Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4864,2,Mod(1,4864)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4864, 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("4864.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4864 = 2^{8} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4864.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: | \(38.8392355432\) |
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: | \( x^{10} - 2x^{9} - 23x^{8} + 44x^{7} + 167x^{6} - 266x^{5} - 491x^{4} + 460x^{3} + 546x^{2} + 56x - 8 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{6} \) |
Twist minimal: | no (minimal twist has level 2432) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(-3.58141\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4864.1 |
$q$-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 | ||||||||
\(3\) | −1.15181 | −0.664999 | −0.332500 | − | 0.943103i | \(-0.607892\pi\) | ||||
−0.332500 | + | 0.943103i | \(0.607892\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.07587 | −0.481146 | −0.240573 | − | 0.970631i | \(-0.577335\pi\) | ||||
−0.240573 | + | 0.970631i | \(0.577335\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.238565 | 0.0901690 | 0.0450845 | − | 0.998983i | \(-0.485644\pi\) | ||||
0.0450845 | + | 0.998983i | \(0.485644\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.67333 | −0.557776 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.84249 | −0.857044 | −0.428522 | − | 0.903531i | \(-0.640966\pi\) | ||||
−0.428522 | + | 0.903531i | \(0.640966\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.31444 | 0.364560 | 0.182280 | − | 0.983247i | \(-0.441652\pi\) | ||||
0.182280 | + | 0.983247i | \(0.441652\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.23921 | 0.319962 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −4.47279 | −1.08481 | −0.542405 | − | 0.840117i | \(-0.682486\pi\) | ||||
−0.542405 | + | 0.840117i | \(0.682486\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.00000 | 0.229416 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.274782 | −0.0599623 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.94338 | 0.405222 | 0.202611 | − | 0.979259i | \(-0.435057\pi\) | ||||
0.202611 | + | 0.979259i | \(0.435057\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3.84249 | −0.768499 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 5.38280 | 1.03592 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 8.83944 | 1.64144 | 0.820721 | − | 0.571329i | \(-0.193572\pi\) | ||||
0.820721 | + | 0.571329i | \(0.193572\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −6.64877 | −1.19415 | −0.597077 | − | 0.802184i | \(-0.703671\pi\) | ||||
−0.597077 | + | 0.802184i | \(0.703671\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 3.27402 | 0.569933 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −0.256666 | −0.0433845 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −4.06763 | −0.668715 | −0.334357 | − | 0.942446i | \(-0.608519\pi\) | ||||
−0.334357 | + | 0.942446i | \(0.608519\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −1.51399 | −0.242432 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −2.78211 | −0.434492 | −0.217246 | − | 0.976117i | \(-0.569707\pi\) | ||||
−0.217246 | + | 0.976117i | \(0.569707\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.21363 | −0.185077 | −0.0925386 | − | 0.995709i | \(-0.529498\pi\) | ||||
−0.0925386 | + | 0.995709i | \(0.529498\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1.80029 | 0.268372 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −10.2695 | −1.49796 | −0.748978 | − | 0.662595i | \(-0.769455\pi\) | ||||
−0.748978 | + | 0.662595i | \(0.769455\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.94309 | −0.991870 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 5.15181 | 0.721398 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −8.36231 | −1.14865 | −0.574326 | − | 0.818627i | \(-0.694736\pi\) | ||||
−0.574326 | + | 0.818627i | \(0.694736\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 3.05817 | 0.412363 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −1.15181 | −0.152561 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 9.25916 | 1.20544 | 0.602720 | − | 0.797953i | \(-0.294084\pi\) | ||||
0.602720 | + | 0.797953i | \(0.294084\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −4.66035 | −0.596697 | −0.298349 | − | 0.954457i | \(-0.596436\pi\) | ||||
−0.298349 | + | 0.954457i | \(0.596436\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −0.399197 | −0.0502941 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −1.41417 | −0.175407 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 4.31849 | 0.527587 | 0.263794 | − | 0.964579i | \(-0.415026\pi\) | ||||
0.263794 | + | 0.964579i | \(0.415026\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −2.23841 | −0.269472 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 2.78069 | 0.330007 | 0.165003 | − | 0.986293i | \(-0.447236\pi\) | ||||
0.165003 | + | 0.986293i | \(0.447236\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −0.134460 | −0.0157373 | −0.00786866 | − | 0.999969i | \(-0.502505\pi\) | ||||
−0.00786866 | + | 0.999969i | \(0.502505\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 4.42583 | 0.511051 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −0.678119 | −0.0772788 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 12.7841 | 1.43832 | 0.719162 | − | 0.694843i | \(-0.244526\pi\) | ||||
0.719162 | + | 0.694843i | \(0.244526\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −1.17998 | −0.131109 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 13.4028 | 1.47115 | 0.735573 | − | 0.677445i | \(-0.236913\pi\) | ||||
0.735573 | + | 0.677445i | \(0.236913\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 4.81216 | 0.521952 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −10.1814 | −1.09156 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 9.20650 | 0.975887 | 0.487944 | − | 0.872875i | \(-0.337747\pi\) | ||||
0.487944 | + | 0.872875i | \(0.337747\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.313579 | 0.0328720 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 7.65814 | 0.794112 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −1.07587 | −0.110382 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −0.247499 | −0.0251297 | −0.0125648 | − | 0.999921i | \(-0.504000\pi\) | ||||
−0.0125648 | + | 0.999921i | \(0.504000\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 4.75643 | 0.478039 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −16.8026 | −1.67193 | −0.835963 | − | 0.548786i | \(-0.815090\pi\) | ||||
−0.835963 | + | 0.548786i | \(0.815090\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 5.40957 | 0.533020 | 0.266510 | − | 0.963832i | \(-0.414129\pi\) | ||||
0.266510 | + | 0.963832i | \(0.414129\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0.295631 | 0.0288506 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 6.39113 | 0.617853 | 0.308927 | − | 0.951086i | \(-0.400030\pi\) | ||||
0.308927 | + | 0.951086i | \(0.400030\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 14.8779 | 1.42505 | 0.712524 | − | 0.701648i | \(-0.247552\pi\) | ||||
0.712524 | + | 0.701648i | \(0.247552\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 4.68515 | 0.444695 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 8.59073 | 0.808148 | 0.404074 | − | 0.914726i | \(-0.367594\pi\) | ||||
0.404074 | + | 0.914726i | \(0.367594\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −2.09083 | −0.194971 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −2.19949 | −0.203343 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −1.06705 | −0.0978163 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −2.92023 | −0.265476 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 3.20446 | 0.288937 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 9.51342 | 0.850906 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1.15983 | −0.102918 | −0.0514592 | − | 0.998675i | \(-0.516387\pi\) | ||||
−0.0514592 | + | 0.998675i | \(0.516387\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 1.39788 | 0.123076 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −3.85559 | −0.336864 | −0.168432 | − | 0.985713i | \(-0.553870\pi\) | ||||
−0.168432 | + | 0.985713i | \(0.553870\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.238565 | 0.0206862 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −5.79122 | −0.498428 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −1.42976 | −0.122152 | −0.0610761 | − | 0.998133i | \(-0.519453\pi\) | ||||
−0.0610761 | + | 0.998133i | \(0.519453\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 3.58190 | 0.303813 | 0.151907 | − | 0.988395i | \(-0.451459\pi\) | ||||
0.151907 | + | 0.988395i | \(0.451459\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 11.8285 | 0.996139 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −3.73629 | −0.312444 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −9.51013 | −0.789773 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 7.99713 | 0.659592 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −16.2763 | −1.33341 | −0.666705 | − | 0.745322i | \(-0.732296\pi\) | ||||
−0.666705 | + | 0.745322i | \(0.732296\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −14.3242 | −1.16569 | −0.582845 | − | 0.812583i | \(-0.698061\pi\) | ||||
−0.582845 | + | 0.812583i | \(0.698061\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 7.48445 | 0.605082 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 7.15325 | 0.574563 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −3.73495 | −0.298081 | −0.149041 | − | 0.988831i | \(-0.547619\pi\) | ||||
−0.149041 | + | 0.988831i | \(0.547619\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 9.63181 | 0.763852 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0.463621 | 0.0365385 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −3.98861 | −0.312412 | −0.156206 | − | 0.987724i | \(-0.549926\pi\) | ||||
−0.156206 | + | 0.987724i | \(0.549926\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −3.52243 | −0.274221 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 8.17158 | 0.632336 | 0.316168 | − | 0.948703i | \(-0.397604\pi\) | ||||
0.316168 | + | 0.948703i | \(0.397604\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −11.2722 | −0.867096 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1.67333 | −0.127963 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −0.351356 | −0.0267131 | −0.0133565 | − | 0.999911i | \(-0.504252\pi\) | ||||
−0.0133565 | + | 0.999911i | \(0.504252\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −0.916684 | −0.0692948 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −10.6648 | −0.801616 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 15.2740 | 1.14163 | 0.570817 | − | 0.821077i | \(-0.306627\pi\) | ||||
0.570817 | + | 0.821077i | \(0.306627\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −8.94630 | −0.664974 | −0.332487 | − | 0.943108i | \(-0.607888\pi\) | ||||
−0.332487 | + | 0.943108i | \(0.607888\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 5.36785 | 0.396803 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 4.37626 | 0.321749 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 12.7139 | 0.929730 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 1.28415 | 0.0934079 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 18.3946 | 1.33098 | 0.665492 | − | 0.746405i | \(-0.268222\pi\) | ||||
0.665492 | + | 0.746405i | \(0.268222\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −5.09902 | −0.367035 | −0.183518 | − | 0.983016i | \(-0.558748\pi\) | ||||
−0.183518 | + | 0.983016i | \(0.558748\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 1.62886 | 0.116645 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 20.2916 | 1.44572 | 0.722860 | − | 0.690995i | \(-0.242827\pi\) | ||||
0.722860 | + | 0.690995i | \(0.242827\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 0.310999 | 0.0220461 | 0.0110231 | − | 0.999939i | \(-0.496491\pi\) | ||||
0.0110231 | + | 0.999939i | \(0.496491\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −4.97408 | −0.350845 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 2.10878 | 0.148007 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 2.99320 | 0.209054 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −3.25191 | −0.226023 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −2.84249 | −0.196619 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 14.3284 | 0.986406 | 0.493203 | − | 0.869914i | \(-0.335826\pi\) | ||||
0.493203 | + | 0.869914i | \(0.335826\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −3.20283 | −0.219454 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 1.30572 | 0.0890491 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1.58616 | −0.107676 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0.154872 | 0.0104653 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −5.87921 | −0.395479 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −12.8621 | −0.861312 | −0.430656 | − | 0.902516i | \(-0.641718\pi\) | ||||
−0.430656 | + | 0.902516i | \(0.641718\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 6.42976 | 0.428650 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 18.4491 | 1.22451 | 0.612256 | − | 0.790659i | \(-0.290262\pi\) | ||||
0.612256 | + | 0.790659i | \(0.290262\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 4.73279 | 0.312751 | 0.156376 | − | 0.987698i | \(-0.450019\pi\) | ||||
0.156376 | + | 0.987698i | \(0.450019\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0.781066 | 0.0513903 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −4.27809 | −0.280267 | −0.140133 | − | 0.990133i | \(-0.544753\pi\) | ||||
−0.140133 | + | 0.990133i | \(0.544753\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 11.0487 | 0.720735 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −14.7249 | −0.956483 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 20.3905 | 1.31895 | 0.659474 | − | 0.751727i | \(-0.270779\pi\) | ||||
0.659474 | + | 0.751727i | \(0.270779\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 25.5877 | 1.64825 | 0.824123 | − | 0.566410i | \(-0.191668\pi\) | ||||
0.824123 | + | 0.566410i | \(0.191668\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −14.7893 | −0.948732 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 7.46989 | 0.477234 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1.31444 | 0.0836358 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −15.4375 | −0.978311 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 28.9847 | 1.82950 | 0.914749 | − | 0.404024i | \(-0.132389\pi\) | ||||
0.914749 | + | 0.404024i | \(0.132389\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −5.52404 | −0.347293 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −5.54270 | −0.347098 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 5.10203 | 0.318256 | 0.159128 | − | 0.987258i | \(-0.449132\pi\) | ||||
0.159128 | + | 0.987258i | \(0.449132\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −0.970394 | −0.0602974 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −14.7913 | −0.915558 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 11.6953 | 0.721160 | 0.360580 | − | 0.932728i | \(-0.382579\pi\) | ||||
0.360580 | + | 0.932728i | \(0.382579\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 8.99680 | 0.552669 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −10.6042 | −0.648964 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −0.163433 | −0.00996466 | −0.00498233 | − | 0.999988i | \(-0.501586\pi\) | ||||
−0.00498233 | + | 0.999988i | \(0.501586\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1.01216 | 0.0614846 | 0.0307423 | − | 0.999527i | \(-0.490213\pi\) | ||||
0.0307423 | + | 0.999527i | \(0.490213\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −0.361184 | −0.0218599 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 10.9223 | 0.658637 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 3.14825 | 0.189160 | 0.0945800 | − | 0.995517i | \(-0.469849\pi\) | ||||
0.0945800 | + | 0.995517i | \(0.469849\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 11.1256 | 0.666071 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 24.6734 | 1.47189 | 0.735946 | − | 0.677040i | \(-0.236738\pi\) | ||||
0.735946 | + | 0.677040i | \(0.236738\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −13.8095 | −0.820889 | −0.410445 | − | 0.911886i | \(-0.634626\pi\) | ||||
−0.410445 | + | 0.911886i | \(0.634626\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 1.23921 | 0.0734042 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −0.663713 | −0.0391777 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 3.00584 | 0.176814 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0.285072 | 0.0167112 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 8.24682 | 0.481784 | 0.240892 | − | 0.970552i | \(-0.422560\pi\) | ||||
0.240892 | + | 0.970552i | \(0.422560\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −9.96169 | −0.579992 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −15.3006 | −0.887829 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 2.55445 | 0.147728 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −0.289530 | −0.0166882 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 19.3535 | 1.11183 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 5.01396 | 0.287098 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 17.4540 | 0.996153 | 0.498076 | − | 0.867133i | \(-0.334040\pi\) | ||||
0.498076 | + | 0.867133i | \(0.334040\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −6.23080 | −0.354458 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 10.5256 | 0.596851 | 0.298425 | − | 0.954433i | \(-0.403539\pi\) | ||||
0.298425 | + | 0.954433i | \(0.403539\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 14.3498 | 0.811098 | 0.405549 | − | 0.914073i | \(-0.367080\pi\) | ||||
0.405549 | + | 0.914073i | \(0.367080\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0.429486 | 0.0241988 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 16.3470 | 0.918138 | 0.459069 | − | 0.888401i | \(-0.348183\pi\) | ||||
0.459069 | + | 0.888401i | \(0.348183\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −25.1260 | −1.40679 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −7.36138 | −0.410872 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −4.47279 | −0.248873 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −5.05073 | −0.280164 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −17.1366 | −0.947656 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −2.44993 | −0.135069 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −15.0118 | −0.825123 | −0.412562 | − | 0.910930i | \(-0.635366\pi\) | ||||
−0.412562 | + | 0.910930i | \(0.635366\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 6.80649 | 0.372993 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −4.64615 | −0.253846 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 0.462187 | 0.0251769 | 0.0125885 | − | 0.999921i | \(-0.495993\pi\) | ||||
0.0125885 | + | 0.999921i | \(0.495993\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −9.89491 | −0.537418 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 18.8991 | 1.02344 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −3.32633 | −0.179605 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 2.40824 | 0.129655 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 17.2669 | 0.926935 | 0.463468 | − | 0.886114i | \(-0.346605\pi\) | ||||
0.463468 | + | 0.886114i | \(0.346605\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −26.1466 | −1.39960 | −0.699798 | − | 0.714341i | \(-0.746727\pi\) | ||||
−0.699798 | + | 0.714341i | \(0.746727\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 7.07536 | 0.377655 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 12.3930 | 0.659614 | 0.329807 | − | 0.944048i | \(-0.393016\pi\) | ||||
0.329807 | + | 0.944048i | \(0.393016\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −2.99167 | −0.158781 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 1.22904 | 0.0650478 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −14.1664 | −0.747673 | −0.373837 | − | 0.927495i | \(-0.621958\pi\) | ||||
−0.373837 | + | 0.927495i | \(0.621958\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 3.36356 | 0.176541 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0.144662 | 0.00757195 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 3.00328 | 0.156770 | 0.0783850 | − | 0.996923i | \(-0.475024\pi\) | ||||
0.0783850 | + | 0.996923i | \(0.475024\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 4.65538 | 0.242349 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −1.99495 | −0.103573 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 38.0432 | 1.96980 | 0.984901 | − | 0.173119i | \(-0.0553845\pi\) | ||||
0.984901 | + | 0.173119i | \(0.0553845\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −10.9577 | −0.565852 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 11.6189 | 0.598404 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 28.6291 | 1.47058 | 0.735290 | − | 0.677753i | \(-0.237046\pi\) | ||||
0.735290 | + | 0.677753i | \(0.237046\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1.33591 | 0.0684407 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −24.1407 | −1.23353 | −0.616767 | − | 0.787146i | \(-0.711558\pi\) | ||||
−0.616767 | + | 0.787146i | \(0.711558\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0.729571 | 0.0371824 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 2.03081 | 0.103232 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −16.2953 | −0.826206 | −0.413103 | − | 0.910684i | \(-0.635555\pi\) | ||||
−0.413103 | + | 0.910684i | \(0.635555\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −8.69231 | −0.439589 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 4.44091 | 0.224014 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −13.7541 | −0.692043 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −36.8139 | −1.84764 | −0.923819 | − | 0.382829i | \(-0.874950\pi\) | ||||
−0.923819 | + | 0.382829i | \(0.874950\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −0.274782 | −0.0137563 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −23.6899 | −1.18302 | −0.591508 | − | 0.806299i | \(-0.701467\pi\) | ||||
−0.591508 | + | 0.806299i | \(0.701467\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −8.73941 | −0.435341 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 1.26951 | 0.0630827 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 11.5622 | 0.573118 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −0.102363 | −0.00506154 | −0.00253077 | − | 0.999997i | \(-0.500806\pi\) | ||||
−0.00253077 | + | 0.999997i | \(0.500806\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 1.64681 | 0.0812311 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 2.20891 | 0.108693 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −14.4197 | −0.707836 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −4.12568 | −0.202035 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 25.7326 | 1.25712 | 0.628560 | − | 0.777761i | \(-0.283645\pi\) | ||||
0.628560 | + | 0.777761i | \(0.283645\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 18.0014 | 0.877334 | 0.438667 | − | 0.898650i | \(-0.355451\pi\) | ||||
0.438667 | + | 0.898650i | \(0.355451\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 17.1842 | 0.835524 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 17.1867 | 0.833675 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −1.11180 | −0.0538036 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 4.30350 | 0.207775 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −27.6392 | −1.33133 | −0.665667 | − | 0.746249i | \(-0.731853\pi\) | ||||
−0.665667 | + | 0.746249i | \(0.731853\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 38.5219 | 1.85124 | 0.925621 | − | 0.378451i | \(-0.123543\pi\) | ||||
0.925621 | + | 0.378451i | \(0.123543\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 10.9539 | 0.525198 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 1.94338 | 0.0929643 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 23.1302 | 1.10394 | 0.551971 | − | 0.833863i | \(-0.313876\pi\) | ||||
0.551971 | + | 0.833863i | \(0.313876\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 11.6181 | 0.553241 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 19.2436 | 0.914290 | 0.457145 | − | 0.889392i | \(-0.348872\pi\) | ||||
0.457145 | + | 0.889392i | \(0.348872\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −9.90505 | −0.469544 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 18.7473 | 0.886716 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 11.0578 | 0.521851 | 0.260926 | − | 0.965359i | \(-0.415972\pi\) | ||||
0.260926 | + | 0.965359i | \(0.415972\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 7.90812 | 0.372379 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 16.4988 | 0.775183 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −0.337372 | −0.0158162 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −4.08310 | −0.190999 | −0.0954996 | − | 0.995429i | \(-0.530445\pi\) | ||||
−0.0954996 | + | 0.995429i | \(0.530445\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −24.0761 | −1.12378 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −7.59017 | −0.353509 | −0.176755 | − | 0.984255i | \(-0.556560\pi\) | ||||
−0.176755 | + | 0.984255i | \(0.556560\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −37.2637 | −1.73179 | −0.865894 | − | 0.500227i | \(-0.833250\pi\) | ||||
−0.865894 | + | 0.500227i | \(0.833250\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −8.23920 | −0.382084 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −8.92480 | −0.412991 | −0.206495 | − | 0.978448i | \(-0.566206\pi\) | ||||
−0.206495 | + | 0.978448i | \(0.566206\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1.03024 | 0.0475720 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 4.30196 | 0.198224 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 3.44974 | 0.158619 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −3.84249 | −0.176306 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 13.9929 | 0.640690 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 19.6241 | 0.896650 | 0.448325 | − | 0.893871i | \(-0.352021\pi\) | ||||
0.448325 | + | 0.893871i | \(0.352021\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −5.34666 | −0.243787 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −0.534005 | −0.0242981 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0.266277 | 0.0120910 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 13.5448 | 0.613775 | 0.306887 | − | 0.951746i | \(-0.400712\pi\) | ||||
0.306887 | + | 0.951746i | \(0.400712\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 4.59413 | 0.207754 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −9.58255 | −0.432454 | −0.216227 | − | 0.976343i | \(-0.569375\pi\) | ||||
−0.216227 | + | 0.976343i | \(0.569375\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −39.5369 | −1.78065 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −5.11732 | −0.230006 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0.663374 | 0.0297564 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 7.24834 | 0.324480 | 0.162240 | − | 0.986751i | \(-0.448128\pi\) | ||||
0.162240 | + | 0.986751i | \(0.448128\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −9.41213 | −0.420503 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −2.19200 | −0.0977367 | −0.0488683 | − | 0.998805i | \(-0.515561\pi\) | ||||
−0.0488683 | + | 0.998805i | \(0.515561\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 18.0775 | 0.804440 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 12.9835 | 0.576618 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −13.5765 | −0.601766 | −0.300883 | − | 0.953661i | \(-0.597281\pi\) | ||||
−0.300883 | + | 0.953661i | \(0.597281\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −0.0320774 | −0.00141902 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 5.38280 | 0.237656 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −5.82002 | −0.256461 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 29.1909 | 1.28381 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0.404696 | 0.0177642 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −6.57594 | −0.288097 | −0.144049 | − | 0.989571i | \(-0.546012\pi\) | ||||
−0.144049 | + | 0.989571i | \(0.546012\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −22.2161 | −0.971443 | −0.485722 | − | 0.874114i | \(-0.661443\pi\) | ||||
−0.485722 | + | 0.874114i | \(0.661443\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 1.05585 | 0.0460810 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 29.7386 | 1.29543 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −19.2233 | −0.835795 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −15.4936 | −0.672366 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −3.65691 | −0.158398 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −6.87605 | −0.297278 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −17.5928 | −0.759185 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 19.7357 | 0.850076 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −22.5004 | −0.967368 | −0.483684 | − | 0.875243i | \(-0.660702\pi\) | ||||
−0.483684 | + | 0.875243i | \(0.660702\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 10.3045 | 0.442207 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −16.0068 | −0.685656 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −24.1551 | −1.03280 | −0.516399 | − | 0.856348i | \(-0.672728\pi\) | ||||
−0.516399 | + | 0.856348i | \(0.672728\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 7.79830 | 0.332823 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 8.83944 | 0.376573 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 3.04984 | 0.129692 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −5.04063 | −0.213963 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 21.4469 | 0.908734 | 0.454367 | − | 0.890815i | \(-0.349865\pi\) | ||||
0.454367 | + | 0.890815i | \(0.349865\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −1.59525 | −0.0674717 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −14.6440 | −0.618270 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 15.3594 | 0.647322 | 0.323661 | − | 0.946173i | \(-0.395086\pi\) | ||||
0.323661 | + | 0.946173i | \(0.395086\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −9.24256 | −0.388837 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −0.281503 | −0.0118220 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 2.05613 | 0.0861973 | 0.0430986 | − | 0.999071i | \(-0.486277\pi\) | ||||
0.0430986 | + | 0.999071i | \(0.486277\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 35.4718 | 1.48445 | 0.742225 | − | 0.670151i | \(-0.233771\pi\) | ||||
0.742225 | + | 0.670151i | \(0.233771\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −21.1871 | −0.885103 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −7.46741 | −0.311413 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 14.6910 | 0.611595 | 0.305798 | − | 0.952097i | \(-0.401077\pi\) | ||||
0.305798 | + | 0.952097i | \(0.401077\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 5.87311 | 0.244078 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 3.19743 | 0.132652 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 23.7698 | 0.984445 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 2.36638 | 0.0978376 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 1.71339 | 0.0707193 | 0.0353596 | − | 0.999375i | \(-0.488742\pi\) | ||||
0.0353596 | + | 0.999375i | \(0.488742\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −6.64877 | −0.273958 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −23.3722 | −0.961402 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 20.3947 | 0.837509 | 0.418754 | − | 0.908100i | \(-0.362467\pi\) | ||||
0.418754 | + | 0.908100i | \(0.362467\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1.14801 | 0.0470639 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −0.358212 | −0.0146607 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −21.9447 | −0.896637 | −0.448318 | − | 0.893874i | \(-0.647977\pi\) | ||||
−0.448318 | + | 0.893874i | \(0.647977\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −3.41894 | −0.139461 | −0.0697306 | − | 0.997566i | \(-0.522214\pi\) | ||||
−0.0697306 | + | 0.997566i | \(0.522214\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −7.22625 | −0.294276 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 3.14180 | 0.127732 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 23.1235 | 0.938555 | 0.469278 | − | 0.883051i | \(-0.344514\pi\) | ||||
0.469278 | + | 0.883051i | \(0.344514\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −2.42892 | −0.0984247 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −13.4986 | −0.546095 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 46.3763 | 1.87312 | 0.936561 | − | 0.350504i | \(-0.113990\pi\) | ||||
0.936561 | + | 0.350504i | \(0.113990\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −3.44760 | −0.139021 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −25.2123 | −1.01501 | −0.507504 | − | 0.861649i | \(-0.669432\pi\) | ||||
−0.507504 | + | 0.861649i | \(0.669432\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −37.2031 | −1.49532 | −0.747660 | − | 0.664082i | \(-0.768822\pi\) | ||||
−0.747660 | + | 0.664082i | \(0.768822\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 10.4608 | 0.419778 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 2.19635 | 0.0879948 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 8.97722 | 0.359089 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 3.27402 | 0.130752 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 18.1937 | 0.725429 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −40.8412 | −1.62586 | −0.812931 | − | 0.582360i | \(-0.802129\pi\) | ||||
−0.812931 | + | 0.582360i | \(0.802129\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −16.5036 | −0.655959 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 1.24783 | 0.0495188 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −9.12627 | −0.361596 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −4.65300 | −0.184070 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 5.87446 | 0.232027 | 0.116014 | − | 0.993248i | \(-0.462988\pi\) | ||||
0.116014 | + | 0.993248i | \(0.462988\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −21.3344 | −0.841347 | −0.420673 | − | 0.907212i | \(-0.638206\pi\) | ||||
−0.420673 | + | 0.907212i | \(0.638206\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −1.50394 | −0.0592176 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −48.1625 | −1.89346 | −0.946732 | − | 0.322024i | \(-0.895637\pi\) | ||||
−0.946732 | + | 0.322024i | \(0.895637\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −26.3191 | −1.03311 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 1.82696 | 0.0716043 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −11.3441 | −0.443929 | −0.221965 | − | 0.975055i | \(-0.571247\pi\) | ||||
−0.221965 | + | 0.975055i | \(0.571247\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 4.14813 | 0.162081 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0.224995 | 0.00877791 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 24.6320 | 0.959526 | 0.479763 | − | 0.877398i | \(-0.340723\pi\) | ||||
0.479763 | + | 0.877398i | \(0.340723\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 47.3409 | 1.84135 | 0.920673 | − | 0.390335i | \(-0.127641\pi\) | ||||
0.920673 | + | 0.390335i | \(0.127641\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 6.77175 | 0.262993 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −0.256666 | −0.00995308 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 17.1784 | 0.665149 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 14.8148 | 0.572772 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 13.2470 | 0.511396 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −35.1767 | −1.35596 | −0.677981 | − | 0.735079i | \(-0.737145\pi\) | ||||
−0.677981 | + | 0.735079i | \(0.737145\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −20.6834 | −0.796103 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −2.71085 | −0.104186 | −0.0520932 | − | 0.998642i | \(-0.516589\pi\) | ||||
−0.0520932 | + | 0.998642i | \(0.516589\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −0.0590444 | −0.00226592 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −21.2499 | −0.814300 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −48.4820 | −1.85511 | −0.927557 | − | 0.373682i | \(-0.878095\pi\) | ||||
−0.927557 | + | 0.373682i | \(0.878095\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 1.53824 | 0.0587730 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −5.45128 | −0.207979 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −10.9917 | −0.418752 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 41.3295 | 1.57225 | 0.786124 | − | 0.618068i | \(-0.212085\pi\) | ||||
0.786124 | + | 0.618068i | \(0.212085\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 1.13472 | 0.0431043 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −3.85368 | −0.146178 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 12.4438 | 0.471342 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 4.92755 | 0.186377 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −15.9692 | −0.603147 | −0.301573 | − | 0.953443i | \(-0.597512\pi\) | ||||
−0.301573 | + | 0.953443i | \(0.597512\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −4.06763 | −0.153414 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −12.7260 | −0.479288 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −4.00852 | −0.150756 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 1.27532 | 0.0478957 | 0.0239478 | − | 0.999713i | \(-0.492376\pi\) | ||||
0.0239478 | + | 0.999713i | \(0.492376\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −21.3920 | −0.802263 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −12.9211 | −0.483898 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 4.01978 | 0.150331 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −23.4860 | −0.877100 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −38.6245 | −1.44045 | −0.720225 | − | 0.693740i | \(-0.755962\pi\) | ||||
−0.720225 | + | 0.693740i | \(0.755962\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1.29053 | 0.0480619 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −29.4722 | −1.09608 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −33.9655 | −1.26145 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −3.96945 | −0.147219 | −0.0736095 | − | 0.997287i | \(-0.523452\pi\) | ||||
−0.0736095 | + | 0.997287i | \(0.523452\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 20.5744 | 0.762015 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 5.42832 | 0.200774 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −23.9821 | −0.885800 | −0.442900 | − | 0.896571i | \(-0.646050\pi\) | ||||
−0.442900 | + | 0.896571i | \(0.646050\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −8.60391 | −0.317360 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −12.2753 | −0.452165 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −34.2553 | −1.26010 | −0.630051 | − | 0.776554i | \(-0.716966\pi\) | ||||
−0.630051 | + | 0.776554i | \(0.716966\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −1.51399 | −0.0556177 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 31.0058 | 1.13749 | 0.568746 | − | 0.822513i | \(-0.307429\pi\) | ||||
0.568746 | + | 0.822513i | \(0.307429\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 17.5113 | 0.641564 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −22.4273 | −0.820571 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 1.52470 | 0.0557112 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 36.0417 | 1.31518 | 0.657590 | − | 0.753376i | \(-0.271576\pi\) | ||||
0.657590 | + | 0.753376i | \(0.271576\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −33.3849 | −1.21661 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 15.4111 | 0.560867 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −26.6253 | −0.967712 | −0.483856 | − | 0.875148i | \(-0.660764\pi\) | ||||
−0.483856 | + | 0.875148i | \(0.660764\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 6.36265 | 0.230950 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −40.0064 | −1.45023 | −0.725115 | − | 0.688628i | \(-0.758213\pi\) | ||||
−0.725115 | + | 0.688628i | \(0.758213\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 3.54935 | 0.128495 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −8.05233 | −0.291133 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 12.1706 | 0.439455 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 19.1147 | 0.689295 | 0.344648 | − | 0.938732i | \(-0.387998\pi\) | ||||
0.344648 | + | 0.938732i | \(0.387998\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −5.87658 | −0.211640 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −42.2244 | −1.51871 | −0.759353 | − | 0.650679i | \(-0.774484\pi\) | ||||
−0.759353 | + | 0.650679i | \(0.774484\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 25.5479 | 0.917706 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 1.11771 | 0.0400977 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −2.78211 | −0.0996793 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −7.90408 | −0.282830 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 47.5809 | 1.70040 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 4.01833 | 0.143421 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −43.6009 | −1.55420 | −0.777102 | − | 0.629375i | \(-0.783311\pi\) | ||||
−0.777102 | + | 0.629375i | \(0.783311\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −13.4707 | −0.479571 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 2.04945 | 0.0728699 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −6.12575 | −0.217532 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −10.3626 | −0.367524 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 14.6901 | 0.520351 | 0.260176 | − | 0.965561i | \(-0.416220\pi\) | ||||
0.260176 | + | 0.965561i | \(0.416220\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 45.9332 | 1.62500 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −15.4055 | −0.544327 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 0.382201 | 0.0134876 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −0.498799 | −0.0175803 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0.188244 | 0.00662649 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −4.76004 | −0.167354 | −0.0836771 | − | 0.996493i | \(-0.526666\pi\) | ||||
−0.0836771 | + | 0.996493i | \(0.526666\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −14.6172 | −0.513279 | −0.256640 | − | 0.966507i | \(-0.582615\pi\) | ||||
−0.256640 | + | 0.966507i | \(0.582615\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −1.16582 | −0.0408872 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 4.29125 | 0.150316 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −1.21363 | −0.0424596 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −0.524721 | −0.0183352 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 32.3079 | 1.12755 | 0.563776 | − | 0.825928i | \(-0.309348\pi\) | ||||
0.563776 | + | 0.825928i | \(0.309348\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −9.79982 | −0.341600 | −0.170800 | − | 0.985306i | \(-0.554635\pi\) | ||||
−0.170800 | + | 0.985306i | \(0.554635\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −12.5804 | −0.437993 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −11.2066 | −0.389691 | −0.194845 | − | 0.980834i | \(-0.562421\pi\) | ||||
−0.194845 | + | 0.980834i | \(0.562421\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 45.4323 | 1.57793 | 0.788965 | − | 0.614438i | \(-0.210617\pi\) | ||||
0.788965 | + | 0.614438i | \(0.210617\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −3.62619 | −0.125791 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 31.0550 | 1.07599 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −8.79160 | −0.304246 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −35.7890 | −1.23705 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −16.8997 | −0.583441 | −0.291721 | − | 0.956504i | \(-0.594228\pi\) | ||||
−0.291721 | + | 0.956504i | \(0.594228\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 49.1356 | 1.69433 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −28.4191 | −0.978807 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 12.1275 | 0.417200 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −0.696664 | −0.0239377 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 15.9059 | 0.545890 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −7.90494 | −0.270978 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 37.7943 | 1.29405 | 0.647027 | − | 0.762467i | \(-0.276012\pi\) | ||||
0.647027 | + | 0.762467i | \(0.276012\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 1.80029 | 0.0615687 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −38.8619 | −1.32750 | −0.663749 | − | 0.747956i | \(-0.731036\pi\) | ||||
−0.663749 | + | 0.747956i | \(0.731036\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −41.1795 | −1.40503 | −0.702513 | − | 0.711671i | \(-0.747939\pi\) | ||||
−0.702513 | + | 0.711671i | \(0.747939\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0.764473 | 0.0260532 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −25.5909 | −0.871125 | −0.435562 | − | 0.900159i | \(-0.643450\pi\) | ||||
−0.435562 | + | 0.900159i | \(0.643450\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0.378015 | 0.0128529 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −3.46216 | −0.117581 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −36.3387 | −1.23271 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 5.67639 | 0.192337 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0.414146 | 0.0140167 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 2.26957 | 0.0767253 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −14.4790 | −0.488920 | −0.244460 | − | 0.969659i | \(-0.578611\pi\) | ||||
−0.244460 | + | 0.969659i | \(0.578611\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −9.49879 | −0.320386 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 48.3407 | 1.62864 | 0.814320 | − | 0.580416i | \(-0.197110\pi\) | ||||
0.814320 | + | 0.580416i | \(0.197110\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −17.2669 | −0.581077 | −0.290539 | − | 0.956863i | \(-0.593834\pi\) | ||||
−0.290539 | + | 0.956863i | \(0.593834\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 11.4740 | 0.385694 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 51.0650 | 1.71460 | 0.857298 | − | 0.514820i | \(-0.172141\pi\) | ||||
0.857298 | + | 0.514820i | \(0.172141\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −0.276695 | −0.00928006 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 3.35410 | 0.112366 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −10.2695 | −0.343655 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −16.4329 | −0.549292 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −2.94225 | −0.0982388 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −58.7714 | −1.96014 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 37.4028 | 1.24607 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0.333484 | 0.0110977 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 9.62510 | 0.319949 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −30.0974 | −0.999367 | −0.499684 | − | 0.866208i | \(-0.666550\pi\) | ||||
−0.499684 | + | 0.866208i | \(0.666550\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 28.1164 | 0.932561 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −9.15413 | −0.303290 | −0.151645 | − | 0.988435i | \(-0.548457\pi\) | ||||
−0.151645 | + | 0.988435i | \(0.548457\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −38.0973 | −1.26084 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −5.77514 | −0.190920 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −0.919807 | −0.0303747 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −7.49270 | −0.247161 | −0.123581 | − | 0.992335i | \(-0.539438\pi\) | ||||
−0.123581 | + | 0.992335i | \(0.539438\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −20.1037 | −0.662440 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 3.65505 | 0.120307 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 15.6299 | 0.513906 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −9.05198 | −0.297306 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −12.0792 | −0.396306 | −0.198153 | − | 0.980171i | \(-0.563494\pi\) | ||||
−0.198153 | + | 0.980171i | \(0.563494\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −6.94309 | −0.227550 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −12.1235 | −0.396905 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −13.6785 | −0.447336 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 16.6732 | 0.544690 | 0.272345 | − | 0.962200i | \(-0.412201\pi\) | ||||
0.272345 | + | 0.962200i | \(0.412201\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −16.5283 | −0.539380 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 29.5263 | 0.962529 | 0.481265 | − | 0.876575i | \(-0.340178\pi\) | ||||
0.481265 | + | 0.876575i | \(0.340178\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −5.40668 | −0.176066 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −1.38158 | −0.0449428 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 24.2099 | 0.786717 | 0.393358 | − | 0.919385i | \(-0.371313\pi\) | ||||
0.393358 | + | 0.919385i | \(0.371313\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −0.176739 | −0.00573720 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −18.8287 | −0.610561 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 18.5304 | 0.600258 | 0.300129 | − | 0.953899i | \(-0.402970\pi\) | ||||
0.300129 | + | 0.953899i | \(0.402970\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −19.7903 | −0.640398 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 28.9405 | 0.935513 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −0.341089 | −0.0110143 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 13.2062 | 0.426005 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −10.6945 | −0.344624 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 5.48590 | 0.176597 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 54.2821 | 1.74559 | 0.872797 | − | 0.488084i | \(-0.162304\pi\) | ||||
0.872797 | + | 0.488084i | \(0.162304\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 5.15181 | 0.165500 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 7.69284 | 0.246875 | 0.123437 | − | 0.992352i | \(-0.460608\pi\) | ||||
0.123437 | + | 0.992352i | \(0.460608\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0.854516 | 0.0273945 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 5.81749 | 0.186309 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −32.8587 | −1.05124 | −0.525621 | − | 0.850719i | \(-0.676167\pi\) | ||||
−0.525621 | + | 0.850719i | \(0.676167\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −26.1694 | −0.836378 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −24.8957 | −0.794858 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −10.4144 | −0.332169 | −0.166084 | − | 0.986112i | \(-0.553112\pi\) | ||||
−0.166084 | + | 0.986112i | \(0.553112\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −21.8313 | −0.695602 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 2.82186 | 0.0898209 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −2.35855 | −0.0749974 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 62.1164 | 1.97319 | 0.986596 | − | 0.163183i | \(-0.0521761\pi\) | ||||
0.986596 | + | 0.163183i | \(0.0521761\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 17.2908 | 0.548706 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −0.334596 | −0.0106074 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −5.60362 | −0.177468 | −0.0887341 | − | 0.996055i | \(-0.528282\pi\) | ||||
−0.0887341 | + | 0.996055i | \(0.528282\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −21.8952 | −0.692735 |
(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 | 4864.2.a.bt.1.3 | 10 | ||
4.3 | odd | 2 | 4864.2.a.bs.1.7 | 10 | |||
8.3 | odd | 2 | inner | 4864.2.a.bt.1.4 | 10 | ||
8.5 | even | 2 | 4864.2.a.bs.1.8 | 10 | |||
16.3 | odd | 4 | 2432.2.c.j.1217.14 | yes | 20 | ||
16.5 | even | 4 | 2432.2.c.j.1217.13 | yes | 20 | ||
16.11 | odd | 4 | 2432.2.c.j.1217.7 | ✓ | 20 | ||
16.13 | even | 4 | 2432.2.c.j.1217.8 | yes | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2432.2.c.j.1217.7 | ✓ | 20 | 16.11 | odd | 4 | ||
2432.2.c.j.1217.8 | yes | 20 | 16.13 | even | 4 | ||
2432.2.c.j.1217.13 | yes | 20 | 16.5 | even | 4 | ||
2432.2.c.j.1217.14 | yes | 20 | 16.3 | odd | 4 | ||
4864.2.a.bs.1.7 | 10 | 4.3 | odd | 2 | |||
4864.2.a.bs.1.8 | 10 | 8.5 | even | 2 | |||
4864.2.a.bt.1.3 | 10 | 1.1 | even | 1 | trivial | ||
4864.2.a.bt.1.4 | 10 | 8.3 | odd | 2 | inner |