Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3432,2,Mod(1,3432)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3432, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("3432.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3432 = 2^{3} \cdot 3 \cdot 11 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3432.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: | \(27.4046579737\) |
Analytic rank: | \(1\) |
Dimension: | \(5\) |
Coefficient field: | 5.5.2172244.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{5} - 2x^{4} - 8x^{3} + 16x^{2} + 5x - 8 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.5 | ||
Root | \(2.60211\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3432.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 3.52882 | 1.57814 | 0.789068 | − | 0.614305i | \(-0.210564\pi\) | ||||
0.789068 | + | 0.614305i | \(0.210564\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −3.24835 | −1.22776 | −0.613881 | − | 0.789399i | \(-0.710393\pi\) | ||||
−0.613881 | + | 0.789399i | \(0.710393\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.00000 | −0.301511 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.00000 | 0.277350 | ||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −3.52882 | −0.911138 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −5.48469 | −1.33023 | −0.665117 | − | 0.746740i | \(-0.731618\pi\) | ||||
−0.665117 | + | 0.746740i | \(0.731618\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.44934 | −0.561917 | −0.280959 | − | 0.959720i | \(-0.590652\pi\) | ||||
−0.280959 | + | 0.959720i | \(0.590652\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 3.24835 | 0.708849 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2.29362 | 0.478252 | 0.239126 | − | 0.970989i | \(-0.423139\pi\) | ||||
0.239126 | + | 0.970989i | \(0.423139\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 7.45258 | 1.49052 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 9.32897 | 1.73235 | 0.866173 | − | 0.499745i | \(-0.166573\pi\) | ||||
0.866173 | + | 0.499745i | \(0.166573\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.32783 | 0.418091 | 0.209045 | − | 0.977906i | \(-0.432964\pi\) | ||||
0.209045 | + | 0.977906i | \(0.432964\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 1.00000 | 0.174078 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −11.4629 | −1.93758 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −11.4537 | −1.88298 | −0.941489 | − | 0.337043i | \(-0.890573\pi\) | ||||
−0.941489 | + | 0.337043i | \(0.890573\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −1.00000 | −0.160128 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −10.0588 | −1.57092 | −0.785459 | − | 0.618914i | \(-0.787573\pi\) | ||||
−0.785459 | + | 0.618914i | \(0.787573\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −7.09186 | −1.08150 | −0.540749 | − | 0.841184i | \(-0.681859\pi\) | ||||
−0.540749 | + | 0.841184i | \(0.681859\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 3.52882 | 0.526046 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −2.48433 | −0.362376 | −0.181188 | − | 0.983448i | \(-0.557994\pi\) | ||||
−0.181188 | + | 0.983448i | \(0.557994\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 3.55179 | 0.507399 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 5.48469 | 0.768010 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 13.6449 | 1.87427 | 0.937134 | − | 0.348970i | \(-0.113468\pi\) | ||||
0.937134 | + | 0.348970i | \(0.113468\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −3.52882 | −0.475826 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 2.44934 | 0.324423 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −5.35995 | −0.697806 | −0.348903 | − | 0.937159i | \(-0.613446\pi\) | ||||
−0.348903 | + | 0.937159i | \(0.613446\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −7.71007 | −0.987173 | −0.493587 | − | 0.869697i | \(-0.664314\pi\) | ||||
−0.493587 | + | 0.869697i | \(0.664314\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −3.24835 | −0.409254 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 3.52882 | 0.437696 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −12.2750 | −1.49963 | −0.749816 | − | 0.661647i | \(-0.769858\pi\) | ||||
−0.749816 | + | 0.661647i | \(0.769858\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −2.29362 | −0.276119 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1.76516 | 0.209486 | 0.104743 | − | 0.994499i | \(-0.466598\pi\) | ||||
0.104743 | + | 0.994499i | \(0.466598\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 1.80929 | 0.211761 | 0.105881 | − | 0.994379i | \(-0.466234\pi\) | ||||
0.105881 | + | 0.994379i | \(0.466234\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −7.45258 | −0.860549 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 3.24835 | 0.370184 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 3.26150 | 0.366948 | 0.183474 | − | 0.983025i | \(-0.441266\pi\) | ||||
0.183474 | + | 0.983025i | \(0.441266\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −13.1482 | −1.44320 | −0.721600 | − | 0.692311i | \(-0.756593\pi\) | ||||
−0.721600 | + | 0.692311i | \(0.756593\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −19.3545 | −2.09929 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −9.32897 | −1.00017 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −2.06824 | −0.219233 | −0.109616 | − | 0.993974i | \(-0.534962\pi\) | ||||
−0.109616 | + | 0.993974i | \(0.534962\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −3.24835 | −0.340520 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −2.32783 | −0.241385 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −8.64329 | −0.886783 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −5.04526 | −0.512269 | −0.256135 | − | 0.966641i | \(-0.582449\pi\) | ||||
−0.256135 | + | 0.966641i | \(0.582449\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −1.00000 | −0.100504 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 0.897457 | 0.0893003 | 0.0446502 | − | 0.999003i | \(-0.485783\pi\) | ||||
0.0446502 | + | 0.999003i | \(0.485783\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1.69769 | 0.167279 | 0.0836394 | − | 0.996496i | \(-0.473346\pi\) | ||||
0.0836394 | + | 0.996496i | \(0.473346\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 11.4629 | 1.11866 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 8.44389 | 0.816301 | 0.408151 | − | 0.912915i | \(-0.366174\pi\) | ||||
0.408151 | + | 0.912915i | \(0.366174\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 5.30344 | 0.507978 | 0.253989 | − | 0.967207i | \(-0.418257\pi\) | ||||
0.253989 | + | 0.967207i | \(0.418257\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 11.4537 | 1.08714 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 13.4569 | 1.26592 | 0.632961 | − | 0.774183i | \(-0.281839\pi\) | ||||
0.632961 | + | 0.774183i | \(0.281839\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 8.09376 | 0.754747 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 1.00000 | 0.0924500 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 17.8162 | 1.63321 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 10.0588 | 0.906969 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 8.65470 | 0.774100 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −9.11492 | −0.808818 | −0.404409 | − | 0.914578i | \(-0.632523\pi\) | ||||
−0.404409 | + | 0.914578i | \(0.632523\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 7.09186 | 0.624403 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −6.88954 | −0.601942 | −0.300971 | − | 0.953633i | \(-0.597311\pi\) | ||||
−0.300971 | + | 0.953633i | \(0.597311\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 7.95632 | 0.689901 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −3.52882 | −0.303713 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −9.28257 | −0.793063 | −0.396532 | − | 0.918021i | \(-0.629786\pi\) | ||||
−0.396532 | + | 0.918021i | \(0.629786\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −16.3512 | −1.38689 | −0.693444 | − | 0.720511i | \(-0.743908\pi\) | ||||
−0.693444 | + | 0.720511i | \(0.743908\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 2.48433 | 0.209218 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −1.00000 | −0.0836242 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 32.9203 | 2.73388 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −3.55179 | −0.292947 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 6.85779 | 0.561812 | 0.280906 | − | 0.959735i | \(-0.409365\pi\) | ||||
0.280906 | + | 0.959735i | \(0.409365\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2.36108 | 0.192142 | 0.0960711 | − | 0.995374i | \(-0.469372\pi\) | ||||
0.0960711 | + | 0.995374i | \(0.469372\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −5.48469 | −0.443411 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 8.21450 | 0.659805 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −17.2539 | −1.37701 | −0.688504 | − | 0.725233i | \(-0.741732\pi\) | ||||
−0.688504 | + | 0.725233i | \(0.741732\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −13.6449 | −1.08211 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −7.45048 | −0.587180 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 8.66881 | 0.678994 | 0.339497 | − | 0.940607i | \(-0.389743\pi\) | ||||
0.339497 | + | 0.940607i | \(0.389743\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 3.52882 | 0.274718 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −13.6094 | −1.05313 | −0.526565 | − | 0.850135i | \(-0.676520\pi\) | ||||
−0.526565 | + | 0.850135i | \(0.676520\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −2.44934 | −0.187306 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −12.2378 | −0.930419 | −0.465210 | − | 0.885201i | \(-0.654021\pi\) | ||||
−0.465210 | + | 0.885201i | \(0.654021\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −24.2086 | −1.83000 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 5.35995 | 0.402878 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −10.7549 | −0.803858 | −0.401929 | − | 0.915671i | \(-0.631660\pi\) | ||||
−0.401929 | + | 0.915671i | \(0.631660\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −8.68491 | −0.645544 | −0.322772 | − | 0.946477i | \(-0.604615\pi\) | ||||
−0.322772 | + | 0.946477i | \(0.604615\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 7.71007 | 0.569945 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −40.4181 | −2.97160 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 5.48469 | 0.401080 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 3.24835 | 0.236283 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 14.8523 | 1.07468 | 0.537339 | − | 0.843367i | \(-0.319430\pi\) | ||||
0.537339 | + | 0.843367i | \(0.319430\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −7.50698 | −0.540364 | −0.270182 | − | 0.962809i | \(-0.587084\pi\) | ||||
−0.270182 | + | 0.962809i | \(0.587084\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −3.52882 | −0.252704 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −3.19553 | −0.227672 | −0.113836 | − | 0.993500i | \(-0.536314\pi\) | ||||
−0.113836 | + | 0.993500i | \(0.536314\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 19.3205 | 1.36959 | 0.684796 | − | 0.728735i | \(-0.259891\pi\) | ||||
0.684796 | + | 0.728735i | \(0.259891\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 12.2750 | 0.865813 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −30.3038 | −2.12691 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −35.4956 | −2.47912 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 2.29362 | 0.159417 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 2.44934 | 0.169424 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 4.58374 | 0.315558 | 0.157779 | − | 0.987474i | \(-0.449567\pi\) | ||||
0.157779 | + | 0.987474i | \(0.449567\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −1.76516 | −0.120947 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −25.0259 | −1.70675 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −7.56162 | −0.513316 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −1.80929 | −0.122260 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −5.48469 | −0.368940 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −15.3212 | −1.02599 | −0.512993 | − | 0.858393i | \(-0.671463\pi\) | ||||
−0.512993 | + | 0.858393i | \(0.671463\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 7.45258 | 0.496838 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 5.66821 | 0.376212 | 0.188106 | − | 0.982149i | \(-0.439765\pi\) | ||||
0.188106 | + | 0.982149i | \(0.439765\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 6.49994 | 0.429528 | 0.214764 | − | 0.976666i | \(-0.431102\pi\) | ||||
0.214764 | + | 0.976666i | \(0.431102\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −3.24835 | −0.213726 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −11.5430 | −0.756208 | −0.378104 | − | 0.925763i | \(-0.623424\pi\) | ||||
−0.378104 | + | 0.925763i | \(0.623424\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −8.76675 | −0.571880 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −3.26150 | −0.211857 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −7.78299 | −0.503440 | −0.251720 | − | 0.967800i | \(-0.580996\pi\) | ||||
−0.251720 | + | 0.967800i | \(0.580996\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −26.6383 | −1.71592 | −0.857961 | − | 0.513714i | \(-0.828269\pi\) | ||||
−0.857961 | + | 0.513714i | \(0.828269\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 12.5336 | 0.800745 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −2.44934 | −0.155848 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 13.1482 | 0.833231 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 18.5880 | 1.17326 | 0.586631 | − | 0.809854i | \(-0.300454\pi\) | ||||
0.586631 | + | 0.809854i | \(0.300454\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2.29362 | −0.144198 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 19.3545 | 1.21203 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −4.23233 | −0.264006 | −0.132003 | − | 0.991249i | \(-0.542141\pi\) | ||||
−0.132003 | + | 0.991249i | \(0.542141\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 37.2057 | 2.31185 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 9.32897 | 0.577449 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 27.2699 | 1.68154 | 0.840768 | − | 0.541396i | \(-0.182104\pi\) | ||||
0.840768 | + | 0.541396i | \(0.182104\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 48.1503 | 2.95785 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 2.06824 | 0.126574 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −17.3334 | −1.05684 | −0.528419 | − | 0.848984i | \(-0.677215\pi\) | ||||
−0.528419 | + | 0.848984i | \(0.677215\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 19.9402 | 1.21128 | 0.605640 | − | 0.795739i | \(-0.292917\pi\) | ||||
0.605640 | + | 0.795739i | \(0.292917\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 3.24835 | 0.196599 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −7.45258 | −0.449407 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 8.21405 | 0.493534 | 0.246767 | − | 0.969075i | \(-0.420632\pi\) | ||||
0.246767 | + | 0.969075i | \(0.420632\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 2.32783 | 0.139364 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −15.8135 | −0.943354 | −0.471677 | − | 0.881772i | \(-0.656351\pi\) | ||||
−0.471677 | + | 0.881772i | \(0.656351\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 11.2407 | 0.668191 | 0.334095 | − | 0.942539i | \(-0.391569\pi\) | ||||
0.334095 | + | 0.942539i | \(0.391569\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 8.64329 | 0.511984 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 32.6745 | 1.92871 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 13.0818 | 0.769520 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 5.04526 | 0.295759 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −16.4756 | −0.962517 | −0.481259 | − | 0.876579i | \(-0.659820\pi\) | ||||
−0.481259 | + | 0.876579i | \(0.659820\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −18.9143 | −1.10123 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 1.00000 | 0.0580259 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 2.29362 | 0.132643 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 23.0368 | 1.32782 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −0.897457 | −0.0515576 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −27.2075 | −1.55789 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −30.0991 | −1.71785 | −0.858924 | − | 0.512102i | \(-0.828867\pi\) | ||||
−0.858924 | + | 0.512102i | \(0.828867\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −1.69769 | −0.0965784 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −18.6929 | −1.05998 | −0.529989 | − | 0.848004i | \(-0.677804\pi\) | ||||
−0.529989 | + | 0.848004i | \(0.677804\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 7.73114 | 0.436990 | 0.218495 | − | 0.975838i | \(-0.429885\pi\) | ||||
0.218495 | + | 0.975838i | \(0.429885\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −11.4629 | −0.645859 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −24.2897 | −1.36424 | −0.682122 | − | 0.731239i | \(-0.738943\pi\) | ||||
−0.682122 | + | 0.731239i | \(0.738943\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −9.32897 | −0.522322 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −8.44389 | −0.471292 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 13.4339 | 0.747481 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 7.45258 | 0.413395 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −5.30344 | −0.293281 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 8.06997 | 0.444912 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −2.62003 | −0.144010 | −0.0720050 | − | 0.997404i | \(-0.522940\pi\) | ||||
−0.0720050 | + | 0.997404i | \(0.522940\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −11.4537 | −0.627659 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −43.3163 | −2.36662 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −14.3625 | −0.782375 | −0.391188 | − | 0.920311i | \(-0.627936\pi\) | ||||
−0.391188 | + | 0.920311i | \(0.627936\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −13.4569 | −0.730881 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −2.32783 | −0.126059 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 11.2010 | 0.604797 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −8.09376 | −0.435754 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −34.3771 | −1.84546 | −0.922731 | − | 0.385445i | \(-0.874048\pi\) | ||||
−0.922731 | + | 0.385445i | \(0.874048\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 14.4553 | 0.773774 | 0.386887 | − | 0.922127i | \(-0.373550\pi\) | ||||
0.386887 | + | 0.922127i | \(0.373550\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1.00000 | −0.0533761 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 14.3564 | 0.764114 | 0.382057 | − | 0.924139i | \(-0.375216\pi\) | ||||
0.382057 | + | 0.924139i | \(0.375216\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 6.22893 | 0.330597 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −17.8162 | −0.942934 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −9.33888 | −0.492887 | −0.246444 | − | 0.969157i | \(-0.579262\pi\) | ||||
−0.246444 | + | 0.969157i | \(0.579262\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −13.0007 | −0.684249 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −1.00000 | −0.0524864 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 6.38466 | 0.334188 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 27.8507 | 1.45379 | 0.726897 | − | 0.686746i | \(-0.240962\pi\) | ||||
0.726897 | + | 0.686746i | \(0.240962\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −10.0588 | −0.523639 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −44.3234 | −2.30115 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 25.1455 | 1.30198 | 0.650992 | − | 0.759084i | \(-0.274353\pi\) | ||||
0.650992 | + | 0.759084i | \(0.274353\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −8.65470 | −0.446927 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 9.32897 | 0.480466 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 33.4424 | 1.71782 | 0.858911 | − | 0.512125i | \(-0.171141\pi\) | ||||
0.858911 | + | 0.512125i | \(0.171141\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 9.11492 | 0.466971 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −28.2495 | −1.44348 | −0.721741 | − | 0.692164i | \(-0.756658\pi\) | ||||
−0.721741 | + | 0.692164i | \(0.756658\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 11.4629 | 0.584201 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −7.09186 | −0.360499 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −15.8301 | −0.802620 | −0.401310 | − | 0.915942i | \(-0.631445\pi\) | ||||
−0.401310 | + | 0.915942i | \(0.631445\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −12.5798 | −0.636187 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 6.88954 | 0.347531 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 11.5093 | 0.579093 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −4.96388 | −0.249130 | −0.124565 | − | 0.992211i | \(-0.539754\pi\) | ||||
−0.124565 | + | 0.992211i | \(0.539754\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −7.95632 | −0.398314 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −28.8698 | −1.44169 | −0.720846 | − | 0.693096i | \(-0.756246\pi\) | ||||
−0.720846 | + | 0.693096i | \(0.756246\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 2.32783 | 0.115958 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 3.52882 | 0.175349 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 11.4537 | 0.567739 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 26.6445 | 1.31748 | 0.658742 | − | 0.752369i | \(-0.271089\pi\) | ||||
0.658742 | + | 0.752369i | \(0.271089\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 9.28257 | 0.457875 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 17.4110 | 0.856739 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −46.3975 | −2.27757 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 16.3512 | 0.800720 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −5.83882 | −0.285245 | −0.142623 | − | 0.989777i | \(-0.545553\pi\) | ||||
−0.142623 | + | 0.989777i | \(0.545553\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 37.3214 | 1.81893 | 0.909466 | − | 0.415778i | \(-0.136491\pi\) | ||||
0.909466 | + | 0.415778i | \(0.136491\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −2.48433 | −0.120792 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −40.8751 | −1.98273 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 25.0450 | 1.21201 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 1.00000 | 0.0482805 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 20.7222 | 0.998152 | 0.499076 | − | 0.866558i | \(-0.333673\pi\) | ||||
0.499076 | + | 0.866558i | \(0.333673\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −24.7204 | −1.18799 | −0.593993 | − | 0.804470i | \(-0.702449\pi\) | ||||
−0.593993 | + | 0.804470i | \(0.702449\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −32.9203 | −1.57841 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −5.61785 | −0.268738 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 1.77211 | 0.0845783 | 0.0422892 | − | 0.999105i | \(-0.486535\pi\) | ||||
0.0422892 | + | 0.999105i | \(0.486535\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 3.55179 | 0.169133 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 6.43320 | 0.305651 | 0.152825 | − | 0.988253i | \(-0.451163\pi\) | ||||
0.152825 | + | 0.988253i | \(0.451163\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −7.29844 | −0.345979 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −6.85779 | −0.324362 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 29.4607 | 1.39034 | 0.695169 | − | 0.718847i | \(-0.255330\pi\) | ||||
0.695169 | + | 0.718847i | \(0.255330\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 10.0588 | 0.473649 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −2.36108 | −0.110933 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −11.4629 | −0.537387 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −40.3142 | −1.88582 | −0.942910 | − | 0.333048i | \(-0.891923\pi\) | ||||
−0.942910 | + | 0.333048i | \(0.891923\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 5.48469 | 0.256003 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 18.1182 | 0.843851 | 0.421925 | − | 0.906631i | \(-0.361354\pi\) | ||||
0.421925 | + | 0.906631i | \(0.361354\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 24.9917 | 1.16146 | 0.580731 | − | 0.814096i | \(-0.302767\pi\) | ||||
0.580731 | + | 0.814096i | \(0.302767\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −8.21450 | −0.380938 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 20.7835 | 0.961743 | 0.480872 | − | 0.876791i | \(-0.340320\pi\) | ||||
0.480872 | + | 0.876791i | \(0.340320\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 39.8736 | 1.84119 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 17.2539 | 0.795016 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 7.09186 | 0.326084 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −18.2539 | −0.837546 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 13.6449 | 0.624756 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −36.5844 | −1.67159 | −0.835793 | − | 0.549045i | \(-0.814992\pi\) | ||||
−0.835793 | + | 0.549045i | \(0.814992\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −11.4537 | −0.522244 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 7.45048 | 0.339008 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −17.8038 | −0.808430 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 21.6052 | 0.979025 | 0.489513 | − | 0.871996i | \(-0.337175\pi\) | ||||
0.489513 | + | 0.871996i | \(0.337175\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −8.66881 | −0.392017 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −17.8732 | −0.806607 | −0.403304 | − | 0.915066i | \(-0.632138\pi\) | ||||
−0.403304 | + | 0.915066i | \(0.632138\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −51.1665 | −2.30442 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −3.52882 | −0.158609 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −5.73386 | −0.257199 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 26.1343 | 1.16993 | 0.584967 | − | 0.811057i | \(-0.301108\pi\) | ||||
0.584967 | + | 0.811057i | \(0.301108\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 13.6094 | 0.608025 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −44.3670 | −1.97823 | −0.989114 | − | 0.147149i | \(-0.952990\pi\) | ||||
−0.989114 | + | 0.147149i | \(0.952990\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 3.16697 | 0.140928 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −1.00000 | −0.0444116 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −0.450386 | −0.0199630 | −0.00998151 | − | 0.999950i | \(-0.503177\pi\) | ||||
−0.00998151 | + | 0.999950i | \(0.503177\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −5.87721 | −0.259992 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 2.44934 | 0.108141 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 5.99086 | 0.263989 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 2.48433 | 0.109261 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 12.2378 | 0.537178 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 38.0188 | 1.66563 | 0.832817 | − | 0.553549i | \(-0.186727\pi\) | ||||
0.832817 | + | 0.553549i | \(0.186727\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 19.7961 | 0.865625 | 0.432812 | − | 0.901484i | \(-0.357521\pi\) | ||||
0.432812 | + | 0.901484i | \(0.357521\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 24.2086 | 1.05655 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −12.7674 | −0.556158 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −17.7393 | −0.771275 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −5.35995 | −0.232602 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −10.0588 | −0.435694 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 29.7970 | 1.28824 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 10.7549 | 0.464107 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −3.55179 | −0.152987 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 3.16993 | 0.136286 | 0.0681429 | − | 0.997676i | \(-0.478293\pi\) | ||||
0.0681429 | + | 0.997676i | \(0.478293\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 8.68491 | 0.372705 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 18.7149 | 0.801658 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 16.1394 | 0.690071 | 0.345035 | − | 0.938590i | \(-0.387867\pi\) | ||||
0.345035 | + | 0.938590i | \(0.387867\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −7.71007 | −0.329058 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −22.8498 | −0.973435 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −10.5945 | −0.450524 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 40.4181 | 1.71565 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 39.5561 | 1.67605 | 0.838023 | − | 0.545635i | \(-0.183711\pi\) | ||||
0.838023 | + | 0.545635i | \(0.183711\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −7.09186 | −0.299954 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −5.48469 | −0.231564 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −7.62505 | −0.321357 | −0.160679 | − | 0.987007i | \(-0.551368\pi\) | ||||
−0.160679 | + | 0.987007i | \(0.551368\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 47.4871 | 1.99780 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −3.24835 | −0.136418 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −14.2286 | −0.596495 | −0.298247 | − | 0.954489i | \(-0.596402\pi\) | ||||
−0.298247 | + | 0.954489i | \(0.596402\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 0.707256 | 0.0295978 | 0.0147989 | − | 0.999890i | \(-0.495289\pi\) | ||||
0.0147989 | + | 0.999890i | \(0.495289\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −14.8523 | −0.620465 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 17.0934 | 0.712842 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 29.3254 | 1.22083 | 0.610416 | − | 0.792081i | \(-0.291002\pi\) | ||||
0.610416 | + | 0.792081i | \(0.291002\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 7.50698 | 0.311980 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 42.7099 | 1.77190 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −13.6449 | −0.565113 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 3.52882 | 0.145899 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 30.0849 | 1.24174 | 0.620869 | − | 0.783914i | \(-0.286780\pi\) | ||||
0.620869 | + | 0.783914i | \(0.286780\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −5.70165 | −0.234933 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 3.19553 | 0.131447 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −21.5857 | −0.886418 | −0.443209 | − | 0.896418i | \(-0.646160\pi\) | ||||
−0.443209 | + | 0.896418i | \(0.646160\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 62.8702 | 2.57743 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −19.3205 | −0.790734 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 31.7749 | 1.29829 | 0.649143 | − | 0.760667i | \(-0.275128\pi\) | ||||
0.649143 | + | 0.760667i | \(0.275128\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −8.09700 | −0.330283 | −0.165142 | − | 0.986270i | \(-0.552808\pi\) | ||||
−0.165142 | + | 0.986270i | \(0.552808\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −12.2750 | −0.499877 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 3.52882 | 0.143467 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −9.11492 | −0.369963 | −0.184982 | − | 0.982742i | \(-0.559223\pi\) | ||||
−0.184982 | + | 0.982742i | \(0.559223\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 30.3038 | 1.22797 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −2.48433 | −0.100505 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −2.60183 | −0.105087 | −0.0525435 | − | 0.998619i | \(-0.516733\pi\) | ||||
−0.0525435 | + | 0.998619i | \(0.516733\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 35.4956 | 1.43132 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −20.8466 | −0.839254 | −0.419627 | − | 0.907697i | \(-0.637839\pi\) | ||||
−0.419627 | + | 0.907697i | \(0.637839\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −31.8886 | −1.28171 | −0.640855 | − | 0.767662i | \(-0.721420\pi\) | ||||
−0.640855 | + | 0.767662i | \(0.721420\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −2.29362 | −0.0920397 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 6.71837 | 0.269166 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −6.72199 | −0.268880 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −2.44934 | −0.0978173 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 62.8201 | 2.50480 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 5.38401 | 0.214334 | 0.107167 | − | 0.994241i | \(-0.465822\pi\) | ||||
0.107167 | + | 0.994241i | \(0.465822\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −4.58374 | −0.182187 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −32.1649 | −1.27643 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 3.55179 | 0.140727 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 1.76516 | 0.0698286 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 16.3920 | 0.647446 | 0.323723 | − | 0.946152i | \(-0.395065\pi\) | ||||
0.323723 | + | 0.946152i | \(0.395065\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 45.9975 | 1.81396 | 0.906981 | − | 0.421171i | \(-0.138381\pi\) | ||||
0.906981 | + | 0.421171i | \(0.138381\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 25.0259 | 0.985393 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 15.2406 | 0.599171 | 0.299585 | − | 0.954069i | \(-0.403152\pi\) | ||||
0.299585 | + | 0.954069i | \(0.403152\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 5.35995 | 0.210396 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 7.56162 | 0.296363 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −3.21660 | −0.125875 | −0.0629376 | − | 0.998017i | \(-0.520047\pi\) | ||||
−0.0629376 | + | 0.998017i | \(0.520047\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −24.3120 | −0.949947 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 1.80929 | 0.0705871 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −1.42094 | −0.0553521 | −0.0276761 | − | 0.999617i | \(-0.508811\pi\) | ||||
−0.0276761 | + | 0.999617i | \(0.508811\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 20.5478 | 0.799215 | 0.399608 | − | 0.916686i | \(-0.369146\pi\) | ||||
0.399608 | + | 0.916686i | \(0.369146\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 5.48469 | 0.213008 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 28.0764 | 1.08876 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 21.3971 | 0.828498 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 15.3212 | 0.592353 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 7.71007 | 0.297644 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 9.13806 | 0.352246 | 0.176123 | − | 0.984368i | \(-0.443644\pi\) | ||||
0.176123 | + | 0.984368i | \(0.443644\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −7.45258 | −0.286850 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 26.6437 | 1.02400 | 0.512000 | − | 0.858985i | \(-0.328905\pi\) | ||||
0.512000 | + | 0.858985i | \(0.328905\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 16.3888 | 0.628944 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −5.66821 | −0.217206 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −22.9749 | −0.879110 | −0.439555 | − | 0.898216i | \(-0.644864\pi\) | ||||
−0.439555 | + | 0.898216i | \(0.644864\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −32.7565 | −1.25156 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −6.49994 | −0.247988 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 13.6449 | 0.519828 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −24.0127 | −0.913488 | −0.456744 | − | 0.889598i | \(-0.650984\pi\) | ||||
−0.456744 | + | 0.889598i | \(0.650984\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 3.24835 | 0.123395 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −57.7003 | −2.18870 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 55.1693 | 2.08969 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 11.5430 | 0.436597 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 4.66740 | 0.176285 | 0.0881425 | − | 0.996108i | \(-0.471907\pi\) | ||||
0.0881425 | + | 0.996108i | \(0.471907\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 28.0540 | 1.05808 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 8.76675 | 0.330175 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −2.91526 | −0.109640 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −13.9375 | −0.523432 | −0.261716 | − | 0.965145i | \(-0.584288\pi\) | ||||
−0.261716 | + | 0.965145i | \(0.584288\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 3.26150 | 0.122316 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 5.33915 | 0.199953 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −3.52882 | −0.131970 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 7.78299 | 0.290661 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −25.7087 | −0.958773 | −0.479386 | − | 0.877604i | \(-0.659141\pi\) | ||||
−0.479386 | + | 0.877604i | \(0.659141\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −5.51471 | −0.205378 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 26.6383 | 0.990688 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 69.5248 | 2.58209 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −7.75698 | −0.287690 | −0.143845 | − | 0.989600i | \(-0.545947\pi\) | ||||
−0.143845 | + | 0.989600i | \(0.545947\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 38.8966 | 1.43864 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 51.9270 | 1.91797 | 0.958984 | − | 0.283461i | \(-0.0914826\pi\) | ||||
0.958984 | + | 0.283461i | \(0.0914826\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −12.5336 | −0.462310 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 12.2750 | 0.452156 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 3.00728 | 0.110625 | 0.0553123 | − | 0.998469i | \(-0.482385\pi\) | ||||
0.0553123 | + | 0.998469i | \(0.482385\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 2.44934 | 0.0899788 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 42.4774 | 1.55834 | 0.779172 | − | 0.626810i | \(-0.215640\pi\) | ||||
0.779172 | + | 0.626810i | \(0.215640\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 24.1999 | 0.886616 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −13.1482 | −0.481066 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −27.4287 | −1.00222 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 4.12506 | 0.150526 | 0.0752628 | − | 0.997164i | \(-0.476020\pi\) | ||||
0.0752628 | + | 0.997164i | \(0.476020\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −18.5880 | −0.677383 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 8.33184 | 0.303227 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −24.6428 | −0.895657 | −0.447828 | − | 0.894119i | \(-0.647802\pi\) | ||||
−0.447828 | + | 0.894119i | \(0.647802\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 2.29362 | 0.0832530 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 51.6672 | 1.87293 | 0.936467 | − | 0.350756i | \(-0.114075\pi\) | ||||
0.936467 | + | 0.350756i | \(0.114075\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −17.2274 | −0.623675 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −19.3545 | −0.699763 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −5.35995 | −0.193536 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −1.60716 | −0.0579558 | −0.0289779 | − | 0.999580i | \(-0.509225\pi\) | ||||
−0.0289779 | + | 0.999580i | \(0.509225\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 4.23233 | 0.152424 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 8.38325 | 0.301524 | 0.150762 | − | 0.988570i | \(-0.451827\pi\) | ||||
0.150762 | + | 0.988570i | \(0.451827\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 17.3483 | 0.623171 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −37.2057 | −1.33475 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 24.6374 | 0.882726 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1.76516 | −0.0631624 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −9.32897 | −0.333390 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −60.8858 | −2.17311 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 37.3531 | 1.33150 | 0.665748 | − | 0.746177i | \(-0.268113\pi\) | ||||
0.665748 | + | 0.746177i | \(0.268113\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −27.2699 | −0.970835 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −43.7129 | −1.55425 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −7.71007 | −0.273793 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −48.1503 | −1.70772 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −4.12175 | −0.146000 | −0.0730000 | − | 0.997332i | \(-0.523257\pi\) | ||||
−0.0730000 | + | 0.997332i | \(0.523257\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 13.6258 | 0.482045 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −2.06824 | −0.0730776 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −1.80929 | −0.0638484 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −26.2914 | −0.926650 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 17.3334 | 0.610166 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 43.6064 | 1.53312 | 0.766560 | − | 0.642172i | \(-0.221967\pi\) | ||||
0.766560 | + | 0.642172i | \(0.221967\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −0.946046 | −0.0332202 | −0.0166101 | − | 0.999862i | \(-0.505287\pi\) | ||||
−0.0166101 | + | 0.999862i | \(0.505287\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −19.9402 | −0.699333 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 30.5907 | 1.07154 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 17.3704 | 0.607713 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −3.24835 | −0.113507 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −13.2226 | −0.461470 | −0.230735 | − | 0.973017i | \(-0.574113\pi\) | ||||
−0.230735 | + | 0.973017i | \(0.574113\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −4.96024 | −0.172903 | −0.0864516 | − | 0.996256i | \(-0.527553\pi\) | ||||
−0.0864516 | + | 0.996256i | \(0.527553\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 7.45258 | 0.259465 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 36.0721 | 1.25435 | 0.627175 | − | 0.778878i | \(-0.284211\pi\) | ||||
0.627175 | + | 0.778878i | \(0.284211\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −11.8500 | −0.411566 | −0.205783 | − | 0.978598i | \(-0.565974\pi\) | ||||
−0.205783 | + | 0.978598i | \(0.565974\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −8.21405 | −0.284942 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −19.4805 | −0.674959 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −48.0253 | −1.66198 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −2.32783 | −0.0804616 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 43.2541 | 1.49330 | 0.746648 | − | 0.665219i | \(-0.231662\pi\) | ||||
0.746648 | + | 0.665219i | \(0.231662\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 58.0296 | 2.00102 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 15.8135 | 0.544645 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 3.52882 | 0.121395 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −3.24835 | −0.111615 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −11.2407 | −0.385780 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −26.2704 | −0.900539 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −0.307251 | −0.0105201 | −0.00526003 | − | 0.999986i | \(-0.501674\pi\) | ||||
−0.00526003 | + | 0.999986i | \(0.501674\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −8.64329 | −0.295594 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 49.7992 | 1.70111 | 0.850553 | − | 0.525889i | \(-0.176267\pi\) | ||||
0.850553 | + | 0.525889i | \(0.176267\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 49.1125 | 1.67570 | 0.837849 | − | 0.545903i | \(-0.183813\pi\) | ||||
0.837849 | + | 0.545903i | \(0.183813\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −32.6745 | −1.11354 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 27.7615 | 0.945013 | 0.472507 | − | 0.881327i | \(-0.343349\pi\) | ||||
0.472507 | + | 0.881327i | \(0.343349\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −43.1848 | −1.46833 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −13.0818 | −0.444283 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −3.26150 | −0.110639 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −12.2750 | −0.415923 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −5.04526 | −0.170756 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −28.1135 | −0.950410 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −1.79857 | −0.0607333 | −0.0303666 | − | 0.999539i | \(-0.509667\pi\) | ||||
−0.0303666 | + | 0.999539i | \(0.509667\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 16.4756 | 0.555710 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 16.1505 | 0.544126 | 0.272063 | − | 0.962279i | \(-0.412294\pi\) | ||||
0.272063 | + | 0.962279i | \(0.412294\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 27.0031 | 0.908725 | 0.454363 | − | 0.890817i | \(-0.349867\pi\) | ||||
0.454363 | + | 0.890817i | \(0.349867\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 18.9143 | 0.635797 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −49.9740 | −1.67796 | −0.838981 | − | 0.544161i | \(-0.816848\pi\) | ||||
−0.838981 | + | 0.544161i | \(0.816848\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 29.6085 | 0.993036 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1.00000 | −0.0335013 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 6.08497 | 0.203626 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −37.9520 | −1.26860 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −2.29362 | −0.0765816 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 21.7163 | 0.724278 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −74.8379 | −2.49321 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −23.0368 | −0.766618 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −30.6475 | −1.01876 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −50.6063 | −1.68036 | −0.840178 | − | 0.542311i | \(-0.817550\pi\) | ||||
−0.840178 | + | 0.542311i | \(0.817550\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0.897457 | 0.0297668 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −46.7755 | −1.54974 | −0.774871 | − | 0.632120i | \(-0.782185\pi\) | ||||
−0.774871 | + | 0.632120i | \(0.782185\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 13.1482 | 0.435141 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 27.2075 | 0.899451 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 22.3797 | 0.739041 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 34.6524 | 1.14308 | 0.571539 | − | 0.820575i | \(-0.306347\pi\) | ||||
0.571539 | + | 0.820575i | \(0.306347\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 30.0991 | 0.991800 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 1.76516 | 0.0581009 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −85.3596 | −2.80661 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 1.69769 | 0.0557596 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −48.8020 | −1.60114 | −0.800570 | − | 0.599239i | \(-0.795470\pi\) | ||||
−0.800570 | + | 0.599239i | \(0.795470\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −8.69956 | −0.285116 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 18.6929 | 0.611979 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 19.3545 | 0.632960 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −7.99427 | −0.261161 | −0.130581 | − | 0.991438i | \(-0.541684\pi\) | ||||
−0.130581 | + | 0.991438i | \(0.541684\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −7.73114 | −0.252296 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 58.2642 | 1.89936 | 0.949679 | − | 0.313225i | \(-0.101409\pi\) | ||||
0.949679 | + | 0.313225i | \(0.101409\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −23.0710 | −0.751295 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 11.4629 | 0.372887 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 31.8587 | 1.03527 | 0.517634 | − | 0.855602i | \(-0.326813\pi\) | ||||
0.517634 | + | 0.855602i | \(0.326813\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1.80929 | 0.0587320 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 24.2897 | 0.787646 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 15.4081 | 0.499117 | 0.249558 | − | 0.968360i | \(-0.419715\pi\) | ||||
0.249558 | + | 0.968360i | \(0.419715\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 52.4112 | 1.69599 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 9.32897 | 0.301563 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 30.1531 | 0.973693 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −25.5812 | −0.825200 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 8.44389 | 0.272100 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −26.4908 | −0.852769 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −37.6657 | −1.21125 | −0.605624 | − | 0.795751i | \(-0.707076\pi\) | ||||
−0.605624 | + | 0.795751i | \(0.707076\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −13.4339 | −0.431558 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −21.2714 | −0.682632 | −0.341316 | − | 0.939949i | \(-0.610873\pi\) | ||||
−0.341316 | + | 0.939949i | \(0.610873\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 53.1144 | 1.70277 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −7.45258 | −0.238673 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −40.9806 | −1.31109 | −0.655543 | − | 0.755158i | \(-0.727560\pi\) | ||||
−0.655543 | + | 0.755158i | \(0.727560\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 2.06824 | 0.0661012 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 5.30344 | 0.169326 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 21.0862 | 0.672546 | 0.336273 | − | 0.941765i | \(-0.390834\pi\) | ||||
0.336273 | + | 0.941765i | \(0.390834\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −11.2765 | −0.359298 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −8.06997 | −0.256870 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −16.2660 | −0.517229 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 33.8837 | 1.07635 | 0.538175 | − | 0.842833i | \(-0.319114\pi\) | ||||
0.538175 | + | 0.842833i | \(0.319114\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 2.62003 | 0.0831442 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 68.1785 | 2.16140 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 30.9741 | 0.980959 | 0.490480 | − | 0.871453i | \(-0.336822\pi\) | ||||
0.490480 | + | 0.871453i | \(0.336822\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 11.4537 | 0.362379 |
(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 | 3432.2.a.w.1.5 | ✓ | 5 | |
4.3 | odd | 2 | 6864.2.a.cf.1.5 | 5 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3432.2.a.w.1.5 | ✓ | 5 | 1.1 | even | 1 | trivial | |
6864.2.a.cf.1.5 | 5 | 4.3 | odd | 2 |