Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [896,2,Mod(1,896)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(896, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("896.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 896 = 2^{7} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 896.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: | \(7.15459602111\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.316.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 4x + 2 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(0.470683\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 896.1 |
$q$-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 | ||||||||
\(3\) | −2.24914 | −1.29854 | −0.649271 | − | 0.760557i | \(-0.724926\pi\) | ||||
−0.649271 | + | 0.760557i | \(0.724926\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −3.30777 | −1.47928 | −0.739641 | − | 0.673002i | \(-0.765005\pi\) | ||||
−0.739641 | + | 0.673002i | \(0.765005\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 2.05863 | 0.686211 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.941367 | 0.283833 | 0.141916 | − | 0.989879i | \(-0.454674\pi\) | ||||
0.141916 | + | 0.989879i | \(0.454674\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −5.19051 | −1.43959 | −0.719794 | − | 0.694188i | \(-0.755764\pi\) | ||||
−0.719794 | + | 0.694188i | \(0.755764\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 7.43965 | 1.92091 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −6.49828 | −1.57606 | −0.788032 | − | 0.615634i | \(-0.788900\pi\) | ||||
−0.788032 | + | 0.615634i | \(0.788900\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.75086 | 0.401675 | 0.200837 | − | 0.979625i | \(-0.435634\pi\) | ||||
0.200837 | + | 0.979625i | \(0.435634\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −2.24914 | −0.490803 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −5.55691 | −1.15870 | −0.579348 | − | 0.815080i | \(-0.696693\pi\) | ||||
−0.579348 | + | 0.815080i | \(0.696693\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 5.94137 | 1.18827 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 2.11727 | 0.407468 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.49828 | 0.463919 | 0.231960 | − | 0.972725i | \(-0.425486\pi\) | ||||
0.231960 | + | 0.972725i | \(0.425486\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 6.61555 | 1.18819 | 0.594094 | − | 0.804396i | \(-0.297511\pi\) | ||||
0.594094 | + | 0.804396i | \(0.297511\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −2.11727 | −0.368569 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −3.30777 | −0.559116 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 4.61555 | 0.758791 | 0.379396 | − | 0.925235i | \(-0.376132\pi\) | ||||
0.379396 | + | 0.925235i | \(0.376132\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 11.6742 | 1.86936 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 10.4983 | 1.63956 | 0.819778 | − | 0.572681i | \(-0.194097\pi\) | ||||
0.819778 | + | 0.572681i | \(0.194097\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 12.0552 | 1.83840 | 0.919200 | − | 0.393791i | \(-0.128837\pi\) | ||||
0.919200 | + | 0.393791i | \(0.128837\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −6.80949 | −1.01510 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −4.49828 | −0.656142 | −0.328071 | − | 0.944653i | \(-0.606398\pi\) | ||||
−0.328071 | + | 0.944653i | \(0.606398\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 14.6155 | 2.04659 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 2.00000 | 0.274721 | 0.137361 | − | 0.990521i | \(-0.456138\pi\) | ||||
0.137361 | + | 0.990521i | \(0.456138\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −3.11383 | −0.419869 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −3.93793 | −0.521591 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 12.6302 | 1.64431 | 0.822153 | − | 0.569266i | \(-0.192773\pi\) | ||||
0.822153 | + | 0.569266i | \(0.192773\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −11.3078 | −1.44781 | −0.723906 | − | 0.689899i | \(-0.757655\pi\) | ||||
−0.723906 | + | 0.689899i | \(0.757655\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 2.05863 | 0.259363 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 17.1690 | 2.12956 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −0.443086 | −0.0541315 | −0.0270658 | − | 0.999634i | \(-0.508616\pi\) | ||||
−0.0270658 | + | 0.999634i | \(0.508616\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 12.4983 | 1.50462 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −0.117266 | −0.0137250 | −0.00686249 | − | 0.999976i | \(-0.502184\pi\) | ||||
−0.00686249 | + | 0.999976i | \(0.502184\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −13.3630 | −1.54302 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0.941367 | 0.107279 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −7.11383 | −0.800368 | −0.400184 | − | 0.916435i | \(-0.631054\pi\) | ||||
−0.400184 | + | 0.916435i | \(0.631054\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −10.9379 | −1.21533 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −12.8647 | −1.41208 | −0.706041 | − | 0.708170i | \(-0.749521\pi\) | ||||
−0.706041 | + | 0.708170i | \(0.749521\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 21.4948 | 2.33144 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −5.61899 | −0.602418 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 10.9966 | 1.16563 | 0.582817 | − | 0.812604i | \(-0.301951\pi\) | ||||
0.582817 | + | 0.812604i | \(0.301951\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −5.19051 | −0.544113 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −14.8793 | −1.54291 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −5.79145 | −0.594190 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 13.6121 | 1.38210 | 0.691050 | − | 0.722807i | \(-0.257148\pi\) | ||||
0.691050 | + | 0.722807i | \(0.257148\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1.93793 | 0.194769 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −15.8061 | −1.57276 | −0.786381 | − | 0.617742i | \(-0.788047\pi\) | ||||
−0.786381 | + | 0.617742i | \(0.788047\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 6.61555 | 0.651849 | 0.325925 | − | 0.945396i | \(-0.394324\pi\) | ||||
0.325925 | + | 0.945396i | \(0.394324\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 7.43965 | 0.726035 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −5.43965 | −0.525871 | −0.262935 | − | 0.964813i | \(-0.584691\pi\) | ||||
−0.262935 | + | 0.964813i | \(0.584691\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 0.381015 | 0.0364946 | 0.0182473 | − | 0.999834i | \(-0.494191\pi\) | ||||
0.0182473 | + | 0.999834i | \(0.494191\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −10.3810 | −0.985322 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −8.05520 | −0.757769 | −0.378885 | − | 0.925444i | \(-0.623692\pi\) | ||||
−0.378885 | + | 0.925444i | \(0.623692\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 18.3810 | 1.71404 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −10.6854 | −0.987861 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −6.49828 | −0.595696 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.1138 | −0.919439 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −23.6121 | −2.12903 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −3.11383 | −0.278509 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 11.6742 | 1.03592 | 0.517958 | − | 0.855406i | \(-0.326692\pi\) | ||||
0.517958 | + | 0.855406i | \(0.326692\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −27.1138 | −2.38724 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0.366407 | 0.0320131 | 0.0160066 | − | 0.999872i | \(-0.494905\pi\) | ||||
0.0160066 | + | 0.999872i | \(0.494905\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.75086 | 0.151819 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −7.00344 | −0.602760 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −3.88273 | −0.331724 | −0.165862 | − | 0.986149i | \(-0.553041\pi\) | ||||
−0.165862 | + | 0.986149i | \(0.553041\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 14.2491 | 1.20860 | 0.604298 | − | 0.796758i | \(-0.293454\pi\) | ||||
0.604298 | + | 0.796758i | \(0.293454\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 10.1173 | 0.852028 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −4.88617 | −0.408602 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −8.26375 | −0.686267 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −2.24914 | −0.185506 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 8.87930 | 0.727420 | 0.363710 | − | 0.931512i | \(-0.381510\pi\) | ||||
0.363710 | + | 0.931512i | \(0.381510\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 22.5535 | 1.83538 | 0.917688 | − | 0.397302i | \(-0.130053\pi\) | ||||
0.917688 | + | 0.397302i | \(0.130053\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −13.3776 | −1.08151 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −21.8827 | −1.75766 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 12.8026 | 1.02176 | 0.510880 | − | 0.859652i | \(-0.329320\pi\) | ||||
0.510880 | + | 0.859652i | \(0.329320\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −4.49828 | −0.356737 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −5.55691 | −0.437946 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −9.93793 | −0.778399 | −0.389199 | − | 0.921154i | \(-0.627248\pi\) | ||||
−0.389199 | + | 0.921154i | \(0.627248\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 7.00344 | 0.545217 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 12.4983 | 0.967146 | 0.483573 | − | 0.875304i | \(-0.339339\pi\) | ||||
0.483573 | + | 0.875304i | \(0.339339\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 13.9414 | 1.07241 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 3.60438 | 0.275634 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 16.0406 | 1.21954 | 0.609772 | − | 0.792577i | \(-0.291261\pi\) | ||||
0.609772 | + | 0.792577i | \(0.291261\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 5.94137 | 0.449125 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −28.4070 | −2.13520 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 12.7880 | 0.955821 | 0.477910 | − | 0.878409i | \(-0.341394\pi\) | ||||
0.477910 | + | 0.878409i | \(0.341394\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −9.68879 | −0.720162 | −0.360081 | − | 0.932921i | \(-0.617251\pi\) | ||||
−0.360081 | + | 0.932921i | \(0.617251\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 25.4328 | 1.88004 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −15.2672 | −1.12247 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −6.11727 | −0.447339 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 2.11727 | 0.154008 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −9.88273 | −0.715090 | −0.357545 | − | 0.933896i | \(-0.616386\pi\) | ||||
−0.357545 | + | 0.933896i | \(0.616386\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 8.70683 | 0.626732 | 0.313366 | − | 0.949632i | \(-0.398543\pi\) | ||||
0.313366 | + | 0.949632i | \(0.398543\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −38.6155 | −2.76532 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 10.0000 | 0.712470 | 0.356235 | − | 0.934396i | \(-0.384060\pi\) | ||||
0.356235 | + | 0.934396i | \(0.384060\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −23.6121 | −1.67382 | −0.836909 | − | 0.547342i | \(-0.815640\pi\) | ||||
−0.836909 | + | 0.547342i | \(0.815640\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0.996562 | 0.0702921 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 2.49828 | 0.175345 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −34.7259 | −2.42536 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −11.4396 | −0.795110 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 1.64820 | 0.114008 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2.32582 | 0.160116 | 0.0800580 | − | 0.996790i | \(-0.474489\pi\) | ||||
0.0800580 | + | 0.996790i | \(0.474489\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −39.8759 | −2.71951 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 6.61555 | 0.449093 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0.263748 | 0.0178225 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 33.7294 | 2.26888 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 6.87930 | 0.460672 | 0.230336 | − | 0.973111i | \(-0.426018\pi\) | ||||
0.230336 | + | 0.973111i | \(0.426018\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 12.2311 | 0.815406 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −14.2491 | −0.945749 | −0.472874 | − | 0.881130i | \(-0.656784\pi\) | ||||
−0.472874 | + | 0.881130i | \(0.656784\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 3.80605 | 0.251511 | 0.125756 | − | 0.992061i | \(-0.459864\pi\) | ||||
0.125756 | + | 0.992061i | \(0.459864\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −2.11727 | −0.139306 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −24.8793 | −1.62990 | −0.814948 | − | 0.579533i | \(-0.803235\pi\) | ||||
−0.814948 | + | 0.579533i | \(0.803235\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 14.8793 | 0.970618 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 16.0000 | 1.03931 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 17.5569 | 1.13566 | 0.567831 | − | 0.823145i | \(-0.307783\pi\) | ||||
0.567831 | + | 0.823145i | \(0.307783\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 0.850080 | 0.0547585 | 0.0273792 | − | 0.999625i | \(-0.491284\pi\) | ||||
0.0273792 | + | 0.999625i | \(0.491284\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 18.2491 | 1.17068 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −3.30777 | −0.211326 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −9.08785 | −0.578246 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 28.9345 | 1.83365 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −8.36641 | −0.528083 | −0.264041 | − | 0.964511i | \(-0.585056\pi\) | ||||
−0.264041 | + | 0.964511i | \(0.585056\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −5.23109 | −0.328876 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −48.3449 | −3.02748 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −14.9966 | −0.935460 | −0.467730 | − | 0.883871i | \(-0.654928\pi\) | ||||
−0.467730 | + | 0.883871i | \(0.654928\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 4.61555 | 0.286796 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 5.14304 | 0.318346 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −14.2277 | −0.877315 | −0.438657 | − | 0.898654i | \(-0.644546\pi\) | ||||
−0.438657 | + | 0.898654i | \(0.644546\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −6.61555 | −0.406390 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −24.7328 | −1.51362 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −4.19395 | −0.255709 | −0.127855 | − | 0.991793i | \(-0.540809\pi\) | ||||
−0.127855 | + | 0.991793i | \(0.540809\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1.64820 | 0.100121 | 0.0500605 | − | 0.998746i | \(-0.484059\pi\) | ||||
0.0500605 | + | 0.998746i | \(0.484059\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 11.6742 | 0.706554 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 5.59301 | 0.337271 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −8.11727 | −0.487719 | −0.243860 | − | 0.969811i | \(-0.578414\pi\) | ||||
−0.243860 | + | 0.969811i | \(0.578414\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 13.6190 | 0.815347 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −14.2345 | −0.849161 | −0.424581 | − | 0.905390i | \(-0.639578\pi\) | ||||
−0.424581 | + | 0.905390i | \(0.639578\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 31.4802 | 1.87131 | 0.935653 | − | 0.352922i | \(-0.114812\pi\) | ||||
0.935653 | + | 0.352922i | \(0.114812\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 13.0258 | 0.771580 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 10.4983 | 0.619694 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 25.2277 | 1.48398 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −30.6155 | −1.79472 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 1.19051 | 0.0695502 | 0.0347751 | − | 0.999395i | \(-0.488929\pi\) | ||||
0.0347751 | + | 0.999395i | \(0.488929\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −41.7777 | −2.43239 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 1.99312 | 0.115653 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 28.8432 | 1.66805 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 12.0552 | 0.694850 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 35.5500 | 2.04230 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 37.4036 | 2.14172 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 4.60094 | 0.262589 | 0.131295 | − | 0.991343i | \(-0.458087\pi\) | ||||
0.131295 | + | 0.991343i | \(0.458087\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −14.8793 | −0.846454 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 13.2311 | 0.750267 | 0.375133 | − | 0.926971i | \(-0.377597\pi\) | ||||
0.375133 | + | 0.926971i | \(0.377597\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 10.4983 | 0.593398 | 0.296699 | − | 0.954971i | \(-0.404114\pi\) | ||||
0.296699 | + | 0.954971i | \(0.404114\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −6.80949 | −0.383671 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 9.00344 | 0.505683 | 0.252842 | − | 0.967508i | \(-0.418635\pi\) | ||||
0.252842 | + | 0.967508i | \(0.418635\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 2.35180 | 0.131675 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 12.2345 | 0.682865 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −11.3776 | −0.633065 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −30.8387 | −1.71062 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −0.856956 | −0.0473898 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −4.49828 | −0.247998 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −10.1725 | −0.559129 | −0.279565 | − | 0.960127i | \(-0.590190\pi\) | ||||
−0.279565 | + | 0.960127i | \(0.590190\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 9.50172 | 0.520691 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 1.46563 | 0.0800758 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 23.8207 | 1.29759 | 0.648797 | − | 0.760961i | \(-0.275272\pi\) | ||||
0.648797 | + | 0.760961i | \(0.275272\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 18.1173 | 0.983995 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 6.22766 | 0.337247 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −41.3415 | −2.22575 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 17.2863 | 0.927977 | 0.463988 | − | 0.885841i | \(-0.346418\pi\) | ||||
0.463988 | + | 0.885841i | \(0.346418\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −16.6922 | −0.893514 | −0.446757 | − | 0.894655i | \(-0.647421\pi\) | ||||
−0.446757 | + | 0.894655i | \(0.647421\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −10.9897 | −0.586586 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −14.3449 | −0.763503 | −0.381752 | − | 0.924265i | \(-0.624679\pi\) | ||||
−0.381752 | + | 0.924265i | \(0.624679\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 14.6155 | 0.773537 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 3.43965 | 0.181538 | 0.0907688 | − | 0.995872i | \(-0.471068\pi\) | ||||
0.0907688 | + | 0.995872i | \(0.471068\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −15.9345 | −0.838657 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 22.7474 | 1.19393 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0.387890 | 0.0203031 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −10.1173 | −0.528117 | −0.264059 | − | 0.964507i | \(-0.585061\pi\) | ||||
−0.264059 | + | 0.964507i | \(0.585061\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 21.6121 | 1.12508 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 2.00000 | 0.103835 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −20.8793 | −1.08109 | −0.540544 | − | 0.841315i | \(-0.681782\pi\) | ||||
−0.540544 | + | 0.841315i | \(0.681782\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 7.00344 | 0.361656 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −12.9673 | −0.667852 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −13.9379 | −0.715943 | −0.357972 | − | 0.933732i | \(-0.616532\pi\) | ||||
−0.357972 | + | 0.933732i | \(0.616532\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −26.2569 | −1.34518 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 22.4914 | 1.14926 | 0.574629 | − | 0.818414i | \(-0.305147\pi\) | ||||
0.574629 | + | 0.818414i | \(0.305147\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −3.11383 | −0.158695 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 24.8172 | 1.26153 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 17.8466 | 0.904861 | 0.452430 | − | 0.891800i | \(-0.350557\pi\) | ||||
0.452430 | + | 0.891800i | \(0.350557\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 36.1104 | 1.82618 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −0.824101 | −0.0415704 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 23.5309 | 1.18397 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −0.692226 | −0.0347418 | −0.0173709 | − | 0.999849i | \(-0.505530\pi\) | ||||
−0.0173709 | + | 0.999849i | \(0.505530\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −3.93793 | −0.197143 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −2.40699 | −0.120200 | −0.0600998 | − | 0.998192i | \(-0.519142\pi\) | ||||
−0.0600998 | + | 0.998192i | \(0.519142\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −34.3380 | −1.71050 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 36.1802 | 1.79781 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 4.34492 | 0.215370 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 21.6121 | 1.06865 | 0.534325 | − | 0.845279i | \(-0.320566\pi\) | ||||
0.534325 | + | 0.845279i | \(0.320566\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 8.73281 | 0.430758 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 12.6302 | 0.621489 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 42.5535 | 2.08887 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −32.0483 | −1.56941 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −9.25258 | −0.452018 | −0.226009 | − | 0.974125i | \(-0.572568\pi\) | ||||
−0.226009 | + | 0.974125i | \(0.572568\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −14.3449 | −0.699129 | −0.349564 | − | 0.936912i | \(-0.613670\pi\) | ||||
−0.349564 | + | 0.936912i | \(0.613670\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −9.26031 | −0.450252 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −38.6087 | −1.87280 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −11.3078 | −0.547222 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 10.9897 | 0.530587 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 24.4362 | 1.17705 | 0.588525 | − | 0.808479i | \(-0.299709\pi\) | ||||
0.588525 | + | 0.808479i | \(0.299709\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −16.4914 | −0.792526 | −0.396263 | − | 0.918137i | \(-0.629693\pi\) | ||||
−0.396263 | + | 0.918137i | \(0.629693\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 18.5863 | 0.891146 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −9.72938 | −0.465419 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 38.8793 | 1.85561 | 0.927804 | − | 0.373069i | \(-0.121694\pi\) | ||||
0.927804 | + | 0.373069i | \(0.121694\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 2.05863 | 0.0980302 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −15.0878 | −0.716845 | −0.358423 | − | 0.933559i | \(-0.616685\pi\) | ||||
−0.358423 | + | 0.933559i | \(0.616685\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −36.3741 | −1.72430 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −19.9708 | −0.944586 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 28.8793 | 1.36290 | 0.681449 | − | 0.731865i | \(-0.261350\pi\) | ||||
0.681449 | + | 0.731865i | \(0.261350\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 9.88273 | 0.465360 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −50.7259 | −2.38331 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 17.1690 | 0.804896 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 24.2897 | 1.13623 | 0.568113 | − | 0.822951i | \(-0.307674\pi\) | ||||
0.568113 | + | 0.822951i | \(0.307674\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −13.7586 | −0.642196 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 10.0767 | 0.469318 | 0.234659 | − | 0.972078i | \(-0.424603\pi\) | ||||
0.234659 | + | 0.972078i | \(0.424603\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 34.8793 | 1.62098 | 0.810489 | − | 0.585754i | \(-0.199201\pi\) | ||||
0.810489 | + | 0.585754i | \(0.199201\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 49.2173 | 2.28240 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 26.7474 | 1.23772 | 0.618862 | − | 0.785500i | \(-0.287594\pi\) | ||||
0.618862 | + | 0.785500i | \(0.287594\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −0.443086 | −0.0204598 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −28.7949 | −1.32680 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 11.3484 | 0.521798 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 10.4025 | 0.477299 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 4.11727 | 0.188517 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 1.38445 | 0.0632573 | 0.0316286 | − | 0.999500i | \(-0.489931\pi\) | ||||
0.0316286 | + | 0.999500i | \(0.489931\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −23.9570 | −1.09235 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 12.4983 | 0.568691 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −45.0258 | −2.04452 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 6.20855 | 0.281336 | 0.140668 | − | 0.990057i | \(-0.455075\pi\) | ||||
0.140668 | + | 0.990057i | \(0.455075\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 22.3518 | 1.01078 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −30.7811 | −1.38913 | −0.694567 | − | 0.719428i | \(-0.744404\pi\) | ||||
−0.694567 | + | 0.719428i | \(0.744404\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −16.2345 | −0.731167 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −6.41023 | −0.288118 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 33.6742 | 1.50746 | 0.753732 | − | 0.657182i | \(-0.228252\pi\) | ||||
0.753732 | + | 0.657182i | \(0.228252\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −28.1104 | −1.25588 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 29.8827 | 1.33241 | 0.666203 | − | 0.745771i | \(-0.267919\pi\) | ||||
0.666203 | + | 0.745771i | \(0.267919\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 52.2829 | 2.32656 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −31.3561 | −1.39257 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 3.54231 | 0.157010 | 0.0785050 | − | 0.996914i | \(-0.474985\pi\) | ||||
0.0785050 | + | 0.996914i | \(0.474985\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −0.117266 | −0.00518756 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 3.70704 | 0.163670 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −21.8827 | −0.964268 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −4.23453 | −0.186235 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −36.0775 | −1.58363 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −38.8432 | −1.70175 | −0.850876 | − | 0.525367i | \(-0.823928\pi\) | ||||
−0.850876 | + | 0.525367i | \(0.823928\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 3.63359 | 0.158886 | 0.0794430 | − | 0.996839i | \(-0.474686\pi\) | ||||
0.0794430 | + | 0.996839i | \(0.474686\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −13.3630 | −0.583208 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −42.9897 | −1.87266 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 7.87930 | 0.342578 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 26.0009 | 1.12834 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −54.4914 | −2.36028 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 17.9931 | 0.777911 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −28.7620 | −1.24117 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0.941367 | 0.0405475 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 22.1104 | 0.950600 | 0.475300 | − | 0.879824i | \(-0.342340\pi\) | ||||
0.475300 | + | 0.879824i | \(0.342340\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 21.7914 | 0.935160 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −1.26031 | −0.0539858 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −39.1690 | −1.67475 | −0.837373 | − | 0.546632i | \(-0.815910\pi\) | ||||
−0.837373 | + | 0.546632i | \(0.815910\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −23.2786 | −0.993505 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 4.37414 | 0.186345 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −7.11383 | −0.302511 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 34.3380 | 1.45757 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 13.7655 | 0.583262 | 0.291631 | − | 0.956531i | \(-0.405802\pi\) | ||||
0.291631 | + | 0.956531i | \(0.405802\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −62.5726 | −2.64654 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 13.7586 | 0.580888 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −21.6267 | −0.911457 | −0.455729 | − | 0.890119i | \(-0.650621\pi\) | ||||
−0.455729 | + | 0.890119i | \(0.650621\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 26.6448 | 1.12095 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −10.9379 | −0.459350 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 7.16902 | 0.300541 | 0.150271 | − | 0.988645i | \(-0.451986\pi\) | ||||
0.150271 | + | 0.988645i | \(0.451986\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 36.0552 | 1.50886 | 0.754431 | − | 0.656379i | \(-0.227913\pi\) | ||||
0.754431 | + | 0.656379i | \(0.227913\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 22.2277 | 0.928574 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −33.0157 | −1.37685 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −34.1104 | −1.42003 | −0.710017 | − | 0.704184i | \(-0.751313\pi\) | ||||
−0.710017 | + | 0.704184i | \(0.751313\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −19.5829 | −0.813837 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −12.8647 | −0.533717 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1.88273 | 0.0779749 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 35.3447 | 1.46132 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −2.74742 | −0.113398 | −0.0566991 | − | 0.998391i | \(-0.518058\pi\) | ||||
−0.0566991 | + | 0.998391i | \(0.518058\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 11.5829 | 0.477265 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −22.4914 | −0.925173 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 32.2277 | 1.32343 | 0.661716 | − | 0.749755i | \(-0.269829\pi\) | ||||
0.661716 | + | 0.749755i | \(0.269829\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 21.4948 | 0.881203 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 53.1070 | 2.17352 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −0.469065 | −0.0191655 | −0.00958274 | − | 0.999954i | \(-0.503050\pi\) | ||||
−0.00958274 | + | 0.999954i | \(0.503050\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 37.4588 | 1.52797 | 0.763987 | − | 0.645231i | \(-0.223239\pi\) | ||||
0.763987 | + | 0.645231i | \(0.223239\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −0.912151 | −0.0371457 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 33.4543 | 1.36011 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 25.4656 | 1.03362 | 0.516809 | − | 0.856101i | \(-0.327120\pi\) | ||||
0.516809 | + | 0.856101i | \(0.327120\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −5.61899 | −0.227693 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 23.3484 | 0.944574 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 1.03265 | 0.0417085 | 0.0208542 | − | 0.999783i | \(-0.493361\pi\) | ||||
0.0208542 | + | 0.999783i | \(0.493361\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 78.1035 | 3.14944 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 6.93449 | 0.279172 | 0.139586 | − | 0.990210i | \(-0.455423\pi\) | ||||
0.139586 | + | 0.990210i | \(0.455423\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −2.98195 | −0.119855 | −0.0599274 | − | 0.998203i | \(-0.519087\pi\) | ||||
−0.0599274 | + | 0.998203i | \(0.519087\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −11.7655 | −0.472132 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 10.9966 | 0.440568 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −19.4070 | −0.776280 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −3.70704 | −0.148045 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −29.9931 | −1.19590 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 38.7552 | 1.54282 | 0.771409 | − | 0.636339i | \(-0.219552\pi\) | ||||
0.771409 | + | 0.636339i | \(0.219552\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −5.23109 | −0.207917 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −38.6155 | −1.53241 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −5.19051 | −0.205655 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 24.0552 | 0.950123 | 0.475062 | − | 0.879953i | \(-0.342426\pi\) | ||||
0.475062 | + | 0.879953i | \(0.342426\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 22.8286 | 0.900272 | 0.450136 | − | 0.892960i | \(-0.351376\pi\) | ||||
0.450136 | + | 0.892960i | \(0.351376\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 89.6864 | 3.53140 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −5.14992 | −0.202464 | −0.101232 | − | 0.994863i | \(-0.532278\pi\) | ||||
−0.101232 | + | 0.994863i | \(0.532278\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 11.8896 | 0.466708 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −14.8793 | −0.583166 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 6.73281 | 0.263475 | 0.131738 | − | 0.991285i | \(-0.457944\pi\) | ||||
0.131738 | + | 0.991285i | \(0.457944\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −1.21199 | −0.0473564 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −0.241408 | −0.00941824 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 36.8172 | 1.43420 | 0.717098 | − | 0.696973i | \(-0.245470\pi\) | ||||
0.717098 | + | 0.696973i | \(0.245470\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 21.4250 | 0.833337 | 0.416669 | − | 0.909058i | \(-0.363198\pi\) | ||||
0.416669 | + | 0.909058i | \(0.363198\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −75.8621 | −2.94624 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −5.79145 | −0.224583 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −13.8827 | −0.537542 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −15.4725 | −0.598202 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −10.6448 | −0.410937 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −6.76203 | −0.260657 | −0.130329 | − | 0.991471i | \(-0.541603\pi\) | ||||
−0.130329 | + | 0.991471i | \(0.541603\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 12.5795 | 0.484183 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 42.2975 | 1.62562 | 0.812812 | − | 0.582526i | \(-0.197936\pi\) | ||||
0.812812 | + | 0.582526i | \(0.197936\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 13.6121 | 0.522385 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 32.0483 | 1.22809 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 32.7880 | 1.25460 | 0.627299 | − | 0.778778i | \(-0.284160\pi\) | ||||
0.627299 | + | 0.778778i | \(0.284160\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 12.8432 | 0.490714 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −8.56035 | −0.326598 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −10.3810 | −0.395485 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 22.1250 | 0.841675 | 0.420837 | − | 0.907136i | \(-0.361736\pi\) | ||||
0.420837 | + | 0.907136i | \(0.361736\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 1.93793 | 0.0736158 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −47.1329 | −1.78785 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −68.2208 | −2.58405 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 55.9570 | 2.11649 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −36.7259 | −1.38712 | −0.693560 | − | 0.720399i | \(-0.743959\pi\) | ||||
−0.693560 | + | 0.720399i | \(0.743959\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 8.08117 | 0.304787 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −33.4656 | −1.26039 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −15.8061 | −0.594448 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 6.38789 | 0.239902 | 0.119951 | − | 0.992780i | \(-0.461726\pi\) | ||||
0.119951 | + | 0.992780i | \(0.461726\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −14.6448 | −0.549222 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −36.7620 | −1.37675 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 16.1623 | 0.604438 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −39.4880 | −1.47471 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 45.4948 | 1.69667 | 0.848336 | − | 0.529459i | \(-0.177605\pi\) | ||||
0.848336 | + | 0.529459i | \(0.177605\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 6.61555 | 0.246376 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −1.91195 | −0.0711062 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 14.8432 | 0.551263 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −50.2569 | −1.86392 | −0.931962 | − | 0.362556i | \(-0.881904\pi\) | ||||
−0.931962 | + | 0.362556i | \(0.881904\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −8.23109 | −0.304855 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −78.3380 | −2.89744 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −13.3009 | −0.491280 | −0.245640 | − | 0.969361i | \(-0.578998\pi\) | ||||
−0.245640 | + | 0.969361i | \(0.578998\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 7.43965 | 0.274416 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −0.417106 | −0.0153643 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −2.40699 | −0.0885427 | −0.0442714 | − | 0.999020i | \(-0.514097\pi\) | ||||
−0.0442714 | + | 0.999020i | \(0.514097\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 20.4398 | 0.750877 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −14.0844 | −0.516707 | −0.258353 | − | 0.966050i | \(-0.583180\pi\) | ||||
−0.258353 | + | 0.966050i | \(0.583180\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −29.3707 | −1.07606 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −26.4837 | −0.968987 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −5.43965 | −0.198760 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −7.78457 | −0.284063 | −0.142032 | − | 0.989862i | \(-0.545363\pi\) | ||||
−0.142032 | + | 0.989862i | \(0.545363\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 18.8172 | 0.685738 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −74.6018 | −2.71504 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −24.4914 | −0.890155 | −0.445078 | − | 0.895492i | \(-0.646824\pi\) | ||||
−0.445078 | + | 0.895492i | \(0.646824\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 11.7655 | 0.427059 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 10.9673 | 0.397566 | 0.198783 | − | 0.980044i | \(-0.436301\pi\) | ||||
0.198783 | + | 0.980044i | \(0.436301\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0.381015 | 0.0137937 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 44.2500 | 1.59986 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −65.5569 | −2.36712 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −6.62242 | −0.238811 | −0.119405 | − | 0.992846i | \(-0.538099\pi\) | ||||
−0.119405 | + | 0.992846i | \(0.538099\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 33.7294 | 1.21473 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 3.91645 | 0.140865 | 0.0704324 | − | 0.997517i | \(-0.477562\pi\) | ||||
0.0704324 | + | 0.997517i | \(0.477562\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 39.3054 | 1.41189 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −10.3810 | −0.372417 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 18.3810 | 0.658568 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 5.28953 | 0.189032 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −42.3482 | −1.51147 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −9.01805 | −0.321459 | −0.160729 | − | 0.986999i | \(-0.551385\pi\) | ||||
−0.160729 | + | 0.986999i | \(0.551385\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 32.0000 | 1.13923 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −8.05520 | −0.286410 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 58.6931 | 2.08425 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 14.8793 | 0.527714 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 23.5715 | 0.834946 | 0.417473 | − | 0.908689i | \(-0.362916\pi\) | ||||
0.417473 | + | 0.908689i | \(0.362916\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 29.2311 | 1.03412 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 22.6379 | 0.799870 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −0.110391 | −0.00389560 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 18.3810 | 0.647846 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 9.43277 | 0.332049 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −20.1656 | −0.708984 | −0.354492 | − | 0.935059i | \(-0.615346\pi\) | ||||
−0.354492 | + | 0.935059i | \(0.615346\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −21.9716 | −0.771529 | −0.385764 | − | 0.922597i | \(-0.626062\pi\) | ||||
−0.385764 | + | 0.922597i | \(0.626062\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −3.70704 | −0.130011 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 32.8724 | 1.15147 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 21.1070 | 0.738439 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −10.6854 | −0.373376 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −3.10695 | −0.108433 | −0.0542167 | − | 0.998529i | \(-0.517266\pi\) | ||||
−0.0542167 | + | 0.998529i | \(0.517266\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −12.7620 | −0.444856 | −0.222428 | − | 0.974949i | \(-0.571398\pi\) | ||||
−0.222428 | + | 0.974949i | \(0.571398\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −12.5795 | −0.437960 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −4.91215 | −0.170812 | −0.0854061 | − | 0.996346i | \(-0.527219\pi\) | ||||
−0.0854061 | + | 0.996346i | \(0.527219\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −33.5354 | −1.16473 | −0.582367 | − | 0.812926i | \(-0.697873\pi\) | ||||
−0.582367 | + | 0.812926i | \(0.697873\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 18.2569 | 0.633324 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −6.49828 | −0.225152 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −41.3415 | −1.43068 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 14.0069 | 0.484148 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −6.61555 | −0.228394 | −0.114197 | − | 0.993458i | \(-0.536430\pi\) | ||||
−0.114197 | + | 0.993458i | \(0.536430\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −22.7586 | −0.784779 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 32.0155 | 1.10267 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −46.1149 | −1.58640 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −10.1138 | −0.347515 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −70.8035 | −2.42997 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −25.6482 | −0.879209 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −30.1871 | −1.03359 | −0.516793 | − | 0.856111i | \(-0.672874\pi\) | ||||
−0.516793 | + | 0.856111i | \(0.672874\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −11.9225 | −0.407740 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 16.3810 | 0.559565 | 0.279782 | − | 0.960063i | \(-0.409738\pi\) | ||||
0.279782 | + | 0.960063i | \(0.409738\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −0.366407 | −0.0125016 | −0.00625082 | − | 0.999980i | \(-0.501990\pi\) | ||||
−0.00625082 | + | 0.999980i | \(0.501990\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −23.6121 | −0.804699 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 13.6482 | 0.464590 | 0.232295 | − | 0.972645i | \(-0.425376\pi\) | ||||
0.232295 | + | 0.972645i | \(0.425376\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −53.0586 | −1.80405 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −56.7405 | −1.92701 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −6.69672 | −0.227171 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 2.29984 | 0.0779271 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 28.0223 | 0.948413 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −3.11383 | −0.105267 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 15.8535 | 0.535335 | 0.267668 | − | 0.963511i | \(-0.413747\pi\) | ||||
0.267668 | + | 0.963511i | \(0.413747\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −2.67762 | −0.0903138 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 7.35524 | 0.247804 | 0.123902 | − | 0.992294i | \(-0.460459\pi\) | ||||
0.123902 | + | 0.992294i | \(0.460459\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −25.2571 | −0.849968 | −0.424984 | − | 0.905201i | \(-0.639720\pi\) | ||||
−0.424984 | + | 0.905201i | \(0.639720\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 93.9639 | 3.15856 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −43.1950 | −1.45035 | −0.725173 | − | 0.688567i | \(-0.758240\pi\) | ||||
−0.725173 | + | 0.688567i | \(0.758240\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 11.6742 | 0.391539 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −10.2966 | −0.344949 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −7.87586 | −0.263556 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −42.2998 | −1.41393 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −64.8724 | −2.16603 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 16.5275 | 0.551223 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −12.9966 | −0.432978 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −27.1138 | −0.902292 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 32.0483 | 1.06532 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −41.0810 | −1.36407 | −0.682036 | − | 0.731319i | \(-0.738905\pi\) | ||||
−0.682036 | + | 0.731319i | \(0.738905\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −32.5389 | −1.07925 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −21.4465 | −0.710555 | −0.355278 | − | 0.934761i | \(-0.615614\pi\) | ||||
−0.355278 | + | 0.934761i | \(0.615614\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −12.1104 | −0.400795 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −84.1259 | −2.78111 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0.366407 | 0.0120998 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −4.76203 | −0.157085 | −0.0785424 | − | 0.996911i | \(-0.525027\pi\) | ||||
−0.0785424 | + | 0.996911i | \(0.525027\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −10.3482 | −0.340983 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 27.4227 | 0.901652 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 13.6190 | 0.447306 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 20.9605 | 0.687691 | 0.343845 | − | 0.939026i | \(-0.388270\pi\) | ||||
0.343845 | + | 0.939026i | \(0.388270\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1.75086 | 0.0573821 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −29.7586 | −0.974253 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 20.2345 | 0.661740 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 7.10695 | 0.232174 | 0.116087 | − | 0.993239i | \(-0.462965\pi\) | ||||
0.116087 | + | 0.993239i | \(0.462965\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −23.6121 | −0.770552 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −3.57152 | −0.116428 | −0.0582141 | − | 0.998304i | \(-0.518541\pi\) | ||||
−0.0582141 | + | 0.998304i | \(0.518541\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −58.3380 | −1.89975 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −7.00344 | −0.227822 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −25.4104 | −0.825728 | −0.412864 | − | 0.910793i | \(-0.635472\pi\) | ||||
−0.412864 | + | 0.910793i | \(0.635472\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0.608672 | 0.0197583 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −20.2500 | −0.656651 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −28.2277 | −0.914383 | −0.457192 | − | 0.889368i | \(-0.651145\pi\) | ||||
−0.457192 | + | 0.889368i | \(0.651145\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 32.6898 | 1.05782 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −5.28953 | −0.170986 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −3.88273 | −0.125380 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 12.7655 | 0.411789 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −11.1982 | −0.360858 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −28.8002 | −0.927112 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −40.0191 | −1.28693 | −0.643464 | − | 0.765477i | \(-0.722503\pi\) | ||||
−0.643464 | + | 0.765477i | \(0.722503\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 25.5898 | 0.822062 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 16.8647 | 0.541214 | 0.270607 | − | 0.962690i | \(-0.412776\pi\) | ||||
0.270607 | + | 0.962690i | \(0.412776\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 14.2491 | 0.456806 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 69.3606 | 2.22132 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −12.1173 | −0.387666 | −0.193833 | − | 0.981035i | \(-0.562092\pi\) | ||||
−0.193833 | + | 0.981035i | \(0.562092\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 10.3518 | 0.330845 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0.784370 | 0.0250430 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 49.6052 | 1.58216 | 0.791081 | − | 0.611712i | \(-0.209519\pi\) | ||||
0.791081 | + | 0.611712i | \(0.209519\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −33.0777 | −1.05394 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 10.1173 | 0.322036 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −66.9897 | −2.13015 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 35.8759 | 1.13963 | 0.569817 | − | 0.821772i | \(-0.307014\pi\) | ||||
0.569817 | + | 0.821772i | \(0.307014\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 22.8793 | 0.726053 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 78.1035 | 2.47605 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 9.45426 | 0.299419 | 0.149710 | − | 0.988730i | \(-0.452166\pi\) | ||||
0.149710 | + | 0.988730i | \(0.452166\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 9.77234 | 0.309183 |
(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 | 896.2.a.k.1.1 | yes | 3 | |
3.2 | odd | 2 | 8064.2.a.ch.1.3 | 3 | |||
4.3 | odd | 2 | 896.2.a.i.1.3 | ✓ | 3 | ||
7.6 | odd | 2 | 6272.2.a.v.1.3 | 3 | |||
8.3 | odd | 2 | 896.2.a.l.1.1 | yes | 3 | ||
8.5 | even | 2 | 896.2.a.j.1.3 | yes | 3 | ||
12.11 | even | 2 | 8064.2.a.ce.1.3 | 3 | |||
16.3 | odd | 4 | 1792.2.b.p.897.5 | 6 | |||
16.5 | even | 4 | 1792.2.b.o.897.5 | 6 | |||
16.11 | odd | 4 | 1792.2.b.p.897.2 | 6 | |||
16.13 | even | 4 | 1792.2.b.o.897.2 | 6 | |||
24.5 | odd | 2 | 8064.2.a.cb.1.1 | 3 | |||
24.11 | even | 2 | 8064.2.a.bu.1.1 | 3 | |||
28.27 | even | 2 | 6272.2.a.x.1.1 | 3 | |||
56.13 | odd | 2 | 6272.2.a.w.1.1 | 3 | |||
56.27 | even | 2 | 6272.2.a.u.1.3 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
896.2.a.i.1.3 | ✓ | 3 | 4.3 | odd | 2 | ||
896.2.a.j.1.3 | yes | 3 | 8.5 | even | 2 | ||
896.2.a.k.1.1 | yes | 3 | 1.1 | even | 1 | trivial | |
896.2.a.l.1.1 | yes | 3 | 8.3 | odd | 2 | ||
1792.2.b.o.897.2 | 6 | 16.13 | even | 4 | |||
1792.2.b.o.897.5 | 6 | 16.5 | even | 4 | |||
1792.2.b.p.897.2 | 6 | 16.11 | odd | 4 | |||
1792.2.b.p.897.5 | 6 | 16.3 | odd | 4 | |||
6272.2.a.u.1.3 | 3 | 56.27 | even | 2 | |||
6272.2.a.v.1.3 | 3 | 7.6 | odd | 2 | |||
6272.2.a.w.1.1 | 3 | 56.13 | odd | 2 | |||
6272.2.a.x.1.1 | 3 | 28.27 | even | 2 | |||
8064.2.a.bu.1.1 | 3 | 24.11 | even | 2 | |||
8064.2.a.cb.1.1 | 3 | 24.5 | odd | 2 | |||
8064.2.a.ce.1.3 | 3 | 12.11 | even | 2 | |||
8064.2.a.ch.1.3 | 3 | 3.2 | odd | 2 |