Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2004,2,Mod(1,2004)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2004, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2004.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2004 = 2^{2} \cdot 3 \cdot 167 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2004.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: | \(16.0020205651\) |
Analytic rank: | \(0\) |
Dimension: | \(9\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{9} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{9} - 29x^{7} - 7x^{6} + 266x^{5} + 69x^{4} - 901x^{3} - 199x^{2} + 875x + 391 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(1.61974\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2004.1 |
$q$-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 | ||||||||
\(5\) | −0.619742 | −0.277157 | −0.138579 | − | 0.990351i | \(-0.544253\pi\) | ||||
−0.138579 | + | 0.990351i | \(0.544253\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.05844 | 0.400051 | 0.200026 | − | 0.979791i | \(-0.435897\pi\) | ||||
0.200026 | + | 0.979791i | \(0.435897\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.94492 | −0.887927 | −0.443963 | − | 0.896045i | \(-0.646428\pi\) | ||||
−0.443963 | + | 0.896045i | \(0.646428\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −6.55099 | −1.81692 | −0.908459 | − | 0.417975i | \(-0.862740\pi\) | ||||
−0.908459 | + | 0.417975i | \(0.862740\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −0.619742 | −0.160017 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 6.19312 | 1.50205 | 0.751026 | − | 0.660272i | \(-0.229559\pi\) | ||||
0.751026 | + | 0.660272i | \(0.229559\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 7.10438 | 1.62986 | 0.814928 | − | 0.579562i | \(-0.196776\pi\) | ||||
0.814928 | + | 0.579562i | \(0.196776\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.05844 | 0.230970 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 4.16491 | 0.868444 | 0.434222 | − | 0.900806i | \(-0.357023\pi\) | ||||
0.434222 | + | 0.900806i | \(0.357023\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.61592 | −0.923184 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −0.996993 | −0.185137 | −0.0925685 | − | 0.995706i | \(-0.529508\pi\) | ||||
−0.0925685 | + | 0.995706i | \(0.529508\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 7.31224 | 1.31332 | 0.656659 | − | 0.754188i | \(-0.271969\pi\) | ||||
0.656659 | + | 0.754188i | \(0.271969\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −2.94492 | −0.512645 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −0.655958 | −0.110877 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 5.89613 | 0.969317 | 0.484659 | − | 0.874703i | \(-0.338944\pi\) | ||||
0.484659 | + | 0.874703i | \(0.338944\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −6.55099 | −1.04900 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 9.96986 | 1.55703 | 0.778515 | − | 0.627626i | \(-0.215973\pi\) | ||||
0.778515 | + | 0.627626i | \(0.215973\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4.82896 | 0.736409 | 0.368205 | − | 0.929745i | \(-0.379973\pi\) | ||||
0.368205 | + | 0.929745i | \(0.379973\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −0.619742 | −0.0923857 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 6.61501 | 0.964898 | 0.482449 | − | 0.875924i | \(-0.339747\pi\) | ||||
0.482449 | + | 0.875924i | \(0.339747\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −5.87971 | −0.839959 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 6.19312 | 0.867211 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 10.9128 | 1.49899 | 0.749497 | − | 0.662007i | \(-0.230295\pi\) | ||||
0.749497 | + | 0.662007i | \(0.230295\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.82509 | 0.246095 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 7.10438 | 0.940998 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −9.89351 | −1.28803 | −0.644013 | − | 0.765015i | \(-0.722732\pi\) | ||||
−0.644013 | + | 0.765015i | \(0.722732\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 10.2882 | 1.31727 | 0.658633 | − | 0.752464i | \(-0.271135\pi\) | ||||
0.658633 | + | 0.752464i | \(0.271135\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 1.05844 | 0.133350 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 4.05992 | 0.503572 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −10.2505 | −1.25230 | −0.626148 | − | 0.779705i | \(-0.715369\pi\) | ||||
−0.626148 | + | 0.779705i | \(0.715369\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 4.16491 | 0.501396 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 11.7281 | 1.39187 | 0.695936 | − | 0.718103i | \(-0.254990\pi\) | ||||
0.695936 | + | 0.718103i | \(0.254990\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −12.2938 | −1.43888 | −0.719442 | − | 0.694552i | \(-0.755602\pi\) | ||||
−0.719442 | + | 0.694552i | \(0.755602\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −4.61592 | −0.533000 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −3.11701 | −0.355216 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −3.71458 | −0.417923 | −0.208962 | − | 0.977924i | \(-0.567008\pi\) | ||||
−0.208962 | + | 0.977924i | \(0.567008\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −5.90125 | −0.647747 | −0.323873 | − | 0.946100i | \(-0.604985\pi\) | ||||
−0.323873 | + | 0.946100i | \(0.604985\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −3.83814 | −0.416305 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −0.996993 | −0.106889 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 9.88073 | 1.04735 | 0.523677 | − | 0.851917i | \(-0.324560\pi\) | ||||
0.523677 | + | 0.851917i | \(0.324560\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −6.93380 | −0.726860 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 7.31224 | 0.758244 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −4.40288 | −0.451726 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −8.96090 | −0.909841 | −0.454921 | − | 0.890532i | \(-0.650332\pi\) | ||||
−0.454921 | + | 0.890532i | \(0.650332\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −2.94492 | −0.295976 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −4.91541 | −0.489101 | −0.244551 | − | 0.969637i | \(-0.578640\pi\) | ||||
−0.244551 | + | 0.969637i | \(0.578640\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 4.72990 | 0.466051 | 0.233026 | − | 0.972471i | \(-0.425137\pi\) | ||||
0.233026 | + | 0.972471i | \(0.425137\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −0.655958 | −0.0640149 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 2.10628 | 0.203622 | 0.101811 | − | 0.994804i | \(-0.467536\pi\) | ||||
0.101811 | + | 0.994804i | \(0.467536\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −6.73056 | −0.644671 | −0.322336 | − | 0.946625i | \(-0.604468\pi\) | ||||
−0.322336 | + | 0.946625i | \(0.604468\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 5.89613 | 0.559636 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 4.21493 | 0.396507 | 0.198254 | − | 0.980151i | \(-0.436473\pi\) | ||||
0.198254 | + | 0.980151i | \(0.436473\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −2.58117 | −0.240695 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −6.55099 | −0.605639 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 6.55503 | 0.600898 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −2.32744 | −0.211586 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 9.96986 | 0.898952 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 5.95939 | 0.533024 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 11.2289 | 0.996401 | 0.498201 | − | 0.867062i | \(-0.333994\pi\) | ||||
0.498201 | + | 0.867062i | \(0.333994\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 4.82896 | 0.425166 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −4.86472 | −0.425032 | −0.212516 | − | 0.977158i | \(-0.568166\pi\) | ||||
−0.212516 | + | 0.977158i | \(0.568166\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 7.51953 | 0.652026 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −0.619742 | −0.0533389 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −1.48097 | −0.126528 | −0.0632640 | − | 0.997997i | \(-0.520151\pi\) | ||||
−0.0632640 | + | 0.997997i | \(0.520151\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −11.8564 | −1.00565 | −0.502823 | − | 0.864389i | \(-0.667705\pi\) | ||||
−0.502823 | + | 0.864389i | \(0.667705\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 6.61501 | 0.557084 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 19.2921 | 1.61329 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0.617879 | 0.0513120 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −5.87971 | −0.484951 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 1.25014 | 0.102415 | 0.0512075 | − | 0.998688i | \(-0.483693\pi\) | ||||
0.0512075 | + | 0.998688i | \(0.483693\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 8.74306 | 0.711500 | 0.355750 | − | 0.934581i | \(-0.384225\pi\) | ||||
0.355750 | + | 0.934581i | \(0.384225\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 6.19312 | 0.500684 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −4.53170 | −0.363995 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1.28243 | 0.102349 | 0.0511747 | − | 0.998690i | \(-0.483703\pi\) | ||||
0.0511747 | + | 0.998690i | \(0.483703\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 10.9128 | 0.865445 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 4.40829 | 0.347422 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 10.2657 | 0.804074 | 0.402037 | − | 0.915623i | \(-0.368302\pi\) | ||||
0.402037 | + | 0.915623i | \(0.368302\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 1.82509 | 0.142083 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 1.00000 | 0.0773823 | ||||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 29.9154 | 2.30119 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 7.10438 | 0.543285 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −1.26599 | −0.0962515 | −0.0481257 | − | 0.998841i | \(-0.515325\pi\) | ||||
−0.0481257 | + | 0.998841i | \(0.515325\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −4.88566 | −0.369321 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −9.89351 | −0.743642 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −7.48456 | −0.559422 | −0.279711 | − | 0.960084i | \(-0.590239\pi\) | ||||
−0.279711 | + | 0.960084i | \(0.590239\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −4.86471 | −0.361591 | −0.180796 | − | 0.983521i | \(-0.557867\pi\) | ||||
−0.180796 | + | 0.983521i | \(0.557867\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 10.2882 | 0.760524 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −3.65408 | −0.268653 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −18.2383 | −1.33371 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 1.05844 | 0.0769899 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 8.37459 | 0.605964 | 0.302982 | − | 0.952996i | \(-0.402018\pi\) | ||||
0.302982 | + | 0.952996i | \(0.402018\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −6.53375 | −0.470309 | −0.235155 | − | 0.971958i | \(-0.575560\pi\) | ||||
−0.235155 | + | 0.971958i | \(0.575560\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 4.05992 | 0.290737 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 2.01768 | 0.143754 | 0.0718768 | − | 0.997414i | \(-0.477101\pi\) | ||||
0.0718768 | + | 0.997414i | \(0.477101\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −18.2648 | −1.29476 | −0.647379 | − | 0.762168i | \(-0.724135\pi\) | ||||
−0.647379 | + | 0.762168i | \(0.724135\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −10.2505 | −0.723013 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −1.05525 | −0.0740643 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −6.17874 | −0.431542 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 4.16491 | 0.289481 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −20.9218 | −1.44719 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 8.93507 | 0.615116 | 0.307558 | − | 0.951529i | \(-0.400488\pi\) | ||||
0.307558 | + | 0.951529i | \(0.400488\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 11.7281 | 0.803598 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −2.99271 | −0.204101 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 7.73954 | 0.525394 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −12.2938 | −0.830740 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −40.5711 | −2.72911 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −17.7607 | −1.18934 | −0.594671 | − | 0.803969i | \(-0.702718\pi\) | ||||
−0.594671 | + | 0.803969i | \(0.702718\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −4.61592 | −0.307728 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −11.3559 | −0.753716 | −0.376858 | − | 0.926271i | \(-0.622996\pi\) | ||||
−0.376858 | + | 0.926271i | \(0.622996\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 14.3141 | 0.945900 | 0.472950 | − | 0.881089i | \(-0.343189\pi\) | ||||
0.472950 | + | 0.881089i | \(0.343189\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −3.11701 | −0.205084 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 20.6800 | 1.35479 | 0.677395 | − | 0.735620i | \(-0.263109\pi\) | ||||
0.677395 | + | 0.735620i | \(0.263109\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −4.09960 | −0.267428 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −3.71458 | −0.241288 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 9.67387 | 0.625750 | 0.312875 | − | 0.949794i | \(-0.398708\pi\) | ||||
0.312875 | + | 0.949794i | \(0.398708\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 7.89334 | 0.508455 | 0.254227 | − | 0.967144i | \(-0.418179\pi\) | ||||
0.254227 | + | 0.967144i | \(0.418179\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 3.64391 | 0.232801 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −46.5407 | −2.96131 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −5.90125 | −0.373977 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −30.8625 | −1.94802 | −0.974011 | − | 0.226500i | \(-0.927272\pi\) | ||||
−0.974011 | + | 0.226500i | \(0.927272\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −12.2653 | −0.771115 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −3.83814 | −0.240354 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −16.5611 | −1.03305 | −0.516525 | − | 0.856272i | \(-0.672775\pi\) | ||||
−0.516525 | + | 0.856272i | \(0.672775\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 6.24067 | 0.387777 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −0.996993 | −0.0617123 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −2.43522 | −0.150162 | −0.0750812 | − | 0.997177i | \(-0.523922\pi\) | ||||
−0.0750812 | + | 0.997177i | \(0.523922\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −6.76315 | −0.415457 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 9.88073 | 0.604691 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 32.6765 | 1.99232 | 0.996162 | − | 0.0875285i | \(-0.0278969\pi\) | ||||
0.996162 | + | 0.0875285i | \(0.0278969\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −0.00431859 | −0.000262335 0 | −0.000131168 | − | 1.00000i | \(-0.500042\pi\) | ||||
−0.000131168 | 1.00000i | \(0.500042\pi\) | ||||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −6.93380 | −0.419653 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 13.5935 | 0.819720 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −25.8726 | −1.55453 | −0.777266 | − | 0.629172i | \(-0.783394\pi\) | ||||
−0.777266 | + | 0.629172i | \(0.783394\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 7.31224 | 0.437772 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 23.4091 | 1.39647 | 0.698236 | − | 0.715868i | \(-0.253969\pi\) | ||||
0.698236 | + | 0.715868i | \(0.253969\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −26.8435 | −1.59568 | −0.797842 | − | 0.602867i | \(-0.794025\pi\) | ||||
−0.797842 | + | 0.602867i | \(0.794025\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −4.40288 | −0.260804 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 10.5525 | 0.622892 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 21.3548 | 1.25616 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −8.96090 | −0.525297 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 23.7852 | 1.38954 | 0.694772 | − | 0.719230i | \(-0.255505\pi\) | ||||
0.694772 | + | 0.719230i | \(0.255505\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 6.13143 | 0.356985 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −2.94492 | −0.170882 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −27.2843 | −1.57789 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 5.11115 | 0.294602 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −4.91541 | −0.282383 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −6.37602 | −0.365090 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −10.0558 | −0.573914 | −0.286957 | − | 0.957943i | \(-0.592644\pi\) | ||||
−0.286957 | + | 0.957943i | \(0.592644\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 4.72990 | 0.269075 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 18.7831 | 1.06509 | 0.532547 | − | 0.846401i | \(-0.321235\pi\) | ||||
0.532547 | + | 0.846401i | \(0.321235\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 14.5269 | 0.821110 | 0.410555 | − | 0.911836i | \(-0.365335\pi\) | ||||
0.410555 | + | 0.911836i | \(0.365335\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −0.655958 | −0.0369590 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −8.74455 | −0.491143 | −0.245571 | − | 0.969379i | \(-0.578976\pi\) | ||||
−0.245571 | + | 0.969379i | \(0.578976\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 2.93606 | 0.164388 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 2.10628 | 0.117561 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 43.9983 | 2.44813 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 30.2388 | 1.67735 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −6.73056 | −0.372201 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 7.00156 | 0.386009 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −4.49622 | −0.247135 | −0.123567 | − | 0.992336i | \(-0.539433\pi\) | ||||
−0.123567 | + | 0.992336i | \(0.539433\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 5.89613 | 0.323106 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 6.35265 | 0.347082 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 11.1496 | 0.607359 | 0.303680 | − | 0.952774i | \(-0.401785\pi\) | ||||
0.303680 | + | 0.952774i | \(0.401785\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 4.21493 | 0.228923 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −21.5340 | −1.16613 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −13.6324 | −0.736078 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −2.58117 | −0.138966 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 31.7784 | 1.70595 | 0.852977 | − | 0.521949i | \(-0.174795\pi\) | ||||
0.852977 | + | 0.521949i | \(0.174795\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −11.4428 | −0.612521 | −0.306261 | − | 0.951948i | \(-0.599078\pi\) | ||||
−0.306261 | + | 0.951948i | \(0.599078\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −6.55099 | −0.349666 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 5.68738 | 0.302709 | 0.151354 | − | 0.988480i | \(-0.451637\pi\) | ||||
0.151354 | + | 0.988480i | \(0.451637\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −7.26842 | −0.385767 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 6.55503 | 0.346929 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −36.8239 | −1.94349 | −0.971745 | − | 0.236031i | \(-0.924153\pi\) | ||||
−0.971745 | + | 0.236031i | \(0.924153\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 31.4722 | 1.65643 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −2.32744 | −0.122159 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 7.61901 | 0.398797 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −22.4128 | −1.16994 | −0.584968 | − | 0.811056i | \(-0.698893\pi\) | ||||
−0.584968 | + | 0.811056i | \(0.698893\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 9.96986 | 0.519010 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 11.5506 | 0.599675 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −20.0874 | −1.04009 | −0.520044 | − | 0.854140i | \(-0.674084\pi\) | ||||
−0.520044 | + | 0.854140i | \(0.674084\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 5.95939 | 0.307742 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 6.53129 | 0.336378 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −13.4368 | −0.690203 | −0.345102 | − | 0.938565i | \(-0.612156\pi\) | ||||
−0.345102 | + | 0.938565i | \(0.612156\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 11.2289 | 0.575273 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −21.1688 | −1.08168 | −0.540838 | − | 0.841127i | \(-0.681893\pi\) | ||||
−0.540838 | + | 0.841127i | \(0.681893\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1.93174 | 0.0984508 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 4.82896 | 0.245470 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 13.8032 | 0.699849 | 0.349924 | − | 0.936778i | \(-0.386207\pi\) | ||||
0.349924 | + | 0.936778i | \(0.386207\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 25.7938 | 1.30445 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −4.86472 | −0.245393 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 2.30208 | 0.115830 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 23.8793 | 1.19847 | 0.599234 | − | 0.800574i | \(-0.295472\pi\) | ||||
0.599234 | + | 0.800574i | \(0.295472\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 7.51953 | 0.376447 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −31.6924 | −1.58265 | −0.791323 | − | 0.611399i | \(-0.790607\pi\) | ||||
−0.791323 | + | 0.611399i | \(0.790607\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −47.9024 | −2.38619 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −0.619742 | −0.0307952 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −17.3636 | −0.860683 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −10.5695 | −0.522626 | −0.261313 | − | 0.965254i | \(-0.584156\pi\) | ||||
−0.261313 | + | 0.965254i | \(0.584156\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −1.48097 | −0.0730510 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −10.4717 | −0.515276 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 3.65726 | 0.179528 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −11.8564 | −0.580610 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −6.09660 | −0.297839 | −0.148919 | − | 0.988849i | \(-0.547579\pi\) | ||||
−0.148919 | + | 0.988849i | \(0.547579\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −8.05451 | −0.392553 | −0.196276 | − | 0.980549i | \(-0.562885\pi\) | ||||
−0.196276 | + | 0.980549i | \(0.562885\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 6.61501 | 0.321633 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −28.5870 | −1.38667 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 10.8894 | 0.526974 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 19.2921 | 0.931433 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 7.89755 | 0.380412 | 0.190206 | − | 0.981744i | \(-0.439084\pi\) | ||||
0.190206 | + | 0.981744i | \(0.439084\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −20.1848 | −0.970021 | −0.485010 | − | 0.874508i | \(-0.661184\pi\) | ||||
−0.485010 | + | 0.874508i | \(0.661184\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0.617879 | 0.0296250 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 29.5891 | 1.41544 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −30.9441 | −1.47688 | −0.738442 | − | 0.674317i | \(-0.764438\pi\) | ||||
−0.738442 | + | 0.674317i | \(0.764438\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −5.87971 | −0.279986 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −33.5088 | −1.59205 | −0.796025 | − | 0.605264i | \(-0.793067\pi\) | ||||
−0.796025 | + | 0.605264i | \(0.793067\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −6.12350 | −0.290282 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 1.25014 | 0.0591294 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −21.8767 | −1.03243 | −0.516213 | − | 0.856460i | \(-0.672659\pi\) | ||||
−0.516213 | + | 0.856460i | \(0.672659\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −29.3604 | −1.38253 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 8.74306 | 0.410785 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 4.29717 | 0.201454 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 21.2520 | 0.994128 | 0.497064 | − | 0.867714i | \(-0.334411\pi\) | ||||
0.497064 | + | 0.867714i | \(0.334411\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 6.19312 | 0.289070 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −2.74130 | −0.127675 | −0.0638375 | − | 0.997960i | \(-0.520334\pi\) | ||||
−0.0638375 | + | 0.997960i | \(0.520334\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 0.939856 | 0.0436788 | 0.0218394 | − | 0.999761i | \(-0.493048\pi\) | ||||
0.0218394 | + | 0.999761i | \(0.493048\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −4.53170 | −0.210153 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 4.00247 | 0.185212 | 0.0926061 | − | 0.995703i | \(-0.470480\pi\) | ||||
0.0926061 | + | 0.995703i | \(0.470480\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −10.8495 | −0.500982 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 1.28243 | 0.0590915 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −14.2209 | −0.653878 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −32.7932 | −1.50466 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 10.9128 | 0.499665 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −9.13204 | −0.417254 | −0.208627 | − | 0.977995i | \(-0.566899\pi\) | ||||
−0.208627 | + | 0.977995i | \(0.566899\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −38.6255 | −1.76117 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 4.40829 | 0.200584 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 5.55345 | 0.252169 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −35.6996 | −1.61770 | −0.808852 | − | 0.588012i | \(-0.799911\pi\) | ||||
−0.808852 | + | 0.588012i | \(0.799911\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 10.2657 | 0.464232 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 38.1762 | 1.72287 | 0.861434 | − | 0.507870i | \(-0.169567\pi\) | ||||
0.861434 | + | 0.507870i | \(0.169567\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −6.17450 | −0.278085 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 1.82509 | 0.0820318 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 12.4135 | 0.556821 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −1.03459 | −0.0463144 | −0.0231572 | − | 0.999732i | \(-0.507372\pi\) | ||||
−0.0231572 | + | 0.999732i | \(0.507372\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 1.00000 | 0.0446767 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 28.2992 | 1.26180 | 0.630900 | − | 0.775864i | \(-0.282686\pi\) | ||||
0.630900 | + | 0.775864i | \(0.282686\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 3.04629 | 0.135558 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 29.9154 | 1.32859 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 9.65536 | 0.427966 | 0.213983 | − | 0.976837i | \(-0.431356\pi\) | ||||
0.213983 | + | 0.976837i | \(0.431356\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −13.0122 | −0.575627 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 7.10438 | 0.313666 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −2.93132 | −0.129169 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −19.4807 | −0.856759 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −1.26599 | −0.0555708 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −0.841870 | −0.0368830 | −0.0184415 | − | 0.999830i | \(-0.505870\pi\) | ||||
−0.0184415 | + | 0.999830i | \(0.505870\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −12.6622 | −0.553679 | −0.276840 | − | 0.960916i | \(-0.589287\pi\) | ||||
−0.276840 | + | 0.960916i | \(0.589287\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −4.88566 | −0.213228 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 45.2856 | 1.97267 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −5.65352 | −0.245805 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −9.89351 | −0.429342 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −65.3124 | −2.82900 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −1.30535 | −0.0564352 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −7.48456 | −0.322982 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 17.3153 | 0.745822 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 10.6265 | 0.456869 | 0.228435 | − | 0.973559i | \(-0.426639\pi\) | ||||
0.228435 | + | 0.973559i | \(0.426639\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −4.86471 | −0.208765 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 4.17122 | 0.178675 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 46.1517 | 1.97330 | 0.986652 | − | 0.162841i | \(-0.0520657\pi\) | ||||
0.986652 | + | 0.162841i | \(0.0520657\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 10.2882 | 0.439089 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −7.08301 | −0.301747 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −3.93165 | −0.167191 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −3.65408 | −0.155107 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −19.0103 | −0.805494 | −0.402747 | − | 0.915311i | \(-0.631944\pi\) | ||||
−0.402747 | + | 0.915311i | \(0.631944\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −31.6345 | −1.33800 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −18.2383 | −0.770020 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −24.1476 | −1.01770 | −0.508850 | − | 0.860855i | \(-0.669929\pi\) | ||||
−0.508850 | + | 0.860855i | \(0.669929\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −2.61217 | −0.109895 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 1.05844 | 0.0444501 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −22.7175 | −0.952369 | −0.476185 | − | 0.879345i | \(-0.657981\pi\) | ||||
−0.476185 | + | 0.879345i | \(0.657981\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −12.5374 | −0.524673 | −0.262337 | − | 0.964976i | \(-0.584493\pi\) | ||||
−0.262337 | + | 0.964976i | \(0.584493\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 8.37459 | 0.349854 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −19.2249 | −0.801733 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 41.0884 | 1.71053 | 0.855267 | − | 0.518188i | \(-0.173393\pi\) | ||||
0.855267 | + | 0.518188i | \(0.173393\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −6.53375 | −0.271533 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −6.24610 | −0.259132 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −32.1375 | −1.33100 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 4.05992 | 0.167857 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −1.04147 | −0.0429861 | −0.0214931 | − | 0.999769i | \(-0.506842\pi\) | ||||
−0.0214931 | + | 0.999769i | \(0.506842\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 51.9489 | 2.14052 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 2.01768 | 0.0829962 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 34.8470 | 1.43100 | 0.715498 | − | 0.698615i | \(-0.246200\pi\) | ||||
0.715498 | + | 0.698615i | \(0.246200\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −4.06243 | −0.166543 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −18.2648 | −0.747529 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −39.0595 | −1.59593 | −0.797965 | − | 0.602704i | \(-0.794090\pi\) | ||||
−0.797965 | + | 0.602704i | \(0.794090\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 9.49751 | 0.387411 | 0.193706 | − | 0.981060i | \(-0.437949\pi\) | ||||
0.193706 | + | 0.981060i | \(0.437949\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −10.2505 | −0.417432 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 1.44241 | 0.0586425 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 18.2746 | 0.741742 | 0.370871 | − | 0.928684i | \(-0.379059\pi\) | ||||
0.370871 | + | 0.928684i | \(0.379059\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −1.05525 | −0.0427610 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −43.3348 | −1.75314 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −33.5367 | −1.35454 | −0.677268 | − | 0.735736i | \(-0.736836\pi\) | ||||
−0.677268 | + | 0.735736i | \(0.736836\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −6.17874 | −0.249151 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 1.66780 | 0.0671429 | 0.0335715 | − | 0.999436i | \(-0.489312\pi\) | ||||
0.0335715 | + | 0.999436i | \(0.489312\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −22.5977 | −0.908278 | −0.454139 | − | 0.890931i | \(-0.650053\pi\) | ||||
−0.454139 | + | 0.890931i | \(0.650053\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 4.16491 | 0.167132 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 10.4581 | 0.418996 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 19.3863 | 0.775452 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −20.9218 | −0.835538 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 36.5154 | 1.45597 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 9.50108 | 0.378232 | 0.189116 | − | 0.981955i | \(-0.439438\pi\) | ||||
0.189116 | + | 0.981955i | \(0.439438\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 8.93507 | 0.355137 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −6.95901 | −0.276160 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 38.5179 | 1.52614 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 11.7281 | 0.463958 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 21.9083 | 0.865325 | 0.432663 | − | 0.901556i | \(-0.357574\pi\) | ||||
0.432663 | + | 0.901556i | \(0.357574\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 41.7641 | 1.64701 | 0.823507 | − | 0.567306i | \(-0.192014\pi\) | ||||
0.823507 | + | 0.567306i | \(0.192014\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −2.99271 | −0.117838 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −4.32773 | −0.170141 | −0.0850703 | − | 0.996375i | \(-0.527111\pi\) | ||||
−0.0850703 | + | 0.996375i | \(0.527111\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 29.1356 | 1.14367 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 7.73954 | 0.303336 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 39.5986 | 1.54961 | 0.774807 | − | 0.632198i | \(-0.217847\pi\) | ||||
0.774807 | + | 0.632198i | \(0.217847\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 3.01487 | 0.117801 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −12.2938 | −0.479628 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −33.0788 | −1.28857 | −0.644284 | − | 0.764786i | \(-0.722845\pi\) | ||||
−0.644284 | + | 0.764786i | \(0.722845\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −14.2897 | −0.555803 | −0.277902 | − | 0.960610i | \(-0.589639\pi\) | ||||
−0.277902 | + | 0.960610i | \(0.589639\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −40.5711 | −1.57565 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −4.66017 | −0.180714 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −4.15239 | −0.160781 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −17.7607 | −0.686667 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −30.2979 | −1.16964 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −43.1679 | −1.66400 | −0.832000 | − | 0.554776i | \(-0.812804\pi\) | ||||
−0.832000 | + | 0.554776i | \(0.812804\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −4.61592 | −0.177667 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 28.8027 | 1.10698 | 0.553489 | − | 0.832857i | \(-0.313296\pi\) | ||||
0.553489 | + | 0.832857i | \(0.313296\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −9.48454 | −0.363983 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −11.3559 | −0.435158 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −28.6388 | −1.09583 | −0.547916 | − | 0.836533i | \(-0.684579\pi\) | ||||
−0.547916 | + | 0.836533i | \(0.684579\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0.917821 | 0.0350682 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 14.3141 | 0.546116 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −71.4899 | −2.72355 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 38.6489 | 1.47027 | 0.735137 | − | 0.677919i | \(-0.237118\pi\) | ||||
0.735137 | + | 0.677919i | \(0.237118\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −3.11701 | −0.118405 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 7.34791 | 0.278722 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 61.7446 | 2.33874 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 20.6800 | 0.782188 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −3.43773 | −0.129841 | −0.0649206 | − | 0.997890i | \(-0.520679\pi\) | ||||
−0.0649206 | + | 0.997890i | \(0.520679\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 41.8883 | 1.57985 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −4.09960 | −0.154400 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −5.20265 | −0.195666 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 20.2732 | 0.761375 | 0.380687 | − | 0.924704i | \(-0.375687\pi\) | ||||
0.380687 | + | 0.924704i | \(0.375687\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −3.71458 | −0.139308 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 30.4548 | 1.14054 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −11.9562 | −0.447135 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 9.67387 | 0.361277 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −30.6813 | −1.14422 | −0.572110 | − | 0.820177i | \(-0.693875\pi\) | ||||
−0.572110 | + | 0.820177i | \(0.693875\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 5.00630 | 0.186444 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 7.89334 | 0.293557 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 4.60204 | 0.170915 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 11.9584 | 0.443512 | 0.221756 | − | 0.975102i | \(-0.428821\pi\) | ||||
0.221756 | + | 0.975102i | \(0.428821\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 29.9063 | 1.10613 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 9.76983 | 0.360857 | 0.180429 | − | 0.983588i | \(-0.442252\pi\) | ||||
0.180429 | + | 0.983588i | \(0.442252\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 3.64391 | 0.134407 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 30.1868 | 1.11195 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −36.8792 | −1.35662 | −0.678312 | − | 0.734774i | \(-0.737288\pi\) | ||||
−0.678312 | + | 0.734774i | \(0.737288\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −46.5407 | −1.70972 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −31.8422 | −1.16818 | −0.584089 | − | 0.811690i | \(-0.698548\pi\) | ||||
−0.584089 | + | 0.811690i | \(0.698548\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −0.774761 | −0.0283851 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −5.90125 | −0.215916 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 2.22936 | 0.0814591 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 7.33017 | 0.267482 | 0.133741 | − | 0.991016i | \(-0.457301\pi\) | ||||
0.133741 | + | 0.991016i | \(0.457301\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −30.8625 | −1.12469 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −5.41844 | −0.197197 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −45.1792 | −1.64206 | −0.821032 | − | 0.570882i | \(-0.806602\pi\) | ||||
−0.821032 | + | 0.570882i | \(0.806602\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −12.2653 | −0.445203 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −28.8565 | −1.04605 | −0.523024 | − | 0.852318i | \(-0.675196\pi\) | ||||
−0.523024 | + | 0.852318i | \(0.675196\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −7.12387 | −0.257902 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −3.83814 | −0.138768 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 64.8123 | 2.34024 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 11.3707 | 0.410039 | 0.205019 | − | 0.978758i | \(-0.434274\pi\) | ||||
0.205019 | + | 0.978758i | \(0.434274\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −16.5611 | −0.596432 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −20.9885 | −0.754904 | −0.377452 | − | 0.926029i | \(-0.623200\pi\) | ||||
−0.377452 | + | 0.926029i | \(0.623200\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −33.7527 | −1.21243 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 6.24067 | 0.223883 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 70.8297 | 2.53774 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −34.5384 | −1.23588 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −0.996993 | −0.0356296 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −0.794779 | −0.0283669 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 41.3812 | 1.47508 | 0.737540 | − | 0.675304i | \(-0.235988\pi\) | ||||
0.737540 | + | 0.675304i | \(0.235988\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −2.43522 | −0.0866963 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 4.46123 | 0.158623 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −67.3977 | −2.39336 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −6.76315 | −0.239864 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −27.3144 | −0.967525 | −0.483762 | − | 0.875199i | \(-0.660730\pi\) | ||||
−0.483762 | + | 0.875199i | \(0.660730\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 40.9676 | 1.44933 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 9.88073 | 0.349118 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 36.2044 | 1.27762 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −2.73200 | −0.0962905 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 32.6765 | 1.15027 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 33.5282 | 1.17879 | 0.589395 | − | 0.807845i | \(-0.299366\pi\) | ||||
0.589395 | + | 0.807845i | \(0.299366\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 33.7840 | 1.18632 | 0.593159 | − | 0.805086i | \(-0.297881\pi\) | ||||
0.593159 | + | 0.805086i | \(0.297881\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −0.00431859 | −0.000151459 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −6.36211 | −0.222855 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 34.3068 | 1.20024 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −6.93380 | −0.242287 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 26.8743 | 0.937919 | 0.468959 | − | 0.883220i | \(-0.344629\pi\) | ||||
0.468959 | + | 0.883220i | \(0.344629\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 10.8499 | 0.378205 | 0.189103 | − | 0.981957i | \(-0.439442\pi\) | ||||
0.189103 | + | 0.981957i | \(0.439442\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 13.5935 | 0.473266 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −45.4359 | −1.57996 | −0.789981 | − | 0.613131i | \(-0.789910\pi\) | ||||
−0.789981 | + | 0.613131i | \(0.789910\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 37.4911 | 1.30212 | 0.651060 | − | 0.759026i | \(-0.274325\pi\) | ||||
0.651060 | + | 0.759026i | \(0.274325\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −25.8726 | −0.897509 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −36.4138 | −1.26166 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −0.619742 | −0.0214471 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 7.31224 | 0.252748 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 23.1675 | 0.799831 | 0.399916 | − | 0.916552i | \(-0.369039\pi\) | ||||
0.399916 | + | 0.916552i | \(0.369039\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.0060 | −0.965724 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 23.4091 | 0.806253 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −18.5399 | −0.637791 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −2.46345 | −0.0846451 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −26.8435 | −0.921268 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 24.5568 | 0.841798 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 24.1133 | 0.825624 | 0.412812 | − | 0.910816i | \(-0.364547\pi\) | ||||
0.412812 | + | 0.910816i | \(0.364547\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −4.40288 | −0.150575 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −10.6072 | −0.362335 | −0.181168 | − | 0.983452i | \(-0.557988\pi\) | ||||
−0.181168 | + | 0.983452i | \(0.557988\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 37.8886 | 1.29274 | 0.646372 | − | 0.763022i | \(-0.276285\pi\) | ||||
0.646372 | + | 0.763022i | \(0.276285\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 10.5525 | 0.359627 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 12.3480 | 0.420332 | 0.210166 | − | 0.977666i | \(-0.432600\pi\) | ||||
0.210166 | + | 0.977666i | \(0.432600\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0.784588 | 0.0266768 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 21.3548 | 0.725246 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 10.9392 | 0.371085 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 67.1508 | 2.27532 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −8.96090 | −0.303280 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 6.30764 | 0.213237 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −49.0918 | −1.65771 | −0.828856 | − | 0.559462i | \(-0.811008\pi\) | ||||
−0.828856 | + | 0.559462i | \(0.811008\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 23.7852 | 0.802254 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 27.4045 | 0.923280 | 0.461640 | − | 0.887067i | \(-0.347261\pi\) | ||||
0.461640 | + | 0.887067i | \(0.347261\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −34.8248 | −1.17195 | −0.585974 | − | 0.810330i | \(-0.699288\pi\) | ||||
−0.585974 | + | 0.810330i | \(0.699288\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 6.13143 | 0.206106 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 0.157909 | 0.00530207 | 0.00265104 | − | 0.999996i | \(-0.499156\pi\) | ||||
0.00265104 | + | 0.999996i | \(0.499156\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 11.8850 | 0.398612 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −2.94492 | −0.0986586 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 46.9955 | 1.57265 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 4.63849 | 0.155048 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −27.2843 | −0.910996 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −7.29025 | −0.243143 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 67.5846 | 2.25157 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 5.11115 | 0.170088 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 3.01487 | 0.100218 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −3.38987 | −0.112559 | −0.0562794 | − | 0.998415i | \(-0.517924\pi\) | ||||
−0.0562794 | + | 0.998415i | \(0.517924\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −4.91541 | −0.163034 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 37.5128 | 1.24285 | 0.621427 | − | 0.783472i | \(-0.286553\pi\) | ||||
0.621427 | + | 0.783472i | \(0.286553\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 17.3787 | 0.575152 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −6.37602 | −0.210785 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −5.14899 | −0.170035 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 3.48351 | 0.114910 | 0.0574552 | − | 0.998348i | \(-0.481701\pi\) | ||||
0.0574552 | + | 0.998348i | \(0.481701\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −10.0558 | −0.331349 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −76.8308 | −2.52892 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −27.2160 | −0.894858 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 4.72990 | 0.155350 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 16.6068 | 0.544851 | 0.272425 | − | 0.962177i | \(-0.412174\pi\) | ||||
0.272425 | + | 0.962177i | \(0.412174\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −41.7717 | −1.36901 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 18.7831 | 0.614932 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 11.3030 | 0.369648 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −41.7410 | −1.36362 | −0.681810 | − | 0.731529i | \(-0.738807\pi\) | ||||
−0.681810 | + | 0.731529i | \(0.738807\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 14.5269 | 0.474068 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 60.1088 | 1.95949 | 0.979746 | − | 0.200246i | \(-0.0641741\pi\) | ||||
0.979746 | + | 0.200246i | \(0.0641741\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 41.5236 | 1.35219 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −0.655958 | −0.0213383 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −14.3268 | −0.465558 | −0.232779 | − | 0.972530i | \(-0.574782\pi\) | ||||
−0.232779 | + | 0.972530i | \(0.574782\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 80.5367 | 2.61433 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −8.74455 | −0.283561 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −53.4836 | −1.73250 | −0.866252 | − | 0.499608i | \(-0.833478\pi\) | ||||
−0.866252 | + | 0.499608i | \(0.833478\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −5.19009 | −0.167947 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 2.93606 | 0.0949095 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −1.56752 | −0.0506177 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 22.4688 | 0.724802 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 2.10628 | 0.0678739 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 4.04924 | 0.130350 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 31.0170 | 0.997440 | 0.498720 | − | 0.866763i | \(-0.333804\pi\) | ||||
0.498720 | + | 0.866763i | \(0.333804\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 43.9983 | 1.41343 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 19.6921 | 0.631949 | 0.315974 | − | 0.948768i | \(-0.397669\pi\) | ||||
0.315974 | + | 0.948768i | \(0.397669\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −12.5492 | −0.402310 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 30.2388 | 0.968418 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −53.4720 | −1.71072 | −0.855360 | − | 0.518033i | \(-0.826664\pi\) | ||||
−0.855360 | + | 0.518033i | \(0.826664\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −29.0980 | −0.929975 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −6.73056 | −0.214890 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 10.0426 | 0.320309 | 0.160154 | − | 0.987092i | \(-0.448801\pi\) | ||||
0.160154 | + | 0.987092i | \(0.448801\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −1.25044 | −0.0398424 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 7.00156 | 0.222862 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 20.1122 | 0.639530 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −23.1529 | −0.735477 | −0.367739 | − | 0.929929i | \(-0.619868\pi\) | ||||
−0.367739 | + | 0.929929i | \(0.619868\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −4.49622 | −0.142683 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 11.3195 | 0.358852 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −14.0835 | −0.446029 | −0.223014 | − | 0.974815i | \(-0.571590\pi\) | ||||
−0.223014 | + | 0.974815i | \(0.571590\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 5.89613 | 0.186545 |
(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 | 2004.2.a.d.1.4 | ✓ | 9 | |
3.2 | odd | 2 | 6012.2.a.h.1.6 | 9 | |||
4.3 | odd | 2 | 8016.2.a.bb.1.4 | 9 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2004.2.a.d.1.4 | ✓ | 9 | 1.1 | even | 1 | trivial | |
6012.2.a.h.1.6 | 9 | 3.2 | odd | 2 | |||
8016.2.a.bb.1.4 | 9 | 4.3 | odd | 2 |