Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [920,2,Mod(1,920)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(920, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("920.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 920 = 2^{3} \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 920.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: | \(7.34623698596\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.229.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - 4x - 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(2.11491\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 920.1 |
$q$-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 | ||||||||
\(3\) | 2.47283 | 1.42769 | 0.713846 | − | 0.700303i | \(-0.246952\pi\) | ||||
0.713846 | + | 0.700303i | \(0.246952\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.527166 | 0.199250 | 0.0996250 | − | 0.995025i | \(-0.468236\pi\) | ||||
0.0996250 | + | 0.995025i | \(0.468236\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 3.11491 | 1.03830 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.11491 | 0.939180 | 0.469590 | − | 0.882885i | \(-0.344402\pi\) | ||||
0.469590 | + | 0.882885i | \(0.344402\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.11491 | 1.14127 | 0.570635 | − | 0.821204i | \(-0.306697\pi\) | ||||
0.570635 | + | 0.821204i | \(0.306697\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 2.47283 | 0.638483 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −4.39905 | −1.06693 | −0.533464 | − | 0.845823i | \(-0.679110\pi\) | ||||
−0.533464 | + | 0.845823i | \(0.679110\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −3.70265 | −0.849446 | −0.424723 | − | 0.905323i | \(-0.639628\pi\) | ||||
−0.424723 | + | 0.905323i | \(0.639628\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.30359 | 0.284468 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.00000 | −0.208514 | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0.284147 | 0.0546842 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −9.10170 | −1.69014 | −0.845072 | − | 0.534653i | \(-0.820442\pi\) | ||||
−0.845072 | + | 0.534653i | \(0.820442\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.83076 | 0.867630 | 0.433815 | − | 0.901002i | \(-0.357167\pi\) | ||||
0.433815 | + | 0.901002i | \(0.357167\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 7.70265 | 1.34086 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0.527166 | 0.0891073 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 9.74378 | 1.60187 | 0.800934 | − | 0.598753i | \(-0.204337\pi\) | ||||
0.800934 | + | 0.598753i | \(0.204337\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 10.1755 | 1.62938 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 6.93246 | 1.08267 | 0.541334 | − | 0.840807i | \(-0.317919\pi\) | ||||
0.541334 | + | 0.840807i | \(0.317919\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −4.45963 | −0.680087 | −0.340044 | − | 0.940410i | \(-0.610442\pi\) | ||||
−0.340044 | + | 0.940410i | \(0.610442\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 3.11491 | 0.464343 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0.642074 | 0.0936561 | 0.0468280 | − | 0.998903i | \(-0.485089\pi\) | ||||
0.0468280 | + | 0.998903i | \(0.485089\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.72210 | −0.960299 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −10.8781 | −1.52324 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −3.89134 | −0.534516 | −0.267258 | − | 0.963625i | \(-0.586118\pi\) | ||||
−0.267258 | + | 0.963625i | \(0.586118\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 3.11491 | 0.420014 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −9.15604 | −1.21275 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 8.79811 | 1.14542 | 0.572708 | − | 0.819759i | \(-0.305893\pi\) | ||||
0.572708 | + | 0.819759i | \(0.305893\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −3.45339 | −0.442161 | −0.221080 | − | 0.975256i | \(-0.570958\pi\) | ||||
−0.221080 | + | 0.975256i | \(0.570958\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 1.64207 | 0.206882 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 4.11491 | 0.510391 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −8.60719 | −1.05154 | −0.525768 | − | 0.850628i | \(-0.676222\pi\) | ||||
−0.525768 | + | 0.850628i | \(0.676222\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −2.47283 | −0.297694 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 12.3642 | 1.46736 | 0.733678 | − | 0.679497i | \(-0.237802\pi\) | ||||
0.733678 | + | 0.679497i | \(0.237802\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −5.81756 | −0.680893 | −0.340447 | − | 0.940264i | \(-0.610578\pi\) | ||||
−0.340447 | + | 0.940264i | \(0.610578\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 2.47283 | 0.285538 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1.64207 | 0.187132 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −3.17548 | −0.357270 | −0.178635 | − | 0.983915i | \(-0.557168\pi\) | ||||
−0.178635 | + | 0.983915i | \(0.557168\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −8.64207 | −0.960230 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 4.71585 | 0.517632 | 0.258816 | − | 0.965927i | \(-0.416668\pi\) | ||||
0.258816 | + | 0.965927i | \(0.416668\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −4.39905 | −0.477144 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −22.5070 | −2.41300 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −5.43171 | −0.575760 | −0.287880 | − | 0.957667i | \(-0.592950\pi\) | ||||
−0.287880 | + | 0.957667i | \(0.592950\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.16924 | 0.227398 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 11.9457 | 1.23871 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −3.70265 | −0.379884 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −4.06058 | −0.412289 | −0.206144 | − | 0.978522i | \(-0.566092\pi\) | ||||
−0.206144 | + | 0.978522i | \(0.566092\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 9.70265 | 0.975153 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −15.5529 | −1.54757 | −0.773784 | − | 0.633450i | \(-0.781638\pi\) | ||||
−0.773784 | + | 0.633450i | \(0.781638\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 17.9519 | 1.76885 | 0.884427 | − | 0.466678i | \(-0.154549\pi\) | ||||
0.884427 | + | 0.466678i | \(0.154549\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 1.30359 | 0.127218 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −12.2298 | −1.18230 | −0.591150 | − | 0.806561i | \(-0.701326\pi\) | ||||
−0.591150 | + | 0.806561i | \(0.701326\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 9.10795 | 0.872383 | 0.436192 | − | 0.899854i | \(-0.356327\pi\) | ||||
0.436192 | + | 0.899854i | \(0.356327\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 24.0947 | 2.28697 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −13.1755 | −1.23945 | −0.619723 | − | 0.784821i | \(-0.712755\pi\) | ||||
−0.619723 | + | 0.784821i | \(0.712755\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1.00000 | −0.0932505 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 12.8176 | 1.18498 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −2.31903 | −0.212585 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.29735 | −0.117941 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 17.1428 | 1.54572 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 19.5613 | 1.73579 | 0.867894 | − | 0.496750i | \(-0.165473\pi\) | ||||
0.867894 | + | 0.496750i | \(0.165473\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −11.0279 | −0.970955 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −4.15604 | −0.363115 | −0.181557 | − | 0.983380i | \(-0.558114\pi\) | ||||
−0.181557 | + | 0.983380i | \(0.558114\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.95191 | −0.169252 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0.284147 | 0.0244555 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −11.1344 | −0.951272 | −0.475636 | − | 0.879642i | \(-0.657782\pi\) | ||||
−0.475636 | + | 0.879642i | \(0.657782\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −6.49452 | −0.550858 | −0.275429 | − | 0.961321i | \(-0.588820\pi\) | ||||
−0.275429 | + | 0.961321i | \(0.588820\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1.58774 | 0.133712 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 12.8176 | 1.07186 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −9.10170 | −0.755855 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −16.6226 | −1.37101 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −5.47283 | −0.448352 | −0.224176 | − | 0.974549i | \(-0.571969\pi\) | ||||
−0.224176 | + | 0.974549i | \(0.571969\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −0.0954606 | −0.00776848 | −0.00388424 | − | 0.999992i | \(-0.501236\pi\) | ||||
−0.00388424 | + | 0.999992i | \(0.501236\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −13.7026 | −1.10779 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 4.83076 | 0.388016 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −3.40530 | −0.271772 | −0.135886 | − | 0.990724i | \(-0.543388\pi\) | ||||
−0.135886 | + | 0.990724i | \(0.543388\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −9.62263 | −0.763124 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −0.527166 | −0.0415465 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 18.5745 | 1.45487 | 0.727435 | − | 0.686177i | \(-0.240712\pi\) | ||||
0.727435 | + | 0.686177i | \(0.240712\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 7.70265 | 0.599650 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −12.4596 | −0.964155 | −0.482078 | − | 0.876129i | \(-0.660118\pi\) | ||||
−0.482078 | + | 0.876129i | \(0.660118\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 3.93246 | 0.302497 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −11.5334 | −0.881982 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 3.49228 | 0.265513 | 0.132757 | − | 0.991149i | \(-0.457617\pi\) | ||||
0.132757 | + | 0.991149i | \(0.457617\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0.527166 | 0.0398500 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 21.7563 | 1.63530 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 6.38585 | 0.477301 | 0.238650 | − | 0.971106i | \(-0.423295\pi\) | ||||
0.238650 | + | 0.971106i | \(0.423295\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −20.8781 | −1.55186 | −0.775930 | − | 0.630819i | \(-0.782719\pi\) | ||||
−0.775930 | + | 0.630819i | \(0.782719\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −8.53965 | −0.631269 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 9.74378 | 0.716377 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −13.7026 | −1.00204 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0.149793 | 0.0108958 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −6.83700 | −0.494708 | −0.247354 | − | 0.968925i | \(-0.579561\pi\) | ||||
−0.247354 | + | 0.968925i | \(0.579561\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 7.10170 | 0.511192 | 0.255596 | − | 0.966784i | \(-0.417728\pi\) | ||||
0.255596 | + | 0.966784i | \(0.417728\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 10.1755 | 0.728681 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 0.850207 | 0.0605748 | 0.0302874 | − | 0.999541i | \(-0.490358\pi\) | ||||
0.0302874 | + | 0.999541i | \(0.490358\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 8.56829 | 0.607390 | 0.303695 | − | 0.952769i | \(-0.401780\pi\) | ||||
0.303695 | + | 0.952769i | \(0.401780\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −21.2841 | −1.50127 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −4.79811 | −0.336761 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 6.93246 | 0.484184 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −3.11491 | −0.216501 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −11.5334 | −0.797783 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 9.63511 | 0.663309 | 0.331654 | − | 0.943401i | \(-0.392393\pi\) | ||||
0.331654 | + | 0.943401i | \(0.392393\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 30.5745 | 2.09493 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −4.45963 | −0.304144 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 2.54661 | 0.172875 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −14.3859 | −0.972106 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −18.1017 | −1.21765 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 9.43171 | 0.631594 | 0.315797 | − | 0.948827i | \(-0.397728\pi\) | ||||
0.315797 | + | 0.948827i | \(0.397728\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 3.11491 | 0.207661 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −3.91774 | −0.260030 | −0.130015 | − | 0.991512i | \(-0.541503\pi\) | ||||
−0.130015 | + | 0.991512i | \(0.541503\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −22.0947 | −1.46006 | −0.730031 | − | 0.683414i | \(-0.760494\pi\) | ||||
−0.730031 | + | 0.683414i | \(0.760494\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 4.06058 | 0.267166 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −12.5334 | −0.821091 | −0.410545 | − | 0.911840i | \(-0.634662\pi\) | ||||
−0.410545 | + | 0.911840i | \(0.634662\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0.642074 | 0.0418843 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −7.85244 | −0.510071 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −12.4123 | −0.802882 | −0.401441 | − | 0.915885i | \(-0.631491\pi\) | ||||
−0.401441 | + | 0.915885i | \(0.631491\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 5.74378 | 0.369989 | 0.184995 | − | 0.982740i | \(-0.440773\pi\) | ||||
0.184995 | + | 0.982740i | \(0.440773\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −22.2229 | −1.42560 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −6.72210 | −0.429459 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −15.2361 | −0.969447 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 11.6615 | 0.739019 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −6.33624 | −0.399940 | −0.199970 | − | 0.979802i | \(-0.564085\pi\) | ||||
−0.199970 | + | 0.979802i | \(0.564085\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −3.11491 | −0.195833 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −10.8781 | −0.681215 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 22.2772 | 1.38961 | 0.694806 | − | 0.719197i | \(-0.255490\pi\) | ||||
0.694806 | + | 0.719197i | \(0.255490\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 5.13659 | 0.319172 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −28.3510 | −1.75488 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −4.66776 | −0.287827 | −0.143913 | − | 0.989590i | \(-0.545969\pi\) | ||||
−0.143913 | + | 0.989590i | \(0.545969\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −3.89134 | −0.239043 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −13.4317 | −0.822007 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 9.70889 | 0.591962 | 0.295981 | − | 0.955194i | \(-0.404354\pi\) | ||||
0.295981 | + | 0.955194i | \(0.404354\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −6.75698 | −0.410457 | −0.205229 | − | 0.978714i | \(-0.565794\pi\) | ||||
−0.205229 | + | 0.978714i | \(0.565794\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 5.36417 | 0.324654 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 3.11491 | 0.187836 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 19.0194 | 1.14277 | 0.571384 | − | 0.820683i | \(-0.306407\pi\) | ||||
0.571384 | + | 0.820683i | \(0.306407\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 15.0474 | 0.900863 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −32.8370 | −1.95889 | −0.979446 | − | 0.201708i | \(-0.935351\pi\) | ||||
−0.979446 | + | 0.201708i | \(0.935351\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 13.7827 | 0.819295 | 0.409647 | − | 0.912244i | \(-0.365652\pi\) | ||||
0.409647 | + | 0.912244i | \(0.365652\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −9.15604 | −0.542357 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 3.65456 | 0.215722 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 2.35168 | 0.138334 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −10.0411 | −0.588621 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 15.0668 | 0.880213 | 0.440106 | − | 0.897946i | \(-0.354941\pi\) | ||||
0.440106 | + | 0.897946i | \(0.354941\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 8.79811 | 0.512246 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0.885092 | 0.0513583 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −4.11491 | −0.237971 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2.35097 | −0.135507 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −38.4596 | −2.20945 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −3.45339 | −0.197740 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −5.91302 | −0.337474 | −0.168737 | − | 0.985661i | \(-0.553969\pi\) | ||||
−0.168737 | + | 0.985661i | \(0.553969\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 44.3921 | 2.52538 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −25.7911 | −1.46248 | −0.731241 | − | 0.682119i | \(-0.761058\pi\) | ||||
−0.731241 | + | 0.682119i | \(0.761058\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 16.7306 | 0.945668 | 0.472834 | − | 0.881152i | \(-0.343231\pi\) | ||||
0.472834 | + | 0.881152i | \(0.343231\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 1.64207 | 0.0925204 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 28.1623 | 1.58175 | 0.790876 | − | 0.611977i | \(-0.209625\pi\) | ||||
0.790876 | + | 0.611977i | \(0.209625\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −28.3510 | −1.58735 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −30.2423 | −1.68796 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 16.2882 | 0.906297 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 4.11491 | 0.228254 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 22.5224 | 1.24549 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0.338479 | 0.0186610 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −25.8176 | −1.41906 | −0.709531 | − | 0.704675i | \(-0.751093\pi\) | ||||
−0.709531 | + | 0.704675i | \(0.751093\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 30.3510 | 1.66322 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −8.60719 | −0.470261 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 33.5676 | 1.82854 | 0.914271 | − | 0.405103i | \(-0.132764\pi\) | ||||
0.914271 | + | 0.405103i | \(0.132764\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −32.5808 | −1.76955 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 15.0474 | 0.814861 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −7.23382 | −0.390590 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −2.47283 | −0.133133 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 7.63984 | 0.410128 | 0.205064 | − | 0.978749i | \(-0.434260\pi\) | ||||
0.205064 | + | 0.978749i | \(0.434260\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 3.01945 | 0.161627 | 0.0808136 | − | 0.996729i | \(-0.474248\pi\) | ||||
0.0808136 | + | 0.996729i | \(0.474248\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.16924 | 0.0624094 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −25.1840 | −1.34041 | −0.670203 | − | 0.742177i | \(-0.733793\pi\) | ||||
−0.670203 | + | 0.742177i | \(0.733793\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 12.3642 | 0.656222 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −5.73458 | −0.303506 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −5.32304 | −0.280939 | −0.140470 | − | 0.990085i | \(-0.544861\pi\) | ||||
−0.140470 | + | 0.990085i | \(0.544861\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −5.29039 | −0.278442 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −3.20813 | −0.168383 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −5.81756 | −0.304505 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 8.24230 | 0.430245 | 0.215122 | − | 0.976587i | \(-0.430985\pi\) | ||||
0.215122 | + | 0.976587i | \(0.430985\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 21.5940 | 1.12414 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −2.05138 | −0.106502 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 1.91774 | 0.0992970 | 0.0496485 | − | 0.998767i | \(-0.484190\pi\) | ||||
0.0496485 | + | 0.998767i | \(0.484190\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 2.47283 | 0.127697 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −37.4527 | −1.92891 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 30.1692 | 1.54969 | 0.774845 | − | 0.632151i | \(-0.217828\pi\) | ||||
0.774845 | + | 0.632151i | \(0.217828\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 48.3719 | 2.47817 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −1.64903 | −0.0842617 | −0.0421309 | − | 0.999112i | \(-0.513415\pi\) | ||||
−0.0421309 | + | 0.999112i | \(0.513415\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1.64207 | 0.0836878 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −13.8913 | −0.706136 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −16.6414 | −0.843750 | −0.421875 | − | 0.906654i | \(-0.638628\pi\) | ||||
−0.421875 | + | 0.906654i | \(0.638628\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 4.39905 | 0.222470 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −10.2772 | −0.518415 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −3.17548 | −0.159776 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 36.0257 | 1.80808 | 0.904039 | − | 0.427450i | \(-0.140588\pi\) | ||||
0.904039 | + | 0.427450i | \(0.140588\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −4.82675 | −0.241640 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −5.62263 | −0.280781 | −0.140390 | − | 0.990096i | \(-0.544836\pi\) | ||||
−0.140390 | + | 0.990096i | \(0.544836\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 19.8781 | 0.990200 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −8.64207 | −0.429428 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 30.3510 | 1.50444 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −2.76546 | −0.136743 | −0.0683716 | − | 0.997660i | \(-0.521780\pi\) | ||||
−0.0683716 | + | 0.997660i | \(0.521780\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −27.5334 | −1.35812 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 4.63807 | 0.228224 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 4.71585 | 0.231492 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −16.0599 | −0.786455 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −17.5962 | −0.859632 | −0.429816 | − | 0.902917i | \(-0.641421\pi\) | ||||
−0.429816 | + | 0.902917i | \(0.641421\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 25.5676 | 1.24609 | 0.623044 | − | 0.782187i | \(-0.285896\pi\) | ||||
0.623044 | + | 0.782187i | \(0.285896\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 2.00000 | 0.0972433 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −4.39905 | −0.213386 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −1.82051 | −0.0881006 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 31.6957 | 1.53028 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 17.9736 | 0.865757 | 0.432879 | − | 0.901452i | \(-0.357498\pi\) | ||||
0.432879 | + | 0.901452i | \(0.357498\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 37.0382 | 1.77994 | 0.889971 | − | 0.456018i | \(-0.150725\pi\) | ||||
0.889971 | + | 0.456018i | \(0.150725\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −22.5070 | −1.07913 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 3.70265 | 0.177122 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 38.8168 | 1.85263 | 0.926313 | − | 0.376754i | \(-0.122960\pi\) | ||||
0.926313 | + | 0.376754i | \(0.122960\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −20.9387 | −0.997081 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 25.3726 | 1.20549 | 0.602745 | − | 0.797934i | \(-0.294073\pi\) | ||||
0.602745 | + | 0.797934i | \(0.294073\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −5.43171 | −0.257488 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −13.5334 | −0.640108 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 33.4589 | 1.57902 | 0.789512 | − | 0.613735i | \(-0.210334\pi\) | ||||
0.789512 | + | 0.613735i | \(0.210334\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 21.5940 | 1.01682 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −0.236058 | −0.0110910 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 2.16924 | 0.101696 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −27.5264 | −1.28763 | −0.643816 | − | 0.765180i | \(-0.722650\pi\) | ||||
−0.643816 | + | 0.765180i | \(0.722650\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −1.24998 | −0.0583440 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 36.3161 | 1.69141 | 0.845704 | − | 0.533652i | \(-0.179181\pi\) | ||||
0.845704 | + | 0.533652i | \(0.179181\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −22.5544 | −1.04819 | −0.524095 | − | 0.851660i | \(-0.675596\pi\) | ||||
−0.524095 | + | 0.851660i | \(0.675596\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 11.9457 | 0.553967 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 22.8370 | 1.05677 | 0.528385 | − | 0.849005i | \(-0.322798\pi\) | ||||
0.528385 | + | 0.849005i | \(0.322798\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −4.53742 | −0.209518 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −8.42074 | −0.388007 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −13.8913 | −0.638724 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −3.70265 | −0.169889 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −12.1212 | −0.554989 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −35.5264 | −1.62324 | −0.811622 | − | 0.584182i | \(-0.801415\pi\) | ||||
−0.811622 | + | 0.584182i | \(0.801415\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 40.0947 | 1.82816 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −1.30359 | −0.0593156 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −4.06058 | −0.184381 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −10.4945 | −0.475552 | −0.237776 | − | 0.971320i | \(-0.576418\pi\) | ||||
−0.237776 | + | 0.971320i | \(0.576418\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 45.9317 | 2.07711 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 42.1685 | 1.90304 | 0.951519 | − | 0.307589i | \(-0.0995221\pi\) | ||||
0.951519 | + | 0.307589i | \(0.0995221\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 40.0389 | 1.80326 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 9.70265 | 0.436102 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 6.51797 | 0.292371 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 30.1560 | 1.34997 | 0.674985 | − | 0.737832i | \(-0.264150\pi\) | ||||
0.674985 | + | 0.737832i | \(0.264150\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −30.8106 | −1.37652 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 22.9729 | 1.02431 | 0.512155 | − | 0.858893i | \(-0.328847\pi\) | ||||
0.512155 | + | 0.858893i | \(0.328847\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −15.5529 | −0.692093 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 9.72433 | 0.431873 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 11.8176 | 0.523804 | 0.261902 | − | 0.965094i | \(-0.415650\pi\) | ||||
0.261902 | + | 0.965094i | \(0.415650\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −3.06682 | −0.135668 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −1.05210 | −0.0464512 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 17.9519 | 0.791056 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 2.00000 | 0.0879599 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 8.63583 | 0.379071 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −35.7438 | −1.56596 | −0.782982 | − | 0.622045i | \(-0.786302\pi\) | ||||
−0.782982 | + | 0.622045i | \(0.786302\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 14.3899 | 0.629225 | 0.314612 | − | 0.949220i | \(-0.398125\pi\) | ||||
0.314612 | + | 0.949220i | \(0.398125\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 1.30359 | 0.0568935 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −21.2508 | −0.925698 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 27.4053 | 1.18929 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 28.5264 | 1.23562 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −12.2298 | −0.528741 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 15.7911 | 0.681438 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −20.9387 | −0.901894 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 14.5209 | 0.624303 | 0.312152 | − | 0.950032i | \(-0.398950\pi\) | ||||
0.312152 | + | 0.950032i | \(0.398950\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −51.6282 | −2.21558 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 9.10795 | 0.390142 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 19.6289 | 0.839270 | 0.419635 | − | 0.907693i | \(-0.362158\pi\) | ||||
0.419635 | + | 0.907693i | \(0.362158\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −10.7570 | −0.459097 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 33.7004 | 1.43569 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −1.67401 | −0.0711860 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 24.0947 | 1.02276 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 1.13659 | 0.0481588 | 0.0240794 | − | 0.999710i | \(-0.492335\pi\) | ||||
0.0240794 | + | 0.999710i | \(0.492335\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −18.3510 | −0.776163 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −33.8844 | −1.43060 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 25.8913 | 1.09119 | 0.545595 | − | 0.838049i | \(-0.316304\pi\) | ||||
0.545595 | + | 0.838049i | \(0.316304\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −13.1755 | −0.554297 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −4.55581 | −0.191326 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −44.0558 | −1.84692 | −0.923459 | − | 0.383698i | \(-0.874650\pi\) | ||||
−0.923459 | + | 0.383698i | \(0.874650\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −41.8991 | −1.75342 | −0.876711 | − | 0.481017i | \(-0.840268\pi\) | ||||
−0.876711 | + | 0.481017i | \(0.840268\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −16.9068 | −0.706291 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −1.00000 | −0.0417029 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 1.34544 | 0.0560114 | 0.0280057 | − | 0.999608i | \(-0.491084\pi\) | ||||
0.0280057 | + | 0.999608i | \(0.491084\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 17.5613 | 0.729824 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 2.48604 | 0.103138 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −12.1212 | −0.502007 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 12.8176 | 0.529941 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 25.0411 | 1.03356 | 0.516779 | − | 0.856119i | \(-0.327131\pi\) | ||||
0.516779 | + | 0.856119i | \(0.327131\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −17.8866 | −0.737005 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 2.10242 | 0.0864821 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −22.5947 | −0.927853 | −0.463927 | − | 0.885874i | \(-0.653560\pi\) | ||||
−0.463927 | + | 0.885874i | \(0.653560\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −2.31903 | −0.0950711 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 21.1880 | 0.867166 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 14.7111 | 0.601080 | 0.300540 | − | 0.953769i | \(-0.402833\pi\) | ||||
0.300540 | + | 0.953769i | \(0.402833\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 19.2904 | 0.786871 | 0.393436 | − | 0.919352i | \(-0.371286\pi\) | ||||
0.393436 | + | 0.919352i | \(0.371286\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −26.8106 | −1.09181 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −1.29735 | −0.0527448 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −20.7547 | −0.842409 | −0.421205 | − | 0.906966i | \(-0.638393\pi\) | ||||
−0.421205 | + | 0.906966i | \(0.638393\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −11.8649 | −0.480791 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 2.64207 | 0.106887 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −43.3091 | −1.74924 | −0.874619 | − | 0.484810i | \(-0.838889\pi\) | ||||
−0.874619 | + | 0.484810i | \(0.838889\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 17.1428 | 0.691266 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 13.5621 | 0.545988 | 0.272994 | − | 0.962016i | \(-0.411986\pi\) | ||||
0.272994 | + | 0.962016i | \(0.411986\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −12.9045 | −0.518677 | −0.259339 | − | 0.965786i | \(-0.583505\pi\) | ||||
−0.259339 | + | 0.965786i | \(0.583505\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −0.284147 | −0.0114024 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −2.86341 | −0.114720 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −28.5202 | −1.13899 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −42.8634 | −1.70908 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 45.0404 | 1.79303 | 0.896515 | − | 0.443013i | \(-0.146090\pi\) | ||||
0.896515 | + | 0.443013i | \(0.146090\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 23.8260 | 0.947000 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 19.5613 | 0.776268 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −27.6608 | −1.09596 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 38.5132 | 1.52356 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −3.08074 | −0.121682 | −0.0608410 | − | 0.998147i | \(-0.519378\pi\) | ||||
−0.0608410 | + | 0.998147i | \(0.519378\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 4.52493 | 0.178446 | 0.0892229 | − | 0.996012i | \(-0.471562\pi\) | ||||
0.0892229 | + | 0.996012i | \(0.471562\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −11.0279 | −0.434224 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 34.8719 | 1.37096 | 0.685478 | − | 0.728094i | \(-0.259593\pi\) | ||||
0.685478 | + | 0.728094i | \(0.259593\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 27.4053 | 1.07575 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 6.29735 | 0.246813 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −35.3726 | −1.38424 | −0.692119 | − | 0.721783i | \(-0.743323\pi\) | ||||
−0.692119 | + | 0.721783i | \(0.743323\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −4.15604 | −0.162390 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −18.1212 | −0.706973 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −2.10866 | −0.0821419 | −0.0410710 | − | 0.999156i | \(-0.513077\pi\) | ||||
−0.0410710 | + | 0.999156i | \(0.513077\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 20.0342 | 0.779239 | 0.389619 | − | 0.920976i | \(-0.372607\pi\) | ||||
0.389619 | + | 0.920976i | \(0.372607\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −44.7625 | −1.73843 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −1.95191 | −0.0756919 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 9.10170 | 0.352419 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 23.3230 | 0.901721 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −10.7570 | −0.415269 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −5.07530 | −0.195638 | −0.0978191 | − | 0.995204i | \(-0.531187\pi\) | ||||
−0.0978191 | + | 0.995204i | \(0.531187\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0.284147 | 0.0109368 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −13.4876 | −0.518369 | −0.259184 | − | 0.965828i | \(-0.583454\pi\) | ||||
−0.259184 | + | 0.965828i | \(0.583454\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −2.14060 | −0.0821486 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −9.68793 | −0.371242 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 25.4379 | 0.973356 | 0.486678 | − | 0.873581i | \(-0.338208\pi\) | ||||
0.486678 | + | 0.873581i | \(0.338208\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −11.1344 | −0.425422 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −54.6366 | −2.08452 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −16.0125 | −0.610027 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 22.6506 | 0.861668 | 0.430834 | − | 0.902431i | \(-0.358220\pi\) | ||||
0.430834 | + | 0.902431i | \(0.358220\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 5.11491 | 0.194299 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −6.49452 | −0.246351 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −30.4963 | −1.15513 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −30.9930 | −1.17226 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −41.8099 | −1.57914 | −0.789569 | − | 0.613662i | \(-0.789696\pi\) | ||||
−0.789569 | + | 0.613662i | \(0.789696\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −36.0778 | −1.36070 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 1.58774 | 0.0597978 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −8.19894 | −0.308353 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 2.87117 | 0.107829 | 0.0539146 | − | 0.998546i | \(-0.482830\pi\) | ||||
0.0539146 | + | 0.998546i | \(0.482830\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −9.89134 | −0.370954 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −4.83076 | −0.180913 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 12.8176 | 0.479349 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −30.6935 | −1.14627 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −50.1623 | −1.87074 | −0.935369 | − | 0.353674i | \(-0.884932\pi\) | ||||
−0.935369 | + | 0.353674i | \(0.884932\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 9.46364 | 0.352444 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 14.2034 | 0.528230 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −9.10170 | −0.338029 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −26.8198 | −0.994691 | −0.497345 | − | 0.867553i | \(-0.665692\pi\) | ||||
−0.497345 | + | 0.867553i | \(0.665692\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −29.0272 | −1.07508 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 19.6182 | 0.725604 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 35.9861 | 1.32918 | 0.664588 | − | 0.747210i | \(-0.268607\pi\) | ||||
0.664588 | + | 0.747210i | \(0.268607\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −16.6226 | −0.613135 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −26.8106 | −0.987581 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 5.84396 | 0.214974 | 0.107487 | − | 0.994207i | \(-0.465720\pi\) | ||||
0.107487 | + | 0.994207i | \(0.465720\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −37.6762 | −1.38407 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 14.2012 | 0.520991 | 0.260495 | − | 0.965475i | \(-0.416114\pi\) | ||||
0.260495 | + | 0.965475i | \(0.416114\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −5.47283 | −0.200509 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 14.6894 | 0.537459 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −6.44714 | −0.235574 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 33.0404 | 1.20566 | 0.602831 | − | 0.797869i | \(-0.294039\pi\) | ||||
0.602831 | + | 0.797869i | \(0.294039\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −15.6685 | −0.570991 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −0.0954606 | −0.00347417 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 18.2034 | 0.661614 | 0.330807 | − | 0.943698i | \(-0.392679\pi\) | ||||
0.330807 | + | 0.943698i | \(0.392679\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −7.70265 | −0.279588 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 34.1010 | 1.23616 | 0.618080 | − | 0.786115i | \(-0.287911\pi\) | ||||
0.618080 | + | 0.786115i | \(0.287911\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 4.80140 | 0.173822 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −13.7026 | −0.495420 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 36.2034 | 1.30723 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 35.1366 | 1.26706 | 0.633529 | − | 0.773719i | \(-0.281606\pi\) | ||||
0.633529 | + | 0.773719i | \(0.281606\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 55.0878 | 1.98394 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 1.13659 | 0.0408803 | 0.0204401 | − | 0.999791i | \(-0.493493\pi\) | ||||
0.0204401 | + | 0.999791i | \(0.493493\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 4.83076 | 0.173526 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 12.7019 | 0.455679 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −25.6685 | −0.919669 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 38.5132 | 1.37811 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −2.58622 | −0.0924241 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −3.40530 | −0.121540 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −8.33848 | −0.297235 | −0.148617 | − | 0.988895i | \(-0.547482\pi\) | ||||
−0.148617 | + | 0.988895i | \(0.547482\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −11.5426 | −0.410928 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −6.94567 | −0.246960 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −14.2104 | −0.504625 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −9.62263 | −0.341279 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −0.190921 | −0.00676278 | −0.00338139 | − | 0.999994i | \(-0.501076\pi\) | ||||
−0.00338139 | + | 0.999994i | \(0.501076\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −2.82452 | −0.0999242 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −16.9193 | −0.597813 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −18.1212 | −0.639482 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −0.527166 | −0.0185802 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 24.0085 | 0.845138 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −14.5202 | −0.510503 | −0.255252 | − | 0.966875i | \(-0.582158\pi\) | ||||
−0.255252 | + | 0.966875i | \(0.582158\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −51.5474 | −1.81007 | −0.905037 | − | 0.425332i | \(-0.860157\pi\) | ||||
−0.905037 | + | 0.425332i | \(0.860157\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −16.7089 | −0.586006 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 18.5745 | 0.650638 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 16.5124 | 0.577697 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 6.75698 | 0.236108 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 13.7827 | 0.481019 | 0.240509 | − | 0.970647i | \(-0.422686\pi\) | ||||
0.240509 | + | 0.970647i | \(0.422686\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −37.1531 | −1.29508 | −0.647538 | − | 0.762034i | \(-0.724201\pi\) | ||||
−0.647538 | + | 0.762034i | \(0.724201\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 7.70265 | 0.268172 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −39.8510 | −1.38576 | −0.692878 | − | 0.721055i | \(-0.743657\pi\) | ||||
−0.692878 | + | 0.721055i | \(0.743657\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 20.5933 | 0.715234 | 0.357617 | − | 0.933868i | \(-0.383589\pi\) | ||||
0.357617 | + | 0.933868i | \(0.383589\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 47.0319 | 1.63152 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 29.5709 | 1.02457 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −12.4596 | −0.431183 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 1.37265 | 0.0474456 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −36.5669 | −1.26243 | −0.631214 | − | 0.775609i | \(-0.717443\pi\) | ||||
−0.631214 | + | 0.775609i | \(0.717443\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 53.8410 | 1.85659 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −81.2005 | −2.79669 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 3.93246 | 0.135281 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −0.683919 | −0.0234998 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 34.0823 | 1.16970 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −9.74378 | −0.334012 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −19.3208 | −0.661532 | −0.330766 | − | 0.943713i | \(-0.607307\pi\) | ||||
−0.330766 | + | 0.943713i | \(0.607307\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −11.5334 | −0.394434 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 54.6017 | 1.86516 | 0.932580 | − | 0.360963i | \(-0.117552\pi\) | ||||
0.932580 | + | 0.360963i | \(0.117552\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −32.9541 | −1.12438 | −0.562190 | − | 0.827008i | \(-0.690041\pi\) | ||||
−0.562190 | + | 0.827008i | \(0.690041\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 9.03712 | 0.307984 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −54.6840 | −1.86147 | −0.930733 | − | 0.365701i | \(-0.880829\pi\) | ||||
−0.930733 | + | 0.365701i | \(0.880829\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 3.49228 | 0.118741 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 5.81532 | 0.197499 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −9.89134 | −0.335541 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −35.4178 | −1.20009 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −12.6483 | −0.428081 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0.527166 | 0.0178215 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 16.7500 | 0.565608 | 0.282804 | − | 0.959178i | \(-0.408735\pi\) | ||||
0.282804 | + | 0.959178i | \(0.408735\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 37.2577 | 1.25667 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −31.7049 | −1.06816 | −0.534082 | − | 0.845432i | \(-0.679343\pi\) | ||||
−0.534082 | + | 0.845432i | \(0.679343\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 51.9185 | 1.74720 | 0.873599 | − | 0.486646i | \(-0.161780\pi\) | ||||
0.873599 | + | 0.486646i | \(0.161780\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 21.7563 | 0.731329 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 36.2897 | 1.21849 | 0.609244 | − | 0.792983i | \(-0.291473\pi\) | ||||
0.609244 | + | 0.792983i | \(0.291473\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 10.3121 | 0.345856 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −26.9193 | −0.901829 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −2.37737 | −0.0795558 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 6.38585 | 0.213455 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −10.1755 | −0.339749 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −43.9681 | −1.46642 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 17.1182 | 0.570290 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −5.81355 | −0.193463 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −20.8781 | −0.694013 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −25.4442 | −0.844861 | −0.422430 | − | 0.906395i | \(-0.638823\pi\) | ||||
−0.422430 | + | 0.906395i | \(0.638823\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −48.4457 | −1.60684 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 47.9597 | 1.58897 | 0.794487 | − | 0.607281i | \(-0.207740\pi\) | ||||
0.794487 | + | 0.607281i | \(0.207740\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 14.6894 | 0.486150 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −8.53965 | −0.282312 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −2.19092 | −0.0723506 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 2.78562 | 0.0918892 | 0.0459446 | − | 0.998944i | \(-0.485370\pi\) | ||||
0.0459446 | + | 0.998944i | \(0.485370\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −14.6219 | −0.481808 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 50.8774 | 1.67465 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 9.74378 | 0.320373 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 55.9185 | 1.83661 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 40.2508 | 1.32059 | 0.660293 | − | 0.751008i | \(-0.270432\pi\) | ||||
0.660293 | + | 0.751008i | \(0.270432\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 24.8896 | 0.815722 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −63.7772 | −2.08797 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −13.7026 | −0.448125 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −38.9868 | −1.27364 | −0.636822 | − | 0.771011i | \(-0.719751\pi\) | ||||
−0.636822 | + | 0.771011i | \(0.719751\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 41.3719 | 1.35012 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 38.3682 | 1.25077 | 0.625383 | − | 0.780318i | \(-0.284943\pi\) | ||||
0.625383 | + | 0.780318i | \(0.284943\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −6.93246 | −0.225752 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0.149793 | 0.00487276 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 15.0217 | 0.488139 | 0.244070 | − | 0.969758i | \(-0.421517\pi\) | ||||
0.244070 | + | 0.969758i | \(0.421517\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −23.9387 | −0.777083 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 69.6406 | 2.25825 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −12.1303 | −0.392940 | −0.196470 | − | 0.980510i | \(-0.562948\pi\) | ||||
−0.196470 | + | 0.980510i | \(0.562948\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −6.83700 | −0.221240 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −70.1072 | −2.26624 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −5.86965 | −0.189541 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −7.66376 | −0.247218 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −38.0947 | −1.22759 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 7.10170 | 0.228612 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 21.2882 | 0.684581 | 0.342290 | − | 0.939594i | \(-0.388797\pi\) | ||||
0.342290 | + | 0.939594i | \(0.388797\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 40.2779 | 1.29391 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 11.4006 | 0.365862 | 0.182931 | − | 0.983126i | \(-0.441442\pi\) | ||||
0.182931 | + | 0.983126i | \(0.441442\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −3.42369 | −0.109758 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 10.1755 | 0.325876 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 41.2849 | 1.32082 | 0.660411 | − | 0.750904i | \(-0.270382\pi\) | ||||
0.660411 | + | 0.750904i | \(0.270382\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −16.9193 | −0.540742 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 28.3704 | 0.905798 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −42.8448 | −1.36654 | −0.683268 | − | 0.730168i | \(-0.739442\pi\) | ||||
−0.683268 | + | 0.730168i | \(0.739442\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0.850207 | 0.0270899 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0.837003 | 0.0266421 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 4.45963 | 0.141808 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 8.73307 | 0.277415 | 0.138707 | − | 0.990333i | \(-0.455705\pi\) | ||||
0.138707 | + | 0.990333i | \(0.455705\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −63.8425 | −2.02598 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 8.56829 | 0.271633 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −44.0808 | −1.39605 | −0.698027 | − | 0.716072i | \(-0.745938\pi\) | ||||
−0.698027 | + | 0.716072i | \(0.745938\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 2.76867 | 0.0875968 |
(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 | 920.2.a.i.1.3 | ✓ | 3 | |
3.2 | odd | 2 | 8280.2.a.bl.1.1 | 3 | |||
4.3 | odd | 2 | 1840.2.a.q.1.1 | 3 | |||
5.2 | odd | 4 | 4600.2.e.q.4049.1 | 6 | |||
5.3 | odd | 4 | 4600.2.e.q.4049.6 | 6 | |||
5.4 | even | 2 | 4600.2.a.v.1.1 | 3 | |||
8.3 | odd | 2 | 7360.2.a.cf.1.3 | 3 | |||
8.5 | even | 2 | 7360.2.a.bw.1.1 | 3 | |||
20.19 | odd | 2 | 9200.2.a.ci.1.3 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
920.2.a.i.1.3 | ✓ | 3 | 1.1 | even | 1 | trivial | |
1840.2.a.q.1.1 | 3 | 4.3 | odd | 2 | |||
4600.2.a.v.1.1 | 3 | 5.4 | even | 2 | |||
4600.2.e.q.4049.1 | 6 | 5.2 | odd | 4 | |||
4600.2.e.q.4049.6 | 6 | 5.3 | odd | 4 | |||
7360.2.a.bw.1.1 | 3 | 8.5 | even | 2 | |||
7360.2.a.cf.1.3 | 3 | 8.3 | odd | 2 | |||
8280.2.a.bl.1.1 | 3 | 3.2 | odd | 2 | |||
9200.2.a.ci.1.3 | 3 | 20.19 | odd | 2 |