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 | 1.50 | ||
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 5.46223 | 1.93119 | 0.965595 | − | 0.260049i | \(-0.0837387\pi\) | ||||
0.965595 | + | 0.260049i | \(0.0837387\pi\) | |||||||
\(3\) | −9.09504 | −1.75034 | −0.875170 | − | 0.483815i | \(-0.839251\pi\) | ||||
−0.875170 | + | 0.483815i | \(0.839251\pi\) | |||||||
\(4\) | 21.8360 | 2.72950 | ||||||||
\(5\) | 6.15202 | 0.550254 | 0.275127 | − | 0.961408i | \(-0.411280\pi\) | ||||
0.275127 | + | 0.961408i | \(0.411280\pi\) | |||||||
\(6\) | −49.6792 | −3.38024 | ||||||||
\(7\) | −2.59059 | −0.139879 | −0.0699394 | − | 0.997551i | \(-0.522281\pi\) | ||||
−0.0699394 | + | 0.997551i | \(0.522281\pi\) | |||||||
\(8\) | 75.5754 | 3.33999 | ||||||||
\(9\) | 55.7197 | 2.06369 | ||||||||
\(10\) | 33.6038 | 1.06264 | ||||||||
\(11\) | −20.0476 | −0.549508 | −0.274754 | − | 0.961515i | \(-0.588596\pi\) | ||||
−0.274754 | + | 0.961515i | \(0.588596\pi\) | |||||||
\(12\) | −198.599 | −4.77755 | ||||||||
\(13\) | −34.1627 | −0.728848 | −0.364424 | − | 0.931233i | \(-0.618734\pi\) | ||||
−0.364424 | + | 0.931233i | \(0.618734\pi\) | |||||||
\(14\) | −14.1504 | −0.270132 | ||||||||
\(15\) | −55.9529 | −0.963131 | ||||||||
\(16\) | 238.122 | 3.72066 | ||||||||
\(17\) | 36.1588 | 0.515870 | 0.257935 | − | 0.966162i | \(-0.416958\pi\) | ||||
0.257935 | + | 0.966162i | \(0.416958\pi\) | |||||||
\(18\) | 304.354 | 3.98538 | ||||||||
\(19\) | −142.784 | −1.72405 | −0.862026 | − | 0.506864i | \(-0.830805\pi\) | ||||
−0.862026 | + | 0.506864i | \(0.830805\pi\) | |||||||
\(20\) | 134.335 | 1.50192 | ||||||||
\(21\) | 23.5615 | 0.244835 | ||||||||
\(22\) | −109.505 | −1.06121 | ||||||||
\(23\) | −132.818 | −1.20410 | −0.602052 | − | 0.798457i | \(-0.705650\pi\) | ||||
−0.602052 | + | 0.798457i | \(0.705650\pi\) | |||||||
\(24\) | −687.361 | −5.84612 | ||||||||
\(25\) | −87.1526 | −0.697221 | ||||||||
\(26\) | −186.604 | −1.40754 | ||||||||
\(27\) | −261.207 | −1.86182 | ||||||||
\(28\) | −56.5681 | −0.381799 | ||||||||
\(29\) | 49.6805 | 0.318118 | 0.159059 | − | 0.987269i | \(-0.449154\pi\) | ||||
0.159059 | + | 0.987269i | \(0.449154\pi\) | |||||||
\(30\) | −305.628 | −1.85999 | ||||||||
\(31\) | −51.3202 | −0.297335 | −0.148667 | − | 0.988887i | \(-0.547498\pi\) | ||||
−0.148667 | + | 0.988887i | \(0.547498\pi\) | |||||||
\(32\) | 696.077 | 3.84532 | ||||||||
\(33\) | 182.334 | 0.961826 | ||||||||
\(34\) | 197.508 | 0.996244 | ||||||||
\(35\) | −15.9374 | −0.0769688 | ||||||||
\(36\) | 1216.69 | 5.63284 | ||||||||
\(37\) | 49.1882 | 0.218554 | 0.109277 | − | 0.994011i | \(-0.465147\pi\) | ||||
0.109277 | + | 0.994011i | \(0.465147\pi\) | |||||||
\(38\) | −779.922 | −3.32947 | ||||||||
\(39\) | 310.711 | 1.27573 | ||||||||
\(40\) | 464.941 | 1.83784 | ||||||||
\(41\) | 71.4324 | 0.272094 | 0.136047 | − | 0.990702i | \(-0.456560\pi\) | ||||
0.136047 | + | 0.990702i | \(0.456560\pi\) | |||||||
\(42\) | 128.698 | 0.472824 | ||||||||
\(43\) | 0 | 0 | ||||||||
\(44\) | −437.760 | −1.49988 | ||||||||
\(45\) | 342.789 | 1.13555 | ||||||||
\(46\) | −725.481 | −2.32536 | ||||||||
\(47\) | −371.774 | −1.15380 | −0.576902 | − | 0.816813i | \(-0.695739\pi\) | ||||
−0.576902 | + | 0.816813i | \(0.695739\pi\) | |||||||
\(48\) | −2165.73 | −6.51243 | ||||||||
\(49\) | −336.289 | −0.980434 | ||||||||
\(50\) | −476.048 | −1.34647 | ||||||||
\(51\) | −328.865 | −0.902948 | ||||||||
\(52\) | −745.976 | −1.98939 | ||||||||
\(53\) | 260.514 | 0.675177 | 0.337588 | − | 0.941294i | \(-0.390389\pi\) | ||||
0.337588 | + | 0.941294i | \(0.390389\pi\) | |||||||
\(54\) | −1426.77 | −3.59554 | ||||||||
\(55\) | −123.333 | −0.302369 | ||||||||
\(56\) | −195.785 | −0.467194 | ||||||||
\(57\) | 1298.63 | 3.01768 | ||||||||
\(58\) | 271.366 | 0.614347 | ||||||||
\(59\) | 29.4340 | 0.0649489 | 0.0324745 | − | 0.999473i | \(-0.489661\pi\) | ||||
0.0324745 | + | 0.999473i | \(0.489661\pi\) | |||||||
\(60\) | −1221.79 | −2.62886 | ||||||||
\(61\) | 461.029 | 0.967683 | 0.483842 | − | 0.875156i | \(-0.339241\pi\) | ||||
0.483842 | + | 0.875156i | \(0.339241\pi\) | |||||||
\(62\) | −280.323 | −0.574210 | ||||||||
\(63\) | −144.347 | −0.288667 | ||||||||
\(64\) | 1897.16 | 3.70538 | ||||||||
\(65\) | −210.169 | −0.401051 | ||||||||
\(66\) | 995.951 | 1.85747 | ||||||||
\(67\) | 891.001 | 1.62467 | 0.812336 | − | 0.583189i | \(-0.198195\pi\) | ||||
0.812336 | + | 0.583189i | \(0.198195\pi\) | |||||||
\(68\) | 789.563 | 1.40807 | ||||||||
\(69\) | 1207.98 | 2.10759 | ||||||||
\(70\) | −87.0536 | −0.148641 | ||||||||
\(71\) | −475.538 | −0.794873 | −0.397436 | − | 0.917630i | \(-0.630100\pi\) | ||||
−0.397436 | + | 0.917630i | \(0.630100\pi\) | |||||||
\(72\) | 4211.04 | 6.89271 | ||||||||
\(73\) | −1027.68 | −1.64768 | −0.823838 | − | 0.566826i | \(-0.808171\pi\) | ||||
−0.823838 | + | 0.566826i | \(0.808171\pi\) | |||||||
\(74\) | 268.677 | 0.422069 | ||||||||
\(75\) | 792.656 | 1.22037 | ||||||||
\(76\) | −3117.84 | −4.70580 | ||||||||
\(77\) | 51.9352 | 0.0768645 | ||||||||
\(78\) | 1697.17 | 2.46368 | ||||||||
\(79\) | −307.975 | −0.438607 | −0.219303 | − | 0.975657i | \(-0.570378\pi\) | ||||
−0.219303 | + | 0.975657i | \(0.570378\pi\) | |||||||
\(80\) | 1464.93 | 2.04731 | ||||||||
\(81\) | 871.251 | 1.19513 | ||||||||
\(82\) | 390.181 | 0.525466 | ||||||||
\(83\) | −1145.51 | −1.51490 | −0.757448 | − | 0.652895i | \(-0.773554\pi\) | ||||
−0.757448 | + | 0.652895i | \(0.773554\pi\) | |||||||
\(84\) | 514.489 | 0.668278 | ||||||||
\(85\) | 222.450 | 0.283859 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −451.846 | −0.556815 | ||||||||
\(88\) | −1515.11 | −1.83535 | ||||||||
\(89\) | 670.531 | 0.798608 | 0.399304 | − | 0.916819i | \(-0.369252\pi\) | ||||
0.399304 | + | 0.916819i | \(0.369252\pi\) | |||||||
\(90\) | 1872.39 | 2.19297 | ||||||||
\(91\) | 88.5015 | 0.101950 | ||||||||
\(92\) | −2900.20 | −3.28660 | ||||||||
\(93\) | 466.759 | 0.520437 | ||||||||
\(94\) | −2030.72 | −2.22822 | ||||||||
\(95\) | −878.413 | −0.948666 | ||||||||
\(96\) | −6330.85 | −6.73062 | ||||||||
\(97\) | −125.357 | −0.131217 | −0.0656085 | − | 0.997845i | \(-0.520899\pi\) | ||||
−0.0656085 | + | 0.997845i | \(0.520899\pi\) | |||||||
\(98\) | −1836.89 | −1.89341 | ||||||||
\(99\) | −1117.05 | −1.13402 | ||||||||
\(100\) | −1903.06 | −1.90306 | ||||||||
\(101\) | −1452.64 | −1.43112 | −0.715558 | − | 0.698554i | \(-0.753827\pi\) | ||||
−0.715558 | + | 0.698554i | \(0.753827\pi\) | |||||||
\(102\) | −1796.34 | −1.74377 | ||||||||
\(103\) | 840.149 | 0.803712 | 0.401856 | − | 0.915703i | \(-0.368365\pi\) | ||||
0.401856 | + | 0.915703i | \(0.368365\pi\) | |||||||
\(104\) | −2581.86 | −2.43434 | ||||||||
\(105\) | 144.951 | 0.134722 | ||||||||
\(106\) | 1422.99 | 1.30390 | ||||||||
\(107\) | −932.647 | −0.842639 | −0.421320 | − | 0.906912i | \(-0.638433\pi\) | ||||
−0.421320 | + | 0.906912i | \(0.638433\pi\) | |||||||
\(108\) | −5703.70 | −5.08184 | ||||||||
\(109\) | −74.7800 | −0.0657122 | −0.0328561 | − | 0.999460i | \(-0.510460\pi\) | ||||
−0.0328561 | + | 0.999460i | \(0.510460\pi\) | |||||||
\(110\) | −673.676 | −0.583932 | ||||||||
\(111\) | −447.368 | −0.382543 | ||||||||
\(112\) | −616.878 | −0.520442 | ||||||||
\(113\) | 2118.16 | 1.76336 | 0.881680 | − | 0.471849i | \(-0.156413\pi\) | ||||
0.881680 | + | 0.471849i | \(0.156413\pi\) | |||||||
\(114\) | 7093.42 | 5.82771 | ||||||||
\(115\) | −817.097 | −0.662563 | ||||||||
\(116\) | 1084.82 | 0.868303 | ||||||||
\(117\) | −1903.53 | −1.50412 | ||||||||
\(118\) | 160.776 | 0.125429 | ||||||||
\(119\) | −93.6726 | −0.0721593 | ||||||||
\(120\) | −4228.66 | −3.21685 | ||||||||
\(121\) | −929.092 | −0.698041 | ||||||||
\(122\) | 2518.25 | 1.86878 | ||||||||
\(123\) | −649.680 | −0.476258 | ||||||||
\(124\) | −1120.63 | −0.811575 | ||||||||
\(125\) | −1305.17 | −0.933902 | ||||||||
\(126\) | −788.456 | −0.557470 | ||||||||
\(127\) | −2054.14 | −1.43524 | −0.717619 | − | 0.696436i | \(-0.754768\pi\) | ||||
−0.717619 | + | 0.696436i | \(0.754768\pi\) | |||||||
\(128\) | 4794.09 | 3.31048 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −1147.99 | −0.774506 | ||||||||
\(131\) | −913.318 | −0.609137 | −0.304569 | − | 0.952490i | \(-0.598512\pi\) | ||||
−0.304569 | + | 0.952490i | \(0.598512\pi\) | |||||||
\(132\) | 3981.44 | 2.62530 | ||||||||
\(133\) | 369.896 | 0.241158 | ||||||||
\(134\) | 4866.85 | 3.13755 | ||||||||
\(135\) | −1606.95 | −1.02447 | ||||||||
\(136\) | 2732.71 | 1.72300 | ||||||||
\(137\) | −585.919 | −0.365390 | −0.182695 | − | 0.983170i | \(-0.558482\pi\) | ||||
−0.182695 | + | 0.983170i | \(0.558482\pi\) | |||||||
\(138\) | 6598.28 | 4.07016 | ||||||||
\(139\) | −670.674 | −0.409250 | −0.204625 | − | 0.978840i | \(-0.565598\pi\) | ||||
−0.204625 | + | 0.978840i | \(0.565598\pi\) | |||||||
\(140\) | −348.008 | −0.210086 | ||||||||
\(141\) | 3381.30 | 2.01955 | ||||||||
\(142\) | −2597.50 | −1.53505 | ||||||||
\(143\) | 684.881 | 0.400508 | ||||||||
\(144\) | 13268.1 | 7.67830 | ||||||||
\(145\) | 305.635 | 0.175046 | ||||||||
\(146\) | −5613.40 | −3.18198 | ||||||||
\(147\) | 3058.56 | 1.71609 | ||||||||
\(148\) | 1074.07 | 0.596542 | ||||||||
\(149\) | 1919.37 | 1.05531 | 0.527653 | − | 0.849460i | \(-0.323072\pi\) | ||||
0.527653 | + | 0.849460i | \(0.323072\pi\) | |||||||
\(150\) | 4329.67 | 2.35678 | ||||||||
\(151\) | 2246.31 | 1.21061 | 0.605304 | − | 0.795994i | \(-0.293052\pi\) | ||||
0.605304 | + | 0.795994i | \(0.293052\pi\) | |||||||
\(152\) | −10791.0 | −5.75832 | ||||||||
\(153\) | 2014.76 | 1.06460 | ||||||||
\(154\) | 283.682 | 0.148440 | ||||||||
\(155\) | −315.723 | −0.163610 | ||||||||
\(156\) | 6784.67 | 3.48211 | ||||||||
\(157\) | −1805.52 | −0.917808 | −0.458904 | − | 0.888486i | \(-0.651758\pi\) | ||||
−0.458904 | + | 0.888486i | \(0.651758\pi\) | |||||||
\(158\) | −1682.23 | −0.847034 | ||||||||
\(159\) | −2369.39 | −1.18179 | ||||||||
\(160\) | 4282.28 | 2.11590 | ||||||||
\(161\) | 344.076 | 0.168429 | ||||||||
\(162\) | 4758.98 | 2.30803 | ||||||||
\(163\) | −3452.86 | −1.65920 | −0.829598 | − | 0.558361i | \(-0.811430\pi\) | ||||
−0.829598 | + | 0.558361i | \(0.811430\pi\) | |||||||
\(164\) | 1559.80 | 0.742681 | ||||||||
\(165\) | 1121.72 | 0.529248 | ||||||||
\(166\) | −6257.06 | −2.92555 | ||||||||
\(167\) | 2197.72 | 1.01835 | 0.509175 | − | 0.860663i | \(-0.329951\pi\) | ||||
0.509175 | + | 0.860663i | \(0.329951\pi\) | |||||||
\(168\) | 1780.67 | 0.817748 | ||||||||
\(169\) | −1029.91 | −0.468781 | ||||||||
\(170\) | 1215.07 | 0.548187 | ||||||||
\(171\) | −7955.90 | −3.55791 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −109.547 | −0.0481427 | −0.0240714 | − | 0.999710i | \(-0.507663\pi\) | ||||
−0.0240714 | + | 0.999710i | \(0.507663\pi\) | |||||||
\(174\) | −2468.09 | −1.07532 | ||||||||
\(175\) | 225.777 | 0.0975264 | ||||||||
\(176\) | −4773.79 | −2.04453 | ||||||||
\(177\) | −267.704 | −0.113683 | ||||||||
\(178\) | 3662.60 | 1.54227 | ||||||||
\(179\) | −2102.20 | −0.877799 | −0.438899 | − | 0.898536i | \(-0.644632\pi\) | ||||
−0.438899 | + | 0.898536i | \(0.644632\pi\) | |||||||
\(180\) | 7485.13 | 3.09949 | ||||||||
\(181\) | −2790.51 | −1.14595 | −0.572975 | − | 0.819573i | \(-0.694211\pi\) | ||||
−0.572975 | + | 0.819573i | \(0.694211\pi\) | |||||||
\(182\) | 483.416 | 0.196885 | ||||||||
\(183\) | −4193.07 | −1.69377 | ||||||||
\(184\) | −10037.7 | −4.02170 | ||||||||
\(185\) | 302.607 | 0.120260 | ||||||||
\(186\) | 2549.55 | 1.00506 | ||||||||
\(187\) | −724.898 | −0.283475 | ||||||||
\(188\) | −8118.05 | −3.14931 | ||||||||
\(189\) | 676.679 | 0.260429 | ||||||||
\(190\) | −4798.10 | −1.83206 | ||||||||
\(191\) | 3833.56 | 1.45229 | 0.726144 | − | 0.687543i | \(-0.241311\pi\) | ||||
0.726144 | + | 0.687543i | \(0.241311\pi\) | |||||||
\(192\) | −17254.7 | −6.48568 | ||||||||
\(193\) | 3873.73 | 1.44475 | 0.722375 | − | 0.691501i | \(-0.243050\pi\) | ||||
0.722375 | + | 0.691501i | \(0.243050\pi\) | |||||||
\(194\) | −684.728 | −0.253405 | ||||||||
\(195\) | 1911.50 | 0.701976 | ||||||||
\(196\) | −7343.20 | −2.67609 | ||||||||
\(197\) | −2456.45 | −0.888401 | −0.444201 | − | 0.895927i | \(-0.646512\pi\) | ||||
−0.444201 | + | 0.895927i | \(0.646512\pi\) | |||||||
\(198\) | −6101.58 | −2.19000 | ||||||||
\(199\) | −162.945 | −0.0580446 | −0.0290223 | − | 0.999579i | \(-0.509239\pi\) | ||||
−0.0290223 | + | 0.999579i | \(0.509239\pi\) | |||||||
\(200\) | −6586.59 | −2.32871 | ||||||||
\(201\) | −8103.68 | −2.84373 | ||||||||
\(202\) | −7934.64 | −2.76376 | ||||||||
\(203\) | −128.702 | −0.0444980 | ||||||||
\(204\) | −7181.10 | −2.46460 | ||||||||
\(205\) | 439.454 | 0.149721 | ||||||||
\(206\) | 4589.09 | 1.55212 | ||||||||
\(207\) | −7400.56 | −2.48490 | ||||||||
\(208\) | −8134.90 | −2.71180 | ||||||||
\(209\) | 2862.49 | 0.947381 | ||||||||
\(210\) | 791.756 | 0.260173 | ||||||||
\(211\) | 975.959 | 0.318426 | 0.159213 | − | 0.987244i | \(-0.449104\pi\) | ||||
0.159213 | + | 0.987244i | \(0.449104\pi\) | |||||||
\(212\) | 5688.58 | 1.84289 | ||||||||
\(213\) | 4325.03 | 1.39130 | ||||||||
\(214\) | −5094.34 | −1.62730 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −19740.8 | −6.21847 | ||||||||
\(217\) | 132.950 | 0.0415908 | ||||||||
\(218\) | −408.466 | −0.126903 | ||||||||
\(219\) | 9346.74 | 2.88399 | ||||||||
\(220\) | −2693.11 | −0.825315 | ||||||||
\(221\) | −1235.28 | −0.375991 | ||||||||
\(222\) | −2443.63 | −0.738764 | ||||||||
\(223\) | −5259.83 | −1.57948 | −0.789740 | − | 0.613441i | \(-0.789785\pi\) | ||||
−0.789740 | + | 0.613441i | \(0.789785\pi\) | |||||||
\(224\) | −1803.25 | −0.537878 | ||||||||
\(225\) | −4856.12 | −1.43885 | ||||||||
\(226\) | 11569.9 | 3.40538 | ||||||||
\(227\) | 2907.49 | 0.850119 | 0.425060 | − | 0.905165i | \(-0.360253\pi\) | ||||
0.425060 | + | 0.905165i | \(0.360253\pi\) | |||||||
\(228\) | 28356.9 | 8.23675 | ||||||||
\(229\) | 1315.09 | 0.379492 | 0.189746 | − | 0.981833i | \(-0.439234\pi\) | ||||
0.189746 | + | 0.981833i | \(0.439234\pi\) | |||||||
\(230\) | −4463.17 | −1.27953 | ||||||||
\(231\) | −472.353 | −0.134539 | ||||||||
\(232\) | 3754.62 | 1.06251 | ||||||||
\(233\) | 1070.36 | 0.300952 | 0.150476 | − | 0.988614i | \(-0.451919\pi\) | ||||
0.150476 | + | 0.988614i | \(0.451919\pi\) | |||||||
\(234\) | −10397.5 | −2.90474 | ||||||||
\(235\) | −2287.16 | −0.634885 | ||||||||
\(236\) | 642.721 | 0.177278 | ||||||||
\(237\) | 2801.05 | 0.767712 | ||||||||
\(238\) | −511.661 | −0.139353 | ||||||||
\(239\) | −3598.65 | −0.973964 | −0.486982 | − | 0.873412i | \(-0.661902\pi\) | ||||
−0.486982 | + | 0.873412i | \(0.661902\pi\) | |||||||
\(240\) | −13323.6 | −3.58349 | ||||||||
\(241\) | 4241.99 | 1.13382 | 0.566910 | − | 0.823780i | \(-0.308139\pi\) | ||||
0.566910 | + | 0.823780i | \(0.308139\pi\) | |||||||
\(242\) | −5074.92 | −1.34805 | ||||||||
\(243\) | −871.487 | −0.230065 | ||||||||
\(244\) | 10067.0 | 2.64129 | ||||||||
\(245\) | −2068.86 | −0.539487 | ||||||||
\(246\) | −3548.71 | −0.919745 | ||||||||
\(247\) | 4877.90 | 1.25657 | ||||||||
\(248\) | −3878.54 | −0.993096 | ||||||||
\(249\) | 10418.5 | 2.65158 | ||||||||
\(250\) | −7129.13 | −1.80354 | ||||||||
\(251\) | −2419.46 | −0.608425 | −0.304212 | − | 0.952604i | \(-0.598393\pi\) | ||||
−0.304212 | + | 0.952604i | \(0.598393\pi\) | |||||||
\(252\) | −3151.96 | −0.787915 | ||||||||
\(253\) | 2662.68 | 0.661665 | ||||||||
\(254\) | −11220.2 | −2.77172 | ||||||||
\(255\) | −2023.19 | −0.496851 | ||||||||
\(256\) | 11009.2 | 2.68779 | ||||||||
\(257\) | −2727.33 | −0.661969 | −0.330984 | − | 0.943636i | \(-0.607381\pi\) | ||||
−0.330984 | + | 0.943636i | \(0.607381\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −127.426 | −0.0305710 | ||||||||
\(260\) | −4589.26 | −1.09467 | ||||||||
\(261\) | 2768.18 | 0.656498 | ||||||||
\(262\) | −4988.76 | −1.17636 | ||||||||
\(263\) | 1524.72 | 0.357485 | 0.178742 | − | 0.983896i | \(-0.442797\pi\) | ||||
0.178742 | + | 0.983896i | \(0.442797\pi\) | |||||||
\(264\) | 13780.0 | 3.21249 | ||||||||
\(265\) | 1602.69 | 0.371518 | ||||||||
\(266\) | 2020.46 | 0.465723 | ||||||||
\(267\) | −6098.50 | −1.39784 | ||||||||
\(268\) | 19455.9 | 4.43454 | ||||||||
\(269\) | −1365.12 | −0.309415 | −0.154707 | − | 0.987960i | \(-0.549444\pi\) | ||||
−0.154707 | + | 0.987960i | \(0.549444\pi\) | |||||||
\(270\) | −8777.53 | −1.97846 | ||||||||
\(271\) | −8496.07 | −1.90443 | −0.952213 | − | 0.305434i | \(-0.901198\pi\) | ||||
−0.952213 | + | 0.305434i | \(0.901198\pi\) | |||||||
\(272\) | 8610.22 | 1.91938 | ||||||||
\(273\) | −804.924 | −0.178448 | ||||||||
\(274\) | −3200.42 | −0.705638 | ||||||||
\(275\) | 1747.20 | 0.383129 | ||||||||
\(276\) | 26377.5 | 5.75267 | ||||||||
\(277\) | 85.6103 | 0.0185698 | 0.00928488 | − | 0.999957i | \(-0.497044\pi\) | ||||
0.00928488 | + | 0.999957i | \(0.497044\pi\) | |||||||
\(278\) | −3663.38 | −0.790340 | ||||||||
\(279\) | −2859.55 | −0.613607 | ||||||||
\(280\) | −1204.47 | −0.257075 | ||||||||
\(281\) | −1787.07 | −0.379387 | −0.189693 | − | 0.981843i | \(-0.560749\pi\) | ||||
−0.189693 | + | 0.981843i | \(0.560749\pi\) | |||||||
\(282\) | 18469.4 | 3.90014 | ||||||||
\(283\) | 4265.75 | 0.896015 | 0.448008 | − | 0.894030i | \(-0.352134\pi\) | ||||
0.448008 | + | 0.894030i | \(0.352134\pi\) | |||||||
\(284\) | −10383.8 | −2.16960 | ||||||||
\(285\) | 7989.20 | 1.66049 | ||||||||
\(286\) | 3740.98 | 0.773457 | ||||||||
\(287\) | −185.052 | −0.0380602 | ||||||||
\(288\) | 38785.2 | 7.93555 | ||||||||
\(289\) | −3605.54 | −0.733878 | ||||||||
\(290\) | 1669.45 | 0.338047 | ||||||||
\(291\) | 1140.12 | 0.229674 | ||||||||
\(292\) | −22440.3 | −4.49733 | ||||||||
\(293\) | 7693.93 | 1.53408 | 0.767038 | − | 0.641601i | \(-0.221730\pi\) | ||||
0.767038 | + | 0.641601i | \(0.221730\pi\) | |||||||
\(294\) | 16706.6 | 3.31410 | ||||||||
\(295\) | 181.079 | 0.0357384 | ||||||||
\(296\) | 3717.41 | 0.729967 | ||||||||
\(297\) | 5236.57 | 1.02309 | ||||||||
\(298\) | 10484.0 | 2.03800 | ||||||||
\(299\) | 4537.41 | 0.877608 | ||||||||
\(300\) | 17308.4 | 3.33101 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 12269.8 | 2.33791 | ||||||||
\(303\) | 13211.8 | 2.50494 | ||||||||
\(304\) | −34000.2 | −6.41462 | ||||||||
\(305\) | 2836.26 | 0.532471 | ||||||||
\(306\) | 11005.1 | 2.05594 | ||||||||
\(307\) | −2173.11 | −0.403993 | −0.201996 | − | 0.979386i | \(-0.564743\pi\) | ||||
−0.201996 | + | 0.979386i | \(0.564743\pi\) | |||||||
\(308\) | 1134.06 | 0.209801 | ||||||||
\(309\) | −7641.19 | −1.40677 | ||||||||
\(310\) | −1724.55 | −0.315961 | ||||||||
\(311\) | 9690.39 | 1.76685 | 0.883427 | − | 0.468568i | \(-0.155230\pi\) | ||||
0.883427 | + | 0.468568i | \(0.155230\pi\) | |||||||
\(312\) | 23482.1 | 4.26093 | ||||||||
\(313\) | −2920.33 | −0.527369 | −0.263685 | − | 0.964609i | \(-0.584938\pi\) | ||||
−0.263685 | + | 0.964609i | \(0.584938\pi\) | |||||||
\(314\) | −9862.15 | −1.77246 | ||||||||
\(315\) | −888.025 | −0.158840 | ||||||||
\(316\) | −6724.95 | −1.19718 | ||||||||
\(317\) | 650.198 | 0.115201 | 0.0576006 | − | 0.998340i | \(-0.481655\pi\) | ||||
0.0576006 | + | 0.998340i | \(0.481655\pi\) | |||||||
\(318\) | −12942.1 | −2.28226 | ||||||||
\(319\) | −995.976 | −0.174809 | ||||||||
\(320\) | 11671.3 | 2.03890 | ||||||||
\(321\) | 8482.46 | 1.47491 | ||||||||
\(322\) | 1879.42 | 0.325268 | ||||||||
\(323\) | −5162.91 | −0.889387 | ||||||||
\(324\) | 19024.6 | 3.26211 | ||||||||
\(325\) | 2977.37 | 0.508168 | ||||||||
\(326\) | −18860.3 | −3.20422 | ||||||||
\(327\) | 680.127 | 0.115019 | ||||||||
\(328\) | 5398.53 | 0.908793 | ||||||||
\(329\) | 963.114 | 0.161393 | ||||||||
\(330\) | 6127.11 | 1.02208 | ||||||||
\(331\) | 2920.97 | 0.485048 | 0.242524 | − | 0.970145i | \(-0.422025\pi\) | ||||
0.242524 | + | 0.970145i | \(0.422025\pi\) | |||||||
\(332\) | −25013.4 | −4.13491 | ||||||||
\(333\) | 2740.75 | 0.451027 | ||||||||
\(334\) | 12004.4 | 1.96663 | ||||||||
\(335\) | 5481.46 | 0.893982 | ||||||||
\(336\) | 5610.52 | 0.910950 | ||||||||
\(337\) | −2962.81 | −0.478916 | −0.239458 | − | 0.970907i | \(-0.576970\pi\) | ||||
−0.239458 | + | 0.970907i | \(0.576970\pi\) | |||||||
\(338\) | −5625.62 | −0.905306 | ||||||||
\(339\) | −19264.7 | −3.08648 | ||||||||
\(340\) | 4857.41 | 0.774794 | ||||||||
\(341\) | 1028.85 | 0.163388 | ||||||||
\(342\) | −43457.0 | −6.87101 | ||||||||
\(343\) | 1759.76 | 0.277021 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 7431.53 | 1.15971 | ||||||||
\(346\) | −598.370 | −0.0929728 | ||||||||
\(347\) | 7999.88 | 1.23763 | 0.618813 | − | 0.785538i | \(-0.287614\pi\) | ||||
0.618813 | + | 0.785538i | \(0.287614\pi\) | |||||||
\(348\) | −9866.49 | −1.51983 | ||||||||
\(349\) | 5314.28 | 0.815091 | 0.407546 | − | 0.913185i | \(-0.366385\pi\) | ||||
0.407546 | + | 0.913185i | \(0.366385\pi\) | |||||||
\(350\) | 1233.25 | 0.188342 | ||||||||
\(351\) | 8923.51 | 1.35699 | ||||||||
\(352\) | −13954.7 | −2.11303 | ||||||||
\(353\) | 2313.24 | 0.348786 | 0.174393 | − | 0.984676i | \(-0.444204\pi\) | ||||
0.174393 | + | 0.984676i | \(0.444204\pi\) | |||||||
\(354\) | −1462.26 | −0.219543 | ||||||||
\(355\) | −2925.52 | −0.437382 | ||||||||
\(356\) | 14641.7 | 2.17980 | ||||||||
\(357\) | 851.955 | 0.126303 | ||||||||
\(358\) | −11482.7 | −1.69520 | ||||||||
\(359\) | 3108.14 | 0.456940 | 0.228470 | − | 0.973551i | \(-0.426628\pi\) | ||||
0.228470 | + | 0.973551i | \(0.426628\pi\) | |||||||
\(360\) | 25906.4 | 3.79274 | ||||||||
\(361\) | 13528.4 | 1.97236 | ||||||||
\(362\) | −15242.4 | −2.21305 | ||||||||
\(363\) | 8450.13 | 1.22181 | ||||||||
\(364\) | 1932.52 | 0.278273 | ||||||||
\(365\) | −6322.28 | −0.906639 | ||||||||
\(366\) | −22903.5 | −3.27100 | ||||||||
\(367\) | 645.178 | 0.0917657 | 0.0458828 | − | 0.998947i | \(-0.485390\pi\) | ||||
0.0458828 | + | 0.998947i | \(0.485390\pi\) | |||||||
\(368\) | −31626.9 | −4.48007 | ||||||||
\(369\) | 3980.19 | 0.561519 | ||||||||
\(370\) | 1652.91 | 0.232245 | ||||||||
\(371\) | −674.885 | −0.0944429 | ||||||||
\(372\) | 10192.1 | 1.42053 | ||||||||
\(373\) | 11994.3 | 1.66498 | 0.832492 | − | 0.554037i | \(-0.186913\pi\) | ||||
0.832492 | + | 0.554037i | \(0.186913\pi\) | |||||||
\(374\) | −3959.56 | −0.547444 | ||||||||
\(375\) | 11870.5 | 1.63465 | ||||||||
\(376\) | −28097.0 | −3.85370 | ||||||||
\(377\) | −1697.22 | −0.231860 | ||||||||
\(378\) | 3696.18 | 0.502939 | ||||||||
\(379\) | −9712.13 | −1.31630 | −0.658151 | − | 0.752886i | \(-0.728661\pi\) | ||||
−0.658151 | + | 0.752886i | \(0.728661\pi\) | |||||||
\(380\) | −19181.0 | −2.58938 | ||||||||
\(381\) | 18682.5 | 2.51215 | ||||||||
\(382\) | 20939.8 | 2.80464 | ||||||||
\(383\) | 11940.6 | 1.59305 | 0.796525 | − | 0.604605i | \(-0.206669\pi\) | ||||
0.796525 | + | 0.604605i | \(0.206669\pi\) | |||||||
\(384\) | −43602.4 | −5.79447 | ||||||||
\(385\) | 319.506 | 0.0422950 | ||||||||
\(386\) | 21159.2 | 2.79009 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −2737.29 | −0.358157 | ||||||||
\(389\) | −2644.94 | −0.344740 | −0.172370 | − | 0.985032i | \(-0.555143\pi\) | ||||
−0.172370 | + | 0.985032i | \(0.555143\pi\) | |||||||
\(390\) | 10441.1 | 1.35565 | ||||||||
\(391\) | −4802.52 | −0.621161 | ||||||||
\(392\) | −25415.2 | −3.27464 | ||||||||
\(393\) | 8306.66 | 1.06620 | ||||||||
\(394\) | −13417.7 | −1.71567 | ||||||||
\(395\) | −1894.67 | −0.241345 | ||||||||
\(396\) | −24391.8 | −3.09529 | ||||||||
\(397\) | −8950.96 | −1.13158 | −0.565788 | − | 0.824551i | \(-0.691428\pi\) | ||||
−0.565788 | + | 0.824551i | \(0.691428\pi\) | |||||||
\(398\) | −890.044 | −0.112095 | ||||||||
\(399\) | −3364.22 | −0.422109 | ||||||||
\(400\) | −20753.0 | −2.59412 | ||||||||
\(401\) | 14096.5 | 1.75547 | 0.877736 | − | 0.479145i | \(-0.159053\pi\) | ||||
0.877736 | + | 0.479145i | \(0.159053\pi\) | |||||||
\(402\) | −44264.2 | −5.49179 | ||||||||
\(403\) | 1753.23 | 0.216712 | ||||||||
\(404\) | −31719.7 | −3.90623 | ||||||||
\(405\) | 5359.96 | 0.657626 | ||||||||
\(406\) | −702.999 | −0.0859341 | ||||||||
\(407\) | −986.106 | −0.120097 | ||||||||
\(408\) | −24854.1 | −3.01584 | ||||||||
\(409\) | −8473.30 | −1.02440 | −0.512198 | − | 0.858868i | \(-0.671169\pi\) | ||||
−0.512198 | + | 0.858868i | \(0.671169\pi\) | |||||||
\(410\) | 2400.40 | 0.289140 | ||||||||
\(411\) | 5328.95 | 0.639557 | ||||||||
\(412\) | 18345.5 | 2.19373 | ||||||||
\(413\) | −76.2515 | −0.00908497 | ||||||||
\(414\) | −40423.6 | −4.79882 | ||||||||
\(415\) | −7047.22 | −0.833577 | ||||||||
\(416\) | −23779.8 | −2.80265 | ||||||||
\(417\) | 6099.80 | 0.716327 | ||||||||
\(418\) | 15635.6 | 1.82957 | ||||||||
\(419\) | 500.922 | 0.0584048 | 0.0292024 | − | 0.999574i | \(-0.490703\pi\) | ||||
0.0292024 | + | 0.999574i | \(0.490703\pi\) | |||||||
\(420\) | 3165.15 | 0.367722 | ||||||||
\(421\) | 13129.3 | 1.51991 | 0.759955 | − | 0.649976i | \(-0.225221\pi\) | ||||
0.759955 | + | 0.649976i | \(0.225221\pi\) | |||||||
\(422\) | 5330.92 | 0.614941 | ||||||||
\(423\) | −20715.1 | −2.38110 | ||||||||
\(424\) | 19688.5 | 2.25508 | ||||||||
\(425\) | −3151.33 | −0.359676 | ||||||||
\(426\) | 23624.3 | 2.68686 | ||||||||
\(427\) | −1194.34 | −0.135358 | ||||||||
\(428\) | −20365.3 | −2.29998 | ||||||||
\(429\) | −6229.01 | −0.701025 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 4610.52 | 0.515269 | 0.257635 | − | 0.966242i | \(-0.417057\pi\) | ||||
0.257635 | + | 0.966242i | \(0.417057\pi\) | |||||||
\(432\) | −62199.1 | −6.92722 | ||||||||
\(433\) | −11366.8 | −1.26155 | −0.630777 | − | 0.775964i | \(-0.717264\pi\) | ||||
−0.630777 | + | 0.775964i | \(0.717264\pi\) | |||||||
\(434\) | 726.202 | 0.0803198 | ||||||||
\(435\) | −2779.76 | −0.306390 | ||||||||
\(436\) | −1632.90 | −0.179361 | ||||||||
\(437\) | 18964.3 | 2.07594 | ||||||||
\(438\) | 51054.1 | 5.56954 | ||||||||
\(439\) | 4689.83 | 0.509871 | 0.254935 | − | 0.966958i | \(-0.417946\pi\) | ||||
0.254935 | + | 0.966958i | \(0.417946\pi\) | |||||||
\(440\) | −9320.98 | −1.00991 | ||||||||
\(441\) | −18737.9 | −2.02331 | ||||||||
\(442\) | −6747.39 | −0.726110 | ||||||||
\(443\) | −1822.08 | −0.195417 | −0.0977086 | − | 0.995215i | \(-0.531151\pi\) | ||||
−0.0977086 | + | 0.995215i | \(0.531151\pi\) | |||||||
\(444\) | −9768.72 | −1.04415 | ||||||||
\(445\) | 4125.12 | 0.439437 | ||||||||
\(446\) | −28730.4 | −3.05028 | ||||||||
\(447\) | −17456.7 | −1.84715 | ||||||||
\(448\) | −4914.75 | −0.518304 | ||||||||
\(449\) | 12923.6 | 1.35836 | 0.679180 | − | 0.733972i | \(-0.262336\pi\) | ||||
0.679180 | + | 0.733972i | \(0.262336\pi\) | |||||||
\(450\) | −26525.2 | −2.77869 | ||||||||
\(451\) | −1432.05 | −0.149518 | ||||||||
\(452\) | 46252.1 | 4.81309 | ||||||||
\(453\) | −20430.2 | −2.11898 | ||||||||
\(454\) | 15881.4 | 1.64174 | ||||||||
\(455\) | 544.463 | 0.0560985 | ||||||||
\(456\) | 98144.4 | 10.0790 | ||||||||
\(457\) | 1087.83 | 0.111349 | 0.0556743 | − | 0.998449i | \(-0.482269\pi\) | ||||
0.0556743 | + | 0.998449i | \(0.482269\pi\) | |||||||
\(458\) | 7183.33 | 0.732871 | ||||||||
\(459\) | −9444.91 | −0.960459 | ||||||||
\(460\) | −17842.1 | −1.80846 | ||||||||
\(461\) | −1854.32 | −0.187341 | −0.0936707 | − | 0.995603i | \(-0.529860\pi\) | ||||
−0.0936707 | + | 0.995603i | \(0.529860\pi\) | |||||||
\(462\) | −2580.10 | −0.259821 | ||||||||
\(463\) | −19191.6 | −1.92637 | −0.963186 | − | 0.268834i | \(-0.913362\pi\) | ||||
−0.963186 | + | 0.268834i | \(0.913362\pi\) | |||||||
\(464\) | 11830.0 | 1.18361 | ||||||||
\(465\) | 2871.51 | 0.286372 | ||||||||
\(466\) | 5846.58 | 0.581196 | ||||||||
\(467\) | −3701.95 | −0.366822 | −0.183411 | − | 0.983036i | \(-0.558714\pi\) | ||||
−0.183411 | + | 0.983036i | \(0.558714\pi\) | |||||||
\(468\) | −41565.5 | −4.10548 | ||||||||
\(469\) | −2308.22 | −0.227257 | ||||||||
\(470\) | −12493.0 | −1.22608 | ||||||||
\(471\) | 16421.2 | 1.60648 | ||||||||
\(472\) | 2224.49 | 0.216929 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 15300.0 | 1.48260 | ||||||||
\(475\) | 12444.0 | 1.20205 | ||||||||
\(476\) | −2045.43 | −0.196959 | ||||||||
\(477\) | 14515.8 | 1.39336 | ||||||||
\(478\) | −19656.7 | −1.88091 | ||||||||
\(479\) | 8304.65 | 0.792169 | 0.396085 | − | 0.918214i | \(-0.370369\pi\) | ||||
0.396085 | + | 0.918214i | \(0.370369\pi\) | |||||||
\(480\) | −38947.5 | −3.70355 | ||||||||
\(481\) | −1680.40 | −0.159292 | ||||||||
\(482\) | 23170.7 | 2.18962 | ||||||||
\(483\) | −3129.38 | −0.294807 | ||||||||
\(484\) | −20287.6 | −1.90530 | ||||||||
\(485\) | −771.197 | −0.0722026 | ||||||||
\(486\) | −4760.26 | −0.444300 | ||||||||
\(487\) | −15674.8 | −1.45851 | −0.729254 | − | 0.684243i | \(-0.760133\pi\) | ||||
−0.729254 | + | 0.684243i | \(0.760133\pi\) | |||||||
\(488\) | 34842.4 | 3.23205 | ||||||||
\(489\) | 31403.9 | 2.90416 | ||||||||
\(490\) | −11300.6 | −1.04185 | ||||||||
\(491\) | 13069.6 | 1.20127 | 0.600636 | − | 0.799522i | \(-0.294914\pi\) | ||||
0.600636 | + | 0.799522i | \(0.294914\pi\) | |||||||
\(492\) | −14186.4 | −1.29995 | ||||||||
\(493\) | 1796.38 | 0.164108 | ||||||||
\(494\) | 26644.2 | 2.42668 | ||||||||
\(495\) | −6872.10 | −0.623996 | ||||||||
\(496\) | −12220.5 | −1.10628 | ||||||||
\(497\) | 1231.92 | 0.111186 | ||||||||
\(498\) | 56908.2 | 5.12072 | ||||||||
\(499\) | −9756.69 | −0.875289 | −0.437645 | − | 0.899148i | \(-0.644187\pi\) | ||||
−0.437645 | + | 0.899148i | \(0.644187\pi\) | |||||||
\(500\) | −28499.6 | −2.54908 | ||||||||
\(501\) | −19988.3 | −1.78246 | ||||||||
\(502\) | −13215.6 | −1.17498 | ||||||||
\(503\) | 14365.4 | 1.27340 | 0.636700 | − | 0.771112i | \(-0.280299\pi\) | ||||
0.636700 | + | 0.771112i | \(0.280299\pi\) | |||||||
\(504\) | −10909.1 | −0.964144 | ||||||||
\(505\) | −8936.65 | −0.787476 | ||||||||
\(506\) | 14544.2 | 1.27780 | ||||||||
\(507\) | 9367.09 | 0.820527 | ||||||||
\(508\) | −44854.1 | −3.91748 | ||||||||
\(509\) | −13972.3 | −1.21672 | −0.608360 | − | 0.793662i | \(-0.708172\pi\) | ||||
−0.608360 | + | 0.793662i | \(0.708172\pi\) | |||||||
\(510\) | −11051.1 | −0.959513 | ||||||||
\(511\) | 2662.29 | 0.230475 | ||||||||
\(512\) | 21782.0 | 1.88015 | ||||||||
\(513\) | 37296.2 | 3.20988 | ||||||||
\(514\) | −14897.3 | −1.27839 | ||||||||
\(515\) | 5168.62 | 0.442246 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 7453.19 | 0.634025 | ||||||||
\(518\) | −696.032 | −0.0590384 | ||||||||
\(519\) | 996.332 | 0.0842662 | ||||||||
\(520\) | −15883.6 | −1.33951 | ||||||||
\(521\) | −13785.0 | −1.15918 | −0.579588 | − | 0.814910i | \(-0.696787\pi\) | ||||
−0.579588 | + | 0.814910i | \(0.696787\pi\) | |||||||
\(522\) | 15120.4 | 1.26782 | ||||||||
\(523\) | 8431.00 | 0.704898 | 0.352449 | − | 0.935831i | \(-0.385349\pi\) | ||||
0.352449 | + | 0.935831i | \(0.385349\pi\) | |||||||
\(524\) | −19943.2 | −1.66264 | ||||||||
\(525\) | −2053.45 | −0.170704 | ||||||||
\(526\) | 8328.40 | 0.690372 | ||||||||
\(527\) | −1855.68 | −0.153386 | ||||||||
\(528\) | 43417.8 | 3.57863 | ||||||||
\(529\) | 5473.53 | 0.449867 | ||||||||
\(530\) | 8754.26 | 0.717473 | ||||||||
\(531\) | 1640.06 | 0.134035 | ||||||||
\(532\) | 8077.04 | 0.658241 | ||||||||
\(533\) | −2440.32 | −0.198315 | ||||||||
\(534\) | −33311.4 | −2.69949 | ||||||||
\(535\) | −5737.67 | −0.463665 | ||||||||
\(536\) | 67337.7 | 5.42639 | ||||||||
\(537\) | 19119.6 | 1.53645 | ||||||||
\(538\) | −7456.58 | −0.597539 | ||||||||
\(539\) | 6741.80 | 0.538756 | ||||||||
\(540\) | −35089.3 | −2.79630 | ||||||||
\(541\) | 375.733 | 0.0298596 | 0.0149298 | − | 0.999889i | \(-0.495248\pi\) | ||||
0.0149298 | + | 0.999889i | \(0.495248\pi\) | |||||||
\(542\) | −46407.5 | −3.67781 | ||||||||
\(543\) | 25379.8 | 2.00580 | ||||||||
\(544\) | 25169.3 | 1.98369 | ||||||||
\(545\) | −460.048 | −0.0361584 | ||||||||
\(546\) | −4396.68 | −0.344617 | ||||||||
\(547\) | 9627.22 | 0.752523 | 0.376261 | − | 0.926514i | \(-0.377209\pi\) | ||||
0.376261 | + | 0.926514i | \(0.377209\pi\) | |||||||
\(548\) | −12794.1 | −0.997331 | ||||||||
\(549\) | 25688.4 | 1.99700 | ||||||||
\(550\) | 9543.64 | 0.739894 | ||||||||
\(551\) | −7093.60 | −0.548453 | ||||||||
\(552\) | 91293.7 | 7.03934 | ||||||||
\(553\) | 797.838 | 0.0613518 | ||||||||
\(554\) | 467.623 | 0.0358618 | ||||||||
\(555\) | −2752.22 | −0.210496 | ||||||||
\(556\) | −14644.8 | −1.11705 | ||||||||
\(557\) | −13673.1 | −1.04012 | −0.520061 | − | 0.854129i | \(-0.674091\pi\) | ||||
−0.520061 | + | 0.854129i | \(0.674091\pi\) | |||||||
\(558\) | −15619.5 | −1.18499 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | −3795.04 | −0.286375 | ||||||||
\(561\) | 6592.97 | 0.496177 | ||||||||
\(562\) | −9761.39 | −0.732668 | ||||||||
\(563\) | −5880.29 | −0.440186 | −0.220093 | − | 0.975479i | \(-0.570636\pi\) | ||||
−0.220093 | + | 0.975479i | \(0.570636\pi\) | |||||||
\(564\) | 73834.0 | 5.51236 | ||||||||
\(565\) | 13031.0 | 0.970295 | ||||||||
\(566\) | 23300.5 | 1.73038 | ||||||||
\(567\) | −2257.06 | −0.167174 | ||||||||
\(568\) | −35939.0 | −2.65487 | ||||||||
\(569\) | −14311.3 | −1.05441 | −0.527207 | − | 0.849737i | \(-0.676761\pi\) | ||||
−0.527207 | + | 0.849737i | \(0.676761\pi\) | |||||||
\(570\) | 43638.9 | 3.20672 | ||||||||
\(571\) | −875.082 | −0.0641349 | −0.0320675 | − | 0.999486i | \(-0.510209\pi\) | ||||
−0.0320675 | + | 0.999486i | \(0.510209\pi\) | |||||||
\(572\) | 14955.0 | 1.09318 | ||||||||
\(573\) | −34866.4 | −2.54200 | ||||||||
\(574\) | −1010.80 | −0.0735015 | ||||||||
\(575\) | 11575.4 | 0.839527 | ||||||||
\(576\) | 105709. | 7.64677 | ||||||||
\(577\) | −1692.97 | −0.122147 | −0.0610737 | − | 0.998133i | \(-0.519452\pi\) | ||||
−0.0610737 | + | 0.998133i | \(0.519452\pi\) | |||||||
\(578\) | −19694.3 | −1.41726 | ||||||||
\(579\) | −35231.7 | −2.52881 | ||||||||
\(580\) | 6673.85 | 0.477787 | ||||||||
\(581\) | 2967.55 | 0.211902 | ||||||||
\(582\) | 6227.62 | 0.443545 | ||||||||
\(583\) | −5222.69 | −0.371015 | ||||||||
\(584\) | −77667.0 | −5.50322 | ||||||||
\(585\) | −11710.6 | −0.827646 | ||||||||
\(586\) | 42026.1 | 2.96259 | ||||||||
\(587\) | −9558.71 | −0.672112 | −0.336056 | − | 0.941842i | \(-0.609093\pi\) | ||||
−0.336056 | + | 0.941842i | \(0.609093\pi\) | |||||||
\(588\) | 66786.7 | 4.68407 | ||||||||
\(589\) | 7327.73 | 0.512621 | ||||||||
\(590\) | 989.095 | 0.0690176 | ||||||||
\(591\) | 22341.5 | 1.55501 | ||||||||
\(592\) | 11712.8 | 0.813164 | ||||||||
\(593\) | −380.686 | −0.0263624 | −0.0131812 | − | 0.999913i | \(-0.504196\pi\) | ||||
−0.0131812 | + | 0.999913i | \(0.504196\pi\) | |||||||
\(594\) | 28603.4 | 1.97578 | ||||||||
\(595\) | −576.276 | −0.0397059 | ||||||||
\(596\) | 41911.3 | 2.88046 | ||||||||
\(597\) | 1481.99 | 0.101598 | ||||||||
\(598\) | 24784.4 | 1.69483 | ||||||||
\(599\) | 18267.5 | 1.24606 | 0.623031 | − | 0.782197i | \(-0.285901\pi\) | ||||
0.623031 | + | 0.782197i | \(0.285901\pi\) | |||||||
\(600\) | 59905.3 | 4.07604 | ||||||||
\(601\) | −3526.45 | −0.239346 | −0.119673 | − | 0.992813i | \(-0.538185\pi\) | ||||
−0.119673 | + | 0.992813i | \(0.538185\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 49646.3 | 3.35282 | ||||||||
\(604\) | 49050.3 | 3.30435 | ||||||||
\(605\) | −5715.80 | −0.384099 | ||||||||
\(606\) | 72165.8 | 4.83752 | ||||||||
\(607\) | 1688.55 | 0.112910 | 0.0564548 | − | 0.998405i | \(-0.482020\pi\) | ||||
0.0564548 | + | 0.998405i | \(0.482020\pi\) | |||||||
\(608\) | −99389.0 | −6.62953 | ||||||||
\(609\) | 1170.55 | 0.0778866 | ||||||||
\(610\) | 15492.3 | 1.02830 | ||||||||
\(611\) | 12700.8 | 0.840948 | ||||||||
\(612\) | 43994.2 | 2.90582 | ||||||||
\(613\) | 19844.4 | 1.30752 | 0.653759 | − | 0.756703i | \(-0.273191\pi\) | ||||
0.653759 | + | 0.756703i | \(0.273191\pi\) | |||||||
\(614\) | −11870.0 | −0.780187 | ||||||||
\(615\) | −3996.85 | −0.262063 | ||||||||
\(616\) | 3925.02 | 0.256727 | ||||||||
\(617\) | 12892.5 | 0.841218 | 0.420609 | − | 0.907242i | \(-0.361816\pi\) | ||||
0.420609 | + | 0.907242i | \(0.361816\pi\) | |||||||
\(618\) | −41738.0 | −2.71674 | ||||||||
\(619\) | −17148.5 | −1.11350 | −0.556751 | − | 0.830679i | \(-0.687952\pi\) | ||||
−0.556751 | + | 0.830679i | \(0.687952\pi\) | |||||||
\(620\) | −6894.12 | −0.446572 | ||||||||
\(621\) | 34692.8 | 2.24183 | ||||||||
\(622\) | 52931.2 | 3.41213 | ||||||||
\(623\) | −1737.07 | −0.111708 | ||||||||
\(624\) | 73987.2 | 4.74657 | ||||||||
\(625\) | 2864.66 | 0.183338 | ||||||||
\(626\) | −15951.5 | −1.01845 | ||||||||
\(627\) | −26034.5 | −1.65824 | ||||||||
\(628\) | −39425.2 | −2.50515 | ||||||||
\(629\) | 1778.58 | 0.112745 | ||||||||
\(630\) | −4850.60 | −0.306750 | ||||||||
\(631\) | 978.279 | 0.0617190 | 0.0308595 | − | 0.999524i | \(-0.490176\pi\) | ||||
0.0308595 | + | 0.999524i | \(0.490176\pi\) | |||||||
\(632\) | −23275.4 | −1.46494 | ||||||||
\(633\) | −8876.38 | −0.557353 | ||||||||
\(634\) | 3551.54 | 0.222476 | ||||||||
\(635\) | −12637.1 | −0.789745 | ||||||||
\(636\) | −51737.9 | −3.22569 | ||||||||
\(637\) | 11488.5 | 0.714587 | ||||||||
\(638\) | −5440.25 | −0.337589 | ||||||||
\(639\) | −26496.8 | −1.64037 | ||||||||
\(640\) | 29493.3 | 1.82160 | ||||||||
\(641\) | −12867.5 | −0.792880 | −0.396440 | − | 0.918061i | \(-0.629754\pi\) | ||||
−0.396440 | + | 0.918061i | \(0.629754\pi\) | |||||||
\(642\) | 46333.2 | 2.84833 | ||||||||
\(643\) | 13732.1 | 0.842211 | 0.421106 | − | 0.907012i | \(-0.361642\pi\) | ||||
0.421106 | + | 0.907012i | \(0.361642\pi\) | |||||||
\(644\) | 7513.24 | 0.459725 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −28201.0 | −1.71758 | ||||||||
\(647\) | −2460.71 | −0.149522 | −0.0747608 | − | 0.997201i | \(-0.523819\pi\) | ||||
−0.0747608 | + | 0.997201i | \(0.523819\pi\) | |||||||
\(648\) | 65845.2 | 3.99173 | ||||||||
\(649\) | −590.083 | −0.0356899 | ||||||||
\(650\) | 16263.1 | 0.981369 | ||||||||
\(651\) | −1209.18 | −0.0727981 | ||||||||
\(652\) | −75396.6 | −4.52877 | ||||||||
\(653\) | 26816.4 | 1.60706 | 0.803528 | − | 0.595267i | \(-0.202954\pi\) | ||||
0.803528 | + | 0.595267i | \(0.202954\pi\) | |||||||
\(654\) | 3715.01 | 0.222123 | ||||||||
\(655\) | −5618.75 | −0.335180 | ||||||||
\(656\) | 17009.7 | 1.01237 | ||||||||
\(657\) | −57261.7 | −3.40029 | ||||||||
\(658\) | 5260.75 | 0.311680 | ||||||||
\(659\) | −943.089 | −0.0557474 | −0.0278737 | − | 0.999611i | \(-0.508874\pi\) | ||||
−0.0278737 | + | 0.999611i | \(0.508874\pi\) | |||||||
\(660\) | 24493.9 | 1.44458 | ||||||||
\(661\) | 14083.2 | 0.828706 | 0.414353 | − | 0.910116i | \(-0.364008\pi\) | ||||
0.414353 | + | 0.910116i | \(0.364008\pi\) | |||||||
\(662\) | 15955.0 | 0.936721 | ||||||||
\(663\) | 11234.9 | 0.658112 | ||||||||
\(664\) | −86572.6 | −5.05974 | ||||||||
\(665\) | 2275.61 | 0.132698 | ||||||||
\(666\) | 14970.6 | 0.871020 | ||||||||
\(667\) | −6598.44 | −0.383048 | ||||||||
\(668\) | 47989.3 | 2.77958 | ||||||||
\(669\) | 47838.3 | 2.76463 | ||||||||
\(670\) | 29941.0 | 1.72645 | ||||||||
\(671\) | −9242.53 | −0.531750 | ||||||||
\(672\) | 16400.6 | 0.941470 | ||||||||
\(673\) | 4292.74 | 0.245873 | 0.122937 | − | 0.992415i | \(-0.460769\pi\) | ||||
0.122937 | + | 0.992415i | \(0.460769\pi\) | |||||||
\(674\) | −16183.6 | −0.924878 | ||||||||
\(675\) | 22764.8 | 1.29810 | ||||||||
\(676\) | −22489.2 | −1.27954 | ||||||||
\(677\) | 19977.3 | 1.13411 | 0.567054 | − | 0.823681i | \(-0.308083\pi\) | ||||
0.567054 | + | 0.823681i | \(0.308083\pi\) | |||||||
\(678\) | −105228. | −5.96058 | ||||||||
\(679\) | 324.748 | 0.0183545 | ||||||||
\(680\) | 16811.7 | 0.948088 | ||||||||
\(681\) | −26443.8 | −1.48800 | ||||||||
\(682\) | 5619.81 | 0.315533 | ||||||||
\(683\) | 16248.8 | 0.910314 | 0.455157 | − | 0.890411i | \(-0.349583\pi\) | ||||
0.455157 | + | 0.890411i | \(0.349583\pi\) | |||||||
\(684\) | −173725. | −9.71132 | ||||||||
\(685\) | −3604.59 | −0.201057 | ||||||||
\(686\) | 9612.21 | 0.534980 | ||||||||
\(687\) | −11960.8 | −0.664239 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −8899.86 | −0.492101 | ||||||||
\(690\) | 40592.7 | 2.23962 | ||||||||
\(691\) | 27470.0 | 1.51231 | 0.756155 | − | 0.654392i | \(-0.227075\pi\) | ||||
0.756155 | + | 0.654392i | \(0.227075\pi\) | |||||||
\(692\) | −2392.06 | −0.131405 | ||||||||
\(693\) | 2893.81 | 0.158625 | ||||||||
\(694\) | 43697.2 | 2.39009 | ||||||||
\(695\) | −4126.00 | −0.225191 | ||||||||
\(696\) | −34148.4 | −1.85976 | ||||||||
\(697\) | 2582.91 | 0.140365 | ||||||||
\(698\) | 29027.8 | 1.57410 | ||||||||
\(699\) | −9735.00 | −0.526769 | ||||||||
\(700\) | 4930.06 | 0.266198 | ||||||||
\(701\) | −5373.47 | −0.289519 | −0.144760 | − | 0.989467i | \(-0.546241\pi\) | ||||
−0.144760 | + | 0.989467i | \(0.546241\pi\) | |||||||
\(702\) | 48742.3 | 2.62060 | ||||||||
\(703\) | −7023.30 | −0.376798 | ||||||||
\(704\) | −38033.5 | −2.03614 | ||||||||
\(705\) | 20801.8 | 1.11126 | ||||||||
\(706\) | 12635.5 | 0.673573 | ||||||||
\(707\) | 3763.18 | 0.200183 | ||||||||
\(708\) | −5845.57 | −0.310297 | ||||||||
\(709\) | 22366.6 | 1.18476 | 0.592380 | − | 0.805658i | \(-0.298188\pi\) | ||||
0.592380 | + | 0.805658i | \(0.298188\pi\) | |||||||
\(710\) | −15979.9 | −0.844667 | ||||||||
\(711\) | −17160.3 | −0.905150 | ||||||||
\(712\) | 50675.6 | 2.66735 | ||||||||
\(713\) | 6816.23 | 0.358022 | ||||||||
\(714\) | 4653.58 | 0.243916 | ||||||||
\(715\) | 4213.40 | 0.220381 | ||||||||
\(716\) | −45903.6 | −2.39595 | ||||||||
\(717\) | 32729.8 | 1.70477 | ||||||||
\(718\) | 16977.4 | 0.882439 | ||||||||
\(719\) | −19417.5 | −1.00716 | −0.503582 | − | 0.863947i | \(-0.667985\pi\) | ||||
−0.503582 | + | 0.863947i | \(0.667985\pi\) | |||||||
\(720\) | 81625.7 | 4.22501 | ||||||||
\(721\) | −2176.48 | −0.112422 | ||||||||
\(722\) | 73895.2 | 3.80900 | ||||||||
\(723\) | −38581.1 | −1.98457 | ||||||||
\(724\) | −60933.5 | −3.12787 | ||||||||
\(725\) | −4329.78 | −0.221799 | ||||||||
\(726\) | 46156.6 | 2.35955 | ||||||||
\(727\) | 5295.15 | 0.270133 | 0.135066 | − | 0.990837i | \(-0.456875\pi\) | ||||
0.135066 | + | 0.990837i | \(0.456875\pi\) | |||||||
\(728\) | 6688.53 | 0.340513 | ||||||||
\(729\) | −15597.6 | −0.792439 | ||||||||
\(730\) | −34533.8 | −1.75089 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | −91559.9 | −4.62316 | ||||||||
\(733\) | 3812.57 | 0.192115 | 0.0960576 | − | 0.995376i | \(-0.469377\pi\) | ||||
0.0960576 | + | 0.995376i | \(0.469377\pi\) | |||||||
\(734\) | 3524.11 | 0.177217 | ||||||||
\(735\) | 18816.3 | 0.944286 | ||||||||
\(736\) | −92451.3 | −4.63016 | ||||||||
\(737\) | −17862.5 | −0.892771 | ||||||||
\(738\) | 21740.7 | 1.08440 | ||||||||
\(739\) | −4166.76 | −0.207411 | −0.103706 | − | 0.994608i | \(-0.533070\pi\) | ||||
−0.103706 | + | 0.994608i | \(0.533070\pi\) | |||||||
\(740\) | 6607.72 | 0.328249 | ||||||||
\(741\) | −44364.6 | −2.19943 | ||||||||
\(742\) | −3686.38 | −0.182387 | ||||||||
\(743\) | 25570.4 | 1.26257 | 0.631284 | − | 0.775552i | \(-0.282528\pi\) | ||||
0.631284 | + | 0.775552i | \(0.282528\pi\) | |||||||
\(744\) | 35275.5 | 1.73826 | ||||||||
\(745\) | 11808.0 | 0.580686 | ||||||||
\(746\) | 65515.4 | 3.21540 | ||||||||
\(747\) | −63827.6 | −3.12628 | ||||||||
\(748\) | −15828.9 | −0.773744 | ||||||||
\(749\) | 2416.11 | 0.117867 | ||||||||
\(750\) | 64839.7 | 3.15681 | ||||||||
\(751\) | −8697.56 | −0.422608 | −0.211304 | − | 0.977420i | \(-0.567771\pi\) | ||||
−0.211304 | + | 0.977420i | \(0.567771\pi\) | |||||||
\(752\) | −88527.7 | −4.29292 | ||||||||
\(753\) | 22005.0 | 1.06495 | ||||||||
\(754\) | −9270.59 | −0.447765 | ||||||||
\(755\) | 13819.3 | 0.666141 | ||||||||
\(756\) | 14776.0 | 0.710842 | ||||||||
\(757\) | 6943.97 | 0.333399 | 0.166699 | − | 0.986008i | \(-0.446689\pi\) | ||||
0.166699 | + | 0.986008i | \(0.446689\pi\) | |||||||
\(758\) | −53049.9 | −2.54203 | ||||||||
\(759\) | −24217.2 | −1.15814 | ||||||||
\(760\) | −66386.4 | −3.16854 | ||||||||
\(761\) | −14571.8 | −0.694121 | −0.347060 | − | 0.937843i | \(-0.612820\pi\) | ||||
−0.347060 | + | 0.937843i | \(0.612820\pi\) | |||||||
\(762\) | 102048. | 4.85145 | ||||||||
\(763\) | 193.724 | 0.00919173 | ||||||||
\(764\) | 83709.6 | 3.96402 | ||||||||
\(765\) | 12394.8 | 0.585798 | ||||||||
\(766\) | 65222.6 | 3.07649 | ||||||||
\(767\) | −1005.55 | −0.0473379 | ||||||||
\(768\) | −100129. | −4.70455 | ||||||||
\(769\) | −32318.2 | −1.51550 | −0.757752 | − | 0.652543i | \(-0.773702\pi\) | ||||
−0.757752 | + | 0.652543i | \(0.773702\pi\) | |||||||
\(770\) | 1745.22 | 0.0816796 | ||||||||
\(771\) | 24805.1 | 1.15867 | ||||||||
\(772\) | 84586.6 | 3.94344 | ||||||||
\(773\) | −1785.68 | −0.0830874 | −0.0415437 | − | 0.999137i | \(-0.513228\pi\) | ||||
−0.0415437 | + | 0.999137i | \(0.513228\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 4472.69 | 0.207308 | ||||||||
\(776\) | −9473.88 | −0.438264 | ||||||||
\(777\) | 1158.95 | 0.0535097 | ||||||||
\(778\) | −14447.3 | −0.665759 | ||||||||
\(779\) | −10199.4 | −0.469105 | ||||||||
\(780\) | 41739.5 | 1.91604 | ||||||||
\(781\) | 9533.41 | 0.436789 | ||||||||
\(782\) | −26232.5 | −1.19958 | ||||||||
\(783\) | −12976.9 | −0.592280 | ||||||||
\(784\) | −80077.9 | −3.64786 | ||||||||
\(785\) | −11107.6 | −0.505027 | ||||||||
\(786\) | 45372.9 | 2.05903 | ||||||||
\(787\) | 7591.08 | 0.343828 | 0.171914 | − | 0.985112i | \(-0.445005\pi\) | ||||
0.171914 | + | 0.985112i | \(0.445005\pi\) | |||||||
\(788\) | −53639.1 | −2.42489 | ||||||||
\(789\) | −13867.4 | −0.625720 | ||||||||
\(790\) | −10349.1 | −0.466083 | ||||||||
\(791\) | −5487.28 | −0.246656 | ||||||||
\(792\) | −84421.3 | −3.78760 | ||||||||
\(793\) | −15750.0 | −0.705293 | ||||||||
\(794\) | −48892.2 | −2.18529 | ||||||||
\(795\) | −14576.5 | −0.650284 | ||||||||
\(796\) | −3558.07 | −0.158433 | ||||||||
\(797\) | −11200.4 | −0.497790 | −0.248895 | − | 0.968531i | \(-0.580067\pi\) | ||||
−0.248895 | + | 0.968531i | \(0.580067\pi\) | |||||||
\(798\) | −18376.1 | −0.815173 | ||||||||
\(799\) | −13442.9 | −0.595213 | ||||||||
\(800\) | −60664.9 | −2.68104 | ||||||||
\(801\) | 37361.8 | 1.64808 | ||||||||
\(802\) | 76998.2 | 3.39015 | ||||||||
\(803\) | 20602.5 | 0.905411 | ||||||||
\(804\) | −176952. | −7.76196 | ||||||||
\(805\) | 2116.76 | 0.0926784 | ||||||||
\(806\) | 9576.58 | 0.418512 | ||||||||
\(807\) | 12415.8 | 0.541582 | ||||||||
\(808\) | −109784. | −4.77991 | ||||||||
\(809\) | −23832.0 | −1.03571 | −0.517854 | − | 0.855469i | \(-0.673269\pi\) | ||||
−0.517854 | + | 0.855469i | \(0.673269\pi\) | |||||||
\(810\) | 29277.3 | 1.27000 | ||||||||
\(811\) | 23707.2 | 1.02648 | 0.513239 | − | 0.858246i | \(-0.328445\pi\) | ||||
0.513239 | + | 0.858246i | \(0.328445\pi\) | |||||||
\(812\) | −2810.33 | −0.121457 | ||||||||
\(813\) | 77272.1 | 3.33339 | ||||||||
\(814\) | −5386.34 | −0.231930 | ||||||||
\(815\) | −21242.1 | −0.912978 | ||||||||
\(816\) | −78310.2 | −3.35957 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | −46283.1 | −1.97830 | ||||||||
\(819\) | 4931.27 | 0.210394 | ||||||||
\(820\) | 9595.91 | 0.408663 | ||||||||
\(821\) | −27578.1 | −1.17233 | −0.586165 | − | 0.810192i | \(-0.699363\pi\) | ||||
−0.586165 | + | 0.810192i | \(0.699363\pi\) | |||||||
\(822\) | 29108.0 | 1.23511 | ||||||||
\(823\) | 14566.9 | 0.616975 | 0.308488 | − | 0.951228i | \(-0.400177\pi\) | ||||
0.308488 | + | 0.951228i | \(0.400177\pi\) | |||||||
\(824\) | 63494.6 | 2.68439 | ||||||||
\(825\) | −15890.9 | −0.670606 | ||||||||
\(826\) | −416.504 | −0.0175448 | ||||||||
\(827\) | 46389.9 | 1.95059 | 0.975293 | − | 0.220917i | \(-0.0709049\pi\) | ||||
0.975293 | + | 0.220917i | \(0.0709049\pi\) | |||||||
\(828\) | −161598. | −6.78253 | ||||||||
\(829\) | −17471.0 | −0.731957 | −0.365979 | − | 0.930623i | \(-0.619266\pi\) | ||||
−0.365979 | + | 0.930623i | \(0.619266\pi\) | |||||||
\(830\) | −38493.6 | −1.60980 | ||||||||
\(831\) | −778.629 | −0.0325034 | ||||||||
\(832\) | −64811.9 | −2.70066 | ||||||||
\(833\) | −12159.8 | −0.505777 | ||||||||
\(834\) | 33318.5 | 1.38336 | ||||||||
\(835\) | 13520.4 | 0.560350 | ||||||||
\(836\) | 62505.3 | 2.58587 | ||||||||
\(837\) | 13405.2 | 0.553585 | ||||||||
\(838\) | 2736.15 | 0.112791 | ||||||||
\(839\) | −31457.8 | −1.29445 | −0.647225 | − | 0.762299i | \(-0.724070\pi\) | ||||
−0.647225 | + | 0.762299i | \(0.724070\pi\) | |||||||
\(840\) | 10954.7 | 0.449969 | ||||||||
\(841\) | −21920.9 | −0.898801 | ||||||||
\(842\) | 71715.2 | 2.93524 | ||||||||
\(843\) | 16253.5 | 0.664056 | ||||||||
\(844\) | 21311.0 | 0.869142 | ||||||||
\(845\) | −6336.04 | −0.257949 | ||||||||
\(846\) | −113151. | −4.59835 | ||||||||
\(847\) | 2406.90 | 0.0976411 | ||||||||
\(848\) | 62034.3 | 2.51211 | ||||||||
\(849\) | −38797.1 | −1.56833 | ||||||||
\(850\) | −17213.3 | −0.694602 | ||||||||
\(851\) | −6533.06 | −0.263161 | ||||||||
\(852\) | 94441.4 | 3.79755 | ||||||||
\(853\) | 12947.7 | 0.519720 | 0.259860 | − | 0.965646i | \(-0.416324\pi\) | ||||
0.259860 | + | 0.965646i | \(0.416324\pi\) | |||||||
\(854\) | −6523.74 | −0.261403 | ||||||||
\(855\) | −48944.9 | −1.95775 | ||||||||
\(856\) | −70485.2 | −2.81441 | ||||||||
\(857\) | −22730.2 | −0.906007 | −0.453004 | − | 0.891509i | \(-0.649648\pi\) | ||||
−0.453004 | + | 0.891509i | \(0.649648\pi\) | |||||||
\(858\) | −34024.3 | −1.35381 | ||||||||
\(859\) | 10019.6 | 0.397980 | 0.198990 | − | 0.980002i | \(-0.436234\pi\) | ||||
0.198990 | + | 0.980002i | \(0.436234\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 1683.06 | 0.0666183 | ||||||||
\(862\) | 25183.8 | 0.995084 | ||||||||
\(863\) | 33745.3 | 1.33106 | 0.665530 | − | 0.746371i | \(-0.268206\pi\) | ||||
0.665530 | + | 0.746371i | \(0.268206\pi\) | |||||||
\(864\) | −181820. | −7.15930 | ||||||||
\(865\) | −673.934 | −0.0264907 | ||||||||
\(866\) | −62088.0 | −2.43630 | ||||||||
\(867\) | 32792.5 | 1.28454 | ||||||||
\(868\) | 2903.09 | 0.113522 | ||||||||
\(869\) | 6174.18 | 0.241018 | ||||||||
\(870\) | −15183.7 | −0.591697 | ||||||||
\(871\) | −30439.0 | −1.18414 | ||||||||
\(872\) | −5651.53 | −0.219478 | ||||||||
\(873\) | −6984.84 | −0.270791 | ||||||||
\(874\) | 103587. | 4.00903 | ||||||||
\(875\) | 3381.15 | 0.130633 | ||||||||
\(876\) | 204095. | 7.87185 | ||||||||
\(877\) | −9357.18 | −0.360285 | −0.180142 | − | 0.983641i | \(-0.557656\pi\) | ||||
−0.180142 | + | 0.983641i | \(0.557656\pi\) | |||||||
\(878\) | 25616.9 | 0.984658 | ||||||||
\(879\) | −69976.6 | −2.68516 | ||||||||
\(880\) | −29368.5 | −1.12501 | ||||||||
\(881\) | 18561.7 | 0.709828 | 0.354914 | − | 0.934899i | \(-0.384510\pi\) | ||||
0.354914 | + | 0.934899i | \(0.384510\pi\) | |||||||
\(882\) | −102351. | −3.90740 | ||||||||
\(883\) | −28177.1 | −1.07388 | −0.536940 | − | 0.843621i | \(-0.680420\pi\) | ||||
−0.536940 | + | 0.843621i | \(0.680420\pi\) | |||||||
\(884\) | −26973.6 | −1.02627 | ||||||||
\(885\) | −1646.92 | −0.0625543 | ||||||||
\(886\) | −9952.65 | −0.377388 | ||||||||
\(887\) | −13672.0 | −0.517543 | −0.258771 | − | 0.965939i | \(-0.583318\pi\) | ||||
−0.258771 | + | 0.965939i | \(0.583318\pi\) | |||||||
\(888\) | −33810.0 | −1.27769 | ||||||||
\(889\) | 5321.43 | 0.200759 | ||||||||
\(890\) | 22532.4 | 0.848637 | ||||||||
\(891\) | −17466.5 | −0.656735 | ||||||||
\(892\) | −114854. | −4.31119 | ||||||||
\(893\) | 53083.5 | 1.98922 | ||||||||
\(894\) | −95352.6 | −3.56719 | ||||||||
\(895\) | −12932.8 | −0.483012 | ||||||||
\(896\) | −12419.5 | −0.463066 | ||||||||
\(897\) | −41267.9 | −1.53611 | ||||||||
\(898\) | 70591.9 | 2.62325 | ||||||||
\(899\) | −2549.61 | −0.0945876 | ||||||||
\(900\) | −106038. | −3.92734 | ||||||||
\(901\) | 9419.87 | 0.348304 | ||||||||
\(902\) | −7822.20 | −0.288748 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 160081. | 5.88960 | ||||||||
\(905\) | −17167.3 | −0.630563 | ||||||||
\(906\) | −111595. | −4.09215 | ||||||||
\(907\) | −9828.52 | −0.359813 | −0.179907 | − | 0.983684i | \(-0.557580\pi\) | ||||
−0.179907 | + | 0.983684i | \(0.557580\pi\) | |||||||
\(908\) | 63488.0 | 2.32040 | ||||||||
\(909\) | −80940.4 | −2.95338 | ||||||||
\(910\) | 2973.98 | 0.108337 | ||||||||
\(911\) | −30471.1 | −1.10818 | −0.554091 | − | 0.832456i | \(-0.686934\pi\) | ||||
−0.554091 | + | 0.832456i | \(0.686934\pi\) | |||||||
\(912\) | 309233. | 11.2278 | ||||||||
\(913\) | 22964.8 | 0.832448 | ||||||||
\(914\) | 5941.95 | 0.215035 | ||||||||
\(915\) | −25795.9 | −0.932006 | ||||||||
\(916\) | 28716.3 | 1.03582 | ||||||||
\(917\) | 2366.03 | 0.0852053 | ||||||||
\(918\) | −51590.3 | −1.85483 | ||||||||
\(919\) | 42727.5 | 1.53368 | 0.766839 | − | 0.641839i | \(-0.221828\pi\) | ||||
0.766839 | + | 0.641839i | \(0.221828\pi\) | |||||||
\(920\) | −61752.4 | −2.21295 | ||||||||
\(921\) | 19764.5 | 0.707125 | ||||||||
\(922\) | −10128.7 | −0.361792 | ||||||||
\(923\) | 16245.6 | 0.579341 | ||||||||
\(924\) | −10314.3 | −0.367224 | ||||||||
\(925\) | −4286.88 | −0.152380 | ||||||||
\(926\) | −104829. | −3.72019 | ||||||||
\(927\) | 46812.9 | 1.65861 | ||||||||
\(928\) | 34581.4 | 1.22327 | ||||||||
\(929\) | 32717.0 | 1.15545 | 0.577723 | − | 0.816233i | \(-0.303941\pi\) | ||||
0.577723 | + | 0.816233i | \(0.303941\pi\) | |||||||
\(930\) | 15684.9 | 0.553040 | ||||||||
\(931\) | 48016.8 | 1.69032 | ||||||||
\(932\) | 23372.4 | 0.821449 | ||||||||
\(933\) | −88134.5 | −3.09260 | ||||||||
\(934\) | −20220.9 | −0.708403 | ||||||||
\(935\) | −4459.59 | −0.155983 | ||||||||
\(936\) | −143860. | −5.02374 | ||||||||
\(937\) | 51528.4 | 1.79654 | 0.898271 | − | 0.439443i | \(-0.144824\pi\) | ||||
0.898271 | + | 0.439443i | \(0.144824\pi\) | |||||||
\(938\) | −12608.0 | −0.438877 | ||||||||
\(939\) | 26560.5 | 0.923076 | ||||||||
\(940\) | −49942.4 | −1.73292 | ||||||||
\(941\) | 26909.6 | 0.932229 | 0.466114 | − | 0.884724i | \(-0.345653\pi\) | ||||
0.466114 | + | 0.884724i | \(0.345653\pi\) | |||||||
\(942\) | 89696.6 | 3.10241 | ||||||||
\(943\) | −9487.49 | −0.327630 | ||||||||
\(944\) | 7008.90 | 0.241653 | ||||||||
\(945\) | 4162.94 | 0.143302 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 18441.8 | 0.632818 | 0.316409 | − | 0.948623i | \(-0.397523\pi\) | ||||
0.316409 | + | 0.948623i | \(0.397523\pi\) | |||||||
\(948\) | 61163.7 | 2.09547 | ||||||||
\(949\) | 35108.1 | 1.20090 | ||||||||
\(950\) | 67972.2 | 2.32138 | ||||||||
\(951\) | −5913.58 | −0.201641 | ||||||||
\(952\) | −7079.34 | −0.241011 | ||||||||
\(953\) | −35819.6 | −1.21754 | −0.608768 | − | 0.793348i | \(-0.708336\pi\) | ||||
−0.608768 | + | 0.793348i | \(0.708336\pi\) | |||||||
\(954\) | 79288.5 | 2.69084 | ||||||||
\(955\) | 23584.2 | 0.799126 | ||||||||
\(956\) | −78580.1 | −2.65843 | ||||||||
\(957\) | 9058.43 | 0.305975 | ||||||||
\(958\) | 45361.9 | 1.52983 | ||||||||
\(959\) | 1517.88 | 0.0511103 | ||||||||
\(960\) | −106151. | −3.56877 | ||||||||
\(961\) | −27157.2 | −0.911592 | ||||||||
\(962\) | −9178.73 | −0.307624 | ||||||||
\(963\) | −51966.8 | −1.73895 | ||||||||
\(964\) | 92628.1 | 3.09476 | ||||||||
\(965\) | 23831.2 | 0.794979 | ||||||||
\(966\) | −17093.4 | −0.569329 | ||||||||
\(967\) | −28557.3 | −0.949680 | −0.474840 | − | 0.880072i | \(-0.657494\pi\) | ||||
−0.474840 | + | 0.880072i | \(0.657494\pi\) | |||||||
\(968\) | −70216.5 | −2.33145 | ||||||||
\(969\) | 46956.9 | 1.55673 | ||||||||
\(970\) | −4212.46 | −0.139437 | ||||||||
\(971\) | −32692.2 | −1.08048 | −0.540238 | − | 0.841513i | \(-0.681666\pi\) | ||||
−0.540238 | + | 0.841513i | \(0.681666\pi\) | |||||||
\(972\) | −19029.8 | −0.627963 | ||||||||
\(973\) | 1737.44 | 0.0572454 | ||||||||
\(974\) | −85619.5 | −2.81666 | ||||||||
\(975\) | −27079.3 | −0.889467 | ||||||||
\(976\) | 109781. | 3.60042 | ||||||||
\(977\) | −2318.74 | −0.0759294 | −0.0379647 | − | 0.999279i | \(-0.512087\pi\) | ||||
−0.0379647 | + | 0.999279i | \(0.512087\pi\) | |||||||
\(978\) | 171535. | 5.60848 | ||||||||
\(979\) | −13442.6 | −0.438842 | ||||||||
\(980\) | −45175.5 | −1.47253 | ||||||||
\(981\) | −4166.72 | −0.135610 | ||||||||
\(982\) | 71389.5 | 2.31989 | ||||||||
\(983\) | −26323.2 | −0.854099 | −0.427050 | − | 0.904228i | \(-0.640447\pi\) | ||||
−0.427050 | + | 0.904228i | \(0.640447\pi\) | |||||||
\(984\) | −49099.8 | −1.59070 | ||||||||
\(985\) | −15112.2 | −0.488846 | ||||||||
\(986\) | 9812.27 | 0.316923 | ||||||||
\(987\) | −8759.56 | −0.282492 | ||||||||
\(988\) | 106514. | 3.42981 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | −37537.0 | −1.20506 | ||||||||
\(991\) | −57890.7 | −1.85566 | −0.927830 | − | 0.373004i | \(-0.878328\pi\) | ||||
−0.927830 | + | 0.373004i | \(0.878328\pi\) | |||||||
\(992\) | −35722.8 | −1.14335 | ||||||||
\(993\) | −26566.3 | −0.849000 | ||||||||
\(994\) | 6729.05 | 0.214721 | ||||||||
\(995\) | −1002.44 | −0.0319392 | ||||||||
\(996\) | 227498. | 7.23749 | ||||||||
\(997\) | −10032.0 | −0.318673 | −0.159337 | − | 0.987224i | \(-0.550936\pi\) | ||||
−0.159337 | + | 0.987224i | \(0.550936\pi\) | |||||||
\(998\) | −53293.3 | −1.69035 | ||||||||
\(999\) | −12848.3 | −0.406908 |
(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.1.50 | yes | 50 | |
43.42 | odd | 2 | 1849.4.a.i.1.1 | ✓ | 50 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1849.4.a.i.1.1 | ✓ | 50 | 43.42 | odd | 2 | ||
1849.4.a.j.1.50 | yes | 50 | 1.1 | even | 1 | trivial |