Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1856,4,Mod(1,1856)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1856, 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("1856.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1856 = 2^{6} \cdot 29 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1856.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: | \(109.507544971\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 245x^{10} + 21294x^{8} - 755514x^{6} + 8955005x^{4} - 27099393x^{2} + 23710340 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{19} \) |
Twist minimal: | no (minimal twist has level 928) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.12 | ||
Root | \(9.17689\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1856.1 |
$q$-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 | ||||||||
\(3\) | 9.17689 | 1.76609 | 0.883046 | − | 0.469286i | \(-0.155489\pi\) | ||||
0.883046 | + | 0.469286i | \(0.155489\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 14.0091 | 1.25301 | 0.626507 | − | 0.779416i | \(-0.284484\pi\) | ||||
0.626507 | + | 0.779416i | \(0.284484\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 13.6574 | 0.737431 | 0.368715 | − | 0.929542i | \(-0.379798\pi\) | ||||
0.368715 | + | 0.929542i | \(0.379798\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 57.2153 | 2.11908 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 4.50774 | 0.123558 | 0.0617788 | − | 0.998090i | \(-0.480323\pi\) | ||||
0.0617788 | + | 0.998090i | \(0.480323\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −7.29514 | −0.155639 | −0.0778195 | − | 0.996967i | \(-0.524796\pi\) | ||||
−0.0778195 | + | 0.996967i | \(0.524796\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 128.560 | 2.21294 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 28.0079 | 0.399584 | 0.199792 | − | 0.979838i | \(-0.435973\pi\) | ||||
0.199792 | + | 0.979838i | \(0.435973\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 100.099 | 1.20864 | 0.604320 | − | 0.796741i | \(-0.293445\pi\) | ||||
0.604320 | + | 0.796741i | \(0.293445\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 125.332 | 1.30237 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −62.4954 | −0.566574 | −0.283287 | − | 0.959035i | \(-0.591425\pi\) | ||||
−0.283287 | + | 0.959035i | \(0.591425\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 71.2554 | 0.570043 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 277.282 | 1.97641 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 29.0000 | 0.185695 | ||||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −156.926 | −0.909183 | −0.454591 | − | 0.890700i | \(-0.650215\pi\) | ||||
−0.454591 | + | 0.890700i | \(0.650215\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 41.3670 | 0.218214 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 191.328 | 0.924011 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 233.828 | 1.03895 | 0.519475 | − | 0.854486i | \(-0.326128\pi\) | ||||
0.519475 | + | 0.854486i | \(0.326128\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −66.9466 | −0.274873 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 7.39085 | 0.0281526 | 0.0140763 | − | 0.999901i | \(-0.495519\pi\) | ||||
0.0140763 | + | 0.999901i | \(0.495519\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 31.0965 | 0.110283 | 0.0551415 | − | 0.998479i | \(-0.482439\pi\) | ||||
0.0551415 | + | 0.998479i | \(0.482439\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 801.535 | 2.65524 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −226.708 | −0.703590 | −0.351795 | − | 0.936077i | \(-0.614429\pi\) | ||||
−0.351795 | + | 0.936077i | \(0.614429\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −156.475 | −0.456196 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 257.026 | 0.705702 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −254.020 | −0.658345 | −0.329172 | − | 0.944270i | \(-0.606770\pi\) | ||||
−0.329172 | + | 0.944270i | \(0.606770\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 63.1495 | 0.154819 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 918.593 | 2.13457 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −33.2971 | −0.0734731 | −0.0367365 | − | 0.999325i | \(-0.511696\pi\) | ||||
−0.0367365 | + | 0.999325i | \(0.511696\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −644.725 | −1.35325 | −0.676627 | − | 0.736326i | \(-0.736559\pi\) | ||||
−0.676627 | + | 0.736326i | \(0.736559\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 781.412 | 1.56268 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −102.198 | −0.195018 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 939.189 | 1.71254 | 0.856270 | − | 0.516528i | \(-0.172776\pi\) | ||||
0.856270 | + | 0.516528i | \(0.172776\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −573.513 | −1.00062 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −842.541 | −1.40833 | −0.704164 | − | 0.710038i | \(-0.748678\pi\) | ||||
−0.704164 | + | 0.710038i | \(0.748678\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 664.251 | 1.06500 | 0.532498 | − | 0.846431i | \(-0.321253\pi\) | ||||
0.532498 | + | 0.846431i | \(0.321253\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 653.903 | 1.00675 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 61.5640 | 0.0911152 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0.292394 | 0.000416416 0 | 0.000208208 | − | 1.00000i | \(-0.499934\pi\) | ||||
0.000208208 | 1.00000i | \(0.499934\pi\) | ||||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 999.774 | 1.37143 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 283.786 | 0.375296 | 0.187648 | − | 0.982236i | \(-0.439914\pi\) | ||||
0.187648 | + | 0.982236i | \(0.439914\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 392.367 | 0.500684 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 266.130 | 0.327955 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 1414.38 | 1.68454 | 0.842270 | − | 0.539056i | \(-0.181219\pi\) | ||||
0.842270 | + | 0.539056i | \(0.181219\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −99.6326 | −0.114773 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −1440.09 | −1.60570 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 1402.29 | 1.51444 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −642.913 | −0.672968 | −0.336484 | − | 0.941689i | \(-0.609238\pi\) | ||||
−0.336484 | + | 0.941689i | \(0.609238\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 257.911 | 0.261829 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1710.19 | −1.68486 | −0.842429 | − | 0.538808i | \(-0.818875\pi\) | ||||
−0.842429 | + | 0.538808i | \(0.818875\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 110.293 | 0.105509 | 0.0527547 | − | 0.998608i | \(-0.483200\pi\) | ||||
0.0527547 | + | 0.998608i | \(0.483200\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 1755.80 | 1.63189 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 1062.68 | 0.960124 | 0.480062 | − | 0.877235i | \(-0.340614\pi\) | ||||
0.480062 | + | 0.877235i | \(0.340614\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −544.198 | −0.478208 | −0.239104 | − | 0.970994i | \(-0.576854\pi\) | ||||
−0.239104 | + | 0.970994i | \(0.576854\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 2145.82 | 1.83488 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −815.771 | −0.679126 | −0.339563 | − | 0.940583i | \(-0.610279\pi\) | ||||
−0.339563 | + | 0.940583i | \(0.610279\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −875.506 | −0.709925 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −417.393 | −0.329812 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 382.516 | 0.294665 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1310.68 | −0.984733 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 67.8250 | 0.0497201 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −752.914 | −0.538742 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1448.39 | 1.01200 | 0.505998 | − | 0.862535i | \(-0.331124\pi\) | ||||
0.505998 | + | 0.862535i | \(0.331124\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 285.369 | 0.194770 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −2671.44 | −1.78172 | −0.890858 | − | 0.454281i | \(-0.849896\pi\) | ||||
−0.890858 | + | 0.454281i | \(0.849896\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1367.09 | 0.891289 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 3884.48 | 2.47646 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 856.732 | 0.534274 | 0.267137 | − | 0.963659i | \(-0.413922\pi\) | ||||
0.267137 | + | 0.963659i | \(0.413922\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −545.813 | −0.333059 | −0.166530 | − | 0.986036i | \(-0.553256\pi\) | ||||
−0.166530 | + | 0.986036i | \(0.553256\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −2080.47 | −1.24261 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −32.8846 | −0.0192304 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 406.264 | 0.232679 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −1435.96 | −0.805685 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 3398.46 | 1.86854 | 0.934271 | − | 0.356564i | \(-0.116052\pi\) | ||||
0.934271 | + | 0.356564i | \(0.116052\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2535.99 | −1.36673 | −0.683365 | − | 0.730077i | \(-0.739484\pi\) | ||||
−0.683365 | + | 0.730077i | \(0.739484\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 1602.48 | 0.846752 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −2198.39 | −1.13922 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1492.77 | 0.758826 | 0.379413 | − | 0.925227i | \(-0.376126\pi\) | ||||
0.379413 | + | 0.925227i | \(0.376126\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −2331.11 | −1.16270 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −853.525 | −0.417809 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −82.3321 | −0.0395629 | −0.0197814 | − | 0.999804i | \(-0.506297\pi\) | ||||
−0.0197814 | + | 0.999804i | \(0.506297\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 579.515 | 0.273426 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 3428.68 | 1.58874 | 0.794368 | − | 0.607437i | \(-0.207802\pi\) | ||||
0.794368 | + | 0.607437i | \(0.207802\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −2143.78 | −0.975777 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 5727.16 | 2.56121 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 1766.93 | 0.776515 | 0.388257 | − | 0.921551i | \(-0.373077\pi\) | ||||
0.388257 | + | 0.921551i | \(0.373077\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 973.164 | 0.420367 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −305.564 | −0.129760 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −3627.06 | −1.51452 | −0.757261 | − | 0.653113i | \(-0.773463\pi\) | ||||
−0.757261 | + | 0.653113i | \(0.773463\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −848.353 | −0.348385 | −0.174192 | − | 0.984712i | \(-0.555731\pi\) | ||||
−0.174192 | + | 0.984712i | \(0.555731\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −5916.57 | −2.38997 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 3275.73 | 1.30182 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 126.253 | 0.0493716 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 3786.95 | 1.45746 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −3990.26 | −1.51165 | −0.755825 | − | 0.654774i | \(-0.772764\pi\) | ||||
−0.755825 | + | 0.654774i | \(0.772764\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 3743.94 | 1.39635 | 0.698173 | − | 0.715929i | \(-0.253997\pi\) | ||||
0.698173 | + | 0.715929i | \(0.253997\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −937.864 | −0.344420 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −366.361 | −0.132498 | −0.0662490 | − | 0.997803i | \(-0.521103\pi\) | ||||
−0.0662490 | + | 0.997803i | \(0.521103\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 2961.91 | 1.05510 | 0.527549 | − | 0.849525i | \(-0.323111\pi\) | ||||
0.527549 | + | 0.849525i | \(0.323111\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 8618.84 | 3.02451 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 396.065 | 0.136937 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 103.539 | 0.0352756 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −3575.69 | −1.20062 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 451.218 | 0.149337 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1425.98 | 0.465252 | 0.232626 | − | 0.972566i | \(-0.425268\pi\) | ||||
0.232626 | + | 0.972566i | \(0.425268\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −7731.91 | −2.48724 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 435.634 | 0.138186 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −2143.20 | −0.670459 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 6095.75 | 1.88088 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −204.322 | −0.0621908 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 843.229 | 0.253214 | 0.126607 | − | 0.991953i | \(-0.459591\pi\) | ||||
0.126607 | + | 0.991953i | \(0.459591\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 4076.90 | 1.20797 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −5480.14 | −1.60233 | −0.801167 | − | 0.598441i | \(-0.795787\pi\) | ||||
−0.801167 | + | 0.598441i | \(0.795787\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1748.22 | 0.504479 | 0.252240 | − | 0.967665i | \(-0.418833\pi\) | ||||
0.252240 | + | 0.967665i | \(0.418833\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 564.966 | 0.160918 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 3627.19 | 1.01985 | 0.509925 | − | 0.860219i | \(-0.329673\pi\) | ||||
0.509925 | + | 0.860219i | \(0.329673\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −3175.98 | −0.881608 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 2.68327 | 0.000735430 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 97.1814 | 0.0263019 | 0.0131509 | − | 0.999914i | \(-0.495814\pi\) | ||||
0.0131509 | + | 0.999914i | \(0.495814\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −5736.63 | −1.53331 | −0.766657 | − | 0.642057i | \(-0.778081\pi\) | ||||
−0.766657 | + | 0.642057i | \(0.778081\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1688.20 | 0.445671 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −2192.08 | −0.571620 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −730.232 | −0.188112 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 2604.27 | 0.662807 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −6981.23 | −1.75558 | −0.877791 | − | 0.479044i | \(-0.840983\pi\) | ||||
−0.877791 | + | 0.479044i | \(0.840983\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −281.713 | −0.0700045 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 3600.70 | 0.884254 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 5232.97 | 1.27013 | 0.635065 | − | 0.772458i | \(-0.280973\pi\) | ||||
0.635065 | + | 0.772458i | \(0.280973\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 3193.49 | 0.766153 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1659.24 | 0.393504 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −2634.50 | −0.617682 | −0.308841 | − | 0.951114i | \(-0.599941\pi\) | ||||
−0.308841 | + | 0.951114i | \(0.599941\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −3558.59 | −0.824915 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 12979.6 | 2.97505 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −163.237 | −0.0369990 | −0.0184995 | − | 0.999829i | \(-0.505889\pi\) | ||||
−0.0184995 | + | 0.999829i | \(0.505889\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1044.55 | 0.234141 | 0.117070 | − | 0.993124i | \(-0.462650\pi\) | ||||
0.117070 | + | 0.993124i | \(0.462650\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −914.317 | −0.202700 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 321.201 | 0.0704332 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 2943.00 | 0.638366 | 0.319183 | − | 0.947693i | \(-0.396591\pi\) | ||||
0.319183 | + | 0.947693i | \(0.396591\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −8978.54 | −1.92663 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 4706.57 | 0.999184 | 0.499592 | − | 0.866261i | \(-0.333483\pi\) | ||||
0.499592 | + | 0.866261i | \(0.333483\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 212.937 | 0.0447271 | 0.0223636 | − | 0.999750i | \(-0.492881\pi\) | ||||
0.0223636 | + | 0.999750i | \(0.492881\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 12868.7 | 2.67465 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 100.940 | 0.0207606 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −4128.56 | −0.840333 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −5899.94 | −1.18852 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −1474.73 | −0.294044 | −0.147022 | − | 0.989133i | \(-0.546969\pi\) | ||||
−0.147022 | + | 0.989133i | \(0.546969\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −466.463 | −0.0920628 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 1249.92 | 0.244200 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 455.913 | 0.0881809 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 424.697 | 0.0813260 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −15694.2 | −2.97561 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −9032.02 | −1.69565 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −6933.89 | −1.28905 | −0.644525 | − | 0.764583i | \(-0.722945\pi\) | ||||
−0.644525 | + | 0.764583i | \(0.722945\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 1012.14 | 0.186339 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −9011.82 | −1.64313 | −0.821565 | − | 0.570114i | \(-0.806899\pi\) | ||||
−0.821565 | + | 0.570114i | \(0.806899\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −4415.44 | −0.797366 | −0.398683 | − | 0.917089i | \(-0.630533\pi\) | ||||
−0.398683 | + | 0.917089i | \(0.630533\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 10946.9 | 1.95806 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −5219.14 | −0.924720 | −0.462360 | − | 0.886692i | \(-0.652997\pi\) | ||||
−0.462360 | + | 0.886692i | \(0.652997\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 130.724 | 0.0229441 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 9752.10 | 1.69567 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 2803.55 | 0.482953 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −519.818 | −0.0887210 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −4994.04 | −0.844560 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −3096.24 | −0.518849 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −4797.61 | −0.796678 | −0.398339 | − | 0.917238i | \(-0.630413\pi\) | ||||
−0.398339 | + | 0.917238i | \(0.630413\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 13378.5 | 2.20162 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 13157.2 | 2.14584 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 4182.15 | 0.676013 | 0.338006 | − | 0.941144i | \(-0.390247\pi\) | ||||
0.338006 | + | 0.941144i | \(0.390247\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −7486.24 | −1.19940 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −707.380 | −0.112337 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −6821.54 | −1.07384 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −8034.42 | −1.25379 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −1391.64 | −0.215294 | −0.107647 | − | 0.994189i | \(-0.534332\pi\) | ||||
−0.107647 | + | 0.994189i | \(0.534332\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 11159.2 | 1.71157 | 0.855787 | − | 0.517328i | \(-0.173073\pi\) | ||||
0.855787 | + | 0.517328i | \(0.173073\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −2022.81 | −0.307606 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 12702.3 | 1.91523 | 0.957613 | − | 0.288059i | \(-0.0930098\pi\) | ||||
0.957613 | + | 0.288059i | \(0.0930098\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −11803.3 | −1.76465 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 3510.30 | 0.520406 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −727.922 | −0.107015 | −0.0535073 | − | 0.998567i | \(-0.517040\pi\) | ||||
−0.0535073 | + | 0.998567i | \(0.517040\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 3160.71 | 0.460813 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −12028.0 | −1.73913 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 9305.57 | 1.33445 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 6792.19 | 0.966075 | 0.483038 | − | 0.875600i | \(-0.339533\pi\) | ||||
0.483038 | + | 0.875600i | \(0.339533\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 422.869 | 0.0596577 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −3469.25 | −0.485484 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −13659.3 | −1.89611 | −0.948057 | − | 0.318100i | \(-0.896955\pi\) | ||||
−0.948057 | + | 0.318100i | \(0.896955\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −6909.41 | −0.951468 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −211.559 | −0.0289014 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 199.856 | 0.0270869 | 0.0135434 | − | 0.999908i | \(-0.495689\pi\) | ||||
0.0135434 | + | 0.999908i | \(0.495689\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 13291.7 | 1.78728 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 6689.13 | 0.892424 | 0.446212 | − | 0.894927i | \(-0.352773\pi\) | ||||
0.446212 | + | 0.894927i | \(0.352773\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 862.458 | 0.114169 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 1779.19 | 0.233699 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 11082.6 | 1.44450 | 0.722248 | − | 0.691634i | \(-0.243109\pi\) | ||||
0.722248 | + | 0.691634i | \(0.243109\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1750.37 | −0.226394 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −24515.5 | −3.14668 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 4.09618 | 0.000521775 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 2941.58 | 0.371873 | 0.185937 | − | 0.982562i | \(-0.440468\pi\) | ||||
0.185937 | + | 0.982562i | \(0.440468\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 12545.6 | 1.57410 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 15343.4 | 1.91075 | 0.955375 | − | 0.295395i | \(-0.0954513\pi\) | ||||
0.955375 | + | 0.295395i | \(0.0954513\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1144.79 | 0.141504 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 14006.0 | 1.71842 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 1054.04 | 0.128370 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 5573.49 | 0.673818 | 0.336909 | − | 0.941537i | \(-0.390619\pi\) | ||||
0.336909 | + | 0.941537i | \(0.390619\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 7862.14 | 0.943578 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −454.752 | −0.0541813 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 3975.59 | 0.470251 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −5008.86 | −0.588213 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 3169.81 | 0.369583 | 0.184792 | − | 0.982778i | \(-0.440839\pi\) | ||||
0.184792 | + | 0.982778i | \(0.440839\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −29.4016 | −0.00340367 | −0.00170183 | − | 0.999999i | \(-0.500542\pi\) | ||||
−0.00170183 | + | 0.999999i | \(0.500542\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −12971.2 | −1.49097 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 1995.72 | 0.227780 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −8805.27 | −0.997931 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −301.778 | −0.0339627 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 12774.5 | 1.42767 | 0.713833 | − | 0.700316i | \(-0.246958\pi\) | ||||
0.713833 | + | 0.700316i | \(0.246958\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 1549.79 | 0.172005 | 0.0860023 | − | 0.996295i | \(-0.472591\pi\) | ||||
0.0860023 | + | 0.996295i | \(0.472591\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 3728.24 | 0.410932 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −6255.70 | −0.684784 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −9161.15 | −0.995986 | −0.497993 | − | 0.867181i | \(-0.665930\pi\) | ||||
−0.497993 | + | 0.867181i | \(0.665930\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −8952.77 | −0.966718 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 12192.8 | 1.30767 | 0.653833 | − | 0.756639i | \(-0.273160\pi\) | ||||
0.653833 | + | 0.756639i | \(0.273160\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 19814.2 | 2.11075 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 31187.3 | 3.30002 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 6856.53 | 0.720667 | 0.360334 | − | 0.932824i | \(-0.382663\pi\) | ||||
0.360334 | + | 0.932824i | \(0.382663\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 33.3160 | 0.00347847 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −23272.5 | −2.41377 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −1395.77 | −0.143812 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 14578.3 | 1.49222 | 0.746111 | − | 0.665821i | \(-0.231919\pi\) | ||||
0.746111 | + | 0.665821i | \(0.231919\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 7766.10 | 0.789740 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 6740.91 | 0.681031 | 0.340516 | − | 0.940239i | \(-0.389398\pi\) | ||||
0.340516 | + | 0.940239i | \(0.389398\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 12058.0 | 1.21033 | 0.605164 | − | 0.796101i | \(-0.293107\pi\) | ||||
0.605164 | + | 0.796101i | \(0.293107\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −20174.4 | −2.01197 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −1459.40 | −0.144610 | −0.0723052 | − | 0.997383i | \(-0.523036\pi\) | ||||
−0.0723052 | + | 0.997383i | \(0.523036\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 12826.9 | 1.26288 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 13698.9 | 1.34016 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 140.175 | 0.0136263 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 7132.56 | 0.688978 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −14533.8 | −1.39509 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −14648.8 | −1.39733 | −0.698666 | − | 0.715448i | \(-0.746223\pi\) | ||||
−0.698666 | + | 0.715448i | \(0.746223\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1705.81 | −0.161701 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −7832.70 | −0.737889 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −9006.64 | −0.843238 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 4557.53 | 0.424069 | 0.212034 | − | 0.977262i | \(-0.431991\pi\) | ||||
0.212034 | + | 0.977262i | \(0.431991\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −755.552 | −0.0698717 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −7563.44 | −0.695179 | −0.347590 | − | 0.937647i | \(-0.613000\pi\) | ||||
−0.347590 | + | 0.937647i | \(0.613000\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 812.230 | 0.0742008 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 3613.11 | 0.328075 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −11506.9 | −1.03854 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 2933.62 | 0.263180 | 0.131590 | − | 0.991304i | \(-0.457992\pi\) | ||||
0.131590 | + | 0.991304i | \(0.457992\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 31464.6 | 2.80586 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −4013.31 | −0.355755 | −0.177877 | − | 0.984053i | \(-0.556923\pi\) | ||||
−0.177877 | + | 0.984053i | \(0.556923\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −23958.3 | −2.11115 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −19673.2 | −1.72331 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 21058.1 | 1.83376 | 0.916880 | − | 0.399163i | \(-0.130699\pi\) | ||||
0.916880 | + | 0.399163i | \(0.130699\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 9071.94 | 0.785360 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 27755.5 | 2.38876 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 1545.10 | 0.132205 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −1021.94 | −0.0869340 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 16214.9 | 1.37140 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 6743.14 | 0.567029 | 0.283515 | − | 0.958968i | \(-0.408500\pi\) | ||||
0.283515 | + | 0.958968i | \(0.408500\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −1918.97 | −0.160441 | −0.0802206 | − | 0.996777i | \(-0.525562\pi\) | ||||
−0.0802206 | + | 0.996777i | \(0.525562\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 8930.62 | 0.742408 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −4395.16 | −0.363295 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −8261.32 | −0.678994 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −1905.10 | −0.155696 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −53.9172 | −0.00438164 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 14887.2 | 1.20305 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −33285.1 | −2.67479 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −705.350 | −0.0563665 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −13747.5 | −1.09252 | −0.546259 | − | 0.837617i | \(-0.683948\pi\) | ||||
−0.546259 | + | 0.837617i | \(0.683948\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −7785.24 | −0.615280 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −7623.74 | −0.599202 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 9785.34 | 0.764883 | 0.382441 | − | 0.923980i | \(-0.375083\pi\) | ||||
0.382441 | + | 0.923980i | \(0.375083\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −36888.1 | −2.86766 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 2902.86 | 0.224439 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 3.99334 | 0.000307078 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 30061.0 | 2.29913 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −21524.5 | −1.63738 | −0.818692 | − | 0.574232i | \(-0.805301\pi\) | ||||
−0.818692 | + | 0.574232i | \(0.805301\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −226.853 | −0.0171643 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 1158.61 | 0.0871949 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −7302.37 | −0.546640 | −0.273320 | − | 0.961923i | \(-0.588122\pi\) | ||||
−0.273320 | + | 0.961923i | \(0.588122\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −11428.2 | −0.850955 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 13654.3 | 1.01134 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −13132.2 | −0.967541 | −0.483771 | − | 0.875195i | \(-0.660733\pi\) | ||||
−0.483771 | + | 0.875195i | \(0.660733\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −11235.4 | −0.823447 | −0.411724 | − | 0.911309i | \(-0.635073\pi\) | ||||
−0.411724 | + | 0.911309i | \(0.635073\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −36618.2 | −2.66971 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −4453.14 | −0.322972 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 21896.6 | 1.57984 | 0.789919 | − | 0.613211i | \(-0.210123\pi\) | ||||
0.789919 | + | 0.613211i | \(0.210123\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 34357.7 | 2.46608 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 3875.78 | 0.276755 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1145.05 | −0.0813436 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −5847.31 | −0.413259 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 1582.58 | 0.111278 | 0.0556388 | − | 0.998451i | \(-0.482280\pi\) | ||||
0.0556388 | + | 0.998451i | \(0.482280\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −15708.0 | −1.09888 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −3362.05 | −0.234004 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −2738.39 | −0.189633 | −0.0948165 | − | 0.995495i | \(-0.530226\pi\) | ||||
−0.0948165 | + | 0.995495i | \(0.530226\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 5358.71 | 0.369220 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 27181.2 | 1.86340 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −1868.85 | −0.127478 | −0.0637390 | − | 0.997967i | \(-0.520303\pi\) | ||||
−0.0637390 | + | 0.997967i | \(0.520303\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −13016.9 | −0.883481 | −0.441741 | − | 0.897143i | \(-0.645639\pi\) | ||||
−0.441741 | + | 0.897143i | \(0.645639\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 53736.0 | 3.62902 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −18361.5 | −1.23388 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 8352.64 | 0.558523 | 0.279261 | − | 0.960215i | \(-0.409910\pi\) | ||||
0.279261 | + | 0.960215i | \(0.409910\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 3634.64 | 0.241844 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1653.86 | 0.109506 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −8937.94 | −0.588907 | −0.294453 | − | 0.955666i | \(-0.595138\pi\) | ||||
−0.294453 | + | 0.955666i | \(0.595138\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 950.168 | 0.0622999 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 4243.94 | 0.276912 | 0.138456 | − | 0.990369i | \(-0.455786\pi\) | ||||
0.138456 | + | 0.990369i | \(0.455786\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −25500.0 | −1.65579 | −0.827894 | − | 0.560885i | \(-0.810461\pi\) | ||||
−0.827894 | + | 0.560885i | \(0.810461\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −17328.9 | −1.11978 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 19316.8 | 1.24223 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −19454.6 | −1.24509 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 4140.78 | 0.263743 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 6549.05 | 0.415147 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −13923.2 | −0.878405 | −0.439203 | − | 0.898388i | \(-0.644739\pi\) | ||||
−0.439203 | + | 0.898388i | \(0.644739\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 13086.0 | 0.821679 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 20290.6 | 1.26804 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1141.51 | 0.0710019 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −48206.2 | −2.98436 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 15525.7 | 0.956672 | 0.478336 | − | 0.878177i | \(-0.341240\pi\) | ||||
0.478336 | + | 0.878177i | \(0.341240\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 30205.1 | 1.85252 | 0.926261 | − | 0.376883i | \(-0.123004\pi\) | ||||
0.926261 | + | 0.376883i | \(0.123004\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 3997.77 | 0.244049 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −3920.67 | −0.238234 | −0.119117 | − | 0.992880i | \(-0.538006\pi\) | ||||
−0.119117 | + | 0.992880i | \(0.538006\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −150.095 | −0.00907816 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −19667.9 | −1.18409 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −21252.6 | −1.27363 | −0.636815 | − | 0.771017i | \(-0.719748\pi\) | ||||
−0.636815 | + | 0.771017i | \(0.719748\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −37424.5 | −2.23252 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 38005.3 | 2.25681 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −6413.43 | −0.379107 | −0.189554 | − | 0.981870i | \(-0.560704\pi\) | ||||
−0.189554 | + | 0.981870i | \(0.560704\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −516.403 | −0.0303869 | −0.0151934 | − | 0.999885i | \(-0.504836\pi\) | ||||
−0.0151934 | + | 0.999885i | \(0.504836\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −1875.04 | −0.109835 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 19151.7 | 1.11680 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1812.37 | −0.105210 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 7738.21 | 0.447200 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −2906.25 | −0.167205 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −16043.0 | −0.918886 | −0.459443 | − | 0.888207i | \(-0.651951\pi\) | ||||
−0.459443 | + | 0.888207i | \(0.651951\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 19757.9 | 1.12664 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −10152.6 | −0.576360 | −0.288180 | − | 0.957576i | \(-0.593050\pi\) | ||||
−0.288180 | + | 0.957576i | \(0.593050\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −8780.52 | −0.496267 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −50290.6 | −2.82987 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −17659.3 | −0.989332 | −0.494666 | − | 0.869083i | \(-0.664710\pi\) | ||||
−0.494666 | + | 0.869083i | \(0.664710\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 12002.1 | 0.669453 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 16043.2 | 0.890957 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 1853.11 | 0.102464 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 21407.0 | 1.17853 | 0.589264 | − | 0.807941i | \(-0.299418\pi\) | ||||
0.589264 | + | 0.807941i | \(0.299418\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 3522.40 | 0.193081 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −7646.35 | −0.417328 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 207.002 | 0.0112493 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 33286.3 | 1.80115 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 4871.91 | 0.262496 | 0.131248 | − | 0.991350i | \(-0.458102\pi\) | ||||
0.131248 | + | 0.991350i | \(0.458102\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 23405.9 | 1.25572 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −29145.6 | −1.55700 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −23356.8 | −1.24247 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −16561.0 | −0.877240 | −0.438620 | − | 0.898673i | \(-0.644533\pi\) | ||||
−0.438620 | + | 0.898673i | \(0.644533\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 16.7294 | 0.000882421 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 9807.13 | 0.515119 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −460.684 | −0.0240959 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 891.823 | 0.0464515 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −20089.0 | −1.04199 | −0.520996 | − | 0.853559i | \(-0.674439\pi\) | ||||
−0.520996 | + | 0.853559i | \(0.674439\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1506.31 | 0.0778059 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −52644.4 | −2.70797 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 2066.41 | 0.105854 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −1212.39 | −0.0618501 | −0.0309250 | − | 0.999522i | \(-0.509845\pi\) | ||||
−0.0309250 | + | 0.999522i | \(0.509845\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −11501.5 | −0.584336 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 870.948 | 0.0440673 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 2250.65 | 0.113410 | 0.0567050 | − | 0.998391i | \(-0.481941\pi\) | ||||
0.0567050 | + | 0.998391i | \(0.481941\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −20116.5 | −1.00953 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 4233.62 | 0.211598 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −33601.0 | −1.67257 | −0.836287 | − | 0.548292i | \(-0.815278\pi\) | ||||
−0.836287 | + | 0.548292i | \(0.815278\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −6701.26 | −0.332223 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −1205.51 | −0.0595236 | −0.0297618 | − | 0.999557i | \(-0.509475\pi\) | ||||
−0.0297618 | + | 0.999557i | \(0.509475\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 47609.4 | 2.34131 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 16236.9 | 0.795283 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 14513.5 | 0.708024 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 24033.9 | 1.16779 | 0.583895 | − | 0.811829i | \(-0.301528\pi\) | ||||
0.583895 | + | 0.811829i | \(0.301528\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −64065.9 | −3.10052 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −35527.0 | −1.71253 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 33709.6 | 1.61849 | 0.809244 | − | 0.587472i | \(-0.199877\pi\) | ||||
0.809244 | + | 0.587472i | \(0.199877\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −2585.25 | −0.123634 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −5472.43 | −0.260677 | −0.130339 | − | 0.991470i | \(-0.541606\pi\) | ||||
−0.130339 | + | 0.991470i | \(0.541606\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −7432.33 | −0.352646 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 22449.4 | 1.06099 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 242.907 | 0.0114353 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −3939.61 | −0.184741 | −0.0923706 | − | 0.995725i | \(-0.529444\pi\) | ||||
−0.0923706 | + | 0.995725i | \(0.529444\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 48022.4 | 2.24317 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 299.990 | 0.0139585 | 0.00697924 | − | 0.999976i | \(-0.497778\pi\) | ||||
0.00697924 | + | 0.999976i | \(0.497778\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −11181.8 | −0.518274 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 29306.3 | 1.35310 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 739.813 | 0.0340264 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −3797.96 | −0.174010 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 8041.18 | 0.367009 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 20912.3 | 0.950819 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −39130.1 | −1.77235 | −0.886174 | − | 0.463352i | \(-0.846646\pi\) | ||||
−0.886174 | + | 0.463352i | \(0.846646\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −24176.5 | −1.09088 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −11141.3 | −0.500809 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 4703.35 | 0.210619 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −32656.8 | −1.45688 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 15591.2 | 0.692933 | 0.346466 | − | 0.938062i | \(-0.387381\pi\) | ||||
0.346466 | + | 0.938062i | \(0.387381\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −6349.62 | −0.281143 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 80924.1 | 3.56968 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 2994.27 | 0.131588 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −11957.1 | −0.523520 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −1498.01 | −0.0653437 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 10085.3 | 0.438296 | 0.219148 | − | 0.975692i | \(-0.429672\pi\) | ||||
0.219148 | + | 0.975692i | \(0.429672\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 4240.62 | 0.183611 | 0.0918053 | − | 0.995777i | \(-0.470736\pi\) | ||||
0.0918053 | + | 0.995777i | \(0.470736\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 9585.75 | 0.413514 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −1153.40 | −0.0495728 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 3112.71 | 0.133292 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −5700.51 | −0.243213 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −2096.00 | −0.0890999 | −0.0445500 | − | 0.999007i | \(-0.514185\pi\) | ||||
−0.0445500 | + | 0.999007i | \(0.514185\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 35843.2 | 1.51812 | 0.759062 | − | 0.651018i | \(-0.225658\pi\) | ||||
0.759062 | + | 0.651018i | \(0.225658\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 2947.62 | 0.124392 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −34088.3 | −1.43333 | −0.716667 | − | 0.697416i | \(-0.754333\pi\) | ||||
−0.716667 | + | 0.697416i | \(0.754333\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 5277.98 | 0.221124 | 0.110562 | − | 0.993869i | \(-0.464735\pi\) | ||||
0.110562 | + | 0.993869i | \(0.464735\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 27007.5 | 1.12741 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −4382.55 | −0.182289 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 48032.7 | 1.99071 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −43512.7 | −1.79691 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −13449.4 | −0.553426 | −0.276713 | − | 0.960953i | \(-0.589245\pi\) | ||||
−0.276713 | + | 0.960953i | \(0.589245\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 841.000 | 0.0344828 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 43191.7 | 1.76465 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −30032.5 | −1.22266 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −17900.5 | −0.726173 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 1954.10 | 0.0789923 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −14613.2 | −0.588641 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −484.372 | −0.0194426 | −0.00972132 | − | 0.999953i | \(-0.503094\pi\) | ||||
−0.00972132 | + | 0.999953i | \(0.503094\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 80232.5 | 3.20923 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 3781.84 | 0.150741 | 0.0753705 | − | 0.997156i | \(-0.475986\pi\) | ||||
0.0753705 | + | 0.997156i | \(0.475986\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 3541.87 | 0.140683 | 0.0703417 | − | 0.997523i | \(-0.477591\pi\) | ||||
0.0703417 | + | 0.997523i | \(0.477591\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 926.313 | 0.0366651 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −43405.8 | −1.71211 | −0.856056 | − | 0.516883i | \(-0.827092\pi\) | ||||
−0.856056 | + | 0.516883i | \(0.827092\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 24753.1 | 0.972984 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −37887.3 | −1.48411 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 1.31804 | 5.14514e−5 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −6851.51 | −0.266538 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −36784.4 | −1.42608 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −10282.9 | −0.397284 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −14767.0 | −0.568583 | −0.284292 | − | 0.958738i | \(-0.591758\pi\) | ||||
−0.284292 | + | 0.958738i | \(0.591758\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −13533.5 | −0.519308 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 18112.9 | 0.692668 | 0.346334 | − | 0.938111i | \(-0.387426\pi\) | ||||
0.346334 | + | 0.938111i | \(0.387426\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −28230.9 | −1.07593 | −0.537964 | − | 0.842968i | \(-0.680807\pi\) | ||||
−0.537964 | + | 0.842968i | \(0.680807\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −4280.68 | −0.162591 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 2372.78 | 0.0898200 | 0.0449100 | − | 0.998991i | \(-0.485700\pi\) | ||||
0.0449100 | + | 0.998991i | \(0.485700\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 19781.2 | 0.746276 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 4506.72 | 0.169451 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −22693.1 | −0.850388 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −50811.9 | −1.89772 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 4183.86 | 0.155736 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −4550.84 | −0.168831 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −7114.57 | −0.263064 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 3897.40 | 0.143629 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −11884.7 | −0.436531 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −38489.1 | −1.40905 | −0.704525 | − | 0.709679i | \(-0.748840\pi\) | ||||
−0.704525 | + | 0.709679i | \(0.748840\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −97849.1 | −3.57035 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 29547.5 | 1.07459 | 0.537295 | − | 0.843394i | \(-0.319446\pi\) | ||||
0.537295 | + | 0.843394i | \(0.319446\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1279.23 | 0.0463707 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −82885.9 | −2.99467 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −36484.9 | −1.31389 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −25068.6 | −0.899822 | −0.449911 | − | 0.893073i | \(-0.648544\pi\) | ||||
−0.449911 | + | 0.893073i | \(0.648544\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −63631.6 | −2.27658 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 6146.45 | 0.219191 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 16661.5 | 0.592246 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 6310.43 | 0.223583 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 30066.2 | 1.06183 | 0.530915 | − | 0.847425i | \(-0.321848\pi\) | ||||
0.530915 | + | 0.847425i | \(0.321848\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −15662.9 | −0.551377 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −82700.5 | −2.90192 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 1768.69 | 0.0618634 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −14590.0 | −0.508682 | −0.254341 | − | 0.967115i | \(-0.581858\pi\) | ||||
−0.254341 | + | 0.967115i | \(0.581858\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −40520.0 | −1.40822 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −51836.7 | −1.79578 | −0.897889 | − | 0.440221i | \(-0.854900\pi\) | ||||
−0.897889 | + | 0.440221i | \(0.854900\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −461.894 | −0.0159505 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 53051.9 | 1.82622 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −29471.8 | −1.01130 | −0.505652 | − | 0.862738i | \(-0.668748\pi\) | ||||
−0.505652 | + | 0.862738i | \(0.668748\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −4845.80 | −0.165755 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −47895.5 | −1.63314 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −43125.7 | −1.46588 | −0.732938 | − | 0.680295i | \(-0.761851\pi\) | ||||
−0.732938 | + | 0.680295i | \(0.761851\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −55900.0 | −1.89412 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 1199.64 | 0.0405214 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 11700.7 | 0.393990 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −5165.36 | −0.173387 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 60801.6 | 2.03458 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 52449.3 | 1.74964 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −12445.3 | −0.413872 | −0.206936 | − | 0.978354i | \(-0.566349\pi\) | ||||
−0.206936 | + | 0.978354i | \(0.566349\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 25727.9 | 0.852940 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −43174.2 | −1.42691 | −0.713453 | − | 0.700704i | \(-0.752870\pi\) | ||||
−0.713453 | + | 0.700704i | \(0.752870\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −7454.38 | −0.245608 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −4770.31 | −0.156689 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −8505.17 | −0.278510 | −0.139255 | − | 0.990257i | \(-0.544471\pi\) | ||||
−0.139255 | + | 0.990257i | \(0.544471\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 6375.66 | 0.208138 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −31136.4 | −1.01336 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −7035.65 | −0.228283 | −0.114142 | − | 0.993464i | \(-0.536412\pi\) | ||||
−0.114142 | + | 0.993464i | \(0.536412\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −5132.39 | −0.166022 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −28413.9 | −0.916335 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −1943.39 | −0.0624834 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −37661.1 | −1.20721 | −0.603605 | − | 0.797283i | \(-0.706270\pi\) | ||||
−0.603605 | + | 0.797283i | \(0.706270\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −44027.1 | −1.40701 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 41493.8 | 1.32205 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −17472.0 | −0.555009 | −0.277504 | − | 0.960724i | \(-0.589507\pi\) | ||||
−0.277504 | + | 0.960724i | \(0.589507\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 64836.4 | 2.05339 |
(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 | 1856.4.a.bk.1.12 | 12 | ||
4.3 | odd | 2 | inner | 1856.4.a.bk.1.1 | 12 | ||
8.3 | odd | 2 | 928.4.a.i.1.12 | yes | 12 | ||
8.5 | even | 2 | 928.4.a.i.1.1 | ✓ | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
928.4.a.i.1.1 | ✓ | 12 | 8.5 | even | 2 | ||
928.4.a.i.1.12 | yes | 12 | 8.3 | odd | 2 | ||
1856.4.a.bk.1.1 | 12 | 4.3 | odd | 2 | inner | ||
1856.4.a.bk.1.12 | 12 | 1.1 | even | 1 | trivial |