Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1440,2,Mod(1439,1440)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1440, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1440.1439");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1440 = 2^{5} \cdot 3^{2} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1440.o (of order \(2\), degree \(1\), 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: | \(11.4984578911\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Coefficient field: | 12.0.426337261060096.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 4x^{9} - 3x^{8} + 4x^{7} + 8x^{6} + 8x^{5} - 12x^{4} - 32x^{3} + 64 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{10} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1439.2 | ||
Root | \(-0.0912546 - 1.41127i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1440.1439 |
Dual form | 1440.2.o.a.1439.1 |
$q$-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 \(\left(\mathbb{Z}/1440\mathbb{Z}\right)^\times\).
\(n\) | \(577\) | \(641\) | \(901\) | \(991\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(1\) | \(-1\) |
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 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −2.20963 | + | 0.342849i | −0.988176 | + | 0.153327i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.64002 | 0.997835 | 0.498918 | − | 0.866649i | \(-0.333731\pi\) | ||||
0.498918 | + | 0.866649i | \(0.333731\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −3.00504 | −0.906054 | −0.453027 | − | 0.891497i | \(-0.649656\pi\) | ||||
−0.453027 | + | 0.891497i | \(0.649656\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 0.640023i | − | 0.177511i | −0.996053 | − | 0.0887553i | \(-0.971711\pi\) | ||
0.996053 | − | 0.0887553i | \(-0.0282889\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −0.685698 | −0.166306 | −0.0831531 | − | 0.996537i | \(-0.526499\pi\) | ||||
−0.0831531 | + | 0.996537i | \(0.526499\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 5.28005i | 1.21133i | 0.795721 | + | 0.605663i | \(0.207092\pi\) | ||||
−0.795721 | + | 0.605663i | \(0.792908\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 2.27653i | − | 0.474689i | −0.971426 | − | 0.237344i | \(-0.923723\pi\) | ||
0.971426 | − | 0.237344i | \(-0.0762770\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 4.76491 | − | 1.51514i | 0.952982 | − | 0.303028i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 8.15281i | 1.51394i | 0.653450 | + | 0.756970i | \(0.273321\pi\) | ||||
−0.653450 | + | 0.756970i | \(0.726679\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.96972i | 0.533378i | 0.963783 | + | 0.266689i | \(0.0859297\pi\) | ||||
−0.963783 | + | 0.266689i | \(0.914070\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −5.83347 | + | 0.905130i | −0.986036 | + | 0.152995i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.60975i | 0.264641i | 0.991207 | + | 0.132320i | \(0.0422428\pi\) | ||||
−0.991207 | + | 0.132320i | \(0.957757\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 7.42430i | 1.15948i | 0.814801 | + | 0.579740i | \(0.196846\pi\) | ||||
−0.814801 | + | 0.579740i | \(0.803154\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −11.2195 | −1.71096 | −0.855478 | − | 0.517838i | \(-0.826737\pi\) | ||||
−0.855478 | + | 0.517838i | \(0.826737\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − | 4.19982i | − | 0.612607i | −0.951934 | − | 0.306304i | \(-0.900908\pi\) | ||
0.951934 | − | 0.306304i | \(-0.0990923\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −0.0302761 | −0.00432516 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 9.60984 | 1.32001 | 0.660007 | − | 0.751260i | \(-0.270553\pi\) | ||||
0.660007 | + | 0.751260i | \(0.270553\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 6.64002 | − | 1.03028i | 0.895341 | − | 0.138922i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −7.20487 | −0.937994 | −0.468997 | − | 0.883200i | \(-0.655384\pi\) | ||||
−0.468997 | + | 0.883200i | \(0.655384\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 10.4995 | 1.34433 | 0.672164 | − | 0.740402i | \(-0.265365\pi\) | ||||
0.672164 | + | 0.740402i | \(0.265365\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0.219432 | + | 1.41421i | 0.0272171 | + | 0.175412i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −8.49954 | −1.03838 | −0.519192 | − | 0.854658i | \(-0.673767\pi\) | ||||
−0.519192 | + | 0.854658i | \(0.673767\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −13.1240 | −1.55753 | −0.778764 | − | 0.627317i | \(-0.784153\pi\) | ||||
−0.778764 | + | 0.627317i | \(0.784153\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 14.2498i | 1.66781i | 0.551908 | + | 0.833905i | \(0.313900\pi\) | ||||
−0.551908 | + | 0.833905i | \(0.686100\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −7.93338 | −0.904093 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 11.4693i | 1.29039i | 0.764017 | + | 0.645197i | \(0.223225\pi\) | ||||
−0.764017 | + | 0.645197i | \(0.776775\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 13.1240i | 1.44054i | 0.693692 | + | 0.720271i | \(0.255983\pi\) | ||||
−0.693692 | + | 0.720271i | \(0.744017\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.51514 | − | 0.235091i | 0.164340 | − | 0.0254992i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 10.2527i | 1.08679i | 0.839478 | + | 0.543393i | \(0.182861\pi\) | ||||
−0.839478 | + | 0.543393i | \(0.817139\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 1.68968i | − | 0.177126i | ||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −1.81026 | − | 11.6669i | −0.185729 | − | 1.19700i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 8.31032i | − | 0.843785i | −0.906646 | − | 0.421893i | \(-0.861366\pi\) | ||
0.906646 | − | 0.421893i | \(-0.138634\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 3.51413i | 0.349669i | 0.984598 | + | 0.174834i | \(0.0559390\pi\) | ||||
−0.984598 | + | 0.174834i | \(0.944061\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 3.13957 | 0.309351 | 0.154675 | − | 0.987965i | \(-0.450567\pi\) | ||||
0.154675 | + | 0.987965i | \(0.450567\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 7.46711i | 0.721873i | 0.932590 | + | 0.360937i | \(0.117543\pi\) | ||||
−0.932590 | + | 0.360937i | \(0.882457\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 2.96972 | 0.284448 | 0.142224 | − | 0.989835i | \(-0.454575\pi\) | ||||
0.142224 | + | 0.989835i | \(0.454575\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −5.67761 | −0.534105 | −0.267053 | − | 0.963682i | \(-0.586050\pi\) | ||||
−0.267053 | + | 0.963682i | \(0.586050\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0.780505 | + | 5.03028i | 0.0727825 | + | 0.469076i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −1.81026 | −0.165946 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.96972 | −0.179066 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −10.0092 | + | 4.98154i | −0.895251 | + | 0.445562i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 19.1396 | 1.69836 | 0.849181 | − | 0.528102i | \(-0.177096\pi\) | ||||
0.849181 | + | 0.528102i | \(0.177096\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 11.5760 | 1.01140 | 0.505698 | − | 0.862711i | \(-0.331235\pi\) | ||||
0.505698 | + | 0.862711i | \(0.331235\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 13.9394i | 1.20870i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 2.49596 | 0.213244 | 0.106622 | − | 0.994300i | \(-0.465997\pi\) | ||||
0.106622 | + | 0.994300i | \(0.465997\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 7.46927i | − | 0.633535i | −0.948503 | − | 0.316767i | \(-0.897403\pi\) | ||
0.948503 | − | 0.316767i | \(-0.102597\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 1.92330i | 0.160834i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −2.79518 | − | 18.0147i | −0.232127 | − | 1.49604i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − | 9.60984i | − | 0.787269i | −0.919267 | − | 0.393634i | \(-0.871218\pi\) | ||
0.919267 | − | 0.393634i | \(-0.128782\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 19.4693i | 1.58439i | 0.610270 | + | 0.792193i | \(0.291061\pi\) | ||||
−0.610270 | + | 0.792193i | \(0.708939\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −1.01817 | − | 6.56198i | −0.0817812 | − | 0.527071i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 12.8292i | − | 1.02388i | −0.859020 | − | 0.511942i | \(-0.828926\pi\) | ||
0.859020 | − | 0.511942i | \(-0.171074\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 6.01008i | − | 0.473661i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −21.2800 | −1.66678 | −0.833391 | − | 0.552684i | \(-0.813604\pi\) | ||||
−0.833391 | + | 0.552684i | \(0.813604\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 22.8676i | − | 1.76955i | −0.466020 | − | 0.884774i | \(-0.654312\pi\) | ||
0.466020 | − | 0.884774i | \(-0.345688\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 12.5904 | 0.968490 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 5.98932 | 0.455360 | 0.227680 | − | 0.973736i | \(-0.426886\pi\) | ||||
0.227680 | + | 0.973736i | \(0.426886\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 12.5795 | − | 4.00000i | 0.950919 | − | 0.302372i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −2.65181 | −0.198206 | −0.0991029 | − | 0.995077i | \(-0.531597\pi\) | ||||
−0.0991029 | + | 0.995077i | \(0.531597\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −11.4693 | −0.852504 | −0.426252 | − | 0.904605i | \(-0.640166\pi\) | ||||
−0.426252 | + | 0.904605i | \(0.640166\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −0.551901 | − | 3.55694i | −0.0405765 | − | 0.261512i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 2.06055 | 0.150682 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −5.30362 | −0.383757 | −0.191878 | − | 0.981419i | \(-0.561458\pi\) | ||||
−0.191878 | + | 0.981419i | \(0.561458\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 10.0606i | 0.724174i | 0.932144 | + | 0.362087i | \(0.117936\pi\) | ||||
−0.932144 | + | 0.362087i | \(0.882064\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 5.79065 | 0.412567 | 0.206283 | − | 0.978492i | \(-0.433863\pi\) | ||||
0.206283 | + | 0.978492i | \(0.433863\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 24.0899i | − | 1.70769i | −0.520529 | − | 0.853844i | \(-0.674265\pi\) | ||
0.520529 | − | 0.853844i | \(-0.325735\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 21.5236i | 1.51066i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −2.54541 | − | 16.4049i | −0.177779 | − | 1.14577i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 15.8668i | − | 1.09753i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 23.4693i | − | 1.61569i | −0.589394 | − | 0.807845i | \(-0.700634\pi\) | ||
0.589394 | − | 0.807845i | \(-0.299366\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 24.7909 | − | 3.84659i | 1.69073 | − | 0.262336i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 7.84014i | 0.532223i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0.438863i | 0.0295211i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −13.3600 | −0.894650 | −0.447325 | − | 0.894371i | \(-0.647623\pi\) | ||||
−0.447325 | + | 0.894371i | \(0.647623\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − | 8.57092i | − | 0.568872i | −0.958695 | − | 0.284436i | \(-0.908194\pi\) | ||
0.958695 | − | 0.284436i | \(-0.0918063\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −8.90917 | −0.588735 | −0.294367 | − | 0.955692i | \(-0.595109\pi\) | ||||
−0.294367 | + | 0.955692i | \(0.595109\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 24.0196 | 1.57357 | 0.786787 | − | 0.617224i | \(-0.211743\pi\) | ||||
0.786787 | + | 0.617224i | \(0.211743\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1.43991 | + | 9.28005i | 0.0939291 | + | 0.605364i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 14.4097 | 0.932088 | 0.466044 | − | 0.884762i | \(-0.345679\pi\) | ||||
0.466044 | + | 0.884762i | \(0.345679\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 3.87890 | 0.249862 | 0.124931 | − | 0.992165i | \(-0.460129\pi\) | ||||
0.124931 | + | 0.992165i | \(0.460129\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0.0668989 | − | 0.0103801i | 0.00427401 | − | 0.000663162i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 3.37935 | 0.215023 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 24.1754 | 1.52594 | 0.762970 | − | 0.646434i | \(-0.223741\pi\) | ||||
0.762970 | + | 0.646434i | \(0.223741\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 6.84106i | 0.430094i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −12.4383 | −0.775878 | −0.387939 | − | 0.921685i | \(-0.626813\pi\) | ||||
−0.387939 | + | 0.921685i | \(0.626813\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 4.24977i | 0.264068i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 19.2471i | 1.18683i | 0.804898 | + | 0.593413i | \(0.202220\pi\) | ||||
−0.804898 | + | 0.593413i | \(0.797780\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −21.2342 | + | 3.29473i | −1.30440 | + | 0.202393i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − | 15.8875i | − | 0.968679i | −0.874880 | − | 0.484340i | \(-0.839060\pi\) | ||
0.874880 | − | 0.484340i | \(-0.160940\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 6.02936i | − | 0.366258i | −0.983089 | − | 0.183129i | \(-0.941377\pi\) | ||
0.983089 | − | 0.183129i | \(-0.0586225\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −14.3188 | + | 4.55305i | −0.863453 | + | 0.274559i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 12.3591i | 0.742584i | 0.928516 | + | 0.371292i | \(0.121085\pi\) | ||||
−0.928516 | + | 0.371292i | \(0.878915\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 17.7198i | − | 1.05708i | −0.848909 | − | 0.528538i | \(-0.822740\pi\) | ||
0.848909 | − | 0.528538i | \(-0.177260\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −20.6206 | −1.22577 | −0.612885 | − | 0.790172i | \(-0.709991\pi\) | ||||
−0.612885 | + | 0.790172i | \(0.709991\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 19.6003i | 1.15697i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.5298 | −0.972342 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 21.6574 | 1.26524 | 0.632620 | − | 0.774463i | \(-0.281980\pi\) | ||||
0.632620 | + | 0.774463i | \(0.281980\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 15.9201 | − | 2.47018i | 0.926902 | − | 0.143820i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −1.45703 | −0.0842622 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −29.6197 | −1.70725 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −23.2001 | + | 3.59976i | −1.32843 | + | 0.206122i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 3.87890 | 0.221380 | 0.110690 | − | 0.993855i | \(-0.464694\pi\) | ||||
0.110690 | + | 0.993855i | \(0.464694\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 6.71654 | 0.380860 | 0.190430 | − | 0.981701i | \(-0.439012\pi\) | ||||
0.190430 | + | 0.981701i | \(0.439012\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 21.9394i | 1.24009i | 0.784566 | + | 0.620045i | \(0.212886\pi\) | ||||
−0.784566 | + | 0.620045i | \(0.787114\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −14.3616 | −0.806626 | −0.403313 | − | 0.915062i | \(-0.632141\pi\) | ||||
−0.403313 | + | 0.915062i | \(0.632141\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 24.4995i | − | 1.37171i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 3.62052i | − | 0.201451i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −0.969724 | − | 3.04965i | −0.0537906 | − | 0.169164i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − | 11.0876i | − | 0.611281i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 4.78051i | − | 0.262760i | −0.991332 | − | 0.131380i | \(-0.958059\pi\) | ||
0.991332 | − | 0.131380i | \(-0.0419409\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 18.7808 | − | 2.91406i | 1.02611 | − | 0.159212i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 33.1883i | − | 1.80788i | −0.427657 | − | 0.903941i | \(-0.640661\pi\) | ||
0.427657 | − | 0.903941i | \(-0.359339\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 8.92414i | − | 0.483270i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −18.5601 | −1.00215 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 13.8304i | 0.742456i | 0.928542 | + | 0.371228i | \(0.121063\pi\) | ||||
−0.928542 | + | 0.371228i | \(0.878937\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 20.4390 | 1.09407 | 0.547037 | − | 0.837108i | \(-0.315756\pi\) | ||||
0.547037 | + | 0.837108i | \(0.315756\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 20.8379 | 1.10909 | 0.554545 | − | 0.832154i | \(-0.312892\pi\) | ||||
0.554545 | + | 0.832154i | \(0.312892\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 28.9991 | − | 4.49954i | 1.53911 | − | 0.238811i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 22.0481 | 1.16365 | 0.581827 | − | 0.813312i | \(-0.302338\pi\) | ||||
0.581827 | + | 0.813312i | \(0.302338\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −8.87890 | −0.467310 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −4.88552 | − | 31.4867i | −0.255720 | − | 1.64809i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 4.70058 | 0.245368 | 0.122684 | − | 0.992446i | \(-0.460850\pi\) | ||||
0.122684 | + | 0.992446i | \(0.460850\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 25.3702 | 1.31716 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 35.5104i | 1.83866i | 0.393486 | + | 0.919330i | \(0.371269\pi\) | ||||
−0.393486 | + | 0.919330i | \(0.628731\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 5.21799 | 0.268740 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 1.52982i | − | 0.0785815i | −0.999228 | − | 0.0392907i | \(-0.987490\pi\) | ||
0.999228 | − | 0.0392907i | \(-0.0125098\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − | 2.16349i | − | 0.110549i | −0.998471 | − | 0.0552746i | \(-0.982397\pi\) | ||
0.998471 | − | 0.0552746i | \(-0.0176034\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 17.5298 | − | 2.71995i | 0.893402 | − | 0.138622i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 0.0207603i | 0.00105259i | 1.00000 | 0.000526294i | \(0.000167524\pi\) | |||||
−1.00000 | 0.000526294i | \(0.999832\pi\) | ||||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.56101i | 0.0789437i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −3.93223 | − | 25.3428i | −0.197852 | − | 1.27513i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 36.6694i | − | 1.84038i | −0.391468 | − | 0.920192i | \(-0.628033\pi\) | ||
0.391468 | − | 0.920192i | \(-0.371967\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 7.59556i | 0.379304i | 0.981851 | + | 0.189652i | \(0.0607360\pi\) | ||||
−0.981851 | + | 0.189652i | \(0.939264\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1.90069 | 0.0946803 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 4.83736i | − | 0.239779i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −26.5289 | −1.31177 | −0.655885 | − | 0.754861i | \(-0.727704\pi\) | ||||
−0.655885 | + | 0.754861i | \(0.727704\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −19.0210 | −0.935963 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −4.49954 | − | 28.9991i | −0.220874 | − | 1.42351i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −0.841553 | −0.0411125 | −0.0205563 | − | 0.999789i | \(-0.506544\pi\) | ||||
−0.0205563 | + | 0.999789i | \(0.506544\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 26.1505 | 1.27450 | 0.637248 | − | 0.770659i | \(-0.280073\pi\) | ||||
0.637248 | + | 0.770659i | \(0.280073\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −3.26729 | + | 1.03893i | −0.158487 | + | 0.0503954i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 27.7190 | 1.34142 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −38.8474 | −1.87121 | −0.935607 | − | 0.353044i | \(-0.885147\pi\) | ||||
−0.935607 | + | 0.353044i | \(0.885147\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 30.7787i | − | 1.47913i | −0.673086 | − | 0.739564i | \(-0.735032\pi\) | ||
0.673086 | − | 0.739564i | \(-0.264968\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 12.0202 | 0.575003 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 26.1505i | 1.24809i | 0.781387 | + | 0.624047i | \(0.214513\pi\) | ||||
−0.781387 | + | 0.624047i | \(0.785487\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − | 13.8304i | − | 0.657103i | −0.944486 | − | 0.328552i | \(-0.893439\pi\) | ||
0.944486 | − | 0.328552i | \(-0.106561\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −3.51514 | − | 22.6547i | −0.166634 | − | 1.07394i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 2.07915i | − | 0.0981212i | −0.998796 | − | 0.0490606i | \(-0.984377\pi\) | ||
0.998796 | − | 0.0490606i | \(-0.0156228\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 22.3103i | − | 1.05055i | ||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0.579304 | + | 3.73356i | 0.0271582 | + | 0.175032i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 18.6282i | 0.871391i | 0.900094 | + | 0.435695i | \(0.143498\pi\) | ||||
−0.900094 | + | 0.435695i | \(0.856502\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 23.0014i | − | 1.07128i | −0.844446 | − | 0.535641i | \(-0.820070\pi\) | ||
0.844446 | − | 0.535641i | \(-0.179930\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −25.9806 | −1.20742 | −0.603711 | − | 0.797203i | \(-0.706312\pi\) | ||||
−0.603711 | + | 0.797203i | \(0.706312\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − | 33.3177i | − | 1.54176i | −0.636981 | − | 0.770880i | \(-0.719817\pi\) | ||
0.636981 | − | 0.770880i | \(-0.280183\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −22.4390 | −1.03614 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 33.7151 | 1.55022 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 8.00000 | + | 25.1589i | 0.367065 | + | 1.15437i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 16.0380 | 0.732796 | 0.366398 | − | 0.930458i | \(-0.380591\pi\) | ||||
0.366398 | + | 0.930458i | \(0.380591\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.03028 | 0.0469765 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 2.84919 | + | 18.3627i | 0.129375 | + | 0.833808i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −19.1396 | −0.867296 | −0.433648 | − | 0.901082i | \(-0.642774\pi\) | ||||
−0.433648 | + | 0.901082i | \(0.642774\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 36.3669 | 1.64121 | 0.820607 | − | 0.571493i | \(-0.193636\pi\) | ||||
0.820607 | + | 0.571493i | \(0.193636\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 5.59037i | − | 0.251778i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −34.6476 | −1.55416 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 8.65940i | 0.387648i | 0.981036 | + | 0.193824i | \(0.0620891\pi\) | ||||
−0.981036 | + | 0.193824i | \(0.937911\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 31.1542i | 1.38910i | 0.719445 | + | 0.694549i | \(0.244396\pi\) | ||||
−0.719445 | + | 0.694549i | \(0.755604\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −1.20482 | − | 7.76491i | −0.0536136 | − | 0.345534i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 28.3907i | 1.25839i | 0.777246 | + | 0.629197i | \(0.216616\pi\) | ||||
−0.777246 | + | 0.629197i | \(0.783384\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 37.6197i | 1.66420i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −6.93727 | + | 1.07640i | −0.305693 | + | 0.0474317i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 12.6206i | 0.555055i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 16.4341i | − | 0.719990i | −0.932954 | − | 0.359995i | \(-0.882778\pi\) | ||
0.932954 | − | 0.359995i | \(-0.117222\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 14.2791 | 0.624383 | 0.312191 | − | 0.950019i | \(-0.398937\pi\) | ||||
0.312191 | + | 0.950019i | \(0.398937\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 2.03633i | − | 0.0887041i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 17.8174 | 0.774671 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 4.75172 | 0.205820 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −2.56009 | − | 16.4995i | −0.110683 | − | 0.713337i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0.0909809 | 0.00391883 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 1.40871 | 0.0605653 | 0.0302827 | − | 0.999541i | \(-0.490359\pi\) | ||||
0.0302827 | + | 0.999541i | \(0.490359\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −6.56198 | + | 1.01817i | −0.281085 | + | 0.0436135i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 15.3406 | 0.655917 | 0.327958 | − | 0.944692i | \(-0.393639\pi\) | ||||
0.327958 | + | 0.944692i | \(0.393639\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −43.0472 | −1.83387 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 30.2791i | 1.28760i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 7.53199 | 0.319141 | 0.159570 | − | 0.987187i | \(-0.448989\pi\) | ||||
0.159570 | + | 0.987187i | \(0.448989\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 7.18074i | 0.303713i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 40.0784i | 1.68910i | 0.535475 | + | 0.844551i | \(0.320132\pi\) | ||||
−0.535475 | + | 0.844551i | \(0.679868\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 12.5454 | − | 1.94657i | 0.527790 | − | 0.0818926i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 28.6803i | 1.20234i | 0.799121 | + | 0.601171i | \(0.205299\pi\) | ||||
−0.799121 | + | 0.601171i | \(0.794701\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 33.9007i | − | 1.41870i | −0.704857 | − | 0.709350i | \(-0.748989\pi\) | ||
0.704857 | − | 0.709350i | \(-0.251011\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −3.44925 | − | 10.8474i | −0.143844 | − | 0.452370i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 18.4002i | 0.766012i | 0.923746 | + | 0.383006i | \(0.125111\pi\) | ||||
−0.923746 | + | 0.383006i | \(0.874889\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 34.6476i | 1.43742i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −28.8780 | −1.19600 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 27.8869i | − | 1.15102i | −0.817796 | − | 0.575508i | \(-0.804804\pi\) | ||
0.817796 | − | 0.575508i | \(-0.195196\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −15.6803 | −0.646095 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −34.2295 | −1.40564 | −0.702818 | − | 0.711370i | \(-0.748075\pi\) | ||||
−0.702818 | + | 0.711370i | \(0.748075\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 4.00000 | − | 0.620646i | 0.163984 | − | 0.0254440i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −22.7546 | −0.929727 | −0.464863 | − | 0.885382i | \(-0.653897\pi\) | ||||
−0.464863 | + | 0.885382i | \(0.653897\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 11.5298 | 0.470311 | 0.235156 | − | 0.971958i | \(-0.424440\pi\) | ||||
0.235156 | + | 0.971958i | \(0.424440\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 4.35236 | − | 0.675318i | 0.176948 | − | 0.0274556i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −17.0790 | −0.693216 | −0.346608 | − | 0.938010i | \(-0.612667\pi\) | ||||
−0.346608 | + | 0.938010i | \(0.612667\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −2.68799 | −0.108744 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 43.1084i | 1.74113i | 0.492053 | + | 0.870565i | \(0.336247\pi\) | ||||
−0.492053 | + | 0.870565i | \(0.663753\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 23.7935 | 0.957890 | 0.478945 | − | 0.877845i | \(-0.341019\pi\) | ||||
0.478945 | + | 0.877845i | \(0.341019\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 32.4683i | 1.30501i | 0.757783 | + | 0.652507i | \(0.226283\pi\) | ||||
−0.757783 | + | 0.652507i | \(0.773717\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 27.0674i | 1.08443i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 20.4087 | − | 14.4390i | 0.816349 | − | 0.577560i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 1.10380i | − | 0.0440114i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 13.0303i | 0.518727i | 0.965780 | + | 0.259364i | \(0.0835128\pi\) | ||||
−0.965780 | + | 0.259364i | \(0.916487\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −42.2913 | + | 6.56198i | −1.67828 | + | 0.260404i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0.0193774i | 0.000767761i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 38.1397i | 1.50643i | 0.657777 | + | 0.753213i | \(0.271497\pi\) | ||||
−0.657777 | + | 0.753213i | \(0.728503\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 17.1589 | 0.676683 | 0.338341 | − | 0.941023i | \(-0.390134\pi\) | ||||
0.338341 | + | 0.941023i | \(0.390134\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 30.4478i | 1.19702i | 0.801113 | + | 0.598512i | \(0.204241\pi\) | ||||
−0.801113 | + | 0.598512i | \(0.795759\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 21.6509 | 0.849873 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −11.7151 | −0.458447 | −0.229224 | − | 0.973374i | \(-0.573619\pi\) | ||||
−0.229224 | + | 0.973374i | \(0.573619\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −25.5786 | + | 3.96881i | −0.999437 | + | 0.155074i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −10.1189 | −0.394177 | −0.197089 | − | 0.980386i | \(-0.563149\pi\) | ||||
−0.197089 | + | 0.980386i | \(0.563149\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 11.1202 | 0.432525 | 0.216263 | − | 0.976335i | \(-0.430613\pi\) | ||||
0.216263 | + | 0.976335i | \(0.430613\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −4.77913 | − | 30.8010i | −0.185327 | − | 1.19441i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 18.5601 | 0.718650 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −31.5516 | −1.21803 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 15.0984i | 0.582000i | 0.956723 | + | 0.291000i | \(0.0939880\pi\) | ||||
−0.956723 | + | 0.291000i | \(0.906012\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −7.82699 | −0.300816 | −0.150408 | − | 0.988624i | \(-0.548059\pi\) | ||||
−0.150408 | + | 0.988624i | \(0.548059\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 21.9394i | − | 0.841959i | ||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 34.4763i | − | 1.31920i | −0.751617 | − | 0.659600i | \(-0.770726\pi\) | ||
0.751617 | − | 0.659600i | \(-0.229274\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −5.51514 | + | 0.855737i | −0.210723 | + | 0.0326960i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − | 6.15052i | − | 0.234316i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 36.7181i | 1.39682i | 0.715696 | + | 0.698412i | \(0.246109\pi\) | ||||
−0.715696 | + | 0.698412i | \(0.753891\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 2.56083 | + | 16.5043i | 0.0971379 | + | 0.626044i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 5.09083i | − | 0.192829i | ||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1.47779i | 0.0558154i | 0.999611 | + | 0.0279077i | \(0.00888445\pi\) | ||||
−0.999611 | + | 0.0279077i | \(0.991116\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −8.49954 | −0.320566 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 9.27737i | 0.348912i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 6.02936 | 0.226437 | 0.113219 | − | 0.993570i | \(-0.463884\pi\) | ||||
0.113219 | + | 0.993570i | \(0.463884\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 6.76066 | 0.253189 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −0.659401 | − | 4.24977i | −0.0246602 | − | 0.158932i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −13.3059 | −0.496227 | −0.248114 | − | 0.968731i | \(-0.579811\pi\) | ||||
−0.248114 | + | 0.968731i | \(0.579811\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 8.28853 | 0.308681 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 12.3526 | + | 38.8474i | 0.458765 | + | 1.44276i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −17.7384 | −0.657881 | −0.328941 | − | 0.944351i | \(-0.606692\pi\) | ||||
−0.328941 | + | 0.944351i | \(0.606692\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 7.69319 | 0.284543 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 29.6391i | − | 1.09475i | −0.836889 | − | 0.547373i | \(-0.815628\pi\) | ||
0.836889 | − | 0.547373i | \(-0.184372\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 25.5415 | 0.940832 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 19.2195i | 0.707001i | 0.935434 | + | 0.353500i | \(0.115009\pi\) | ||||
−0.935434 | + | 0.353500i | \(0.884991\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 21.8768i | − | 0.802584i | −0.915950 | − | 0.401292i | \(-0.868561\pi\) | ||
0.915950 | − | 0.401292i | \(-0.131439\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 3.29473 | + | 21.2342i | 0.120709 | + | 0.777960i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 19.7134i | 0.720310i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 14.5913i | 0.532444i | 0.963912 | + | 0.266222i | \(0.0857754\pi\) | ||||
−0.963912 | + | 0.266222i | \(0.914225\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −6.67502 | − | 43.0198i | −0.242929 | − | 1.56565i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 5.26067i | − | 0.191202i | −0.995420 | − | 0.0956011i | \(-0.969523\pi\) | ||
0.995420 | − | 0.0956011i | \(-0.0304773\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 22.6261i | 0.820196i | 0.912041 | + | 0.410098i | \(0.134506\pi\) | ||||
−0.912041 | + | 0.410098i | \(0.865494\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 7.84014 | 0.283832 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 4.61128i | 0.166504i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 0.150464 | 0.00542586 | 0.00271293 | − | 0.999996i | \(-0.499136\pi\) | ||||
0.00271293 | + | 0.999996i | \(0.499136\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −1.23760 | −0.0445133 | −0.0222567 | − | 0.999752i | \(-0.507085\pi\) | ||||
−0.0222567 | + | 0.999752i | \(0.507085\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 4.49954 | + | 14.1505i | 0.161628 | + | 0.508300i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −39.2006 | −1.40451 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 39.4381 | 1.41121 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 4.39850 | + | 28.3478i | 0.156989 | + | 1.01178i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −6.84106 | −0.243857 | −0.121929 | − | 0.992539i | \(-0.538908\pi\) | ||||
−0.121929 | + | 0.992539i | \(0.538908\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −14.9890 | −0.532949 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 6.71995i | − | 0.238633i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −32.9437 | −1.16693 | −0.583463 | − | 0.812140i | \(-0.698303\pi\) | ||||
−0.583463 | + | 0.812140i | \(0.698303\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 2.87981i | 0.101880i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − | 42.8212i | − | 1.51113i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 2.06055 | + | 13.2800i | 0.0726249 | + | 0.468060i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 53.6532i | 1.88635i | 0.332303 | + | 0.943173i | \(0.392174\pi\) | ||||
−0.332303 | + | 0.943173i | \(0.607826\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 19.5904i | − | 0.687911i | −0.938986 | − | 0.343955i | \(-0.888233\pi\) | ||
0.938986 | − | 0.343955i | \(-0.111767\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 47.0210 | − | 7.29585i | 1.64707 | − | 0.255562i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 59.2395i | − | 2.07253i | ||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 2.49596i | 0.0871095i | 0.999051 | + | 0.0435548i | \(0.0138683\pi\) | ||||
−0.999051 | + | 0.0435548i | \(0.986132\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 4.04117 | 0.140866 | 0.0704332 | − | 0.997516i | \(-0.477562\pi\) | ||||
0.0704332 | + | 0.997516i | \(0.477562\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 6.76066i | 0.235091i | 0.993067 | + | 0.117546i | \(0.0375026\pi\) | ||||
−0.993067 | + | 0.117546i | \(0.962497\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 29.5298 | 1.02561 | 0.512806 | − | 0.858504i | \(-0.328606\pi\) | ||||
0.512806 | + | 0.858504i | \(0.328606\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0.0207603 | 0.000719301 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 7.84014 | + | 50.5289i | 0.271319 | + | 1.74862i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 10.7344 | 0.370593 | 0.185296 | − | 0.982683i | \(-0.440675\pi\) | ||||
0.185296 | + | 0.982683i | \(0.440675\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −37.4683 | −1.29201 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −27.8200 | + | 4.31660i | −0.957038 | + | 0.148495i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −5.20012 | −0.178678 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 3.66463 | 0.125622 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 19.0109i | − | 0.650921i | −0.945556 | − | 0.325460i | \(-0.894481\pi\) | ||
0.945556 | − | 0.325460i | \(-0.105519\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −24.4584 | −0.835484 | −0.417742 | − | 0.908566i | \(-0.637178\pi\) | ||||
−0.417742 | + | 0.908566i | \(0.637178\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 23.4693i | 0.800761i | 0.916349 | + | 0.400381i | \(0.131122\pi\) | ||||
−0.916349 | + | 0.400381i | \(0.868878\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 11.5539i | 0.393299i | 0.980474 | + | 0.196650i | \(0.0630062\pi\) | ||||
−0.980474 | + | 0.196650i | \(0.936994\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −13.2342 | + | 2.05343i | −0.449975 | + | 0.0698189i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 34.4656i | − | 1.16917i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 5.43991i | 0.184324i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −26.4246 | + | 13.1514i | −0.893313 | + | 0.444598i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 7.38934i | 0.249520i | 0.992187 | + | 0.124760i | \(0.0398161\pi\) | ||||
−0.992187 | + | 0.124760i | \(0.960184\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 3.05321i | − | 0.102865i | −0.998676 | − | 0.0514326i | \(-0.983621\pi\) | ||
0.998676 | − | 0.0514326i | \(-0.0163787\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 21.2800 | 0.716131 | 0.358065 | − | 0.933697i | \(-0.383437\pi\) | ||||
0.358065 | + | 0.933697i | \(0.383437\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − | 31.9737i | − | 1.07357i | −0.843718 | − | 0.536786i | \(-0.819638\pi\) | ||
0.843718 | − | 0.536786i | \(-0.180362\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 50.5289 | 1.69468 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 22.1753 | 0.742067 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 5.85952 | − | 0.909172i | 0.195862 | − | 0.0303903i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −24.2116 | −0.807502 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −6.58945 | −0.219527 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 25.3428 | − | 3.93223i | 0.842423 | − | 0.130712i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −16.6594 | −0.553166 | −0.276583 | − | 0.960990i | \(-0.589202\pi\) | ||||
−0.276583 | + | 0.960990i | \(0.589202\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −23.3339 | −0.773086 | −0.386543 | − | 0.922271i | \(-0.626331\pi\) | ||||
−0.386543 | + | 0.922271i | \(0.626331\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 39.4381i | − | 1.30521i | ||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 30.5608 | 1.00921 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 21.0303i | − | 0.693725i | −0.937916 | − | 0.346862i | \(-0.887247\pi\) | ||
0.937916 | − | 0.346862i | \(-0.112753\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 8.39965i | 0.276478i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 2.43899 | + | 7.67030i | 0.0801935 | + | 0.252198i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − | 39.8536i | − | 1.30755i | −0.756687 | − | 0.653777i | \(-0.773184\pi\) | ||
0.756687 | − | 0.653777i | \(-0.226816\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − | 0.159859i | − | 0.00523917i | ||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −4.55305 | + | 0.706459i | −0.148901 | + | 0.0231037i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 42.5601i | 1.39038i | 0.718827 | + | 0.695189i | \(0.244679\pi\) | ||||
−0.718827 | + | 0.695189i | \(0.755321\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 2.05710i | − | 0.0670594i | −0.999438 | − | 0.0335297i | \(-0.989325\pi\) | ||
0.999438 | − | 0.0335297i | \(-0.0106748\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 16.9016 | 0.550392 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − | 26.4740i | − | 0.860290i | −0.902760 | − | 0.430145i | \(-0.858462\pi\) | ||
0.902760 | − | 0.430145i | \(-0.141538\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 9.12019 | 0.296054 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −42.9717 | −1.39199 | −0.695994 | − | 0.718047i | \(-0.745036\pi\) | ||||
−0.695994 | + | 0.718047i | \(0.745036\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 11.7190 | − | 1.81834i | 0.379219 | − | 0.0588402i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 6.58939 | 0.212782 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 22.1807 | 0.715508 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −3.44925 | − | 22.2301i | −0.111035 | − | 0.715611i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 11.7990 | 0.379429 | 0.189715 | − | 0.981839i | \(-0.439244\pi\) | ||||
0.189715 | + | 0.981839i | \(0.439244\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 3.23112 | 0.103691 | 0.0518457 | − | 0.998655i | \(-0.483490\pi\) | ||||
0.0518457 | + | 0.998655i | \(0.483490\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − | 19.7190i | − | 0.632163i | ||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −47.6210 | −1.52353 | −0.761766 | − | 0.647852i | \(-0.775667\pi\) | ||||
−0.761766 | + | 0.647852i | \(0.775667\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 30.8099i | − | 0.984688i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − | 13.4772i | − | 0.429856i | −0.976630 | − | 0.214928i | \(-0.931048\pi\) | ||
0.976630 | − | 0.214928i | \(-0.0689517\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −12.7952 | + | 1.98532i | −0.407688 | + | 0.0632576i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 25.5415i | 0.812172i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 47.0284i | 1.49391i | 0.664876 | + | 0.746954i | \(0.268484\pi\) | ||||
−0.664876 | + | 0.746954i | \(0.731516\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 8.25921 | + | 53.2297i | 0.261834 | + | 1.68750i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 31.2295i | 0.989047i | 0.869164 | + | 0.494524i | \(0.164657\pi\) | ||||
−0.869164 | + | 0.494524i | \(0.835343\pi\) | |||||||
\(998\) | 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 | 1440.2.o.a.1439.2 | yes | 12 | |
3.2 | odd | 2 | inner | 1440.2.o.a.1439.11 | yes | 12 | |
4.3 | odd | 2 | 1440.2.o.b.1439.2 | yes | 12 | ||
5.2 | odd | 4 | 7200.2.h.m.1151.9 | 12 | |||
5.3 | odd | 4 | 7200.2.h.l.1151.3 | 12 | |||
5.4 | even | 2 | 1440.2.o.b.1439.12 | yes | 12 | ||
8.3 | odd | 2 | 2880.2.o.e.2879.11 | 12 | |||
8.5 | even | 2 | 2880.2.o.f.2879.11 | 12 | |||
12.11 | even | 2 | 1440.2.o.b.1439.11 | yes | 12 | ||
15.2 | even | 4 | 7200.2.h.m.1151.10 | 12 | |||
15.8 | even | 4 | 7200.2.h.l.1151.4 | 12 | |||
15.14 | odd | 2 | 1440.2.o.b.1439.1 | yes | 12 | ||
20.3 | even | 4 | 7200.2.h.l.1151.10 | 12 | |||
20.7 | even | 4 | 7200.2.h.m.1151.4 | 12 | |||
20.19 | odd | 2 | inner | 1440.2.o.a.1439.12 | yes | 12 | |
24.5 | odd | 2 | 2880.2.o.f.2879.2 | 12 | |||
24.11 | even | 2 | 2880.2.o.e.2879.2 | 12 | |||
40.19 | odd | 2 | 2880.2.o.f.2879.1 | 12 | |||
40.29 | even | 2 | 2880.2.o.e.2879.1 | 12 | |||
60.23 | odd | 4 | 7200.2.h.l.1151.9 | 12 | |||
60.47 | odd | 4 | 7200.2.h.m.1151.3 | 12 | |||
60.59 | even | 2 | inner | 1440.2.o.a.1439.1 | ✓ | 12 | |
120.29 | odd | 2 | 2880.2.o.e.2879.12 | 12 | |||
120.59 | even | 2 | 2880.2.o.f.2879.12 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1440.2.o.a.1439.1 | ✓ | 12 | 60.59 | even | 2 | inner | |
1440.2.o.a.1439.2 | yes | 12 | 1.1 | even | 1 | trivial | |
1440.2.o.a.1439.11 | yes | 12 | 3.2 | odd | 2 | inner | |
1440.2.o.a.1439.12 | yes | 12 | 20.19 | odd | 2 | inner | |
1440.2.o.b.1439.1 | yes | 12 | 15.14 | odd | 2 | ||
1440.2.o.b.1439.2 | yes | 12 | 4.3 | odd | 2 | ||
1440.2.o.b.1439.11 | yes | 12 | 12.11 | even | 2 | ||
1440.2.o.b.1439.12 | yes | 12 | 5.4 | even | 2 | ||
2880.2.o.e.2879.1 | 12 | 40.29 | even | 2 | |||
2880.2.o.e.2879.2 | 12 | 24.11 | even | 2 | |||
2880.2.o.e.2879.11 | 12 | 8.3 | odd | 2 | |||
2880.2.o.e.2879.12 | 12 | 120.29 | odd | 2 | |||
2880.2.o.f.2879.1 | 12 | 40.19 | odd | 2 | |||
2880.2.o.f.2879.2 | 12 | 24.5 | odd | 2 | |||
2880.2.o.f.2879.11 | 12 | 8.5 | even | 2 | |||
2880.2.o.f.2879.12 | 12 | 120.59 | even | 2 | |||
7200.2.h.l.1151.3 | 12 | 5.3 | odd | 4 | |||
7200.2.h.l.1151.4 | 12 | 15.8 | even | 4 | |||
7200.2.h.l.1151.9 | 12 | 60.23 | odd | 4 | |||
7200.2.h.l.1151.10 | 12 | 20.3 | even | 4 | |||
7200.2.h.m.1151.3 | 12 | 60.47 | odd | 4 | |||
7200.2.h.m.1151.4 | 12 | 20.7 | even | 4 | |||
7200.2.h.m.1151.9 | 12 | 5.2 | odd | 4 | |||
7200.2.h.m.1151.10 | 12 | 15.2 | even | 4 |