Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6348,2,Mod(1,6348)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6348, 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("6348.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6348 = 2^{2} \cdot 3 \cdot 23^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6348.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: | \(50.6890352031\) |
Analytic rank: | \(0\) |
Dimension: | \(10\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} - 4x^{9} - 14x^{8} + 65x^{7} + 57x^{6} - 354x^{5} - 46x^{4} + 714x^{3} - 74x^{2} - 323x - 23 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 276) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(2.46393\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6348.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.04710 | −0.468279 | −0.234140 | − | 0.972203i | \(-0.575227\pi\) | ||||
−0.234140 | + | 0.972203i | \(0.575227\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.46307 | −0.552988 | −0.276494 | − | 0.961016i | \(-0.589173\pi\) | ||||
−0.276494 | + | 0.961016i | \(0.589173\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.04776 | 0.617423 | 0.308712 | − | 0.951156i | \(-0.400102\pi\) | ||||
0.308712 | + | 0.951156i | \(0.400102\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −6.89348 | −1.91191 | −0.955953 | − | 0.293519i | \(-0.905173\pi\) | ||||
−0.955953 | + | 0.293519i | \(0.905173\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.04710 | −0.270361 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 7.77763 | 1.88635 | 0.943176 | − | 0.332294i | \(-0.107823\pi\) | ||||
0.943176 | + | 0.332294i | \(0.107823\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −6.37212 | −1.46187 | −0.730933 | − | 0.682450i | \(-0.760915\pi\) | ||||
−0.730933 | + | 0.682450i | \(0.760915\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.46307 | −0.319268 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0 | 0 | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3.90357 | −0.780714 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 4.14709 | 0.770095 | 0.385048 | − | 0.922897i | \(-0.374185\pi\) | ||||
0.385048 | + | 0.922897i | \(0.374185\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.909997 | 0.163440 | 0.0817201 | − | 0.996655i | \(-0.473959\pi\) | ||||
0.0817201 | + | 0.996655i | \(0.473959\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 2.04776 | 0.356469 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1.53199 | 0.258953 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −4.07919 | −0.670614 | −0.335307 | − | 0.942109i | \(-0.608840\pi\) | ||||
−0.335307 | + | 0.942109i | \(0.608840\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −6.89348 | −1.10384 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 4.89363 | 0.764257 | 0.382129 | − | 0.924109i | \(-0.375191\pi\) | ||||
0.382129 | + | 0.924109i | \(0.375191\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 3.50314 | 0.534224 | 0.267112 | − | 0.963665i | \(-0.413931\pi\) | ||||
0.267112 | + | 0.963665i | \(0.413931\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.04710 | −0.156093 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −1.92699 | −0.281080 | −0.140540 | − | 0.990075i | \(-0.544884\pi\) | ||||
−0.140540 | + | 0.990075i | \(0.544884\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −4.85943 | −0.694205 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 7.77763 | 1.08909 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 7.82919 | 1.07542 | 0.537711 | − | 0.843129i | \(-0.319289\pi\) | ||||
0.537711 | + | 0.843129i | \(0.319289\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −2.14422 | −0.289127 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −6.37212 | −0.844008 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 14.4629 | 1.88291 | 0.941453 | − | 0.337145i | \(-0.109461\pi\) | ||||
0.941453 | + | 0.337145i | \(0.109461\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 7.53528 | 0.964794 | 0.482397 | − | 0.875953i | \(-0.339766\pi\) | ||||
0.482397 | + | 0.875953i | \(0.339766\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −1.46307 | −0.184329 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 7.21819 | 0.895306 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 10.0950 | 1.23330 | 0.616650 | − | 0.787237i | \(-0.288489\pi\) | ||||
0.616650 | + | 0.787237i | \(0.288489\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −0.197482 | −0.0234368 | −0.0117184 | − | 0.999931i | \(-0.503730\pi\) | ||||
−0.0117184 | + | 0.999931i | \(0.503730\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −7.96038 | −0.931692 | −0.465846 | − | 0.884866i | \(-0.654250\pi\) | ||||
−0.465846 | + | 0.884866i | \(0.654250\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −3.90357 | −0.450746 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −2.99601 | −0.341427 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 4.62746 | 0.520630 | 0.260315 | − | 0.965524i | \(-0.416174\pi\) | ||||
0.260315 | + | 0.965524i | \(0.416174\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −8.28322 | −0.909201 | −0.454601 | − | 0.890695i | \(-0.650218\pi\) | ||||
−0.454601 | + | 0.890695i | \(0.650218\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −8.14399 | −0.883340 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 4.14709 | 0.444615 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 0.275247 | 0.0291762 | 0.0145881 | − | 0.999894i | \(-0.495356\pi\) | ||||
0.0145881 | + | 0.999894i | \(0.495356\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 10.0856 | 1.05726 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0.909997 | 0.0943623 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 6.67228 | 0.684561 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 7.35665 | 0.746954 | 0.373477 | − | 0.927639i | \(-0.378165\pi\) | ||||
0.373477 | + | 0.927639i | \(0.378165\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 2.04776 | 0.205808 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −14.3167 | −1.42456 | −0.712282 | − | 0.701893i | \(-0.752338\pi\) | ||||
−0.712282 | + | 0.701893i | \(0.752338\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 4.01467 | 0.395577 | 0.197788 | − | 0.980245i | \(-0.436624\pi\) | ||||
0.197788 | + | 0.980245i | \(0.436624\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 1.53199 | 0.149506 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 13.0252 | 1.25919 | 0.629597 | − | 0.776922i | \(-0.283220\pi\) | ||||
0.629597 | + | 0.776922i | \(0.283220\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 3.54533 | 0.339581 | 0.169791 | − | 0.985480i | \(-0.445691\pi\) | ||||
0.169791 | + | 0.985480i | \(0.445691\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −4.07919 | −0.387179 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 15.3074 | 1.43999 | 0.719997 | − | 0.693977i | \(-0.244143\pi\) | ||||
0.719997 | + | 0.693977i | \(0.244143\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −6.89348 | −0.637302 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −11.3792 | −1.04313 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −6.80668 | −0.618789 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 4.89363 | 0.441244 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 9.32297 | 0.833872 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 13.7788 | 1.22267 | 0.611335 | − | 0.791372i | \(-0.290633\pi\) | ||||
0.611335 | + | 0.791372i | \(0.290633\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 3.50314 | 0.308434 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −9.61471 | −0.840041 | −0.420020 | − | 0.907515i | \(-0.637977\pi\) | ||||
−0.420020 | + | 0.907515i | \(0.637977\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 9.32285 | 0.808393 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −1.04710 | −0.0901204 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −3.53079 | −0.301656 | −0.150828 | − | 0.988560i | \(-0.548194\pi\) | ||||
−0.150828 | + | 0.988560i | \(0.548194\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2.28333 | 0.193670 | 0.0968349 | − | 0.995300i | \(-0.469128\pi\) | ||||
0.0968349 | + | 0.995300i | \(0.469128\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −1.92699 | −0.162282 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −14.1162 | −1.18046 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −4.34244 | −0.360620 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −4.85943 | −0.400799 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 13.5130 | 1.10703 | 0.553515 | − | 0.832839i | \(-0.313286\pi\) | ||||
0.553515 | + | 0.832839i | \(0.313286\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2.31041 | −0.188019 | −0.0940093 | − | 0.995571i | \(-0.529968\pi\) | ||||
−0.0940093 | + | 0.995571i | \(0.529968\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 7.77763 | 0.628784 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −0.952862 | −0.0765357 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 12.0945 | 0.965245 | 0.482622 | − | 0.875829i | \(-0.339684\pi\) | ||||
0.482622 | + | 0.875829i | \(0.339684\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 7.82919 | 0.620895 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −21.6370 | −1.69474 | −0.847371 | − | 0.531001i | \(-0.821816\pi\) | ||||
−0.847371 | + | 0.531001i | \(0.821816\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −2.14422 | −0.166927 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −5.53960 | −0.428667 | −0.214333 | − | 0.976761i | \(-0.568758\pi\) | ||||
−0.214333 | + | 0.976761i | \(0.568758\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 34.5200 | 2.65539 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −6.37212 | −0.487288 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 10.9773 | 0.834590 | 0.417295 | − | 0.908771i | \(-0.362978\pi\) | ||||
0.417295 | + | 0.908771i | \(0.362978\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 5.71119 | 0.431725 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 14.4629 | 1.08710 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 18.9602 | 1.41715 | 0.708576 | − | 0.705634i | \(-0.249338\pi\) | ||||
0.708576 | + | 0.705634i | \(0.249338\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 16.7037 | 1.24158 | 0.620789 | − | 0.783978i | \(-0.286812\pi\) | ||||
0.620789 | + | 0.783978i | \(0.286812\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 7.53528 | 0.557024 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 4.27134 | 0.314035 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 15.9267 | 1.16468 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −1.46307 | −0.106423 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −10.1256 | −0.732663 | −0.366332 | − | 0.930484i | \(-0.619386\pi\) | ||||
−0.366332 | + | 0.930484i | \(0.619386\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 14.1573 | 1.01906 | 0.509532 | − | 0.860452i | \(-0.329819\pi\) | ||||
0.509532 | + | 0.860452i | \(0.329819\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 7.21819 | 0.516905 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −25.3524 | −1.80628 | −0.903140 | − | 0.429346i | \(-0.858744\pi\) | ||||
−0.903140 | + | 0.429346i | \(0.858744\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −13.2342 | −0.938148 | −0.469074 | − | 0.883159i | \(-0.655412\pi\) | ||||
−0.469074 | + | 0.883159i | \(0.655412\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 10.0950 | 0.712047 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −6.06748 | −0.425853 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −5.12415 | −0.357886 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −13.0486 | −0.902589 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1.29644 | −0.0892509 | −0.0446254 | − | 0.999004i | \(-0.514209\pi\) | ||||
−0.0446254 | + | 0.999004i | \(0.514209\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −0.197482 | −0.0135313 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −3.66816 | −0.250166 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1.33139 | −0.0903804 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −7.96038 | −0.537913 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −53.6149 | −3.60653 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −12.1561 | −0.814030 | −0.407015 | − | 0.913422i | \(-0.633430\pi\) | ||||
−0.407015 | + | 0.913422i | \(0.633430\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −3.90357 | −0.260238 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 23.5950 | 1.56606 | 0.783029 | − | 0.621985i | \(-0.213674\pi\) | ||||
0.783029 | + | 0.621985i | \(0.213674\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −15.4803 | −1.02296 | −0.511482 | − | 0.859294i | \(-0.670903\pi\) | ||||
−0.511482 | + | 0.859294i | \(0.670903\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −2.99601 | −0.197123 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 12.4984 | 0.818800 | 0.409400 | − | 0.912355i | \(-0.365738\pi\) | ||||
0.409400 | + | 0.912355i | \(0.365738\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 2.01776 | 0.131624 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 4.62746 | 0.300586 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 20.8825 | 1.35078 | 0.675390 | − | 0.737461i | \(-0.263975\pi\) | ||||
0.675390 | + | 0.737461i | \(0.263975\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −2.57940 | −0.166154 | −0.0830768 | − | 0.996543i | \(-0.526475\pi\) | ||||
−0.0830768 | + | 0.996543i | \(0.526475\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 5.08833 | 0.325082 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 43.9261 | 2.79495 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −8.28322 | −0.524928 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −6.31385 | −0.398527 | −0.199263 | − | 0.979946i | \(-0.563855\pi\) | ||||
−0.199263 | + | 0.979946i | \(0.563855\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −8.14399 | −0.509996 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 12.3028 | 0.767425 | 0.383713 | − | 0.923453i | \(-0.374645\pi\) | ||||
0.383713 | + | 0.923453i | \(0.374645\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 5.96813 | 0.370842 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 4.14709 | 0.256698 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −7.09090 | −0.437244 | −0.218622 | − | 0.975810i | \(-0.570156\pi\) | ||||
−0.218622 | + | 0.975810i | \(0.570156\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −8.19798 | −0.503598 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0.275247 | 0.0168449 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −14.9741 | −0.912989 | −0.456494 | − | 0.889726i | \(-0.650895\pi\) | ||||
−0.456494 | + | 0.889726i | \(0.650895\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 18.3737 | 1.11612 | 0.558061 | − | 0.829800i | \(-0.311545\pi\) | ||||
0.558061 | + | 0.829800i | \(0.311545\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 10.0856 | 0.610410 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −7.99358 | −0.482031 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 13.9414 | 0.837657 | 0.418829 | − | 0.908065i | \(-0.362441\pi\) | ||||
0.418829 | + | 0.908065i | \(0.362441\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0.909997 | 0.0544801 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 7.75769 | 0.462785 | 0.231392 | − | 0.972861i | \(-0.425672\pi\) | ||||
0.231392 | + | 0.972861i | \(0.425672\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 32.5795 | 1.93665 | 0.968325 | − | 0.249693i | \(-0.0803297\pi\) | ||||
0.968325 | + | 0.249693i | \(0.0803297\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 6.67228 | 0.395232 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −7.15972 | −0.422625 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 43.4915 | 2.55832 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 7.35665 | 0.431254 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −21.4612 | −1.25378 | −0.626889 | − | 0.779108i | \(-0.715672\pi\) | ||||
−0.626889 | + | 0.779108i | \(0.715672\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −15.1441 | −0.881726 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 2.04776 | 0.118823 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −5.12533 | −0.295419 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −14.3167 | −0.822473 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −7.89023 | −0.451793 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −4.31387 | −0.246205 | −0.123103 | − | 0.992394i | \(-0.539284\pi\) | ||||
−0.123103 | + | 0.992394i | \(0.539284\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 4.01467 | 0.228386 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 12.9425 | 0.733899 | 0.366950 | − | 0.930241i | \(-0.380402\pi\) | ||||
0.366950 | + | 0.930241i | \(0.380402\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −3.69404 | −0.208800 | −0.104400 | − | 0.994535i | \(-0.533292\pi\) | ||||
−0.104400 | + | 0.994535i | \(0.533292\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 1.53199 | 0.0863176 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 18.7068 | 1.05068 | 0.525339 | − | 0.850893i | \(-0.323938\pi\) | ||||
0.525339 | + | 0.850893i | \(0.323938\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 8.49225 | 0.475475 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 13.0252 | 0.726996 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −49.5600 | −2.75759 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 26.9092 | 1.49265 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 3.54533 | 0.196057 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 2.81931 | 0.155434 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −4.54026 | −0.249555 | −0.124778 | − | 0.992185i | \(-0.539822\pi\) | ||||
−0.124778 | + | 0.992185i | \(0.539822\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −4.07919 | −0.223538 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −10.5705 | −0.577530 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 22.6085 | 1.23156 | 0.615782 | − | 0.787917i | \(-0.288840\pi\) | ||||
0.615782 | + | 0.787917i | \(0.288840\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 15.3074 | 0.831381 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1.86346 | 0.100912 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 17.3512 | 0.936874 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 18.0403 | 0.968452 | 0.484226 | − | 0.874943i | \(-0.339101\pi\) | ||||
0.484226 | + | 0.874943i | \(0.339101\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −5.02311 | −0.268881 | −0.134441 | − | 0.990922i | \(-0.542924\pi\) | ||||
−0.134441 | + | 0.990922i | \(0.542924\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −6.89348 | −0.367947 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 12.7057 | 0.676254 | 0.338127 | − | 0.941100i | \(-0.390207\pi\) | ||||
0.338127 | + | 0.941100i | \(0.390207\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0.206785 | 0.0109750 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −11.3792 | −0.602251 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −5.33498 | −0.281569 | −0.140785 | − | 0.990040i | \(-0.544963\pi\) | ||||
−0.140785 | + | 0.990040i | \(0.544963\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 21.6039 | 1.13705 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −6.80668 | −0.357258 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 8.33535 | 0.436292 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 1.47822 | 0.0771624 | 0.0385812 | − | 0.999255i | \(-0.487716\pi\) | ||||
0.0385812 | + | 0.999255i | \(0.487716\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 4.89363 | 0.254752 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −11.4546 | −0.594695 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −17.5700 | −0.909740 | −0.454870 | − | 0.890558i | \(-0.650314\pi\) | ||||
−0.454870 | + | 0.890558i | \(0.650314\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 9.32297 | 0.481436 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −28.5879 | −1.47235 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 5.17831 | 0.265992 | 0.132996 | − | 0.991117i | \(-0.457540\pi\) | ||||
0.132996 | + | 0.991117i | \(0.457540\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 13.7788 | 0.705909 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 27.7003 | 1.41542 | 0.707708 | − | 0.706505i | \(-0.249729\pi\) | ||||
0.707708 | + | 0.706505i | \(0.249729\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 3.13714 | 0.159883 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 3.50314 | 0.178075 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −5.37281 | −0.272412 | −0.136206 | − | 0.990681i | \(-0.543491\pi\) | ||||
−0.136206 | + | 0.990681i | \(0.543491\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −9.61471 | −0.484998 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −4.84543 | −0.243800 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −36.1923 | −1.81644 | −0.908219 | − | 0.418496i | \(-0.862557\pi\) | ||||
−0.908219 | + | 0.418496i | \(0.862557\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 9.32285 | 0.466726 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 9.19341 | 0.459097 | 0.229549 | − | 0.973297i | \(-0.426275\pi\) | ||||
0.229549 | + | 0.973297i | \(0.426275\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −6.27304 | −0.312482 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −1.04710 | −0.0520311 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −8.35320 | −0.414053 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −0.848516 | −0.0419564 | −0.0209782 | − | 0.999780i | \(-0.506678\pi\) | ||||
−0.0209782 | + | 0.999780i | \(0.506678\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −3.53079 | −0.174161 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −21.1602 | −1.04122 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 8.67340 | 0.425760 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 2.28333 | 0.111815 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −24.7145 | −1.20738 | −0.603691 | − | 0.797219i | \(-0.706304\pi\) | ||||
−0.603691 | + | 0.797219i | \(0.706304\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −15.6587 | −0.763157 | −0.381578 | − | 0.924336i | \(-0.624619\pi\) | ||||
−0.381578 | + | 0.924336i | \(0.624619\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −1.92699 | −0.0936933 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −30.3605 | −1.47270 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −11.0246 | −0.533519 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −14.1162 | −0.681536 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 6.65212 | 0.320421 | 0.160211 | − | 0.987083i | \(-0.448783\pi\) | ||||
0.160211 | + | 0.987083i | \(0.448783\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −20.2388 | −0.972613 | −0.486306 | − | 0.873788i | \(-0.661656\pi\) | ||||
−0.486306 | + | 0.873788i | \(0.661656\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −4.34244 | −0.208204 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 4.12378 | 0.196817 | 0.0984087 | − | 0.995146i | \(-0.468625\pi\) | ||||
0.0984087 | + | 0.995146i | \(0.468625\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −4.85943 | −0.231402 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 30.6761 | 1.45747 | 0.728733 | − | 0.684798i | \(-0.240110\pi\) | ||||
0.728733 | + | 0.684798i | \(0.240110\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −0.288213 | −0.0136626 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 13.5130 | 0.639144 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 22.6823 | 1.07045 | 0.535223 | − | 0.844711i | \(-0.320228\pi\) | ||||
0.535223 | + | 0.844711i | \(0.320228\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 10.0210 | 0.471870 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −2.31041 | −0.108553 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −10.5607 | −0.495093 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 28.1141 | 1.31512 | 0.657561 | − | 0.753401i | \(-0.271588\pi\) | ||||
0.657561 | + | 0.753401i | \(0.271588\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 7.77763 | 0.363029 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −4.98643 | −0.232241 | −0.116121 | − | 0.993235i | \(-0.537046\pi\) | ||||
−0.116121 | + | 0.993235i | \(0.537046\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −26.2974 | −1.22214 | −0.611072 | − | 0.791575i | \(-0.709261\pi\) | ||||
−0.611072 | + | 0.791575i | \(0.709261\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −0.952862 | −0.0441879 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −35.6620 | −1.65024 | −0.825119 | − | 0.564959i | \(-0.808892\pi\) | ||||
−0.825119 | + | 0.564959i | \(0.808892\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −14.7697 | −0.682000 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 12.0945 | 0.557284 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 7.17360 | 0.329842 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 24.8740 | 1.14130 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 7.82919 | 0.358474 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 42.3745 | 1.93614 | 0.968069 | − | 0.250682i | \(-0.0806550\pi\) | ||||
0.968069 | + | 0.250682i | \(0.0806550\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 28.1198 | 1.28215 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −7.70318 | −0.349783 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −29.8140 | −1.35100 | −0.675501 | − | 0.737359i | \(-0.736073\pi\) | ||||
−0.675501 | + | 0.737359i | \(0.736073\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −21.6370 | −0.978460 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 13.0685 | 0.589773 | 0.294886 | − | 0.955532i | \(-0.404718\pi\) | ||||
0.294886 | + | 0.955532i | \(0.404718\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 32.2545 | 1.45267 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −2.14422 | −0.0963755 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0.288930 | 0.0129603 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −21.7301 | −0.972773 | −0.486386 | − | 0.873744i | \(-0.661685\pi\) | ||||
−0.486386 | + | 0.873744i | \(0.661685\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −5.53960 | −0.247491 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 18.2149 | 0.812161 | 0.406080 | − | 0.913837i | \(-0.366895\pi\) | ||||
0.406080 | + | 0.913837i | \(0.366895\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 14.9911 | 0.667094 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 34.5200 | 1.53309 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −1.51886 | −0.0673224 | −0.0336612 | − | 0.999433i | \(-0.510717\pi\) | ||||
−0.0336612 | + | 0.999433i | \(0.510717\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 11.6466 | 0.515214 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −6.37212 | −0.281336 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −4.20378 | −0.185240 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −3.94601 | −0.173545 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 10.9773 | 0.481851 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −14.7934 | −0.648112 | −0.324056 | − | 0.946038i | \(-0.605047\pi\) | ||||
−0.324056 | + | 0.946038i | \(0.605047\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −19.5761 | −0.856001 | −0.428001 | − | 0.903778i | \(-0.640782\pi\) | ||||
−0.428001 | + | 0.903778i | \(0.640782\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 5.71119 | 0.249257 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 7.07761 | 0.308306 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 0 | 0 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 14.4629 | 0.627635 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −33.7341 | −1.46119 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −13.6387 | −0.589654 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 18.9602 | 0.818193 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −9.95095 | −0.428618 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −1.41169 | −0.0606934 | −0.0303467 | − | 0.999539i | \(-0.509661\pi\) | ||||
−0.0303467 | + | 0.999539i | \(0.509661\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 16.7037 | 0.716825 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −3.71233 | −0.159019 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −22.4315 | −0.959102 | −0.479551 | − | 0.877514i | \(-0.659200\pi\) | ||||
−0.479551 | + | 0.877514i | \(0.659200\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 7.53528 | 0.321598 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −26.4258 | −1.12578 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −6.77028 | −0.287902 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 4.27134 | 0.181308 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −34.8082 | −1.47487 | −0.737436 | − | 0.675417i | \(-0.763964\pi\) | ||||
−0.737436 | + | 0.675417i | \(0.763964\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −24.1488 | −1.02139 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 15.9267 | 0.672427 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 46.7994 | 1.97236 | 0.986179 | − | 0.165685i | \(-0.0529834\pi\) | ||||
0.986179 | + | 0.165685i | \(0.0529834\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −16.0284 | −0.674320 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −1.46307 | −0.0614431 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 8.73896 | 0.366356 | 0.183178 | − | 0.983080i | \(-0.441361\pi\) | ||||
0.183178 | + | 0.983080i | \(0.441361\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −19.7017 | −0.824491 | −0.412246 | − | 0.911073i | \(-0.635255\pi\) | ||||
−0.412246 | + | 0.911073i | \(0.635255\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −10.1256 | −0.423003 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −17.2532 | −0.718260 | −0.359130 | − | 0.933288i | \(-0.616927\pi\) | ||||
−0.359130 | + | 0.933288i | \(0.616927\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 14.1573 | 0.588357 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 12.1189 | 0.502777 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 16.0323 | 0.663990 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 7.21819 | 0.298435 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 23.3777 | 0.964900 | 0.482450 | − | 0.875923i | \(-0.339747\pi\) | ||||
0.482450 | + | 0.875923i | \(0.339747\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −5.79861 | −0.238928 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −25.3524 | −1.04286 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 14.6390 | 0.601152 | 0.300576 | − | 0.953758i | \(-0.402821\pi\) | ||||
0.300576 | + | 0.953758i | \(0.402821\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 11.9152 | 0.488476 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −13.2342 | −0.541640 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −18.2295 | −0.744838 | −0.372419 | − | 0.928065i | \(-0.621472\pi\) | ||||
−0.372419 | + | 0.928065i | \(0.621472\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −33.9613 | −1.38531 | −0.692655 | − | 0.721269i | \(-0.743559\pi\) | ||||
−0.692655 | + | 0.721269i | \(0.743559\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 10.0950 | 0.411100 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 7.12730 | 0.289766 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 48.9794 | 1.98801 | 0.994007 | − | 0.109314i | \(-0.0348655\pi\) | ||||
0.994007 | + | 0.109314i | \(0.0348655\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −6.06748 | −0.245866 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 13.2836 | 0.537398 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −20.6235 | −0.832974 | −0.416487 | − | 0.909142i | \(-0.636739\pi\) | ||||
−0.416487 | + | 0.909142i | \(0.636739\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −5.12415 | −0.206626 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 27.0051 | 1.08718 | 0.543592 | − | 0.839350i | \(-0.317064\pi\) | ||||
0.543592 | + | 0.839350i | \(0.317064\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −27.3293 | −1.09846 | −0.549228 | − | 0.835673i | \(-0.685078\pi\) | ||||
−0.549228 | + | 0.835673i | \(0.685078\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −0.402706 | −0.0161341 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 9.75573 | 0.390229 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −13.0486 | −0.521110 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −31.7264 | −1.26501 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −40.2664 | −1.60298 | −0.801491 | − | 0.598007i | \(-0.795959\pi\) | ||||
−0.801491 | + | 0.598007i | \(0.795959\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −1.29644 | −0.0515290 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −14.4278 | −0.572551 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 33.4984 | 1.32725 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −0.197482 | −0.00781227 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 3.44875 | 0.136217 | 0.0681087 | − | 0.997678i | \(-0.478304\pi\) | ||||
0.0681087 | + | 0.997678i | \(0.478304\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 23.4827 | 0.926065 | 0.463033 | − | 0.886341i | \(-0.346761\pi\) | ||||
0.463033 | + | 0.886341i | \(0.346761\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −3.66816 | −0.144434 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 39.1906 | 1.54074 | 0.770371 | − | 0.637595i | \(-0.220071\pi\) | ||||
0.770371 | + | 0.637595i | \(0.220071\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 29.6165 | 1.16255 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −1.33139 | −0.0521812 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −4.39915 | −0.172152 | −0.0860760 | − | 0.996289i | \(-0.527433\pi\) | ||||
−0.0860760 | + | 0.996289i | \(0.527433\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 10.0676 | 0.393374 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −7.96038 | −0.310564 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −15.4695 | −0.602606 | −0.301303 | − | 0.953528i | \(-0.597422\pi\) | ||||
−0.301303 | + | 0.953528i | \(0.597422\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 25.5574 | 0.994069 | 0.497035 | − | 0.867731i | \(-0.334422\pi\) | ||||
0.497035 | + | 0.867731i | \(0.334422\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −53.6149 | −2.08223 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −9.76200 | −0.378554 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −12.1561 | −0.469980 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 15.4305 | 0.595686 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −16.4470 | −0.633986 | −0.316993 | − | 0.948428i | \(-0.602673\pi\) | ||||
−0.316993 | + | 0.948428i | \(0.602673\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −3.90357 | −0.150249 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −44.9835 | −1.72886 | −0.864429 | − | 0.502755i | \(-0.832320\pi\) | ||||
−0.864429 | + | 0.502755i | \(0.832320\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −10.7633 | −0.413057 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 23.5950 | 0.904164 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 5.31043 | 0.203198 | 0.101599 | − | 0.994825i | \(-0.467604\pi\) | ||||
0.101599 | + | 0.994825i | \(0.467604\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 3.69711 | 0.141259 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −15.4803 | −0.590609 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −53.9703 | −2.05611 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −22.2506 | −0.846454 | −0.423227 | − | 0.906024i | \(-0.639103\pi\) | ||||
−0.423227 | + | 0.906024i | \(0.639103\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −2.99601 | −0.113809 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −2.39089 | −0.0906916 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 38.0609 | 1.44166 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 12.4984 | 0.472734 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −31.1228 | −1.17549 | −0.587745 | − | 0.809046i | \(-0.699984\pi\) | ||||
−0.587745 | + | 0.809046i | \(0.699984\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 25.9931 | 0.980348 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 2.01776 | 0.0759931 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 20.9463 | 0.787767 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −22.9277 | −0.861067 | −0.430534 | − | 0.902575i | \(-0.641675\pi\) | ||||
−0.430534 | + | 0.902575i | \(0.641675\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 4.62746 | 0.173543 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 14.7811 | 0.552783 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 20.8825 | 0.779873 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 45.9238 | 1.71267 | 0.856335 | − | 0.516421i | \(-0.172736\pi\) | ||||
0.856335 | + | 0.516421i | \(0.172736\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −5.87373 | −0.218749 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −2.57940 | −0.0959288 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −16.1885 | −0.601224 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −20.6813 | −0.767028 | −0.383514 | − | 0.923535i | \(-0.625286\pi\) | ||||
−0.383514 | + | 0.923535i | \(0.625286\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 27.2461 | 1.00773 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −38.9570 | −1.43891 | −0.719454 | − | 0.694540i | \(-0.755608\pi\) | ||||
−0.719454 | + | 0.694540i | \(0.755608\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 5.08833 | 0.187686 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 20.6722 | 0.761469 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 29.1549 | 1.07248 | 0.536239 | − | 0.844066i | \(-0.319844\pi\) | ||||
0.536239 | + | 0.844066i | \(0.319844\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 43.9261 | 1.61366 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 2.48734 | 0.0912516 | 0.0456258 | − | 0.998959i | \(-0.485472\pi\) | ||||
0.0456258 | + | 0.998959i | \(0.485472\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −14.1495 | −0.518399 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −8.28322 | −0.303067 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −19.0567 | −0.696318 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 26.9151 | 0.982146 | 0.491073 | − | 0.871118i | \(-0.336605\pi\) | ||||
0.491073 | + | 0.871118i | \(0.336605\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −6.31385 | −0.230089 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 2.41924 | 0.0880453 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −15.0755 | −0.547928 | −0.273964 | − | 0.961740i | \(-0.588335\pi\) | ||||
−0.273964 | + | 0.961740i | \(0.588335\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 20.1657 | 0.731005 | 0.365502 | − | 0.930810i | \(-0.380897\pi\) | ||||
0.365502 | + | 0.930810i | \(0.380897\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −5.18706 | −0.187784 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −8.14399 | −0.294447 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −99.6994 | −3.59994 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 31.0151 | 1.11843 | 0.559216 | − | 0.829022i | \(-0.311102\pi\) | ||||
0.559216 | + | 0.829022i | \(0.311102\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 12.3028 | 0.443073 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −14.8542 | −0.534269 | −0.267135 | − | 0.963659i | \(-0.586077\pi\) | ||||
−0.267135 | + | 0.963659i | \(0.586077\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −3.55224 | −0.127600 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 5.96813 | 0.214105 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −31.1828 | −1.11724 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −0.404396 | −0.0144704 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 4.14709 | 0.148205 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −12.6642 | −0.452004 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 23.8432 | 0.849919 | 0.424959 | − | 0.905212i | \(-0.360288\pi\) | ||||
0.424959 | + | 0.905212i | \(0.360288\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −7.09090 | −0.252443 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −22.3957 | −0.796299 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −51.9443 | −1.84460 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −8.19798 | −0.290752 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 0.0152420 | 0.000539900 0 | 0.000269950 | − | 1.00000i | \(-0.499914\pi\) | ||||
0.000269950 | 1.00000i | \(0.499914\pi\) | ||||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −14.9874 | −0.530215 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0.275247 | 0.00972539 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −16.3010 | −0.575248 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −14.9741 | −0.527114 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −34.3498 | −1.20767 | −0.603836 | − | 0.797108i | \(-0.706362\pi\) | ||||
−0.603836 | + | 0.797108i | \(0.706362\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −35.6554 | −1.25203 | −0.626016 | − | 0.779810i | \(-0.715315\pi\) | ||||
−0.626016 | + | 0.779810i | \(0.715315\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 18.3737 | 0.644394 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 22.6562 | 0.793613 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −22.3224 | −0.780964 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 10.0856 | 0.352420 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 34.7214 | 1.21178 | 0.605892 | − | 0.795547i | \(-0.292816\pi\) | ||||
0.605892 | + | 0.795547i | \(0.292816\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −26.4728 | −0.922783 | −0.461391 | − | 0.887197i | \(-0.652650\pi\) | ||||
−0.461391 | + | 0.887197i | \(0.652650\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −7.99358 | −0.278301 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 25.7194 | 0.894351 | 0.447176 | − | 0.894446i | \(-0.352430\pi\) | ||||
0.447176 | + | 0.894446i | \(0.352430\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 2.78348 | 0.0966741 | 0.0483371 | − | 0.998831i | \(-0.484608\pi\) | ||||
0.0483371 | + | 0.998831i | \(0.484608\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 13.9414 | 0.483622 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −37.7948 | −1.30951 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 5.80054 | 0.200736 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0.909997 | 0.0314541 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 41.7432 | 1.44113 | 0.720567 | − | 0.693385i | \(-0.243882\pi\) | ||||
0.720567 | + | 0.693385i | \(0.243882\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −11.8016 | −0.406953 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 7.75769 | 0.267189 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −36.1461 | −1.24346 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 9.95863 | 0.342183 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 32.5795 | 1.11813 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −27.0756 | −0.927050 | −0.463525 | − | 0.886084i | \(-0.653416\pi\) | ||||
−0.463525 | + | 0.886084i | \(0.653416\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 6.67228 | 0.228187 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 31.7827 | 1.08568 | 0.542838 | − | 0.839837i | \(-0.317350\pi\) | ||||
0.542838 | + | 0.839837i | \(0.317350\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 15.5728 | 0.531338 | 0.265669 | − | 0.964064i | \(-0.414407\pi\) | ||||
0.265669 | + | 0.964064i | \(0.414407\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −7.15972 | −0.244003 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 3.13566 | 0.106739 | 0.0533695 | − | 0.998575i | \(-0.483004\pi\) | ||||
0.0533695 | + | 0.998575i | \(0.483004\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −11.4944 | −0.390821 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 43.4915 | 1.47705 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 9.47593 | 0.321449 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −69.5897 | −2.35796 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 7.35665 | 0.248985 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −13.6401 | −0.461121 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −7.55790 | −0.255212 | −0.127606 | − | 0.991825i | \(-0.540729\pi\) | ||||
−0.127606 | + | 0.991825i | \(0.540729\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −21.4612 | −0.723869 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 21.8132 | 0.734905 | 0.367453 | − | 0.930042i | \(-0.380230\pi\) | ||||
0.367453 | + | 0.930042i | \(0.380230\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1.98696 | 0.0668664 | 0.0334332 | − | 0.999441i | \(-0.489356\pi\) | ||||
0.0334332 | + | 0.999441i | \(0.489356\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −15.1441 | −0.509065 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −14.7683 | −0.495870 | −0.247935 | − | 0.968777i | \(-0.579752\pi\) | ||||
−0.247935 | + | 0.968777i | \(0.579752\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −20.1593 | −0.676121 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 2.04776 | 0.0686026 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 12.2790 | 0.410901 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −19.8533 | −0.663623 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 3.77384 | 0.125865 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 60.8925 | 2.02862 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −5.12533 | −0.170560 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −17.4905 | −0.581405 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −7.95757 | −0.264227 | −0.132113 | − | 0.991235i | \(-0.542176\pi\) | ||||
−0.132113 | + | 0.991235i | \(0.542176\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −14.3167 | −0.474855 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −28.6491 | −0.949186 | −0.474593 | − | 0.880205i | \(-0.657405\pi\) | ||||
−0.474593 | + | 0.880205i | \(0.657405\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −16.9620 | −0.561362 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −7.89023 | −0.260843 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 14.0670 | 0.464532 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 33.7887 | 1.11458 | 0.557292 | − | 0.830316i | \(-0.311840\pi\) | ||||
0.557292 | + | 0.830316i | \(0.311840\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −4.31387 | −0.142147 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 1.36134 | 0.0448090 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 15.9234 | 0.523558 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 4.01467 | 0.131859 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −33.5555 | −1.10092 | −0.550460 | − | 0.834862i | \(-0.685547\pi\) | ||||
−0.550460 | + | 0.834862i | \(0.685547\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 30.9649 | 1.01483 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 12.9425 | 0.423717 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −16.6769 | −0.545394 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −21.9489 | −0.717039 | −0.358520 | − | 0.933522i | \(-0.616718\pi\) | ||||
−0.358520 | + | 0.933522i | \(0.616718\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −3.69404 | −0.120551 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −32.7362 | −1.06717 | −0.533585 | − | 0.845746i | \(-0.679156\pi\) | ||||
−0.533585 | + | 0.845746i | \(0.679156\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 1.53199 | 0.0498355 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 32.0690 | 1.04210 | 0.521051 | − | 0.853526i | \(-0.325540\pi\) | ||||
0.521051 | + | 0.853526i | \(0.325540\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 54.8747 | 1.78131 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 18.7068 | 0.606609 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 24.4717 | 0.792717 | 0.396358 | − | 0.918096i | \(-0.370274\pi\) | ||||
0.396358 | + | 0.918096i | \(0.370274\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 10.6026 | 0.343091 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 8.49225 | 0.274515 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 5.16579 | 0.166812 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.1719 | −0.973287 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 13.0252 | 0.419731 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −14.8242 | −0.477207 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 17.6787 | 0.568508 | 0.284254 | − | 0.958749i | \(-0.408254\pi\) | ||||
0.284254 | + | 0.958749i | \(0.408254\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −49.5600 | −1.59210 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −5.19762 | −0.166799 | −0.0833997 | − | 0.996516i | \(-0.526578\pi\) | ||||
−0.0833997 | + | 0.996516i | \(0.526578\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −3.34067 | −0.107097 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 26.9092 | 0.861783 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 23.3734 | 0.747783 | 0.373891 | − | 0.927473i | \(-0.378023\pi\) | ||||
0.373891 | + | 0.927473i | \(0.378023\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0.563641 | 0.0180140 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 3.54533 | 0.113194 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −33.4288 | −1.06621 | −0.533107 | − | 0.846048i | \(-0.678976\pi\) | ||||
−0.533107 | + | 0.846048i | \(0.678976\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 26.5466 | 0.845844 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 2.81931 | 0.0897397 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 0.897557 | 0.0285118 | 0.0142559 | − | 0.999898i | \(-0.495462\pi\) | ||||
0.0142559 | + | 0.999898i | \(0.495462\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −4.54026 | −0.144081 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 13.8576 | 0.439316 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 50.0344 | 1.58460 | 0.792302 | − | 0.610129i | \(-0.208882\pi\) | ||||
0.792302 | + | 0.610129i | \(0.208882\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −4.07919 | −0.129060 |
(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 | 6348.2.a.t.1.4 | 10 | ||
23.15 | odd | 22 | 276.2.i.a.133.1 | ✓ | 20 | ||
23.20 | odd | 22 | 276.2.i.a.193.1 | yes | 20 | ||
23.22 | odd | 2 | 6348.2.a.s.1.7 | 10 | |||
69.20 | even | 22 | 828.2.q.c.469.2 | 20 | |||
69.38 | even | 22 | 828.2.q.c.685.2 | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
276.2.i.a.133.1 | ✓ | 20 | 23.15 | odd | 22 | ||
276.2.i.a.193.1 | yes | 20 | 23.20 | odd | 22 | ||
828.2.q.c.469.2 | 20 | 69.20 | even | 22 | |||
828.2.q.c.685.2 | 20 | 69.38 | even | 22 | |||
6348.2.a.s.1.7 | 10 | 23.22 | odd | 2 | |||
6348.2.a.t.1.4 | 10 | 1.1 | even | 1 | trivial |