Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4014,2,Mod(1,4014)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4014, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4014.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4014 = 2 \cdot 3^{2} \cdot 223 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4014.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: | \(32.0519513713\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | 6.6.103354048.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 2x^{5} - 8x^{4} + 14x^{3} + 13x^{2} - 16x + 3 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(0.605879\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4014.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −2.63291 | −1.17747 | −0.588737 | − | 0.808325i | \(-0.700375\pi\) | ||||
−0.588737 | + | 0.808325i | \(0.700375\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.24656 | −0.849118 | −0.424559 | − | 0.905400i | \(-0.639571\pi\) | ||||
−0.424559 | + | 0.905400i | \(0.639571\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −2.63291 | −0.832600 | ||||||||
\(11\) | −4.09429 | −1.23447 | −0.617237 | − | 0.786777i | \(-0.711748\pi\) | ||||
−0.617237 | + | 0.786777i | \(0.711748\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.00776648 | 0.00215403 | 0.00107702 | − | 0.999999i | \(-0.499657\pi\) | ||||
0.00107702 | + | 0.999999i | \(0.499657\pi\) | |||||||
\(14\) | −2.24656 | −0.600417 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 0.673658 | 0.163386 | 0.0816931 | − | 0.996658i | \(-0.473967\pi\) | ||||
0.0816931 | + | 0.996658i | \(0.473967\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −3.57290 | −0.819679 | −0.409839 | − | 0.912158i | \(-0.634415\pi\) | ||||
−0.409839 | + | 0.912158i | \(0.634415\pi\) | |||||||
\(20\) | −2.63291 | −0.588737 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −4.09429 | −0.872905 | ||||||||
\(23\) | 3.39412 | 0.707723 | 0.353862 | − | 0.935298i | \(-0.384868\pi\) | ||||
0.353862 | + | 0.935298i | \(0.384868\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.93222 | 0.386444 | ||||||||
\(26\) | 0.00776648 | 0.00152313 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −2.24656 | −0.424559 | ||||||||
\(29\) | 8.00809 | 1.48706 | 0.743532 | − | 0.668700i | \(-0.233149\pi\) | ||||
0.743532 | + | 0.668700i | \(0.233149\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −6.93425 | −1.24543 | −0.622714 | − | 0.782450i | \(-0.713970\pi\) | ||||
−0.622714 | + | 0.782450i | \(0.713970\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0.673658 | 0.115531 | ||||||||
\(35\) | 5.91498 | 0.999815 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0.651332 | 0.107078 | 0.0535391 | − | 0.998566i | \(-0.482950\pi\) | ||||
0.0535391 | + | 0.998566i | \(0.482950\pi\) | |||||||
\(38\) | −3.57290 | −0.579601 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −2.63291 | −0.416300 | ||||||||
\(41\) | 4.43181 | 0.692132 | 0.346066 | − | 0.938210i | \(-0.387517\pi\) | ||||
0.346066 | + | 0.938210i | \(0.387517\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 9.59164 | 1.46271 | 0.731355 | − | 0.681996i | \(-0.238888\pi\) | ||||
0.731355 | + | 0.681996i | \(0.238888\pi\) | |||||||
\(44\) | −4.09429 | −0.617237 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 3.39412 | 0.500436 | ||||||||
\(47\) | 10.6264 | 1.55003 | 0.775013 | − | 0.631946i | \(-0.217744\pi\) | ||||
0.775013 | + | 0.631946i | \(0.217744\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.95299 | −0.278998 | ||||||||
\(50\) | 1.93222 | 0.273257 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0.00776648 | 0.00107702 | ||||||||
\(53\) | 4.64357 | 0.637843 | 0.318921 | − | 0.947781i | \(-0.396679\pi\) | ||||
0.318921 | + | 0.947781i | \(0.396679\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 10.7799 | 1.45356 | ||||||||
\(56\) | −2.24656 | −0.300209 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 8.00809 | 1.05151 | ||||||||
\(59\) | 7.95351 | 1.03546 | 0.517730 | − | 0.855544i | \(-0.326777\pi\) | ||||
0.517730 | + | 0.855544i | \(0.326777\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −11.0517 | −1.41502 | −0.707510 | − | 0.706703i | \(-0.750182\pi\) | ||||
−0.707510 | + | 0.706703i | \(0.750182\pi\) | |||||||
\(62\) | −6.93425 | −0.880650 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −0.0204485 | −0.00253632 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 15.2010 | 1.85710 | 0.928551 | − | 0.371204i | \(-0.121055\pi\) | ||||
0.928551 | + | 0.371204i | \(0.121055\pi\) | |||||||
\(68\) | 0.673658 | 0.0816931 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 5.91498 | 0.706976 | ||||||||
\(71\) | −9.64824 | −1.14504 | −0.572518 | − | 0.819892i | \(-0.694033\pi\) | ||||
−0.572518 | + | 0.819892i | \(0.694033\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 0.995761 | 0.116545 | 0.0582725 | − | 0.998301i | \(-0.481441\pi\) | ||||
0.0582725 | + | 0.998301i | \(0.481441\pi\) | |||||||
\(74\) | 0.651332 | 0.0757157 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −3.57290 | −0.409839 | ||||||||
\(77\) | 9.19804 | 1.04821 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1.27648 | −0.143615 | −0.0718074 | − | 0.997419i | \(-0.522877\pi\) | ||||
−0.0718074 | + | 0.997419i | \(0.522877\pi\) | |||||||
\(80\) | −2.63291 | −0.294368 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 4.43181 | 0.489411 | ||||||||
\(83\) | 5.75391 | 0.631574 | 0.315787 | − | 0.948830i | \(-0.397732\pi\) | ||||
0.315787 | + | 0.948830i | \(0.397732\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.77368 | −0.192383 | ||||||||
\(86\) | 9.59164 | 1.03429 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −4.09429 | −0.436452 | ||||||||
\(89\) | −2.07485 | −0.219933 | −0.109967 | − | 0.993935i | \(-0.535074\pi\) | ||||
−0.109967 | + | 0.993935i | \(0.535074\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −0.0174478 | −0.00182903 | ||||||||
\(92\) | 3.39412 | 0.353862 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 10.6264 | 1.09603 | ||||||||
\(95\) | 9.40712 | 0.965150 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −17.5825 | −1.78523 | −0.892615 | − | 0.450819i | \(-0.851132\pi\) | ||||
−0.892615 | + | 0.450819i | \(0.851132\pi\) | |||||||
\(98\) | −1.95299 | −0.197281 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 1.93222 | 0.193222 | ||||||||
\(101\) | −8.56611 | −0.852359 | −0.426180 | − | 0.904639i | \(-0.640141\pi\) | ||||
−0.426180 | + | 0.904639i | \(0.640141\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 19.9320 | 1.96396 | 0.981978 | − | 0.188996i | \(-0.0605234\pi\) | ||||
0.981978 | + | 0.188996i | \(0.0605234\pi\) | |||||||
\(104\) | 0.00776648 | 0.000761566 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 4.64357 | 0.451023 | ||||||||
\(107\) | 13.1728 | 1.27347 | 0.636733 | − | 0.771085i | \(-0.280285\pi\) | ||||
0.636733 | + | 0.771085i | \(0.280285\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −5.10676 | −0.489139 | −0.244569 | − | 0.969632i | \(-0.578647\pi\) | ||||
−0.244569 | + | 0.969632i | \(0.578647\pi\) | |||||||
\(110\) | 10.7799 | 1.02782 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −2.24656 | −0.212280 | ||||||||
\(113\) | 15.5553 | 1.46332 | 0.731659 | − | 0.681671i | \(-0.238746\pi\) | ||||
0.731659 | + | 0.681671i | \(0.238746\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −8.93642 | −0.833325 | ||||||||
\(116\) | 8.00809 | 0.743532 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 7.95351 | 0.732180 | ||||||||
\(119\) | −1.51341 | −0.138734 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 5.76317 | 0.523925 | ||||||||
\(122\) | −11.0517 | −1.00057 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −6.93425 | −0.622714 | ||||||||
\(125\) | 8.07719 | 0.722446 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 15.4106 | 1.36747 | 0.683737 | − | 0.729729i | \(-0.260354\pi\) | ||||
0.683737 | + | 0.729729i | \(0.260354\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −0.0204485 | −0.00179345 | ||||||||
\(131\) | −21.0190 | −1.83644 | −0.918219 | − | 0.396073i | \(-0.870373\pi\) | ||||
−0.918219 | + | 0.396073i | \(0.870373\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 8.02672 | 0.696005 | ||||||||
\(134\) | 15.2010 | 1.31317 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0.673658 | 0.0577657 | ||||||||
\(137\) | 12.5823 | 1.07498 | 0.537490 | − | 0.843270i | \(-0.319373\pi\) | ||||
0.537490 | + | 0.843270i | \(0.319373\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −9.51306 | −0.806887 | −0.403444 | − | 0.915004i | \(-0.632187\pi\) | ||||
−0.403444 | + | 0.915004i | \(0.632187\pi\) | |||||||
\(140\) | 5.91498 | 0.499907 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −9.64824 | −0.809662 | ||||||||
\(143\) | −0.0317982 | −0.00265910 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −21.0846 | −1.75098 | ||||||||
\(146\) | 0.995761 | 0.0824097 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0.651332 | 0.0535391 | ||||||||
\(149\) | −2.73070 | −0.223708 | −0.111854 | − | 0.993725i | \(-0.535679\pi\) | ||||
−0.111854 | + | 0.993725i | \(0.535679\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 7.96037 | 0.647806 | 0.323903 | − | 0.946090i | \(-0.395005\pi\) | ||||
0.323903 | + | 0.946090i | \(0.395005\pi\) | |||||||
\(152\) | −3.57290 | −0.289800 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 9.19804 | 0.741199 | ||||||||
\(155\) | 18.2573 | 1.46646 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 12.4903 | 0.996831 | 0.498416 | − | 0.866938i | \(-0.333915\pi\) | ||||
0.498416 | + | 0.866938i | \(0.333915\pi\) | |||||||
\(158\) | −1.27648 | −0.101551 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −2.63291 | −0.208150 | ||||||||
\(161\) | −7.62508 | −0.600941 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −6.27007 | −0.491109 | −0.245555 | − | 0.969383i | \(-0.578970\pi\) | ||||
−0.245555 | + | 0.969383i | \(0.578970\pi\) | |||||||
\(164\) | 4.43181 | 0.346066 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 5.75391 | 0.446590 | ||||||||
\(167\) | 2.90654 | 0.224915 | 0.112458 | − | 0.993657i | \(-0.464128\pi\) | ||||
0.112458 | + | 0.993657i | \(0.464128\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.9999 | −0.999995 | ||||||||
\(170\) | −1.77368 | −0.136035 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 9.59164 | 0.731355 | ||||||||
\(173\) | −9.28984 | −0.706293 | −0.353147 | − | 0.935568i | \(-0.614888\pi\) | ||||
−0.353147 | + | 0.935568i | \(0.614888\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −4.34084 | −0.328137 | ||||||||
\(176\) | −4.09429 | −0.308618 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −2.07485 | −0.155516 | ||||||||
\(179\) | 21.1054 | 1.57749 | 0.788745 | − | 0.614721i | \(-0.210731\pi\) | ||||
0.788745 | + | 0.614721i | \(0.210731\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 0.543334 | 0.0403857 | 0.0201928 | − | 0.999796i | \(-0.493572\pi\) | ||||
0.0201928 | + | 0.999796i | \(0.493572\pi\) | |||||||
\(182\) | −0.0174478 | −0.00129332 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 3.39412 | 0.250218 | ||||||||
\(185\) | −1.71490 | −0.126082 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −2.75815 | −0.201696 | ||||||||
\(188\) | 10.6264 | 0.775013 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 9.40712 | 0.682464 | ||||||||
\(191\) | 14.0400 | 1.01590 | 0.507950 | − | 0.861387i | \(-0.330404\pi\) | ||||
0.507950 | + | 0.861387i | \(0.330404\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −9.77786 | −0.703826 | −0.351913 | − | 0.936033i | \(-0.614469\pi\) | ||||
−0.351913 | + | 0.936033i | \(0.614469\pi\) | |||||||
\(194\) | −17.5825 | −1.26235 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −1.95299 | −0.139499 | ||||||||
\(197\) | −14.5046 | −1.03341 | −0.516705 | − | 0.856163i | \(-0.672842\pi\) | ||||
−0.516705 | + | 0.856163i | \(0.672842\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 22.6203 | 1.60351 | 0.801755 | − | 0.597653i | \(-0.203900\pi\) | ||||
0.801755 | + | 0.597653i | \(0.203900\pi\) | |||||||
\(200\) | 1.93222 | 0.136629 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −8.56611 | −0.602709 | ||||||||
\(203\) | −17.9906 | −1.26269 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −11.6686 | −0.814967 | ||||||||
\(206\) | 19.9320 | 1.38873 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0.00776648 | 0.000538508 0 | ||||||||
\(209\) | 14.6285 | 1.01187 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −10.0332 | −0.690715 | −0.345358 | − | 0.938471i | \(-0.612242\pi\) | ||||
−0.345358 | + | 0.938471i | \(0.612242\pi\) | |||||||
\(212\) | 4.64357 | 0.318921 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 13.1728 | 0.900476 | ||||||||
\(215\) | −25.2539 | −1.72230 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 15.5782 | 1.05752 | ||||||||
\(218\) | −5.10676 | −0.345873 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 10.7799 | 0.726780 | ||||||||
\(221\) | 0.00523195 | 0.000351939 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1.00000 | −0.0669650 | ||||||||
\(224\) | −2.24656 | −0.150104 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 15.5553 | 1.03472 | ||||||||
\(227\) | −20.8914 | −1.38661 | −0.693305 | − | 0.720645i | \(-0.743846\pi\) | ||||
−0.693305 | + | 0.720645i | \(0.743846\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 20.5829 | 1.36015 | 0.680077 | − | 0.733141i | \(-0.261946\pi\) | ||||
0.680077 | + | 0.733141i | \(0.261946\pi\) | |||||||
\(230\) | −8.93642 | −0.589250 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 8.00809 | 0.525757 | ||||||||
\(233\) | 9.41577 | 0.616848 | 0.308424 | − | 0.951249i | \(-0.400198\pi\) | ||||
0.308424 | + | 0.951249i | \(0.400198\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −27.9785 | −1.82511 | ||||||||
\(236\) | 7.95351 | 0.517730 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −1.51341 | −0.0980999 | ||||||||
\(239\) | −14.6538 | −0.947877 | −0.473939 | − | 0.880558i | \(-0.657168\pi\) | ||||
−0.473939 | + | 0.880558i | \(0.657168\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 17.1216 | 1.10290 | 0.551448 | − | 0.834209i | \(-0.314075\pi\) | ||||
0.551448 | + | 0.834209i | \(0.314075\pi\) | |||||||
\(242\) | 5.76317 | 0.370471 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −11.0517 | −0.707510 | ||||||||
\(245\) | 5.14204 | 0.328513 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −0.0277488 | −0.00176562 | ||||||||
\(248\) | −6.93425 | −0.440325 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 8.07719 | 0.510846 | ||||||||
\(251\) | 22.7295 | 1.43467 | 0.717337 | − | 0.696727i | \(-0.245361\pi\) | ||||
0.717337 | + | 0.696727i | \(0.245361\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −13.8965 | −0.873666 | ||||||||
\(254\) | 15.4106 | 0.966950 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −7.48452 | −0.466872 | −0.233436 | − | 0.972372i | \(-0.574997\pi\) | ||||
−0.233436 | + | 0.972372i | \(0.574997\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1.46325 | −0.0909221 | ||||||||
\(260\) | −0.0204485 | −0.00126816 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −21.0190 | −1.29856 | ||||||||
\(263\) | −7.82448 | −0.482478 | −0.241239 | − | 0.970466i | \(-0.577554\pi\) | ||||
−0.241239 | + | 0.970466i | \(0.577554\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −12.2261 | −0.751043 | ||||||||
\(266\) | 8.02672 | 0.492150 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 15.2010 | 0.928551 | ||||||||
\(269\) | 31.3794 | 1.91324 | 0.956619 | − | 0.291342i | \(-0.0941016\pi\) | ||||
0.956619 | + | 0.291342i | \(0.0941016\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1.63798 | −0.0995000 | −0.0497500 | − | 0.998762i | \(-0.515842\pi\) | ||||
−0.0497500 | + | 0.998762i | \(0.515842\pi\) | |||||||
\(272\) | 0.673658 | 0.0408465 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 12.5823 | 0.760125 | ||||||||
\(275\) | −7.91106 | −0.477055 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 8.78445 | 0.527806 | 0.263903 | − | 0.964549i | \(-0.414990\pi\) | ||||
0.263903 | + | 0.964549i | \(0.414990\pi\) | |||||||
\(278\) | −9.51306 | −0.570555 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 5.91498 | 0.353488 | ||||||||
\(281\) | −13.1236 | −0.782887 | −0.391444 | − | 0.920202i | \(-0.628024\pi\) | ||||
−0.391444 | + | 0.920202i | \(0.628024\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 21.8961 | 1.30159 | 0.650795 | − | 0.759253i | \(-0.274436\pi\) | ||||
0.650795 | + | 0.759253i | \(0.274436\pi\) | |||||||
\(284\) | −9.64824 | −0.572518 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −0.0317982 | −0.00188027 | ||||||||
\(287\) | −9.95630 | −0.587702 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.5462 | −0.973305 | ||||||||
\(290\) | −21.0846 | −1.23813 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0.995761 | 0.0582725 | ||||||||
\(293\) | −15.4295 | −0.901402 | −0.450701 | − | 0.892675i | \(-0.648826\pi\) | ||||
−0.450701 | + | 0.892675i | \(0.648826\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −20.9409 | −1.21923 | ||||||||
\(296\) | 0.651332 | 0.0378579 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −2.73070 | −0.158185 | ||||||||
\(299\) | 0.0263604 | 0.00152446 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −21.5482 | −1.24201 | ||||||||
\(302\) | 7.96037 | 0.458068 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −3.57290 | −0.204920 | ||||||||
\(305\) | 29.0980 | 1.66615 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −18.6854 | −1.06643 | −0.533216 | − | 0.845979i | \(-0.679017\pi\) | ||||
−0.533216 | + | 0.845979i | \(0.679017\pi\) | |||||||
\(308\) | 9.19804 | 0.524107 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 18.2573 | 1.03694 | ||||||||
\(311\) | 21.9347 | 1.24380 | 0.621902 | − | 0.783095i | \(-0.286360\pi\) | ||||
0.621902 | + | 0.783095i | \(0.286360\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −5.51529 | −0.311743 | −0.155871 | − | 0.987777i | \(-0.549819\pi\) | ||||
−0.155871 | + | 0.987777i | \(0.549819\pi\) | |||||||
\(314\) | 12.4903 | 0.704866 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −1.27648 | −0.0718074 | ||||||||
\(317\) | 10.2843 | 0.577622 | 0.288811 | − | 0.957386i | \(-0.406740\pi\) | ||||
0.288811 | + | 0.957386i | \(0.406740\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −32.7874 | −1.83574 | ||||||||
\(320\) | −2.63291 | −0.147184 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −7.62508 | −0.424929 | ||||||||
\(323\) | −2.40691 | −0.133924 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0.0150066 | 0.000832414 0 | ||||||||
\(326\) | −6.27007 | −0.347267 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 4.43181 | 0.244706 | ||||||||
\(329\) | −23.8729 | −1.31615 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −23.9394 | −1.31583 | −0.657913 | − | 0.753094i | \(-0.728561\pi\) | ||||
−0.657913 | + | 0.753094i | \(0.728561\pi\) | |||||||
\(332\) | 5.75391 | 0.315787 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 2.90654 | 0.159039 | ||||||||
\(335\) | −40.0230 | −2.18669 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 4.45595 | 0.242731 | 0.121366 | − | 0.992608i | \(-0.461273\pi\) | ||||
0.121366 | + | 0.992608i | \(0.461273\pi\) | |||||||
\(338\) | −12.9999 | −0.707104 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −1.77368 | −0.0961914 | ||||||||
\(341\) | 28.3908 | 1.53745 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 20.1134 | 1.08602 | ||||||||
\(344\) | 9.59164 | 0.517146 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −9.28984 | −0.499425 | ||||||||
\(347\) | 30.7768 | 1.65219 | 0.826093 | − | 0.563534i | \(-0.190558\pi\) | ||||
0.826093 | + | 0.563534i | \(0.190558\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 10.6268 | 0.568837 | 0.284419 | − | 0.958700i | \(-0.408199\pi\) | ||||
0.284419 | + | 0.958700i | \(0.408199\pi\) | |||||||
\(350\) | −4.34084 | −0.232028 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −4.09429 | −0.218226 | ||||||||
\(353\) | −23.9565 | −1.27508 | −0.637538 | − | 0.770419i | \(-0.720047\pi\) | ||||
−0.637538 | + | 0.770419i | \(0.720047\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 25.4029 | 1.34825 | ||||||||
\(356\) | −2.07485 | −0.109967 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 21.1054 | 1.11545 | ||||||||
\(359\) | −17.1370 | −0.904457 | −0.452229 | − | 0.891902i | \(-0.649371\pi\) | ||||
−0.452229 | + | 0.891902i | \(0.649371\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −6.23440 | −0.328126 | ||||||||
\(362\) | 0.543334 | 0.0285570 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −0.0174478 | −0.000914515 0 | ||||||||
\(365\) | −2.62175 | −0.137229 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −11.9256 | −0.622511 | −0.311255 | − | 0.950326i | \(-0.600749\pi\) | ||||
−0.311255 | + | 0.950326i | \(0.600749\pi\) | |||||||
\(368\) | 3.39412 | 0.176931 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −1.71490 | −0.0891533 | ||||||||
\(371\) | −10.4320 | −0.541604 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −3.91021 | −0.202463 | −0.101232 | − | 0.994863i | \(-0.532278\pi\) | ||||
−0.101232 | + | 0.994863i | \(0.532278\pi\) | |||||||
\(374\) | −2.75815 | −0.142621 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 10.6264 | 0.548017 | ||||||||
\(377\) | 0.0621946 | 0.00320319 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 10.4984 | 0.539268 | 0.269634 | − | 0.962963i | \(-0.413097\pi\) | ||||
0.269634 | + | 0.962963i | \(0.413097\pi\) | |||||||
\(380\) | 9.40712 | 0.482575 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 14.0400 | 0.718350 | ||||||||
\(383\) | 8.52206 | 0.435457 | 0.217729 | − | 0.976009i | \(-0.430135\pi\) | ||||
0.217729 | + | 0.976009i | \(0.430135\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −24.2176 | −1.23424 | ||||||||
\(386\) | −9.77786 | −0.497680 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −17.5825 | −0.892615 | ||||||||
\(389\) | 31.7085 | 1.60768 | 0.803842 | − | 0.594843i | \(-0.202786\pi\) | ||||
0.803842 | + | 0.594843i | \(0.202786\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2.28648 | 0.115632 | ||||||||
\(392\) | −1.95299 | −0.0986407 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −14.5046 | −0.730732 | ||||||||
\(395\) | 3.36085 | 0.169103 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −5.92081 | −0.297157 | −0.148578 | − | 0.988901i | \(-0.547470\pi\) | ||||
−0.148578 | + | 0.988901i | \(0.547470\pi\) | |||||||
\(398\) | 22.6203 | 1.13385 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 1.93222 | 0.0966110 | ||||||||
\(401\) | 8.12974 | 0.405980 | 0.202990 | − | 0.979181i | \(-0.434934\pi\) | ||||
0.202990 | + | 0.979181i | \(0.434934\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −0.0538547 | −0.00268269 | ||||||||
\(404\) | −8.56611 | −0.426180 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −17.9906 | −0.892859 | ||||||||
\(407\) | −2.66674 | −0.132185 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 12.9592 | 0.640791 | 0.320395 | − | 0.947284i | \(-0.396184\pi\) | ||||
0.320395 | + | 0.947284i | \(0.396184\pi\) | |||||||
\(410\) | −11.6686 | −0.576269 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 19.9320 | 0.981978 | ||||||||
\(413\) | −17.8680 | −0.879228 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −15.1495 | −0.743661 | ||||||||
\(416\) | 0.00776648 | 0.000380783 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 14.6285 | 0.715502 | ||||||||
\(419\) | 30.4806 | 1.48907 | 0.744537 | − | 0.667581i | \(-0.232670\pi\) | ||||
0.744537 | + | 0.667581i | \(0.232670\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −38.0654 | −1.85520 | −0.927598 | − | 0.373581i | \(-0.878130\pi\) | ||||
−0.927598 | + | 0.373581i | \(0.878130\pi\) | |||||||
\(422\) | −10.0332 | −0.488409 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 4.64357 | 0.225511 | ||||||||
\(425\) | 1.30166 | 0.0631396 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 24.8282 | 1.20152 | ||||||||
\(428\) | 13.1728 | 0.636733 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −25.2539 | −1.21785 | ||||||||
\(431\) | 21.5664 | 1.03881 | 0.519407 | − | 0.854527i | \(-0.326153\pi\) | ||||
0.519407 | + | 0.854527i | \(0.326153\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −8.92010 | −0.428673 | −0.214336 | − | 0.976760i | \(-0.568759\pi\) | ||||
−0.214336 | + | 0.976760i | \(0.568759\pi\) | |||||||
\(434\) | 15.5782 | 0.747776 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −5.10676 | −0.244569 | ||||||||
\(437\) | −12.1268 | −0.580106 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −26.0102 | −1.24140 | −0.620700 | − | 0.784048i | \(-0.713152\pi\) | ||||
−0.620700 | + | 0.784048i | \(0.713152\pi\) | |||||||
\(440\) | 10.7799 | 0.513911 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0.00523195 | 0.000248859 0 | ||||||||
\(443\) | −10.7806 | −0.512200 | −0.256100 | − | 0.966650i | \(-0.582438\pi\) | ||||
−0.256100 | + | 0.966650i | \(0.582438\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 5.46289 | 0.258966 | ||||||||
\(446\) | −1.00000 | −0.0473514 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −2.24656 | −0.106140 | ||||||||
\(449\) | 20.0819 | 0.947722 | 0.473861 | − | 0.880600i | \(-0.342860\pi\) | ||||
0.473861 | + | 0.880600i | \(0.342860\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −18.1451 | −0.854419 | ||||||||
\(452\) | 15.5553 | 0.731659 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −20.8914 | −0.980481 | ||||||||
\(455\) | 0.0459386 | 0.00215363 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −35.5020 | −1.66071 | −0.830357 | − | 0.557232i | \(-0.811863\pi\) | ||||
−0.830357 | + | 0.557232i | \(0.811863\pi\) | |||||||
\(458\) | 20.5829 | 0.961774 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −8.93642 | −0.416663 | ||||||||
\(461\) | 3.26003 | 0.151835 | 0.0759173 | − | 0.997114i | \(-0.475811\pi\) | ||||
0.0759173 | + | 0.997114i | \(0.475811\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 5.67209 | 0.263604 | 0.131802 | − | 0.991276i | \(-0.457924\pi\) | ||||
0.131802 | + | 0.991276i | \(0.457924\pi\) | |||||||
\(464\) | 8.00809 | 0.371766 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 9.41577 | 0.436177 | ||||||||
\(467\) | 10.7885 | 0.499231 | 0.249616 | − | 0.968345i | \(-0.419696\pi\) | ||||
0.249616 | + | 0.968345i | \(0.419696\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −34.1500 | −1.57690 | ||||||||
\(470\) | −27.9785 | −1.29055 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 7.95351 | 0.366090 | ||||||||
\(473\) | −39.2709 | −1.80568 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −6.90363 | −0.316760 | ||||||||
\(476\) | −1.51341 | −0.0693671 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −14.6538 | −0.670250 | ||||||||
\(479\) | −17.5354 | −0.801211 | −0.400605 | − | 0.916251i | \(-0.631200\pi\) | ||||
−0.400605 | + | 0.916251i | \(0.631200\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0.00505855 | 0.000230650 0 | ||||||||
\(482\) | 17.1216 | 0.779866 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 5.76317 | 0.261962 | ||||||||
\(485\) | 46.2931 | 2.10206 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 21.6167 | 0.979547 | 0.489774 | − | 0.871850i | \(-0.337079\pi\) | ||||
0.489774 | + | 0.871850i | \(0.337079\pi\) | |||||||
\(488\) | −11.0517 | −0.500285 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 5.14204 | 0.232294 | ||||||||
\(491\) | 11.0429 | 0.498359 | 0.249180 | − | 0.968457i | \(-0.419839\pi\) | ||||
0.249180 | + | 0.968457i | \(0.419839\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 5.39471 | 0.242966 | ||||||||
\(494\) | −0.0277488 | −0.00124848 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −6.93425 | −0.311357 | ||||||||
\(497\) | 21.6753 | 0.972270 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −9.24468 | −0.413849 | −0.206924 | − | 0.978357i | \(-0.566345\pi\) | ||||
−0.206924 | + | 0.978357i | \(0.566345\pi\) | |||||||
\(500\) | 8.07719 | 0.361223 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 22.7295 | 1.01447 | ||||||||
\(503\) | −42.2295 | −1.88292 | −0.941461 | − | 0.337123i | \(-0.890546\pi\) | ||||
−0.941461 | + | 0.337123i | \(0.890546\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 22.5538 | 1.00363 | ||||||||
\(506\) | −13.8965 | −0.617775 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 15.4106 | 0.683737 | ||||||||
\(509\) | 38.2695 | 1.69627 | 0.848134 | − | 0.529782i | \(-0.177726\pi\) | ||||
0.848134 | + | 0.529782i | \(0.177726\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −2.23703 | −0.0989605 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −7.48452 | −0.330128 | ||||||||
\(515\) | −52.4791 | −2.31251 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −43.5077 | −1.91346 | ||||||||
\(518\) | −1.46325 | −0.0642916 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −0.0204485 | −0.000896724 0 | ||||||||
\(521\) | −20.1266 | −0.881760 | −0.440880 | − | 0.897566i | \(-0.645334\pi\) | ||||
−0.440880 | + | 0.897566i | \(0.645334\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −3.72087 | −0.162702 | −0.0813512 | − | 0.996686i | \(-0.525924\pi\) | ||||
−0.0813512 | + | 0.996686i | \(0.525924\pi\) | |||||||
\(524\) | −21.0190 | −0.918219 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −7.82448 | −0.341163 | ||||||||
\(527\) | −4.67131 | −0.203486 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −11.4799 | −0.499128 | ||||||||
\(530\) | −12.2261 | −0.531068 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 8.02672 | 0.348002 | ||||||||
\(533\) | 0.0344195 | 0.00149088 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −34.6829 | −1.49947 | ||||||||
\(536\) | 15.2010 | 0.656585 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 31.3794 | 1.35286 | ||||||||
\(539\) | 7.99608 | 0.344416 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −22.9511 | −0.986745 | −0.493373 | − | 0.869818i | \(-0.664236\pi\) | ||||
−0.493373 | + | 0.869818i | \(0.664236\pi\) | |||||||
\(542\) | −1.63798 | −0.0703571 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0.673658 | 0.0288829 | ||||||||
\(545\) | 13.4456 | 0.575948 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −2.69925 | −0.115412 | −0.0577058 | − | 0.998334i | \(-0.518379\pi\) | ||||
−0.0577058 | + | 0.998334i | \(0.518379\pi\) | |||||||
\(548\) | 12.5823 | 0.537490 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −7.91106 | −0.337329 | ||||||||
\(551\) | −28.6121 | −1.21892 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 2.86768 | 0.121946 | ||||||||
\(554\) | 8.78445 | 0.373215 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −9.51306 | −0.403444 | ||||||||
\(557\) | 19.9531 | 0.845440 | 0.422720 | − | 0.906260i | \(-0.361075\pi\) | ||||
0.422720 | + | 0.906260i | \(0.361075\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0.0744933 | 0.00315073 | ||||||||
\(560\) | 5.91498 | 0.249954 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −13.1236 | −0.553585 | ||||||||
\(563\) | 1.38362 | 0.0583125 | 0.0291563 | − | 0.999575i | \(-0.490718\pi\) | ||||
0.0291563 | + | 0.999575i | \(0.490718\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −40.9557 | −1.72302 | ||||||||
\(566\) | 21.8961 | 0.920364 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −9.64824 | −0.404831 | ||||||||
\(569\) | 12.6605 | 0.530757 | 0.265379 | − | 0.964144i | \(-0.414503\pi\) | ||||
0.265379 | + | 0.964144i | \(0.414503\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 46.7306 | 1.95562 | 0.977808 | − | 0.209503i | \(-0.0671846\pi\) | ||||
0.977808 | + | 0.209503i | \(0.0671846\pi\) | |||||||
\(572\) | −0.0317982 | −0.00132955 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −9.95630 | −0.415568 | ||||||||
\(575\) | 6.55819 | 0.273495 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −18.8790 | −0.785944 | −0.392972 | − | 0.919550i | \(-0.628553\pi\) | ||||
−0.392972 | + | 0.919550i | \(0.628553\pi\) | |||||||
\(578\) | −16.5462 | −0.688231 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −21.0846 | −0.875489 | ||||||||
\(581\) | −12.9265 | −0.536281 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −19.0121 | −0.787400 | ||||||||
\(584\) | 0.995761 | 0.0412049 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −15.4295 | −0.637387 | ||||||||
\(587\) | −7.31271 | −0.301828 | −0.150914 | − | 0.988547i | \(-0.548222\pi\) | ||||
−0.150914 | + | 0.988547i | \(0.548222\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 24.7754 | 1.02085 | ||||||||
\(590\) | −20.9409 | −0.862123 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0.651332 | 0.0267696 | ||||||||
\(593\) | 0.674078 | 0.0276811 | 0.0138405 | − | 0.999904i | \(-0.495594\pi\) | ||||
0.0138405 | + | 0.999904i | \(0.495594\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 3.98468 | 0.163356 | ||||||||
\(596\) | −2.73070 | −0.111854 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0.0263604 | 0.00107796 | ||||||||
\(599\) | −9.80274 | −0.400529 | −0.200265 | − | 0.979742i | \(-0.564180\pi\) | ||||
−0.200265 | + | 0.979742i | \(0.564180\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 22.8526 | 0.932178 | 0.466089 | − | 0.884738i | \(-0.345663\pi\) | ||||
0.466089 | + | 0.884738i | \(0.345663\pi\) | |||||||
\(602\) | −21.5482 | −0.878237 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 7.96037 | 0.323903 | ||||||||
\(605\) | −15.1739 | −0.616908 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 44.0179 | 1.78663 | 0.893316 | − | 0.449428i | \(-0.148372\pi\) | ||||
0.893316 | + | 0.449428i | \(0.148372\pi\) | |||||||
\(608\) | −3.57290 | −0.144900 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 29.0980 | 1.17815 | ||||||||
\(611\) | 0.0825300 | 0.00333881 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 23.4729 | 0.948063 | 0.474031 | − | 0.880508i | \(-0.342798\pi\) | ||||
0.474031 | + | 0.880508i | \(0.342798\pi\) | |||||||
\(614\) | −18.6854 | −0.754082 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 9.19804 | 0.370600 | ||||||||
\(617\) | −24.9763 | −1.00551 | −0.502753 | − | 0.864430i | \(-0.667679\pi\) | ||||
−0.502753 | + | 0.864430i | \(0.667679\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −9.73956 | −0.391466 | −0.195733 | − | 0.980657i | \(-0.562709\pi\) | ||||
−0.195733 | + | 0.980657i | \(0.562709\pi\) | |||||||
\(620\) | 18.2573 | 0.733229 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 21.9347 | 0.879502 | ||||||||
\(623\) | 4.66126 | 0.186749 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −30.9276 | −1.23711 | ||||||||
\(626\) | −5.51529 | −0.220435 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 12.4903 | 0.498416 | ||||||||
\(629\) | 0.438775 | 0.0174951 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −23.1790 | −0.922740 | −0.461370 | − | 0.887208i | \(-0.652642\pi\) | ||||
−0.461370 | + | 0.887208i | \(0.652642\pi\) | |||||||
\(632\) | −1.27648 | −0.0507755 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 10.2843 | 0.408440 | ||||||||
\(635\) | −40.5749 | −1.61016 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −0.0151678 | −0.000600971 0 | ||||||||
\(638\) | −32.7874 | −1.29807 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −2.63291 | −0.104075 | ||||||||
\(641\) | −11.3880 | −0.449799 | −0.224900 | − | 0.974382i | \(-0.572205\pi\) | ||||
−0.224900 | + | 0.974382i | \(0.572205\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 7.09359 | 0.279744 | 0.139872 | − | 0.990170i | \(-0.455331\pi\) | ||||
0.139872 | + | 0.990170i | \(0.455331\pi\) | |||||||
\(644\) | −7.62508 | −0.300470 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −2.40691 | −0.0946987 | ||||||||
\(647\) | −26.4990 | −1.04178 | −0.520892 | − | 0.853623i | \(-0.674400\pi\) | ||||
−0.520892 | + | 0.853623i | \(0.674400\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −32.5640 | −1.27825 | ||||||||
\(650\) | 0.0150066 | 0.000588605 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −6.27007 | −0.245555 | ||||||||
\(653\) | −11.3962 | −0.445966 | −0.222983 | − | 0.974822i | \(-0.571579\pi\) | ||||
−0.222983 | + | 0.974822i | \(0.571579\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 55.3412 | 2.16236 | ||||||||
\(656\) | 4.43181 | 0.173033 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −23.8729 | −0.930662 | ||||||||
\(659\) | 41.0879 | 1.60056 | 0.800278 | − | 0.599629i | \(-0.204685\pi\) | ||||
0.800278 | + | 0.599629i | \(0.204685\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 43.6409 | 1.69743 | 0.848716 | − | 0.528849i | \(-0.177376\pi\) | ||||
0.848716 | + | 0.528849i | \(0.177376\pi\) | |||||||
\(662\) | −23.9394 | −0.930430 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 5.75391 | 0.223295 | ||||||||
\(665\) | −21.1336 | −0.819527 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 27.1804 | 1.05243 | ||||||||
\(668\) | 2.90654 | 0.112458 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −40.0230 | −1.54622 | ||||||||
\(671\) | 45.2487 | 1.74680 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 22.3619 | 0.861987 | 0.430994 | − | 0.902355i | \(-0.358163\pi\) | ||||
0.430994 | + | 0.902355i | \(0.358163\pi\) | |||||||
\(674\) | 4.45595 | 0.171637 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −12.9999 | −0.499998 | ||||||||
\(677\) | −34.4169 | −1.32275 | −0.661374 | − | 0.750056i | \(-0.730026\pi\) | ||||
−0.661374 | + | 0.750056i | \(0.730026\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 39.5000 | 1.51587 | ||||||||
\(680\) | −1.77368 | −0.0680176 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 28.3908 | 1.08714 | ||||||||
\(683\) | 10.4429 | 0.399588 | 0.199794 | − | 0.979838i | \(-0.435973\pi\) | ||||
0.199794 | + | 0.979838i | \(0.435973\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −33.1281 | −1.26576 | ||||||||
\(686\) | 20.1134 | 0.767933 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 9.59164 | 0.365678 | ||||||||
\(689\) | 0.0360642 | 0.00137393 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 45.0269 | 1.71290 | 0.856452 | − | 0.516227i | \(-0.172664\pi\) | ||||
0.856452 | + | 0.516227i | \(0.172664\pi\) | |||||||
\(692\) | −9.28984 | −0.353147 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 30.7768 | 1.16827 | ||||||||
\(695\) | 25.0470 | 0.950088 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 2.98552 | 0.113085 | ||||||||
\(698\) | 10.6268 | 0.402229 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −4.34084 | −0.164068 | ||||||||
\(701\) | −19.7764 | −0.746944 | −0.373472 | − | 0.927641i | \(-0.621833\pi\) | ||||
−0.373472 | + | 0.927641i | \(0.621833\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −2.32714 | −0.0877698 | ||||||||
\(704\) | −4.09429 | −0.154309 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −23.9565 | −0.901615 | ||||||||
\(707\) | 19.2442 | 0.723754 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 11.3226 | 0.425230 | 0.212615 | − | 0.977136i | \(-0.431802\pi\) | ||||
0.212615 | + | 0.977136i | \(0.431802\pi\) | |||||||
\(710\) | 25.4029 | 0.953356 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −2.07485 | −0.0777582 | ||||||||
\(713\) | −23.5357 | −0.881418 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0.0837218 | 0.00313102 | ||||||||
\(716\) | 21.1054 | 0.788745 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −17.1370 | −0.639548 | ||||||||
\(719\) | −42.4365 | −1.58261 | −0.791307 | − | 0.611419i | \(-0.790599\pi\) | ||||
−0.791307 | + | 0.611419i | \(0.790599\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −44.7783 | −1.66763 | ||||||||
\(722\) | −6.23440 | −0.232020 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0.543334 | 0.0201928 | ||||||||
\(725\) | 15.4734 | 0.574667 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 16.3993 | 0.608218 | 0.304109 | − | 0.952637i | \(-0.401641\pi\) | ||||
0.304109 | + | 0.952637i | \(0.401641\pi\) | |||||||
\(728\) | −0.0174478 | −0.000646660 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −2.62175 | −0.0970353 | ||||||||
\(731\) | 6.46149 | 0.238987 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −21.4011 | −0.790468 | −0.395234 | − | 0.918580i | \(-0.629337\pi\) | ||||
−0.395234 | + | 0.918580i | \(0.629337\pi\) | |||||||
\(734\) | −11.9256 | −0.440182 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 3.39412 | 0.125109 | ||||||||
\(737\) | −62.2374 | −2.29254 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 5.23739 | 0.192661 | 0.0963303 | − | 0.995349i | \(-0.469289\pi\) | ||||
0.0963303 | + | 0.995349i | \(0.469289\pi\) | |||||||
\(740\) | −1.71490 | −0.0630409 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −10.4320 | −0.382972 | ||||||||
\(743\) | 37.6115 | 1.37983 | 0.689916 | − | 0.723889i | \(-0.257647\pi\) | ||||
0.689916 | + | 0.723889i | \(0.257647\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 7.18969 | 0.263410 | ||||||||
\(746\) | −3.91021 | −0.143163 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −2.75815 | −0.100848 | ||||||||
\(749\) | −29.5935 | −1.08132 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 15.3955 | 0.561790 | 0.280895 | − | 0.959738i | \(-0.409369\pi\) | ||||
0.280895 | + | 0.959738i | \(0.409369\pi\) | |||||||
\(752\) | 10.6264 | 0.387506 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0.0621946 | 0.00226500 | ||||||||
\(755\) | −20.9589 | −0.762774 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 45.9995 | 1.67188 | 0.835941 | − | 0.548819i | \(-0.184923\pi\) | ||||
0.835941 | + | 0.548819i | \(0.184923\pi\) | |||||||
\(758\) | 10.4984 | 0.381320 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 9.40712 | 0.341232 | ||||||||
\(761\) | 23.9738 | 0.869050 | 0.434525 | − | 0.900660i | \(-0.356916\pi\) | ||||
0.434525 | + | 0.900660i | \(0.356916\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 11.4726 | 0.415337 | ||||||||
\(764\) | 14.0400 | 0.507950 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 8.52206 | 0.307915 | ||||||||
\(767\) | 0.0617708 | 0.00223041 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 31.3460 | 1.13037 | 0.565183 | − | 0.824966i | \(-0.308806\pi\) | ||||
0.565183 | + | 0.824966i | \(0.308806\pi\) | |||||||
\(770\) | −24.2176 | −0.872743 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −9.77786 | −0.351913 | ||||||||
\(773\) | 43.8102 | 1.57574 | 0.787871 | − | 0.615840i | \(-0.211183\pi\) | ||||
0.787871 | + | 0.615840i | \(0.211183\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −13.3985 | −0.481288 | ||||||||
\(776\) | −17.5825 | −0.631174 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 31.7085 | 1.13680 | ||||||||
\(779\) | −15.8344 | −0.567326 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 39.5026 | 1.41352 | ||||||||
\(782\) | 2.28648 | 0.0817643 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −1.95299 | −0.0697495 | ||||||||
\(785\) | −32.8857 | −1.17374 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 8.20309 | 0.292409 | 0.146204 | − | 0.989254i | \(-0.453294\pi\) | ||||
0.146204 | + | 0.989254i | \(0.453294\pi\) | |||||||
\(788\) | −14.5046 | −0.516705 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 3.36085 | 0.119574 | ||||||||
\(791\) | −34.9458 | −1.24253 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −0.0858325 | −0.00304800 | ||||||||
\(794\) | −5.92081 | −0.210122 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 22.6203 | 0.801755 | ||||||||
\(797\) | −22.7577 | −0.806118 | −0.403059 | − | 0.915174i | \(-0.632053\pi\) | ||||
−0.403059 | + | 0.915174i | \(0.632053\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 7.15859 | 0.253253 | ||||||||
\(800\) | 1.93222 | 0.0683143 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 8.12974 | 0.287071 | ||||||||
\(803\) | −4.07693 | −0.143872 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 20.0762 | 0.707592 | ||||||||
\(806\) | −0.0538547 | −0.00189695 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −8.56611 | −0.301355 | ||||||||
\(809\) | 27.2179 | 0.956930 | 0.478465 | − | 0.878107i | \(-0.341193\pi\) | ||||
0.478465 | + | 0.878107i | \(0.341193\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −9.81625 | −0.344695 | −0.172348 | − | 0.985036i | \(-0.555135\pi\) | ||||
−0.172348 | + | 0.985036i | \(0.555135\pi\) | |||||||
\(812\) | −17.9906 | −0.631347 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −2.66674 | −0.0934691 | ||||||||
\(815\) | 16.5085 | 0.578268 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −34.2699 | −1.19895 | ||||||||
\(818\) | 12.9592 | 0.453108 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −11.6686 | −0.407484 | ||||||||
\(821\) | 17.8972 | 0.624616 | 0.312308 | − | 0.949981i | \(-0.398898\pi\) | ||||
0.312308 | + | 0.949981i | \(0.398898\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 16.0259 | 0.558627 | 0.279313 | − | 0.960200i | \(-0.409893\pi\) | ||||
0.279313 | + | 0.960200i | \(0.409893\pi\) | |||||||
\(824\) | 19.9320 | 0.694363 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −17.8680 | −0.621708 | ||||||||
\(827\) | 18.7380 | 0.651584 | 0.325792 | − | 0.945441i | \(-0.394369\pi\) | ||||
0.325792 | + | 0.945441i | \(0.394369\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −0.931833 | −0.0323639 | −0.0161820 | − | 0.999869i | \(-0.505151\pi\) | ||||
−0.0161820 | + | 0.999869i | \(0.505151\pi\) | |||||||
\(830\) | −15.1495 | −0.525848 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0.00776648 | 0.000269254 0 | ||||||||
\(833\) | −1.31564 | −0.0455844 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −7.65267 | −0.264832 | ||||||||
\(836\) | 14.6285 | 0.505936 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 30.4806 | 1.05293 | ||||||||
\(839\) | −10.4652 | −0.361300 | −0.180650 | − | 0.983547i | \(-0.557820\pi\) | ||||
−0.180650 | + | 0.983547i | \(0.557820\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 35.1294 | 1.21136 | ||||||||
\(842\) | −38.0654 | −1.31182 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −10.0332 | −0.345358 | ||||||||
\(845\) | 34.2277 | 1.17747 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −12.9473 | −0.444874 | ||||||||
\(848\) | 4.64357 | 0.159461 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 1.30166 | 0.0446464 | ||||||||
\(851\) | 2.21070 | 0.0757818 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 28.7039 | 0.982801 | 0.491401 | − | 0.870934i | \(-0.336485\pi\) | ||||
0.491401 | + | 0.870934i | \(0.336485\pi\) | |||||||
\(854\) | 24.8282 | 0.849603 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 13.1728 | 0.450238 | ||||||||
\(857\) | 10.0329 | 0.342717 | 0.171359 | − | 0.985209i | \(-0.445184\pi\) | ||||
0.171359 | + | 0.985209i | \(0.445184\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −32.0157 | −1.09236 | −0.546181 | − | 0.837667i | \(-0.683919\pi\) | ||||
−0.546181 | + | 0.837667i | \(0.683919\pi\) | |||||||
\(860\) | −25.2539 | −0.861152 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 21.5664 | 0.734553 | ||||||||
\(863\) | −4.53904 | −0.154511 | −0.0772553 | − | 0.997011i | \(-0.524616\pi\) | ||||
−0.0772553 | + | 0.997011i | \(0.524616\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 24.4593 | 0.831642 | ||||||||
\(866\) | −8.92010 | −0.303117 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 15.5782 | 0.528758 | ||||||||
\(869\) | 5.22626 | 0.177289 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0.118059 | 0.00400026 | ||||||||
\(872\) | −5.10676 | −0.172937 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −12.1268 | −0.410197 | ||||||||
\(875\) | −18.1459 | −0.613442 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 40.9646 | 1.38328 | 0.691639 | − | 0.722243i | \(-0.256889\pi\) | ||||
0.691639 | + | 0.722243i | \(0.256889\pi\) | |||||||
\(878\) | −26.0102 | −0.877802 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 10.7799 | 0.363390 | ||||||||
\(881\) | 0.505607 | 0.0170343 | 0.00851716 | − | 0.999964i | \(-0.497289\pi\) | ||||
0.00851716 | + | 0.999964i | \(0.497289\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 27.7967 | 0.935434 | 0.467717 | − | 0.883878i | \(-0.345077\pi\) | ||||
0.467717 | + | 0.883878i | \(0.345077\pi\) | |||||||
\(884\) | 0.00523195 | 0.000175970 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −10.7806 | −0.362180 | ||||||||
\(887\) | 6.73644 | 0.226188 | 0.113094 | − | 0.993584i | \(-0.463924\pi\) | ||||
0.113094 | + | 0.993584i | \(0.463924\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −34.6209 | −1.16115 | ||||||||
\(890\) | 5.46289 | 0.183116 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −1.00000 | −0.0334825 | ||||||||
\(893\) | −37.9672 | −1.27052 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −55.5686 | −1.85745 | ||||||||
\(896\) | −2.24656 | −0.0750522 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 20.0819 | 0.670140 | ||||||||
\(899\) | −55.5301 | −1.85203 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 3.12818 | 0.104215 | ||||||||
\(902\) | −18.1451 | −0.604165 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 15.5553 | 0.517361 | ||||||||
\(905\) | −1.43055 | −0.0475531 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −21.5625 | −0.715972 | −0.357986 | − | 0.933727i | \(-0.616536\pi\) | ||||
−0.357986 | + | 0.933727i | \(0.616536\pi\) | |||||||
\(908\) | −20.8914 | −0.693305 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0.0459386 | 0.00152285 | ||||||||
\(911\) | −59.1815 | −1.96077 | −0.980386 | − | 0.197088i | \(-0.936852\pi\) | ||||
−0.980386 | + | 0.197088i | \(0.936852\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −23.5581 | −0.779661 | ||||||||
\(914\) | −35.5020 | −1.17430 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 20.5829 | 0.680077 | ||||||||
\(917\) | 47.2204 | 1.55935 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −28.4787 | −0.939426 | −0.469713 | − | 0.882819i | \(-0.655643\pi\) | ||||
−0.469713 | + | 0.882819i | \(0.655643\pi\) | |||||||
\(920\) | −8.93642 | −0.294625 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 3.26003 | 0.107363 | ||||||||
\(923\) | −0.0749328 | −0.00246644 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1.25852 | 0.0413798 | ||||||||
\(926\) | 5.67209 | 0.186397 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 8.00809 | 0.262878 | ||||||||
\(929\) | −32.6469 | −1.07111 | −0.535555 | − | 0.844500i | \(-0.679898\pi\) | ||||
−0.535555 | + | 0.844500i | \(0.679898\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 6.97782 | 0.228689 | ||||||||
\(932\) | 9.41577 | 0.308424 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 10.7885 | 0.353010 | ||||||||
\(935\) | 7.26196 | 0.237492 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −26.4204 | −0.863118 | −0.431559 | − | 0.902085i | \(-0.642036\pi\) | ||||
−0.431559 | + | 0.902085i | \(0.642036\pi\) | |||||||
\(938\) | −34.1500 | −1.11504 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −27.9785 | −0.912557 | ||||||||
\(941\) | −27.0639 | −0.882259 | −0.441130 | − | 0.897443i | \(-0.645422\pi\) | ||||
−0.441130 | + | 0.897443i | \(0.645422\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 15.0421 | 0.489838 | ||||||||
\(944\) | 7.95351 | 0.258865 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −39.2709 | −1.27681 | ||||||||
\(947\) | −15.7697 | −0.512447 | −0.256223 | − | 0.966618i | \(-0.582478\pi\) | ||||
−0.256223 | + | 0.966618i | \(0.582478\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0.00773355 | 0.000251042 0 | ||||||||
\(950\) | −6.90363 | −0.223983 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −1.51341 | −0.0490499 | ||||||||
\(953\) | −25.0914 | −0.812791 | −0.406395 | − | 0.913697i | \(-0.633214\pi\) | ||||
−0.406395 | + | 0.913697i | \(0.633214\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −36.9661 | −1.19620 | ||||||||
\(956\) | −14.6538 | −0.473939 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −17.5354 | −0.566542 | ||||||||
\(959\) | −28.2669 | −0.912785 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 17.0838 | 0.551090 | ||||||||
\(962\) | 0.00505855 | 0.000163094 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 17.1216 | 0.551448 | ||||||||
\(965\) | 25.7442 | 0.828737 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 40.5703 | 1.30465 | 0.652327 | − | 0.757938i | \(-0.273793\pi\) | ||||
0.652327 | + | 0.757938i | \(0.273793\pi\) | |||||||
\(968\) | 5.76317 | 0.185235 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 46.2931 | 1.48638 | ||||||||
\(971\) | −32.4433 | −1.04116 | −0.520578 | − | 0.853814i | \(-0.674283\pi\) | ||||
−0.520578 | + | 0.853814i | \(0.674283\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 21.3716 | 0.685143 | ||||||||
\(974\) | 21.6167 | 0.692645 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −11.0517 | −0.353755 | ||||||||
\(977\) | 32.0199 | 1.02441 | 0.512204 | − | 0.858864i | \(-0.328829\pi\) | ||||
0.512204 | + | 0.858864i | \(0.328829\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 8.49501 | 0.271502 | ||||||||
\(980\) | 5.14204 | 0.164256 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 11.0429 | 0.352393 | ||||||||
\(983\) | 11.3623 | 0.362400 | 0.181200 | − | 0.983446i | \(-0.442002\pi\) | ||||
0.181200 | + | 0.983446i | \(0.442002\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 38.1894 | 1.21681 | ||||||||
\(986\) | 5.39471 | 0.171803 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −0.0277488 | −0.000882808 0 | ||||||||
\(989\) | 32.5552 | 1.03519 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 57.7380 | 1.83411 | 0.917054 | − | 0.398764i | \(-0.130561\pi\) | ||||
0.917054 | + | 0.398764i | \(0.130561\pi\) | |||||||
\(992\) | −6.93425 | −0.220163 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 21.6753 | 0.687499 | ||||||||
\(995\) | −59.5572 | −1.88809 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −48.5327 | −1.53705 | −0.768524 | − | 0.639821i | \(-0.779008\pi\) | ||||
−0.768524 | + | 0.639821i | \(0.779008\pi\) | |||||||
\(998\) | −9.24468 | −0.292635 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 4014.2.a.u.1.2 | yes | 6 | |
3.2 | odd | 2 | 4014.2.a.t.1.5 | ✓ | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4014.2.a.t.1.5 | ✓ | 6 | 3.2 | odd | 2 | ||
4014.2.a.u.1.2 | yes | 6 | 1.1 | even | 1 | trivial |