Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4014,2,Mod(1,4014)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4014, 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("4014.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4014 = 2 \cdot 3^{2} \cdot 223 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4014.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: | \(32.0519513713\) |
Analytic rank: | \(1\) |
Dimension: | \(5\) |
Coefficient field: | 5.5.356173.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{5} - 2x^{4} - 7x^{3} + 9x^{2} + 14x - 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 1338) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-1.38363\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4014.1 |
$q$-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 | 0 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −4.35484 | −1.94754 | −0.973772 | − | 0.227528i | \(-0.926936\pi\) | ||||
−0.973772 | + | 0.227528i | \(0.926936\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.05676 | 1.15535 | 0.577674 | − | 0.816268i | \(-0.303961\pi\) | ||||
0.577674 | + | 0.816268i | \(0.303961\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −4.35484 | −1.37712 | ||||||||
\(11\) | 0.734963 | 0.221600 | 0.110800 | − | 0.993843i | \(-0.464659\pi\) | ||||
0.110800 | + | 0.993843i | \(0.464659\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.43689 | −0.675871 | −0.337935 | − | 0.941169i | \(-0.609728\pi\) | ||||
−0.337935 | + | 0.941169i | \(0.609728\pi\) | |||||||
\(14\) | 3.05676 | 0.816954 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 0.681711 | 0.165339 | 0.0826696 | − | 0.996577i | \(-0.473655\pi\) | ||||
0.0826696 | + | 0.996577i | \(0.473655\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.87811 | −0.430868 | −0.215434 | − | 0.976518i | \(-0.569117\pi\) | ||||
−0.215434 | + | 0.976518i | \(0.569117\pi\) | |||||||
\(20\) | −4.35484 | −0.973772 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0.734963 | 0.156695 | ||||||||
\(23\) | −6.91115 | −1.44107 | −0.720537 | − | 0.693416i | \(-0.756105\pi\) | ||||
−0.720537 | + | 0.693416i | \(0.756105\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 13.9646 | 2.79292 | ||||||||
\(26\) | −2.43689 | −0.477913 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 3.05676 | 0.577674 | ||||||||
\(29\) | −0.113306 | −0.0210404 | −0.0105202 | − | 0.999945i | \(-0.503349\pi\) | ||||
−0.0105202 | + | 0.999945i | \(0.503349\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.56736 | 0.281506 | 0.140753 | − | 0.990045i | \(-0.455048\pi\) | ||||
0.140753 | + | 0.990045i | \(0.455048\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0.681711 | 0.116912 | ||||||||
\(35\) | −13.3117 | −2.25009 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −3.71884 | −0.611374 | −0.305687 | − | 0.952132i | \(-0.598886\pi\) | ||||
−0.305687 | + | 0.952132i | \(0.598886\pi\) | |||||||
\(38\) | −1.87811 | −0.304670 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −4.35484 | −0.688560 | ||||||||
\(41\) | 11.1102 | 1.73513 | 0.867563 | − | 0.497327i | \(-0.165685\pi\) | ||||
0.867563 | + | 0.497327i | \(0.165685\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −10.9512 | −1.67004 | −0.835022 | − | 0.550217i | \(-0.814545\pi\) | ||||
−0.835022 | + | 0.550217i | \(0.814545\pi\) | |||||||
\(44\) | 0.734963 | 0.110800 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −6.91115 | −1.01899 | ||||||||
\(47\) | 6.22966 | 0.908689 | 0.454344 | − | 0.890826i | \(-0.349874\pi\) | ||||
0.454344 | + | 0.890826i | \(0.349874\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 2.34379 | 0.334827 | ||||||||
\(50\) | 13.9646 | 1.97490 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −2.43689 | −0.337935 | ||||||||
\(53\) | −6.47426 | −0.889309 | −0.444654 | − | 0.895702i | \(-0.646673\pi\) | ||||
−0.444654 | + | 0.895702i | \(0.646673\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −3.20064 | −0.431575 | ||||||||
\(56\) | 3.05676 | 0.408477 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −0.113306 | −0.0148778 | ||||||||
\(59\) | −7.94099 | −1.03383 | −0.516915 | − | 0.856037i | \(-0.672920\pi\) | ||||
−0.516915 | + | 0.856037i | \(0.672920\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −4.54537 | −0.581974 | −0.290987 | − | 0.956727i | \(-0.593984\pi\) | ||||
−0.290987 | + | 0.956727i | \(0.593984\pi\) | |||||||
\(62\) | 1.56736 | 0.199055 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 10.6122 | 1.31629 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −2.23117 | −0.272581 | −0.136290 | − | 0.990669i | \(-0.543518\pi\) | ||||
−0.136290 | + | 0.990669i | \(0.543518\pi\) | |||||||
\(68\) | 0.681711 | 0.0826696 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −13.3117 | −1.59105 | ||||||||
\(71\) | −10.5641 | −1.25372 | −0.626862 | − | 0.779130i | \(-0.715661\pi\) | ||||
−0.626862 | + | 0.779130i | \(0.715661\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −3.30232 | −0.386507 | −0.193254 | − | 0.981149i | \(-0.561904\pi\) | ||||
−0.193254 | + | 0.981149i | \(0.561904\pi\) | |||||||
\(74\) | −3.71884 | −0.432307 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −1.87811 | −0.215434 | ||||||||
\(77\) | 2.24661 | 0.256024 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −3.98486 | −0.448332 | −0.224166 | − | 0.974551i | \(-0.571966\pi\) | ||||
−0.224166 | + | 0.974551i | \(0.571966\pi\) | |||||||
\(80\) | −4.35484 | −0.486886 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 11.1102 | 1.22692 | ||||||||
\(83\) | 9.77231 | 1.07265 | 0.536325 | − | 0.844011i | \(-0.319812\pi\) | ||||
0.536325 | + | 0.844011i | \(0.319812\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −2.96874 | −0.322005 | ||||||||
\(86\) | −10.9512 | −1.18090 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0.734963 | 0.0783473 | ||||||||
\(89\) | 3.23802 | 0.343230 | 0.171615 | − | 0.985164i | \(-0.445102\pi\) | ||||
0.171615 | + | 0.985164i | \(0.445102\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −7.44898 | −0.780865 | ||||||||
\(92\) | −6.91115 | −0.720537 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 6.22966 | 0.642540 | ||||||||
\(95\) | 8.17887 | 0.839134 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −11.1019 | −1.12723 | −0.563613 | − | 0.826039i | \(-0.690589\pi\) | ||||
−0.563613 | + | 0.826039i | \(0.690589\pi\) | |||||||
\(98\) | 2.34379 | 0.236759 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 13.9646 | 1.39646 | ||||||||
\(101\) | −19.8419 | −1.97434 | −0.987171 | − | 0.159664i | \(-0.948959\pi\) | ||||
−0.987171 | + | 0.159664i | \(0.948959\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −4.42428 | −0.435937 | −0.217968 | − | 0.975956i | \(-0.569943\pi\) | ||||
−0.217968 | + | 0.975956i | \(0.569943\pi\) | |||||||
\(104\) | −2.43689 | −0.238956 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −6.47426 | −0.628836 | ||||||||
\(107\) | −11.4126 | −1.10330 | −0.551651 | − | 0.834075i | \(-0.686002\pi\) | ||||
−0.551651 | + | 0.834075i | \(0.686002\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −15.1912 | −1.45506 | −0.727528 | − | 0.686078i | \(-0.759331\pi\) | ||||
−0.727528 | + | 0.686078i | \(0.759331\pi\) | |||||||
\(110\) | −3.20064 | −0.305169 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 3.05676 | 0.288837 | ||||||||
\(113\) | 0.723916 | 0.0681003 | 0.0340501 | − | 0.999420i | \(-0.489159\pi\) | ||||
0.0340501 | + | 0.999420i | \(0.489159\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 30.0969 | 2.80655 | ||||||||
\(116\) | −0.113306 | −0.0105202 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −7.94099 | −0.731028 | ||||||||
\(119\) | 2.08383 | 0.191024 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.4598 | −0.950894 | ||||||||
\(122\) | −4.54537 | −0.411518 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 1.56736 | 0.140753 | ||||||||
\(125\) | −39.0395 | −3.49180 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 17.7134 | 1.57181 | 0.785905 | − | 0.618347i | \(-0.212197\pi\) | ||||
0.785905 | + | 0.618347i | \(0.212197\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 10.6122 | 0.930755 | ||||||||
\(131\) | 4.62868 | 0.404409 | 0.202205 | − | 0.979343i | \(-0.435189\pi\) | ||||
0.202205 | + | 0.979343i | \(0.435189\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −5.74094 | −0.497802 | ||||||||
\(134\) | −2.23117 | −0.192744 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0.681711 | 0.0584562 | ||||||||
\(137\) | 6.95121 | 0.593882 | 0.296941 | − | 0.954896i | \(-0.404034\pi\) | ||||
0.296941 | + | 0.954896i | \(0.404034\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 23.4964 | 1.99294 | 0.996468 | − | 0.0839681i | \(-0.0267594\pi\) | ||||
0.996468 | + | 0.0839681i | \(0.0267594\pi\) | |||||||
\(140\) | −13.3117 | −1.12504 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −10.5641 | −0.886517 | ||||||||
\(143\) | −1.79102 | −0.149773 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0.493430 | 0.0409772 | ||||||||
\(146\) | −3.30232 | −0.273302 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −3.71884 | −0.305687 | ||||||||
\(149\) | 8.25494 | 0.676271 | 0.338136 | − | 0.941097i | \(-0.390204\pi\) | ||||
0.338136 | + | 0.941097i | \(0.390204\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −15.3701 | −1.25080 | −0.625402 | − | 0.780303i | \(-0.715065\pi\) | ||||
−0.625402 | + | 0.780303i | \(0.715065\pi\) | |||||||
\(152\) | −1.87811 | −0.152335 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 2.24661 | 0.181037 | ||||||||
\(155\) | −6.82559 | −0.548245 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 5.70675 | 0.455448 | 0.227724 | − | 0.973726i | \(-0.426872\pi\) | ||||
0.227724 | + | 0.973726i | \(0.426872\pi\) | |||||||
\(158\) | −3.98486 | −0.317019 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −4.35484 | −0.344280 | ||||||||
\(161\) | −21.1257 | −1.66494 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1.46144 | 0.114469 | 0.0572343 | − | 0.998361i | \(-0.481772\pi\) | ||||
0.0572343 | + | 0.998361i | \(0.481772\pi\) | |||||||
\(164\) | 11.1102 | 0.867563 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 9.77231 | 0.758478 | ||||||||
\(167\) | 0.335943 | 0.0259960 | 0.0129980 | − | 0.999916i | \(-0.495862\pi\) | ||||
0.0129980 | + | 0.999916i | \(0.495862\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −7.06159 | −0.543199 | ||||||||
\(170\) | −2.96874 | −0.227692 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −10.9512 | −0.835022 | ||||||||
\(173\) | −3.25577 | −0.247532 | −0.123766 | − | 0.992311i | \(-0.539497\pi\) | ||||
−0.123766 | + | 0.992311i | \(0.539497\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 42.6865 | 3.22680 | ||||||||
\(176\) | 0.734963 | 0.0553999 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 3.23802 | 0.242700 | ||||||||
\(179\) | −2.01680 | −0.150743 | −0.0753715 | − | 0.997156i | \(-0.524014\pi\) | ||||
−0.0753715 | + | 0.997156i | \(0.524014\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −0.718726 | −0.0534225 | −0.0267113 | − | 0.999643i | \(-0.508503\pi\) | ||||
−0.0267113 | + | 0.999643i | \(0.508503\pi\) | |||||||
\(182\) | −7.44898 | −0.552155 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −6.91115 | −0.509497 | ||||||||
\(185\) | 16.1950 | 1.19068 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0.501032 | 0.0366391 | ||||||||
\(188\) | 6.22966 | 0.454344 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 8.17887 | 0.593357 | ||||||||
\(191\) | −4.95760 | −0.358719 | −0.179360 | − | 0.983784i | \(-0.557403\pi\) | ||||
−0.179360 | + | 0.983784i | \(0.557403\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −8.59130 | −0.618415 | −0.309208 | − | 0.950995i | \(-0.600064\pi\) | ||||
−0.309208 | + | 0.950995i | \(0.600064\pi\) | |||||||
\(194\) | −11.1019 | −0.797070 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 2.34379 | 0.167414 | ||||||||
\(197\) | −17.0864 | −1.21736 | −0.608678 | − | 0.793417i | \(-0.708300\pi\) | ||||
−0.608678 | + | 0.793417i | \(0.708300\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −0.350646 | −0.0248566 | −0.0124283 | − | 0.999923i | \(-0.503956\pi\) | ||||
−0.0124283 | + | 0.999923i | \(0.503956\pi\) | |||||||
\(200\) | 13.9646 | 0.987448 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −19.8419 | −1.39607 | ||||||||
\(203\) | −0.346350 | −0.0243090 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −48.3833 | −3.37923 | ||||||||
\(206\) | −4.42428 | −0.308254 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −2.43689 | −0.168968 | ||||||||
\(209\) | −1.38034 | −0.0954802 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −12.3103 | −0.847475 | −0.423738 | − | 0.905785i | \(-0.639282\pi\) | ||||
−0.423738 | + | 0.905785i | \(0.639282\pi\) | |||||||
\(212\) | −6.47426 | −0.444654 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −11.4126 | −0.780152 | ||||||||
\(215\) | 47.6907 | 3.25248 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 4.79104 | 0.325237 | ||||||||
\(218\) | −15.1912 | −1.02888 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −3.20064 | −0.215787 | ||||||||
\(221\) | −1.66125 | −0.111748 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1.00000 | −0.0669650 | ||||||||
\(224\) | 3.05676 | 0.204238 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0.723916 | 0.0481542 | ||||||||
\(227\) | −11.9814 | −0.795233 | −0.397616 | − | 0.917552i | \(-0.630162\pi\) | ||||
−0.397616 | + | 0.917552i | \(0.630162\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −0.278694 | −0.0184166 | −0.00920831 | − | 0.999958i | \(-0.502931\pi\) | ||||
−0.00920831 | + | 0.999958i | \(0.502931\pi\) | |||||||
\(230\) | 30.0969 | 1.98453 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −0.113306 | −0.00743892 | ||||||||
\(233\) | 12.2226 | 0.800732 | 0.400366 | − | 0.916355i | \(-0.368883\pi\) | ||||
0.400366 | + | 0.916355i | \(0.368883\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −27.1291 | −1.76971 | ||||||||
\(236\) | −7.94099 | −0.516915 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 2.08383 | 0.135074 | ||||||||
\(239\) | −22.2407 | −1.43863 | −0.719316 | − | 0.694683i | \(-0.755545\pi\) | ||||
−0.719316 | + | 0.694683i | \(0.755545\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −22.3491 | −1.43963 | −0.719814 | − | 0.694166i | \(-0.755773\pi\) | ||||
−0.719814 | + | 0.694166i | \(0.755773\pi\) | |||||||
\(242\) | −10.4598 | −0.672383 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −4.54537 | −0.290987 | ||||||||
\(245\) | −10.2068 | −0.652091 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 4.57674 | 0.291211 | ||||||||
\(248\) | 1.56736 | 0.0995274 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −39.0395 | −2.46907 | ||||||||
\(251\) | −19.7825 | −1.24866 | −0.624331 | − | 0.781160i | \(-0.714628\pi\) | ||||
−0.624331 | + | 0.781160i | \(0.714628\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −5.07944 | −0.319341 | ||||||||
\(254\) | 17.7134 | 1.11144 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 11.4401 | 0.713617 | 0.356808 | − | 0.934178i | \(-0.383865\pi\) | ||||
0.356808 | + | 0.934178i | \(0.383865\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −11.3676 | −0.706349 | ||||||||
\(260\) | 10.6122 | 0.658143 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 4.62868 | 0.285961 | ||||||||
\(263\) | −13.3295 | −0.821929 | −0.410965 | − | 0.911651i | \(-0.634808\pi\) | ||||
−0.410965 | + | 0.911651i | \(0.634808\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 28.1944 | 1.73197 | ||||||||
\(266\) | −5.74094 | −0.351999 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −2.23117 | −0.136290 | ||||||||
\(269\) | −3.03055 | −0.184776 | −0.0923878 | − | 0.995723i | \(-0.529450\pi\) | ||||
−0.0923878 | + | 0.995723i | \(0.529450\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 21.4604 | 1.30362 | 0.651812 | − | 0.758381i | \(-0.274009\pi\) | ||||
0.651812 | + | 0.758381i | \(0.274009\pi\) | |||||||
\(272\) | 0.681711 | 0.0413348 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 6.95121 | 0.419938 | ||||||||
\(275\) | 10.2635 | 0.618911 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 28.2695 | 1.69855 | 0.849276 | − | 0.527950i | \(-0.177039\pi\) | ||||
0.849276 | + | 0.527950i | \(0.177039\pi\) | |||||||
\(278\) | 23.4964 | 1.40922 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −13.3117 | −0.795526 | ||||||||
\(281\) | 12.7637 | 0.761420 | 0.380710 | − | 0.924694i | \(-0.375680\pi\) | ||||
0.380710 | + | 0.924694i | \(0.375680\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 32.5585 | 1.93540 | 0.967702 | − | 0.252098i | \(-0.0811205\pi\) | ||||
0.967702 | + | 0.252098i | \(0.0811205\pi\) | |||||||
\(284\) | −10.5641 | −0.626862 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −1.79102 | −0.105905 | ||||||||
\(287\) | 33.9613 | 2.00467 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.5353 | −0.972663 | ||||||||
\(290\) | 0.493430 | 0.0289752 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −3.30232 | −0.193254 | ||||||||
\(293\) | −28.3976 | −1.65901 | −0.829503 | − | 0.558503i | \(-0.811376\pi\) | ||||
−0.829503 | + | 0.558503i | \(0.811376\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 34.5817 | 2.01343 | ||||||||
\(296\) | −3.71884 | −0.216153 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 8.25494 | 0.478196 | ||||||||
\(299\) | 16.8417 | 0.973980 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −33.4752 | −1.92948 | ||||||||
\(302\) | −15.3701 | −0.884452 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −1.87811 | −0.107717 | ||||||||
\(305\) | 19.7943 | 1.13342 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −27.9578 | −1.59563 | −0.797817 | − | 0.602900i | \(-0.794012\pi\) | ||||
−0.797817 | + | 0.602900i | \(0.794012\pi\) | |||||||
\(308\) | 2.24661 | 0.128012 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −6.82559 | −0.387668 | ||||||||
\(311\) | 3.59459 | 0.203831 | 0.101915 | − | 0.994793i | \(-0.467503\pi\) | ||||
0.101915 | + | 0.994793i | \(0.467503\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 11.4643 | 0.647998 | 0.323999 | − | 0.946057i | \(-0.394972\pi\) | ||||
0.323999 | + | 0.946057i | \(0.394972\pi\) | |||||||
\(314\) | 5.70675 | 0.322050 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −3.98486 | −0.224166 | ||||||||
\(317\) | 33.3632 | 1.87386 | 0.936931 | − | 0.349514i | \(-0.113653\pi\) | ||||
0.936931 | + | 0.349514i | \(0.113653\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −0.0832759 | −0.00466255 | ||||||||
\(320\) | −4.35484 | −0.243443 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −21.1257 | −1.17729 | ||||||||
\(323\) | −1.28033 | −0.0712394 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −34.0302 | −1.88765 | ||||||||
\(326\) | 1.46144 | 0.0809415 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 11.1102 | 0.613460 | ||||||||
\(329\) | 19.0426 | 1.04985 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −11.6186 | −0.638615 | −0.319308 | − | 0.947651i | \(-0.603450\pi\) | ||||
−0.319308 | + | 0.947651i | \(0.603450\pi\) | |||||||
\(332\) | 9.77231 | 0.536325 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0.335943 | 0.0183820 | ||||||||
\(335\) | 9.71638 | 0.530862 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −7.91263 | −0.431029 | −0.215514 | − | 0.976501i | \(-0.569143\pi\) | ||||
−0.215514 | + | 0.976501i | \(0.569143\pi\) | |||||||
\(338\) | −7.06159 | −0.384100 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −2.96874 | −0.161003 | ||||||||
\(341\) | 1.15195 | 0.0623816 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −14.2329 | −0.768505 | ||||||||
\(344\) | −10.9512 | −0.590450 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −3.25577 | −0.175031 | ||||||||
\(347\) | 21.1718 | 1.13656 | 0.568280 | − | 0.822835i | \(-0.307609\pi\) | ||||
0.568280 | + | 0.822835i | \(0.307609\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −11.3838 | −0.609360 | −0.304680 | − | 0.952455i | \(-0.598550\pi\) | ||||
−0.304680 | + | 0.952455i | \(0.598550\pi\) | |||||||
\(350\) | 42.6865 | 2.28169 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0.734963 | 0.0391736 | ||||||||
\(353\) | 20.6961 | 1.10154 | 0.550772 | − | 0.834656i | \(-0.314333\pi\) | ||||
0.550772 | + | 0.834656i | \(0.314333\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 46.0048 | 2.44168 | ||||||||
\(356\) | 3.23802 | 0.171615 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −2.01680 | −0.106591 | ||||||||
\(359\) | 13.4560 | 0.710183 | 0.355092 | − | 0.934832i | \(-0.384450\pi\) | ||||
0.355092 | + | 0.934832i | \(0.384450\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −15.4727 | −0.814353 | ||||||||
\(362\) | −0.718726 | −0.0377754 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −7.44898 | −0.390433 | ||||||||
\(365\) | 14.3811 | 0.752740 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 8.80612 | 0.459675 | 0.229838 | − | 0.973229i | \(-0.426180\pi\) | ||||
0.229838 | + | 0.973229i | \(0.426180\pi\) | |||||||
\(368\) | −6.91115 | −0.360269 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 16.1950 | 0.841936 | ||||||||
\(371\) | −19.7903 | −1.02746 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 5.86346 | 0.303598 | 0.151799 | − | 0.988411i | \(-0.451493\pi\) | ||||
0.151799 | + | 0.988411i | \(0.451493\pi\) | |||||||
\(374\) | 0.501032 | 0.0259078 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 6.22966 | 0.321270 | ||||||||
\(377\) | 0.276114 | 0.0142206 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −20.7423 | −1.06546 | −0.532729 | − | 0.846286i | \(-0.678833\pi\) | ||||
−0.532729 | + | 0.846286i | \(0.678833\pi\) | |||||||
\(380\) | 8.17887 | 0.419567 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −4.95760 | −0.253653 | ||||||||
\(383\) | −25.8637 | −1.32158 | −0.660788 | − | 0.750573i | \(-0.729778\pi\) | ||||
−0.660788 | + | 0.750573i | \(0.729778\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −9.78361 | −0.498619 | ||||||||
\(386\) | −8.59130 | −0.437286 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −11.1019 | −0.563613 | ||||||||
\(389\) | −2.44929 | −0.124184 | −0.0620920 | − | 0.998070i | \(-0.519777\pi\) | ||||
−0.0620920 | + | 0.998070i | \(0.519777\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −4.71141 | −0.238266 | ||||||||
\(392\) | 2.34379 | 0.118379 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −17.0864 | −0.860801 | ||||||||
\(395\) | 17.3534 | 0.873146 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 19.7131 | 0.989370 | 0.494685 | − | 0.869072i | \(-0.335283\pi\) | ||||
0.494685 | + | 0.869072i | \(0.335283\pi\) | |||||||
\(398\) | −0.350646 | −0.0175763 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 13.9646 | 0.698231 | ||||||||
\(401\) | −11.7643 | −0.587483 | −0.293742 | − | 0.955885i | \(-0.594900\pi\) | ||||
−0.293742 | + | 0.955885i | \(0.594900\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −3.81947 | −0.190262 | ||||||||
\(404\) | −19.8419 | −0.987171 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −0.346350 | −0.0171891 | ||||||||
\(407\) | −2.73321 | −0.135480 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 29.9196 | 1.47943 | 0.739715 | − | 0.672920i | \(-0.234960\pi\) | ||||
0.739715 | + | 0.672920i | \(0.234960\pi\) | |||||||
\(410\) | −48.3833 | −2.38948 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −4.42428 | −0.217968 | ||||||||
\(413\) | −24.2737 | −1.19443 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −42.5568 | −2.08903 | ||||||||
\(416\) | −2.43689 | −0.119478 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −1.38034 | −0.0675147 | ||||||||
\(419\) | 36.6787 | 1.79187 | 0.895935 | − | 0.444185i | \(-0.146507\pi\) | ||||
0.895935 | + | 0.444185i | \(0.146507\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 30.9616 | 1.50898 | 0.754488 | − | 0.656313i | \(-0.227885\pi\) | ||||
0.754488 | + | 0.656313i | \(0.227885\pi\) | |||||||
\(422\) | −12.3103 | −0.599255 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −6.47426 | −0.314418 | ||||||||
\(425\) | 9.51983 | 0.461780 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −13.8941 | −0.672383 | ||||||||
\(428\) | −11.4126 | −0.551651 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 47.6907 | 2.29985 | ||||||||
\(431\) | 32.4852 | 1.56476 | 0.782378 | − | 0.622804i | \(-0.214006\pi\) | ||||
0.782378 | + | 0.622804i | \(0.214006\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −24.9126 | −1.19722 | −0.598612 | − | 0.801039i | \(-0.704281\pi\) | ||||
−0.598612 | + | 0.801039i | \(0.704281\pi\) | |||||||
\(434\) | 4.79104 | 0.229977 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −15.1912 | −0.727528 | ||||||||
\(437\) | 12.9799 | 0.620913 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 31.8189 | 1.51863 | 0.759317 | − | 0.650721i | \(-0.225533\pi\) | ||||
0.759317 | + | 0.650721i | \(0.225533\pi\) | |||||||
\(440\) | −3.20064 | −0.152585 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −1.66125 | −0.0790177 | ||||||||
\(443\) | 22.4064 | 1.06456 | 0.532281 | − | 0.846568i | \(-0.321335\pi\) | ||||
0.532281 | + | 0.846568i | \(0.321335\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −14.1011 | −0.668455 | ||||||||
\(446\) | −1.00000 | −0.0473514 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 3.05676 | 0.144418 | ||||||||
\(449\) | −27.5968 | −1.30237 | −0.651187 | − | 0.758917i | \(-0.725729\pi\) | ||||
−0.651187 | + | 0.758917i | \(0.725729\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 8.16560 | 0.384503 | ||||||||
\(452\) | 0.723916 | 0.0340501 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −11.9814 | −0.562314 | ||||||||
\(455\) | 32.4391 | 1.52077 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 6.26270 | 0.292957 | 0.146478 | − | 0.989214i | \(-0.453206\pi\) | ||||
0.146478 | + | 0.989214i | \(0.453206\pi\) | |||||||
\(458\) | −0.278694 | −0.0130225 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 30.0969 | 1.40328 | ||||||||
\(461\) | 24.4624 | 1.13933 | 0.569664 | − | 0.821878i | \(-0.307074\pi\) | ||||
0.569664 | + | 0.821878i | \(0.307074\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −10.5467 | −0.490146 | −0.245073 | − | 0.969505i | \(-0.578812\pi\) | ||||
−0.245073 | + | 0.969505i | \(0.578812\pi\) | |||||||
\(464\) | −0.113306 | −0.00526011 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 12.2226 | 0.566203 | ||||||||
\(467\) | 27.0318 | 1.25088 | 0.625442 | − | 0.780271i | \(-0.284919\pi\) | ||||
0.625442 | + | 0.780271i | \(0.284919\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −6.82015 | −0.314925 | ||||||||
\(470\) | −27.1291 | −1.25137 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −7.94099 | −0.365514 | ||||||||
\(473\) | −8.04873 | −0.370081 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −26.2271 | −1.20338 | ||||||||
\(476\) | 2.08383 | 0.0955121 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −22.2407 | −1.01727 | ||||||||
\(479\) | −23.9419 | −1.09393 | −0.546967 | − | 0.837154i | \(-0.684218\pi\) | ||||
−0.546967 | + | 0.837154i | \(0.684218\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 9.06239 | 0.413210 | ||||||||
\(482\) | −22.3491 | −1.01797 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −10.4598 | −0.475447 | ||||||||
\(485\) | 48.3470 | 2.19532 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −2.04679 | −0.0927490 | −0.0463745 | − | 0.998924i | \(-0.514767\pi\) | ||||
−0.0463745 | + | 0.998924i | \(0.514767\pi\) | |||||||
\(488\) | −4.54537 | −0.205759 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −10.2068 | −0.461098 | ||||||||
\(491\) | 30.6746 | 1.38433 | 0.692163 | − | 0.721741i | \(-0.256658\pi\) | ||||
0.692163 | + | 0.721741i | \(0.256658\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −0.0772421 | −0.00347881 | ||||||||
\(494\) | 4.57674 | 0.205917 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 1.56736 | 0.0703765 | ||||||||
\(497\) | −32.2918 | −1.44849 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 29.0813 | 1.30186 | 0.650929 | − | 0.759138i | \(-0.274379\pi\) | ||||
0.650929 | + | 0.759138i | \(0.274379\pi\) | |||||||
\(500\) | −39.0395 | −1.74590 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −19.7825 | −0.882937 | ||||||||
\(503\) | −32.4064 | −1.44493 | −0.722466 | − | 0.691407i | \(-0.756991\pi\) | ||||
−0.722466 | + | 0.691407i | \(0.756991\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 86.4083 | 3.84512 | ||||||||
\(506\) | −5.07944 | −0.225809 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 17.7134 | 0.785905 | ||||||||
\(509\) | 20.3134 | 0.900376 | 0.450188 | − | 0.892934i | \(-0.351357\pi\) | ||||
0.450188 | + | 0.892934i | \(0.351357\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −10.0944 | −0.446550 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 11.4401 | 0.504603 | ||||||||
\(515\) | 19.2670 | 0.849006 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 4.57856 | 0.201365 | ||||||||
\(518\) | −11.3676 | −0.499464 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 10.6122 | 0.465378 | ||||||||
\(521\) | 23.8912 | 1.04669 | 0.523346 | − | 0.852120i | \(-0.324683\pi\) | ||||
0.523346 | + | 0.852120i | \(0.324683\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 26.0276 | 1.13811 | 0.569054 | − | 0.822300i | \(-0.307309\pi\) | ||||
0.569054 | + | 0.822300i | \(0.307309\pi\) | |||||||
\(524\) | 4.62868 | 0.202205 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −13.3295 | −0.581192 | ||||||||
\(527\) | 1.06849 | 0.0465440 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 24.7640 | 1.07670 | ||||||||
\(530\) | 28.1944 | 1.22469 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −5.74094 | −0.248901 | ||||||||
\(533\) | −27.0744 | −1.17272 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 49.7002 | 2.14873 | ||||||||
\(536\) | −2.23117 | −0.0963718 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −3.03055 | −0.130656 | ||||||||
\(539\) | 1.72260 | 0.0741976 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −5.46873 | −0.235119 | −0.117559 | − | 0.993066i | \(-0.537507\pi\) | ||||
−0.117559 | + | 0.993066i | \(0.537507\pi\) | |||||||
\(542\) | 21.4604 | 0.921801 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0.681711 | 0.0292281 | ||||||||
\(545\) | 66.1554 | 2.83378 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 0.600980 | 0.0256961 | 0.0128480 | − | 0.999917i | \(-0.495910\pi\) | ||||
0.0128480 | + | 0.999917i | \(0.495910\pi\) | |||||||
\(548\) | 6.95121 | 0.296941 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 10.2635 | 0.437636 | ||||||||
\(551\) | 0.212802 | 0.00906565 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −12.1808 | −0.517979 | ||||||||
\(554\) | 28.2695 | 1.20106 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 23.4964 | 0.996468 | ||||||||
\(557\) | 33.5046 | 1.41963 | 0.709817 | − | 0.704386i | \(-0.248778\pi\) | ||||
0.709817 | + | 0.704386i | \(0.248778\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 26.6868 | 1.12873 | ||||||||
\(560\) | −13.3117 | −0.562522 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 12.7637 | 0.538405 | ||||||||
\(563\) | 0.0190630 | 0.000803411 0 | 0.000401705 | − | 1.00000i | \(-0.499872\pi\) | ||||
0.000401705 | 1.00000i | \(0.499872\pi\) | ||||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −3.15254 | −0.132628 | ||||||||
\(566\) | 32.5585 | 1.36854 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −10.5641 | −0.443258 | ||||||||
\(569\) | −17.4587 | −0.731908 | −0.365954 | − | 0.930633i | \(-0.619257\pi\) | ||||
−0.365954 | + | 0.930633i | \(0.619257\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 18.0879 | 0.756955 | 0.378477 | − | 0.925611i | \(-0.376448\pi\) | ||||
0.378477 | + | 0.925611i | \(0.376448\pi\) | |||||||
\(572\) | −1.79102 | −0.0748863 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 33.9613 | 1.41752 | ||||||||
\(575\) | −96.5116 | −4.02481 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 35.8487 | 1.49240 | 0.746200 | − | 0.665722i | \(-0.231876\pi\) | ||||
0.746200 | + | 0.665722i | \(0.231876\pi\) | |||||||
\(578\) | −16.5353 | −0.687777 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0.493430 | 0.0204886 | ||||||||
\(581\) | 29.8716 | 1.23928 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −4.75834 | −0.197070 | ||||||||
\(584\) | −3.30232 | −0.136651 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −28.3976 | −1.17309 | ||||||||
\(587\) | −2.69524 | −0.111244 | −0.0556222 | − | 0.998452i | \(-0.517714\pi\) | ||||
−0.0556222 | + | 0.998452i | \(0.517714\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −2.94367 | −0.121292 | ||||||||
\(590\) | 34.5817 | 1.42371 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −3.71884 | −0.152843 | ||||||||
\(593\) | 31.1847 | 1.28060 | 0.640302 | − | 0.768124i | \(-0.278809\pi\) | ||||
0.640302 | + | 0.768124i | \(0.278809\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −9.07473 | −0.372028 | ||||||||
\(596\) | 8.25494 | 0.338136 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 16.8417 | 0.688708 | ||||||||
\(599\) | 5.49303 | 0.224439 | 0.112220 | − | 0.993683i | \(-0.464204\pi\) | ||||
0.112220 | + | 0.993683i | \(0.464204\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −25.3653 | −1.03467 | −0.517335 | − | 0.855783i | \(-0.673076\pi\) | ||||
−0.517335 | + | 0.855783i | \(0.673076\pi\) | |||||||
\(602\) | −33.4752 | −1.36435 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −15.3701 | −0.625402 | ||||||||
\(605\) | 45.5509 | 1.85191 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −12.3964 | −0.503154 | −0.251577 | − | 0.967837i | \(-0.580949\pi\) | ||||
−0.251577 | + | 0.967837i | \(0.580949\pi\) | |||||||
\(608\) | −1.87811 | −0.0761674 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 19.7943 | 0.801449 | ||||||||
\(611\) | −15.1810 | −0.614156 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 11.0514 | 0.446363 | 0.223181 | − | 0.974777i | \(-0.428356\pi\) | ||||
0.223181 | + | 0.974777i | \(0.428356\pi\) | |||||||
\(614\) | −27.9578 | −1.12828 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 2.24661 | 0.0905183 | ||||||||
\(617\) | −24.7403 | −0.996006 | −0.498003 | − | 0.867175i | \(-0.665933\pi\) | ||||
−0.498003 | + | 0.867175i | \(0.665933\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −4.37667 | −0.175913 | −0.0879566 | − | 0.996124i | \(-0.528034\pi\) | ||||
−0.0879566 | + | 0.996124i | \(0.528034\pi\) | |||||||
\(620\) | −6.82559 | −0.274122 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 3.59459 | 0.144130 | ||||||||
\(623\) | 9.89786 | 0.396550 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 100.187 | 4.00750 | ||||||||
\(626\) | 11.4643 | 0.458204 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 5.70675 | 0.227724 | ||||||||
\(629\) | −2.53518 | −0.101084 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −39.8325 | −1.58571 | −0.792854 | − | 0.609411i | \(-0.791406\pi\) | ||||
−0.792854 | + | 0.609411i | \(0.791406\pi\) | |||||||
\(632\) | −3.98486 | −0.158509 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 33.3632 | 1.32502 | ||||||||
\(635\) | −77.1390 | −3.06117 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −5.71155 | −0.226300 | ||||||||
\(638\) | −0.0832759 | −0.00329692 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −4.35484 | −0.172140 | ||||||||
\(641\) | 44.5598 | 1.76000 | 0.880002 | − | 0.474969i | \(-0.157541\pi\) | ||||
0.880002 | + | 0.474969i | \(0.157541\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 33.6455 | 1.32685 | 0.663425 | − | 0.748243i | \(-0.269102\pi\) | ||||
0.663425 | + | 0.748243i | \(0.269102\pi\) | |||||||
\(644\) | −21.1257 | −0.832471 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −1.28033 | −0.0503738 | ||||||||
\(647\) | 7.69538 | 0.302537 | 0.151268 | − | 0.988493i | \(-0.451664\pi\) | ||||
0.151268 | + | 0.988493i | \(0.451664\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −5.83633 | −0.229096 | ||||||||
\(650\) | −34.0302 | −1.33477 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 1.46144 | 0.0572343 | ||||||||
\(653\) | −11.4671 | −0.448742 | −0.224371 | − | 0.974504i | \(-0.572033\pi\) | ||||
−0.224371 | + | 0.974504i | \(0.572033\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −20.1571 | −0.787605 | ||||||||
\(656\) | 11.1102 | 0.433782 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 19.0426 | 0.742357 | ||||||||
\(659\) | −35.9351 | −1.39983 | −0.699916 | − | 0.714225i | \(-0.746779\pi\) | ||||
−0.699916 | + | 0.714225i | \(0.746779\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −45.1850 | −1.75749 | −0.878747 | − | 0.477288i | \(-0.841620\pi\) | ||||
−0.878747 | + | 0.477288i | \(0.841620\pi\) | |||||||
\(662\) | −11.6186 | −0.451569 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 9.77231 | 0.379239 | ||||||||
\(665\) | 25.0009 | 0.969491 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0.783076 | 0.0303208 | ||||||||
\(668\) | 0.335943 | 0.0129980 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 9.71638 | 0.375376 | ||||||||
\(671\) | −3.34067 | −0.128965 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 1.54949 | 0.0597284 | 0.0298642 | − | 0.999554i | \(-0.490493\pi\) | ||||
0.0298642 | + | 0.999554i | \(0.490493\pi\) | |||||||
\(674\) | −7.91263 | −0.304783 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −7.06159 | −0.271600 | ||||||||
\(677\) | 18.2028 | 0.699590 | 0.349795 | − | 0.936826i | \(-0.386251\pi\) | ||||
0.349795 | + | 0.936826i | \(0.386251\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −33.9358 | −1.30234 | ||||||||
\(680\) | −2.96874 | −0.113846 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 1.15195 | 0.0441104 | ||||||||
\(683\) | −32.0454 | −1.22618 | −0.613092 | − | 0.790012i | \(-0.710074\pi\) | ||||
−0.613092 | + | 0.790012i | \(0.710074\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −30.2714 | −1.15661 | ||||||||
\(686\) | −14.2329 | −0.543415 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −10.9512 | −0.417511 | ||||||||
\(689\) | 15.7770 | 0.601057 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 8.17206 | 0.310880 | 0.155440 | − | 0.987845i | \(-0.450321\pi\) | ||||
0.155440 | + | 0.987845i | \(0.450321\pi\) | |||||||
\(692\) | −3.25577 | −0.123766 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 21.1718 | 0.803669 | ||||||||
\(695\) | −102.323 | −3.88133 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 7.57397 | 0.286884 | ||||||||
\(698\) | −11.3838 | −0.430883 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 42.6865 | 1.61340 | ||||||||
\(701\) | 25.3718 | 0.958281 | 0.479140 | − | 0.877738i | \(-0.340948\pi\) | ||||
0.479140 | + | 0.877738i | \(0.340948\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 6.98440 | 0.263422 | ||||||||
\(704\) | 0.734963 | 0.0276999 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 20.6961 | 0.778910 | ||||||||
\(707\) | −60.6520 | −2.28105 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 7.95024 | 0.298578 | 0.149289 | − | 0.988794i | \(-0.452302\pi\) | ||||
0.149289 | + | 0.988794i | \(0.452302\pi\) | |||||||
\(710\) | 46.0048 | 1.72653 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 3.23802 | 0.121350 | ||||||||
\(713\) | −10.8322 | −0.405671 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 7.79960 | 0.291689 | ||||||||
\(716\) | −2.01680 | −0.0753715 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 13.4560 | 0.502175 | ||||||||
\(719\) | 31.5123 | 1.17521 | 0.587606 | − | 0.809147i | \(-0.300071\pi\) | ||||
0.587606 | + | 0.809147i | \(0.300071\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −13.5240 | −0.503658 | ||||||||
\(722\) | −15.4727 | −0.575834 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −0.718726 | −0.0267113 | ||||||||
\(725\) | −1.58228 | −0.0587643 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −41.5993 | −1.54283 | −0.771416 | − | 0.636332i | \(-0.780451\pi\) | ||||
−0.771416 | + | 0.636332i | \(0.780451\pi\) | |||||||
\(728\) | −7.44898 | −0.276078 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 14.3811 | 0.532267 | ||||||||
\(731\) | −7.46556 | −0.276124 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −0.280816 | −0.0103722 | −0.00518608 | − | 0.999987i | \(-0.501651\pi\) | ||||
−0.00518608 | + | 0.999987i | \(0.501651\pi\) | |||||||
\(734\) | 8.80612 | 0.325040 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −6.91115 | −0.254748 | ||||||||
\(737\) | −1.63983 | −0.0604038 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 30.0973 | 1.10715 | 0.553574 | − | 0.832800i | \(-0.313264\pi\) | ||||
0.553574 | + | 0.832800i | \(0.313264\pi\) | |||||||
\(740\) | 16.1950 | 0.595339 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −19.7903 | −0.726524 | ||||||||
\(743\) | −1.49835 | −0.0549692 | −0.0274846 | − | 0.999622i | \(-0.508750\pi\) | ||||
−0.0274846 | + | 0.999622i | \(0.508750\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −35.9489 | −1.31707 | ||||||||
\(746\) | 5.86346 | 0.214676 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0.501032 | 0.0183195 | ||||||||
\(749\) | −34.8857 | −1.27470 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 19.0975 | 0.696878 | 0.348439 | − | 0.937331i | \(-0.386712\pi\) | ||||
0.348439 | + | 0.937331i | \(0.386712\pi\) | |||||||
\(752\) | 6.22966 | 0.227172 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0.276114 | 0.0100555 | ||||||||
\(755\) | 66.9344 | 2.43599 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −29.6151 | −1.07638 | −0.538189 | − | 0.842824i | \(-0.680891\pi\) | ||||
−0.538189 | + | 0.842824i | \(0.680891\pi\) | |||||||
\(758\) | −20.7423 | −0.753392 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 8.17887 | 0.296679 | ||||||||
\(761\) | −14.8382 | −0.537886 | −0.268943 | − | 0.963156i | \(-0.586674\pi\) | ||||
−0.268943 | + | 0.963156i | \(0.586674\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −46.4360 | −1.68110 | ||||||||
\(764\) | −4.95760 | −0.179360 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −25.8637 | −0.934495 | ||||||||
\(767\) | 19.3513 | 0.698735 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −23.8346 | −0.859498 | −0.429749 | − | 0.902948i | \(-0.641398\pi\) | ||||
−0.429749 | + | 0.902948i | \(0.641398\pi\) | |||||||
\(770\) | −9.78361 | −0.352577 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −8.59130 | −0.309208 | ||||||||
\(773\) | −55.4521 | −1.99447 | −0.997237 | − | 0.0742897i | \(-0.976331\pi\) | ||||
−0.997237 | + | 0.0742897i | \(0.976331\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 21.8876 | 0.786224 | ||||||||
\(776\) | −11.1019 | −0.398535 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −2.44929 | −0.0878113 | ||||||||
\(779\) | −20.8662 | −0.747611 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −7.76419 | −0.277825 | ||||||||
\(782\) | −4.71141 | −0.168480 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 2.34379 | 0.0837068 | ||||||||
\(785\) | −24.8520 | −0.887005 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 33.1602 | 1.18203 | 0.591017 | − | 0.806659i | \(-0.298726\pi\) | ||||
0.591017 | + | 0.806659i | \(0.298726\pi\) | |||||||
\(788\) | −17.0864 | −0.608678 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 17.3534 | 0.617407 | ||||||||
\(791\) | 2.21284 | 0.0786795 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 11.0765 | 0.393339 | ||||||||
\(794\) | 19.7131 | 0.699590 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −0.350646 | −0.0124283 | ||||||||
\(797\) | −15.2713 | −0.540936 | −0.270468 | − | 0.962729i | \(-0.587179\pi\) | ||||
−0.270468 | + | 0.962729i | \(0.587179\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 4.24682 | 0.150242 | ||||||||
\(800\) | 13.9646 | 0.493724 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −11.7643 | −0.415413 | ||||||||
\(803\) | −2.42708 | −0.0856499 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 91.9992 | 3.24255 | ||||||||
\(806\) | −3.81947 | −0.134535 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −19.8419 | −0.698036 | ||||||||
\(809\) | −39.8830 | −1.40221 | −0.701106 | − | 0.713057i | \(-0.747310\pi\) | ||||
−0.701106 | + | 0.713057i | \(0.747310\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −21.4838 | −0.754400 | −0.377200 | − | 0.926132i | \(-0.623113\pi\) | ||||
−0.377200 | + | 0.926132i | \(0.623113\pi\) | |||||||
\(812\) | −0.346350 | −0.0121545 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −2.73321 | −0.0957990 | ||||||||
\(815\) | −6.36432 | −0.222932 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 20.5676 | 0.719569 | ||||||||
\(818\) | 29.9196 | 1.04611 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −48.3833 | −1.68962 | ||||||||
\(821\) | −14.5566 | −0.508029 | −0.254014 | − | 0.967200i | \(-0.581751\pi\) | ||||
−0.254014 | + | 0.967200i | \(0.581751\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 3.79452 | 0.132269 | 0.0661344 | − | 0.997811i | \(-0.478933\pi\) | ||||
0.0661344 | + | 0.997811i | \(0.478933\pi\) | |||||||
\(824\) | −4.42428 | −0.154127 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −24.2737 | −0.844591 | ||||||||
\(827\) | −56.9287 | −1.97960 | −0.989802 | − | 0.142452i | \(-0.954501\pi\) | ||||
−0.989802 | + | 0.142452i | \(0.954501\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −44.0562 | −1.53013 | −0.765067 | − | 0.643951i | \(-0.777294\pi\) | ||||
−0.765067 | + | 0.643951i | \(0.777294\pi\) | |||||||
\(830\) | −42.5568 | −1.47717 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −2.43689 | −0.0844838 | ||||||||
\(833\) | 1.59779 | 0.0553601 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −1.46298 | −0.0506284 | ||||||||
\(836\) | −1.38034 | −0.0477401 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 36.6787 | 1.26704 | ||||||||
\(839\) | −2.03615 | −0.0702957 | −0.0351479 | − | 0.999382i | \(-0.511190\pi\) | ||||
−0.0351479 | + | 0.999382i | \(0.511190\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.9872 | −0.999557 | ||||||||
\(842\) | 30.9616 | 1.06701 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −12.3103 | −0.423738 | ||||||||
\(845\) | 30.7521 | 1.05790 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −31.9732 | −1.09861 | ||||||||
\(848\) | −6.47426 | −0.222327 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 9.51983 | 0.326528 | ||||||||
\(851\) | 25.7015 | 0.881035 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 45.1825 | 1.54702 | 0.773510 | − | 0.633785i | \(-0.218499\pi\) | ||||
0.773510 | + | 0.633785i | \(0.218499\pi\) | |||||||
\(854\) | −13.8941 | −0.475446 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −11.4126 | −0.390076 | ||||||||
\(857\) | 13.9020 | 0.474883 | 0.237442 | − | 0.971402i | \(-0.423691\pi\) | ||||
0.237442 | + | 0.971402i | \(0.423691\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 25.9715 | 0.886134 | 0.443067 | − | 0.896488i | \(-0.353890\pi\) | ||||
0.443067 | + | 0.896488i | \(0.353890\pi\) | |||||||
\(860\) | 47.6907 | 1.62624 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 32.4852 | 1.10645 | ||||||||
\(863\) | −24.8717 | −0.846642 | −0.423321 | − | 0.905980i | \(-0.639136\pi\) | ||||
−0.423321 | + | 0.905980i | \(0.639136\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 14.1784 | 0.482079 | ||||||||
\(866\) | −24.9126 | −0.846566 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 4.79104 | 0.162619 | ||||||||
\(869\) | −2.92872 | −0.0993502 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 5.43710 | 0.184229 | ||||||||
\(872\) | −15.1912 | −0.514440 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 12.9799 | 0.439052 | ||||||||
\(875\) | −119.334 | −4.03424 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −41.9092 | −1.41517 | −0.707586 | − | 0.706627i | \(-0.750216\pi\) | ||||
−0.707586 | + | 0.706627i | \(0.750216\pi\) | |||||||
\(878\) | 31.8189 | 1.07384 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −3.20064 | −0.107894 | ||||||||
\(881\) | −0.208232 | −0.00701552 | −0.00350776 | − | 0.999994i | \(-0.501117\pi\) | ||||
−0.00350776 | + | 0.999994i | \(0.501117\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −4.62099 | −0.155509 | −0.0777544 | − | 0.996973i | \(-0.524775\pi\) | ||||
−0.0777544 | + | 0.996973i | \(0.524775\pi\) | |||||||
\(884\) | −1.66125 | −0.0558739 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 22.4064 | 0.752759 | ||||||||
\(887\) | 11.1644 | 0.374865 | 0.187433 | − | 0.982277i | \(-0.439983\pi\) | ||||
0.187433 | + | 0.982277i | \(0.439983\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 54.1457 | 1.81599 | ||||||||
\(890\) | −14.1011 | −0.472669 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −1.00000 | −0.0334825 | ||||||||
\(893\) | −11.7000 | −0.391525 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 8.78285 | 0.293578 | ||||||||
\(896\) | 3.05676 | 0.102119 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −27.5968 | −0.920918 | ||||||||
\(899\) | −0.177591 | −0.00592301 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −4.41358 | −0.147038 | ||||||||
\(902\) | 8.16560 | 0.271885 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0.723916 | 0.0240771 | ||||||||
\(905\) | 3.12994 | 0.104043 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 0.749208 | 0.0248770 | 0.0124385 | − | 0.999923i | \(-0.496041\pi\) | ||||
0.0124385 | + | 0.999923i | \(0.496041\pi\) | |||||||
\(908\) | −11.9814 | −0.397616 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 32.4391 | 1.07535 | ||||||||
\(911\) | 45.7170 | 1.51467 | 0.757336 | − | 0.653026i | \(-0.226501\pi\) | ||||
0.757336 | + | 0.653026i | \(0.226501\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 7.18228 | 0.237699 | ||||||||
\(914\) | 6.26270 | 0.207152 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −0.278694 | −0.00920831 | ||||||||
\(917\) | 14.1488 | 0.467233 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −4.43703 | −0.146364 | −0.0731821 | − | 0.997319i | \(-0.523315\pi\) | ||||
−0.0731821 | + | 0.997319i | \(0.523315\pi\) | |||||||
\(920\) | 30.0969 | 0.992267 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 24.4624 | 0.805626 | ||||||||
\(923\) | 25.7434 | 0.847355 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −51.9322 | −1.70752 | ||||||||
\(926\) | −10.5467 | −0.346585 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −0.113306 | −0.00371946 | ||||||||
\(929\) | −0.789965 | −0.0259179 | −0.0129590 | − | 0.999916i | \(-0.504125\pi\) | ||||
−0.0129590 | + | 0.999916i | \(0.504125\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −4.40190 | −0.144266 | ||||||||
\(932\) | 12.2226 | 0.400366 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 27.0318 | 0.884508 | ||||||||
\(935\) | −2.18191 | −0.0713562 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 11.0887 | 0.362252 | 0.181126 | − | 0.983460i | \(-0.442026\pi\) | ||||
0.181126 | + | 0.983460i | \(0.442026\pi\) | |||||||
\(938\) | −6.82015 | −0.222686 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −27.1291 | −0.884855 | ||||||||
\(941\) | 49.8346 | 1.62456 | 0.812281 | − | 0.583267i | \(-0.198226\pi\) | ||||
0.812281 | + | 0.583267i | \(0.198226\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −76.7845 | −2.50045 | ||||||||
\(944\) | −7.94099 | −0.258457 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −8.04873 | −0.261687 | ||||||||
\(947\) | −3.22300 | −0.104733 | −0.0523667 | − | 0.998628i | \(-0.516676\pi\) | ||||
−0.0523667 | + | 0.998628i | \(0.516676\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 8.04738 | 0.261229 | ||||||||
\(950\) | −26.2271 | −0.850919 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 2.08383 | 0.0675372 | ||||||||
\(953\) | −35.4866 | −1.14952 | −0.574762 | − | 0.818320i | \(-0.694905\pi\) | ||||
−0.574762 | + | 0.818320i | \(0.694905\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 21.5895 | 0.698621 | ||||||||
\(956\) | −22.2407 | −0.719316 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −23.9419 | −0.773528 | ||||||||
\(959\) | 21.2482 | 0.686140 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −28.5434 | −0.920754 | ||||||||
\(962\) | 9.06239 | 0.292183 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −22.3491 | −0.719814 | ||||||||
\(965\) | 37.4137 | 1.20439 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −4.41806 | −0.142075 | −0.0710376 | − | 0.997474i | \(-0.522631\pi\) | ||||
−0.0710376 | + | 0.997474i | \(0.522631\pi\) | |||||||
\(968\) | −10.4598 | −0.336192 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 48.3470 | 1.55233 | ||||||||
\(971\) | −12.8435 | −0.412169 | −0.206084 | − | 0.978534i | \(-0.566072\pi\) | ||||
−0.206084 | + | 0.978534i | \(0.566072\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 71.8228 | 2.30253 | ||||||||
\(974\) | −2.04679 | −0.0655834 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −4.54537 | −0.145494 | ||||||||
\(977\) | −14.9739 | −0.479057 | −0.239528 | − | 0.970889i | \(-0.576993\pi\) | ||||
−0.239528 | + | 0.970889i | \(0.576993\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 2.37983 | 0.0760596 | ||||||||
\(980\) | −10.2068 | −0.326045 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 30.6746 | 0.978866 | ||||||||
\(983\) | 22.0615 | 0.703652 | 0.351826 | − | 0.936065i | \(-0.385561\pi\) | ||||
0.351826 | + | 0.936065i | \(0.385561\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 74.4086 | 2.37085 | ||||||||
\(986\) | −0.0772421 | −0.00245989 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 4.57674 | 0.145606 | ||||||||
\(989\) | 75.6855 | 2.40666 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −8.96101 | −0.284656 | −0.142328 | − | 0.989820i | \(-0.545459\pi\) | ||||
−0.142328 | + | 0.989820i | \(0.545459\pi\) | |||||||
\(992\) | 1.56736 | 0.0497637 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −32.2918 | −1.02423 | ||||||||
\(995\) | 1.52701 | 0.0484093 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 51.5423 | 1.63236 | 0.816180 | − | 0.577798i | \(-0.196088\pi\) | ||||
0.816180 | + | 0.577798i | \(0.196088\pi\) | |||||||
\(998\) | 29.0813 | 0.920553 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 4014.2.a.r.1.1 | 5 | ||
3.2 | odd | 2 | 1338.2.a.h.1.5 | ✓ | 5 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1338.2.a.h.1.5 | ✓ | 5 | 3.2 | odd | 2 | ||
4014.2.a.r.1.1 | 5 | 1.1 | even | 1 | trivial |