Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3234,2,Mod(1,3234)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3234, 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("3234.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3234 = 2 \cdot 3 \cdot 7^{2} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3234.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: | \(25.8236200137\) |
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: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(+1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-1.41421\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3234.1 |
$q$-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 | ||||||||
\(5\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(6\) | −1.00000 | −0.408248 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | 1.00000 | 0.288675 | ||||||||
\(13\) | 1.41421 | 0.392232 | 0.196116 | − | 0.980581i | \(-0.437167\pi\) | ||||
0.196116 | + | 0.980581i | \(0.437167\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −4.00000 | −0.970143 | −0.485071 | − | 0.874475i | \(-0.661206\pi\) | ||||
−0.485071 | + | 0.874475i | \(0.661206\pi\) | |||||||
\(18\) | −1.00000 | −0.235702 | ||||||||
\(19\) | −2.58579 | −0.593220 | −0.296610 | − | 0.954999i | \(-0.595856\pi\) | ||||
−0.296610 | + | 0.954999i | \(0.595856\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −1.00000 | −0.213201 | ||||||||
\(23\) | −3.65685 | −0.762507 | −0.381253 | − | 0.924471i | \(-0.624507\pi\) | ||||
−0.381253 | + | 0.924471i | \(0.624507\pi\) | |||||||
\(24\) | −1.00000 | −0.204124 | ||||||||
\(25\) | −5.00000 | −1.00000 | ||||||||
\(26\) | −1.41421 | −0.277350 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 5.65685 | 1.05045 | 0.525226 | − | 0.850963i | \(-0.323981\pi\) | ||||
0.525226 | + | 0.850963i | \(0.323981\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −11.0711 | −1.98842 | −0.994211 | − | 0.107443i | \(-0.965734\pi\) | ||||
−0.994211 | + | 0.107443i | \(0.965734\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 1.00000 | 0.174078 | ||||||||
\(34\) | 4.00000 | 0.685994 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | −7.65685 | −1.25878 | −0.629390 | − | 0.777090i | \(-0.716695\pi\) | ||||
−0.629390 | + | 0.777090i | \(0.716695\pi\) | |||||||
\(38\) | 2.58579 | 0.419470 | ||||||||
\(39\) | 1.41421 | 0.226455 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.65685 | 0.258757 | 0.129379 | − | 0.991595i | \(-0.458702\pi\) | ||||
0.129379 | + | 0.991595i | \(0.458702\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −10.0000 | −1.52499 | −0.762493 | − | 0.646997i | \(-0.776025\pi\) | ||||
−0.762493 | + | 0.646997i | \(0.776025\pi\) | |||||||
\(44\) | 1.00000 | 0.150756 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 3.65685 | 0.539174 | ||||||||
\(47\) | −1.41421 | −0.206284 | −0.103142 | − | 0.994667i | \(-0.532890\pi\) | ||||
−0.103142 | + | 0.994667i | \(0.532890\pi\) | |||||||
\(48\) | 1.00000 | 0.144338 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 5.00000 | 0.707107 | ||||||||
\(51\) | −4.00000 | −0.560112 | ||||||||
\(52\) | 1.41421 | 0.196116 | ||||||||
\(53\) | 7.65685 | 1.05175 | 0.525875 | − | 0.850562i | \(-0.323738\pi\) | ||||
0.525875 | + | 0.850562i | \(0.323738\pi\) | |||||||
\(54\) | −1.00000 | −0.136083 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −2.58579 | −0.342496 | ||||||||
\(58\) | −5.65685 | −0.742781 | ||||||||
\(59\) | −1.17157 | −0.152526 | −0.0762629 | − | 0.997088i | \(-0.524299\pi\) | ||||
−0.0762629 | + | 0.997088i | \(0.524299\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.41421 | −0.181071 | −0.0905357 | − | 0.995893i | \(-0.528858\pi\) | ||||
−0.0905357 | + | 0.995893i | \(0.528858\pi\) | |||||||
\(62\) | 11.0711 | 1.40603 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −1.00000 | −0.123091 | ||||||||
\(67\) | 11.3137 | 1.38219 | 0.691095 | − | 0.722764i | \(-0.257129\pi\) | ||||
0.691095 | + | 0.722764i | \(0.257129\pi\) | |||||||
\(68\) | −4.00000 | −0.485071 | ||||||||
\(69\) | −3.65685 | −0.440234 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 2.34315 | 0.278080 | 0.139040 | − | 0.990287i | \(-0.455598\pi\) | ||||
0.139040 | + | 0.990287i | \(0.455598\pi\) | |||||||
\(72\) | −1.00000 | −0.117851 | ||||||||
\(73\) | −4.00000 | −0.468165 | −0.234082 | − | 0.972217i | \(-0.575209\pi\) | ||||
−0.234082 | + | 0.972217i | \(0.575209\pi\) | |||||||
\(74\) | 7.65685 | 0.890091 | ||||||||
\(75\) | −5.00000 | −0.577350 | ||||||||
\(76\) | −2.58579 | −0.296610 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −1.41421 | −0.160128 | ||||||||
\(79\) | −9.65685 | −1.08648 | −0.543240 | − | 0.839577i | \(-0.682803\pi\) | ||||
−0.543240 | + | 0.839577i | \(0.682803\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −1.65685 | −0.182969 | ||||||||
\(83\) | 0.928932 | 0.101964 | 0.0509818 | − | 0.998700i | \(-0.483765\pi\) | ||||
0.0509818 | + | 0.998700i | \(0.483765\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 10.0000 | 1.07833 | ||||||||
\(87\) | 5.65685 | 0.606478 | ||||||||
\(88\) | −1.00000 | −0.106600 | ||||||||
\(89\) | −5.41421 | −0.573905 | −0.286953 | − | 0.957945i | \(-0.592642\pi\) | ||||
−0.286953 | + | 0.957945i | \(0.592642\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −3.65685 | −0.381253 | ||||||||
\(93\) | −11.0711 | −1.14802 | ||||||||
\(94\) | 1.41421 | 0.145865 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −1.00000 | −0.102062 | ||||||||
\(97\) | 12.7279 | 1.29232 | 0.646162 | − | 0.763200i | \(-0.276373\pi\) | ||||
0.646162 | + | 0.763200i | \(0.276373\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1.00000 | 0.100504 | ||||||||
\(100\) | −5.00000 | −0.500000 | ||||||||
\(101\) | −8.24264 | −0.820173 | −0.410087 | − | 0.912047i | \(-0.634502\pi\) | ||||
−0.410087 | + | 0.912047i | \(0.634502\pi\) | |||||||
\(102\) | 4.00000 | 0.396059 | ||||||||
\(103\) | 5.89949 | 0.581295 | 0.290647 | − | 0.956830i | \(-0.406129\pi\) | ||||
0.290647 | + | 0.956830i | \(0.406129\pi\) | |||||||
\(104\) | −1.41421 | −0.138675 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −7.65685 | −0.743699 | ||||||||
\(107\) | −5.31371 | −0.513696 | −0.256848 | − | 0.966452i | \(-0.582684\pi\) | ||||
−0.256848 | + | 0.966452i | \(0.582684\pi\) | |||||||
\(108\) | 1.00000 | 0.0962250 | ||||||||
\(109\) | −10.0000 | −0.957826 | −0.478913 | − | 0.877862i | \(-0.658969\pi\) | ||||
−0.478913 | + | 0.877862i | \(0.658969\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −7.65685 | −0.726756 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 5.65685 | 0.532152 | 0.266076 | − | 0.963952i | \(-0.414273\pi\) | ||||
0.266076 | + | 0.963952i | \(0.414273\pi\) | |||||||
\(114\) | 2.58579 | 0.242181 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 5.65685 | 0.525226 | ||||||||
\(117\) | 1.41421 | 0.130744 | ||||||||
\(118\) | 1.17157 | 0.107852 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 1.41421 | 0.128037 | ||||||||
\(123\) | 1.65685 | 0.149394 | ||||||||
\(124\) | −11.0711 | −0.994211 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 7.31371 | 0.648987 | 0.324493 | − | 0.945888i | \(-0.394806\pi\) | ||||
0.324493 | + | 0.945888i | \(0.394806\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | −10.0000 | −0.880451 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −12.2426 | −1.06964 | −0.534822 | − | 0.844965i | \(-0.679621\pi\) | ||||
−0.534822 | + | 0.844965i | \(0.679621\pi\) | |||||||
\(132\) | 1.00000 | 0.0870388 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −11.3137 | −0.977356 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 4.00000 | 0.342997 | ||||||||
\(137\) | 13.3137 | 1.13747 | 0.568733 | − | 0.822522i | \(-0.307434\pi\) | ||||
0.568733 | + | 0.822522i | \(0.307434\pi\) | |||||||
\(138\) | 3.65685 | 0.311292 | ||||||||
\(139\) | −21.8995 | −1.85749 | −0.928745 | − | 0.370718i | \(-0.879112\pi\) | ||||
−0.928745 | + | 0.370718i | \(0.879112\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −1.41421 | −0.119098 | ||||||||
\(142\) | −2.34315 | −0.196632 | ||||||||
\(143\) | 1.41421 | 0.118262 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 4.00000 | 0.331042 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −7.65685 | −0.629390 | ||||||||
\(149\) | −20.9706 | −1.71798 | −0.858988 | − | 0.511996i | \(-0.828906\pi\) | ||||
−0.858988 | + | 0.511996i | \(0.828906\pi\) | |||||||
\(150\) | 5.00000 | 0.408248 | ||||||||
\(151\) | 9.65685 | 0.785864 | 0.392932 | − | 0.919568i | \(-0.371461\pi\) | ||||
0.392932 | + | 0.919568i | \(0.371461\pi\) | |||||||
\(152\) | 2.58579 | 0.209735 | ||||||||
\(153\) | −4.00000 | −0.323381 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 1.41421 | 0.113228 | ||||||||
\(157\) | −2.82843 | −0.225733 | −0.112867 | − | 0.993610i | \(-0.536003\pi\) | ||||
−0.112867 | + | 0.993610i | \(0.536003\pi\) | |||||||
\(158\) | 9.65685 | 0.768258 | ||||||||
\(159\) | 7.65685 | 0.607228 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −1.00000 | −0.0785674 | ||||||||
\(163\) | −5.65685 | −0.443079 | −0.221540 | − | 0.975151i | \(-0.571108\pi\) | ||||
−0.221540 | + | 0.975151i | \(0.571108\pi\) | |||||||
\(164\) | 1.65685 | 0.129379 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −0.928932 | −0.0720991 | ||||||||
\(167\) | −5.17157 | −0.400188 | −0.200094 | − | 0.979777i | \(-0.564125\pi\) | ||||
−0.200094 | + | 0.979777i | \(0.564125\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −11.0000 | −0.846154 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −2.58579 | −0.197740 | ||||||||
\(172\) | −10.0000 | −0.762493 | ||||||||
\(173\) | −19.0711 | −1.44995 | −0.724973 | − | 0.688777i | \(-0.758148\pi\) | ||||
−0.724973 | + | 0.688777i | \(0.758148\pi\) | |||||||
\(174\) | −5.65685 | −0.428845 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 1.00000 | 0.0753778 | ||||||||
\(177\) | −1.17157 | −0.0880608 | ||||||||
\(178\) | 5.41421 | 0.405812 | ||||||||
\(179\) | 13.6569 | 1.02076 | 0.510381 | − | 0.859949i | \(-0.329505\pi\) | ||||
0.510381 | + | 0.859949i | \(0.329505\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 10.3431 | 0.768800 | 0.384400 | − | 0.923167i | \(-0.374408\pi\) | ||||
0.384400 | + | 0.923167i | \(0.374408\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −1.41421 | −0.104542 | ||||||||
\(184\) | 3.65685 | 0.269587 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 11.0711 | 0.811770 | ||||||||
\(187\) | −4.00000 | −0.292509 | ||||||||
\(188\) | −1.41421 | −0.103142 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 22.9706 | 1.66209 | 0.831046 | − | 0.556204i | \(-0.187743\pi\) | ||||
0.831046 | + | 0.556204i | \(0.187743\pi\) | |||||||
\(192\) | 1.00000 | 0.0721688 | ||||||||
\(193\) | −3.65685 | −0.263226 | −0.131613 | − | 0.991301i | \(-0.542016\pi\) | ||||
−0.131613 | + | 0.991301i | \(0.542016\pi\) | |||||||
\(194\) | −12.7279 | −0.913812 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −1.31371 | −0.0935979 | −0.0467989 | − | 0.998904i | \(-0.514902\pi\) | ||||
−0.0467989 | + | 0.998904i | \(0.514902\pi\) | |||||||
\(198\) | −1.00000 | −0.0710669 | ||||||||
\(199\) | −13.4142 | −0.950908 | −0.475454 | − | 0.879740i | \(-0.657716\pi\) | ||||
−0.475454 | + | 0.879740i | \(0.657716\pi\) | |||||||
\(200\) | 5.00000 | 0.353553 | ||||||||
\(201\) | 11.3137 | 0.798007 | ||||||||
\(202\) | 8.24264 | 0.579950 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −4.00000 | −0.280056 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −5.89949 | −0.411037 | ||||||||
\(207\) | −3.65685 | −0.254169 | ||||||||
\(208\) | 1.41421 | 0.0980581 | ||||||||
\(209\) | −2.58579 | −0.178863 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −5.31371 | −0.365811 | −0.182905 | − | 0.983131i | \(-0.558550\pi\) | ||||
−0.182905 | + | 0.983131i | \(0.558550\pi\) | |||||||
\(212\) | 7.65685 | 0.525875 | ||||||||
\(213\) | 2.34315 | 0.160550 | ||||||||
\(214\) | 5.31371 | 0.363238 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −1.00000 | −0.0680414 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 10.0000 | 0.677285 | ||||||||
\(219\) | −4.00000 | −0.270295 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −5.65685 | −0.380521 | ||||||||
\(222\) | 7.65685 | 0.513894 | ||||||||
\(223\) | 11.5563 | 0.773870 | 0.386935 | − | 0.922107i | \(-0.373534\pi\) | ||||
0.386935 | + | 0.922107i | \(0.373534\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −5.00000 | −0.333333 | ||||||||
\(226\) | −5.65685 | −0.376288 | ||||||||
\(227\) | 7.55635 | 0.501533 | 0.250766 | − | 0.968048i | \(-0.419317\pi\) | ||||
0.250766 | + | 0.968048i | \(0.419317\pi\) | |||||||
\(228\) | −2.58579 | −0.171248 | ||||||||
\(229\) | 5.65685 | 0.373815 | 0.186908 | − | 0.982377i | \(-0.440153\pi\) | ||||
0.186908 | + | 0.982377i | \(0.440153\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −5.65685 | −0.371391 | ||||||||
\(233\) | 23.6569 | 1.54981 | 0.774906 | − | 0.632076i | \(-0.217797\pi\) | ||||
0.774906 | + | 0.632076i | \(0.217797\pi\) | |||||||
\(234\) | −1.41421 | −0.0924500 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −1.17157 | −0.0762629 | ||||||||
\(237\) | −9.65685 | −0.627280 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 25.6569 | 1.65960 | 0.829802 | − | 0.558058i | \(-0.188453\pi\) | ||||
0.829802 | + | 0.558058i | \(0.188453\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −15.3137 | −0.986443 | −0.493221 | − | 0.869904i | \(-0.664181\pi\) | ||||
−0.493221 | + | 0.869904i | \(0.664181\pi\) | |||||||
\(242\) | −1.00000 | −0.0642824 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | −1.41421 | −0.0905357 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −1.65685 | −0.105637 | ||||||||
\(247\) | −3.65685 | −0.232680 | ||||||||
\(248\) | 11.0711 | 0.703014 | ||||||||
\(249\) | 0.928932 | 0.0588687 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −9.17157 | −0.578905 | −0.289452 | − | 0.957192i | \(-0.593473\pi\) | ||||
−0.289452 | + | 0.957192i | \(0.593473\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −3.65685 | −0.229904 | ||||||||
\(254\) | −7.31371 | −0.458903 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −8.72792 | −0.544433 | −0.272216 | − | 0.962236i | \(-0.587757\pi\) | ||||
−0.272216 | + | 0.962236i | \(0.587757\pi\) | |||||||
\(258\) | 10.0000 | 0.622573 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 5.65685 | 0.350150 | ||||||||
\(262\) | 12.2426 | 0.756353 | ||||||||
\(263\) | 2.34315 | 0.144485 | 0.0722423 | − | 0.997387i | \(-0.476985\pi\) | ||||
0.0722423 | + | 0.997387i | \(0.476985\pi\) | |||||||
\(264\) | −1.00000 | −0.0615457 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −5.41421 | −0.331344 | ||||||||
\(268\) | 11.3137 | 0.691095 | ||||||||
\(269\) | 22.6274 | 1.37962 | 0.689809 | − | 0.723991i | \(-0.257694\pi\) | ||||
0.689809 | + | 0.723991i | \(0.257694\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −26.8284 | −1.62971 | −0.814855 | − | 0.579664i | \(-0.803184\pi\) | ||||
−0.814855 | + | 0.579664i | \(0.803184\pi\) | |||||||
\(272\) | −4.00000 | −0.242536 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −13.3137 | −0.804311 | ||||||||
\(275\) | −5.00000 | −0.301511 | ||||||||
\(276\) | −3.65685 | −0.220117 | ||||||||
\(277\) | 4.00000 | 0.240337 | 0.120168 | − | 0.992754i | \(-0.461657\pi\) | ||||
0.120168 | + | 0.992754i | \(0.461657\pi\) | |||||||
\(278\) | 21.8995 | 1.31344 | ||||||||
\(279\) | −11.0711 | −0.662807 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 14.9706 | 0.893069 | 0.446534 | − | 0.894766i | \(-0.352658\pi\) | ||||
0.446534 | + | 0.894766i | \(0.352658\pi\) | |||||||
\(282\) | 1.41421 | 0.0842152 | ||||||||
\(283\) | −24.2426 | −1.44108 | −0.720538 | − | 0.693416i | \(-0.756105\pi\) | ||||
−0.720538 | + | 0.693416i | \(0.756105\pi\) | |||||||
\(284\) | 2.34315 | 0.139040 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −1.41421 | −0.0836242 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −1.00000 | −0.0589256 | ||||||||
\(289\) | −1.00000 | −0.0588235 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 12.7279 | 0.746124 | ||||||||
\(292\) | −4.00000 | −0.234082 | ||||||||
\(293\) | −11.0711 | −0.646779 | −0.323389 | − | 0.946266i | \(-0.604822\pi\) | ||||
−0.323389 | + | 0.946266i | \(0.604822\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 7.65685 | 0.445046 | ||||||||
\(297\) | 1.00000 | 0.0580259 | ||||||||
\(298\) | 20.9706 | 1.21479 | ||||||||
\(299\) | −5.17157 | −0.299080 | ||||||||
\(300\) | −5.00000 | −0.288675 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −9.65685 | −0.555690 | ||||||||
\(303\) | −8.24264 | −0.473527 | ||||||||
\(304\) | −2.58579 | −0.148305 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 4.00000 | 0.228665 | ||||||||
\(307\) | −24.7279 | −1.41130 | −0.705649 | − | 0.708562i | \(-0.749344\pi\) | ||||
−0.705649 | + | 0.708562i | \(0.749344\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 5.89949 | 0.335611 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −11.7574 | −0.666699 | −0.333349 | − | 0.942803i | \(-0.608179\pi\) | ||||
−0.333349 | + | 0.942803i | \(0.608179\pi\) | |||||||
\(312\) | −1.41421 | −0.0800641 | ||||||||
\(313\) | 3.75736 | 0.212379 | 0.106189 | − | 0.994346i | \(-0.466135\pi\) | ||||
0.106189 | + | 0.994346i | \(0.466135\pi\) | |||||||
\(314\) | 2.82843 | 0.159617 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −9.65685 | −0.543240 | ||||||||
\(317\) | 17.3137 | 0.972435 | 0.486217 | − | 0.873838i | \(-0.338376\pi\) | ||||
0.486217 | + | 0.873838i | \(0.338376\pi\) | |||||||
\(318\) | −7.65685 | −0.429375 | ||||||||
\(319\) | 5.65685 | 0.316723 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −5.31371 | −0.296582 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 10.3431 | 0.575508 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | −7.07107 | −0.392232 | ||||||||
\(326\) | 5.65685 | 0.313304 | ||||||||
\(327\) | −10.0000 | −0.553001 | ||||||||
\(328\) | −1.65685 | −0.0914845 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −4.97056 | −0.273207 | −0.136603 | − | 0.990626i | \(-0.543619\pi\) | ||||
−0.136603 | + | 0.990626i | \(0.543619\pi\) | |||||||
\(332\) | 0.928932 | 0.0509818 | ||||||||
\(333\) | −7.65685 | −0.419593 | ||||||||
\(334\) | 5.17157 | 0.282976 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 5.31371 | 0.289456 | 0.144728 | − | 0.989471i | \(-0.453769\pi\) | ||||
0.144728 | + | 0.989471i | \(0.453769\pi\) | |||||||
\(338\) | 11.0000 | 0.598321 | ||||||||
\(339\) | 5.65685 | 0.307238 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −11.0711 | −0.599532 | ||||||||
\(342\) | 2.58579 | 0.139823 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 10.0000 | 0.539164 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 19.0711 | 1.02527 | ||||||||
\(347\) | −2.00000 | −0.107366 | −0.0536828 | − | 0.998558i | \(-0.517096\pi\) | ||||
−0.0536828 | + | 0.998558i | \(0.517096\pi\) | |||||||
\(348\) | 5.65685 | 0.303239 | ||||||||
\(349\) | −25.4142 | −1.36039 | −0.680196 | − | 0.733030i | \(-0.738105\pi\) | ||||
−0.680196 | + | 0.733030i | \(0.738105\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.41421 | 0.0754851 | ||||||||
\(352\) | −1.00000 | −0.0533002 | ||||||||
\(353\) | −5.89949 | −0.313998 | −0.156999 | − | 0.987599i | \(-0.550182\pi\) | ||||
−0.156999 | + | 0.987599i | \(0.550182\pi\) | |||||||
\(354\) | 1.17157 | 0.0622684 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −5.41421 | −0.286953 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −13.6569 | −0.721787 | ||||||||
\(359\) | −4.00000 | −0.211112 | −0.105556 | − | 0.994413i | \(-0.533662\pi\) | ||||
−0.105556 | + | 0.994413i | \(0.533662\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −12.3137 | −0.648090 | ||||||||
\(362\) | −10.3431 | −0.543624 | ||||||||
\(363\) | 1.00000 | 0.0524864 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 1.41421 | 0.0739221 | ||||||||
\(367\) | −22.8701 | −1.19381 | −0.596904 | − | 0.802313i | \(-0.703603\pi\) | ||||
−0.596904 | + | 0.802313i | \(0.703603\pi\) | |||||||
\(368\) | −3.65685 | −0.190627 | ||||||||
\(369\) | 1.65685 | 0.0862524 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −11.0711 | −0.574008 | ||||||||
\(373\) | 8.62742 | 0.446711 | 0.223355 | − | 0.974737i | \(-0.428299\pi\) | ||||
0.223355 | + | 0.974737i | \(0.428299\pi\) | |||||||
\(374\) | 4.00000 | 0.206835 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 1.41421 | 0.0729325 | ||||||||
\(377\) | 8.00000 | 0.412021 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −6.34315 | −0.325826 | −0.162913 | − | 0.986640i | \(-0.552089\pi\) | ||||
−0.162913 | + | 0.986640i | \(0.552089\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 7.31371 | 0.374693 | ||||||||
\(382\) | −22.9706 | −1.17528 | ||||||||
\(383\) | −23.5563 | −1.20367 | −0.601837 | − | 0.798619i | \(-0.705564\pi\) | ||||
−0.601837 | + | 0.798619i | \(0.705564\pi\) | |||||||
\(384\) | −1.00000 | −0.0510310 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 3.65685 | 0.186129 | ||||||||
\(387\) | −10.0000 | −0.508329 | ||||||||
\(388\) | 12.7279 | 0.646162 | ||||||||
\(389\) | −32.6274 | −1.65428 | −0.827138 | − | 0.561999i | \(-0.810032\pi\) | ||||
−0.827138 | + | 0.561999i | \(0.810032\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 14.6274 | 0.739740 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −12.2426 | −0.617560 | ||||||||
\(394\) | 1.31371 | 0.0661837 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 1.00000 | 0.0502519 | ||||||||
\(397\) | 27.7990 | 1.39519 | 0.697596 | − | 0.716492i | \(-0.254253\pi\) | ||||
0.697596 | + | 0.716492i | \(0.254253\pi\) | |||||||
\(398\) | 13.4142 | 0.672394 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −5.00000 | −0.250000 | ||||||||
\(401\) | −6.00000 | −0.299626 | −0.149813 | − | 0.988714i | \(-0.547867\pi\) | ||||
−0.149813 | + | 0.988714i | \(0.547867\pi\) | |||||||
\(402\) | −11.3137 | −0.564276 | ||||||||
\(403\) | −15.6569 | −0.779923 | ||||||||
\(404\) | −8.24264 | −0.410087 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −7.65685 | −0.379536 | ||||||||
\(408\) | 4.00000 | 0.198030 | ||||||||
\(409\) | −4.48528 | −0.221783 | −0.110891 | − | 0.993833i | \(-0.535371\pi\) | ||||
−0.110891 | + | 0.993833i | \(0.535371\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 13.3137 | 0.656717 | ||||||||
\(412\) | 5.89949 | 0.290647 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 3.65685 | 0.179725 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −1.41421 | −0.0693375 | ||||||||
\(417\) | −21.8995 | −1.07242 | ||||||||
\(418\) | 2.58579 | 0.126475 | ||||||||
\(419\) | 40.2843 | 1.96802 | 0.984008 | − | 0.178126i | \(-0.0570034\pi\) | ||||
0.984008 | + | 0.178126i | \(0.0570034\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 18.9706 | 0.924569 | 0.462284 | − | 0.886732i | \(-0.347030\pi\) | ||||
0.462284 | + | 0.886732i | \(0.347030\pi\) | |||||||
\(422\) | 5.31371 | 0.258667 | ||||||||
\(423\) | −1.41421 | −0.0687614 | ||||||||
\(424\) | −7.65685 | −0.371850 | ||||||||
\(425\) | 20.0000 | 0.970143 | ||||||||
\(426\) | −2.34315 | −0.113526 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −5.31371 | −0.256848 | ||||||||
\(429\) | 1.41421 | 0.0682789 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 16.0000 | 0.770693 | 0.385346 | − | 0.922772i | \(-0.374082\pi\) | ||||
0.385346 | + | 0.922772i | \(0.374082\pi\) | |||||||
\(432\) | 1.00000 | 0.0481125 | ||||||||
\(433\) | 5.21320 | 0.250531 | 0.125265 | − | 0.992123i | \(-0.460022\pi\) | ||||
0.125265 | + | 0.992123i | \(0.460022\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −10.0000 | −0.478913 | ||||||||
\(437\) | 9.45584 | 0.452334 | ||||||||
\(438\) | 4.00000 | 0.191127 | ||||||||
\(439\) | 3.79899 | 0.181316 | 0.0906579 | − | 0.995882i | \(-0.471103\pi\) | ||||
0.0906579 | + | 0.995882i | \(0.471103\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 5.65685 | 0.269069 | ||||||||
\(443\) | −28.2843 | −1.34383 | −0.671913 | − | 0.740630i | \(-0.734527\pi\) | ||||
−0.671913 | + | 0.740630i | \(0.734527\pi\) | |||||||
\(444\) | −7.65685 | −0.363378 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −11.5563 | −0.547209 | ||||||||
\(447\) | −20.9706 | −0.991874 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 21.6569 | 1.02205 | 0.511025 | − | 0.859566i | \(-0.329266\pi\) | ||||
0.511025 | + | 0.859566i | \(0.329266\pi\) | |||||||
\(450\) | 5.00000 | 0.235702 | ||||||||
\(451\) | 1.65685 | 0.0780182 | ||||||||
\(452\) | 5.65685 | 0.266076 | ||||||||
\(453\) | 9.65685 | 0.453719 | ||||||||
\(454\) | −7.55635 | −0.354637 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 2.58579 | 0.121091 | ||||||||
\(457\) | 8.34315 | 0.390276 | 0.195138 | − | 0.980776i | \(-0.437485\pi\) | ||||
0.195138 | + | 0.980776i | \(0.437485\pi\) | |||||||
\(458\) | −5.65685 | −0.264327 | ||||||||
\(459\) | −4.00000 | −0.186704 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −18.1005 | −0.843025 | −0.421512 | − | 0.906823i | \(-0.638501\pi\) | ||||
−0.421512 | + | 0.906823i | \(0.638501\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −4.68629 | −0.217790 | −0.108895 | − | 0.994053i | \(-0.534731\pi\) | ||||
−0.108895 | + | 0.994053i | \(0.534731\pi\) | |||||||
\(464\) | 5.65685 | 0.262613 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −23.6569 | −1.09588 | ||||||||
\(467\) | −29.9411 | −1.38551 | −0.692755 | − | 0.721173i | \(-0.743603\pi\) | ||||
−0.692755 | + | 0.721173i | \(0.743603\pi\) | |||||||
\(468\) | 1.41421 | 0.0653720 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −2.82843 | −0.130327 | ||||||||
\(472\) | 1.17157 | 0.0539260 | ||||||||
\(473\) | −10.0000 | −0.459800 | ||||||||
\(474\) | 9.65685 | 0.443554 | ||||||||
\(475\) | 12.9289 | 0.593220 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 7.65685 | 0.350583 | ||||||||
\(478\) | −25.6569 | −1.17352 | ||||||||
\(479\) | 0.970563 | 0.0443461 | 0.0221731 | − | 0.999754i | \(-0.492942\pi\) | ||||
0.0221731 | + | 0.999754i | \(0.492942\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −10.8284 | −0.493734 | ||||||||
\(482\) | 15.3137 | 0.697520 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 1.00000 | 0.0454545 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −1.00000 | −0.0453609 | ||||||||
\(487\) | −11.6569 | −0.528222 | −0.264111 | − | 0.964492i | \(-0.585079\pi\) | ||||
−0.264111 | + | 0.964492i | \(0.585079\pi\) | |||||||
\(488\) | 1.41421 | 0.0640184 | ||||||||
\(489\) | −5.65685 | −0.255812 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 20.0000 | 0.902587 | 0.451294 | − | 0.892375i | \(-0.350963\pi\) | ||||
0.451294 | + | 0.892375i | \(0.350963\pi\) | |||||||
\(492\) | 1.65685 | 0.0746968 | ||||||||
\(493\) | −22.6274 | −1.01909 | ||||||||
\(494\) | 3.65685 | 0.164530 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −11.0711 | −0.497106 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −0.928932 | −0.0416264 | ||||||||
\(499\) | 34.6274 | 1.55014 | 0.775068 | − | 0.631878i | \(-0.217716\pi\) | ||||
0.775068 | + | 0.631878i | \(0.217716\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −5.17157 | −0.231049 | ||||||||
\(502\) | 9.17157 | 0.409347 | ||||||||
\(503\) | −16.4853 | −0.735042 | −0.367521 | − | 0.930015i | \(-0.619793\pi\) | ||||
−0.367521 | + | 0.930015i | \(0.619793\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 3.65685 | 0.162567 | ||||||||
\(507\) | −11.0000 | −0.488527 | ||||||||
\(508\) | 7.31371 | 0.324493 | ||||||||
\(509\) | −25.9411 | −1.14982 | −0.574910 | − | 0.818217i | \(-0.694963\pi\) | ||||
−0.574910 | + | 0.818217i | \(0.694963\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | −2.58579 | −0.114165 | ||||||||
\(514\) | 8.72792 | 0.384972 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −10.0000 | −0.440225 | ||||||||
\(517\) | −1.41421 | −0.0621970 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −19.0711 | −0.837127 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 32.7279 | 1.43384 | 0.716918 | − | 0.697157i | \(-0.245552\pi\) | ||||
0.716918 | + | 0.697157i | \(0.245552\pi\) | |||||||
\(522\) | −5.65685 | −0.247594 | ||||||||
\(523\) | 40.2426 | 1.75969 | 0.879844 | − | 0.475263i | \(-0.157647\pi\) | ||||
0.879844 | + | 0.475263i | \(0.157647\pi\) | |||||||
\(524\) | −12.2426 | −0.534822 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −2.34315 | −0.102166 | ||||||||
\(527\) | 44.2843 | 1.92905 | ||||||||
\(528\) | 1.00000 | 0.0435194 | ||||||||
\(529\) | −9.62742 | −0.418583 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −1.17157 | −0.0508419 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 2.34315 | 0.101493 | ||||||||
\(534\) | 5.41421 | 0.234296 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −11.3137 | −0.488678 | ||||||||
\(537\) | 13.6569 | 0.589337 | ||||||||
\(538\) | −22.6274 | −0.975537 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 36.6274 | 1.57474 | 0.787368 | − | 0.616483i | \(-0.211443\pi\) | ||||
0.787368 | + | 0.616483i | \(0.211443\pi\) | |||||||
\(542\) | 26.8284 | 1.15238 | ||||||||
\(543\) | 10.3431 | 0.443867 | ||||||||
\(544\) | 4.00000 | 0.171499 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 9.65685 | 0.412897 | 0.206449 | − | 0.978457i | \(-0.433809\pi\) | ||||
0.206449 | + | 0.978457i | \(0.433809\pi\) | |||||||
\(548\) | 13.3137 | 0.568733 | ||||||||
\(549\) | −1.41421 | −0.0603572 | ||||||||
\(550\) | 5.00000 | 0.213201 | ||||||||
\(551\) | −14.6274 | −0.623149 | ||||||||
\(552\) | 3.65685 | 0.155646 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −4.00000 | −0.169944 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −21.8995 | −0.928745 | ||||||||
\(557\) | −35.9411 | −1.52287 | −0.761437 | − | 0.648239i | \(-0.775506\pi\) | ||||
−0.761437 | + | 0.648239i | \(0.775506\pi\) | |||||||
\(558\) | 11.0711 | 0.468676 | ||||||||
\(559\) | −14.1421 | −0.598149 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −4.00000 | −0.168880 | ||||||||
\(562\) | −14.9706 | −0.631495 | ||||||||
\(563\) | 25.4142 | 1.07108 | 0.535541 | − | 0.844509i | \(-0.320108\pi\) | ||||
0.535541 | + | 0.844509i | \(0.320108\pi\) | |||||||
\(564\) | −1.41421 | −0.0595491 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 24.2426 | 1.01899 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −2.34315 | −0.0983162 | ||||||||
\(569\) | −29.3137 | −1.22889 | −0.614447 | − | 0.788958i | \(-0.710621\pi\) | ||||
−0.614447 | + | 0.788958i | \(0.710621\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −16.2843 | −0.681476 | −0.340738 | − | 0.940158i | \(-0.610677\pi\) | ||||
−0.340738 | + | 0.940158i | \(0.610677\pi\) | |||||||
\(572\) | 1.41421 | 0.0591312 | ||||||||
\(573\) | 22.9706 | 0.959609 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 18.2843 | 0.762507 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | 36.2426 | 1.50880 | 0.754400 | − | 0.656414i | \(-0.227928\pi\) | ||||
0.754400 | + | 0.656414i | \(0.227928\pi\) | |||||||
\(578\) | 1.00000 | 0.0415945 | ||||||||
\(579\) | −3.65685 | −0.151974 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −12.7279 | −0.527589 | ||||||||
\(583\) | 7.65685 | 0.317115 | ||||||||
\(584\) | 4.00000 | 0.165521 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 11.0711 | 0.457342 | ||||||||
\(587\) | −20.4853 | −0.845518 | −0.422759 | − | 0.906242i | \(-0.638938\pi\) | ||||
−0.422759 | + | 0.906242i | \(0.638938\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 28.6274 | 1.17957 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −1.31371 | −0.0540387 | ||||||||
\(592\) | −7.65685 | −0.314695 | ||||||||
\(593\) | 0.686292 | 0.0281826 | 0.0140913 | − | 0.999901i | \(-0.495514\pi\) | ||||
0.0140913 | + | 0.999901i | \(0.495514\pi\) | |||||||
\(594\) | −1.00000 | −0.0410305 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −20.9706 | −0.858988 | ||||||||
\(597\) | −13.4142 | −0.549007 | ||||||||
\(598\) | 5.17157 | 0.211481 | ||||||||
\(599\) | 0.970563 | 0.0396561 | 0.0198281 | − | 0.999803i | \(-0.493688\pi\) | ||||
0.0198281 | + | 0.999803i | \(0.493688\pi\) | |||||||
\(600\) | 5.00000 | 0.204124 | ||||||||
\(601\) | 37.4558 | 1.52786 | 0.763928 | − | 0.645302i | \(-0.223268\pi\) | ||||
0.763928 | + | 0.645302i | \(0.223268\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 11.3137 | 0.460730 | ||||||||
\(604\) | 9.65685 | 0.392932 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 8.24264 | 0.334834 | ||||||||
\(607\) | 19.3137 | 0.783919 | 0.391960 | − | 0.919982i | \(-0.371797\pi\) | ||||
0.391960 | + | 0.919982i | \(0.371797\pi\) | |||||||
\(608\) | 2.58579 | 0.104867 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −2.00000 | −0.0809113 | ||||||||
\(612\) | −4.00000 | −0.161690 | ||||||||
\(613\) | 12.0000 | 0.484675 | 0.242338 | − | 0.970192i | \(-0.422086\pi\) | ||||
0.242338 | + | 0.970192i | \(0.422086\pi\) | |||||||
\(614\) | 24.7279 | 0.997938 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 25.6569 | 1.03291 | 0.516453 | − | 0.856316i | \(-0.327252\pi\) | ||||
0.516453 | + | 0.856316i | \(0.327252\pi\) | |||||||
\(618\) | −5.89949 | −0.237312 | ||||||||
\(619\) | −15.3137 | −0.615510 | −0.307755 | − | 0.951466i | \(-0.599578\pi\) | ||||
−0.307755 | + | 0.951466i | \(0.599578\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −3.65685 | −0.146745 | ||||||||
\(622\) | 11.7574 | 0.471427 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 1.41421 | 0.0566139 | ||||||||
\(625\) | 25.0000 | 1.00000 | ||||||||
\(626\) | −3.75736 | −0.150174 | ||||||||
\(627\) | −2.58579 | −0.103266 | ||||||||
\(628\) | −2.82843 | −0.112867 | ||||||||
\(629\) | 30.6274 | 1.22120 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −41.5980 | −1.65599 | −0.827995 | − | 0.560736i | \(-0.810518\pi\) | ||||
−0.827995 | + | 0.560736i | \(0.810518\pi\) | |||||||
\(632\) | 9.65685 | 0.384129 | ||||||||
\(633\) | −5.31371 | −0.211201 | ||||||||
\(634\) | −17.3137 | −0.687615 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 7.65685 | 0.303614 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −5.65685 | −0.223957 | ||||||||
\(639\) | 2.34315 | 0.0926934 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −48.2843 | −1.90711 | −0.953557 | − | 0.301213i | \(-0.902609\pi\) | ||||
−0.953557 | + | 0.301213i | \(0.902609\pi\) | |||||||
\(642\) | 5.31371 | 0.209715 | ||||||||
\(643\) | 41.1716 | 1.62365 | 0.811824 | − | 0.583902i | \(-0.198475\pi\) | ||||
0.811824 | + | 0.583902i | \(0.198475\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −10.3431 | −0.406946 | ||||||||
\(647\) | 1.89949 | 0.0746769 | 0.0373384 | − | 0.999303i | \(-0.488112\pi\) | ||||
0.0373384 | + | 0.999303i | \(0.488112\pi\) | |||||||
\(648\) | −1.00000 | −0.0392837 | ||||||||
\(649\) | −1.17157 | −0.0459883 | ||||||||
\(650\) | 7.07107 | 0.277350 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −5.65685 | −0.221540 | ||||||||
\(653\) | 12.6274 | 0.494149 | 0.247075 | − | 0.968996i | \(-0.420531\pi\) | ||||
0.247075 | + | 0.968996i | \(0.420531\pi\) | |||||||
\(654\) | 10.0000 | 0.391031 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 1.65685 | 0.0646893 | ||||||||
\(657\) | −4.00000 | −0.156055 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −2.68629 | −0.104643 | −0.0523215 | − | 0.998630i | \(-0.516662\pi\) | ||||
−0.0523215 | + | 0.998630i | \(0.516662\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −8.97056 | −0.348914 | −0.174457 | − | 0.984665i | \(-0.555817\pi\) | ||||
−0.174457 | + | 0.984665i | \(0.555817\pi\) | |||||||
\(662\) | 4.97056 | 0.193186 | ||||||||
\(663\) | −5.65685 | −0.219694 | ||||||||
\(664\) | −0.928932 | −0.0360496 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 7.65685 | 0.296697 | ||||||||
\(667\) | −20.6863 | −0.800976 | ||||||||
\(668\) | −5.17157 | −0.200094 | ||||||||
\(669\) | 11.5563 | 0.446794 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −1.41421 | −0.0545951 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 8.34315 | 0.321605 | 0.160802 | − | 0.986987i | \(-0.448592\pi\) | ||||
0.160802 | + | 0.986987i | \(0.448592\pi\) | |||||||
\(674\) | −5.31371 | −0.204676 | ||||||||
\(675\) | −5.00000 | −0.192450 | ||||||||
\(676\) | −11.0000 | −0.423077 | ||||||||
\(677\) | 21.4142 | 0.823015 | 0.411508 | − | 0.911406i | \(-0.365002\pi\) | ||||
0.411508 | + | 0.911406i | \(0.365002\pi\) | |||||||
\(678\) | −5.65685 | −0.217250 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 7.55635 | 0.289560 | ||||||||
\(682\) | 11.0711 | 0.423933 | ||||||||
\(683\) | 8.28427 | 0.316989 | 0.158494 | − | 0.987360i | \(-0.449336\pi\) | ||||
0.158494 | + | 0.987360i | \(0.449336\pi\) | |||||||
\(684\) | −2.58579 | −0.0988700 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 5.65685 | 0.215822 | ||||||||
\(688\) | −10.0000 | −0.381246 | ||||||||
\(689\) | 10.8284 | 0.412530 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 12.4853 | 0.474962 | 0.237481 | − | 0.971392i | \(-0.423678\pi\) | ||||
0.237481 | + | 0.971392i | \(0.423678\pi\) | |||||||
\(692\) | −19.0711 | −0.724973 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 2.00000 | 0.0759190 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −5.65685 | −0.214423 | ||||||||
\(697\) | −6.62742 | −0.251031 | ||||||||
\(698\) | 25.4142 | 0.961942 | ||||||||
\(699\) | 23.6569 | 0.894784 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −18.6863 | −0.705771 | −0.352886 | − | 0.935666i | \(-0.614800\pi\) | ||||
−0.352886 | + | 0.935666i | \(0.614800\pi\) | |||||||
\(702\) | −1.41421 | −0.0533761 | ||||||||
\(703\) | 19.7990 | 0.746733 | ||||||||
\(704\) | 1.00000 | 0.0376889 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 5.89949 | 0.222030 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −1.17157 | −0.0440304 | ||||||||
\(709\) | −44.6274 | −1.67602 | −0.838009 | − | 0.545657i | \(-0.816280\pi\) | ||||
−0.838009 | + | 0.545657i | \(0.816280\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −9.65685 | −0.362160 | ||||||||
\(712\) | 5.41421 | 0.202906 | ||||||||
\(713\) | 40.4853 | 1.51619 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 13.6569 | 0.510381 | ||||||||
\(717\) | 25.6569 | 0.958173 | ||||||||
\(718\) | 4.00000 | 0.149279 | ||||||||
\(719\) | −17.4142 | −0.649441 | −0.324720 | − | 0.945810i | \(-0.605270\pi\) | ||||
−0.324720 | + | 0.945810i | \(0.605270\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 12.3137 | 0.458269 | ||||||||
\(723\) | −15.3137 | −0.569523 | ||||||||
\(724\) | 10.3431 | 0.384400 | ||||||||
\(725\) | −28.2843 | −1.05045 | ||||||||
\(726\) | −1.00000 | −0.0371135 | ||||||||
\(727\) | −31.3553 | −1.16291 | −0.581453 | − | 0.813580i | \(-0.697515\pi\) | ||||
−0.581453 | + | 0.813580i | \(0.697515\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 40.0000 | 1.47945 | ||||||||
\(732\) | −1.41421 | −0.0522708 | ||||||||
\(733\) | 44.2426 | 1.63414 | 0.817070 | − | 0.576539i | \(-0.195597\pi\) | ||||
0.817070 | + | 0.576539i | \(0.195597\pi\) | |||||||
\(734\) | 22.8701 | 0.844149 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 3.65685 | 0.134793 | ||||||||
\(737\) | 11.3137 | 0.416746 | ||||||||
\(738\) | −1.65685 | −0.0609896 | ||||||||
\(739\) | 17.6569 | 0.649518 | 0.324759 | − | 0.945797i | \(-0.394717\pi\) | ||||
0.324759 | + | 0.945797i | \(0.394717\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −3.65685 | −0.134338 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 28.9706 | 1.06283 | 0.531413 | − | 0.847113i | \(-0.321661\pi\) | ||||
0.531413 | + | 0.847113i | \(0.321661\pi\) | |||||||
\(744\) | 11.0711 | 0.405885 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −8.62742 | −0.315872 | ||||||||
\(747\) | 0.928932 | 0.0339879 | ||||||||
\(748\) | −4.00000 | −0.146254 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −6.97056 | −0.254359 | −0.127180 | − | 0.991880i | \(-0.540592\pi\) | ||||
−0.127180 | + | 0.991880i | \(0.540592\pi\) | |||||||
\(752\) | −1.41421 | −0.0515711 | ||||||||
\(753\) | −9.17157 | −0.334231 | ||||||||
\(754\) | −8.00000 | −0.291343 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −29.3137 | −1.06542 | −0.532712 | − | 0.846296i | \(-0.678827\pi\) | ||||
−0.532712 | + | 0.846296i | \(0.678827\pi\) | |||||||
\(758\) | 6.34315 | 0.230393 | ||||||||
\(759\) | −3.65685 | −0.132735 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 42.1421 | 1.52765 | 0.763826 | − | 0.645423i | \(-0.223319\pi\) | ||||
0.763826 | + | 0.645423i | \(0.223319\pi\) | |||||||
\(762\) | −7.31371 | −0.264948 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 22.9706 | 0.831046 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 23.5563 | 0.851125 | ||||||||
\(767\) | −1.65685 | −0.0598255 | ||||||||
\(768\) | 1.00000 | 0.0360844 | ||||||||
\(769\) | −0.201010 | −0.00724861 | −0.00362431 | − | 0.999993i | \(-0.501154\pi\) | ||||
−0.00362431 | + | 0.999993i | \(0.501154\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −8.72792 | −0.314328 | ||||||||
\(772\) | −3.65685 | −0.131613 | ||||||||
\(773\) | −14.1421 | −0.508657 | −0.254329 | − | 0.967118i | \(-0.581854\pi\) | ||||
−0.254329 | + | 0.967118i | \(0.581854\pi\) | |||||||
\(774\) | 10.0000 | 0.359443 | ||||||||
\(775\) | 55.3553 | 1.98842 | ||||||||
\(776\) | −12.7279 | −0.456906 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 32.6274 | 1.16975 | ||||||||
\(779\) | −4.28427 | −0.153500 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 2.34315 | 0.0838443 | ||||||||
\(782\) | −14.6274 | −0.523075 | ||||||||
\(783\) | 5.65685 | 0.202159 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 12.2426 | 0.436681 | ||||||||
\(787\) | 1.61522 | 0.0575765 | 0.0287883 | − | 0.999586i | \(-0.490835\pi\) | ||||
0.0287883 | + | 0.999586i | \(0.490835\pi\) | |||||||
\(788\) | −1.31371 | −0.0467989 | ||||||||
\(789\) | 2.34315 | 0.0834182 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −1.00000 | −0.0355335 | ||||||||
\(793\) | −2.00000 | −0.0710221 | ||||||||
\(794\) | −27.7990 | −0.986549 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −13.4142 | −0.475454 | ||||||||
\(797\) | 45.1716 | 1.60006 | 0.800030 | − | 0.599961i | \(-0.204817\pi\) | ||||
0.800030 | + | 0.599961i | \(0.204817\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 5.65685 | 0.200125 | ||||||||
\(800\) | 5.00000 | 0.176777 | ||||||||
\(801\) | −5.41421 | −0.191302 | ||||||||
\(802\) | 6.00000 | 0.211867 | ||||||||
\(803\) | −4.00000 | −0.141157 | ||||||||
\(804\) | 11.3137 | 0.399004 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 15.6569 | 0.551489 | ||||||||
\(807\) | 22.6274 | 0.796523 | ||||||||
\(808\) | 8.24264 | 0.289975 | ||||||||
\(809\) | −14.9706 | −0.526337 | −0.263168 | − | 0.964750i | \(-0.584768\pi\) | ||||
−0.263168 | + | 0.964750i | \(0.584768\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −54.8701 | −1.92675 | −0.963374 | − | 0.268161i | \(-0.913584\pi\) | ||||
−0.963374 | + | 0.268161i | \(0.913584\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −26.8284 | −0.940914 | ||||||||
\(814\) | 7.65685 | 0.268373 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −4.00000 | −0.140028 | ||||||||
\(817\) | 25.8579 | 0.904652 | ||||||||
\(818\) | 4.48528 | 0.156824 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 36.9706 | 1.29028 | 0.645141 | − | 0.764064i | \(-0.276799\pi\) | ||||
0.645141 | + | 0.764064i | \(0.276799\pi\) | |||||||
\(822\) | −13.3137 | −0.464369 | ||||||||
\(823\) | 25.5980 | 0.892289 | 0.446145 | − | 0.894961i | \(-0.352797\pi\) | ||||
0.446145 | + | 0.894961i | \(0.352797\pi\) | |||||||
\(824\) | −5.89949 | −0.205519 | ||||||||
\(825\) | −5.00000 | −0.174078 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 28.0000 | 0.973655 | 0.486828 | − | 0.873498i | \(-0.338154\pi\) | ||||
0.486828 | + | 0.873498i | \(0.338154\pi\) | |||||||
\(828\) | −3.65685 | −0.127084 | ||||||||
\(829\) | 3.31371 | 0.115090 | 0.0575449 | − | 0.998343i | \(-0.481673\pi\) | ||||
0.0575449 | + | 0.998343i | \(0.481673\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 4.00000 | 0.138758 | ||||||||
\(832\) | 1.41421 | 0.0490290 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 21.8995 | 0.758317 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −2.58579 | −0.0894313 | ||||||||
\(837\) | −11.0711 | −0.382672 | ||||||||
\(838\) | −40.2843 | −1.39160 | ||||||||
\(839\) | 12.7279 | 0.439417 | 0.219708 | − | 0.975566i | \(-0.429489\pi\) | ||||
0.219708 | + | 0.975566i | \(0.429489\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 3.00000 | 0.103448 | ||||||||
\(842\) | −18.9706 | −0.653769 | ||||||||
\(843\) | 14.9706 | 0.515614 | ||||||||
\(844\) | −5.31371 | −0.182905 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 1.41421 | 0.0486217 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 7.65685 | 0.262937 | ||||||||
\(849\) | −24.2426 | −0.832005 | ||||||||
\(850\) | −20.0000 | −0.685994 | ||||||||
\(851\) | 28.0000 | 0.959828 | ||||||||
\(852\) | 2.34315 | 0.0802749 | ||||||||
\(853\) | 27.2721 | 0.933778 | 0.466889 | − | 0.884316i | \(-0.345375\pi\) | ||||
0.466889 | + | 0.884316i | \(0.345375\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 5.31371 | 0.181619 | ||||||||
\(857\) | 9.17157 | 0.313295 | 0.156647 | − | 0.987655i | \(-0.449931\pi\) | ||||
0.156647 | + | 0.987655i | \(0.449931\pi\) | |||||||
\(858\) | −1.41421 | −0.0482805 | ||||||||
\(859\) | 38.4264 | 1.31109 | 0.655546 | − | 0.755155i | \(-0.272439\pi\) | ||||
0.655546 | + | 0.755155i | \(0.272439\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −16.0000 | −0.544962 | ||||||||
\(863\) | −29.5980 | −1.00753 | −0.503763 | − | 0.863842i | \(-0.668052\pi\) | ||||
−0.503763 | + | 0.863842i | \(0.668052\pi\) | |||||||
\(864\) | −1.00000 | −0.0340207 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −5.21320 | −0.177152 | ||||||||
\(867\) | −1.00000 | −0.0339618 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −9.65685 | −0.327586 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 16.0000 | 0.542139 | ||||||||
\(872\) | 10.0000 | 0.338643 | ||||||||
\(873\) | 12.7279 | 0.430775 | ||||||||
\(874\) | −9.45584 | −0.319849 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −4.00000 | −0.135147 | ||||||||
\(877\) | 30.6863 | 1.03620 | 0.518101 | − | 0.855319i | \(-0.326639\pi\) | ||||
0.518101 | + | 0.855319i | \(0.326639\pi\) | |||||||
\(878\) | −3.79899 | −0.128210 | ||||||||
\(879\) | −11.0711 | −0.373418 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 2.10051 | 0.0707678 | 0.0353839 | − | 0.999374i | \(-0.488735\pi\) | ||||
0.0353839 | + | 0.999374i | \(0.488735\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 18.6274 | 0.626862 | 0.313431 | − | 0.949611i | \(-0.398521\pi\) | ||||
0.313431 | + | 0.949611i | \(0.398521\pi\) | |||||||
\(884\) | −5.65685 | −0.190261 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 28.2843 | 0.950229 | ||||||||
\(887\) | −52.2843 | −1.75553 | −0.877767 | − | 0.479088i | \(-0.840968\pi\) | ||||
−0.877767 | + | 0.479088i | \(0.840968\pi\) | |||||||
\(888\) | 7.65685 | 0.256947 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1.00000 | 0.0335013 | ||||||||
\(892\) | 11.5563 | 0.386935 | ||||||||
\(893\) | 3.65685 | 0.122372 | ||||||||
\(894\) | 20.9706 | 0.701361 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −5.17157 | −0.172674 | ||||||||
\(898\) | −21.6569 | −0.722699 | ||||||||
\(899\) | −62.6274 | −2.08874 | ||||||||
\(900\) | −5.00000 | −0.166667 | ||||||||
\(901\) | −30.6274 | −1.02035 | ||||||||
\(902\) | −1.65685 | −0.0551672 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −5.65685 | −0.188144 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −9.65685 | −0.320827 | ||||||||
\(907\) | 33.9411 | 1.12700 | 0.563498 | − | 0.826117i | \(-0.309455\pi\) | ||||
0.563498 | + | 0.826117i | \(0.309455\pi\) | |||||||
\(908\) | 7.55635 | 0.250766 | ||||||||
\(909\) | −8.24264 | −0.273391 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −37.5980 | −1.24568 | −0.622838 | − | 0.782351i | \(-0.714021\pi\) | ||||
−0.622838 | + | 0.782351i | \(0.714021\pi\) | |||||||
\(912\) | −2.58579 | −0.0856239 | ||||||||
\(913\) | 0.928932 | 0.0307432 | ||||||||
\(914\) | −8.34315 | −0.275967 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 5.65685 | 0.186908 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 4.00000 | 0.132020 | ||||||||
\(919\) | −30.6274 | −1.01031 | −0.505153 | − | 0.863030i | \(-0.668564\pi\) | ||||
−0.505153 | + | 0.863030i | \(0.668564\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −24.7279 | −0.814813 | ||||||||
\(922\) | 18.1005 | 0.596108 | ||||||||
\(923\) | 3.31371 | 0.109072 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 38.2843 | 1.25878 | ||||||||
\(926\) | 4.68629 | 0.154001 | ||||||||
\(927\) | 5.89949 | 0.193765 | ||||||||
\(928\) | −5.65685 | −0.185695 | ||||||||
\(929\) | 20.9289 | 0.686656 | 0.343328 | − | 0.939216i | \(-0.388446\pi\) | ||||
0.343328 | + | 0.939216i | \(0.388446\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 23.6569 | 0.774906 | ||||||||
\(933\) | −11.7574 | −0.384919 | ||||||||
\(934\) | 29.9411 | 0.979704 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −1.41421 | −0.0462250 | ||||||||
\(937\) | 5.37258 | 0.175515 | 0.0877573 | − | 0.996142i | \(-0.472030\pi\) | ||||
0.0877573 | + | 0.996142i | \(0.472030\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 3.75736 | 0.122617 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 57.6985 | 1.88092 | 0.940458 | − | 0.339909i | \(-0.110396\pi\) | ||||
0.940458 | + | 0.339909i | \(0.110396\pi\) | |||||||
\(942\) | 2.82843 | 0.0921551 | ||||||||
\(943\) | −6.05887 | −0.197304 | ||||||||
\(944\) | −1.17157 | −0.0381314 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 10.0000 | 0.325128 | ||||||||
\(947\) | −47.3137 | −1.53749 | −0.768744 | − | 0.639556i | \(-0.779118\pi\) | ||||
−0.768744 | + | 0.639556i | \(0.779118\pi\) | |||||||
\(948\) | −9.65685 | −0.313640 | ||||||||
\(949\) | −5.65685 | −0.183629 | ||||||||
\(950\) | −12.9289 | −0.419470 | ||||||||
\(951\) | 17.3137 | 0.561435 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −26.0000 | −0.842223 | −0.421111 | − | 0.907009i | \(-0.638360\pi\) | ||||
−0.421111 | + | 0.907009i | \(0.638360\pi\) | |||||||
\(954\) | −7.65685 | −0.247900 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 25.6569 | 0.829802 | ||||||||
\(957\) | 5.65685 | 0.182860 | ||||||||
\(958\) | −0.970563 | −0.0313575 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 91.5685 | 2.95382 | ||||||||
\(962\) | 10.8284 | 0.349123 | ||||||||
\(963\) | −5.31371 | −0.171232 | ||||||||
\(964\) | −15.3137 | −0.493221 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −12.2843 | −0.395036 | −0.197518 | − | 0.980299i | \(-0.563288\pi\) | ||||
−0.197518 | + | 0.980299i | \(0.563288\pi\) | |||||||
\(968\) | −1.00000 | −0.0321412 | ||||||||
\(969\) | 10.3431 | 0.332270 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 54.9117 | 1.76220 | 0.881100 | − | 0.472930i | \(-0.156804\pi\) | ||||
0.881100 | + | 0.472930i | \(0.156804\pi\) | |||||||
\(972\) | 1.00000 | 0.0320750 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 11.6569 | 0.373510 | ||||||||
\(975\) | −7.07107 | −0.226455 | ||||||||
\(976\) | −1.41421 | −0.0452679 | ||||||||
\(977\) | 37.6569 | 1.20475 | 0.602375 | − | 0.798213i | \(-0.294221\pi\) | ||||
0.602375 | + | 0.798213i | \(0.294221\pi\) | |||||||
\(978\) | 5.65685 | 0.180886 | ||||||||
\(979\) | −5.41421 | −0.173039 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −10.0000 | −0.319275 | ||||||||
\(982\) | −20.0000 | −0.638226 | ||||||||
\(983\) | 41.0122 | 1.30809 | 0.654043 | − | 0.756457i | \(-0.273072\pi\) | ||||
0.654043 | + | 0.756457i | \(0.273072\pi\) | |||||||
\(984\) | −1.65685 | −0.0528186 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 22.6274 | 0.720604 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −3.65685 | −0.116340 | ||||||||
\(989\) | 36.5685 | 1.16281 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 20.6863 | 0.657122 | 0.328561 | − | 0.944483i | \(-0.393436\pi\) | ||||
0.328561 | + | 0.944483i | \(0.393436\pi\) | |||||||
\(992\) | 11.0711 | 0.351507 | ||||||||
\(993\) | −4.97056 | −0.157736 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0.928932 | 0.0294343 | ||||||||
\(997\) | 9.89949 | 0.313520 | 0.156760 | − | 0.987637i | \(-0.449895\pi\) | ||||
0.156760 | + | 0.987637i | \(0.449895\pi\) | |||||||
\(998\) | −34.6274 | −1.09611 | ||||||||
\(999\) | −7.65685 | −0.242252 |
(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 | 3234.2.a.z.1.2 | yes | 2 | |
3.2 | odd | 2 | 9702.2.a.dl.1.2 | 2 | |||
7.6 | odd | 2 | 3234.2.a.y.1.1 | ✓ | 2 | ||
21.20 | even | 2 | 9702.2.a.de.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3234.2.a.y.1.1 | ✓ | 2 | 7.6 | odd | 2 | ||
3234.2.a.z.1.2 | yes | 2 | 1.1 | even | 1 | trivial | |
9702.2.a.de.1.1 | 2 | 21.20 | even | 2 | |||
9702.2.a.dl.1.2 | 2 | 3.2 | odd | 2 |