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: | \( x^{12} - 5 x^{11} - 21 x^{10} + 116 x^{9} + 106 x^{8} - 774 x^{7} - 63 x^{6} + 2013 x^{5} - 417 x^{4} + \cdots - 375 \) |
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 | 1.9 | ||
Root | \(1.53008\) 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 | ||||||||
\(5\) | 1.53008 | 0.684272 | 0.342136 | − | 0.939650i | \(-0.388850\pi\) | ||||
0.342136 | + | 0.939650i | \(0.388850\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 5.04291 | 1.90604 | 0.953021 | − | 0.302905i | \(-0.0979563\pi\) | ||||
0.953021 | + | 0.302905i | \(0.0979563\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −1.53008 | −0.483854 | ||||||||
\(11\) | 2.19639 | 0.662237 | 0.331118 | − | 0.943589i | \(-0.392574\pi\) | ||||
0.331118 | + | 0.943589i | \(0.392574\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.71640 | −1.03074 | −0.515372 | − | 0.856966i | \(-0.672346\pi\) | ||||
−0.515372 | + | 0.856966i | \(0.672346\pi\) | |||||||
\(14\) | −5.04291 | −1.34778 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 2.18832 | 0.530745 | 0.265372 | − | 0.964146i | \(-0.414505\pi\) | ||||
0.265372 | + | 0.964146i | \(0.414505\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.428199 | 0.0982357 | 0.0491178 | − | 0.998793i | \(-0.484359\pi\) | ||||
0.0491178 | + | 0.998793i | \(0.484359\pi\) | |||||||
\(20\) | 1.53008 | 0.342136 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −2.19639 | −0.468272 | ||||||||
\(23\) | 2.68792 | 0.560471 | 0.280235 | − | 0.959931i | \(-0.409587\pi\) | ||||
0.280235 | + | 0.959931i | \(0.409587\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.65886 | −0.531772 | ||||||||
\(26\) | 3.71640 | 0.728846 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 5.04291 | 0.953021 | ||||||||
\(29\) | 1.03044 | 0.191348 | 0.0956738 | − | 0.995413i | \(-0.469499\pi\) | ||||
0.0956738 | + | 0.995413i | \(0.469499\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.812378 | 0.145907 | 0.0729537 | − | 0.997335i | \(-0.476757\pi\) | ||||
0.0729537 | + | 0.997335i | \(0.476757\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −2.18832 | −0.375293 | ||||||||
\(35\) | 7.71606 | 1.30425 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −2.71746 | −0.446747 | −0.223374 | − | 0.974733i | \(-0.571707\pi\) | ||||
−0.223374 | + | 0.974733i | \(0.571707\pi\) | |||||||
\(38\) | −0.428199 | −0.0694631 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −1.53008 | −0.241927 | ||||||||
\(41\) | 3.18736 | 0.497782 | 0.248891 | − | 0.968532i | \(-0.419934\pi\) | ||||
0.248891 | + | 0.968532i | \(0.419934\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −10.6001 | −1.61649 | −0.808247 | − | 0.588843i | \(-0.799583\pi\) | ||||
−0.808247 | + | 0.588843i | \(0.799583\pi\) | |||||||
\(44\) | 2.19639 | 0.331118 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −2.68792 | −0.396313 | ||||||||
\(47\) | 3.13589 | 0.457416 | 0.228708 | − | 0.973495i | \(-0.426550\pi\) | ||||
0.228708 | + | 0.973495i | \(0.426550\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 18.4310 | 2.63300 | ||||||||
\(50\) | 2.65886 | 0.376019 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −3.71640 | −0.515372 | ||||||||
\(53\) | −7.68548 | −1.05568 | −0.527841 | − | 0.849343i | \(-0.676998\pi\) | ||||
−0.527841 | + | 0.849343i | \(0.676998\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 3.36065 | 0.453150 | ||||||||
\(56\) | −5.04291 | −0.673888 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −1.03044 | −0.135303 | ||||||||
\(59\) | 11.9319 | 1.55340 | 0.776701 | − | 0.629870i | \(-0.216892\pi\) | ||||
0.776701 | + | 0.629870i | \(0.216892\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0.845814 | 0.108295 | 0.0541477 | − | 0.998533i | \(-0.482756\pi\) | ||||
0.0541477 | + | 0.998533i | \(0.482756\pi\) | |||||||
\(62\) | −0.812378 | −0.103172 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −5.68639 | −0.705310 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −4.18466 | −0.511237 | −0.255619 | − | 0.966778i | \(-0.582279\pi\) | ||||
−0.255619 | + | 0.966778i | \(0.582279\pi\) | |||||||
\(68\) | 2.18832 | 0.265372 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −7.71606 | −0.922245 | ||||||||
\(71\) | 9.74208 | 1.15617 | 0.578086 | − | 0.815976i | \(-0.303800\pi\) | ||||
0.578086 | + | 0.815976i | \(0.303800\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −14.1375 | −1.65467 | −0.827333 | − | 0.561712i | \(-0.810143\pi\) | ||||
−0.827333 | + | 0.561712i | \(0.810143\pi\) | |||||||
\(74\) | 2.71746 | 0.315898 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0.428199 | 0.0491178 | ||||||||
\(77\) | 11.0762 | 1.26225 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 14.8966 | 1.67600 | 0.838000 | − | 0.545670i | \(-0.183725\pi\) | ||||
0.838000 | + | 0.545670i | \(0.183725\pi\) | |||||||
\(80\) | 1.53008 | 0.171068 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −3.18736 | −0.351985 | ||||||||
\(83\) | −1.50002 | −0.164649 | −0.0823245 | − | 0.996606i | \(-0.526234\pi\) | ||||
−0.0823245 | + | 0.996606i | \(0.526234\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 3.34830 | 0.363174 | ||||||||
\(86\) | 10.6001 | 1.14303 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −2.19639 | −0.234136 | ||||||||
\(89\) | 6.94999 | 0.736697 | 0.368348 | − | 0.929688i | \(-0.379923\pi\) | ||||
0.368348 | + | 0.929688i | \(0.379923\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −18.7415 | −1.96464 | ||||||||
\(92\) | 2.68792 | 0.280235 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −3.13589 | −0.323442 | ||||||||
\(95\) | 0.655179 | 0.0672199 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −15.0130 | −1.52434 | −0.762168 | − | 0.647379i | \(-0.775865\pi\) | ||||
−0.762168 | + | 0.647379i | \(0.775865\pi\) | |||||||
\(98\) | −18.4310 | −1.86181 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −2.65886 | −0.265886 | ||||||||
\(101\) | 18.5580 | 1.84659 | 0.923293 | − | 0.384096i | \(-0.125487\pi\) | ||||
0.923293 | + | 0.384096i | \(0.125487\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 17.8293 | 1.75677 | 0.878386 | − | 0.477952i | \(-0.158621\pi\) | ||||
0.878386 | + | 0.477952i | \(0.158621\pi\) | |||||||
\(104\) | 3.71640 | 0.364423 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 7.68548 | 0.746480 | ||||||||
\(107\) | 16.8615 | 1.63007 | 0.815033 | − | 0.579414i | \(-0.196719\pi\) | ||||
0.815033 | + | 0.579414i | \(0.196719\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 13.4120 | 1.28464 | 0.642320 | − | 0.766436i | \(-0.277972\pi\) | ||||
0.642320 | + | 0.766436i | \(0.277972\pi\) | |||||||
\(110\) | −3.36065 | −0.320426 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 5.04291 | 0.476510 | ||||||||
\(113\) | 4.50527 | 0.423820 | 0.211910 | − | 0.977289i | \(-0.432032\pi\) | ||||
0.211910 | + | 0.977289i | \(0.432032\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 4.11274 | 0.383515 | ||||||||
\(116\) | 1.03044 | 0.0956738 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −11.9319 | −1.09842 | ||||||||
\(119\) | 11.0355 | 1.01162 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −6.17587 | −0.561443 | ||||||||
\(122\) | −0.845814 | −0.0765764 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0.812378 | 0.0729537 | ||||||||
\(125\) | −11.7187 | −1.04815 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 11.1412 | 0.988619 | 0.494309 | − | 0.869286i | \(-0.335421\pi\) | ||||
0.494309 | + | 0.869286i | \(0.335421\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 5.68639 | 0.498729 | ||||||||
\(131\) | −14.1460 | −1.23594 | −0.617972 | − | 0.786200i | \(-0.712046\pi\) | ||||
−0.617972 | + | 0.786200i | \(0.712046\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2.15937 | 0.187241 | ||||||||
\(134\) | 4.18466 | 0.361499 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −2.18832 | −0.187647 | ||||||||
\(137\) | −3.26025 | −0.278542 | −0.139271 | − | 0.990254i | \(-0.544476\pi\) | ||||
−0.139271 | + | 0.990254i | \(0.544476\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 18.1889 | 1.54276 | 0.771381 | − | 0.636374i | \(-0.219566\pi\) | ||||
0.771381 | + | 0.636374i | \(0.219566\pi\) | |||||||
\(140\) | 7.71606 | 0.652126 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −9.74208 | −0.817537 | ||||||||
\(143\) | −8.16267 | −0.682597 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1.57665 | 0.130934 | ||||||||
\(146\) | 14.1375 | 1.17003 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −2.71746 | −0.223374 | ||||||||
\(149\) | 1.00000 | 0.0819232 | ||||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 13.8103 | 1.12386 | 0.561932 | − | 0.827183i | \(-0.310058\pi\) | ||||
0.561932 | + | 0.827183i | \(0.310058\pi\) | |||||||
\(152\) | −0.428199 | −0.0347315 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −11.0762 | −0.892546 | ||||||||
\(155\) | 1.24300 | 0.0998403 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 15.5334 | 1.23970 | 0.619849 | − | 0.784721i | \(-0.287194\pi\) | ||||
0.619849 | + | 0.784721i | \(0.287194\pi\) | |||||||
\(158\) | −14.8966 | −1.18511 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −1.53008 | −0.120963 | ||||||||
\(161\) | 13.5550 | 1.06828 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −15.8819 | −1.24396 | −0.621982 | − | 0.783031i | \(-0.713672\pi\) | ||||
−0.621982 | + | 0.783031i | \(0.713672\pi\) | |||||||
\(164\) | 3.18736 | 0.248891 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 1.50002 | 0.116424 | ||||||||
\(167\) | −21.1258 | −1.63476 | −0.817381 | − | 0.576097i | \(-0.804575\pi\) | ||||
−0.817381 | + | 0.576097i | \(0.804575\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 0.811642 | 0.0624340 | ||||||||
\(170\) | −3.34830 | −0.256803 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −10.6001 | −0.808247 | ||||||||
\(173\) | −12.1765 | −0.925765 | −0.462882 | − | 0.886420i | \(-0.653185\pi\) | ||||
−0.462882 | + | 0.886420i | \(0.653185\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −13.4084 | −1.01358 | ||||||||
\(176\) | 2.19639 | 0.165559 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −6.94999 | −0.520923 | ||||||||
\(179\) | 22.3807 | 1.67281 | 0.836406 | − | 0.548110i | \(-0.184652\pi\) | ||||
0.836406 | + | 0.548110i | \(0.184652\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −16.5525 | −1.23034 | −0.615170 | − | 0.788395i | \(-0.710913\pi\) | ||||
−0.615170 | + | 0.788395i | \(0.710913\pi\) | |||||||
\(182\) | 18.7415 | 1.38921 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −2.68792 | −0.198156 | ||||||||
\(185\) | −4.15793 | −0.305697 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 4.80640 | 0.351479 | ||||||||
\(188\) | 3.13589 | 0.228708 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −0.655179 | −0.0475317 | ||||||||
\(191\) | 20.5627 | 1.48787 | 0.743933 | − | 0.668254i | \(-0.232958\pi\) | ||||
0.743933 | + | 0.668254i | \(0.232958\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 16.6431 | 1.19800 | 0.598998 | − | 0.800751i | \(-0.295566\pi\) | ||||
0.598998 | + | 0.800751i | \(0.295566\pi\) | |||||||
\(194\) | 15.0130 | 1.07787 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 18.4310 | 1.31650 | ||||||||
\(197\) | 21.4204 | 1.52614 | 0.763069 | − | 0.646317i | \(-0.223691\pi\) | ||||
0.763069 | + | 0.646317i | \(0.223691\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 6.13385 | 0.434817 | 0.217409 | − | 0.976081i | \(-0.430240\pi\) | ||||
0.217409 | + | 0.976081i | \(0.430240\pi\) | |||||||
\(200\) | 2.65886 | 0.188010 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −18.5580 | −1.30573 | ||||||||
\(203\) | 5.19641 | 0.364717 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 4.87691 | 0.340618 | ||||||||
\(206\) | −17.8293 | −1.24223 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −3.71640 | −0.257686 | ||||||||
\(209\) | 0.940493 | 0.0650553 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1.92401 | −0.132454 | −0.0662272 | − | 0.997805i | \(-0.521096\pi\) | ||||
−0.0662272 | + | 0.997805i | \(0.521096\pi\) | |||||||
\(212\) | −7.68548 | −0.527841 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −16.8615 | −1.15263 | ||||||||
\(215\) | −16.2189 | −1.10612 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 4.09675 | 0.278105 | ||||||||
\(218\) | −13.4120 | −0.908378 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 3.36065 | 0.226575 | ||||||||
\(221\) | −8.13267 | −0.547062 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 11.4543 | 0.767040 | 0.383520 | − | 0.923533i | \(-0.374712\pi\) | ||||
0.383520 | + | 0.923533i | \(0.374712\pi\) | |||||||
\(224\) | −5.04291 | −0.336944 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −4.50527 | −0.299686 | ||||||||
\(227\) | −7.54669 | −0.500891 | −0.250446 | − | 0.968131i | \(-0.580577\pi\) | ||||
−0.250446 | + | 0.968131i | \(0.580577\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −27.8224 | −1.83855 | −0.919277 | − | 0.393610i | \(-0.871226\pi\) | ||||
−0.919277 | + | 0.393610i | \(0.871226\pi\) | |||||||
\(230\) | −4.11274 | −0.271186 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −1.03044 | −0.0676516 | ||||||||
\(233\) | 26.3727 | 1.72773 | 0.863867 | − | 0.503720i | \(-0.168036\pi\) | ||||
0.863867 | + | 0.503720i | \(0.168036\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 4.79816 | 0.312997 | ||||||||
\(236\) | 11.9319 | 0.776701 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −11.0355 | −0.715325 | ||||||||
\(239\) | −19.1553 | −1.23905 | −0.619527 | − | 0.784975i | \(-0.712676\pi\) | ||||
−0.619527 | + | 0.784975i | \(0.712676\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −18.2493 | −1.17554 | −0.587772 | − | 0.809027i | \(-0.699995\pi\) | ||||
−0.587772 | + | 0.809027i | \(0.699995\pi\) | |||||||
\(242\) | 6.17587 | 0.397000 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0.845814 | 0.0541477 | ||||||||
\(245\) | 28.2008 | 1.80169 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1.59136 | −0.101256 | ||||||||
\(248\) | −0.812378 | −0.0515860 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 11.7187 | 0.741153 | ||||||||
\(251\) | −3.34068 | −0.210862 | −0.105431 | − | 0.994427i | \(-0.533622\pi\) | ||||
−0.105431 | + | 0.994427i | \(0.533622\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 5.90373 | 0.371164 | ||||||||
\(254\) | −11.1412 | −0.699059 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −1.84462 | −0.115064 | −0.0575320 | − | 0.998344i | \(-0.518323\pi\) | ||||
−0.0575320 | + | 0.998344i | \(0.518323\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −13.7039 | −0.851519 | ||||||||
\(260\) | −5.68639 | −0.352655 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 14.1460 | 0.873945 | ||||||||
\(263\) | 0.236331 | 0.0145728 | 0.00728638 | − | 0.999973i | \(-0.497681\pi\) | ||||
0.00728638 | + | 0.999973i | \(0.497681\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −11.7594 | −0.722374 | ||||||||
\(266\) | −2.15937 | −0.132400 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −4.18466 | −0.255619 | ||||||||
\(269\) | 0.492739 | 0.0300428 | 0.0150214 | − | 0.999887i | \(-0.495218\pi\) | ||||
0.0150214 | + | 0.999887i | \(0.495218\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 7.28712 | 0.442661 | 0.221330 | − | 0.975199i | \(-0.428960\pi\) | ||||
0.221330 | + | 0.975199i | \(0.428960\pi\) | |||||||
\(272\) | 2.18832 | 0.132686 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 3.26025 | 0.196959 | ||||||||
\(275\) | −5.83989 | −0.352159 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −26.1050 | −1.56850 | −0.784248 | − | 0.620447i | \(-0.786951\pi\) | ||||
−0.784248 | + | 0.620447i | \(0.786951\pi\) | |||||||
\(278\) | −18.1889 | −1.09090 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −7.71606 | −0.461123 | ||||||||
\(281\) | −26.6711 | −1.59106 | −0.795531 | − | 0.605913i | \(-0.792808\pi\) | ||||
−0.795531 | + | 0.605913i | \(0.792808\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 17.0033 | 1.01074 | 0.505371 | − | 0.862902i | \(-0.331356\pi\) | ||||
0.505371 | + | 0.862902i | \(0.331356\pi\) | |||||||
\(284\) | 9.74208 | 0.578086 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 8.16267 | 0.482669 | ||||||||
\(287\) | 16.0736 | 0.948793 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −12.2113 | −0.718310 | ||||||||
\(290\) | −1.57665 | −0.0925842 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −14.1375 | −0.827333 | ||||||||
\(293\) | −24.2864 | −1.41882 | −0.709412 | − | 0.704794i | \(-0.751040\pi\) | ||||
−0.709412 | + | 0.704794i | \(0.751040\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 18.2568 | 1.06295 | ||||||||
\(296\) | 2.71746 | 0.157949 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −1.00000 | −0.0579284 | ||||||||
\(299\) | −9.98941 | −0.577702 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −53.4552 | −3.08111 | ||||||||
\(302\) | −13.8103 | −0.794692 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0.428199 | 0.0245589 | ||||||||
\(305\) | 1.29416 | 0.0741035 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 1.13742 | 0.0649161 | 0.0324581 | − | 0.999473i | \(-0.489666\pi\) | ||||
0.0324581 | + | 0.999473i | \(0.489666\pi\) | |||||||
\(308\) | 11.0762 | 0.631125 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −1.24300 | −0.0705978 | ||||||||
\(311\) | −0.447203 | −0.0253586 | −0.0126793 | − | 0.999920i | \(-0.504036\pi\) | ||||
−0.0126793 | + | 0.999920i | \(0.504036\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 12.9333 | 0.731031 | 0.365516 | − | 0.930805i | \(-0.380893\pi\) | ||||
0.365516 | + | 0.930805i | \(0.380893\pi\) | |||||||
\(314\) | −15.5334 | −0.876599 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 14.8966 | 0.838000 | ||||||||
\(317\) | 4.60730 | 0.258772 | 0.129386 | − | 0.991594i | \(-0.458699\pi\) | ||||
0.129386 | + | 0.991594i | \(0.458699\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 2.26324 | 0.126717 | ||||||||
\(320\) | 1.53008 | 0.0855340 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −13.5550 | −0.755389 | ||||||||
\(323\) | 0.937036 | 0.0521381 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 9.88138 | 0.548121 | ||||||||
\(326\) | 15.8819 | 0.879616 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −3.18736 | −0.175992 | ||||||||
\(329\) | 15.8140 | 0.871854 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −9.54771 | −0.524789 | −0.262395 | − | 0.964961i | \(-0.584512\pi\) | ||||
−0.262395 | + | 0.964961i | \(0.584512\pi\) | |||||||
\(332\) | −1.50002 | −0.0823245 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 21.1258 | 1.15595 | ||||||||
\(335\) | −6.40286 | −0.349825 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1.90607 | 0.103830 | 0.0519151 | − | 0.998651i | \(-0.483467\pi\) | ||||
0.0519151 | + | 0.998651i | \(0.483467\pi\) | |||||||
\(338\) | −0.811642 | −0.0441475 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 3.34830 | 0.181587 | ||||||||
\(341\) | 1.78430 | 0.0966252 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 57.6454 | 3.11256 | ||||||||
\(344\) | 10.6001 | 0.571517 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 12.1765 | 0.654615 | ||||||||
\(347\) | −31.8251 | −1.70846 | −0.854230 | − | 0.519896i | \(-0.825971\pi\) | ||||
−0.854230 | + | 0.519896i | \(0.825971\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −14.2839 | −0.764602 | −0.382301 | − | 0.924038i | \(-0.624868\pi\) | ||||
−0.382301 | + | 0.924038i | \(0.624868\pi\) | |||||||
\(350\) | 13.4084 | 0.716708 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −2.19639 | −0.117068 | ||||||||
\(353\) | −4.35738 | −0.231920 | −0.115960 | − | 0.993254i | \(-0.536994\pi\) | ||||
−0.115960 | + | 0.993254i | \(0.536994\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 14.9062 | 0.791136 | ||||||||
\(356\) | 6.94999 | 0.368348 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −22.3807 | −1.18286 | ||||||||
\(359\) | −17.6460 | −0.931319 | −0.465659 | − | 0.884964i | \(-0.654183\pi\) | ||||
−0.465659 | + | 0.884964i | \(0.654183\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.8166 | −0.990350 | ||||||||
\(362\) | 16.5525 | 0.869981 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −18.7415 | −0.982321 | ||||||||
\(365\) | −21.6314 | −1.13224 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −12.9361 | −0.675257 | −0.337628 | − | 0.941280i | \(-0.609625\pi\) | ||||
−0.337628 | + | 0.941280i | \(0.609625\pi\) | |||||||
\(368\) | 2.68792 | 0.140118 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 4.15793 | 0.216160 | ||||||||
\(371\) | −38.7572 | −2.01217 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −8.95023 | −0.463425 | −0.231713 | − | 0.972784i | \(-0.574433\pi\) | ||||
−0.231713 | + | 0.972784i | \(0.574433\pi\) | |||||||
\(374\) | −4.80640 | −0.248533 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −3.13589 | −0.161721 | ||||||||
\(377\) | −3.82952 | −0.197230 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −25.4453 | −1.30704 | −0.653520 | − | 0.756910i | \(-0.726708\pi\) | ||||
−0.653520 | + | 0.756910i | \(0.726708\pi\) | |||||||
\(380\) | 0.655179 | 0.0336100 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −20.5627 | −1.05208 | ||||||||
\(383\) | 20.2374 | 1.03408 | 0.517042 | − | 0.855960i | \(-0.327033\pi\) | ||||
0.517042 | + | 0.855960i | \(0.327033\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 16.9475 | 0.863723 | ||||||||
\(386\) | −16.6431 | −0.847111 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −15.0130 | −0.762168 | ||||||||
\(389\) | 15.5789 | 0.789880 | 0.394940 | − | 0.918707i | \(-0.370765\pi\) | ||||
0.394940 | + | 0.918707i | \(0.370765\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 5.88203 | 0.297467 | ||||||||
\(392\) | −18.4310 | −0.930904 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −21.4204 | −1.07914 | ||||||||
\(395\) | 22.7930 | 1.14684 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −21.5619 | −1.08216 | −0.541081 | − | 0.840970i | \(-0.681985\pi\) | ||||
−0.541081 | + | 0.840970i | \(0.681985\pi\) | |||||||
\(398\) | −6.13385 | −0.307462 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −2.65886 | −0.132943 | ||||||||
\(401\) | 20.2428 | 1.01088 | 0.505439 | − | 0.862862i | \(-0.331330\pi\) | ||||
0.505439 | + | 0.862862i | \(0.331330\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −3.01912 | −0.150393 | ||||||||
\(404\) | 18.5580 | 0.923293 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −5.19641 | −0.257894 | ||||||||
\(407\) | −5.96860 | −0.295852 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 7.78181 | 0.384786 | 0.192393 | − | 0.981318i | \(-0.438375\pi\) | ||||
0.192393 | + | 0.981318i | \(0.438375\pi\) | |||||||
\(410\) | −4.87691 | −0.240854 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 17.8293 | 0.878386 | ||||||||
\(413\) | 60.1715 | 2.96085 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −2.29515 | −0.112665 | ||||||||
\(416\) | 3.71640 | 0.182212 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −0.940493 | −0.0460010 | ||||||||
\(419\) | 29.8913 | 1.46029 | 0.730143 | − | 0.683295i | \(-0.239454\pi\) | ||||
0.730143 | + | 0.683295i | \(0.239454\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 3.47305 | 0.169266 | 0.0846331 | − | 0.996412i | \(-0.473028\pi\) | ||||
0.0846331 | + | 0.996412i | \(0.473028\pi\) | |||||||
\(422\) | 1.92401 | 0.0936594 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 7.68548 | 0.373240 | ||||||||
\(425\) | −5.81843 | −0.282235 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 4.26536 | 0.206415 | ||||||||
\(428\) | 16.8615 | 0.815033 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 16.2189 | 0.782146 | ||||||||
\(431\) | 26.4524 | 1.27416 | 0.637082 | − | 0.770796i | \(-0.280141\pi\) | ||||
0.637082 | + | 0.770796i | \(0.280141\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 9.06980 | 0.435867 | 0.217933 | − | 0.975964i | \(-0.430068\pi\) | ||||
0.217933 | + | 0.975964i | \(0.430068\pi\) | |||||||
\(434\) | −4.09675 | −0.196650 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 13.4120 | 0.642320 | ||||||||
\(437\) | 1.15097 | 0.0550582 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 14.3151 | 0.683224 | 0.341612 | − | 0.939841i | \(-0.389027\pi\) | ||||
0.341612 | + | 0.939841i | \(0.389027\pi\) | |||||||
\(440\) | −3.36065 | −0.160213 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 8.13267 | 0.386832 | ||||||||
\(443\) | 18.3436 | 0.871529 | 0.435764 | − | 0.900061i | \(-0.356478\pi\) | ||||
0.435764 | + | 0.900061i | \(0.356478\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 10.6340 | 0.504101 | ||||||||
\(446\) | −11.4543 | −0.542379 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 5.04291 | 0.238255 | ||||||||
\(449\) | 5.91128 | 0.278971 | 0.139485 | − | 0.990224i | \(-0.455455\pi\) | ||||
0.139485 | + | 0.990224i | \(0.455455\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 7.00068 | 0.329649 | ||||||||
\(452\) | 4.50527 | 0.211910 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 7.54669 | 0.354184 | ||||||||
\(455\) | −28.6760 | −1.34435 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −4.51467 | −0.211187 | −0.105594 | − | 0.994409i | \(-0.533674\pi\) | ||||
−0.105594 | + | 0.994409i | \(0.533674\pi\) | |||||||
\(458\) | 27.8224 | 1.30005 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 4.11274 | 0.191757 | ||||||||
\(461\) | −17.7809 | −0.828140 | −0.414070 | − | 0.910245i | \(-0.635893\pi\) | ||||
−0.414070 | + | 0.910245i | \(0.635893\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −34.2340 | −1.59099 | −0.795495 | − | 0.605960i | \(-0.792789\pi\) | ||||
−0.795495 | + | 0.605960i | \(0.792789\pi\) | |||||||
\(464\) | 1.03044 | 0.0478369 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −26.3727 | −1.22169 | ||||||||
\(467\) | −2.79934 | −0.129538 | −0.0647689 | − | 0.997900i | \(-0.520631\pi\) | ||||
−0.0647689 | + | 0.997900i | \(0.520631\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −21.1029 | −0.974440 | ||||||||
\(470\) | −4.79816 | −0.221322 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −11.9319 | −0.549210 | ||||||||
\(473\) | −23.2819 | −1.07050 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1.13852 | −0.0522389 | ||||||||
\(476\) | 11.0355 | 0.505811 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 19.1553 | 0.876144 | ||||||||
\(479\) | −3.83579 | −0.175262 | −0.0876308 | − | 0.996153i | \(-0.527930\pi\) | ||||
−0.0876308 | + | 0.996153i | \(0.527930\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 10.0992 | 0.460482 | ||||||||
\(482\) | 18.2493 | 0.831235 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −6.17587 | −0.280721 | ||||||||
\(485\) | −22.9710 | −1.04306 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 26.3377 | 1.19347 | 0.596737 | − | 0.802437i | \(-0.296464\pi\) | ||||
0.596737 | + | 0.802437i | \(0.296464\pi\) | |||||||
\(488\) | −0.845814 | −0.0382882 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −28.2008 | −1.27398 | ||||||||
\(491\) | −22.8728 | −1.03224 | −0.516119 | − | 0.856517i | \(-0.672624\pi\) | ||||
−0.516119 | + | 0.856517i | \(0.672624\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 2.25493 | 0.101557 | ||||||||
\(494\) | 1.59136 | 0.0715987 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0.812378 | 0.0364768 | ||||||||
\(497\) | 49.1284 | 2.20371 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 3.17734 | 0.142237 | 0.0711187 | − | 0.997468i | \(-0.477343\pi\) | ||||
0.0711187 | + | 0.997468i | \(0.477343\pi\) | |||||||
\(500\) | −11.7187 | −0.524074 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 3.34068 | 0.149102 | ||||||||
\(503\) | 31.6477 | 1.41110 | 0.705550 | − | 0.708660i | \(-0.250700\pi\) | ||||
0.705550 | + | 0.708660i | \(0.250700\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 28.3951 | 1.26357 | ||||||||
\(506\) | −5.90373 | −0.262453 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 11.1412 | 0.494309 | ||||||||
\(509\) | 23.9531 | 1.06170 | 0.530851 | − | 0.847465i | \(-0.321872\pi\) | ||||
0.530851 | + | 0.847465i | \(0.321872\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −71.2940 | −3.15386 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 1.84462 | 0.0813625 | ||||||||
\(515\) | 27.2802 | 1.20211 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 6.88763 | 0.302918 | ||||||||
\(518\) | 13.7039 | 0.602115 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 5.68639 | 0.249365 | ||||||||
\(521\) | −4.11740 | −0.180387 | −0.0901934 | − | 0.995924i | \(-0.528749\pi\) | ||||
−0.0901934 | + | 0.995924i | \(0.528749\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 16.4484 | 0.719238 | 0.359619 | − | 0.933099i | \(-0.382907\pi\) | ||||
0.359619 | + | 0.933099i | \(0.382907\pi\) | |||||||
\(524\) | −14.1460 | −0.617972 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −0.236331 | −0.0103045 | ||||||||
\(527\) | 1.77774 | 0.0774396 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −15.7751 | −0.685872 | ||||||||
\(530\) | 11.7594 | 0.510796 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 2.15937 | 0.0936206 | ||||||||
\(533\) | −11.8455 | −0.513086 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 25.7995 | 1.11541 | ||||||||
\(536\) | 4.18466 | 0.180750 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −0.492739 | −0.0212435 | ||||||||
\(539\) | 40.4816 | 1.74367 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 19.6792 | 0.846076 | 0.423038 | − | 0.906112i | \(-0.360964\pi\) | ||||
0.423038 | + | 0.906112i | \(0.360964\pi\) | |||||||
\(542\) | −7.28712 | −0.313009 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −2.18832 | −0.0938233 | ||||||||
\(545\) | 20.5215 | 0.879044 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −23.7784 | −1.01669 | −0.508345 | − | 0.861154i | \(-0.669742\pi\) | ||||
−0.508345 | + | 0.861154i | \(0.669742\pi\) | |||||||
\(548\) | −3.26025 | −0.139271 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 5.83989 | 0.249014 | ||||||||
\(551\) | 0.441233 | 0.0187972 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 75.1224 | 3.19453 | ||||||||
\(554\) | 26.1050 | 1.10909 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 18.1889 | 0.771381 | ||||||||
\(557\) | 7.29901 | 0.309269 | 0.154635 | − | 0.987972i | \(-0.450580\pi\) | ||||
0.154635 | + | 0.987972i | \(0.450580\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 39.3941 | 1.66619 | ||||||||
\(560\) | 7.71606 | 0.326063 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 26.6711 | 1.12505 | ||||||||
\(563\) | −2.03753 | −0.0858716 | −0.0429358 | − | 0.999078i | \(-0.513671\pi\) | ||||
−0.0429358 | + | 0.999078i | \(0.513671\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 6.89342 | 0.290008 | ||||||||
\(566\) | −17.0033 | −0.714702 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −9.74208 | −0.408768 | ||||||||
\(569\) | 17.2444 | 0.722921 | 0.361461 | − | 0.932387i | \(-0.382278\pi\) | ||||
0.361461 | + | 0.932387i | \(0.382278\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −19.9527 | −0.834993 | −0.417496 | − | 0.908679i | \(-0.637092\pi\) | ||||
−0.417496 | + | 0.908679i | \(0.637092\pi\) | |||||||
\(572\) | −8.16267 | −0.341298 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −16.0736 | −0.670898 | ||||||||
\(575\) | −7.14681 | −0.298042 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 8.77032 | 0.365113 | 0.182557 | − | 0.983195i | \(-0.441563\pi\) | ||||
0.182557 | + | 0.983195i | \(0.441563\pi\) | |||||||
\(578\) | 12.2113 | 0.507922 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 1.57665 | 0.0654669 | ||||||||
\(581\) | −7.56449 | −0.313828 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −16.8803 | −0.699111 | ||||||||
\(584\) | 14.1375 | 0.585013 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 24.2864 | 1.00326 | ||||||||
\(587\) | −3.84784 | −0.158817 | −0.0794087 | − | 0.996842i | \(-0.525303\pi\) | ||||
−0.0794087 | + | 0.996842i | \(0.525303\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0.347860 | 0.0143333 | ||||||||
\(590\) | −18.2568 | −0.751619 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −2.71746 | −0.111687 | ||||||||
\(593\) | −22.2185 | −0.912404 | −0.456202 | − | 0.889876i | \(-0.650790\pi\) | ||||
−0.456202 | + | 0.889876i | \(0.650790\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 16.8852 | 0.692225 | ||||||||
\(596\) | 1.00000 | 0.0409616 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 9.98941 | 0.408497 | ||||||||
\(599\) | −37.4024 | −1.52822 | −0.764110 | − | 0.645086i | \(-0.776822\pi\) | ||||
−0.764110 | + | 0.645086i | \(0.776822\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 20.9418 | 0.854234 | 0.427117 | − | 0.904196i | \(-0.359529\pi\) | ||||
0.427117 | + | 0.904196i | \(0.359529\pi\) | |||||||
\(602\) | 53.4552 | 2.17867 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 13.8103 | 0.561932 | ||||||||
\(605\) | −9.44957 | −0.384180 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −8.43905 | −0.342531 | −0.171265 | − | 0.985225i | \(-0.554786\pi\) | ||||
−0.171265 | + | 0.985225i | \(0.554786\pi\) | |||||||
\(608\) | −0.428199 | −0.0173658 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −1.29416 | −0.0523991 | ||||||||
\(611\) | −11.6542 | −0.471479 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −16.8275 | −0.679656 | −0.339828 | − | 0.940488i | \(-0.610369\pi\) | ||||
−0.339828 | + | 0.940488i | \(0.610369\pi\) | |||||||
\(614\) | −1.13742 | −0.0459026 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −11.0762 | −0.446273 | ||||||||
\(617\) | −43.7674 | −1.76201 | −0.881005 | − | 0.473108i | \(-0.843132\pi\) | ||||
−0.881005 | + | 0.473108i | \(0.843132\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 32.3525 | 1.30036 | 0.650178 | − | 0.759782i | \(-0.274694\pi\) | ||||
0.650178 | + | 0.759782i | \(0.274694\pi\) | |||||||
\(620\) | 1.24300 | 0.0499202 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0.447203 | 0.0179312 | ||||||||
\(623\) | 35.0482 | 1.40418 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −4.63619 | −0.185448 | ||||||||
\(626\) | −12.9333 | −0.516917 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 15.5334 | 0.619849 | ||||||||
\(629\) | −5.94666 | −0.237109 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 5.92934 | 0.236043 | 0.118022 | − | 0.993011i | \(-0.462345\pi\) | ||||
0.118022 | + | 0.993011i | \(0.462345\pi\) | |||||||
\(632\) | −14.8966 | −0.592556 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −4.60730 | −0.182979 | ||||||||
\(635\) | 17.0469 | 0.676484 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −68.4969 | −2.71395 | ||||||||
\(638\) | −2.26324 | −0.0896027 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −1.53008 | −0.0604817 | ||||||||
\(641\) | 10.6182 | 0.419394 | 0.209697 | − | 0.977766i | \(-0.432752\pi\) | ||||
0.209697 | + | 0.977766i | \(0.432752\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −8.30984 | −0.327708 | −0.163854 | − | 0.986485i | \(-0.552393\pi\) | ||||
−0.163854 | + | 0.986485i | \(0.552393\pi\) | |||||||
\(644\) | 13.5550 | 0.534140 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −0.937036 | −0.0368672 | ||||||||
\(647\) | 2.82555 | 0.111084 | 0.0555419 | − | 0.998456i | \(-0.482311\pi\) | ||||
0.0555419 | + | 0.998456i | \(0.482311\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 26.2071 | 1.02872 | ||||||||
\(650\) | −9.88138 | −0.387580 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −15.8819 | −0.621982 | ||||||||
\(653\) | −14.4243 | −0.564465 | −0.282232 | − | 0.959346i | \(-0.591075\pi\) | ||||
−0.282232 | + | 0.959346i | \(0.591075\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −21.6446 | −0.845723 | ||||||||
\(656\) | 3.18736 | 0.124445 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −15.8140 | −0.616494 | ||||||||
\(659\) | 1.31140 | 0.0510848 | 0.0255424 | − | 0.999674i | \(-0.491869\pi\) | ||||
0.0255424 | + | 0.999674i | \(0.491869\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −0.269664 | −0.0104887 | −0.00524436 | − | 0.999986i | \(-0.501669\pi\) | ||||
−0.00524436 | + | 0.999986i | \(0.501669\pi\) | |||||||
\(662\) | 9.54771 | 0.371082 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 1.50002 | 0.0582122 | ||||||||
\(665\) | 3.30401 | 0.128124 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 2.76974 | 0.107245 | ||||||||
\(668\) | −21.1258 | −0.817381 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 6.40286 | 0.247364 | ||||||||
\(671\) | 1.85774 | 0.0717171 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 13.5720 | 0.523164 | 0.261582 | − | 0.965181i | \(-0.415756\pi\) | ||||
0.261582 | + | 0.965181i | \(0.415756\pi\) | |||||||
\(674\) | −1.90607 | −0.0734191 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0.811642 | 0.0312170 | ||||||||
\(677\) | 23.7120 | 0.911324 | 0.455662 | − | 0.890153i | \(-0.349403\pi\) | ||||
0.455662 | + | 0.890153i | \(0.349403\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −75.7091 | −2.90545 | ||||||||
\(680\) | −3.34830 | −0.128401 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −1.78430 | −0.0683243 | ||||||||
\(683\) | 21.4299 | 0.819993 | 0.409997 | − | 0.912087i | \(-0.365530\pi\) | ||||
0.409997 | + | 0.912087i | \(0.365530\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −4.98844 | −0.190598 | ||||||||
\(686\) | −57.6454 | −2.20091 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −10.6001 | −0.404124 | ||||||||
\(689\) | 28.5623 | 1.08814 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −25.3951 | −0.966076 | −0.483038 | − | 0.875599i | \(-0.660467\pi\) | ||||
−0.483038 | + | 0.875599i | \(0.660467\pi\) | |||||||
\(692\) | −12.1765 | −0.462882 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 31.8251 | 1.20806 | ||||||||
\(695\) | 27.8304 | 1.05567 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 6.97495 | 0.264195 | ||||||||
\(698\) | 14.2839 | 0.540655 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −13.4084 | −0.506789 | ||||||||
\(701\) | −18.3848 | −0.694384 | −0.347192 | − | 0.937794i | \(-0.612865\pi\) | ||||
−0.347192 | + | 0.937794i | \(0.612865\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −1.16361 | −0.0438865 | ||||||||
\(704\) | 2.19639 | 0.0827796 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 4.35738 | 0.163992 | ||||||||
\(707\) | 93.5862 | 3.51967 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −0.380764 | −0.0142999 | −0.00714995 | − | 0.999974i | \(-0.502276\pi\) | ||||
−0.00714995 | + | 0.999974i | \(0.502276\pi\) | |||||||
\(710\) | −14.9062 | −0.559418 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −6.94999 | −0.260462 | ||||||||
\(713\) | 2.18361 | 0.0817768 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −12.4895 | −0.467082 | ||||||||
\(716\) | 22.3807 | 0.836406 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 17.6460 | 0.658542 | ||||||||
\(719\) | 5.68886 | 0.212159 | 0.106079 | − | 0.994358i | \(-0.466170\pi\) | ||||
0.106079 | + | 0.994358i | \(0.466170\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 89.9115 | 3.34848 | ||||||||
\(722\) | 18.8166 | 0.700283 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −16.5525 | −0.615170 | ||||||||
\(725\) | −2.73979 | −0.101753 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −18.4997 | −0.686115 | −0.343058 | − | 0.939314i | \(-0.611463\pi\) | ||||
−0.343058 | + | 0.939314i | \(0.611463\pi\) | |||||||
\(728\) | 18.7415 | 0.694606 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 21.6314 | 0.800616 | ||||||||
\(731\) | −23.1963 | −0.857946 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −0.985838 | −0.0364127 | −0.0182064 | − | 0.999834i | \(-0.505796\pi\) | ||||
−0.0182064 | + | 0.999834i | \(0.505796\pi\) | |||||||
\(734\) | 12.9361 | 0.477479 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −2.68792 | −0.0990782 | ||||||||
\(737\) | −9.19114 | −0.338560 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 14.4601 | 0.531925 | 0.265962 | − | 0.963983i | \(-0.414310\pi\) | ||||
0.265962 | + | 0.963983i | \(0.414310\pi\) | |||||||
\(740\) | −4.15793 | −0.152848 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 38.7572 | 1.42282 | ||||||||
\(743\) | 30.5301 | 1.12004 | 0.560020 | − | 0.828479i | \(-0.310793\pi\) | ||||
0.560020 | + | 0.828479i | \(0.310793\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 1.53008 | 0.0560578 | ||||||||
\(746\) | 8.95023 | 0.327691 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 4.80640 | 0.175739 | ||||||||
\(749\) | 85.0313 | 3.10698 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 39.7575 | 1.45077 | 0.725385 | − | 0.688343i | \(-0.241662\pi\) | ||||
0.725385 | + | 0.688343i | \(0.241662\pi\) | |||||||
\(752\) | 3.13589 | 0.114354 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 3.82952 | 0.139463 | ||||||||
\(755\) | 21.1308 | 0.769029 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 16.0332 | 0.582737 | 0.291369 | − | 0.956611i | \(-0.405889\pi\) | ||||
0.291369 | + | 0.956611i | \(0.405889\pi\) | |||||||
\(758\) | 25.4453 | 0.924216 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −0.655179 | −0.0237658 | ||||||||
\(761\) | 22.2255 | 0.805674 | 0.402837 | − | 0.915272i | \(-0.368024\pi\) | ||||
0.402837 | + | 0.915272i | \(0.368024\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 67.6357 | 2.44858 | ||||||||
\(764\) | 20.5627 | 0.743933 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −20.2374 | −0.731208 | ||||||||
\(767\) | −44.3437 | −1.60116 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −47.0661 | −1.69725 | −0.848623 | − | 0.528998i | \(-0.822568\pi\) | ||||
−0.848623 | + | 0.528998i | \(0.822568\pi\) | |||||||
\(770\) | −16.9475 | −0.610744 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 16.6431 | 0.598998 | ||||||||
\(773\) | 15.0500 | 0.541312 | 0.270656 | − | 0.962676i | \(-0.412759\pi\) | ||||
0.270656 | + | 0.962676i | \(0.412759\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −2.16000 | −0.0775894 | ||||||||
\(776\) | 15.0130 | 0.538934 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −15.5789 | −0.558529 | ||||||||
\(779\) | 1.36482 | 0.0488999 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 21.3974 | 0.765659 | ||||||||
\(782\) | −5.88203 | −0.210341 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 18.4310 | 0.658249 | ||||||||
\(785\) | 23.7673 | 0.848291 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −14.4696 | −0.515786 | −0.257893 | − | 0.966174i | \(-0.583028\pi\) | ||||
−0.257893 | + | 0.966174i | \(0.583028\pi\) | |||||||
\(788\) | 21.4204 | 0.763069 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −22.7930 | −0.810939 | ||||||||
\(791\) | 22.7197 | 0.807819 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −3.14338 | −0.111625 | ||||||||
\(794\) | 21.5619 | 0.765204 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 6.13385 | 0.217409 | ||||||||
\(797\) | −20.3370 | −0.720374 | −0.360187 | − | 0.932880i | \(-0.617287\pi\) | ||||
−0.360187 | + | 0.932880i | \(0.617287\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 6.86232 | 0.242771 | ||||||||
\(800\) | 2.65886 | 0.0940048 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −20.2428 | −0.714799 | ||||||||
\(803\) | −31.0514 | −1.09578 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 20.7402 | 0.730995 | ||||||||
\(806\) | 3.01912 | 0.106344 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −18.5580 | −0.652867 | ||||||||
\(809\) | −19.2164 | −0.675614 | −0.337807 | − | 0.941215i | \(-0.609685\pi\) | ||||
−0.337807 | + | 0.941215i | \(0.609685\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 37.5596 | 1.31890 | 0.659448 | − | 0.751750i | \(-0.270790\pi\) | ||||
0.659448 | + | 0.751750i | \(0.270790\pi\) | |||||||
\(812\) | 5.19641 | 0.182358 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 5.96860 | 0.209199 | ||||||||
\(815\) | −24.3005 | −0.851211 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −4.53894 | −0.158797 | ||||||||
\(818\) | −7.78181 | −0.272085 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 4.87691 | 0.170309 | ||||||||
\(821\) | −37.2215 | −1.29904 | −0.649520 | − | 0.760344i | \(-0.725030\pi\) | ||||
−0.649520 | + | 0.760344i | \(0.725030\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −4.34491 | −0.151454 | −0.0757270 | − | 0.997129i | \(-0.524128\pi\) | ||||
−0.0757270 | + | 0.997129i | \(0.524128\pi\) | |||||||
\(824\) | −17.8293 | −0.621113 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −60.1715 | −2.09364 | ||||||||
\(827\) | 21.0032 | 0.730355 | 0.365177 | − | 0.930938i | \(-0.381008\pi\) | ||||
0.365177 | + | 0.930938i | \(0.381008\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 19.1963 | 0.666716 | 0.333358 | − | 0.942800i | \(-0.391818\pi\) | ||||
0.333358 | + | 0.942800i | \(0.391818\pi\) | |||||||
\(830\) | 2.29515 | 0.0796660 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −3.71640 | −0.128843 | ||||||||
\(833\) | 40.3328 | 1.39745 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −32.3241 | −1.11862 | ||||||||
\(836\) | 0.940493 | 0.0325276 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −29.8913 | −1.03258 | ||||||||
\(839\) | −30.8957 | −1.06664 | −0.533320 | − | 0.845914i | \(-0.679056\pi\) | ||||
−0.533320 | + | 0.845914i | \(0.679056\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −27.9382 | −0.963386 | ||||||||
\(842\) | −3.47305 | −0.119689 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −1.92401 | −0.0662272 | ||||||||
\(845\) | 1.24188 | 0.0427218 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −31.1444 | −1.07013 | ||||||||
\(848\) | −7.68548 | −0.263921 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 5.81843 | 0.199570 | ||||||||
\(851\) | −7.30432 | −0.250389 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 51.8321 | 1.77470 | 0.887349 | − | 0.461099i | \(-0.152545\pi\) | ||||
0.887349 | + | 0.461099i | \(0.152545\pi\) | |||||||
\(854\) | −4.26536 | −0.145958 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −16.8615 | −0.576316 | ||||||||
\(857\) | 38.9753 | 1.33137 | 0.665685 | − | 0.746233i | \(-0.268140\pi\) | ||||
0.665685 | + | 0.746233i | \(0.268140\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −29.0741 | −0.991996 | −0.495998 | − | 0.868324i | \(-0.665198\pi\) | ||||
−0.495998 | + | 0.868324i | \(0.665198\pi\) | |||||||
\(860\) | −16.2189 | −0.553061 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −26.4524 | −0.900971 | ||||||||
\(863\) | −43.1294 | −1.46814 | −0.734071 | − | 0.679072i | \(-0.762382\pi\) | ||||
−0.734071 | + | 0.679072i | \(0.762382\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −18.6311 | −0.633475 | ||||||||
\(866\) | −9.06980 | −0.308204 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 4.09675 | 0.139053 | ||||||||
\(869\) | 32.7188 | 1.10991 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 15.5519 | 0.526955 | ||||||||
\(872\) | −13.4120 | −0.454189 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −1.15097 | −0.0389320 | ||||||||
\(875\) | −59.0962 | −1.99782 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 51.7592 | 1.74778 | 0.873892 | − | 0.486120i | \(-0.161588\pi\) | ||||
0.873892 | + | 0.486120i | \(0.161588\pi\) | |||||||
\(878\) | −14.3151 | −0.483112 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 3.36065 | 0.113288 | ||||||||
\(881\) | −11.2445 | −0.378838 | −0.189419 | − | 0.981896i | \(-0.560660\pi\) | ||||
−0.189419 | + | 0.981896i | \(0.560660\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −35.2347 | −1.18574 | −0.592872 | − | 0.805297i | \(-0.702006\pi\) | ||||
−0.592872 | + | 0.805297i | \(0.702006\pi\) | |||||||
\(884\) | −8.13267 | −0.273531 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −18.3436 | −0.616264 | ||||||||
\(887\) | 5.09499 | 0.171073 | 0.0855366 | − | 0.996335i | \(-0.472740\pi\) | ||||
0.0855366 | + | 0.996335i | \(0.472740\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 56.1839 | 1.88435 | ||||||||
\(890\) | −10.6340 | −0.356453 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 11.4543 | 0.383520 | ||||||||
\(893\) | 1.34278 | 0.0449346 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 34.2443 | 1.14466 | ||||||||
\(896\) | −5.04291 | −0.168472 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −5.91128 | −0.197262 | ||||||||
\(899\) | 0.837105 | 0.0279190 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −16.8183 | −0.560298 | ||||||||
\(902\) | −7.00068 | −0.233097 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −4.50527 | −0.149843 | ||||||||
\(905\) | −25.3267 | −0.841887 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −36.8786 | −1.22453 | −0.612266 | − | 0.790652i | \(-0.709742\pi\) | ||||
−0.612266 | + | 0.790652i | \(0.709742\pi\) | |||||||
\(908\) | −7.54669 | −0.250446 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 28.6760 | 0.950599 | ||||||||
\(911\) | −33.3860 | −1.10613 | −0.553064 | − | 0.833139i | \(-0.686542\pi\) | ||||
−0.553064 | + | 0.833139i | \(0.686542\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −3.29464 | −0.109037 | ||||||||
\(914\) | 4.51467 | 0.149332 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −27.8224 | −0.919277 | ||||||||
\(917\) | −71.3372 | −2.35576 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 42.0441 | 1.38691 | 0.693454 | − | 0.720501i | \(-0.256088\pi\) | ||||
0.693454 | + | 0.720501i | \(0.256088\pi\) | |||||||
\(920\) | −4.11274 | −0.135593 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 17.7809 | 0.585583 | ||||||||
\(923\) | −36.2055 | −1.19172 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 7.22533 | 0.237568 | ||||||||
\(926\) | 34.2340 | 1.12500 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −1.03044 | −0.0338258 | ||||||||
\(929\) | −26.8964 | −0.882441 | −0.441221 | − | 0.897399i | \(-0.645454\pi\) | ||||
−0.441221 | + | 0.897399i | \(0.645454\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 7.89213 | 0.258654 | ||||||||
\(932\) | 26.3727 | 0.863867 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 2.79934 | 0.0915971 | ||||||||
\(935\) | 7.35417 | 0.240507 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −3.40736 | −0.111314 | −0.0556568 | − | 0.998450i | \(-0.517725\pi\) | ||||
−0.0556568 | + | 0.998450i | \(0.517725\pi\) | |||||||
\(938\) | 21.1029 | 0.689033 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 4.79816 | 0.156499 | ||||||||
\(941\) | −31.5304 | −1.02786 | −0.513931 | − | 0.857832i | \(-0.671811\pi\) | ||||
−0.513931 | + | 0.857832i | \(0.671811\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 8.56738 | 0.278992 | ||||||||
\(944\) | 11.9319 | 0.388350 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 23.2819 | 0.756959 | ||||||||
\(947\) | −25.3895 | −0.825048 | −0.412524 | − | 0.910947i | \(-0.635353\pi\) | ||||
−0.412524 | + | 0.910947i | \(0.635353\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 52.5405 | 1.70554 | ||||||||
\(950\) | 1.13852 | 0.0369385 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −11.0355 | −0.357662 | ||||||||
\(953\) | −28.2057 | −0.913673 | −0.456837 | − | 0.889551i | \(-0.651018\pi\) | ||||
−0.456837 | + | 0.889551i | \(0.651018\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 31.4626 | 1.01811 | ||||||||
\(956\) | −19.1553 | −0.619527 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 3.83579 | 0.123929 | ||||||||
\(959\) | −16.4411 | −0.530912 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.3400 | −0.978711 | ||||||||
\(962\) | −10.0992 | −0.325610 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −18.2493 | −0.587772 | ||||||||
\(965\) | 25.4652 | 0.819755 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −16.4498 | −0.528991 | −0.264495 | − | 0.964387i | \(-0.585205\pi\) | ||||
−0.264495 | + | 0.964387i | \(0.585205\pi\) | |||||||
\(968\) | 6.17587 | 0.198500 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 22.9710 | 0.737555 | ||||||||
\(971\) | 45.5948 | 1.46321 | 0.731604 | − | 0.681730i | \(-0.238772\pi\) | ||||
0.731604 | + | 0.681730i | \(0.238772\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 91.7250 | 2.94057 | ||||||||
\(974\) | −26.3377 | −0.843913 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0.845814 | 0.0270738 | ||||||||
\(977\) | −8.73458 | −0.279444 | −0.139722 | − | 0.990191i | \(-0.544621\pi\) | ||||
−0.139722 | + | 0.990191i | \(0.544621\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 15.2649 | 0.487868 | ||||||||
\(980\) | 28.2008 | 0.900843 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 22.8728 | 0.729902 | ||||||||
\(983\) | −43.3752 | −1.38345 | −0.691726 | − | 0.722160i | \(-0.743150\pi\) | ||||
−0.691726 | + | 0.722160i | \(0.743150\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 32.7749 | 1.04429 | ||||||||
\(986\) | −2.25493 | −0.0718115 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −1.59136 | −0.0506279 | ||||||||
\(989\) | −28.4922 | −0.905998 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 7.62311 | 0.242156 | 0.121078 | − | 0.992643i | \(-0.461365\pi\) | ||||
0.121078 | + | 0.992643i | \(0.461365\pi\) | |||||||
\(992\) | −0.812378 | −0.0257930 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −49.1284 | −1.55826 | ||||||||
\(995\) | 9.38528 | 0.297533 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −43.7993 | −1.38714 | −0.693569 | − | 0.720390i | \(-0.743963\pi\) | ||||
−0.693569 | + | 0.720390i | \(0.743963\pi\) | |||||||
\(998\) | −3.17734 | −0.100577 | ||||||||
\(999\) | 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.l.1.9 | ✓ | 12 | |
3.2 | odd | 2 | 8046.2.a.m.1.4 | yes | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8046.2.a.l.1.9 | ✓ | 12 | 1.1 | even | 1 | trivial | |
8046.2.a.m.1.4 | yes | 12 | 3.2 | odd | 2 |