Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8020,2,Mod(1,8020)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8020, 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("8020.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8020 = 2^{2} \cdot 5 \cdot 401 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8020.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: | \(64.0400224211\) |
Analytic rank: | \(1\) |
Dimension: | \(28\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.12 | ||
Character | \(\chi\) | \(=\) | 8020.1 |
$q$-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 | ||||||||
\(3\) | −0.324068 | −0.187101 | −0.0935503 | − | 0.995615i | \(-0.529822\pi\) | ||||
−0.0935503 | + | 0.995615i | \(0.529822\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.35293 | −0.511358 | −0.255679 | − | 0.966762i | \(-0.582299\pi\) | ||||
−0.255679 | + | 0.966762i | \(0.582299\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.89498 | −0.964993 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.28388 | −0.688615 | −0.344307 | − | 0.938857i | \(-0.611886\pi\) | ||||
−0.344307 | + | 0.938857i | \(0.611886\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.54867 | −0.429524 | −0.214762 | − | 0.976666i | \(-0.568898\pi\) | ||||
−0.214762 | + | 0.976666i | \(0.568898\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.324068 | 0.0836740 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 7.82804 | 1.89858 | 0.949289 | − | 0.314403i | \(-0.101804\pi\) | ||||
0.949289 | + | 0.314403i | \(0.101804\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.53890 | 1.04129 | 0.520647 | − | 0.853772i | \(-0.325691\pi\) | ||||
0.520647 | + | 0.853772i | \(0.325691\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.438440 | 0.0956754 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0.446041 | 0.0930060 | 0.0465030 | − | 0.998918i | \(-0.485192\pi\) | ||||
0.0465030 | + | 0.998918i | \(0.485192\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.91037 | 0.367652 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.54869 | 0.473279 | 0.236640 | − | 0.971597i | \(-0.423954\pi\) | ||||
0.236640 | + | 0.971597i | \(0.423954\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.39570 | −0.789491 | −0.394745 | − | 0.918791i | \(-0.629167\pi\) | ||||
−0.394745 | + | 0.918791i | \(0.629167\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0.740131 | 0.128840 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1.35293 | 0.228686 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −5.52615 | −0.908494 | −0.454247 | − | 0.890876i | \(-0.650092\pi\) | ||||
−0.454247 | + | 0.890876i | \(0.650092\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0.501874 | 0.0803642 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 2.55237 | 0.398613 | 0.199307 | − | 0.979937i | \(-0.436131\pi\) | ||||
0.199307 | + | 0.979937i | \(0.436131\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.78802 | −0.272670 | −0.136335 | − | 0.990663i | \(-0.543532\pi\) | ||||
−0.136335 | + | 0.990663i | \(0.543532\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 2.89498 | 0.431558 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −5.32558 | −0.776816 | −0.388408 | − | 0.921488i | \(-0.626975\pi\) | ||||
−0.388408 | + | 0.921488i | \(0.626975\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −5.16959 | −0.738513 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −2.53682 | −0.355225 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0.0646043 | 0.00887408 | 0.00443704 | − | 0.999990i | \(-0.498588\pi\) | ||||
0.00443704 | + | 0.999990i | \(0.498588\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 2.28388 | 0.307958 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −1.47091 | −0.194827 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 8.28181 | 1.07820 | 0.539100 | − | 0.842242i | \(-0.318765\pi\) | ||||
0.539100 | + | 0.842242i | \(0.318765\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −4.00052 | −0.512214 | −0.256107 | − | 0.966648i | \(-0.582440\pi\) | ||||
−0.256107 | + | 0.966648i | \(0.582440\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 3.91669 | 0.493457 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 1.54867 | 0.192089 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 12.9447 | 1.58145 | 0.790723 | − | 0.612174i | \(-0.209705\pi\) | ||||
0.790723 | + | 0.612174i | \(0.209705\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −0.144548 | −0.0174015 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 10.6888 | 1.26853 | 0.634265 | − | 0.773116i | \(-0.281303\pi\) | ||||
0.634265 | + | 0.773116i | \(0.281303\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −8.01456 | −0.938033 | −0.469016 | − | 0.883189i | \(-0.655392\pi\) | ||||
−0.469016 | + | 0.883189i | \(0.655392\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −0.324068 | −0.0374201 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 3.08992 | 0.352129 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 2.47993 | 0.279014 | 0.139507 | − | 0.990221i | \(-0.455448\pi\) | ||||
0.139507 | + | 0.990221i | \(0.455448\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 8.06585 | 0.896206 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −4.09191 | −0.449146 | −0.224573 | − | 0.974457i | \(-0.572099\pi\) | ||||
−0.224573 | + | 0.974457i | \(0.572099\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −7.82804 | −0.849070 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −0.825948 | −0.0885509 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 8.32346 | 0.882285 | 0.441143 | − | 0.897437i | \(-0.354573\pi\) | ||||
0.441143 | + | 0.897437i | \(0.354573\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.09524 | 0.219640 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 1.42450 | 0.147714 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −4.53890 | −0.465681 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 13.1809 | 1.33832 | 0.669158 | − | 0.743120i | \(-0.266655\pi\) | ||||
0.669158 | + | 0.743120i | \(0.266655\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 6.61178 | 0.664509 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 5.23850 | 0.521250 | 0.260625 | − | 0.965440i | \(-0.416071\pi\) | ||||
0.260625 | + | 0.965440i | \(0.416071\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 5.76758 | 0.568297 | 0.284148 | − | 0.958780i | \(-0.408289\pi\) | ||||
0.284148 | + | 0.958780i | \(0.408289\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −0.438440 | −0.0427873 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 1.21818 | 0.117766 | 0.0588829 | − | 0.998265i | \(-0.481246\pi\) | ||||
0.0588829 | + | 0.998265i | \(0.481246\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −10.1815 | −0.975210 | −0.487605 | − | 0.873064i | \(-0.662129\pi\) | ||||
−0.487605 | + | 0.873064i | \(0.662129\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 1.79085 | 0.169980 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 4.07269 | 0.383126 | 0.191563 | − | 0.981480i | \(-0.438644\pi\) | ||||
0.191563 | + | 0.981480i | \(0.438644\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −0.446041 | −0.0415936 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 4.48337 | 0.414488 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −10.5908 | −0.970853 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −5.78391 | −0.525810 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −0.827141 | −0.0745808 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −10.7603 | −0.954822 | −0.477411 | − | 0.878680i | \(-0.658425\pi\) | ||||
−0.477411 | + | 0.878680i | \(0.658425\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0.579440 | 0.0510168 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −12.5848 | −1.09954 | −0.549771 | − | 0.835315i | \(-0.685285\pi\) | ||||
−0.549771 | + | 0.835315i | \(0.685285\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −6.14079 | −0.532474 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −1.91037 | −0.164419 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −12.0756 | −1.03169 | −0.515843 | − | 0.856683i | \(-0.672521\pi\) | ||||
−0.515843 | + | 0.856683i | \(0.672521\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 11.0398 | 0.936387 | 0.468193 | − | 0.883626i | \(-0.344905\pi\) | ||||
0.468193 | + | 0.883626i | \(0.344905\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1.72585 | 0.145343 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 3.53697 | 0.295776 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −2.54869 | −0.211657 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 1.67530 | 0.138176 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 6.04694 | 0.495385 | 0.247692 | − | 0.968839i | \(-0.420328\pi\) | ||||
0.247692 | + | 0.968839i | \(0.420328\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −5.39115 | −0.438725 | −0.219363 | − | 0.975643i | \(-0.570398\pi\) | ||||
−0.219363 | + | 0.975643i | \(0.570398\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −22.6620 | −1.83212 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 4.39570 | 0.353071 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −20.2708 | −1.61779 | −0.808894 | − | 0.587955i | \(-0.799933\pi\) | ||||
−0.808894 | + | 0.587955i | \(0.799933\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −0.0209362 | −0.00166035 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −0.603461 | −0.0475594 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 12.0931 | 0.947202 | 0.473601 | − | 0.880740i | \(-0.342954\pi\) | ||||
0.473601 | + | 0.880740i | \(0.342954\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −0.740131 | −0.0576191 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −3.51510 | −0.272007 | −0.136003 | − | 0.990708i | \(-0.543426\pi\) | ||||
−0.136003 | + | 0.990708i | \(0.543426\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −10.6016 | −0.815509 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −13.1400 | −1.00484 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −15.6538 | −1.19014 | −0.595068 | − | 0.803675i | \(-0.702875\pi\) | ||||
−0.595068 | + | 0.803675i | \(0.702875\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1.35293 | −0.102272 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −2.68387 | −0.201732 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −4.73613 | −0.353995 | −0.176997 | − | 0.984211i | \(-0.556638\pi\) | ||||
−0.176997 | + | 0.984211i | \(0.556638\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2.57853 | 0.191661 | 0.0958303 | − | 0.995398i | \(-0.469449\pi\) | ||||
0.0958303 | + | 0.995398i | \(0.469449\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 1.29644 | 0.0958356 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 5.52615 | 0.406291 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −17.8783 | −1.30739 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −2.58459 | −0.188001 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −19.1099 | −1.38275 | −0.691373 | − | 0.722498i | \(-0.742994\pi\) | ||||
−0.691373 | + | 0.722498i | \(0.742994\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −2.69558 | −0.194032 | −0.0970159 | − | 0.995283i | \(-0.530930\pi\) | ||||
−0.0970159 | + | 0.995283i | \(0.530930\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −0.501874 | −0.0359400 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −1.74637 | −0.124424 | −0.0622120 | − | 0.998063i | \(-0.519815\pi\) | ||||
−0.0622120 | + | 0.998063i | \(0.519815\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −6.19135 | −0.438893 | −0.219447 | − | 0.975624i | \(-0.570425\pi\) | ||||
−0.219447 | + | 0.975624i | \(0.570425\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −4.19496 | −0.295890 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −3.44818 | −0.242015 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −2.55237 | −0.178265 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −1.29128 | −0.0897502 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −10.3663 | −0.717050 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 4.40624 | 0.303338 | 0.151669 | − | 0.988431i | \(-0.451535\pi\) | ||||
0.151669 | + | 0.988431i | \(0.451535\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −3.46390 | −0.237343 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 1.78802 | 0.121942 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 5.94705 | 0.403712 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 2.59726 | 0.175507 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −12.1231 | −0.815485 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −10.0677 | −0.674182 | −0.337091 | − | 0.941472i | \(-0.609443\pi\) | ||||
−0.337091 | + | 0.941472i | \(0.609443\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −2.89498 | −0.192999 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −18.9259 | −1.25615 | −0.628076 | − | 0.778152i | \(-0.716157\pi\) | ||||
−0.628076 | + | 0.778152i | \(0.716157\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 5.73467 | 0.378958 | 0.189479 | − | 0.981885i | \(-0.439320\pi\) | ||||
0.189479 | + | 0.981885i | \(0.439320\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −1.00134 | −0.0658835 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 0.359235 | 0.0235342 | 0.0117671 | − | 0.999931i | \(-0.496254\pi\) | ||||
0.0117671 | + | 0.999931i | \(0.496254\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 5.32558 | 0.347402 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −0.803665 | −0.0522037 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −13.5999 | −0.879701 | −0.439851 | − | 0.898071i | \(-0.644969\pi\) | ||||
−0.439851 | + | 0.898071i | \(0.644969\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −15.0718 | −0.970857 | −0.485428 | − | 0.874276i | \(-0.661336\pi\) | ||||
−0.485428 | + | 0.874276i | \(0.661336\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −8.34500 | −0.535332 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 5.16959 | 0.330273 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −7.02925 | −0.447261 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 1.32606 | 0.0840354 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −12.8089 | −0.808490 | −0.404245 | − | 0.914651i | \(-0.632466\pi\) | ||||
−0.404245 | + | 0.914651i | \(0.632466\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1.01870 | −0.0640453 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 2.53682 | 0.158862 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 23.1041 | 1.44119 | 0.720597 | − | 0.693355i | \(-0.243868\pi\) | ||||
0.720597 | + | 0.693355i | \(0.243868\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 7.47648 | 0.464566 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −7.37840 | −0.456711 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −6.90942 | −0.426053 | −0.213026 | − | 0.977046i | \(-0.568332\pi\) | ||||
−0.213026 | + | 0.977046i | \(0.568332\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −0.0646043 | −0.00396861 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −2.69737 | −0.165076 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −16.0076 | −0.975999 | −0.488000 | − | 0.872844i | \(-0.662273\pi\) | ||||
−0.488000 | + | 0.872844i | \(0.662273\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −12.1477 | −0.737921 | −0.368961 | − | 0.929445i | \(-0.620286\pi\) | ||||
−0.368961 | + | 0.929445i | \(0.620286\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −0.678999 | −0.0410949 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −2.28388 | −0.137723 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −19.9737 | −1.20011 | −0.600053 | − | 0.799960i | \(-0.704854\pi\) | ||||
−0.600053 | + | 0.799960i | \(0.704854\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 12.7255 | 0.761853 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −10.6807 | −0.637157 | −0.318578 | − | 0.947896i | \(-0.603205\pi\) | ||||
−0.318578 | + | 0.947896i | \(0.603205\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 0.732385 | 0.0435358 | 0.0217679 | − | 0.999763i | \(-0.493071\pi\) | ||||
0.0217679 | + | 0.999763i | \(0.493071\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 1.47091 | 0.0871292 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −3.45317 | −0.203834 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 44.2782 | 2.60460 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −4.27150 | −0.250400 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 24.9233 | 1.45604 | 0.728018 | − | 0.685559i | \(-0.240442\pi\) | ||||
0.728018 | + | 0.685559i | \(0.240442\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −8.28181 | −0.482186 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −4.36306 | −0.253170 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −0.690771 | −0.0399483 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2.41906 | 0.139432 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −1.69763 | −0.0975262 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 4.00052 | 0.229069 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −5.62747 | −0.321176 | −0.160588 | − | 0.987021i | \(-0.551339\pi\) | ||||
−0.160588 | + | 0.987021i | \(0.551339\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −1.86909 | −0.106329 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −12.5854 | −0.713653 | −0.356827 | − | 0.934171i | \(-0.616141\pi\) | ||||
−0.356827 | + | 0.934171i | \(0.616141\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −7.47883 | −0.422728 | −0.211364 | − | 0.977407i | \(-0.567791\pi\) | ||||
−0.211364 | + | 0.977407i | \(0.567791\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −3.91669 | −0.220681 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −18.4388 | −1.03563 | −0.517813 | − | 0.855494i | \(-0.673254\pi\) | ||||
−0.517813 | + | 0.855494i | \(0.673254\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −5.82089 | −0.325907 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −0.394773 | −0.0220341 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 35.5307 | 1.97698 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1.54867 | −0.0859048 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 3.29950 | 0.182462 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 7.20511 | 0.397231 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 13.9905 | 0.768988 | 0.384494 | − | 0.923127i | \(-0.374376\pi\) | ||||
0.384494 | + | 0.923127i | \(0.374376\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 15.9981 | 0.876691 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −12.9447 | −0.707244 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −8.52906 | −0.464608 | −0.232304 | − | 0.972643i | \(-0.574626\pi\) | ||||
−0.232304 | + | 0.972643i | \(0.574626\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −1.31983 | −0.0716831 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 10.0392 | 0.543655 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 16.4646 | 0.889002 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0.144548 | 0.00778218 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −6.21504 | −0.333641 | −0.166821 | − | 0.985987i | \(-0.553350\pi\) | ||||
−0.166821 | + | 0.985987i | \(0.553350\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −10.6095 | −0.567913 | −0.283957 | − | 0.958837i | \(-0.591647\pi\) | ||||
−0.283957 | + | 0.958837i | \(0.591647\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −2.95854 | −0.157915 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −16.8299 | −0.895763 | −0.447881 | − | 0.894093i | \(-0.647821\pi\) | ||||
−0.447881 | + | 0.894093i | \(0.647821\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −10.6888 | −0.567304 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 3.43212 | 0.181647 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −26.7261 | −1.41055 | −0.705275 | − | 0.708933i | \(-0.749177\pi\) | ||||
−0.705275 | + | 0.708933i | \(0.749177\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.60157 | 0.0842933 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 1.87438 | 0.0983793 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 8.01456 | 0.419501 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 23.5577 | 1.22970 | 0.614852 | − | 0.788643i | \(-0.289216\pi\) | ||||
0.614852 | + | 0.788643i | \(0.289216\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −7.38906 | −0.384659 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −0.0874048 | −0.00453783 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 31.9026 | 1.65185 | 0.825926 | − | 0.563778i | \(-0.190653\pi\) | ||||
0.825926 | + | 0.563778i | \(0.190653\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0.324068 | 0.0167348 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −3.94708 | −0.203285 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −26.8107 | −1.37717 | −0.688587 | − | 0.725154i | \(-0.741769\pi\) | ||||
−0.688587 | + | 0.725154i | \(0.741769\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 3.48707 | 0.178648 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 0.260208 | 0.0132960 | 0.00664800 | − | 0.999978i | \(-0.497884\pi\) | ||||
0.00664800 | + | 0.999978i | \(0.497884\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −3.08992 | −0.157477 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 5.17628 | 0.263125 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −31.3007 | −1.58701 | −0.793504 | − | 0.608565i | \(-0.791746\pi\) | ||||
−0.793504 | + | 0.608565i | \(0.791746\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 3.49163 | 0.176579 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 4.07834 | 0.205725 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −2.47993 | −0.124779 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −19.6343 | −0.985417 | −0.492708 | − | 0.870195i | \(-0.663993\pi\) | ||||
−0.492708 | + | 0.870195i | \(0.663993\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 1.99003 | 0.0996262 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 1.00000 | 0.0499376 | ||||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 6.80749 | 0.339105 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −8.06585 | −0.400795 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 12.6211 | 0.625602 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −33.1279 | −1.63807 | −0.819035 | − | 0.573744i | \(-0.805491\pi\) | ||||
−0.819035 | + | 0.573744i | \(0.805491\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 3.91330 | 0.193029 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −11.2047 | −0.551346 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 4.09191 | 0.200864 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −3.57766 | −0.175199 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 29.0081 | 1.41714 | 0.708569 | − | 0.705642i | \(-0.249341\pi\) | ||||
0.708569 | + | 0.705642i | \(0.249341\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 31.5495 | 1.53763 | 0.768814 | − | 0.639473i | \(-0.220847\pi\) | ||||
0.768814 | + | 0.639473i | \(0.220847\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 15.4174 | 0.749622 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 7.82804 | 0.379716 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 5.41241 | 0.261925 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −1.14622 | −0.0553400 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −19.2499 | −0.927234 | −0.463617 | − | 0.886036i | \(-0.653449\pi\) | ||||
−0.463617 | + | 0.886036i | \(0.653449\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −40.7631 | −1.95895 | −0.979476 | − | 0.201562i | \(-0.935398\pi\) | ||||
−0.979476 | + | 0.201562i | \(0.935398\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0.825948 | 0.0396012 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 2.02453 | 0.0968466 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 15.6415 | 0.746526 | 0.373263 | − | 0.927725i | \(-0.378239\pi\) | ||||
0.373263 | + | 0.927725i | \(0.378239\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 14.9659 | 0.712660 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 27.1649 | 1.29064 | 0.645322 | − | 0.763910i | \(-0.276723\pi\) | ||||
0.645322 | + | 0.763910i | \(0.276723\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −8.32346 | −0.394570 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −1.95962 | −0.0926868 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −2.87709 | −0.135778 | −0.0678890 | − | 0.997693i | \(-0.521626\pi\) | ||||
−0.0678890 | + | 0.997693i | \(0.521626\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −5.82930 | −0.274491 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 1.74710 | 0.0820858 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −2.09524 | −0.0982262 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 37.1709 | 1.73878 | 0.869390 | − | 0.494127i | \(-0.164512\pi\) | ||||
0.869390 | + | 0.494127i | \(0.164512\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 14.9545 | 0.698015 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −11.3487 | −0.528561 | −0.264280 | − | 0.964446i | \(-0.585134\pi\) | ||||
−0.264280 | + | 0.964446i | \(0.585134\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 38.6067 | 1.79420 | 0.897102 | − | 0.441823i | \(-0.145668\pi\) | ||||
0.897102 | + | 0.441823i | \(0.145668\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −1.42450 | −0.0660598 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −18.0206 | −0.833896 | −0.416948 | − | 0.908930i | \(-0.636900\pi\) | ||||
−0.416948 | + | 0.908930i | \(0.636900\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −17.5132 | −0.808685 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 6.56912 | 0.302689 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 4.08362 | 0.187765 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 4.53890 | 0.208259 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −0.187028 | −0.00856343 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 19.6971 | 0.899982 | 0.449991 | − | 0.893033i | \(-0.351427\pi\) | ||||
0.449991 | + | 0.893033i | \(0.351427\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 8.55819 | 0.390220 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0.195562 | 0.00889839 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −13.1809 | −0.598513 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 14.6410 | 0.663445 | 0.331722 | − | 0.943377i | \(-0.392370\pi\) | ||||
0.331722 | + | 0.943377i | \(0.392370\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −3.91897 | −0.177222 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 11.2088 | 0.505848 | 0.252924 | − | 0.967486i | \(-0.418608\pi\) | ||||
0.252924 | + | 0.967486i | \(0.418608\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 19.9512 | 0.898558 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −6.61178 | −0.297177 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −14.4612 | −0.648672 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 12.0196 | 0.538071 | 0.269036 | − | 0.963130i | \(-0.413295\pi\) | ||||
0.269036 | + | 0.963130i | \(0.413295\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 1.13913 | 0.0508926 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −6.98878 | −0.311614 | −0.155807 | − | 0.987788i | \(-0.549798\pi\) | ||||
−0.155807 | + | 0.987788i | \(0.549798\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −5.23850 | −0.233110 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 3.43564 | 0.152582 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −33.7782 | −1.49719 | −0.748595 | − | 0.663027i | \(-0.769271\pi\) | ||||
−0.748595 | + | 0.663027i | \(0.769271\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 10.8431 | 0.479670 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 8.67098 | 0.382833 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −5.76758 | −0.254150 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 12.1630 | 0.534927 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 5.07289 | 0.222675 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 9.05093 | 0.396528 | 0.198264 | − | 0.980149i | \(-0.436470\pi\) | ||||
0.198264 | + | 0.980149i | \(0.436470\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 29.7700 | 1.30175 | 0.650876 | − | 0.759184i | \(-0.274402\pi\) | ||||
0.650876 | + | 0.759184i | \(0.274402\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0.438440 | 0.0191351 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −34.4097 | −1.49891 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −22.8010 | −0.991350 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −23.9757 | −1.04046 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −3.95278 | −0.171214 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −1.21818 | −0.0526665 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 1.53483 | 0.0662326 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 11.8067 | 0.508551 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 3.38789 | 0.145657 | 0.0728284 | − | 0.997344i | \(-0.476797\pi\) | ||||
0.0728284 | + | 0.997344i | \(0.476797\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −0.835619 | −0.0358598 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 10.1815 | 0.436127 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −36.2477 | −1.54984 | −0.774920 | − | 0.632059i | \(-0.782210\pi\) | ||||
−0.774920 | + | 0.632059i | \(0.782210\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 11.5814 | 0.494283 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 11.5682 | 0.492823 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −3.35516 | −0.142676 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −1.79085 | −0.0760173 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −34.6813 | −1.46949 | −0.734747 | − | 0.678342i | \(-0.762699\pi\) | ||||
−0.734747 | + | 0.678342i | \(0.762699\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 2.76905 | 0.117118 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 5.79378 | 0.244613 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 17.7505 | 0.748096 | 0.374048 | − | 0.927409i | \(-0.377970\pi\) | ||||
0.374048 | + | 0.927409i | \(0.377970\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −4.07269 | −0.171339 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −10.9125 | −0.458282 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −2.32248 | −0.0973634 | −0.0486817 | − | 0.998814i | \(-0.515502\pi\) | ||||
−0.0486817 | + | 0.998814i | \(0.515502\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −29.8713 | −1.25007 | −0.625037 | − | 0.780595i | \(-0.714916\pi\) | ||||
−0.625037 | + | 0.780595i | \(0.714916\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 6.19292 | 0.258713 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0.446041 | 0.0186012 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −41.0344 | −1.70828 | −0.854142 | − | 0.520040i | \(-0.825917\pi\) | ||||
−0.854142 | + | 0.520040i | \(0.825917\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0.873550 | 0.0363035 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 5.53605 | 0.229674 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −0.147548 | −0.00611083 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −4.48337 | −0.185365 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −6.28562 | −0.259435 | −0.129718 | − | 0.991551i | \(-0.541407\pi\) | ||||
−0.129718 | + | 0.991551i | \(0.541407\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −19.9516 | −0.822092 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0.565943 | 0.0232798 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −3.36345 | −0.138120 | −0.0690601 | − | 0.997613i | \(-0.522000\pi\) | ||||
−0.0690601 | + | 0.997613i | \(0.522000\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 10.5908 | 0.434179 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 2.00642 | 0.0821172 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −27.4182 | −1.12028 | −0.560139 | − | 0.828399i | \(-0.689252\pi\) | ||||
−0.560139 | + | 0.828399i | \(0.689252\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −36.1687 | −1.47535 | −0.737675 | − | 0.675155i | \(-0.764077\pi\) | ||||
−0.737675 | + | 0.675155i | \(0.764077\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −37.4746 | −1.52609 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 5.78391 | 0.235149 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −12.4228 | −0.504224 | −0.252112 | − | 0.967698i | \(-0.581125\pi\) | ||||
−0.252112 | + | 0.967698i | \(0.581125\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 1.11745 | 0.0452812 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 8.24757 | 0.333661 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 36.1432 | 1.45981 | 0.729905 | − | 0.683548i | \(-0.239564\pi\) | ||||
0.729905 | + | 0.683548i | \(0.239564\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0.827141 | 0.0333535 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 30.8006 | 1.23999 | 0.619993 | − | 0.784607i | \(-0.287135\pi\) | ||||
0.619993 | + | 0.784607i | \(0.287135\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 10.0643 | 0.404518 | 0.202259 | − | 0.979332i | \(-0.435172\pi\) | ||||
0.202259 | + | 0.979332i | \(0.435172\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0.852105 | 0.0341938 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −11.2610 | −0.451163 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 3.35938 | 0.134161 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −43.2590 | −1.72485 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −44.2366 | −1.76103 | −0.880516 | − | 0.474017i | \(-0.842804\pi\) | ||||
−0.880516 | + | 0.474017i | \(0.842804\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −1.42792 | −0.0567547 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 10.7603 | 0.427009 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 8.00599 | 0.317209 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −30.9439 | −1.22412 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −2.50430 | −0.0989139 | −0.0494570 | − | 0.998776i | \(-0.515749\pi\) | ||||
−0.0494570 | + | 0.998776i | \(0.515749\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 22.0101 | 0.867992 | 0.433996 | − | 0.900915i | \(-0.357103\pi\) | ||||
0.433996 | + | 0.900915i | \(0.357103\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −0.579440 | −0.0228154 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −4.04488 | −0.159021 | −0.0795103 | − | 0.996834i | \(-0.525336\pi\) | ||||
−0.0795103 | + | 0.996834i | \(0.525336\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −18.9146 | −0.742464 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −1.92725 | −0.0755348 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −17.2195 | −0.673851 | −0.336925 | − | 0.941531i | \(-0.609387\pi\) | ||||
−0.336925 | + | 0.941531i | \(0.609387\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 12.5848 | 0.491730 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 23.2020 | 0.905196 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 15.6550 | 0.609832 | 0.304916 | − | 0.952379i | \(-0.401372\pi\) | ||||
0.304916 | + | 0.952379i | \(0.401372\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −31.6730 | −1.23194 | −0.615968 | − | 0.787771i | \(-0.711235\pi\) | ||||
−0.615968 | + | 0.787771i | \(0.711235\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 3.92869 | 0.152578 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 6.14079 | 0.238130 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.13682 | 0.0440178 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 3.26261 | 0.126140 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 9.13669 | 0.352718 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 18.2786 | 0.704590 | 0.352295 | − | 0.935889i | \(-0.385401\pi\) | ||||
0.352295 | + | 0.935889i | \(0.385401\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 1.91037 | 0.0735303 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −29.5683 | −1.13640 | −0.568202 | − | 0.822889i | \(-0.692361\pi\) | ||||
−0.568202 | + | 0.822889i | \(0.692361\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −17.8328 | −0.684358 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 6.13326 | 0.235027 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −0.237407 | −0.00908414 | −0.00454207 | − | 0.999990i | \(-0.501446\pi\) | ||||
−0.00454207 | + | 0.999990i | \(0.501446\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 12.0756 | 0.461384 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −1.85842 | −0.0709032 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −0.100051 | −0.00381163 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −3.38838 | −0.128900 | −0.0644500 | − | 0.997921i | \(-0.520529\pi\) | ||||
−0.0644500 | + | 0.997921i | \(0.520529\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −8.94524 | −0.339802 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −11.0398 | −0.418765 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 19.9801 | 0.756799 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −0.116416 | −0.00440327 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 21.7522 | 0.821571 | 0.410785 | − | 0.911732i | \(-0.365255\pi\) | ||||
0.410785 | + | 0.911732i | \(0.365255\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −25.0826 | −0.946010 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −1.72585 | −0.0649992 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −7.08730 | −0.266545 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 33.8533 | 1.27139 | 0.635693 | − | 0.771942i | \(-0.280714\pi\) | ||||
0.635693 | + | 0.771942i | \(0.280714\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −7.17935 | −0.269247 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −1.96066 | −0.0734274 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −3.53697 | −0.132275 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 4.40727 | 0.164593 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −5.13757 | −0.191599 | −0.0957996 | − | 0.995401i | \(-0.530541\pi\) | ||||
−0.0957996 | + | 0.995401i | \(0.530541\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −7.80311 | −0.290603 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 4.88427 | 0.181648 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 2.54869 | 0.0946559 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 50.3092 | 1.86586 | 0.932932 | − | 0.360052i | \(-0.117241\pi\) | ||||
0.932932 | + | 0.360052i | \(0.117241\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −21.4932 | −0.796045 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −13.9967 | −0.517686 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 8.89863 | 0.328678 | 0.164339 | − | 0.986404i | \(-0.447451\pi\) | ||||
0.164339 | + | 0.986404i | \(0.447451\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −1.67530 | −0.0617943 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −29.5641 | −1.08901 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 1.48800 | 0.0547369 | 0.0273684 | − | 0.999625i | \(-0.491287\pi\) | ||||
0.0273684 | + | 0.999625i | \(0.491287\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 2.27795 | 0.0836828 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −1.81572 | −0.0666125 | −0.0333062 | − | 0.999445i | \(-0.510604\pi\) | ||||
−0.0333062 | + | 0.999445i | \(0.510604\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −6.04694 | −0.221543 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 11.8460 | 0.433423 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −1.64811 | −0.0602205 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −11.4691 | −0.418513 | −0.209256 | − | 0.977861i | \(-0.567104\pi\) | ||||
−0.209256 | + | 0.977861i | \(0.567104\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 4.15095 | 0.151269 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 5.39115 | 0.196204 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 28.6945 | 1.04292 | 0.521460 | − | 0.853276i | \(-0.325388\pi\) | ||||
0.521460 | + | 0.853276i | \(0.325388\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0.330129 | 0.0119829 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −52.5333 | −1.90433 | −0.952166 | − | 0.305582i | \(-0.901149\pi\) | ||||
−0.952166 | + | 0.305582i | \(0.901149\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 13.7748 | 0.498681 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 22.6620 | 0.819347 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −12.8258 | −0.463113 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −19.5173 | −0.703813 | −0.351907 | − | 0.936035i | \(-0.614467\pi\) | ||||
−0.351907 | + | 0.936035i | \(0.614467\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −7.48729 | −0.269648 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −7.80828 | −0.280844 | −0.140422 | − | 0.990092i | \(-0.544846\pi\) | ||||
−0.140422 | + | 0.990092i | \(0.544846\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −4.39570 | −0.157898 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −2.42289 | −0.0869205 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 11.5849 | 0.415074 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −24.4119 | −0.873528 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 4.86894 | 0.174002 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 20.2708 | 0.723497 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 30.2113 | 1.07692 | 0.538458 | − | 0.842652i | \(-0.319007\pi\) | ||||
0.538458 | + | 0.842652i | \(0.319007\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 2.23912 | 0.0797148 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −5.51004 | −0.195914 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 6.19549 | 0.220008 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0.0209362 | 0.000742530 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 10.0463 | 0.355857 | 0.177929 | − | 0.984043i | \(-0.443060\pi\) | ||||
0.177929 | + | 0.984043i | \(0.443060\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −41.6889 | −1.47485 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −24.0963 | −0.851399 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 18.3043 | 0.645943 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0.603461 | 0.0212692 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 5.18754 | 0.182610 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 45.2492 | 1.59088 | 0.795439 | − | 0.606034i | \(-0.207241\pi\) | ||||
0.795439 | + | 0.606034i | \(0.207241\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −2.67838 | −0.0940506 | −0.0470253 | − | 0.998894i | \(-0.514974\pi\) | ||||
−0.0470253 | + | 0.998894i | \(0.514974\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 3.93668 | 0.138065 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −12.0931 | −0.423601 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −8.11563 | −0.283930 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −6.06567 | −0.211952 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −0.00264638 | −9.23594e−5 0 | −4.61797e−5 | − | 1.00000i | \(-0.500015\pi\) | ||||
−4.61797e−5 | 1.00000i | \(0.500015\pi\) | ||||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 4.56917 | 0.159271 | 0.0796356 | − | 0.996824i | \(-0.474624\pi\) | ||||
0.0796356 | + | 0.996824i | \(0.474624\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0.740131 | 0.0257681 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −1.89854 | −0.0660188 | −0.0330094 | − | 0.999455i | \(-0.510509\pi\) | ||||
−0.0330094 | + | 0.999455i | \(0.510509\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −6.38272 | −0.221681 | −0.110840 | − | 0.993838i | \(-0.535354\pi\) | ||||
−0.110840 | + | 0.993838i | \(0.535354\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 6.47285 | 0.224541 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −40.4678 | −1.40213 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 3.51510 | 0.121645 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −8.39742 | −0.290257 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 2.09516 | 0.0723331 | 0.0361665 | − | 0.999346i | \(-0.488485\pi\) | ||||
0.0361665 | + | 0.999346i | \(0.488485\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −22.5042 | −0.776007 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 3.46127 | 0.119212 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 10.6016 | 0.364707 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 7.82520 | 0.268877 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −0.237342 | −0.00814557 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −2.46489 | −0.0844954 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 9.34390 | 0.319929 | 0.159965 | − | 0.987123i | \(-0.448862\pi\) | ||||
0.159965 | + | 0.987123i | \(0.448862\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 13.1400 | 0.449379 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −7.37661 | −0.251980 | −0.125990 | − | 0.992031i | \(-0.540211\pi\) | ||||
−0.125990 | + | 0.992031i | \(0.540211\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 50.8509 | 1.73501 | 0.867506 | − | 0.497428i | \(-0.165722\pi\) | ||||
0.867506 | + | 0.497428i | \(0.165722\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 1.11906 | 0.0381375 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 40.3542 | 1.37367 | 0.686836 | − | 0.726813i | \(-0.258999\pi\) | ||||
0.686836 | + | 0.726813i | \(0.258999\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 15.6538 | 0.532245 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −14.3492 | −0.487323 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −5.66385 | −0.192133 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −20.0471 | −0.679269 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −38.1584 | −1.29147 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 1.35293 | 0.0457372 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −46.1310 | −1.55773 | −0.778867 | − | 0.627189i | \(-0.784205\pi\) | ||||
−0.778867 | + | 0.627189i | \(0.784205\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −8.07684 | −0.272425 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 44.7364 | 1.50721 | 0.753605 | − | 0.657328i | \(-0.228313\pi\) | ||||
0.753605 | + | 0.657328i | \(0.228313\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −1.68377 | −0.0566633 | −0.0283316 | − | 0.999599i | \(-0.509019\pi\) | ||||
−0.0283316 | + | 0.999599i | \(0.509019\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 2.68387 | 0.0902172 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 7.16442 | 0.240558 | 0.120279 | − | 0.992740i | \(-0.461621\pi\) | ||||
0.120279 | + | 0.992740i | \(0.461621\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 14.5579 | 0.488256 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −18.4214 | −0.617140 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −24.1722 | −0.808893 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 4.73613 | 0.158311 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0.223857 | 0.00747435 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −11.2033 | −0.373650 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0.505725 | 0.0168482 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −0.783939 | −0.0260878 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −2.57853 | −0.0857133 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 44.9100 | 1.49121 | 0.745605 | − | 0.666388i | \(-0.232160\pi\) | ||||
0.745605 | + | 0.666388i | \(0.232160\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −15.1654 | −0.503003 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 13.4452 | 0.445459 | 0.222730 | − | 0.974880i | \(-0.428503\pi\) | ||||
0.222730 | + | 0.974880i | \(0.428503\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 9.34542 | 0.309288 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −1.29644 | −0.0428590 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 17.0263 | 0.562259 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 39.4959 | 1.30285 | 0.651425 | − | 0.758713i | \(-0.274171\pi\) | ||||
0.651425 | + | 0.758713i | \(0.274171\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 1.82368 | 0.0600923 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −16.5535 | −0.544864 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −5.52615 | −0.181699 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −16.6970 | −0.548403 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −17.2776 | −0.566860 | −0.283430 | − | 0.958993i | \(-0.591472\pi\) | ||||
−0.283430 | + | 0.958993i | \(0.591472\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −23.4642 | −0.769009 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 4.07853 | 0.133525 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 17.8783 | 0.584682 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −15.0352 | −0.491179 | −0.245590 | − | 0.969374i | \(-0.578982\pi\) | ||||
−0.245590 | + | 0.969374i | \(0.578982\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 2.42365 | 0.0790927 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 28.8958 | 0.941977 | 0.470989 | − | 0.882139i | \(-0.343897\pi\) | ||||
0.470989 | + | 0.882139i | \(0.343897\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1.13846 | 0.0370734 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 2.58459 | 0.0840768 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 57.1262 | 1.85635 | 0.928176 | − | 0.372142i | \(-0.121377\pi\) | ||||
0.928176 | + | 0.372142i | \(0.121377\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 12.4119 | 0.402908 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 5.97542 | 0.193766 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −5.55064 | −0.179803 | −0.0899014 | − | 0.995951i | \(-0.528655\pi\) | ||||
−0.0899014 | + | 0.995951i | \(0.528655\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 19.1099 | 0.618383 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 1.88636 | 0.0609774 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 16.3374 | 0.527561 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −11.6778 | −0.376704 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −3.52660 | −0.113643 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 2.69558 | 0.0867737 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 50.9437 | 1.63824 | 0.819119 | − | 0.573624i | \(-0.194463\pi\) | ||||
0.819119 | + | 0.573624i | \(0.194463\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −11.5143 | −0.369894 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −39.9308 | −1.28144 | −0.640719 | − | 0.767775i | \(-0.721364\pi\) | ||||
−0.640719 | + | 0.767775i | \(0.721364\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −14.9361 | −0.478829 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0.501874 | 0.0160728 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −39.7986 | −1.27327 | −0.636635 | − | 0.771165i | \(-0.719674\pi\) | ||||
−0.636635 | + | 0.771165i | \(0.719674\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −19.0098 | −0.607554 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 29.4752 | 0.941072 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −5.22196 | −0.166555 | −0.0832773 | − | 0.996526i | \(-0.526539\pi\) | ||||
−0.0832773 | + | 0.996526i | \(0.526539\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1.74637 | 0.0556441 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −2.33495 | −0.0743221 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −0.797530 | −0.0253600 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −45.3443 | −1.44041 | −0.720204 | − | 0.693763i | \(-0.755952\pi\) | ||||
−0.720204 | + | 0.693763i | \(0.755952\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −4.53388 | −0.143878 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 6.19135 | 0.196279 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 47.1591 | 1.49354 | 0.746772 | − | 0.665080i | \(-0.231603\pi\) | ||||
0.746772 | + | 0.665080i | \(0.231603\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −10.5570 | −0.334009 |
(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 | 8020.2.a.c.1.12 | ✓ | 28 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8020.2.a.c.1.12 | ✓ | 28 | 1.1 | even | 1 | trivial |