Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3640,2,Mod(1,3640)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3640, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 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("3640.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3640 = 2^{3} \cdot 5 \cdot 7 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3640.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: | \(29.0655463357\) |
Analytic rank: | \(1\) |
Dimension: | \(5\) |
Coefficient field: | 5.5.1194649.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{5} - 8x^{3} - 3x^{2} + 10x + 4 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.5 | ||
Root | \(-2.24233\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3640.1 |
$q$-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 | ||||||||
\(3\) | 2.24233 | 1.29461 | 0.647305 | − | 0.762231i | \(-0.275896\pi\) | ||||
0.647305 | + | 0.762231i | \(0.275896\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 2.02804 | 0.676014 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −5.09092 | −1.53497 | −0.767485 | − | 0.641067i | \(-0.778492\pi\) | ||||
−0.767485 | + | 0.641067i | \(0.778492\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.00000 | −0.277350 | ||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −2.24233 | −0.578967 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −2.63792 | −0.639790 | −0.319895 | − | 0.947453i | \(-0.603648\pi\) | ||||
−0.319895 | + | 0.947453i | \(0.603648\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 6.11896 | 1.40379 | 0.701893 | − | 0.712282i | \(-0.252338\pi\) | ||||
0.701893 | + | 0.712282i | \(0.252338\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 2.24233 | 0.489316 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −5.44982 | −1.13637 | −0.568183 | − | 0.822902i | \(-0.692354\pi\) | ||||
−0.568183 | + | 0.822902i | \(0.692354\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −2.17945 | −0.419435 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −6.47239 | −1.20189 | −0.600947 | − | 0.799289i | \(-0.705210\pi\) | ||||
−0.600947 | + | 0.799289i | \(0.705210\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.50723 | −0.629917 | −0.314959 | − | 0.949105i | \(-0.601991\pi\) | ||||
−0.314959 | + | 0.949105i | \(0.601991\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −11.4155 | −1.98719 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −1.00000 | −0.169031 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0.458471 | 0.0753721 | 0.0376860 | − | 0.999290i | \(-0.488001\pi\) | ||||
0.0376860 | + | 0.999290i | \(0.488001\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −2.24233 | −0.359060 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −7.15380 | −1.11724 | −0.558618 | − | 0.829425i | \(-0.688668\pi\) | ||||
−0.558618 | + | 0.829425i | \(0.688668\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.62019 | 0.399575 | 0.199787 | − | 0.979839i | \(-0.435975\pi\) | ||||
0.199787 | + | 0.979839i | \(0.435975\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −2.02804 | −0.302323 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −8.09454 | −1.18071 | −0.590355 | − | 0.807144i | \(-0.701012\pi\) | ||||
−0.590355 | + | 0.807144i | \(0.701012\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −5.91509 | −0.828278 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 3.74956 | 0.515042 | 0.257521 | − | 0.966273i | \(-0.417094\pi\) | ||||
0.257521 | + | 0.966273i | \(0.417094\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 5.09092 | 0.686460 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 13.7207 | 1.81736 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 9.17319 | 1.19425 | 0.597124 | − | 0.802149i | \(-0.296310\pi\) | ||||
0.597124 | + | 0.802149i | \(0.296310\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 9.41552 | 1.20553 | 0.602767 | − | 0.797917i | \(-0.294065\pi\) | ||||
0.602767 | + | 0.797917i | \(0.294065\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 2.02804 | 0.255509 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 1.00000 | 0.124035 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −5.80828 | −0.709595 | −0.354797 | − | 0.934943i | \(-0.615450\pi\) | ||||
−0.354797 | + | 0.934943i | \(0.615450\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −12.2203 | −1.47115 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −5.83994 | −0.693074 | −0.346537 | − | 0.938036i | \(-0.612642\pi\) | ||||
−0.346537 | + | 0.938036i | \(0.612642\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −8.27638 | −0.968677 | −0.484339 | − | 0.874881i | \(-0.660940\pi\) | ||||
−0.484339 | + | 0.874881i | \(0.660940\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 2.24233 | 0.258922 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −5.09092 | −0.580164 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 3.86437 | 0.434775 | 0.217388 | − | 0.976085i | \(-0.430246\pi\) | ||||
0.217388 | + | 0.976085i | \(0.430246\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −10.9712 | −1.21902 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −8.61042 | −0.945116 | −0.472558 | − | 0.881300i | \(-0.656669\pi\) | ||||
−0.472558 | + | 0.881300i | \(0.656669\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 2.63792 | 0.286123 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −14.5132 | −1.55598 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −11.7618 | −1.24675 | −0.623376 | − | 0.781923i | \(-0.714239\pi\) | ||||
−0.623376 | + | 0.781923i | \(0.714239\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.00000 | −0.104828 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −7.86437 | −0.815497 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −6.11896 | −0.627792 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 8.15062 | 0.827570 | 0.413785 | − | 0.910375i | \(-0.364206\pi\) | ||||
0.413785 | + | 0.910375i | \(0.364206\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −10.3246 | −1.03766 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −14.9869 | −1.49126 | −0.745629 | − | 0.666362i | \(-0.767851\pi\) | ||||
−0.745629 | + | 0.666362i | \(0.767851\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −13.4923 | −1.32944 | −0.664719 | − | 0.747093i | \(-0.731449\pi\) | ||||
−0.664719 | + | 0.747093i | \(0.731449\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −2.24233 | −0.218829 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −5.04876 | −0.488082 | −0.244041 | − | 0.969765i | \(-0.578473\pi\) | ||||
−0.244041 | + | 0.969765i | \(0.578473\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 6.11217 | 0.585440 | 0.292720 | − | 0.956198i | \(-0.405440\pi\) | ||||
0.292720 | + | 0.956198i | \(0.405440\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 1.02804 | 0.0975774 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 13.9002 | 1.30762 | 0.653810 | − | 0.756659i | \(-0.273170\pi\) | ||||
0.653810 | + | 0.756659i | \(0.273170\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 5.44982 | 0.508199 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −2.02804 | −0.187493 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −2.63792 | −0.241818 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 14.9175 | 1.35613 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −16.0412 | −1.44638 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 16.1687 | 1.43474 | 0.717370 | − | 0.696692i | \(-0.245346\pi\) | ||||
0.717370 | + | 0.696692i | \(0.245346\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 5.87532 | 0.517293 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 19.9423 | 1.74237 | 0.871185 | − | 0.490954i | \(-0.163352\pi\) | ||||
0.871185 | + | 0.490954i | \(0.163352\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 6.11896 | 0.530581 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 2.17945 | 0.187577 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 22.5405 | 1.92576 | 0.962882 | − | 0.269922i | \(-0.0869978\pi\) | ||||
0.962882 | + | 0.269922i | \(0.0869978\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −19.4855 | −1.65274 | −0.826371 | − | 0.563127i | \(-0.809598\pi\) | ||||
−0.826371 | + | 0.563127i | \(0.809598\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −18.1506 | −1.52856 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 5.09092 | 0.425724 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 6.47239 | 0.537503 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 2.24233 | 0.184944 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −10.5159 | −0.861494 | −0.430747 | − | 0.902473i | \(-0.641750\pi\) | ||||
−0.430747 | + | 0.902473i | \(0.641750\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −14.4613 | −1.17684 | −0.588422 | − | 0.808554i | \(-0.700251\pi\) | ||||
−0.588422 | + | 0.808554i | \(0.700251\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −5.34981 | −0.432507 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 3.50723 | 0.281708 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1.74790 | 0.139498 | 0.0697489 | − | 0.997565i | \(-0.477780\pi\) | ||||
0.0697489 | + | 0.997565i | \(0.477780\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 8.40775 | 0.666778 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −5.44982 | −0.429506 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −4.80345 | −0.376235 | −0.188118 | − | 0.982147i | \(-0.560239\pi\) | ||||
−0.188118 | + | 0.982147i | \(0.560239\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 11.4155 | 0.888697 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −12.1367 | −0.939166 | −0.469583 | − | 0.882888i | \(-0.655596\pi\) | ||||
−0.469583 | + | 0.882888i | \(0.655596\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 12.4095 | 0.948979 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 5.45901 | 0.415041 | 0.207520 | − | 0.978231i | \(-0.433461\pi\) | ||||
0.207520 | + | 0.978231i | \(0.433461\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1.00000 | 0.0755929 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 20.5693 | 1.54609 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −12.0323 | −0.899335 | −0.449668 | − | 0.893196i | \(-0.648458\pi\) | ||||
−0.449668 | + | 0.893196i | \(0.648458\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −3.50142 | −0.260258 | −0.130129 | − | 0.991497i | \(-0.541539\pi\) | ||||
−0.130129 | + | 0.991497i | \(0.541539\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 21.1127 | 1.56070 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −0.458471 | −0.0337074 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 13.4294 | 0.982058 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −2.17945 | −0.158532 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −0.371166 | −0.0268566 | −0.0134283 | − | 0.999910i | \(-0.504274\pi\) | ||||
−0.0134283 | + | 0.999910i | \(0.504274\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −14.3314 | −1.03160 | −0.515798 | − | 0.856710i | \(-0.672505\pi\) | ||||
−0.515798 | + | 0.856710i | \(0.672505\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 2.24233 | 0.160577 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −18.6403 | −1.32807 | −0.664034 | − | 0.747703i | \(-0.731157\pi\) | ||||
−0.664034 | + | 0.747703i | \(0.731157\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 8.80477 | 0.624154 | 0.312077 | − | 0.950057i | \(-0.398975\pi\) | ||||
0.312077 | + | 0.950057i | \(0.398975\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −13.0241 | −0.918648 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −6.47239 | −0.454273 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 7.15380 | 0.499643 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −11.0525 | −0.768200 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −31.1512 | −2.15477 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 16.8270 | 1.15842 | 0.579209 | − | 0.815179i | \(-0.303361\pi\) | ||||
0.579209 | + | 0.815179i | \(0.303361\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −13.0951 | −0.897260 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −2.62019 | −0.178695 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −3.50723 | −0.238086 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −18.5584 | −1.25406 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 2.63792 | 0.177446 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 14.7610 | 0.988472 | 0.494236 | − | 0.869328i | \(-0.335448\pi\) | ||||
0.494236 | + | 0.869328i | \(0.335448\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 2.02804 | 0.135203 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 21.2596 | 1.41105 | 0.705525 | − | 0.708685i | \(-0.250711\pi\) | ||||
0.705525 | + | 0.708685i | \(0.250711\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −19.6072 | −1.29568 | −0.647841 | − | 0.761775i | \(-0.724328\pi\) | ||||
−0.647841 | + | 0.761775i | \(0.724328\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −11.4155 | −0.751086 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 4.45714 | 0.291997 | 0.145999 | − | 0.989285i | \(-0.453360\pi\) | ||||
0.145999 | + | 0.989285i | \(0.453360\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 8.09454 | 0.528029 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 8.66519 | 0.562864 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 14.5871 | 0.943558 | 0.471779 | − | 0.881717i | \(-0.343612\pi\) | ||||
0.471779 | + | 0.881717i | \(0.343612\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 23.8588 | 1.53688 | 0.768439 | − | 0.639923i | \(-0.221034\pi\) | ||||
0.768439 | + | 0.639923i | \(0.221034\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −18.0626 | −1.15872 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −1.00000 | −0.0638877 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −6.11896 | −0.389340 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −19.3074 | −1.22356 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 2.99946 | 0.189324 | 0.0946621 | − | 0.995509i | \(-0.469823\pi\) | ||||
0.0946621 | + | 0.995509i | \(0.469823\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 27.7446 | 1.74429 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 5.91509 | 0.370417 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 12.4674 | 0.777693 | 0.388846 | − | 0.921303i | \(-0.372874\pi\) | ||||
0.388846 | + | 0.921303i | \(0.372874\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0.458471 | 0.0284880 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −13.1263 | −0.812497 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 13.3601 | 0.823817 | 0.411909 | − | 0.911225i | \(-0.364862\pi\) | ||||
0.411909 | + | 0.911225i | \(0.364862\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −3.74956 | −0.230334 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −26.3739 | −1.61406 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 2.98695 | 0.182117 | 0.0910587 | − | 0.995846i | \(-0.470975\pi\) | ||||
0.0910587 | + | 0.995846i | \(0.470975\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −15.0296 | −0.912981 | −0.456490 | − | 0.889728i | \(-0.650894\pi\) | ||||
−0.456490 | + | 0.889728i | \(0.650894\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −2.24233 | −0.135712 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −5.09092 | −0.306994 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −28.5000 | −1.71240 | −0.856199 | − | 0.516646i | \(-0.827180\pi\) | ||||
−0.856199 | + | 0.516646i | \(0.827180\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −7.11281 | −0.425833 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 21.2145 | 1.26555 | 0.632775 | − | 0.774336i | \(-0.281916\pi\) | ||||
0.632775 | + | 0.774336i | \(0.281916\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 10.9340 | 0.649956 | 0.324978 | − | 0.945722i | \(-0.394643\pi\) | ||||
0.324978 | + | 0.945722i | \(0.394643\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −13.7207 | −0.812746 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −7.15380 | −0.422276 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −10.0414 | −0.590669 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 18.2764 | 1.07138 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −28.5931 | −1.67043 | −0.835214 | − | 0.549925i | \(-0.814656\pi\) | ||||
−0.835214 | + | 0.549925i | \(0.814656\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −9.17319 | −0.534084 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 11.0954 | 0.643821 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 5.44982 | 0.315171 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2.62019 | 0.151025 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −33.6057 | −1.93060 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −9.41552 | −0.539131 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −23.1899 | −1.32352 | −0.661760 | − | 0.749716i | \(-0.730190\pi\) | ||||
−0.661760 | + | 0.749716i | \(0.730190\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −30.2542 | −1.72110 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 31.7370 | 1.79964 | 0.899821 | − | 0.436258i | \(-0.143697\pi\) | ||||
0.899821 | + | 0.436258i | \(0.143697\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 20.8433 | 1.17813 | 0.589067 | − | 0.808084i | \(-0.299495\pi\) | ||||
0.589067 | + | 0.808084i | \(0.299495\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −2.02804 | −0.114267 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 2.80140 | 0.157342 | 0.0786711 | − | 0.996901i | \(-0.474932\pi\) | ||||
0.0786711 | + | 0.996901i | \(0.474932\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 32.9504 | 1.84487 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −11.3210 | −0.631876 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −16.1413 | −0.898128 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1.00000 | −0.0554700 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 13.7055 | 0.757916 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −8.09454 | −0.446266 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 0.789678 | 0.0434046 | 0.0217023 | − | 0.999764i | \(-0.493091\pi\) | ||||
0.0217023 | + | 0.999764i | \(0.493091\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0.929797 | 0.0509526 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 5.80828 | 0.317340 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −15.4083 | −0.839343 | −0.419672 | − | 0.907676i | \(-0.637855\pi\) | ||||
−0.419672 | + | 0.907676i | \(0.637855\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 31.1688 | 1.69286 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 17.8550 | 0.966905 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 12.2203 | 0.657919 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 29.2569 | 1.57059 | 0.785296 | − | 0.619121i | \(-0.212511\pi\) | ||||
0.785296 | + | 0.619121i | \(0.212511\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −32.5918 | −1.74460 | −0.872299 | − | 0.488972i | \(-0.837372\pi\) | ||||
−0.872299 | + | 0.488972i | \(0.837372\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 2.17945 | 0.116330 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 4.27160 | 0.227354 | 0.113677 | − | 0.993518i | \(-0.463737\pi\) | ||||
0.113677 | + | 0.993518i | \(0.463737\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 5.83994 | 0.309952 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −5.91509 | −0.313060 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −20.0108 | −1.05613 | −0.528066 | − | 0.849203i | \(-0.677083\pi\) | ||||
−0.528066 | + | 0.849203i | \(0.677083\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 18.4417 | 0.970616 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 33.4499 | 1.75566 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 8.27638 | 0.433206 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 22.6944 | 1.18464 | 0.592320 | − | 0.805703i | \(-0.298212\pi\) | ||||
0.592320 | + | 0.805703i | \(0.298212\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −14.5082 | −0.755267 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 3.74956 | 0.194668 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −22.2489 | −1.15200 | −0.576001 | − | 0.817449i | \(-0.695388\pi\) | ||||
−0.576001 | + | 0.817449i | \(0.695388\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −2.24233 | −0.115793 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 6.47239 | 0.333345 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 5.53342 | 0.284233 | 0.142116 | − | 0.989850i | \(-0.454609\pi\) | ||||
0.142116 | + | 0.989850i | \(0.454609\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 36.2556 | 1.85743 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 37.6545 | 1.92406 | 0.962028 | − | 0.272950i | \(-0.0879993\pi\) | ||||
0.962028 | + | 0.272950i | \(0.0879993\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 5.09092 | 0.259457 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 5.31385 | 0.270118 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 13.3921 | 0.679004 | 0.339502 | − | 0.940605i | \(-0.389741\pi\) | ||||
0.339502 | + | 0.940605i | \(0.389741\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 14.3762 | 0.727036 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 44.7173 | 2.25569 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −3.86437 | −0.194437 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −33.7589 | −1.69431 | −0.847156 | − | 0.531344i | \(-0.821687\pi\) | ||||
−0.847156 | + | 0.531344i | \(0.821687\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 13.7207 | 0.686896 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −28.5245 | −1.42445 | −0.712223 | − | 0.701953i | \(-0.752312\pi\) | ||||
−0.712223 | + | 0.701953i | \(0.752312\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 3.50723 | 0.174708 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 10.9712 | 0.545162 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −2.33404 | −0.115694 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −13.6113 | −0.673035 | −0.336517 | − | 0.941677i | \(-0.609249\pi\) | ||||
−0.336517 | + | 0.941677i | \(0.609249\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 50.5432 | 2.49311 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 9.17319 | 0.451383 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 8.61042 | 0.422669 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −43.6930 | −2.13965 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 19.8892 | 0.971653 | 0.485827 | − | 0.874055i | \(-0.338519\pi\) | ||||
0.485827 | + | 0.874055i | \(0.338519\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −4.98324 | −0.242868 | −0.121434 | − | 0.992599i | \(-0.538749\pi\) | ||||
−0.121434 | + | 0.992599i | \(0.538749\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −16.4161 | −0.798176 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −2.63792 | −0.127958 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 9.41552 | 0.455649 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 11.4155 | 0.551147 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 30.2146 | 1.45538 | 0.727692 | − | 0.685904i | \(-0.240593\pi\) | ||||
0.727692 | + | 0.685904i | \(0.240593\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −7.49507 | −0.360190 | −0.180095 | − | 0.983649i | \(-0.557641\pi\) | ||||
−0.180095 | + | 0.983649i | \(0.557641\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 14.5132 | 0.695857 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −33.3473 | −1.59522 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −9.97390 | −0.476028 | −0.238014 | − | 0.971262i | \(-0.576496\pi\) | ||||
−0.238014 | + | 0.971262i | \(0.576496\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 2.02804 | 0.0965734 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −19.5073 | −0.926821 | −0.463410 | − | 0.886144i | \(-0.653374\pi\) | ||||
−0.463410 | + | 0.886144i | \(0.653374\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 11.7618 | 0.557564 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −23.5801 | −1.11530 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −38.6895 | −1.82587 | −0.912934 | − | 0.408107i | \(-0.866189\pi\) | ||||
−0.912934 | + | 0.408107i | \(0.866189\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 36.4194 | 1.71492 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −32.4270 | −1.52355 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 1.00000 | 0.0468807 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 33.6615 | 1.57462 | 0.787308 | − | 0.616559i | \(-0.211474\pi\) | ||||
0.787308 | + | 0.616559i | \(0.211474\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 5.74922 | 0.268350 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 6.26378 | 0.291733 | 0.145867 | − | 0.989304i | \(-0.453403\pi\) | ||||
0.145867 | + | 0.989304i | \(0.453403\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −36.6265 | −1.70218 | −0.851089 | − | 0.525022i | \(-0.824057\pi\) | ||||
−0.851089 | + | 0.525022i | \(0.824057\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 7.86437 | 0.364701 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −19.6170 | −0.907767 | −0.453883 | − | 0.891061i | \(-0.649962\pi\) | ||||
−0.453883 | + | 0.891061i | \(0.649962\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −5.80828 | −0.268202 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 3.91937 | 0.180595 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −13.3392 | −0.613335 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 6.11896 | 0.280757 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 7.60427 | 0.348175 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −4.13528 | −0.188946 | −0.0944729 | − | 0.995527i | \(-0.530117\pi\) | ||||
−0.0944729 | + | 0.995527i | \(0.530117\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −0.458471 | −0.0209045 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −12.2203 | −0.556043 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −8.15062 | −0.370101 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 6.35387 | 0.287921 | 0.143961 | − | 0.989583i | \(-0.454016\pi\) | ||||
0.143961 | + | 0.989583i | \(0.454016\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −10.7709 | −0.487078 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −7.82665 | −0.353212 | −0.176606 | − | 0.984282i | \(-0.556512\pi\) | ||||
−0.176606 | + | 0.984282i | \(0.556512\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 17.0737 | 0.768959 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 10.3246 | 0.464056 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −5.83994 | −0.261957 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 8.51929 | 0.381376 | 0.190688 | − | 0.981651i | \(-0.438928\pi\) | ||||
0.190688 | + | 0.981651i | \(0.438928\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −27.2145 | −1.21585 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −23.1975 | −1.03432 | −0.517162 | − | 0.855887i | \(-0.673012\pi\) | ||||
−0.517162 | + | 0.855887i | \(0.673012\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 14.9869 | 0.666910 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 2.24233 | 0.0995854 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −20.4922 | −0.908302 | −0.454151 | − | 0.890925i | \(-0.650057\pi\) | ||||
−0.454151 | + | 0.890925i | \(0.650057\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −8.27638 | −0.366126 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −13.3360 | −0.588798 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 13.4923 | 0.594543 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 41.2087 | 1.81235 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 12.2409 | 0.537316 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 9.14638 | 0.400710 | 0.200355 | − | 0.979723i | \(-0.435790\pi\) | ||||
0.200355 | + | 0.979723i | \(0.435790\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 3.33395 | 0.145783 | 0.0728917 | − | 0.997340i | \(-0.476777\pi\) | ||||
0.0728917 | + | 0.997340i | \(0.476777\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 2.24233 | 0.0978633 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 9.25180 | 0.403015 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 6.70056 | 0.291329 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 18.6036 | 0.807328 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 7.15380 | 0.309866 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 5.04876 | 0.218277 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −26.9804 | −1.16429 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −5.09092 | −0.219282 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 19.9936 | 0.859594 | 0.429797 | − | 0.902926i | \(-0.358585\pi\) | ||||
0.429797 | + | 0.902926i | \(0.358585\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −7.85133 | −0.336933 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −6.11217 | −0.261817 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 26.7271 | 1.14277 | 0.571384 | − | 0.820683i | \(-0.306407\pi\) | ||||
0.571384 | + | 0.820683i | \(0.306407\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 19.0951 | 0.814958 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −39.6043 | −1.68720 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 3.86437 | 0.164330 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −1.02804 | −0.0436380 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −1.05415 | −0.0446656 | −0.0223328 | − | 0.999751i | \(-0.507109\pi\) | ||||
−0.0223328 | + | 0.999751i | \(0.507109\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −2.62019 | −0.110822 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 30.1132 | 1.27138 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 15.3526 | 0.647037 | 0.323518 | − | 0.946222i | \(-0.395134\pi\) | ||||
0.323518 | + | 0.946222i | \(0.395134\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −13.9002 | −0.584785 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −10.9712 | −0.460746 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 37.9806 | 1.59223 | 0.796114 | − | 0.605147i | \(-0.206886\pi\) | ||||
0.796114 | + | 0.605147i | \(0.206886\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 15.5848 | 0.652202 | 0.326101 | − | 0.945335i | \(-0.394265\pi\) | ||||
0.326101 | + | 0.945335i | \(0.394265\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −0.832276 | −0.0347688 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −5.44982 | −0.227273 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −20.0473 | −0.834579 | −0.417290 | − | 0.908774i | \(-0.637020\pi\) | ||||
−0.417290 | + | 0.908774i | \(0.637020\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −32.1357 | −1.33551 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −8.61042 | −0.357220 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −19.0887 | −0.790574 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 2.02804 | 0.0838492 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 39.1180 | 1.61457 | 0.807287 | − | 0.590159i | \(-0.200935\pi\) | ||||
0.807287 | + | 0.590159i | \(0.200935\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −21.4606 | −0.884269 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −41.7977 | −1.71933 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 6.30917 | 0.259087 | 0.129543 | − | 0.991574i | \(-0.458649\pi\) | ||||
0.129543 | + | 0.991574i | \(0.458649\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 2.63792 | 0.108144 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 19.7432 | 0.808036 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 30.9916 | 1.26628 | 0.633140 | − | 0.774037i | \(-0.281766\pi\) | ||||
0.633140 | + | 0.774037i | \(0.281766\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 2.65801 | 0.108423 | 0.0542113 | − | 0.998529i | \(-0.482736\pi\) | ||||
0.0542113 | + | 0.998529i | \(0.482736\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −11.7794 | −0.479696 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −14.9175 | −0.606482 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −3.48607 | −0.141495 | −0.0707477 | − | 0.997494i | \(-0.522539\pi\) | ||||
−0.0707477 | + | 0.997494i | \(0.522539\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −14.5132 | −0.588106 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 8.09454 | 0.327470 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −41.1579 | −1.66235 | −0.831175 | − | 0.556011i | \(-0.812331\pi\) | ||||
−0.831175 | + | 0.556011i | \(0.812331\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 16.0412 | 0.646843 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −6.57548 | −0.264719 | −0.132359 | − | 0.991202i | \(-0.542255\pi\) | ||||
−0.132359 | + | 0.991202i | \(0.542255\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 12.0917 | 0.486007 | 0.243003 | − | 0.970025i | \(-0.421867\pi\) | ||||
0.243003 | + | 0.970025i | \(0.421867\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 11.8776 | 0.476632 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −11.7618 | −0.471228 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −69.8512 | −2.78959 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −1.20941 | −0.0482223 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −8.45054 | −0.336411 | −0.168205 | − | 0.985752i | \(-0.553797\pi\) | ||||
−0.168205 | + | 0.985752i | \(0.553797\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 37.7317 | 1.49970 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −16.1687 | −0.641635 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.00000 | −0.0396214 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −11.8436 | −0.468528 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 7.16904 | 0.283160 | 0.141580 | − | 0.989927i | \(-0.454782\pi\) | ||||
0.141580 | + | 0.989927i | \(0.454782\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −29.0789 | −1.14676 | −0.573379 | − | 0.819290i | \(-0.694368\pi\) | ||||
−0.573379 | + | 0.819290i | \(0.694368\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −5.87532 | −0.231340 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 28.9981 | 1.14003 | 0.570016 | − | 0.821633i | \(-0.306937\pi\) | ||||
0.570016 | + | 0.821633i | \(0.306937\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −46.7000 | −1.83314 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −7.86437 | −0.308229 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −5.94499 | −0.232646 | −0.116323 | − | 0.993211i | \(-0.537111\pi\) | ||||
−0.116323 | + | 0.993211i | \(0.537111\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −19.9423 | −0.779212 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −16.7848 | −0.654839 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −14.2339 | −0.554473 | −0.277237 | − | 0.960802i | \(-0.589419\pi\) | ||||
−0.277237 | + | 0.960802i | \(0.589419\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −2.19138 | −0.0852349 | −0.0426175 | − | 0.999091i | \(-0.513570\pi\) | ||||
−0.0426175 | + | 0.999091i | \(0.513570\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 5.91509 | 0.229723 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −6.11896 | −0.237283 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 35.2734 | 1.36579 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 33.0991 | 1.27969 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −47.9337 | −1.85046 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 9.31430 | 0.359040 | 0.179520 | − | 0.983754i | \(-0.442546\pi\) | ||||
0.179520 | + | 0.983754i | \(0.442546\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −2.17945 | −0.0838871 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 1.32289 | 0.0508428 | 0.0254214 | − | 0.999677i | \(-0.491907\pi\) | ||||
0.0254214 | + | 0.999677i | \(0.491907\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 8.15062 | 0.312792 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 47.6711 | 1.82676 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −16.3381 | −0.625160 | −0.312580 | − | 0.949892i | \(-0.601193\pi\) | ||||
−0.312580 | + | 0.949892i | \(0.601193\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −22.5405 | −0.861228 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −43.9659 | −1.67740 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −3.74956 | −0.142847 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 28.7187 | 1.09251 | 0.546256 | − | 0.837618i | \(-0.316053\pi\) | ||||
0.546256 | + | 0.837618i | \(0.316053\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −10.3246 | −0.392199 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 19.4855 | 0.739128 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 18.8712 | 0.714796 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 9.99439 | 0.378022 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 2.41572 | 0.0912404 | 0.0456202 | − | 0.998959i | \(-0.485474\pi\) | ||||
0.0456202 | + | 0.998959i | \(0.485474\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 2.80536 | 0.105806 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 18.1506 | 0.683592 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −14.9869 | −0.563642 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −19.2385 | −0.722516 | −0.361258 | − | 0.932466i | \(-0.617653\pi\) | ||||
−0.361258 | + | 0.932466i | \(0.617653\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 7.83710 | 0.293914 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 19.1138 | 0.715817 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −5.09092 | −0.190390 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 32.7090 | 1.22154 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −40.1912 | −1.49888 | −0.749440 | − | 0.662073i | \(-0.769677\pi\) | ||||
−0.749440 | + | 0.662073i | \(0.769677\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −13.4923 | −0.502480 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 53.4992 | 1.98966 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −6.47239 | −0.240379 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −38.8861 | −1.44221 | −0.721103 | − | 0.692828i | \(-0.756364\pi\) | ||||
−0.721103 | + | 0.692828i | \(0.756364\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −7.58886 | −0.281069 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −6.91184 | −0.255644 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −32.8166 | −1.21211 | −0.606054 | − | 0.795423i | \(-0.707248\pi\) | ||||
−0.606054 | + | 0.795423i | \(0.707248\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −2.24233 | −0.0827096 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 29.5695 | 1.08921 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 53.2128 | 1.95746 | 0.978732 | − | 0.205141i | \(-0.0657653\pi\) | ||||
0.978732 | + | 0.205141i | \(0.0657653\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −13.7207 | −0.504044 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −10.5818 | −0.388210 | −0.194105 | − | 0.980981i | \(-0.562180\pi\) | ||||
−0.194105 | + | 0.980981i | \(0.562180\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 10.5159 | 0.385272 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −17.4623 | −0.638912 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −5.04876 | −0.184478 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −19.8391 | −0.723938 | −0.361969 | − | 0.932190i | \(-0.617895\pi\) | ||||
−0.361969 | + | 0.932190i | \(0.617895\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 6.72578 | 0.245101 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 14.4613 | 0.526301 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −26.3012 | −0.955935 | −0.477967 | − | 0.878378i | \(-0.658626\pi\) | ||||
−0.477967 | + | 0.878378i | \(0.658626\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 62.2126 | 2.25817 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 45.4116 | 1.64617 | 0.823084 | − | 0.567920i | \(-0.192252\pi\) | ||||
0.823084 | + | 0.567920i | \(0.192252\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 6.11217 | 0.221275 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 5.34981 | 0.193423 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −9.17319 | −0.331225 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 6.40438 | 0.230948 | 0.115474 | − | 0.993311i | \(-0.463161\pi\) | ||||
0.115474 | + | 0.993311i | \(0.463161\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 27.9559 | 1.00681 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −15.4161 | −0.554477 | −0.277239 | − | 0.960801i | \(-0.589419\pi\) | ||||
−0.277239 | + | 0.960801i | \(0.589419\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −3.50723 | −0.125983 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 1.02804 | 0.0368808 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −43.7738 | −1.56836 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 29.7307 | 1.06385 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 14.1063 | 0.504117 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −1.74790 | −0.0623853 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −11.4713 | −0.408907 | −0.204453 | − | 0.978876i | \(-0.565542\pi\) | ||||
−0.204453 | + | 0.978876i | \(0.565542\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 29.9577 | 1.06652 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 13.9002 | 0.494234 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −9.41552 | −0.334355 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −8.40775 | −0.298192 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 38.9694 | 1.38037 | 0.690184 | − | 0.723634i | \(-0.257530\pi\) | ||||
0.690184 | + | 0.723634i | \(0.257530\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 21.3527 | 0.755406 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −23.8535 | −0.842821 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 42.1344 | 1.48689 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 5.44982 | 0.192081 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 6.69772 | 0.235771 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −19.1824 | −0.674416 | −0.337208 | − | 0.941430i | \(-0.609483\pi\) | ||||
−0.337208 | + | 0.941430i | \(0.609483\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 8.52598 | 0.299388 | 0.149694 | − | 0.988732i | \(-0.452171\pi\) | ||||
0.149694 | + | 0.988732i | \(0.452171\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −33.7012 | −1.18195 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 4.80345 | 0.168257 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 16.0328 | 0.560917 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −2.02804 | −0.0708655 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 18.5580 | 0.647680 | 0.323840 | − | 0.946112i | \(-0.395026\pi\) | ||||
0.323840 | + | 0.946112i | \(0.395026\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 31.6231 | 1.10231 | 0.551155 | − | 0.834403i | \(-0.314187\pi\) | ||||
0.551155 | + | 0.834403i | \(0.314187\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −11.4155 | −0.397438 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −40.8572 | −1.42074 | −0.710371 | − | 0.703827i | \(-0.751473\pi\) | ||||
−0.710371 | + | 0.703827i | \(0.751473\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 16.4917 | 0.572780 | 0.286390 | − | 0.958113i | \(-0.407545\pi\) | ||||
0.286390 | + | 0.958113i | \(0.407545\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −63.9064 | −2.21689 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −2.63792 | −0.0913985 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 12.1367 | 0.420008 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 7.64384 | 0.264210 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 2.49868 | 0.0862639 | 0.0431319 | − | 0.999069i | \(-0.486266\pi\) | ||||
0.0431319 | + | 0.999069i | \(0.486266\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 12.8919 | 0.444548 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 47.5699 | 1.63839 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −1.00000 | −0.0344010 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 14.9175 | 0.512571 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 24.5175 | 0.841439 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −2.49858 | −0.0856503 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 20.9813 | 0.718387 | 0.359194 | − | 0.933263i | \(-0.383052\pi\) | ||||
0.359194 | + | 0.933263i | \(0.383052\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −12.4095 | −0.424396 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −40.0604 | −1.36844 | −0.684219 | − | 0.729277i | \(-0.739857\pi\) | ||||
−0.684219 | + | 0.729277i | \(0.739857\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 1.19224 | 0.0406788 | 0.0203394 | − | 0.999793i | \(-0.493525\pi\) | ||||
0.0203394 | + | 0.999793i | \(0.493525\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −16.0412 | −0.546682 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 17.4481 | 0.593942 | 0.296971 | − | 0.954887i | \(-0.404024\pi\) | ||||
0.296971 | + | 0.954887i | \(0.404024\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −5.45901 | −0.185612 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −22.5161 | −0.764686 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −19.6732 | −0.667367 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 5.80828 | 0.196806 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 16.5298 | 0.559449 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −1.00000 | −0.0338062 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −40.9281 | −1.38204 | −0.691021 | − | 0.722834i | \(-0.742839\pi\) | ||||
−0.691021 | + | 0.722834i | \(0.742839\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −64.1152 | −2.16255 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 13.0769 | 0.440572 | 0.220286 | − | 0.975435i | \(-0.429301\pi\) | ||||
0.220286 | + | 0.975435i | \(0.429301\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 9.18193 | 0.308997 | 0.154498 | − | 0.987993i | \(-0.450624\pi\) | ||||
0.154498 | + | 0.987993i | \(0.450624\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −20.5693 | −0.691430 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −27.0349 | −0.907744 | −0.453872 | − | 0.891067i | \(-0.649958\pi\) | ||||
−0.453872 | + | 0.891067i | \(0.649958\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 16.1687 | 0.542281 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 55.8534 | 1.87116 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −49.5302 | −1.65746 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 12.0323 | 0.402195 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 12.2203 | 0.408024 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 22.7002 | 0.757093 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −9.89104 | −0.329518 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 5.87532 | 0.195518 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 3.50142 | 0.116391 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 49.5193 | 1.64426 | 0.822131 | − | 0.569298i | \(-0.192785\pi\) | ||||
0.822131 | + | 0.569298i | \(0.192785\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −30.3942 | −1.00811 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 24.5483 | 0.813322 | 0.406661 | − | 0.913579i | \(-0.366693\pi\) | ||||
0.406661 | + | 0.913579i | \(0.366693\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 43.8350 | 1.45073 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −21.1127 | −0.697965 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 19.9423 | 0.658554 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −10.5408 | −0.347710 | −0.173855 | − | 0.984771i | \(-0.555622\pi\) | ||||
−0.173855 | + | 0.984771i | \(0.555622\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −51.9995 | −1.71344 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 5.83994 | 0.192224 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0.458471 | 0.0150744 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −27.3630 | −0.898719 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 49.6214 | 1.62803 | 0.814013 | − | 0.580846i | \(-0.197278\pi\) | ||||
0.814013 | + | 0.580846i | \(0.197278\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 6.11896 | 0.200541 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 71.1649 | 2.32983 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −13.4294 | −0.439190 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −42.4164 | −1.38568 | −0.692842 | − | 0.721090i | \(-0.743642\pi\) | ||||
−0.692842 | + | 0.721090i | \(0.743642\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 46.7376 | 1.52522 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 29.0006 | 0.945391 | 0.472695 | − | 0.881226i | \(-0.343281\pi\) | ||||
0.472695 | + | 0.881226i | \(0.343281\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 38.9869 | 1.26959 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 2.17945 | 0.0708975 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 4.42169 | 0.143685 | 0.0718427 | − | 0.997416i | \(-0.477112\pi\) | ||||
0.0718427 | + | 0.997416i | \(0.477112\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 8.27638 | 0.268663 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 6.28166 | 0.203697 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −21.5536 | −0.698191 | −0.349095 | − | 0.937087i | \(-0.613511\pi\) | ||||
−0.349095 | + | 0.937087i | \(0.613511\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0.371166 | 0.0120106 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 73.8858 | 2.38839 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 22.5405 | 0.727871 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −18.6993 | −0.603204 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −10.2391 | −0.329950 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 14.3314 | 0.461344 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 14.9791 | 0.481697 | 0.240848 | − | 0.970563i | \(-0.422574\pi\) | ||||
0.240848 | + | 0.970563i | \(0.422574\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −36.1942 | −1.16273 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 9.31800 | 0.299029 | 0.149514 | − | 0.988760i | \(-0.452229\pi\) | ||||
0.149514 | + | 0.988760i | \(0.452229\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −19.4855 | −0.624677 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −2.24233 | −0.0718120 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −18.9661 | −0.606780 | −0.303390 | − | 0.952866i | \(-0.598119\pi\) | ||||
−0.303390 | + | 0.952866i | \(0.598119\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 59.8785 | 1.91373 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 12.3957 | 0.395765 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 41.5464 | 1.32512 | 0.662562 | − | 0.749007i | \(-0.269469\pi\) | ||||
0.662562 | + | 0.749007i | \(0.269469\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 18.6403 | 0.593930 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −18.1506 | −0.577741 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −14.2795 | −0.454063 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 6.23529 | 0.198070 | 0.0990352 | − | 0.995084i | \(-0.468424\pi\) | ||||
0.0990352 | + | 0.995084i | \(0.468424\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 1.77072 | 0.0561920 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −8.80477 | −0.279130 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 28.6321 | 0.906788 | 0.453394 | − | 0.891310i | \(-0.350213\pi\) | ||||
0.453394 | + | 0.891310i | \(0.350213\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −0.999214 | −0.0316137 |
(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 | 3640.2.a.y.1.5 | ✓ | 5 | |
4.3 | odd | 2 | 7280.2.a.cc.1.1 | 5 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3640.2.a.y.1.5 | ✓ | 5 | 1.1 | even | 1 | trivial | |
7280.2.a.cc.1.1 | 5 | 4.3 | odd | 2 |