Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8046,2,Mod(1,8046)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8046, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("8046.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8046 = 2 \cdot 3^{3} \cdot 149 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8046.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: | \(64.2476334663\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 3 x^{11} - 31 x^{10} + 82 x^{9} + 334 x^{8} - 684 x^{7} - 1561 x^{6} + 1551 x^{5} + 3573 x^{4} + 345 x^{3} - 1607 x^{2} - 594 x - 3 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.8 | ||
Root | \(0.761360\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8046.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 0.761360 | 0.340491 | 0.170245 | − | 0.985402i | \(-0.445544\pi\) | ||||
0.170245 | + | 0.985402i | \(0.445544\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.23946 | 0.468474 | 0.234237 | − | 0.972180i | \(-0.424741\pi\) | ||||
0.234237 | + | 0.972180i | \(0.424741\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −0.761360 | −0.240763 | ||||||||
\(11\) | 4.16498 | 1.25579 | 0.627894 | − | 0.778299i | \(-0.283917\pi\) | ||||
0.627894 | + | 0.778299i | \(0.283917\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.92984 | 0.812591 | 0.406296 | − | 0.913742i | \(-0.366820\pi\) | ||||
0.406296 | + | 0.913742i | \(0.366820\pi\) | |||||||
\(14\) | −1.23946 | −0.331261 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 2.05222 | 0.497737 | 0.248868 | − | 0.968537i | \(-0.419941\pi\) | ||||
0.248868 | + | 0.968537i | \(0.419941\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.666318 | 0.152864 | 0.0764319 | − | 0.997075i | \(-0.475647\pi\) | ||||
0.0764319 | + | 0.997075i | \(0.475647\pi\) | |||||||
\(20\) | 0.761360 | 0.170245 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −4.16498 | −0.887976 | ||||||||
\(23\) | 8.48075 | 1.76836 | 0.884179 | − | 0.467148i | \(-0.154719\pi\) | ||||
0.884179 | + | 0.467148i | \(0.154719\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.42033 | −0.884066 | ||||||||
\(26\) | −2.92984 | −0.574589 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 1.23946 | 0.234237 | ||||||||
\(29\) | −1.77307 | −0.329250 | −0.164625 | − | 0.986356i | \(-0.552641\pi\) | ||||
−0.164625 | + | 0.986356i | \(0.552641\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.84602 | 0.690765 | 0.345382 | − | 0.938462i | \(-0.387749\pi\) | ||||
0.345382 | + | 0.938462i | \(0.387749\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −2.05222 | −0.351953 | ||||||||
\(35\) | 0.943679 | 0.159511 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 4.44887 | 0.731390 | 0.365695 | − | 0.930735i | \(-0.380831\pi\) | ||||
0.365695 | + | 0.930735i | \(0.380831\pi\) | |||||||
\(38\) | −0.666318 | −0.108091 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −0.761360 | −0.120382 | ||||||||
\(41\) | −2.52486 | −0.394317 | −0.197158 | − | 0.980372i | \(-0.563171\pi\) | ||||
−0.197158 | + | 0.980372i | \(0.563171\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 5.24402 | 0.799706 | 0.399853 | − | 0.916579i | \(-0.369061\pi\) | ||||
0.399853 | + | 0.916579i | \(0.369061\pi\) | |||||||
\(44\) | 4.16498 | 0.627894 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −8.48075 | −1.25042 | ||||||||
\(47\) | −3.71322 | −0.541630 | −0.270815 | − | 0.962631i | \(-0.587293\pi\) | ||||
−0.270815 | + | 0.962631i | \(0.587293\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −5.46373 | −0.780533 | ||||||||
\(50\) | 4.42033 | 0.625129 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 2.92984 | 0.406296 | ||||||||
\(53\) | 8.26592 | 1.13541 | 0.567706 | − | 0.823231i | \(-0.307831\pi\) | ||||
0.567706 | + | 0.823231i | \(0.307831\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 3.17105 | 0.427584 | ||||||||
\(56\) | −1.23946 | −0.165630 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 1.77307 | 0.232815 | ||||||||
\(59\) | 9.37120 | 1.22003 | 0.610013 | − | 0.792391i | \(-0.291164\pi\) | ||||
0.610013 | + | 0.792391i | \(0.291164\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 10.0229 | 1.28330 | 0.641649 | − | 0.766998i | \(-0.278251\pi\) | ||||
0.641649 | + | 0.766998i | \(0.278251\pi\) | |||||||
\(62\) | −3.84602 | −0.488445 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 2.23066 | 0.276680 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1.45888 | −0.178231 | −0.0891155 | − | 0.996021i | \(-0.528404\pi\) | ||||
−0.0891155 | + | 0.996021i | \(0.528404\pi\) | |||||||
\(68\) | 2.05222 | 0.248868 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −0.943679 | −0.112791 | ||||||||
\(71\) | 6.19297 | 0.734970 | 0.367485 | − | 0.930029i | \(-0.380219\pi\) | ||||
0.367485 | + | 0.930029i | \(0.380219\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −10.9177 | −1.27782 | −0.638910 | − | 0.769281i | \(-0.720614\pi\) | ||||
−0.638910 | + | 0.769281i | \(0.720614\pi\) | |||||||
\(74\) | −4.44887 | −0.517171 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0.666318 | 0.0764319 | ||||||||
\(77\) | 5.16234 | 0.588304 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −9.54970 | −1.07443 | −0.537213 | − | 0.843447i | \(-0.680523\pi\) | ||||
−0.537213 | + | 0.843447i | \(0.680523\pi\) | |||||||
\(80\) | 0.761360 | 0.0851227 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 2.52486 | 0.278824 | ||||||||
\(83\) | 5.69162 | 0.624737 | 0.312368 | − | 0.949961i | \(-0.398878\pi\) | ||||
0.312368 | + | 0.949961i | \(0.398878\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.56248 | 0.169475 | ||||||||
\(86\) | −5.24402 | −0.565477 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −4.16498 | −0.443988 | ||||||||
\(89\) | 7.72882 | 0.819253 | 0.409627 | − | 0.912253i | \(-0.365659\pi\) | ||||
0.409627 | + | 0.912253i | \(0.365659\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 3.63143 | 0.380678 | ||||||||
\(92\) | 8.48075 | 0.884179 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 3.71322 | 0.382990 | ||||||||
\(95\) | 0.507308 | 0.0520487 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −18.6599 | −1.89463 | −0.947315 | − | 0.320304i | \(-0.896215\pi\) | ||||
−0.947315 | + | 0.320304i | \(0.896215\pi\) | |||||||
\(98\) | 5.46373 | 0.551920 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −4.42033 | −0.442033 | ||||||||
\(101\) | 5.89482 | 0.586557 | 0.293278 | − | 0.956027i | \(-0.405254\pi\) | ||||
0.293278 | + | 0.956027i | \(0.405254\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −3.77939 | −0.372395 | −0.186197 | − | 0.982512i | \(-0.559616\pi\) | ||||
−0.186197 | + | 0.982512i | \(0.559616\pi\) | |||||||
\(104\) | −2.92984 | −0.287294 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −8.26592 | −0.802858 | ||||||||
\(107\) | 7.59349 | 0.734090 | 0.367045 | − | 0.930203i | \(-0.380369\pi\) | ||||
0.367045 | + | 0.930203i | \(0.380369\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1.05733 | 0.101274 | 0.0506371 | − | 0.998717i | \(-0.483875\pi\) | ||||
0.0506371 | + | 0.998717i | \(0.483875\pi\) | |||||||
\(110\) | −3.17105 | −0.302348 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 1.23946 | 0.117118 | ||||||||
\(113\) | −9.52892 | −0.896405 | −0.448203 | − | 0.893932i | \(-0.647936\pi\) | ||||
−0.448203 | + | 0.893932i | \(0.647936\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 6.45691 | 0.602110 | ||||||||
\(116\) | −1.77307 | −0.164625 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −9.37120 | −0.862689 | ||||||||
\(119\) | 2.54366 | 0.233177 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 6.34704 | 0.577004 | ||||||||
\(122\) | −10.0229 | −0.907429 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 3.84602 | 0.345382 | ||||||||
\(125\) | −7.17227 | −0.641507 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −15.5448 | −1.37938 | −0.689689 | − | 0.724106i | \(-0.742253\pi\) | ||||
−0.689689 | + | 0.724106i | \(0.742253\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −2.23066 | −0.195642 | ||||||||
\(131\) | 5.51152 | 0.481544 | 0.240772 | − | 0.970582i | \(-0.422599\pi\) | ||||
0.240772 | + | 0.970582i | \(0.422599\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.825877 | 0.0716127 | ||||||||
\(134\) | 1.45888 | 0.126028 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −2.05222 | −0.175977 | ||||||||
\(137\) | −10.2474 | −0.875495 | −0.437747 | − | 0.899098i | \(-0.644224\pi\) | ||||
−0.437747 | + | 0.899098i | \(0.644224\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −9.23075 | −0.782942 | −0.391471 | − | 0.920190i | \(-0.628034\pi\) | ||||
−0.391471 | + | 0.920190i | \(0.628034\pi\) | |||||||
\(140\) | 0.943679 | 0.0797555 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −6.19297 | −0.519702 | ||||||||
\(143\) | 12.2027 | 1.02044 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1.34994 | −0.112107 | ||||||||
\(146\) | 10.9177 | 0.903555 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 4.44887 | 0.365695 | ||||||||
\(149\) | −1.00000 | −0.0819232 | ||||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 8.58020 | 0.698247 | 0.349124 | − | 0.937077i | \(-0.386479\pi\) | ||||
0.349124 | + | 0.937077i | \(0.386479\pi\) | |||||||
\(152\) | −0.666318 | −0.0540455 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −5.16234 | −0.415993 | ||||||||
\(155\) | 2.92821 | 0.235199 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 9.08853 | 0.725344 | 0.362672 | − | 0.931917i | \(-0.381865\pi\) | ||||
0.362672 | + | 0.931917i | \(0.381865\pi\) | |||||||
\(158\) | 9.54970 | 0.759733 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −0.761360 | −0.0601908 | ||||||||
\(161\) | 10.5116 | 0.828429 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 13.3116 | 1.04264 | 0.521322 | − | 0.853360i | \(-0.325439\pi\) | ||||
0.521322 | + | 0.853360i | \(0.325439\pi\) | |||||||
\(164\) | −2.52486 | −0.197158 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −5.69162 | −0.441756 | ||||||||
\(167\) | −6.38977 | −0.494455 | −0.247228 | − | 0.968957i | \(-0.579520\pi\) | ||||
−0.247228 | + | 0.968957i | \(0.579520\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −4.41604 | −0.339695 | ||||||||
\(170\) | −1.56248 | −0.119837 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 5.24402 | 0.399853 | ||||||||
\(173\) | 1.23167 | 0.0936421 | 0.0468211 | − | 0.998903i | \(-0.485091\pi\) | ||||
0.0468211 | + | 0.998903i | \(0.485091\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −5.47884 | −0.414162 | ||||||||
\(176\) | 4.16498 | 0.313947 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −7.72882 | −0.579299 | ||||||||
\(179\) | −10.4034 | −0.777585 | −0.388792 | − | 0.921325i | \(-0.627108\pi\) | ||||
−0.388792 | + | 0.921325i | \(0.627108\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 5.03575 | 0.374304 | 0.187152 | − | 0.982331i | \(-0.440074\pi\) | ||||
0.187152 | + | 0.982331i | \(0.440074\pi\) | |||||||
\(182\) | −3.63143 | −0.269180 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −8.48075 | −0.625209 | ||||||||
\(185\) | 3.38720 | 0.249032 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 8.54746 | 0.625052 | ||||||||
\(188\) | −3.71322 | −0.270815 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −0.507308 | −0.0368040 | ||||||||
\(191\) | −14.0973 | −1.02004 | −0.510022 | − | 0.860161i | \(-0.670363\pi\) | ||||
−0.510022 | + | 0.860161i | \(0.670363\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 7.50264 | 0.540052 | 0.270026 | − | 0.962853i | \(-0.412968\pi\) | ||||
0.270026 | + | 0.962853i | \(0.412968\pi\) | |||||||
\(194\) | 18.6599 | 1.33971 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −5.46373 | −0.390266 | ||||||||
\(197\) | −8.01296 | −0.570900 | −0.285450 | − | 0.958394i | \(-0.592143\pi\) | ||||
−0.285450 | + | 0.958394i | \(0.592143\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −14.7857 | −1.04813 | −0.524064 | − | 0.851679i | \(-0.675585\pi\) | ||||
−0.524064 | + | 0.851679i | \(0.675585\pi\) | |||||||
\(200\) | 4.42033 | 0.312565 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −5.89482 | −0.414758 | ||||||||
\(203\) | −2.19765 | −0.154245 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1.92233 | −0.134261 | ||||||||
\(206\) | 3.77939 | 0.263323 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 2.92984 | 0.203148 | ||||||||
\(209\) | 2.77520 | 0.191965 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 3.54316 | 0.243921 | 0.121961 | − | 0.992535i | \(-0.461082\pi\) | ||||
0.121961 | + | 0.992535i | \(0.461082\pi\) | |||||||
\(212\) | 8.26592 | 0.567706 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −7.59349 | −0.519080 | ||||||||
\(215\) | 3.99259 | 0.272292 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 4.76700 | 0.323605 | ||||||||
\(218\) | −1.05733 | −0.0716117 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 3.17105 | 0.213792 | ||||||||
\(221\) | 6.01268 | 0.404457 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 12.5260 | 0.838806 | 0.419403 | − | 0.907800i | \(-0.362239\pi\) | ||||
0.419403 | + | 0.907800i | \(0.362239\pi\) | |||||||
\(224\) | −1.23946 | −0.0828152 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 9.52892 | 0.633854 | ||||||||
\(227\) | 14.2435 | 0.945376 | 0.472688 | − | 0.881230i | \(-0.343284\pi\) | ||||
0.472688 | + | 0.881230i | \(0.343284\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −22.3396 | −1.47624 | −0.738120 | − | 0.674670i | \(-0.764286\pi\) | ||||
−0.738120 | + | 0.674670i | \(0.764286\pi\) | |||||||
\(230\) | −6.45691 | −0.425756 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 1.77307 | 0.116407 | ||||||||
\(233\) | −13.9412 | −0.913316 | −0.456658 | − | 0.889642i | \(-0.650954\pi\) | ||||
−0.456658 | + | 0.889642i | \(0.650954\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −2.82710 | −0.184420 | ||||||||
\(236\) | 9.37120 | 0.610013 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −2.54366 | −0.164881 | ||||||||
\(239\) | 15.8580 | 1.02577 | 0.512883 | − | 0.858458i | \(-0.328577\pi\) | ||||
0.512883 | + | 0.858458i | \(0.328577\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −13.2150 | −0.851253 | −0.425626 | − | 0.904899i | \(-0.639946\pi\) | ||||
−0.425626 | + | 0.904899i | \(0.639946\pi\) | |||||||
\(242\) | −6.34704 | −0.408003 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 10.0229 | 0.641649 | ||||||||
\(245\) | −4.15987 | −0.265764 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1.95220 | 0.124216 | ||||||||
\(248\) | −3.84602 | −0.244222 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 7.17227 | 0.453614 | ||||||||
\(251\) | 8.73531 | 0.551368 | 0.275684 | − | 0.961248i | \(-0.411096\pi\) | ||||
0.275684 | + | 0.961248i | \(0.411096\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 35.3221 | 2.22068 | ||||||||
\(254\) | 15.5448 | 0.975367 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 17.0182 | 1.06157 | 0.530785 | − | 0.847507i | \(-0.321897\pi\) | ||||
0.530785 | + | 0.847507i | \(0.321897\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 5.51422 | 0.342637 | ||||||||
\(260\) | 2.23066 | 0.138340 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −5.51152 | −0.340503 | ||||||||
\(263\) | 1.87735 | 0.115762 | 0.0578811 | − | 0.998323i | \(-0.481566\pi\) | ||||
0.0578811 | + | 0.998323i | \(0.481566\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 6.29335 | 0.386597 | ||||||||
\(266\) | −0.825877 | −0.0506378 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −1.45888 | −0.0891155 | ||||||||
\(269\) | −17.0976 | −1.04246 | −0.521230 | − | 0.853416i | \(-0.674527\pi\) | ||||
−0.521230 | + | 0.853416i | \(0.674527\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2.52171 | 0.153183 | 0.0765916 | − | 0.997063i | \(-0.475596\pi\) | ||||
0.0765916 | + | 0.997063i | \(0.475596\pi\) | |||||||
\(272\) | 2.05222 | 0.124434 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 10.2474 | 0.619068 | ||||||||
\(275\) | −18.4106 | −1.11020 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 20.3576 | 1.22317 | 0.611586 | − | 0.791178i | \(-0.290532\pi\) | ||||
0.611586 | + | 0.791178i | \(0.290532\pi\) | |||||||
\(278\) | 9.23075 | 0.553624 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −0.943679 | −0.0563956 | ||||||||
\(281\) | −26.7498 | −1.59576 | −0.797880 | − | 0.602816i | \(-0.794045\pi\) | ||||
−0.797880 | + | 0.602816i | \(0.794045\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −29.9892 | −1.78267 | −0.891336 | − | 0.453344i | \(-0.850231\pi\) | ||||
−0.891336 | + | 0.453344i | \(0.850231\pi\) | |||||||
\(284\) | 6.19297 | 0.367485 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −12.2027 | −0.721562 | ||||||||
\(287\) | −3.12947 | −0.184727 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −12.7884 | −0.752258 | ||||||||
\(290\) | 1.34994 | 0.0792713 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −10.9177 | −0.638910 | ||||||||
\(293\) | 5.78618 | 0.338032 | 0.169016 | − | 0.985613i | \(-0.445941\pi\) | ||||
0.169016 | + | 0.985613i | \(0.445941\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 7.13486 | 0.415408 | ||||||||
\(296\) | −4.44887 | −0.258586 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 1.00000 | 0.0579284 | ||||||||
\(299\) | 24.8472 | 1.43695 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 6.49978 | 0.374641 | ||||||||
\(302\) | −8.58020 | −0.493735 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0.666318 | 0.0382160 | ||||||||
\(305\) | 7.63102 | 0.436951 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −15.9386 | −0.909665 | −0.454832 | − | 0.890577i | \(-0.650301\pi\) | ||||
−0.454832 | + | 0.890577i | \(0.650301\pi\) | |||||||
\(308\) | 5.16234 | 0.294152 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −2.92821 | −0.166311 | ||||||||
\(311\) | 18.5036 | 1.04924 | 0.524621 | − | 0.851336i | \(-0.324207\pi\) | ||||
0.524621 | + | 0.851336i | \(0.324207\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −8.94571 | −0.505641 | −0.252821 | − | 0.967513i | \(-0.581358\pi\) | ||||
−0.252821 | + | 0.967513i | \(0.581358\pi\) | |||||||
\(314\) | −9.08853 | −0.512896 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −9.54970 | −0.537213 | ||||||||
\(317\) | 33.2027 | 1.86485 | 0.932424 | − | 0.361365i | \(-0.117689\pi\) | ||||
0.932424 | + | 0.361365i | \(0.117689\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −7.38478 | −0.413468 | ||||||||
\(320\) | 0.761360 | 0.0425613 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −10.5116 | −0.585788 | ||||||||
\(323\) | 1.36743 | 0.0760859 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −12.9509 | −0.718384 | ||||||||
\(326\) | −13.3116 | −0.737260 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 2.52486 | 0.139412 | ||||||||
\(329\) | −4.60241 | −0.253739 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −26.3503 | −1.44834 | −0.724172 | − | 0.689620i | \(-0.757778\pi\) | ||||
−0.724172 | + | 0.689620i | \(0.757778\pi\) | |||||||
\(332\) | 5.69162 | 0.312368 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 6.38977 | 0.349633 | ||||||||
\(335\) | −1.11074 | −0.0606860 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 4.70544 | 0.256322 | 0.128161 | − | 0.991753i | \(-0.459093\pi\) | ||||
0.128161 | + | 0.991753i | \(0.459093\pi\) | |||||||
\(338\) | 4.41604 | 0.240201 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 1.56248 | 0.0847374 | ||||||||
\(341\) | 16.0186 | 0.867454 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −15.4483 | −0.834132 | ||||||||
\(344\) | −5.24402 | −0.282739 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −1.23167 | −0.0662150 | ||||||||
\(347\) | 27.0511 | 1.45218 | 0.726091 | − | 0.687599i | \(-0.241335\pi\) | ||||
0.726091 | + | 0.687599i | \(0.241335\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 9.98625 | 0.534552 | 0.267276 | − | 0.963620i | \(-0.413877\pi\) | ||||
0.267276 | + | 0.963620i | \(0.413877\pi\) | |||||||
\(350\) | 5.47884 | 0.292856 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −4.16498 | −0.221994 | ||||||||
\(353\) | 9.07685 | 0.483112 | 0.241556 | − | 0.970387i | \(-0.422342\pi\) | ||||
0.241556 | + | 0.970387i | \(0.422342\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 4.71508 | 0.250251 | ||||||||
\(356\) | 7.72882 | 0.409627 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 10.4034 | 0.549836 | ||||||||
\(359\) | −13.4684 | −0.710836 | −0.355418 | − | 0.934707i | \(-0.615661\pi\) | ||||
−0.355418 | + | 0.934707i | \(0.615661\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.5560 | −0.976633 | ||||||||
\(362\) | −5.03575 | −0.264673 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 3.63143 | 0.190339 | ||||||||
\(365\) | −8.31230 | −0.435086 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 18.1866 | 0.949331 | 0.474665 | − | 0.880166i | \(-0.342569\pi\) | ||||
0.474665 | + | 0.880166i | \(0.342569\pi\) | |||||||
\(368\) | 8.48075 | 0.442089 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −3.38720 | −0.176092 | ||||||||
\(371\) | 10.2453 | 0.531911 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 15.9422 | 0.825456 | 0.412728 | − | 0.910854i | \(-0.364576\pi\) | ||||
0.412728 | + | 0.910854i | \(0.364576\pi\) | |||||||
\(374\) | −8.54746 | −0.441978 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 3.71322 | 0.191495 | ||||||||
\(377\) | −5.19480 | −0.267546 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −29.0734 | −1.49340 | −0.746701 | − | 0.665160i | \(-0.768363\pi\) | ||||
−0.746701 | + | 0.665160i | \(0.768363\pi\) | |||||||
\(380\) | 0.507308 | 0.0260244 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 14.0973 | 0.721280 | ||||||||
\(383\) | 25.2617 | 1.29081 | 0.645407 | − | 0.763839i | \(-0.276688\pi\) | ||||
0.645407 | + | 0.763839i | \(0.276688\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 3.93040 | 0.200312 | ||||||||
\(386\) | −7.50264 | −0.381874 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −18.6599 | −0.947315 | ||||||||
\(389\) | 1.32764 | 0.0673138 | 0.0336569 | − | 0.999433i | \(-0.489285\pi\) | ||||
0.0336569 | + | 0.999433i | \(0.489285\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 17.4044 | 0.880177 | ||||||||
\(392\) | 5.46373 | 0.275960 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 8.01296 | 0.403687 | ||||||||
\(395\) | −7.27077 | −0.365832 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −2.12240 | −0.106520 | −0.0532601 | − | 0.998581i | \(-0.516961\pi\) | ||||
−0.0532601 | + | 0.998581i | \(0.516961\pi\) | |||||||
\(398\) | 14.7857 | 0.741138 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −4.42033 | −0.221017 | ||||||||
\(401\) | 26.4011 | 1.31841 | 0.659204 | − | 0.751964i | \(-0.270893\pi\) | ||||
0.659204 | + | 0.751964i | \(0.270893\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 11.2682 | 0.561310 | ||||||||
\(404\) | 5.89482 | 0.293278 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 2.19765 | 0.109068 | ||||||||
\(407\) | 18.5295 | 0.918471 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −10.0056 | −0.494744 | −0.247372 | − | 0.968921i | \(-0.579567\pi\) | ||||
−0.247372 | + | 0.968921i | \(0.579567\pi\) | |||||||
\(410\) | 1.92233 | 0.0949370 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −3.77939 | −0.186197 | ||||||||
\(413\) | 11.6153 | 0.571550 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 4.33338 | 0.212717 | ||||||||
\(416\) | −2.92984 | −0.143647 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −2.77520 | −0.135739 | ||||||||
\(419\) | −20.0307 | −0.978562 | −0.489281 | − | 0.872126i | \(-0.662741\pi\) | ||||
−0.489281 | + | 0.872126i | \(0.662741\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 26.9452 | 1.31323 | 0.656614 | − | 0.754227i | \(-0.271988\pi\) | ||||
0.656614 | + | 0.754227i | \(0.271988\pi\) | |||||||
\(422\) | −3.54316 | −0.172478 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −8.26592 | −0.401429 | ||||||||
\(425\) | −9.07150 | −0.440032 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 12.4230 | 0.601191 | ||||||||
\(428\) | 7.59349 | 0.367045 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −3.99259 | −0.192540 | ||||||||
\(431\) | −16.9357 | −0.815763 | −0.407881 | − | 0.913035i | \(-0.633732\pi\) | ||||
−0.407881 | + | 0.913035i | \(0.633732\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −10.1849 | −0.489453 | −0.244727 | − | 0.969592i | \(-0.578698\pi\) | ||||
−0.244727 | + | 0.969592i | \(0.578698\pi\) | |||||||
\(434\) | −4.76700 | −0.228823 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 1.05733 | 0.0506371 | ||||||||
\(437\) | 5.65087 | 0.270318 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 32.8283 | 1.56681 | 0.783405 | − | 0.621511i | \(-0.213481\pi\) | ||||
0.783405 | + | 0.621511i | \(0.213481\pi\) | |||||||
\(440\) | −3.17105 | −0.151174 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −6.01268 | −0.285994 | ||||||||
\(443\) | −13.1581 | −0.625162 | −0.312581 | − | 0.949891i | \(-0.601194\pi\) | ||||
−0.312581 | + | 0.949891i | \(0.601194\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 5.88442 | 0.278948 | ||||||||
\(446\) | −12.5260 | −0.593126 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 1.23946 | 0.0585592 | ||||||||
\(449\) | 1.34071 | 0.0632721 | 0.0316361 | − | 0.999499i | \(-0.489928\pi\) | ||||
0.0316361 | + | 0.999499i | \(0.489928\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −10.5160 | −0.495178 | ||||||||
\(452\) | −9.52892 | −0.448203 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −14.2435 | −0.668482 | ||||||||
\(455\) | 2.76483 | 0.129617 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 4.66820 | 0.218369 | 0.109185 | − | 0.994021i | \(-0.465176\pi\) | ||||
0.109185 | + | 0.994021i | \(0.465176\pi\) | |||||||
\(458\) | 22.3396 | 1.04386 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 6.45691 | 0.301055 | ||||||||
\(461\) | −7.86962 | −0.366525 | −0.183262 | − | 0.983064i | \(-0.558666\pi\) | ||||
−0.183262 | + | 0.983064i | \(0.558666\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 19.3249 | 0.898106 | 0.449053 | − | 0.893505i | \(-0.351761\pi\) | ||||
0.449053 | + | 0.893505i | \(0.351761\pi\) | |||||||
\(464\) | −1.77307 | −0.0823125 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 13.9412 | 0.645812 | ||||||||
\(467\) | −35.3122 | −1.63405 | −0.817026 | − | 0.576601i | \(-0.804379\pi\) | ||||
−0.817026 | + | 0.576601i | \(0.804379\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −1.80824 | −0.0834965 | ||||||||
\(470\) | 2.82710 | 0.130405 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −9.37120 | −0.431345 | ||||||||
\(473\) | 21.8412 | 1.00426 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −2.94535 | −0.135142 | ||||||||
\(476\) | 2.54366 | 0.116588 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −15.8580 | −0.725326 | ||||||||
\(479\) | −5.70156 | −0.260511 | −0.130255 | − | 0.991480i | \(-0.541580\pi\) | ||||
−0.130255 | + | 0.991480i | \(0.541580\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 13.0345 | 0.594322 | ||||||||
\(482\) | 13.2150 | 0.601927 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 6.34704 | 0.288502 | ||||||||
\(485\) | −14.2069 | −0.645104 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −24.4051 | −1.10590 | −0.552950 | − | 0.833214i | \(-0.686498\pi\) | ||||
−0.552950 | + | 0.833214i | \(0.686498\pi\) | |||||||
\(488\) | −10.0229 | −0.453714 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 4.15987 | 0.187924 | ||||||||
\(491\) | 14.7538 | 0.665828 | 0.332914 | − | 0.942957i | \(-0.391968\pi\) | ||||
0.332914 | + | 0.942957i | \(0.391968\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −3.63872 | −0.163880 | ||||||||
\(494\) | −1.95220 | −0.0878338 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 3.84602 | 0.172691 | ||||||||
\(497\) | 7.67597 | 0.344314 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 3.13631 | 0.140400 | 0.0702002 | − | 0.997533i | \(-0.477636\pi\) | ||||
0.0702002 | + | 0.997533i | \(0.477636\pi\) | |||||||
\(500\) | −7.17227 | −0.320754 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −8.73531 | −0.389876 | ||||||||
\(503\) | −32.1683 | −1.43431 | −0.717157 | − | 0.696912i | \(-0.754557\pi\) | ||||
−0.717157 | + | 0.696912i | \(0.754557\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 4.48808 | 0.199717 | ||||||||
\(506\) | −35.3221 | −1.57026 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −15.5448 | −0.689689 | ||||||||
\(509\) | 12.2885 | 0.544677 | 0.272339 | − | 0.962202i | \(-0.412203\pi\) | ||||
0.272339 | + | 0.962202i | \(0.412203\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −13.5321 | −0.598625 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −17.0182 | −0.750643 | ||||||||
\(515\) | −2.87748 | −0.126797 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −15.4655 | −0.680172 | ||||||||
\(518\) | −5.51422 | −0.242281 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −2.23066 | −0.0978211 | ||||||||
\(521\) | 24.8807 | 1.09004 | 0.545022 | − | 0.838421i | \(-0.316521\pi\) | ||||
0.545022 | + | 0.838421i | \(0.316521\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 5.95819 | 0.260534 | 0.130267 | − | 0.991479i | \(-0.458417\pi\) | ||||
0.130267 | + | 0.991479i | \(0.458417\pi\) | |||||||
\(524\) | 5.51152 | 0.240772 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −1.87735 | −0.0818562 | ||||||||
\(527\) | 7.89288 | 0.343819 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 48.9231 | 2.12709 | ||||||||
\(530\) | −6.29335 | −0.273366 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0.825877 | 0.0358063 | ||||||||
\(533\) | −7.39743 | −0.320418 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 5.78138 | 0.249951 | ||||||||
\(536\) | 1.45888 | 0.0630142 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 17.0976 | 0.737130 | ||||||||
\(539\) | −22.7563 | −0.980183 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 19.2533 | 0.827762 | 0.413881 | − | 0.910331i | \(-0.364173\pi\) | ||||
0.413881 | + | 0.910331i | \(0.364173\pi\) | |||||||
\(542\) | −2.52171 | −0.108317 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −2.05222 | −0.0879883 | ||||||||
\(545\) | 0.805012 | 0.0344829 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −21.0064 | −0.898171 | −0.449085 | − | 0.893489i | \(-0.648250\pi\) | ||||
−0.449085 | + | 0.893489i | \(0.648250\pi\) | |||||||
\(548\) | −10.2474 | −0.437747 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 18.4106 | 0.785030 | ||||||||
\(551\) | −1.18143 | −0.0503304 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −11.8365 | −0.503340 | ||||||||
\(554\) | −20.3576 | −0.864913 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −9.23075 | −0.391471 | ||||||||
\(557\) | −6.48989 | −0.274986 | −0.137493 | − | 0.990503i | \(-0.543904\pi\) | ||||
−0.137493 | + | 0.990503i | \(0.543904\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 15.3641 | 0.649834 | ||||||||
\(560\) | 0.943679 | 0.0398777 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 26.7498 | 1.12837 | ||||||||
\(563\) | 44.9514 | 1.89447 | 0.947237 | − | 0.320533i | \(-0.103862\pi\) | ||||
0.947237 | + | 0.320533i | \(0.103862\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −7.25494 | −0.305218 | ||||||||
\(566\) | 29.9892 | 1.26054 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −6.19297 | −0.259851 | ||||||||
\(569\) | −18.5364 | −0.777085 | −0.388542 | − | 0.921431i | \(-0.627021\pi\) | ||||
−0.388542 | + | 0.921431i | \(0.627021\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 11.1531 | 0.466741 | 0.233370 | − | 0.972388i | \(-0.425025\pi\) | ||||
0.233370 | + | 0.972388i | \(0.425025\pi\) | |||||||
\(572\) | 12.2027 | 0.510221 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 3.12947 | 0.130622 | ||||||||
\(575\) | −37.4877 | −1.56335 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 4.89010 | 0.203578 | 0.101789 | − | 0.994806i | \(-0.467543\pi\) | ||||
0.101789 | + | 0.994806i | \(0.467543\pi\) | |||||||
\(578\) | 12.7884 | 0.531927 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −1.34994 | −0.0560533 | ||||||||
\(581\) | 7.05456 | 0.292673 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 34.4274 | 1.42584 | ||||||||
\(584\) | 10.9177 | 0.451778 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −5.78618 | −0.239025 | ||||||||
\(587\) | −37.4879 | −1.54729 | −0.773646 | − | 0.633618i | \(-0.781569\pi\) | ||||
−0.773646 | + | 0.633618i | \(0.781569\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 2.56267 | 0.105593 | ||||||||
\(590\) | −7.13486 | −0.293738 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 4.44887 | 0.182848 | ||||||||
\(593\) | −11.4627 | −0.470719 | −0.235359 | − | 0.971908i | \(-0.575627\pi\) | ||||
−0.235359 | + | 0.971908i | \(0.575627\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1.93664 | 0.0793944 | ||||||||
\(596\) | −1.00000 | −0.0409616 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −24.8472 | −1.01608 | ||||||||
\(599\) | −4.91928 | −0.200996 | −0.100498 | − | 0.994937i | \(-0.532044\pi\) | ||||
−0.100498 | + | 0.994937i | \(0.532044\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 3.31114 | 0.135064 | 0.0675321 | − | 0.997717i | \(-0.478487\pi\) | ||||
0.0675321 | + | 0.997717i | \(0.478487\pi\) | |||||||
\(602\) | −6.49978 | −0.264911 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 8.58020 | 0.349124 | ||||||||
\(605\) | 4.83239 | 0.196464 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −36.6659 | −1.48822 | −0.744112 | − | 0.668055i | \(-0.767127\pi\) | ||||
−0.744112 | + | 0.668055i | \(0.767127\pi\) | |||||||
\(608\) | −0.666318 | −0.0270228 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −7.63102 | −0.308971 | ||||||||
\(611\) | −10.8792 | −0.440123 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 23.5176 | 0.949865 | 0.474932 | − | 0.880022i | \(-0.342472\pi\) | ||||
0.474932 | + | 0.880022i | \(0.342472\pi\) | |||||||
\(614\) | 15.9386 | 0.643230 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −5.16234 | −0.207997 | ||||||||
\(617\) | 9.64068 | 0.388119 | 0.194060 | − | 0.980990i | \(-0.437834\pi\) | ||||
0.194060 | + | 0.980990i | \(0.437834\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 11.9779 | 0.481431 | 0.240715 | − | 0.970596i | \(-0.422618\pi\) | ||||
0.240715 | + | 0.970596i | \(0.422618\pi\) | |||||||
\(620\) | 2.92821 | 0.117600 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −18.5036 | −0.741927 | ||||||||
\(623\) | 9.57960 | 0.383798 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 16.6410 | 0.665639 | ||||||||
\(626\) | 8.94571 | 0.357542 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 9.08853 | 0.362672 | ||||||||
\(629\) | 9.13007 | 0.364040 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −26.2849 | −1.04638 | −0.523192 | − | 0.852215i | \(-0.675259\pi\) | ||||
−0.523192 | + | 0.852215i | \(0.675259\pi\) | |||||||
\(632\) | 9.54970 | 0.379867 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −33.2027 | −1.31865 | ||||||||
\(635\) | −11.8352 | −0.469665 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −16.0078 | −0.634254 | ||||||||
\(638\) | 7.38478 | 0.292366 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −0.761360 | −0.0300954 | ||||||||
\(641\) | −3.50080 | −0.138273 | −0.0691366 | − | 0.997607i | \(-0.522024\pi\) | ||||
−0.0691366 | + | 0.997607i | \(0.522024\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 4.61292 | 0.181916 | 0.0909578 | − | 0.995855i | \(-0.471007\pi\) | ||||
0.0909578 | + | 0.995855i | \(0.471007\pi\) | |||||||
\(644\) | 10.5116 | 0.414214 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −1.36743 | −0.0538009 | ||||||||
\(647\) | −17.2644 | −0.678735 | −0.339368 | − | 0.940654i | \(-0.610213\pi\) | ||||
−0.339368 | + | 0.940654i | \(0.610213\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 39.0309 | 1.53210 | ||||||||
\(650\) | 12.9509 | 0.507974 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 13.3116 | 0.521322 | ||||||||
\(653\) | 7.86506 | 0.307784 | 0.153892 | − | 0.988088i | \(-0.450819\pi\) | ||||
0.153892 | + | 0.988088i | \(0.450819\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 4.19625 | 0.163961 | ||||||||
\(656\) | −2.52486 | −0.0985792 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 4.60241 | 0.179421 | ||||||||
\(659\) | 25.2923 | 0.985247 | 0.492623 | − | 0.870243i | \(-0.336038\pi\) | ||||
0.492623 | + | 0.870243i | \(0.336038\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 18.4738 | 0.718546 | 0.359273 | − | 0.933233i | \(-0.383025\pi\) | ||||
0.359273 | + | 0.933233i | \(0.383025\pi\) | |||||||
\(662\) | 26.3503 | 1.02413 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −5.69162 | −0.220878 | ||||||||
\(665\) | 0.628790 | 0.0243834 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −15.0369 | −0.582232 | ||||||||
\(668\) | −6.38977 | −0.247228 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 1.11074 | 0.0429115 | ||||||||
\(671\) | 41.7451 | 1.61155 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 38.6055 | 1.48813 | 0.744067 | − | 0.668105i | \(-0.232895\pi\) | ||||
0.744067 | + | 0.668105i | \(0.232895\pi\) | |||||||
\(674\) | −4.70544 | −0.181247 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −4.41604 | −0.169848 | ||||||||
\(677\) | 8.94930 | 0.343950 | 0.171975 | − | 0.985101i | \(-0.444985\pi\) | ||||
0.171975 | + | 0.985101i | \(0.444985\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −23.1283 | −0.887584 | ||||||||
\(680\) | −1.56248 | −0.0599184 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −16.0186 | −0.613383 | ||||||||
\(683\) | 24.7539 | 0.947182 | 0.473591 | − | 0.880745i | \(-0.342958\pi\) | ||||
0.473591 | + | 0.880745i | \(0.342958\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −7.80197 | −0.298098 | ||||||||
\(686\) | 15.4483 | 0.589821 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 5.24402 | 0.199926 | ||||||||
\(689\) | 24.2178 | 0.922626 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 17.9206 | 0.681733 | 0.340867 | − | 0.940112i | \(-0.389280\pi\) | ||||
0.340867 | + | 0.940112i | \(0.389280\pi\) | |||||||
\(692\) | 1.23167 | 0.0468211 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −27.0511 | −1.02685 | ||||||||
\(695\) | −7.02793 | −0.266585 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −5.18157 | −0.196266 | ||||||||
\(698\) | −9.98625 | −0.377985 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −5.47884 | −0.207081 | ||||||||
\(701\) | 29.8120 | 1.12598 | 0.562992 | − | 0.826463i | \(-0.309650\pi\) | ||||
0.562992 | + | 0.826463i | \(0.309650\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 2.96436 | 0.111803 | ||||||||
\(704\) | 4.16498 | 0.156974 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −9.07685 | −0.341612 | ||||||||
\(707\) | 7.30642 | 0.274786 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 17.8874 | 0.671776 | 0.335888 | − | 0.941902i | \(-0.390964\pi\) | ||||
0.335888 | + | 0.941902i | \(0.390964\pi\) | |||||||
\(710\) | −4.71508 | −0.176954 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −7.72882 | −0.289650 | ||||||||
\(713\) | 32.6171 | 1.22152 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 9.29067 | 0.347451 | ||||||||
\(716\) | −10.4034 | −0.388792 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 13.4684 | 0.502637 | ||||||||
\(719\) | 31.1012 | 1.15988 | 0.579939 | − | 0.814660i | \(-0.303076\pi\) | ||||
0.579939 | + | 0.814660i | \(0.303076\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −4.68442 | −0.174457 | ||||||||
\(722\) | 18.5560 | 0.690584 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 5.03575 | 0.187152 | ||||||||
\(725\) | 7.83754 | 0.291079 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 39.7921 | 1.47581 | 0.737904 | − | 0.674906i | \(-0.235816\pi\) | ||||
0.737904 | + | 0.674906i | \(0.235816\pi\) | |||||||
\(728\) | −3.63143 | −0.134590 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 8.31230 | 0.307652 | ||||||||
\(731\) | 10.7619 | 0.398043 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −28.9878 | −1.07069 | −0.535344 | − | 0.844634i | \(-0.679818\pi\) | ||||
−0.535344 | + | 0.844634i | \(0.679818\pi\) | |||||||
\(734\) | −18.1866 | −0.671278 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −8.48075 | −0.312604 | ||||||||
\(737\) | −6.07622 | −0.223820 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −9.23444 | −0.339694 | −0.169847 | − | 0.985470i | \(-0.554327\pi\) | ||||
−0.169847 | + | 0.985470i | \(0.554327\pi\) | |||||||
\(740\) | 3.38720 | 0.124516 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −10.2453 | −0.376118 | ||||||||
\(743\) | 4.29294 | 0.157493 | 0.0787463 | − | 0.996895i | \(-0.474908\pi\) | ||||
0.0787463 | + | 0.996895i | \(0.474908\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −0.761360 | −0.0278941 | ||||||||
\(746\) | −15.9422 | −0.583685 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 8.54746 | 0.312526 | ||||||||
\(749\) | 9.41186 | 0.343902 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 33.4787 | 1.22165 | 0.610827 | − | 0.791764i | \(-0.290837\pi\) | ||||
0.610827 | + | 0.791764i | \(0.290837\pi\) | |||||||
\(752\) | −3.71322 | −0.135407 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 5.19480 | 0.189183 | ||||||||
\(755\) | 6.53263 | 0.237747 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −40.1690 | −1.45997 | −0.729984 | − | 0.683464i | \(-0.760473\pi\) | ||||
−0.729984 | + | 0.683464i | \(0.760473\pi\) | |||||||
\(758\) | 29.0734 | 1.05599 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −0.507308 | −0.0184020 | ||||||||
\(761\) | −27.1823 | −0.985356 | −0.492678 | − | 0.870212i | \(-0.663982\pi\) | ||||
−0.492678 | + | 0.870212i | \(0.663982\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1.31053 | 0.0474443 | ||||||||
\(764\) | −14.0973 | −0.510022 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −25.2617 | −0.912744 | ||||||||
\(767\) | 27.4561 | 0.991383 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 27.1059 | 0.977464 | 0.488732 | − | 0.872434i | \(-0.337460\pi\) | ||||
0.488732 | + | 0.872434i | \(0.337460\pi\) | |||||||
\(770\) | −3.93040 | −0.141642 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 7.50264 | 0.270026 | ||||||||
\(773\) | −30.4154 | −1.09397 | −0.546984 | − | 0.837143i | \(-0.684224\pi\) | ||||
−0.546984 | + | 0.837143i | \(0.684224\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −17.0007 | −0.610682 | ||||||||
\(776\) | 18.6599 | 0.669853 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −1.32764 | −0.0475980 | ||||||||
\(779\) | −1.68236 | −0.0602768 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 25.7936 | 0.922967 | ||||||||
\(782\) | −17.4044 | −0.622379 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −5.46373 | −0.195133 | ||||||||
\(785\) | 6.91965 | 0.246973 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −17.2434 | −0.614660 | −0.307330 | − | 0.951603i | \(-0.599436\pi\) | ||||
−0.307330 | + | 0.951603i | \(0.599436\pi\) | |||||||
\(788\) | −8.01296 | −0.285450 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 7.27077 | 0.258682 | ||||||||
\(791\) | −11.8108 | −0.419942 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 29.3654 | 1.04280 | ||||||||
\(794\) | 2.12240 | 0.0753211 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −14.7857 | −0.524064 | ||||||||
\(797\) | −53.3978 | −1.89145 | −0.945724 | − | 0.324971i | \(-0.894645\pi\) | ||||
−0.945724 | + | 0.324971i | \(0.894645\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −7.62036 | −0.269589 | ||||||||
\(800\) | 4.42033 | 0.156282 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −26.4011 | −0.932256 | ||||||||
\(803\) | −45.4720 | −1.60467 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 8.00311 | 0.282072 | ||||||||
\(806\) | −11.2682 | −0.396906 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −5.89482 | −0.207379 | ||||||||
\(809\) | 33.8973 | 1.19177 | 0.595883 | − | 0.803071i | \(-0.296802\pi\) | ||||
0.595883 | + | 0.803071i | \(0.296802\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 8.67149 | 0.304497 | 0.152249 | − | 0.988342i | \(-0.451349\pi\) | ||||
0.152249 | + | 0.988342i | \(0.451349\pi\) | |||||||
\(812\) | −2.19765 | −0.0771225 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −18.5295 | −0.649457 | ||||||||
\(815\) | 10.1349 | 0.355010 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 3.49418 | 0.122246 | ||||||||
\(818\) | 10.0056 | 0.349837 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −1.92233 | −0.0671306 | ||||||||
\(821\) | −12.9393 | −0.451585 | −0.225793 | − | 0.974175i | \(-0.572497\pi\) | ||||
−0.225793 | + | 0.974175i | \(0.572497\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 2.76391 | 0.0963437 | 0.0481719 | − | 0.998839i | \(-0.484660\pi\) | ||||
0.0481719 | + | 0.998839i | \(0.484660\pi\) | |||||||
\(824\) | 3.77939 | 0.131661 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −11.6153 | −0.404147 | ||||||||
\(827\) | −10.9901 | −0.382163 | −0.191082 | − | 0.981574i | \(-0.561200\pi\) | ||||
−0.191082 | + | 0.981574i | \(0.561200\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −9.82219 | −0.341139 | −0.170569 | − | 0.985346i | \(-0.554561\pi\) | ||||
−0.170569 | + | 0.985346i | \(0.554561\pi\) | |||||||
\(830\) | −4.33338 | −0.150414 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 2.92984 | 0.101574 | ||||||||
\(833\) | −11.2128 | −0.388500 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −4.86492 | −0.168357 | ||||||||
\(836\) | 2.77520 | 0.0959823 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 20.0307 | 0.691948 | ||||||||
\(839\) | 4.03589 | 0.139334 | 0.0696671 | − | 0.997570i | \(-0.477806\pi\) | ||||
0.0696671 | + | 0.997570i | \(0.477806\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −25.8562 | −0.891594 | ||||||||
\(842\) | −26.9452 | −0.928592 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 3.54316 | 0.121961 | ||||||||
\(845\) | −3.36220 | −0.115663 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 7.86693 | 0.270311 | ||||||||
\(848\) | 8.26592 | 0.283853 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 9.07150 | 0.311150 | ||||||||
\(851\) | 37.7298 | 1.29336 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 11.3792 | 0.389616 | 0.194808 | − | 0.980841i | \(-0.437592\pi\) | ||||
0.194808 | + | 0.980841i | \(0.437592\pi\) | |||||||
\(854\) | −12.4230 | −0.425106 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −7.59349 | −0.259540 | ||||||||
\(857\) | 28.3238 | 0.967522 | 0.483761 | − | 0.875200i | \(-0.339270\pi\) | ||||
0.483761 | + | 0.875200i | \(0.339270\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 52.8590 | 1.80352 | 0.901762 | − | 0.432233i | \(-0.142274\pi\) | ||||
0.901762 | + | 0.432233i | \(0.142274\pi\) | |||||||
\(860\) | 3.99259 | 0.136146 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 16.9357 | 0.576831 | ||||||||
\(863\) | −19.7991 | −0.673968 | −0.336984 | − | 0.941510i | \(-0.609407\pi\) | ||||
−0.336984 | + | 0.941510i | \(0.609407\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0.937745 | 0.0318843 | ||||||||
\(866\) | 10.1849 | 0.346096 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 4.76700 | 0.161803 | ||||||||
\(869\) | −39.7743 | −1.34925 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −4.27430 | −0.144829 | ||||||||
\(872\) | −1.05733 | −0.0358059 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −5.65087 | −0.191144 | ||||||||
\(875\) | −8.88977 | −0.300529 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −13.9418 | −0.470781 | −0.235391 | − | 0.971901i | \(-0.575637\pi\) | ||||
−0.235391 | + | 0.971901i | \(0.575637\pi\) | |||||||
\(878\) | −32.8283 | −1.10790 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 3.17105 | 0.106896 | ||||||||
\(881\) | 35.1454 | 1.18408 | 0.592039 | − | 0.805910i | \(-0.298323\pi\) | ||||
0.592039 | + | 0.805910i | \(0.298323\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 22.9553 | 0.772506 | 0.386253 | − | 0.922393i | \(-0.373769\pi\) | ||||
0.386253 | + | 0.922393i | \(0.373769\pi\) | |||||||
\(884\) | 6.01268 | 0.202228 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 13.1581 | 0.442056 | ||||||||
\(887\) | −4.29374 | −0.144170 | −0.0720849 | − | 0.997398i | \(-0.522965\pi\) | ||||
−0.0720849 | + | 0.997398i | \(0.522965\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −19.2672 | −0.646202 | ||||||||
\(890\) | −5.88442 | −0.197246 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 12.5260 | 0.419403 | ||||||||
\(893\) | −2.47419 | −0.0827956 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −7.92072 | −0.264760 | ||||||||
\(896\) | −1.23946 | −0.0414076 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −1.34071 | −0.0447401 | ||||||||
\(899\) | −6.81924 | −0.227434 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 16.9635 | 0.565136 | ||||||||
\(902\) | 10.5160 | 0.350144 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 9.52892 | 0.316927 | ||||||||
\(905\) | 3.83402 | 0.127447 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −16.0955 | −0.534442 | −0.267221 | − | 0.963635i | \(-0.586105\pi\) | ||||
−0.267221 | + | 0.963635i | \(0.586105\pi\) | |||||||
\(908\) | 14.2435 | 0.472688 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −2.76483 | −0.0916532 | ||||||||
\(911\) | 29.8829 | 0.990063 | 0.495032 | − | 0.868875i | \(-0.335157\pi\) | ||||
0.495032 | + | 0.868875i | \(0.335157\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 23.7055 | 0.784537 | ||||||||
\(914\) | −4.66820 | −0.154410 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −22.3396 | −0.738120 | ||||||||
\(917\) | 6.83134 | 0.225591 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 32.2582 | 1.06410 | 0.532050 | − | 0.846713i | \(-0.321422\pi\) | ||||
0.532050 | + | 0.846713i | \(0.321422\pi\) | |||||||
\(920\) | −6.45691 | −0.212878 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 7.86962 | 0.259172 | ||||||||
\(923\) | 18.1444 | 0.597230 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −19.6655 | −0.646597 | ||||||||
\(926\) | −19.3249 | −0.635057 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 1.77307 | 0.0582037 | ||||||||
\(929\) | 3.07707 | 0.100955 | 0.0504777 | − | 0.998725i | \(-0.483926\pi\) | ||||
0.0504777 | + | 0.998725i | \(0.483926\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −3.64058 | −0.119315 | ||||||||
\(932\) | −13.9412 | −0.456658 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 35.3122 | 1.15545 | ||||||||
\(935\) | 6.50770 | 0.212824 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 22.4776 | 0.734311 | 0.367156 | − | 0.930160i | \(-0.380332\pi\) | ||||
0.367156 | + | 0.930160i | \(0.380332\pi\) | |||||||
\(938\) | 1.80824 | 0.0590410 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −2.82710 | −0.0922099 | ||||||||
\(941\) | 22.0470 | 0.718712 | 0.359356 | − | 0.933201i | \(-0.382996\pi\) | ||||
0.359356 | + | 0.933201i | \(0.382996\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −21.4127 | −0.697293 | ||||||||
\(944\) | 9.37120 | 0.305007 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −21.8412 | −0.710120 | ||||||||
\(947\) | −5.17219 | −0.168073 | −0.0840367 | − | 0.996463i | \(-0.526781\pi\) | ||||
−0.0840367 | + | 0.996463i | \(0.526781\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −31.9871 | −1.03835 | ||||||||
\(950\) | 2.94535 | 0.0955596 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −2.54366 | −0.0824403 | ||||||||
\(953\) | −32.0348 | −1.03771 | −0.518855 | − | 0.854862i | \(-0.673642\pi\) | ||||
−0.518855 | + | 0.854862i | \(0.673642\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −10.7331 | −0.347316 | ||||||||
\(956\) | 15.8580 | 0.512883 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 5.70156 | 0.184209 | ||||||||
\(959\) | −12.7013 | −0.410146 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −16.2082 | −0.522844 | ||||||||
\(962\) | −13.0345 | −0.420249 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −13.2150 | −0.425626 | ||||||||
\(965\) | 5.71221 | 0.183883 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −10.9279 | −0.351419 | −0.175709 | − | 0.984442i | \(-0.556222\pi\) | ||||
−0.175709 | + | 0.984442i | \(0.556222\pi\) | |||||||
\(968\) | −6.34704 | −0.204002 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 14.2069 | 0.456157 | ||||||||
\(971\) | −1.27203 | −0.0408214 | −0.0204107 | − | 0.999792i | \(-0.506497\pi\) | ||||
−0.0204107 | + | 0.999792i | \(0.506497\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −11.4412 | −0.366788 | ||||||||
\(974\) | 24.4051 | 0.781990 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 10.0229 | 0.320825 | ||||||||
\(977\) | 59.6830 | 1.90943 | 0.954714 | − | 0.297526i | \(-0.0961615\pi\) | ||||
0.954714 | + | 0.297526i | \(0.0961615\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 32.1904 | 1.02881 | ||||||||
\(980\) | −4.15987 | −0.132882 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −14.7538 | −0.470811 | ||||||||
\(983\) | −39.9669 | −1.27475 | −0.637374 | − | 0.770555i | \(-0.719979\pi\) | ||||
−0.637374 | + | 0.770555i | \(0.719979\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −6.10075 | −0.194386 | ||||||||
\(986\) | 3.63872 | 0.115881 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 1.95220 | 0.0621079 | ||||||||
\(989\) | 44.4732 | 1.41417 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −18.7853 | −0.596735 | −0.298368 | − | 0.954451i | \(-0.596442\pi\) | ||||
−0.298368 | + | 0.954451i | \(0.596442\pi\) | |||||||
\(992\) | −3.84602 | −0.122111 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −7.67597 | −0.243467 | ||||||||
\(995\) | −11.2572 | −0.356878 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 42.9444 | 1.36006 | 0.680032 | − | 0.733183i | \(-0.261966\pi\) | ||||
0.680032 | + | 0.733183i | \(0.261966\pi\) | |||||||
\(998\) | −3.13631 | −0.0992781 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 8046.2.a.k.1.8 | ✓ | 12 | |
3.2 | odd | 2 | 8046.2.a.n.1.5 | yes | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8046.2.a.k.1.8 | ✓ | 12 | 1.1 | even | 1 | trivial | |
8046.2.a.n.1.5 | yes | 12 | 3.2 | odd | 2 |