Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8020,2,Mod(1,8020)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8020, 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("8020.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8020 = 2^{2} \cdot 5 \cdot 401 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8020.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: | \(64.0400224211\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{12})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - 3 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-1.73205\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8020.1 |
$q$-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 | ||||||||
\(3\) | −2.73205 | −1.57735 | −0.788675 | − | 0.614810i | \(-0.789233\pi\) | ||||
−0.788675 | + | 0.614810i | \(0.789233\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −3.46410 | −1.30931 | −0.654654 | − | 0.755929i | \(-0.727186\pi\) | ||||
−0.654654 | + | 0.755929i | \(0.727186\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 4.46410 | 1.48803 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.46410 | 1.04447 | 0.522233 | − | 0.852803i | \(-0.325099\pi\) | ||||
0.522233 | + | 0.852803i | \(0.325099\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −6.73205 | −1.86713 | −0.933567 | − | 0.358402i | \(-0.883322\pi\) | ||||
−0.933567 | + | 0.358402i | \(0.883322\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 2.73205 | 0.705412 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 2.73205 | 0.662620 | 0.331310 | − | 0.943522i | \(-0.392509\pi\) | ||||
0.331310 | + | 0.943522i | \(0.392509\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 6.92820 | 1.58944 | 0.794719 | − | 0.606977i | \(-0.207618\pi\) | ||||
0.794719 | + | 0.606977i | \(0.207618\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 9.46410 | 2.06524 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 8.19615 | 1.70902 | 0.854508 | − | 0.519438i | \(-0.173859\pi\) | ||||
0.854508 | + | 0.519438i | \(0.173859\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −4.00000 | −0.769800 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 5.46410 | 1.01466 | 0.507329 | − | 0.861752i | \(-0.330633\pi\) | ||||
0.507329 | + | 0.861752i | \(0.330633\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −5.46410 | −0.981382 | −0.490691 | − | 0.871334i | \(-0.663256\pi\) | ||||
−0.490691 | + | 0.871334i | \(0.663256\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −9.46410 | −1.64749 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 3.46410 | 0.585540 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −0.196152 | −0.0322473 | −0.0161236 | − | 0.999870i | \(-0.505133\pi\) | ||||
−0.0161236 | + | 0.999870i | \(0.505133\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 18.3923 | 2.94513 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −12.3923 | −1.93535 | −0.967676 | − | 0.252195i | \(-0.918848\pi\) | ||||
−0.967676 | + | 0.252195i | \(0.918848\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −2.00000 | −0.304997 | −0.152499 | − | 0.988304i | \(-0.548732\pi\) | ||||
−0.152499 | + | 0.988304i | \(0.548732\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −4.46410 | −0.665469 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −8.92820 | −1.30231 | −0.651156 | − | 0.758944i | \(-0.725716\pi\) | ||||
−0.651156 | + | 0.758944i | \(0.725716\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 5.00000 | 0.714286 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −7.46410 | −1.04518 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 12.1962 | 1.67527 | 0.837635 | − | 0.546230i | \(-0.183938\pi\) | ||||
0.837635 | + | 0.546230i | \(0.183938\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −3.46410 | −0.467099 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −18.9282 | −2.50710 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −8.00000 | −1.04151 | −0.520756 | − | 0.853706i | \(-0.674350\pi\) | ||||
−0.520756 | + | 0.853706i | \(0.674350\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 8.92820 | 1.14314 | 0.571570 | − | 0.820554i | \(-0.306335\pi\) | ||||
0.571570 | + | 0.820554i | \(0.306335\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −15.4641 | −1.94829 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 6.73205 | 0.835008 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −8.19615 | −1.00132 | −0.500660 | − | 0.865644i | \(-0.666909\pi\) | ||||
−0.500660 | + | 0.865644i | \(0.666909\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −22.3923 | −2.69572 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 2.53590 | 0.300956 | 0.150478 | − | 0.988613i | \(-0.451919\pi\) | ||||
0.150478 | + | 0.988613i | \(0.451919\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −0.928203 | −0.108638 | −0.0543190 | − | 0.998524i | \(-0.517299\pi\) | ||||
−0.0543190 | + | 0.998524i | \(0.517299\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −2.73205 | −0.315470 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −12.0000 | −1.36753 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −2.46410 | −0.273789 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −15.8564 | −1.74047 | −0.870233 | − | 0.492640i | \(-0.836032\pi\) | ||||
−0.870233 | + | 0.492640i | \(0.836032\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −2.73205 | −0.296333 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −14.9282 | −1.60047 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −15.8564 | −1.68078 | −0.840388 | − | 0.541985i | \(-0.817673\pi\) | ||||
−0.840388 | + | 0.541985i | \(0.817673\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 23.3205 | 2.44465 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 14.9282 | 1.54798 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −6.92820 | −0.710819 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 10.7321 | 1.08967 | 0.544837 | − | 0.838542i | \(-0.316591\pi\) | ||||
0.544837 | + | 0.838542i | \(0.316591\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 15.4641 | 1.55420 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 3.07180 | 0.305655 | 0.152828 | − | 0.988253i | \(-0.451162\pi\) | ||||
0.152828 | + | 0.988253i | \(0.451162\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −10.3923 | −1.02398 | −0.511992 | − | 0.858990i | \(-0.671092\pi\) | ||||
−0.511992 | + | 0.858990i | \(0.671092\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −9.46410 | −0.923602 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −12.5885 | −1.21697 | −0.608486 | − | 0.793565i | \(-0.708223\pi\) | ||||
−0.608486 | + | 0.793565i | \(0.708223\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 15.3205 | 1.46744 | 0.733719 | − | 0.679453i | \(-0.237783\pi\) | ||||
0.733719 | + | 0.679453i | \(0.237783\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0.535898 | 0.0508652 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 15.4641 | 1.45474 | 0.727370 | − | 0.686245i | \(-0.240742\pi\) | ||||
0.727370 | + | 0.686245i | \(0.240742\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −8.19615 | −0.764295 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −30.0526 | −2.77836 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −9.46410 | −0.867573 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 33.8564 | 3.05273 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 10.7321 | 0.952316 | 0.476158 | − | 0.879360i | \(-0.342029\pi\) | ||||
0.476158 | + | 0.879360i | \(0.342029\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 5.46410 | 0.481087 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 6.53590 | 0.571044 | 0.285522 | − | 0.958372i | \(-0.407833\pi\) | ||||
0.285522 | + | 0.958372i | \(0.407833\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −24.0000 | −2.08106 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 4.00000 | 0.344265 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −9.66025 | −0.825331 | −0.412666 | − | 0.910883i | \(-0.635402\pi\) | ||||
−0.412666 | + | 0.910883i | \(0.635402\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 10.9282 | 0.926918 | 0.463459 | − | 0.886118i | \(-0.346608\pi\) | ||||
0.463459 | + | 0.886118i | \(0.346608\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 24.3923 | 2.05420 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −23.3205 | −1.95016 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −5.46410 | −0.453769 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −13.6603 | −1.12668 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −3.07180 | −0.251651 | −0.125826 | − | 0.992052i | \(-0.540158\pi\) | ||||
−0.125826 | + | 0.992052i | \(0.540158\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 15.4641 | 1.25845 | 0.629225 | − | 0.777223i | \(-0.283372\pi\) | ||||
0.629225 | + | 0.777223i | \(0.283372\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 12.1962 | 0.986000 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 5.46410 | 0.438887 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1.26795 | 0.101193 | 0.0505967 | − | 0.998719i | \(-0.483888\pi\) | ||||
0.0505967 | + | 0.998719i | \(0.483888\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −33.3205 | −2.64249 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −28.3923 | −2.23763 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −12.1962 | −0.955276 | −0.477638 | − | 0.878557i | \(-0.658507\pi\) | ||||
−0.477638 | + | 0.878557i | \(0.658507\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 9.46410 | 0.736779 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 12.1962 | 0.943767 | 0.471883 | − | 0.881661i | \(-0.343574\pi\) | ||||
0.471883 | + | 0.881661i | \(0.343574\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 32.3205 | 2.48619 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 30.9282 | 2.36514 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −7.46410 | −0.567485 | −0.283743 | − | 0.958900i | \(-0.591576\pi\) | ||||
−0.283743 | + | 0.958900i | \(0.591576\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −3.46410 | −0.261861 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 21.8564 | 1.64283 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −25.3205 | −1.89254 | −0.946272 | − | 0.323372i | \(-0.895183\pi\) | ||||
−0.946272 | + | 0.323372i | \(0.895183\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −10.0000 | −0.743294 | −0.371647 | − | 0.928374i | \(-0.621207\pi\) | ||||
−0.371647 | + | 0.928374i | \(0.621207\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −24.3923 | −1.80313 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0.196152 | 0.0144214 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 9.46410 | 0.692084 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 13.8564 | 1.00791 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 16.3923 | 1.18611 | 0.593053 | − | 0.805164i | \(-0.297923\pi\) | ||||
0.593053 | + | 0.805164i | \(0.297923\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 4.19615 | 0.302046 | 0.151023 | − | 0.988530i | \(-0.451743\pi\) | ||||
0.151023 | + | 0.988530i | \(0.451743\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −18.3923 | −1.31710 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 3.46410 | 0.246807 | 0.123404 | − | 0.992357i | \(-0.460619\pi\) | ||||
0.123404 | + | 0.992357i | \(0.460619\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 16.7846 | 1.18983 | 0.594915 | − | 0.803789i | \(-0.297186\pi\) | ||||
0.594915 | + | 0.803789i | \(0.297186\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 22.3923 | 1.57943 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −18.9282 | −1.32850 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 12.3923 | 0.865516 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 36.5885 | 2.54307 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 24.0000 | 1.66011 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −10.5359 | −0.725321 | −0.362661 | − | 0.931921i | \(-0.618132\pi\) | ||||
−0.362661 | + | 0.931921i | \(0.618132\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −6.92820 | −0.474713 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 2.00000 | 0.136399 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 18.9282 | 1.28493 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 2.53590 | 0.171360 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −18.3923 | −1.23720 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −21.3205 | −1.42773 | −0.713863 | − | 0.700285i | \(-0.753056\pi\) | ||||
−0.713863 | + | 0.700285i | \(0.753056\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 4.46410 | 0.297607 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −24.1962 | −1.60596 | −0.802978 | − | 0.596009i | \(-0.796752\pi\) | ||||
−0.802978 | + | 0.596009i | \(0.796752\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 7.07180 | 0.467317 | 0.233659 | − | 0.972319i | \(-0.424930\pi\) | ||||
0.233659 | + | 0.972319i | \(0.424930\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 32.7846 | 2.15707 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 15.8038 | 1.03534 | 0.517672 | − | 0.855579i | \(-0.326799\pi\) | ||||
0.517672 | + | 0.855579i | \(0.326799\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 8.92820 | 0.582412 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −27.4641 | −1.77651 | −0.888253 | − | 0.459355i | \(-0.848080\pi\) | ||||
−0.888253 | + | 0.459355i | \(0.848080\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 15.8564 | 1.02140 | 0.510700 | − | 0.859759i | \(-0.329386\pi\) | ||||
0.510700 | + | 0.859759i | \(0.329386\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 18.7321 | 1.20166 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −5.00000 | −0.319438 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −46.6410 | −2.96770 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 43.3205 | 2.74533 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 27.3205 | 1.72446 | 0.862228 | − | 0.506521i | \(-0.169069\pi\) | ||||
0.862228 | + | 0.506521i | \(0.169069\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 28.3923 | 1.78501 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 7.46410 | 0.467420 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 7.46410 | 0.465598 | 0.232799 | − | 0.972525i | \(-0.425212\pi\) | ||||
0.232799 | + | 0.972525i | \(0.425212\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0.679492 | 0.0422216 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 24.3923 | 1.50985 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −12.9282 | −0.797187 | −0.398594 | − | 0.917128i | \(-0.630502\pi\) | ||||
−0.398594 | + | 0.917128i | \(0.630502\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −12.1962 | −0.749204 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 43.3205 | 2.65117 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 3.46410 | 0.211210 | 0.105605 | − | 0.994408i | \(-0.466322\pi\) | ||||
0.105605 | + | 0.994408i | \(0.466322\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 0.392305 | 0.0238308 | 0.0119154 | − | 0.999929i | \(-0.496207\pi\) | ||||
0.0119154 | + | 0.999929i | \(0.496207\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −63.7128 | −3.85607 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 3.46410 | 0.208893 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −11.8038 | −0.709224 | −0.354612 | − | 0.935013i | \(-0.615387\pi\) | ||||
−0.354612 | + | 0.935013i | \(0.615387\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −24.3923 | −1.46033 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 27.8564 | 1.66177 | 0.830887 | − | 0.556441i | \(-0.187834\pi\) | ||||
0.830887 | + | 0.556441i | \(0.187834\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −5.66025 | −0.336467 | −0.168234 | − | 0.985747i | \(-0.553806\pi\) | ||||
−0.168234 | + | 0.985747i | \(0.553806\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 18.9282 | 1.12121 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 42.9282 | 2.53397 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −9.53590 | −0.560935 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −29.3205 | −1.71880 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 4.19615 | 0.245142 | 0.122571 | − | 0.992460i | \(-0.460886\pi\) | ||||
0.122571 | + | 0.992460i | \(0.460886\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 8.00000 | 0.465778 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −13.8564 | −0.804030 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −55.1769 | −3.19096 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 6.92820 | 0.399335 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −8.39230 | −0.482125 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −8.92820 | −0.511227 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −4.92820 | −0.281267 | −0.140634 | − | 0.990062i | \(-0.544914\pi\) | ||||
−0.140634 | + | 0.990062i | \(0.544914\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 28.3923 | 1.61518 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 6.92820 | 0.392862 | 0.196431 | − | 0.980518i | \(-0.437065\pi\) | ||||
0.196431 | + | 0.980518i | \(0.437065\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −5.60770 | −0.316966 | −0.158483 | − | 0.987362i | \(-0.550660\pi\) | ||||
−0.158483 | + | 0.987362i | \(0.550660\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 15.4641 | 0.871303 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 0.588457 | 0.0330511 | 0.0165255 | − | 0.999863i | \(-0.494740\pi\) | ||||
0.0165255 | + | 0.999863i | \(0.494740\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 18.9282 | 1.05978 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 34.3923 | 1.91959 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 18.9282 | 1.05319 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −6.73205 | −0.373427 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −41.8564 | −2.31466 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 30.9282 | 1.70513 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −26.3923 | −1.45065 | −0.725326 | − | 0.688405i | \(-0.758311\pi\) | ||||
−0.725326 | + | 0.688405i | \(0.758311\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −0.875644 | −0.0479850 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 8.19615 | 0.447804 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 33.7128 | 1.83645 | 0.918227 | − | 0.396055i | \(-0.129621\pi\) | ||||
0.918227 | + | 0.396055i | \(0.129621\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −42.2487 | −2.29464 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −18.9282 | −1.02502 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 6.92820 | 0.374088 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 22.3923 | 1.20556 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −30.0526 | −1.61331 | −0.806653 | − | 0.591025i | \(-0.798723\pi\) | ||||
−0.806653 | + | 0.591025i | \(0.798723\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −7.46410 | −0.399544 | −0.199772 | − | 0.979842i | \(-0.564020\pi\) | ||||
−0.199772 | + | 0.979842i | \(0.564020\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 26.9282 | 1.43732 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 1.26795 | 0.0674861 | 0.0337431 | − | 0.999431i | \(-0.489257\pi\) | ||||
0.0337431 | + | 0.999431i | \(0.489257\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −2.53590 | −0.134592 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 25.8564 | 1.36847 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 6.92820 | 0.365657 | 0.182828 | − | 0.983145i | \(-0.441475\pi\) | ||||
0.182828 | + | 0.983145i | \(0.441475\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 29.0000 | 1.52632 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −2.73205 | −0.143395 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0.928203 | 0.0485844 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 26.7321 | 1.39540 | 0.697701 | − | 0.716389i | \(-0.254206\pi\) | ||||
0.697701 | + | 0.716389i | \(0.254206\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −55.3205 | −2.87987 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −42.2487 | −2.19344 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −25.7128 | −1.33136 | −0.665679 | − | 0.746238i | \(-0.731858\pi\) | ||||
−0.665679 | + | 0.746238i | \(0.731858\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 2.73205 | 0.141082 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −36.7846 | −1.89450 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −7.46410 | −0.383405 | −0.191703 | − | 0.981453i | \(-0.561401\pi\) | ||||
−0.191703 | + | 0.981453i | \(0.561401\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −29.3205 | −1.50214 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 26.7846 | 1.36863 | 0.684315 | − | 0.729187i | \(-0.260101\pi\) | ||||
0.684315 | + | 0.729187i | \(0.260101\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 12.0000 | 0.611577 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −8.92820 | −0.453846 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −18.3923 | −0.932527 | −0.466263 | − | 0.884646i | \(-0.654400\pi\) | ||||
−0.466263 | + | 0.884646i | \(0.654400\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 22.3923 | 1.13243 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −17.8564 | −0.900737 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 0.535898 | 0.0268960 | 0.0134480 | − | 0.999910i | \(-0.495719\pi\) | ||||
0.0134480 | + | 0.999910i | \(0.495719\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 65.5692 | 3.28257 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −1.00000 | −0.0499376 | ||||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 36.7846 | 1.83237 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 2.46410 | 0.122442 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −0.679492 | −0.0336812 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −16.3923 | −0.810547 | −0.405274 | − | 0.914195i | \(-0.632824\pi\) | ||||
−0.405274 | + | 0.914195i | \(0.632824\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 26.3923 | 1.30184 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 27.7128 | 1.36366 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 15.8564 | 0.778360 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −29.8564 | −1.46207 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 1.32051 | 0.0645110 | 0.0322555 | − | 0.999480i | \(-0.489731\pi\) | ||||
0.0322555 | + | 0.999480i | \(0.489731\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 13.4641 | 0.656200 | 0.328100 | − | 0.944643i | \(-0.393592\pi\) | ||||
0.328100 | + | 0.944643i | \(0.393592\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −39.8564 | −1.93788 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 2.73205 | 0.132524 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −30.9282 | −1.49672 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 63.7128 | 3.07608 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 11.6077 | 0.559123 | 0.279562 | − | 0.960128i | \(-0.409811\pi\) | ||||
0.279562 | + | 0.960128i | \(0.409811\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 5.60770 | 0.269489 | 0.134744 | − | 0.990880i | \(-0.456979\pi\) | ||||
0.134744 | + | 0.990880i | \(0.456979\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 14.9282 | 0.715753 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 56.7846 | 2.71638 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 0.784610 | 0.0374474 | 0.0187237 | − | 0.999825i | \(-0.494040\pi\) | ||||
0.0187237 | + | 0.999825i | \(0.494040\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 22.3205 | 1.06288 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 16.1962 | 0.769502 | 0.384751 | − | 0.923020i | \(-0.374287\pi\) | ||||
0.384751 | + | 0.923020i | \(0.374287\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 15.8564 | 0.751666 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 8.39230 | 0.396942 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 37.3205 | 1.76126 | 0.880632 | − | 0.473801i | \(-0.157118\pi\) | ||||
0.880632 | + | 0.473801i | \(0.157118\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −42.9282 | −2.02141 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −42.2487 | −1.98502 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −23.3205 | −1.09328 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −1.32051 | −0.0617708 | −0.0308854 | − | 0.999523i | \(-0.509833\pi\) | ||||
−0.0308854 | + | 0.999523i | \(0.509833\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −10.9282 | −0.510085 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 10.0000 | 0.465746 | 0.232873 | − | 0.972507i | \(-0.425187\pi\) | ||||
0.232873 | + | 0.972507i | \(0.425187\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −16.5885 | −0.770931 | −0.385465 | − | 0.922722i | \(-0.625959\pi\) | ||||
−0.385465 | + | 0.922722i | \(0.625959\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −14.9282 | −0.692279 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −3.12436 | −0.144578 | −0.0722890 | − | 0.997384i | \(-0.523030\pi\) | ||||
−0.0722890 | + | 0.997384i | \(0.523030\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 28.3923 | 1.31103 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −3.46410 | −0.159617 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −6.92820 | −0.318559 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 6.92820 | 0.317888 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 54.4449 | 2.49286 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −24.7846 | −1.13244 | −0.566219 | − | 0.824255i | \(-0.691594\pi\) | ||||
−0.566219 | + | 0.824255i | \(0.691594\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.32051 | 0.0602100 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 77.5692 | 3.52952 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −10.7321 | −0.487317 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −11.8564 | −0.537265 | −0.268633 | − | 0.963243i | \(-0.586572\pi\) | ||||
−0.268633 | + | 0.963243i | \(0.586572\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 33.3205 | 1.50681 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 10.1436 | 0.457774 | 0.228887 | − | 0.973453i | \(-0.426491\pi\) | ||||
0.228887 | + | 0.973453i | \(0.426491\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 14.9282 | 0.672332 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −15.4641 | −0.695060 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −8.78461 | −0.394044 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 14.9282 | 0.668278 | 0.334139 | − | 0.942524i | \(-0.391554\pi\) | ||||
0.334139 | + | 0.942524i | \(0.391554\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −33.3205 | −1.48865 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 4.14359 | 0.184754 | 0.0923769 | − | 0.995724i | \(-0.470554\pi\) | ||||
0.0923769 | + | 0.995724i | \(0.470554\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −3.07180 | −0.136693 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −88.3013 | −3.92160 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 5.60770 | 0.248557 | 0.124278 | − | 0.992247i | \(-0.460338\pi\) | ||||
0.124278 | + | 0.992247i | \(0.460338\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 3.21539 | 0.142240 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −27.7128 | −1.22355 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 10.3923 | 0.457940 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −30.9282 | −1.36022 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 20.3923 | 0.895123 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 7.85641 | 0.344195 | 0.172098 | − | 0.985080i | \(-0.444946\pi\) | ||||
0.172098 | + | 0.985080i | \(0.444946\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 28.5885 | 1.25009 | 0.625043 | − | 0.780590i | \(-0.285081\pi\) | ||||
0.625043 | + | 0.780590i | \(0.285081\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 9.46410 | 0.413047 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −14.9282 | −0.650283 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 44.1769 | 1.92074 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −35.7128 | −1.54980 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 83.4256 | 3.61356 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 12.5885 | 0.544246 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 69.1769 | 2.98520 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 17.3205 | 0.746047 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −25.7128 | −1.10548 | −0.552740 | − | 0.833354i | \(-0.686418\pi\) | ||||
−0.552740 | + | 0.833354i | \(0.686418\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 27.3205 | 1.17244 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −15.3205 | −0.656258 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −22.3923 | −0.957426 | −0.478713 | − | 0.877971i | \(-0.658897\pi\) | ||||
−0.478713 | + | 0.877971i | \(0.658897\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 39.8564 | 1.70103 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 37.8564 | 1.61274 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −0.535898 | −0.0227476 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 42.0000 | 1.77960 | 0.889799 | − | 0.456354i | \(-0.150845\pi\) | ||||
0.889799 | + | 0.456354i | \(0.150845\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 13.4641 | 0.569471 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −25.8564 | −1.09166 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −18.3923 | −0.775143 | −0.387572 | − | 0.921840i | \(-0.626686\pi\) | ||||
−0.387572 | + | 0.921840i | \(0.626686\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −15.4641 | −0.650580 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 8.53590 | 0.358474 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −8.24871 | −0.345804 | −0.172902 | − | 0.984939i | \(-0.555314\pi\) | ||||
−0.172902 | + | 0.984939i | \(0.555314\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 27.3205 | 1.14333 | 0.571664 | − | 0.820488i | \(-0.306298\pi\) | ||||
0.571664 | + | 0.820488i | \(0.306298\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −44.7846 | −1.87090 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 8.19615 | 0.341803 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −17.3205 | −0.721062 | −0.360531 | − | 0.932747i | \(-0.617405\pi\) | ||||
−0.360531 | + | 0.932747i | \(0.617405\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −11.4641 | −0.476432 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 54.9282 | 2.27881 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 42.2487 | 1.74976 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 30.0526 | 1.24252 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 35.1769 | 1.45191 | 0.725953 | − | 0.687744i | \(-0.241399\pi\) | ||||
0.725953 | + | 0.687744i | \(0.241399\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −37.8564 | −1.55985 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −9.46410 | −0.389301 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 15.1244 | 0.621083 | 0.310541 | − | 0.950560i | \(-0.399490\pi\) | ||||
0.310541 | + | 0.950560i | \(0.399490\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 9.46410 | 0.387990 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −45.8564 | −1.87678 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −19.1769 | −0.783547 | −0.391774 | − | 0.920062i | \(-0.628138\pi\) | ||||
−0.391774 | + | 0.920062i | \(0.628138\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 14.0000 | 0.571072 | 0.285536 | − | 0.958368i | \(-0.407828\pi\) | ||||
0.285536 | + | 0.958368i | \(0.407828\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −36.5885 | −1.49000 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −1.00000 | −0.0406558 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 45.7128 | 1.85543 | 0.927713 | − | 0.373294i | \(-0.121772\pi\) | ||||
0.927713 | + | 0.373294i | \(0.121772\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 51.7128 | 2.09551 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 60.1051 | 2.43159 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 45.6603 | 1.84420 | 0.922100 | − | 0.386951i | \(-0.126472\pi\) | ||||
0.922100 | + | 0.386951i | \(0.126472\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −33.8564 | −1.36522 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 7.80385 | 0.314171 | 0.157086 | − | 0.987585i | \(-0.449790\pi\) | ||||
0.157086 | + | 0.987585i | \(0.449790\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −13.3205 | −0.535396 | −0.267698 | − | 0.963503i | \(-0.586263\pi\) | ||||
−0.267698 | + | 0.963503i | \(0.586263\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −32.7846 | −1.31560 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 54.9282 | 2.20065 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −65.5692 | −2.61858 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −0.535898 | −0.0213677 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 36.1051 | 1.43732 | 0.718661 | − | 0.695361i | \(-0.244755\pi\) | ||||
0.718661 | + | 0.695361i | \(0.244755\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 28.7846 | 1.14409 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −10.7321 | −0.425888 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −33.6603 | −1.33367 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 11.3205 | 0.447832 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −23.8564 | −0.942271 | −0.471136 | − | 0.882061i | \(-0.656156\pi\) | ||||
−0.471136 | + | 0.882061i | \(0.656156\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −19.0718 | −0.752118 | −0.376059 | − | 0.926596i | \(-0.622721\pi\) | ||||
−0.376059 | + | 0.926596i | \(0.622721\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −5.46410 | −0.215149 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 29.6603 | 1.16606 | 0.583032 | − | 0.812449i | \(-0.301866\pi\) | ||||
0.583032 | + | 0.812449i | \(0.301866\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −27.7128 | −1.08782 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −51.7128 | −2.02678 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 44.2487 | 1.73159 | 0.865793 | − | 0.500402i | \(-0.166815\pi\) | ||||
0.865793 | + | 0.500402i | \(0.166815\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −6.53590 | −0.255379 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −4.14359 | −0.161657 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 6.92820 | 0.269884 | 0.134942 | − | 0.990853i | \(-0.456915\pi\) | ||||
0.134942 | + | 0.990853i | \(0.456915\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 23.8564 | 0.927907 | 0.463953 | − | 0.885860i | \(-0.346431\pi\) | ||||
0.463953 | + | 0.885860i | \(0.346431\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 50.2487 | 1.95150 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 24.0000 | 0.930680 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 44.7846 | 1.73407 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 58.2487 | 2.25203 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 30.9282 | 1.19397 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 38.4449 | 1.48194 | 0.740970 | − | 0.671538i | \(-0.234366\pi\) | ||||
0.740970 | + | 0.671538i | \(0.234366\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −4.00000 | −0.153960 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −1.60770 | −0.0617887 | −0.0308944 | − | 0.999523i | \(-0.509836\pi\) | ||||
−0.0308944 | + | 0.999523i | \(0.509836\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −37.1769 | −1.42672 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 66.1051 | 2.53315 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −29.6603 | −1.13492 | −0.567459 | − | 0.823402i | \(-0.692073\pi\) | ||||
−0.567459 | + | 0.823402i | \(0.692073\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 9.66025 | 0.369099 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −19.3205 | −0.737123 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −82.1051 | −3.12796 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −16.0000 | −0.608669 | −0.304334 | − | 0.952565i | \(-0.598434\pi\) | ||||
−0.304334 | + | 0.952565i | \(0.598434\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −53.5692 | −2.03493 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −10.9282 | −0.414530 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −33.8564 | −1.28240 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −43.1769 | −1.63310 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −11.0718 | −0.418176 | −0.209088 | − | 0.977897i | \(-0.567050\pi\) | ||||
−0.209088 | + | 0.977897i | \(0.567050\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −1.35898 | −0.0512550 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −24.3923 | −0.918667 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −10.6410 | −0.400197 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 1.21539 | 0.0456449 | 0.0228225 | − | 0.999740i | \(-0.492735\pi\) | ||||
0.0228225 | + | 0.999740i | \(0.492735\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −44.7846 | −1.67720 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 23.3205 | 0.872138 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 75.0333 | 2.80217 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 0.248711 | 0.00927537 | 0.00463768 | − | 0.999989i | \(-0.498524\pi\) | ||||
0.00463768 | + | 0.999989i | \(0.498524\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 36.0000 | 1.34071 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −43.3205 | −1.61111 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 5.46410 | 0.202932 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 26.7321 | 0.991437 | 0.495718 | − | 0.868483i | \(-0.334905\pi\) | ||||
0.495718 | + | 0.868483i | \(0.334905\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −43.7846 | −1.62165 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −5.46410 | −0.202097 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −12.5359 | −0.463024 | −0.231512 | − | 0.972832i | \(-0.574367\pi\) | ||||
−0.231512 | + | 0.972832i | \(0.574367\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 13.6603 | 0.503866 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −28.3923 | −1.04584 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −20.5359 | −0.755425 | −0.377713 | − | 0.925923i | \(-0.623289\pi\) | ||||
−0.377713 | + | 0.925923i | \(0.623289\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 127.426 | 4.68110 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −36.9808 | −1.35669 | −0.678346 | − | 0.734742i | \(-0.737303\pi\) | ||||
−0.678346 | + | 0.734742i | \(0.737303\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 3.07180 | 0.112542 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −70.7846 | −2.58987 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 43.6077 | 1.59339 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −12.0000 | −0.437886 | −0.218943 | − | 0.975738i | \(-0.570261\pi\) | ||||
−0.218943 | + | 0.975738i | \(0.570261\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −74.6410 | −2.72007 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −15.4641 | −0.562796 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 9.32051 | 0.338760 | 0.169380 | − | 0.985551i | \(-0.445824\pi\) | ||||
0.169380 | + | 0.985551i | \(0.445824\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −77.5692 | −2.81558 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 2.53590 | 0.0919262 | 0.0459631 | − | 0.998943i | \(-0.485364\pi\) | ||||
0.0459631 | + | 0.998943i | \(0.485364\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −53.0718 | −1.92133 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −12.1962 | −0.440953 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 53.8564 | 1.94464 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −46.1051 | −1.66259 | −0.831297 | − | 0.555829i | \(-0.812401\pi\) | ||||
−0.831297 | + | 0.555829i | \(0.812401\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −20.3923 | −0.734411 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 38.7846 | 1.39499 | 0.697493 | − | 0.716592i | \(-0.254299\pi\) | ||||
0.697493 | + | 0.716592i | \(0.254299\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −5.46410 | −0.196276 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −1.85641 | −0.0665982 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −85.8564 | −3.07612 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 8.78461 | 0.314338 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −21.8564 | −0.781084 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −1.26795 | −0.0452550 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 41.2679 | 1.47104 | 0.735522 | − | 0.677501i | \(-0.236937\pi\) | ||||
0.735522 | + | 0.677501i | \(0.236937\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 35.3205 | 1.25744 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −53.5692 | −1.90470 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −60.1051 | −2.13440 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 33.3205 | 1.18176 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −13.6077 | −0.482009 | −0.241005 | − | 0.970524i | \(-0.577477\pi\) | ||||
−0.241005 | + | 0.970524i | \(0.577477\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −24.3923 | −0.862938 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −70.7846 | −2.50105 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −3.21539 | −0.113469 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 28.3923 | 1.00070 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −9.46410 | −0.333152 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −14.7846 | −0.519799 | −0.259900 | − | 0.965636i | \(-0.583689\pi\) | ||||
−0.259900 | + | 0.965636i | \(0.583689\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 5.07180 | 0.178095 | 0.0890474 | − | 0.996027i | \(-0.471618\pi\) | ||||
0.0890474 | + | 0.996027i | \(0.471618\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −1.07180 | −0.0375896 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 12.1962 | 0.427213 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −13.8564 | −0.484774 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 104.105 | 3.63773 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −35.5692 | −1.24137 | −0.620687 | − | 0.784058i | \(-0.713146\pi\) | ||||
−0.620687 | + | 0.784058i | \(0.713146\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −42.0526 | −1.46586 | −0.732930 | − | 0.680304i | \(-0.761848\pi\) | ||||
−0.732930 | + | 0.680304i | \(0.761848\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −9.46410 | −0.329498 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 3.75129 | 0.130445 | 0.0652225 | − | 0.997871i | \(-0.479224\pi\) | ||||
0.0652225 | + | 0.997871i | \(0.479224\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −26.1051 | −0.906668 | −0.453334 | − | 0.891341i | \(-0.649766\pi\) | ||||
−0.453334 | + | 0.891341i | \(0.649766\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 32.2487 | 1.11870 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 13.6603 | 0.473300 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −12.1962 | −0.422065 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 21.8564 | 0.755468 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 49.8564 | 1.72123 | 0.860617 | − | 0.509253i | \(-0.170078\pi\) | ||||
0.860617 | + | 0.509253i | \(0.170078\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 0.856406 | 0.0295313 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −76.1051 | −2.62120 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −32.3205 | −1.11186 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −3.46410 | −0.119028 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 15.4641 | 0.530727 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −1.60770 | −0.0551111 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 7.07180 | 0.242134 | 0.121067 | − | 0.992644i | \(-0.461368\pi\) | ||||
0.121067 | + | 0.992644i | \(0.461368\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −30.9282 | −1.05772 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 56.2487 | 1.92142 | 0.960710 | − | 0.277555i | \(-0.0895241\pi\) | ||||
0.960710 | + | 0.277555i | \(0.0895241\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −4.24871 | −0.144964 | −0.0724821 | − | 0.997370i | \(-0.523092\pi\) | ||||
−0.0724821 | + | 0.997370i | \(0.523092\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −117.282 | −3.99696 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 40.1962 | 1.36829 | 0.684146 | − | 0.729345i | \(-0.260175\pi\) | ||||
0.684146 | + | 0.729345i | \(0.260175\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 7.46410 | 0.253787 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 26.0526 | 0.884791 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 55.1769 | 1.86960 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 47.9090 | 1.62147 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 3.46410 | 0.117108 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −12.4833 | −0.421532 | −0.210766 | − | 0.977536i | \(-0.567596\pi\) | ||||
−0.210766 | + | 0.977536i | \(0.567596\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −11.4641 | −0.386675 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 29.7128 | 1.00105 | 0.500525 | − | 0.865722i | \(-0.333140\pi\) | ||||
0.500525 | + | 0.865722i | \(0.333140\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 37.7128 | 1.26914 | 0.634569 | − | 0.772867i | \(-0.281178\pi\) | ||||
0.634569 | + | 0.772867i | \(0.281178\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −21.8564 | −0.734695 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −26.4449 | −0.887932 | −0.443966 | − | 0.896044i | \(-0.646429\pi\) | ||||
−0.443966 | + | 0.896044i | \(0.646429\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −37.1769 | −1.24687 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −8.53590 | −0.285963 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −61.8564 | −2.06995 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 25.3205 | 0.846371 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 150.746 | 5.03327 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −29.8564 | −0.995767 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 33.3205 | 1.11007 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −18.9282 | −0.629891 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 10.0000 | 0.332411 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −21.2679 | −0.706191 | −0.353095 | − | 0.935587i | \(-0.614871\pi\) | ||||
−0.353095 | + | 0.935587i | \(0.614871\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 13.7128 | 0.454825 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −31.7128 | −1.05069 | −0.525346 | − | 0.850889i | \(-0.676064\pi\) | ||||
−0.525346 | + | 0.850889i | \(0.676064\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −54.9282 | −1.81786 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 24.3923 | 0.806385 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −22.6410 | −0.747672 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −40.7846 | −1.34536 | −0.672680 | − | 0.739933i | \(-0.734857\pi\) | ||||
−0.672680 | + | 0.739933i | \(0.734857\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 13.4641 | 0.443657 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −17.0718 | −0.561925 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −0.196152 | −0.00644945 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −46.3923 | −1.52372 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −0.535898 | −0.0175823 | −0.00879113 | − | 0.999961i | \(-0.502798\pi\) | ||||
−0.00879113 | + | 0.999961i | \(0.502798\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 34.6410 | 1.13531 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −18.9282 | −0.619682 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −9.46410 | −0.309509 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 41.3731 | 1.35160 | 0.675800 | − | 0.737085i | \(-0.263798\pi\) | ||||
0.675800 | + | 0.737085i | \(0.263798\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 15.3205 | 0.499966 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −17.7128 | −0.577421 | −0.288711 | − | 0.957416i | \(-0.593227\pi\) | ||||
−0.288711 | + | 0.957416i | \(0.593227\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −101.569 | −3.30755 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −13.8564 | −0.450749 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −48.6410 | −1.58062 | −0.790310 | − | 0.612707i | \(-0.790081\pi\) | ||||
−0.790310 | + | 0.612707i | \(0.790081\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 6.24871 | 0.202842 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −1.60770 | −0.0521331 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 10.3923 | 0.336640 | 0.168320 | − | 0.985732i | \(-0.446166\pi\) | ||||
0.168320 | + | 0.985732i | \(0.446166\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −16.3923 | −0.530443 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −51.7128 | −1.67164 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 33.4641 | 1.08061 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −1.14359 | −0.0368901 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −56.1962 | −1.81090 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −4.19615 | −0.135079 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 22.4449 | 0.721778 | 0.360889 | − | 0.932609i | \(-0.382473\pi\) | ||||
0.360889 | + | 0.932609i | \(0.382473\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −51.7128 | −1.66125 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −16.0000 | −0.513464 | −0.256732 | − | 0.966483i | \(-0.582646\pi\) | ||||
−0.256732 | + | 0.966483i | \(0.582646\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −37.8564 | −1.21362 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 18.3923 | 0.589025 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −11.4641 | −0.366769 | −0.183385 | − | 0.983041i | \(-0.558705\pi\) | ||||
−0.183385 | + | 0.983041i | \(0.558705\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −54.9282 | −1.75551 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 68.3923 | 2.18360 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 27.1769 | 0.866809 | 0.433404 | − | 0.901200i | \(-0.357312\pi\) | ||||
0.433404 | + | 0.901200i | \(0.357312\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −3.46410 | −0.110375 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −84.4974 | −2.68958 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −16.3923 | −0.521245 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −0.392305 | −0.0124620 | −0.00623099 | − | 0.999981i | \(-0.501983\pi\) | ||||
−0.00623099 | + | 0.999981i | \(0.501983\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 72.1051 | 2.28819 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −16.7846 | −0.532108 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 19.0718 | 0.604010 | 0.302005 | − | 0.953306i | \(-0.402344\pi\) | ||||
0.302005 | + | 0.953306i | \(0.402344\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0.784610 | 0.0248240 |
(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 | 8020.2.a.b.1.1 | ✓ | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8020.2.a.b.1.1 | ✓ | 2 | 1.1 | even | 1 | trivial |