Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1152,4,Mod(577,1152)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1152, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1152.577");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1152 = 2^{7} \cdot 3^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1152.d (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: | \(67.9702003266\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(i, \sqrt{7})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 3x^{2} + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{10} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 577.4 | ||
Root | \(1.32288 + 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1152.577 |
Dual form | 1152.4.d.k.577.2 |
$q$-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 \(\left(\mathbb{Z}/1152\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(641\) | \(901\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 6.00000i | 0.536656i | 0.963328 | + | 0.268328i | \(0.0864711\pi\) | ||||
−0.963328 | + | 0.268328i | \(0.913529\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 21.1660 | 1.14286 | 0.571429 | − | 0.820652i | \(-0.306389\pi\) | ||||
0.571429 | + | 0.820652i | \(0.306389\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 42.3320i | 1.16033i | 0.814500 | + | 0.580163i | \(0.197011\pi\) | ||||
−0.814500 | + | 0.580163i | \(0.802989\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − 20.0000i | − 0.426692i | −0.976977 | − | 0.213346i | \(-0.931564\pi\) | ||||
0.976977 | − | 0.213346i | \(-0.0684362\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −8.00000 | −0.114134 | −0.0570672 | − | 0.998370i | \(-0.518175\pi\) | ||||
−0.0570672 | + | 0.998370i | \(0.518175\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − 84.6640i | − 1.02228i | −0.859498 | − | 0.511139i | \(-0.829224\pi\) | ||||
0.859498 | − | 0.511139i | \(-0.170776\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 169.328 | 1.53510 | 0.767551 | − | 0.640988i | \(-0.221475\pi\) | ||||
0.767551 | + | 0.640988i | \(0.221475\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 89.0000 | 0.712000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 46.0000i | 0.294551i | 0.989095 | + | 0.147276i | \(0.0470504\pi\) | ||||
−0.989095 | + | 0.147276i | \(0.952950\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −21.1660 | −0.122630 | −0.0613150 | − | 0.998118i | \(-0.519529\pi\) | ||||
−0.0613150 | + | 0.998118i | \(0.519529\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 126.996i | 0.613322i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − 164.000i | − 0.728687i | −0.931265 | − | 0.364344i | \(-0.881293\pi\) | ||||
0.931265 | − | 0.364344i | \(-0.118707\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 312.000 | 1.18844 | 0.594222 | − | 0.804301i | \(-0.297460\pi\) | ||||
0.594222 | + | 0.804301i | \(0.297460\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 423.320i | 1.50130i | 0.660702 | + | 0.750648i | \(0.270259\pi\) | ||||
−0.660702 | + | 0.750648i | \(0.729741\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −169.328 | −0.525511 | −0.262756 | − | 0.964862i | \(-0.584631\pi\) | ||||
−0.262756 | + | 0.964862i | \(0.584631\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 105.000 | 0.306122 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 266.000i | 0.689395i | 0.938714 | + | 0.344697i | \(0.112018\pi\) | ||||
−0.938714 | + | 0.344697i | \(0.887982\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −253.992 | −0.622696 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − 253.992i | − 0.560457i | −0.959933 | − | 0.280228i | \(-0.909590\pi\) | ||||
0.959933 | − | 0.280228i | \(-0.0904102\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 132.000i | 0.277063i | 0.990358 | + | 0.138532i | \(0.0442383\pi\) | ||||
−0.990358 | + | 0.138532i | \(0.955762\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 120.000 | 0.228987 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − 507.984i | − 0.926271i | −0.886287 | − | 0.463135i | \(-0.846724\pi\) | ||||
0.886287 | − | 0.463135i | \(-0.153276\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −677.312 | −1.13214 | −0.566072 | − | 0.824356i | \(-0.691537\pi\) | ||||
−0.566072 | + | 0.824356i | \(0.691537\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −246.000 | −0.394413 | −0.197206 | − | 0.980362i | \(-0.563187\pi\) | ||||
−0.197206 | + | 0.980362i | \(0.563187\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 896.000i | 1.32609i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 232.826 | 0.331582 | 0.165791 | − | 0.986161i | \(-0.446982\pi\) | ||||
0.165791 | + | 0.986161i | \(0.446982\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − 973.636i | − 1.28760i | −0.765195 | − | 0.643798i | \(-0.777358\pi\) | ||||
0.765195 | − | 0.643798i | \(-0.222642\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − 48.0000i | − 0.0612510i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 1392.00 | 1.65788 | 0.828942 | − | 0.559334i | \(-0.188943\pi\) | ||||
0.828942 | + | 0.559334i | \(0.188943\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − 423.320i | − 0.487649i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 507.984 | 0.548611 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −302.000 | −0.316118 | −0.158059 | − | 0.987430i | \(-0.550524\pi\) | ||||
−0.158059 | + | 0.987430i | \(0.550524\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1466.00i | 1.44428i | 0.691746 | + | 0.722141i | \(0.256842\pi\) | ||||
−0.691746 | + | 0.722141i | \(0.743158\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1248.79 | 1.19463 | 0.597317 | − | 0.802005i | \(-0.296233\pi\) | ||||
0.597317 | + | 0.802005i | \(0.296233\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 423.320i | 0.382466i | 0.981545 | + | 0.191233i | \(0.0612487\pi\) | ||||
−0.981545 | + | 0.191233i | \(0.938751\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1564.00i | 1.37435i | 0.726492 | + | 0.687174i | \(0.241149\pi\) | ||||
−0.726492 | + | 0.687174i | \(0.758851\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1552.00 | 1.29203 | 0.646017 | − | 0.763323i | \(-0.276433\pi\) | ||||
0.646017 | + | 0.763323i | \(0.276433\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1015.97i | 0.823822i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −169.328 | −0.130439 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −461.000 | −0.346356 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1284.00i | 0.918756i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −994.802 | −0.695074 | −0.347537 | − | 0.937666i | \(-0.612982\pi\) | ||||
−0.347537 | + | 0.937666i | \(0.612982\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 2539.92i | 1.69400i | 0.531593 | + | 0.847000i | \(0.321594\pi\) | ||||
−0.531593 | + | 0.847000i | \(0.678406\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − 1792.00i | − 1.16832i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 1992.00 | 1.24225 | 0.621124 | − | 0.783712i | \(-0.286676\pi\) | ||||
0.621124 | + | 0.783712i | \(0.286676\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − 1185.30i | − 0.723277i | −0.932318 | − | 0.361639i | \(-0.882217\pi\) | ||||
0.932318 | − | 0.361639i | \(-0.117783\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 846.640 | 0.495102 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −276.000 | −0.158073 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 1974.00i | 1.08534i | 0.839944 | + | 0.542672i | \(0.182587\pi\) | ||||
−0.839944 | + | 0.542672i | \(0.817413\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −3111.40 | −1.67684 | −0.838419 | − | 0.545027i | \(-0.816519\pi\) | ||||
−0.838419 | + | 0.545027i | \(0.816519\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − 126.996i | − 0.0658101i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1796.00i | 0.912971i | 0.889731 | + | 0.456485i | \(0.150892\pi\) | ||||
−0.889731 | + | 0.456485i | \(0.849108\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 3584.00 | 1.75440 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 2624.59i | 1.26119i | 0.776114 | + | 0.630593i | \(0.217188\pi\) | ||||
−0.776114 | + | 0.630593i | \(0.782812\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 3555.89 | 1.64768 | 0.823841 | − | 0.566820i | \(-0.191827\pi\) | ||||
0.823841 | + | 0.566820i | \(0.191827\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1797.00 | 0.817934 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 4290.00i | 1.88533i | 0.333736 | + | 0.942667i | \(0.391691\pi\) | ||||
−0.333736 | + | 0.942667i | \(0.608309\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1883.77 | 0.813714 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − 1608.62i | − 0.671696i | −0.941916 | − | 0.335848i | \(-0.890977\pi\) | ||||
0.941916 | − | 0.335848i | \(-0.109023\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − 3196.00i | − 1.31247i | −0.754557 | − | 0.656234i | \(-0.772148\pi\) | ||||
0.754557 | − | 0.656234i | \(-0.227852\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 984.000 | 0.391055 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − 338.656i | − 0.132433i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −3217.23 | −1.21880 | −0.609400 | − | 0.792863i | \(-0.708590\pi\) | ||||
−0.609400 | + | 0.792863i | \(0.708590\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 462.000 | 0.172308 | 0.0861541 | − | 0.996282i | \(-0.472542\pi\) | ||||
0.0861541 | + | 0.996282i | \(0.472542\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 3834.00i | 1.38661i | 0.720647 | + | 0.693303i | \(0.243845\pi\) | ||||
−0.720647 | + | 0.693303i | \(0.756155\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 3788.72 | 1.34962 | 0.674811 | − | 0.737990i | \(-0.264225\pi\) | ||||
0.674811 | + | 0.737990i | \(0.264225\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 973.636i | 0.336630i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1872.00i | 0.637786i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 3584.00 | 1.18617 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − 2878.58i | − 0.939192i | −0.882882 | − | 0.469596i | \(-0.844400\pi\) | ||||
0.882882 | − | 0.469596i | \(-0.155600\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −2539.92 | −0.805680 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −448.000 | −0.140148 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 160.000i | 0.0487003i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −910.138 | −0.273307 | −0.136653 | − | 0.990619i | \(-0.543635\pi\) | ||||
−0.136653 | + | 0.990619i | \(0.543635\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − 3259.57i | − 0.953062i | −0.879158 | − | 0.476531i | \(-0.841894\pi\) | ||||
0.879158 | − | 0.476531i | \(-0.158106\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − 5260.00i | − 1.51786i | −0.651171 | − | 0.758931i | \(-0.725722\pi\) | ||||
0.651171 | − | 0.758931i | \(-0.274278\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 1936.00 | 0.544342 | 0.272171 | − | 0.962249i | \(-0.412258\pi\) | ||||
0.272171 | + | 0.962249i | \(0.412258\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − 1015.97i | − 0.282019i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −1523.95 | −0.412453 | −0.206227 | − | 0.978504i | \(-0.566118\pi\) | ||||
−0.206227 | + | 0.978504i | \(0.566118\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 3202.00 | 0.855846 | 0.427923 | − | 0.903815i | \(-0.359245\pi\) | ||||
0.427923 | + | 0.903815i | \(0.359245\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 630.000i | 0.164283i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1693.28 | −0.436198 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − 2666.92i | − 0.670655i | −0.942102 | − | 0.335327i | \(-0.891153\pi\) | ||||
0.942102 | − | 0.335327i | \(-0.108847\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 7168.00i | 1.78122i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 3104.00 | 0.753394 | 0.376697 | − | 0.926337i | \(-0.377060\pi\) | ||||
0.376697 | + | 0.926337i | \(0.377060\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − 3471.23i | − 0.832786i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −4741.19 | −1.11161 | −0.555806 | − | 0.831312i | \(-0.687590\pi\) | ||||
−0.555806 | + | 0.831312i | \(0.687590\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1596.00 | −0.369968 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 4350.00i | 0.985963i | 0.870040 | + | 0.492982i | \(0.164093\pi\) | ||||
−0.870040 | + | 0.492982i | \(0.835907\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1079.47 | −0.241967 | −0.120983 | − | 0.992655i | \(-0.538605\pi\) | ||||
−0.120983 | + | 0.992655i | \(0.538605\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 3767.55i | 0.826152i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − 7532.00i | − 1.63377i | −0.576801 | − | 0.816885i | \(-0.695699\pi\) | ||||
0.576801 | − | 0.816885i | \(-0.304301\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1824.00 | 0.387227 | 0.193613 | − | 0.981078i | \(-0.437979\pi\) | ||||
0.193613 | + | 0.981078i | \(0.437979\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 8805.06i | 1.84949i | 0.380584 | + | 0.924746i | \(0.375723\pi\) | ||||
−0.380584 | + | 0.924746i | \(0.624277\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 6603.80 | 1.35822 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −4849.00 | −0.986973 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 858.000i | 0.171075i | 0.996335 | + | 0.0855374i | \(0.0272607\pi\) | ||||
−0.996335 | + | 0.0855374i | \(0.972739\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1523.95 | 0.300773 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − 3386.56i | − 0.655016i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 8960.00i | 1.71577i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −792.000 | −0.148688 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 1523.95i | 0.283311i | 0.989916 | + | 0.141656i | \(0.0452426\pi\) | ||||
−0.989916 | + | 0.141656i | \(0.954757\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 4402.53 | 0.802716 | 0.401358 | − | 0.915921i | \(-0.368538\pi\) | ||||
0.401358 | + | 0.915921i | \(0.368538\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −118.000 | −0.0213091 | −0.0106546 | − | 0.999943i | \(-0.503392\pi\) | ||||
−0.0106546 | + | 0.999943i | \(0.503392\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − 4594.00i | − 0.813958i | −0.913437 | − | 0.406979i | \(-0.866582\pi\) | ||||
0.913437 | − | 0.406979i | \(-0.133418\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1947.27 | −0.341775 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 677.312i | 0.116677i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − 1780.00i | − 0.303805i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −3584.00 | −0.600585 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 3725.22i | 0.618600i | 0.950965 | + | 0.309300i | \(0.100095\pi\) | ||||
−0.950965 | + | 0.309300i | \(0.899905\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 3047.91 | 0.497089 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1166.00 | 0.188475 | 0.0942375 | − | 0.995550i | \(-0.469959\pi\) | ||||
0.0942375 | + | 0.995550i | \(0.469959\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − 896.000i | − 0.142291i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −5037.51 | −0.793003 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 11302.6i | 1.74858i | 0.485402 | + | 0.874291i | \(0.338673\pi\) | ||||
−0.485402 | + | 0.874291i | \(0.661327\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 6388.00i | 0.979776i | 0.871785 | + | 0.489888i | \(0.162962\pi\) | ||||
−0.871785 | + | 0.489888i | \(0.837038\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −8432.00 | −1.27136 | −0.635680 | − | 0.771953i | \(-0.719280\pi\) | ||||
−0.635680 | + | 0.771953i | \(0.719280\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − 4063.87i | − 0.607572i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −2031.94 | −0.298723 | −0.149361 | − | 0.988783i | \(-0.547722\pi\) | ||||
−0.149361 | + | 0.988783i | \(0.547722\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −309.000 | −0.0450503 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − 1476.00i | − 0.211664i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 5397.33 | 0.767680 | 0.383840 | − | 0.923400i | \(-0.374601\pi\) | ||||
0.383840 | + | 0.923400i | \(0.374601\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 5630.16i | 0.787879i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − 8276.00i | − 1.14883i | −0.818563 | − | 0.574417i | \(-0.805229\pi\) | ||||
0.818563 | − | 0.574417i | \(-0.194771\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 920.000 | 0.125683 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − 13800.2i | − 1.87037i | −0.354158 | − | 0.935186i | \(-0.615233\pi\) | ||||
0.354158 | − | 0.935186i | \(-0.384767\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −1862.61 | −0.248498 | −0.124249 | − | 0.992251i | \(-0.539652\pi\) | ||||
−0.124249 | + | 0.992251i | \(0.539652\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −5376.00 | −0.711653 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − 6170.00i | − 0.804194i | −0.915597 | − | 0.402097i | \(-0.868281\pi\) | ||||
0.915597 | − | 0.402097i | \(-0.131719\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1354.62 | −0.175208 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 1396.96i | 0.177946i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 8644.00i | 1.09277i | 0.837534 | + | 0.546385i | \(0.183997\pi\) | ||||
−0.837534 | + | 0.546385i | \(0.816003\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −8152.00 | −1.01519 | −0.507595 | − | 0.861596i | \(-0.669465\pi\) | ||||
−0.507595 | + | 0.861596i | \(0.669465\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 423.320i | 0.0523253i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 6942.45 | 0.845515 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −874.000 | −0.105664 | −0.0528319 | − | 0.998603i | \(-0.516825\pi\) | ||||
−0.0528319 | + | 0.998603i | \(0.516825\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − 5376.00i | − 0.640522i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 5841.82 | 0.690997 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − 14265.9i | − 1.66333i | −0.555279 | − | 0.831664i | \(-0.687389\pi\) | ||||
0.555279 | − | 0.831664i | \(-0.312611\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − 11564.0i | − 1.33871i | −0.742945 | − | 0.669353i | \(-0.766572\pi\) | ||||
0.742945 | − | 0.669353i | \(-0.233428\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −712.000 | −0.0812637 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 2793.91i | 0.316644i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −7619.76 | −0.851580 | −0.425790 | − | 0.904822i | \(-0.640004\pi\) | ||||
−0.425790 | + | 0.904822i | \(0.640004\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 7550.00 | 0.837944 | 0.418972 | − | 0.907999i | \(-0.362391\pi\) | ||||
0.418972 | + | 0.907999i | \(0.362391\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − 14336.0i | − 1.56930i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 17335.0 | 1.88463 | 0.942315 | − | 0.334727i | \(-0.108644\pi\) | ||||
0.942315 | + | 0.334727i | \(0.108644\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − 9016.72i | − 0.967037i | −0.875334 | − | 0.483518i | \(-0.839359\pi\) | ||||
0.875334 | − | 0.483518i | \(-0.160641\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 8352.00i | 0.889714i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −6568.00 | −0.690341 | −0.345170 | − | 0.938540i | \(-0.612179\pi\) | ||||
−0.345170 | + | 0.938540i | \(0.612179\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 13207.6i | 1.37898i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 2539.92 | 0.261700 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 9478.00 | 0.970158 | 0.485079 | − | 0.874470i | \(-0.338791\pi\) | ||||
0.485079 | + | 0.874470i | \(0.338791\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − 12606.0i | − 1.27358i | −0.771038 | − | 0.636790i | \(-0.780262\pi\) | ||||
0.771038 | − | 0.636790i | \(-0.219738\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −14371.7 | −1.44257 | −0.721286 | − | 0.692638i | \(-0.756448\pi\) | ||||
−0.721286 | + | 0.692638i | \(0.756448\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 4698.85i | 0.465604i | 0.972524 | + | 0.232802i | \(0.0747894\pi\) | ||||
−0.972524 | + | 0.232802i | \(0.925211\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − 10752.0i | − 1.05860i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −17920.0 | −1.74199 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − 7535.10i | − 0.727861i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −10837.0 | −1.03373 | −0.516863 | − | 0.856068i | \(-0.672900\pi\) | ||||
−0.516863 | + | 0.856068i | \(0.672900\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −3280.00 | −0.310925 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − 1812.00i | − 0.169647i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −13355.8 | −1.24272 | −0.621362 | − | 0.783523i | \(-0.713420\pi\) | ||||
−0.621362 | + | 0.783523i | \(0.713420\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − 13715.6i | − 1.26064i | −0.776335 | − | 0.630321i | \(-0.782923\pi\) | ||||
0.776335 | − | 0.630321i | \(-0.217077\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − 368.000i | − 0.0336184i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −14336.0 | −1.29388 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 6773.12i | 0.607629i | 0.952731 | + | 0.303814i | \(0.0982602\pi\) | ||||
−0.952731 | + | 0.303814i | \(0.901740\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −11175.7 | −0.990652 | −0.495326 | − | 0.868707i | \(-0.664951\pi\) | ||||
−0.495326 | + | 0.868707i | \(0.664951\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −8796.00 | −0.775083 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − 13458.0i | − 1.17194i | −0.810334 | − | 0.585968i | \(-0.800714\pi\) | ||||
0.810334 | − | 0.585968i | \(-0.199286\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −5206.84 | −0.450757 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 7492.77i | 0.641108i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − 7168.00i | − 0.609765i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −5352.00 | −0.450049 | −0.225024 | − | 0.974353i | \(-0.572246\pi\) | ||||
−0.225024 | + | 0.974353i | \(0.572246\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − 6011.15i | − 0.502580i | −0.967912 | − | 0.251290i | \(-0.919145\pi\) | ||||
0.967912 | − | 0.251290i | \(-0.0808547\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 169.328 | 0.0139963 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 16505.0 | 1.35654 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − 6240.00i | − 0.507100i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −2539.92 | −0.205253 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 4444.86i | 0.355202i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 2396.00i | 0.190411i | 0.995458 | + | 0.0952053i | \(0.0303507\pi\) | ||||
−0.995458 | + | 0.0952053i | \(0.969649\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −9384.00 | −0.737553 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − 1269.96i | − 0.0992680i | −0.998767 | − | 0.0496340i | \(-0.984195\pi\) | ||||
0.998767 | − | 0.0496340i | \(-0.0158055\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 3894.55 | 0.301113 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 4928.00 | 0.378951 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − 254.000i | − 0.0193219i | −0.999953 | − | 0.00966097i | \(-0.996925\pi\) | ||||
0.999953 | − | 0.00966097i | \(-0.00307523\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 8466.40 | 0.640592 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − 10032.7i | − 0.751026i | −0.926817 | − | 0.375513i | \(-0.877467\pi\) | ||||
0.926817 | − | 0.375513i | \(-0.122533\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 9312.00i | 0.693378i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −9320.00 | −0.686669 | −0.343335 | − | 0.939213i | \(-0.611556\pi\) | ||||
−0.343335 | + | 0.939213i | \(0.611556\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 13376.9i | 0.980397i | 0.871611 | + | 0.490198i | \(0.163076\pi\) | ||||
−0.871611 | + | 0.490198i | \(0.836924\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 15070.2 | 1.09299 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −13758.0 | −0.992640 | −0.496320 | − | 0.868140i | \(-0.665316\pi\) | ||||
−0.496320 | + | 0.868140i | \(0.665316\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − 20608.0i | − 1.47154i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −11260.3 | −0.799922 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 26076.5i | 1.83355i | 0.399405 | + | 0.916775i | \(0.369217\pi\) | ||||
−0.399405 | + | 0.916775i | \(0.630783\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1792.00i | 0.125362i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 4080.00 | 0.282539 | 0.141269 | − | 0.989971i | \(-0.454882\pi\) | ||||
0.141269 | + | 0.989971i | \(0.454882\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − 1015.97i | − 0.0700011i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −15747.5 | −1.07417 | −0.537083 | − | 0.843529i | \(-0.680474\pi\) | ||||
−0.537083 | + | 0.843529i | \(0.680474\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −10298.0 | −0.698942 | −0.349471 | − | 0.936947i | \(-0.613639\pi\) | ||||
−0.349471 | + | 0.936947i | \(0.613639\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | − 2766.00i | − 0.185874i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 23219.1 | 1.55261 | 0.776305 | − | 0.630357i | \(-0.217091\pi\) | ||||
0.776305 | + | 0.630357i | \(0.217091\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 3386.56i | 0.224232i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − 5652.00i | − 0.372402i | −0.982512 | − | 0.186201i | \(-0.940383\pi\) | ||||
0.982512 | − | 0.186201i | \(-0.0596175\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −26848.0 | −1.75180 | −0.875899 | − | 0.482494i | \(-0.839731\pi\) | ||||
−0.875899 | + | 0.482494i | \(0.839731\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − 3725.22i | − 0.241889i | −0.992659 | − | 0.120944i | \(-0.961408\pi\) | ||||
0.992659 | − | 0.120944i | \(-0.0385923\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 29463.1 | 1.89472 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 3421.00 | 0.218944 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 1312.00i | 0.0831683i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 27452.3 | 1.73195 | 0.865974 | − | 0.500089i | \(-0.166699\pi\) | ||||
0.865974 | + | 0.500089i | \(0.166699\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | − 5968.81i | − 0.373016i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − 2100.00i | − 0.130620i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −6024.00 | −0.371191 | −0.185596 | − | 0.982626i | \(-0.559421\pi\) | ||||
−0.185596 | + | 0.982626i | \(0.559421\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − 24637.2i | − 1.51104i | −0.655126 | − | 0.755519i | \(-0.727385\pi\) | ||||
0.655126 | − | 0.755519i | \(-0.272615\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 20827.4 | 1.26555 | 0.632773 | − | 0.774338i | \(-0.281917\pi\) | ||||
0.632773 | + | 0.774338i | \(0.281917\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 10752.0 | 0.650313 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − 29054.0i | − 1.74115i | −0.492036 | − | 0.870575i | \(-0.663747\pi\) | ||||
0.492036 | − | 0.870575i | \(-0.336253\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −15239.5 | −0.909096 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − 3047.91i | − 0.180166i | −0.995934 | − | 0.0900831i | \(-0.971287\pi\) | ||||
0.995934 | − | 0.0900831i | \(-0.0287133\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 9628.00i | 0.566544i | 0.959040 | + | 0.283272i | \(0.0914200\pi\) | ||||
−0.959040 | + | 0.283272i | \(0.908580\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 10752.0 | 0.626984 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 7789.09i | 0.452166i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −5587.83 | −0.321484 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −28690.0 | −1.64327 | −0.821633 | − | 0.570017i | \(-0.806937\pi\) | ||||
−0.821633 | + | 0.570017i | \(0.806937\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − 4922.00i | − 0.279421i | −0.990192 | − | 0.139710i | \(-0.955383\pi\) | ||||
0.990192 | − | 0.139710i | \(-0.0446171\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −6392.14 | −0.361278 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 42.3320i | 0.00237158i | 0.999999 | + | 0.00118579i | \(0.000377449\pi\) | ||||
−0.999999 | + | 0.00118579i | \(0.999623\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 11952.0i | 0.666661i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 5320.00 | 0.294159 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − 18372.1i | − 1.01144i | −0.862697 | − | 0.505722i | \(-0.831226\pi\) | ||||
0.862697 | − | 0.505722i | \(-0.168774\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 7111.78 | 0.388151 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −2496.00 | −0.135642 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 19310.0i | 1.04041i | 0.854041 | + | 0.520206i | \(0.174145\pi\) | ||||
−0.854041 | + | 0.520206i | \(0.825855\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −13884.9 | −0.744920 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 31029.4i | 1.65061i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 18820.0i | 0.996897i | 0.866919 | + | 0.498448i | \(0.166097\pi\) | ||||
−0.866919 | + | 0.498448i | \(0.833903\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −3584.00 | −0.188249 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 5079.84i | 0.265700i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −27431.1 | −1.42282 | −0.711411 | − | 0.702776i | \(-0.751944\pi\) | ||||
−0.711411 | + | 0.702776i | \(0.751944\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 26432.0 | 1.36530 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 4094.00i | 0.209720i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −10561.8 | −0.538813 | −0.269406 | − | 0.963027i | \(-0.586827\pi\) | ||||
−0.269406 | + | 0.963027i | \(0.586827\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − 3386.56i | − 0.171350i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − 16468.0i | − 0.829822i | −0.909862 | − | 0.414911i | \(-0.863813\pi\) | ||||
0.909862 | − | 0.414911i | \(-0.136187\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 21504.0 | 1.07478 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 15070.2i | 0.750157i | 0.926993 | + | 0.375079i | \(0.122384\pi\) | ||||
−0.926993 | + | 0.375079i | \(0.877616\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −34373.6 | −1.69723 | −0.848617 | − | 0.529007i | \(-0.822564\pi\) | ||||
−0.848617 | + | 0.529007i | \(0.822564\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −11844.0 | −0.582457 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 8960.00i | 0.437105i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1756.78 | 0.0853605 | 0.0426803 | − | 0.999089i | \(-0.486410\pi\) | ||||
0.0426803 | + | 0.999089i | \(0.486410\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − 18668.4i | − 0.899885i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1572.00i | 0.0754760i | 0.999288 | + | 0.0377380i | \(0.0120152\pi\) | ||||
−0.999288 | + | 0.0377380i | \(0.987985\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −17816.0 | −0.848659 | −0.424329 | − | 0.905508i | \(-0.639490\pi\) | ||||
−0.424329 | + | 0.905508i | \(0.639490\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 33103.6i | 1.57068i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −5079.84 | −0.239143 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −21746.0 | −1.01974 | −0.509870 | − | 0.860251i | \(-0.670307\pi\) | ||||
−0.509870 | + | 0.860251i | \(0.670307\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 13978.0i | 0.650393i | 0.945646 | + | 0.325196i | \(0.105430\pi\) | ||||
−0.945646 | + | 0.325196i | \(0.894570\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −1883.77 | −0.0873125 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − 26415.2i | − 1.21492i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − 28672.0i | − 1.31366i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −10776.0 | −0.489952 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 1777.94i | 0.0805297i | 0.999189 | + | 0.0402649i | \(0.0128202\pi\) | ||||
−0.999189 | + | 0.0402649i | \(0.987180\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 32849.6 | 1.47661 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 2640.00 | 0.118221 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 9650.00i | 0.428884i | 0.976737 | + | 0.214442i | \(0.0687933\pi\) | ||||
−0.976737 | + | 0.214442i | \(0.931207\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1354.62 | 0.0599789 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − 10413.7i | − 0.457647i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 21504.0i | 0.941511i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 38024.0 | 1.65248 | 0.826238 | − | 0.563322i | \(-0.190477\pi\) | ||||
0.826238 | + | 0.563322i | \(0.190477\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 931.304i | 0.0403237i | 0.999797 | + | 0.0201619i | \(0.00641815\pi\) | ||||
−0.999797 | + | 0.0201619i | \(0.993582\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −15747.5 | −0.676824 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 35840.0 | 1.53474 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 6858.00i | 0.291530i | 0.989319 | + | 0.145765i | \(0.0465643\pi\) | ||||
−0.989319 | + | 0.145765i | \(0.953436\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 18816.6 | 0.796968 | 0.398484 | − | 0.917175i | \(-0.369536\pi\) | ||||
0.398484 | + | 0.917175i | \(0.369536\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − 8212.41i | − 0.345313i | −0.984982 | − | 0.172656i | \(-0.944765\pi\) | ||||
0.984982 | − | 0.172656i | \(-0.0552350\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − 25124.0i | − 1.05258i | −0.850304 | − | 0.526292i | \(-0.823582\pi\) | ||||
0.850304 | − | 0.526292i | \(-0.176418\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −840.000 | −0.0349391 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 21335.3i | 0.884239i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −6095.81 | −0.250835 | −0.125418 | − | 0.992104i | \(-0.540027\pi\) | ||||
−0.125418 | + | 0.992104i | \(0.540027\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 22273.0 | 0.913240 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 10782.0i | 0.438949i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −9757.53 | −0.395836 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − 27769.8i | − 1.11861i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 32812.0i | 1.31707i | 0.752550 | + | 0.658535i | \(0.228824\pi\) | ||||
−0.752550 | + | 0.658535i | \(0.771176\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 21944.0 | 0.874671 | 0.437335 | − | 0.899299i | \(-0.355922\pi\) | ||||
0.437335 | + | 0.899299i | \(0.355922\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − 48173.8i | − 1.91347i | −0.290962 | − | 0.956735i | \(-0.593975\pi\) | ||||
0.290962 | − | 0.956735i | \(-0.406025\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −12361.0 | −0.487569 | −0.243784 | − | 0.969829i | \(-0.578389\pi\) | ||||
−0.243784 | + | 0.969829i | \(0.578389\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −25740.0 | −1.01178 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 9856.00i | 0.384743i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −10159.7 | −0.395233 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 27177.2i | 1.05001i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − 33212.0i | − 1.27878i | −0.768883 | − | 0.639390i | \(-0.779187\pi\) | ||||
0.768883 | − | 0.639390i | \(-0.220813\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 34336.0 | 1.31306 | 0.656532 | − | 0.754298i | \(-0.272023\pi\) | ||||
0.656532 | + | 0.754298i | \(0.272023\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − 16678.8i | − 0.635659i | −0.948148 | − | 0.317829i | \(-0.897046\pi\) | ||||
0.948148 | − | 0.317829i | \(-0.102954\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 5079.84 | 0.192294 | 0.0961468 | − | 0.995367i | \(-0.469348\pi\) | ||||
0.0961468 | + | 0.995367i | \(0.469348\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −21056.0 | −0.794371 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 14336.0i | 0.537218i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 9651.70 | 0.360470 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − 973.636i | − 0.0361208i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − 2128.00i | − 0.0786836i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 19176.0 | 0.704345 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − 13292.3i | − 0.486617i | −0.969949 | − | 0.243309i | \(-0.921767\pi\) | ||||
0.969949 | − | 0.243309i | \(-0.0782328\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 2539.92 | 0.0923725 | 0.0461862 | − | 0.998933i | \(-0.485293\pi\) | ||||
0.0461862 | + | 0.998933i | \(0.485293\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 41216.0 | 1.49403 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 53760.0i | 1.93600i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −35368.4 | −1.26953 | −0.634764 | − | 0.772706i | \(-0.718903\pi\) | ||||
−0.634764 | + | 0.772706i | \(0.718903\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 13546.2i | 0.483077i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − 14596.0i | − 0.518825i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 17576.0 | 0.620721 | 0.310361 | − | 0.950619i | \(-0.399550\pi\) | ||||
0.310361 | + | 0.950619i | \(0.399550\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − 8889.72i | − 0.312942i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 2031.94 | 0.0710711 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 21526.0 | 0.750506 | 0.375253 | − | 0.926923i | \(-0.377556\pi\) | ||||
0.375253 | + | 0.926923i | \(0.377556\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 5218.00i | 0.180767i | 0.995907 | + | 0.0903836i | \(0.0288093\pi\) | ||||
−0.995907 | + | 0.0903836i | \(0.971191\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 52830.4 | 1.82438 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 29717.1i | 1.01972i | 0.860257 | + | 0.509860i | \(0.170303\pi\) | ||||
−0.860257 | + | 0.509860i | \(0.829697\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 4920.00i | 0.168293i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 48888.0 | 1.66174 | 0.830870 | − | 0.556467i | \(-0.187843\pi\) | ||||
0.830870 | + | 0.556467i | \(0.187843\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − 19303.4i | − 0.654077i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 42162.7 | 1.41971 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −29343.0 | −0.984962 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 2772.00i | 0.0924703i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 42988.2 | 1.42958 | 0.714791 | − | 0.699338i | \(-0.246522\pi\) | ||||
0.714791 | + | 0.699338i | \(0.246522\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 12403.3i | 0.409928i | 0.978769 | + | 0.204964i | \(0.0657078\pi\) | ||||
−0.978769 | + | 0.204964i | \(0.934292\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − 25088.0i | − 0.826603i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −2040.00 | −0.0668018 | −0.0334009 | − | 0.999442i | \(-0.510634\pi\) | ||||
−0.0334009 | + | 0.999442i | \(0.510634\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 58926.2i | 1.92369i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −20658.0 | −0.670284 | −0.335142 | − | 0.942168i | \(-0.608784\pi\) | ||||
−0.335142 | + | 0.942168i | \(0.608784\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −23004.0 | −0.744130 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 71680.0i | 2.30464i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −10773.5 | −0.345340 | −0.172670 | − | 0.984980i | \(-0.555239\pi\) | ||||
−0.172670 | + | 0.984980i | \(0.555239\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 22732.3i | 0.724284i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 62044.0i | 1.97087i | 0.170065 | + | 0.985433i | \(0.445602\pi\) | ||||
−0.170065 | + | 0.985433i | \(0.554398\pi\) | |||||||
\(998\) | 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 | 1152.4.d.k.577.4 | yes | 4 | |
3.2 | odd | 2 | 1152.4.d.m.577.2 | yes | 4 | ||
4.3 | odd | 2 | inner | 1152.4.d.k.577.3 | yes | 4 | |
8.3 | odd | 2 | inner | 1152.4.d.k.577.1 | ✓ | 4 | |
8.5 | even | 2 | inner | 1152.4.d.k.577.2 | yes | 4 | |
12.11 | even | 2 | 1152.4.d.m.577.1 | yes | 4 | ||
16.3 | odd | 4 | 2304.4.a.bs.1.2 | 2 | |||
16.5 | even | 4 | 2304.4.a.q.1.1 | 2 | |||
16.11 | odd | 4 | 2304.4.a.q.1.2 | 2 | |||
16.13 | even | 4 | 2304.4.a.bs.1.1 | 2 | |||
24.5 | odd | 2 | 1152.4.d.m.577.4 | yes | 4 | ||
24.11 | even | 2 | 1152.4.d.m.577.3 | yes | 4 | ||
48.5 | odd | 4 | 2304.4.a.br.1.1 | 2 | |||
48.11 | even | 4 | 2304.4.a.br.1.2 | 2 | |||
48.29 | odd | 4 | 2304.4.a.r.1.1 | 2 | |||
48.35 | even | 4 | 2304.4.a.r.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1152.4.d.k.577.1 | ✓ | 4 | 8.3 | odd | 2 | inner | |
1152.4.d.k.577.2 | yes | 4 | 8.5 | even | 2 | inner | |
1152.4.d.k.577.3 | yes | 4 | 4.3 | odd | 2 | inner | |
1152.4.d.k.577.4 | yes | 4 | 1.1 | even | 1 | trivial | |
1152.4.d.m.577.1 | yes | 4 | 12.11 | even | 2 | ||
1152.4.d.m.577.2 | yes | 4 | 3.2 | odd | 2 | ||
1152.4.d.m.577.3 | yes | 4 | 24.11 | even | 2 | ||
1152.4.d.m.577.4 | yes | 4 | 24.5 | odd | 2 | ||
2304.4.a.q.1.1 | 2 | 16.5 | even | 4 | |||
2304.4.a.q.1.2 | 2 | 16.11 | odd | 4 | |||
2304.4.a.r.1.1 | 2 | 48.29 | odd | 4 | |||
2304.4.a.r.1.2 | 2 | 48.35 | even | 4 | |||
2304.4.a.br.1.1 | 2 | 48.5 | odd | 4 | |||
2304.4.a.br.1.2 | 2 | 48.11 | even | 4 | |||
2304.4.a.bs.1.1 | 2 | 16.13 | even | 4 | |||
2304.4.a.bs.1.2 | 2 | 16.3 | odd | 4 |