Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1521,2,Mod(1,1521)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1521, 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("1521.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1521 = 3^{2} \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1521.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: | \(12.1452461474\) |
Analytic rank: | \(1\) |
Dimension: | \(6\) |
Coefficient field: | 6.6.1997632.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 8x^{4} + 19x^{2} - 13 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(-2.06082\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1521.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.14367 | −0.808696 | −0.404348 | − | 0.914605i | \(-0.632502\pi\) | ||||
−0.404348 | + | 0.914605i | \(0.632502\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −0.692021 | −0.346011 | ||||||||
\(5\) | −3.48695 | −1.55941 | −0.779706 | − | 0.626146i | \(-0.784632\pi\) | ||||
−0.779706 | + | 0.626146i | \(0.784632\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −3.35690 | −1.26879 | −0.634394 | − | 0.773010i | \(-0.718750\pi\) | ||||
−0.634394 | + | 0.773010i | \(0.718750\pi\) | |||||||
\(8\) | 3.07878 | 1.08851 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 3.98792 | 1.26109 | ||||||||
\(11\) | 2.97797 | 0.897892 | 0.448946 | − | 0.893559i | \(-0.351800\pi\) | ||||
0.448946 | + | 0.893559i | \(0.351800\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | 3.83918 | 1.02606 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −2.13706 | −0.534266 | ||||||||
\(17\) | 6.91796 | 1.67785 | 0.838926 | − | 0.544246i | \(-0.183184\pi\) | ||||
0.838926 | + | 0.544246i | \(0.183184\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.295897 | 0.0678834 | 0.0339417 | − | 0.999424i | \(-0.489194\pi\) | ||||
0.0339417 | + | 0.999424i | \(0.489194\pi\) | |||||||
\(20\) | 2.41305 | 0.539573 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −3.40581 | −0.726122 | ||||||||
\(23\) | 2.46899 | 0.514820 | 0.257410 | − | 0.966302i | \(-0.417131\pi\) | ||||
0.257410 | + | 0.966302i | \(0.417131\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 7.15883 | 1.43177 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 2.32304 | 0.439014 | ||||||||
\(29\) | 0.609790 | 0.113235 | 0.0566176 | − | 0.998396i | \(-0.481968\pi\) | ||||
0.0566176 | + | 0.998396i | \(0.481968\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −9.93900 | −1.78510 | −0.892549 | − | 0.450951i | \(-0.851085\pi\) | ||||
−0.892549 | + | 0.450951i | \(0.851085\pi\) | |||||||
\(32\) | −3.71347 | −0.656455 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −7.91185 | −1.35687 | ||||||||
\(35\) | 11.7053 | 1.97856 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 8.50365 | 1.39799 | 0.698996 | − | 0.715126i | \(-0.253631\pi\) | ||||
0.698996 | + | 0.715126i | \(0.253631\pi\) | |||||||
\(38\) | −0.338408 | −0.0548970 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −10.7356 | −1.69744 | ||||||||
\(41\) | 7.30123 | 1.14026 | 0.570130 | − | 0.821554i | \(-0.306893\pi\) | ||||
0.570130 | + | 0.821554i | \(0.306893\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −6.60388 | −1.00708 | −0.503541 | − | 0.863971i | \(-0.667970\pi\) | ||||
−0.503541 | + | 0.863971i | \(0.667970\pi\) | |||||||
\(44\) | −2.06082 | −0.310680 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −2.82371 | −0.416333 | ||||||||
\(47\) | −4.63062 | −0.675445 | −0.337723 | − | 0.941246i | \(-0.609657\pi\) | ||||
−0.337723 | + | 0.941246i | \(0.609657\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 4.26875 | 0.609821 | ||||||||
\(50\) | −8.18734 | −1.15786 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −9.38695 | −1.28940 | −0.644698 | − | 0.764437i | \(-0.723017\pi\) | ||||
−0.644698 | + | 0.764437i | \(0.723017\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −10.3840 | −1.40018 | ||||||||
\(56\) | −10.3351 | −1.38109 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −0.697398 | −0.0915729 | ||||||||
\(59\) | 0.816341 | 0.106279 | 0.0531393 | − | 0.998587i | \(-0.483077\pi\) | ||||
0.0531393 | + | 0.998587i | \(0.483077\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 5.08815 | 0.651470 | 0.325735 | − | 0.945461i | \(-0.394388\pi\) | ||||
0.325735 | + | 0.945461i | \(0.394388\pi\) | |||||||
\(62\) | 11.3669 | 1.44360 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 8.52111 | 1.06514 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −10.2349 | −1.25039 | −0.625196 | − | 0.780468i | \(-0.714981\pi\) | ||||
−0.625196 | + | 0.780468i | \(0.714981\pi\) | |||||||
\(68\) | −4.78738 | −0.580555 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −13.3870 | −1.60006 | ||||||||
\(71\) | −10.1224 | −1.20131 | −0.600657 | − | 0.799507i | \(-0.705094\pi\) | ||||
−0.600657 | + | 0.799507i | \(0.705094\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −8.74094 | −1.02305 | −0.511525 | − | 0.859269i | \(-0.670919\pi\) | ||||
−0.511525 | + | 0.859269i | \(0.670919\pi\) | |||||||
\(74\) | −9.72536 | −1.13055 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −0.204767 | −0.0234884 | ||||||||
\(77\) | −9.99674 | −1.13923 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 3.52111 | 0.396155 | 0.198078 | − | 0.980186i | \(-0.436530\pi\) | ||||
0.198078 | + | 0.980186i | \(0.436530\pi\) | |||||||
\(80\) | 7.45184 | 0.833141 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −8.35019 | −0.922124 | ||||||||
\(83\) | 11.7751 | 1.29248 | 0.646242 | − | 0.763132i | \(-0.276339\pi\) | ||||
0.646242 | + | 0.763132i | \(0.276339\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −24.1226 | −2.61646 | ||||||||
\(86\) | 7.55265 | 0.814423 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 9.16852 | 0.977368 | ||||||||
\(89\) | 7.77916 | 0.824590 | 0.412295 | − | 0.911050i | \(-0.364727\pi\) | ||||
0.412295 | + | 0.911050i | \(0.364727\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −1.70859 | −0.178133 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 5.29590 | 0.546230 | ||||||||
\(95\) | −1.03178 | −0.105858 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −2.56033 | −0.259963 | −0.129981 | − | 0.991516i | \(-0.541492\pi\) | ||||
−0.129981 | + | 0.991516i | \(0.541492\pi\) | |||||||
\(98\) | −4.88204 | −0.493160 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −4.95407 | −0.495407 | ||||||||
\(101\) | −14.7841 | −1.47107 | −0.735537 | − | 0.677484i | \(-0.763070\pi\) | ||||
−0.735537 | + | 0.677484i | \(0.763070\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 2.09783 | 0.206706 | 0.103353 | − | 0.994645i | \(-0.467043\pi\) | ||||
0.103353 | + | 0.994645i | \(0.467043\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 10.7356 | 1.04273 | ||||||||
\(107\) | 6.64658 | 0.642549 | 0.321274 | − | 0.946986i | \(-0.395889\pi\) | ||||
0.321274 | + | 0.946986i | \(0.395889\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −3.06100 | −0.293191 | −0.146595 | − | 0.989197i | \(-0.546831\pi\) | ||||
−0.146595 | + | 0.989197i | \(0.546831\pi\) | |||||||
\(110\) | 11.8759 | 1.13232 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 7.17390 | 0.677870 | ||||||||
\(113\) | −5.81915 | −0.547420 | −0.273710 | − | 0.961812i | \(-0.588251\pi\) | ||||
−0.273710 | + | 0.961812i | \(0.588251\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −8.60925 | −0.802817 | ||||||||
\(116\) | −0.421988 | −0.0391806 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −0.933624 | −0.0859471 | ||||||||
\(119\) | −23.2229 | −2.12884 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −2.13169 | −0.193790 | ||||||||
\(122\) | −5.81915 | −0.526841 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 6.87800 | 0.617663 | ||||||||
\(125\) | −7.52775 | −0.673302 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 15.9879 | 1.41870 | 0.709349 | − | 0.704857i | \(-0.248989\pi\) | ||||
0.709349 | + | 0.704857i | \(0.248989\pi\) | |||||||
\(128\) | −2.31839 | −0.204918 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 2.80740 | 0.245284 | 0.122642 | − | 0.992451i | \(-0.460863\pi\) | ||||
0.122642 | + | 0.992451i | \(0.460863\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −0.993295 | −0.0861296 | ||||||||
\(134\) | 11.7053 | 1.01119 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 21.2989 | 1.82636 | ||||||||
\(137\) | −1.80326 | −0.154062 | −0.0770312 | − | 0.997029i | \(-0.524544\pi\) | ||||
−0.0770312 | + | 0.997029i | \(0.524544\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −4.26875 | −0.362071 | −0.181035 | − | 0.983477i | \(-0.557945\pi\) | ||||
−0.181035 | + | 0.983477i | \(0.557945\pi\) | |||||||
\(140\) | −8.10034 | −0.684604 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 11.5767 | 0.971497 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −2.12631 | −0.176580 | ||||||||
\(146\) | 9.99674 | 0.827336 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −5.88471 | −0.483720 | ||||||||
\(149\) | 21.9784 | 1.80054 | 0.900270 | − | 0.435332i | \(-0.143369\pi\) | ||||
0.900270 | + | 0.435332i | \(0.143369\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −7.08277 | −0.576388 | −0.288194 | − | 0.957572i | \(-0.593055\pi\) | ||||
−0.288194 | + | 0.957572i | \(0.593055\pi\) | |||||||
\(152\) | 0.911002 | 0.0738920 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 11.4330 | 0.921294 | ||||||||
\(155\) | 34.6568 | 2.78370 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −2.95646 | −0.235951 | −0.117976 | − | 0.993016i | \(-0.537640\pi\) | ||||
−0.117976 | + | 0.993016i | \(0.537640\pi\) | |||||||
\(158\) | −4.02698 | −0.320369 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 12.9487 | 1.02368 | ||||||||
\(161\) | −8.28815 | −0.653197 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 6.18060 | 0.484102 | 0.242051 | − | 0.970263i | \(-0.422180\pi\) | ||||
0.242051 | + | 0.970263i | \(0.422180\pi\) | |||||||
\(164\) | −5.05261 | −0.394542 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −13.4668 | −1.04523 | ||||||||
\(167\) | 3.78938 | 0.293231 | 0.146616 | − | 0.989194i | \(-0.453162\pi\) | ||||
0.146616 | + | 0.989194i | \(0.453162\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | 27.5883 | 2.11592 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 4.57002 | 0.348461 | ||||||||
\(173\) | −10.4858 | −0.797217 | −0.398609 | − | 0.917121i | \(-0.630507\pi\) | ||||
−0.398609 | + | 0.917121i | \(0.630507\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −24.0315 | −1.81661 | ||||||||
\(176\) | −6.36411 | −0.479713 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −8.89679 | −0.666842 | ||||||||
\(179\) | −10.1473 | −0.758448 | −0.379224 | − | 0.925305i | \(-0.623809\pi\) | ||||
−0.379224 | + | 0.925305i | \(0.623809\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −21.4426 | −1.59382 | −0.796910 | − | 0.604098i | \(-0.793533\pi\) | ||||
−0.796910 | + | 0.604098i | \(0.793533\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 7.60148 | 0.560389 | ||||||||
\(185\) | −29.6518 | −2.18004 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 20.6015 | 1.50653 | ||||||||
\(188\) | 3.20449 | 0.233711 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 1.18001 | 0.0856071 | ||||||||
\(191\) | −21.3637 | −1.54582 | −0.772910 | − | 0.634515i | \(-0.781200\pi\) | ||||
−0.772910 | + | 0.634515i | \(0.781200\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 2.23191 | 0.160657 | 0.0803283 | − | 0.996768i | \(-0.474403\pi\) | ||||
0.0803283 | + | 0.996768i | \(0.474403\pi\) | |||||||
\(194\) | 2.92818 | 0.210231 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −2.95407 | −0.211005 | ||||||||
\(197\) | −2.51386 | −0.179105 | −0.0895524 | − | 0.995982i | \(-0.528544\pi\) | ||||
−0.0895524 | + | 0.995982i | \(0.528544\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −11.5646 | −0.819796 | −0.409898 | − | 0.912131i | \(-0.634436\pi\) | ||||
−0.409898 | + | 0.912131i | \(0.634436\pi\) | |||||||
\(200\) | 22.0405 | 1.55850 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 16.9081 | 1.18965 | ||||||||
\(203\) | −2.04700 | −0.143671 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −25.4590 | −1.77814 | ||||||||
\(206\) | −2.39923 | −0.167162 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0.881173 | 0.0609520 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −19.9041 | −1.37025 | −0.685127 | − | 0.728424i | \(-0.740253\pi\) | ||||
−0.685127 | + | 0.728424i | \(0.740253\pi\) | |||||||
\(212\) | 6.49597 | 0.446145 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −7.60148 | −0.519627 | ||||||||
\(215\) | 23.0274 | 1.57046 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 33.3642 | 2.26491 | ||||||||
\(218\) | 3.50077 | 0.237102 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 7.18598 | 0.484479 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −18.1468 | −1.21520 | −0.607598 | − | 0.794245i | \(-0.707867\pi\) | ||||
−0.607598 | + | 0.794245i | \(0.707867\pi\) | |||||||
\(224\) | 12.4657 | 0.832902 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 6.65519 | 0.442696 | ||||||||
\(227\) | −11.5796 | −0.768567 | −0.384283 | − | 0.923215i | \(-0.625551\pi\) | ||||
−0.384283 | + | 0.923215i | \(0.625551\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 11.8605 | 0.783767 | 0.391883 | − | 0.920015i | \(-0.371824\pi\) | ||||
0.391883 | + | 0.920015i | \(0.371824\pi\) | |||||||
\(230\) | 9.84613 | 0.649235 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 1.87741 | 0.123258 | ||||||||
\(233\) | −19.2331 | −1.26000 | −0.630001 | − | 0.776595i | \(-0.716945\pi\) | ||||
−0.630001 | + | 0.776595i | \(0.716945\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 16.1468 | 1.05330 | ||||||||
\(236\) | −0.564926 | −0.0367735 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 26.5593 | 1.72158 | ||||||||
\(239\) | −1.35637 | −0.0877362 | −0.0438681 | − | 0.999037i | \(-0.513968\pi\) | ||||
−0.0438681 | + | 0.999037i | \(0.513968\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −9.64310 | −0.621167 | −0.310583 | − | 0.950546i | \(-0.600524\pi\) | ||||
−0.310583 | + | 0.950546i | \(0.600524\pi\) | |||||||
\(242\) | 2.43794 | 0.156717 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −3.52111 | −0.225416 | ||||||||
\(245\) | −14.8849 | −0.950963 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −30.6000 | −1.94310 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 8.60925 | 0.544497 | ||||||||
\(251\) | −26.9114 | −1.69863 | −0.849317 | − | 0.527882i | \(-0.822986\pi\) | ||||
−0.849317 | + | 0.527882i | \(0.822986\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 7.35258 | 0.462253 | ||||||||
\(254\) | −18.2849 | −1.14730 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −14.3907 | −0.899422 | ||||||||
\(257\) | −9.72536 | −0.606651 | −0.303326 | − | 0.952887i | \(-0.598097\pi\) | ||||
−0.303326 | + | 0.952887i | \(0.598097\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −28.5459 | −1.77375 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −3.21073 | −0.198360 | ||||||||
\(263\) | 15.2061 | 0.937649 | 0.468824 | − | 0.883291i | \(-0.344678\pi\) | ||||
0.468824 | + | 0.883291i | \(0.344678\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 32.7318 | 2.01070 | ||||||||
\(266\) | 1.13600 | 0.0696527 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 7.08277 | 0.432649 | ||||||||
\(269\) | −1.43721 | −0.0876284 | −0.0438142 | − | 0.999040i | \(-0.513951\pi\) | ||||
−0.0438142 | + | 0.999040i | \(0.513951\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −7.32006 | −0.444662 | −0.222331 | − | 0.974971i | \(-0.571367\pi\) | ||||
−0.222331 | + | 0.974971i | \(0.571367\pi\) | |||||||
\(272\) | −14.7841 | −0.896419 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 2.06233 | 0.124590 | ||||||||
\(275\) | 21.3188 | 1.28557 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −0.610580 | −0.0366862 | −0.0183431 | − | 0.999832i | \(-0.505839\pi\) | ||||
−0.0183431 | + | 0.999832i | \(0.505839\pi\) | |||||||
\(278\) | 4.88204 | 0.292805 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 36.0382 | 2.15369 | ||||||||
\(281\) | 11.2772 | 0.672741 | 0.336371 | − | 0.941730i | \(-0.390801\pi\) | ||||
0.336371 | + | 0.941730i | \(0.390801\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −10.5894 | −0.629475 | −0.314737 | − | 0.949179i | \(-0.601916\pi\) | ||||
−0.314737 | + | 0.949179i | \(0.601916\pi\) | |||||||
\(284\) | 7.00495 | 0.415667 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −24.5095 | −1.44675 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 30.8582 | 1.81519 | ||||||||
\(290\) | 2.43179 | 0.142800 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 6.04892 | 0.353986 | ||||||||
\(293\) | −13.4028 | −0.783003 | −0.391501 | − | 0.920178i | \(-0.628044\pi\) | ||||
−0.391501 | + | 0.920178i | \(0.628044\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −2.84654 | −0.165732 | ||||||||
\(296\) | 26.1809 | 1.52173 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −25.1360 | −1.45609 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 22.1685 | 1.27777 | ||||||||
\(302\) | 8.10034 | 0.466122 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −0.632351 | −0.0362678 | ||||||||
\(305\) | −17.7421 | −1.01591 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 18.0476 | 1.03003 | 0.515015 | − | 0.857181i | \(-0.327786\pi\) | ||||
0.515015 | + | 0.857181i | \(0.327786\pi\) | |||||||
\(308\) | 6.91796 | 0.394187 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −39.6359 | −2.25117 | ||||||||
\(311\) | −28.4993 | −1.61604 | −0.808022 | − | 0.589152i | \(-0.799462\pi\) | ||||
−0.808022 | + | 0.589152i | \(0.799462\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 20.2911 | 1.14692 | 0.573461 | − | 0.819233i | \(-0.305601\pi\) | ||||
0.573461 | + | 0.819233i | \(0.305601\pi\) | |||||||
\(314\) | 3.38121 | 0.190813 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −2.43668 | −0.137074 | ||||||||
\(317\) | −2.54983 | −0.143213 | −0.0716065 | − | 0.997433i | \(-0.522813\pi\) | ||||
−0.0716065 | + | 0.997433i | \(0.522813\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1.81594 | 0.101673 | ||||||||
\(320\) | −29.7127 | −1.66099 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 9.47889 | 0.528238 | ||||||||
\(323\) | 2.04700 | 0.113898 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −7.06856 | −0.391492 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 22.4789 | 1.24119 | ||||||||
\(329\) | 15.5445 | 0.856997 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 0.993295 | 0.0545964 | 0.0272982 | − | 0.999627i | \(-0.491310\pi\) | ||||
0.0272982 | + | 0.999627i | \(0.491310\pi\) | |||||||
\(332\) | −8.14862 | −0.447214 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −4.33380 | −0.237135 | ||||||||
\(335\) | 35.6886 | 1.94988 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 20.4959 | 1.11648 | 0.558241 | − | 0.829679i | \(-0.311477\pi\) | ||||
0.558241 | + | 0.829679i | \(0.311477\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 16.6933 | 0.905324 | ||||||||
\(341\) | −29.5981 | −1.60282 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 9.16852 | 0.495054 | ||||||||
\(344\) | −20.3319 | −1.09622 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 11.9922 | 0.644706 | ||||||||
\(347\) | 15.3939 | 0.826388 | 0.413194 | − | 0.910643i | \(-0.364413\pi\) | ||||
0.413194 | + | 0.910643i | \(0.364413\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −3.72587 | −0.199441 | −0.0997207 | − | 0.995015i | \(-0.531795\pi\) | ||||
−0.0997207 | + | 0.995015i | \(0.531795\pi\) | |||||||
\(350\) | 27.4840 | 1.46908 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −11.0586 | −0.589426 | ||||||||
\(353\) | 13.0307 | 0.693552 | 0.346776 | − | 0.937948i | \(-0.387276\pi\) | ||||
0.346776 | + | 0.937948i | \(0.387276\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 35.2965 | 1.87334 | ||||||||
\(356\) | −5.38335 | −0.285317 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 11.6052 | 0.613354 | ||||||||
\(359\) | 25.2339 | 1.33179 | 0.665897 | − | 0.746044i | \(-0.268049\pi\) | ||||
0.665897 | + | 0.746044i | \(0.268049\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.9124 | −0.995392 | ||||||||
\(362\) | 24.5233 | 1.28892 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 30.4792 | 1.59536 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 5.87369 | 0.306604 | 0.153302 | − | 0.988179i | \(-0.451009\pi\) | ||||
0.153302 | + | 0.988179i | \(0.451009\pi\) | |||||||
\(368\) | −5.27639 | −0.275051 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 33.9119 | 1.76299 | ||||||||
\(371\) | 31.5110 | 1.63597 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 11.4330 | 0.591976 | 0.295988 | − | 0.955192i | \(-0.404351\pi\) | ||||
0.295988 | + | 0.955192i | \(0.404351\pi\) | |||||||
\(374\) | −23.5613 | −1.21832 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −14.2567 | −0.735232 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −26.5773 | −1.36519 | −0.682593 | − | 0.730799i | \(-0.739148\pi\) | ||||
−0.682593 | + | 0.730799i | \(0.739148\pi\) | |||||||
\(380\) | 0.714013 | 0.0366281 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 24.4330 | 1.25010 | ||||||||
\(383\) | −3.74725 | −0.191476 | −0.0957379 | − | 0.995407i | \(-0.530521\pi\) | ||||
−0.0957379 | + | 0.995407i | \(0.530521\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 34.8582 | 1.77654 | ||||||||
\(386\) | −2.55257 | −0.129922 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 1.77181 | 0.0899499 | ||||||||
\(389\) | 6.57955 | 0.333596 | 0.166798 | − | 0.985991i | \(-0.446657\pi\) | ||||
0.166798 | + | 0.985991i | \(0.446657\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 17.0804 | 0.863792 | ||||||||
\(392\) | 13.1425 | 0.663799 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 2.87502 | 0.144841 | ||||||||
\(395\) | −12.2779 | −0.617770 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 11.2101 | 0.562621 | 0.281310 | − | 0.959617i | \(-0.409231\pi\) | ||||
0.281310 | + | 0.959617i | \(0.409231\pi\) | |||||||
\(398\) | 13.2261 | 0.662966 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −15.2989 | −0.764944 | ||||||||
\(401\) | −20.8547 | −1.04143 | −0.520717 | − | 0.853730i | \(-0.674335\pi\) | ||||
−0.520717 | + | 0.853730i | \(0.674335\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 10.2309 | 0.509008 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 2.34109 | 0.116187 | ||||||||
\(407\) | 25.3236 | 1.25525 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −36.5163 | −1.80562 | −0.902808 | − | 0.430044i | \(-0.858498\pi\) | ||||
−0.902808 | + | 0.430044i | \(0.858498\pi\) | |||||||
\(410\) | 29.1167 | 1.43797 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −1.45175 | −0.0715224 | ||||||||
\(413\) | −2.74037 | −0.134845 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −41.0592 | −2.01552 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −1.00777 | −0.0492916 | ||||||||
\(419\) | 9.99674 | 0.488373 | 0.244186 | − | 0.969728i | \(-0.421479\pi\) | ||||
0.244186 | + | 0.969728i | \(0.421479\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 0.770479 | 0.0375508 | 0.0187754 | − | 0.999824i | \(-0.494023\pi\) | ||||
0.0187754 | + | 0.999824i | \(0.494023\pi\) | |||||||
\(422\) | 22.7637 | 1.10812 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −28.9004 | −1.40353 | ||||||||
\(425\) | 49.5245 | 2.40229 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −17.0804 | −0.826577 | ||||||||
\(428\) | −4.59957 | −0.222329 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −26.3357 | −1.27002 | ||||||||
\(431\) | −30.2838 | −1.45872 | −0.729359 | − | 0.684131i | \(-0.760181\pi\) | ||||
−0.729359 | + | 0.684131i | \(0.760181\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −28.0713 | −1.34902 | −0.674510 | − | 0.738266i | \(-0.735645\pi\) | ||||
−0.674510 | + | 0.738266i | \(0.735645\pi\) | |||||||
\(434\) | −38.1576 | −1.83162 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 2.11828 | 0.101447 | ||||||||
\(437\) | 0.730567 | 0.0349478 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −20.1347 | −0.960975 | −0.480488 | − | 0.877001i | \(-0.659540\pi\) | ||||
−0.480488 | + | 0.877001i | \(0.659540\pi\) | |||||||
\(440\) | −31.9702 | −1.52412 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 31.8494 | 1.51321 | 0.756606 | − | 0.653871i | \(-0.226856\pi\) | ||||
0.756606 | + | 0.653871i | \(0.226856\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −27.1256 | −1.28588 | ||||||||
\(446\) | 20.7539 | 0.982724 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −28.6045 | −1.35143 | ||||||||
\(449\) | −3.47313 | −0.163907 | −0.0819537 | − | 0.996636i | \(-0.526116\pi\) | ||||
−0.0819537 | + | 0.996636i | \(0.526116\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 21.7429 | 1.02383 | ||||||||
\(452\) | 4.02698 | 0.189413 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 13.2433 | 0.621537 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −21.1021 | −0.987117 | −0.493558 | − | 0.869713i | \(-0.664304\pi\) | ||||
−0.493558 | + | 0.869713i | \(0.664304\pi\) | |||||||
\(458\) | −13.5645 | −0.633829 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 5.95779 | 0.277783 | ||||||||
\(461\) | −7.19427 | −0.335071 | −0.167535 | − | 0.985866i | \(-0.553581\pi\) | ||||
−0.167535 | + | 0.985866i | \(0.553581\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −33.1594 | −1.54105 | −0.770525 | − | 0.637410i | \(-0.780006\pi\) | ||||
−0.770525 | + | 0.637410i | \(0.780006\pi\) | |||||||
\(464\) | −1.30316 | −0.0604977 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 21.9963 | 1.01896 | ||||||||
\(467\) | 21.6350 | 1.00115 | 0.500575 | − | 0.865693i | \(-0.333122\pi\) | ||||
0.500575 | + | 0.865693i | \(0.333122\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 34.3575 | 1.58648 | ||||||||
\(470\) | −18.4665 | −0.851798 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 2.51334 | 0.115686 | ||||||||
\(473\) | −19.6662 | −0.904251 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 2.11828 | 0.0971932 | ||||||||
\(476\) | 16.0707 | 0.736600 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 1.55124 | 0.0709519 | ||||||||
\(479\) | 31.0020 | 1.41652 | 0.708259 | − | 0.705952i | \(-0.249481\pi\) | ||||
0.708259 | + | 0.705952i | \(0.249481\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 11.0285 | 0.502335 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 1.47517 | 0.0670533 | ||||||||
\(485\) | 8.92776 | 0.405389 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 27.3478 | 1.23925 | 0.619624 | − | 0.784899i | \(-0.287285\pi\) | ||||
0.619624 | + | 0.784899i | \(0.287285\pi\) | |||||||
\(488\) | 15.6653 | 0.709134 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 17.0234 | 0.769040 | ||||||||
\(491\) | 15.0017 | 0.677019 | 0.338510 | − | 0.940963i | \(-0.390077\pi\) | ||||
0.338510 | + | 0.940963i | \(0.390077\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 4.21850 | 0.189992 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 21.2403 | 0.953716 | ||||||||
\(497\) | 33.9800 | 1.52421 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −5.85862 | −0.262268 | −0.131134 | − | 0.991365i | \(-0.541862\pi\) | ||||
−0.131134 | + | 0.991365i | \(0.541862\pi\) | |||||||
\(500\) | 5.20936 | 0.232970 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 30.7778 | 1.37368 | ||||||||
\(503\) | −25.8797 | −1.15392 | −0.576958 | − | 0.816773i | \(-0.695761\pi\) | ||||
−0.576958 | + | 0.816773i | \(0.695761\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 51.5515 | 2.29401 | ||||||||
\(506\) | −8.40892 | −0.373822 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −11.0640 | −0.490885 | ||||||||
\(509\) | 10.5306 | 0.466761 | 0.233381 | − | 0.972385i | \(-0.425021\pi\) | ||||
0.233381 | + | 0.972385i | \(0.425021\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 29.3424 | 1.29803 | ||||||||
\(512\) | 21.0950 | 0.932277 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 11.1226 | 0.490596 | ||||||||
\(515\) | −7.31505 | −0.322340 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −13.7899 | −0.606477 | ||||||||
\(518\) | 32.6470 | 1.43443 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −10.5395 | −0.461744 | −0.230872 | − | 0.972984i | \(-0.574158\pi\) | ||||
−0.230872 | + | 0.972984i | \(0.574158\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −4.97152 | −0.217390 | −0.108695 | − | 0.994075i | \(-0.534667\pi\) | ||||
−0.108695 | + | 0.994075i | \(0.534667\pi\) | |||||||
\(524\) | −1.94278 | −0.0848708 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −17.3907 | −0.758273 | ||||||||
\(527\) | −68.7576 | −2.99513 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −16.9041 | −0.734960 | ||||||||
\(530\) | −37.4344 | −1.62605 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0.687382 | 0.0298018 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −23.1763 | −1.00200 | ||||||||
\(536\) | −31.5110 | −1.36107 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 1.64370 | 0.0708647 | ||||||||
\(539\) | 12.7122 | 0.547554 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 1.99462 | 0.0857555 | 0.0428778 | − | 0.999080i | \(-0.486347\pi\) | ||||
0.0428778 | + | 0.999080i | \(0.486347\pi\) | |||||||
\(542\) | 8.37173 | 0.359596 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −25.6896 | −1.10143 | ||||||||
\(545\) | 10.6736 | 0.457205 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −37.6872 | −1.61139 | −0.805695 | − | 0.592331i | \(-0.798208\pi\) | ||||
−0.805695 | + | 0.592331i | \(0.798208\pi\) | |||||||
\(548\) | 1.24789 | 0.0533073 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −24.3817 | −1.03964 | ||||||||
\(551\) | 0.180435 | 0.00768679 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −11.8200 | −0.502637 | ||||||||
\(554\) | 0.698302 | 0.0296680 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 2.95407 | 0.125280 | ||||||||
\(557\) | 26.4695 | 1.12155 | 0.560774 | − | 0.827969i | \(-0.310504\pi\) | ||||
0.560774 | + | 0.827969i | \(0.310504\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | −25.0150 | −1.05708 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −12.8974 | −0.544043 | ||||||||
\(563\) | 6.79718 | 0.286467 | 0.143234 | − | 0.989689i | \(-0.454250\pi\) | ||||
0.143234 | + | 0.989689i | \(0.454250\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 20.2911 | 0.853653 | ||||||||
\(566\) | 12.1108 | 0.509054 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −31.1648 | −1.30765 | ||||||||
\(569\) | 38.2784 | 1.60471 | 0.802356 | − | 0.596845i | \(-0.203579\pi\) | ||||
0.802356 | + | 0.596845i | \(0.203579\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 29.7375 | 1.24447 | 0.622237 | − | 0.782829i | \(-0.286224\pi\) | ||||
0.622237 | + | 0.782829i | \(0.286224\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 28.0307 | 1.16998 | ||||||||
\(575\) | 17.6751 | 0.737102 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −11.7549 | −0.489365 | −0.244682 | − | 0.969603i | \(-0.578684\pi\) | ||||
−0.244682 | + | 0.969603i | \(0.578684\pi\) | |||||||
\(578\) | −35.2915 | −1.46793 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 1.47145 | 0.0610987 | ||||||||
\(581\) | −39.5278 | −1.63989 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −27.9541 | −1.15774 | ||||||||
\(584\) | −26.9114 | −1.11360 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 15.3284 | 0.633211 | ||||||||
\(587\) | 18.2090 | 0.751565 | 0.375782 | − | 0.926708i | \(-0.377374\pi\) | ||||
0.375782 | + | 0.926708i | \(0.377374\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −2.94092 | −0.121178 | ||||||||
\(590\) | 3.25550 | 0.134027 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −18.1728 | −0.746899 | ||||||||
\(593\) | −31.5421 | −1.29528 | −0.647639 | − | 0.761948i | \(-0.724243\pi\) | ||||
−0.647639 | + | 0.761948i | \(0.724243\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 80.9770 | 3.31973 | ||||||||
\(596\) | −15.2095 | −0.623006 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −32.4592 | −1.32625 | −0.663124 | − | 0.748510i | \(-0.730770\pi\) | ||||
−0.663124 | + | 0.748510i | \(0.730770\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 8.47112 | 0.345544 | 0.172772 | − | 0.984962i | \(-0.444728\pi\) | ||||
0.172772 | + | 0.984962i | \(0.444728\pi\) | |||||||
\(602\) | −25.3534 | −1.03333 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 4.90143 | 0.199436 | ||||||||
\(605\) | 7.43309 | 0.302198 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −23.9342 | −0.971460 | −0.485730 | − | 0.874109i | \(-0.661446\pi\) | ||||
−0.485730 | + | 0.874109i | \(0.661446\pi\) | |||||||
\(608\) | −1.09880 | −0.0445624 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 20.2911 | 0.821563 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 38.8864 | 1.57061 | 0.785303 | − | 0.619112i | \(-0.212507\pi\) | ||||
0.785303 | + | 0.619112i | \(0.212507\pi\) | |||||||
\(614\) | −20.6405 | −0.832981 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −30.7778 | −1.24007 | ||||||||
\(617\) | 34.1927 | 1.37655 | 0.688273 | − | 0.725452i | \(-0.258369\pi\) | ||||
0.688273 | + | 0.725452i | \(0.258369\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −43.0398 | −1.72992 | −0.864958 | − | 0.501844i | \(-0.832655\pi\) | ||||
−0.864958 | + | 0.501844i | \(0.832655\pi\) | |||||||
\(620\) | −23.9833 | −0.963191 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 32.5937 | 1.30689 | ||||||||
\(623\) | −26.1138 | −1.04623 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −9.54527 | −0.381811 | ||||||||
\(626\) | −23.2063 | −0.927511 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 2.04593 | 0.0816416 | ||||||||
\(629\) | 58.8279 | 2.34562 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −4.92394 | −0.196019 | −0.0980094 | − | 0.995185i | \(-0.531248\pi\) | ||||
−0.0980094 | + | 0.995185i | \(0.531248\pi\) | |||||||
\(632\) | 10.8407 | 0.431221 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 2.91617 | 0.115816 | ||||||||
\(635\) | −55.7491 | −2.21234 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −2.07683 | −0.0822226 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 8.08410 | 0.319552 | ||||||||
\(641\) | −29.8396 | −1.17859 | −0.589297 | − | 0.807917i | \(-0.700595\pi\) | ||||
−0.589297 | + | 0.807917i | \(0.700595\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −13.7885 | −0.543766 | −0.271883 | − | 0.962330i | \(-0.587646\pi\) | ||||
−0.271883 | + | 0.962330i | \(0.587646\pi\) | |||||||
\(644\) | 5.73557 | 0.226013 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −2.34109 | −0.0921091 | ||||||||
\(647\) | −41.4540 | −1.62972 | −0.814862 | − | 0.579654i | \(-0.803188\pi\) | ||||
−0.814862 | + | 0.579654i | \(0.803188\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 2.43104 | 0.0954267 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −4.27711 | −0.167505 | ||||||||
\(653\) | 39.5948 | 1.54946 | 0.774732 | − | 0.632290i | \(-0.217885\pi\) | ||||
0.774732 | + | 0.632290i | \(0.217885\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −9.78927 | −0.382498 | ||||||||
\(656\) | −15.6032 | −0.609202 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −17.7778 | −0.693050 | ||||||||
\(659\) | 24.7437 | 0.963876 | 0.481938 | − | 0.876205i | \(-0.339933\pi\) | ||||
0.481938 | + | 0.876205i | \(0.339933\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −21.2664 | −0.827165 | −0.413583 | − | 0.910467i | \(-0.635723\pi\) | ||||
−0.413583 | + | 0.910467i | \(0.635723\pi\) | |||||||
\(662\) | −1.13600 | −0.0441519 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 36.2529 | 1.40689 | ||||||||
\(665\) | 3.46357 | 0.134312 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.50557 | 0.0582958 | ||||||||
\(668\) | −2.62233 | −0.101461 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −40.8159 | −1.57686 | ||||||||
\(671\) | 15.1524 | 0.584950 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 12.7821 | 0.492713 | 0.246357 | − | 0.969179i | \(-0.420767\pi\) | ||||
0.246357 | + | 0.969179i | \(0.420767\pi\) | |||||||
\(674\) | −23.4405 | −0.902894 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −17.5915 | −0.676097 | −0.338048 | − | 0.941129i | \(-0.609767\pi\) | ||||
−0.338048 | + | 0.941129i | \(0.609767\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 8.59478 | 0.329837 | ||||||||
\(680\) | −74.2682 | −2.84805 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 33.8504 | 1.29620 | ||||||||
\(683\) | −27.2609 | −1.04311 | −0.521555 | − | 0.853218i | \(-0.674648\pi\) | ||||
−0.521555 | + | 0.853218i | \(0.674648\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 6.28786 | 0.240247 | ||||||||
\(686\) | −10.4858 | −0.400348 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 14.1129 | 0.538049 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −27.5851 | −1.04939 | −0.524693 | − | 0.851291i | \(-0.675820\pi\) | ||||
−0.524693 | + | 0.851291i | \(0.675820\pi\) | |||||||
\(692\) | 7.25637 | 0.275846 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −17.6055 | −0.668297 | ||||||||
\(695\) | 14.8849 | 0.564617 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 50.5096 | 1.91319 | ||||||||
\(698\) | 4.26117 | 0.161287 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 16.6303 | 0.628566 | ||||||||
\(701\) | 20.1813 | 0.762236 | 0.381118 | − | 0.924526i | \(-0.375539\pi\) | ||||
0.381118 | + | 0.924526i | \(0.375539\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 2.51620 | 0.0949004 | ||||||||
\(704\) | 25.3756 | 0.956379 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −14.9028 | −0.560873 | ||||||||
\(707\) | 49.6287 | 1.86648 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −36.9764 | −1.38868 | −0.694339 | − | 0.719648i | \(-0.744303\pi\) | ||||
−0.694339 | + | 0.719648i | \(0.744303\pi\) | |||||||
\(710\) | −40.3675 | −1.51497 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 23.9503 | 0.897577 | ||||||||
\(713\) | −24.5393 | −0.919004 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 7.02218 | 0.262431 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −28.8592 | −1.07702 | ||||||||
\(719\) | −2.87442 | −0.107198 | −0.0535990 | − | 0.998563i | \(-0.517069\pi\) | ||||
−0.0535990 | + | 0.998563i | \(0.517069\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −7.04221 | −0.262266 | ||||||||
\(722\) | 21.6296 | 0.804969 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 14.8388 | 0.551479 | ||||||||
\(725\) | 4.36539 | 0.162126 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 15.5459 | 0.576564 | 0.288282 | − | 0.957546i | \(-0.406916\pi\) | ||||
0.288282 | + | 0.957546i | \(0.406916\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −34.8582 | −1.29016 | ||||||||
\(731\) | −45.6853 | −1.68973 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −37.2723 | −1.37668 | −0.688342 | − | 0.725386i | \(-0.741661\pi\) | ||||
−0.688342 | + | 0.725386i | \(0.741661\pi\) | |||||||
\(734\) | −6.71756 | −0.247950 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −9.16852 | −0.337956 | ||||||||
\(737\) | −30.4792 | −1.12272 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 29.5652 | 1.08757 | 0.543787 | − | 0.839223i | \(-0.316990\pi\) | ||||
0.543787 | + | 0.839223i | \(0.316990\pi\) | |||||||
\(740\) | 20.5197 | 0.754319 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −36.0382 | −1.32300 | ||||||||
\(743\) | 5.28528 | 0.193898 | 0.0969490 | − | 0.995289i | \(-0.469092\pi\) | ||||
0.0969490 | + | 0.995289i | \(0.469092\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −76.6376 | −2.80778 | ||||||||
\(746\) | −13.0755 | −0.478729 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −14.2567 | −0.521275 | ||||||||
\(749\) | −22.3119 | −0.815258 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 11.7616 | 0.429188 | 0.214594 | − | 0.976703i | \(-0.431157\pi\) | ||||
0.214594 | + | 0.976703i | \(0.431157\pi\) | |||||||
\(752\) | 9.89593 | 0.360867 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 24.6973 | 0.898826 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −50.1226 | −1.82174 | −0.910868 | − | 0.412697i | \(-0.864587\pi\) | ||||
−0.910868 | + | 0.412697i | \(0.864587\pi\) | |||||||
\(758\) | 30.3957 | 1.10402 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −3.17662 | −0.115228 | ||||||||
\(761\) | 20.5473 | 0.744840 | 0.372420 | − | 0.928064i | \(-0.378528\pi\) | ||||
0.372420 | + | 0.928064i | \(0.378528\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 10.2755 | 0.371996 | ||||||||
\(764\) | 14.7841 | 0.534871 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 4.28562 | 0.154846 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 40.8745 | 1.47397 | 0.736987 | − | 0.675907i | \(-0.236248\pi\) | ||||
0.736987 | + | 0.675907i | \(0.236248\pi\) | |||||||
\(770\) | −39.8662 | −1.43668 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −1.54453 | −0.0555889 | ||||||||
\(773\) | 26.7857 | 0.963416 | 0.481708 | − | 0.876332i | \(-0.340017\pi\) | ||||
0.481708 | + | 0.876332i | \(0.340017\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −71.1517 | −2.55584 | ||||||||
\(776\) | −7.88271 | −0.282973 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −7.52483 | −0.269778 | ||||||||
\(779\) | 2.16041 | 0.0774048 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −30.1444 | −1.07865 | ||||||||
\(782\) | −19.5343 | −0.698545 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −9.12259 | −0.325807 | ||||||||
\(785\) | 10.3090 | 0.367945 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −31.3631 | −1.11797 | −0.558987 | − | 0.829176i | \(-0.688810\pi\) | ||||
−0.558987 | + | 0.829176i | \(0.688810\pi\) | |||||||
\(788\) | 1.73964 | 0.0619722 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 14.0419 | 0.499588 | ||||||||
\(791\) | 19.5343 | 0.694560 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | −12.8207 | −0.454989 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 8.00298 | 0.283658 | ||||||||
\(797\) | 18.4727 | 0.654336 | 0.327168 | − | 0.944966i | \(-0.393906\pi\) | ||||
0.327168 | + | 0.944966i | \(0.393906\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −32.0344 | −1.13330 | ||||||||
\(800\) | −26.5841 | −0.939890 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 23.8509 | 0.842203 | ||||||||
\(803\) | −26.0303 | −0.918588 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 28.9004 | 1.01860 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −45.5171 | −1.60128 | ||||||||
\(809\) | 37.1258 | 1.30527 | 0.652637 | − | 0.757671i | \(-0.273663\pi\) | ||||
0.652637 | + | 0.757671i | \(0.273663\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −5.15319 | −0.180953 | −0.0904766 | − | 0.995899i | \(-0.528839\pi\) | ||||
−0.0904766 | + | 0.995899i | \(0.528839\pi\) | |||||||
\(812\) | 1.41657 | 0.0497119 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −28.9618 | −1.01511 | ||||||||
\(815\) | −21.5515 | −0.754915 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −1.95407 | −0.0683641 | ||||||||
\(818\) | 41.7626 | 1.46019 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 17.6182 | 0.615254 | ||||||||
\(821\) | −14.4368 | −0.503849 | −0.251924 | − | 0.967747i | \(-0.581063\pi\) | ||||
−0.251924 | + | 0.967747i | \(0.581063\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 29.8568 | 1.04074 | 0.520372 | − | 0.853940i | \(-0.325793\pi\) | ||||
0.520372 | + | 0.853940i | \(0.325793\pi\) | |||||||
\(824\) | 6.45877 | 0.225002 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 3.13408 | 0.109049 | ||||||||
\(827\) | −43.5486 | −1.51433 | −0.757167 | − | 0.653222i | \(-0.773417\pi\) | ||||
−0.757167 | + | 0.653222i | \(0.773417\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −35.3327 | −1.22716 | −0.613578 | − | 0.789634i | \(-0.710270\pi\) | ||||
−0.613578 | + | 0.789634i | \(0.710270\pi\) | |||||||
\(830\) | 46.9581 | 1.62994 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 29.5310 | 1.02319 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −13.2134 | −0.457268 | ||||||||
\(836\) | −0.609790 | −0.0210900 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −11.4330 | −0.394945 | ||||||||
\(839\) | −36.6107 | −1.26394 | −0.631971 | − | 0.774992i | \(-0.717754\pi\) | ||||
−0.631971 | + | 0.774992i | \(0.717754\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.6282 | −0.987178 | ||||||||
\(842\) | −0.881173 | −0.0303672 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 13.7741 | 0.474122 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 7.15585 | 0.245878 | ||||||||
\(848\) | 20.0605 | 0.688881 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −56.6396 | −1.94272 | ||||||||
\(851\) | 20.9954 | 0.719714 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −8.47757 | −0.290266 | −0.145133 | − | 0.989412i | \(-0.546361\pi\) | ||||
−0.145133 | + | 0.989412i | \(0.546361\pi\) | |||||||
\(854\) | 19.5343 | 0.668450 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 20.4634 | 0.699423 | ||||||||
\(857\) | 15.0555 | 0.514286 | 0.257143 | − | 0.966373i | \(-0.417219\pi\) | ||||
0.257143 | + | 0.966373i | \(0.417219\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −53.1952 | −1.81500 | −0.907498 | − | 0.420056i | \(-0.862011\pi\) | ||||
−0.907498 | + | 0.420056i | \(0.862011\pi\) | |||||||
\(860\) | −15.9355 | −0.543394 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 34.6346 | 1.17966 | ||||||||
\(863\) | −42.7433 | −1.45500 | −0.727500 | − | 0.686107i | \(-0.759318\pi\) | ||||
−0.727500 | + | 0.686107i | \(0.759318\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 36.5633 | 1.24319 | ||||||||
\(866\) | 32.1042 | 1.09095 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −23.0887 | −0.783683 | ||||||||
\(869\) | 10.4858 | 0.355705 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | −9.42415 | −0.319142 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −0.835527 | −0.0282621 | ||||||||
\(875\) | 25.2699 | 0.854278 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 15.7767 | 0.532742 | 0.266371 | − | 0.963871i | \(-0.414175\pi\) | ||||
0.266371 | + | 0.963871i | \(0.414175\pi\) | |||||||
\(878\) | 23.0274 | 0.777137 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 22.1914 | 0.748071 | ||||||||
\(881\) | −7.46072 | −0.251358 | −0.125679 | − | 0.992071i | \(-0.540111\pi\) | ||||
−0.125679 | + | 0.992071i | \(0.540111\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −2.54586 | −0.0856750 | −0.0428375 | − | 0.999082i | \(-0.513640\pi\) | ||||
−0.0428375 | + | 0.999082i | \(0.513640\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −36.4252 | −1.22373 | ||||||||
\(887\) | −3.48422 | −0.116988 | −0.0584942 | − | 0.998288i | \(-0.518630\pi\) | ||||
−0.0584942 | + | 0.998288i | \(0.518630\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −53.6698 | −1.80003 | ||||||||
\(890\) | 31.0227 | 1.03988 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 12.5579 | 0.420471 | ||||||||
\(893\) | −1.37019 | −0.0458515 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 35.3833 | 1.18273 | ||||||||
\(896\) | 7.78258 | 0.259998 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 3.97212 | 0.132551 | ||||||||
\(899\) | −6.06071 | −0.202136 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −64.9385 | −2.16342 | ||||||||
\(902\) | −24.8666 | −0.827968 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −17.9159 | −0.595874 | ||||||||
\(905\) | 74.7695 | 2.48542 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 40.4209 | 1.34215 | 0.671077 | − | 0.741388i | \(-0.265832\pi\) | ||||
0.671077 | + | 0.741388i | \(0.265832\pi\) | |||||||
\(908\) | 8.01335 | 0.265932 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 48.5763 | 1.60941 | 0.804703 | − | 0.593678i | \(-0.202325\pi\) | ||||
0.804703 | + | 0.593678i | \(0.202325\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 35.0659 | 1.16051 | ||||||||
\(914\) | 24.1339 | 0.798277 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −8.20775 | −0.271192 | ||||||||
\(917\) | −9.42415 | −0.311213 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −35.6937 | −1.17743 | −0.588713 | − | 0.808342i | \(-0.700365\pi\) | ||||
−0.588713 | + | 0.808342i | \(0.700365\pi\) | |||||||
\(920\) | −26.5060 | −0.873877 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 8.22787 | 0.270970 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 60.8762 | 2.00160 | ||||||||
\(926\) | 37.9234 | 1.24624 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −2.26444 | −0.0743338 | ||||||||
\(929\) | −22.5411 | −0.739550 | −0.369775 | − | 0.929121i | \(-0.620565\pi\) | ||||
−0.369775 | + | 0.929121i | \(0.620565\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1.26311 | 0.0413968 | ||||||||
\(932\) | 13.3097 | 0.435974 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −24.7433 | −0.809627 | ||||||||
\(935\) | −71.8364 | −2.34930 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −32.0344 | −1.04652 | −0.523260 | − | 0.852173i | \(-0.675284\pi\) | ||||
−0.523260 | + | 0.852173i | \(0.675284\pi\) | |||||||
\(938\) | −39.2936 | −1.28298 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −11.1739 | −0.364452 | ||||||||
\(941\) | −45.6156 | −1.48703 | −0.743513 | − | 0.668722i | \(-0.766842\pi\) | ||||
−0.743513 | + | 0.668722i | \(0.766842\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 18.0267 | 0.587029 | ||||||||
\(944\) | −1.74457 | −0.0567810 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 22.4916 | 0.731264 | ||||||||
\(947\) | −39.7494 | −1.29168 | −0.645840 | − | 0.763473i | \(-0.723493\pi\) | ||||
−0.645840 | + | 0.763473i | \(0.723493\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | −2.42261 | −0.0785998 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −71.4981 | −2.31727 | ||||||||
\(953\) | 14.3621 | 0.465235 | 0.232617 | − | 0.972568i | \(-0.425271\pi\) | ||||
0.232617 | + | 0.972568i | \(0.425271\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 74.4941 | 2.41057 | ||||||||
\(956\) | 0.938637 | 0.0303577 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −35.4561 | −1.14553 | ||||||||
\(959\) | 6.05334 | 0.195473 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 67.7837 | 2.18657 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 6.67324 | 0.214930 | ||||||||
\(965\) | −7.78258 | −0.250530 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 33.2261 | 1.06848 | 0.534239 | − | 0.845333i | \(-0.320598\pi\) | ||||
0.534239 | + | 0.845333i | \(0.320598\pi\) | |||||||
\(968\) | −6.56300 | −0.210943 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −10.2104 | −0.327836 | ||||||||
\(971\) | 25.0522 | 0.803965 | 0.401982 | − | 0.915647i | \(-0.368321\pi\) | ||||
0.401982 | + | 0.915647i | \(0.368321\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 14.3297 | 0.459391 | ||||||||
\(974\) | −31.2768 | −1.00217 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −10.8737 | −0.348058 | ||||||||
\(977\) | −55.6599 | −1.78072 | −0.890359 | − | 0.455259i | \(-0.849547\pi\) | ||||
−0.890359 | + | 0.455259i | \(0.849547\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 23.1661 | 0.740393 | ||||||||
\(980\) | 10.3007 | 0.329043 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −17.1570 | −0.547503 | ||||||||
\(983\) | 28.2878 | 0.902240 | 0.451120 | − | 0.892463i | \(-0.351025\pi\) | ||||
0.451120 | + | 0.892463i | \(0.351025\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 8.76569 | 0.279298 | ||||||||
\(986\) | −4.82457 | −0.153646 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −16.3049 | −0.518466 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 41.0863 | 1.30515 | 0.652575 | − | 0.757724i | \(-0.273689\pi\) | ||||
0.652575 | + | 0.757724i | \(0.273689\pi\) | |||||||
\(992\) | 36.9082 | 1.17184 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −38.8619 | −1.23262 | ||||||||
\(995\) | 40.3254 | 1.27840 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 45.7663 | 1.44943 | 0.724716 | − | 0.689047i | \(-0.241971\pi\) | ||||
0.724716 | + | 0.689047i | \(0.241971\pi\) | |||||||
\(998\) | 6.70033 | 0.212095 | ||||||||
\(999\) | 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 | 1521.2.a.v.1.3 | ✓ | 6 | |
3.2 | odd | 2 | inner | 1521.2.a.v.1.4 | yes | 6 | |
13.5 | odd | 4 | 1521.2.b.n.1351.7 | 12 | |||
13.8 | odd | 4 | 1521.2.b.n.1351.6 | 12 | |||
13.12 | even | 2 | 1521.2.a.w.1.4 | yes | 6 | ||
39.5 | even | 4 | 1521.2.b.n.1351.5 | 12 | |||
39.8 | even | 4 | 1521.2.b.n.1351.8 | 12 | |||
39.38 | odd | 2 | 1521.2.a.w.1.3 | yes | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1521.2.a.v.1.3 | ✓ | 6 | 1.1 | even | 1 | trivial | |
1521.2.a.v.1.4 | yes | 6 | 3.2 | odd | 2 | inner | |
1521.2.a.w.1.3 | yes | 6 | 39.38 | odd | 2 | ||
1521.2.a.w.1.4 | yes | 6 | 13.12 | even | 2 | ||
1521.2.b.n.1351.5 | 12 | 39.5 | even | 4 | |||
1521.2.b.n.1351.6 | 12 | 13.8 | odd | 4 | |||
1521.2.b.n.1351.7 | 12 | 13.5 | odd | 4 | |||
1521.2.b.n.1351.8 | 12 | 39.8 | even | 4 |