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: | \(0\) |
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 | \(-0.507818\pi\) | ||||
−0.0245596 | + | 0.999698i | \(0.507818\pi\) | |||||||
\(12\) | 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 | \(-0.344880\pi\) | ||||
0.468264 | + | 0.883589i | \(0.344880\pi\) | |||||||
\(18\) | 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 | \(-0.236215\pi\) | ||||
0.737057 | + | 0.675831i | \(0.236215\pi\) | |||||||
\(30\) | 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 | \(-0.531978\pi\) | ||||
−0.100292 | + | 0.994958i | \(0.531978\pi\) | |||||||
\(42\) | 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 | \(-0.604406\pi\) | ||||
−0.322150 | + | 0.946689i | \(0.604406\pi\) | |||||||
\(48\) | 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 | \(-0.482664\pi\) | ||||
0.0544352 | + | 0.998517i | \(0.482664\pi\) | |||||||
\(54\) | 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 | \(-0.600125\pi\) | ||||
−0.309392 | + | 0.950935i | \(0.600125\pi\) | |||||||
\(60\) | 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 | \(-0.249616\pi\) | ||||
0.707958 | + | 0.706254i | \(0.249616\pi\) | |||||||
\(72\) | 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 | \(-0.357131\pi\) | ||||
0.433917 | + | 0.900953i | \(0.357131\pi\) | |||||||
\(84\) | 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 | \(-0.683641\pi\) | ||||
−0.545449 | + | 0.838144i | \(0.683641\pi\) | |||||||
\(90\) | 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 | \(-0.790773\pi\) | ||||
−0.791642 | + | 0.610985i | \(0.790773\pi\) | |||||||
\(102\) | 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 | \(-0.745543\pi\) | ||||
−0.697138 | + | 0.716937i | \(0.745543\pi\) | |||||||
\(108\) | 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 | \(-0.336587\pi\) | ||||
0.491123 | + | 0.871090i | \(0.336587\pi\) | |||||||
\(114\) | 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 | \(-0.291920\pi\) | ||||
0.608131 | + | 0.793837i | \(0.291920\pi\) | |||||||
\(132\) | 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 | \(-0.687565\pi\) | ||||
−0.555739 | + | 0.831357i | \(0.687565\pi\) | |||||||
\(138\) | 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 | \(-0.298059\pi\) | ||||
0.592707 | + | 0.805418i | \(0.298059\pi\) | |||||||
\(150\) | 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 | \(-0.375217\pi\) | ||||
0.382053 | + | 0.924141i | \(0.375217\pi\) | |||||||
\(168\) | 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 | \(-0.414296\pi\) | ||||
0.266007 | + | 0.963971i | \(0.414296\pi\) | |||||||
\(174\) | 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 | \(-0.214358\pi\) | ||||
0.781691 | + | 0.623666i | \(0.214358\pi\) | |||||||
\(180\) | 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 | \(-0.544677\pi\) | ||||
−0.139896 | + | 0.990166i | \(0.544677\pi\) | |||||||
\(192\) | 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 | \(-0.299931\pi\) | ||||
0.587961 | + | 0.808889i | \(0.299931\pi\) | |||||||
\(198\) | 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 | \(-0.314751\pi\) | ||||
0.549677 | + | 0.835377i | \(0.314751\pi\) | |||||||
\(228\) | 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 | \(-0.495675\pi\) | ||||
0.0135880 | + | 0.999908i | \(0.495675\pi\) | |||||||
\(234\) | 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 | \(-0.206252\pi\) | ||||
0.797317 | + | 0.603561i | \(0.206252\pi\) | |||||||
\(240\) | 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 | \(-0.225996\pi\) | ||||
0.758371 | + | 0.651824i | \(0.225996\pi\) | |||||||
\(252\) | 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 | \(-0.223748\pi\) | ||||
0.762955 | + | 0.646452i | \(0.223748\pi\) | |||||||
\(258\) | 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 | \(-0.538453\pi\) | ||||
−0.120510 | + | 0.992712i | \(0.538453\pi\) | |||||||
\(264\) | 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 | \(-0.671861\pi\) | ||||
−0.514065 | + | 0.857751i | \(0.671861\pi\) | |||||||
\(270\) | 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 | \(-0.404313\pi\) | ||||
0.296101 | + | 0.955157i | \(0.404313\pi\) | |||||||
\(282\) | 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 | \(-0.263422\pi\) | ||||
0.676671 | + | 0.736285i | \(0.263422\pi\) | |||||||
\(294\) | 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 | \(-0.0768570\pi\) | ||||
0.970991 | + | 0.239114i | \(0.0768570\pi\) | |||||||
\(312\) | 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 | \(-0.732238\pi\) | ||||
−0.666569 | + | 0.745443i | \(0.732238\pi\) | |||||||
\(318\) | 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 | \(-0.336014\pi\) | ||||
0.492688 | + | 0.870206i | \(0.336014\pi\) | |||||||
\(348\) | 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 | \(-0.498174\pi\) | ||||
0.00573808 | + | 0.999984i | \(0.498174\pi\) | |||||||
\(354\) | 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 | \(-0.481283\pi\) | ||||
0.0587660 | + | 0.998272i | \(0.481283\pi\) | |||||||
\(360\) | 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 | \(-0.362603\pi\) | ||||
0.418367 | + | 0.908278i | \(0.362603\pi\) | |||||||
\(384\) | 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 | \(-0.171687\pi\) | ||||
0.858032 | + | 0.513596i | \(0.171687\pi\) | |||||||
\(390\) | 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 | \(-0.615603\pi\) | ||||
−0.355248 | + | 0.934772i | \(0.615603\pi\) | |||||||
\(402\) | 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 | \(-0.807976\pi\) | ||||
−0.823490 | + | 0.567330i | \(0.807976\pi\) | |||||||
\(420\) | 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 | \(-0.632217\pi\) | ||||
−0.403529 | + | 0.914967i | \(0.632217\pi\) | |||||||
\(432\) | 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 | \(-0.666388\pi\) | ||||
−0.499242 | + | 0.866463i | \(0.666388\pi\) | |||||||
\(444\) | 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 | \(-0.494318\pi\) | ||||
0.0178507 | + | 0.999841i | \(0.494318\pi\) | |||||||
\(450\) | 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 | \(-0.567011\pi\) | ||||
−0.208970 | + | 0.977922i | \(0.567011\pi\) | |||||||
\(462\) | 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 | \(-0.252561\pi\) | ||||
0.701396 | + | 0.712772i | \(0.252561\pi\) | |||||||
\(468\) | 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 | \(-0.310655\pi\) | ||||
0.560381 | + | 0.828235i | \(0.310655\pi\) | |||||||
\(480\) | 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 | \(-0.440153\pi\) | ||||
0.186910 | + | 0.982377i | \(0.440153\pi\) | |||||||
\(492\) | 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 | \(-0.427024\pi\) | ||||
0.227256 | + | 0.973835i | \(0.427024\pi\) | |||||||
\(504\) | 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 | \(-0.532302\pi\) | ||||
−0.101304 | + | 0.994855i | \(0.532302\pi\) | |||||||
\(510\) | 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 | \(-0.678891\pi\) | ||||
−0.532883 | + | 0.846189i | \(0.678891\pi\) | |||||||
\(522\) | 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 | \(-0.464353\pi\) | ||||
0.111753 | + | 0.993736i | \(0.464353\pi\) | |||||||
\(558\) | 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 | \(-0.443853\pi\) | ||||
0.175479 | + | 0.984483i | \(0.443853\pi\) | |||||||
\(564\) | 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 | \(-0.631880\pi\) | ||||
−0.402560 | + | 0.915394i | \(0.631880\pi\) | |||||||
\(570\) | 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 | \(-0.550231\pi\) | ||||
−0.157150 | + | 0.987575i | \(0.550231\pi\) | |||||||
\(588\) | 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 | \(-0.527315\pi\) | ||||
−0.0857071 | + | 0.996320i | \(0.527315\pi\) | |||||||
\(594\) | 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 | \(-0.514162\pi\) | ||||
−0.0444781 | + | 0.999010i | \(0.514162\pi\) | |||||||
\(600\) | 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 | \(-0.479450\pi\) | ||||
0.0645155 | + | 0.997917i | \(0.479450\pi\) | |||||||
\(618\) | 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 | \(-0.611403\pi\) | ||||
−0.342880 | + | 0.939379i | \(0.611403\pi\) | |||||||
\(642\) | 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 | \(-0.722535\pi\) | ||||
−0.643541 | + | 0.765412i | \(0.722535\pi\) | |||||||
\(648\) | 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 | \(-0.541011\pi\) | ||||
−0.128482 | + | 0.991712i | \(0.541011\pi\) | |||||||
\(654\) | 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 | \(-0.262236\pi\) | ||||
0.679409 | + | 0.733760i | \(0.262236\pi\) | |||||||
\(660\) | 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 | \(-0.607151\pi\) | ||||
−0.330304 | + | 0.943875i | \(0.607151\pi\) | |||||||
\(678\) | 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 | \(-0.361656\pi\) | ||||
0.421066 | + | 0.907030i | \(0.361656\pi\) | |||||||
\(684\) | 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 | \(-0.278807\pi\) | ||||
0.640308 | + | 0.768118i | \(0.278807\pi\) | |||||||
\(702\) | 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 | \(-0.688987\pi\) | ||||
−0.559449 | + | 0.828864i | \(0.688987\pi\) | |||||||
\(720\) | 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 | \(-0.301653\pi\) | ||||
0.583575 | + | 0.812059i | \(0.301653\pi\) | |||||||
\(744\) | 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 | \(-0.406062\pi\) | ||||
0.290851 | + | 0.956769i | \(0.406062\pi\) | |||||||
\(762\) | 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 | \(-0.682344\pi\) | ||||
−0.542031 | + | 0.840359i | \(0.682344\pi\) | |||||||
\(774\) | 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 | \(-0.565507\pi\) | ||||
−0.204347 | + | 0.978898i | \(0.565507\pi\) | |||||||
\(798\) | 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 | \(-0.697782\pi\) | ||||
−0.582134 | + | 0.813093i | \(0.697782\pi\) | |||||||
\(810\) | 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 | \(-0.354900\pi\) | ||||
0.440221 | + | 0.897889i | \(0.354900\pi\) | |||||||
\(822\) | 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 | \(-0.658304\pi\) | ||||
−0.477078 | + | 0.878861i | \(0.658304\pi\) | |||||||
\(828\) | 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 | \(-0.749117\pi\) | ||||
−0.705142 | + | 0.709067i | \(0.749117\pi\) | |||||||
\(840\) | 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 | \(-0.0745780\pi\) | ||||
0.972679 | + | 0.232156i | \(0.0745780\pi\) | |||||||
\(858\) | 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 | \(-0.487748\pi\) | ||||
0.0384815 | + | 0.999259i | \(0.487748\pi\) | |||||||
\(864\) | 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 | \(-0.801929\pi\) | ||||
−0.812564 | + | 0.582872i | \(0.801929\pi\) | |||||||
\(882\) | 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 | \(-0.288294\pi\) | ||||
0.617134 | + | 0.786858i | \(0.288294\pi\) | |||||||
\(888\) | 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 | \(-0.420176\pi\) | ||||
0.248155 | + | 0.968720i | \(0.420176\pi\) | |||||||
\(912\) | 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 | \(-0.622099\pi\) | ||||
−0.374247 | + | 0.927329i | \(0.622099\pi\) | |||||||
\(930\) | 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 | \(-0.532621\pi\) | ||||
−0.102303 | + | 0.994753i | \(0.532621\pi\) | |||||||
\(942\) | 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 | \(-0.334998\pi\) | ||||
0.495464 | + | 0.868629i | \(0.334998\pi\) | |||||||
\(948\) | 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 | \(-0.831976\pi\) | ||||
−0.863885 | + | 0.503689i | \(0.831976\pi\) | |||||||
\(954\) | 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 | \(-0.389307\pi\) | ||||
0.340786 | + | 0.940141i | \(0.389307\pi\) | |||||||
\(972\) | 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 | \(-0.290143\pi\) | ||||
0.612552 | + | 0.790430i | \(0.290143\pi\) | |||||||
\(978\) | 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 | \(-0.731265\pi\) | ||||
−0.664288 | + | 0.747477i | \(0.731265\pi\) | |||||||
\(984\) | 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.bu.1.3 | yes | 6 | |
3.2 | odd | 2 | 8280.2.a.bt.1.3 | ✓ | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8280.2.a.bt.1.3 | ✓ | 6 | 3.2 | odd | 2 | ||
8280.2.a.bu.1.3 | yes | 6 | 1.1 | even | 1 | trivial |