Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4400,2,Mod(1,4400)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4400, 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("4400.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4400 = 2^{4} \cdot 5^{2} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4400.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: | \(35.1341768894\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.837.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - 6x - 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 2200) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(2.52892\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4400.1 |
$q$-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 | ||||||||
\(3\) | −1.52892 | −0.882721 | −0.441361 | − | 0.897330i | \(-0.645504\pi\) | ||||
−0.441361 | + | 0.897330i | \(0.645504\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.39543 | −0.527421 | −0.263711 | − | 0.964602i | \(-0.584946\pi\) | ||||
−0.263711 | + | 0.964602i | \(0.584946\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −0.662410 | −0.220803 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 6.05784 | 1.68014 | 0.840071 | − | 0.542477i | \(-0.182513\pi\) | ||||
0.840071 | + | 0.542477i | \(0.182513\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 3.26193 | 0.791135 | 0.395568 | − | 0.918437i | \(-0.370548\pi\) | ||||
0.395568 | + | 0.918437i | \(0.370548\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.00000 | −0.229416 | −0.114708 | − | 0.993399i | \(-0.536593\pi\) | ||||
−0.114708 | + | 0.993399i | \(0.536593\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 2.13349 | 0.465566 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −0.528918 | −0.110287 | −0.0551435 | − | 0.998478i | \(-0.517562\pi\) | ||||
−0.0551435 | + | 0.998478i | \(0.517562\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 5.59952 | 1.07763 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.60457 | 0.297962 | 0.148981 | − | 0.988840i | \(-0.452401\pi\) | ||||
0.148981 | + | 0.988840i | \(0.452401\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.79085 | −0.680857 | −0.340429 | − | 0.940270i | \(-0.610572\pi\) | ||||
−0.340429 | + | 0.940270i | \(0.610572\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −1.52892 | −0.266150 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −8.92434 | −1.46715 | −0.733577 | − | 0.679607i | \(-0.762150\pi\) | ||||
−0.733577 | + | 0.679607i | \(0.762150\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −9.26193 | −1.48310 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.86651 | 0.291500 | 0.145750 | − | 0.989321i | \(-0.453441\pi\) | ||||
0.145750 | + | 0.989321i | \(0.453441\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −0.866508 | −0.132141 | −0.0660706 | − | 0.997815i | \(-0.521046\pi\) | ||||
−0.0660706 | + | 0.997815i | \(0.521046\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −1.19133 | −0.173773 | −0.0868865 | − | 0.996218i | \(-0.527692\pi\) | ||||
−0.0868865 | + | 0.996218i | \(0.527692\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −5.05279 | −0.721827 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −4.98723 | −0.698352 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 10.7202 | 1.47254 | 0.736270 | − | 0.676688i | \(-0.236586\pi\) | ||||
0.736270 | + | 0.676688i | \(0.236586\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1.52892 | 0.202510 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −13.1913 | −1.71736 | −0.858682 | − | 0.512508i | \(-0.828716\pi\) | ||||
−0.858682 | + | 0.512508i | \(0.828716\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −3.12844 | −0.400556 | −0.200278 | − | 0.979739i | \(-0.564185\pi\) | ||||
−0.200278 | + | 0.979739i | \(0.564185\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0.924344 | 0.116456 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2.26698 | 0.276956 | 0.138478 | − | 0.990365i | \(-0.455779\pi\) | ||||
0.138478 | + | 0.990365i | \(0.455779\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0.808672 | 0.0973527 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −10.0400 | −1.19153 | −0.595765 | − | 0.803159i | \(-0.703151\pi\) | ||||
−0.595765 | + | 0.803159i | \(0.703151\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 13.3954 | 1.56782 | 0.783908 | − | 0.620877i | \(-0.213223\pi\) | ||||
0.783908 | + | 0.620877i | \(0.213223\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −1.39543 | −0.159024 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 2.58675 | 0.291033 | 0.145516 | − | 0.989356i | \(-0.453516\pi\) | ||||
0.145516 | + | 0.989356i | \(0.453516\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −6.57398 | −0.730443 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −0.128442 | −0.0140984 | −0.00704918 | − | 0.999975i | \(-0.502244\pi\) | ||||
−0.00704918 | + | 0.999975i | \(0.502244\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −2.45326 | −0.263017 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 4.12844 | 0.437614 | 0.218807 | − | 0.975768i | \(-0.429783\pi\) | ||||
0.218807 | + | 0.975768i | \(0.429783\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −8.45326 | −0.886143 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 5.79590 | 0.601007 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −11.4354 | −1.16109 | −0.580547 | − | 0.814227i | \(-0.697161\pi\) | ||||
−0.580547 | + | 0.814227i | \(0.697161\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −0.662410 | −0.0665747 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 14.2619 | 1.41912 | 0.709558 | − | 0.704647i | \(-0.248895\pi\) | ||||
0.709558 | + | 0.704647i | \(0.248895\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 18.3598 | 1.80904 | 0.904522 | − | 0.426428i | \(-0.140228\pi\) | ||||
0.904522 | + | 0.426428i | \(0.140228\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 5.11567 | 0.494551 | 0.247275 | − | 0.968945i | \(-0.420465\pi\) | ||||
0.247275 | + | 0.968945i | \(0.420465\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 8.24411 | 0.789643 | 0.394821 | − | 0.918758i | \(-0.370806\pi\) | ||||
0.394821 | + | 0.918758i | \(0.370806\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 13.6446 | 1.29509 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 10.9243 | 1.02768 | 0.513838 | − | 0.857887i | \(-0.328223\pi\) | ||||
0.513838 | + | 0.857887i | \(0.328223\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −4.01277 | −0.370981 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −4.55179 | −0.417262 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −2.85374 | −0.257313 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 8.47108 | 0.751687 | 0.375843 | − | 0.926683i | \(-0.377353\pi\) | ||||
0.375843 | + | 0.926683i | \(0.377353\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 1.32482 | 0.116644 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 11.4354 | 0.999119 | 0.499560 | − | 0.866280i | \(-0.333495\pi\) | ||||
0.499560 | + | 0.866280i | \(0.333495\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.39543 | 0.120999 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 6.66241 | 0.569208 | 0.284604 | − | 0.958645i | \(-0.408138\pi\) | ||||
0.284604 | + | 0.958645i | \(0.408138\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −12.8487 | −1.08981 | −0.544906 | − | 0.838497i | \(-0.683435\pi\) | ||||
−0.544906 | + | 0.838497i | \(0.683435\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1.82144 | 0.153393 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 6.05784 | 0.506582 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 7.72530 | 0.637172 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −1.73302 | −0.141974 | −0.0709871 | − | 0.997477i | \(-0.522615\pi\) | ||||
−0.0709871 | + | 0.997477i | \(0.522615\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 12.9243 | 1.05177 | 0.525884 | − | 0.850556i | \(-0.323735\pi\) | ||||
0.525884 | + | 0.850556i | \(0.323735\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −2.16074 | −0.174685 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −12.6496 | −1.00955 | −0.504776 | − | 0.863251i | \(-0.668425\pi\) | ||||
−0.504776 | + | 0.863251i | \(0.668425\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −16.3904 | −1.29984 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0.738066 | 0.0581677 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 10.9771 | 0.859795 | 0.429898 | − | 0.902878i | \(-0.358550\pi\) | ||||
0.429898 | + | 0.902878i | \(0.358550\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 2.66746 | 0.206414 | 0.103207 | − | 0.994660i | \(-0.467090\pi\) | ||||
0.103207 | + | 0.994660i | \(0.467090\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 23.6974 | 1.82288 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0.662410 | 0.0506557 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −15.1157 | −1.14922 | −0.574612 | − | 0.818426i | \(-0.694847\pi\) | ||||
−0.574612 | + | 0.818426i | \(0.694847\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 20.1685 | 1.51595 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −13.6624 | −1.02118 | −0.510588 | − | 0.859825i | \(-0.670572\pi\) | ||||
−0.510588 | + | 0.859825i | \(0.670572\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 8.98723 | 0.668016 | 0.334008 | − | 0.942570i | \(-0.391599\pi\) | ||||
0.334008 | + | 0.942570i | \(0.391599\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 4.78313 | 0.353579 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 3.26193 | 0.238536 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −7.81372 | −0.568365 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 4.24411 | 0.307093 | 0.153547 | − | 0.988141i | \(-0.450930\pi\) | ||||
0.153547 | + | 0.988141i | \(0.450930\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 4.53397 | 0.326362 | 0.163181 | − | 0.986596i | \(-0.447825\pi\) | ||||
0.163181 | + | 0.986596i | \(0.447825\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 3.72797 | 0.265607 | 0.132803 | − | 0.991142i | \(-0.457602\pi\) | ||||
0.132803 | + | 0.991142i | \(0.457602\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 12.5111 | 0.886888 | 0.443444 | − | 0.896302i | \(-0.353756\pi\) | ||||
0.443444 | + | 0.896302i | \(0.353756\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −3.46603 | −0.244475 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −2.23906 | −0.157152 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0.350360 | 0.0243517 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −1.00000 | −0.0691714 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 23.0400 | 1.58614 | 0.793070 | − | 0.609130i | \(-0.208481\pi\) | ||||
0.793070 | + | 0.609130i | \(0.208481\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 15.3504 | 1.05179 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 5.28985 | 0.359099 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −20.4805 | −1.38394 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 19.7603 | 1.32922 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −9.19133 | −0.615497 | −0.307748 | − | 0.951468i | \(-0.599576\pi\) | ||||
−0.307748 | + | 0.951468i | \(0.599576\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 15.0350 | 0.997906 | 0.498953 | − | 0.866629i | \(-0.333718\pi\) | ||||
0.498953 | + | 0.866629i | \(0.333718\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −4.58675 | −0.303101 | −0.151551 | − | 0.988449i | \(-0.548427\pi\) | ||||
−0.151551 | + | 0.988449i | \(0.548427\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 2.13349 | 0.140373 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 0.337590 | 0.0221163 | 0.0110581 | − | 0.999939i | \(-0.496480\pi\) | ||||
0.0110581 | + | 0.999939i | \(0.496480\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −3.95493 | −0.256901 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 25.5111 | 1.65018 | 0.825088 | − | 0.565004i | \(-0.191126\pi\) | ||||
0.825088 | + | 0.565004i | \(0.191126\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1.93711 | −0.124781 | −0.0623903 | − | 0.998052i | \(-0.519872\pi\) | ||||
−0.0623903 | + | 0.998052i | \(0.519872\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −6.74749 | −0.432852 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −6.05784 | −0.385451 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0.196378 | 0.0124449 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −17.3776 | −1.09686 | −0.548432 | − | 0.836195i | \(-0.684775\pi\) | ||||
−0.548432 | + | 0.836195i | \(0.684775\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −0.528918 | −0.0332528 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −2.98218 | −0.186023 | −0.0930116 | − | 0.995665i | \(-0.529649\pi\) | ||||
−0.0930116 | + | 0.995665i | \(0.529649\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 12.4533 | 0.773808 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1.06289 | −0.0657910 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 22.7730 | 1.40425 | 0.702123 | − | 0.712056i | \(-0.252236\pi\) | ||||
0.702123 | + | 0.712056i | \(0.252236\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −6.31205 | −0.386291 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −25.4933 | −1.55435 | −0.777176 | − | 0.629283i | \(-0.783349\pi\) | ||||
−0.777176 | + | 0.629283i | \(0.783349\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −9.18123 | −0.557720 | −0.278860 | − | 0.960332i | \(-0.589957\pi\) | ||||
−0.278860 | + | 0.960332i | \(0.589957\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 12.9243 | 0.782217 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 24.0979 | 1.44790 | 0.723950 | − | 0.689853i | \(-0.242325\pi\) | ||||
0.723950 | + | 0.689853i | \(0.242325\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 2.51110 | 0.150335 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 27.4126 | 1.63530 | 0.817648 | − | 0.575718i | \(-0.195277\pi\) | ||||
0.817648 | + | 0.575718i | \(0.195277\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 17.6446 | 1.04886 | 0.524431 | − | 0.851453i | \(-0.324278\pi\) | ||||
0.524431 | + | 0.851453i | \(0.324278\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −2.60457 | −0.153743 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −6.35979 | −0.374105 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 17.4839 | 1.02492 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −25.1634 | −1.47006 | −0.735031 | − | 0.678033i | \(-0.762832\pi\) | ||||
−0.735031 | + | 0.678033i | \(0.762832\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 5.59952 | 0.324917 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −3.20410 | −0.185298 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.20915 | 0.0696941 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −21.8053 | −1.25268 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 29.6089 | 1.68987 | 0.844936 | − | 0.534867i | \(-0.179638\pi\) | ||||
0.844936 | + | 0.534867i | \(0.179638\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −28.0706 | −1.59688 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −10.7330 | −0.608614 | −0.304307 | − | 0.952574i | \(-0.598425\pi\) | ||||
−0.304307 | + | 0.952574i | \(0.598425\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 33.2892 | 1.88162 | 0.940808 | − | 0.338940i | \(-0.110069\pi\) | ||||
0.940808 | + | 0.338940i | \(0.110069\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −18.5511 | −1.04193 | −0.520967 | − | 0.853577i | \(-0.674429\pi\) | ||||
−0.520967 | + | 0.853577i | \(0.674429\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1.60457 | 0.0898389 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −7.82144 | −0.436550 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −3.26193 | −0.181499 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −12.6046 | −0.697035 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 1.66241 | 0.0916516 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 5.86651 | 0.322452 | 0.161226 | − | 0.986917i | \(-0.448455\pi\) | ||||
0.161226 | + | 0.986917i | \(0.448455\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 5.91157 | 0.323952 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 7.58170 | 0.413002 | 0.206501 | − | 0.978446i | \(-0.433792\pi\) | ||||
0.206501 | + | 0.978446i | \(0.433792\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −16.7024 | −0.907151 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −3.79085 | −0.205286 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 16.8188 | 0.908128 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −25.3954 | −1.36330 | −0.681649 | − | 0.731679i | \(-0.738737\pi\) | ||||
−0.681649 | + | 0.731679i | \(0.738737\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −21.2670 | −1.13840 | −0.569198 | − | 0.822201i | \(-0.692746\pi\) | ||||
−0.569198 | + | 0.822201i | \(0.692746\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 33.9210 | 1.81057 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −8.88433 | −0.472865 | −0.236433 | − | 0.971648i | \(-0.575978\pi\) | ||||
−0.236433 | + | 0.971648i | \(0.575978\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 6.95931 | 0.368326 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −11.1990 | −0.591063 | −0.295532 | − | 0.955333i | \(-0.595497\pi\) | ||||
−0.295532 | + | 0.955333i | \(0.595497\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.0000 | −0.947368 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −1.52892 | −0.0802474 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −1.58675 | −0.0828279 | −0.0414139 | − | 0.999142i | \(-0.513186\pi\) | ||||
−0.0414139 | + | 0.999142i | \(0.513186\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −1.23639 | −0.0643641 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −14.9593 | −0.776649 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −33.2714 | −1.72273 | −0.861363 | − | 0.507990i | \(-0.830389\pi\) | ||||
−0.861363 | + | 0.507990i | \(0.830389\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 9.72025 | 0.500618 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 24.0979 | 1.23782 | 0.618912 | − | 0.785461i | \(-0.287574\pi\) | ||||
0.618912 | + | 0.785461i | \(0.287574\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −12.9516 | −0.663530 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 15.3648 | 0.785106 | 0.392553 | − | 0.919729i | \(-0.371592\pi\) | ||||
0.392553 | + | 0.919729i | \(0.371592\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0.573984 | 0.0291772 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −1.88433 | −0.0955392 | −0.0477696 | − | 0.998858i | \(-0.515211\pi\) | ||||
−0.0477696 | + | 0.998858i | \(0.515211\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1.72530 | −0.0872519 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −17.4839 | −0.881944 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 7.27203 | 0.364973 | 0.182486 | − | 0.983208i | \(-0.441585\pi\) | ||||
0.182486 | + | 0.983208i | \(0.441585\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −2.13349 | −0.106808 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 12.8665 | 0.642523 | 0.321261 | − | 0.946991i | \(-0.395893\pi\) | ||||
0.321261 | + | 0.946991i | \(0.395893\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −22.9644 | −1.14394 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −8.92434 | −0.442363 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 5.15569 | 0.254932 | 0.127466 | − | 0.991843i | \(-0.459316\pi\) | ||||
0.127466 | + | 0.991843i | \(0.459316\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −10.1863 | −0.502452 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 18.4075 | 0.905775 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 19.6446 | 0.962000 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 39.0145 | 1.90598 | 0.952991 | − | 0.302999i | \(-0.0979878\pi\) | ||||
0.952991 | + | 0.302999i | \(0.0979878\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 28.9415 | 1.41052 | 0.705261 | − | 0.708948i | \(-0.250830\pi\) | ||||
0.705261 | + | 0.708948i | \(0.250830\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0.789147 | 0.0383697 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 4.36551 | 0.211262 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −9.26193 | −0.447170 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 17.2969 | 0.833162 | 0.416581 | − | 0.909099i | \(-0.363228\pi\) | ||||
0.416581 | + | 0.909099i | \(0.363228\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 17.8010 | 0.855459 | 0.427730 | − | 0.903907i | \(-0.359314\pi\) | ||||
0.427730 | + | 0.903907i | \(0.359314\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0.528918 | 0.0253016 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 28.9694 | 1.38263 | 0.691317 | − | 0.722551i | \(-0.257031\pi\) | ||||
0.691317 | + | 0.722551i | \(0.257031\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 3.34702 | 0.159382 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −5.70748 | −0.271170 | −0.135585 | − | 0.990766i | \(-0.543291\pi\) | ||||
−0.135585 | + | 0.990766i | \(0.543291\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 2.64964 | 0.125324 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 21.8436 | 1.03087 | 0.515433 | − | 0.856930i | \(-0.327631\pi\) | ||||
0.515433 | + | 0.856930i | \(0.327631\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.86651 | 0.0878904 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −19.7603 | −0.928418 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 19.2441 | 0.900202 | 0.450101 | − | 0.892978i | \(-0.351388\pi\) | ||||
0.450101 | + | 0.892978i | \(0.351388\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 18.2653 | 0.852550 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 10.6574 | 0.496363 | 0.248181 | − | 0.968714i | \(-0.420167\pi\) | ||||
0.248181 | + | 0.968714i | \(0.420167\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −6.98990 | −0.324848 | −0.162424 | − | 0.986721i | \(-0.551931\pi\) | ||||
−0.162424 | + | 0.986721i | \(0.551931\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −10.3904 | −0.480809 | −0.240405 | − | 0.970673i | \(-0.577280\pi\) | ||||
−0.240405 | + | 0.970673i | \(0.577280\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −3.16341 | −0.146073 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 19.3403 | 0.891152 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −0.866508 | −0.0398421 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −7.10120 | −0.325141 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 37.0044 | 1.69077 | 0.845387 | − | 0.534155i | \(-0.179370\pi\) | ||||
0.845387 | + | 0.534155i | \(0.179370\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −54.0622 | −2.46502 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −1.12844 | −0.0513459 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 24.0578 | 1.09016 | 0.545082 | − | 0.838383i | \(-0.316498\pi\) | ||||
0.545082 | + | 0.838383i | \(0.316498\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −16.7831 | −0.758959 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 0.314720 | 0.0142031 | 0.00710156 | − | 0.999975i | \(-0.497739\pi\) | ||||
0.00710156 | + | 0.999975i | \(0.497739\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 5.23401 | 0.235728 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 14.0101 | 0.628439 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −39.6268 | −1.77394 | −0.886969 | − | 0.461829i | \(-0.847193\pi\) | ||||
−0.886969 | + | 0.461829i | \(0.847193\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −4.07833 | −0.182206 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 21.2892 | 0.949238 | 0.474619 | − | 0.880191i | \(-0.342586\pi\) | ||||
0.474619 | + | 0.880191i | \(0.342586\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −36.2313 | −1.60909 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 12.3019 | 0.545274 | 0.272637 | − | 0.962117i | \(-0.412104\pi\) | ||||
0.272637 | + | 0.962117i | \(0.412104\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −18.6923 | −0.826900 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −5.59952 | −0.247225 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −1.19133 | −0.0523945 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 23.1106 | 1.01444 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 36.4227 | 1.59571 | 0.797853 | − | 0.602852i | \(-0.205969\pi\) | ||||
0.797853 | + | 0.602852i | \(0.205969\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −23.6675 | −1.03491 | −0.517453 | − | 0.855712i | \(-0.673120\pi\) | ||||
−0.517453 | + | 0.855712i | \(0.673120\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −12.3655 | −0.538650 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −22.7202 | −0.987837 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 8.73807 | 0.379200 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 11.3070 | 0.489761 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 20.8887 | 0.901414 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −5.05279 | −0.217639 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 12.9015 | 0.554678 | 0.277339 | − | 0.960772i | \(-0.410548\pi\) | ||||
0.277339 | + | 0.960772i | \(0.410548\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −13.7407 | −0.589671 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −35.2841 | −1.50864 | −0.754320 | − | 0.656507i | \(-0.772033\pi\) | ||||
−0.754320 | + | 0.656507i | \(0.772033\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 2.07231 | 0.0884441 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −1.60457 | −0.0683571 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −3.60962 | −0.153497 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −24.9745 | −1.05820 | −0.529101 | − | 0.848559i | \(-0.677471\pi\) | ||||
−0.529101 | + | 0.848559i | \(0.677471\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −5.24916 | −0.222016 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −4.98723 | −0.210561 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 40.8258 | 1.72060 | 0.860302 | − | 0.509785i | \(-0.170275\pi\) | ||||
0.860302 | + | 0.509785i | \(0.170275\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 9.17351 | 0.385251 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −18.6046 | −0.779944 | −0.389972 | − | 0.920827i | \(-0.627515\pi\) | ||||
−0.389972 | + | 0.920827i | \(0.627515\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 9.44554 | 0.395284 | 0.197642 | − | 0.980274i | \(-0.436672\pi\) | ||||
0.197642 | + | 0.980274i | \(0.436672\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −6.48890 | −0.271078 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 13.5646 | 0.564700 | 0.282350 | − | 0.959311i | \(-0.408886\pi\) | ||||
0.282350 | + | 0.959311i | \(0.408886\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −6.93206 | −0.288087 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0.179232 | 0.00743578 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 10.7202 | 0.443987 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 35.2263 | 1.45394 | 0.726972 | − | 0.686667i | \(-0.240927\pi\) | ||||
0.726972 | + | 0.686667i | \(0.240927\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 3.79085 | 0.156199 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −5.69975 | −0.234457 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −39.7952 | −1.63419 | −0.817097 | − | 0.576500i | \(-0.804418\pi\) | ||||
−0.817097 | + | 0.576500i | \(0.804418\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −19.1284 | −0.782875 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −19.1207 | −0.781252 | −0.390626 | − | 0.920550i | \(-0.627741\pi\) | ||||
−0.390626 | + | 0.920550i | \(0.627741\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −22.1964 | −0.905409 | −0.452705 | − | 0.891661i | \(-0.649541\pi\) | ||||
−0.452705 | + | 0.891661i | \(0.649541\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −1.50167 | −0.0611528 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 12.9321 | 0.524896 | 0.262448 | − | 0.964946i | \(-0.415470\pi\) | ||||
0.262448 | + | 0.964946i | \(0.415470\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 3.42335 | 0.138721 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −7.21687 | −0.291963 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −18.4711 | −0.746040 | −0.373020 | − | 0.927823i | \(-0.621678\pi\) | ||||
−0.373020 | + | 0.927823i | \(0.621678\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 22.6096 | 0.910229 | 0.455115 | − | 0.890433i | \(-0.349598\pi\) | ||||
0.455115 | + | 0.890433i | \(0.349598\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 37.1557 | 1.49341 | 0.746707 | − | 0.665154i | \(-0.231634\pi\) | ||||
0.746707 | + | 0.665154i | \(0.231634\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −2.96169 | −0.118848 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −5.76094 | −0.230807 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 1.52892 | 0.0610591 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −29.1106 | −1.16072 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 24.1506 | 0.961422 | 0.480711 | − | 0.876879i | \(-0.340379\pi\) | ||||
0.480711 | + | 0.876879i | \(0.340379\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −35.2263 | −1.40012 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −30.6089 | −1.21277 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 6.65061 | 0.263094 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −34.3948 | −1.35851 | −0.679256 | − | 0.733902i | \(-0.737697\pi\) | ||||
−0.679256 | + | 0.733902i | \(0.737697\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 44.4983 | 1.75484 | 0.877421 | − | 0.479720i | \(-0.159262\pi\) | ||||
0.877421 | + | 0.479720i | \(0.159262\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −40.2135 | −1.58096 | −0.790478 | − | 0.612490i | \(-0.790168\pi\) | ||||
−0.790478 | + | 0.612490i | \(0.790168\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −13.1913 | −0.517805 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −8.08775 | −0.316984 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −31.3420 | −1.22651 | −0.613253 | − | 0.789887i | \(-0.710139\pi\) | ||||
−0.613253 | + | 0.789887i | \(0.710139\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −8.87326 | −0.346179 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −32.3598 | −1.26056 | −0.630279 | − | 0.776369i | \(-0.717060\pi\) | ||||
−0.630279 | + | 0.776369i | \(0.717060\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −22.8087 | −0.887155 | −0.443577 | − | 0.896236i | \(-0.646291\pi\) | ||||
−0.443577 | + | 0.896236i | \(0.646291\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −30.2118 | −1.17333 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −0.848688 | −0.0328613 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 14.0528 | 0.543312 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −3.12844 | −0.120772 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 27.7152 | 1.06834 | 0.534171 | − | 0.845376i | \(-0.320624\pi\) | ||||
0.534171 | + | 0.845376i | \(0.320624\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −16.0400 | −0.616468 | −0.308234 | − | 0.951311i | \(-0.599738\pi\) | ||||
−0.308234 | + | 0.951311i | \(0.599738\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 15.9573 | 0.612385 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −22.9872 | −0.880873 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 35.8208 | 1.37064 | 0.685322 | − | 0.728240i | \(-0.259662\pi\) | ||||
0.685322 | + | 0.728240i | \(0.259662\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 7.01277 | 0.267554 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 64.9415 | 2.47407 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −38.5333 | −1.46588 | −0.732938 | − | 0.680296i | \(-0.761851\pi\) | ||||
−0.732938 | + | 0.680296i | \(0.761851\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0.924344 | 0.0351129 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 6.08843 | 0.230616 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −0.516148 | −0.0195225 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −52.7596 | −1.99270 | −0.996351 | − | 0.0853497i | \(-0.972799\pi\) | ||||
−0.996351 | + | 0.0853497i | \(0.972799\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 8.92434 | 0.336588 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −19.9015 | −0.748472 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 5.04774 | 0.189572 | 0.0947859 | − | 0.995498i | \(-0.469783\pi\) | ||||
0.0947859 | + | 0.995498i | \(0.469783\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −1.71349 | −0.0642609 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 2.00505 | 0.0750897 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −39.0044 | −1.45665 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −16.2848 | −0.607321 | −0.303660 | − | 0.952780i | \(-0.598209\pi\) | ||||
−0.303660 | + | 0.952780i | \(0.598209\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −25.6197 | −0.954128 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 2.96169 | 0.110146 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 9.68461 | 0.359182 | 0.179591 | − | 0.983741i | \(-0.442523\pi\) | ||||
0.179591 | + | 0.983741i | \(0.442523\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 30.0383 | 1.11253 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −2.82649 | −0.104542 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 13.8964 | 0.513276 | 0.256638 | − | 0.966508i | \(-0.417385\pi\) | ||||
0.256638 | + | 0.966508i | \(0.417385\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 2.26698 | 0.0835054 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 17.9092 | 0.658800 | 0.329400 | − | 0.944190i | \(-0.393153\pi\) | ||||
0.329400 | + | 0.944190i | \(0.393153\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 9.26193 | 0.340246 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −9.77808 | −0.358723 | −0.179362 | − | 0.983783i | \(-0.557403\pi\) | ||||
−0.179362 | + | 0.983783i | \(0.557403\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0.0850814 | 0.00311296 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −7.13854 | −0.260837 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −24.5212 | −0.894791 | −0.447396 | − | 0.894336i | \(-0.647648\pi\) | ||||
−0.447396 | + | 0.894336i | \(0.647648\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 26.5689 | 0.968226 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −43.9822 | −1.59856 | −0.799280 | − | 0.600959i | \(-0.794785\pi\) | ||||
−0.799280 | + | 0.600959i | \(0.794785\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0.808672 | 0.0293529 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 24.2313 | 0.878386 | 0.439193 | − | 0.898393i | \(-0.355265\pi\) | ||||
0.439193 | + | 0.898393i | \(0.355265\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −11.5041 | −0.416475 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −79.9109 | −2.88542 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −23.5282 | −0.848450 | −0.424225 | − | 0.905557i | \(-0.639453\pi\) | ||||
−0.424225 | + | 0.905557i | \(0.639453\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 4.55951 | 0.164207 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −2.74579 | −0.0987591 | −0.0493795 | − | 0.998780i | \(-0.515724\pi\) | ||||
−0.0493795 | + | 0.998780i | \(0.515724\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −19.0400 | −0.683057 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −1.86651 | −0.0668746 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −10.0400 | −0.359260 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 8.98485 | 0.321092 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 31.4482 | 1.12101 | 0.560504 | − | 0.828152i | \(-0.310608\pi\) | ||||
0.560504 | + | 0.828152i | \(0.310608\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −34.8181 | −1.23956 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −15.2441 | −0.542018 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −18.9516 | −0.672991 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −12.1685 | −0.431029 | −0.215514 | − | 0.976501i | \(-0.569143\pi\) | ||||
−0.215514 | + | 0.976501i | \(0.569143\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −3.88603 | −0.137478 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −2.73472 | −0.0966266 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 13.3954 | 0.472714 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 38.9771 | 1.37206 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 49.1480 | 1.72795 | 0.863975 | − | 0.503534i | \(-0.167967\pi\) | ||||
0.863975 | + | 0.503534i | \(0.167967\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −29.7253 | −1.04380 | −0.521898 | − | 0.853008i | \(-0.674776\pi\) | ||||
−0.521898 | + | 0.853008i | \(0.674776\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 14.0373 | 0.492311 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0.866508 | 0.0303153 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 5.59952 | 0.195663 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 49.3648 | 1.72284 | 0.861422 | − | 0.507889i | \(-0.169574\pi\) | ||||
0.861422 | + | 0.507889i | \(0.169574\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −37.5817 | −1.31002 | −0.655008 | − | 0.755622i | \(-0.727335\pi\) | ||||
−0.655008 | + | 0.755622i | \(0.727335\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −35.3749 | −1.23011 | −0.615054 | − | 0.788485i | \(-0.710866\pi\) | ||||
−0.615054 | + | 0.788485i | \(0.710866\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 44.1786 | 1.53438 | 0.767192 | − | 0.641417i | \(-0.221653\pi\) | ||||
0.767192 | + | 0.641417i | \(0.221653\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −36.8436 | −1.27809 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −16.4819 | −0.571062 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −21.2270 | −0.733711 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −47.7424 | −1.64825 | −0.824126 | − | 0.566406i | \(-0.808333\pi\) | ||||
−0.824126 | + | 0.566406i | \(0.808333\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −26.4253 | −0.911219 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −41.9116 | −1.44351 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −1.39543 | −0.0479474 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −26.9771 | −0.925853 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 4.72025 | 0.161808 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −39.7502 | −1.36102 | −0.680510 | − | 0.732739i | \(-0.738242\pi\) | ||||
−0.680510 | + | 0.732739i | \(0.738242\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 12.1080 | 0.413600 | 0.206800 | − | 0.978383i | \(-0.433695\pi\) | ||||
0.206800 | + | 0.978383i | \(0.433695\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 55.4049 | 1.89039 | 0.945195 | − | 0.326508i | \(-0.105872\pi\) | ||||
0.945195 | + | 0.326508i | \(0.105872\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 3.98218 | 0.135712 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −10.4660 | −0.356268 | −0.178134 | − | 0.984006i | \(-0.557006\pi\) | ||||
−0.178134 | + | 0.984006i | \(0.557006\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 9.72359 | 0.330230 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 2.58675 | 0.0877496 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 13.7330 | 0.465326 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 7.57495 | 0.256373 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 21.4959 | 0.725867 | 0.362933 | − | 0.931815i | \(-0.381775\pi\) | ||||
0.362933 | + | 0.931815i | \(0.381775\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 38.4728 | 1.29765 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −38.3521 | −1.29211 | −0.646057 | − | 0.763289i | \(-0.723583\pi\) | ||||
−0.646057 | + | 0.763289i | \(0.723583\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −25.8665 | −0.870477 | −0.435239 | − | 0.900315i | \(-0.643336\pi\) | ||||
−0.435239 | + | 0.900315i | \(0.643336\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 7.19133 | 0.241461 | 0.120731 | − | 0.992685i | \(-0.461476\pi\) | ||||
0.120731 | + | 0.992685i | \(0.461476\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −11.8208 | −0.396456 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −6.57398 | −0.220237 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 1.19133 | 0.0398663 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 4.89880 | 0.163566 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −6.08270 | −0.202869 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 34.9687 | 1.16498 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −1.84869 | −0.0615205 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 14.0356 | 0.466046 | 0.233023 | − | 0.972471i | \(-0.425138\pi\) | ||||
0.233023 | + | 0.972471i | \(0.425138\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −9.44725 | −0.313345 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −18.9166 | −0.626736 | −0.313368 | − | 0.949632i | \(-0.601457\pi\) | ||||
−0.313368 | + | 0.949632i | \(0.601457\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −0.128442 | −0.00425082 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −15.9573 | −0.526957 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −32.7451 | −1.08016 | −0.540081 | − | 0.841613i | \(-0.681606\pi\) | ||||
−0.540081 | + | 0.841613i | \(0.681606\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −45.2697 | −1.49169 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −60.8208 | −2.00194 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −12.1617 | −0.399443 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −9.37256 | −0.307504 | −0.153752 | − | 0.988110i | \(-0.549136\pi\) | ||||
−0.153752 | + | 0.988110i | \(0.549136\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 5.05279 | 0.165598 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 16.4099 | 0.537236 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 49.6617 | 1.62238 | 0.811189 | − | 0.584784i | \(-0.198821\pi\) | ||||
0.811189 | + | 0.584784i | \(0.198821\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −50.8964 | −1.66094 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 18.0178 | 0.587364 | 0.293682 | − | 0.955903i | \(-0.405119\pi\) | ||||
0.293682 | + | 0.955903i | \(0.405119\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −0.987230 | −0.0321486 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −29.6096 | −0.962183 | −0.481092 | − | 0.876670i | \(-0.659760\pi\) | ||||
−0.481092 | + | 0.876670i | \(0.659760\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 81.1473 | 2.63415 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 28.3631 | 0.919738 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 0.649640 | 0.0210439 | 0.0105219 | − | 0.999945i | \(-0.496651\pi\) | ||||
0.0105219 | + | 0.999945i | \(0.496651\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −2.45326 | −0.0793027 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −9.29690 | −0.300213 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −16.6294 | −0.536434 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −3.38867 | −0.109198 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 30.7381 | 0.988470 | 0.494235 | − | 0.869328i | \(-0.335448\pi\) | ||||
0.494235 | + | 0.869328i | \(0.335448\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 4.98723 | 0.160213 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −24.4634 | −0.785067 | −0.392533 | − | 0.919738i | \(-0.628401\pi\) | ||||
−0.392533 | + | 0.919738i | \(0.628401\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 17.9294 | 0.574790 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −2.14359 | −0.0685796 | −0.0342898 | − | 0.999412i | \(-0.510917\pi\) | ||||
−0.0342898 | + | 0.999412i | \(0.510917\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 4.12844 | 0.131946 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −5.46098 | −0.174356 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −6.56388 | −0.209355 | −0.104678 | − | 0.994506i | \(-0.533381\pi\) | ||||
−0.104678 | + | 0.994506i | \(0.533381\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −2.54169 | −0.0809028 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0.458312 | 0.0145735 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −27.6345 | −0.877839 | −0.438919 | − | 0.898527i | \(-0.644639\pi\) | ||||
−0.438919 | + | 0.898527i | \(0.644639\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −8.96941 | −0.284636 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 19.2008 | 0.608094 | 0.304047 | − | 0.952657i | \(-0.401662\pi\) | ||||
0.304047 | + | 0.952657i | \(0.401662\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −49.9721 | −1.58105 |
(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 | 4400.2.a.ca.1.1 | 3 | ||
4.3 | odd | 2 | 2200.2.a.t.1.3 | ✓ | 3 | ||
5.2 | odd | 4 | 4400.2.b.bc.4049.5 | 6 | |||
5.3 | odd | 4 | 4400.2.b.bc.4049.2 | 6 | |||
5.4 | even | 2 | 4400.2.a.bx.1.3 | 3 | |||
20.3 | even | 4 | 2200.2.b.l.1849.5 | 6 | |||
20.7 | even | 4 | 2200.2.b.l.1849.2 | 6 | |||
20.19 | odd | 2 | 2200.2.a.w.1.1 | yes | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2200.2.a.t.1.3 | ✓ | 3 | 4.3 | odd | 2 | ||
2200.2.a.w.1.1 | yes | 3 | 20.19 | odd | 2 | ||
2200.2.b.l.1849.2 | 6 | 20.7 | even | 4 | |||
2200.2.b.l.1849.5 | 6 | 20.3 | even | 4 | |||
4400.2.a.bx.1.3 | 3 | 5.4 | even | 2 | |||
4400.2.a.ca.1.1 | 3 | 1.1 | even | 1 | trivial | ||
4400.2.b.bc.4049.2 | 6 | 5.3 | odd | 4 | |||
4400.2.b.bc.4049.5 | 6 | 5.2 | odd | 4 |