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 | 1.2 | ||
Root | \(2.34292\) 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 | ||||||||
\(3\) | −1.14637 | −0.661854 | −0.330927 | − | 0.943656i | \(-0.607361\pi\) | ||||
−0.330927 | + | 0.943656i | \(0.607361\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −3.83221 | −1.71382 | −0.856909 | − | 0.515468i | \(-0.827618\pi\) | ||||
−0.856909 | + | 0.515468i | \(0.827618\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.68585 | −0.561949 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −4.68585 | −1.41284 | −0.706418 | − | 0.707795i | \(-0.749690\pi\) | ||||
−0.706418 | + | 0.707795i | \(0.749690\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 5.53948 | 1.53638 | 0.768188 | − | 0.640225i | \(-0.221159\pi\) | ||||
0.768188 | + | 0.640225i | \(0.221159\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 4.39312 | 1.13430 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0.292731 | 0.0709977 | 0.0354988 | − | 0.999370i | \(-0.488698\pi\) | ||||
0.0354988 | + | 0.999370i | \(0.488698\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −5.14637 | −1.18066 | −0.590329 | − | 0.807163i | \(-0.701002\pi\) | ||||
−0.590329 | + | 0.807163i | \(0.701002\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.14637 | −0.250157 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 4.97858 | 1.03811 | 0.519053 | − | 0.854742i | \(-0.326285\pi\) | ||||
0.519053 | + | 0.854742i | \(0.326285\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 9.68585 | 1.93717 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 5.37169 | 1.03378 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 4.29273 | 0.797140 | 0.398570 | − | 0.917138i | \(-0.369507\pi\) | ||||
0.398570 | + | 0.917138i | \(0.369507\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −7.66442 | −1.37657 | −0.688286 | − | 0.725440i | \(-0.741636\pi\) | ||||
−0.688286 | + | 0.725440i | \(0.741636\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 5.37169 | 0.935092 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −3.83221 | −0.647762 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 9.66442 | 1.58882 | 0.794411 | − | 0.607381i | \(-0.207780\pi\) | ||||
0.794411 | + | 0.607381i | \(0.207780\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −6.35027 | −1.01686 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 3.70727 | 0.578978 | 0.289489 | − | 0.957181i | \(-0.406515\pi\) | ||||
0.289489 | + | 0.957181i | \(0.406515\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 5.27131 | 0.803867 | 0.401933 | − | 0.915669i | \(-0.368338\pi\) | ||||
0.401933 | + | 0.915669i | \(0.368338\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 6.46052 | 0.963077 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 2.29273 | 0.334429 | 0.167215 | − | 0.985921i | \(-0.446523\pi\) | ||||
0.167215 | + | 0.985921i | \(0.446523\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −0.335577 | −0.0469901 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −2.00000 | −0.274721 | −0.137361 | − | 0.990521i | \(-0.543862\pi\) | ||||
−0.137361 | + | 0.990521i | \(0.543862\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 17.9572 | 2.42134 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 5.89962 | 0.781423 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −9.93260 | −1.29311 | −0.646557 | − | 0.762866i | \(-0.723792\pi\) | ||||
−0.646557 | + | 0.762866i | \(0.723792\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 4.16779 | 0.533631 | 0.266815 | − | 0.963748i | \(-0.414029\pi\) | ||||
0.266815 | + | 0.963748i | \(0.414029\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −1.68585 | −0.212397 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −21.2285 | −2.63307 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 10.9786 | 1.34125 | 0.670623 | − | 0.741798i | \(-0.266027\pi\) | ||||
0.670623 | + | 0.741798i | \(0.266027\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −5.70727 | −0.687074 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 7.37169 | 0.862791 | 0.431396 | − | 0.902163i | \(-0.358021\pi\) | ||||
0.431396 | + | 0.902163i | \(0.358021\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −11.1035 | −1.28212 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −4.68585 | −0.534002 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 13.9572 | 1.57030 | 0.785151 | − | 0.619304i | \(-0.212585\pi\) | ||||
0.785151 | + | 0.619304i | \(0.212585\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −1.10038 | −0.122265 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −4.81079 | −0.528053 | −0.264026 | − | 0.964515i | \(-0.585051\pi\) | ||||
−0.264026 | + | 0.964515i | \(0.585051\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.12181 | −0.121677 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −4.92104 | −0.527591 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −2.58546 | −0.274058 | −0.137029 | − | 0.990567i | \(-0.543755\pi\) | ||||
−0.137029 | + | 0.990567i | \(0.543755\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 5.53948 | 0.580695 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 8.78623 | 0.911090 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 19.7220 | 2.02343 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −14.2499 | −1.44686 | −0.723428 | − | 0.690399i | \(-0.757435\pi\) | ||||
−0.723428 | + | 0.690399i | \(0.757435\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 7.89962 | 0.793941 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1.87506 | 0.186575 | 0.0932876 | − | 0.995639i | \(-0.470262\pi\) | ||||
0.0932876 | + | 0.995639i | \(0.470262\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −7.66442 | −0.755198 | −0.377599 | − | 0.925969i | \(-0.623250\pi\) | ||||
−0.377599 | + | 0.925969i | \(0.623250\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 4.39312 | 0.428724 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 2.39312 | 0.231351 | 0.115676 | − | 0.993287i | \(-0.463097\pi\) | ||||
0.115676 | + | 0.993287i | \(0.463097\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1.07896 | −0.103346 | −0.0516729 | − | 0.998664i | \(-0.516455\pi\) | ||||
−0.0516729 | + | 0.998664i | \(0.516455\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −11.0790 | −1.05157 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 9.27131 | 0.872171 | 0.436086 | − | 0.899905i | \(-0.356364\pi\) | ||||
0.436086 | + | 0.899905i | \(0.356364\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −19.0790 | −1.77912 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −9.33871 | −0.863364 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0.292731 | 0.0268346 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 10.9572 | 0.996105 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −4.24989 | −0.383199 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −17.9572 | −1.60614 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −6.35027 | −0.563495 | −0.281748 | − | 0.959489i | \(-0.590914\pi\) | ||||
−0.281748 | + | 0.959489i | \(0.590914\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −6.04285 | −0.532043 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 10.5181 | 0.918967 | 0.459483 | − | 0.888186i | \(-0.348035\pi\) | ||||
0.459483 | + | 0.888186i | \(0.348035\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −5.14637 | −0.446246 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −20.5855 | −1.77171 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −11.3717 | −0.971549 | −0.485775 | − | 0.874084i | \(-0.661462\pi\) | ||||
−0.485775 | + | 0.874084i | \(0.661462\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −10.8536 | −0.920593 | −0.460297 | − | 0.887765i | \(-0.652257\pi\) | ||||
−0.460297 | + | 0.887765i | \(0.652257\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −2.62831 | −0.221343 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −25.9572 | −2.17065 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −16.4507 | −1.36615 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −1.14637 | −0.0945506 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −2.78623 | −0.228257 | −0.114128 | − | 0.993466i | \(-0.536408\pi\) | ||||
−0.114128 | + | 0.993466i | \(0.536408\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1.56404 | −0.127280 | −0.0636398 | − | 0.997973i | \(-0.520271\pi\) | ||||
−0.0636398 | + | 0.997973i | \(0.520271\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −0.493499 | −0.0398971 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 29.3717 | 2.35919 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 14.7104 | 1.17402 | 0.587009 | − | 0.809580i | \(-0.300305\pi\) | ||||
0.587009 | + | 0.809580i | \(0.300305\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 2.29273 | 0.181825 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 4.97858 | 0.392367 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 0.100384 | 0.00786270 | 0.00393135 | − | 0.999992i | \(-0.498749\pi\) | ||||
0.00393135 | + | 0.999992i | \(0.498749\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −20.5855 | −1.60258 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 5.70727 | 0.441642 | 0.220821 | − | 0.975314i | \(-0.429126\pi\) | ||||
0.220821 | + | 0.975314i | \(0.429126\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 17.6858 | 1.36045 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 8.67598 | 0.663469 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 12.8683 | 0.978361 | 0.489180 | − | 0.872183i | \(-0.337296\pi\) | ||||
0.489180 | + | 0.872183i | \(0.337296\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 9.68585 | 0.732181 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 11.3864 | 0.855853 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 26.3074 | 1.96631 | 0.983155 | − | 0.182776i | \(-0.0585083\pi\) | ||||
0.983155 | + | 0.182776i | \(0.0585083\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 3.24675 | 0.241329 | 0.120665 | − | 0.992693i | \(-0.461497\pi\) | ||||
0.120665 | + | 0.992693i | \(0.461497\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −4.77781 | −0.353186 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −37.0361 | −2.72295 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1.37169 | −0.100308 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 5.37169 | 0.390733 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −17.3717 | −1.25697 | −0.628486 | − | 0.777821i | \(-0.716325\pi\) | ||||
−0.628486 | + | 0.777821i | \(0.716325\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 27.4292 | 1.97440 | 0.987200 | − | 0.159490i | \(-0.0509848\pi\) | ||||
0.987200 | + | 0.159490i | \(0.0509848\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 24.3356 | 1.74271 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −10.0000 | −0.712470 | −0.356235 | − | 0.934396i | \(-0.615940\pi\) | ||||
−0.356235 | + | 0.934396i | \(0.615940\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 4.24989 | 0.301266 | 0.150633 | − | 0.988590i | \(-0.451869\pi\) | ||||
0.150633 | + | 0.988590i | \(0.451869\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −12.5855 | −0.887710 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 4.29273 | 0.301291 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −14.2070 | −0.992263 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −8.39312 | −0.583362 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 24.1151 | 1.66807 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −20.3503 | −1.40097 | −0.700485 | − | 0.713667i | \(-0.747033\pi\) | ||||
−0.700485 | + | 0.713667i | \(0.747033\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −20.2008 | −1.37768 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −7.66442 | −0.520295 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −8.45065 | −0.571042 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1.62158 | 0.109079 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 0.786230 | 0.0526499 | 0.0263249 | − | 0.999653i | \(-0.491620\pi\) | ||||
0.0263249 | + | 0.999653i | \(0.491620\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −16.3288 | −1.08859 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 10.8536 | 0.720381 | 0.360191 | − | 0.932879i | \(-0.382712\pi\) | ||||
0.360191 | + | 0.932879i | \(0.382712\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 10.1249 | 0.669075 | 0.334538 | − | 0.942382i | \(-0.391420\pi\) | ||||
0.334538 | + | 0.942382i | \(0.391420\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 5.37169 | 0.353431 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −18.7862 | −1.23073 | −0.615363 | − | 0.788244i | \(-0.710991\pi\) | ||||
−0.615363 | + | 0.788244i | \(0.710991\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −8.78623 | −0.573150 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −16.0000 | −1.03931 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 7.02142 | 0.454178 | 0.227089 | − | 0.973874i | \(-0.427079\pi\) | ||||
0.227089 | + | 0.973874i | \(0.427079\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −28.4078 | −1.82991 | −0.914954 | − | 0.403558i | \(-0.867773\pi\) | ||||
−0.914954 | + | 0.403558i | \(0.867773\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −14.8536 | −0.952861 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −3.83221 | −0.244831 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −28.5082 | −1.81393 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 5.51492 | 0.349494 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −2.51806 | −0.158938 | −0.0794692 | − | 0.996837i | \(-0.525323\pi\) | ||||
−0.0794692 | + | 0.996837i | \(0.525323\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −23.3288 | −1.46667 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 1.28600 | 0.0805325 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −1.41454 | −0.0882365 | −0.0441182 | − | 0.999026i | \(-0.514048\pi\) | ||||
−0.0441182 | + | 0.999026i | \(0.514048\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 9.66442 | 0.600518 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −7.23688 | −0.447952 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 27.9143 | 1.72127 | 0.860635 | − | 0.509222i | \(-0.170067\pi\) | ||||
0.860635 | + | 0.509222i | \(0.170067\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 7.66442 | 0.470822 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 2.96388 | 0.181387 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 18.1249 | 1.10510 | 0.552549 | − | 0.833481i | \(-0.313655\pi\) | ||||
0.552549 | + | 0.833481i | \(0.313655\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 24.1151 | 1.46489 | 0.732443 | − | 0.680828i | \(-0.238380\pi\) | ||||
0.732443 | + | 0.680828i | \(0.238380\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −6.35027 | −0.384336 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −45.3864 | −2.73690 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 0.628308 | 0.0377513 | 0.0188757 | − | 0.999822i | \(-0.493991\pi\) | ||||
0.0188757 | + | 0.999822i | \(0.493991\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 12.9210 | 0.773562 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 0.743385 | 0.0443466 | 0.0221733 | − | 0.999754i | \(-0.492941\pi\) | ||||
0.0221733 | + | 0.999754i | \(0.492941\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 0.475212 | 0.0282484 | 0.0141242 | − | 0.999900i | \(-0.495504\pi\) | ||||
0.0141242 | + | 0.999900i | \(0.495504\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −22.6086 | −1.33922 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 3.70727 | 0.218833 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.9143 | −0.994959 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 16.3356 | 0.957608 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −1.53948 | −0.0899374 | −0.0449687 | − | 0.998988i | \(-0.514319\pi\) | ||||
−0.0449687 | + | 0.998988i | \(0.514319\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 38.0638 | 2.21616 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −25.1709 | −1.46057 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 27.5787 | 1.59492 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 5.27131 | 0.303833 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −2.14950 | −0.123486 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −15.9718 | −0.914545 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 21.2614 | 1.21345 | 0.606727 | − | 0.794910i | \(-0.292482\pi\) | ||||
0.606727 | + | 0.794910i | \(0.292482\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 8.78623 | 0.499831 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −15.3288 | −0.869219 | −0.434610 | − | 0.900619i | \(-0.643114\pi\) | ||||
−0.434610 | + | 0.900619i | \(0.643114\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 3.70727 | 0.209547 | 0.104774 | − | 0.994496i | \(-0.466588\pi\) | ||||
0.104774 | + | 0.994496i | \(0.466588\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 6.46052 | 0.364009 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −22.5855 | −1.26853 | −0.634263 | − | 0.773117i | \(-0.718696\pi\) | ||||
−0.634263 | + | 0.773117i | \(0.718696\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −20.1151 | −1.12623 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −2.74338 | −0.153121 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −1.50650 | −0.0838239 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 53.6546 | 2.97622 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 1.23688 | 0.0683998 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 2.29273 | 0.126402 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −14.6430 | −0.804852 | −0.402426 | − | 0.915452i | \(-0.631833\pi\) | ||||
−0.402426 | + | 0.915452i | \(0.631833\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −16.2927 | −0.892836 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −42.0722 | −2.29865 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 21.4721 | 1.16966 | 0.584829 | − | 0.811156i | \(-0.301162\pi\) | ||||
0.584829 | + | 0.811156i | \(0.301162\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −10.6283 | −0.577250 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 35.9143 | 1.94487 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 21.8715 | 1.17752 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 28.6002 | 1.53534 | 0.767668 | − | 0.640847i | \(-0.221417\pi\) | ||||
0.767668 | + | 0.640847i | \(0.221417\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 23.8322 | 1.27571 | 0.637855 | − | 0.770157i | \(-0.279822\pi\) | ||||
0.637855 | + | 0.770157i | \(0.279822\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 29.7564 | 1.58828 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 35.2860 | 1.87808 | 0.939042 | − | 0.343802i | \(-0.111715\pi\) | ||||
0.939042 | + | 0.343802i | \(0.111715\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −0.335577 | −0.0177606 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 0.393115 | 0.0207478 | 0.0103739 | − | 0.999946i | \(-0.496698\pi\) | ||||
0.0103739 | + | 0.999946i | \(0.496698\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 7.48508 | 0.393951 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −12.5609 | −0.659276 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −28.2499 | −1.47867 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −2.62831 | −0.137197 | −0.0685983 | − | 0.997644i | \(-0.521853\pi\) | ||||
−0.0685983 | + | 0.997644i | \(0.521853\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −6.24989 | −0.325356 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −2.00000 | −0.103835 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 14.7862 | 0.765602 | 0.382801 | − | 0.923831i | \(-0.374959\pi\) | ||||
0.382801 | + | 0.923831i | \(0.374959\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 20.5855 | 1.06303 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 23.7795 | 1.22471 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 4.10038 | 0.210623 | 0.105311 | − | 0.994439i | \(-0.466416\pi\) | ||||
0.105311 | + | 0.994439i | \(0.466416\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 7.27973 | 0.372952 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −11.4637 | −0.585765 | −0.292883 | − | 0.956148i | \(-0.594615\pi\) | ||||
−0.292883 | + | 0.956148i | \(0.594615\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 17.9572 | 0.915181 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −8.88661 | −0.451732 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 24.9933 | 1.26721 | 0.633605 | − | 0.773657i | \(-0.281575\pi\) | ||||
0.633605 | + | 0.773657i | \(0.281575\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.45738 | 0.0737031 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −12.0575 | −0.608222 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −53.4868 | −2.69121 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 7.83221 | 0.393087 | 0.196544 | − | 0.980495i | \(-0.437028\pi\) | ||||
0.196544 | + | 0.980495i | \(0.437028\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 5.89962 | 0.295350 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 37.3864 | 1.86699 | 0.933493 | − | 0.358594i | \(-0.116744\pi\) | ||||
0.933493 | + | 0.358594i | \(0.116744\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −42.4569 | −2.11493 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 4.21691 | 0.209540 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −45.2860 | −2.24474 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −6.24989 | −0.309037 | −0.154518 | − | 0.987990i | \(-0.549383\pi\) | ||||
−0.154518 | + | 0.987990i | \(0.549383\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 13.0361 | 0.643024 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −9.93260 | −0.488751 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 18.4360 | 0.904986 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 12.4422 | 0.609299 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 19.4391 | 0.949662 | 0.474831 | − | 0.880077i | \(-0.342509\pi\) | ||||
0.474831 | + | 0.880077i | \(0.342509\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −35.2860 | −1.71973 | −0.859867 | − | 0.510518i | \(-0.829454\pi\) | ||||
−0.859867 | + | 0.510518i | \(0.829454\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −3.86519 | −0.187932 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 2.83535 | 0.137535 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 4.16779 | 0.201693 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 29.7564 | 1.43665 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 7.80765 | 0.376081 | 0.188041 | − | 0.982161i | \(-0.439786\pi\) | ||||
0.188041 | + | 0.982161i | \(0.439786\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 17.4637 | 0.839250 | 0.419625 | − | 0.907698i | \(-0.362162\pi\) | ||||
0.419625 | + | 0.907698i | \(0.362162\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 18.8585 | 0.904194 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −25.6216 | −1.22565 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 32.7862 | 1.56480 | 0.782401 | − | 0.622775i | \(-0.213995\pi\) | ||||
0.782401 | + | 0.622775i | \(0.213995\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −1.68585 | −0.0802784 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 34.5082 | 1.63953 | 0.819767 | − | 0.572697i | \(-0.194103\pi\) | ||||
0.819767 | + | 0.572697i | \(0.194103\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 9.90804 | 0.469686 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 3.19404 | 0.151073 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 22.7862 | 1.07535 | 0.537674 | − | 0.843153i | \(-0.319303\pi\) | ||||
0.537674 | + | 0.843153i | \(0.319303\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −17.3717 | −0.818001 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 1.79296 | 0.0842406 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −21.2285 | −0.995206 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −8.01469 | −0.374912 | −0.187456 | − | 0.982273i | \(-0.560024\pi\) | ||||
−0.187456 | + | 0.982273i | \(0.560024\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 1.57246 | 0.0733962 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −31.4966 | −1.46694 | −0.733472 | − | 0.679719i | \(-0.762102\pi\) | ||||
−0.733472 | + | 0.679719i | \(0.762102\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 28.7862 | 1.33781 | 0.668905 | − | 0.743348i | \(-0.266763\pi\) | ||||
0.668905 | + | 0.743348i | \(0.266763\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −33.6707 | −1.56144 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −16.5609 | −0.766347 | −0.383174 | − | 0.923676i | \(-0.625169\pi\) | ||||
−0.383174 | + | 0.923676i | \(0.625169\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 10.9786 | 0.506944 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −16.8635 | −0.777029 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −24.7005 | −1.13573 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −49.8469 | −2.28713 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 3.37169 | 0.154379 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 15.6644 | 0.715726 | 0.357863 | − | 0.933774i | \(-0.383506\pi\) | ||||
0.357863 | + | 0.933774i | \(0.383506\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 53.5359 | 2.44103 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −5.70727 | −0.259690 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 54.6086 | 2.47965 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 31.7220 | 1.43746 | 0.718730 | − | 0.695290i | \(-0.244724\pi\) | ||||
0.718730 | + | 0.695290i | \(0.244724\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −0.115077 | −0.00520396 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −35.4783 | −1.60112 | −0.800558 | − | 0.599256i | \(-0.795463\pi\) | ||||
−0.800558 | + | 0.599256i | \(0.795463\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1.25662 | 0.0565951 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −30.2730 | −1.36067 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −15.6497 | −0.700578 | −0.350289 | − | 0.936642i | \(-0.613917\pi\) | ||||
−0.350289 | + | 0.936642i | \(0.613917\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −6.54262 | −0.292303 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 37.3717 | 1.66632 | 0.833161 | − | 0.553031i | \(-0.186529\pi\) | ||||
0.833161 | + | 0.553031i | \(0.186529\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −7.18562 | −0.319756 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −20.2744 | −0.900420 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 18.5756 | 0.823349 | 0.411674 | − | 0.911331i | \(-0.364944\pi\) | ||||
0.411674 | + | 0.911331i | \(0.364944\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 7.37169 | 0.326104 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −27.6447 | −1.22054 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 29.3717 | 1.29427 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −10.7434 | −0.472494 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −14.7518 | −0.647532 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 17.5787 | 0.770138 | 0.385069 | − | 0.922888i | \(-0.374178\pi\) | ||||
0.385069 | + | 0.922888i | \(0.374178\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −14.5181 | −0.634830 | −0.317415 | − | 0.948287i | \(-0.602815\pi\) | ||||
−0.317415 | + | 0.948287i | \(0.602815\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −11.1035 | −0.484597 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −2.24361 | −0.0977334 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.78623 | 0.0776622 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 16.7448 | 0.726664 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 20.5363 | 0.889528 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −9.17092 | −0.396494 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −30.1579 | −1.30141 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −4.68585 | −0.201834 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 12.5426 | 0.539249 | 0.269625 | − | 0.962966i | \(-0.413100\pi\) | ||||
0.269625 | + | 0.962966i | \(0.413100\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −3.72196 | −0.159725 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 4.13481 | 0.177116 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 0.771538 | 0.0329886 | 0.0164943 | − | 0.999864i | \(-0.494749\pi\) | ||||
0.0164943 | + | 0.999864i | \(0.494749\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −7.02625 | −0.299873 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −22.0920 | −0.941149 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 13.9572 | 0.593519 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 42.4569 | 1.80220 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −28.7434 | −1.21790 | −0.608948 | − | 0.793210i | \(-0.708408\pi\) | ||||
−0.608948 | + | 0.793210i | \(0.708408\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 29.2003 | 1.23504 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 1.57246 | 0.0663893 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 5.34713 | 0.225355 | 0.112677 | − | 0.993632i | \(-0.464057\pi\) | ||||
0.112677 | + | 0.993632i | \(0.464057\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −35.5296 | −1.49474 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −1.10038 | −0.0462118 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −31.2285 | −1.30917 | −0.654583 | − | 0.755990i | \(-0.727156\pi\) | ||||
−0.654583 | + | 0.755990i | \(0.727156\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −18.7287 | −0.783771 | −0.391886 | − | 0.920014i | \(-0.628177\pi\) | ||||
−0.391886 | + | 0.920014i | \(0.628177\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 19.9143 | 0.831932 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 48.2217 | 2.01099 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 0.542616 | 0.0225894 | 0.0112947 | − | 0.999936i | \(-0.496405\pi\) | ||||
0.0112947 | + | 0.999936i | \(0.496405\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −31.4439 | −1.30676 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −4.81079 | −0.199585 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 9.37169 | 0.388136 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 35.7879 | 1.47965 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −7.43910 | −0.307044 | −0.153522 | − | 0.988145i | \(-0.549062\pi\) | ||||
−0.153522 | + | 0.988145i | \(0.549062\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 39.4439 | 1.62526 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 11.4637 | 0.471552 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −9.91431 | −0.407132 | −0.203566 | − | 0.979061i | \(-0.565253\pi\) | ||||
−0.203566 | + | 0.979061i | \(0.565253\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −1.12181 | −0.0459896 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −4.87192 | −0.199394 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 29.4868 | 1.20480 | 0.602398 | − | 0.798196i | \(-0.294212\pi\) | ||||
0.602398 | + | 0.798196i | \(0.294212\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −33.2432 | −1.35602 | −0.678008 | − | 0.735054i | \(-0.737157\pi\) | ||||
−0.678008 | + | 0.735054i | \(0.737157\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −18.5082 | −0.753712 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −41.9901 | −1.70714 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −18.0722 | −0.733529 | −0.366765 | − | 0.930314i | \(-0.619535\pi\) | ||||
−0.366765 | + | 0.930314i | \(0.619535\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −4.92104 | −0.199411 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 12.7005 | 0.513809 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −37.7795 | −1.52590 | −0.762950 | − | 0.646458i | \(-0.776250\pi\) | ||||
−0.762950 | + | 0.646458i | \(0.776250\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 16.2865 | 0.656733 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −16.4851 | −0.663664 | −0.331832 | − | 0.943338i | \(-0.607667\pi\) | ||||
−0.331832 | + | 0.943338i | \(0.607667\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −22.1825 | −0.891589 | −0.445795 | − | 0.895135i | \(-0.647079\pi\) | ||||
−0.445795 | + | 0.895135i | \(0.647079\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 26.7434 | 1.07318 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −2.58546 | −0.103584 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 20.3864 | 0.815455 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −27.6447 | −1.10402 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 2.82908 | 0.112803 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 12.9870 | 0.517004 | 0.258502 | − | 0.966011i | \(-0.416771\pi\) | ||||
0.258502 | + | 0.966011i | \(0.416771\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 23.3288 | 0.927238 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 24.3356 | 0.965728 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 5.53948 | 0.219482 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 6.72869 | 0.265767 | 0.132884 | − | 0.991132i | \(-0.457576\pi\) | ||||
0.132884 | + | 0.991132i | \(0.457576\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 45.1758 | 1.78156 | 0.890779 | − | 0.454437i | \(-0.150160\pi\) | ||||
0.890779 | + | 0.454437i | \(0.150160\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 23.1575 | 0.911824 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −34.4078 | −1.35271 | −0.676355 | − | 0.736576i | \(-0.736442\pi\) | ||||
−0.676355 | + | 0.736576i | \(0.736442\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 46.5426 | 1.82696 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 8.78623 | 0.344360 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 15.0361 | 0.588409 | 0.294204 | − | 0.955743i | \(-0.404945\pi\) | ||||
0.294204 | + | 0.955743i | \(0.404945\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −40.3074 | −1.57494 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −12.4275 | −0.484844 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −20.8866 | −0.813627 | −0.406813 | − | 0.913511i | \(-0.633360\pi\) | ||||
−0.406813 | + | 0.913511i | \(0.633360\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −6.79610 | −0.264337 | −0.132169 | − | 0.991227i | \(-0.542194\pi\) | ||||
−0.132169 | + | 0.991227i | \(0.542194\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −1.85892 | −0.0721945 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 19.7220 | 0.764785 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 21.3717 | 0.827515 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −0.901307 | −0.0348466 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −19.5296 | −0.753932 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −8.15792 | −0.314465 | −0.157232 | − | 0.987562i | \(-0.550257\pi\) | ||||
−0.157232 | + | 0.987562i | \(0.550257\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 52.0294 | 2.00261 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 5.58860 | 0.214787 | 0.107394 | − | 0.994217i | \(-0.465749\pi\) | ||||
0.107394 | + | 0.994217i | \(0.465749\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −14.2499 | −0.546860 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −12.4422 | −0.476787 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 6.30742 | 0.241347 | 0.120673 | − | 0.992692i | \(-0.461495\pi\) | ||||
0.120673 | + | 0.992692i | \(0.461495\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 43.5787 | 1.66506 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −11.6069 | −0.442830 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −11.0790 | −0.422075 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 0.945597 | 0.0359722 | 0.0179861 | − | 0.999838i | \(-0.494275\pi\) | ||||
0.0179861 | + | 0.999838i | \(0.494275\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 7.89962 | 0.300082 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 41.5934 | 1.57773 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1.08523 | 0.0411061 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 21.5359 | 0.814562 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −12.2070 | −0.461054 | −0.230527 | − | 0.973066i | \(-0.574045\pi\) | ||||
−0.230527 | + | 0.973066i | \(0.574045\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −49.7367 | −1.87585 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 10.0722 | 0.379342 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 1.87506 | 0.0705188 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −34.2499 | −1.28628 | −0.643141 | − | 0.765748i | \(-0.722369\pi\) | ||||
−0.643141 | + | 0.765748i | \(0.722369\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −23.5296 | −0.882430 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −38.1579 | −1.42903 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 99.4733 | 3.72009 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −8.04912 | −0.300600 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 25.1218 | 0.936885 | 0.468443 | − | 0.883494i | \(-0.344815\pi\) | ||||
0.468443 | + | 0.883494i | \(0.344815\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −7.66442 | −0.285438 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 32.5657 | 1.21113 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 41.5787 | 1.54420 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −31.2797 | −1.16010 | −0.580050 | − | 0.814581i | \(-0.696967\pi\) | ||||
−0.580050 | + | 0.814581i | \(0.696967\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 20.3288 | 0.752920 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1.54308 | 0.0570727 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −21.0031 | −0.775769 | −0.387884 | − | 0.921708i | \(-0.626794\pi\) | ||||
−0.387884 | + | 0.921708i | \(0.626794\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 4.39312 | 0.162042 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −51.4439 | −1.89496 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −37.3864 | −1.37528 | −0.687640 | − | 0.726052i | \(-0.741353\pi\) | ||||
−0.687640 | + | 0.726052i | \(0.741353\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 32.6808 | 1.20056 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −19.9227 | −0.730894 | −0.365447 | − | 0.930832i | \(-0.619084\pi\) | ||||
−0.365447 | + | 0.930832i | \(0.619084\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 10.6774 | 0.391191 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 8.11025 | 0.296739 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 2.39312 | 0.0874425 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 44.8929 | 1.63816 | 0.819082 | − | 0.573676i | \(-0.194483\pi\) | ||||
0.819082 | + | 0.573676i | \(0.194483\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 2.88661 | 0.105194 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 5.99373 | 0.218134 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −9.46365 | −0.343962 | −0.171981 | − | 0.985100i | \(-0.555017\pi\) | ||||
−0.171981 | + | 0.985100i | \(0.555017\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 26.7434 | 0.970723 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −25.7795 | −0.934506 | −0.467253 | − | 0.884124i | \(-0.654756\pi\) | ||||
−0.467253 | + | 0.884124i | \(0.654756\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −1.07896 | −0.0390610 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 1.89119 | 0.0683763 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −55.0214 | −1.98671 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −19.5065 | −0.703422 | −0.351711 | − | 0.936109i | \(-0.614400\pi\) | ||||
−0.351711 | + | 0.936109i | \(0.614400\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1.62158 | 0.0583997 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 44.6676 | 1.60658 | 0.803290 | − | 0.595588i | \(-0.203081\pi\) | ||||
0.803290 | + | 0.595588i | \(0.203081\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −74.2364 | −2.66665 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −11.0790 | −0.397456 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −19.0790 | −0.683575 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 23.0592 | 0.824070 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −56.3734 | −2.01205 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 34.1825 | 1.21847 | 0.609237 | − | 0.792988i | \(-0.291476\pi\) | ||||
0.609237 | + | 0.792988i | \(0.291476\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −32.0000 | −1.13923 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 9.27131 | 0.329650 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 23.0874 | 0.819857 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −8.78623 | −0.311615 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −24.6184 | −0.872030 | −0.436015 | − | 0.899939i | \(-0.643611\pi\) | ||||
−0.436015 | + | 0.899939i | \(0.643611\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0.671153 | 0.0237437 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 4.35869 | 0.154007 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −34.5426 | −1.21898 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −19.0790 | −0.672445 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −20.7778 | −0.731414 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 31.8139 | 1.11852 | 0.559259 | − | 0.828993i | \(-0.311086\pi\) | ||||
0.559259 | + | 0.828993i | \(0.311086\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −43.9389 | −1.54290 | −0.771451 | − | 0.636289i | \(-0.780469\pi\) | ||||
−0.771451 | + | 0.636289i | \(0.780469\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −27.6447 | −0.969542 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −0.384694 | −0.0134752 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −27.1281 | −0.949091 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −9.33871 | −0.326321 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −45.1281 | −1.57498 | −0.787490 | − | 0.616327i | \(-0.788620\pi\) | ||||
−0.787490 | + | 0.616327i | \(0.788620\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −14.1579 | −0.493514 | −0.246757 | − | 0.969077i | \(-0.579365\pi\) | ||||
−0.246757 | + | 0.969077i | \(0.579365\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 52.0294 | 1.81143 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −14.5082 | −0.504499 | −0.252250 | − | 0.967662i | \(-0.581170\pi\) | ||||
−0.252250 | + | 0.967662i | \(0.581170\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −15.7465 | −0.546899 | −0.273450 | − | 0.961886i | \(-0.588165\pi\) | ||||
−0.273450 | + | 0.961886i | \(0.588165\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −0.720270 | −0.0249859 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0.292731 | 0.0101425 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −21.8715 | −0.756893 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −41.1709 | −1.42308 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 7.66442 | 0.264605 | 0.132303 | − | 0.991209i | \(-0.457763\pi\) | ||||
0.132303 | + | 0.991209i | \(0.457763\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −10.5725 | −0.364568 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −0.852191 | −0.0293510 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −67.7759 | −2.33156 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 10.9572 | 0.376492 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −0.544767 | −0.0186963 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 48.1151 | 1.64936 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 16.9540 | 0.580495 | 0.290247 | − | 0.956952i | \(-0.406262\pi\) | ||||
0.290247 | + | 0.956952i | \(0.406262\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −33.2482 | −1.13706 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 17.0790 | 0.583406 | 0.291703 | − | 0.956509i | \(-0.405778\pi\) | ||||
0.291703 | + | 0.956509i | \(0.405778\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −10.5181 | −0.358872 | −0.179436 | − | 0.983770i | \(-0.557427\pi\) | ||||
−0.179436 | + | 0.983770i | \(0.557427\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −4.24989 | −0.144836 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 36.1151 | 1.22937 | 0.614686 | − | 0.788772i | \(-0.289283\pi\) | ||||
0.614686 | + | 0.788772i | \(0.289283\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −49.3142 | −1.67673 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 19.3900 | 0.658518 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −65.4011 | −2.21858 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 60.8156 | 2.06066 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 24.0231 | 0.813059 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −17.9572 | −0.607063 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −0.177654 | −0.00599895 | −0.00299947 | − | 0.999996i | \(-0.500955\pi\) | ||||
−0.00299947 | + | 0.999996i | \(0.500955\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 1.76481 | 0.0595255 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −1.52962 | −0.0515340 | −0.0257670 | − | 0.999668i | \(-0.508203\pi\) | ||||
−0.0257670 | + | 0.999668i | \(0.508203\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −43.7942 | −1.47379 | −0.736896 | − | 0.676006i | \(-0.763709\pi\) | ||||
−0.736896 | + | 0.676006i | \(0.763709\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −43.6350 | −1.46678 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 35.6938 | 1.19848 | 0.599240 | − | 0.800569i | \(-0.295469\pi\) | ||||
0.599240 | + | 0.800569i | \(0.295469\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −6.35027 | −0.212981 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 5.15623 | 0.172740 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −11.7992 | −0.394846 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −100.816 | −3.36989 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −31.6153 | −1.05560 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −32.9013 | −1.09732 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −0.585462 | −0.0195046 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −6.04285 | −0.201093 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −12.4422 | −0.413594 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 33.3373 | 1.10695 | 0.553473 | − | 0.832867i | \(-0.313302\pi\) | ||||
0.553473 | + | 0.832867i | \(0.313302\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −3.16106 | −0.104846 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −45.5640 | −1.50960 | −0.754802 | − | 0.655953i | \(-0.772267\pi\) | ||||
−0.754802 | + | 0.655953i | \(0.772267\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 22.5426 | 0.746052 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 18.3096 | 0.605296 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 10.5181 | 0.347337 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −6.15792 | −0.203131 | −0.101566 | − | 0.994829i | \(-0.532385\pi\) | ||||
−0.101566 | + | 0.994829i | \(0.532385\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −24.3734 | −0.803130 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 93.6081 | 3.07782 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 12.9210 | 0.424383 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −42.9504 | −1.40916 | −0.704579 | − | 0.709626i | \(-0.748864\pi\) | ||||
−0.704579 | + | 0.709626i | \(0.748864\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −5.14637 | −0.168665 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 17.5725 | 0.575297 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 5.25662 | 0.171910 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −41.1281 | −1.34360 | −0.671798 | − | 0.740735i | \(-0.734478\pi\) | ||||
−0.671798 | + | 0.740735i | \(0.734478\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −4.24989 | −0.138690 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 4.61844 | 0.150557 | 0.0752785 | − | 0.997163i | \(-0.476015\pi\) | ||||
0.0752785 | + | 0.997163i | \(0.476015\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 18.4569 | 0.601040 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −20.5855 | −0.669645 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −0.800923 | −0.0260265 | −0.0130133 | − | 0.999915i | \(-0.504142\pi\) | ||||
−0.0130133 | + | 0.999915i | \(0.504142\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 40.8353 | 1.32557 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 25.8912 | 0.839579 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 13.9143 | 0.450729 | 0.225364 | − | 0.974275i | \(-0.427643\pi\) | ||||
0.225364 | + | 0.974275i | \(0.427643\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 66.5720 | 2.15422 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 23.0592 | 0.745399 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −11.3717 | −0.367211 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 27.7434 | 0.894948 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −4.03442 | −0.130007 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −105.115 | −3.38376 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 27.6363 | 0.888723 | 0.444361 | − | 0.895848i | \(-0.353431\pi\) | ||||
0.444361 | + | 0.895848i | \(0.353431\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 1.72700 | 0.0554792 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 0.810789 | 0.0260195 | 0.0130097 | − | 0.999915i | \(-0.495859\pi\) | ||||
0.0130097 | + | 0.999915i | \(0.495859\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −10.8536 | −0.347952 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −61.5077 | −1.96982 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −4.62831 | −0.148073 | −0.0740363 | − | 0.997256i | \(-0.523588\pi\) | ||||
−0.0740363 | + | 0.997256i | \(0.523588\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 12.1151 | 0.387200 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 1.81896 | 0.0580750 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −5.42081 | −0.172897 | −0.0864485 | − | 0.996256i | \(-0.527552\pi\) | ||||
−0.0864485 | + | 0.996256i | \(0.527552\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 38.3221 | 1.22104 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −2.62831 | −0.0836600 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 26.2436 | 0.834498 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 16.2008 | 0.514634 | 0.257317 | − | 0.966327i | \(-0.417161\pi\) | ||||
0.257317 | + | 0.966327i | \(0.417161\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 16.7862 | 0.532695 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −16.2865 | −0.516315 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −17.9901 | −0.569753 | −0.284877 | − | 0.958564i | \(-0.591953\pi\) | ||||
−0.284877 | + | 0.958564i | \(0.591953\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 51.9143 | 1.64250 |
(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.j.1.2 | yes | 3 | |
3.2 | odd | 2 | 8064.2.a.cb.1.3 | 3 | |||
4.3 | odd | 2 | 896.2.a.l.1.2 | yes | 3 | ||
7.6 | odd | 2 | 6272.2.a.w.1.2 | 3 | |||
8.3 | odd | 2 | 896.2.a.i.1.2 | ✓ | 3 | ||
8.5 | even | 2 | 896.2.a.k.1.2 | yes | 3 | ||
12.11 | even | 2 | 8064.2.a.bu.1.3 | 3 | |||
16.3 | odd | 4 | 1792.2.b.p.897.4 | 6 | |||
16.5 | even | 4 | 1792.2.b.o.897.4 | 6 | |||
16.11 | odd | 4 | 1792.2.b.p.897.3 | 6 | |||
16.13 | even | 4 | 1792.2.b.o.897.3 | 6 | |||
24.5 | odd | 2 | 8064.2.a.ch.1.1 | 3 | |||
24.11 | even | 2 | 8064.2.a.ce.1.1 | 3 | |||
28.27 | even | 2 | 6272.2.a.u.1.2 | 3 | |||
56.13 | odd | 2 | 6272.2.a.v.1.2 | 3 | |||
56.27 | even | 2 | 6272.2.a.x.1.2 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
896.2.a.i.1.2 | ✓ | 3 | 8.3 | odd | 2 | ||
896.2.a.j.1.2 | yes | 3 | 1.1 | even | 1 | trivial | |
896.2.a.k.1.2 | yes | 3 | 8.5 | even | 2 | ||
896.2.a.l.1.2 | yes | 3 | 4.3 | odd | 2 | ||
1792.2.b.o.897.3 | 6 | 16.13 | even | 4 | |||
1792.2.b.o.897.4 | 6 | 16.5 | even | 4 | |||
1792.2.b.p.897.3 | 6 | 16.11 | odd | 4 | |||
1792.2.b.p.897.4 | 6 | 16.3 | odd | 4 | |||
6272.2.a.u.1.2 | 3 | 28.27 | even | 2 | |||
6272.2.a.v.1.2 | 3 | 56.13 | odd | 2 | |||
6272.2.a.w.1.2 | 3 | 7.6 | odd | 2 | |||
6272.2.a.x.1.2 | 3 | 56.27 | even | 2 | |||
8064.2.a.bu.1.3 | 3 | 12.11 | even | 2 | |||
8064.2.a.cb.1.3 | 3 | 3.2 | odd | 2 | |||
8064.2.a.ce.1.1 | 3 | 24.11 | even | 2 | |||
8064.2.a.ch.1.1 | 3 | 24.5 | odd | 2 |