101146 | ||||||||
\(292\) | 0.332356 | 0.0194497 | ||||||||
\(293\) | 23.5594 | 1.37636 | 0.688178 | − | 0.725541i | \(-0.258411\pi\) | ||||
0.688178 | + | 0.725541i | \(0.258411\pi\) | |||||||
\(294\) | −2.53855 | −0.148051 | ||||||||
\(295\) | 3.10187 | 0.180598 | ||||||||
\(296\) | 5.49422 | 0.319345 | ||||||||
\(297\) | 0.206934 | 0.0120076 | ||||||||
\(298\) | −5.02747 | −0.291234 | ||||||||
\(299\) | −0.720644 | −0.0416759 | ||||||||
\(300\) | 0.344098 | 0.0198665 | ||||||||
\(301\) | 19.1526 | 1.10394 | ||||||||
\(302\) | 31.8444 | 1.83244 | ||||||||
\(303\) | 5.34150 | 0.306861 | ||||||||
\(304\) | 15.6390 | 0.896956 | ||||||||
\(305\) | 23.5646 | 1.34930 | ||||||||
\(306\) | −2.98157 | −0.170445 | ||||||||
\(307\) | 11.0124 | 0.628509 | 0.314254 | − | 0.949339i | \(-0.398245\pi\) | ||||
0.314254 | + | 0.949339i | \(0.398245\pi\) | |||||||
\(308\) | −0.121640 | −0.00693107 | ||||||||
\(309\) | 8.03732 | 0.457227 | ||||||||
\(310\) | 2.03969 | 0.115846 | ||||||||
\(311\) | −4.46225 | −0.253031 | −0.126515 | − | 0.991965i | \(-0.540379\pi\) | ||||
−0.126515 | + | 0.991965i | \(0.540379\pi\) | |||||||
\(312\) | 2.14866 | 0.121644 | ||||||||
\(313\) | 11.9157 | 0.673516 | 0.336758 | − | 0.941591i | \(-0.390670\pi\) | ||||
0.336758 | + | 0.941591i | \(0.390670\pi\) | |||||||
\(314\) | −18.0839 | −1.02053 | ||||||||
\(315\) | −5.66284 | −0.319065 | ||||||||
\(316\) | −2.44250 | −0.137402 | ||||||||
\(317\) | −2.70900 | −0.152153 | −0.0760764 | − | 0.997102i | \(-0.524239\pi\) | ||||
−0.0760764 | + | 0.997102i | \(0.524239\pi\) | |||||||
\(318\) | 7.41006 | 0.415535 | ||||||||
\(319\) | −0.206934 | −0.0115861 | ||||||||
\(320\) | 22.0041 | 1.23006 | ||||||||
\(321\) | 3.51280 | 0.196065 | ||||||||
\(322\) | 2.97083 | 0.165558 | ||||||||
\(323\) | −10.3689 | −0.576942 | ||||||||
\(324\) | −0.260930 | −0.0144961 | ||||||||
\(325\) | −0.950341 | −0.0527155 | ||||||||
\(326\) | −1.48335 | −0.0821553 | ||||||||
\(327\) | −18.5175 | −1.02402 | ||||||||
\(328\) | −10.1353 | −0.559628 | ||||||||
\(329\) | −13.2887 | −0.732627 | ||||||||
\(330\) | −0.685972 | −0.0377615 | ||||||||
\(331\) | −10.9224 | −0.600349 | −0.300175 | − | 0.953884i | \(-0.597045\pi\) | ||||
−0.300175 | + | 0.953884i | \(0.597045\pi\) | |||||||
\(332\) | 3.51316 | 0.192809 | ||||||||
\(333\) | 1.84272 | 0.100981 | ||||||||
\(334\) | −9.46790 | −0.518061 | ||||||||
\(335\) | −23.7123 | −1.29554 | ||||||||
\(336\) | −7.68211 | −0.419093 | ||||||||
\(337\) | 35.6784 | 1.94353 | 0.971763 | − | 0.235960i | \(-0.0758235\pi\) | ||||
0.971763 | + | 0.235960i | \(0.0758235\pi\) | |||||||
\(338\) | 16.4587 | 0.895237 | ||||||||
\(339\) | 17.2446 | 0.936599 | ||||||||
\(340\) | −1.48295 | −0.0804242 | ||||||||
\(341\) | 0.127328 | 0.00689518 | ||||||||
\(342\) | 6.04791 | 0.327033 | ||||||||
\(343\) | 20.1060 | 1.08562 | ||||||||
\(344\) | −25.3486 | −1.36670 | ||||||||
\(345\) | −2.51371 | −0.135334 | ||||||||
\(346\) | −4.47477 | −0.240565 | ||||||||
\(347\) | 11.2710 | 0.605060 | 0.302530 | − | 0.953140i | \(-0.402169\pi\) | ||||
0.302530 | + | 0.953140i | \(0.402169\pi\) | |||||||
\(348\) | 0.260930 | 0.0139873 | ||||||||
\(349\) | −12.9056 | −0.690823 | −0.345412 | − | 0.938451i | \(-0.612261\pi\) | ||||
−0.345412 | + | 0.938451i | \(0.612261\pi\) | |||||||
\(350\) | 3.91774 | 0.209412 | ||||||||
\(351\) | 0.720644 | 0.0384652 | ||||||||
\(352\) | 0.303403 | 0.0161714 | ||||||||
\(353\) | 6.75930 | 0.359761 | 0.179881 | − | 0.983688i | \(-0.442429\pi\) | ||||
0.179881 | + | 0.983688i | \(0.442429\pi\) | |||||||
\(354\) | 1.62730 | 0.0864899 | ||||||||
\(355\) | 3.41392 | 0.181192 | ||||||||
\(356\) | 0.942786 | 0.0499675 | ||||||||
\(357\) | 5.09338 | 0.269570 | ||||||||
\(358\) | 16.3216 | 0.862624 | ||||||||
\(359\) | 33.2370 | 1.75418 | 0.877091 | − | 0.480325i | \(-0.159481\pi\) | ||||
0.877091 | + | 0.480325i | \(0.159481\pi\) | |||||||
\(360\) | 7.49481 | 0.395011 | ||||||||
\(361\) | 2.03260 | 0.106979 | ||||||||
\(362\) | 28.3958 | 1.49245 | ||||||||
\(363\) | 10.9572 | 0.575103 | ||||||||
\(364\) | −0.423607 | −0.0222031 | ||||||||
\(365\) | −3.20181 | −0.167590 | ||||||||
\(366\) | 12.3624 | 0.646193 | ||||||||
\(367\) | 12.7646 | 0.666308 | 0.333154 | − | 0.942872i | \(-0.391887\pi\) | ||||
0.333154 | + | 0.942872i | \(0.391887\pi\) | |||||||
\(368\) | −3.41006 | −0.177761 | ||||||||
\(369\) | −3.39931 | −0.176961 | ||||||||
\(370\) | −6.10849 | −0.317565 | ||||||||
\(371\) | −12.6585 | −0.657196 | ||||||||
\(372\) | −0.160551 | −0.00832419 | ||||||||
\(373\) | −18.6085 | −0.963511 | −0.481756 | − | 0.876306i | \(-0.660001\pi\) | ||||
−0.481756 | + | 0.876306i | \(0.660001\pi\) | |||||||
\(374\) | 0.616990 | 0.0319038 | ||||||||
\(375\) | 9.25362 | 0.477855 | ||||||||
\(376\) | 17.5876 | 0.907014 | ||||||||
\(377\) | −0.720644 | −0.0371151 | ||||||||
\(378\) | −2.97083 | −0.152803 | ||||||||
\(379\) | −7.61409 | −0.391109 | −0.195555 | − | 0.980693i | \(-0.562651\pi\) | ||||
−0.195555 | + | 0.980693i | \(0.562651\pi\) | |||||||
\(380\) | 3.00805 | 0.154310 | ||||||||
\(381\) | −14.4331 | −0.739429 | ||||||||
\(382\) | 24.5941 | 1.25834 | ||||||||
\(383\) | −6.30303 | −0.322070 | −0.161035 | − | 0.986949i | \(-0.551483\pi\) | ||||
−0.161035 | + | 0.986949i | \(0.551483\pi\) | |||||||
\(384\) | 8.61137 | 0.439447 | ||||||||
\(385\) | 1.17184 | 0.0597223 | ||||||||
\(386\) | 10.7613 | 0.547736 | ||||||||
\(387\) | −8.50175 | −0.432168 | ||||||||
\(388\) | −0.450214 | −0.0228561 | ||||||||
\(389\) | −19.1940 | −0.973175 | −0.486588 | − | 0.873632i | \(-0.661759\pi\) | ||||
−0.486588 | + | 0.873632i | \(0.661759\pi\) | |||||||
\(390\) | −2.38888 | −0.120966 | ||||||||
\(391\) | 2.26093 | 0.114340 | ||||||||
\(392\) | −5.73947 | −0.289887 | ||||||||
\(393\) | 9.95272 | 0.502048 | ||||||||
\(394\) | −17.8425 | −0.898890 | ||||||||
\(395\) | 23.5303 | 1.18394 | ||||||||
\(396\) | 0.0539954 | 0.00271337 | ||||||||
\(397\) | 3.97724 | 0.199612 | 0.0998059 | − | 0.995007i | \(-0.468178\pi\) | ||||
0.0998059 | + | 0.995007i | \(0.468178\pi\) | |||||||
\(398\) | 5.05894 | 0.253582 | ||||||||
\(399\) | −10.3315 | −0.517224 | ||||||||
\(400\) | −4.49697 | −0.224849 | ||||||||
\(401\) | −7.76968 | −0.387999 | −0.194000 | − | 0.981002i | \(-0.562146\pi\) | ||||
−0.194000 | + | 0.981002i | \(0.562146\pi\) | |||||||
\(402\) | −12.4399 | −0.620446 | ||||||||
\(403\) | 0.443415 | 0.0220881 | ||||||||
\(404\) | 1.39376 | 0.0693420 | ||||||||
\(405\) | 2.51371 | 0.124907 | ||||||||
\(406\) | 2.97083 | 0.147440 | ||||||||
\(407\) | −0.381323 | −0.0189015 | ||||||||
\(408\) | −6.74113 | −0.333736 | ||||||||
\(409\) | 24.8374 | 1.22813 | 0.614066 | − | 0.789255i | \(-0.289533\pi\) | ||||
0.614066 | + | 0.789255i | \(0.289533\pi\) | |||||||
\(410\) | 11.2685 | 0.556509 | ||||||||
\(411\) | 21.7145 | 1.07110 | ||||||||
\(412\) | 2.09718 | 0.103321 | ||||||||
\(413\) | −2.77989 | −0.136789 | ||||||||
\(414\) | −1.31874 | −0.0648124 | ||||||||
\(415\) | −33.8446 | −1.66136 | ||||||||
\(416\) | 1.05659 | 0.0518037 | ||||||||
\(417\) | 9.64007 | 0.472076 | ||||||||
\(418\) | −1.25152 | −0.0612138 | ||||||||
\(419\) | 2.53323 | 0.123756 | 0.0618782 | − | 0.998084i | \(-0.480291\pi\) | ||||
0.0618782 | + | 0.998084i | \(0.480291\pi\) | |||||||
\(420\) | −1.47760 | −0.0720996 | ||||||||
\(421\) | −0.486597 | −0.0237153 | −0.0118576 | − | 0.999930i | \(-0.503774\pi\) | ||||
−0.0118576 | + | 0.999930i | \(0.503774\pi\) | |||||||
\(422\) | 23.8219 | 1.15963 | ||||||||
\(423\) | 5.89878 | 0.286808 | ||||||||
\(424\) | 16.7536 | 0.813628 | ||||||||
\(425\) | 2.98157 | 0.144628 | ||||||||
\(426\) | 1.79101 | 0.0867745 | ||||||||
\(427\) | −21.1185 | −1.02200 | ||||||||
\(428\) | 0.916594 | 0.0443052 | ||||||||
\(429\) | −0.149126 | −0.00719988 | ||||||||
\(430\) | 28.1827 | 1.35909 | ||||||||
\(431\) | 17.1122 | 0.824267 | 0.412133 | − | 0.911123i | \(-0.364784\pi\) | ||||
0.412133 | + | 0.911123i | \(0.364784\pi\) | |||||||
\(432\) | 3.41006 | 0.164066 | ||||||||
\(433\) | −25.5910 | −1.22982 | −0.614912 | − | 0.788596i | \(-0.710808\pi\) | ||||
−0.614912 | + | 0.788596i | \(0.710808\pi\) | |||||||
\(434\) | −1.82796 | −0.0877450 | ||||||||
\(435\) | −2.51371 | −0.120523 | ||||||||
\(436\) | −4.83177 | −0.231400 | ||||||||
\(437\) | −4.58613 | −0.219384 | ||||||||
\(438\) | −1.67973 | −0.0802604 | ||||||||
\(439\) | −7.57936 | −0.361743 | −0.180872 | − | 0.983507i | \(-0.557892\pi\) | ||||
−0.180872 | + | 0.983507i | \(0.557892\pi\) | |||||||
\(440\) | −1.55094 | −0.0739379 | ||||||||
\(441\) | −1.92498 | −0.0916658 | ||||||||
\(442\) | 2.14866 | 0.102201 | ||||||||
\(443\) | 8.39708 | 0.398958 | 0.199479 | − | 0.979902i | \(-0.436075\pi\) | ||||
0.199479 | + | 0.979902i | \(0.436075\pi\) | |||||||
\(444\) | 0.480822 | 0.0228188 | ||||||||
\(445\) | −9.08248 | −0.430551 | ||||||||
\(446\) | −7.67505 | −0.363424 | ||||||||
\(447\) | −3.81234 | −0.180317 | ||||||||
\(448\) | −19.7200 | −0.931681 | ||||||||
\(449\) | 30.7310 | 1.45029 | 0.725144 | − | 0.688597i | \(-0.241773\pi\) | ||||
0.725144 | + | 0.688597i | \(0.241773\pi\) | |||||||
\(450\) | −1.73907 | −0.0819806 | ||||||||
\(451\) | 0.703434 | 0.0331234 | ||||||||
\(452\) | 4.49963 | 0.211645 | ||||||||
\(453\) | 24.1476 | 1.13455 | ||||||||
\(454\) | 20.2404 | 0.949931 | ||||||||
\(455\) | 4.08089 | 0.191315 | ||||||||
\(456\) | 13.6739 | 0.640339 | ||||||||
\(457\) | 1.32954 | 0.0621932 | 0.0310966 | − | 0.999516i | \(-0.490100\pi\) | ||||
0.0310966 | + | 0.999516i | \(0.490100\pi\) | |||||||
\(458\) | 20.8595 | 0.974700 | ||||||||
\(459\) | −2.26093 | −0.105531 | ||||||||
\(460\) | −0.655902 | −0.0305816 | ||||||||
\(461\) | −7.33804 | −0.341767 | −0.170883 | − | 0.985291i | \(-0.554662\pi\) | ||||
−0.170883 | + | 0.985291i | \(0.554662\pi\) | |||||||
\(462\) | 0.614766 | 0.0286015 | ||||||||
\(463\) | −2.68755 | −0.124901 | −0.0624506 | − | 0.998048i | \(-0.519892\pi\) | ||||
−0.0624506 | + | 0.998048i | \(0.519892\pi\) | |||||||
\(464\) | −3.41006 | −0.158308 | ||||||||
\(465\) | 1.54670 | 0.0717263 | ||||||||
\(466\) | −14.2508 | −0.660156 | ||||||||
\(467\) | 6.84657 | 0.316821 | 0.158411 | − | 0.987373i | \(-0.449363\pi\) | ||||
0.158411 | + | 0.987373i | \(0.449363\pi\) | |||||||
\(468\) | 0.188038 | 0.00869204 | ||||||||
\(469\) | 21.2509 | 0.981276 | ||||||||
\(470\) | −19.5540 | −0.901959 | ||||||||
\(471\) | −13.7130 | −0.631863 | ||||||||
\(472\) | 3.67921 | 0.169349 | ||||||||
\(473\) | 1.75930 | 0.0808929 | ||||||||
\(474\) | 12.3444 | 0.566997 | ||||||||
\(475\) | −6.04791 | −0.277497 | ||||||||
\(476\) | 1.32901 | 0.0609153 | ||||||||
\(477\) | 5.61905 | 0.257279 | ||||||||
\(478\) | 16.4661 | 0.753143 | ||||||||
\(479\) | 15.1503 | 0.692236 | 0.346118 | − | 0.938191i | \(-0.387500\pi\) | ||||
0.346118 | + | 0.938191i | \(0.387500\pi\) | |||||||
\(480\) | 3.68555 | 0.168221 | ||||||||
\(481\) | −1.32795 | −0.0605493 | ||||||||
\(482\) | 5.19865 | 0.236792 | ||||||||
\(483\) | 2.25278 | 0.102505 | ||||||||
\(484\) | 2.85905 | 0.129957 | ||||||||
\(485\) | 4.33721 | 0.196942 | ||||||||
\(486\) | 1.31874 | 0.0598192 | ||||||||
\(487\) | −2.30603 | −0.104496 | −0.0522481 | − | 0.998634i | \(-0.516639\pi\) | ||||
−0.0522481 | + | 0.998634i | \(0.516639\pi\) | |||||||
\(488\) | 27.9505 | 1.26526 | ||||||||
\(489\) | −1.12483 | −0.0508665 | ||||||||
\(490\) | 6.38117 | 0.288272 | ||||||||
\(491\) | −30.1262 | −1.35958 | −0.679789 | − | 0.733408i | \(-0.737929\pi\) | ||||
−0.679789 | + | 0.733408i | \(0.737929\pi\) | |||||||
\(492\) | −0.886981 | −0.0399882 | ||||||||
\(493\) | 2.26093 | 0.101827 | ||||||||
\(494\) | −4.35839 | −0.196093 | ||||||||
\(495\) | −0.520173 | −0.0233800 | ||||||||
\(496\) | 2.09822 | 0.0942129 | ||||||||
\(497\) | −3.05955 | −0.137239 | ||||||||
\(498\) | −17.7555 | −0.795642 | ||||||||
\(499\) | 14.1251 | 0.632328 | 0.316164 | − | 0.948705i | \(-0.397605\pi\) | ||||
0.316164 | + | 0.948705i | \(0.397605\pi\) | |||||||
\(500\) | 2.41455 | 0.107982 | ||||||||
\(501\) | −7.17952 | −0.320757 | ||||||||
\(502\) | −8.96729 | −0.400230 | ||||||||
\(503\) | −28.0963 | −1.25275 | −0.626377 | − | 0.779521i | \(-0.715463\pi\) | ||||
−0.626377 | + | 0.779521i | \(0.715463\pi\) | |||||||
\(504\) | −6.71683 | −0.299191 | ||||||||
\(505\) | −13.4270 | −0.597493 | ||||||||
\(506\) | 0.272892 | 0.0121315 | ||||||||
\(507\) | 12.4807 | 0.554286 | ||||||||
\(508\) | −3.76602 | −0.167090 | ||||||||
\(509\) | −5.49940 | −0.243757 | −0.121878 | − | 0.992545i | \(-0.538892\pi\) | ||||
−0.121878 | + | 0.992545i | \(0.538892\pi\) | |||||||
\(510\) | 7.49481 | 0.331876 | ||||||||
\(511\) | 2.86945 | 0.126937 | ||||||||
\(512\) | 25.3344 | 1.11963 | ||||||||
\(513\) | 4.58613 | 0.202483 | ||||||||
\(514\) | 33.6191 | 1.48287 | ||||||||
\(515\) | −20.2035 | −0.890273 | ||||||||
\(516\) | −2.21836 | −0.0976578 | ||||||||
\(517\) | −1.22066 | −0.0536846 | ||||||||
\(518\) | 5.47442 | 0.240532 | ||||||||
\(519\) | −3.39322 | −0.148946 | ||||||||
\(520\) | −5.40110 | −0.236854 | ||||||||
\(521\) | 19.0771 | 0.835783 | 0.417892 | − | 0.908497i | \(-0.362769\pi\) | ||||
0.417892 | + | 0.908497i | \(0.362769\pi\) | |||||||
\(522\) | −1.31874 | −0.0577196 | ||||||||
\(523\) | −5.59256 | −0.244545 | −0.122273 | − | 0.992497i | \(-0.539018\pi\) | ||||
−0.122273 | + | 0.992497i | \(0.539018\pi\) | |||||||
\(524\) | 2.59696 | 0.113449 | ||||||||
\(525\) | 2.97083 | 0.129658 | ||||||||
\(526\) | −7.74961 | −0.337899 | ||||||||
\(527\) | −1.39116 | −0.0605998 | ||||||||
\(528\) | −0.705658 | −0.0307098 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | −18.6267 | −0.809094 | ||||||||
\(531\) | 1.23398 | 0.0535502 | ||||||||
\(532\) | −2.69581 | −0.116878 | ||||||||
\(533\) | 2.44969 | 0.106108 | ||||||||
\(534\) | −4.76483 | −0.206195 | ||||||||
\(535\) | −8.83016 | −0.381761 | ||||||||
\(536\) | −28.1258 | −1.21485 | ||||||||
\(537\) | 12.3767 | 0.534094 | ||||||||
\(538\) | 4.76303 | 0.205349 | ||||||||
\(539\) | 0.398345 | 0.0171579 | ||||||||
\(540\) | 0.655902 | 0.0282255 | ||||||||
\(541\) | 12.7925 | 0.549994 | 0.274997 | − | 0.961445i | \(-0.411323\pi\) | ||||
0.274997 | + | 0.961445i | \(0.411323\pi\) | |||||||
\(542\) | 30.5222 | 1.31104 | ||||||||
\(543\) | 21.5325 | 0.924050 | ||||||||
\(544\) | −3.31493 | −0.142126 | ||||||||
\(545\) | 46.5476 | 1.99388 | ||||||||
\(546\) | 2.14091 | 0.0916225 | ||||||||
\(547\) | −28.1352 | −1.20298 | −0.601488 | − | 0.798882i | \(-0.705425\pi\) | ||||
−0.601488 | + | 0.798882i | \(0.705425\pi\) | |||||||
\(548\) | 5.66596 | 0.242038 | ||||||||
\(549\) | 9.37442 | 0.400090 | ||||||||
\(550\) | 0.359874 | 0.0153451 | ||||||||
\(551\) | −4.58613 | −0.195376 | ||||||||
\(552\) | −2.98157 | −0.126904 | ||||||||
\(553\) | −21.0878 | −0.896743 | ||||||||
\(554\) | −21.0416 | −0.893970 | ||||||||
\(555\) | −4.63207 | −0.196621 | ||||||||
\(556\) | 2.51538 | 0.106676 | ||||||||
\(557\) | −0.823300 | −0.0348843 | −0.0174422 | − | 0.999848i | \(-0.505552\pi\) | ||||
−0.0174422 | + | 0.999848i | \(0.505552\pi\) | |||||||
\(558\) | 0.811425 | 0.0343504 | ||||||||
\(559\) | 6.12674 | 0.259133 | ||||||||
\(560\) | 19.3106 | 0.816021 | ||||||||
\(561\) | 0.467864 | 0.0197532 | ||||||||
\(562\) | 4.29710 | 0.181262 | ||||||||
\(563\) | 20.8016 | 0.876684 | 0.438342 | − | 0.898808i | \(-0.355566\pi\) | ||||
0.438342 | + | 0.898808i | \(0.355566\pi\) | |||||||
\(564\) | 1.53917 | 0.0648106 | ||||||||
\(565\) | −43.3480 | −1.82366 | ||||||||
\(566\) | −10.2263 | −0.429845 | ||||||||
\(567\) | −2.25278 | −0.0946079 | ||||||||
\(568\) | 4.04934 | 0.169906 | ||||||||
\(569\) | −8.48857 | −0.355859 | −0.177930 | − | 0.984043i | \(-0.556940\pi\) | ||||
−0.177930 | + | 0.984043i | \(0.556940\pi\) | |||||||
\(570\) | −15.2027 | −0.636770 | ||||||||
\(571\) | 1.08653 | 0.0454698 | 0.0227349 | − | 0.999742i | \(-0.492763\pi\) | ||||
0.0227349 | + | 0.999742i | \(0.492763\pi\) | |||||||
\(572\) | −0.0389115 | −0.00162697 | ||||||||
\(573\) | 18.6497 | 0.779102 | ||||||||
\(574\) | −10.0988 | −0.421514 | ||||||||
\(575\) | 1.31874 | 0.0549952 | ||||||||
\(576\) | 8.75362 | 0.364734 | ||||||||
\(577\) | 39.2324 | 1.63327 | 0.816634 | − | 0.577156i | \(-0.195838\pi\) | ||||
0.816634 | + | 0.577156i | \(0.195838\pi\) | |||||||
\(578\) | 15.6774 | 0.652095 | ||||||||
\(579\) | 8.16030 | 0.339130 | ||||||||
\(580\) | −0.655902 | −0.0272348 | ||||||||
\(581\) | 30.3314 | 1.25836 | ||||||||
\(582\) | 2.27538 | 0.0943175 | ||||||||
\(583\) | −1.16278 | −0.0481572 | ||||||||
\(584\) | −3.79774 | −0.157152 | ||||||||
\(585\) | −1.81149 | −0.0748959 | ||||||||
\(586\) | −31.0687 | −1.28344 | ||||||||
\(587\) | −13.3533 | −0.551152 | −0.275576 | − | 0.961279i | \(-0.588869\pi\) | ||||
−0.275576 | + | 0.961279i | \(0.588869\pi\) | |||||||
\(588\) | −0.502285 | −0.0207139 | ||||||||
\(589\) | 2.82186 | 0.116273 | ||||||||
\(590\) | −4.09055 | −0.168405 | ||||||||
\(591\) | −13.5299 | −0.556547 | ||||||||
\(592\) | −6.28379 | −0.258262 | ||||||||
\(593\) | 11.9242 | 0.489668 | 0.244834 | − | 0.969565i | \(-0.421267\pi\) | ||||
0.244834 | + | 0.969565i | \(0.421267\pi\) | |||||||
\(594\) | −0.272892 | −0.0111969 | ||||||||
\(595\) | −12.8033 | −0.524883 | ||||||||
\(596\) | −0.994752 | −0.0407466 | ||||||||
\(597\) | 3.83619 | 0.157005 | ||||||||
\(598\) | 0.950341 | 0.0388623 | ||||||||
\(599\) | 19.6776 | 0.804004 | 0.402002 | − | 0.915639i | \(-0.368315\pi\) | ||||
0.402002 | + | 0.915639i | \(0.368315\pi\) | |||||||
\(600\) | −3.93192 | −0.160520 | ||||||||
\(601\) | −2.28447 | −0.0931854 | −0.0465927 | − | 0.998914i | \(-0.514836\pi\) | ||||
−0.0465927 | + | 0.998914i | \(0.514836\pi\) | |||||||
\(602\) | −25.2572 | −1.02941 | ||||||||
\(603\) | −9.43319 | −0.384149 | ||||||||
\(604\) | 6.30084 | 0.256377 | ||||||||
\(605\) | −27.5432 | −1.11979 | ||||||||
\(606\) | −7.04404 | −0.286145 | ||||||||
\(607\) | 35.5364 | 1.44238 | 0.721188 | − | 0.692739i | \(-0.243596\pi\) | ||||
0.721188 | + | 0.692739i | \(0.243596\pi\) | |||||||
\(608\) | 6.72408 | 0.272698 | ||||||||
\(609\) | 2.25278 | 0.0912873 | ||||||||
\(610\) | −31.0755 | −1.25821 | ||||||||
\(611\) | −4.25092 | −0.171974 | ||||||||
\(612\) | −0.589944 | −0.0238471 | ||||||||
\(613\) | −6.04229 | −0.244046 | −0.122023 | − | 0.992527i | \(-0.538938\pi\) | ||||
−0.122023 | + | 0.992527i | \(0.538938\pi\) | |||||||
\(614\) | −14.5224 | −0.586078 | ||||||||
\(615\) | 8.54488 | 0.344563 | ||||||||
\(616\) | 1.38994 | 0.0560024 | ||||||||
\(617\) | 12.1271 | 0.488220 | 0.244110 | − | 0.969748i | \(-0.421504\pi\) | ||||
0.244110 | + | 0.969748i | \(0.421504\pi\) | |||||||
\(618\) | −10.5991 | −0.426359 | ||||||||
\(619\) | 40.4628 | 1.62634 | 0.813168 | − | 0.582028i | \(-0.197741\pi\) | ||||
0.813168 | + | 0.582028i | \(0.197741\pi\) | |||||||
\(620\) | 0.403579 | 0.0162081 | ||||||||
\(621\) | −1.00000 | −0.0401286 | ||||||||
\(622\) | 5.88453 | 0.235948 | ||||||||
\(623\) | 8.13969 | 0.326110 | ||||||||
\(624\) | −2.45744 | −0.0983763 | ||||||||
\(625\) | −29.8546 | −1.19418 | ||||||||
\(626\) | −15.7137 | −0.628046 | ||||||||
\(627\) | −0.949029 | −0.0379005 | ||||||||
\(628\) | −3.57814 | −0.142783 | ||||||||
\(629\) | 4.16627 | 0.166120 | ||||||||
\(630\) | 7.46780 | 0.297524 | ||||||||
\(631\) | −26.9996 | −1.07484 | −0.537418 | − | 0.843316i | \(-0.680600\pi\) | ||||
−0.537418 | + | 0.843316i | \(0.680600\pi\) | |||||||
\(632\) | 27.9098 | 1.11019 | ||||||||
\(633\) | 18.0641 | 0.717985 | ||||||||
\(634\) | 3.57247 | 0.141881 | ||||||||
\(635\) | 36.2806 | 1.43975 | ||||||||
\(636\) | 1.46618 | 0.0581377 | ||||||||
\(637\) | 1.38723 | 0.0549639 | ||||||||
\(638\) | 0.272892 | 0.0108039 | ||||||||
\(639\) | 1.35812 | 0.0537264 | ||||||||
\(640\) | −21.6465 | −0.855653 | ||||||||
\(641\) | −3.52991 | −0.139423 | −0.0697116 | − | 0.997567i | \(-0.522208\pi\) | ||||
−0.0697116 | + | 0.997567i | \(0.522208\pi\) | |||||||
\(642\) | −4.63246 | −0.182829 | ||||||||
\(643\) | −24.7084 | −0.974405 | −0.487203 | − | 0.873289i | \(-0.661983\pi\) | ||||
−0.487203 | + | 0.873289i | \(0.661983\pi\) | |||||||
\(644\) | 0.587818 | 0.0231633 | ||||||||
\(645\) | 21.3709 | 0.841479 | ||||||||
\(646\) | 13.6739 | 0.537992 | ||||||||
\(647\) | 9.56460 | 0.376023 | 0.188012 | − | 0.982167i | \(-0.439796\pi\) | ||||
0.188012 | + | 0.982167i | \(0.439796\pi\) | |||||||
\(648\) | 2.98157 | 0.117127 | ||||||||
\(649\) | −0.255353 | −0.0100235 | ||||||||
\(650\) | 1.25325 | 0.0491566 | ||||||||
\(651\) | −1.38614 | −0.0543273 | ||||||||
\(652\) | −0.293501 | −0.0114944 | ||||||||
\(653\) | −9.70004 | −0.379592 | −0.189796 | − | 0.981824i | \(-0.560783\pi\) | ||||
−0.189796 | + | 0.981824i | \(0.560783\pi\) | |||||||
\(654\) | 24.4197 | 0.954888 | ||||||||
\(655\) | −25.0183 | −0.977544 | ||||||||
\(656\) | 11.5918 | 0.452585 | ||||||||
\(657\) | −1.27374 | −0.0496932 | ||||||||
\(658\) | 17.5243 | 0.683167 | ||||||||
\(659\) | 16.1697 | 0.629881 | 0.314940 | − | 0.949111i | \(-0.398015\pi\) | ||||
0.314940 | + | 0.949111i | \(0.398015\pi\) | |||||||
\(660\) | −0.135729 | −0.00528323 | ||||||||
\(661\) | 15.2278 | 0.592295 | 0.296147 | − | 0.955142i | \(-0.404298\pi\) | ||||
0.296147 | + | 0.955142i | \(0.404298\pi\) | |||||||
\(662\) | 14.4038 | 0.559819 | ||||||||
\(663\) | 1.62933 | 0.0632778 | ||||||||
\(664\) | −40.1439 | −1.55788 | ||||||||
\(665\) | 25.9705 | 1.00709 | ||||||||
\(666\) | −2.43007 | −0.0941633 | ||||||||
\(667\) | 1.00000 | 0.0387202 | ||||||||
\(668\) | −1.87335 | −0.0724821 | ||||||||
\(669\) | −5.81999 | −0.225014 | ||||||||
\(670\) | 31.2703 | 1.20808 | ||||||||
\(671\) | −1.93989 | −0.0748886 | ||||||||
\(672\) | −3.30298 | −0.127415 | ||||||||
\(673\) | −30.1373 | −1.16171 | −0.580854 | − | 0.814008i | \(-0.697281\pi\) | ||||
−0.580854 | + | 0.814008i | \(0.697281\pi\) | |||||||
\(674\) | −47.0504 | −1.81232 | ||||||||
\(675\) | −1.31874 | −0.0507583 | ||||||||
\(676\) | 3.25658 | 0.125253 | ||||||||
\(677\) | −4.23918 | −0.162925 | −0.0814624 | − | 0.996676i | \(-0.525959\pi\) | ||||
−0.0814624 | + | 0.996676i | \(0.525959\pi\) | |||||||
\(678\) | −22.7411 | −0.873368 | ||||||||
\(679\) | −3.88699 | −0.149169 | ||||||||
\(680\) | 16.9452 | 0.649821 | ||||||||
\(681\) | 15.3483 | 0.588150 | ||||||||
\(682\) | −0.167912 | −0.00642967 | ||||||||
\(683\) | −45.8651 | −1.75498 | −0.877490 | − | 0.479596i | \(-0.840783\pi\) | ||||
−0.877490 | + | 0.479596i | \(0.840783\pi\) | |||||||
\(684\) | 1.19666 | 0.0457554 | ||||||||
\(685\) | −54.5839 | −2.08554 | ||||||||
\(686\) | −26.5146 | −1.01233 | ||||||||
\(687\) | 15.8178 | 0.603486 | ||||||||
\(688\) | 28.9914 | 1.10529 | ||||||||
\(689\) | −4.04934 | −0.154267 | ||||||||
\(690\) | 3.31493 | 0.126197 | ||||||||
\(691\) | 32.6070 | 1.24043 | 0.620215 | − | 0.784432i | \(-0.287046\pi\) | ||||
0.620215 | + | 0.784432i | \(0.287046\pi\) | |||||||
\(692\) | −0.885392 | −0.0336576 | ||||||||
\(693\) | 0.466178 | 0.0177086 | ||||||||
\(694\) | −14.8635 | −0.564212 | ||||||||
\(695\) | −24.2324 | −0.919185 | ||||||||
\(696\) | −2.98157 | −0.113016 | ||||||||
\(697\) | −7.68560 | −0.291113 | ||||||||
\(698\) | 17.0192 | 0.644185 | ||||||||
\(699\) | −10.8064 | −0.408735 | ||||||||
\(700\) | 0.775177 | 0.0292990 | ||||||||
\(701\) | −35.5331 | −1.34207 | −0.671033 | − | 0.741427i | \(-0.734149\pi\) | ||||
−0.671033 | + | 0.741427i | \(0.734149\pi\) | |||||||
\(702\) | −0.950341 | −0.0358683 | ||||||||
\(703\) | −8.45097 | −0.318735 | ||||||||
\(704\) | −1.81142 | −0.0682706 | ||||||||
\(705\) | −14.8278 | −0.558448 | ||||||||
\(706\) | −8.91375 | −0.335473 | ||||||||
\(707\) | 12.0332 | 0.452556 | ||||||||
\(708\) | 0.321982 | 0.0121008 | ||||||||
\(709\) | −45.4945 | −1.70858 | −0.854290 | − | 0.519796i | \(-0.826008\pi\) | ||||
−0.854290 | + | 0.519796i | \(0.826008\pi\) | |||||||
\(710\) | −4.50207 | −0.168960 | ||||||||
\(711\) | 9.36077 | 0.351056 | ||||||||
\(712\) | −10.7730 | −0.403734 | ||||||||
\(713\) | −0.615304 | −0.0230433 | ||||||||
\(714\) | −6.71683 | −0.251371 | ||||||||
\(715\) | 0.374860 | 0.0140190 | ||||||||
\(716\) | 3.22945 | 0.120690 | ||||||||
\(717\) | 12.4863 | 0.466309 | ||||||||
\(718\) | −43.8309 | −1.63575 | ||||||||
\(719\) | −20.5160 | −0.765119 | −0.382560 | − | 0.923931i | \(-0.624957\pi\) | ||||
−0.382560 | + | 0.923931i | \(0.624957\pi\) | |||||||
\(720\) | −8.57189 | −0.319456 | ||||||||
\(721\) | 18.1063 | 0.674315 | ||||||||
\(722\) | −2.68047 | −0.0997566 | ||||||||
\(723\) | 3.94214 | 0.146610 | ||||||||
\(724\) | 5.61848 | 0.208809 | ||||||||
\(725\) | 1.31874 | 0.0489767 | ||||||||
\(726\) | −14.4496 | −0.536277 | ||||||||
\(727\) | −28.3740 | −1.05233 | −0.526167 | − | 0.850382i | \(-0.676371\pi\) | ||||
−0.526167 | + | 0.850382i | \(0.676371\pi\) | |||||||
\(728\) | 4.84045 | 0.179399 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 4.22234 | 0.156276 | ||||||||
\(731\) | −19.2219 | −0.710946 | ||||||||
\(732\) | 2.44607 | 0.0904092 | ||||||||
\(733\) | 50.2037 | 1.85432 | 0.927158 | − | 0.374672i | \(-0.122245\pi\) | ||||
0.927158 | + | 0.374672i | \(0.122245\pi\) | |||||||
\(734\) | −16.8332 | −0.621324 | ||||||||
\(735\) | 4.83884 | 0.178483 | ||||||||
\(736\) | −1.46618 | −0.0540440 | ||||||||
\(737\) | 1.95205 | 0.0719048 | ||||||||
\(738\) | 4.48280 | 0.165014 | ||||||||
\(739\) | −19.7992 | −0.728326 | −0.364163 | − | 0.931335i | \(-0.618645\pi\) | ||||
−0.364163 | + | 0.931335i | \(0.618645\pi\) | |||||||
\(740\) | −1.20865 | −0.0444307 | ||||||||
\(741\) | −3.30497 | −0.121411 | ||||||||
\(742\) | 16.6932 | 0.612828 | ||||||||
\(743\) | −46.4475 | −1.70399 | −0.851997 | − | 0.523546i | \(-0.824609\pi\) | ||||
−0.851997 | + | 0.523546i | \(0.824609\pi\) | |||||||
\(744\) | 1.83457 | 0.0672588 | ||||||||
\(745\) | 9.58311 | 0.351098 | ||||||||
\(746\) | 24.5397 | 0.898463 | ||||||||
\(747\) | −13.4640 | −0.492621 | ||||||||
\(748\) | 0.122080 | 0.00446368 | ||||||||
\(749\) | 7.91356 | 0.289155 | ||||||||
\(750\) | −12.2031 | −0.445594 | ||||||||
\(751\) | 36.9387 | 1.34791 | 0.673956 | − | 0.738772i | \(-0.264594\pi\) | ||||
0.673956 | + | 0.738772i | \(0.264594\pi\) | |||||||
\(752\) | −20.1152 | −0.733525 | ||||||||
\(753\) | −6.79990 | −0.247802 | ||||||||
\(754\) | 0.950341 | 0.0346094 | ||||||||
\(755\) | −60.7001 | −2.20910 | ||||||||
\(756\) | −0.587818 | −0.0213787 | ||||||||
\(757\) | 15.5417 | 0.564872 | 0.282436 | − | 0.959286i | \(-0.408857\pi\) | ||||
0.282436 | + | 0.959286i | \(0.408857\pi\) | |||||||
\(758\) | 10.0410 | 0.364705 | ||||||||
\(759\) | 0.206934 | 0.00751124 | ||||||||
\(760\) | −34.3722 | −1.24681 | ||||||||
\(761\) | −40.6429 | −1.47330 | −0.736652 | − | 0.676272i | \(-0.763594\pi\) | ||||
−0.736652 | + | 0.676272i | \(0.763594\pi\) | |||||||
\(762\) | 19.0334 | 0.689509 | ||||||||
\(763\) | −41.7159 | −1.51022 | ||||||||
\(764\) | 4.86626 | 0.176055 | ||||||||
\(765\) | 5.68332 | 0.205481 | ||||||||
\(766\) | 8.31204 | 0.300326 | ||||||||
\(767\) | −0.889262 | −0.0321094 | ||||||||
\(768\) | 6.15109 | 0.221958 | ||||||||
\(769\) | −5.13554 | −0.185192 | −0.0925962 | − | 0.995704i | \(-0.529517\pi\) | ||||
−0.0925962 | + | 0.995704i | \(0.529517\pi\) | |||||||
\(770\) | −1.54534 | −0.0556904 | ||||||||
\(771\) | 25.4934 | 0.918121 | ||||||||
\(772\) | 2.12927 | 0.0766339 | ||||||||
\(773\) | 0.211642 | 0.00761222 | 0.00380611 | − | 0.999993i | \(-0.498788\pi\) | ||||
0.00380611 | + | 0.999993i | \(0.498788\pi\) | |||||||
\(774\) | 11.2116 | 0.402992 | ||||||||
\(775\) | −0.811425 | −0.0291472 | ||||||||
\(776\) | 5.14447 | 0.184676 | ||||||||
\(777\) | 4.15125 | 0.148925 | ||||||||
\(778\) | 25.3119 | 0.907475 | ||||||||
\(779\) | 15.5897 | 0.558558 | ||||||||
\(780\) | −0.472672 | −0.0169244 | ||||||||
\(781\) | −0.281042 | −0.0100565 | ||||||||
\(782\) | −2.98157 | −0.106621 | ||||||||
\(783\) | −1.00000 | −0.0357371 | ||||||||
\(784\) | 6.56429 | 0.234439 | ||||||||
\(785\) | 34.4706 | 1.23031 | ||||||||
\(786\) | −13.1250 | −0.468154 | ||||||||
\(787\) | 19.8563 | 0.707799 | 0.353900 | − | 0.935283i | \(-0.384855\pi\) | ||||
0.353900 | + | 0.935283i | \(0.384855\pi\) | |||||||
\(788\) | −3.53037 | −0.125764 | ||||||||
\(789\) | −5.87654 | −0.209210 | ||||||||
\(790\) | −31.0303 | −1.10401 | ||||||||
\(791\) | 38.8483 | 1.38129 | ||||||||
\(792\) | −0.616990 | −0.0219238 | ||||||||
\(793\) | −6.75562 | −0.239899 | ||||||||
\(794\) | −5.24493 | −0.186136 | ||||||||
\(795\) | −14.1247 | −0.500950 | ||||||||
\(796\) | 1.00098 | 0.0354787 | ||||||||
\(797\) | −6.41446 | −0.227212 | −0.113606 | − | 0.993526i | \(-0.536240\pi\) | ||||
−0.113606 | + | 0.993526i | \(0.536240\pi\) | |||||||
\(798\) | 13.6246 | 0.482306 | ||||||||
\(799\) | 13.3367 | 0.471819 | ||||||||
\(800\) | −1.93350 | −0.0683597 | ||||||||
\(801\) | −3.61318 | −0.127665 | ||||||||
\(802\) | 10.2462 | 0.361805 | ||||||||
\(803\) | 0.263580 | 0.00930154 | ||||||||
\(804\) | −2.46140 | −0.0868069 | ||||||||
\(805\) | −5.66284 | −0.199589 | ||||||||
\(806\) | −0.584749 | −0.0205969 | ||||||||
\(807\) | 3.61181 | 0.127142 | ||||||||
\(808\) | −15.9261 | −0.560278 | ||||||||
\(809\) | 47.7649 | 1.67932 | 0.839662 | − | 0.543109i | \(-0.182753\pi\) | ||||
0.839662 | + | 0.543109i | \(0.182753\pi\) | |||||||
\(810\) | −3.31493 | −0.116475 | ||||||||
\(811\) | −12.0735 | −0.423959 | −0.211979 | − | 0.977274i | \(-0.567991\pi\) | ||||
−0.211979 | + | 0.977274i | \(0.567991\pi\) | |||||||
\(812\) | 0.587818 | 0.0206284 | ||||||||
\(813\) | 23.1450 | 0.811732 | ||||||||
\(814\) | 0.502865 | 0.0176254 | ||||||||
\(815\) | 2.82749 | 0.0990427 | ||||||||
\(816\) | 7.70990 | 0.269900 | ||||||||
\(817\) | 38.9901 | 1.36409 | ||||||||
\(818\) | −32.7540 | −1.14522 | ||||||||
\(819\) | 1.62345 | 0.0567281 | ||||||||
\(820\) | 2.22961 | 0.0778615 | ||||||||
\(821\) | 2.12441 | 0.0741424 | 0.0370712 | − | 0.999313i | \(-0.488197\pi\) | ||||
0.0370712 | + | 0.999313i | \(0.488197\pi\) | |||||||
\(822\) | −28.6357 | −0.998786 | ||||||||
\(823\) | 14.3341 | 0.499656 | 0.249828 | − | 0.968290i | \(-0.419626\pi\) | ||||
0.249828 | + | 0.968290i | \(0.419626\pi\) | |||||||
\(824\) | −23.9639 | −0.834821 | ||||||||
\(825\) | 0.272892 | 0.00950089 | ||||||||
\(826\) | 3.66594 | 0.127554 | ||||||||
\(827\) | 27.0920 | 0.942082 | 0.471041 | − | 0.882111i | \(-0.343878\pi\) | ||||
0.471041 | + | 0.882111i | \(0.343878\pi\) | |||||||
\(828\) | −0.260930 | −0.00906794 | ||||||||
\(829\) | 14.1735 | 0.492268 | 0.246134 | − | 0.969236i | \(-0.420840\pi\) | ||||
0.246134 | + | 0.969236i | \(0.420840\pi\) | |||||||
\(830\) | 44.6321 | 1.54920 | ||||||||
\(831\) | −15.9558 | −0.553502 | ||||||||
\(832\) | −6.30825 | −0.218699 | ||||||||
\(833\) | −4.35225 | −0.150796 | ||||||||
\(834\) | −12.7127 | −0.440206 | ||||||||
\(835\) | 18.0472 | 0.624550 | ||||||||
\(836\) | −0.247630 | −0.00856446 | ||||||||
\(837\) | 0.615304 | 0.0212680 | ||||||||
\(838\) | −3.34067 | −0.115402 | ||||||||
\(839\) | −41.6889 | −1.43926 | −0.719631 | − | 0.694357i | \(-0.755689\pi\) | ||||
−0.719631 | + | 0.694357i | \(0.755689\pi\) | |||||||
\(840\) | 16.8842 | 0.582559 | ||||||||
\(841\) | 1.00000 | 0.0344828 | ||||||||
\(842\) | 0.641694 | 0.0221142 | ||||||||
\(843\) | 3.25850 | 0.112229 | ||||||||
\(844\) | 4.71347 | 0.162244 | ||||||||
\(845\) | −31.3728 | −1.07926 | ||||||||
\(846\) | −7.77895 | −0.267446 | ||||||||
\(847\) | 24.6841 | 0.848156 | ||||||||
\(848\) | −19.1613 | −0.658001 | ||||||||
\(849\) | −7.75465 | −0.266139 | ||||||||
\(850\) | −3.93192 | −0.134864 | ||||||||
\(851\) | 1.84272 | 0.0631678 | ||||||||
\(852\) | 0.354374 | 0.0121407 | ||||||||
\(853\) | 24.0066 | 0.821970 | 0.410985 | − | 0.911642i | \(-0.365185\pi\) | ||||
0.410985 | + | 0.911642i | \(0.365185\pi\) | |||||||
\(854\) | 27.8498 | 0.953000 | ||||||||
\(855\) | −11.5282 | −0.394256 | ||||||||
\(856\) | −10.4737 | −0.357983 | ||||||||
\(857\) | 28.3597 | 0.968749 | 0.484374 | − | 0.874861i | \(-0.339047\pi\) | ||||
0.484374 | + | 0.874861i | \(0.339047\pi\) | |||||||
\(858\) | 0.196658 | 0.00671381 | ||||||||
\(859\) | −12.0011 | −0.409474 | −0.204737 | − | 0.978817i | \(-0.565634\pi\) | ||||
−0.204737 | + | 0.978817i | \(0.565634\pi\) | |||||||
\(860\) | 5.57631 | 0.190151 | ||||||||
\(861\) | −7.65790 | −0.260980 | ||||||||
\(862\) | −22.5665 | −0.768620 | ||||||||
\(863\) | 31.8630 | 1.08463 | 0.542314 | − | 0.840176i | \(-0.317548\pi\) | ||||
0.542314 | + | 0.840176i | \(0.317548\pi\) | |||||||
\(864\) | 1.46618 | 0.0498804 | ||||||||
\(865\) | 8.52957 | 0.290014 | ||||||||
\(866\) | 33.7478 | 1.14680 | ||||||||
\(867\) | 11.8882 | 0.403744 | ||||||||
\(868\) | −0.361686 | −0.0122764 | ||||||||
\(869\) | −1.93707 | −0.0657105 | ||||||||
\(870\) | 3.31493 | 0.112386 | ||||||||
\(871\) | 6.79798 | 0.230341 | ||||||||
\(872\) | 55.2113 | 1.86969 | ||||||||
\(873\) | 1.72542 | 0.0583967 | ||||||||
\(874\) | 6.04791 | 0.204573 | ||||||||
\(875\) | 20.8464 | 0.704736 | ||||||||
\(876\) | −0.332356 | −0.0112293 | ||||||||
\(877\) | 5.74793 | 0.194094 | 0.0970469 | − | 0.995280i | \(-0.469060\pi\) | ||||
0.0970469 | + | 0.995280i | \(0.469060\pi\) | |||||||
\(878\) | 9.99519 | 0.337321 | ||||||||
\(879\) | −23.5594 | −0.794640 | ||||||||
\(880\) | 1.77382 | 0.0597955 | ||||||||
\(881\) | −11.9952 | −0.404128 | −0.202064 | − | 0.979372i | \(-0.564765\pi\) | ||||
−0.202064 | + | 0.979372i | \(0.564765\pi\) | |||||||
\(882\) | 2.53855 | 0.0854773 | ||||||||
\(883\) | 30.2919 | 1.01940 | 0.509701 | − | 0.860352i | \(-0.329756\pi\) | ||||
0.509701 | + | 0.860352i | \(0.329756\pi\) | |||||||
\(884\) | 0.425140 | 0.0142990 | ||||||||
\(885\) | −3.10187 | −0.104268 | ||||||||
\(886\) | −11.0736 | −0.372023 | ||||||||
\(887\) | −28.8927 | −0.970123 | −0.485062 | − | 0.874480i | \(-0.661203\pi\) | ||||
−0.485062 | + | 0.874480i | \(0.661203\pi\) | |||||||
\(888\) | −5.49422 | −0.184374 | ||||||||
\(889\) | −32.5145 | −1.09050 | ||||||||
\(890\) | 11.9774 | 0.401484 | ||||||||
\(891\) | −0.206934 | −0.00693256 | ||||||||
\(892\) | −1.51861 | −0.0508468 | ||||||||
\(893\) | −27.0526 | −0.905280 | ||||||||
\(894\) | 5.02747 | 0.168144 | ||||||||
\(895\) | −31.1114 | −1.03994 | ||||||||
\(896\) | 19.3995 | 0.648093 | ||||||||
\(897\) | 0.720644 | 0.0240616 | ||||||||
\(898\) | −40.5262 | −1.35238 | ||||||||
\(899\) | −0.615304 | −0.0205215 | ||||||||
\(900\) | −0.344098 | −0.0114699 | ||||||||
\(901\) | 12.7043 | 0.423241 | ||||||||
\(902\) | −0.927645 | −0.0308872 | ||||||||
\(903\) | −19.1526 | −0.637358 | ||||||||
\(904\) | −51.4161 | −1.71007 | ||||||||
\(905\) | −54.1266 | −1.79923 | ||||||||
\(906\) | −31.8444 | −1.05796 | ||||||||
\(907\) | 40.3737 | 1.34059 | 0.670293 | − | 0.742097i | \(-0.266168\pi\) | ||||
0.670293 | + | 0.742097i | \(0.266168\pi\) | |||||||
\(908\) | 4.00484 | 0.132905 | ||||||||
\(909\) | −5.34150 | −0.177166 | ||||||||
\(910\) | −5.38163 | −0.178399 | ||||||||
\(911\) | −8.30349 | −0.275107 | −0.137553 | − | 0.990494i | \(-0.543924\pi\) | ||||
−0.137553 | + | 0.990494i | \(0.543924\pi\) | |||||||
\(912\) | −15.6390 | −0.517858 | ||||||||
\(913\) | 2.78616 | 0.0922085 | ||||||||
\(914\) | −1.75331 | −0.0579944 | ||||||||
\(915\) | −23.5646 | −0.779021 | ||||||||
\(916\) | 4.12733 | 0.136371 | ||||||||
\(917\) | 22.4213 | 0.740416 | ||||||||
\(918\) | 2.98157 | 0.0984066 | ||||||||
\(919\) | −39.2171 | −1.29365 | −0.646827 | − | 0.762637i | \(-0.723904\pi\) | ||||
−0.646827 | + | 0.762637i | \(0.723904\pi\) | |||||||
\(920\) | 7.49481 | 0.247097 | ||||||||
\(921\) | −11.0124 | −0.362870 | ||||||||
\(922\) | 9.67695 | 0.318693 | ||||||||
\(923\) | −0.978722 | −0.0322150 | ||||||||
\(924\) | 0.121640 | 0.00400165 | ||||||||
\(925\) | 2.43007 | 0.0799002 | ||||||||
\(926\) | 3.54418 | 0.116469 | ||||||||
\(927\) | −8.03732 | −0.263980 | ||||||||
\(928\) | −1.46618 | −0.0481296 | ||||||||
\(929\) | 40.1694 | 1.31792 | 0.658958 | − | 0.752180i | \(-0.270998\pi\) | ||||
0.658958 | + | 0.752180i | \(0.270998\pi\) | |||||||
\(930\) | −2.03969 | −0.0668840 | ||||||||
\(931\) | 8.82822 | 0.289333 | ||||||||
\(932\) | −2.81971 | −0.0923627 | ||||||||
\(933\) | 4.46225 | 0.146087 | ||||||||
\(934\) | −9.02883 | −0.295432 | ||||||||
\(935\) | −1.17608 | −0.0384618 | ||||||||
\(936\) | −2.14866 | −0.0702310 | ||||||||
\(937\) | −26.5512 | −0.867390 | −0.433695 | − | 0.901060i | \(-0.642791\pi\) | ||||
−0.433695 | + | 0.901060i | \(0.642791\pi\) | |||||||
\(938\) | −28.0244 | −0.915029 | ||||||||
\(939\) | −11.9157 | −0.388855 | ||||||||
\(940\) | −3.86902 | −0.126194 | ||||||||
\(941\) | −17.2684 | −0.562934 | −0.281467 | − | 0.959571i | \(-0.590821\pi\) | ||||
−0.281467 | + | 0.959571i | \(0.590821\pi\) | |||||||
\(942\) | 18.0839 | 0.589205 | ||||||||
\(943\) | −3.39931 | −0.110697 | ||||||||
\(944\) | −4.20794 | −0.136957 | ||||||||
\(945\) | 5.66284 | 0.184212 | ||||||||
\(946\) | −2.32006 | −0.0754317 | ||||||||
\(947\) | 44.4634 | 1.44487 | 0.722434 | − | 0.691440i | \(-0.243023\pi\) | ||||
0.722434 | + | 0.691440i | \(0.243023\pi\) | |||||||
\(948\) | 2.44250 | 0.0793289 | ||||||||
\(949\) | 0.917912 | 0.0297967 | ||||||||
\(950\) | 7.97560 | 0.258763 | ||||||||
\(951\) | 2.70900 | 0.0878454 | ||||||||
\(952\) | −15.1863 | −0.492190 | ||||||||
\(953\) | −22.6887 | −0.734958 | −0.367479 | − | 0.930032i | \(-0.619779\pi\) | ||||
−0.367479 | + | 0.930032i | \(0.619779\pi\) | |||||||
\(954\) | −7.41006 | −0.239909 | ||||||||
\(955\) | −46.8799 | −1.51700 | ||||||||
\(956\) | 3.25804 | 0.105373 | ||||||||
\(957\) | 0.206934 | 0.00668924 | ||||||||
\(958\) | −19.9793 | −0.645502 | ||||||||
\(959\) | 48.9180 | 1.57964 | ||||||||
\(960\) | −22.0041 | −0.710178 | ||||||||
\(961\) | −30.6214 | −0.987787 | ||||||||
\(962\) | 1.75122 | 0.0564615 | ||||||||
\(963\) | −3.51280 | −0.113198 | ||||||||
\(964\) | 1.02862 | 0.0331297 | ||||||||
\(965\) | −20.5126 | −0.660325 | ||||||||
\(966\) | −2.97083 | −0.0955848 | ||||||||
\(967\) | 4.31252 | 0.138681 | 0.0693406 | − | 0.997593i | \(-0.477910\pi\) | ||||
0.0693406 | + | 0.997593i | \(0.477910\pi\) | |||||||
\(968\) | −32.6696 | −1.05004 | ||||||||
\(969\) | 10.3689 | 0.333098 | ||||||||
\(970\) | −5.71964 | −0.183647 | ||||||||
\(971\) | 46.8188 | 1.50249 | 0.751243 | − | 0.660025i | \(-0.229454\pi\) | ||||
0.751243 | + | 0.660025i | \(0.229454\pi\) | |||||||
\(972\) | 0.260930 | 0.00836933 | ||||||||
\(973\) | 21.7170 | 0.696214 | ||||||||
\(974\) | 3.04105 | 0.0974414 | ||||||||
\(975\) | 0.950341 | 0.0304353 | ||||||||
\(976\) | −31.9673 | −1.02325 | ||||||||
\(977\) | 51.8522 | 1.65890 | 0.829450 | − | 0.558581i | \(-0.188654\pi\) | ||||
0.829450 | + | 0.558581i | \(0.188654\pi\) | |||||||
\(978\) | 1.48335 | 0.0474324 | ||||||||
\(979\) | 0.747691 | 0.0238963 | ||||||||
\(980\) | 1.26260 | 0.0403322 | ||||||||
\(981\) | 18.5175 | 0.591219 | ||||||||
\(982\) | 39.7286 | 1.26779 | ||||||||
\(983\) | 2.68187 | 0.0855382 | 0.0427691 | − | 0.999085i | \(-0.486382\pi\) | ||||
0.0427691 | + | 0.999085i | \(0.486382\pi\) | |||||||
\(984\) | 10.1353 | 0.323101 | ||||||||
\(985\) | 34.0104 | 1.08366 | ||||||||
\(986\) | −2.98157 | −0.0949527 | ||||||||
\(987\) | 13.2887 | 0.422983 | ||||||||
\(988\) | −0.862365 | −0.0274355 | ||||||||
\(989\) | −8.50175 | −0.270340 | ||||||||
\(990\) | 0.685972 | 0.0218016 | ||||||||
\(991\) | 11.1114 | 0.352966 | 0.176483 | − | 0.984304i | \(-0.443528\pi\) | ||||
0.176483 | + | 0.984304i | \(0.443528\pi\) | |||||||
\(992\) | 0.902145 | 0.0286431 | ||||||||
\(993\) | 10.9224 | 0.346612 | ||||||||
\(994\) | 4.03474 | 0.127974 | ||||||||
\(995\) | −9.64308 | −0.305706 | ||||||||
\(996\) | −3.51316 | −0.111319 | ||||||||
\(997\) | 35.6328 | 1.12850 | 0.564251 | − | 0.825603i | \(-0.309165\pi\) | ||||
0.564251 | + | 0.825603i | \(0.309165\pi\) | |||||||
\(998\) | −18.6274 | −0.589639 | ||||||||
\(999\) | −1.84272 | −0.0583012 |
(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 | 2001.2.a.h.1.3 | ✓ | 5 | |
3.2 | odd | 2 | 6003.2.a.h.1.3 | 5 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2001.2.a.h.1.3 | ✓ | 5 | 1.1 | even | 1 | trivial | |
6003.2.a.h.1.3 | 5 | 3.2 | odd | 2 |