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: | \(4\) |
Coefficient field: | \(\Q(\sqrt{3}, \sqrt{19})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 11x^{2} + 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 1216) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(1.31342\) 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 | ||||||||
\(3\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.31342 | 0.587381 | 0.293691 | − | 0.955901i | \(-0.405116\pi\) | ||||
0.293691 | + | 0.955901i | \(0.405116\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −4.77753 | −1.80573 | −0.902867 | − | 0.429919i | \(-0.858542\pi\) | ||||
−0.902867 | + | 0.429919i | \(0.858542\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −3.00000 | −1.00000 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.27492 | −0.685913 | −0.342957 | − | 0.939351i | \(-0.611428\pi\) | ||||
−0.342957 | + | 0.939351i | \(0.611428\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 6.09095 | 1.68933 | 0.844663 | − | 0.535299i | \(-0.179801\pi\) | ||||
0.844663 | + | 0.535299i | \(0.179801\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −4.27492 | −1.03682 | −0.518410 | − | 0.855132i | \(-0.673476\pi\) | ||||
−0.518410 | + | 0.855132i | \(0.673476\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.00000 | −0.229416 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −3.46410 | −0.722315 | −0.361158 | − | 0.932505i | \(-0.617618\pi\) | ||||
−0.361158 | + | 0.932505i | \(0.617618\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3.27492 | −0.654983 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 6.09095 | 1.13106 | 0.565530 | − | 0.824727i | \(-0.308671\pi\) | ||||
0.565530 | + | 0.824727i | \(0.308671\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.62685 | −0.471796 | −0.235898 | − | 0.971778i | \(-0.575803\pi\) | ||||
−0.235898 | + | 0.971778i | \(0.575803\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −6.27492 | −1.06065 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −0.837253 | −0.137644 | −0.0688218 | − | 0.997629i | \(-0.521924\pi\) | ||||
−0.0688218 | + | 0.997629i | \(0.521924\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 10.5498 | 1.64761 | 0.823804 | − | 0.566875i | \(-0.191848\pi\) | ||||
0.823804 | + | 0.566875i | \(0.191848\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 10.2749 | 1.56691 | 0.783455 | − | 0.621448i | \(-0.213455\pi\) | ||||
0.783455 | + | 0.621448i | \(0.213455\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −3.94027 | −0.587381 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −4.77753 | −0.696874 | −0.348437 | − | 0.937332i | \(-0.613287\pi\) | ||||
−0.348437 | + | 0.937332i | \(0.613287\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 15.8248 | 2.26068 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −10.3923 | −1.42749 | −0.713746 | − | 0.700404i | \(-0.753003\pi\) | ||||
−0.713746 | + | 0.700404i | \(0.753003\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −2.98793 | −0.402893 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 8.54983 | 1.11309 | 0.556547 | − | 0.830816i | \(-0.312126\pi\) | ||||
0.556547 | + | 0.830816i | \(0.312126\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.31342 | −0.168167 | −0.0840834 | − | 0.996459i | \(-0.526796\pi\) | ||||
−0.0840834 | + | 0.996459i | \(0.526796\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 14.3326 | 1.80573 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 8.00000 | 0.992278 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −8.54983 | −1.04453 | −0.522264 | − | 0.852784i | \(-0.674913\pi\) | ||||
−0.522264 | + | 0.852784i | \(0.674913\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −14.8087 | −1.75748 | −0.878738 | − | 0.477305i | \(-0.841614\pi\) | ||||
−0.878738 | + | 0.477305i | \(0.841614\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −4.27492 | −0.500341 | −0.250171 | − | 0.968202i | \(-0.580487\pi\) | ||||
−0.250171 | + | 0.968202i | \(0.580487\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 10.8685 | 1.23858 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 4.30136 | 0.483940 | 0.241970 | − | 0.970284i | \(-0.422206\pi\) | ||||
0.241970 | + | 0.970284i | \(0.422206\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 9.00000 | 1.00000 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 13.0997 | 1.43788 | 0.718938 | − | 0.695074i | \(-0.244629\pi\) | ||||
0.718938 | + | 0.695074i | \(0.244629\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −5.61478 | −0.609008 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 10.0000 | 1.06000 | 0.529999 | − | 0.847998i | \(-0.322192\pi\) | ||||
0.529999 | + | 0.847998i | \(0.322192\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −29.0997 | −3.05047 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −1.31342 | −0.134754 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1.45017 | 0.147242 | 0.0736210 | − | 0.997286i | \(-0.476544\pi\) | ||||
0.0736210 | + | 0.997286i | \(0.476544\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 6.82475 | 0.685913 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 13.8564 | 1.37876 | 0.689382 | − | 0.724398i | \(-0.257882\pi\) | ||||
0.689382 | + | 0.724398i | \(0.257882\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 2.62685 | 0.258831 | 0.129416 | − | 0.991590i | \(-0.458690\pi\) | ||||
0.129416 | + | 0.991590i | \(0.458690\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 16.5498 | 1.59993 | 0.799966 | − | 0.600045i | \(-0.204851\pi\) | ||||
0.799966 | + | 0.600045i | \(0.204851\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −3.46410 | −0.331801 | −0.165900 | − | 0.986143i | \(-0.553053\pi\) | ||||
−0.165900 | + | 0.986143i | \(0.553053\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −2.54983 | −0.239868 | −0.119934 | − | 0.992782i | \(-0.538268\pi\) | ||||
−0.119934 | + | 0.992782i | \(0.538268\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −4.54983 | −0.424274 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −18.2728 | −1.68933 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 20.4235 | 1.87222 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −5.82475 | −0.529523 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −10.8685 | −0.972106 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 17.4356 | 1.54716 | 0.773579 | − | 0.633699i | \(-0.218464\pi\) | ||||
0.773579 | + | 0.633699i | \(0.218464\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 2.27492 | 0.198760 | 0.0993802 | − | 0.995050i | \(-0.468314\pi\) | ||||
0.0993802 | + | 0.995050i | \(0.468314\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 4.77753 | 0.414264 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 20.2749 | 1.73220 | 0.866102 | − | 0.499868i | \(-0.166618\pi\) | ||||
0.866102 | + | 0.499868i | \(0.166618\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 10.2749 | 0.871507 | 0.435754 | − | 0.900066i | \(-0.356482\pi\) | ||||
0.435754 | + | 0.900066i | \(0.356482\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −13.8564 | −1.15873 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 8.00000 | 0.664364 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 2.98793 | 0.244781 | 0.122390 | − | 0.992482i | \(-0.460944\pi\) | ||||
0.122390 | + | 0.992482i | \(0.460944\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 9.55505 | 0.777579 | 0.388790 | − | 0.921327i | \(-0.372893\pi\) | ||||
0.388790 | + | 0.921327i | \(0.372893\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 12.8248 | 1.03682 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −3.45017 | −0.277124 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −5.25370 | −0.419291 | −0.209645 | − | 0.977778i | \(-0.567231\pi\) | ||||
−0.209645 | + | 0.977778i | \(0.567231\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 16.5498 | 1.30431 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −4.00000 | −0.313304 | −0.156652 | − | 0.987654i | \(-0.550070\pi\) | ||||
−0.156652 | + | 0.987654i | \(0.550070\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 1.67451 | 0.129577 | 0.0647886 | − | 0.997899i | \(-0.479363\pi\) | ||||
0.0647886 | + | 0.997899i | \(0.479363\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 24.0997 | 1.85382 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 3.00000 | 0.229416 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 8.71780 | 0.662802 | 0.331401 | − | 0.943490i | \(-0.392479\pi\) | ||||
0.331401 | + | 0.943490i | \(0.392479\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 15.6460 | 1.18273 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −9.09967 | −0.680141 | −0.340071 | − | 0.940400i | \(-0.610451\pi\) | ||||
−0.340071 | + | 0.940400i | \(0.610451\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −3.46410 | −0.257485 | −0.128742 | − | 0.991678i | \(-0.541094\pi\) | ||||
−0.128742 | + | 0.991678i | \(0.541094\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −1.09967 | −0.0808493 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 9.72508 | 0.711168 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −10.0312 | −0.725834 | −0.362917 | − | 0.931822i | \(-0.618219\pi\) | ||||
−0.362917 | + | 0.931822i | \(0.618219\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −19.0997 | −1.37482 | −0.687412 | − | 0.726268i | \(-0.741253\pi\) | ||||
−0.687412 | + | 0.726268i | \(0.741253\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 12.1819 | 0.867924 | 0.433962 | − | 0.900931i | \(-0.357115\pi\) | ||||
0.433962 | + | 0.900931i | \(0.357115\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 18.6339 | 1.32092 | 0.660462 | − | 0.750859i | \(-0.270360\pi\) | ||||
0.660462 | + | 0.750859i | \(0.270360\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −29.0997 | −2.04240 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 13.8564 | 0.967773 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 10.3923 | 0.722315 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 2.27492 | 0.157359 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 11.4502 | 0.788262 | 0.394131 | − | 0.919054i | \(-0.371046\pi\) | ||||
0.394131 | + | 0.919054i | \(0.371046\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 13.4953 | 0.920373 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 12.5498 | 0.851938 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −26.0383 | −1.75153 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −17.4356 | −1.16757 | −0.583787 | − | 0.811907i | \(-0.698430\pi\) | ||||
−0.583787 | + | 0.811907i | \(0.698430\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 9.82475 | 0.654983 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −4.00000 | −0.265489 | −0.132745 | − | 0.991150i | \(-0.542379\pi\) | ||||
−0.132745 | + | 0.991150i | \(0.542379\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 22.0980 | 1.46028 | 0.730140 | − | 0.683298i | \(-0.239455\pi\) | ||||
0.730140 | + | 0.683298i | \(0.239455\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −17.3746 | −1.13825 | −0.569123 | − | 0.822252i | \(-0.692717\pi\) | ||||
−0.569123 | + | 0.822252i | \(0.692717\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −6.27492 | −0.409330 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −3.82518 | −0.247431 | −0.123715 | − | 0.992318i | \(-0.539481\pi\) | ||||
−0.123715 | + | 0.992318i | \(0.539481\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 2.54983 | 0.164249 | 0.0821246 | − | 0.996622i | \(-0.473829\pi\) | ||||
0.0821246 | + | 0.996622i | \(0.473829\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 20.7846 | 1.32788 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −6.09095 | −0.387558 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −18.2749 | −1.15350 | −0.576751 | − | 0.816920i | \(-0.695680\pi\) | ||||
−0.576751 | + | 0.816920i | \(0.695680\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 7.88054 | 0.495446 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 22.5498 | 1.40662 | 0.703310 | − | 0.710883i | \(-0.251705\pi\) | ||||
0.703310 | + | 0.710883i | \(0.251705\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 4.00000 | 0.248548 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −18.2728 | −1.13106 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −14.3326 | −0.883785 | −0.441892 | − | 0.897068i | \(-0.645693\pi\) | ||||
−0.441892 | + | 0.897068i | \(0.645693\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −13.6495 | −0.838482 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −22.5742 | −1.37637 | −0.688187 | − | 0.725534i | \(-0.741593\pi\) | ||||
−0.688187 | + | 0.725534i | \(0.741593\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 7.04329 | 0.427849 | 0.213925 | − | 0.976850i | \(-0.431375\pi\) | ||||
0.213925 | + | 0.976850i | \(0.431375\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 7.45017 | 0.449262 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −2.98793 | −0.179527 | −0.0897637 | − | 0.995963i | \(-0.528611\pi\) | ||||
−0.0897637 | + | 0.995963i | \(0.528611\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 7.88054 | 0.471796 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 19.0997 | 1.13939 | 0.569695 | − | 0.821856i | \(-0.307061\pi\) | ||||
0.569695 | + | 0.821856i | \(0.307061\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 11.3746 | 0.676149 | 0.338074 | − | 0.941119i | \(-0.390224\pi\) | ||||
0.338074 | + | 0.941119i | \(0.390224\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −50.4021 | −2.97514 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1.27492 | 0.0749951 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 21.6219 | 1.26316 | 0.631581 | − | 0.775310i | \(-0.282406\pi\) | ||||
0.631581 | + | 0.775310i | \(0.282406\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 11.2296 | 0.653810 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −21.0997 | −1.22023 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −49.0887 | −2.82942 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −1.72508 | −0.0987780 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 16.5498 | 0.944549 | 0.472274 | − | 0.881452i | \(-0.343433\pi\) | ||||
0.472274 | + | 0.881452i | \(0.343433\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −5.72987 | −0.324911 | −0.162455 | − | 0.986716i | \(-0.551941\pi\) | ||||
−0.162455 | + | 0.986716i | \(0.551941\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 15.0997 | 0.853484 | 0.426742 | − | 0.904373i | \(-0.359661\pi\) | ||||
0.426742 | + | 0.904373i | \(0.359661\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 18.8248 | 1.06065 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −8.71780 | −0.489640 | −0.244820 | − | 0.969569i | \(-0.578729\pi\) | ||||
−0.244820 | + | 0.969569i | \(0.578729\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −13.8564 | −0.775810 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 4.27492 | 0.237863 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −19.9474 | −1.10648 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 22.8248 | 1.25837 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 24.5498 | 1.34938 | 0.674690 | − | 0.738101i | \(-0.264277\pi\) | ||||
0.674690 | + | 0.738101i | \(0.264277\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 2.51176 | 0.137644 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −11.2296 | −0.613536 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −11.6495 | −0.634589 | −0.317294 | − | 0.948327i | \(-0.602774\pi\) | ||||
−0.317294 | + | 0.948327i | \(0.602774\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 5.97586 | 0.323611 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −42.1605 | −2.27645 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −14.8248 | −0.795834 | −0.397917 | − | 0.917421i | \(-0.630267\pi\) | ||||
−0.397917 | + | 0.917421i | \(0.630267\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 35.2323 | 1.88594 | 0.942970 | − | 0.332877i | \(-0.108019\pi\) | ||||
0.942970 | + | 0.332877i | \(0.108019\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −10.0000 | −0.532246 | −0.266123 | − | 0.963939i | \(-0.585743\pi\) | ||||
−0.266123 | + | 0.963939i | \(0.585743\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −19.4502 | −1.03231 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −0.476171 | −0.0251313 | −0.0125657 | − | 0.999921i | \(-0.504000\pi\) | ||||
−0.0125657 | + | 0.999921i | \(0.504000\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −5.61478 | −0.293891 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −1.78959 | −0.0934161 | −0.0467080 | − | 0.998909i | \(-0.514873\pi\) | ||||
−0.0467080 | + | 0.998909i | \(0.514873\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −31.6495 | −1.64761 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 49.6495 | 2.57767 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −25.2011 | −1.30486 | −0.652431 | − | 0.757849i | \(-0.726251\pi\) | ||||
−0.652431 | + | 0.757849i | \(0.726251\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 37.0997 | 1.91073 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −21.6495 | −1.11206 | −0.556030 | − | 0.831162i | \(-0.687676\pi\) | ||||
−0.556030 | + | 0.831162i | \(0.687676\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −5.97586 | −0.305352 | −0.152676 | − | 0.988276i | \(-0.548789\pi\) | ||||
−0.152676 | + | 0.988276i | \(0.548789\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 14.2749 | 0.727517 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −30.8248 | −1.56691 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −17.7967 | −0.902327 | −0.451164 | − | 0.892441i | \(-0.648991\pi\) | ||||
−0.451164 | + | 0.892441i | \(0.648991\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 14.8087 | 0.748911 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 5.64950 | 0.284257 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 24.0027 | 1.20466 | 0.602331 | − | 0.798247i | \(-0.294239\pi\) | ||||
0.602331 | + | 0.798247i | \(0.294239\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 4.90033 | 0.244711 | 0.122355 | − | 0.992486i | \(-0.460955\pi\) | ||||
0.122355 | + | 0.992486i | \(0.460955\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −16.0000 | −0.797017 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 11.8208 | 0.587381 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 1.90468 | 0.0944116 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −18.0000 | −0.890043 | −0.445021 | − | 0.895520i | \(-0.646804\pi\) | ||||
−0.445021 | + | 0.895520i | \(0.646804\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −40.8471 | −2.00995 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 17.2054 | 0.844581 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −12.0000 | −0.586238 | −0.293119 | − | 0.956076i | \(-0.594693\pi\) | ||||
−0.293119 | + | 0.956076i | \(0.594693\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −24.2487 | −1.18181 | −0.590905 | − | 0.806741i | \(-0.701229\pi\) | ||||
−0.590905 | + | 0.806741i | \(0.701229\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 14.3326 | 0.696874 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 14.0000 | 0.679100 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 6.27492 | 0.303665 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 19.1101 | 0.920501 | 0.460251 | − | 0.887789i | \(-0.347760\pi\) | ||||
0.460251 | + | 0.887789i | \(0.347760\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 27.6495 | 1.32875 | 0.664375 | − | 0.747399i | \(-0.268698\pi\) | ||||
0.664375 | + | 0.747399i | \(0.268698\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 3.46410 | 0.165710 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −3.57919 | −0.170825 | −0.0854127 | − | 0.996346i | \(-0.527221\pi\) | ||||
−0.0854127 | + | 0.996346i | \(0.527221\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −47.4743 | −2.26068 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 27.3746 | 1.30061 | 0.650303 | − | 0.759675i | \(-0.274642\pi\) | ||||
0.650303 | + | 0.759675i | \(0.274642\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 13.1342 | 0.622623 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −5.45017 | −0.257209 | −0.128605 | − | 0.991696i | \(-0.541050\pi\) | ||||
−0.128605 | + | 0.991696i | \(0.541050\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −24.0000 | −1.13012 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −38.2202 | −1.79179 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 7.72508 | 0.361364 | 0.180682 | − | 0.983542i | \(-0.442169\pi\) | ||||
0.180682 | + | 0.983542i | \(0.442169\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 35.2323 | 1.64093 | 0.820465 | − | 0.571696i | \(-0.193714\pi\) | ||||
0.820465 | + | 0.571696i | \(0.193714\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −33.4427 | −1.55421 | −0.777107 | − | 0.629369i | \(-0.783313\pi\) | ||||
−0.777107 | + | 0.629369i | \(0.783313\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 30.8248 | 1.42640 | 0.713200 | − | 0.700961i | \(-0.247245\pi\) | ||||
0.713200 | + | 0.700961i | \(0.247245\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 40.8471 | 1.88614 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −23.3746 | −1.07476 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 3.27492 | 0.150264 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 31.1769 | 1.42749 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −17.3205 | −0.791394 | −0.395697 | − | 0.918381i | \(-0.629497\pi\) | ||||
−0.395697 | + | 0.918381i | \(0.629497\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −5.09967 | −0.232525 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 1.90468 | 0.0864872 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −12.9041 | −0.584739 | −0.292370 | − | 0.956305i | \(-0.594444\pi\) | ||||
−0.292370 | + | 0.956305i | \(0.594444\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 12.0000 | 0.541552 | 0.270776 | − | 0.962642i | \(-0.412720\pi\) | ||||
0.270776 | + | 0.962642i | \(0.412720\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −26.0383 | −1.17271 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 8.96379 | 0.402893 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 70.7492 | 3.17353 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 34.2749 | 1.53436 | 0.767178 | − | 0.641434i | \(-0.221660\pi\) | ||||
0.767178 | + | 0.641434i | \(0.221660\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 6.81312 | 0.303782 | 0.151891 | − | 0.988397i | \(-0.451464\pi\) | ||||
0.151891 | + | 0.988397i | \(0.451464\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 18.1993 | 0.809860 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 13.0192 | 0.577064 | 0.288532 | − | 0.957470i | \(-0.406833\pi\) | ||||
0.288532 | + | 0.957470i | \(0.406833\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 20.4235 | 0.903484 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 3.45017 | 0.152032 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 10.8685 | 0.477995 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −3.09967 | −0.135799 | −0.0678995 | − | 0.997692i | \(-0.521630\pi\) | ||||
−0.0678995 | + | 0.997692i | \(0.521630\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −20.5498 | −0.898582 | −0.449291 | − | 0.893386i | \(-0.648323\pi\) | ||||
−0.449291 | + | 0.893386i | \(0.648323\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 11.2296 | 0.489167 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −11.0000 | −0.478261 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −25.6495 | −1.11309 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 64.2585 | 2.78335 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 21.7370 | 0.939770 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −36.0000 | −1.55063 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 7.28929 | 0.313391 | 0.156695 | − | 0.987647i | \(-0.449916\pi\) | ||||
0.156695 | + | 0.987647i | \(0.449916\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −4.54983 | −0.194893 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −32.0000 | −1.36822 | −0.684111 | − | 0.729378i | \(-0.739809\pi\) | ||||
−0.684111 | + | 0.729378i | \(0.739809\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 3.94027 | 0.168167 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −6.09095 | −0.259483 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −20.5498 | −0.873868 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 16.8443 | 0.713717 | 0.356859 | − | 0.934158i | \(-0.383848\pi\) | ||||
0.356859 | + | 0.934158i | \(0.383848\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 62.5840 | 2.64702 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 24.0000 | 1.01148 | 0.505740 | − | 0.862686i | \(-0.331220\pi\) | ||||
0.505740 | + | 0.862686i | \(0.331220\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −3.34901 | −0.140894 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −42.9977 | −1.80573 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 34.5498 | 1.44840 | 0.724202 | − | 0.689588i | \(-0.242208\pi\) | ||||
0.724202 | + | 0.689588i | \(0.242208\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 10.9003 | 0.456165 | 0.228082 | − | 0.973642i | \(-0.426754\pi\) | ||||
0.228082 | + | 0.973642i | \(0.426754\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 11.3446 | 0.473104 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 15.7251 | 0.654644 | 0.327322 | − | 0.944913i | \(-0.393854\pi\) | ||||
0.327322 | + | 0.944913i | \(0.393854\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −62.5840 | −2.59642 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 23.6416 | 0.979136 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −24.0000 | −0.992278 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 29.7251 | 1.22689 | 0.613443 | − | 0.789739i | \(-0.289784\pi\) | ||||
0.613443 | + | 0.789739i | \(0.289784\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 2.62685 | 0.108237 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −11.0997 | −0.455809 | −0.227904 | − | 0.973684i | \(-0.573187\pi\) | ||||
−0.227904 | + | 0.973684i | \(0.573187\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 26.8248 | 1.09971 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 35.5934 | 1.45431 | 0.727153 | − | 0.686476i | \(-0.240843\pi\) | ||||
0.727153 | + | 0.686476i | \(0.240843\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 19.0997 | 0.779092 | 0.389546 | − | 0.921007i | \(-0.372632\pi\) | ||||
0.389546 | + | 0.921007i | \(0.372632\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 25.6495 | 1.04453 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −7.65037 | −0.311032 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 46.8229 | 1.90048 | 0.950242 | − | 0.311513i | \(-0.100836\pi\) | ||||
0.950242 | + | 0.311513i | \(0.100836\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −29.0997 | −1.17725 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −16.8443 | −0.680336 | −0.340168 | − | 0.940365i | \(-0.610484\pi\) | ||||
−0.340168 | + | 0.940365i | \(0.610484\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −20.2749 | −0.816237 | −0.408119 | − | 0.912929i | \(-0.633815\pi\) | ||||
−0.408119 | + | 0.912929i | \(0.633815\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −4.00000 | −0.160774 | −0.0803868 | − | 0.996764i | \(-0.525616\pi\) | ||||
−0.0803868 | + | 0.996764i | \(0.525616\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −47.7753 | −1.91408 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 2.09967 | 0.0839868 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 3.57919 | 0.142712 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −9.07888 | −0.361425 | −0.180712 | − | 0.983536i | \(-0.557840\pi\) | ||||
−0.180712 | + | 0.983536i | \(0.557840\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 22.9003 | 0.908772 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 96.3878 | 3.81902 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 44.4262 | 1.75748 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 2.54983 | 0.100712 | 0.0503562 | − | 0.998731i | \(-0.483964\pi\) | ||||
0.0503562 | + | 0.998731i | \(0.483964\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 7.92442 | 0.312509 | 0.156254 | − | 0.987717i | \(-0.450058\pi\) | ||||
0.156254 | + | 0.987717i | \(0.450058\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −3.82518 | −0.150384 | −0.0751918 | − | 0.997169i | \(-0.523957\pi\) | ||||
−0.0751918 | + | 0.997169i | \(0.523957\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −19.4502 | −0.763486 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 2.98793 | 0.116927 | 0.0584634 | − | 0.998290i | \(-0.481380\pi\) | ||||
0.0584634 | + | 0.998290i | \(0.481380\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 2.98793 | 0.116748 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 12.8248 | 0.500341 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −28.5498 | −1.11214 | −0.556072 | − | 0.831134i | \(-0.687692\pi\) | ||||
−0.556072 | + | 0.831134i | \(0.687692\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −0.837253 | −0.0325654 | −0.0162827 | − | 0.999867i | \(-0.505183\pi\) | ||||
−0.0162827 | + | 0.999867i | \(0.505183\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 6.27492 | 0.243331 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −21.0997 | −0.816982 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 2.98793 | 0.115348 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −16.9003 | −0.651460 | −0.325730 | − | 0.945463i | \(-0.605610\pi\) | ||||
−0.325730 | + | 0.945463i | \(0.605610\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −44.3112 | −1.70302 | −0.851508 | − | 0.524342i | \(-0.824312\pi\) | ||||
−0.851508 | + | 0.524342i | \(0.824312\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −6.92820 | −0.265880 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 38.1993 | 1.46166 | 0.730829 | − | 0.682561i | \(-0.239134\pi\) | ||||
0.730829 | + | 0.682561i | \(0.239134\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 26.6296 | 1.01746 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −63.2990 | −2.41150 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −44.4743 | −1.69188 | −0.845940 | − | 0.533278i | \(-0.820960\pi\) | ||||
−0.845940 | + | 0.533278i | \(0.820960\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −32.6054 | −1.23858 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 13.4953 | 0.511907 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −45.0997 | −1.70827 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −48.7276 | −1.84042 | −0.920208 | − | 0.391430i | \(-0.871981\pi\) | ||||
−0.920208 | + | 0.391430i | \(0.871981\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0.837253 | 0.0315776 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −66.1993 | −2.48968 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 3.34901 | 0.125775 | 0.0628874 | − | 0.998021i | \(-0.479969\pi\) | ||||
0.0628874 | + | 0.998021i | \(0.479969\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −12.9041 | −0.483940 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 9.09967 | 0.340785 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −18.1993 | −0.680617 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 12.4279 | 0.463482 | 0.231741 | − | 0.972777i | \(-0.425558\pi\) | ||||
0.231741 | + | 0.972777i | \(0.425558\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −12.5498 | −0.467380 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −19.9474 | −0.740826 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −19.5863 | −0.726415 | −0.363207 | − | 0.931708i | \(-0.618318\pi\) | ||||
−0.363207 | + | 0.931708i | \(0.618318\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −27.0000 | −1.00000 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −43.9244 | −1.62460 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 1.67451 | 0.0618493 | 0.0309247 | − | 0.999522i | \(-0.490155\pi\) | ||||
0.0309247 | + | 0.999522i | \(0.490155\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 19.4502 | 0.716456 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −14.8248 | −0.545337 | −0.272669 | − | 0.962108i | \(-0.587906\pi\) | ||||
−0.272669 | + | 0.962108i | \(0.587906\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 26.7605 | 0.981746 | 0.490873 | − | 0.871231i | \(-0.336678\pi\) | ||||
0.490873 | + | 0.871231i | \(0.336678\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 3.92442 | 0.143780 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −39.2990 | −1.43788 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −79.0673 | −2.88905 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −53.7511 | −1.96141 | −0.980703 | − | 0.195503i | \(-0.937366\pi\) | ||||
−0.980703 | + | 0.195503i | \(0.937366\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 12.5498 | 0.456735 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −1.31342 | −0.0477372 | −0.0238686 | − | 0.999715i | \(-0.507598\pi\) | ||||
−0.0238686 | + | 0.999715i | \(0.507598\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 4.27492 | 0.154966 | 0.0774828 | − | 0.996994i | \(-0.475312\pi\) | ||||
0.0774828 | + | 0.996994i | \(0.475312\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 16.5498 | 0.599144 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 16.8443 | 0.609008 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 52.0766 | 1.88038 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 8.82475 | 0.318229 | 0.159114 | − | 0.987260i | \(-0.449136\pi\) | ||||
0.159114 | + | 0.987260i | \(0.449136\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −0.115088 | −0.00413942 | −0.00206971 | − | 0.999998i | \(-0.500659\pi\) | ||||
−0.00206971 | + | 0.999998i | \(0.500659\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 8.60271 | 0.309018 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −10.5498 | −0.377987 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 33.6887 | 1.20548 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −6.90033 | −0.246283 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 46.1993 | 1.64683 | 0.823414 | − | 0.567441i | \(-0.192066\pi\) | ||||
0.823414 | + | 0.567441i | \(0.192066\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 12.1819 | 0.433138 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −8.00000 | −0.284088 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −24.2487 | −0.858933 | −0.429467 | − | 0.903083i | \(-0.641298\pi\) | ||||
−0.429467 | + | 0.903083i | \(0.641298\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 20.4235 | 0.722532 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −30.0000 | −1.06000 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 9.72508 | 0.343191 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 21.7370 | 0.766127 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −16.8248 | −0.591527 | −0.295763 | − | 0.955261i | \(-0.595574\pi\) | ||||
−0.295763 | + | 0.955261i | \(0.595574\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 43.2990 | 1.52043 | 0.760217 | − | 0.649669i | \(-0.225093\pi\) | ||||
0.760217 | + | 0.649669i | \(0.225093\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −5.25370 | −0.184029 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −10.2749 | −0.359474 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 87.2990 | 3.05047 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −21.3759 | −0.746023 | −0.373011 | − | 0.927827i | \(-0.621675\pi\) | ||||
−0.373011 | + | 0.927827i | \(0.621675\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −43.9501 | −1.53200 | −0.766002 | − | 0.642839i | \(-0.777757\pi\) | ||||
−0.766002 | + | 0.642839i | \(0.777757\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −2.35050 | −0.0817348 | −0.0408674 | − | 0.999165i | \(-0.513012\pi\) | ||||
−0.0408674 | + | 0.999165i | \(0.513012\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −35.7084 | −1.24021 | −0.620103 | − | 0.784521i | \(-0.712909\pi\) | ||||
−0.620103 | + | 0.784521i | \(0.712909\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −67.6495 | −2.34392 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 2.19934 | 0.0761112 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 38.9424 | 1.34444 | 0.672220 | − | 0.740351i | \(-0.265341\pi\) | ||||
0.672220 | + | 0.740351i | \(0.265341\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 8.09967 | 0.279299 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 31.6531 | 1.08890 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 27.8279 | 0.956178 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 2.90033 | 0.0994221 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 15.5309 | 0.531768 | 0.265884 | − | 0.964005i | \(-0.414336\pi\) | ||||
0.265884 | + | 0.964005i | \(0.414336\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 3.94027 | 0.134754 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −44.1993 | −1.50982 | −0.754910 | − | 0.655828i | \(-0.772320\pi\) | ||||
−0.754910 | + | 0.655828i | \(0.772320\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 12.4743 | 0.425616 | 0.212808 | − | 0.977094i | \(-0.431739\pi\) | ||||
0.212808 | + | 0.977094i | \(0.431739\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 27.9430 | 0.951190 | 0.475595 | − | 0.879664i | \(-0.342233\pi\) | ||||
0.475595 | + | 0.879664i | \(0.342233\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 11.4502 | 0.389317 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −9.78523 | −0.331941 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −52.0766 | −1.76455 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −4.35050 | −0.147242 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 51.9244 | 1.75537 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −38.3353 | −1.29449 | −0.647245 | − | 0.762282i | \(-0.724079\pi\) | ||||
−0.647245 | + | 0.762282i | \(0.724079\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −20.8248 | −0.701604 | −0.350802 | − | 0.936450i | \(-0.614091\pi\) | ||||
−0.350802 | + | 0.936450i | \(0.614091\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 51.3746 | 1.72889 | 0.864446 | − | 0.502725i | \(-0.167669\pi\) | ||||
0.864446 | + | 0.502725i | \(0.167669\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −9.55505 | −0.320827 | −0.160414 | − | 0.987050i | \(-0.551283\pi\) | ||||
−0.160414 | + | 0.987050i | \(0.551283\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −83.2990 | −2.79376 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −20.4743 | −0.685913 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 4.77753 | 0.159874 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −11.9517 | −0.399502 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −16.0000 | −0.533630 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 44.4262 | 1.48005 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −4.54983 | −0.151242 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 21.6495 | 0.718860 | 0.359430 | − | 0.933172i | \(-0.382971\pi\) | ||||
0.359430 | + | 0.933172i | \(0.382971\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −41.5692 | −1.37876 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −44.4262 | −1.47191 | −0.735954 | − | 0.677032i | \(-0.763266\pi\) | ||||
−0.735954 | + | 0.677032i | \(0.763266\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −29.8007 | −0.986258 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −10.8685 | −0.358909 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 34.7561 | 1.14650 | 0.573249 | − | 0.819381i | \(-0.305683\pi\) | ||||
0.573249 | + | 0.819381i | \(0.305683\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −90.1993 | −2.96895 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 2.74194 | 0.0901543 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −7.88054 | −0.258831 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 23.0997 | 0.757876 | 0.378938 | − | 0.925422i | \(-0.376289\pi\) | ||||
0.378938 | + | 0.925422i | \(0.376289\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −15.8248 | −0.518635 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 12.7732 | 0.417727 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −37.9244 | −1.23894 | −0.619468 | − | 0.785022i | \(-0.712652\pi\) | ||||
−0.619468 | + | 0.785022i | \(0.712652\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 31.1769 | 1.01634 | 0.508169 | − | 0.861257i | \(-0.330322\pi\) | ||||
0.508169 | + | 0.861257i | \(0.330322\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −36.5457 | −1.19009 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −30.1993 | −0.981347 | −0.490673 | − | 0.871344i | \(-0.663249\pi\) | ||||
−0.490673 | + | 0.871344i | \(0.663249\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −26.0383 | −0.845239 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −45.2990 | −1.46738 | −0.733689 | − | 0.679485i | \(-0.762203\pi\) | ||||
−0.733689 | + | 0.679485i | \(0.762203\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −13.1752 | −0.426341 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −96.8639 | −3.12790 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −24.0997 | −0.777409 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −49.6495 | −1.59993 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −25.0860 | −0.807546 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −20.6695 | −0.664687 | −0.332344 | − | 0.943158i | \(-0.607839\pi\) | ||||
−0.332344 | + | 0.943158i | \(0.607839\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 44.0000 | 1.41203 | 0.706014 | − | 0.708198i | \(-0.250492\pi\) | ||||
0.706014 | + | 0.708198i | \(0.250492\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −49.0887 | −1.57371 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 32.1993 | 1.03015 | 0.515074 | − | 0.857146i | \(-0.327764\pi\) | ||||
0.515074 | + | 0.857146i | \(0.327764\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −22.7492 | −0.727067 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 10.3923 | 0.331801 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −29.6175 | −0.944651 | −0.472326 | − | 0.881424i | \(-0.656585\pi\) | ||||
−0.472326 | + | 0.881424i | \(0.656585\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 16.0000 | 0.509802 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −35.5934 | −1.13180 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −40.1249 | −1.27461 | −0.637305 | − | 0.770612i | \(-0.719951\pi\) | ||||
−0.637305 | + | 0.770612i | \(0.719951\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 24.4743 | 0.775886 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −11.5906 | −0.367079 | −0.183540 | − | 0.983012i | \(-0.558756\pi\) | ||||
−0.183540 | + | 0.983012i | \(0.558756\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(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.bk.1.3 | 4 | ||
4.3 | odd | 2 | 4864.2.a.bj.1.3 | 4 | |||
8.3 | odd | 2 | inner | 4864.2.a.bk.1.2 | 4 | ||
8.5 | even | 2 | 4864.2.a.bj.1.2 | 4 | |||
16.3 | odd | 4 | 1216.2.c.i.609.3 | ✓ | 8 | ||
16.5 | even | 4 | 1216.2.c.i.609.6 | yes | 8 | ||
16.11 | odd | 4 | 1216.2.c.i.609.5 | yes | 8 | ||
16.13 | even | 4 | 1216.2.c.i.609.4 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1216.2.c.i.609.3 | ✓ | 8 | 16.3 | odd | 4 | ||
1216.2.c.i.609.4 | yes | 8 | 16.13 | even | 4 | ||
1216.2.c.i.609.5 | yes | 8 | 16.11 | odd | 4 | ||
1216.2.c.i.609.6 | yes | 8 | 16.5 | even | 4 | ||
4864.2.a.bj.1.2 | 4 | 8.5 | even | 2 | |||
4864.2.a.bj.1.3 | 4 | 4.3 | odd | 2 | |||
4864.2.a.bk.1.2 | 4 | 8.3 | odd | 2 | inner | ||
4864.2.a.bk.1.3 | 4 | 1.1 | even | 1 | trivial |