Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [9075,2,Mod(1,9075)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(9075, 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("9075.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 9075 = 3 \cdot 5^{2} \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 9075.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: | \(72.4642398343\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.5725.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} - 8x^{2} + 6x + 11 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 165) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(2.55157\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 9075.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.933531 | 0.660106 | 0.330053 | − | 0.943962i | \(-0.392933\pi\) | ||||
0.330053 | + | 0.943962i | \(0.392933\pi\) | |||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | −1.12852 | −0.564260 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0.933531 | 0.381113 | ||||||||
\(7\) | 2.04108 | 0.771456 | 0.385728 | − | 0.922613i | \(-0.373950\pi\) | ||||
0.385728 | + | 0.922613i | \(0.373950\pi\) | |||||||
\(8\) | −2.92057 | −1.03258 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | −1.12852 | −0.325775 | ||||||||
\(13\) | 1.44843 | 0.401724 | 0.200862 | − | 0.979620i | \(-0.435626\pi\) | ||||
0.200862 | + | 0.979620i | \(0.435626\pi\) | |||||||
\(14\) | 1.90541 | 0.509243 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.469405 | −0.117351 | ||||||||
\(17\) | −0.867063 | −0.210294 | −0.105147 | − | 0.994457i | \(-0.533531\pi\) | ||||
−0.105147 | + | 0.994457i | \(0.533531\pi\) | |||||||
\(18\) | 0.933531 | 0.220035 | ||||||||
\(19\) | 3.12852 | 0.717732 | 0.358866 | − | 0.933389i | \(-0.383164\pi\) | ||||
0.358866 | + | 0.933389i | \(0.383164\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 2.04108 | 0.445400 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 4.70547 | 0.981159 | 0.490580 | − | 0.871396i | \(-0.336785\pi\) | ||||
0.490580 | + | 0.871396i | \(0.336785\pi\) | |||||||
\(24\) | −2.92057 | −0.596159 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 1.35216 | 0.265180 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | −2.30340 | −0.435301 | ||||||||
\(29\) | 2.03835 | 0.378512 | 0.189256 | − | 0.981928i | \(-0.439392\pi\) | ||||
0.189256 | + | 0.981928i | \(0.439392\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 10.6136 | 1.90626 | 0.953131 | − | 0.302558i | \(-0.0978407\pi\) | ||||
0.953131 | + | 0.302558i | \(0.0978407\pi\) | |||||||
\(32\) | 5.40294 | 0.955113 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −0.809430 | −0.138816 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −1.12852 | −0.188087 | ||||||||
\(37\) | −4.15664 | −0.683347 | −0.341674 | − | 0.939819i | \(-0.610994\pi\) | ||||
−0.341674 | + | 0.939819i | \(0.610994\pi\) | |||||||
\(38\) | 2.92057 | 0.473779 | ||||||||
\(39\) | 1.44843 | 0.231935 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −0.805012 | −0.125722 | −0.0628609 | − | 0.998022i | \(-0.520022\pi\) | ||||
−0.0628609 | + | 0.998022i | \(0.520022\pi\) | |||||||
\(42\) | 1.90541 | 0.294011 | ||||||||
\(43\) | 2.34089 | 0.356982 | 0.178491 | − | 0.983942i | \(-0.442878\pi\) | ||||
0.178491 | + | 0.983942i | \(0.442878\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 4.39271 | 0.647669 | ||||||||
\(47\) | −10.3803 | −1.51412 | −0.757060 | − | 0.653346i | \(-0.773365\pi\) | ||||
−0.757060 | + | 0.653346i | \(0.773365\pi\) | |||||||
\(48\) | −0.469405 | −0.0677528 | ||||||||
\(49\) | −2.83399 | −0.404856 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −0.867063 | −0.121413 | ||||||||
\(52\) | −1.63459 | −0.226676 | ||||||||
\(53\) | −7.21596 | −0.991188 | −0.495594 | − | 0.868554i | \(-0.665050\pi\) | ||||
−0.495594 | + | 0.868554i | \(0.665050\pi\) | |||||||
\(54\) | 0.933531 | 0.127038 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −5.96112 | −0.796588 | ||||||||
\(57\) | 3.12852 | 0.414383 | ||||||||
\(58\) | 1.90286 | 0.249858 | ||||||||
\(59\) | −8.32351 | −1.08363 | −0.541814 | − | 0.840498i | \(-0.682262\pi\) | ||||
−0.541814 | + | 0.840498i | \(0.682262\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −8.76752 | −1.12257 | −0.561283 | − | 0.827624i | \(-0.689692\pi\) | ||||
−0.561283 | + | 0.827624i | \(0.689692\pi\) | |||||||
\(62\) | 9.90814 | 1.25834 | ||||||||
\(63\) | 2.04108 | 0.257152 | ||||||||
\(64\) | 5.98262 | 0.747828 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 3.15664 | 0.385645 | 0.192822 | − | 0.981234i | \(-0.438236\pi\) | ||||
0.192822 | + | 0.981234i | \(0.438236\pi\) | |||||||
\(68\) | 0.978497 | 0.118660 | ||||||||
\(69\) | 4.70547 | 0.566472 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 12.8707 | 1.52747 | 0.763733 | − | 0.645532i | \(-0.223364\pi\) | ||||
0.763733 | + | 0.645532i | \(0.223364\pi\) | |||||||
\(72\) | −2.92057 | −0.344193 | ||||||||
\(73\) | 14.7184 | 1.72266 | 0.861331 | − | 0.508044i | \(-0.169631\pi\) | ||||
0.861331 | + | 0.508044i | \(0.169631\pi\) | |||||||
\(74\) | −3.88035 | −0.451082 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −3.53059 | −0.404987 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 1.35216 | 0.153102 | ||||||||
\(79\) | −16.9992 | −1.91256 | −0.956278 | − | 0.292458i | \(-0.905527\pi\) | ||||
−0.956278 | + | 0.292458i | \(0.905527\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −0.751504 | −0.0829897 | ||||||||
\(83\) | −6.14148 | −0.674115 | −0.337058 | − | 0.941484i | \(-0.609432\pi\) | ||||
−0.337058 | + | 0.941484i | \(0.609432\pi\) | |||||||
\(84\) | −2.30340 | −0.251321 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 2.18529 | 0.235646 | ||||||||
\(87\) | 2.03835 | 0.218534 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 3.77194 | 0.399825 | 0.199913 | − | 0.979814i | \(-0.435934\pi\) | ||||
0.199913 | + | 0.979814i | \(0.435934\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.95637 | 0.309912 | ||||||||
\(92\) | −5.31022 | −0.553628 | ||||||||
\(93\) | 10.6136 | 1.10058 | ||||||||
\(94\) | −9.69031 | −0.999480 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 5.40294 | 0.551435 | ||||||||
\(97\) | 1.93795 | 0.196769 | 0.0983845 | − | 0.995148i | \(-0.468633\pi\) | ||||
0.0983845 | + | 0.995148i | \(0.468633\pi\) | |||||||
\(98\) | −2.64562 | −0.267248 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −5.25176 | −0.522570 | −0.261285 | − | 0.965262i | \(-0.584146\pi\) | ||||
−0.261285 | + | 0.965262i | \(0.584146\pi\) | |||||||
\(102\) | −0.809430 | −0.0801455 | ||||||||
\(103\) | 13.6007 | 1.34011 | 0.670056 | − | 0.742310i | \(-0.266270\pi\) | ||||
0.670056 | + | 0.742310i | \(0.266270\pi\) | |||||||
\(104\) | −4.23026 | −0.414811 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −6.73632 | −0.654290 | ||||||||
\(107\) | 9.99063 | 0.965831 | 0.482915 | − | 0.875667i | \(-0.339578\pi\) | ||||
0.482915 | + | 0.875667i | \(0.339578\pi\) | |||||||
\(108\) | −1.12852 | −0.108592 | ||||||||
\(109\) | −6.75183 | −0.646708 | −0.323354 | − | 0.946278i | \(-0.604811\pi\) | ||||
−0.323354 | + | 0.946278i | \(0.604811\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −4.15664 | −0.394531 | ||||||||
\(112\) | −0.958094 | −0.0905314 | ||||||||
\(113\) | 5.24461 | 0.493371 | 0.246686 | − | 0.969096i | \(-0.420658\pi\) | ||||
0.246686 | + | 0.969096i | \(0.420658\pi\) | |||||||
\(114\) | 2.92057 | 0.273537 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −2.30032 | −0.213579 | ||||||||
\(117\) | 1.44843 | 0.133908 | ||||||||
\(118\) | −7.77025 | −0.715310 | ||||||||
\(119\) | −1.76974 | −0.162232 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | −8.18476 | −0.741013 | ||||||||
\(123\) | −0.805012 | −0.0725855 | ||||||||
\(124\) | −11.9777 | −1.07563 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 1.90541 | 0.169748 | ||||||||
\(127\) | 20.6751 | 1.83462 | 0.917311 | − | 0.398172i | \(-0.130355\pi\) | ||||
0.917311 | + | 0.398172i | \(0.130355\pi\) | |||||||
\(128\) | −5.22091 | −0.461468 | ||||||||
\(129\) | 2.34089 | 0.206104 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 20.3089 | 1.77439 | 0.887197 | − | 0.461392i | \(-0.152650\pi\) | ||||
0.887197 | + | 0.461392i | \(0.152650\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 6.38556 | 0.553698 | ||||||||
\(134\) | 2.94682 | 0.254567 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 2.53232 | 0.217144 | ||||||||
\(137\) | 3.47982 | 0.297301 | 0.148650 | − | 0.988890i | \(-0.452507\pi\) | ||||
0.148650 | + | 0.988890i | \(0.452507\pi\) | |||||||
\(138\) | 4.39271 | 0.373932 | ||||||||
\(139\) | 2.73086 | 0.231629 | 0.115814 | − | 0.993271i | \(-0.463052\pi\) | ||||
0.115814 | + | 0.993271i | \(0.463052\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −10.3803 | −0.874177 | ||||||||
\(142\) | 12.0152 | 1.00829 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −0.469405 | −0.0391171 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 13.7401 | 1.13714 | ||||||||
\(147\) | −2.83399 | −0.233744 | ||||||||
\(148\) | 4.69085 | 0.385585 | ||||||||
\(149\) | −9.10841 | −0.746190 | −0.373095 | − | 0.927793i | \(-0.621703\pi\) | ||||
−0.373095 | + | 0.927793i | \(0.621703\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 21.5744 | 1.75570 | 0.877852 | − | 0.478933i | \(-0.158976\pi\) | ||||
0.877852 | + | 0.478933i | \(0.158976\pi\) | |||||||
\(152\) | −9.13706 | −0.741114 | ||||||||
\(153\) | −0.867063 | −0.0700979 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −1.63459 | −0.130872 | ||||||||
\(157\) | 23.7940 | 1.89896 | 0.949482 | − | 0.313821i | \(-0.101609\pi\) | ||||
0.949482 | + | 0.313821i | \(0.101609\pi\) | |||||||
\(158\) | −15.8693 | −1.26249 | ||||||||
\(159\) | −7.21596 | −0.572263 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 9.60425 | 0.756921 | ||||||||
\(162\) | 0.933531 | 0.0733451 | ||||||||
\(163\) | 1.80332 | 0.141247 | 0.0706236 | − | 0.997503i | \(-0.477501\pi\) | ||||
0.0706236 | + | 0.997503i | \(0.477501\pi\) | |||||||
\(164\) | 0.908472 | 0.0709397 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −5.73326 | −0.444988 | ||||||||
\(167\) | 24.5874 | 1.90263 | 0.951315 | − | 0.308220i | \(-0.0997333\pi\) | ||||
0.951315 | + | 0.308220i | \(0.0997333\pi\) | |||||||
\(168\) | −5.96112 | −0.459910 | ||||||||
\(169\) | −10.9020 | −0.838618 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 3.12852 | 0.239244 | ||||||||
\(172\) | −2.64174 | −0.201430 | ||||||||
\(173\) | 16.2115 | 1.23254 | 0.616270 | − | 0.787535i | \(-0.288643\pi\) | ||||
0.616270 | + | 0.787535i | \(0.288643\pi\) | |||||||
\(174\) | 1.90286 | 0.144256 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −8.32351 | −0.625633 | ||||||||
\(178\) | 3.52123 | 0.263927 | ||||||||
\(179\) | 16.9697 | 1.26837 | 0.634186 | − | 0.773181i | \(-0.281335\pi\) | ||||
0.634186 | + | 0.773181i | \(0.281335\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 18.3508 | 1.36400 | 0.682002 | − | 0.731350i | \(-0.261109\pi\) | ||||
0.682002 | + | 0.731350i | \(0.261109\pi\) | |||||||
\(182\) | 2.75986 | 0.204575 | ||||||||
\(183\) | −8.76752 | −0.648114 | ||||||||
\(184\) | −13.7427 | −1.01312 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 9.90814 | 0.726500 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 11.7143 | 0.854356 | ||||||||
\(189\) | 2.04108 | 0.148467 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −15.3985 | −1.11420 | −0.557099 | − | 0.830446i | \(-0.688086\pi\) | ||||
−0.557099 | + | 0.830446i | \(0.688086\pi\) | |||||||
\(192\) | 5.98262 | 0.431759 | ||||||||
\(193\) | 7.37942 | 0.531182 | 0.265591 | − | 0.964086i | \(-0.414433\pi\) | ||||
0.265591 | + | 0.964086i | \(0.414433\pi\) | |||||||
\(194\) | 1.80914 | 0.129888 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 3.19822 | 0.228444 | ||||||||
\(197\) | −3.14676 | −0.224197 | −0.112099 | − | 0.993697i | \(-0.535757\pi\) | ||||
−0.112099 | + | 0.993697i | \(0.535757\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −3.25757 | −0.230923 | −0.115462 | − | 0.993312i | \(-0.536835\pi\) | ||||
−0.115462 | + | 0.993312i | \(0.536835\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 3.15664 | 0.222652 | ||||||||
\(202\) | −4.90268 | −0.344951 | ||||||||
\(203\) | 4.16043 | 0.292005 | ||||||||
\(204\) | 0.978497 | 0.0685085 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 12.6966 | 0.884617 | ||||||||
\(207\) | 4.70547 | 0.327053 | ||||||||
\(208\) | −0.679903 | −0.0471428 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 19.9242 | 1.37164 | 0.685818 | − | 0.727773i | \(-0.259445\pi\) | ||||
0.685818 | + | 0.727773i | \(0.259445\pi\) | |||||||
\(212\) | 8.14335 | 0.559288 | ||||||||
\(213\) | 12.8707 | 0.881883 | ||||||||
\(214\) | 9.32657 | 0.637551 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −2.92057 | −0.198720 | ||||||||
\(217\) | 21.6632 | 1.47060 | ||||||||
\(218\) | −6.30305 | −0.426896 | ||||||||
\(219\) | 14.7184 | 0.994580 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1.25588 | −0.0844799 | ||||||||
\(222\) | −3.88035 | −0.260432 | ||||||||
\(223\) | −10.4801 | −0.701802 | −0.350901 | − | 0.936412i | \(-0.614125\pi\) | ||||
−0.350901 | + | 0.936412i | \(0.614125\pi\) | |||||||
\(224\) | 11.0278 | 0.736828 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 4.89601 | 0.325678 | ||||||||
\(227\) | −17.6731 | −1.17301 | −0.586503 | − | 0.809947i | \(-0.699496\pi\) | ||||
−0.586503 | + | 0.809947i | \(0.699496\pi\) | |||||||
\(228\) | −3.53059 | −0.233819 | ||||||||
\(229\) | 4.12967 | 0.272897 | 0.136448 | − | 0.990647i | \(-0.456431\pi\) | ||||
0.136448 | + | 0.990647i | \(0.456431\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −5.95314 | −0.390843 | ||||||||
\(233\) | −13.5990 | −0.890898 | −0.445449 | − | 0.895307i | \(-0.646956\pi\) | ||||
−0.445449 | + | 0.895307i | \(0.646956\pi\) | |||||||
\(234\) | 1.35216 | 0.0883934 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 9.39324 | 0.611448 | ||||||||
\(237\) | −16.9992 | −1.10422 | ||||||||
\(238\) | −1.65211 | −0.107090 | ||||||||
\(239\) | 8.00632 | 0.517886 | 0.258943 | − | 0.965893i | \(-0.416626\pi\) | ||||
0.258943 | + | 0.965893i | \(0.416626\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −0.501943 | −0.0323330 | −0.0161665 | − | 0.999869i | \(-0.505146\pi\) | ||||
−0.0161665 | + | 0.999869i | \(0.505146\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 9.89432 | 0.633419 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −0.751504 | −0.0479141 | ||||||||
\(247\) | 4.53146 | 0.288330 | ||||||||
\(248\) | −30.9978 | −1.96836 | ||||||||
\(249\) | −6.14148 | −0.389200 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −18.5405 | −1.17027 | −0.585133 | − | 0.810937i | \(-0.698958\pi\) | ||||
−0.585133 | + | 0.810937i | \(0.698958\pi\) | |||||||
\(252\) | −2.30340 | −0.145100 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 19.3009 | 1.21105 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −16.8391 | −1.05245 | ||||||||
\(257\) | −7.38010 | −0.460358 | −0.230179 | − | 0.973148i | \(-0.573931\pi\) | ||||
−0.230179 | + | 0.973148i | \(0.573931\pi\) | |||||||
\(258\) | 2.18529 | 0.136050 | ||||||||
\(259\) | −8.48403 | −0.527172 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 2.03835 | 0.126171 | ||||||||
\(262\) | 18.9590 | 1.17129 | ||||||||
\(263\) | 3.05950 | 0.188657 | 0.0943285 | − | 0.995541i | \(-0.469930\pi\) | ||||
0.0943285 | + | 0.995541i | \(0.469930\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 5.96112 | 0.365500 | ||||||||
\(267\) | 3.77194 | 0.230839 | ||||||||
\(268\) | −3.56233 | −0.217604 | ||||||||
\(269\) | −17.6801 | −1.07797 | −0.538987 | − | 0.842314i | \(-0.681193\pi\) | ||||
−0.538987 | + | 0.842314i | \(0.681193\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −15.2992 | −0.929358 | −0.464679 | − | 0.885479i | \(-0.653830\pi\) | ||||
−0.464679 | + | 0.885479i | \(0.653830\pi\) | |||||||
\(272\) | 0.407004 | 0.0246782 | ||||||||
\(273\) | 2.95637 | 0.178928 | ||||||||
\(274\) | 3.24852 | 0.196250 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −5.31022 | −0.319638 | ||||||||
\(277\) | 17.8238 | 1.07093 | 0.535463 | − | 0.844559i | \(-0.320137\pi\) | ||||
0.535463 | + | 0.844559i | \(0.320137\pi\) | |||||||
\(278\) | 2.54935 | 0.152900 | ||||||||
\(279\) | 10.6136 | 0.635421 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −17.2990 | −1.03197 | −0.515985 | − | 0.856597i | \(-0.672574\pi\) | ||||
−0.515985 | + | 0.856597i | \(0.672574\pi\) | |||||||
\(282\) | −9.69031 | −0.577050 | ||||||||
\(283\) | 25.7764 | 1.53225 | 0.766124 | − | 0.642693i | \(-0.222183\pi\) | ||||
0.766124 | + | 0.642693i | \(0.222183\pi\) | |||||||
\(284\) | −14.5248 | −0.861887 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −1.64309 | −0.0969888 | ||||||||
\(288\) | 5.40294 | 0.318371 | ||||||||
\(289\) | −16.2482 | −0.955777 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 1.93795 | 0.113605 | ||||||||
\(292\) | −16.6100 | −0.972029 | ||||||||
\(293\) | −13.5306 | −0.790468 | −0.395234 | − | 0.918581i | \(-0.629336\pi\) | ||||
−0.395234 | + | 0.918581i | \(0.629336\pi\) | |||||||
\(294\) | −2.64562 | −0.154296 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 12.1398 | 0.705609 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −8.50299 | −0.492565 | ||||||||
\(299\) | 6.81557 | 0.394155 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 4.77794 | 0.275396 | ||||||||
\(302\) | 20.1404 | 1.15895 | ||||||||
\(303\) | −5.25176 | −0.301706 | ||||||||
\(304\) | −1.46854 | −0.0842268 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −0.809430 | −0.0462720 | ||||||||
\(307\) | 13.0268 | 0.743478 | 0.371739 | − | 0.928337i | \(-0.378762\pi\) | ||||
0.371739 | + | 0.928337i | \(0.378762\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 13.6007 | 0.773714 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 1.90319 | 0.107920 | 0.0539601 | − | 0.998543i | \(-0.482816\pi\) | ||||
0.0539601 | + | 0.998543i | \(0.482816\pi\) | |||||||
\(312\) | −4.23026 | −0.239491 | ||||||||
\(313\) | −10.9324 | −0.617934 | −0.308967 | − | 0.951073i | \(-0.599983\pi\) | ||||
−0.308967 | + | 0.951073i | \(0.599983\pi\) | |||||||
\(314\) | 22.2124 | 1.25352 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 19.1839 | 1.07918 | ||||||||
\(317\) | 16.0723 | 0.902708 | 0.451354 | − | 0.892345i | \(-0.350941\pi\) | ||||
0.451354 | + | 0.892345i | \(0.350941\pi\) | |||||||
\(318\) | −6.73632 | −0.377754 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 9.99063 | 0.557623 | ||||||||
\(322\) | 8.96587 | 0.499648 | ||||||||
\(323\) | −2.71262 | −0.150934 | ||||||||
\(324\) | −1.12852 | −0.0626955 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 1.68346 | 0.0932382 | ||||||||
\(327\) | −6.75183 | −0.373377 | ||||||||
\(328\) | 2.35109 | 0.129817 | ||||||||
\(329\) | −21.1870 | −1.16808 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1.39579 | 0.0767195 | 0.0383597 | − | 0.999264i | \(-0.487787\pi\) | ||||
0.0383597 | + | 0.999264i | \(0.487787\pi\) | |||||||
\(332\) | 6.93078 | 0.380376 | ||||||||
\(333\) | −4.15664 | −0.227782 | ||||||||
\(334\) | 22.9531 | 1.25594 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −0.958094 | −0.0522683 | ||||||||
\(337\) | 2.76340 | 0.150532 | 0.0752660 | − | 0.997163i | \(-0.476019\pi\) | ||||
0.0752660 | + | 0.997163i | \(0.476019\pi\) | |||||||
\(338\) | −10.1774 | −0.553577 | ||||||||
\(339\) | 5.24461 | 0.284848 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 2.92057 | 0.157926 | ||||||||
\(343\) | −20.0720 | −1.08378 | ||||||||
\(344\) | −6.83672 | −0.368611 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 15.1340 | 0.813608 | ||||||||
\(347\) | 3.12683 | 0.167857 | 0.0839286 | − | 0.996472i | \(-0.473253\pi\) | ||||
0.0839286 | + | 0.996472i | \(0.473253\pi\) | |||||||
\(348\) | −2.30032 | −0.123310 | ||||||||
\(349\) | 13.1277 | 0.702709 | 0.351355 | − | 0.936242i | \(-0.385721\pi\) | ||||
0.351355 | + | 0.936242i | \(0.385721\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.44843 | 0.0773117 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −10.7984 | −0.574739 | −0.287370 | − | 0.957820i | \(-0.592781\pi\) | ||||
−0.287370 | + | 0.957820i | \(0.592781\pi\) | |||||||
\(354\) | −7.77025 | −0.412984 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −4.25671 | −0.225605 | ||||||||
\(357\) | −1.76974 | −0.0936648 | ||||||||
\(358\) | 15.8417 | 0.837260 | ||||||||
\(359\) | 23.9716 | 1.26517 | 0.632585 | − | 0.774491i | \(-0.281994\pi\) | ||||
0.632585 | + | 0.774491i | \(0.281994\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −9.21237 | −0.484861 | ||||||||
\(362\) | 17.1310 | 0.900388 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −3.33632 | −0.174871 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −8.18476 | −0.427824 | ||||||||
\(367\) | −8.87287 | −0.463160 | −0.231580 | − | 0.972816i | \(-0.574390\pi\) | ||||
−0.231580 | + | 0.972816i | \(0.574390\pi\) | |||||||
\(368\) | −2.20877 | −0.115140 | ||||||||
\(369\) | −0.805012 | −0.0419072 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −14.7283 | −0.764658 | ||||||||
\(372\) | −11.9777 | −0.621013 | ||||||||
\(373\) | 26.3389 | 1.36378 | 0.681888 | − | 0.731456i | \(-0.261159\pi\) | ||||
0.681888 | + | 0.731456i | \(0.261159\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 30.3163 | 1.56345 | ||||||||
\(377\) | 2.95242 | 0.152057 | ||||||||
\(378\) | 1.90541 | 0.0980038 | ||||||||
\(379\) | 4.69610 | 0.241223 | 0.120611 | − | 0.992700i | \(-0.461515\pi\) | ||||
0.120611 | + | 0.992700i | \(0.461515\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 20.6751 | 1.05922 | ||||||||
\(382\) | −14.3750 | −0.735489 | ||||||||
\(383\) | 6.89931 | 0.352538 | 0.176269 | − | 0.984342i | \(-0.443597\pi\) | ||||
0.176269 | + | 0.984342i | \(0.443597\pi\) | |||||||
\(384\) | −5.22091 | −0.266428 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 6.88892 | 0.350637 | ||||||||
\(387\) | 2.34089 | 0.118994 | ||||||||
\(388\) | −2.18701 | −0.111029 | ||||||||
\(389\) | 2.40462 | 0.121919 | 0.0609596 | − | 0.998140i | \(-0.480584\pi\) | ||||
0.0609596 | + | 0.998140i | \(0.480584\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −4.07994 | −0.206331 | ||||||||
\(392\) | 8.27688 | 0.418045 | ||||||||
\(393\) | 20.3089 | 1.02445 | ||||||||
\(394\) | −2.93760 | −0.147994 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −37.6715 | −1.89068 | −0.945338 | − | 0.326091i | \(-0.894268\pi\) | ||||
−0.945338 | + | 0.326091i | \(0.894268\pi\) | |||||||
\(398\) | −3.04104 | −0.152434 | ||||||||
\(399\) | 6.38556 | 0.319678 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −12.5168 | −0.625060 | −0.312530 | − | 0.949908i | \(-0.601176\pi\) | ||||
−0.312530 | + | 0.949908i | \(0.601176\pi\) | |||||||
\(402\) | 2.94682 | 0.146974 | ||||||||
\(403\) | 15.3731 | 0.765790 | ||||||||
\(404\) | 5.92671 | 0.294865 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 3.88390 | 0.192754 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 2.53232 | 0.125368 | ||||||||
\(409\) | −26.4622 | −1.30847 | −0.654237 | − | 0.756290i | \(-0.727010\pi\) | ||||
−0.654237 | + | 0.756290i | \(0.727010\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 3.47982 | 0.171647 | ||||||||
\(412\) | −15.3486 | −0.756171 | ||||||||
\(413\) | −16.9889 | −0.835971 | ||||||||
\(414\) | 4.39271 | 0.215890 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 7.82580 | 0.383691 | ||||||||
\(417\) | 2.73086 | 0.133731 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 30.9711 | 1.51304 | 0.756518 | − | 0.653973i | \(-0.226899\pi\) | ||||
0.756518 | + | 0.653973i | \(0.226899\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 18.2435 | 0.889132 | 0.444566 | − | 0.895746i | \(-0.353358\pi\) | ||||
0.444566 | + | 0.895746i | \(0.353358\pi\) | |||||||
\(422\) | 18.5998 | 0.905426 | ||||||||
\(423\) | −10.3803 | −0.504706 | ||||||||
\(424\) | 21.0747 | 1.02348 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 12.0152 | 0.582136 | ||||||||
\(427\) | −17.8952 | −0.866010 | ||||||||
\(428\) | −11.2746 | −0.544979 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 30.3488 | 1.46185 | 0.730925 | − | 0.682458i | \(-0.239089\pi\) | ||||
0.730925 | + | 0.682458i | \(0.239089\pi\) | |||||||
\(432\) | −0.469405 | −0.0225843 | ||||||||
\(433\) | −12.7012 | −0.610382 | −0.305191 | − | 0.952291i | \(-0.598720\pi\) | ||||
−0.305191 | + | 0.952291i | \(0.598720\pi\) | |||||||
\(434\) | 20.2233 | 0.970750 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 7.61957 | 0.364911 | ||||||||
\(437\) | 14.7212 | 0.704209 | ||||||||
\(438\) | 13.7401 | 0.656528 | ||||||||
\(439\) | −25.6564 | −1.22451 | −0.612257 | − | 0.790659i | \(-0.709738\pi\) | ||||
−0.612257 | + | 0.790659i | \(0.709738\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −2.83399 | −0.134952 | ||||||||
\(442\) | −1.17241 | −0.0557657 | ||||||||
\(443\) | 26.2148 | 1.24550 | 0.622751 | − | 0.782420i | \(-0.286015\pi\) | ||||
0.622751 | + | 0.782420i | \(0.286015\pi\) | |||||||
\(444\) | 4.69085 | 0.222618 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −9.78354 | −0.463264 | ||||||||
\(447\) | −9.10841 | −0.430813 | ||||||||
\(448\) | 12.2110 | 0.576916 | ||||||||
\(449\) | −12.0061 | −0.566605 | −0.283302 | − | 0.959031i | \(-0.591430\pi\) | ||||
−0.283302 | + | 0.959031i | \(0.591430\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | −5.91864 | −0.278390 | ||||||||
\(453\) | 21.5744 | 1.01366 | ||||||||
\(454\) | −16.4984 | −0.774309 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −9.13706 | −0.427882 | ||||||||
\(457\) | −13.7890 | −0.645022 | −0.322511 | − | 0.946566i | \(-0.604527\pi\) | ||||
−0.322511 | + | 0.946566i | \(0.604527\pi\) | |||||||
\(458\) | 3.85518 | 0.180141 | ||||||||
\(459\) | −0.867063 | −0.0404710 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 11.3262 | 0.527515 | 0.263758 | − | 0.964589i | \(-0.415038\pi\) | ||||
0.263758 | + | 0.964589i | \(0.415038\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −6.18784 | −0.287573 | −0.143787 | − | 0.989609i | \(-0.545928\pi\) | ||||
−0.143787 | + | 0.989609i | \(0.545928\pi\) | |||||||
\(464\) | −0.956812 | −0.0444189 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −12.6951 | −0.588087 | ||||||||
\(467\) | −8.48288 | −0.392541 | −0.196270 | − | 0.980550i | \(-0.562883\pi\) | ||||
−0.196270 | + | 0.980550i | \(0.562883\pi\) | |||||||
\(468\) | −1.63459 | −0.0755588 | ||||||||
\(469\) | 6.44295 | 0.297508 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 23.7940 | 1.09637 | ||||||||
\(472\) | 24.3094 | 1.11893 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | −15.8693 | −0.728899 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 1.99719 | 0.0915411 | ||||||||
\(477\) | −7.21596 | −0.330396 | ||||||||
\(478\) | 7.47415 | 0.341860 | ||||||||
\(479\) | 9.23554 | 0.421982 | 0.210991 | − | 0.977488i | \(-0.432331\pi\) | ||||
0.210991 | + | 0.977488i | \(0.432331\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −6.02062 | −0.274517 | ||||||||
\(482\) | −0.468579 | −0.0213432 | ||||||||
\(483\) | 9.60425 | 0.437008 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0.933531 | 0.0423458 | ||||||||
\(487\) | −20.1708 | −0.914024 | −0.457012 | − | 0.889460i | \(-0.651080\pi\) | ||||
−0.457012 | + | 0.889460i | \(0.651080\pi\) | |||||||
\(488\) | 25.6062 | 1.15914 | ||||||||
\(489\) | 1.80332 | 0.0815491 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −5.33594 | −0.240807 | −0.120404 | − | 0.992725i | \(-0.538419\pi\) | ||||
−0.120404 | + | 0.992725i | \(0.538419\pi\) | |||||||
\(492\) | 0.908472 | 0.0409571 | ||||||||
\(493\) | −1.76738 | −0.0795986 | ||||||||
\(494\) | 4.23026 | 0.190328 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −4.98209 | −0.223702 | ||||||||
\(497\) | 26.2700 | 1.17837 | ||||||||
\(498\) | −5.73326 | −0.256914 | ||||||||
\(499\) | −39.2816 | −1.75849 | −0.879243 | − | 0.476374i | \(-0.841951\pi\) | ||||
−0.879243 | + | 0.476374i | \(0.841951\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 24.5874 | 1.09848 | ||||||||
\(502\) | −17.3081 | −0.772500 | ||||||||
\(503\) | −32.4181 | −1.44545 | −0.722727 | − | 0.691134i | \(-0.757111\pi\) | ||||
−0.722727 | + | 0.691134i | \(0.757111\pi\) | |||||||
\(504\) | −5.96112 | −0.265529 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −10.9020 | −0.484176 | ||||||||
\(508\) | −23.3323 | −1.03520 | ||||||||
\(509\) | −17.0656 | −0.756421 | −0.378211 | − | 0.925720i | \(-0.623461\pi\) | ||||
−0.378211 | + | 0.925720i | \(0.623461\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 30.0415 | 1.32896 | ||||||||
\(512\) | −5.27803 | −0.233258 | ||||||||
\(513\) | 3.12852 | 0.138128 | ||||||||
\(514\) | −6.88955 | −0.303885 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −2.64174 | −0.116296 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | −7.92011 | −0.347990 | ||||||||
\(519\) | 16.2115 | 0.711608 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −15.0471 | −0.659224 | −0.329612 | − | 0.944116i | \(-0.606918\pi\) | ||||
−0.329612 | + | 0.944116i | \(0.606918\pi\) | |||||||
\(522\) | 1.90286 | 0.0832860 | ||||||||
\(523\) | 37.0416 | 1.61972 | 0.809859 | − | 0.586624i | \(-0.199544\pi\) | ||||
0.809859 | + | 0.586624i | \(0.199544\pi\) | |||||||
\(524\) | −22.9189 | −1.00122 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 2.85614 | 0.124534 | ||||||||
\(527\) | −9.20267 | −0.400875 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −0.858520 | −0.0373270 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −8.32351 | −0.361209 | ||||||||
\(532\) | −7.20623 | −0.312430 | ||||||||
\(533\) | −1.16601 | −0.0505054 | ||||||||
\(534\) | 3.52123 | 0.152378 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −9.21919 | −0.398208 | ||||||||
\(537\) | 16.9697 | 0.732295 | ||||||||
\(538\) | −16.5049 | −0.711577 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 0.177099 | 0.00761407 | 0.00380704 | − | 0.999993i | \(-0.498788\pi\) | ||||
0.00380704 | + | 0.999993i | \(0.498788\pi\) | |||||||
\(542\) | −14.2822 | −0.613475 | ||||||||
\(543\) | 18.3508 | 0.787508 | ||||||||
\(544\) | −4.68468 | −0.200854 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 2.75986 | 0.118111 | ||||||||
\(547\) | −1.21270 | −0.0518511 | −0.0259256 | − | 0.999664i | \(-0.508253\pi\) | ||||
−0.0259256 | + | 0.999664i | \(0.508253\pi\) | |||||||
\(548\) | −3.92704 | −0.167755 | ||||||||
\(549\) | −8.76752 | −0.374189 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 6.37702 | 0.271670 | ||||||||
\(552\) | −13.7427 | −0.584927 | ||||||||
\(553\) | −34.6967 | −1.47545 | ||||||||
\(554\) | 16.6390 | 0.706925 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −3.08183 | −0.130699 | ||||||||
\(557\) | −1.93846 | −0.0821352 | −0.0410676 | − | 0.999156i | \(-0.513076\pi\) | ||||
−0.0410676 | + | 0.999156i | \(0.513076\pi\) | |||||||
\(558\) | 9.90814 | 0.419445 | ||||||||
\(559\) | 3.39062 | 0.143408 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −16.1491 | −0.681210 | ||||||||
\(563\) | 20.9958 | 0.884866 | 0.442433 | − | 0.896802i | \(-0.354115\pi\) | ||||
0.442433 | + | 0.896802i | \(0.354115\pi\) | |||||||
\(564\) | 11.7143 | 0.493263 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 24.0631 | 1.01145 | ||||||||
\(567\) | 2.04108 | 0.0857173 | ||||||||
\(568\) | −37.5897 | −1.57723 | ||||||||
\(569\) | −39.3757 | −1.65071 | −0.825357 | − | 0.564612i | \(-0.809026\pi\) | ||||
−0.825357 | + | 0.564612i | \(0.809026\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 30.6796 | 1.28390 | 0.641950 | − | 0.766746i | \(-0.278126\pi\) | ||||
0.641950 | + | 0.766746i | \(0.278126\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −15.3985 | −0.643282 | ||||||||
\(574\) | −1.53388 | −0.0640229 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 5.98262 | 0.249276 | ||||||||
\(577\) | 34.7038 | 1.44474 | 0.722369 | − | 0.691508i | \(-0.243053\pi\) | ||||
0.722369 | + | 0.691508i | \(0.243053\pi\) | |||||||
\(578\) | −15.1682 | −0.630914 | ||||||||
\(579\) | 7.37942 | 0.306678 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −12.5353 | −0.520050 | ||||||||
\(582\) | 1.80914 | 0.0749911 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | −42.9862 | −1.77878 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −12.6313 | −0.521793 | ||||||||
\(587\) | −8.05710 | −0.332552 | −0.166276 | − | 0.986079i | \(-0.553174\pi\) | ||||
−0.166276 | + | 0.986079i | \(0.553174\pi\) | |||||||
\(588\) | 3.19822 | 0.131892 | ||||||||
\(589\) | 33.2049 | 1.36818 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −3.14676 | −0.129440 | ||||||||
\(592\) | 1.95115 | 0.0801917 | ||||||||
\(593\) | 28.1409 | 1.15561 | 0.577805 | − | 0.816175i | \(-0.303909\pi\) | ||||
0.577805 | + | 0.816175i | \(0.303909\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 10.2790 | 0.421045 | ||||||||
\(597\) | −3.25757 | −0.133324 | ||||||||
\(598\) | 6.36255 | 0.260184 | ||||||||
\(599\) | −28.5988 | −1.16851 | −0.584257 | − | 0.811568i | \(-0.698614\pi\) | ||||
−0.584257 | + | 0.811568i | \(0.698614\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −7.27610 | −0.296799 | −0.148399 | − | 0.988928i | \(-0.547412\pi\) | ||||
−0.148399 | + | 0.988928i | \(0.547412\pi\) | |||||||
\(602\) | 4.46035 | 0.181790 | ||||||||
\(603\) | 3.15664 | 0.128548 | ||||||||
\(604\) | −24.3472 | −0.990672 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −4.90268 | −0.199158 | ||||||||
\(607\) | 5.34785 | 0.217063 | 0.108531 | − | 0.994093i | \(-0.465385\pi\) | ||||
0.108531 | + | 0.994093i | \(0.465385\pi\) | |||||||
\(608\) | 16.9032 | 0.685515 | ||||||||
\(609\) | 4.16043 | 0.168589 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −15.0352 | −0.608257 | ||||||||
\(612\) | 0.978497 | 0.0395534 | ||||||||
\(613\) | 4.64099 | 0.187448 | 0.0937238 | − | 0.995598i | \(-0.470123\pi\) | ||||
0.0937238 | + | 0.995598i | \(0.470123\pi\) | |||||||
\(614\) | 12.1609 | 0.490774 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −24.5843 | −0.989727 | −0.494864 | − | 0.868971i | \(-0.664782\pi\) | ||||
−0.494864 | + | 0.868971i | \(0.664782\pi\) | |||||||
\(618\) | 12.6966 | 0.510734 | ||||||||
\(619\) | −6.13789 | −0.246703 | −0.123351 | − | 0.992363i | \(-0.539364\pi\) | ||||
−0.123351 | + | 0.992363i | \(0.539364\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 4.70547 | 0.188824 | ||||||||
\(622\) | 1.77669 | 0.0712387 | ||||||||
\(623\) | 7.69884 | 0.308447 | ||||||||
\(624\) | −0.679903 | −0.0272179 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −10.2057 | −0.407902 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −26.8519 | −1.07151 | ||||||||
\(629\) | 3.60407 | 0.143704 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −17.7085 | −0.704966 | −0.352483 | − | 0.935818i | \(-0.614662\pi\) | ||||
−0.352483 | + | 0.935818i | \(0.614662\pi\) | |||||||
\(632\) | 49.6473 | 1.97486 | ||||||||
\(633\) | 19.9242 | 0.791914 | ||||||||
\(634\) | 15.0040 | 0.595883 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 8.14335 | 0.322905 | ||||||||
\(637\) | −4.10485 | −0.162640 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 12.8707 | 0.509155 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 39.8621 | 1.57446 | 0.787230 | − | 0.616659i | \(-0.211514\pi\) | ||||
0.787230 | + | 0.616659i | \(0.211514\pi\) | |||||||
\(642\) | 9.32657 | 0.368090 | ||||||||
\(643\) | 17.8662 | 0.704576 | 0.352288 | − | 0.935892i | \(-0.385404\pi\) | ||||
0.352288 | + | 0.935892i | \(0.385404\pi\) | |||||||
\(644\) | −10.8386 | −0.427100 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −2.53232 | −0.0996327 | ||||||||
\(647\) | −5.04075 | −0.198172 | −0.0990862 | − | 0.995079i | \(-0.531592\pi\) | ||||
−0.0990862 | + | 0.995079i | \(0.531592\pi\) | |||||||
\(648\) | −2.92057 | −0.114731 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 21.6632 | 0.849049 | ||||||||
\(652\) | −2.03509 | −0.0797001 | ||||||||
\(653\) | −40.7212 | −1.59354 | −0.796771 | − | 0.604281i | \(-0.793460\pi\) | ||||
−0.796771 | + | 0.604281i | \(0.793460\pi\) | |||||||
\(654\) | −6.30305 | −0.246469 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0.377877 | 0.0147536 | ||||||||
\(657\) | 14.7184 | 0.574221 | ||||||||
\(658\) | −19.7787 | −0.771054 | ||||||||
\(659\) | 48.7556 | 1.89925 | 0.949624 | − | 0.313390i | \(-0.101465\pi\) | ||||
0.949624 | + | 0.313390i | \(0.101465\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −41.0061 | −1.59495 | −0.797477 | − | 0.603350i | \(-0.793832\pi\) | ||||
−0.797477 | + | 0.603350i | \(0.793832\pi\) | |||||||
\(662\) | 1.30301 | 0.0506430 | ||||||||
\(663\) | −1.25588 | −0.0487745 | ||||||||
\(664\) | 17.9366 | 0.696076 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −3.88035 | −0.150361 | ||||||||
\(667\) | 9.59140 | 0.371380 | ||||||||
\(668\) | −27.7474 | −1.07358 | ||||||||
\(669\) | −10.4801 | −0.405186 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 11.0278 | 0.425408 | ||||||||
\(673\) | 30.4936 | 1.17544 | 0.587722 | − | 0.809063i | \(-0.300025\pi\) | ||||
0.587722 | + | 0.809063i | \(0.300025\pi\) | |||||||
\(674\) | 2.57972 | 0.0993671 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 12.3032 | 0.473198 | ||||||||
\(677\) | 43.4424 | 1.66963 | 0.834813 | − | 0.550534i | \(-0.185576\pi\) | ||||
0.834813 | + | 0.550534i | \(0.185576\pi\) | |||||||
\(678\) | 4.89601 | 0.188030 | ||||||||
\(679\) | 3.95551 | 0.151799 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −17.6731 | −0.677235 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 43.5970 | 1.66819 | 0.834096 | − | 0.551619i | \(-0.185990\pi\) | ||||
0.834096 | + | 0.551619i | \(0.185990\pi\) | |||||||
\(684\) | −3.53059 | −0.134996 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −18.7378 | −0.715413 | ||||||||
\(687\) | 4.12967 | 0.157557 | ||||||||
\(688\) | −1.09882 | −0.0418923 | ||||||||
\(689\) | −10.4518 | −0.398184 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −8.30897 | −0.316088 | −0.158044 | − | 0.987432i | \(-0.550519\pi\) | ||||
−0.158044 | + | 0.987432i | \(0.550519\pi\) | |||||||
\(692\) | −18.2950 | −0.695473 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 2.91900 | 0.110804 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −5.95314 | −0.225653 | ||||||||
\(697\) | 0.697996 | 0.0264385 | ||||||||
\(698\) | 12.2551 | 0.463863 | ||||||||
\(699\) | −13.5990 | −0.514360 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 9.08744 | 0.343228 | 0.171614 | − | 0.985164i | \(-0.445102\pi\) | ||||
0.171614 | + | 0.985164i | \(0.445102\pi\) | |||||||
\(702\) | 1.35216 | 0.0510340 | ||||||||
\(703\) | −13.0041 | −0.490460 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −10.0806 | −0.379389 | ||||||||
\(707\) | −10.7193 | −0.403139 | ||||||||
\(708\) | 9.39324 | 0.353020 | ||||||||
\(709\) | −4.85568 | −0.182359 | −0.0911794 | − | 0.995834i | \(-0.529064\pi\) | ||||
−0.0911794 | + | 0.995834i | \(0.529064\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −16.9992 | −0.637519 | ||||||||
\(712\) | −11.0162 | −0.412850 | ||||||||
\(713\) | 49.9421 | 1.87035 | ||||||||
\(714\) | −1.65211 | −0.0618287 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −19.1506 | −0.715691 | ||||||||
\(717\) | 8.00632 | 0.299002 | ||||||||
\(718\) | 22.3782 | 0.835147 | ||||||||
\(719\) | 23.9034 | 0.891448 | 0.445724 | − | 0.895171i | \(-0.352946\pi\) | ||||
0.445724 | + | 0.895171i | \(0.352946\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 27.7600 | 1.03384 | ||||||||
\(722\) | −8.60003 | −0.320060 | ||||||||
\(723\) | −0.501943 | −0.0186675 | ||||||||
\(724\) | −20.7092 | −0.769653 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 11.3674 | 0.421592 | 0.210796 | − | 0.977530i | \(-0.432394\pi\) | ||||
0.210796 | + | 0.977530i | \(0.432394\pi\) | |||||||
\(728\) | −8.63429 | −0.320008 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −2.02969 | −0.0750710 | ||||||||
\(732\) | 9.89432 | 0.365705 | ||||||||
\(733\) | 34.1178 | 1.26017 | 0.630085 | − | 0.776526i | \(-0.283020\pi\) | ||||
0.630085 | + | 0.776526i | \(0.283020\pi\) | |||||||
\(734\) | −8.28311 | −0.305735 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 25.4234 | 0.937118 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | −0.751504 | −0.0276632 | ||||||||
\(739\) | 2.33848 | 0.0860225 | 0.0430113 | − | 0.999075i | \(-0.486305\pi\) | ||||
0.0430113 | + | 0.999075i | \(0.486305\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 4.53146 | 0.166467 | ||||||||
\(742\) | −13.7494 | −0.504755 | ||||||||
\(743\) | −14.4885 | −0.531533 | −0.265767 | − | 0.964037i | \(-0.585625\pi\) | ||||
−0.265767 | + | 0.964037i | \(0.585625\pi\) | |||||||
\(744\) | −30.9978 | −1.13644 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 24.5882 | 0.900238 | ||||||||
\(747\) | −6.14148 | −0.224705 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 20.3917 | 0.745096 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 33.3203 | 1.21587 | 0.607937 | − | 0.793985i | \(-0.291997\pi\) | ||||
0.607937 | + | 0.793985i | \(0.291997\pi\) | |||||||
\(752\) | 4.87256 | 0.177684 | ||||||||
\(753\) | −18.5405 | −0.675654 | ||||||||
\(754\) | 2.75617 | 0.100374 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −2.30340 | −0.0837738 | ||||||||
\(757\) | −40.3778 | −1.46755 | −0.733777 | − | 0.679390i | \(-0.762244\pi\) | ||||
−0.733777 | + | 0.679390i | \(0.762244\pi\) | |||||||
\(758\) | 4.38396 | 0.159233 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −49.8971 | −1.80877 | −0.904384 | − | 0.426720i | \(-0.859669\pi\) | ||||
−0.904384 | + | 0.426720i | \(0.859669\pi\) | |||||||
\(762\) | 19.3009 | 0.699197 | ||||||||
\(763\) | −13.7810 | −0.498907 | ||||||||
\(764\) | 17.3775 | 0.628697 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 6.44072 | 0.232713 | ||||||||
\(767\) | −12.0561 | −0.435319 | ||||||||
\(768\) | −16.8391 | −0.607630 | ||||||||
\(769\) | 4.93932 | 0.178116 | 0.0890582 | − | 0.996026i | \(-0.471614\pi\) | ||||
0.0890582 | + | 0.996026i | \(0.471614\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −7.38010 | −0.265788 | ||||||||
\(772\) | −8.32781 | −0.299725 | ||||||||
\(773\) | 33.4710 | 1.20387 | 0.601934 | − | 0.798546i | \(-0.294397\pi\) | ||||
0.601934 | + | 0.798546i | \(0.294397\pi\) | |||||||
\(774\) | 2.18529 | 0.0785486 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −5.65992 | −0.203179 | ||||||||
\(777\) | −8.48403 | −0.304363 | ||||||||
\(778\) | 2.24479 | 0.0804797 | ||||||||
\(779\) | −2.51850 | −0.0902345 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | −3.80875 | −0.136201 | ||||||||
\(783\) | 2.03835 | 0.0728447 | ||||||||
\(784\) | 1.33029 | 0.0475104 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 18.9590 | 0.676244 | ||||||||
\(787\) | −25.9400 | −0.924661 | −0.462331 | − | 0.886708i | \(-0.652987\pi\) | ||||
−0.462331 | + | 0.886708i | \(0.652987\pi\) | |||||||
\(788\) | 3.55118 | 0.126506 | ||||||||
\(789\) | 3.05950 | 0.108921 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 10.7047 | 0.380614 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −12.6992 | −0.450961 | ||||||||
\(794\) | −35.1675 | −1.24805 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 3.67623 | 0.130301 | ||||||||
\(797\) | −9.86264 | −0.349353 | −0.174676 | − | 0.984626i | \(-0.555888\pi\) | ||||
−0.174676 | + | 0.984626i | \(0.555888\pi\) | |||||||
\(798\) | 5.96112 | 0.211021 | ||||||||
\(799\) | 9.00035 | 0.318410 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 3.77194 | 0.133275 | ||||||||
\(802\) | −11.6848 | −0.412606 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | −3.56233 | −0.125634 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 14.3513 | 0.505503 | ||||||||
\(807\) | −17.6801 | −0.622368 | ||||||||
\(808\) | 15.3381 | 0.539594 | ||||||||
\(809\) | −33.0590 | −1.16229 | −0.581146 | − | 0.813799i | \(-0.697396\pi\) | ||||
−0.581146 | + | 0.813799i | \(0.697396\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 5.21312 | 0.183057 | 0.0915286 | − | 0.995802i | \(-0.470825\pi\) | ||||
0.0915286 | + | 0.995802i | \(0.470825\pi\) | |||||||
\(812\) | −4.69513 | −0.164767 | ||||||||
\(813\) | −15.2992 | −0.536565 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0.407004 | 0.0142480 | ||||||||
\(817\) | 7.32351 | 0.256217 | ||||||||
\(818\) | −24.7033 | −0.863731 | ||||||||
\(819\) | 2.95637 | 0.103304 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −1.63933 | −0.0572131 | −0.0286066 | − | 0.999591i | \(-0.509107\pi\) | ||||
−0.0286066 | + | 0.999591i | \(0.509107\pi\) | |||||||
\(822\) | 3.24852 | 0.113305 | ||||||||
\(823\) | 17.8894 | 0.623586 | 0.311793 | − | 0.950150i | \(-0.399070\pi\) | ||||
0.311793 | + | 0.950150i | \(0.399070\pi\) | |||||||
\(824\) | −39.7217 | −1.38377 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −15.8597 | −0.551830 | ||||||||
\(827\) | −35.5449 | −1.23602 | −0.618009 | − | 0.786171i | \(-0.712061\pi\) | ||||
−0.618009 | + | 0.786171i | \(0.712061\pi\) | |||||||
\(828\) | −5.31022 | −0.184543 | ||||||||
\(829\) | −26.9512 | −0.936053 | −0.468026 | − | 0.883715i | \(-0.655035\pi\) | ||||
−0.468026 | + | 0.883715i | \(0.655035\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 17.8238 | 0.618299 | ||||||||
\(832\) | 8.66544 | 0.300420 | ||||||||
\(833\) | 2.45725 | 0.0851386 | ||||||||
\(834\) | 2.54935 | 0.0882766 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 10.6136 | 0.366860 | ||||||||
\(838\) | 28.9124 | 0.998764 | ||||||||
\(839\) | −11.8373 | −0.408667 | −0.204334 | − | 0.978901i | \(-0.565503\pi\) | ||||
−0.204334 | + | 0.978901i | \(0.565503\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −24.8451 | −0.856729 | ||||||||
\(842\) | 17.0308 | 0.586921 | ||||||||
\(843\) | −17.2990 | −0.595809 | ||||||||
\(844\) | −22.4848 | −0.773959 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −9.69031 | −0.333160 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 3.38721 | 0.116317 | ||||||||
\(849\) | 25.7764 | 0.884644 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −19.5590 | −0.670472 | ||||||||
\(852\) | −14.5248 | −0.497611 | ||||||||
\(853\) | 30.3043 | 1.03760 | 0.518799 | − | 0.854896i | \(-0.326379\pi\) | ||||
0.518799 | + | 0.854896i | \(0.326379\pi\) | |||||||
\(854\) | −16.7057 | −0.571659 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −29.1783 | −0.997295 | ||||||||
\(857\) | 29.2318 | 0.998540 | 0.499270 | − | 0.866446i | \(-0.333602\pi\) | ||||
0.499270 | + | 0.866446i | \(0.333602\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −36.7151 | −1.25270 | −0.626351 | − | 0.779541i | \(-0.715452\pi\) | ||||
−0.626351 | + | 0.779541i | \(0.715452\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −1.64309 | −0.0559965 | ||||||||
\(862\) | 28.3315 | 0.964976 | ||||||||
\(863\) | −43.5758 | −1.48334 | −0.741669 | − | 0.670766i | \(-0.765966\pi\) | ||||
−0.741669 | + | 0.670766i | \(0.765966\pi\) | |||||||
\(864\) | 5.40294 | 0.183812 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −11.8570 | −0.402917 | ||||||||
\(867\) | −16.2482 | −0.551818 | ||||||||
\(868\) | −24.4474 | −0.829798 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 4.57219 | 0.154923 | ||||||||
\(872\) | 19.7192 | 0.667777 | ||||||||
\(873\) | 1.93795 | 0.0655896 | ||||||||
\(874\) | 13.7427 | 0.464853 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −16.6100 | −0.561201 | ||||||||
\(877\) | 11.1173 | 0.375404 | 0.187702 | − | 0.982226i | \(-0.439896\pi\) | ||||
0.187702 | + | 0.982226i | \(0.439896\pi\) | |||||||
\(878\) | −23.9511 | −0.808309 | ||||||||
\(879\) | −13.5306 | −0.456377 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −39.1155 | −1.31783 | −0.658917 | − | 0.752216i | \(-0.728985\pi\) | ||||
−0.658917 | + | 0.752216i | \(0.728985\pi\) | |||||||
\(882\) | −2.64562 | −0.0890827 | ||||||||
\(883\) | −19.5187 | −0.656857 | −0.328428 | − | 0.944529i | \(-0.606519\pi\) | ||||
−0.328428 | + | 0.944529i | \(0.606519\pi\) | |||||||
\(884\) | 1.41729 | 0.0476686 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 24.4723 | 0.822164 | ||||||||
\(887\) | 5.19108 | 0.174299 | 0.0871497 | − | 0.996195i | \(-0.472224\pi\) | ||||
0.0871497 | + | 0.996195i | \(0.472224\pi\) | |||||||
\(888\) | 12.1398 | 0.407384 | ||||||||
\(889\) | 42.1996 | 1.41533 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 11.8270 | 0.395999 | ||||||||
\(893\) | −32.4749 | −1.08673 | ||||||||
\(894\) | −8.50299 | −0.284382 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −10.6563 | −0.356002 | ||||||||
\(897\) | 6.81557 | 0.227565 | ||||||||
\(898\) | −11.2081 | −0.374019 | ||||||||
\(899\) | 21.6343 | 0.721543 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 6.25669 | 0.208440 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 4.77794 | 0.159000 | ||||||||
\(904\) | −15.3173 | −0.509444 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 20.1404 | 0.669120 | ||||||||
\(907\) | 42.4379 | 1.40913 | 0.704563 | − | 0.709641i | \(-0.251143\pi\) | ||||
0.704563 | + | 0.709641i | \(0.251143\pi\) | |||||||
\(908\) | 19.9445 | 0.661880 | ||||||||
\(909\) | −5.25176 | −0.174190 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −19.7499 | −0.654344 | −0.327172 | − | 0.944965i | \(-0.606096\pi\) | ||||
−0.327172 | + | 0.944965i | \(0.606096\pi\) | |||||||
\(912\) | −1.46854 | −0.0486283 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | −12.8725 | −0.425783 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −4.66042 | −0.153985 | ||||||||
\(917\) | 41.4520 | 1.36887 | ||||||||
\(918\) | −0.809430 | −0.0267152 | ||||||||
\(919\) | −24.4853 | −0.807696 | −0.403848 | − | 0.914826i | \(-0.632328\pi\) | ||||
−0.403848 | + | 0.914826i | \(0.632328\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 13.0268 | 0.429247 | ||||||||
\(922\) | 10.5734 | 0.348216 | ||||||||
\(923\) | 18.6423 | 0.613619 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −5.77654 | −0.189829 | ||||||||
\(927\) | 13.6007 | 0.446704 | ||||||||
\(928\) | 11.0131 | 0.361522 | ||||||||
\(929\) | −6.05289 | −0.198589 | −0.0992944 | − | 0.995058i | \(-0.531659\pi\) | ||||
−0.0992944 | + | 0.995058i | \(0.531659\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −8.86620 | −0.290578 | ||||||||
\(932\) | 15.3467 | 0.502698 | ||||||||
\(933\) | 1.90319 | 0.0623077 | ||||||||
\(934\) | −7.91903 | −0.259119 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −4.23026 | −0.138270 | ||||||||
\(937\) | −6.83865 | −0.223409 | −0.111704 | − | 0.993741i | \(-0.535631\pi\) | ||||
−0.111704 | + | 0.993741i | \(0.535631\pi\) | |||||||
\(938\) | 6.01470 | 0.196387 | ||||||||
\(939\) | −10.9324 | −0.356765 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −3.95417 | −0.128902 | −0.0644512 | − | 0.997921i | \(-0.520530\pi\) | ||||
−0.0644512 | + | 0.997921i | \(0.520530\pi\) | |||||||
\(942\) | 22.2124 | 0.723719 | ||||||||
\(943\) | −3.78796 | −0.123353 | ||||||||
\(944\) | 3.90710 | 0.127165 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 40.1742 | 1.30549 | 0.652743 | − | 0.757579i | \(-0.273618\pi\) | ||||
0.652743 | + | 0.757579i | \(0.273618\pi\) | |||||||
\(948\) | 19.1839 | 0.623064 | ||||||||
\(949\) | 21.3187 | 0.692034 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 16.0723 | 0.521179 | ||||||||
\(952\) | 5.16866 | 0.167517 | ||||||||
\(953\) | 41.2470 | 1.33612 | 0.668061 | − | 0.744106i | \(-0.267124\pi\) | ||||
0.668061 | + | 0.744106i | \(0.267124\pi\) | |||||||
\(954\) | −6.73632 | −0.218097 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −9.03529 | −0.292222 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 8.62166 | 0.278553 | ||||||||
\(959\) | 7.10258 | 0.229354 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 81.6488 | 2.63383 | ||||||||
\(962\) | −5.62044 | −0.181210 | ||||||||
\(963\) | 9.99063 | 0.321944 | ||||||||
\(964\) | 0.566452 | 0.0182442 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 8.96587 | 0.288472 | ||||||||
\(967\) | −9.16826 | −0.294831 | −0.147416 | − | 0.989075i | \(-0.547096\pi\) | ||||
−0.147416 | + | 0.989075i | \(0.547096\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −2.71262 | −0.0871420 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −3.71264 | −0.119144 | −0.0595722 | − | 0.998224i | \(-0.518974\pi\) | ||||
−0.0595722 | + | 0.998224i | \(0.518974\pi\) | |||||||
\(972\) | −1.12852 | −0.0361973 | ||||||||
\(973\) | 5.57391 | 0.178691 | ||||||||
\(974\) | −18.8300 | −0.603353 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 4.11552 | 0.131735 | ||||||||
\(977\) | −12.3932 | −0.396495 | −0.198247 | − | 0.980152i | \(-0.563525\pi\) | ||||
−0.198247 | + | 0.980152i | \(0.563525\pi\) | |||||||
\(978\) | 1.68346 | 0.0538311 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −6.75183 | −0.215569 | ||||||||
\(982\) | −4.98126 | −0.158958 | ||||||||
\(983\) | −23.2949 | −0.742992 | −0.371496 | − | 0.928435i | \(-0.621155\pi\) | ||||
−0.371496 | + | 0.928435i | \(0.621155\pi\) | |||||||
\(984\) | 2.35109 | 0.0749501 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −1.64990 | −0.0525436 | ||||||||
\(987\) | −21.1870 | −0.674389 | ||||||||
\(988\) | −5.11384 | −0.162693 | ||||||||
\(989\) | 11.0150 | 0.350256 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −37.7826 | −1.20020 | −0.600101 | − | 0.799924i | \(-0.704873\pi\) | ||||
−0.600101 | + | 0.799924i | \(0.704873\pi\) | |||||||
\(992\) | 57.3447 | 1.82070 | ||||||||
\(993\) | 1.39579 | 0.0442940 | ||||||||
\(994\) | 24.5239 | 0.777851 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 6.93078 | 0.219610 | ||||||||
\(997\) | −7.87590 | −0.249432 | −0.124716 | − | 0.992192i | \(-0.539802\pi\) | ||||
−0.124716 | + | 0.992192i | \(0.539802\pi\) | |||||||
\(998\) | −36.6706 | −1.16079 | ||||||||
\(999\) | −4.15664 | −0.131510 |
(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 | 9075.2.a.cq.1.3 | 4 | ||
5.4 | even | 2 | 1815.2.a.v.1.2 | 4 | |||
11.3 | even | 5 | 825.2.n.i.526.2 | 8 | |||
11.4 | even | 5 | 825.2.n.i.676.2 | 8 | |||
11.10 | odd | 2 | 9075.2.a.dg.1.2 | 4 | |||
15.14 | odd | 2 | 5445.2.a.bk.1.3 | 4 | |||
55.3 | odd | 20 | 825.2.bx.g.724.2 | 16 | |||
55.4 | even | 10 | 165.2.m.b.16.1 | ✓ | 8 | ||
55.14 | even | 10 | 165.2.m.b.31.1 | yes | 8 | ||
55.37 | odd | 20 | 825.2.bx.g.49.2 | 16 | |||
55.47 | odd | 20 | 825.2.bx.g.724.3 | 16 | |||
55.48 | odd | 20 | 825.2.bx.g.49.3 | 16 | |||
55.54 | odd | 2 | 1815.2.a.r.1.3 | 4 | |||
165.14 | odd | 10 | 495.2.n.b.361.2 | 8 | |||
165.59 | odd | 10 | 495.2.n.b.181.2 | 8 | |||
165.164 | even | 2 | 5445.2.a.br.1.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
165.2.m.b.16.1 | ✓ | 8 | 55.4 | even | 10 | ||
165.2.m.b.31.1 | yes | 8 | 55.14 | even | 10 | ||
495.2.n.b.181.2 | 8 | 165.59 | odd | 10 | |||
495.2.n.b.361.2 | 8 | 165.14 | odd | 10 | |||
825.2.n.i.526.2 | 8 | 11.3 | even | 5 | |||
825.2.n.i.676.2 | 8 | 11.4 | even | 5 | |||
825.2.bx.g.49.2 | 16 | 55.37 | odd | 20 | |||
825.2.bx.g.49.3 | 16 | 55.48 | odd | 20 | |||
825.2.bx.g.724.2 | 16 | 55.3 | odd | 20 | |||
825.2.bx.g.724.3 | 16 | 55.47 | odd | 20 | |||
1815.2.a.r.1.3 | 4 | 55.54 | odd | 2 | |||
1815.2.a.v.1.2 | 4 | 5.4 | even | 2 | |||
5445.2.a.bk.1.3 | 4 | 15.14 | odd | 2 | |||
5445.2.a.br.1.2 | 4 | 165.164 | even | 2 | |||
9075.2.a.cq.1.3 | 4 | 1.1 | even | 1 | trivial | ||
9075.2.a.dg.1.2 | 4 | 11.10 | odd | 2 |