Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8048,2,Mod(1,8048)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8048, 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("8048.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8048 = 2^{4} \cdot 503 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8048.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(64.2636035467\) |
Analytic rank: | \(1\) |
Dimension: | \(28\) |
Twist minimal: | no (minimal twist has level 4024) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.22 | ||
Character | \(\chi\) | \(=\) | 8048.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 1.73728 | 1.00302 | 0.501509 | − | 0.865153i | \(-0.332779\pi\) | ||||
0.501509 | + | 0.865153i | \(0.332779\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 2.58604 | 1.15651 | 0.578257 | − | 0.815855i | \(-0.303733\pi\) | ||||
0.578257 | + | 0.815855i | \(0.303733\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.10260 | −0.794708 | −0.397354 | − | 0.917665i | \(-0.630071\pi\) | ||||
−0.397354 | + | 0.917665i | \(0.630071\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0.0181326 | 0.00604419 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.62289 | 0.790832 | 0.395416 | − | 0.918502i | \(-0.370600\pi\) | ||||
0.395416 | + | 0.918502i | \(0.370600\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.715213 | 0.198364 | 0.0991822 | − | 0.995069i | \(-0.468377\pi\) | ||||
0.0991822 | + | 0.995069i | \(0.468377\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 4.49267 | 1.16000 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −5.38011 | −1.30487 | −0.652434 | − | 0.757846i | \(-0.726252\pi\) | ||||
−0.652434 | + | 0.757846i | \(0.726252\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.38337 | −0.317367 | −0.158684 | − | 0.987330i | \(-0.550725\pi\) | ||||
−0.158684 | + | 0.987330i | \(0.550725\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −3.65280 | −0.797106 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −6.72492 | −1.40224 | −0.701122 | − | 0.713041i | \(-0.747317\pi\) | ||||
−0.701122 | + | 0.713041i | \(0.747317\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.68762 | 0.337523 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −5.18033 | −0.996955 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −4.19384 | −0.778776 | −0.389388 | − | 0.921074i | \(-0.627313\pi\) | ||||
−0.389388 | + | 0.921074i | \(0.627313\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 5.92164 | 1.06356 | 0.531779 | − | 0.846883i | \(-0.321524\pi\) | ||||
0.531779 | + | 0.846883i | \(0.321524\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 4.55669 | 0.793218 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −5.43741 | −0.919090 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −7.49843 | −1.23273 | −0.616367 | − | 0.787459i | \(-0.711396\pi\) | ||||
−0.616367 | + | 0.787459i | \(0.711396\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 1.24252 | 0.198963 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −2.29080 | −0.357763 | −0.178882 | − | 0.983871i | \(-0.557248\pi\) | ||||
−0.178882 | + | 0.983871i | \(0.557248\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −7.41206 | −1.13033 | −0.565164 | − | 0.824979i | \(-0.691187\pi\) | ||||
−0.565164 | + | 0.824979i | \(0.691187\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0.0468916 | 0.00699019 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 7.28843 | 1.06313 | 0.531564 | − | 0.847018i | \(-0.321605\pi\) | ||||
0.531564 | + | 0.847018i | \(0.321605\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −2.57908 | −0.368440 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −9.34674 | −1.30881 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −11.8850 | −1.63253 | −0.816266 | − | 0.577677i | \(-0.803959\pi\) | ||||
−0.816266 | + | 0.577677i | \(0.803959\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 6.78291 | 0.914608 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −2.40330 | −0.318325 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 7.39694 | 0.963000 | 0.481500 | − | 0.876446i | \(-0.340092\pi\) | ||||
0.481500 | + | 0.876446i | \(0.340092\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.47413 | −0.188743 | −0.0943717 | − | 0.995537i | \(-0.530084\pi\) | ||||
−0.0943717 | + | 0.995537i | \(0.530084\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −0.0381255 | −0.00480337 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 1.84957 | 0.229411 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 4.45942 | 0.544805 | 0.272402 | − | 0.962183i | \(-0.412182\pi\) | ||||
0.272402 | + | 0.962183i | \(0.412182\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −11.6831 | −1.40648 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −8.17012 | −0.969615 | −0.484807 | − | 0.874621i | \(-0.661110\pi\) | ||||
−0.484807 | + | 0.874621i | \(0.661110\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −9.67286 | −1.13212 | −0.566061 | − | 0.824363i | \(-0.691533\pi\) | ||||
−0.566061 | + | 0.824363i | \(0.691533\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 2.93186 | 0.338542 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −5.51489 | −0.628480 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −9.04789 | −1.01797 | −0.508983 | − | 0.860776i | \(-0.669979\pi\) | ||||
−0.508983 | + | 0.860776i | \(0.669979\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −9.05407 | −1.00601 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −4.25798 | −0.467374 | −0.233687 | − | 0.972312i | \(-0.575079\pi\) | ||||
−0.233687 | + | 0.972312i | \(0.575079\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −13.9132 | −1.50910 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −7.28586 | −0.781126 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 9.05608 | 0.959943 | 0.479972 | − | 0.877284i | \(-0.340647\pi\) | ||||
0.479972 | + | 0.877284i | \(0.340647\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.50381 | −0.157642 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 10.2875 | 1.06677 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −3.57746 | −0.367039 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 8.08527 | 0.820934 | 0.410467 | − | 0.911875i | \(-0.365366\pi\) | ||||
0.410467 | + | 0.911875i | \(0.365366\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0.0475598 | 0.00477994 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 18.8020 | 1.87087 | 0.935436 | − | 0.353497i | \(-0.115008\pi\) | ||||
0.935436 | + | 0.353497i | \(0.115008\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1.20257 | −0.118492 | −0.0592462 | − | 0.998243i | \(-0.518870\pi\) | ||||
−0.0592462 | + | 0.998243i | \(0.518870\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −9.44629 | −0.921863 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 16.6032 | 1.60509 | 0.802544 | − | 0.596593i | \(-0.203479\pi\) | ||||
0.802544 | + | 0.596593i | \(0.203479\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 10.9284 | 1.04675 | 0.523376 | − | 0.852102i | \(-0.324672\pi\) | ||||
0.523376 | + | 0.852102i | \(0.324672\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −13.0269 | −1.23645 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −18.5233 | −1.74252 | −0.871261 | − | 0.490820i | \(-0.836697\pi\) | ||||
−0.871261 | + | 0.490820i | \(0.836697\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −17.3909 | −1.62171 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0.0129687 | 0.00119895 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 11.3122 | 1.03699 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −4.12043 | −0.374585 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −3.97976 | −0.358843 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −8.56597 | −0.766163 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −10.1838 | −0.903668 | −0.451834 | − | 0.892102i | \(-0.649230\pi\) | ||||
−0.451834 | + | 0.892102i | \(0.649230\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −12.8768 | −1.13374 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1.75144 | 0.153024 | 0.0765121 | − | 0.997069i | \(-0.475622\pi\) | ||||
0.0765121 | + | 0.997069i | \(0.475622\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2.90867 | 0.252214 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −13.3966 | −1.15299 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −15.0405 | −1.28499 | −0.642496 | − | 0.766289i | \(-0.722101\pi\) | ||||
−0.642496 | + | 0.766289i | \(0.722101\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 8.98840 | 0.762386 | 0.381193 | − | 0.924495i | \(-0.375513\pi\) | ||||
0.381193 | + | 0.924495i | \(0.375513\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 12.6620 | 1.06634 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 1.87593 | 0.156873 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −10.8454 | −0.900665 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −4.48057 | −0.369551 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 18.8981 | 1.54819 | 0.774097 | − | 0.633067i | \(-0.218204\pi\) | ||||
0.774097 | + | 0.633067i | \(0.218204\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −17.6152 | −1.43351 | −0.716754 | − | 0.697326i | \(-0.754373\pi\) | ||||
−0.716754 | + | 0.697326i | \(0.754373\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −0.0975552 | −0.00788687 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 15.3136 | 1.23002 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 21.9626 | 1.75280 | 0.876401 | − | 0.481582i | \(-0.159937\pi\) | ||||
0.876401 | + | 0.481582i | \(0.159937\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −20.6476 | −1.63746 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 14.1398 | 1.11437 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 21.4671 | 1.68143 | 0.840717 | − | 0.541474i | \(-0.182134\pi\) | ||||
0.840717 | + | 0.541474i | \(0.182134\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 11.7838 | 0.917368 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −2.18943 | −0.169423 | −0.0847114 | − | 0.996406i | \(-0.526997\pi\) | ||||
−0.0847114 | + | 0.996406i | \(0.526997\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.4885 | −0.960652 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −0.0250841 | −0.00191823 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 2.58894 | 0.196833 | 0.0984167 | − | 0.995145i | \(-0.468622\pi\) | ||||
0.0984167 | + | 0.995145i | \(0.468622\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −3.54838 | −0.268232 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 12.8505 | 0.965906 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 14.8091 | 1.10688 | 0.553442 | − | 0.832888i | \(-0.313314\pi\) | ||||
0.553442 | + | 0.832888i | \(0.313314\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −26.5615 | −1.97430 | −0.987152 | − | 0.159784i | \(-0.948920\pi\) | ||||
−0.987152 | + | 0.159784i | \(0.948920\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −2.56098 | −0.189313 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −19.3913 | −1.42567 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −14.1115 | −1.03193 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 10.8922 | 0.792288 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 7.64557 | 0.553214 | 0.276607 | − | 0.960983i | \(-0.410790\pi\) | ||||
0.276607 | + | 0.960983i | \(0.410790\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 18.6737 | 1.34417 | 0.672083 | − | 0.740476i | \(-0.265400\pi\) | ||||
0.672083 | + | 0.740476i | \(0.265400\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 3.21322 | 0.230103 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −23.8450 | −1.69889 | −0.849443 | − | 0.527680i | \(-0.823062\pi\) | ||||
−0.849443 | + | 0.527680i | \(0.823062\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 21.5661 | 1.52878 | 0.764390 | − | 0.644754i | \(-0.223040\pi\) | ||||
0.764390 | + | 0.644754i | \(0.223040\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 7.74724 | 0.546448 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 8.81796 | 0.618899 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −5.92411 | −0.413758 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −0.121940 | −0.00847543 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −3.62843 | −0.250984 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 13.1034 | 0.902078 | 0.451039 | − | 0.892504i | \(-0.351054\pi\) | ||||
0.451039 | + | 0.892504i | \(0.351054\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −14.1938 | −0.972541 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −19.1679 | −1.30724 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −12.4508 | −0.845218 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −16.8044 | −1.13554 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −3.84792 | −0.258839 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −7.00682 | −0.469211 | −0.234606 | − | 0.972091i | \(-0.575380\pi\) | ||||
−0.234606 | + | 0.972091i | \(0.575380\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0.0306008 | 0.00204005 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 11.6164 | 0.771006 | 0.385503 | − | 0.922707i | \(-0.374028\pi\) | ||||
0.385503 | + | 0.922707i | \(0.374028\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −19.2049 | −1.26909 | −0.634547 | − | 0.772884i | \(-0.718813\pi\) | ||||
−0.634547 | + | 0.772884i | \(0.718813\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −9.58090 | −0.630377 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 2.65846 | 0.174161 | 0.0870807 | − | 0.996201i | \(-0.472246\pi\) | ||||
0.0870807 | + | 0.996201i | \(0.472246\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 18.8482 | 1.22952 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −15.7187 | −1.02104 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 9.78193 | 0.632740 | 0.316370 | − | 0.948636i | \(-0.397536\pi\) | ||||
0.316370 | + | 0.948636i | \(0.397536\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 14.1847 | 0.913718 | 0.456859 | − | 0.889539i | \(-0.348974\pi\) | ||||
0.456859 | + | 0.889539i | \(0.348974\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −0.188437 | −0.0120882 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −6.66960 | −0.426105 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −0.989405 | −0.0629543 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −7.39730 | −0.468785 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −7.28945 | −0.460106 | −0.230053 | − | 0.973178i | \(-0.573890\pi\) | ||||
−0.230053 | + | 0.973178i | \(0.573890\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −17.6388 | −1.10894 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −24.1711 | −1.51365 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −24.3811 | −1.52085 | −0.760424 | − | 0.649427i | \(-0.775009\pi\) | ||||
−0.760424 | + | 0.649427i | \(0.775009\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 15.7662 | 0.979664 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −0.0760451 | −0.00470707 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −10.9637 | −0.676052 | −0.338026 | − | 0.941137i | \(-0.609759\pi\) | ||||
−0.338026 | + | 0.941137i | \(0.609759\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −30.7351 | −1.88804 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 15.7329 | 0.962840 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 6.72724 | 0.410167 | 0.205084 | − | 0.978744i | \(-0.434253\pi\) | ||||
0.205084 | + | 0.978744i | \(0.434253\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 6.57983 | 0.399696 | 0.199848 | − | 0.979827i | \(-0.435955\pi\) | ||||
0.199848 | + | 0.979827i | \(0.435955\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −2.61253 | −0.158117 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 4.42643 | 0.266924 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 5.65170 | 0.339577 | 0.169789 | − | 0.985480i | \(-0.445691\pi\) | ||||
0.169789 | + | 0.985480i | \(0.445691\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0.107375 | 0.00642835 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 6.49270 | 0.387322 | 0.193661 | − | 0.981069i | \(-0.437964\pi\) | ||||
0.193661 | + | 0.981069i | \(0.437964\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 15.3968 | 0.915246 | 0.457623 | − | 0.889146i | \(-0.348701\pi\) | ||||
0.457623 | + | 0.889146i | \(0.348701\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −6.21503 | −0.368147 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 4.81664 | 0.284317 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 11.9456 | 0.702681 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 14.0464 | 0.823412 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −25.3812 | −1.48279 | −0.741393 | − | 0.671071i | \(-0.765835\pi\) | ||||
−0.741393 | + | 0.671071i | \(0.765835\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 19.1288 | 1.11372 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −13.5875 | −0.788424 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −4.80975 | −0.278155 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 15.5846 | 0.898281 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 32.6643 | 1.87652 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −3.81217 | −0.218284 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −24.9503 | −1.42399 | −0.711993 | − | 0.702186i | \(-0.752207\pi\) | ||||
−0.711993 | + | 0.702186i | \(0.752207\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −2.08919 | −0.118850 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −9.38125 | −0.531962 | −0.265981 | − | 0.963978i | \(-0.585696\pi\) | ||||
−0.265981 | + | 0.963978i | \(0.585696\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −7.27785 | −0.411368 | −0.205684 | − | 0.978618i | \(-0.565942\pi\) | ||||
−0.205684 | + | 0.978618i | \(0.565942\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −0.0985943 | −0.00555516 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 4.69633 | 0.263772 | 0.131886 | − | 0.991265i | \(-0.457897\pi\) | ||||
0.131886 | + | 0.991265i | \(0.457897\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −11.0000 | −0.615881 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 28.8443 | 1.60993 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 7.44268 | 0.414122 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1.20700 | 0.0669525 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 18.9857 | 1.04991 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −15.3247 | −0.844875 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 19.3105 | 1.06140 | 0.530700 | − | 0.847560i | \(-0.321929\pi\) | ||||
0.530700 | + | 0.847560i | \(0.321929\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −0.135966 | −0.00745088 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 11.5322 | 0.630074 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 17.1916 | 0.936488 | 0.468244 | − | 0.883599i | \(-0.344887\pi\) | ||||
0.468244 | + | 0.883599i | \(0.344887\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −32.1800 | −1.74778 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 15.5318 | 0.841096 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 20.1410 | 1.08751 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −30.2129 | −1.62661 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 14.6384 | 0.785832 | 0.392916 | − | 0.919574i | \(-0.371466\pi\) | ||||
0.392916 | + | 0.919574i | \(0.371466\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −9.91051 | −0.530497 | −0.265249 | − | 0.964180i | \(-0.585454\pi\) | ||||
−0.265249 | + | 0.964180i | \(0.585454\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −3.70504 | −0.197760 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −30.7124 | −1.63466 | −0.817329 | − | 0.576171i | \(-0.804546\pi\) | ||||
−0.817329 | + | 0.576171i | \(0.804546\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −21.1283 | −1.12137 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 19.6524 | 1.04012 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −35.5684 | −1.87723 | −0.938614 | − | 0.344968i | \(-0.887890\pi\) | ||||
−0.938614 | + | 0.344968i | \(0.887890\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −17.0863 | −0.899278 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −7.15833 | −0.375715 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −25.0144 | −1.30931 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −32.6083 | −1.70214 | −0.851070 | − | 0.525052i | \(-0.824046\pi\) | ||||
−0.851070 | + | 0.525052i | \(0.824046\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −0.0415382 | −0.00216239 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 24.9894 | 1.29739 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 31.6305 | 1.63777 | 0.818883 | − | 0.573961i | \(-0.194594\pi\) | ||||
0.818883 | + | 0.573961i | \(0.194594\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −14.8815 | −0.768475 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −2.99949 | −0.154481 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −25.6286 | −1.31645 | −0.658227 | − | 0.752820i | \(-0.728693\pi\) | ||||
−0.658227 | + | 0.752820i | \(0.728693\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −17.6921 | −0.906394 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −29.2140 | −1.49276 | −0.746382 | − | 0.665518i | \(-0.768211\pi\) | ||||
−0.746382 | + | 0.665518i | \(0.768211\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −14.2617 | −0.726846 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −0.134400 | −0.00683192 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −18.4995 | −0.937962 | −0.468981 | − | 0.883208i | \(-0.655379\pi\) | ||||
−0.468981 | + | 0.883208i | \(0.655379\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 36.1808 | 1.82974 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 3.04274 | 0.153486 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −23.3982 | −1.17729 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −3.21806 | −0.161510 | −0.0807550 | − | 0.996734i | \(-0.525733\pi\) | ||||
−0.0807550 | + | 0.996734i | \(0.525733\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 5.05317 | 0.252975 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 28.4986 | 1.42315 | 0.711576 | − | 0.702609i | \(-0.247982\pi\) | ||||
0.711576 | + | 0.702609i | \(0.247982\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 4.23523 | 0.210972 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −23.4142 | −1.16346 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −19.6676 | −0.974886 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 9.38723 | 0.464168 | 0.232084 | − | 0.972696i | \(-0.425446\pi\) | ||||
0.232084 | + | 0.972696i | \(0.425446\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −26.1294 | −1.28887 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −15.5528 | −0.765303 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −11.0113 | −0.540525 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 15.6153 | 0.764687 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 24.9405 | 1.21842 | 0.609211 | − | 0.793008i | \(-0.291486\pi\) | ||||
0.609211 | + | 0.793008i | \(0.291486\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −30.2102 | −1.47236 | −0.736178 | − | 0.676788i | \(-0.763371\pi\) | ||||
−0.736178 | + | 0.676788i | \(0.763371\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0.132158 | 0.00642574 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −9.07955 | −0.440423 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 3.09951 | 0.149996 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 3.25901 | 0.157346 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 36.8695 | 1.77594 | 0.887970 | − | 0.459902i | \(-0.152116\pi\) | ||||
0.887970 | + | 0.459902i | \(0.152116\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −18.5932 | −0.893530 | −0.446765 | − | 0.894651i | \(-0.647424\pi\) | ||||
−0.446765 | + | 0.894651i | \(0.647424\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −18.8415 | −0.903383 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 9.30306 | 0.445026 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 5.25442 | 0.250780 | 0.125390 | − | 0.992108i | \(-0.459982\pi\) | ||||
0.125390 | + | 0.992108i | \(0.459982\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −0.0467653 | −0.00222692 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −16.1896 | −0.769190 | −0.384595 | − | 0.923085i | \(-0.625659\pi\) | ||||
−0.384595 | + | 0.923085i | \(0.625659\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 23.4194 | 1.11019 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 32.8313 | 1.55287 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −0.629326 | −0.0296997 | −0.0148499 | − | 0.999890i | \(-0.504727\pi\) | ||||
−0.0148499 | + | 0.999890i | \(0.504727\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −6.00853 | −0.282931 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −30.6026 | −1.43783 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −3.88891 | −0.182315 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 13.6403 | 0.638066 | 0.319033 | − | 0.947744i | \(-0.396642\pi\) | ||||
0.319033 | + | 0.947744i | \(0.396642\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 27.8707 | 1.30089 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 13.8122 | 0.643298 | 0.321649 | − | 0.946859i | \(-0.395763\pi\) | ||||
0.321649 | + | 0.946859i | \(0.395763\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −6.86831 | −0.319197 | −0.159599 | − | 0.987182i | \(-0.551020\pi\) | ||||
−0.159599 | + | 0.987182i | \(0.551020\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 26.6040 | 1.23373 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −1.48619 | −0.0687728 | −0.0343864 | − | 0.999409i | \(-0.510948\pi\) | ||||
−0.0343864 | + | 0.999409i | \(0.510948\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −9.37637 | −0.432960 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 38.1550 | 1.75809 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −19.4410 | −0.893900 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −2.33460 | −0.107119 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −0.215506 | −0.00986733 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 0.419481 | 0.0191666 | 0.00958329 | − | 0.999954i | \(-0.496949\pi\) | ||||
0.00958329 | + | 0.999954i | \(0.496949\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −5.36297 | −0.244531 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 24.5648 | 1.11774 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 20.9088 | 0.949422 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 25.9633 | 1.17651 | 0.588255 | − | 0.808676i | \(-0.299815\pi\) | ||||
0.588255 | + | 0.808676i | \(0.299815\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 37.2943 | 1.68651 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 36.8094 | 1.66119 | 0.830594 | − | 0.556879i | \(-0.188001\pi\) | ||||
0.830594 | + | 0.556879i | \(0.188001\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 22.5633 | 1.01620 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0.122992 | 0.00552807 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 17.1785 | 0.770561 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −2.13357 | −0.0955116 | −0.0477558 | − | 0.998859i | \(-0.515207\pi\) | ||||
−0.0477558 | + | 0.998859i | \(0.515207\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −3.80364 | −0.169934 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −1.00000 | −0.0445878 | ||||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 48.6228 | 2.16369 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −21.6959 | −0.963550 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −30.2938 | −1.34275 | −0.671375 | − | 0.741118i | \(-0.734296\pi\) | ||||
−0.671375 | + | 0.741118i | \(0.734296\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 20.3381 | 0.899706 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 7.16632 | 0.316401 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −3.10989 | −0.137038 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 19.1168 | 0.840755 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 4.49771 | 0.197427 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −27.1463 | −1.18930 | −0.594650 | − | 0.803985i | \(-0.702709\pi\) | ||||
−0.594650 | + | 0.803985i | \(0.702709\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −21.3731 | −0.934580 | −0.467290 | − | 0.884104i | \(-0.654770\pi\) | ||||
−0.467290 | + | 0.884104i | \(0.654770\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −6.16452 | −0.269042 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −31.8591 | −1.38780 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 22.2246 | 0.966287 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0.134126 | 0.00582056 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −1.63841 | −0.0709675 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 42.9365 | 1.85631 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 25.7275 | 1.11022 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −6.76464 | −0.291374 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 29.9286 | 1.28673 | 0.643366 | − | 0.765559i | \(-0.277537\pi\) | ||||
0.643366 | + | 0.765559i | \(0.277537\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −46.1448 | −1.98026 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 28.2613 | 1.21058 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 29.9207 | 1.27931 | 0.639657 | − | 0.768660i | \(-0.279076\pi\) | ||||
0.639657 | + | 0.768660i | \(0.279076\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −0.0267298 | −0.00114080 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 5.80163 | 0.247158 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 19.0241 | 0.808986 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −33.6880 | −1.42998 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −13.2317 | −0.560644 | −0.280322 | − | 0.959906i | \(-0.590441\pi\) | ||||
−0.280322 | + | 0.959906i | \(0.590441\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −5.30120 | −0.224217 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −24.5155 | −1.03505 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −15.4871 | −0.652701 | −0.326351 | − | 0.945249i | \(-0.605819\pi\) | ||||
−0.326351 | + | 0.945249i | \(0.605819\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −47.9019 | −2.01525 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 19.0371 | 0.799482 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 16.7971 | 0.704170 | 0.352085 | − | 0.935968i | \(-0.385473\pi\) | ||||
0.352085 | + | 0.935968i | \(0.385473\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 30.2291 | 1.26505 | 0.632525 | − | 0.774540i | \(-0.282018\pi\) | ||||
0.632525 | + | 0.774540i | \(0.282018\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 13.2825 | 0.554883 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −11.3491 | −0.473290 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 1.03748 | 0.0431910 | 0.0215955 | − | 0.999767i | \(-0.493125\pi\) | ||||
0.0215955 | + | 0.999767i | \(0.493125\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 32.4415 | 1.34822 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 8.95283 | 0.371426 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −31.1731 | −1.29106 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0.0335375 | 0.00138660 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 26.9328 | 1.11164 | 0.555818 | − | 0.831304i | \(-0.312405\pi\) | ||||
0.555818 | + | 0.831304i | \(0.312405\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −8.19183 | −0.337538 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −41.4254 | −1.70401 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 8.67227 | 0.356127 | 0.178064 | − | 0.984019i | \(-0.443017\pi\) | ||||
0.178064 | + | 0.984019i | \(0.443017\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 29.2539 | 1.19929 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 37.4663 | 1.53339 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −7.03128 | −0.287290 | −0.143645 | − | 0.989629i | \(-0.545882\pi\) | ||||
−0.143645 | + | 0.989629i | \(0.545882\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 16.9913 | 0.693088 | 0.346544 | − | 0.938034i | \(-0.387355\pi\) | ||||
0.346544 | + | 0.938034i | \(0.387355\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0.0808607 | 0.00329290 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −10.6556 | −0.433212 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −33.6055 | −1.36400 | −0.682002 | − | 0.731350i | \(-0.738890\pi\) | ||||
−0.682002 | + | 0.731350i | \(0.738890\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 15.3192 | 0.620767 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 5.21278 | 0.210887 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −41.5746 | −1.67918 | −0.839591 | − | 0.543219i | \(-0.817205\pi\) | ||||
−0.839591 | + | 0.543219i | \(0.817205\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −10.2918 | −0.415007 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 10.0211 | 0.403434 | 0.201717 | − | 0.979444i | \(-0.435348\pi\) | ||||
0.201717 | + | 0.979444i | \(0.435348\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 10.8542 | 0.436267 | 0.218133 | − | 0.975919i | \(-0.430003\pi\) | ||||
0.218133 | + | 0.975919i | \(0.430003\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 34.8373 | 1.39797 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −19.0413 | −0.762874 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −30.5900 | −1.22360 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −6.30360 | −0.251741 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 40.3424 | 1.60856 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −18.4761 | −0.735524 | −0.367762 | − | 0.929920i | \(-0.619876\pi\) | ||||
−0.367762 | + | 0.929920i | \(0.619876\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 22.7643 | 0.904800 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −26.3358 | −1.04510 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.84459 | −0.0730853 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −0.148145 | −0.00586054 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 0.947579 | 0.0374271 | 0.0187136 | − | 0.999825i | \(-0.494043\pi\) | ||||
0.0187136 | + | 0.999825i | \(0.494043\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 22.9716 | 0.905913 | 0.452956 | − | 0.891533i | \(-0.350369\pi\) | ||||
0.452956 | + | 0.891533i | \(0.350369\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −33.2999 | −1.31118 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −29.7014 | −1.16768 | −0.583842 | − | 0.811868i | \(-0.698451\pi\) | ||||
−0.583842 | + | 0.811868i | \(0.698451\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 19.4014 | 0.761571 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −21.6306 | −0.847768 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 42.3223 | 1.65620 | 0.828099 | − | 0.560581i | \(-0.189422\pi\) | ||||
0.828099 | + | 0.560581i | \(0.189422\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 4.52930 | 0.176974 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −0.175394 | −0.00684276 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −15.9106 | −0.619789 | −0.309895 | − | 0.950771i | \(-0.600294\pi\) | ||||
−0.309895 | + | 0.950771i | \(0.600294\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 0.347986 | 0.0135351 | 0.00676755 | − | 0.999977i | \(-0.497846\pi\) | ||||
0.00676755 | + | 0.999977i | \(0.497846\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −6.68491 | −0.259620 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 7.52195 | 0.291689 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 28.2032 | 1.09203 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −12.1728 | −0.470627 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −3.86649 | −0.149264 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 18.8705 | 0.727406 | 0.363703 | − | 0.931515i | \(-0.381512\pi\) | ||||
0.363703 | + | 0.931515i | \(0.381512\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −8.74241 | −0.336495 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 15.1564 | 0.582508 | 0.291254 | − | 0.956646i | \(-0.405928\pi\) | ||||
0.291254 | + | 0.956646i | \(0.405928\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −17.0001 | −0.652403 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 20.1809 | 0.773332 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −39.5457 | −1.51318 | −0.756588 | − | 0.653892i | \(-0.773135\pi\) | ||||
−0.756588 | + | 0.653892i | \(0.773135\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −38.8953 | −1.48611 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −33.3642 | −1.27292 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −8.50031 | −0.323836 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 33.2527 | 1.26499 | 0.632495 | − | 0.774564i | \(-0.282031\pi\) | ||||
0.632495 | + | 0.774564i | \(0.282031\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −0.0999992 | −0.00379866 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 23.2444 | 0.881710 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 12.3248 | 0.466834 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 4.61848 | 0.174687 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 38.7601 | 1.46395 | 0.731975 | − | 0.681331i | \(-0.238599\pi\) | ||||
0.731975 | + | 0.681331i | \(0.238599\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 10.3731 | 0.391229 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 32.7445 | 1.23323 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −39.5331 | −1.48680 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 30.6093 | 1.14956 | 0.574778 | − | 0.818310i | \(-0.305089\pi\) | ||||
0.574778 | + | 0.818310i | \(0.305089\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −0.164061 | −0.00615279 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −39.8226 | −1.49137 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 4.85123 | 0.181426 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 16.9939 | 0.634650 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −51.1073 | −1.90598 | −0.952990 | − | 0.303002i | \(-0.902011\pi\) | ||||
−0.952990 | + | 0.303002i | \(0.902011\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 2.52851 | 0.0941668 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 24.6428 | 0.916475 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −7.07758 | −0.262855 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −2.23928 | −0.0830505 | −0.0415252 | − | 0.999137i | \(-0.513222\pi\) | ||||
−0.0415252 | + | 0.999137i | \(0.513222\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 26.8348 | 0.993883 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 39.8777 | 1.47493 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 2.66853 | 0.0985643 | 0.0492821 | − | 0.998785i | \(-0.484307\pi\) | ||||
0.0492821 | + | 0.998785i | \(0.484307\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −11.5869 | −0.427391 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 11.6966 | 0.430849 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −23.9717 | −0.881815 | −0.440907 | − | 0.897553i | \(-0.645343\pi\) | ||||
−0.440907 | + | 0.897553i | \(0.645343\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −1.71887 | −0.0631443 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 6.79980 | 0.249460 | 0.124730 | − | 0.992191i | \(-0.460193\pi\) | ||||
0.124730 | + | 0.992191i | \(0.460193\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 48.8713 | 1.79051 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −0.0772082 | −0.00282490 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −34.9098 | −1.27558 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 28.4576 | 1.03843 | 0.519217 | − | 0.854642i | \(-0.326224\pi\) | ||||
0.519217 | + | 0.854642i | \(0.326224\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −12.6638 | −0.461495 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −45.5538 | −1.65787 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −25.9573 | −0.943434 | −0.471717 | − | 0.881750i | \(-0.656366\pi\) | ||||
−0.471717 | + | 0.881750i | \(0.656366\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −30.6434 | −1.11229 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −38.7281 | −1.40389 | −0.701946 | − | 0.712230i | \(-0.747685\pi\) | ||||
−0.701946 | + | 0.712230i | \(0.747685\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −22.9781 | −0.831862 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −0.252282 | −0.00912127 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 5.29039 | 0.191025 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −31.1088 | −1.12181 | −0.560906 | − | 0.827879i | \(-0.689547\pi\) | ||||
−0.560906 | + | 0.827879i | \(0.689547\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −42.3567 | −1.52544 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 38.9856 | 1.40222 | 0.701108 | − | 0.713055i | \(-0.252689\pi\) | ||||
0.701108 | + | 0.713055i | \(0.252689\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 9.99345 | 0.358975 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 27.3903 | 0.982620 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 3.16903 | 0.113542 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −21.4294 | −0.766803 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 21.7255 | 0.776405 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 56.7961 | 2.02714 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 9.31965 | 0.332210 | 0.166105 | − | 0.986108i | \(-0.446881\pi\) | ||||
0.166105 | + | 0.986108i | \(0.446881\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −19.0470 | −0.678092 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 38.9470 | 1.38480 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −1.05432 | −0.0374399 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −53.3954 | −1.89374 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −6.06555 | −0.214853 | −0.107426 | − | 0.994213i | \(-0.534261\pi\) | ||||
−0.107426 | + | 0.994213i | \(0.534261\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −39.2126 | −1.38724 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0.164210 | 0.00580208 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −25.3709 | −0.895319 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 36.5662 | 1.28879 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 11.6871 | 0.411405 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −10.5655 | −0.371463 | −0.185732 | − | 0.982601i | \(-0.559466\pi\) | ||||
−0.185732 | + | 0.982601i | \(0.559466\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −29.8315 | −1.04752 | −0.523762 | − | 0.851865i | \(-0.675472\pi\) | ||||
−0.523762 | + | 0.851865i | \(0.675472\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 11.4310 | 0.400902 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 55.5149 | 1.94460 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 10.2536 | 0.358729 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −0.0272679 | −0.000952817 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −23.0775 | −0.805409 | −0.402705 | − | 0.915330i | \(-0.631930\pi\) | ||||
−0.402705 | + | 0.915330i | \(0.631930\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −5.76982 | −0.201123 | −0.100562 | − | 0.994931i | \(-0.532064\pi\) | ||||
−0.100562 | + | 0.994931i | \(0.532064\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 7.68994 | 0.267730 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 6.15648 | 0.214082 | 0.107041 | − | 0.994255i | \(-0.465862\pi\) | ||||
0.107041 | + | 0.994255i | \(0.465862\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −20.9851 | −0.728842 | −0.364421 | − | 0.931234i | \(-0.618733\pi\) | ||||
−0.364421 | + | 0.931234i | \(0.618733\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 9.81856 | 0.340602 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 13.8757 | 0.480765 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −5.66195 | −0.195940 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −30.6761 | −1.06032 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −32.9640 | −1.13804 | −0.569022 | − | 0.822323i | \(-0.692678\pi\) | ||||
−0.569022 | + | 0.822323i | \(0.692678\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −11.4117 | −0.393508 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 11.2796 | 0.388491 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −32.2957 | −1.11101 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 8.66361 | 0.297685 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 26.7486 | 0.918008 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 50.4264 | 1.72859 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −46.8181 | −1.60302 | −0.801511 | − | 0.597980i | \(-0.795970\pi\) | ||||
−0.801511 | + | 0.597980i | \(0.795970\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −0.0648685 | −0.00221846 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −21.3371 | −0.728861 | −0.364430 | − | 0.931231i | \(-0.618736\pi\) | ||||
−0.364430 | + | 0.931231i | \(0.618736\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 3.48916 | 0.119049 | 0.0595243 | − | 0.998227i | \(-0.481042\pi\) | ||||
0.0595243 | + | 0.998227i | \(0.481042\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 8.36784 | 0.285175 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −37.4202 | −1.27380 | −0.636900 | − | 0.770947i | \(-0.719783\pi\) | ||||
−0.636900 | + | 0.770947i | \(0.719783\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 6.69511 | 0.227641 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 20.7528 | 0.704801 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −23.7316 | −0.805041 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 3.18943 | 0.108070 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0.146607 | 0.00496189 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 18.0108 | 0.608876 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 27.9015 | 0.942166 | 0.471083 | − | 0.882089i | \(-0.343863\pi\) | ||||
0.471083 | + | 0.882089i | \(0.343863\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −44.0942 | −1.48726 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −40.3310 | −1.35879 | −0.679393 | − | 0.733775i | \(-0.737757\pi\) | ||||
−0.679393 | + | 0.733775i | \(0.737757\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −52.3288 | −1.76100 | −0.880502 | − | 0.474043i | \(-0.842794\pi\) | ||||
−0.880502 | + | 0.474043i | \(0.842794\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 33.2320 | 1.11708 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −28.4277 | −0.954510 | −0.477255 | − | 0.878765i | \(-0.658368\pi\) | ||||
−0.477255 | + | 0.878765i | \(0.658368\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 21.4125 | 0.718152 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −23.7479 | −0.795583 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −10.0826 | −0.337401 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 38.2970 | 1.28013 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −8.35587 | −0.278995 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −24.8344 | −0.828274 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 63.9426 | 2.13024 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 27.0747 | 0.900991 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −68.6893 | −2.28331 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −48.2852 | −1.60328 | −0.801641 | − | 0.597805i | \(-0.796040\pi\) | ||||
−0.801641 | + | 0.597805i | \(0.796040\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0.340929 | 0.0113079 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 19.7120 | 0.653087 | 0.326543 | − | 0.945182i | \(-0.394116\pi\) | ||||
0.326543 | + | 0.945182i | \(0.394116\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −11.1682 | −0.369615 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −6.62279 | −0.218943 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −3.68258 | −0.121609 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −28.4127 | −0.937248 | −0.468624 | − | 0.883398i | \(-0.655250\pi\) | ||||
−0.468624 | + | 0.883398i | \(0.655250\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −43.3455 | −1.42828 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −5.84338 | −0.192337 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −12.6545 | −0.416076 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −0.0218056 | −0.000716190 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −53.6116 | −1.75894 | −0.879470 | − | 0.475954i | \(-0.842103\pi\) | ||||
−0.879470 | + | 0.475954i | \(0.842103\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 3.56782 | 0.116931 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −16.2978 | −0.533567 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −36.4928 | −1.19344 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 37.8601 | 1.23684 | 0.618418 | − | 0.785849i | \(-0.287774\pi\) | ||||
0.618418 | + | 0.785849i | \(0.287774\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −12.6436 | −0.412610 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −56.8829 | −1.85433 | −0.927165 | − | 0.374652i | \(-0.877762\pi\) | ||||
−0.927165 | + | 0.374652i | \(0.877762\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 15.4055 | 0.501671 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 28.1676 | 0.916292 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −0.601397 | −0.0195428 | −0.00977140 | − | 0.999952i | \(-0.503110\pi\) | ||||
−0.00977140 | + | 0.999952i | \(0.503110\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −6.91815 | −0.224573 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 8.15883 | 0.264568 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −11.9862 | −0.388270 | −0.194135 | − | 0.980975i | \(-0.562190\pi\) | ||||
−0.194135 | + | 0.980975i | \(0.562190\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 19.7718 | 0.639799 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −19.1100 | −0.617740 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 31.6240 | 1.02119 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 4.06584 | 0.131156 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0.301058 | 0.00970146 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 48.2911 | 1.55455 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −40.9121 | −1.31564 | −0.657822 | − | 0.753173i | \(-0.728522\pi\) | ||||
−0.657822 | + | 0.753173i | \(0.728522\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 12.9300 | 0.415372 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 55.2770 | 1.77392 | 0.886962 | − | 0.461842i | \(-0.152811\pi\) | ||||
0.886962 | + | 0.461842i | \(0.152811\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −18.8990 | −0.605874 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 2.09690 | 0.0671546 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 13.0269 | 0.416767 | 0.208384 | − | 0.978047i | \(-0.433180\pi\) | ||||
0.208384 | + | 0.978047i | \(0.433180\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 23.7531 | 0.759154 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0.198160 | 0.00632677 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −45.8814 | −1.46339 | −0.731695 | − | 0.681632i | \(-0.761270\pi\) | ||||
−0.731695 | + | 0.681632i | \(0.761270\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −61.6642 | −1.96478 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −26.6232 | −0.847425 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 49.8455 | 1.58500 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −50.5955 | −1.60722 | −0.803609 | − | 0.595158i | \(-0.797090\pi\) | ||||
−0.803609 | + | 0.595158i | \(0.797090\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 33.5477 | 1.06460 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 55.7708 | 1.76805 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 42.6441 | 1.35055 | 0.675276 | − | 0.737565i | \(-0.264025\pi\) | ||||
0.675276 | + | 0.737565i | \(0.264025\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 38.8444 | 1.22898 |
(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 | 8048.2.a.v.1.22 | 28 | ||
4.3 | odd | 2 | 4024.2.a.d.1.7 | ✓ | 28 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4024.2.a.d.1.7 | ✓ | 28 | 4.3 | odd | 2 | ||
8048.2.a.v.1.22 | 28 | 1.1 | even | 1 | trivial |