Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4600,2,Mod(1,4600)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4600, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("4600.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4600 = 2^{3} \cdot 5^{2} \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4600.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: | \(36.7311849298\) |
Analytic rank: | \(1\) |
Dimension: | \(5\) |
Coefficient field: | 5.5.791953.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{5} - 2x^{4} - 7x^{3} + 7x^{2} + 9x + 2 \)
|
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(+1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(-0.336890\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4600.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −1.33689 | −0.771854 | −0.385927 | − | 0.922529i | \(-0.626118\pi\) | ||||
−0.385927 | + | 0.922529i | \(0.626118\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −3.16736 | −1.19715 | −0.598575 | − | 0.801067i | \(-0.704266\pi\) | ||||
−0.598575 | + | 0.801067i | \(0.704266\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.21273 | −0.404242 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.0955192 | −0.0288001 | −0.0144001 | − | 0.999896i | \(-0.504584\pi\) | ||||
−0.0144001 | + | 0.999896i | \(0.504584\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.44343 | 0.400335 | 0.200167 | − | 0.979762i | \(-0.435851\pi\) | ||||
0.200167 | + | 0.979762i | \(0.435851\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −2.29775 | −0.557287 | −0.278643 | − | 0.960395i | \(-0.589885\pi\) | ||||
−0.278643 | + | 0.960395i | \(0.589885\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 7.00371 | 1.60676 | 0.803381 | − | 0.595466i | \(-0.203032\pi\) | ||||
0.803381 | + | 0.595466i | \(0.203032\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 4.23441 | 0.924025 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.00000 | −0.208514 | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 5.63195 | 1.08387 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 5.39076 | 1.00104 | 0.500519 | − | 0.865725i | \(-0.333142\pi\) | ||||
0.500519 | + | 0.865725i | \(0.333142\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −0.584488 | −0.104977 | −0.0524886 | − | 0.998622i | \(-0.516715\pi\) | ||||
−0.0524886 | + | 0.998622i | \(0.516715\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0.127699 | 0.0222295 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −9.29985 | −1.52889 | −0.764443 | − | 0.644691i | \(-0.776986\pi\) | ||||
−0.764443 | + | 0.644691i | \(0.776986\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −1.92970 | −0.309000 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −2.86534 | −0.447492 | −0.223746 | − | 0.974648i | \(-0.571829\pi\) | ||||
−0.223746 | + | 0.974648i | \(0.571829\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 9.50208 | 1.44905 | 0.724527 | − | 0.689246i | \(-0.242058\pi\) | ||||
0.724527 | + | 0.689246i | \(0.242058\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 7.09353 | 1.03470 | 0.517349 | − | 0.855775i | \(-0.326919\pi\) | ||||
0.517349 | + | 0.855775i | \(0.326919\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 3.03218 | 0.433168 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 3.07184 | 0.430144 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −7.73922 | −1.06306 | −0.531532 | − | 0.847038i | \(-0.678383\pi\) | ||||
−0.531532 | + | 0.847038i | \(0.678383\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −9.36319 | −1.24018 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 13.6426 | 1.77612 | 0.888059 | − | 0.459730i | \(-0.152054\pi\) | ||||
0.888059 | + | 0.459730i | \(0.152054\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0.234413 | 0.0300135 | 0.0150068 | − | 0.999887i | \(-0.495223\pi\) | ||||
0.0150068 | + | 0.999887i | \(0.495223\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 3.84114 | 0.483938 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 7.49729 | 0.915940 | 0.457970 | − | 0.888968i | \(-0.348577\pi\) | ||||
0.457970 | + | 0.888968i | \(0.348577\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 1.33689 | 0.160943 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −5.18426 | −0.615258 | −0.307629 | − | 0.951506i | \(-0.599536\pi\) | ||||
−0.307629 | + | 0.951506i | \(0.599536\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −1.52384 | −0.178352 | −0.0891760 | − | 0.996016i | \(-0.528423\pi\) | ||||
−0.0891760 | + | 0.996016i | \(0.528423\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0.302544 | 0.0344781 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −3.04068 | −0.342103 | −0.171052 | − | 0.985262i | \(-0.554717\pi\) | ||||
−0.171052 | + | 0.985262i | \(0.554717\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −3.89112 | −0.432347 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −15.9909 | −1.75523 | −0.877613 | − | 0.479369i | \(-0.840865\pi\) | ||||
−0.877613 | + | 0.479369i | \(0.840865\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −7.20685 | −0.772655 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 5.53325 | 0.586523 | 0.293261 | − | 0.956032i | \(-0.405259\pi\) | ||||
0.293261 | + | 0.956032i | \(0.405259\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −4.57186 | −0.479261 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0.781396 | 0.0810270 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 2.58305 | 0.262269 | 0.131135 | − | 0.991365i | \(-0.458138\pi\) | ||||
0.131135 | + | 0.991365i | \(0.458138\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0.115839 | 0.0116422 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −6.65615 | −0.662312 | −0.331156 | − | 0.943576i | \(-0.607439\pi\) | ||||
−0.331156 | + | 0.943576i | \(0.607439\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −17.6668 | −1.74076 | −0.870378 | − | 0.492383i | \(-0.836126\pi\) | ||||
−0.870378 | + | 0.492383i | \(0.836126\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −5.83635 | −0.564221 | −0.282111 | − | 0.959382i | \(-0.591035\pi\) | ||||
−0.282111 | + | 0.959382i | \(0.591035\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 7.02096 | 0.672486 | 0.336243 | − | 0.941775i | \(-0.390844\pi\) | ||||
0.336243 | + | 0.941775i | \(0.390844\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 12.4329 | 1.18008 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −17.1003 | −1.60866 | −0.804328 | − | 0.594185i | \(-0.797475\pi\) | ||||
−0.804328 | + | 0.594185i | \(0.797475\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −1.75048 | −0.161832 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 7.27781 | 0.667156 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.9909 | −0.999171 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 3.83065 | 0.345398 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −10.8050 | −0.958787 | −0.479394 | − | 0.877600i | \(-0.659143\pi\) | ||||
−0.479394 | + | 0.877600i | \(0.659143\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −12.7032 | −1.11846 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −8.45211 | −0.738464 | −0.369232 | − | 0.929337i | \(-0.620379\pi\) | ||||
−0.369232 | + | 0.929337i | \(0.620379\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −22.1833 | −1.92354 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −18.5322 | −1.58331 | −0.791655 | − | 0.610969i | \(-0.790780\pi\) | ||||
−0.791655 | + | 0.610969i | \(0.790780\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 7.42618 | 0.629880 | 0.314940 | − | 0.949112i | \(-0.398016\pi\) | ||||
0.314940 | + | 0.949112i | \(0.398016\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −9.48327 | −0.798635 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −0.137875 | −0.0115297 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −4.05369 | −0.334343 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −4.53968 | −0.371905 | −0.185952 | − | 0.982559i | \(-0.559537\pi\) | ||||
−0.185952 | + | 0.982559i | \(0.559537\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 0.00675366 | 0.000549605 0 | 0.000274803 | − | 1.00000i | \(-0.499913\pi\) | ||||
0.000274803 | 1.00000i | \(0.499913\pi\) | ||||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 2.78654 | 0.225279 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 12.1721 | 0.971439 | 0.485719 | − | 0.874115i | \(-0.338558\pi\) | ||||
0.485719 | + | 0.874115i | \(0.338558\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 10.3465 | 0.820529 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 3.16736 | 0.249623 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 20.2201 | 1.58376 | 0.791879 | − | 0.610677i | \(-0.209103\pi\) | ||||
0.791879 | + | 0.610677i | \(0.209103\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 8.04709 | 0.622702 | 0.311351 | − | 0.950295i | \(-0.399218\pi\) | ||||
0.311351 | + | 0.950295i | \(0.399218\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −10.9165 | −0.839732 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −8.49358 | −0.649520 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 16.8394 | 1.28028 | 0.640139 | − | 0.768259i | \(-0.278877\pi\) | ||||
0.640139 | + | 0.768259i | \(0.278877\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −18.2387 | −1.37090 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 23.7641 | 1.77621 | 0.888105 | − | 0.459641i | \(-0.152022\pi\) | ||||
0.888105 | + | 0.459641i | \(0.152022\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −3.13518 | −0.233036 | −0.116518 | − | 0.993189i | \(-0.537173\pi\) | ||||
−0.116518 | + | 0.993189i | \(0.537173\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −0.313385 | −0.0231661 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0.219479 | 0.0160499 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −17.8384 | −1.29755 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 6.17586 | 0.446870 | 0.223435 | − | 0.974719i | \(-0.428273\pi\) | ||||
0.223435 | + | 0.974719i | \(0.428273\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 7.22267 | 0.519899 | 0.259949 | − | 0.965622i | \(-0.416294\pi\) | ||||
0.259949 | + | 0.965622i | \(0.416294\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −13.0019 | −0.926349 | −0.463174 | − | 0.886267i | \(-0.653290\pi\) | ||||
−0.463174 | + | 0.886267i | \(0.653290\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1.84114 | −0.130515 | −0.0652575 | − | 0.997868i | \(-0.520787\pi\) | ||||
−0.0652575 | + | 0.997868i | \(0.520787\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −10.0231 | −0.706972 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −17.0745 | −1.19839 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 1.21273 | 0.0842903 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −0.668989 | −0.0462749 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −24.8791 | −1.71275 | −0.856375 | − | 0.516354i | \(-0.827289\pi\) | ||||
−0.856375 | + | 0.516354i | \(0.827289\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 6.93078 | 0.474889 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1.85128 | 0.125673 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 2.03721 | 0.137662 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −3.31664 | −0.223101 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −4.04924 | −0.271157 | −0.135579 | − | 0.990767i | \(-0.543289\pi\) | ||||
−0.135579 | + | 0.990767i | \(0.543289\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −17.3916 | −1.15432 | −0.577162 | − | 0.816630i | \(-0.695840\pi\) | ||||
−0.577162 | + | 0.816630i | \(0.695840\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −3.51761 | −0.232450 | −0.116225 | − | 0.993223i | \(-0.537079\pi\) | ||||
−0.116225 | + | 0.993223i | \(0.537079\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −0.404468 | −0.0266120 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 10.7910 | 0.706941 | 0.353471 | − | 0.935446i | \(-0.385001\pi\) | ||||
0.353471 | + | 0.935446i | \(0.385001\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 4.06506 | 0.264054 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −2.86944 | −0.185608 | −0.0928042 | − | 0.995684i | \(-0.529583\pi\) | ||||
−0.0928042 | + | 0.995684i | \(0.529583\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 27.0486 | 1.74235 | 0.871176 | − | 0.490972i | \(-0.163358\pi\) | ||||
0.871176 | + | 0.490972i | \(0.163358\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −11.6939 | −0.750161 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 10.1093 | 0.643242 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 21.3780 | 1.35478 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −11.7794 | −0.743510 | −0.371755 | − | 0.928331i | \(-0.621244\pi\) | ||||
−0.371755 | + | 0.928331i | \(0.621244\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0.0955192 | 0.00600524 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −8.47742 | −0.528807 | −0.264404 | − | 0.964412i | \(-0.585175\pi\) | ||||
−0.264404 | + | 0.964412i | \(0.585175\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 29.4560 | 1.83031 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −6.53751 | −0.404662 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −18.5118 | −1.14149 | −0.570745 | − | 0.821128i | \(-0.693345\pi\) | ||||
−0.570745 | + | 0.821128i | \(0.693345\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −7.39734 | −0.452710 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −25.4583 | −1.55222 | −0.776109 | − | 0.630599i | \(-0.782809\pi\) | ||||
−0.776109 | + | 0.630599i | \(0.782809\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −14.1812 | −0.861446 | −0.430723 | − | 0.902484i | \(-0.641741\pi\) | ||||
−0.430723 | + | 0.902484i | \(0.641741\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 6.11207 | 0.369919 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −21.4281 | −1.28749 | −0.643744 | − | 0.765241i | \(-0.722620\pi\) | ||||
−0.643744 | + | 0.765241i | \(0.722620\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0.708823 | 0.0424361 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −8.90281 | −0.531097 | −0.265548 | − | 0.964098i | \(-0.585553\pi\) | ||||
−0.265548 | + | 0.964098i | \(0.585553\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 13.0369 | 0.774966 | 0.387483 | − | 0.921877i | \(-0.373345\pi\) | ||||
0.387483 | + | 0.921877i | \(0.373345\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 9.07558 | 0.535715 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −11.7203 | −0.689431 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −3.45325 | −0.202433 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 6.74772 | 0.394206 | 0.197103 | − | 0.980383i | \(-0.436847\pi\) | ||||
0.197103 | + | 0.980383i | \(0.436847\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −0.537959 | −0.0312156 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −1.44343 | −0.0834755 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −30.0965 | −1.73474 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 8.89854 | 0.511208 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −15.6667 | −0.894143 | −0.447071 | − | 0.894498i | \(-0.647533\pi\) | ||||
−0.447071 | + | 0.894498i | \(0.647533\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 23.6185 | 1.34361 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 8.27922 | 0.469472 | 0.234736 | − | 0.972059i | \(-0.424577\pi\) | ||||
0.234736 | + | 0.972059i | \(0.424577\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −15.4898 | −0.875534 | −0.437767 | − | 0.899088i | \(-0.644231\pi\) | ||||
−0.437767 | + | 0.899088i | \(0.644231\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 10.5803 | 0.594251 | 0.297125 | − | 0.954838i | \(-0.403972\pi\) | ||||
0.297125 | + | 0.954838i | \(0.403972\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −0.514921 | −0.0288300 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 7.80256 | 0.435496 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −16.0928 | −0.895427 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −9.38625 | −0.519061 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −22.4678 | −1.23869 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1.32836 | −0.0730133 | −0.0365067 | − | 0.999333i | \(-0.511623\pi\) | ||||
−0.0365067 | + | 0.999333i | \(0.511623\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 11.2782 | 0.618040 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −33.1297 | −1.80469 | −0.902345 | − | 0.431014i | \(-0.858156\pi\) | ||||
−0.902345 | + | 0.431014i | \(0.858156\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 22.8611 | 1.24165 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0.0558298 | 0.00302335 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 12.5675 | 0.678582 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −15.7579 | −0.845926 | −0.422963 | − | 0.906147i | \(-0.639010\pi\) | ||||
−0.422963 | + | 0.906147i | \(0.639010\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −14.5904 | −0.781004 | −0.390502 | − | 0.920602i | \(-0.627699\pi\) | ||||
−0.390502 | + | 0.920602i | \(0.627699\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 8.12931 | 0.433910 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 28.0097 | 1.49080 | 0.745402 | − | 0.666615i | \(-0.232258\pi\) | ||||
0.745402 | + | 0.666615i | \(0.232258\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −9.72964 | −0.514947 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 0.214689 | 0.0113308 | 0.00566542 | − | 0.999984i | \(-0.498197\pi\) | ||||
0.00566542 | + | 0.999984i | \(0.498197\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 30.0520 | 1.58168 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 14.6936 | 0.771213 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −21.0197 | −1.09722 | −0.548610 | − | 0.836079i | \(-0.684843\pi\) | ||||
−0.548610 | + | 0.836079i | \(0.684843\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 3.47488 | 0.180895 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 24.5129 | 1.27265 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 10.2558 | 0.531023 | 0.265511 | − | 0.964108i | \(-0.414459\pi\) | ||||
0.265511 | + | 0.964108i | \(0.414459\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 7.78116 | 0.400750 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −20.6274 | −1.05956 | −0.529780 | − | 0.848135i | \(-0.677726\pi\) | ||||
−0.529780 | + | 0.848135i | \(0.677726\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 14.4451 | 0.740044 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −18.7419 | −0.957667 | −0.478833 | − | 0.877906i | \(-0.658940\pi\) | ||||
−0.478833 | + | 0.877906i | \(0.658940\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −11.5234 | −0.585769 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −3.07719 | −0.156020 | −0.0780100 | − | 0.996953i | \(-0.524857\pi\) | ||||
−0.0780100 | + | 0.996953i | \(0.524857\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2.29775 | 0.116202 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 11.2995 | 0.569986 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −11.4670 | −0.575513 | −0.287756 | − | 0.957704i | \(-0.592909\pi\) | ||||
−0.287756 | + | 0.957704i | \(0.592909\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 29.6566 | 1.48469 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 14.1227 | 0.705252 | 0.352626 | − | 0.935764i | \(-0.385289\pi\) | ||||
0.352626 | + | 0.935764i | \(0.385289\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −0.843666 | −0.0420260 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0.888314 | 0.0440321 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −0.851429 | −0.0421005 | −0.0210502 | − | 0.999778i | \(-0.506701\pi\) | ||||
−0.0210502 | + | 0.999778i | \(0.506701\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 24.7755 | 1.22208 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −43.2111 | −2.12628 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −9.92799 | −0.486176 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 0.680728 | 0.0332557 | 0.0166279 | − | 0.999862i | \(-0.494707\pi\) | ||||
0.0166279 | + | 0.999862i | \(0.494707\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −35.9671 | −1.75293 | −0.876466 | − | 0.481465i | \(-0.840105\pi\) | ||||
−0.876466 | + | 0.481465i | \(0.840105\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −8.60251 | −0.418268 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −0.742472 | −0.0359307 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0.184324 | 0.00889923 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 15.2881 | 0.736402 | 0.368201 | − | 0.929746i | \(-0.379974\pi\) | ||||
0.368201 | + | 0.929746i | \(0.379974\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 13.2632 | 0.637390 | 0.318695 | − | 0.947857i | \(-0.396755\pi\) | ||||
0.318695 | + | 0.947857i | \(0.396755\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −7.00371 | −0.335033 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 18.7740 | 0.896035 | 0.448018 | − | 0.894025i | \(-0.352130\pi\) | ||||
0.448018 | + | 0.894025i | \(0.352130\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −3.67720 | −0.175105 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −5.49270 | −0.260966 | −0.130483 | − | 0.991451i | \(-0.541653\pi\) | ||||
−0.130483 | + | 0.991451i | \(0.541653\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 6.06905 | 0.287056 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 13.1705 | 0.621553 | 0.310777 | − | 0.950483i | \(-0.399411\pi\) | ||||
0.310777 | + | 0.950483i | \(0.399411\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0.273695 | 0.0128878 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −0.00902890 | −0.000424215 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 20.9676 | 0.980821 | 0.490410 | − | 0.871492i | \(-0.336847\pi\) | ||||
0.490410 | + | 0.871492i | \(0.336847\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −12.9408 | −0.604026 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 6.27335 | 0.292179 | 0.146089 | − | 0.989271i | \(-0.453331\pi\) | ||||
0.146089 | + | 0.989271i | \(0.453331\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 9.49565 | 0.441300 | 0.220650 | − | 0.975353i | \(-0.429182\pi\) | ||||
0.220650 | + | 0.975353i | \(0.429182\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 13.9066 | 0.643518 | 0.321759 | − | 0.946822i | \(-0.395726\pi\) | ||||
0.321759 | + | 0.946822i | \(0.395726\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −23.7466 | −1.09652 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −16.2727 | −0.749809 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −0.907631 | −0.0417329 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 9.38555 | 0.429735 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 3.66220 | 0.167330 | 0.0836652 | − | 0.996494i | \(-0.473337\pi\) | ||||
0.0836652 | + | 0.996494i | \(0.473337\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −13.4237 | −0.612066 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −4.23441 | −0.192672 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 28.9654 | 1.31255 | 0.656274 | − | 0.754523i | \(-0.272132\pi\) | ||||
0.656274 | + | 0.754523i | \(0.272132\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −27.0320 | −1.22243 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −37.8991 | −1.71036 | −0.855182 | − | 0.518328i | \(-0.826554\pi\) | ||||
−0.855182 | + | 0.518328i | \(0.826554\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −12.3866 | −0.557866 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 16.4204 | 0.736557 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −26.6914 | −1.19487 | −0.597436 | − | 0.801917i | \(-0.703814\pi\) | ||||
−0.597436 | + | 0.801917i | \(0.703814\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −10.7581 | −0.480635 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −18.2182 | −0.812309 | −0.406154 | − | 0.913804i | \(-0.633130\pi\) | ||||
−0.406154 | + | 0.913804i | \(0.633130\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 14.5942 | 0.648150 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −31.0138 | −1.37466 | −0.687332 | − | 0.726344i | \(-0.741218\pi\) | ||||
−0.687332 | + | 0.726344i | \(0.741218\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 4.82655 | 0.213514 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 39.4446 | 1.74152 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −0.677568 | −0.0297994 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −22.5125 | −0.988188 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −39.9824 | −1.75166 | −0.875831 | − | 0.482618i | \(-0.839686\pi\) | ||||
−0.875831 | + | 0.482618i | \(0.839686\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 10.3111 | 0.450873 | 0.225437 | − | 0.974258i | \(-0.427619\pi\) | ||||
0.225437 | + | 0.974258i | \(0.427619\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 1.34301 | 0.0585024 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −16.5448 | −0.717981 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −4.13592 | −0.179146 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −31.7699 | −1.37097 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −0.289631 | −0.0124753 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −42.5472 | −1.82925 | −0.914623 | − | 0.404307i | \(-0.867513\pi\) | ||||
−0.914623 | + | 0.404307i | \(0.867513\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 4.19139 | 0.179870 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 2.47986 | 0.106031 | 0.0530156 | − | 0.998594i | \(-0.483117\pi\) | ||||
0.0530156 | + | 0.998594i | \(0.483117\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −0.284279 | −0.0121327 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 37.7553 | 1.60843 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 9.63094 | 0.409549 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 22.9814 | 0.973755 | 0.486877 | − | 0.873470i | \(-0.338136\pi\) | ||||
0.486877 | + | 0.873470i | \(0.338136\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 13.7156 | 0.580107 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −0.293420 | −0.0123882 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −18.4939 | −0.779427 | −0.389713 | − | 0.920936i | \(-0.627426\pi\) | ||||
−0.389713 | + | 0.920936i | \(0.627426\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 12.3246 | 0.517584 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 35.6081 | 1.49277 | 0.746385 | − | 0.665514i | \(-0.231788\pi\) | ||||
0.746385 | + | 0.665514i | \(0.231788\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 20.5827 | 0.861359 | 0.430680 | − | 0.902505i | \(-0.358274\pi\) | ||||
0.430680 | + | 0.902505i | \(0.358274\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −8.25645 | −0.344918 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −19.0378 | −0.792554 | −0.396277 | − | 0.918131i | \(-0.629698\pi\) | ||||
−0.396277 | + | 0.918131i | \(0.629698\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −9.65591 | −0.401286 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 50.6489 | 2.10127 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0.739244 | 0.0306163 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 7.29062 | 0.300916 | 0.150458 | − | 0.988616i | \(-0.451925\pi\) | ||||
0.150458 | + | 0.988616i | \(0.451925\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −4.09358 | −0.168673 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 17.3821 | 0.715006 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 10.5832 | 0.434598 | 0.217299 | − | 0.976105i | \(-0.430275\pi\) | ||||
0.217299 | + | 0.976105i | \(0.430275\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 2.46140 | 0.100739 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −5.63520 | −0.230248 | −0.115124 | − | 0.993351i | \(-0.536727\pi\) | ||||
−0.115124 | + | 0.993351i | \(0.536727\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −17.7093 | −0.722377 | −0.361188 | − | 0.932493i | \(-0.617629\pi\) | ||||
−0.361188 | + | 0.932493i | \(0.617629\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −9.09216 | −0.370261 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 22.0996 | 0.896996 | 0.448498 | − | 0.893784i | \(-0.351959\pi\) | ||||
0.448498 | + | 0.893784i | \(0.351959\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 22.8267 | 0.924984 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 10.2390 | 0.414225 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 5.08532 | 0.205394 | 0.102697 | − | 0.994713i | \(-0.467253\pi\) | ||||
0.102697 | + | 0.994713i | \(0.467253\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 7.63073 | 0.307202 | 0.153601 | − | 0.988133i | \(-0.450913\pi\) | ||||
0.153601 | + | 0.988133i | \(0.450913\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 38.5591 | 1.54982 | 0.774910 | − | 0.632072i | \(-0.217795\pi\) | ||||
0.774910 | + | 0.632072i | \(0.217795\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −5.63195 | −0.226002 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −17.5258 | −0.702156 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0.894364 | 0.0357175 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 21.3688 | 0.852028 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1.86751 | −0.0743444 | −0.0371722 | − | 0.999309i | \(-0.511835\pi\) | ||||
−0.0371722 | + | 0.999309i | \(0.511835\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 33.2607 | 1.32199 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 4.37673 | 0.173412 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 6.28708 | 0.248713 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −1.91236 | −0.0755338 | −0.0377669 | − | 0.999287i | \(-0.512024\pi\) | ||||
−0.0377669 | + | 0.999287i | \(0.512024\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 5.06670 | 0.199811 | 0.0999055 | − | 0.994997i | \(-0.468146\pi\) | ||||
0.0999055 | + | 0.994997i | \(0.468146\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 37.0429 | 1.45631 | 0.728153 | − | 0.685414i | \(-0.240379\pi\) | ||||
0.728153 | + | 0.685414i | \(0.240379\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −1.30313 | −0.0511524 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −2.47496 | −0.0970014 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −11.9884 | −0.469143 | −0.234572 | − | 0.972099i | \(-0.575369\pi\) | ||||
−0.234572 | + | 0.972099i | \(0.575369\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 1.84800 | 0.0720974 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −2.82513 | −0.110051 | −0.0550257 | − | 0.998485i | \(-0.517524\pi\) | ||||
−0.0550257 | + | 0.998485i | \(0.517524\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −26.5004 | −1.03075 | −0.515374 | − | 0.856965i | \(-0.672347\pi\) | ||||
−0.515374 | + | 0.856965i | \(0.672347\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 4.43398 | 0.172202 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −5.39076 | −0.208731 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 5.41339 | 0.209294 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −0.0223910 | −0.000864393 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −19.0620 | −0.734784 | −0.367392 | − | 0.930066i | \(-0.619749\pi\) | ||||
−0.367392 | + | 0.930066i | \(0.619749\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −2.54346 | −0.0977533 | −0.0488766 | − | 0.998805i | \(-0.515564\pi\) | ||||
−0.0488766 | + | 0.998805i | \(0.515564\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −8.18146 | −0.313975 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 23.2507 | 0.890969 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 0.377109 | 0.0144297 | 0.00721483 | − | 0.999974i | \(-0.497703\pi\) | ||||
0.00721483 | + | 0.999974i | \(0.497703\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 4.70266 | 0.179418 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −11.1710 | −0.425581 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 7.24743 | 0.275705 | 0.137853 | − | 0.990453i | \(-0.455980\pi\) | ||||
0.137853 | + | 0.990453i | \(0.455980\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −0.366903 | −0.0139375 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 6.58385 | 0.249381 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −14.4264 | −0.545655 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −15.7381 | −0.594420 | −0.297210 | − | 0.954812i | \(-0.596056\pi\) | ||||
−0.297210 | + | 0.954812i | \(0.596056\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −65.1335 | −2.45656 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 21.0824 | 0.792887 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −45.9062 | −1.72404 | −0.862022 | − | 0.506870i | \(-0.830802\pi\) | ||||
−0.862022 | + | 0.506870i | \(0.830802\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 3.68751 | 0.138293 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0.584488 | 0.0218892 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 3.83612 | 0.143263 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −50.4975 | −1.88324 | −0.941619 | − | 0.336682i | \(-0.890695\pi\) | ||||
−0.941619 | + | 0.336682i | \(0.890695\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 55.9570 | 2.08395 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −36.1609 | −1.34484 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 19.0273 | 0.705685 | 0.352842 | − | 0.935683i | \(-0.385215\pi\) | ||||
0.352842 | + | 0.935683i | \(0.385215\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 27.3067 | 1.01136 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −21.8334 | −0.807539 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 42.1027 | 1.55510 | 0.777549 | − | 0.628822i | \(-0.216463\pi\) | ||||
0.777549 | + | 0.628822i | \(0.216463\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −0.716135 | −0.0263792 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 47.9212 | 1.76281 | 0.881405 | − | 0.472361i | \(-0.156598\pi\) | ||||
0.881405 | + | 0.472361i | \(0.156598\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −13.5151 | −0.496489 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −21.3492 | −0.783225 | −0.391613 | − | 0.920130i | \(-0.628083\pi\) | ||||
−0.391613 | + | 0.920130i | \(0.628083\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 19.3925 | 0.709536 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 18.4858 | 0.675458 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −27.8218 | −1.01523 | −0.507617 | − | 0.861583i | \(-0.669473\pi\) | ||||
−0.507617 | + | 0.861583i | \(0.669473\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 15.7478 | 0.573881 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −8.74990 | −0.318020 | −0.159010 | − | 0.987277i | \(-0.550830\pi\) | ||||
−0.159010 | + | 0.987277i | \(0.550830\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −0.127699 | −0.00463517 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 21.9923 | 0.797221 | 0.398610 | − | 0.917120i | \(-0.369493\pi\) | ||||
0.398610 | + | 0.917120i | \(0.369493\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −22.2379 | −0.805066 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 19.6921 | 0.711041 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −31.3229 | −1.12953 | −0.564766 | − | 0.825251i | \(-0.691034\pi\) | ||||
−0.564766 | + | 0.825251i | \(0.691034\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 11.3334 | 0.408162 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −32.3308 | −1.16286 | −0.581429 | − | 0.813597i | \(-0.697506\pi\) | ||||
−0.581429 | + | 0.813597i | \(0.697506\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −39.3794 | −1.41273 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −20.0680 | −0.719012 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0.495196 | 0.0177195 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 30.3605 | 1.08499 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 18.5712 | 0.661990 | 0.330995 | − | 0.943632i | \(-0.392616\pi\) | ||||
0.330995 | + | 0.943632i | \(0.392616\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 24.7483 | 0.881063 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 54.1627 | 1.92580 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0.338358 | 0.0120155 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 24.1985 | 0.857154 | 0.428577 | − | 0.903505i | \(-0.359015\pi\) | ||||
0.428577 | + | 0.903505i | \(0.359015\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −16.2992 | −0.576624 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −6.71031 | −0.237097 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 0.145556 | 0.00513656 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 34.0349 | 1.19809 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −30.4574 | −1.07082 | −0.535412 | − | 0.844591i | \(-0.679844\pi\) | ||||
−0.535412 | + | 0.844591i | \(0.679844\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 4.05626 | 0.142435 | 0.0712174 | − | 0.997461i | \(-0.477312\pi\) | ||||
0.0712174 | + | 0.997461i | \(0.477312\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 18.9587 | 0.664910 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 66.5499 | 2.32829 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 5.54441 | 0.193737 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 19.0615 | 0.665252 | 0.332626 | − | 0.943059i | \(-0.392065\pi\) | ||||
0.332626 | + | 0.943059i | \(0.392065\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 42.9810 | 1.49822 | 0.749111 | − | 0.662444i | \(-0.230481\pi\) | ||||
0.749111 | + | 0.662444i | \(0.230481\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −51.6777 | −1.79701 | −0.898505 | − | 0.438963i | \(-0.855346\pi\) | ||||
−0.898505 | + | 0.438963i | \(0.855346\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 25.6228 | 0.889915 | 0.444958 | − | 0.895552i | \(-0.353219\pi\) | ||||
0.444958 | + | 0.895552i | \(0.353219\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 28.6470 | 0.993753 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −6.96720 | −0.241399 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −3.29181 | −0.113781 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −53.0313 | −1.83084 | −0.915422 | − | 0.402495i | \(-0.868143\pi\) | ||||
−0.915422 | + | 0.402495i | \(0.868143\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 0.0602571 | 0.00207783 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 11.9021 | 0.409929 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 34.8121 | 1.19616 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −17.4290 | −0.598160 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 9.29985 | 0.318795 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −13.8668 | −0.474791 | −0.237395 | − | 0.971413i | \(-0.576294\pi\) | ||||
−0.237395 | + | 0.971413i | \(0.576294\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −16.3518 | −0.558567 | −0.279283 | − | 0.960209i | \(-0.590097\pi\) | ||||
−0.279283 | + | 0.960209i | \(0.590097\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 42.1443 | 1.43795 | 0.718973 | − | 0.695038i | \(-0.244612\pi\) | ||||
0.718973 | + | 0.695038i | \(0.244612\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −12.1331 | −0.413493 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 15.2130 | 0.517856 | 0.258928 | − | 0.965897i | \(-0.416631\pi\) | ||||
0.258928 | + | 0.965897i | \(0.416631\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 15.6688 | 0.532140 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0.290443 | 0.00985262 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 10.8218 | 0.366683 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −3.13253 | −0.106020 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 53.6934 | 1.81310 | 0.906549 | − | 0.422101i | \(-0.138707\pi\) | ||||
0.906549 | + | 0.422101i | \(0.138707\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −9.02096 | −0.304269 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 46.5787 | 1.56928 | 0.784638 | − | 0.619954i | \(-0.212849\pi\) | ||||
0.784638 | + | 0.619954i | \(0.212849\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 19.9787 | 0.672337 | 0.336169 | − | 0.941802i | \(-0.390869\pi\) | ||||
0.336169 | + | 0.941802i | \(0.390869\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −51.9251 | −1.74347 | −0.871737 | − | 0.489974i | \(-0.837006\pi\) | ||||
−0.871737 | + | 0.489974i | \(0.837006\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 34.2233 | 1.14781 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0.371676 | 0.0124516 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 49.6810 | 1.66251 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 1.92970 | 0.0644309 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −3.15083 | −0.105086 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 17.7828 | 0.592431 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 40.2358 | 1.33896 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 6.64335 | 0.220589 | 0.110294 | − | 0.993899i | \(-0.464821\pi\) | ||||
0.110294 | + | 0.993899i | \(0.464821\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 8.07209 | 0.267734 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 15.2064 | 0.503811 | 0.251905 | − | 0.967752i | \(-0.418943\pi\) | ||||
0.251905 | + | 0.967752i | \(0.418943\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1.52744 | 0.0505507 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 26.7709 | 0.884052 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 41.2068 | 1.35929 | 0.679644 | − | 0.733542i | \(-0.262134\pi\) | ||||
0.679644 | + | 0.733542i | \(0.262134\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 20.9446 | 0.690148 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −7.48310 | −0.246309 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 21.4249 | 0.703687 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −4.86715 | −0.159686 | −0.0798431 | − | 0.996807i | \(-0.525442\pi\) | ||||
−0.0798431 | + | 0.996807i | \(0.525442\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 21.2365 | 0.695999 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −11.0684 | −0.362364 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 3.44469 | 0.112533 | 0.0562666 | − | 0.998416i | \(-0.482080\pi\) | ||||
0.0562666 | + | 0.998416i | \(0.482080\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 20.7081 | 0.675784 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −34.8591 | −1.13637 | −0.568187 | − | 0.822900i | \(-0.692355\pi\) | ||||
−0.568187 | + | 0.822900i | \(0.692355\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 2.86534 | 0.0933084 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 5.17298 | 0.168099 | 0.0840496 | − | 0.996462i | \(-0.473215\pi\) | ||||
0.0840496 | + | 0.996462i | \(0.473215\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −2.19955 | −0.0714005 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −14.1447 | −0.458675 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −3.41090 | −0.110490 | −0.0552449 | − | 0.998473i | \(-0.517594\pi\) | ||||
−0.0552449 | + | 0.998473i | \(0.517594\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0.688392 | 0.0222526 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 58.6981 | 1.89546 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.6584 | −0.988980 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 7.07789 | 0.228082 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −17.5047 | −0.562914 | −0.281457 | − | 0.959574i | \(-0.590818\pi\) | ||||
−0.281457 | + | 0.959574i | \(0.590818\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 21.5143 | 0.691139 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 35.9954 | 1.15515 | 0.577574 | − | 0.816338i | \(-0.303999\pi\) | ||||
0.577574 | + | 0.816338i | \(0.303999\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −23.5214 | −0.754062 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 31.3634 | 1.00340 | 0.501702 | − | 0.865040i | \(-0.332707\pi\) | ||||
0.501702 | + | 0.865040i | \(0.332707\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −0.528531 | −0.0168919 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −8.51450 | −0.271847 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 36.4262 | 1.16182 | 0.580908 | − | 0.813969i | \(-0.302698\pi\) | ||||
0.580908 | + | 0.813969i | \(0.302698\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 30.0369 | 0.956086 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −9.50208 | −0.302149 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 6.22316 | 0.197685 | 0.0988426 | − | 0.995103i | \(-0.468486\pi\) | ||||
0.0988426 | + | 0.995103i | \(0.468486\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 1.77587 | 0.0563556 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 24.0896 | 0.762925 | 0.381463 | − | 0.924384i | \(-0.375420\pi\) | ||||
0.381463 | + | 0.924384i | \(0.375420\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −52.3763 | −1.65711 |
(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 | 4600.2.a.bc.1.3 | ✓ | 5 | |
4.3 | odd | 2 | 9200.2.a.cw.1.3 | 5 | |||
5.2 | odd | 4 | 4600.2.e.v.4049.7 | 10 | |||
5.3 | odd | 4 | 4600.2.e.v.4049.4 | 10 | |||
5.4 | even | 2 | 4600.2.a.bg.1.3 | yes | 5 | ||
20.19 | odd | 2 | 9200.2.a.cs.1.3 | 5 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4600.2.a.bc.1.3 | ✓ | 5 | 1.1 | even | 1 | trivial | |
4600.2.a.bg.1.3 | yes | 5 | 5.4 | even | 2 | ||
4600.2.e.v.4049.4 | 10 | 5.3 | odd | 4 | |||
4600.2.e.v.4049.7 | 10 | 5.2 | odd | 4 | |||
9200.2.a.cs.1.3 | 5 | 20.19 | odd | 2 | |||
9200.2.a.cw.1.3 | 5 | 4.3 | odd | 2 |