Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8100,2,Mod(1,8100)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8100, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("8100.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8100 = 2^{2} \cdot 3^{4} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8100.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: | \(64.6788256372\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.3981.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} - 4x^{2} + 2x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 3^{2} \) |
Twist minimal: | no (minimal twist has level 900) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-1.75080\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8100.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −4.99574 | −1.88821 | −0.944105 | − | 0.329644i | \(-0.893071\pi\) | ||||
−0.944105 | + | 0.329644i | \(0.893071\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −3.99574 | −1.20476 | −0.602380 | − | 0.798210i | \(-0.705781\pi\) | ||||
−0.602380 | + | 0.798210i | \(0.705781\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.54316 | 0.427997 | 0.213998 | − | 0.976834i | \(-0.431351\pi\) | ||||
0.213998 | + | 0.976834i | \(0.431351\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 6.99574 | 1.69672 | 0.848358 | − | 0.529424i | \(-0.177592\pi\) | ||||
0.848358 | + | 0.529424i | \(0.177592\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.25667 | −0.517715 | −0.258857 | − | 0.965916i | \(-0.583346\pi\) | ||||
−0.258857 | + | 0.965916i | \(0.583346\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −7.79556 | −1.62549 | −0.812744 | − | 0.582621i | \(-0.802027\pi\) | ||||
−0.812744 | + | 0.582621i | \(0.802027\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −6.16607 | −1.14501 | −0.572506 | − | 0.819901i | \(-0.694029\pi\) | ||||
−0.572506 | + | 0.819901i | \(0.694029\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −0.543164 | −0.0975551 | −0.0487775 | − | 0.998810i | \(-0.515533\pi\) | ||||
−0.0487775 | + | 0.998810i | \(0.515533\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −6.25240 | −1.02789 | −0.513944 | − | 0.857824i | \(-0.671816\pi\) | ||||
−0.513944 | + | 0.857824i | \(0.671816\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −0.195906 | −0.0305954 | −0.0152977 | − | 0.999883i | \(-0.504870\pi\) | ||||
−0.0152977 | + | 0.999883i | \(0.504870\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −0.0863273 | −0.0131648 | −0.00658239 | − | 0.999978i | \(-0.502095\pi\) | ||||
−0.00658239 | + | 0.999978i | \(0.502095\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 3.82966 | 0.558614 | 0.279307 | − | 0.960202i | \(-0.409895\pi\) | ||||
0.279307 | + | 0.960202i | \(0.409895\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 17.9574 | 2.56534 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −4.19164 | −0.575766 | −0.287883 | − | 0.957666i | \(-0.592951\pi\) | ||||
−0.287883 | + | 0.957666i | \(0.592951\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −7.02557 | −0.914651 | −0.457326 | − | 0.889299i | \(-0.651193\pi\) | ||||
−0.457326 | + | 0.889299i | \(0.651193\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.90941 | −0.372512 | −0.186256 | − | 0.982501i | \(-0.559635\pi\) | ||||
−0.186256 | + | 0.982501i | \(0.559635\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 8.96590 | 1.09536 | 0.547680 | − | 0.836688i | \(-0.315511\pi\) | ||||
0.547680 | + | 0.836688i | \(0.315511\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −8.79130 | −1.04334 | −0.521668 | − | 0.853149i | \(-0.674690\pi\) | ||||
−0.521668 | + | 0.853149i | \(0.674690\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −2.28650 | −0.267614 | −0.133807 | − | 0.991007i | \(-0.542720\pi\) | ||||
−0.133807 | + | 0.991007i | \(0.542720\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 19.9616 | 2.27484 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −12.6442 | −1.42259 | −0.711293 | − | 0.702896i | \(-0.751890\pi\) | ||||
−0.711293 | + | 0.702896i | \(0.751890\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 13.9616 | 1.53249 | 0.766244 | − | 0.642549i | \(-0.222123\pi\) | ||||
0.766244 | + | 0.642549i | \(0.222123\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 10.3577 | 1.09792 | 0.548958 | − | 0.835850i | \(-0.315025\pi\) | ||||
0.548958 | + | 0.835850i | \(0.315025\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −7.70924 | −0.808148 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 9.33873 | 0.948204 | 0.474102 | − | 0.880470i | \(-0.342773\pi\) | ||||
0.474102 | + | 0.880470i | \(0.342773\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −7.96164 | −0.792213 | −0.396106 | − | 0.918205i | \(-0.629639\pi\) | ||||
−0.396106 | + | 0.918205i | \(0.629639\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −16.4142 | −1.61734 | −0.808670 | − | 0.588262i | \(-0.799812\pi\) | ||||
−0.808670 | + | 0.588262i | \(0.799812\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 11.3662 | 1.09882 | 0.549408 | − | 0.835554i | \(-0.314853\pi\) | ||||
0.549408 | + | 0.835554i | \(0.314853\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −2.22683 | −0.213292 | −0.106646 | − | 0.994297i | \(-0.534011\pi\) | ||||
−0.106646 | + | 0.994297i | \(0.534011\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 2.83393 | 0.266593 | 0.133297 | − | 0.991076i | \(-0.457444\pi\) | ||||
0.133297 | + | 0.991076i | \(0.457444\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −34.9488 | −3.20376 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 4.96590 | 0.451446 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 7.02130 | 0.623040 | 0.311520 | − | 0.950240i | \(-0.399162\pi\) | ||||
0.311520 | + | 0.950240i | \(0.399162\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 8.36624 | 0.730962 | 0.365481 | − | 0.930819i | \(-0.380904\pi\) | ||||
0.365481 | + | 0.930819i | \(0.380904\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 11.2737 | 0.977554 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −2.79130 | −0.238477 | −0.119238 | − | 0.992866i | \(-0.538045\pi\) | ||||
−0.119238 | + | 0.992866i | \(0.538045\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −3.91599 | −0.332150 | −0.166075 | − | 0.986113i | \(-0.553109\pi\) | ||||
−0.166075 | + | 0.986113i | \(0.553109\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −6.16607 | −0.515633 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 12.7572 | 1.04511 | 0.522555 | − | 0.852605i | \(-0.324979\pi\) | ||||
0.522555 | + | 0.852605i | \(0.324979\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −0.377090 | −0.0306871 | −0.0153436 | − | 0.999882i | \(-0.504884\pi\) | ||||
−0.0153436 | + | 0.999882i | \(0.504884\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 12.0968 | 0.965429 | 0.482714 | − | 0.875778i | \(-0.339651\pi\) | ||||
0.482714 | + | 0.875778i | \(0.339651\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 38.9446 | 3.06926 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 10.8563 | 0.850333 | 0.425166 | − | 0.905115i | \(-0.360216\pi\) | ||||
0.425166 | + | 0.905115i | \(0.360216\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −5.18738 | −0.401411 | −0.200706 | − | 0.979652i | \(-0.564323\pi\) | ||||
−0.200706 | + | 0.979652i | \(0.564323\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −10.6186 | −0.816819 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 3.37477 | 0.256579 | 0.128290 | − | 0.991737i | \(-0.459051\pi\) | ||||
0.128290 | + | 0.991737i | \(0.459051\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −19.5997 | −1.46495 | −0.732474 | − | 0.680795i | \(-0.761634\pi\) | ||||
−0.732474 | + | 0.680795i | \(0.761634\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 5.84865 | 0.434727 | 0.217363 | − | 0.976091i | \(-0.430254\pi\) | ||||
0.217363 | + | 0.976091i | \(0.430254\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −27.9531 | −2.04413 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 24.5911 | 1.77935 | 0.889676 | − | 0.456593i | \(-0.150930\pi\) | ||||
0.889676 | + | 0.456593i | \(0.150930\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −10.3430 | −0.744505 | −0.372252 | − | 0.928132i | \(-0.621414\pi\) | ||||
−0.372252 | + | 0.928132i | \(0.621414\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 16.0256 | 1.14177 | 0.570887 | − | 0.821028i | \(-0.306599\pi\) | ||||
0.570887 | + | 0.821028i | \(0.306599\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −22.2353 | −1.57622 | −0.788111 | − | 0.615533i | \(-0.788941\pi\) | ||||
−0.788111 | + | 0.615533i | \(0.788941\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 30.8041 | 2.16202 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 9.01704 | 0.623722 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 24.3558 | 1.67672 | 0.838360 | − | 0.545117i | \(-0.183515\pi\) | ||||
0.838360 | + | 0.545117i | \(0.183515\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 2.71350 | 0.184205 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 10.7956 | 0.726188 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 11.2481 | 0.753231 | 0.376615 | − | 0.926370i | \(-0.377088\pi\) | ||||
0.376615 | + | 0.926370i | \(0.377088\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −10.1490 | −0.673614 | −0.336807 | − | 0.941574i | \(-0.609347\pi\) | ||||
−0.336807 | + | 0.941574i | \(0.609347\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −2.36856 | −0.156519 | −0.0782595 | − | 0.996933i | \(-0.524936\pi\) | ||||
−0.0782595 | + | 0.996933i | \(0.524936\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 24.1831 | 1.58429 | 0.792144 | − | 0.610334i | \(-0.208965\pi\) | ||||
0.792144 | + | 0.610334i | \(0.208965\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 1.79556 | 0.116145 | 0.0580727 | − | 0.998312i | \(-0.481504\pi\) | ||||
0.0580727 | + | 0.998312i | \(0.481504\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −14.8668 | −0.957654 | −0.478827 | − | 0.877909i | \(-0.658938\pi\) | ||||
−0.478827 | + | 0.877909i | \(0.658938\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −3.48240 | −0.221580 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 15.8297 | 0.999159 | 0.499580 | − | 0.866268i | \(-0.333488\pi\) | ||||
0.499580 | + | 0.866268i | \(0.333488\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 31.1490 | 1.95832 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 21.9957 | 1.37206 | 0.686028 | − | 0.727575i | \(-0.259353\pi\) | ||||
0.686028 | + | 0.727575i | \(0.259353\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 31.2353 | 1.94087 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 15.1533 | 0.934391 | 0.467196 | − | 0.884154i | \(-0.345264\pi\) | ||||
0.467196 | + | 0.884154i | \(0.345264\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 7.99147 | 0.487249 | 0.243624 | − | 0.969870i | \(-0.421664\pi\) | ||||
0.243624 | + | 0.969870i | \(0.421664\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 3.97248 | 0.241311 | 0.120656 | − | 0.992694i | \(-0.461500\pi\) | ||||
0.120656 | + | 0.992694i | \(0.461500\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 18.2140 | 1.09438 | 0.547188 | − | 0.837010i | \(-0.315698\pi\) | ||||
0.547188 | + | 0.837010i | \(0.315698\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 22.2087 | 1.32486 | 0.662429 | − | 0.749124i | \(-0.269525\pi\) | ||||
0.662429 | + | 0.749124i | \(0.269525\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 11.6527 | 0.692684 | 0.346342 | − | 0.938108i | \(-0.387424\pi\) | ||||
0.346342 | + | 0.938108i | \(0.387424\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0.978696 | 0.0577706 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 31.9403 | 1.87884 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −6.18311 | −0.361221 | −0.180611 | − | 0.983555i | \(-0.557807\pi\) | ||||
−0.180611 | + | 0.983555i | \(0.557807\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −12.0298 | −0.695703 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0.431268 | 0.0248579 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −12.9872 | −0.741219 | −0.370610 | − | 0.928789i | \(-0.620851\pi\) | ||||
−0.370610 | + | 0.928789i | \(0.620851\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 22.1916 | 1.25837 | 0.629186 | − | 0.777255i | \(-0.283388\pi\) | ||||
0.629186 | + | 0.777255i | \(0.283388\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −16.6922 | −0.943498 | −0.471749 | − | 0.881733i | \(-0.656377\pi\) | ||||
−0.471749 | + | 0.881733i | \(0.656377\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 32.9574 | 1.85107 | 0.925535 | − | 0.378661i | \(-0.123615\pi\) | ||||
0.925535 | + | 0.378661i | \(0.123615\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 24.6380 | 1.37946 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −15.7870 | −0.878414 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −19.1320 | −1.05478 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 28.6666 | 1.57566 | 0.787830 | − | 0.615893i | \(-0.211205\pi\) | ||||
0.787830 | + | 0.615893i | \(0.211205\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −29.8540 | −1.62625 | −0.813125 | − | 0.582089i | \(-0.802236\pi\) | ||||
−0.813125 | + | 0.582089i | \(0.802236\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 2.17034 | 0.117530 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −54.7401 | −2.95569 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 4.83819 | 0.259728 | 0.129864 | − | 0.991532i | \(-0.458546\pi\) | ||||
0.129864 | + | 0.991532i | \(0.458546\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −32.0650 | −1.71640 | −0.858200 | − | 0.513315i | \(-0.828417\pi\) | ||||
−0.858200 | + | 0.513315i | \(0.828417\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 9.85949 | 0.524768 | 0.262384 | − | 0.964964i | \(-0.415491\pi\) | ||||
0.262384 | + | 0.964964i | \(0.415491\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −9.93266 | −0.524226 | −0.262113 | − | 0.965037i | \(-0.584419\pi\) | ||||
−0.262113 | + | 0.965037i | \(0.584419\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −13.9075 | −0.731972 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 19.0213 | 0.992904 | 0.496452 | − | 0.868064i | \(-0.334636\pi\) | ||||
0.496452 | + | 0.868064i | \(0.334636\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 20.9403 | 1.08717 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −1.87848 | −0.0972641 | −0.0486320 | − | 0.998817i | \(-0.515486\pi\) | ||||
−0.0486320 | + | 0.998817i | \(0.515486\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −9.51526 | −0.490061 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 22.8435 | 1.17339 | 0.586697 | − | 0.809807i | \(-0.300428\pi\) | ||||
0.586697 | + | 0.809807i | \(0.300428\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 4.70266 | 0.240295 | 0.120147 | − | 0.992756i | \(-0.461663\pi\) | ||||
0.120147 | + | 0.992756i | \(0.461663\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 10.7657 | 0.545844 | 0.272922 | − | 0.962036i | \(-0.412010\pi\) | ||||
0.272922 | + | 0.962036i | \(0.412010\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −54.5357 | −2.75799 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −8.10958 | −0.407008 | −0.203504 | − | 0.979074i | \(-0.565233\pi\) | ||||
−0.203504 | + | 0.979074i | \(0.565233\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 12.4549 | 0.621967 | 0.310984 | − | 0.950415i | \(-0.399342\pi\) | ||||
0.310984 | + | 0.950415i | \(0.399342\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −0.838190 | −0.0417532 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 24.9829 | 1.23836 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −31.4332 | −1.55427 | −0.777136 | − | 0.629333i | \(-0.783328\pi\) | ||||
−0.777136 | + | 0.629333i | \(0.783328\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 35.0979 | 1.72705 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −26.3697 | −1.28824 | −0.644121 | − | 0.764924i | \(-0.722777\pi\) | ||||
−0.644121 | + | 0.764924i | \(0.722777\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −13.2311 | −0.644844 | −0.322422 | − | 0.946596i | \(-0.604497\pi\) | ||||
−0.322422 | + | 0.946596i | \(0.604497\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 14.5346 | 0.703380 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −24.2895 | −1.16999 | −0.584993 | − | 0.811039i | \(-0.698903\pi\) | ||||
−0.584993 | + | 0.811039i | \(0.698903\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −17.9840 | −0.864258 | −0.432129 | − | 0.901812i | \(-0.642237\pi\) | ||||
−0.432129 | + | 0.901812i | \(0.642237\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 17.5920 | 0.841539 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 22.7154 | 1.08415 | 0.542074 | − | 0.840331i | \(-0.317639\pi\) | ||||
0.542074 | + | 0.840331i | \(0.317639\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −22.9156 | −1.08875 | −0.544377 | − | 0.838841i | \(-0.683234\pi\) | ||||
−0.544377 | + | 0.838841i | \(0.683234\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 5.36966 | 0.253410 | 0.126705 | − | 0.991940i | \(-0.459560\pi\) | ||||
0.126705 | + | 0.991940i | \(0.459560\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0.782790 | 0.0368601 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −19.2462 | −0.900299 | −0.450149 | − | 0.892953i | \(-0.648629\pi\) | ||||
−0.450149 | + | 0.892953i | \(0.648629\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −35.3739 | −1.64753 | −0.823763 | − | 0.566934i | \(-0.808130\pi\) | ||||
−0.823763 | + | 0.566934i | \(0.808130\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 17.1215 | 0.795704 | 0.397852 | − | 0.917450i | \(-0.369756\pi\) | ||||
0.397852 | + | 0.917450i | \(0.369756\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 25.9318 | 1.19998 | 0.599990 | − | 0.800007i | \(-0.295171\pi\) | ||||
0.599990 | + | 0.800007i | \(0.295171\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −44.7913 | −2.06827 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0.344941 | 0.0158604 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 20.9147 | 0.955619 | 0.477810 | − | 0.878463i | \(-0.341431\pi\) | ||||
0.477810 | + | 0.878463i | \(0.341431\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −9.64848 | −0.439933 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 20.2373 | 0.917039 | 0.458520 | − | 0.888684i | \(-0.348380\pi\) | ||||
0.458520 | + | 0.888684i | \(0.348380\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 14.2002 | 0.640845 | 0.320422 | − | 0.947275i | \(-0.396175\pi\) | ||||
0.320422 | + | 0.947275i | \(0.396175\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −43.1362 | −1.94276 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 43.9190 | 1.97004 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −28.2767 | −1.26584 | −0.632920 | − | 0.774217i | \(-0.718144\pi\) | ||||
−0.632920 | + | 0.774217i | \(0.718144\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 17.4165 | 0.776565 | 0.388282 | − | 0.921540i | \(-0.373069\pi\) | ||||
0.388282 | + | 0.921540i | \(0.373069\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −22.2121 | −0.984534 | −0.492267 | − | 0.870444i | \(-0.663832\pi\) | ||||
−0.492267 | + | 0.870444i | \(0.663832\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 11.4227 | 0.505312 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −15.3023 | −0.672995 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −5.48898 | −0.240477 | −0.120238 | − | 0.992745i | \(-0.538366\pi\) | ||||
−0.120238 | + | 0.992745i | \(0.538366\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 26.0991 | 1.14123 | 0.570617 | − | 0.821216i | \(-0.306704\pi\) | ||||
0.570617 | + | 0.821216i | \(0.306704\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −3.79983 | −0.165523 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 37.7708 | 1.64221 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −0.302316 | −0.0130947 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −71.7529 | −3.09062 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 18.7828 | 0.807534 | 0.403767 | − | 0.914862i | \(-0.367701\pi\) | ||||
0.403767 | + | 0.914862i | \(0.367701\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −9.05649 | −0.387228 | −0.193614 | − | 0.981078i | \(-0.562021\pi\) | ||||
−0.193614 | + | 0.981078i | \(0.562021\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 13.9148 | 0.592789 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 63.1672 | 2.68614 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 24.8467 | 1.05279 | 0.526394 | − | 0.850241i | \(-0.323544\pi\) | ||||
0.526394 | + | 0.850241i | \(0.323544\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −0.133217 | −0.00563448 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −23.3535 | −0.984231 | −0.492115 | − | 0.870530i | \(-0.663776\pi\) | ||||
−0.492115 | + | 0.870530i | \(0.663776\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 15.0902 | 0.632614 | 0.316307 | − | 0.948657i | \(-0.397557\pi\) | ||||
0.316307 | + | 0.948657i | \(0.397557\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −6.53573 | −0.273512 | −0.136756 | − | 0.990605i | \(-0.543668\pi\) | ||||
−0.136756 | + | 0.990605i | \(0.543668\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −8.12662 | −0.338316 | −0.169158 | − | 0.985589i | \(-0.554105\pi\) | ||||
−0.169158 | + | 0.985589i | \(0.554105\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −69.7487 | −2.89366 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 16.7487 | 0.693660 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 13.0987 | 0.540643 | 0.270321 | − | 0.962770i | \(-0.412870\pi\) | ||||
0.270321 | + | 0.962770i | \(0.412870\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1.22574 | 0.0505057 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 8.60478 | 0.353356 | 0.176678 | − | 0.984269i | \(-0.443465\pi\) | ||||
0.176678 | + | 0.984269i | \(0.443465\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −24.3654 | −0.995543 | −0.497771 | − | 0.867308i | \(-0.665848\pi\) | ||||
−0.497771 | + | 0.867308i | \(0.665848\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −24.1799 | −0.986320 | −0.493160 | − | 0.869938i | \(-0.664158\pi\) | ||||
−0.493160 | + | 0.869938i | \(0.664158\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −1.42700 | −0.0579203 | −0.0289602 | − | 0.999581i | \(-0.509220\pi\) | ||||
−0.0289602 | + | 0.999581i | \(0.509220\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 5.90979 | 0.239085 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −6.92878 | −0.279851 | −0.139925 | − | 0.990162i | \(-0.544686\pi\) | ||||
−0.139925 | + | 0.990162i | \(0.544686\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −26.4931 | −1.06657 | −0.533286 | − | 0.845935i | \(-0.679043\pi\) | ||||
−0.533286 | + | 0.845935i | \(0.679043\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −26.9597 | −1.08360 | −0.541801 | − | 0.840507i | \(-0.682257\pi\) | ||||
−0.541801 | + | 0.840507i | \(0.682257\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −51.7444 | −2.07310 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −43.7401 | −1.74403 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −15.9350 | −0.634361 | −0.317181 | − | 0.948365i | \(-0.602736\pi\) | ||||
−0.317181 | + | 0.948365i | \(0.602736\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 27.7112 | 1.09796 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 7.16181 | 0.282874 | 0.141437 | − | 0.989947i | \(-0.454828\pi\) | ||||
0.141437 | + | 0.989947i | \(0.454828\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −7.06308 | −0.278541 | −0.139270 | − | 0.990254i | \(-0.544476\pi\) | ||||
−0.139270 | + | 0.990254i | \(0.544476\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 26.4037 | 1.03804 | 0.519019 | − | 0.854763i | \(-0.326297\pi\) | ||||
0.519019 | + | 0.854763i | \(0.326297\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 28.0723 | 1.10193 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −7.71970 | −0.302095 | −0.151048 | − | 0.988527i | \(-0.548265\pi\) | ||||
−0.151048 | + | 0.988527i | \(0.548265\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 22.2853 | 0.868110 | 0.434055 | − | 0.900886i | \(-0.357082\pi\) | ||||
0.434055 | + | 0.900886i | \(0.357082\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 32.1087 | 1.24888 | 0.624442 | − | 0.781071i | \(-0.285326\pi\) | ||||
0.624442 | + | 0.781071i | \(0.285326\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 48.0680 | 1.86120 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 11.6252 | 0.448787 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −7.83161 | −0.301886 | −0.150943 | − | 0.988542i | \(-0.548231\pi\) | ||||
−0.150943 | + | 0.988542i | \(0.548231\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 18.0034 | 0.691927 | 0.345964 | − | 0.938248i | \(-0.387552\pi\) | ||||
0.345964 | + | 0.938248i | \(0.387552\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −46.6538 | −1.79041 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −30.3356 | −1.16076 | −0.580379 | − | 0.814347i | \(-0.697096\pi\) | ||||
−0.580379 | + | 0.814347i | \(0.697096\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −6.46839 | −0.246426 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 28.1149 | 1.06954 | 0.534771 | − | 0.844997i | \(-0.320398\pi\) | ||||
0.534771 | + | 0.844997i | \(0.320398\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1.37051 | −0.0519117 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −28.4378 | −1.07408 | −0.537041 | − | 0.843556i | \(-0.680458\pi\) | ||||
−0.537041 | + | 0.843556i | \(0.680458\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 14.1096 | 0.532153 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 39.7742 | 1.49586 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 30.9000 | 1.16047 | 0.580237 | − | 0.814447i | \(-0.302960\pi\) | ||||
0.580237 | + | 0.814447i | \(0.302960\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 4.23427 | 0.158575 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 21.2462 | 0.792349 | 0.396175 | − | 0.918175i | \(-0.370338\pi\) | ||||
0.396175 | + | 0.918175i | \(0.370338\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 82.0011 | 3.05388 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 24.9821 | 0.926534 | 0.463267 | − | 0.886219i | \(-0.346677\pi\) | ||||
0.463267 | + | 0.886219i | \(0.346677\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −0.603923 | −0.0223369 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −10.4677 | −0.386633 | −0.193316 | − | 0.981136i | \(-0.561924\pi\) | ||||
−0.193316 | + | 0.981136i | \(0.561924\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −35.8254 | −1.31964 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 35.6244 | 1.31046 | 0.655232 | − | 0.755428i | \(-0.272571\pi\) | ||||
0.655232 | + | 0.755428i | \(0.272571\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −10.0554 | −0.368897 | −0.184448 | − | 0.982842i | \(-0.559050\pi\) | ||||
−0.184448 | + | 0.982842i | \(0.559050\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −56.7828 | −2.07480 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 17.7348 | 0.647152 | 0.323576 | − | 0.946202i | \(-0.395115\pi\) | ||||
0.323576 | + | 0.946202i | \(0.395115\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −6.42042 | −0.233354 | −0.116677 | − | 0.993170i | \(-0.537224\pi\) | ||||
−0.116677 | + | 0.993170i | \(0.537224\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −25.3910 | −0.920422 | −0.460211 | − | 0.887810i | \(-0.652226\pi\) | ||||
−0.460211 | + | 0.887810i | \(0.652226\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 11.1247 | 0.402740 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −10.8416 | −0.391468 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −14.8018 | −0.533765 | −0.266883 | − | 0.963729i | \(-0.585994\pi\) | ||||
−0.266883 | + | 0.963729i | \(0.585994\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −7.48046 | −0.269053 | −0.134527 | − | 0.990910i | \(-0.542951\pi\) | ||||
−0.134527 | + | 0.990910i | \(0.542951\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0.442095 | 0.0158397 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 35.1277 | 1.25697 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −52.3174 | −1.86491 | −0.932457 | − | 0.361281i | \(-0.882340\pi\) | ||||
−0.932457 | + | 0.361281i | \(0.882340\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −14.1575 | −0.503384 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −4.48969 | −0.159434 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 53.7359 | 1.90342 | 0.951711 | − | 0.306994i | \(-0.0993233\pi\) | ||||
0.951711 | + | 0.306994i | \(0.0993233\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 26.7913 | 0.947808 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 9.13624 | 0.322411 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 26.1908 | 0.920819 | 0.460410 | − | 0.887707i | \(-0.347703\pi\) | ||||
0.460410 | + | 0.887707i | \(0.347703\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −52.3506 | −1.83828 | −0.919140 | − | 0.393931i | \(-0.871115\pi\) | ||||
−0.919140 | + | 0.393931i | \(0.871115\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0.194812 | 0.00681560 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 4.85864 | 0.169568 | 0.0847839 | − | 0.996399i | \(-0.472980\pi\) | ||||
0.0847839 | + | 0.996399i | \(0.472980\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 1.17777 | 0.0410546 | 0.0205273 | − | 0.999789i | \(-0.493466\pi\) | ||||
0.0205273 | + | 0.999789i | \(0.493466\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −32.7188 | −1.13775 | −0.568873 | − | 0.822426i | \(-0.692620\pi\) | ||||
−0.568873 | + | 0.822426i | \(0.692620\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −5.99342 | −0.208160 | −0.104080 | − | 0.994569i | \(-0.533190\pi\) | ||||
−0.104080 | + | 0.994569i | \(0.533190\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 125.625 | 4.35265 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 38.3867 | 1.32526 | 0.662628 | − | 0.748949i | \(-0.269441\pi\) | ||||
0.662628 | + | 0.748949i | \(0.269441\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 9.02047 | 0.311051 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −24.8083 | −0.852425 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 48.7410 | 1.67082 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 21.7190 | 0.743644 | 0.371822 | − | 0.928304i | \(-0.378733\pi\) | ||||
0.371822 | + | 0.928304i | \(0.378733\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 4.59966 | 0.157121 | 0.0785607 | − | 0.996909i | \(-0.474968\pi\) | ||||
0.0785607 | + | 0.996909i | \(0.474968\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 14.9179 | 0.508993 | 0.254496 | − | 0.967074i | \(-0.418090\pi\) | ||||
0.254496 | + | 0.967074i | \(0.418090\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −11.4089 | −0.388362 | −0.194181 | − | 0.980966i | \(-0.562205\pi\) | ||||
−0.194181 | + | 0.980966i | \(0.562205\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 50.5229 | 1.71387 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 13.8359 | 0.468810 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 27.9284 | 0.943075 | 0.471537 | − | 0.881846i | \(-0.343699\pi\) | ||||
0.471537 | + | 0.881846i | \(0.343699\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 42.3270 | 1.42603 | 0.713017 | − | 0.701147i | \(-0.247328\pi\) | ||||
0.713017 | + | 0.701147i | \(0.247328\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −20.3895 | −0.686161 | −0.343081 | − | 0.939306i | \(-0.611470\pi\) | ||||
−0.343081 | + | 0.939306i | \(0.611470\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −39.5451 | −1.32779 | −0.663897 | − | 0.747824i | \(-0.731099\pi\) | ||||
−0.663897 | + | 0.747824i | \(0.731099\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −35.0766 | −1.17643 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −8.64227 | −0.289202 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 3.34919 | 0.111702 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −29.3236 | −0.976911 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 36.9597 | 1.22723 | 0.613613 | − | 0.789607i | \(-0.289715\pi\) | ||||
0.613613 | + | 0.789607i | \(0.289715\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 9.84670 | 0.326236 | 0.163118 | − | 0.986607i | \(-0.447845\pi\) | ||||
0.163118 | + | 0.986607i | \(0.447845\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −55.7870 | −1.84628 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −41.7955 | −1.38021 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −8.42079 | −0.277776 | −0.138888 | − | 0.990308i | \(-0.544353\pi\) | ||||
−0.138888 | + | 0.990308i | \(0.544353\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −13.5664 | −0.446544 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 28.3875 | 0.931365 | 0.465683 | − | 0.884952i | \(-0.345809\pi\) | ||||
0.465683 | + | 0.884952i | \(0.345809\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −40.5238 | −1.32811 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −4.69342 | −0.153327 | −0.0766637 | − | 0.997057i | \(-0.524427\pi\) | ||||
−0.0766637 | + | 0.997057i | \(0.524427\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −19.0256 | −0.620216 | −0.310108 | − | 0.950701i | \(-0.600365\pi\) | ||||
−0.310108 | + | 0.950701i | \(0.600365\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1.52720 | 0.0497325 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 12.8169 | 0.416492 | 0.208246 | − | 0.978076i | \(-0.433224\pi\) | ||||
0.208246 | + | 0.978076i | \(0.433224\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −3.52844 | −0.114538 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 45.9701 | 1.48912 | 0.744560 | − | 0.667556i | \(-0.232660\pi\) | ||||
0.744560 | + | 0.667556i | \(0.232660\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 13.9446 | 0.450295 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.7050 | −0.990483 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 5.14709 | 0.165519 | 0.0827596 | − | 0.996570i | \(-0.473627\pi\) | ||||
0.0827596 | + | 0.996570i | \(0.473627\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 10.3875 | 0.333352 | 0.166676 | − | 0.986012i | \(-0.446697\pi\) | ||||
0.166676 | + | 0.986012i | \(0.446697\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 19.5632 | 0.627169 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −39.5621 | −1.26570 | −0.632852 | − | 0.774272i | \(-0.718116\pi\) | ||||
−0.632852 | + | 0.774272i | \(0.718116\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −41.3867 | −1.32272 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −20.4719 | −0.652954 | −0.326477 | − | 0.945205i | \(-0.605862\pi\) | ||||
−0.326477 | + | 0.945205i | \(0.605862\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0.672970 | 0.0213992 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −19.2415 | −0.611228 | −0.305614 | − | 0.952156i | \(-0.598862\pi\) | ||||
−0.305614 | + | 0.952156i | \(0.598862\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −23.2385 | −0.735971 | −0.367986 | − | 0.929832i | \(-0.619952\pi\) | ||||
−0.367986 | + | 0.929832i | \(0.619952\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 8100.2.a.y.1.1 | 4 | ||
3.2 | odd | 2 | 8100.2.a.x.1.1 | 4 | |||
5.2 | odd | 4 | 8100.2.d.s.649.1 | 8 | |||
5.3 | odd | 4 | 8100.2.d.s.649.8 | 8 | |||
5.4 | even | 2 | 8100.2.a.ba.1.4 | 4 | |||
9.2 | odd | 6 | 900.2.i.d.301.2 | ✓ | 8 | ||
9.4 | even | 3 | 2700.2.i.e.1801.4 | 8 | |||
9.5 | odd | 6 | 900.2.i.d.601.2 | yes | 8 | ||
9.7 | even | 3 | 2700.2.i.e.901.4 | 8 | |||
15.2 | even | 4 | 8100.2.d.q.649.1 | 8 | |||
15.8 | even | 4 | 8100.2.d.q.649.8 | 8 | |||
15.14 | odd | 2 | 8100.2.a.z.1.4 | 4 | |||
45.2 | even | 12 | 900.2.s.d.49.2 | 16 | |||
45.4 | even | 6 | 2700.2.i.d.1801.1 | 8 | |||
45.7 | odd | 12 | 2700.2.s.d.1549.1 | 16 | |||
45.13 | odd | 12 | 2700.2.s.d.2449.1 | 16 | |||
45.14 | odd | 6 | 900.2.i.e.601.3 | yes | 8 | ||
45.22 | odd | 12 | 2700.2.s.d.2449.8 | 16 | |||
45.23 | even | 12 | 900.2.s.d.349.2 | 16 | |||
45.29 | odd | 6 | 900.2.i.e.301.3 | yes | 8 | ||
45.32 | even | 12 | 900.2.s.d.349.7 | 16 | |||
45.34 | even | 6 | 2700.2.i.d.901.1 | 8 | |||
45.38 | even | 12 | 900.2.s.d.49.7 | 16 | |||
45.43 | odd | 12 | 2700.2.s.d.1549.8 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
900.2.i.d.301.2 | ✓ | 8 | 9.2 | odd | 6 | ||
900.2.i.d.601.2 | yes | 8 | 9.5 | odd | 6 | ||
900.2.i.e.301.3 | yes | 8 | 45.29 | odd | 6 | ||
900.2.i.e.601.3 | yes | 8 | 45.14 | odd | 6 | ||
900.2.s.d.49.2 | 16 | 45.2 | even | 12 | |||
900.2.s.d.49.7 | 16 | 45.38 | even | 12 | |||
900.2.s.d.349.2 | 16 | 45.23 | even | 12 | |||
900.2.s.d.349.7 | 16 | 45.32 | even | 12 | |||
2700.2.i.d.901.1 | 8 | 45.34 | even | 6 | |||
2700.2.i.d.1801.1 | 8 | 45.4 | even | 6 | |||
2700.2.i.e.901.4 | 8 | 9.7 | even | 3 | |||
2700.2.i.e.1801.4 | 8 | 9.4 | even | 3 | |||
2700.2.s.d.1549.1 | 16 | 45.7 | odd | 12 | |||
2700.2.s.d.1549.8 | 16 | 45.43 | odd | 12 | |||
2700.2.s.d.2449.1 | 16 | 45.13 | odd | 12 | |||
2700.2.s.d.2449.8 | 16 | 45.22 | odd | 12 | |||
8100.2.a.x.1.1 | 4 | 3.2 | odd | 2 | |||
8100.2.a.y.1.1 | 4 | 1.1 | even | 1 | trivial | ||
8100.2.a.z.1.4 | 4 | 15.14 | odd | 2 | |||
8100.2.a.ba.1.4 | 4 | 5.4 | even | 2 | |||
8100.2.d.q.649.1 | 8 | 15.2 | even | 4 | |||
8100.2.d.q.649.8 | 8 | 15.8 | even | 4 | |||
8100.2.d.s.649.1 | 8 | 5.2 | odd | 4 | |||
8100.2.d.s.649.8 | 8 | 5.3 | odd | 4 |