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: | \(0\) |
Dimension: | \(7\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{7} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{7} - 18x^{5} - 8x^{4} + 51x^{3} + 47x^{2} - 2x - 8 \) |
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 | 1.7 | ||
Root | \(-0.788998\) 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 | ||||||||
\(5\) | 3.73564 | 1.67063 | 0.835314 | − | 0.549774i | \(-0.185286\pi\) | ||||
0.835314 | + | 0.549774i | \(0.185286\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.27800 | 0.861004 | 0.430502 | − | 0.902590i | \(-0.358337\pi\) | ||||
0.430502 | + | 0.902590i | \(0.358337\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −3.73564 | −1.18131 | ||||||||
\(11\) | 6.01441 | 1.81341 | 0.906706 | − | 0.421763i | \(-0.138589\pi\) | ||||
0.906706 | + | 0.421763i | \(0.138589\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.852078 | 0.236324 | 0.118162 | − | 0.992994i | \(-0.462300\pi\) | ||||
0.118162 | + | 0.992994i | \(0.462300\pi\) | |||||||
\(14\) | −2.27800 | −0.608822 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −4.60921 | −1.11790 | −0.558949 | − | 0.829202i | \(-0.688795\pi\) | ||||
−0.558949 | + | 0.829202i | \(0.688795\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.48612 | 0.340940 | 0.170470 | − | 0.985363i | \(-0.445471\pi\) | ||||
0.170470 | + | 0.985363i | \(0.445471\pi\) | |||||||
\(20\) | 3.73564 | 0.835314 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −6.01441 | −1.28228 | ||||||||
\(23\) | −4.21204 | −0.878271 | −0.439136 | − | 0.898421i | \(-0.644715\pi\) | ||||
−0.439136 | + | 0.898421i | \(0.644715\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 8.95498 | 1.79100 | ||||||||
\(26\) | −0.852078 | −0.167106 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 2.27800 | 0.430502 | ||||||||
\(29\) | −1.52437 | −0.283068 | −0.141534 | − | 0.989933i | \(-0.545203\pi\) | ||||
−0.141534 | + | 0.989933i | \(0.545203\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 6.58406 | 1.18253 | 0.591266 | − | 0.806476i | \(-0.298628\pi\) | ||||
0.591266 | + | 0.806476i | \(0.298628\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 4.60921 | 0.790473 | ||||||||
\(35\) | 8.50979 | 1.43842 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 4.42642 | 0.727699 | 0.363850 | − | 0.931458i | \(-0.381462\pi\) | ||||
0.363850 | + | 0.931458i | \(0.381462\pi\) | |||||||
\(38\) | −1.48612 | −0.241081 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −3.73564 | −0.590656 | ||||||||
\(41\) | −10.1716 | −1.58853 | −0.794267 | − | 0.607568i | \(-0.792145\pi\) | ||||
−0.794267 | + | 0.607568i | \(0.792145\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0.917382 | 0.139899 | 0.0699497 | − | 0.997551i | \(-0.477716\pi\) | ||||
0.0699497 | + | 0.997551i | \(0.477716\pi\) | |||||||
\(44\) | 6.01441 | 0.906706 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 4.21204 | 0.621032 | ||||||||
\(47\) | 8.32897 | 1.21490 | 0.607452 | − | 0.794356i | \(-0.292192\pi\) | ||||
0.607452 | + | 0.794356i | \(0.292192\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.81071 | −0.258673 | ||||||||
\(50\) | −8.95498 | −1.26643 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0.852078 | 0.118162 | ||||||||
\(53\) | 6.28830 | 0.863764 | 0.431882 | − | 0.901930i | \(-0.357850\pi\) | ||||
0.431882 | + | 0.901930i | \(0.357850\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 22.4676 | 3.02954 | ||||||||
\(56\) | −2.27800 | −0.304411 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 1.52437 | 0.200159 | ||||||||
\(59\) | −4.62427 | −0.602029 | −0.301014 | − | 0.953620i | \(-0.597325\pi\) | ||||
−0.301014 | + | 0.953620i | \(0.597325\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.47563 | 0.316973 | 0.158486 | − | 0.987361i | \(-0.449339\pi\) | ||||
0.158486 | + | 0.987361i | \(0.449339\pi\) | |||||||
\(62\) | −6.58406 | −0.836177 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 3.18305 | 0.394809 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 3.43979 | 0.420238 | 0.210119 | − | 0.977676i | \(-0.432615\pi\) | ||||
0.210119 | + | 0.977676i | \(0.432615\pi\) | |||||||
\(68\) | −4.60921 | −0.558949 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −8.50979 | −1.01711 | ||||||||
\(71\) | −0.919349 | −0.109107 | −0.0545533 | − | 0.998511i | \(-0.517373\pi\) | ||||
−0.0545533 | + | 0.998511i | \(0.517373\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −1.20422 | −0.140944 | −0.0704718 | − | 0.997514i | \(-0.522450\pi\) | ||||
−0.0704718 | + | 0.997514i | \(0.522450\pi\) | |||||||
\(74\) | −4.42642 | −0.514561 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 1.48612 | 0.170470 | ||||||||
\(77\) | 13.7008 | 1.56135 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 12.3064 | 1.38457 | 0.692287 | − | 0.721623i | \(-0.256603\pi\) | ||||
0.692287 | + | 0.721623i | \(0.256603\pi\) | |||||||
\(80\) | 3.73564 | 0.417657 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 10.1716 | 1.12326 | ||||||||
\(83\) | −12.1582 | −1.33453 | −0.667266 | − | 0.744820i | \(-0.732535\pi\) | ||||
−0.667266 | + | 0.744820i | \(0.732535\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −17.2183 | −1.86759 | ||||||||
\(86\) | −0.917382 | −0.0989239 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −6.01441 | −0.641138 | ||||||||
\(89\) | 1.06503 | 0.112893 | 0.0564466 | − | 0.998406i | \(-0.482023\pi\) | ||||
0.0564466 | + | 0.998406i | \(0.482023\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.94104 | 0.203476 | ||||||||
\(92\) | −4.21204 | −0.439136 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −8.32897 | −0.859067 | ||||||||
\(95\) | 5.55162 | 0.569584 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −2.53493 | −0.257383 | −0.128692 | − | 0.991685i | \(-0.541078\pi\) | ||||
−0.128692 | + | 0.991685i | \(0.541078\pi\) | |||||||
\(98\) | 1.81071 | 0.182909 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 8.95498 | 0.895498 | ||||||||
\(101\) | −4.75076 | −0.472718 | −0.236359 | − | 0.971666i | \(-0.575954\pi\) | ||||
−0.236359 | + | 0.971666i | \(0.575954\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 8.46155 | 0.833742 | 0.416871 | − | 0.908966i | \(-0.363127\pi\) | ||||
0.416871 | + | 0.908966i | \(0.363127\pi\) | |||||||
\(104\) | −0.852078 | −0.0835531 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −6.28830 | −0.610773 | ||||||||
\(107\) | −1.43645 | −0.138867 | −0.0694333 | − | 0.997587i | \(-0.522119\pi\) | ||||
−0.0694333 | + | 0.997587i | \(0.522119\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 12.5744 | 1.20441 | 0.602205 | − | 0.798342i | \(-0.294289\pi\) | ||||
0.602205 | + | 0.798342i | \(0.294289\pi\) | |||||||
\(110\) | −22.4676 | −2.14221 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 2.27800 | 0.215251 | ||||||||
\(113\) | −1.42716 | −0.134256 | −0.0671279 | − | 0.997744i | \(-0.521384\pi\) | ||||
−0.0671279 | + | 0.997744i | \(0.521384\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −15.7347 | −1.46726 | ||||||||
\(116\) | −1.52437 | −0.141534 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 4.62427 | 0.425699 | ||||||||
\(119\) | −10.4998 | −0.962514 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 25.1731 | 2.28846 | ||||||||
\(122\) | −2.47563 | −0.224133 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 6.58406 | 0.591266 | ||||||||
\(125\) | 14.7744 | 1.32146 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −21.3436 | −1.89394 | −0.946971 | − | 0.321319i | \(-0.895874\pi\) | ||||
−0.946971 | + | 0.321319i | \(0.895874\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −3.18305 | −0.279172 | ||||||||
\(131\) | −17.7225 | −1.54842 | −0.774209 | − | 0.632930i | \(-0.781852\pi\) | ||||
−0.774209 | + | 0.632930i | \(0.781852\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 3.38539 | 0.293551 | ||||||||
\(134\) | −3.43979 | −0.297153 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 4.60921 | 0.395236 | ||||||||
\(137\) | −8.40769 | −0.718318 | −0.359159 | − | 0.933276i | \(-0.616936\pi\) | ||||
−0.359159 | + | 0.933276i | \(0.616936\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −16.6796 | −1.41474 | −0.707371 | − | 0.706842i | \(-0.750119\pi\) | ||||
−0.707371 | + | 0.706842i | \(0.750119\pi\) | |||||||
\(140\) | 8.50979 | 0.719208 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0.919349 | 0.0771500 | ||||||||
\(143\) | 5.12474 | 0.428553 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −5.69448 | −0.472900 | ||||||||
\(146\) | 1.20422 | 0.0996622 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 4.42642 | 0.363850 | ||||||||
\(149\) | 20.0642 | 1.64372 | 0.821861 | − | 0.569688i | \(-0.192936\pi\) | ||||
0.821861 | + | 0.569688i | \(0.192936\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −17.7405 | −1.44370 | −0.721852 | − | 0.692048i | \(-0.756709\pi\) | ||||
−0.721852 | + | 0.692048i | \(0.756709\pi\) | |||||||
\(152\) | −1.48612 | −0.120541 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −13.7008 | −1.10404 | ||||||||
\(155\) | 24.5957 | 1.97557 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −2.78869 | −0.222562 | −0.111281 | − | 0.993789i | \(-0.535495\pi\) | ||||
−0.111281 | + | 0.993789i | \(0.535495\pi\) | |||||||
\(158\) | −12.3064 | −0.979041 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −3.73564 | −0.295328 | ||||||||
\(161\) | −9.59504 | −0.756195 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −14.9595 | −1.17172 | −0.585859 | − | 0.810413i | \(-0.699243\pi\) | ||||
−0.585859 | + | 0.810413i | \(0.699243\pi\) | |||||||
\(164\) | −10.1716 | −0.794267 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 12.1582 | 0.943656 | ||||||||
\(167\) | −8.34896 | −0.646062 | −0.323031 | − | 0.946388i | \(-0.604702\pi\) | ||||
−0.323031 | + | 0.946388i | \(0.604702\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.2740 | −0.944151 | ||||||||
\(170\) | 17.2183 | 1.32059 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0.917382 | 0.0699497 | ||||||||
\(173\) | 1.30257 | 0.0990327 | 0.0495163 | − | 0.998773i | \(-0.484232\pi\) | ||||
0.0495163 | + | 0.998773i | \(0.484232\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 20.3995 | 1.54205 | ||||||||
\(176\) | 6.01441 | 0.453353 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −1.06503 | −0.0798276 | ||||||||
\(179\) | 24.7249 | 1.84803 | 0.924014 | − | 0.382359i | \(-0.124888\pi\) | ||||
0.924014 | + | 0.382359i | \(0.124888\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 24.6587 | 1.83287 | 0.916435 | − | 0.400184i | \(-0.131054\pi\) | ||||
0.916435 | + | 0.400184i | \(0.131054\pi\) | |||||||
\(182\) | −1.94104 | −0.143879 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 4.21204 | 0.310516 | ||||||||
\(185\) | 16.5355 | 1.21571 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −27.7217 | −2.02721 | ||||||||
\(188\) | 8.32897 | 0.607452 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −5.55162 | −0.402757 | ||||||||
\(191\) | 18.6689 | 1.35084 | 0.675418 | − | 0.737435i | \(-0.263963\pi\) | ||||
0.675418 | + | 0.737435i | \(0.263963\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −21.4822 | −1.54633 | −0.773163 | − | 0.634207i | \(-0.781327\pi\) | ||||
−0.773163 | + | 0.634207i | \(0.781327\pi\) | |||||||
\(194\) | 2.53493 | 0.181997 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −1.81071 | −0.129336 | ||||||||
\(197\) | −1.74494 | −0.124322 | −0.0621610 | − | 0.998066i | \(-0.519799\pi\) | ||||
−0.0621610 | + | 0.998066i | \(0.519799\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −21.8960 | −1.55217 | −0.776084 | − | 0.630630i | \(-0.782797\pi\) | ||||
−0.776084 | + | 0.630630i | \(0.782797\pi\) | |||||||
\(200\) | −8.95498 | −0.633213 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 4.75076 | 0.334262 | ||||||||
\(203\) | −3.47251 | −0.243722 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −37.9973 | −2.65385 | ||||||||
\(206\) | −8.46155 | −0.589544 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0.852078 | 0.0590810 | ||||||||
\(209\) | 8.93815 | 0.618265 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 22.6920 | 1.56218 | 0.781091 | − | 0.624417i | \(-0.214663\pi\) | ||||
0.781091 | + | 0.624417i | \(0.214663\pi\) | |||||||
\(212\) | 6.28830 | 0.431882 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 1.43645 | 0.0981935 | ||||||||
\(215\) | 3.42701 | 0.233720 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 14.9985 | 1.01817 | ||||||||
\(218\) | −12.5744 | −0.851646 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 22.4676 | 1.51477 | ||||||||
\(221\) | −3.92740 | −0.264186 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1.00000 | −0.0669650 | ||||||||
\(224\) | −2.27800 | −0.152205 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 1.42716 | 0.0949332 | ||||||||
\(227\) | 22.2803 | 1.47880 | 0.739399 | − | 0.673268i | \(-0.235110\pi\) | ||||
0.739399 | + | 0.673268i | \(0.235110\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 14.5880 | 0.964000 | 0.482000 | − | 0.876171i | \(-0.339910\pi\) | ||||
0.482000 | + | 0.876171i | \(0.339910\pi\) | |||||||
\(230\) | 15.7347 | 1.03751 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 1.52437 | 0.100080 | ||||||||
\(233\) | −4.82251 | −0.315933 | −0.157967 | − | 0.987444i | \(-0.550494\pi\) | ||||
−0.157967 | + | 0.987444i | \(0.550494\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 31.1140 | 2.02965 | ||||||||
\(236\) | −4.62427 | −0.301014 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 10.4998 | 0.680600 | ||||||||
\(239\) | −13.8013 | −0.892730 | −0.446365 | − | 0.894851i | \(-0.647282\pi\) | ||||
−0.446365 | + | 0.894851i | \(0.647282\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 10.5058 | 0.676738 | 0.338369 | − | 0.941014i | \(-0.390125\pi\) | ||||
0.338369 | + | 0.941014i | \(0.390125\pi\) | |||||||
\(242\) | −25.1731 | −1.61819 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 2.47563 | 0.158486 | ||||||||
\(245\) | −6.76415 | −0.432145 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1.26629 | 0.0805723 | ||||||||
\(248\) | −6.58406 | −0.418088 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −14.7744 | −0.934413 | ||||||||
\(251\) | −10.4874 | −0.661958 | −0.330979 | − | 0.943638i | \(-0.607379\pi\) | ||||
−0.330979 | + | 0.943638i | \(0.607379\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −25.3329 | −1.59267 | ||||||||
\(254\) | 21.3436 | 1.33922 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −12.5438 | −0.782460 | −0.391230 | − | 0.920293i | \(-0.627950\pi\) | ||||
−0.391230 | + | 0.920293i | \(0.627950\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 10.0834 | 0.626552 | ||||||||
\(260\) | 3.18305 | 0.197405 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 17.7225 | 1.09490 | ||||||||
\(263\) | −25.8499 | −1.59397 | −0.796986 | − | 0.603997i | \(-0.793574\pi\) | ||||
−0.796986 | + | 0.603997i | \(0.793574\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 23.4908 | 1.44303 | ||||||||
\(266\) | −3.38539 | −0.207572 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 3.43979 | 0.210119 | ||||||||
\(269\) | −19.2755 | −1.17525 | −0.587623 | − | 0.809135i | \(-0.699936\pi\) | ||||
−0.587623 | + | 0.809135i | \(0.699936\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −21.8099 | −1.32486 | −0.662428 | − | 0.749125i | \(-0.730474\pi\) | ||||
−0.662428 | + | 0.749125i | \(0.730474\pi\) | |||||||
\(272\) | −4.60921 | −0.279474 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 8.40769 | 0.507927 | ||||||||
\(275\) | 53.8589 | 3.24781 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 19.4696 | 1.16981 | 0.584907 | − | 0.811100i | \(-0.301131\pi\) | ||||
0.584907 | + | 0.811100i | \(0.301131\pi\) | |||||||
\(278\) | 16.6796 | 1.00037 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −8.50979 | −0.508557 | ||||||||
\(281\) | −16.7963 | −1.00198 | −0.500992 | − | 0.865452i | \(-0.667031\pi\) | ||||
−0.500992 | + | 0.865452i | \(0.667031\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −24.1812 | −1.43743 | −0.718713 | − | 0.695307i | \(-0.755268\pi\) | ||||
−0.718713 | + | 0.695307i | \(0.755268\pi\) | |||||||
\(284\) | −0.919349 | −0.0545533 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −5.12474 | −0.303033 | ||||||||
\(287\) | −23.1709 | −1.36773 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 4.24479 | 0.249694 | ||||||||
\(290\) | 5.69448 | 0.334391 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −1.20422 | −0.0704718 | ||||||||
\(293\) | −26.0052 | −1.51924 | −0.759619 | − | 0.650368i | \(-0.774615\pi\) | ||||
−0.759619 | + | 0.650368i | \(0.774615\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −17.2746 | −1.00577 | ||||||||
\(296\) | −4.42642 | −0.257281 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −20.0642 | −1.16229 | ||||||||
\(299\) | −3.58899 | −0.207556 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2.08980 | 0.120454 | ||||||||
\(302\) | 17.7405 | 1.02085 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 1.48612 | 0.0852350 | ||||||||
\(305\) | 9.24807 | 0.529543 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 26.1554 | 1.49277 | 0.746383 | − | 0.665516i | \(-0.231789\pi\) | ||||
0.746383 | + | 0.665516i | \(0.231789\pi\) | |||||||
\(308\) | 13.7008 | 0.780677 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −24.5957 | −1.39694 | ||||||||
\(311\) | −2.36626 | −0.134178 | −0.0670892 | − | 0.997747i | \(-0.521371\pi\) | ||||
−0.0670892 | + | 0.997747i | \(0.521371\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −11.2794 | −0.637548 | −0.318774 | − | 0.947831i | \(-0.603271\pi\) | ||||
−0.318774 | + | 0.947831i | \(0.603271\pi\) | |||||||
\(314\) | 2.78869 | 0.157375 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 12.3064 | 0.692287 | ||||||||
\(317\) | 28.7306 | 1.61367 | 0.806835 | − | 0.590777i | \(-0.201179\pi\) | ||||
0.806835 | + | 0.590777i | \(0.201179\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −9.16816 | −0.513318 | ||||||||
\(320\) | 3.73564 | 0.208828 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 9.59504 | 0.534711 | ||||||||
\(323\) | −6.84985 | −0.381136 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 7.63034 | 0.423255 | ||||||||
\(326\) | 14.9595 | 0.828530 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 10.1716 | 0.561632 | ||||||||
\(329\) | 18.9734 | 1.04604 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 7.33457 | 0.403145 | 0.201572 | − | 0.979474i | \(-0.435395\pi\) | ||||
0.201572 | + | 0.979474i | \(0.435395\pi\) | |||||||
\(332\) | −12.1582 | −0.667266 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 8.34896 | 0.456835 | ||||||||
\(335\) | 12.8498 | 0.702060 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 6.40802 | 0.349067 | 0.174534 | − | 0.984651i | \(-0.444158\pi\) | ||||
0.174534 | + | 0.984651i | \(0.444158\pi\) | |||||||
\(338\) | 12.2740 | 0.667616 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −17.2183 | −0.933795 | ||||||||
\(341\) | 39.5992 | 2.14442 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −20.0708 | −1.08372 | ||||||||
\(344\) | −0.917382 | −0.0494619 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −1.30257 | −0.0700267 | ||||||||
\(347\) | −7.39309 | −0.396882 | −0.198441 | − | 0.980113i | \(-0.563588\pi\) | ||||
−0.198441 | + | 0.980113i | \(0.563588\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 20.8521 | 1.11619 | 0.558093 | − | 0.829778i | \(-0.311533\pi\) | ||||
0.558093 | + | 0.829778i | \(0.311533\pi\) | |||||||
\(350\) | −20.3995 | −1.09040 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −6.01441 | −0.320569 | ||||||||
\(353\) | −3.49981 | −0.186276 | −0.0931381 | − | 0.995653i | \(-0.529690\pi\) | ||||
−0.0931381 | + | 0.995653i | \(0.529690\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −3.43435 | −0.182277 | ||||||||
\(356\) | 1.06503 | 0.0564466 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −24.7249 | −1.30675 | ||||||||
\(359\) | 30.5897 | 1.61446 | 0.807232 | − | 0.590234i | \(-0.200965\pi\) | ||||
0.807232 | + | 0.590234i | \(0.200965\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −16.7914 | −0.883760 | ||||||||
\(362\) | −24.6587 | −1.29603 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 1.94104 | 0.101738 | ||||||||
\(365\) | −4.49854 | −0.235464 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 10.9138 | 0.569697 | 0.284848 | − | 0.958573i | \(-0.408057\pi\) | ||||
0.284848 | + | 0.958573i | \(0.408057\pi\) | |||||||
\(368\) | −4.21204 | −0.219568 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −16.5355 | −0.859640 | ||||||||
\(371\) | 14.3247 | 0.743704 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 23.2262 | 1.20261 | 0.601304 | − | 0.799020i | \(-0.294648\pi\) | ||||
0.601304 | + | 0.799020i | \(0.294648\pi\) | |||||||
\(374\) | 27.7217 | 1.43345 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −8.32897 | −0.429534 | ||||||||
\(377\) | −1.29888 | −0.0668956 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 7.46237 | 0.383316 | 0.191658 | − | 0.981462i | \(-0.438613\pi\) | ||||
0.191658 | + | 0.981462i | \(0.438613\pi\) | |||||||
\(380\) | 5.55162 | 0.284792 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −18.6689 | −0.955186 | ||||||||
\(383\) | −9.04126 | −0.461987 | −0.230993 | − | 0.972955i | \(-0.574198\pi\) | ||||
−0.230993 | + | 0.972955i | \(0.574198\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 51.1813 | 2.60844 | ||||||||
\(386\) | 21.4822 | 1.09342 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −2.53493 | −0.128692 | ||||||||
\(389\) | 23.3946 | 1.18615 | 0.593076 | − | 0.805147i | \(-0.297914\pi\) | ||||
0.593076 | + | 0.805147i | \(0.297914\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 19.4142 | 0.981817 | ||||||||
\(392\) | 1.81071 | 0.0914546 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 1.74494 | 0.0879090 | ||||||||
\(395\) | 45.9721 | 2.31311 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 37.9849 | 1.90641 | 0.953203 | − | 0.302331i | \(-0.0977649\pi\) | ||||
0.953203 | + | 0.302331i | \(0.0977649\pi\) | |||||||
\(398\) | 21.8960 | 1.09755 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 8.95498 | 0.447749 | ||||||||
\(401\) | 11.8561 | 0.592064 | 0.296032 | − | 0.955178i | \(-0.404337\pi\) | ||||
0.296032 | + | 0.955178i | \(0.404337\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 5.61014 | 0.279461 | ||||||||
\(404\) | −4.75076 | −0.236359 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 3.47251 | 0.172338 | ||||||||
\(407\) | 26.6223 | 1.31962 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 25.8663 | 1.27900 | 0.639502 | − | 0.768789i | \(-0.279140\pi\) | ||||
0.639502 | + | 0.768789i | \(0.279140\pi\) | |||||||
\(410\) | 37.9973 | 1.87655 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 8.46155 | 0.416871 | ||||||||
\(413\) | −10.5341 | −0.518349 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −45.4185 | −2.22950 | ||||||||
\(416\) | −0.852078 | −0.0417766 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −8.93815 | −0.437179 | ||||||||
\(419\) | −19.7538 | −0.965036 | −0.482518 | − | 0.875886i | \(-0.660278\pi\) | ||||
−0.482518 | + | 0.875886i | \(0.660278\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −4.44190 | −0.216485 | −0.108243 | − | 0.994125i | \(-0.534522\pi\) | ||||
−0.108243 | + | 0.994125i | \(0.534522\pi\) | |||||||
\(422\) | −22.6920 | −1.10463 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −6.28830 | −0.305387 | ||||||||
\(425\) | −41.2754 | −2.00215 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 5.63950 | 0.272915 | ||||||||
\(428\) | −1.43645 | −0.0694333 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −3.42701 | −0.165265 | ||||||||
\(431\) | −10.1940 | −0.491026 | −0.245513 | − | 0.969393i | \(-0.578956\pi\) | ||||
−0.245513 | + | 0.969393i | \(0.578956\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 18.5071 | 0.889396 | 0.444698 | − | 0.895681i | \(-0.353311\pi\) | ||||
0.444698 | + | 0.895681i | \(0.353311\pi\) | |||||||
\(434\) | −14.9985 | −0.719951 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 12.5744 | 0.602205 | ||||||||
\(437\) | −6.25961 | −0.299438 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 10.4648 | 0.499456 | 0.249728 | − | 0.968316i | \(-0.419659\pi\) | ||||
0.249728 | + | 0.968316i | \(0.419659\pi\) | |||||||
\(440\) | −22.4676 | −1.07110 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 3.92740 | 0.186808 | ||||||||
\(443\) | −19.2885 | −0.916427 | −0.458213 | − | 0.888842i | \(-0.651510\pi\) | ||||
−0.458213 | + | 0.888842i | \(0.651510\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 3.97858 | 0.188603 | ||||||||
\(446\) | 1.00000 | 0.0473514 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 2.27800 | 0.107625 | ||||||||
\(449\) | 2.34935 | 0.110873 | 0.0554364 | − | 0.998462i | \(-0.482345\pi\) | ||||
0.0554364 | + | 0.998462i | \(0.482345\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −61.1761 | −2.88067 | ||||||||
\(452\) | −1.42716 | −0.0671279 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −22.2803 | −1.04567 | ||||||||
\(455\) | 7.25100 | 0.339932 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 1.65175 | 0.0772657 | 0.0386329 | − | 0.999253i | \(-0.487700\pi\) | ||||
0.0386329 | + | 0.999253i | \(0.487700\pi\) | |||||||
\(458\) | −14.5880 | −0.681651 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −15.7347 | −0.733632 | ||||||||
\(461\) | 24.2317 | 1.12858 | 0.564291 | − | 0.825576i | \(-0.309149\pi\) | ||||
0.564291 | + | 0.825576i | \(0.309149\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 13.6909 | 0.636272 | 0.318136 | − | 0.948045i | \(-0.396943\pi\) | ||||
0.318136 | + | 0.948045i | \(0.396943\pi\) | |||||||
\(464\) | −1.52437 | −0.0707669 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 4.82251 | 0.223399 | ||||||||
\(467\) | 26.6189 | 1.23177 | 0.615887 | − | 0.787835i | \(-0.288798\pi\) | ||||
0.615887 | + | 0.787835i | \(0.288798\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 7.83585 | 0.361826 | ||||||||
\(470\) | −31.1140 | −1.43518 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 4.62427 | 0.212849 | ||||||||
\(473\) | 5.51751 | 0.253695 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 13.3082 | 0.610622 | ||||||||
\(476\) | −10.4998 | −0.481257 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 13.8013 | 0.631255 | ||||||||
\(479\) | 31.6473 | 1.44600 | 0.723000 | − | 0.690848i | \(-0.242763\pi\) | ||||
0.723000 | + | 0.690848i | \(0.242763\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 3.77166 | 0.171973 | ||||||||
\(482\) | −10.5058 | −0.478526 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 25.1731 | 1.14423 | ||||||||
\(485\) | −9.46958 | −0.429991 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −9.72175 | −0.440535 | −0.220267 | − | 0.975440i | \(-0.570693\pi\) | ||||
−0.220267 | + | 0.975440i | \(0.570693\pi\) | |||||||
\(488\) | −2.47563 | −0.112067 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 6.76415 | 0.305573 | ||||||||
\(491\) | 26.5785 | 1.19947 | 0.599736 | − | 0.800198i | \(-0.295272\pi\) | ||||
0.599736 | + | 0.800198i | \(0.295272\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 7.02612 | 0.316440 | ||||||||
\(494\) | −1.26629 | −0.0569732 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 6.58406 | 0.295633 | ||||||||
\(497\) | −2.09428 | −0.0939412 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −0.377594 | −0.0169034 | −0.00845172 | − | 0.999964i | \(-0.502690\pi\) | ||||
−0.00845172 | + | 0.999964i | \(0.502690\pi\) | |||||||
\(500\) | 14.7744 | 0.660730 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 10.4874 | 0.468075 | ||||||||
\(503\) | −6.34075 | −0.282720 | −0.141360 | − | 0.989958i | \(-0.545148\pi\) | ||||
−0.141360 | + | 0.989958i | \(0.545148\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −17.7471 | −0.789735 | ||||||||
\(506\) | 25.3329 | 1.12619 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −21.3436 | −0.946971 | ||||||||
\(509\) | −17.3369 | −0.768445 | −0.384223 | − | 0.923240i | \(-0.625530\pi\) | ||||
−0.384223 | + | 0.923240i | \(0.625530\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −2.74322 | −0.121353 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 12.5438 | 0.553283 | ||||||||
\(515\) | 31.6093 | 1.39287 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 50.0938 | 2.20312 | ||||||||
\(518\) | −10.0834 | −0.443039 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −3.18305 | −0.139586 | ||||||||
\(521\) | −24.0104 | −1.05191 | −0.525957 | − | 0.850511i | \(-0.676293\pi\) | ||||
−0.525957 | + | 0.850511i | \(0.676293\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −36.1593 | −1.58114 | −0.790569 | − | 0.612373i | \(-0.790215\pi\) | ||||
−0.790569 | + | 0.612373i | \(0.790215\pi\) | |||||||
\(524\) | −17.7225 | −0.774209 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 25.8499 | 1.12711 | ||||||||
\(527\) | −30.3473 | −1.32195 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −5.25871 | −0.228640 | ||||||||
\(530\) | −23.4908 | −1.02037 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 3.38539 | 0.146775 | ||||||||
\(533\) | −8.66698 | −0.375409 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −5.36605 | −0.231994 | ||||||||
\(536\) | −3.43979 | −0.148576 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 19.2755 | 0.831025 | ||||||||
\(539\) | −10.8903 | −0.469080 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 13.5548 | 0.582764 | 0.291382 | − | 0.956607i | \(-0.405885\pi\) | ||||
0.291382 | + | 0.956607i | \(0.405885\pi\) | |||||||
\(542\) | 21.8099 | 0.936815 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 4.60921 | 0.197618 | ||||||||
\(545\) | 46.9734 | 2.01212 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −3.67323 | −0.157056 | −0.0785279 | − | 0.996912i | \(-0.525022\pi\) | ||||
−0.0785279 | + | 0.996912i | \(0.525022\pi\) | |||||||
\(548\) | −8.40769 | −0.359159 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −53.8589 | −2.29655 | ||||||||
\(551\) | −2.26540 | −0.0965091 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 28.0339 | 1.19212 | ||||||||
\(554\) | −19.4696 | −0.827183 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −16.6796 | −0.707371 | ||||||||
\(557\) | −14.4915 | −0.614023 | −0.307011 | − | 0.951706i | \(-0.599329\pi\) | ||||
−0.307011 | + | 0.951706i | \(0.599329\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0.781681 | 0.0330616 | ||||||||
\(560\) | 8.50979 | 0.359604 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 16.7963 | 0.708510 | ||||||||
\(563\) | 18.2302 | 0.768312 | 0.384156 | − | 0.923268i | \(-0.374493\pi\) | ||||
0.384156 | + | 0.923268i | \(0.374493\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −5.33135 | −0.224291 | ||||||||
\(566\) | 24.1812 | 1.01641 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0.919349 | 0.0385750 | ||||||||
\(569\) | 1.40032 | 0.0587045 | 0.0293523 | − | 0.999569i | \(-0.490656\pi\) | ||||
0.0293523 | + | 0.999569i | \(0.490656\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 38.5377 | 1.61275 | 0.806376 | − | 0.591403i | \(-0.201426\pi\) | ||||
0.806376 | + | 0.591403i | \(0.201426\pi\) | |||||||
\(572\) | 5.12474 | 0.214276 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 23.1709 | 0.967134 | ||||||||
\(575\) | −37.7187 | −1.57298 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −39.6408 | −1.65027 | −0.825135 | − | 0.564936i | \(-0.808901\pi\) | ||||
−0.825135 | + | 0.564936i | \(0.808901\pi\) | |||||||
\(578\) | −4.24479 | −0.176560 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −5.69448 | −0.236450 | ||||||||
\(581\) | −27.6963 | −1.14904 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 37.8204 | 1.56636 | ||||||||
\(584\) | 1.20422 | 0.0498311 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 26.0052 | 1.07426 | ||||||||
\(587\) | −9.32442 | −0.384860 | −0.192430 | − | 0.981311i | \(-0.561637\pi\) | ||||
−0.192430 | + | 0.981311i | \(0.561637\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 9.78473 | 0.403173 | ||||||||
\(590\) | 17.2746 | 0.711184 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 4.42642 | 0.181925 | ||||||||
\(593\) | 19.6791 | 0.808123 | 0.404062 | − | 0.914732i | \(-0.367598\pi\) | ||||
0.404062 | + | 0.914732i | \(0.367598\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −39.2234 | −1.60800 | ||||||||
\(596\) | 20.0642 | 0.821861 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 3.58899 | 0.146765 | ||||||||
\(599\) | −12.7036 | −0.519057 | −0.259528 | − | 0.965735i | \(-0.583567\pi\) | ||||
−0.259528 | + | 0.965735i | \(0.583567\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −15.7787 | −0.643627 | −0.321813 | − | 0.946803i | \(-0.604292\pi\) | ||||
−0.321813 | + | 0.946803i | \(0.604292\pi\) | |||||||
\(602\) | −2.08980 | −0.0851738 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −17.7405 | −0.721852 | ||||||||
\(605\) | 94.0376 | 3.82317 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −3.28948 | −0.133516 | −0.0667579 | − | 0.997769i | \(-0.521266\pi\) | ||||
−0.0667579 | + | 0.997769i | \(0.521266\pi\) | |||||||
\(608\) | −1.48612 | −0.0602703 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −9.24807 | −0.374443 | ||||||||
\(611\) | 7.09693 | 0.287111 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 5.83172 | 0.235541 | 0.117771 | − | 0.993041i | \(-0.462425\pi\) | ||||
0.117771 | + | 0.993041i | \(0.462425\pi\) | |||||||
\(614\) | −26.1554 | −1.05555 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −13.7008 | −0.552022 | ||||||||
\(617\) | −8.27184 | −0.333012 | −0.166506 | − | 0.986040i | \(-0.553248\pi\) | ||||
−0.166506 | + | 0.986040i | \(0.553248\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −36.3235 | −1.45997 | −0.729983 | − | 0.683466i | \(-0.760472\pi\) | ||||
−0.729983 | + | 0.683466i | \(0.760472\pi\) | |||||||
\(620\) | 24.5957 | 0.987786 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 2.36626 | 0.0948784 | ||||||||
\(623\) | 2.42615 | 0.0972015 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 10.4168 | 0.416670 | ||||||||
\(626\) | 11.2794 | 0.450814 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −2.78869 | −0.111281 | ||||||||
\(629\) | −20.4023 | −0.813493 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −31.2758 | −1.24507 | −0.622536 | − | 0.782592i | \(-0.713897\pi\) | ||||
−0.622536 | + | 0.782592i | \(0.713897\pi\) | |||||||
\(632\) | −12.3064 | −0.489520 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −28.7306 | −1.14104 | ||||||||
\(635\) | −79.7321 | −3.16407 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.54286 | −0.0611305 | ||||||||
\(638\) | 9.16816 | 0.362971 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −3.73564 | −0.147664 | ||||||||
\(641\) | −7.82219 | −0.308958 | −0.154479 | − | 0.987996i | \(-0.549370\pi\) | ||||
−0.154479 | + | 0.987996i | \(0.549370\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 16.2715 | 0.641686 | 0.320843 | − | 0.947132i | \(-0.396034\pi\) | ||||
0.320843 | + | 0.947132i | \(0.396034\pi\) | |||||||
\(644\) | −9.59504 | −0.378097 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 6.84985 | 0.269504 | ||||||||
\(647\) | −12.1262 | −0.476731 | −0.238366 | − | 0.971175i | \(-0.576612\pi\) | ||||
−0.238366 | + | 0.971175i | \(0.576612\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −27.8123 | −1.09173 | ||||||||
\(650\) | −7.63034 | −0.299287 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −14.9595 | −0.585859 | ||||||||
\(653\) | −14.2664 | −0.558287 | −0.279144 | − | 0.960249i | \(-0.590051\pi\) | ||||
−0.279144 | + | 0.960249i | \(0.590051\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −66.2047 | −2.58683 | ||||||||
\(656\) | −10.1716 | −0.397134 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −18.9734 | −0.739660 | ||||||||
\(659\) | 17.3036 | 0.674054 | 0.337027 | − | 0.941495i | \(-0.390579\pi\) | ||||
0.337027 | + | 0.941495i | \(0.390579\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 13.7700 | 0.535591 | 0.267795 | − | 0.963476i | \(-0.413705\pi\) | ||||
0.267795 | + | 0.963476i | \(0.413705\pi\) | |||||||
\(662\) | −7.33457 | −0.285066 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 12.1582 | 0.471828 | ||||||||
\(665\) | 12.6466 | 0.490414 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 6.42069 | 0.248610 | ||||||||
\(668\) | −8.34896 | −0.323031 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −12.8498 | −0.496432 | ||||||||
\(671\) | 14.8895 | 0.574802 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −24.4926 | −0.944121 | −0.472061 | − | 0.881566i | \(-0.656490\pi\) | ||||
−0.472061 | + | 0.881566i | \(0.656490\pi\) | |||||||
\(674\) | −6.40802 | −0.246828 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −12.2740 | −0.472076 | ||||||||
\(677\) | −27.4584 | −1.05531 | −0.527656 | − | 0.849458i | \(-0.676929\pi\) | ||||
−0.527656 | + | 0.849458i | \(0.676929\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −5.77458 | −0.221608 | ||||||||
\(680\) | 17.2183 | 0.660293 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −39.5992 | −1.51633 | ||||||||
\(683\) | 42.0591 | 1.60935 | 0.804673 | − | 0.593718i | \(-0.202340\pi\) | ||||
0.804673 | + | 0.593718i | \(0.202340\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −31.4081 | −1.20004 | ||||||||
\(686\) | 20.0708 | 0.766307 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0.917382 | 0.0349749 | ||||||||
\(689\) | 5.35812 | 0.204128 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −29.3603 | −1.11692 | −0.558459 | − | 0.829532i | \(-0.688607\pi\) | ||||
−0.558459 | + | 0.829532i | \(0.688607\pi\) | |||||||
\(692\) | 1.30257 | 0.0495163 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 7.39309 | 0.280638 | ||||||||
\(695\) | −62.3088 | −2.36351 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 46.8829 | 1.77582 | ||||||||
\(698\) | −20.8521 | −0.789263 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 20.3995 | 0.771027 | ||||||||
\(701\) | 24.2185 | 0.914720 | 0.457360 | − | 0.889282i | \(-0.348795\pi\) | ||||
0.457360 | + | 0.889282i | \(0.348795\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 6.57821 | 0.248102 | ||||||||
\(704\) | 6.01441 | 0.226677 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 3.49981 | 0.131717 | ||||||||
\(707\) | −10.8222 | −0.407012 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 25.4904 | 0.957312 | 0.478656 | − | 0.878002i | \(-0.341124\pi\) | ||||
0.478656 | + | 0.878002i | \(0.341124\pi\) | |||||||
\(710\) | 3.43435 | 0.128889 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −1.06503 | −0.0399138 | ||||||||
\(713\) | −27.7323 | −1.03858 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 19.1442 | 0.715952 | ||||||||
\(716\) | 24.7249 | 0.924014 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −30.5897 | −1.14160 | ||||||||
\(719\) | −33.6674 | −1.25558 | −0.627792 | − | 0.778381i | \(-0.716041\pi\) | ||||
−0.627792 | + | 0.778381i | \(0.716041\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 19.2754 | 0.717855 | ||||||||
\(722\) | 16.7914 | 0.624913 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 24.6587 | 0.916435 | ||||||||
\(725\) | −13.6507 | −0.506973 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −29.1086 | −1.07958 | −0.539788 | − | 0.841801i | \(-0.681496\pi\) | ||||
−0.539788 | + | 0.841801i | \(0.681496\pi\) | |||||||
\(728\) | −1.94104 | −0.0719395 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 4.49854 | 0.166498 | ||||||||
\(731\) | −4.22840 | −0.156393 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 1.05662 | 0.0390273 | 0.0195137 | − | 0.999810i | \(-0.493788\pi\) | ||||
0.0195137 | + | 0.999810i | \(0.493788\pi\) | |||||||
\(734\) | −10.9138 | −0.402836 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 4.21204 | 0.155258 | ||||||||
\(737\) | 20.6883 | 0.762064 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −53.2785 | −1.95988 | −0.979941 | − | 0.199289i | \(-0.936137\pi\) | ||||
−0.979941 | + | 0.199289i | \(0.936137\pi\) | |||||||
\(740\) | 16.5355 | 0.607857 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −14.3247 | −0.525878 | ||||||||
\(743\) | −49.6908 | −1.82298 | −0.911489 | − | 0.411325i | \(-0.865066\pi\) | ||||
−0.911489 | + | 0.411325i | \(0.865066\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 74.9525 | 2.74605 | ||||||||
\(746\) | −23.2262 | −0.850373 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −27.7217 | −1.01360 | ||||||||
\(749\) | −3.27223 | −0.119565 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −13.5295 | −0.493697 | −0.246849 | − | 0.969054i | \(-0.579395\pi\) | ||||
−0.246849 | + | 0.969054i | \(0.579395\pi\) | |||||||
\(752\) | 8.32897 | 0.303726 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 1.29888 | 0.0473024 | ||||||||
\(755\) | −66.2722 | −2.41189 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 46.9354 | 1.70589 | 0.852947 | − | 0.521997i | \(-0.174813\pi\) | ||||
0.852947 | + | 0.521997i | \(0.174813\pi\) | |||||||
\(758\) | −7.46237 | −0.271046 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −5.55162 | −0.201378 | ||||||||
\(761\) | 27.4191 | 0.993940 | 0.496970 | − | 0.867768i | \(-0.334446\pi\) | ||||
0.496970 | + | 0.867768i | \(0.334446\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 28.6445 | 1.03700 | ||||||||
\(764\) | 18.6689 | 0.675418 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 9.04126 | 0.326674 | ||||||||
\(767\) | −3.94024 | −0.142274 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 33.1069 | 1.19386 | 0.596932 | − | 0.802292i | \(-0.296386\pi\) | ||||
0.596932 | + | 0.802292i | \(0.296386\pi\) | |||||||
\(770\) | −51.1813 | −1.84445 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −21.4822 | −0.773163 | ||||||||
\(773\) | −34.4021 | −1.23736 | −0.618678 | − | 0.785645i | \(-0.712331\pi\) | ||||
−0.618678 | + | 0.785645i | \(0.712331\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 58.9602 | 2.11791 | ||||||||
\(776\) | 2.53493 | 0.0909987 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −23.3946 | −0.838736 | ||||||||
\(779\) | −15.1162 | −0.541595 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −5.52934 | −0.197855 | ||||||||
\(782\) | −19.4142 | −0.694249 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −1.81071 | −0.0646681 | ||||||||
\(785\) | −10.4175 | −0.371818 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −8.78386 | −0.313111 | −0.156555 | − | 0.987669i | \(-0.550039\pi\) | ||||
−0.156555 | + | 0.987669i | \(0.550039\pi\) | |||||||
\(788\) | −1.74494 | −0.0621610 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −45.9721 | −1.63561 | ||||||||
\(791\) | −3.25107 | −0.115595 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 2.10943 | 0.0749082 | ||||||||
\(794\) | −37.9849 | −1.34803 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −21.8960 | −0.776084 | ||||||||
\(797\) | −9.49402 | −0.336295 | −0.168148 | − | 0.985762i | \(-0.553779\pi\) | ||||
−0.168148 | + | 0.985762i | \(0.553779\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −38.3899 | −1.35814 | ||||||||
\(800\) | −8.95498 | −0.316606 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −11.8561 | −0.418652 | ||||||||
\(803\) | −7.24269 | −0.255589 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −35.8436 | −1.26332 | ||||||||
\(806\) | −5.61014 | −0.197609 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 4.75076 | 0.167131 | ||||||||
\(809\) | 19.8140 | 0.696624 | 0.348312 | − | 0.937379i | \(-0.386755\pi\) | ||||
0.348312 | + | 0.937379i | \(0.386755\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −35.4976 | −1.24649 | −0.623245 | − | 0.782026i | \(-0.714186\pi\) | ||||
−0.623245 | + | 0.782026i | \(0.714186\pi\) | |||||||
\(812\) | −3.47251 | −0.121861 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −26.6223 | −0.933112 | ||||||||
\(815\) | −55.8833 | −1.95751 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1.36334 | 0.0476973 | ||||||||
\(818\) | −25.8663 | −0.904393 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −37.9973 | −1.32692 | ||||||||
\(821\) | 14.8442 | 0.518066 | 0.259033 | − | 0.965869i | \(-0.416596\pi\) | ||||
0.259033 | + | 0.965869i | \(0.416596\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −5.84581 | −0.203772 | −0.101886 | − | 0.994796i | \(-0.532488\pi\) | ||||
−0.101886 | + | 0.994796i | \(0.532488\pi\) | |||||||
\(824\) | −8.46155 | −0.294772 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 10.5341 | 0.366528 | ||||||||
\(827\) | −34.7754 | −1.20926 | −0.604630 | − | 0.796507i | \(-0.706679\pi\) | ||||
−0.604630 | + | 0.796507i | \(0.706679\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −36.0468 | −1.25196 | −0.625979 | − | 0.779840i | \(-0.715300\pi\) | ||||
−0.625979 | + | 0.779840i | \(0.715300\pi\) | |||||||
\(830\) | 45.4185 | 1.57650 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0.852078 | 0.0295405 | ||||||||
\(833\) | 8.34593 | 0.289169 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −31.1887 | −1.07933 | ||||||||
\(836\) | 8.93815 | 0.309133 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 19.7538 | 0.682384 | ||||||||
\(839\) | 23.3118 | 0.804812 | 0.402406 | − | 0.915461i | \(-0.368174\pi\) | ||||
0.402406 | + | 0.915461i | \(0.368174\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −26.6763 | −0.919873 | ||||||||
\(842\) | 4.44190 | 0.153078 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 22.6920 | 0.781091 | ||||||||
\(845\) | −45.8511 | −1.57732 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 57.3444 | 1.97038 | ||||||||
\(848\) | 6.28830 | 0.215941 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 41.2754 | 1.41573 | ||||||||
\(851\) | −18.6443 | −0.639118 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −32.6519 | −1.11798 | −0.558990 | − | 0.829174i | \(-0.688811\pi\) | ||||
−0.558990 | + | 0.829174i | \(0.688811\pi\) | |||||||
\(854\) | −5.63950 | −0.192980 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 1.43645 | 0.0490968 | ||||||||
\(857\) | −31.0079 | −1.05921 | −0.529605 | − | 0.848245i | \(-0.677660\pi\) | ||||
−0.529605 | + | 0.848245i | \(0.677660\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −31.8330 | −1.08613 | −0.543064 | − | 0.839691i | \(-0.682736\pi\) | ||||
−0.543064 | + | 0.839691i | \(0.682736\pi\) | |||||||
\(860\) | 3.42701 | 0.116860 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 10.1940 | 0.347208 | ||||||||
\(863\) | 44.5320 | 1.51589 | 0.757944 | − | 0.652319i | \(-0.226204\pi\) | ||||
0.757944 | + | 0.652319i | \(0.226204\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 4.86593 | 0.165447 | ||||||||
\(866\) | −18.5071 | −0.628898 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 14.9985 | 0.509083 | ||||||||
\(869\) | 74.0154 | 2.51080 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 2.93097 | 0.0993122 | ||||||||
\(872\) | −12.5744 | −0.425823 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 6.25961 | 0.211735 | ||||||||
\(875\) | 33.6560 | 1.13778 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 25.9629 | 0.876703 | 0.438352 | − | 0.898804i | \(-0.355562\pi\) | ||||
0.438352 | + | 0.898804i | \(0.355562\pi\) | |||||||
\(878\) | −10.4648 | −0.353169 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 22.4676 | 0.757384 | ||||||||
\(881\) | 4.76702 | 0.160605 | 0.0803025 | − | 0.996771i | \(-0.474411\pi\) | ||||
0.0803025 | + | 0.996771i | \(0.474411\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −11.8426 | −0.398536 | −0.199268 | − | 0.979945i | \(-0.563856\pi\) | ||||
−0.199268 | + | 0.979945i | \(0.563856\pi\) | |||||||
\(884\) | −3.92740 | −0.132093 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 19.2885 | 0.648011 | ||||||||
\(887\) | −43.4389 | −1.45853 | −0.729267 | − | 0.684229i | \(-0.760139\pi\) | ||||
−0.729267 | + | 0.684229i | \(0.760139\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −48.6209 | −1.63069 | ||||||||
\(890\) | −3.97858 | −0.133362 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −1.00000 | −0.0334825 | ||||||||
\(893\) | 12.3779 | 0.414210 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 92.3633 | 3.08737 | ||||||||
\(896\) | −2.27800 | −0.0761027 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −2.34935 | −0.0783990 | ||||||||
\(899\) | −10.0365 | −0.334737 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −28.9841 | −0.965599 | ||||||||
\(902\) | 61.1761 | 2.03694 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 1.42716 | 0.0474666 | ||||||||
\(905\) | 92.1161 | 3.06204 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 3.63494 | 0.120696 | 0.0603481 | − | 0.998177i | \(-0.480779\pi\) | ||||
0.0603481 | + | 0.998177i | \(0.480779\pi\) | |||||||
\(908\) | 22.2803 | 0.739399 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −7.25100 | −0.240368 | ||||||||
\(911\) | −9.04333 | −0.299619 | −0.149810 | − | 0.988715i | \(-0.547866\pi\) | ||||
−0.149810 | + | 0.988715i | \(0.547866\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −73.1241 | −2.42006 | ||||||||
\(914\) | −1.65175 | −0.0546351 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 14.5880 | 0.482000 | ||||||||
\(917\) | −40.3718 | −1.33319 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 32.5562 | 1.07393 | 0.536965 | − | 0.843604i | \(-0.319571\pi\) | ||||
0.536965 | + | 0.843604i | \(0.319571\pi\) | |||||||
\(920\) | 15.7347 | 0.518756 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −24.2317 | −0.798028 | ||||||||
\(923\) | −0.783357 | −0.0257845 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 39.6385 | 1.30331 | ||||||||
\(926\) | −13.6909 | −0.449912 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 1.52437 | 0.0500398 | ||||||||
\(929\) | 3.06405 | 0.100528 | 0.0502642 | − | 0.998736i | \(-0.483994\pi\) | ||||
0.0502642 | + | 0.998736i | \(0.483994\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −2.69094 | −0.0881919 | ||||||||
\(932\) | −4.82251 | −0.157967 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −26.6189 | −0.870995 | ||||||||
\(935\) | −103.558 | −3.38671 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −27.1123 | −0.885720 | −0.442860 | − | 0.896591i | \(-0.646036\pi\) | ||||
−0.442860 | + | 0.896591i | \(0.646036\pi\) | |||||||
\(938\) | −7.83585 | −0.255850 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 31.1140 | 1.01483 | ||||||||
\(941\) | 34.5485 | 1.12625 | 0.563124 | − | 0.826372i | \(-0.309599\pi\) | ||||
0.563124 | + | 0.826372i | \(0.309599\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 42.8431 | 1.39516 | ||||||||
\(944\) | −4.62427 | −0.150507 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −5.51751 | −0.179390 | ||||||||
\(947\) | 9.62266 | 0.312694 | 0.156347 | − | 0.987702i | \(-0.450028\pi\) | ||||
0.156347 | + | 0.987702i | \(0.450028\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −1.02609 | −0.0333084 | ||||||||
\(950\) | −13.3082 | −0.431775 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 10.4998 | 0.340300 | ||||||||
\(953\) | −42.5824 | −1.37938 | −0.689689 | − | 0.724105i | \(-0.742253\pi\) | ||||
−0.689689 | + | 0.724105i | \(0.742253\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 69.7403 | 2.25674 | ||||||||
\(956\) | −13.8013 | −0.446365 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −31.6473 | −1.02248 | ||||||||
\(959\) | −19.1527 | −0.618474 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 12.3499 | 0.398384 | ||||||||
\(962\) | −3.77166 | −0.121603 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 10.5058 | 0.338369 | ||||||||
\(965\) | −80.2499 | −2.58333 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −24.1986 | −0.778175 | −0.389088 | − | 0.921201i | \(-0.627210\pi\) | ||||
−0.389088 | + | 0.921201i | \(0.627210\pi\) | |||||||
\(968\) | −25.1731 | −0.809094 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 9.46958 | 0.304050 | ||||||||
\(971\) | 9.35231 | 0.300130 | 0.150065 | − | 0.988676i | \(-0.452052\pi\) | ||||
0.150065 | + | 0.988676i | \(0.452052\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −37.9961 | −1.21810 | ||||||||
\(974\) | 9.72175 | 0.311505 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 2.47563 | 0.0792431 | ||||||||
\(977\) | 51.7697 | 1.65626 | 0.828129 | − | 0.560537i | \(-0.189405\pi\) | ||||
0.828129 | + | 0.560537i | \(0.189405\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 6.40554 | 0.204722 | ||||||||
\(980\) | −6.76415 | −0.216073 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −26.5785 | −0.848155 | ||||||||
\(983\) | 61.4372 | 1.95954 | 0.979772 | − | 0.200119i | \(-0.0641327\pi\) | ||||
0.979772 | + | 0.200119i | \(0.0641327\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −6.51847 | −0.207696 | ||||||||
\(986\) | −7.02612 | −0.223757 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 1.26629 | 0.0402861 | ||||||||
\(989\) | −3.86405 | −0.122870 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 12.3245 | 0.391501 | 0.195750 | − | 0.980654i | \(-0.437286\pi\) | ||||
0.195750 | + | 0.980654i | \(0.437286\pi\) | |||||||
\(992\) | −6.58406 | −0.209044 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 2.09428 | 0.0664265 | ||||||||
\(995\) | −81.7956 | −2.59309 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 38.2719 | 1.21208 | 0.606041 | − | 0.795433i | \(-0.292757\pi\) | ||||
0.606041 | + | 0.795433i | \(0.292757\pi\) | |||||||
\(998\) | 0.377594 | 0.0119525 | ||||||||
\(999\) | 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.v.1.7 | 7 | ||
3.2 | odd | 2 | 1338.2.a.j.1.1 | ✓ | 7 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1338.2.a.j.1.1 | ✓ | 7 | 3.2 | odd | 2 | ||
4014.2.a.v.1.7 | 7 | 1.1 | even | 1 | trivial |