Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [7600,2,Mod(1,7600)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(7600, 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("7600.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 7600 = 2^{4} \cdot 5^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 7600.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: | \(60.6863055362\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.257.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 4x + 3 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 1900) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(-1.91223\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 7600.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 2.91223 | 1.68138 | 0.840688 | − | 0.541520i | \(-0.182151\pi\) | ||||
0.840688 | + | 0.541520i | \(0.182151\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.91223 | 1.10072 | 0.550360 | − | 0.834928i | \(-0.314491\pi\) | ||||
0.550360 | + | 0.834928i | \(0.314491\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 5.48108 | 1.82703 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.598988 | −0.180602 | −0.0903009 | − | 0.995915i | \(-0.528783\pi\) | ||||
−0.0903009 | + | 0.995915i | \(0.528783\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.56885 | 0.712471 | 0.356235 | − | 0.934396i | \(-0.384060\pi\) | ||||
0.356235 | + | 0.934396i | \(0.384060\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −2.91223 | −0.706319 | −0.353160 | − | 0.935563i | \(-0.614893\pi\) | ||||
−0.353160 | + | 0.935563i | \(0.614893\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.00000 | 0.229416 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 8.48108 | 1.85072 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.16784 | −0.243511 | −0.121756 | − | 0.992560i | \(-0.538852\pi\) | ||||
−0.121756 | + | 0.992560i | \(0.538852\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 7.22547 | 1.39054 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −1.40101 | −0.260161 | −0.130081 | − | 0.991503i | \(-0.541524\pi\) | ||||
−0.130081 | + | 0.991503i | \(0.541524\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −7.88209 | −1.41567 | −0.707833 | − | 0.706380i | \(-0.750327\pi\) | ||||
−0.707833 | + | 0.706380i | \(0.750327\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −1.74439 | −0.303660 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 6.53871 | 1.07496 | 0.537479 | − | 0.843277i | \(-0.319377\pi\) | ||||
0.537479 | + | 0.843277i | \(0.319377\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 7.48108 | 1.19793 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 9.48108 | 1.48070 | 0.740348 | − | 0.672224i | \(-0.234661\pi\) | ||||
0.740348 | + | 0.672224i | \(0.234661\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −0.824458 | −0.125729 | −0.0628644 | − | 0.998022i | \(-0.520024\pi\) | ||||
−0.0628644 | + | 0.998022i | \(0.520024\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 6.05763 | 0.883596 | 0.441798 | − | 0.897114i | \(-0.354341\pi\) | ||||
0.441798 | + | 0.897114i | \(0.354341\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.48108 | 0.211583 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −8.48108 | −1.18759 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0.824458 | 0.113248 | 0.0566240 | − | 0.998396i | \(-0.481966\pi\) | ||||
0.0566240 | + | 0.998396i | \(0.481966\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 2.91223 | 0.385734 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 14.1601 | 1.84349 | 0.921746 | − | 0.387794i | \(-0.126763\pi\) | ||||
0.921746 | + | 0.387794i | \(0.126763\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.88209 | −0.240977 | −0.120488 | − | 0.992715i | \(-0.538446\pi\) | ||||
−0.120488 | + | 0.992715i | \(0.538446\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 15.9622 | 2.01104 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 5.11021 | 0.624311 | 0.312156 | − | 0.950031i | \(-0.398949\pi\) | ||||
0.312156 | + | 0.950031i | \(0.398949\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −3.40101 | −0.409434 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 11.9622 | 1.41965 | 0.709823 | − | 0.704380i | \(-0.248775\pi\) | ||||
0.709823 | + | 0.704380i | \(0.248775\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −1.03014 | −0.120569 | −0.0602843 | − | 0.998181i | \(-0.519201\pi\) | ||||
−0.0602843 | + | 0.998181i | \(0.519201\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −1.74439 | −0.198792 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 15.3632 | 1.72849 | 0.864246 | − | 0.503070i | \(-0.167796\pi\) | ||||
0.864246 | + | 0.503070i | \(0.167796\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 4.59899 | 0.510999 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −15.7565 | −1.72950 | −0.864749 | − | 0.502204i | \(-0.832523\pi\) | ||||
−0.864749 | + | 0.502204i | \(0.832523\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −4.08007 | −0.437429 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 15.4432 | 1.63698 | 0.818490 | − | 0.574521i | \(-0.194812\pi\) | ||||
0.818490 | + | 0.574521i | \(0.194812\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 7.48108 | 0.784230 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −22.9545 | −2.38027 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −7.70655 | −0.782481 | −0.391241 | − | 0.920288i | \(-0.627954\pi\) | ||||
−0.391241 | + | 0.920288i | \(0.627954\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −3.28310 | −0.329964 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 4.40101 | 0.437917 | 0.218959 | − | 0.975734i | \(-0.429734\pi\) | ||||
0.218959 | + | 0.975734i | \(0.429734\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 17.3632 | 1.71084 | 0.855422 | − | 0.517932i | \(-0.173298\pi\) | ||||
0.855422 | + | 0.517932i | \(0.173298\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 14.1903 | 1.37183 | 0.685913 | − | 0.727684i | \(-0.259403\pi\) | ||||
0.685913 | + | 0.727684i | \(0.259403\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −10.6791 | −1.02287 | −0.511434 | − | 0.859323i | \(-0.670886\pi\) | ||||
−0.511434 | + | 0.859323i | \(0.670886\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 19.0422 | 1.80741 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −8.25561 | −0.776622 | −0.388311 | − | 0.921528i | \(-0.626941\pi\) | ||||
−0.388311 | + | 0.921528i | \(0.626941\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 14.0801 | 1.30170 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −8.48108 | −0.777459 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.6412 | −0.967383 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 27.6111 | 2.48961 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −12.1300 | −1.07636 | −0.538182 | − | 0.842829i | \(-0.680889\pi\) | ||||
−0.538182 | + | 0.842829i | \(0.680889\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −2.40101 | −0.211397 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −5.48108 | −0.478884 | −0.239442 | − | 0.970911i | \(-0.576965\pi\) | ||||
−0.239442 | + | 0.970911i | \(0.576965\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2.91223 | 0.252522 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −7.59634 | −0.648999 | −0.324500 | − | 0.945886i | \(-0.605196\pi\) | ||||
−0.324500 | + | 0.945886i | \(0.605196\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −7.16013 | −0.607315 | −0.303657 | − | 0.952781i | \(-0.598208\pi\) | ||||
−0.303657 | + | 0.952781i | \(0.598208\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 17.6412 | 1.48566 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −1.53871 | −0.128673 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 4.31324 | 0.355750 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −18.4432 | −1.51093 | −0.755464 | − | 0.655190i | \(-0.772589\pi\) | ||||
−0.755464 | + | 0.655190i | \(0.772589\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 9.27804 | 0.755036 | 0.377518 | − | 0.926002i | \(-0.376778\pi\) | ||||
0.377518 | + | 0.926002i | \(0.376778\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −15.9622 | −1.29046 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 14.1903 | 1.13251 | 0.566254 | − | 0.824231i | \(-0.308392\pi\) | ||||
0.566254 | + | 0.824231i | \(0.308392\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 2.40101 | 0.190413 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −3.40101 | −0.268037 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −25.1799 | −1.97224 | −0.986122 | − | 0.166023i | \(-0.946907\pi\) | ||||
−0.986122 | + | 0.166023i | \(0.946907\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 11.0301 | 0.853538 | 0.426769 | − | 0.904361i | \(-0.359652\pi\) | ||||
0.426769 | + | 0.904361i | \(0.359652\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −6.40101 | −0.492386 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 5.48108 | 0.419149 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −15.3029 | −1.16346 | −0.581729 | − | 0.813383i | \(-0.697623\pi\) | ||||
−0.581729 | + | 0.813383i | \(0.697623\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 41.2376 | 3.09960 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 14.9243 | 1.11550 | 0.557748 | − | 0.830010i | \(-0.311666\pi\) | ||||
0.557748 | + | 0.830010i | \(0.311666\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 3.80202 | 0.282602 | 0.141301 | − | 0.989967i | \(-0.454871\pi\) | ||||
0.141301 | + | 0.989967i | \(0.454871\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −5.48108 | −0.405173 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1.74439 | 0.127563 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 21.0422 | 1.53060 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 10.5990 | 0.766916 | 0.383458 | − | 0.923558i | \(-0.374733\pi\) | ||||
0.383458 | + | 0.923558i | \(0.374733\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −22.2677 | −1.60286 | −0.801432 | − | 0.598086i | \(-0.795928\pi\) | ||||
−0.801432 | + | 0.598086i | \(0.795928\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 15.1652 | 1.08048 | 0.540238 | − | 0.841513i | \(-0.318334\pi\) | ||||
0.540238 | + | 0.841513i | \(0.318334\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −16.3632 | −1.15995 | −0.579977 | − | 0.814633i | \(-0.696939\pi\) | ||||
−0.579977 | + | 0.814633i | \(0.696939\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 14.8821 | 1.04970 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −4.08007 | −0.286365 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −6.40101 | −0.444901 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −0.598988 | −0.0414329 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 5.80202 | 0.399428 | 0.199714 | − | 0.979854i | \(-0.435999\pi\) | ||||
0.199714 | + | 0.979854i | \(0.435999\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 34.8365 | 2.38696 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −22.9545 | −1.55825 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −3.00000 | −0.202721 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −7.48108 | −0.503232 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −10.1377 | −0.678871 | −0.339435 | − | 0.940629i | \(-0.610236\pi\) | ||||
−0.339435 | + | 0.940629i | \(0.610236\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 14.5189 | 0.963655 | 0.481827 | − | 0.876266i | \(-0.339973\pi\) | ||||
0.481827 | + | 0.876266i | \(0.339973\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −27.2024 | −1.79758 | −0.898791 | − | 0.438377i | \(-0.855554\pi\) | ||||
−0.898791 | + | 0.438377i | \(0.855554\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −5.08007 | −0.334244 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 1.40101 | 0.0917833 | 0.0458917 | − | 0.998946i | \(-0.485387\pi\) | ||||
0.0458917 | + | 0.998946i | \(0.485387\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 44.7411 | 2.90624 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −9.88209 | −0.639219 | −0.319610 | − | 0.947549i | \(-0.603552\pi\) | ||||
−0.319610 | + | 0.947549i | \(0.603552\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −3.08513 | −0.198730 | −0.0993652 | − | 0.995051i | \(-0.531681\pi\) | ||||
−0.0993652 | + | 0.995051i | \(0.531681\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −8.28310 | −0.531361 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 2.56885 | 0.163452 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −45.8865 | −2.90794 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −6.08007 | −0.383770 | −0.191885 | − | 0.981417i | \(-0.561460\pi\) | ||||
−0.191885 | + | 0.981417i | \(0.561460\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0.699521 | 0.0439785 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −19.0121 | −1.18594 | −0.592971 | − | 0.805224i | \(-0.702045\pi\) | ||||
−0.592971 | + | 0.805224i | \(0.702045\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 19.0422 | 1.18323 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −7.67906 | −0.475322 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −0.453585 | −0.0279693 | −0.0139846 | − | 0.999902i | \(-0.504452\pi\) | ||||
−0.0139846 | + | 0.999902i | \(0.504452\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 44.9742 | 2.75238 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 23.8442 | 1.45381 | 0.726905 | − | 0.686738i | \(-0.240958\pi\) | ||||
0.726905 | + | 0.686738i | \(0.240958\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −12.7591 | −0.775061 | −0.387531 | − | 0.921857i | \(-0.626672\pi\) | ||||
−0.387531 | + | 0.921857i | \(0.626672\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 21.7866 | 1.31859 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −8.29783 | −0.498568 | −0.249284 | − | 0.968430i | \(-0.580195\pi\) | ||||
−0.249284 | + | 0.968430i | \(0.580195\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −43.2024 | −2.58646 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −9.19798 | −0.548705 | −0.274353 | − | 0.961629i | \(-0.588464\pi\) | ||||
−0.274353 | + | 0.961629i | \(0.588464\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −19.8770 | −1.18157 | −0.590783 | − | 0.806830i | \(-0.701181\pi\) | ||||
−0.590783 | + | 0.806830i | \(0.701181\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 27.6111 | 1.62983 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −8.51892 | −0.501113 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −22.4432 | −1.31565 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 8.14540 | 0.475860 | 0.237930 | − | 0.971282i | \(-0.423531\pi\) | ||||
0.237930 | + | 0.971282i | \(0.423531\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −4.32797 | −0.251134 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −3.00000 | −0.173494 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2.40101 | −0.138392 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 12.8168 | 0.736303 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 10.7565 | 0.613905 | 0.306952 | − | 0.951725i | \(-0.400691\pi\) | ||||
0.306952 | + | 0.951725i | \(0.400691\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 50.5655 | 2.87657 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 30.8442 | 1.74902 | 0.874508 | − | 0.485010i | \(-0.161184\pi\) | ||||
0.874508 | + | 0.485010i | \(0.161184\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −6.53871 | −0.369590 | −0.184795 | − | 0.982777i | \(-0.559162\pi\) | ||||
−0.184795 | + | 0.982777i | \(0.559162\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −11.3055 | −0.634982 | −0.317491 | − | 0.948261i | \(-0.602840\pi\) | ||||
−0.317491 | + | 0.948261i | \(0.602840\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0.839190 | 0.0469856 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 41.3253 | 2.30655 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −2.91223 | −0.162041 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −31.0999 | −1.71983 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 17.6412 | 0.972592 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −22.8064 | −1.25355 | −0.626777 | − | 0.779199i | \(-0.715626\pi\) | ||||
−0.626777 | + | 0.779199i | \(0.715626\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 35.8392 | 1.96398 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 17.7065 | 0.964537 | 0.482269 | − | 0.876023i | \(-0.339813\pi\) | ||||
0.482269 | + | 0.876023i | \(0.339813\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −24.0422 | −1.30579 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 4.72128 | 0.255672 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −16.0724 | −0.867826 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 6.26331 | 0.336232 | 0.168116 | − | 0.985767i | \(-0.446232\pi\) | ||||
0.168116 | + | 0.985767i | \(0.446232\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −14.8821 | −0.796620 | −0.398310 | − | 0.917251i | \(-0.630403\pi\) | ||||
−0.398310 | + | 0.917251i | \(0.630403\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 18.5611 | 0.990721 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 5.45359 | 0.290265 | 0.145133 | − | 0.989412i | \(-0.453639\pi\) | ||||
0.145133 | + | 0.989412i | \(0.453639\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −24.6988 | −1.30720 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −2.11791 | −0.111779 | −0.0558895 | − | 0.998437i | \(-0.517799\pi\) | ||||
−0.0558895 | + | 0.998437i | \(0.517799\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −30.9897 | −1.62653 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −17.5414 | −0.915651 | −0.457826 | − | 0.889042i | \(-0.651372\pi\) | ||||
−0.457826 | + | 0.889042i | \(0.651372\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 51.9665 | 2.70527 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 2.40101 | 0.124654 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 29.0801 | 1.50571 | 0.752854 | − | 0.658187i | \(-0.228676\pi\) | ||||
0.752854 | + | 0.658187i | \(0.228676\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −3.59899 | −0.185357 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −26.2780 | −1.34981 | −0.674906 | − | 0.737904i | \(-0.735816\pi\) | ||||
−0.674906 | + | 0.737904i | \(0.735816\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −35.3253 | −1.80977 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 21.6911 | 1.10837 | 0.554183 | − | 0.832395i | \(-0.313031\pi\) | ||||
0.554183 | + | 0.832395i | \(0.313031\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −4.51892 | −0.229710 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 2.43380 | 0.123398 | 0.0616992 | − | 0.998095i | \(-0.480348\pi\) | ||||
0.0616992 | + | 0.998095i | \(0.480348\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 3.40101 | 0.171997 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −15.9622 | −0.805184 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 31.2780 | 1.56980 | 0.784900 | − | 0.619622i | \(-0.212714\pi\) | ||||
0.784900 | + | 0.619622i | \(0.212714\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 8.48108 | 0.424585 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −8.95710 | −0.447296 | −0.223648 | − | 0.974670i | \(-0.571797\pi\) | ||||
−0.223648 | + | 0.974670i | \(0.571797\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −20.2479 | −1.00862 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −3.91661 | −0.194139 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −24.6412 | −1.21843 | −0.609215 | − | 0.793005i | \(-0.708515\pi\) | ||||
−0.609215 | + | 0.793005i | \(0.708515\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −22.1223 | −1.09121 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 41.2376 | 2.02917 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −20.8520 | −1.02112 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −13.9199 | −0.680033 | −0.340017 | − | 0.940419i | \(-0.610433\pi\) | ||||
−0.340017 | + | 0.940419i | \(0.610433\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 4.91993 | 0.239783 | 0.119891 | − | 0.992787i | \(-0.461745\pi\) | ||||
0.119891 | + | 0.992787i | \(0.461745\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 33.2024 | 1.61435 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −5.48108 | −0.265248 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −4.48108 | −0.216349 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −20.2875 | −0.977214 | −0.488607 | − | 0.872504i | \(-0.662495\pi\) | ||||
−0.488607 | + | 0.872504i | \(0.662495\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 20.9769 | 1.00808 | 0.504042 | − | 0.863679i | \(-0.331845\pi\) | ||||
0.504042 | + | 0.863679i | \(0.331845\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −1.16784 | −0.0558653 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 18.7591 | 0.895324 | 0.447662 | − | 0.894203i | \(-0.352257\pi\) | ||||
0.447662 | + | 0.894203i | \(0.352257\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 8.11791 | 0.386567 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 40.4828 | 1.92340 | 0.961698 | − | 0.274110i | \(-0.0883833\pi\) | ||||
0.961698 | + | 0.274110i | \(0.0883833\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −53.7109 | −2.54044 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −19.2402 | −0.908001 | −0.454001 | − | 0.891001i | \(-0.650004\pi\) | ||||
−0.454001 | + | 0.891001i | \(0.650004\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −5.67906 | −0.267416 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 27.0198 | 1.26950 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 8.44829 | 0.395195 | 0.197597 | − | 0.980283i | \(-0.436686\pi\) | ||||
0.197597 | + | 0.980283i | \(0.436686\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −21.0422 | −0.982167 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −25.2780 | −1.17732 | −0.588658 | − | 0.808382i | \(-0.700343\pi\) | ||||
−0.588658 | + | 0.808382i | \(0.700343\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 7.15749 | 0.332637 | 0.166318 | − | 0.986072i | \(-0.446812\pi\) | ||||
0.166318 | + | 0.986072i | \(0.446812\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 1.71690 | 0.0794486 | 0.0397243 | − | 0.999211i | \(-0.487352\pi\) | ||||
0.0397243 | + | 0.999211i | \(0.487352\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 14.8821 | 0.687191 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 41.3253 | 1.90417 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0.493841 | 0.0227068 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 4.51892 | 0.206907 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 31.6885 | 1.44788 | 0.723942 | − | 0.689861i | \(-0.242328\pi\) | ||||
0.723942 | + | 0.689861i | \(0.242328\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 16.7970 | 0.765876 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −9.90453 | −0.450672 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 1.08513 | 0.0491717 | 0.0245859 | − | 0.999698i | \(-0.492173\pi\) | ||||
0.0245859 | + | 0.999698i | \(0.492173\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −73.3297 | −3.31608 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 10.9149 | 0.492581 | 0.246291 | − | 0.969196i | \(-0.420788\pi\) | ||||
0.246291 | + | 0.969196i | \(0.420788\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 4.08007 | 0.183757 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 34.8365 | 1.56263 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −38.8814 | −1.74057 | −0.870286 | − | 0.492547i | \(-0.836066\pi\) | ||||
−0.870286 | + | 0.492547i | \(0.836066\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 32.1223 | 1.43512 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 20.3306 | 0.906497 | 0.453249 | − | 0.891384i | \(-0.350265\pi\) | ||||
0.453249 | + | 0.891384i | \(0.350265\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −18.6412 | −0.827885 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 10.5189 | 0.466243 | 0.233121 | − | 0.972448i | \(-0.425106\pi\) | ||||
0.233121 | + | 0.972448i | \(0.425106\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −3.00000 | −0.132712 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 7.22547 | 0.319012 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −3.62845 | −0.159579 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −44.5655 | −1.95621 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −25.7642 | −1.12875 | −0.564375 | − | 0.825519i | \(-0.690883\pi\) | ||||
−0.564375 | + | 0.825519i | \(0.690883\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 30.8814 | 1.35035 | 0.675175 | − | 0.737658i | \(-0.264068\pi\) | ||||
0.675175 | + | 0.737658i | \(0.264068\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 22.9545 | 0.999912 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −21.6362 | −0.940702 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 77.6128 | 3.36811 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 24.3555 | 1.05495 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 43.4630 | 1.87557 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −0.887149 | −0.0382122 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 13.3253 | 0.572901 | 0.286450 | − | 0.958095i | \(-0.407525\pi\) | ||||
0.286450 | + | 0.958095i | \(0.407525\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 11.0724 | 0.475161 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 26.8821 | 1.14940 | 0.574698 | − | 0.818366i | \(-0.305120\pi\) | ||||
0.574698 | + | 0.818366i | \(0.305120\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −10.3159 | −0.440271 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −1.40101 | −0.0596851 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 44.7411 | 1.90258 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 27.3082 | 1.15708 | 0.578542 | − | 0.815652i | \(-0.303622\pi\) | ||||
0.578542 | + | 0.815652i | \(0.303622\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −2.11791 | −0.0895780 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 5.08007 | 0.214481 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −40.3324 | −1.69981 | −0.849903 | − | 0.526939i | \(-0.823340\pi\) | ||||
−0.849903 | + | 0.526939i | \(0.823340\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 13.3933 | 0.562466 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 11.8399 | 0.496353 | 0.248176 | − | 0.968715i | \(-0.420169\pi\) | ||||
0.248176 | + | 0.968715i | \(0.420169\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1.71690 | 0.0718499 | 0.0359250 | − | 0.999354i | \(-0.488562\pi\) | ||||
0.0359250 | + | 0.999354i | \(0.488562\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 30.8667 | 1.28947 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 0.0552190 | 0.00229880 | 0.00114940 | − | 0.999999i | \(-0.499634\pi\) | ||||
0.00114940 | + | 0.999999i | \(0.499634\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −64.8486 | −2.69502 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −45.8865 | −1.90369 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −0.493841 | −0.0204528 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −11.4010 | −0.470570 | −0.235285 | − | 0.971926i | \(-0.575602\pi\) | ||||
−0.235285 | + | 0.971926i | \(0.575602\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −7.88209 | −0.324776 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 44.1645 | 1.81669 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −36.8288 | −1.51238 | −0.756190 | − | 0.654353i | \(-0.772941\pi\) | ||||
−0.756190 | + | 0.654353i | \(0.772941\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −47.6533 | −1.95032 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 22.7591 | 0.929913 | 0.464956 | − | 0.885334i | \(-0.346070\pi\) | ||||
0.464956 | + | 0.885334i | \(0.346070\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −36.5277 | −1.49000 | −0.744998 | − | 0.667067i | \(-0.767549\pi\) | ||||
−0.744998 | + | 0.667067i | \(0.767549\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 28.0094 | 1.14063 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 10.1230 | 0.410879 | 0.205439 | − | 0.978670i | \(-0.434138\pi\) | ||||
0.205439 | + | 0.978670i | \(0.434138\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −11.8821 | −0.481487 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 15.5611 | 0.629537 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −35.5930 | −1.43759 | −0.718794 | − | 0.695223i | \(-0.755306\pi\) | ||||
−0.718794 | + | 0.695223i | \(0.755306\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −13.2134 | −0.531951 | −0.265975 | − | 0.963980i | \(-0.585694\pi\) | ||||
−0.265975 | + | 0.963980i | \(0.585694\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 23.2453 | 0.934306 | 0.467153 | − | 0.884177i | \(-0.345280\pi\) | ||||
0.467153 | + | 0.884177i | \(0.345280\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −8.43818 | −0.338612 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 44.9742 | 1.80186 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −1.74439 | −0.0696643 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −19.0422 | −0.759263 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −3.88715 | −0.154745 | −0.0773725 | − | 0.997002i | \(-0.524653\pi\) | ||||
−0.0773725 | + | 0.997002i | \(0.524653\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 16.8968 | 0.671588 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 3.80467 | 0.150746 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 65.5655 | 2.59373 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −34.1223 | −1.34775 | −0.673875 | − | 0.738846i | \(-0.735371\pi\) | ||||
−0.673875 | + | 0.738846i | \(0.735371\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 31.9243 | 1.25897 | 0.629486 | − | 0.777012i | \(-0.283265\pi\) | ||||
0.629486 | + | 0.777012i | \(0.283265\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 35.3434 | 1.38949 | 0.694746 | − | 0.719255i | \(-0.255517\pi\) | ||||
0.694746 | + | 0.719255i | \(0.255517\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −8.48175 | −0.332938 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −66.8486 | −2.62000 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −27.5431 | −1.07784 | −0.538922 | − | 0.842356i | \(-0.681168\pi\) | ||||
−0.538922 | + | 0.842356i | \(0.681168\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −5.64627 | −0.220282 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −29.6740 | −1.15593 | −0.577967 | − | 0.816060i | \(-0.696154\pi\) | ||||
−0.577967 | + | 0.816060i | \(0.696154\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −16.3159 | −0.634614 | −0.317307 | − | 0.948323i | \(-0.602779\pi\) | ||||
−0.317307 | + | 0.948323i | \(0.602779\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −21.7866 | −0.846122 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.63615 | 0.0633522 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −29.5233 | −1.14144 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 1.12735 | 0.0435209 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −13.6945 | −0.527883 | −0.263941 | − | 0.964539i | \(-0.585023\pi\) | ||||
−0.263941 | + | 0.964539i | \(0.585023\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −18.2426 | −0.701121 | −0.350560 | − | 0.936540i | \(-0.614009\pi\) | ||||
−0.350560 | + | 0.936540i | \(0.614009\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −22.4432 | −0.861292 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 42.2824 | 1.62027 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 8.92764 | 0.341607 | 0.170803 | − | 0.985305i | \(-0.445364\pi\) | ||||
0.170803 | + | 0.985305i | \(0.445364\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −79.2195 | −3.02241 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 2.11791 | 0.0806859 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −37.5284 | −1.42765 | −0.713823 | − | 0.700326i | \(-0.753038\pi\) | ||||
−0.713823 | + | 0.700326i | \(0.753038\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −9.56115 | −0.363198 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −27.6111 | −1.04584 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 4.08007 | 0.154322 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −42.1746 | −1.59291 | −0.796457 | − | 0.604695i | \(-0.793295\pi\) | ||||
−0.796457 | + | 0.604695i | \(0.793295\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 6.53871 | 0.246612 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 12.8168 | 0.482024 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −4.35373 | −0.163508 | −0.0817539 | − | 0.996653i | \(-0.526052\pi\) | ||||
−0.0817539 | + | 0.996653i | \(0.526052\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 84.2067 | 3.15800 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 9.20500 | 0.344730 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −28.7789 | −1.07477 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −14.2780 | −0.532481 | −0.266241 | − | 0.963907i | \(-0.585782\pi\) | ||||
−0.266241 | + | 0.963907i | \(0.585782\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 50.5655 | 1.88316 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −8.98459 | −0.334141 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −29.7538 | −1.10351 | −0.551754 | − | 0.834007i | \(-0.686041\pi\) | ||||
−0.551754 | + | 0.834007i | \(0.686041\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −37.9193 | −1.40442 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 2.40101 | 0.0888046 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −16.4580 | −0.607889 | −0.303944 | − | 0.952690i | \(-0.598304\pi\) | ||||
−0.303944 | + | 0.952690i | \(0.598304\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −3.06095 | −0.112752 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −11.2024 | −0.412085 | −0.206043 | − | 0.978543i | \(-0.566059\pi\) | ||||
−0.206043 | + | 0.978543i | \(0.566059\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 7.48108 | 0.274824 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −28.5053 | −1.04576 | −0.522878 | − | 0.852407i | \(-0.675142\pi\) | ||||
−0.522878 | + | 0.852407i | \(0.675142\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −86.3625 | −3.15984 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 41.3253 | 1.50999 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 24.9716 | 0.911227 | 0.455613 | − | 0.890178i | \(-0.349420\pi\) | ||||
0.455613 | + | 0.890178i | \(0.349420\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −17.7065 | −0.645263 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 12.8717 | 0.467831 | 0.233916 | − | 0.972257i | \(-0.424846\pi\) | ||||
0.233916 | + | 0.972257i | \(0.424846\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 2.03717 | 0.0739445 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −26.6791 | −0.967115 | −0.483558 | − | 0.875313i | \(-0.660656\pi\) | ||||
−0.483558 | + | 0.875313i | \(0.660656\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −31.0999 | −1.12589 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 36.3753 | 1.31343 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 29.7541 | 1.07296 | 0.536479 | − | 0.843913i | \(-0.319754\pi\) | ||||
0.536479 | + | 0.843913i | \(0.319754\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −55.3676 | −1.99401 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −50.5655 | −1.81872 | −0.909358 | − | 0.416015i | \(-0.863426\pi\) | ||||
−0.909358 | + | 0.416015i | \(0.863426\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 55.4553 | 1.98945 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 9.48108 | 0.339695 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −7.16519 | −0.256391 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −10.1230 | −0.361765 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −54.8530 | −1.95530 | −0.977649 | − | 0.210242i | \(-0.932575\pi\) | ||||
−0.977649 | + | 0.210242i | \(0.932575\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −1.32094 | −0.0470269 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −24.0422 | −0.854843 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −4.83481 | −0.171689 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −30.3434 | −1.07482 | −0.537409 | − | 0.843322i | \(-0.680597\pi\) | ||||
−0.537409 | + | 0.843322i | \(0.680597\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −17.6412 | −0.624101 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 84.6456 | 2.99081 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 0.617041 | 0.0217749 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 69.4399 | 2.44440 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −11.0801 | −0.389554 | −0.194777 | − | 0.980848i | \(-0.562398\pi\) | ||||
−0.194777 | + | 0.980848i | \(0.562398\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −39.3625 | −1.38220 | −0.691102 | − | 0.722757i | \(-0.742874\pi\) | ||||
−0.691102 | + | 0.722757i | \(0.742874\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −37.1575 | −1.30317 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −0.824458 | −0.0288441 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 41.0044 | 1.43281 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 34.8493 | 1.21625 | 0.608125 | − | 0.793842i | \(-0.291922\pi\) | ||||
0.608125 | + | 0.793842i | \(0.291922\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −22.7615 | −0.793417 | −0.396709 | − | 0.917945i | \(-0.629848\pi\) | ||||
−0.396709 | + | 0.917945i | \(0.629848\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 32.7615 | 1.13923 | 0.569615 | − | 0.821912i | \(-0.307092\pi\) | ||||
0.569615 | + | 0.821912i | \(0.307092\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 36.4905 | 1.26737 | 0.633684 | − | 0.773592i | \(-0.281542\pi\) | ||||
0.633684 | + | 0.773592i | \(0.281542\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −24.1652 | −0.838281 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −4.31324 | −0.149445 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −56.9518 | −1.96854 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −47.4949 | −1.63971 | −0.819853 | − | 0.572574i | \(-0.805945\pi\) | ||||
−0.819853 | + | 0.572574i | \(0.805945\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −27.0372 | −0.932316 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −26.7866 | −0.922580 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −30.9897 | −1.06482 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −57.8865 | −1.98666 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −7.63615 | −0.261764 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −1.86736 | −0.0639372 | −0.0319686 | − | 0.999489i | \(-0.510178\pi\) | ||||
−0.0319686 | + | 0.999489i | \(0.510178\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −16.3608 | −0.558873 | −0.279436 | − | 0.960164i | \(-0.590148\pi\) | ||||
−0.279436 | + | 0.960164i | \(0.590148\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 21.0851 | 0.719415 | 0.359708 | − | 0.933065i | \(-0.382876\pi\) | ||||
0.359708 | + | 0.933065i | \(0.382876\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 80.4098 | 2.74036 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 25.6868 | 0.874387 | 0.437194 | − | 0.899367i | \(-0.355972\pi\) | ||||
0.437194 | + | 0.899367i | \(0.355972\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −24.8091 | −0.842560 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −9.20236 | −0.312169 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 13.1274 | 0.444803 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −42.2402 | −1.42961 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 43.2978 | 1.46206 | 0.731032 | − | 0.682343i | \(-0.239039\pi\) | ||||
0.731032 | + | 0.682343i | \(0.239039\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 23.7213 | 0.800099 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 22.0750 | 0.743726 | 0.371863 | − | 0.928288i | \(-0.378719\pi\) | ||||
0.371863 | + | 0.928288i | \(0.378719\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −0.385604 | −0.0129766 | −0.00648831 | − | 0.999979i | \(-0.502065\pi\) | ||||
−0.00648831 | + | 0.999979i | \(0.502065\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −54.9210 | −1.84407 | −0.922033 | − | 0.387111i | \(-0.873473\pi\) | ||||
−0.922033 | + | 0.387111i | \(0.873473\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −35.3253 | −1.18477 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −2.75474 | −0.0922873 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 6.05763 | 0.202711 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −8.73669 | −0.291710 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 11.0429 | 0.368301 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −2.40101 | −0.0799893 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −6.99230 | −0.232689 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 41.4727 | 1.37708 | 0.688539 | − | 0.725199i | \(-0.258252\pi\) | ||||
0.688539 | + | 0.725199i | \(0.258252\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 24.1223 | 0.800086 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −41.8909 | −1.38791 | −0.693953 | − | 0.720020i | \(-0.744132\pi\) | ||||
−0.693953 | + | 0.720020i | \(0.744132\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 9.43795 | 0.312350 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −15.9622 | −0.527117 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 36.0044 | 1.18767 | 0.593837 | − | 0.804585i | \(-0.297612\pi\) | ||||
0.593837 | + | 0.804585i | \(0.297612\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 31.3253 | 1.03220 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 30.7290 | 1.01146 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 95.1689 | 3.12576 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 59.4898 | 1.95180 | 0.975899 | − | 0.218222i | \(-0.0700256\pi\) | ||||
0.975899 | + | 0.218222i | \(0.0700256\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1.48108 | 0.0485404 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 89.8255 | 2.94076 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 35.7143 | 1.16673 | 0.583367 | − | 0.812209i | \(-0.301735\pi\) | ||||
0.583367 | + | 0.812209i | \(0.301735\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −19.0422 | −0.621420 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 20.2074 | 0.658743 | 0.329371 | − | 0.944200i | \(-0.393163\pi\) | ||||
0.329371 | + | 0.944200i | \(0.393163\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −11.0724 | −0.360566 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 51.4982 | 1.67347 | 0.836734 | − | 0.547610i | \(-0.184462\pi\) | ||||
0.836734 | + | 0.547610i | \(0.184462\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −2.64627 | −0.0859016 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −32.9243 | −1.06764 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −7.95272 | −0.257614 | −0.128807 | − | 0.991670i | \(-0.541115\pi\) | ||||
−0.128807 | + | 0.991670i | \(0.541115\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 2.44391 | 0.0790005 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −22.1223 | −0.714366 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 31.1274 | 1.00411 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 77.7780 | 2.50636 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 32.5706 | 1.04740 | 0.523700 | − | 0.851903i | \(-0.324551\pi\) | ||||
0.523700 | + | 0.851903i | \(0.324551\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −8.48108 | −0.272452 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −21.0378 | −0.675136 | −0.337568 | − | 0.941301i | \(-0.609604\pi\) | ||||
−0.337568 | + | 0.941301i | \(0.609604\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −20.8520 | −0.668483 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −46.9648 | −1.50254 | −0.751269 | − | 0.659997i | \(-0.770558\pi\) | ||||
−0.751269 | + | 0.659997i | \(0.770558\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −9.25032 | −0.295641 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −58.5327 | −1.86881 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −18.5182 | −0.590640 | −0.295320 | − | 0.955398i | \(-0.595426\pi\) | ||||
−0.295320 | + | 0.955398i | \(0.595426\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 51.3753 | 1.63529 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0.962834 | 0.0306163 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 5.40539 | 0.171708 | 0.0858540 | − | 0.996308i | \(-0.472638\pi\) | ||||
0.0858540 | + | 0.996308i | \(0.472638\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −66.4175 | −2.10770 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −8.55676 | −0.270995 | −0.135498 | − | 0.990778i | \(-0.543263\pi\) | ||||
−0.135498 | + | 0.990778i | \(0.543263\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 47.2453 | 1.49477 |
(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 | 7600.2.a.by.1.3 | 3 | ||
4.3 | odd | 2 | 1900.2.a.f.1.1 | ✓ | 3 | ||
5.4 | even | 2 | 7600.2.a.bj.1.1 | 3 | |||
20.3 | even | 4 | 1900.2.c.g.1749.1 | 6 | |||
20.7 | even | 4 | 1900.2.c.g.1749.6 | 6 | |||
20.19 | odd | 2 | 1900.2.a.h.1.3 | yes | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1900.2.a.f.1.1 | ✓ | 3 | 4.3 | odd | 2 | ||
1900.2.a.h.1.3 | yes | 3 | 20.19 | odd | 2 | ||
1900.2.c.g.1749.1 | 6 | 20.3 | even | 4 | |||
1900.2.c.g.1749.6 | 6 | 20.7 | even | 4 | |||
7600.2.a.bj.1.1 | 3 | 5.4 | even | 2 | |||
7600.2.a.by.1.3 | 3 | 1.1 | even | 1 | trivial |