Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1288,2,Mod(1,1288)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1288, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("1288.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1288 = 2^{3} \cdot 7 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1288.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: | \(10.2847317803\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.148.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 3x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-1.48119\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1288.1 |
$q$-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 | ||||||||
\(3\) | −1.67513 | −0.967137 | −0.483569 | − | 0.875306i | \(-0.660660\pi\) | ||||
−0.483569 | + | 0.875306i | \(0.660660\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 3.28726 | 1.47011 | 0.735053 | − | 0.678009i | \(-0.237157\pi\) | ||||
0.735053 | + | 0.678009i | \(0.237157\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −0.193937 | −0.0646455 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.15633 | 0.650157 | 0.325078 | − | 0.945687i | \(-0.394609\pi\) | ||||
0.325078 | + | 0.945687i | \(0.394609\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.96239 | 0.821619 | 0.410809 | − | 0.911721i | \(-0.365246\pi\) | ||||
0.410809 | + | 0.911721i | \(0.365246\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −5.50659 | −1.42179 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −0.637519 | −0.154621 | −0.0773106 | − | 0.997007i | \(-0.524633\pi\) | ||||
−0.0773106 | + | 0.997007i | \(0.524633\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.67513 | 0.365544 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.00000 | 0.208514 | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 5.80606 | 1.16121 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 5.35026 | 1.02966 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 3.19394 | 0.593099 | 0.296550 | − | 0.955017i | \(-0.404164\pi\) | ||||
0.296550 | + | 0.955017i | \(0.404164\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −5.59991 | −1.00577 | −0.502887 | − | 0.864352i | \(-0.667729\pi\) | ||||
−0.502887 | + | 0.864352i | \(0.667729\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −3.61213 | −0.628791 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −3.28726 | −0.555648 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 10.9624 | 1.80221 | 0.901103 | − | 0.433606i | \(-0.142759\pi\) | ||||
0.901103 | + | 0.433606i | \(0.142759\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −4.96239 | −0.794618 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.22425 | 0.191196 | 0.0955982 | − | 0.995420i | \(-0.469524\pi\) | ||||
0.0955982 | + | 0.995420i | \(0.469524\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −5.73813 | −0.875057 | −0.437529 | − | 0.899204i | \(-0.644146\pi\) | ||||
−0.437529 | + | 0.899204i | \(0.644146\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −0.637519 | −0.0950358 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −4.63752 | −0.676452 | −0.338226 | − | 0.941065i | \(-0.609827\pi\) | ||||
−0.338226 | + | 0.941065i | \(0.609827\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 1.06793 | 0.149540 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −5.22425 | −0.717606 | −0.358803 | − | 0.933413i | \(-0.616815\pi\) | ||||
−0.358803 | + | 0.933413i | \(0.616815\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 7.08840 | 0.955799 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 1.98778 | 0.258787 | 0.129394 | − | 0.991593i | \(-0.458697\pi\) | ||||
0.129394 | + | 0.991593i | \(0.458697\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 5.80114 | 0.742760 | 0.371380 | − | 0.928481i | \(-0.378885\pi\) | ||||
0.371380 | + | 0.928481i | \(0.378885\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0.193937 | 0.0244337 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 9.73813 | 1.20787 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 8.08110 | 0.987264 | 0.493632 | − | 0.869671i | \(-0.335669\pi\) | ||||
0.493632 | + | 0.869671i | \(0.335669\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −1.67513 | −0.201662 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 6.70052 | 0.795206 | 0.397603 | − | 0.917558i | \(-0.369842\pi\) | ||||
0.397603 | + | 0.917558i | \(0.369842\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 12.0508 | 1.41044 | 0.705219 | − | 0.708990i | \(-0.250849\pi\) | ||||
0.705219 | + | 0.708990i | \(0.250849\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −9.72592 | −1.12305 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −2.15633 | −0.245736 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 7.76845 | 0.874019 | 0.437010 | − | 0.899457i | \(-0.356038\pi\) | ||||
0.437010 | + | 0.899457i | \(0.356038\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −8.38058 | −0.931175 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 0.962389 | 0.105636 | 0.0528179 | − | 0.998604i | \(-0.483180\pi\) | ||||
0.0528179 | + | 0.998604i | \(0.483180\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −2.09569 | −0.227310 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −5.35026 | −0.573608 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 14.3757 | 1.52382 | 0.761908 | − | 0.647685i | \(-0.224263\pi\) | ||||
0.761908 | + | 0.647685i | \(0.224263\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.96239 | −0.310543 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 9.38058 | 0.972721 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 14.1138 | 1.43304 | 0.716519 | − | 0.697567i | \(-0.245734\pi\) | ||||
0.716519 | + | 0.697567i | \(0.245734\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −0.418190 | −0.0420297 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −0.574515 | −0.0571664 | −0.0285832 | − | 0.999591i | \(-0.509100\pi\) | ||||
−0.0285832 | + | 0.999591i | \(0.509100\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 5.92478 | 0.583786 | 0.291893 | − | 0.956451i | \(-0.405715\pi\) | ||||
0.291893 | + | 0.956451i | \(0.405715\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 5.50659 | 0.537388 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 12.4387 | 1.20249 | 0.601245 | − | 0.799065i | \(-0.294671\pi\) | ||||
0.601245 | + | 0.799065i | \(0.294671\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −17.9756 | −1.72175 | −0.860873 | − | 0.508819i | \(-0.830082\pi\) | ||||
−0.860873 | + | 0.508819i | \(0.830082\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −18.3634 | −1.74298 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −8.70052 | −0.818476 | −0.409238 | − | 0.912428i | \(-0.634205\pi\) | ||||
−0.409238 | + | 0.912428i | \(0.634205\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 3.28726 | 0.306538 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −0.574515 | −0.0531140 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0.637519 | 0.0584413 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −6.35026 | −0.577297 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −2.05079 | −0.184913 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 2.64974 | 0.237000 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −8.96239 | −0.795283 | −0.397642 | − | 0.917541i | \(-0.630171\pi\) | ||||
−0.397642 | + | 0.917541i | \(0.630171\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 9.61213 | 0.846301 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 8.45088 | 0.738357 | 0.369178 | − | 0.929359i | \(-0.379639\pi\) | ||||
0.369178 | + | 0.929359i | \(0.379639\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 17.5877 | 1.51371 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −12.8872 | −1.10102 | −0.550512 | − | 0.834827i | \(-0.685568\pi\) | ||||
−0.550512 | + | 0.834827i | \(0.685568\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 9.98778 | 0.847153 | 0.423576 | − | 0.905860i | \(-0.360775\pi\) | ||||
0.423576 | + | 0.905860i | \(0.360775\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 7.76845 | 0.654222 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 6.38787 | 0.534181 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 10.4993 | 0.871919 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −1.67513 | −0.138162 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −1.47627 | −0.120941 | −0.0604704 | − | 0.998170i | \(-0.519260\pi\) | ||||
−0.0604704 | + | 0.998170i | \(0.519260\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 10.1114 | 0.822856 | 0.411428 | − | 0.911442i | \(-0.365030\pi\) | ||||
0.411428 | + | 0.911442i | \(0.365030\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0.123638 | 0.00999557 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −18.4083 | −1.47859 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −3.67513 | −0.293307 | −0.146654 | − | 0.989188i | \(-0.546850\pi\) | ||||
−0.146654 | + | 0.989188i | \(0.546850\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 8.75131 | 0.694024 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1.00000 | −0.0788110 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 20.1622 | 1.57923 | 0.789613 | − | 0.613605i | \(-0.210281\pi\) | ||||
0.789613 | + | 0.613605i | \(0.210281\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −11.8740 | −0.924389 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 14.5017 | 1.12217 | 0.561086 | − | 0.827757i | \(-0.310384\pi\) | ||||
0.561086 | + | 0.827757i | \(0.310384\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −4.22425 | −0.324943 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 8.07522 | 0.613948 | 0.306974 | − | 0.951718i | \(-0.400684\pi\) | ||||
0.306974 | + | 0.951718i | \(0.400684\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −5.80606 | −0.438897 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −3.32979 | −0.250283 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −11.6629 | −0.871727 | −0.435863 | − | 0.900013i | \(-0.643557\pi\) | ||||
−0.435863 | + | 0.900013i | \(0.643557\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −10.1890 | −0.757343 | −0.378672 | − | 0.925531i | \(-0.623619\pi\) | ||||
−0.378672 | + | 0.925531i | \(0.623619\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −9.71767 | −0.718351 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 36.0362 | 2.64943 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1.37470 | −0.100528 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −5.35026 | −0.389174 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −14.8872 | −1.07720 | −0.538599 | − | 0.842562i | \(-0.681046\pi\) | ||||
−0.538599 | + | 0.842562i | \(0.681046\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −3.27504 | −0.235742 | −0.117871 | − | 0.993029i | \(-0.537607\pi\) | ||||
−0.117871 | + | 0.993029i | \(0.537607\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −16.3127 | −1.16817 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −18.6253 | −1.32700 | −0.663499 | − | 0.748177i | \(-0.730929\pi\) | ||||
−0.663499 | + | 0.748177i | \(0.730929\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1.92478 | −0.136444 | −0.0682219 | − | 0.997670i | \(-0.521733\pi\) | ||||
−0.0682219 | + | 0.997670i | \(0.521733\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −13.5369 | −0.954820 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −3.19394 | −0.224170 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 4.02444 | 0.281079 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −0.193937 | −0.0134795 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −26.8872 | −1.85099 | −0.925494 | − | 0.378761i | \(-0.876350\pi\) | ||||
−0.925494 | + | 0.378761i | \(0.876350\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −11.2243 | −0.769073 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −18.8627 | −1.28643 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 5.59991 | 0.380147 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −20.1866 | −1.36409 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1.88858 | −0.127040 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1.98778 | −0.133112 | −0.0665558 | − | 0.997783i | \(-0.521201\pi\) | ||||
−0.0665558 | + | 0.997783i | \(0.521201\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −1.12601 | −0.0750672 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 3.68735 | 0.244738 | 0.122369 | − | 0.992485i | \(-0.460951\pi\) | ||||
0.122369 | + | 0.992485i | \(0.460951\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −15.3987 | −1.01757 | −0.508787 | − | 0.860893i | \(-0.669906\pi\) | ||||
−0.508787 | + | 0.860893i | \(0.669906\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 3.61213 | 0.237660 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −6.73084 | −0.440952 | −0.220476 | − | 0.975392i | \(-0.570761\pi\) | ||||
−0.220476 | + | 0.975392i | \(0.570761\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −15.2447 | −0.994456 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −13.0132 | −0.845296 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 14.8872 | 0.962971 | 0.481485 | − | 0.876454i | \(-0.340097\pi\) | ||||
0.481485 | + | 0.876454i | \(0.340097\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −15.3380 | −0.988010 | −0.494005 | − | 0.869459i | \(-0.664468\pi\) | ||||
−0.494005 | + | 0.869459i | \(0.664468\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −2.01222 | −0.129084 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 3.28726 | 0.210015 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −1.61213 | −0.102164 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −12.3733 | −0.780995 | −0.390497 | − | 0.920604i | \(-0.627697\pi\) | ||||
−0.390497 | + | 0.920604i | \(0.627697\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2.15633 | 0.135567 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 3.51056 | 0.219840 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 10.6253 | 0.662788 | 0.331394 | − | 0.943492i | \(-0.392481\pi\) | ||||
0.331394 | + | 0.943492i | \(0.392481\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −10.9624 | −0.681170 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −0.619421 | −0.0383412 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −7.61801 | −0.469746 | −0.234873 | − | 0.972026i | \(-0.575467\pi\) | ||||
−0.234873 | + | 0.972026i | \(0.575467\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −17.1735 | −1.05496 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −24.0811 | −1.47374 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 1.22425 | 0.0746441 | 0.0373220 | − | 0.999303i | \(-0.488117\pi\) | ||||
0.0373220 | + | 0.999303i | \(0.488117\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −4.96476 | −0.301588 | −0.150794 | − | 0.988565i | \(-0.548183\pi\) | ||||
−0.150794 | + | 0.988565i | \(0.548183\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 4.96239 | 0.300337 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 12.5198 | 0.754970 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 12.1319 | 0.728934 | 0.364467 | − | 0.931216i | \(-0.381251\pi\) | ||||
0.364467 | + | 0.931216i | \(0.381251\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 1.08603 | 0.0650187 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −14.7513 | −0.879989 | −0.439995 | − | 0.898000i | \(-0.645020\pi\) | ||||
−0.439995 | + | 0.898000i | \(0.645020\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −28.9380 | −1.72018 | −0.860091 | − | 0.510140i | \(-0.829594\pi\) | ||||
−0.860091 | + | 0.510140i | \(0.829594\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −1.22425 | −0.0722654 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.5936 | −0.976092 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −23.6424 | −1.38594 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 5.15140 | 0.300948 | 0.150474 | − | 0.988614i | \(-0.451920\pi\) | ||||
0.150474 | + | 0.988614i | \(0.451920\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 6.53435 | 0.380445 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 11.5369 | 0.669439 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 2.96239 | 0.171319 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 5.73813 | 0.330741 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0.962389 | 0.0552878 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 19.0698 | 1.09194 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −14.5867 | −0.832509 | −0.416254 | − | 0.909248i | \(-0.636657\pi\) | ||||
−0.416254 | + | 0.909248i | \(0.636657\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −9.92478 | −0.564601 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −15.1368 | −0.858330 | −0.429165 | − | 0.903226i | \(-0.641192\pi\) | ||||
−0.429165 | + | 0.903226i | \(0.641192\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 11.2727 | 0.637169 | 0.318584 | − | 0.947894i | \(-0.396793\pi\) | ||||
0.318584 | + | 0.947894i | \(0.396793\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0.637519 | 0.0359202 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −11.4460 | −0.642869 | −0.321434 | − | 0.946932i | \(-0.604165\pi\) | ||||
−0.321434 | + | 0.946932i | \(0.604165\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 6.88717 | 0.385607 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −20.8364 | −1.16297 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 17.1998 | 0.954074 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 30.1114 | 1.66517 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 4.63752 | 0.255675 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −11.8740 | −0.652654 | −0.326327 | − | 0.945257i | \(-0.605811\pi\) | ||||
−0.326327 | + | 0.945257i | \(0.605811\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −2.12601 | −0.116505 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 26.5647 | 1.45138 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 22.1260 | 1.20528 | 0.602640 | − | 0.798013i | \(-0.294115\pi\) | ||||
0.602640 | + | 0.798013i | \(0.294115\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 14.5745 | 0.791579 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −12.0752 | −0.653910 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −5.50659 | −0.296465 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 29.3357 | 1.57482 | 0.787411 | − | 0.616429i | \(-0.211421\pi\) | ||||
0.787411 | + | 0.616429i | \(0.211421\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −30.1622 | −1.61455 | −0.807273 | − | 0.590178i | \(-0.799057\pi\) | ||||
−0.807273 | + | 0.590178i | \(0.799057\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 15.8496 | 0.845987 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 32.3634 | 1.72253 | 0.861266 | − | 0.508154i | \(-0.169672\pi\) | ||||
0.861266 | + | 0.508154i | \(0.169672\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 22.0263 | 1.16904 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −1.06793 | −0.0565208 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −1.84367 | −0.0973054 | −0.0486527 | − | 0.998816i | \(-0.515493\pi\) | ||||
−0.0486527 | + | 0.998816i | \(0.515493\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −19.0000 | −1.00000 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 10.6375 | 0.558325 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 39.6140 | 2.07349 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 23.0376 | 1.20255 | 0.601277 | − | 0.799041i | \(-0.294659\pi\) | ||||
0.601277 | + | 0.799041i | \(0.294659\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −0.237428 | −0.0123600 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 5.22425 | 0.271230 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −11.7743 | −0.609652 | −0.304826 | − | 0.952408i | \(-0.598598\pi\) | ||||
−0.304826 | + | 0.952408i | \(0.598598\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −4.43866 | −0.229211 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 9.46168 | 0.487301 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −37.0191 | −1.90154 | −0.950771 | − | 0.309896i | \(-0.899706\pi\) | ||||
−0.950771 | + | 0.309896i | \(0.899706\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 15.0132 | 0.769148 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −22.9887 | −1.17467 | −0.587335 | − | 0.809344i | \(-0.699823\pi\) | ||||
−0.587335 | + | 0.809344i | \(0.699823\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −7.08840 | −0.361258 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 1.11283 | 0.0565685 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 3.17347 | 0.160901 | 0.0804506 | − | 0.996759i | \(-0.474364\pi\) | ||||
0.0804506 | + | 0.996759i | \(0.474364\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −0.637519 | −0.0322407 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −14.1563 | −0.714092 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 25.5369 | 1.28490 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 30.2882 | 1.52012 | 0.760061 | − | 0.649852i | \(-0.225169\pi\) | ||||
0.760061 | + | 0.649852i | \(0.225169\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 0.201231 | 0.0100490 | 0.00502449 | − | 0.999987i | \(-0.498401\pi\) | ||||
0.00502449 | + | 0.999987i | \(0.498401\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −16.5891 | −0.826362 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −27.5491 | −1.36893 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 23.6385 | 1.17172 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −7.73813 | −0.382626 | −0.191313 | − | 0.981529i | \(-0.561275\pi\) | ||||
−0.191313 | + | 0.981529i | \(0.561275\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 21.5877 | 1.06484 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −1.98778 | −0.0978123 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 3.16362 | 0.155296 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −16.7308 | −0.819313 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 24.2228 | 1.18336 | 0.591682 | − | 0.806172i | \(-0.298464\pi\) | ||||
0.591682 | + | 0.806172i | \(0.298464\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −34.9986 | −1.70573 | −0.852863 | − | 0.522134i | \(-0.825136\pi\) | ||||
−0.852863 | + | 0.522134i | \(0.825136\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0.899385 | 0.0437296 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −3.70148 | −0.179548 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −5.80114 | −0.280737 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −10.7005 | −0.516626 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 18.5501 | 0.893526 | 0.446763 | − | 0.894652i | \(-0.352577\pi\) | ||||
0.446763 | + | 0.894652i | \(0.352577\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −33.5247 | −1.61109 | −0.805547 | − | 0.592532i | \(-0.798128\pi\) | ||||
−0.805547 | + | 0.592532i | \(0.798128\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −17.5877 | −0.843265 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 22.6982 | 1.08332 | 0.541662 | − | 0.840596i | \(-0.317795\pi\) | ||||
0.541662 | + | 0.840596i | \(0.317795\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −0.193937 | −0.00923507 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −9.46168 | −0.449538 | −0.224769 | − | 0.974412i | \(-0.572163\pi\) | ||||
−0.224769 | + | 0.974412i | \(0.572163\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 47.2565 | 2.24017 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 2.47295 | 0.116966 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −21.8945 | −1.03326 | −0.516632 | − | 0.856208i | \(-0.672814\pi\) | ||||
−0.516632 | + | 0.856208i | \(0.672814\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 2.63989 | 0.124308 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −16.9380 | −0.795814 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −9.73813 | −0.456531 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 1.93937 | 0.0907197 | 0.0453598 | − | 0.998971i | \(-0.485557\pi\) | ||||
0.0453598 | + | 0.998971i | \(0.485557\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −3.41090 | −0.159207 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 42.4749 | 1.97825 | 0.989126 | − | 0.147073i | \(-0.0469853\pi\) | ||||
0.989126 | + | 0.147073i | \(0.0469853\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −7.50071 | −0.348587 | −0.174294 | − | 0.984694i | \(-0.555764\pi\) | ||||
−0.174294 | + | 0.984694i | \(0.555764\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 30.8364 | 1.43000 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −18.5501 | −0.858395 | −0.429198 | − | 0.903211i | \(-0.641204\pi\) | ||||
−0.429198 | + | 0.903211i | \(0.641204\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −8.08110 | −0.373151 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 6.15633 | 0.283668 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −12.3733 | −0.568924 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 1.01317 | 0.0463900 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 27.9102 | 1.27525 | 0.637625 | − | 0.770347i | \(-0.279917\pi\) | ||||
0.637625 | + | 0.770347i | \(0.279917\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 32.4749 | 1.48073 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 1.67513 | 0.0762211 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 46.3957 | 2.10672 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 20.2520 | 0.917706 | 0.458853 | − | 0.888512i | \(-0.348260\pi\) | ||||
0.458853 | + | 0.888512i | \(0.348260\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −33.7743 | −1.52733 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 15.0738 | 0.680271 | 0.340136 | − | 0.940376i | \(-0.389527\pi\) | ||||
0.340136 | + | 0.940376i | \(0.389527\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −2.03620 | −0.0917057 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −1.37470 | −0.0617881 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −6.70052 | −0.300560 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 4.90175 | 0.219433 | 0.109716 | − | 0.993963i | \(-0.465006\pi\) | ||||
0.109716 | + | 0.993963i | \(0.465006\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −24.2922 | −1.08529 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 4.98683 | 0.222352 | 0.111176 | − | 0.993801i | \(-0.464538\pi\) | ||||
0.111176 | + | 0.993801i | \(0.464538\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −1.88858 | −0.0840407 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 7.07618 | 0.314264 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −11.6121 | −0.514698 | −0.257349 | − | 0.966318i | \(-0.582849\pi\) | ||||
−0.257349 | + | 0.966318i | \(0.582849\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −12.0508 | −0.533095 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 19.4763 | 0.858227 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −10.0000 | −0.439799 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −13.5271 | −0.593772 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 18.6375 | 0.816525 | 0.408262 | − | 0.912865i | \(-0.366135\pi\) | ||||
0.408262 | + | 0.912865i | \(0.366135\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −39.6385 | −1.73327 | −0.866635 | − | 0.498943i | \(-0.833722\pi\) | ||||
−0.866635 | + | 0.498943i | \(0.833722\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 9.72592 | 0.424474 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 3.57005 | 0.155514 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −0.385503 | −0.0167294 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 3.62672 | 0.157090 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 40.8891 | 1.76779 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 19.5369 | 0.843080 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 2.15633 | 0.0928795 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 23.3561 | 1.00416 | 0.502079 | − | 0.864821i | \(-0.332568\pi\) | ||||
0.502079 | + | 0.864821i | \(0.332568\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 17.0679 | 0.732455 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −59.0903 | −2.53115 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −20.9624 | −0.896287 | −0.448144 | − | 0.893962i | \(-0.647915\pi\) | ||||
−0.448144 | + | 0.893962i | \(0.647915\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −1.12505 | −0.0480161 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −7.76845 | −0.330348 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −60.3653 | −2.56237 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 1.62672 | 0.0689261 | 0.0344631 | − | 0.999406i | \(-0.489028\pi\) | ||||
0.0344631 | + | 0.999406i | \(0.489028\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −16.9986 | −0.718964 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 2.30280 | 0.0972243 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 18.9116 | 0.797029 | 0.398515 | − | 0.917162i | \(-0.369526\pi\) | ||||
0.398515 | + | 0.917162i | \(0.369526\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −28.6009 | −1.20325 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 8.38058 | 0.351951 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −0.111420 | −0.00467095 | −0.00233548 | − | 0.999997i | \(-0.500743\pi\) | ||||
−0.00233548 | + | 0.999997i | \(0.500743\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −37.0640 | −1.55108 | −0.775539 | − | 0.631299i | \(-0.782522\pi\) | ||||
−0.775539 | + | 0.631299i | \(0.782522\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 24.9380 | 1.04180 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 5.80606 | 0.242130 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −11.8594 | −0.493713 | −0.246857 | − | 0.969052i | \(-0.579398\pi\) | ||||
−0.246857 | + | 0.969052i | \(0.579398\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 5.48612 | 0.227995 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −0.962389 | −0.0399266 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −11.2652 | −0.466556 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −1.88858 | −0.0780832 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 27.2873 | 1.12627 | 0.563133 | − | 0.826366i | \(-0.309596\pi\) | ||||
0.563133 | + | 0.826366i | \(0.309596\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 31.1998 | 1.28339 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 3.08840 | 0.126825 | 0.0634126 | − | 0.997987i | \(-0.479802\pi\) | ||||
0.0634126 | + | 0.997987i | \(0.479802\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 2.09569 | 0.0859149 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 3.22425 | 0.131960 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 8.58910 | 0.350941 | 0.175471 | − | 0.984485i | \(-0.443855\pi\) | ||||
0.175471 | + | 0.984485i | \(0.443855\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −17.8134 | −0.726622 | −0.363311 | − | 0.931668i | \(-0.618354\pi\) | ||||
−0.363311 | + | 0.931668i | \(0.618354\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −1.56722 | −0.0638222 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −20.8749 | −0.848687 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −16.4871 | −0.669190 | −0.334595 | − | 0.942362i | \(-0.608599\pi\) | ||||
−0.334595 | + | 0.942362i | \(0.608599\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 5.35026 | 0.216804 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −13.7381 | −0.555785 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −27.7499 | −1.12081 | −0.560404 | − | 0.828220i | \(-0.689354\pi\) | ||||
−0.560404 | + | 0.828220i | \(0.689354\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −6.74146 | −0.271842 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 15.5877 | 0.627537 | 0.313768 | − | 0.949500i | \(-0.398408\pi\) | ||||
0.313768 | + | 0.949500i | \(0.398408\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −3.41090 | −0.137095 | −0.0685477 | − | 0.997648i | \(-0.521837\pi\) | ||||
−0.0685477 | + | 0.997648i | \(0.521837\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 5.35026 | 0.214699 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −14.3757 | −0.575948 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −20.3199 | −0.812798 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −6.98874 | −0.278659 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 36.6458 | 1.45885 | 0.729423 | − | 0.684063i | \(-0.239789\pi\) | ||||
0.729423 | + | 0.684063i | \(0.239789\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 45.0395 | 1.79016 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −29.4617 | −1.16915 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 2.96239 | 0.117374 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −1.29948 | −0.0514065 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −48.3146 | −1.90831 | −0.954155 | − | 0.299312i | \(-0.903243\pi\) | ||||
−0.954155 | + | 0.299312i | \(0.903243\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 29.1900 | 1.15114 | 0.575570 | − | 0.817753i | \(-0.304780\pi\) | ||||
0.575570 | + | 0.817753i | \(0.304780\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 31.5975 | 1.24415 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 34.7127 | 1.36470 | 0.682349 | − | 0.731026i | \(-0.260958\pi\) | ||||
0.682349 | + | 0.731026i | \(0.260958\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 4.28630 | 0.168252 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −9.38058 | −0.367654 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 18.2228 | 0.713115 | 0.356557 | − | 0.934273i | \(-0.383950\pi\) | ||||
0.356557 | + | 0.934273i | \(0.383950\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 27.7802 | 1.08546 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −2.33709 | −0.0911785 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 4.00000 | 0.155818 | 0.0779089 | − | 0.996960i | \(-0.475176\pi\) | ||||
0.0779089 | + | 0.996960i | \(0.475176\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −21.9878 | −0.855226 | −0.427613 | − | 0.903962i | \(-0.640645\pi\) | ||||
−0.427613 | + | 0.903962i | \(0.640645\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 3.16362 | 0.122865 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 3.19394 | 0.123670 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 3.32979 | 0.128737 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 12.5091 | 0.482910 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −2.47882 | −0.0955517 | −0.0477758 | − | 0.998858i | \(-0.515213\pi\) | ||||
−0.0477758 | + | 0.998858i | \(0.515213\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 31.0640 | 1.19565 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −4.37565 | −0.168170 | −0.0840850 | − | 0.996459i | \(-0.526797\pi\) | ||||
−0.0840850 | + | 0.996459i | \(0.526797\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −14.1138 | −0.541638 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −6.17679 | −0.236695 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −44.7875 | −1.71375 | −0.856873 | − | 0.515527i | \(-0.827596\pi\) | ||||
−0.856873 | + | 0.515527i | \(0.827596\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −42.3634 | −1.61862 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 25.7948 | 0.984133 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −15.4763 | −0.589599 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −8.76353 | −0.333380 | −0.166690 | − | 0.986009i | \(-0.553308\pi\) | ||||
−0.166690 | + | 0.986009i | \(0.553308\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0.418190 | 0.0158857 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 32.8324 | 1.24540 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −0.780486 | −0.0295630 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 11.2750 | 0.426461 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −26.9135 | −1.01651 | −0.508255 | − | 0.861207i | \(-0.669709\pi\) | ||||
−0.508255 | + | 0.861207i | \(0.669709\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 25.5369 | 0.961775 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0.574515 | 0.0216069 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 29.3503 | 1.10227 | 0.551136 | − | 0.834415i | \(-0.314195\pi\) | ||||
0.551136 | + | 0.834415i | \(0.314195\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −1.50659 | −0.0565014 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −5.59991 | −0.209718 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 20.9986 | 0.785303 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −24.9380 | −0.931325 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 6.81431 | 0.254131 | 0.127065 | − | 0.991894i | \(-0.459444\pi\) | ||||
0.127065 | + | 0.991894i | \(0.459444\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −5.92478 | −0.220650 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 25.6932 | 0.955541 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 18.5442 | 0.688714 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 14.5501 | 0.539633 | 0.269816 | − | 0.962912i | \(-0.413037\pi\) | ||||
0.269816 | + | 0.962912i | \(0.413037\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 28.5125 | 1.05602 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 3.65817 | 0.135302 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 30.4626 | 1.12516 | 0.562582 | − | 0.826742i | \(-0.309808\pi\) | ||||
0.562582 | + | 0.826742i | \(0.309808\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −5.50659 | −0.203114 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 17.4255 | 0.641876 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −27.4471 | −1.00966 | −0.504829 | − | 0.863219i | \(-0.668444\pi\) | ||||
−0.504829 | + | 0.863219i | \(0.668444\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 22.0665 | 0.809542 | 0.404771 | − | 0.914418i | \(-0.367351\pi\) | ||||
0.404771 | + | 0.914418i | \(0.367351\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −4.85288 | −0.177796 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −0.186642 | −0.00682889 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −12.4387 | −0.454499 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 18.6312 | 0.679861 | 0.339931 | − | 0.940450i | \(-0.389596\pi\) | ||||
0.339931 | + | 0.940450i | \(0.389596\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 20.7269 | 0.755329 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 33.2388 | 1.20969 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 50.5402 | 1.83692 | 0.918458 | − | 0.395519i | \(-0.129435\pi\) | ||||
0.918458 | + | 0.395519i | \(0.129435\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −3.61213 | −0.131112 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 5.62198 | 0.203796 | 0.101898 | − | 0.994795i | \(-0.467508\pi\) | ||||
0.101898 | + | 0.994795i | \(0.467508\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 17.9756 | 0.650759 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0.406431 | 0.0146945 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 5.88858 | 0.212624 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −3.12696 | −0.112761 | −0.0563806 | − | 0.998409i | \(-0.517956\pi\) | ||||
−0.0563806 | + | 0.998409i | \(0.517956\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −17.7988 | −0.641007 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −40.2106 | −1.44628 | −0.723138 | − | 0.690704i | \(-0.757301\pi\) | ||||
−0.723138 | + | 0.690704i | \(0.757301\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −32.5134 | −1.16792 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 18.3634 | 0.658785 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 14.4485 | 0.517008 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 17.0884 | 0.610689 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −12.0811 | −0.431193 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −46.0019 | −1.63979 | −0.819896 | − | 0.572513i | \(-0.805969\pi\) | ||||
−0.819896 | + | 0.572513i | \(0.805969\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 12.7612 | 0.454309 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 8.70052 | 0.309355 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 17.1852 | 0.610265 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 28.7678 | 1.02029 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 55.0127 | 1.94865 | 0.974325 | − | 0.225145i | \(-0.0722857\pi\) | ||||
0.974325 | + | 0.225145i | \(0.0722857\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 2.95651 | 0.104594 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −2.78797 | −0.0985079 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 25.9854 | 0.917005 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −3.28726 | −0.115861 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −2.05079 | −0.0721911 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −15.4255 | −0.542331 | −0.271166 | − | 0.962533i | \(-0.587409\pi\) | ||||
−0.271166 | + | 0.962533i | \(0.587409\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −25.1006 | −0.881402 | −0.440701 | − | 0.897654i | \(-0.645270\pi\) | ||||
−0.440701 | + | 0.897654i | \(0.645270\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 8.31662 | 0.291677 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 66.2784 | 2.32163 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0.574515 | 0.0200752 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 10.8930 | 0.380170 | 0.190085 | − | 0.981768i | \(-0.439124\pi\) | ||||
0.190085 | + | 0.981768i | \(0.439124\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −49.1608 | −1.71364 | −0.856819 | − | 0.515618i | \(-0.827562\pi\) | ||||
−0.856819 | + | 0.515618i | \(0.827562\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −20.9722 | −0.730160 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 49.7255 | 1.72912 | 0.864562 | − | 0.502527i | \(-0.167596\pi\) | ||||
0.864562 | + | 0.502527i | \(0.167596\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 14.8364 | 0.515289 | 0.257644 | − | 0.966240i | \(-0.417054\pi\) | ||||
0.257644 | + | 0.966240i | \(0.417054\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −20.3225 | −0.704980 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −0.637519 | −0.0220887 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 47.6707 | 1.64971 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −29.9610 | −1.03560 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −19.4109 | −0.670139 | −0.335069 | − | 0.942193i | \(-0.608760\pi\) | ||||
−0.335069 | + | 0.942193i | \(0.608760\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −18.7988 | −0.648233 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 24.7104 | 0.851070 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −13.8862 | −0.477700 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 6.35026 | 0.218198 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 48.4749 | 1.66365 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 10.9624 | 0.375786 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −39.5877 | −1.35546 | −0.677728 | − | 0.735312i | \(-0.737035\pi\) | ||||
−0.677728 | + | 0.735312i | \(0.737035\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −36.9234 | −1.26128 | −0.630639 | − | 0.776076i | \(-0.717207\pi\) | ||||
−0.630639 | + | 0.776076i | \(0.717207\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −1.50025 | −0.0511878 | −0.0255939 | − | 0.999672i | \(-0.508148\pi\) | ||||
−0.0255939 | + | 0.999672i | \(0.508148\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 2.05079 | 0.0698906 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −56.9789 | −1.93958 | −0.969792 | − | 0.243934i | \(-0.921562\pi\) | ||||
−0.969792 | + | 0.243934i | \(0.921562\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 26.5453 | 0.902569 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 27.7964 | 0.944015 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 16.7513 | 0.568249 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 23.9394 | 0.811154 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −2.73718 | −0.0926395 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −2.64974 | −0.0895775 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 21.4920 | 0.725733 | 0.362867 | − | 0.931841i | \(-0.381798\pi\) | ||||
0.362867 | + | 0.931841i | \(0.381798\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −8.62927 | −0.291058 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −28.3004 | −0.953466 | −0.476733 | − | 0.879048i | \(-0.658179\pi\) | ||||
−0.476733 | + | 0.879048i | \(0.658179\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −15.6629 | −0.527099 | −0.263549 | − | 0.964646i | \(-0.584893\pi\) | ||||
−0.263549 | + | 0.964646i | \(0.584893\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −10.9459 | −0.367942 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −21.5247 | −0.722728 | −0.361364 | − | 0.932425i | \(-0.617689\pi\) | ||||
−0.361364 | + | 0.932425i | \(0.617689\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 8.96239 | 0.300589 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −18.0713 | −0.605410 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −38.3390 | −1.28153 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −4.96239 | −0.165689 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −17.8858 | −0.596523 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 3.33056 | 0.110957 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −9.61213 | −0.319872 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −33.4939 | −1.11338 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 39.2243 | 1.30242 | 0.651210 | − | 0.758898i | \(-0.274262\pi\) | ||||
0.651210 | + | 0.758898i | \(0.274262\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0.111420 | 0.00369555 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −42.9029 | −1.42144 | −0.710718 | − | 0.703477i | \(-0.751630\pi\) | ||||
−0.710718 | + | 0.703477i | \(0.751630\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 2.07522 | 0.0686799 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −31.9445 | −1.05605 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −8.45088 | −0.279073 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −17.4215 | −0.574683 | −0.287341 | − | 0.957828i | \(-0.592771\pi\) | ||||
−0.287341 | + | 0.957828i | \(0.592771\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 24.4347 | 0.805150 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 19.8496 | 0.653356 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 63.6483 | 2.09274 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −1.14903 | −0.0377391 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 50.1740 | 1.64615 | 0.823077 | − | 0.567930i | \(-0.192255\pi\) | ||||
0.823077 | + | 0.567930i | \(0.192255\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 25.3561 | 0.830123 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −4.51899 | −0.147787 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −1.18569 | −0.0387347 | −0.0193674 | − | 0.999812i | \(-0.506165\pi\) | ||||
−0.0193674 | + | 0.999812i | \(0.506165\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −18.8832 | −0.616230 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −26.9962 | −0.880051 | −0.440026 | − | 0.897985i | \(-0.645031\pi\) | ||||
−0.440026 | + | 0.897985i | \(0.645031\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1.22425 | 0.0398672 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −17.5877 | −0.572128 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 41.7499 | 1.35669 | 0.678345 | − | 0.734744i | \(-0.262698\pi\) | ||||
0.678345 | + | 0.734744i | \(0.262698\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 35.6991 | 1.15884 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 19.1735 | 0.621742 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −15.6121 | −0.505726 | −0.252863 | − | 0.967502i | \(-0.581372\pi\) | ||||
−0.252863 | + | 0.967502i | \(0.581372\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −48.9380 | −1.58359 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −11.5369 | −0.372935 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 12.8872 | 0.416148 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 0.358971 | 0.0115797 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −2.41231 | −0.0777356 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −10.7659 | −0.346566 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −34.6107 | −1.11301 | −0.556503 | − | 0.830846i | \(-0.687857\pi\) | ||||
−0.556503 | + | 0.830846i | \(0.687857\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −25.7988 | −0.827922 | −0.413961 | − | 0.910295i | \(-0.635855\pi\) | ||||
−0.413961 | + | 0.910295i | \(0.635855\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −9.98778 | −0.320194 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −28.8119 | −0.922721 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 13.2487 | 0.423863 | 0.211932 | − | 0.977285i | \(-0.432025\pi\) | ||||
0.211932 | + | 0.977285i | \(0.432025\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 30.9986 | 0.990719 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 3.48612 | 0.111303 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −1.01126 | −0.0322543 | −0.0161272 | − | 0.999870i | \(-0.505134\pi\) | ||||
−0.0161272 | + | 0.999870i | \(0.505134\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −61.2262 | −1.95083 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −7.76845 | −0.247273 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −5.73813 | −0.182462 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −27.5778 | −0.876039 | −0.438019 | − | 0.898965i | \(-0.644320\pi\) | ||||
−0.438019 | + | 0.898965i | \(0.644320\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 19.8905 | 0.631206 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −6.32724 | −0.200587 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −3.40105 | −0.107712 | −0.0538561 | − | 0.998549i | \(-0.517151\pi\) | ||||
−0.0538561 | + | 0.998549i | \(0.517151\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 58.6516 | 1.85566 |
(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 | 1288.2.a.l.1.1 | ✓ | 3 | |
4.3 | odd | 2 | 2576.2.a.y.1.3 | 3 | |||
7.6 | odd | 2 | 9016.2.a.z.1.3 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1288.2.a.l.1.1 | ✓ | 3 | 1.1 | even | 1 | trivial | |
2576.2.a.y.1.3 | 3 | 4.3 | odd | 2 | |||
9016.2.a.z.1.3 | 3 | 7.6 | odd | 2 |