Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3864,2,Mod(1,3864)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3864, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3864.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3864 = 2^{3} \cdot 3 \cdot 7 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3864.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: | \(30.8541953410\) |
Analytic rank: | \(1\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.733.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 7x + 8 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-2.69639\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3864.1 |
$q$-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 | ||||||||
\(5\) | −3.27053 | −1.46263 | −0.731314 | − | 0.682041i | \(-0.761092\pi\) | ||||
−0.731314 | + | 0.682041i | \(0.761092\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.42586 | −0.429913 | −0.214956 | − | 0.976624i | \(-0.568961\pi\) | ||||
−0.214956 | + | 0.976624i | \(0.568961\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.69639 | 1.30254 | 0.651272 | − | 0.758844i | \(-0.274235\pi\) | ||||
0.651272 | + | 0.758844i | \(0.274235\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −3.27053 | −0.844448 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 3.96693 | 0.962121 | 0.481061 | − | 0.876687i | \(-0.340252\pi\) | ||||
0.481061 | + | 0.876687i | \(0.340252\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −5.42586 | −1.24478 | −0.622389 | − | 0.782708i | \(-0.713838\pi\) | ||||
−0.622389 | + | 0.782708i | \(0.713838\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.00000 | −0.218218 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.00000 | 0.208514 | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 5.69639 | 1.13928 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 3.96693 | 0.736640 | 0.368320 | − | 0.929699i | \(-0.379933\pi\) | ||||
0.368320 | + | 0.929699i | \(0.379933\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −8.81864 | −1.58388 | −0.791938 | − | 0.610602i | \(-0.790928\pi\) | ||||
−0.791938 | + | 0.610602i | \(0.790928\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −1.42586 | −0.248210 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 3.27053 | 0.552821 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 4.81864 | 0.792180 | 0.396090 | − | 0.918212i | \(-0.370367\pi\) | ||||
0.396090 | + | 0.918212i | \(0.370367\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 4.69639 | 0.752025 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 2.57414 | 0.402013 | 0.201007 | − | 0.979590i | \(-0.435579\pi\) | ||||
0.201007 | + | 0.979590i | \(0.435579\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −11.5481 | −1.76107 | −0.880535 | − | 0.473981i | \(-0.842817\pi\) | ||||
−0.880535 | + | 0.473981i | \(0.842817\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −3.27053 | −0.487542 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 5.39279 | 0.786619 | 0.393309 | − | 0.919406i | \(-0.371330\pi\) | ||||
0.393309 | + | 0.919406i | \(0.371330\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 3.96693 | 0.555481 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −12.6633 | −1.73944 | −0.869720 | − | 0.493545i | \(-0.835701\pi\) | ||||
−0.869720 | + | 0.493545i | \(0.835701\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 4.66332 | 0.628802 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −5.42586 | −0.718673 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 11.5150 | 1.49913 | 0.749565 | − | 0.661931i | \(-0.230263\pi\) | ||||
0.749565 | + | 0.661931i | \(0.230263\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −13.2375 | −1.69488 | −0.847442 | − | 0.530889i | \(-0.821858\pi\) | ||||
−0.847442 | + | 0.530889i | \(0.821858\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −1.00000 | −0.125988 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −15.3597 | −1.90514 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 5.51504 | 0.673769 | 0.336885 | − | 0.941546i | \(-0.390627\pi\) | ||||
0.336885 | + | 0.941546i | \(0.390627\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 1.00000 | 0.120386 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −2.69639 | −0.320003 | −0.160001 | − | 0.987117i | \(-0.551150\pi\) | ||||
−0.160001 | + | 0.987117i | \(0.551150\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −9.35971 | −1.09547 | −0.547736 | − | 0.836651i | \(-0.684510\pi\) | ||||
−0.547736 | + | 0.836651i | \(0.684510\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 5.69639 | 0.657763 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1.42586 | 0.162492 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −4.57414 | −0.514631 | −0.257316 | − | 0.966327i | \(-0.582838\pi\) | ||||
−0.257316 | + | 0.966327i | \(0.582838\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −0.277576 | −0.0304680 | −0.0152340 | − | 0.999884i | \(-0.504849\pi\) | ||||
−0.0152340 | + | 0.999884i | \(0.504849\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −12.9740 | −1.40722 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 3.96693 | 0.425299 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 11.4820 | 1.21709 | 0.608543 | − | 0.793521i | \(-0.291754\pi\) | ||||
0.608543 | + | 0.793521i | \(0.291754\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −4.69639 | −0.492316 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −8.81864 | −0.914451 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 17.7455 | 1.82065 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 7.96693 | 0.808919 | 0.404459 | − | 0.914556i | \(-0.367460\pi\) | ||||
0.404459 | + | 0.914556i | \(0.367460\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −1.42586 | −0.143304 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 6.97397 | 0.693936 | 0.346968 | − | 0.937877i | \(-0.387211\pi\) | ||||
0.346968 | + | 0.937877i | \(0.387211\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −19.8677 | −1.95762 | −0.978812 | − | 0.204763i | \(-0.934358\pi\) | ||||
−0.978812 | + | 0.204763i | \(0.934358\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 3.27053 | 0.319171 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −10.3998 | −1.00539 | −0.502695 | − | 0.864464i | \(-0.667658\pi\) | ||||
−0.502695 | + | 0.864464i | \(0.667658\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −12.3527 | −1.18317 | −0.591586 | − | 0.806242i | \(-0.701498\pi\) | ||||
−0.591586 | + | 0.806242i | \(0.701498\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 4.81864 | 0.457365 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −2.41882 | −0.227543 | −0.113772 | − | 0.993507i | \(-0.536293\pi\) | ||||
−0.113772 | + | 0.993507i | \(0.536293\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −3.27053 | −0.304979 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 4.69639 | 0.434182 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −3.96693 | −0.363648 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −8.96693 | −0.815175 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 2.57414 | 0.232102 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −2.27758 | −0.203713 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −16.9268 | −1.50201 | −0.751006 | − | 0.660296i | \(-0.770431\pi\) | ||||
−0.751006 | + | 0.660296i | \(0.770431\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −11.5481 | −1.01675 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −19.2936 | −1.68569 | −0.842843 | − | 0.538159i | \(-0.819120\pi\) | ||||
−0.842843 | + | 0.538159i | \(0.819120\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 5.42586 | 0.470482 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −3.27053 | −0.281483 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 4.27758 | 0.365458 | 0.182729 | − | 0.983163i | \(-0.441507\pi\) | ||||
0.182729 | + | 0.983163i | \(0.441507\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −2.18840 | −0.185617 | −0.0928087 | − | 0.995684i | \(-0.529585\pi\) | ||||
−0.0928087 | + | 0.995684i | \(0.529585\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 5.39279 | 0.454154 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −6.69639 | −0.559980 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −12.9740 | −1.07743 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 1.00000 | 0.0824786 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −15.6894 | −1.28532 | −0.642661 | − | 0.766151i | \(-0.722170\pi\) | ||||
−0.642661 | + | 0.766151i | \(0.722170\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 11.0962 | 0.902998 | 0.451499 | − | 0.892272i | \(-0.350890\pi\) | ||||
0.451499 | + | 0.892272i | \(0.350890\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 3.96693 | 0.320707 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 28.8417 | 2.31662 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −6.54107 | −0.522034 | −0.261017 | − | 0.965334i | \(-0.584058\pi\) | ||||
−0.261017 | + | 0.965334i | \(0.584058\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −12.6633 | −1.00427 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1.00000 | −0.0788110 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 3.51504 | 0.275319 | 0.137659 | − | 0.990480i | \(-0.456042\pi\) | ||||
0.137659 | + | 0.990480i | \(0.456042\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 4.66332 | 0.363039 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −2.27758 | −0.176244 | −0.0881221 | − | 0.996110i | \(-0.528087\pi\) | ||||
−0.0881221 | + | 0.996110i | \(0.528087\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 9.05611 | 0.696623 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −5.42586 | −0.414926 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −9.35971 | −0.711606 | −0.355803 | − | 0.934561i | \(-0.615793\pi\) | ||||
−0.355803 | + | 0.934561i | \(0.615793\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −5.69639 | −0.430607 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 11.5150 | 0.865523 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −4.66332 | −0.348553 | −0.174276 | − | 0.984697i | \(-0.555759\pi\) | ||||
−0.174276 | + | 0.984697i | \(0.555759\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −17.3738 | −1.29138 | −0.645692 | − | 0.763598i | \(-0.723431\pi\) | ||||
−0.645692 | + | 0.763598i | \(0.723431\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −13.2375 | −0.978541 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −15.7595 | −1.15866 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −5.65628 | −0.413628 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −1.00000 | −0.0727393 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −11.6894 | −0.845812 | −0.422906 | − | 0.906174i | \(-0.638990\pi\) | ||||
−0.422906 | + | 0.906174i | \(0.638990\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 4.60721 | 0.331635 | 0.165817 | − | 0.986156i | \(-0.446974\pi\) | ||||
0.165817 | + | 0.986156i | \(0.446974\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −15.3597 | −1.09993 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −24.8747 | −1.77225 | −0.886126 | − | 0.463444i | \(-0.846614\pi\) | ||||
−0.886126 | + | 0.463444i | \(0.846614\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 7.44889 | 0.528038 | 0.264019 | − | 0.964517i | \(-0.414952\pi\) | ||||
0.264019 | + | 0.964517i | \(0.414952\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 5.51504 | 0.389001 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −3.96693 | −0.278424 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −8.41882 | −0.587996 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 1.00000 | 0.0695048 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 7.73651 | 0.535145 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 11.9810 | 0.824807 | 0.412403 | − | 0.911001i | \(-0.364689\pi\) | ||||
0.412403 | + | 0.911001i | \(0.364689\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −2.69639 | −0.184754 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 37.7685 | 2.57579 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 8.81864 | 0.598649 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −9.35971 | −0.632471 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 18.6302 | 1.25321 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −10.1884 | −0.682266 | −0.341133 | − | 0.940015i | \(-0.610811\pi\) | ||||
−0.341133 | + | 0.940015i | \(0.610811\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 5.69639 | 0.379760 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −20.0561 | −1.33117 | −0.665585 | − | 0.746322i | \(-0.731818\pi\) | ||||
−0.665585 | + | 0.746322i | \(0.731818\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 9.28462 | 0.613545 | 0.306772 | − | 0.951783i | \(-0.400751\pi\) | ||||
0.306772 | + | 0.951783i | \(0.400751\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1.42586 | 0.0938146 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 5.20439 | 0.340951 | 0.170475 | − | 0.985362i | \(-0.445470\pi\) | ||||
0.170475 | + | 0.985362i | \(0.445470\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −17.6373 | −1.15053 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −4.57414 | −0.297122 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −23.1382 | −1.49669 | −0.748344 | − | 0.663311i | \(-0.769151\pi\) | ||||
−0.748344 | + | 0.663311i | \(0.769151\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1.11521 | 0.0718369 | 0.0359185 | − | 0.999355i | \(-0.488564\pi\) | ||||
0.0359185 | + | 0.999355i | \(0.488564\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −3.27053 | −0.208947 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −25.4820 | −1.62138 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −0.277576 | −0.0175907 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 23.8818 | 1.50741 | 0.753703 | − | 0.657216i | \(-0.228266\pi\) | ||||
0.753703 | + | 0.657216i | \(0.228266\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1.42586 | −0.0896430 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −12.9740 | −0.812461 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −22.1122 | −1.37932 | −0.689661 | − | 0.724132i | \(-0.742240\pi\) | ||||
−0.689661 | + | 0.724132i | \(0.742240\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −4.81864 | −0.299416 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 3.96693 | 0.245547 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 16.1973 | 0.998771 | 0.499386 | − | 0.866380i | \(-0.333559\pi\) | ||||
0.499386 | + | 0.866380i | \(0.333559\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 41.4158 | 2.54415 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 11.4820 | 0.702685 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 20.3196 | 1.23891 | 0.619454 | − | 0.785033i | \(-0.287354\pi\) | ||||
0.619454 | + | 0.785033i | \(0.287354\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −16.5080 | −1.00279 | −0.501395 | − | 0.865219i | \(-0.667180\pi\) | ||||
−0.501395 | + | 0.865219i | \(0.667180\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −4.69639 | −0.284239 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −8.12225 | −0.489790 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −3.30361 | −0.198495 | −0.0992473 | − | 0.995063i | \(-0.531643\pi\) | ||||
−0.0992473 | + | 0.995063i | \(0.531643\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −8.81864 | −0.527958 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 32.4749 | 1.93729 | 0.968646 | − | 0.248446i | \(-0.0799199\pi\) | ||||
0.968646 | + | 0.248446i | \(0.0799199\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 6.66332 | 0.396093 | 0.198047 | − | 0.980193i | \(-0.436540\pi\) | ||||
0.198047 | + | 0.980193i | \(0.436540\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 17.7455 | 1.05115 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −2.57414 | −0.151947 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1.26349 | −0.0743230 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 7.96693 | 0.467030 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −1.08214 | −0.0632191 | −0.0316095 | − | 0.999500i | \(-0.510063\pi\) | ||||
−0.0316095 | + | 0.999500i | \(0.510063\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −37.6603 | −2.19267 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −1.42586 | −0.0827367 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 4.69639 | 0.271599 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 11.5481 | 0.665622 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 6.97397 | 0.400644 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 43.2936 | 2.47898 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −8.88479 | −0.507082 | −0.253541 | − | 0.967325i | \(-0.581595\pi\) | ||||
−0.253541 | + | 0.967325i | \(0.581595\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −19.8677 | −1.13023 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 15.2515 | 0.864836 | 0.432418 | − | 0.901673i | \(-0.357661\pi\) | ||||
0.432418 | + | 0.901673i | \(0.357661\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 33.3126 | 1.88294 | 0.941468 | − | 0.337101i | \(-0.109446\pi\) | ||||
0.941468 | + | 0.337101i | \(0.109446\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 3.27053 | 0.184274 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −17.2044 | −0.966295 | −0.483147 | − | 0.875539i | \(-0.660506\pi\) | ||||
−0.483147 | + | 0.875539i | \(0.660506\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −5.65628 | −0.316691 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −10.3998 | −0.580462 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −21.5240 | −1.19763 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 26.7525 | 1.48396 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −12.3527 | −0.683104 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −5.39279 | −0.297314 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 5.14828 | 0.282975 | 0.141488 | − | 0.989940i | \(-0.454811\pi\) | ||||
0.141488 | + | 0.989940i | \(0.454811\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 4.81864 | 0.264060 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −18.0371 | −0.985473 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −6.71048 | −0.365543 | −0.182771 | − | 0.983155i | \(-0.558507\pi\) | ||||
−0.182771 | + | 0.983155i | \(0.558507\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −2.41882 | −0.131372 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 12.5741 | 0.680928 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −3.27053 | −0.176080 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −6.83273 | −0.366800 | −0.183400 | − | 0.983038i | \(-0.558710\pi\) | ||||
−0.183400 | + | 0.983038i | \(0.558710\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 15.7455 | 0.842835 | 0.421417 | − | 0.906867i | \(-0.361533\pi\) | ||||
0.421417 | + | 0.906867i | \(0.361533\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 4.69639 | 0.250675 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 3.78857 | 0.201645 | 0.100823 | − | 0.994904i | \(-0.467853\pi\) | ||||
0.100823 | + | 0.994904i | \(0.467853\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 8.81864 | 0.468045 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −3.96693 | −0.209952 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 34.8276 | 1.83813 | 0.919065 | − | 0.394106i | \(-0.128946\pi\) | ||||
0.919065 | + | 0.394106i | \(0.128946\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 10.4399 | 0.549471 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −8.96693 | −0.470642 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 30.6113 | 1.60227 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 0.926811 | 0.0483792 | 0.0241896 | − | 0.999707i | \(-0.492299\pi\) | ||||
0.0241896 | + | 0.999707i | \(0.492299\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 2.57414 | 0.134004 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 12.6633 | 0.657447 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 7.60422 | 0.393731 | 0.196866 | − | 0.980430i | \(-0.436924\pi\) | ||||
0.196866 | + | 0.980430i | \(0.436924\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −2.27758 | −0.117614 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 18.6302 | 0.959507 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 32.7194 | 1.68068 | 0.840342 | − | 0.542057i | \(-0.182354\pi\) | ||||
0.840342 | + | 0.542057i | \(0.182354\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −16.9268 | −0.867187 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −1.78857 | −0.0913917 | −0.0456958 | − | 0.998955i | \(-0.514551\pi\) | ||||
−0.0456958 | + | 0.998955i | \(0.514551\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −4.66332 | −0.237665 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −11.5481 | −0.587023 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −30.4559 | −1.54418 | −0.772089 | − | 0.635515i | \(-0.780788\pi\) | ||||
−0.772089 | + | 0.635515i | \(0.780788\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 3.96693 | 0.200616 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −19.2936 | −0.973232 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 14.9599 | 0.752713 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 26.7053 | 1.34030 | 0.670151 | − | 0.742225i | \(-0.266229\pi\) | ||||
0.670151 | + | 0.742225i | \(0.266229\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 5.42586 | 0.271633 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −15.9669 | −0.797350 | −0.398675 | − | 0.917092i | \(-0.630530\pi\) | ||||
−0.398675 | + | 0.917092i | \(0.630530\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −41.4158 | −2.06307 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −3.27053 | −0.162514 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −6.87071 | −0.340568 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 0.560057 | 0.0276930 | 0.0138465 | − | 0.999904i | \(-0.495592\pi\) | ||||
0.0138465 | + | 0.999904i | \(0.495592\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 4.27758 | 0.210997 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −11.5150 | −0.566618 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0.907823 | 0.0445633 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −2.18840 | −0.107166 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −16.8937 | −0.825313 | −0.412657 | − | 0.910887i | \(-0.635399\pi\) | ||||
−0.412657 | + | 0.910887i | \(0.635399\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 12.0892 | 0.589191 | 0.294595 | − | 0.955622i | \(-0.404815\pi\) | ||||
0.294595 | + | 0.955622i | \(0.404815\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 5.39279 | 0.262206 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 22.5972 | 1.09612 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 13.2375 | 0.640606 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −6.69639 | −0.323305 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 10.1412 | 0.488486 | 0.244243 | − | 0.969714i | \(-0.421460\pi\) | ||||
0.244243 | + | 0.969714i | \(0.421460\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 40.4749 | 1.94510 | 0.972550 | − | 0.232693i | \(-0.0747536\pi\) | ||||
0.972550 | + | 0.232693i | \(0.0747536\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −12.9740 | −0.622054 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −5.42586 | −0.259554 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −6.03307 | −0.287943 | −0.143971 | − | 0.989582i | \(-0.545987\pi\) | ||||
−0.143971 | + | 0.989582i | \(0.545987\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.00000 | 0.0476190 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 0.621299 | 0.0295188 | 0.0147594 | − | 0.999891i | \(-0.495302\pi\) | ||||
0.0147594 | + | 0.999891i | \(0.495302\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −37.5522 | −1.78014 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −15.6894 | −0.742081 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 31.7455 | 1.49816 | 0.749080 | − | 0.662479i | \(-0.230496\pi\) | ||||
0.749080 | + | 0.662479i | \(0.230496\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −3.67036 | −0.172831 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 11.0962 | 0.521346 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 15.3597 | 0.720074 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −41.3166 | −1.93271 | −0.966354 | − | 0.257214i | \(-0.917195\pi\) | ||||
−0.966354 | + | 0.257214i | \(0.917195\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 3.96693 | 0.185160 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 13.7595 | 0.640846 | 0.320423 | − | 0.947275i | \(-0.396175\pi\) | ||||
0.320423 | + | 0.947275i | \(0.396175\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 20.1312 | 0.935576 | 0.467788 | − | 0.883841i | \(-0.345051\pi\) | ||||
0.467788 | + | 0.883841i | \(0.345051\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 28.8417 | 1.33750 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −25.2936 | −1.17045 | −0.585223 | − | 0.810872i | \(-0.698993\pi\) | ||||
−0.585223 | + | 0.810872i | \(0.698993\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −5.51504 | −0.254661 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −6.54107 | −0.301397 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 16.4660 | 0.757106 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −30.9078 | −1.41815 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −12.6633 | −0.579814 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 24.6864 | 1.12795 | 0.563974 | − | 0.825792i | \(-0.309272\pi\) | ||||
0.563974 | + | 0.825792i | \(0.309272\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 22.6302 | 1.03185 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −1.00000 | −0.0455016 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −26.0561 | −1.18315 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −37.2415 | −1.68757 | −0.843787 | − | 0.536678i | \(-0.819679\pi\) | ||||
−0.843787 | + | 0.536678i | \(0.819679\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 3.51504 | 0.158955 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −39.1193 | −1.76543 | −0.882714 | − | 0.469911i | \(-0.844286\pi\) | ||||
−0.882714 | + | 0.469911i | \(0.844286\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 15.7365 | 0.708737 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 4.66332 | 0.209601 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 2.69639 | 0.120950 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −19.3367 | −0.865629 | −0.432814 | − | 0.901483i | \(-0.642479\pi\) | ||||
−0.432814 | + | 0.901483i | \(0.642479\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −2.27758 | −0.101755 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 2.95988 | 0.131975 | 0.0659874 | − | 0.997820i | \(-0.478980\pi\) | ||||
0.0659874 | + | 0.997820i | \(0.478980\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −22.8086 | −1.01497 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 9.05611 | 0.402196 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −22.2445 | −0.985970 | −0.492985 | − | 0.870038i | \(-0.664094\pi\) | ||||
−0.492985 | + | 0.870038i | \(0.664094\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 9.35971 | 0.414049 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −5.42586 | −0.239558 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 64.9780 | 2.86327 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −7.68935 | −0.338177 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −9.35971 | −0.410846 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 42.4890 | 1.86148 | 0.930739 | − | 0.365685i | \(-0.119165\pi\) | ||||
0.930739 | + | 0.365685i | \(0.119165\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 37.7354 | 1.65005 | 0.825027 | − | 0.565093i | \(-0.191160\pi\) | ||||
0.825027 | + | 0.565093i | \(0.191160\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −5.69639 | −0.248611 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −34.9829 | −1.52388 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 11.5150 | 0.499710 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 12.0892 | 0.523640 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 34.0130 | 1.47051 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −4.66332 | −0.201237 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −1.42586 | −0.0614161 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −23.9479 | −1.02960 | −0.514801 | − | 0.857310i | \(-0.672134\pi\) | ||||
−0.514801 | + | 0.857310i | \(0.672134\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −17.3738 | −0.745581 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 40.3998 | 1.73054 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 3.44889 | 0.147464 | 0.0737320 | − | 0.997278i | \(-0.476509\pi\) | ||||
0.0737320 | + | 0.997278i | \(0.476509\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −13.2375 | −0.564961 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −21.5240 | −0.916953 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 4.57414 | 0.194512 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −15.7595 | −0.668955 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −19.0301 | −0.806330 | −0.403165 | − | 0.915127i | \(-0.632090\pi\) | ||||
−0.403165 | + | 0.915127i | \(0.632090\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −54.2345 | −2.29387 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −5.65628 | −0.238808 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −3.76444 | −0.158652 | −0.0793262 | − | 0.996849i | \(-0.525277\pi\) | ||||
−0.0793262 | + | 0.996849i | \(0.525277\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 7.91082 | 0.332811 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −1.00000 | −0.0419961 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −33.9339 | −1.42258 | −0.711291 | − | 0.702898i | \(-0.751889\pi\) | ||||
−0.711291 | + | 0.702898i | \(0.751889\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 24.0791 | 1.00768 | 0.503840 | − | 0.863797i | \(-0.331920\pi\) | ||||
0.503840 | + | 0.863797i | \(0.331920\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −11.6894 | −0.488330 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 5.69639 | 0.237556 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 28.1924 | 1.17367 | 0.586833 | − | 0.809708i | \(-0.300374\pi\) | ||||
0.586833 | + | 0.809708i | \(0.300374\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 4.60721 | 0.191469 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0.277576 | 0.0115158 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 18.0561 | 0.747807 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −15.3597 | −0.635046 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 24.8888 | 1.02727 | 0.513636 | − | 0.858008i | \(-0.328298\pi\) | ||||
0.513636 | + | 0.858008i | \(0.328298\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 47.8487 | 1.97157 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −24.8747 | −1.02321 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 19.3928 | 0.796366 | 0.398183 | − | 0.917306i | \(-0.369641\pi\) | ||||
0.398183 | + | 0.917306i | \(0.369641\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 12.9740 | 0.531881 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 7.44889 | 0.304863 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 4.15532 | 0.169782 | 0.0848910 | − | 0.996390i | \(-0.472946\pi\) | ||||
0.0848910 | + | 0.996390i | \(0.472946\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −0.300608 | −0.0122621 | −0.00613103 | − | 0.999981i | \(-0.501952\pi\) | ||||
−0.00613103 | + | 0.999981i | \(0.501952\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 5.51504 | 0.224590 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 29.3266 | 1.19230 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −29.3497 | −1.19127 | −0.595633 | − | 0.803257i | \(-0.703099\pi\) | ||||
−0.595633 | + | 0.803257i | \(0.703099\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −3.96693 | −0.160748 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 25.3266 | 1.02461 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −5.72242 | −0.231127 | −0.115563 | − | 0.993300i | \(-0.536867\pi\) | ||||
−0.115563 | + | 0.993300i | \(0.536867\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −8.41882 | −0.339479 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 24.6964 | 0.994239 | 0.497120 | − | 0.867682i | \(-0.334391\pi\) | ||||
0.497120 | + | 0.867682i | \(0.334391\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −40.7425 | −1.63758 | −0.818789 | − | 0.574095i | \(-0.805354\pi\) | ||||
−0.818789 | + | 0.574095i | \(0.805354\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.00000 | 0.0401286 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −11.4820 | −0.460015 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −21.0331 | −0.841323 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 7.73651 | 0.308966 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 19.1152 | 0.762173 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −10.5221 | −0.418877 | −0.209439 | − | 0.977822i | \(-0.567164\pi\) | ||||
−0.209439 | + | 0.977822i | \(0.567164\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 11.9810 | 0.476202 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 55.3597 | 2.19688 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 4.69639 | 0.186078 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −2.69639 | −0.106668 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −2.64433 | −0.104445 | −0.0522224 | − | 0.998635i | \(-0.516630\pi\) | ||||
−0.0522224 | + | 0.998635i | \(0.516630\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 5.18540 | 0.204492 | 0.102246 | − | 0.994759i | \(-0.467397\pi\) | ||||
0.102246 | + | 0.994759i | \(0.467397\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 37.7685 | 1.48713 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 17.2564 | 0.678421 | 0.339211 | − | 0.940710i | \(-0.389840\pi\) | ||||
0.339211 | + | 0.940710i | \(0.389840\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −16.4188 | −0.644495 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 8.81864 | 0.345630 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −31.1523 | −1.21908 | −0.609542 | − | 0.792754i | \(-0.708647\pi\) | ||||
−0.609542 | + | 0.792754i | \(0.708647\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 63.1003 | 2.46553 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −9.35971 | −0.365157 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 5.84872 | 0.227834 | 0.113917 | − | 0.993490i | \(-0.463660\pi\) | ||||
0.113917 | + | 0.993490i | \(0.463660\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −7.64219 | −0.297247 | −0.148623 | − | 0.988894i | \(-0.547484\pi\) | ||||
−0.148623 | + | 0.988894i | \(0.547484\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 18.6302 | 0.723539 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −17.7455 | −0.688139 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 3.96693 | 0.153600 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −10.1884 | −0.393906 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 18.8747 | 0.728652 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 2.26349 | 0.0872512 | 0.0436256 | − | 0.999048i | \(-0.486109\pi\) | ||||
0.0436256 | + | 0.999048i | \(0.486109\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 5.69639 | 0.219254 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 22.8747 | 0.879148 | 0.439574 | − | 0.898206i | \(-0.355129\pi\) | ||||
0.439574 | + | 0.898206i | \(0.355129\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −7.96693 | −0.305743 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −20.0561 | −0.768552 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 10.3437 | 0.395792 | 0.197896 | − | 0.980223i | \(-0.436589\pi\) | ||||
0.197896 | + | 0.980223i | \(0.436589\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −13.9900 | −0.534529 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 9.28462 | 0.354230 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −59.4719 | −2.26570 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −37.6603 | −1.43267 | −0.716333 | − | 0.697759i | \(-0.754181\pi\) | ||||
−0.716333 | + | 0.697759i | \(0.754181\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 1.42586 | 0.0541639 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 7.15723 | 0.271489 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 10.2114 | 0.386785 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 5.20439 | 0.196848 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −26.1223 | −0.986624 | −0.493312 | − | 0.869852i | \(-0.664214\pi\) | ||||
−0.493312 | + | 0.869852i | \(0.664214\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −26.1453 | −0.986088 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −17.6373 | −0.664259 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −6.97397 | −0.262283 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 18.1412 | 0.681309 | 0.340654 | − | 0.940189i | \(-0.389351\pi\) | ||||
0.340654 | + | 0.940189i | \(0.389351\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −4.57414 | −0.171544 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −8.81864 | −0.330261 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 21.9008 | 0.819043 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −23.1382 | −0.864113 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −18.4559 | −0.688290 | −0.344145 | − | 0.938916i | \(-0.611831\pi\) | ||||
−0.344145 | + | 0.938916i | \(0.611831\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 19.8677 | 0.739912 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 1.11521 | 0.0414751 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 22.5972 | 0.839238 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 17.6563 | 0.654835 | 0.327418 | − | 0.944880i | \(-0.393822\pi\) | ||||
0.327418 | + | 0.944880i | \(0.393822\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −45.8105 | −1.69436 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −36.1122 | −1.33383 | −0.666917 | − | 0.745132i | \(-0.732387\pi\) | ||||
−0.666917 | + | 0.745132i | \(0.732387\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −3.27053 | −0.120635 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −7.86366 | −0.289662 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −19.9149 | −0.732580 | −0.366290 | − | 0.930501i | \(-0.619372\pi\) | ||||
−0.366290 | + | 0.930501i | \(0.619372\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −25.4820 | −0.936103 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −40.2865 | −1.47797 | −0.738985 | − | 0.673722i | \(-0.764694\pi\) | ||||
−0.738985 | + | 0.673722i | \(0.764694\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 51.3126 | 1.87995 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −0.277576 | −0.0101560 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 10.3998 | 0.380001 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −49.6793 | −1.81282 | −0.906412 | − | 0.422395i | \(-0.861190\pi\) | ||||
−0.906412 | + | 0.422395i | \(0.861190\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 23.8818 | 0.870301 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −36.2906 | −1.32075 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −37.7685 | −1.37272 | −0.686360 | − | 0.727262i | \(-0.740792\pi\) | ||||
−0.686360 | + | 0.727262i | \(0.740792\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −1.42586 | −0.0517554 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 3.14828 | 0.114125 | 0.0570626 | − | 0.998371i | \(-0.481827\pi\) | ||||
0.0570626 | + | 0.998371i | \(0.481827\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 12.3527 | 0.447197 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −12.9740 | −0.469075 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 54.0791 | 1.95268 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 19.2605 | 0.694551 | 0.347276 | − | 0.937763i | \(-0.387107\pi\) | ||||
0.347276 | + | 0.937763i | \(0.387107\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −22.1122 | −0.796352 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −13.0631 | −0.469849 | −0.234924 | − | 0.972014i | \(-0.575484\pi\) | ||||
−0.234924 | + | 0.972014i | \(0.575484\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −50.2345 | −1.80448 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −4.81864 | −0.172868 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −13.9669 | −0.500417 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 3.84468 | 0.137573 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 3.96693 | 0.141766 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 21.3928 | 0.763541 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −45.7595 | −1.63115 | −0.815576 | − | 0.578650i | \(-0.803580\pi\) | ||||
−0.815576 | + | 0.578650i | \(0.803580\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 16.1973 | 0.576641 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 2.41882 | 0.0860032 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −62.1683 | −2.20766 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 41.4158 | 1.46887 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 10.4749 | 0.371041 | 0.185520 | − | 0.982640i | \(-0.440603\pi\) | ||||
0.185520 | + | 0.982640i | \(0.440603\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 21.3928 | 0.756822 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 11.4820 | 0.405695 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 13.3456 | 0.470957 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 3.27053 | 0.115271 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 20.3196 | 0.715284 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 14.0230 | 0.493024 | 0.246512 | − | 0.969140i | \(-0.420716\pi\) | ||||
0.246512 | + | 0.969140i | \(0.420716\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 30.0791 | 1.05622 | 0.528111 | − | 0.849176i | \(-0.322901\pi\) | ||||
0.528111 | + | 0.849176i | \(0.322901\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −16.5080 | −0.578961 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −11.4960 | −0.402689 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 62.6584 | 2.19214 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −4.69639 | −0.164105 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 44.4088 | 1.54988 | 0.774938 | − | 0.632037i | \(-0.217781\pi\) | ||||
0.774938 | + | 0.632037i | \(0.217781\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −14.8276 | −0.516857 | −0.258429 | − | 0.966030i | \(-0.583205\pi\) | ||||
−0.258429 | + | 0.966030i | \(0.583205\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −8.12225 | −0.282781 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −27.0401 | −0.940277 | −0.470138 | − | 0.882593i | \(-0.655796\pi\) | ||||
−0.470138 | + | 0.882593i | \(0.655796\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −11.9669 | −0.415629 | −0.207814 | − | 0.978168i | \(-0.566635\pi\) | ||||
−0.207814 | + | 0.978168i | \(0.566635\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −3.30361 | −0.114601 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 3.96693 | 0.137446 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 7.44889 | 0.257779 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −8.81864 | −0.304817 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −42.2535 | −1.45875 | −0.729376 | − | 0.684114i | \(-0.760189\pi\) | ||||
−0.729376 | + | 0.684114i | \(0.760189\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −13.2635 | −0.457362 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 32.4749 | 1.11850 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −29.6183 | −1.01890 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 8.96693 | 0.308107 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 6.66332 | 0.228685 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 4.81864 | 0.165181 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 20.4749 | 0.701048 | 0.350524 | − | 0.936554i | \(-0.386004\pi\) | ||||
0.350524 | + | 0.936554i | \(0.386004\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 17.7455 | 0.606882 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 17.6894 | 0.604257 | 0.302128 | − | 0.953267i | \(-0.402303\pi\) | ||||
0.302128 | + | 0.953267i | \(0.402303\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −5.01599 | −0.171143 | −0.0855717 | − | 0.996332i | \(-0.527272\pi\) | ||||
−0.0855717 | + | 0.996332i | \(0.527272\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −2.57414 | −0.0877265 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 16.9699 | 0.577663 | 0.288831 | − | 0.957380i | \(-0.406733\pi\) | ||||
0.288831 | + | 0.957380i | \(0.406733\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 30.6113 | 1.04081 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −1.26349 | −0.0429104 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 6.52208 | 0.221246 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 25.9008 | 0.877614 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 7.96693 | 0.269640 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 2.27758 | 0.0769961 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 0.851718 | 0.0287605 | 0.0143802 | − | 0.999897i | \(-0.495422\pi\) | ||||
0.0143802 | + | 0.999897i | \(0.495422\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −1.08214 | −0.0364995 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −44.8316 | −1.51042 | −0.755208 | − | 0.655485i | \(-0.772464\pi\) | ||||
−0.755208 | + | 0.655485i | \(0.772464\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 51.6462 | 1.73803 | 0.869017 | − | 0.494782i | \(-0.164752\pi\) | ||||
0.869017 | + | 0.494782i | \(0.164752\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −37.6603 | −1.26594 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 54.9870 | 1.84628 | 0.923141 | − | 0.384462i | \(-0.125613\pi\) | ||||
0.923141 | + | 0.384462i | \(0.125613\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 16.9268 | 0.567707 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1.42586 | −0.0477681 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −29.2605 | −0.979165 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 15.2515 | 0.509803 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 4.69639 | 0.156808 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −34.9829 | −1.16675 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −50.2345 | −1.67355 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 11.5481 | 0.384297 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 56.8216 | 1.88881 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −27.6132 | −0.916880 | −0.458440 | − | 0.888725i | \(-0.651592\pi\) | ||||
−0.458440 | + | 0.888725i | \(0.651592\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 6.97397 | 0.231312 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 25.3928 | 0.841301 | 0.420650 | − | 0.907223i | \(-0.361802\pi\) | ||||
0.420650 | + | 0.907223i | \(0.361802\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0.395785 | 0.0130986 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 43.2936 | 1.43124 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 19.2936 | 0.637130 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 52.6202 | 1.73578 | 0.867890 | − | 0.496756i | \(-0.165476\pi\) | ||||
0.867890 | + | 0.496756i | \(0.165476\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −8.88479 | −0.292764 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −12.6633 | −0.416818 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 27.4489 | 0.902514 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −19.8677 | −0.652541 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −39.9900 | −1.31203 | −0.656014 | − | 0.754749i | \(-0.727759\pi\) | ||||
−0.656014 | + | 0.754749i | \(0.727759\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −5.42586 | −0.177825 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 15.2515 | 0.499313 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 18.4990 | 0.604984 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −36.6061 | −1.19587 | −0.597935 | − | 0.801545i | \(-0.704012\pi\) | ||||
−0.597935 | + | 0.801545i | \(0.704012\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 33.3126 | 1.08711 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 31.4069 | 1.02383 | 0.511917 | − | 0.859035i | \(-0.328935\pi\) | ||||
0.511917 | + | 0.859035i | \(0.328935\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 2.57414 | 0.0838256 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 3.27053 | 0.106390 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −28.0661 | −0.912027 | −0.456014 | − | 0.889973i | \(-0.650723\pi\) | ||||
−0.456014 | + | 0.889973i | \(0.650723\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −43.9569 | −1.42690 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −17.2044 | −0.557890 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 51.8105 | 1.67831 | 0.839153 | − | 0.543895i | \(-0.183051\pi\) | ||||
0.839153 | + | 0.543895i | \(0.183051\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 38.2304 | 1.23711 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −5.65628 | −0.182841 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −4.27758 | −0.138130 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 46.7685 | 1.50866 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −10.3998 | −0.335130 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −15.0681 | −0.485058 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 25.0160 | 0.804460 | 0.402230 | − | 0.915539i | \(-0.368235\pi\) | ||||
0.402230 | + | 0.915539i | \(0.368235\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −21.5240 | −0.691450 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 38.5782 | 1.23803 | 0.619016 | − | 0.785378i | \(-0.287531\pi\) | ||||
0.619016 | + | 0.785378i | \(0.287531\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 2.18840 | 0.0701568 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 26.7525 | 0.856766 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −10.0230 | −0.320665 | −0.160333 | − | 0.987063i | \(-0.551257\pi\) | ||||
−0.160333 | + | 0.987063i | \(0.551257\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −16.3717 | −0.523240 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −12.3527 | −0.394390 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 10.3437 | 0.329914 | 0.164957 | − | 0.986301i | \(-0.447252\pi\) | ||||
0.164957 | + | 0.986301i | \(0.447252\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 81.3537 | 2.59214 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −5.39279 | −0.171654 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −11.5481 | −0.367209 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 38.6302 | 1.22713 | 0.613565 | − | 0.789644i | \(-0.289735\pi\) | ||||
0.613565 | + | 0.789644i | \(0.289735\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 5.14828 | 0.163376 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −24.3619 | −0.772323 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 28.0331 | 0.887816 | 0.443908 | − | 0.896072i | \(-0.353592\pi\) | ||||
0.443908 | + | 0.896072i | \(0.353592\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 4.81864 | 0.152455 |
(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 | 3864.2.a.o.1.1 | ✓ | 3 | |
4.3 | odd | 2 | 7728.2.a.bq.1.1 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3864.2.a.o.1.1 | ✓ | 3 | 1.1 | even | 1 | trivial | |
7728.2.a.bq.1.1 | 3 | 4.3 | odd | 2 |