Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1900,2,Mod(1,1900)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1900, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1900.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1900 = 2^{2} \cdot 5^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1900.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: | \(15.1715763840\) |
Analytic rank: | \(1\) |
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: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-1.91223\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1900.1 |
$q$-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 | \(-0.817849\pi\) | ||||
−0.840688 | + | 0.541520i | \(0.817849\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.91223 | −1.10072 | −0.550360 | − | 0.834928i | \(-0.685509\pi\) | ||||
−0.550360 | + | 0.834928i | \(0.685509\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 5.48108 | 1.82703 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.598988 | 0.180602 | 0.0903009 | − | 0.995915i | \(-0.471217\pi\) | ||||
0.0903009 | + | 0.995915i | \(0.471217\pi\) | |||||||
\(12\) | 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 | \(-0.461148\pi\) | ||||
0.121756 | + | 0.992560i | \(0.461148\pi\) | |||||||
\(24\) | 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 | \(-0.249673\pi\) | ||||
0.707833 | + | 0.706380i | \(0.249673\pi\) | |||||||
\(32\) | 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 | \(-0.479976\pi\) | ||||
0.0628644 | + | 0.998022i | \(0.479976\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −6.05763 | −0.883596 | −0.441798 | − | 0.897114i | \(-0.645659\pi\) | ||||
−0.441798 | + | 0.897114i | \(0.645659\pi\) | |||||||
\(48\) | 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 | \(-0.873237\pi\) | ||||
−0.921746 | + | 0.387794i | \(0.873237\pi\) | |||||||
\(60\) | 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 | \(-0.601051\pi\) | ||||
−0.312156 | + | 0.950031i | \(0.601051\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −3.40101 | −0.409434 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −11.9622 | −1.41965 | −0.709823 | − | 0.704380i | \(-0.751225\pi\) | ||||
−0.709823 | + | 0.704380i | \(0.751225\pi\) | |||||||
\(72\) | 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 | \(-0.832204\pi\) | ||||
−0.864246 | + | 0.503070i | \(0.832204\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 4.59899 | 0.510999 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 15.7565 | 1.72950 | 0.864749 | − | 0.502204i | \(-0.167477\pi\) | ||||
0.864749 | + | 0.502204i | \(0.167477\pi\) | |||||||
\(84\) | 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 | \(-0.826702\pi\) | ||||
−0.855422 | + | 0.517932i | \(0.826702\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −14.1903 | −1.37183 | −0.685913 | − | 0.727684i | \(-0.740597\pi\) | ||||
−0.685913 | + | 0.727684i | \(0.740597\pi\) | |||||||
\(108\) | 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 | \(-0.319111\pi\) | ||||
0.538182 | + | 0.842829i | \(0.319111\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −2.40101 | −0.211397 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 5.48108 | 0.478884 | 0.239442 | − | 0.970911i | \(-0.423035\pi\) | ||||
0.239442 | + | 0.970911i | \(0.423035\pi\) | |||||||
\(132\) | 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 | \(-0.401792\pi\) | ||||
0.303657 | + | 0.952781i | \(0.401792\pi\) | |||||||
\(140\) | 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 | \(-0.623222\pi\) | ||||
−0.377518 | + | 0.926002i | \(0.623222\pi\) | |||||||
\(152\) | 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 | \(-0.0530925\pi\) | ||||
0.986122 | + | 0.166023i | \(0.0530925\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −11.0301 | −0.853538 | −0.426769 | − | 0.904361i | \(-0.640348\pi\) | ||||
−0.426769 | + | 0.904361i | \(0.640348\pi\) | |||||||
\(168\) | 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 | \(-0.688334\pi\) | ||||
−0.557748 | + | 0.830010i | \(0.688334\pi\) | |||||||
\(180\) | 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 | \(-0.625267\pi\) | ||||
−0.383458 | + | 0.923558i | \(0.625267\pi\) | |||||||
\(192\) | 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 | \(-0.303061\pi\) | ||||
0.579977 | + | 0.814633i | \(0.303061\pi\) | |||||||
\(200\) | 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 | \(-0.564001\pi\) | ||||
−0.199714 | + | 0.979854i | \(0.564001\pi\) | |||||||
\(212\) | 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 | \(-0.389764\pi\) | ||||
0.339435 | + | 0.940629i | \(0.389764\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −14.5189 | −0.963655 | −0.481827 | − | 0.876266i | \(-0.660027\pi\) | ||||
−0.481827 | + | 0.876266i | \(0.660027\pi\) | |||||||
\(228\) | 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 | \(-0.396448\pi\) | ||||
0.319610 | + | 0.947549i | \(0.396448\pi\) | |||||||
\(240\) | 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 | \(-0.438540\pi\) | ||||
0.191885 | + | 0.981417i | \(0.438540\pi\) | |||||||
\(252\) | 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 | \(-0.495548\pi\) | ||||
0.0139846 | + | 0.999902i | \(0.495548\pi\) | |||||||
\(264\) | 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 | \(-0.373328\pi\) | ||||
0.387531 | + | 0.921857i | \(0.373328\pi\) | |||||||
\(272\) | 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 | \(-0.298819\pi\) | ||||
0.590783 | + | 0.806830i | \(0.298819\pi\) | |||||||
\(284\) | 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 | \(-0.599309\pi\) | ||||
−0.306952 | + | 0.951725i | \(0.599309\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 50.5655 | 2.87657 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −30.8442 | −1.74902 | −0.874508 | − | 0.485010i | \(-0.838816\pi\) | ||||
−0.874508 | + | 0.485010i | \(0.838816\pi\) | |||||||
\(312\) | 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 | \(-0.284374\pi\) | ||||
0.626777 | + | 0.779199i | \(0.284374\pi\) | |||||||
\(332\) | 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 | \(-0.553768\pi\) | ||||
−0.168116 | + | 0.985767i | \(0.553768\pi\) | |||||||
\(348\) | 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 | \(-0.482201\pi\) | ||||
0.0558895 | + | 0.998437i | \(0.482201\pi\) | |||||||
\(360\) | 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 | \(-0.348628\pi\) | ||||
0.457826 | + | 0.889042i | \(0.348628\pi\) | |||||||
\(368\) | 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 | \(-0.264184\pi\) | ||||
0.674906 | + | 0.737904i | \(0.264184\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −35.3253 | −1.80977 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −21.6911 | −1.10837 | −0.554183 | − | 0.832395i | \(-0.686969\pi\) | ||||
−0.554183 | + | 0.832395i | \(0.686969\pi\) | |||||||
\(384\) | 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 | \(-0.389567\pi\) | ||||
0.340017 | + | 0.940419i | \(0.389567\pi\) | |||||||
\(420\) | 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 | \(-0.337505\pi\) | ||||
0.488607 | + | 0.872504i | \(0.337505\pi\) | |||||||
\(432\) | 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 | \(-0.647743\pi\) | ||||
−0.447662 | + | 0.894203i | \(0.647743\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 8.11791 | 0.386567 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −40.4828 | −1.92340 | −0.961698 | − | 0.274110i | \(-0.911617\pi\) | ||||
−0.961698 | + | 0.274110i | \(0.911617\pi\) | |||||||
\(444\) | 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 | \(-0.553188\pi\) | ||||
−0.166318 | + | 0.986072i | \(0.553188\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −1.71690 | −0.0794486 | −0.0397243 | − | 0.999211i | \(-0.512648\pi\) | ||||
−0.0397243 | + | 0.999211i | \(0.512648\pi\) | |||||||
\(468\) | 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 | \(-0.757672\pi\) | ||||
−0.723942 | + | 0.689861i | \(0.757672\pi\) | |||||||
\(480\) | 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 | \(-0.507827\pi\) | ||||
−0.0245859 | + | 0.999698i | \(0.507827\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −73.3297 | −3.31608 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −10.9149 | −0.492581 | −0.246291 | − | 0.969196i | \(-0.579212\pi\) | ||||
−0.246291 | + | 0.969196i | \(0.579212\pi\) | |||||||
\(492\) | 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 | \(-0.163934\pi\) | ||||
0.870286 | + | 0.492547i | \(0.163934\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 32.1223 | 1.43512 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −20.3306 | −0.906497 | −0.453249 | − | 0.891384i | \(-0.649735\pi\) | ||||
−0.453249 | + | 0.891384i | \(0.649735\pi\) | |||||||
\(504\) | 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 | \(-0.735932\pi\) | ||||
−0.675175 | + | 0.737658i | \(0.735932\pi\) | |||||||
\(524\) | 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 | \(-0.694880\pi\) | ||||
−0.574698 | + | 0.818366i | \(0.694880\pi\) | |||||||
\(548\) | 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 | \(-0.176660\pi\) | ||||
0.849903 | + | 0.526939i | \(0.176660\pi\) | |||||||
\(564\) | 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 | \(-0.511438\pi\) | ||||
−0.0359250 | + | 0.999354i | \(0.511438\pi\) | |||||||
\(572\) | 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 | \(-0.424398\pi\) | ||||
0.235285 | + | 0.971926i | \(0.424398\pi\) | |||||||
\(588\) | 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 | \(-0.653930\pi\) | ||||
−0.464956 | + | 0.885334i | \(0.653930\pi\) | |||||||
\(600\) | 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 | \(-0.565862\pi\) | ||||
−0.205439 | + | 0.978670i | \(0.565862\pi\) | |||||||
\(608\) | 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 | \(-0.654720\pi\) | ||||
−0.467153 | + | 0.884177i | \(0.654720\pi\) | |||||||
\(620\) | 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 | \(-0.475347\pi\) | ||||
0.0773725 | + | 0.997002i | \(0.475347\pi\) | |||||||
\(632\) | 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 | \(-0.716735\pi\) | ||||
−0.629486 | + | 0.777012i | \(0.716735\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −35.3434 | −1.38949 | −0.694746 | − | 0.719255i | \(-0.744483\pi\) | ||||
−0.694746 | + | 0.719255i | \(0.744483\pi\) | |||||||
\(648\) | 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 | \(-0.303846\pi\) | ||||
0.577967 | + | 0.816060i | \(0.303846\pi\) | |||||||
\(660\) | 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 | \(-0.554636\pi\) | ||||
−0.170803 | + | 0.985305i | \(0.554636\pi\) | |||||||
\(684\) | 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 | \(-0.246962\pi\) | ||||
0.713823 | + | 0.700326i | \(0.246962\pi\) | |||||||
\(692\) | 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 | \(-0.414218\pi\) | ||||
0.266241 | + | 0.963907i | \(0.414218\pi\) | |||||||
\(720\) | 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 | \(-0.313959\pi\) | ||||
0.551754 | + | 0.834007i | \(0.313959\pi\) | |||||||
\(728\) | 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 | \(-0.433941\pi\) | ||||
0.206043 | + | 0.978543i | \(0.433941\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 7.48108 | 0.274824 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 28.5053 | 1.04576 | 0.522878 | − | 0.852407i | \(-0.324858\pi\) | ||||
0.522878 | + | 0.852407i | \(0.324858\pi\) | |||||||
\(744\) | 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 | \(-0.650580\pi\) | ||||
−0.455613 | + | 0.890178i | \(0.650580\pi\) | |||||||
\(752\) | 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 | \(-0.0674252\pi\) | ||||
0.977649 | + | 0.210242i | \(0.0674252\pi\) | |||||||
\(788\) | 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 | \(-0.257126\pi\) | ||||
0.691102 | + | 0.722757i | \(0.257126\pi\) | |||||||
\(812\) | 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 | \(-0.370152\pi\) | ||||
0.396709 | + | 0.917945i | \(0.370152\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −32.7615 | −1.13923 | −0.569615 | − | 0.821912i | \(-0.692908\pi\) | ||||
−0.569615 | + | 0.821912i | \(0.692908\pi\) | |||||||
\(828\) | 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 | \(-0.194055\pi\) | ||||
0.819853 | + | 0.572574i | \(0.194055\pi\) | |||||||
\(840\) | 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 | \(-0.617124\pi\) | ||||
−0.359708 | + | 0.933065i | \(0.617124\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 80.4098 | 2.74036 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −25.6868 | −0.874387 | −0.437194 | − | 0.899367i | \(-0.644028\pi\) | ||||
−0.437194 | + | 0.899367i | \(0.644028\pi\) | |||||||
\(864\) | 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 | \(-0.497935\pi\) | ||||
0.00648831 | + | 0.999979i | \(0.497935\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 54.9210 | 1.84407 | 0.922033 | − | 0.387111i | \(-0.126527\pi\) | ||||
0.922033 | + | 0.387111i | \(0.126527\pi\) | |||||||
\(888\) | 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 | \(-0.741748\pi\) | ||||
−0.688539 | + | 0.725199i | \(0.741748\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 24.1223 | 0.800086 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 41.8909 | 1.38791 | 0.693953 | − | 0.720020i | \(-0.255868\pi\) | ||||
0.693953 | + | 0.720020i | \(0.255868\pi\) | |||||||
\(912\) | 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 | \(-0.702388\pi\) | ||||
−0.593837 | + | 0.804585i | \(0.702388\pi\) | |||||||
\(920\) | 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 | \(-0.815538\pi\) | ||||
−0.836734 | + | 0.547610i | \(0.815538\pi\) | |||||||
\(948\) | 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 | \(-0.675449\pi\) | ||||
−0.523700 | + | 0.851903i | \(0.675449\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −8.48108 | −0.272452 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 21.0378 | 0.675136 | 0.337568 | − | 0.941301i | \(-0.390396\pi\) | ||||
0.337568 | + | 0.941301i | \(0.390396\pi\) | |||||||
\(972\) | 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 | \(-0.404574\pi\) | ||||
0.295320 | + | 0.955398i | \(0.404574\pi\) | |||||||
\(984\) | 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 | \(-0.527362\pi\) | ||||
−0.0858540 | + | 0.996308i | \(0.527362\pi\) | |||||||
\(992\) | 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 | 1900.2.a.f.1.1 | ✓ | 3 | |
4.3 | odd | 2 | 7600.2.a.by.1.3 | 3 | |||
5.2 | odd | 4 | 1900.2.c.g.1749.6 | 6 | |||
5.3 | odd | 4 | 1900.2.c.g.1749.1 | 6 | |||
5.4 | even | 2 | 1900.2.a.h.1.3 | yes | 3 | ||
20.19 | odd | 2 | 7600.2.a.bj.1.1 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1900.2.a.f.1.1 | ✓ | 3 | 1.1 | even | 1 | trivial | |
1900.2.a.h.1.3 | yes | 3 | 5.4 | even | 2 | ||
1900.2.c.g.1749.1 | 6 | 5.3 | odd | 4 | |||
1900.2.c.g.1749.6 | 6 | 5.2 | odd | 4 | |||
7600.2.a.bj.1.1 | 3 | 20.19 | odd | 2 | |||
7600.2.a.by.1.3 | 3 | 4.3 | odd | 2 |