Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8550,2,Mod(1,8550)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8550, 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("8550.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8550 = 2 \cdot 3^{2} \cdot 5^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8550.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: | \(68.2720937282\) |
Analytic rank: | \(1\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.788.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 7x - 3 \) |
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 | 1.3 | ||
Root | \(3.35386\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8550.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.35386 | 0.889674 | 0.444837 | − | 0.895612i | \(-0.353262\pi\) | ||||
0.444837 | + | 0.895612i | \(0.353262\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −4.89449 | −1.47575 | −0.737873 | − | 0.674940i | \(-0.764169\pi\) | ||||
−0.737873 | + | 0.674940i | \(0.764169\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.89449 | 0.525438 | 0.262719 | − | 0.964872i | \(-0.415381\pi\) | ||||
0.262719 | + | 0.964872i | \(0.415381\pi\) | |||||||
\(14\) | 2.35386 | 0.629094 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −2.35386 | −0.570894 | −0.285447 | − | 0.958395i | \(-0.592142\pi\) | ||||
−0.285447 | + | 0.958395i | \(0.592142\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.00000 | −0.229416 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −4.89449 | −1.04351 | ||||||||
\(23\) | −6.16707 | −1.28592 | −0.642962 | − | 0.765898i | \(-0.722295\pi\) | ||||
−0.642962 | + | 0.765898i | \(0.722295\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 1.89449 | 0.371541 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 2.35386 | 0.444837 | ||||||||
\(29\) | −4.27258 | −0.793398 | −0.396699 | − | 0.917949i | \(-0.629844\pi\) | ||||
−0.396699 | + | 0.917949i | \(0.629844\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 7.70771 | 1.38435 | 0.692173 | − | 0.721732i | \(-0.256654\pi\) | ||||
0.692173 | + | 0.721732i | \(0.256654\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −2.35386 | −0.403683 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −7.78899 | −1.28050 | −0.640251 | − | 0.768166i | \(-0.721170\pi\) | ||||
−0.640251 | + | 0.768166i | \(0.721170\pi\) | |||||||
\(38\) | −1.00000 | −0.162221 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −3.54064 | −0.552955 | −0.276477 | − | 0.961020i | \(-0.589167\pi\) | ||||
−0.276477 | + | 0.961020i | \(0.589167\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.73194 | 0.264119 | 0.132060 | − | 0.991242i | \(-0.457841\pi\) | ||||
0.132060 | + | 0.991242i | \(0.457841\pi\) | |||||||
\(44\) | −4.89449 | −0.737873 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −6.16707 | −0.909286 | ||||||||
\(47\) | −5.32962 | −0.777405 | −0.388703 | − | 0.921363i | \(-0.627077\pi\) | ||||
−0.388703 | + | 0.921363i | \(0.627077\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.45936 | −0.208480 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 1.89449 | 0.262719 | ||||||||
\(53\) | −1.97577 | −0.271392 | −0.135696 | − | 0.990750i | \(-0.543327\pi\) | ||||
−0.135696 | + | 0.990750i | \(0.543327\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 2.35386 | 0.314547 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −4.27258 | −0.561017 | ||||||||
\(59\) | −6.81322 | −0.887006 | −0.443503 | − | 0.896273i | \(-0.646264\pi\) | ||||
−0.443503 | + | 0.896273i | \(0.646264\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 3.97577 | 0.509045 | 0.254522 | − | 0.967067i | \(-0.418082\pi\) | ||||
0.254522 | + | 0.967067i | \(0.418082\pi\) | |||||||
\(62\) | 7.70771 | 0.978880 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −5.19131 | −0.634219 | −0.317110 | − | 0.948389i | \(-0.602712\pi\) | ||||
−0.317110 | + | 0.948389i | \(0.602712\pi\) | |||||||
\(68\) | −2.35386 | −0.285447 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 4.14284 | 0.491665 | 0.245832 | − | 0.969312i | \(-0.420939\pi\) | ||||
0.245832 | + | 0.969312i | \(0.420939\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −4.37809 | −0.512417 | −0.256208 | − | 0.966622i | \(-0.582473\pi\) | ||||
−0.256208 | + | 0.966622i | \(0.582473\pi\) | |||||||
\(74\) | −7.78899 | −0.905451 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −1.00000 | −0.114708 | ||||||||
\(77\) | −11.5209 | −1.31293 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 9.49670 | 1.06846 | 0.534231 | − | 0.845339i | \(-0.320601\pi\) | ||||
0.534231 | + | 0.845339i | \(0.320601\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −3.54064 | −0.390998 | ||||||||
\(83\) | −4.43513 | −0.486819 | −0.243409 | − | 0.969924i | \(-0.578266\pi\) | ||||
−0.243409 | + | 0.969924i | \(0.578266\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 1.73194 | 0.186760 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −4.89449 | −0.521755 | ||||||||
\(89\) | −3.62191 | −0.383922 | −0.191961 | − | 0.981403i | \(-0.561485\pi\) | ||||
−0.191961 | + | 0.981403i | \(0.561485\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 4.45936 | 0.467468 | ||||||||
\(92\) | −6.16707 | −0.642962 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −5.32962 | −0.549709 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −7.06157 | −0.716994 | −0.358497 | − | 0.933531i | \(-0.616711\pi\) | ||||
−0.358497 | + | 0.933531i | \(0.616711\pi\) | |||||||
\(98\) | −1.45936 | −0.147418 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −6.10551 | −0.607521 | −0.303760 | − | 0.952748i | \(-0.598242\pi\) | ||||
−0.303760 | + | 0.952748i | \(0.598242\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −11.2483 | −1.10833 | −0.554166 | − | 0.832406i | \(-0.686963\pi\) | ||||
−0.554166 | + | 0.832406i | \(0.686963\pi\) | |||||||
\(104\) | 1.89449 | 0.185770 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −1.97577 | −0.191903 | ||||||||
\(107\) | 15.3099 | 1.48007 | 0.740033 | − | 0.672571i | \(-0.234810\pi\) | ||||
0.740033 | + | 0.672571i | \(0.234810\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −14.7077 | −1.40874 | −0.704372 | − | 0.709831i | \(-0.748771\pi\) | ||||
−0.704372 | + | 0.709831i | \(0.748771\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 2.35386 | 0.222418 | ||||||||
\(113\) | −3.29681 | −0.310138 | −0.155069 | − | 0.987904i | \(-0.549560\pi\) | ||||
−0.155069 | + | 0.987904i | \(0.549560\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −4.27258 | −0.396699 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −6.81322 | −0.627208 | ||||||||
\(119\) | −5.54064 | −0.507909 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 12.9561 | 1.17782 | ||||||||
\(122\) | 3.97577 | 0.359949 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 7.70771 | 0.692173 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 6.62644 | 0.588001 | 0.294001 | − | 0.955805i | \(-0.405013\pi\) | ||||
0.294001 | + | 0.955805i | \(0.405013\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −16.9803 | −1.48358 | −0.741788 | − | 0.670635i | \(-0.766022\pi\) | ||||
−0.741788 | + | 0.670635i | \(0.766022\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −2.35386 | −0.204105 | ||||||||
\(134\) | −5.19131 | −0.448461 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −2.35386 | −0.201841 | ||||||||
\(137\) | 12.8703 | 1.09958 | 0.549790 | − | 0.835303i | \(-0.314708\pi\) | ||||
0.549790 | + | 0.835303i | \(0.314708\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 9.30992 | 0.789657 | 0.394828 | − | 0.918755i | \(-0.370804\pi\) | ||||
0.394828 | + | 0.918755i | \(0.370804\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 4.14284 | 0.347660 | ||||||||
\(143\) | −9.27258 | −0.775412 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −4.37809 | −0.362333 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −7.78899 | −0.640251 | ||||||||
\(149\) | 16.1231 | 1.32086 | 0.660429 | − | 0.750888i | \(-0.270374\pi\) | ||||
0.660429 | + | 0.750888i | \(0.270374\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −15.6638 | −1.27470 | −0.637350 | − | 0.770575i | \(-0.719969\pi\) | ||||
−0.637350 | + | 0.770575i | \(0.719969\pi\) | |||||||
\(152\) | −1.00000 | −0.0811107 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −11.5209 | −0.928383 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 14.2483 | 1.13714 | 0.568571 | − | 0.822634i | \(-0.307496\pi\) | ||||
0.568571 | + | 0.822634i | \(0.307496\pi\) | |||||||
\(158\) | 9.49670 | 0.755517 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −14.5164 | −1.14405 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −6.00000 | −0.469956 | −0.234978 | − | 0.972001i | \(-0.575502\pi\) | ||||
−0.234978 | + | 0.972001i | \(0.575502\pi\) | |||||||
\(164\) | −3.54064 | −0.276477 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −4.43513 | −0.344233 | ||||||||
\(167\) | 0.756178 | 0.0585148 | 0.0292574 | − | 0.999572i | \(-0.490686\pi\) | ||||
0.0292574 | + | 0.999572i | \(0.490686\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −9.41090 | −0.723915 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 1.73194 | 0.132060 | ||||||||
\(173\) | 13.6880 | 1.04068 | 0.520340 | − | 0.853959i | \(-0.325805\pi\) | ||||
0.520340 | + | 0.853959i | \(0.325805\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −4.89449 | −0.368936 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −3.62191 | −0.271474 | ||||||||
\(179\) | −23.2044 | −1.73438 | −0.867189 | − | 0.497978i | \(-0.834076\pi\) | ||||
−0.867189 | + | 0.497978i | \(0.834076\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 6.65067 | 0.494340 | 0.247170 | − | 0.968972i | \(-0.420499\pi\) | ||||
0.247170 | + | 0.968972i | \(0.420499\pi\) | |||||||
\(182\) | 4.45936 | 0.330550 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −6.16707 | −0.454643 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 11.5209 | 0.842494 | ||||||||
\(188\) | −5.32962 | −0.388703 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −14.7890 | −1.07009 | −0.535047 | − | 0.844822i | \(-0.679706\pi\) | ||||
−0.535047 | + | 0.844822i | \(0.679706\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −11.5977 | −0.834819 | −0.417410 | − | 0.908718i | \(-0.637062\pi\) | ||||
−0.417410 | + | 0.908718i | \(0.637062\pi\) | |||||||
\(194\) | −7.06157 | −0.506991 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −1.45936 | −0.104240 | ||||||||
\(197\) | 12.6022 | 0.897870 | 0.448935 | − | 0.893564i | \(-0.351803\pi\) | ||||
0.448935 | + | 0.893564i | \(0.351803\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −23.7405 | −1.68292 | −0.841460 | − | 0.540319i | \(-0.818304\pi\) | ||||
−0.841460 | + | 0.540319i | \(0.818304\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −6.10551 | −0.429582 | ||||||||
\(203\) | −10.0570 | −0.705866 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −11.2483 | −0.783710 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 1.89449 | 0.131359 | ||||||||
\(209\) | 4.89449 | 0.338559 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 19.9848 | 1.37581 | 0.687906 | − | 0.725800i | \(-0.258530\pi\) | ||||
0.687906 | + | 0.725800i | \(0.258530\pi\) | |||||||
\(212\) | −1.97577 | −0.135696 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 15.3099 | 1.04656 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 18.1428 | 1.23162 | ||||||||
\(218\) | −14.7077 | −0.996132 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −4.45936 | −0.299969 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −18.7122 | −1.25306 | −0.626532 | − | 0.779396i | \(-0.715526\pi\) | ||||
−0.626532 | + | 0.779396i | \(0.715526\pi\) | |||||||
\(224\) | 2.35386 | 0.157274 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −3.29681 | −0.219301 | ||||||||
\(227\) | 13.0813 | 0.868235 | 0.434117 | − | 0.900856i | \(-0.357060\pi\) | ||||
0.434117 | + | 0.900856i | \(0.357060\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −9.89902 | −0.654146 | −0.327073 | − | 0.944999i | \(-0.606062\pi\) | ||||
−0.327073 | + | 0.944999i | \(0.606062\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −4.27258 | −0.280509 | ||||||||
\(233\) | 12.6395 | 0.828044 | 0.414022 | − | 0.910267i | \(-0.364124\pi\) | ||||
0.414022 | + | 0.910267i | \(0.364124\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −6.81322 | −0.443503 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −5.54064 | −0.359146 | ||||||||
\(239\) | 20.1605 | 1.30407 | 0.652036 | − | 0.758188i | \(-0.273915\pi\) | ||||
0.652036 | + | 0.758188i | \(0.273915\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −11.7693 | −0.758126 | −0.379063 | − | 0.925371i | \(-0.623754\pi\) | ||||
−0.379063 | + | 0.925371i | \(0.623754\pi\) | |||||||
\(242\) | 12.9561 | 0.832847 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 3.97577 | 0.254522 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1.89449 | −0.120544 | ||||||||
\(248\) | 7.70771 | 0.489440 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 18.3715 | 1.15960 | 0.579799 | − | 0.814760i | \(-0.303131\pi\) | ||||
0.579799 | + | 0.814760i | \(0.303131\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 30.1847 | 1.89770 | ||||||||
\(254\) | 6.62644 | 0.415780 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 3.83293 | 0.239091 | 0.119546 | − | 0.992829i | \(-0.461856\pi\) | ||||
0.119546 | + | 0.992829i | \(0.461856\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −18.3341 | −1.13923 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −16.9803 | −1.04905 | ||||||||
\(263\) | −21.2483 | −1.31023 | −0.655115 | − | 0.755529i | \(-0.727380\pi\) | ||||
−0.655115 | + | 0.755529i | \(0.727380\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −2.35386 | −0.144324 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −5.19131 | −0.317110 | ||||||||
\(269\) | −5.78899 | −0.352961 | −0.176480 | − | 0.984304i | \(-0.556471\pi\) | ||||
−0.176480 | + | 0.984304i | \(0.556471\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 4.01971 | 0.244180 | 0.122090 | − | 0.992519i | \(-0.461040\pi\) | ||||
0.122090 | + | 0.992519i | \(0.461040\pi\) | |||||||
\(272\) | −2.35386 | −0.142723 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 12.8703 | 0.777521 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −12.0989 | −0.726953 | −0.363476 | − | 0.931603i | \(-0.618410\pi\) | ||||
−0.363476 | + | 0.931603i | \(0.618410\pi\) | |||||||
\(278\) | 9.30992 | 0.558372 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −9.21101 | −0.549483 | −0.274742 | − | 0.961518i | \(-0.588592\pi\) | ||||
−0.274742 | + | 0.961518i | \(0.588592\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 8.49670 | 0.505076 | 0.252538 | − | 0.967587i | \(-0.418735\pi\) | ||||
0.252538 | + | 0.967587i | \(0.418735\pi\) | |||||||
\(284\) | 4.14284 | 0.245832 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −9.27258 | −0.548299 | ||||||||
\(287\) | −8.33415 | −0.491949 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −11.4594 | −0.674080 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −4.37809 | −0.256208 | ||||||||
\(293\) | 12.0989 | 0.706825 | 0.353413 | − | 0.935468i | \(-0.385021\pi\) | ||||
0.353413 | + | 0.935468i | \(0.385021\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −7.78899 | −0.452726 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 16.1231 | 0.933988 | ||||||||
\(299\) | −11.6835 | −0.675673 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 4.07675 | 0.234980 | ||||||||
\(302\) | −15.6638 | −0.901349 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −1.00000 | −0.0573539 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 20.9318 | 1.19464 | 0.597321 | − | 0.802002i | \(-0.296232\pi\) | ||||
0.597321 | + | 0.802002i | \(0.296232\pi\) | |||||||
\(308\) | −11.5209 | −0.656466 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −14.9561 | −0.848080 | −0.424040 | − | 0.905643i | \(-0.639388\pi\) | ||||
−0.424040 | + | 0.905643i | \(0.639388\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 32.2902 | 1.82515 | 0.912575 | − | 0.408909i | \(-0.134091\pi\) | ||||
0.912575 | + | 0.408909i | \(0.134091\pi\) | |||||||
\(314\) | 14.2483 | 0.804081 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 9.49670 | 0.534231 | ||||||||
\(317\) | 24.2726 | 1.36328 | 0.681642 | − | 0.731686i | \(-0.261266\pi\) | ||||
0.681642 | + | 0.731686i | \(0.261266\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 20.9121 | 1.17085 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −14.5164 | −0.808968 | ||||||||
\(323\) | 2.35386 | 0.130972 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −6.00000 | −0.332309 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −3.54064 | −0.195499 | ||||||||
\(329\) | −12.5452 | −0.691637 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 6.80869 | 0.374240 | 0.187120 | − | 0.982337i | \(-0.440085\pi\) | ||||
0.187120 | + | 0.982337i | \(0.440085\pi\) | |||||||
\(332\) | −4.43513 | −0.243409 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0.756178 | 0.0413762 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −16.1231 | −0.878283 | −0.439142 | − | 0.898418i | \(-0.644717\pi\) | ||||
−0.439142 | + | 0.898418i | \(0.644717\pi\) | |||||||
\(338\) | −9.41090 | −0.511885 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −37.7253 | −2.04294 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −19.9121 | −1.07515 | ||||||||
\(344\) | 1.73194 | 0.0933802 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 13.6880 | 0.735872 | ||||||||
\(347\) | 23.3670 | 1.25440 | 0.627202 | − | 0.778857i | \(-0.284200\pi\) | ||||
0.627202 | + | 0.778857i | \(0.284200\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 16.5977 | 0.888453 | 0.444227 | − | 0.895914i | \(-0.353478\pi\) | ||||
0.444227 | + | 0.895914i | \(0.353478\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −4.89449 | −0.260877 | ||||||||
\(353\) | −5.32105 | −0.283211 | −0.141605 | − | 0.989923i | \(-0.545226\pi\) | ||||
−0.141605 | + | 0.989923i | \(0.545226\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −3.62191 | −0.191961 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −23.2044 | −1.22639 | ||||||||
\(359\) | −6.67038 | −0.352049 | −0.176025 | − | 0.984386i | \(-0.556324\pi\) | ||||
−0.176025 | + | 0.984386i | \(0.556324\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 6.65067 | 0.349551 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 4.45936 | 0.233734 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −8.14284 | −0.425053 | −0.212526 | − | 0.977155i | \(-0.568169\pi\) | ||||
−0.212526 | + | 0.977155i | \(0.568169\pi\) | |||||||
\(368\) | −6.16707 | −0.321481 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −4.65067 | −0.241451 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −3.94296 | −0.204159 | −0.102079 | − | 0.994776i | \(-0.532550\pi\) | ||||
−0.102079 | + | 0.994776i | \(0.532550\pi\) | |||||||
\(374\) | 11.5209 | 0.595733 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −5.32962 | −0.274854 | ||||||||
\(377\) | −8.09438 | −0.416882 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −33.2044 | −1.70560 | −0.852798 | − | 0.522241i | \(-0.825096\pi\) | ||||
−0.852798 | + | 0.522241i | \(0.825096\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −14.7890 | −0.756670 | ||||||||
\(383\) | −19.3867 | −0.990612 | −0.495306 | − | 0.868719i | \(-0.664944\pi\) | ||||
−0.495306 | + | 0.868719i | \(0.664944\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −11.5977 | −0.590306 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −7.06157 | −0.358497 | ||||||||
\(389\) | 6.87026 | 0.348336 | 0.174168 | − | 0.984716i | \(-0.444276\pi\) | ||||
0.174168 | + | 0.984716i | \(0.444276\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 14.5164 | 0.734126 | ||||||||
\(392\) | −1.45936 | −0.0737090 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 12.6022 | 0.634890 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −21.8879 | −1.09852 | −0.549261 | − | 0.835651i | \(-0.685091\pi\) | ||||
−0.549261 | + | 0.835651i | \(0.685091\pi\) | |||||||
\(398\) | −23.7405 | −1.19000 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −7.49670 | −0.374367 | −0.187184 | − | 0.982325i | \(-0.559936\pi\) | ||||
−0.187184 | + | 0.982325i | \(0.559936\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 14.6022 | 0.727388 | ||||||||
\(404\) | −6.10551 | −0.303760 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −10.0570 | −0.499123 | ||||||||
\(407\) | 38.1231 | 1.88969 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 4.21101 | 0.208221 | 0.104111 | − | 0.994566i | \(-0.466800\pi\) | ||||
0.104111 | + | 0.994566i | \(0.466800\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −11.2483 | −0.554166 | ||||||||
\(413\) | −16.0373 | −0.789146 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 1.89449 | 0.0928852 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 4.89449 | 0.239397 | ||||||||
\(419\) | −10.8703 | −0.531047 | −0.265523 | − | 0.964104i | \(-0.585545\pi\) | ||||
−0.265523 | + | 0.964104i | \(0.585545\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 33.7496 | 1.64485 | 0.822427 | − | 0.568871i | \(-0.192620\pi\) | ||||
0.822427 | + | 0.568871i | \(0.192620\pi\) | |||||||
\(422\) | 19.9848 | 0.972846 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −1.97577 | −0.0959517 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 9.35838 | 0.452884 | ||||||||
\(428\) | 15.3099 | 0.740033 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 15.7011 | 0.756296 | 0.378148 | − | 0.925745i | \(-0.376561\pi\) | ||||
0.378148 | + | 0.925745i | \(0.376561\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −15.1847 | −0.729730 | −0.364865 | − | 0.931060i | \(-0.618885\pi\) | ||||
−0.364865 | + | 0.931060i | \(0.618885\pi\) | |||||||
\(434\) | 18.1428 | 0.870884 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −14.7077 | −0.704372 | ||||||||
\(437\) | 6.16707 | 0.295011 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −25.4482 | −1.21458 | −0.607289 | − | 0.794481i | \(-0.707743\pi\) | ||||
−0.607289 | + | 0.794481i | \(0.707743\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −4.45936 | −0.212110 | ||||||||
\(443\) | −24.4351 | −1.16095 | −0.580474 | − | 0.814279i | \(-0.697133\pi\) | ||||
−0.580474 | + | 0.814279i | \(0.697133\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −18.7122 | −0.886050 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 2.35386 | 0.111209 | ||||||||
\(449\) | −26.5012 | −1.25067 | −0.625335 | − | 0.780356i | \(-0.715038\pi\) | ||||
−0.625335 | + | 0.780356i | \(0.715038\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 17.3296 | 0.816020 | ||||||||
\(452\) | −3.29681 | −0.155069 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 13.0813 | 0.613935 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 36.3230 | 1.69912 | 0.849560 | − | 0.527493i | \(-0.176868\pi\) | ||||
0.849560 | + | 0.527493i | \(0.176868\pi\) | |||||||
\(458\) | −9.89902 | −0.462551 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −23.0813 | −1.07500 | −0.537501 | − | 0.843263i | \(-0.680632\pi\) | ||||
−0.537501 | + | 0.843263i | \(0.680632\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −31.0419 | −1.44264 | −0.721319 | − | 0.692603i | \(-0.756464\pi\) | ||||
−0.721319 | + | 0.692603i | \(0.756464\pi\) | |||||||
\(464\) | −4.27258 | −0.198350 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 12.6395 | 0.585515 | ||||||||
\(467\) | −16.6925 | −0.772438 | −0.386219 | − | 0.922407i | \(-0.626219\pi\) | ||||
−0.386219 | + | 0.922407i | \(0.626219\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −12.2196 | −0.564248 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −6.81322 | −0.313604 | ||||||||
\(473\) | −8.47699 | −0.389772 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −5.54064 | −0.253955 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 20.1605 | 0.922118 | ||||||||
\(479\) | 12.5891 | 0.575211 | 0.287605 | − | 0.957749i | \(-0.407141\pi\) | ||||
0.287605 | + | 0.957749i | \(0.407141\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −14.7562 | −0.672824 | ||||||||
\(482\) | −11.7693 | −0.536076 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 12.9561 | 0.588912 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −20.7077 | −0.938356 | −0.469178 | − | 0.883104i | \(-0.655450\pi\) | ||||
−0.469178 | + | 0.883104i | \(0.655450\pi\) | |||||||
\(488\) | 3.97577 | 0.179975 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −20.0747 | −0.905957 | −0.452979 | − | 0.891521i | \(-0.649639\pi\) | ||||
−0.452979 | + | 0.891521i | \(0.649639\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 10.0570 | 0.452946 | ||||||||
\(494\) | −1.89449 | −0.0852373 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 7.70771 | 0.346086 | ||||||||
\(497\) | 9.75165 | 0.437421 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 41.5956 | 1.86207 | 0.931037 | − | 0.364924i | \(-0.118905\pi\) | ||||
0.931037 | + | 0.364924i | \(0.118905\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 18.3715 | 0.819959 | ||||||||
\(503\) | −16.0000 | −0.713405 | −0.356702 | − | 0.934218i | \(-0.616099\pi\) | ||||
−0.356702 | + | 0.934218i | \(0.616099\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 30.1847 | 1.34187 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 6.62644 | 0.294001 | ||||||||
\(509\) | −25.8879 | −1.14746 | −0.573730 | − | 0.819044i | \(-0.694504\pi\) | ||||
−0.573730 | + | 0.819044i | \(0.694504\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −10.3054 | −0.455884 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 3.83293 | 0.169063 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 26.0858 | 1.14725 | ||||||||
\(518\) | −18.3341 | −0.805556 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 24.5386 | 1.07505 | 0.537527 | − | 0.843247i | \(-0.319359\pi\) | ||||
0.537527 | + | 0.843247i | \(0.319359\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 4.21101 | 0.184135 | 0.0920674 | − | 0.995753i | \(-0.470652\pi\) | ||||
0.0920674 | + | 0.995753i | \(0.470652\pi\) | |||||||
\(524\) | −16.9803 | −0.741788 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −21.2483 | −0.926472 | ||||||||
\(527\) | −18.1428 | −0.790315 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 15.0328 | 0.653600 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −2.35386 | −0.102053 | ||||||||
\(533\) | −6.70771 | −0.290543 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −5.19131 | −0.224230 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −5.78899 | −0.249581 | ||||||||
\(539\) | 7.14284 | 0.307664 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −12.7208 | −0.546910 | −0.273455 | − | 0.961885i | \(-0.588167\pi\) | ||||
−0.273455 | + | 0.961885i | \(0.588167\pi\) | |||||||
\(542\) | 4.01971 | 0.172661 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −2.35386 | −0.100921 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 5.97577 | 0.255505 | 0.127753 | − | 0.991806i | \(-0.459224\pi\) | ||||
0.127753 | + | 0.991806i | \(0.459224\pi\) | |||||||
\(548\) | 12.8703 | 0.549790 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 4.27258 | 0.182018 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 22.3539 | 0.950583 | ||||||||
\(554\) | −12.0989 | −0.514033 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 9.30992 | 0.394828 | ||||||||
\(557\) | 29.6441 | 1.25606 | 0.628030 | − | 0.778189i | \(-0.283862\pi\) | ||||
0.628030 | + | 0.778189i | \(0.283862\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 3.28116 | 0.138778 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −9.21101 | −0.388543 | ||||||||
\(563\) | 24.3427 | 1.02592 | 0.512962 | − | 0.858411i | \(-0.328548\pi\) | ||||
0.512962 | + | 0.858411i | \(0.328548\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 8.49670 | 0.357143 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 4.14284 | 0.173830 | ||||||||
\(569\) | 23.6264 | 0.990472 | 0.495236 | − | 0.868759i | \(-0.335082\pi\) | ||||
0.495236 | + | 0.868759i | \(0.335082\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 8.81322 | 0.368822 | 0.184411 | − | 0.982849i | \(-0.440962\pi\) | ||||
0.184411 | + | 0.982849i | \(0.440962\pi\) | |||||||
\(572\) | −9.27258 | −0.387706 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −8.33415 | −0.347861 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 36.9121 | 1.53667 | 0.768336 | − | 0.640047i | \(-0.221085\pi\) | ||||
0.768336 | + | 0.640047i | \(0.221085\pi\) | |||||||
\(578\) | −11.4594 | −0.476647 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −10.4397 | −0.433110 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 9.67038 | 0.400506 | ||||||||
\(584\) | −4.37809 | −0.181167 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 12.0989 | 0.499801 | ||||||||
\(587\) | −15.9737 | −0.659305 | −0.329652 | − | 0.944102i | \(-0.606932\pi\) | ||||
−0.329652 | + | 0.944102i | \(0.606932\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −7.70771 | −0.317591 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −7.78899 | −0.320125 | ||||||||
\(593\) | 4.22007 | 0.173297 | 0.0866487 | − | 0.996239i | \(-0.472384\pi\) | ||||
0.0866487 | + | 0.996239i | \(0.472384\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 16.1231 | 0.660429 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −11.6835 | −0.477773 | ||||||||
\(599\) | 21.6552 | 0.884807 | 0.442404 | − | 0.896816i | \(-0.354126\pi\) | ||||
0.442404 | + | 0.896816i | \(0.354126\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −30.0944 | −1.22758 | −0.613788 | − | 0.789471i | \(-0.710355\pi\) | ||||
−0.613788 | + | 0.789471i | \(0.710355\pi\) | |||||||
\(602\) | 4.07675 | 0.166156 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −15.6638 | −0.637350 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 14.9979 | 0.608747 | 0.304373 | − | 0.952553i | \(-0.401553\pi\) | ||||
0.304373 | + | 0.952553i | \(0.401553\pi\) | |||||||
\(608\) | −1.00000 | −0.0405554 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −10.0969 | −0.408478 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 16.7562 | 0.676776 | 0.338388 | − | 0.941007i | \(-0.390118\pi\) | ||||
0.338388 | + | 0.941007i | \(0.390118\pi\) | |||||||
\(614\) | 20.9318 | 0.844740 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −11.5209 | −0.464192 | ||||||||
\(617\) | 18.1141 | 0.729245 | 0.364623 | − | 0.931155i | \(-0.381198\pi\) | ||||
0.364623 | + | 0.931155i | \(0.381198\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −36.0176 | −1.44767 | −0.723835 | − | 0.689973i | \(-0.757622\pi\) | ||||
−0.723835 | + | 0.689973i | \(0.757622\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −14.9561 | −0.599683 | ||||||||
\(623\) | −8.52546 | −0.341565 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 32.2902 | 1.29058 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 14.2483 | 0.568571 | ||||||||
\(629\) | 18.3341 | 0.731030 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 17.6749 | 0.703627 | 0.351813 | − | 0.936070i | \(-0.385565\pi\) | ||||
0.351813 | + | 0.936070i | \(0.385565\pi\) | |||||||
\(632\) | 9.49670 | 0.377758 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 24.2726 | 0.963987 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −2.76475 | −0.109543 | ||||||||
\(638\) | 20.9121 | 0.827919 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 2.08580 | 0.0823842 | 0.0411921 | − | 0.999151i | \(-0.486884\pi\) | ||||
0.0411921 | + | 0.999151i | \(0.486884\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −37.5295 | −1.48002 | −0.740010 | − | 0.672596i | \(-0.765179\pi\) | ||||
−0.740010 | + | 0.672596i | \(0.765179\pi\) | |||||||
\(644\) | −14.5164 | −0.572026 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 2.35386 | 0.0926112 | ||||||||
\(647\) | −9.12521 | −0.358749 | −0.179375 | − | 0.983781i | \(-0.557407\pi\) | ||||
−0.179375 | + | 0.983781i | \(0.557407\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 33.3473 | 1.30899 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −6.00000 | −0.234978 | ||||||||
\(653\) | −13.2529 | −0.518625 | −0.259313 | − | 0.965793i | \(-0.583496\pi\) | ||||
−0.259313 | + | 0.965793i | \(0.583496\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −3.54064 | −0.138239 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −12.5452 | −0.489061 | ||||||||
\(659\) | −24.9364 | −0.971382 | −0.485691 | − | 0.874130i | \(-0.661432\pi\) | ||||
−0.485691 | + | 0.874130i | \(0.661432\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −29.9606 | −1.16533 | −0.582666 | − | 0.812712i | \(-0.697990\pi\) | ||||
−0.582666 | + | 0.812712i | \(0.697990\pi\) | |||||||
\(662\) | 6.80869 | 0.264627 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −4.43513 | −0.172116 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 26.3493 | 1.02025 | ||||||||
\(668\) | 0.756178 | 0.0292574 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −19.4594 | −0.751220 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −2.85055 | −0.109881 | −0.0549404 | − | 0.998490i | \(-0.517497\pi\) | ||||
−0.0549404 | + | 0.998490i | \(0.517497\pi\) | |||||||
\(674\) | −16.1231 | −0.621040 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −9.41090 | −0.361958 | ||||||||
\(677\) | 42.5562 | 1.63557 | 0.817784 | − | 0.575526i | \(-0.195203\pi\) | ||||
0.817784 | + | 0.575526i | \(0.195203\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −16.6219 | −0.637890 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −37.7253 | −1.44458 | ||||||||
\(683\) | 12.2286 | 0.467916 | 0.233958 | − | 0.972247i | \(-0.424832\pi\) | ||||
0.233958 | + | 0.972247i | \(0.424832\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −19.9121 | −0.760248 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 1.73194 | 0.0660298 | ||||||||
\(689\) | −3.74308 | −0.142600 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 21.7581 | 0.827719 | 0.413859 | − | 0.910341i | \(-0.364180\pi\) | ||||
0.413859 | + | 0.910341i | \(0.364180\pi\) | |||||||
\(692\) | 13.6880 | 0.520340 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 23.3670 | 0.886998 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 8.33415 | 0.315678 | ||||||||
\(698\) | 16.5977 | 0.628231 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −28.6592 | −1.08244 | −0.541222 | − | 0.840880i | \(-0.682038\pi\) | ||||
−0.541222 | + | 0.840880i | \(0.682038\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 7.78899 | 0.293767 | ||||||||
\(704\) | −4.89449 | −0.184468 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −5.32105 | −0.200260 | ||||||||
\(707\) | −14.3715 | −0.540495 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 6.69461 | 0.251421 | 0.125711 | − | 0.992067i | \(-0.459879\pi\) | ||||
0.125711 | + | 0.992067i | \(0.459879\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −3.62191 | −0.135737 | ||||||||
\(713\) | −47.5340 | −1.78016 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −23.2044 | −0.867189 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −6.67038 | −0.248936 | ||||||||
\(719\) | −24.7980 | −0.924811 | −0.462405 | − | 0.886669i | \(-0.653014\pi\) | ||||
−0.462405 | + | 0.886669i | \(0.653014\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −26.4770 | −0.986055 | ||||||||
\(722\) | 1.00000 | 0.0372161 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 6.65067 | 0.247170 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 33.0328 | 1.22512 | 0.612560 | − | 0.790424i | \(-0.290140\pi\) | ||||
0.612560 | + | 0.790424i | \(0.290140\pi\) | |||||||
\(728\) | 4.45936 | 0.165275 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −4.07675 | −0.150784 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 42.5098 | 1.57014 | 0.785068 | − | 0.619410i | \(-0.212628\pi\) | ||||
0.785068 | + | 0.619410i | \(0.212628\pi\) | |||||||
\(734\) | −8.14284 | −0.300558 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −6.16707 | −0.227321 | ||||||||
\(737\) | 25.4088 | 0.935946 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 1.20441 | 0.0443049 | 0.0221524 | − | 0.999755i | \(-0.492948\pi\) | ||||
0.0221524 | + | 0.999755i | \(0.492948\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −4.65067 | −0.170731 | ||||||||
\(743\) | −21.5870 | −0.791951 | −0.395976 | − | 0.918261i | \(-0.629594\pi\) | ||||
−0.395976 | + | 0.918261i | \(0.629594\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −3.94296 | −0.144362 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 11.5209 | 0.421247 | ||||||||
\(749\) | 36.0373 | 1.31678 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −42.2089 | −1.54023 | −0.770113 | − | 0.637908i | \(-0.779800\pi\) | ||||
−0.770113 | + | 0.637908i | \(0.779800\pi\) | |||||||
\(752\) | −5.32962 | −0.194351 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −8.09438 | −0.294780 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 32.3867 | 1.17711 | 0.588557 | − | 0.808456i | \(-0.299696\pi\) | ||||
0.588557 | + | 0.808456i | \(0.299696\pi\) | |||||||
\(758\) | −33.2044 | −1.20604 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 43.1362 | 1.56369 | 0.781844 | − | 0.623475i | \(-0.214279\pi\) | ||||
0.781844 | + | 0.623475i | \(0.214279\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −34.6198 | −1.25332 | ||||||||
\(764\) | −14.7890 | −0.535047 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −19.3867 | −0.700469 | ||||||||
\(767\) | −12.9076 | −0.466066 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −33.7541 | −1.21720 | −0.608602 | − | 0.793476i | \(-0.708269\pi\) | ||||
−0.608602 | + | 0.793476i | \(0.708269\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −11.5977 | −0.417410 | ||||||||
\(773\) | −44.9055 | −1.61514 | −0.807570 | − | 0.589772i | \(-0.799217\pi\) | ||||
−0.807570 | + | 0.589772i | \(0.799217\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −7.06157 | −0.253495 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 6.87026 | 0.246311 | ||||||||
\(779\) | 3.54064 | 0.126856 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −20.2771 | −0.725572 | ||||||||
\(782\) | 14.5164 | 0.519106 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −1.45936 | −0.0521201 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −23.0550 | −0.821821 | −0.410910 | − | 0.911676i | \(-0.634789\pi\) | ||||
−0.410910 | + | 0.911676i | \(0.634789\pi\) | |||||||
\(788\) | 12.6022 | 0.448935 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −7.76023 | −0.275922 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 7.53206 | 0.267471 | ||||||||
\(794\) | −21.8879 | −0.776772 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −23.7405 | −0.841460 | ||||||||
\(797\) | −35.7384 | −1.26592 | −0.632960 | − | 0.774184i | \(-0.718160\pi\) | ||||
−0.632960 | + | 0.774184i | \(0.718160\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 12.5452 | 0.443816 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −7.49670 | −0.264718 | ||||||||
\(803\) | 21.4285 | 0.756196 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 14.6022 | 0.514341 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −6.10551 | −0.214791 | ||||||||
\(809\) | −21.0525 | −0.740167 | −0.370084 | − | 0.928998i | \(-0.620671\pi\) | ||||
−0.370084 | + | 0.928998i | \(0.620671\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 17.3912 | 0.610687 | 0.305344 | − | 0.952242i | \(-0.401229\pi\) | ||||
0.305344 | + | 0.952242i | \(0.401229\pi\) | |||||||
\(812\) | −10.0570 | −0.352933 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 38.1231 | 1.33622 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −1.73194 | −0.0605931 | ||||||||
\(818\) | 4.21101 | 0.147235 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −6.43966 | −0.224746 | −0.112373 | − | 0.993666i | \(-0.535845\pi\) | ||||
−0.112373 | + | 0.993666i | \(0.535845\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 22.8308 | 0.795833 | 0.397917 | − | 0.917422i | \(-0.369733\pi\) | ||||
0.397917 | + | 0.917422i | \(0.369733\pi\) | |||||||
\(824\) | −11.2483 | −0.391855 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −16.0373 | −0.558010 | ||||||||
\(827\) | 29.2705 | 1.01784 | 0.508918 | − | 0.860815i | \(-0.330046\pi\) | ||||
0.508918 | + | 0.860815i | \(0.330046\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −22.5053 | −0.781640 | −0.390820 | − | 0.920467i | \(-0.627809\pi\) | ||||
−0.390820 | + | 0.920467i | \(0.627809\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 1.89449 | 0.0656797 | ||||||||
\(833\) | 3.43513 | 0.119020 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 4.89449 | 0.169280 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −10.8703 | −0.375507 | ||||||||
\(839\) | 25.2241 | 0.870833 | 0.435417 | − | 0.900229i | \(-0.356601\pi\) | ||||
0.435417 | + | 0.900229i | \(0.356601\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −10.7450 | −0.370519 | ||||||||
\(842\) | 33.7496 | 1.16309 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 19.9848 | 0.687906 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 30.4967 | 1.04788 | ||||||||
\(848\) | −1.97577 | −0.0678481 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 48.0353 | 1.64663 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 19.4548 | 0.666121 | 0.333060 | − | 0.942905i | \(-0.391919\pi\) | ||||
0.333060 | + | 0.942905i | \(0.391919\pi\) | |||||||
\(854\) | 9.35838 | 0.320237 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 15.3099 | 0.523282 | ||||||||
\(857\) | −50.2351 | −1.71600 | −0.858000 | − | 0.513650i | \(-0.828293\pi\) | ||||
−0.858000 | + | 0.513650i | \(0.828293\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −5.82840 | −0.198862 | −0.0994312 | − | 0.995044i | \(-0.531702\pi\) | ||||
−0.0994312 | + | 0.995044i | \(0.531702\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 15.7011 | 0.534782 | ||||||||
\(863\) | −8.37356 | −0.285039 | −0.142520 | − | 0.989792i | \(-0.545520\pi\) | ||||
−0.142520 | + | 0.989792i | \(0.545520\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −15.1847 | −0.515997 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 18.1428 | 0.615808 | ||||||||
\(869\) | −46.4815 | −1.57678 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −9.83490 | −0.333243 | ||||||||
\(872\) | −14.7077 | −0.498066 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 6.16707 | 0.208604 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 23.9031 | 0.807149 | 0.403575 | − | 0.914947i | \(-0.367768\pi\) | ||||
0.403575 | + | 0.914947i | \(0.367768\pi\) | |||||||
\(878\) | −25.4482 | −0.858836 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −25.0419 | −0.843682 | −0.421841 | − | 0.906670i | \(-0.638616\pi\) | ||||
−0.421841 | + | 0.906670i | \(0.638616\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 9.51188 | 0.320100 | 0.160050 | − | 0.987109i | \(-0.448834\pi\) | ||||
0.160050 | + | 0.987109i | \(0.448834\pi\) | |||||||
\(884\) | −4.45936 | −0.149985 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −24.4351 | −0.820914 | ||||||||
\(887\) | −40.7824 | −1.36934 | −0.684669 | − | 0.728854i | \(-0.740053\pi\) | ||||
−0.684669 | + | 0.728854i | \(0.740053\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 15.5977 | 0.523129 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −18.7122 | −0.626532 | ||||||||
\(893\) | 5.32962 | 0.178349 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 2.35386 | 0.0786368 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −26.5012 | −0.884357 | ||||||||
\(899\) | −32.9318 | −1.09834 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 4.65067 | 0.154936 | ||||||||
\(902\) | 17.3296 | 0.577013 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −3.29681 | −0.109650 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 9.05299 | 0.300600 | 0.150300 | − | 0.988640i | \(-0.451976\pi\) | ||||
0.150300 | + | 0.988640i | \(0.451976\pi\) | |||||||
\(908\) | 13.0813 | 0.434117 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −28.2947 | −0.937446 | −0.468723 | − | 0.883345i | \(-0.655286\pi\) | ||||
−0.468723 | + | 0.883345i | \(0.655286\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 21.7077 | 0.718420 | ||||||||
\(914\) | 36.3230 | 1.20146 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −9.89902 | −0.327073 | ||||||||
\(917\) | −39.9692 | −1.31990 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 42.3801 | 1.39799 | 0.698995 | − | 0.715127i | \(-0.253631\pi\) | ||||
0.698995 | + | 0.715127i | \(0.253631\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −23.0813 | −0.760141 | ||||||||
\(923\) | 7.84858 | 0.258339 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −31.0419 | −1.02010 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −4.27258 | −0.140254 | ||||||||
\(929\) | 38.7430 | 1.27112 | 0.635558 | − | 0.772053i | \(-0.280770\pi\) | ||||
0.635558 | + | 0.772053i | \(0.280770\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1.45936 | 0.0478287 | ||||||||
\(932\) | 12.6395 | 0.414022 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −16.6925 | −0.546196 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −3.20441 | −0.104683 | −0.0523417 | − | 0.998629i | \(-0.516669\pi\) | ||||
−0.0523417 | + | 0.998629i | \(0.516669\pi\) | |||||||
\(938\) | −12.2196 | −0.398984 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 3.14492 | 0.102521 | 0.0512607 | − | 0.998685i | \(-0.483676\pi\) | ||||
0.0512607 | + | 0.998685i | \(0.483676\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 21.8354 | 0.711058 | ||||||||
\(944\) | −6.81322 | −0.221751 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −8.47699 | −0.275611 | ||||||||
\(947\) | −29.0509 | −0.944028 | −0.472014 | − | 0.881591i | \(-0.656473\pi\) | ||||
−0.472014 | + | 0.881591i | \(0.656473\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −8.29426 | −0.269243 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −5.54064 | −0.179573 | ||||||||
\(953\) | −11.5452 | −0.373985 | −0.186992 | − | 0.982361i | \(-0.559874\pi\) | ||||
−0.186992 | + | 0.982361i | \(0.559874\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 20.1605 | 0.652036 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 12.5891 | 0.406735 | ||||||||
\(959\) | 30.2947 | 0.978268 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 28.4088 | 0.916413 | ||||||||
\(962\) | −14.7562 | −0.475758 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −11.7693 | −0.379063 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 17.2044 | 0.553256 | 0.276628 | − | 0.960977i | \(-0.410783\pi\) | ||||
0.276628 | + | 0.960977i | \(0.410783\pi\) | |||||||
\(968\) | 12.9561 | 0.416424 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 38.2771 | 1.22837 | 0.614185 | − | 0.789162i | \(-0.289485\pi\) | ||||
0.614185 | + | 0.789162i | \(0.289485\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 21.9142 | 0.702537 | ||||||||
\(974\) | −20.7077 | −0.663518 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 3.97577 | 0.127261 | ||||||||
\(977\) | 16.5340 | 0.528971 | 0.264485 | − | 0.964390i | \(-0.414798\pi\) | ||||
0.264485 | + | 0.964390i | \(0.414798\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 17.7274 | 0.566571 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −20.0747 | −0.640608 | ||||||||
\(983\) | 41.7783 | 1.33252 | 0.666261 | − | 0.745719i | \(-0.267894\pi\) | ||||
0.666261 | + | 0.745719i | \(0.267894\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 10.0570 | 0.320281 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −1.89449 | −0.0602718 | ||||||||
\(989\) | −10.6810 | −0.339637 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 27.7845 | 0.882602 | 0.441301 | − | 0.897359i | \(-0.354517\pi\) | ||||
0.441301 | + | 0.897359i | \(0.354517\pi\) | |||||||
\(992\) | 7.70771 | 0.244720 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 9.75165 | 0.309304 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −16.9297 | −0.536170 | −0.268085 | − | 0.963395i | \(-0.586391\pi\) | ||||
−0.268085 | + | 0.963395i | \(0.586391\pi\) | |||||||
\(998\) | 41.5956 | 1.31669 | ||||||||
\(999\) | 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 | 8550.2.a.cm.1.3 | yes | 3 | |
3.2 | odd | 2 | 8550.2.a.cc.1.3 | ✓ | 3 | ||
5.4 | even | 2 | 8550.2.a.ch.1.1 | yes | 3 | ||
15.14 | odd | 2 | 8550.2.a.ct.1.1 | yes | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8550.2.a.cc.1.3 | ✓ | 3 | 3.2 | odd | 2 | ||
8550.2.a.ch.1.1 | yes | 3 | 5.4 | even | 2 | ||
8550.2.a.cm.1.3 | yes | 3 | 1.1 | even | 1 | trivial | |
8550.2.a.ct.1.1 | yes | 3 | 15.14 | odd | 2 |