Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4024,2,Mod(1,4024)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4024, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4024.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4024 = 2^{3} \cdot 503 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4024.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: | \(32.1318017734\) |
Analytic rank: | \(1\) |
Dimension: | \(28\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.10 | ||
Character | \(\chi\) | \(=\) | 4024.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −0.893789 | −0.516029 | −0.258015 | − | 0.966141i | \(-0.583068\pi\) | ||||
−0.258015 | + | 0.966141i | \(0.583068\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −3.85908 | −1.72583 | −0.862917 | − | 0.505346i | \(-0.831365\pi\) | ||||
−0.862917 | + | 0.505346i | \(0.831365\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.77625 | 1.42729 | 0.713644 | − | 0.700509i | \(-0.247043\pi\) | ||||
0.713644 | + | 0.700509i | \(0.247043\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.20114 | −0.733714 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −4.71894 | −1.42281 | −0.711407 | − | 0.702780i | \(-0.751942\pi\) | ||||
−0.711407 | + | 0.702780i | \(0.751942\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.511554 | −0.141880 | −0.0709398 | − | 0.997481i | \(-0.522600\pi\) | ||||
−0.0709398 | + | 0.997481i | \(0.522600\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 3.44921 | 0.890581 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 5.63108 | 1.36574 | 0.682869 | − | 0.730541i | \(-0.260732\pi\) | ||||
0.682869 | + | 0.730541i | \(0.260732\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.0695678 | 0.0159600 | 0.00797998 | − | 0.999968i | \(-0.497460\pi\) | ||||
0.00797998 | + | 0.999968i | \(0.497460\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −3.37517 | −0.736523 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 5.20252 | 1.08480 | 0.542401 | − | 0.840120i | \(-0.317515\pi\) | ||||
0.542401 | + | 0.840120i | \(0.317515\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 9.89252 | 1.97850 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 4.64872 | 0.894647 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −1.66971 | −0.310057 | −0.155028 | − | 0.987910i | \(-0.549547\pi\) | ||||
−0.155028 | + | 0.987910i | \(0.549547\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −0.370767 | −0.0665918 | −0.0332959 | − | 0.999446i | \(-0.510600\pi\) | ||||
−0.0332959 | + | 0.999446i | \(0.510600\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 4.21774 | 0.734214 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −14.5729 | −2.46326 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0.932872 | 0.153363 | 0.0766816 | − | 0.997056i | \(-0.475568\pi\) | ||||
0.0766816 | + | 0.997056i | \(0.475568\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0.457221 | 0.0732140 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 5.06469 | 0.790972 | 0.395486 | − | 0.918472i | \(-0.370576\pi\) | ||||
0.395486 | + | 0.918472i | \(0.370576\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −6.38770 | −0.974115 | −0.487058 | − | 0.873370i | \(-0.661930\pi\) | ||||
−0.487058 | + | 0.873370i | \(0.661930\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 8.49438 | 1.26627 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −4.19872 | −0.612447 | −0.306223 | − | 0.951960i | \(-0.599065\pi\) | ||||
−0.306223 | + | 0.951960i | \(0.599065\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 7.26006 | 1.03715 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −5.03300 | −0.704761 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 1.31018 | 0.179968 | 0.0899839 | − | 0.995943i | \(-0.471318\pi\) | ||||
0.0899839 | + | 0.995943i | \(0.471318\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 18.2108 | 2.45554 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −0.0621790 | −0.00823581 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −13.0216 | −1.69527 | −0.847635 | − | 0.530579i | \(-0.821974\pi\) | ||||
−0.847635 | + | 0.530579i | \(0.821974\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 10.4141 | 1.33339 | 0.666696 | − | 0.745330i | \(-0.267708\pi\) | ||||
0.666696 | + | 0.745330i | \(0.267708\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −8.31206 | −1.04722 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 1.97413 | 0.244861 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2.09964 | 0.256512 | 0.128256 | − | 0.991741i | \(-0.459062\pi\) | ||||
0.128256 | + | 0.991741i | \(0.459062\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −4.64996 | −0.559789 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 3.30951 | 0.392767 | 0.196383 | − | 0.980527i | \(-0.437080\pi\) | ||||
0.196383 | + | 0.980527i | \(0.437080\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 1.07644 | 0.125987 | 0.0629937 | − | 0.998014i | \(-0.479935\pi\) | ||||
0.0629937 | + | 0.998014i | \(0.479935\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −8.84182 | −1.02097 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −17.8199 | −2.03077 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 10.1610 | 1.14320 | 0.571598 | − | 0.820534i | \(-0.306324\pi\) | ||||
0.571598 | + | 0.820534i | \(0.306324\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 2.44844 | 0.272049 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 11.7519 | 1.28993 | 0.644967 | − | 0.764210i | \(-0.276871\pi\) | ||||
0.644967 | + | 0.764210i | \(0.276871\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −21.7308 | −2.35704 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 1.49237 | 0.159999 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −16.5010 | −1.74910 | −0.874551 | − | 0.484933i | \(-0.838844\pi\) | ||||
−0.874551 | + | 0.484933i | \(0.838844\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.93176 | −0.202503 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0.331388 | 0.0343633 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −0.268468 | −0.0275442 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −12.5981 | −1.27914 | −0.639572 | − | 0.768731i | \(-0.720889\pi\) | ||||
−0.639572 | + | 0.768731i | \(0.720889\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 10.3871 | 1.04394 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −16.9935 | −1.69091 | −0.845457 | − | 0.534044i | \(-0.820672\pi\) | ||||
−0.845457 | + | 0.534044i | \(0.820672\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −15.7173 | −1.54867 | −0.774336 | − | 0.632775i | \(-0.781916\pi\) | ||||
−0.774336 | + | 0.632775i | \(0.781916\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 13.0251 | 1.27112 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −7.81103 | −0.755121 | −0.377561 | − | 0.925985i | \(-0.623237\pi\) | ||||
−0.377561 | + | 0.925985i | \(0.623237\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1.47716 | −0.141486 | −0.0707430 | − | 0.997495i | \(-0.522537\pi\) | ||||
−0.0707430 | + | 0.997495i | \(0.522537\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −0.833791 | −0.0791399 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −4.93874 | −0.464598 | −0.232299 | − | 0.972644i | \(-0.574625\pi\) | ||||
−0.232299 | + | 0.972644i | \(0.574625\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −20.0770 | −1.87219 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 1.12600 | 0.104099 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 21.2644 | 1.94930 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 11.2684 | 1.02440 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −4.52677 | −0.408165 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −18.8806 | −1.68873 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −12.0431 | −1.06865 | −0.534325 | − | 0.845279i | \(-0.679434\pi\) | ||||
−0.534325 | + | 0.845279i | \(0.679434\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 5.70926 | 0.502672 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0.173395 | 0.0151496 | 0.00757479 | − | 0.999971i | \(-0.497589\pi\) | ||||
0.00757479 | + | 0.999971i | \(0.497589\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.262705 | 0.0227795 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −17.9398 | −1.54401 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −10.3811 | −0.886914 | −0.443457 | − | 0.896296i | \(-0.646248\pi\) | ||||
−0.443457 | + | 0.896296i | \(0.646248\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 14.1517 | 1.20033 | 0.600166 | − | 0.799875i | \(-0.295101\pi\) | ||||
0.600166 | + | 0.799875i | \(0.295101\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 3.75277 | 0.316041 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 2.41399 | 0.201868 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 6.44354 | 0.535107 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −6.48896 | −0.535201 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 19.1922 | 1.57228 | 0.786142 | − | 0.618046i | \(-0.212076\pi\) | ||||
0.786142 | + | 0.618046i | \(0.212076\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −7.33354 | −0.596795 | −0.298397 | − | 0.954442i | \(-0.596452\pi\) | ||||
−0.298397 | + | 0.954442i | \(0.596452\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −12.3948 | −1.00206 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1.43082 | 0.114926 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 20.3956 | 1.62775 | 0.813873 | − | 0.581043i | \(-0.197355\pi\) | ||||
0.813873 | + | 0.581043i | \(0.197355\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −1.17103 | −0.0928687 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 19.6460 | 1.54832 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1.52868 | 0.119735 | 0.0598677 | − | 0.998206i | \(-0.480932\pi\) | ||||
0.0598677 | + | 0.998206i | \(0.480932\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −16.2766 | −1.26713 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 6.89472 | 0.533530 | 0.266765 | − | 0.963762i | \(-0.414045\pi\) | ||||
0.266765 | + | 0.963762i | \(0.414045\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.7383 | −0.979870 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −0.153129 | −0.0117100 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −24.2254 | −1.84182 | −0.920912 | − | 0.389770i | \(-0.872555\pi\) | ||||
−0.920912 | + | 0.389770i | \(0.872555\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 37.3566 | 2.82389 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 11.6386 | 0.874810 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 17.5123 | 1.30893 | 0.654467 | − | 0.756091i | \(-0.272893\pi\) | ||||
0.654467 | + | 0.756091i | \(0.272893\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −14.0756 | −1.04623 | −0.523115 | − | 0.852262i | \(-0.675230\pi\) | ||||
−0.523115 | + | 0.852262i | \(0.675230\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −9.30803 | −0.688069 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −3.60003 | −0.264679 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −26.5728 | −1.94319 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 17.5547 | 1.27692 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −18.0871 | −1.30874 | −0.654370 | − | 0.756175i | \(-0.727066\pi\) | ||||
−0.654370 | + | 0.756175i | \(0.727066\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −4.16569 | −0.299853 | −0.149926 | − | 0.988697i | \(-0.547904\pi\) | ||||
−0.149926 | + | 0.988697i | \(0.547904\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −1.76446 | −0.126355 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −17.9008 | −1.27538 | −0.637689 | − | 0.770294i | \(-0.720109\pi\) | ||||
−0.637689 | + | 0.770294i | \(0.720109\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 18.8700 | 1.33766 | 0.668830 | − | 0.743415i | \(-0.266795\pi\) | ||||
0.668830 | + | 0.743415i | \(0.266795\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −1.87664 | −0.132368 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −6.30523 | −0.442541 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −19.5451 | −1.36509 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −11.4515 | −0.795933 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −0.328287 | −0.0227081 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 18.2052 | 1.25330 | 0.626649 | − | 0.779302i | \(-0.284426\pi\) | ||||
0.626649 | + | 0.779302i | \(0.284426\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −2.95801 | −0.202679 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 24.6507 | 1.68116 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1.40011 | −0.0950457 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −0.962107 | −0.0650132 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −2.88060 | −0.193770 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 3.04587 | 0.203967 | 0.101983 | − | 0.994786i | \(-0.467481\pi\) | ||||
0.101983 | + | 0.994786i | \(0.467481\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −21.7748 | −1.45165 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −7.06816 | −0.469130 | −0.234565 | − | 0.972100i | \(-0.575367\pi\) | ||||
−0.234565 | + | 0.972100i | \(0.575367\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 3.43621 | 0.227071 | 0.113536 | − | 0.993534i | \(-0.463782\pi\) | ||||
0.113536 | + | 0.993534i | \(0.463782\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 15.9272 | 1.04794 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −19.0437 | −1.24759 | −0.623797 | − | 0.781586i | \(-0.714411\pi\) | ||||
−0.623797 | + | 0.781586i | \(0.714411\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 16.2032 | 1.05698 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −9.08175 | −0.589923 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −20.8015 | −1.34553 | −0.672767 | − | 0.739854i | \(-0.734894\pi\) | ||||
−0.672767 | + | 0.739854i | \(0.734894\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 4.43572 | 0.285730 | 0.142865 | − | 0.989742i | \(-0.454369\pi\) | ||||
0.142865 | + | 0.989742i | \(0.454369\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −16.1346 | −1.03503 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −28.0172 | −1.78995 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −0.0355877 | −0.00226439 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −10.5037 | −0.665644 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −22.4720 | −1.41842 | −0.709210 | − | 0.704997i | \(-0.750948\pi\) | ||||
−0.709210 | + | 0.704997i | \(0.750948\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −24.5504 | −1.54347 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 19.4228 | 1.21630 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 0.369671 | 0.0230595 | 0.0115297 | − | 0.999934i | \(-0.496330\pi\) | ||||
0.0115297 | + | 0.999934i | \(0.496330\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 3.52276 | 0.218893 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 3.67526 | 0.227493 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 2.44589 | 0.150820 | 0.0754099 | − | 0.997153i | \(-0.475973\pi\) | ||||
0.0754099 | + | 0.997153i | \(0.475973\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −5.05611 | −0.310594 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 14.7484 | 0.902588 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −3.85067 | −0.234780 | −0.117390 | − | 0.993086i | \(-0.537453\pi\) | ||||
−0.117390 | + | 0.993086i | \(0.537453\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −29.7078 | −1.80462 | −0.902310 | − | 0.431087i | \(-0.858130\pi\) | ||||
−0.902310 | + | 0.431087i | \(0.858130\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 1.72658 | 0.104498 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −46.6822 | −2.81504 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 21.6836 | 1.30284 | 0.651420 | − | 0.758717i | \(-0.274173\pi\) | ||||
0.651420 | + | 0.758717i | \(0.274173\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0.816111 | 0.0488593 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −2.96764 | −0.177035 | −0.0885174 | − | 0.996075i | \(-0.528213\pi\) | ||||
−0.0885174 | + | 0.996075i | \(0.528213\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −0.541058 | −0.0321626 | −0.0160813 | − | 0.999871i | \(-0.505119\pi\) | ||||
−0.0160813 | + | 0.999871i | \(0.505119\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0.239954 | 0.0142136 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 19.1255 | 1.12894 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 14.7091 | 0.865241 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 11.2601 | 0.660076 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −11.3653 | −0.663966 | −0.331983 | − | 0.943285i | \(-0.607718\pi\) | ||||
−0.331983 | + | 0.943285i | \(0.607718\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 50.2515 | 2.92576 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −21.9371 | −1.27292 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −2.66137 | −0.153911 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −24.1216 | −1.39034 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 15.1886 | 0.872561 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −40.1889 | −2.30121 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 8.95952 | 0.511347 | 0.255674 | − | 0.966763i | \(-0.417703\pi\) | ||||
0.255674 | + | 0.966763i | \(0.417703\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 14.0480 | 0.799160 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −22.9435 | −1.30101 | −0.650503 | − | 0.759504i | \(-0.725442\pi\) | ||||
−0.650503 | + | 0.759504i | \(0.725442\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −29.0611 | −1.64263 | −0.821314 | − | 0.570477i | \(-0.806759\pi\) | ||||
−0.821314 | + | 0.570477i | \(0.806759\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 32.0769 | 1.80733 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 22.3051 | 1.25278 | 0.626390 | − | 0.779510i | \(-0.284532\pi\) | ||||
0.626390 | + | 0.779510i | \(0.284532\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 7.87926 | 0.441154 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 6.98142 | 0.389665 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0.391742 | 0.0217971 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −5.06056 | −0.280709 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 1.32027 | 0.0730109 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −15.8554 | −0.874138 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 16.7757 | 0.922076 | 0.461038 | − | 0.887380i | \(-0.347477\pi\) | ||||
0.461038 | + | 0.887380i | \(0.347477\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −2.05338 | −0.112525 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −8.10269 | −0.442697 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −27.7893 | −1.51378 | −0.756890 | − | 0.653542i | \(-0.773282\pi\) | ||||
−0.756890 | + | 0.653542i | \(0.773282\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 4.41420 | 0.239746 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1.74963 | 0.0947478 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0.982048 | 0.0530256 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 17.9446 | 0.966104 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 1.80385 | 0.0968359 | 0.0484179 | − | 0.998827i | \(-0.484582\pi\) | ||||
0.0484179 | + | 0.998827i | \(0.484582\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 24.4308 | 1.30775 | 0.653876 | − | 0.756602i | \(-0.273142\pi\) | ||||
0.653876 | + | 0.756602i | \(0.273142\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −2.37807 | −0.126932 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −9.08469 | −0.483530 | −0.241765 | − | 0.970335i | \(-0.577726\pi\) | ||||
−0.241765 | + | 0.970335i | \(0.577726\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −12.7717 | −0.677850 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −19.0059 | −1.00590 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −24.4405 | −1.28992 | −0.644961 | − | 0.764215i | \(-0.723127\pi\) | ||||
−0.644961 | + | 0.764215i | \(0.723127\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.9952 | −0.999745 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −10.0716 | −0.528622 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −4.15406 | −0.217433 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 34.6446 | 1.80843 | 0.904216 | − | 0.427075i | \(-0.140456\pi\) | ||||
0.904216 | + | 0.427075i | \(0.140456\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −11.1481 | −0.580347 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 4.94758 | 0.256866 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −28.5395 | −1.47772 | −0.738859 | − | 0.673860i | \(-0.764635\pi\) | ||||
−0.738859 | + | 0.673860i | \(0.764635\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 16.8753 | 0.871437 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0.854146 | 0.0439907 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 5.70976 | 0.293291 | 0.146645 | − | 0.989189i | \(-0.453152\pi\) | ||||
0.146645 | + | 0.989189i | \(0.453152\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 10.7640 | 0.551455 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 20.8571 | 1.06575 | 0.532873 | − | 0.846195i | \(-0.321112\pi\) | ||||
0.532873 | + | 0.846195i | \(0.321112\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 68.7685 | 3.50477 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 14.0602 | 0.714722 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −23.3177 | −1.18225 | −0.591126 | − | 0.806579i | \(-0.701316\pi\) | ||||
−0.591126 | + | 0.806579i | \(0.701316\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 29.2958 | 1.48155 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −0.154979 | −0.00781763 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −39.2120 | −1.97297 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −33.4612 | −1.67937 | −0.839684 | − | 0.543076i | \(-0.817260\pi\) | ||||
−0.839684 | + | 0.543076i | \(0.817260\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −0.234803 | −0.0117549 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −27.3510 | −1.36584 | −0.682922 | − | 0.730491i | \(-0.739291\pi\) | ||||
−0.682922 | + | 0.730491i | \(0.739291\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0.189668 | 0.00944801 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −9.44874 | −0.469512 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −4.40217 | −0.218207 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −2.71339 | −0.134169 | −0.0670843 | − | 0.997747i | \(-0.521370\pi\) | ||||
−0.0670843 | + | 0.997747i | \(0.521370\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 9.27848 | 0.457674 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −49.1729 | −2.41964 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −45.3514 | −2.22621 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −12.6487 | −0.619407 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −4.86004 | −0.237428 | −0.118714 | − | 0.992928i | \(-0.537877\pi\) | ||||
−0.118714 | + | 0.992928i | \(0.537877\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 13.2128 | 0.643952 | 0.321976 | − | 0.946748i | \(-0.395653\pi\) | ||||
0.321976 | + | 0.946748i | \(0.395653\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 9.24198 | 0.449360 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 55.7056 | 2.70212 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 39.3263 | 1.90313 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −2.15760 | −0.104170 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 23.1046 | 1.11291 | 0.556455 | − | 0.830878i | \(-0.312161\pi\) | ||||
0.556455 | + | 0.830878i | \(0.312161\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 2.97652 | 0.143043 | 0.0715213 | − | 0.997439i | \(-0.477215\pi\) | ||||
0.0715213 | + | 0.997439i | \(0.477215\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −5.75917 | −0.276131 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0.361928 | 0.0173134 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 26.2388 | 1.25231 | 0.626155 | − | 0.779699i | \(-0.284628\pi\) | ||||
0.626155 | + | 0.779699i | \(0.284628\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −15.9804 | −0.760972 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −28.1621 | −1.33802 | −0.669012 | − | 0.743252i | \(-0.733282\pi\) | ||||
−0.669012 | + | 0.743252i | \(0.733282\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 63.6787 | 3.01866 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −17.1537 | −0.811344 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 14.4204 | 0.680541 | 0.340271 | − | 0.940328i | \(-0.389481\pi\) | ||||
0.340271 | + | 0.940328i | \(0.389481\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −23.9000 | −1.12541 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 6.55464 | 0.307964 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 7.45480 | 0.349487 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 3.73893 | 0.174900 | 0.0874499 | − | 0.996169i | \(-0.472128\pi\) | ||||
0.0874499 | + | 0.996169i | \(0.472128\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 26.1774 | 1.22185 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −12.1666 | −0.566654 | −0.283327 | − | 0.959023i | \(-0.591438\pi\) | ||||
−0.283327 | + | 0.959023i | \(0.591438\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −25.0242 | −1.16298 | −0.581488 | − | 0.813555i | \(-0.697529\pi\) | ||||
−0.581488 | + | 0.813555i | \(0.697529\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −1.27885 | −0.0593054 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −2.41158 | −0.111594 | −0.0557972 | − | 0.998442i | \(-0.517770\pi\) | ||||
−0.0557972 | + | 0.998442i | \(0.517770\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 7.92877 | 0.366117 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −18.2294 | −0.839965 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 30.1432 | 1.38599 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0.688201 | 0.0315768 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −2.88390 | −0.132045 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −12.3217 | −0.562992 | −0.281496 | − | 0.959562i | \(-0.590831\pi\) | ||||
−0.281496 | + | 0.959562i | \(0.590831\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −0.477214 | −0.0217591 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −17.5594 | −0.798981 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 48.6172 | 2.20759 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −34.7800 | −1.57603 | −0.788016 | − | 0.615655i | \(-0.788891\pi\) | ||||
−0.788016 | + | 0.615655i | \(0.788891\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −1.36632 | −0.0617870 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −6.56397 | −0.296228 | −0.148114 | − | 0.988970i | \(-0.547320\pi\) | ||||
−0.148114 | + | 0.988970i | \(0.547320\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −9.40226 | −0.423457 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −40.0845 | −1.80166 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 12.4975 | 0.560591 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 27.2924 | 1.22178 | 0.610888 | − | 0.791717i | \(-0.290813\pi\) | ||||
0.610888 | + | 0.791717i | \(0.290813\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −6.16243 | −0.275317 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 1.00000 | 0.0445878 | ||||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 65.5792 | 2.91824 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 11.3854 | 0.505642 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 3.54941 | 0.157325 | 0.0786625 | − | 0.996901i | \(-0.474935\pi\) | ||||
0.0786625 | + | 0.996901i | \(0.474935\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 4.06489 | 0.179820 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0.323402 | 0.0142785 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 60.6544 | 2.67275 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 19.8135 | 0.871398 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 21.6524 | 0.950436 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 10.8364 | 0.474751 | 0.237376 | − | 0.971418i | \(-0.423713\pi\) | ||||
0.237376 | + | 0.971418i | \(0.423713\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 11.3289 | 0.495377 | 0.247689 | − | 0.968840i | \(-0.420329\pi\) | ||||
0.247689 | + | 0.968840i | \(0.420329\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −33.3889 | −1.45721 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −2.08782 | −0.0909470 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 4.06626 | 0.176794 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 28.6624 | 1.24384 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −2.59086 | −0.112223 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 30.1434 | 1.30321 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −15.6523 | −0.675449 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −34.2598 | −1.47567 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −20.4018 | −0.877140 | −0.438570 | − | 0.898697i | \(-0.644515\pi\) | ||||
−0.438570 | + | 0.898697i | \(0.644515\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 12.5806 | 0.539886 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 5.70047 | 0.244181 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 24.3885 | 1.04278 | 0.521388 | − | 0.853319i | \(-0.325414\pi\) | ||||
0.521388 | + | 0.853319i | \(0.325414\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −22.9229 | −0.978327 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −0.116158 | −0.00494849 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 38.3703 | 1.63167 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 3.21767 | 0.136582 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −12.3148 | −0.521793 | −0.260897 | − | 0.965367i | \(-0.584018\pi\) | ||||
−0.260897 | + | 0.965367i | \(0.584018\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 3.26765 | 0.138207 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 23.7505 | 1.00274 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 29.9321 | 1.26149 | 0.630745 | − | 0.775990i | \(-0.282750\pi\) | ||||
0.630745 | + | 0.775990i | \(0.282750\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 19.0590 | 0.801819 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 9.24593 | 0.388293 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 19.1154 | 0.801360 | 0.400680 | − | 0.916218i | \(-0.368774\pi\) | ||||
0.400680 | + | 0.916218i | \(0.368774\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 15.4172 | 0.645191 | 0.322595 | − | 0.946537i | \(-0.395445\pi\) | ||||
0.322595 | + | 0.946537i | \(0.395445\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 16.1661 | 0.675348 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 51.4661 | 2.14628 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 4.37226 | 0.182019 | 0.0910097 | − | 0.995850i | \(-0.470991\pi\) | ||||
0.0910097 | + | 0.995850i | \(0.470991\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 3.72325 | 0.154733 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 44.3780 | 1.84111 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −6.18269 | −0.256061 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −4.34534 | −0.179657 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 16.8749 | 0.696500 | 0.348250 | − | 0.937402i | \(-0.386776\pi\) | ||||
0.348250 | + | 0.937402i | \(0.386776\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −0.0257935 | −0.00106280 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 15.9995 | 0.658133 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 25.1993 | 1.03481 | 0.517405 | − | 0.855741i | \(-0.326898\pi\) | ||||
0.517405 | + | 0.855741i | \(0.326898\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −82.0610 | −3.36417 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −16.8658 | −0.690272 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 33.5870 | 1.37233 | 0.686165 | − | 0.727446i | \(-0.259293\pi\) | ||||
0.686165 | + | 0.727446i | \(0.259293\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 19.6769 | 0.802636 | 0.401318 | − | 0.915939i | \(-0.368552\pi\) | ||||
0.401318 | + | 0.915939i | \(0.368552\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −4.62161 | −0.188206 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −43.4858 | −1.76795 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −0.481239 | −0.0195329 | −0.00976644 | − | 0.999952i | \(-0.503109\pi\) | ||||
−0.00976644 | + | 0.999952i | \(0.503109\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 5.63555 | 0.228364 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 2.14787 | 0.0868937 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −7.08677 | −0.286232 | −0.143116 | − | 0.989706i | \(-0.545712\pi\) | ||||
−0.143116 | + | 0.989706i | \(0.545712\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 17.4692 | 0.704425 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 5.30571 | 0.213600 | 0.106800 | − | 0.994281i | \(-0.465940\pi\) | ||||
0.106800 | + | 0.994281i | \(0.465940\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 30.7918 | 1.23763 | 0.618813 | − | 0.785539i | \(-0.287614\pi\) | ||||
0.618813 | + | 0.785539i | \(0.287614\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 24.1851 | 0.970515 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −62.3119 | −2.49647 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 23.3993 | 0.935972 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0.293419 | 0.0117180 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 5.25308 | 0.209454 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −35.2732 | −1.40421 | −0.702103 | − | 0.712076i | \(-0.747755\pi\) | ||||
−0.702103 | + | 0.712076i | \(0.747755\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −16.2716 | −0.646739 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 46.4752 | 1.84431 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −3.71391 | −0.147151 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −7.28470 | −0.288178 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 17.8655 | 0.705644 | 0.352822 | − | 0.935690i | \(-0.385222\pi\) | ||||
0.352822 | + | 0.935690i | \(0.385222\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −8.61818 | −0.339868 | −0.169934 | − | 0.985455i | \(-0.554355\pi\) | ||||
−0.169934 | + | 0.985455i | \(0.554355\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −22.0325 | −0.867529 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 15.4910 | 0.609016 | 0.304508 | − | 0.952510i | \(-0.401508\pi\) | ||||
0.304508 | + | 0.952510i | \(0.401508\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 61.4483 | 2.41206 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 1.25140 | 0.0490464 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 21.5939 | 0.845035 | 0.422517 | − | 0.906355i | \(-0.361147\pi\) | ||||
0.422517 | + | 0.906355i | \(0.361147\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −0.669145 | −0.0261457 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −2.36939 | −0.0924386 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 25.2479 | 0.983517 | 0.491759 | − | 0.870731i | \(-0.336354\pi\) | ||||
0.491759 | + | 0.870731i | \(0.336354\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −26.7554 | −1.04067 | −0.520333 | − | 0.853964i | \(-0.674192\pi\) | ||||
−0.520333 | + | 0.853964i | \(0.674192\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 2.57465 | 0.0999912 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −1.01380 | −0.0393136 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −8.68670 | −0.336350 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −2.72237 | −0.105253 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −49.1436 | −1.89717 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 44.1952 | 1.70360 | 0.851801 | − | 0.523866i | \(-0.175511\pi\) | ||||
0.851801 | + | 0.523866i | \(0.175511\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 45.9876 | 1.77006 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −25.5496 | −0.981952 | −0.490976 | − | 0.871173i | \(-0.663360\pi\) | ||||
−0.490976 | + | 0.871173i | \(0.663360\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −47.5736 | −1.82571 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 6.31745 | 0.242085 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −4.16513 | −0.159374 | −0.0796872 | − | 0.996820i | \(-0.525392\pi\) | ||||
−0.0796872 | + | 0.996820i | \(0.525392\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 40.0614 | 1.53067 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −3.07125 | −0.117175 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −0.670230 | −0.0255337 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 34.4452 | 1.31036 | 0.655179 | − | 0.755474i | \(-0.272593\pi\) | ||||
0.655179 | + | 0.755474i | \(0.272593\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 39.2241 | 1.49000 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −54.6126 | −2.07158 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 28.5197 | 1.08026 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 17.0210 | 0.643795 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −19.9463 | −0.753363 | −0.376682 | − | 0.926343i | \(-0.622935\pi\) | ||||
−0.376682 | + | 0.926343i | \(0.622935\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0.0648979 | 0.00244767 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −14.4823 | −0.545434 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −64.1716 | −2.41342 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −42.3849 | −1.59180 | −0.795900 | − | 0.605429i | \(-0.793002\pi\) | ||||
−0.795900 | + | 0.605429i | \(0.793002\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −22.3657 | −0.838779 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −1.92893 | −0.0722389 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −9.31580 | −0.348391 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 18.5921 | 0.694336 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −29.6547 | −1.10593 | −0.552967 | − | 0.833203i | \(-0.686505\pi\) | ||||
−0.552967 | + | 0.833203i | \(0.686505\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −59.3525 | −2.21040 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −3.96460 | −0.147445 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −16.5176 | −0.613449 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 9.18661 | 0.340713 | 0.170356 | − | 0.985383i | \(-0.445508\pi\) | ||||
0.170356 | + | 0.985383i | \(0.445508\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 7.07557 | 0.262058 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −35.9697 | −1.33039 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −3.92172 | −0.144852 | −0.0724260 | − | 0.997374i | \(-0.523074\pi\) | ||||
−0.0724260 | + | 0.997374i | \(0.523074\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 25.0414 | 0.923668 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −9.90809 | −0.364969 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −40.3182 | −1.48313 | −0.741564 | − | 0.670882i | \(-0.765916\pi\) | ||||
−0.741564 | + | 0.670882i | \(0.765916\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0.0318079 | 0.00116849 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 12.1172 | 0.444535 | 0.222268 | − | 0.974986i | \(-0.428654\pi\) | ||||
0.222268 | + | 0.974986i | \(0.428654\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −74.0641 | −2.71350 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −25.8675 | −0.946442 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −29.4964 | −1.07778 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −15.8609 | −0.578771 | −0.289386 | − | 0.957213i | \(-0.593451\pi\) | ||||
−0.289386 | + | 0.957213i | \(0.593451\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 20.0852 | 0.731947 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 28.3007 | 1.02997 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 24.4267 | 0.887805 | 0.443902 | − | 0.896075i | \(-0.353594\pi\) | ||||
0.443902 | + | 0.896075i | \(0.353594\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 21.9429 | 0.796477 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 20.2267 | 0.733216 | 0.366608 | − | 0.930375i | \(-0.380519\pi\) | ||||
0.366608 | + | 0.930375i | \(0.380519\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −5.57811 | −0.201941 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 47.8326 | 1.72939 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 6.66126 | 0.240524 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −2.17563 | −0.0784551 | −0.0392275 | − | 0.999230i | \(-0.512490\pi\) | ||||
−0.0392275 | + | 0.999230i | \(0.512490\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −0.330408 | −0.0118994 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 3.49777 | 0.125806 | 0.0629030 | − | 0.998020i | \(-0.479964\pi\) | ||||
0.0629030 | + | 0.998020i | \(0.479964\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −3.66782 | −0.131752 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −3.14860 | −0.112955 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0.352339 | 0.0126239 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −15.6174 | −0.558834 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −7.76201 | −0.277392 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −78.7083 | −2.80922 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −25.5395 | −0.910384 | −0.455192 | − | 0.890393i | \(-0.650429\pi\) | ||||
−0.455192 | + | 0.890393i | \(0.650429\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −2.18611 | −0.0778275 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −18.6499 | −0.663115 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −5.32738 | −0.189181 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 4.51910 | 0.160276 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −31.0283 | −1.09908 | −0.549540 | − | 0.835467i | \(-0.685197\pi\) | ||||
−0.549540 | + | 0.835467i | \(0.685197\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −23.6434 | −0.836442 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 36.3210 | 1.28334 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −5.07964 | −0.179257 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −75.8156 | −2.67215 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 3.44169 | 0.121153 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 33.7935 | 1.18812 | 0.594059 | − | 0.804422i | \(-0.297525\pi\) | ||||
0.594059 | + | 0.804422i | \(0.297525\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −14.3158 | −0.502697 | −0.251348 | − | 0.967897i | \(-0.580874\pi\) | ||||
−0.251348 | + | 0.967897i | \(0.580874\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 26.5525 | 0.931237 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −5.89930 | −0.206643 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −0.444378 | −0.0155468 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 4.25207 | 0.148579 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −46.7093 | −1.63017 | −0.815083 | − | 0.579344i | \(-0.803309\pi\) | ||||
−0.815083 | + | 0.579344i | \(0.803309\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 8.77876 | 0.306008 | 0.153004 | − | 0.988226i | \(-0.451105\pi\) | ||||
0.153004 | + | 0.988226i | \(0.451105\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 41.7241 | 1.45265 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −40.5870 | −1.41135 | −0.705674 | − | 0.708537i | \(-0.749356\pi\) | ||||
−0.705674 | + | 0.708537i | \(0.749356\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 36.2857 | 1.26025 | 0.630127 | − | 0.776492i | \(-0.283003\pi\) | ||||
0.630127 | + | 0.776492i | \(0.283003\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −19.3806 | −0.672304 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 40.8820 | 1.41648 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −26.6073 | −0.920784 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −1.72360 | −0.0595762 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −18.1603 | −0.626963 | −0.313481 | − | 0.949594i | \(-0.601495\pi\) | ||||
−0.313481 | + | 0.949594i | \(0.601495\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −26.2121 | −0.903865 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 2.65245 | 0.0913551 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 49.1582 | 1.69109 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 42.5524 | 1.46212 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0.483592 | 0.0165968 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 4.85329 | 0.166369 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −42.2922 | −1.44806 | −0.724028 | − | 0.689771i | \(-0.757711\pi\) | ||||
−0.724028 | + | 0.689771i | \(0.757711\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0.590936 | 0.0202096 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 39.9946 | 1.36619 | 0.683095 | − | 0.730330i | \(-0.260633\pi\) | ||||
0.683095 | + | 0.730330i | \(0.260633\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 55.2653 | 1.88563 | 0.942813 | − | 0.333322i | \(-0.108170\pi\) | ||||
0.942813 | + | 0.333322i | \(0.108170\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −17.0942 | −0.582569 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 14.9582 | 0.509185 | 0.254592 | − | 0.967048i | \(-0.418059\pi\) | ||||
0.254592 | + | 0.967048i | \(0.418059\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 93.4879 | 3.17868 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −13.1468 | −0.446490 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −47.9490 | −1.62656 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1.07408 | −0.0363938 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 27.7302 | 0.938526 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −71.2979 | −2.41031 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −33.7083 | −1.13825 | −0.569124 | − | 0.822252i | \(-0.692717\pi\) | ||||
−0.569124 | + | 0.822252i | \(0.692717\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 10.1582 | 0.342626 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 24.4774 | 0.824666 | 0.412333 | − | 0.911033i | \(-0.364714\pi\) | ||||
0.412333 | + | 0.911033i | \(0.364714\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 22.1930 | 0.746853 | 0.373426 | − | 0.927660i | \(-0.378183\pi\) | ||||
0.373426 | + | 0.927660i | \(0.378183\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −44.9143 | −1.50978 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 8.44417 | 0.283528 | 0.141764 | − | 0.989901i | \(-0.454723\pi\) | ||||
0.141764 | + | 0.989901i | \(0.454723\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −45.4777 | −1.52527 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −11.5541 | −0.387076 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −0.292096 | −0.00977462 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −67.5816 | −2.25900 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 2.37871 | 0.0794227 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0.619073 | 0.0206472 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 7.37776 | 0.245789 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 21.5596 | 0.717458 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 54.3188 | 1.80562 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 16.7572 | 0.556413 | 0.278207 | − | 0.960521i | \(-0.410260\pi\) | ||||
0.278207 | + | 0.960521i | \(0.410260\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 37.4050 | 1.24065 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −48.2461 | −1.59847 | −0.799233 | − | 0.601021i | \(-0.794761\pi\) | ||||
−0.799233 | + | 0.601021i | \(0.794761\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −55.4564 | −1.83534 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 35.9204 | 1.18749 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0.654782 | 0.0216228 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 18.0249 | 0.594587 | 0.297294 | − | 0.954786i | \(-0.403916\pi\) | ||||
0.297294 | + | 0.954786i | \(0.403916\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −8.00793 | −0.263870 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −1.69299 | −0.0557256 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 9.22845 | 0.303430 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 34.5960 | 1.13628 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 9.46901 | 0.310668 | 0.155334 | − | 0.987862i | \(-0.450355\pi\) | ||||
0.155334 | + | 0.987862i | \(0.450355\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0.505066 | 0.0165529 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 20.5067 | 0.671358 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 102.546 | 3.35363 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −29.3194 | −0.957824 | −0.478912 | − | 0.877863i | \(-0.658969\pi\) | ||||
−0.478912 | + | 0.877863i | \(0.658969\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 25.9745 | 0.847644 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 54.4765 | 1.77588 | 0.887942 | − | 0.459956i | \(-0.152135\pi\) | ||||
0.887942 | + | 0.459956i | \(0.152135\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 26.3492 | 0.858047 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −67.7452 | −2.20375 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −0.898972 | −0.0292127 | −0.0146063 | − | 0.999893i | \(-0.504650\pi\) | ||||
−0.0146063 | + | 0.999893i | \(0.504650\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −0.550655 | −0.0178750 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −19.9361 | −0.646472 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −47.1222 | −1.52644 | −0.763218 | − | 0.646141i | \(-0.776382\pi\) | ||||
−0.763218 | + | 0.646141i | \(0.776382\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 69.7998 | 2.25867 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −7.04239 | −0.227648 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −39.2015 | −1.26588 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.8625 | −0.995566 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 17.1932 | 0.554043 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 16.0757 | 0.517496 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 24.3871 | 0.784235 | 0.392118 | − | 0.919915i | \(-0.371743\pi\) | ||||
0.392118 | + | 0.919915i | \(0.371743\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −0.350135 | −0.0112480 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −36.8714 | −1.18326 | −0.591630 | − | 0.806209i | \(-0.701515\pi\) | ||||
−0.591630 | + | 0.806209i | \(0.701515\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 53.4404 | 1.71322 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 4.52307 | 0.144854 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 10.0886 | 0.322763 | 0.161382 | − | 0.986892i | \(-0.448405\pi\) | ||||
0.161382 | + | 0.986892i | \(0.448405\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 77.8673 | 2.48865 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 3.25143 | 0.103810 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 29.7977 | 0.950399 | 0.475200 | − | 0.879878i | \(-0.342376\pi\) | ||||
0.475200 | + | 0.879878i | \(0.342376\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 69.0806 | 2.20109 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 14.1714 | 0.451081 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −33.2322 | −1.05672 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −14.3363 | −0.455408 | −0.227704 | − | 0.973730i | \(-0.573122\pi\) | ||||
−0.227704 | + | 0.973730i | \(0.573122\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −14.9939 | −0.475818 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −72.8209 | −2.30858 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −5.98970 | −0.189696 | −0.0948478 | − | 0.995492i | \(-0.530236\pi\) | ||||
−0.0948478 | + | 0.995492i | \(0.530236\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 4.33666 | 0.137206 |
(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 | 4024.2.a.d.1.10 | ✓ | 28 | |
4.3 | odd | 2 | 8048.2.a.v.1.19 | 28 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4024.2.a.d.1.10 | ✓ | 28 | 1.1 | even | 1 | trivial | |
8048.2.a.v.1.19 | 28 | 4.3 | odd | 2 |