Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [9680,2,Mod(1,9680)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(9680, 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("9680.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 9680 = 2^{4} \cdot 5 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 9680.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: | \(77.2951891566\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.725.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} - 3x^{2} + x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 440) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-0.477260\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 9680.1 |
$q$-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 | ||||||||
\(3\) | −0.294963 | −0.170297 | −0.0851485 | − | 0.996368i | \(-0.527136\pi\) | ||||
−0.0851485 | + | 0.996368i | \(0.527136\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 4.39026 | 1.65936 | 0.829681 | − | 0.558238i | \(-0.188523\pi\) | ||||
0.829681 | + | 0.558238i | \(0.188523\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.91300 | −0.970999 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 5.96281 | 1.65379 | 0.826893 | − | 0.562359i | \(-0.190106\pi\) | ||||
0.826893 | + | 0.562359i | \(0.190106\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −0.294963 | −0.0761591 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1.66785 | −0.404513 | −0.202256 | − | 0.979333i | \(-0.564827\pi\) | ||||
−0.202256 | + | 0.979333i | \(0.564827\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −7.69351 | −1.76501 | −0.882506 | − | 0.470301i | \(-0.844145\pi\) | ||||
−0.882506 | + | 0.470301i | \(0.844145\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.29496 | −0.282584 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0.904706 | 0.188644 | 0.0943221 | − | 0.995542i | \(-0.469932\pi\) | ||||
0.0943221 | + | 0.995542i | \(0.469932\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.74411 | 0.335655 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −4.73899 | −0.880008 | −0.440004 | − | 0.897996i | \(-0.645023\pi\) | ||||
−0.440004 | + | 0.897996i | \(0.645023\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 5.12608 | 0.920671 | 0.460336 | − | 0.887745i | \(-0.347729\pi\) | ||||
0.460336 | + | 0.887745i | \(0.347729\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 4.39026 | 0.742089 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −0.184976 | −0.0304098 | −0.0152049 | − | 0.999884i | \(-0.504840\pi\) | ||||
−0.0152049 | + | 0.999884i | \(0.504840\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −1.75881 | −0.281635 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −2.62237 | −0.409545 | −0.204773 | − | 0.978810i | \(-0.565645\pi\) | ||||
−0.204773 | + | 0.978810i | \(0.565645\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −3.59822 | −0.548723 | −0.274361 | − | 0.961627i | \(-0.588466\pi\) | ||||
−0.274361 | + | 0.961627i | \(0.588466\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −2.91300 | −0.434244 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0.776180 | 0.113217 | 0.0566087 | − | 0.998396i | \(-0.481971\pi\) | ||||
0.0566087 | + | 0.998396i | \(0.481971\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 12.2744 | 1.75348 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0.491953 | 0.0688872 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −9.59554 | −1.31805 | −0.659024 | − | 0.752122i | \(-0.729031\pi\) | ||||
−0.659024 | + | 0.752122i | \(0.729031\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 2.26930 | 0.300576 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 11.2538 | 1.46512 | 0.732561 | − | 0.680701i | \(-0.238325\pi\) | ||||
0.732561 | + | 0.680701i | \(0.238325\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 13.1898 | 1.68878 | 0.844390 | − | 0.535729i | \(-0.179963\pi\) | ||||
0.844390 | + | 0.535729i | \(0.179963\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −12.7888 | −1.61124 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 5.96281 | 0.739596 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 7.79954 | 0.952866 | 0.476433 | − | 0.879211i | \(-0.341930\pi\) | ||||
0.476433 | + | 0.879211i | \(0.341930\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −0.266855 | −0.0321255 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 6.97072 | 0.827273 | 0.413636 | − | 0.910442i | \(-0.364258\pi\) | ||||
0.413636 | + | 0.910442i | \(0.364258\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 12.7541 | 1.49275 | 0.746375 | − | 0.665526i | \(-0.231793\pi\) | ||||
0.746375 | + | 0.665526i | \(0.231793\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −0.294963 | −0.0340594 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 10.0313 | 1.12861 | 0.564303 | − | 0.825568i | \(-0.309145\pi\) | ||||
0.564303 | + | 0.825568i | \(0.309145\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 8.22454 | 0.913838 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −4.09529 | −0.449517 | −0.224758 | − | 0.974415i | \(-0.572159\pi\) | ||||
−0.224758 | + | 0.974415i | \(0.572159\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.66785 | −0.180904 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 1.39783 | 0.149863 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −0.466291 | −0.0494267 | −0.0247134 | − | 0.999695i | \(-0.507867\pi\) | ||||
−0.0247134 | + | 0.999695i | \(0.507867\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 26.1783 | 2.74423 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −1.51200 | −0.156787 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −7.69351 | −0.789338 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 7.09963 | 0.720858 | 0.360429 | − | 0.932787i | \(-0.382630\pi\) | ||||
0.360429 | + | 0.932787i | \(0.382630\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −16.2851 | −1.62043 | −0.810214 | − | 0.586135i | \(-0.800649\pi\) | ||||
−0.810214 | + | 0.586135i | \(0.800649\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −3.19059 | −0.314378 | −0.157189 | − | 0.987569i | \(-0.550243\pi\) | ||||
−0.157189 | + | 0.987569i | \(0.550243\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −1.29496 | −0.126375 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 13.1644 | 1.27265 | 0.636324 | − | 0.771422i | \(-0.280454\pi\) | ||||
0.636324 | + | 0.771422i | \(0.280454\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1.33532 | 0.127900 | 0.0639502 | − | 0.997953i | \(-0.479630\pi\) | ||||
0.0639502 | + | 0.997953i | \(0.479630\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0.0545610 | 0.00517870 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −1.67448 | −0.157522 | −0.0787611 | − | 0.996894i | \(-0.525096\pi\) | ||||
−0.0787611 | + | 0.996894i | \(0.525096\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0.904706 | 0.0843643 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −17.3696 | −1.60582 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −7.32228 | −0.671232 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0.773501 | 0.0697443 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −0.901470 | −0.0799926 | −0.0399963 | − | 0.999200i | \(-0.512735\pi\) | ||||
−0.0399963 | + | 0.999200i | \(0.512735\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 1.06134 | 0.0934458 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 14.5527 | 1.27148 | 0.635739 | − | 0.771904i | \(-0.280695\pi\) | ||||
0.635739 | + | 0.771904i | \(0.280695\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −33.7765 | −2.92879 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 1.74411 | 0.150109 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −20.5895 | −1.75908 | −0.879540 | − | 0.475824i | \(-0.842150\pi\) | ||||
−0.879540 | + | 0.475824i | \(0.842150\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 14.9841 | 1.27094 | 0.635469 | − | 0.772126i | \(-0.280807\pi\) | ||||
0.635469 | + | 0.772126i | \(0.280807\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −0.228944 | −0.0192806 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −4.73899 | −0.393552 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −3.62048 | −0.298612 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 10.9626 | 0.898089 | 0.449045 | − | 0.893509i | \(-0.351764\pi\) | ||||
0.449045 | + | 0.893509i | \(0.351764\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 5.91172 | 0.481089 | 0.240544 | − | 0.970638i | \(-0.422674\pi\) | ||||
0.240544 | + | 0.970638i | \(0.422674\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 4.85844 | 0.392781 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 5.12608 | 0.411737 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −4.42628 | −0.353256 | −0.176628 | − | 0.984278i | \(-0.556519\pi\) | ||||
−0.176628 | + | 0.984278i | \(0.556519\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 2.83033 | 0.224460 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 3.97189 | 0.313029 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 7.38464 | 0.578410 | 0.289205 | − | 0.957267i | \(-0.406609\pi\) | ||||
0.289205 | + | 0.957267i | \(0.406609\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 19.4876 | 1.50799 | 0.753996 | − | 0.656879i | \(-0.228124\pi\) | ||||
0.753996 | + | 0.656879i | \(0.228124\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 22.5551 | 1.73501 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 22.4112 | 1.71383 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 9.50805 | 0.722883 | 0.361442 | − | 0.932395i | \(-0.382285\pi\) | ||||
0.361442 | + | 0.932395i | \(0.382285\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 4.39026 | 0.331872 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −3.31946 | −0.249506 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −7.21253 | −0.539090 | −0.269545 | − | 0.962988i | \(-0.586873\pi\) | ||||
−0.269545 | + | 0.962988i | \(0.586873\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −23.3895 | −1.73853 | −0.869263 | − | 0.494350i | \(-0.835406\pi\) | ||||
−0.869263 | + | 0.494350i | \(0.835406\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −3.89050 | −0.287594 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −0.184976 | −0.0135997 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 7.65711 | 0.556973 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 4.16572 | 0.301421 | 0.150710 | − | 0.988578i | \(-0.451844\pi\) | ||||
0.150710 | + | 0.988578i | \(0.451844\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −23.1660 | −1.66753 | −0.833763 | − | 0.552122i | \(-0.813818\pi\) | ||||
−0.833763 | + | 0.552122i | \(0.813818\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −1.75881 | −0.125951 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 10.1507 | 0.723209 | 0.361604 | − | 0.932332i | \(-0.382229\pi\) | ||||
0.361604 | + | 0.932332i | \(0.382229\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 17.0131 | 1.20603 | 0.603014 | − | 0.797731i | \(-0.293966\pi\) | ||||
0.603014 | + | 0.797731i | \(0.293966\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −2.30058 | −0.162270 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −20.8054 | −1.46025 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −2.62237 | −0.183154 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −2.63541 | −0.183173 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 6.01620 | 0.414173 | 0.207086 | − | 0.978323i | \(-0.433602\pi\) | ||||
0.207086 | + | 0.978323i | \(0.433602\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −2.05611 | −0.140882 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −3.59822 | −0.245396 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 22.5048 | 1.52773 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −3.76197 | −0.254211 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −9.94506 | −0.668977 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −2.49407 | −0.167016 | −0.0835078 | − | 0.996507i | \(-0.526612\pi\) | ||||
−0.0835078 | + | 0.996507i | \(0.526612\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −2.91300 | −0.194200 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 24.9953 | 1.65899 | 0.829497 | − | 0.558512i | \(-0.188627\pi\) | ||||
0.829497 | + | 0.558512i | \(0.188627\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −2.77082 | −0.183101 | −0.0915506 | − | 0.995800i | \(-0.529182\pi\) | ||||
−0.0915506 | + | 0.995800i | \(0.529182\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −9.60025 | −0.628933 | −0.314467 | − | 0.949269i | \(-0.601826\pi\) | ||||
−0.314467 | + | 0.949269i | \(0.601826\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0.776180 | 0.0506324 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −2.95885 | −0.192198 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −14.7692 | −0.955341 | −0.477671 | − | 0.878539i | \(-0.658519\pi\) | ||||
−0.477671 | + | 0.878539i | \(0.658519\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −10.4338 | −0.672099 | −0.336049 | − | 0.941844i | \(-0.609091\pi\) | ||||
−0.336049 | + | 0.941844i | \(0.609091\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −7.65828 | −0.491279 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 12.2744 | 0.784180 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −45.8749 | −2.91895 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 1.20796 | 0.0765513 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 6.73394 | 0.425042 | 0.212521 | − | 0.977156i | \(-0.431833\pi\) | ||||
0.212521 | + | 0.977156i | \(0.431833\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0.491953 | 0.0308073 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 7.74192 | 0.482928 | 0.241464 | − | 0.970410i | \(-0.422372\pi\) | ||||
0.241464 | + | 0.970410i | \(0.422372\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −0.812091 | −0.0504609 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 13.8047 | 0.854487 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −18.1618 | −1.11990 | −0.559952 | − | 0.828525i | \(-0.689181\pi\) | ||||
−0.559952 | + | 0.828525i | \(0.689181\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −9.59554 | −0.589449 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0.137538 | 0.00841721 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −10.7267 | −0.654021 | −0.327011 | − | 0.945021i | \(-0.606041\pi\) | ||||
−0.327011 | + | 0.945021i | \(0.606041\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 18.7875 | 1.14126 | 0.570630 | − | 0.821207i | \(-0.306699\pi\) | ||||
0.570630 | + | 0.821207i | \(0.306699\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −7.72162 | −0.467334 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 28.8467 | 1.73323 | 0.866614 | − | 0.498978i | \(-0.166291\pi\) | ||||
0.866614 | + | 0.498978i | \(0.166291\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −14.9323 | −0.893971 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 27.0542 | 1.61392 | 0.806959 | − | 0.590608i | \(-0.201112\pi\) | ||||
0.806959 | + | 0.590608i | \(0.201112\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −12.8731 | −0.765228 | −0.382614 | − | 0.923908i | \(-0.624976\pi\) | ||||
−0.382614 | + | 0.923908i | \(0.624976\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 2.26930 | 0.134422 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −11.5129 | −0.679583 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −14.2183 | −0.836370 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −2.09413 | −0.122760 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 5.88873 | 0.344024 | 0.172012 | − | 0.985095i | \(-0.444973\pi\) | ||||
0.172012 | + | 0.985095i | \(0.444973\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 11.2538 | 0.655223 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 5.39459 | 0.311977 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −15.7971 | −0.910529 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 4.80350 | 0.275954 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 13.1898 | 0.755246 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −6.85844 | −0.391432 | −0.195716 | − | 0.980661i | \(-0.562703\pi\) | ||||
−0.195716 | + | 0.980661i | \(0.562703\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0.941105 | 0.0535376 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 14.2693 | 0.809138 | 0.404569 | − | 0.914508i | \(-0.367422\pi\) | ||||
0.404569 | + | 0.914508i | \(0.367422\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 1.59973 | 0.0904220 | 0.0452110 | − | 0.998977i | \(-0.485604\pi\) | ||||
0.0452110 | + | 0.998977i | \(0.485604\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −12.7888 | −0.720568 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −30.8556 | −1.73302 | −0.866511 | − | 0.499158i | \(-0.833643\pi\) | ||||
−0.866511 | + | 0.499158i | \(0.833643\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −3.88300 | −0.216728 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 12.8316 | 0.713970 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 5.96281 | 0.330757 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −0.393870 | −0.0217810 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 3.40763 | 0.187869 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1.16816 | 0.0642079 | 0.0321040 | − | 0.999485i | \(-0.489779\pi\) | ||||
0.0321040 | + | 0.999485i | \(0.489779\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0.538833 | 0.0295279 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 7.79954 | 0.426134 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 14.0291 | 0.764212 | 0.382106 | − | 0.924119i | \(-0.375199\pi\) | ||||
0.382106 | + | 0.924119i | \(0.375199\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0.493910 | 0.0268255 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 23.1558 | 1.25029 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −0.266855 | −0.0143670 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −33.3514 | −1.79040 | −0.895198 | − | 0.445669i | \(-0.852966\pi\) | ||||
−0.895198 | + | 0.445669i | \(0.852966\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −35.3268 | −1.89100 | −0.945500 | − | 0.325623i | \(-0.894426\pi\) | ||||
−0.945500 | + | 0.325623i | \(0.894426\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 10.3998 | 0.555102 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 11.7558 | 0.625698 | 0.312849 | − | 0.949803i | \(-0.398717\pi\) | ||||
0.312849 | + | 0.949803i | \(0.398717\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 6.97072 | 0.369968 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 2.15980 | 0.114309 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 2.72101 | 0.143609 | 0.0718047 | − | 0.997419i | \(-0.477124\pi\) | ||||
0.0718047 | + | 0.997419i | \(0.477124\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 40.1901 | 2.11527 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 12.7541 | 0.667578 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −3.10358 | −0.162006 | −0.0810029 | − | 0.996714i | \(-0.525812\pi\) | ||||
−0.0810029 | + | 0.996714i | \(0.525812\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 7.63895 | 0.397668 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −42.1269 | −2.18712 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −27.4604 | −1.42185 | −0.710924 | − | 0.703269i | \(-0.751723\pi\) | ||||
−0.710924 | + | 0.703269i | \(0.751723\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −0.294963 | −0.0152318 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −28.2577 | −1.45535 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −13.9435 | −0.716229 | −0.358114 | − | 0.933678i | \(-0.616580\pi\) | ||||
−0.358114 | + | 0.933678i | \(0.616580\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0.265900 | 0.0136225 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −8.15608 | −0.416756 | −0.208378 | − | 0.978048i | \(-0.566818\pi\) | ||||
−0.208378 | + | 0.978048i | \(0.566818\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 10.4816 | 0.532809 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −3.10121 | −0.157237 | −0.0786187 | − | 0.996905i | \(-0.525051\pi\) | ||||
−0.0786187 | + | 0.996905i | \(0.525051\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1.50891 | −0.0763090 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −4.29252 | −0.216529 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 10.0313 | 0.504728 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 23.1546 | 1.16209 | 0.581047 | − | 0.813870i | \(-0.302643\pi\) | ||||
0.581047 | + | 0.813870i | \(0.302643\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 9.96281 | 0.498764 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −8.24375 | −0.411673 | −0.205837 | − | 0.978586i | \(-0.565992\pi\) | ||||
−0.205837 | + | 0.978586i | \(0.565992\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 30.5658 | 1.52259 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 8.22454 | 0.408681 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 2.18649 | 0.108115 | 0.0540574 | − | 0.998538i | \(-0.482785\pi\) | ||||
0.0540574 | + | 0.998538i | \(0.482785\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 6.07314 | 0.299566 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 49.4071 | 2.43117 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −4.09529 | −0.201030 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −4.41977 | −0.216437 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −10.7348 | −0.524429 | −0.262215 | − | 0.965010i | \(-0.584453\pi\) | ||||
−0.262215 | + | 0.965010i | \(0.584453\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 18.7885 | 0.915696 | 0.457848 | − | 0.889031i | \(-0.348620\pi\) | ||||
0.457848 | + | 0.889031i | \(0.348620\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −2.26101 | −0.109934 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −1.66785 | −0.0809025 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 57.9066 | 2.80230 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 8.97878 | 0.432493 | 0.216246 | − | 0.976339i | \(-0.430619\pi\) | ||||
0.216246 | + | 0.976339i | \(0.430619\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 31.5059 | 1.51408 | 0.757039 | − | 0.653370i | \(-0.226645\pi\) | ||||
0.757039 | + | 0.653370i | \(0.226645\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 1.39783 | 0.0670206 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −6.96037 | −0.332959 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −27.4750 | −1.31131 | −0.655655 | − | 0.755060i | \(-0.727607\pi\) | ||||
−0.655655 | + | 0.755060i | \(0.727607\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −35.7552 | −1.70263 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 30.1960 | 1.43466 | 0.717328 | − | 0.696736i | \(-0.245365\pi\) | ||||
0.717328 | + | 0.696736i | \(0.245365\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −0.466291 | −0.0221043 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −3.23355 | −0.152942 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −27.3820 | −1.29224 | −0.646118 | − | 0.763237i | \(-0.723609\pi\) | ||||
−0.646118 | + | 0.763237i | \(0.723609\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −1.74374 | −0.0819279 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 26.1783 | 1.22726 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 14.2884 | 0.668385 | 0.334193 | − | 0.942505i | \(-0.391536\pi\) | ||||
0.334193 | + | 0.942505i | \(0.391536\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −2.90892 | −0.135777 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 8.78738 | 0.409269 | 0.204635 | − | 0.978838i | \(-0.434399\pi\) | ||||
0.204635 | + | 0.978838i | \(0.434399\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 13.8394 | 0.643172 | 0.321586 | − | 0.946880i | \(-0.395784\pi\) | ||||
0.321586 | + | 0.946880i | \(0.395784\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −1.51200 | −0.0701175 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −24.8893 | −1.15174 | −0.575871 | − | 0.817541i | \(-0.695337\pi\) | ||||
−0.575871 | + | 0.817541i | \(0.695337\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 34.2420 | 1.58115 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 1.30559 | 0.0601583 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −7.69351 | −0.353002 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 27.9518 | 1.27982 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 28.5906 | 1.30634 | 0.653169 | − | 0.757212i | \(-0.273439\pi\) | ||||
0.653169 | + | 0.757212i | \(0.273439\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1.10297 | −0.0502913 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −1.17156 | −0.0533079 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 7.09963 | 0.322377 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −4.65371 | −0.210880 | −0.105440 | − | 0.994426i | \(-0.533625\pi\) | ||||
−0.105440 | + | 0.994426i | \(0.533625\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −2.17820 | −0.0985014 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −24.9360 | −1.12535 | −0.562673 | − | 0.826680i | \(-0.690227\pi\) | ||||
−0.562673 | + | 0.826680i | \(0.690227\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 7.90392 | 0.355974 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 30.6033 | 1.37274 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −15.3848 | −0.688719 | −0.344359 | − | 0.938838i | \(-0.611904\pi\) | ||||
−0.344359 | + | 0.938838i | \(0.611904\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −5.74810 | −0.256806 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 32.7511 | 1.46030 | 0.730149 | − | 0.683288i | \(-0.239451\pi\) | ||||
0.730149 | + | 0.683288i | \(0.239451\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −16.2851 | −0.724677 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −6.65292 | −0.295467 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 15.7017 | 0.695964 | 0.347982 | − | 0.937501i | \(-0.386867\pi\) | ||||
0.347982 | + | 0.937501i | \(0.386867\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 55.9936 | 2.47701 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −13.4184 | −0.592435 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −3.19059 | −0.140594 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −2.80452 | −0.123105 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −33.6243 | −1.47311 | −0.736553 | − | 0.676380i | \(-0.763548\pi\) | ||||
−0.736553 | + | 0.676380i | \(0.763548\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 22.9574 | 1.00386 | 0.501928 | − | 0.864910i | \(-0.332624\pi\) | ||||
0.501928 | + | 0.864910i | \(0.332624\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −1.29496 | −0.0565168 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −8.54952 | −0.372423 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −22.1815 | −0.964413 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −32.7823 | −1.42263 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −15.6367 | −0.677300 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 13.1644 | 0.569145 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 2.12743 | 0.0918053 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −18.7777 | −0.807314 | −0.403657 | − | 0.914910i | \(-0.632261\pi\) | ||||
−0.403657 | + | 0.914910i | \(0.632261\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 6.89902 | 0.296065 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 1.33532 | 0.0571988 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −19.2785 | −0.824291 | −0.412146 | − | 0.911118i | \(-0.635220\pi\) | ||||
−0.412146 | + | 0.911118i | \(0.635220\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −38.4218 | −1.63980 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 36.4595 | 1.55323 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 44.0399 | 1.87277 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0.0545610 | 0.00231598 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −17.9380 | −0.760057 | −0.380028 | − | 0.924975i | \(-0.624086\pi\) | ||||
−0.380028 | + | 0.924975i | \(0.624086\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −21.4555 | −0.907470 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 1.81288 | 0.0764038 | 0.0382019 | − | 0.999270i | \(-0.487837\pi\) | ||||
0.0382019 | + | 0.999270i | \(0.487837\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −1.67448 | −0.0704460 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 36.1079 | 1.51639 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 8.53549 | 0.357826 | 0.178913 | − | 0.983865i | \(-0.442742\pi\) | ||||
0.178913 | + | 0.983865i | \(0.442742\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 32.2491 | 1.34958 | 0.674792 | − | 0.738008i | \(-0.264233\pi\) | ||||
0.674792 | + | 0.738008i | \(0.264233\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −1.22873 | −0.0513310 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0.904706 | 0.0377288 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 29.9652 | 1.24747 | 0.623734 | − | 0.781637i | \(-0.285615\pi\) | ||||
0.623734 | + | 0.781637i | \(0.285615\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 6.83312 | 0.283975 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −17.9794 | −0.745911 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −17.3696 | −0.718147 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −9.80339 | −0.404629 | −0.202315 | − | 0.979321i | \(-0.564846\pi\) | ||||
−0.202315 | + | 0.979321i | \(0.564846\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −39.4376 | −1.62500 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −2.99409 | −0.123160 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 15.4666 | 0.635136 | 0.317568 | − | 0.948235i | \(-0.397134\pi\) | ||||
0.317568 | + | 0.948235i | \(0.397134\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −7.32228 | −0.300184 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −5.01824 | −0.205383 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 0.278191 | 0.0113666 | 0.00568328 | − | 0.999984i | \(-0.498191\pi\) | ||||
0.00568328 | + | 0.999984i | \(0.498191\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 30.0055 | 1.22395 | 0.611974 | − | 0.790878i | \(-0.290376\pi\) | ||||
0.611974 | + | 0.790878i | \(0.290376\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −22.7200 | −0.925232 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 22.2971 | 0.905011 | 0.452505 | − | 0.891762i | \(-0.350530\pi\) | ||||
0.452505 | + | 0.891762i | \(0.350530\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 6.13682 | 0.248676 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 4.62821 | 0.187237 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −28.3748 | −1.14605 | −0.573024 | − | 0.819539i | \(-0.694230\pi\) | ||||
−0.573024 | + | 0.819539i | \(0.694230\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0.773501 | 0.0311906 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −15.1603 | −0.610332 | −0.305166 | − | 0.952299i | \(-0.598712\pi\) | ||||
−0.305166 | + | 0.952299i | \(0.598712\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 29.5238 | 1.18666 | 0.593331 | − | 0.804959i | \(-0.297813\pi\) | ||||
0.593331 | + | 0.804959i | \(0.297813\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.57791 | 0.0633194 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −2.04714 | −0.0820167 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 0.308511 | 0.0123011 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 45.6894 | 1.81887 | 0.909433 | − | 0.415849i | \(-0.136516\pi\) | ||||
0.909433 | + | 0.415849i | \(0.136516\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −1.77456 | −0.0705323 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −0.901470 | −0.0357738 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 73.1897 | 2.89988 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −20.3057 | −0.803281 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 36.1151 | 1.42646 | 0.713231 | − | 0.700929i | \(-0.247231\pi\) | ||||
0.713231 | + | 0.700929i | \(0.247231\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 33.4972 | 1.32100 | 0.660500 | − | 0.750826i | \(-0.270344\pi\) | ||||
0.660500 | + | 0.750826i | \(0.270344\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 1.06134 | 0.0417902 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −39.2066 | −1.54137 | −0.770686 | − | 0.637215i | \(-0.780086\pi\) | ||||
−0.770686 | + | 0.637215i | \(0.780086\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −6.63808 | −0.260167 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 24.7595 | 0.968913 | 0.484456 | − | 0.874815i | \(-0.339017\pi\) | ||||
0.484456 | + | 0.874815i | \(0.339017\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 14.5527 | 0.568622 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −37.1525 | −1.44946 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −24.8813 | −0.969238 | −0.484619 | − | 0.874725i | \(-0.661042\pi\) | ||||
−0.484619 | + | 0.874725i | \(0.661042\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −5.94396 | −0.231193 | −0.115597 | − | 0.993296i | \(-0.536878\pi\) | ||||
−0.115597 | + | 0.993296i | \(0.536878\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 2.93342 | 0.113925 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −33.7765 | −1.30980 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −4.28739 | −0.166009 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0.735660 | 0.0284422 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 37.8500 | 1.45901 | 0.729505 | − | 0.683975i | \(-0.239750\pi\) | ||||
0.729505 | + | 0.683975i | \(0.239750\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 1.74411 | 0.0671310 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 0.190100 | 0.00730612 | 0.00365306 | − | 0.999993i | \(-0.498837\pi\) | ||||
0.00365306 | + | 0.999993i | \(0.498837\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 31.1692 | 1.19616 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −7.37267 | −0.282521 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −23.0773 | −0.883030 | −0.441515 | − | 0.897254i | \(-0.645559\pi\) | ||||
−0.441515 | + | 0.897254i | \(0.645559\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −20.5895 | −0.786685 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0.817290 | 0.0311816 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −57.2164 | −2.17977 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −46.7082 | −1.77686 | −0.888432 | − | 0.459008i | \(-0.848205\pi\) | ||||
−0.888432 | + | 0.459008i | \(0.848205\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 14.9841 | 0.568381 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 4.37371 | 0.165666 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 2.83172 | 0.107105 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 4.17239 | 0.157589 | 0.0787946 | − | 0.996891i | \(-0.474893\pi\) | ||||
0.0787946 | + | 0.996891i | \(0.474893\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1.42311 | 0.0536737 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −0.228944 | −0.00862254 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −71.4957 | −2.68887 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −8.74277 | −0.328342 | −0.164171 | − | 0.986432i | \(-0.552495\pi\) | ||||
−0.164171 | + | 0.986432i | \(0.552495\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −29.2211 | −1.09588 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 4.63760 | 0.173679 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 4.35637 | 0.162692 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 7.40160 | 0.276033 | 0.138017 | − | 0.990430i | \(-0.455927\pi\) | ||||
0.138017 | + | 0.990430i | \(0.455927\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −14.0075 | −0.521667 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 3.07758 | 0.114456 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −4.73899 | −0.176002 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −18.0187 | −0.668275 | −0.334137 | − | 0.942524i | \(-0.608445\pi\) | ||||
−0.334137 | + | 0.942524i | \(0.608445\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −22.4147 | −0.830175 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 6.00128 | 0.221965 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −36.3939 | −1.34424 | −0.672120 | − | 0.740442i | \(-0.734616\pi\) | ||||
−0.672120 | + | 0.740442i | \(0.734616\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −3.62048 | −0.133543 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 12.4319 | 0.457313 | 0.228657 | − | 0.973507i | \(-0.426567\pi\) | ||||
0.228657 | + | 0.973507i | \(0.426567\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 13.5314 | 0.497089 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −37.3696 | −1.37096 | −0.685479 | − | 0.728092i | \(-0.740407\pi\) | ||||
−0.685479 | + | 0.728092i | \(0.740407\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 10.9626 | 0.401638 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 11.9296 | 0.436480 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 57.7950 | 2.11178 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 7.89958 | 0.288260 | 0.144130 | − | 0.989559i | \(-0.453962\pi\) | ||||
0.144130 | + | 0.989559i | \(0.453962\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −1.98626 | −0.0723834 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 5.91172 | 0.215149 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −3.17036 | −0.115229 | −0.0576143 | − | 0.998339i | \(-0.518349\pi\) | ||||
−0.0576143 | + | 0.998339i | \(0.518349\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 46.7689 | 1.69537 | 0.847685 | − | 0.530499i | \(-0.177996\pi\) | ||||
0.847685 | + | 0.530499i | \(0.177996\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 5.86239 | 0.212233 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 4.85844 | 0.175657 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 67.1044 | 2.42300 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −1.95610 | −0.0705388 | −0.0352694 | − | 0.999378i | \(-0.511229\pi\) | ||||
−0.0352694 | + | 0.999378i | \(0.511229\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −2.28358 | −0.0822411 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −20.4428 | −0.735277 | −0.367639 | − | 0.929969i | \(-0.619834\pi\) | ||||
−0.367639 | + | 0.929969i | \(0.619834\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 5.12608 | 0.184134 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0.239537 | 0.00859333 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 20.1752 | 0.722852 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −8.26534 | −0.295379 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −4.42628 | −0.157981 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 2.59196 | 0.0923933 | 0.0461967 | − | 0.998932i | \(-0.485290\pi\) | ||||
0.0461967 | + | 0.998932i | \(0.485290\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 5.35706 | 0.190716 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −7.35141 | −0.261386 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 78.6483 | 2.79288 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 2.83033 | 0.100381 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 22.3867 | 0.792977 | 0.396488 | − | 0.918040i | \(-0.370229\pi\) | ||||
0.396488 | + | 0.918040i | \(0.370229\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −1.29455 | −0.0457979 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 1.35830 | 0.0479933 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 3.97189 | 0.139991 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 3.16399 | 0.111378 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 11.9561 | 0.420354 | 0.210177 | − | 0.977663i | \(-0.432596\pi\) | ||||
0.210177 | + | 0.977663i | \(0.432596\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −18.4696 | −0.648554 | −0.324277 | − | 0.945962i | \(-0.605121\pi\) | ||||
−0.324277 | + | 0.945962i | \(0.605121\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −5.54162 | −0.194353 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 7.38464 | 0.258673 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 27.6829 | 0.968503 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −76.2572 | −2.66464 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 55.4734 | 1.93604 | 0.968018 | − | 0.250881i | \(-0.0807201\pi\) | ||||
0.968018 | + | 0.250881i | \(0.0807201\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −43.7133 | −1.52375 | −0.761874 | − | 0.647725i | \(-0.775721\pi\) | ||||
−0.761874 | + | 0.647725i | \(0.775721\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −31.7396 | −1.10369 | −0.551846 | − | 0.833946i | \(-0.686076\pi\) | ||||
−0.551846 | + | 0.833946i | \(0.686076\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −35.0302 | −1.21665 | −0.608325 | − | 0.793688i | \(-0.708158\pi\) | ||||
−0.608325 | + | 0.793688i | \(0.708158\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −8.50870 | −0.295164 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −20.4718 | −0.709304 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 19.4876 | 0.674394 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 8.94047 | 0.309028 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 15.8542 | 0.547349 | 0.273674 | − | 0.961822i | \(-0.411761\pi\) | ||||
0.273674 | + | 0.961822i | \(0.411761\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −6.54197 | −0.225585 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −7.97998 | −0.274845 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 22.5551 | 0.775919 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 3.79710 | 0.130316 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −0.167349 | −0.00573664 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −22.5865 | −0.773346 | −0.386673 | − | 0.922217i | \(-0.626376\pi\) | ||||
−0.386673 | + | 0.922217i | \(0.626376\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 22.4112 | 0.766446 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 40.9108 | 1.39749 | 0.698744 | − | 0.715372i | \(-0.253743\pi\) | ||||
0.698744 | + | 0.715372i | \(0.253743\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −15.9523 | −0.544284 | −0.272142 | − | 0.962257i | \(-0.587732\pi\) | ||||
−0.272142 | + | 0.962257i | \(0.587732\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 3.39587 | 0.115731 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −7.28894 | −0.248118 | −0.124059 | − | 0.992275i | \(-0.539591\pi\) | ||||
−0.124059 | + | 0.992275i | \(0.539591\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 9.50805 | 0.323283 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 4.19387 | 0.142431 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 46.5072 | 1.57584 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −20.6812 | −0.699952 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 4.39026 | 0.148418 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 7.14718 | 0.241343 | 0.120671 | − | 0.992692i | \(-0.461495\pi\) | ||||
0.120671 | + | 0.992692i | \(0.461495\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −1.73696 | −0.0585861 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −17.5763 | −0.592160 | −0.296080 | − | 0.955163i | \(-0.595680\pi\) | ||||
−0.296080 | + | 0.955163i | \(0.595680\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 6.26855 | 0.210954 | 0.105477 | − | 0.994422i | \(-0.466363\pi\) | ||||
0.105477 | + | 0.994422i | \(0.466363\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −3.31946 | −0.111582 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 24.6894 | 0.828989 | 0.414495 | − | 0.910052i | \(-0.363958\pi\) | ||||
0.414495 | + | 0.910052i | \(0.363958\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −3.95769 | −0.132737 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −5.97155 | −0.199830 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −7.21253 | −0.241088 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −1.59120 | −0.0531288 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −24.2924 | −0.810199 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 16.0039 | 0.533167 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 4.65956 | 0.155060 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −23.3895 | −0.777492 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −25.4380 | −0.844655 | −0.422327 | − | 0.906443i | \(-0.638787\pi\) | ||||
−0.422327 | + | 0.906443i | \(0.638787\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 47.4384 | 1.57343 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 24.5296 | 0.812701 | 0.406350 | − | 0.913717i | \(-0.366801\pi\) | ||||
0.406350 | + | 0.913717i | \(0.366801\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −3.89050 | −0.128616 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 63.8903 | 2.10984 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −21.2250 | −0.700148 | −0.350074 | − | 0.936722i | \(-0.613844\pi\) | ||||
−0.350074 | + | 0.936722i | \(0.613844\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 2.02298 | 0.0666596 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 41.5651 | 1.36813 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −0.184976 | −0.00608196 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 9.29417 | 0.305261 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 34.2535 | 1.12382 | 0.561910 | − | 0.827198i | \(-0.310067\pi\) | ||||
0.561910 | + | 0.827198i | \(0.310067\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −94.4329 | −3.09491 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −4.20891 | −0.137794 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 34.9322 | 1.14119 | 0.570593 | − | 0.821233i | \(-0.306713\pi\) | ||||
0.570593 | + | 0.821233i | \(0.306713\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −0.471860 | −0.0153986 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −18.7014 | −0.609649 | −0.304825 | − | 0.952409i | \(-0.598598\pi\) | ||||
−0.304825 | + | 0.952409i | \(0.598598\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −2.37247 | −0.0772583 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 7.65711 | 0.249086 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −12.7418 | −0.414052 | −0.207026 | − | 0.978335i | \(-0.566379\pi\) | ||||
−0.207026 | + | 0.978335i | \(0.566379\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 76.0501 | 2.46869 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 9.10125 | 0.295128 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 5.77686 | 0.187131 | 0.0935654 | − | 0.995613i | \(-0.470174\pi\) | ||||
0.0935654 | + | 0.995613i | \(0.470174\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 4.16572 | 0.134799 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −90.3933 | −2.91895 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −4.72330 | −0.152364 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −38.3478 | −1.23574 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −23.1660 | −0.745741 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 36.2900 | 1.16701 | 0.583504 | − | 0.812110i | \(-0.301681\pi\) | ||||
0.583504 | + | 0.812110i | \(0.301681\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −3.78485 | −0.121587 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 6.98883 | 0.224282 | 0.112141 | − | 0.993692i | \(-0.464229\pi\) | ||||
0.112141 | + | 0.993692i | \(0.464229\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 65.7842 | 2.10895 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −1.75881 | −0.0563269 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 25.9994 | 0.831795 | 0.415897 | − | 0.909412i | \(-0.363468\pi\) | ||||
0.415897 | + | 0.909412i | \(0.363468\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −3.88978 | −0.124191 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −28.6461 | −0.913669 | −0.456834 | − | 0.889552i | \(-0.651017\pi\) | ||||
−0.456834 | + | 0.889552i | \(0.651017\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 10.1507 | 0.323429 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −1.00512 | −0.0319935 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −3.25533 | −0.103513 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −27.9673 | −0.888409 | −0.444205 | − | 0.895925i | \(-0.646514\pi\) | ||||
−0.444205 | + | 0.895925i | \(0.646514\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −0.344564 | −0.0109344 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 17.0131 | 0.539352 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 13.0579 | 0.413547 | 0.206773 | − | 0.978389i | \(-0.433704\pi\) | ||||
0.206773 | + | 0.978389i | \(0.433704\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −0.322619 | −0.0102072 |
(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 | 9680.2.a.cu.1.2 | 4 | ||
4.3 | odd | 2 | 4840.2.a.y.1.3 | 4 | |||
11.5 | even | 5 | 880.2.bo.d.641.1 | 8 | |||
11.9 | even | 5 | 880.2.bo.d.81.1 | 8 | |||
11.10 | odd | 2 | 9680.2.a.ct.1.2 | 4 | |||
44.27 | odd | 10 | 440.2.y.a.201.2 | yes | 8 | ||
44.31 | odd | 10 | 440.2.y.a.81.2 | ✓ | 8 | ||
44.43 | even | 2 | 4840.2.a.z.1.3 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
440.2.y.a.81.2 | ✓ | 8 | 44.31 | odd | 10 | ||
440.2.y.a.201.2 | yes | 8 | 44.27 | odd | 10 | ||
880.2.bo.d.81.1 | 8 | 11.9 | even | 5 | |||
880.2.bo.d.641.1 | 8 | 11.5 | even | 5 | |||
4840.2.a.y.1.3 | 4 | 4.3 | odd | 2 | |||
4840.2.a.z.1.3 | 4 | 44.43 | even | 2 | |||
9680.2.a.ct.1.2 | 4 | 11.10 | odd | 2 | |||
9680.2.a.cu.1.2 | 4 | 1.1 | even | 1 | trivial |