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 | 1439.10 | ||
Root | \(1.19252 - 0.760198i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1440.1439 |
Dual form | 1440.2.o.b.1439.9 |
$q$-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 | ||||||||
\(5\) | 1.24561 | + | 1.85700i | 0.557053 | + | 0.830477i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.864641 | −0.326804 | −0.163402 | − | 0.986560i | \(-0.552247\pi\) | ||||
−0.163402 | + | 0.986560i | \(0.552247\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −3.90543 | −1.17753 | −0.588766 | − | 0.808304i | \(-0.700386\pi\) | ||||
−0.588766 | + | 0.808304i | \(0.700386\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 1.13536i | − | 0.314892i | −0.987528 | − | 0.157446i | \(-0.949674\pi\) | ||
0.987528 | − | 0.157446i | \(-0.0503260\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 3.71400 | 0.900779 | 0.450389 | − | 0.892832i | \(-0.351285\pi\) | ||||
0.450389 | + | 0.892832i | \(0.351285\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.72928i | 0.396724i | 0.980129 | + | 0.198362i | \(0.0635622\pi\) | ||||
−0.980129 | + | 0.198362i | \(0.936438\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 9.03365i | 1.88365i | 0.336109 | + | 0.941823i | \(0.390889\pi\) | ||||
−0.336109 | + | 0.941823i | \(0.609111\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.89692 | + | 4.62620i | −0.379383 | + | 0.925240i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.26843i | 0.235542i | 0.993041 | + | 0.117771i | \(0.0375748\pi\) | ||||
−0.993041 | + | 0.117771i | \(0.962425\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 3.25240i | − | 0.584148i | −0.956396 | − | 0.292074i | \(-0.905655\pi\) | ||
0.956396 | − | 0.292074i | \(-0.0943453\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −1.07700 | − | 1.60564i | −0.182047 | − | 0.271403i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 6.38776i | 1.05014i | 0.851059 | + | 0.525070i | \(0.175961\pi\) | ||||
−0.851059 | + | 0.525070i | \(0.824039\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 6.39665i | 0.998989i | 0.866317 | + | 0.499494i | \(0.166481\pi\) | ||||
−0.866317 | + | 0.499494i | \(0.833519\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −4.77551 | −0.728259 | −0.364129 | − | 0.931348i | \(-0.618633\pi\) | ||||
−0.364129 | + | 0.931348i | \(0.618633\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 4.59958i | 0.670918i | 0.942055 | + | 0.335459i | \(0.108891\pi\) | ||||
−0.942055 | + | 0.335459i | \(0.891109\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.25240 | −0.893199 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 8.98801 | 1.23460 | 0.617299 | − | 0.786729i | \(-0.288227\pi\) | ||||
0.617299 | + | 0.786729i | \(0.288227\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −4.86464 | − | 7.25240i | −0.655948 | − | 0.977913i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −8.50501 | −1.10726 | −0.553629 | − | 0.832763i | \(-0.686758\pi\) | ||||
−0.553629 | + | 0.832763i | \(0.686758\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −9.04623 | −1.15825 | −0.579125 | − | 0.815238i | \(-0.696606\pi\) | ||||
−0.579125 | + | 0.815238i | \(0.696606\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 2.10836 | − | 1.41421i | 0.261510 | − | 0.175412i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −11.0462 | −1.34951 | −0.674756 | − | 0.738041i | \(-0.735751\pi\) | ||||
−0.674756 | + | 0.738041i | \(0.735751\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 8.10243 | 0.961581 | 0.480791 | − | 0.876835i | \(-0.340350\pi\) | ||||
0.480791 | + | 0.876835i | \(0.340350\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 4.47689i | − | 0.523980i | −0.965071 | − | 0.261990i | \(-0.915621\pi\) | ||
0.965071 | − | 0.261990i | \(-0.0843787\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 3.37680 | 0.384822 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 14.2986i | − | 1.60872i | −0.594142 | − | 0.804360i | \(-0.702508\pi\) | ||
0.594142 | − | 0.804360i | \(-0.297492\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 8.10243i | 0.889357i | 0.895690 | + | 0.444679i | \(0.146682\pi\) | ||||
−0.895690 | + | 0.444679i | \(0.853318\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 4.62620 | + | 6.89692i | 0.501782 | + | 0.748076i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 3.56822i | 0.378231i | 0.981955 | + | 0.189115i | \(0.0605620\pi\) | ||||
−0.981955 | + | 0.189115i | \(0.939438\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.981678i | 0.102908i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −3.21128 | + | 2.15401i | −0.329470 | + | 0.220997i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 10.9817i | 1.11502i | 0.830170 | + | 0.557510i | \(0.188243\pi\) | ||||
−0.830170 | + | 0.557510i | \(0.811757\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 0.885578i | 0.0881183i | 0.999029 | + | 0.0440591i | \(0.0140290\pi\) | ||||
−0.999029 | + | 0.0440591i | \(0.985971\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 18.1816 | 1.79149 | 0.895743 | − | 0.444573i | \(-0.146645\pi\) | ||||
0.895743 | + | 0.444573i | \(0.146645\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 2.44557i | 0.236423i | 0.992988 | + | 0.118211i | \(0.0377160\pi\) | ||||
−0.992988 | + | 0.118211i | \(0.962284\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −3.25240 | −0.311523 | −0.155762 | − | 0.987795i | \(-0.549783\pi\) | ||||
−0.155762 | + | 0.987795i | \(0.549783\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 17.5646 | 1.65234 | 0.826168 | − | 0.563424i | \(-0.190516\pi\) | ||||
0.826168 | + | 0.563424i | \(0.190516\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −16.7755 | + | 11.2524i | −1.56432 | + | 1.04929i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −3.21128 | −0.294378 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 4.25240 | 0.386581 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −10.9537 | + | 2.23986i | −0.979727 | + | 0.200339i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 2.18159 | 0.193585 | 0.0967923 | − | 0.995305i | \(-0.469142\pi\) | ||||
0.0967923 | + | 0.995305i | \(0.469142\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −22.2643 | −1.94524 | −0.972620 | − | 0.232400i | \(-0.925342\pi\) | ||||
−0.972620 | + | 0.232400i | \(0.925342\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − | 1.49521i | − | 0.129651i | ||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −6.92529 | −0.591667 | −0.295834 | − | 0.955240i | \(-0.595597\pi\) | ||||
−0.295834 | + | 0.955240i | \(0.595597\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 18.2986i | 1.55207i | 0.630690 | + | 0.776035i | \(0.282772\pi\) | ||||
−0.630690 | + | 0.776035i | \(0.717228\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 4.43407i | 0.370795i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −2.35548 | + | 1.57997i | −0.195612 | + | 0.131209i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 8.98801i | 0.736326i | 0.929761 | + | 0.368163i | \(0.120013\pi\) | ||||
−0.929761 | + | 0.368163i | \(0.879987\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 6.29862i | − | 0.512575i | −0.966601 | − | 0.256287i | \(-0.917501\pi\) | ||
0.966601 | − | 0.256287i | \(-0.0824994\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 6.03971 | − | 4.05121i | 0.485121 | − | 0.325401i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 11.1633i | − | 0.890926i | −0.895300 | − | 0.445463i | \(-0.853039\pi\) | ||
0.895300 | − | 0.445463i | \(-0.146961\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 7.81086i | − | 0.615582i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 17.7293 | 1.38866 | 0.694332 | − | 0.719655i | \(-0.255700\pi\) | ||||
0.694332 | + | 0.719655i | \(0.255700\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 1.51435i | − | 0.117184i | −0.998282 | − | 0.0585920i | \(-0.981339\pi\) | ||
0.998282 | − | 0.0585920i | \(-0.0186611\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 11.7110 | 0.900843 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 15.4106 | 1.17164 | 0.585822 | − | 0.810440i | \(-0.300772\pi\) | ||||
0.585822 | + | 0.810440i | \(0.300772\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1.64015 | − | 4.00000i | 0.123984 | − | 0.302372i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 9.56229 | 0.714719 | 0.357359 | − | 0.933967i | \(-0.383677\pi\) | ||||
0.357359 | + | 0.933967i | \(0.383677\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 14.2986 | 1.06281 | 0.531404 | − | 0.847118i | \(-0.321665\pi\) | ||||
0.531404 | + | 0.847118i | \(0.321665\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −11.8621 | + | 7.95665i | −0.872117 | + | 0.584984i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −14.5048 | −1.06070 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 19.1246 | 1.38381 | 0.691903 | − | 0.721991i | \(-0.256773\pi\) | ||||
0.691903 | + | 0.721991i | \(0.256773\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − | 22.5048i | − | 1.61993i | −0.586478 | − | 0.809965i | \(-0.699486\pi\) | ||
0.586478 | − | 0.809965i | \(-0.300514\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −9.91923 | −0.706716 | −0.353358 | − | 0.935488i | \(-0.614960\pi\) | ||||
−0.353358 | + | 0.935488i | \(0.614960\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 3.66473i | − | 0.259786i | −0.991528 | − | 0.129893i | \(-0.958537\pi\) | ||
0.991528 | − | 0.129893i | \(-0.0414634\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − | 1.09674i | − | 0.0769759i | ||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −11.8786 | + | 7.96772i | −0.829637 | + | 0.556490i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 6.75359i | − | 0.467156i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2.29862i | 0.158244i | 0.996865 | + | 0.0791219i | \(0.0252116\pi\) | ||||
−0.996865 | + | 0.0791219i | \(0.974788\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −5.94842 | − | 8.86813i | −0.405679 | − | 0.604802i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 2.81215i | 0.190901i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 4.21673i | − | 0.283648i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 15.1354 | 1.01354 | 0.506769 | − | 0.862082i | \(-0.330840\pi\) | ||||
0.506769 | + | 0.862082i | \(0.330840\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − | 26.1697i | − | 1.73695i | −0.495737 | − | 0.868473i | \(-0.665102\pi\) | ||
0.495737 | − | 0.868473i | \(-0.334898\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 9.75719 | 0.644773 | 0.322387 | − | 0.946608i | \(-0.395515\pi\) | ||||
0.322387 | + | 0.946608i | \(0.395515\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −8.02202 | −0.525540 | −0.262770 | − | 0.964858i | \(-0.584636\pi\) | ||||
−0.262770 | + | 0.964858i | \(0.584636\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −8.54144 | + | 5.72928i | −0.557182 | + | 0.373737i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 17.0100 | 1.10029 | 0.550144 | − | 0.835070i | \(-0.314573\pi\) | ||||
0.550144 | + | 0.835070i | \(0.314573\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −21.0096 | −1.35335 | −0.676673 | − | 0.736284i | \(-0.736579\pi\) | ||||
−0.676673 | + | 0.736284i | \(0.736579\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −7.78804 | − | 11.6107i | −0.497560 | − | 0.741781i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1.96336 | 0.124925 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −8.46555 | −0.534341 | −0.267170 | − | 0.963649i | \(-0.586089\pi\) | ||||
−0.267170 | + | 0.963649i | \(0.586089\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 35.2803i | − | 2.21805i | ||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −11.8164 | −0.737089 | −0.368544 | − | 0.929610i | \(-0.620144\pi\) | ||||
−0.368544 | + | 0.929610i | \(0.620144\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 5.52311i | − | 0.343190i | ||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 7.93691i | 0.489411i | 0.969597 | + | 0.244705i | \(0.0786913\pi\) | ||||
−0.969597 | + | 0.244705i | \(0.921309\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 11.1955 | + | 16.6907i | 0.687737 | + | 1.02530i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − | 29.9750i | − | 1.82761i | −0.406154 | − | 0.913805i | \(-0.633130\pi\) | ||
0.406154 | − | 0.913805i | \(-0.366870\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 26.8401i | 1.63042i | 0.579167 | + | 0.815209i | \(0.303378\pi\) | ||||
−0.579167 | + | 0.815209i | \(0.696622\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 7.40828 | − | 18.0673i | 0.446736 | − | 1.08950i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 24.9571i | 1.49953i | 0.661706 | + | 0.749763i | \(0.269833\pi\) | ||||
−0.661706 | + | 0.749763i | \(0.730167\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 1.12265i | − | 0.0669716i | −0.999439 | − | 0.0334858i | \(-0.989339\pi\) | ||
0.999439 | − | 0.0334858i | \(-0.0106609\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 25.9634 | 1.54336 | 0.771681 | − | 0.636010i | \(-0.219416\pi\) | ||||
0.771681 | + | 0.636010i | \(0.219416\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − | 5.53080i | − | 0.326473i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −3.20617 | −0.188598 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −16.6728 | −0.974037 | −0.487018 | − | 0.873392i | \(-0.661915\pi\) | ||||
−0.487018 | + | 0.873392i | \(0.661915\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −10.5939 | − | 15.7938i | −0.616802 | − | 0.919552i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 10.2564 | 0.593145 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 4.12910 | 0.237997 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −11.2681 | − | 16.7989i | −0.645207 | − | 0.961900i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 21.0096 | 1.19908 | 0.599540 | − | 0.800345i | \(-0.295350\pi\) | ||||
0.599540 | + | 0.800345i | \(0.295350\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 34.7463 | 1.97028 | 0.985141 | − | 0.171748i | \(-0.0549415\pi\) | ||||
0.985141 | + | 0.171748i | \(0.0549415\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 9.49521i | − | 0.536701i | −0.963321 | − | 0.268350i | \(-0.913521\pi\) | ||
0.963321 | − | 0.268350i | \(-0.0864785\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −16.2505 | −0.912719 | −0.456360 | − | 0.889795i | \(-0.650847\pi\) | ||||
−0.456360 | + | 0.889795i | \(0.650847\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 4.95377i | − | 0.277358i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 6.42256i | 0.357361i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 5.25240 | + | 2.15368i | 0.291351 | + | 0.119465i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − | 3.97699i | − | 0.219258i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 20.7755i | − | 1.14193i | −0.820976 | − | 0.570963i | \(-0.806570\pi\) | ||
0.820976 | − | 0.570963i | \(-0.193430\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −13.7593 | − | 20.5129i | −0.751750 | − | 1.12074i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 28.1204i | − | 1.53181i | −0.642951 | − | 0.765907i | \(-0.722290\pi\) | ||
0.642951 | − | 0.765907i | \(-0.277710\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 12.7020i | 0.687852i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 11.4586 | 0.618704 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − | 18.8330i | − | 1.01101i | −0.862824 | − | 0.505504i | \(-0.831306\pi\) | ||
0.862824 | − | 0.505504i | \(-0.168694\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −11.5510 | −0.618312 | −0.309156 | − | 0.951011i | \(-0.600047\pi\) | ||||
−0.309156 | + | 0.951011i | \(0.600047\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 2.61727 | 0.139303 | 0.0696515 | − | 0.997571i | \(-0.477811\pi\) | ||||
0.0696515 | + | 0.997571i | \(0.477811\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 10.0925 | + | 15.0462i | 0.535652 | + | 0.798571i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −20.8044 | −1.09802 | −0.549008 | − | 0.835817i | \(-0.684994\pi\) | ||||
−0.549008 | + | 0.835817i | \(0.684994\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 16.0096 | 0.842610 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 8.31359 | − | 5.57645i | 0.435153 | − | 0.291885i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −15.3694 | −0.802278 | −0.401139 | − | 0.916017i | \(-0.631386\pi\) | ||||
−0.401139 | + | 0.916017i | \(0.631386\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −7.77140 | −0.403471 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 29.3049i | − | 1.51735i | −0.651470 | − | 0.758675i | \(-0.725847\pi\) | ||
0.651470 | − | 0.758675i | \(-0.274153\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 1.44012 | 0.0741702 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 11.7938i | 0.605808i | 0.953021 | + | 0.302904i | \(0.0979562\pi\) | ||||
−0.953021 | + | 0.302904i | \(0.902044\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 16.6790i | 0.852257i | 0.904663 | + | 0.426128i | \(0.140123\pi\) | ||||
−0.904663 | + | 0.426128i | \(0.859877\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 4.20617 | + | 6.27072i | 0.214366 | + | 0.319585i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 23.2214i | 1.17737i | 0.808361 | + | 0.588687i | \(0.200355\pi\) | ||||
−0.808361 | + | 0.588687i | \(0.799645\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 33.5510i | 1.69675i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 26.5526 | − | 17.8105i | 1.33601 | − | 0.896143i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 2.02458i | 0.101611i | 0.998709 | + | 0.0508054i | \(0.0161788\pi\) | ||||
−0.998709 | + | 0.0508054i | \(0.983821\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 28.9722i | − | 1.44680i | −0.690427 | − | 0.723402i | \(-0.742577\pi\) | ||
0.690427 | − | 0.723402i | \(-0.257423\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −3.69264 | −0.183943 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 24.9469i | − | 1.23657i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 25.8863 | 1.27999 | 0.639997 | − | 0.768377i | \(-0.278935\pi\) | ||||
0.639997 | + | 0.768377i | \(0.278935\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 7.35378 | 0.361856 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −15.0462 | + | 10.0925i | −0.738590 | + | 0.495419i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 12.7736 | 0.624030 | 0.312015 | − | 0.950077i | \(-0.398996\pi\) | ||||
0.312015 | + | 0.950077i | \(0.398996\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 18.1695 | 0.885528 | 0.442764 | − | 0.896638i | \(-0.353998\pi\) | ||||
0.442764 | + | 0.896638i | \(0.353998\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −7.04516 | + | 17.1817i | −0.341740 | + | 0.833436i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 7.82174 | 0.378520 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 2.40611 | 0.115898 | 0.0579491 | − | 0.998320i | \(-0.481544\pi\) | ||||
0.0579491 | + | 0.998320i | \(0.481544\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 31.4094i | − | 1.50944i | −0.656047 | − | 0.754720i | \(-0.727773\pi\) | ||
0.656047 | − | 0.754720i | \(-0.272227\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −15.6217 | −0.747289 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 18.1695i | 0.867184i | 0.901109 | + | 0.433592i | \(0.142754\pi\) | ||||
−0.901109 | + | 0.433592i | \(0.857246\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 18.8330i | 0.894783i | 0.894338 | + | 0.447392i | \(0.147647\pi\) | ||||
−0.894338 | + | 0.447392i | \(0.852353\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −6.62620 | + | 4.44461i | −0.314112 | + | 0.210695i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 20.9216i | 0.987353i | 0.869646 | + | 0.493677i | \(0.164347\pi\) | ||||
−0.869646 | + | 0.493677i | \(0.835653\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 24.9817i | − | 1.17634i | ||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −1.82298 | + | 1.22279i | −0.0854625 | + | 0.0573251i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 35.5789i | 1.66431i | 0.554542 | + | 0.832156i | \(0.312894\pi\) | ||||
−0.554542 | + | 0.832156i | \(0.687106\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 14.0617i | − | 0.654920i | −0.944865 | − | 0.327460i | \(-0.893807\pi\) | ||
0.944865 | − | 0.327460i | \(-0.106193\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 33.0987 | 1.53823 | 0.769114 | − | 0.639112i | \(-0.220698\pi\) | ||||
0.769114 | + | 0.639112i | \(0.220698\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 32.0092i | 1.48121i | 0.671942 | + | 0.740604i | \(0.265460\pi\) | ||||
−0.671942 | + | 0.740604i | \(0.734540\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 9.55102 | 0.441025 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 18.6504 | 0.857548 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −8.00000 | − | 3.28030i | −0.367065 | − | 0.150511i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −28.6153 | −1.30747 | −0.653733 | − | 0.756725i | \(-0.726798\pi\) | ||||
−0.653733 | + | 0.756725i | \(0.726798\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 7.25240 | 0.330681 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −20.3930 | + | 13.6789i | −0.925999 | + | 0.621126i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −2.18159 | −0.0988572 | −0.0494286 | − | 0.998778i | \(-0.515740\pi\) | ||||
−0.0494286 | + | 0.998778i | \(0.515740\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −28.2127 | −1.27322 | −0.636611 | − | 0.771185i | \(-0.719664\pi\) | ||||
−0.636611 | + | 0.771185i | \(0.719664\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 4.71096i | 0.212171i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −7.00569 | −0.314248 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 0.234074i | − | 0.0104786i | −0.999986 | − | 0.00523930i | \(-0.998332\pi\) | ||
0.999986 | − | 0.00523930i | \(-0.00166773\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 15.3302i | − | 0.683538i | −0.939784 | − | 0.341769i | \(-0.888974\pi\) | ||
0.939784 | − | 0.341769i | \(-0.111026\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −1.64452 | + | 1.10308i | −0.0731802 | + | 0.0490866i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − | 22.7473i | − | 1.00826i | −0.863629 | − | 0.504128i | \(-0.831814\pi\) | ||
0.863629 | − | 0.504128i | \(-0.168186\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 3.87090i | 0.171238i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 22.6471 | + | 33.7633i | 0.997953 | + | 1.48779i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 17.9634i | − | 0.790027i | ||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 23.9898i | 1.05101i | 0.850790 | + | 0.525506i | \(0.176124\pi\) | ||||
−0.850790 | + | 0.525506i | \(0.823876\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 28.3632 | 1.24024 | 0.620118 | − | 0.784509i | \(-0.287085\pi\) | ||||
0.620118 | + | 0.784509i | \(0.287085\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 12.0794i | − | 0.526188i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −58.6068 | −2.54812 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 7.26249 | 0.314574 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −4.54144 | + | 3.04623i | −0.196343 | + | 0.131700i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 24.4183 | 1.05177 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −36.8034 | −1.58230 | −0.791151 | − | 0.611621i | \(-0.790518\pi\) | ||||
−0.791151 | + | 0.611621i | \(0.790518\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −4.05121 | − | 6.03971i | −0.173535 | − | 0.258713i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −24.2341 | −1.03617 | −0.518087 | − | 0.855328i | \(-0.673356\pi\) | ||||
−0.518087 | + | 0.855328i | \(0.673356\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −2.19347 | −0.0934452 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 12.3632i | 0.525736i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 43.3515 | 1.83686 | 0.918430 | − | 0.395584i | \(-0.129458\pi\) | ||||
0.918430 | + | 0.395584i | \(0.129458\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 5.42192i | 0.229323i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − | 2.62815i | − | 0.110763i | −0.998465 | − | 0.0553817i | \(-0.982362\pi\) | ||
0.998465 | − | 0.0553817i | \(-0.0176376\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 21.8786 | + | 32.6175i | 0.920439 | + | 1.37223i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 23.6588i | − | 0.991828i | −0.868372 | − | 0.495914i | \(-0.834833\pi\) | ||
0.868372 | − | 0.495914i | \(-0.165167\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 35.6926i | − | 1.49369i | −0.664998 | − | 0.746845i | \(-0.731568\pi\) | ||
0.664998 | − | 0.746845i | \(-0.268432\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −41.7915 | − | 17.1361i | −1.74282 | − | 0.714624i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 0.646409i | − | 0.0269104i | −0.999909 | − | 0.0134552i | \(-0.995717\pi\) | ||
0.999909 | − | 0.0134552i | \(-0.00428304\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − | 7.00569i | − | 0.290645i | ||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −35.1020 | −1.45378 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 22.3753i | 0.923528i | 0.887003 | + | 0.461764i | \(0.152783\pi\) | ||||
−0.887003 | + | 0.461764i | \(0.847217\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 5.62431 | 0.231746 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 20.4325 | 0.839061 | 0.419530 | − | 0.907741i | \(-0.362195\pi\) | ||||
0.419530 | + | 0.907741i | \(0.362195\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −4.00000 | − | 5.96336i | −0.163984 | − | 0.244474i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −6.13100 | −0.250506 | −0.125253 | − | 0.992125i | \(-0.539974\pi\) | ||||
−0.125253 | + | 0.992125i | \(0.539974\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −1.79383 | −0.0731720 | −0.0365860 | − | 0.999331i | \(-0.511648\pi\) | ||||
−0.0365860 | + | 0.999331i | \(0.511648\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 5.29682 | + | 7.89671i | 0.215346 | + | 0.321047i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −16.6864 | −0.677279 | −0.338640 | − | 0.940916i | \(-0.609967\pi\) | ||||
−0.338640 | + | 0.940916i | \(0.609967\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 5.22218 | 0.211267 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 23.5264i | 0.950224i | 0.879925 | + | 0.475112i | \(0.157592\pi\) | ||||
−0.879925 | + | 0.475112i | \(0.842408\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −23.3127 | −0.938535 | −0.469267 | − | 0.883056i | \(-0.655482\pi\) | ||||
−0.469267 | + | 0.883056i | \(0.655482\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 32.3911i | − | 1.30191i | −0.759117 | − | 0.650954i | \(-0.774369\pi\) | ||
0.759117 | − | 0.650954i | \(-0.225631\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − | 3.08523i | − | 0.123607i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −17.8034 | − | 17.5510i | −0.712137 | − | 0.702041i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 23.7242i | 0.945944i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 19.2524i | 0.766426i | 0.923660 | + | 0.383213i | \(0.125182\pi\) | ||||
−0.923660 | + | 0.383213i | \(0.874818\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 2.71741 | + | 4.05121i | 0.107837 | + | 0.160768i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 7.09871i | 0.281261i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 25.9435i | 1.02471i | 0.858774 | + | 0.512354i | \(0.171226\pi\) | ||||
−0.858774 | + | 0.512354i | \(0.828774\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 11.2803 | 0.444852 | 0.222426 | − | 0.974950i | \(-0.428602\pi\) | ||||
0.222426 | + | 0.974950i | \(0.428602\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 11.6053i | 0.456250i | 0.973632 | + | 0.228125i | \(0.0732595\pi\) | ||||
−0.973632 | + | 0.228125i | \(0.926740\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 33.2158 | 1.30383 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 35.4145 | 1.38588 | 0.692939 | − | 0.720996i | \(-0.256316\pi\) | ||||
0.692939 | + | 0.720996i | \(0.256316\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −27.7326 | − | 41.3449i | −1.08360 | − | 1.61548i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 12.0079 | 0.467760 | 0.233880 | − | 0.972265i | \(-0.424858\pi\) | ||||
0.233880 | + | 0.972265i | \(0.424858\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −3.08287 | −0.119910 | −0.0599549 | − | 0.998201i | \(-0.519096\pi\) | ||||
−0.0599549 | + | 0.998201i | \(0.519096\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 2.77660 | − | 1.86244i | 0.107672 | − | 0.0722225i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −11.4586 | −0.443677 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 35.3294 | 1.36388 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 25.7851i | 0.993942i | 0.867767 | + | 0.496971i | \(0.165555\pi\) | ||||
−0.867767 | + | 0.496971i | \(0.834445\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −2.16019 | −0.0830227 | −0.0415114 | − | 0.999138i | \(-0.513217\pi\) | ||||
−0.0415114 | + | 0.999138i | \(0.513217\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 9.49521i | − | 0.364393i | ||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 28.3632i | 1.08529i | 0.839963 | + | 0.542644i | \(0.182577\pi\) | ||||
−0.839963 | + | 0.542644i | \(0.817423\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −8.62620 | − | 12.8603i | −0.329590 | − | 0.491366i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − | 10.2046i | − | 0.388765i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 37.9142i | − | 1.44232i | −0.692766 | − | 0.721162i | \(-0.743608\pi\) | ||
0.692766 | − | 0.721162i | \(-0.256392\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −33.9806 | + | 22.7929i | −1.28896 | + | 0.864585i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 23.7572i | 0.899868i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 12.9650i | 0.489681i | 0.969563 | + | 0.244841i | \(0.0787356\pi\) | ||||
−0.969563 | + | 0.244841i | \(0.921264\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −11.0462 | −0.416616 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − | 0.765707i | − | 0.0287974i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −26.8401 | −1.00800 | −0.504000 | − | 0.863704i | \(-0.668139\pi\) | ||||
−0.504000 | + | 0.863704i | \(0.668139\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 29.3810 | 1.10033 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −8.23407 | + | 5.52311i | −0.307937 | + | 0.206553i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −40.7342 | −1.51913 | −0.759564 | − | 0.650432i | \(-0.774588\pi\) | ||||
−0.759564 | + | 0.650432i | \(0.774588\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −15.7205 | −0.585464 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −5.86801 | − | 2.40611i | −0.217933 | − | 0.0893606i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −24.9205 | −0.924248 | −0.462124 | − | 0.886815i | \(-0.652913\pi\) | ||||
−0.462124 | + | 0.886815i | \(0.652913\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −17.7363 | −0.656000 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 11.2278i | − | 0.414709i | −0.978266 | − | 0.207354i | \(-0.933515\pi\) | ||
0.978266 | − | 0.207354i | \(-0.0664853\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 43.1403 | 1.58909 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 3.22449i | 0.118615i | 0.998240 | + | 0.0593074i | \(0.0188892\pi\) | ||||
−0.998240 | + | 0.0593074i | \(0.981111\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 14.5645i | 0.534318i | 0.963652 | + | 0.267159i | \(0.0860849\pi\) | ||||
−0.963652 | + | 0.267159i | \(0.913915\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −16.6907 | + | 11.1955i | −0.611502 | + | 0.410173i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − | 2.11454i | − | 0.0772637i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 52.8034i | 1.92682i | 0.268025 | + | 0.963412i | \(0.413629\pi\) | ||||
−0.268025 | + | 0.963412i | \(0.586371\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 11.6966 | − | 7.84562i | 0.425681 | − | 0.285531i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 8.82800i | 0.320859i | 0.987047 | + | 0.160429i | \(0.0512879\pi\) | ||||
−0.987047 | + | 0.160429i | \(0.948712\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 32.6577i | 1.18384i | 0.805997 | + | 0.591920i | \(0.201630\pi\) | ||||
−0.805997 | + | 0.591920i | \(0.798370\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 2.81215 | 0.101807 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 9.65625i | 0.348667i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −7.83048 | −0.282374 | −0.141187 | − | 0.989983i | \(-0.545092\pi\) | ||||
−0.141187 | + | 0.989983i | \(0.545092\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −8.14807 | −0.293066 | −0.146533 | − | 0.989206i | \(-0.546811\pi\) | ||||
−0.146533 | + | 0.989206i | \(0.546811\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 15.0462 | + | 6.16952i | 0.540476 | + | 0.221616i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −11.0616 | −0.396323 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −31.6435 | −1.13229 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 20.7302 | − | 13.9051i | 0.739893 | − | 0.496293i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 35.2803 | 1.25761 | 0.628803 | − | 0.777564i | \(-0.283545\pi\) | ||||
0.628803 | + | 0.777564i | \(0.283545\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −15.1871 | −0.539989 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 10.2707i | 0.364724i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −4.67999 | −0.165774 | −0.0828868 | − | 0.996559i | \(-0.526414\pi\) | ||||
−0.0828868 | + | 0.996559i | \(0.526414\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 17.0829i | 0.604349i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 17.4842i | 0.617003i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 14.5048 | − | 9.72928i | 0.511227 | − | 0.342912i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 19.2294i | 0.676070i | 0.941133 | + | 0.338035i | \(0.109762\pi\) | ||||
−0.941133 | + | 0.338035i | \(0.890238\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 18.7110i | − | 0.657031i | −0.944499 | − | 0.328515i | \(-0.893452\pi\) | ||
0.944499 | − | 0.328515i | \(-0.106548\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 22.0838 | + | 32.9233i | 0.773560 | + | 1.15325i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 8.25820i | − | 0.288918i | ||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 6.92529i | 0.241694i | 0.992671 | + | 0.120847i | \(0.0385611\pi\) | ||||
−0.992671 | + | 0.120847i | \(0.961439\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −23.6035 | −0.822767 | −0.411383 | − | 0.911462i | \(-0.634954\pi\) | ||||
−0.411383 | + | 0.911462i | \(0.634954\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 29.3810i | 1.02168i | 0.859676 | + | 0.510839i | \(0.170665\pi\) | ||||
−0.859676 | + | 0.510839i | \(0.829335\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 16.2062 | 0.562863 | 0.281432 | − | 0.959581i | \(-0.409191\pi\) | ||||
0.281432 | + | 0.959581i | \(0.409191\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −23.2214 | −0.804575 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 2.81215 | − | 1.88629i | 0.0973186 | − | 0.0652778i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −9.49073 | −0.327656 | −0.163828 | − | 0.986489i | \(-0.552384\pi\) | ||||
−0.163828 | + | 0.986489i | \(0.552384\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 27.3911 | 0.944520 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 14.5873 | + | 21.7473i | 0.501818 | + | 0.748129i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −3.67680 | −0.126336 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −57.7047 | −1.97809 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 32.3511i | 1.10768i | 0.832623 | + | 0.553840i | \(0.186838\pi\) | ||||
−0.832623 | + | 0.553840i | \(0.813162\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 3.80529 | 0.129986 | 0.0649932 | − | 0.997886i | \(-0.479297\pi\) | ||||
0.0649932 | + | 0.997886i | \(0.479297\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 2.29862i | − | 0.0784281i | −0.999231 | − | 0.0392140i | \(-0.987515\pi\) | ||
0.999231 | − | 0.0392140i | \(-0.0124854\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 9.79936i | − | 0.333574i | −0.985993 | − | 0.166787i | \(-0.946661\pi\) | ||
0.985993 | − | 0.166787i | \(-0.0533392\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 19.1955 | + | 28.6175i | 0.652668 | + | 0.973023i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 55.8423i | 1.89432i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 12.5414i | 0.424950i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 9.47100 | − | 1.93667i | 0.320178 | − | 0.0654714i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 23.7047i | 0.800451i | 0.916417 | + | 0.400225i | \(0.131068\pi\) | ||||
−0.916417 | + | 0.400225i | \(0.868932\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 37.1660i | − | 1.25215i | −0.779762 | − | 0.626077i | \(-0.784660\pi\) | ||
0.779762 | − | 0.626077i | \(-0.215340\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −17.7293 | −0.596638 | −0.298319 | − | 0.954466i | \(-0.596426\pi\) | ||||
−0.298319 | + | 0.954466i | \(0.596426\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 34.6202i | 1.16243i | 0.813749 | + | 0.581217i | \(0.197423\pi\) | ||||
−0.813749 | + | 0.581217i | \(0.802577\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1.88629 | −0.0632641 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −7.95397 | −0.266170 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 11.9109 | + | 17.7572i | 0.398136 | + | 0.593557i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 4.12544 | 0.137591 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 33.3815 | 1.11210 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 17.8105 | + | 26.5526i | 0.592041 | + | 0.882638i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 7.76593 | 0.257863 | 0.128932 | − | 0.991653i | \(-0.458845\pi\) | ||||
0.128932 | + | 0.991653i | \(0.458845\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −4.30802 | −0.142731 | −0.0713655 | − | 0.997450i | \(-0.522736\pi\) | ||||
−0.0713655 | + | 0.997450i | \(0.522736\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 31.6435i | − | 1.04725i | ||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 19.2506 | 0.635712 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 27.2524i | − | 0.898974i | −0.893287 | − | 0.449487i | \(-0.851607\pi\) | ||
0.893287 | − | 0.449487i | \(-0.148393\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − | 9.19917i | − | 0.302794i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −29.5510 | − | 12.1170i | −0.971632 | − | 0.398406i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 37.3662i | 1.22595i | 0.790104 | + | 0.612973i | \(0.210027\pi\) | ||||
−0.790104 | + | 0.612973i | \(0.789973\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − | 10.8122i | − | 0.354354i | ||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −18.0673 | − | 26.9354i | −0.590864 | − | 0.880883i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 35.4586i | − | 1.15838i | −0.815192 | − | 0.579190i | \(-0.803369\pi\) | ||
0.815192 | − | 0.579190i | \(-0.196631\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 11.1420i | − | 0.363219i | −0.983371 | − | 0.181610i | \(-0.941869\pi\) | ||
0.983371 | − | 0.181610i | \(-0.0581307\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −57.7851 | −1.88174 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − | 31.4956i | − | 1.02347i | −0.859144 | − | 0.511734i | \(-0.829003\pi\) | ||
0.859144 | − | 0.511734i | \(-0.170997\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −5.08287 | −0.164997 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −41.1062 | −1.33156 | −0.665779 | − | 0.746149i | \(-0.731901\pi\) | ||||
−0.665779 | + | 0.746149i | \(0.731901\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 23.8217 | + | 35.5144i | 0.770853 | + | 1.14922i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 5.98788 | 0.193359 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 20.4219 | 0.658772 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 41.7915 | − | 28.0322i | 1.34531 | − | 0.902388i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 18.4157 | 0.592208 | 0.296104 | − | 0.955156i | \(-0.404313\pi\) | ||||
0.296104 | + | 0.955156i | \(0.404313\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −11.3853 | −0.365371 | −0.182685 | − | 0.983171i | \(-0.558479\pi\) | ||||
−0.182685 | + | 0.983171i | \(0.558479\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − | 15.8217i | − | 0.507222i | ||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 43.4822 | 1.39112 | 0.695559 | − | 0.718469i | \(-0.255157\pi\) | ||||
0.695559 | + | 0.718469i | \(0.255157\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 13.9354i | − | 0.445379i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 5.36529i | 0.171126i | 0.996333 | + | 0.0855631i | \(0.0272689\pi\) | ||||
−0.996333 | + | 0.0855631i | \(0.972731\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −12.3555 | − | 18.4200i | −0.393678 | − | 0.586911i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 43.1403i | − | 1.37178i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 24.9325i | − | 0.792008i | −0.918249 | − | 0.396004i | \(-0.870397\pi\) | ||
0.918249 | − | 0.396004i | \(-0.129603\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 6.80541 | − | 4.56482i | 0.215746 | − | 0.144715i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 10.5169i | 0.333072i | 0.986035 | + | 0.166536i | \(0.0532582\pi\) | ||||
−0.986035 | + | 0.166536i | \(0.946742\pi\) | |||||||
\(998\) | 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.b.1439.10 | yes | 12 | |
3.2 | odd | 2 | inner | 1440.2.o.b.1439.3 | yes | 12 | |
4.3 | odd | 2 | 1440.2.o.a.1439.10 | yes | 12 | ||
5.2 | odd | 4 | 7200.2.h.l.1151.5 | 12 | |||
5.3 | odd | 4 | 7200.2.h.m.1151.7 | 12 | |||
5.4 | even | 2 | 1440.2.o.a.1439.4 | yes | 12 | ||
8.3 | odd | 2 | 2880.2.o.f.2879.3 | 12 | |||
8.5 | even | 2 | 2880.2.o.e.2879.3 | 12 | |||
12.11 | even | 2 | 1440.2.o.a.1439.3 | ✓ | 12 | ||
15.2 | even | 4 | 7200.2.h.l.1151.6 | 12 | |||
15.8 | even | 4 | 7200.2.h.m.1151.8 | 12 | |||
15.14 | odd | 2 | 1440.2.o.a.1439.9 | yes | 12 | ||
20.3 | even | 4 | 7200.2.h.m.1151.6 | 12 | |||
20.7 | even | 4 | 7200.2.h.l.1151.8 | 12 | |||
20.19 | odd | 2 | inner | 1440.2.o.b.1439.4 | yes | 12 | |
24.5 | odd | 2 | 2880.2.o.e.2879.10 | 12 | |||
24.11 | even | 2 | 2880.2.o.f.2879.10 | 12 | |||
40.19 | odd | 2 | 2880.2.o.e.2879.9 | 12 | |||
40.29 | even | 2 | 2880.2.o.f.2879.9 | 12 | |||
60.23 | odd | 4 | 7200.2.h.m.1151.5 | 12 | |||
60.47 | odd | 4 | 7200.2.h.l.1151.7 | 12 | |||
60.59 | even | 2 | inner | 1440.2.o.b.1439.9 | yes | 12 | |
120.29 | odd | 2 | 2880.2.o.f.2879.4 | 12 | |||
120.59 | even | 2 | 2880.2.o.e.2879.4 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1440.2.o.a.1439.3 | ✓ | 12 | 12.11 | even | 2 | ||
1440.2.o.a.1439.4 | yes | 12 | 5.4 | even | 2 | ||
1440.2.o.a.1439.9 | yes | 12 | 15.14 | odd | 2 | ||
1440.2.o.a.1439.10 | yes | 12 | 4.3 | odd | 2 | ||
1440.2.o.b.1439.3 | yes | 12 | 3.2 | odd | 2 | inner | |
1440.2.o.b.1439.4 | yes | 12 | 20.19 | odd | 2 | inner | |
1440.2.o.b.1439.9 | yes | 12 | 60.59 | even | 2 | inner | |
1440.2.o.b.1439.10 | yes | 12 | 1.1 | even | 1 | trivial | |
2880.2.o.e.2879.3 | 12 | 8.5 | even | 2 | |||
2880.2.o.e.2879.4 | 12 | 120.59 | even | 2 | |||
2880.2.o.e.2879.9 | 12 | 40.19 | odd | 2 | |||
2880.2.o.e.2879.10 | 12 | 24.5 | odd | 2 | |||
2880.2.o.f.2879.3 | 12 | 8.3 | odd | 2 | |||
2880.2.o.f.2879.4 | 12 | 120.29 | odd | 2 | |||
2880.2.o.f.2879.9 | 12 | 40.29 | even | 2 | |||
2880.2.o.f.2879.10 | 12 | 24.11 | even | 2 | |||
7200.2.h.l.1151.5 | 12 | 5.2 | odd | 4 | |||
7200.2.h.l.1151.6 | 12 | 15.2 | even | 4 | |||
7200.2.h.l.1151.7 | 12 | 60.47 | odd | 4 | |||
7200.2.h.l.1151.8 | 12 | 20.7 | even | 4 | |||
7200.2.h.m.1151.5 | 12 | 60.23 | odd | 4 | |||
7200.2.h.m.1151.6 | 12 | 20.3 | even | 4 | |||
7200.2.h.m.1151.7 | 12 | 5.3 | odd | 4 | |||
7200.2.h.m.1151.8 | 12 | 15.8 | even | 4 |