Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [224,3,Mod(15,224)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(224, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 0]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("224.15");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 224 = 2^{5} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 224.g (of order \(2\), degree \(1\), not minimal) |
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: | no |
Analytic conductor: | \(6.10355792167\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.0.292213762624.3 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{7} - 2x^{6} - 2x^{5} + 24x^{4} - 8x^{3} - 32x^{2} - 64x + 256 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{10} \) |
Twist minimal: | no (minimal twist has level 56) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 15.2 | ||
Root | \(-1.67467 - 1.09337i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 224.15 |
Dual form | 224.3.g.b.15.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/224\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(129\) | \(197\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(-1\) |
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 | ||||||||
\(3\) | −4.56747 | −1.52249 | −0.761245 | − | 0.648464i | \(-0.775412\pi\) | ||||
−0.761245 | + | 0.648464i | \(0.775412\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 5.73252i | 1.14650i | 0.819379 | + | 0.573252i | \(0.194318\pi\) | ||||
−0.819379 | + | 0.573252i | \(0.805682\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.64575i | 0.377964i | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 11.8618 | 1.31798 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.40065 | 0.127332 | 0.0636658 | − | 0.997971i | \(-0.479721\pi\) | ||||
0.0636658 | + | 0.997971i | \(0.479721\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − 19.0821i | − 1.46785i | −0.679228 | − | 0.733927i | \(-0.737685\pi\) | ||||
0.679228 | − | 0.733927i | \(-0.262315\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | − 26.1831i | − 1.74554i | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −32.2699 | −1.89823 | −0.949114 | − | 0.314932i | \(-0.898018\pi\) | ||||
−0.949114 | + | 0.314932i | \(0.898018\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −12.5675 | −0.661446 | −0.330723 | − | 0.943728i | \(-0.607293\pi\) | ||||
−0.330723 | + | 0.943728i | \(0.607293\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | − 12.0844i | − 0.575447i | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − 15.8893i | − 0.690839i | −0.938448 | − | 0.345419i | \(-0.887737\pi\) | ||||
0.938448 | − | 0.345419i | \(-0.112263\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −7.86180 | −0.314472 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −13.0712 | −0.484118 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − 3.29194i | − 0.113515i | −0.998388 | − | 0.0567576i | \(-0.981924\pi\) | ||||
0.998388 | − | 0.0567576i | \(-0.0180762\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − 22.6705i | − 0.731306i | −0.930751 | − | 0.365653i | \(-0.880846\pi\) | ||||
0.930751 | − | 0.365653i | \(-0.119154\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −6.39741 | −0.193861 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −15.1668 | −0.433338 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − 54.1537i | − 1.46361i | −0.681512 | − | 0.731807i | \(-0.738677\pi\) | ||||
0.681512 | − | 0.731807i | \(-0.261323\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 87.1569i | 2.23479i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −7.59607 | −0.185270 | −0.0926350 | − | 0.995700i | \(-0.529529\pi\) | ||||
−0.0926350 | + | 0.995700i | \(0.529529\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 20.8478 | 0.484833 | 0.242417 | − | 0.970172i | \(-0.422060\pi\) | ||||
0.242417 | + | 0.970172i | \(0.422060\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 67.9980i | 1.51107i | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − 21.6384i | − 0.460392i | −0.973144 | − | 0.230196i | \(-0.926063\pi\) | ||||
0.973144 | − | 0.230196i | \(-0.0739367\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −7.00000 | −0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 147.392 | 2.89004 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0.356667i | 0.00672957i | 0.999994 | + | 0.00336479i | \(0.00107105\pi\) | ||||
−0.999994 | + | 0.00336479i | \(0.998929\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 8.02924i | 0.145986i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 57.4016 | 1.00705 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −26.8583 | −0.455226 | −0.227613 | − | 0.973752i | \(-0.573092\pi\) | ||||
−0.227613 | + | 0.973752i | \(0.573092\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 86.2287i | 1.41359i | 0.707420 | + | 0.706793i | \(0.249859\pi\) | ||||
−0.707420 | + | 0.706793i | \(0.750141\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 31.3834i | 0.498149i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 109.389 | 1.68290 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −114.523 | −1.70929 | −0.854646 | − | 0.519211i | \(-0.826226\pi\) | ||||
−0.854646 | + | 0.519211i | \(0.826226\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 72.5739i | 1.05180i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 104.792i | 1.47594i | 0.674834 | + | 0.737969i | \(0.264215\pi\) | ||||
−0.674834 | + | 0.737969i | \(0.735785\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −24.3974 | −0.334211 | −0.167106 | − | 0.985939i | \(-0.553442\pi\) | ||||
−0.167106 | + | 0.985939i | \(0.553442\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 35.9085 | 0.478781 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 3.70576i | 0.0481268i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − 117.128i | − 1.48263i | −0.671157 | − | 0.741315i | \(-0.734202\pi\) | ||||
0.671157 | − | 0.741315i | \(-0.265798\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −47.0539 | −0.580913 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −79.2706 | −0.955067 | −0.477534 | − | 0.878614i | \(-0.658469\pi\) | ||||
−0.477534 | + | 0.878614i | \(0.658469\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − 184.988i | − 2.17633i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 15.0359i | 0.172826i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 2.66078 | 0.0298964 | 0.0149482 | − | 0.999888i | \(-0.495242\pi\) | ||||
0.0149482 | + | 0.999888i | \(0.495242\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 50.4865 | 0.554797 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 103.547i | 1.11341i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | − 72.0433i | − 0.758350i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −52.0930 | −0.537042 | −0.268521 | − | 0.963274i | \(-0.586535\pi\) | ||||
−0.268521 | + | 0.963274i | \(0.586535\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 16.6142 | 0.167820 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 91.4742i | 0.905685i | 0.891591 | + | 0.452842i | \(0.149590\pi\) | ||||
−0.891591 | + | 0.452842i | \(0.850410\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − 39.7891i | − 0.386302i | −0.981169 | − | 0.193151i | \(-0.938129\pi\) | ||||
0.981169 | − | 0.193151i | \(-0.0618708\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 69.2740 | 0.659753 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −82.6631 | −0.772552 | −0.386276 | − | 0.922383i | \(-0.626239\pi\) | ||||
−0.386276 | + | 0.922383i | \(0.626239\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − 29.4719i | − 0.270384i | −0.990819 | − | 0.135192i | \(-0.956835\pi\) | ||||
0.990819 | − | 0.135192i | \(-0.0431652\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 247.346i | 2.22834i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 159.133 | 1.40826 | 0.704130 | − | 0.710071i | \(-0.251337\pi\) | ||||
0.704130 | + | 0.710071i | \(0.251337\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 91.0857 | 0.792049 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | − 226.348i | − 1.93460i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − 85.3781i | − 0.717463i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −119.038 | −0.983787 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 34.6948 | 0.282072 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 98.2451i | 0.785961i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − 16.0834i | − 0.126641i | −0.997993 | − | 0.0633205i | \(-0.979831\pi\) | ||||
0.997993 | − | 0.0633205i | \(-0.0201690\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −95.2219 | −0.738154 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 118.136 | 0.901799 | 0.450899 | − | 0.892575i | \(-0.351103\pi\) | ||||
0.450899 | + | 0.892575i | \(0.351103\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − 33.2504i | − 0.250003i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | − 74.9308i | − 0.555043i | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −19.1708 | −0.139933 | −0.0699664 | − | 0.997549i | \(-0.522289\pi\) | ||||
−0.0699664 | + | 0.997549i | \(0.522289\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −104.954 | −0.755062 | −0.377531 | − | 0.925997i | \(-0.623227\pi\) | ||||
−0.377531 | + | 0.925997i | \(0.623227\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 98.8329i | 0.700942i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − 26.7273i | − 0.186904i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 18.8711 | 0.130146 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 31.9723 | 0.217499 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − 82.3906i | − 0.552957i | −0.961020 | − | 0.276478i | \(-0.910833\pi\) | ||||
0.961020 | − | 0.276478i | \(-0.0891674\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 57.7395i | 0.382381i | 0.981553 | + | 0.191190i | \(0.0612347\pi\) | ||||
−0.981553 | + | 0.191190i | \(0.938765\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −382.779 | −2.50182 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 129.959 | 0.838445 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 3.72975i | 0.0237564i | 0.999929 | + | 0.0118782i | \(0.00378104\pi\) | ||||
−0.999929 | + | 0.0118782i | \(0.996219\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | − 1.62907i | − 0.0102457i | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 42.0391 | 0.261112 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −77.7069 | −0.476729 | −0.238365 | − | 0.971176i | \(-0.576611\pi\) | ||||
−0.238365 | + | 0.971176i | \(0.576611\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | − 36.6733i | − 0.222262i | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − 62.0837i | − 0.371759i | −0.982573 | − | 0.185879i | \(-0.940487\pi\) | ||||
0.982573 | − | 0.185879i | \(-0.0595133\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −195.127 | −1.15459 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −149.073 | −0.871771 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − 195.614i | − 1.13072i | −0.824846 | − | 0.565358i | \(-0.808738\pi\) | ||||
0.824846 | − | 0.565358i | \(-0.191262\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − 20.8004i | − 0.118859i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 122.675 | 0.693077 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −72.2099 | −0.403407 | −0.201704 | − | 0.979447i | \(-0.564648\pi\) | ||||
−0.201704 | + | 0.979447i | \(0.564648\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − 140.980i | − 0.778895i | −0.921049 | − | 0.389448i | \(-0.872666\pi\) | ||||
0.921049 | − | 0.389448i | \(-0.127334\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − 393.847i | − 2.15217i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 310.437 | 1.67804 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −45.1987 | −0.241704 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | − 34.5831i | − 0.182979i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 284.473i | 1.48939i | 0.667407 | + | 0.744693i | \(0.267404\pi\) | ||||
−0.667407 | + | 0.744693i | \(0.732596\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −123.850 | −0.641710 | −0.320855 | − | 0.947128i | \(-0.603970\pi\) | ||||
−0.320855 | + | 0.947128i | \(0.603970\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −499.629 | −2.56220 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 108.098i | 0.548721i | 0.961627 | + | 0.274361i | \(0.0884662\pi\) | ||||
−0.961627 | + | 0.274361i | \(0.911534\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − 331.854i | − 1.66761i | −0.552060 | − | 0.833804i | \(-0.686158\pi\) | ||||
0.552060 | − | 0.833804i | \(-0.313842\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 523.079 | 2.60238 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 8.70966 | 0.0429047 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − 43.5446i | − 0.212413i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | − 188.476i | − 0.910510i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −17.6026 | −0.0842229 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −26.3950 | −0.125095 | −0.0625475 | − | 0.998042i | \(-0.519922\pi\) | ||||
−0.0625475 | + | 0.998042i | \(0.519922\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − 478.633i | − 2.24710i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 119.511i | 0.555864i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 59.9804 | 0.276408 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 111.434 | 0.508833 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 615.777i | 2.78632i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 161.183i | 0.722796i | 0.932412 | + | 0.361398i | \(0.117700\pi\) | ||||
−0.932412 | + | 0.361398i | \(0.882300\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −93.2551 | −0.414467 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 171.279 | 0.754533 | 0.377266 | − | 0.926105i | \(-0.376864\pi\) | ||||
0.377266 | + | 0.926105i | \(0.376864\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 229.251i | 1.00110i | 0.865709 | + | 0.500548i | \(0.166868\pi\) | ||||
−0.865709 | + | 0.500548i | \(0.833132\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | − 16.9260i | − 0.0732726i | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −270.154 | −1.15946 | −0.579730 | − | 0.814808i | \(-0.696842\pi\) | ||||
−0.579730 | + | 0.814808i | \(0.696842\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 124.043 | 0.527841 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 534.978i | 2.25729i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 157.155i | 0.657551i | 0.944408 | + | 0.328776i | \(0.106636\pi\) | ||||
−0.944408 | + | 0.328776i | \(0.893364\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −97.7124 | −0.405445 | −0.202723 | − | 0.979236i | \(-0.564979\pi\) | ||||
−0.202723 | + | 0.979236i | \(0.564979\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 332.558 | 1.36855 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | − 40.1276i | − 0.163786i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 239.814i | 0.970906i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 362.066 | 1.45408 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 313.145 | 1.24759 | 0.623796 | − | 0.781587i | \(-0.285590\pi\) | ||||
0.623796 | + | 0.781587i | \(0.285590\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − 22.2553i | − 0.0879655i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 844.927i | 3.31344i | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −348.855 | −1.35741 | −0.678707 | − | 0.734409i | \(-0.737459\pi\) | ||||
−0.678707 | + | 0.734409i | \(0.737459\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 143.277 | 0.553194 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | − 39.0484i | − 0.149611i | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 384.364i | 1.46146i | 0.682667 | + | 0.730729i | \(0.260820\pi\) | ||||
−0.682667 | + | 0.730729i | \(0.739180\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −2.04460 | −0.00771548 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −12.1530 | −0.0455170 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − 37.7613i | − 0.140376i | −0.997534 | − | 0.0701882i | \(-0.977640\pi\) | ||||
0.997534 | − | 0.0701882i | \(-0.0223600\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − 308.730i | − 1.13922i | −0.821914 | − | 0.569612i | \(-0.807093\pi\) | ||||
0.821914 | − | 0.569612i | \(-0.192907\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −230.596 | −0.844673 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −11.0116 | −0.0400422 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − 244.210i | − 0.881623i | −0.897600 | − | 0.440812i | \(-0.854691\pi\) | ||||
0.897600 | − | 0.440812i | \(-0.145309\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | − 268.913i | − 0.963845i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 266.569 | 0.948646 | 0.474323 | − | 0.880351i | \(-0.342693\pi\) | ||||
0.474323 | + | 0.880351i | \(0.342693\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −165.605 | −0.585177 | −0.292589 | − | 0.956238i | \(-0.594517\pi\) | ||||
−0.292589 | + | 0.956238i | \(0.594517\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 329.056i | 1.15458i | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − 20.0973i | − 0.0700255i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 752.346 | 2.60327 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 237.933 | 0.817641 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − 34.3652i | − 0.117288i | −0.998279 | − | 0.0586438i | \(-0.981322\pi\) | ||||
0.998279 | − | 0.0586438i | \(-0.0186776\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − 153.966i | − 0.521918i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −18.3081 | −0.0616434 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −303.201 | −1.01405 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 55.1582i | 0.183250i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − 417.806i | − 1.37890i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −494.308 | −1.62068 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 222.934 | 0.726170 | 0.363085 | − | 0.931756i | \(-0.381724\pi\) | ||||
0.363085 | + | 0.931756i | \(0.381724\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 181.736i | 0.588141i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 419.934i | 1.35027i | 0.737694 | + | 0.675135i | \(0.235915\pi\) | ||||
−0.737694 | + | 0.675135i | \(0.764085\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −293.869 | −0.938878 | −0.469439 | − | 0.882965i | \(-0.655544\pi\) | ||||
−0.469439 | + | 0.882965i | \(0.655544\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −179.906 | −0.571130 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − 423.461i | − 1.33584i | −0.744234 | − | 0.667919i | \(-0.767185\pi\) | ||||
0.744234 | − | 0.667919i | \(-0.232815\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − 4.61085i | − 0.0144541i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 377.561 | 1.17620 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 405.551 | 1.25558 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 150.020i | 0.461599i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 134.612i | 0.411658i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 57.2499 | 0.174012 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 126.666 | 0.382678 | 0.191339 | − | 0.981524i | \(-0.438717\pi\) | ||||
0.191339 | + | 0.981524i | \(0.438717\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − 642.361i | − 1.92901i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | − 656.503i | − 1.95971i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 302.404 | 0.897341 | 0.448671 | − | 0.893697i | \(-0.351898\pi\) | ||||
0.448671 | + | 0.893697i | \(0.351898\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −726.838 | −2.14406 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − 31.7533i | − 0.0931183i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − 18.5203i | − 0.0539949i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −416.031 | −1.20589 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −320.532 | −0.923724 | −0.461862 | − | 0.886952i | \(-0.652818\pi\) | ||||
−0.461862 | + | 0.886952i | \(0.652818\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − 380.678i | − 1.09077i | −0.838186 | − | 0.545385i | \(-0.816384\pi\) | ||||
0.838186 | − | 0.545385i | \(-0.183616\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 249.426i | 0.710614i | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −364.369 | −1.03221 | −0.516104 | − | 0.856526i | \(-0.672618\pi\) | ||||
−0.516104 | + | 0.856526i | \(0.672618\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −600.720 | −1.69217 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 389.962i | 1.09233i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 111.995i | 0.311965i | 0.987760 | + | 0.155982i | \(0.0498543\pi\) | ||||
−0.987760 | + | 0.155982i | \(0.950146\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −203.059 | −0.562489 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 543.704 | 1.49781 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − 139.859i | − 0.383174i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − 439.042i | − 1.19630i | −0.801384 | − | 0.598150i | \(-0.795903\pi\) | ||||
0.801384 | − | 0.598150i | \(-0.204097\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −90.1030 | −0.244182 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −0.943653 | −0.00254354 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 254.996i | 0.683637i | 0.939766 | + | 0.341818i | \(0.111043\pi\) | ||||
−0.939766 | + | 0.341818i | \(0.888957\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | − 448.732i | − 1.19662i | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −62.8172 | −0.166624 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −603.048 | −1.59116 | −0.795578 | − | 0.605852i | \(-0.792833\pi\) | ||||
−0.795578 | + | 0.605852i | \(0.792833\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 73.4605i | 0.192810i | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − 73.3855i | − 0.191607i | −0.995400 | − | 0.0958035i | \(-0.969458\pi\) | ||||
0.995400 | − | 0.0958035i | \(-0.0305420\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −21.2434 | −0.0551776 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 247.293 | 0.639000 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 340.800i | 0.876092i | 0.898953 | + | 0.438046i | \(0.144329\pi\) | ||||
−0.898953 | + | 0.438046i | \(0.855671\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 512.745i | 1.31137i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −539.581 | −1.37298 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 671.438 | 1.69984 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − 111.540i | − 0.280957i | −0.990084 | − | 0.140478i | \(-0.955136\pi\) | ||||
0.990084 | − | 0.140478i | \(-0.0448640\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 151.870i | 0.380627i | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 340.535 | 0.849215 | 0.424607 | − | 0.905378i | \(-0.360412\pi\) | ||||
0.424607 | + | 0.905378i | \(0.360412\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −432.600 | −1.07345 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | − 269.738i | − 0.666019i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − 75.8502i | − 0.186364i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 666.959 | 1.63071 | 0.815354 | − | 0.578963i | \(-0.196543\pi\) | ||||
0.815354 | + | 0.578963i | \(0.196543\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 87.5620 | 0.213046 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − 71.0604i | − 0.172059i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − 454.420i | − 1.09499i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 479.373 | 1.14958 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 200.191 | 0.477783 | 0.238891 | − | 0.971046i | \(-0.423216\pi\) | ||||
0.238891 | + | 0.971046i | \(0.423216\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − 15.9136i | − 0.0377996i | −0.999821 | − | 0.0188998i | \(-0.993984\pi\) | ||||
0.999821 | − | 0.0188998i | \(-0.00601636\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | − 256.671i | − 0.606786i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 253.699 | 0.596940 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −228.140 | −0.534285 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 122.076i | 0.284560i | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − 628.013i | − 1.45711i | −0.684989 | − | 0.728553i | \(-0.740193\pi\) | ||||
0.684989 | − | 0.728553i | \(-0.259807\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 789.232 | 1.82271 | 0.911353 | − | 0.411625i | \(-0.135039\pi\) | ||||
0.911353 | + | 0.411625i | \(0.135039\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −86.1933 | −0.198146 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 199.688i | 0.456952i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 665.570i | 1.51610i | 0.652194 | + | 0.758052i | \(0.273849\pi\) | ||||
−0.652194 | + | 0.758052i | \(0.726151\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −83.0326 | −0.188283 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −507.152 | −1.14481 | −0.572406 | − | 0.819970i | \(-0.693990\pi\) | ||||
−0.572406 | + | 0.819970i | \(0.693990\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 15.2530i | 0.0342764i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 376.317i | 0.841872i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −279.029 | −0.621446 | −0.310723 | − | 0.950501i | \(-0.600571\pi\) | ||||
−0.310723 | + | 0.950501i | \(0.600571\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −10.6394 | −0.0235907 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | − 263.723i | − 0.582171i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 289.415i | 0.636077i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −720.881 | −1.57742 | −0.788710 | − | 0.614765i | \(-0.789251\pi\) | ||||
−0.788710 | + | 0.614765i | \(0.789251\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 421.805 | 0.918966 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − 483.262i | − 1.04829i | −0.851629 | − | 0.524145i | \(-0.824385\pi\) | ||||
0.851629 | − | 0.524145i | \(-0.175615\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − 39.6326i | − 0.0855995i | −0.999084 | − | 0.0427997i | \(-0.986372\pi\) | ||||
0.999084 | − | 0.0427997i | \(-0.0136277\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −593.584 | −1.27652 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −17.7868 | −0.0380874 | −0.0190437 | − | 0.999819i | \(-0.506062\pi\) | ||||
−0.0190437 | + | 0.999819i | \(0.506062\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − 302.998i | − 0.646052i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | − 17.0355i | − 0.0361689i | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 29.2005 | 0.0617346 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 98.8029 | 0.208006 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 4.23072i | 0.00886943i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | − 668.616i | − 1.39586i | −0.716166 | − | 0.697930i | \(-0.754105\pi\) | ||||
0.716166 | − | 0.697930i | \(-0.245895\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1033.37 | −2.14837 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −192.012 | −0.397541 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − 298.624i | − 0.615720i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 418.484i | 0.859311i | 0.902993 | + | 0.429656i | \(0.141365\pi\) | ||||
−0.902993 | + | 0.429656i | \(0.858635\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 354.924 | 0.725816 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −381.031 | −0.776030 | −0.388015 | − | 0.921653i | \(-0.626839\pi\) | ||||
−0.388015 | + | 0.921653i | \(0.626839\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 106.231i | 0.215478i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 95.2412i | 0.192406i | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −277.253 | −0.557852 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 438.392 | 0.878541 | 0.439271 | − | 0.898355i | \(-0.355237\pi\) | ||||
0.439271 | + | 0.898355i | \(0.355237\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 283.565i | 0.565999i | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − 754.754i | − 1.50050i | −0.661151 | − | 0.750252i | \(-0.729932\pi\) | ||||
0.661151 | − | 0.750252i | \(-0.270068\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −524.378 | −1.03837 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 891.235 | 1.75786 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − 494.029i | − 0.970588i | −0.874351 | − | 0.485294i | \(-0.838713\pi\) | ||||
0.874351 | − | 0.485294i | \(-0.161287\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − 64.5495i | − 0.126320i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 164.272 | 0.320218 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 228.092 | 0.442897 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − 30.3078i | − 0.0586224i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 893.460i | 1.72150i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −32.8747 | −0.0630993 | −0.0315496 | − | 0.999502i | \(-0.510044\pi\) | ||||
−0.0315496 | + | 0.999502i | \(0.510044\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 28.2755 | 0.0540640 | 0.0270320 | − | 0.999635i | \(-0.491394\pi\) | ||||
0.0270320 | + | 0.999635i | \(0.491394\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 95.0051i | 0.180962i | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 731.574i | 1.38819i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 276.531 | 0.522742 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −318.588 | −0.599977 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 144.949i | 0.271949i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − 473.868i | − 0.885735i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 329.817 | 0.614183 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −9.80453 | −0.0181902 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 1071.59i | 1.98077i | 0.138352 | + | 0.990383i | \(0.455820\pi\) | ||||
−0.138352 | + | 0.990383i | \(0.544180\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 643.922i | 1.18586i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 168.948 | 0.309997 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 986.888 | 1.80418 | 0.902091 | − | 0.431545i | \(-0.142032\pi\) | ||||
0.902091 | + | 0.431545i | \(0.142032\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 1022.83i | 1.86307i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 41.3714i | 0.0750842i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 309.891 | 0.560382 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −1417.91 | −2.55480 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − 483.550i | − 0.868133i | −0.900881 | − | 0.434067i | \(-0.857078\pi\) | ||||
0.900881 | − | 0.434067i | \(-0.142922\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − 397.821i | − 0.711665i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 206.444 | 0.367993 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −520.893 | −0.925210 | −0.462605 | − | 0.886564i | \(-0.653085\pi\) | ||||
−0.462605 | + | 0.886564i | \(0.653085\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 912.236i | 1.61458i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | − 124.493i | − 0.219564i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −732.959 | −1.28815 | −0.644077 | − | 0.764961i | \(-0.722758\pi\) | ||||
−0.644077 | + | 0.764961i | \(0.722758\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 999.584 | 1.75058 | 0.875292 | − | 0.483595i | \(-0.160669\pi\) | ||||
0.875292 | + | 0.483595i | \(0.160669\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − 1299.32i | − 2.26758i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 124.918i | 0.217249i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 465.859 | 0.807381 | 0.403690 | − | 0.914896i | \(-0.367727\pi\) | ||||
0.403690 | + | 0.914896i | \(0.367727\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 565.682 | 0.976998 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − 209.730i | − 0.360981i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0.499565i | 0 0.000856887i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 1297.54 | 2.21803 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 574.851 | 0.979303 | 0.489651 | − | 0.871918i | \(-0.337124\pi\) | ||||
0.489651 | + | 0.871918i | \(0.337124\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 284.911i | 0.483719i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | − 493.735i | − 0.835423i | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 943.055 | 1.59031 | 0.795156 | − | 0.606405i | \(-0.207389\pi\) | ||||
0.795156 | + | 0.606405i | \(0.207389\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 489.432 | 0.822574 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 1515.73i | 2.53892i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − 9.26699i | − 0.0154708i | −0.999970 | − | 0.00773538i | \(-0.997538\pi\) | ||||
0.999970 | − | 0.00773538i | \(-0.00246227\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 57.7003 | 0.0960072 | 0.0480036 | − | 0.998847i | \(-0.484714\pi\) | ||||
0.0480036 | + | 0.998847i | \(0.484714\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −1358.44 | −2.25281 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | − 682.389i | − 1.12792i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 1024.68i | 1.68810i | 0.536264 | + | 0.844050i | \(0.319835\pi\) | ||||
−0.536264 | + | 0.844050i | \(0.680165\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −39.7811 | −0.0653221 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −412.906 | −0.675788 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − 404.818i | − 0.660389i | −0.943913 | − | 0.330195i | \(-0.892886\pi\) | ||||
0.943913 | − | 0.330195i | \(-0.107114\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 198.889i | 0.323396i | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 894.209 | 1.44928 | 0.724642 | − | 0.689125i | \(-0.242005\pi\) | ||||
0.724642 | + | 0.689125i | \(0.242005\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 779.388 | 1.25911 | 0.629554 | − | 0.776957i | \(-0.283238\pi\) | ||||
0.629554 | + | 0.776957i | \(0.283238\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 207.692i | 0.334447i | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 7.03977i | 0.0112998i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −759.737 | −1.21558 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 80.3993 | 0.128229 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 1747.53i | 2.77827i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 780.191i | 1.23644i | 0.786007 | + | 0.618218i | \(0.212145\pi\) | ||||
−0.786007 | + | 0.618218i | \(0.787855\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 120.559 | 0.190456 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 92.1985 | 0.145194 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 133.575i | 0.209693i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 1243.02i | 1.94525i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −23.3139 | −0.0363712 | −0.0181856 | − | 0.999835i | \(-0.505789\pi\) | ||||
−0.0181856 | + | 0.999835i | \(0.505789\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −530.706 | −0.825360 | −0.412680 | − | 0.910876i | \(-0.635407\pi\) | ||||
−0.412680 | + | 0.910876i | \(0.635407\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | − 545.862i | − 0.846297i | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 213.435i | 0.329883i | 0.986303 | + | 0.164942i | \(0.0527436\pi\) | ||||
−0.986303 | + | 0.164942i | \(0.947256\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −37.6190 | −0.0579646 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −273.959 | −0.420828 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 274.874i | 0.420941i | 0.977600 | + | 0.210470i | \(0.0674995\pi\) | ||||
−0.977600 | + | 0.210470i | \(0.932500\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 677.215i | 1.03392i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −289.397 | −0.440483 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −1234.48 | −1.87327 | −0.936633 | − | 0.350313i | \(-0.886075\pi\) | ||||
−0.936633 | + | 0.350313i | \(0.886075\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − 582.733i | − 0.881593i | −0.897607 | − | 0.440797i | \(-0.854696\pi\) | ||||
0.897607 | − | 0.440797i | \(-0.145304\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | − 2812.54i | − 4.24215i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 190.609 | 0.286630 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −52.3066 | −0.0784207 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | − 736.201i | − 1.10045i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 120.776i | 0.179994i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −399.145 | −0.593083 | −0.296542 | − | 0.955020i | \(-0.595833\pi\) | ||||
−0.296542 | + | 0.955020i | \(0.595833\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 102.763 | 0.152241 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 754.467i | 1.11443i | 0.830369 | + | 0.557214i | \(0.188130\pi\) | ||||
−0.830369 | + | 0.557214i | \(0.811870\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − 137.825i | − 0.202983i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −782.312 | −1.14877 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −288.264 | −0.422055 | −0.211028 | − | 0.977480i | \(-0.567681\pi\) | ||||
−0.211028 | + | 0.977480i | \(0.567681\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − 109.897i | − 0.160433i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − 1047.10i | − 1.52416i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 6.80596 | 0.00987803 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 156.692 | 0.226761 | 0.113380 | − | 0.993552i | \(-0.463832\pi\) | ||||
0.113380 | + | 0.993552i | \(0.463832\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 43.9570i | 0.0634300i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − 601.649i | − 0.865682i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 245.124 | 0.351685 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 1233.92 | 1.76527 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − 1126.50i | − 1.60700i | −0.595307 | − | 0.803498i | \(-0.702970\pi\) | ||||
0.595307 | − | 0.803498i | \(-0.297030\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 680.575i | 0.968102i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −566.562 | −0.803633 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −242.018 | −0.342317 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − 1096.17i | − 1.54608i | −0.634356 | − | 0.773041i | \(-0.718734\pi\) | ||||
0.634356 | − | 0.773041i | \(-0.281266\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | − 1389.35i | − 1.95407i | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −360.218 | −0.505214 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 153.215 | 0.214286 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − 717.800i | − 1.00112i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − 605.362i | − 0.841949i | −0.907072 | − | 0.420975i | \(-0.861688\pi\) | ||||
0.907072 | − | 0.420975i | \(-0.138312\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 105.272 | 0.146009 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 446.298 | 0.617287 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 25.8806i | 0.0356974i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 443.659i | 0.610260i | 0.952311 | + | 0.305130i | \(0.0986999\pi\) | ||||
−0.952311 | + | 0.305130i | \(0.901300\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −1095.46 | −1.50269 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −672.757 | −0.920325 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 750.026i | 1.02323i | 0.859216 | + | 0.511614i | \(0.170952\pi\) | ||||
−0.859216 | + | 0.511614i | \(0.829048\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 183.282i | 0.249363i | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −160.406 | −0.217647 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −619.293 | −0.838015 | −0.419007 | − | 0.907983i | \(-0.637622\pi\) | ||||
−0.419007 | + | 0.907983i | \(0.637622\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | − 1095.34i | − 1.47819i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 30.5255i | 0.0410842i | 0.999789 | + | 0.0205421i | \(0.00653921\pi\) | ||||
−0.999789 | + | 0.0205421i | \(0.993461\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 472.306 | 0.633967 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −940.291 | −1.25876 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − 218.706i | − 0.291997i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − 968.214i | − 1.28923i | −0.764506 | − | 0.644616i | \(-0.777017\pi\) | ||||
0.764506 | − | 0.644616i | \(-0.222983\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −1430.28 | −1.89945 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −330.993 | −0.438401 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1171.15i | 1.54710i | 0.633736 | + | 0.773550i | \(0.281521\pi\) | ||||
−0.633736 | + | 0.773550i | \(0.718479\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 101.650i | 0.133927i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 235.996 | 0.310113 | 0.155057 | − | 0.987906i | \(-0.450444\pi\) | ||||
0.155057 | + | 0.987906i | \(0.450444\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 77.9753 | 0.102196 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | − 2194.29i | − 2.86835i | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 512.513i | 0.668205i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −124.257 | −0.161582 | −0.0807912 | − | 0.996731i | \(-0.525745\pi\) | ||||
−0.0807912 | + | 0.996731i | \(0.525745\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1593.39 | 2.06665 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − 178.223i | − 0.230560i | −0.993333 | − | 0.115280i | \(-0.963224\pi\) | ||||
0.993333 | − | 0.115280i | \(-0.0367765\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 178.231i | 0.229975i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −654.415 | −0.842233 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 95.4634 | 0.122546 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 146.776i | 0.187933i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 43.0296i | 0.0549548i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −21.3809 | −0.0272368 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 1107.90 | 1.40775 | 0.703873 | − | 0.710326i | \(-0.251453\pi\) | ||||
0.703873 | + | 0.710326i | \(0.251453\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | − 1755.57i | − 2.22506i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 421.028i | 0.532273i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1645.43 | 2.07494 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 9.33867 | 0.0117468 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 1094.69i | 1.37351i | 0.726889 | + | 0.686755i | \(0.240966\pi\) | ||||
−0.726889 | + | 0.686755i | \(0.759034\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 698.269i | 0.873929i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 31.5617 | 0.0394028 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −34.1722 | −0.0425556 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 240.990i | 0.299367i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 172.473i | 0.213722i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −1386.75 | −1.71416 | −0.857079 | − | 0.515185i | \(-0.827723\pi\) | ||||
−0.857079 | + | 0.515185i | \(0.827723\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 312.204 | 0.384962 | 0.192481 | − | 0.981301i | \(-0.438347\pi\) | ||||
0.192481 | + | 0.981301i | \(0.438347\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 1410.11i | 1.73446i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | − 445.456i | − 0.546572i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −262.005 | −0.320691 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 598.861 | 0.731209 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 1092.89i | 1.33117i | 0.746324 | + | 0.665583i | \(0.231817\pi\) | ||||
−0.746324 | + | 0.665583i | \(0.768183\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − 907.162i | − 1.10226i | −0.834419 | − | 0.551131i | \(-0.814196\pi\) | ||||
0.834419 | − | 0.551131i | \(-0.185804\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 50.2952 | 0.0609638 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 607.144 | 0.734152 | 0.367076 | − | 0.930191i | \(-0.380359\pi\) | ||||
0.367076 | + | 0.930191i | \(0.380359\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 427.969i | 0.516247i | 0.966112 | + | 0.258124i | \(0.0831042\pi\) | ||||
−0.966112 | + | 0.258124i | \(0.916896\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 1115.42i | 1.34226i | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 225.889 | 0.271176 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 355.896 | 0.426223 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 296.330i | 0.354038i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − 1133.09i | − 1.35053i | −0.737575 | − | 0.675265i | \(-0.764029\pi\) | ||||
0.737575 | − | 0.675265i | \(-0.235971\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 830.163 | 0.987114 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −1217.55 | −1.44430 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − 1118.57i | − 1.32375i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − 314.945i | − 0.371836i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 756.397 | 0.890927 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −860.464 | −1.01112 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 169.502i | 0.198712i | 0.995052 | + | 0.0993562i | \(0.0316783\pi\) | ||||
−0.995052 | + | 0.0993562i | \(0.968322\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | − 854.563i | − 0.999489i | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −234.079 | −0.273138 | −0.136569 | − | 0.990631i | \(-0.543607\pi\) | ||||
−0.136569 | + | 0.990631i | \(0.543607\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −894.342 | −1.04114 | −0.520571 | − | 0.853818i | \(-0.674281\pi\) | ||||
−0.520571 | + | 0.853818i | \(0.674281\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 91.7939i | 0.106613i | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 778.580i | 0.902178i | 0.892479 | + | 0.451089i | \(0.148964\pi\) | ||||
−0.892479 | + | 0.451089i | \(0.851036\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 1121.36 | 1.29637 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −3436.32 | −3.96346 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − 164.055i | − 0.188786i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 2185.33i | 2.50899i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −617.917 | −0.707809 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −259.932 | −0.297065 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − 17.2780i | − 0.0197013i | −0.999951 | − | 0.00985064i | \(-0.996864\pi\) | ||||
0.999951 | − | 0.00985064i | \(-0.00313561\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 156.962i | 0.178569i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 770.918 | 0.875049 | 0.437524 | − | 0.899207i | \(-0.355855\pi\) | ||||
0.437524 | + | 0.899207i | \(0.355855\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −776.362 | −0.879232 | −0.439616 | − | 0.898186i | \(-0.644886\pi\) | ||||
−0.439616 | + | 0.898186i | \(0.644886\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 703.235i | 0.794616i | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 1630.80i | 1.83856i | 0.393603 | + | 0.919280i | \(0.371228\pi\) | ||||
−0.393603 | + | 0.919280i | \(0.628772\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 42.5527 | 0.0478658 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −65.9059 | −0.0739685 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 271.940i | 0.304524i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − 413.945i | − 0.462508i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 1384.86 | 1.54388 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −74.6299 | −0.0830144 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − 11.5096i | − 0.0127743i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | − 251.933i | − 0.278996i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 808.171 | 0.893007 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 953.863 | 1.05167 | 0.525834 | − | 0.850587i | \(-0.323753\pi\) | ||||
0.525834 | + | 0.850587i | \(0.323753\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 1085.05i | 1.19367i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − 1681.15i | − 1.84539i | −0.385534 | − | 0.922694i | \(-0.625983\pi\) | ||||
0.385534 | − | 0.922694i | \(-0.374017\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −111.030 | −0.121610 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 2257.74 | 2.46747 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 312.557i | 0.340848i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − 504.991i | − 0.549500i | −0.961516 | − | 0.274750i | \(-0.911405\pi\) | ||||
0.961516 | − | 0.274750i | \(-0.0885952\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −1018.24 | −1.10559 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 1999.64 | 2.16646 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 425.746i | 0.460266i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | − 471.971i | − 0.509138i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 983.851 | 1.05904 | 0.529521 | − | 0.848297i | \(-0.322372\pi\) | ||||
0.529521 | + | 0.848297i | \(0.322372\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 87.9723 | 0.0944923 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | − 1918.04i | − 2.05577i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − 259.103i | − 0.277115i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −389.648 | −0.415846 | −0.207923 | − | 0.978145i | \(-0.566670\pi\) | ||||
−0.207923 | + | 0.978145i | \(0.566670\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 1342.24 | 1.42943 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 875.465i | 0.930356i | 0.885217 | + | 0.465178i | \(0.154010\pi\) | ||||
−0.885217 | + | 0.465178i | \(0.845990\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 120.696i | 0.127992i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 198.248 | 0.209787 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 1251.29 | 1.32132 | 0.660661 | − | 0.750685i | \(-0.270276\pi\) | ||||
0.660661 | + | 0.750685i | \(0.270276\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 465.554i | 0.490573i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 1934.14i | 2.03380i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −882.129 | −0.925633 | −0.462817 | − | 0.886454i | \(-0.653161\pi\) | ||||
−0.462817 | + | 0.886454i | \(0.653161\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −1630.75 | −1.70759 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 21.0599i | 0.0220062i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | − 50.7211i | − 0.0528896i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 447.049 | 0.465192 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −980.533 | −1.01821 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − 709.973i | − 0.735724i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − 1410.24i | − 1.45836i | −0.684320 | − | 0.729182i | \(-0.739901\pi\) | ||||
0.684320 | − | 0.729182i | \(-0.260099\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −1852.34 | −1.91160 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −678.550 | −0.698815 | −0.349408 | − | 0.936971i | \(-0.613617\pi\) | ||||
−0.349408 | + | 0.936971i | \(0.613617\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − 277.681i | − 0.285387i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | − 685.210i | − 0.702780i | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 111.815 | 0.114447 | 0.0572235 | − | 0.998361i | \(-0.481775\pi\) | ||||
0.0572235 | + | 0.998361i | \(0.481775\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 3.72682 | 0.00380676 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − 349.590i | − 0.356360i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 202.226i | 0.205723i | 0.994696 | + | 0.102862i | \(0.0327999\pi\) | ||||
−0.994696 | + | 0.102862i | \(0.967200\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −619.675 | −0.629111 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −261.487 | −0.264931 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − 331.257i | − 0.334942i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − 189.064i | − 0.190781i | −0.995440 | − | 0.0953907i | \(-0.969590\pi\) | ||||
0.995440 | − | 0.0953907i | \(-0.0304100\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −578.546 | −0.582624 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 1902.36 | 1.91192 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − 1632.91i | − 1.63783i | −0.573917 | − | 0.818914i | \(-0.694577\pi\) | ||||
0.573917 | − | 0.818914i | \(-0.305423\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 707.853i | 0.708562i |
(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 | 224.3.g.b.15.2 | 8 | ||
3.2 | odd | 2 | 2016.3.g.b.1135.2 | 8 | |||
4.3 | odd | 2 | 56.3.g.b.43.1 | ✓ | 8 | ||
7.6 | odd | 2 | 1568.3.g.m.687.7 | 8 | |||
8.3 | odd | 2 | inner | 224.3.g.b.15.1 | 8 | ||
8.5 | even | 2 | 56.3.g.b.43.2 | yes | 8 | ||
12.11 | even | 2 | 504.3.g.b.379.8 | 8 | |||
16.3 | odd | 4 | 1792.3.d.j.1023.14 | 16 | |||
16.5 | even | 4 | 1792.3.d.j.1023.13 | 16 | |||
16.11 | odd | 4 | 1792.3.d.j.1023.3 | 16 | |||
16.13 | even | 4 | 1792.3.d.j.1023.4 | 16 | |||
24.5 | odd | 2 | 504.3.g.b.379.7 | 8 | |||
24.11 | even | 2 | 2016.3.g.b.1135.7 | 8 | |||
28.3 | even | 6 | 392.3.k.n.275.7 | 16 | |||
28.11 | odd | 6 | 392.3.k.o.275.7 | 16 | |||
28.19 | even | 6 | 392.3.k.n.67.5 | 16 | |||
28.23 | odd | 6 | 392.3.k.o.67.5 | 16 | |||
28.27 | even | 2 | 392.3.g.m.99.1 | 8 | |||
56.5 | odd | 6 | 392.3.k.n.67.7 | 16 | |||
56.13 | odd | 2 | 392.3.g.m.99.2 | 8 | |||
56.27 | even | 2 | 1568.3.g.m.687.8 | 8 | |||
56.37 | even | 6 | 392.3.k.o.67.7 | 16 | |||
56.45 | odd | 6 | 392.3.k.n.275.5 | 16 | |||
56.53 | even | 6 | 392.3.k.o.275.5 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
56.3.g.b.43.1 | ✓ | 8 | 4.3 | odd | 2 | ||
56.3.g.b.43.2 | yes | 8 | 8.5 | even | 2 | ||
224.3.g.b.15.1 | 8 | 8.3 | odd | 2 | inner | ||
224.3.g.b.15.2 | 8 | 1.1 | even | 1 | trivial | ||
392.3.g.m.99.1 | 8 | 28.27 | even | 2 | |||
392.3.g.m.99.2 | 8 | 56.13 | odd | 2 | |||
392.3.k.n.67.5 | 16 | 28.19 | even | 6 | |||
392.3.k.n.67.7 | 16 | 56.5 | odd | 6 | |||
392.3.k.n.275.5 | 16 | 56.45 | odd | 6 | |||
392.3.k.n.275.7 | 16 | 28.3 | even | 6 | |||
392.3.k.o.67.5 | 16 | 28.23 | odd | 6 | |||
392.3.k.o.67.7 | 16 | 56.37 | even | 6 | |||
392.3.k.o.275.5 | 16 | 56.53 | even | 6 | |||
392.3.k.o.275.7 | 16 | 28.11 | odd | 6 | |||
504.3.g.b.379.7 | 8 | 24.5 | odd | 2 | |||
504.3.g.b.379.8 | 8 | 12.11 | even | 2 | |||
1568.3.g.m.687.7 | 8 | 7.6 | odd | 2 | |||
1568.3.g.m.687.8 | 8 | 56.27 | even | 2 | |||
1792.3.d.j.1023.3 | 16 | 16.11 | odd | 4 | |||
1792.3.d.j.1023.4 | 16 | 16.13 | even | 4 | |||
1792.3.d.j.1023.13 | 16 | 16.5 | even | 4 | |||
1792.3.d.j.1023.14 | 16 | 16.3 | odd | 4 | |||
2016.3.g.b.1135.2 | 8 | 3.2 | odd | 2 | |||
2016.3.g.b.1135.7 | 8 | 24.11 | even | 2 |