Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4016,2,Mod(1,4016)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4016, 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("4016.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4016 = 2^{4} \cdot 251 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4016.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: | \(32.0679214517\) |
Analytic rank: | \(0\) |
Dimension: | \(23\) |
Twist minimal: | no (minimal twist has level 2008) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.18 | ||
Character | \(\chi\) | \(=\) | 4016.1 |
$q$-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 | ||||||||
\(3\) | 2.13165 | 1.23071 | 0.615356 | − | 0.788250i | \(-0.289012\pi\) | ||||
0.615356 | + | 0.788250i | \(0.289012\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.257423 | 0.115123 | 0.0575615 | − | 0.998342i | \(-0.481667\pi\) | ||||
0.0575615 | + | 0.998342i | \(0.481667\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.578263 | −0.218563 | −0.109281 | − | 0.994011i | \(-0.534855\pi\) | ||||
−0.109281 | + | 0.994011i | \(0.534855\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.54395 | 0.514650 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.44278 | 0.435015 | 0.217507 | − | 0.976059i | \(-0.430207\pi\) | ||||
0.217507 | + | 0.976059i | \(0.430207\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.23315 | 0.342015 | 0.171008 | − | 0.985270i | \(-0.445298\pi\) | ||||
0.171008 | + | 0.985270i | \(0.445298\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.548737 | 0.141683 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 3.22998 | 0.783386 | 0.391693 | − | 0.920096i | \(-0.371890\pi\) | ||||
0.391693 | + | 0.920096i | \(0.371890\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.16232 | 0.496071 | 0.248036 | − | 0.968751i | \(-0.420215\pi\) | ||||
0.248036 | + | 0.968751i | \(0.420215\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.23266 | −0.268988 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 3.59035 | 0.748639 | 0.374320 | − | 0.927300i | \(-0.377876\pi\) | ||||
0.374320 | + | 0.927300i | \(0.377876\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.93373 | −0.986747 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −3.10379 | −0.597325 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.34015 | 0.248860 | 0.124430 | − | 0.992228i | \(-0.460290\pi\) | ||||
0.124430 | + | 0.992228i | \(0.460290\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.91300 | −0.523191 | −0.261595 | − | 0.965178i | \(-0.584249\pi\) | ||||
−0.261595 | + | 0.965178i | \(0.584249\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 3.07551 | 0.535377 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −0.148858 | −0.0251616 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 7.43825 | 1.22284 | 0.611421 | − | 0.791306i | \(-0.290598\pi\) | ||||
0.611421 | + | 0.791306i | \(0.290598\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 2.62866 | 0.420922 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 9.61132 | 1.50104 | 0.750518 | − | 0.660850i | \(-0.229804\pi\) | ||||
0.750518 | + | 0.660850i | \(0.229804\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4.00610 | 0.610925 | 0.305462 | − | 0.952204i | \(-0.401189\pi\) | ||||
0.305462 | + | 0.952204i | \(0.401189\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0.397448 | 0.0592481 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 7.55848 | 1.10252 | 0.551259 | − | 0.834334i | \(-0.314148\pi\) | ||||
0.551259 | + | 0.834334i | \(0.314148\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.66561 | −0.952230 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 6.88521 | 0.964122 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −5.08800 | −0.698890 | −0.349445 | − | 0.936957i | \(-0.613630\pi\) | ||||
−0.349445 | + | 0.936957i | \(0.613630\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0.371405 | 0.0500802 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 4.60933 | 0.610520 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 4.79877 | 0.624747 | 0.312374 | − | 0.949959i | \(-0.398876\pi\) | ||||
0.312374 | + | 0.949959i | \(0.398876\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −0.119891 | −0.0153504 | −0.00767522 | − | 0.999971i | \(-0.502443\pi\) | ||||
−0.00767522 | + | 0.999971i | \(0.502443\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −0.892809 | −0.112483 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0.317442 | 0.0393738 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 8.76927 | 1.07134 | 0.535668 | − | 0.844429i | \(-0.320060\pi\) | ||||
0.535668 | + | 0.844429i | \(0.320060\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 7.65338 | 0.921359 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −14.2487 | −1.69101 | −0.845504 | − | 0.533969i | \(-0.820700\pi\) | ||||
−0.845504 | + | 0.533969i | \(0.820700\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 10.5417 | 1.23381 | 0.616905 | − | 0.787038i | \(-0.288386\pi\) | ||||
0.616905 | + | 0.787038i | \(0.288386\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −10.5170 | −1.21440 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −0.834306 | −0.0950780 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −14.7249 | −1.65669 | −0.828343 | − | 0.560222i | \(-0.810716\pi\) | ||||
−0.828343 | + | 0.560222i | \(0.810716\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −11.2481 | −1.24979 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −9.70080 | −1.06480 | −0.532401 | − | 0.846492i | \(-0.678710\pi\) | ||||
−0.532401 | + | 0.846492i | \(0.678710\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0.831472 | 0.0901858 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 2.85674 | 0.306275 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 15.5478 | 1.64807 | 0.824034 | − | 0.566540i | \(-0.191718\pi\) | ||||
0.824034 | + | 0.566540i | \(0.191718\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −0.713087 | −0.0747518 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −6.20952 | −0.643897 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0.556632 | 0.0571092 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 17.4458 | 1.77135 | 0.885676 | − | 0.464303i | \(-0.153695\pi\) | ||||
0.885676 | + | 0.464303i | \(0.153695\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 2.22758 | 0.223880 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 11.4484 | 1.13916 | 0.569580 | − | 0.821936i | \(-0.307106\pi\) | ||||
0.569580 | + | 0.821936i | \(0.307106\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −0.147959 | −0.0145789 | −0.00728943 | − | 0.999973i | \(-0.502320\pi\) | ||||
−0.00728943 | + | 0.999973i | \(0.502320\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −0.317314 | −0.0309667 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 0.777070 | 0.0751221 | 0.0375611 | − | 0.999294i | \(-0.488041\pi\) | ||||
0.0375611 | + | 0.999294i | \(0.488041\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −2.23762 | −0.214325 | −0.107162 | − | 0.994242i | \(-0.534176\pi\) | ||||
−0.107162 | + | 0.994242i | \(0.534176\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 15.8558 | 1.50496 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 10.2350 | 0.962831 | 0.481416 | − | 0.876492i | \(-0.340123\pi\) | ||||
0.481416 | + | 0.876492i | \(0.340123\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0.924238 | 0.0861857 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 1.90393 | 0.176018 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −1.86778 | −0.171219 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −8.91839 | −0.810762 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 20.4880 | 1.84734 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −2.55717 | −0.228720 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −18.6170 | −1.65200 | −0.825998 | − | 0.563674i | \(-0.809388\pi\) | ||||
−0.825998 | + | 0.563674i | \(0.809388\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 8.53962 | 0.751872 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 6.50800 | 0.568607 | 0.284303 | − | 0.958734i | \(-0.408238\pi\) | ||||
0.284303 | + | 0.958734i | \(0.408238\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.25039 | −0.108423 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −0.798988 | −0.0687659 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 18.2925 | 1.56283 | 0.781415 | − | 0.624012i | \(-0.214498\pi\) | ||||
0.781415 | + | 0.624012i | \(0.214498\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 12.7384 | 1.08046 | 0.540231 | − | 0.841517i | \(-0.318337\pi\) | ||||
0.540231 | + | 0.841517i | \(0.318337\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 16.1121 | 1.35688 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 1.77917 | 0.148782 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0.344986 | 0.0286495 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −14.2088 | −1.17192 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 3.89636 | 0.319203 | 0.159601 | − | 0.987182i | \(-0.448979\pi\) | ||||
0.159601 | + | 0.987182i | \(0.448979\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −14.6934 | −1.19573 | −0.597865 | − | 0.801597i | \(-0.703984\pi\) | ||||
−0.597865 | + | 0.801597i | \(0.703984\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 4.98694 | 0.403170 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −0.749874 | −0.0602313 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 9.49373 | 0.757682 | 0.378841 | − | 0.925462i | \(-0.376323\pi\) | ||||
0.378841 | + | 0.925462i | \(0.376323\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −10.8458 | −0.860132 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −2.07617 | −0.163625 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 16.6323 | 1.30274 | 0.651369 | − | 0.758761i | \(-0.274195\pi\) | ||||
0.651369 | + | 0.758761i | \(0.274195\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0.791707 | 0.0616343 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −5.05080 | −0.390843 | −0.195421 | − | 0.980719i | \(-0.562607\pi\) | ||||
−0.195421 | + | 0.980719i | \(0.562607\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −11.4793 | −0.883026 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 3.33852 | 0.255303 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 5.19947 | 0.395308 | 0.197654 | − | 0.980272i | \(-0.436668\pi\) | ||||
0.197654 | + | 0.980272i | \(0.436668\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 2.85299 | 0.215666 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 10.2293 | 0.768883 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −4.38408 | −0.327681 | −0.163841 | − | 0.986487i | \(-0.552388\pi\) | ||||
−0.163841 | + | 0.986487i | \(0.552388\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 12.9053 | 0.959241 | 0.479621 | − | 0.877476i | \(-0.340774\pi\) | ||||
0.479621 | + | 0.877476i | \(0.340774\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −0.255566 | −0.0188920 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 1.91478 | 0.140777 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 4.66016 | 0.340784 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 1.79481 | 0.130553 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −14.6014 | −1.05652 | −0.528261 | − | 0.849082i | \(-0.677156\pi\) | ||||
−0.528261 | + | 0.849082i | \(0.677156\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 0.612232 | 0.0440694 | 0.0220347 | − | 0.999757i | \(-0.492986\pi\) | ||||
0.0220347 | + | 0.999757i | \(0.492986\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0.676677 | 0.0484578 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −11.7607 | −0.837914 | −0.418957 | − | 0.908006i | \(-0.637604\pi\) | ||||
−0.418957 | + | 0.908006i | \(0.637604\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 5.95001 | 0.421785 | 0.210892 | − | 0.977509i | \(-0.432363\pi\) | ||||
0.210892 | + | 0.977509i | \(0.432363\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 18.6930 | 1.31851 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −0.774961 | −0.0543916 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 2.47417 | 0.172804 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 5.54332 | 0.385287 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 3.11976 | 0.215798 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −23.4565 | −1.61481 | −0.807407 | − | 0.589995i | \(-0.799130\pi\) | ||||
−0.807407 | + | 0.589995i | \(0.799130\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −30.3733 | −2.08114 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 1.03126 | 0.0703315 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1.68448 | 0.114350 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 22.4712 | 1.51846 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 3.98306 | 0.267930 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 13.7654 | 0.921800 | 0.460900 | − | 0.887452i | \(-0.347527\pi\) | ||||
0.460900 | + | 0.887452i | \(0.347527\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −7.61744 | −0.507829 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −25.3420 | −1.68201 | −0.841005 | − | 0.541028i | \(-0.818035\pi\) | ||||
−0.841005 | + | 0.541028i | \(0.818035\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −8.16364 | −0.539468 | −0.269734 | − | 0.962935i | \(-0.586936\pi\) | ||||
−0.269734 | + | 0.962935i | \(0.586936\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −1.77845 | −0.117014 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 4.62470 | 0.302974 | 0.151487 | − | 0.988459i | \(-0.451594\pi\) | ||||
0.151487 | + | 0.988459i | \(0.451594\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1.94573 | 0.126925 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −31.3885 | −2.03890 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 4.88042 | 0.315688 | 0.157844 | − | 0.987464i | \(-0.449546\pi\) | ||||
0.157844 | + | 0.987464i | \(0.449546\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 0.652332 | 0.0420204 | 0.0210102 | − | 0.999779i | \(-0.493312\pi\) | ||||
0.0210102 | + | 0.999779i | \(0.493312\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −14.6656 | −0.940800 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −1.71588 | −0.109624 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 2.66648 | 0.169664 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −20.6788 | −1.31046 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1.00000 | 0.0631194 | ||||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 5.18008 | 0.325669 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 1.77241 | 0.110993 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −21.6636 | −1.35134 | −0.675670 | − | 0.737205i | \(-0.736145\pi\) | ||||
−0.675670 | + | 0.737205i | \(0.736145\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −4.30127 | −0.267268 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 2.06913 | 0.128076 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −24.1926 | −1.49178 | −0.745889 | − | 0.666070i | \(-0.767975\pi\) | ||||
−0.745889 | + | 0.666070i | \(0.767975\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1.30977 | −0.0804584 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 33.1426 | 2.02830 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −16.0347 | −0.977652 | −0.488826 | − | 0.872381i | \(-0.662575\pi\) | ||||
−0.488826 | + | 0.872381i | \(0.662575\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 28.6525 | 1.74051 | 0.870257 | − | 0.492598i | \(-0.163953\pi\) | ||||
0.870257 | + | 0.492598i | \(0.163953\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −1.52005 | −0.0919979 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −7.11829 | −0.429249 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 19.8294 | 1.19143 | 0.595717 | − | 0.803194i | \(-0.296868\pi\) | ||||
0.595717 | + | 0.803194i | \(0.296868\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −4.49753 | −0.269260 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 7.04601 | 0.420330 | 0.210165 | − | 0.977666i | \(-0.432600\pi\) | ||||
0.210165 | + | 0.977666i | \(0.432600\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −16.2260 | −0.964534 | −0.482267 | − | 0.876024i | \(-0.660186\pi\) | ||||
−0.482267 | + | 0.876024i | \(0.660186\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 1.18655 | 0.0702850 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −5.55787 | −0.328070 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −6.56721 | −0.386306 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 37.1884 | 2.18002 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 9.06228 | 0.529424 | 0.264712 | − | 0.964327i | \(-0.414723\pi\) | ||||
0.264712 | + | 0.964327i | \(0.414723\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1.23531 | 0.0719228 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −4.47809 | −0.259845 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 4.42745 | 0.256046 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2.31658 | −0.133525 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 24.4041 | 1.40198 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −0.0308626 | −0.00176719 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 23.0105 | 1.31328 | 0.656638 | − | 0.754206i | \(-0.271978\pi\) | ||||
0.656638 | + | 0.754206i | \(0.271978\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −0.315398 | −0.0179424 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 9.22635 | 0.523179 | 0.261589 | − | 0.965179i | \(-0.415753\pi\) | ||||
0.261589 | + | 0.965179i | \(0.415753\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 11.6420 | 0.658045 | 0.329022 | − | 0.944322i | \(-0.393281\pi\) | ||||
0.329022 | + | 0.944322i | \(0.393281\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −0.229830 | −0.0129494 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −11.7025 | −0.657276 | −0.328638 | − | 0.944456i | \(-0.606590\pi\) | ||||
−0.328638 | + | 0.944456i | \(0.606590\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1.93355 | 0.108258 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 1.65644 | 0.0924537 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 6.98427 | 0.388615 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −6.08405 | −0.337482 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −4.76983 | −0.263772 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −4.37079 | −0.240969 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 2.26578 | 0.124539 | 0.0622694 | − | 0.998059i | \(-0.480166\pi\) | ||||
0.0622694 | + | 0.998059i | \(0.480166\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 11.4843 | 0.629336 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 2.25741 | 0.123336 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −8.58164 | −0.467472 | −0.233736 | − | 0.972300i | \(-0.575095\pi\) | ||||
−0.233736 | + | 0.972300i | \(0.575095\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 21.8176 | 1.18497 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −4.20282 | −0.227596 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 7.90232 | 0.426685 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 1.97016 | 0.106070 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −17.8709 | −0.959361 | −0.479681 | − | 0.877443i | \(-0.659248\pi\) | ||||
−0.479681 | + | 0.877443i | \(0.659248\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −22.8884 | −1.22519 | −0.612594 | − | 0.790398i | \(-0.709874\pi\) | ||||
−0.612594 | + | 0.790398i | \(0.709874\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −3.82745 | −0.204294 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −12.4512 | −0.662710 | −0.331355 | − | 0.943506i | \(-0.607506\pi\) | ||||
−0.331355 | + | 0.943506i | \(0.607506\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −3.66794 | −0.194674 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −3.98146 | −0.210721 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −25.4272 | −1.34200 | −0.670998 | − | 0.741459i | \(-0.734134\pi\) | ||||
−0.670998 | + | 0.741459i | \(0.734134\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −14.3244 | −0.753913 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −19.0109 | −0.997814 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 2.71367 | 0.142040 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −34.2480 | −1.78773 | −0.893866 | − | 0.448335i | \(-0.852017\pi\) | ||||
−0.893866 | + | 0.448335i | \(0.852017\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 14.8394 | 0.772508 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 2.94220 | 0.152751 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 25.8031 | 1.33603 | 0.668017 | − | 0.744146i | \(-0.267143\pi\) | ||||
0.668017 | + | 0.744146i | \(0.267143\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −5.45101 | −0.281489 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 1.65261 | 0.0851139 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 4.65289 | 0.239003 | 0.119502 | − | 0.992834i | \(-0.461870\pi\) | ||||
0.119502 | + | 0.992834i | \(0.461870\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −39.6851 | −2.03313 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 10.8385 | 0.553823 | 0.276912 | − | 0.960895i | \(-0.410689\pi\) | ||||
0.276912 | + | 0.960895i | \(0.410689\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −0.214770 | −0.0109457 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 6.18522 | 0.314413 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −31.2682 | −1.58536 | −0.792679 | − | 0.609639i | \(-0.791314\pi\) | ||||
−0.792679 | + | 0.609639i | \(0.791314\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 11.5968 | 0.586474 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 13.8728 | 0.699791 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −3.79054 | −0.190723 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −18.4742 | −0.927195 | −0.463597 | − | 0.886046i | \(-0.653442\pi\) | ||||
−0.463597 | + | 0.886046i | \(0.653442\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −2.66540 | −0.133437 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 10.3634 | 0.517525 | 0.258762 | − | 0.965941i | \(-0.416685\pi\) | ||||
0.258762 | + | 0.965941i | \(0.416685\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −3.59218 | −0.178939 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −2.89551 | −0.143879 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 10.7318 | 0.531954 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −33.5152 | −1.65722 | −0.828611 | − | 0.559825i | \(-0.810868\pi\) | ||||
−0.828611 | + | 0.559825i | \(0.810868\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 38.9932 | 1.92339 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −2.77495 | −0.136546 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −2.49721 | −0.122583 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 27.1540 | 1.32974 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −8.01559 | −0.391587 | −0.195794 | − | 0.980645i | \(-0.562728\pi\) | ||||
−0.195794 | + | 0.980645i | \(0.562728\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −13.1527 | −0.641025 | −0.320512 | − | 0.947244i | \(-0.603855\pi\) | ||||
−0.320512 | + | 0.947244i | \(0.603855\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 11.6699 | 0.567411 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −15.9359 | −0.773004 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0.0693284 | 0.00335504 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 3.79257 | 0.183107 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −2.41216 | −0.116190 | −0.0580948 | − | 0.998311i | \(-0.518503\pi\) | ||||
−0.0580948 | + | 0.998311i | \(0.518503\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −15.1889 | −0.729930 | −0.364965 | − | 0.931021i | \(-0.618919\pi\) | ||||
−0.364965 | + | 0.931021i | \(0.618919\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0.735391 | 0.0352593 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 7.76350 | 0.371378 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 5.98083 | 0.285449 | 0.142725 | − | 0.989762i | \(-0.454414\pi\) | ||||
0.142725 | + | 0.989762i | \(0.454414\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −10.2914 | −0.490066 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 22.3495 | 1.06186 | 0.530928 | − | 0.847417i | \(-0.321843\pi\) | ||||
0.530928 | + | 0.847417i | \(0.321843\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 4.00237 | 0.189731 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 8.30570 | 0.392846 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −13.5528 | −0.639598 | −0.319799 | − | 0.947485i | \(-0.603615\pi\) | ||||
−0.319799 | + | 0.947485i | \(0.603615\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 13.8670 | 0.652972 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −31.3212 | −1.47160 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −0.183565 | −0.00860565 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 8.19148 | 0.383181 | 0.191591 | − | 0.981475i | \(-0.438635\pi\) | ||||
0.191591 | + | 0.981475i | \(0.438635\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −10.0252 | −0.467936 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 13.1494 | 0.612430 | 0.306215 | − | 0.951962i | \(-0.400937\pi\) | ||||
0.306215 | + | 0.951962i | \(0.400937\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −9.03105 | −0.419708 | −0.209854 | − | 0.977733i | \(-0.567299\pi\) | ||||
−0.209854 | + | 0.977733i | \(0.567299\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −1.59847 | −0.0741274 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −11.3433 | −0.524908 | −0.262454 | − | 0.964945i | \(-0.584532\pi\) | ||||
−0.262454 | + | 0.964945i | \(0.584532\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −5.07094 | −0.234154 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 20.2373 | 0.932488 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 5.77992 | 0.265761 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −10.6683 | −0.489497 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −7.85562 | −0.359684 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 5.01937 | 0.229341 | 0.114670 | − | 0.993404i | \(-0.463419\pi\) | ||||
0.114670 | + | 0.993404i | \(0.463419\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 9.17251 | 0.418230 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −4.42567 | −0.201375 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 4.49095 | 0.203924 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 2.51042 | 0.113758 | 0.0568789 | − | 0.998381i | \(-0.481885\pi\) | ||||
0.0568789 | + | 0.998381i | \(0.481885\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 35.4542 | 1.60330 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 2.31426 | 0.104441 | 0.0522205 | − | 0.998636i | \(-0.483370\pi\) | ||||
0.0522205 | + | 0.998636i | \(0.483370\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 4.32867 | 0.194954 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0.573431 | 0.0257738 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 8.23948 | 0.369591 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 8.76208 | 0.392244 | 0.196122 | − | 0.980579i | \(-0.437165\pi\) | ||||
0.196122 | + | 0.980579i | \(0.437165\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −10.7666 | −0.481015 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 4.97063 | 0.221630 | 0.110815 | − | 0.993841i | \(-0.464654\pi\) | ||||
0.110815 | + | 0.993841i | \(0.464654\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 2.94709 | 0.131144 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −24.4700 | −1.08675 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −11.5632 | −0.512529 | −0.256265 | − | 0.966607i | \(-0.582492\pi\) | ||||
−0.256265 | + | 0.966607i | \(0.582492\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −6.09586 | −0.269665 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −6.71141 | −0.296316 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −0.0380881 | −0.00167836 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 10.9052 | 0.479611 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 11.0835 | 0.486511 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 22.1108 | 0.968691 | 0.484346 | − | 0.874877i | \(-0.339058\pi\) | ||||
0.484346 | + | 0.874877i | \(0.339058\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −18.6154 | −0.813993 | −0.406997 | − | 0.913430i | \(-0.633424\pi\) | ||||
−0.406997 | + | 0.913430i | \(0.633424\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 6.08160 | 0.265423 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −9.40895 | −0.409860 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −10.1094 | −0.439539 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 7.40907 | 0.321526 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 11.8522 | 0.513377 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0.200036 | 0.00864829 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −9.34533 | −0.403281 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −9.61701 | −0.414234 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −36.3161 | −1.56135 | −0.780675 | − | 0.624937i | \(-0.785124\pi\) | ||||
−0.780675 | + | 0.624937i | \(0.785124\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 27.5096 | 1.18055 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −0.576014 | −0.0246737 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 2.47047 | 0.105630 | 0.0528148 | − | 0.998604i | \(-0.483181\pi\) | ||||
0.0528148 | + | 0.998604i | \(0.483181\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −0.185105 | −0.00790011 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 2.89784 | 0.123452 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 8.51489 | 0.362090 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 4.08164 | 0.173256 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −39.3494 | −1.66729 | −0.833644 | − | 0.552302i | \(-0.813749\pi\) | ||||
−0.833644 | + | 0.552302i | \(0.813749\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 4.94014 | 0.208945 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 9.93384 | 0.419407 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 12.6798 | 0.534389 | 0.267195 | − | 0.963643i | \(-0.413903\pi\) | ||||
0.267195 | + | 0.963643i | \(0.413903\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 2.63473 | 0.110844 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 6.50434 | 0.273157 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 39.6216 | 1.66102 | 0.830512 | − | 0.557000i | \(-0.188048\pi\) | ||||
0.830512 | + | 0.557000i | \(0.188048\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 10.9909 | 0.459954 | 0.229977 | − | 0.973196i | \(-0.426135\pi\) | ||||
0.229977 | + | 0.973196i | \(0.426135\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −31.1252 | −1.30027 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −17.7138 | −0.738717 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 22.5319 | 0.938017 | 0.469008 | − | 0.883194i | \(-0.344611\pi\) | ||||
0.469008 | + | 0.883194i | \(0.344611\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 1.30507 | 0.0542367 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 5.60961 | 0.232726 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −7.34086 | −0.304027 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0.490115 | 0.0202638 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −39.4321 | −1.62754 | −0.813769 | − | 0.581189i | \(-0.802588\pi\) | ||||
−0.813769 | + | 0.581189i | \(0.802588\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −6.29886 | −0.259540 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −25.0697 | −1.03123 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −41.9828 | −1.72403 | −0.862013 | − | 0.506887i | \(-0.830796\pi\) | ||||
−0.862013 | + | 0.506887i | \(0.830796\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −0.480809 | −0.0197113 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 12.6834 | 0.519096 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 15.8875 | 0.649146 | 0.324573 | − | 0.945861i | \(-0.394779\pi\) | ||||
0.324573 | + | 0.945861i | \(0.394779\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 39.4266 | 1.60825 | 0.804123 | − | 0.594463i | \(-0.202635\pi\) | ||||
0.804123 | + | 0.594463i | \(0.202635\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 13.5393 | 0.551364 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −2.29580 | −0.0933374 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −5.29224 | −0.214805 | −0.107403 | − | 0.994216i | \(-0.534253\pi\) | ||||
−0.107403 | + | 0.994216i | \(0.534253\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −1.65195 | −0.0669403 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 9.32077 | 0.377078 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 34.1195 | 1.37808 | 0.689038 | − | 0.724725i | \(-0.258033\pi\) | ||||
0.689038 | + | 0.724725i | \(0.258033\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 5.27408 | 0.212672 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 29.4738 | 1.18657 | 0.593285 | − | 0.804992i | \(-0.297831\pi\) | ||||
0.593285 | + | 0.804992i | \(0.297831\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 32.8210 | 1.31919 | 0.659593 | − | 0.751623i | \(-0.270729\pi\) | ||||
0.659593 | + | 0.751623i | \(0.270729\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −11.1437 | −0.447181 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −8.99074 | −0.360206 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 24.0104 | 0.960416 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 6.65025 | 0.265585 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 24.0254 | 0.957957 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 13.2532 | 0.527601 | 0.263801 | − | 0.964577i | \(-0.415024\pi\) | ||||
0.263801 | + | 0.964577i | \(0.415024\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −50.0012 | −1.98737 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −4.79245 | −0.190183 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −8.21972 | −0.325677 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −21.9993 | −0.870278 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 1.34546 | 0.0531426 | 0.0265713 | − | 0.999647i | \(-0.491541\pi\) | ||||
0.0265713 | + | 0.999647i | \(0.491541\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 12.2114 | 0.481569 | 0.240785 | − | 0.970579i | \(-0.422595\pi\) | ||||
0.240785 | + | 0.970579i | \(0.422595\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 2.19830 | 0.0865578 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −28.5704 | −1.12322 | −0.561608 | − | 0.827403i | \(-0.689817\pi\) | ||||
−0.561608 | + | 0.827403i | \(0.689817\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 6.92358 | 0.271774 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 3.59073 | 0.140732 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 15.3953 | 0.602463 | 0.301231 | − | 0.953551i | \(-0.402602\pi\) | ||||
0.301231 | + | 0.953551i | \(0.402602\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 1.67531 | 0.0654597 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 16.2758 | 0.634981 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −24.7538 | −0.964272 | −0.482136 | − | 0.876096i | \(-0.660139\pi\) | ||||
−0.482136 | + | 0.876096i | \(0.660139\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −19.0121 | −0.739487 | −0.369743 | − | 0.929134i | \(-0.620554\pi\) | ||||
−0.369743 | + | 0.929134i | \(0.620554\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 8.49052 | 0.329744 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −0.321879 | −0.0124820 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 4.81162 | 0.186306 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 29.3431 | 1.13447 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −0.172976 | −0.00667767 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 16.1863 | 0.623935 | 0.311967 | − | 0.950093i | \(-0.399012\pi\) | ||||
0.311967 | + | 0.950093i | \(0.399012\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 15.3133 | 0.589409 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 34.9382 | 1.34278 | 0.671392 | − | 0.741102i | \(-0.265697\pi\) | ||||
0.671392 | + | 0.741102i | \(0.265697\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −10.0883 | −0.387152 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −54.0204 | −2.07007 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −39.9757 | −1.52963 | −0.764813 | − | 0.644252i | \(-0.777169\pi\) | ||||
−0.764813 | + | 0.644252i | \(0.777169\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 4.70890 | 0.179918 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −17.4021 | −0.663930 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −6.27428 | −0.239031 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 3.27679 | 0.124655 | 0.0623275 | − | 0.998056i | \(-0.480148\pi\) | ||||
0.0623275 | + | 0.998056i | \(0.480148\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −1.28813 | −0.0489319 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 3.27917 | 0.124386 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 31.0444 | 1.17589 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 9.85826 | 0.372873 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −22.9428 | −0.866538 | −0.433269 | − | 0.901265i | \(-0.642640\pi\) | ||||
−0.433269 | + | 0.901265i | \(0.642640\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 16.0839 | 0.606616 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 4.14762 | 0.156208 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −6.62020 | −0.248978 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −51.3035 | −1.92674 | −0.963371 | − | 0.268173i | \(-0.913580\pi\) | ||||
−0.963371 | + | 0.268173i | \(0.913580\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −22.7346 | −0.852614 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −10.4587 | −0.391681 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0.457999 | 0.0171282 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 10.4034 | 0.388521 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 4.63057 | 0.172691 | 0.0863456 | − | 0.996265i | \(-0.472481\pi\) | ||||
0.0863456 | + | 0.996265i | \(0.472481\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0.0855594 | 0.00318640 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 1.39055 | 0.0517149 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −6.61196 | −0.245562 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 0.697832 | 0.0258812 | 0.0129406 | − | 0.999916i | \(-0.495881\pi\) | ||||
0.0129406 | + | 0.999916i | \(0.495881\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 2.48218 | 0.0919327 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 12.9396 | 0.478590 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −13.5235 | −0.499502 | −0.249751 | − | 0.968310i | \(-0.580349\pi\) | ||||
−0.249751 | + | 0.968310i | \(0.580349\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −3.65767 | −0.134915 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 12.6521 | 0.466047 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −49.4982 | −1.82082 | −0.910410 | − | 0.413708i | \(-0.864233\pi\) | ||||
−0.910410 | + | 0.413708i | \(0.864233\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 5.68401 | 0.208807 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −28.6466 | −1.05094 | −0.525472 | − | 0.850811i | \(-0.676111\pi\) | ||||
−0.525472 | + | 0.850811i | \(0.676111\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 1.00301 | 0.0367476 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −14.9776 | −0.548000 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −0.449350 | −0.0164189 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 12.6351 | 0.461061 | 0.230530 | − | 0.973065i | \(-0.425954\pi\) | ||||
0.230530 | + | 0.973065i | \(0.425954\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 2.13165 | 0.0776818 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −3.78241 | −0.137656 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 27.6027 | 1.00324 | 0.501619 | − | 0.865089i | \(-0.332738\pi\) | ||||
0.501619 | + | 0.865089i | \(0.332738\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 11.0421 | 0.400805 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 15.9504 | 0.578201 | 0.289100 | − | 0.957299i | \(-0.406644\pi\) | ||||
0.289100 | + | 0.957299i | \(0.406644\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1.29393 | 0.0468434 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 1.28375 | 0.0464141 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 5.91762 | 0.213673 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 42.2253 | 1.52268 | 0.761342 | − | 0.648350i | \(-0.224541\pi\) | ||||
0.761342 | + | 0.648350i | \(0.224541\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −46.1793 | −1.66311 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 14.9447 | 0.537523 | 0.268761 | − | 0.963207i | \(-0.413386\pi\) | ||||
0.268761 | + | 0.963207i | \(0.413386\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 14.3720 | 0.516257 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −9.16881 | −0.328929 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 20.7828 | 0.744620 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −20.5577 | −0.735613 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −4.15956 | −0.148650 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 2.44390 | 0.0872267 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 19.8262 | 0.706727 | 0.353364 | − | 0.935486i | \(-0.385038\pi\) | ||||
0.353364 | + | 0.935486i | \(0.385038\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −51.5702 | −1.83595 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −5.91854 | −0.210439 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −0.147844 | −0.00525008 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −2.79197 | −0.0990210 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 12.3151 | 0.436224 | 0.218112 | − | 0.975924i | \(-0.430010\pi\) | ||||
0.218112 | + | 0.975924i | \(0.430010\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 24.4138 | 0.863697 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 24.0051 | 0.848179 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 15.2093 | 0.536725 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −0.534453 | −0.0188370 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −34.1804 | −1.20321 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 1.95284 | 0.0686581 | 0.0343291 | − | 0.999411i | \(-0.489071\pi\) | ||||
0.0343291 | + | 0.999411i | \(0.489071\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 4.28269 | 0.150386 | 0.0751928 | − | 0.997169i | \(-0.476043\pi\) | ||||
0.0751928 | + | 0.997169i | \(0.476043\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 61.0772 | 2.14207 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 4.28153 | 0.149975 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 8.66249 | 0.303062 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −1.10097 | −0.0384710 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −10.1730 | −0.355040 | −0.177520 | − | 0.984117i | \(-0.556808\pi\) | ||||
−0.177520 | + | 0.984117i | \(0.556808\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 9.65644 | 0.336602 | 0.168301 | − | 0.985736i | \(-0.446172\pi\) | ||||
0.168301 | + | 0.985736i | \(0.446172\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −15.1737 | −0.528282 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −55.4357 | −1.92769 | −0.963845 | − | 0.266464i | \(-0.914145\pi\) | ||||
−0.963845 | + | 0.266464i | \(0.914145\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −20.0529 | −0.696465 | −0.348232 | − | 0.937408i | \(-0.613218\pi\) | ||||
−0.348232 | + | 0.937408i | \(0.613218\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 42.2695 | 1.46631 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −21.5298 | −0.745964 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −1.30019 | −0.0449950 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 9.04136 | 0.312515 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −33.8398 | −1.16828 | −0.584139 | − | 0.811654i | \(-0.698568\pi\) | ||||
−0.584139 | + | 0.811654i | \(0.698568\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −27.2040 | −0.938069 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 15.0197 | 0.517305 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −2.95504 | −0.101657 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 5.15717 | 0.177202 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −34.5882 | −1.18706 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 26.7059 | 0.915467 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −43.8531 | −1.50150 | −0.750751 | − | 0.660586i | \(-0.770308\pi\) | ||||
−0.750751 | + | 0.660586i | \(0.770308\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0.859412 | 0.0293913 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −16.7010 | −0.570496 | −0.285248 | − | 0.958454i | \(-0.592076\pi\) | ||||
−0.285248 | + | 0.958454i | \(0.592076\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −31.2057 | −1.06473 | −0.532363 | − | 0.846516i | \(-0.678696\pi\) | ||||
−0.532363 | + | 0.846516i | \(0.678696\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −11.8475 | −0.403760 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −28.2924 | −0.963083 | −0.481542 | − | 0.876423i | \(-0.659923\pi\) | ||||
−0.481542 | + | 0.876423i | \(0.659923\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 1.33846 | 0.0455091 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −13.9990 | −0.475431 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −21.2449 | −0.720682 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 10.8138 | 0.366413 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 26.9355 | 0.911627 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 1.47872 | 0.0499898 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −42.6838 | −1.44133 | −0.720665 | − | 0.693284i | \(-0.756163\pi\) | ||||
−0.720665 | + | 0.693284i | \(0.756163\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 19.3177 | 0.651568 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 20.3040 | 0.684060 | 0.342030 | − | 0.939689i | \(-0.388885\pi\) | ||||
0.342030 | + | 0.939689i | \(0.388885\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −47.4337 | −1.59627 | −0.798135 | − | 0.602479i | \(-0.794180\pi\) | ||||
−0.798135 | + | 0.602479i | \(0.794180\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 2.63326 | 0.0885162 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −21.3167 | −0.715746 | −0.357873 | − | 0.933770i | \(-0.616498\pi\) | ||||
−0.357873 | + | 0.933770i | \(0.616498\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 10.7655 | 0.361065 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −16.2285 | −0.543675 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 16.3439 | 0.546927 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −1.12856 | −0.0377237 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 9.43779 | 0.315119 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −3.90387 | −0.130201 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −16.4341 | −0.547501 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −4.93815 | −0.164331 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 3.32211 | 0.110431 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 17.8871 | 0.593931 | 0.296966 | − | 0.954888i | \(-0.404025\pi\) | ||||
0.296966 | + | 0.954888i | \(0.404025\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 17.6758 | 0.586269 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 4.03861 | 0.133805 | 0.0669026 | − | 0.997760i | \(-0.478688\pi\) | ||||
0.0669026 | + | 0.997760i | \(0.478688\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −13.9961 | −0.463204 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −0.0657885 | −0.00217490 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −3.76334 | −0.124276 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −17.2681 | −0.569624 | −0.284812 | − | 0.958583i | \(-0.591931\pi\) | ||||
−0.284812 | + | 0.958583i | \(0.591931\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 49.0504 | 1.61626 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −17.5708 | −0.578350 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −36.6984 | −1.20663 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −0.228442 | −0.00750302 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −32.2922 | −1.05947 | −0.529737 | − | 0.848162i | \(-0.677709\pi\) | ||||
−0.529737 | + | 0.848162i | \(0.677709\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −14.4132 | −0.472374 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 19.6674 | 0.643882 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 1.19963 | 0.0392321 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −11.5818 | −0.378362 | −0.189181 | − | 0.981942i | \(-0.560583\pi\) | ||||
−0.189181 | + | 0.981942i | \(0.560583\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 24.8167 | 0.809863 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −32.0018 | −1.04323 | −0.521614 | − | 0.853182i | \(-0.674670\pi\) | ||||
−0.521614 | + | 0.853182i | \(0.674670\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 34.5080 | 1.12373 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0.462025 | 0.0150297 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −28.0987 | −0.913085 | −0.456543 | − | 0.889702i | \(-0.650912\pi\) | ||||
−0.456543 | + | 0.889702i | \(0.650912\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 12.9995 | 0.421982 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −24.9456 | −0.808917 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 11.9394 | 0.386755 | 0.193377 | − | 0.981124i | \(-0.438056\pi\) | ||||
0.193377 | + | 0.981124i | \(0.438056\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −3.75874 | −0.121630 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 4.12165 | 0.133234 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −10.5778 | −0.341576 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −22.5144 | −0.726271 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 1.19976 | 0.0386616 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0.157603 | 0.00507341 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 37.0856 | 1.19259 | 0.596296 | − | 0.802764i | \(-0.296638\pi\) | ||||
0.596296 | + | 0.802764i | \(0.296638\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 14.8881 | 0.478273 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −3.36029 | −0.107837 | −0.0539184 | − | 0.998545i | \(-0.517171\pi\) | ||||
−0.0539184 | + | 0.998545i | \(0.517171\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −7.36617 | −0.236149 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −12.9691 | −0.415343 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −24.6162 | −0.787543 | −0.393772 | − | 0.919208i | \(-0.628830\pi\) | ||||
−0.393772 | + | 0.919208i | \(0.628830\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 22.4321 | 0.716934 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −3.45477 | −0.110302 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 38.0516 | 1.21366 | 0.606829 | − | 0.794832i | \(-0.292441\pi\) | ||||
0.606829 | + | 0.794832i | \(0.292441\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −3.02747 | −0.0964632 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −9.31701 | −0.296564 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 14.3833 | 0.457362 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 41.3513 | 1.31357 | 0.656783 | − | 0.754080i | \(-0.271917\pi\) | ||||
0.656783 | + | 0.754080i | \(0.271917\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 4.82987 | 0.153271 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 1.53167 | 0.0485572 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −5.97938 | −0.189369 | −0.0946845 | − | 0.995507i | \(-0.530184\pi\) | ||||
−0.0946845 | + | 0.995507i | \(0.530184\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −23.0868 | −0.730434 |
(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 | 4016.2.a.m.1.18 | 23 | ||
4.3 | odd | 2 | 2008.2.a.d.1.6 | ✓ | 23 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2008.2.a.d.1.6 | ✓ | 23 | 4.3 | odd | 2 | ||
4016.2.a.m.1.18 | 23 | 1.1 | even | 1 | trivial |