Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1080,2,Mod(1,1080)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1080, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1080.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1080 = 2^{3} \cdot 3^{3} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1080.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: | \(8.62384341830\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{73}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 18 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(4.77200\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1080.1 |
$q$-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 | ||||||||
\(7\) | 4.77200 | 1.80365 | 0.901824 | − | 0.432104i | \(-0.142229\pi\) | ||||
0.901824 | + | 0.432104i | \(0.142229\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −3.77200 | −1.13730 | −0.568651 | − | 0.822579i | \(-0.692534\pi\) | ||||
−0.568651 | + | 0.822579i | \(0.692534\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.00000 | 0.832050 | 0.416025 | − | 0.909353i | \(-0.363423\pi\) | ||||
0.416025 | + | 0.909353i | \(0.363423\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.77200 | 0.429774 | 0.214887 | − | 0.976639i | \(-0.431062\pi\) | ||||
0.214887 | + | 0.976639i | \(0.431062\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.77200 | −0.635941 | −0.317970 | − | 0.948101i | \(-0.603001\pi\) | ||||
−0.317970 | + | 0.948101i | \(0.603001\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 7.77200 | 1.62057 | 0.810287 | − | 0.586033i | \(-0.199311\pi\) | ||||
0.810287 | + | 0.586033i | \(0.199311\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 3.77200 | 0.700443 | 0.350222 | − | 0.936667i | \(-0.386106\pi\) | ||||
0.350222 | + | 0.936667i | \(0.386106\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.22800 | 0.400160 | 0.200080 | − | 0.979780i | \(-0.435880\pi\) | ||||
0.200080 | + | 0.979780i | \(0.435880\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −4.77200 | −0.806616 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −0.772002 | −0.126916 | −0.0634582 | − | 0.997984i | \(-0.520213\pi\) | ||||
−0.0634582 | + | 0.997984i | \(0.520213\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −9.54400 | −1.49052 | −0.745261 | − | 0.666772i | \(-0.767675\pi\) | ||||
−0.745261 | + | 0.666772i | \(0.767675\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.77200 | −0.270228 | −0.135114 | − | 0.990830i | \(-0.543140\pi\) | ||||
−0.135114 | + | 0.990830i | \(0.543140\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 5.77200 | 0.841933 | 0.420967 | − | 0.907076i | \(-0.361691\pi\) | ||||
0.420967 | + | 0.907076i | \(0.361691\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 15.7720 | 2.25314 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −9.54400 | −1.31097 | −0.655485 | − | 0.755208i | \(-0.727536\pi\) | ||||
−0.655485 | + | 0.755208i | \(0.727536\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 3.77200 | 0.508617 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 12.0000 | 1.56227 | 0.781133 | − | 0.624364i | \(-0.214642\pi\) | ||||
0.781133 | + | 0.624364i | \(0.214642\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0.772002 | 0.0988447 | 0.0494224 | − | 0.998778i | \(-0.484262\pi\) | ||||
0.0494224 | + | 0.998778i | \(0.484262\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −3.00000 | −0.372104 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 14.7720 | 1.80469 | 0.902344 | − | 0.431017i | \(-0.141845\pi\) | ||||
0.902344 | + | 0.431017i | \(0.141845\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 13.5440 | 1.60738 | 0.803689 | − | 0.595050i | \(-0.202868\pi\) | ||||
0.803689 | + | 0.595050i | \(0.202868\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 4.77200 | 0.558521 | 0.279260 | − | 0.960215i | \(-0.409911\pi\) | ||||
0.279260 | + | 0.960215i | \(0.409911\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −18.0000 | −2.05129 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −5.00000 | −0.562544 | −0.281272 | − | 0.959628i | \(-0.590756\pi\) | ||||
−0.281272 | + | 0.959628i | \(0.590756\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 6.00000 | 0.658586 | 0.329293 | − | 0.944228i | \(-0.393190\pi\) | ||||
0.329293 | + | 0.944228i | \(0.393190\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.77200 | −0.192201 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 8.00000 | 0.847998 | 0.423999 | − | 0.905663i | \(-0.360626\pi\) | ||||
0.423999 | + | 0.905663i | \(0.360626\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 14.3160 | 1.50073 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 2.77200 | 0.284401 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −18.3160 | −1.85971 | −0.929854 | − | 0.367928i | \(-0.880067\pi\) | ||||
−0.929854 | + | 0.367928i | \(0.880067\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −10.2280 | −1.01772 | −0.508862 | − | 0.860848i | \(-0.669934\pi\) | ||||
−0.508862 | + | 0.860848i | \(0.669934\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 16.7720 | 1.65259 | 0.826297 | − | 0.563234i | \(-0.190443\pi\) | ||||
0.826297 | + | 0.563234i | \(0.190443\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −14.0000 | −1.35343 | −0.676716 | − | 0.736245i | \(-0.736597\pi\) | ||||
−0.676716 | + | 0.736245i | \(0.736597\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 9.54400 | 0.914150 | 0.457075 | − | 0.889428i | \(-0.348897\pi\) | ||||
0.457075 | + | 0.889428i | \(0.348897\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 11.3160 | 1.06452 | 0.532260 | − | 0.846581i | \(-0.321343\pi\) | ||||
0.532260 | + | 0.846581i | \(0.321343\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −7.77200 | −0.724743 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 8.45600 | 0.775160 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 3.22800 | 0.293454 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −11.5440 | −1.02436 | −0.512182 | − | 0.858877i | \(-0.671163\pi\) | ||||
−0.512182 | + | 0.858877i | \(0.671163\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 6.22800 | 0.544143 | 0.272071 | − | 0.962277i | \(-0.412291\pi\) | ||||
0.272071 | + | 0.962277i | \(0.412291\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −13.2280 | −1.14701 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −21.0880 | −1.80167 | −0.900835 | − | 0.434162i | \(-0.857045\pi\) | ||||
−0.900835 | + | 0.434162i | \(0.857045\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −12.7720 | −1.08331 | −0.541654 | − | 0.840602i | \(-0.682202\pi\) | ||||
−0.541654 | + | 0.840602i | \(0.682202\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −11.3160 | −0.946292 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −3.77200 | −0.313248 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −9.77200 | −0.800554 | −0.400277 | − | 0.916394i | \(-0.631086\pi\) | ||||
−0.400277 | + | 0.916394i | \(0.631086\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −24.0880 | −1.96025 | −0.980127 | − | 0.198370i | \(-0.936435\pi\) | ||||
−0.980127 | + | 0.198370i | \(0.936435\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −2.22800 | −0.178957 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 7.77200 | 0.620273 | 0.310137 | − | 0.950692i | \(-0.399625\pi\) | ||||
0.310137 | + | 0.950692i | \(0.399625\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 37.0880 | 2.92294 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −8.54400 | −0.669218 | −0.334609 | − | 0.942357i | \(-0.608604\pi\) | ||||
−0.334609 | + | 0.942357i | \(0.608604\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −23.0880 | −1.78660 | −0.893302 | − | 0.449457i | \(-0.851617\pi\) | ||||
−0.893302 | + | 0.449457i | \(0.851617\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −4.00000 | −0.307692 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 7.54400 | 0.573560 | 0.286780 | − | 0.957996i | \(-0.407415\pi\) | ||||
0.286780 | + | 0.957996i | \(0.407415\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 4.77200 | 0.360729 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 9.54400 | 0.713352 | 0.356676 | − | 0.934228i | \(-0.383910\pi\) | ||||
0.356676 | + | 0.934228i | \(0.383910\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −24.3160 | −1.80739 | −0.903697 | − | 0.428172i | \(-0.859158\pi\) | ||||
−0.903697 | + | 0.428172i | \(0.859158\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0.772002 | 0.0567587 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −6.68399 | −0.488782 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 3.54400 | 0.256435 | 0.128218 | − | 0.991746i | \(-0.459074\pi\) | ||||
0.128218 | + | 0.991746i | \(0.459074\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −12.7720 | −0.919349 | −0.459674 | − | 0.888088i | \(-0.652034\pi\) | ||||
−0.459674 | + | 0.888088i | \(0.652034\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −20.0000 | −1.42494 | −0.712470 | − | 0.701702i | \(-0.752424\pi\) | ||||
−0.712470 | + | 0.701702i | \(0.752424\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −15.0000 | −1.06332 | −0.531661 | − | 0.846957i | \(-0.678432\pi\) | ||||
−0.531661 | + | 0.846957i | \(0.678432\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 18.0000 | 1.26335 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 9.54400 | 0.666582 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 10.4560 | 0.723256 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 14.3160 | 0.985554 | 0.492777 | − | 0.870156i | \(-0.335982\pi\) | ||||
0.492777 | + | 0.870156i | \(0.335982\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 1.77200 | 0.120850 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 10.6320 | 0.721748 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 5.31601 | 0.357593 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 15.0880 | 1.01037 | 0.505184 | − | 0.863012i | \(-0.331425\pi\) | ||||
0.505184 | + | 0.863012i | \(0.331425\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 1.54400 | 0.102479 | 0.0512396 | − | 0.998686i | \(-0.483683\pi\) | ||||
0.0512396 | + | 0.998686i | \(0.483683\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 10.4560 | 0.690952 | 0.345476 | − | 0.938428i | \(-0.387718\pi\) | ||||
0.345476 | + | 0.938428i | \(0.387718\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 12.4560 | 0.816019 | 0.408010 | − | 0.912978i | \(-0.366223\pi\) | ||||
0.408010 | + | 0.912978i | \(0.366223\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −5.77200 | −0.376524 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 6.00000 | 0.388108 | 0.194054 | − | 0.980991i | \(-0.437836\pi\) | ||||
0.194054 | + | 0.980991i | \(0.437836\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 8.08801 | 0.520994 | 0.260497 | − | 0.965475i | \(-0.416114\pi\) | ||||
0.260497 | + | 0.965475i | \(0.416114\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −15.7720 | −1.00764 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −8.31601 | −0.529135 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 0.227998 | 0.0143911 | 0.00719556 | − | 0.999974i | \(-0.497710\pi\) | ||||
0.00719556 | + | 0.999974i | \(0.497710\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −29.3160 | −1.84308 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −2.22800 | −0.138979 | −0.0694894 | − | 0.997583i | \(-0.522137\pi\) | ||||
−0.0694894 | + | 0.997583i | \(0.522137\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −3.68399 | −0.228912 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 12.0000 | 0.739952 | 0.369976 | − | 0.929041i | \(-0.379366\pi\) | ||||
0.369976 | + | 0.929041i | \(0.379366\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 9.54400 | 0.586283 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −5.31601 | −0.324123 | −0.162061 | − | 0.986781i | \(-0.551814\pi\) | ||||
−0.162061 | + | 0.986781i | \(0.551814\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −10.7720 | −0.654353 | −0.327176 | − | 0.944963i | \(-0.606097\pi\) | ||||
−0.327176 | + | 0.944963i | \(0.606097\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −3.77200 | −0.227460 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 10.0000 | 0.600842 | 0.300421 | − | 0.953807i | \(-0.402873\pi\) | ||||
0.300421 | + | 0.953807i | \(0.402873\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −11.5440 | −0.688658 | −0.344329 | − | 0.938849i | \(-0.611893\pi\) | ||||
−0.344329 | + | 0.938849i | \(0.611893\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −11.0880 | −0.659114 | −0.329557 | − | 0.944136i | \(-0.606899\pi\) | ||||
−0.329557 | + | 0.944136i | \(0.606899\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −45.5440 | −2.68838 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −13.8600 | −0.815295 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −29.0880 | −1.69934 | −0.849670 | − | 0.527315i | \(-0.823199\pi\) | ||||
−0.849670 | + | 0.527315i | \(0.823199\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −12.0000 | −0.698667 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 23.3160 | 1.34840 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −8.45600 | −0.487396 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −0.772002 | −0.0442047 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −5.77200 | −0.329426 | −0.164713 | − | 0.986342i | \(-0.552670\pi\) | ||||
−0.164713 | + | 0.986342i | \(0.552670\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 4.00000 | 0.226819 | 0.113410 | − | 0.993548i | \(-0.463823\pi\) | ||||
0.113410 | + | 0.993548i | \(0.463823\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −28.3160 | −1.60052 | −0.800258 | − | 0.599656i | \(-0.795304\pi\) | ||||
−0.800258 | + | 0.599656i | \(0.795304\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 11.0880 | 0.622765 | 0.311382 | − | 0.950285i | \(-0.399208\pi\) | ||||
0.311382 | + | 0.950285i | \(0.399208\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −14.2280 | −0.796615 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −4.91199 | −0.273311 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 3.00000 | 0.166410 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 27.5440 | 1.51855 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 3.22800 | 0.177427 | 0.0887134 | − | 0.996057i | \(-0.471724\pi\) | ||||
0.0887134 | + | 0.996057i | \(0.471724\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −14.7720 | −0.807081 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −26.7720 | −1.45836 | −0.729182 | − | 0.684320i | \(-0.760099\pi\) | ||||
−0.729182 | + | 0.684320i | \(0.760099\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −8.40401 | −0.455103 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 41.8600 | 2.26023 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 28.6320 | 1.53705 | 0.768523 | − | 0.639822i | \(-0.220992\pi\) | ||||
0.768523 | + | 0.639822i | \(0.220992\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −25.4040 | −1.35985 | −0.679923 | − | 0.733284i | \(-0.737987\pi\) | ||||
−0.679923 | + | 0.733284i | \(0.737987\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 14.2280 | 0.757280 | 0.378640 | − | 0.925544i | \(-0.376392\pi\) | ||||
0.378640 | + | 0.925544i | \(0.376392\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −13.5440 | −0.718841 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −2.45600 | −0.129623 | −0.0648113 | − | 0.997898i | \(-0.520645\pi\) | ||||
−0.0648113 | + | 0.997898i | \(0.520645\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −11.3160 | −0.595579 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −4.77200 | −0.249778 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −10.3160 | −0.538491 | −0.269246 | − | 0.963072i | \(-0.586774\pi\) | ||||
−0.269246 | + | 0.963072i | \(0.586774\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −45.5440 | −2.36453 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 20.0880 | 1.04012 | 0.520059 | − | 0.854130i | \(-0.325910\pi\) | ||||
0.520059 | + | 0.854130i | \(0.325910\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 11.3160 | 0.582804 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 0.316006 | 0.0162321 | 0.00811606 | − | 0.999967i | \(-0.497417\pi\) | ||||
0.00811606 | + | 0.999967i | \(0.497417\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −13.7720 | −0.703716 | −0.351858 | − | 0.936053i | \(-0.614450\pi\) | ||||
−0.351858 | + | 0.936053i | \(0.614450\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 18.0000 | 0.917365 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 29.3160 | 1.48638 | 0.743190 | − | 0.669080i | \(-0.233312\pi\) | ||||
0.743190 | + | 0.669080i | \(0.233312\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 13.7720 | 0.696480 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 5.00000 | 0.251577 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 31.3160 | 1.57171 | 0.785853 | − | 0.618414i | \(-0.212224\pi\) | ||||
0.785853 | + | 0.618414i | \(0.212224\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −1.54400 | −0.0771039 | −0.0385519 | − | 0.999257i | \(-0.512275\pi\) | ||||
−0.0385519 | + | 0.999257i | \(0.512275\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 6.68399 | 0.332953 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 2.91199 | 0.144342 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 20.5440 | 1.01584 | 0.507918 | − | 0.861406i | \(-0.330415\pi\) | ||||
0.507918 | + | 0.861406i | \(0.330415\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 57.2640 | 2.81778 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −6.00000 | −0.294528 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −1.77200 | −0.0865680 | −0.0432840 | − | 0.999063i | \(-0.513782\pi\) | ||||
−0.0432840 | + | 0.999063i | \(0.513782\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −5.22800 | −0.254797 | −0.127399 | − | 0.991852i | \(-0.540663\pi\) | ||||
−0.127399 | + | 0.991852i | \(0.540663\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 1.77200 | 0.0859547 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 3.68399 | 0.178281 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −24.6320 | −1.18648 | −0.593241 | − | 0.805025i | \(-0.702152\pi\) | ||||
−0.593241 | + | 0.805025i | \(0.702152\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 1.08801 | 0.0522863 | 0.0261432 | − | 0.999658i | \(-0.491677\pi\) | ||||
0.0261432 | + | 0.999658i | \(0.491677\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −21.5440 | −1.03059 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 16.0000 | 0.763638 | 0.381819 | − | 0.924237i | \(-0.375298\pi\) | ||||
0.381819 | + | 0.924237i | \(0.375298\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −27.0880 | −1.28699 | −0.643495 | − | 0.765450i | \(-0.722516\pi\) | ||||
−0.643495 | + | 0.765450i | \(0.722516\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −8.00000 | −0.379236 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 27.5440 | 1.29988 | 0.649941 | − | 0.759985i | \(-0.274794\pi\) | ||||
0.649941 | + | 0.759985i | \(0.274794\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 36.0000 | 1.69517 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −14.3160 | −0.671145 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 17.5440 | 0.820674 | 0.410337 | − | 0.911934i | \(-0.365411\pi\) | ||||
0.410337 | + | 0.911934i | \(0.365411\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −35.5440 | −1.65545 | −0.827725 | − | 0.561134i | \(-0.810365\pi\) | ||||
−0.827725 | + | 0.561134i | \(0.810365\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 7.86001 | 0.365286 | 0.182643 | − | 0.983179i | \(-0.441535\pi\) | ||||
0.182643 | + | 0.983179i | \(0.441535\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −32.0000 | −1.48078 | −0.740392 | − | 0.672176i | \(-0.765360\pi\) | ||||
−0.740392 | + | 0.672176i | \(0.765360\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 70.4920 | 3.25502 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 6.68399 | 0.307330 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −2.77200 | −0.127188 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 10.4560 | 0.477747 | 0.238873 | − | 0.971051i | \(-0.423222\pi\) | ||||
0.238873 | + | 0.971051i | \(0.423222\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −2.31601 | −0.105601 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 18.3160 | 0.831687 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −6.77200 | −0.306869 | −0.153434 | − | 0.988159i | \(-0.549033\pi\) | ||||
−0.153434 | + | 0.988159i | \(0.549033\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 33.5440 | 1.51382 | 0.756910 | − | 0.653519i | \(-0.226708\pi\) | ||||
0.756910 | + | 0.653519i | \(0.226708\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 6.68399 | 0.301032 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 64.6320 | 2.89914 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −0.911993 | −0.0408264 | −0.0204132 | − | 0.999792i | \(-0.506498\pi\) | ||||
−0.0204132 | + | 0.999792i | \(0.506498\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 18.8600 | 0.840926 | 0.420463 | − | 0.907310i | \(-0.361868\pi\) | ||||
0.420463 | + | 0.907310i | \(0.361868\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 10.2280 | 0.455140 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −8.22800 | −0.364700 | −0.182350 | − | 0.983234i | \(-0.558370\pi\) | ||||
−0.182350 | + | 0.983234i | \(0.558370\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 22.7720 | 1.00737 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −16.7720 | −0.739063 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −21.7720 | −0.957532 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 26.4560 | 1.15906 | 0.579529 | − | 0.814952i | \(-0.303236\pi\) | ||||
0.579529 | + | 0.814952i | \(0.303236\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 1.45600 | 0.0636663 | 0.0318331 | − | 0.999493i | \(-0.489865\pi\) | ||||
0.0318331 | + | 0.999493i | \(0.489865\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 3.94802 | 0.171978 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 37.4040 | 1.62626 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −28.6320 | −1.24019 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 14.0000 | 0.605273 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −59.4920 | −2.56250 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −16.7720 | −0.721085 | −0.360542 | − | 0.932743i | \(-0.617408\pi\) | ||||
−0.360542 | + | 0.932743i | \(0.617408\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −9.54400 | −0.408820 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −0.544004 | −0.0232599 | −0.0116300 | − | 0.999932i | \(-0.503702\pi\) | ||||
−0.0116300 | + | 0.999932i | \(0.503702\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −10.4560 | −0.445440 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −23.8600 | −1.01463 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −38.1760 | −1.61757 | −0.808785 | − | 0.588105i | \(-0.799874\pi\) | ||||
−0.808785 | + | 0.588105i | \(0.799874\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −5.31601 | −0.224843 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −7.54400 | −0.317942 | −0.158971 | − | 0.987283i | \(-0.550818\pi\) | ||||
−0.158971 | + | 0.987283i | \(0.550818\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −11.3160 | −0.476068 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 19.0880 | 0.800211 | 0.400105 | − | 0.916469i | \(-0.368973\pi\) | ||||
0.400105 | + | 0.916469i | \(0.368973\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −19.2280 | −0.804667 | −0.402333 | − | 0.915493i | \(-0.631801\pi\) | ||||
−0.402333 | + | 0.915493i | \(0.631801\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 7.77200 | 0.324115 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −19.4040 | −0.807800 | −0.403900 | − | 0.914803i | \(-0.632346\pi\) | ||||
−0.403900 | + | 0.914803i | \(0.632346\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 28.6320 | 1.18786 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 36.0000 | 1.49097 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 2.91199 | 0.120191 | 0.0600954 | − | 0.998193i | \(-0.480860\pi\) | ||||
0.0600954 | + | 0.998193i | \(0.480860\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −6.17601 | −0.254478 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −14.8600 | −0.610227 | −0.305114 | − | 0.952316i | \(-0.598694\pi\) | ||||
−0.305114 | + | 0.952316i | \(0.598694\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −8.45600 | −0.346662 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 5.08801 | 0.207890 | 0.103945 | − | 0.994583i | \(-0.466853\pi\) | ||||
0.103945 | + | 0.994583i | \(0.466853\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 20.6840 | 0.843718 | 0.421859 | − | 0.906662i | \(-0.361378\pi\) | ||||
0.421859 | + | 0.906662i | \(0.361378\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −3.22800 | −0.131237 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 39.8600 | 1.61787 | 0.808934 | − | 0.587900i | \(-0.200045\pi\) | ||||
0.808934 | + | 0.587900i | \(0.200045\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 17.3160 | 0.700531 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −2.54400 | −0.102751 | −0.0513757 | − | 0.998679i | \(-0.516361\pi\) | ||||
−0.0513757 | + | 0.998679i | \(0.516361\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −7.31601 | −0.294531 | −0.147266 | − | 0.989097i | \(-0.547047\pi\) | ||||
−0.147266 | + | 0.989097i | \(0.547047\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 5.68399 | 0.228459 | 0.114230 | − | 0.993454i | \(-0.463560\pi\) | ||||
0.114230 | + | 0.993454i | \(0.463560\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 38.1760 | 1.52949 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −1.36799 | −0.0545453 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −2.77200 | −0.110352 | −0.0551758 | − | 0.998477i | \(-0.517572\pi\) | ||||
−0.0551758 | + | 0.998477i | \(0.517572\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 11.5440 | 0.458110 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 47.3160 | 1.87473 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 10.6320 | 0.419939 | 0.209970 | − | 0.977708i | \(-0.432663\pi\) | ||||
0.209970 | + | 0.977708i | \(0.432663\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −9.77200 | −0.385370 | −0.192685 | − | 0.981261i | \(-0.561720\pi\) | ||||
−0.192685 | + | 0.981261i | \(0.561720\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 28.6320 | 1.12564 | 0.562820 | − | 0.826579i | \(-0.309716\pi\) | ||||
0.562820 | + | 0.826579i | \(0.309716\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −45.2640 | −1.77677 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −27.0880 | −1.06004 | −0.530018 | − | 0.847987i | \(-0.677815\pi\) | ||||
−0.530018 | + | 0.847987i | \(0.677815\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −6.22800 | −0.243348 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −40.0000 | −1.55818 | −0.779089 | − | 0.626913i | \(-0.784318\pi\) | ||||
−0.779089 | + | 0.626913i | \(0.784318\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −7.22800 | −0.281137 | −0.140568 | − | 0.990071i | \(-0.544893\pi\) | ||||
−0.140568 | + | 0.990071i | \(0.544893\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 13.2280 | 0.512960 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 29.3160 | 1.13512 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −2.91199 | −0.112416 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 13.4040 | 0.516687 | 0.258343 | − | 0.966053i | \(-0.416823\pi\) | ||||
0.258343 | + | 0.966053i | \(0.416823\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 8.91199 | 0.342516 | 0.171258 | − | 0.985226i | \(-0.445217\pi\) | ||||
0.171258 | + | 0.985226i | \(0.445217\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −87.4040 | −3.35426 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 10.4560 | 0.400088 | 0.200044 | − | 0.979787i | \(-0.435892\pi\) | ||||
0.200044 | + | 0.979787i | \(0.435892\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 21.0880 | 0.805731 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −28.6320 | −1.09079 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 38.6320 | 1.46963 | 0.734815 | − | 0.678267i | \(-0.237269\pi\) | ||||
0.734815 | + | 0.678267i | \(0.237269\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 12.7720 | 0.484470 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −16.9120 | −0.640587 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 19.7720 | 0.746778 | 0.373389 | − | 0.927675i | \(-0.378196\pi\) | ||||
0.373389 | + | 0.927675i | \(0.378196\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 2.13999 | 0.0807113 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −48.8080 | −1.83561 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 49.8600 | 1.87253 | 0.936266 | − | 0.351292i | \(-0.114258\pi\) | ||||
0.936266 | + | 0.351292i | \(0.114258\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 17.3160 | 0.648490 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 11.3160 | 0.423195 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −18.0000 | −0.671287 | −0.335643 | − | 0.941989i | \(-0.608954\pi\) | ||||
−0.335643 | + | 0.941989i | \(0.608954\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 80.0360 | 2.98070 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 3.77200 | 0.140089 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −0.911993 | −0.0338239 | −0.0169120 | − | 0.999857i | \(-0.505384\pi\) | ||||
−0.0169120 | + | 0.999857i | \(0.505384\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −3.13999 | −0.116137 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −6.91199 | −0.255300 | −0.127650 | − | 0.991819i | \(-0.540743\pi\) | ||||
−0.127650 | + | 0.991819i | \(0.540743\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −55.7200 | −2.05247 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −35.0880 | −1.29073 | −0.645367 | − | 0.763873i | \(-0.723295\pi\) | ||||
−0.645367 | + | 0.763873i | \(0.723295\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −44.4040 | −1.62903 | −0.814513 | − | 0.580146i | \(-0.802996\pi\) | ||||
−0.814513 | + | 0.580146i | \(0.802996\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 9.77200 | 0.358018 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −66.8080 | −2.44111 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −39.1760 | −1.42955 | −0.714777 | − | 0.699353i | \(-0.753472\pi\) | ||||
−0.714777 | + | 0.699353i | \(0.753472\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 24.0880 | 0.876652 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −46.7200 | −1.69807 | −0.849034 | − | 0.528338i | \(-0.822815\pi\) | ||||
−0.849034 | + | 0.528338i | \(0.822815\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 29.0880 | 1.05444 | 0.527220 | − | 0.849729i | \(-0.323234\pi\) | ||||
0.527220 | + | 0.849729i | \(0.323234\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 45.5440 | 1.64880 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 36.0000 | 1.29988 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 48.2640 | 1.74045 | 0.870223 | − | 0.492659i | \(-0.163975\pi\) | ||||
0.870223 | + | 0.492659i | \(0.163975\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −10.9120 | −0.392477 | −0.196239 | − | 0.980556i | \(-0.562873\pi\) | ||||
−0.196239 | + | 0.980556i | \(0.562873\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 2.22800 | 0.0800321 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 26.4560 | 0.947884 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −51.0880 | −1.82807 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −7.77200 | −0.277395 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 39.1760 | 1.39647 | 0.698237 | − | 0.715867i | \(-0.253968\pi\) | ||||
0.698237 | + | 0.715867i | \(0.253968\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 54.0000 | 1.92002 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 2.31601 | 0.0822438 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 46.1760 | 1.63564 | 0.817819 | − | 0.575475i | \(-0.195183\pi\) | ||||
0.817819 | + | 0.575475i | \(0.195183\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 10.2280 | 0.361841 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −18.0000 | −0.635206 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −37.0880 | −1.30718 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −24.0000 | −0.843795 | −0.421898 | − | 0.906644i | \(-0.638636\pi\) | ||||
−0.421898 | + | 0.906644i | \(0.638636\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −31.5440 | −1.10766 | −0.553830 | − | 0.832630i | \(-0.686834\pi\) | ||||
−0.553830 | + | 0.832630i | \(0.686834\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 8.54400 | 0.299283 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 4.91199 | 0.171849 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −23.5440 | −0.821691 | −0.410846 | − | 0.911705i | \(-0.634767\pi\) | ||||
−0.410846 | + | 0.911705i | \(0.634767\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −39.4040 | −1.37354 | −0.686769 | − | 0.726876i | \(-0.740972\pi\) | ||||
−0.686769 | + | 0.726876i | \(0.740972\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −3.54400 | −0.123237 | −0.0616185 | − | 0.998100i | \(-0.519626\pi\) | ||||
−0.0616185 | + | 0.998100i | \(0.519626\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 38.7720 | 1.34661 | 0.673304 | − | 0.739366i | \(-0.264875\pi\) | ||||
0.673304 | + | 0.739366i | \(0.264875\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 27.9480 | 0.968341 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 23.0880 | 0.798993 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 54.6320 | 1.88611 | 0.943053 | − | 0.332642i | \(-0.107940\pi\) | ||||
0.943053 | + | 0.332642i | \(0.107940\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −14.7720 | −0.509379 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 4.00000 | 0.137604 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 15.4040 | 0.529288 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −6.00000 | −0.205677 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −15.4560 | −0.529203 | −0.264602 | − | 0.964358i | \(-0.585240\pi\) | ||||
−0.264602 | + | 0.964358i | \(0.585240\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 41.0880 | 1.40354 | 0.701770 | − | 0.712404i | \(-0.252394\pi\) | ||||
0.701770 | + | 0.712404i | \(0.252394\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −24.7720 | −0.845210 | −0.422605 | − | 0.906314i | \(-0.638884\pi\) | ||||
−0.422605 | + | 0.906314i | \(0.638884\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −25.3160 | −0.861767 | −0.430883 | − | 0.902408i | \(-0.641798\pi\) | ||||
−0.430883 | + | 0.902408i | \(0.641798\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −7.54400 | −0.256504 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 18.8600 | 0.639782 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 44.3160 | 1.50159 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −4.77200 | −0.161323 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −23.0000 | −0.776655 | −0.388327 | − | 0.921521i | \(-0.626947\pi\) | ||||
−0.388327 | + | 0.921521i | \(0.626947\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −6.91199 | −0.232871 | −0.116435 | − | 0.993198i | \(-0.537147\pi\) | ||||
−0.116435 | + | 0.993198i | \(0.537147\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 12.3160 | 0.414467 | 0.207233 | − | 0.978292i | \(-0.433554\pi\) | ||||
0.207233 | + | 0.978292i | \(0.433554\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 6.68399 | 0.224427 | 0.112213 | − | 0.993684i | \(-0.464206\pi\) | ||||
0.112213 | + | 0.993684i | \(0.464206\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −55.0880 | −1.84759 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −16.0000 | −0.535420 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −9.54400 | −0.319021 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 8.40401 | 0.280290 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −16.9120 | −0.563420 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 24.3160 | 0.808291 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −35.0000 | −1.16216 | −0.581078 | − | 0.813848i | \(-0.697369\pi\) | ||||
−0.581078 | + | 0.813848i | \(0.697369\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −38.1760 | −1.26483 | −0.632414 | − | 0.774631i | \(-0.717936\pi\) | ||||
−0.632414 | + | 0.774631i | \(0.717936\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −22.6320 | −0.749010 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 29.7200 | 0.981441 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 4.86001 | 0.160317 | 0.0801585 | − | 0.996782i | \(-0.474457\pi\) | ||||
0.0801585 | + | 0.996782i | \(0.474457\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 40.6320 | 1.33742 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −0.772002 | −0.0253833 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −16.6320 | −0.545679 | −0.272839 | − | 0.962060i | \(-0.587963\pi\) | ||||
−0.272839 | + | 0.962060i | \(0.587963\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −43.7200 | −1.43287 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 6.68399 | 0.218590 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −16.7720 | −0.547917 | −0.273959 | − | 0.961741i | \(-0.588333\pi\) | ||||
−0.273959 | + | 0.961741i | \(0.588333\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −22.4040 | −0.730350 | −0.365175 | − | 0.930939i | \(-0.618991\pi\) | ||||
−0.365175 | + | 0.930939i | \(0.618991\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −74.1760 | −2.41550 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 8.45600 | 0.274783 | 0.137391 | − | 0.990517i | \(-0.456128\pi\) | ||||
0.137391 | + | 0.990517i | \(0.456128\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 14.3160 | 0.464717 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −48.8600 | −1.58273 | −0.791365 | − | 0.611343i | \(-0.790629\pi\) | ||||
−0.791365 | + | 0.611343i | \(0.790629\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −3.54400 | −0.114681 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −100.632 | −3.24958 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −26.0360 | −0.839872 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 12.7720 | 0.411145 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −4.77200 | −0.153457 | −0.0767286 | − | 0.997052i | \(-0.524448\pi\) | ||||
−0.0767286 | + | 0.997052i | \(0.524448\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 37.7720 | 1.21216 | 0.606081 | − | 0.795403i | \(-0.292741\pi\) | ||||
0.606081 | + | 0.795403i | \(0.292741\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −60.9480 | −1.95390 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 0.227998 | 0.00729431 | 0.00364715 | − | 0.999993i | \(-0.498839\pi\) | ||||
0.00364715 | + | 0.999993i | \(0.498839\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −30.1760 | −0.964430 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −14.4040 | −0.459417 | −0.229708 | − | 0.973260i | \(-0.573777\pi\) | ||||
−0.229708 | + | 0.973260i | \(0.573777\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 20.0000 | 0.637253 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −13.7720 | −0.437924 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 8.08801 | 0.256924 | 0.128462 | − | 0.991714i | \(-0.458996\pi\) | ||||
0.128462 | + | 0.991714i | \(0.458996\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 15.0000 | 0.475532 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 12.6840 | 0.401706 | 0.200853 | − | 0.979621i | \(-0.435629\pi\) | ||||
0.200853 | + | 0.979621i | \(0.435629\pi\) | |||||||
\(998\) | 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 | 1080.2.a.m.1.2 | ✓ | 2 | |
3.2 | odd | 2 | 1080.2.a.n.1.2 | yes | 2 | ||
4.3 | odd | 2 | 2160.2.a.z.1.1 | 2 | |||
5.2 | odd | 4 | 5400.2.f.be.649.4 | 4 | |||
5.3 | odd | 4 | 5400.2.f.be.649.1 | 4 | |||
5.4 | even | 2 | 5400.2.a.cb.1.1 | 2 | |||
8.3 | odd | 2 | 8640.2.a.db.1.1 | 2 | |||
8.5 | even | 2 | 8640.2.a.de.1.2 | 2 | |||
9.2 | odd | 6 | 3240.2.q.z.1081.1 | 4 | |||
9.4 | even | 3 | 3240.2.q.bc.2161.1 | 4 | |||
9.5 | odd | 6 | 3240.2.q.z.2161.1 | 4 | |||
9.7 | even | 3 | 3240.2.q.bc.1081.1 | 4 | |||
12.11 | even | 2 | 2160.2.a.bb.1.1 | 2 | |||
15.2 | even | 4 | 5400.2.f.bd.649.4 | 4 | |||
15.8 | even | 4 | 5400.2.f.bd.649.1 | 4 | |||
15.14 | odd | 2 | 5400.2.a.ca.1.1 | 2 | |||
24.5 | odd | 2 | 8640.2.a.cq.1.2 | 2 | |||
24.11 | even | 2 | 8640.2.a.cn.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1080.2.a.m.1.2 | ✓ | 2 | 1.1 | even | 1 | trivial | |
1080.2.a.n.1.2 | yes | 2 | 3.2 | odd | 2 | ||
2160.2.a.z.1.1 | 2 | 4.3 | odd | 2 | |||
2160.2.a.bb.1.1 | 2 | 12.11 | even | 2 | |||
3240.2.q.z.1081.1 | 4 | 9.2 | odd | 6 | |||
3240.2.q.z.2161.1 | 4 | 9.5 | odd | 6 | |||
3240.2.q.bc.1081.1 | 4 | 9.7 | even | 3 | |||
3240.2.q.bc.2161.1 | 4 | 9.4 | even | 3 | |||
5400.2.a.ca.1.1 | 2 | 15.14 | odd | 2 | |||
5400.2.a.cb.1.1 | 2 | 5.4 | even | 2 | |||
5400.2.f.bd.649.1 | 4 | 15.8 | even | 4 | |||
5400.2.f.bd.649.4 | 4 | 15.2 | even | 4 | |||
5400.2.f.be.649.1 | 4 | 5.3 | odd | 4 | |||
5400.2.f.be.649.4 | 4 | 5.2 | odd | 4 | |||
8640.2.a.cn.1.1 | 2 | 24.11 | even | 2 | |||
8640.2.a.cq.1.2 | 2 | 24.5 | odd | 2 | |||
8640.2.a.db.1.1 | 2 | 8.3 | odd | 2 | |||
8640.2.a.de.1.2 | 2 | 8.5 | even | 2 |