Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8280,2,Mod(1,8280)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8280, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8280.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8280 = 2^{3} \cdot 3^{2} \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8280.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: | \(66.1161328736\) |
Analytic rank: | \(1\) |
Dimension: | \(6\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{6} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 2x^{5} - 16x^{4} + 26x^{3} + 52x^{2} - 48x + 9 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(3.58888\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8280.1 |
$q$-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 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.26189 | −0.854912 | −0.427456 | − | 0.904036i | \(-0.640590\pi\) | ||||
−0.427456 | + | 0.904036i | \(0.640590\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.162910 | 0.0491191 | 0.0245596 | − | 0.999698i | \(-0.492182\pi\) | ||||
0.0245596 | + | 0.999698i | \(0.492182\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 7.01485 | 1.94557 | 0.972785 | − | 0.231711i | \(-0.0744322\pi\) | ||||
0.972785 | + | 0.231711i | \(0.0744322\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −3.86140 | −0.936527 | −0.468264 | − | 0.883589i | \(-0.655120\pi\) | ||||
−0.468264 | + | 0.883589i | \(0.655120\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.83709 | 0.421457 | 0.210729 | − | 0.977545i | \(-0.432416\pi\) | ||||
0.210729 | + | 0.977545i | \(0.432416\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.00000 | −0.208514 | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −7.93835 | −1.47411 | −0.737057 | − | 0.675831i | \(-0.763785\pi\) | ||||
−0.737057 | + | 0.675831i | \(0.763785\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −5.15345 | −0.925587 | −0.462794 | − | 0.886466i | \(-0.653153\pi\) | ||||
−0.462794 | + | 0.886466i | \(0.653153\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 2.26189 | 0.382328 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 6.51608 | 1.07124 | 0.535618 | − | 0.844460i | \(-0.320079\pi\) | ||||
0.535618 | + | 0.844460i | \(0.320079\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.28436 | 0.200583 | 0.100292 | − | 0.994958i | \(-0.468022\pi\) | ||||
0.100292 | + | 0.994958i | \(0.468022\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −5.17776 | −0.789601 | −0.394801 | − | 0.918767i | \(-0.629186\pi\) | ||||
−0.394801 | + | 0.918767i | \(0.629186\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 4.41710 | 0.644301 | 0.322150 | − | 0.946689i | \(-0.395594\pi\) | ||||
0.322150 | + | 0.946689i | \(0.395594\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.88387 | −0.269125 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −0.792589 | −0.108870 | −0.0544352 | − | 0.998517i | \(-0.517336\pi\) | ||||
−0.0544352 | + | 0.998517i | \(0.517336\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −0.162910 | −0.0219667 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 4.75296 | 0.618783 | 0.309392 | − | 0.950935i | \(-0.399875\pi\) | ||||
0.309392 | + | 0.950935i | \(0.399875\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 13.0522 | 1.67116 | 0.835580 | − | 0.549369i | \(-0.185132\pi\) | ||||
0.835580 | + | 0.549369i | \(0.185132\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −7.01485 | −0.870085 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1.99231 | −0.243399 | −0.121700 | − | 0.992567i | \(-0.538834\pi\) | ||||
−0.121700 | + | 0.992567i | \(0.538834\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −11.9307 | −1.41592 | −0.707958 | − | 0.706254i | \(-0.750384\pi\) | ||||
−0.707958 | + | 0.706254i | \(0.750384\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −11.9230 | −1.39549 | −0.697743 | − | 0.716348i | \(-0.745812\pi\) | ||||
−0.697743 | + | 0.716348i | \(0.745812\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −0.368483 | −0.0419926 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 9.21508 | 1.03678 | 0.518389 | − | 0.855145i | \(-0.326532\pi\) | ||||
0.518389 | + | 0.855145i | \(0.326532\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −7.90634 | −0.867834 | −0.433917 | − | 0.900953i | \(-0.642869\pi\) | ||||
−0.433917 | + | 0.900953i | \(0.642869\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 3.86140 | 0.418828 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 10.2915 | 1.09090 | 0.545449 | − | 0.838144i | \(-0.316359\pi\) | ||||
0.545449 | + | 0.838144i | \(0.316359\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −15.8668 | −1.66329 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −1.83709 | −0.188481 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 0.560425 | 0.0569025 | 0.0284513 | − | 0.999595i | \(-0.490942\pi\) | ||||
0.0284513 | + | 0.999595i | \(0.490942\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 15.9118 | 1.58328 | 0.791642 | − | 0.610985i | \(-0.209227\pi\) | ||||
0.791642 | + | 0.610985i | \(0.209227\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −13.1588 | −1.29658 | −0.648290 | − | 0.761394i | \(-0.724515\pi\) | ||||
−0.648290 | + | 0.761394i | \(0.724515\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 14.4225 | 1.39428 | 0.697138 | − | 0.716937i | \(-0.254457\pi\) | ||||
0.697138 | + | 0.716937i | \(0.254457\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 7.28443 | 0.697722 | 0.348861 | − | 0.937175i | \(-0.386569\pi\) | ||||
0.348861 | + | 0.937175i | \(0.386569\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −10.4414 | −0.982246 | −0.491123 | − | 0.871090i | \(-0.663413\pi\) | ||||
−0.491123 | + | 0.871090i | \(0.663413\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.00000 | 0.0932505 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 8.73405 | 0.800649 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.9735 | −0.997587 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −2.90590 | −0.257857 | −0.128929 | − | 0.991654i | \(-0.541154\pi\) | ||||
−0.128929 | + | 0.991654i | \(0.541154\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −13.9208 | −1.21626 | −0.608131 | − | 0.793837i | \(-0.708080\pi\) | ||||
−0.608131 | + | 0.793837i | \(0.708080\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −4.15529 | −0.360309 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 13.0095 | 1.11148 | 0.555739 | − | 0.831357i | \(-0.312435\pi\) | ||||
0.555739 | + | 0.831357i | \(0.312435\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 16.9136 | 1.43459 | 0.717295 | − | 0.696769i | \(-0.245380\pi\) | ||||
0.717295 | + | 0.696769i | \(0.245380\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 1.14279 | 0.0955647 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 7.93835 | 0.659244 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −14.4698 | −1.18541 | −0.592707 | − | 0.805418i | \(-0.701941\pi\) | ||||
−0.592707 | + | 0.805418i | \(0.701941\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −14.7780 | −1.20261 | −0.601307 | − | 0.799018i | \(-0.705353\pi\) | ||||
−0.601307 | + | 0.799018i | \(0.705353\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 5.15345 | 0.413935 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 7.32835 | 0.584866 | 0.292433 | − | 0.956286i | \(-0.405535\pi\) | ||||
0.292433 | + | 0.956286i | \(0.405535\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 2.26189 | 0.178262 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 20.3366 | 1.59289 | 0.796443 | − | 0.604714i | \(-0.206713\pi\) | ||||
0.796443 | + | 0.604714i | \(0.206713\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −9.87441 | −0.764105 | −0.382053 | − | 0.924141i | \(-0.624783\pi\) | ||||
−0.382053 | + | 0.924141i | \(0.624783\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 36.2081 | 2.78524 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −6.99754 | −0.532013 | −0.266007 | − | 0.963971i | \(-0.585704\pi\) | ||||
−0.266007 | + | 0.963971i | \(0.585704\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −2.26189 | −0.170982 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −20.9166 | −1.56338 | −0.781691 | − | 0.623666i | \(-0.785642\pi\) | ||||
−0.781691 | + | 0.623666i | \(0.785642\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −9.62991 | −0.715785 | −0.357893 | − | 0.933763i | \(-0.616505\pi\) | ||||
−0.357893 | + | 0.933763i | \(0.616505\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −6.51608 | −0.479072 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −0.629060 | −0.0460014 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 3.86679 | 0.279791 | 0.139896 | − | 0.990166i | \(-0.455323\pi\) | ||||
0.139896 | + | 0.990166i | \(0.455323\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 2.45977 | 0.177058 | 0.0885290 | − | 0.996074i | \(-0.471783\pi\) | ||||
0.0885290 | + | 0.996074i | \(0.471783\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −16.5049 | −1.17592 | −0.587961 | − | 0.808889i | \(-0.700069\pi\) | ||||
−0.587961 | + | 0.808889i | \(0.700069\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −13.1665 | −0.933346 | −0.466673 | − | 0.884430i | \(-0.654547\pi\) | ||||
−0.466673 | + | 0.884430i | \(0.654547\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 17.9556 | 1.26024 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1.28436 | −0.0897035 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0.299280 | 0.0207016 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 12.4538 | 0.857355 | 0.428678 | − | 0.903457i | \(-0.358980\pi\) | ||||
0.428678 | + | 0.903457i | \(0.358980\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 5.17776 | 0.353120 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 11.6565 | 0.791296 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −27.0871 | −1.82208 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −17.5813 | −1.17733 | −0.588665 | − | 0.808377i | \(-0.700346\pi\) | ||||
−0.588665 | + | 0.808377i | \(0.700346\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −16.5634 | −1.09935 | −0.549677 | − | 0.835377i | \(-0.685249\pi\) | ||||
−0.549677 | + | 0.835377i | \(0.685249\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −14.6273 | −0.966600 | −0.483300 | − | 0.875455i | \(-0.660562\pi\) | ||||
−0.483300 | + | 0.875455i | \(0.660562\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −0.414823 | −0.0271759 | −0.0135880 | − | 0.999908i | \(-0.504325\pi\) | ||||
−0.0135880 | + | 0.999908i | \(0.504325\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −4.41710 | −0.288140 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −24.6524 | −1.59463 | −0.797317 | − | 0.603561i | \(-0.793748\pi\) | ||||
−0.797317 | + | 0.603561i | \(0.793748\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −11.3040 | −0.728156 | −0.364078 | − | 0.931369i | \(-0.618616\pi\) | ||||
−0.364078 | + | 0.931369i | \(0.618616\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 1.88387 | 0.120356 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 12.8869 | 0.819975 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −24.0297 | −1.51674 | −0.758371 | − | 0.651824i | \(-0.774004\pi\) | ||||
−0.758371 | + | 0.651824i | \(0.774004\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −0.162910 | −0.0102420 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −24.4622 | −1.52591 | −0.762955 | − | 0.646452i | \(-0.776252\pi\) | ||||
−0.762955 | + | 0.646452i | \(0.776252\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −14.7386 | −0.915814 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 3.90869 | 0.241020 | 0.120510 | − | 0.992712i | \(-0.461547\pi\) | ||||
0.120510 | + | 0.992712i | \(0.461547\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0.792589 | 0.0486883 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 16.8626 | 1.02813 | 0.514065 | − | 0.857751i | \(-0.328139\pi\) | ||||
0.514065 | + | 0.857751i | \(0.328139\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −30.6128 | −1.85959 | −0.929796 | − | 0.368075i | \(-0.880017\pi\) | ||||
−0.929796 | + | 0.368075i | \(0.880017\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0.162910 | 0.00982383 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 14.4699 | 0.869411 | 0.434705 | − | 0.900573i | \(-0.356852\pi\) | ||||
0.434705 | + | 0.900573i | \(0.356852\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −9.92712 | −0.592202 | −0.296101 | − | 0.955157i | \(-0.595687\pi\) | ||||
−0.296101 | + | 0.955157i | \(0.595687\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −13.5212 | −0.803755 | −0.401877 | − | 0.915694i | \(-0.631642\pi\) | ||||
−0.401877 | + | 0.915694i | \(0.631642\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −2.90507 | −0.171481 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −2.08959 | −0.122917 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −23.1655 | −1.35334 | −0.676671 | − | 0.736285i | \(-0.736578\pi\) | ||||
−0.676671 | + | 0.736285i | \(0.736578\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −4.75296 | −0.276728 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −7.01485 | −0.405679 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 11.7115 | 0.675040 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −13.0522 | −0.747365 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 32.6898 | 1.86571 | 0.932854 | − | 0.360255i | \(-0.117310\pi\) | ||||
0.932854 | + | 0.360255i | \(0.117310\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −34.2472 | −1.94198 | −0.970991 | − | 0.239114i | \(-0.923143\pi\) | ||||
−0.970991 | + | 0.239114i | \(0.923143\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −26.6997 | −1.50915 | −0.754577 | − | 0.656211i | \(-0.772158\pi\) | ||||
−0.754577 | + | 0.656211i | \(0.772158\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 23.7359 | 1.33314 | 0.666569 | − | 0.745443i | \(-0.267762\pi\) | ||||
0.666569 | + | 0.745443i | \(0.267762\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1.29323 | −0.0724072 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −7.09374 | −0.394706 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 7.01485 | 0.389114 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −9.99098 | −0.550821 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −5.10483 | −0.280587 | −0.140293 | − | 0.990110i | \(-0.544805\pi\) | ||||
−0.140293 | + | 0.990110i | \(0.544805\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 1.99231 | 0.108851 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 6.87848 | 0.374695 | 0.187347 | − | 0.982294i | \(-0.440011\pi\) | ||||
0.187347 | + | 0.982294i | \(0.440011\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −0.839547 | −0.0454640 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 20.0943 | 1.08499 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −18.3555 | −0.985376 | −0.492688 | − | 0.870206i | \(-0.663986\pi\) | ||||
−0.492688 | + | 0.870206i | \(0.663986\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −26.1280 | −1.39860 | −0.699300 | − | 0.714829i | \(-0.746505\pi\) | ||||
−0.699300 | + | 0.714829i | \(0.746505\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −0.215617 | −0.0114762 | −0.00573808 | − | 0.999984i | \(-0.501826\pi\) | ||||
−0.00573808 | + | 0.999984i | \(0.501826\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 11.9307 | 0.633217 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −2.22691 | −0.117532 | −0.0587660 | − | 0.998272i | \(-0.518717\pi\) | ||||
−0.0587660 | + | 0.998272i | \(0.518717\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −15.6251 | −0.822374 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 11.9230 | 0.624080 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 20.3289 | 1.06116 | 0.530580 | − | 0.847635i | \(-0.321974\pi\) | ||||
0.530580 | + | 0.847635i | \(0.321974\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1.79274 | 0.0930747 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 14.4704 | 0.749247 | 0.374623 | − | 0.927177i | \(-0.377772\pi\) | ||||
0.374623 | + | 0.927177i | \(0.377772\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −55.6863 | −2.86799 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 10.7514 | 0.552264 | 0.276132 | − | 0.961120i | \(-0.410947\pi\) | ||||
0.276132 | + | 0.961120i | \(0.410947\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −16.3752 | −0.836734 | −0.418367 | − | 0.908278i | \(-0.637397\pi\) | ||||
−0.418367 | + | 0.908278i | \(0.637397\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0.368483 | 0.0187796 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −33.8461 | −1.71606 | −0.858032 | − | 0.513596i | \(-0.828313\pi\) | ||||
−0.858032 | + | 0.513596i | \(0.828313\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 3.86140 | 0.195279 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −9.21508 | −0.463661 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 13.6249 | 0.683812 | 0.341906 | − | 0.939734i | \(-0.388928\pi\) | ||||
0.341906 | + | 0.939734i | \(0.388928\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 14.2277 | 0.710495 | 0.355248 | − | 0.934772i | \(-0.384397\pi\) | ||||
0.355248 | + | 0.934772i | \(0.384397\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −36.1507 | −1.80079 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 1.06153 | 0.0526182 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −27.3581 | −1.35277 | −0.676385 | − | 0.736548i | \(-0.736455\pi\) | ||||
−0.676385 | + | 0.736548i | \(0.736455\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −10.7507 | −0.529006 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 7.90634 | 0.388107 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 33.7129 | 1.64698 | 0.823490 | − | 0.567330i | \(-0.192024\pi\) | ||||
0.823490 | + | 0.567330i | \(0.192024\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −21.6839 | −1.05681 | −0.528404 | − | 0.848993i | \(-0.677209\pi\) | ||||
−0.528404 | + | 0.848993i | \(0.677209\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −3.86140 | −0.187305 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −29.5225 | −1.42870 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 16.7550 | 0.807058 | 0.403529 | − | 0.914967i | \(-0.367783\pi\) | ||||
0.403529 | + | 0.914967i | \(0.367783\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −5.18372 | −0.249113 | −0.124557 | − | 0.992212i | \(-0.539751\pi\) | ||||
−0.124557 | + | 0.992212i | \(0.539751\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −1.83709 | −0.0878799 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −23.9780 | −1.14441 | −0.572204 | − | 0.820111i | \(-0.693912\pi\) | ||||
−0.572204 | + | 0.820111i | \(0.693912\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 21.0157 | 0.998484 | 0.499242 | − | 0.866463i | \(-0.333612\pi\) | ||||
0.499242 | + | 0.866463i | \(0.333612\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −10.2915 | −0.487865 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −0.756499 | −0.0357014 | −0.0178507 | − | 0.999841i | \(-0.505682\pi\) | ||||
−0.0178507 | + | 0.999841i | \(0.505682\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0.209234 | 0.00985246 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 15.8668 | 0.743847 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 40.0031 | 1.87127 | 0.935633 | − | 0.352975i | \(-0.114830\pi\) | ||||
0.935633 | + | 0.352975i | \(0.114830\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 8.97357 | 0.417941 | 0.208970 | − | 0.977922i | \(-0.432989\pi\) | ||||
0.208970 | + | 0.977922i | \(0.432989\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 11.3218 | 0.526166 | 0.263083 | − | 0.964773i | \(-0.415261\pi\) | ||||
0.263083 | + | 0.964773i | \(0.415261\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −30.3146 | −1.40279 | −0.701396 | − | 0.712772i | \(-0.747439\pi\) | ||||
−0.701396 | + | 0.712772i | \(0.747439\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 4.50637 | 0.208085 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −0.843508 | −0.0387845 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1.83709 | 0.0842915 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −24.5291 | −1.12076 | −0.560381 | − | 0.828235i | \(-0.689345\pi\) | ||||
−0.560381 | + | 0.828235i | \(0.689345\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 45.7093 | 2.08417 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −0.560425 | −0.0254476 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −10.8620 | −0.492204 | −0.246102 | − | 0.969244i | \(-0.579150\pi\) | ||||
−0.246102 | + | 0.969244i | \(0.579150\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −8.28328 | −0.373819 | −0.186910 | − | 0.982377i | \(-0.559847\pi\) | ||||
−0.186910 | + | 0.982377i | \(0.559847\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 30.6531 | 1.38055 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 26.9859 | 1.21048 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −21.5719 | −0.965693 | −0.482847 | − | 0.875705i | \(-0.660397\pi\) | ||||
−0.482847 | + | 0.875705i | \(0.660397\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −10.1937 | −0.454513 | −0.227256 | − | 0.973835i | \(-0.572976\pi\) | ||||
−0.227256 | + | 0.973835i | \(0.572976\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −15.9118 | −0.708066 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 4.57107 | 0.202609 | 0.101304 | − | 0.994855i | \(-0.467698\pi\) | ||||
0.101304 | + | 0.994855i | \(0.467698\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 26.9685 | 1.19302 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 13.1588 | 0.579848 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0.719589 | 0.0316475 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 24.3266 | 1.06577 | 0.532883 | − | 0.846189i | \(-0.321109\pi\) | ||||
0.532883 | + | 0.846189i | \(0.321109\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −15.8263 | −0.692037 | −0.346019 | − | 0.938228i | \(-0.612467\pi\) | ||||
−0.346019 | + | 0.938228i | \(0.612467\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 19.8995 | 0.866837 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 9.00958 | 0.390248 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −14.4225 | −0.623539 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −0.306901 | −0.0132192 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −29.7922 | −1.28087 | −0.640434 | − | 0.768013i | \(-0.721246\pi\) | ||||
−0.640434 | + | 0.768013i | \(0.721246\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −7.28443 | −0.312031 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −4.87562 | −0.208466 | −0.104233 | − | 0.994553i | \(-0.533239\pi\) | ||||
−0.104233 | + | 0.994553i | \(0.533239\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −14.5835 | −0.621276 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −20.8435 | −0.886354 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −5.27495 | −0.223507 | −0.111753 | − | 0.993736i | \(-0.535647\pi\) | ||||
−0.111753 | + | 0.993736i | \(0.535647\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −36.3212 | −1.53622 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −8.32741 | −0.350958 | −0.175479 | − | 0.984483i | \(-0.556147\pi\) | ||||
−0.175479 | + | 0.984483i | \(0.556147\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 10.4414 | 0.439274 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 19.2051 | 0.805120 | 0.402560 | − | 0.915394i | \(-0.368120\pi\) | ||||
0.402560 | + | 0.915394i | \(0.368120\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 41.9511 | 1.75560 | 0.877799 | − | 0.479030i | \(-0.159012\pi\) | ||||
0.877799 | + | 0.479030i | \(0.159012\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −1.00000 | −0.0417029 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 29.4610 | 1.22648 | 0.613238 | − | 0.789898i | \(-0.289866\pi\) | ||||
0.613238 | + | 0.789898i | \(0.289866\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 17.8832 | 0.741922 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −0.129120 | −0.00534762 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 7.61488 | 0.314300 | 0.157150 | − | 0.987575i | \(-0.449769\pi\) | ||||
0.157150 | + | 0.987575i | \(0.449769\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −9.46735 | −0.390096 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 4.17421 | 0.171414 | 0.0857071 | − | 0.996320i | \(-0.472685\pi\) | ||||
0.0857071 | + | 0.996320i | \(0.472685\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −8.73405 | −0.358061 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 2.17716 | 0.0889562 | 0.0444781 | − | 0.999010i | \(-0.485838\pi\) | ||||
0.0444781 | + | 0.999010i | \(0.485838\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 30.1253 | 1.22884 | 0.614418 | − | 0.788981i | \(-0.289391\pi\) | ||||
0.614418 | + | 0.788981i | \(0.289391\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 10.9735 | 0.446135 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −12.7789 | −0.518680 | −0.259340 | − | 0.965786i | \(-0.583505\pi\) | ||||
−0.259340 | + | 0.965786i | \(0.583505\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 30.9853 | 1.25353 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 13.6889 | 0.552888 | 0.276444 | − | 0.961030i | \(-0.410844\pi\) | ||||
0.276444 | + | 0.961030i | \(0.410844\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −3.20506 | −0.129031 | −0.0645155 | − | 0.997917i | \(-0.520550\pi\) | ||||
−0.0645155 | + | 0.997917i | \(0.520550\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −23.2889 | −0.936061 | −0.468030 | − | 0.883712i | \(-0.655036\pi\) | ||||
−0.468030 | + | 0.883712i | \(0.655036\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −23.2782 | −0.932623 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −25.1612 | −1.00324 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −28.6706 | −1.14136 | −0.570679 | − | 0.821173i | \(-0.693320\pi\) | ||||
−0.570679 | + | 0.821173i | \(0.693320\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 2.90590 | 0.115317 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −13.2151 | −0.523601 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 17.3621 | 0.685761 | 0.342880 | − | 0.939379i | \(-0.388597\pi\) | ||||
0.342880 | + | 0.939379i | \(0.388597\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 27.2117 | 1.07313 | 0.536563 | − | 0.843860i | \(-0.319722\pi\) | ||||
0.536563 | + | 0.843860i | \(0.319722\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 32.7385 | 1.28708 | 0.643541 | − | 0.765412i | \(-0.277465\pi\) | ||||
0.643541 | + | 0.765412i | \(0.277465\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0.774304 | 0.0303941 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 6.56644 | 0.256964 | 0.128482 | − | 0.991712i | \(-0.458989\pi\) | ||||
0.128482 | + | 0.991712i | \(0.458989\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 13.9208 | 0.543929 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −34.8822 | −1.35882 | −0.679409 | − | 0.733760i | \(-0.737764\pi\) | ||||
−0.679409 | + | 0.733760i | \(0.737764\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 5.68921 | 0.221285 | 0.110642 | − | 0.993860i | \(-0.464709\pi\) | ||||
0.110642 | + | 0.993860i | \(0.464709\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 4.15529 | 0.161135 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 7.93835 | 0.307374 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 2.12633 | 0.0820859 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 6.24380 | 0.240681 | 0.120340 | − | 0.992733i | \(-0.461601\pi\) | ||||
0.120340 | + | 0.992733i | \(0.461601\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 17.1885 | 0.660607 | 0.330304 | − | 0.943875i | \(-0.392849\pi\) | ||||
0.330304 | + | 0.943875i | \(0.392849\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −1.26762 | −0.0486467 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −22.0085 | −0.842132 | −0.421066 | − | 0.907030i | \(-0.638344\pi\) | ||||
−0.421066 | + | 0.907030i | \(0.638344\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −13.0095 | −0.497068 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −5.55989 | −0.211815 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −5.82031 | −0.221415 | −0.110708 | − | 0.993853i | \(-0.535312\pi\) | ||||
−0.110708 | + | 0.993853i | \(0.535312\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −16.9136 | −0.641568 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −4.95942 | −0.187851 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −33.9061 | −1.28062 | −0.640308 | − | 0.768118i | \(-0.721193\pi\) | ||||
−0.640308 | + | 0.768118i | \(0.721193\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 11.9706 | 0.451481 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −35.9907 | −1.35357 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 3.80820 | 0.143020 | 0.0715100 | − | 0.997440i | \(-0.477218\pi\) | ||||
0.0715100 | + | 0.997440i | \(0.477218\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 5.15345 | 0.192998 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1.14279 | −0.0427378 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 30.0024 | 1.11890 | 0.559449 | − | 0.828864i | \(-0.311013\pi\) | ||||
0.559449 | + | 0.828864i | \(0.311013\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 29.7638 | 1.10846 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −7.93835 | −0.294823 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −45.0419 | −1.67051 | −0.835257 | − | 0.549860i | \(-0.814681\pi\) | ||||
−0.835257 | + | 0.549860i | \(0.814681\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 19.9934 | 0.739483 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 35.2270 | 1.30114 | 0.650569 | − | 0.759447i | \(-0.274530\pi\) | ||||
0.650569 | + | 0.759447i | \(0.274530\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −0.324566 | −0.0119556 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −31.9520 | −1.17537 | −0.587686 | − | 0.809089i | \(-0.699961\pi\) | ||||
−0.587686 | + | 0.809089i | \(0.699961\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −31.8142 | −1.16715 | −0.583575 | − | 0.812059i | \(-0.698347\pi\) | ||||
−0.583575 | + | 0.812059i | \(0.698347\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 14.4698 | 0.530133 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −32.6220 | −1.19198 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1.82206 | 0.0664880 | 0.0332440 | − | 0.999447i | \(-0.489416\pi\) | ||||
0.0332440 | + | 0.999447i | \(0.489416\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 14.7780 | 0.537825 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 18.2276 | 0.662493 | 0.331246 | − | 0.943544i | \(-0.392531\pi\) | ||||
0.331246 | + | 0.943544i | \(0.392531\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −16.0469 | −0.581701 | −0.290851 | − | 0.956769i | \(-0.593938\pi\) | ||||
−0.290851 | + | 0.956769i | \(0.593938\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −16.4765 | −0.596491 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 33.3413 | 1.20389 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 15.9910 | 0.576650 | 0.288325 | − | 0.957533i | \(-0.406902\pi\) | ||||
0.288325 | + | 0.957533i | \(0.406902\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 30.1400 | 1.08406 | 0.542031 | − | 0.840359i | \(-0.317656\pi\) | ||||
0.542031 | + | 0.840359i | \(0.317656\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −5.15345 | −0.185117 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 2.35948 | 0.0845372 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1.94363 | −0.0695486 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −7.32835 | −0.261560 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 24.4650 | 0.872083 | 0.436042 | − | 0.899926i | \(-0.356380\pi\) | ||||
0.436042 | + | 0.899926i | \(0.356380\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 23.6173 | 0.839734 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 91.5591 | 3.25136 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 11.5379 | 0.408694 | 0.204347 | − | 0.978898i | \(-0.434493\pi\) | ||||
0.204347 | + | 0.978898i | \(0.434493\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −17.0562 | −0.603405 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −1.94238 | −0.0685450 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −2.26189 | −0.0797210 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 33.1152 | 1.16427 | 0.582134 | − | 0.813093i | \(-0.302218\pi\) | ||||
0.582134 | + | 0.813093i | \(0.302218\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −23.2159 | −0.815221 | −0.407611 | − | 0.913156i | \(-0.633638\pi\) | ||||
−0.407611 | + | 0.913156i | \(0.633638\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −20.3366 | −0.712360 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −9.51201 | −0.332783 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −25.2274 | −0.880442 | −0.440221 | − | 0.897889i | \(-0.645100\pi\) | ||||
−0.440221 | + | 0.897889i | \(0.645100\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −30.6014 | −1.06670 | −0.533349 | − | 0.845895i | \(-0.679067\pi\) | ||||
−0.533349 | + | 0.845895i | \(0.679067\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 27.4393 | 0.954157 | 0.477078 | − | 0.878861i | \(-0.341696\pi\) | ||||
0.477078 | + | 0.878861i | \(0.341696\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 34.5658 | 1.20052 | 0.600260 | − | 0.799805i | \(-0.295064\pi\) | ||||
0.600260 | + | 0.799805i | \(0.295064\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 7.27439 | 0.252043 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 9.87441 | 0.341718 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 40.8496 | 1.41028 | 0.705142 | − | 0.709067i | \(-0.250883\pi\) | ||||
0.705142 | + | 0.709067i | \(0.250883\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 34.0173 | 1.17301 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −36.2081 | −1.24560 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 24.8207 | 0.852850 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −6.51608 | −0.223368 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −16.3456 | −0.559661 | −0.279830 | − | 0.960049i | \(-0.590278\pi\) | ||||
−0.279830 | + | 0.960049i | \(0.590278\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −56.9495 | −1.94536 | −0.972679 | − | 0.232156i | \(-0.925422\pi\) | ||||
−0.972679 | + | 0.232156i | \(0.925422\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −40.5938 | −1.38504 | −0.692522 | − | 0.721397i | \(-0.743500\pi\) | ||||
−0.692522 | + | 0.721397i | \(0.743500\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −2.26093 | −0.0769629 | −0.0384815 | − | 0.999259i | \(-0.512252\pi\) | ||||
−0.0384815 | + | 0.999259i | \(0.512252\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 6.99754 | 0.237924 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 1.50123 | 0.0509256 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −13.9757 | −0.473550 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 2.26189 | 0.0764657 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 15.3501 | 0.518336 | 0.259168 | − | 0.965832i | \(-0.416552\pi\) | ||||
0.259168 | + | 0.965832i | \(0.416552\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 48.2365 | 1.62513 | 0.812564 | − | 0.582872i | \(-0.198071\pi\) | ||||
0.812564 | + | 0.582872i | \(0.198071\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −11.9832 | −0.403267 | −0.201634 | − | 0.979461i | \(-0.564625\pi\) | ||||
−0.201634 | + | 0.979461i | \(0.564625\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −36.7597 | −1.23427 | −0.617134 | − | 0.786858i | \(-0.711706\pi\) | ||||
−0.617134 | + | 0.786858i | \(0.711706\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 6.57282 | 0.220445 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 8.11462 | 0.271545 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 20.9166 | 0.699165 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 40.9099 | 1.36442 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 3.06050 | 0.101960 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 9.62991 | 0.320109 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 42.8633 | 1.42325 | 0.711627 | − | 0.702558i | \(-0.247959\pi\) | ||||
0.711627 | + | 0.702558i | \(0.247959\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −14.9800 | −0.496310 | −0.248155 | − | 0.968720i | \(-0.579824\pi\) | ||||
−0.248155 | + | 0.968720i | \(0.579824\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −1.28802 | −0.0426273 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 31.4872 | 1.03980 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −18.9236 | −0.624231 | −0.312115 | − | 0.950044i | \(-0.601038\pi\) | ||||
−0.312115 | + | 0.950044i | \(0.601038\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −83.6923 | −2.75476 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 6.51608 | 0.214247 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 22.8137 | 0.748495 | 0.374247 | − | 0.927329i | \(-0.377901\pi\) | ||||
0.374247 | + | 0.927329i | \(0.377901\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −3.46084 | −0.113425 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0.629060 | 0.0205725 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 47.4243 | 1.54929 | 0.774643 | − | 0.632399i | \(-0.217930\pi\) | ||||
0.774643 | + | 0.632399i | \(0.217930\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 6.27642 | 0.204605 | 0.102303 | − | 0.994753i | \(-0.467379\pi\) | ||||
0.102303 | + | 0.994753i | \(0.467379\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −1.28436 | −0.0418244 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −30.4942 | −0.990927 | −0.495464 | − | 0.868629i | \(-0.665002\pi\) | ||||
−0.495464 | + | 0.868629i | \(0.665002\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −83.6383 | −2.71501 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 53.3375 | 1.72777 | 0.863885 | − | 0.503689i | \(-0.168024\pi\) | ||||
0.863885 | + | 0.503689i | \(0.168024\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −3.86679 | −0.125126 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −29.4260 | −0.950216 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −4.44195 | −0.143289 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −2.45977 | −0.0791827 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 33.1227 | 1.06516 | 0.532578 | − | 0.846381i | \(-0.321223\pi\) | ||||
0.532578 | + | 0.846381i | \(0.321223\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −21.2383 | −0.681571 | −0.340786 | − | 0.940141i | \(-0.610693\pi\) | ||||
−0.340786 | + | 0.940141i | \(0.610693\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −38.2566 | −1.22645 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −38.2931 | −1.22510 | −0.612552 | − | 0.790430i | \(-0.709857\pi\) | ||||
−0.612552 | + | 0.790430i | \(0.709857\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1.67659 | 0.0535840 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 41.6546 | 1.32858 | 0.664288 | − | 0.747477i | \(-0.268735\pi\) | ||||
0.664288 | + | 0.747477i | \(0.268735\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 16.5049 | 0.525888 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 5.17776 | 0.164643 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 47.1319 | 1.49719 | 0.748597 | − | 0.663025i | \(-0.230728\pi\) | ||||
0.748597 | + | 0.663025i | \(0.230728\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 13.1665 | 0.417405 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −5.83363 | −0.184753 | −0.0923764 | − | 0.995724i | \(-0.529446\pi\) | ||||
−0.0923764 | + | 0.995724i | \(0.529446\pi\) | |||||||
\(998\) | 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 | 8280.2.a.bt.1.3 | ✓ | 6 | |
3.2 | odd | 2 | 8280.2.a.bu.1.3 | yes | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8280.2.a.bt.1.3 | ✓ | 6 | 1.1 | even | 1 | trivial | |
8280.2.a.bu.1.3 | yes | 6 | 3.2 | odd | 2 |