Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3675,2,Mod(1,3675)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3675, 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("3675.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3675 = 3 \cdot 5^{2} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3675.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: | \(29.3450227428\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{8})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - 2 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 105) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(1.41421\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3675.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.41421 | 1.00000 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −1.41421 | −0.577350 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −2.82843 | −1.00000 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.585786 | 0.176621 | 0.0883106 | − | 0.996093i | \(-0.471853\pi\) | ||||
0.0883106 | + | 0.996093i | \(0.471853\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −4.41421 | −1.22428 | −0.612141 | − | 0.790748i | \(-0.709692\pi\) | ||||
−0.612141 | + | 0.790748i | \(0.709692\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −4.00000 | −1.00000 | ||||||||
\(17\) | 2.24264 | 0.543920 | 0.271960 | − | 0.962309i | \(-0.412328\pi\) | ||||
0.271960 | + | 0.962309i | \(0.412328\pi\) | |||||||
\(18\) | 1.41421 | 0.333333 | ||||||||
\(19\) | −4.65685 | −1.06836 | −0.534178 | − | 0.845372i | \(-0.679379\pi\) | ||||
−0.534178 | + | 0.845372i | \(0.679379\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0.828427 | 0.176621 | ||||||||
\(23\) | −2.24264 | −0.467623 | −0.233811 | − | 0.972282i | \(-0.575120\pi\) | ||||
−0.233811 | + | 0.972282i | \(0.575120\pi\) | |||||||
\(24\) | 2.82843 | 0.577350 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −6.24264 | −1.22428 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 8.24264 | 1.53062 | 0.765310 | − | 0.643662i | \(-0.222586\pi\) | ||||
0.765310 | + | 0.643662i | \(0.222586\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 5.82843 | 1.04682 | 0.523408 | − | 0.852082i | \(-0.324660\pi\) | ||||
0.523408 | + | 0.852082i | \(0.324660\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −0.585786 | −0.101972 | ||||||||
\(34\) | 3.17157 | 0.543920 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 8.41421 | 1.38329 | 0.691644 | − | 0.722238i | \(-0.256887\pi\) | ||||
0.691644 | + | 0.722238i | \(0.256887\pi\) | |||||||
\(38\) | −6.58579 | −1.06836 | ||||||||
\(39\) | 4.41421 | 0.706840 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 6.24264 | 0.974937 | 0.487468 | − | 0.873141i | \(-0.337920\pi\) | ||||
0.487468 | + | 0.873141i | \(0.337920\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 7.58579 | 1.15682 | 0.578411 | − | 0.815746i | \(-0.303673\pi\) | ||||
0.578411 | + | 0.815746i | \(0.303673\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −3.17157 | −0.467623 | ||||||||
\(47\) | −13.3137 | −1.94200 | −0.971002 | − | 0.239071i | \(-0.923157\pi\) | ||||
−0.971002 | + | 0.239071i | \(0.923157\pi\) | |||||||
\(48\) | 4.00000 | 0.577350 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −2.24264 | −0.314033 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −6.82843 | −0.937957 | −0.468978 | − | 0.883210i | \(-0.655378\pi\) | ||||
−0.468978 | + | 0.883210i | \(0.655378\pi\) | |||||||
\(54\) | −1.41421 | −0.192450 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 4.65685 | 0.616815 | ||||||||
\(58\) | 11.6569 | 1.53062 | ||||||||
\(59\) | 1.41421 | 0.184115 | 0.0920575 | − | 0.995754i | \(-0.470656\pi\) | ||||
0.0920575 | + | 0.995754i | \(0.470656\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 4.48528 | 0.574281 | 0.287141 | − | 0.957888i | \(-0.407295\pi\) | ||||
0.287141 | + | 0.957888i | \(0.407295\pi\) | |||||||
\(62\) | 8.24264 | 1.04682 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 8.00000 | 1.00000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −0.828427 | −0.101972 | ||||||||
\(67\) | 13.7279 | 1.67713 | 0.838566 | − | 0.544800i | \(-0.183394\pi\) | ||||
0.838566 | + | 0.544800i | \(0.183394\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 2.24264 | 0.269982 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −0.585786 | −0.0695201 | −0.0347600 | − | 0.999396i | \(-0.511067\pi\) | ||||
−0.0347600 | + | 0.999396i | \(0.511067\pi\) | |||||||
\(72\) | −2.82843 | −0.333333 | ||||||||
\(73\) | −12.0711 | −1.41281 | −0.706406 | − | 0.707807i | \(-0.749685\pi\) | ||||
−0.706406 | + | 0.707807i | \(0.749685\pi\) | |||||||
\(74\) | 11.8995 | 1.38329 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 6.24264 | 0.706840 | ||||||||
\(79\) | 6.65685 | 0.748955 | 0.374477 | − | 0.927236i | \(-0.377822\pi\) | ||||
0.374477 | + | 0.927236i | \(0.377822\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 8.82843 | 0.974937 | ||||||||
\(83\) | 2.58579 | 0.283827 | 0.141913 | − | 0.989879i | \(-0.454675\pi\) | ||||
0.141913 | + | 0.989879i | \(0.454675\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 10.7279 | 1.15682 | ||||||||
\(87\) | −8.24264 | −0.883704 | ||||||||
\(88\) | −1.65685 | −0.176621 | ||||||||
\(89\) | 12.2426 | 1.29772 | 0.648859 | − | 0.760909i | \(-0.275247\pi\) | ||||
0.648859 | + | 0.760909i | \(0.275247\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −5.82843 | −0.604380 | ||||||||
\(94\) | −18.8284 | −1.94200 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −5.17157 | −0.525094 | −0.262547 | − | 0.964919i | \(-0.584562\pi\) | ||||
−0.262547 | + | 0.964919i | \(0.584562\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0.585786 | 0.0588738 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −2.24264 | −0.223151 | −0.111576 | − | 0.993756i | \(-0.535590\pi\) | ||||
−0.111576 | + | 0.993756i | \(0.535590\pi\) | |||||||
\(102\) | −3.17157 | −0.314033 | ||||||||
\(103\) | 7.24264 | 0.713639 | 0.356819 | − | 0.934173i | \(-0.383861\pi\) | ||||
0.356819 | + | 0.934173i | \(0.383861\pi\) | |||||||
\(104\) | 12.4853 | 1.22428 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −9.65685 | −0.937957 | ||||||||
\(107\) | −12.5858 | −1.21671 | −0.608357 | − | 0.793664i | \(-0.708171\pi\) | ||||
−0.608357 | + | 0.793664i | \(0.708171\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 3.48528 | 0.333829 | 0.166915 | − | 0.985971i | \(-0.446620\pi\) | ||||
0.166915 | + | 0.985971i | \(0.446620\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −8.41421 | −0.798642 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 15.6569 | 1.47287 | 0.736436 | − | 0.676507i | \(-0.236507\pi\) | ||||
0.736436 | + | 0.676507i | \(0.236507\pi\) | |||||||
\(114\) | 6.58579 | 0.616815 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −4.41421 | −0.408094 | ||||||||
\(118\) | 2.00000 | 0.184115 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.6569 | −0.968805 | ||||||||
\(122\) | 6.34315 | 0.574281 | ||||||||
\(123\) | −6.24264 | −0.562880 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 3.92893 | 0.348636 | 0.174318 | − | 0.984689i | \(-0.444228\pi\) | ||||
0.174318 | + | 0.984689i | \(0.444228\pi\) | |||||||
\(128\) | 11.3137 | 1.00000 | ||||||||
\(129\) | −7.58579 | −0.667891 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −6.48528 | −0.566622 | −0.283311 | − | 0.959028i | \(-0.591433\pi\) | ||||
−0.283311 | + | 0.959028i | \(0.591433\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 19.4142 | 1.67713 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −6.34315 | −0.543920 | ||||||||
\(137\) | 17.0711 | 1.45848 | 0.729240 | − | 0.684258i | \(-0.239874\pi\) | ||||
0.729240 | + | 0.684258i | \(0.239874\pi\) | |||||||
\(138\) | 3.17157 | 0.269982 | ||||||||
\(139\) | 5.48528 | 0.465255 | 0.232628 | − | 0.972566i | \(-0.425268\pi\) | ||||
0.232628 | + | 0.972566i | \(0.425268\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 13.3137 | 1.12122 | ||||||||
\(142\) | −0.828427 | −0.0695201 | ||||||||
\(143\) | −2.58579 | −0.216234 | ||||||||
\(144\) | −4.00000 | −0.333333 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −17.0711 | −1.41281 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 6.34315 | 0.519651 | 0.259825 | − | 0.965656i | \(-0.416335\pi\) | ||||
0.259825 | + | 0.965656i | \(0.416335\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 10.4853 | 0.853280 | 0.426640 | − | 0.904422i | \(-0.359697\pi\) | ||||
0.426640 | + | 0.904422i | \(0.359697\pi\) | |||||||
\(152\) | 13.1716 | 1.06836 | ||||||||
\(153\) | 2.24264 | 0.181307 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 12.1421 | 0.969048 | 0.484524 | − | 0.874778i | \(-0.338993\pi\) | ||||
0.484524 | + | 0.874778i | \(0.338993\pi\) | |||||||
\(158\) | 9.41421 | 0.748955 | ||||||||
\(159\) | 6.82843 | 0.541529 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 1.41421 | 0.111111 | ||||||||
\(163\) | −3.31371 | −0.259550 | −0.129775 | − | 0.991543i | \(-0.541425\pi\) | ||||
−0.129775 | + | 0.991543i | \(0.541425\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 3.65685 | 0.283827 | ||||||||
\(167\) | 20.2426 | 1.56642 | 0.783211 | − | 0.621756i | \(-0.213580\pi\) | ||||
0.783211 | + | 0.621756i | \(0.213580\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 6.48528 | 0.498868 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −4.65685 | −0.356119 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 2.82843 | 0.215041 | 0.107521 | − | 0.994203i | \(-0.465709\pi\) | ||||
0.107521 | + | 0.994203i | \(0.465709\pi\) | |||||||
\(174\) | −11.6569 | −0.883704 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −2.34315 | −0.176621 | ||||||||
\(177\) | −1.41421 | −0.106299 | ||||||||
\(178\) | 17.3137 | 1.29772 | ||||||||
\(179\) | 8.34315 | 0.623596 | 0.311798 | − | 0.950148i | \(-0.399069\pi\) | ||||
0.311798 | + | 0.950148i | \(0.399069\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 10.6569 | 0.792118 | 0.396059 | − | 0.918225i | \(-0.370378\pi\) | ||||
0.396059 | + | 0.918225i | \(0.370378\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −4.48528 | −0.331562 | ||||||||
\(184\) | 6.34315 | 0.467623 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −8.24264 | −0.604380 | ||||||||
\(187\) | 1.31371 | 0.0960679 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −14.9706 | −1.08323 | −0.541616 | − | 0.840626i | \(-0.682187\pi\) | ||||
−0.541616 | + | 0.840626i | \(0.682187\pi\) | |||||||
\(192\) | −8.00000 | −0.577350 | ||||||||
\(193\) | 15.2426 | 1.09719 | 0.548595 | − | 0.836088i | \(-0.315163\pi\) | ||||
0.548595 | + | 0.836088i | \(0.315163\pi\) | |||||||
\(194\) | −7.31371 | −0.525094 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 25.5563 | 1.82081 | 0.910407 | − | 0.413713i | \(-0.135768\pi\) | ||||
0.910407 | + | 0.413713i | \(0.135768\pi\) | |||||||
\(198\) | 0.828427 | 0.0588738 | ||||||||
\(199\) | −22.4853 | −1.59394 | −0.796970 | − | 0.604019i | \(-0.793565\pi\) | ||||
−0.796970 | + | 0.604019i | \(0.793565\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −13.7279 | −0.968293 | ||||||||
\(202\) | −3.17157 | −0.223151 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 10.2426 | 0.713639 | ||||||||
\(207\) | −2.24264 | −0.155874 | ||||||||
\(208\) | 17.6569 | 1.22428 | ||||||||
\(209\) | −2.72792 | −0.188694 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −28.1421 | −1.93738 | −0.968692 | − | 0.248265i | \(-0.920140\pi\) | ||||
−0.968692 | + | 0.248265i | \(0.920140\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0.585786 | 0.0401374 | ||||||||
\(214\) | −17.7990 | −1.21671 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 2.82843 | 0.192450 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 4.92893 | 0.333829 | ||||||||
\(219\) | 12.0711 | 0.815687 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −9.89949 | −0.665912 | ||||||||
\(222\) | −11.8995 | −0.798642 | ||||||||
\(223\) | 22.8284 | 1.52870 | 0.764352 | − | 0.644799i | \(-0.223059\pi\) | ||||
0.764352 | + | 0.644799i | \(0.223059\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 22.1421 | 1.47287 | ||||||||
\(227\) | 8.92893 | 0.592634 | 0.296317 | − | 0.955090i | \(-0.404242\pi\) | ||||
0.296317 | + | 0.955090i | \(0.404242\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −8.31371 | −0.549385 | −0.274693 | − | 0.961532i | \(-0.588576\pi\) | ||||
−0.274693 | + | 0.961532i | \(0.588576\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −23.3137 | −1.53062 | ||||||||
\(233\) | 5.51472 | 0.361281 | 0.180641 | − | 0.983549i | \(-0.442183\pi\) | ||||
0.180641 | + | 0.983549i | \(0.442183\pi\) | |||||||
\(234\) | −6.24264 | −0.408094 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −6.65685 | −0.432409 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −5.31371 | −0.343715 | −0.171858 | − | 0.985122i | \(-0.554977\pi\) | ||||
−0.171858 | + | 0.985122i | \(0.554977\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 21.6569 | 1.39504 | 0.697520 | − | 0.716565i | \(-0.254287\pi\) | ||||
0.697520 | + | 0.716565i | \(0.254287\pi\) | |||||||
\(242\) | −15.0711 | −0.968805 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −8.82843 | −0.562880 | ||||||||
\(247\) | 20.5563 | 1.30797 | ||||||||
\(248\) | −16.4853 | −1.04682 | ||||||||
\(249\) | −2.58579 | −0.163868 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 2.58579 | 0.163213 | 0.0816067 | − | 0.996665i | \(-0.473995\pi\) | ||||
0.0816067 | + | 0.996665i | \(0.473995\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1.31371 | −0.0825921 | ||||||||
\(254\) | 5.55635 | 0.348636 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −10.1005 | −0.630052 | −0.315026 | − | 0.949083i | \(-0.602013\pi\) | ||||
−0.315026 | + | 0.949083i | \(0.602013\pi\) | |||||||
\(258\) | −10.7279 | −0.667891 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 8.24264 | 0.510207 | ||||||||
\(262\) | −9.17157 | −0.566622 | ||||||||
\(263\) | −6.82843 | −0.421059 | −0.210529 | − | 0.977588i | \(-0.567519\pi\) | ||||
−0.210529 | + | 0.977588i | \(0.567519\pi\) | |||||||
\(264\) | 1.65685 | 0.101972 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −12.2426 | −0.749237 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 20.1421 | 1.22809 | 0.614044 | − | 0.789272i | \(-0.289542\pi\) | ||||
0.614044 | + | 0.789272i | \(0.289542\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 8.14214 | 0.494600 | 0.247300 | − | 0.968939i | \(-0.420457\pi\) | ||||
0.247300 | + | 0.968939i | \(0.420457\pi\) | |||||||
\(272\) | −8.97056 | −0.543920 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 24.1421 | 1.45848 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −13.3848 | −0.804213 | −0.402107 | − | 0.915593i | \(-0.631722\pi\) | ||||
−0.402107 | + | 0.915593i | \(0.631722\pi\) | |||||||
\(278\) | 7.75736 | 0.465255 | ||||||||
\(279\) | 5.82843 | 0.348939 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −1.65685 | −0.0988396 | −0.0494198 | − | 0.998778i | \(-0.515737\pi\) | ||||
−0.0494198 | + | 0.998778i | \(0.515737\pi\) | |||||||
\(282\) | 18.8284 | 1.12122 | ||||||||
\(283\) | −4.75736 | −0.282796 | −0.141398 | − | 0.989953i | \(-0.545160\pi\) | ||||
−0.141398 | + | 0.989953i | \(0.545160\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −3.65685 | −0.216234 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −11.9706 | −0.704151 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 5.17157 | 0.303163 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 7.31371 | 0.427271 | 0.213636 | − | 0.976913i | \(-0.431469\pi\) | ||||
0.213636 | + | 0.976913i | \(0.431469\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −23.7990 | −1.38329 | ||||||||
\(297\) | −0.585786 | −0.0339908 | ||||||||
\(298\) | 8.97056 | 0.519651 | ||||||||
\(299\) | 9.89949 | 0.572503 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 14.8284 | 0.853280 | ||||||||
\(303\) | 2.24264 | 0.128836 | ||||||||
\(304\) | 18.6274 | 1.06836 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 3.17157 | 0.181307 | ||||||||
\(307\) | 4.41421 | 0.251932 | 0.125966 | − | 0.992035i | \(-0.459797\pi\) | ||||
0.125966 | + | 0.992035i | \(0.459797\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −7.24264 | −0.412019 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 2.92893 | 0.166085 | 0.0830423 | − | 0.996546i | \(-0.473536\pi\) | ||||
0.0830423 | + | 0.996546i | \(0.473536\pi\) | |||||||
\(312\) | −12.4853 | −0.706840 | ||||||||
\(313\) | −16.2132 | −0.916424 | −0.458212 | − | 0.888843i | \(-0.651510\pi\) | ||||
−0.458212 | + | 0.888843i | \(0.651510\pi\) | |||||||
\(314\) | 17.1716 | 0.969048 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −19.8995 | −1.11767 | −0.558833 | − | 0.829280i | \(-0.688751\pi\) | ||||
−0.558833 | + | 0.829280i | \(0.688751\pi\) | |||||||
\(318\) | 9.65685 | 0.541529 | ||||||||
\(319\) | 4.82843 | 0.270340 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 12.5858 | 0.702470 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −10.4437 | −0.581100 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −4.68629 | −0.259550 | ||||||||
\(327\) | −3.48528 | −0.192737 | ||||||||
\(328\) | −17.6569 | −0.974937 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 17.6274 | 0.968890 | 0.484445 | − | 0.874822i | \(-0.339021\pi\) | ||||
0.484445 | + | 0.874822i | \(0.339021\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 8.41421 | 0.461096 | ||||||||
\(334\) | 28.6274 | 1.56642 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −18.8995 | −1.02952 | −0.514761 | − | 0.857334i | \(-0.672119\pi\) | ||||
−0.514761 | + | 0.857334i | \(0.672119\pi\) | |||||||
\(338\) | 9.17157 | 0.498868 | ||||||||
\(339\) | −15.6569 | −0.850364 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 3.41421 | 0.184890 | ||||||||
\(342\) | −6.58579 | −0.356119 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −21.4558 | −1.15682 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 4.00000 | 0.215041 | ||||||||
\(347\) | −8.97056 | −0.481565 | −0.240783 | − | 0.970579i | \(-0.577404\pi\) | ||||
−0.240783 | + | 0.970579i | \(0.577404\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −28.6274 | −1.53239 | −0.766195 | − | 0.642608i | \(-0.777852\pi\) | ||||
−0.766195 | + | 0.642608i | \(0.777852\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 4.41421 | 0.235613 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −13.8995 | −0.739795 | −0.369898 | − | 0.929072i | \(-0.620607\pi\) | ||||
−0.369898 | + | 0.929072i | \(0.620607\pi\) | |||||||
\(354\) | −2.00000 | −0.106299 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 11.7990 | 0.623596 | ||||||||
\(359\) | −29.4142 | −1.55242 | −0.776211 | − | 0.630473i | \(-0.782861\pi\) | ||||
−0.776211 | + | 0.630473i | \(0.782861\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 2.68629 | 0.141384 | ||||||||
\(362\) | 15.0711 | 0.792118 | ||||||||
\(363\) | 10.6569 | 0.559340 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −6.34315 | −0.331562 | ||||||||
\(367\) | −22.4142 | −1.17001 | −0.585006 | − | 0.811029i | \(-0.698908\pi\) | ||||
−0.585006 | + | 0.811029i | \(0.698908\pi\) | |||||||
\(368\) | 8.97056 | 0.467623 | ||||||||
\(369\) | 6.24264 | 0.324979 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −10.7574 | −0.556995 | −0.278497 | − | 0.960437i | \(-0.589836\pi\) | ||||
−0.278497 | + | 0.960437i | \(0.589836\pi\) | |||||||
\(374\) | 1.85786 | 0.0960679 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 37.6569 | 1.94200 | ||||||||
\(377\) | −36.3848 | −1.87391 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −24.7990 | −1.27384 | −0.636919 | − | 0.770931i | \(-0.719792\pi\) | ||||
−0.636919 | + | 0.770931i | \(0.719792\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −3.92893 | −0.201285 | ||||||||
\(382\) | −21.1716 | −1.08323 | ||||||||
\(383\) | −4.48528 | −0.229187 | −0.114594 | − | 0.993412i | \(-0.536557\pi\) | ||||
−0.114594 | + | 0.993412i | \(0.536557\pi\) | |||||||
\(384\) | −11.3137 | −0.577350 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 21.5563 | 1.09719 | ||||||||
\(387\) | 7.58579 | 0.385607 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −36.8701 | −1.86939 | −0.934693 | − | 0.355456i | \(-0.884326\pi\) | ||||
−0.934693 | + | 0.355456i | \(0.884326\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −5.02944 | −0.254350 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 6.48528 | 0.327139 | ||||||||
\(394\) | 36.1421 | 1.82081 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 18.2132 | 0.914094 | 0.457047 | − | 0.889442i | \(-0.348907\pi\) | ||||
0.457047 | + | 0.889442i | \(0.348907\pi\) | |||||||
\(398\) | −31.7990 | −1.59394 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −16.4853 | −0.823236 | −0.411618 | − | 0.911357i | \(-0.635036\pi\) | ||||
−0.411618 | + | 0.911357i | \(0.635036\pi\) | |||||||
\(402\) | −19.4142 | −0.968293 | ||||||||
\(403\) | −25.7279 | −1.28160 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 4.92893 | 0.244318 | ||||||||
\(408\) | 6.34315 | 0.314033 | ||||||||
\(409\) | 3.68629 | 0.182275 | 0.0911377 | − | 0.995838i | \(-0.470950\pi\) | ||||
0.0911377 | + | 0.995838i | \(0.470950\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −17.0711 | −0.842054 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −3.17157 | −0.155874 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −5.48528 | −0.268615 | ||||||||
\(418\) | −3.85786 | −0.188694 | ||||||||
\(419\) | 8.82843 | 0.431297 | 0.215648 | − | 0.976471i | \(-0.430813\pi\) | ||||
0.215648 | + | 0.976471i | \(0.430813\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 10.5147 | 0.512456 | 0.256228 | − | 0.966616i | \(-0.417520\pi\) | ||||
0.256228 | + | 0.966616i | \(0.417520\pi\) | |||||||
\(422\) | −39.7990 | −1.93738 | ||||||||
\(423\) | −13.3137 | −0.647335 | ||||||||
\(424\) | 19.3137 | 0.937957 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0.828427 | 0.0401374 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 2.58579 | 0.124843 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 31.1716 | 1.50148 | 0.750741 | − | 0.660597i | \(-0.229697\pi\) | ||||
0.750741 | + | 0.660597i | \(0.229697\pi\) | |||||||
\(432\) | 4.00000 | 0.192450 | ||||||||
\(433\) | 6.55635 | 0.315078 | 0.157539 | − | 0.987513i | \(-0.449644\pi\) | ||||
0.157539 | + | 0.987513i | \(0.449644\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 10.4437 | 0.499588 | ||||||||
\(438\) | 17.0711 | 0.815687 | ||||||||
\(439\) | −11.6569 | −0.556351 | −0.278176 | − | 0.960530i | \(-0.589730\pi\) | ||||
−0.278176 | + | 0.960530i | \(0.589730\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −14.0000 | −0.665912 | ||||||||
\(443\) | 16.4853 | 0.783239 | 0.391620 | − | 0.920127i | \(-0.371915\pi\) | ||||
0.391620 | + | 0.920127i | \(0.371915\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 32.2843 | 1.52870 | ||||||||
\(447\) | −6.34315 | −0.300020 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 26.9706 | 1.27282 | 0.636410 | − | 0.771351i | \(-0.280419\pi\) | ||||
0.636410 | + | 0.771351i | \(0.280419\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 3.65685 | 0.172195 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −10.4853 | −0.492641 | ||||||||
\(454\) | 12.6274 | 0.592634 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −13.1716 | −0.616815 | ||||||||
\(457\) | 1.10051 | 0.0514795 | 0.0257397 | − | 0.999669i | \(-0.491806\pi\) | ||||
0.0257397 | + | 0.999669i | \(0.491806\pi\) | |||||||
\(458\) | −11.7574 | −0.549385 | ||||||||
\(459\) | −2.24264 | −0.104678 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 12.9289 | 0.602160 | 0.301080 | − | 0.953599i | \(-0.402653\pi\) | ||||
0.301080 | + | 0.953599i | \(0.402653\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 7.58579 | 0.352541 | 0.176271 | − | 0.984342i | \(-0.443597\pi\) | ||||
0.176271 | + | 0.984342i | \(0.443597\pi\) | |||||||
\(464\) | −32.9706 | −1.53062 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 7.79899 | 0.361281 | ||||||||
\(467\) | 29.3137 | 1.35648 | 0.678238 | − | 0.734842i | \(-0.262744\pi\) | ||||
0.678238 | + | 0.734842i | \(0.262744\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −12.1421 | −0.559480 | ||||||||
\(472\) | −4.00000 | −0.184115 | ||||||||
\(473\) | 4.44365 | 0.204319 | ||||||||
\(474\) | −9.41421 | −0.432409 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −6.82843 | −0.312652 | ||||||||
\(478\) | −7.51472 | −0.343715 | ||||||||
\(479\) | −10.6274 | −0.485579 | −0.242790 | − | 0.970079i | \(-0.578062\pi\) | ||||
−0.242790 | + | 0.970079i | \(0.578062\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −37.1421 | −1.69354 | ||||||||
\(482\) | 30.6274 | 1.39504 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −1.41421 | −0.0641500 | ||||||||
\(487\) | 18.8995 | 0.856418 | 0.428209 | − | 0.903680i | \(-0.359145\pi\) | ||||
0.428209 | + | 0.903680i | \(0.359145\pi\) | |||||||
\(488\) | −12.6863 | −0.574281 | ||||||||
\(489\) | 3.31371 | 0.149851 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 18.1421 | 0.818743 | 0.409372 | − | 0.912368i | \(-0.365748\pi\) | ||||
0.409372 | + | 0.912368i | \(0.365748\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 18.4853 | 0.832535 | ||||||||
\(494\) | 29.0711 | 1.30797 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −23.3137 | −1.04682 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −3.65685 | −0.163868 | ||||||||
\(499\) | −30.7990 | −1.37875 | −0.689376 | − | 0.724404i | \(-0.742115\pi\) | ||||
−0.689376 | + | 0.724404i | \(0.742115\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −20.2426 | −0.904374 | ||||||||
\(502\) | 3.65685 | 0.163213 | ||||||||
\(503\) | −1.51472 | −0.0675380 | −0.0337690 | − | 0.999430i | \(-0.510751\pi\) | ||||
−0.0337690 | + | 0.999430i | \(0.510751\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −1.85786 | −0.0825921 | ||||||||
\(507\) | −6.48528 | −0.288021 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 25.7990 | 1.14352 | 0.571760 | − | 0.820421i | \(-0.306261\pi\) | ||||
0.571760 | + | 0.820421i | \(0.306261\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −22.6274 | −1.00000 | ||||||||
\(513\) | 4.65685 | 0.205605 | ||||||||
\(514\) | −14.2843 | −0.630052 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −7.79899 | −0.342999 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −2.82843 | −0.124154 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −23.1127 | −1.01259 | −0.506293 | − | 0.862362i | \(-0.668985\pi\) | ||||
−0.506293 | + | 0.862362i | \(0.668985\pi\) | |||||||
\(522\) | 11.6569 | 0.510207 | ||||||||
\(523\) | −10.4142 | −0.455382 | −0.227691 | − | 0.973733i | \(-0.573118\pi\) | ||||
−0.227691 | + | 0.973733i | \(0.573118\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −9.65685 | −0.421059 | ||||||||
\(527\) | 13.0711 | 0.569385 | ||||||||
\(528\) | 2.34315 | 0.101972 | ||||||||
\(529\) | −17.9706 | −0.781329 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 1.41421 | 0.0613716 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −27.5563 | −1.19360 | ||||||||
\(534\) | −17.3137 | −0.749237 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −38.8284 | −1.67713 | ||||||||
\(537\) | −8.34315 | −0.360033 | ||||||||
\(538\) | 28.4853 | 1.22809 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 9.68629 | 0.416446 | 0.208223 | − | 0.978081i | \(-0.433232\pi\) | ||||
0.208223 | + | 0.978081i | \(0.433232\pi\) | |||||||
\(542\) | 11.5147 | 0.494600 | ||||||||
\(543\) | −10.6569 | −0.457329 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −7.79899 | −0.333461 | −0.166730 | − | 0.986003i | \(-0.553321\pi\) | ||||
−0.166730 | + | 0.986003i | \(0.553321\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 4.48528 | 0.191427 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −38.3848 | −1.63525 | ||||||||
\(552\) | −6.34315 | −0.269982 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −18.9289 | −0.804213 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 19.6569 | 0.832888 | 0.416444 | − | 0.909161i | \(-0.363276\pi\) | ||||
0.416444 | + | 0.909161i | \(0.363276\pi\) | |||||||
\(558\) | 8.24264 | 0.348939 | ||||||||
\(559\) | −33.4853 | −1.41628 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −1.31371 | −0.0554648 | ||||||||
\(562\) | −2.34315 | −0.0988396 | ||||||||
\(563\) | 42.2843 | 1.78207 | 0.891035 | − | 0.453935i | \(-0.149980\pi\) | ||||
0.891035 | + | 0.453935i | \(0.149980\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −6.72792 | −0.282796 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 1.65685 | 0.0695201 | ||||||||
\(569\) | 16.8701 | 0.707230 | 0.353615 | − | 0.935391i | \(-0.384952\pi\) | ||||
0.353615 | + | 0.935391i | \(0.384952\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −5.97056 | −0.249860 | −0.124930 | − | 0.992166i | \(-0.539871\pi\) | ||||
−0.124930 | + | 0.992166i | \(0.539871\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 14.9706 | 0.625404 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 8.00000 | 0.333333 | ||||||||
\(577\) | −24.5563 | −1.02229 | −0.511147 | − | 0.859493i | \(-0.670779\pi\) | ||||
−0.511147 | + | 0.859493i | \(0.670779\pi\) | |||||||
\(578\) | −16.9289 | −0.704151 | ||||||||
\(579\) | −15.2426 | −0.633463 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 7.31371 | 0.303163 | ||||||||
\(583\) | −4.00000 | −0.165663 | ||||||||
\(584\) | 34.1421 | 1.41281 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 10.3431 | 0.427271 | ||||||||
\(587\) | 21.7574 | 0.898022 | 0.449011 | − | 0.893526i | \(-0.351776\pi\) | ||||
0.449011 | + | 0.893526i | \(0.351776\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −27.1421 | −1.11837 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −25.5563 | −1.05125 | ||||||||
\(592\) | −33.6569 | −1.38329 | ||||||||
\(593\) | 10.5858 | 0.434706 | 0.217353 | − | 0.976093i | \(-0.430258\pi\) | ||||
0.217353 | + | 0.976093i | \(0.430258\pi\) | |||||||
\(594\) | −0.828427 | −0.0339908 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 22.4853 | 0.920261 | ||||||||
\(598\) | 14.0000 | 0.572503 | ||||||||
\(599\) | −13.8579 | −0.566217 | −0.283108 | − | 0.959088i | \(-0.591366\pi\) | ||||
−0.283108 | + | 0.959088i | \(0.591366\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 29.8284 | 1.21673 | 0.608363 | − | 0.793659i | \(-0.291826\pi\) | ||||
0.608363 | + | 0.793659i | \(0.291826\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 13.7279 | 0.559044 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 3.17157 | 0.128836 | ||||||||
\(607\) | 7.24264 | 0.293970 | 0.146985 | − | 0.989139i | \(-0.453043\pi\) | ||||
0.146985 | + | 0.989139i | \(0.453043\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 58.7696 | 2.37756 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 18.1421 | 0.732754 | 0.366377 | − | 0.930467i | \(-0.380598\pi\) | ||||
0.366377 | + | 0.930467i | \(0.380598\pi\) | |||||||
\(614\) | 6.24264 | 0.251932 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 3.17157 | 0.127683 | 0.0638414 | − | 0.997960i | \(-0.479665\pi\) | ||||
0.0638414 | + | 0.997960i | \(0.479665\pi\) | |||||||
\(618\) | −10.2426 | −0.412019 | ||||||||
\(619\) | −6.02944 | −0.242344 | −0.121172 | − | 0.992632i | \(-0.538665\pi\) | ||||
−0.121172 | + | 0.992632i | \(0.538665\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 2.24264 | 0.0899941 | ||||||||
\(622\) | 4.14214 | 0.166085 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −17.6569 | −0.706840 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −22.9289 | −0.916424 | ||||||||
\(627\) | 2.72792 | 0.108943 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 18.8701 | 0.752398 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 16.0000 | 0.636950 | 0.318475 | − | 0.947931i | \(-0.396829\pi\) | ||||
0.318475 | + | 0.947931i | \(0.396829\pi\) | |||||||
\(632\) | −18.8284 | −0.748955 | ||||||||
\(633\) | 28.1421 | 1.11855 | ||||||||
\(634\) | −28.1421 | −1.11767 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 6.82843 | 0.270340 | ||||||||
\(639\) | −0.585786 | −0.0231734 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 29.2132 | 1.15385 | 0.576926 | − | 0.816796i | \(-0.304252\pi\) | ||||
0.576926 | + | 0.816796i | \(0.304252\pi\) | |||||||
\(642\) | 17.7990 | 0.702470 | ||||||||
\(643\) | −6.55635 | −0.258557 | −0.129279 | − | 0.991608i | \(-0.541266\pi\) | ||||
−0.129279 | + | 0.991608i | \(0.541266\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −14.7696 | −0.581100 | ||||||||
\(647\) | 46.3848 | 1.82357 | 0.911787 | − | 0.410664i | \(-0.134703\pi\) | ||||
0.911787 | + | 0.410664i | \(0.134703\pi\) | |||||||
\(648\) | −2.82843 | −0.111111 | ||||||||
\(649\) | 0.828427 | 0.0325186 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −16.2426 | −0.635624 | −0.317812 | − | 0.948154i | \(-0.602948\pi\) | ||||
−0.317812 | + | 0.948154i | \(0.602948\pi\) | |||||||
\(654\) | −4.92893 | −0.192737 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −24.9706 | −0.974937 | ||||||||
\(657\) | −12.0711 | −0.470937 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −4.68629 | −0.182552 | −0.0912760 | − | 0.995826i | \(-0.529095\pi\) | ||||
−0.0912760 | + | 0.995826i | \(0.529095\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −9.68629 | −0.376753 | −0.188377 | − | 0.982097i | \(-0.560323\pi\) | ||||
−0.188377 | + | 0.982097i | \(0.560323\pi\) | |||||||
\(662\) | 24.9289 | 0.968890 | ||||||||
\(663\) | 9.89949 | 0.384465 | ||||||||
\(664\) | −7.31371 | −0.283827 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 11.8995 | 0.461096 | ||||||||
\(667\) | −18.4853 | −0.715753 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −22.8284 | −0.882598 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 2.62742 | 0.101430 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −27.7279 | −1.06883 | −0.534416 | − | 0.845221i | \(-0.679469\pi\) | ||||
−0.534416 | + | 0.845221i | \(0.679469\pi\) | |||||||
\(674\) | −26.7279 | −1.02952 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −15.8995 | −0.611067 | −0.305534 | − | 0.952181i | \(-0.598835\pi\) | ||||
−0.305534 | + | 0.952181i | \(0.598835\pi\) | |||||||
\(678\) | −22.1421 | −0.850364 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −8.92893 | −0.342157 | ||||||||
\(682\) | 4.82843 | 0.184890 | ||||||||
\(683\) | −23.4142 | −0.895920 | −0.447960 | − | 0.894054i | \(-0.647849\pi\) | ||||
−0.447960 | + | 0.894054i | \(0.647849\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 8.31371 | 0.317188 | ||||||||
\(688\) | −30.3431 | −1.15682 | ||||||||
\(689\) | 30.1421 | 1.14832 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −7.68629 | −0.292400 | −0.146200 | − | 0.989255i | \(-0.546704\pi\) | ||||
−0.146200 | + | 0.989255i | \(0.546704\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −12.6863 | −0.481565 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 23.3137 | 0.883704 | ||||||||
\(697\) | 14.0000 | 0.530288 | ||||||||
\(698\) | −40.4853 | −1.53239 | ||||||||
\(699\) | −5.51472 | −0.208586 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −1.21320 | −0.0458221 | −0.0229110 | − | 0.999738i | \(-0.507293\pi\) | ||||
−0.0229110 | + | 0.999738i | \(0.507293\pi\) | |||||||
\(702\) | 6.24264 | 0.235613 | ||||||||
\(703\) | −39.1838 | −1.47784 | ||||||||
\(704\) | 4.68629 | 0.176621 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −19.6569 | −0.739795 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 51.1127 | 1.91958 | 0.959789 | − | 0.280723i | \(-0.0905742\pi\) | ||||
0.959789 | + | 0.280723i | \(0.0905742\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 6.65685 | 0.249652 | ||||||||
\(712\) | −34.6274 | −1.29772 | ||||||||
\(713\) | −13.0711 | −0.489515 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 5.31371 | 0.198444 | ||||||||
\(718\) | −41.5980 | −1.55242 | ||||||||
\(719\) | −34.4853 | −1.28608 | −0.643042 | − | 0.765831i | \(-0.722328\pi\) | ||||
−0.643042 | + | 0.765831i | \(0.722328\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 3.79899 | 0.141384 | ||||||||
\(723\) | −21.6569 | −0.805427 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 15.0711 | 0.559340 | ||||||||
\(727\) | 13.2426 | 0.491142 | 0.245571 | − | 0.969379i | \(-0.421024\pi\) | ||||
0.245571 | + | 0.969379i | \(0.421024\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 17.0122 | 0.629219 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −19.2426 | −0.710743 | −0.355372 | − | 0.934725i | \(-0.615646\pi\) | ||||
−0.355372 | + | 0.934725i | \(0.615646\pi\) | |||||||
\(734\) | −31.6985 | −1.17001 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 8.04163 | 0.296217 | ||||||||
\(738\) | 8.82843 | 0.324979 | ||||||||
\(739\) | −6.85786 | −0.252271 | −0.126135 | − | 0.992013i | \(-0.540257\pi\) | ||||
−0.126135 | + | 0.992013i | \(0.540257\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −20.5563 | −0.755156 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −20.7279 | −0.760434 | −0.380217 | − | 0.924897i | \(-0.624151\pi\) | ||||
−0.380217 | + | 0.924897i | \(0.624151\pi\) | |||||||
\(744\) | 16.4853 | 0.604380 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −15.2132 | −0.556995 | ||||||||
\(747\) | 2.58579 | 0.0946090 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −25.6274 | −0.935158 | −0.467579 | − | 0.883951i | \(-0.654874\pi\) | ||||
−0.467579 | + | 0.883951i | \(0.654874\pi\) | |||||||
\(752\) | 53.2548 | 1.94200 | ||||||||
\(753\) | −2.58579 | −0.0942313 | ||||||||
\(754\) | −51.4558 | −1.87391 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 37.5980 | 1.36652 | 0.683261 | − | 0.730174i | \(-0.260561\pi\) | ||||
0.683261 | + | 0.730174i | \(0.260561\pi\) | |||||||
\(758\) | −35.0711 | −1.27384 | ||||||||
\(759\) | 1.31371 | 0.0476846 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 35.0711 | 1.27133 | 0.635663 | − | 0.771967i | \(-0.280727\pi\) | ||||
0.635663 | + | 0.771967i | \(0.280727\pi\) | |||||||
\(762\) | −5.55635 | −0.201285 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −6.34315 | −0.229187 | ||||||||
\(767\) | −6.24264 | −0.225409 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −17.9706 | −0.648035 | −0.324018 | − | 0.946051i | \(-0.605034\pi\) | ||||
−0.324018 | + | 0.946051i | \(0.605034\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 10.1005 | 0.363761 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 39.0711 | 1.40529 | 0.702644 | − | 0.711541i | \(-0.252003\pi\) | ||||
0.702644 | + | 0.711541i | \(0.252003\pi\) | |||||||
\(774\) | 10.7279 | 0.385607 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 14.6274 | 0.525094 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −52.1421 | −1.86939 | ||||||||
\(779\) | −29.0711 | −1.04158 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −0.343146 | −0.0122787 | ||||||||
\(782\) | −7.11270 | −0.254350 | ||||||||
\(783\) | −8.24264 | −0.294568 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 9.17157 | 0.327139 | ||||||||
\(787\) | 18.8284 | 0.671161 | 0.335580 | − | 0.942012i | \(-0.391068\pi\) | ||||
0.335580 | + | 0.942012i | \(0.391068\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 6.82843 | 0.243098 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −1.65685 | −0.0588738 | ||||||||
\(793\) | −19.7990 | −0.703083 | ||||||||
\(794\) | 25.7574 | 0.914094 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 41.5563 | 1.47200 | 0.736001 | − | 0.676981i | \(-0.236712\pi\) | ||||
0.736001 | + | 0.676981i | \(0.236712\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −29.8579 | −1.05630 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 12.2426 | 0.432572 | ||||||||
\(802\) | −23.3137 | −0.823236 | ||||||||
\(803\) | −7.07107 | −0.249533 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −36.3848 | −1.28160 | ||||||||
\(807\) | −20.1421 | −0.709037 | ||||||||
\(808\) | 6.34315 | 0.223151 | ||||||||
\(809\) | 40.6274 | 1.42838 | 0.714192 | − | 0.699950i | \(-0.246794\pi\) | ||||
0.714192 | + | 0.699950i | \(0.246794\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −10.9706 | −0.385229 | −0.192614 | − | 0.981275i | \(-0.561697\pi\) | ||||
−0.192614 | + | 0.981275i | \(0.561697\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −8.14214 | −0.285557 | ||||||||
\(814\) | 6.97056 | 0.244318 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 8.97056 | 0.314033 | ||||||||
\(817\) | −35.3259 | −1.23590 | ||||||||
\(818\) | 5.21320 | 0.182275 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −17.5563 | −0.612721 | −0.306360 | − | 0.951916i | \(-0.599111\pi\) | ||||
−0.306360 | + | 0.951916i | \(0.599111\pi\) | |||||||
\(822\) | −24.1421 | −0.842054 | ||||||||
\(823\) | 34.2843 | 1.19507 | 0.597537 | − | 0.801841i | \(-0.296146\pi\) | ||||
0.597537 | + | 0.801841i | \(0.296146\pi\) | |||||||
\(824\) | −20.4853 | −0.713639 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −7.17157 | −0.249380 | −0.124690 | − | 0.992196i | \(-0.539794\pi\) | ||||
−0.124690 | + | 0.992196i | \(0.539794\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 7.34315 | 0.255038 | 0.127519 | − | 0.991836i | \(-0.459299\pi\) | ||||
0.127519 | + | 0.991836i | \(0.459299\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 13.3848 | 0.464313 | ||||||||
\(832\) | −35.3137 | −1.22428 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −7.75736 | −0.268615 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −5.82843 | −0.201460 | ||||||||
\(838\) | 12.4853 | 0.431297 | ||||||||
\(839\) | 32.7279 | 1.12989 | 0.564947 | − | 0.825127i | \(-0.308897\pi\) | ||||
0.564947 | + | 0.825127i | \(0.308897\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 38.9411 | 1.34280 | ||||||||
\(842\) | 14.8701 | 0.512456 | ||||||||
\(843\) | 1.65685 | 0.0570651 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −18.8284 | −0.647335 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 27.3137 | 0.937957 | ||||||||
\(849\) | 4.75736 | 0.163272 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −18.8701 | −0.646857 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −44.0122 | −1.50695 | −0.753474 | − | 0.657477i | \(-0.771624\pi\) | ||||
−0.753474 | + | 0.657477i | \(0.771624\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 35.5980 | 1.21671 | ||||||||
\(857\) | 2.24264 | 0.0766071 | 0.0383036 | − | 0.999266i | \(-0.487805\pi\) | ||||
0.0383036 | + | 0.999266i | \(0.487805\pi\) | |||||||
\(858\) | 3.65685 | 0.124843 | ||||||||
\(859\) | −4.34315 | −0.148186 | −0.0740931 | − | 0.997251i | \(-0.523606\pi\) | ||||
−0.0740931 | + | 0.997251i | \(0.523606\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 44.0833 | 1.50148 | ||||||||
\(863\) | −29.7990 | −1.01437 | −0.507185 | − | 0.861837i | \(-0.669314\pi\) | ||||
−0.507185 | + | 0.861837i | \(0.669314\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 9.27208 | 0.315078 | ||||||||
\(867\) | 11.9706 | 0.406542 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 3.89949 | 0.132281 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −60.5980 | −2.05328 | ||||||||
\(872\) | −9.85786 | −0.333829 | ||||||||
\(873\) | −5.17157 | −0.175031 | ||||||||
\(874\) | 14.7696 | 0.499588 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 18.0000 | 0.607817 | 0.303908 | − | 0.952701i | \(-0.401708\pi\) | ||||
0.303908 | + | 0.952701i | \(0.401708\pi\) | |||||||
\(878\) | −16.4853 | −0.556351 | ||||||||
\(879\) | −7.31371 | −0.246685 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 10.3431 | 0.348469 | 0.174235 | − | 0.984704i | \(-0.444255\pi\) | ||||
0.174235 | + | 0.984704i | \(0.444255\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 6.07107 | 0.204308 | 0.102154 | − | 0.994769i | \(-0.467427\pi\) | ||||
0.102154 | + | 0.994769i | \(0.467427\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 23.3137 | 0.783239 | ||||||||
\(887\) | −37.2132 | −1.24950 | −0.624749 | − | 0.780826i | \(-0.714799\pi\) | ||||
−0.624749 | + | 0.780826i | \(0.714799\pi\) | |||||||
\(888\) | 23.7990 | 0.798642 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0.585786 | 0.0196246 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 62.0000 | 2.07475 | ||||||||
\(894\) | −8.97056 | −0.300020 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −9.89949 | −0.330535 | ||||||||
\(898\) | 38.1421 | 1.27282 | ||||||||
\(899\) | 48.0416 | 1.60228 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −15.3137 | −0.510174 | ||||||||
\(902\) | 5.17157 | 0.172195 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −44.2843 | −1.47287 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −14.8284 | −0.492641 | ||||||||
\(907\) | 45.3848 | 1.50698 | 0.753488 | − | 0.657461i | \(-0.228370\pi\) | ||||
0.753488 | + | 0.657461i | \(0.228370\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −2.24264 | −0.0743837 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −4.24264 | −0.140565 | −0.0702825 | − | 0.997527i | \(-0.522390\pi\) | ||||
−0.0702825 | + | 0.997527i | \(0.522390\pi\) | |||||||
\(912\) | −18.6274 | −0.616815 | ||||||||
\(913\) | 1.51472 | 0.0501299 | ||||||||
\(914\) | 1.55635 | 0.0514795 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −3.17157 | −0.104678 | ||||||||
\(919\) | −35.3431 | −1.16586 | −0.582931 | − | 0.812521i | \(-0.698094\pi\) | ||||
−0.582931 | + | 0.812521i | \(0.698094\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −4.41421 | −0.145453 | ||||||||
\(922\) | 18.2843 | 0.602160 | ||||||||
\(923\) | 2.58579 | 0.0851122 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 10.7279 | 0.352541 | ||||||||
\(927\) | 7.24264 | 0.237880 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −31.0122 | −1.01748 | −0.508739 | − | 0.860921i | \(-0.669888\pi\) | ||||
−0.508739 | + | 0.860921i | \(0.669888\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −2.92893 | −0.0958889 | ||||||||
\(934\) | 41.4558 | 1.35648 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 12.4853 | 0.408094 | ||||||||
\(937\) | −22.0711 | −0.721030 | −0.360515 | − | 0.932753i | \(-0.617399\pi\) | ||||
−0.360515 | + | 0.932753i | \(0.617399\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 16.2132 | 0.529098 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 36.7279 | 1.19730 | 0.598648 | − | 0.801012i | \(-0.295705\pi\) | ||||
0.598648 | + | 0.801012i | \(0.295705\pi\) | |||||||
\(942\) | −17.1716 | −0.559480 | ||||||||
\(943\) | −14.0000 | −0.455903 | ||||||||
\(944\) | −5.65685 | −0.184115 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 6.28427 | 0.204319 | ||||||||
\(947\) | 19.0711 | 0.619726 | 0.309863 | − | 0.950781i | \(-0.399717\pi\) | ||||
0.309863 | + | 0.950781i | \(0.399717\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 53.2843 | 1.72968 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 19.8995 | 0.645285 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −31.5147 | −1.02086 | −0.510431 | − | 0.859919i | \(-0.670514\pi\) | ||||
−0.510431 | + | 0.859919i | \(0.670514\pi\) | |||||||
\(954\) | −9.65685 | −0.312652 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −4.82843 | −0.156081 | ||||||||
\(958\) | −15.0294 | −0.485579 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 2.97056 | 0.0958246 | ||||||||
\(962\) | −52.5269 | −1.69354 | ||||||||
\(963\) | −12.5858 | −0.405571 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 13.3848 | 0.430425 | 0.215213 | − | 0.976567i | \(-0.430956\pi\) | ||||
0.215213 | + | 0.976567i | \(0.430956\pi\) | |||||||
\(968\) | 30.1421 | 0.968805 | ||||||||
\(969\) | 10.4437 | 0.335498 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −25.6569 | −0.823368 | −0.411684 | − | 0.911327i | \(-0.635059\pi\) | ||||
−0.411684 | + | 0.911327i | \(0.635059\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 26.7279 | 0.856418 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −17.9411 | −0.574281 | ||||||||
\(977\) | 45.6985 | 1.46202 | 0.731012 | − | 0.682365i | \(-0.239048\pi\) | ||||
0.731012 | + | 0.682365i | \(0.239048\pi\) | |||||||
\(978\) | 4.68629 | 0.149851 | ||||||||
\(979\) | 7.17157 | 0.229204 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 3.48528 | 0.111276 | ||||||||
\(982\) | 25.6569 | 0.818743 | ||||||||
\(983\) | −57.1543 | −1.82294 | −0.911470 | − | 0.411367i | \(-0.865052\pi\) | ||||
−0.911470 | + | 0.411367i | \(0.865052\pi\) | |||||||
\(984\) | 17.6569 | 0.562880 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 26.1421 | 0.832535 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −17.0122 | −0.540956 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −19.3431 | −0.614455 | −0.307228 | − | 0.951636i | \(-0.599401\pi\) | ||||
−0.307228 | + | 0.951636i | \(0.599401\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −17.6274 | −0.559389 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 9.24264 | 0.292717 | 0.146359 | − | 0.989232i | \(-0.453245\pi\) | ||||
0.146359 | + | 0.989232i | \(0.453245\pi\) | |||||||
\(998\) | −43.5563 | −1.37875 | ||||||||
\(999\) | −8.41421 | −0.266214 |
(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 | 3675.2.a.x.1.2 | 2 | ||
5.4 | even | 2 | 735.2.a.j.1.1 | 2 | |||
7.3 | odd | 6 | 525.2.i.g.226.1 | 4 | |||
7.5 | odd | 6 | 525.2.i.g.151.1 | 4 | |||
7.6 | odd | 2 | 3675.2.a.z.1.2 | 2 | |||
15.14 | odd | 2 | 2205.2.a.s.1.2 | 2 | |||
35.3 | even | 12 | 525.2.r.g.499.4 | 8 | |||
35.4 | even | 6 | 735.2.i.j.226.2 | 4 | |||
35.9 | even | 6 | 735.2.i.j.361.2 | 4 | |||
35.12 | even | 12 | 525.2.r.g.424.4 | 8 | |||
35.17 | even | 12 | 525.2.r.g.499.1 | 8 | |||
35.19 | odd | 6 | 105.2.i.c.46.2 | yes | 4 | ||
35.24 | odd | 6 | 105.2.i.c.16.2 | ✓ | 4 | ||
35.33 | even | 12 | 525.2.r.g.424.1 | 8 | |||
35.34 | odd | 2 | 735.2.a.i.1.1 | 2 | |||
105.59 | even | 6 | 315.2.j.d.226.1 | 4 | |||
105.89 | even | 6 | 315.2.j.d.46.1 | 4 | |||
105.104 | even | 2 | 2205.2.a.u.1.2 | 2 | |||
140.19 | even | 6 | 1680.2.bg.p.1201.2 | 4 | |||
140.59 | even | 6 | 1680.2.bg.p.961.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
105.2.i.c.16.2 | ✓ | 4 | 35.24 | odd | 6 | ||
105.2.i.c.46.2 | yes | 4 | 35.19 | odd | 6 | ||
315.2.j.d.46.1 | 4 | 105.89 | even | 6 | |||
315.2.j.d.226.1 | 4 | 105.59 | even | 6 | |||
525.2.i.g.151.1 | 4 | 7.5 | odd | 6 | |||
525.2.i.g.226.1 | 4 | 7.3 | odd | 6 | |||
525.2.r.g.424.1 | 8 | 35.33 | even | 12 | |||
525.2.r.g.424.4 | 8 | 35.12 | even | 12 | |||
525.2.r.g.499.1 | 8 | 35.17 | even | 12 | |||
525.2.r.g.499.4 | 8 | 35.3 | even | 12 | |||
735.2.a.i.1.1 | 2 | 35.34 | odd | 2 | |||
735.2.a.j.1.1 | 2 | 5.4 | even | 2 | |||
735.2.i.j.226.2 | 4 | 35.4 | even | 6 | |||
735.2.i.j.361.2 | 4 | 35.9 | even | 6 | |||
1680.2.bg.p.961.2 | 4 | 140.59 | even | 6 | |||
1680.2.bg.p.1201.2 | 4 | 140.19 | even | 6 | |||
2205.2.a.s.1.2 | 2 | 15.14 | odd | 2 | |||
2205.2.a.u.1.2 | 2 | 105.104 | even | 2 | |||
3675.2.a.x.1.2 | 2 | 1.1 | even | 1 | trivial | ||
3675.2.a.z.1.2 | 2 | 7.6 | odd | 2 |