Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3800,2,Mod(1,3800)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3800, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("3800.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3800 = 2^{3} \cdot 5^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3800.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: | \(30.3431527681\) |
Analytic rank: | \(1\) |
Dimension: | \(6\) |
Coefficient field: | 6.6.253565184.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 2x^{5} - 11x^{4} + 20x^{3} + 22x^{2} - 32x + 8 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 760) |
Fricke sign: | \(+1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(0.664406\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3800.1 |
$q$-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 | ||||||||
\(3\) | −0.664406 | −0.383595 | −0.191798 | − | 0.981434i | \(-0.561432\pi\) | ||||
−0.191798 | + | 0.981434i | \(0.561432\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.345799 | 0.130700 | 0.0653499 | − | 0.997862i | \(-0.479184\pi\) | ||||
0.0653499 | + | 0.997862i | \(0.479184\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.55856 | −0.852855 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.51609 | 1.06014 | 0.530071 | − | 0.847954i | \(-0.322165\pi\) | ||||
0.530071 | + | 0.847954i | \(0.322165\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.22452 | 0.894320 | 0.447160 | − | 0.894454i | \(-0.352435\pi\) | ||||
0.447160 | + | 0.894454i | \(0.352435\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −4.88550 | −1.18491 | −0.592454 | − | 0.805604i | \(-0.701841\pi\) | ||||
−0.592454 | + | 0.805604i | \(0.701841\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.00000 | 0.229416 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.229751 | −0.0501358 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −7.62861 | −1.59067 | −0.795337 | − | 0.606167i | \(-0.792706\pi\) | ||||
−0.795337 | + | 0.606167i | \(0.792706\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 3.69315 | 0.710746 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −1.73968 | −0.323051 | −0.161526 | − | 0.986869i | \(-0.551641\pi\) | ||||
−0.161526 | + | 0.986869i | \(0.551641\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.76164 | −0.855216 | −0.427608 | − | 0.903964i | \(-0.640644\pi\) | ||||
−0.427608 | + | 0.903964i | \(0.640644\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −2.33611 | −0.406665 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.86749 | 0.307013 | 0.153506 | − | 0.988148i | \(-0.450943\pi\) | ||||
0.153506 | + | 0.988148i | \(0.450943\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −2.14239 | −0.343057 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 6.76164 | 1.05599 | 0.527996 | − | 0.849247i | \(-0.322944\pi\) | ||||
0.527996 | + | 0.849247i | \(0.322944\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −0.606115 | −0.0924317 | −0.0462158 | − | 0.998931i | \(-0.514716\pi\) | ||||
−0.0462158 | + | 0.998931i | \(0.514716\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −3.34735 | −0.488261 | −0.244130 | − | 0.969742i | \(-0.578502\pi\) | ||||
−0.244130 | + | 0.969742i | \(0.578502\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.88042 | −0.982918 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 3.24596 | 0.454525 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0.107390 | 0.0147512 | 0.00737559 | − | 0.999973i | \(-0.497652\pi\) | ||||
0.00737559 | + | 0.999973i | \(0.497652\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −0.664406 | −0.0880028 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 12.3233 | 1.60436 | 0.802179 | − | 0.597084i | \(-0.203674\pi\) | ||||
0.802179 | + | 0.597084i | \(0.203674\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −8.41231 | −1.07709 | −0.538543 | − | 0.842598i | \(-0.681025\pi\) | ||||
−0.538543 | + | 0.842598i | \(0.681025\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −0.884749 | −0.111468 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −2.23888 | −0.273522 | −0.136761 | − | 0.990604i | \(-0.543669\pi\) | ||||
−0.136761 | + | 0.990604i | \(0.543669\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 5.06850 | 0.610175 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −0.536605 | −0.0636833 | −0.0318417 | − | 0.999493i | \(-0.510137\pi\) | ||||
−0.0318417 | + | 0.999493i | \(0.510137\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −5.57710 | −0.652750 | −0.326375 | − | 0.945240i | \(-0.605827\pi\) | ||||
−0.326375 | + | 0.945240i | \(0.605827\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1.21586 | 0.138560 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −2.67119 | −0.300532 | −0.150266 | − | 0.988646i | \(-0.548013\pi\) | ||||
−0.150266 | + | 0.988646i | \(0.548013\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 5.22194 | 0.580216 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −1.79847 | −0.197408 | −0.0987038 | − | 0.995117i | \(-0.531470\pi\) | ||||
−0.0987038 | + | 0.995117i | \(0.531470\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 1.15586 | 0.123921 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 8.94482 | 0.948149 | 0.474075 | − | 0.880485i | \(-0.342783\pi\) | ||||
0.474075 | + | 0.880485i | \(0.342783\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.11504 | 0.116887 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 3.16367 | 0.328057 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −10.1560 | −1.03119 | −0.515594 | − | 0.856833i | \(-0.672429\pi\) | ||||
−0.515594 | + | 0.856833i | \(0.672429\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −8.99614 | −0.904146 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 16.5089 | 1.64270 | 0.821350 | − | 0.570425i | \(-0.193221\pi\) | ||||
0.821350 | + | 0.570425i | \(0.193221\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −11.5212 | −1.13522 | −0.567610 | − | 0.823298i | \(-0.692132\pi\) | ||||
−0.567610 | + | 0.823298i | \(0.692132\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −10.0340 | −0.970027 | −0.485014 | − | 0.874507i | \(-0.661185\pi\) | ||||
−0.485014 | + | 0.874507i | \(0.661185\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 12.2737 | 1.17560 | 0.587802 | − | 0.809005i | \(-0.299993\pi\) | ||||
0.587802 | + | 0.809005i | \(0.299993\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −1.24077 | −0.117769 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 0.700723 | 0.0659185 | 0.0329593 | − | 0.999457i | \(-0.489507\pi\) | ||||
0.0329593 | + | 0.999457i | \(0.489507\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −8.25014 | −0.762725 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −1.68940 | −0.154867 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.36289 | 0.123899 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −4.49248 | −0.405073 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −11.8369 | −1.05036 | −0.525178 | − | 0.850992i | \(-0.676001\pi\) | ||||
−0.525178 | + | 0.850992i | \(0.676001\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0.402707 | 0.0354563 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −22.0556 | −1.92701 | −0.963503 | − | 0.267699i | \(-0.913737\pi\) | ||||
−0.963503 | + | 0.267699i | \(0.913737\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.345799 | 0.0299846 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −19.4858 | −1.66478 | −0.832390 | − | 0.554190i | \(-0.813028\pi\) | ||||
−0.832390 | + | 0.554190i | \(0.813028\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −14.5867 | −1.23723 | −0.618613 | − | 0.785696i | \(-0.712305\pi\) | ||||
−0.618613 | + | 0.785696i | \(0.712305\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 2.22400 | 0.187294 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 11.3377 | 0.948106 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 4.57140 | 0.377043 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 15.3918 | 1.26094 | 0.630471 | − | 0.776213i | \(-0.282862\pi\) | ||||
0.630471 | + | 0.776213i | \(0.282862\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −3.55281 | −0.289124 | −0.144562 | − | 0.989496i | \(-0.546177\pi\) | ||||
−0.144562 | + | 0.989496i | \(0.546177\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 12.4999 | 1.01055 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −10.9812 | −0.876393 | −0.438196 | − | 0.898879i | \(-0.644383\pi\) | ||||
−0.438196 | + | 0.898879i | \(0.644383\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −0.0713507 | −0.00565848 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −2.63797 | −0.207901 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −7.88687 | −0.617747 | −0.308874 | − | 0.951103i | \(-0.599952\pi\) | ||||
−0.308874 | + | 0.951103i | \(0.599952\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −14.1924 | −1.09824 | −0.549121 | − | 0.835743i | \(-0.685037\pi\) | ||||
−0.549121 | + | 0.835743i | \(0.685037\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −2.60248 | −0.200191 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −2.55856 | −0.195658 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 0.654185 | 0.0497368 | 0.0248684 | − | 0.999691i | \(-0.492083\pi\) | ||||
0.0248684 | + | 0.999691i | \(0.492083\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −8.18768 | −0.615424 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 0.893129 | 0.0667556 | 0.0333778 | − | 0.999443i | \(-0.489374\pi\) | ||||
0.0333778 | + | 0.999443i | \(0.489374\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −20.8542 | −1.55008 | −0.775039 | − | 0.631914i | \(-0.782270\pi\) | ||||
−0.775039 | + | 0.631914i | \(0.782270\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 5.58920 | 0.413165 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −17.1779 | −1.25617 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 1.27709 | 0.0928944 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −13.8797 | −1.00430 | −0.502151 | − | 0.864780i | \(-0.667458\pi\) | ||||
−0.502151 | + | 0.864780i | \(0.667458\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −9.98613 | −0.718817 | −0.359409 | − | 0.933180i | \(-0.617022\pi\) | ||||
−0.359409 | + | 0.933180i | \(0.617022\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 12.3247 | 0.878099 | 0.439050 | − | 0.898463i | \(-0.355315\pi\) | ||||
0.439050 | + | 0.898463i | \(0.355315\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −16.0086 | −1.13482 | −0.567410 | − | 0.823435i | \(-0.692055\pi\) | ||||
−0.567410 | + | 0.823435i | \(0.692055\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1.48752 | 0.104922 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −0.601581 | −0.0422227 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 19.5183 | 1.35661 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 3.51609 | 0.243213 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 19.0558 | 1.31185 | 0.655926 | − | 0.754825i | \(-0.272278\pi\) | ||||
0.655926 | + | 0.754825i | \(0.272278\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0.356524 | 0.0244286 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1.64657 | −0.111777 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 3.70546 | 0.250392 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −15.7534 | −1.05969 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 8.68798 | 0.581790 | 0.290895 | − | 0.956755i | \(-0.406047\pi\) | ||||
0.290895 | + | 0.956755i | \(0.406047\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −28.8077 | −1.91203 | −0.956017 | − | 0.293311i | \(-0.905243\pi\) | ||||
−0.956017 | + | 0.293311i | \(0.905243\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 8.27464 | 0.546803 | 0.273402 | − | 0.961900i | \(-0.411851\pi\) | ||||
0.273402 | + | 0.961900i | \(0.411851\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −0.807826 | −0.0531510 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 29.0199 | 1.90116 | 0.950580 | − | 0.310480i | \(-0.100490\pi\) | ||||
0.950580 | + | 0.310480i | \(0.100490\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 1.77475 | 0.115283 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −15.3744 | −0.994486 | −0.497243 | − | 0.867611i | \(-0.665654\pi\) | ||||
−0.497243 | + | 0.867611i | \(0.665654\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 24.8583 | 1.60126 | 0.800632 | − | 0.599157i | \(-0.204497\pi\) | ||||
0.800632 | + | 0.599157i | \(0.204497\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −14.5489 | −0.933314 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 3.22452 | 0.205171 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 1.19491 | 0.0757246 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −14.3807 | −0.907702 | −0.453851 | − | 0.891077i | \(-0.649950\pi\) | ||||
−0.453851 | + | 0.891077i | \(0.649950\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −26.8229 | −1.68634 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −21.9784 | −1.37097 | −0.685486 | − | 0.728086i | \(-0.740410\pi\) | ||||
−0.685486 | + | 0.728086i | \(0.740410\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0.645775 | 0.0401265 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 4.45109 | 0.275516 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 2.24444 | 0.138398 | 0.0691990 | − | 0.997603i | \(-0.477956\pi\) | ||||
0.0691990 | + | 0.997603i | \(0.477956\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −5.94300 | −0.363705 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 19.3526 | 1.17995 | 0.589975 | − | 0.807421i | \(-0.299137\pi\) | ||||
0.589975 | + | 0.807421i | \(0.299137\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −4.18631 | −0.254300 | −0.127150 | − | 0.991883i | \(-0.540583\pi\) | ||||
−0.127150 | + | 0.991883i | \(0.540583\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −0.740837 | −0.0448375 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 15.2206 | 0.914518 | 0.457259 | − | 0.889334i | \(-0.348831\pi\) | ||||
0.457259 | + | 0.889334i | \(0.348831\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 12.1830 | 0.729375 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 7.96393 | 0.475088 | 0.237544 | − | 0.971377i | \(-0.423658\pi\) | ||||
0.237544 | + | 0.971377i | \(0.423658\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 31.6286 | 1.88013 | 0.940064 | − | 0.340998i | \(-0.110765\pi\) | ||||
0.940064 | + | 0.340998i | \(0.110765\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 2.33817 | 0.138018 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 6.86811 | 0.404006 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 6.74773 | 0.395559 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −32.6323 | −1.90640 | −0.953199 | − | 0.302342i | \(-0.902231\pi\) | ||||
−0.953199 | + | 0.302342i | \(0.902231\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 12.9854 | 0.753491 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −24.5986 | −1.42257 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −0.209594 | −0.0120808 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −10.9686 | −0.630132 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −4.85468 | −0.277071 | −0.138536 | − | 0.990357i | \(-0.544240\pi\) | ||||
−0.138536 | + | 0.990357i | \(0.544240\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 7.65477 | 0.435465 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −0.509761 | −0.0289059 | −0.0144530 | − | 0.999896i | \(-0.504601\pi\) | ||||
−0.0144530 | + | 0.999896i | \(0.504601\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −5.33353 | −0.301469 | −0.150734 | − | 0.988574i | \(-0.548164\pi\) | ||||
−0.150734 | + | 0.988574i | \(0.548164\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 15.1325 | 0.849927 | 0.424963 | − | 0.905211i | \(-0.360287\pi\) | ||||
0.424963 | + | 0.905211i | \(0.360287\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −6.11689 | −0.342480 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 6.66668 | 0.372098 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −4.88550 | −0.271836 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −8.15470 | −0.450956 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −1.15751 | −0.0638156 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 4.21378 | 0.231610 | 0.115805 | − | 0.993272i | \(-0.463055\pi\) | ||||
0.115805 | + | 0.993272i | \(0.463055\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −4.77808 | −0.261837 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 16.5707 | 0.902664 | 0.451332 | − | 0.892356i | \(-0.350949\pi\) | ||||
0.451332 | + | 0.892356i | \(0.350949\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −0.465565 | −0.0252860 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −16.7424 | −0.906650 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −4.79984 | −0.259167 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −5.17123 | −0.277606 | −0.138803 | − | 0.990320i | \(-0.544325\pi\) | ||||
−0.138803 | + | 0.990320i | \(0.544325\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −12.5843 | −0.673624 | −0.336812 | − | 0.941572i | \(-0.609349\pi\) | ||||
−0.336812 | + | 0.941572i | \(0.609349\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 11.9086 | 0.635635 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 13.2242 | 0.703853 | 0.351927 | − | 0.936028i | \(-0.385527\pi\) | ||||
0.351927 | + | 0.936028i | \(0.385527\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 1.12245 | 0.0594063 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −9.77950 | −0.516142 | −0.258071 | − | 0.966126i | \(-0.583087\pi\) | ||||
−0.258071 | + | 0.966126i | \(0.583087\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −0.905512 | −0.0475271 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 19.7113 | 1.02892 | 0.514460 | − | 0.857515i | \(-0.327993\pi\) | ||||
0.514460 | + | 0.857515i | \(0.327993\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −17.3001 | −0.900607 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0.0371354 | 0.00192798 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −33.0128 | −1.70934 | −0.854670 | − | 0.519172i | \(-0.826240\pi\) | ||||
−0.854670 | + | 0.519172i | \(0.826240\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −5.60964 | −0.288911 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −29.3422 | −1.50721 | −0.753604 | − | 0.657329i | \(-0.771686\pi\) | ||||
−0.753604 | + | 0.657329i | \(0.771686\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 7.86453 | 0.402912 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 29.9938 | 1.53261 | 0.766305 | − | 0.642477i | \(-0.222093\pi\) | ||||
0.766305 | + | 0.642477i | \(0.222093\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 1.55078 | 0.0788308 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 7.64392 | 0.387562 | 0.193781 | − | 0.981045i | \(-0.437925\pi\) | ||||
0.193781 | + | 0.981045i | \(0.437925\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 37.2696 | 1.88480 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 14.6539 | 0.739190 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 4.48509 | 0.225100 | 0.112550 | − | 0.993646i | \(-0.464098\pi\) | ||||
0.112550 | + | 0.993646i | \(0.464098\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −0.229751 | −0.0115019 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 3.11631 | 0.155621 | 0.0778105 | − | 0.996968i | \(-0.475207\pi\) | ||||
0.0778105 | + | 0.996968i | \(0.475207\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −15.3540 | −0.764837 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 6.56625 | 0.325477 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 9.88207 | 0.488637 | 0.244319 | − | 0.969695i | \(-0.421436\pi\) | ||||
0.244319 | + | 0.969695i | \(0.421436\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 12.9465 | 0.638602 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 4.26139 | 0.209689 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 9.69148 | 0.474594 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −4.05273 | −0.197989 | −0.0989944 | − | 0.995088i | \(-0.531563\pi\) | ||||
−0.0989944 | + | 0.995088i | \(0.531563\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −34.5916 | −1.68589 | −0.842945 | − | 0.538000i | \(-0.819180\pi\) | ||||
−0.842945 | + | 0.538000i | \(0.819180\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 8.56440 | 0.416415 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −2.90897 | −0.140775 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −7.53284 | −0.363689 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −22.8014 | −1.09831 | −0.549153 | − | 0.835722i | \(-0.685050\pi\) | ||||
−0.549153 | + | 0.835722i | \(0.685050\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −19.8043 | −0.951733 | −0.475867 | − | 0.879517i | \(-0.657866\pi\) | ||||
−0.475867 | + | 0.879517i | \(0.657866\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −7.62861 | −0.364926 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −24.5069 | −1.16965 | −0.584825 | − | 0.811160i | \(-0.698837\pi\) | ||||
−0.584825 | + | 0.811160i | \(0.698837\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 17.6040 | 0.838286 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −29.8226 | −1.41692 | −0.708458 | − | 0.705753i | \(-0.750609\pi\) | ||||
−0.708458 | + | 0.705753i | \(0.750609\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −10.2264 | −0.483692 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −10.8675 | −0.512869 | −0.256435 | − | 0.966562i | \(-0.582548\pi\) | ||||
−0.256435 | + | 0.966562i | \(0.582548\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 23.7745 | 1.11950 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 2.36051 | 0.110906 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −0.604334 | −0.0282696 | −0.0141348 | − | 0.999900i | \(-0.504499\pi\) | ||||
−0.0141348 | + | 0.999900i | \(0.504499\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −18.0429 | −0.842169 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −31.2349 | −1.45475 | −0.727376 | − | 0.686239i | \(-0.759261\pi\) | ||||
−0.727376 | + | 0.686239i | \(0.759261\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −33.5246 | −1.55802 | −0.779010 | − | 0.627011i | \(-0.784278\pi\) | ||||
−0.779010 | + | 0.627011i | \(0.784278\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 37.0124 | 1.71273 | 0.856364 | − | 0.516372i | \(-0.172718\pi\) | ||||
0.856364 | + | 0.516372i | \(0.172718\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −0.774201 | −0.0357493 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 7.29596 | 0.336180 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −2.13115 | −0.0979906 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −0.274765 | −0.0125806 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 14.1388 | 0.646020 | 0.323010 | − | 0.946396i | \(-0.395305\pi\) | ||||
0.323010 | + | 0.946396i | \(0.395305\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 6.02174 | 0.274568 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 1.75268 | 0.0797498 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −36.2708 | −1.64359 | −0.821793 | − | 0.569785i | \(-0.807026\pi\) | ||||
−0.821793 | + | 0.569785i | \(0.807026\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 5.24009 | 0.236965 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −12.8630 | −0.580498 | −0.290249 | − | 0.956951i | \(-0.593738\pi\) | ||||
−0.290249 | + | 0.956951i | \(0.593738\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 8.49923 | 0.382786 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −0.185558 | −0.00832339 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 30.9889 | 1.38725 | 0.693626 | − | 0.720336i | \(-0.256012\pi\) | ||||
0.693626 | + | 0.720336i | \(0.256012\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 9.42953 | 0.421280 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 3.17853 | 0.141724 | 0.0708619 | − | 0.997486i | \(-0.477425\pi\) | ||||
0.0708619 | + | 0.997486i | \(0.477425\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 1.72911 | 0.0767923 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −10.6322 | −0.471265 | −0.235632 | − | 0.971842i | \(-0.575716\pi\) | ||||
−0.235632 | + | 0.971842i | \(0.575716\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1.92856 | −0.0853143 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 3.69315 | 0.163056 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −11.7696 | −0.517625 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −0.434645 | −0.0190788 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 31.4792 | 1.37913 | 0.689564 | − | 0.724225i | \(-0.257802\pi\) | ||||
0.689564 | + | 0.724225i | \(0.257802\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 2.60906 | 0.114086 | 0.0570430 | − | 0.998372i | \(-0.481833\pi\) | ||||
0.0570430 | + | 0.998372i | \(0.481833\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 23.2630 | 1.01335 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 35.1957 | 1.53025 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −31.5300 | −1.36828 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 21.8030 | 0.944395 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −0.593401 | −0.0256071 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −24.1922 | −1.04203 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 8.22279 | 0.353525 | 0.176763 | − | 0.984254i | \(-0.443438\pi\) | ||||
0.176763 | + | 0.984254i | \(0.443438\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 13.8556 | 0.594602 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 14.9776 | 0.640394 | 0.320197 | − | 0.947351i | \(-0.396251\pi\) | ||||
0.320197 | + | 0.947351i | \(0.396251\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 21.5234 | 0.918598 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −1.73968 | −0.0741130 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −0.923694 | −0.0392795 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −22.5965 | −0.957443 | −0.478722 | − | 0.877967i | \(-0.658900\pi\) | ||||
−0.478722 | + | 0.877967i | \(0.658900\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −1.95443 | −0.0826635 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 11.4131 | 0.481861 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 21.7518 | 0.916728 | 0.458364 | − | 0.888765i | \(-0.348436\pi\) | ||||
0.458364 | + | 0.888765i | \(0.348436\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 1.80574 | 0.0758341 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 32.5606 | 1.36501 | 0.682506 | − | 0.730880i | \(-0.260890\pi\) | ||||
0.682506 | + | 0.730880i | \(0.260890\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −11.4285 | −0.478267 | −0.239134 | − | 0.970987i | \(-0.576863\pi\) | ||||
−0.239134 | + | 0.970987i | \(0.576863\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 9.22179 | 0.385246 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 23.4277 | 0.975307 | 0.487654 | − | 0.873037i | \(-0.337853\pi\) | ||||
0.487654 | + | 0.873037i | \(0.337853\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 6.63485 | 0.275735 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −0.621909 | −0.0258011 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0.377594 | 0.0156383 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −1.85818 | −0.0766953 | −0.0383477 | − | 0.999264i | \(-0.512209\pi\) | ||||
−0.0383477 | + | 0.999264i | \(0.512209\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −4.76164 | −0.196200 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −8.18862 | −0.336835 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −1.37788 | −0.0565829 | −0.0282914 | − | 0.999600i | \(-0.509007\pi\) | ||||
−0.0282914 | + | 0.999600i | \(0.509007\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 10.6362 | 0.435312 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 33.9275 | 1.38624 | 0.693120 | − | 0.720822i | \(-0.256235\pi\) | ||||
0.693120 | + | 0.720822i | \(0.256235\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −15.9368 | −0.650076 | −0.325038 | − | 0.945701i | \(-0.605377\pi\) | ||||
−0.325038 | + | 0.945701i | \(0.605377\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 5.72831 | 0.233275 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 32.3921 | 1.31475 | 0.657377 | − | 0.753562i | \(-0.271666\pi\) | ||||
0.657377 | + | 0.753562i | \(0.271666\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0.399694 | 0.0161964 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −10.7936 | −0.436662 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −8.44582 | −0.341123 | −0.170562 | − | 0.985347i | \(-0.554558\pi\) | ||||
−0.170562 | + | 0.985347i | \(0.554558\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 37.4621 | 1.50817 | 0.754084 | − | 0.656778i | \(-0.228081\pi\) | ||||
0.754084 | + | 0.656778i | \(0.228081\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −7.35835 | −0.295757 | −0.147878 | − | 0.989006i | \(-0.547244\pi\) | ||||
−0.147878 | + | 0.989006i | \(0.547244\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −28.1736 | −1.13057 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 3.09311 | 0.123923 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −2.33611 | −0.0932954 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −9.12360 | −0.363782 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 35.8314 | 1.42642 | 0.713212 | − | 0.700948i | \(-0.247240\pi\) | ||||
0.713212 | + | 0.700948i | \(0.247240\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −12.6608 | −0.503220 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −22.1860 | −0.879043 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 1.37294 | 0.0543126 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 15.5827 | 0.615479 | 0.307740 | − | 0.951471i | \(-0.400427\pi\) | ||||
0.307740 | + | 0.951471i | \(0.400427\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 44.5775 | 1.75797 | 0.878983 | − | 0.476852i | \(-0.158222\pi\) | ||||
0.878983 | + | 0.476852i | \(0.158222\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 13.9836 | 0.549752 | 0.274876 | − | 0.961480i | \(-0.411363\pi\) | ||||
0.274876 | + | 0.961480i | \(0.411363\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 43.3298 | 1.70085 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 1.09399 | 0.0428770 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 18.9179 | 0.740314 | 0.370157 | − | 0.928969i | \(-0.379304\pi\) | ||||
0.370157 | + | 0.928969i | \(0.379304\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 14.2694 | 0.556701 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 35.9816 | 1.40164 | 0.700822 | − | 0.713337i | \(-0.252817\pi\) | ||||
0.700822 | + | 0.713337i | \(0.252817\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 7.69177 | 0.299175 | 0.149588 | − | 0.988748i | \(-0.452205\pi\) | ||||
0.149588 | + | 0.988748i | \(0.452205\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 10.4667 | 0.406491 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 13.2714 | 0.513870 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −5.77235 | −0.223172 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −29.5785 | −1.14186 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −19.0426 | −0.734040 | −0.367020 | − | 0.930213i | \(-0.619622\pi\) | ||||
−0.367020 | + | 0.930213i | \(0.619622\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 4.61140 | 0.177230 | 0.0886152 | − | 0.996066i | \(-0.471756\pi\) | ||||
0.0886152 | + | 0.996066i | \(0.471756\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −3.51194 | −0.134776 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 19.1400 | 0.733447 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 37.5087 | 1.43523 | 0.717614 | − | 0.696441i | \(-0.245234\pi\) | ||||
0.717614 | + | 0.696441i | \(0.245234\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −5.49772 | −0.209751 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0.346282 | 0.0131923 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −18.3081 | −0.696473 | −0.348236 | − | 0.937407i | \(-0.613219\pi\) | ||||
−0.348236 | + | 0.937407i | \(0.613219\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −3.11086 | −0.118172 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −33.0340 | −1.25125 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −19.2810 | −0.729276 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 6.22677 | 0.235182 | 0.117591 | − | 0.993062i | \(-0.462483\pi\) | ||||
0.117591 | + | 0.993062i | \(0.462483\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1.86749 | 0.0704335 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 5.70877 | 0.214700 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −30.0878 | −1.12997 | −0.564986 | − | 0.825100i | \(-0.691119\pi\) | ||||
−0.564986 | + | 0.825100i | \(0.691119\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 6.83440 | 0.256310 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 36.3247 | 1.36037 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 10.2148 | 0.381480 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −32.7649 | −1.22193 | −0.610963 | − | 0.791659i | \(-0.709218\pi\) | ||||
−0.610963 | + | 0.791659i | \(0.709218\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −3.98403 | −0.148373 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −16.5160 | −0.614237 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −24.9335 | −0.924733 | −0.462367 | − | 0.886689i | \(-0.653000\pi\) | ||||
−0.462367 | + | 0.886689i | \(0.653000\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −5.99942 | −0.222201 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 2.96117 | 0.109523 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −16.3618 | −0.604338 | −0.302169 | − | 0.953254i | \(-0.597711\pi\) | ||||
−0.302169 | + | 0.953254i | \(0.597711\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −7.87209 | −0.289972 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 14.0239 | 0.515876 | 0.257938 | − | 0.966162i | \(-0.416957\pi\) | ||||
0.257938 | + | 0.966162i | \(0.416957\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −2.14239 | −0.0787027 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 48.2145 | 1.76882 | 0.884408 | − | 0.466714i | \(-0.154562\pi\) | ||||
0.884408 | + | 0.466714i | \(0.154562\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 4.60150 | 0.168360 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −3.46976 | −0.126782 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −29.4639 | −1.07515 | −0.537577 | − | 0.843214i | \(-0.680660\pi\) | ||||
−0.537577 | + | 0.843214i | \(0.680660\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 9.55464 | 0.348190 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 17.8966 | 0.650464 | 0.325232 | − | 0.945634i | \(-0.394558\pi\) | ||||
0.325232 | + | 0.945634i | \(0.394558\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 17.8213 | 0.646872 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 38.1996 | 1.38474 | 0.692368 | − | 0.721545i | \(-0.256568\pi\) | ||||
0.692368 | + | 0.721545i | \(0.256568\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 4.24422 | 0.153651 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 39.7367 | 1.43481 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 39.5374 | 1.42576 | 0.712878 | − | 0.701289i | \(-0.247392\pi\) | ||||
0.712878 | + | 0.701289i | \(0.247392\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 14.6026 | 0.525898 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 51.3427 | 1.84667 | 0.923335 | − | 0.383995i | \(-0.125452\pi\) | ||||
0.923335 | + | 0.383995i | \(0.125452\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −0.429057 | −0.0153923 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 6.76164 | 0.242261 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1.88675 | −0.0675133 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −6.42491 | −0.229607 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 41.6629 | 1.48512 | 0.742560 | − | 0.669779i | \(-0.233611\pi\) | ||||
0.742560 | + | 0.669779i | \(0.233611\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −1.49122 | −0.0530888 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0.242309 | 0.00861553 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −27.1257 | −0.963261 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −12.4446 | −0.440812 | −0.220406 | − | 0.975408i | \(-0.570738\pi\) | ||||
−0.220406 | + | 0.975408i | \(0.570738\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 16.3535 | 0.578544 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −22.8859 | −0.808633 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −19.6096 | −0.692007 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −12.8580 | −0.452624 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 0.283694 | 0.00997414 | 0.00498707 | − | 0.999988i | \(-0.498413\pi\) | ||||
0.00498707 | + | 0.999988i | \(0.498413\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −46.2273 | −1.62326 | −0.811631 | − | 0.584171i | \(-0.801420\pi\) | ||||
−0.811631 | + | 0.584171i | \(0.801420\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 2.78141 | 0.0975483 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −0.606115 | −0.0212053 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −2.85289 | −0.0996880 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 24.7448 | 0.863600 | 0.431800 | − | 0.901969i | \(-0.357879\pi\) | ||||
0.431800 | + | 0.901969i | \(0.357879\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −29.5937 | −1.03157 | −0.515786 | − | 0.856717i | \(-0.672500\pi\) | ||||
−0.515786 | + | 0.856717i | \(0.672500\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 52.8976 | 1.83943 | 0.919715 | − | 0.392587i | \(-0.128420\pi\) | ||||
0.919715 | + | 0.392587i | \(0.128420\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 7.44924 | 0.258723 | 0.129361 | − | 0.991598i | \(-0.458707\pi\) | ||||
0.129361 | + | 0.991598i | \(0.458707\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −10.1127 | −0.350805 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 33.6143 | 1.16467 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −17.5854 | −0.607842 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 7.89398 | 0.272531 | 0.136265 | − | 0.990672i | \(-0.456490\pi\) | ||||
0.136265 | + | 0.990672i | \(0.456490\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −25.9735 | −0.895638 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −5.29128 | −0.182242 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0.471286 | 0.0161936 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −21.0143 | −0.721208 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −14.2463 | −0.488357 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 46.6687 | 1.59791 | 0.798953 | − | 0.601393i | \(-0.205387\pi\) | ||||
0.798953 | + | 0.601393i | \(0.205387\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 7.92083 | 0.270570 | 0.135285 | − | 0.990807i | \(-0.456805\pi\) | ||||
0.135285 | + | 0.990807i | \(0.456805\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 8.42793 | 0.287557 | 0.143779 | − | 0.989610i | \(-0.454075\pi\) | ||||
0.143779 | + | 0.989610i | \(0.454075\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −1.55350 | −0.0529430 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −28.2751 | −0.962495 | −0.481248 | − | 0.876585i | \(-0.659816\pi\) | ||||
−0.481248 | + | 0.876585i | \(0.659816\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −4.56322 | −0.154975 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −9.39213 | −0.318606 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −7.21930 | −0.244617 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 25.9848 | 0.879453 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 32.0169 | 1.08113 | 0.540567 | − | 0.841301i | \(-0.318210\pi\) | ||||
0.540567 | + | 0.841301i | \(0.318210\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 21.6811 | 0.731286 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 55.6183 | 1.87383 | 0.936914 | − | 0.349560i | \(-0.113669\pi\) | ||||
0.936914 | + | 0.349560i | \(0.113669\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −16.1272 | −0.542723 | −0.271362 | − | 0.962477i | \(-0.587474\pi\) | ||||
−0.271362 | + | 0.962477i | \(0.587474\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 14.9850 | 0.503146 | 0.251573 | − | 0.967838i | \(-0.419052\pi\) | ||||
0.251573 | + | 0.967838i | \(0.419052\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −4.09320 | −0.137281 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 18.3608 | 0.615111 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −3.34735 | −0.112015 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 16.3435 | 0.545692 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 8.28375 | 0.276279 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −0.524655 | −0.0174788 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0.139256 | 0.00463414 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −45.0654 | −1.49637 | −0.748185 | − | 0.663490i | \(-0.769075\pi\) | ||||
−0.748185 | + | 0.663490i | \(0.769075\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −42.2391 | −1.40098 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −3.86130 | −0.127930 | −0.0639652 | − | 0.997952i | \(-0.520375\pi\) | ||||
−0.0639652 | + | 0.997952i | \(0.520375\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −6.32358 | −0.209280 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −7.62680 | −0.251859 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −4.62296 | −0.152497 | −0.0762487 | − | 0.997089i | \(-0.524294\pi\) | ||||
−0.0762487 | + | 0.997089i | \(0.524294\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 3.22548 | 0.106283 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −1.73029 | −0.0569533 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 29.4778 | 0.968177 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −31.0613 | −1.01909 | −0.509543 | − | 0.860445i | \(-0.670186\pi\) | ||||
−0.509543 | + | 0.860445i | \(0.670186\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −6.88042 | −0.225497 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0.338689 | 0.0110882 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 27.5290 | 0.899334 | 0.449667 | − | 0.893196i | \(-0.351543\pi\) | ||||
0.449667 | + | 0.893196i | \(0.351543\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 3.54363 | 0.115642 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −40.2018 | −1.31054 | −0.655271 | − | 0.755394i | \(-0.727445\pi\) | ||||
−0.655271 | + | 0.755394i | \(0.727445\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −51.5819 | −1.67974 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −18.8753 | −0.613363 | −0.306682 | − | 0.951812i | \(-0.599219\pi\) | ||||
−0.306682 | + | 0.951812i | \(0.599219\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −17.9835 | −0.583768 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −10.0541 | −0.326028 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −46.2885 | −1.49943 | −0.749715 | − | 0.661760i | \(-0.769810\pi\) | ||||
−0.749715 | + | 0.661760i | \(0.769810\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 4.06410 | 0.131374 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −6.73815 | −0.217586 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −8.32676 | −0.268605 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 25.6727 | 0.827292 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 6.98996 | 0.224782 | 0.112391 | − | 0.993664i | \(-0.464149\pi\) | ||||
0.112391 | + | 0.993664i | \(0.464149\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 3.24596 | 0.104275 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 2.02077 | 0.0648496 | 0.0324248 | − | 0.999474i | \(-0.489677\pi\) | ||||
0.0324248 | + | 0.999474i | \(0.489677\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −5.04406 | −0.161705 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 6.12836 | 0.196064 | 0.0980318 | − | 0.995183i | \(-0.468745\pi\) | ||||
0.0980318 | + | 0.995183i | \(0.468745\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 31.4508 | 1.00517 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −31.4030 | −1.00262 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −30.8941 | −0.985370 | −0.492685 | − | 0.870208i | \(-0.663984\pi\) | ||||
−0.492685 | + | 0.870208i | \(0.663984\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0.769057 | 0.0244793 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 4.62381 | 0.147029 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −4.01803 | −0.127637 | −0.0638185 | − | 0.997962i | \(-0.520328\pi\) | ||||
−0.0638185 | + | 0.997962i | \(0.520328\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −2.79966 | −0.0888446 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −5.96552 | −0.188930 | −0.0944650 | − | 0.995528i | \(-0.530114\pi\) | ||||
−0.0944650 | + | 0.995528i | \(0.530114\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 6.89690 | 0.218208 |
(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 | 3800.2.a.z.1.3 | 6 | ||
4.3 | odd | 2 | 7600.2.a.cn.1.4 | 6 | |||
5.2 | odd | 4 | 760.2.d.e.609.8 | yes | 12 | ||
5.3 | odd | 4 | 760.2.d.e.609.5 | ✓ | 12 | ||
5.4 | even | 2 | 3800.2.a.be.1.4 | 6 | |||
20.3 | even | 4 | 1520.2.d.k.609.8 | 12 | |||
20.7 | even | 4 | 1520.2.d.k.609.5 | 12 | |||
20.19 | odd | 2 | 7600.2.a.cg.1.3 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
760.2.d.e.609.5 | ✓ | 12 | 5.3 | odd | 4 | ||
760.2.d.e.609.8 | yes | 12 | 5.2 | odd | 4 | ||
1520.2.d.k.609.5 | 12 | 20.7 | even | 4 | |||
1520.2.d.k.609.8 | 12 | 20.3 | even | 4 | |||
3800.2.a.z.1.3 | 6 | 1.1 | even | 1 | trivial | ||
3800.2.a.be.1.4 | 6 | 5.4 | even | 2 | |||
7600.2.a.cg.1.3 | 6 | 20.19 | odd | 2 | |||
7600.2.a.cn.1.4 | 6 | 4.3 | odd | 2 |