Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8036,2,Mod(1,8036)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8036, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8036.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8036 = 2^{2} \cdot 7^{2} \cdot 41 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8036.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: | \(64.1677830643\) |
Analytic rank: | \(1\) |
Dimension: | \(20\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} - 4 x^{19} - 30 x^{18} + 128 x^{17} + 348 x^{16} - 1644 x^{15} - 1934 x^{14} + 10948 x^{13} + \cdots + 9 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{3} \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.18 | ||
Root | \(-2.32542\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8036.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 2.32542 | 1.34258 | 0.671292 | − | 0.741193i | \(-0.265740\pi\) | ||||
0.671292 | + | 0.741193i | \(0.265740\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.16439 | −0.520730 | −0.260365 | − | 0.965510i | \(-0.583843\pi\) | ||||
−0.260365 | + | 0.965510i | \(0.583843\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 2.40759 | 0.802531 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.577754 | 0.174199 | 0.0870997 | − | 0.996200i | \(-0.472240\pi\) | ||||
0.0870997 | + | 0.996200i | \(0.472240\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.18295 | −0.605442 | −0.302721 | − | 0.953079i | \(-0.597895\pi\) | ||||
−0.302721 | + | 0.953079i | \(0.597895\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −2.70769 | −0.699123 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −6.65536 | −1.61416 | −0.807081 | − | 0.590441i | \(-0.798954\pi\) | ||||
−0.807081 | + | 0.590441i | \(0.798954\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.12850 | 0.488312 | 0.244156 | − | 0.969736i | \(-0.421489\pi\) | ||||
0.244156 | + | 0.969736i | \(0.421489\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 8.32156 | 1.73516 | 0.867582 | − | 0.497294i | \(-0.165673\pi\) | ||||
0.867582 | + | 0.497294i | \(0.165673\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3.64420 | −0.728840 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.37760 | −0.265119 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −6.30024 | −1.16993 | −0.584963 | − | 0.811060i | \(-0.698891\pi\) | ||||
−0.584963 | + | 0.811060i | \(0.698891\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.38664 | 0.249047 | 0.124524 | − | 0.992217i | \(-0.460260\pi\) | ||||
0.124524 | + | 0.992217i | \(0.460260\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 1.34352 | 0.233877 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.86577 | 0.471130 | 0.235565 | − | 0.971859i | \(-0.424306\pi\) | ||||
0.235565 | + | 0.971859i | \(0.424306\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −5.07629 | −0.812856 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.00000 | 0.156174 | ||||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 6.21582 | 0.947904 | 0.473952 | − | 0.880551i | \(-0.342827\pi\) | ||||
0.473952 | + | 0.880551i | \(0.342827\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −2.80337 | −0.417902 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −12.3492 | −1.80132 | −0.900658 | − | 0.434528i | \(-0.856915\pi\) | ||||
−0.900658 | + | 0.434528i | \(0.856915\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −15.4765 | −2.16715 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 13.0449 | 1.79185 | 0.895925 | − | 0.444204i | \(-0.146514\pi\) | ||||
0.895925 | + | 0.444204i | \(0.146514\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −0.672730 | −0.0907109 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 4.94967 | 0.655600 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 3.27380 | 0.426213 | 0.213106 | − | 0.977029i | \(-0.431642\pi\) | ||||
0.213106 | + | 0.977029i | \(0.431642\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −5.15551 | −0.660095 | −0.330048 | − | 0.943964i | \(-0.607065\pi\) | ||||
−0.330048 | + | 0.943964i | \(0.607065\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 2.54180 | 0.315272 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −5.35143 | −0.653781 | −0.326890 | − | 0.945062i | \(-0.606001\pi\) | ||||
−0.326890 | + | 0.945062i | \(0.606001\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 19.3511 | 2.32960 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −14.3919 | −1.70801 | −0.854004 | − | 0.520267i | \(-0.825833\pi\) | ||||
−0.854004 | + | 0.520267i | \(0.825833\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −8.30995 | −0.972606 | −0.486303 | − | 0.873790i | \(-0.661655\pi\) | ||||
−0.486303 | + | 0.873790i | \(0.661655\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −8.47431 | −0.978529 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −14.6782 | −1.65143 | −0.825716 | − | 0.564086i | \(-0.809229\pi\) | ||||
−0.825716 | + | 0.564086i | \(0.809229\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −10.4263 | −1.15848 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 11.7691 | 1.29182 | 0.645911 | − | 0.763413i | \(-0.276478\pi\) | ||||
0.645911 | + | 0.763413i | \(0.276478\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 7.74941 | 0.840542 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −14.6507 | −1.57072 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −6.56350 | −0.695730 | −0.347865 | − | 0.937545i | \(-0.613093\pi\) | ||||
−0.347865 | + | 0.937545i | \(0.613093\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 3.22452 | 0.334367 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −2.47840 | −0.254279 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 2.09480 | 0.212695 | 0.106347 | − | 0.994329i | \(-0.466084\pi\) | ||||
0.106347 | + | 0.994329i | \(0.466084\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1.39100 | 0.139800 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −4.73209 | −0.470861 | −0.235430 | − | 0.971891i | \(-0.575650\pi\) | ||||
−0.235430 | + | 0.971891i | \(0.575650\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −15.6314 | −1.54021 | −0.770106 | − | 0.637916i | \(-0.779796\pi\) | ||||
−0.770106 | + | 0.637916i | \(0.779796\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −4.34990 | −0.420520 | −0.210260 | − | 0.977645i | \(-0.567431\pi\) | ||||
−0.210260 | + | 0.977645i | \(0.567431\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 14.7394 | 1.41178 | 0.705890 | − | 0.708321i | \(-0.250547\pi\) | ||||
0.705890 | + | 0.708321i | \(0.250547\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 6.66413 | 0.632531 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −1.29851 | −0.122153 | −0.0610766 | − | 0.998133i | \(-0.519453\pi\) | ||||
−0.0610766 | + | 0.998133i | \(0.519453\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −9.68951 | −0.903552 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −5.25566 | −0.485886 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.6662 | −0.969655 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 2.32542 | 0.209676 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 10.0652 | 0.900259 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −16.6554 | −1.47793 | −0.738964 | − | 0.673745i | \(-0.764685\pi\) | ||||
−0.738964 | + | 0.673745i | \(0.764685\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 14.4544 | 1.27264 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −18.9750 | −1.65785 | −0.828926 | − | 0.559359i | \(-0.811047\pi\) | ||||
−0.828926 | + | 0.559359i | \(0.811047\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 1.60406 | 0.138055 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −3.44151 | −0.294028 | −0.147014 | − | 0.989134i | \(-0.546966\pi\) | ||||
−0.147014 | + | 0.989134i | \(0.546966\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 4.88501 | 0.414341 | 0.207171 | − | 0.978305i | \(-0.433574\pi\) | ||||
0.207171 | + | 0.978305i | \(0.433574\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −28.7171 | −2.41842 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −1.26121 | −0.105468 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 7.33592 | 0.609215 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 22.0258 | 1.80442 | 0.902210 | − | 0.431297i | \(-0.141944\pi\) | ||||
0.902210 | + | 0.431297i | \(0.141944\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −9.59867 | −0.781128 | −0.390564 | − | 0.920576i | \(-0.627720\pi\) | ||||
−0.390564 | + | 0.920576i | \(0.627720\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −16.0234 | −1.29541 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −1.61458 | −0.129686 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −2.53129 | −0.202019 | −0.101010 | − | 0.994885i | \(-0.532207\pi\) | ||||
−0.101010 | + | 0.994885i | \(0.532207\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 30.3348 | 2.40571 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −18.9641 | −1.48539 | −0.742693 | − | 0.669632i | \(-0.766452\pi\) | ||||
−0.742693 | + | 0.669632i | \(0.766452\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −1.56438 | −0.121787 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 1.39051 | 0.107601 | 0.0538004 | − | 0.998552i | \(-0.482867\pi\) | ||||
0.0538004 | + | 0.998552i | \(0.482867\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −8.23472 | −0.633440 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 5.12457 | 0.391885 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −20.1903 | −1.53504 | −0.767518 | − | 0.641027i | \(-0.778509\pi\) | ||||
−0.767518 | + | 0.641027i | \(0.778509\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 7.61298 | 0.572226 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 0.927522 | 0.0693262 | 0.0346631 | − | 0.999399i | \(-0.488964\pi\) | ||||
0.0346631 | + | 0.999399i | \(0.488964\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 3.28822 | 0.244412 | 0.122206 | − | 0.992505i | \(-0.461003\pi\) | ||||
0.122206 | + | 0.992505i | \(0.461003\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −11.9887 | −0.886233 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −3.33687 | −0.245331 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −3.84516 | −0.281186 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −14.1671 | −1.02509 | −0.512547 | − | 0.858659i | \(-0.671298\pi\) | ||||
−0.512547 | + | 0.858659i | \(0.671298\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −20.1435 | −1.44996 | −0.724982 | − | 0.688768i | \(-0.758152\pi\) | ||||
−0.724982 | + | 0.688768i | \(0.758152\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 5.91076 | 0.423279 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 26.5834 | 1.89399 | 0.946996 | − | 0.321246i | \(-0.104102\pi\) | ||||
0.946996 | + | 0.321246i | \(0.104102\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 14.9769 | 1.06168 | 0.530841 | − | 0.847471i | \(-0.321876\pi\) | ||||
0.530841 | + | 0.847471i | \(0.321876\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −12.4443 | −0.877755 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1.16439 | −0.0813243 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 20.0349 | 1.39252 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 1.22975 | 0.0850637 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 8.62894 | 0.594041 | 0.297020 | − | 0.954871i | \(-0.404007\pi\) | ||||
0.297020 | + | 0.954871i | \(0.404007\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −33.4673 | −2.29314 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −7.23762 | −0.493602 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −19.3242 | −1.30581 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 14.5283 | 0.977281 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1.53527 | 0.102809 | 0.0514045 | − | 0.998678i | \(-0.483630\pi\) | ||||
0.0514045 | + | 0.998678i | \(0.483630\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −8.77375 | −0.584917 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −20.1904 | −1.34008 | −0.670042 | − | 0.742323i | \(-0.733724\pi\) | ||||
−0.670042 | + | 0.742323i | \(0.733724\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 5.96534 | 0.394201 | 0.197100 | − | 0.980383i | \(-0.436847\pi\) | ||||
0.197100 | + | 0.980383i | \(0.436847\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −0.959514 | −0.0628599 | −0.0314299 | − | 0.999506i | \(-0.510006\pi\) | ||||
−0.0314299 | + | 0.999506i | \(0.510006\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 14.3793 | 0.937999 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −34.1331 | −2.21719 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 6.77258 | 0.438082 | 0.219041 | − | 0.975716i | \(-0.429707\pi\) | ||||
0.219041 | + | 0.975716i | \(0.429707\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −17.7945 | −1.14625 | −0.573123 | − | 0.819469i | \(-0.694268\pi\) | ||||
−0.573123 | + | 0.819469i | \(0.694268\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −20.1127 | −1.29023 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −4.64642 | −0.295644 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 27.3680 | 1.73438 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 21.5340 | 1.35922 | 0.679608 | − | 0.733575i | \(-0.262150\pi\) | ||||
0.679608 | + | 0.733575i | \(0.262150\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 4.80781 | 0.302265 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 18.0207 | 1.12850 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 22.1592 | 1.38225 | 0.691127 | − | 0.722733i | \(-0.257115\pi\) | ||||
0.691127 | + | 0.722733i | \(0.257115\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −15.1684 | −0.938901 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 17.7048 | 1.09173 | 0.545863 | − | 0.837874i | \(-0.316202\pi\) | ||||
0.545863 | + | 0.837874i | \(0.316202\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −15.1893 | −0.933070 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −15.2629 | −0.934075 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −18.4884 | −1.12726 | −0.563628 | − | 0.826029i | \(-0.690595\pi\) | ||||
−0.563628 | + | 0.826029i | \(0.690595\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 14.1700 | 0.860765 | 0.430383 | − | 0.902647i | \(-0.358379\pi\) | ||||
0.430383 | + | 0.902647i | \(0.358379\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −2.10545 | −0.126964 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 15.7359 | 0.945481 | 0.472740 | − | 0.881202i | \(-0.343265\pi\) | ||||
0.472740 | + | 0.881202i | \(0.343265\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 3.33846 | 0.199868 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 26.1380 | 1.55926 | 0.779632 | − | 0.626237i | \(-0.215406\pi\) | ||||
0.779632 | + | 0.626237i | \(0.215406\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 15.2769 | 0.908119 | 0.454059 | − | 0.890971i | \(-0.349975\pi\) | ||||
0.454059 | + | 0.890971i | \(0.349975\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −5.76333 | −0.341390 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 27.2938 | 1.60552 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 4.87130 | 0.285561 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −8.49926 | −0.496532 | −0.248266 | − | 0.968692i | \(-0.579861\pi\) | ||||
−0.248266 | + | 0.968692i | \(0.579861\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −3.81197 | −0.221942 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −0.795913 | −0.0461836 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −18.1656 | −1.05054 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −11.0041 | −0.632170 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 6.00301 | 0.343731 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 9.03457 | 0.515630 | 0.257815 | − | 0.966194i | \(-0.416998\pi\) | ||||
0.257815 | + | 0.966194i | \(0.416998\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −36.3497 | −2.06786 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 24.0195 | 1.36202 | 0.681010 | − | 0.732274i | \(-0.261541\pi\) | ||||
0.681010 | + | 0.732274i | \(0.261541\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −25.9450 | −1.46650 | −0.733249 | − | 0.679960i | \(-0.761997\pi\) | ||||
−0.733249 | + | 0.679960i | \(0.761997\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −31.0716 | −1.74515 | −0.872576 | − | 0.488478i | \(-0.837552\pi\) | ||||
−0.872576 | + | 0.488478i | \(0.837552\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −3.63999 | −0.203800 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −10.1153 | −0.564584 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −14.1659 | −0.788214 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 7.95512 | 0.441270 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 34.2754 | 1.89543 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1.05839 | 0.0581746 | 0.0290873 | − | 0.999577i | \(-0.490740\pi\) | ||||
0.0290873 | + | 0.999577i | \(0.490740\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 6.89961 | 0.378096 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 6.23113 | 0.340443 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 22.0487 | 1.20107 | 0.600536 | − | 0.799598i | \(-0.294954\pi\) | ||||
0.600536 | + | 0.799598i | \(0.294954\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −3.01958 | −0.164001 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0.801135 | 0.0433839 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −22.5322 | −1.21309 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −17.4946 | −0.939161 | −0.469581 | − | 0.882890i | \(-0.655595\pi\) | ||||
−0.469581 | + | 0.882890i | \(0.655595\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 9.53548 | 0.510423 | 0.255211 | − | 0.966885i | \(-0.417855\pi\) | ||||
0.255211 | + | 0.966885i | \(0.417855\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 3.00723 | 0.160514 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −5.45842 | −0.290522 | −0.145261 | − | 0.989393i | \(-0.546402\pi\) | ||||
−0.145261 | + | 0.989393i | \(0.546402\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 16.7578 | 0.889411 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 28.2188 | 1.48933 | 0.744665 | − | 0.667439i | \(-0.232609\pi\) | ||||
0.744665 | + | 0.667439i | \(0.232609\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −14.4695 | −0.761551 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −24.8034 | −1.30184 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 9.67600 | 0.506465 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −12.6548 | −0.660578 | −0.330289 | − | 0.943880i | \(-0.607146\pi\) | ||||
−0.330289 | + | 0.943880i | \(0.607146\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 2.40759 | 0.125334 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 16.0610 | 0.831605 | 0.415803 | − | 0.909455i | \(-0.363501\pi\) | ||||
0.415803 | + | 0.909455i | \(0.363501\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 23.4058 | 1.20867 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 13.7531 | 0.708322 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −3.85863 | −0.198205 | −0.0991023 | − | 0.995077i | \(-0.531597\pi\) | ||||
−0.0991023 | + | 0.995077i | \(0.531597\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −38.7308 | −1.98424 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −9.73227 | −0.497296 | −0.248648 | − | 0.968594i | \(-0.579986\pi\) | ||||
−0.248648 | + | 0.968594i | \(0.579986\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 14.9652 | 0.760722 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 4.65923 | 0.236232 | 0.118116 | − | 0.993000i | \(-0.462315\pi\) | ||||
0.118116 | + | 0.993000i | \(0.462315\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −55.3829 | −2.80084 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −44.1248 | −2.22580 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 17.0912 | 0.859950 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −23.7699 | −1.19298 | −0.596489 | − | 0.802622i | \(-0.703438\pi\) | ||||
−0.596489 | + | 0.802622i | \(0.703438\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −16.1934 | −0.808658 | −0.404329 | − | 0.914614i | \(-0.632495\pi\) | ||||
−0.404329 | + | 0.914614i | \(0.632495\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −3.02696 | −0.150784 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 12.1402 | 0.603253 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 1.65571 | 0.0820706 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −27.8628 | −1.37773 | −0.688863 | − | 0.724891i | \(-0.741890\pi\) | ||||
−0.688863 | + | 0.724891i | \(0.741890\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −8.00297 | −0.394758 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −13.7037 | −0.672690 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 11.3597 | 0.556288 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −16.5549 | −0.808759 | −0.404380 | − | 0.914591i | \(-0.632513\pi\) | ||||
−0.404380 | + | 0.914591i | \(0.632513\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −14.7753 | −0.720104 | −0.360052 | − | 0.932932i | \(-0.617241\pi\) | ||||
−0.360052 | + | 0.932932i | \(0.617241\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −29.7319 | −1.44561 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 24.2535 | 1.17647 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −2.93285 | −0.141599 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −11.4352 | −0.550815 | −0.275407 | − | 0.961328i | \(-0.588813\pi\) | ||||
−0.275407 | + | 0.961328i | \(0.588813\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −0.174657 | −0.00839348 | −0.00419674 | − | 0.999991i | \(-0.501336\pi\) | ||||
−0.00419674 | + | 0.999991i | \(0.501336\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 17.0591 | 0.817922 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 17.7125 | 0.847302 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −8.45595 | −0.403580 | −0.201790 | − | 0.979429i | \(-0.564676\pi\) | ||||
−0.201790 | + | 0.979429i | \(0.564676\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 2.89323 | 0.137461 | 0.0687307 | − | 0.997635i | \(-0.478105\pi\) | ||||
0.0687307 | + | 0.997635i | \(0.478105\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 7.64246 | 0.362287 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 51.2192 | 2.42258 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −8.62766 | −0.407164 | −0.203582 | − | 0.979058i | \(-0.565258\pi\) | ||||
−0.203582 | + | 0.979058i | \(0.565258\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0.577754 | 0.0272054 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −22.3210 | −1.04873 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 25.3212 | 1.18448 | 0.592238 | − | 0.805763i | \(-0.298245\pi\) | ||||
0.592238 | + | 0.805763i | \(0.298245\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 9.16841 | 0.427945 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 13.1693 | 0.613354 | 0.306677 | − | 0.951814i | \(-0.400783\pi\) | ||||
0.306677 | + | 0.951814i | \(0.400783\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 21.7893 | 1.01264 | 0.506318 | − | 0.862347i | \(-0.331006\pi\) | ||||
0.506318 | + | 0.862347i | \(0.331006\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −3.75459 | −0.174115 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −28.9339 | −1.33890 | −0.669451 | − | 0.742856i | \(-0.733471\pi\) | ||||
−0.669451 | + | 0.742856i | \(0.733471\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −5.88633 | −0.271228 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 3.59122 | 0.165124 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −7.75669 | −0.355902 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 31.4067 | 1.43802 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −7.12399 | −0.325503 | −0.162752 | − | 0.986667i | \(-0.552037\pi\) | ||||
−0.162752 | + | 0.986667i | \(0.552037\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −6.25584 | −0.285242 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −2.43916 | −0.110757 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 33.1983 | 1.50436 | 0.752179 | − | 0.658959i | \(-0.229003\pi\) | ||||
0.752179 | + | 0.658959i | \(0.229003\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −44.0997 | −1.99426 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −0.0506885 | −0.00228754 | −0.00114377 | − | 0.999999i | \(-0.500364\pi\) | ||||
−0.00114377 | + | 0.999999i | \(0.500364\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 41.9303 | 1.88845 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −1.61966 | −0.0727983 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −27.6020 | −1.23563 | −0.617817 | − | 0.786322i | \(-0.711983\pi\) | ||||
−0.617817 | + | 0.786322i | \(0.711983\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 3.23352 | 0.144463 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −31.7270 | −1.41464 | −0.707318 | − | 0.706895i | \(-0.750095\pi\) | ||||
−0.707318 | + | 0.706895i | \(0.750095\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 5.50999 | 0.245191 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −19.1492 | −0.850446 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 5.24465 | 0.232465 | 0.116233 | − | 0.993222i | \(-0.462918\pi\) | ||||
0.116233 | + | 0.993222i | \(0.462918\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −2.93222 | −0.129461 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 18.2010 | 0.802034 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −7.13481 | −0.313788 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −46.9509 | −2.06092 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 7.11443 | 0.311689 | 0.155844 | − | 0.987782i | \(-0.450190\pi\) | ||||
0.155844 | + | 0.987782i | \(0.450190\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 7.45011 | 0.325770 | 0.162885 | − | 0.986645i | \(-0.447920\pi\) | ||||
0.162885 | + | 0.986645i | \(0.447920\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −9.22856 | −0.402003 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 46.2483 | 2.01080 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 7.88198 | 0.342049 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −2.18295 | −0.0945541 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 5.06496 | 0.218977 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 2.15688 | 0.0930762 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −2.23267 | −0.0959899 | −0.0479949 | − | 0.998848i | \(-0.515283\pi\) | ||||
−0.0479949 | + | 0.998848i | \(0.515283\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 7.64651 | 0.328143 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −17.1624 | −0.735156 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 20.7822 | 0.888582 | 0.444291 | − | 0.895882i | \(-0.353456\pi\) | ||||
0.444291 | + | 0.895882i | \(0.353456\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −12.4124 | −0.529747 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −13.4101 | −0.571288 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −7.75963 | −0.329378 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −0.0133890 | −0.000567310 0 | −0.000283655 | − | 1.00000i | \(-0.500090\pi\) | ||||
−0.000283655 | 1.00000i | \(0.500090\pi\) | ||||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −13.5688 | −0.573901 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −8.94163 | −0.377516 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 17.7441 | 0.747824 | 0.373912 | − | 0.927464i | \(-0.378016\pi\) | ||||
0.373912 | + | 0.927464i | \(0.378016\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 1.51196 | 0.0636088 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 34.4381 | 1.44372 | 0.721859 | − | 0.692040i | \(-0.243288\pi\) | ||||
0.721859 | + | 0.692040i | \(0.243288\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −26.8148 | −1.12216 | −0.561081 | − | 0.827761i | \(-0.689615\pi\) | ||||
−0.561081 | + | 0.827761i | \(0.689615\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −32.9444 | −1.37627 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −30.3254 | −1.26466 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 2.11828 | 0.0881853 | 0.0440926 | − | 0.999027i | \(-0.485960\pi\) | ||||
0.0440926 | + | 0.999027i | \(0.485960\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −46.8422 | −1.94670 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 7.53673 | 0.312140 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 6.11962 | 0.253015 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −32.6369 | −1.34707 | −0.673534 | − | 0.739156i | \(-0.735225\pi\) | ||||
−0.673534 | + | 0.739156i | \(0.735225\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 2.95146 | 0.121613 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 61.8177 | 2.54284 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 10.8698 | 0.446371 | 0.223186 | − | 0.974776i | \(-0.428354\pi\) | ||||
0.223186 | + | 0.974776i | \(0.428354\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 34.8276 | 1.42540 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 13.0873 | 0.534731 | 0.267366 | − | 0.963595i | \(-0.413847\pi\) | ||||
0.267366 | + | 0.963595i | \(0.413847\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 6.48319 | 0.264455 | 0.132227 | − | 0.991219i | \(-0.457787\pi\) | ||||
0.132227 | + | 0.991219i | \(0.457787\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −12.8841 | −0.524679 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 12.4196 | 0.504928 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −29.4411 | −1.19498 | −0.597488 | − | 0.801878i | \(-0.703834\pi\) | ||||
−0.597488 | + | 0.801878i | \(0.703834\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 26.9577 | 1.09059 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −0.185150 | −0.00747814 | −0.00373907 | − | 0.999993i | \(-0.501190\pi\) | ||||
−0.00373907 | + | 0.999993i | \(0.501190\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −2.70769 | −0.109185 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −37.6266 | −1.51479 | −0.757395 | − | 0.652957i | \(-0.773528\pi\) | ||||
−0.757395 | + | 0.652957i | \(0.773528\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −34.9704 | −1.40558 | −0.702790 | − | 0.711397i | \(-0.748063\pi\) | ||||
−0.702790 | + | 0.711397i | \(0.748063\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −11.4638 | −0.460025 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 6.50122 | 0.260049 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 2.85969 | 0.114205 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −19.0727 | −0.760480 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 39.4821 | 1.57176 | 0.785878 | − | 0.618381i | \(-0.212211\pi\) | ||||
0.785878 | + | 0.618381i | \(0.212211\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 20.0659 | 0.797550 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 19.3933 | 0.769601 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −34.6499 | −1.37073 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 26.1071 | 1.03117 | 0.515583 | − | 0.856839i | \(-0.327575\pi\) | ||||
0.515583 | + | 0.856839i | \(0.327575\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −13.0439 | −0.514403 | −0.257201 | − | 0.966358i | \(-0.582800\pi\) | ||||
−0.257201 | + | 0.966358i | \(0.582800\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −16.8305 | −0.662702 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −25.3524 | −0.996704 | −0.498352 | − | 0.866975i | \(-0.666061\pi\) | ||||
−0.498352 | + | 0.866975i | \(0.666061\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1.89145 | 0.0742461 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 32.7755 | 1.28260 | 0.641301 | − | 0.767289i | \(-0.278395\pi\) | ||||
0.641301 | + | 0.767289i | \(0.278395\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 22.0942 | 0.863293 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −20.0070 | −0.780546 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 18.6120 | 0.725019 | 0.362509 | − | 0.931980i | \(-0.381920\pi\) | ||||
0.362509 | + | 0.931980i | \(0.381920\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 21.6989 | 0.843991 | 0.421995 | − | 0.906598i | \(-0.361330\pi\) | ||||
0.421995 | + | 0.906598i | \(0.361330\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 33.7845 | 1.31208 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −52.4278 | −2.03001 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 3.57014 | 0.138030 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −2.97862 | −0.114988 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −4.48404 | −0.172847 | −0.0864235 | − | 0.996258i | \(-0.527544\pi\) | ||||
−0.0864235 | + | 0.996258i | \(0.527544\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 5.02024 | 0.193229 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 24.7715 | 0.952047 | 0.476023 | − | 0.879433i | \(-0.342078\pi\) | ||||
0.476023 | + | 0.879433i | \(0.342078\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −46.9512 | −1.79917 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 34.2572 | 1.31082 | 0.655408 | − | 0.755275i | \(-0.272497\pi\) | ||||
0.655408 | + | 0.755275i | \(0.272497\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 4.00725 | 0.153109 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 13.8719 | 0.529248 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −28.4763 | −1.08486 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −50.4922 | −1.92081 | −0.960407 | − | 0.278600i | \(-0.910130\pi\) | ||||
−0.960407 | + | 0.278600i | \(0.910130\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −5.68804 | −0.215760 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −6.65536 | −0.252090 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −2.23128 | −0.0843946 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 35.6345 | 1.34590 | 0.672948 | − | 0.739690i | \(-0.265028\pi\) | ||||
0.672948 | + | 0.739690i | \(0.265028\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 6.09980 | 0.230058 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 33.4379 | 1.25934 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 4.63467 | 0.174059 | 0.0870294 | − | 0.996206i | \(-0.472263\pi\) | ||||
0.0870294 | + | 0.996206i | \(0.472263\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −35.3392 | −1.32533 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 11.5390 | 0.432138 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1.46854 | 0.0549202 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 15.7491 | 0.588161 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 38.0114 | 1.41759 | 0.708794 | − | 0.705416i | \(-0.249240\pi\) | ||||
0.708794 | + | 0.705416i | \(0.249240\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −41.3798 | −1.53893 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 22.9593 | 0.852689 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 8.03179 | 0.297882 | 0.148941 | − | 0.988846i | \(-0.452413\pi\) | ||||
0.148941 | + | 0.988846i | \(0.452413\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −15.4917 | −0.573768 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −41.3685 | −1.53007 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 17.0042 | 0.628063 | 0.314032 | − | 0.949413i | \(-0.398320\pi\) | ||||
0.314032 | + | 0.949413i | \(0.398320\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −3.09181 | −0.113888 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 50.4482 | 1.85577 | 0.927883 | − | 0.372871i | \(-0.121626\pi\) | ||||
0.927883 | + | 0.372871i | \(0.121626\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −10.8049 | −0.396927 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 49.1625 | 1.80360 | 0.901799 | − | 0.432156i | \(-0.142247\pi\) | ||||
0.901799 | + | 0.432156i | \(0.142247\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −25.6465 | −0.939615 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 28.3351 | 1.03673 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −0.812005 | −0.0296305 | −0.0148152 | − | 0.999890i | \(-0.504716\pi\) | ||||
−0.0148152 | + | 0.999890i | \(0.504716\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 50.0758 | 1.82486 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 11.1766 | 0.406757 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −6.57037 | −0.238804 | −0.119402 | − | 0.992846i | \(-0.538098\pi\) | ||||
−0.119402 | + | 0.992846i | \(0.538098\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 11.1802 | 0.405816 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −20.4663 | −0.741904 | −0.370952 | − | 0.928652i | \(-0.620969\pi\) | ||||
−0.370952 | + | 0.928652i | \(0.620969\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 18.6574 | 0.674561 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −7.14655 | −0.258047 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 12.6132 | 0.454844 | 0.227422 | − | 0.973796i | \(-0.426970\pi\) | ||||
0.227422 | + | 0.973796i | \(0.426970\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 51.5295 | 1.85579 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 46.2197 | 1.66241 | 0.831203 | − | 0.555969i | \(-0.187653\pi\) | ||||
0.831203 | + | 0.555969i | \(0.187653\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −5.05318 | −0.181516 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 2.12850 | 0.0762615 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −8.31500 | −0.297534 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 8.67920 | 0.310169 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 2.94741 | 0.105197 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 42.1247 | 1.50158 | 0.750791 | − | 0.660539i | \(-0.229672\pi\) | ||||
0.750791 | + | 0.660539i | \(0.229672\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 41.1712 | 1.46573 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 11.2542 | 0.399649 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −35.3215 | −1.25272 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 20.2562 | 0.717510 | 0.358755 | − | 0.933432i | \(-0.383201\pi\) | ||||
0.358755 | + | 0.933432i | \(0.383201\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 82.1884 | 2.90762 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −15.8022 | −0.558344 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −4.80111 | −0.169427 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −42.9933 | −1.51344 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −43.4001 | −1.52587 | −0.762934 | − | 0.646477i | \(-0.776242\pi\) | ||||
−0.762934 | + | 0.646477i | \(0.776242\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 3.14538 | 0.110449 | 0.0552246 | − | 0.998474i | \(-0.482413\pi\) | ||||
0.0552246 | + | 0.998474i | \(0.482413\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 32.9512 | 1.15565 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 22.0816 | 0.773485 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 13.2304 | 0.462873 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 39.9800 | 1.39531 | 0.697656 | − | 0.716432i | \(-0.254226\pi\) | ||||
0.697656 | + | 0.716432i | \(0.254226\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −38.4780 | −1.34126 | −0.670630 | − | 0.741792i | \(-0.733976\pi\) | ||||
−0.670630 | + | 0.741792i | \(0.733976\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −4.89607 | −0.170459 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 23.8196 | 0.828289 | 0.414145 | − | 0.910211i | \(-0.364081\pi\) | ||||
0.414145 | + | 0.910211i | \(0.364081\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −25.5478 | −0.887311 | −0.443655 | − | 0.896197i | \(-0.646319\pi\) | ||||
−0.443655 | + | 0.896197i | \(0.646319\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 36.5927 | 1.26939 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −1.61909 | −0.0560310 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −1.91023 | −0.0660271 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 35.2200 | 1.21593 | 0.607966 | − | 0.793963i | \(-0.291986\pi\) | ||||
0.607966 | + | 0.793963i | \(0.291986\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 10.6930 | 0.368725 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 60.7820 | 2.09344 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 9.58841 | 0.329851 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 35.5253 | 1.21923 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 23.8477 | 0.817488 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 23.5636 | 0.806803 | 0.403401 | − | 0.915023i | \(-0.367828\pi\) | ||||
0.403401 | + | 0.915023i | \(0.367828\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −5.96698 | −0.204066 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 13.1481 | 0.449131 | 0.224565 | − | 0.974459i | \(-0.427904\pi\) | ||||
0.224565 | + | 0.974459i | \(0.427904\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −41.6355 | −1.42058 | −0.710292 | − | 0.703907i | \(-0.751437\pi\) | ||||
−0.710292 | + | 0.703907i | \(0.751437\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −36.6615 | −1.24797 | −0.623986 | − | 0.781435i | \(-0.714488\pi\) | ||||
−0.623986 | + | 0.781435i | \(0.714488\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 23.5093 | 0.799339 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 63.4696 | 2.15554 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −8.48042 | −0.287679 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 11.6819 | 0.395826 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 5.04343 | 0.170694 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 23.3610 | 0.788844 | 0.394422 | − | 0.918929i | \(-0.370945\pi\) | ||||
0.394422 | + | 0.918929i | \(0.370945\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −19.7644 | −0.666636 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −34.3795 | −1.15827 | −0.579137 | − | 0.815230i | \(-0.696611\pi\) | ||||
−0.579137 | + | 0.815230i | \(0.696611\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 6.66499 | 0.224295 | 0.112147 | − | 0.993692i | \(-0.464227\pi\) | ||||
0.112147 | + | 0.993692i | \(0.464227\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −8.86445 | −0.297975 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −12.1283 | −0.407229 | −0.203615 | − | 0.979051i | \(-0.565269\pi\) | ||||
−0.203615 | + | 0.979051i | \(0.565269\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −6.02383 | −0.201806 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −26.2853 | −0.879604 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −1.07999 | −0.0361002 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −42.2426 | −1.41044 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −8.73614 | −0.291367 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −86.8183 | −2.89234 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −3.82876 | −0.127272 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 8.69194 | 0.288611 | 0.144306 | − | 0.989533i | \(-0.453905\pi\) | ||||
0.144306 | + | 0.989533i | \(0.453905\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −11.3929 | −0.377880 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −10.6870 | −0.354076 | −0.177038 | − | 0.984204i | \(-0.556652\pi\) | ||||
−0.177038 | + | 0.984204i | \(0.556652\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 6.79963 | 0.225035 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 13.9595 | 0.461488 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 37.0944 | 1.22363 | 0.611815 | − | 0.791001i | \(-0.290440\pi\) | ||||
0.611815 | + | 0.791001i | \(0.290440\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 21.0092 | 0.692276 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 31.4169 | 1.03410 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −10.4435 | −0.343379 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −37.6341 | −1.23607 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 13.7333 | 0.450574 | 0.225287 | − | 0.974292i | \(-0.427668\pi\) | ||||
0.225287 | + | 0.974292i | \(0.427668\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 55.8555 | 1.82863 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 4.47726 | 0.146422 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 14.5987 | 0.476920 | 0.238460 | − | 0.971152i | \(-0.423357\pi\) | ||||
0.238460 | + | 0.971152i | \(0.423357\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −60.3331 | −1.96890 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 10.5934 | 0.345334 | 0.172667 | − | 0.984980i | \(-0.444762\pi\) | ||||
0.172667 | + | 0.984980i | \(0.444762\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 8.32156 | 0.270987 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 8.15610 | 0.265038 | 0.132519 | − | 0.991180i | \(-0.457693\pi\) | ||||
0.132519 | + | 0.991180i | \(0.457693\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 18.1402 | 0.588856 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −72.2545 | −2.34301 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −58.9994 | −1.91118 | −0.955589 | − | 0.294703i | \(-0.904779\pi\) | ||||
−0.955589 | + | 0.294703i | \(0.904779\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 16.4960 | 0.533797 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −8.46452 | −0.273619 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −29.0772 | −0.937975 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −10.4728 | −0.337480 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 23.4549 | 0.755039 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −22.9767 | −0.738880 | −0.369440 | − | 0.929255i | \(-0.620450\pi\) | ||||
−0.369440 | + | 0.929255i | \(0.620450\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −32.9418 | −1.05824 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 53.3603 | 1.71241 | 0.856206 | − | 0.516634i | \(-0.172815\pi\) | ||||
0.856206 | + | 0.516634i | \(0.172815\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 18.4990 | 0.592443 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 14.6210 | 0.467769 | 0.233884 | − | 0.972264i | \(-0.424856\pi\) | ||||
0.233884 | + | 0.972264i | \(0.424856\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −3.79209 | −0.121196 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 35.4865 | 1.13300 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −21.9944 | −0.701512 | −0.350756 | − | 0.936467i | \(-0.614075\pi\) | ||||
−0.350756 | + | 0.936467i | \(0.614075\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −30.9534 | −0.986258 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 51.7253 | 1.64477 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −28.0746 | −0.891820 | −0.445910 | − | 0.895078i | \(-0.647120\pi\) | ||||
−0.445910 | + | 0.895078i | \(0.647120\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 2.46122 | 0.0781043 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −17.4389 | −0.552850 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −28.3418 | −0.897593 | −0.448797 | − | 0.893634i | \(-0.648147\pi\) | ||||
−0.448797 | + | 0.893634i | \(0.648147\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −3.94788 | −0.124905 |
(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 | 8036.2.a.s.1.18 | ✓ | 20 | |
7.6 | odd | 2 | 8036.2.a.t.1.3 | yes | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8036.2.a.s.1.18 | ✓ | 20 | 1.1 | even | 1 | trivial | |
8036.2.a.t.1.3 | yes | 20 | 7.6 | odd | 2 |