Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2013,4,Mod(1,2013)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2013, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2013.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2013 = 3 \cdot 11 \cdot 61 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 2013.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: | \(118.770844842\) |
Analytic rank: | \(1\) |
Dimension: | \(36\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.17 | ||
Character | \(\chi\) | \(=\) | 2013.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.11376 | −0.393773 | −0.196886 | − | 0.980426i | \(-0.563083\pi\) | ||||
−0.196886 | + | 0.980426i | \(0.563083\pi\) | |||||||
\(3\) | 3.00000 | 0.577350 | ||||||||
\(4\) | −6.75954 | −0.844943 | ||||||||
\(5\) | −13.8886 | −1.24223 | −0.621116 | − | 0.783719i | \(-0.713320\pi\) | ||||
−0.621116 | + | 0.783719i | \(0.713320\pi\) | |||||||
\(6\) | −3.34127 | −0.227345 | ||||||||
\(7\) | −3.42861 | −0.185128 | −0.0925639 | − | 0.995707i | \(-0.529506\pi\) | ||||
−0.0925639 | + | 0.995707i | \(0.529506\pi\) | |||||||
\(8\) | 16.4385 | 0.726488 | ||||||||
\(9\) | 9.00000 | 0.333333 | ||||||||
\(10\) | 15.4685 | 0.489157 | ||||||||
\(11\) | 11.0000 | 0.301511 | ||||||||
\(12\) | −20.2786 | −0.487828 | ||||||||
\(13\) | 0.489230 | 0.0104375 | 0.00521876 | − | 0.999986i | \(-0.498339\pi\) | ||||
0.00521876 | + | 0.999986i | \(0.498339\pi\) | |||||||
\(14\) | 3.81864 | 0.0728983 | ||||||||
\(15\) | −41.6657 | −0.717202 | ||||||||
\(16\) | 35.7678 | 0.558872 | ||||||||
\(17\) | 22.7800 | 0.324998 | 0.162499 | − | 0.986709i | \(-0.448045\pi\) | ||||
0.162499 | + | 0.986709i | \(0.448045\pi\) | |||||||
\(18\) | −10.0238 | −0.131258 | ||||||||
\(19\) | −110.746 | −1.33720 | −0.668600 | − | 0.743622i | \(-0.733106\pi\) | ||||
−0.668600 | + | 0.743622i | \(0.733106\pi\) | |||||||
\(20\) | 93.8804 | 1.04961 | ||||||||
\(21\) | −10.2858 | −0.106884 | ||||||||
\(22\) | −12.2513 | −0.118727 | ||||||||
\(23\) | −49.8649 | −0.452067 | −0.226034 | − | 0.974119i | \(-0.572576\pi\) | ||||
−0.226034 | + | 0.974119i | \(0.572576\pi\) | |||||||
\(24\) | 49.3156 | 0.419438 | ||||||||
\(25\) | 67.8923 | 0.543138 | ||||||||
\(26\) | −0.544883 | −0.00411001 | ||||||||
\(27\) | 27.0000 | 0.192450 | ||||||||
\(28\) | 23.1759 | 0.156422 | ||||||||
\(29\) | −152.448 | −0.976170 | −0.488085 | − | 0.872796i | \(-0.662304\pi\) | ||||
−0.488085 | + | 0.872796i | \(0.662304\pi\) | |||||||
\(30\) | 46.4055 | 0.282415 | ||||||||
\(31\) | 263.015 | 1.52384 | 0.761919 | − | 0.647672i | \(-0.224257\pi\) | ||||
0.761919 | + | 0.647672i | \(0.224257\pi\) | |||||||
\(32\) | −171.345 | −0.946557 | ||||||||
\(33\) | 33.0000 | 0.174078 | ||||||||
\(34\) | −25.3714 | −0.127975 | ||||||||
\(35\) | 47.6185 | 0.229972 | ||||||||
\(36\) | −60.8359 | −0.281648 | ||||||||
\(37\) | 257.140 | 1.14253 | 0.571264 | − | 0.820766i | \(-0.306453\pi\) | ||||
0.571264 | + | 0.820766i | \(0.306453\pi\) | |||||||
\(38\) | 123.344 | 0.526553 | ||||||||
\(39\) | 1.46769 | 0.00602611 | ||||||||
\(40\) | −228.308 | −0.902466 | ||||||||
\(41\) | −47.7543 | −0.181902 | −0.0909508 | − | 0.995855i | \(-0.528991\pi\) | ||||
−0.0909508 | + | 0.995855i | \(0.528991\pi\) | |||||||
\(42\) | 11.4559 | 0.0420878 | ||||||||
\(43\) | −50.6012 | −0.179456 | −0.0897280 | − | 0.995966i | \(-0.528600\pi\) | ||||
−0.0897280 | + | 0.995966i | \(0.528600\pi\) | |||||||
\(44\) | −74.3550 | −0.254760 | ||||||||
\(45\) | −124.997 | −0.414077 | ||||||||
\(46\) | 55.5374 | 0.178012 | ||||||||
\(47\) | 463.322 | 1.43793 | 0.718963 | − | 0.695049i | \(-0.244617\pi\) | ||||
0.718963 | + | 0.695049i | \(0.244617\pi\) | |||||||
\(48\) | 107.303 | 0.322665 | ||||||||
\(49\) | −331.245 | −0.965728 | ||||||||
\(50\) | −75.6155 | −0.213873 | ||||||||
\(51\) | 68.3400 | 0.187637 | ||||||||
\(52\) | −3.30697 | −0.00881912 | ||||||||
\(53\) | 205.122 | 0.531617 | 0.265808 | − | 0.964026i | \(-0.414361\pi\) | ||||
0.265808 | + | 0.964026i | \(0.414361\pi\) | |||||||
\(54\) | −30.0714 | −0.0757816 | ||||||||
\(55\) | −152.774 | −0.374547 | ||||||||
\(56\) | −56.3615 | −0.134493 | ||||||||
\(57\) | −332.237 | −0.772032 | ||||||||
\(58\) | 169.790 | 0.384389 | ||||||||
\(59\) | 582.033 | 1.28431 | 0.642155 | − | 0.766575i | \(-0.278041\pi\) | ||||
0.642155 | + | 0.766575i | \(0.278041\pi\) | |||||||
\(60\) | 281.641 | 0.605995 | ||||||||
\(61\) | 61.0000 | 0.128037 | ||||||||
\(62\) | −292.935 | −0.600046 | ||||||||
\(63\) | −30.8575 | −0.0617093 | ||||||||
\(64\) | −95.3056 | −0.186144 | ||||||||
\(65\) | −6.79470 | −0.0129658 | ||||||||
\(66\) | −36.7540 | −0.0685470 | ||||||||
\(67\) | 794.216 | 1.44819 | 0.724097 | − | 0.689698i | \(-0.242257\pi\) | ||||
0.724097 | + | 0.689698i | \(0.242257\pi\) | |||||||
\(68\) | −153.982 | −0.274604 | ||||||||
\(69\) | −149.595 | −0.261001 | ||||||||
\(70\) | −53.0355 | −0.0905565 | ||||||||
\(71\) | 164.319 | 0.274663 | 0.137332 | − | 0.990525i | \(-0.456147\pi\) | ||||
0.137332 | + | 0.990525i | \(0.456147\pi\) | |||||||
\(72\) | 147.947 | 0.242163 | ||||||||
\(73\) | −2.82106 | −0.00452301 | −0.00226151 | − | 0.999997i | \(-0.500720\pi\) | ||||
−0.00226151 | + | 0.999997i | \(0.500720\pi\) | |||||||
\(74\) | −286.392 | −0.449896 | ||||||||
\(75\) | 203.677 | 0.313581 | ||||||||
\(76\) | 748.590 | 1.12986 | ||||||||
\(77\) | −37.7148 | −0.0558181 | ||||||||
\(78\) | −1.63465 | −0.00237292 | ||||||||
\(79\) | −1183.00 | −1.68479 | −0.842394 | − | 0.538862i | \(-0.818855\pi\) | ||||
−0.842394 | + | 0.538862i | \(0.818855\pi\) | |||||||
\(80\) | −496.764 | −0.694248 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | 53.1867 | 0.0716279 | ||||||||
\(83\) | 1507.01 | 1.99296 | 0.996481 | − | 0.0838228i | \(-0.0267130\pi\) | ||||
0.996481 | + | 0.0838228i | \(0.0267130\pi\) | |||||||
\(84\) | 69.5276 | 0.0903106 | ||||||||
\(85\) | −316.381 | −0.403722 | ||||||||
\(86\) | 56.3574 | 0.0706649 | ||||||||
\(87\) | −457.345 | −0.563592 | ||||||||
\(88\) | 180.824 | 0.219044 | ||||||||
\(89\) | −152.669 | −0.181830 | −0.0909152 | − | 0.995859i | \(-0.528979\pi\) | ||||
−0.0909152 | + | 0.995859i | \(0.528979\pi\) | |||||||
\(90\) | 139.216 | 0.163052 | ||||||||
\(91\) | −1.67738 | −0.00193228 | ||||||||
\(92\) | 337.064 | 0.381971 | ||||||||
\(93\) | 789.046 | 0.879788 | ||||||||
\(94\) | −516.029 | −0.566216 | ||||||||
\(95\) | 1538.10 | 1.66111 | ||||||||
\(96\) | −514.035 | −0.546495 | ||||||||
\(97\) | 1147.09 | 1.20071 | 0.600355 | − | 0.799734i | \(-0.295026\pi\) | ||||
0.600355 | + | 0.799734i | \(0.295026\pi\) | |||||||
\(98\) | 368.926 | 0.380277 | ||||||||
\(99\) | 99.0000 | 0.100504 | ||||||||
\(100\) | −458.921 | −0.458921 | ||||||||
\(101\) | −653.484 | −0.643803 | −0.321901 | − | 0.946773i | \(-0.604322\pi\) | ||||
−0.321901 | + | 0.946773i | \(0.604322\pi\) | |||||||
\(102\) | −76.1141 | −0.0738865 | ||||||||
\(103\) | 1125.98 | 1.07715 | 0.538573 | − | 0.842579i | \(-0.318964\pi\) | ||||
0.538573 | + | 0.842579i | \(0.318964\pi\) | |||||||
\(104\) | 8.04222 | 0.00758274 | ||||||||
\(105\) | 142.856 | 0.132774 | ||||||||
\(106\) | −228.456 | −0.209336 | ||||||||
\(107\) | 273.530 | 0.247132 | 0.123566 | − | 0.992336i | \(-0.460567\pi\) | ||||
0.123566 | + | 0.992336i | \(0.460567\pi\) | |||||||
\(108\) | −182.508 | −0.162609 | ||||||||
\(109\) | −960.583 | −0.844103 | −0.422051 | − | 0.906572i | \(-0.638690\pi\) | ||||
−0.422051 | + | 0.906572i | \(0.638690\pi\) | |||||||
\(110\) | 170.153 | 0.147486 | ||||||||
\(111\) | 771.420 | 0.659639 | ||||||||
\(112\) | −122.634 | −0.103463 | ||||||||
\(113\) | −1867.87 | −1.55500 | −0.777498 | − | 0.628885i | \(-0.783512\pi\) | ||||
−0.777498 | + | 0.628885i | \(0.783512\pi\) | |||||||
\(114\) | 370.031 | 0.304005 | ||||||||
\(115\) | 692.552 | 0.561572 | ||||||||
\(116\) | 1030.48 | 0.824808 | ||||||||
\(117\) | 4.40307 | 0.00347918 | ||||||||
\(118\) | −648.244 | −0.505726 | ||||||||
\(119\) | −78.1038 | −0.0601661 | ||||||||
\(120\) | −684.924 | −0.521039 | ||||||||
\(121\) | 121.000 | 0.0909091 | ||||||||
\(122\) | −67.9392 | −0.0504174 | ||||||||
\(123\) | −143.263 | −0.105021 | ||||||||
\(124\) | −1777.86 | −1.28756 | ||||||||
\(125\) | 793.145 | 0.567528 | ||||||||
\(126\) | 34.3678 | 0.0242994 | ||||||||
\(127\) | −1426.24 | −0.996519 | −0.498260 | − | 0.867028i | \(-0.666027\pi\) | ||||
−0.498260 | + | 0.867028i | \(0.666027\pi\) | |||||||
\(128\) | 1476.91 | 1.01985 | ||||||||
\(129\) | −151.804 | −0.103609 | ||||||||
\(130\) | 7.56764 | 0.00510559 | ||||||||
\(131\) | −1794.21 | −1.19665 | −0.598325 | − | 0.801254i | \(-0.704167\pi\) | ||||
−0.598325 | + | 0.801254i | \(0.704167\pi\) | |||||||
\(132\) | −223.065 | −0.147086 | ||||||||
\(133\) | 379.704 | 0.247553 | ||||||||
\(134\) | −884.564 | −0.570259 | ||||||||
\(135\) | −374.991 | −0.239067 | ||||||||
\(136\) | 374.470 | 0.236107 | ||||||||
\(137\) | −884.505 | −0.551594 | −0.275797 | − | 0.961216i | \(-0.588942\pi\) | ||||
−0.275797 | + | 0.961216i | \(0.588942\pi\) | |||||||
\(138\) | 166.612 | 0.102775 | ||||||||
\(139\) | 375.996 | 0.229436 | 0.114718 | − | 0.993398i | \(-0.463404\pi\) | ||||
0.114718 | + | 0.993398i | \(0.463404\pi\) | |||||||
\(140\) | −321.880 | −0.194313 | ||||||||
\(141\) | 1389.97 | 0.830187 | ||||||||
\(142\) | −183.012 | −0.108155 | ||||||||
\(143\) | 5.38152 | 0.00314703 | ||||||||
\(144\) | 321.910 | 0.186291 | ||||||||
\(145\) | 2117.29 | 1.21263 | ||||||||
\(146\) | 3.14197 | 0.00178104 | ||||||||
\(147\) | −993.734 | −0.557563 | ||||||||
\(148\) | −1738.15 | −0.965372 | ||||||||
\(149\) | −2081.04 | −1.14420 | −0.572099 | − | 0.820185i | \(-0.693871\pi\) | ||||
−0.572099 | + | 0.820185i | \(0.693871\pi\) | |||||||
\(150\) | −226.846 | −0.123480 | ||||||||
\(151\) | −297.787 | −0.160487 | −0.0802437 | − | 0.996775i | \(-0.525570\pi\) | ||||
−0.0802437 | + | 0.996775i | \(0.525570\pi\) | |||||||
\(152\) | −1820.50 | −0.971460 | ||||||||
\(153\) | 205.020 | 0.108333 | ||||||||
\(154\) | 42.0051 | 0.0219797 | ||||||||
\(155\) | −3652.91 | −1.89296 | ||||||||
\(156\) | −9.92091 | −0.00509172 | ||||||||
\(157\) | 2606.19 | 1.32482 | 0.662409 | − | 0.749142i | \(-0.269534\pi\) | ||||
0.662409 | + | 0.749142i | \(0.269534\pi\) | |||||||
\(158\) | 1317.58 | 0.663424 | ||||||||
\(159\) | 615.366 | 0.306929 | ||||||||
\(160\) | 2379.74 | 1.17584 | ||||||||
\(161\) | 170.967 | 0.0836902 | ||||||||
\(162\) | −90.2143 | −0.0437525 | ||||||||
\(163\) | −1490.70 | −0.716324 | −0.358162 | − | 0.933659i | \(-0.616596\pi\) | ||||
−0.358162 | + | 0.933659i | \(0.616596\pi\) | |||||||
\(164\) | 322.797 | 0.153697 | ||||||||
\(165\) | −458.323 | −0.216245 | ||||||||
\(166\) | −1678.44 | −0.784774 | ||||||||
\(167\) | −2050.04 | −0.949923 | −0.474962 | − | 0.880007i | \(-0.657538\pi\) | ||||
−0.474962 | + | 0.880007i | \(0.657538\pi\) | |||||||
\(168\) | −169.084 | −0.0776497 | ||||||||
\(169\) | −2196.76 | −0.999891 | ||||||||
\(170\) | 352.372 | 0.158975 | ||||||||
\(171\) | −996.711 | −0.445733 | ||||||||
\(172\) | 342.041 | 0.151630 | ||||||||
\(173\) | −3715.79 | −1.63298 | −0.816491 | − | 0.577358i | \(-0.804084\pi\) | ||||
−0.816491 | + | 0.577358i | \(0.804084\pi\) | |||||||
\(174\) | 509.371 | 0.221927 | ||||||||
\(175\) | −232.776 | −0.100550 | ||||||||
\(176\) | 393.446 | 0.168506 | ||||||||
\(177\) | 1746.10 | 0.741497 | ||||||||
\(178\) | 170.036 | 0.0715998 | ||||||||
\(179\) | −151.765 | −0.0633711 | −0.0316856 | − | 0.999498i | \(-0.510088\pi\) | ||||
−0.0316856 | + | 0.999498i | \(0.510088\pi\) | |||||||
\(180\) | 844.923 | 0.349872 | ||||||||
\(181\) | 1068.80 | 0.438913 | 0.219457 | − | 0.975622i | \(-0.429572\pi\) | ||||
0.219457 | + | 0.975622i | \(0.429572\pi\) | |||||||
\(182\) | 1.86819 | 0.000760878 0 | ||||||||
\(183\) | 183.000 | 0.0739221 | ||||||||
\(184\) | −819.706 | −0.328422 | ||||||||
\(185\) | −3571.31 | −1.41928 | ||||||||
\(186\) | −878.806 | −0.346437 | ||||||||
\(187\) | 250.580 | 0.0979904 | ||||||||
\(188\) | −3131.85 | −1.21497 | ||||||||
\(189\) | −92.5726 | −0.0356279 | ||||||||
\(190\) | −1713.07 | −0.654100 | ||||||||
\(191\) | −4168.98 | −1.57935 | −0.789677 | − | 0.613522i | \(-0.789752\pi\) | ||||
−0.789677 | + | 0.613522i | \(0.789752\pi\) | |||||||
\(192\) | −285.917 | −0.107470 | ||||||||
\(193\) | 801.403 | 0.298892 | 0.149446 | − | 0.988770i | \(-0.452251\pi\) | ||||
0.149446 | + | 0.988770i | \(0.452251\pi\) | |||||||
\(194\) | −1277.57 | −0.472807 | ||||||||
\(195\) | −20.3841 | −0.00748582 | ||||||||
\(196\) | 2239.06 | 0.815985 | ||||||||
\(197\) | −561.099 | −0.202927 | −0.101464 | − | 0.994839i | \(-0.532353\pi\) | ||||
−0.101464 | + | 0.994839i | \(0.532353\pi\) | |||||||
\(198\) | −110.262 | −0.0395756 | ||||||||
\(199\) | −4943.61 | −1.76102 | −0.880510 | − | 0.474028i | \(-0.842800\pi\) | ||||
−0.880510 | + | 0.474028i | \(0.842800\pi\) | |||||||
\(200\) | 1116.05 | 0.394583 | ||||||||
\(201\) | 2382.65 | 0.836115 | ||||||||
\(202\) | 727.823 | 0.253512 | ||||||||
\(203\) | 522.686 | 0.180716 | ||||||||
\(204\) | −461.947 | −0.158543 | ||||||||
\(205\) | 663.239 | 0.225964 | ||||||||
\(206\) | −1254.07 | −0.424151 | ||||||||
\(207\) | −448.784 | −0.150689 | ||||||||
\(208\) | 17.4987 | 0.00583324 | ||||||||
\(209\) | −1218.20 | −0.403181 | ||||||||
\(210\) | −159.106 | −0.0522828 | ||||||||
\(211\) | −2261.41 | −0.737827 | −0.368914 | − | 0.929464i | \(-0.620270\pi\) | ||||
−0.368914 | + | 0.929464i | \(0.620270\pi\) | |||||||
\(212\) | −1386.53 | −0.449186 | ||||||||
\(213\) | 492.957 | 0.158577 | ||||||||
\(214\) | −304.646 | −0.0973138 | ||||||||
\(215\) | 702.778 | 0.222926 | ||||||||
\(216\) | 443.841 | 0.139813 | ||||||||
\(217\) | −901.779 | −0.282105 | ||||||||
\(218\) | 1069.86 | 0.332385 | ||||||||
\(219\) | −8.46317 | −0.00261136 | ||||||||
\(220\) | 1032.68 | 0.316471 | ||||||||
\(221\) | 11.1446 | 0.00339217 | ||||||||
\(222\) | −859.175 | −0.259748 | ||||||||
\(223\) | 119.361 | 0.0358430 | 0.0179215 | − | 0.999839i | \(-0.494295\pi\) | ||||
0.0179215 | + | 0.999839i | \(0.494295\pi\) | |||||||
\(224\) | 587.476 | 0.175234 | ||||||||
\(225\) | 611.030 | 0.181046 | ||||||||
\(226\) | 2080.36 | 0.612315 | ||||||||
\(227\) | −1490.13 | −0.435697 | −0.217849 | − | 0.975983i | \(-0.569904\pi\) | ||||
−0.217849 | + | 0.975983i | \(0.569904\pi\) | |||||||
\(228\) | 2245.77 | 0.652323 | ||||||||
\(229\) | 821.195 | 0.236970 | 0.118485 | − | 0.992956i | \(-0.462196\pi\) | ||||
0.118485 | + | 0.992956i | \(0.462196\pi\) | |||||||
\(230\) | −771.335 | −0.221132 | ||||||||
\(231\) | −113.144 | −0.0322266 | ||||||||
\(232\) | −2506.03 | −0.709176 | ||||||||
\(233\) | −4979.85 | −1.40018 | −0.700088 | − | 0.714056i | \(-0.746856\pi\) | ||||
−0.700088 | + | 0.714056i | \(0.746856\pi\) | |||||||
\(234\) | −4.90395 | −0.00137000 | ||||||||
\(235\) | −6434.88 | −1.78624 | ||||||||
\(236\) | −3934.28 | −1.08517 | ||||||||
\(237\) | −3549.01 | −0.972713 | ||||||||
\(238\) | 86.9887 | 0.0236918 | ||||||||
\(239\) | 2742.36 | 0.742211 | 0.371105 | − | 0.928591i | \(-0.378979\pi\) | ||||
0.371105 | + | 0.928591i | \(0.378979\pi\) | |||||||
\(240\) | −1490.29 | −0.400824 | ||||||||
\(241\) | −1172.32 | −0.313343 | −0.156672 | − | 0.987651i | \(-0.550076\pi\) | ||||
−0.156672 | + | 0.987651i | \(0.550076\pi\) | |||||||
\(242\) | −134.765 | −0.0357975 | ||||||||
\(243\) | 243.000 | 0.0641500 | ||||||||
\(244\) | −412.332 | −0.108184 | ||||||||
\(245\) | 4600.51 | 1.19966 | ||||||||
\(246\) | 159.560 | 0.0413544 | ||||||||
\(247\) | −54.1800 | −0.0139571 | ||||||||
\(248\) | 4323.59 | 1.10705 | ||||||||
\(249\) | 4521.03 | 1.15064 | ||||||||
\(250\) | −883.371 | −0.223477 | ||||||||
\(251\) | −1911.00 | −0.480562 | −0.240281 | − | 0.970703i | \(-0.577240\pi\) | ||||
−0.240281 | + | 0.970703i | \(0.577240\pi\) | |||||||
\(252\) | 208.583 | 0.0521408 | ||||||||
\(253\) | −548.514 | −0.136303 | ||||||||
\(254\) | 1588.48 | 0.392402 | ||||||||
\(255\) | −949.144 | −0.233089 | ||||||||
\(256\) | −882.472 | −0.215447 | ||||||||
\(257\) | −1333.36 | −0.323630 | −0.161815 | − | 0.986821i | \(-0.551735\pi\) | ||||
−0.161815 | + | 0.986821i | \(0.551735\pi\) | |||||||
\(258\) | 169.072 | 0.0407984 | ||||||||
\(259\) | −881.634 | −0.211514 | ||||||||
\(260\) | 45.9291 | 0.0109554 | ||||||||
\(261\) | −1372.03 | −0.325390 | ||||||||
\(262\) | 1998.32 | 0.471208 | ||||||||
\(263\) | 2494.19 | 0.584784 | 0.292392 | − | 0.956298i | \(-0.405549\pi\) | ||||
0.292392 | + | 0.956298i | \(0.405549\pi\) | |||||||
\(264\) | 542.472 | 0.126465 | ||||||||
\(265\) | −2848.85 | −0.660391 | ||||||||
\(266\) | −422.898 | −0.0974795 | ||||||||
\(267\) | −458.007 | −0.104980 | ||||||||
\(268\) | −5368.54 | −1.22364 | ||||||||
\(269\) | 99.4858 | 0.0225493 | 0.0112746 | − | 0.999936i | \(-0.496411\pi\) | ||||
0.0112746 | + | 0.999936i | \(0.496411\pi\) | |||||||
\(270\) | 417.649 | 0.0941382 | ||||||||
\(271\) | 16.1354 | 0.00361680 | 0.00180840 | − | 0.999998i | \(-0.499424\pi\) | ||||
0.00180840 | + | 0.999998i | \(0.499424\pi\) | |||||||
\(272\) | 814.790 | 0.181632 | ||||||||
\(273\) | −5.03214 | −0.00111560 | ||||||||
\(274\) | 985.123 | 0.217203 | ||||||||
\(275\) | 746.815 | 0.163762 | ||||||||
\(276\) | 1011.19 | 0.220531 | ||||||||
\(277\) | −5786.17 | −1.25508 | −0.627540 | − | 0.778584i | \(-0.715938\pi\) | ||||
−0.627540 | + | 0.778584i | \(0.715938\pi\) | |||||||
\(278\) | −418.769 | −0.0903456 | ||||||||
\(279\) | 2367.14 | 0.507946 | ||||||||
\(280\) | 782.780 | 0.167072 | ||||||||
\(281\) | 1100.01 | 0.233526 | 0.116763 | − | 0.993160i | \(-0.462748\pi\) | ||||
0.116763 | + | 0.993160i | \(0.462748\pi\) | |||||||
\(282\) | −1548.09 | −0.326905 | ||||||||
\(283\) | 4837.01 | 1.01601 | 0.508004 | − | 0.861355i | \(-0.330383\pi\) | ||||
0.508004 | + | 0.861355i | \(0.330383\pi\) | |||||||
\(284\) | −1110.72 | −0.232075 | ||||||||
\(285\) | 4614.29 | 0.959043 | ||||||||
\(286\) | −5.99371 | −0.00123922 | ||||||||
\(287\) | 163.731 | 0.0336751 | ||||||||
\(288\) | −1542.11 | −0.315519 | ||||||||
\(289\) | −4394.07 | −0.894377 | ||||||||
\(290\) | −2358.14 | −0.477500 | ||||||||
\(291\) | 3441.26 | 0.693230 | ||||||||
\(292\) | 19.0691 | 0.00382169 | ||||||||
\(293\) | 5422.52 | 1.08118 | 0.540592 | − | 0.841285i | \(-0.318200\pi\) | ||||
0.540592 | + | 0.841285i | \(0.318200\pi\) | |||||||
\(294\) | 1106.78 | 0.219553 | ||||||||
\(295\) | −8083.61 | −1.59541 | ||||||||
\(296\) | 4227.01 | 0.830033 | ||||||||
\(297\) | 297.000 | 0.0580259 | ||||||||
\(298\) | 2317.77 | 0.450554 | ||||||||
\(299\) | −24.3954 | −0.00471846 | ||||||||
\(300\) | −1376.76 | −0.264958 | ||||||||
\(301\) | 173.492 | 0.0332223 | ||||||||
\(302\) | 331.663 | 0.0631955 | ||||||||
\(303\) | −1960.45 | −0.371700 | ||||||||
\(304\) | −3961.13 | −0.747323 | ||||||||
\(305\) | −847.203 | −0.159051 | ||||||||
\(306\) | −228.342 | −0.0426584 | ||||||||
\(307\) | 6417.34 | 1.19302 | 0.596509 | − | 0.802606i | \(-0.296554\pi\) | ||||
0.596509 | + | 0.802606i | \(0.296554\pi\) | |||||||
\(308\) | 254.935 | 0.0471631 | ||||||||
\(309\) | 3377.94 | 0.621890 | ||||||||
\(310\) | 4068.45 | 0.745395 | ||||||||
\(311\) | 6012.22 | 1.09621 | 0.548105 | − | 0.836409i | \(-0.315349\pi\) | ||||
0.548105 | + | 0.836409i | \(0.315349\pi\) | |||||||
\(312\) | 24.1267 | 0.00437790 | ||||||||
\(313\) | −4551.74 | −0.821979 | −0.410989 | − | 0.911640i | \(-0.634817\pi\) | ||||
−0.410989 | + | 0.911640i | \(0.634817\pi\) | |||||||
\(314\) | −2902.66 | −0.521677 | ||||||||
\(315\) | 428.567 | 0.0766572 | ||||||||
\(316\) | 7996.57 | 1.42355 | ||||||||
\(317\) | 3268.10 | 0.579037 | 0.289519 | − | 0.957172i | \(-0.406505\pi\) | ||||
0.289519 | + | 0.957172i | \(0.406505\pi\) | |||||||
\(318\) | −685.369 | −0.120860 | ||||||||
\(319\) | −1676.93 | −0.294326 | ||||||||
\(320\) | 1323.66 | 0.231234 | ||||||||
\(321\) | 820.589 | 0.142682 | ||||||||
\(322\) | −190.416 | −0.0329549 | ||||||||
\(323\) | −2522.78 | −0.434586 | ||||||||
\(324\) | −547.523 | −0.0938826 | ||||||||
\(325\) | 33.2149 | 0.00566902 | ||||||||
\(326\) | 1660.28 | 0.282069 | ||||||||
\(327\) | −2881.75 | −0.487343 | ||||||||
\(328\) | −785.011 | −0.132149 | ||||||||
\(329\) | −1588.55 | −0.266200 | ||||||||
\(330\) | 510.460 | 0.0851512 | ||||||||
\(331\) | 1134.94 | 0.188465 | 0.0942323 | − | 0.995550i | \(-0.469960\pi\) | ||||
0.0942323 | + | 0.995550i | \(0.469960\pi\) | |||||||
\(332\) | −10186.7 | −1.68394 | ||||||||
\(333\) | 2314.26 | 0.380843 | ||||||||
\(334\) | 2283.25 | 0.374054 | ||||||||
\(335\) | −11030.5 | −1.79899 | ||||||||
\(336\) | −367.902 | −0.0597342 | ||||||||
\(337\) | 5871.98 | 0.949161 | 0.474580 | − | 0.880212i | \(-0.342600\pi\) | ||||
0.474580 | + | 0.880212i | \(0.342600\pi\) | |||||||
\(338\) | 2446.66 | 0.393730 | ||||||||
\(339\) | −5603.62 | −0.897778 | ||||||||
\(340\) | 2138.59 | 0.341122 | ||||||||
\(341\) | 2893.17 | 0.459454 | ||||||||
\(342\) | 1110.09 | 0.175518 | ||||||||
\(343\) | 2311.73 | 0.363911 | ||||||||
\(344\) | −831.810 | −0.130373 | ||||||||
\(345\) | 2077.66 | 0.324224 | ||||||||
\(346\) | 4138.48 | 0.643024 | ||||||||
\(347\) | −1086.86 | −0.168143 | −0.0840716 | − | 0.996460i | \(-0.526792\pi\) | ||||
−0.0840716 | + | 0.996460i | \(0.526792\pi\) | |||||||
\(348\) | 3091.44 | 0.476203 | ||||||||
\(349\) | −3249.90 | −0.498462 | −0.249231 | − | 0.968444i | \(-0.580178\pi\) | ||||
−0.249231 | + | 0.968444i | \(0.580178\pi\) | |||||||
\(350\) | 259.256 | 0.0395938 | ||||||||
\(351\) | 13.2092 | 0.00200870 | ||||||||
\(352\) | −1884.80 | −0.285398 | ||||||||
\(353\) | −1106.80 | −0.166881 | −0.0834406 | − | 0.996513i | \(-0.526591\pi\) | ||||
−0.0834406 | + | 0.996513i | \(0.526591\pi\) | |||||||
\(354\) | −1944.73 | −0.291981 | ||||||||
\(355\) | −2282.16 | −0.341195 | ||||||||
\(356\) | 1031.97 | 0.153636 | ||||||||
\(357\) | −234.311 | −0.0347369 | ||||||||
\(358\) | 169.029 | 0.0249538 | ||||||||
\(359\) | −2204.35 | −0.324069 | −0.162035 | − | 0.986785i | \(-0.551806\pi\) | ||||
−0.162035 | + | 0.986785i | \(0.551806\pi\) | |||||||
\(360\) | −2054.77 | −0.300822 | ||||||||
\(361\) | 5405.59 | 0.788102 | ||||||||
\(362\) | −1190.38 | −0.172832 | ||||||||
\(363\) | 363.000 | 0.0524864 | ||||||||
\(364\) | 11.3383 | 0.00163266 | ||||||||
\(365\) | 39.1804 | 0.00561862 | ||||||||
\(366\) | −203.818 | −0.0291085 | ||||||||
\(367\) | 10749.8 | 1.52897 | 0.764487 | − | 0.644640i | \(-0.222993\pi\) | ||||
0.764487 | + | 0.644640i | \(0.222993\pi\) | |||||||
\(368\) | −1783.56 | −0.252648 | ||||||||
\(369\) | −429.789 | −0.0606339 | ||||||||
\(370\) | 3977.57 | 0.558875 | ||||||||
\(371\) | −703.285 | −0.0984170 | ||||||||
\(372\) | −5333.59 | −0.743371 | ||||||||
\(373\) | 4949.70 | 0.687093 | 0.343547 | − | 0.939136i | \(-0.388372\pi\) | ||||
0.343547 | + | 0.939136i | \(0.388372\pi\) | |||||||
\(374\) | −279.085 | −0.0385860 | ||||||||
\(375\) | 2379.43 | 0.327663 | ||||||||
\(376\) | 7616.35 | 1.04464 | ||||||||
\(377\) | −74.5822 | −0.0101888 | ||||||||
\(378\) | 103.103 | 0.0140293 | ||||||||
\(379\) | 1603.57 | 0.217335 | 0.108667 | − | 0.994078i | \(-0.465342\pi\) | ||||
0.108667 | + | 0.994078i | \(0.465342\pi\) | |||||||
\(380\) | −10396.8 | −1.40354 | ||||||||
\(381\) | −4278.71 | −0.575341 | ||||||||
\(382\) | 4643.23 | 0.621907 | ||||||||
\(383\) | −3241.02 | −0.432398 | −0.216199 | − | 0.976349i | \(-0.569366\pi\) | ||||
−0.216199 | + | 0.976349i | \(0.569366\pi\) | |||||||
\(384\) | 4430.72 | 0.588814 | ||||||||
\(385\) | 523.804 | 0.0693390 | ||||||||
\(386\) | −892.568 | −0.117696 | ||||||||
\(387\) | −455.411 | −0.0598187 | ||||||||
\(388\) | −7753.77 | −1.01453 | ||||||||
\(389\) | −1400.30 | −0.182514 | −0.0912570 | − | 0.995827i | \(-0.529088\pi\) | ||||
−0.0912570 | + | 0.995827i | \(0.529088\pi\) | |||||||
\(390\) | 22.7029 | 0.00294771 | ||||||||
\(391\) | −1135.92 | −0.146921 | ||||||||
\(392\) | −5445.18 | −0.701590 | ||||||||
\(393\) | −5382.64 | −0.690886 | ||||||||
\(394\) | 624.929 | 0.0799072 | ||||||||
\(395\) | 16430.2 | 2.09290 | ||||||||
\(396\) | −669.195 | −0.0849200 | ||||||||
\(397\) | 7029.71 | 0.888693 | 0.444346 | − | 0.895855i | \(-0.353436\pi\) | ||||
0.444346 | + | 0.895855i | \(0.353436\pi\) | |||||||
\(398\) | 5505.98 | 0.693441 | ||||||||
\(399\) | 1139.11 | 0.142925 | ||||||||
\(400\) | 2428.36 | 0.303545 | ||||||||
\(401\) | −8738.60 | −1.08824 | −0.544121 | − | 0.839007i | \(-0.683137\pi\) | ||||
−0.544121 | + | 0.839007i | \(0.683137\pi\) | |||||||
\(402\) | −2653.69 | −0.329239 | ||||||||
\(403\) | 128.675 | 0.0159051 | ||||||||
\(404\) | 4417.25 | 0.543977 | ||||||||
\(405\) | −1124.97 | −0.138026 | ||||||||
\(406\) | −582.146 | −0.0711611 | ||||||||
\(407\) | 2828.54 | 0.344485 | ||||||||
\(408\) | 1123.41 | 0.136316 | ||||||||
\(409\) | 9983.94 | 1.20703 | 0.603513 | − | 0.797353i | \(-0.293767\pi\) | ||||
0.603513 | + | 0.797353i | \(0.293767\pi\) | |||||||
\(410\) | −738.687 | −0.0889784 | ||||||||
\(411\) | −2653.51 | −0.318463 | ||||||||
\(412\) | −7611.11 | −0.910127 | ||||||||
\(413\) | −1995.57 | −0.237761 | ||||||||
\(414\) | 499.836 | 0.0593372 | ||||||||
\(415\) | −20930.2 | −2.47572 | ||||||||
\(416\) | −83.8271 | −0.00987971 | ||||||||
\(417\) | 1127.99 | 0.132465 | ||||||||
\(418\) | 1356.78 | 0.158762 | ||||||||
\(419\) | −3759.10 | −0.438291 | −0.219146 | − | 0.975692i | \(-0.570327\pi\) | ||||
−0.219146 | + | 0.975692i | \(0.570327\pi\) | |||||||
\(420\) | −965.639 | −0.112187 | ||||||||
\(421\) | 6359.47 | 0.736204 | 0.368102 | − | 0.929785i | \(-0.380008\pi\) | ||||
0.368102 | + | 0.929785i | \(0.380008\pi\) | |||||||
\(422\) | 2518.66 | 0.290536 | ||||||||
\(423\) | 4169.90 | 0.479308 | ||||||||
\(424\) | 3371.91 | 0.386213 | ||||||||
\(425\) | 1546.58 | 0.176519 | ||||||||
\(426\) | −549.035 | −0.0624432 | ||||||||
\(427\) | −209.146 | −0.0237032 | ||||||||
\(428\) | −1848.94 | −0.208812 | ||||||||
\(429\) | 16.1446 | 0.00181694 | ||||||||
\(430\) | −782.724 | −0.0877821 | ||||||||
\(431\) | −7539.85 | −0.842649 | −0.421325 | − | 0.906910i | \(-0.638435\pi\) | ||||
−0.421325 | + | 0.906910i | \(0.638435\pi\) | |||||||
\(432\) | 965.731 | 0.107555 | ||||||||
\(433\) | 986.955 | 0.109538 | 0.0547691 | − | 0.998499i | \(-0.482558\pi\) | ||||
0.0547691 | + | 0.998499i | \(0.482558\pi\) | |||||||
\(434\) | 1004.36 | 0.111085 | ||||||||
\(435\) | 6351.86 | 0.700112 | ||||||||
\(436\) | 6493.10 | 0.713219 | ||||||||
\(437\) | 5522.32 | 0.604504 | ||||||||
\(438\) | 9.42592 | 0.00102828 | ||||||||
\(439\) | −5759.02 | −0.626112 | −0.313056 | − | 0.949735i | \(-0.601353\pi\) | ||||
−0.313056 | + | 0.949735i | \(0.601353\pi\) | |||||||
\(440\) | −2511.39 | −0.272104 | ||||||||
\(441\) | −2981.20 | −0.321909 | ||||||||
\(442\) | −12.4124 | −0.00133574 | ||||||||
\(443\) | −11330.2 | −1.21516 | −0.607579 | − | 0.794259i | \(-0.707859\pi\) | ||||
−0.607579 | + | 0.794259i | \(0.707859\pi\) | |||||||
\(444\) | −5214.45 | −0.557358 | ||||||||
\(445\) | 2120.36 | 0.225875 | ||||||||
\(446\) | −132.939 | −0.0141140 | ||||||||
\(447\) | −6243.12 | −0.660603 | ||||||||
\(448\) | 326.766 | 0.0344604 | ||||||||
\(449\) | −7997.54 | −0.840595 | −0.420297 | − | 0.907386i | \(-0.638074\pi\) | ||||
−0.420297 | + | 0.907386i | \(0.638074\pi\) | |||||||
\(450\) | −680.539 | −0.0712910 | ||||||||
\(451\) | −525.297 | −0.0548454 | ||||||||
\(452\) | 12626.0 | 1.31388 | ||||||||
\(453\) | −893.362 | −0.0926574 | ||||||||
\(454\) | 1659.64 | 0.171566 | ||||||||
\(455\) | 23.2964 | 0.00240033 | ||||||||
\(456\) | −5461.49 | −0.560872 | ||||||||
\(457\) | −5553.97 | −0.568499 | −0.284249 | − | 0.958750i | \(-0.591744\pi\) | ||||
−0.284249 | + | 0.958750i | \(0.591744\pi\) | |||||||
\(458\) | −914.612 | −0.0933122 | ||||||||
\(459\) | 615.060 | 0.0625458 | ||||||||
\(460\) | −4681.33 | −0.474496 | ||||||||
\(461\) | −11687.1 | −1.18074 | −0.590369 | − | 0.807133i | \(-0.701018\pi\) | ||||
−0.590369 | + | 0.807133i | \(0.701018\pi\) | |||||||
\(462\) | 126.015 | 0.0126900 | ||||||||
\(463\) | −2021.79 | −0.202939 | −0.101469 | − | 0.994839i | \(-0.532354\pi\) | ||||
−0.101469 | + | 0.994839i | \(0.532354\pi\) | |||||||
\(464\) | −5452.74 | −0.545554 | ||||||||
\(465\) | −10958.7 | −1.09290 | ||||||||
\(466\) | 5546.35 | 0.551351 | ||||||||
\(467\) | −5216.13 | −0.516860 | −0.258430 | − | 0.966030i | \(-0.583205\pi\) | ||||
−0.258430 | + | 0.966030i | \(0.583205\pi\) | |||||||
\(468\) | −29.7627 | −0.00293971 | ||||||||
\(469\) | −2723.06 | −0.268101 | ||||||||
\(470\) | 7166.90 | 0.703371 | ||||||||
\(471\) | 7818.57 | 0.764884 | ||||||||
\(472\) | 9567.78 | 0.933036 | ||||||||
\(473\) | −556.613 | −0.0541080 | ||||||||
\(474\) | 3952.74 | 0.383028 | ||||||||
\(475\) | −7518.77 | −0.726284 | ||||||||
\(476\) | 527.946 | 0.0508369 | ||||||||
\(477\) | 1846.10 | 0.177206 | ||||||||
\(478\) | −3054.32 | −0.292262 | ||||||||
\(479\) | 12182.3 | 1.16205 | 0.581027 | − | 0.813884i | \(-0.302651\pi\) | ||||
0.581027 | + | 0.813884i | \(0.302651\pi\) | |||||||
\(480\) | 7139.21 | 0.678873 | ||||||||
\(481\) | 125.800 | 0.0119252 | ||||||||
\(482\) | 1305.68 | 0.123386 | ||||||||
\(483\) | 512.902 | 0.0483186 | ||||||||
\(484\) | −817.905 | −0.0768130 | ||||||||
\(485\) | −15931.4 | −1.49156 | ||||||||
\(486\) | −270.643 | −0.0252605 | ||||||||
\(487\) | 10645.4 | 0.990533 | 0.495267 | − | 0.868741i | \(-0.335070\pi\) | ||||
0.495267 | + | 0.868741i | \(0.335070\pi\) | |||||||
\(488\) | 1002.75 | 0.0930173 | ||||||||
\(489\) | −4472.11 | −0.413570 | ||||||||
\(490\) | −5123.85 | −0.472392 | ||||||||
\(491\) | −5022.23 | −0.461609 | −0.230805 | − | 0.973000i | \(-0.574136\pi\) | ||||
−0.230805 | + | 0.973000i | \(0.574136\pi\) | |||||||
\(492\) | 968.392 | 0.0887367 | ||||||||
\(493\) | −3472.77 | −0.317253 | ||||||||
\(494\) | 60.3434 | 0.00549591 | ||||||||
\(495\) | −1374.97 | −0.124849 | ||||||||
\(496\) | 9407.49 | 0.851630 | ||||||||
\(497\) | −563.387 | −0.0508478 | ||||||||
\(498\) | −5035.33 | −0.453089 | ||||||||
\(499\) | −11480.2 | −1.02991 | −0.514955 | − | 0.857217i | \(-0.672192\pi\) | ||||
−0.514955 | + | 0.857217i | \(0.672192\pi\) | |||||||
\(500\) | −5361.30 | −0.479529 | ||||||||
\(501\) | −6150.13 | −0.548438 | ||||||||
\(502\) | 2128.39 | 0.189232 | ||||||||
\(503\) | −16697.3 | −1.48011 | −0.740057 | − | 0.672545i | \(-0.765201\pi\) | ||||
−0.740057 | + | 0.672545i | \(0.765201\pi\) | |||||||
\(504\) | −507.253 | −0.0448311 | ||||||||
\(505\) | 9075.96 | 0.799752 | ||||||||
\(506\) | 610.911 | 0.0536726 | ||||||||
\(507\) | −6590.28 | −0.577287 | ||||||||
\(508\) | 9640.70 | 0.842002 | ||||||||
\(509\) | −21307.9 | −1.85551 | −0.927756 | − | 0.373188i | \(-0.878265\pi\) | ||||
−0.927756 | + | 0.373188i | \(0.878265\pi\) | |||||||
\(510\) | 1057.12 | 0.0917841 | ||||||||
\(511\) | 9.67232 | 0.000837335 0 | ||||||||
\(512\) | −10832.4 | −0.935018 | ||||||||
\(513\) | −2990.13 | −0.257344 | ||||||||
\(514\) | 1485.04 | 0.127436 | ||||||||
\(515\) | −15638.2 | −1.33806 | ||||||||
\(516\) | 1026.12 | 0.0875437 | ||||||||
\(517\) | 5096.54 | 0.433551 | ||||||||
\(518\) | 981.926 | 0.0832883 | ||||||||
\(519\) | −11147.4 | −0.942803 | ||||||||
\(520\) | −111.695 | −0.00941952 | ||||||||
\(521\) | −16365.1 | −1.37614 | −0.688071 | − | 0.725644i | \(-0.741542\pi\) | ||||
−0.688071 | + | 0.725644i | \(0.741542\pi\) | |||||||
\(522\) | 1528.11 | 0.128130 | ||||||||
\(523\) | 2312.73 | 0.193363 | 0.0966813 | − | 0.995315i | \(-0.469177\pi\) | ||||
0.0966813 | + | 0.995315i | \(0.469177\pi\) | |||||||
\(524\) | 12128.1 | 1.01110 | ||||||||
\(525\) | −698.329 | −0.0580525 | ||||||||
\(526\) | −2777.92 | −0.230272 | ||||||||
\(527\) | 5991.49 | 0.495243 | ||||||||
\(528\) | 1180.34 | 0.0972871 | ||||||||
\(529\) | −9680.49 | −0.795635 | ||||||||
\(530\) | 3172.93 | 0.260044 | ||||||||
\(531\) | 5238.30 | 0.428103 | ||||||||
\(532\) | −2566.63 | −0.209168 | ||||||||
\(533\) | −23.3628 | −0.00189860 | ||||||||
\(534\) | 510.109 | 0.0413382 | ||||||||
\(535\) | −3798.94 | −0.306995 | ||||||||
\(536\) | 13055.8 | 1.05210 | ||||||||
\(537\) | −455.294 | −0.0365873 | ||||||||
\(538\) | −110.803 | −0.00887929 | ||||||||
\(539\) | −3643.69 | −0.291178 | ||||||||
\(540\) | 2534.77 | 0.201998 | ||||||||
\(541\) | −13996.7 | −1.11232 | −0.556160 | − | 0.831075i | \(-0.687726\pi\) | ||||
−0.556160 | + | 0.831075i | \(0.687726\pi\) | |||||||
\(542\) | −17.9709 | −0.00142420 | ||||||||
\(543\) | 3206.40 | 0.253407 | ||||||||
\(544\) | −3903.24 | −0.307629 | ||||||||
\(545\) | 13341.1 | 1.04857 | ||||||||
\(546\) | 5.60458 | 0.000439293 0 | ||||||||
\(547\) | −14956.8 | −1.16912 | −0.584558 | − | 0.811352i | \(-0.698732\pi\) | ||||
−0.584558 | + | 0.811352i | \(0.698732\pi\) | |||||||
\(548\) | 5978.85 | 0.466065 | ||||||||
\(549\) | 549.000 | 0.0426790 | ||||||||
\(550\) | −831.770 | −0.0644851 | ||||||||
\(551\) | 16883.0 | 1.30533 | ||||||||
\(552\) | −2459.12 | −0.189614 | ||||||||
\(553\) | 4056.06 | 0.311901 | ||||||||
\(554\) | 6444.39 | 0.494216 | ||||||||
\(555\) | −10713.9 | −0.819424 | ||||||||
\(556\) | −2541.57 | −0.193860 | ||||||||
\(557\) | −8051.60 | −0.612491 | −0.306245 | − | 0.951953i | \(-0.599073\pi\) | ||||
−0.306245 | + | 0.951953i | \(0.599073\pi\) | |||||||
\(558\) | −2636.42 | −0.200015 | ||||||||
\(559\) | −24.7556 | −0.00187308 | ||||||||
\(560\) | 1703.21 | 0.128525 | ||||||||
\(561\) | 751.739 | 0.0565748 | ||||||||
\(562\) | −1225.14 | −0.0919562 | ||||||||
\(563\) | −9291.89 | −0.695571 | −0.347786 | − | 0.937574i | \(-0.613066\pi\) | ||||
−0.347786 | + | 0.937574i | \(0.613066\pi\) | |||||||
\(564\) | −9395.54 | −0.701460 | ||||||||
\(565\) | 25942.1 | 1.93167 | ||||||||
\(566\) | −5387.25 | −0.400076 | ||||||||
\(567\) | −277.718 | −0.0205698 | ||||||||
\(568\) | 2701.17 | 0.199540 | ||||||||
\(569\) | 6825.11 | 0.502853 | 0.251426 | − | 0.967876i | \(-0.419100\pi\) | ||||
0.251426 | + | 0.967876i | \(0.419100\pi\) | |||||||
\(570\) | −5139.20 | −0.377645 | ||||||||
\(571\) | 26015.7 | 1.90669 | 0.953347 | − | 0.301876i | \(-0.0976129\pi\) | ||||
0.953347 | + | 0.301876i | \(0.0976129\pi\) | |||||||
\(572\) | −36.3767 | −0.00265906 | ||||||||
\(573\) | −12506.9 | −0.911841 | ||||||||
\(574\) | −182.357 | −0.0132603 | ||||||||
\(575\) | −3385.44 | −0.245535 | ||||||||
\(576\) | −857.751 | −0.0620479 | ||||||||
\(577\) | 16764.2 | 1.20953 | 0.604767 | − | 0.796402i | \(-0.293266\pi\) | ||||
0.604767 | + | 0.796402i | \(0.293266\pi\) | |||||||
\(578\) | 4893.93 | 0.352181 | ||||||||
\(579\) | 2404.21 | 0.172566 | ||||||||
\(580\) | −14311.9 | −1.02460 | ||||||||
\(581\) | −5166.96 | −0.368953 | ||||||||
\(582\) | −3832.72 | −0.272975 | ||||||||
\(583\) | 2256.34 | 0.160288 | ||||||||
\(584\) | −46.3741 | −0.00328591 | ||||||||
\(585\) | −61.1523 | −0.00432194 | ||||||||
\(586\) | −6039.37 | −0.425741 | ||||||||
\(587\) | 925.271 | 0.0650597 | 0.0325298 | − | 0.999471i | \(-0.489644\pi\) | ||||
0.0325298 | + | 0.999471i | \(0.489644\pi\) | |||||||
\(588\) | 6717.19 | 0.471109 | ||||||||
\(589\) | −29127.8 | −2.03768 | ||||||||
\(590\) | 9003.18 | 0.628229 | ||||||||
\(591\) | −1683.30 | −0.117160 | ||||||||
\(592\) | 9197.33 | 0.638527 | ||||||||
\(593\) | 21641.2 | 1.49865 | 0.749323 | − | 0.662204i | \(-0.230379\pi\) | ||||
0.749323 | + | 0.662204i | \(0.230379\pi\) | |||||||
\(594\) | −330.786 | −0.0228490 | ||||||||
\(595\) | 1084.75 | 0.0747402 | ||||||||
\(596\) | 14066.9 | 0.966782 | ||||||||
\(597\) | −14830.8 | −1.01673 | ||||||||
\(598\) | 27.1705 | 0.00185800 | ||||||||
\(599\) | −10575.2 | −0.721352 | −0.360676 | − | 0.932691i | \(-0.617454\pi\) | ||||
−0.360676 | + | 0.932691i | \(0.617454\pi\) | |||||||
\(600\) | 3348.15 | 0.227813 | ||||||||
\(601\) | −15680.6 | −1.06427 | −0.532134 | − | 0.846660i | \(-0.678610\pi\) | ||||
−0.532134 | + | 0.846660i | \(0.678610\pi\) | |||||||
\(602\) | −193.228 | −0.0130820 | ||||||||
\(603\) | 7147.95 | 0.482731 | ||||||||
\(604\) | 2012.91 | 0.135603 | ||||||||
\(605\) | −1680.52 | −0.112930 | ||||||||
\(606\) | 2183.47 | 0.146365 | ||||||||
\(607\) | 8864.90 | 0.592776 | 0.296388 | − | 0.955068i | \(-0.404218\pi\) | ||||
0.296388 | + | 0.955068i | \(0.404218\pi\) | |||||||
\(608\) | 18975.7 | 1.26573 | ||||||||
\(609\) | 1568.06 | 0.104337 | ||||||||
\(610\) | 943.578 | 0.0626301 | ||||||||
\(611\) | 226.671 | 0.0150084 | ||||||||
\(612\) | −1385.84 | −0.0915348 | ||||||||
\(613\) | −15664.1 | −1.03209 | −0.516043 | − | 0.856563i | \(-0.672595\pi\) | ||||
−0.516043 | + | 0.856563i | \(0.672595\pi\) | |||||||
\(614\) | −7147.35 | −0.469778 | ||||||||
\(615\) | 1989.72 | 0.130460 | ||||||||
\(616\) | −619.976 | −0.0405512 | ||||||||
\(617\) | −418.541 | −0.0273093 | −0.0136546 | − | 0.999907i | \(-0.504347\pi\) | ||||
−0.0136546 | + | 0.999907i | \(0.504347\pi\) | |||||||
\(618\) | −3762.20 | −0.244883 | ||||||||
\(619\) | 16521.1 | 1.07276 | 0.536381 | − | 0.843976i | \(-0.319791\pi\) | ||||
0.536381 | + | 0.843976i | \(0.319791\pi\) | |||||||
\(620\) | 24692.0 | 1.59944 | ||||||||
\(621\) | −1346.35 | −0.0870004 | ||||||||
\(622\) | −6696.15 | −0.431658 | ||||||||
\(623\) | 523.444 | 0.0336618 | ||||||||
\(624\) | 52.4960 | 0.00336782 | ||||||||
\(625\) | −19502.2 | −1.24814 | ||||||||
\(626\) | 5069.53 | 0.323673 | ||||||||
\(627\) | −3654.61 | −0.232777 | ||||||||
\(628\) | −17616.6 | −1.11940 | ||||||||
\(629\) | 5857.64 | 0.371319 | ||||||||
\(630\) | −477.319 | −0.0301855 | ||||||||
\(631\) | 14714.5 | 0.928329 | 0.464164 | − | 0.885749i | \(-0.346355\pi\) | ||||
0.464164 | + | 0.885749i | \(0.346355\pi\) | |||||||
\(632\) | −19446.9 | −1.22398 | ||||||||
\(633\) | −6784.22 | −0.425985 | ||||||||
\(634\) | −3639.87 | −0.228009 | ||||||||
\(635\) | 19808.4 | 1.23791 | ||||||||
\(636\) | −4159.60 | −0.259338 | ||||||||
\(637\) | −162.055 | −0.0100798 | ||||||||
\(638\) | 1867.69 | 0.115898 | ||||||||
\(639\) | 1478.87 | 0.0915544 | ||||||||
\(640\) | −20512.1 | −1.26690 | ||||||||
\(641\) | 2027.44 | 0.124928 | 0.0624642 | − | 0.998047i | \(-0.480104\pi\) | ||||
0.0624642 | + | 0.998047i | \(0.480104\pi\) | |||||||
\(642\) | −913.937 | −0.0561842 | ||||||||
\(643\) | 12686.6 | 0.778086 | 0.389043 | − | 0.921220i | \(-0.372806\pi\) | ||||
0.389043 | + | 0.921220i | \(0.372806\pi\) | |||||||
\(644\) | −1155.66 | −0.0707135 | ||||||||
\(645\) | 2108.33 | 0.128706 | ||||||||
\(646\) | 2809.77 | 0.171128 | ||||||||
\(647\) | −29492.8 | −1.79209 | −0.896044 | − | 0.443966i | \(-0.853571\pi\) | ||||
−0.896044 | + | 0.443966i | \(0.853571\pi\) | |||||||
\(648\) | 1331.52 | 0.0807209 | ||||||||
\(649\) | 6402.37 | 0.387234 | ||||||||
\(650\) | −36.9933 | −0.00223230 | ||||||||
\(651\) | −2705.34 | −0.162873 | ||||||||
\(652\) | 10076.5 | 0.605253 | ||||||||
\(653\) | −28852.0 | −1.72905 | −0.864524 | − | 0.502592i | \(-0.832380\pi\) | ||||
−0.864524 | + | 0.502592i | \(0.832380\pi\) | |||||||
\(654\) | 3209.57 | 0.191902 | ||||||||
\(655\) | 24919.0 | 1.48651 | ||||||||
\(656\) | −1708.07 | −0.101660 | ||||||||
\(657\) | −25.3895 | −0.00150767 | ||||||||
\(658\) | 1769.26 | 0.104822 | ||||||||
\(659\) | −27394.0 | −1.61930 | −0.809649 | − | 0.586915i | \(-0.800342\pi\) | ||||
−0.809649 | + | 0.586915i | \(0.800342\pi\) | |||||||
\(660\) | 3098.05 | 0.182714 | ||||||||
\(661\) | −9956.80 | −0.585892 | −0.292946 | − | 0.956129i | \(-0.594636\pi\) | ||||
−0.292946 | + | 0.956129i | \(0.594636\pi\) | |||||||
\(662\) | −1264.04 | −0.0742122 | ||||||||
\(663\) | 33.4339 | 0.00195847 | ||||||||
\(664\) | 24773.1 | 1.44786 | ||||||||
\(665\) | −5273.55 | −0.307518 | ||||||||
\(666\) | −2577.52 | −0.149965 | ||||||||
\(667\) | 7601.82 | 0.441295 | ||||||||
\(668\) | 13857.4 | 0.802631 | ||||||||
\(669\) | 358.082 | 0.0206939 | ||||||||
\(670\) | 12285.3 | 0.708393 | ||||||||
\(671\) | 671.000 | 0.0386046 | ||||||||
\(672\) | 1762.43 | 0.101171 | ||||||||
\(673\) | −3762.58 | −0.215508 | −0.107754 | − | 0.994178i | \(-0.534366\pi\) | ||||
−0.107754 | + | 0.994178i | \(0.534366\pi\) | |||||||
\(674\) | −6539.96 | −0.373754 | ||||||||
\(675\) | 1833.09 | 0.104527 | ||||||||
\(676\) | 14849.1 | 0.844851 | ||||||||
\(677\) | 4823.83 | 0.273848 | 0.136924 | − | 0.990582i | \(-0.456278\pi\) | ||||
0.136924 | + | 0.990582i | \(0.456278\pi\) | |||||||
\(678\) | 6241.07 | 0.353520 | ||||||||
\(679\) | −3932.91 | −0.222285 | ||||||||
\(680\) | −5200.85 | −0.293299 | ||||||||
\(681\) | −4470.38 | −0.251550 | ||||||||
\(682\) | −3222.29 | −0.180921 | ||||||||
\(683\) | 25032.8 | 1.40242 | 0.701210 | − | 0.712955i | \(-0.252644\pi\) | ||||
0.701210 | + | 0.712955i | \(0.252644\pi\) | |||||||
\(684\) | 6737.31 | 0.376619 | ||||||||
\(685\) | 12284.5 | 0.685207 | ||||||||
\(686\) | −2574.70 | −0.143298 | ||||||||
\(687\) | 2463.58 | 0.136815 | ||||||||
\(688\) | −1809.89 | −0.100293 | ||||||||
\(689\) | 100.352 | 0.00554876 | ||||||||
\(690\) | −2314.00 | −0.127670 | ||||||||
\(691\) | −11744.4 | −0.646566 | −0.323283 | − | 0.946302i | \(-0.604787\pi\) | ||||
−0.323283 | + | 0.946302i | \(0.604787\pi\) | |||||||
\(692\) | 25117.0 | 1.37978 | ||||||||
\(693\) | −339.433 | −0.0186060 | ||||||||
\(694\) | 1210.50 | 0.0662102 | ||||||||
\(695\) | −5222.05 | −0.285013 | ||||||||
\(696\) | −7518.09 | −0.409443 | ||||||||
\(697\) | −1087.84 | −0.0591176 | ||||||||
\(698\) | 3619.60 | 0.196281 | ||||||||
\(699\) | −14939.6 | −0.808392 | ||||||||
\(700\) | 1573.46 | 0.0849590 | ||||||||
\(701\) | −5016.91 | −0.270308 | −0.135154 | − | 0.990825i | \(-0.543153\pi\) | ||||
−0.135154 | + | 0.990825i | \(0.543153\pi\) | |||||||
\(702\) | −14.7118 | −0.000790972 0 | ||||||||
\(703\) | −28477.1 | −1.52779 | ||||||||
\(704\) | −1048.36 | −0.0561245 | ||||||||
\(705\) | −19304.6 | −1.03128 | ||||||||
\(706\) | 1232.71 | 0.0657133 | ||||||||
\(707\) | 2240.55 | 0.119186 | ||||||||
\(708\) | −11802.8 | −0.626523 | ||||||||
\(709\) | −8781.09 | −0.465135 | −0.232567 | − | 0.972580i | \(-0.574713\pi\) | ||||
−0.232567 | + | 0.972580i | \(0.574713\pi\) | |||||||
\(710\) | 2541.77 | 0.134353 | ||||||||
\(711\) | −10647.0 | −0.561596 | ||||||||
\(712\) | −2509.66 | −0.132098 | ||||||||
\(713\) | −13115.2 | −0.688877 | ||||||||
\(714\) | 260.966 | 0.0136784 | ||||||||
\(715\) | −74.7417 | −0.00390934 | ||||||||
\(716\) | 1025.86 | 0.0535450 | ||||||||
\(717\) | 8227.07 | 0.428515 | ||||||||
\(718\) | 2455.11 | 0.127610 | ||||||||
\(719\) | 35971.2 | 1.86578 | 0.932891 | − | 0.360158i | \(-0.117277\pi\) | ||||
0.932891 | + | 0.360158i | \(0.117277\pi\) | |||||||
\(720\) | −4470.87 | −0.231416 | ||||||||
\(721\) | −3860.55 | −0.199410 | ||||||||
\(722\) | −6020.52 | −0.310333 | ||||||||
\(723\) | −3516.96 | −0.180909 | ||||||||
\(724\) | −7224.60 | −0.370857 | ||||||||
\(725\) | −10350.1 | −0.530195 | ||||||||
\(726\) | −404.294 | −0.0206677 | ||||||||
\(727\) | −7885.61 | −0.402285 | −0.201142 | − | 0.979562i | \(-0.564465\pi\) | ||||
−0.201142 | + | 0.979562i | \(0.564465\pi\) | |||||||
\(728\) | −27.5737 | −0.00140378 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | −43.6375 | −0.00221246 | ||||||||
\(731\) | −1152.69 | −0.0583227 | ||||||||
\(732\) | −1237.00 | −0.0624600 | ||||||||
\(733\) | −18910.6 | −0.952906 | −0.476453 | − | 0.879200i | \(-0.658078\pi\) | ||||
−0.476453 | + | 0.879200i | \(0.658078\pi\) | |||||||
\(734\) | −11972.6 | −0.602068 | ||||||||
\(735\) | 13801.5 | 0.692622 | ||||||||
\(736\) | 8544.10 | 0.427907 | ||||||||
\(737\) | 8736.38 | 0.436647 | ||||||||
\(738\) | 478.680 | 0.0238760 | ||||||||
\(739\) | 27942.6 | 1.39091 | 0.695456 | − | 0.718568i | \(-0.255202\pi\) | ||||
0.695456 | + | 0.718568i | \(0.255202\pi\) | |||||||
\(740\) | 24140.4 | 1.19921 | ||||||||
\(741\) | −162.540 | −0.00805811 | ||||||||
\(742\) | 783.288 | 0.0387539 | ||||||||
\(743\) | −18727.4 | −0.924685 | −0.462342 | − | 0.886702i | \(-0.652991\pi\) | ||||
−0.462342 | + | 0.886702i | \(0.652991\pi\) | |||||||
\(744\) | 12970.8 | 0.639156 | ||||||||
\(745\) | 28902.7 | 1.42136 | ||||||||
\(746\) | −5512.76 | −0.270558 | ||||||||
\(747\) | 13563.1 | 0.664320 | ||||||||
\(748\) | −1693.81 | −0.0827963 | ||||||||
\(749\) | −937.828 | −0.0457510 | ||||||||
\(750\) | −2650.11 | −0.129025 | ||||||||
\(751\) | 35045.9 | 1.70285 | 0.851426 | − | 0.524475i | \(-0.175738\pi\) | ||||
0.851426 | + | 0.524475i | \(0.175738\pi\) | |||||||
\(752\) | 16572.0 | 0.803616 | ||||||||
\(753\) | −5732.99 | −0.277453 | ||||||||
\(754\) | 83.0665 | 0.00401207 | ||||||||
\(755\) | 4135.84 | 0.199362 | ||||||||
\(756\) | 625.749 | 0.0301035 | ||||||||
\(757\) | 40352.7 | 1.93744 | 0.968722 | − | 0.248150i | \(-0.0798227\pi\) | ||||
0.968722 | + | 0.248150i | \(0.0798227\pi\) | |||||||
\(758\) | −1785.99 | −0.0855804 | ||||||||
\(759\) | −1645.54 | −0.0786948 | ||||||||
\(760\) | 25284.1 | 1.20678 | ||||||||
\(761\) | −18421.6 | −0.877508 | −0.438754 | − | 0.898607i | \(-0.644580\pi\) | ||||
−0.438754 | + | 0.898607i | \(0.644580\pi\) | |||||||
\(762\) | 4765.44 | 0.226553 | ||||||||
\(763\) | 3293.47 | 0.156267 | ||||||||
\(764\) | 28180.4 | 1.33446 | ||||||||
\(765\) | −2847.43 | −0.134574 | ||||||||
\(766\) | 3609.71 | 0.170266 | ||||||||
\(767\) | 284.748 | 0.0134050 | ||||||||
\(768\) | −2647.41 | −0.124388 | ||||||||
\(769\) | 30675.0 | 1.43845 | 0.719226 | − | 0.694776i | \(-0.244497\pi\) | ||||
0.719226 | + | 0.694776i | \(0.244497\pi\) | |||||||
\(770\) | −583.390 | −0.0273038 | ||||||||
\(771\) | −4000.08 | −0.186848 | ||||||||
\(772\) | −5417.12 | −0.252547 | ||||||||
\(773\) | −37656.4 | −1.75214 | −0.876071 | − | 0.482181i | \(-0.839845\pi\) | ||||
−0.876071 | + | 0.482181i | \(0.839845\pi\) | |||||||
\(774\) | 507.217 | 0.0235550 | ||||||||
\(775\) | 17856.7 | 0.827654 | ||||||||
\(776\) | 18856.4 | 0.872301 | ||||||||
\(777\) | −2644.90 | −0.122118 | ||||||||
\(778\) | 1559.59 | 0.0718690 | ||||||||
\(779\) | 5288.58 | 0.243239 | ||||||||
\(780\) | 137.787 | 0.00632509 | ||||||||
\(781\) | 1807.51 | 0.0828141 | ||||||||
\(782\) | 1265.14 | 0.0578534 | ||||||||
\(783\) | −4116.10 | −0.187864 | ||||||||
\(784\) | −11847.9 | −0.539718 | ||||||||
\(785\) | −36196.2 | −1.64573 | ||||||||
\(786\) | 5994.95 | 0.272052 | ||||||||
\(787\) | −15315.4 | −0.693689 | −0.346845 | − | 0.937923i | \(-0.612747\pi\) | ||||
−0.346845 | + | 0.937923i | \(0.612747\pi\) | |||||||
\(788\) | 3792.78 | 0.171462 | ||||||||
\(789\) | 7482.57 | 0.337625 | ||||||||
\(790\) | −18299.3 | −0.824125 | ||||||||
\(791\) | 6404.21 | 0.287873 | ||||||||
\(792\) | 1627.42 | 0.0730148 | ||||||||
\(793\) | 29.8430 | 0.00133639 | ||||||||
\(794\) | −7829.39 | −0.349943 | ||||||||
\(795\) | −8546.56 | −0.381277 | ||||||||
\(796\) | 33416.5 | 1.48796 | ||||||||
\(797\) | 13591.3 | 0.604050 | 0.302025 | − | 0.953300i | \(-0.402337\pi\) | ||||
0.302025 | + | 0.953300i | \(0.402337\pi\) | |||||||
\(798\) | −1268.69 | −0.0562798 | ||||||||
\(799\) | 10554.5 | 0.467322 | ||||||||
\(800\) | −11633.0 | −0.514111 | ||||||||
\(801\) | −1374.02 | −0.0606101 | ||||||||
\(802\) | 9732.68 | 0.428520 | ||||||||
\(803\) | −31.0316 | −0.00136374 | ||||||||
\(804\) | −16105.6 | −0.706470 | ||||||||
\(805\) | −2374.49 | −0.103963 | ||||||||
\(806\) | −143.313 | −0.00626299 | ||||||||
\(807\) | 298.457 | 0.0130188 | ||||||||
\(808\) | −10742.3 | −0.467715 | ||||||||
\(809\) | −15190.3 | −0.660153 | −0.330077 | − | 0.943954i | \(-0.607075\pi\) | ||||
−0.330077 | + | 0.943954i | \(0.607075\pi\) | |||||||
\(810\) | 1252.95 | 0.0543507 | ||||||||
\(811\) | −17169.9 | −0.743424 | −0.371712 | − | 0.928348i | \(-0.621229\pi\) | ||||
−0.371712 | + | 0.928348i | \(0.621229\pi\) | |||||||
\(812\) | −3533.12 | −0.152695 | ||||||||
\(813\) | 48.4061 | 0.00208816 | ||||||||
\(814\) | −3150.31 | −0.135649 | ||||||||
\(815\) | 20703.7 | 0.889840 | ||||||||
\(816\) | 2444.37 | 0.104865 | ||||||||
\(817\) | 5603.86 | 0.239968 | ||||||||
\(818\) | −11119.7 | −0.475294 | ||||||||
\(819\) | −15.0964 | −0.000644092 0 | ||||||||
\(820\) | −4483.19 | −0.190927 | ||||||||
\(821\) | −19114.6 | −0.812551 | −0.406276 | − | 0.913751i | \(-0.633173\pi\) | ||||
−0.406276 | + | 0.913751i | \(0.633173\pi\) | |||||||
\(822\) | 2955.37 | 0.125402 | ||||||||
\(823\) | 33203.8 | 1.40633 | 0.703166 | − | 0.711026i | \(-0.251769\pi\) | ||||
0.703166 | + | 0.711026i | \(0.251769\pi\) | |||||||
\(824\) | 18509.5 | 0.782534 | ||||||||
\(825\) | 2240.44 | 0.0945482 | ||||||||
\(826\) | 2222.58 | 0.0936240 | ||||||||
\(827\) | −38018.7 | −1.59860 | −0.799298 | − | 0.600934i | \(-0.794795\pi\) | ||||
−0.799298 | + | 0.600934i | \(0.794795\pi\) | |||||||
\(828\) | 3033.58 | 0.127324 | ||||||||
\(829\) | 12718.7 | 0.532855 | 0.266428 | − | 0.963855i | \(-0.414157\pi\) | ||||
0.266428 | + | 0.963855i | \(0.414157\pi\) | |||||||
\(830\) | 23311.2 | 0.974870 | ||||||||
\(831\) | −17358.5 | −0.724621 | ||||||||
\(832\) | −46.6263 | −0.00194288 | ||||||||
\(833\) | −7545.75 | −0.313859 | ||||||||
\(834\) | −1256.31 | −0.0521611 | ||||||||
\(835\) | 28472.2 | 1.18002 | ||||||||
\(836\) | 8234.49 | 0.340665 | ||||||||
\(837\) | 7101.42 | 0.293263 | ||||||||
\(838\) | 4186.72 | 0.172587 | ||||||||
\(839\) | −8352.31 | −0.343688 | −0.171844 | − | 0.985124i | \(-0.554972\pi\) | ||||
−0.171844 | + | 0.985124i | \(0.554972\pi\) | |||||||
\(840\) | 2348.34 | 0.0964588 | ||||||||
\(841\) | −1148.52 | −0.0470919 | ||||||||
\(842\) | −7082.91 | −0.289897 | ||||||||
\(843\) | 3300.02 | 0.134826 | ||||||||
\(844\) | 15286.1 | 0.623422 | ||||||||
\(845\) | 30509.9 | 1.24210 | ||||||||
\(846\) | −4644.26 | −0.188739 | ||||||||
\(847\) | −414.862 | −0.0168298 | ||||||||
\(848\) | 7336.77 | 0.297106 | ||||||||
\(849\) | 14511.0 | 0.586593 | ||||||||
\(850\) | −1722.52 | −0.0695082 | ||||||||
\(851\) | −12822.3 | −0.516500 | ||||||||
\(852\) | −3332.17 | −0.133988 | ||||||||
\(853\) | −13708.7 | −0.550266 | −0.275133 | − | 0.961406i | \(-0.588722\pi\) | ||||
−0.275133 | + | 0.961406i | \(0.588722\pi\) | |||||||
\(854\) | 232.937 | 0.00933367 | ||||||||
\(855\) | 13842.9 | 0.553704 | ||||||||
\(856\) | 4496.43 | 0.179538 | ||||||||
\(857\) | 20442.1 | 0.814806 | 0.407403 | − | 0.913249i | \(-0.366434\pi\) | ||||
0.407403 | + | 0.913249i | \(0.366434\pi\) | |||||||
\(858\) | −17.9811 | −0.000715461 0 | ||||||||
\(859\) | 325.152 | 0.0129151 | 0.00645753 | − | 0.999979i | \(-0.497944\pi\) | ||||
0.00645753 | + | 0.999979i | \(0.497944\pi\) | |||||||
\(860\) | −4750.46 | −0.188360 | ||||||||
\(861\) | 491.193 | 0.0194423 | ||||||||
\(862\) | 8397.56 | 0.331812 | ||||||||
\(863\) | 21814.7 | 0.860465 | 0.430232 | − | 0.902718i | \(-0.358432\pi\) | ||||
0.430232 | + | 0.902718i | \(0.358432\pi\) | |||||||
\(864\) | −4626.32 | −0.182165 | ||||||||
\(865\) | 51606.9 | 2.02854 | ||||||||
\(866\) | −1099.23 | −0.0431332 | ||||||||
\(867\) | −13182.2 | −0.516369 | ||||||||
\(868\) | 6095.61 | 0.238362 | ||||||||
\(869\) | −13013.0 | −0.507983 | ||||||||
\(870\) | −7074.43 | −0.275685 | ||||||||
\(871\) | 388.554 | 0.0151156 | ||||||||
\(872\) | −15790.6 | −0.613230 | ||||||||
\(873\) | 10323.8 | 0.400237 | ||||||||
\(874\) | −6150.52 | −0.238037 | ||||||||
\(875\) | −2719.39 | −0.105065 | ||||||||
\(876\) | 57.2072 | 0.00220645 | ||||||||
\(877\) | 35454.8 | 1.36514 | 0.682568 | − | 0.730822i | \(-0.260863\pi\) | ||||
0.682568 | + | 0.730822i | \(0.260863\pi\) | |||||||
\(878\) | 6414.15 | 0.246546 | ||||||||
\(879\) | 16267.6 | 0.624222 | ||||||||
\(880\) | −5464.40 | −0.209324 | ||||||||
\(881\) | 21157.5 | 0.809097 | 0.404549 | − | 0.914517i | \(-0.367429\pi\) | ||||
0.404549 | + | 0.914517i | \(0.367429\pi\) | |||||||
\(882\) | 3320.33 | 0.126759 | ||||||||
\(883\) | −18201.4 | −0.693689 | −0.346844 | − | 0.937923i | \(-0.612747\pi\) | ||||
−0.346844 | + | 0.937923i | \(0.612747\pi\) | |||||||
\(884\) | −75.3327 | −0.00286619 | ||||||||
\(885\) | −24250.8 | −0.921110 | ||||||||
\(886\) | 12619.1 | 0.478496 | ||||||||
\(887\) | 44392.8 | 1.68046 | 0.840229 | − | 0.542232i | \(-0.182421\pi\) | ||||
0.840229 | + | 0.542232i | \(0.182421\pi\) | |||||||
\(888\) | 12681.0 | 0.479220 | ||||||||
\(889\) | 4890.01 | 0.184483 | ||||||||
\(890\) | −2361.56 | −0.0889435 | ||||||||
\(891\) | 891.000 | 0.0335013 | ||||||||
\(892\) | −806.824 | −0.0302853 | ||||||||
\(893\) | −51310.9 | −1.92279 | ||||||||
\(894\) | 6953.32 | 0.260127 | ||||||||
\(895\) | 2107.79 | 0.0787216 | ||||||||
\(896\) | −5063.75 | −0.188804 | ||||||||
\(897\) | −73.1861 | −0.00272421 | ||||||||
\(898\) | 8907.31 | 0.331003 | ||||||||
\(899\) | −40096.3 | −1.48752 | ||||||||
\(900\) | −4130.29 | −0.152974 | ||||||||
\(901\) | 4672.68 | 0.172774 | ||||||||
\(902\) | 585.054 | 0.0215966 | ||||||||
\(903\) | 520.476 | 0.0191809 | ||||||||
\(904\) | −30705.1 | −1.12969 | ||||||||
\(905\) | −14844.1 | −0.545232 | ||||||||
\(906\) | 994.988 | 0.0364860 | ||||||||
\(907\) | −39412.3 | −1.44285 | −0.721425 | − | 0.692492i | \(-0.756513\pi\) | ||||
−0.721425 | + | 0.692492i | \(0.756513\pi\) | |||||||
\(908\) | 10072.6 | 0.368139 | ||||||||
\(909\) | −5881.36 | −0.214601 | ||||||||
\(910\) | −25.9465 | −0.000945186 0 | ||||||||
\(911\) | −11227.1 | −0.408309 | −0.204155 | − | 0.978939i | \(-0.565445\pi\) | ||||
−0.204155 | + | 0.978939i | \(0.565445\pi\) | |||||||
\(912\) | −11883.4 | −0.431467 | ||||||||
\(913\) | 16577.1 | 0.600900 | ||||||||
\(914\) | 6185.78 | 0.223859 | ||||||||
\(915\) | −2541.61 | −0.0918284 | ||||||||
\(916\) | −5550.90 | −0.200226 | ||||||||
\(917\) | 6151.66 | 0.221533 | ||||||||
\(918\) | −685.027 | −0.0246288 | ||||||||
\(919\) | −8366.39 | −0.300307 | −0.150153 | − | 0.988663i | \(-0.547977\pi\) | ||||
−0.150153 | + | 0.988663i | \(0.547977\pi\) | |||||||
\(920\) | 11384.5 | 0.407975 | ||||||||
\(921\) | 19252.0 | 0.688790 | ||||||||
\(922\) | 13016.5 | 0.464943 | ||||||||
\(923\) | 80.3897 | 0.00286680 | ||||||||
\(924\) | 764.804 | 0.0272297 | ||||||||
\(925\) | 17457.8 | 0.620551 | ||||||||
\(926\) | 2251.79 | 0.0799117 | ||||||||
\(927\) | 10133.8 | 0.359049 | ||||||||
\(928\) | 26121.3 | 0.924000 | ||||||||
\(929\) | 5243.41 | 0.185178 | 0.0925891 | − | 0.995704i | \(-0.470486\pi\) | ||||
0.0925891 | + | 0.995704i | \(0.470486\pi\) | |||||||
\(930\) | 12205.4 | 0.430354 | ||||||||
\(931\) | 36683.9 | 1.29137 | ||||||||
\(932\) | 33661.5 | 1.18307 | ||||||||
\(933\) | 18036.6 | 0.632898 | ||||||||
\(934\) | 5809.50 | 0.203525 | ||||||||
\(935\) | −3480.19 | −0.121727 | ||||||||
\(936\) | 72.3800 | 0.00252758 | ||||||||
\(937\) | 27264.9 | 0.950592 | 0.475296 | − | 0.879826i | \(-0.342341\pi\) | ||||
0.475296 | + | 0.879826i | \(0.342341\pi\) | |||||||
\(938\) | 3032.83 | 0.105571 | ||||||||
\(939\) | −13655.2 | −0.474570 | ||||||||
\(940\) | 43496.9 | 1.50927 | ||||||||
\(941\) | −1697.70 | −0.0588134 | −0.0294067 | − | 0.999568i | \(-0.509362\pi\) | ||||
−0.0294067 | + | 0.999568i | \(0.509362\pi\) | |||||||
\(942\) | −8707.98 | −0.301190 | ||||||||
\(943\) | 2381.26 | 0.0822318 | ||||||||
\(944\) | 20818.1 | 0.717765 | ||||||||
\(945\) | 1285.70 | 0.0442580 | ||||||||
\(946\) | 619.932 | 0.0213063 | ||||||||
\(947\) | 46288.1 | 1.58834 | 0.794172 | − | 0.607693i | \(-0.207905\pi\) | ||||
0.794172 | + | 0.607693i | \(0.207905\pi\) | |||||||
\(948\) | 23989.7 | 0.821887 | ||||||||
\(949\) | −1.38014 | −4.72090e−5 0 | ||||||||
\(950\) | 8374.09 | 0.285991 | ||||||||
\(951\) | 9804.30 | 0.334307 | ||||||||
\(952\) | −1283.91 | −0.0437099 | ||||||||
\(953\) | 17967.7 | 0.610737 | 0.305368 | − | 0.952234i | \(-0.401220\pi\) | ||||
0.305368 | + | 0.952234i | \(0.401220\pi\) | |||||||
\(954\) | −2056.11 | −0.0697787 | ||||||||
\(955\) | 57901.1 | 1.96192 | ||||||||
\(956\) | −18537.1 | −0.627126 | ||||||||
\(957\) | −5030.79 | −0.169929 | ||||||||
\(958\) | −13568.1 | −0.457585 | ||||||||
\(959\) | 3032.63 | 0.102115 | ||||||||
\(960\) | 3970.98 | 0.133503 | ||||||||
\(961\) | 39386.1 | 1.32208 | ||||||||
\(962\) | −140.111 | −0.00469581 | ||||||||
\(963\) | 2461.77 | 0.0823773 | ||||||||
\(964\) | 7924.35 | 0.264757 | ||||||||
\(965\) | −11130.3 | −0.371293 | ||||||||
\(966\) | −571.249 | −0.0190265 | ||||||||
\(967\) | 34702.6 | 1.15404 | 0.577022 | − | 0.816729i | \(-0.304215\pi\) | ||||
0.577022 | + | 0.816729i | \(0.304215\pi\) | |||||||
\(968\) | 1989.06 | 0.0660444 | ||||||||
\(969\) | −7568.35 | −0.250909 | ||||||||
\(970\) | 17743.7 | 0.587335 | ||||||||
\(971\) | 22424.8 | 0.741138 | 0.370569 | − | 0.928805i | \(-0.379163\pi\) | ||||
0.370569 | + | 0.928805i | \(0.379163\pi\) | |||||||
\(972\) | −1642.57 | −0.0542031 | ||||||||
\(973\) | −1289.15 | −0.0424750 | ||||||||
\(974\) | −11856.4 | −0.390045 | ||||||||
\(975\) | 99.6447 | 0.00327301 | ||||||||
\(976\) | 2181.84 | 0.0715562 | ||||||||
\(977\) | 21620.2 | 0.707974 | 0.353987 | − | 0.935250i | \(-0.384826\pi\) | ||||
0.353987 | + | 0.935250i | \(0.384826\pi\) | |||||||
\(978\) | 4980.84 | 0.162852 | ||||||||
\(979\) | −1679.36 | −0.0548239 | ||||||||
\(980\) | −31097.4 | −1.01364 | ||||||||
\(981\) | −8645.25 | −0.281368 | ||||||||
\(982\) | 5593.54 | 0.181769 | ||||||||
\(983\) | −37331.7 | −1.21129 | −0.605644 | − | 0.795736i | \(-0.707084\pi\) | ||||
−0.605644 | + | 0.795736i | \(0.707084\pi\) | |||||||
\(984\) | −2355.03 | −0.0762965 | ||||||||
\(985\) | 7792.87 | 0.252083 | ||||||||
\(986\) | 3867.82 | 0.124925 | ||||||||
\(987\) | −4765.66 | −0.153691 | ||||||||
\(988\) | 366.232 | 0.0117929 | ||||||||
\(989\) | 2523.22 | 0.0811262 | ||||||||
\(990\) | 1531.38 | 0.0491621 | ||||||||
\(991\) | −59665.6 | −1.91255 | −0.956276 | − | 0.292465i | \(-0.905524\pi\) | ||||
−0.956276 | + | 0.292465i | \(0.905524\pi\) | |||||||
\(992\) | −45066.4 | −1.44240 | ||||||||
\(993\) | 3404.81 | 0.108810 | ||||||||
\(994\) | 627.476 | 0.0200225 | ||||||||
\(995\) | 68659.6 | 2.18759 | ||||||||
\(996\) | −30560.1 | −0.972223 | ||||||||
\(997\) | −57929.4 | −1.84016 | −0.920081 | − | 0.391728i | \(-0.871877\pi\) | ||||
−0.920081 | + | 0.391728i | \(0.871877\pi\) | |||||||
\(998\) | 12786.2 | 0.405551 | ||||||||
\(999\) | 6942.78 | 0.219880 |
(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 | 2013.4.a.a.1.17 | ✓ | 36 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2013.4.a.a.1.17 | ✓ | 36 | 1.1 | even | 1 | trivial |