Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3856,2,Mod(1,3856)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3856, 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("3856.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3856 = 2^{4} \cdot 241 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3856.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: | \(30.7903150194\) |
Analytic rank: | \(0\) |
Dimension: | \(7\) |
Coefficient field: | 7.7.31056073.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{7} - 3x^{6} - 3x^{5} + 11x^{4} + x^{3} - 9x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 241) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(-0.911223\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3856.1 |
$q$-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 | ||||||||
\(3\) | 0.186202 | 0.107504 | 0.0537520 | − | 0.998554i | \(-0.482882\pi\) | ||||
0.0537520 | + | 0.998554i | \(0.482882\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −2.25110 | −1.00672 | −0.503361 | − | 0.864076i | \(-0.667903\pi\) | ||||
−0.503361 | + | 0.864076i | \(0.667903\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −3.52970 | −1.33410 | −0.667050 | − | 0.745013i | \(-0.732443\pi\) | ||||
−0.667050 | + | 0.745013i | \(0.732443\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.96533 | −0.988443 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.515564 | −0.155448 | −0.0777242 | − | 0.996975i | \(-0.524765\pi\) | ||||
−0.0777242 | + | 0.996975i | \(0.524765\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −5.38098 | −1.49242 | −0.746208 | − | 0.665712i | \(-0.768128\pi\) | ||||
−0.746208 | + | 0.665712i | \(0.768128\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −0.419160 | −0.108227 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −4.16566 | −1.01032 | −0.505161 | − | 0.863025i | \(-0.668567\pi\) | ||||
−0.505161 | + | 0.863025i | \(0.668567\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −4.92935 | −1.13087 | −0.565436 | − | 0.824792i | \(-0.691292\pi\) | ||||
−0.565436 | + | 0.824792i | \(0.691292\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.657237 | −0.143421 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 7.69193 | 1.60388 | 0.801940 | − | 0.597405i | \(-0.203802\pi\) | ||||
0.801940 | + | 0.597405i | \(0.203802\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0.0674429 | 0.0134886 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.11076 | −0.213765 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −8.93755 | −1.65966 | −0.829831 | − | 0.558015i | \(-0.811563\pi\) | ||||
−0.829831 | + | 0.558015i | \(0.811563\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.43182 | 0.795978 | 0.397989 | − | 0.917390i | \(-0.369708\pi\) | ||||
0.397989 | + | 0.917390i | \(0.369708\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −0.0959992 | −0.0167113 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 7.94569 | 1.34307 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 5.99816 | 0.986091 | 0.493046 | − | 0.870003i | \(-0.335884\pi\) | ||||
0.493046 | + | 0.870003i | \(0.335884\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −1.00195 | −0.160441 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −8.99946 | −1.40548 | −0.702740 | − | 0.711447i | \(-0.748040\pi\) | ||||
−0.702740 | + | 0.711447i | \(0.748040\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.66336 | 0.253660 | 0.126830 | − | 0.991924i | \(-0.459520\pi\) | ||||
0.126830 | + | 0.991924i | \(0.459520\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 6.67525 | 0.995087 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −8.55484 | −1.24785 | −0.623926 | − | 0.781483i | \(-0.714463\pi\) | ||||
−0.623926 | + | 0.781483i | \(0.714463\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 5.45876 | 0.779823 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −0.775656 | −0.108614 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 13.1736 | 1.80954 | 0.904769 | − | 0.425903i | \(-0.140043\pi\) | ||||
0.904769 | + | 0.425903i | \(0.140043\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.16059 | 0.156493 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −0.917857 | −0.121573 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −9.25521 | −1.20493 | −0.602463 | − | 0.798147i | \(-0.705814\pi\) | ||||
−0.602463 | + | 0.798147i | \(0.705814\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −10.4203 | −1.33418 | −0.667090 | − | 0.744978i | \(-0.732460\pi\) | ||||
−0.667090 | + | 0.744978i | \(0.732460\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 10.4667 | 1.31868 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 12.1131 | 1.50245 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 3.91715 | 0.478555 | 0.239278 | − | 0.970951i | \(-0.423089\pi\) | ||||
0.239278 | + | 0.970951i | \(0.423089\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 1.43226 | 0.172423 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 13.6724 | 1.62262 | 0.811308 | − | 0.584619i | \(-0.198756\pi\) | ||||
0.811308 | + | 0.584619i | \(0.198756\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 11.5529 | 1.35217 | 0.676083 | − | 0.736825i | \(-0.263676\pi\) | ||||
0.676083 | + | 0.736825i | \(0.263676\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0.0125580 | 0.00145007 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1.81979 | 0.207384 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1.43448 | 0.161391 | 0.0806956 | − | 0.996739i | \(-0.474286\pi\) | ||||
0.0806956 | + | 0.996739i | \(0.474286\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 8.68916 | 0.965462 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −1.73047 | −0.189944 | −0.0949720 | − | 0.995480i | \(-0.530276\pi\) | ||||
−0.0949720 | + | 0.995480i | \(0.530276\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 9.37732 | 1.01711 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −1.66419 | −0.178420 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −1.07999 | −0.114478 | −0.0572392 | − | 0.998360i | \(-0.518230\pi\) | ||||
−0.0572392 | + | 0.998360i | \(0.518230\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 18.9932 | 1.99103 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0.825214 | 0.0855707 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 11.0965 | 1.13847 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −16.0883 | −1.63352 | −0.816759 | − | 0.576979i | \(-0.804231\pi\) | ||||
−0.816759 | + | 0.576979i | \(0.804231\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1.52882 | 0.153652 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1.23922 | −0.123307 | −0.0616536 | − | 0.998098i | \(-0.519637\pi\) | ||||
−0.0616536 | + | 0.998098i | \(0.519637\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −5.27633 | −0.519892 | −0.259946 | − | 0.965623i | \(-0.583705\pi\) | ||||
−0.259946 | + | 0.965623i | \(0.583705\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 1.47951 | 0.144385 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −10.7822 | −1.04236 | −0.521178 | − | 0.853448i | \(-0.674507\pi\) | ||||
−0.521178 | + | 0.853448i | \(0.674507\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1.15255 | −0.110394 | −0.0551972 | − | 0.998475i | \(-0.517579\pi\) | ||||
−0.0551972 | + | 0.998475i | \(0.517579\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 1.11687 | 0.106009 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −8.70999 | −0.819367 | −0.409684 | − | 0.912228i | \(-0.634361\pi\) | ||||
−0.409684 | + | 0.912228i | \(0.634361\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −17.3153 | −1.61466 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 15.9564 | 1.47517 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 14.7035 | 1.34787 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.7342 | −0.975836 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −1.67572 | −0.151095 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 11.1037 | 0.993142 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 8.22063 | 0.729463 | 0.364732 | − | 0.931113i | \(-0.381161\pi\) | ||||
0.364732 | + | 0.931113i | \(0.381161\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0.309722 | 0.0272695 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 7.30323 | 0.638086 | 0.319043 | − | 0.947740i | \(-0.396638\pi\) | ||||
0.319043 | + | 0.947740i | \(0.396638\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 17.3991 | 1.50870 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 2.50042 | 0.215202 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 5.95317 | 0.508614 | 0.254307 | − | 0.967124i | \(-0.418153\pi\) | ||||
0.254307 | + | 0.967124i | \(0.418153\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −14.9650 | −1.26931 | −0.634656 | − | 0.772795i | \(-0.718858\pi\) | ||||
−0.634656 | + | 0.772795i | \(0.718858\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −1.59293 | −0.134149 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 2.77424 | 0.231994 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 20.1193 | 1.67082 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 1.01643 | 0.0838340 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −0.130576 | −0.0106972 | −0.00534860 | − | 0.999986i | \(-0.501703\pi\) | ||||
−0.00534860 | + | 0.999986i | \(0.501703\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −0.276102 | −0.0224688 | −0.0112344 | − | 0.999937i | \(-0.503576\pi\) | ||||
−0.0112344 | + | 0.999937i | \(0.503576\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 12.3526 | 0.998645 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −9.97646 | −0.801328 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 16.1044 | 1.28527 | 0.642636 | − | 0.766172i | \(-0.277841\pi\) | ||||
0.642636 | + | 0.766172i | \(0.277841\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 2.45296 | 0.194532 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −27.1502 | −2.13973 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 18.5215 | 1.45071 | 0.725357 | − | 0.688373i | \(-0.241675\pi\) | ||||
0.725357 | + | 0.688373i | \(0.241675\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0.216104 | 0.0168236 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −15.5017 | −1.19956 | −0.599779 | − | 0.800166i | \(-0.704745\pi\) | ||||
−0.599779 | + | 0.800166i | \(0.704745\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 15.9550 | 1.22731 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 14.6172 | 1.11780 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −0.366438 | −0.0278597 | −0.0139299 | − | 0.999903i | \(-0.504434\pi\) | ||||
−0.0139299 | + | 0.999903i | \(0.504434\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −0.238053 | −0.0179951 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −1.72334 | −0.129534 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −12.8719 | −0.962090 | −0.481045 | − | 0.876696i | \(-0.659743\pi\) | ||||
−0.481045 | + | 0.876696i | \(0.659743\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −12.2125 | −0.907746 | −0.453873 | − | 0.891066i | \(-0.649958\pi\) | ||||
−0.453873 | + | 0.891066i | \(0.649958\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −1.94028 | −0.143429 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −13.5024 | −0.992719 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 2.14767 | 0.157053 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 3.92064 | 0.285184 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 3.92400 | 0.283930 | 0.141965 | − | 0.989872i | \(-0.454658\pi\) | ||||
0.141965 | + | 0.989872i | \(0.454658\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1.69319 | −0.121879 | −0.0609393 | − | 0.998141i | \(-0.519410\pi\) | ||||
−0.0609393 | + | 0.998141i | \(0.519410\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 2.25549 | 0.161519 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −2.20382 | −0.157016 | −0.0785080 | − | 0.996913i | \(-0.525016\pi\) | ||||
−0.0785080 | + | 0.996913i | \(0.525016\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 15.5533 | 1.10255 | 0.551274 | − | 0.834324i | \(-0.314142\pi\) | ||||
0.551274 | + | 0.834324i | \(0.314142\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0.729381 | 0.0514466 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 31.5468 | 2.21415 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 20.2587 | 1.41493 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −22.8091 | −1.58534 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 2.54140 | 0.175792 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −6.55996 | −0.451606 | −0.225803 | − | 0.974173i | \(-0.572501\pi\) | ||||
−0.225803 | + | 0.974173i | \(0.572501\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 2.54583 | 0.174438 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −3.74439 | −0.255365 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −15.6430 | −1.06191 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 2.15118 | 0.145363 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 22.4154 | 1.50782 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −6.53800 | −0.437817 | −0.218908 | − | 0.975745i | \(-0.570250\pi\) | ||||
−0.218908 | + | 0.975745i | \(0.570250\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −0.199990 | −0.0133327 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −16.1673 | −1.07306 | −0.536530 | − | 0.843881i | \(-0.680265\pi\) | ||||
−0.536530 | + | 0.843881i | \(0.680265\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 0.0208412 | 0.00137722 | 0.000688612 | − | 1.00000i | \(-0.499781\pi\) | ||||
0.000688612 | 1.00000i | \(0.499781\pi\) | ||||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0.338848 | 0.0222946 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −0.651845 | −0.0427038 | −0.0213519 | − | 0.999772i | \(-0.506797\pi\) | ||||
−0.0213519 | + | 0.999772i | \(0.506797\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 19.2578 | 1.25624 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0.267103 | 0.0173502 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 8.99997 | 0.582160 | 0.291080 | − | 0.956699i | \(-0.405985\pi\) | ||||
0.291080 | + | 0.956699i | \(0.405985\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1.00000 | −0.0644157 | ||||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 4.95021 | 0.317556 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −12.2882 | −0.785064 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 26.5248 | 1.68773 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −0.322218 | −0.0204197 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −16.4986 | −1.04138 | −0.520691 | − | 0.853745i | \(-0.674326\pi\) | ||||
−0.520691 | + | 0.853745i | \(0.674326\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −3.96569 | −0.249321 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 1.74608 | 0.109344 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 7.99029 | 0.498420 | 0.249210 | − | 0.968449i | \(-0.419829\pi\) | ||||
0.249210 | + | 0.968449i | \(0.419829\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −21.1717 | −1.31554 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 26.5028 | 1.64048 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 5.47488 | 0.337595 | 0.168798 | − | 0.985651i | \(-0.446012\pi\) | ||||
0.168798 | + | 0.985651i | \(0.446012\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −29.6551 | −1.82170 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −0.201096 | −0.0123069 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −2.34697 | −0.143097 | −0.0715486 | − | 0.997437i | \(-0.522794\pi\) | ||||
−0.0715486 | + | 0.997437i | \(0.522794\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1.60301 | −0.0973758 | −0.0486879 | − | 0.998814i | \(-0.515504\pi\) | ||||
−0.0486879 | + | 0.998814i | \(0.515504\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 3.53658 | 0.214044 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −0.0347711 | −0.00209678 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −21.6775 | −1.30247 | −0.651237 | − | 0.758875i | \(-0.725750\pi\) | ||||
−0.651237 | + | 0.758875i | \(0.725750\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −13.1418 | −0.786779 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 26.9010 | 1.60478 | 0.802388 | − | 0.596802i | \(-0.203562\pi\) | ||||
0.802388 | + | 0.596802i | \(0.203562\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −3.89230 | −0.231373 | −0.115687 | − | 0.993286i | \(-0.536907\pi\) | ||||
−0.115687 | + | 0.993286i | \(0.536907\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 2.06619 | 0.122390 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 31.7654 | 1.87505 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 0.352752 | 0.0207501 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −2.99567 | −0.175610 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −5.57389 | −0.325630 | −0.162815 | − | 0.986657i | \(-0.552057\pi\) | ||||
−0.162815 | + | 0.986657i | \(0.552057\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 20.8344 | 1.21302 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0.572667 | 0.0332295 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −41.3902 | −2.39366 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −5.87116 | −0.338408 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −0.230746 | −0.0132560 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 23.4571 | 1.34315 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −23.0795 | −1.31722 | −0.658608 | − | 0.752486i | \(-0.728854\pi\) | ||||
−0.658608 | + | 0.752486i | \(0.728854\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −0.982465 | −0.0558905 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 14.9884 | 0.849916 | 0.424958 | − | 0.905213i | \(-0.360289\pi\) | ||||
0.424958 | + | 0.905213i | \(0.360289\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −2.31082 | −0.130615 | −0.0653076 | − | 0.997865i | \(-0.520803\pi\) | ||||
−0.0653076 | + | 0.997865i | \(0.520803\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −23.5616 | −1.32755 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −18.3630 | −1.03137 | −0.515684 | − | 0.856779i | \(-0.672462\pi\) | ||||
−0.515684 | + | 0.856779i | \(0.672462\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 4.60788 | 0.257992 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −2.00767 | −0.112057 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 20.5340 | 1.14254 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −0.362909 | −0.0201306 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −0.214608 | −0.0118678 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 30.1960 | 1.66476 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 6.47933 | 0.356136 | 0.178068 | − | 0.984018i | \(-0.443015\pi\) | ||||
0.178068 | + | 0.984018i | \(0.443015\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −17.7865 | −0.974695 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −8.81788 | −0.481772 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −3.54257 | −0.192976 | −0.0964880 | − | 0.995334i | \(-0.530761\pi\) | ||||
−0.0964880 | + | 0.995334i | \(0.530761\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −1.62182 | −0.0880852 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −2.28489 | −0.123734 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 5.44011 | 0.293739 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −3.22415 | −0.173582 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 14.4844 | 0.777566 | 0.388783 | − | 0.921329i | \(-0.372896\pi\) | ||||
0.388783 | + | 0.921329i | \(0.372896\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −23.6287 | −1.26482 | −0.632408 | − | 0.774636i | \(-0.717933\pi\) | ||||
−0.632408 | + | 0.774636i | \(0.717933\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 5.97697 | 0.319027 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −18.2662 | −0.972209 | −0.486105 | − | 0.873901i | \(-0.661583\pi\) | ||||
−0.486105 | + | 0.873901i | \(0.661583\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −30.7779 | −1.63352 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 2.73783 | 0.144901 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 20.3758 | 1.07539 | 0.537697 | − | 0.843138i | \(-0.319294\pi\) | ||||
0.537697 | + | 0.843138i | \(0.319294\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 5.29852 | 0.278870 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −1.99873 | −0.104906 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −26.0067 | −1.36125 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 1.76412 | 0.0920862 | 0.0460431 | − | 0.998939i | \(-0.485339\pi\) | ||||
0.0460431 | + | 0.998939i | \(0.485339\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 26.6864 | 1.38924 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −46.4989 | −2.41410 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −32.1736 | −1.66589 | −0.832943 | − | 0.553359i | \(-0.813346\pi\) | ||||
−0.832943 | + | 0.553359i | \(0.813346\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 2.06753 | 0.106767 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 48.0928 | 2.47691 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 31.3680 | 1.61126 | 0.805632 | − | 0.592416i | \(-0.201826\pi\) | ||||
0.805632 | + | 0.592416i | \(0.201826\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1.53070 | 0.0784201 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −16.8623 | −0.861624 | −0.430812 | − | 0.902442i | \(-0.641773\pi\) | ||||
−0.430812 | + | 0.902442i | \(0.641773\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −4.09651 | −0.208778 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −4.93242 | −0.250729 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −0.816001 | −0.0413729 | −0.0206864 | − | 0.999786i | \(-0.506585\pi\) | ||||
−0.0206864 | + | 0.999786i | \(0.506585\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −32.0420 | −1.62043 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 1.35988 | 0.0685968 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −3.22915 | −0.162476 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −21.8279 | −1.09551 | −0.547755 | − | 0.836639i | \(-0.684517\pi\) | ||||
−0.547755 | + | 0.836639i | \(0.684517\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 3.23976 | 0.162191 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −15.4857 | −0.773321 | −0.386661 | − | 0.922222i | \(-0.626372\pi\) | ||||
−0.386661 | + | 0.922222i | \(0.626372\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −23.8475 | −1.18793 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −19.5602 | −0.971952 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −3.09244 | −0.153286 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 26.0377 | 1.28748 | 0.643740 | − | 0.765245i | \(-0.277382\pi\) | ||||
0.643740 | + | 0.765245i | \(0.277382\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 1.10849 | 0.0546780 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 32.6681 | 1.60749 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 3.89546 | 0.191221 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −2.78651 | −0.136456 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 33.2204 | 1.62292 | 0.811462 | − | 0.584406i | \(-0.198672\pi\) | ||||
0.811462 | + | 0.584406i | \(0.198672\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 2.90586 | 0.141623 | 0.0708115 | − | 0.997490i | \(-0.477441\pi\) | ||||
0.0708115 | + | 0.997490i | \(0.477441\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 25.3679 | 1.23343 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −0.280944 | −0.0136278 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 36.7804 | 1.77993 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0.516570 | 0.0249402 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 28.4892 | 1.37228 | 0.686139 | − | 0.727471i | \(-0.259304\pi\) | ||||
0.686139 | + | 0.727471i | \(0.259304\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −28.9311 | −1.39034 | −0.695169 | − | 0.718846i | \(-0.744671\pi\) | ||||
−0.695169 | + | 0.718846i | \(0.744671\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 3.74626 | 0.179619 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −37.9163 | −1.81378 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 8.92156 | 0.425803 | 0.212901 | − | 0.977074i | \(-0.431709\pi\) | ||||
0.212901 | + | 0.977074i | \(0.431709\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −16.1870 | −0.770810 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −24.8216 | −1.17931 | −0.589656 | − | 0.807655i | \(-0.700736\pi\) | ||||
−0.589656 | + | 0.807655i | \(0.700736\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 2.43116 | 0.115248 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −0.0243136 | −0.00114999 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 11.9254 | 0.562793 | 0.281397 | − | 0.959592i | \(-0.409202\pi\) | ||||
0.281397 | + | 0.959592i | \(0.409202\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 4.63980 | 0.218480 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −0.0514107 | −0.00241549 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −42.7557 | −2.00442 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 8.44205 | 0.394902 | 0.197451 | − | 0.980313i | \(-0.436734\pi\) | ||||
0.197451 | + | 0.980313i | \(0.436734\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 4.62704 | 0.215972 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 23.2925 | 1.08484 | 0.542419 | − | 0.840108i | \(-0.317509\pi\) | ||||
0.542419 | + | 0.840108i | \(0.317509\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −1.66578 | −0.0774152 | −0.0387076 | − | 0.999251i | \(-0.512324\pi\) | ||||
−0.0387076 | + | 0.999251i | \(0.512324\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −1.85764 | −0.0861459 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 6.66428 | 0.308386 | 0.154193 | − | 0.988041i | \(-0.450722\pi\) | ||||
0.154193 | + | 0.988041i | \(0.450722\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −13.8263 | −0.638441 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 2.99868 | 0.138172 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −0.857570 | −0.0394311 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −0.332450 | −0.0152538 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −39.0642 | −1.78863 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 13.6902 | 0.625523 | 0.312762 | − | 0.949832i | \(-0.398746\pi\) | ||||
0.312762 | + | 0.949832i | \(0.398746\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −32.2760 | −1.47166 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −5.05543 | −0.230030 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 36.2163 | 1.64450 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −31.9634 | −1.44840 | −0.724200 | − | 0.689590i | \(-0.757791\pi\) | ||||
−0.724200 | + | 0.689590i | \(0.757791\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 3.44874 | 0.155957 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 10.0550 | 0.453777 | 0.226889 | − | 0.973921i | \(-0.427145\pi\) | ||||
0.226889 | + | 0.973921i | \(0.427145\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 37.2308 | 1.67679 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −3.44152 | −0.154685 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −48.2594 | −2.16473 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −9.14295 | −0.409295 | −0.204647 | − | 0.978836i | \(-0.565605\pi\) | ||||
−0.204647 | + | 0.978836i | \(0.565605\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −2.88645 | −0.128957 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 27.2050 | 1.21301 | 0.606506 | − | 0.795079i | \(-0.292571\pi\) | ||||
0.606506 | + | 0.795079i | \(0.292571\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 2.78961 | 0.124136 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 2.97086 | 0.131940 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 7.79598 | 0.345551 | 0.172775 | − | 0.984961i | \(-0.444726\pi\) | ||||
0.172775 | + | 0.984961i | \(0.444726\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −40.7783 | −1.80392 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 5.47532 | 0.241741 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 11.8775 | 0.523387 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 4.41057 | 0.193977 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −0.0682315 | −0.00299503 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 32.6959 | 1.43243 | 0.716216 | − | 0.697878i | \(-0.245872\pi\) | ||||
0.716216 | + | 0.697878i | \(0.245872\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 7.80136 | 0.341129 | 0.170565 | − | 0.985346i | \(-0.445441\pi\) | ||||
0.170565 | + | 0.985346i | \(0.445441\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −0.0443260 | −0.00193454 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −18.4615 | −0.804194 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 36.1658 | 1.57243 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 27.4447 | 1.19100 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 48.4260 | 2.09756 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 24.2718 | 1.04936 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −2.39677 | −0.103428 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −2.81434 | −0.121222 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 22.3971 | 0.962926 | 0.481463 | − | 0.876467i | \(-0.340106\pi\) | ||||
0.481463 | + | 0.876467i | \(0.340106\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −2.27399 | −0.0975863 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 2.59451 | 0.111136 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −37.2322 | −1.59193 | −0.795966 | − | 0.605341i | \(-0.793037\pi\) | ||||
−0.795966 | + | 0.605341i | \(0.793037\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 30.8995 | 1.31876 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 44.0563 | 1.87686 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −5.06326 | −0.215312 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −2.51419 | −0.106721 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −27.6457 | −1.17139 | −0.585693 | − | 0.810533i | \(-0.699177\pi\) | ||||
−0.585693 | + | 0.810533i | \(0.699177\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −8.95053 | −0.378567 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0.399900 | 0.0168838 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 23.3454 | 0.983891 | 0.491945 | − | 0.870626i | \(-0.336286\pi\) | ||||
0.491945 | + | 0.870626i | \(0.336286\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 19.6070 | 0.824875 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −30.6701 | −1.28802 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 2.61346 | 0.109562 | 0.0547811 | − | 0.998498i | \(-0.482554\pi\) | ||||
0.0547811 | + | 0.998498i | \(0.482554\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −16.9259 | −0.708326 | −0.354163 | − | 0.935184i | \(-0.615234\pi\) | ||||
−0.354163 | + | 0.935184i | \(0.615234\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0.730657 | 0.0305236 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0.518766 | 0.0216340 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 4.67534 | 0.194637 | 0.0973185 | − | 0.995253i | \(-0.468973\pi\) | ||||
0.0973185 | + | 0.995253i | \(0.468973\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −0.315276 | −0.0131024 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 6.10804 | 0.253404 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −6.79185 | −0.281290 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −35.9194 | −1.48508 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 3.78940 | 0.156405 | 0.0782027 | − | 0.996937i | \(-0.475082\pi\) | ||||
0.0782027 | + | 0.996937i | \(0.475082\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −21.8460 | −0.900148 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −0.410357 | −0.0168798 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −6.81434 | −0.279831 | −0.139916 | − | 0.990163i | \(-0.544683\pi\) | ||||
−0.139916 | + | 0.990163i | \(0.544683\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −33.0991 | −1.35693 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 2.89607 | 0.118528 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 39.7739 | 1.62512 | 0.812559 | − | 0.582879i | \(-0.198074\pi\) | ||||
0.812559 | + | 0.582879i | \(0.198074\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 27.4256 | 1.11871 | 0.559356 | − | 0.828927i | \(-0.311048\pi\) | ||||
0.559356 | + | 0.828927i | \(0.311048\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −11.6156 | −0.473025 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 24.1637 | 0.982395 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −20.6168 | −0.836811 | −0.418405 | − | 0.908260i | \(-0.637411\pi\) | ||||
−0.418405 | + | 0.908260i | \(0.637411\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 5.87409 | 0.238030 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 46.0335 | 1.86232 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −12.9127 | −0.521540 | −0.260770 | − | 0.965401i | \(-0.583976\pi\) | ||||
−0.260770 | + | 0.965401i | \(0.583976\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 3.77221 | 0.152110 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 26.3856 | 1.06225 | 0.531123 | − | 0.847295i | \(-0.321770\pi\) | ||||
0.531123 | + | 0.847295i | \(0.321770\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 2.30850 | 0.0927866 | 0.0463933 | − | 0.998923i | \(-0.485227\pi\) | ||||
0.0463933 | + | 0.998923i | \(0.485227\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −8.54387 | −0.342854 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 3.81203 | 0.152726 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −25.3327 | −1.01331 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0.473214 | 0.0188983 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −24.9863 | −0.996270 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 8.60820 | 0.342687 | 0.171343 | − | 0.985211i | \(-0.445189\pi\) | ||||
0.171343 | + | 0.985211i | \(0.445189\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −1.22148 | −0.0485494 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −18.5054 | −0.734366 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −29.3735 | −1.16382 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −40.5432 | −1.60386 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −11.7479 | −0.464014 | −0.232007 | − | 0.972714i | \(-0.574529\pi\) | ||||
−0.232007 | + | 0.972714i | \(0.574529\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −15.0808 | −0.594729 | −0.297364 | − | 0.954764i | \(-0.596108\pi\) | ||||
−0.297364 | + | 0.954764i | \(0.596108\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −0.697214 | −0.0274528 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 5.68014 | 0.223309 | 0.111655 | − | 0.993747i | \(-0.464385\pi\) | ||||
0.111655 | + | 0.993747i | \(0.464385\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 4.77166 | 0.187304 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −2.91276 | −0.114160 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −48.9941 | −1.91729 | −0.958644 | − | 0.284608i | \(-0.908137\pi\) | ||||
−0.958644 | + | 0.284608i | \(0.908137\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −16.4403 | −0.642375 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −34.2582 | −1.33654 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 23.5789 | 0.918505 | 0.459252 | − | 0.888306i | \(-0.348117\pi\) | ||||
0.459252 | + | 0.888306i | \(0.348117\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −38.6322 | −1.50262 | −0.751310 | − | 0.659949i | \(-0.770578\pi\) | ||||
−0.751310 | + | 0.659949i | \(0.770578\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 4.17379 | 0.162097 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −39.1671 | −1.51884 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −68.7470 | −2.66190 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −1.21739 | −0.0470670 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 5.37232 | 0.207396 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −37.4530 | −1.44371 | −0.721853 | − | 0.692047i | \(-0.756709\pi\) | ||||
−0.721853 | + | 0.692047i | \(0.756709\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −0.0749127 | −0.00288339 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 16.0616 | 0.617297 | 0.308649 | − | 0.951176i | \(-0.400123\pi\) | ||||
0.308649 | + | 0.951176i | \(0.400123\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 56.7868 | 2.17928 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −3.01038 | −0.115358 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −13.5819 | −0.519696 | −0.259848 | − | 0.965649i | \(-0.583673\pi\) | ||||
−0.259848 | + | 0.965649i | \(0.583673\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −13.4012 | −0.512032 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0.00388067 | 0.000148057 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −70.8871 | −2.70058 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 5.72328 | 0.217724 | 0.108862 | − | 0.994057i | \(-0.465279\pi\) | ||||
0.108862 | + | 0.994057i | \(0.465279\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −5.39626 | −0.204987 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 33.6876 | 1.27784 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 37.4887 | 1.41999 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −0.121375 | −0.00459083 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −20.2921 | −0.766421 | −0.383211 | − | 0.923661i | \(-0.625182\pi\) | ||||
−0.383211 | + | 0.923661i | \(0.625182\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −29.5670 | −1.11514 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 3.58584 | 0.135051 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 4.37408 | 0.164504 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −31.5398 | −1.18450 | −0.592251 | − | 0.805754i | \(-0.701761\pi\) | ||||
−0.592251 | + | 0.805754i | \(0.701761\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −4.25369 | −0.159526 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 34.0892 | 1.27665 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −6.24509 | −0.233553 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 1.67581 | 0.0625844 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 11.0676 | 0.412753 | 0.206376 | − | 0.978473i | \(-0.433833\pi\) | ||||
0.206376 | + | 0.978473i | \(0.433833\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 18.6238 | 0.693588 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −0.186202 | −0.00692494 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −0.602774 | −0.0223865 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 49.5631 | 1.83819 | 0.919096 | − | 0.394033i | \(-0.128921\pi\) | ||||
0.919096 | + | 0.394033i | \(0.128921\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −25.1457 | −0.931324 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −6.92901 | −0.256279 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −2.44508 | −0.0903110 | −0.0451555 | − | 0.998980i | \(-0.514378\pi\) | ||||
−0.0451555 | + | 0.998980i | \(0.514378\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −2.28809 | −0.0843975 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −2.01954 | −0.0743907 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −36.9067 | −1.35764 | −0.678818 | − | 0.734307i | \(-0.737508\pi\) | ||||
−0.678818 | + | 0.734307i | \(0.737508\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 4.93897 | 0.181438 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −40.6188 | −1.49016 | −0.745079 | − | 0.666976i | \(-0.767588\pi\) | ||||
−0.745079 | + | 0.666976i | \(0.767588\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0.293940 | 0.0107691 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 5.13142 | 0.187749 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 38.0579 | 1.39061 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 14.0406 | 0.512349 | 0.256174 | − | 0.966631i | \(-0.417538\pi\) | ||||
0.256174 | + | 0.966631i | \(0.417538\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −3.07207 | −0.111953 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0.621532 | 0.0226199 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 24.6936 | 0.897505 | 0.448752 | − | 0.893656i | \(-0.351869\pi\) | ||||
0.448752 | + | 0.893656i | \(0.351869\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −0.738419 | −0.0268029 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 12.6083 | 0.457051 | 0.228525 | − | 0.973538i | \(-0.426610\pi\) | ||||
0.228525 | + | 0.973538i | \(0.426610\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 4.06816 | 0.147277 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −27.8068 | −1.00536 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 49.8021 | 1.79825 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 42.1413 | 1.51965 | 0.759827 | − | 0.650125i | \(-0.225283\pi\) | ||||
0.759827 | + | 0.650125i | \(0.225283\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1.48781 | 0.0535821 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −9.62659 | −0.346244 | −0.173122 | − | 0.984900i | \(-0.555386\pi\) | ||||
−0.173122 | + | 0.984900i | \(0.555386\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0.298895 | 0.0107366 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −3.94221 | −0.141426 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 44.3615 | 1.58942 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −7.04900 | −0.252233 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 9.92745 | 0.354778 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −36.2526 | −1.29391 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −50.4413 | −1.79804 | −0.899019 | − | 0.437909i | \(-0.855719\pi\) | ||||
−0.899019 | + | 0.437909i | \(0.855719\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 1.01943 | 0.0362928 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 30.7436 | 1.09312 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 56.0713 | 1.99115 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −5.52185 | −0.195840 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 34.3043 | 1.21512 | 0.607561 | − | 0.794273i | \(-0.292148\pi\) | ||||
0.607561 | + | 0.794273i | \(0.292148\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 35.6366 | 1.26073 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 3.20252 | 0.113155 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −5.95627 | −0.210192 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 61.1177 | 2.15412 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −0.437011 | −0.0153835 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −43.9886 | −1.54656 | −0.773279 | − | 0.634066i | \(-0.781385\pi\) | ||||
−0.773279 | + | 0.634066i | \(0.781385\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 43.0270 | 1.51088 | 0.755440 | − | 0.655217i | \(-0.227423\pi\) | ||||
0.755440 | + | 0.655217i | \(0.227423\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −0.298484 | −0.0104683 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −41.6937 | −1.46047 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −8.19930 | −0.286857 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −56.3212 | −1.96802 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 18.7704 | 0.655090 | 0.327545 | − | 0.944836i | \(-0.393779\pi\) | ||||
0.327545 | + | 0.944836i | \(0.393779\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −27.1588 | −0.946695 | −0.473348 | − | 0.880876i | \(-0.656955\pi\) | ||||
−0.473348 | + | 0.880876i | \(0.656955\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −0.00647446 | −0.000225412 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −41.5157 | −1.44364 | −0.721821 | − | 0.692079i | \(-0.756695\pi\) | ||||
−0.721821 | + | 0.692079i | \(0.756695\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −30.6349 | −1.06399 | −0.531997 | − | 0.846746i | \(-0.678558\pi\) | ||||
−0.531997 | + | 0.846746i | \(0.678558\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −4.03640 | −0.140021 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −22.7394 | −0.787872 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 34.8959 | 1.20762 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −4.92267 | −0.170153 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −30.2456 | −1.04419 | −0.522097 | − | 0.852886i | \(-0.674850\pi\) | ||||
−0.522097 | + | 0.852886i | \(0.674850\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 50.8798 | 1.75447 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 5.00902 | 0.172520 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −35.9163 | −1.23556 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 37.8884 | 1.30186 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −0.724755 | −0.0248735 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 46.1374 | 1.58157 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 42.7734 | 1.46453 | 0.732267 | − | 0.681018i | \(-0.238462\pi\) | ||||
0.732267 | + | 0.681018i | \(0.238462\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −32.9046 | −1.12532 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −18.8048 | −0.642361 | −0.321181 | − | 0.947018i | \(-0.604080\pi\) | ||||
−0.321181 | + | 0.947018i | \(0.604080\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 8.22676 | 0.280693 | 0.140347 | − | 0.990102i | \(-0.455178\pi\) | ||||
0.140347 | + | 0.990102i | \(0.455178\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 5.91478 | 0.201575 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 41.8464 | 1.42447 | 0.712235 | − | 0.701941i | \(-0.247683\pi\) | ||||
0.712235 | + | 0.701941i | \(0.247683\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0.824887 | 0.0280470 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0.0656832 | 0.00223072 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −0.739564 | −0.0250880 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −21.0781 | −0.714204 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 47.7071 | 1.61464 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −39.1926 | −1.32495 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −6.11483 | −0.206483 | −0.103242 | − | 0.994656i | \(-0.532921\pi\) | ||||
−0.103242 | + | 0.994656i | \(0.532921\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −1.03787 | −0.0350065 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −13.5157 | −0.455355 | −0.227678 | − | 0.973737i | \(-0.573113\pi\) | ||||
−0.227678 | + | 0.973737i | \(0.573113\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −38.5489 | −1.29727 | −0.648637 | − | 0.761098i | \(-0.724661\pi\) | ||||
−0.648637 | + | 0.761098i | \(0.724661\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 3.87941 | 0.130405 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −40.8386 | −1.37123 | −0.685613 | − | 0.727966i | \(-0.740466\pi\) | ||||
−0.685613 | + | 0.727966i | \(0.740466\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −29.0163 | −0.973177 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −4.47982 | −0.150080 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 42.1698 | 1.41116 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 28.9759 | 0.968557 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −7.70694 | −0.257327 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −39.6096 | −1.32105 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −54.8769 | −1.82822 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −1.09322 | −0.0363802 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 27.4915 | 0.913848 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 34.3321 | 1.13998 | 0.569989 | − | 0.821652i | \(-0.306947\pi\) | ||||
0.569989 | + | 0.821652i | \(0.306947\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 3.67470 | 0.121882 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −49.0410 | −1.62480 | −0.812400 | − | 0.583100i | \(-0.801840\pi\) | ||||
−0.812400 | + | 0.583100i | \(0.801840\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0.892169 | 0.0295265 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 4.36776 | 0.144394 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −25.7782 | −0.851271 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −48.7329 | −1.60755 | −0.803775 | − | 0.594934i | \(-0.797178\pi\) | ||||
−0.803775 | + | 0.594934i | \(0.797178\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −4.29745 | −0.141606 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −73.5710 | −2.42162 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0.404533 | 0.0133010 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 15.6461 | 0.513884 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 52.9031 | 1.73569 | 0.867847 | − | 0.496832i | \(-0.165504\pi\) | ||||
0.867847 | + | 0.496832i | \(0.165504\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −26.9081 | −0.881879 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 2.79088 | 0.0913693 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −4.83461 | −0.158109 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −16.1310 | −0.526976 | −0.263488 | − | 0.964663i | \(-0.584873\pi\) | ||||
−0.263488 | + | 0.964663i | \(0.584873\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −0.430280 | −0.0140416 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 10.7225 | 0.349544 | 0.174772 | − | 0.984609i | \(-0.444081\pi\) | ||||
0.174772 | + | 0.984609i | \(0.444081\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −69.2233 | −2.25422 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −8.82574 | −0.287101 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 21.9984 | 0.714851 | 0.357426 | − | 0.933942i | \(-0.383655\pi\) | ||||
0.357426 | + | 0.933942i | \(0.383655\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −62.1660 | −2.01800 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −3.41923 | −0.110876 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −40.5214 | −1.31262 | −0.656309 | − | 0.754492i | \(-0.727883\pi\) | ||||
−0.656309 | + | 0.754492i | \(0.727883\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −8.83330 | −0.285839 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0.857998 | 0.0277351 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −21.0129 | −0.678542 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −11.3590 | −0.366419 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 31.9728 | 1.03031 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 3.81154 | 0.122698 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 46.5645 | 1.49741 | 0.748706 | − | 0.662902i | \(-0.230676\pi\) | ||||
0.748706 | + | 0.662902i | \(0.230676\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 3.82348 | 0.122828 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −2.03099 | −0.0651775 | −0.0325887 | − | 0.999469i | \(-0.510375\pi\) | ||||
−0.0325887 | + | 0.999469i | \(0.510375\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 52.8218 | 1.69339 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −0.0675745 | −0.00216412 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −45.7170 | −1.46262 | −0.731308 | − | 0.682047i | \(-0.761090\pi\) | ||||
−0.731308 | + | 0.682047i | \(0.761090\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0.556803 | 0.0177955 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 3.41770 | 0.109119 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 47.0190 | 1.49967 | 0.749837 | − | 0.661623i | \(-0.230132\pi\) | ||||
0.749837 | + | 0.661623i | \(0.230132\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 4.96103 | 0.158071 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 5.62256 | 0.178968 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 12.7945 | 0.406841 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −54.4626 | −1.73006 | −0.865031 | − | 0.501718i | \(-0.832702\pi\) | ||||
−0.865031 | + | 0.501718i | \(0.832702\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 1.20647 | 0.0382860 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −35.0121 | −1.10996 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 13.5868 | 0.430297 | 0.215149 | − | 0.976581i | \(-0.430976\pi\) | ||||
0.215149 | + | 0.976581i | \(0.430976\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −6.66250 | −0.210792 |
(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 | 3856.2.a.j.1.3 | 7 | ||
4.3 | odd | 2 | 241.2.a.a.1.2 | ✓ | 7 | ||
12.11 | even | 2 | 2169.2.a.e.1.6 | 7 | |||
20.19 | odd | 2 | 6025.2.a.f.1.6 | 7 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
241.2.a.a.1.2 | ✓ | 7 | 4.3 | odd | 2 | ||
2169.2.a.e.1.6 | 7 | 12.11 | even | 2 | |||
3856.2.a.j.1.3 | 7 | 1.1 | even | 1 | trivial | ||
6025.2.a.f.1.6 | 7 | 20.19 | odd | 2 |