Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [5625,2,Mod(1,5625)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(5625, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("5625.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 5625 = 3^{2} \cdot 5^{4} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 5625.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: | \(44.9158511370\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 15x^{6} + 70x^{4} - 105x^{2} + 45 \) |
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 | 1.8 | ||
Root | \(2.66202\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 5625.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.66202 | 1.88233 | 0.941166 | − | 0.337946i | \(-0.109732\pi\) | ||||
0.941166 | + | 0.337946i | \(0.109732\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 5.08634 | 2.54317 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.46831 | 1.31090 | 0.655448 | − | 0.755240i | \(-0.272480\pi\) | ||||
0.655448 | + | 0.755240i | \(0.272480\pi\) | |||||||
\(8\) | 8.21589 | 2.90476 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.43248 | 1.03493 | 0.517466 | − | 0.855703i | \(-0.326875\pi\) | ||||
0.517466 | + | 0.855703i | \(0.326875\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 5.70437 | 1.58211 | 0.791054 | − | 0.611746i | \(-0.209532\pi\) | ||||
0.791054 | + | 0.611746i | \(0.209532\pi\) | |||||||
\(14\) | 9.23269 | 2.46754 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 11.6982 | 2.92454 | ||||||||
\(17\) | −1.89155 | −0.458769 | −0.229384 | − | 0.973336i | \(-0.573671\pi\) | ||||
−0.229384 | + | 0.973336i | \(0.573671\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.46831 | 0.566268 | 0.283134 | − | 0.959080i | \(-0.408626\pi\) | ||||
0.283134 | + | 0.959080i | \(0.408626\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 9.13733 | 1.94809 | ||||||||
\(23\) | −8.84431 | −1.84417 | −0.922083 | − | 0.386992i | \(-0.873514\pi\) | ||||
−0.922083 | + | 0.386992i | \(0.873514\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 15.1851 | 2.97805 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 17.6410 | 3.33383 | ||||||||
\(29\) | −8.98636 | −1.66873 | −0.834363 | − | 0.551216i | \(-0.814164\pi\) | ||||
−0.834363 | + | 0.551216i | \(0.814164\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.90746 | −0.342591 | −0.171295 | − | 0.985220i | \(-0.554795\pi\) | ||||
−0.171295 | + | 0.985220i | \(0.554795\pi\) | |||||||
\(32\) | 14.7090 | 2.60020 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −5.03535 | −0.863555 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 5.09254 | 0.837208 | 0.418604 | − | 0.908169i | \(-0.362520\pi\) | ||||
0.418604 | + | 0.908169i | \(0.362520\pi\) | |||||||
\(38\) | 6.57068 | 1.06590 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −6.35103 | −0.991864 | −0.495932 | − | 0.868361i | \(-0.665174\pi\) | ||||
−0.495932 | + | 0.868361i | \(0.665174\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −3.43296 | −0.523522 | −0.261761 | − | 0.965133i | \(-0.584303\pi\) | ||||
−0.261761 | + | 0.965133i | \(0.584303\pi\) | |||||||
\(44\) | 17.4588 | 2.63201 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −23.5437 | −3.47133 | ||||||||
\(47\) | −8.61447 | −1.25655 | −0.628275 | − | 0.777991i | \(-0.716239\pi\) | ||||
−0.628275 | + | 0.777991i | \(0.716239\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 5.02915 | 0.718450 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 29.0144 | 4.02357 | ||||||||
\(53\) | −2.03360 | −0.279337 | −0.139668 | − | 0.990198i | \(-0.544604\pi\) | ||||
−0.139668 | + | 0.990198i | \(0.544604\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 28.4952 | 3.80784 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −23.9219 | −3.14109 | ||||||||
\(59\) | 8.47242 | 1.10302 | 0.551508 | − | 0.834170i | \(-0.314053\pi\) | ||||
0.551508 | + | 0.834170i | \(0.314053\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −7.90746 | −1.01245 | −0.506223 | − | 0.862402i | \(-0.668959\pi\) | ||||
−0.506223 | + | 0.862402i | \(0.668959\pi\) | |||||||
\(62\) | −5.07770 | −0.644869 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 15.7592 | 1.96990 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 6.95846 | 0.850111 | 0.425055 | − | 0.905167i | \(-0.360255\pi\) | ||||
0.425055 | + | 0.905167i | \(0.360255\pi\) | |||||||
\(68\) | −9.62108 | −1.16673 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −2.91855 | −0.346368 | −0.173184 | − | 0.984890i | \(-0.555405\pi\) | ||||
−0.173184 | + | 0.984890i | \(0.555405\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −11.9280 | −1.39607 | −0.698036 | − | 0.716062i | \(-0.745943\pi\) | ||||
−0.698036 | + | 0.716062i | \(0.745943\pi\) | |||||||
\(74\) | 13.5564 | 1.57590 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 12.5546 | 1.44012 | ||||||||
\(77\) | 11.9049 | 1.35669 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −6.60564 | −0.743193 | −0.371596 | − | 0.928394i | \(-0.621189\pi\) | ||||
−0.371596 | + | 0.928394i | \(0.621189\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −16.9066 | −1.86702 | ||||||||
\(83\) | −12.9993 | −1.42686 | −0.713429 | − | 0.700727i | \(-0.752859\pi\) | ||||
−0.713429 | + | 0.700727i | \(0.752859\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −9.13860 | −0.985441 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 28.2009 | 3.00623 | ||||||||
\(89\) | 11.5873 | 1.22825 | 0.614124 | − | 0.789209i | \(-0.289509\pi\) | ||||
0.614124 | + | 0.789209i | \(0.289509\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 19.7845 | 2.07398 | ||||||||
\(92\) | −44.9852 | −4.69003 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −22.9319 | −2.36524 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −2.17888 | −0.221231 | −0.110616 | − | 0.993863i | \(-0.535282\pi\) | ||||
−0.110616 | + | 0.993863i | \(0.535282\pi\) | |||||||
\(98\) | 13.3877 | 1.35236 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −9.30399 | −0.925782 | −0.462891 | − | 0.886415i | \(-0.653188\pi\) | ||||
−0.462891 | + | 0.886415i | \(0.653188\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −0.176510 | −0.0173921 | −0.00869604 | − | 0.999962i | \(-0.502768\pi\) | ||||
−0.00869604 | + | 0.999962i | \(0.502768\pi\) | |||||||
\(104\) | 46.8665 | 4.59564 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −5.41348 | −0.525804 | ||||||||
\(107\) | 1.37761 | 0.133179 | 0.0665895 | − | 0.997780i | \(-0.478788\pi\) | ||||
0.0665895 | + | 0.997780i | \(0.478788\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1.89744 | 0.181742 | 0.0908708 | − | 0.995863i | \(-0.471035\pi\) | ||||
0.0908708 | + | 0.995863i | \(0.471035\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 40.5729 | 3.83378 | ||||||||
\(113\) | −2.35123 | −0.221185 | −0.110593 | − | 0.993866i | \(-0.535275\pi\) | ||||
−0.110593 | + | 0.993866i | \(0.535275\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −45.7077 | −4.24385 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 22.5537 | 2.07624 | ||||||||
\(119\) | −6.56048 | −0.601398 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0.781947 | 0.0710861 | ||||||||
\(122\) | −21.0498 | −1.90576 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −9.70201 | −0.871266 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −3.78069 | −0.335482 | −0.167741 | − | 0.985831i | \(-0.553647\pi\) | ||||
−0.167741 | + | 0.985831i | \(0.553647\pi\) | |||||||
\(128\) | 12.5333 | 1.10780 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0.797155 | 0.0696477 | 0.0348239 | − | 0.999393i | \(-0.488913\pi\) | ||||
0.0348239 | + | 0.999393i | \(0.488913\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 8.56084 | 0.742319 | ||||||||
\(134\) | 18.5235 | 1.60019 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −15.5408 | −1.33261 | ||||||||
\(137\) | 12.4188 | 1.06101 | 0.530507 | − | 0.847681i | \(-0.322002\pi\) | ||||
0.530507 | + | 0.847681i | \(0.322002\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 12.2399 | 1.03817 | 0.519087 | − | 0.854721i | \(-0.326272\pi\) | ||||
0.519087 | + | 0.854721i | \(0.326272\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −7.76922 | −0.651979 | ||||||||
\(143\) | 19.5802 | 1.63738 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −31.7527 | −2.62787 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 25.9024 | 2.12916 | ||||||||
\(149\) | 1.31109 | 0.107409 | 0.0537044 | − | 0.998557i | \(-0.482897\pi\) | ||||
0.0537044 | + | 0.998557i | \(0.482897\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2.57266 | 0.209360 | 0.104680 | − | 0.994506i | \(-0.466618\pi\) | ||||
0.104680 | + | 0.994506i | \(0.466618\pi\) | |||||||
\(152\) | 20.2793 | 1.64487 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 31.6911 | 2.55374 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 15.7038 | 1.25330 | 0.626650 | − | 0.779301i | \(-0.284426\pi\) | ||||
0.626650 | + | 0.779301i | \(0.284426\pi\) | |||||||
\(158\) | −17.5843 | −1.39893 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −30.6748 | −2.41751 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −7.42913 | −0.581894 | −0.290947 | − | 0.956739i | \(-0.593970\pi\) | ||||
−0.290947 | + | 0.956739i | \(0.593970\pi\) | |||||||
\(164\) | −32.3035 | −2.52248 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −34.6044 | −2.68582 | ||||||||
\(167\) | 4.12200 | 0.318970 | 0.159485 | − | 0.987200i | \(-0.449017\pi\) | ||||
0.159485 | + | 0.987200i | \(0.449017\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 19.5399 | 1.50307 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −17.4612 | −1.33140 | ||||||||
\(173\) | 19.7765 | 1.50358 | 0.751789 | − | 0.659404i | \(-0.229191\pi\) | ||||
0.751789 | + | 0.659404i | \(0.229191\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 40.1538 | 3.02671 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 30.8455 | 2.31197 | ||||||||
\(179\) | 7.18260 | 0.536853 | 0.268426 | − | 0.963300i | \(-0.413496\pi\) | ||||
0.268426 | + | 0.963300i | \(0.413496\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 15.9100 | 1.18258 | 0.591292 | − | 0.806458i | \(-0.298618\pi\) | ||||
0.591292 | + | 0.806458i | \(0.298618\pi\) | |||||||
\(182\) | 52.6667 | 3.90392 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −72.6639 | −5.35686 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −6.49272 | −0.474795 | ||||||||
\(188\) | −43.8161 | −3.19562 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −14.5190 | −1.05056 | −0.525278 | − | 0.850931i | \(-0.676039\pi\) | ||||
−0.525278 | + | 0.850931i | \(0.676039\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −13.0763 | −0.941254 | −0.470627 | − | 0.882332i | \(-0.655972\pi\) | ||||
−0.470627 | + | 0.882332i | \(0.655972\pi\) | |||||||
\(194\) | −5.80021 | −0.416431 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 25.5800 | 1.82714 | ||||||||
\(197\) | 17.8849 | 1.27425 | 0.637124 | − | 0.770761i | \(-0.280124\pi\) | ||||
0.637124 | + | 0.770761i | \(0.280124\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −21.1565 | −1.49974 | −0.749871 | − | 0.661584i | \(-0.769884\pi\) | ||||
−0.749871 | + | 0.661584i | \(0.769884\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −24.7674 | −1.74263 | ||||||||
\(203\) | −31.1675 | −2.18753 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −0.469874 | −0.0327377 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 66.7308 | 4.62695 | ||||||||
\(209\) | 8.47242 | 0.586050 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 13.4002 | 0.922507 | 0.461253 | − | 0.887268i | \(-0.347400\pi\) | ||||
0.461253 | + | 0.887268i | \(0.347400\pi\) | |||||||
\(212\) | −10.3436 | −0.710400 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 3.66724 | 0.250687 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −6.61567 | −0.449101 | ||||||||
\(218\) | 5.05101 | 0.342098 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −10.7901 | −0.725822 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 25.2555 | 1.69124 | 0.845618 | − | 0.533788i | \(-0.179232\pi\) | ||||
0.845618 | + | 0.533788i | \(0.179232\pi\) | |||||||
\(224\) | 51.0152 | 3.40860 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −6.25902 | −0.416344 | ||||||||
\(227\) | 1.89155 | 0.125547 | 0.0627734 | − | 0.998028i | \(-0.480005\pi\) | ||||
0.0627734 | + | 0.998028i | \(0.480005\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −4.78069 | −0.315917 | −0.157958 | − | 0.987446i | \(-0.550491\pi\) | ||||
−0.157958 | + | 0.987446i | \(0.550491\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −73.8310 | −4.84724 | ||||||||
\(233\) | 3.44563 | 0.225731 | 0.112865 | − | 0.993610i | \(-0.463997\pi\) | ||||
0.112865 | + | 0.993610i | \(0.463997\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 43.0936 | 2.80516 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −17.4641 | −1.13203 | ||||||||
\(239\) | 24.8164 | 1.60524 | 0.802620 | − | 0.596490i | \(-0.203439\pi\) | ||||
0.802620 | + | 0.596490i | \(0.203439\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −20.5045 | −1.32081 | −0.660407 | − | 0.750908i | \(-0.729616\pi\) | ||||
−0.660407 | + | 0.750908i | \(0.729616\pi\) | |||||||
\(242\) | 2.08156 | 0.133808 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −40.2201 | −2.57482 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 14.0801 | 0.895898 | ||||||||
\(248\) | −15.6715 | −0.995142 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −2.10825 | −0.133071 | −0.0665357 | − | 0.997784i | \(-0.521195\pi\) | ||||
−0.0665357 | + | 0.997784i | \(0.521195\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −30.3580 | −1.90859 | ||||||||
\(254\) | −10.0643 | −0.631488 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.84554 | 0.115346 | ||||||||
\(257\) | 1.45314 | 0.0906445 | 0.0453222 | − | 0.998972i | \(-0.485569\pi\) | ||||
0.0453222 | + | 0.998972i | \(0.485569\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 17.6625 | 1.09749 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 2.12204 | 0.131100 | ||||||||
\(263\) | 25.7688 | 1.58897 | 0.794485 | − | 0.607284i | \(-0.207741\pi\) | ||||
0.794485 | + | 0.607284i | \(0.207741\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 22.7891 | 1.39729 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 35.3931 | 2.16198 | ||||||||
\(269\) | 31.9778 | 1.94972 | 0.974859 | − | 0.222823i | \(-0.0715272\pi\) | ||||
0.974859 | + | 0.222823i | \(0.0715272\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 25.1821 | 1.52971 | 0.764853 | − | 0.644205i | \(-0.222812\pi\) | ||||
0.764853 | + | 0.644205i | \(0.222812\pi\) | |||||||
\(272\) | −22.1277 | −1.34169 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 33.0592 | 1.99718 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 16.8847 | 1.01450 | 0.507252 | − | 0.861798i | \(-0.330661\pi\) | ||||
0.507252 | + | 0.861798i | \(0.330661\pi\) | |||||||
\(278\) | 32.5828 | 1.95419 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −7.35764 | −0.438920 | −0.219460 | − | 0.975622i | \(-0.570430\pi\) | ||||
−0.219460 | + | 0.975622i | \(0.570430\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 12.1220 | 0.720581 | 0.360290 | − | 0.932840i | \(-0.382678\pi\) | ||||
0.360290 | + | 0.932840i | \(0.382678\pi\) | |||||||
\(284\) | −14.8447 | −0.880872 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 52.1228 | 3.08208 | ||||||||
\(287\) | −22.0273 | −1.30023 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −13.4220 | −0.789531 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −60.6701 | −3.55045 | ||||||||
\(293\) | 24.6612 | 1.44072 | 0.720362 | − | 0.693598i | \(-0.243976\pi\) | ||||
0.720362 | + | 0.693598i | \(0.243976\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 41.8397 | 2.43189 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 3.49015 | 0.202179 | ||||||||
\(299\) | −50.4513 | −2.91767 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −11.9066 | −0.686283 | ||||||||
\(302\) | 6.84847 | 0.394085 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 28.8747 | 1.65608 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −19.9964 | −1.14125 | −0.570627 | − | 0.821210i | \(-0.693300\pi\) | ||||
−0.570627 | + | 0.821210i | \(0.693300\pi\) | |||||||
\(308\) | 60.5524 | 3.45029 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 3.11485 | 0.176627 | 0.0883136 | − | 0.996093i | \(-0.471852\pi\) | ||||
0.0883136 | + | 0.996093i | \(0.471852\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −10.1492 | −0.573664 | −0.286832 | − | 0.957981i | \(-0.592602\pi\) | ||||
−0.286832 | + | 0.957981i | \(0.592602\pi\) | |||||||
\(314\) | 41.8038 | 2.35913 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −33.5985 | −1.89007 | ||||||||
\(317\) | −8.18921 | −0.459952 | −0.229976 | − | 0.973196i | \(-0.573865\pi\) | ||||
−0.229976 | + | 0.973196i | \(0.573865\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −30.8455 | −1.72702 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −81.6568 | −4.55056 | ||||||||
\(323\) | −4.66893 | −0.259786 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −19.7765 | −1.09532 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −52.1794 | −2.88113 | ||||||||
\(329\) | −29.8776 | −1.64721 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 19.3339 | 1.06269 | 0.531344 | − | 0.847156i | \(-0.321687\pi\) | ||||
0.531344 | + | 0.847156i | \(0.321687\pi\) | |||||||
\(332\) | −66.1189 | −3.62875 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 10.9728 | 0.600408 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −0.902375 | −0.0491555 | −0.0245778 | − | 0.999698i | \(-0.507824\pi\) | ||||
−0.0245778 | + | 0.999698i | \(0.507824\pi\) | |||||||
\(338\) | 52.0155 | 2.82927 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −6.54734 | −0.354558 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −6.83551 | −0.369083 | ||||||||
\(344\) | −28.2048 | −1.52070 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 52.6454 | 2.83023 | ||||||||
\(347\) | −0.676375 | −0.0363097 | −0.0181548 | − | 0.999835i | \(-0.505779\pi\) | ||||
−0.0181548 | + | 0.999835i | \(0.505779\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 10.0604 | 0.538523 | 0.269262 | − | 0.963067i | \(-0.413220\pi\) | ||||
0.269262 | + | 0.963067i | \(0.413220\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 50.4883 | 2.69104 | ||||||||
\(353\) | −7.29023 | −0.388020 | −0.194010 | − | 0.981000i | \(-0.562149\pi\) | ||||
−0.194010 | + | 0.981000i | \(0.562149\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 58.9368 | 3.12365 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 19.1202 | 1.01053 | ||||||||
\(359\) | −15.8301 | −0.835479 | −0.417739 | − | 0.908567i | \(-0.637177\pi\) | ||||
−0.417739 | + | 0.908567i | \(0.637177\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −12.9075 | −0.679340 | ||||||||
\(362\) | 42.3528 | 2.22601 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 100.631 | 5.27449 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 23.5116 | 1.22730 | 0.613649 | − | 0.789579i | \(-0.289701\pi\) | ||||
0.613649 | + | 0.789579i | \(0.289701\pi\) | |||||||
\(368\) | −103.462 | −5.39335 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −7.05315 | −0.366181 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −8.27467 | −0.428446 | −0.214223 | − | 0.976785i | \(-0.568722\pi\) | ||||
−0.214223 | + | 0.976785i | \(0.568722\pi\) | |||||||
\(374\) | −17.2837 | −0.893721 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −70.7756 | −3.64997 | ||||||||
\(377\) | −51.2616 | −2.64010 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −27.3648 | −1.40564 | −0.702819 | − | 0.711369i | \(-0.748075\pi\) | ||||
−0.702819 | + | 0.711369i | \(0.748075\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −38.6498 | −1.97749 | ||||||||
\(383\) | −15.6880 | −0.801620 | −0.400810 | − | 0.916161i | \(-0.631271\pi\) | ||||
−0.400810 | + | 0.916161i | \(0.631271\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −34.8094 | −1.77175 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −11.0825 | −0.562629 | ||||||||
\(389\) | 20.6950 | 1.04928 | 0.524638 | − | 0.851325i | \(-0.324201\pi\) | ||||
0.524638 | + | 0.851325i | \(0.324201\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 16.7295 | 0.846046 | ||||||||
\(392\) | 41.3190 | 2.08692 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 47.6100 | 2.39856 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 10.3616 | 0.520033 | 0.260016 | − | 0.965604i | \(-0.416272\pi\) | ||||
0.260016 | + | 0.965604i | \(0.416272\pi\) | |||||||
\(398\) | −56.3189 | −2.82301 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −0.600848 | −0.0300049 | −0.0150025 | − | 0.999887i | \(-0.504776\pi\) | ||||
−0.0150025 | + | 0.999887i | \(0.504776\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −10.8809 | −0.542015 | ||||||||
\(404\) | −47.3233 | −2.35442 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −82.9683 | −4.11765 | ||||||||
\(407\) | 17.4801 | 0.866454 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −20.0064 | −0.989253 | −0.494626 | − | 0.869106i | \(-0.664695\pi\) | ||||
−0.494626 | + | 0.869106i | \(0.664695\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −0.897792 | −0.0442310 | ||||||||
\(413\) | 29.3850 | 1.44594 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 83.9055 | 4.11381 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 22.5537 | 1.10314 | ||||||||
\(419\) | 10.8245 | 0.528813 | 0.264407 | − | 0.964411i | \(-0.414824\pi\) | ||||
0.264407 | + | 0.964411i | \(0.414824\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −31.3321 | −1.52703 | −0.763516 | − | 0.645789i | \(-0.776528\pi\) | ||||
−0.763516 | + | 0.645789i | \(0.776528\pi\) | |||||||
\(422\) | 35.6715 | 1.73646 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −16.7078 | −0.811405 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −27.4255 | −1.32721 | ||||||||
\(428\) | 7.00702 | 0.338697 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −31.6470 | −1.52438 | −0.762191 | − | 0.647353i | \(-0.775876\pi\) | ||||
−0.762191 | + | 0.647353i | \(0.775876\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 19.9075 | 0.956692 | 0.478346 | − | 0.878172i | \(-0.341237\pi\) | ||||
0.478346 | + | 0.878172i | \(0.341237\pi\) | |||||||
\(434\) | −17.6110 | −0.845356 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 9.65101 | 0.462200 | ||||||||
\(437\) | −21.8305 | −1.04429 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −23.7707 | −1.13451 | −0.567256 | − | 0.823542i | \(-0.691995\pi\) | ||||
−0.567256 | + | 0.823542i | \(0.691995\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −28.7235 | −1.36624 | ||||||||
\(443\) | 8.36336 | 0.397355 | 0.198678 | − | 0.980065i | \(-0.436335\pi\) | ||||
0.198678 | + | 0.980065i | \(0.436335\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 67.2307 | 3.18347 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 54.6577 | 2.58234 | ||||||||
\(449\) | −35.2889 | −1.66539 | −0.832693 | − | 0.553734i | \(-0.813202\pi\) | ||||
−0.832693 | + | 0.553734i | \(0.813202\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −21.7998 | −1.02651 | ||||||||
\(452\) | −11.9592 | −0.562512 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 5.03535 | 0.236320 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 12.9534 | 0.605933 | 0.302967 | − | 0.953001i | \(-0.402023\pi\) | ||||
0.302967 | + | 0.953001i | \(0.402023\pi\) | |||||||
\(458\) | −12.7263 | −0.594660 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 29.8908 | 1.39215 | 0.696076 | − | 0.717968i | \(-0.254928\pi\) | ||||
0.696076 | + | 0.717968i | \(0.254928\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −14.1155 | −0.656002 | −0.328001 | − | 0.944677i | \(-0.606375\pi\) | ||||
−0.328001 | + | 0.944677i | \(0.606375\pi\) | |||||||
\(464\) | −105.124 | −4.88026 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 9.17233 | 0.424900 | ||||||||
\(467\) | −4.00068 | −0.185129 | −0.0925647 | − | 0.995707i | \(-0.529506\pi\) | ||||
−0.0925647 | + | 0.995707i | \(0.529506\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 24.1341 | 1.11441 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 69.6085 | 3.20399 | ||||||||
\(473\) | −11.7836 | −0.541810 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −33.3688 | −1.52946 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 66.0618 | 3.02159 | ||||||||
\(479\) | −19.2413 | −0.879156 | −0.439578 | − | 0.898204i | \(-0.644872\pi\) | ||||
−0.439578 | + | 0.898204i | \(0.644872\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 29.0497 | 1.32455 | ||||||||
\(482\) | −54.5835 | −2.48621 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 3.97725 | 0.180784 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −13.9219 | −0.630859 | −0.315430 | − | 0.948949i | \(-0.602149\pi\) | ||||
−0.315430 | + | 0.948949i | \(0.602149\pi\) | |||||||
\(488\) | −64.9669 | −2.94091 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 14.5058 | 0.654639 | 0.327319 | − | 0.944914i | \(-0.393855\pi\) | ||||
0.327319 | + | 0.944914i | \(0.393855\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 16.9982 | 0.765559 | ||||||||
\(494\) | 37.4816 | 1.68638 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −22.3138 | −1.00192 | ||||||||
\(497\) | −10.1224 | −0.454052 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 1.26905 | 0.0568103 | 0.0284052 | − | 0.999596i | \(-0.490957\pi\) | ||||
0.0284052 | + | 0.999596i | \(0.490957\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −5.61219 | −0.250484 | ||||||||
\(503\) | −8.50684 | −0.379301 | −0.189651 | − | 0.981852i | \(-0.560736\pi\) | ||||
−0.189651 | + | 0.981852i | \(0.560736\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −80.8134 | −3.59260 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −19.2299 | −0.853188 | ||||||||
\(509\) | 36.4250 | 1.61451 | 0.807254 | − | 0.590204i | \(-0.200953\pi\) | ||||
0.807254 | + | 0.590204i | \(0.200953\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −41.3701 | −1.83011 | ||||||||
\(512\) | −20.1538 | −0.890680 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 3.86829 | 0.170623 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −29.5690 | −1.30044 | ||||||||
\(518\) | 47.0178 | 2.06585 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −31.9990 | −1.40190 | −0.700951 | − | 0.713209i | \(-0.747241\pi\) | ||||
−0.700951 | + | 0.713209i | \(0.747241\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 29.0448 | 1.27004 | 0.635020 | − | 0.772496i | \(-0.280992\pi\) | ||||
0.635020 | + | 0.772496i | \(0.280992\pi\) | |||||||
\(524\) | 4.05460 | 0.177126 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 68.5969 | 2.99097 | ||||||||
\(527\) | 3.60807 | 0.157170 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 55.2218 | 2.40095 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 43.5434 | 1.88784 | ||||||||
\(533\) | −36.2287 | −1.56924 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 57.1700 | 2.46937 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 85.1254 | 3.67001 | ||||||||
\(539\) | 17.2625 | 0.743547 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −18.2546 | −0.784827 | −0.392414 | − | 0.919789i | \(-0.628360\pi\) | ||||
−0.392414 | + | 0.919789i | \(0.628360\pi\) | |||||||
\(542\) | 67.0353 | 2.87941 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −27.8228 | −1.19289 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 6.92805 | 0.296222 | 0.148111 | − | 0.988971i | \(-0.452681\pi\) | ||||
0.148111 | + | 0.988971i | \(0.452681\pi\) | |||||||
\(548\) | 63.1665 | 2.69834 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −22.1811 | −0.944946 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −22.9104 | −0.974249 | ||||||||
\(554\) | 44.9474 | 1.90963 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 62.2563 | 2.64025 | ||||||||
\(557\) | −11.5873 | −0.490969 | −0.245484 | − | 0.969401i | \(-0.578947\pi\) | ||||
−0.245484 | + | 0.969401i | \(0.578947\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −19.5829 | −0.828268 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −19.5862 | −0.826192 | ||||||||
\(563\) | −4.92004 | −0.207355 | −0.103677 | − | 0.994611i | \(-0.533061\pi\) | ||||
−0.103677 | + | 0.994611i | \(0.533061\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 32.2691 | 1.35637 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −23.9785 | −1.00611 | ||||||||
\(569\) | −37.5316 | −1.57341 | −0.786704 | − | 0.617331i | \(-0.788214\pi\) | ||||
−0.786704 | + | 0.617331i | \(0.788214\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −31.5956 | −1.32224 | −0.661118 | − | 0.750282i | \(-0.729918\pi\) | ||||
−0.661118 | + | 0.750282i | \(0.729918\pi\) | |||||||
\(572\) | 99.5914 | 4.16413 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −58.6371 | −2.44747 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 36.4055 | 1.51558 | 0.757790 | − | 0.652499i | \(-0.226279\pi\) | ||||
0.757790 | + | 0.652499i | \(0.226279\pi\) | |||||||
\(578\) | −35.7297 | −1.48616 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −45.0856 | −1.87046 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −6.98030 | −0.289095 | ||||||||
\(584\) | −97.9996 | −4.05525 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 65.6486 | 2.71192 | ||||||||
\(587\) | 35.5061 | 1.46550 | 0.732748 | − | 0.680500i | \(-0.238237\pi\) | ||||
0.732748 | + | 0.680500i | \(0.238237\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −4.70820 | −0.193998 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 59.5734 | 2.44845 | ||||||||
\(593\) | 45.7086 | 1.87703 | 0.938513 | − | 0.345244i | \(-0.112204\pi\) | ||||
0.938513 | + | 0.345244i | \(0.112204\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 6.66866 | 0.273159 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −134.302 | −5.49202 | ||||||||
\(599\) | −3.58625 | −0.146530 | −0.0732652 | − | 0.997312i | \(-0.523342\pi\) | ||||
−0.0732652 | + | 0.997312i | \(0.523342\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 10.0366 | 0.409400 | 0.204700 | − | 0.978825i | \(-0.434378\pi\) | ||||
0.204700 | + | 0.978825i | \(0.434378\pi\) | |||||||
\(602\) | −31.6955 | −1.29181 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 13.0854 | 0.532439 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 34.8691 | 1.41529 | 0.707646 | − | 0.706567i | \(-0.249757\pi\) | ||||
0.707646 | + | 0.706567i | \(0.249757\pi\) | |||||||
\(608\) | 36.3063 | 1.47241 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −49.1402 | −1.98800 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 23.8674 | 0.963994 | 0.481997 | − | 0.876173i | \(-0.339912\pi\) | ||||
0.481997 | + | 0.876173i | \(0.339912\pi\) | |||||||
\(614\) | −53.2307 | −2.14822 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 97.8095 | 3.94086 | ||||||||
\(617\) | −6.81159 | −0.274224 | −0.137112 | − | 0.990556i | \(-0.543782\pi\) | ||||
−0.137112 | + | 0.990556i | \(0.543782\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −24.7256 | −0.993808 | −0.496904 | − | 0.867806i | \(-0.665530\pi\) | ||||
−0.496904 | + | 0.867806i | \(0.665530\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 8.29180 | 0.332471 | ||||||||
\(623\) | 40.1882 | 1.61011 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −27.0172 | −1.07983 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 79.8749 | 3.18735 | ||||||||
\(629\) | −9.63280 | −0.384085 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −23.4178 | −0.932250 | −0.466125 | − | 0.884719i | \(-0.654350\pi\) | ||||
−0.466125 | + | 0.884719i | \(0.654350\pi\) | |||||||
\(632\) | −54.2713 | −2.15879 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −21.7998 | −0.865781 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 28.6882 | 1.13667 | ||||||||
\(638\) | −82.1114 | −3.25082 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −26.9591 | −1.06482 | −0.532410 | − | 0.846487i | \(-0.678713\pi\) | ||||
−0.532410 | + | 0.846487i | \(0.678713\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −9.56996 | −0.377403 | −0.188701 | − | 0.982035i | \(-0.560428\pi\) | ||||
−0.188701 | + | 0.982035i | \(0.560428\pi\) | |||||||
\(644\) | −156.022 | −6.14814 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −12.4288 | −0.489004 | ||||||||
\(647\) | −20.0941 | −0.789981 | −0.394991 | − | 0.918685i | \(-0.629252\pi\) | ||||
−0.394991 | + | 0.918685i | \(0.629252\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 29.0815 | 1.14155 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −37.7871 | −1.47986 | ||||||||
\(653\) | −40.7211 | −1.59354 | −0.796770 | − | 0.604282i | \(-0.793460\pi\) | ||||
−0.796770 | + | 0.604282i | \(0.793460\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −74.2955 | −2.90075 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −79.5348 | −3.10059 | ||||||||
\(659\) | −11.4254 | −0.445070 | −0.222535 | − | 0.974925i | \(-0.571433\pi\) | ||||
−0.222535 | + | 0.974925i | \(0.571433\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −33.5985 | −1.30683 | −0.653416 | − | 0.756999i | \(-0.726665\pi\) | ||||
−0.653416 | + | 0.756999i | \(0.726665\pi\) | |||||||
\(662\) | 51.4672 | 2.00033 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −106.801 | −4.14468 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 79.4782 | 3.07741 | ||||||||
\(668\) | 20.9659 | 0.811196 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −27.1422 | −1.04781 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 27.7871 | 1.07111 | 0.535557 | − | 0.844499i | \(-0.320102\pi\) | ||||
0.535557 | + | 0.844499i | \(0.320102\pi\) | |||||||
\(674\) | −2.40214 | −0.0925270 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 99.3865 | 3.82256 | ||||||||
\(677\) | 31.3520 | 1.20496 | 0.602478 | − | 0.798135i | \(-0.294180\pi\) | ||||
0.602478 | + | 0.798135i | \(0.294180\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −7.55701 | −0.290012 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −17.4291 | −0.667396 | ||||||||
\(683\) | 0.655106 | 0.0250669 | 0.0125335 | − | 0.999921i | \(-0.496010\pi\) | ||||
0.0125335 | + | 0.999921i | \(0.496010\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −18.1963 | −0.694736 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −40.1594 | −1.53106 | ||||||||
\(689\) | −11.6004 | −0.441941 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 28.9381 | 1.10086 | 0.550428 | − | 0.834883i | \(-0.314464\pi\) | ||||
0.550428 | + | 0.834883i | \(0.314464\pi\) | |||||||
\(692\) | 100.590 | 3.82385 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −1.80052 | −0.0683469 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 12.0133 | 0.455036 | ||||||||
\(698\) | 26.7811 | 1.01368 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −31.0249 | −1.17179 | −0.585896 | − | 0.810386i | \(-0.699257\pi\) | ||||
−0.585896 | + | 0.810386i | \(0.699257\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 12.5699 | 0.474084 | ||||||||
\(704\) | 54.0932 | 2.03871 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −19.4067 | −0.730382 | ||||||||
\(707\) | −32.2691 | −1.21360 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 41.2676 | 1.54984 | 0.774918 | − | 0.632062i | \(-0.217791\pi\) | ||||
0.774918 | + | 0.632062i | \(0.217791\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 95.1998 | 3.56776 | ||||||||
\(713\) | 16.8702 | 0.631794 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 36.5331 | 1.36531 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −42.1399 | −1.57265 | ||||||||
\(719\) | −2.15581 | −0.0803980 | −0.0401990 | − | 0.999192i | \(-0.512799\pi\) | ||||
−0.0401990 | + | 0.999192i | \(0.512799\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −0.612192 | −0.0227992 | ||||||||
\(722\) | −34.3599 | −1.27874 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 80.9239 | 3.00751 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 43.8091 | 1.62479 | 0.812396 | − | 0.583107i | \(-0.198163\pi\) | ||||
0.812396 | + | 0.583107i | \(0.198163\pi\) | |||||||
\(728\) | 162.548 | 6.02441 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 6.49362 | 0.240175 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −38.6326 | −1.42693 | −0.713464 | − | 0.700692i | \(-0.752875\pi\) | ||||
−0.713464 | + | 0.700692i | \(0.752875\pi\) | |||||||
\(734\) | 62.5884 | 2.31018 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −130.091 | −4.79521 | ||||||||
\(737\) | 23.8848 | 0.879808 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 20.4743 | 0.753159 | 0.376579 | − | 0.926384i | \(-0.377100\pi\) | ||||
0.376579 | + | 0.926384i | \(0.377100\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −18.7756 | −0.689275 | ||||||||
\(743\) | −4.86490 | −0.178476 | −0.0892379 | − | 0.996010i | \(-0.528443\pi\) | ||||
−0.0892379 | + | 0.996010i | \(0.528443\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −22.0273 | −0.806478 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −33.0242 | −1.20748 | ||||||||
\(749\) | 4.77799 | 0.174584 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −36.7353 | −1.34049 | −0.670245 | − | 0.742140i | \(-0.733811\pi\) | ||||
−0.670245 | + | 0.742140i | \(0.733811\pi\) | |||||||
\(752\) | −100.774 | −3.67484 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −136.459 | −4.96955 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 13.1609 | 0.478340 | 0.239170 | − | 0.970978i | \(-0.423125\pi\) | ||||
0.239170 | + | 0.970978i | \(0.423125\pi\) | |||||||
\(758\) | −72.8457 | −2.64587 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −17.9859 | −0.651987 | −0.325994 | − | 0.945372i | \(-0.605699\pi\) | ||||
−0.325994 | + | 0.945372i | \(0.605699\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 6.58089 | 0.238244 | ||||||||
\(764\) | −73.8484 | −2.67174 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −41.7618 | −1.50891 | ||||||||
\(767\) | 48.3299 | 1.74509 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 3.28562 | 0.118483 | 0.0592413 | − | 0.998244i | \(-0.481132\pi\) | ||||
0.0592413 | + | 0.998244i | \(0.481132\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −66.5106 | −2.39377 | ||||||||
\(773\) | −10.0265 | −0.360628 | −0.180314 | − | 0.983609i | \(-0.557711\pi\) | ||||
−0.180314 | + | 0.983609i | \(0.557711\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −17.9014 | −0.642624 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 55.0904 | 1.97509 | ||||||||
\(779\) | −15.6763 | −0.561661 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −10.0179 | −0.358467 | ||||||||
\(782\) | 44.5342 | 1.59254 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 58.8319 | 2.10114 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 43.1508 | 1.53816 | 0.769080 | − | 0.639153i | \(-0.220715\pi\) | ||||
0.769080 | + | 0.639153i | \(0.220715\pi\) | |||||||
\(788\) | 90.9688 | 3.24063 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −8.15479 | −0.289951 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −45.1071 | −1.60180 | ||||||||
\(794\) | 27.5827 | 0.978874 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −107.609 | −3.81410 | ||||||||
\(797\) | 23.2836 | 0.824748 | 0.412374 | − | 0.911015i | \(-0.364700\pi\) | ||||
0.412374 | + | 0.911015i | \(0.364700\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 16.2947 | 0.576466 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −1.59947 | −0.0564792 | ||||||||
\(803\) | −40.9428 | −1.44484 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −28.9651 | −1.02025 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −76.4406 | −2.68917 | ||||||||
\(809\) | 6.18914 | 0.217598 | 0.108799 | − | 0.994064i | \(-0.465299\pi\) | ||||
0.108799 | + | 0.994064i | \(0.465299\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −2.53809 | −0.0891245 | −0.0445623 | − | 0.999007i | \(-0.514189\pi\) | ||||
−0.0445623 | + | 0.999007i | \(0.514189\pi\) | |||||||
\(812\) | −158.528 | −5.56325 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 46.5322 | 1.63095 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −8.47360 | −0.296454 | ||||||||
\(818\) | −53.2574 | −1.86210 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 44.4179 | 1.55019 | 0.775097 | − | 0.631842i | \(-0.217701\pi\) | ||||
0.775097 | + | 0.631842i | \(0.217701\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 19.6434 | 0.684724 | 0.342362 | − | 0.939568i | \(-0.388773\pi\) | ||||
0.342362 | + | 0.939568i | \(0.388773\pi\) | |||||||
\(824\) | −1.45019 | −0.0505198 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 78.2233 | 2.72174 | ||||||||
\(827\) | 31.1557 | 1.08339 | 0.541695 | − | 0.840575i | \(-0.317783\pi\) | ||||
0.541695 | + | 0.840575i | \(0.317783\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 2.46831 | 0.0857278 | 0.0428639 | − | 0.999081i | \(-0.486352\pi\) | ||||
0.0428639 | + | 0.999081i | \(0.486352\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 89.8964 | 3.11660 | ||||||||
\(833\) | −9.51290 | −0.329602 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 43.0936 | 1.49042 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 28.8151 | 0.995401 | ||||||||
\(839\) | 46.0334 | 1.58925 | 0.794625 | − | 0.607100i | \(-0.207667\pi\) | ||||
0.794625 | + | 0.607100i | \(0.207667\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 51.7547 | 1.78464 | ||||||||
\(842\) | −83.4065 | −2.87438 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 68.1579 | 2.34609 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 2.71203 | 0.0931866 | ||||||||
\(848\) | −23.7894 | −0.816932 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −45.0400 | −1.54395 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −9.24700 | −0.316611 | −0.158306 | − | 0.987390i | \(-0.550603\pi\) | ||||
−0.158306 | + | 0.987390i | \(0.550603\pi\) | |||||||
\(854\) | −73.0072 | −2.49825 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 11.3183 | 0.386853 | ||||||||
\(857\) | −32.3505 | −1.10507 | −0.552536 | − | 0.833489i | \(-0.686340\pi\) | ||||
−0.552536 | + | 0.833489i | \(0.686340\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −14.0883 | −0.480688 | −0.240344 | − | 0.970688i | \(-0.577260\pi\) | ||||
−0.240344 | + | 0.970688i | \(0.577260\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −84.2448 | −2.86939 | ||||||||
\(863\) | −52.5301 | −1.78815 | −0.894073 | − | 0.447921i | \(-0.852164\pi\) | ||||
−0.894073 | + | 0.447921i | \(0.852164\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 52.9940 | 1.80081 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −33.6495 | −1.14214 | ||||||||
\(869\) | −22.6738 | −0.769155 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 39.6936 | 1.34497 | ||||||||
\(872\) | 15.5891 | 0.527915 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −58.1131 | −1.96571 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −6.58359 | −0.222312 | −0.111156 | − | 0.993803i | \(-0.535455\pi\) | ||||
−0.111156 | + | 0.993803i | \(0.535455\pi\) | |||||||
\(878\) | −63.2779 | −2.13553 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 36.4594 | 1.22835 | 0.614174 | − | 0.789171i | \(-0.289489\pi\) | ||||
0.614174 | + | 0.789171i | \(0.289489\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 17.5190 | 0.589560 | 0.294780 | − | 0.955565i | \(-0.404754\pi\) | ||||
0.294780 | + | 0.955565i | \(0.404754\pi\) | |||||||
\(884\) | −54.8822 | −1.84589 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 22.2634 | 0.747954 | ||||||||
\(887\) | −24.6277 | −0.826917 | −0.413459 | − | 0.910523i | \(-0.635679\pi\) | ||||
−0.413459 | + | 0.910523i | \(0.635679\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −13.1126 | −0.439782 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 128.458 | 4.30110 | ||||||||
\(893\) | −21.2632 | −0.711544 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 43.4694 | 1.45221 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −93.9397 | −3.13481 | ||||||||
\(899\) | 17.1412 | 0.571689 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 3.84666 | 0.128151 | ||||||||
\(902\) | −58.0315 | −1.93224 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −19.3175 | −0.642490 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −4.47955 | −0.148741 | −0.0743705 | − | 0.997231i | \(-0.523695\pi\) | ||||
−0.0743705 | + | 0.997231i | \(0.523695\pi\) | |||||||
\(908\) | 9.62108 | 0.319287 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −41.9576 | −1.39012 | −0.695058 | − | 0.718953i | \(-0.744621\pi\) | ||||
−0.695058 | + | 0.718953i | \(0.744621\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −44.6199 | −1.47670 | ||||||||
\(914\) | 34.4821 | 1.14057 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −24.3162 | −0.803430 | ||||||||
\(917\) | 2.76478 | 0.0913010 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −37.6692 | −1.24259 | −0.621297 | − | 0.783575i | \(-0.713394\pi\) | ||||
−0.621297 | + | 0.783575i | \(0.713394\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 79.5698 | 2.62049 | ||||||||
\(923\) | −16.6485 | −0.547992 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −37.5757 | −1.23481 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −132.180 | −4.33903 | ||||||||
\(929\) | −17.1493 | −0.562649 | −0.281325 | − | 0.959613i | \(-0.590774\pi\) | ||||
−0.281325 | + | 0.959613i | \(0.590774\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 12.4135 | 0.406835 | ||||||||
\(932\) | 17.5256 | 0.574071 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −10.6499 | −0.348475 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 37.1944 | 1.21509 | 0.607544 | − | 0.794286i | \(-0.292155\pi\) | ||||
0.607544 | + | 0.794286i | \(0.292155\pi\) | |||||||
\(938\) | 64.2453 | 2.09768 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 29.5387 | 0.962935 | 0.481468 | − | 0.876464i | \(-0.340104\pi\) | ||||
0.481468 | + | 0.876464i | \(0.340104\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 56.1705 | 1.82916 | ||||||||
\(944\) | 99.1119 | 3.22582 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −31.3681 | −1.01987 | ||||||||
\(947\) | 34.0869 | 1.10767 | 0.553837 | − | 0.832625i | \(-0.313163\pi\) | ||||
0.553837 | + | 0.832625i | \(0.313163\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −68.0421 | −2.20874 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −53.9002 | −1.74692 | ||||||||
\(953\) | −9.67588 | −0.313432 | −0.156716 | − | 0.987644i | \(-0.550091\pi\) | ||||
−0.156716 | + | 0.987644i | \(0.550091\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 126.225 | 4.08240 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −51.2206 | −1.65486 | ||||||||
\(959\) | 43.0724 | 1.39088 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −27.3616 | −0.882632 | ||||||||
\(962\) | 77.3309 | 2.49325 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −104.293 | −3.35905 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −17.2537 | −0.554842 | −0.277421 | − | 0.960748i | \(-0.589480\pi\) | ||||
−0.277421 | + | 0.960748i | \(0.589480\pi\) | |||||||
\(968\) | 6.42440 | 0.206488 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −1.92509 | −0.0617789 | −0.0308895 | − | 0.999523i | \(-0.509834\pi\) | ||||
−0.0308895 | + | 0.999523i | \(0.509834\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 42.4517 | 1.36094 | ||||||||
\(974\) | −37.0602 | −1.18749 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −92.5029 | −2.96095 | ||||||||
\(977\) | 26.1185 | 0.835605 | 0.417803 | − | 0.908538i | \(-0.362800\pi\) | ||||
0.417803 | + | 0.908538i | \(0.362800\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 39.7731 | 1.27116 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 38.6148 | 1.23225 | ||||||||
\(983\) | 9.28360 | 0.296101 | 0.148050 | − | 0.988980i | \(-0.452700\pi\) | ||||
0.148050 | + | 0.988980i | \(0.452700\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 45.2494 | 1.44104 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 71.6164 | 2.27842 | ||||||||
\(989\) | 30.3622 | 0.965461 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 41.1337 | 1.30666 | 0.653328 | − | 0.757075i | \(-0.273372\pi\) | ||||
0.653328 | + | 0.757075i | \(0.273372\pi\) | |||||||
\(992\) | −28.0568 | −0.890805 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −26.9461 | −0.854677 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 4.60496 | 0.145840 | 0.0729202 | − | 0.997338i | \(-0.476768\pi\) | ||||
0.0729202 | + | 0.997338i | \(0.476768\pi\) | |||||||
\(998\) | 3.37823 | 0.106936 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 5625.2.a.bb.1.8 | yes | 8 | |
3.2 | odd | 2 | inner | 5625.2.a.bb.1.1 | yes | 8 | |
5.4 | even | 2 | 5625.2.a.z.1.1 | ✓ | 8 | ||
15.14 | odd | 2 | 5625.2.a.z.1.8 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
5625.2.a.z.1.1 | ✓ | 8 | 5.4 | even | 2 | ||
5625.2.a.z.1.8 | yes | 8 | 15.14 | odd | 2 | ||
5625.2.a.bb.1.1 | yes | 8 | 3.2 | odd | 2 | inner | |
5625.2.a.bb.1.8 | yes | 8 | 1.1 | even | 1 | trivial |