Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4028,2,Mod(1,4028)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4028, 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("4028.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4028 = 2^{2} \cdot 19 \cdot 53 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4028.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: | \(32.1637419342\) |
Analytic rank: | \(1\) |
Dimension: | \(19\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{19} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{19} - 5 x^{18} - 27 x^{17} + 161 x^{16} + 253 x^{15} - 2103 x^{14} - 683 x^{13} + 14442 x^{12} - 4144 x^{11} - 56325 x^{10} + 37245 x^{9} + 124233 x^{8} - 117486 x^{7} + \cdots - 4088 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 3^{3} \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.19 | ||
Root | \(-3.04822\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4028.1 |
$q$-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 | ||||||||
\(3\) | 3.04822 | 1.75989 | 0.879946 | − | 0.475074i | \(-0.157579\pi\) | ||||
0.879946 | + | 0.475074i | \(0.157579\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.16277 | −0.520009 | −0.260004 | − | 0.965607i | \(-0.583724\pi\) | ||||
−0.260004 | + | 0.965607i | \(0.583724\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −3.09586 | −1.17012 | −0.585062 | − | 0.810988i | \(-0.698930\pi\) | ||||
−0.585062 | + | 0.810988i | \(0.698930\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 6.29166 | 2.09722 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.740609 | −0.223302 | −0.111651 | − | 0.993747i | \(-0.535614\pi\) | ||||
−0.111651 | + | 0.993747i | \(0.535614\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −7.01696 | −1.94616 | −0.973078 | − | 0.230476i | \(-0.925972\pi\) | ||||
−0.973078 | + | 0.230476i | \(0.925972\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −3.54439 | −0.915159 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 5.39632 | 1.30880 | 0.654400 | − | 0.756149i | \(-0.272921\pi\) | ||||
0.654400 | + | 0.756149i | \(0.272921\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.00000 | 0.229416 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −9.43686 | −2.05929 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.27050 | −0.264918 | −0.132459 | − | 0.991188i | \(-0.542287\pi\) | ||||
−0.132459 | + | 0.991188i | \(0.542287\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3.64796 | −0.729591 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 10.0337 | 1.93099 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −5.83714 | −1.08393 | −0.541965 | − | 0.840401i | \(-0.682319\pi\) | ||||
−0.541965 | + | 0.840401i | \(0.682319\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.81429 | 0.864672 | 0.432336 | − | 0.901713i | \(-0.357690\pi\) | ||||
0.432336 | + | 0.901713i | \(0.357690\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −2.25754 | −0.392987 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 3.59979 | 0.608475 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −4.16138 | −0.684127 | −0.342063 | − | 0.939677i | \(-0.611126\pi\) | ||||
−0.342063 | + | 0.939677i | \(0.611126\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −21.3893 | −3.42502 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −7.66017 | −1.19632 | −0.598158 | − | 0.801378i | \(-0.704101\pi\) | ||||
−0.598158 | + | 0.801378i | \(0.704101\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 8.98019 | 1.36947 | 0.684733 | − | 0.728794i | \(-0.259919\pi\) | ||||
0.684733 | + | 0.728794i | \(0.259919\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −7.31578 | −1.09057 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −7.19701 | −1.04979 | −0.524896 | − | 0.851167i | \(-0.675896\pi\) | ||||
−0.524896 | + | 0.851167i | \(0.675896\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 2.58434 | 0.369191 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 16.4492 | 2.30335 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −1.00000 | −0.137361 | ||||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0.861161 | 0.116119 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 3.04822 | 0.403747 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −4.18347 | −0.544642 | −0.272321 | − | 0.962206i | \(-0.587791\pi\) | ||||
−0.272321 | + | 0.962206i | \(0.587791\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.39640 | 0.306828 | 0.153414 | − | 0.988162i | \(-0.450973\pi\) | ||||
0.153414 | + | 0.988162i | \(0.450973\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −19.4781 | −2.45401 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 8.15915 | 1.01202 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −12.6421 | −1.54448 | −0.772238 | − | 0.635334i | \(-0.780863\pi\) | ||||
−0.772238 | + | 0.635334i | \(0.780863\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −3.87278 | −0.466228 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −15.0821 | −1.78991 | −0.894957 | − | 0.446152i | \(-0.852794\pi\) | ||||
−0.894957 | + | 0.446152i | \(0.852794\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −13.9346 | −1.63093 | −0.815463 | − | 0.578809i | \(-0.803518\pi\) | ||||
−0.815463 | + | 0.578809i | \(0.803518\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −11.1198 | −1.28400 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 2.29282 | 0.261291 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 11.9623 | 1.34587 | 0.672934 | − | 0.739703i | \(-0.265034\pi\) | ||||
0.672934 | + | 0.739703i | \(0.265034\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 11.7100 | 1.30111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −2.76424 | −0.303415 | −0.151708 | − | 0.988425i | \(-0.548477\pi\) | ||||
−0.151708 | + | 0.988425i | \(0.548477\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −6.27470 | −0.680587 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −17.7929 | −1.90760 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −0.783312 | −0.0830309 | −0.0415155 | − | 0.999138i | \(-0.513219\pi\) | ||||
−0.0415155 | + | 0.999138i | \(0.513219\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 21.7235 | 2.27724 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 14.6750 | 1.52173 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −1.16277 | −0.119298 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −12.2450 | −1.24329 | −0.621647 | − | 0.783297i | \(-0.713536\pi\) | ||||
−0.621647 | + | 0.783297i | \(0.713536\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −4.65966 | −0.468313 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 15.0356 | 1.49609 | 0.748047 | − | 0.663646i | \(-0.230992\pi\) | ||||
0.748047 | + | 0.663646i | \(0.230992\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 7.36543 | 0.725737 | 0.362869 | − | 0.931840i | \(-0.381797\pi\) | ||||
0.362869 | + | 0.931840i | \(0.381797\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 10.9729 | 1.07085 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −4.04862 | −0.391395 | −0.195697 | − | 0.980664i | \(-0.562697\pi\) | ||||
−0.195697 | + | 0.980664i | \(0.562697\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −7.89989 | −0.756673 | −0.378336 | − | 0.925668i | \(-0.623504\pi\) | ||||
−0.378336 | + | 0.925668i | \(0.623504\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −12.6848 | −1.20399 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 6.64480 | 0.625090 | 0.312545 | − | 0.949903i | \(-0.398819\pi\) | ||||
0.312545 | + | 0.949903i | \(0.398819\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.47731 | 0.137760 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −44.1483 | −4.08151 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −16.7062 | −1.53146 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.4515 | −0.950136 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −23.3499 | −2.10539 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 10.0556 | 0.899402 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1.17268 | −0.104058 | −0.0520292 | − | 0.998646i | \(-0.516569\pi\) | ||||
−0.0520292 | + | 0.998646i | \(0.516569\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 27.3736 | 2.41011 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −10.3480 | −0.904112 | −0.452056 | − | 0.891990i | \(-0.649309\pi\) | ||||
−0.452056 | + | 0.891990i | \(0.649309\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −3.09586 | −0.268445 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −11.6669 | −1.00413 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 7.99811 | 0.683324 | 0.341662 | − | 0.939823i | \(-0.389010\pi\) | ||||
0.341662 | + | 0.939823i | \(0.389010\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 16.5659 | 1.40510 | 0.702551 | − | 0.711633i | \(-0.252044\pi\) | ||||
0.702551 | + | 0.711633i | \(0.252044\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −21.9381 | −1.84752 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 5.19682 | 0.434580 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 6.78728 | 0.563653 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 7.87764 | 0.649737 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −5.13277 | −0.420493 | −0.210246 | − | 0.977648i | \(-0.567427\pi\) | ||||
−0.210246 | + | 0.977648i | \(0.567427\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −11.7033 | −0.952398 | −0.476199 | − | 0.879337i | \(-0.657986\pi\) | ||||
−0.476199 | + | 0.879337i | \(0.657986\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 33.9518 | 2.74484 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −5.59793 | −0.449637 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 20.2992 | 1.62005 | 0.810026 | − | 0.586393i | \(-0.199453\pi\) | ||||
0.810026 | + | 0.586393i | \(0.199453\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −3.04822 | −0.241740 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 3.93330 | 0.309987 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 14.5405 | 1.13890 | 0.569449 | − | 0.822027i | \(-0.307157\pi\) | ||||
0.569449 | + | 0.822027i | \(0.307157\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 2.62501 | 0.204357 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 2.10737 | 0.163073 | 0.0815366 | − | 0.996670i | \(-0.474017\pi\) | ||||
0.0815366 | + | 0.996670i | \(0.474017\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 36.2378 | 2.78752 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 6.29166 | 0.481135 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −20.9904 | −1.59587 | −0.797935 | − | 0.602743i | \(-0.794074\pi\) | ||||
−0.797935 | + | 0.602743i | \(0.794074\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 11.2936 | 0.853712 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −12.7522 | −0.958511 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −21.3043 | −1.59236 | −0.796179 | − | 0.605062i | \(-0.793148\pi\) | ||||
−0.796179 | + | 0.605062i | \(0.793148\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −13.2130 | −0.982111 | −0.491055 | − | 0.871128i | \(-0.663389\pi\) | ||||
−0.491055 | + | 0.871128i | \(0.663389\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 7.30476 | 0.539983 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 4.83875 | 0.355752 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −3.99656 | −0.292257 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −31.0629 | −2.25949 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −16.2450 | −1.17544 | −0.587722 | − | 0.809063i | \(-0.699975\pi\) | ||||
−0.587722 | + | 0.809063i | \(0.699975\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 16.3832 | 1.17929 | 0.589644 | − | 0.807663i | \(-0.299268\pi\) | ||||
0.589644 | + | 0.807663i | \(0.299268\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 24.8709 | 1.78104 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 10.0911 | 0.718960 | 0.359480 | − | 0.933153i | \(-0.382954\pi\) | ||||
0.359480 | + | 0.933153i | \(0.382954\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −11.3050 | −0.801391 | −0.400695 | − | 0.916211i | \(-0.631231\pi\) | ||||
−0.400695 | + | 0.916211i | \(0.631231\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −38.5359 | −2.71811 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 18.0710 | 1.26833 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 8.90705 | 0.622095 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −7.99357 | −0.555592 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −0.740609 | −0.0512290 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 9.97727 | 0.686864 | 0.343432 | − | 0.939178i | \(-0.388411\pi\) | ||||
0.343432 | + | 0.939178i | \(0.388411\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −45.9735 | −3.15006 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −10.4419 | −0.712134 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −14.9044 | −1.01177 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −42.4759 | −2.87025 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −37.8658 | −2.54713 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −7.63982 | −0.511600 | −0.255800 | − | 0.966730i | \(-0.582339\pi\) | ||||
−0.255800 | + | 0.966730i | \(0.582339\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −22.9517 | −1.53011 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 25.9854 | 1.72471 | 0.862356 | − | 0.506303i | \(-0.168988\pi\) | ||||
0.862356 | + | 0.506303i | \(0.168988\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −10.1641 | −0.671664 | −0.335832 | − | 0.941922i | \(-0.609017\pi\) | ||||
−0.335832 | + | 0.941922i | \(0.609017\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 6.98902 | 0.459844 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −10.3490 | −0.677984 | −0.338992 | − | 0.940789i | \(-0.610086\pi\) | ||||
−0.338992 | + | 0.940789i | \(0.610086\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 8.36849 | 0.545900 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 36.4639 | 2.36858 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 20.8350 | 1.34770 | 0.673850 | − | 0.738868i | \(-0.264639\pi\) | ||||
0.673850 | + | 0.738868i | \(0.264639\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 19.5401 | 1.25869 | 0.629345 | − | 0.777126i | \(-0.283323\pi\) | ||||
0.629345 | + | 0.777126i | \(0.283323\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 5.59350 | 0.358823 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −3.00500 | −0.191983 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −7.01696 | −0.446479 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −8.42602 | −0.533978 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 22.4084 | 1.41441 | 0.707204 | − | 0.707010i | \(-0.249956\pi\) | ||||
0.707204 | + | 0.707010i | \(0.249956\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0.940946 | 0.0591568 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −19.1267 | −1.19776 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −4.89503 | −0.305344 | −0.152672 | − | 0.988277i | \(-0.548788\pi\) | ||||
−0.152672 | + | 0.988277i | \(0.548788\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 12.8830 | 0.800514 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −36.7253 | −2.27324 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 19.6614 | 1.21237 | 0.606186 | − | 0.795323i | \(-0.292699\pi\) | ||||
0.606186 | + | 0.795323i | \(0.292699\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1.16277 | 0.0714287 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −2.38771 | −0.146125 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −12.7626 | −0.778146 | −0.389073 | − | 0.921207i | \(-0.627205\pi\) | ||||
−0.389073 | + | 0.921207i | \(0.627205\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 20.5820 | 1.25027 | 0.625134 | − | 0.780517i | \(-0.285044\pi\) | ||||
0.625134 | + | 0.780517i | \(0.285044\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 66.2181 | 4.00770 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 2.70171 | 0.162919 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −1.81797 | −0.109231 | −0.0546155 | − | 0.998507i | \(-0.517393\pi\) | ||||
−0.0546155 | + | 0.998507i | \(0.517393\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 30.2898 | 1.81341 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 18.1060 | 1.08011 | 0.540057 | − | 0.841628i | \(-0.318403\pi\) | ||||
0.540057 | + | 0.841628i | \(0.318403\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −17.1952 | −1.02215 | −0.511075 | − | 0.859536i | \(-0.670752\pi\) | ||||
−0.511075 | + | 0.859536i | \(0.670752\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −3.54439 | −0.209952 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 23.7148 | 1.39984 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 12.1203 | 0.712956 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −37.3256 | −2.18806 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −26.7819 | −1.56461 | −0.782307 | − | 0.622893i | \(-0.785957\pi\) | ||||
−0.782307 | + | 0.622893i | \(0.785957\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 4.86444 | 0.283218 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −7.43104 | −0.431193 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 8.91508 | 0.515572 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −27.8014 | −1.60245 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 45.8317 | 2.63296 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −2.78647 | −0.159553 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −25.6481 | −1.46382 | −0.731909 | − | 0.681403i | \(-0.761370\pi\) | ||||
−0.731909 | + | 0.681403i | \(0.761370\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 22.4515 | 1.27722 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 21.6832 | 1.22954 | 0.614771 | − | 0.788706i | \(-0.289248\pi\) | ||||
0.614771 | + | 0.788706i | \(0.289248\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 19.9277 | 1.12638 | 0.563189 | − | 0.826328i | \(-0.309574\pi\) | ||||
0.563189 | + | 0.826328i | \(0.309574\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 22.6486 | 1.27610 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 17.9589 | 1.00867 | 0.504335 | − | 0.863508i | \(-0.331738\pi\) | ||||
0.504335 | + | 0.863508i | \(0.331738\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 4.32303 | 0.242043 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −12.3411 | −0.688813 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 5.39632 | 0.300259 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 25.5976 | 1.41990 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −24.0806 | −1.33166 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 22.2809 | 1.22839 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −24.0397 | −1.32134 | −0.660671 | − | 0.750676i | \(-0.729728\pi\) | ||||
−0.660671 | + | 0.750676i | \(0.729728\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −26.1820 | −1.43476 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 14.6999 | 0.803141 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 4.89808 | 0.266815 | 0.133408 | − | 0.991061i | \(-0.457408\pi\) | ||||
0.133408 | + | 0.991061i | \(0.457408\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 20.2548 | 1.10009 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −3.56550 | −0.193083 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 13.6703 | 0.738125 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 4.50317 | 0.242442 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 18.3665 | 0.985968 | 0.492984 | − | 0.870038i | \(-0.335906\pi\) | ||||
0.492984 | + | 0.870038i | \(0.335906\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 26.6377 | 1.42589 | 0.712943 | − | 0.701222i | \(-0.247362\pi\) | ||||
0.712943 | + | 0.701222i | \(0.247362\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −70.4061 | −3.75800 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −4.76409 | −0.253567 | −0.126783 | − | 0.991930i | \(-0.540465\pi\) | ||||
−0.126783 | + | 0.991930i | \(0.540465\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 17.5371 | 0.930771 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −50.9243 | −2.69520 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 11.0425 | 0.582800 | 0.291400 | − | 0.956601i | \(-0.405879\pi\) | ||||
0.291400 | + | 0.956601i | \(0.405879\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −31.8585 | −1.67214 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 16.2028 | 0.848096 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −0.880221 | −0.0459472 | −0.0229736 | − | 0.999736i | \(-0.507313\pi\) | ||||
−0.0229736 | + | 0.999736i | \(0.507313\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −48.1951 | −2.50894 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 3.09586 | 0.160729 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −2.50328 | −0.129615 | −0.0648075 | − | 0.997898i | \(-0.520643\pi\) | ||||
−0.0648075 | + | 0.997898i | \(0.520643\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 30.6518 | 1.58285 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 40.9590 | 2.10950 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −24.5729 | −1.26222 | −0.631112 | − | 0.775692i | \(-0.717401\pi\) | ||||
−0.631112 | + | 0.775692i | \(0.717401\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −3.57459 | −0.183132 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 7.34290 | 0.375204 | 0.187602 | − | 0.982245i | \(-0.439928\pi\) | ||||
0.187602 | + | 0.982245i | \(0.439928\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −2.66603 | −0.135874 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 56.5003 | 2.87207 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 36.1517 | 1.83296 | 0.916482 | − | 0.400075i | \(-0.131016\pi\) | ||||
0.916482 | + | 0.400075i | \(0.131016\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −6.85604 | −0.346725 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −31.5431 | −1.59114 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −13.9095 | −0.699863 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −11.4015 | −0.572224 | −0.286112 | − | 0.958196i | \(-0.592363\pi\) | ||||
−0.286112 | + | 0.958196i | \(0.592363\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −9.43686 | −0.472434 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −28.8683 | −1.44161 | −0.720806 | − | 0.693137i | \(-0.756228\pi\) | ||||
−0.720806 | + | 0.693137i | \(0.756228\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −33.7817 | −1.68279 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −13.6161 | −0.676587 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 3.08195 | 0.152767 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −25.2528 | −1.24867 | −0.624336 | − | 0.781156i | \(-0.714630\pi\) | ||||
−0.624336 | + | 0.781156i | \(0.714630\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 24.3800 | 1.20258 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 12.9514 | 0.637299 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 3.21419 | 0.157778 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 50.4966 | 2.47283 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 19.5676 | 0.955942 | 0.477971 | − | 0.878376i | \(-0.341372\pi\) | ||||
0.477971 | + | 0.878376i | \(0.341372\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 35.8639 | 1.74790 | 0.873950 | − | 0.486015i | \(-0.161550\pi\) | ||||
0.873950 | + | 0.486015i | \(0.161550\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −45.2811 | −2.20164 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −19.6855 | −0.954888 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −7.41892 | −0.359027 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 15.8411 | 0.764814 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 37.6114 | 1.81168 | 0.905839 | − | 0.423621i | \(-0.139241\pi\) | ||||
0.905839 | + | 0.423621i | \(0.139241\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −28.6407 | −1.37638 | −0.688191 | − | 0.725530i | \(-0.741595\pi\) | ||||
−0.688191 | + | 0.725530i | \(0.741595\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 20.6891 | 0.991967 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −1.27050 | −0.0607764 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 26.9827 | 1.28781 | 0.643907 | − | 0.765103i | \(-0.277312\pi\) | ||||
0.643907 | + | 0.765103i | \(0.277312\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 16.2598 | 0.774275 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 8.11043 | 0.385338 | 0.192669 | − | 0.981264i | \(-0.438286\pi\) | ||||
0.192669 | + | 0.981264i | \(0.438286\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0.910815 | 0.0431768 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −15.6458 | −0.740022 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 25.7519 | 1.21531 | 0.607654 | − | 0.794202i | \(-0.292111\pi\) | ||||
0.607654 | + | 0.794202i | \(0.292111\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 5.67319 | 0.267140 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −35.6741 | −1.67612 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −25.2596 | −1.18419 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 20.4909 | 0.958524 | 0.479262 | − | 0.877672i | \(-0.340904\pi\) | ||||
0.479262 | + | 0.877672i | \(0.340904\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 54.1450 | 2.52727 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 1.41508 | 0.0659068 | 0.0329534 | − | 0.999457i | \(-0.489509\pi\) | ||||
0.0329534 | + | 0.999457i | \(0.489509\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −13.8270 | −0.642594 | −0.321297 | − | 0.946978i | \(-0.604119\pi\) | ||||
−0.321297 | + | 0.946978i | \(0.604119\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −17.0637 | −0.791312 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −33.2695 | −1.53953 | −0.769764 | − | 0.638329i | \(-0.779626\pi\) | ||||
−0.769764 | + | 0.638329i | \(0.779626\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 39.1381 | 1.80723 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 61.8765 | 2.85112 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −6.65081 | −0.305805 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −3.64796 | −0.167380 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −6.29166 | −0.288075 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −6.22234 | −0.284306 | −0.142153 | − | 0.989845i | \(-0.545402\pi\) | ||||
−0.142153 | + | 0.989845i | \(0.545402\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 29.2003 | 1.33142 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 11.9896 | 0.545544 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 14.2382 | 0.646524 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −13.4589 | −0.609881 | −0.304941 | − | 0.952371i | \(-0.598637\pi\) | ||||
−0.304941 | + | 0.952371i | \(0.598637\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 44.3226 | 2.00434 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −23.0456 | −1.04003 | −0.520016 | − | 0.854156i | \(-0.674074\pi\) | ||||
−0.520016 | + | 0.854156i | \(0.674074\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −31.4991 | −1.41865 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 5.41813 | 0.243527 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 46.6920 | 2.09442 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 19.9850 | 0.894650 | 0.447325 | − | 0.894372i | \(-0.352377\pi\) | ||||
0.447325 | + | 0.894372i | \(0.352377\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 6.42373 | 0.286991 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −7.04829 | −0.314268 | −0.157134 | − | 0.987577i | \(-0.550225\pi\) | ||||
−0.157134 | + | 0.987577i | \(0.550225\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −17.4830 | −0.777982 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 110.461 | 4.90574 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 18.2695 | 0.809780 | 0.404890 | − | 0.914365i | \(-0.367310\pi\) | ||||
0.404890 | + | 0.914365i | \(0.367310\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 43.1397 | 1.90839 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 10.0337 | 0.442999 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −8.56433 | −0.377390 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 5.33016 | 0.234420 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −63.9834 | −2.80856 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −35.5708 | −1.55839 | −0.779193 | − | 0.626784i | \(-0.784371\pi\) | ||||
−0.779193 | + | 0.626784i | \(0.784371\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −17.0717 | −0.746495 | −0.373248 | − | 0.927732i | \(-0.621756\pi\) | ||||
−0.373248 | + | 0.927732i | \(0.621756\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 34.4253 | 1.50244 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 25.9794 | 1.13168 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −21.3858 | −0.929818 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −26.3210 | −1.14223 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 53.7511 | 2.32822 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 4.70763 | 0.203529 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −64.9402 | −2.80238 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −1.91398 | −0.0824411 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −43.1129 | −1.85357 | −0.926785 | − | 0.375592i | \(-0.877439\pi\) | ||||
−0.926785 | + | 0.375592i | \(0.877439\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −40.2760 | −1.72841 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 9.18580 | 0.393476 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −21.0629 | −0.900586 | −0.450293 | − | 0.892881i | \(-0.648680\pi\) | ||||
−0.450293 | + | 0.892881i | \(0.648680\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 15.0773 | 0.643485 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −5.83714 | −0.248670 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −37.0337 | −1.57483 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 14.7496 | 0.626085 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −7.64874 | −0.324088 | −0.162044 | − | 0.986784i | \(-0.551809\pi\) | ||||
−0.162044 | + | 0.986784i | \(0.551809\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −63.0137 | −2.66520 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −12.1824 | −0.514341 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −36.5312 | −1.53961 | −0.769803 | − | 0.638282i | \(-0.779645\pi\) | ||||
−0.769803 | + | 0.638282i | \(0.779645\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −7.72640 | −0.325052 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −36.2524 | −1.52246 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −17.1777 | −0.720125 | −0.360063 | − | 0.932928i | \(-0.617245\pi\) | ||||
−0.360063 | + | 0.932928i | \(0.617245\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −31.0730 | −1.30037 | −0.650183 | − | 0.759777i | \(-0.725308\pi\) | ||||
−0.650183 | + | 0.759777i | \(0.725308\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −49.5182 | −2.06865 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 4.63474 | 0.193282 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −12.0608 | −0.502096 | −0.251048 | − | 0.967975i | \(-0.580775\pi\) | ||||
−0.251048 | + | 0.967975i | \(0.580775\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 49.9396 | 2.07542 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 8.55770 | 0.355033 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0.740609 | 0.0306729 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 51.3346 | 2.12242 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 35.7852 | 1.47701 | 0.738507 | − | 0.674245i | \(-0.235531\pi\) | ||||
0.738507 | + | 0.674245i | \(0.235531\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 4.81429 | 0.198369 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 30.7599 | 1.26529 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 40.8186 | 1.67622 | 0.838110 | − | 0.545501i | \(-0.183661\pi\) | ||||
0.838110 | + | 0.545501i | \(0.183661\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 19.4256 | 0.796372 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −34.4602 | −1.41036 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 7.09856 | 0.290039 | 0.145020 | − | 0.989429i | \(-0.453675\pi\) | ||||
0.145020 | + | 0.989429i | \(0.453675\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 16.6077 | 0.677443 | 0.338722 | − | 0.940887i | \(-0.390006\pi\) | ||||
0.338722 | + | 0.940887i | \(0.390006\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −79.5396 | −3.23910 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 12.1527 | 0.494079 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −36.8221 | −1.49456 | −0.747281 | − | 0.664508i | \(-0.768641\pi\) | ||||
−0.747281 | + | 0.664508i | \(0.768641\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 55.0843 | 2.23213 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 50.5011 | 2.04306 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −12.0996 | −0.488699 | −0.244350 | − | 0.969687i | \(-0.578574\pi\) | ||||
−0.244350 | + | 0.969687i | \(0.578574\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 27.1507 | 1.09482 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −0.604854 | −0.0243505 | −0.0121752 | − | 0.999926i | \(-0.503876\pi\) | ||||
−0.0121752 | + | 0.999926i | \(0.503876\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −16.5794 | −0.666383 | −0.333191 | − | 0.942859i | \(-0.608126\pi\) | ||||
−0.333191 | + | 0.942859i | \(0.608126\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −12.7479 | −0.511554 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 2.42502 | 0.0971565 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 6.54735 | 0.261894 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −2.25754 | −0.0901574 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −22.4561 | −0.895385 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 21.7550 | 0.866052 | 0.433026 | − | 0.901381i | \(-0.357446\pi\) | ||||
0.433026 | + | 0.901381i | \(0.357446\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 30.4129 | 1.20881 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 1.36356 | 0.0541113 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −18.1342 | −0.718504 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −94.8913 | −3.75384 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −0.517139 | −0.0204257 | −0.0102129 | − | 0.999948i | \(-0.503251\pi\) | ||||
−0.0102129 | + | 0.999948i | \(0.503251\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −33.9671 | −1.33953 | −0.669766 | − | 0.742572i | \(-0.733606\pi\) | ||||
−0.669766 | + | 0.742572i | \(0.733606\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −31.8294 | −1.25328 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −32.8904 | −1.29305 | −0.646527 | − | 0.762891i | \(-0.723779\pi\) | ||||
−0.646527 | + | 0.762891i | \(0.723779\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 3.09832 | 0.121620 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −45.4318 | −1.78061 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −1.17030 | −0.0457975 | −0.0228988 | − | 0.999738i | \(-0.507290\pi\) | ||||
−0.0228988 | + | 0.999738i | \(0.507290\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 12.0324 | 0.470146 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −87.6720 | −3.42041 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −3.49037 | −0.135966 | −0.0679828 | − | 0.997686i | \(-0.521656\pi\) | ||||
−0.0679828 | + | 0.997686i | \(0.521656\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 12.2910 | 0.478064 | 0.239032 | − | 0.971012i | \(-0.423170\pi\) | ||||
0.239032 | + | 0.971012i | \(0.423170\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −115.423 | −4.48267 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 3.59979 | 0.139594 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 7.41611 | 0.287153 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −23.2879 | −0.900361 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −1.77479 | −0.0685152 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −2.72180 | −0.104918 | −0.0524588 | − | 0.998623i | \(-0.516706\pi\) | ||||
−0.0524588 | + | 0.998623i | \(0.516706\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −36.6025 | −1.40883 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −32.6667 | −1.25548 | −0.627742 | − | 0.778421i | \(-0.716021\pi\) | ||||
−0.627742 | + | 0.778421i | \(0.716021\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 37.9089 | 1.45481 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 79.2093 | 3.03531 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −41.0703 | −1.57151 | −0.785757 | − | 0.618536i | \(-0.787726\pi\) | ||||
−0.785757 | + | 0.618536i | \(0.787726\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −9.29999 | −0.355334 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −30.9825 | −1.18206 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 7.01696 | 0.267325 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −27.3355 | −1.03989 | −0.519946 | − | 0.854199i | \(-0.674048\pi\) | ||||
−0.519946 | + | 0.854199i | \(0.674048\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 14.4256 | 0.547984 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −19.2624 | −0.730665 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −41.3367 | −1.56574 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −31.5460 | −1.19318 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 12.7553 | 0.481760 | 0.240880 | − | 0.970555i | \(-0.422564\pi\) | ||||
0.240880 | + | 0.970555i | \(0.422564\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −4.16138 | −0.156949 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 25.5090 | 0.960726 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −46.5480 | −1.75062 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 3.78797 | 0.142260 | 0.0711302 | − | 0.997467i | \(-0.477339\pi\) | ||||
0.0711302 | + | 0.997467i | \(0.477339\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 75.2629 | 2.82258 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −6.11657 | −0.229067 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −6.04274 | −0.225985 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 63.5096 | 2.37181 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −35.4850 | −1.32337 | −0.661685 | − | 0.749782i | \(-0.730158\pi\) | ||||
−0.661685 | + | 0.749782i | \(0.730158\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −22.8023 | −0.849203 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 59.5627 | 2.21516 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 21.2936 | 0.790825 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −19.8987 | −0.738002 | −0.369001 | − | 0.929429i | \(-0.620300\pi\) | ||||
−0.369001 | + | 0.929429i | \(0.620300\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −18.0797 | −0.669619 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 48.4600 | 1.79236 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −26.2945 | −0.971210 | −0.485605 | − | 0.874178i | \(-0.661401\pi\) | ||||
−0.485605 | + | 0.874178i | \(0.661401\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −9.15992 | −0.337869 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 9.36283 | 0.344884 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −16.4215 | −0.604076 | −0.302038 | − | 0.953296i | \(-0.597667\pi\) | ||||
−0.302038 | + | 0.953296i | \(0.597667\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −21.3893 | −0.785754 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 4.23096 | 0.155219 | 0.0776094 | − | 0.996984i | \(-0.475271\pi\) | ||||
0.0776094 | + | 0.996984i | \(0.475271\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 5.96825 | 0.218660 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −17.3917 | −0.636328 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 12.5340 | 0.457981 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −32.4440 | −1.18390 | −0.591948 | − | 0.805976i | \(-0.701641\pi\) | ||||
−0.591948 | + | 0.805976i | \(0.701641\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 68.3059 | 2.48920 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 13.6083 | 0.495255 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −28.9795 | −1.05328 | −0.526640 | − | 0.850089i | \(-0.676548\pi\) | ||||
−0.526640 | + | 0.850089i | \(0.676548\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 2.86821 | 0.104110 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −8.20808 | −0.297543 | −0.148771 | − | 0.988872i | \(-0.547532\pi\) | ||||
−0.148771 | + | 0.988872i | \(0.547532\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 24.4570 | 0.885401 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −39.4783 | −1.42734 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 29.3553 | 1.05996 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 17.0560 | 0.615056 | 0.307528 | − | 0.951539i | \(-0.400498\pi\) | ||||
0.307528 | + | 0.951539i | \(0.400498\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −14.9212 | −0.537372 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 2.48355 | 0.0893271 | 0.0446636 | − | 0.999002i | \(-0.485778\pi\) | ||||
0.0446636 | + | 0.999002i | \(0.485778\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −17.5623 | −0.630857 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 39.2704 | 1.40882 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −7.66017 | −0.274454 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 11.1699 | 0.399691 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −58.5681 | −2.09305 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −23.6034 | −0.842441 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 19.2381 | 0.685764 | 0.342882 | − | 0.939378i | \(-0.388597\pi\) | ||||
0.342882 | + | 0.939378i | \(0.388597\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 59.9322 | 2.13364 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −20.5713 | −0.731433 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −16.8155 | −0.597134 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 3.54439 | 0.125707 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 24.9359 | 0.883275 | 0.441637 | − | 0.897194i | \(-0.354398\pi\) | ||||
0.441637 | + | 0.897194i | \(0.354398\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −38.8373 | −1.37397 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −4.92833 | −0.174134 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 10.3201 | 0.364189 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −4.57354 | −0.161196 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −38.9031 | −1.36945 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 12.2484 | 0.430631 | 0.215316 | − | 0.976545i | \(-0.430922\pi\) | ||||
0.215316 | + | 0.976545i | \(0.430922\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 24.1065 | 0.846494 | 0.423247 | − | 0.906014i | \(-0.360890\pi\) | ||||
0.423247 | + | 0.906014i | \(0.360890\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 62.7386 | 2.20034 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −16.9073 | −0.592236 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 8.98019 | 0.314177 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 136.677 | 4.77588 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −4.27035 | −0.149036 | −0.0745181 | − | 0.997220i | \(-0.523742\pi\) | ||||
−0.0745181 | + | 0.997220i | \(0.523742\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 1.20527 | 0.0420129 | 0.0210065 | − | 0.999779i | \(-0.493313\pi\) | ||||
0.0210065 | + | 0.999779i | \(0.493313\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 8.23540 | 0.286720 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −0.801213 | −0.0278609 | −0.0139305 | − | 0.999903i | \(-0.504434\pi\) | ||||
−0.0139305 | + | 0.999903i | \(0.504434\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 30.5026 | 1.05940 | 0.529699 | − | 0.848186i | \(-0.322305\pi\) | ||||
0.529699 | + | 0.848186i | \(0.322305\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −5.54157 | −0.192235 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 13.9459 | 0.483197 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −2.45040 | −0.0847995 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 48.3051 | 1.66967 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 8.03688 | 0.277464 | 0.138732 | − | 0.990330i | \(-0.455697\pi\) | ||||
0.138732 | + | 0.990330i | \(0.455697\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 5.07218 | 0.174903 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 55.1911 | 1.90088 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −42.1364 | −1.44954 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 32.3564 | 1.11178 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −52.4148 | −1.79887 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 5.28705 | 0.181238 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −10.3377 | −0.353956 | −0.176978 | − | 0.984215i | \(-0.556632\pi\) | ||||
−0.176978 | + | 0.984215i | \(0.556632\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −7.31578 | −0.250194 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −7.72909 | −0.264021 | −0.132010 | − | 0.991248i | \(-0.542143\pi\) | ||||
−0.132010 | + | 0.991248i | \(0.542143\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −12.0954 | −0.412689 | −0.206345 | − | 0.978479i | \(-0.566157\pi\) | ||||
−0.206345 | + | 0.978479i | \(0.566157\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 72.2879 | 2.46357 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −19.6215 | −0.667925 | −0.333963 | − | 0.942586i | \(-0.608386\pi\) | ||||
−0.333963 | + | 0.942586i | \(0.608386\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 24.4071 | 0.829866 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 36.9452 | 1.25473 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −8.85941 | −0.300535 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 88.7090 | 3.00579 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −77.0415 | −2.60746 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −31.1308 | −1.05241 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −0.158867 | −0.00536456 | −0.00268228 | − | 0.999996i | \(-0.500854\pi\) | ||||
−0.00268228 | + | 0.999996i | \(0.500854\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −81.6371 | −2.75355 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 0.142683 | 0.00480710 | 0.00240355 | − | 0.999997i | \(-0.499235\pi\) | ||||
0.00240355 | + | 0.999997i | \(0.499235\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −12.5685 | −0.422964 | −0.211482 | − | 0.977382i | \(-0.567829\pi\) | ||||
−0.211482 | + | 0.977382i | \(0.567829\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 14.8279 | 0.498434 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 9.10854 | 0.305835 | 0.152917 | − | 0.988239i | \(-0.451133\pi\) | ||||
0.152917 | + | 0.988239i | \(0.451133\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 3.63045 | 0.121761 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −8.67251 | −0.290540 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −7.19701 | −0.240839 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 24.7721 | 0.828040 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 27.1751 | 0.907352 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −28.1017 | −0.937243 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −5.39632 | −0.179777 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −84.7449 | −2.82013 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 15.3637 | 0.510706 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 48.1536 | 1.59891 | 0.799457 | − | 0.600723i | \(-0.205121\pi\) | ||||
0.799457 | + | 0.600723i | \(0.205121\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 94.5986 | 3.13764 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 26.1851 | 0.867552 | 0.433776 | − | 0.901021i | \(-0.357181\pi\) | ||||
0.433776 | + | 0.901021i | \(0.357181\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 2.04722 | 0.0677531 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −8.49379 | −0.280796 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 32.0360 | 1.05792 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −27.3973 | −0.903755 | −0.451878 | − | 0.892080i | \(-0.649246\pi\) | ||||
−0.451878 | + | 0.892080i | \(0.649246\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −78.1812 | −2.57616 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 105.830 | 3.48345 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 15.1805 | 0.499133 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 46.3408 | 1.52203 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 0.708375 | 0.0232410 | 0.0116205 | − | 0.999932i | \(-0.496301\pi\) | ||||
0.0116205 | + | 0.999932i | \(0.496301\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 2.58434 | 0.0846983 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 66.0952 | 2.16386 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 4.64710 | 0.151976 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −0.0101807 | −0.000332587 0 | −0.000166294 | − | 1.00000i | \(-0.500053\pi\) | ||||
−0.000166294 | 1.00000i | \(0.500053\pi\) | ||||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 60.7439 | 1.98230 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 19.8896 | 0.648381 | 0.324191 | − | 0.945992i | \(-0.394908\pi\) | ||||
0.324191 | + | 0.945992i | \(0.394908\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 9.73227 | 0.316926 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 36.1192 | 1.17496 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −6.65944 | −0.216403 | −0.108201 | − | 0.994129i | \(-0.534509\pi\) | ||||
−0.108201 | + | 0.994129i | \(0.534509\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 97.7789 | 3.17404 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 54.7426 | 1.77515 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 27.1133 | 0.878286 | 0.439143 | − | 0.898417i | \(-0.355282\pi\) | ||||
0.439143 | + | 0.898417i | \(0.355282\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 18.8892 | 0.611241 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 13.1776 | 0.425970 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −24.7610 | −0.799574 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −7.82263 | −0.252343 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −25.4725 | −0.820841 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −19.0500 | −0.613240 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 12.9830 | 0.417504 | 0.208752 | − | 0.977969i | \(-0.433060\pi\) | ||||
0.208752 | + | 0.977969i | \(0.433060\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 16.4492 | 0.528424 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 3.01652 | 0.0968047 | 0.0484024 | − | 0.998828i | \(-0.484587\pi\) | ||||
0.0484024 | + | 0.998828i | \(0.484587\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −51.2857 | −1.64414 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 78.0271 | 2.49887 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 52.7315 | 1.68703 | 0.843515 | − | 0.537105i | \(-0.180482\pi\) | ||||
0.843515 | + | 0.537105i | \(0.180482\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0.580128 | 0.0185410 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −49.7034 | −1.58691 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 2.56594 | 0.0818409 | 0.0409204 | − | 0.999162i | \(-0.486971\pi\) | ||||
0.0409204 | + | 0.999162i | \(0.486971\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −11.7337 | −0.373866 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 67.9172 | 2.16183 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −11.4094 | −0.362797 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −27.2810 | −0.866608 | −0.433304 | − | 0.901248i | \(-0.642652\pi\) | ||||
−0.433304 | + | 0.901248i | \(0.642652\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −73.2784 | −2.32542 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 13.1452 | 0.416730 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 54.1487 | 1.71491 | 0.857453 | − | 0.514562i | \(-0.172046\pi\) | ||||
0.857453 | + | 0.514562i | \(0.172046\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −41.7540 | −1.32104 |
(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 | 4028.2.a.c.1.19 | ✓ | 19 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4028.2.a.c.1.19 | ✓ | 19 | 1.1 | even | 1 | trivial |