Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2352,4,Mod(1,2352)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2352, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("2352.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2352 = 2^{4} \cdot 3 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 2352.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: | \(138.772492334\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{8})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 147) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(1.41421\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2352.1 |
$q$-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 | ||||||||
\(3\) | −3.00000 | −0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.100505 | −0.00898945 | −0.00449472 | − | 0.999990i | \(-0.501431\pi\) | ||||
−0.00449472 | + | 0.999990i | \(0.501431\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 9.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 43.9411 | 1.20443 | 0.602216 | − | 0.798333i | \(-0.294285\pi\) | ||||
0.602216 | + | 0.798333i | \(0.294285\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −16.6447 | −0.355108 | −0.177554 | − | 0.984111i | \(-0.556818\pi\) | ||||
−0.177554 | + | 0.984111i | \(0.556818\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.301515 | 0.00519006 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −121.640 | −1.73541 | −0.867704 | − | 0.497081i | \(-0.834405\pi\) | ||||
−0.867704 | + | 0.497081i | \(0.834405\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 127.113 | 1.53482 | 0.767412 | − | 0.641154i | \(-0.221544\pi\) | ||||
0.767412 | + | 0.641154i | \(0.221544\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −53.5980 | −0.485911 | −0.242955 | − | 0.970037i | \(-0.578117\pi\) | ||||
−0.242955 | + | 0.970037i | \(0.578117\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −124.990 | −0.999919 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −27.0000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 235.681 | 1.50913 | 0.754567 | − | 0.656223i | \(-0.227847\pi\) | ||||
0.754567 | + | 0.656223i | \(0.227847\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 18.7107 | 0.108404 | 0.0542022 | − | 0.998530i | \(-0.482738\pi\) | ||||
0.0542022 | + | 0.998530i | \(0.482738\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −131.823 | −0.695379 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −191.882 | −0.852574 | −0.426287 | − | 0.904588i | \(-0.640179\pi\) | ||||
−0.426287 | + | 0.904588i | \(0.640179\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 49.9340 | 0.205021 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −319.713 | −1.21782 | −0.608912 | − | 0.793238i | \(-0.708394\pi\) | ||||
−0.608912 | + | 0.793238i | \(0.708394\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 218.579 | 0.775184 | 0.387592 | − | 0.921831i | \(-0.373307\pi\) | ||||
0.387592 | + | 0.921831i | \(0.373307\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −0.904546 | −0.00299648 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −401.553 | −1.24623 | −0.623113 | − | 0.782132i | \(-0.714132\pi\) | ||||
−0.623113 | + | 0.782132i | \(0.714132\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 364.919 | 1.00194 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 643.117 | 1.66677 | 0.833386 | − | 0.552692i | \(-0.186399\pi\) | ||||
0.833386 | + | 0.552692i | \(0.186399\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −4.41631 | −0.0108272 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −381.338 | −0.886131 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 11.6123 | 0.0256235 | 0.0128118 | − | 0.999918i | \(-0.495922\pi\) | ||||
0.0128118 | + | 0.999918i | \(0.495922\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −12.2426 | −0.0256969 | −0.0128484 | − | 0.999917i | \(-0.504090\pi\) | ||||
−0.0128484 | + | 0.999917i | \(0.504090\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 1.67287 | 0.00319222 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −669.048 | −1.21996 | −0.609979 | − | 0.792417i | \(-0.708822\pi\) | ||||
−0.609979 | + | 0.792417i | \(0.708822\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 160.794 | 0.280541 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −822.098 | −1.37416 | −0.687078 | − | 0.726584i | \(-0.741107\pi\) | ||||
−0.687078 | + | 0.726584i | \(0.741107\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 515.100 | 0.825861 | 0.412930 | − | 0.910763i | \(-0.364505\pi\) | ||||
0.412930 | + | 0.910763i | \(0.364505\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 374.970 | 0.577304 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 805.754 | 1.14752 | 0.573762 | − | 0.819022i | \(-0.305483\pi\) | ||||
0.573762 | + | 0.819022i | \(0.305483\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 394.863 | 0.522191 | 0.261095 | − | 0.965313i | \(-0.415916\pi\) | ||||
0.261095 | + | 0.965313i | \(0.415916\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 12.2254 | 0.0156004 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −707.044 | −0.871299 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 673.418 | 0.802047 | 0.401024 | − | 0.916068i | \(-0.368655\pi\) | ||||
0.401024 | + | 0.916068i | \(0.368655\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −56.1320 | −0.0625873 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −12.7755 | −0.0137972 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1091.11 | −1.14212 | −0.571061 | − | 0.820908i | \(-0.693468\pi\) | ||||
−0.571061 | + | 0.820908i | \(0.693468\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 395.470 | 0.401477 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1370.79 | −1.35048 | −0.675242 | − | 0.737597i | \(-0.735961\pi\) | ||||
−0.675242 | + | 0.737597i | \(0.735961\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1413.96 | 1.35263 | 0.676316 | − | 0.736611i | \(-0.263575\pi\) | ||||
0.676316 | + | 0.736611i | \(0.263575\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 343.539 | 0.310385 | 0.155192 | − | 0.987884i | \(-0.450400\pi\) | ||||
0.155192 | + | 0.987884i | \(0.450400\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −317.657 | −0.279138 | −0.139569 | − | 0.990212i | \(-0.544572\pi\) | ||||
−0.139569 | + | 0.990212i | \(0.544572\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 575.647 | 0.492234 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 798.373 | 0.664643 | 0.332321 | − | 0.943166i | \(-0.392168\pi\) | ||||
0.332321 | + | 0.943166i | \(0.392168\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 5.38687 | 0.00436807 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −149.802 | −0.118369 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 599.823 | 0.450656 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 959.138 | 0.703110 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 25.1253 | 0.0179782 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1071.40 | −0.748593 | −0.374297 | − | 0.927309i | \(-0.622116\pi\) | ||||
−0.374297 | + | 0.927309i | \(0.622116\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −655.736 | −0.447553 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 2515.02 | 1.67739 | 0.838695 | − | 0.544601i | \(-0.183319\pi\) | ||||
0.838695 | + | 0.544601i | \(0.183319\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 2.71364 | 0.00173002 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 251.064 | 0.156568 | 0.0782841 | − | 0.996931i | \(-0.475056\pi\) | ||||
0.0782841 | + | 0.996931i | \(0.475056\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −886.067 | −0.540685 | −0.270343 | − | 0.962764i | \(-0.587137\pi\) | ||||
−0.270343 | + | 0.962764i | \(0.587137\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1204.66 | 0.719508 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −731.385 | −0.427703 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −23.6872 | −0.0135663 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 582.626 | 0.320339 | 0.160170 | − | 0.987090i | \(-0.448796\pi\) | ||||
0.160170 | + | 0.987090i | \(0.448796\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2811.76 | 1.51535 | 0.757676 | − | 0.652631i | \(-0.226335\pi\) | ||||
0.757676 | + | 0.652631i | \(0.226335\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −1094.76 | −0.578469 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −1.88052 | −0.000974496 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1691.34 | −0.859770 | −0.429885 | − | 0.902884i | \(-0.641446\pi\) | ||||
−0.429885 | + | 0.902884i | \(0.641446\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −1929.35 | −0.962311 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 40.7232 | 0.0195686 | 0.00978432 | − | 0.999952i | \(-0.496886\pi\) | ||||
0.00978432 | + | 0.999952i | \(0.496886\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 13.2489 | 0.00625107 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −2900.47 | −1.34398 | −0.671990 | − | 0.740560i | \(-0.734560\pi\) | ||||
−0.671990 | + | 0.740560i | \(0.734560\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1919.96 | −0.873899 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1144.01 | 0.511608 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −2146.15 | −0.943171 | −0.471585 | − | 0.881820i | \(-0.656318\pi\) | ||||
−0.471585 | + | 0.881820i | \(0.656318\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −34.8368 | −0.0147938 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −1203.54 | −0.502552 | −0.251276 | − | 0.967916i | \(-0.580850\pi\) | ||||
−0.251276 | + | 0.967916i | \(0.580850\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −2990.47 | −1.22807 | −0.614033 | − | 0.789280i | \(-0.710454\pi\) | ||||
−0.614033 | + | 0.789280i | \(0.710454\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 36.7279 | 0.0148361 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 19.2851 | 0.00766417 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −5344.98 | −2.09018 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 2807.41 | 1.06354 | 0.531772 | − | 0.846887i | \(-0.321526\pi\) | ||||
0.531772 | + | 0.846887i | \(0.321526\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 3336.37 | 1.24434 | 0.622169 | − | 0.782883i | \(-0.286252\pi\) | ||||
0.622169 | + | 0.782883i | \(0.286252\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −5.01862 | −0.00184303 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −4226.65 | −1.52861 | −0.764305 | − | 0.644855i | \(-0.776918\pi\) | ||||
−0.764305 | + | 0.644855i | \(0.776918\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −4385.69 | −1.56228 | −0.781140 | − | 0.624356i | \(-0.785361\pi\) | ||||
−0.781140 | + | 0.624356i | \(0.785361\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 2007.14 | 0.704343 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 32.1328 | 0.0109476 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −482.382 | −0.161970 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 5585.48 | 1.84859 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −2291.56 | −0.747665 | −0.373833 | − | 0.927496i | \(-0.621957\pi\) | ||||
−0.373833 | + | 0.927496i | \(0.621957\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 2466.29 | 0.793369 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −21.9683 | −0.00696848 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −1545.30 | −0.476811 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 2024.65 | 0.616257 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 217.970 | 0.0654544 | 0.0327272 | − | 0.999464i | \(-0.489581\pi\) | ||||
0.0327272 | + | 0.999464i | \(0.489581\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −1124.91 | −0.333306 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −1835.36 | −0.536639 | −0.268320 | − | 0.963330i | \(-0.586468\pi\) | ||||
−0.268320 | + | 0.963330i | \(0.586468\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 2774.01 | 0.800488 | 0.400244 | − | 0.916409i | \(-0.368925\pi\) | ||||
0.400244 | + | 0.916409i | \(0.368925\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −988.712 | −0.277994 | −0.138997 | − | 0.990293i | \(-0.544388\pi\) | ||||
−0.138997 | + | 0.990293i | \(0.544388\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 40.3581 | 0.0112029 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −2417.26 | −0.662524 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 837.928 | 0.226783 | 0.113391 | − | 0.993550i | \(-0.463829\pi\) | ||||
0.113391 | + | 0.993550i | \(0.463829\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −3454.99 | −0.923466 | −0.461733 | − | 0.887019i | \(-0.652772\pi\) | ||||
−0.461733 | + | 0.887019i | \(0.652772\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −243.000 | −0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −2115.75 | −0.545028 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −1184.59 | −0.301487 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −5635.01 | −1.41705 | −0.708523 | − | 0.705688i | \(-0.750638\pi\) | ||||
−0.708523 | + | 0.705688i | \(0.750638\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2355.16 | −0.585246 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −36.6762 | −0.00900687 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −2271.16 | −0.551248 | −0.275624 | − | 0.961265i | \(-0.588885\pi\) | ||||
−0.275624 | + | 0.961265i | \(0.588885\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 2121.13 | 0.503045 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −163.867 | −0.0384201 | −0.0192101 | − | 0.999815i | \(-0.506115\pi\) | ||||
−0.0192101 | + | 0.999815i | \(0.506115\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −64.6365 | −0.0149834 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −2020.26 | −0.463062 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −5167.10 | −1.17116 | −0.585582 | − | 0.810613i | \(-0.699134\pi\) | ||||
−0.585582 | + | 0.810613i | \(0.699134\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1622.27 | 0.363638 | 0.181819 | − | 0.983332i | \(-0.441801\pi\) | ||||
0.181819 | + | 0.983332i | \(0.441801\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −5492.20 | −1.20433 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −4612.37 | −1.00047 | −0.500235 | − | 0.865890i | \(-0.666753\pi\) | ||||
−0.500235 | + | 0.865890i | \(0.666753\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 168.396 | 0.0361348 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −2125.22 | −0.451174 | −0.225587 | − | 0.974223i | \(-0.572430\pi\) | ||||
−0.225587 | + | 0.974223i | \(0.572430\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −2571.54 | −0.540149 | −0.270075 | − | 0.962839i | \(-0.587048\pi\) | ||||
−0.270075 | + | 0.962839i | \(0.587048\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 38.3264 | 0.00796583 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 9883.19 | 2.01164 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 3273.34 | 0.659404 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −3324.96 | −0.662957 | −0.331478 | − | 0.943463i | \(-0.607547\pi\) | ||||
−0.331478 | + | 0.943463i | \(0.607547\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1.16709 | −0.000230341 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −1186.41 | −0.231793 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 892.120 | 0.172551 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 4112.37 | 0.779702 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 1.23045 | 0.000231001 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −887.096 | −0.164916 | −0.0824580 | − | 0.996595i | \(-0.526277\pi\) | ||||
−0.0824580 | + | 0.996595i | \(0.526277\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −4241.87 | −0.780943 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −4510.82 | −0.822460 | −0.411230 | − | 0.911532i | \(-0.634901\pi\) | ||||
−0.411230 | + | 0.911532i | \(0.634901\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −3715.78 | −0.671018 | −0.335509 | − | 0.942037i | \(-0.608908\pi\) | ||||
−0.335509 | + | 0.942037i | \(0.608908\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 6954.52 | 1.23219 | 0.616096 | − | 0.787671i | \(-0.288713\pi\) | ||||
0.616096 | + | 0.787671i | \(0.288713\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 10356.1 | 1.81765 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −1030.62 | −0.179201 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −15461.9 | −2.66355 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 2080.41 | 0.355079 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 952.971 | 0.161160 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 9863.18 | 1.63785 | 0.818926 | − | 0.573899i | \(-0.194570\pi\) | ||||
0.818926 | + | 0.573899i | \(0.194570\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −1726.94 | −0.284191 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 67.2427 | 0.0109668 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −5945.06 | −0.960974 | −0.480487 | − | 0.877002i | \(-0.659540\pi\) | ||||
−0.480487 | + | 0.877002i | \(0.659540\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −2395.12 | −0.383732 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 822.168 | 0.130566 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −16.1606 | −0.00252191 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −1169.57 | −0.180939 | −0.0904697 | − | 0.995899i | \(-0.528837\pi\) | ||||
−0.0904697 | + | 0.995899i | \(0.528837\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 9176.66 | 1.40749 | 0.703747 | − | 0.710451i | \(-0.251509\pi\) | ||||
0.703747 | + | 0.710451i | \(0.251509\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 449.406 | 0.0683405 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −10587.2 | −1.59632 | −0.798158 | − | 0.602448i | \(-0.794192\pi\) | ||||
−0.798158 | + | 0.602448i | \(0.794192\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 82.6250 | 0.0123529 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −8615.21 | −1.26656 | −0.633278 | − | 0.773924i | \(-0.718291\pi\) | ||||
−0.633278 | + | 0.773924i | \(0.718291\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 9298.64 | 1.35568 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −1799.47 | −0.260186 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −51.7701 | −0.00742403 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 8297.79 | 1.18022 | 0.590110 | − | 0.807323i | \(-0.299084\pi\) | ||||
0.590110 | + | 0.807323i | \(0.299084\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −2877.41 | −0.405941 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −5123.86 | −0.711269 | −0.355634 | − | 0.934625i | \(-0.615735\pi\) | ||||
−0.355634 | + | 0.934625i | \(0.615735\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −75.3758 | −0.0103797 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −3922.83 | −0.535905 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 1502.49 | 0.203635 | 0.101817 | − | 0.994803i | \(-0.467534\pi\) | ||||
0.101817 | + | 0.994803i | \(0.467534\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 3214.20 | 0.432200 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −10872.9 | −1.45060 | −0.725301 | − | 0.688431i | \(-0.758300\pi\) | ||||
−0.725301 | + | 0.688431i | \(0.758300\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 1967.21 | 0.258395 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 4618.99 | 0.602036 | 0.301018 | − | 0.953618i | \(-0.402674\pi\) | ||||
0.301018 | + | 0.953618i | \(0.402674\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 6519.64 | 0.843254 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −7545.05 | −0.968442 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −80.9824 | −0.0103156 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −9606.95 | −1.21451 | −0.607253 | − | 0.794508i | \(-0.707729\pi\) | ||||
−0.607253 | + | 0.794508i | \(0.707729\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −10501.0 | −1.30772 | −0.653862 | − | 0.756614i | \(-0.726852\pi\) | ||||
−0.653862 | + | 0.756614i | \(0.726852\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −311.433 | −0.0384952 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −8.14091 | −0.000998827 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −8431.52 | −1.02687 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 12066.9 | 1.45885 | 0.729427 | − | 0.684059i | \(-0.239787\pi\) | ||||
0.729427 | + | 0.684059i | \(0.239787\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −753.192 | −0.0903947 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −39.6857 | −0.00469421 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 2658.20 | 0.312165 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −6366.31 | −0.742278 | −0.371139 | − | 0.928577i | \(-0.621033\pi\) | ||||
−0.371139 | + | 0.928577i | \(0.621033\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −4731.84 | −0.547781 | −0.273890 | − | 0.961761i | \(-0.588311\pi\) | ||||
−0.273890 | + | 0.961761i | \(0.588311\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −3613.98 | −0.415408 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 15203.7 | 1.73527 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 2194.16 | 0.246934 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −3752.78 | −0.419409 | −0.209704 | − | 0.977765i | \(-0.567250\pi\) | ||||
−0.209704 | + | 0.977765i | \(0.567250\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −11709.2 | −1.29956 | −0.649780 | − | 0.760122i | \(-0.725139\pi\) | ||||
−0.649780 | + | 0.760122i | \(0.725139\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 71.0615 | 0.00783250 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −6812.98 | −0.745788 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −14924.7 | −1.62259 | −0.811296 | − | 0.584635i | \(-0.801238\pi\) | ||||
−0.811296 | + | 0.584635i | \(0.801238\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 8517.66 | 0.913513 | 0.456756 | − | 0.889592i | \(-0.349011\pi\) | ||||
0.456756 | + | 0.889592i | \(0.349011\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −67.6820 | −0.00720996 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −1747.88 | −0.184948 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −5965.73 | −0.627038 | −0.313519 | − | 0.949582i | \(-0.601508\pi\) | ||||
−0.313519 | + | 0.949582i | \(0.601508\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −14048.5 | −1.46678 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −8435.29 | −0.874889 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −13860.6 | −1.41875 | −0.709376 | − | 0.704830i | \(-0.751023\pi\) | ||||
−0.709376 | + | 0.704830i | \(0.751023\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 3284.27 | 0.333979 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 149.312 | 0.0150850 | 0.00754249 | − | 0.999972i | \(-0.497599\pi\) | ||||
0.00754249 | + | 0.999972i | \(0.497599\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −5403.95 | −0.542425 | −0.271213 | − | 0.962519i | \(-0.587425\pi\) | ||||
−0.271213 | + | 0.962519i | \(0.587425\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 5.64155 | 0.000562625 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 3704.66 | 0.367090 | 0.183545 | − | 0.983011i | \(-0.441243\pi\) | ||||
0.183545 | + | 0.983011i | \(0.441243\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 5074.03 | 0.496389 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 9604.59 | 0.933657 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −15887.8 | −1.53470 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 5788.05 | 0.555591 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −10671.8 | −1.01796 | −0.508982 | − | 0.860777i | \(-0.669978\pi\) | ||||
−0.508982 | + | 0.860777i | \(0.669978\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 3193.82 | 0.302756 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 109.662 | 0.0102670 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −5853.92 | −0.544695 | −0.272348 | − | 0.962199i | \(-0.587800\pi\) | ||||
−0.272348 | + | 0.962199i | \(0.587800\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −122.170 | −0.0112980 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −4065.31 | −0.373656 | −0.186828 | − | 0.982393i | \(-0.559821\pi\) | ||||
−0.186828 | + | 0.982393i | \(0.559821\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −28668.2 | −2.61896 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −39.7468 | −0.00360906 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −4811.19 | −0.431620 | −0.215810 | − | 0.976435i | \(-0.569239\pi\) | ||||
−0.215810 | + | 0.976435i | \(0.569239\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 8701.40 | 0.775947 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 17001.2 | 1.50705 | 0.753526 | − | 0.657418i | \(-0.228351\pi\) | ||||
0.753526 | + | 0.657418i | \(0.228351\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 137.771 | 0.0121401 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 5759.87 | 0.504546 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −13797.2 | −1.20148 | −0.600738 | − | 0.799446i | \(-0.705126\pi\) | ||||
−0.600738 | + | 0.799446i | \(0.705126\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −3432.04 | −0.295377 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −142.110 | −0.0121594 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −17644.7 | −1.50099 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 6438.44 | 0.544540 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −3936.61 | −0.331029 | −0.165515 | − | 0.986207i | \(-0.552928\pi\) | ||||
−0.165515 | + | 0.986207i | \(0.552928\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 17459.3 | 1.45973 | 0.729866 | − | 0.683590i | \(-0.239582\pi\) | ||||
0.729866 | + | 0.683590i | \(0.239582\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −2275.96 | −0.188126 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −9294.26 | −0.763891 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 104.510 | 0.00854118 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 5321.51 | 0.432458 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −34.5274 | −0.00279019 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 3610.62 | 0.290148 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 19101.3 | 1.51798 | 0.758992 | − | 0.651100i | \(-0.225692\pi\) | ||||
0.758992 | + | 0.651100i | \(0.225692\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 8971.41 | 0.709024 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 31.9261 | 0.00250929 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −15413.5 | −1.20481 | −0.602407 | − | 0.798189i | \(-0.705792\pi\) | ||||
−0.602407 | + | 0.798189i | \(0.705792\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −110.184 | −0.00856563 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 29958.1 | 2.31626 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −57.8554 | −0.00442491 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −20492.9 | −1.55891 | −0.779453 | − | 0.626460i | \(-0.784503\pi\) | ||||
−0.779453 | + | 0.626460i | \(0.784503\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −3638.17 | −0.275274 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 16034.9 | 1.20677 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −7142.49 | −0.534671 | −0.267336 | − | 0.963603i | \(-0.586143\pi\) | ||||
−0.267336 | + | 0.963603i | \(0.586143\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −80.2406 | −0.00597477 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 4097.91 | 0.301922 | 0.150961 | − | 0.988540i | \(-0.451763\pi\) | ||||
0.150961 | + | 0.988540i | \(0.451763\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 2838.48 | 0.208033 | 0.104016 | − | 0.994576i | \(-0.466831\pi\) | ||||
0.104016 | + | 0.994576i | \(0.466831\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −8422.23 | −0.614038 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 6699.21 | 0.485872 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 15464.5 | 1.11576 | 0.557881 | − | 0.829921i | \(-0.311615\pi\) | ||||
0.557881 | + | 0.829921i | \(0.311615\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −10009.1 | −0.718418 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 28259.3 | 2.00751 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 15.0559 | 0.00106407 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 14003.6 | 0.984652 | 0.492326 | − | 0.870411i | \(-0.336147\pi\) | ||||
0.492326 | + | 0.870411i | \(0.336147\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 2378.36 | 0.166382 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 12679.9 | 0.882543 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −6504.50 | −0.450435 | −0.225217 | − | 0.974309i | \(-0.572309\pi\) | ||||
−0.225217 | + | 0.974309i | \(0.572309\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 13157.1 | 0.901982 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 12616.1 | 0.860567 | 0.430284 | − | 0.902694i | \(-0.358414\pi\) | ||||
0.430284 | + | 0.902694i | \(0.358414\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −8270.87 | −0.561358 | −0.280679 | − | 0.959802i | \(-0.590560\pi\) | ||||
−0.280679 | + | 0.959802i | \(0.590560\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −6021.43 | −0.406653 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −60.2852 | −0.00405114 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 3811.84 | 0.254889 | 0.127445 | − | 0.991846i | \(-0.459323\pi\) | ||||
0.127445 | + | 0.991846i | \(0.459323\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 6683.72 | 0.442544 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 11359.3 | 0.748445 | 0.374222 | − | 0.927339i | \(-0.377910\pi\) | ||||
0.374222 | + | 0.927339i | \(0.377910\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −96.3983 | −0.00632057 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −18272.2 | −1.19224 | −0.596118 | − | 0.802896i | \(-0.703291\pi\) | ||||
−0.596118 | + | 0.802896i | \(0.703291\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 29600.2 | 1.92203 | 0.961013 | − | 0.276503i | \(-0.0891756\pi\) | ||||
0.961013 | + | 0.276503i | \(0.0891756\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1447.15 | 0.0935136 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 15621.2 | 0.999758 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −16756.4 | −1.06728 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 23340.5 | 1.47956 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −7185.41 | −0.453322 | −0.226661 | − | 0.973974i | \(-0.572781\pi\) | ||||
−0.226661 | + | 0.973974i | \(0.572781\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 6874.67 | 0.431665 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 107.681 | 0.00672944 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −7398.88 | −0.458052 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −232.982 | −0.0143561 | −0.00717803 | − | 0.999974i | \(-0.502285\pi\) | ||||
−0.00717803 | + | 0.999974i | \(0.502285\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −1837.96 | −0.112725 | −0.0563624 | − | 0.998410i | \(-0.517950\pi\) | ||||
−0.0563624 | + | 0.998410i | \(0.517950\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 65.9048 | 0.00402325 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −18594.7 | −1.12988 | −0.564941 | − | 0.825131i | \(-0.691101\pi\) | ||||
−0.564941 | + | 0.825131i | \(0.691101\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 510.256 | 0.0308618 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −28864.7 | −1.72980 | −0.864902 | − | 0.501940i | \(-0.832620\pi\) | ||||
−0.864902 | + | 0.501940i | \(0.832620\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −252.772 | −0.0150788 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 4635.90 | 0.275287 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 29066.3 | 1.71815 | 0.859076 | − | 0.511847i | \(-0.171039\pi\) | ||||
0.859076 | + | 0.511847i | \(0.171039\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 3979.51 | 0.234168 | 0.117084 | − | 0.993122i | \(-0.462645\pi\) | ||||
0.117084 | + | 0.993122i | \(0.462645\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −6073.95 | −0.355796 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −12632.0 | −0.733305 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −653.909 | −0.0377901 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −537.955 | −0.0309501 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −184.229 | −0.0105520 | −0.00527601 | − | 0.999986i | \(-0.501679\pi\) | ||||
−0.00527601 | + | 0.999986i | \(0.501679\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 3374.73 | 0.192435 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 16683.5 | 0.947116 | 0.473558 | − | 0.880763i | \(-0.342969\pi\) | ||||
0.473558 | + | 0.880763i | \(0.342969\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 5506.08 | 0.309829 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −17808.2 | −0.997676 | −0.498838 | − | 0.866695i | \(-0.666240\pi\) | ||||
−0.498838 | + | 0.866695i | \(0.666240\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −25.2332 | −0.00140746 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −8322.03 | −0.462162 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −10704.5 | −0.591883 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −20145.7 | −1.10908 | −0.554542 | − | 0.832156i | \(-0.687106\pi\) | ||||
−0.554542 | + | 0.832156i | \(0.687106\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 89.0542 | 0.00486046 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 38889.7 | 2.11342 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 2966.14 | 0.160500 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −2719.67 | −0.146534 | −0.0732672 | − | 0.997312i | \(-0.523343\pi\) | ||||
−0.0732672 | + | 0.997312i | \(0.523343\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −24390.7 | −1.30855 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −121.074 | −0.00646798 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −625.708 | −0.0331438 | −0.0165719 | − | 0.999863i | \(-0.505275\pi\) | ||||
−0.0165719 | + | 0.999863i | \(0.505275\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 7251.79 | 0.382508 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −1002.85 | −0.0526749 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 73.5079 | 0.00384481 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −2513.78 | −0.130933 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −9577.54 | −0.496776 | −0.248388 | − | 0.968661i | \(-0.579901\pi\) | ||||
−0.248388 | + | 0.968661i | \(0.579901\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 10365.0 | 0.533163 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −29457.8 | −1.50901 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −16741.2 | −0.854053 | −0.427027 | − | 0.904239i | \(-0.640439\pi\) | ||||
−0.427027 | + | 0.904239i | \(0.640439\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −26587.8 | −1.34526 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 6496.04 | 0.327335 | 0.163668 | − | 0.986516i | \(-0.447668\pi\) | ||||
0.163668 | + | 0.986516i | \(0.447668\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −29398.7 | −1.46936 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −499.280 | −0.0248529 | −0.0124265 | − | 0.999923i | \(-0.503956\pi\) | ||||
−0.0124265 | + | 0.999923i | \(0.503956\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 6347.24 | 0.314672 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 6367.30 | 0.314393 | 0.157196 | − | 0.987567i | \(-0.449754\pi\) | ||||
0.157196 | + | 0.987567i | \(0.449754\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −58.5568 | −0.00287967 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 3553.77 | 0.174064 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −496.098 | −0.0241050 | −0.0120525 | − | 0.999927i | \(-0.503837\pi\) | ||||
−0.0120525 | + | 0.999927i | \(0.503837\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 16905.0 | 0.818132 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −282.597 | −0.0136222 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 13025.9 | 0.625408 | 0.312704 | − | 0.949851i | \(-0.398765\pi\) | ||||
0.312704 | + | 0.949851i | \(0.398765\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 7065.47 | 0.337892 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 25474.6 | 1.21347 | 0.606736 | − | 0.794904i | \(-0.292479\pi\) | ||||
0.606736 | + | 0.794904i | \(0.292479\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 110.029 | 0.00520012 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −193.282 | −0.00909911 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 29054.0 | 1.36244 | 0.681218 | − | 0.732080i | \(-0.261450\pi\) | ||||
0.681218 | + | 0.732080i | \(0.261450\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 6813.47 | 0.318263 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −1897.35 | −0.0882834 | −0.0441417 | − | 0.999025i | \(-0.514055\pi\) | ||||
−0.0441417 | + | 0.999025i | \(0.514055\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −2338.65 | −0.108396 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −40639.6 | −1.86914 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −36123.9 | −1.65508 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −6363.39 | −0.290433 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 169.989 | 0.00772886 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 42650.3 | 1.93179 | 0.965895 | − | 0.258936i | \(-0.0833718\pi\) | ||||
0.965895 | + | 0.258936i | \(0.0833718\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 491.602 | 0.0221819 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 203.775 | 0.00912516 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 193.910 | 0.00865064 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −36822.8 | −1.63655 | −0.818275 | − | 0.574828i | \(-0.805069\pi\) | ||||
−0.818275 | + | 0.574828i | \(0.805069\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 48844.8 | 2.16271 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 6060.77 | 0.267349 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 22634.1 | 0.994693 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 15501.3 | 0.676172 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 5081.94 | 0.220855 | 0.110427 | − | 0.993884i | \(-0.464778\pi\) | ||||
0.110427 | + | 0.993884i | \(0.464778\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 11873.4 | 0.514097 | 0.257048 | − | 0.966399i | \(-0.417250\pi\) | ||||
0.257048 | + | 0.966399i | \(0.417250\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −4866.82 | −0.209947 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −4.09289 | −0.000175911 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 27784.1 | 1.18977 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 16969.4 | 0.721361 | 0.360681 | − | 0.932689i | \(-0.382544\pi\) | ||||
0.360681 | + | 0.932689i | \(0.382544\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −3995.94 | −0.169246 | −0.0846231 | − | 0.996413i | \(-0.526969\pi\) | ||||
−0.0846231 | + | 0.996413i | \(0.526969\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 16476.6 | 0.695323 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 13589.7 | 0.571417 | 0.285708 | − | 0.958317i | \(-0.407771\pi\) | ||||
0.285708 | + | 0.958317i | \(0.407771\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 30646.0 | 1.28393 | 0.641966 | − | 0.766733i | \(-0.278119\pi\) | ||||
0.641966 | + | 0.766733i | \(0.278119\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 13837.1 | 0.577622 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 291.511 | 0.0120816 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −505.188 | −0.0208624 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −7497.57 | −0.308516 | −0.154258 | − | 0.988031i | \(-0.549299\pi\) | ||||
−0.154258 | + | 0.988031i | \(0.549299\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 31156.6 | 1.27749 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 6375.65 | 0.260485 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 192.965 | 0.00785586 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 7714.62 | 0.311855 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 10284.5 | 0.414275 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 10347.6 | 0.415352 | 0.207676 | − | 0.978198i | \(-0.433410\pi\) | ||||
0.207676 | + | 0.978198i | \(0.433410\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −114.979 | −0.00459907 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −1550.00 | −0.0617817 | −0.0308909 | − | 0.999523i | \(-0.509834\pi\) | ||||
−0.0308909 | + | 0.999523i | \(0.509834\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 15187.5 | 0.603250 | 0.301625 | − | 0.953427i | \(-0.402471\pi\) | ||||
0.301625 | + | 0.953427i | \(0.402471\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −41550.2 | −1.63892 | −0.819459 | − | 0.573138i | \(-0.805726\pi\) | ||||
−0.819459 | + | 0.573138i | \(0.805726\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 215.699 | 0.00847858 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −29649.6 | −1.16142 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 35405.8 | 1.38212 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 11136.1 | 0.433216 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −9820.03 | −0.380707 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 27837.4 | 1.07184 | 0.535919 | − | 0.844269i | \(-0.319965\pi\) | ||||
0.535919 | + | 0.844269i | \(0.319965\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 9974.89 | 0.382758 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 2587.85 | 0.0989635 | 0.0494817 | − | 0.998775i | \(-0.484243\pi\) | ||||
0.0494817 | + | 0.998775i | \(0.484243\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 16382.0 | 0.624346 | 0.312173 | − | 0.950025i | \(-0.398943\pi\) | ||||
0.312173 | + | 0.950025i | \(0.398943\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 3.50127 | 0.000132988 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −22980.2 | −0.869896 | −0.434948 | − | 0.900456i | \(-0.643233\pi\) | ||||
−0.434948 | + | 0.900456i | \(0.643233\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 3559.23 | 0.133826 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −51042.5 | −1.91274 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 120.962 | 0.00451766 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −2676.36 | −0.0996222 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 4409.76 | 0.163597 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −78228.5 | −2.89253 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 300.557 | 0.0110396 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 22715.4 | 0.831590 | 0.415795 | − | 0.909458i | \(-0.363503\pi\) | ||||
0.415795 | + | 0.909458i | \(0.363503\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −12337.1 | −0.450161 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −34922.3 | −1.27006 | −0.635031 | − | 0.772487i | \(-0.719013\pi\) | ||||
−0.635031 | + | 0.772487i | \(0.719013\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 17350.7 | 0.628943 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −3.69134 | −0.000133368 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −11702.6 | −0.420059 | −0.210030 | − | 0.977695i | \(-0.567356\pi\) | ||||
−0.210030 | + | 0.977695i | \(0.567356\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 2661.29 | 0.0952144 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 13683.5 | 0.487973 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 23983.3 | 0.852505 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 12725.6 | 0.450878 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 53096.5 | 1.87518 | 0.937588 | − | 0.347747i | \(-0.113053\pi\) | ||||
0.937588 | + | 0.347747i | \(0.113053\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 13532.5 | 0.474848 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 537.198 | 0.0187896 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 39020.6 | 1.36046 | 0.680229 | − | 0.733000i | \(-0.261880\pi\) | ||||
0.680229 | + | 0.733000i | \(0.261880\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 11147.4 | 0.387412 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −30743.8 | −1.06506 | −0.532528 | − | 0.846412i | \(-0.678758\pi\) | ||||
−0.532528 | + | 0.846412i | \(0.678758\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 17136.0 | 0.591754 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −16300.3 | −0.559332 | −0.279666 | − | 0.960097i | \(-0.590224\pi\) | ||||
−0.279666 | + | 0.960097i | \(0.590224\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −8573.66 | −0.293269 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −20863.6 | −0.711406 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −11512.7 | −0.391325 | −0.195663 | − | 0.980671i | \(-0.562686\pi\) | ||||
−0.195663 | + | 0.980671i | \(0.562686\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −282.159 | −0.00956068 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −31068.3 | −1.04942 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −29440.9 | −0.988248 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 3091.85 | 0.103462 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −335.322 | −0.0111859 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 18178.4 | 0.604528 | 0.302264 | − | 0.953224i | \(-0.402258\pi\) | ||||
0.302264 | + | 0.953224i | \(0.402258\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 46385.8 | 1.53780 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −28276.7 | −0.934543 | −0.467271 | − | 0.884114i | \(-0.654763\pi\) | ||||
−0.467271 | + | 0.884114i | \(0.654763\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −6241.24 | −0.205005 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −13947.1 | −0.456710 | −0.228355 | − | 0.973578i | \(-0.573335\pi\) | ||||
−0.228355 | + | 0.973578i | \(0.573335\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 29590.8 | 0.966011 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −2858.91 | −0.0930459 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 26576.8 | 0.862327 | 0.431164 | − | 0.902274i | \(-0.358103\pi\) | ||||
0.431164 | + | 0.902274i | \(0.358103\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 424.799 | 0.0137414 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −11715.4 | −0.376671 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −16249.9 | −0.520884 | −0.260442 | − | 0.965490i | \(-0.583868\pi\) | ||||
−0.260442 | + | 0.965490i | \(0.583868\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −29589.5 | −0.945615 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 440.784 | 0.0140440 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 18814.1 | 0.597642 | 0.298821 | − | 0.954309i | \(-0.403407\pi\) | ||||
0.298821 | + | 0.954309i | \(0.403407\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 5180.82 | 0.164078 |
(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 | 2352.4.a.bl.1.2 | 2 | ||
4.3 | odd | 2 | 147.4.a.k.1.1 | yes | 2 | ||
7.6 | odd | 2 | 2352.4.a.cf.1.1 | 2 | |||
12.11 | even | 2 | 441.4.a.o.1.2 | 2 | |||
28.3 | even | 6 | 147.4.e.k.79.2 | 4 | |||
28.11 | odd | 6 | 147.4.e.j.79.2 | 4 | |||
28.19 | even | 6 | 147.4.e.k.67.2 | 4 | |||
28.23 | odd | 6 | 147.4.e.j.67.2 | 4 | |||
28.27 | even | 2 | 147.4.a.j.1.1 | ✓ | 2 | ||
84.11 | even | 6 | 441.4.e.u.226.1 | 4 | |||
84.23 | even | 6 | 441.4.e.u.361.1 | 4 | |||
84.47 | odd | 6 | 441.4.e.v.361.1 | 4 | |||
84.59 | odd | 6 | 441.4.e.v.226.1 | 4 | |||
84.83 | odd | 2 | 441.4.a.n.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
147.4.a.j.1.1 | ✓ | 2 | 28.27 | even | 2 | ||
147.4.a.k.1.1 | yes | 2 | 4.3 | odd | 2 | ||
147.4.e.j.67.2 | 4 | 28.23 | odd | 6 | |||
147.4.e.j.79.2 | 4 | 28.11 | odd | 6 | |||
147.4.e.k.67.2 | 4 | 28.19 | even | 6 | |||
147.4.e.k.79.2 | 4 | 28.3 | even | 6 | |||
441.4.a.n.1.2 | 2 | 84.83 | odd | 2 | |||
441.4.a.o.1.2 | 2 | 12.11 | even | 2 | |||
441.4.e.u.226.1 | 4 | 84.11 | even | 6 | |||
441.4.e.u.361.1 | 4 | 84.23 | even | 6 | |||
441.4.e.v.226.1 | 4 | 84.59 | odd | 6 | |||
441.4.e.v.361.1 | 4 | 84.47 | odd | 6 | |||
2352.4.a.bl.1.2 | 2 | 1.1 | even | 1 | trivial | ||
2352.4.a.cf.1.1 | 2 | 7.6 | odd | 2 |