Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1849,4,Mod(1,1849)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1849, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1849.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1849 = 43^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1849.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: | \(109.094531601\) |
Analytic rank: | \(1\) |
Dimension: | \(50\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.27 | ||
Character | \(\chi\) | \(=\) | 1849.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.902811 | 0.319192 | 0.159596 | − | 0.987182i | \(-0.448981\pi\) | ||||
0.159596 | + | 0.987182i | \(0.448981\pi\) | |||||||
\(3\) | 9.58399 | 1.84444 | 0.922220 | − | 0.386667i | \(-0.126374\pi\) | ||||
0.922220 | + | 0.386667i | \(0.126374\pi\) | |||||||
\(4\) | −7.18493 | −0.898117 | ||||||||
\(5\) | 2.03345 | 0.181877 | 0.0909387 | − | 0.995856i | \(-0.471013\pi\) | ||||
0.0909387 | + | 0.995856i | \(0.471013\pi\) | |||||||
\(6\) | 8.65253 | 0.588730 | ||||||||
\(7\) | −26.8278 | −1.44857 | −0.724284 | − | 0.689502i | \(-0.757829\pi\) | ||||
−0.724284 | + | 0.689502i | \(0.757829\pi\) | |||||||
\(8\) | −13.7091 | −0.605863 | ||||||||
\(9\) | 64.8528 | 2.40196 | ||||||||
\(10\) | 1.83582 | 0.0580538 | ||||||||
\(11\) | 38.6799 | 1.06022 | 0.530110 | − | 0.847929i | \(-0.322151\pi\) | ||||
0.530110 | + | 0.847929i | \(0.322151\pi\) | |||||||
\(12\) | −68.8603 | −1.65652 | ||||||||
\(13\) | −37.4866 | −0.799762 | −0.399881 | − | 0.916567i | \(-0.630949\pi\) | ||||
−0.399881 | + | 0.916567i | \(0.630949\pi\) | |||||||
\(14\) | −24.2205 | −0.462371 | ||||||||
\(15\) | 19.4886 | 0.335462 | ||||||||
\(16\) | 45.1027 | 0.704730 | ||||||||
\(17\) | −12.0881 | −0.172459 | −0.0862294 | − | 0.996275i | \(-0.527482\pi\) | ||||
−0.0862294 | + | 0.996275i | \(0.527482\pi\) | |||||||
\(18\) | 58.5498 | 0.766685 | ||||||||
\(19\) | 64.0712 | 0.773628 | 0.386814 | − | 0.922158i | \(-0.373576\pi\) | ||||
0.386814 | + | 0.922158i | \(0.373576\pi\) | |||||||
\(20\) | −14.6102 | −0.163347 | ||||||||
\(21\) | −257.118 | −2.67179 | ||||||||
\(22\) | 34.9206 | 0.338414 | ||||||||
\(23\) | −85.2739 | −0.773080 | −0.386540 | − | 0.922273i | \(-0.626330\pi\) | ||||
−0.386540 | + | 0.922273i | \(0.626330\pi\) | |||||||
\(24\) | −131.388 | −1.11748 | ||||||||
\(25\) | −120.865 | −0.966921 | ||||||||
\(26\) | −33.8433 | −0.255278 | ||||||||
\(27\) | 362.781 | 2.58582 | ||||||||
\(28\) | 192.756 | 1.30098 | ||||||||
\(29\) | −129.469 | −0.829029 | −0.414514 | − | 0.910043i | \(-0.636049\pi\) | ||||
−0.414514 | + | 0.910043i | \(0.636049\pi\) | |||||||
\(30\) | 17.5945 | 0.107077 | ||||||||
\(31\) | 261.836 | 1.51700 | 0.758501 | − | 0.651671i | \(-0.225932\pi\) | ||||
0.758501 | + | 0.651671i | \(0.225932\pi\) | |||||||
\(32\) | 150.392 | 0.830808 | ||||||||
\(33\) | 370.707 | 1.95551 | ||||||||
\(34\) | −10.9133 | −0.0550474 | ||||||||
\(35\) | −54.5531 | −0.263462 | ||||||||
\(36\) | −465.963 | −2.15724 | ||||||||
\(37\) | −310.147 | −1.37805 | −0.689024 | − | 0.724739i | \(-0.741961\pi\) | ||||
−0.689024 | + | 0.724739i | \(0.741961\pi\) | |||||||
\(38\) | 57.8442 | 0.246936 | ||||||||
\(39\) | −359.271 | −1.47511 | ||||||||
\(40\) | −27.8768 | −0.110193 | ||||||||
\(41\) | −333.686 | −1.27105 | −0.635524 | − | 0.772081i | \(-0.719216\pi\) | ||||
−0.635524 | + | 0.772081i | \(0.719216\pi\) | |||||||
\(42\) | −232.129 | −0.852815 | ||||||||
\(43\) | 0 | 0 | ||||||||
\(44\) | −277.912 | −0.952201 | ||||||||
\(45\) | 131.875 | 0.436861 | ||||||||
\(46\) | −76.9862 | −0.246761 | ||||||||
\(47\) | −475.663 | −1.47622 | −0.738112 | − | 0.674678i | \(-0.764282\pi\) | ||||
−0.738112 | + | 0.674678i | \(0.764282\pi\) | |||||||
\(48\) | 432.264 | 1.29983 | ||||||||
\(49\) | 376.733 | 1.09835 | ||||||||
\(50\) | −109.118 | −0.308633 | ||||||||
\(51\) | −115.852 | −0.318090 | ||||||||
\(52\) | 269.339 | 0.718280 | ||||||||
\(53\) | 14.1574 | 0.0366919 | 0.0183460 | − | 0.999832i | \(-0.494160\pi\) | ||||
0.0183460 | + | 0.999832i | \(0.494160\pi\) | |||||||
\(54\) | 327.523 | 0.825374 | ||||||||
\(55\) | 78.6536 | 0.192830 | ||||||||
\(56\) | 367.786 | 0.877634 | ||||||||
\(57\) | 614.057 | 1.42691 | ||||||||
\(58\) | −116.886 | −0.264619 | ||||||||
\(59\) | −652.202 | −1.43914 | −0.719571 | − | 0.694419i | \(-0.755662\pi\) | ||||
−0.719571 | + | 0.694419i | \(0.755662\pi\) | |||||||
\(60\) | −140.024 | −0.301284 | ||||||||
\(61\) | 233.602 | 0.490323 | 0.245162 | − | 0.969482i | \(-0.421159\pi\) | ||||
0.245162 | + | 0.969482i | \(0.421159\pi\) | |||||||
\(62\) | 236.388 | 0.484215 | ||||||||
\(63\) | −1739.86 | −3.47939 | ||||||||
\(64\) | −225.046 | −0.439543 | ||||||||
\(65\) | −76.2271 | −0.145459 | ||||||||
\(66\) | 334.679 | 0.624183 | ||||||||
\(67\) | 963.472 | 1.75682 | 0.878409 | − | 0.477909i | \(-0.158605\pi\) | ||||
0.878409 | + | 0.477909i | \(0.158605\pi\) | |||||||
\(68\) | 86.8523 | 0.154888 | ||||||||
\(69\) | −817.264 | −1.42590 | ||||||||
\(70\) | −49.2511 | −0.0840948 | ||||||||
\(71\) | −887.185 | −1.48295 | −0.741475 | − | 0.670980i | \(-0.765874\pi\) | ||||
−0.741475 | + | 0.670980i | \(0.765874\pi\) | |||||||
\(72\) | −889.075 | −1.45526 | ||||||||
\(73\) | 345.150 | 0.553380 | 0.276690 | − | 0.960959i | \(-0.410762\pi\) | ||||
0.276690 | + | 0.960959i | \(0.410762\pi\) | |||||||
\(74\) | −280.004 | −0.439862 | ||||||||
\(75\) | −1158.37 | −1.78343 | ||||||||
\(76\) | −460.347 | −0.694808 | ||||||||
\(77\) | −1037.70 | −1.53580 | ||||||||
\(78\) | −324.354 | −0.470844 | ||||||||
\(79\) | −396.269 | −0.564351 | −0.282176 | − | 0.959363i | \(-0.591056\pi\) | ||||
−0.282176 | + | 0.959363i | \(0.591056\pi\) | |||||||
\(80\) | 91.7141 | 0.128174 | ||||||||
\(81\) | 1725.86 | 2.36744 | ||||||||
\(82\) | −301.255 | −0.405708 | ||||||||
\(83\) | 539.877 | 0.713966 | 0.356983 | − | 0.934111i | \(-0.383805\pi\) | ||||
0.356983 | + | 0.934111i | \(0.383805\pi\) | |||||||
\(84\) | 1847.37 | 2.39958 | ||||||||
\(85\) | −24.5806 | −0.0313663 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −1240.83 | −1.52909 | ||||||||
\(88\) | −530.267 | −0.642349 | ||||||||
\(89\) | −295.412 | −0.351838 | −0.175919 | − | 0.984405i | \(-0.556290\pi\) | ||||
−0.175919 | + | 0.984405i | \(0.556290\pi\) | |||||||
\(90\) | 119.058 | 0.139443 | ||||||||
\(91\) | 1005.68 | 1.15851 | ||||||||
\(92\) | 612.687 | 0.694316 | ||||||||
\(93\) | 2509.43 | 2.79802 | ||||||||
\(94\) | −429.433 | −0.471199 | ||||||||
\(95\) | 130.286 | 0.140705 | ||||||||
\(96\) | 1441.36 | 1.53237 | ||||||||
\(97\) | 191.963 | 0.200937 | 0.100469 | − | 0.994940i | \(-0.467966\pi\) | ||||
0.100469 | + | 0.994940i | \(0.467966\pi\) | |||||||
\(98\) | 340.119 | 0.350584 | ||||||||
\(99\) | 2508.50 | 2.54660 | ||||||||
\(100\) | 868.407 | 0.868407 | ||||||||
\(101\) | −1717.20 | −1.69176 | −0.845878 | − | 0.533377i | \(-0.820923\pi\) | ||||
−0.845878 | + | 0.533377i | \(0.820923\pi\) | |||||||
\(102\) | −104.593 | −0.101532 | ||||||||
\(103\) | −31.9437 | −0.0305583 | −0.0152792 | − | 0.999883i | \(-0.504864\pi\) | ||||
−0.0152792 | + | 0.999883i | \(0.504864\pi\) | |||||||
\(104\) | 513.908 | 0.484547 | ||||||||
\(105\) | −522.836 | −0.485939 | ||||||||
\(106\) | 12.7815 | 0.0117118 | ||||||||
\(107\) | 1275.01 | 1.15196 | 0.575980 | − | 0.817463i | \(-0.304620\pi\) | ||||
0.575980 | + | 0.817463i | \(0.304620\pi\) | |||||||
\(108\) | −2606.56 | −2.32237 | ||||||||
\(109\) | −1181.87 | −1.03856 | −0.519278 | − | 0.854606i | \(-0.673799\pi\) | ||||
−0.519278 | + | 0.854606i | \(0.673799\pi\) | |||||||
\(110\) | 71.0094 | 0.0615498 | ||||||||
\(111\) | −2972.44 | −2.54173 | ||||||||
\(112\) | −1210.01 | −1.02085 | ||||||||
\(113\) | −1007.21 | −0.838495 | −0.419248 | − | 0.907872i | \(-0.637706\pi\) | ||||
−0.419248 | + | 0.907872i | \(0.637706\pi\) | |||||||
\(114\) | 554.378 | 0.455458 | ||||||||
\(115\) | −173.400 | −0.140606 | ||||||||
\(116\) | 930.228 | 0.744564 | ||||||||
\(117\) | −2431.11 | −1.92099 | ||||||||
\(118\) | −588.815 | −0.459363 | ||||||||
\(119\) | 324.298 | 0.249818 | ||||||||
\(120\) | −267.171 | −0.203244 | ||||||||
\(121\) | 165.132 | 0.124066 | ||||||||
\(122\) | 210.899 | 0.156507 | ||||||||
\(123\) | −3198.04 | −2.34437 | ||||||||
\(124\) | −1881.27 | −1.36245 | ||||||||
\(125\) | −499.955 | −0.357738 | ||||||||
\(126\) | −1570.77 | −1.11059 | ||||||||
\(127\) | −694.035 | −0.484926 | −0.242463 | − | 0.970161i | \(-0.577955\pi\) | ||||
−0.242463 | + | 0.970161i | \(0.577955\pi\) | |||||||
\(128\) | −1406.31 | −0.971106 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −68.8187 | −0.0464292 | ||||||||
\(131\) | 1014.00 | 0.676286 | 0.338143 | − | 0.941095i | \(-0.390201\pi\) | ||||
0.338143 | + | 0.941095i | \(0.390201\pi\) | |||||||
\(132\) | −2663.51 | −1.75628 | ||||||||
\(133\) | −1718.89 | −1.12065 | ||||||||
\(134\) | 869.833 | 0.560762 | ||||||||
\(135\) | 737.697 | 0.470303 | ||||||||
\(136\) | 165.717 | 0.104486 | ||||||||
\(137\) | −633.186 | −0.394867 | −0.197433 | − | 0.980316i | \(-0.563261\pi\) | ||||
−0.197433 | + | 0.980316i | \(0.563261\pi\) | |||||||
\(138\) | −737.835 | −0.455135 | ||||||||
\(139\) | −437.269 | −0.266825 | −0.133412 | − | 0.991061i | \(-0.542594\pi\) | ||||
−0.133412 | + | 0.991061i | \(0.542594\pi\) | |||||||
\(140\) | 391.960 | 0.236619 | ||||||||
\(141\) | −4558.74 | −2.72280 | ||||||||
\(142\) | −800.961 | −0.473346 | ||||||||
\(143\) | −1449.98 | −0.847924 | ||||||||
\(144\) | 2925.04 | 1.69273 | ||||||||
\(145\) | −263.269 | −0.150782 | ||||||||
\(146\) | 311.605 | 0.176635 | ||||||||
\(147\) | 3610.60 | 2.02583 | ||||||||
\(148\) | 2228.38 | 1.23765 | ||||||||
\(149\) | −2052.33 | −1.12841 | −0.564205 | − | 0.825635i | \(-0.690817\pi\) | ||||
−0.564205 | + | 0.825635i | \(0.690817\pi\) | |||||||
\(150\) | −1045.79 | −0.569255 | ||||||||
\(151\) | −1021.62 | −0.550583 | −0.275292 | − | 0.961361i | \(-0.588774\pi\) | ||||
−0.275292 | + | 0.961361i | \(0.588774\pi\) | |||||||
\(152\) | −878.360 | −0.468713 | ||||||||
\(153\) | −783.948 | −0.414238 | ||||||||
\(154\) | −936.845 | −0.490215 | ||||||||
\(155\) | 532.430 | 0.275909 | ||||||||
\(156\) | 2581.34 | 1.32482 | ||||||||
\(157\) | −183.529 | −0.0932942 | −0.0466471 | − | 0.998911i | \(-0.514854\pi\) | ||||
−0.0466471 | + | 0.998911i | \(0.514854\pi\) | |||||||
\(158\) | −357.756 | −0.180136 | ||||||||
\(159\) | 135.685 | 0.0676760 | ||||||||
\(160\) | 305.815 | 0.151105 | ||||||||
\(161\) | 2287.71 | 1.11986 | ||||||||
\(162\) | 1558.13 | 0.755666 | ||||||||
\(163\) | −832.248 | −0.399918 | −0.199959 | − | 0.979804i | \(-0.564081\pi\) | ||||
−0.199959 | + | 0.979804i | \(0.564081\pi\) | |||||||
\(164\) | 2397.51 | 1.14155 | ||||||||
\(165\) | 753.815 | 0.355663 | ||||||||
\(166\) | 487.407 | 0.227892 | ||||||||
\(167\) | −319.899 | −0.148231 | −0.0741153 | − | 0.997250i | \(-0.523613\pi\) | ||||
−0.0741153 | + | 0.997250i | \(0.523613\pi\) | |||||||
\(168\) | 3524.86 | 1.61874 | ||||||||
\(169\) | −791.756 | −0.360380 | ||||||||
\(170\) | −22.1916 | −0.0100119 | ||||||||
\(171\) | 4155.20 | 1.85822 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −3014.11 | −1.32462 | −0.662309 | − | 0.749231i | \(-0.730423\pi\) | ||||
−0.662309 | + | 0.749231i | \(0.730423\pi\) | |||||||
\(174\) | −1120.24 | −0.488074 | ||||||||
\(175\) | 3242.55 | 1.40065 | ||||||||
\(176\) | 1744.57 | 0.747169 | ||||||||
\(177\) | −6250.69 | −2.65441 | ||||||||
\(178\) | −266.701 | −0.112304 | ||||||||
\(179\) | −3477.58 | −1.45211 | −0.726053 | − | 0.687639i | \(-0.758647\pi\) | ||||
−0.726053 | + | 0.687639i | \(0.758647\pi\) | |||||||
\(180\) | −947.513 | −0.392352 | ||||||||
\(181\) | 7.73635 | 0.00317701 | 0.00158850 | − | 0.999999i | \(-0.499494\pi\) | ||||
0.00158850 | + | 0.999999i | \(0.499494\pi\) | |||||||
\(182\) | 907.943 | 0.369787 | ||||||||
\(183\) | 2238.84 | 0.904372 | ||||||||
\(184\) | 1169.03 | 0.468381 | ||||||||
\(185\) | −630.668 | −0.250636 | ||||||||
\(186\) | 2265.54 | 0.893105 | ||||||||
\(187\) | −467.567 | −0.182844 | ||||||||
\(188\) | 3417.60 | 1.32582 | ||||||||
\(189\) | −9732.63 | −3.74574 | ||||||||
\(190\) | 117.623 | 0.0449121 | ||||||||
\(191\) | 1301.75 | 0.493147 | 0.246574 | − | 0.969124i | \(-0.420695\pi\) | ||||
0.246574 | + | 0.969124i | \(0.420695\pi\) | |||||||
\(192\) | −2156.84 | −0.810710 | ||||||||
\(193\) | −760.523 | −0.283646 | −0.141823 | − | 0.989892i | \(-0.545296\pi\) | ||||
−0.141823 | + | 0.989892i | \(0.545296\pi\) | |||||||
\(194\) | 173.306 | 0.0641375 | ||||||||
\(195\) | −730.560 | −0.268290 | ||||||||
\(196\) | −2706.80 | −0.986444 | ||||||||
\(197\) | −200.537 | −0.0725263 | −0.0362632 | − | 0.999342i | \(-0.511545\pi\) | ||||
−0.0362632 | + | 0.999342i | \(0.511545\pi\) | |||||||
\(198\) | 2264.70 | 0.812855 | ||||||||
\(199\) | 1878.65 | 0.669217 | 0.334608 | − | 0.942357i | \(-0.391396\pi\) | ||||
0.334608 | + | 0.942357i | \(0.391396\pi\) | |||||||
\(200\) | 1656.95 | 0.585822 | ||||||||
\(201\) | 9233.90 | 3.24034 | ||||||||
\(202\) | −1550.30 | −0.539995 | ||||||||
\(203\) | 3473.38 | 1.20090 | ||||||||
\(204\) | 832.391 | 0.285682 | ||||||||
\(205\) | −678.534 | −0.231175 | ||||||||
\(206\) | −28.8391 | −0.00975397 | ||||||||
\(207\) | −5530.25 | −1.85690 | ||||||||
\(208\) | −1690.75 | −0.563616 | ||||||||
\(209\) | 2478.26 | 0.820216 | ||||||||
\(210\) | −472.022 | −0.155108 | ||||||||
\(211\) | 907.815 | 0.296192 | 0.148096 | − | 0.988973i | \(-0.452685\pi\) | ||||
0.148096 | + | 0.988973i | \(0.452685\pi\) | |||||||
\(212\) | −101.720 | −0.0329536 | ||||||||
\(213\) | −8502.77 | −2.73521 | ||||||||
\(214\) | 1151.09 | 0.367697 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −4973.41 | −1.56666 | ||||||||
\(217\) | −7024.49 | −2.19748 | ||||||||
\(218\) | −1067.00 | −0.331498 | ||||||||
\(219\) | 3307.91 | 1.02068 | ||||||||
\(220\) | −565.121 | −0.173184 | ||||||||
\(221\) | 453.142 | 0.137926 | ||||||||
\(222\) | −2683.55 | −0.811298 | ||||||||
\(223\) | 2724.67 | 0.818193 | 0.409097 | − | 0.912491i | \(-0.365844\pi\) | ||||
0.409097 | + | 0.912491i | \(0.365844\pi\) | |||||||
\(224\) | −4034.70 | −1.20348 | ||||||||
\(225\) | −7838.44 | −2.32250 | ||||||||
\(226\) | −909.317 | −0.267641 | ||||||||
\(227\) | −2297.13 | −0.671655 | −0.335828 | − | 0.941923i | \(-0.609016\pi\) | ||||
−0.335828 | + | 0.941923i | \(0.609016\pi\) | |||||||
\(228\) | −4411.96 | −1.28153 | ||||||||
\(229\) | 3034.87 | 0.875763 | 0.437882 | − | 0.899033i | \(-0.355729\pi\) | ||||
0.437882 | + | 0.899033i | \(0.355729\pi\) | |||||||
\(230\) | −156.548 | −0.0448802 | ||||||||
\(231\) | −9945.28 | −2.83269 | ||||||||
\(232\) | 1774.91 | 0.502278 | ||||||||
\(233\) | −4994.74 | −1.40436 | −0.702180 | − | 0.711999i | \(-0.747790\pi\) | ||||
−0.702180 | + | 0.711999i | \(0.747790\pi\) | |||||||
\(234\) | −2194.83 | −0.613166 | ||||||||
\(235\) | −967.237 | −0.268492 | ||||||||
\(236\) | 4686.02 | 1.29252 | ||||||||
\(237\) | −3797.84 | −1.04091 | ||||||||
\(238\) | 292.780 | 0.0797399 | ||||||||
\(239\) | −2939.14 | −0.795470 | −0.397735 | − | 0.917500i | \(-0.630204\pi\) | ||||
−0.397735 | + | 0.917500i | \(0.630204\pi\) | |||||||
\(240\) | 878.987 | 0.236410 | ||||||||
\(241\) | 4981.47 | 1.33147 | 0.665736 | − | 0.746187i | \(-0.268118\pi\) | ||||
0.665736 | + | 0.746187i | \(0.268118\pi\) | |||||||
\(242\) | 149.083 | 0.0396010 | ||||||||
\(243\) | 6745.54 | 1.78077 | ||||||||
\(244\) | −1678.42 | −0.440368 | ||||||||
\(245\) | 766.068 | 0.199765 | ||||||||
\(246\) | −2887.23 | −0.748304 | ||||||||
\(247\) | −2401.81 | −0.618719 | ||||||||
\(248\) | −3589.54 | −0.919097 | ||||||||
\(249\) | 5174.17 | 1.31687 | ||||||||
\(250\) | −451.365 | −0.114187 | ||||||||
\(251\) | 5028.93 | 1.26463 | 0.632317 | − | 0.774709i | \(-0.282104\pi\) | ||||
0.632317 | + | 0.774709i | \(0.282104\pi\) | |||||||
\(252\) | 12500.8 | 3.12490 | ||||||||
\(253\) | −3298.38 | −0.819634 | ||||||||
\(254\) | −626.583 | −0.154785 | ||||||||
\(255\) | −235.580 | −0.0578533 | ||||||||
\(256\) | 530.733 | 0.129573 | ||||||||
\(257\) | 846.260 | 0.205402 | 0.102701 | − | 0.994712i | \(-0.467252\pi\) | ||||
0.102701 | + | 0.994712i | \(0.467252\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 8320.56 | 1.99620 | ||||||||
\(260\) | 547.687 | 0.130639 | ||||||||
\(261\) | −8396.44 | −1.99129 | ||||||||
\(262\) | 915.449 | 0.215865 | ||||||||
\(263\) | 7725.74 | 1.81137 | 0.905684 | − | 0.423954i | \(-0.139358\pi\) | ||||
0.905684 | + | 0.423954i | \(0.139358\pi\) | |||||||
\(264\) | −5082.07 | −1.18477 | ||||||||
\(265\) | 28.7884 | 0.00667343 | ||||||||
\(266\) | −1551.83 | −0.357703 | ||||||||
\(267\) | −2831.23 | −0.648944 | ||||||||
\(268\) | −6922.48 | −1.57783 | ||||||||
\(269\) | −1281.93 | −0.290559 | −0.145279 | − | 0.989391i | \(-0.546408\pi\) | ||||
−0.145279 | + | 0.989391i | \(0.546408\pi\) | |||||||
\(270\) | 666.001 | 0.150117 | ||||||||
\(271\) | 1156.22 | 0.259171 | 0.129585 | − | 0.991568i | \(-0.458635\pi\) | ||||
0.129585 | + | 0.991568i | \(0.458635\pi\) | |||||||
\(272\) | −545.207 | −0.121537 | ||||||||
\(273\) | 9638.46 | 2.13680 | ||||||||
\(274\) | −571.648 | −0.126038 | ||||||||
\(275\) | −4675.05 | −1.02515 | ||||||||
\(276\) | 5871.98 | 1.28062 | ||||||||
\(277\) | −2086.27 | −0.452533 | −0.226266 | − | 0.974065i | \(-0.572652\pi\) | ||||
−0.226266 | + | 0.974065i | \(0.572652\pi\) | |||||||
\(278\) | −394.771 | −0.0851684 | ||||||||
\(279\) | 16980.8 | 3.64377 | ||||||||
\(280\) | 747.875 | 0.159622 | ||||||||
\(281\) | 1154.08 | 0.245006 | 0.122503 | − | 0.992468i | \(-0.460908\pi\) | ||||
0.122503 | + | 0.992468i | \(0.460908\pi\) | |||||||
\(282\) | −4115.68 | −0.869097 | ||||||||
\(283\) | 5288.51 | 1.11085 | 0.555423 | − | 0.831568i | \(-0.312556\pi\) | ||||
0.555423 | + | 0.831568i | \(0.312556\pi\) | |||||||
\(284\) | 6374.37 | 1.33186 | ||||||||
\(285\) | 1248.66 | 0.259523 | ||||||||
\(286\) | −1309.05 | −0.270650 | ||||||||
\(287\) | 8952.07 | 1.84120 | ||||||||
\(288\) | 9753.36 | 1.99556 | ||||||||
\(289\) | −4766.88 | −0.970258 | ||||||||
\(290\) | −237.683 | −0.0481283 | ||||||||
\(291\) | 1839.77 | 0.370616 | ||||||||
\(292\) | −2479.88 | −0.497000 | ||||||||
\(293\) | −3079.73 | −0.614060 | −0.307030 | − | 0.951700i | \(-0.599335\pi\) | ||||
−0.307030 | + | 0.951700i | \(0.599335\pi\) | |||||||
\(294\) | 3259.69 | 0.646630 | ||||||||
\(295\) | −1326.22 | −0.261747 | ||||||||
\(296\) | 4251.84 | 0.834909 | ||||||||
\(297\) | 14032.3 | 2.74154 | ||||||||
\(298\) | −1852.86 | −0.360179 | ||||||||
\(299\) | 3196.63 | 0.618280 | ||||||||
\(300\) | 8322.80 | 1.60172 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −922.328 | −0.175742 | ||||||||
\(303\) | −16457.6 | −3.12034 | ||||||||
\(304\) | 2889.78 | 0.545199 | ||||||||
\(305\) | 475.019 | 0.0891787 | ||||||||
\(306\) | −707.757 | −0.132222 | ||||||||
\(307\) | −639.484 | −0.118884 | −0.0594419 | − | 0.998232i | \(-0.518932\pi\) | ||||
−0.0594419 | + | 0.998232i | \(0.518932\pi\) | |||||||
\(308\) | 7455.79 | 1.37933 | ||||||||
\(309\) | −306.148 | −0.0563630 | ||||||||
\(310\) | 480.684 | 0.0880678 | ||||||||
\(311\) | 7068.39 | 1.28878 | 0.644391 | − | 0.764696i | \(-0.277111\pi\) | ||||
0.644391 | + | 0.764696i | \(0.277111\pi\) | |||||||
\(312\) | 4925.29 | 0.893717 | ||||||||
\(313\) | −5479.55 | −0.989528 | −0.494764 | − | 0.869027i | \(-0.664746\pi\) | ||||
−0.494764 | + | 0.869027i | \(0.664746\pi\) | |||||||
\(314\) | −165.692 | −0.0297787 | ||||||||
\(315\) | −3537.92 | −0.632823 | ||||||||
\(316\) | 2847.17 | 0.506853 | ||||||||
\(317\) | 6514.68 | 1.15426 | 0.577131 | − | 0.816652i | \(-0.304172\pi\) | ||||
0.577131 | + | 0.816652i | \(0.304172\pi\) | |||||||
\(318\) | 122.498 | 0.0216016 | ||||||||
\(319\) | −5007.85 | −0.878953 | ||||||||
\(320\) | −457.620 | −0.0799429 | ||||||||
\(321\) | 12219.7 | 2.12472 | ||||||||
\(322\) | 2065.37 | 0.357450 | ||||||||
\(323\) | −774.500 | −0.133419 | ||||||||
\(324\) | −12400.2 | −2.12623 | ||||||||
\(325\) | 4530.82 | 0.773307 | ||||||||
\(326\) | −751.363 | −0.127651 | ||||||||
\(327\) | −11327.0 | −1.91555 | ||||||||
\(328\) | 4574.54 | 0.770081 | ||||||||
\(329\) | 12761.0 | 2.13841 | ||||||||
\(330\) | 680.553 | 0.113525 | ||||||||
\(331\) | 3774.59 | 0.626799 | 0.313399 | − | 0.949621i | \(-0.398532\pi\) | ||||
0.313399 | + | 0.949621i | \(0.398532\pi\) | |||||||
\(332\) | −3878.98 | −0.641225 | ||||||||
\(333\) | −20113.9 | −3.31001 | ||||||||
\(334\) | −288.808 | −0.0473140 | ||||||||
\(335\) | 1959.17 | 0.319526 | ||||||||
\(336\) | −11596.7 | −1.88289 | ||||||||
\(337\) | 11690.7 | 1.88972 | 0.944859 | − | 0.327478i | \(-0.106199\pi\) | ||||
0.944859 | + | 0.327478i | \(0.106199\pi\) | |||||||
\(338\) | −714.806 | −0.115031 | ||||||||
\(339\) | −9653.05 | −1.54655 | ||||||||
\(340\) | 176.610 | 0.0281706 | ||||||||
\(341\) | 10127.8 | 1.60836 | ||||||||
\(342\) | 3751.36 | 0.593129 | ||||||||
\(343\) | −904.985 | −0.142462 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −1661.87 | −0.259339 | ||||||||
\(346\) | −2721.18 | −0.422807 | ||||||||
\(347\) | 11140.5 | 1.72349 | 0.861746 | − | 0.507340i | \(-0.169371\pi\) | ||||
0.861746 | + | 0.507340i | \(0.169371\pi\) | |||||||
\(348\) | 8915.29 | 1.37330 | ||||||||
\(349\) | −1226.84 | −0.188170 | −0.0940852 | − | 0.995564i | \(-0.529993\pi\) | ||||
−0.0940852 | + | 0.995564i | \(0.529993\pi\) | |||||||
\(350\) | 2927.41 | 0.447076 | ||||||||
\(351\) | −13599.4 | −2.06804 | ||||||||
\(352\) | 5817.15 | 0.880839 | ||||||||
\(353\) | −1582.18 | −0.238558 | −0.119279 | − | 0.992861i | \(-0.538058\pi\) | ||||
−0.119279 | + | 0.992861i | \(0.538058\pi\) | |||||||
\(354\) | −5643.19 | −0.847267 | ||||||||
\(355\) | −1804.05 | −0.269715 | ||||||||
\(356\) | 2122.52 | 0.315992 | ||||||||
\(357\) | 3108.07 | 0.460774 | ||||||||
\(358\) | −3139.60 | −0.463500 | ||||||||
\(359\) | −613.266 | −0.0901586 | −0.0450793 | − | 0.998983i | \(-0.514354\pi\) | ||||
−0.0450793 | + | 0.998983i | \(0.514354\pi\) | |||||||
\(360\) | −1807.89 | −0.264678 | ||||||||
\(361\) | −2753.88 | −0.401499 | ||||||||
\(362\) | 6.98446 | 0.00101407 | ||||||||
\(363\) | 1582.63 | 0.228833 | ||||||||
\(364\) | −7225.77 | −1.04048 | ||||||||
\(365\) | 701.846 | 0.100647 | ||||||||
\(366\) | 2021.25 | 0.288668 | ||||||||
\(367\) | 2202.45 | 0.313261 | 0.156631 | − | 0.987657i | \(-0.449937\pi\) | ||||
0.156631 | + | 0.987657i | \(0.449937\pi\) | |||||||
\(368\) | −3846.08 | −0.544812 | ||||||||
\(369\) | −21640.5 | −3.05300 | ||||||||
\(370\) | −569.374 | −0.0800009 | ||||||||
\(371\) | −379.813 | −0.0531507 | ||||||||
\(372\) | −18030.1 | −2.51295 | ||||||||
\(373\) | −6268.78 | −0.870201 | −0.435101 | − | 0.900382i | \(-0.643287\pi\) | ||||
−0.435101 | + | 0.900382i | \(0.643287\pi\) | |||||||
\(374\) | −422.124 | −0.0583624 | ||||||||
\(375\) | −4791.56 | −0.659827 | ||||||||
\(376\) | 6520.92 | 0.894390 | ||||||||
\(377\) | 4853.36 | 0.663026 | ||||||||
\(378\) | −8786.72 | −1.19561 | ||||||||
\(379\) | 3247.19 | 0.440097 | 0.220049 | − | 0.975489i | \(-0.429378\pi\) | ||||
0.220049 | + | 0.975489i | \(0.429378\pi\) | |||||||
\(380\) | −936.093 | −0.126370 | ||||||||
\(381\) | −6651.62 | −0.894417 | ||||||||
\(382\) | 1175.23 | 0.157409 | ||||||||
\(383\) | 8938.80 | 1.19256 | 0.596281 | − | 0.802776i | \(-0.296644\pi\) | ||||
0.596281 | + | 0.802776i | \(0.296644\pi\) | |||||||
\(384\) | −13478.1 | −1.79115 | ||||||||
\(385\) | −2110.11 | −0.279327 | ||||||||
\(386\) | −686.609 | −0.0905375 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −1379.24 | −0.180465 | ||||||||
\(389\) | 4626.84 | 0.603060 | 0.301530 | − | 0.953457i | \(-0.402503\pi\) | ||||
0.301530 | + | 0.953457i | \(0.402503\pi\) | |||||||
\(390\) | −659.558 | −0.0856359 | ||||||||
\(391\) | 1030.80 | 0.133324 | ||||||||
\(392\) | −5164.68 | −0.665448 | ||||||||
\(393\) | 9718.15 | 1.24737 | ||||||||
\(394\) | −181.047 | −0.0231498 | ||||||||
\(395\) | −805.794 | −0.102643 | ||||||||
\(396\) | −18023.4 | −2.28714 | ||||||||
\(397\) | 10840.9 | 1.37051 | 0.685253 | − | 0.728305i | \(-0.259692\pi\) | ||||
0.685253 | + | 0.728305i | \(0.259692\pi\) | |||||||
\(398\) | 1696.07 | 0.213609 | ||||||||
\(399\) | −16473.8 | −2.06698 | ||||||||
\(400\) | −5451.34 | −0.681418 | ||||||||
\(401\) | −12391.8 | −1.54319 | −0.771594 | − | 0.636116i | \(-0.780540\pi\) | ||||
−0.771594 | + | 0.636116i | \(0.780540\pi\) | |||||||
\(402\) | 8336.47 | 1.03429 | ||||||||
\(403\) | −9815.33 | −1.21324 | ||||||||
\(404\) | 12337.9 | 1.51939 | ||||||||
\(405\) | 3509.45 | 0.430583 | ||||||||
\(406\) | 3135.81 | 0.383319 | ||||||||
\(407\) | −11996.4 | −1.46103 | ||||||||
\(408\) | 1588.23 | 0.192719 | ||||||||
\(409\) | −7910.71 | −0.956380 | −0.478190 | − | 0.878256i | \(-0.658707\pi\) | ||||
−0.478190 | + | 0.878256i | \(0.658707\pi\) | |||||||
\(410\) | −612.588 | −0.0737891 | ||||||||
\(411\) | −6068.45 | −0.728308 | ||||||||
\(412\) | 229.513 | 0.0274449 | ||||||||
\(413\) | 17497.2 | 2.08469 | ||||||||
\(414\) | −4992.77 | −0.592708 | ||||||||
\(415\) | 1097.81 | 0.129854 | ||||||||
\(416\) | −5637.69 | −0.664448 | ||||||||
\(417\) | −4190.78 | −0.492142 | ||||||||
\(418\) | 2237.41 | 0.261806 | ||||||||
\(419\) | 12901.8 | 1.50428 | 0.752142 | − | 0.659001i | \(-0.229021\pi\) | ||||
0.752142 | + | 0.659001i | \(0.229021\pi\) | |||||||
\(420\) | 3756.54 | 0.436430 | ||||||||
\(421\) | 16075.1 | 1.86093 | 0.930464 | − | 0.366382i | \(-0.119404\pi\) | ||||
0.930464 | + | 0.366382i | \(0.119404\pi\) | |||||||
\(422\) | 819.586 | 0.0945422 | ||||||||
\(423\) | −30848.1 | −3.54582 | ||||||||
\(424\) | −194.086 | −0.0222303 | ||||||||
\(425\) | 1461.03 | 0.166754 | ||||||||
\(426\) | −7676.40 | −0.873058 | ||||||||
\(427\) | −6267.05 | −0.710266 | ||||||||
\(428\) | −9160.86 | −1.03460 | ||||||||
\(429\) | −13896.6 | −1.56394 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −9277.47 | −1.03684 | −0.518422 | − | 0.855125i | \(-0.673480\pi\) | ||||
−0.518422 | + | 0.855125i | \(0.673480\pi\) | |||||||
\(432\) | 16362.4 | 1.82231 | ||||||||
\(433\) | 182.499 | 0.0202548 | 0.0101274 | − | 0.999949i | \(-0.496776\pi\) | ||||
0.0101274 | + | 0.999949i | \(0.496776\pi\) | |||||||
\(434\) | −6341.79 | −0.701418 | ||||||||
\(435\) | −2523.17 | −0.278107 | ||||||||
\(436\) | 8491.65 | 0.932744 | ||||||||
\(437\) | −5463.60 | −0.598076 | ||||||||
\(438\) | 2986.42 | 0.325792 | ||||||||
\(439\) | −5806.09 | −0.631229 | −0.315614 | − | 0.948888i | \(-0.602211\pi\) | ||||
−0.315614 | + | 0.948888i | \(0.602211\pi\) | |||||||
\(440\) | −1078.27 | −0.116829 | ||||||||
\(441\) | 24432.2 | 2.63818 | ||||||||
\(442\) | 409.102 | 0.0440249 | ||||||||
\(443\) | 13300.1 | 1.42643 | 0.713214 | − | 0.700946i | \(-0.247239\pi\) | ||||
0.713214 | + | 0.700946i | \(0.247239\pi\) | |||||||
\(444\) | 21356.8 | 2.28277 | ||||||||
\(445\) | −600.706 | −0.0639914 | ||||||||
\(446\) | 2459.86 | 0.261161 | ||||||||
\(447\) | −19669.5 | −2.08128 | ||||||||
\(448\) | 6037.49 | 0.636707 | ||||||||
\(449\) | −7189.18 | −0.755631 | −0.377815 | − | 0.925881i | \(-0.623325\pi\) | ||||
−0.377815 | + | 0.925881i | \(0.623325\pi\) | |||||||
\(450\) | −7076.63 | −0.741323 | ||||||||
\(451\) | −12906.9 | −1.34759 | ||||||||
\(452\) | 7236.71 | 0.753066 | ||||||||
\(453\) | −9791.17 | −1.01552 | ||||||||
\(454\) | −2073.87 | −0.214387 | ||||||||
\(455\) | 2045.01 | 0.210707 | ||||||||
\(456\) | −8418.19 | −0.864513 | ||||||||
\(457\) | 4199.15 | 0.429820 | 0.214910 | − | 0.976634i | \(-0.431054\pi\) | ||||
0.214910 | + | 0.976634i | \(0.431054\pi\) | |||||||
\(458\) | 2739.91 | 0.279537 | ||||||||
\(459\) | −4385.34 | −0.445948 | ||||||||
\(460\) | 1245.87 | 0.126280 | ||||||||
\(461\) | −1185.60 | −0.119781 | −0.0598905 | − | 0.998205i | \(-0.519075\pi\) | ||||
−0.0598905 | + | 0.998205i | \(0.519075\pi\) | |||||||
\(462\) | −8978.71 | −0.904172 | ||||||||
\(463\) | 2522.44 | 0.253192 | 0.126596 | − | 0.991954i | \(-0.459595\pi\) | ||||
0.126596 | + | 0.991954i | \(0.459595\pi\) | |||||||
\(464\) | −5839.41 | −0.584241 | ||||||||
\(465\) | 5102.80 | 0.508897 | ||||||||
\(466\) | −4509.30 | −0.448261 | ||||||||
\(467\) | −9629.56 | −0.954182 | −0.477091 | − | 0.878854i | \(-0.658309\pi\) | ||||
−0.477091 | + | 0.878854i | \(0.658309\pi\) | |||||||
\(468\) | 17467.4 | 1.72528 | ||||||||
\(469\) | −25847.9 | −2.54487 | ||||||||
\(470\) | −873.232 | −0.0857004 | ||||||||
\(471\) | −1758.94 | −0.172075 | ||||||||
\(472\) | 8941.11 | 0.871924 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | −3428.73 | −0.332251 | ||||||||
\(475\) | −7743.97 | −0.748037 | ||||||||
\(476\) | −2330.06 | −0.224366 | ||||||||
\(477\) | 918.149 | 0.0881324 | ||||||||
\(478\) | −2653.49 | −0.253908 | ||||||||
\(479\) | 12358.5 | 1.17886 | 0.589431 | − | 0.807819i | \(-0.299352\pi\) | ||||
0.589431 | + | 0.807819i | \(0.299352\pi\) | |||||||
\(480\) | 2930.93 | 0.278704 | ||||||||
\(481\) | 11626.3 | 1.10211 | ||||||||
\(482\) | 4497.33 | 0.424995 | ||||||||
\(483\) | 21925.4 | 2.06551 | ||||||||
\(484\) | −1186.47 | −0.111426 | ||||||||
\(485\) | 390.348 | 0.0365459 | ||||||||
\(486\) | 6089.95 | 0.568407 | ||||||||
\(487\) | 2723.31 | 0.253398 | 0.126699 | − | 0.991941i | \(-0.459562\pi\) | ||||
0.126699 | + | 0.991941i | \(0.459562\pi\) | |||||||
\(488\) | −3202.49 | −0.297069 | ||||||||
\(489\) | −7976.25 | −0.737625 | ||||||||
\(490\) | 691.615 | 0.0637632 | ||||||||
\(491\) | 4199.46 | 0.385986 | 0.192993 | − | 0.981200i | \(-0.438181\pi\) | ||||
0.192993 | + | 0.981200i | \(0.438181\pi\) | |||||||
\(492\) | 22977.7 | 2.10552 | ||||||||
\(493\) | 1565.04 | 0.142973 | ||||||||
\(494\) | −2168.38 | −0.197490 | ||||||||
\(495\) | 5100.91 | 0.463169 | ||||||||
\(496\) | 11809.5 | 1.06908 | ||||||||
\(497\) | 23801.3 | 2.14815 | ||||||||
\(498\) | 4671.30 | 0.420333 | ||||||||
\(499\) | −19985.3 | −1.79292 | −0.896458 | − | 0.443129i | \(-0.853868\pi\) | ||||
−0.896458 | + | 0.443129i | \(0.853868\pi\) | |||||||
\(500\) | 3592.14 | 0.321291 | ||||||||
\(501\) | −3065.90 | −0.273402 | ||||||||
\(502\) | 4540.18 | 0.403661 | ||||||||
\(503\) | −520.717 | −0.0461583 | −0.0230792 | − | 0.999734i | \(-0.507347\pi\) | ||||
−0.0230792 | + | 0.999734i | \(0.507347\pi\) | |||||||
\(504\) | 23852.0 | 2.10804 | ||||||||
\(505\) | −3491.83 | −0.307692 | ||||||||
\(506\) | −2977.82 | −0.261621 | ||||||||
\(507\) | −7588.18 | −0.664700 | ||||||||
\(508\) | 4986.60 | 0.435520 | ||||||||
\(509\) | 1746.69 | 0.152103 | 0.0760517 | − | 0.997104i | \(-0.475769\pi\) | ||||
0.0760517 | + | 0.997104i | \(0.475769\pi\) | |||||||
\(510\) | −212.684 | −0.0184663 | ||||||||
\(511\) | −9259.63 | −0.801609 | ||||||||
\(512\) | 11729.6 | 1.01246 | ||||||||
\(513\) | 23243.8 | 2.00046 | ||||||||
\(514\) | 764.013 | 0.0655626 | ||||||||
\(515\) | −64.9560 | −0.00555787 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −18398.6 | −1.56512 | ||||||||
\(518\) | 7511.90 | 0.637169 | ||||||||
\(519\) | −28887.2 | −2.44318 | ||||||||
\(520\) | 1045.01 | 0.0881281 | ||||||||
\(521\) | 12223.8 | 1.02790 | 0.513948 | − | 0.857821i | \(-0.328182\pi\) | ||||
0.513948 | + | 0.857821i | \(0.328182\pi\) | |||||||
\(522\) | −7580.40 | −0.635604 | ||||||||
\(523\) | 12923.8 | 1.08053 | 0.540265 | − | 0.841495i | \(-0.318324\pi\) | ||||
0.540265 | + | 0.841495i | \(0.318324\pi\) | |||||||
\(524\) | −7285.51 | −0.607383 | ||||||||
\(525\) | 31076.5 | 2.58341 | ||||||||
\(526\) | 6974.88 | 0.578174 | ||||||||
\(527\) | −3165.10 | −0.261620 | ||||||||
\(528\) | 16719.9 | 1.37811 | ||||||||
\(529\) | −4895.37 | −0.402348 | ||||||||
\(530\) | 25.9905 | 0.00213011 | ||||||||
\(531\) | −42297.1 | −3.45676 | ||||||||
\(532\) | 12350.1 | 1.00648 | ||||||||
\(533\) | 12508.7 | 1.01654 | ||||||||
\(534\) | −2556.06 | −0.207138 | ||||||||
\(535\) | 2592.67 | 0.209516 | ||||||||
\(536\) | −13208.4 | −1.06439 | ||||||||
\(537\) | −33329.1 | −2.67832 | ||||||||
\(538\) | −1157.34 | −0.0927441 | ||||||||
\(539\) | 14572.0 | 1.16449 | ||||||||
\(540\) | −5300.30 | −0.422387 | ||||||||
\(541\) | −10061.3 | −0.799574 | −0.399787 | − | 0.916608i | \(-0.630916\pi\) | ||||
−0.399787 | + | 0.916608i | \(0.630916\pi\) | |||||||
\(542\) | 1043.85 | 0.0827252 | ||||||||
\(543\) | 74.1451 | 0.00585980 | ||||||||
\(544\) | −1817.96 | −0.143280 | ||||||||
\(545\) | −2403.27 | −0.188890 | ||||||||
\(546\) | 8701.71 | 0.682049 | ||||||||
\(547\) | −23951.3 | −1.87218 | −0.936090 | − | 0.351761i | \(-0.885583\pi\) | ||||
−0.936090 | + | 0.351761i | \(0.885583\pi\) | |||||||
\(548\) | 4549.40 | 0.354636 | ||||||||
\(549\) | 15149.8 | 1.17774 | ||||||||
\(550\) | −4220.68 | −0.327219 | ||||||||
\(551\) | −8295.25 | −0.641360 | ||||||||
\(552\) | 11204.0 | 0.863900 | ||||||||
\(553\) | 10631.0 | 0.817501 | ||||||||
\(554\) | −1883.50 | −0.144445 | ||||||||
\(555\) | −6044.31 | −0.462282 | ||||||||
\(556\) | 3141.75 | 0.239640 | ||||||||
\(557\) | 8803.19 | 0.669665 | 0.334832 | − | 0.942278i | \(-0.391320\pi\) | ||||
0.334832 | + | 0.942278i | \(0.391320\pi\) | |||||||
\(558\) | 15330.4 | 1.16306 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | −2460.49 | −0.185669 | ||||||||
\(561\) | −4481.15 | −0.337245 | ||||||||
\(562\) | 1041.92 | 0.0782038 | ||||||||
\(563\) | −21876.5 | −1.63762 | −0.818812 | − | 0.574061i | \(-0.805367\pi\) | ||||
−0.818812 | + | 0.574061i | \(0.805367\pi\) | |||||||
\(564\) | 32754.3 | 2.44540 | ||||||||
\(565\) | −2048.10 | −0.152503 | ||||||||
\(566\) | 4774.53 | 0.354573 | ||||||||
\(567\) | −46301.1 | −3.42939 | ||||||||
\(568\) | 12162.5 | 0.898466 | ||||||||
\(569\) | −22198.4 | −1.63551 | −0.817756 | − | 0.575565i | \(-0.804782\pi\) | ||||
−0.817756 | + | 0.575565i | \(0.804782\pi\) | |||||||
\(570\) | 1127.30 | 0.0828376 | ||||||||
\(571\) | 13270.8 | 0.972619 | 0.486310 | − | 0.873787i | \(-0.338343\pi\) | ||||
0.486310 | + | 0.873787i | \(0.338343\pi\) | |||||||
\(572\) | 10418.0 | 0.761534 | ||||||||
\(573\) | 12475.9 | 0.909580 | ||||||||
\(574\) | 8082.03 | 0.587696 | ||||||||
\(575\) | 10306.6 | 0.747507 | ||||||||
\(576\) | −14594.9 | −1.05576 | ||||||||
\(577\) | 15373.6 | 1.10921 | 0.554603 | − | 0.832115i | \(-0.312870\pi\) | ||||
0.554603 | + | 0.832115i | \(0.312870\pi\) | |||||||
\(578\) | −4303.59 | −0.309699 | ||||||||
\(579\) | −7288.85 | −0.523168 | ||||||||
\(580\) | 1891.57 | 0.135419 | ||||||||
\(581\) | −14483.7 | −1.03423 | ||||||||
\(582\) | 1660.97 | 0.118298 | ||||||||
\(583\) | 547.607 | 0.0389015 | ||||||||
\(584\) | −4731.71 | −0.335273 | ||||||||
\(585\) | −4943.54 | −0.349385 | ||||||||
\(586\) | −2780.41 | −0.196003 | ||||||||
\(587\) | −863.918 | −0.0607457 | −0.0303728 | − | 0.999539i | \(-0.509669\pi\) | ||||
−0.0303728 | + | 0.999539i | \(0.509669\pi\) | |||||||
\(588\) | −25942.0 | −1.81944 | ||||||||
\(589\) | 16776.1 | 1.17360 | ||||||||
\(590\) | −1197.33 | −0.0835477 | ||||||||
\(591\) | −1921.95 | −0.133770 | ||||||||
\(592\) | −13988.4 | −0.971151 | ||||||||
\(593\) | 1387.83 | 0.0961071 | 0.0480536 | − | 0.998845i | \(-0.484698\pi\) | ||||
0.0480536 | + | 0.998845i | \(0.484698\pi\) | |||||||
\(594\) | 12668.5 | 0.875078 | ||||||||
\(595\) | 659.444 | 0.0454363 | ||||||||
\(596\) | 14745.8 | 1.01344 | ||||||||
\(597\) | 18005.0 | 1.23433 | ||||||||
\(598\) | 2885.95 | 0.197350 | ||||||||
\(599\) | −23119.8 | −1.57704 | −0.788521 | − | 0.615008i | \(-0.789153\pi\) | ||||
−0.788521 | + | 0.615008i | \(0.789153\pi\) | |||||||
\(600\) | 15880.2 | 1.08051 | ||||||||
\(601\) | −29375.9 | −1.99379 | −0.996897 | − | 0.0787233i | \(-0.974916\pi\) | ||||
−0.996897 | + | 0.0787233i | \(0.974916\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 62483.9 | 4.21980 | ||||||||
\(604\) | 7340.26 | 0.494488 | ||||||||
\(605\) | 335.789 | 0.0225649 | ||||||||
\(606\) | −14858.1 | −0.995987 | ||||||||
\(607\) | 10354.5 | 0.692383 | 0.346191 | − | 0.938164i | \(-0.387475\pi\) | ||||
0.346191 | + | 0.938164i | \(0.387475\pi\) | |||||||
\(608\) | 9635.81 | 0.642736 | ||||||||
\(609\) | 33288.8 | 2.21499 | ||||||||
\(610\) | 428.853 | 0.0284651 | ||||||||
\(611\) | 17831.0 | 1.18063 | ||||||||
\(612\) | 5632.61 | 0.372034 | ||||||||
\(613\) | −9960.96 | −0.656312 | −0.328156 | − | 0.944624i | \(-0.606427\pi\) | ||||
−0.328156 | + | 0.944624i | \(0.606427\pi\) | |||||||
\(614\) | −577.334 | −0.0379467 | ||||||||
\(615\) | −6503.06 | −0.426388 | ||||||||
\(616\) | 14225.9 | 0.930485 | ||||||||
\(617\) | −13796.7 | −0.900218 | −0.450109 | − | 0.892974i | \(-0.648615\pi\) | ||||
−0.450109 | + | 0.892974i | \(0.648615\pi\) | |||||||
\(618\) | −276.394 | −0.0179906 | ||||||||
\(619\) | 25631.5 | 1.66432 | 0.832162 | − | 0.554533i | \(-0.187103\pi\) | ||||
0.832162 | + | 0.554533i | \(0.187103\pi\) | |||||||
\(620\) | −3825.47 | −0.247798 | ||||||||
\(621\) | −30935.7 | −1.99905 | ||||||||
\(622\) | 6381.42 | 0.411369 | ||||||||
\(623\) | 7925.27 | 0.509662 | ||||||||
\(624\) | −16204.1 | −1.03956 | ||||||||
\(625\) | 14091.5 | 0.901856 | ||||||||
\(626\) | −4947.00 | −0.315849 | ||||||||
\(627\) | 23751.7 | 1.51284 | ||||||||
\(628\) | 1318.64 | 0.0837890 | ||||||||
\(629\) | 3749.09 | 0.237656 | ||||||||
\(630\) | −3194.08 | −0.201992 | ||||||||
\(631\) | 17655.1 | 1.11385 | 0.556925 | − | 0.830563i | \(-0.311981\pi\) | ||||
0.556925 | + | 0.830563i | \(0.311981\pi\) | |||||||
\(632\) | 5432.50 | 0.341920 | ||||||||
\(633\) | 8700.49 | 0.546309 | ||||||||
\(634\) | 5881.53 | 0.368431 | ||||||||
\(635\) | −1411.29 | −0.0881972 | ||||||||
\(636\) | −974.884 | −0.0607809 | ||||||||
\(637\) | −14122.4 | −0.878417 | ||||||||
\(638\) | −4521.15 | −0.280555 | ||||||||
\(639\) | −57536.5 | −3.56198 | ||||||||
\(640\) | −2859.67 | −0.176622 | ||||||||
\(641\) | −374.249 | −0.0230608 | −0.0115304 | − | 0.999934i | \(-0.503670\pi\) | ||||
−0.0115304 | + | 0.999934i | \(0.503670\pi\) | |||||||
\(642\) | 11032.1 | 0.678194 | ||||||||
\(643\) | −18264.0 | −1.12016 | −0.560080 | − | 0.828438i | \(-0.689230\pi\) | ||||
−0.560080 | + | 0.828438i | \(0.689230\pi\) | |||||||
\(644\) | −16437.1 | −1.00576 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −699.227 | −0.0425863 | ||||||||
\(647\) | 1121.95 | 0.0681735 | 0.0340868 | − | 0.999419i | \(-0.489148\pi\) | ||||
0.0340868 | + | 0.999419i | \(0.489148\pi\) | |||||||
\(648\) | −23660.0 | −1.43434 | ||||||||
\(649\) | −25227.1 | −1.52581 | ||||||||
\(650\) | 4090.47 | 0.246833 | ||||||||
\(651\) | −67322.6 | −4.05312 | ||||||||
\(652\) | 5979.65 | 0.359173 | ||||||||
\(653\) | 14019.2 | 0.840142 | 0.420071 | − | 0.907491i | \(-0.362005\pi\) | ||||
0.420071 | + | 0.907491i | \(0.362005\pi\) | |||||||
\(654\) | −10226.2 | −0.611429 | ||||||||
\(655\) | 2061.92 | 0.123001 | ||||||||
\(656\) | −15050.1 | −0.895745 | ||||||||
\(657\) | 22384.0 | 1.32920 | ||||||||
\(658\) | 11520.8 | 0.682563 | ||||||||
\(659\) | −26897.3 | −1.58994 | −0.794969 | − | 0.606650i | \(-0.792513\pi\) | ||||
−0.794969 | + | 0.606650i | \(0.792513\pi\) | |||||||
\(660\) | −5416.11 | −0.319427 | ||||||||
\(661\) | 4456.60 | 0.262241 | 0.131121 | − | 0.991366i | \(-0.458142\pi\) | ||||
0.131121 | + | 0.991366i | \(0.458142\pi\) | |||||||
\(662\) | 3407.74 | 0.200069 | ||||||||
\(663\) | 4342.91 | 0.254396 | ||||||||
\(664\) | −7401.24 | −0.432566 | ||||||||
\(665\) | −3495.28 | −0.203821 | ||||||||
\(666\) | −18159.0 | −1.05653 | ||||||||
\(667\) | 11040.3 | 0.640905 | ||||||||
\(668\) | 2298.45 | 0.133128 | ||||||||
\(669\) | 26113.2 | 1.50911 | ||||||||
\(670\) | 1768.76 | 0.101990 | ||||||||
\(671\) | 9035.71 | 0.519851 | ||||||||
\(672\) | −38668.5 | −2.21975 | ||||||||
\(673\) | −12270.1 | −0.702787 | −0.351394 | − | 0.936228i | \(-0.614292\pi\) | ||||
−0.351394 | + | 0.936228i | \(0.614292\pi\) | |||||||
\(674\) | 10554.5 | 0.603183 | ||||||||
\(675\) | −43847.5 | −2.50028 | ||||||||
\(676\) | 5688.71 | 0.323664 | ||||||||
\(677\) | −5587.24 | −0.317186 | −0.158593 | − | 0.987344i | \(-0.550696\pi\) | ||||
−0.158593 | + | 0.987344i | \(0.550696\pi\) | |||||||
\(678\) | −8714.88 | −0.493647 | ||||||||
\(679\) | −5149.96 | −0.291071 | ||||||||
\(680\) | 336.978 | 0.0190037 | ||||||||
\(681\) | −22015.7 | −1.23883 | ||||||||
\(682\) | 9143.47 | 0.513375 | ||||||||
\(683\) | −16419.2 | −0.919860 | −0.459930 | − | 0.887955i | \(-0.652126\pi\) | ||||
−0.459930 | + | 0.887955i | \(0.652126\pi\) | |||||||
\(684\) | −29854.8 | −1.66890 | ||||||||
\(685\) | −1287.55 | −0.0718173 | ||||||||
\(686\) | −817.031 | −0.0454729 | ||||||||
\(687\) | 29086.1 | 1.61529 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −530.714 | −0.0293448 | ||||||||
\(690\) | −1500.35 | −0.0827788 | ||||||||
\(691\) | 21390.2 | 1.17760 | 0.588801 | − | 0.808278i | \(-0.299600\pi\) | ||||
0.588801 | + | 0.808278i | \(0.299600\pi\) | |||||||
\(692\) | 21656.2 | 1.18966 | ||||||||
\(693\) | −67297.6 | −3.68892 | ||||||||
\(694\) | 10057.7 | 0.550125 | ||||||||
\(695\) | −889.165 | −0.0485294 | ||||||||
\(696\) | 17010.7 | 0.926422 | ||||||||
\(697\) | 4033.63 | 0.219203 | ||||||||
\(698\) | −1107.61 | −0.0600625 | ||||||||
\(699\) | −47869.5 | −2.59026 | ||||||||
\(700\) | −23297.5 | −1.25795 | ||||||||
\(701\) | 2029.82 | 0.109365 | 0.0546827 | − | 0.998504i | \(-0.482585\pi\) | ||||
0.0546827 | + | 0.998504i | \(0.482585\pi\) | |||||||
\(702\) | −12277.7 | −0.660103 | ||||||||
\(703\) | −19871.5 | −1.06610 | ||||||||
\(704\) | −8704.74 | −0.466012 | ||||||||
\(705\) | −9269.98 | −0.495217 | ||||||||
\(706\) | −1428.41 | −0.0761459 | ||||||||
\(707\) | 46068.6 | 2.45062 | ||||||||
\(708\) | 44910.8 | 2.38397 | ||||||||
\(709\) | 17269.2 | 0.914751 | 0.457376 | − | 0.889274i | \(-0.348789\pi\) | ||||
0.457376 | + | 0.889274i | \(0.348789\pi\) | |||||||
\(710\) | −1628.71 | −0.0860909 | ||||||||
\(711\) | −25699.2 | −1.35555 | ||||||||
\(712\) | 4049.84 | 0.213166 | ||||||||
\(713\) | −22327.7 | −1.17276 | ||||||||
\(714\) | 2806.00 | 0.147075 | ||||||||
\(715\) | −2948.46 | −0.154218 | ||||||||
\(716\) | 24986.2 | 1.30416 | ||||||||
\(717\) | −28168.7 | −1.46720 | ||||||||
\(718\) | −553.663 | −0.0287779 | ||||||||
\(719\) | 13317.0 | 0.690739 | 0.345369 | − | 0.938467i | \(-0.387754\pi\) | ||||
0.345369 | + | 0.938467i | \(0.387754\pi\) | |||||||
\(720\) | 5947.92 | 0.307869 | ||||||||
\(721\) | 856.981 | 0.0442658 | ||||||||
\(722\) | −2486.24 | −0.128155 | ||||||||
\(723\) | 47742.4 | 2.45582 | ||||||||
\(724\) | −55.5851 | −0.00285332 | ||||||||
\(725\) | 15648.3 | 0.801605 | ||||||||
\(726\) | 1428.81 | 0.0730416 | ||||||||
\(727\) | 22136.1 | 1.12927 | 0.564636 | − | 0.825340i | \(-0.309017\pi\) | ||||
0.564636 | + | 0.825340i | \(0.309017\pi\) | |||||||
\(728\) | −13787.1 | −0.701899 | ||||||||
\(729\) | 18051.0 | 0.917084 | ||||||||
\(730\) | 633.634 | 0.0321258 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | −16085.9 | −0.812231 | ||||||||
\(733\) | 17545.9 | 0.884139 | 0.442069 | − | 0.896981i | \(-0.354244\pi\) | ||||
0.442069 | + | 0.896981i | \(0.354244\pi\) | |||||||
\(734\) | 1988.39 | 0.0999904 | ||||||||
\(735\) | 7341.99 | 0.368453 | ||||||||
\(736\) | −12824.5 | −0.642280 | ||||||||
\(737\) | 37267.0 | 1.86261 | ||||||||
\(738\) | −19537.2 | −0.974493 | ||||||||
\(739\) | 13702.8 | 0.682094 | 0.341047 | − | 0.940046i | \(-0.389219\pi\) | ||||
0.341047 | + | 0.940046i | \(0.389219\pi\) | |||||||
\(740\) | 4531.31 | 0.225100 | ||||||||
\(741\) | −23018.9 | −1.14119 | ||||||||
\(742\) | −342.900 | −0.0169653 | ||||||||
\(743\) | 12371.8 | 0.610871 | 0.305435 | − | 0.952213i | \(-0.401198\pi\) | ||||
0.305435 | + | 0.952213i | \(0.401198\pi\) | |||||||
\(744\) | −34402.1 | −1.69522 | ||||||||
\(745\) | −4173.30 | −0.205232 | ||||||||
\(746\) | −5659.52 | −0.277761 | ||||||||
\(747\) | 35012.5 | 1.71492 | ||||||||
\(748\) | 3359.44 | 0.164215 | ||||||||
\(749\) | −34205.7 | −1.66869 | ||||||||
\(750\) | −4325.87 | −0.210611 | ||||||||
\(751\) | −9938.30 | −0.482895 | −0.241447 | − | 0.970414i | \(-0.577622\pi\) | ||||
−0.241447 | + | 0.970414i | \(0.577622\pi\) | |||||||
\(752\) | −21453.7 | −1.04034 | ||||||||
\(753\) | 48197.2 | 2.33254 | ||||||||
\(754\) | 4381.67 | 0.211633 | ||||||||
\(755\) | −2077.41 | −0.100139 | ||||||||
\(756\) | 69928.3 | 3.36411 | ||||||||
\(757\) | 10311.6 | 0.495088 | 0.247544 | − | 0.968877i | \(-0.420377\pi\) | ||||
0.247544 | + | 0.968877i | \(0.420377\pi\) | |||||||
\(758\) | 2931.60 | 0.140475 | ||||||||
\(759\) | −31611.7 | −1.51177 | ||||||||
\(760\) | −1786.10 | −0.0852483 | ||||||||
\(761\) | −19234.7 | −0.916238 | −0.458119 | − | 0.888891i | \(-0.651477\pi\) | ||||
−0.458119 | + | 0.888891i | \(0.651477\pi\) | |||||||
\(762\) | −6005.16 | −0.285491 | ||||||||
\(763\) | 31707.0 | 1.50442 | ||||||||
\(764\) | −9352.97 | −0.442904 | ||||||||
\(765\) | −1594.12 | −0.0753406 | ||||||||
\(766\) | 8070.05 | 0.380656 | ||||||||
\(767\) | 24448.8 | 1.15097 | ||||||||
\(768\) | 5086.54 | 0.238990 | ||||||||
\(769\) | 13634.6 | 0.639370 | 0.319685 | − | 0.947524i | \(-0.396423\pi\) | ||||
0.319685 | + | 0.947524i | \(0.396423\pi\) | |||||||
\(770\) | −1905.03 | −0.0891590 | ||||||||
\(771\) | 8110.55 | 0.378851 | ||||||||
\(772\) | 5464.31 | 0.254747 | ||||||||
\(773\) | −11204.3 | −0.521335 | −0.260667 | − | 0.965429i | \(-0.583943\pi\) | ||||
−0.260667 | + | 0.965429i | \(0.583943\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −31646.8 | −1.46682 | ||||||||
\(776\) | −2631.65 | −0.121740 | ||||||||
\(777\) | 79744.2 | 3.68186 | ||||||||
\(778\) | 4177.17 | 0.192492 | ||||||||
\(779\) | −21379.6 | −0.983318 | ||||||||
\(780\) | 5249.02 | 0.240955 | ||||||||
\(781\) | −34316.2 | −1.57225 | ||||||||
\(782\) | 930.618 | 0.0425561 | ||||||||
\(783\) | −46969.0 | −2.14372 | ||||||||
\(784\) | 16991.7 | 0.774038 | ||||||||
\(785\) | −373.197 | −0.0169681 | ||||||||
\(786\) | 8773.65 | 0.398150 | ||||||||
\(787\) | −40995.2 | −1.85683 | −0.928413 | − | 0.371551i | \(-0.878826\pi\) | ||||
−0.928413 | + | 0.371551i | \(0.878826\pi\) | |||||||
\(788\) | 1440.85 | 0.0651371 | ||||||||
\(789\) | 74043.4 | 3.34096 | ||||||||
\(790\) | −727.480 | −0.0327627 | ||||||||
\(791\) | 27021.2 | 1.21462 | ||||||||
\(792\) | −34389.3 | −1.54289 | ||||||||
\(793\) | −8756.96 | −0.392142 | ||||||||
\(794\) | 9787.31 | 0.437454 | ||||||||
\(795\) | 275.908 | 0.0123087 | ||||||||
\(796\) | −13498.0 | −0.601034 | ||||||||
\(797\) | −1380.09 | −0.0613368 | −0.0306684 | − | 0.999530i | \(-0.509764\pi\) | ||||
−0.0306684 | + | 0.999530i | \(0.509764\pi\) | |||||||
\(798\) | −14872.8 | −0.659762 | ||||||||
\(799\) | 5749.86 | 0.254588 | ||||||||
\(800\) | −18177.2 | −0.803325 | ||||||||
\(801\) | −19158.3 | −0.845100 | ||||||||
\(802\) | −11187.5 | −0.492573 | ||||||||
\(803\) | 13350.4 | 0.586705 | ||||||||
\(804\) | −66345.0 | −2.91021 | ||||||||
\(805\) | 4651.95 | 0.203677 | ||||||||
\(806\) | −8861.39 | −0.387257 | ||||||||
\(807\) | −12286.0 | −0.535918 | ||||||||
\(808\) | 23541.2 | 1.02497 | ||||||||
\(809\) | −18158.2 | −0.789131 | −0.394566 | − | 0.918868i | \(-0.629105\pi\) | ||||
−0.394566 | + | 0.918868i | \(0.629105\pi\) | |||||||
\(810\) | 3168.37 | 0.137439 | ||||||||
\(811\) | 478.154 | 0.0207031 | 0.0103516 | − | 0.999946i | \(-0.496705\pi\) | ||||
0.0103516 | + | 0.999946i | \(0.496705\pi\) | |||||||
\(812\) | −24956.0 | −1.07855 | ||||||||
\(813\) | 11081.2 | 0.478024 | ||||||||
\(814\) | −10830.5 | −0.466350 | ||||||||
\(815\) | −1692.34 | −0.0727361 | ||||||||
\(816\) | −5225.25 | −0.224167 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | −7141.88 | −0.305269 | ||||||||
\(819\) | 65221.4 | 2.78269 | ||||||||
\(820\) | 4875.22 | 0.207622 | ||||||||
\(821\) | 7722.38 | 0.328274 | 0.164137 | − | 0.986438i | \(-0.447516\pi\) | ||||
0.164137 | + | 0.986438i | \(0.447516\pi\) | |||||||
\(822\) | −5478.66 | −0.232470 | ||||||||
\(823\) | −1765.67 | −0.0747842 | −0.0373921 | − | 0.999301i | \(-0.511905\pi\) | ||||
−0.0373921 | + | 0.999301i | \(0.511905\pi\) | |||||||
\(824\) | 437.920 | 0.0185142 | ||||||||
\(825\) | −44805.6 | −1.89082 | ||||||||
\(826\) | 15796.6 | 0.665418 | ||||||||
\(827\) | −19472.6 | −0.818776 | −0.409388 | − | 0.912360i | \(-0.634258\pi\) | ||||
−0.409388 | + | 0.912360i | \(0.634258\pi\) | |||||||
\(828\) | 39734.5 | 1.66772 | ||||||||
\(829\) | −26318.0 | −1.10261 | −0.551304 | − | 0.834304i | \(-0.685870\pi\) | ||||
−0.551304 | + | 0.834304i | \(0.685870\pi\) | |||||||
\(830\) | 991.118 | 0.0414485 | ||||||||
\(831\) | −19994.7 | −0.834669 | ||||||||
\(832\) | 8436.20 | 0.351530 | ||||||||
\(833\) | −4553.99 | −0.189420 | ||||||||
\(834\) | −3783.48 | −0.157088 | ||||||||
\(835\) | −650.498 | −0.0269598 | ||||||||
\(836\) | −17806.2 | −0.736650 | ||||||||
\(837\) | 94989.0 | 3.92270 | ||||||||
\(838\) | 11647.9 | 0.480156 | ||||||||
\(839\) | −6566.60 | −0.270208 | −0.135104 | − | 0.990831i | \(-0.543137\pi\) | ||||
−0.135104 | + | 0.990831i | \(0.543137\pi\) | |||||||
\(840\) | 7167.63 | 0.294413 | ||||||||
\(841\) | −7626.71 | −0.312711 | ||||||||
\(842\) | 14512.8 | 0.593994 | ||||||||
\(843\) | 11060.7 | 0.451898 | ||||||||
\(844\) | −6522.59 | −0.266015 | ||||||||
\(845\) | −1610.00 | −0.0655450 | ||||||||
\(846\) | −27850.0 | −1.13180 | ||||||||
\(847\) | −4430.15 | −0.179719 | ||||||||
\(848\) | 638.538 | 0.0258579 | ||||||||
\(849\) | 50685.0 | 2.04889 | ||||||||
\(850\) | 1319.04 | 0.0532265 | ||||||||
\(851\) | 26447.4 | 1.06534 | ||||||||
\(852\) | 61091.8 | 2.45654 | ||||||||
\(853\) | 39036.9 | 1.56694 | 0.783468 | − | 0.621432i | \(-0.213449\pi\) | ||||
0.783468 | + | 0.621432i | \(0.213449\pi\) | |||||||
\(854\) | −5657.96 | −0.226711 | ||||||||
\(855\) | 8449.39 | 0.337968 | ||||||||
\(856\) | −17479.3 | −0.697931 | ||||||||
\(857\) | −6060.17 | −0.241554 | −0.120777 | − | 0.992680i | \(-0.538539\pi\) | ||||
−0.120777 | + | 0.992680i | \(0.538539\pi\) | |||||||
\(858\) | −12546.0 | −0.499198 | ||||||||
\(859\) | −13664.8 | −0.542767 | −0.271383 | − | 0.962471i | \(-0.587481\pi\) | ||||
−0.271383 | + | 0.962471i | \(0.587481\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 85796.5 | 3.39598 | ||||||||
\(862\) | −8375.80 | −0.330952 | ||||||||
\(863\) | 8805.11 | 0.347311 | 0.173655 | − | 0.984806i | \(-0.444442\pi\) | ||||
0.173655 | + | 0.984806i | \(0.444442\pi\) | |||||||
\(864\) | 54559.4 | 2.14832 | ||||||||
\(865\) | −6129.05 | −0.240918 | ||||||||
\(866\) | 164.762 | 0.00646517 | ||||||||
\(867\) | −45685.7 | −1.78958 | ||||||||
\(868\) | 50470.5 | 1.97359 | ||||||||
\(869\) | −15327.6 | −0.598337 | ||||||||
\(870\) | −2277.95 | −0.0887697 | ||||||||
\(871\) | −36117.3 | −1.40504 | ||||||||
\(872\) | 16202.4 | 0.629223 | ||||||||
\(873\) | 12449.3 | 0.482642 | ||||||||
\(874\) | −4932.60 | −0.190901 | ||||||||
\(875\) | 13412.7 | 0.518208 | ||||||||
\(876\) | −23767.1 | −0.916686 | ||||||||
\(877\) | 24442.4 | 0.941120 | 0.470560 | − | 0.882368i | \(-0.344052\pi\) | ||||
0.470560 | + | 0.882368i | \(0.344052\pi\) | |||||||
\(878\) | −5241.80 | −0.201483 | ||||||||
\(879\) | −29516.1 | −1.13260 | ||||||||
\(880\) | 3547.49 | 0.135893 | ||||||||
\(881\) | −21839.8 | −0.835190 | −0.417595 | − | 0.908633i | \(-0.637127\pi\) | ||||
−0.417595 | + | 0.908633i | \(0.637127\pi\) | |||||||
\(882\) | 22057.7 | 0.842086 | ||||||||
\(883\) | 17757.9 | 0.676785 | 0.338393 | − | 0.941005i | \(-0.390117\pi\) | ||||
0.338393 | + | 0.941005i | \(0.390117\pi\) | |||||||
\(884\) | −3255.80 | −0.123874 | ||||||||
\(885\) | −12710.5 | −0.482777 | ||||||||
\(886\) | 12007.5 | 0.455304 | ||||||||
\(887\) | 42106.9 | 1.59392 | 0.796962 | − | 0.604030i | \(-0.206439\pi\) | ||||
0.796962 | + | 0.604030i | \(0.206439\pi\) | |||||||
\(888\) | 40749.6 | 1.53994 | ||||||||
\(889\) | 18619.5 | 0.702449 | ||||||||
\(890\) | −542.324 | −0.0204256 | ||||||||
\(891\) | 66756.1 | 2.51000 | ||||||||
\(892\) | −19576.5 | −0.734833 | ||||||||
\(893\) | −30476.3 | −1.14205 | ||||||||
\(894\) | −17757.8 | −0.664329 | ||||||||
\(895\) | −7071.50 | −0.264105 | ||||||||
\(896\) | 37728.3 | 1.40671 | ||||||||
\(897\) | 30636.4 | 1.14038 | ||||||||
\(898\) | −6490.47 | −0.241191 | ||||||||
\(899\) | −33899.7 | −1.25764 | ||||||||
\(900\) | 56318.7 | 2.08588 | ||||||||
\(901\) | −171.137 | −0.00632784 | ||||||||
\(902\) | −11652.5 | −0.430140 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 13807.9 | 0.508014 | ||||||||
\(905\) | 15.7315 | 0.000577826 0 | ||||||||
\(906\) | −8839.58 | −0.324145 | ||||||||
\(907\) | 1377.33 | 0.0504227 | 0.0252114 | − | 0.999682i | \(-0.491974\pi\) | ||||
0.0252114 | + | 0.999682i | \(0.491974\pi\) | |||||||
\(908\) | 16504.7 | 0.603225 | ||||||||
\(909\) | −111365. | −4.06352 | ||||||||
\(910\) | 1846.26 | 0.0672559 | ||||||||
\(911\) | 39864.1 | 1.44979 | 0.724895 | − | 0.688860i | \(-0.241888\pi\) | ||||
0.724895 | + | 0.688860i | \(0.241888\pi\) | |||||||
\(912\) | 27695.6 | 1.00559 | ||||||||
\(913\) | 20882.4 | 0.756961 | ||||||||
\(914\) | 3791.04 | 0.137195 | ||||||||
\(915\) | 4552.58 | 0.164485 | ||||||||
\(916\) | −21805.3 | −0.786537 | ||||||||
\(917\) | −27203.4 | −0.979646 | ||||||||
\(918\) | −3959.13 | −0.142343 | ||||||||
\(919\) | 5830.88 | 0.209296 | 0.104648 | − | 0.994509i | \(-0.466628\pi\) | ||||
0.104648 | + | 0.994509i | \(0.466628\pi\) | |||||||
\(920\) | 2377.17 | 0.0851879 | ||||||||
\(921\) | −6128.81 | −0.219274 | ||||||||
\(922\) | −1070.38 | −0.0382331 | ||||||||
\(923\) | 33257.5 | 1.18601 | ||||||||
\(924\) | 71456.2 | 2.54409 | ||||||||
\(925\) | 37485.9 | 1.33246 | ||||||||
\(926\) | 2277.29 | 0.0808169 | ||||||||
\(927\) | −2071.64 | −0.0733998 | ||||||||
\(928\) | −19471.2 | −0.688763 | ||||||||
\(929\) | 4121.82 | 0.145568 | 0.0727840 | − | 0.997348i | \(-0.476812\pi\) | ||||
0.0727840 | + | 0.997348i | \(0.476812\pi\) | |||||||
\(930\) | 4606.87 | 0.162436 | ||||||||
\(931\) | 24137.7 | 0.849712 | ||||||||
\(932\) | 35886.8 | 1.26128 | ||||||||
\(933\) | 67743.3 | 2.37708 | ||||||||
\(934\) | −8693.67 | −0.304567 | ||||||||
\(935\) | −950.774 | −0.0332552 | ||||||||
\(936\) | 33328.4 | 1.16386 | ||||||||
\(937\) | −33608.5 | −1.17176 | −0.585881 | − | 0.810397i | \(-0.699251\pi\) | ||||
−0.585881 | + | 0.810397i | \(0.699251\pi\) | |||||||
\(938\) | −23335.7 | −0.812302 | ||||||||
\(939\) | −52515.9 | −1.82512 | ||||||||
\(940\) | 6949.53 | 0.241137 | ||||||||
\(941\) | −30075.8 | −1.04192 | −0.520958 | − | 0.853582i | \(-0.674425\pi\) | ||||
−0.520958 | + | 0.853582i | \(0.674425\pi\) | |||||||
\(942\) | −1587.99 | −0.0549251 | ||||||||
\(943\) | 28454.7 | 0.982621 | ||||||||
\(944\) | −29416.1 | −1.01421 | ||||||||
\(945\) | −19790.8 | −0.681265 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 8945.08 | 0.306944 | 0.153472 | − | 0.988153i | \(-0.450955\pi\) | ||||
0.153472 | + | 0.988153i | \(0.450955\pi\) | |||||||
\(948\) | 27287.2 | 0.934860 | ||||||||
\(949\) | −12938.5 | −0.442573 | ||||||||
\(950\) | −6991.34 | −0.238767 | ||||||||
\(951\) | 62436.6 | 2.12897 | ||||||||
\(952\) | −4445.84 | −0.151356 | ||||||||
\(953\) | 51373.5 | 1.74622 | 0.873112 | − | 0.487519i | \(-0.162098\pi\) | ||||
0.873112 | + | 0.487519i | \(0.162098\pi\) | |||||||
\(954\) | 828.915 | 0.0281311 | ||||||||
\(955\) | 2647.04 | 0.0896924 | ||||||||
\(956\) | 21117.5 | 0.714425 | ||||||||
\(957\) | −47995.2 | −1.62118 | ||||||||
\(958\) | 11157.4 | 0.376283 | ||||||||
\(959\) | 16987.0 | 0.571991 | ||||||||
\(960\) | −4385.82 | −0.147450 | ||||||||
\(961\) | 38767.0 | 1.30130 | ||||||||
\(962\) | 10496.4 | 0.351785 | ||||||||
\(963\) | 82687.9 | 2.76696 | ||||||||
\(964\) | −35791.5 | −1.19582 | ||||||||
\(965\) | −1546.49 | −0.0515888 | ||||||||
\(966\) | 19794.5 | 0.659294 | ||||||||
\(967\) | 22479.1 | 0.747549 | 0.373775 | − | 0.927520i | \(-0.378063\pi\) | ||||
0.373775 | + | 0.927520i | \(0.378063\pi\) | |||||||
\(968\) | −2263.82 | −0.0751673 | ||||||||
\(969\) | −7422.80 | −0.246083 | ||||||||
\(970\) | 352.410 | 0.0116652 | ||||||||
\(971\) | 45003.4 | 1.48736 | 0.743680 | − | 0.668536i | \(-0.233079\pi\) | ||||
0.743680 | + | 0.668536i | \(0.233079\pi\) | |||||||
\(972\) | −48466.3 | −1.59934 | ||||||||
\(973\) | 11731.0 | 0.386514 | ||||||||
\(974\) | 2458.63 | 0.0808826 | ||||||||
\(975\) | 43423.3 | 1.42632 | ||||||||
\(976\) | 10536.1 | 0.345545 | ||||||||
\(977\) | −21946.4 | −0.718657 | −0.359329 | − | 0.933211i | \(-0.616994\pi\) | ||||
−0.359329 | + | 0.933211i | \(0.616994\pi\) | |||||||
\(978\) | −7201.05 | −0.235444 | ||||||||
\(979\) | −11426.5 | −0.373026 | ||||||||
\(980\) | −5504.15 | −0.179412 | ||||||||
\(981\) | −76647.5 | −2.49456 | ||||||||
\(982\) | 3791.32 | 0.123204 | ||||||||
\(983\) | −950.865 | −0.0308524 | −0.0154262 | − | 0.999881i | \(-0.504911\pi\) | ||||
−0.0154262 | + | 0.999881i | \(0.504911\pi\) | |||||||
\(984\) | 43842.3 | 1.42037 | ||||||||
\(985\) | −407.783 | −0.0131909 | ||||||||
\(986\) | 1412.93 | 0.0456359 | ||||||||
\(987\) | 122301. | 3.94417 | ||||||||
\(988\) | 17256.8 | 0.555681 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 4605.16 | 0.147840 | ||||||||
\(991\) | −51696.8 | −1.65712 | −0.828559 | − | 0.559901i | \(-0.810839\pi\) | ||||
−0.828559 | + | 0.559901i | \(0.810839\pi\) | |||||||
\(992\) | 39378.1 | 1.26034 | ||||||||
\(993\) | 36175.6 | 1.15609 | ||||||||
\(994\) | 21488.0 | 0.685674 | ||||||||
\(995\) | 3820.15 | 0.121715 | ||||||||
\(996\) | −37176.1 | −1.18270 | ||||||||
\(997\) | −44474.6 | −1.41276 | −0.706381 | − | 0.707832i | \(-0.749674\pi\) | ||||
−0.706381 | + | 0.707832i | \(0.749674\pi\) | |||||||
\(998\) | −18042.9 | −0.572284 | ||||||||
\(999\) | −112515. | −3.56339 |
(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 | 1849.4.a.j.1.27 | yes | 50 | |
43.42 | odd | 2 | 1849.4.a.i.1.24 | ✓ | 50 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1849.4.a.i.1.24 | ✓ | 50 | 43.42 | odd | 2 | ||
1849.4.a.j.1.27 | yes | 50 | 1.1 | even | 1 | trivial |