Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [289,4,Mod(1,289)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(289, 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("289.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 289 = 17^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 289.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: | \(17.0515519917\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 72 x^{10} - 17 x^{9} + 1872 x^{8} + 627 x^{7} - 20922 x^{6} - 5163 x^{5} + 93255 x^{4} - 4607 x^{3} - 117822 x^{2} + 21960 x + 29352 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{3}\cdot 17^{2} \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.8 | ||
Root | \(-1.26162\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 289.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.26162 | 0.446051 | 0.223026 | − | 0.974813i | \(-0.428407\pi\) | ||||
0.223026 | + | 0.974813i | \(0.428407\pi\) | |||||||
\(3\) | −6.09538 | −1.17306 | −0.586528 | − | 0.809929i | \(-0.699506\pi\) | ||||
−0.586528 | + | 0.809929i | \(0.699506\pi\) | |||||||
\(4\) | −6.40830 | −0.801038 | ||||||||
\(5\) | 13.2627 | 1.18625 | 0.593124 | − | 0.805111i | \(-0.297894\pi\) | ||||
0.593124 | + | 0.805111i | \(0.297894\pi\) | |||||||
\(6\) | −7.69007 | −0.523243 | ||||||||
\(7\) | −27.2593 | −1.47186 | −0.735932 | − | 0.677055i | \(-0.763256\pi\) | ||||
−0.735932 | + | 0.677055i | \(0.763256\pi\) | |||||||
\(8\) | −18.1779 | −0.803356 | ||||||||
\(9\) | 10.1536 | 0.376059 | ||||||||
\(10\) | 16.7325 | 0.529128 | ||||||||
\(11\) | 45.5149 | 1.24757 | 0.623785 | − | 0.781596i | \(-0.285594\pi\) | ||||
0.623785 | + | 0.781596i | \(0.285594\pi\) | |||||||
\(12\) | 39.0610 | 0.939662 | ||||||||
\(13\) | −52.5379 | −1.12088 | −0.560438 | − | 0.828196i | \(-0.689367\pi\) | ||||
−0.560438 | + | 0.828196i | \(0.689367\pi\) | |||||||
\(14\) | −34.3910 | −0.656527 | ||||||||
\(15\) | −80.8409 | −1.39153 | ||||||||
\(16\) | 28.3328 | 0.442700 | ||||||||
\(17\) | 0 | 0 | ||||||||
\(18\) | 12.8100 | 0.167742 | ||||||||
\(19\) | 3.08418 | 0.0372400 | 0.0186200 | − | 0.999827i | \(-0.494073\pi\) | ||||
0.0186200 | + | 0.999827i | \(0.494073\pi\) | |||||||
\(20\) | −84.9911 | −0.950230 | ||||||||
\(21\) | 166.156 | 1.72658 | ||||||||
\(22\) | 57.4227 | 0.556480 | ||||||||
\(23\) | 112.369 | 1.01872 | 0.509359 | − | 0.860554i | \(-0.329882\pi\) | ||||
0.509359 | + | 0.860554i | \(0.329882\pi\) | |||||||
\(24\) | 110.801 | 0.942381 | ||||||||
\(25\) | 50.8981 | 0.407185 | ||||||||
\(26\) | −66.2831 | −0.499968 | ||||||||
\(27\) | 102.685 | 0.731917 | ||||||||
\(28\) | 174.686 | 1.17902 | ||||||||
\(29\) | −18.6294 | −0.119290 | −0.0596448 | − | 0.998220i | \(-0.518997\pi\) | ||||
−0.0596448 | + | 0.998220i | \(0.518997\pi\) | |||||||
\(30\) | −101.991 | −0.620696 | ||||||||
\(31\) | 238.763 | 1.38333 | 0.691664 | − | 0.722219i | \(-0.256878\pi\) | ||||
0.691664 | + | 0.722219i | \(0.256878\pi\) | |||||||
\(32\) | 181.168 | 1.00082 | ||||||||
\(33\) | −277.430 | −1.46347 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −361.531 | −1.74600 | ||||||||
\(36\) | −65.0674 | −0.301238 | ||||||||
\(37\) | −162.717 | −0.722986 | −0.361493 | − | 0.932375i | \(-0.617733\pi\) | ||||
−0.361493 | + | 0.932375i | \(0.617733\pi\) | |||||||
\(38\) | 3.89108 | 0.0166110 | ||||||||
\(39\) | 320.238 | 1.31485 | ||||||||
\(40\) | −241.087 | −0.952979 | ||||||||
\(41\) | 383.816 | 1.46200 | 0.730999 | − | 0.682378i | \(-0.239054\pi\) | ||||
0.730999 | + | 0.682378i | \(0.239054\pi\) | |||||||
\(42\) | 209.626 | 0.770143 | ||||||||
\(43\) | 468.761 | 1.66245 | 0.831226 | − | 0.555935i | \(-0.187640\pi\) | ||||
0.831226 | + | 0.555935i | \(0.187640\pi\) | |||||||
\(44\) | −291.673 | −0.999350 | ||||||||
\(45\) | 134.664 | 0.446100 | ||||||||
\(46\) | 141.767 | 0.454401 | ||||||||
\(47\) | −199.727 | −0.619856 | −0.309928 | − | 0.950760i | \(-0.600305\pi\) | ||||
−0.309928 | + | 0.950760i | \(0.600305\pi\) | |||||||
\(48\) | −172.699 | −0.519312 | ||||||||
\(49\) | 400.071 | 1.16639 | ||||||||
\(50\) | 64.2142 | 0.181625 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 336.679 | 0.897864 | ||||||||
\(53\) | −105.679 | −0.273889 | −0.136944 | − | 0.990579i | \(-0.543728\pi\) | ||||
−0.136944 | + | 0.990579i | \(0.543728\pi\) | |||||||
\(54\) | 129.550 | 0.326473 | ||||||||
\(55\) | 603.649 | 1.47993 | ||||||||
\(56\) | 495.516 | 1.18243 | ||||||||
\(57\) | −18.7993 | −0.0436846 | ||||||||
\(58\) | −23.5033 | −0.0532093 | ||||||||
\(59\) | 207.142 | 0.457078 | 0.228539 | − | 0.973535i | \(-0.426605\pi\) | ||||
0.228539 | + | 0.973535i | \(0.426605\pi\) | |||||||
\(60\) | 518.053 | 1.11467 | ||||||||
\(61\) | 586.101 | 1.23021 | 0.615103 | − | 0.788447i | \(-0.289114\pi\) | ||||
0.615103 | + | 0.788447i | \(0.289114\pi\) | |||||||
\(62\) | 301.230 | 0.617036 | ||||||||
\(63\) | −276.780 | −0.553508 | ||||||||
\(64\) | 1.90375 | 0.00371826 | ||||||||
\(65\) | −696.792 | −1.32964 | ||||||||
\(66\) | −350.013 | −0.652782 | ||||||||
\(67\) | 401.953 | 0.732931 | 0.366466 | − | 0.930432i | \(-0.380568\pi\) | ||||
0.366466 | + | 0.930432i | \(0.380568\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −684.930 | −1.19501 | ||||||||
\(70\) | −456.116 | −0.778805 | ||||||||
\(71\) | −481.559 | −0.804937 | −0.402468 | − | 0.915434i | \(-0.631848\pi\) | ||||
−0.402468 | + | 0.915434i | \(0.631848\pi\) | |||||||
\(72\) | −184.571 | −0.302109 | ||||||||
\(73\) | −725.281 | −1.16285 | −0.581423 | − | 0.813602i | \(-0.697504\pi\) | ||||
−0.581423 | + | 0.813602i | \(0.697504\pi\) | |||||||
\(74\) | −205.287 | −0.322489 | ||||||||
\(75\) | −310.243 | −0.477650 | ||||||||
\(76\) | −19.7644 | −0.0298307 | ||||||||
\(77\) | −1240.71 | −1.83625 | ||||||||
\(78\) | 404.020 | 0.586491 | ||||||||
\(79\) | −382.621 | −0.544914 | −0.272457 | − | 0.962168i | \(-0.587836\pi\) | ||||
−0.272457 | + | 0.962168i | \(0.587836\pi\) | |||||||
\(80\) | 375.768 | 0.525152 | ||||||||
\(81\) | −900.052 | −1.23464 | ||||||||
\(82\) | 484.231 | 0.652127 | ||||||||
\(83\) | −182.391 | −0.241204 | −0.120602 | − | 0.992701i | \(-0.538483\pi\) | ||||
−0.120602 | + | 0.992701i | \(0.538483\pi\) | |||||||
\(84\) | −1064.78 | −1.38306 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 591.401 | 0.741539 | ||||||||
\(87\) | 113.553 | 0.139933 | ||||||||
\(88\) | −827.364 | −1.00224 | ||||||||
\(89\) | −623.009 | −0.742010 | −0.371005 | − | 0.928631i | \(-0.620987\pi\) | ||||
−0.371005 | + | 0.928631i | \(0.620987\pi\) | |||||||
\(90\) | 169.895 | 0.198983 | ||||||||
\(91\) | 1432.15 | 1.64978 | ||||||||
\(92\) | −720.094 | −0.816032 | ||||||||
\(93\) | −1455.35 | −1.62272 | ||||||||
\(94\) | −251.981 | −0.276488 | ||||||||
\(95\) | 40.9045 | 0.0441759 | ||||||||
\(96\) | −1104.29 | −1.17402 | ||||||||
\(97\) | −369.544 | −0.386820 | −0.193410 | − | 0.981118i | \(-0.561955\pi\) | ||||
−0.193410 | + | 0.981118i | \(0.561955\pi\) | |||||||
\(98\) | 504.739 | 0.520268 | ||||||||
\(99\) | 462.140 | 0.469160 | ||||||||
\(100\) | −326.170 | −0.326170 | ||||||||
\(101\) | 810.381 | 0.798375 | 0.399188 | − | 0.916869i | \(-0.369292\pi\) | ||||
0.399188 | + | 0.916869i | \(0.369292\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 772.683 | 0.739172 | 0.369586 | − | 0.929197i | \(-0.379500\pi\) | ||||
0.369586 | + | 0.929197i | \(0.379500\pi\) | |||||||
\(104\) | 955.026 | 0.900462 | ||||||||
\(105\) | 2203.67 | 2.04815 | ||||||||
\(106\) | −133.327 | −0.122169 | ||||||||
\(107\) | −996.966 | −0.900751 | −0.450375 | − | 0.892839i | \(-0.648710\pi\) | ||||
−0.450375 | + | 0.892839i | \(0.648710\pi\) | |||||||
\(108\) | −658.038 | −0.586293 | ||||||||
\(109\) | 700.996 | 0.615993 | 0.307996 | − | 0.951388i | \(-0.400342\pi\) | ||||
0.307996 | + | 0.951388i | \(0.400342\pi\) | |||||||
\(110\) | 761.578 | 0.660123 | ||||||||
\(111\) | 991.820 | 0.848102 | ||||||||
\(112\) | −772.333 | −0.651595 | ||||||||
\(113\) | 1459.26 | 1.21483 | 0.607415 | − | 0.794384i | \(-0.292206\pi\) | ||||
0.607415 | + | 0.794384i | \(0.292206\pi\) | |||||||
\(114\) | −23.7176 | −0.0194856 | ||||||||
\(115\) | 1490.31 | 1.20845 | ||||||||
\(116\) | 119.383 | 0.0955554 | ||||||||
\(117\) | −533.449 | −0.421516 | ||||||||
\(118\) | 261.335 | 0.203880 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 1469.51 | 1.11790 | ||||||||
\(121\) | 740.607 | 0.556429 | ||||||||
\(122\) | 739.439 | 0.548735 | ||||||||
\(123\) | −2339.50 | −1.71501 | ||||||||
\(124\) | −1530.07 | −1.10810 | ||||||||
\(125\) | −982.788 | −0.703226 | ||||||||
\(126\) | −349.193 | −0.246893 | ||||||||
\(127\) | 426.418 | 0.297941 | 0.148970 | − | 0.988842i | \(-0.452404\pi\) | ||||
0.148970 | + | 0.988842i | \(0.452404\pi\) | |||||||
\(128\) | −1446.94 | −0.999164 | ||||||||
\(129\) | −2857.28 | −1.95015 | ||||||||
\(130\) | −879.089 | −0.593086 | ||||||||
\(131\) | −19.9037 | −0.0132747 | −0.00663737 | − | 0.999978i | \(-0.502113\pi\) | ||||
−0.00663737 | + | 0.999978i | \(0.502113\pi\) | |||||||
\(132\) | 1777.86 | 1.17229 | ||||||||
\(133\) | −84.0728 | −0.0548123 | ||||||||
\(134\) | 507.114 | 0.326925 | ||||||||
\(135\) | 1361.88 | 0.868235 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −1824.89 | −1.13804 | −0.569019 | − | 0.822324i | \(-0.692677\pi\) | ||||
−0.569019 | + | 0.822324i | \(0.692677\pi\) | |||||||
\(138\) | −864.125 | −0.533037 | ||||||||
\(139\) | 1803.87 | 1.10074 | 0.550368 | − | 0.834922i | \(-0.314488\pi\) | ||||
0.550368 | + | 0.834922i | \(0.314488\pi\) | |||||||
\(140\) | 2316.80 | 1.39861 | ||||||||
\(141\) | 1217.41 | 0.727126 | ||||||||
\(142\) | −607.546 | −0.359043 | ||||||||
\(143\) | −2391.26 | −1.39837 | ||||||||
\(144\) | 287.680 | 0.166482 | ||||||||
\(145\) | −247.076 | −0.141507 | ||||||||
\(146\) | −915.032 | −0.518689 | ||||||||
\(147\) | −2438.58 | −1.36824 | ||||||||
\(148\) | 1042.74 | 0.579139 | ||||||||
\(149\) | 2742.46 | 1.50786 | 0.753929 | − | 0.656955i | \(-0.228156\pi\) | ||||
0.753929 | + | 0.656955i | \(0.228156\pi\) | |||||||
\(150\) | −391.410 | −0.213057 | ||||||||
\(151\) | 2085.22 | 1.12379 | 0.561896 | − | 0.827208i | \(-0.310072\pi\) | ||||
0.561896 | + | 0.827208i | \(0.310072\pi\) | |||||||
\(152\) | −56.0639 | −0.0299170 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −1565.30 | −0.819063 | ||||||||
\(155\) | 3166.64 | 1.64097 | ||||||||
\(156\) | −2052.18 | −1.05324 | ||||||||
\(157\) | −2703.53 | −1.37430 | −0.687149 | − | 0.726516i | \(-0.741138\pi\) | ||||
−0.687149 | + | 0.726516i | \(0.741138\pi\) | |||||||
\(158\) | −482.724 | −0.243060 | ||||||||
\(159\) | 644.152 | 0.321287 | ||||||||
\(160\) | 2402.77 | 1.18722 | ||||||||
\(161\) | −3063.10 | −1.49942 | ||||||||
\(162\) | −1135.53 | −0.550712 | ||||||||
\(163\) | 2923.57 | 1.40486 | 0.702428 | − | 0.711755i | \(-0.252099\pi\) | ||||
0.702428 | + | 0.711755i | \(0.252099\pi\) | |||||||
\(164\) | −2459.61 | −1.17112 | ||||||||
\(165\) | −3679.46 | −1.73604 | ||||||||
\(166\) | −230.108 | −0.107590 | ||||||||
\(167\) | 2419.31 | 1.12103 | 0.560514 | − | 0.828145i | \(-0.310603\pi\) | ||||
0.560514 | + | 0.828145i | \(0.310603\pi\) | |||||||
\(168\) | −3020.36 | −1.38706 | ||||||||
\(169\) | 563.229 | 0.256363 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 31.3156 | 0.0140045 | ||||||||
\(172\) | −3003.97 | −1.33169 | ||||||||
\(173\) | 393.655 | 0.173000 | 0.0865000 | − | 0.996252i | \(-0.472432\pi\) | ||||
0.0865000 | + | 0.996252i | \(0.472432\pi\) | |||||||
\(174\) | 143.262 | 0.0624174 | ||||||||
\(175\) | −1387.45 | −0.599321 | ||||||||
\(176\) | 1289.57 | 0.552299 | ||||||||
\(177\) | −1262.61 | −0.536178 | ||||||||
\(178\) | −786.004 | −0.330975 | ||||||||
\(179\) | 1918.60 | 0.801133 | 0.400567 | − | 0.916268i | \(-0.368813\pi\) | ||||
0.400567 | + | 0.916268i | \(0.368813\pi\) | |||||||
\(180\) | −862.966 | −0.357343 | ||||||||
\(181\) | 1677.03 | 0.688688 | 0.344344 | − | 0.938844i | \(-0.388101\pi\) | ||||
0.344344 | + | 0.938844i | \(0.388101\pi\) | |||||||
\(182\) | 1806.83 | 0.735886 | ||||||||
\(183\) | −3572.51 | −1.44310 | ||||||||
\(184\) | −2042.63 | −0.818393 | ||||||||
\(185\) | −2158.06 | −0.857640 | ||||||||
\(186\) | −1836.11 | −0.723817 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 1279.91 | 0.496529 | ||||||||
\(189\) | −2799.13 | −1.07728 | ||||||||
\(190\) | 51.6061 | 0.0197047 | ||||||||
\(191\) | 2347.19 | 0.889196 | 0.444598 | − | 0.895730i | \(-0.353347\pi\) | ||||
0.444598 | + | 0.895730i | \(0.353347\pi\) | |||||||
\(192\) | −11.6041 | −0.00436173 | ||||||||
\(193\) | −650.982 | −0.242791 | −0.121396 | − | 0.992604i | \(-0.538737\pi\) | ||||
−0.121396 | + | 0.992604i | \(0.538737\pi\) | |||||||
\(194\) | −466.226 | −0.172542 | ||||||||
\(195\) | 4247.21 | 1.55974 | ||||||||
\(196\) | −2563.77 | −0.934320 | ||||||||
\(197\) | 2681.01 | 0.969614 | 0.484807 | − | 0.874621i | \(-0.338890\pi\) | ||||
0.484807 | + | 0.874621i | \(0.338890\pi\) | |||||||
\(198\) | 583.047 | 0.209269 | ||||||||
\(199\) | 1784.74 | 0.635762 | 0.317881 | − | 0.948131i | \(-0.397029\pi\) | ||||
0.317881 | + | 0.948131i | \(0.397029\pi\) | |||||||
\(200\) | −925.218 | −0.327114 | ||||||||
\(201\) | −2450.06 | −0.859769 | ||||||||
\(202\) | 1022.40 | 0.356116 | ||||||||
\(203\) | 507.825 | 0.175578 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 5090.42 | 1.73429 | ||||||||
\(206\) | 974.835 | 0.329709 | ||||||||
\(207\) | 1140.95 | 0.383099 | ||||||||
\(208\) | −1488.55 | −0.496212 | ||||||||
\(209\) | 140.376 | 0.0464595 | ||||||||
\(210\) | 2780.20 | 0.913581 | ||||||||
\(211\) | −68.5651 | −0.0223707 | −0.0111853 | − | 0.999937i | \(-0.503560\pi\) | ||||
−0.0111853 | + | 0.999937i | \(0.503560\pi\) | |||||||
\(212\) | 677.222 | 0.219395 | ||||||||
\(213\) | 2935.28 | 0.944235 | ||||||||
\(214\) | −1257.80 | −0.401781 | ||||||||
\(215\) | 6217.02 | 1.97208 | ||||||||
\(216\) | −1866.60 | −0.587990 | ||||||||
\(217\) | −6508.53 | −2.03607 | ||||||||
\(218\) | 884.393 | 0.274765 | ||||||||
\(219\) | 4420.86 | 1.36408 | ||||||||
\(220\) | −3868.36 | −1.18548 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 1251.30 | 0.378297 | ||||||||
\(223\) | 4734.22 | 1.42164 | 0.710822 | − | 0.703372i | \(-0.248323\pi\) | ||||
0.710822 | + | 0.703372i | \(0.248323\pi\) | |||||||
\(224\) | −4938.52 | −1.47308 | ||||||||
\(225\) | 516.799 | 0.153126 | ||||||||
\(226\) | 1841.04 | 0.541877 | ||||||||
\(227\) | −1722.86 | −0.503745 | −0.251873 | − | 0.967760i | \(-0.581046\pi\) | ||||
−0.251873 | + | 0.967760i | \(0.581046\pi\) | |||||||
\(228\) | 120.471 | 0.0349930 | ||||||||
\(229\) | −313.375 | −0.0904297 | −0.0452149 | − | 0.998977i | \(-0.514397\pi\) | ||||
−0.0452149 | + | 0.998977i | \(0.514397\pi\) | |||||||
\(230\) | 1880.21 | 0.539032 | ||||||||
\(231\) | 7562.57 | 2.15403 | ||||||||
\(232\) | 338.643 | 0.0958319 | ||||||||
\(233\) | 2101.61 | 0.590905 | 0.295453 | − | 0.955357i | \(-0.404530\pi\) | ||||
0.295453 | + | 0.955357i | \(0.404530\pi\) | |||||||
\(234\) | −673.012 | −0.188018 | ||||||||
\(235\) | −2648.92 | −0.735303 | ||||||||
\(236\) | −1327.43 | −0.366137 | ||||||||
\(237\) | 2332.22 | 0.639215 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −5525.44 | −1.49544 | −0.747721 | − | 0.664013i | \(-0.768852\pi\) | ||||
−0.747721 | + | 0.664013i | \(0.768852\pi\) | |||||||
\(240\) | −2290.45 | −0.616033 | ||||||||
\(241\) | −2005.92 | −0.536153 | −0.268076 | − | 0.963398i | \(-0.586388\pi\) | ||||
−0.268076 | + | 0.963398i | \(0.586388\pi\) | |||||||
\(242\) | 934.367 | 0.248196 | ||||||||
\(243\) | 2713.65 | 0.716383 | ||||||||
\(244\) | −3755.91 | −0.985442 | ||||||||
\(245\) | 5306.00 | 1.38362 | ||||||||
\(246\) | −2951.57 | −0.764981 | ||||||||
\(247\) | −162.037 | −0.0417414 | ||||||||
\(248\) | −4340.21 | −1.11130 | ||||||||
\(249\) | 1111.74 | 0.282946 | ||||||||
\(250\) | −1239.91 | −0.313675 | ||||||||
\(251\) | 4427.81 | 1.11347 | 0.556735 | − | 0.830690i | \(-0.312054\pi\) | ||||
0.556735 | + | 0.830690i | \(0.312054\pi\) | |||||||
\(252\) | 1773.69 | 0.443381 | ||||||||
\(253\) | 5114.46 | 1.27092 | ||||||||
\(254\) | 537.979 | 0.132897 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −1840.73 | −0.449397 | ||||||||
\(257\) | −6198.01 | −1.50436 | −0.752182 | − | 0.658956i | \(-0.770998\pi\) | ||||
−0.752182 | + | 0.658956i | \(0.770998\pi\) | |||||||
\(258\) | −3604.81 | −0.869867 | ||||||||
\(259\) | 4435.55 | 1.06414 | ||||||||
\(260\) | 4465.26 | 1.06509 | ||||||||
\(261\) | −189.156 | −0.0448599 | ||||||||
\(262\) | −25.1109 | −0.00592122 | ||||||||
\(263\) | 477.072 | 0.111854 | 0.0559269 | − | 0.998435i | \(-0.482189\pi\) | ||||
0.0559269 | + | 0.998435i | \(0.482189\pi\) | |||||||
\(264\) | 5043.09 | 1.17569 | ||||||||
\(265\) | −1401.58 | −0.324900 | ||||||||
\(266\) | −106.068 | −0.0244491 | ||||||||
\(267\) | 3797.48 | 0.870419 | ||||||||
\(268\) | −2575.84 | −0.587106 | ||||||||
\(269\) | 7583.93 | 1.71896 | 0.859481 | − | 0.511168i | \(-0.170787\pi\) | ||||
0.859481 | + | 0.511168i | \(0.170787\pi\) | |||||||
\(270\) | 1718.18 | 0.387278 | ||||||||
\(271\) | −5431.92 | −1.21759 | −0.608793 | − | 0.793329i | \(-0.708346\pi\) | ||||
−0.608793 | + | 0.793329i | \(0.708346\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −8729.47 | −1.93528 | ||||||||
\(274\) | −2302.33 | −0.507624 | ||||||||
\(275\) | 2316.62 | 0.507991 | ||||||||
\(276\) | 4389.24 | 0.957251 | ||||||||
\(277\) | 4091.98 | 0.887594 | 0.443797 | − | 0.896127i | \(-0.353631\pi\) | ||||
0.443797 | + | 0.896127i | \(0.353631\pi\) | |||||||
\(278\) | 2275.81 | 0.490985 | ||||||||
\(279\) | 2424.31 | 0.520213 | ||||||||
\(280\) | 6571.86 | 1.40266 | ||||||||
\(281\) | −3410.26 | −0.723983 | −0.361991 | − | 0.932181i | \(-0.617903\pi\) | ||||
−0.361991 | + | 0.932181i | \(0.617903\pi\) | |||||||
\(282\) | 1535.92 | 0.324336 | ||||||||
\(283\) | −4322.86 | −0.908011 | −0.454006 | − | 0.890999i | \(-0.650005\pi\) | ||||
−0.454006 | + | 0.890999i | \(0.650005\pi\) | |||||||
\(284\) | 3085.97 | 0.644785 | ||||||||
\(285\) | −249.328 | −0.0518208 | ||||||||
\(286\) | −3016.87 | −0.623745 | ||||||||
\(287\) | −10462.6 | −2.15186 | ||||||||
\(288\) | 1839.51 | 0.376369 | ||||||||
\(289\) | 0 | 0 | ||||||||
\(290\) | −311.716 | −0.0631194 | ||||||||
\(291\) | 2252.51 | 0.453761 | ||||||||
\(292\) | 4647.82 | 0.931484 | ||||||||
\(293\) | 3073.56 | 0.612831 | 0.306416 | − | 0.951898i | \(-0.400870\pi\) | ||||
0.306416 | + | 0.951898i | \(0.400870\pi\) | |||||||
\(294\) | −3076.57 | −0.610304 | ||||||||
\(295\) | 2747.26 | 0.542208 | ||||||||
\(296\) | 2957.84 | 0.580815 | ||||||||
\(297\) | 4673.70 | 0.913117 | ||||||||
\(298\) | 3459.95 | 0.672583 | ||||||||
\(299\) | −5903.62 | −1.14186 | ||||||||
\(300\) | 1988.13 | 0.382616 | ||||||||
\(301\) | −12778.1 | −2.44690 | ||||||||
\(302\) | 2630.76 | 0.501269 | ||||||||
\(303\) | −4939.57 | −0.936538 | ||||||||
\(304\) | 87.3836 | 0.0164862 | ||||||||
\(305\) | 7773.26 | 1.45933 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −3954.45 | −0.735154 | −0.367577 | − | 0.929993i | \(-0.619813\pi\) | ||||
−0.367577 | + | 0.929993i | \(0.619813\pi\) | |||||||
\(308\) | 7950.82 | 1.47091 | ||||||||
\(309\) | −4709.79 | −0.867089 | ||||||||
\(310\) | 3995.11 | 0.731957 | ||||||||
\(311\) | 8984.40 | 1.63813 | 0.819065 | − | 0.573701i | \(-0.194493\pi\) | ||||
0.819065 | + | 0.573701i | \(0.194493\pi\) | |||||||
\(312\) | −5821.24 | −1.05629 | ||||||||
\(313\) | 1737.01 | 0.313680 | 0.156840 | − | 0.987624i | \(-0.449869\pi\) | ||||
0.156840 | + | 0.987624i | \(0.449869\pi\) | |||||||
\(314\) | −3410.83 | −0.613008 | ||||||||
\(315\) | −3670.84 | −0.656598 | ||||||||
\(316\) | 2451.95 | 0.436497 | ||||||||
\(317\) | 8232.55 | 1.45863 | 0.729316 | − | 0.684177i | \(-0.239838\pi\) | ||||
0.729316 | + | 0.684177i | \(0.239838\pi\) | |||||||
\(318\) | 812.678 | 0.143310 | ||||||||
\(319\) | −847.916 | −0.148822 | ||||||||
\(320\) | 25.2488 | 0.00441078 | ||||||||
\(321\) | 6076.88 | 1.05663 | ||||||||
\(322\) | −3864.48 | −0.668817 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 5767.81 | 0.988993 | ||||||||
\(325\) | −2674.08 | −0.456403 | ||||||||
\(326\) | 3688.44 | 0.626638 | ||||||||
\(327\) | −4272.83 | −0.722594 | ||||||||
\(328\) | −6976.95 | −1.17451 | ||||||||
\(329\) | 5444.44 | 0.912345 | ||||||||
\(330\) | −4642.10 | −0.774361 | ||||||||
\(331\) | −4153.12 | −0.689655 | −0.344828 | − | 0.938666i | \(-0.612063\pi\) | ||||
−0.344828 | + | 0.938666i | \(0.612063\pi\) | |||||||
\(332\) | 1168.81 | 0.193214 | ||||||||
\(333\) | −1652.16 | −0.271885 | ||||||||
\(334\) | 3052.26 | 0.500037 | ||||||||
\(335\) | 5330.97 | 0.869439 | ||||||||
\(336\) | 4707.66 | 0.764357 | ||||||||
\(337\) | 6569.49 | 1.06191 | 0.530954 | − | 0.847401i | \(-0.321834\pi\) | ||||
0.530954 | + | 0.847401i | \(0.321834\pi\) | |||||||
\(338\) | 710.584 | 0.114351 | ||||||||
\(339\) | −8894.75 | −1.42506 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 10867.3 | 1.72580 | ||||||||
\(342\) | 39.5085 | 0.00624671 | ||||||||
\(343\) | −1555.70 | −0.244898 | ||||||||
\(344\) | −8521.08 | −1.33554 | ||||||||
\(345\) | −9084.00 | −1.41758 | ||||||||
\(346\) | 496.644 | 0.0771669 | ||||||||
\(347\) | −2038.58 | −0.315380 | −0.157690 | − | 0.987489i | \(-0.550405\pi\) | ||||
−0.157690 | + | 0.987489i | \(0.550405\pi\) | |||||||
\(348\) | −727.684 | −0.112092 | ||||||||
\(349\) | −1791.21 | −0.274731 | −0.137365 | − | 0.990520i | \(-0.543863\pi\) | ||||
−0.137365 | + | 0.990520i | \(0.543863\pi\) | |||||||
\(350\) | −1750.44 | −0.267328 | ||||||||
\(351\) | −5394.86 | −0.820388 | ||||||||
\(352\) | 8245.86 | 1.24860 | ||||||||
\(353\) | −5928.71 | −0.893919 | −0.446959 | − | 0.894554i | \(-0.647493\pi\) | ||||
−0.446959 | + | 0.894554i | \(0.647493\pi\) | |||||||
\(354\) | −1592.94 | −0.239163 | ||||||||
\(355\) | −6386.75 | −0.954854 | ||||||||
\(356\) | 3992.43 | 0.594378 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 2420.55 | 0.357347 | ||||||||
\(359\) | 413.998 | 0.0608634 | 0.0304317 | − | 0.999537i | \(-0.490312\pi\) | ||||
0.0304317 | + | 0.999537i | \(0.490312\pi\) | |||||||
\(360\) | −2447.90 | −0.358377 | ||||||||
\(361\) | −6849.49 | −0.998613 | ||||||||
\(362\) | 2115.78 | 0.307190 | ||||||||
\(363\) | −4514.28 | −0.652722 | ||||||||
\(364\) | −9177.63 | −1.32154 | ||||||||
\(365\) | −9619.15 | −1.37942 | ||||||||
\(366\) | −4507.16 | −0.643697 | ||||||||
\(367\) | 6979.15 | 0.992667 | 0.496334 | − | 0.868132i | \(-0.334679\pi\) | ||||
0.496334 | + | 0.868132i | \(0.334679\pi\) | |||||||
\(368\) | 3183.73 | 0.450987 | ||||||||
\(369\) | 3897.11 | 0.549798 | ||||||||
\(370\) | −2722.66 | −0.382552 | ||||||||
\(371\) | 2880.73 | 0.403127 | ||||||||
\(372\) | 9326.34 | 1.29986 | ||||||||
\(373\) | 6855.64 | 0.951667 | 0.475833 | − | 0.879535i | \(-0.342147\pi\) | ||||
0.475833 | + | 0.879535i | \(0.342147\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 5990.46 | 0.824923 | ||||||||
\(376\) | 3630.62 | 0.497965 | ||||||||
\(377\) | 978.750 | 0.133709 | ||||||||
\(378\) | −3531.45 | −0.480524 | ||||||||
\(379\) | −8206.78 | −1.11228 | −0.556140 | − | 0.831089i | \(-0.687718\pi\) | ||||
−0.556140 | + | 0.831089i | \(0.687718\pi\) | |||||||
\(380\) | −262.128 | −0.0353866 | ||||||||
\(381\) | −2599.18 | −0.349501 | ||||||||
\(382\) | 2961.27 | 0.396627 | ||||||||
\(383\) | −889.401 | −0.118659 | −0.0593293 | − | 0.998238i | \(-0.518896\pi\) | ||||
−0.0593293 | + | 0.998238i | \(0.518896\pi\) | |||||||
\(384\) | 8819.67 | 1.17208 | ||||||||
\(385\) | −16455.1 | −2.17825 | ||||||||
\(386\) | −821.294 | −0.108297 | ||||||||
\(387\) | 4759.62 | 0.625180 | ||||||||
\(388\) | 2368.15 | 0.309857 | ||||||||
\(389\) | −12992.8 | −1.69347 | −0.846736 | − | 0.532013i | \(-0.821436\pi\) | ||||
−0.846736 | + | 0.532013i | \(0.821436\pi\) | |||||||
\(390\) | 5358.38 | 0.695723 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | −7272.43 | −0.937023 | ||||||||
\(393\) | 121.320 | 0.0155720 | ||||||||
\(394\) | 3382.42 | 0.432498 | ||||||||
\(395\) | −5074.57 | −0.646403 | ||||||||
\(396\) | −2961.54 | −0.375815 | ||||||||
\(397\) | 4325.29 | 0.546801 | 0.273400 | − | 0.961900i | \(-0.411852\pi\) | ||||
0.273400 | + | 0.961900i | \(0.411852\pi\) | |||||||
\(398\) | 2251.67 | 0.283583 | ||||||||
\(399\) | 512.455 | 0.0642979 | ||||||||
\(400\) | 1442.09 | 0.180261 | ||||||||
\(401\) | −11849.1 | −1.47560 | −0.737798 | − | 0.675022i | \(-0.764134\pi\) | ||||
−0.737798 | + | 0.675022i | \(0.764134\pi\) | |||||||
\(402\) | −3091.05 | −0.383501 | ||||||||
\(403\) | −12544.1 | −1.55054 | ||||||||
\(404\) | −5193.17 | −0.639529 | ||||||||
\(405\) | −11937.1 | −1.46459 | ||||||||
\(406\) | 640.685 | 0.0783168 | ||||||||
\(407\) | −7406.04 | −0.901975 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 7677.24 | 0.928154 | 0.464077 | − | 0.885795i | \(-0.346386\pi\) | ||||
0.464077 | + | 0.885795i | \(0.346386\pi\) | |||||||
\(410\) | 6422.19 | 0.773584 | ||||||||
\(411\) | 11123.4 | 1.33498 | ||||||||
\(412\) | −4951.59 | −0.592105 | ||||||||
\(413\) | −5646.55 | −0.672757 | ||||||||
\(414\) | 1439.45 | 0.170882 | ||||||||
\(415\) | −2418.98 | −0.286128 | ||||||||
\(416\) | −9518.20 | −1.12180 | ||||||||
\(417\) | −10995.3 | −1.29122 | ||||||||
\(418\) | 177.102 | 0.0207233 | ||||||||
\(419\) | −3235.83 | −0.377280 | −0.188640 | − | 0.982046i | \(-0.560408\pi\) | ||||
−0.188640 | + | 0.982046i | \(0.560408\pi\) | |||||||
\(420\) | −14121.8 | −1.64065 | ||||||||
\(421\) | 14496.6 | 1.67820 | 0.839100 | − | 0.543977i | \(-0.183082\pi\) | ||||
0.839100 | + | 0.543977i | \(0.183082\pi\) | |||||||
\(422\) | −86.5033 | −0.00997848 | ||||||||
\(423\) | −2027.95 | −0.233103 | ||||||||
\(424\) | 1921.02 | 0.220030 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 3703.22 | 0.421178 | ||||||||
\(427\) | −15976.7 | −1.81070 | ||||||||
\(428\) | 6388.86 | 0.721536 | ||||||||
\(429\) | 14575.6 | 1.64037 | ||||||||
\(430\) | 7843.54 | 0.879649 | ||||||||
\(431\) | 7136.25 | 0.797543 | 0.398771 | − | 0.917050i | \(-0.369437\pi\) | ||||
0.398771 | + | 0.917050i | \(0.369437\pi\) | |||||||
\(432\) | 2909.36 | 0.324020 | ||||||||
\(433\) | 11434.3 | 1.26904 | 0.634521 | − | 0.772905i | \(-0.281197\pi\) | ||||
0.634521 | + | 0.772905i | \(0.281197\pi\) | |||||||
\(434\) | −8211.32 | −0.908193 | ||||||||
\(435\) | 1506.02 | 0.165996 | ||||||||
\(436\) | −4492.20 | −0.493434 | ||||||||
\(437\) | 346.566 | 0.0379371 | ||||||||
\(438\) | 5577.46 | 0.608451 | ||||||||
\(439\) | −13308.0 | −1.44682 | −0.723412 | − | 0.690417i | \(-0.757427\pi\) | ||||
−0.723412 | + | 0.690417i | \(0.757427\pi\) | |||||||
\(440\) | −10973.0 | −1.18891 | ||||||||
\(441\) | 4062.16 | 0.438630 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −10897.9 | −1.16880 | −0.584398 | − | 0.811467i | \(-0.698669\pi\) | ||||
−0.584398 | + | 0.811467i | \(0.698669\pi\) | |||||||
\(444\) | −6355.88 | −0.679362 | ||||||||
\(445\) | −8262.76 | −0.880208 | ||||||||
\(446\) | 5972.80 | 0.634126 | ||||||||
\(447\) | −16716.3 | −1.76880 | ||||||||
\(448\) | −51.8949 | −0.00547278 | ||||||||
\(449\) | −16756.4 | −1.76121 | −0.880603 | − | 0.473855i | \(-0.842862\pi\) | ||||
−0.880603 | + | 0.473855i | \(0.842862\pi\) | |||||||
\(450\) | 652.006 | 0.0683019 | ||||||||
\(451\) | 17469.3 | 1.82394 | ||||||||
\(452\) | −9351.40 | −0.973126 | ||||||||
\(453\) | −12710.2 | −1.31827 | ||||||||
\(454\) | −2173.60 | −0.224696 | ||||||||
\(455\) | 18994.1 | 1.95705 | ||||||||
\(456\) | 341.730 | 0.0350943 | ||||||||
\(457\) | 13561.8 | 1.38817 | 0.694087 | − | 0.719891i | \(-0.255808\pi\) | ||||
0.694087 | + | 0.719891i | \(0.255808\pi\) | |||||||
\(458\) | −395.361 | −0.0403363 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −9550.36 | −0.968017 | ||||||||
\(461\) | 15516.4 | 1.56762 | 0.783810 | − | 0.621000i | \(-0.213273\pi\) | ||||
0.783810 | + | 0.621000i | \(0.213273\pi\) | |||||||
\(462\) | 9541.11 | 0.960807 | ||||||||
\(463\) | −15186.4 | −1.52435 | −0.762174 | − | 0.647372i | \(-0.775868\pi\) | ||||
−0.762174 | + | 0.647372i | \(0.775868\pi\) | |||||||
\(464\) | −527.824 | −0.0528095 | ||||||||
\(465\) | −19301.8 | −1.92495 | ||||||||
\(466\) | 2651.44 | 0.263574 | ||||||||
\(467\) | 10544.3 | 1.04482 | 0.522412 | − | 0.852693i | \(-0.325032\pi\) | ||||
0.522412 | + | 0.852693i | \(0.325032\pi\) | |||||||
\(468\) | 3418.50 | 0.337650 | ||||||||
\(469\) | −10957.0 | −1.07878 | ||||||||
\(470\) | −3341.94 | −0.327983 | ||||||||
\(471\) | 16479.0 | 1.61213 | ||||||||
\(472\) | −3765.40 | −0.367196 | ||||||||
\(473\) | 21335.6 | 2.07402 | ||||||||
\(474\) | 2942.38 | 0.285123 | ||||||||
\(475\) | 156.979 | 0.0151636 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −1073.02 | −0.102998 | ||||||||
\(478\) | −6971.02 | −0.667044 | ||||||||
\(479\) | −5762.22 | −0.549650 | −0.274825 | − | 0.961494i | \(-0.588620\pi\) | ||||
−0.274825 | + | 0.961494i | \(0.588620\pi\) | |||||||
\(480\) | −14645.8 | −1.39268 | ||||||||
\(481\) | 8548.79 | 0.810377 | ||||||||
\(482\) | −2530.72 | −0.239152 | ||||||||
\(483\) | 18670.7 | 1.75890 | ||||||||
\(484\) | −4746.03 | −0.445721 | ||||||||
\(485\) | −4901.14 | −0.458864 | ||||||||
\(486\) | 3423.61 | 0.319544 | ||||||||
\(487\) | 5369.36 | 0.499608 | 0.249804 | − | 0.968296i | \(-0.419634\pi\) | ||||
0.249804 | + | 0.968296i | \(0.419634\pi\) | |||||||
\(488\) | −10654.1 | −0.988293 | ||||||||
\(489\) | −17820.2 | −1.64797 | ||||||||
\(490\) | 6694.18 | 0.617167 | ||||||||
\(491\) | 17878.0 | 1.64322 | 0.821611 | − | 0.570049i | \(-0.193076\pi\) | ||||
0.821611 | + | 0.570049i | \(0.193076\pi\) | |||||||
\(492\) | 14992.2 | 1.37378 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | −204.429 | −0.0186188 | ||||||||
\(495\) | 6129.21 | 0.556540 | ||||||||
\(496\) | 6764.84 | 0.612400 | ||||||||
\(497\) | 13127.0 | 1.18476 | ||||||||
\(498\) | 1402.60 | 0.126209 | ||||||||
\(499\) | −3507.03 | −0.314622 | −0.157311 | − | 0.987549i | \(-0.550282\pi\) | ||||
−0.157311 | + | 0.987549i | \(0.550282\pi\) | |||||||
\(500\) | 6298.01 | 0.563311 | ||||||||
\(501\) | −14746.6 | −1.31503 | ||||||||
\(502\) | 5586.23 | 0.496665 | ||||||||
\(503\) | 1207.56 | 0.107043 | 0.0535214 | − | 0.998567i | \(-0.482955\pi\) | ||||
0.0535214 | + | 0.998567i | \(0.482955\pi\) | |||||||
\(504\) | 5031.27 | 0.444664 | ||||||||
\(505\) | 10747.8 | 0.947071 | ||||||||
\(506\) | 6452.52 | 0.566897 | ||||||||
\(507\) | −3433.09 | −0.300728 | ||||||||
\(508\) | −2732.62 | −0.238662 | ||||||||
\(509\) | −14092.1 | −1.22716 | −0.613578 | − | 0.789634i | \(-0.710270\pi\) | ||||
−0.613578 | + | 0.789634i | \(0.710270\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 19770.7 | 1.71155 | ||||||||
\(512\) | 9253.25 | 0.798710 | ||||||||
\(513\) | 316.700 | 0.0272566 | ||||||||
\(514\) | −7819.56 | −0.671023 | ||||||||
\(515\) | 10247.8 | 0.876841 | ||||||||
\(516\) | 18310.3 | 1.56214 | ||||||||
\(517\) | −9090.58 | −0.773314 | ||||||||
\(518\) | 5595.99 | 0.474660 | ||||||||
\(519\) | −2399.47 | −0.202939 | ||||||||
\(520\) | 12666.2 | 1.06817 | ||||||||
\(521\) | 10080.1 | 0.847635 | 0.423818 | − | 0.905748i | \(-0.360690\pi\) | ||||
0.423818 | + | 0.905748i | \(0.360690\pi\) | |||||||
\(522\) | −238.643 | −0.0200098 | ||||||||
\(523\) | 12330.2 | 1.03090 | 0.515452 | − | 0.856919i | \(-0.327624\pi\) | ||||
0.515452 | + | 0.856919i | \(0.327624\pi\) | |||||||
\(524\) | 127.549 | 0.0106336 | ||||||||
\(525\) | 8457.01 | 0.703036 | ||||||||
\(526\) | 601.886 | 0.0498925 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | −7860.38 | −0.647877 | ||||||||
\(529\) | 459.760 | 0.0377875 | ||||||||
\(530\) | −1768.27 | −0.144922 | ||||||||
\(531\) | 2103.24 | 0.171888 | ||||||||
\(532\) | 538.764 | 0.0439067 | ||||||||
\(533\) | −20164.9 | −1.63872 | ||||||||
\(534\) | 4790.99 | 0.388252 | ||||||||
\(535\) | −13222.4 | −1.06851 | ||||||||
\(536\) | −7306.65 | −0.588805 | ||||||||
\(537\) | −11694.6 | −0.939774 | ||||||||
\(538\) | 9568.07 | 0.766745 | ||||||||
\(539\) | 18209.2 | 1.45515 | ||||||||
\(540\) | −8727.33 | −0.695490 | ||||||||
\(541\) | −7122.72 | −0.566044 | −0.283022 | − | 0.959113i | \(-0.591337\pi\) | ||||
−0.283022 | + | 0.959113i | \(0.591337\pi\) | |||||||
\(542\) | −6853.04 | −0.543106 | ||||||||
\(543\) | −10222.1 | −0.807869 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 9297.07 | 0.730720 | ||||||||
\(546\) | −11013.3 | −0.863235 | ||||||||
\(547\) | −14919.7 | −1.16622 | −0.583109 | − | 0.812394i | \(-0.698164\pi\) | ||||
−0.583109 | + | 0.812394i | \(0.698164\pi\) | |||||||
\(548\) | 11694.5 | 0.911612 | ||||||||
\(549\) | 5951.04 | 0.462630 | ||||||||
\(550\) | 2922.70 | 0.226590 | ||||||||
\(551\) | −57.4566 | −0.00444234 | ||||||||
\(552\) | 12450.6 | 0.960021 | ||||||||
\(553\) | 10430.0 | 0.802040 | ||||||||
\(554\) | 5162.55 | 0.395913 | ||||||||
\(555\) | 13154.2 | 1.00606 | ||||||||
\(556\) | −11559.7 | −0.881731 | ||||||||
\(557\) | −18935.0 | −1.44039 | −0.720197 | − | 0.693769i | \(-0.755949\pi\) | ||||
−0.720197 | + | 0.693769i | \(0.755949\pi\) | |||||||
\(558\) | 3058.57 | 0.232042 | ||||||||
\(559\) | −24627.7 | −1.86340 | ||||||||
\(560\) | −10243.2 | −0.772953 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −4302.47 | −0.322934 | ||||||||
\(563\) | 8150.42 | 0.610123 | 0.305062 | − | 0.952333i | \(-0.401323\pi\) | ||||
0.305062 | + | 0.952333i | \(0.401323\pi\) | |||||||
\(564\) | −7801.56 | −0.582456 | ||||||||
\(565\) | 19353.7 | 1.44109 | ||||||||
\(566\) | −5453.82 | −0.405020 | ||||||||
\(567\) | 24534.8 | 1.81722 | ||||||||
\(568\) | 8753.71 | 0.646650 | ||||||||
\(569\) | 18218.2 | 1.34226 | 0.671131 | − | 0.741338i | \(-0.265809\pi\) | ||||
0.671131 | + | 0.741338i | \(0.265809\pi\) | |||||||
\(570\) | −314.558 | −0.0231147 | ||||||||
\(571\) | −2443.35 | −0.179073 | −0.0895367 | − | 0.995984i | \(-0.528539\pi\) | ||||
−0.0895367 | + | 0.995984i | \(0.528539\pi\) | |||||||
\(572\) | 15323.9 | 1.12015 | ||||||||
\(573\) | −14307.0 | −1.04308 | ||||||||
\(574\) | −13199.8 | −0.959842 | ||||||||
\(575\) | 5719.36 | 0.414806 | ||||||||
\(576\) | 19.3299 | 0.00139829 | ||||||||
\(577\) | −852.752 | −0.0615261 | −0.0307630 | − | 0.999527i | \(-0.509794\pi\) | ||||
−0.0307630 | + | 0.999527i | \(0.509794\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 3967.98 | 0.284807 | ||||||||
\(580\) | 1583.34 | 0.113352 | ||||||||
\(581\) | 4971.84 | 0.355020 | ||||||||
\(582\) | 2841.82 | 0.202401 | ||||||||
\(583\) | −4809.96 | −0.341695 | ||||||||
\(584\) | 13184.1 | 0.934179 | ||||||||
\(585\) | −7074.95 | −0.500022 | ||||||||
\(586\) | 3877.68 | 0.273354 | ||||||||
\(587\) | 900.272 | 0.0633019 | 0.0316509 | − | 0.999499i | \(-0.489924\pi\) | ||||
0.0316509 | + | 0.999499i | \(0.489924\pi\) | |||||||
\(588\) | 15627.2 | 1.09601 | ||||||||
\(589\) | 736.390 | 0.0515152 | ||||||||
\(590\) | 3466.00 | 0.241853 | ||||||||
\(591\) | −16341.7 | −1.13741 | ||||||||
\(592\) | −4610.22 | −0.320066 | ||||||||
\(593\) | −25007.2 | −1.73174 | −0.865870 | − | 0.500268i | \(-0.833235\pi\) | ||||
−0.865870 | + | 0.500268i | \(0.833235\pi\) | |||||||
\(594\) | 5896.46 | 0.407297 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −17574.5 | −1.20785 | ||||||||
\(597\) | −10878.6 | −0.745784 | ||||||||
\(598\) | −7448.15 | −0.509327 | ||||||||
\(599\) | −3448.82 | −0.235251 | −0.117625 | − | 0.993058i | \(-0.537528\pi\) | ||||
−0.117625 | + | 0.993058i | \(0.537528\pi\) | |||||||
\(600\) | 5639.55 | 0.383723 | ||||||||
\(601\) | −942.873 | −0.0639943 | −0.0319972 | − | 0.999488i | \(-0.510187\pi\) | ||||
−0.0319972 | + | 0.999488i | \(0.510187\pi\) | |||||||
\(602\) | −16121.2 | −1.09145 | ||||||||
\(603\) | 4081.27 | 0.275626 | ||||||||
\(604\) | −13362.7 | −0.900201 | ||||||||
\(605\) | 9822.41 | 0.660063 | ||||||||
\(606\) | −6231.89 | −0.417744 | ||||||||
\(607\) | 10173.9 | 0.680306 | 0.340153 | − | 0.940370i | \(-0.389521\pi\) | ||||
0.340153 | + | 0.940370i | \(0.389521\pi\) | |||||||
\(608\) | 558.756 | 0.0372707 | ||||||||
\(609\) | −3095.39 | −0.205963 | ||||||||
\(610\) | 9806.93 | 0.650936 | ||||||||
\(611\) | 10493.3 | 0.694782 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −17327.0 | −1.14165 | −0.570824 | − | 0.821073i | \(-0.693376\pi\) | ||||
−0.570824 | + | 0.821073i | \(0.693376\pi\) | |||||||
\(614\) | −4989.03 | −0.327916 | ||||||||
\(615\) | −31028.0 | −2.03442 | ||||||||
\(616\) | 22553.4 | 1.47516 | ||||||||
\(617\) | 19782.8 | 1.29080 | 0.645401 | − | 0.763844i | \(-0.276690\pi\) | ||||
0.645401 | + | 0.763844i | \(0.276690\pi\) | |||||||
\(618\) | −5941.98 | −0.386766 | ||||||||
\(619\) | 15033.2 | 0.976147 | 0.488074 | − | 0.872802i | \(-0.337700\pi\) | ||||
0.488074 | + | 0.872802i | \(0.337700\pi\) | |||||||
\(620\) | −20292.8 | −1.31448 | ||||||||
\(621\) | 11538.6 | 0.745618 | ||||||||
\(622\) | 11334.9 | 0.730690 | ||||||||
\(623\) | 16982.8 | 1.09214 | ||||||||
\(624\) | 9073.25 | 0.582084 | ||||||||
\(625\) | −19396.6 | −1.24139 | ||||||||
\(626\) | 2191.46 | 0.139917 | ||||||||
\(627\) | −855.647 | −0.0544996 | ||||||||
\(628\) | 17325.0 | 1.10087 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | −4631.22 | −0.292877 | ||||||||
\(631\) | −24060.5 | −1.51796 | −0.758979 | − | 0.651115i | \(-0.774302\pi\) | ||||
−0.758979 | + | 0.651115i | \(0.774302\pi\) | |||||||
\(632\) | 6955.23 | 0.437760 | ||||||||
\(633\) | 417.930 | 0.0262421 | ||||||||
\(634\) | 10386.4 | 0.650625 | ||||||||
\(635\) | 5655.44 | 0.353432 | ||||||||
\(636\) | −4127.92 | −0.257363 | ||||||||
\(637\) | −21018.9 | −1.30737 | ||||||||
\(638\) | −1069.75 | −0.0663822 | ||||||||
\(639\) | −4889.55 | −0.302704 | ||||||||
\(640\) | −19190.3 | −1.18526 | ||||||||
\(641\) | −4886.07 | −0.301074 | −0.150537 | − | 0.988604i | \(-0.548100\pi\) | ||||
−0.150537 | + | 0.988604i | \(0.548100\pi\) | |||||||
\(642\) | 7666.74 | 0.471312 | ||||||||
\(643\) | −24508.4 | −1.50314 | −0.751568 | − | 0.659655i | \(-0.770702\pi\) | ||||
−0.751568 | + | 0.659655i | \(0.770702\pi\) | |||||||
\(644\) | 19629.3 | 1.20109 | ||||||||
\(645\) | −37895.1 | −2.31336 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 2932.50 | 0.178189 | 0.0890947 | − | 0.996023i | \(-0.471603\pi\) | ||||
0.0890947 | + | 0.996023i | \(0.471603\pi\) | |||||||
\(648\) | 16361.0 | 0.991854 | ||||||||
\(649\) | 9428.06 | 0.570237 | ||||||||
\(650\) | −3373.68 | −0.203579 | ||||||||
\(651\) | 39671.9 | 2.38843 | ||||||||
\(652\) | −18735.1 | −1.12534 | ||||||||
\(653\) | 19977.8 | 1.19723 | 0.598617 | − | 0.801035i | \(-0.295717\pi\) | ||||
0.598617 | + | 0.801035i | \(0.295717\pi\) | |||||||
\(654\) | −5390.71 | −0.322314 | ||||||||
\(655\) | −263.975 | −0.0157471 | ||||||||
\(656\) | 10874.6 | 0.647227 | ||||||||
\(657\) | −7364.21 | −0.437299 | ||||||||
\(658\) | 6868.83 | 0.406953 | ||||||||
\(659\) | 28222.7 | 1.66829 | 0.834143 | − | 0.551548i | \(-0.185963\pi\) | ||||
0.834143 | + | 0.551548i | \(0.185963\pi\) | |||||||
\(660\) | 23579.1 | 1.39063 | ||||||||
\(661\) | 20712.8 | 1.21881 | 0.609405 | − | 0.792859i | \(-0.291408\pi\) | ||||
0.609405 | + | 0.792859i | \(0.291408\pi\) | |||||||
\(662\) | −5239.67 | −0.307622 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 3315.47 | 0.193773 | ||||||||
\(665\) | −1115.03 | −0.0650210 | ||||||||
\(666\) | −2084.41 | −0.121275 | ||||||||
\(667\) | −2093.37 | −0.121522 | ||||||||
\(668\) | −15503.7 | −0.897987 | ||||||||
\(669\) | −28856.8 | −1.66767 | ||||||||
\(670\) | 6725.68 | 0.387814 | ||||||||
\(671\) | 26676.3 | 1.53477 | ||||||||
\(672\) | 30102.2 | 1.72800 | ||||||||
\(673\) | 395.468 | 0.0226511 | 0.0113255 | − | 0.999936i | \(-0.496395\pi\) | ||||
0.0113255 | + | 0.999936i | \(0.496395\pi\) | |||||||
\(674\) | 8288.23 | 0.473666 | ||||||||
\(675\) | 5226.48 | 0.298025 | ||||||||
\(676\) | −3609.34 | −0.205356 | ||||||||
\(677\) | −2297.47 | −0.130427 | −0.0652135 | − | 0.997871i | \(-0.520773\pi\) | ||||
−0.0652135 | + | 0.997871i | \(0.520773\pi\) | |||||||
\(678\) | −11221.8 | −0.635652 | ||||||||
\(679\) | 10073.5 | 0.569347 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 10501.5 | 0.590921 | ||||||||
\(682\) | 13710.4 | 0.769794 | ||||||||
\(683\) | −28611.7 | −1.60292 | −0.801461 | − | 0.598048i | \(-0.795943\pi\) | ||||
−0.801461 | + | 0.598048i | \(0.795943\pi\) | |||||||
\(684\) | −200.680 | −0.0112181 | ||||||||
\(685\) | −24202.9 | −1.35000 | ||||||||
\(686\) | −1962.71 | −0.109237 | ||||||||
\(687\) | 1910.14 | 0.106079 | ||||||||
\(688\) | 13281.3 | 0.735968 | ||||||||
\(689\) | 5552.14 | 0.306995 | ||||||||
\(690\) | −11460.6 | −0.632315 | ||||||||
\(691\) | 4902.87 | 0.269919 | 0.134959 | − | 0.990851i | \(-0.456910\pi\) | ||||
0.134959 | + | 0.990851i | \(0.456910\pi\) | |||||||
\(692\) | −2522.66 | −0.138580 | ||||||||
\(693\) | −12597.6 | −0.690540 | ||||||||
\(694\) | −2571.93 | −0.140676 | ||||||||
\(695\) | 23924.1 | 1.30575 | ||||||||
\(696\) | −2064.16 | −0.112416 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | −2259.83 | −0.122544 | ||||||||
\(699\) | −12810.1 | −0.693165 | ||||||||
\(700\) | 8891.18 | 0.480079 | ||||||||
\(701\) | 1714.99 | 0.0924027 | 0.0462014 | − | 0.998932i | \(-0.485288\pi\) | ||||
0.0462014 | + | 0.998932i | \(0.485288\pi\) | |||||||
\(702\) | −6806.28 | −0.365935 | ||||||||
\(703\) | −501.849 | −0.0269240 | ||||||||
\(704\) | 86.6490 | 0.00463879 | ||||||||
\(705\) | 16146.1 | 0.862552 | ||||||||
\(706\) | −7479.80 | −0.398734 | ||||||||
\(707\) | −22090.4 | −1.17510 | ||||||||
\(708\) | 8091.18 | 0.429499 | ||||||||
\(709\) | −13939.8 | −0.738393 | −0.369196 | − | 0.929351i | \(-0.620367\pi\) | ||||
−0.369196 | + | 0.929351i | \(0.620367\pi\) | |||||||
\(710\) | −8057.67 | −0.425914 | ||||||||
\(711\) | −3884.98 | −0.204920 | ||||||||
\(712\) | 11325.0 | 0.596098 | ||||||||
\(713\) | 26829.6 | 1.40922 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −31714.4 | −1.65881 | ||||||||
\(716\) | −12295.0 | −0.641738 | ||||||||
\(717\) | 33679.6 | 1.75424 | ||||||||
\(718\) | 522.310 | 0.0271482 | ||||||||
\(719\) | −1779.18 | −0.0922839 | −0.0461419 | − | 0.998935i | \(-0.514693\pi\) | ||||
−0.0461419 | + | 0.998935i | \(0.514693\pi\) | |||||||
\(720\) | 3815.40 | 0.197488 | ||||||||
\(721\) | −21062.8 | −1.08796 | ||||||||
\(722\) | −8641.48 | −0.445433 | ||||||||
\(723\) | 12226.9 | 0.628937 | ||||||||
\(724\) | −10746.9 | −0.551665 | ||||||||
\(725\) | −948.201 | −0.0485729 | ||||||||
\(726\) | −5695.32 | −0.291148 | ||||||||
\(727\) | 9141.02 | 0.466330 | 0.233165 | − | 0.972437i | \(-0.425092\pi\) | ||||
0.233165 | + | 0.972437i | \(0.425092\pi\) | |||||||
\(728\) | −26033.4 | −1.32536 | ||||||||
\(729\) | 7760.65 | 0.394282 | ||||||||
\(730\) | −12135.8 | −0.615294 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 22893.7 | 1.15598 | ||||||||
\(733\) | 12176.0 | 0.613547 | 0.306773 | − | 0.951783i | \(-0.400751\pi\) | ||||
0.306773 | + | 0.951783i | \(0.400751\pi\) | |||||||
\(734\) | 8805.07 | 0.442781 | ||||||||
\(735\) | −32342.1 | −1.62307 | ||||||||
\(736\) | 20357.7 | 1.01956 | ||||||||
\(737\) | 18294.9 | 0.914383 | ||||||||
\(738\) | 4916.69 | 0.245238 | ||||||||
\(739\) | 25025.4 | 1.24570 | 0.622852 | − | 0.782339i | \(-0.285974\pi\) | ||||
0.622852 | + | 0.782339i | \(0.285974\pi\) | |||||||
\(740\) | 13829.5 | 0.687003 | ||||||||
\(741\) | 987.673 | 0.0489650 | ||||||||
\(742\) | 3634.40 | 0.179816 | ||||||||
\(743\) | −10781.3 | −0.532339 | −0.266170 | − | 0.963926i | \(-0.585758\pi\) | ||||
−0.266170 | + | 0.963926i | \(0.585758\pi\) | |||||||
\(744\) | 26455.2 | 1.30362 | ||||||||
\(745\) | 36372.3 | 1.78869 | ||||||||
\(746\) | 8649.24 | 0.424492 | ||||||||
\(747\) | −1851.92 | −0.0907072 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 27176.6 | 1.32578 | ||||||||
\(750\) | 7557.71 | 0.367958 | ||||||||
\(751\) | 33910.7 | 1.64769 | 0.823847 | − | 0.566812i | \(-0.191823\pi\) | ||||
0.823847 | + | 0.566812i | \(0.191823\pi\) | |||||||
\(752\) | −5658.84 | −0.274410 | ||||||||
\(753\) | −26989.2 | −1.30616 | ||||||||
\(754\) | 1234.81 | 0.0596410 | ||||||||
\(755\) | 27655.5 | 1.33310 | ||||||||
\(756\) | 17937.7 | 0.862945 | ||||||||
\(757\) | −31545.0 | −1.51456 | −0.757281 | − | 0.653090i | \(-0.773472\pi\) | ||||
−0.757281 | + | 0.653090i | \(0.773472\pi\) | |||||||
\(758\) | −10353.9 | −0.496134 | ||||||||
\(759\) | −31174.5 | −1.49086 | ||||||||
\(760\) | −743.556 | −0.0354890 | ||||||||
\(761\) | 9150.51 | 0.435881 | 0.217941 | − | 0.975962i | \(-0.430066\pi\) | ||||
0.217941 | + | 0.975962i | \(0.430066\pi\) | |||||||
\(762\) | −3279.19 | −0.155895 | ||||||||
\(763\) | −19108.7 | −0.906658 | ||||||||
\(764\) | −15041.5 | −0.712280 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −1122.09 | −0.0529279 | ||||||||
\(767\) | −10882.8 | −0.512328 | ||||||||
\(768\) | 11219.9 | 0.527168 | ||||||||
\(769\) | 33797.5 | 1.58488 | 0.792438 | − | 0.609952i | \(-0.208811\pi\) | ||||
0.792438 | + | 0.609952i | \(0.208811\pi\) | |||||||
\(770\) | −20760.1 | −0.971612 | ||||||||
\(771\) | 37779.2 | 1.76470 | ||||||||
\(772\) | 4171.69 | 0.194485 | ||||||||
\(773\) | −33969.4 | −1.58059 | −0.790295 | − | 0.612727i | \(-0.790073\pi\) | ||||
−0.790295 | + | 0.612727i | \(0.790073\pi\) | |||||||
\(774\) | 6004.85 | 0.278863 | ||||||||
\(775\) | 12152.6 | 0.563270 | ||||||||
\(776\) | 6717.52 | 0.310754 | ||||||||
\(777\) | −27036.3 | −1.24829 | ||||||||
\(778\) | −16392.0 | −0.755376 | ||||||||
\(779\) | 1183.76 | 0.0544449 | ||||||||
\(780\) | −27217.4 | −1.24941 | ||||||||
\(781\) | −21918.1 | −1.00421 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −1912.96 | −0.0873100 | ||||||||
\(784\) | 11335.1 | 0.516359 | ||||||||
\(785\) | −35856.0 | −1.63026 | ||||||||
\(786\) | 153.061 | 0.00694592 | ||||||||
\(787\) | −10962.7 | −0.496543 | −0.248271 | − | 0.968691i | \(-0.579862\pi\) | ||||
−0.248271 | + | 0.968691i | \(0.579862\pi\) | |||||||
\(788\) | −17180.7 | −0.776698 | ||||||||
\(789\) | −2907.93 | −0.131211 | ||||||||
\(790\) | −6402.20 | −0.288329 | ||||||||
\(791\) | −39778.5 | −1.78807 | ||||||||
\(792\) | −8400.72 | −0.376902 | ||||||||
\(793\) | −30792.5 | −1.37891 | ||||||||
\(794\) | 5456.89 | 0.243901 | ||||||||
\(795\) | 8543.17 | 0.381126 | ||||||||
\(796\) | −11437.1 | −0.509270 | ||||||||
\(797\) | −8041.29 | −0.357386 | −0.178693 | − | 0.983905i | \(-0.557187\pi\) | ||||
−0.178693 | + | 0.983905i | \(0.557187\pi\) | |||||||
\(798\) | 646.526 | 0.0286802 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 9221.12 | 0.407520 | ||||||||
\(801\) | −6325.79 | −0.279040 | ||||||||
\(802\) | −14949.1 | −0.658192 | ||||||||
\(803\) | −33011.1 | −1.45073 | ||||||||
\(804\) | 15700.7 | 0.688708 | ||||||||
\(805\) | −40624.8 | −1.77868 | ||||||||
\(806\) | −15826.0 | −0.691620 | ||||||||
\(807\) | −46226.9 | −2.01644 | ||||||||
\(808\) | −14731.0 | −0.641379 | ||||||||
\(809\) | 36568.0 | 1.58920 | 0.794599 | − | 0.607134i | \(-0.207681\pi\) | ||||
0.794599 | + | 0.607134i | \(0.207681\pi\) | |||||||
\(810\) | −15060.1 | −0.653282 | ||||||||
\(811\) | 37315.7 | 1.61570 | 0.807849 | − | 0.589390i | \(-0.200632\pi\) | ||||
0.807849 | + | 0.589390i | \(0.200632\pi\) | |||||||
\(812\) | −3254.30 | −0.140645 | ||||||||
\(813\) | 33109.6 | 1.42830 | ||||||||
\(814\) | −9343.64 | −0.402327 | ||||||||
\(815\) | 38774.3 | 1.66651 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1445.75 | 0.0619097 | ||||||||
\(818\) | 9685.79 | 0.414005 | ||||||||
\(819\) | 14541.4 | 0.620414 | ||||||||
\(820\) | −32620.9 | −1.38924 | ||||||||
\(821\) | −27365.1 | −1.16328 | −0.581638 | − | 0.813448i | \(-0.697588\pi\) | ||||
−0.581638 | + | 0.813448i | \(0.697588\pi\) | |||||||
\(822\) | 14033.6 | 0.595471 | ||||||||
\(823\) | −21138.4 | −0.895308 | −0.447654 | − | 0.894207i | \(-0.647740\pi\) | ||||
−0.447654 | + | 0.894207i | \(0.647740\pi\) | |||||||
\(824\) | −14045.7 | −0.593818 | ||||||||
\(825\) | −14120.7 | −0.595902 | ||||||||
\(826\) | −7123.83 | −0.300084 | ||||||||
\(827\) | −43453.3 | −1.82711 | −0.913554 | − | 0.406717i | \(-0.866673\pi\) | ||||
−0.913554 | + | 0.406717i | \(0.866673\pi\) | |||||||
\(828\) | −7311.55 | −0.306877 | ||||||||
\(829\) | 36460.2 | 1.52752 | 0.763760 | − | 0.645501i | \(-0.223351\pi\) | ||||
0.763760 | + | 0.645501i | \(0.223351\pi\) | |||||||
\(830\) | −3051.85 | −0.127628 | ||||||||
\(831\) | −24942.2 | −1.04120 | ||||||||
\(832\) | −100.019 | −0.00416771 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −13871.9 | −0.575952 | ||||||||
\(835\) | 32086.5 | 1.32982 | ||||||||
\(836\) | −899.575 | −0.0372158 | ||||||||
\(837\) | 24517.4 | 1.01248 | ||||||||
\(838\) | −4082.39 | −0.168286 | ||||||||
\(839\) | 20236.0 | 0.832687 | 0.416344 | − | 0.909207i | \(-0.363311\pi\) | ||||
0.416344 | + | 0.909207i | \(0.363311\pi\) | |||||||
\(840\) | −40058.0 | −1.64539 | ||||||||
\(841\) | −24041.9 | −0.985770 | ||||||||
\(842\) | 18289.3 | 0.748564 | ||||||||
\(843\) | 20786.8 | 0.849272 | ||||||||
\(844\) | 439.386 | 0.0179198 | ||||||||
\(845\) | 7469.92 | 0.304110 | ||||||||
\(846\) | −2558.51 | −0.103976 | ||||||||
\(847\) | −20188.4 | −0.818988 | ||||||||
\(848\) | −2994.18 | −0.121251 | ||||||||
\(849\) | 26349.4 | 1.06515 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −18284.3 | −0.736519 | ||||||||
\(852\) | −18810.2 | −0.756368 | ||||||||
\(853\) | −6934.19 | −0.278338 | −0.139169 | − | 0.990269i | \(-0.544443\pi\) | ||||
−0.139169 | + | 0.990269i | \(0.544443\pi\) | |||||||
\(854\) | −20156.6 | −0.807664 | ||||||||
\(855\) | 415.328 | 0.0166128 | ||||||||
\(856\) | 18122.7 | 0.723623 | ||||||||
\(857\) | −19207.8 | −0.765607 | −0.382803 | − | 0.923830i | \(-0.625041\pi\) | ||||
−0.382803 | + | 0.923830i | \(0.625041\pi\) | |||||||
\(858\) | 18388.9 | 0.731688 | ||||||||
\(859\) | −9954.55 | −0.395395 | −0.197698 | − | 0.980263i | \(-0.563346\pi\) | ||||
−0.197698 | + | 0.980263i | \(0.563346\pi\) | |||||||
\(860\) | −39840.6 | −1.57971 | ||||||||
\(861\) | 63773.2 | 2.52426 | ||||||||
\(862\) | 9003.26 | 0.355745 | ||||||||
\(863\) | −33698.0 | −1.32919 | −0.664596 | − | 0.747203i | \(-0.731396\pi\) | ||||
−0.664596 | + | 0.747203i | \(0.731396\pi\) | |||||||
\(864\) | 18603.3 | 0.732519 | ||||||||
\(865\) | 5220.91 | 0.205221 | ||||||||
\(866\) | 14425.7 | 0.566058 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 41708.6 | 1.63097 | ||||||||
\(869\) | −17415.0 | −0.679818 | ||||||||
\(870\) | 1900.03 | 0.0740425 | ||||||||
\(871\) | −21117.8 | −0.821525 | ||||||||
\(872\) | −12742.6 | −0.494861 | ||||||||
\(873\) | −3752.20 | −0.145467 | ||||||||
\(874\) | 437.236 | 0.0169219 | ||||||||
\(875\) | 26790.1 | 1.03505 | ||||||||
\(876\) | −28330.2 | −1.09268 | ||||||||
\(877\) | −4469.65 | −0.172097 | −0.0860487 | − | 0.996291i | \(-0.527424\pi\) | ||||
−0.0860487 | + | 0.996291i | \(0.527424\pi\) | |||||||
\(878\) | −16789.7 | −0.645358 | ||||||||
\(879\) | −18734.5 | −0.718885 | ||||||||
\(880\) | 17103.1 | 0.655164 | ||||||||
\(881\) | −2081.32 | −0.0795930 | −0.0397965 | − | 0.999208i | \(-0.512671\pi\) | ||||
−0.0397965 | + | 0.999208i | \(0.512671\pi\) | |||||||
\(882\) | 5124.91 | 0.195652 | ||||||||
\(883\) | 10124.4 | 0.385857 | 0.192929 | − | 0.981213i | \(-0.438201\pi\) | ||||
0.192929 | + | 0.981213i | \(0.438201\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −16745.6 | −0.636040 | ||||||||
\(886\) | −13749.1 | −0.521343 | ||||||||
\(887\) | 42725.3 | 1.61733 | 0.808666 | − | 0.588268i | \(-0.200190\pi\) | ||||
0.808666 | + | 0.588268i | \(0.200190\pi\) | |||||||
\(888\) | −18029.2 | −0.681328 | ||||||||
\(889\) | −11623.9 | −0.438529 | ||||||||
\(890\) | −10424.5 | −0.392618 | ||||||||
\(891\) | −40965.8 | −1.54030 | ||||||||
\(892\) | −30338.3 | −1.13879 | ||||||||
\(893\) | −615.996 | −0.0230835 | ||||||||
\(894\) | −21089.7 | −0.788977 | ||||||||
\(895\) | 25445.7 | 0.950343 | ||||||||
\(896\) | 39442.7 | 1.47063 | ||||||||
\(897\) | 35984.8 | 1.33946 | ||||||||
\(898\) | −21140.2 | −0.785588 | ||||||||
\(899\) | −4448.02 | −0.165017 | ||||||||
\(900\) | −3311.80 | −0.122659 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 22039.7 | 0.813573 | ||||||||
\(903\) | 77887.4 | 2.87036 | ||||||||
\(904\) | −26526.3 | −0.975941 | ||||||||
\(905\) | 22241.8 | 0.816954 | ||||||||
\(906\) | −16035.5 | −0.588017 | ||||||||
\(907\) | 21767.6 | 0.796893 | 0.398446 | − | 0.917192i | \(-0.369550\pi\) | ||||
0.398446 | + | 0.917192i | \(0.369550\pi\) | |||||||
\(908\) | 11040.6 | 0.403519 | ||||||||
\(909\) | 8228.28 | 0.300236 | ||||||||
\(910\) | 23963.4 | 0.872943 | ||||||||
\(911\) | 21654.2 | 0.787524 | 0.393762 | − | 0.919212i | \(-0.371173\pi\) | ||||
0.393762 | + | 0.919212i | \(0.371173\pi\) | |||||||
\(912\) | −532.636 | −0.0193392 | ||||||||
\(913\) | −8301.49 | −0.300919 | ||||||||
\(914\) | 17109.9 | 0.619197 | ||||||||
\(915\) | −47380.9 | −1.71187 | ||||||||
\(916\) | 2008.20 | 0.0724376 | ||||||||
\(917\) | 542.560 | 0.0195386 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 21445.1 | 0.769760 | 0.384880 | − | 0.922967i | \(-0.374243\pi\) | ||||
0.384880 | + | 0.922967i | \(0.374243\pi\) | |||||||
\(920\) | −27090.6 | −0.970818 | ||||||||
\(921\) | 24103.8 | 0.862376 | ||||||||
\(922\) | 19575.9 | 0.699239 | ||||||||
\(923\) | 25300.1 | 0.902234 | ||||||||
\(924\) | −48463.2 | −1.72546 | ||||||||
\(925\) | −8281.97 | −0.294389 | ||||||||
\(926\) | −19159.6 | −0.679938 | ||||||||
\(927\) | 7845.51 | 0.277972 | ||||||||
\(928\) | −3375.06 | −0.119388 | ||||||||
\(929\) | −24271.4 | −0.857177 | −0.428589 | − | 0.903500i | \(-0.640989\pi\) | ||||
−0.428589 | + | 0.903500i | \(0.640989\pi\) | |||||||
\(930\) | −24351.7 | −0.858626 | ||||||||
\(931\) | 1233.89 | 0.0434363 | ||||||||
\(932\) | −13467.7 | −0.473338 | ||||||||
\(933\) | −54763.3 | −1.92162 | ||||||||
\(934\) | 13303.0 | 0.466046 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 9696.96 | 0.338627 | ||||||||
\(937\) | 38491.5 | 1.34201 | 0.671005 | − | 0.741453i | \(-0.265863\pi\) | ||||
0.671005 | + | 0.741453i | \(0.265863\pi\) | |||||||
\(938\) | −13823.6 | −0.481190 | ||||||||
\(939\) | −10587.7 | −0.367964 | ||||||||
\(940\) | 16975.1 | 0.589006 | ||||||||
\(941\) | −31323.4 | −1.08514 | −0.542568 | − | 0.840012i | \(-0.682548\pi\) | ||||
−0.542568 | + | 0.840012i | \(0.682548\pi\) | |||||||
\(942\) | 20790.3 | 0.719092 | ||||||||
\(943\) | 43128.9 | 1.48937 | ||||||||
\(944\) | 5868.92 | 0.202349 | ||||||||
\(945\) | −37123.9 | −1.27793 | ||||||||
\(946\) | 26917.5 | 0.925121 | ||||||||
\(947\) | −32096.4 | −1.10136 | −0.550682 | − | 0.834715i | \(-0.685632\pi\) | ||||
−0.550682 | + | 0.834715i | \(0.685632\pi\) | |||||||
\(948\) | −14945.6 | −0.512035 | ||||||||
\(949\) | 38104.7 | 1.30341 | ||||||||
\(950\) | 198.049 | 0.00676373 | ||||||||
\(951\) | −50180.5 | −1.71106 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 10493.3 | 0.356675 | 0.178338 | − | 0.983969i | \(-0.442928\pi\) | ||||
0.178338 | + | 0.983969i | \(0.442928\pi\) | |||||||
\(954\) | −1353.75 | −0.0459426 | ||||||||
\(955\) | 31129.9 | 1.05481 | ||||||||
\(956\) | 35408.7 | 1.19791 | ||||||||
\(957\) | 5168.37 | 0.174576 | ||||||||
\(958\) | −7269.75 | −0.245172 | ||||||||
\(959\) | 49745.4 | 1.67504 | ||||||||
\(960\) | −153.901 | −0.00517409 | ||||||||
\(961\) | 27217.0 | 0.913597 | ||||||||
\(962\) | 10785.4 | 0.361470 | ||||||||
\(963\) | −10122.8 | −0.338736 | ||||||||
\(964\) | 12854.6 | 0.429479 | ||||||||
\(965\) | −8633.74 | −0.288010 | ||||||||
\(966\) | 23555.4 | 0.784559 | ||||||||
\(967\) | 31468.2 | 1.04648 | 0.523242 | − | 0.852184i | \(-0.324722\pi\) | ||||
0.523242 | + | 0.852184i | \(0.324722\pi\) | |||||||
\(968\) | −13462.6 | −0.447010 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −6183.39 | −0.204677 | ||||||||
\(971\) | −46923.8 | −1.55083 | −0.775415 | − | 0.631452i | \(-0.782459\pi\) | ||||
−0.775415 | + | 0.631452i | \(0.782459\pi\) | |||||||
\(972\) | −17389.9 | −0.573850 | ||||||||
\(973\) | −49172.3 | −1.62013 | ||||||||
\(974\) | 6774.11 | 0.222851 | ||||||||
\(975\) | 16299.5 | 0.535387 | ||||||||
\(976\) | 16605.9 | 0.544612 | ||||||||
\(977\) | 8666.25 | 0.283785 | 0.141893 | − | 0.989882i | \(-0.454681\pi\) | ||||
0.141893 | + | 0.989882i | \(0.454681\pi\) | |||||||
\(978\) | −22482.4 | −0.735081 | ||||||||
\(979\) | −28356.2 | −0.925709 | ||||||||
\(980\) | −34002.5 | −1.10834 | ||||||||
\(981\) | 7117.63 | 0.231650 | ||||||||
\(982\) | 22555.3 | 0.732961 | ||||||||
\(983\) | 35155.3 | 1.14067 | 0.570336 | − | 0.821412i | \(-0.306813\pi\) | ||||
0.570336 | + | 0.821412i | \(0.306813\pi\) | |||||||
\(984\) | 42527.1 | 1.37776 | ||||||||
\(985\) | 35557.3 | 1.15020 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −33185.9 | −1.07023 | ||||||||
\(988\) | 1038.38 | 0.0334365 | ||||||||
\(989\) | 52674.2 | 1.69357 | ||||||||
\(990\) | 7732.75 | 0.248246 | ||||||||
\(991\) | −11236.2 | −0.360170 | −0.180085 | − | 0.983651i | \(-0.557637\pi\) | ||||
−0.180085 | + | 0.983651i | \(0.557637\pi\) | |||||||
\(992\) | 43256.3 | 1.38447 | ||||||||
\(993\) | 25314.8 | 0.809004 | ||||||||
\(994\) | 16561.3 | 0.528463 | ||||||||
\(995\) | 23670.4 | 0.754172 | ||||||||
\(996\) | −7124.36 | −0.226651 | ||||||||
\(997\) | 18825.0 | 0.597987 | 0.298994 | − | 0.954255i | \(-0.403349\pi\) | ||||
0.298994 | + | 0.954255i | \(0.403349\pi\) | |||||||
\(998\) | −4424.56 | −0.140338 | ||||||||
\(999\) | −16708.6 | −0.529166 |
(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 | 289.4.a.i.1.8 | yes | 12 | |
17.4 | even | 4 | 289.4.b.f.288.9 | 24 | |||
17.13 | even | 4 | 289.4.b.f.288.10 | 24 | |||
17.16 | even | 2 | 289.4.a.h.1.8 | ✓ | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
289.4.a.h.1.8 | ✓ | 12 | 17.16 | even | 2 | ||
289.4.a.i.1.8 | yes | 12 | 1.1 | even | 1 | trivial | |
289.4.b.f.288.9 | 24 | 17.4 | even | 4 | |||
289.4.b.f.288.10 | 24 | 17.13 | even | 4 |