Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2304,4,Mod(1,2304)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2304, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2304.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2304 = 2^{8} \cdot 3^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 2304.a (trivial) |
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: | yes |
Analytic conductor: | \(135.940400653\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{7}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - 7 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{3} \) |
Twist minimal: | no (minimal twist has level 1152) |
Fricke sign: | \(+1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(2.64575\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2304.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
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 | ||||||||
\(5\) | 6.00000 | 0.536656 | 0.268328 | − | 0.963328i | \(-0.413529\pi\) | ||||
0.268328 | + | 0.963328i | \(0.413529\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −21.1660 | −1.14286 | −0.571429 | − | 0.820652i | \(-0.693611\pi\) | ||||
−0.571429 | + | 0.820652i | \(0.693611\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 42.3320 | 1.16033 | 0.580163 | − | 0.814500i | \(-0.302989\pi\) | ||||
0.580163 | + | 0.814500i | \(0.302989\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −20.0000 | −0.426692 | −0.213346 | − | 0.976977i | \(-0.568436\pi\) | ||||
−0.213346 | + | 0.976977i | \(0.568436\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 8.00000 | 0.114134 | 0.0570672 | − | 0.998370i | \(-0.481825\pi\) | ||||
0.0570672 | + | 0.998370i | \(0.481825\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −84.6640 | −1.02228 | −0.511139 | − | 0.859498i | \(-0.670776\pi\) | ||||
−0.511139 | + | 0.859498i | \(0.670776\pi\) | |||||||
\(20\) | 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 | ||||||||
\(29\) | −46.0000 | −0.294551 | −0.147276 | − | 0.989095i | \(-0.547050\pi\) | ||||
−0.147276 | + | 0.989095i | \(0.547050\pi\) | |||||||
\(30\) | 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 | ||||||||
\(35\) | −126.996 | −0.613322 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 164.000 | 0.728687 | 0.364344 | − | 0.931265i | \(-0.381293\pi\) | ||||
0.364344 | + | 0.931265i | \(0.381293\pi\) | |||||||
\(38\) | 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 | ||||||||
\(43\) | −423.320 | −1.50130 | −0.750648 | − | 0.660702i | \(-0.770259\pi\) | ||||
−0.750648 | + | 0.660702i | \(0.770259\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 169.328 | 0.525511 | 0.262756 | − | 0.964862i | \(-0.415369\pi\) | ||||
0.262756 | + | 0.964862i | \(0.415369\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 105.000 | 0.306122 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 266.000 | 0.689395 | 0.344697 | − | 0.938714i | \(-0.387982\pi\) | ||||
0.344697 | + | 0.938714i | \(0.387982\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 253.992 | 0.622696 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −253.992 | −0.560457 | −0.280228 | − | 0.959933i | \(-0.590410\pi\) | ||||
−0.280228 | + | 0.959933i | \(0.590410\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 132.000 | 0.277063 | 0.138532 | − | 0.990358i | \(-0.455762\pi\) | ||||
0.138532 | + | 0.990358i | \(0.455762\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −120.000 | −0.228987 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −507.984 | −0.926271 | −0.463135 | − | 0.886287i | \(-0.653276\pi\) | ||||
−0.463135 | + | 0.886287i | \(0.653276\pi\) | |||||||
\(68\) | 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 | \(-0.436813\pi\) | ||||
0.197206 | + | 0.980362i | \(0.436813\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −896.000 | −1.32609 | ||||||||
\(78\) | 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 | ||||||||
\(83\) | 973.636 | 1.28760 | 0.643798 | − | 0.765195i | \(-0.277358\pi\) | ||||
0.643798 | + | 0.765195i | \(0.277358\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 48.0000 | 0.0612510 | ||||||||
\(86\) | 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 | ||||||||
\(91\) | 423.320 | 0.487649 | ||||||||
\(92\) | 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 | ||||||||
\(101\) | 1466.00 | 1.44428 | 0.722141 | − | 0.691746i | \(-0.243158\pi\) | ||||
0.722141 | + | 0.691746i | \(0.243158\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1248.79 | −1.19463 | −0.597317 | − | 0.802005i | \(-0.703767\pi\) | ||||
−0.597317 | + | 0.802005i | \(0.703767\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 423.320 | 0.382466 | 0.191233 | − | 0.981545i | \(-0.438751\pi\) | ||||
0.191233 | + | 0.981545i | \(0.438751\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1564.00 | 1.37435 | 0.687174 | − | 0.726492i | \(-0.258851\pi\) | ||||
0.687174 | + | 0.726492i | \(0.258851\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −1552.00 | −1.29203 | −0.646017 | − | 0.763323i | \(-0.723567\pi\) | ||||
−0.646017 | + | 0.763323i | \(0.723567\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1015.97 | 0.823822 | ||||||||
\(116\) | 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 | ||||||||
\(125\) | −1284.00 | −0.918756 | ||||||||
\(126\) | 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 | ||||||||
\(131\) | −2539.92 | −1.69400 | −0.847000 | − | 0.531593i | \(-0.821594\pi\) | ||||
−0.847000 | + | 0.531593i | \(0.821594\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1792.00 | 1.16832 | ||||||||
\(134\) | 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 | ||||||||
\(139\) | 1185.30 | 0.723277 | 0.361639 | − | 0.932318i | \(-0.382217\pi\) | ||||
0.361639 | + | 0.932318i | \(0.382217\pi\) | |||||||
\(140\) | 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 | ||||||||
\(149\) | 1974.00 | 1.08534 | 0.542672 | − | 0.839944i | \(-0.317413\pi\) | ||||
0.542672 | + | 0.839944i | \(0.317413\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 3111.40 | 1.67684 | 0.838419 | − | 0.545027i | \(-0.183481\pi\) | ||||
0.838419 | + | 0.545027i | \(0.183481\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −126.996 | −0.0658101 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1796.00 | 0.912971 | 0.456485 | − | 0.889731i | \(-0.349108\pi\) | ||||
0.456485 | + | 0.889731i | \(0.349108\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −3584.00 | −1.75440 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 2624.59 | 1.26119 | 0.630593 | − | 0.776114i | \(-0.282812\pi\) | ||||
0.630593 | + | 0.776114i | \(0.282812\pi\) | |||||||
\(164\) | 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 | ||||||||
\(173\) | −4290.00 | −1.88533 | −0.942667 | − | 0.333736i | \(-0.891691\pi\) | ||||
−0.942667 | + | 0.333736i | \(0.891691\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1883.77 | 0.813714 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 1608.62 | 0.671696 | 0.335848 | − | 0.941916i | \(-0.390977\pi\) | ||||
0.335848 | + | 0.941916i | \(0.390977\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 3196.00 | 1.31247 | 0.656234 | − | 0.754557i | \(-0.272148\pi\) | ||||
0.656234 | + | 0.754557i | \(0.272148\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 984.000 | 0.391055 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 338.656 | 0.132433 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 3217.23 | 1.21880 | 0.609400 | − | 0.792863i | \(-0.291410\pi\) | ||||
0.609400 | + | 0.792863i | \(0.291410\pi\) | |||||||
\(192\) | 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 | ||||||||
\(197\) | 3834.00 | 1.38661 | 0.693303 | − | 0.720647i | \(-0.256155\pi\) | ||||
0.693303 | + | 0.720647i | \(0.256155\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −3788.72 | −1.34962 | −0.674811 | − | 0.737990i | \(-0.735775\pi\) | ||||
−0.674811 | + | 0.737990i | \(0.735775\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 973.636 | 0.336630 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1872.00 | 0.637786 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −3584.00 | −1.18617 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −2878.58 | −0.939192 | −0.469596 | − | 0.882882i | \(-0.655600\pi\) | ||||
−0.469596 | + | 0.882882i | \(0.655600\pi\) | |||||||
\(212\) | 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 | ||||||||
\(221\) | −160.000 | −0.0487003 | ||||||||
\(222\) | 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 | ||||||||
\(227\) | 3259.57 | 0.953062 | 0.476531 | − | 0.879158i | \(-0.341894\pi\) | ||||
0.476531 | + | 0.879158i | \(0.341894\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 5260.00 | 1.51786 | 0.758931 | − | 0.651171i | \(-0.225722\pi\) | ||||
0.758931 | + | 0.651171i | \(0.225722\pi\) | |||||||
\(230\) | 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 | ||||||||
\(235\) | 1015.97 | 0.282019 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 1523.95 | 0.412453 | 0.206227 | − | 0.978504i | \(-0.433882\pi\) | ||||
0.206227 | + | 0.978504i | \(0.433882\pi\) | |||||||
\(240\) | 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 | ||||||||
\(245\) | 630.000 | 0.164283 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1693.28 | 0.436198 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −2666.92 | −0.670655 | −0.335327 | − | 0.942102i | \(-0.608847\pi\) | ||||
−0.335327 | + | 0.942102i | \(0.608847\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 7168.00 | 1.78122 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −3104.00 | −0.753394 | −0.376697 | − | 0.926337i | \(-0.622940\pi\) | ||||
−0.376697 | + | 0.926337i | \(0.622940\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −3471.23 | −0.832786 | ||||||||
\(260\) | 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 | ||||||||
\(269\) | −4350.00 | −0.985963 | −0.492982 | − | 0.870040i | \(-0.664093\pi\) | ||||
−0.492982 | + | 0.870040i | \(0.664093\pi\) | |||||||
\(270\) | 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 | ||||||||
\(275\) | −3767.55 | −0.826152 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 7532.00 | 1.63377 | 0.816885 | − | 0.576801i | \(-0.195699\pi\) | ||||
0.816885 | + | 0.576801i | \(0.195699\pi\) | |||||||
\(278\) | 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 | ||||||||
\(283\) | −8805.06 | −1.84949 | −0.924746 | − | 0.380584i | \(-0.875723\pi\) | ||||
−0.924746 | + | 0.380584i | \(0.875723\pi\) | |||||||
\(284\) | 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 | ||||||||
\(293\) | 858.000 | 0.171075 | 0.0855374 | − | 0.996335i | \(-0.472739\pi\) | ||||
0.0855374 | + | 0.996335i | \(0.472739\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1523.95 | −0.300773 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −3386.56 | −0.655016 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 8960.00 | 1.71577 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 792.000 | 0.148688 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 1523.95 | 0.283311 | 0.141656 | − | 0.989916i | \(-0.454757\pi\) | ||||
0.141656 | + | 0.989916i | \(0.454757\pi\) | |||||||
\(308\) | 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 | \(-0.496608\pi\) | ||||
0.0106546 | + | 0.999943i | \(0.496608\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 4594.00 | 0.813958 | 0.406979 | − | 0.913437i | \(-0.366582\pi\) | ||||
0.406979 | + | 0.913437i | \(0.366582\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1947.27 | −0.341775 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −677.312 | −0.116677 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1780.00 | 0.303805 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −3584.00 | −0.600585 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −3725.22 | −0.618600 | −0.309300 | − | 0.950965i | \(-0.600095\pi\) | ||||
−0.309300 | + | 0.950965i | \(0.600095\pi\) | |||||||
\(332\) | 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 | ||||||||
\(341\) | −896.000 | −0.142291 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 5037.51 | 0.793003 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 11302.6 | 1.74858 | 0.874291 | − | 0.485402i | \(-0.161327\pi\) | ||||
0.874291 | + | 0.485402i | \(0.161327\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 6388.00 | 0.979776 | 0.489888 | − | 0.871785i | \(-0.337038\pi\) | ||||
0.489888 | + | 0.871785i | \(0.337038\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 8432.00 | 1.27136 | 0.635680 | − | 0.771953i | \(-0.280720\pi\) | ||||
0.635680 | + | 0.771953i | \(0.280720\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −4063.87 | −0.607572 | ||||||||
\(356\) | 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 | ||||||||
\(365\) | 1476.00 | 0.211664 | ||||||||
\(366\) | 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 | ||||||||
\(371\) | −5630.16 | −0.787879 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 8276.00 | 1.14883 | 0.574417 | − | 0.818563i | \(-0.305229\pi\) | ||||
0.574417 | + | 0.818563i | \(0.305229\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 920.000 | 0.125683 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 13800.2 | 1.87037 | 0.935186 | − | 0.354158i | \(-0.115233\pi\) | ||||
0.935186 | + | 0.354158i | \(0.115233\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 1862.61 | 0.248498 | 0.124249 | − | 0.992251i | \(-0.460348\pi\) | ||||
0.124249 | + | 0.992251i | \(0.460348\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −5376.00 | −0.711653 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −6170.00 | −0.804194 | −0.402097 | − | 0.915597i | \(-0.631719\pi\) | ||||
−0.402097 | + | 0.915597i | \(0.631719\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1354.62 | 0.175208 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 1396.96 | 0.177946 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 8644.00 | 1.09277 | 0.546385 | − | 0.837534i | \(-0.316003\pi\) | ||||
0.546385 | + | 0.837534i | \(0.316003\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 8152.00 | 1.01519 | 0.507595 | − | 0.861596i | \(-0.330535\pi\) | ||||
0.507595 | + | 0.861596i | \(0.330535\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 423.320 | 0.0523253 | ||||||||
\(404\) | 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 | \(-0.483175\pi\) | ||||
0.0528319 | + | 0.998603i | \(0.483175\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 5376.00 | 0.640522 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 5841.82 | 0.690997 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 14265.9 | 1.66333 | 0.831664 | − | 0.555279i | \(-0.187389\pi\) | ||||
0.831664 | + | 0.555279i | \(0.187389\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 11564.0 | 1.33871 | 0.669353 | − | 0.742945i | \(-0.266572\pi\) | ||||
0.669353 | + | 0.742945i | \(0.266572\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −712.000 | −0.0812637 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −2793.91 | −0.316644 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 7619.76 | 0.851580 | 0.425790 | − | 0.904822i | \(-0.359996\pi\) | ||||
0.425790 | + | 0.904822i | \(0.359996\pi\) | |||||||
\(432\) | 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 | ||||||||
\(437\) | −14336.0 | −1.56930 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −17335.0 | −1.88463 | −0.942315 | − | 0.334727i | \(-0.891356\pi\) | ||||
−0.942315 | + | 0.334727i | \(0.891356\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −9016.72 | −0.967037 | −0.483518 | − | 0.875334i | \(-0.660641\pi\) | ||||
−0.483518 | + | 0.875334i | \(0.660641\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 8352.00 | 0.889714 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 6568.00 | 0.690341 | 0.345170 | − | 0.938540i | \(-0.387821\pi\) | ||||
0.345170 | + | 0.938540i | \(0.387821\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 13207.6 | 1.37898 | ||||||||
\(452\) | 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 | \(-0.661209\pi\) | ||||
−0.485079 | + | 0.874470i | \(0.661209\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 12606.0 | 1.27358 | 0.636790 | − | 0.771038i | \(-0.280262\pi\) | ||||
0.636790 | + | 0.771038i | \(0.280262\pi\) | |||||||
\(462\) | 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 | ||||||||
\(467\) | −4698.85 | −0.465604 | −0.232802 | − | 0.972524i | \(-0.574789\pi\) | ||||
−0.232802 | + | 0.972524i | \(0.574789\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 10752.0 | 1.05860 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −17920.0 | −1.74199 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 7535.10 | 0.727861 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 10837.0 | 1.03373 | 0.516863 | − | 0.856068i | \(-0.327100\pi\) | ||||
0.516863 | + | 0.856068i | \(0.327100\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −3280.00 | −0.310925 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −1812.00 | −0.169647 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 13355.8 | 1.24272 | 0.621362 | − | 0.783523i | \(-0.286580\pi\) | ||||
0.621362 | + | 0.783523i | \(0.286580\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −13715.6 | −1.26064 | −0.630321 | − | 0.776335i | \(-0.717077\pi\) | ||||
−0.630321 | + | 0.776335i | \(0.717077\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −368.000 | −0.0336184 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 14336.0 | 1.29388 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 6773.12 | 0.607629 | 0.303814 | − | 0.952731i | \(-0.401740\pi\) | ||||
0.303814 | + | 0.952731i | \(0.401740\pi\) | |||||||
\(500\) | 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 | ||||||||
\(509\) | 13458.0 | 1.17194 | 0.585968 | − | 0.810334i | \(-0.300714\pi\) | ||||
0.585968 | + | 0.810334i | \(0.300714\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −5206.84 | −0.450757 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −7492.77 | −0.641108 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 7168.00 | 0.609765 | ||||||||
\(518\) | 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 | ||||||||
\(523\) | 6011.15 | 0.502580 | 0.251290 | − | 0.967912i | \(-0.419145\pi\) | ||||
0.251290 | + | 0.967912i | \(0.419145\pi\) | |||||||
\(524\) | 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 | ||||||||
\(533\) | −6240.00 | −0.507100 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 2539.92 | 0.205253 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 4444.86 | 0.355202 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 2396.00 | 0.190411 | 0.0952053 | − | 0.995458i | \(-0.469649\pi\) | ||||
0.0952053 | + | 0.995458i | \(0.469649\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 9384.00 | 0.737553 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −1269.96 | −0.0992680 | −0.0496340 | − | 0.998767i | \(-0.515805\pi\) | ||||
−0.0496340 | + | 0.998767i | \(0.515805\pi\) | |||||||
\(548\) | 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 | ||||||||
\(557\) | 254.000 | 0.0193219 | 0.00966097 | − | 0.999953i | \(-0.496925\pi\) | ||||
0.00966097 | + | 0.999953i | \(0.496925\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 8466.40 | 0.640592 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 10032.7 | 0.751026 | 0.375513 | − | 0.926817i | \(-0.377467\pi\) | ||||
0.375513 | + | 0.926817i | \(0.377467\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −9312.00 | −0.693378 | ||||||||
\(566\) | 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 | ||||||||
\(571\) | −13376.9 | −0.980397 | −0.490198 | − | 0.871611i | \(-0.663076\pi\) | ||||
−0.490198 | + | 0.871611i | \(0.663076\pi\) | |||||||
\(572\) | 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 | ||||||||
\(581\) | −20608.0 | −1.47154 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 11260.3 | 0.799922 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 26076.5 | 1.83355 | 0.916775 | − | 0.399405i | \(-0.130783\pi\) | ||||
0.916775 | + | 0.399405i | \(0.130783\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1792.00 | 0.125362 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −4080.00 | −0.282539 | −0.141269 | − | 0.989971i | \(-0.545118\pi\) | ||||
−0.141269 | + | 0.989971i | \(0.545118\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −1015.97 | −0.0700011 | ||||||||
\(596\) | 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 | \(-0.386361\pi\) | ||||
0.349471 | + | 0.936947i | \(0.386361\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 2766.00 | 0.185874 | ||||||||
\(606\) | 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 | ||||||||
\(611\) | −3386.56 | −0.224232 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 5652.00 | 0.372402 | 0.186201 | − | 0.982512i | \(-0.440383\pi\) | ||||
0.186201 | + | 0.982512i | \(0.440383\pi\) | |||||||
\(614\) | 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 | ||||||||
\(619\) | 3725.22 | 0.241889 | 0.120944 | − | 0.992659i | \(-0.461408\pi\) | ||||
0.120944 | + | 0.992659i | \(0.461408\pi\) | |||||||
\(620\) | 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 | ||||||||
\(629\) | 1312.00 | 0.0831683 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −27452.3 | −1.73195 | −0.865974 | − | 0.500089i | \(-0.833301\pi\) | ||||
−0.865974 | + | 0.500089i | \(0.833301\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −5968.81 | −0.373016 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −2100.00 | −0.130620 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 6024.00 | 0.371191 | 0.185596 | − | 0.982626i | \(-0.440579\pi\) | ||||
0.185596 | + | 0.982626i | \(0.440579\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −24637.2 | −1.51104 | −0.755519 | − | 0.655126i | \(-0.772615\pi\) | ||||
−0.755519 | + | 0.655126i | \(0.772615\pi\) | |||||||
\(644\) | 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 | ||||||||
\(653\) | 29054.0 | 1.74115 | 0.870575 | − | 0.492036i | \(-0.163747\pi\) | ||||
0.870575 | + | 0.492036i | \(0.163747\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −15239.5 | −0.909096 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 3047.91 | 0.180166 | 0.0900831 | − | 0.995934i | \(-0.471287\pi\) | ||||
0.0900831 | + | 0.995934i | \(0.471287\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −9628.00 | −0.566544 | −0.283272 | − | 0.959040i | \(-0.591420\pi\) | ||||
−0.283272 | + | 0.959040i | \(0.591420\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 10752.0 | 0.626984 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −7789.09 | −0.452166 | ||||||||
\(668\) | 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 | ||||||||
\(677\) | −4922.00 | −0.279421 | −0.139710 | − | 0.990192i | \(-0.544617\pi\) | ||||
−0.139710 | + | 0.990192i | \(0.544617\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 6392.14 | 0.361278 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 42.3320 | 0.00237158 | 0.00118579 | − | 0.999999i | \(-0.499623\pi\) | ||||
0.00118579 | + | 0.999999i | \(0.499623\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 11952.0 | 0.666661 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −5320.00 | −0.294159 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −18372.1 | −1.01144 | −0.505722 | − | 0.862697i | \(-0.668774\pi\) | ||||
−0.505722 | + | 0.862697i | \(0.668774\pi\) | |||||||
\(692\) | 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 | ||||||||
\(701\) | −19310.0 | −1.04041 | −0.520206 | − | 0.854041i | \(-0.674145\pi\) | ||||
−0.520206 | + | 0.854041i | \(0.674145\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −13884.9 | −0.744920 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −31029.4 | −1.65061 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −18820.0 | −0.996897 | −0.498448 | − | 0.866919i | \(-0.666097\pi\) | ||||
−0.498448 | + | 0.866919i | \(0.666097\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −3584.00 | −0.188249 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −5079.84 | −0.265700 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 27431.1 | 1.42282 | 0.711411 | − | 0.702776i | \(-0.248056\pi\) | ||||
0.711411 | + | 0.702776i | \(0.248056\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 26432.0 | 1.36530 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 4094.00 | 0.209720 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 10561.8 | 0.538813 | 0.269406 | − | 0.963027i | \(-0.413173\pi\) | ||||
0.269406 | + | 0.963027i | \(0.413173\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −3386.56 | −0.171350 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −16468.0 | −0.829822 | −0.414911 | − | 0.909862i | \(-0.636187\pi\) | ||||
−0.414911 | + | 0.909862i | \(0.636187\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −21504.0 | −1.07478 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 15070.2 | 0.750157 | 0.375079 | − | 0.926993i | \(-0.377616\pi\) | ||||
0.375079 | + | 0.926993i | \(0.377616\pi\) | |||||||
\(740\) | 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 | ||||||||
\(749\) | −8960.00 | −0.437105 | ||||||||
\(750\) | 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 | ||||||||
\(755\) | 18668.4 | 0.899885 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −1572.00 | −0.0754760 | −0.0377380 | − | 0.999288i | \(-0.512015\pi\) | ||||
−0.0377380 | + | 0.999288i | \(0.512015\pi\) | |||||||
\(758\) | 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 | ||||||||
\(763\) | −33103.6 | −1.57068 | ||||||||
\(764\) | 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 | ||||||||
\(773\) | 13978.0 | 0.650393 | 0.325196 | − | 0.945646i | \(-0.394570\pi\) | ||||
0.325196 | + | 0.945646i | \(0.394570\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1883.77 | 0.0873125 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −26415.2 | −1.21492 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −28672.0 | −1.31366 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 10776.0 | 0.489952 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 1777.94 | 0.0805297 | 0.0402649 | − | 0.999189i | \(-0.487180\pi\) | ||||
0.0402649 | + | 0.999189i | \(0.487180\pi\) | |||||||
\(788\) | 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 | ||||||||
\(797\) | −9650.00 | −0.428884 | −0.214442 | − | 0.976737i | \(-0.568793\pi\) | ||||
−0.214442 | + | 0.976737i | \(0.568793\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1354.62 | 0.0599789 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 10413.7 | 0.457647 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −21504.0 | −0.941511 | ||||||||
\(806\) | 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 | ||||||||
\(811\) | −931.304 | −0.0403237 | −0.0201619 | − | 0.999797i | \(-0.506418\pi\) | ||||
−0.0201619 | + | 0.999797i | \(0.506418\pi\) | |||||||
\(812\) | 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 | ||||||||
\(821\) | 6858.00 | 0.291530 | 0.145765 | − | 0.989319i | \(-0.453436\pi\) | ||||
0.145765 | + | 0.989319i | \(0.453436\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −18816.6 | −0.796968 | −0.398484 | − | 0.917175i | \(-0.630464\pi\) | ||||
−0.398484 | + | 0.917175i | \(0.630464\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −8212.41 | −0.345313 | −0.172656 | − | 0.984982i | \(-0.555235\pi\) | ||||
−0.172656 | + | 0.984982i | \(0.555235\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −25124.0 | −1.05258 | −0.526292 | − | 0.850304i | \(-0.676418\pi\) | ||||
−0.526292 | + | 0.850304i | \(0.676418\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 840.000 | 0.0349391 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 21335.3 | 0.884239 | ||||||||
\(836\) | 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 | ||||||||
\(845\) | −10782.0 | −0.438949 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −9757.53 | −0.395836 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 27769.8 | 1.11861 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −32812.0 | −1.31707 | −0.658535 | − | 0.752550i | \(-0.728824\pi\) | ||||
−0.658535 | + | 0.752550i | \(0.728824\pi\) | |||||||
\(854\) | 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 | ||||||||
\(859\) | 48173.8 | 1.91347 | 0.956735 | − | 0.290962i | \(-0.0939752\pi\) | ||||
0.956735 | + | 0.290962i | \(0.0939752\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 12361.0 | 0.487569 | 0.243784 | − | 0.969829i | \(-0.421611\pi\) | ||||
0.243784 | + | 0.969829i | \(0.421611\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −25740.0 | −1.01178 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 9856.00 | 0.384743 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 10159.7 | 0.395233 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 27177.2 | 1.05001 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −33212.0 | −1.27878 | −0.639390 | − | 0.768883i | \(-0.720813\pi\) | ||||
−0.639390 | + | 0.768883i | \(0.720813\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −34336.0 | −1.31306 | −0.656532 | − | 0.754298i | \(-0.727977\pi\) | ||||
−0.656532 | + | 0.754298i | \(0.727977\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −16678.8 | −0.635659 | −0.317829 | − | 0.948148i | \(-0.602954\pi\) | ||||
−0.317829 | + | 0.948148i | \(0.602954\pi\) | |||||||
\(884\) | 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 | ||||||||
\(893\) | −14336.0 | −0.537218 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 9651.70 | 0.360470 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 973.636 | 0.0361208 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 2128.00 | 0.0786836 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 19176.0 | 0.704345 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 13292.3 | 0.486617 | 0.243309 | − | 0.969949i | \(-0.421767\pi\) | ||||
0.243309 | + | 0.969949i | \(0.421767\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −2539.92 | −0.0923725 | −0.0461862 | − | 0.998933i | \(-0.514707\pi\) | ||||
−0.0461862 | + | 0.998933i | \(0.514707\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 41216.0 | 1.49403 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 53760.0 | 1.93600 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 35368.4 | 1.26953 | 0.634764 | − | 0.772706i | \(-0.281097\pi\) | ||||
0.634764 | + | 0.772706i | \(0.281097\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 13546.2 | 0.483077 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −14596.0 | −0.518825 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −17576.0 | −0.620721 | −0.310361 | − | 0.950619i | \(-0.600450\pi\) | ||||
−0.310361 | + | 0.950619i | \(0.600450\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −8889.72 | −0.312942 | ||||||||
\(932\) | 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 | \(-0.622444\pi\) | ||||
−0.375253 | + | 0.926923i | \(0.622444\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −5218.00 | −0.180767 | −0.0903836 | − | 0.995907i | \(-0.528809\pi\) | ||||
−0.0903836 | + | 0.995907i | \(0.528809\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 52830.4 | 1.82438 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −29717.1 | −1.01972 | −0.509860 | − | 0.860257i | \(-0.670303\pi\) | ||||
−0.509860 | + | 0.860257i | \(0.670303\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −4920.00 | −0.168293 | ||||||||
\(950\) | 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 | ||||||||
\(955\) | 19303.4 | 0.654077 | ||||||||
\(956\) | 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 | ||||||||
\(965\) | 2772.00 | 0.0924703 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −42988.2 | −1.42958 | −0.714791 | − | 0.699338i | \(-0.753478\pi\) | ||||
−0.714791 | + | 0.699338i | \(0.753478\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 12403.3 | 0.409928 | 0.204964 | − | 0.978769i | \(-0.434292\pi\) | ||||
0.204964 | + | 0.978769i | \(0.434292\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −25088.0 | −0.826603 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 2040.00 | 0.0668018 | 0.0334009 | − | 0.999442i | \(-0.489366\pi\) | ||||
0.0334009 | + | 0.999442i | \(0.489366\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 58926.2 | 1.92369 | ||||||||
\(980\) | 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 | ||||||||
\(989\) | −71680.0 | −2.30464 | ||||||||
\(990\) | 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 | ||||||||
\(995\) | −22732.3 | −0.724284 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −62044.0 | −1.97087 | −0.985433 | − | 0.170065i | \(-0.945602\pi\) | ||||
−0.985433 | + | 0.170065i | \(0.945602\pi\) | |||||||
\(998\) | 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 | 2304.4.a.br.1.1 | 2 | ||
3.2 | odd | 2 | 2304.4.a.q.1.1 | 2 | |||
4.3 | odd | 2 | inner | 2304.4.a.br.1.2 | 2 | ||
8.3 | odd | 2 | 2304.4.a.r.1.2 | 2 | |||
8.5 | even | 2 | 2304.4.a.r.1.1 | 2 | |||
12.11 | even | 2 | 2304.4.a.q.1.2 | 2 | |||
16.3 | odd | 4 | 1152.4.d.m.577.1 | yes | 4 | ||
16.5 | even | 4 | 1152.4.d.m.577.4 | yes | 4 | ||
16.11 | odd | 4 | 1152.4.d.m.577.3 | yes | 4 | ||
16.13 | even | 4 | 1152.4.d.m.577.2 | yes | 4 | ||
24.5 | odd | 2 | 2304.4.a.bs.1.1 | 2 | |||
24.11 | even | 2 | 2304.4.a.bs.1.2 | 2 | |||
48.5 | odd | 4 | 1152.4.d.k.577.2 | yes | 4 | ||
48.11 | even | 4 | 1152.4.d.k.577.1 | ✓ | 4 | ||
48.29 | odd | 4 | 1152.4.d.k.577.4 | yes | 4 | ||
48.35 | even | 4 | 1152.4.d.k.577.3 | yes | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1152.4.d.k.577.1 | ✓ | 4 | 48.11 | even | 4 | ||
1152.4.d.k.577.2 | yes | 4 | 48.5 | odd | 4 | ||
1152.4.d.k.577.3 | yes | 4 | 48.35 | even | 4 | ||
1152.4.d.k.577.4 | yes | 4 | 48.29 | odd | 4 | ||
1152.4.d.m.577.1 | yes | 4 | 16.3 | odd | 4 | ||
1152.4.d.m.577.2 | yes | 4 | 16.13 | even | 4 | ||
1152.4.d.m.577.3 | yes | 4 | 16.11 | odd | 4 | ||
1152.4.d.m.577.4 | yes | 4 | 16.5 | even | 4 | ||
2304.4.a.q.1.1 | 2 | 3.2 | odd | 2 | |||
2304.4.a.q.1.2 | 2 | 12.11 | even | 2 | |||
2304.4.a.r.1.1 | 2 | 8.5 | even | 2 | |||
2304.4.a.r.1.2 | 2 | 8.3 | odd | 2 | |||
2304.4.a.br.1.1 | 2 | 1.1 | even | 1 | trivial | ||
2304.4.a.br.1.2 | 2 | 4.3 | odd | 2 | inner | ||
2304.4.a.bs.1.1 | 2 | 24.5 | odd | 2 | |||
2304.4.a.bs.1.2 | 2 | 24.11 | even | 2 |