Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1560,2,Mod(1,1560)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1560, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("1560.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1560 = 2^{3} \cdot 3 \cdot 5 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1560.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: | \(12.4566627153\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.940.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - 7x - 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(-0.602705\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1560.1 |
$q$-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 | ||||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.43134 | 1.29692 | 0.648462 | − | 0.761247i | \(-0.275413\pi\) | ||||
0.648462 | + | 0.761247i | \(0.275413\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.63675 | −0.795009 | −0.397505 | − | 0.917600i | \(-0.630124\pi\) | ||||
−0.397505 | + | 0.917600i | \(0.630124\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.00000 | −0.277350 | ||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.00000 | 0.258199 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 7.84216 | 1.90200 | 0.951001 | − | 0.309187i | \(-0.100057\pi\) | ||||
0.951001 | + | 0.309187i | \(0.100057\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.794590 | 0.182291 | 0.0911457 | − | 0.995838i | \(-0.470947\pi\) | ||||
0.0911457 | + | 0.995838i | \(0.470947\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 3.43134 | 0.748779 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −3.43134 | −0.715483 | −0.357742 | − | 0.933821i | \(-0.616453\pi\) | ||||
−0.357742 | + | 0.933821i | \(0.616453\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −4.06808 | −0.755424 | −0.377712 | − | 0.925923i | \(-0.623289\pi\) | ||||
−0.377712 | + | 0.925923i | \(0.623289\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 9.27349 | 1.66557 | 0.832784 | − | 0.553598i | \(-0.186745\pi\) | ||||
0.832784 | + | 0.553598i | \(0.186745\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −2.63675 | −0.458999 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 3.43134 | 0.580002 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −0.636747 | −0.104681 | −0.0523403 | − | 0.998629i | \(-0.516668\pi\) | ||||
−0.0523403 | + | 0.998629i | \(0.516668\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −1.00000 | −0.160128 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −4.63675 | −0.724138 | −0.362069 | − | 0.932151i | \(-0.617930\pi\) | ||||
−0.362069 | + | 0.932151i | \(0.617930\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.41082 | 0.367647 | 0.183823 | − | 0.982959i | \(-0.441153\pi\) | ||||
0.183823 | + | 0.982959i | \(0.441153\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1.00000 | 0.149071 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 5.27349 | 0.769218 | 0.384609 | − | 0.923080i | \(-0.374336\pi\) | ||||
0.384609 | + | 0.923080i | \(0.374336\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 4.77407 | 0.682010 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 7.84216 | 1.09812 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 11.4994 | 1.57957 | 0.789783 | − | 0.613386i | \(-0.210193\pi\) | ||||
0.789783 | + | 0.613386i | \(0.210193\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −2.63675 | −0.355539 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0.794590 | 0.105246 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −12.1362 | −1.57999 | −0.789997 | − | 0.613110i | \(-0.789918\pi\) | ||||
−0.789997 | + | 0.613110i | \(0.789918\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −11.4994 | −1.47235 | −0.736175 | − | 0.676791i | \(-0.763370\pi\) | ||||
−0.736175 | + | 0.676791i | \(0.763370\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 3.43134 | 0.432308 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −1.00000 | −0.124035 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −6.41082 | −0.783206 | −0.391603 | − | 0.920134i | \(-0.628079\pi\) | ||||
−0.391603 | + | 0.920134i | \(0.628079\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −3.43134 | −0.413084 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −10.6367 | −1.26235 | −0.631175 | − | 0.775641i | \(-0.717427\pi\) | ||||
−0.631175 | + | 0.775641i | \(0.717427\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 16.0681 | 1.88063 | 0.940313 | − | 0.340310i | \(-0.110532\pi\) | ||||
0.940313 | + | 0.340310i | \(0.110532\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 1.00000 | 0.115470 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −9.04757 | −1.03107 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 10.6367 | 1.19673 | 0.598364 | − | 0.801225i | \(-0.295818\pi\) | ||||
0.598364 | + | 0.801225i | \(0.295818\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −16.1362 | −1.77117 | −0.885587 | − | 0.464473i | \(-0.846244\pi\) | ||||
−0.885587 | + | 0.464473i | \(0.846244\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 7.84216 | 0.850601 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −4.06808 | −0.436144 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 8.63675 | 0.915493 | 0.457747 | − | 0.889083i | \(-0.348657\pi\) | ||||
0.457747 | + | 0.889083i | \(0.348657\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −3.43134 | −0.359702 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 9.27349 | 0.961616 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0.794590 | 0.0815232 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 12.2940 | 1.24827 | 0.624134 | − | 0.781317i | \(-0.285452\pi\) | ||||
0.624134 | + | 0.781317i | \(0.285452\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −2.63675 | −0.265003 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 5.34158 | 0.531507 | 0.265753 | − | 0.964041i | \(-0.414379\pi\) | ||||
0.265753 | + | 0.964041i | \(0.414379\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −10.4108 | −1.02581 | −0.512904 | − | 0.858446i | \(-0.671430\pi\) | ||||
−0.512904 | + | 0.858446i | \(0.671430\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 3.43134 | 0.334864 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 5.04757 | 0.487967 | 0.243983 | − | 0.969779i | \(-0.421546\pi\) | ||||
0.243983 | + | 0.969779i | \(0.421546\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 6.79459 | 0.650804 | 0.325402 | − | 0.945576i | \(-0.394500\pi\) | ||||
0.325402 | + | 0.945576i | \(0.394500\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −0.636747 | −0.0604373 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −8.06808 | −0.758981 | −0.379491 | − | 0.925196i | \(-0.623901\pi\) | ||||
−0.379491 | + | 0.925196i | \(0.623901\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −3.43134 | −0.319974 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −1.00000 | −0.0924500 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 26.9091 | 2.46675 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −4.04757 | −0.367961 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −4.63675 | −0.418081 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −15.6843 | −1.39176 | −0.695879 | − | 0.718159i | \(-0.744985\pi\) | ||||
−0.695879 | + | 0.718159i | \(0.744985\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 2.41082 | 0.212261 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 12.9308 | 1.12977 | 0.564883 | − | 0.825171i | \(-0.308921\pi\) | ||||
0.564883 | + | 0.825171i | \(0.308921\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2.72651 | 0.236418 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 1.00000 | 0.0860663 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 2.00000 | 0.170872 | 0.0854358 | − | 0.996344i | \(-0.472772\pi\) | ||||
0.0854358 | + | 0.996344i | \(0.472772\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 19.9102 | 1.68876 | 0.844382 | − | 0.535741i | \(-0.179968\pi\) | ||||
0.844382 | + | 0.535741i | \(0.179968\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 5.27349 | 0.444108 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 2.63675 | 0.220496 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −4.06808 | −0.337836 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 4.77407 | 0.393759 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 8.63675 | 0.707550 | 0.353775 | − | 0.935331i | \(-0.384898\pi\) | ||||
0.353775 | + | 0.935331i | \(0.384898\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −17.7253 | −1.44247 | −0.721234 | − | 0.692691i | \(-0.756425\pi\) | ||||
−0.721234 | + | 0.692691i | \(0.756425\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 7.84216 | 0.634001 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 9.27349 | 0.744865 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 20.5470 | 1.63983 | 0.819914 | − | 0.572487i | \(-0.194021\pi\) | ||||
0.819914 | + | 0.572487i | \(0.194021\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 11.4994 | 0.911963 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −11.7741 | −0.927927 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −4.22593 | −0.331000 | −0.165500 | − | 0.986210i | \(-0.552924\pi\) | ||||
−0.165500 | + | 0.986210i | \(0.552924\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −2.63675 | −0.205270 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −14.4108 | −1.11514 | −0.557571 | − | 0.830129i | \(-0.688267\pi\) | ||||
−0.557571 | + | 0.830129i | \(0.688267\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0.794590 | 0.0607638 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −6.00000 | −0.456172 | −0.228086 | − | 0.973641i | \(-0.573247\pi\) | ||||
−0.228086 | + | 0.973641i | \(0.573247\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 3.43134 | 0.259385 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −12.1362 | −0.912210 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −20.9308 | −1.56444 | −0.782219 | − | 0.623003i | \(-0.785912\pi\) | ||||
−0.782219 | + | 0.623003i | \(0.785912\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −5.08860 | −0.378233 | −0.189116 | − | 0.981955i | \(-0.560562\pi\) | ||||
−0.189116 | + | 0.981955i | \(0.560562\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −11.4994 | −0.850062 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −0.636747 | −0.0468146 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −20.6778 | −1.51211 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 3.43134 | 0.249593 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −13.7253 | −0.993131 | −0.496566 | − | 0.867999i | \(-0.665406\pi\) | ||||
−0.496566 | + | 0.867999i | \(0.665406\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −5.11565 | −0.368233 | −0.184116 | − | 0.982904i | \(-0.558942\pi\) | ||||
−0.184116 | + | 0.982904i | \(0.558942\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −1.00000 | −0.0716115 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −20.9988 | −1.49611 | −0.748053 | − | 0.663639i | \(-0.769011\pi\) | ||||
−0.748053 | + | 0.663639i | \(0.769011\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 9.58918 | 0.679759 | 0.339879 | − | 0.940469i | \(-0.389614\pi\) | ||||
0.339879 | + | 0.940469i | \(0.389614\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −6.41082 | −0.452184 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −13.9590 | −0.979727 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −4.63675 | −0.323844 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −3.43134 | −0.238494 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −2.09513 | −0.144923 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −8.82164 | −0.607307 | −0.303653 | − | 0.952783i | \(-0.598206\pi\) | ||||
−0.303653 | + | 0.952783i | \(0.598206\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −10.6367 | −0.728818 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 2.41082 | 0.164417 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 31.8205 | 2.16011 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 16.0681 | 1.08578 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −7.84216 | −0.527521 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −9.93192 | −0.665090 | −0.332545 | − | 0.943087i | \(-0.607907\pi\) | ||||
−0.332545 | + | 0.943087i | \(0.607907\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.00000 | 0.0666667 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 9.27349 | 0.615503 | 0.307752 | − | 0.951467i | \(-0.400423\pi\) | ||||
0.307752 | + | 0.951467i | \(0.400423\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 12.0681 | 0.797481 | 0.398741 | − | 0.917064i | \(-0.369447\pi\) | ||||
0.398741 | + | 0.917064i | \(0.369447\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −9.04757 | −0.595286 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 13.1157 | 0.859235 | 0.429617 | − | 0.903011i | \(-0.358648\pi\) | ||||
0.429617 | + | 0.903011i | \(0.358648\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 5.27349 | 0.344005 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 10.6367 | 0.690931 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −22.7729 | −1.47306 | −0.736529 | − | 0.676406i | \(-0.763536\pi\) | ||||
−0.736529 | + | 0.676406i | \(0.763536\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 6.82164 | 0.439420 | 0.219710 | − | 0.975565i | \(-0.429489\pi\) | ||||
0.219710 | + | 0.975565i | \(0.429489\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 4.77407 | 0.305004 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −0.794590 | −0.0505586 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −16.1362 | −1.02259 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 9.24644 | 0.583630 | 0.291815 | − | 0.956475i | \(-0.405741\pi\) | ||||
0.291815 | + | 0.956475i | \(0.405741\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 9.04757 | 0.568816 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 7.84216 | 0.491095 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −11.2464 | −0.701534 | −0.350767 | − | 0.936463i | \(-0.614079\pi\) | ||||
−0.350767 | + | 0.936463i | \(0.614079\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −2.18489 | −0.135763 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −4.06808 | −0.251808 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −22.0681 | −1.36078 | −0.680388 | − | 0.732852i | \(-0.738189\pi\) | ||||
−0.680388 | + | 0.732852i | \(0.738189\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 11.4994 | 0.706404 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 8.63675 | 0.528560 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −13.2054 | −0.805148 | −0.402574 | − | 0.915387i | \(-0.631884\pi\) | ||||
−0.402574 | + | 0.915387i | \(0.631884\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 14.0951 | 0.856218 | 0.428109 | − | 0.903727i | \(-0.359180\pi\) | ||||
0.428109 | + | 0.903727i | \(0.359180\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −3.43134 | −0.207674 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −2.63675 | −0.159002 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −30.2723 | −1.81889 | −0.909444 | − | 0.415826i | \(-0.863493\pi\) | ||||
−0.909444 | + | 0.415826i | \(0.863493\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 9.27349 | 0.555190 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 2.13617 | 0.127433 | 0.0637165 | − | 0.997968i | \(-0.479705\pi\) | ||||
0.0637165 | + | 0.997968i | \(0.479705\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 0.136167 | 0.00809431 | 0.00404715 | − | 0.999992i | \(-0.498712\pi\) | ||||
0.00404715 | + | 0.999992i | \(0.498712\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0.794590 | 0.0470675 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −15.9102 | −0.939152 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 44.4994 | 2.61761 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 12.2940 | 0.720688 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −15.2735 | −0.892287 | −0.446144 | − | 0.894961i | \(-0.647203\pi\) | ||||
−0.446144 | + | 0.894961i | \(0.647203\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −12.1362 | −0.706595 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −2.63675 | −0.153000 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 3.43134 | 0.198439 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 8.27233 | 0.476809 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 5.34158 | 0.306866 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −11.4994 | −0.658455 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 7.91024 | 0.451461 | 0.225731 | − | 0.974190i | \(-0.427523\pi\) | ||||
0.225731 | + | 0.974190i | \(0.427523\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −10.4108 | −0.592251 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 2.54699 | 0.144426 | 0.0722132 | − | 0.997389i | \(-0.476994\pi\) | ||||
0.0722132 | + | 0.997389i | \(0.476994\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 19.5892 | 1.10725 | 0.553623 | − | 0.832767i | \(-0.313245\pi\) | ||||
0.553623 | + | 0.832767i | \(0.313245\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 3.43134 | 0.193334 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −23.2735 | −1.30717 | −0.653585 | − | 0.756853i | \(-0.726736\pi\) | ||||
−0.653585 | + | 0.756853i | \(0.726736\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 10.7265 | 0.600569 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 5.04757 | 0.281728 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 6.23130 | 0.346719 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1.00000 | −0.0554700 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 6.79459 | 0.375742 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 18.0951 | 0.997617 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −20.4789 | −1.12562 | −0.562811 | − | 0.826586i | \(-0.690280\pi\) | ||||
−0.562811 | + | 0.826586i | \(0.690280\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −0.636747 | −0.0348935 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −6.41082 | −0.350260 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −25.6843 | −1.39911 | −0.699557 | − | 0.714577i | \(-0.746619\pi\) | ||||
−0.699557 | + | 0.714577i | \(0.746619\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −8.06808 | −0.438198 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −24.4519 | −1.32414 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −7.63791 | −0.412408 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −3.43134 | −0.184737 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 9.81511 | 0.526903 | 0.263451 | − | 0.964673i | \(-0.415139\pi\) | ||||
0.263451 | + | 0.964673i | \(0.415139\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 12.5199 | 0.670177 | 0.335088 | − | 0.942187i | \(-0.391234\pi\) | ||||
0.335088 | + | 0.942187i | \(0.391234\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1.00000 | −0.0533761 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −14.0000 | −0.745145 | −0.372572 | − | 0.928003i | \(-0.621524\pi\) | ||||
−0.372572 | + | 0.928003i | \(0.621524\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −10.6367 | −0.564540 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 26.9091 | 1.42418 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −28.1362 | −1.48497 | −0.742485 | − | 0.669863i | \(-0.766353\pi\) | ||||
−0.742485 | + | 0.669863i | \(0.766353\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.3686 | −0.966770 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −4.04757 | −0.212442 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 16.0681 | 0.841042 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 2.41082 | 0.125844 | 0.0629219 | − | 0.998018i | \(-0.479958\pi\) | ||||
0.0629219 | + | 0.998018i | \(0.479958\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −4.63675 | −0.241379 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 39.4584 | 2.04858 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −5.54815 | −0.287272 | −0.143636 | − | 0.989631i | \(-0.545879\pi\) | ||||
−0.143636 | + | 0.989631i | \(0.545879\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 1.00000 | 0.0516398 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 4.06808 | 0.209517 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −14.5199 | −0.745839 | −0.372920 | − | 0.927864i | \(-0.621643\pi\) | ||||
−0.372920 | + | 0.927864i | \(0.621643\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −15.6843 | −0.803532 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −22.8627 | −1.16823 | −0.584114 | − | 0.811672i | \(-0.698558\pi\) | ||||
−0.584114 | + | 0.811672i | \(0.698558\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −9.04757 | −0.461107 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 2.41082 | 0.122549 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 5.34158 | 0.270829 | 0.135414 | − | 0.990789i | \(-0.456763\pi\) | ||||
0.135414 | + | 0.990789i | \(0.456763\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −26.9091 | −1.36085 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 12.9308 | 0.652270 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 10.6367 | 0.535193 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −21.4584 | −1.07697 | −0.538483 | − | 0.842637i | \(-0.681002\pi\) | ||||
−0.538483 | + | 0.842637i | \(0.681002\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 2.72651 | 0.136496 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −17.3145 | −0.864646 | −0.432323 | − | 0.901719i | \(-0.642306\pi\) | ||||
−0.432323 | + | 0.901719i | \(0.642306\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −9.27349 | −0.461946 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 1.00000 | 0.0496904 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 1.67894 | 0.0832220 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 16.4108 | 0.811463 | 0.405731 | − | 0.913992i | \(-0.367017\pi\) | ||||
0.405731 | + | 0.913992i | \(0.367017\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 2.00000 | 0.0986527 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −41.6433 | −2.04913 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −16.1362 | −0.792093 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 19.9102 | 0.975009 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 25.7524 | 1.25809 | 0.629043 | − | 0.777370i | \(-0.283447\pi\) | ||||
0.629043 | + | 0.777370i | \(0.283447\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 13.4777 | 0.656865 | 0.328433 | − | 0.944527i | \(-0.393480\pi\) | ||||
0.328433 | + | 0.944527i | \(0.393480\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 5.27349 | 0.256406 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 7.84216 | 0.380400 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −39.4584 | −1.90953 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 2.63675 | 0.127303 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −24.2723 | −1.16916 | −0.584579 | − | 0.811337i | \(-0.698740\pi\) | ||||
−0.584579 | + | 0.811337i | \(0.698740\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 3.13733 | 0.150770 | 0.0753851 | − | 0.997154i | \(-0.475981\pi\) | ||||
0.0753851 | + | 0.997154i | \(0.475981\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −4.06808 | −0.195050 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −2.72651 | −0.130426 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 8.59571 | 0.410251 | 0.205125 | − | 0.978736i | \(-0.434240\pi\) | ||||
0.205125 | + | 0.978736i | \(0.434240\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 4.77407 | 0.227337 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 0.911399 | 0.0433019 | 0.0216509 | − | 0.999766i | \(-0.493108\pi\) | ||||
0.0216509 | + | 0.999766i | \(0.493108\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 8.63675 | 0.409421 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 8.63675 | 0.408504 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 38.8139 | 1.83174 | 0.915872 | − | 0.401471i | \(-0.131501\pi\) | ||||
0.915872 | + | 0.401471i | \(0.131501\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 12.2259 | 0.575696 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −17.7253 | −0.832809 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −3.43134 | −0.160864 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −6.25298 | −0.292502 | −0.146251 | − | 0.989248i | \(-0.546721\pi\) | ||||
−0.146251 | + | 0.989248i | \(0.546721\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 7.84216 | 0.366041 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −27.9513 | −1.30182 | −0.650910 | − | 0.759155i | \(-0.725613\pi\) | ||||
−0.650910 | + | 0.759155i | \(0.725613\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −11.8832 | −0.552259 | −0.276129 | − | 0.961120i | \(-0.589052\pi\) | ||||
−0.276129 | + | 0.961120i | \(0.589052\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 9.27349 | 0.430048 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −28.8680 | −1.33585 | −0.667927 | − | 0.744227i | \(-0.732818\pi\) | ||||
−0.667927 | + | 0.744227i | \(0.732818\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −21.9977 | −1.01576 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 20.5470 | 0.946755 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −6.35672 | −0.292282 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0.794590 | 0.0364583 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 11.4994 | 0.526522 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −12.0464 | −0.550414 | −0.275207 | − | 0.961385i | \(-0.588746\pi\) | ||||
−0.275207 | + | 0.961385i | \(0.588746\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0.636747 | 0.0290332 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −11.7741 | −0.535739 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 12.2940 | 0.558242 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 11.2518 | 0.509869 | 0.254934 | − | 0.966958i | \(-0.417946\pi\) | ||||
0.254934 | + | 0.966958i | \(0.417946\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −4.22593 | −0.191103 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 31.0259 | 1.40018 | 0.700089 | − | 0.714055i | \(-0.253143\pi\) | ||||
0.700089 | + | 0.714055i | \(0.253143\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −31.9025 | −1.43682 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −2.63675 | −0.118513 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −36.4983 | −1.63717 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −5.61623 | −0.251417 | −0.125708 | − | 0.992067i | \(-0.540120\pi\) | ||||
−0.125708 | + | 0.992067i | \(0.540120\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −14.4108 | −0.643828 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −3.52110 | −0.156998 | −0.0784990 | − | 0.996914i | \(-0.525013\pi\) | ||||
−0.0784990 | + | 0.996914i | \(0.525013\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 5.34158 | 0.237697 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 1.00000 | 0.0444116 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −13.7741 | −0.610525 | −0.305263 | − | 0.952268i | \(-0.598744\pi\) | ||||
−0.305263 | + | 0.952268i | \(0.598744\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 55.1350 | 2.43903 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0.794590 | 0.0350820 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −10.4108 | −0.458756 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −13.9049 | −0.611535 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −6.00000 | −0.263371 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 25.3145 | 1.10905 | 0.554525 | − | 0.832167i | \(-0.312900\pi\) | ||||
0.554525 | + | 0.832167i | \(0.312900\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −4.00000 | −0.174908 | −0.0874539 | − | 0.996169i | \(-0.527873\pi\) | ||||
−0.0874539 | + | 0.996169i | \(0.527873\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 3.43134 | 0.149756 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 72.7242 | 3.16792 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −11.2259 | −0.488084 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −12.1362 | −0.526665 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 4.63675 | 0.200840 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 5.04757 | 0.218225 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −20.9308 | −0.903229 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −12.5880 | −0.542204 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −26.6151 | −1.14427 | −0.572136 | − | 0.820159i | \(-0.693885\pi\) | ||||
−0.572136 | + | 0.820159i | \(0.693885\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −5.08860 | −0.218373 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 6.79459 | 0.291048 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −17.7253 | −0.757881 | −0.378941 | − | 0.925421i | \(-0.623712\pi\) | ||||
−0.378941 | + | 0.925421i | \(0.623712\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −11.4994 | −0.490783 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −3.23246 | −0.137707 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 36.4983 | 1.55206 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −0.636747 | −0.0270284 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 30.2723 | 1.28268 | 0.641340 | − | 0.767257i | \(-0.278379\pi\) | ||||
0.641340 | + | 0.767257i | \(0.278379\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −2.41082 | −0.101967 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −20.6778 | −0.873017 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 22.6367 | 0.954025 | 0.477013 | − | 0.878896i | \(-0.341720\pi\) | ||||
0.477013 | + | 0.878896i | \(0.341720\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −8.06808 | −0.339427 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 3.43134 | 0.144103 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 20.0410 | 0.840164 | 0.420082 | − | 0.907486i | \(-0.362001\pi\) | ||||
0.420082 | + | 0.907486i | \(0.362001\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 20.3621 | 0.852127 | 0.426064 | − | 0.904693i | \(-0.359900\pi\) | ||||
0.426064 | + | 0.904693i | \(0.359900\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −13.7253 | −0.573385 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −3.43134 | −0.143097 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 2.70483 | 0.112604 | 0.0563018 | − | 0.998414i | \(-0.482069\pi\) | ||||
0.0563018 | + | 0.998414i | \(0.482069\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −5.11565 | −0.212599 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −55.3686 | −2.29708 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −30.3211 | −1.25577 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −1.00000 | −0.0413449 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 33.2735 | 1.37334 | 0.686672 | − | 0.726967i | \(-0.259071\pi\) | ||||
0.686672 | + | 0.726967i | \(0.259071\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 7.36863 | 0.303619 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −20.9988 | −0.863777 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −28.2313 | −1.15932 | −0.579660 | − | 0.814858i | \(-0.696815\pi\) | ||||
−0.579660 | + | 0.814858i | \(0.696815\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 26.9091 | 1.10316 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 9.58918 | 0.392459 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 29.0940 | 1.18875 | 0.594374 | − | 0.804189i | \(-0.297400\pi\) | ||||
0.594374 | + | 0.804189i | \(0.297400\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 46.0464 | 1.87827 | 0.939136 | − | 0.343545i | \(-0.111628\pi\) | ||||
0.939136 | + | 0.343545i | \(0.111628\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −6.41082 | −0.261069 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −4.04757 | −0.164557 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 24.1362 | 0.979657 | 0.489828 | − | 0.871819i | \(-0.337059\pi\) | ||||
0.489828 | + | 0.871819i | \(0.337059\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −13.9590 | −0.565646 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −5.27349 | −0.213343 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 3.73304 | 0.150776 | 0.0753880 | − | 0.997154i | \(-0.475980\pi\) | ||||
0.0753880 | + | 0.997154i | \(0.475980\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −4.63675 | −0.186972 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −13.3686 | −0.538201 | −0.269100 | − | 0.963112i | \(-0.586726\pi\) | ||||
−0.269100 | + | 0.963112i | \(0.586726\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −21.8886 | −0.879776 | −0.439888 | − | 0.898053i | \(-0.644982\pi\) | ||||
−0.439888 | + | 0.898053i | \(0.644982\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −3.43134 | −0.137695 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 29.6356 | 1.18732 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −2.09513 | −0.0836716 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −4.99347 | −0.199103 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 21.5892 | 0.859452 | 0.429726 | − | 0.902959i | \(-0.358610\pi\) | ||||
0.429726 | + | 0.902959i | \(0.358610\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −8.82164 | −0.350629 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −15.6843 | −0.622413 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −4.77407 | −0.189156 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −10.6367 | −0.420783 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −5.54815 | −0.219139 | −0.109569 | − | 0.993979i | \(-0.534947\pi\) | ||||
−0.109569 | + | 0.993979i | \(0.534947\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −34.6367 | −1.36594 | −0.682970 | − | 0.730446i | \(-0.739312\pi\) | ||||
−0.682970 | + | 0.730446i | \(0.739312\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 2.41082 | 0.0949259 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 29.9783 | 1.17857 | 0.589285 | − | 0.807925i | \(-0.299410\pi\) | ||||
0.589285 | + | 0.807925i | \(0.299410\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 32.0000 | 1.25611 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 31.8205 | 1.24714 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 32.6832 | 1.27899 | 0.639495 | − | 0.768795i | \(-0.279143\pi\) | ||||
0.639495 | + | 0.768795i | \(0.279143\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 12.9308 | 0.505247 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 16.0681 | 0.626876 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 23.9296 | 0.932165 | 0.466082 | − | 0.884741i | \(-0.345665\pi\) | ||||
0.466082 | + | 0.884741i | \(0.345665\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −34.1632 | −1.32880 | −0.664398 | − | 0.747379i | \(-0.731312\pi\) | ||||
−0.664398 | + | 0.747379i | \(0.731312\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −7.84216 | −0.304564 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 2.72651 | 0.105729 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 13.9590 | 0.540493 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −9.93192 | −0.383990 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 30.3211 | 1.17053 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −6.90371 | −0.266118 | −0.133059 | − | 0.991108i | \(-0.542480\pi\) | ||||
−0.133059 | + | 0.991108i | \(0.542480\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 1.00000 | 0.0384900 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 49.2789 | 1.89394 | 0.946970 | − | 0.321321i | \(-0.104127\pi\) | ||||
0.946970 | + | 0.321321i | \(0.104127\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 42.1849 | 1.61891 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 9.27349 | 0.355361 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 3.04219 | 0.116406 | 0.0582031 | − | 0.998305i | \(-0.481463\pi\) | ||||
0.0582031 | + | 0.998305i | \(0.481463\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 2.00000 | 0.0764161 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 12.0681 | 0.460426 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −11.4994 | −0.438093 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 13.8886 | 0.528346 | 0.264173 | − | 0.964475i | \(-0.414901\pi\) | ||||
0.264173 | + | 0.964475i | \(0.414901\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −9.04757 | −0.343689 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 19.9102 | 0.755238 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −36.3621 | −1.37731 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 13.1157 | 0.496079 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −5.20541 | −0.196606 | −0.0983028 | − | 0.995157i | \(-0.531341\pi\) | ||||
−0.0983028 | + | 0.995157i | \(0.531341\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −0.505953 | −0.0190824 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 5.27349 | 0.198611 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 18.3288 | 0.689324 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −19.7524 | −0.741817 | −0.370908 | − | 0.928669i | \(-0.620954\pi\) | ||||
−0.370908 | + | 0.928669i | \(0.620954\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 10.6367 | 0.398909 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −31.8205 | −1.19169 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 2.63675 | 0.0986087 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −22.7729 | −0.850470 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −4.13617 | −0.154253 | −0.0771265 | − | 0.997021i | \(-0.524575\pi\) | ||||
−0.0771265 | + | 0.997021i | \(0.524575\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −35.7230 | −1.33040 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 6.82164 | 0.253700 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −4.06808 | −0.151085 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 6.09513 | 0.226056 | 0.113028 | − | 0.993592i | \(-0.463945\pi\) | ||||
0.113028 | + | 0.993592i | \(0.463945\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 18.9060 | 0.699265 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −40.0054 | −1.47763 | −0.738816 | − | 0.673907i | \(-0.764615\pi\) | ||||
−0.738816 | + | 0.673907i | \(0.764615\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 4.77407 | 0.176094 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 16.9037 | 0.622656 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 12.0270 | 0.442422 | 0.221211 | − | 0.975226i | \(-0.428999\pi\) | ||||
0.221211 | + | 0.975226i | \(0.428999\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −0.794590 | −0.0291900 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 10.0410 | 0.368370 | 0.184185 | − | 0.982892i | \(-0.441035\pi\) | ||||
0.184185 | + | 0.982892i | \(0.441035\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 8.63675 | 0.316426 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −16.1362 | −0.590391 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 17.3199 | 0.632855 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 12.6778 | 0.462619 | 0.231309 | − | 0.972880i | \(-0.425699\pi\) | ||||
0.231309 | + | 0.972880i | \(0.425699\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 9.24644 | 0.336959 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −17.7253 | −0.645091 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 13.6302 | 0.495399 | 0.247699 | − | 0.968837i | \(-0.420326\pi\) | ||||
0.247699 | + | 0.968837i | \(0.420326\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 9.04757 | 0.328406 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −11.8615 | −0.429980 | −0.214990 | − | 0.976616i | \(-0.568972\pi\) | ||||
−0.214990 | + | 0.976616i | \(0.568972\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 23.3145 | 0.844043 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 7.84216 | 0.283534 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 12.1362 | 0.438212 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 20.9988 | 0.757238 | 0.378619 | − | 0.925553i | \(-0.376399\pi\) | ||||
0.378619 | + | 0.925553i | \(0.376399\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −11.2464 | −0.405031 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 14.4519 | 0.519797 | 0.259899 | − | 0.965636i | \(-0.416311\pi\) | ||||
0.259899 | + | 0.965636i | \(0.416311\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 9.27349 | 0.333114 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −2.18489 | −0.0783826 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −3.68431 | −0.132004 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 28.0464 | 1.00358 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −4.06808 | −0.145381 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 20.5470 | 0.733353 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −10.5470 | −0.375959 | −0.187980 | − | 0.982173i | \(-0.560194\pi\) | ||||
−0.187980 | + | 0.982173i | \(0.560194\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −22.0681 | −0.785645 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −27.6843 | −0.984341 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 11.4994 | 0.408356 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 11.4994 | 0.407842 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 40.7729 | 1.44425 | 0.722125 | − | 0.691762i | \(-0.243165\pi\) | ||||
0.722125 | + | 0.691762i | \(0.243165\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 41.3556 | 1.46305 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 8.63675 | 0.305164 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −42.3675 | −1.49512 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −11.7741 | −0.414982 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −13.2054 | −0.464852 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 20.2747 | 0.712819 | 0.356409 | − | 0.934330i | \(-0.384001\pi\) | ||||
0.356409 | + | 0.934330i | \(0.384001\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −15.0259 | −0.527630 | −0.263815 | − | 0.964573i | \(-0.584981\pi\) | ||||
−0.263815 | + | 0.964573i | \(0.584981\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 14.0951 | 0.494338 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −4.22593 | −0.148028 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1.91561 | 0.0670188 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −3.43134 | −0.119901 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −2.36209 | −0.0824377 | −0.0412188 | − | 0.999150i | \(-0.513124\pi\) | ||||
−0.0412188 | + | 0.999150i | \(0.513124\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −16.1362 | −0.562471 | −0.281236 | − | 0.959639i | \(-0.590744\pi\) | ||||
−0.281236 | + | 0.959639i | \(0.590744\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −2.63675 | −0.0917997 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 24.5880 | 0.855009 | 0.427505 | − | 0.904013i | \(-0.359393\pi\) | ||||
0.427505 | + | 0.904013i | \(0.359393\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −22.8216 | −0.792628 | −0.396314 | − | 0.918115i | \(-0.629711\pi\) | ||||
−0.396314 | + | 0.918115i | \(0.629711\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −30.2723 | −1.05014 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 37.4390 | 1.29719 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −14.4108 | −0.498707 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 9.27349 | 0.320539 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 46.3211 | 1.59918 | 0.799590 | − | 0.600546i | \(-0.205050\pi\) | ||||
0.799590 | + | 0.600546i | \(0.205050\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −12.4507 | −0.429334 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 2.13617 | 0.0735735 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 1.00000 | 0.0344010 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −13.8886 | −0.477217 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0.136167 | 0.00467325 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 2.18489 | 0.0748972 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 47.1837 | 1.61554 | 0.807770 | − | 0.589498i | \(-0.200674\pi\) | ||||
0.807770 | + | 0.589498i | \(0.200674\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0.794590 | 0.0271744 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −11.8422 | −0.404520 | −0.202260 | − | 0.979332i | \(-0.564829\pi\) | ||||
−0.202260 | + | 0.979332i | \(0.564829\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 10.3211 | 0.352150 | 0.176075 | − | 0.984377i | \(-0.443660\pi\) | ||||
0.176075 | + | 0.984377i | \(0.443660\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −15.9102 | −0.542220 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 1.13733 | 0.0387150 | 0.0193575 | − | 0.999813i | \(-0.493838\pi\) | ||||
0.0193575 | + | 0.999813i | \(0.493838\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −6.00000 | −0.204006 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 44.4994 | 1.51128 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −28.0464 | −0.951409 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 6.41082 | 0.217222 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 12.2940 | 0.416089 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 3.43134 | 0.116000 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −54.5447 | −1.84184 | −0.920921 | − | 0.389749i | \(-0.872562\pi\) | ||||
−0.920921 | + | 0.389749i | \(0.872562\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −15.2735 | −0.515162 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 48.9555 | 1.64935 | 0.824676 | − | 0.565605i | \(-0.191357\pi\) | ||||
0.824676 | + | 0.565605i | \(0.191357\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 27.3686 | 0.921028 | 0.460514 | − | 0.887653i | \(-0.347665\pi\) | ||||
0.460514 | + | 0.887653i | \(0.347665\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −12.1362 | −0.407953 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −21.5265 | −0.722788 | −0.361394 | − | 0.932413i | \(-0.617699\pi\) | ||||
−0.361394 | + | 0.932413i | \(0.617699\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −53.8182 | −1.80500 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −2.63675 | −0.0883343 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 4.19027 | 0.140222 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −20.9308 | −0.699638 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 3.43134 | 0.114569 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −37.7253 | −1.25821 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 90.1803 | 3.00434 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 8.27233 | 0.275286 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −5.08860 | −0.169151 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −39.6843 | −1.31770 | −0.658848 | − | 0.752276i | \(-0.728956\pi\) | ||||
−0.658848 | + | 0.752276i | \(0.728956\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 5.34158 | 0.177169 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −4.13617 | −0.137037 | −0.0685187 | − | 0.997650i | \(-0.521827\pi\) | ||||
−0.0685187 | + | 0.997650i | \(0.521827\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 42.5470 | 1.40810 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −11.4994 | −0.380159 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 44.3698 | 1.46522 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 17.6789 | 0.583174 | 0.291587 | − | 0.956544i | \(-0.405817\pi\) | ||||
0.291587 | + | 0.956544i | \(0.405817\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 7.91024 | 0.260651 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 10.6367 | 0.350113 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −0.636747 | −0.0209361 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −10.4108 | −0.341936 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 27.8151 | 0.912584 | 0.456292 | − | 0.889830i | \(-0.349177\pi\) | ||||
0.456292 | + | 0.889830i | \(0.349177\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 3.79343 | 0.124325 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 2.54699 | 0.0833846 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −20.6778 | −0.676236 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −54.5447 | −1.78190 | −0.890948 | − | 0.454105i | \(-0.849959\pi\) | ||||
−0.890948 | + | 0.454105i | \(0.849959\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 19.5892 | 0.639269 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −12.1849 | −0.397216 | −0.198608 | − | 0.980079i | \(-0.563642\pi\) | ||||
−0.198608 | + | 0.980079i | \(0.563642\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 15.9102 | 0.518109 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 3.43134 | 0.111621 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 39.5048 | 1.28373 | 0.641867 | − | 0.766816i | \(-0.278160\pi\) | ||||
0.641867 | + | 0.766816i | \(0.278160\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −16.0681 | −0.521592 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −23.2735 | −0.754695 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 19.0205 | 0.616135 | 0.308067 | − | 0.951365i | \(-0.400318\pi\) | ||||
0.308067 | + | 0.951365i | \(0.400318\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −13.7253 | −0.444142 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 10.7265 | 0.346739 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 6.86267 | 0.221607 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 54.9977 | 1.77412 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 5.04757 | 0.162656 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −5.11565 | −0.164679 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −38.3404 | −1.23294 | −0.616472 | − | 0.787377i | \(-0.711439\pi\) | ||||
−0.616472 | + | 0.787377i | \(0.711439\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 6.23130 | 0.200178 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 15.7114 | 0.504202 | 0.252101 | − | 0.967701i | \(-0.418879\pi\) | ||||
0.252101 | + | 0.967701i | \(0.418879\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 68.3187 | 2.19020 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −1.00000 | −0.0320256 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 53.9566 | 1.72623 | 0.863113 | − | 0.505011i | \(-0.168511\pi\) | ||||
0.863113 | + | 0.505011i | \(0.168511\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −22.7729 | −0.727825 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 6.79459 | 0.216935 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −45.0399 | −1.43655 | −0.718274 | − | 0.695760i | \(-0.755068\pi\) | ||||
−0.718274 | + | 0.695760i | \(0.755068\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −20.9988 | −0.669079 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 18.0951 | 0.575974 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −8.27233 | −0.263045 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 7.63791 | 0.242626 | 0.121313 | − | 0.992614i | \(-0.461290\pi\) | ||||
0.121313 | + | 0.992614i | \(0.461290\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −20.4789 | −0.649878 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 9.58918 | 0.303997 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −16.0951 | −0.509738 | −0.254869 | − | 0.966976i | \(-0.582032\pi\) | ||||
−0.254869 | + | 0.966976i | \(0.582032\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −0.636747 | −0.0201458 |
(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 | 1560.2.a.q.1.3 | ✓ | 3 | |
3.2 | odd | 2 | 4680.2.a.bh.1.3 | 3 | |||
4.3 | odd | 2 | 3120.2.a.bi.1.1 | 3 | |||
5.4 | even | 2 | 7800.2.a.bi.1.1 | 3 | |||
12.11 | even | 2 | 9360.2.a.cy.1.1 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1560.2.a.q.1.3 | ✓ | 3 | 1.1 | even | 1 | trivial | |
3120.2.a.bi.1.1 | 3 | 4.3 | odd | 2 | |||
4680.2.a.bh.1.3 | 3 | 3.2 | odd | 2 | |||
7800.2.a.bi.1.1 | 3 | 5.4 | even | 2 | |||
9360.2.a.cy.1.1 | 3 | 12.11 | even | 2 |