Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3822,2,Mod(1,3822)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3822, 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("3822.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3822 = 2 \cdot 3 \cdot 7^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3822.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: | \(30.5188236525\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{8})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 546) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(1.41421\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3822.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 1.41421 | 0.632456 | 0.316228 | − | 0.948683i | \(-0.397584\pi\) | ||||
0.316228 | + | 0.948683i | \(0.397584\pi\) | |||||||
\(6\) | −1.00000 | −0.408248 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 1.41421 | 0.447214 | ||||||||
\(11\) | 0.414214 | 0.124890 | 0.0624450 | − | 0.998048i | \(-0.480110\pi\) | ||||
0.0624450 | + | 0.998048i | \(0.480110\pi\) | |||||||
\(12\) | −1.00000 | −0.288675 | ||||||||
\(13\) | −1.00000 | −0.277350 | ||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.41421 | −0.365148 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −5.24264 | −1.27153 | −0.635764 | − | 0.771884i | \(-0.719315\pi\) | ||||
−0.635764 | + | 0.771884i | \(0.719315\pi\) | |||||||
\(18\) | 1.00000 | 0.235702 | ||||||||
\(19\) | −3.00000 | −0.688247 | −0.344124 | − | 0.938924i | \(-0.611824\pi\) | ||||
−0.344124 | + | 0.938924i | \(0.611824\pi\) | |||||||
\(20\) | 1.41421 | 0.316228 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0.414214 | 0.0883106 | ||||||||
\(23\) | −9.07107 | −1.89145 | −0.945724 | − | 0.324970i | \(-0.894646\pi\) | ||||
−0.945724 | + | 0.324970i | \(0.894646\pi\) | |||||||
\(24\) | −1.00000 | −0.204124 | ||||||||
\(25\) | −3.00000 | −0.600000 | ||||||||
\(26\) | −1.00000 | −0.196116 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 5.00000 | 0.928477 | 0.464238 | − | 0.885710i | \(-0.346328\pi\) | ||||
0.464238 | + | 0.885710i | \(0.346328\pi\) | |||||||
\(30\) | −1.41421 | −0.258199 | ||||||||
\(31\) | −6.82843 | −1.22642 | −0.613211 | − | 0.789919i | \(-0.710122\pi\) | ||||
−0.613211 | + | 0.789919i | \(0.710122\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | −0.414214 | −0.0721053 | ||||||||
\(34\) | −5.24264 | −0.899105 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | −5.07107 | −0.833678 | −0.416839 | − | 0.908980i | \(-0.636862\pi\) | ||||
−0.416839 | + | 0.908980i | \(0.636862\pi\) | |||||||
\(38\) | −3.00000 | −0.486664 | ||||||||
\(39\) | 1.00000 | 0.160128 | ||||||||
\(40\) | 1.41421 | 0.223607 | ||||||||
\(41\) | −4.58579 | −0.716180 | −0.358090 | − | 0.933687i | \(-0.616572\pi\) | ||||
−0.358090 | + | 0.933687i | \(0.616572\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4.82843 | 0.736328 | 0.368164 | − | 0.929761i | \(-0.379986\pi\) | ||||
0.368164 | + | 0.929761i | \(0.379986\pi\) | |||||||
\(44\) | 0.414214 | 0.0624450 | ||||||||
\(45\) | 1.41421 | 0.210819 | ||||||||
\(46\) | −9.07107 | −1.33746 | ||||||||
\(47\) | −9.00000 | −1.31278 | −0.656392 | − | 0.754420i | \(-0.727918\pi\) | ||||
−0.656392 | + | 0.754420i | \(0.727918\pi\) | |||||||
\(48\) | −1.00000 | −0.144338 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −3.00000 | −0.424264 | ||||||||
\(51\) | 5.24264 | 0.734117 | ||||||||
\(52\) | −1.00000 | −0.138675 | ||||||||
\(53\) | 12.3137 | 1.69142 | 0.845709 | − | 0.533644i | \(-0.179178\pi\) | ||||
0.845709 | + | 0.533644i | \(0.179178\pi\) | |||||||
\(54\) | −1.00000 | −0.136083 | ||||||||
\(55\) | 0.585786 | 0.0789874 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 3.00000 | 0.397360 | ||||||||
\(58\) | 5.00000 | 0.656532 | ||||||||
\(59\) | −7.58579 | −0.987585 | −0.493793 | − | 0.869580i | \(-0.664390\pi\) | ||||
−0.493793 | + | 0.869580i | \(0.664390\pi\) | |||||||
\(60\) | −1.41421 | −0.182574 | ||||||||
\(61\) | 5.24264 | 0.671251 | 0.335626 | − | 0.941995i | \(-0.391052\pi\) | ||||
0.335626 | + | 0.941995i | \(0.391052\pi\) | |||||||
\(62\) | −6.82843 | −0.867211 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −1.41421 | −0.175412 | ||||||||
\(66\) | −0.414214 | −0.0509862 | ||||||||
\(67\) | −14.6569 | −1.79062 | −0.895310 | − | 0.445444i | \(-0.853046\pi\) | ||||
−0.895310 | + | 0.445444i | \(0.853046\pi\) | |||||||
\(68\) | −5.24264 | −0.635764 | ||||||||
\(69\) | 9.07107 | 1.09203 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −1.00000 | −0.118678 | −0.0593391 | − | 0.998238i | \(-0.518899\pi\) | ||||
−0.0593391 | + | 0.998238i | \(0.518899\pi\) | |||||||
\(72\) | 1.00000 | 0.117851 | ||||||||
\(73\) | 1.07107 | 0.125359 | 0.0626795 | − | 0.998034i | \(-0.480035\pi\) | ||||
0.0626795 | + | 0.998034i | \(0.480035\pi\) | |||||||
\(74\) | −5.07107 | −0.589500 | ||||||||
\(75\) | 3.00000 | 0.346410 | ||||||||
\(76\) | −3.00000 | −0.344124 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 1.00000 | 0.113228 | ||||||||
\(79\) | 13.3137 | 1.49791 | 0.748955 | − | 0.662621i | \(-0.230556\pi\) | ||||
0.748955 | + | 0.662621i | \(0.230556\pi\) | |||||||
\(80\) | 1.41421 | 0.158114 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −4.58579 | −0.506415 | ||||||||
\(83\) | 7.65685 | 0.840449 | 0.420224 | − | 0.907420i | \(-0.361951\pi\) | ||||
0.420224 | + | 0.907420i | \(0.361951\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −7.41421 | −0.804184 | ||||||||
\(86\) | 4.82843 | 0.520663 | ||||||||
\(87\) | −5.00000 | −0.536056 | ||||||||
\(88\) | 0.414214 | 0.0441553 | ||||||||
\(89\) | 6.24264 | 0.661719 | 0.330859 | − | 0.943680i | \(-0.392661\pi\) | ||||
0.330859 | + | 0.943680i | \(0.392661\pi\) | |||||||
\(90\) | 1.41421 | 0.149071 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −9.07107 | −0.945724 | ||||||||
\(93\) | 6.82843 | 0.708075 | ||||||||
\(94\) | −9.00000 | −0.928279 | ||||||||
\(95\) | −4.24264 | −0.435286 | ||||||||
\(96\) | −1.00000 | −0.102062 | ||||||||
\(97\) | −7.89949 | −0.802072 | −0.401036 | − | 0.916062i | \(-0.631350\pi\) | ||||
−0.401036 | + | 0.916062i | \(0.631350\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0.414214 | 0.0416300 | ||||||||
\(100\) | −3.00000 | −0.300000 | ||||||||
\(101\) | 1.17157 | 0.116576 | 0.0582879 | − | 0.998300i | \(-0.481436\pi\) | ||||
0.0582879 | + | 0.998300i | \(0.481436\pi\) | |||||||
\(102\) | 5.24264 | 0.519099 | ||||||||
\(103\) | −6.48528 | −0.639014 | −0.319507 | − | 0.947584i | \(-0.603517\pi\) | ||||
−0.319507 | + | 0.947584i | \(0.603517\pi\) | |||||||
\(104\) | −1.00000 | −0.0980581 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 12.3137 | 1.19601 | ||||||||
\(107\) | 13.6569 | 1.32026 | 0.660129 | − | 0.751152i | \(-0.270502\pi\) | ||||
0.660129 | + | 0.751152i | \(0.270502\pi\) | |||||||
\(108\) | −1.00000 | −0.0962250 | ||||||||
\(109\) | 1.65685 | 0.158698 | 0.0793489 | − | 0.996847i | \(-0.474716\pi\) | ||||
0.0793489 | + | 0.996847i | \(0.474716\pi\) | |||||||
\(110\) | 0.585786 | 0.0558525 | ||||||||
\(111\) | 5.07107 | 0.481324 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −6.07107 | −0.571118 | −0.285559 | − | 0.958361i | \(-0.592179\pi\) | ||||
−0.285559 | + | 0.958361i | \(0.592179\pi\) | |||||||
\(114\) | 3.00000 | 0.280976 | ||||||||
\(115\) | −12.8284 | −1.19626 | ||||||||
\(116\) | 5.00000 | 0.464238 | ||||||||
\(117\) | −1.00000 | −0.0924500 | ||||||||
\(118\) | −7.58579 | −0.698328 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −1.41421 | −0.129099 | ||||||||
\(121\) | −10.8284 | −0.984402 | ||||||||
\(122\) | 5.24264 | 0.474646 | ||||||||
\(123\) | 4.58579 | 0.413486 | ||||||||
\(124\) | −6.82843 | −0.613211 | ||||||||
\(125\) | −11.3137 | −1.01193 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 9.89949 | 0.878438 | 0.439219 | − | 0.898380i | \(-0.355255\pi\) | ||||
0.439219 | + | 0.898380i | \(0.355255\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | −4.82843 | −0.425119 | ||||||||
\(130\) | −1.41421 | −0.124035 | ||||||||
\(131\) | −9.89949 | −0.864923 | −0.432461 | − | 0.901652i | \(-0.642355\pi\) | ||||
−0.432461 | + | 0.901652i | \(0.642355\pi\) | |||||||
\(132\) | −0.414214 | −0.0360527 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −14.6569 | −1.26616 | ||||||||
\(135\) | −1.41421 | −0.121716 | ||||||||
\(136\) | −5.24264 | −0.449553 | ||||||||
\(137\) | −13.0711 | −1.11674 | −0.558368 | − | 0.829593i | \(-0.688572\pi\) | ||||
−0.558368 | + | 0.829593i | \(0.688572\pi\) | |||||||
\(138\) | 9.07107 | 0.772181 | ||||||||
\(139\) | 21.2132 | 1.79928 | 0.899640 | − | 0.436632i | \(-0.143829\pi\) | ||||
0.899640 | + | 0.436632i | \(0.143829\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 9.00000 | 0.757937 | ||||||||
\(142\) | −1.00000 | −0.0839181 | ||||||||
\(143\) | −0.414214 | −0.0346383 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | 7.07107 | 0.587220 | ||||||||
\(146\) | 1.07107 | 0.0886422 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −5.07107 | −0.416839 | ||||||||
\(149\) | 15.8995 | 1.30254 | 0.651269 | − | 0.758847i | \(-0.274237\pi\) | ||||
0.651269 | + | 0.758847i | \(0.274237\pi\) | |||||||
\(150\) | 3.00000 | 0.244949 | ||||||||
\(151\) | −7.58579 | −0.617323 | −0.308661 | − | 0.951172i | \(-0.599881\pi\) | ||||
−0.308661 | + | 0.951172i | \(0.599881\pi\) | |||||||
\(152\) | −3.00000 | −0.243332 | ||||||||
\(153\) | −5.24264 | −0.423842 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −9.65685 | −0.775657 | ||||||||
\(156\) | 1.00000 | 0.0800641 | ||||||||
\(157\) | −7.92893 | −0.632798 | −0.316399 | − | 0.948626i | \(-0.602474\pi\) | ||||
−0.316399 | + | 0.948626i | \(0.602474\pi\) | |||||||
\(158\) | 13.3137 | 1.05918 | ||||||||
\(159\) | −12.3137 | −0.976541 | ||||||||
\(160\) | 1.41421 | 0.111803 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 1.00000 | 0.0785674 | ||||||||
\(163\) | 17.1421 | 1.34268 | 0.671338 | − | 0.741151i | \(-0.265720\pi\) | ||||
0.671338 | + | 0.741151i | \(0.265720\pi\) | |||||||
\(164\) | −4.58579 | −0.358090 | ||||||||
\(165\) | −0.585786 | −0.0456034 | ||||||||
\(166\) | 7.65685 | 0.594287 | ||||||||
\(167\) | −12.3137 | −0.952863 | −0.476432 | − | 0.879211i | \(-0.658070\pi\) | ||||
−0.476432 | + | 0.879211i | \(0.658070\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | −7.41421 | −0.568644 | ||||||||
\(171\) | −3.00000 | −0.229416 | ||||||||
\(172\) | 4.82843 | 0.368164 | ||||||||
\(173\) | −20.3137 | −1.54442 | −0.772211 | − | 0.635366i | \(-0.780849\pi\) | ||||
−0.772211 | + | 0.635366i | \(0.780849\pi\) | |||||||
\(174\) | −5.00000 | −0.379049 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0.414214 | 0.0312225 | ||||||||
\(177\) | 7.58579 | 0.570183 | ||||||||
\(178\) | 6.24264 | 0.467906 | ||||||||
\(179\) | −12.3431 | −0.922570 | −0.461285 | − | 0.887252i | \(-0.652611\pi\) | ||||
−0.461285 | + | 0.887252i | \(0.652611\pi\) | |||||||
\(180\) | 1.41421 | 0.105409 | ||||||||
\(181\) | 11.5858 | 0.861165 | 0.430582 | − | 0.902551i | \(-0.358308\pi\) | ||||
0.430582 | + | 0.902551i | \(0.358308\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −5.24264 | −0.387547 | ||||||||
\(184\) | −9.07107 | −0.668728 | ||||||||
\(185\) | −7.17157 | −0.527265 | ||||||||
\(186\) | 6.82843 | 0.500685 | ||||||||
\(187\) | −2.17157 | −0.158801 | ||||||||
\(188\) | −9.00000 | −0.656392 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −4.24264 | −0.307794 | ||||||||
\(191\) | 2.34315 | 0.169544 | 0.0847720 | − | 0.996400i | \(-0.472984\pi\) | ||||
0.0847720 | + | 0.996400i | \(0.472984\pi\) | |||||||
\(192\) | −1.00000 | −0.0721688 | ||||||||
\(193\) | −15.7574 | −1.13424 | −0.567120 | − | 0.823635i | \(-0.691942\pi\) | ||||
−0.567120 | + | 0.823635i | \(0.691942\pi\) | |||||||
\(194\) | −7.89949 | −0.567151 | ||||||||
\(195\) | 1.41421 | 0.101274 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 9.55635 | 0.680862 | 0.340431 | − | 0.940270i | \(-0.389427\pi\) | ||||
0.340431 | + | 0.940270i | \(0.389427\pi\) | |||||||
\(198\) | 0.414214 | 0.0294369 | ||||||||
\(199\) | −10.5858 | −0.750407 | −0.375203 | − | 0.926943i | \(-0.622427\pi\) | ||||
−0.375203 | + | 0.926943i | \(0.622427\pi\) | |||||||
\(200\) | −3.00000 | −0.212132 | ||||||||
\(201\) | 14.6569 | 1.03381 | ||||||||
\(202\) | 1.17157 | 0.0824316 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 5.24264 | 0.367058 | ||||||||
\(205\) | −6.48528 | −0.452952 | ||||||||
\(206\) | −6.48528 | −0.451851 | ||||||||
\(207\) | −9.07107 | −0.630483 | ||||||||
\(208\) | −1.00000 | −0.0693375 | ||||||||
\(209\) | −1.24264 | −0.0859553 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −28.3848 | −1.95409 | −0.977044 | − | 0.213036i | \(-0.931665\pi\) | ||||
−0.977044 | + | 0.213036i | \(0.931665\pi\) | |||||||
\(212\) | 12.3137 | 0.845709 | ||||||||
\(213\) | 1.00000 | 0.0685189 | ||||||||
\(214\) | 13.6569 | 0.933563 | ||||||||
\(215\) | 6.82843 | 0.465695 | ||||||||
\(216\) | −1.00000 | −0.0680414 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 1.65685 | 0.112216 | ||||||||
\(219\) | −1.07107 | −0.0723761 | ||||||||
\(220\) | 0.585786 | 0.0394937 | ||||||||
\(221\) | 5.24264 | 0.352658 | ||||||||
\(222\) | 5.07107 | 0.340348 | ||||||||
\(223\) | −21.3848 | −1.43203 | −0.716015 | − | 0.698085i | \(-0.754036\pi\) | ||||
−0.716015 | + | 0.698085i | \(0.754036\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −3.00000 | −0.200000 | ||||||||
\(226\) | −6.07107 | −0.403841 | ||||||||
\(227\) | 26.1421 | 1.73511 | 0.867557 | − | 0.497337i | \(-0.165689\pi\) | ||||
0.867557 | + | 0.497337i | \(0.165689\pi\) | |||||||
\(228\) | 3.00000 | 0.198680 | ||||||||
\(229\) | 7.17157 | 0.473911 | 0.236955 | − | 0.971521i | \(-0.423850\pi\) | ||||
0.236955 | + | 0.971521i | \(0.423850\pi\) | |||||||
\(230\) | −12.8284 | −0.845881 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 5.00000 | 0.328266 | ||||||||
\(233\) | −3.72792 | −0.244224 | −0.122112 | − | 0.992516i | \(-0.538967\pi\) | ||||
−0.122112 | + | 0.992516i | \(0.538967\pi\) | |||||||
\(234\) | −1.00000 | −0.0653720 | ||||||||
\(235\) | −12.7279 | −0.830278 | ||||||||
\(236\) | −7.58579 | −0.493793 | ||||||||
\(237\) | −13.3137 | −0.864818 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −2.51472 | −0.162664 | −0.0813318 | − | 0.996687i | \(-0.525917\pi\) | ||||
−0.0813318 | + | 0.996687i | \(0.525917\pi\) | |||||||
\(240\) | −1.41421 | −0.0912871 | ||||||||
\(241\) | 16.4853 | 1.06191 | 0.530955 | − | 0.847400i | \(-0.321833\pi\) | ||||
0.530955 | + | 0.847400i | \(0.321833\pi\) | |||||||
\(242\) | −10.8284 | −0.696078 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 5.24264 | 0.335626 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 4.58579 | 0.292379 | ||||||||
\(247\) | 3.00000 | 0.190885 | ||||||||
\(248\) | −6.82843 | −0.433606 | ||||||||
\(249\) | −7.65685 | −0.485233 | ||||||||
\(250\) | −11.3137 | −0.715542 | ||||||||
\(251\) | −12.8284 | −0.809723 | −0.404862 | − | 0.914378i | \(-0.632680\pi\) | ||||
−0.404862 | + | 0.914378i | \(0.632680\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −3.75736 | −0.236223 | ||||||||
\(254\) | 9.89949 | 0.621150 | ||||||||
\(255\) | 7.41421 | 0.464296 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 21.7990 | 1.35978 | 0.679892 | − | 0.733312i | \(-0.262027\pi\) | ||||
0.679892 | + | 0.733312i | \(0.262027\pi\) | |||||||
\(258\) | −4.82843 | −0.300605 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −1.41421 | −0.0877058 | ||||||||
\(261\) | 5.00000 | 0.309492 | ||||||||
\(262\) | −9.89949 | −0.611593 | ||||||||
\(263\) | −7.55635 | −0.465944 | −0.232972 | − | 0.972483i | \(-0.574845\pi\) | ||||
−0.232972 | + | 0.972483i | \(0.574845\pi\) | |||||||
\(264\) | −0.414214 | −0.0254931 | ||||||||
\(265\) | 17.4142 | 1.06975 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −6.24264 | −0.382043 | ||||||||
\(268\) | −14.6569 | −0.895310 | ||||||||
\(269\) | 3.68629 | 0.224757 | 0.112379 | − | 0.993665i | \(-0.464153\pi\) | ||||
0.112379 | + | 0.993665i | \(0.464153\pi\) | |||||||
\(270\) | −1.41421 | −0.0860663 | ||||||||
\(271\) | 15.3848 | 0.934559 | 0.467279 | − | 0.884110i | \(-0.345234\pi\) | ||||
0.467279 | + | 0.884110i | \(0.345234\pi\) | |||||||
\(272\) | −5.24264 | −0.317882 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −13.0711 | −0.789652 | ||||||||
\(275\) | −1.24264 | −0.0749341 | ||||||||
\(276\) | 9.07107 | 0.546014 | ||||||||
\(277\) | −16.4142 | −0.986235 | −0.493117 | − | 0.869963i | \(-0.664143\pi\) | ||||
−0.493117 | + | 0.869963i | \(0.664143\pi\) | |||||||
\(278\) | 21.2132 | 1.27228 | ||||||||
\(279\) | −6.82843 | −0.408807 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 7.31371 | 0.436299 | 0.218150 | − | 0.975915i | \(-0.429998\pi\) | ||||
0.218150 | + | 0.975915i | \(0.429998\pi\) | |||||||
\(282\) | 9.00000 | 0.535942 | ||||||||
\(283\) | −17.0711 | −1.01477 | −0.507385 | − | 0.861720i | \(-0.669388\pi\) | ||||
−0.507385 | + | 0.861720i | \(0.669388\pi\) | |||||||
\(284\) | −1.00000 | −0.0593391 | ||||||||
\(285\) | 4.24264 | 0.251312 | ||||||||
\(286\) | −0.414214 | −0.0244930 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 1.00000 | 0.0589256 | ||||||||
\(289\) | 10.4853 | 0.616781 | ||||||||
\(290\) | 7.07107 | 0.415227 | ||||||||
\(291\) | 7.89949 | 0.463077 | ||||||||
\(292\) | 1.07107 | 0.0626795 | ||||||||
\(293\) | 18.7279 | 1.09410 | 0.547048 | − | 0.837101i | \(-0.315751\pi\) | ||||
0.547048 | + | 0.837101i | \(0.315751\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −10.7279 | −0.624604 | ||||||||
\(296\) | −5.07107 | −0.294750 | ||||||||
\(297\) | −0.414214 | −0.0240351 | ||||||||
\(298\) | 15.8995 | 0.921033 | ||||||||
\(299\) | 9.07107 | 0.524593 | ||||||||
\(300\) | 3.00000 | 0.173205 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −7.58579 | −0.436513 | ||||||||
\(303\) | −1.17157 | −0.0673051 | ||||||||
\(304\) | −3.00000 | −0.172062 | ||||||||
\(305\) | 7.41421 | 0.424537 | ||||||||
\(306\) | −5.24264 | −0.299702 | ||||||||
\(307\) | 19.6274 | 1.12020 | 0.560098 | − | 0.828426i | \(-0.310763\pi\) | ||||
0.560098 | + | 0.828426i | \(0.310763\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 6.48528 | 0.368935 | ||||||||
\(310\) | −9.65685 | −0.548472 | ||||||||
\(311\) | 6.58579 | 0.373446 | 0.186723 | − | 0.982413i | \(-0.440213\pi\) | ||||
0.186723 | + | 0.982413i | \(0.440213\pi\) | |||||||
\(312\) | 1.00000 | 0.0566139 | ||||||||
\(313\) | −18.1421 | −1.02545 | −0.512727 | − | 0.858552i | \(-0.671365\pi\) | ||||
−0.512727 | + | 0.858552i | \(0.671365\pi\) | |||||||
\(314\) | −7.92893 | −0.447456 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 13.3137 | 0.748955 | ||||||||
\(317\) | 0.828427 | 0.0465291 | 0.0232646 | − | 0.999729i | \(-0.492594\pi\) | ||||
0.0232646 | + | 0.999729i | \(0.492594\pi\) | |||||||
\(318\) | −12.3137 | −0.690518 | ||||||||
\(319\) | 2.07107 | 0.115958 | ||||||||
\(320\) | 1.41421 | 0.0790569 | ||||||||
\(321\) | −13.6569 | −0.762251 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 15.7279 | 0.875125 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | 3.00000 | 0.166410 | ||||||||
\(326\) | 17.1421 | 0.949415 | ||||||||
\(327\) | −1.65685 | −0.0916242 | ||||||||
\(328\) | −4.58579 | −0.253208 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −0.585786 | −0.0322465 | ||||||||
\(331\) | −22.4853 | −1.23590 | −0.617951 | − | 0.786216i | \(-0.712037\pi\) | ||||
−0.617951 | + | 0.786216i | \(0.712037\pi\) | |||||||
\(332\) | 7.65685 | 0.420224 | ||||||||
\(333\) | −5.07107 | −0.277893 | ||||||||
\(334\) | −12.3137 | −0.673776 | ||||||||
\(335\) | −20.7279 | −1.13249 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 28.6569 | 1.56104 | 0.780519 | − | 0.625132i | \(-0.214955\pi\) | ||||
0.780519 | + | 0.625132i | \(0.214955\pi\) | |||||||
\(338\) | 1.00000 | 0.0543928 | ||||||||
\(339\) | 6.07107 | 0.329735 | ||||||||
\(340\) | −7.41421 | −0.402092 | ||||||||
\(341\) | −2.82843 | −0.153168 | ||||||||
\(342\) | −3.00000 | −0.162221 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 4.82843 | 0.260331 | ||||||||
\(345\) | 12.8284 | 0.690659 | ||||||||
\(346\) | −20.3137 | −1.09207 | ||||||||
\(347\) | 5.75736 | 0.309071 | 0.154536 | − | 0.987987i | \(-0.450612\pi\) | ||||
0.154536 | + | 0.987987i | \(0.450612\pi\) | |||||||
\(348\) | −5.00000 | −0.268028 | ||||||||
\(349\) | −5.41421 | −0.289816 | −0.144908 | − | 0.989445i | \(-0.546289\pi\) | ||||
−0.144908 | + | 0.989445i | \(0.546289\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.00000 | 0.0533761 | ||||||||
\(352\) | 0.414214 | 0.0220777 | ||||||||
\(353\) | −12.6274 | −0.672090 | −0.336045 | − | 0.941846i | \(-0.609089\pi\) | ||||
−0.336045 | + | 0.941846i | \(0.609089\pi\) | |||||||
\(354\) | 7.58579 | 0.403180 | ||||||||
\(355\) | −1.41421 | −0.0750587 | ||||||||
\(356\) | 6.24264 | 0.330859 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −12.3431 | −0.652356 | ||||||||
\(359\) | −15.4558 | −0.815728 | −0.407864 | − | 0.913043i | \(-0.633726\pi\) | ||||
−0.407864 | + | 0.913043i | \(0.633726\pi\) | |||||||
\(360\) | 1.41421 | 0.0745356 | ||||||||
\(361\) | −10.0000 | −0.526316 | ||||||||
\(362\) | 11.5858 | 0.608935 | ||||||||
\(363\) | 10.8284 | 0.568345 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 1.51472 | 0.0792840 | ||||||||
\(366\) | −5.24264 | −0.274037 | ||||||||
\(367\) | −14.0000 | −0.730794 | −0.365397 | − | 0.930852i | \(-0.619067\pi\) | ||||
−0.365397 | + | 0.930852i | \(0.619067\pi\) | |||||||
\(368\) | −9.07107 | −0.472862 | ||||||||
\(369\) | −4.58579 | −0.238727 | ||||||||
\(370\) | −7.17157 | −0.372832 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 6.82843 | 0.354037 | ||||||||
\(373\) | −11.1005 | −0.574762 | −0.287381 | − | 0.957816i | \(-0.592785\pi\) | ||||
−0.287381 | + | 0.957816i | \(0.592785\pi\) | |||||||
\(374\) | −2.17157 | −0.112289 | ||||||||
\(375\) | 11.3137 | 0.584237 | ||||||||
\(376\) | −9.00000 | −0.464140 | ||||||||
\(377\) | −5.00000 | −0.257513 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −33.6569 | −1.72884 | −0.864418 | − | 0.502773i | \(-0.832313\pi\) | ||||
−0.864418 | + | 0.502773i | \(0.832313\pi\) | |||||||
\(380\) | −4.24264 | −0.217643 | ||||||||
\(381\) | −9.89949 | −0.507166 | ||||||||
\(382\) | 2.34315 | 0.119886 | ||||||||
\(383\) | −6.48528 | −0.331382 | −0.165691 | − | 0.986178i | \(-0.552985\pi\) | ||||
−0.165691 | + | 0.986178i | \(0.552985\pi\) | |||||||
\(384\) | −1.00000 | −0.0510310 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −15.7574 | −0.802028 | ||||||||
\(387\) | 4.82843 | 0.245443 | ||||||||
\(388\) | −7.89949 | −0.401036 | ||||||||
\(389\) | 23.0000 | 1.16615 | 0.583073 | − | 0.812420i | \(-0.301850\pi\) | ||||
0.583073 | + | 0.812420i | \(0.301850\pi\) | |||||||
\(390\) | 1.41421 | 0.0716115 | ||||||||
\(391\) | 47.5563 | 2.40503 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 9.89949 | 0.499363 | ||||||||
\(394\) | 9.55635 | 0.481442 | ||||||||
\(395\) | 18.8284 | 0.947361 | ||||||||
\(396\) | 0.414214 | 0.0208150 | ||||||||
\(397\) | 19.7574 | 0.991593 | 0.495797 | − | 0.868439i | \(-0.334876\pi\) | ||||
0.495797 | + | 0.868439i | \(0.334876\pi\) | |||||||
\(398\) | −10.5858 | −0.530618 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −3.00000 | −0.150000 | ||||||||
\(401\) | 19.0711 | 0.952364 | 0.476182 | − | 0.879347i | \(-0.342020\pi\) | ||||
0.476182 | + | 0.879347i | \(0.342020\pi\) | |||||||
\(402\) | 14.6569 | 0.731017 | ||||||||
\(403\) | 6.82843 | 0.340148 | ||||||||
\(404\) | 1.17157 | 0.0582879 | ||||||||
\(405\) | 1.41421 | 0.0702728 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −2.10051 | −0.104118 | ||||||||
\(408\) | 5.24264 | 0.259549 | ||||||||
\(409\) | 2.58579 | 0.127859 | 0.0639295 | − | 0.997954i | \(-0.479637\pi\) | ||||
0.0639295 | + | 0.997954i | \(0.479637\pi\) | |||||||
\(410\) | −6.48528 | −0.320285 | ||||||||
\(411\) | 13.0711 | 0.644748 | ||||||||
\(412\) | −6.48528 | −0.319507 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −9.07107 | −0.445819 | ||||||||
\(415\) | 10.8284 | 0.531547 | ||||||||
\(416\) | −1.00000 | −0.0490290 | ||||||||
\(417\) | −21.2132 | −1.03882 | ||||||||
\(418\) | −1.24264 | −0.0607795 | ||||||||
\(419\) | 27.4558 | 1.34131 | 0.670653 | − | 0.741771i | \(-0.266014\pi\) | ||||
0.670653 | + | 0.741771i | \(0.266014\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 10.5858 | 0.515920 | 0.257960 | − | 0.966156i | \(-0.416950\pi\) | ||||
0.257960 | + | 0.966156i | \(0.416950\pi\) | |||||||
\(422\) | −28.3848 | −1.38175 | ||||||||
\(423\) | −9.00000 | −0.437595 | ||||||||
\(424\) | 12.3137 | 0.598007 | ||||||||
\(425\) | 15.7279 | 0.762916 | ||||||||
\(426\) | 1.00000 | 0.0484502 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 13.6569 | 0.660129 | ||||||||
\(429\) | 0.414214 | 0.0199984 | ||||||||
\(430\) | 6.82843 | 0.329296 | ||||||||
\(431\) | 14.4853 | 0.697731 | 0.348866 | − | 0.937173i | \(-0.386567\pi\) | ||||
0.348866 | + | 0.937173i | \(0.386567\pi\) | |||||||
\(432\) | −1.00000 | −0.0481125 | ||||||||
\(433\) | 19.0000 | 0.913082 | 0.456541 | − | 0.889702i | \(-0.349088\pi\) | ||||
0.456541 | + | 0.889702i | \(0.349088\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −7.07107 | −0.339032 | ||||||||
\(436\) | 1.65685 | 0.0793489 | ||||||||
\(437\) | 27.2132 | 1.30178 | ||||||||
\(438\) | −1.07107 | −0.0511776 | ||||||||
\(439\) | 10.5858 | 0.505232 | 0.252616 | − | 0.967567i | \(-0.418709\pi\) | ||||
0.252616 | + | 0.967567i | \(0.418709\pi\) | |||||||
\(440\) | 0.585786 | 0.0279263 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 5.24264 | 0.249367 | ||||||||
\(443\) | 22.7279 | 1.07984 | 0.539918 | − | 0.841718i | \(-0.318455\pi\) | ||||
0.539918 | + | 0.841718i | \(0.318455\pi\) | |||||||
\(444\) | 5.07107 | 0.240662 | ||||||||
\(445\) | 8.82843 | 0.418508 | ||||||||
\(446\) | −21.3848 | −1.01260 | ||||||||
\(447\) | −15.8995 | −0.752020 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −33.9411 | −1.60178 | −0.800890 | − | 0.598811i | \(-0.795640\pi\) | ||||
−0.800890 | + | 0.598811i | \(0.795640\pi\) | |||||||
\(450\) | −3.00000 | −0.141421 | ||||||||
\(451\) | −1.89949 | −0.0894437 | ||||||||
\(452\) | −6.07107 | −0.285559 | ||||||||
\(453\) | 7.58579 | 0.356411 | ||||||||
\(454\) | 26.1421 | 1.22691 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 3.00000 | 0.140488 | ||||||||
\(457\) | −15.2132 | −0.711644 | −0.355822 | − | 0.934554i | \(-0.615799\pi\) | ||||
−0.355822 | + | 0.934554i | \(0.615799\pi\) | |||||||
\(458\) | 7.17157 | 0.335106 | ||||||||
\(459\) | 5.24264 | 0.244706 | ||||||||
\(460\) | −12.8284 | −0.598128 | ||||||||
\(461\) | 33.4558 | 1.55819 | 0.779097 | − | 0.626903i | \(-0.215678\pi\) | ||||
0.779097 | + | 0.626903i | \(0.215678\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −37.9411 | −1.76327 | −0.881637 | − | 0.471929i | \(-0.843558\pi\) | ||||
−0.881637 | + | 0.471929i | \(0.843558\pi\) | |||||||
\(464\) | 5.00000 | 0.232119 | ||||||||
\(465\) | 9.65685 | 0.447826 | ||||||||
\(466\) | −3.72792 | −0.172693 | ||||||||
\(467\) | 0.242641 | 0.0112281 | 0.00561404 | − | 0.999984i | \(-0.498213\pi\) | ||||
0.00561404 | + | 0.999984i | \(0.498213\pi\) | |||||||
\(468\) | −1.00000 | −0.0462250 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −12.7279 | −0.587095 | ||||||||
\(471\) | 7.92893 | 0.365346 | ||||||||
\(472\) | −7.58579 | −0.349164 | ||||||||
\(473\) | 2.00000 | 0.0919601 | ||||||||
\(474\) | −13.3137 | −0.611519 | ||||||||
\(475\) | 9.00000 | 0.412948 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 12.3137 | 0.563806 | ||||||||
\(478\) | −2.51472 | −0.115021 | ||||||||
\(479\) | 31.1421 | 1.42292 | 0.711460 | − | 0.702726i | \(-0.248034\pi\) | ||||
0.711460 | + | 0.702726i | \(0.248034\pi\) | |||||||
\(480\) | −1.41421 | −0.0645497 | ||||||||
\(481\) | 5.07107 | 0.231221 | ||||||||
\(482\) | 16.4853 | 0.750884 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −10.8284 | −0.492201 | ||||||||
\(485\) | −11.1716 | −0.507275 | ||||||||
\(486\) | −1.00000 | −0.0453609 | ||||||||
\(487\) | −23.7279 | −1.07521 | −0.537607 | − | 0.843195i | \(-0.680672\pi\) | ||||
−0.537607 | + | 0.843195i | \(0.680672\pi\) | |||||||
\(488\) | 5.24264 | 0.237323 | ||||||||
\(489\) | −17.1421 | −0.775194 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −26.2843 | −1.18619 | −0.593096 | − | 0.805132i | \(-0.702095\pi\) | ||||
−0.593096 | + | 0.805132i | \(0.702095\pi\) | |||||||
\(492\) | 4.58579 | 0.206743 | ||||||||
\(493\) | −26.2132 | −1.18058 | ||||||||
\(494\) | 3.00000 | 0.134976 | ||||||||
\(495\) | 0.585786 | 0.0263291 | ||||||||
\(496\) | −6.82843 | −0.306605 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −7.65685 | −0.343112 | ||||||||
\(499\) | −30.0000 | −1.34298 | −0.671492 | − | 0.741012i | \(-0.734346\pi\) | ||||
−0.671492 | + | 0.741012i | \(0.734346\pi\) | |||||||
\(500\) | −11.3137 | −0.505964 | ||||||||
\(501\) | 12.3137 | 0.550136 | ||||||||
\(502\) | −12.8284 | −0.572561 | ||||||||
\(503\) | −35.7990 | −1.59620 | −0.798099 | − | 0.602526i | \(-0.794161\pi\) | ||||
−0.798099 | + | 0.602526i | \(0.794161\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 1.65685 | 0.0737290 | ||||||||
\(506\) | −3.75736 | −0.167035 | ||||||||
\(507\) | −1.00000 | −0.0444116 | ||||||||
\(508\) | 9.89949 | 0.439219 | ||||||||
\(509\) | −12.9706 | −0.574910 | −0.287455 | − | 0.957794i | \(-0.592809\pi\) | ||||
−0.287455 | + | 0.957794i | \(0.592809\pi\) | |||||||
\(510\) | 7.41421 | 0.328307 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 3.00000 | 0.132453 | ||||||||
\(514\) | 21.7990 | 0.961512 | ||||||||
\(515\) | −9.17157 | −0.404148 | ||||||||
\(516\) | −4.82843 | −0.212560 | ||||||||
\(517\) | −3.72792 | −0.163954 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 20.3137 | 0.891673 | ||||||||
\(520\) | −1.41421 | −0.0620174 | ||||||||
\(521\) | 14.0000 | 0.613351 | 0.306676 | − | 0.951814i | \(-0.400783\pi\) | ||||
0.306676 | + | 0.951814i | \(0.400783\pi\) | |||||||
\(522\) | 5.00000 | 0.218844 | ||||||||
\(523\) | 3.85786 | 0.168693 | 0.0843463 | − | 0.996437i | \(-0.473120\pi\) | ||||
0.0843463 | + | 0.996437i | \(0.473120\pi\) | |||||||
\(524\) | −9.89949 | −0.432461 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −7.55635 | −0.329472 | ||||||||
\(527\) | 35.7990 | 1.55943 | ||||||||
\(528\) | −0.414214 | −0.0180263 | ||||||||
\(529\) | 59.2843 | 2.57758 | ||||||||
\(530\) | 17.4142 | 0.756425 | ||||||||
\(531\) | −7.58579 | −0.329195 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 4.58579 | 0.198632 | ||||||||
\(534\) | −6.24264 | −0.270145 | ||||||||
\(535\) | 19.3137 | 0.835004 | ||||||||
\(536\) | −14.6569 | −0.633080 | ||||||||
\(537\) | 12.3431 | 0.532646 | ||||||||
\(538\) | 3.68629 | 0.158927 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −1.41421 | −0.0608581 | ||||||||
\(541\) | 12.8701 | 0.553327 | 0.276663 | − | 0.960967i | \(-0.410771\pi\) | ||||
0.276663 | + | 0.960967i | \(0.410771\pi\) | |||||||
\(542\) | 15.3848 | 0.660833 | ||||||||
\(543\) | −11.5858 | −0.497194 | ||||||||
\(544\) | −5.24264 | −0.224776 | ||||||||
\(545\) | 2.34315 | 0.100369 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −5.75736 | −0.246167 | −0.123083 | − | 0.992396i | \(-0.539278\pi\) | ||||
−0.123083 | + | 0.992396i | \(0.539278\pi\) | |||||||
\(548\) | −13.0711 | −0.558368 | ||||||||
\(549\) | 5.24264 | 0.223750 | ||||||||
\(550\) | −1.24264 | −0.0529864 | ||||||||
\(551\) | −15.0000 | −0.639021 | ||||||||
\(552\) | 9.07107 | 0.386090 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −16.4142 | −0.697373 | ||||||||
\(555\) | 7.17157 | 0.304416 | ||||||||
\(556\) | 21.2132 | 0.899640 | ||||||||
\(557\) | −10.9706 | −0.464838 | −0.232419 | − | 0.972616i | \(-0.574664\pi\) | ||||
−0.232419 | + | 0.972616i | \(0.574664\pi\) | |||||||
\(558\) | −6.82843 | −0.289070 | ||||||||
\(559\) | −4.82843 | −0.204221 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 2.17157 | 0.0916839 | ||||||||
\(562\) | 7.31371 | 0.308510 | ||||||||
\(563\) | 0.485281 | 0.0204522 | 0.0102261 | − | 0.999948i | \(-0.496745\pi\) | ||||
0.0102261 | + | 0.999948i | \(0.496745\pi\) | |||||||
\(564\) | 9.00000 | 0.378968 | ||||||||
\(565\) | −8.58579 | −0.361207 | ||||||||
\(566\) | −17.0711 | −0.717551 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −1.00000 | −0.0419591 | ||||||||
\(569\) | −25.5858 | −1.07261 | −0.536306 | − | 0.844024i | \(-0.680181\pi\) | ||||
−0.536306 | + | 0.844024i | \(0.680181\pi\) | |||||||
\(570\) | 4.24264 | 0.177705 | ||||||||
\(571\) | −1.65685 | −0.0693372 | −0.0346686 | − | 0.999399i | \(-0.511038\pi\) | ||||
−0.0346686 | + | 0.999399i | \(0.511038\pi\) | |||||||
\(572\) | −0.414214 | −0.0173191 | ||||||||
\(573\) | −2.34315 | −0.0978863 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 27.2132 | 1.13487 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | 18.0000 | 0.749350 | 0.374675 | − | 0.927156i | \(-0.377754\pi\) | ||||
0.374675 | + | 0.927156i | \(0.377754\pi\) | |||||||
\(578\) | 10.4853 | 0.436130 | ||||||||
\(579\) | 15.7574 | 0.654854 | ||||||||
\(580\) | 7.07107 | 0.293610 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 7.89949 | 0.327445 | ||||||||
\(583\) | 5.10051 | 0.211241 | ||||||||
\(584\) | 1.07107 | 0.0443211 | ||||||||
\(585\) | −1.41421 | −0.0584705 | ||||||||
\(586\) | 18.7279 | 0.773643 | ||||||||
\(587\) | −11.2426 | −0.464033 | −0.232017 | − | 0.972712i | \(-0.574532\pi\) | ||||
−0.232017 | + | 0.972712i | \(0.574532\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 20.4853 | 0.844081 | ||||||||
\(590\) | −10.7279 | −0.441662 | ||||||||
\(591\) | −9.55635 | −0.393096 | ||||||||
\(592\) | −5.07107 | −0.208420 | ||||||||
\(593\) | 28.5858 | 1.17388 | 0.586939 | − | 0.809631i | \(-0.300333\pi\) | ||||
0.586939 | + | 0.809631i | \(0.300333\pi\) | |||||||
\(594\) | −0.414214 | −0.0169954 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 15.8995 | 0.651269 | ||||||||
\(597\) | 10.5858 | 0.433247 | ||||||||
\(598\) | 9.07107 | 0.370944 | ||||||||
\(599\) | −14.8701 | −0.607574 | −0.303787 | − | 0.952740i | \(-0.598251\pi\) | ||||
−0.303787 | + | 0.952740i | \(0.598251\pi\) | |||||||
\(600\) | 3.00000 | 0.122474 | ||||||||
\(601\) | 17.8284 | 0.727237 | 0.363618 | − | 0.931548i | \(-0.381541\pi\) | ||||
0.363618 | + | 0.931548i | \(0.381541\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −14.6569 | −0.596873 | ||||||||
\(604\) | −7.58579 | −0.308661 | ||||||||
\(605\) | −15.3137 | −0.622591 | ||||||||
\(606\) | −1.17157 | −0.0475919 | ||||||||
\(607\) | −27.0711 | −1.09878 | −0.549390 | − | 0.835566i | \(-0.685140\pi\) | ||||
−0.549390 | + | 0.835566i | \(0.685140\pi\) | |||||||
\(608\) | −3.00000 | −0.121666 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 7.41421 | 0.300193 | ||||||||
\(611\) | 9.00000 | 0.364101 | ||||||||
\(612\) | −5.24264 | −0.211921 | ||||||||
\(613\) | −35.7990 | −1.44591 | −0.722954 | − | 0.690896i | \(-0.757216\pi\) | ||||
−0.722954 | + | 0.690896i | \(0.757216\pi\) | |||||||
\(614\) | 19.6274 | 0.792098 | ||||||||
\(615\) | 6.48528 | 0.261512 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −6.48528 | −0.261088 | −0.130544 | − | 0.991443i | \(-0.541672\pi\) | ||||
−0.130544 | + | 0.991443i | \(0.541672\pi\) | |||||||
\(618\) | 6.48528 | 0.260876 | ||||||||
\(619\) | −43.4558 | −1.74664 | −0.873319 | − | 0.487149i | \(-0.838037\pi\) | ||||
−0.873319 | + | 0.487149i | \(0.838037\pi\) | |||||||
\(620\) | −9.65685 | −0.387829 | ||||||||
\(621\) | 9.07107 | 0.364009 | ||||||||
\(622\) | 6.58579 | 0.264066 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 1.00000 | 0.0400320 | ||||||||
\(625\) | −1.00000 | −0.0400000 | ||||||||
\(626\) | −18.1421 | −0.725106 | ||||||||
\(627\) | 1.24264 | 0.0496263 | ||||||||
\(628\) | −7.92893 | −0.316399 | ||||||||
\(629\) | 26.5858 | 1.06004 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 36.6274 | 1.45811 | 0.729057 | − | 0.684453i | \(-0.239959\pi\) | ||||
0.729057 | + | 0.684453i | \(0.239959\pi\) | |||||||
\(632\) | 13.3137 | 0.529591 | ||||||||
\(633\) | 28.3848 | 1.12819 | ||||||||
\(634\) | 0.828427 | 0.0329010 | ||||||||
\(635\) | 14.0000 | 0.555573 | ||||||||
\(636\) | −12.3137 | −0.488270 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 2.07107 | 0.0819944 | ||||||||
\(639\) | −1.00000 | −0.0395594 | ||||||||
\(640\) | 1.41421 | 0.0559017 | ||||||||
\(641\) | 33.1716 | 1.31020 | 0.655099 | − | 0.755543i | \(-0.272627\pi\) | ||||
0.655099 | + | 0.755543i | \(0.272627\pi\) | |||||||
\(642\) | −13.6569 | −0.538993 | ||||||||
\(643\) | −36.3137 | −1.43207 | −0.716036 | − | 0.698063i | \(-0.754046\pi\) | ||||
−0.716036 | + | 0.698063i | \(0.754046\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −6.82843 | −0.268869 | ||||||||
\(646\) | 15.7279 | 0.618807 | ||||||||
\(647\) | −28.6274 | −1.12546 | −0.562730 | − | 0.826641i | \(-0.690249\pi\) | ||||
−0.562730 | + | 0.826641i | \(0.690249\pi\) | |||||||
\(648\) | 1.00000 | 0.0392837 | ||||||||
\(649\) | −3.14214 | −0.123340 | ||||||||
\(650\) | 3.00000 | 0.117670 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 17.1421 | 0.671338 | ||||||||
\(653\) | 15.1127 | 0.591406 | 0.295703 | − | 0.955280i | \(-0.404446\pi\) | ||||
0.295703 | + | 0.955280i | \(0.404446\pi\) | |||||||
\(654\) | −1.65685 | −0.0647881 | ||||||||
\(655\) | −14.0000 | −0.547025 | ||||||||
\(656\) | −4.58579 | −0.179045 | ||||||||
\(657\) | 1.07107 | 0.0417863 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 30.7279 | 1.19699 | 0.598495 | − | 0.801127i | \(-0.295766\pi\) | ||||
0.598495 | + | 0.801127i | \(0.295766\pi\) | |||||||
\(660\) | −0.585786 | −0.0228017 | ||||||||
\(661\) | 13.5563 | 0.527281 | 0.263640 | − | 0.964621i | \(-0.415077\pi\) | ||||
0.263640 | + | 0.964621i | \(0.415077\pi\) | |||||||
\(662\) | −22.4853 | −0.873915 | ||||||||
\(663\) | −5.24264 | −0.203607 | ||||||||
\(664\) | 7.65685 | 0.297144 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −5.07107 | −0.196500 | ||||||||
\(667\) | −45.3553 | −1.75617 | ||||||||
\(668\) | −12.3137 | −0.476432 | ||||||||
\(669\) | 21.3848 | 0.826783 | ||||||||
\(670\) | −20.7279 | −0.800789 | ||||||||
\(671\) | 2.17157 | 0.0838326 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −1.17157 | −0.0451608 | −0.0225804 | − | 0.999745i | \(-0.507188\pi\) | ||||
−0.0225804 | + | 0.999745i | \(0.507188\pi\) | |||||||
\(674\) | 28.6569 | 1.10382 | ||||||||
\(675\) | 3.00000 | 0.115470 | ||||||||
\(676\) | 1.00000 | 0.0384615 | ||||||||
\(677\) | −28.1716 | −1.08272 | −0.541361 | − | 0.840790i | \(-0.682091\pi\) | ||||
−0.541361 | + | 0.840790i | \(0.682091\pi\) | |||||||
\(678\) | 6.07107 | 0.233158 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −7.41421 | −0.284322 | ||||||||
\(681\) | −26.1421 | −1.00177 | ||||||||
\(682\) | −2.82843 | −0.108306 | ||||||||
\(683\) | 5.45584 | 0.208762 | 0.104381 | − | 0.994537i | \(-0.466714\pi\) | ||||
0.104381 | + | 0.994537i | \(0.466714\pi\) | |||||||
\(684\) | −3.00000 | −0.114708 | ||||||||
\(685\) | −18.4853 | −0.706286 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −7.17157 | −0.273613 | ||||||||
\(688\) | 4.82843 | 0.184082 | ||||||||
\(689\) | −12.3137 | −0.469115 | ||||||||
\(690\) | 12.8284 | 0.488370 | ||||||||
\(691\) | −11.1421 | −0.423867 | −0.211933 | − | 0.977284i | \(-0.567976\pi\) | ||||
−0.211933 | + | 0.977284i | \(0.567976\pi\) | |||||||
\(692\) | −20.3137 | −0.772211 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 5.75736 | 0.218546 | ||||||||
\(695\) | 30.0000 | 1.13796 | ||||||||
\(696\) | −5.00000 | −0.189525 | ||||||||
\(697\) | 24.0416 | 0.910642 | ||||||||
\(698\) | −5.41421 | −0.204931 | ||||||||
\(699\) | 3.72792 | 0.141003 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 48.4853 | 1.83126 | 0.915632 | − | 0.402018i | \(-0.131691\pi\) | ||||
0.915632 | + | 0.402018i | \(0.131691\pi\) | |||||||
\(702\) | 1.00000 | 0.0377426 | ||||||||
\(703\) | 15.2132 | 0.573777 | ||||||||
\(704\) | 0.414214 | 0.0156113 | ||||||||
\(705\) | 12.7279 | 0.479361 | ||||||||
\(706\) | −12.6274 | −0.475239 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 7.58579 | 0.285091 | ||||||||
\(709\) | −32.0416 | −1.20335 | −0.601674 | − | 0.798741i | \(-0.705499\pi\) | ||||
−0.601674 | + | 0.798741i | \(0.705499\pi\) | |||||||
\(710\) | −1.41421 | −0.0530745 | ||||||||
\(711\) | 13.3137 | 0.499303 | ||||||||
\(712\) | 6.24264 | 0.233953 | ||||||||
\(713\) | 61.9411 | 2.31971 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −0.585786 | −0.0219072 | ||||||||
\(716\) | −12.3431 | −0.461285 | ||||||||
\(717\) | 2.51472 | 0.0939139 | ||||||||
\(718\) | −15.4558 | −0.576807 | ||||||||
\(719\) | 22.2843 | 0.831063 | 0.415532 | − | 0.909579i | \(-0.363596\pi\) | ||||
0.415532 | + | 0.909579i | \(0.363596\pi\) | |||||||
\(720\) | 1.41421 | 0.0527046 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −10.0000 | −0.372161 | ||||||||
\(723\) | −16.4853 | −0.613094 | ||||||||
\(724\) | 11.5858 | 0.430582 | ||||||||
\(725\) | −15.0000 | −0.557086 | ||||||||
\(726\) | 10.8284 | 0.401881 | ||||||||
\(727\) | 38.8284 | 1.44007 | 0.720033 | − | 0.693939i | \(-0.244126\pi\) | ||||
0.720033 | + | 0.693939i | \(0.244126\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 1.51472 | 0.0560623 | ||||||||
\(731\) | −25.3137 | −0.936261 | ||||||||
\(732\) | −5.24264 | −0.193774 | ||||||||
\(733\) | 29.0122 | 1.07159 | 0.535795 | − | 0.844348i | \(-0.320012\pi\) | ||||
0.535795 | + | 0.844348i | \(0.320012\pi\) | |||||||
\(734\) | −14.0000 | −0.516749 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −9.07107 | −0.334364 | ||||||||
\(737\) | −6.07107 | −0.223631 | ||||||||
\(738\) | −4.58579 | −0.168805 | ||||||||
\(739\) | 6.97056 | 0.256416 | 0.128208 | − | 0.991747i | \(-0.459077\pi\) | ||||
0.128208 | + | 0.991747i | \(0.459077\pi\) | |||||||
\(740\) | −7.17157 | −0.263632 | ||||||||
\(741\) | −3.00000 | −0.110208 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 11.4853 | 0.421354 | 0.210677 | − | 0.977556i | \(-0.432433\pi\) | ||||
0.210677 | + | 0.977556i | \(0.432433\pi\) | |||||||
\(744\) | 6.82843 | 0.250342 | ||||||||
\(745\) | 22.4853 | 0.823797 | ||||||||
\(746\) | −11.1005 | −0.406418 | ||||||||
\(747\) | 7.65685 | 0.280150 | ||||||||
\(748\) | −2.17157 | −0.0794006 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 11.3137 | 0.413118 | ||||||||
\(751\) | −34.3431 | −1.25320 | −0.626600 | − | 0.779341i | \(-0.715554\pi\) | ||||
−0.626600 | + | 0.779341i | \(0.715554\pi\) | |||||||
\(752\) | −9.00000 | −0.328196 | ||||||||
\(753\) | 12.8284 | 0.467494 | ||||||||
\(754\) | −5.00000 | −0.182089 | ||||||||
\(755\) | −10.7279 | −0.390429 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 23.4437 | 0.852074 | 0.426037 | − | 0.904706i | \(-0.359909\pi\) | ||||
0.426037 | + | 0.904706i | \(0.359909\pi\) | |||||||
\(758\) | −33.6569 | −1.22247 | ||||||||
\(759\) | 3.75736 | 0.136384 | ||||||||
\(760\) | −4.24264 | −0.153897 | ||||||||
\(761\) | 17.8579 | 0.647347 | 0.323674 | − | 0.946169i | \(-0.395082\pi\) | ||||
0.323674 | + | 0.946169i | \(0.395082\pi\) | |||||||
\(762\) | −9.89949 | −0.358621 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 2.34315 | 0.0847720 | ||||||||
\(765\) | −7.41421 | −0.268061 | ||||||||
\(766\) | −6.48528 | −0.234323 | ||||||||
\(767\) | 7.58579 | 0.273907 | ||||||||
\(768\) | −1.00000 | −0.0360844 | ||||||||
\(769\) | 6.92893 | 0.249864 | 0.124932 | − | 0.992165i | \(-0.460129\pi\) | ||||
0.124932 | + | 0.992165i | \(0.460129\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −21.7990 | −0.785071 | ||||||||
\(772\) | −15.7574 | −0.567120 | ||||||||
\(773\) | 29.5980 | 1.06457 | 0.532283 | − | 0.846567i | \(-0.321334\pi\) | ||||
0.532283 | + | 0.846567i | \(0.321334\pi\) | |||||||
\(774\) | 4.82843 | 0.173554 | ||||||||
\(775\) | 20.4853 | 0.735853 | ||||||||
\(776\) | −7.89949 | −0.283575 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 23.0000 | 0.824590 | ||||||||
\(779\) | 13.7574 | 0.492909 | ||||||||
\(780\) | 1.41421 | 0.0506370 | ||||||||
\(781\) | −0.414214 | −0.0148217 | ||||||||
\(782\) | 47.5563 | 1.70061 | ||||||||
\(783\) | −5.00000 | −0.178685 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −11.2132 | −0.400216 | ||||||||
\(786\) | 9.89949 | 0.353103 | ||||||||
\(787\) | 8.17157 | 0.291285 | 0.145643 | − | 0.989337i | \(-0.453475\pi\) | ||||
0.145643 | + | 0.989337i | \(0.453475\pi\) | |||||||
\(788\) | 9.55635 | 0.340431 | ||||||||
\(789\) | 7.55635 | 0.269013 | ||||||||
\(790\) | 18.8284 | 0.669885 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0.414214 | 0.0147184 | ||||||||
\(793\) | −5.24264 | −0.186172 | ||||||||
\(794\) | 19.7574 | 0.701162 | ||||||||
\(795\) | −17.4142 | −0.617619 | ||||||||
\(796\) | −10.5858 | −0.375203 | ||||||||
\(797\) | 36.9706 | 1.30956 | 0.654782 | − | 0.755818i | \(-0.272760\pi\) | ||||
0.654782 | + | 0.755818i | \(0.272760\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 47.1838 | 1.66924 | ||||||||
\(800\) | −3.00000 | −0.106066 | ||||||||
\(801\) | 6.24264 | 0.220573 | ||||||||
\(802\) | 19.0711 | 0.673423 | ||||||||
\(803\) | 0.443651 | 0.0156561 | ||||||||
\(804\) | 14.6569 | 0.516907 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 6.82843 | 0.240521 | ||||||||
\(807\) | −3.68629 | −0.129764 | ||||||||
\(808\) | 1.17157 | 0.0412158 | ||||||||
\(809\) | 35.0416 | 1.23200 | 0.615999 | − | 0.787747i | \(-0.288753\pi\) | ||||
0.615999 | + | 0.787747i | \(0.288753\pi\) | |||||||
\(810\) | 1.41421 | 0.0496904 | ||||||||
\(811\) | −26.7696 | −0.940006 | −0.470003 | − | 0.882665i | \(-0.655747\pi\) | ||||
−0.470003 | + | 0.882665i | \(0.655747\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −15.3848 | −0.539568 | ||||||||
\(814\) | −2.10051 | −0.0736227 | ||||||||
\(815\) | 24.2426 | 0.849183 | ||||||||
\(816\) | 5.24264 | 0.183529 | ||||||||
\(817\) | −14.4853 | −0.506776 | ||||||||
\(818\) | 2.58579 | 0.0904099 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −6.48528 | −0.226476 | ||||||||
\(821\) | −9.61522 | −0.335574 | −0.167787 | − | 0.985823i | \(-0.553662\pi\) | ||||
−0.167787 | + | 0.985823i | \(0.553662\pi\) | |||||||
\(822\) | 13.0711 | 0.455906 | ||||||||
\(823\) | −8.10051 | −0.282366 | −0.141183 | − | 0.989984i | \(-0.545091\pi\) | ||||
−0.141183 | + | 0.989984i | \(0.545091\pi\) | |||||||
\(824\) | −6.48528 | −0.225925 | ||||||||
\(825\) | 1.24264 | 0.0432632 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 13.5269 | 0.470377 | 0.235188 | − | 0.971950i | \(-0.424429\pi\) | ||||
0.235188 | + | 0.971950i | \(0.424429\pi\) | |||||||
\(828\) | −9.07107 | −0.315241 | ||||||||
\(829\) | −18.6985 | −0.649425 | −0.324713 | − | 0.945813i | \(-0.605268\pi\) | ||||
−0.324713 | + | 0.945813i | \(0.605268\pi\) | |||||||
\(830\) | 10.8284 | 0.375860 | ||||||||
\(831\) | 16.4142 | 0.569403 | ||||||||
\(832\) | −1.00000 | −0.0346688 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −21.2132 | −0.734553 | ||||||||
\(835\) | −17.4142 | −0.602644 | ||||||||
\(836\) | −1.24264 | −0.0429776 | ||||||||
\(837\) | 6.82843 | 0.236025 | ||||||||
\(838\) | 27.4558 | 0.948446 | ||||||||
\(839\) | −2.51472 | −0.0868177 | −0.0434089 | − | 0.999057i | \(-0.513822\pi\) | ||||
−0.0434089 | + | 0.999057i | \(0.513822\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −4.00000 | −0.137931 | ||||||||
\(842\) | 10.5858 | 0.364810 | ||||||||
\(843\) | −7.31371 | −0.251898 | ||||||||
\(844\) | −28.3848 | −0.977044 | ||||||||
\(845\) | 1.41421 | 0.0486504 | ||||||||
\(846\) | −9.00000 | −0.309426 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 12.3137 | 0.422854 | ||||||||
\(849\) | 17.0711 | 0.585878 | ||||||||
\(850\) | 15.7279 | 0.539463 | ||||||||
\(851\) | 46.0000 | 1.57686 | ||||||||
\(852\) | 1.00000 | 0.0342594 | ||||||||
\(853\) | 17.6985 | 0.605985 | 0.302992 | − | 0.952993i | \(-0.402014\pi\) | ||||
0.302992 | + | 0.952993i | \(0.402014\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −4.24264 | −0.145095 | ||||||||
\(856\) | 13.6569 | 0.466782 | ||||||||
\(857\) | 51.3848 | 1.75527 | 0.877635 | − | 0.479329i | \(-0.159120\pi\) | ||||
0.877635 | + | 0.479329i | \(0.159120\pi\) | |||||||
\(858\) | 0.414214 | 0.0141410 | ||||||||
\(859\) | −0.201010 | −0.00685838 | −0.00342919 | − | 0.999994i | \(-0.501092\pi\) | ||||
−0.00342919 | + | 0.999994i | \(0.501092\pi\) | |||||||
\(860\) | 6.82843 | 0.232847 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 14.4853 | 0.493371 | ||||||||
\(863\) | 4.00000 | 0.136162 | 0.0680808 | − | 0.997680i | \(-0.478312\pi\) | ||||
0.0680808 | + | 0.997680i | \(0.478312\pi\) | |||||||
\(864\) | −1.00000 | −0.0340207 | ||||||||
\(865\) | −28.7279 | −0.976779 | ||||||||
\(866\) | 19.0000 | 0.645646 | ||||||||
\(867\) | −10.4853 | −0.356099 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 5.51472 | 0.187074 | ||||||||
\(870\) | −7.07107 | −0.239732 | ||||||||
\(871\) | 14.6569 | 0.496629 | ||||||||
\(872\) | 1.65685 | 0.0561082 | ||||||||
\(873\) | −7.89949 | −0.267357 | ||||||||
\(874\) | 27.2132 | 0.920500 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −1.07107 | −0.0361880 | ||||||||
\(877\) | 23.4142 | 0.790642 | 0.395321 | − | 0.918543i | \(-0.370633\pi\) | ||||
0.395321 | + | 0.918543i | \(0.370633\pi\) | |||||||
\(878\) | 10.5858 | 0.357253 | ||||||||
\(879\) | −18.7279 | −0.631677 | ||||||||
\(880\) | 0.585786 | 0.0197469 | ||||||||
\(881\) | 41.1127 | 1.38512 | 0.692561 | − | 0.721359i | \(-0.256482\pi\) | ||||
0.692561 | + | 0.721359i | \(0.256482\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −0.928932 | −0.0312611 | −0.0156305 | − | 0.999878i | \(-0.504976\pi\) | ||||
−0.0156305 | + | 0.999878i | \(0.504976\pi\) | |||||||
\(884\) | 5.24264 | 0.176329 | ||||||||
\(885\) | 10.7279 | 0.360615 | ||||||||
\(886\) | 22.7279 | 0.763559 | ||||||||
\(887\) | −41.3137 | −1.38718 | −0.693589 | − | 0.720371i | \(-0.743972\pi\) | ||||
−0.693589 | + | 0.720371i | \(0.743972\pi\) | |||||||
\(888\) | 5.07107 | 0.170174 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 8.82843 | 0.295930 | ||||||||
\(891\) | 0.414214 | 0.0138767 | ||||||||
\(892\) | −21.3848 | −0.716015 | ||||||||
\(893\) | 27.0000 | 0.903521 | ||||||||
\(894\) | −15.8995 | −0.531759 | ||||||||
\(895\) | −17.4558 | −0.583485 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −9.07107 | −0.302874 | ||||||||
\(898\) | −33.9411 | −1.13263 | ||||||||
\(899\) | −34.1421 | −1.13870 | ||||||||
\(900\) | −3.00000 | −0.100000 | ||||||||
\(901\) | −64.5563 | −2.15068 | ||||||||
\(902\) | −1.89949 | −0.0632463 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −6.07107 | −0.201921 | ||||||||
\(905\) | 16.3848 | 0.544648 | ||||||||
\(906\) | 7.58579 | 0.252021 | ||||||||
\(907\) | −32.1005 | −1.06588 | −0.532940 | − | 0.846153i | \(-0.678913\pi\) | ||||
−0.532940 | + | 0.846153i | \(0.678913\pi\) | |||||||
\(908\) | 26.1421 | 0.867557 | ||||||||
\(909\) | 1.17157 | 0.0388586 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 54.0000 | 1.78910 | 0.894550 | − | 0.446968i | \(-0.147496\pi\) | ||||
0.894550 | + | 0.446968i | \(0.147496\pi\) | |||||||
\(912\) | 3.00000 | 0.0993399 | ||||||||
\(913\) | 3.17157 | 0.104964 | ||||||||
\(914\) | −15.2132 | −0.503208 | ||||||||
\(915\) | −7.41421 | −0.245106 | ||||||||
\(916\) | 7.17157 | 0.236955 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 5.24264 | 0.173033 | ||||||||
\(919\) | −25.7990 | −0.851030 | −0.425515 | − | 0.904951i | \(-0.639907\pi\) | ||||
−0.425515 | + | 0.904951i | \(0.639907\pi\) | |||||||
\(920\) | −12.8284 | −0.422941 | ||||||||
\(921\) | −19.6274 | −0.646745 | ||||||||
\(922\) | 33.4558 | 1.10181 | ||||||||
\(923\) | 1.00000 | 0.0329154 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 15.2132 | 0.500207 | ||||||||
\(926\) | −37.9411 | −1.24682 | ||||||||
\(927\) | −6.48528 | −0.213005 | ||||||||
\(928\) | 5.00000 | 0.164133 | ||||||||
\(929\) | −18.2843 | −0.599887 | −0.299944 | − | 0.953957i | \(-0.596968\pi\) | ||||
−0.299944 | + | 0.953957i | \(0.596968\pi\) | |||||||
\(930\) | 9.65685 | 0.316661 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −3.72792 | −0.122112 | ||||||||
\(933\) | −6.58579 | −0.215609 | ||||||||
\(934\) | 0.242641 | 0.00793945 | ||||||||
\(935\) | −3.07107 | −0.100435 | ||||||||
\(936\) | −1.00000 | −0.0326860 | ||||||||
\(937\) | −40.5980 | −1.32628 | −0.663139 | − | 0.748496i | \(-0.730776\pi\) | ||||
−0.663139 | + | 0.748496i | \(0.730776\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 18.1421 | 0.592046 | ||||||||
\(940\) | −12.7279 | −0.415139 | ||||||||
\(941\) | 20.9706 | 0.683621 | 0.341810 | − | 0.939769i | \(-0.388960\pi\) | ||||
0.341810 | + | 0.939769i | \(0.388960\pi\) | |||||||
\(942\) | 7.92893 | 0.258339 | ||||||||
\(943\) | 41.5980 | 1.35462 | ||||||||
\(944\) | −7.58579 | −0.246896 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 2.00000 | 0.0650256 | ||||||||
\(947\) | 17.2426 | 0.560311 | 0.280155 | − | 0.959955i | \(-0.409614\pi\) | ||||
0.280155 | + | 0.959955i | \(0.409614\pi\) | |||||||
\(948\) | −13.3137 | −0.432409 | ||||||||
\(949\) | −1.07107 | −0.0347683 | ||||||||
\(950\) | 9.00000 | 0.291999 | ||||||||
\(951\) | −0.828427 | −0.0268636 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −10.2132 | −0.330838 | −0.165419 | − | 0.986223i | \(-0.552898\pi\) | ||||
−0.165419 | + | 0.986223i | \(0.552898\pi\) | |||||||
\(954\) | 12.3137 | 0.398671 | ||||||||
\(955\) | 3.31371 | 0.107229 | ||||||||
\(956\) | −2.51472 | −0.0813318 | ||||||||
\(957\) | −2.07107 | −0.0669481 | ||||||||
\(958\) | 31.1421 | 1.00616 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −1.41421 | −0.0456435 | ||||||||
\(961\) | 15.6274 | 0.504110 | ||||||||
\(962\) | 5.07107 | 0.163498 | ||||||||
\(963\) | 13.6569 | 0.440086 | ||||||||
\(964\) | 16.4853 | 0.530955 | ||||||||
\(965\) | −22.2843 | −0.717356 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 9.38478 | 0.301794 | 0.150897 | − | 0.988549i | \(-0.451784\pi\) | ||||
0.150897 | + | 0.988549i | \(0.451784\pi\) | |||||||
\(968\) | −10.8284 | −0.348039 | ||||||||
\(969\) | −15.7279 | −0.505254 | ||||||||
\(970\) | −11.1716 | −0.358698 | ||||||||
\(971\) | −57.5563 | −1.84707 | −0.923536 | − | 0.383513i | \(-0.874714\pi\) | ||||
−0.923536 | + | 0.383513i | \(0.874714\pi\) | |||||||
\(972\) | −1.00000 | −0.0320750 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −23.7279 | −0.760292 | ||||||||
\(975\) | −3.00000 | −0.0960769 | ||||||||
\(976\) | 5.24264 | 0.167813 | ||||||||
\(977\) | 2.48528 | 0.0795112 | 0.0397556 | − | 0.999209i | \(-0.487342\pi\) | ||||
0.0397556 | + | 0.999209i | \(0.487342\pi\) | |||||||
\(978\) | −17.1421 | −0.548145 | ||||||||
\(979\) | 2.58579 | 0.0826421 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 1.65685 | 0.0528993 | ||||||||
\(982\) | −26.2843 | −0.838765 | ||||||||
\(983\) | 22.1716 | 0.707163 | 0.353582 | − | 0.935404i | \(-0.384964\pi\) | ||||
0.353582 | + | 0.935404i | \(0.384964\pi\) | |||||||
\(984\) | 4.58579 | 0.146190 | ||||||||
\(985\) | 13.5147 | 0.430615 | ||||||||
\(986\) | −26.2132 | −0.834798 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 3.00000 | 0.0954427 | ||||||||
\(989\) | −43.7990 | −1.39273 | ||||||||
\(990\) | 0.585786 | 0.0186175 | ||||||||
\(991\) | −7.31371 | −0.232328 | −0.116164 | − | 0.993230i | \(-0.537060\pi\) | ||||
−0.116164 | + | 0.993230i | \(0.537060\pi\) | |||||||
\(992\) | −6.82843 | −0.216803 | ||||||||
\(993\) | 22.4853 | 0.713549 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −14.9706 | −0.474599 | ||||||||
\(996\) | −7.65685 | −0.242617 | ||||||||
\(997\) | −6.69848 | −0.212143 | −0.106072 | − | 0.994358i | \(-0.533827\pi\) | ||||
−0.106072 | + | 0.994358i | \(0.533827\pi\) | |||||||
\(998\) | −30.0000 | −0.949633 | ||||||||
\(999\) | 5.07107 | 0.160441 |
(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 | 3822.2.a.bp.1.2 | 2 | ||
7.3 | odd | 6 | 546.2.i.h.79.2 | ✓ | 4 | ||
7.5 | odd | 6 | 546.2.i.h.235.2 | yes | 4 | ||
7.6 | odd | 2 | 3822.2.a.bs.1.1 | 2 | |||
21.5 | even | 6 | 1638.2.j.n.235.1 | 4 | |||
21.17 | even | 6 | 1638.2.j.n.1171.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
546.2.i.h.79.2 | ✓ | 4 | 7.3 | odd | 6 | ||
546.2.i.h.235.2 | yes | 4 | 7.5 | odd | 6 | ||
1638.2.j.n.235.1 | 4 | 21.5 | even | 6 | |||
1638.2.j.n.1171.1 | 4 | 21.17 | even | 6 | |||
3822.2.a.bp.1.2 | 2 | 1.1 | even | 1 | trivial | ||
3822.2.a.bs.1.1 | 2 | 7.6 | odd | 2 |