Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8046,2,Mod(1,8046)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8046, 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("8046.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8046 = 2 \cdot 3^{3} \cdot 149 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8046.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(64.2476334663\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 3 x^{11} - 29 x^{10} + 76 x^{9} + 320 x^{8} - 724 x^{7} - 1643 x^{6} + 3265 x^{5} + 3921 x^{4} + \cdots + 423 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-2.89416\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8046.1 |
$q$-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 | 0 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −2.89416 | −1.29431 | −0.647153 | − | 0.762360i | \(-0.724041\pi\) | ||||
−0.647153 | + | 0.762360i | \(0.724041\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.647278 | 0.244648 | 0.122324 | − | 0.992490i | \(-0.460965\pi\) | ||||
0.122324 | + | 0.992490i | \(0.460965\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −2.89416 | −0.915213 | ||||||||
\(11\) | 3.72846 | 1.12417 | 0.562086 | − | 0.827078i | \(-0.309999\pi\) | ||||
0.562086 | + | 0.827078i | \(0.309999\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.715732 | 0.198508 | 0.0992542 | − | 0.995062i | \(-0.468354\pi\) | ||||
0.0992542 | + | 0.995062i | \(0.468354\pi\) | |||||||
\(14\) | 0.647278 | 0.172992 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 0.587143 | 0.142403 | 0.0712015 | − | 0.997462i | \(-0.477317\pi\) | ||||
0.0712015 | + | 0.997462i | \(0.477317\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 6.18007 | 1.41781 | 0.708903 | − | 0.705306i | \(-0.249190\pi\) | ||||
0.708903 | + | 0.705306i | \(0.249190\pi\) | |||||||
\(20\) | −2.89416 | −0.647153 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 3.72846 | 0.794910 | ||||||||
\(23\) | 7.30961 | 1.52416 | 0.762079 | − | 0.647484i | \(-0.224179\pi\) | ||||
0.762079 | + | 0.647484i | \(0.224179\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 3.37615 | 0.675230 | ||||||||
\(26\) | 0.715732 | 0.140367 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0.647278 | 0.122324 | ||||||||
\(29\) | 0.536329 | 0.0995937 | 0.0497969 | − | 0.998759i | \(-0.484143\pi\) | ||||
0.0497969 | + | 0.998759i | \(0.484143\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −8.61374 | −1.54707 | −0.773536 | − | 0.633752i | \(-0.781514\pi\) | ||||
−0.773536 | + | 0.633752i | \(0.781514\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0.587143 | 0.100694 | ||||||||
\(35\) | −1.87333 | −0.316650 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −2.58020 | −0.424183 | −0.212091 | − | 0.977250i | \(-0.568027\pi\) | ||||
−0.212091 | + | 0.977250i | \(0.568027\pi\) | |||||||
\(38\) | 6.18007 | 1.00254 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −2.89416 | −0.457607 | ||||||||
\(41\) | −6.06139 | −0.946630 | −0.473315 | − | 0.880893i | \(-0.656943\pi\) | ||||
−0.473315 | + | 0.880893i | \(0.656943\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0.0254145 | 0.00387567 | 0.00193784 | − | 0.999998i | \(-0.499383\pi\) | ||||
0.00193784 | + | 0.999998i | \(0.499383\pi\) | |||||||
\(44\) | 3.72846 | 0.562086 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 7.30961 | 1.07774 | ||||||||
\(47\) | 3.03761 | 0.443081 | 0.221540 | − | 0.975151i | \(-0.428892\pi\) | ||||
0.221540 | + | 0.975151i | \(0.428892\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.58103 | −0.940147 | ||||||||
\(50\) | 3.37615 | 0.477460 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0.715732 | 0.0992542 | ||||||||
\(53\) | 13.3216 | 1.82987 | 0.914933 | − | 0.403607i | \(-0.132244\pi\) | ||||
0.914933 | + | 0.403607i | \(0.132244\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −10.7908 | −1.45502 | ||||||||
\(56\) | 0.647278 | 0.0864962 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0.536329 | 0.0704234 | ||||||||
\(59\) | −8.44682 | −1.09968 | −0.549841 | − | 0.835269i | \(-0.685312\pi\) | ||||
−0.549841 | + | 0.835269i | \(0.685312\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.72772 | −0.221212 | −0.110606 | − | 0.993864i | \(-0.535279\pi\) | ||||
−0.110606 | + | 0.993864i | \(0.535279\pi\) | |||||||
\(62\) | −8.61374 | −1.09395 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −2.07144 | −0.256931 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1.14341 | −0.139689 | −0.0698447 | − | 0.997558i | \(-0.522250\pi\) | ||||
−0.0698447 | + | 0.997558i | \(0.522250\pi\) | |||||||
\(68\) | 0.587143 | 0.0712015 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −1.87333 | −0.223905 | ||||||||
\(71\) | 6.82877 | 0.810425 | 0.405213 | − | 0.914222i | \(-0.367197\pi\) | ||||
0.405213 | + | 0.914222i | \(0.367197\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 7.14332 | 0.836063 | 0.418031 | − | 0.908433i | \(-0.362720\pi\) | ||||
0.418031 | + | 0.908433i | \(0.362720\pi\) | |||||||
\(74\) | −2.58020 | −0.299942 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 6.18007 | 0.708903 | ||||||||
\(77\) | 2.41335 | 0.275027 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 3.34399 | 0.376228 | 0.188114 | − | 0.982147i | \(-0.439763\pi\) | ||||
0.188114 | + | 0.982147i | \(0.439763\pi\) | |||||||
\(80\) | −2.89416 | −0.323577 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −6.06139 | −0.669369 | ||||||||
\(83\) | −12.5992 | −1.38294 | −0.691472 | − | 0.722404i | \(-0.743037\pi\) | ||||
−0.691472 | + | 0.722404i | \(0.743037\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.69928 | −0.184313 | ||||||||
\(86\) | 0.0254145 | 0.00274051 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 3.72846 | 0.397455 | ||||||||
\(89\) | 12.7234 | 1.34868 | 0.674341 | − | 0.738420i | \(-0.264428\pi\) | ||||
0.674341 | + | 0.738420i | \(0.264428\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.463278 | 0.0485647 | ||||||||
\(92\) | 7.30961 | 0.762079 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 3.03761 | 0.313305 | ||||||||
\(95\) | −17.8861 | −1.83508 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −15.1212 | −1.53533 | −0.767663 | − | 0.640853i | \(-0.778581\pi\) | ||||
−0.767663 | + | 0.640853i | \(0.778581\pi\) | |||||||
\(98\) | −6.58103 | −0.664785 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 3.37615 | 0.337615 | ||||||||
\(101\) | 4.60974 | 0.458687 | 0.229343 | − | 0.973346i | \(-0.426342\pi\) | ||||
0.229343 | + | 0.973346i | \(0.426342\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 19.7923 | 1.95019 | 0.975095 | − | 0.221788i | \(-0.0711892\pi\) | ||||
0.975095 | + | 0.221788i | \(0.0711892\pi\) | |||||||
\(104\) | 0.715732 | 0.0701833 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 13.3216 | 1.29391 | ||||||||
\(107\) | −0.116319 | −0.0112449 | −0.00562247 | − | 0.999984i | \(-0.501790\pi\) | ||||
−0.00562247 | + | 0.999984i | \(0.501790\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −17.4189 | −1.66843 | −0.834216 | − | 0.551438i | \(-0.814079\pi\) | ||||
−0.834216 | + | 0.551438i | \(0.814079\pi\) | |||||||
\(110\) | −10.7908 | −1.02886 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0.647278 | 0.0611620 | ||||||||
\(113\) | 14.7319 | 1.38586 | 0.692928 | − | 0.721007i | \(-0.256320\pi\) | ||||
0.692928 | + | 0.721007i | \(0.256320\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −21.1552 | −1.97273 | ||||||||
\(116\) | 0.536329 | 0.0497969 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −8.44682 | −0.777593 | ||||||||
\(119\) | 0.380045 | 0.0348386 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 2.90141 | 0.263765 | ||||||||
\(122\) | −1.72772 | −0.156421 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −8.61374 | −0.773536 | ||||||||
\(125\) | 4.69968 | 0.420352 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 16.5659 | 1.46999 | 0.734993 | − | 0.678074i | \(-0.237185\pi\) | ||||
0.734993 | + | 0.678074i | \(0.237185\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −2.07144 | −0.181677 | ||||||||
\(131\) | 3.97969 | 0.347707 | 0.173853 | − | 0.984772i | \(-0.444378\pi\) | ||||
0.173853 | + | 0.984772i | \(0.444378\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 4.00023 | 0.346864 | ||||||||
\(134\) | −1.14341 | −0.0987753 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0.587143 | 0.0503471 | ||||||||
\(137\) | 17.7470 | 1.51622 | 0.758112 | − | 0.652124i | \(-0.226122\pi\) | ||||
0.758112 | + | 0.652124i | \(0.226122\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −3.40466 | −0.288779 | −0.144390 | − | 0.989521i | \(-0.546122\pi\) | ||||
−0.144390 | + | 0.989521i | \(0.546122\pi\) | |||||||
\(140\) | −1.87333 | −0.158325 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 6.82877 | 0.573057 | ||||||||
\(143\) | 2.66858 | 0.223158 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1.55222 | −0.128905 | ||||||||
\(146\) | 7.14332 | 0.591186 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −2.58020 | −0.212091 | ||||||||
\(149\) | 1.00000 | 0.0819232 | ||||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −10.6585 | −0.867373 | −0.433687 | − | 0.901064i | \(-0.642787\pi\) | ||||
−0.433687 | + | 0.901064i | \(0.642787\pi\) | |||||||
\(152\) | 6.18007 | 0.501270 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 2.41335 | 0.194473 | ||||||||
\(155\) | 24.9295 | 2.00239 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 10.8183 | 0.863397 | 0.431699 | − | 0.902018i | \(-0.357914\pi\) | ||||
0.431699 | + | 0.902018i | \(0.357914\pi\) | |||||||
\(158\) | 3.34399 | 0.266034 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −2.89416 | −0.228803 | ||||||||
\(161\) | 4.73135 | 0.372883 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 6.33240 | 0.495992 | 0.247996 | − | 0.968761i | \(-0.420228\pi\) | ||||
0.247996 | + | 0.968761i | \(0.420228\pi\) | |||||||
\(164\) | −6.06139 | −0.473315 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −12.5992 | −0.977888 | ||||||||
\(167\) | −20.0433 | −1.55099 | −0.775497 | − | 0.631351i | \(-0.782501\pi\) | ||||
−0.775497 | + | 0.631351i | \(0.782501\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.4877 | −0.960594 | ||||||||
\(170\) | −1.69928 | −0.130329 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0.0254145 | 0.00193784 | ||||||||
\(173\) | 19.7813 | 1.50395 | 0.751974 | − | 0.659193i | \(-0.229102\pi\) | ||||
0.751974 | + | 0.659193i | \(0.229102\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 2.18531 | 0.165194 | ||||||||
\(176\) | 3.72846 | 0.281043 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 12.7234 | 0.953662 | ||||||||
\(179\) | 8.80643 | 0.658224 | 0.329112 | − | 0.944291i | \(-0.393251\pi\) | ||||
0.329112 | + | 0.944291i | \(0.393251\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −2.53023 | −0.188070 | −0.0940352 | − | 0.995569i | \(-0.529977\pi\) | ||||
−0.0940352 | + | 0.995569i | \(0.529977\pi\) | |||||||
\(182\) | 0.463278 | 0.0343404 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 7.30961 | 0.538872 | ||||||||
\(185\) | 7.46751 | 0.549022 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 2.18914 | 0.160086 | ||||||||
\(188\) | 3.03761 | 0.221540 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −17.8861 | −1.29759 | ||||||||
\(191\) | 11.0216 | 0.797497 | 0.398748 | − | 0.917060i | \(-0.369445\pi\) | ||||
0.398748 | + | 0.917060i | \(0.369445\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 13.0378 | 0.938481 | 0.469240 | − | 0.883070i | \(-0.344528\pi\) | ||||
0.469240 | + | 0.883070i | \(0.344528\pi\) | |||||||
\(194\) | −15.1212 | −1.08564 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −6.58103 | −0.470074 | ||||||||
\(197\) | 6.51445 | 0.464136 | 0.232068 | − | 0.972700i | \(-0.425451\pi\) | ||||
0.232068 | + | 0.972700i | \(0.425451\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 8.24335 | 0.584356 | 0.292178 | − | 0.956364i | \(-0.405620\pi\) | ||||
0.292178 | + | 0.956364i | \(0.405620\pi\) | |||||||
\(200\) | 3.37615 | 0.238730 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 4.60974 | 0.324340 | ||||||||
\(203\) | 0.347154 | 0.0243654 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 17.5426 | 1.22523 | ||||||||
\(206\) | 19.7923 | 1.37899 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0.715732 | 0.0496271 | ||||||||
\(209\) | 23.0422 | 1.59386 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 14.4493 | 0.994729 | 0.497364 | − | 0.867542i | \(-0.334301\pi\) | ||||
0.497364 | + | 0.867542i | \(0.334301\pi\) | |||||||
\(212\) | 13.3216 | 0.914933 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −0.116319 | −0.00795137 | ||||||||
\(215\) | −0.0735535 | −0.00501631 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −5.57548 | −0.378489 | ||||||||
\(218\) | −17.4189 | −1.17976 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −10.7908 | −0.727512 | ||||||||
\(221\) | 0.420237 | 0.0282682 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −14.0558 | −0.941249 | −0.470624 | − | 0.882334i | \(-0.655971\pi\) | ||||
−0.470624 | + | 0.882334i | \(0.655971\pi\) | |||||||
\(224\) | 0.647278 | 0.0432481 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 14.7319 | 0.979948 | ||||||||
\(227\) | 17.2851 | 1.14725 | 0.573626 | − | 0.819118i | \(-0.305536\pi\) | ||||
0.573626 | + | 0.819118i | \(0.305536\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −9.37902 | −0.619783 | −0.309892 | − | 0.950772i | \(-0.600293\pi\) | ||||
−0.309892 | + | 0.950772i | \(0.600293\pi\) | |||||||
\(230\) | −21.1552 | −1.39493 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0.536329 | 0.0352117 | ||||||||
\(233\) | 17.5605 | 1.15043 | 0.575213 | − | 0.818003i | \(-0.304919\pi\) | ||||
0.575213 | + | 0.818003i | \(0.304919\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −8.79132 | −0.573482 | ||||||||
\(236\) | −8.44682 | −0.549841 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0.380045 | 0.0246346 | ||||||||
\(239\) | −28.9074 | −1.86987 | −0.934933 | − | 0.354823i | \(-0.884541\pi\) | ||||
−0.934933 | + | 0.354823i | \(0.884541\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 22.3729 | 1.44117 | 0.720583 | − | 0.693369i | \(-0.243874\pi\) | ||||
0.720583 | + | 0.693369i | \(0.243874\pi\) | |||||||
\(242\) | 2.90141 | 0.186510 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −1.72772 | −0.110606 | ||||||||
\(245\) | 19.0465 | 1.21684 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 4.42328 | 0.281446 | ||||||||
\(248\) | −8.61374 | −0.546973 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 4.69968 | 0.297234 | ||||||||
\(251\) | 14.0275 | 0.885410 | 0.442705 | − | 0.896667i | \(-0.354019\pi\) | ||||
0.442705 | + | 0.896667i | \(0.354019\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 27.2536 | 1.71342 | ||||||||
\(254\) | 16.5659 | 1.03944 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 9.63634 | 0.601099 | 0.300549 | − | 0.953766i | \(-0.402830\pi\) | ||||
0.300549 | + | 0.953766i | \(0.402830\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1.67011 | −0.103776 | ||||||||
\(260\) | −2.07144 | −0.128465 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 3.97969 | 0.245866 | ||||||||
\(263\) | −21.5566 | −1.32924 | −0.664620 | − | 0.747182i | \(-0.731406\pi\) | ||||
−0.664620 | + | 0.747182i | \(0.731406\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −38.5549 | −2.36841 | ||||||||
\(266\) | 4.00023 | 0.245270 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −1.14341 | −0.0698447 | ||||||||
\(269\) | 26.4569 | 1.61311 | 0.806554 | − | 0.591161i | \(-0.201330\pi\) | ||||
0.806554 | + | 0.591161i | \(0.201330\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 11.9830 | 0.727915 | 0.363958 | − | 0.931415i | \(-0.381425\pi\) | ||||
0.363958 | + | 0.931415i | \(0.381425\pi\) | |||||||
\(272\) | 0.587143 | 0.0356008 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 17.7470 | 1.07213 | ||||||||
\(275\) | 12.5878 | 0.759075 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 23.0482 | 1.38483 | 0.692416 | − | 0.721499i | \(-0.256546\pi\) | ||||
0.692416 | + | 0.721499i | \(0.256546\pi\) | |||||||
\(278\) | −3.40466 | −0.204198 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −1.87333 | −0.111953 | ||||||||
\(281\) | 16.6551 | 0.993561 | 0.496781 | − | 0.867876i | \(-0.334515\pi\) | ||||
0.496781 | + | 0.867876i | \(0.334515\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −4.34695 | −0.258399 | −0.129200 | − | 0.991619i | \(-0.541241\pi\) | ||||
−0.129200 | + | 0.991619i | \(0.541241\pi\) | |||||||
\(284\) | 6.82877 | 0.405213 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 2.66858 | 0.157796 | ||||||||
\(287\) | −3.92341 | −0.231591 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.6553 | −0.979721 | ||||||||
\(290\) | −1.55222 | −0.0911495 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 7.14332 | 0.418031 | ||||||||
\(293\) | −17.5782 | −1.02693 | −0.513464 | − | 0.858111i | \(-0.671638\pi\) | ||||
−0.513464 | + | 0.858111i | \(0.671638\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 24.4464 | 1.42333 | ||||||||
\(296\) | −2.58020 | −0.149971 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 1.00000 | 0.0579284 | ||||||||
\(299\) | 5.23172 | 0.302558 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0.0164502 | 0.000948176 0 | ||||||||
\(302\) | −10.6585 | −0.613325 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 6.18007 | 0.354452 | ||||||||
\(305\) | 5.00030 | 0.286316 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −13.8702 | −0.791612 | −0.395806 | − | 0.918334i | \(-0.629535\pi\) | ||||
−0.395806 | + | 0.918334i | \(0.629535\pi\) | |||||||
\(308\) | 2.41335 | 0.137513 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 24.9295 | 1.41590 | ||||||||
\(311\) | −9.97478 | −0.565618 | −0.282809 | − | 0.959176i | \(-0.591266\pi\) | ||||
−0.282809 | + | 0.959176i | \(0.591266\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 22.0525 | 1.24648 | 0.623240 | − | 0.782031i | \(-0.285816\pi\) | ||||
0.623240 | + | 0.782031i | \(0.285816\pi\) | |||||||
\(314\) | 10.8183 | 0.610514 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 3.34399 | 0.188114 | ||||||||
\(317\) | 2.36150 | 0.132635 | 0.0663176 | − | 0.997799i | \(-0.478875\pi\) | ||||
0.0663176 | + | 0.997799i | \(0.478875\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1.99968 | 0.111961 | ||||||||
\(320\) | −2.89416 | −0.161788 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 4.73135 | 0.263668 | ||||||||
\(323\) | 3.62859 | 0.201900 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 2.41642 | 0.134039 | ||||||||
\(326\) | 6.33240 | 0.350719 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −6.06139 | −0.334684 | ||||||||
\(329\) | 1.96618 | 0.108399 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −24.6246 | −1.35349 | −0.676745 | − | 0.736217i | \(-0.736610\pi\) | ||||
−0.676745 | + | 0.736217i | \(0.736610\pi\) | |||||||
\(332\) | −12.5992 | −0.691472 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −20.0433 | −1.09672 | ||||||||
\(335\) | 3.30920 | 0.180801 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 4.12734 | 0.224831 | 0.112415 | − | 0.993661i | \(-0.464141\pi\) | ||||
0.112415 | + | 0.993661i | \(0.464141\pi\) | |||||||
\(338\) | −12.4877 | −0.679243 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −1.69928 | −0.0921566 | ||||||||
\(341\) | −32.1160 | −1.73918 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −8.79070 | −0.474653 | ||||||||
\(344\) | 0.0254145 | 0.00137026 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 19.7813 | 1.06345 | ||||||||
\(347\) | 1.66183 | 0.0892120 | 0.0446060 | − | 0.999005i | \(-0.485797\pi\) | ||||
0.0446060 | + | 0.999005i | \(0.485797\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −9.67092 | −0.517673 | −0.258836 | − | 0.965921i | \(-0.583339\pi\) | ||||
−0.258836 | + | 0.965921i | \(0.583339\pi\) | |||||||
\(350\) | 2.18531 | 0.116810 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 3.72846 | 0.198728 | ||||||||
\(353\) | −28.8909 | −1.53771 | −0.768853 | − | 0.639426i | \(-0.779172\pi\) | ||||
−0.768853 | + | 0.639426i | \(0.779172\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −19.7635 | −1.04894 | ||||||||
\(356\) | 12.7234 | 0.674341 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 8.80643 | 0.465434 | ||||||||
\(359\) | 6.28476 | 0.331697 | 0.165849 | − | 0.986151i | \(-0.446964\pi\) | ||||
0.165849 | + | 0.986151i | \(0.446964\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 19.1933 | 1.01017 | ||||||||
\(362\) | −2.53023 | −0.132986 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0.463278 | 0.0242823 | ||||||||
\(365\) | −20.6739 | −1.08212 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −23.5043 | −1.22691 | −0.613457 | − | 0.789728i | \(-0.710221\pi\) | ||||
−0.613457 | + | 0.789728i | \(0.710221\pi\) | |||||||
\(368\) | 7.30961 | 0.381040 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 7.46751 | 0.388218 | ||||||||
\(371\) | 8.62279 | 0.447673 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 8.22391 | 0.425818 | 0.212909 | − | 0.977072i | \(-0.431706\pi\) | ||||
0.212909 | + | 0.977072i | \(0.431706\pi\) | |||||||
\(374\) | 2.18914 | 0.113198 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 3.03761 | 0.156653 | ||||||||
\(377\) | 0.383868 | 0.0197702 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 17.0746 | 0.877065 | 0.438533 | − | 0.898715i | \(-0.355498\pi\) | ||||
0.438533 | + | 0.898715i | \(0.355498\pi\) | |||||||
\(380\) | −17.8861 | −0.917538 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 11.0216 | 0.563915 | ||||||||
\(383\) | −9.91645 | −0.506707 | −0.253354 | − | 0.967374i | \(-0.581534\pi\) | ||||
−0.253354 | + | 0.967374i | \(0.581534\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −6.98462 | −0.355969 | ||||||||
\(386\) | 13.0378 | 0.663606 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −15.1212 | −0.767663 | ||||||||
\(389\) | −20.6837 | −1.04871 | −0.524353 | − | 0.851501i | \(-0.675693\pi\) | ||||
−0.524353 | + | 0.851501i | \(0.675693\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 4.29178 | 0.217045 | ||||||||
\(392\) | −6.58103 | −0.332392 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 6.51445 | 0.328193 | ||||||||
\(395\) | −9.67804 | −0.486955 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −10.8701 | −0.545557 | −0.272778 | − | 0.962077i | \(-0.587943\pi\) | ||||
−0.272778 | + | 0.962077i | \(0.587943\pi\) | |||||||
\(398\) | 8.24335 | 0.413202 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 3.37615 | 0.168807 | ||||||||
\(401\) | −27.8798 | −1.39225 | −0.696125 | − | 0.717921i | \(-0.745094\pi\) | ||||
−0.696125 | + | 0.717921i | \(0.745094\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −6.16513 | −0.307107 | ||||||||
\(404\) | 4.60974 | 0.229343 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0.347154 | 0.0172290 | ||||||||
\(407\) | −9.62018 | −0.476855 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −21.3723 | −1.05679 | −0.528397 | − | 0.848997i | \(-0.677207\pi\) | ||||
−0.528397 | + | 0.848997i | \(0.677207\pi\) | |||||||
\(410\) | 17.5426 | 0.866368 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 19.7923 | 0.975095 | ||||||||
\(413\) | −5.46744 | −0.269035 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 36.4641 | 1.78995 | ||||||||
\(416\) | 0.715732 | 0.0350916 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 23.0422 | 1.12703 | ||||||||
\(419\) | 0.754815 | 0.0368751 | 0.0184376 | − | 0.999830i | \(-0.494131\pi\) | ||||
0.0184376 | + | 0.999830i | \(0.494131\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 24.0721 | 1.17320 | 0.586601 | − | 0.809876i | \(-0.300466\pi\) | ||||
0.586601 | + | 0.809876i | \(0.300466\pi\) | |||||||
\(422\) | 14.4493 | 0.703379 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 13.3216 | 0.646955 | ||||||||
\(425\) | 1.98228 | 0.0961548 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −1.11832 | −0.0541191 | ||||||||
\(428\) | −0.116319 | −0.00562247 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −0.0735535 | −0.00354707 | ||||||||
\(431\) | 10.4667 | 0.504162 | 0.252081 | − | 0.967706i | \(-0.418885\pi\) | ||||
0.252081 | + | 0.967706i | \(0.418885\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 2.47142 | 0.118769 | 0.0593843 | − | 0.998235i | \(-0.481086\pi\) | ||||
0.0593843 | + | 0.998235i | \(0.481086\pi\) | |||||||
\(434\) | −5.57548 | −0.267632 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −17.4189 | −0.834216 | ||||||||
\(437\) | 45.1739 | 2.16096 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 37.7653 | 1.80244 | 0.901221 | − | 0.433361i | \(-0.142672\pi\) | ||||
0.901221 | + | 0.433361i | \(0.142672\pi\) | |||||||
\(440\) | −10.7908 | −0.514429 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0.420237 | 0.0199886 | ||||||||
\(443\) | 10.3172 | 0.490184 | 0.245092 | − | 0.969500i | \(-0.421182\pi\) | ||||
0.245092 | + | 0.969500i | \(0.421182\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −36.8237 | −1.74561 | ||||||||
\(446\) | −14.0558 | −0.665563 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0.647278 | 0.0305810 | ||||||||
\(449\) | −18.1795 | −0.857946 | −0.428973 | − | 0.903317i | \(-0.641124\pi\) | ||||
−0.428973 | + | 0.903317i | \(0.641124\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −22.5996 | −1.06418 | ||||||||
\(452\) | 14.7319 | 0.692928 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 17.2851 | 0.811229 | ||||||||
\(455\) | −1.34080 | −0.0628576 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 34.7422 | 1.62517 | 0.812587 | − | 0.582841i | \(-0.198059\pi\) | ||||
0.812587 | + | 0.582841i | \(0.198059\pi\) | |||||||
\(458\) | −9.37902 | −0.438253 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −21.1552 | −0.986365 | ||||||||
\(461\) | −28.6089 | −1.33245 | −0.666224 | − | 0.745752i | \(-0.732091\pi\) | ||||
−0.666224 | + | 0.745752i | \(0.732091\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 19.6770 | 0.914470 | 0.457235 | − | 0.889346i | \(-0.348840\pi\) | ||||
0.457235 | + | 0.889346i | \(0.348840\pi\) | |||||||
\(464\) | 0.536329 | 0.0248984 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 17.5605 | 0.813475 | ||||||||
\(467\) | −35.9243 | −1.66238 | −0.831188 | − | 0.555991i | \(-0.812339\pi\) | ||||
−0.831188 | + | 0.555991i | \(0.812339\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −0.740102 | −0.0341747 | ||||||||
\(470\) | −8.79132 | −0.405513 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −8.44682 | −0.388796 | ||||||||
\(473\) | 0.0947569 | 0.00435693 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 20.8648 | 0.957345 | ||||||||
\(476\) | 0.380045 | 0.0174193 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −28.9074 | −1.32220 | ||||||||
\(479\) | 23.7403 | 1.08472 | 0.542360 | − | 0.840146i | \(-0.317531\pi\) | ||||
0.542360 | + | 0.840146i | \(0.317531\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1.84673 | −0.0842038 | ||||||||
\(482\) | 22.3729 | 1.01906 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 2.90141 | 0.131882 | ||||||||
\(485\) | 43.7632 | 1.98718 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −17.2993 | −0.783906 | −0.391953 | − | 0.919985i | \(-0.628200\pi\) | ||||
−0.391953 | + | 0.919985i | \(0.628200\pi\) | |||||||
\(488\) | −1.72772 | −0.0782103 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 19.0465 | 0.860435 | ||||||||
\(491\) | 0.651841 | 0.0294172 | 0.0147086 | − | 0.999892i | \(-0.495318\pi\) | ||||
0.0147086 | + | 0.999892i | \(0.495318\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0.314902 | 0.0141825 | ||||||||
\(494\) | 4.42328 | 0.199013 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −8.61374 | −0.386768 | ||||||||
\(497\) | 4.42011 | 0.198269 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −15.6414 | −0.700203 | −0.350102 | − | 0.936712i | \(-0.613853\pi\) | ||||
−0.350102 | + | 0.936712i | \(0.613853\pi\) | |||||||
\(500\) | 4.69968 | 0.210176 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 14.0275 | 0.626079 | ||||||||
\(503\) | 9.68777 | 0.431956 | 0.215978 | − | 0.976398i | \(-0.430706\pi\) | ||||
0.215978 | + | 0.976398i | \(0.430706\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −13.3413 | −0.593681 | ||||||||
\(506\) | 27.2536 | 1.21157 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 16.5659 | 0.734993 | ||||||||
\(509\) | −4.48613 | −0.198844 | −0.0994222 | − | 0.995045i | \(-0.531699\pi\) | ||||
−0.0994222 | + | 0.995045i | \(0.531699\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 4.62372 | 0.204541 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 9.63634 | 0.425041 | ||||||||
\(515\) | −57.2819 | −2.52414 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 11.3256 | 0.498099 | ||||||||
\(518\) | −1.67011 | −0.0733804 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −2.07144 | −0.0908387 | ||||||||
\(521\) | 29.3370 | 1.28528 | 0.642638 | − | 0.766170i | \(-0.277840\pi\) | ||||
0.642638 | + | 0.766170i | \(0.277840\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −1.24942 | −0.0546335 | −0.0273167 | − | 0.999627i | \(-0.508696\pi\) | ||||
−0.0273167 | + | 0.999627i | \(0.508696\pi\) | |||||||
\(524\) | 3.97969 | 0.173853 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −21.5566 | −0.939914 | ||||||||
\(527\) | −5.05749 | −0.220308 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 30.4304 | 1.32306 | ||||||||
\(530\) | −38.5549 | −1.67472 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 4.00023 | 0.173432 | ||||||||
\(533\) | −4.33833 | −0.187914 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0.336644 | 0.0145544 | ||||||||
\(536\) | −1.14341 | −0.0493877 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 26.4569 | 1.14064 | ||||||||
\(539\) | −24.5371 | −1.05689 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 23.0580 | 0.991341 | 0.495670 | − | 0.868511i | \(-0.334922\pi\) | ||||
0.495670 | + | 0.868511i | \(0.334922\pi\) | |||||||
\(542\) | 11.9830 | 0.514714 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0.587143 | 0.0251735 | ||||||||
\(545\) | 50.4131 | 2.15946 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −45.8753 | −1.96149 | −0.980744 | − | 0.195298i | \(-0.937433\pi\) | ||||
−0.980744 | + | 0.195298i | \(0.937433\pi\) | |||||||
\(548\) | 17.7470 | 0.758112 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 12.5878 | 0.536747 | ||||||||
\(551\) | 3.31455 | 0.141205 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 2.16449 | 0.0920436 | ||||||||
\(554\) | 23.0482 | 0.979224 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −3.40466 | −0.144390 | ||||||||
\(557\) | 40.9294 | 1.73424 | 0.867118 | − | 0.498103i | \(-0.165970\pi\) | ||||
0.867118 | + | 0.498103i | \(0.165970\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0.0181900 | 0.000769353 0 | ||||||||
\(560\) | −1.87333 | −0.0791624 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 16.6551 | 0.702554 | ||||||||
\(563\) | 41.8178 | 1.76241 | 0.881205 | − | 0.472734i | \(-0.156733\pi\) | ||||
0.881205 | + | 0.472734i | \(0.156733\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −42.6363 | −1.79372 | ||||||||
\(566\) | −4.34695 | −0.182716 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 6.82877 | 0.286529 | ||||||||
\(569\) | 12.9590 | 0.543271 | 0.271635 | − | 0.962400i | \(-0.412436\pi\) | ||||
0.271635 | + | 0.962400i | \(0.412436\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 2.26520 | 0.0947956 | 0.0473978 | − | 0.998876i | \(-0.484907\pi\) | ||||
0.0473978 | + | 0.998876i | \(0.484907\pi\) | |||||||
\(572\) | 2.66858 | 0.111579 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −3.92341 | −0.163760 | ||||||||
\(575\) | 24.6783 | 1.02916 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −45.8681 | −1.90951 | −0.954757 | − | 0.297388i | \(-0.903884\pi\) | ||||
−0.954757 | + | 0.297388i | \(0.903884\pi\) | |||||||
\(578\) | −16.6553 | −0.692768 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −1.55222 | −0.0644524 | ||||||||
\(581\) | −8.15519 | −0.338334 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 49.6691 | 2.05708 | ||||||||
\(584\) | 7.14332 | 0.295593 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −17.5782 | −0.726147 | ||||||||
\(587\) | 24.5809 | 1.01456 | 0.507282 | − | 0.861780i | \(-0.330650\pi\) | ||||
0.507282 | + | 0.861780i | \(0.330650\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −53.2335 | −2.19345 | ||||||||
\(590\) | 24.4464 | 1.00644 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −2.58020 | −0.106046 | ||||||||
\(593\) | −34.9322 | −1.43449 | −0.717246 | − | 0.696820i | \(-0.754598\pi\) | ||||
−0.717246 | + | 0.696820i | \(0.754598\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −1.09991 | −0.0450919 | ||||||||
\(596\) | 1.00000 | 0.0409616 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 5.23172 | 0.213941 | ||||||||
\(599\) | 24.6003 | 1.00514 | 0.502571 | − | 0.864536i | \(-0.332387\pi\) | ||||
0.502571 | + | 0.864536i | \(0.332387\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −27.8018 | −1.13406 | −0.567029 | − | 0.823698i | \(-0.691907\pi\) | ||||
−0.567029 | + | 0.823698i | \(0.691907\pi\) | |||||||
\(602\) | 0.0164502 | 0.000670462 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −10.6585 | −0.433687 | ||||||||
\(605\) | −8.39715 | −0.341393 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 19.6853 | 0.799000 | 0.399500 | − | 0.916733i | \(-0.369184\pi\) | ||||
0.399500 | + | 0.916733i | \(0.369184\pi\) | |||||||
\(608\) | 6.18007 | 0.250635 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 5.00030 | 0.202456 | ||||||||
\(611\) | 2.17411 | 0.0879552 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −41.9191 | −1.69310 | −0.846548 | − | 0.532313i | \(-0.821323\pi\) | ||||
−0.846548 | + | 0.532313i | \(0.821323\pi\) | |||||||
\(614\) | −13.8702 | −0.559754 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 2.41335 | 0.0972367 | ||||||||
\(617\) | 47.4315 | 1.90952 | 0.954760 | − | 0.297378i | \(-0.0961123\pi\) | ||||
0.954760 | + | 0.297378i | \(0.0961123\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −32.0158 | −1.28682 | −0.643412 | − | 0.765520i | \(-0.722482\pi\) | ||||
−0.643412 | + | 0.765520i | \(0.722482\pi\) | |||||||
\(620\) | 24.9295 | 1.00119 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −9.97478 | −0.399952 | ||||||||
\(623\) | 8.23561 | 0.329953 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −30.4824 | −1.21929 | ||||||||
\(626\) | 22.0525 | 0.881394 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 10.8183 | 0.431699 | ||||||||
\(629\) | −1.51495 | −0.0604049 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −11.8268 | −0.470817 | −0.235408 | − | 0.971897i | \(-0.575643\pi\) | ||||
−0.235408 | + | 0.971897i | \(0.575643\pi\) | |||||||
\(632\) | 3.34399 | 0.133017 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 2.36150 | 0.0937873 | ||||||||
\(635\) | −47.9443 | −1.90261 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −4.71025 | −0.186627 | ||||||||
\(638\) | 1.99968 | 0.0791681 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −2.89416 | −0.114402 | ||||||||
\(641\) | −26.3481 | −1.04069 | −0.520344 | − | 0.853957i | \(-0.674196\pi\) | ||||
−0.520344 | + | 0.853957i | \(0.674196\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −1.08450 | −0.0427687 | −0.0213843 | − | 0.999771i | \(-0.506807\pi\) | ||||
−0.0213843 | + | 0.999771i | \(0.506807\pi\) | |||||||
\(644\) | 4.73135 | 0.186441 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 3.62859 | 0.142765 | ||||||||
\(647\) | −26.9245 | −1.05851 | −0.529256 | − | 0.848462i | \(-0.677529\pi\) | ||||
−0.529256 | + | 0.848462i | \(0.677529\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −31.4936 | −1.23623 | ||||||||
\(650\) | 2.41642 | 0.0947797 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 6.33240 | 0.247996 | ||||||||
\(653\) | −7.23572 | −0.283156 | −0.141578 | − | 0.989927i | \(-0.545218\pi\) | ||||
−0.141578 | + | 0.989927i | \(0.545218\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −11.5178 | −0.450039 | ||||||||
\(656\) | −6.06139 | −0.236658 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 1.96618 | 0.0766496 | ||||||||
\(659\) | 21.4670 | 0.836237 | 0.418119 | − | 0.908392i | \(-0.362690\pi\) | ||||
0.418119 | + | 0.908392i | \(0.362690\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 3.65121 | 0.142016 | 0.0710078 | − | 0.997476i | \(-0.477378\pi\) | ||||
0.0710078 | + | 0.997476i | \(0.477378\pi\) | |||||||
\(662\) | −24.6246 | −0.957063 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −12.5992 | −0.488944 | ||||||||
\(665\) | −11.5773 | −0.448948 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 3.92035 | 0.151797 | ||||||||
\(668\) | −20.0433 | −0.775497 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 3.30920 | 0.127846 | ||||||||
\(671\) | −6.44174 | −0.248681 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −12.0356 | −0.463939 | −0.231970 | − | 0.972723i | \(-0.574517\pi\) | ||||
−0.231970 | + | 0.972723i | \(0.574517\pi\) | |||||||
\(674\) | 4.12734 | 0.158979 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −12.4877 | −0.480297 | ||||||||
\(677\) | 42.7141 | 1.64163 | 0.820817 | − | 0.571191i | \(-0.193518\pi\) | ||||
0.820817 | + | 0.571191i | \(0.193518\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −9.78763 | −0.375615 | ||||||||
\(680\) | −1.69928 | −0.0651646 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −32.1160 | −1.22978 | ||||||||
\(683\) | −33.1663 | −1.26907 | −0.634537 | − | 0.772892i | \(-0.718809\pi\) | ||||
−0.634537 | + | 0.772892i | \(0.718809\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −51.3625 | −1.96246 | ||||||||
\(686\) | −8.79070 | −0.335631 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0.0254145 | 0.000968918 0 | ||||||||
\(689\) | 9.53471 | 0.363243 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 9.66686 | 0.367745 | 0.183872 | − | 0.982950i | \(-0.441137\pi\) | ||||
0.183872 | + | 0.982950i | \(0.441137\pi\) | |||||||
\(692\) | 19.7813 | 0.751974 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 1.66183 | 0.0630824 | ||||||||
\(695\) | 9.85362 | 0.373769 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −3.55890 | −0.134803 | ||||||||
\(698\) | −9.67092 | −0.366050 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 2.18531 | 0.0825969 | ||||||||
\(701\) | 13.0861 | 0.494256 | 0.247128 | − | 0.968983i | \(-0.420513\pi\) | ||||
0.247128 | + | 0.968983i | \(0.420513\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −15.9458 | −0.601409 | ||||||||
\(704\) | 3.72846 | 0.140522 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −28.8909 | −1.08732 | ||||||||
\(707\) | 2.98379 | 0.112217 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 23.8607 | 0.896108 | 0.448054 | − | 0.894006i | \(-0.352117\pi\) | ||||
0.448054 | + | 0.894006i | \(0.352117\pi\) | |||||||
\(710\) | −19.7635 | −0.741712 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 12.7234 | 0.476831 | ||||||||
\(713\) | −62.9631 | −2.35798 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −7.72329 | −0.288835 | ||||||||
\(716\) | 8.80643 | 0.329112 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 6.28476 | 0.234545 | ||||||||
\(719\) | −2.06440 | −0.0769893 | −0.0384946 | − | 0.999259i | \(-0.512256\pi\) | ||||
−0.0384946 | + | 0.999259i | \(0.512256\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 12.8111 | 0.477110 | ||||||||
\(722\) | 19.1933 | 0.714301 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −2.53023 | −0.0940352 | ||||||||
\(725\) | 1.81073 | 0.0672487 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 13.8825 | 0.514875 | 0.257437 | − | 0.966295i | \(-0.417122\pi\) | ||||
0.257437 | + | 0.966295i | \(0.417122\pi\) | |||||||
\(728\) | 0.463278 | 0.0171702 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −20.6739 | −0.765176 | ||||||||
\(731\) | 0.0149219 | 0.000551908 0 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 34.2164 | 1.26381 | 0.631906 | − | 0.775045i | \(-0.282273\pi\) | ||||
0.631906 | + | 0.775045i | \(0.282273\pi\) | |||||||
\(734\) | −23.5043 | −0.867559 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 7.30961 | 0.269436 | ||||||||
\(737\) | −4.26315 | −0.157035 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −19.0265 | −0.699901 | −0.349950 | − | 0.936768i | \(-0.613802\pi\) | ||||
−0.349950 | + | 0.936768i | \(0.613802\pi\) | |||||||
\(740\) | 7.46751 | 0.274511 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 8.62279 | 0.316553 | ||||||||
\(743\) | 6.44555 | 0.236464 | 0.118232 | − | 0.992986i | \(-0.462277\pi\) | ||||
0.118232 | + | 0.992986i | \(0.462277\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −2.89416 | −0.106034 | ||||||||
\(746\) | 8.22391 | 0.301099 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 2.18914 | 0.0800428 | ||||||||
\(749\) | −0.0752904 | −0.00275105 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −17.8606 | −0.651741 | −0.325870 | − | 0.945414i | \(-0.605657\pi\) | ||||
−0.325870 | + | 0.945414i | \(0.605657\pi\) | |||||||
\(752\) | 3.03761 | 0.110770 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0.383868 | 0.0139796 | ||||||||
\(755\) | 30.8473 | 1.12265 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −4.27617 | −0.155420 | −0.0777099 | − | 0.996976i | \(-0.524761\pi\) | ||||
−0.0777099 | + | 0.996976i | \(0.524761\pi\) | |||||||
\(758\) | 17.0746 | 0.620179 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −17.8861 | −0.648797 | ||||||||
\(761\) | −8.11840 | −0.294292 | −0.147146 | − | 0.989115i | \(-0.547009\pi\) | ||||
−0.147146 | + | 0.989115i | \(0.547009\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −11.2749 | −0.408179 | ||||||||
\(764\) | 11.0216 | 0.398748 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −9.91645 | −0.358296 | ||||||||
\(767\) | −6.04566 | −0.218296 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 15.0788 | 0.543755 | 0.271878 | − | 0.962332i | \(-0.412355\pi\) | ||||
0.271878 | + | 0.962332i | \(0.412355\pi\) | |||||||
\(770\) | −6.98462 | −0.251708 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 13.0378 | 0.469240 | ||||||||
\(773\) | 15.9177 | 0.572520 | 0.286260 | − | 0.958152i | \(-0.407588\pi\) | ||||
0.286260 | + | 0.958152i | \(0.407588\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −29.0813 | −1.04463 | ||||||||
\(776\) | −15.1212 | −0.542820 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −20.6837 | −0.741548 | ||||||||
\(779\) | −37.4598 | −1.34214 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 25.4608 | 0.911058 | ||||||||
\(782\) | 4.29178 | 0.153474 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −6.58103 | −0.235037 | ||||||||
\(785\) | −31.3100 | −1.11750 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −51.4233 | −1.83304 | −0.916521 | − | 0.399986i | \(-0.869015\pi\) | ||||
−0.916521 | + | 0.399986i | \(0.869015\pi\) | |||||||
\(788\) | 6.51445 | 0.232068 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −9.67804 | −0.344329 | ||||||||
\(791\) | 9.53561 | 0.339047 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −1.23659 | −0.0439125 | ||||||||
\(794\) | −10.8701 | −0.385767 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 8.24335 | 0.292178 | ||||||||
\(797\) | −37.6677 | −1.33426 | −0.667129 | − | 0.744942i | \(-0.732477\pi\) | ||||
−0.667129 | + | 0.744942i | \(0.732477\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1.78351 | 0.0630960 | ||||||||
\(800\) | 3.37615 | 0.119365 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −27.8798 | −0.984469 | ||||||||
\(803\) | 26.6336 | 0.939879 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −13.6933 | −0.482624 | ||||||||
\(806\) | −6.16513 | −0.217157 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 4.60974 | 0.162170 | ||||||||
\(809\) | −1.00886 | −0.0354696 | −0.0177348 | − | 0.999843i | \(-0.505645\pi\) | ||||
−0.0177348 | + | 0.999843i | \(0.505645\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −12.6227 | −0.443244 | −0.221622 | − | 0.975133i | \(-0.571135\pi\) | ||||
−0.221622 | + | 0.975133i | \(0.571135\pi\) | |||||||
\(812\) | 0.347154 | 0.0121827 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −9.62018 | −0.337187 | ||||||||
\(815\) | −18.3270 | −0.641965 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0.157063 | 0.00549495 | ||||||||
\(818\) | −21.3723 | −0.747267 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 17.5426 | 0.612615 | ||||||||
\(821\) | 31.5916 | 1.10256 | 0.551278 | − | 0.834322i | \(-0.314140\pi\) | ||||
0.551278 | + | 0.834322i | \(0.314140\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 31.7590 | 1.10705 | 0.553525 | − | 0.832832i | \(-0.313282\pi\) | ||||
0.553525 | + | 0.832832i | \(0.313282\pi\) | |||||||
\(824\) | 19.7923 | 0.689496 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −5.46744 | −0.190237 | ||||||||
\(827\) | 0.680815 | 0.0236743 | 0.0118371 | − | 0.999930i | \(-0.496232\pi\) | ||||
0.0118371 | + | 0.999930i | \(0.496232\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 18.9640 | 0.658648 | 0.329324 | − | 0.944217i | \(-0.393179\pi\) | ||||
0.329324 | + | 0.944217i | \(0.393179\pi\) | |||||||
\(830\) | 36.4641 | 1.26569 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0.715732 | 0.0248135 | ||||||||
\(833\) | −3.86401 | −0.133880 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 58.0084 | 2.00746 | ||||||||
\(836\) | 23.0422 | 0.796930 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0.754815 | 0.0260747 | ||||||||
\(839\) | 19.3566 | 0.668263 | 0.334132 | − | 0.942526i | \(-0.391557\pi\) | ||||
0.334132 | + | 0.942526i | \(0.391557\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.7124 | −0.990081 | ||||||||
\(842\) | 24.0721 | 0.829579 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 14.4493 | 0.497364 | ||||||||
\(845\) | 36.1415 | 1.24330 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1.87802 | 0.0645296 | ||||||||
\(848\) | 13.3216 | 0.457466 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 1.98228 | 0.0679917 | ||||||||
\(851\) | −18.8603 | −0.646522 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −42.7432 | −1.46350 | −0.731750 | − | 0.681573i | \(-0.761296\pi\) | ||||
−0.731750 | + | 0.681573i | \(0.761296\pi\) | |||||||
\(854\) | −1.11832 | −0.0382680 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −0.116319 | −0.00397568 | ||||||||
\(857\) | −8.25018 | −0.281821 | −0.140910 | − | 0.990022i | \(-0.545003\pi\) | ||||
−0.140910 | + | 0.990022i | \(0.545003\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 44.8257 | 1.52943 | 0.764716 | − | 0.644368i | \(-0.222879\pi\) | ||||
0.764716 | + | 0.644368i | \(0.222879\pi\) | |||||||
\(860\) | −0.0735535 | −0.00250815 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 10.4667 | 0.356496 | ||||||||
\(863\) | 11.2994 | 0.384635 | 0.192317 | − | 0.981333i | \(-0.438400\pi\) | ||||
0.192317 | + | 0.981333i | \(0.438400\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −57.2503 | −1.94657 | ||||||||
\(866\) | 2.47142 | 0.0839821 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −5.57548 | −0.189244 | ||||||||
\(869\) | 12.4679 | 0.422946 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −0.818373 | −0.0277295 | ||||||||
\(872\) | −17.4189 | −0.589880 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 45.1739 | 1.52803 | ||||||||
\(875\) | 3.04200 | 0.102838 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −34.5953 | −1.16820 | −0.584101 | − | 0.811681i | \(-0.698553\pi\) | ||||
−0.584101 | + | 0.811681i | \(0.698553\pi\) | |||||||
\(878\) | 37.7653 | 1.27452 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −10.7908 | −0.363756 | ||||||||
\(881\) | 18.6458 | 0.628192 | 0.314096 | − | 0.949391i | \(-0.398299\pi\) | ||||
0.314096 | + | 0.949391i | \(0.398299\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −19.6055 | −0.659777 | −0.329889 | − | 0.944020i | \(-0.607011\pi\) | ||||
−0.329889 | + | 0.944020i | \(0.607011\pi\) | |||||||
\(884\) | 0.420237 | 0.0141341 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 10.3172 | 0.346613 | ||||||||
\(887\) | −14.3840 | −0.482969 | −0.241484 | − | 0.970405i | \(-0.577634\pi\) | ||||
−0.241484 | + | 0.970405i | \(0.577634\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 10.7227 | 0.359629 | ||||||||
\(890\) | −36.8237 | −1.23433 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −14.0558 | −0.470624 | ||||||||
\(893\) | 18.7726 | 0.628202 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −25.4872 | −0.851943 | ||||||||
\(896\) | 0.647278 | 0.0216240 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −18.1795 | −0.606659 | ||||||||
\(899\) | −4.61979 | −0.154079 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 7.82169 | 0.260578 | ||||||||
\(902\) | −22.5996 | −0.752486 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 14.7319 | 0.489974 | ||||||||
\(905\) | 7.32288 | 0.243421 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 49.7539 | 1.65205 | 0.826026 | − | 0.563632i | \(-0.190596\pi\) | ||||
0.826026 | + | 0.563632i | \(0.190596\pi\) | |||||||
\(908\) | 17.2851 | 0.573626 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −1.34080 | −0.0444470 | ||||||||
\(911\) | −59.1494 | −1.95971 | −0.979853 | − | 0.199721i | \(-0.935997\pi\) | ||||
−0.979853 | + | 0.199721i | \(0.935997\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −46.9757 | −1.55467 | ||||||||
\(914\) | 34.7422 | 1.14917 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −9.37902 | −0.309892 | ||||||||
\(917\) | 2.57596 | 0.0850658 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 3.31621 | 0.109392 | 0.0546959 | − | 0.998503i | \(-0.482581\pi\) | ||||
0.0546959 | + | 0.998503i | \(0.482581\pi\) | |||||||
\(920\) | −21.1552 | −0.697465 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −28.6089 | −0.942183 | ||||||||
\(923\) | 4.88757 | 0.160876 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −8.71115 | −0.286421 | ||||||||
\(926\) | 19.6770 | 0.646628 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0.536329 | 0.0176059 | ||||||||
\(929\) | −5.62665 | −0.184604 | −0.0923021 | − | 0.995731i | \(-0.529423\pi\) | ||||
−0.0923021 | + | 0.995731i | \(0.529423\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −40.6713 | −1.33295 | ||||||||
\(932\) | 17.5605 | 0.575213 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −35.9243 | −1.17548 | ||||||||
\(935\) | −6.33571 | −0.207200 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −35.2604 | −1.15191 | −0.575953 | − | 0.817483i | \(-0.695369\pi\) | ||||
−0.575953 | + | 0.817483i | \(0.695369\pi\) | |||||||
\(938\) | −0.740102 | −0.0241652 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −8.79132 | −0.286741 | ||||||||
\(941\) | −41.3278 | −1.34725 | −0.673624 | − | 0.739074i | \(-0.735263\pi\) | ||||
−0.673624 | + | 0.739074i | \(0.735263\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −44.3064 | −1.44281 | ||||||||
\(944\) | −8.44682 | −0.274921 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0.0947569 | 0.00308081 | ||||||||
\(947\) | −23.3912 | −0.760112 | −0.380056 | − | 0.924963i | \(-0.624095\pi\) | ||||
−0.380056 | + | 0.924963i | \(0.624095\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 5.11270 | 0.165965 | ||||||||
\(950\) | 20.8648 | 0.676945 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0.380045 | 0.0123173 | ||||||||
\(953\) | −4.73330 | −0.153327 | −0.0766633 | − | 0.997057i | \(-0.524427\pi\) | ||||
−0.0766633 | + | 0.997057i | \(0.524427\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −31.8983 | −1.03221 | ||||||||
\(956\) | −28.9074 | −0.934933 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 23.7403 | 0.767013 | ||||||||
\(959\) | 11.4872 | 0.370941 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 43.1965 | 1.39343 | ||||||||
\(962\) | −1.84673 | −0.0595411 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 22.3729 | 0.720583 | ||||||||
\(965\) | −37.7334 | −1.21468 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 43.4553 | 1.39743 | 0.698714 | − | 0.715401i | \(-0.253756\pi\) | ||||
0.698714 | + | 0.715401i | \(0.253756\pi\) | |||||||
\(968\) | 2.90141 | 0.0932550 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 43.7632 | 1.40515 | ||||||||
\(971\) | −37.4142 | −1.20068 | −0.600340 | − | 0.799745i | \(-0.704968\pi\) | ||||
−0.600340 | + | 0.799745i | \(0.704968\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −2.20376 | −0.0706493 | ||||||||
\(974\) | −17.2993 | −0.554305 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −1.72772 | −0.0553030 | ||||||||
\(977\) | −55.4340 | −1.77349 | −0.886746 | − | 0.462258i | \(-0.847040\pi\) | ||||
−0.886746 | + | 0.462258i | \(0.847040\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 47.4389 | 1.51615 | ||||||||
\(980\) | 19.0465 | 0.608419 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0.651841 | 0.0208011 | ||||||||
\(983\) | 37.5297 | 1.19701 | 0.598506 | − | 0.801118i | \(-0.295761\pi\) | ||||
0.598506 | + | 0.801118i | \(0.295761\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −18.8539 | −0.600734 | ||||||||
\(986\) | 0.314902 | 0.0100285 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 4.42328 | 0.140723 | ||||||||
\(989\) | 0.185770 | 0.00590714 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −11.4603 | −0.364049 | −0.182025 | − | 0.983294i | \(-0.558265\pi\) | ||||
−0.182025 | + | 0.983294i | \(0.558265\pi\) | |||||||
\(992\) | −8.61374 | −0.273486 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 4.42011 | 0.140197 | ||||||||
\(995\) | −23.8576 | −0.756336 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 5.94633 | 0.188322 | 0.0941611 | − | 0.995557i | \(-0.469983\pi\) | ||||
0.0941611 | + | 0.995557i | \(0.469983\pi\) | |||||||
\(998\) | −15.6414 | −0.495118 | ||||||||
\(999\) | 0 | 0 |
(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 | 8046.2.a.o.1.1 | yes | 12 | |
3.2 | odd | 2 | 8046.2.a.j.1.12 | ✓ | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8046.2.a.j.1.12 | ✓ | 12 | 3.2 | odd | 2 | ||
8046.2.a.o.1.1 | yes | 12 | 1.1 | even | 1 | trivial |