Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2832,2,Mod(1,2832)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2832, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("2832.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2832 = 2^{4} \cdot 3 \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2832.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: | \(22.6136338524\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{10})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 177) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-0.618034\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2832.1 |
$q$-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 | ||||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 2.23607 | 1.00000 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 4.61803 | 1.74545 | 0.872726 | − | 0.488210i | \(-0.162350\pi\) | ||||
0.872726 | + | 0.488210i | \(0.162350\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.23607 | 0.674200 | 0.337100 | − | 0.941469i | \(-0.390554\pi\) | ||||
0.337100 | + | 0.941469i | \(0.390554\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.76393 | −0.489227 | −0.244613 | − | 0.969621i | \(-0.578661\pi\) | ||||
−0.244613 | + | 0.969621i | \(0.578661\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 2.23607 | 0.577350 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −4.85410 | −1.17729 | −0.588646 | − | 0.808391i | \(-0.700339\pi\) | ||||
−0.588646 | + | 0.808391i | \(0.700339\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 8.09017 | 1.85601 | 0.928006 | − | 0.372565i | \(-0.121522\pi\) | ||||
0.928006 | + | 0.372565i | \(0.121522\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 4.61803 | 1.00774 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2.38197 | 0.496674 | 0.248337 | − | 0.968674i | \(-0.420116\pi\) | ||||
0.248337 | + | 0.968674i | \(0.420116\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 8.61803 | 1.60033 | 0.800164 | − | 0.599781i | \(-0.204746\pi\) | ||||
0.800164 | + | 0.599781i | \(0.204746\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −9.56231 | −1.71744 | −0.858720 | − | 0.512444i | \(-0.828740\pi\) | ||||
−0.858720 | + | 0.512444i | \(0.828740\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 2.23607 | 0.389249 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 10.3262 | 1.74545 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −6.85410 | −1.12681 | −0.563404 | − | 0.826182i | \(-0.690508\pi\) | ||||
−0.563404 | + | 0.826182i | \(0.690508\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −1.76393 | −0.282455 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −3.09017 | −0.482603 | −0.241302 | − | 0.970450i | \(-0.577574\pi\) | ||||
−0.241302 | + | 0.970450i | \(0.577574\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −4.70820 | −0.717994 | −0.358997 | − | 0.933339i | \(-0.616881\pi\) | ||||
−0.358997 | + | 0.933339i | \(0.616881\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 2.23607 | 0.333333 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 4.14590 | 0.604741 | 0.302371 | − | 0.953190i | \(-0.402222\pi\) | ||||
0.302371 | + | 0.953190i | \(0.402222\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 14.3262 | 2.04661 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −4.85410 | −0.679710 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 1.76393 | 0.242295 | 0.121147 | − | 0.992635i | \(-0.461343\pi\) | ||||
0.121147 | + | 0.992635i | \(0.461343\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 5.00000 | 0.674200 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 8.09017 | 1.07157 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 1.00000 | 0.130189 | ||||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −9.85410 | −1.26169 | −0.630844 | − | 0.775909i | \(-0.717291\pi\) | ||||
−0.630844 | + | 0.775909i | \(0.717291\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 4.61803 | 0.581818 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −3.94427 | −0.489227 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2.70820 | 0.330860 | 0.165430 | − | 0.986222i | \(-0.447099\pi\) | ||||
0.165430 | + | 0.986222i | \(0.447099\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 2.38197 | 0.286755 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −9.94427 | −1.18017 | −0.590084 | − | 0.807342i | \(-0.700905\pi\) | ||||
−0.590084 | + | 0.807342i | \(0.700905\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −5.85410 | −0.685171 | −0.342585 | − | 0.939487i | \(-0.611303\pi\) | ||||
−0.342585 | + | 0.939487i | \(0.611303\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 10.3262 | 1.17678 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 3.00000 | 0.337526 | 0.168763 | − | 0.985657i | \(-0.446023\pi\) | ||||
0.168763 | + | 0.985657i | \(0.446023\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −0.618034 | −0.0678380 | −0.0339190 | − | 0.999425i | \(-0.510799\pi\) | ||||
−0.0339190 | + | 0.999425i | \(0.510799\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −10.8541 | −1.17729 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 8.61803 | 0.923950 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 10.7984 | 1.14463 | 0.572313 | − | 0.820035i | \(-0.306046\pi\) | ||||
0.572313 | + | 0.820035i | \(0.306046\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −8.14590 | −0.853922 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −9.56231 | −0.991565 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 18.0902 | 1.85601 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 3.00000 | 0.304604 | 0.152302 | − | 0.988334i | \(-0.451331\pi\) | ||||
0.152302 | + | 0.988334i | \(0.451331\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 2.23607 | 0.224733 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −9.70820 | −0.966002 | −0.483001 | − | 0.875620i | \(-0.660453\pi\) | ||||
−0.483001 | + | 0.875620i | \(0.660453\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1.23607 | −0.121793 | −0.0608967 | − | 0.998144i | \(-0.519396\pi\) | ||||
−0.0608967 | + | 0.998144i | \(0.519396\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 10.3262 | 1.00774 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −12.0902 | −1.16880 | −0.584400 | − | 0.811465i | \(-0.698670\pi\) | ||||
−0.584400 | + | 0.811465i | \(0.698670\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −10.8541 | −1.03963 | −0.519817 | − | 0.854278i | \(-0.674000\pi\) | ||||
−0.519817 | + | 0.854278i | \(0.674000\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −6.85410 | −0.650563 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −9.00000 | −0.846649 | −0.423324 | − | 0.905978i | \(-0.639137\pi\) | ||||
−0.423324 | + | 0.905978i | \(0.639137\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 5.32624 | 0.496674 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −1.76393 | −0.163076 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −22.4164 | −2.05491 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −6.00000 | −0.545455 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −3.09017 | −0.278631 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −11.1803 | −1.00000 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1.94427 | 0.172526 | 0.0862631 | − | 0.996272i | \(-0.472507\pi\) | ||||
0.0862631 | + | 0.996272i | \(0.472507\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −4.70820 | −0.414534 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −10.6525 | −0.930711 | −0.465356 | − | 0.885124i | \(-0.654074\pi\) | ||||
−0.465356 | + | 0.885124i | \(0.654074\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 37.3607 | 3.23958 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 2.23607 | 0.192450 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 7.76393 | 0.663317 | 0.331659 | − | 0.943399i | \(-0.392392\pi\) | ||||
0.331659 | + | 0.943399i | \(0.392392\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −16.2361 | −1.37713 | −0.688563 | − | 0.725177i | \(-0.741758\pi\) | ||||
−0.688563 | + | 0.725177i | \(0.741758\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 4.14590 | 0.349148 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −3.94427 | −0.329837 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 19.2705 | 1.60033 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 14.3262 | 1.18161 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 7.90983 | 0.647999 | 0.323999 | − | 0.946057i | \(-0.394972\pi\) | ||||
0.323999 | + | 0.946057i | \(0.394972\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 17.5623 | 1.42920 | 0.714600 | − | 0.699533i | \(-0.246609\pi\) | ||||
0.714600 | + | 0.699533i | \(0.246609\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −4.85410 | −0.392431 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −21.3820 | −1.71744 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 9.00000 | 0.718278 | 0.359139 | − | 0.933284i | \(-0.383070\pi\) | ||||
0.359139 | + | 0.933284i | \(0.383070\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 1.76393 | 0.139889 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 11.0000 | 0.866921 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1.56231 | −0.122369 | −0.0611846 | − | 0.998126i | \(-0.519488\pi\) | ||||
−0.0611846 | + | 0.998126i | \(0.519488\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 5.00000 | 0.389249 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 22.0344 | 1.70508 | 0.852538 | − | 0.522665i | \(-0.175062\pi\) | ||||
0.852538 | + | 0.522665i | \(0.175062\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −9.88854 | −0.760657 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 8.09017 | 0.618671 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 14.6180 | 1.11139 | 0.555694 | − | 0.831387i | \(-0.312453\pi\) | ||||
0.555694 | + | 0.831387i | \(0.312453\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 1.00000 | 0.0751646 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 9.47214 | 0.707981 | 0.353990 | − | 0.935249i | \(-0.384825\pi\) | ||||
0.353990 | + | 0.935249i | \(0.384825\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −11.2705 | −0.837730 | −0.418865 | − | 0.908048i | \(-0.637572\pi\) | ||||
−0.418865 | + | 0.908048i | \(0.637572\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −9.85410 | −0.728436 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −15.3262 | −1.12681 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −10.8541 | −0.793731 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 4.61803 | 0.335913 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 10.4164 | 0.753705 | 0.376852 | − | 0.926273i | \(-0.377006\pi\) | ||||
0.376852 | + | 0.926273i | \(0.377006\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 8.00000 | 0.575853 | 0.287926 | − | 0.957653i | \(-0.407034\pi\) | ||||
0.287926 | + | 0.957653i | \(0.407034\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −3.94427 | −0.282455 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 10.6525 | 0.758957 | 0.379479 | − | 0.925200i | \(-0.376103\pi\) | ||||
0.379479 | + | 0.925200i | \(0.376103\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −3.56231 | −0.252525 | −0.126263 | − | 0.991997i | \(-0.540298\pi\) | ||||
−0.126263 | + | 0.991997i | \(0.540298\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 2.70820 | 0.191022 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 39.7984 | 2.79330 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −6.90983 | −0.482603 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 2.38197 | 0.165558 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 18.0902 | 1.25132 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 8.85410 | 0.609542 | 0.304771 | − | 0.952426i | \(-0.401420\pi\) | ||||
0.304771 | + | 0.952426i | \(0.401420\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −9.94427 | −0.681370 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −10.5279 | −0.717994 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −44.1591 | −2.99771 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −5.85410 | −0.395584 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 8.56231 | 0.575963 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 18.4721 | 1.23699 | 0.618493 | − | 0.785790i | \(-0.287744\pi\) | ||||
0.618493 | + | 0.785790i | \(0.287744\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 28.8541 | 1.91511 | 0.957557 | − | 0.288244i | \(-0.0930714\pi\) | ||||
0.957557 | + | 0.288244i | \(0.0930714\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −15.8541 | −1.04767 | −0.523834 | − | 0.851820i | \(-0.675499\pi\) | ||||
−0.523834 | + | 0.851820i | \(0.675499\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 10.3262 | 0.679417 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −21.7082 | −1.42215 | −0.711076 | − | 0.703115i | \(-0.751792\pi\) | ||||
−0.711076 | + | 0.703115i | \(0.751792\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 9.27051 | 0.604741 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 3.00000 | 0.194871 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −7.47214 | −0.483332 | −0.241666 | − | 0.970359i | \(-0.577694\pi\) | ||||
−0.241666 | + | 0.970359i | \(0.577694\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 3.41641 | 0.220070 | 0.110035 | − | 0.993928i | \(-0.464904\pi\) | ||||
0.110035 | + | 0.993928i | \(0.464904\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 32.0344 | 2.04661 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −14.2705 | −0.908011 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −0.618034 | −0.0391663 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 7.18034 | 0.453219 | 0.226610 | − | 0.973986i | \(-0.427236\pi\) | ||||
0.226610 | + | 0.973986i | \(0.427236\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 5.32624 | 0.334858 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −10.8541 | −0.679710 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 7.41641 | 0.462623 | 0.231311 | − | 0.972880i | \(-0.425698\pi\) | ||||
0.231311 | + | 0.972880i | \(0.425698\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −31.6525 | −1.96679 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 8.61803 | 0.533443 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 0.618034 | 0.0381096 | 0.0190548 | − | 0.999818i | \(-0.493934\pi\) | ||||
0.0190548 | + | 0.999818i | \(0.493934\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 3.94427 | 0.242295 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 10.7984 | 0.660850 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −2.52786 | −0.154127 | −0.0770633 | − | 0.997026i | \(-0.524554\pi\) | ||||
−0.0770633 | + | 0.997026i | \(0.524554\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 12.2361 | 0.743288 | 0.371644 | − | 0.928375i | \(-0.378794\pi\) | ||||
0.371644 | + | 0.928375i | \(0.378794\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −8.14590 | −0.493012 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 3.47214 | 0.208620 | 0.104310 | − | 0.994545i | \(-0.466737\pi\) | ||||
0.104310 | + | 0.994545i | \(0.466737\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −9.56231 | −0.572480 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −3.70820 | −0.221213 | −0.110606 | − | 0.993864i | \(-0.535279\pi\) | ||||
−0.110606 | + | 0.993864i | \(0.535279\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −10.2705 | −0.610518 | −0.305259 | − | 0.952269i | \(-0.598743\pi\) | ||||
−0.305259 | + | 0.952269i | \(0.598743\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 18.0902 | 1.07157 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −14.2705 | −0.842362 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 6.56231 | 0.386018 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 3.00000 | 0.175863 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 21.6180 | 1.26294 | 0.631470 | − | 0.775401i | \(-0.282452\pi\) | ||||
0.631470 | + | 0.775401i | \(0.282452\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 2.23607 | 0.130189 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 2.23607 | 0.129750 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −4.20163 | −0.242986 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −21.7426 | −1.25323 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −9.70820 | −0.557722 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −22.0344 | −1.26169 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −9.88854 | −0.564369 | −0.282185 | − | 0.959360i | \(-0.591059\pi\) | ||||
−0.282185 | + | 0.959360i | \(0.591059\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −1.23607 | −0.0703175 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 28.4508 | 1.61330 | 0.806650 | − | 0.591030i | \(-0.201278\pi\) | ||||
0.806650 | + | 0.591030i | \(0.201278\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 3.79837 | 0.214697 | 0.107348 | − | 0.994221i | \(-0.465764\pi\) | ||||
0.107348 | + | 0.994221i | \(0.465764\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 10.3262 | 0.581818 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −6.81966 | −0.383030 | −0.191515 | − | 0.981490i | \(-0.561340\pi\) | ||||
−0.191515 | + | 0.981490i | \(0.561340\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 19.2705 | 1.07894 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −12.0902 | −0.674807 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −39.2705 | −2.18507 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −10.8541 | −0.600233 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 19.1459 | 1.05555 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −29.1246 | −1.60083 | −0.800417 | − | 0.599444i | \(-0.795388\pi\) | ||||
−0.800417 | + | 0.599444i | \(0.795388\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −6.85410 | −0.375602 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 6.05573 | 0.330860 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −26.0902 | −1.42122 | −0.710611 | − | 0.703585i | \(-0.751581\pi\) | ||||
−0.710611 | + | 0.703585i | \(0.751581\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −9.00000 | −0.488813 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −21.3820 | −1.15790 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 33.8328 | 1.82680 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 5.32624 | 0.286755 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −1.96556 | −0.105517 | −0.0527583 | − | 0.998607i | \(-0.516801\pi\) | ||||
−0.0527583 | + | 0.998607i | \(0.516801\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −27.0000 | −1.44528 | −0.722638 | − | 0.691226i | \(-0.757071\pi\) | ||||
−0.722638 | + | 0.691226i | \(0.757071\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1.76393 | −0.0941517 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 13.0344 | 0.693753 | 0.346877 | − | 0.937911i | \(-0.387242\pi\) | ||||
0.346877 | + | 0.937911i | \(0.387242\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −22.2361 | −1.18017 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −22.4164 | −1.18640 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −13.8885 | −0.733009 | −0.366505 | − | 0.930416i | \(-0.619446\pi\) | ||||
−0.366505 | + | 0.930416i | \(0.619446\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 46.4508 | 2.44478 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −6.00000 | −0.314918 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −13.0902 | −0.685171 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 23.8328 | 1.24406 | 0.622031 | − | 0.782992i | \(-0.286308\pi\) | ||||
0.622031 | + | 0.782992i | \(0.286308\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −3.09017 | −0.160868 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 8.14590 | 0.422914 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 18.6738 | 0.966891 | 0.483445 | − | 0.875375i | \(-0.339385\pi\) | ||||
0.483445 | + | 0.875375i | \(0.339385\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −11.1803 | −0.577350 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −15.2016 | −0.782924 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 4.41641 | 0.226856 | 0.113428 | − | 0.993546i | \(-0.463817\pi\) | ||||
0.113428 | + | 0.993546i | \(0.463817\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1.94427 | 0.0996081 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 13.7639 | 0.703304 | 0.351652 | − | 0.936131i | \(-0.385620\pi\) | ||||
0.351652 | + | 0.936131i | \(0.385620\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 23.0902 | 1.17678 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −4.70820 | −0.239331 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 23.5279 | 1.19291 | 0.596455 | − | 0.802646i | \(-0.296575\pi\) | ||||
0.596455 | + | 0.802646i | \(0.296575\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −11.5623 | −0.584731 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −10.6525 | −0.537346 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 6.70820 | 0.337526 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 3.00000 | 0.150566 | 0.0752828 | − | 0.997162i | \(-0.476014\pi\) | ||||
0.0752828 | + | 0.997162i | \(0.476014\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 37.3607 | 1.87037 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −5.90983 | −0.295123 | −0.147561 | − | 0.989053i | \(-0.547142\pi\) | ||||
−0.147561 | + | 0.989053i | \(0.547142\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 16.8673 | 0.840218 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 2.23607 | 0.111111 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −15.3262 | −0.759693 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −37.4164 | −1.85012 | −0.925061 | − | 0.379818i | \(-0.875987\pi\) | ||||
−0.925061 | + | 0.379818i | \(0.875987\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 7.76393 | 0.382967 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 4.61803 | 0.227239 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −1.38197 | −0.0678380 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −16.2361 | −0.795084 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −31.3050 | −1.52935 | −0.764673 | − | 0.644418i | \(-0.777100\pi\) | ||||
−0.764673 | + | 0.644418i | \(0.777100\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 1.00000 | 0.0487370 | 0.0243685 | − | 0.999703i | \(-0.492242\pi\) | ||||
0.0243685 | + | 0.999703i | \(0.492242\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 4.14590 | 0.201580 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −45.5066 | −2.20222 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −3.94427 | −0.190431 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −14.6180 | −0.704126 | −0.352063 | − | 0.935976i | \(-0.614520\pi\) | ||||
−0.352063 | + | 0.935976i | \(0.614520\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 19.3262 | 0.928760 | 0.464380 | − | 0.885636i | \(-0.346277\pi\) | ||||
0.464380 | + | 0.885636i | \(0.346277\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 19.2705 | 0.923950 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 19.2705 | 0.921833 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 32.3820 | 1.54551 | 0.772753 | − | 0.634706i | \(-0.218879\pi\) | ||||
0.772753 | + | 0.634706i | \(0.218879\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 14.3262 | 0.682202 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −5.61803 | −0.266921 | −0.133460 | − | 0.991054i | \(-0.542609\pi\) | ||||
−0.133460 | + | 0.991054i | \(0.542609\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 24.1459 | 1.14463 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 7.90983 | 0.374122 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −28.8885 | −1.36333 | −0.681667 | − | 0.731662i | \(-0.738745\pi\) | ||||
−0.681667 | + | 0.731662i | \(0.738745\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −6.90983 | −0.325371 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 17.5623 | 0.825149 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −18.2148 | −0.853922 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −26.6869 | −1.24836 | −0.624181 | − | 0.781280i | \(-0.714567\pi\) | ||||
−0.624181 | + | 0.781280i | \(0.714567\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −4.85410 | −0.226570 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −18.7426 | −0.872932 | −0.436466 | − | 0.899721i | \(-0.643770\pi\) | ||||
−0.436466 | + | 0.899721i | \(0.643770\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −10.8541 | −0.504433 | −0.252216 | − | 0.967671i | \(-0.581159\pi\) | ||||
−0.252216 | + | 0.967671i | \(0.581159\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −21.3820 | −0.991565 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 38.8328 | 1.79697 | 0.898484 | − | 0.439006i | \(-0.144669\pi\) | ||||
0.898484 | + | 0.439006i | \(0.144669\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 12.5066 | 0.577500 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 9.00000 | 0.414698 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −10.5279 | −0.484072 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 1.76393 | 0.0807649 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 26.0902 | 1.19209 | 0.596045 | − | 0.802951i | \(-0.296738\pi\) | ||||
0.596045 | + | 0.802951i | \(0.296738\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 12.0902 | 0.551264 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 11.0000 | 0.500517 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 6.70820 | 0.304604 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −36.7426 | −1.66497 | −0.832484 | − | 0.554049i | \(-0.813082\pi\) | ||||
−0.832484 | + | 0.554049i | \(0.813082\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −1.56231 | −0.0706499 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −26.5066 | −1.19623 | −0.598113 | − | 0.801412i | \(-0.704082\pi\) | ||||
−0.598113 | + | 0.801412i | \(0.704082\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −41.8328 | −1.88406 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 5.00000 | 0.224733 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −45.9230 | −2.05993 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −12.4164 | −0.555835 | −0.277917 | − | 0.960605i | \(-0.589644\pi\) | ||||
−0.277917 | + | 0.960605i | \(0.589644\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 22.0344 | 0.984426 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 20.7984 | 0.927354 | 0.463677 | − | 0.886004i | \(-0.346530\pi\) | ||||
0.463677 | + | 0.886004i | \(0.346530\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −21.7082 | −0.966002 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −9.88854 | −0.439166 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −29.9230 | −1.32631 | −0.663157 | − | 0.748481i | \(-0.730784\pi\) | ||||
−0.663157 | + | 0.748481i | \(0.730784\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −27.0344 | −1.19593 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 8.09017 | 0.357190 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −2.76393 | −0.121793 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 9.27051 | 0.407717 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 14.6180 | 0.641660 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −14.5066 | −0.635545 | −0.317772 | − | 0.948167i | \(-0.602935\pi\) | ||||
−0.317772 | + | 0.948167i | \(0.602935\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −31.9443 | −1.39683 | −0.698413 | − | 0.715695i | \(-0.746110\pi\) | ||||
−0.698413 | + | 0.715695i | \(0.746110\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 46.4164 | 2.02193 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −17.3262 | −0.753315 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 1.00000 | 0.0433963 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 5.45085 | 0.236103 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −27.0344 | −1.16880 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 9.47214 | 0.408753 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 32.0344 | 1.37982 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 14.1246 | 0.607264 | 0.303632 | − | 0.952789i | \(-0.401801\pi\) | ||||
0.303632 | + | 0.952789i | \(0.401801\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −11.2705 | −0.483664 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −24.2705 | −1.03963 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −32.5623 | −1.39226 | −0.696132 | − | 0.717914i | \(-0.745097\pi\) | ||||
−0.696132 | + | 0.717914i | \(0.745097\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −9.85410 | −0.420563 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 69.7214 | 2.97023 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 13.8541 | 0.589136 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −15.3262 | −0.650563 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 1.41641 | 0.0600151 | 0.0300076 | − | 0.999550i | \(-0.490447\pi\) | ||||
0.0300076 | + | 0.999550i | \(0.490447\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 8.30495 | 0.351262 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −10.8541 | −0.458261 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −28.5967 | −1.20521 | −0.602605 | − | 0.798040i | \(-0.705870\pi\) | ||||
−0.602605 | + | 0.798040i | \(0.705870\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −20.1246 | −0.846649 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 4.61803 | 0.193939 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 26.5066 | 1.11121 | 0.555607 | − | 0.831445i | \(-0.312486\pi\) | ||||
0.555607 | + | 0.831445i | \(0.312486\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −28.4164 | −1.18919 | −0.594595 | − | 0.804025i | \(-0.702688\pi\) | ||||
−0.594595 | + | 0.804025i | \(0.702688\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 10.4164 | 0.435152 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 21.4721 | 0.893897 | 0.446948 | − | 0.894560i | \(-0.352511\pi\) | ||||
0.446948 | + | 0.894560i | \(0.352511\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 8.00000 | 0.332469 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −2.85410 | −0.118408 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 3.94427 | 0.163355 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −3.94427 | −0.163076 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −29.3607 | −1.21184 | −0.605922 | − | 0.795524i | \(-0.707196\pi\) | ||||
−0.605922 | + | 0.795524i | \(0.707196\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −77.3607 | −3.18759 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 10.6525 | 0.438184 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 4.90983 | 0.201623 | 0.100811 | − | 0.994906i | \(-0.467856\pi\) | ||||
0.100811 | + | 0.994906i | \(0.467856\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −50.1246 | −2.05491 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −3.56231 | −0.145795 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 28.6525 | 1.17071 | 0.585354 | − | 0.810778i | \(-0.300955\pi\) | ||||
0.585354 | + | 0.810778i | \(0.300955\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 25.6180 | 1.04498 | 0.522491 | − | 0.852645i | \(-0.325003\pi\) | ||||
0.522491 | + | 0.852645i | \(0.325003\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 2.70820 | 0.110287 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −13.4164 | −0.545455 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −17.6525 | −0.716492 | −0.358246 | − | 0.933627i | \(-0.616625\pi\) | ||||
−0.358246 | + | 0.933627i | \(0.616625\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 39.7984 | 1.61271 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −7.31308 | −0.295856 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −7.34752 | −0.296764 | −0.148382 | − | 0.988930i | \(-0.547406\pi\) | ||||
−0.148382 | + | 0.988930i | \(0.547406\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −6.90983 | −0.278631 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 28.8541 | 1.16162 | 0.580811 | − | 0.814038i | \(-0.302735\pi\) | ||||
0.580811 | + | 0.814038i | \(0.302735\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 28.1246 | 1.13042 | 0.565212 | − | 0.824946i | \(-0.308794\pi\) | ||||
0.565212 | + | 0.824946i | \(0.308794\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 2.38197 | 0.0955850 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 49.8673 | 1.99789 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −25.0000 | −1.00000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 18.0902 | 0.722452 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 33.2705 | 1.32658 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 13.5836 | 0.540754 | 0.270377 | − | 0.962754i | \(-0.412852\pi\) | ||||
0.270377 | + | 0.962754i | \(0.412852\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 8.85410 | 0.351919 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 4.34752 | 0.172526 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −25.2705 | −1.00125 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −9.94427 | −0.393389 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −10.0557 | −0.397177 | −0.198589 | − | 0.980083i | \(-0.563636\pi\) | ||||
−0.198589 | + | 0.980083i | \(0.563636\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 13.1459 | 0.518424 | 0.259212 | − | 0.965821i | \(-0.416537\pi\) | ||||
0.259212 | + | 0.965821i | \(0.416537\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −10.5279 | −0.414534 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −27.0557 | −1.06367 | −0.531835 | − | 0.846848i | \(-0.678497\pi\) | ||||
−0.531835 | + | 0.846848i | \(0.678497\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 2.23607 | 0.0877733 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −44.1591 | −1.73073 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 28.9098 | 1.13133 | 0.565665 | − | 0.824635i | \(-0.308620\pi\) | ||||
0.565665 | + | 0.824635i | \(0.308620\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −23.8197 | −0.930711 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −5.85410 | −0.228390 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 4.85410 | 0.189089 | 0.0945445 | − | 0.995521i | \(-0.469861\pi\) | ||||
0.0945445 | + | 0.995521i | \(0.469861\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −11.7426 | −0.456736 | −0.228368 | − | 0.973575i | \(-0.573339\pi\) | ||||
−0.228368 | + | 0.973575i | \(0.573339\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 8.56231 | 0.332532 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 83.5410 | 3.23958 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 20.5279 | 0.794842 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 18.4721 | 0.714174 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −22.0344 | −0.850630 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 0.472136 | 0.0181995 | 0.00909975 | − | 0.999959i | \(-0.497103\pi\) | ||||
0.00909975 | + | 0.999959i | \(0.497103\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −50.1803 | −1.92859 | −0.964294 | − | 0.264836i | \(-0.914682\pi\) | ||||
−0.964294 | + | 0.264836i | \(0.914682\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 13.8541 | 0.531672 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 28.8541 | 1.10569 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −39.0000 | −1.49229 | −0.746147 | − | 0.665782i | \(-0.768098\pi\) | ||||
−0.746147 | + | 0.665782i | \(0.768098\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 17.3607 | 0.663317 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −15.8541 | −0.604872 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −3.11146 | −0.118537 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 5.12461 | 0.194949 | 0.0974747 | − | 0.995238i | \(-0.468923\pi\) | ||||
0.0974747 | + | 0.995238i | \(0.468923\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 10.3262 | 0.392261 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −36.3050 | −1.37713 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 15.0000 | 0.568166 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −21.7082 | −0.821080 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 42.7984 | 1.61647 | 0.808236 | − | 0.588859i | \(-0.200422\pi\) | ||||
0.808236 | + | 0.588859i | \(0.200422\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −55.4508 | −2.09137 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 9.27051 | 0.349148 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −44.8328 | −1.68611 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −14.2918 | −0.536740 | −0.268370 | − | 0.963316i | \(-0.586485\pi\) | ||||
−0.268370 | + | 0.963316i | \(0.586485\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 3.00000 | 0.112509 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −22.7771 | −0.853009 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −8.81966 | −0.329837 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −7.47214 | −0.279052 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −12.3820 | −0.461769 | −0.230885 | − | 0.972981i | \(-0.574162\pi\) | ||||
−0.230885 | + | 0.972981i | \(0.574162\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −5.70820 | −0.212585 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 3.41641 | 0.127058 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −26.0000 | −0.964287 | −0.482143 | − | 0.876092i | \(-0.660142\pi\) | ||||
−0.482143 | + | 0.876092i | \(0.660142\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 22.8541 | 0.845289 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 29.4721 | 1.08858 | 0.544289 | − | 0.838898i | \(-0.316799\pi\) | ||||
0.544289 | + | 0.838898i | \(0.316799\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 32.0344 | 1.18161 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 6.05573 | 0.223066 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 39.1033 | 1.43844 | 0.719220 | − | 0.694783i | \(-0.244500\pi\) | ||||
0.719220 | + | 0.694783i | \(0.244500\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −14.2705 | −0.524240 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 22.3820 | 0.821115 | 0.410557 | − | 0.911835i | \(-0.365334\pi\) | ||||
0.410557 | + | 0.911835i | \(0.365334\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 17.6869 | 0.647999 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −0.618034 | −0.0226127 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −55.8328 | −2.04009 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 45.1246 | 1.64662 | 0.823310 | − | 0.567592i | \(-0.192125\pi\) | ||||
0.823310 | + | 0.567592i | \(0.192125\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 7.18034 | 0.261666 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 39.2705 | 1.42920 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −43.6180 | −1.58532 | −0.792662 | − | 0.609661i | \(-0.791306\pi\) | ||||
−0.792662 | + | 0.609661i | \(0.791306\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 5.32624 | 0.193330 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 17.2918 | 0.626827 | 0.313414 | − | 0.949617i | \(-0.398527\pi\) | ||||
0.313414 | + | 0.949617i | \(0.398527\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −50.1246 | −1.81463 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −10.8541 | −0.392431 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −1.76393 | −0.0636919 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −35.9787 | −1.29743 | −0.648713 | − | 0.761033i | \(-0.724692\pi\) | ||||
−0.648713 | + | 0.761033i | \(0.724692\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 7.41641 | 0.267095 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −2.65248 | −0.0954029 | −0.0477015 | − | 0.998862i | \(-0.515190\pi\) | ||||
−0.0477015 | + | 0.998862i | \(0.515190\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −31.6525 | −1.13553 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −25.0000 | −0.895718 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −22.2361 | −0.795669 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 8.61803 | 0.307983 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 20.1246 | 0.718278 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 17.7082 | 0.631229 | 0.315615 | − | 0.948887i | \(-0.397789\pi\) | ||||
0.315615 | + | 0.948887i | \(0.397789\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0.618034 | 0.0220026 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −41.5623 | −1.47779 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 17.3820 | 0.617252 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 3.94427 | 0.139889 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 3.23607 | 0.114627 | 0.0573137 | − | 0.998356i | \(-0.481746\pi\) | ||||
0.0573137 | + | 0.998356i | \(0.481746\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −20.1246 | −0.711958 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 10.7984 | 0.381542 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −13.0902 | −0.461942 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 24.5967 | 0.866921 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −2.52786 | −0.0889850 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 23.3262 | 0.820107 | 0.410053 | − | 0.912062i | \(-0.365510\pi\) | ||||
0.410053 | + | 0.912062i | \(0.365510\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 16.6525 | 0.584748 | 0.292374 | − | 0.956304i | \(-0.405555\pi\) | ||||
0.292374 | + | 0.956304i | \(0.405555\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 12.2361 | 0.429138 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −3.49342 | −0.122369 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −38.0902 | −1.33261 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −8.14590 | −0.284641 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 23.9230 | 0.834918 | 0.417459 | − | 0.908696i | \(-0.362921\pi\) | ||||
0.417459 | + | 0.908696i | \(0.362921\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −24.7082 | −0.861274 | −0.430637 | − | 0.902525i | \(-0.641711\pi\) | ||||
−0.430637 | + | 0.902525i | \(0.641711\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 25.1803 | 0.875606 | 0.437803 | − | 0.899071i | \(-0.355757\pi\) | ||||
0.437803 | + | 0.899071i | \(0.355757\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 14.6869 | 0.510098 | 0.255049 | − | 0.966928i | \(-0.417908\pi\) | ||||
0.255049 | + | 0.966928i | \(0.417908\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 3.47214 | 0.120447 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −69.5410 | −2.40945 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 49.2705 | 1.70508 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −9.56231 | −0.330522 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 47.1803 | 1.62885 | 0.814423 | − | 0.580271i | \(-0.197054\pi\) | ||||
0.814423 | + | 0.580271i | \(0.197054\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 45.2705 | 1.56105 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −3.70820 | −0.127717 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −22.1115 | −0.760657 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −27.7082 | −0.952065 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −10.2705 | −0.352483 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −16.3262 | −0.559656 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −33.0344 | −1.13108 | −0.565539 | − | 0.824722i | \(-0.691332\pi\) | ||||
−0.565539 | + | 0.824722i | \(0.691332\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 18.0902 | 0.618671 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 42.7771 | 1.46124 | 0.730619 | − | 0.682786i | \(-0.239232\pi\) | ||||
0.730619 | + | 0.682786i | \(0.239232\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −24.4721 | −0.834979 | −0.417489 | − | 0.908682i | \(-0.637090\pi\) | ||||
−0.417489 | + | 0.908682i | \(0.637090\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −14.2705 | −0.486338 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −43.7984 | −1.49091 | −0.745457 | − | 0.666554i | \(-0.767769\pi\) | ||||
−0.745457 | + | 0.666554i | \(0.767769\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 32.6869 | 1.11139 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 6.56231 | 0.222868 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 6.70820 | 0.227560 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −4.77709 | −0.161865 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 3.00000 | 0.101535 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −51.6312 | −1.74545 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −51.8885 | −1.75215 | −0.876076 | − | 0.482173i | \(-0.839848\pi\) | ||||
−0.876076 | + | 0.482173i | \(0.839848\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 21.6180 | 0.729158 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −2.29180 | −0.0772126 | −0.0386063 | − | 0.999254i | \(-0.512292\pi\) | ||||
−0.0386063 | + | 0.999254i | \(0.512292\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −3.41641 | −0.114971 | −0.0574856 | − | 0.998346i | \(-0.518308\pi\) | ||||
−0.0574856 | + | 0.998346i | \(0.518308\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 2.23607 | 0.0751646 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 31.4721 | 1.05673 | 0.528365 | − | 0.849017i | \(-0.322805\pi\) | ||||
0.528365 | + | 0.849017i | \(0.322805\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 8.97871 | 0.301136 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 2.23607 | 0.0749111 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 33.5410 | 1.12241 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 21.1803 | 0.707981 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −4.20163 | −0.140288 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −82.4083 | −2.74847 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −8.56231 | −0.285252 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −21.7426 | −0.723550 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −25.2016 | −0.837730 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 2.05573 | 0.0682593 | 0.0341297 | − | 0.999417i | \(-0.489134\pi\) | ||||
0.0341297 | + | 0.999417i | \(0.489134\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −9.70820 | −0.322001 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −42.1033 | −1.39495 | −0.697473 | − | 0.716611i | \(-0.745692\pi\) | ||||
−0.697473 | + | 0.716611i | \(0.745692\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −1.38197 | −0.0457364 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −22.0344 | −0.728436 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −49.1935 | −1.62451 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −35.5967 | −1.17423 | −0.587114 | − | 0.809504i | \(-0.699736\pi\) | ||||
−0.587114 | + | 0.809504i | \(0.699736\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −9.88854 | −0.325839 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 17.5410 | 0.577370 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −1.23607 | −0.0405978 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −35.2918 | −1.15789 | −0.578943 | − | 0.815368i | \(-0.696535\pi\) | ||||
−0.578943 | + | 0.815368i | \(0.696535\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 115.902 | 3.79852 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 28.4508 | 0.931439 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −24.2705 | −0.793731 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −37.7214 | −1.23230 | −0.616152 | − | 0.787628i | \(-0.711309\pi\) | ||||
−0.616152 | + | 0.787628i | \(0.711309\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 3.79837 | 0.123955 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −22.3050 | −0.727121 | −0.363560 | − | 0.931571i | \(-0.618439\pi\) | ||||
−0.363560 | + | 0.931571i | \(0.618439\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −7.36068 | −0.239697 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 10.3262 | 0.335913 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 4.03444 | 0.131102 | 0.0655509 | − | 0.997849i | \(-0.479120\pi\) | ||||
0.0655509 | + | 0.997849i | \(0.479120\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 10.3262 | 0.335204 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −6.81966 | −0.221143 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −12.9443 | −0.419306 | −0.209653 | − | 0.977776i | \(-0.567233\pi\) | ||||
−0.209653 | + | 0.977776i | \(0.567233\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 23.2918 | 0.753705 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 19.2705 | 0.622927 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 35.8541 | 1.15779 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 60.4377 | 1.94960 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −12.0902 | −0.389600 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 17.8885 | 0.575853 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 18.2705 | 0.587540 | 0.293770 | − | 0.955876i | \(-0.405090\pi\) | ||||
0.293770 | + | 0.955876i | \(0.405090\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −39.2705 | −1.26155 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −22.2016 | −0.712484 | −0.356242 | − | 0.934394i | \(-0.615942\pi\) | ||||
−0.356242 | + | 0.934394i | \(0.615942\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −74.9787 | −2.40371 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 14.8885 | 0.476327 | 0.238163 | − | 0.971225i | \(-0.423455\pi\) | ||||
0.238163 | + | 0.971225i | \(0.423455\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 24.1459 | 0.771706 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −10.8541 | −0.346545 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 58.5967 | 1.86895 | 0.934473 | − | 0.356034i | \(-0.115871\pi\) | ||||
0.934473 | + | 0.356034i | \(0.115871\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 23.8197 | 0.758957 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 19.1459 | 0.609421 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −11.2148 | −0.356609 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 18.7426 | 0.595380 | 0.297690 | − | 0.954663i | \(-0.403784\pi\) | ||||
0.297690 | + | 0.954663i | \(0.403784\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −29.1246 | −0.924242 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −7.96556 | −0.252525 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1.78522 | 0.0565384 | 0.0282692 | − | 0.999600i | \(-0.491000\pi\) | ||||
0.0282692 | + | 0.999600i | \(0.491000\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −6.85410 | −0.216854 |
(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 | 2832.2.a.o.1.2 | 2 | ||
3.2 | odd | 2 | 8496.2.a.bb.1.1 | 2 | |||
4.3 | odd | 2 | 177.2.a.b.1.1 | ✓ | 2 | ||
12.11 | even | 2 | 531.2.a.b.1.2 | 2 | |||
20.19 | odd | 2 | 4425.2.a.t.1.2 | 2 | |||
28.27 | even | 2 | 8673.2.a.k.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
177.2.a.b.1.1 | ✓ | 2 | 4.3 | odd | 2 | ||
531.2.a.b.1.2 | 2 | 12.11 | even | 2 | |||
2832.2.a.o.1.2 | 2 | 1.1 | even | 1 | trivial | ||
4425.2.a.t.1.2 | 2 | 20.19 | odd | 2 | |||
8496.2.a.bb.1.1 | 2 | 3.2 | odd | 2 | |||
8673.2.a.k.1.1 | 2 | 28.27 | even | 2 |