Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4018,2,Mod(1,4018)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4018, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4018.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4018 = 2 \cdot 7^{2} \cdot 41 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4018.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: | \(32.0838915322\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.11348.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} - 5x^{2} + x + 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 574) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(2.64119\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4018.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | −0.757235 | −0.437190 | −0.218595 | − | 0.975816i | \(-0.570147\pi\) | ||||
−0.218595 | + | 0.975816i | \(0.570147\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −1.30651 | −0.584288 | −0.292144 | − | 0.956374i | \(-0.594369\pi\) | ||||
−0.292144 | + | 0.956374i | \(0.594369\pi\) | |||||||
\(6\) | 0.757235 | 0.309140 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | −2.42659 | −0.808865 | ||||||||
\(10\) | 1.30651 | 0.413154 | ||||||||
\(11\) | 1.45073 | 0.437411 | 0.218706 | − | 0.975791i | \(-0.429817\pi\) | ||||
0.218706 | + | 0.975791i | \(0.429817\pi\) | |||||||
\(12\) | −0.757235 | −0.218595 | ||||||||
\(13\) | −3.28237 | −0.910366 | −0.455183 | − | 0.890398i | \(-0.650426\pi\) | ||||
−0.455183 | + | 0.890398i | \(0.650426\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.989333 | 0.255445 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −7.19450 | −1.74492 | −0.872461 | − | 0.488684i | \(-0.837477\pi\) | ||||
−0.872461 | + | 0.488684i | \(0.837477\pi\) | |||||||
\(18\) | 2.42659 | 0.571954 | ||||||||
\(19\) | −5.28237 | −1.21186 | −0.605930 | − | 0.795518i | \(-0.707199\pi\) | ||||
−0.605930 | + | 0.795518i | \(0.707199\pi\) | |||||||
\(20\) | −1.30651 | −0.292144 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −1.45073 | −0.309296 | ||||||||
\(23\) | −3.28237 | −0.684422 | −0.342211 | − | 0.939623i | \(-0.611176\pi\) | ||||
−0.342211 | + | 0.939623i | \(0.611176\pi\) | |||||||
\(24\) | 0.757235 | 0.154570 | ||||||||
\(25\) | −3.29304 | −0.658608 | ||||||||
\(26\) | 3.28237 | 0.643726 | ||||||||
\(27\) | 4.10921 | 0.790818 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 6.46140 | 1.19985 | 0.599925 | − | 0.800056i | \(-0.295197\pi\) | ||||
0.599925 | + | 0.800056i | \(0.295197\pi\) | |||||||
\(30\) | −0.989333 | −0.180627 | ||||||||
\(31\) | −3.01067 | −0.540732 | −0.270366 | − | 0.962758i | \(-0.587145\pi\) | ||||
−0.270366 | + | 0.962758i | \(0.587145\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | −1.09854 | −0.191232 | ||||||||
\(34\) | 7.19450 | 1.23385 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −2.42659 | −0.404432 | ||||||||
\(37\) | −3.51447 | −0.577775 | −0.288888 | − | 0.957363i | \(-0.593285\pi\) | ||||
−0.288888 | + | 0.957363i | \(0.593285\pi\) | |||||||
\(38\) | 5.28237 | 0.856914 | ||||||||
\(39\) | 2.48553 | 0.398003 | ||||||||
\(40\) | 1.30651 | 0.206577 | ||||||||
\(41\) | −1.00000 | −0.156174 | ||||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0.525138 | 0.0800827 | 0.0400414 | − | 0.999198i | \(-0.487251\pi\) | ||||
0.0400414 | + | 0.999198i | \(0.487251\pi\) | |||||||
\(44\) | 1.45073 | 0.218706 | ||||||||
\(45\) | 3.17036 | 0.472610 | ||||||||
\(46\) | 3.28237 | 0.483959 | ||||||||
\(47\) | −3.15489 | −0.460188 | −0.230094 | − | 0.973168i | \(-0.573903\pi\) | ||||
−0.230094 | + | 0.973168i | \(0.573903\pi\) | |||||||
\(48\) | −0.757235 | −0.109298 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 3.29304 | 0.465706 | ||||||||
\(51\) | 5.44793 | 0.762862 | ||||||||
\(52\) | −3.28237 | −0.455183 | ||||||||
\(53\) | 11.6874 | 1.60539 | 0.802696 | − | 0.596389i | \(-0.203398\pi\) | ||||
0.802696 | + | 0.596389i | \(0.203398\pi\) | |||||||
\(54\) | −4.10921 | −0.559193 | ||||||||
\(55\) | −1.89539 | −0.255574 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 4.00000 | 0.529813 | ||||||||
\(58\) | −6.46140 | −0.848423 | ||||||||
\(59\) | −1.68283 | −0.219085 | −0.109543 | − | 0.993982i | \(-0.534939\pi\) | ||||
−0.109543 | + | 0.993982i | \(0.534939\pi\) | |||||||
\(60\) | 0.989333 | 0.127722 | ||||||||
\(61\) | 0.842311 | 0.107847 | 0.0539234 | − | 0.998545i | \(-0.482827\pi\) | ||||
0.0539234 | + | 0.998545i | \(0.482827\pi\) | |||||||
\(62\) | 3.01067 | 0.382355 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 4.28844 | 0.531916 | ||||||||
\(66\) | 1.09854 | 0.135221 | ||||||||
\(67\) | 7.88799 | 0.963671 | 0.481836 | − | 0.876262i | \(-0.339970\pi\) | ||||
0.481836 | + | 0.876262i | \(0.339970\pi\) | |||||||
\(68\) | −7.19450 | −0.872461 | ||||||||
\(69\) | 2.48553 | 0.299223 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −16.4286 | −1.94972 | −0.974858 | − | 0.222826i | \(-0.928472\pi\) | ||||
−0.974858 | + | 0.222826i | \(0.928472\pi\) | |||||||
\(72\) | 2.42659 | 0.285977 | ||||||||
\(73\) | 13.9035 | 1.62728 | 0.813639 | − | 0.581371i | \(-0.197483\pi\) | ||||
0.813639 | + | 0.581371i | \(0.197483\pi\) | |||||||
\(74\) | 3.51447 | 0.408549 | ||||||||
\(75\) | 2.49361 | 0.287937 | ||||||||
\(76\) | −5.28237 | −0.605930 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −2.48553 | −0.281431 | ||||||||
\(79\) | −11.4266 | −1.28559 | −0.642796 | − | 0.766037i | \(-0.722226\pi\) | ||||
−0.642796 | + | 0.766037i | \(0.722226\pi\) | |||||||
\(80\) | −1.30651 | −0.146072 | ||||||||
\(81\) | 4.16814 | 0.463127 | ||||||||
\(82\) | 1.00000 | 0.110432 | ||||||||
\(83\) | 0.168356 | 0.0184794 | 0.00923971 | − | 0.999957i | \(-0.497059\pi\) | ||||
0.00923971 | + | 0.999957i | \(0.497059\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 9.39966 | 1.01954 | ||||||||
\(86\) | −0.525138 | −0.0566270 | ||||||||
\(87\) | −4.89280 | −0.524563 | ||||||||
\(88\) | −1.45073 | −0.154648 | ||||||||
\(89\) | −11.9121 | −1.26268 | −0.631341 | − | 0.775505i | \(-0.717495\pi\) | ||||
−0.631341 | + | 0.775505i | \(0.717495\pi\) | |||||||
\(90\) | −3.17036 | −0.334186 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −3.28237 | −0.342211 | ||||||||
\(93\) | 2.27978 | 0.236403 | ||||||||
\(94\) | 3.15489 | 0.325402 | ||||||||
\(95\) | 6.90146 | 0.708075 | ||||||||
\(96\) | 0.757235 | 0.0772850 | ||||||||
\(97\) | 3.62368 | 0.367929 | 0.183965 | − | 0.982933i | \(-0.441107\pi\) | ||||
0.183965 | + | 0.982933i | \(0.441107\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −3.52033 | −0.353806 | ||||||||
\(100\) | −3.29304 | −0.329304 | ||||||||
\(101\) | −4.38092 | −0.435917 | −0.217959 | − | 0.975958i | \(-0.569940\pi\) | ||||
−0.217959 | + | 0.975958i | \(0.569940\pi\) | |||||||
\(102\) | −5.44793 | −0.539425 | ||||||||
\(103\) | 10.3281 | 1.01765 | 0.508827 | − | 0.860869i | \(-0.330079\pi\) | ||||
0.508827 | + | 0.860869i | \(0.330079\pi\) | |||||||
\(104\) | 3.28237 | 0.321863 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −11.6874 | −1.13518 | ||||||||
\(107\) | 0.284962 | 0.0275484 | 0.0137742 | − | 0.999905i | \(-0.495615\pi\) | ||||
0.0137742 | + | 0.999905i | \(0.495615\pi\) | |||||||
\(108\) | 4.10921 | 0.395409 | ||||||||
\(109\) | 2.47967 | 0.237509 | 0.118755 | − | 0.992924i | \(-0.462110\pi\) | ||||
0.118755 | + | 0.992924i | \(0.462110\pi\) | |||||||
\(110\) | 1.89539 | 0.180718 | ||||||||
\(111\) | 2.66128 | 0.252598 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −5.80751 | −0.546325 | −0.273162 | − | 0.961968i | \(-0.588070\pi\) | ||||
−0.273162 | + | 0.961968i | \(0.588070\pi\) | |||||||
\(114\) | −4.00000 | −0.374634 | ||||||||
\(115\) | 4.28844 | 0.399899 | ||||||||
\(116\) | 6.46140 | 0.599925 | ||||||||
\(117\) | 7.96499 | 0.736363 | ||||||||
\(118\) | 1.68283 | 0.154917 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −0.989333 | −0.0903134 | ||||||||
\(121\) | −8.89539 | −0.808672 | ||||||||
\(122\) | −0.842311 | −0.0762593 | ||||||||
\(123\) | 0.757235 | 0.0682776 | ||||||||
\(124\) | −3.01067 | −0.270366 | ||||||||
\(125\) | 10.8349 | 0.969104 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −7.74657 | −0.687397 | −0.343698 | − | 0.939080i | \(-0.611680\pi\) | ||||
−0.343698 | + | 0.939080i | \(0.611680\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | −0.397653 | −0.0350114 | ||||||||
\(130\) | −4.28844 | −0.376121 | ||||||||
\(131\) | −4.24757 | −0.371112 | −0.185556 | − | 0.982634i | \(-0.559409\pi\) | ||||
−0.185556 | + | 0.982634i | \(0.559409\pi\) | |||||||
\(132\) | −1.09854 | −0.0956159 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −7.88799 | −0.681419 | ||||||||
\(135\) | −5.36871 | −0.462065 | ||||||||
\(136\) | 7.19450 | 0.616923 | ||||||||
\(137\) | 7.93040 | 0.677540 | 0.338770 | − | 0.940869i | \(-0.389989\pi\) | ||||
0.338770 | + | 0.940869i | \(0.389989\pi\) | |||||||
\(138\) | −2.48553 | −0.211582 | ||||||||
\(139\) | 6.44466 | 0.546629 | 0.273314 | − | 0.961925i | \(-0.411880\pi\) | ||||
0.273314 | + | 0.961925i | \(0.411880\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 2.38899 | 0.201190 | ||||||||
\(142\) | 16.4286 | 1.37866 | ||||||||
\(143\) | −4.76183 | −0.398204 | ||||||||
\(144\) | −2.42659 | −0.202216 | ||||||||
\(145\) | −8.44186 | −0.701058 | ||||||||
\(146\) | −13.9035 | −1.15066 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −3.51447 | −0.288888 | ||||||||
\(149\) | 11.2232 | 0.919443 | 0.459721 | − | 0.888063i | \(-0.347949\pi\) | ||||
0.459721 | + | 0.888063i | \(0.347949\pi\) | |||||||
\(150\) | −2.49361 | −0.203602 | ||||||||
\(151\) | −19.6333 | −1.59773 | −0.798867 | − | 0.601507i | \(-0.794567\pi\) | ||||
−0.798867 | + | 0.601507i | \(0.794567\pi\) | |||||||
\(152\) | 5.28237 | 0.428457 | ||||||||
\(153\) | 17.4581 | 1.41141 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 3.93346 | 0.315943 | ||||||||
\(156\) | 2.48553 | 0.199002 | ||||||||
\(157\) | −12.3326 | −0.984252 | −0.492126 | − | 0.870524i | \(-0.663780\pi\) | ||||
−0.492126 | + | 0.870524i | \(0.663780\pi\) | |||||||
\(158\) | 11.4266 | 0.909051 | ||||||||
\(159\) | −8.85013 | −0.701861 | ||||||||
\(160\) | 1.30651 | 0.103288 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −4.16814 | −0.327480 | ||||||||
\(163\) | −13.0020 | −1.01840 | −0.509198 | − | 0.860649i | \(-0.670058\pi\) | ||||
−0.509198 | + | 0.860649i | \(0.670058\pi\) | |||||||
\(164\) | −1.00000 | −0.0780869 | ||||||||
\(165\) | 1.43525 | 0.111734 | ||||||||
\(166\) | −0.168356 | −0.0130669 | ||||||||
\(167\) | 22.9324 | 1.77456 | 0.887281 | − | 0.461228i | \(-0.152591\pi\) | ||||
0.887281 | + | 0.461228i | \(0.152591\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −2.22603 | −0.171233 | ||||||||
\(170\) | −9.39966 | −0.720921 | ||||||||
\(171\) | 12.8182 | 0.980231 | ||||||||
\(172\) | 0.525138 | 0.0400414 | ||||||||
\(173\) | 23.3588 | 1.77594 | 0.887968 | − | 0.459905i | \(-0.152117\pi\) | ||||
0.887968 | + | 0.459905i | \(0.152117\pi\) | |||||||
\(174\) | 4.89280 | 0.370922 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 1.45073 | 0.109353 | ||||||||
\(177\) | 1.27430 | 0.0957819 | ||||||||
\(178\) | 11.9121 | 0.892851 | ||||||||
\(179\) | 20.9865 | 1.56861 | 0.784304 | − | 0.620377i | \(-0.213020\pi\) | ||||
0.784304 | + | 0.620377i | \(0.213020\pi\) | |||||||
\(180\) | 3.17036 | 0.236305 | ||||||||
\(181\) | 5.13355 | 0.381574 | 0.190787 | − | 0.981631i | \(-0.438896\pi\) | ||||
0.190787 | + | 0.981631i | \(0.438896\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −0.637828 | −0.0471496 | ||||||||
\(184\) | 3.28237 | 0.241980 | ||||||||
\(185\) | 4.59168 | 0.337587 | ||||||||
\(186\) | −2.27978 | −0.167162 | ||||||||
\(187\) | −10.4373 | −0.763248 | ||||||||
\(188\) | −3.15489 | −0.230094 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −6.90146 | −0.500684 | ||||||||
\(191\) | 13.1112 | 0.948694 | 0.474347 | − | 0.880338i | \(-0.342684\pi\) | ||||
0.474347 | + | 0.880338i | \(0.342684\pi\) | |||||||
\(192\) | −0.757235 | −0.0546488 | ||||||||
\(193\) | −1.24736 | −0.0897870 | −0.0448935 | − | 0.998992i | \(-0.514295\pi\) | ||||
−0.0448935 | + | 0.998992i | \(0.514295\pi\) | |||||||
\(194\) | −3.62368 | −0.260165 | ||||||||
\(195\) | −3.24736 | −0.232548 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −7.29045 | −0.519423 | −0.259712 | − | 0.965686i | \(-0.583627\pi\) | ||||
−0.259712 | + | 0.965686i | \(0.583627\pi\) | |||||||
\(198\) | 3.52033 | 0.250179 | ||||||||
\(199\) | 2.86645 | 0.203197 | 0.101598 | − | 0.994825i | \(-0.467604\pi\) | ||||
0.101598 | + | 0.994825i | \(0.467604\pi\) | |||||||
\(200\) | 3.29304 | 0.232853 | ||||||||
\(201\) | −5.97307 | −0.421308 | ||||||||
\(202\) | 4.38092 | 0.308240 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 5.44793 | 0.381431 | ||||||||
\(205\) | 1.30651 | 0.0912504 | ||||||||
\(206\) | −10.3281 | −0.719589 | ||||||||
\(207\) | 7.96499 | 0.553605 | ||||||||
\(208\) | −3.28237 | −0.227592 | ||||||||
\(209\) | −7.66329 | −0.530081 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −19.0871 | −1.31401 | −0.657004 | − | 0.753887i | \(-0.728177\pi\) | ||||
−0.657004 | + | 0.753887i | \(0.728177\pi\) | |||||||
\(212\) | 11.6874 | 0.802696 | ||||||||
\(213\) | 12.4403 | 0.852397 | ||||||||
\(214\) | −0.284962 | −0.0194796 | ||||||||
\(215\) | −0.686096 | −0.0467913 | ||||||||
\(216\) | −4.10921 | −0.279596 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −2.47967 | −0.167944 | ||||||||
\(219\) | −10.5282 | −0.711430 | ||||||||
\(220\) | −1.89539 | −0.127787 | ||||||||
\(221\) | 23.6150 | 1.58852 | ||||||||
\(222\) | −2.66128 | −0.178614 | ||||||||
\(223\) | 23.2174 | 1.55475 | 0.777375 | − | 0.629037i | \(-0.216551\pi\) | ||||
0.777375 | + | 0.629037i | \(0.216551\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 7.99087 | 0.532725 | ||||||||
\(226\) | 5.80751 | 0.386310 | ||||||||
\(227\) | 18.4419 | 1.22403 | 0.612015 | − | 0.790847i | \(-0.290359\pi\) | ||||
0.612015 | + | 0.790847i | \(0.290359\pi\) | |||||||
\(228\) | 4.00000 | 0.264906 | ||||||||
\(229\) | −18.0081 | −1.19001 | −0.595004 | − | 0.803723i | \(-0.702849\pi\) | ||||
−0.595004 | + | 0.803723i | \(0.702849\pi\) | |||||||
\(230\) | −4.28844 | −0.282772 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −6.46140 | −0.424211 | ||||||||
\(233\) | 4.38899 | 0.287533 | 0.143766 | − | 0.989612i | \(-0.454079\pi\) | ||||
0.143766 | + | 0.989612i | \(0.454079\pi\) | |||||||
\(234\) | −7.96499 | −0.520688 | ||||||||
\(235\) | 4.12188 | 0.268882 | ||||||||
\(236\) | −1.68283 | −0.109543 | ||||||||
\(237\) | 8.65262 | 0.562048 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 25.0020 | 1.61725 | 0.808623 | − | 0.588328i | \(-0.200213\pi\) | ||||
0.808623 | + | 0.588328i | \(0.200213\pi\) | |||||||
\(240\) | 0.989333 | 0.0638612 | ||||||||
\(241\) | −15.5145 | −0.999375 | −0.499687 | − | 0.866206i | \(-0.666552\pi\) | ||||
−0.499687 | + | 0.866206i | \(0.666552\pi\) | |||||||
\(242\) | 8.89539 | 0.571817 | ||||||||
\(243\) | −15.4839 | −0.993292 | ||||||||
\(244\) | 0.842311 | 0.0539234 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −0.757235 | −0.0482796 | ||||||||
\(247\) | 17.3387 | 1.10324 | ||||||||
\(248\) | 3.01067 | 0.191178 | ||||||||
\(249\) | −0.127485 | −0.00807902 | ||||||||
\(250\) | −10.8349 | −0.685260 | ||||||||
\(251\) | 15.6076 | 0.985144 | 0.492572 | − | 0.870272i | \(-0.336057\pi\) | ||||
0.492572 | + | 0.870272i | \(0.336057\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −4.76183 | −0.299374 | ||||||||
\(254\) | 7.74657 | 0.486063 | ||||||||
\(255\) | −7.11776 | −0.445731 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 24.0706 | 1.50148 | 0.750740 | − | 0.660598i | \(-0.229697\pi\) | ||||
0.750740 | + | 0.660598i | \(0.229697\pi\) | |||||||
\(258\) | 0.397653 | 0.0247568 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 4.28844 | 0.265958 | ||||||||
\(261\) | −15.6792 | −0.970517 | ||||||||
\(262\) | 4.24757 | 0.262416 | ||||||||
\(263\) | −10.1971 | −0.628779 | −0.314390 | − | 0.949294i | \(-0.601800\pi\) | ||||
−0.314390 | + | 0.949294i | \(0.601800\pi\) | |||||||
\(264\) | 1.09854 | 0.0676106 | ||||||||
\(265\) | −15.2697 | −0.938010 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 9.02028 | 0.552032 | ||||||||
\(268\) | 7.88799 | 0.481836 | ||||||||
\(269\) | −20.0988 | −1.22544 | −0.612721 | − | 0.790299i | \(-0.709925\pi\) | ||||
−0.612721 | + | 0.790299i | \(0.709925\pi\) | |||||||
\(270\) | 5.36871 | 0.326729 | ||||||||
\(271\) | −11.9035 | −0.723084 | −0.361542 | − | 0.932356i | \(-0.617750\pi\) | ||||
−0.361542 | + | 0.932356i | \(0.617750\pi\) | |||||||
\(272\) | −7.19450 | −0.436230 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −7.93040 | −0.479093 | ||||||||
\(275\) | −4.77731 | −0.288082 | ||||||||
\(276\) | 2.48553 | 0.149611 | ||||||||
\(277\) | −14.4586 | −0.868733 | −0.434366 | − | 0.900736i | \(-0.643028\pi\) | ||||
−0.434366 | + | 0.900736i | \(0.643028\pi\) | |||||||
\(278\) | −6.44466 | −0.386525 | ||||||||
\(279\) | 7.30567 | 0.437379 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 7.80291 | 0.465483 | 0.232741 | − | 0.972539i | \(-0.425230\pi\) | ||||
0.232741 | + | 0.972539i | \(0.425230\pi\) | |||||||
\(282\) | −2.38899 | −0.142262 | ||||||||
\(283\) | 15.8316 | 0.941094 | 0.470547 | − | 0.882375i | \(-0.344057\pi\) | ||||
0.470547 | + | 0.882375i | \(0.344057\pi\) | |||||||
\(284\) | −16.4286 | −0.974858 | ||||||||
\(285\) | −5.22603 | −0.309563 | ||||||||
\(286\) | 4.76183 | 0.281573 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 2.42659 | 0.142988 | ||||||||
\(289\) | 34.7608 | 2.04475 | ||||||||
\(290\) | 8.44186 | 0.495723 | ||||||||
\(291\) | −2.74398 | −0.160855 | ||||||||
\(292\) | 13.9035 | 0.813639 | ||||||||
\(293\) | −24.2361 | −1.41589 | −0.707944 | − | 0.706268i | \(-0.750377\pi\) | ||||
−0.707944 | + | 0.706268i | \(0.750377\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 2.19862 | 0.128009 | ||||||||
\(296\) | 3.51447 | 0.204274 | ||||||||
\(297\) | 5.96135 | 0.345912 | ||||||||
\(298\) | −11.2232 | −0.650144 | ||||||||
\(299\) | 10.7740 | 0.623075 | ||||||||
\(300\) | 2.49361 | 0.143968 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 19.6333 | 1.12977 | ||||||||
\(303\) | 3.31738 | 0.190579 | ||||||||
\(304\) | −5.28237 | −0.302965 | ||||||||
\(305\) | −1.10049 | −0.0630136 | ||||||||
\(306\) | −17.4581 | −0.998015 | ||||||||
\(307\) | −18.2689 | −1.04266 | −0.521331 | − | 0.853355i | \(-0.674564\pi\) | ||||
−0.521331 | + | 0.853355i | \(0.674564\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −7.82077 | −0.444908 | ||||||||
\(310\) | −3.93346 | −0.223405 | ||||||||
\(311\) | −7.66175 | −0.434458 | −0.217229 | − | 0.976121i | \(-0.569702\pi\) | ||||
−0.217229 | + | 0.976121i | \(0.569702\pi\) | |||||||
\(312\) | −2.48553 | −0.140715 | ||||||||
\(313\) | 0.599758 | 0.0339003 | 0.0169502 | − | 0.999856i | \(-0.494604\pi\) | ||||
0.0169502 | + | 0.999856i | \(0.494604\pi\) | |||||||
\(314\) | 12.3326 | 0.695972 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −11.4266 | −0.642796 | ||||||||
\(317\) | −18.7773 | −1.05464 | −0.527319 | − | 0.849667i | \(-0.676803\pi\) | ||||
−0.527319 | + | 0.849667i | \(0.676803\pi\) | |||||||
\(318\) | 8.85013 | 0.496291 | ||||||||
\(319\) | 9.37373 | 0.524828 | ||||||||
\(320\) | −1.30651 | −0.0730360 | ||||||||
\(321\) | −0.215784 | −0.0120439 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 38.0040 | 2.11460 | ||||||||
\(324\) | 4.16814 | 0.231564 | ||||||||
\(325\) | 10.8090 | 0.599575 | ||||||||
\(326\) | 13.0020 | 0.720115 | ||||||||
\(327\) | −1.87769 | −0.103837 | ||||||||
\(328\) | 1.00000 | 0.0552158 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −1.43525 | −0.0790081 | ||||||||
\(331\) | −20.2074 | −1.11070 | −0.555349 | − | 0.831617i | \(-0.687415\pi\) | ||||
−0.555349 | + | 0.831617i | \(0.687415\pi\) | |||||||
\(332\) | 0.168356 | 0.00923971 | ||||||||
\(333\) | 8.52820 | 0.467342 | ||||||||
\(334\) | −22.9324 | −1.25481 | ||||||||
\(335\) | −10.3057 | −0.563061 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 14.3977 | 0.784290 | 0.392145 | − | 0.919903i | \(-0.371733\pi\) | ||||
0.392145 | + | 0.919903i | \(0.371733\pi\) | |||||||
\(338\) | 2.22603 | 0.121080 | ||||||||
\(339\) | 4.39765 | 0.238848 | ||||||||
\(340\) | 9.39966 | 0.509768 | ||||||||
\(341\) | −4.36766 | −0.236522 | ||||||||
\(342\) | −12.8182 | −0.693128 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −0.525138 | −0.0283135 | ||||||||
\(345\) | −3.24736 | −0.174832 | ||||||||
\(346\) | −23.3588 | −1.25578 | ||||||||
\(347\) | 26.2826 | 1.41092 | 0.705462 | − | 0.708748i | \(-0.250740\pi\) | ||||
0.705462 | + | 0.708748i | \(0.250740\pi\) | |||||||
\(348\) | −4.89280 | −0.262281 | ||||||||
\(349\) | −18.2420 | −0.976470 | −0.488235 | − | 0.872712i | \(-0.662359\pi\) | ||||
−0.488235 | + | 0.872712i | \(0.662359\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −13.4880 | −0.719934 | ||||||||
\(352\) | −1.45073 | −0.0773241 | ||||||||
\(353\) | 16.3407 | 0.869729 | 0.434865 | − | 0.900496i | \(-0.356796\pi\) | ||||
0.434865 | + | 0.900496i | \(0.356796\pi\) | |||||||
\(354\) | −1.27430 | −0.0677281 | ||||||||
\(355\) | 21.4641 | 1.13920 | ||||||||
\(356\) | −11.9121 | −0.631341 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −20.9865 | −1.10917 | ||||||||
\(359\) | −1.69022 | −0.0892066 | −0.0446033 | − | 0.999005i | \(-0.514202\pi\) | ||||
−0.0446033 | + | 0.999005i | \(0.514202\pi\) | |||||||
\(360\) | −3.17036 | −0.167093 | ||||||||
\(361\) | 8.90346 | 0.468603 | ||||||||
\(362\) | −5.13355 | −0.269814 | ||||||||
\(363\) | 6.73590 | 0.353543 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −18.1650 | −0.950798 | ||||||||
\(366\) | 0.637828 | 0.0333398 | ||||||||
\(367\) | 12.9411 | 0.675518 | 0.337759 | − | 0.941233i | \(-0.390331\pi\) | ||||
0.337759 | + | 0.941233i | \(0.390331\pi\) | |||||||
\(368\) | −3.28237 | −0.171106 | ||||||||
\(369\) | 2.42659 | 0.126323 | ||||||||
\(370\) | −4.59168 | −0.238710 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 2.27978 | 0.118201 | ||||||||
\(373\) | 16.6440 | 0.861792 | 0.430896 | − | 0.902402i | \(-0.358198\pi\) | ||||
0.430896 | + | 0.902402i | \(0.358198\pi\) | |||||||
\(374\) | 10.4373 | 0.539698 | ||||||||
\(375\) | −8.20458 | −0.423683 | ||||||||
\(376\) | 3.15489 | 0.162701 | ||||||||
\(377\) | −21.2087 | −1.09230 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 25.0995 | 1.28927 | 0.644637 | − | 0.764489i | \(-0.277008\pi\) | ||||
0.644637 | + | 0.764489i | \(0.277008\pi\) | |||||||
\(380\) | 6.90146 | 0.354037 | ||||||||
\(381\) | 5.86598 | 0.300523 | ||||||||
\(382\) | −13.1112 | −0.670828 | ||||||||
\(383\) | 4.00000 | 0.204390 | 0.102195 | − | 0.994764i | \(-0.467413\pi\) | ||||
0.102195 | + | 0.994764i | \(0.467413\pi\) | |||||||
\(384\) | 0.757235 | 0.0386425 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 1.24736 | 0.0634890 | ||||||||
\(387\) | −1.27430 | −0.0647761 | ||||||||
\(388\) | 3.62368 | 0.183965 | ||||||||
\(389\) | −1.24736 | −0.0632437 | −0.0316219 | − | 0.999500i | \(-0.510067\pi\) | ||||
−0.0316219 | + | 0.999500i | \(0.510067\pi\) | |||||||
\(390\) | 3.24736 | 0.164437 | ||||||||
\(391\) | 23.6150 | 1.19426 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 3.21641 | 0.162247 | ||||||||
\(394\) | 7.29045 | 0.367288 | ||||||||
\(395\) | 14.9289 | 0.751156 | ||||||||
\(396\) | −3.52033 | −0.176903 | ||||||||
\(397\) | 27.3133 | 1.37082 | 0.685408 | − | 0.728159i | \(-0.259624\pi\) | ||||
0.685408 | + | 0.728159i | \(0.259624\pi\) | |||||||
\(398\) | −2.86645 | −0.143682 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −3.29304 | −0.164652 | ||||||||
\(401\) | 13.4133 | 0.669830 | 0.334915 | − | 0.942248i | \(-0.391292\pi\) | ||||
0.334915 | + | 0.942248i | \(0.391292\pi\) | |||||||
\(402\) | 5.97307 | 0.297909 | ||||||||
\(403\) | 9.88213 | 0.492264 | ||||||||
\(404\) | −4.38092 | −0.217959 | ||||||||
\(405\) | −5.44571 | −0.270599 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −5.09854 | −0.252725 | ||||||||
\(408\) | −5.44793 | −0.269713 | ||||||||
\(409\) | −18.5434 | −0.916913 | −0.458456 | − | 0.888717i | \(-0.651597\pi\) | ||||
−0.458456 | + | 0.888717i | \(0.651597\pi\) | |||||||
\(410\) | −1.30651 | −0.0645238 | ||||||||
\(411\) | −6.00518 | −0.296214 | ||||||||
\(412\) | 10.3281 | 0.508827 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −7.96499 | −0.391458 | ||||||||
\(415\) | −0.219958 | −0.0107973 | ||||||||
\(416\) | 3.28237 | 0.160932 | ||||||||
\(417\) | −4.88012 | −0.238981 | ||||||||
\(418\) | 7.66329 | 0.374824 | ||||||||
\(419\) | 25.8265 | 1.26171 | 0.630853 | − | 0.775903i | \(-0.282705\pi\) | ||||
0.630853 | + | 0.775903i | \(0.282705\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 12.1460 | 0.591961 | 0.295980 | − | 0.955194i | \(-0.404354\pi\) | ||||
0.295980 | + | 0.955194i | \(0.404354\pi\) | |||||||
\(422\) | 19.0871 | 0.929145 | ||||||||
\(423\) | 7.65563 | 0.372230 | ||||||||
\(424\) | −11.6874 | −0.567591 | ||||||||
\(425\) | 23.6918 | 1.14922 | ||||||||
\(426\) | −12.4403 | −0.602735 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0.284962 | 0.0137742 | ||||||||
\(429\) | 3.60583 | 0.174091 | ||||||||
\(430\) | 0.686096 | 0.0330865 | ||||||||
\(431\) | −26.8009 | −1.29095 | −0.645476 | − | 0.763781i | \(-0.723341\pi\) | ||||
−0.645476 | + | 0.763781i | \(0.723341\pi\) | |||||||
\(432\) | 4.10921 | 0.197704 | ||||||||
\(433\) | −13.6058 | −0.653854 | −0.326927 | − | 0.945050i | \(-0.606013\pi\) | ||||
−0.326927 | + | 0.945050i | \(0.606013\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 6.39247 | 0.306496 | ||||||||
\(436\) | 2.47967 | 0.118755 | ||||||||
\(437\) | 17.3387 | 0.829423 | ||||||||
\(438\) | 10.5282 | 0.503057 | ||||||||
\(439\) | 15.4433 | 0.737070 | 0.368535 | − | 0.929614i | \(-0.379859\pi\) | ||||
0.368535 | + | 0.929614i | \(0.379859\pi\) | |||||||
\(440\) | 1.89539 | 0.0903590 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −23.6150 | −1.12325 | ||||||||
\(443\) | −20.2367 | −0.961474 | −0.480737 | − | 0.876865i | \(-0.659631\pi\) | ||||
−0.480737 | + | 0.876865i | \(0.659631\pi\) | |||||||
\(444\) | 2.66128 | 0.126299 | ||||||||
\(445\) | 15.5633 | 0.737770 | ||||||||
\(446\) | −23.2174 | −1.09937 | ||||||||
\(447\) | −8.49863 | −0.401971 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 36.1832 | 1.70759 | 0.853797 | − | 0.520607i | \(-0.174294\pi\) | ||||
0.853797 | + | 0.520607i | \(0.174294\pi\) | |||||||
\(450\) | −7.99087 | −0.376693 | ||||||||
\(451\) | −1.45073 | −0.0683121 | ||||||||
\(452\) | −5.80751 | −0.273162 | ||||||||
\(453\) | 14.8670 | 0.698514 | ||||||||
\(454\) | −18.4419 | −0.865519 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −4.00000 | −0.187317 | ||||||||
\(457\) | 41.7369 | 1.95237 | 0.976185 | − | 0.216940i | \(-0.0696075\pi\) | ||||
0.976185 | + | 0.216940i | \(0.0696075\pi\) | |||||||
\(458\) | 18.0081 | 0.841462 | ||||||||
\(459\) | −29.5637 | −1.37992 | ||||||||
\(460\) | 4.28844 | 0.199950 | ||||||||
\(461\) | 19.1038 | 0.889754 | 0.444877 | − | 0.895592i | \(-0.353247\pi\) | ||||
0.444877 | + | 0.895592i | \(0.353247\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −27.1874 | −1.26350 | −0.631752 | − | 0.775170i | \(-0.717664\pi\) | ||||
−0.631752 | + | 0.775170i | \(0.717664\pi\) | |||||||
\(464\) | 6.46140 | 0.299963 | ||||||||
\(465\) | −2.97855 | −0.138127 | ||||||||
\(466\) | −4.38899 | −0.203316 | ||||||||
\(467\) | −20.5787 | −0.952268 | −0.476134 | − | 0.879373i | \(-0.657962\pi\) | ||||
−0.476134 | + | 0.879373i | \(0.657962\pi\) | |||||||
\(468\) | 7.96499 | 0.368182 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −4.12188 | −0.190128 | ||||||||
\(471\) | 9.33872 | 0.430305 | ||||||||
\(472\) | 1.68283 | 0.0774584 | ||||||||
\(473\) | 0.761832 | 0.0350291 | ||||||||
\(474\) | −8.65262 | −0.397428 | ||||||||
\(475\) | 17.3951 | 0.798140 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −28.3606 | −1.29854 | ||||||||
\(478\) | −25.0020 | −1.14357 | ||||||||
\(479\) | 23.4525 | 1.07157 | 0.535787 | − | 0.844353i | \(-0.320015\pi\) | ||||
0.535787 | + | 0.844353i | \(0.320015\pi\) | |||||||
\(480\) | −0.989333 | −0.0451567 | ||||||||
\(481\) | 11.5358 | 0.525987 | ||||||||
\(482\) | 15.5145 | 0.706665 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −8.89539 | −0.404336 | ||||||||
\(485\) | −4.73436 | −0.214976 | ||||||||
\(486\) | 15.4839 | 0.702364 | ||||||||
\(487\) | 23.0381 | 1.04396 | 0.521979 | − | 0.852958i | \(-0.325194\pi\) | ||||
0.521979 | + | 0.852958i | \(0.325194\pi\) | |||||||
\(488\) | −0.842311 | −0.0381296 | ||||||||
\(489\) | 9.84558 | 0.445233 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 30.4073 | 1.37226 | 0.686130 | − | 0.727479i | \(-0.259308\pi\) | ||||
0.686130 | + | 0.727479i | \(0.259308\pi\) | |||||||
\(492\) | 0.757235 | 0.0341388 | ||||||||
\(493\) | −46.4865 | −2.09365 | ||||||||
\(494\) | −17.3387 | −0.780106 | ||||||||
\(495\) | 4.59934 | 0.206725 | ||||||||
\(496\) | −3.01067 | −0.135183 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0.127485 | 0.00571273 | ||||||||
\(499\) | 25.0657 | 1.12210 | 0.561049 | − | 0.827783i | \(-0.310398\pi\) | ||||
0.561049 | + | 0.827783i | \(0.310398\pi\) | |||||||
\(500\) | 10.8349 | 0.484552 | ||||||||
\(501\) | −17.3652 | −0.775821 | ||||||||
\(502\) | −15.6076 | −0.696602 | ||||||||
\(503\) | 25.3052 | 1.12831 | 0.564153 | − | 0.825671i | \(-0.309203\pi\) | ||||
0.564153 | + | 0.825671i | \(0.309203\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 5.72370 | 0.254701 | ||||||||
\(506\) | 4.76183 | 0.211689 | ||||||||
\(507\) | 1.68563 | 0.0748613 | ||||||||
\(508\) | −7.74657 | −0.343698 | ||||||||
\(509\) | 37.2289 | 1.65014 | 0.825072 | − | 0.565028i | \(-0.191135\pi\) | ||||
0.825072 | + | 0.565028i | \(0.191135\pi\) | |||||||
\(510\) | 7.11776 | 0.315180 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | −21.7064 | −0.958360 | ||||||||
\(514\) | −24.0706 | −1.06171 | ||||||||
\(515\) | −13.4937 | −0.594602 | ||||||||
\(516\) | −0.397653 | −0.0175057 | ||||||||
\(517\) | −4.57689 | −0.201291 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −17.6881 | −0.776422 | ||||||||
\(520\) | −4.28844 | −0.188061 | ||||||||
\(521\) | −43.5748 | −1.90905 | −0.954524 | − | 0.298134i | \(-0.903636\pi\) | ||||
−0.954524 | + | 0.298134i | \(0.903636\pi\) | |||||||
\(522\) | 15.6792 | 0.686259 | ||||||||
\(523\) | 15.8534 | 0.693221 | 0.346610 | − | 0.938009i | \(-0.387333\pi\) | ||||
0.346610 | + | 0.938009i | \(0.387333\pi\) | |||||||
\(524\) | −4.24757 | −0.185556 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 10.1971 | 0.444614 | ||||||||
\(527\) | 21.6602 | 0.943534 | ||||||||
\(528\) | −1.09854 | −0.0478079 | ||||||||
\(529\) | −12.2260 | −0.531566 | ||||||||
\(530\) | 15.2697 | 0.663273 | ||||||||
\(531\) | 4.08354 | 0.177210 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 3.28237 | 0.142175 | ||||||||
\(534\) | −9.02028 | −0.390346 | ||||||||
\(535\) | −0.372305 | −0.0160962 | ||||||||
\(536\) | −7.88799 | −0.340709 | ||||||||
\(537\) | −15.8917 | −0.685779 | ||||||||
\(538\) | 20.0988 | 0.866519 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −5.36871 | −0.231033 | ||||||||
\(541\) | −24.7567 | −1.06437 | −0.532186 | − | 0.846628i | \(-0.678629\pi\) | ||||
−0.532186 | + | 0.846628i | \(0.678629\pi\) | |||||||
\(542\) | 11.9035 | 0.511298 | ||||||||
\(543\) | −3.88731 | −0.166820 | ||||||||
\(544\) | 7.19450 | 0.308461 | ||||||||
\(545\) | −3.23971 | −0.138774 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 20.6072 | 0.881098 | 0.440549 | − | 0.897728i | \(-0.354784\pi\) | ||||
0.440549 | + | 0.897728i | \(0.354784\pi\) | |||||||
\(548\) | 7.93040 | 0.338770 | ||||||||
\(549\) | −2.04395 | −0.0872336 | ||||||||
\(550\) | 4.77731 | 0.203705 | ||||||||
\(551\) | −34.1315 | −1.45405 | ||||||||
\(552\) | −2.48553 | −0.105791 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 14.4586 | 0.614287 | ||||||||
\(555\) | −3.47698 | −0.147590 | ||||||||
\(556\) | 6.44466 | 0.273314 | ||||||||
\(557\) | −13.1388 | −0.556710 | −0.278355 | − | 0.960478i | \(-0.589789\pi\) | ||||
−0.278355 | + | 0.960478i | \(0.589789\pi\) | |||||||
\(558\) | −7.30567 | −0.309274 | ||||||||
\(559\) | −1.72370 | −0.0729046 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 7.90346 | 0.333685 | ||||||||
\(562\) | −7.80291 | −0.329146 | ||||||||
\(563\) | −7.84712 | −0.330717 | −0.165358 | − | 0.986234i | \(-0.552878\pi\) | ||||
−0.165358 | + | 0.986234i | \(0.552878\pi\) | |||||||
\(564\) | 2.38899 | 0.100595 | ||||||||
\(565\) | 7.58755 | 0.319211 | ||||||||
\(566\) | −15.8316 | −0.665454 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 16.4286 | 0.689329 | ||||||||
\(569\) | −39.5231 | −1.65689 | −0.828447 | − | 0.560068i | \(-0.810775\pi\) | ||||
−0.828447 | + | 0.560068i | \(0.810775\pi\) | |||||||
\(570\) | 5.22603 | 0.218894 | ||||||||
\(571\) | −18.5437 | −0.776028 | −0.388014 | − | 0.921653i | \(-0.626839\pi\) | ||||
−0.388014 | + | 0.921653i | \(0.626839\pi\) | |||||||
\(572\) | −4.76183 | −0.199102 | ||||||||
\(573\) | −9.92828 | −0.414760 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 10.8090 | 0.450766 | ||||||||
\(576\) | −2.42659 | −0.101108 | ||||||||
\(577\) | −28.3905 | −1.18191 | −0.590957 | − | 0.806703i | \(-0.701250\pi\) | ||||
−0.590957 | + | 0.806703i | \(0.701250\pi\) | |||||||
\(578\) | −34.7608 | −1.44586 | ||||||||
\(579\) | 0.944546 | 0.0392540 | ||||||||
\(580\) | −8.44186 | −0.350529 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 2.74398 | 0.113742 | ||||||||
\(583\) | 16.9553 | 0.702216 | ||||||||
\(584\) | −13.9035 | −0.575329 | ||||||||
\(585\) | −10.4063 | −0.430248 | ||||||||
\(586\) | 24.2361 | 1.00118 | ||||||||
\(587\) | −13.3433 | −0.550738 | −0.275369 | − | 0.961339i | \(-0.588800\pi\) | ||||
−0.275369 | + | 0.961339i | \(0.588800\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 15.9035 | 0.655291 | ||||||||
\(590\) | −2.19862 | −0.0905159 | ||||||||
\(591\) | 5.52059 | 0.227087 | ||||||||
\(592\) | −3.51447 | −0.144444 | ||||||||
\(593\) | 3.51795 | 0.144465 | 0.0722325 | − | 0.997388i | \(-0.476988\pi\) | ||||
0.0722325 | + | 0.997388i | \(0.476988\pi\) | |||||||
\(594\) | −5.96135 | −0.244597 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 11.2232 | 0.459721 | ||||||||
\(597\) | −2.17057 | −0.0888357 | ||||||||
\(598\) | −10.7740 | −0.440580 | ||||||||
\(599\) | 21.6729 | 0.885531 | 0.442765 | − | 0.896637i | \(-0.353997\pi\) | ||||
0.442765 | + | 0.896637i | \(0.353997\pi\) | |||||||
\(600\) | −2.49361 | −0.101801 | ||||||||
\(601\) | −19.7014 | −0.803635 | −0.401818 | − | 0.915720i | \(-0.631621\pi\) | ||||
−0.401818 | + | 0.915720i | \(0.631621\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −19.1410 | −0.779480 | ||||||||
\(604\) | −19.6333 | −0.798867 | ||||||||
\(605\) | 11.6219 | 0.472497 | ||||||||
\(606\) | −3.31738 | −0.134760 | ||||||||
\(607\) | 10.7105 | 0.434726 | 0.217363 | − | 0.976091i | \(-0.430254\pi\) | ||||
0.217363 | + | 0.976091i | \(0.430254\pi\) | |||||||
\(608\) | 5.28237 | 0.214229 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 1.10049 | 0.0445573 | ||||||||
\(611\) | 10.3555 | 0.418939 | ||||||||
\(612\) | 17.4581 | 0.705703 | ||||||||
\(613\) | −38.5744 | −1.55800 | −0.779002 | − | 0.627022i | \(-0.784274\pi\) | ||||
−0.779002 | + | 0.627022i | \(0.784274\pi\) | |||||||
\(614\) | 18.2689 | 0.737273 | ||||||||
\(615\) | −0.989333 | −0.0398938 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 28.5607 | 1.14981 | 0.574905 | − | 0.818220i | \(-0.305039\pi\) | ||||
0.574905 | + | 0.818220i | \(0.305039\pi\) | |||||||
\(618\) | 7.82077 | 0.314597 | ||||||||
\(619\) | −10.1562 | −0.408213 | −0.204106 | − | 0.978949i | \(-0.565429\pi\) | ||||
−0.204106 | + | 0.978949i | \(0.565429\pi\) | |||||||
\(620\) | 3.93346 | 0.157971 | ||||||||
\(621\) | −13.4880 | −0.541253 | ||||||||
\(622\) | 7.66175 | 0.307208 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 2.48553 | 0.0995008 | ||||||||
\(625\) | 2.30931 | 0.0923723 | ||||||||
\(626\) | −0.599758 | −0.0239711 | ||||||||
\(627\) | 5.80291 | 0.231746 | ||||||||
\(628\) | −12.3326 | −0.492126 | ||||||||
\(629\) | 25.2848 | 1.00817 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 14.4079 | 0.573567 | 0.286784 | − | 0.957995i | \(-0.407414\pi\) | ||||
0.286784 | + | 0.957995i | \(0.407414\pi\) | |||||||
\(632\) | 11.4266 | 0.454526 | ||||||||
\(633\) | 14.4534 | 0.574472 | ||||||||
\(634\) | 18.7773 | 0.745742 | ||||||||
\(635\) | 10.1209 | 0.401637 | ||||||||
\(636\) | −8.85013 | −0.350931 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −9.37373 | −0.371110 | ||||||||
\(639\) | 39.8656 | 1.57706 | ||||||||
\(640\) | 1.30651 | 0.0516442 | ||||||||
\(641\) | 12.8624 | 0.508034 | 0.254017 | − | 0.967200i | \(-0.418248\pi\) | ||||
0.254017 | + | 0.967200i | \(0.418248\pi\) | |||||||
\(642\) | 0.215784 | 0.00851630 | ||||||||
\(643\) | −37.9442 | −1.49637 | −0.748186 | − | 0.663489i | \(-0.769075\pi\) | ||||
−0.748186 | + | 0.663489i | \(0.769075\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0.519536 | 0.0204567 | ||||||||
\(646\) | −38.0040 | −1.49525 | ||||||||
\(647\) | −11.4749 | −0.451123 | −0.225562 | − | 0.974229i | \(-0.572422\pi\) | ||||
−0.225562 | + | 0.974229i | \(0.572422\pi\) | |||||||
\(648\) | −4.16814 | −0.163740 | ||||||||
\(649\) | −2.44132 | −0.0958304 | ||||||||
\(650\) | −10.8090 | −0.423963 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −13.0020 | −0.509198 | ||||||||
\(653\) | −41.3455 | −1.61798 | −0.808988 | − | 0.587825i | \(-0.799984\pi\) | ||||
−0.808988 | + | 0.587825i | \(0.799984\pi\) | |||||||
\(654\) | 1.87769 | 0.0734237 | ||||||||
\(655\) | 5.54948 | 0.216836 | ||||||||
\(656\) | −1.00000 | −0.0390434 | ||||||||
\(657\) | −33.7381 | −1.31625 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 24.2191 | 0.943442 | 0.471721 | − | 0.881748i | \(-0.343633\pi\) | ||||
0.471721 | + | 0.881748i | \(0.343633\pi\) | |||||||
\(660\) | 1.43525 | 0.0558672 | ||||||||
\(661\) | −9.66149 | −0.375789 | −0.187894 | − | 0.982189i | \(-0.560166\pi\) | ||||
−0.187894 | + | 0.982189i | \(0.560166\pi\) | |||||||
\(662\) | 20.2074 | 0.785382 | ||||||||
\(663\) | −17.8821 | −0.694484 | ||||||||
\(664\) | −0.168356 | −0.00653346 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −8.52820 | −0.330461 | ||||||||
\(667\) | −21.2087 | −0.821204 | ||||||||
\(668\) | 22.9324 | 0.887281 | ||||||||
\(669\) | −17.5810 | −0.679721 | ||||||||
\(670\) | 10.3057 | 0.398144 | ||||||||
\(671\) | 1.22196 | 0.0471734 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −40.1650 | −1.54825 | −0.774123 | − | 0.633035i | \(-0.781809\pi\) | ||||
−0.774123 | + | 0.633035i | \(0.781809\pi\) | |||||||
\(674\) | −14.3977 | −0.554577 | ||||||||
\(675\) | −13.5318 | −0.520839 | ||||||||
\(676\) | −2.22603 | −0.0856165 | ||||||||
\(677\) | 27.1852 | 1.04481 | 0.522405 | − | 0.852697i | \(-0.325035\pi\) | ||||
0.522405 | + | 0.852697i | \(0.325035\pi\) | |||||||
\(678\) | −4.39765 | −0.168891 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −9.39966 | −0.360460 | ||||||||
\(681\) | −13.9648 | −0.535133 | ||||||||
\(682\) | 4.36766 | 0.167246 | ||||||||
\(683\) | 19.2994 | 0.738470 | 0.369235 | − | 0.929336i | \(-0.379620\pi\) | ||||
0.369235 | + | 0.929336i | \(0.379620\pi\) | |||||||
\(684\) | 12.8182 | 0.490115 | ||||||||
\(685\) | −10.3611 | −0.395878 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 13.6364 | 0.520259 | ||||||||
\(688\) | 0.525138 | 0.0200207 | ||||||||
\(689\) | −38.3625 | −1.46149 | ||||||||
\(690\) | 3.24736 | 0.123625 | ||||||||
\(691\) | −21.4926 | −0.817615 | −0.408808 | − | 0.912621i | \(-0.634055\pi\) | ||||
−0.408808 | + | 0.912621i | \(0.634055\pi\) | |||||||
\(692\) | 23.3588 | 0.887968 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −26.2826 | −0.997673 | ||||||||
\(695\) | −8.41999 | −0.319388 | ||||||||
\(696\) | 4.89280 | 0.185461 | ||||||||
\(697\) | 7.19450 | 0.272511 | ||||||||
\(698\) | 18.2420 | 0.690469 | ||||||||
\(699\) | −3.32350 | −0.125706 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −37.2300 | −1.40616 | −0.703080 | − | 0.711111i | \(-0.748192\pi\) | ||||
−0.703080 | + | 0.711111i | \(0.748192\pi\) | |||||||
\(702\) | 13.4880 | 0.509070 | ||||||||
\(703\) | 18.5647 | 0.700183 | ||||||||
\(704\) | 1.45073 | 0.0546764 | ||||||||
\(705\) | −3.12124 | −0.117553 | ||||||||
\(706\) | −16.3407 | −0.614991 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 1.27430 | 0.0478910 | ||||||||
\(709\) | −35.4003 | −1.32949 | −0.664744 | − | 0.747071i | \(-0.731459\pi\) | ||||
−0.664744 | + | 0.747071i | \(0.731459\pi\) | |||||||
\(710\) | −21.4641 | −0.805533 | ||||||||
\(711\) | 27.7277 | 1.03987 | ||||||||
\(712\) | 11.9121 | 0.446426 | ||||||||
\(713\) | 9.88213 | 0.370089 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 6.22137 | 0.232666 | ||||||||
\(716\) | 20.9865 | 0.784304 | ||||||||
\(717\) | −18.9324 | −0.707044 | ||||||||
\(718\) | 1.69022 | 0.0630786 | ||||||||
\(719\) | 13.8821 | 0.517716 | 0.258858 | − | 0.965915i | \(-0.416654\pi\) | ||||
0.258858 | + | 0.965915i | \(0.416654\pi\) | |||||||
\(720\) | 3.17036 | 0.118152 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −8.90346 | −0.331353 | ||||||||
\(723\) | 11.7481 | 0.436917 | ||||||||
\(724\) | 5.13355 | 0.190787 | ||||||||
\(725\) | −21.2776 | −0.790231 | ||||||||
\(726\) | −6.73590 | −0.249993 | ||||||||
\(727\) | −19.8069 | −0.734598 | −0.367299 | − | 0.930103i | \(-0.619717\pi\) | ||||
−0.367299 | + | 0.930103i | \(0.619717\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −0.779478 | −0.0288696 | ||||||||
\(730\) | 18.1650 | 0.672316 | ||||||||
\(731\) | −3.77810 | −0.139738 | ||||||||
\(732\) | −0.637828 | −0.0235748 | ||||||||
\(733\) | 16.1262 | 0.595636 | 0.297818 | − | 0.954623i | \(-0.403741\pi\) | ||||
0.297818 | + | 0.954623i | \(0.403741\pi\) | |||||||
\(734\) | −12.9411 | −0.477663 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 3.28237 | 0.120990 | ||||||||
\(737\) | 11.4433 | 0.421521 | ||||||||
\(738\) | −2.42659 | −0.0893242 | ||||||||
\(739\) | 31.5002 | 1.15875 | 0.579377 | − | 0.815060i | \(-0.303296\pi\) | ||||
0.579377 | + | 0.815060i | \(0.303296\pi\) | |||||||
\(740\) | 4.59168 | 0.168794 | ||||||||
\(741\) | −13.1295 | −0.482324 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −3.98268 | −0.146110 | −0.0730552 | − | 0.997328i | \(-0.523275\pi\) | ||||
−0.0730552 | + | 0.997328i | \(0.523275\pi\) | |||||||
\(744\) | −2.27978 | −0.0835809 | ||||||||
\(745\) | −14.6632 | −0.537219 | ||||||||
\(746\) | −16.6440 | −0.609379 | ||||||||
\(747\) | −0.408531 | −0.0149474 | ||||||||
\(748\) | −10.4373 | −0.381624 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 8.20458 | 0.299589 | ||||||||
\(751\) | 32.1436 | 1.17294 | 0.586469 | − | 0.809972i | \(-0.300518\pi\) | ||||
0.586469 | + | 0.809972i | \(0.300518\pi\) | |||||||
\(752\) | −3.15489 | −0.115047 | ||||||||
\(753\) | −11.8186 | −0.430695 | ||||||||
\(754\) | 21.2087 | 0.772376 | ||||||||
\(755\) | 25.6510 | 0.933537 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 0.403512 | 0.0146659 | 0.00733294 | − | 0.999973i | \(-0.497666\pi\) | ||||
0.00733294 | + | 0.999973i | \(0.497666\pi\) | |||||||
\(758\) | −25.0995 | −0.911655 | ||||||||
\(759\) | 3.60583 | 0.130883 | ||||||||
\(760\) | −6.90146 | −0.250342 | ||||||||
\(761\) | −0.997993 | −0.0361772 | −0.0180886 | − | 0.999836i | \(-0.505758\pi\) | ||||
−0.0180886 | + | 0.999836i | \(0.505758\pi\) | |||||||
\(762\) | −5.86598 | −0.212502 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 13.1112 | 0.474347 | ||||||||
\(765\) | −22.8092 | −0.824667 | ||||||||
\(766\) | −4.00000 | −0.144526 | ||||||||
\(767\) | 5.52366 | 0.199448 | ||||||||
\(768\) | −0.757235 | −0.0273244 | ||||||||
\(769\) | 0.595695 | 0.0214813 | 0.0107406 | − | 0.999942i | \(-0.496581\pi\) | ||||
0.0107406 | + | 0.999942i | \(0.496581\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −18.2271 | −0.656432 | ||||||||
\(772\) | −1.24736 | −0.0448935 | ||||||||
\(773\) | −34.2148 | −1.23062 | −0.615310 | − | 0.788285i | \(-0.710969\pi\) | ||||
−0.615310 | + | 0.788285i | \(0.710969\pi\) | |||||||
\(774\) | 1.27430 | 0.0458036 | ||||||||
\(775\) | 9.91424 | 0.356130 | ||||||||
\(776\) | −3.62368 | −0.130083 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 1.24736 | 0.0447201 | ||||||||
\(779\) | 5.28237 | 0.189261 | ||||||||
\(780\) | −3.24736 | −0.116274 | ||||||||
\(781\) | −23.8334 | −0.852828 | ||||||||
\(782\) | −23.6150 | −0.844471 | ||||||||
\(783\) | 26.5512 | 0.948863 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 16.1127 | 0.575087 | ||||||||
\(786\) | −3.21641 | −0.114726 | ||||||||
\(787\) | −37.5690 | −1.33919 | −0.669595 | − | 0.742727i | \(-0.733532\pi\) | ||||
−0.669595 | + | 0.742727i | \(0.733532\pi\) | |||||||
\(788\) | −7.29045 | −0.259712 | ||||||||
\(789\) | 7.72159 | 0.274896 | ||||||||
\(790\) | −14.9289 | −0.531147 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 3.52033 | 0.125089 | ||||||||
\(793\) | −2.76478 | −0.0981802 | ||||||||
\(794\) | −27.3133 | −0.969314 | ||||||||
\(795\) | 11.5628 | 0.410089 | ||||||||
\(796\) | 2.86645 | 0.101598 | ||||||||
\(797\) | −21.5101 | −0.761928 | −0.380964 | − | 0.924590i | \(-0.624408\pi\) | ||||
−0.380964 | + | 0.924590i | \(0.624408\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 22.6978 | 0.802992 | ||||||||
\(800\) | 3.29304 | 0.116427 | ||||||||
\(801\) | 28.9059 | 1.02134 | ||||||||
\(802\) | −13.4133 | −0.473641 | ||||||||
\(803\) | 20.1702 | 0.711789 | ||||||||
\(804\) | −5.97307 | −0.210654 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −9.88213 | −0.348083 | ||||||||
\(807\) | 15.2195 | 0.535751 | ||||||||
\(808\) | 4.38092 | 0.154120 | ||||||||
\(809\) | −20.5982 | −0.724195 | −0.362097 | − | 0.932140i | \(-0.617939\pi\) | ||||
−0.362097 | + | 0.932140i | \(0.617939\pi\) | |||||||
\(810\) | 5.44571 | 0.191343 | ||||||||
\(811\) | −30.3481 | −1.06567 | −0.532833 | − | 0.846220i | \(-0.678873\pi\) | ||||
−0.532833 | + | 0.846220i | \(0.678873\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 9.01372 | 0.316125 | ||||||||
\(814\) | 5.09854 | 0.178704 | ||||||||
\(815\) | 16.9872 | 0.595036 | ||||||||
\(816\) | 5.44793 | 0.190716 | ||||||||
\(817\) | −2.77397 | −0.0970490 | ||||||||
\(818\) | 18.5434 | 0.648355 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 1.30651 | 0.0456252 | ||||||||
\(821\) | 16.5865 | 0.578873 | 0.289436 | − | 0.957197i | \(-0.406532\pi\) | ||||
0.289436 | + | 0.957197i | \(0.406532\pi\) | |||||||
\(822\) | 6.00518 | 0.209455 | ||||||||
\(823\) | −23.9217 | −0.833859 | −0.416930 | − | 0.908939i | \(-0.636894\pi\) | ||||
−0.416930 | + | 0.908939i | \(0.636894\pi\) | |||||||
\(824\) | −10.3281 | −0.359795 | ||||||||
\(825\) | 3.61755 | 0.125947 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −29.1394 | −1.01327 | −0.506637 | − | 0.862159i | \(-0.669112\pi\) | ||||
−0.506637 | + | 0.862159i | \(0.669112\pi\) | |||||||
\(828\) | 7.96499 | 0.276802 | ||||||||
\(829\) | 18.9911 | 0.659589 | 0.329795 | − | 0.944053i | \(-0.393021\pi\) | ||||
0.329795 | + | 0.944053i | \(0.393021\pi\) | |||||||
\(830\) | 0.219958 | 0.00763484 | ||||||||
\(831\) | 10.9486 | 0.379801 | ||||||||
\(832\) | −3.28237 | −0.113796 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 4.88012 | 0.168985 | ||||||||
\(835\) | −29.9613 | −1.03686 | ||||||||
\(836\) | −7.66329 | −0.265040 | ||||||||
\(837\) | −12.3715 | −0.427620 | ||||||||
\(838\) | −25.8265 | −0.892160 | ||||||||
\(839\) | −42.7434 | −1.47567 | −0.737833 | − | 0.674983i | \(-0.764151\pi\) | ||||
−0.737833 | + | 0.674983i | \(0.764151\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 12.7496 | 0.439642 | ||||||||
\(842\) | −12.1460 | −0.418579 | ||||||||
\(843\) | −5.90864 | −0.203504 | ||||||||
\(844\) | −19.0871 | −0.657004 | ||||||||
\(845\) | 2.90832 | 0.100049 | ||||||||
\(846\) | −7.65563 | −0.263206 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 11.6874 | 0.401348 | ||||||||
\(849\) | −11.9883 | −0.411437 | ||||||||
\(850\) | −23.6918 | −0.812621 | ||||||||
\(851\) | 11.5358 | 0.395442 | ||||||||
\(852\) | 12.4403 | 0.426198 | ||||||||
\(853\) | 30.4304 | 1.04192 | 0.520958 | − | 0.853582i | \(-0.325575\pi\) | ||||
0.520958 | + | 0.853582i | \(0.325575\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −16.7470 | −0.572737 | ||||||||
\(856\) | −0.284962 | −0.00973982 | ||||||||
\(857\) | 39.5672 | 1.35159 | 0.675794 | − | 0.737090i | \(-0.263801\pi\) | ||||
0.675794 | + | 0.737090i | \(0.263801\pi\) | |||||||
\(858\) | −3.60583 | −0.123101 | ||||||||
\(859\) | 17.7286 | 0.604891 | 0.302445 | − | 0.953167i | \(-0.402197\pi\) | ||||
0.302445 | + | 0.953167i | \(0.402197\pi\) | |||||||
\(860\) | −0.686096 | −0.0233957 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 26.8009 | 0.912841 | ||||||||
\(863\) | −6.52820 | −0.222222 | −0.111111 | − | 0.993808i | \(-0.535441\pi\) | ||||
−0.111111 | + | 0.993808i | \(0.535441\pi\) | |||||||
\(864\) | −4.10921 | −0.139798 | ||||||||
\(865\) | −30.5184 | −1.03766 | ||||||||
\(866\) | 13.6058 | 0.462345 | ||||||||
\(867\) | −26.3221 | −0.893945 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −16.5769 | −0.562332 | ||||||||
\(870\) | −6.39247 | −0.216725 | ||||||||
\(871\) | −25.8913 | −0.877294 | ||||||||
\(872\) | −2.47967 | −0.0839722 | ||||||||
\(873\) | −8.79320 | −0.297605 | ||||||||
\(874\) | −17.3387 | −0.586491 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −10.5282 | −0.355715 | ||||||||
\(877\) | 20.0065 | 0.675573 | 0.337786 | − | 0.941223i | \(-0.390322\pi\) | ||||
0.337786 | + | 0.941223i | \(0.390322\pi\) | |||||||
\(878\) | −15.4433 | −0.521187 | ||||||||
\(879\) | 18.3524 | 0.619013 | ||||||||
\(880\) | −1.89539 | −0.0638935 | ||||||||
\(881\) | 4.03613 | 0.135981 | 0.0679903 | − | 0.997686i | \(-0.478341\pi\) | ||||
0.0679903 | + | 0.997686i | \(0.478341\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −57.2725 | −1.92737 | −0.963686 | − | 0.267039i | \(-0.913955\pi\) | ||||
−0.963686 | + | 0.267039i | \(0.913955\pi\) | |||||||
\(884\) | 23.6150 | 0.794259 | ||||||||
\(885\) | −1.66488 | −0.0559642 | ||||||||
\(886\) | 20.2367 | 0.679865 | ||||||||
\(887\) | 5.83232 | 0.195830 | 0.0979151 | − | 0.995195i | \(-0.468783\pi\) | ||||
0.0979151 | + | 0.995195i | \(0.468783\pi\) | |||||||
\(888\) | −2.66128 | −0.0893068 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −15.5633 | −0.521682 | ||||||||
\(891\) | 6.04685 | 0.202577 | ||||||||
\(892\) | 23.2174 | 0.777375 | ||||||||
\(893\) | 16.6653 | 0.557683 | ||||||||
\(894\) | 8.49863 | 0.284237 | ||||||||
\(895\) | −27.4191 | −0.916518 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −8.15843 | −0.272402 | ||||||||
\(898\) | −36.1832 | −1.20745 | ||||||||
\(899\) | −19.4531 | −0.648797 | ||||||||
\(900\) | 7.99087 | 0.266362 | ||||||||
\(901\) | −84.0851 | −2.80128 | ||||||||
\(902\) | 1.45073 | 0.0483040 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 5.80751 | 0.193155 | ||||||||
\(905\) | −6.70703 | −0.222949 | ||||||||
\(906\) | −14.8670 | −0.493924 | ||||||||
\(907\) | −4.33323 | −0.143883 | −0.0719413 | − | 0.997409i | \(-0.522919\pi\) | ||||
−0.0719413 | + | 0.997409i | \(0.522919\pi\) | |||||||
\(908\) | 18.4419 | 0.612015 | ||||||||
\(909\) | 10.6307 | 0.352598 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −25.3737 | −0.840669 | −0.420335 | − | 0.907369i | \(-0.638087\pi\) | ||||
−0.420335 | + | 0.907369i | \(0.638087\pi\) | |||||||
\(912\) | 4.00000 | 0.132453 | ||||||||
\(913\) | 0.244238 | 0.00808310 | ||||||||
\(914\) | −41.7369 | −1.38053 | ||||||||
\(915\) | 0.833326 | 0.0275489 | ||||||||
\(916\) | −18.0081 | −0.595004 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 29.5637 | 0.975747 | ||||||||
\(919\) | 23.7552 | 0.783611 | 0.391806 | − | 0.920048i | \(-0.371851\pi\) | ||||
0.391806 | + | 0.920048i | \(0.371851\pi\) | |||||||
\(920\) | −4.28844 | −0.141386 | ||||||||
\(921\) | 13.8339 | 0.455841 | ||||||||
\(922\) | −19.1038 | −0.629151 | ||||||||
\(923\) | 53.9248 | 1.77496 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 11.5733 | 0.380527 | ||||||||
\(926\) | 27.1874 | 0.893433 | ||||||||
\(927\) | −25.0620 | −0.823144 | ||||||||
\(928\) | −6.46140 | −0.212106 | ||||||||
\(929\) | 23.5906 | 0.773983 | 0.386991 | − | 0.922083i | \(-0.373514\pi\) | ||||
0.386991 | + | 0.922083i | \(0.373514\pi\) | |||||||
\(930\) | 2.97855 | 0.0976706 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 4.38899 | 0.143766 | ||||||||
\(933\) | 5.80175 | 0.189941 | ||||||||
\(934\) | 20.5787 | 0.673355 | ||||||||
\(935\) | 13.6364 | 0.445956 | ||||||||
\(936\) | −7.96499 | −0.260344 | ||||||||
\(937\) | 13.9954 | 0.457208 | 0.228604 | − | 0.973519i | \(-0.426584\pi\) | ||||
0.228604 | + | 0.973519i | \(0.426584\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −0.454158 | −0.0148209 | ||||||||
\(940\) | 4.12188 | 0.134441 | ||||||||
\(941\) | −10.1293 | −0.330205 | −0.165103 | − | 0.986276i | \(-0.552796\pi\) | ||||
−0.165103 | + | 0.986276i | \(0.552796\pi\) | |||||||
\(942\) | −9.33872 | −0.304272 | ||||||||
\(943\) | 3.28237 | 0.106889 | ||||||||
\(944\) | −1.68283 | −0.0547713 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −0.761832 | −0.0247693 | ||||||||
\(947\) | −48.3434 | −1.57095 | −0.785474 | − | 0.618894i | \(-0.787581\pi\) | ||||
−0.785474 | + | 0.618894i | \(0.787581\pi\) | |||||||
\(948\) | 8.65262 | 0.281024 | ||||||||
\(949\) | −45.6364 | −1.48142 | ||||||||
\(950\) | −17.3951 | −0.564370 | ||||||||
\(951\) | 14.2188 | 0.461078 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 36.5180 | 1.18293 | 0.591467 | − | 0.806329i | \(-0.298549\pi\) | ||||
0.591467 | + | 0.806329i | \(0.298549\pi\) | |||||||
\(954\) | 28.3606 | 0.918209 | ||||||||
\(955\) | −17.1299 | −0.554310 | ||||||||
\(956\) | 25.0020 | 0.808623 | ||||||||
\(957\) | −7.09812 | −0.229450 | ||||||||
\(958\) | −23.4525 | −0.757717 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0.989333 | 0.0319306 | ||||||||
\(961\) | −21.9359 | −0.707609 | ||||||||
\(962\) | −11.5358 | −0.371929 | ||||||||
\(963\) | −0.691488 | −0.0222829 | ||||||||
\(964\) | −15.5145 | −0.499687 | ||||||||
\(965\) | 1.62969 | 0.0524614 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 56.5388 | 1.81816 | 0.909082 | − | 0.416617i | \(-0.136784\pi\) | ||||
0.909082 | + | 0.416617i | \(0.136784\pi\) | |||||||
\(968\) | 8.89539 | 0.285909 | ||||||||
\(969\) | −28.7780 | −0.924482 | ||||||||
\(970\) | 4.73436 | 0.152011 | ||||||||
\(971\) | −7.33370 | −0.235350 | −0.117675 | − | 0.993052i | \(-0.537544\pi\) | ||||
−0.117675 | + | 0.993052i | \(0.537544\pi\) | |||||||
\(972\) | −15.4839 | −0.496646 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −23.0381 | −0.738189 | ||||||||
\(975\) | −8.18495 | −0.262128 | ||||||||
\(976\) | 0.842311 | 0.0269617 | ||||||||
\(977\) | −52.2738 | −1.67239 | −0.836193 | − | 0.548435i | \(-0.815224\pi\) | ||||
−0.836193 | + | 0.548435i | \(0.815224\pi\) | |||||||
\(978\) | −9.84558 | −0.314827 | ||||||||
\(979\) | −17.2813 | −0.552311 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −6.01715 | −0.192113 | ||||||||
\(982\) | −30.4073 | −0.970335 | ||||||||
\(983\) | −22.8014 | −0.727253 | −0.363627 | − | 0.931545i | \(-0.618462\pi\) | ||||
−0.363627 | + | 0.931545i | \(0.618462\pi\) | |||||||
\(984\) | −0.757235 | −0.0241398 | ||||||||
\(985\) | 9.52502 | 0.303492 | ||||||||
\(986\) | 46.4865 | 1.48043 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 17.3387 | 0.551618 | ||||||||
\(989\) | −1.72370 | −0.0548104 | ||||||||
\(990\) | −4.59934 | −0.146176 | ||||||||
\(991\) | −41.1147 | −1.30605 | −0.653026 | − | 0.757336i | \(-0.726501\pi\) | ||||
−0.653026 | + | 0.757336i | \(0.726501\pi\) | |||||||
\(992\) | 3.01067 | 0.0955888 | ||||||||
\(993\) | 15.3017 | 0.485586 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −3.74503 | −0.118725 | ||||||||
\(996\) | −0.127485 | −0.00403951 | ||||||||
\(997\) | 45.2747 | 1.43386 | 0.716932 | − | 0.697144i | \(-0.245546\pi\) | ||||
0.716932 | + | 0.697144i | \(0.245546\pi\) | |||||||
\(998\) | −25.0657 | −0.793442 | ||||||||
\(999\) | −14.4417 | −0.456915 |
(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 | 4018.2.a.bj.1.2 | 4 | ||
7.6 | odd | 2 | 574.2.a.m.1.3 | ✓ | 4 | ||
21.20 | even | 2 | 5166.2.a.bx.1.3 | 4 | |||
28.27 | even | 2 | 4592.2.a.ba.1.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
574.2.a.m.1.3 | ✓ | 4 | 7.6 | odd | 2 | ||
4018.2.a.bj.1.2 | 4 | 1.1 | even | 1 | trivial | ||
4592.2.a.ba.1.2 | 4 | 28.27 | even | 2 | |||
5166.2.a.bx.1.3 | 4 | 21.20 | even | 2 |