Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1512,2,Mod(377,1512)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1512, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("1512.377");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1512 = 2^{3} \cdot 3^{3} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1512.k (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: | \(12.0733807856\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 24x^{14} + 230x^{12} - 1052x^{10} + 2139x^{8} - 1244x^{6} + 1134x^{4} - 104x^{2} + 169 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{20} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 377.1 | ||
Root | \(2.62616 - 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1512.377 |
Dual form | 1512.2.k.a.377.2 |
$q$-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 \(\left(\mathbb{Z}/1512\mathbb{Z}\right)^\times\).
\(n\) | \(757\) | \(785\) | \(1081\) | \(1135\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(-1\) | \(1\) |
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 | ||||||||
\(5\) | −2.86833 | −1.28275 | −0.641377 | − | 0.767226i | \(-0.721637\pi\) | ||||
−0.641377 | + | 0.767226i | \(0.721637\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.43500 | − | 1.03478i | 0.920344 | − | 0.391110i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 3.32538i | − | 1.00264i | −0.865262 | − | 0.501319i | \(-0.832848\pi\) | ||
0.865262 | − | 0.501319i | \(-0.167152\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.821835i | 0.227936i | 0.993484 | + | 0.113968i | \(0.0363561\pi\) | ||||
−0.993484 | + | 0.113968i | \(0.963644\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −3.52027 | −0.853792 | −0.426896 | − | 0.904301i | \(-0.640393\pi\) | ||||
−0.426896 | + | 0.904301i | \(0.640393\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 5.25233i | 1.20497i | 0.798132 | + | 0.602483i | \(0.205822\pi\) | ||||
−0.798132 | + | 0.602483i | \(0.794178\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 5.12921i | − | 1.06951i | −0.845006 | − | 0.534757i | \(-0.820403\pi\) | ||
0.845006 | − | 0.534757i | \(-0.179597\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 3.22729 | 0.645459 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.64271i | 0.305044i | 0.988300 | + | 0.152522i | \(0.0487394\pi\) | ||||
−0.988300 | + | 0.152522i | \(0.951261\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 2.55389i | − | 0.458691i | −0.973345 | − | 0.229346i | \(-0.926341\pi\) | ||
0.973345 | − | 0.229346i | \(-0.0736586\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −6.98438 | + | 2.96809i | −1.18058 | + | 0.501698i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −8.93617 | −1.46910 | −0.734549 | − | 0.678556i | \(-0.762606\pi\) | ||||
−0.734549 | + | 0.678556i | \(0.762606\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −3.49721 | −0.546172 | −0.273086 | − | 0.961990i | \(-0.588044\pi\) | ||||
−0.273086 | + | 0.961990i | \(0.588044\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −0.161123 | −0.0245710 | −0.0122855 | − | 0.999925i | \(-0.503911\pi\) | ||||
−0.0122855 | + | 0.999925i | \(0.503911\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −5.34071 | −0.779022 | −0.389511 | − | 0.921022i | \(-0.627356\pi\) | ||||
−0.389511 | + | 0.921022i | \(0.627356\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 4.85846 | − | 5.03938i | 0.694066 | − | 0.719912i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 3.28542i | 0.451287i | 0.974210 | + | 0.225644i | \(0.0724485\pi\) | ||||
−0.974210 | + | 0.225644i | \(0.927552\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 9.53826i | 1.28614i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 4.08295 | 0.531554 | 0.265777 | − | 0.964034i | \(-0.414371\pi\) | ||||
0.265777 | + | 0.964034i | \(0.414371\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 8.43509i | − | 1.08000i | −0.841664 | − | 0.540001i | \(-0.818424\pi\) | ||
0.841664 | − | 0.540001i | \(-0.181576\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | − | 2.35729i | − | 0.292386i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −11.8780 | −1.45113 | −0.725567 | − | 0.688151i | \(-0.758422\pi\) | ||||
−0.725567 | + | 0.688151i | \(0.758422\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 5.68267i | − | 0.674408i | −0.941432 | − | 0.337204i | \(-0.890519\pi\) | ||
0.941432 | − | 0.337204i | \(-0.109481\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 7.86238i | − | 0.920223i | −0.887861 | − | 0.460111i | \(-0.847810\pi\) | ||
0.887861 | − | 0.460111i | \(-0.152190\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −3.44103 | − | 8.09729i | −0.392142 | − | 0.922772i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −15.1635 | −1.70602 | −0.853012 | − | 0.521892i | \(-0.825226\pi\) | ||||
−0.853012 | + | 0.521892i | \(0.825226\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −15.6686 | −1.71985 | −0.859926 | − | 0.510419i | \(-0.829490\pi\) | ||||
−0.859926 | + | 0.510419i | \(0.829490\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 10.0973 | 1.09521 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −16.2082 | −1.71807 | −0.859033 | − | 0.511921i | \(-0.828934\pi\) | ||||
−0.859033 | + | 0.511921i | \(0.828934\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.850418 | + | 2.00117i | 0.0891481 | + | 0.209780i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | − | 15.0654i | − | 1.54568i | ||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 12.8678i | − | 1.30653i | −0.757129 | − | 0.653266i | \(-0.773398\pi\) | ||
0.757129 | − | 0.653266i | \(-0.226602\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 3.40793 | 0.339102 | 0.169551 | − | 0.985521i | \(-0.445768\pi\) | ||||
0.169551 | + | 0.985521i | \(0.445768\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0.484326i | 0.0477220i | 0.999715 | + | 0.0238610i | \(0.00759592\pi\) | ||||
−0.999715 | + | 0.0238610i | \(0.992404\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 17.3827i | 1.68045i | 0.542238 | + | 0.840225i | \(0.317577\pi\) | ||||
−0.542238 | + | 0.840225i | \(0.682423\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1.13804 | 0.109005 | 0.0545023 | − | 0.998514i | \(-0.482643\pi\) | ||||
0.0545023 | + | 0.998514i | \(0.482643\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 16.1946i | − | 1.52346i | −0.647895 | − | 0.761729i | \(-0.724351\pi\) | ||
0.647895 | − | 0.761729i | \(-0.275649\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 14.7122i | 1.37192i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −8.57187 | + | 3.64271i | −0.785782 | + | 0.333927i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −0.0581269 | −0.00528426 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 5.08470 | 0.454790 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 16.0335 | 1.42274 | 0.711370 | − | 0.702818i | \(-0.248075\pi\) | ||||
0.711370 | + | 0.702818i | \(0.248075\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −7.27801 | −0.635883 | −0.317941 | − | 0.948110i | \(-0.602992\pi\) | ||||
−0.317941 | + | 0.948110i | \(0.602992\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 5.43500 | + | 12.7894i | 0.471274 | + | 1.10898i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 14.2296i | 1.21572i | 0.794044 | + | 0.607860i | \(0.207972\pi\) | ||||
−0.794044 | + | 0.607860i | \(0.792028\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 21.7288i | 1.84301i | 0.388361 | + | 0.921507i | \(0.373042\pi\) | ||||
−0.388361 | + | 0.921507i | \(0.626958\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 2.73291 | 0.228537 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 4.71183i | − | 0.391296i | ||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − | 19.8723i | − | 1.62801i | −0.580861 | − | 0.814003i | \(-0.697284\pi\) | ||
0.580861 | − | 0.814003i | \(-0.302716\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −0.870002 | −0.0707998 | −0.0353999 | − | 0.999373i | \(-0.511270\pi\) | ||||
−0.0353999 | + | 0.999373i | \(0.511270\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 7.32538i | 0.588388i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 3.47414i | − | 0.277266i | −0.990344 | − | 0.138633i | \(-0.955729\pi\) | ||
0.990344 | − | 0.138633i | \(-0.0442709\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −5.30760 | − | 12.4896i | −0.418298 | − | 0.984321i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −2.13804 | −0.167464 | −0.0837321 | − | 0.996488i | \(-0.526684\pi\) | ||||
−0.0837321 | + | 0.996488i | \(0.526684\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 19.7515 | 1.52842 | 0.764210 | − | 0.644967i | \(-0.223129\pi\) | ||||
0.764210 | + | 0.644967i | \(0.223129\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 12.3246 | 0.948045 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −14.5084 | −1.10305 | −0.551525 | − | 0.834158i | \(-0.685954\pi\) | ||||
−0.551525 | + | 0.834158i | \(0.685954\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 7.85846 | − | 3.33954i | 0.594044 | − | 0.252445i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 6.81188i | 0.509143i | 0.967054 | + | 0.254572i | \(0.0819345\pi\) | ||||
−0.967054 | + | 0.254572i | \(0.918066\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 23.6415i | − | 1.75726i | −0.477502 | − | 0.878631i | \(-0.658458\pi\) | ||
0.477502 | − | 0.878631i | \(-0.341542\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 25.6319 | 1.88449 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 11.7062i | 0.856045i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 7.06538i | 0.511233i | 0.966778 | + | 0.255617i | \(0.0822784\pi\) | ||||
−0.966778 | + | 0.255617i | \(0.917722\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −5.71692 | −0.411513 | −0.205757 | − | 0.978603i | \(-0.565965\pi\) | ||||
−0.205757 | + | 0.978603i | \(0.565965\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 24.7815i | 1.76561i | 0.469740 | + | 0.882805i | \(0.344348\pi\) | ||||
−0.469740 | + | 0.882805i | \(0.655652\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 5.15001i | − | 0.365075i | −0.983199 | − | 0.182537i | \(-0.941569\pi\) | ||
0.983199 | − | 0.182537i | \(-0.0584311\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 1.69984 | + | 4.00000i | 0.119306 | + | 0.280745i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 10.0311 | 0.700604 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 17.4660 | 1.20815 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −12.0392 | −0.828810 | −0.414405 | − | 0.910092i | \(-0.636010\pi\) | ||||
−0.414405 | + | 0.910092i | \(0.636010\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0.462153 | 0.0315186 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −2.64271 | − | 6.21871i | −0.179399 | − | 0.422154i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 2.89308i | − | 0.194610i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 22.7676i | − | 1.52463i | −0.647206 | − | 0.762315i | \(-0.724063\pi\) | ||
0.647206 | − | 0.762315i | \(-0.275937\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 25.3297 | 1.68119 | 0.840596 | − | 0.541663i | \(-0.182205\pi\) | ||||
0.840596 | + | 0.541663i | \(0.182205\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 2.49545i | 0.164904i | 0.996595 | + | 0.0824520i | \(0.0262751\pi\) | ||||
−0.996595 | + | 0.0824520i | \(0.973725\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 16.0000i | 1.04819i | 0.851658 | + | 0.524097i | \(0.175597\pi\) | ||||
−0.851658 | + | 0.524097i | \(0.824403\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 15.3189 | 0.999294 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 8.66813i | − | 0.560695i | −0.959899 | − | 0.280347i | \(-0.909550\pi\) | ||
0.959899 | − | 0.280347i | \(-0.0904497\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 30.2907i | 1.95119i | 0.219571 | + | 0.975597i | \(0.429534\pi\) | ||||
−0.219571 | + | 0.975597i | \(0.570466\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −13.9356 | + | 14.4546i | −0.890316 | + | 0.923470i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −4.31654 | −0.274655 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −5.78279 | −0.365006 | −0.182503 | − | 0.983205i | \(-0.558420\pi\) | ||||
−0.182503 | + | 0.983205i | \(0.558420\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −17.0565 | −1.07234 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 17.3454 | 1.08197 | 0.540987 | − | 0.841031i | \(-0.318051\pi\) | ||||
0.540987 | + | 0.841031i | \(0.318051\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −21.7596 | + | 9.24697i | −1.35208 | + | 0.574579i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 8.80696i | − | 0.543061i | −0.962430 | − | 0.271530i | \(-0.912470\pi\) | ||
0.962430 | − | 0.271530i | \(-0.0875297\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 9.42365i | − | 0.578890i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 28.4310 | 1.73347 | 0.866733 | − | 0.498772i | \(-0.166215\pi\) | ||||
0.866733 | + | 0.498772i | \(0.166215\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 2.47554i | − | 0.150378i | −0.997169 | − | 0.0751892i | \(-0.976044\pi\) | ||
0.997169 | − | 0.0751892i | \(-0.0239561\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | − | 10.7320i | − | 0.647162i | ||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −5.93383 | −0.356529 | −0.178265 | − | 0.983983i | \(-0.557048\pi\) | ||||
−0.178265 | + | 0.983983i | \(0.557048\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 9.96496i | 0.594459i | 0.954806 | + | 0.297230i | \(0.0960627\pi\) | ||||
−0.954806 | + | 0.297230i | \(0.903937\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 13.6796i | − | 0.813170i | −0.913613 | − | 0.406585i | \(-0.866719\pi\) | ||
0.913613 | − | 0.406585i | \(-0.133281\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −8.51570 | + | 3.61884i | −0.502666 | + | 0.213613i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −4.60767 | −0.271039 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 1.47062 | 0.0859148 | 0.0429574 | − | 0.999077i | \(-0.486322\pi\) | ||||
0.0429574 | + | 0.999077i | \(0.486322\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −11.7112 | −0.681854 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 4.21536 | 0.243781 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −0.392335 | + | 0.166727i | −0.0226138 | + | 0.00960997i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 24.1946i | 1.38538i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 31.6829i | 1.80824i | 0.427277 | + | 0.904121i | \(0.359473\pi\) | ||||
−0.427277 | + | 0.904121i | \(0.640527\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 19.1971 | 1.08857 | 0.544284 | − | 0.838901i | \(-0.316801\pi\) | ||||
0.544284 | + | 0.838901i | \(0.316801\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 13.4406i | − | 0.759705i | −0.925047 | − | 0.379852i | \(-0.875975\pi\) | ||
0.925047 | − | 0.379852i | \(-0.124025\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − | 29.5151i | − | 1.65773i | −0.559448 | − | 0.828865i | \(-0.688987\pi\) | ||
0.559448 | − | 0.828865i | \(-0.311013\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 5.46263 | 0.305848 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 18.4896i | − | 1.02879i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 2.65230i | 0.147123i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −13.0046 | + | 5.52646i | −0.716968 | + | 0.304683i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 0.547756 | 0.0301074 | 0.0150537 | − | 0.999887i | \(-0.495208\pi\) | ||||
0.0150537 | + | 0.999887i | \(0.495208\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 34.0701 | 1.86145 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −17.1946 | −0.936649 | −0.468324 | − | 0.883557i | \(-0.655142\pi\) | ||||
−0.468324 | + | 0.883557i | \(0.655142\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −8.49263 | −0.459902 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 6.61571 | − | 17.2983i | 0.357215 | − | 0.934022i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − | 22.6443i | − | 1.21561i | −0.794087 | − | 0.607804i | \(-0.792051\pi\) | ||
0.794087 | − | 0.607804i | \(-0.207949\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 24.2288i | − | 1.29694i | −0.761241 | − | 0.648469i | \(-0.775410\pi\) | ||
0.761241 | − | 0.648469i | \(-0.224590\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 16.0497 | 0.854240 | 0.427120 | − | 0.904195i | \(-0.359528\pi\) | ||||
0.427120 | + | 0.904195i | \(0.359528\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 16.2997i | 0.865100i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 26.8119i | 1.41508i | 0.706675 | + | 0.707538i | \(0.250194\pi\) | ||||
−0.706675 | + | 0.707538i | \(0.749806\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −8.58692 | −0.451943 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 22.5519i | 1.18042i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 22.9643i | − | 1.19872i | −0.800478 | − | 0.599362i | \(-0.795421\pi\) | ||
0.800478 | − | 0.599362i | \(-0.204579\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 3.39969 | + | 8.00000i | 0.176503 | + | 0.415339i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 17.6043 | 0.911516 | 0.455758 | − | 0.890104i | \(-0.349368\pi\) | ||||
0.455758 | + | 0.890104i | \(0.349368\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −1.35004 | −0.0695304 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −14.7250 | −0.756371 | −0.378185 | − | 0.925730i | \(-0.623452\pi\) | ||||
−0.378185 | + | 0.925730i | \(0.623452\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −36.8030 | −1.88055 | −0.940273 | − | 0.340421i | \(-0.889430\pi\) | ||||
−0.940273 | + | 0.340421i | \(0.889430\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 9.87000 | + | 23.2257i | 0.503022 | + | 1.18369i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 4.32225i | 0.219147i | 0.993979 | + | 0.109573i | \(0.0349484\pi\) | ||||
−0.993979 | + | 0.109573i | \(0.965052\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 18.0562i | 0.913143i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 43.4938 | 2.18841 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 3.84549i | − | 0.192999i | −0.995333 | − | 0.0964997i | \(-0.969235\pi\) | ||
0.995333 | − | 0.0964997i | \(-0.0307647\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 3.33655i | 0.166619i | 0.996524 | + | 0.0833097i | \(0.0265491\pi\) | ||||
−0.996524 | + | 0.0833097i | \(0.973451\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 2.09887 | 0.104552 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 29.7161i | 1.47297i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 5.99402i | 0.296385i | 0.988959 | + | 0.148193i | \(0.0473456\pi\) | ||||
−0.988959 | + | 0.148193i | \(0.952654\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 9.94198 | − | 4.22495i | 0.489213 | − | 0.207896i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 44.9426 | 2.20615 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 31.1326 | 1.52093 | 0.760463 | − | 0.649382i | \(-0.224972\pi\) | ||||
0.760463 | + | 0.649382i | \(0.224972\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 2.93617 | 0.143100 | 0.0715501 | − | 0.997437i | \(-0.477205\pi\) | ||||
0.0715501 | + | 0.997437i | \(0.477205\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −11.3610 | −0.551087 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −8.72846 | − | 20.5395i | −0.422400 | − | 0.993974i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 23.0654i | 1.11102i | 0.831510 | + | 0.555510i | \(0.187477\pi\) | ||||
−0.831510 | + | 0.555510i | \(0.812523\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 27.8831i | 1.33998i | 0.742371 | + | 0.669989i | \(0.233701\pi\) | ||||
−0.742371 | + | 0.669989i | \(0.766299\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 26.9403 | 1.28873 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 25.7312i | − | 1.22808i | −0.789274 | − | 0.614041i | \(-0.789543\pi\) | ||
0.789274 | − | 0.614041i | \(-0.210457\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − | 6.73845i | − | 0.320154i | −0.987105 | − | 0.160077i | \(-0.948826\pi\) | ||
0.987105 | − | 0.160077i | \(-0.0511742\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 46.4904 | 2.20386 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 38.7654i | − | 1.82945i | −0.404073 | − | 0.914727i | \(-0.632406\pi\) | ||
0.404073 | − | 0.914727i | \(-0.367594\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 11.6295i | 0.547613i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −2.43928 | − | 5.74000i | −0.114355 | − | 0.269096i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 31.7423 | 1.48484 | 0.742422 | − | 0.669932i | \(-0.233677\pi\) | ||||
0.742422 | + | 0.669932i | \(0.233677\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −3.14740 | −0.146589 | −0.0732945 | − | 0.997310i | \(-0.523351\pi\) | ||||
−0.0732945 | + | 0.997310i | \(0.523351\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 5.46833 | 0.254135 | 0.127067 | − | 0.991894i | \(-0.459444\pi\) | ||||
0.127067 | + | 0.991894i | \(0.459444\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −20.5471 | −0.950809 | −0.475404 | − | 0.879767i | \(-0.657698\pi\) | ||||
−0.475404 | + | 0.879767i | \(0.657698\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −28.9231 | + | 12.2912i | −1.33554 | + | 0.567553i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0.535795i | 0.0246359i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 16.9508i | 0.777756i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 13.0645 | 0.596933 | 0.298466 | − | 0.954420i | \(-0.403525\pi\) | ||||
0.298466 | + | 0.954420i | \(0.403525\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | − | 7.34406i | − | 0.334860i | ||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 36.9092i | 1.67596i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 1.74571 | 0.0791055 | 0.0395527 | − | 0.999217i | \(-0.487407\pi\) | ||||
0.0395527 | + | 0.999217i | \(0.487407\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 4.51350i | 0.203691i | 0.994800 | + | 0.101846i | \(0.0324748\pi\) | ||||
−0.994800 | + | 0.101846i | \(0.967525\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 5.78279i | − | 0.260444i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −5.88031 | − | 13.8373i | −0.263768 | − | 0.620688i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 14.7320 | 0.659493 | 0.329747 | − | 0.944069i | \(-0.393037\pi\) | ||||
0.329747 | + | 0.944069i | \(0.393037\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −8.64812 | −0.385600 | −0.192800 | − | 0.981238i | \(-0.561757\pi\) | ||||
−0.192800 | + | 0.981238i | \(0.561757\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −9.77505 | −0.434984 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 29.8666 | 1.32381 | 0.661906 | − | 0.749587i | \(-0.269748\pi\) | ||||
0.661906 | + | 0.749587i | \(0.269748\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −8.13584 | − | 19.1449i | −0.359908 | − | 0.846921i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − | 1.38920i | − | 0.0612157i | ||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 17.7599i | 0.781078i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 12.5756 | 0.550946 | 0.275473 | − | 0.961309i | \(-0.411166\pi\) | ||||
0.275473 | + | 0.961309i | \(0.411166\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 24.9477i | 1.09089i | 0.838148 | + | 0.545443i | \(0.183639\pi\) | ||||
−0.838148 | + | 0.545443i | \(0.816361\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 8.99038i | 0.391627i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −3.30878 | −0.143860 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 2.87413i | − | 0.124492i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − | 49.8593i | − | 2.15560i | ||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −16.7578 | − | 16.1562i | −0.721811 | − | 0.695897i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −12.5438 | −0.539302 | −0.269651 | − | 0.962958i | \(-0.586908\pi\) | ||||
−0.269651 | + | 0.962958i | \(0.586908\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −3.26427 | −0.139826 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −8.87000 | −0.379254 | −0.189627 | − | 0.981856i | \(-0.560728\pi\) | ||||
−0.189627 | + | 0.981856i | \(0.560728\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −8.62805 | −0.367567 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −36.9231 | + | 15.6908i | −1.57013 | + | 0.667243i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 32.7815i | − | 1.38900i | −0.719494 | − | 0.694499i | \(-0.755626\pi\) | ||
0.719494 | − | 0.694499i | \(-0.244374\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 0.132416i | − | 0.00560062i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 3.97060 | 0.167341 | 0.0836704 | − | 0.996493i | \(-0.473336\pi\) | ||||
0.0836704 | + | 0.996493i | \(0.473336\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 46.4514i | 1.95422i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 20.0669i | 0.841250i | 0.907235 | + | 0.420625i | \(0.138189\pi\) | ||||
−0.907235 | + | 0.420625i | \(0.861811\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −22.9323 | −0.959685 | −0.479842 | − | 0.877355i | \(-0.659306\pi\) | ||||
−0.479842 | + | 0.877355i | \(0.659306\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 16.5535i | − | 0.690327i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 27.5760i | 1.14801i | 0.818853 | + | 0.574003i | \(0.194610\pi\) | ||||
−0.818853 | + | 0.574003i | \(0.805390\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −38.1530 | + | 16.2135i | −1.58286 | + | 0.672651i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 10.9253 | 0.452478 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −14.6684 | −0.605428 | −0.302714 | − | 0.953081i | \(-0.597893\pi\) | ||||
−0.302714 | + | 0.953081i | \(0.597893\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 13.4138 | 0.552708 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −27.7560 | −1.13980 | −0.569900 | − | 0.821714i | \(-0.693018\pi\) | ||||
−0.569900 | + | 0.821714i | \(0.693018\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 24.5869 | − | 10.4485i | 1.00797 | − | 0.428346i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 31.2600i | 1.27725i | 0.769519 | + | 0.638624i | \(0.220496\pi\) | ||||
−0.769519 | + | 0.638624i | \(0.779504\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 26.8665i | − | 1.09591i | −0.836508 | − | 0.547955i | \(-0.815407\pi\) | ||
0.836508 | − | 0.547955i | \(-0.184593\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0.166727 | 0.00677841 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 22.6331i | − | 0.918648i | −0.888269 | − | 0.459324i | \(-0.848092\pi\) | ||
0.888269 | − | 0.459324i | \(-0.151908\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 4.38918i | − | 0.177567i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −42.8518 | −1.73077 | −0.865384 | − | 0.501109i | \(-0.832926\pi\) | ||||
−0.865384 | + | 0.501109i | \(0.832926\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 10.9442i | − | 0.440597i | −0.975432 | − | 0.220299i | \(-0.929297\pi\) | ||
0.975432 | − | 0.220299i | \(-0.0707032\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 14.4430i | − | 0.580515i | −0.956949 | − | 0.290257i | \(-0.906259\pi\) | ||
0.956949 | − | 0.290257i | \(-0.0937409\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −39.4670 | + | 16.7719i | −1.58121 | + | 0.671953i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −30.7210 | −1.22884 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 31.4578 | 1.25430 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 14.3326 | 0.570573 | 0.285286 | − | 0.958442i | \(-0.407911\pi\) | ||||
0.285286 | + | 0.958442i | \(0.407911\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −45.9892 | −1.82503 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 4.14154 | + | 3.99285i | 0.164094 | + | 0.158203i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 31.8023i | − | 1.25611i | −0.778168 | − | 0.628057i | \(-0.783851\pi\) | ||
0.778168 | − | 0.628057i | \(-0.216149\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 0.345751i | 0.0136351i | 0.999977 | + | 0.00681755i | \(0.00217011\pi\) | ||||
−0.999977 | + | 0.00681755i | \(0.997830\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −8.85274 | −0.348037 | −0.174019 | − | 0.984742i | \(-0.555675\pi\) | ||||
−0.174019 | + | 0.984742i | \(0.555675\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 13.5773i | − | 0.532957i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − | 40.9603i | − | 1.60290i | −0.598062 | − | 0.801450i | \(-0.704062\pi\) | ||
0.598062 | − | 0.801450i | \(-0.295938\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 20.8757 | 0.815681 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 5.38920i | 0.209934i | 0.994476 | + | 0.104967i | \(0.0334736\pi\) | ||||
−0.994476 | + | 0.104967i | \(0.966526\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 25.9703i | 1.01013i | 0.863083 | + | 0.505063i | \(0.168531\pi\) | ||||
−0.863083 | + | 0.505063i | \(0.831469\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −15.5894 | − | 36.6842i | −0.604529 | − | 1.42255i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 8.42580 | 0.326248 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −28.0499 | −1.08285 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −28.0553 | −1.08145 | −0.540725 | − | 0.841199i | \(-0.681850\pi\) | ||||
−0.540725 | + | 0.841199i | \(0.681850\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −31.5977 | −1.21440 | −0.607200 | − | 0.794549i | \(-0.707707\pi\) | ||||
−0.607200 | + | 0.794549i | \(0.707707\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −13.3154 | − | 31.3332i | −0.510998 | − | 1.20246i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 8.55679i | − | 0.327417i | −0.986509 | − | 0.163708i | \(-0.947654\pi\) | ||
0.986509 | − | 0.163708i | \(-0.0523456\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 40.8152i | − | 1.55947i | ||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −2.70007 | −0.102865 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 19.5748i | − | 0.744660i | −0.928100 | − | 0.372330i | \(-0.878559\pi\) | ||
0.928100 | − | 0.372330i | \(-0.121441\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − | 62.3254i | − | 2.36414i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 12.3111 | 0.466317 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 31.9810i | − | 1.20791i | −0.797019 | − | 0.603954i | \(-0.793591\pi\) | ||
0.797019 | − | 0.603954i | \(-0.206409\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 46.9357i | − | 1.77021i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 8.29831 | − | 3.52646i | 0.312090 | − | 0.132626i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −2.07029 | −0.0777515 | −0.0388757 | − | 0.999244i | \(-0.512378\pi\) | ||||
−0.0388757 | + | 0.999244i | \(0.512378\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −13.0994 | −0.490577 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −7.83888 | −0.293157 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 33.4828 | 1.24870 | 0.624350 | − | 0.781145i | \(-0.285364\pi\) | ||||
0.624350 | + | 0.781145i | \(0.285364\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0.501171 | + | 1.17933i | 0.0186646 | + | 0.0439207i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 5.30150i | 0.196893i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 12.7754i | 0.473814i | 0.971532 | + | 0.236907i | \(0.0761336\pi\) | ||||
−0.971532 | + | 0.236907i | \(0.923866\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0.567197 | 0.0209785 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 30.2462i | 1.11717i | 0.829448 | + | 0.558584i | \(0.188655\pi\) | ||||
−0.829448 | + | 0.558584i | \(0.811345\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 39.4990i | 1.45496i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −9.10692 | −0.335003 | −0.167502 | − | 0.985872i | \(-0.553570\pi\) | ||||
−0.167502 | + | 0.985872i | \(0.553570\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 36.9551i | 1.35575i | 0.735177 | + | 0.677876i | \(0.237099\pi\) | ||||
−0.735177 | + | 0.677876i | \(0.762901\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 57.0004i | 2.08833i | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 17.9873 | + | 42.3269i | 0.657241 | + | 1.54659i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 6.89879 | 0.251740 | 0.125870 | − | 0.992047i | \(-0.459828\pi\) | ||||
0.125870 | + | 0.992047i | \(0.459828\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 2.49545 | 0.0908187 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −12.8861 | −0.468353 | −0.234176 | − | 0.972194i | \(-0.575239\pi\) | ||||
−0.234176 | + | 0.972194i | \(0.575239\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −32.8078 | −1.18928 | −0.594641 | − | 0.803991i | \(-0.702706\pi\) | ||||
−0.594641 | + | 0.803991i | \(0.702706\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 2.77113 | − | 1.17762i | 0.100322 | − | 0.0426328i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 3.35551i | 0.121160i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 18.9096i | − | 0.681899i | −0.940082 | − | 0.340949i | \(-0.889251\pi\) | ||
0.940082 | − | 0.340949i | \(-0.110749\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −15.6195 | −0.561793 | −0.280896 | − | 0.959738i | \(-0.590632\pi\) | ||||
−0.280896 | + | 0.959738i | \(0.590632\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 8.24214i | − | 0.296066i | ||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − | 18.3685i | − | 0.658118i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −18.8970 | −0.676188 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 9.96496i | 0.355665i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 14.4471i | 0.514983i | 0.966281 | + | 0.257492i | \(0.0828960\pi\) | ||||
−0.966281 | + | 0.257492i | \(0.917104\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −16.7578 | − | 39.4338i | −0.595840 | − | 1.40211i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 6.93225 | 0.246172 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −46.1246 | −1.63382 | −0.816909 | − | 0.576767i | \(-0.804314\pi\) | ||||
−0.816909 | + | 0.576767i | \(0.804314\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 18.8008 | 0.665123 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −26.1454 | −0.922651 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 15.2239 | + | 35.8243i | 0.536573 | + | 1.26264i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 4.17879i | 0.146918i | 0.997298 | + | 0.0734591i | \(0.0234039\pi\) | ||||
−0.997298 | + | 0.0734591i | \(0.976596\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 14.7767i | 0.518879i | 0.965759 | + | 0.259439i | \(0.0835378\pi\) | ||||
−0.965759 | + | 0.259439i | \(0.916462\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 6.13260 | 0.214815 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 0.846270i | − | 0.0296073i | ||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 46.5519i | − | 1.62467i | −0.583190 | − | 0.812336i | \(-0.698196\pi\) | ||
0.583190 | − | 0.812336i | \(-0.301804\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 3.20833 | 0.111835 | 0.0559177 | − | 0.998435i | \(-0.482192\pi\) | ||||
0.0559177 | + | 0.998435i | \(0.482192\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 17.7927i | − | 0.618711i | −0.950946 | − | 0.309356i | \(-0.899887\pi\) | ||
0.950946 | − | 0.309356i | \(-0.100113\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 6.66451i | − | 0.231468i | −0.993280 | − | 0.115734i | \(-0.963078\pi\) | ||
0.993280 | − | 0.115734i | \(-0.0369220\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −17.1031 | + | 17.7400i | −0.592588 | + | 0.614655i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −56.6539 | −1.96059 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −2.14564 | −0.0740758 | −0.0370379 | − | 0.999314i | \(-0.511792\pi\) | ||||
−0.0370379 | + | 0.999314i | \(0.511792\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 26.3015 | 0.906948 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −35.3509 | −1.21611 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −0.141539 | + | 0.0601485i | −0.00486334 | + | 0.00206673i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 45.8355i | 1.57122i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 18.8954i | 0.646966i | 0.946234 | + | 0.323483i | \(0.104854\pi\) | ||||
−0.946234 | + | 0.323483i | \(0.895146\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 35.2140 | 1.20289 | 0.601443 | − | 0.798915i | \(-0.294593\pi\) | ||||
0.601443 | + | 0.798915i | \(0.294593\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 23.6538i | 0.807058i | 0.914967 | + | 0.403529i | \(0.132217\pi\) | ||||
−0.914967 | + | 0.403529i | \(0.867783\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 0.993535i | 0.0338203i | 0.999857 | + | 0.0169102i | \(0.00538293\pi\) | ||||
−0.999857 | + | 0.0169102i | \(0.994617\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 41.6147 | 1.41494 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 50.4242i | 1.71052i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 9.76179i | − | 0.330766i | ||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 12.3813 | − | 5.26155i | 0.418563 | − | 0.177873i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −14.9401 | −0.504491 | −0.252246 | − | 0.967663i | \(-0.581169\pi\) | ||||
−0.252246 | + | 0.967663i | \(0.581169\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 17.6044 | 0.593106 | 0.296553 | − | 0.955016i | \(-0.404163\pi\) | ||||
0.296553 | + | 0.955016i | \(0.404163\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 42.0439 | 1.41489 | 0.707444 | − | 0.706769i | \(-0.249848\pi\) | ||||
0.707444 | + | 0.706769i | \(0.249848\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −14.3186 | −0.480770 | −0.240385 | − | 0.970678i | \(-0.577274\pi\) | ||||
−0.240385 | + | 0.970678i | \(0.577274\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 39.0415 | − | 16.5911i | 1.30941 | − | 0.556448i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − | 28.0511i | − | 0.938695i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 19.5387i | − | 0.653106i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 4.19529 | 0.139921 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 11.5656i | − | 0.385305i | ||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 67.8116i | 2.25413i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 9.43616 | 0.313322 | 0.156661 | − | 0.987652i | \(-0.449927\pi\) | ||||
0.156661 | + | 0.987652i | \(0.449927\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 36.1803i | − | 1.19871i | −0.800484 | − | 0.599354i | \(-0.795424\pi\) | ||
0.800484 | − | 0.599354i | \(-0.204576\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 52.1040i | 1.72439i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −17.7220 | + | 7.53114i | −0.585231 | + | 0.248700i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 13.4292 | 0.442987 | 0.221494 | − | 0.975162i | \(-0.428907\pi\) | ||||
0.221494 | + | 0.975162i | \(0.428907\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 4.67021 | 0.153722 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −28.8396 | −0.948242 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −10.4485 | −0.342803 | −0.171402 | − | 0.985201i | \(-0.554830\pi\) | ||||
−0.171402 | + | 0.985201i | \(0.554830\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 26.4685 | + | 25.5182i | 0.867469 | + | 0.836326i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − | 33.5773i | − | 1.09810i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 46.0300i | − | 1.50373i | −0.659315 | − | 0.751867i | \(-0.729153\pi\) | ||
0.659315 | − | 0.751867i | \(-0.270847\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −16.4836 | −0.537349 | −0.268674 | − | 0.963231i | \(-0.586586\pi\) | ||||
−0.268674 | + | 0.963231i | \(0.586586\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 17.9379i | 0.584138i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − | 49.0527i | − | 1.59400i | −0.603981 | − | 0.796999i | \(-0.706420\pi\) | ||
0.603981 | − | 0.796999i | \(-0.293580\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 6.46158 | 0.209752 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 42.9442i | − | 1.39110i | −0.718478 | − | 0.695550i | \(-0.755161\pi\) | ||
0.718478 | − | 0.695550i | \(-0.244839\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − | 20.2658i | − | 0.655786i | ||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 14.7245 | + | 34.6492i | 0.475480 | + | 1.11888i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 24.4777 | 0.789602 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 16.3980 | 0.527870 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −4.03917 | −0.129891 | −0.0649454 | − | 0.997889i | \(-0.520687\pi\) | ||||
−0.0649454 | + | 0.997889i | \(0.520687\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 18.7312 | 0.601114 | 0.300557 | − | 0.953764i | \(-0.402827\pi\) | ||||
0.300557 | + | 0.953764i | \(0.402827\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 22.4846 | + | 52.9097i | 0.720822 | + | 1.69621i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 35.1899i | − | 1.12583i | −0.826516 | − | 0.562913i | \(-0.809681\pi\) | ||
0.826516 | − | 0.562913i | \(-0.190319\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 53.8984i | 1.72260i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −11.0312 | −0.351841 | −0.175921 | − | 0.984404i | \(-0.556290\pi\) | ||||
−0.175921 | + | 0.984404i | \(0.556290\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | − | 71.0815i | − | 2.26484i | ||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0.826433i | 0.0262791i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 4.31654 | 0.137120 | 0.0685598 | − | 0.997647i | \(-0.478160\pi\) | ||||
0.0685598 | + | 0.997647i | \(0.478160\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 14.7719i | 0.468301i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − | 10.5691i | − | 0.334726i | −0.985895 | − | 0.167363i | \(-0.946475\pi\) | ||
0.985895 | − | 0.167363i | \(-0.0535251\pi\) | |||||||
\(998\) | 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 | 1512.2.k.a.377.1 | ✓ | 16 | |
3.2 | odd | 2 | inner | 1512.2.k.a.377.15 | yes | 16 | |
4.3 | odd | 2 | 3024.2.k.k.1889.2 | 16 | |||
7.6 | odd | 2 | inner | 1512.2.k.a.377.16 | yes | 16 | |
12.11 | even | 2 | 3024.2.k.k.1889.16 | 16 | |||
21.20 | even | 2 | inner | 1512.2.k.a.377.2 | yes | 16 | |
28.27 | even | 2 | 3024.2.k.k.1889.15 | 16 | |||
84.83 | odd | 2 | 3024.2.k.k.1889.1 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1512.2.k.a.377.1 | ✓ | 16 | 1.1 | even | 1 | trivial | |
1512.2.k.a.377.2 | yes | 16 | 21.20 | even | 2 | inner | |
1512.2.k.a.377.15 | yes | 16 | 3.2 | odd | 2 | inner | |
1512.2.k.a.377.16 | yes | 16 | 7.6 | odd | 2 | inner | |
3024.2.k.k.1889.1 | 16 | 84.83 | odd | 2 | |||
3024.2.k.k.1889.2 | 16 | 4.3 | odd | 2 | |||
3024.2.k.k.1889.15 | 16 | 28.27 | even | 2 | |||
3024.2.k.k.1889.16 | 16 | 12.11 | even | 2 |