Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1859,4,Mod(1,1859)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1859, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1859.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1859 = 11 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1859.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: | \(109.684550701\) |
Analytic rank: | \(1\) |
Dimension: | \(39\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.6 | ||
Character | \(\chi\) | \(=\) | 1859.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −3.79953 | −1.34334 | −0.671668 | − | 0.740852i | \(-0.734422\pi\) | ||||
−0.671668 | + | 0.740852i | \(0.734422\pi\) | |||||||
\(3\) | 4.80997 | 0.925679 | 0.462839 | − | 0.886442i | \(-0.346831\pi\) | ||||
0.462839 | + | 0.886442i | \(0.346831\pi\) | |||||||
\(4\) | 6.43642 | 0.804553 | ||||||||
\(5\) | 1.29866 | 0.116155 | 0.0580777 | − | 0.998312i | \(-0.481503\pi\) | ||||
0.0580777 | + | 0.998312i | \(0.481503\pi\) | |||||||
\(6\) | −18.2756 | −1.24350 | ||||||||
\(7\) | −1.62019 | −0.0874820 | −0.0437410 | − | 0.999043i | \(-0.513928\pi\) | ||||
−0.0437410 | + | 0.999043i | \(0.513928\pi\) | |||||||
\(8\) | 5.94086 | 0.262551 | ||||||||
\(9\) | −3.86420 | −0.143119 | ||||||||
\(10\) | −4.93429 | −0.156036 | ||||||||
\(11\) | −11.0000 | −0.301511 | ||||||||
\(12\) | 30.9590 | 0.744758 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | 6.15596 | 0.117518 | ||||||||
\(15\) | 6.24650 | 0.107523 | ||||||||
\(16\) | −74.0638 | −1.15725 | ||||||||
\(17\) | 42.5920 | 0.607651 | 0.303826 | − | 0.952728i | \(-0.401736\pi\) | ||||
0.303826 | + | 0.952728i | \(0.401736\pi\) | |||||||
\(18\) | 14.6822 | 0.192256 | ||||||||
\(19\) | 62.5307 | 0.755028 | 0.377514 | − | 0.926004i | \(-0.376779\pi\) | ||||
0.377514 | + | 0.926004i | \(0.376779\pi\) | |||||||
\(20\) | 8.35871 | 0.0934532 | ||||||||
\(21\) | −7.79306 | −0.0809802 | ||||||||
\(22\) | 41.7948 | 0.405031 | ||||||||
\(23\) | −35.1144 | −0.318342 | −0.159171 | − | 0.987251i | \(-0.550882\pi\) | ||||
−0.159171 | + | 0.987251i | \(0.550882\pi\) | |||||||
\(24\) | 28.5753 | 0.243038 | ||||||||
\(25\) | −123.313 | −0.986508 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −148.456 | −1.05816 | ||||||||
\(28\) | −10.4282 | −0.0703839 | ||||||||
\(29\) | −43.3864 | −0.277815 | −0.138908 | − | 0.990305i | \(-0.544359\pi\) | ||||
−0.138908 | + | 0.990305i | \(0.544359\pi\) | |||||||
\(30\) | −23.7338 | −0.144439 | ||||||||
\(31\) | 216.323 | 1.25332 | 0.626658 | − | 0.779294i | \(-0.284422\pi\) | ||||
0.626658 | + | 0.779294i | \(0.284422\pi\) | |||||||
\(32\) | 233.881 | 1.29202 | ||||||||
\(33\) | −52.9097 | −0.279103 | ||||||||
\(34\) | −161.829 | −0.816280 | ||||||||
\(35\) | −2.10407 | −0.0101615 | ||||||||
\(36\) | −24.8716 | −0.115147 | ||||||||
\(37\) | 169.251 | 0.752018 | 0.376009 | − | 0.926616i | \(-0.377296\pi\) | ||||
0.376009 | + | 0.926616i | \(0.377296\pi\) | |||||||
\(38\) | −237.587 | −1.01426 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 7.71514 | 0.0304968 | ||||||||
\(41\) | 89.5980 | 0.341289 | 0.170645 | − | 0.985333i | \(-0.445415\pi\) | ||||
0.170645 | + | 0.985333i | \(0.445415\pi\) | |||||||
\(42\) | 29.6100 | 0.108784 | ||||||||
\(43\) | 38.3091 | 0.135862 | 0.0679312 | − | 0.997690i | \(-0.478360\pi\) | ||||
0.0679312 | + | 0.997690i | \(0.478360\pi\) | |||||||
\(44\) | −70.8007 | −0.242582 | ||||||||
\(45\) | −5.01828 | −0.0166240 | ||||||||
\(46\) | 133.418 | 0.427640 | ||||||||
\(47\) | −325.682 | −1.01076 | −0.505379 | − | 0.862897i | \(-0.668647\pi\) | ||||
−0.505379 | + | 0.862897i | \(0.668647\pi\) | |||||||
\(48\) | −356.245 | −1.07124 | ||||||||
\(49\) | −340.375 | −0.992347 | ||||||||
\(50\) | 468.533 | 1.32521 | ||||||||
\(51\) | 204.866 | 0.562490 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 341.422 | 0.884867 | 0.442434 | − | 0.896801i | \(-0.354115\pi\) | ||||
0.442434 | + | 0.896801i | \(0.354115\pi\) | |||||||
\(54\) | 564.062 | 1.42147 | ||||||||
\(55\) | −14.2852 | −0.0350222 | ||||||||
\(56\) | −9.62531 | −0.0229685 | ||||||||
\(57\) | 300.771 | 0.698913 | ||||||||
\(58\) | 164.848 | 0.373200 | ||||||||
\(59\) | −67.2154 | −0.148317 | −0.0741584 | − | 0.997246i | \(-0.523627\pi\) | ||||
−0.0741584 | + | 0.997246i | \(0.523627\pi\) | |||||||
\(60\) | 40.2051 | 0.0865077 | ||||||||
\(61\) | 332.978 | 0.698910 | 0.349455 | − | 0.936953i | \(-0.386367\pi\) | ||||
0.349455 | + | 0.936953i | \(0.386367\pi\) | |||||||
\(62\) | −821.926 | −1.68362 | ||||||||
\(63\) | 6.26074 | 0.0125203 | ||||||||
\(64\) | −296.127 | −0.578372 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 201.032 | 0.374929 | ||||||||
\(67\) | −253.227 | −0.461741 | −0.230871 | − | 0.972984i | \(-0.574157\pi\) | ||||
−0.230871 | + | 0.972984i | \(0.574157\pi\) | |||||||
\(68\) | 274.140 | 0.488888 | ||||||||
\(69\) | −168.899 | −0.294682 | ||||||||
\(70\) | 7.99448 | 0.0136503 | ||||||||
\(71\) | 113.430 | 0.189601 | 0.0948007 | − | 0.995496i | \(-0.469779\pi\) | ||||
0.0948007 | + | 0.995496i | \(0.469779\pi\) | |||||||
\(72\) | −22.9567 | −0.0375760 | ||||||||
\(73\) | −638.923 | −1.02439 | −0.512193 | − | 0.858870i | \(-0.671167\pi\) | ||||
−0.512193 | + | 0.858870i | \(0.671167\pi\) | |||||||
\(74\) | −643.074 | −1.01021 | ||||||||
\(75\) | −593.134 | −0.913190 | ||||||||
\(76\) | 402.474 | 0.607460 | ||||||||
\(77\) | 17.8221 | 0.0263768 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −339.850 | −0.484002 | −0.242001 | − | 0.970276i | \(-0.577804\pi\) | ||||
−0.242001 | + | 0.970276i | \(0.577804\pi\) | |||||||
\(80\) | −96.1836 | −0.134421 | ||||||||
\(81\) | −609.734 | −0.836398 | ||||||||
\(82\) | −340.430 | −0.458466 | ||||||||
\(83\) | 884.850 | 1.17018 | 0.585090 | − | 0.810969i | \(-0.301059\pi\) | ||||
0.585090 | + | 0.810969i | \(0.301059\pi\) | |||||||
\(84\) | −50.1594 | −0.0651529 | ||||||||
\(85\) | 55.3124 | 0.0705820 | ||||||||
\(86\) | −145.557 | −0.182509 | ||||||||
\(87\) | −208.687 | −0.257168 | ||||||||
\(88\) | −65.3494 | −0.0791622 | ||||||||
\(89\) | −467.941 | −0.557322 | −0.278661 | − | 0.960389i | \(-0.589891\pi\) | ||||
−0.278661 | + | 0.960389i | \(0.589891\pi\) | |||||||
\(90\) | 19.0671 | 0.0223316 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −226.011 | −0.256123 | ||||||||
\(93\) | 1040.51 | 1.16017 | ||||||||
\(94\) | 1237.44 | 1.35779 | ||||||||
\(95\) | 81.2060 | 0.0877006 | ||||||||
\(96\) | 1124.96 | 1.19600 | ||||||||
\(97\) | 661.757 | 0.692693 | 0.346347 | − | 0.938107i | \(-0.387422\pi\) | ||||
0.346347 | + | 0.938107i | \(0.387422\pi\) | |||||||
\(98\) | 1293.26 | 1.33306 | ||||||||
\(99\) | 42.5062 | 0.0431519 | ||||||||
\(100\) | −793.698 | −0.793698 | ||||||||
\(101\) | −2016.44 | −1.98656 | −0.993282 | − | 0.115720i | \(-0.963083\pi\) | ||||
−0.993282 | + | 0.115720i | \(0.963083\pi\) | |||||||
\(102\) | −778.395 | −0.755613 | ||||||||
\(103\) | 689.014 | 0.659132 | 0.329566 | − | 0.944133i | \(-0.393098\pi\) | ||||
0.329566 | + | 0.944133i | \(0.393098\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −10.1205 | −0.00940630 | ||||||||
\(106\) | −1297.24 | −1.18867 | ||||||||
\(107\) | −570.871 | −0.515778 | −0.257889 | − | 0.966175i | \(-0.583027\pi\) | ||||
−0.257889 | + | 0.966175i | \(0.583027\pi\) | |||||||
\(108\) | −955.525 | −0.851346 | ||||||||
\(109\) | −408.229 | −0.358727 | −0.179363 | − | 0.983783i | \(-0.557404\pi\) | ||||
−0.179363 | + | 0.983783i | \(0.557404\pi\) | |||||||
\(110\) | 54.2772 | 0.0470466 | ||||||||
\(111\) | 814.091 | 0.696127 | ||||||||
\(112\) | 119.997 | 0.101238 | ||||||||
\(113\) | −543.756 | −0.452675 | −0.226337 | − | 0.974049i | \(-0.572675\pi\) | ||||
−0.226337 | + | 0.974049i | \(0.572675\pi\) | |||||||
\(114\) | −1142.79 | −0.938876 | ||||||||
\(115\) | −45.6016 | −0.0369772 | ||||||||
\(116\) | −279.253 | −0.223517 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 255.387 | 0.199239 | ||||||||
\(119\) | −69.0070 | −0.0531585 | ||||||||
\(120\) | 37.1096 | 0.0282302 | ||||||||
\(121\) | 121.000 | 0.0909091 | ||||||||
\(122\) | −1265.16 | −0.938871 | ||||||||
\(123\) | 430.964 | 0.315924 | ||||||||
\(124\) | 1392.35 | 1.00836 | ||||||||
\(125\) | −322.474 | −0.230744 | ||||||||
\(126\) | −23.7879 | −0.0168190 | ||||||||
\(127\) | −1245.78 | −0.870431 | −0.435215 | − | 0.900326i | \(-0.643328\pi\) | ||||
−0.435215 | + | 0.900326i | \(0.643328\pi\) | |||||||
\(128\) | −745.906 | −0.515073 | ||||||||
\(129\) | 184.266 | 0.125765 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1092.78 | −0.728826 | −0.364413 | − | 0.931237i | \(-0.618730\pi\) | ||||
−0.364413 | + | 0.931237i | \(0.618730\pi\) | |||||||
\(132\) | −340.549 | −0.224553 | ||||||||
\(133\) | −101.312 | −0.0660513 | ||||||||
\(134\) | 962.145 | 0.620274 | ||||||||
\(135\) | −192.793 | −0.122911 | ||||||||
\(136\) | 253.033 | 0.159540 | ||||||||
\(137\) | 315.651 | 0.196846 | 0.0984230 | − | 0.995145i | \(-0.468620\pi\) | ||||
0.0984230 | + | 0.995145i | \(0.468620\pi\) | |||||||
\(138\) | 641.738 | 0.395858 | ||||||||
\(139\) | −1688.81 | −1.03053 | −0.515264 | − | 0.857032i | \(-0.672306\pi\) | ||||
−0.515264 | + | 0.857032i | \(0.672306\pi\) | |||||||
\(140\) | −13.5427 | −0.00817547 | ||||||||
\(141\) | −1566.52 | −0.935638 | ||||||||
\(142\) | −430.982 | −0.254698 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 286.198 | 0.165624 | ||||||||
\(145\) | −56.3441 | −0.0322698 | ||||||||
\(146\) | 2427.61 | 1.37610 | ||||||||
\(147\) | −1637.19 | −0.918595 | ||||||||
\(148\) | 1089.37 | 0.605038 | ||||||||
\(149\) | 2749.48 | 1.51172 | 0.755860 | − | 0.654733i | \(-0.227219\pi\) | ||||
0.755860 | + | 0.654733i | \(0.227219\pi\) | |||||||
\(150\) | 2253.63 | 1.22672 | ||||||||
\(151\) | −1801.51 | −0.970895 | −0.485447 | − | 0.874266i | \(-0.661343\pi\) | ||||
−0.485447 | + | 0.874266i | \(0.661343\pi\) | |||||||
\(152\) | 371.486 | 0.198233 | ||||||||
\(153\) | −164.584 | −0.0869662 | ||||||||
\(154\) | −67.7155 | −0.0354329 | ||||||||
\(155\) | 280.930 | 0.145580 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1850.87 | 0.940863 | 0.470432 | − | 0.882436i | \(-0.344098\pi\) | ||||
0.470432 | + | 0.882436i | \(0.344098\pi\) | |||||||
\(158\) | 1291.27 | 0.650177 | ||||||||
\(159\) | 1642.23 | 0.819103 | ||||||||
\(160\) | 303.731 | 0.150075 | ||||||||
\(161\) | 56.8920 | 0.0278492 | ||||||||
\(162\) | 2316.70 | 1.12356 | ||||||||
\(163\) | 551.212 | 0.264873 | 0.132436 | − | 0.991192i | \(-0.457720\pi\) | ||||
0.132436 | + | 0.991192i | \(0.457720\pi\) | |||||||
\(164\) | 576.691 | 0.274585 | ||||||||
\(165\) | −68.7115 | −0.0324193 | ||||||||
\(166\) | −3362.01 | −1.57194 | ||||||||
\(167\) | 89.7313 | 0.0415785 | 0.0207893 | − | 0.999784i | \(-0.493382\pi\) | ||||
0.0207893 | + | 0.999784i | \(0.493382\pi\) | |||||||
\(168\) | −46.2974 | −0.0212615 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | −210.161 | −0.0948154 | ||||||||
\(171\) | −241.631 | −0.108059 | ||||||||
\(172\) | 246.574 | 0.109309 | ||||||||
\(173\) | −2921.16 | −1.28377 | −0.641884 | − | 0.766801i | \(-0.721847\pi\) | ||||
−0.641884 | + | 0.766801i | \(0.721847\pi\) | |||||||
\(174\) | 792.913 | 0.345463 | ||||||||
\(175\) | 199.791 | 0.0863017 | ||||||||
\(176\) | 814.702 | 0.348923 | ||||||||
\(177\) | −323.304 | −0.137294 | ||||||||
\(178\) | 1777.96 | 0.748671 | ||||||||
\(179\) | −1282.91 | −0.535695 | −0.267848 | − | 0.963461i | \(-0.586312\pi\) | ||||
−0.267848 | + | 0.963461i | \(0.586312\pi\) | |||||||
\(180\) | −32.2998 | −0.0133749 | ||||||||
\(181\) | 58.6272 | 0.0240758 | 0.0120379 | − | 0.999928i | \(-0.496168\pi\) | ||||
0.0120379 | + | 0.999928i | \(0.496168\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 1601.62 | 0.646966 | ||||||||
\(184\) | −208.610 | −0.0835811 | ||||||||
\(185\) | 219.799 | 0.0873510 | ||||||||
\(186\) | −3953.44 | −1.55850 | ||||||||
\(187\) | −468.512 | −0.183214 | ||||||||
\(188\) | −2096.23 | −0.813209 | ||||||||
\(189\) | 240.527 | 0.0925700 | ||||||||
\(190\) | −308.545 | −0.117811 | ||||||||
\(191\) | 1856.77 | 0.703408 | 0.351704 | − | 0.936111i | \(-0.385602\pi\) | ||||
0.351704 | + | 0.936111i | \(0.385602\pi\) | |||||||
\(192\) | −1424.36 | −0.535387 | ||||||||
\(193\) | −3214.97 | −1.19906 | −0.599530 | − | 0.800352i | \(-0.704646\pi\) | ||||
−0.599530 | + | 0.800352i | \(0.704646\pi\) | |||||||
\(194\) | −2514.36 | −0.930520 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −2190.80 | −0.798396 | ||||||||
\(197\) | 1826.74 | 0.660660 | 0.330330 | − | 0.943865i | \(-0.392840\pi\) | ||||
0.330330 | + | 0.943865i | \(0.392840\pi\) | |||||||
\(198\) | −161.504 | −0.0579675 | ||||||||
\(199\) | 2856.48 | 1.01754 | 0.508770 | − | 0.860903i | \(-0.330101\pi\) | ||||
0.508770 | + | 0.860903i | \(0.330101\pi\) | |||||||
\(200\) | −732.588 | −0.259009 | ||||||||
\(201\) | −1218.02 | −0.427424 | ||||||||
\(202\) | 7661.51 | 2.66862 | ||||||||
\(203\) | 70.2941 | 0.0243038 | ||||||||
\(204\) | 1318.60 | 0.452553 | ||||||||
\(205\) | 116.357 | 0.0396426 | ||||||||
\(206\) | −2617.93 | −0.885436 | ||||||||
\(207\) | 135.689 | 0.0455606 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −687.838 | −0.227649 | ||||||||
\(210\) | 38.4532 | 0.0126358 | ||||||||
\(211\) | 2705.92 | 0.882859 | 0.441430 | − | 0.897296i | \(-0.354472\pi\) | ||||
0.441430 | + | 0.897296i | \(0.354472\pi\) | |||||||
\(212\) | 2197.54 | 0.711922 | ||||||||
\(213\) | 545.596 | 0.175510 | ||||||||
\(214\) | 2169.04 | 0.692863 | ||||||||
\(215\) | 49.7504 | 0.0157812 | ||||||||
\(216\) | −881.955 | −0.277821 | ||||||||
\(217\) | −350.484 | −0.109643 | ||||||||
\(218\) | 1551.08 | 0.481891 | ||||||||
\(219\) | −3073.20 | −0.948253 | ||||||||
\(220\) | −91.9458 | −0.0281772 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | −3093.16 | −0.935133 | ||||||||
\(223\) | −4218.90 | −1.26690 | −0.633449 | − | 0.773784i | \(-0.718361\pi\) | ||||
−0.633449 | + | 0.773784i | \(0.718361\pi\) | |||||||
\(224\) | −378.931 | −0.113029 | ||||||||
\(225\) | 476.508 | 0.141188 | ||||||||
\(226\) | 2066.02 | 0.608095 | ||||||||
\(227\) | −1887.07 | −0.551758 | −0.275879 | − | 0.961192i | \(-0.588969\pi\) | ||||
−0.275879 | + | 0.961192i | \(0.588969\pi\) | |||||||
\(228\) | 1935.89 | 0.562313 | ||||||||
\(229\) | −1730.30 | −0.499308 | −0.249654 | − | 0.968335i | \(-0.580317\pi\) | ||||
−0.249654 | + | 0.968335i | \(0.580317\pi\) | |||||||
\(230\) | 173.265 | 0.0496728 | ||||||||
\(231\) | 85.7236 | 0.0244165 | ||||||||
\(232\) | −257.752 | −0.0729408 | ||||||||
\(233\) | −2161.58 | −0.607767 | −0.303884 | − | 0.952709i | \(-0.598283\pi\) | ||||
−0.303884 | + | 0.952709i | \(0.598283\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −422.950 | −0.117405 | ||||||||
\(236\) | −432.626 | −0.119329 | ||||||||
\(237\) | −1634.67 | −0.448030 | ||||||||
\(238\) | 262.194 | 0.0714098 | ||||||||
\(239\) | 2760.79 | 0.747198 | 0.373599 | − | 0.927590i | \(-0.378124\pi\) | ||||
0.373599 | + | 0.927590i | \(0.378124\pi\) | |||||||
\(240\) | −462.640 | −0.124430 | ||||||||
\(241\) | 2291.05 | 0.612364 | 0.306182 | − | 0.951973i | \(-0.400948\pi\) | ||||
0.306182 | + | 0.951973i | \(0.400948\pi\) | |||||||
\(242\) | −459.743 | −0.122121 | ||||||||
\(243\) | 1075.50 | 0.283924 | ||||||||
\(244\) | 2143.19 | 0.562310 | ||||||||
\(245\) | −442.031 | −0.115267 | ||||||||
\(246\) | −1637.46 | −0.424393 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 1285.14 | 0.329060 | ||||||||
\(249\) | 4256.10 | 1.08321 | ||||||||
\(250\) | 1225.25 | 0.309967 | ||||||||
\(251\) | −751.912 | −0.189085 | −0.0945423 | − | 0.995521i | \(-0.530139\pi\) | ||||
−0.0945423 | + | 0.995521i | \(0.530139\pi\) | |||||||
\(252\) | 40.2968 | 0.0100732 | ||||||||
\(253\) | 386.259 | 0.0959837 | ||||||||
\(254\) | 4733.36 | 1.16928 | ||||||||
\(255\) | 266.051 | 0.0653363 | ||||||||
\(256\) | 5203.10 | 1.27029 | ||||||||
\(257\) | 920.883 | 0.223514 | 0.111757 | − | 0.993736i | \(-0.464352\pi\) | ||||
0.111757 | + | 0.993736i | \(0.464352\pi\) | |||||||
\(258\) | −700.123 | −0.168945 | ||||||||
\(259\) | −274.218 | −0.0657880 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 167.654 | 0.0397606 | ||||||||
\(262\) | 4152.03 | 0.979059 | ||||||||
\(263\) | −5979.43 | −1.40193 | −0.700964 | − | 0.713196i | \(-0.747247\pi\) | ||||
−0.700964 | + | 0.713196i | \(0.747247\pi\) | |||||||
\(264\) | −314.329 | −0.0732788 | ||||||||
\(265\) | 443.391 | 0.102782 | ||||||||
\(266\) | 384.936 | 0.0887291 | ||||||||
\(267\) | −2250.78 | −0.515901 | ||||||||
\(268\) | −1629.88 | −0.371495 | ||||||||
\(269\) | 6780.92 | 1.53695 | 0.768476 | − | 0.639878i | \(-0.221015\pi\) | ||||
0.768476 | + | 0.639878i | \(0.221015\pi\) | |||||||
\(270\) | 732.524 | 0.165111 | ||||||||
\(271\) | −2241.91 | −0.502532 | −0.251266 | − | 0.967918i | \(-0.580847\pi\) | ||||
−0.251266 | + | 0.967918i | \(0.580847\pi\) | |||||||
\(272\) | −3154.53 | −0.703203 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −1199.33 | −0.264430 | ||||||||
\(275\) | 1356.45 | 0.297443 | ||||||||
\(276\) | −1087.11 | −0.237088 | ||||||||
\(277\) | 4135.48 | 0.897028 | 0.448514 | − | 0.893776i | \(-0.351953\pi\) | ||||
0.448514 | + | 0.893776i | \(0.351953\pi\) | |||||||
\(278\) | 6416.70 | 1.38434 | ||||||||
\(279\) | −835.917 | −0.179373 | ||||||||
\(280\) | −12.5000 | −0.00266792 | ||||||||
\(281\) | −2574.08 | −0.546466 | −0.273233 | − | 0.961948i | \(-0.588093\pi\) | ||||
−0.273233 | + | 0.961948i | \(0.588093\pi\) | |||||||
\(282\) | 5952.05 | 1.25688 | ||||||||
\(283\) | 3140.17 | 0.659589 | 0.329794 | − | 0.944053i | \(-0.393021\pi\) | ||||
0.329794 | + | 0.944053i | \(0.393021\pi\) | |||||||
\(284\) | 730.085 | 0.152544 | ||||||||
\(285\) | 390.598 | 0.0811826 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −145.166 | −0.0298567 | ||||||||
\(288\) | −903.763 | −0.184912 | ||||||||
\(289\) | −3098.92 | −0.630760 | ||||||||
\(290\) | 214.081 | 0.0433492 | ||||||||
\(291\) | 3183.03 | 0.641211 | ||||||||
\(292\) | −4112.38 | −0.824173 | ||||||||
\(293\) | −36.1446 | −0.00720679 | −0.00360339 | − | 0.999994i | \(-0.501147\pi\) | ||||
−0.00360339 | + | 0.999994i | \(0.501147\pi\) | |||||||
\(294\) | 6220.56 | 1.23398 | ||||||||
\(295\) | −87.2897 | −0.0172278 | ||||||||
\(296\) | 1005.49 | 0.197443 | ||||||||
\(297\) | 1633.01 | 0.319047 | ||||||||
\(298\) | −10446.7 | −2.03075 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | −3817.66 | −0.734709 | ||||||||
\(301\) | −62.0680 | −0.0118855 | ||||||||
\(302\) | 6844.90 | 1.30424 | ||||||||
\(303\) | −9699.00 | −1.83892 | ||||||||
\(304\) | −4631.26 | −0.873754 | ||||||||
\(305\) | 432.425 | 0.0811822 | ||||||||
\(306\) | 625.342 | 0.116825 | ||||||||
\(307\) | −6834.17 | −1.27051 | −0.635256 | − | 0.772302i | \(-0.719105\pi\) | ||||
−0.635256 | + | 0.772302i | \(0.719105\pi\) | |||||||
\(308\) | 114.710 | 0.0212215 | ||||||||
\(309\) | 3314.14 | 0.610145 | ||||||||
\(310\) | −1067.40 | −0.195562 | ||||||||
\(311\) | −5088.06 | −0.927709 | −0.463855 | − | 0.885911i | \(-0.653534\pi\) | ||||
−0.463855 | + | 0.885911i | \(0.653534\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −5990.28 | −1.08176 | −0.540879 | − | 0.841100i | \(-0.681908\pi\) | ||||
−0.540879 | + | 0.841100i | \(0.681908\pi\) | |||||||
\(314\) | −7032.44 | −1.26390 | ||||||||
\(315\) | 8.13056 | 0.00145430 | ||||||||
\(316\) | −2187.42 | −0.389405 | ||||||||
\(317\) | 4293.56 | 0.760727 | 0.380364 | − | 0.924837i | \(-0.375799\pi\) | ||||
0.380364 | + | 0.924837i | \(0.375799\pi\) | |||||||
\(318\) | −6239.70 | −1.10033 | ||||||||
\(319\) | 477.250 | 0.0837645 | ||||||||
\(320\) | −384.567 | −0.0671811 | ||||||||
\(321\) | −2745.87 | −0.477445 | ||||||||
\(322\) | −216.163 | −0.0374108 | ||||||||
\(323\) | 2663.31 | 0.458794 | ||||||||
\(324\) | −3924.51 | −0.672927 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −2094.34 | −0.355813 | ||||||||
\(327\) | −1963.57 | −0.332066 | ||||||||
\(328\) | 532.289 | 0.0896059 | ||||||||
\(329\) | 527.667 | 0.0884232 | ||||||||
\(330\) | 261.072 | 0.0435500 | ||||||||
\(331\) | 3249.44 | 0.539593 | 0.269797 | − | 0.962917i | \(-0.413044\pi\) | ||||
0.269797 | + | 0.962917i | \(0.413044\pi\) | |||||||
\(332\) | 5695.27 | 0.941471 | ||||||||
\(333\) | −654.020 | −0.107628 | ||||||||
\(334\) | −340.937 | −0.0558540 | ||||||||
\(335\) | −328.856 | −0.0536338 | ||||||||
\(336\) | 577.184 | 0.0937142 | ||||||||
\(337\) | −223.966 | −0.0362023 | −0.0181012 | − | 0.999836i | \(-0.505762\pi\) | ||||
−0.0181012 | + | 0.999836i | \(0.505762\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −2615.45 | −0.419032 | ||||||||
\(340\) | 356.014 | 0.0567870 | ||||||||
\(341\) | −2379.55 | −0.377889 | ||||||||
\(342\) | 918.085 | 0.145159 | ||||||||
\(343\) | 1107.20 | 0.174294 | ||||||||
\(344\) | 227.589 | 0.0356708 | ||||||||
\(345\) | −219.342 | −0.0342290 | ||||||||
\(346\) | 11099.1 | 1.72453 | ||||||||
\(347\) | 3954.54 | 0.611789 | 0.305895 | − | 0.952065i | \(-0.401044\pi\) | ||||
0.305895 | + | 0.952065i | \(0.401044\pi\) | |||||||
\(348\) | −1343.20 | −0.206905 | ||||||||
\(349\) | −6151.61 | −0.943519 | −0.471759 | − | 0.881727i | \(-0.656381\pi\) | ||||
−0.471759 | + | 0.881727i | \(0.656381\pi\) | |||||||
\(350\) | −759.112 | −0.115932 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −2572.69 | −0.389559 | ||||||||
\(353\) | −10687.8 | −1.61149 | −0.805746 | − | 0.592261i | \(-0.798235\pi\) | ||||
−0.805746 | + | 0.592261i | \(0.798235\pi\) | |||||||
\(354\) | 1228.40 | 0.184432 | ||||||||
\(355\) | 147.307 | 0.0220232 | ||||||||
\(356\) | −3011.87 | −0.448395 | ||||||||
\(357\) | −331.922 | −0.0492077 | ||||||||
\(358\) | 4874.47 | 0.719619 | ||||||||
\(359\) | −6082.74 | −0.894247 | −0.447124 | − | 0.894472i | \(-0.647552\pi\) | ||||
−0.447124 | + | 0.894472i | \(0.647552\pi\) | |||||||
\(360\) | −29.8129 | −0.00436466 | ||||||||
\(361\) | −2948.91 | −0.429933 | ||||||||
\(362\) | −222.756 | −0.0323419 | ||||||||
\(363\) | 582.006 | 0.0841526 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −829.742 | −0.118988 | ||||||||
\(366\) | −6085.38 | −0.869093 | ||||||||
\(367\) | −9224.66 | −1.31205 | −0.656026 | − | 0.754738i | \(-0.727764\pi\) | ||||
−0.656026 | + | 0.754738i | \(0.727764\pi\) | |||||||
\(368\) | 2600.71 | 0.368400 | ||||||||
\(369\) | −346.225 | −0.0488449 | ||||||||
\(370\) | −835.133 | −0.117342 | ||||||||
\(371\) | −553.169 | −0.0774099 | ||||||||
\(372\) | 6697.15 | 0.933416 | ||||||||
\(373\) | −13664.5 | −1.89684 | −0.948419 | − | 0.317018i | \(-0.897318\pi\) | ||||
−0.948419 | + | 0.317018i | \(0.897318\pi\) | |||||||
\(374\) | 1780.12 | 0.246118 | ||||||||
\(375\) | −1551.09 | −0.213595 | ||||||||
\(376\) | −1934.83 | −0.265376 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | −913.888 | −0.124353 | ||||||||
\(379\) | −13259.5 | −1.79708 | −0.898542 | − | 0.438888i | \(-0.855372\pi\) | ||||
−0.898542 | + | 0.438888i | \(0.855372\pi\) | |||||||
\(380\) | 522.676 | 0.0705598 | ||||||||
\(381\) | −5992.14 | −0.805740 | ||||||||
\(382\) | −7054.84 | −0.944913 | ||||||||
\(383\) | −12584.6 | −1.67896 | −0.839482 | − | 0.543388i | \(-0.817141\pi\) | ||||
−0.839482 | + | 0.543388i | \(0.817141\pi\) | |||||||
\(384\) | −3587.78 | −0.476792 | ||||||||
\(385\) | 23.1448 | 0.00306381 | ||||||||
\(386\) | 12215.4 | 1.61074 | ||||||||
\(387\) | −148.034 | −0.0194444 | ||||||||
\(388\) | 4259.35 | 0.557308 | ||||||||
\(389\) | 7210.38 | 0.939797 | 0.469898 | − | 0.882720i | \(-0.344291\pi\) | ||||
0.469898 | + | 0.882720i | \(0.344291\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1495.59 | −0.193441 | ||||||||
\(392\) | −2022.12 | −0.260542 | ||||||||
\(393\) | −5256.22 | −0.674659 | ||||||||
\(394\) | −6940.76 | −0.887489 | ||||||||
\(395\) | −441.349 | −0.0562195 | ||||||||
\(396\) | 273.588 | 0.0347180 | ||||||||
\(397\) | −8393.51 | −1.06110 | −0.530552 | − | 0.847652i | \(-0.678015\pi\) | ||||
−0.530552 | + | 0.847652i | \(0.678015\pi\) | |||||||
\(398\) | −10853.3 | −1.36690 | ||||||||
\(399\) | −487.305 | −0.0611423 | ||||||||
\(400\) | 9133.07 | 1.14163 | ||||||||
\(401\) | 8267.45 | 1.02957 | 0.514784 | − | 0.857320i | \(-0.327872\pi\) | ||||
0.514784 | + | 0.857320i | \(0.327872\pi\) | |||||||
\(402\) | 4627.89 | 0.574174 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | −12978.6 | −1.59830 | ||||||||
\(405\) | −791.836 | −0.0971523 | ||||||||
\(406\) | −267.085 | −0.0326482 | ||||||||
\(407\) | −1861.76 | −0.226742 | ||||||||
\(408\) | 1217.08 | 0.147682 | ||||||||
\(409\) | −7210.94 | −0.871780 | −0.435890 | − | 0.900000i | \(-0.643566\pi\) | ||||
−0.435890 | + | 0.900000i | \(0.643566\pi\) | |||||||
\(410\) | −442.103 | −0.0532534 | ||||||||
\(411\) | 1518.27 | 0.182216 | ||||||||
\(412\) | 4434.79 | 0.530307 | ||||||||
\(413\) | 108.902 | 0.0129750 | ||||||||
\(414\) | −515.555 | −0.0612033 | ||||||||
\(415\) | 1149.12 | 0.135923 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −8123.14 | −0.953937 | ||||||||
\(418\) | 2613.46 | 0.305810 | ||||||||
\(419\) | −6344.57 | −0.739743 | −0.369872 | − | 0.929083i | \(-0.620598\pi\) | ||||
−0.369872 | + | 0.929083i | \(0.620598\pi\) | |||||||
\(420\) | −65.1399 | −0.00756786 | ||||||||
\(421\) | −66.2152 | −0.00766540 | −0.00383270 | − | 0.999993i | \(-0.501220\pi\) | ||||
−0.00383270 | + | 0.999993i | \(0.501220\pi\) | |||||||
\(422\) | −10281.2 | −1.18598 | ||||||||
\(423\) | 1258.50 | 0.144658 | ||||||||
\(424\) | 2028.34 | 0.232323 | ||||||||
\(425\) | −5252.17 | −0.599453 | ||||||||
\(426\) | −2073.01 | −0.235769 | ||||||||
\(427\) | −539.488 | −0.0611420 | ||||||||
\(428\) | −3674.37 | −0.414971 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −189.028 | −0.0211994 | ||||||||
\(431\) | −892.273 | −0.0997200 | −0.0498600 | − | 0.998756i | \(-0.515878\pi\) | ||||
−0.0498600 | + | 0.998756i | \(0.515878\pi\) | |||||||
\(432\) | 10995.2 | 1.22455 | ||||||||
\(433\) | −17502.0 | −1.94247 | −0.971236 | − | 0.238119i | \(-0.923469\pi\) | ||||
−0.971236 | + | 0.238119i | \(0.923469\pi\) | |||||||
\(434\) | 1331.68 | 0.147287 | ||||||||
\(435\) | −271.013 | −0.0298715 | ||||||||
\(436\) | −2627.53 | −0.288615 | ||||||||
\(437\) | −2195.73 | −0.240357 | ||||||||
\(438\) | 11676.7 | 1.27382 | ||||||||
\(439\) | 5997.88 | 0.652080 | 0.326040 | − | 0.945356i | \(-0.394286\pi\) | ||||
0.326040 | + | 0.945356i | \(0.394286\pi\) | |||||||
\(440\) | −84.8665 | −0.00919512 | ||||||||
\(441\) | 1315.28 | 0.142023 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 5219.81 | 0.559821 | 0.279910 | − | 0.960026i | \(-0.409695\pi\) | ||||
0.279910 | + | 0.960026i | \(0.409695\pi\) | |||||||
\(444\) | 5239.84 | 0.560071 | ||||||||
\(445\) | −607.696 | −0.0647360 | ||||||||
\(446\) | 16029.8 | 1.70187 | ||||||||
\(447\) | 13224.9 | 1.39937 | ||||||||
\(448\) | 479.781 | 0.0505971 | ||||||||
\(449\) | −8050.74 | −0.846187 | −0.423093 | − | 0.906086i | \(-0.639056\pi\) | ||||
−0.423093 | + | 0.906086i | \(0.639056\pi\) | |||||||
\(450\) | −1810.51 | −0.189663 | ||||||||
\(451\) | −985.578 | −0.102903 | ||||||||
\(452\) | −3499.84 | −0.364201 | ||||||||
\(453\) | −8665.22 | −0.898737 | ||||||||
\(454\) | 7169.97 | 0.741197 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 1786.84 | 0.183501 | ||||||||
\(457\) | −18660.7 | −1.91009 | −0.955043 | − | 0.296468i | \(-0.904191\pi\) | ||||
−0.955043 | + | 0.296468i | \(0.904191\pi\) | |||||||
\(458\) | 6574.33 | 0.670739 | ||||||||
\(459\) | −6323.03 | −0.642993 | ||||||||
\(460\) | −293.511 | −0.0297501 | ||||||||
\(461\) | −13917.5 | −1.40608 | −0.703040 | − | 0.711151i | \(-0.748174\pi\) | ||||
−0.703040 | + | 0.711151i | \(0.748174\pi\) | |||||||
\(462\) | −325.709 | −0.0327995 | ||||||||
\(463\) | 1262.35 | 0.126709 | 0.0633544 | − | 0.997991i | \(-0.479820\pi\) | ||||
0.0633544 | + | 0.997991i | \(0.479820\pi\) | |||||||
\(464\) | 3213.36 | 0.321501 | ||||||||
\(465\) | 1351.26 | 0.134760 | ||||||||
\(466\) | 8212.98 | 0.816436 | ||||||||
\(467\) | −3161.82 | −0.313301 | −0.156650 | − | 0.987654i | \(-0.550070\pi\) | ||||
−0.156650 | + | 0.987654i | \(0.550070\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 410.276 | 0.0403940 | ||||||||
\(470\) | 1607.01 | 0.157715 | ||||||||
\(471\) | 8902.63 | 0.870937 | ||||||||
\(472\) | −399.317 | −0.0389408 | ||||||||
\(473\) | −421.400 | −0.0409641 | ||||||||
\(474\) | 6210.97 | 0.601855 | ||||||||
\(475\) | −7710.88 | −0.744841 | ||||||||
\(476\) | −444.159 | −0.0427689 | ||||||||
\(477\) | −1319.33 | −0.126641 | ||||||||
\(478\) | −10489.7 | −1.00374 | ||||||||
\(479\) | 11469.9 | 1.09410 | 0.547049 | − | 0.837100i | \(-0.315751\pi\) | ||||
0.547049 | + | 0.837100i | \(0.315751\pi\) | |||||||
\(480\) | 1460.94 | 0.138922 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | −8704.92 | −0.822611 | ||||||||
\(483\) | 273.649 | 0.0257794 | ||||||||
\(484\) | 778.807 | 0.0731412 | ||||||||
\(485\) | 859.396 | 0.0804601 | ||||||||
\(486\) | −4086.41 | −0.381406 | ||||||||
\(487\) | −6505.89 | −0.605360 | −0.302680 | − | 0.953092i | \(-0.597881\pi\) | ||||
−0.302680 | + | 0.953092i | \(0.597881\pi\) | |||||||
\(488\) | 1978.18 | 0.183500 | ||||||||
\(489\) | 2651.31 | 0.245187 | ||||||||
\(490\) | 1679.51 | 0.154842 | ||||||||
\(491\) | 7742.24 | 0.711614 | 0.355807 | − | 0.934559i | \(-0.384206\pi\) | ||||
0.355807 | + | 0.934559i | \(0.384206\pi\) | |||||||
\(492\) | 2773.86 | 0.254178 | ||||||||
\(493\) | −1847.91 | −0.168815 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 55.2011 | 0.00501233 | ||||||||
\(496\) | −16021.7 | −1.45040 | ||||||||
\(497\) | −183.778 | −0.0165867 | ||||||||
\(498\) | −16171.2 | −1.45512 | ||||||||
\(499\) | −4385.54 | −0.393435 | −0.196717 | − | 0.980460i | \(-0.563028\pi\) | ||||
−0.196717 | + | 0.980460i | \(0.563028\pi\) | |||||||
\(500\) | −2075.58 | −0.185646 | ||||||||
\(501\) | 431.605 | 0.0384884 | ||||||||
\(502\) | 2856.91 | 0.254004 | ||||||||
\(503\) | −15340.1 | −1.35980 | −0.679901 | − | 0.733304i | \(-0.737977\pi\) | ||||
−0.679901 | + | 0.733304i | \(0.737977\pi\) | |||||||
\(504\) | 37.1942 | 0.00328722 | ||||||||
\(505\) | −2618.66 | −0.230750 | ||||||||
\(506\) | −1467.60 | −0.128938 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −8018.34 | −0.700308 | ||||||||
\(509\) | 5860.56 | 0.510343 | 0.255172 | − | 0.966896i | \(-0.417868\pi\) | ||||
0.255172 | + | 0.966896i | \(0.417868\pi\) | |||||||
\(510\) | −1010.87 | −0.0877686 | ||||||||
\(511\) | 1035.18 | 0.0896154 | ||||||||
\(512\) | −13802.1 | −1.19135 | ||||||||
\(513\) | −9283.05 | −0.798941 | ||||||||
\(514\) | −3498.92 | −0.300255 | ||||||||
\(515\) | 894.794 | 0.0765618 | ||||||||
\(516\) | 1186.01 | 0.101185 | ||||||||
\(517\) | 3582.51 | 0.304755 | ||||||||
\(518\) | 1041.90 | 0.0883755 | ||||||||
\(519\) | −14050.7 | −1.18836 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 8279.11 | 0.696189 | 0.348095 | − | 0.937459i | \(-0.386829\pi\) | ||||
0.348095 | + | 0.937459i | \(0.386829\pi\) | |||||||
\(522\) | −637.005 | −0.0534118 | ||||||||
\(523\) | −11446.6 | −0.957025 | −0.478512 | − | 0.878081i | \(-0.658824\pi\) | ||||
−0.478512 | + | 0.878081i | \(0.658824\pi\) | |||||||
\(524\) | −7033.57 | −0.586379 | ||||||||
\(525\) | 960.989 | 0.0798876 | ||||||||
\(526\) | 22719.0 | 1.88326 | ||||||||
\(527\) | 9213.63 | 0.761579 | ||||||||
\(528\) | 3918.69 | 0.322991 | ||||||||
\(529\) | −10934.0 | −0.898658 | ||||||||
\(530\) | −1684.68 | −0.138071 | ||||||||
\(531\) | 259.734 | 0.0212269 | ||||||||
\(532\) | −652.084 | −0.0531418 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 8551.92 | 0.693029 | ||||||||
\(535\) | −741.367 | −0.0599104 | ||||||||
\(536\) | −1504.39 | −0.121231 | ||||||||
\(537\) | −6170.77 | −0.495882 | ||||||||
\(538\) | −25764.3 | −2.06464 | ||||||||
\(539\) | 3744.12 | 0.299204 | ||||||||
\(540\) | −1240.90 | −0.0988885 | ||||||||
\(541\) | 1021.06 | 0.0811439 | 0.0405719 | − | 0.999177i | \(-0.487082\pi\) | ||||
0.0405719 | + | 0.999177i | \(0.487082\pi\) | |||||||
\(542\) | 8518.19 | 0.675070 | ||||||||
\(543\) | 281.995 | 0.0222865 | ||||||||
\(544\) | 9961.45 | 0.785099 | ||||||||
\(545\) | −530.150 | −0.0416681 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −19405.8 | −1.51688 | −0.758438 | − | 0.651746i | \(-0.774037\pi\) | ||||
−0.758438 | + | 0.651746i | \(0.774037\pi\) | |||||||
\(548\) | 2031.66 | 0.158373 | ||||||||
\(549\) | −1286.70 | −0.100027 | ||||||||
\(550\) | −5153.87 | −0.399566 | ||||||||
\(551\) | −2712.98 | −0.209758 | ||||||||
\(552\) | −1003.41 | −0.0773692 | ||||||||
\(553\) | 550.622 | 0.0423414 | ||||||||
\(554\) | −15712.9 | −1.20501 | ||||||||
\(555\) | 1057.23 | 0.0808590 | ||||||||
\(556\) | −10869.9 | −0.829114 | ||||||||
\(557\) | 1980.10 | 0.150627 | 0.0753136 | − | 0.997160i | \(-0.476004\pi\) | ||||
0.0753136 | + | 0.997160i | \(0.476004\pi\) | |||||||
\(558\) | 3176.09 | 0.240958 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 155.836 | 0.0117594 | ||||||||
\(561\) | −2253.53 | −0.169597 | ||||||||
\(562\) | 9780.30 | 0.734087 | ||||||||
\(563\) | 1526.82 | 0.114294 | 0.0571471 | − | 0.998366i | \(-0.481800\pi\) | ||||
0.0571471 | + | 0.998366i | \(0.481800\pi\) | |||||||
\(564\) | −10082.8 | −0.752770 | ||||||||
\(565\) | −706.153 | −0.0525807 | ||||||||
\(566\) | −11931.2 | −0.886050 | ||||||||
\(567\) | 987.885 | 0.0731698 | ||||||||
\(568\) | 673.873 | 0.0497801 | ||||||||
\(569\) | 13753.6 | 1.01333 | 0.506663 | − | 0.862144i | \(-0.330879\pi\) | ||||
0.506663 | + | 0.862144i | \(0.330879\pi\) | |||||||
\(570\) | −1484.09 | −0.109056 | ||||||||
\(571\) | −21668.9 | −1.58812 | −0.794059 | − | 0.607841i | \(-0.792036\pi\) | ||||
−0.794059 | + | 0.607841i | \(0.792036\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 8930.98 | 0.651130 | ||||||||
\(574\) | 551.561 | 0.0401075 | ||||||||
\(575\) | 4330.08 | 0.314047 | ||||||||
\(576\) | 1144.29 | 0.0827758 | ||||||||
\(577\) | 11200.1 | 0.808086 | 0.404043 | − | 0.914740i | \(-0.367605\pi\) | ||||
0.404043 | + | 0.914740i | \(0.367605\pi\) | |||||||
\(578\) | 11774.5 | 0.847323 | ||||||||
\(579\) | −15463.9 | −1.10995 | ||||||||
\(580\) | −362.654 | −0.0259628 | ||||||||
\(581\) | −1433.62 | −0.102370 | ||||||||
\(582\) | −12094.0 | −0.861363 | ||||||||
\(583\) | −3755.65 | −0.266797 | ||||||||
\(584\) | −3795.75 | −0.268954 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 137.332 | 0.00968114 | ||||||||
\(587\) | 19830.4 | 1.39436 | 0.697181 | − | 0.716895i | \(-0.254438\pi\) | ||||
0.697181 | + | 0.716895i | \(0.254438\pi\) | |||||||
\(588\) | −10537.7 | −0.739058 | ||||||||
\(589\) | 13526.8 | 0.946288 | ||||||||
\(590\) | 331.660 | 0.0231428 | ||||||||
\(591\) | 8786.58 | 0.611559 | ||||||||
\(592\) | −12535.4 | −0.870271 | ||||||||
\(593\) | −24271.4 | −1.68079 | −0.840395 | − | 0.541975i | \(-0.817677\pi\) | ||||
−0.840395 | + | 0.541975i | \(0.817677\pi\) | |||||||
\(594\) | −6204.69 | −0.428588 | ||||||||
\(595\) | −89.6165 | −0.00617466 | ||||||||
\(596\) | 17696.8 | 1.21626 | ||||||||
\(597\) | 13739.6 | 0.941914 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 27754.4 | 1.89318 | 0.946589 | − | 0.322443i | \(-0.104504\pi\) | ||||
0.946589 | + | 0.322443i | \(0.104504\pi\) | |||||||
\(600\) | −3523.72 | −0.239759 | ||||||||
\(601\) | 13670.1 | 0.927813 | 0.463906 | − | 0.885884i | \(-0.346447\pi\) | ||||
0.463906 | + | 0.885884i | \(0.346447\pi\) | |||||||
\(602\) | 235.829 | 0.0159662 | ||||||||
\(603\) | 978.522 | 0.0660838 | ||||||||
\(604\) | −11595.3 | −0.781136 | ||||||||
\(605\) | 157.138 | 0.0105596 | ||||||||
\(606\) | 36851.6 | 2.47029 | ||||||||
\(607\) | −20558.4 | −1.37470 | −0.687348 | − | 0.726328i | \(-0.741225\pi\) | ||||
−0.687348 | + | 0.726328i | \(0.741225\pi\) | |||||||
\(608\) | 14624.7 | 0.975512 | ||||||||
\(609\) | 338.113 | 0.0224976 | ||||||||
\(610\) | −1643.01 | −0.109055 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | −1059.33 | −0.0699689 | ||||||||
\(613\) | 6803.68 | 0.448284 | 0.224142 | − | 0.974557i | \(-0.428042\pi\) | ||||
0.224142 | + | 0.974557i | \(0.428042\pi\) | |||||||
\(614\) | 25966.6 | 1.70672 | ||||||||
\(615\) | 559.674 | 0.0366963 | ||||||||
\(616\) | 105.878 | 0.00692526 | ||||||||
\(617\) | 29749.4 | 1.94111 | 0.970555 | − | 0.240880i | \(-0.0774362\pi\) | ||||
0.970555 | + | 0.240880i | \(0.0774362\pi\) | |||||||
\(618\) | −12592.2 | −0.819630 | ||||||||
\(619\) | −124.952 | −0.00811351 | −0.00405676 | − | 0.999992i | \(-0.501291\pi\) | ||||
−0.00405676 | + | 0.999992i | \(0.501291\pi\) | |||||||
\(620\) | 1808.18 | 0.117126 | ||||||||
\(621\) | 5212.94 | 0.336857 | ||||||||
\(622\) | 19332.2 | 1.24623 | ||||||||
\(623\) | 758.153 | 0.0487557 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 14995.4 | 0.959706 | ||||||||
\(626\) | 22760.2 | 1.45317 | ||||||||
\(627\) | −3308.48 | −0.210730 | ||||||||
\(628\) | 11913.0 | 0.756974 | ||||||||
\(629\) | 7208.73 | 0.456965 | ||||||||
\(630\) | −30.8923 | −0.00195362 | ||||||||
\(631\) | 24670.9 | 1.55647 | 0.778237 | − | 0.627971i | \(-0.216114\pi\) | ||||
0.778237 | + | 0.627971i | \(0.216114\pi\) | |||||||
\(632\) | −2019.00 | −0.127075 | ||||||||
\(633\) | 13015.4 | 0.817244 | ||||||||
\(634\) | −16313.5 | −1.02191 | ||||||||
\(635\) | −1617.84 | −0.101105 | ||||||||
\(636\) | 10570.1 | 0.659012 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −1813.33 | −0.112524 | ||||||||
\(639\) | −438.318 | −0.0271355 | ||||||||
\(640\) | −968.676 | −0.0598286 | ||||||||
\(641\) | −964.516 | −0.0594323 | −0.0297161 | − | 0.999558i | \(-0.509460\pi\) | ||||
−0.0297161 | + | 0.999558i | \(0.509460\pi\) | |||||||
\(642\) | 10433.0 | 0.641369 | ||||||||
\(643\) | 25364.2 | 1.55562 | 0.777811 | − | 0.628499i | \(-0.216330\pi\) | ||||
0.777811 | + | 0.628499i | \(0.216330\pi\) | |||||||
\(644\) | 366.181 | 0.0224061 | ||||||||
\(645\) | 239.298 | 0.0146083 | ||||||||
\(646\) | −10119.3 | −0.616314 | ||||||||
\(647\) | 17180.8 | 1.04397 | 0.521984 | − | 0.852955i | \(-0.325192\pi\) | ||||
0.521984 | + | 0.852955i | \(0.325192\pi\) | |||||||
\(648\) | −3622.35 | −0.219597 | ||||||||
\(649\) | 739.369 | 0.0447192 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −1685.82 | −0.101494 | ||||||||
\(652\) | 3547.83 | 0.213104 | ||||||||
\(653\) | −29381.5 | −1.76078 | −0.880388 | − | 0.474255i | \(-0.842718\pi\) | ||||
−0.880388 | + | 0.474255i | \(0.842718\pi\) | |||||||
\(654\) | 7460.63 | 0.446076 | ||||||||
\(655\) | −1419.14 | −0.0846572 | ||||||||
\(656\) | −6635.97 | −0.394956 | ||||||||
\(657\) | 2468.93 | 0.146609 | ||||||||
\(658\) | −2004.89 | −0.118782 | ||||||||
\(659\) | −11890.6 | −0.702872 | −0.351436 | − | 0.936212i | \(-0.614306\pi\) | ||||
−0.351436 | + | 0.936212i | \(0.614306\pi\) | |||||||
\(660\) | −442.257 | −0.0260830 | ||||||||
\(661\) | 7083.25 | 0.416803 | 0.208401 | − | 0.978043i | \(-0.433174\pi\) | ||||
0.208401 | + | 0.978043i | \(0.433174\pi\) | |||||||
\(662\) | −12346.3 | −0.724855 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 5256.77 | 0.307232 | ||||||||
\(665\) | −131.569 | −0.00767222 | ||||||||
\(666\) | 2484.97 | 0.144580 | ||||||||
\(667\) | 1523.49 | 0.0884403 | ||||||||
\(668\) | 577.549 | 0.0334521 | ||||||||
\(669\) | −20292.8 | −1.17274 | ||||||||
\(670\) | 1249.50 | 0.0720482 | ||||||||
\(671\) | −3662.76 | −0.210729 | ||||||||
\(672\) | −1822.65 | −0.104628 | ||||||||
\(673\) | 7492.85 | 0.429165 | 0.214583 | − | 0.976706i | \(-0.431161\pi\) | ||||
0.214583 | + | 0.976706i | \(0.431161\pi\) | |||||||
\(674\) | 850.964 | 0.0486319 | ||||||||
\(675\) | 18306.6 | 1.04388 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 21186.3 | 1.20274 | 0.601370 | − | 0.798971i | \(-0.294622\pi\) | ||||
0.601370 | + | 0.798971i | \(0.294622\pi\) | |||||||
\(678\) | 9937.48 | 0.562900 | ||||||||
\(679\) | −1072.17 | −0.0605982 | ||||||||
\(680\) | 328.603 | 0.0185314 | ||||||||
\(681\) | −9076.74 | −0.510751 | ||||||||
\(682\) | 9041.19 | 0.507632 | ||||||||
\(683\) | 11337.7 | 0.635176 | 0.317588 | − | 0.948229i | \(-0.397127\pi\) | ||||
0.317588 | + | 0.948229i | \(0.397127\pi\) | |||||||
\(684\) | −1555.24 | −0.0869388 | ||||||||
\(685\) | 409.923 | 0.0228647 | ||||||||
\(686\) | −4206.83 | −0.234136 | ||||||||
\(687\) | −8322.70 | −0.462199 | ||||||||
\(688\) | −2837.32 | −0.157226 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 833.398 | 0.0459810 | ||||||||
\(691\) | 10680.7 | 0.588005 | 0.294002 | − | 0.955805i | \(-0.405013\pi\) | ||||
0.294002 | + | 0.955805i | \(0.405013\pi\) | |||||||
\(692\) | −18801.9 | −1.03286 | ||||||||
\(693\) | −68.8681 | −0.00377501 | ||||||||
\(694\) | −15025.4 | −0.821839 | ||||||||
\(695\) | −2193.19 | −0.119701 | ||||||||
\(696\) | −1239.78 | −0.0675197 | ||||||||
\(697\) | 3816.16 | 0.207385 | ||||||||
\(698\) | 23373.2 | 1.26746 | ||||||||
\(699\) | −10397.1 | −0.562597 | ||||||||
\(700\) | 1285.94 | 0.0694342 | ||||||||
\(701\) | −8351.67 | −0.449983 | −0.224992 | − | 0.974361i | \(-0.572236\pi\) | ||||
−0.224992 | + | 0.974361i | \(0.572236\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 10583.4 | 0.567794 | ||||||||
\(704\) | 3257.39 | 0.174386 | ||||||||
\(705\) | −2034.38 | −0.108680 | ||||||||
\(706\) | 40608.8 | 2.16478 | ||||||||
\(707\) | 3267.01 | 0.173789 | ||||||||
\(708\) | −2080.92 | −0.110460 | ||||||||
\(709\) | −17277.7 | −0.915201 | −0.457601 | − | 0.889158i | \(-0.651291\pi\) | ||||
−0.457601 | + | 0.889158i | \(0.651291\pi\) | |||||||
\(710\) | −559.698 | −0.0295846 | ||||||||
\(711\) | 1313.25 | 0.0692697 | ||||||||
\(712\) | −2779.97 | −0.146326 | ||||||||
\(713\) | −7596.06 | −0.398983 | ||||||||
\(714\) | 1261.15 | 0.0661025 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −8257.37 | −0.430995 | ||||||||
\(717\) | 13279.3 | 0.691666 | ||||||||
\(718\) | 23111.5 | 1.20127 | ||||||||
\(719\) | −21149.6 | −1.09700 | −0.548502 | − | 0.836149i | \(-0.684802\pi\) | ||||
−0.548502 | + | 0.836149i | \(0.684802\pi\) | |||||||
\(720\) | 371.673 | 0.0192381 | ||||||||
\(721\) | −1116.33 | −0.0576622 | ||||||||
\(722\) | 11204.5 | 0.577545 | ||||||||
\(723\) | 11019.9 | 0.566852 | ||||||||
\(724\) | 377.349 | 0.0193703 | ||||||||
\(725\) | 5350.13 | 0.274067 | ||||||||
\(726\) | −2211.35 | −0.113045 | ||||||||
\(727\) | 5227.37 | 0.266675 | 0.133337 | − | 0.991071i | \(-0.457431\pi\) | ||||
0.133337 | + | 0.991071i | \(0.457431\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 21636.0 | 1.09922 | ||||||||
\(730\) | 3152.63 | 0.159841 | ||||||||
\(731\) | 1631.66 | 0.0825570 | ||||||||
\(732\) | 10308.7 | 0.520518 | ||||||||
\(733\) | −6152.37 | −0.310018 | −0.155009 | − | 0.987913i | \(-0.549541\pi\) | ||||
−0.155009 | + | 0.987913i | \(0.549541\pi\) | |||||||
\(734\) | 35049.4 | 1.76253 | ||||||||
\(735\) | −2126.15 | −0.106700 | ||||||||
\(736\) | −8212.59 | −0.411305 | ||||||||
\(737\) | 2785.50 | 0.139220 | ||||||||
\(738\) | 1315.49 | 0.0656151 | ||||||||
\(739\) | −31210.2 | −1.55356 | −0.776782 | − | 0.629769i | \(-0.783149\pi\) | ||||
−0.776782 | + | 0.629769i | \(0.783149\pi\) | |||||||
\(740\) | 1414.72 | 0.0702785 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 2101.78 | 0.103988 | ||||||||
\(743\) | 8135.91 | 0.401719 | 0.200860 | − | 0.979620i | \(-0.435626\pi\) | ||||
0.200860 | + | 0.979620i | \(0.435626\pi\) | |||||||
\(744\) | 6181.51 | 0.304604 | ||||||||
\(745\) | 3570.64 | 0.175595 | ||||||||
\(746\) | 51918.7 | 2.54809 | ||||||||
\(747\) | −3419.24 | −0.167474 | ||||||||
\(748\) | −3015.54 | −0.147405 | ||||||||
\(749\) | 924.920 | 0.0451213 | ||||||||
\(750\) | 5893.42 | 0.286930 | ||||||||
\(751\) | −19772.7 | −0.960739 | −0.480369 | − | 0.877066i | \(-0.659497\pi\) | ||||
−0.480369 | + | 0.877066i | \(0.659497\pi\) | |||||||
\(752\) | 24121.3 | 1.16970 | ||||||||
\(753\) | −3616.67 | −0.175032 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −2339.55 | −0.112775 | ||||||||
\(756\) | 1548.13 | 0.0744775 | ||||||||
\(757\) | −451.352 | −0.0216706 | −0.0108353 | − | 0.999941i | \(-0.503449\pi\) | ||||
−0.0108353 | + | 0.999941i | \(0.503449\pi\) | |||||||
\(758\) | 50379.8 | 2.41409 | ||||||||
\(759\) | 1857.89 | 0.0888501 | ||||||||
\(760\) | 482.433 | 0.0230259 | ||||||||
\(761\) | −9138.05 | −0.435288 | −0.217644 | − | 0.976028i | \(-0.569837\pi\) | ||||
−0.217644 | + | 0.976028i | \(0.569837\pi\) | |||||||
\(762\) | 22767.3 | 1.08238 | ||||||||
\(763\) | 661.408 | 0.0313821 | ||||||||
\(764\) | 11950.9 | 0.565929 | ||||||||
\(765\) | −213.738 | −0.0101016 | ||||||||
\(766\) | 47815.6 | 2.25541 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 25026.8 | 1.17588 | ||||||||
\(769\) | 22827.4 | 1.07045 | 0.535225 | − | 0.844710i | \(-0.320227\pi\) | ||||
0.535225 | + | 0.844710i | \(0.320227\pi\) | |||||||
\(770\) | −87.9393 | −0.00411573 | ||||||||
\(771\) | 4429.42 | 0.206902 | ||||||||
\(772\) | −20692.9 | −0.964708 | ||||||||
\(773\) | 3026.40 | 0.140818 | 0.0704088 | − | 0.997518i | \(-0.477570\pi\) | ||||
0.0704088 | + | 0.997518i | \(0.477570\pi\) | |||||||
\(774\) | 562.460 | 0.0261204 | ||||||||
\(775\) | −26675.6 | −1.23641 | ||||||||
\(776\) | 3931.40 | 0.181867 | ||||||||
\(777\) | −1318.98 | −0.0608986 | ||||||||
\(778\) | −27396.1 | −1.26246 | ||||||||
\(779\) | 5602.63 | 0.257683 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1247.73 | −0.0571670 | ||||||||
\(782\) | 5682.55 | 0.259856 | ||||||||
\(783\) | 6440.96 | 0.293973 | ||||||||
\(784\) | 25209.5 | 1.14839 | ||||||||
\(785\) | 2403.65 | 0.109286 | ||||||||
\(786\) | 19971.1 | 0.906294 | ||||||||
\(787\) | 38985.6 | 1.76580 | 0.882901 | − | 0.469560i | \(-0.155587\pi\) | ||||
0.882901 | + | 0.469560i | \(0.155587\pi\) | |||||||
\(788\) | 11757.7 | 0.531536 | ||||||||
\(789\) | −28760.9 | −1.29774 | ||||||||
\(790\) | 1676.92 | 0.0755217 | ||||||||
\(791\) | 880.988 | 0.0396009 | ||||||||
\(792\) | 252.523 | 0.0113296 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 31891.4 | 1.42542 | ||||||||
\(795\) | 2132.70 | 0.0951433 | ||||||||
\(796\) | 18385.5 | 0.818664 | ||||||||
\(797\) | 3263.88 | 0.145060 | 0.0725299 | − | 0.997366i | \(-0.476893\pi\) | ||||
0.0725299 | + | 0.997366i | \(0.476893\pi\) | |||||||
\(798\) | 1851.53 | 0.0821347 | ||||||||
\(799\) | −13871.5 | −0.614189 | ||||||||
\(800\) | −28840.7 | −1.27459 | ||||||||
\(801\) | 1808.22 | 0.0797632 | ||||||||
\(802\) | −31412.4 | −1.38306 | ||||||||
\(803\) | 7028.15 | 0.308864 | ||||||||
\(804\) | −7839.67 | −0.343885 | ||||||||
\(805\) | 73.8832 | 0.00323483 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 32616.0 | 1.42272 | ||||||||
\(808\) | −11979.4 | −0.521575 | ||||||||
\(809\) | −19749.4 | −0.858282 | −0.429141 | − | 0.903237i | \(-0.641184\pi\) | ||||
−0.429141 | + | 0.903237i | \(0.641184\pi\) | |||||||
\(810\) | 3008.61 | 0.130508 | ||||||||
\(811\) | −19881.6 | −0.860836 | −0.430418 | − | 0.902630i | \(-0.641634\pi\) | ||||
−0.430418 | + | 0.902630i | \(0.641634\pi\) | |||||||
\(812\) | 452.443 | 0.0195537 | ||||||||
\(813\) | −10783.5 | −0.465183 | ||||||||
\(814\) | 7073.81 | 0.304591 | ||||||||
\(815\) | 715.835 | 0.0307664 | ||||||||
\(816\) | −15173.2 | −0.650940 | ||||||||
\(817\) | 2395.50 | 0.102580 | ||||||||
\(818\) | 27398.2 | 1.17109 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 748.924 | 0.0318946 | ||||||||
\(821\) | 32107.5 | 1.36487 | 0.682436 | − | 0.730945i | \(-0.260920\pi\) | ||||
0.682436 | + | 0.730945i | \(0.260920\pi\) | |||||||
\(822\) | −5768.72 | −0.244778 | ||||||||
\(823\) | −39149.9 | −1.65818 | −0.829089 | − | 0.559117i | \(-0.811140\pi\) | ||||
−0.829089 | + | 0.559117i | \(0.811140\pi\) | |||||||
\(824\) | 4093.34 | 0.173056 | ||||||||
\(825\) | 6524.47 | 0.275337 | ||||||||
\(826\) | −413.775 | −0.0174299 | ||||||||
\(827\) | −25509.4 | −1.07261 | −0.536306 | − | 0.844024i | \(-0.680181\pi\) | ||||
−0.536306 | + | 0.844024i | \(0.680181\pi\) | |||||||
\(828\) | 873.353 | 0.0366560 | ||||||||
\(829\) | 8456.68 | 0.354298 | 0.177149 | − | 0.984184i | \(-0.443313\pi\) | ||||
0.177149 | + | 0.984184i | \(0.443313\pi\) | |||||||
\(830\) | −4366.10 | −0.182590 | ||||||||
\(831\) | 19891.5 | 0.830360 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −14497.2 | −0.603001 | ||||||||
\(834\) | 30864.1 | 1.28146 | ||||||||
\(835\) | 116.530 | 0.00482958 | ||||||||
\(836\) | −4427.21 | −0.183156 | ||||||||
\(837\) | −32114.4 | −1.32621 | ||||||||
\(838\) | 24106.4 | 0.993724 | ||||||||
\(839\) | 1705.10 | 0.0701628 | 0.0350814 | − | 0.999384i | \(-0.488831\pi\) | ||||
0.0350814 | + | 0.999384i | \(0.488831\pi\) | |||||||
\(840\) | −60.1245 | −0.00246964 | ||||||||
\(841\) | −22506.6 | −0.922819 | ||||||||
\(842\) | 251.587 | 0.0102972 | ||||||||
\(843\) | −12381.3 | −0.505852 | ||||||||
\(844\) | 17416.5 | 0.710307 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −4781.72 | −0.194325 | ||||||||
\(847\) | −196.043 | −0.00795291 | ||||||||
\(848\) | −25287.0 | −1.02401 | ||||||||
\(849\) | 15104.1 | 0.610567 | ||||||||
\(850\) | 19955.8 | 0.805267 | ||||||||
\(851\) | −5943.14 | −0.239399 | ||||||||
\(852\) | 3511.69 | 0.141207 | ||||||||
\(853\) | 10491.0 | 0.421108 | 0.210554 | − | 0.977582i | \(-0.432473\pi\) | ||||
0.210554 | + | 0.977582i | \(0.432473\pi\) | |||||||
\(854\) | 2049.80 | 0.0821343 | ||||||||
\(855\) | −313.796 | −0.0125516 | ||||||||
\(856\) | −3391.47 | −0.135418 | ||||||||
\(857\) | 28256.3 | 1.12627 | 0.563136 | − | 0.826364i | \(-0.309595\pi\) | ||||
0.563136 | + | 0.826364i | \(0.309595\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −22451.2 | −0.891764 | −0.445882 | − | 0.895092i | \(-0.647110\pi\) | ||||
−0.445882 | + | 0.895092i | \(0.647110\pi\) | |||||||
\(860\) | 320.215 | 0.0126968 | ||||||||
\(861\) | −698.243 | −0.0276377 | ||||||||
\(862\) | 3390.22 | 0.133957 | ||||||||
\(863\) | 25472.8 | 1.00476 | 0.502378 | − | 0.864648i | \(-0.332459\pi\) | ||||
0.502378 | + | 0.864648i | \(0.332459\pi\) | |||||||
\(864\) | −34721.0 | −1.36717 | ||||||||
\(865\) | −3793.59 | −0.149117 | ||||||||
\(866\) | 66499.2 | 2.60939 | ||||||||
\(867\) | −14905.7 | −0.583881 | ||||||||
\(868\) | −2255.87 | −0.0882132 | ||||||||
\(869\) | 3738.35 | 0.145932 | ||||||||
\(870\) | 1029.72 | 0.0401274 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | −2425.23 | −0.0941842 | ||||||||
\(873\) | −2557.16 | −0.0991373 | ||||||||
\(874\) | 8342.74 | 0.322880 | ||||||||
\(875\) | 522.469 | 0.0201859 | ||||||||
\(876\) | −19780.4 | −0.762920 | ||||||||
\(877\) | 43584.1 | 1.67814 | 0.839070 | − | 0.544023i | \(-0.183100\pi\) | ||||
0.839070 | + | 0.544023i | \(0.183100\pi\) | |||||||
\(878\) | −22789.1 | −0.875963 | ||||||||
\(879\) | −173.854 | −0.00667117 | ||||||||
\(880\) | 1058.02 | 0.0405294 | ||||||||
\(881\) | −15725.7 | −0.601374 | −0.300687 | − | 0.953723i | \(-0.597216\pi\) | ||||
−0.300687 | + | 0.953723i | \(0.597216\pi\) | |||||||
\(882\) | −4997.44 | −0.190785 | ||||||||
\(883\) | 29859.6 | 1.13800 | 0.569000 | − | 0.822338i | \(-0.307330\pi\) | ||||
0.569000 | + | 0.822338i | \(0.307330\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −419.861 | −0.0159474 | ||||||||
\(886\) | −19832.8 | −0.752028 | ||||||||
\(887\) | 32321.3 | 1.22350 | 0.611749 | − | 0.791052i | \(-0.290466\pi\) | ||||
0.611749 | + | 0.791052i | \(0.290466\pi\) | |||||||
\(888\) | 4836.40 | 0.182769 | ||||||||
\(889\) | 2018.39 | 0.0761470 | ||||||||
\(890\) | 2308.96 | 0.0869623 | ||||||||
\(891\) | 6707.08 | 0.252184 | ||||||||
\(892\) | −27154.6 | −1.01929 | ||||||||
\(893\) | −20365.2 | −0.763151 | ||||||||
\(894\) | −50248.5 | −1.87982 | ||||||||
\(895\) | −1666.07 | −0.0622239 | ||||||||
\(896\) | 1208.51 | 0.0450596 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 30589.0 | 1.13671 | ||||||||
\(899\) | −9385.48 | −0.348190 | ||||||||
\(900\) | 3067.01 | 0.113593 | ||||||||
\(901\) | 14541.9 | 0.537691 | ||||||||
\(902\) | 3744.73 | 0.138233 | ||||||||
\(903\) | −298.545 | −0.0110022 | ||||||||
\(904\) | −3230.38 | −0.118850 | ||||||||
\(905\) | 76.1366 | 0.00279654 | ||||||||
\(906\) | 32923.8 | 1.20731 | ||||||||
\(907\) | 8207.50 | 0.300469 | 0.150235 | − | 0.988650i | \(-0.451997\pi\) | ||||
0.150235 | + | 0.988650i | \(0.451997\pi\) | |||||||
\(908\) | −12146.0 | −0.443919 | ||||||||
\(909\) | 7791.92 | 0.284314 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −11642.2 | −0.423405 | −0.211702 | − | 0.977334i | \(-0.567901\pi\) | ||||
−0.211702 | + | 0.977334i | \(0.567901\pi\) | |||||||
\(912\) | −22276.2 | −0.808816 | ||||||||
\(913\) | −9733.35 | −0.352822 | ||||||||
\(914\) | 70901.7 | 2.56589 | ||||||||
\(915\) | 2079.95 | 0.0751487 | ||||||||
\(916\) | −11137.0 | −0.401720 | ||||||||
\(917\) | 1770.50 | 0.0637592 | ||||||||
\(918\) | 24024.5 | 0.863756 | ||||||||
\(919\) | −32053.4 | −1.15054 | −0.575269 | − | 0.817964i | \(-0.695103\pi\) | ||||
−0.575269 | + | 0.817964i | \(0.695103\pi\) | |||||||
\(920\) | −270.913 | −0.00970840 | ||||||||
\(921\) | −32872.2 | −1.17609 | ||||||||
\(922\) | 52880.0 | 1.88884 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 551.754 | 0.0196443 | ||||||||
\(925\) | −20870.9 | −0.741872 | ||||||||
\(926\) | −4796.32 | −0.170212 | ||||||||
\(927\) | −2662.49 | −0.0943341 | ||||||||
\(928\) | −10147.2 | −0.358944 | ||||||||
\(929\) | −556.250 | −0.0196447 | −0.00982237 | − | 0.999952i | \(-0.503127\pi\) | ||||
−0.00982237 | + | 0.999952i | \(0.503127\pi\) | |||||||
\(930\) | −5134.17 | −0.181028 | ||||||||
\(931\) | −21283.9 | −0.749249 | ||||||||
\(932\) | −13912.8 | −0.488981 | ||||||||
\(933\) | −24473.4 | −0.858761 | ||||||||
\(934\) | 12013.4 | 0.420868 | ||||||||
\(935\) | −608.436 | −0.0212813 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −18812.9 | −0.655913 | −0.327957 | − | 0.944693i | \(-0.606360\pi\) | ||||
−0.327957 | + | 0.944693i | \(0.606360\pi\) | |||||||
\(938\) | −1558.86 | −0.0542628 | ||||||||
\(939\) | −28813.0 | −1.00136 | ||||||||
\(940\) | −2722.29 | −0.0944587 | ||||||||
\(941\) | −12297.7 | −0.426029 | −0.213015 | − | 0.977049i | \(-0.568328\pi\) | ||||
−0.213015 | + | 0.977049i | \(0.568328\pi\) | |||||||
\(942\) | −33825.8 | −1.16996 | ||||||||
\(943\) | −3146.18 | −0.108647 | ||||||||
\(944\) | 4978.23 | 0.171639 | ||||||||
\(945\) | 312.362 | 0.0107525 | ||||||||
\(946\) | 1601.12 | 0.0550285 | ||||||||
\(947\) | −21301.5 | −0.730946 | −0.365473 | − | 0.930822i | \(-0.619093\pi\) | ||||
−0.365473 | + | 0.930822i | \(0.619093\pi\) | |||||||
\(948\) | −10521.4 | −0.360464 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 29297.7 | 1.00057 | ||||||||
\(951\) | 20651.9 | 0.704189 | ||||||||
\(952\) | −409.961 | −0.0139568 | ||||||||
\(953\) | −1006.35 | −0.0342067 | −0.0171033 | − | 0.999854i | \(-0.505444\pi\) | ||||
−0.0171033 | + | 0.999854i | \(0.505444\pi\) | |||||||
\(954\) | 5012.81 | 0.170121 | ||||||||
\(955\) | 2411.30 | 0.0817047 | ||||||||
\(956\) | 17769.6 | 0.601161 | ||||||||
\(957\) | 2295.56 | 0.0775390 | ||||||||
\(958\) | −43580.2 | −1.46974 | ||||||||
\(959\) | −511.415 | −0.0172205 | ||||||||
\(960\) | −1849.76 | −0.0621881 | ||||||||
\(961\) | 17004.7 | 0.570800 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 2205.96 | 0.0738174 | ||||||||
\(964\) | 14746.2 | 0.492679 | ||||||||
\(965\) | −4175.15 | −0.139278 | ||||||||
\(966\) | −1039.74 | −0.0346304 | ||||||||
\(967\) | −10139.9 | −0.337205 | −0.168602 | − | 0.985684i | \(-0.553925\pi\) | ||||
−0.168602 | + | 0.985684i | \(0.553925\pi\) | |||||||
\(968\) | 718.844 | 0.0238683 | ||||||||
\(969\) | 12810.4 | 0.424696 | ||||||||
\(970\) | −3265.30 | −0.108085 | ||||||||
\(971\) | 40199.7 | 1.32860 | 0.664299 | − | 0.747467i | \(-0.268730\pi\) | ||||
0.664299 | + | 0.747467i | \(0.268730\pi\) | |||||||
\(972\) | 6922.40 | 0.228432 | ||||||||
\(973\) | 2736.20 | 0.0901526 | ||||||||
\(974\) | 24719.3 | 0.813202 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −24661.7 | −0.808812 | ||||||||
\(977\) | 49085.4 | 1.60735 | 0.803675 | − | 0.595068i | \(-0.202875\pi\) | ||||
0.803675 | + | 0.595068i | \(0.202875\pi\) | |||||||
\(978\) | −10073.7 | −0.329368 | ||||||||
\(979\) | 5147.35 | 0.168039 | ||||||||
\(980\) | −2845.10 | −0.0927380 | ||||||||
\(981\) | 1577.48 | 0.0513405 | ||||||||
\(982\) | −29416.9 | −0.955937 | ||||||||
\(983\) | −33803.0 | −1.09680 | −0.548398 | − | 0.836218i | \(-0.684762\pi\) | ||||
−0.548398 | + | 0.836218i | \(0.684762\pi\) | |||||||
\(984\) | 2560.29 | 0.0829463 | ||||||||
\(985\) | 2372.31 | 0.0767393 | ||||||||
\(986\) | 7021.19 | 0.226775 | ||||||||
\(987\) | 2538.06 | 0.0818515 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −1345.20 | −0.0432507 | ||||||||
\(990\) | −209.738 | −0.00673324 | ||||||||
\(991\) | −51713.3 | −1.65764 | −0.828822 | − | 0.559512i | \(-0.810989\pi\) | ||||
−0.828822 | + | 0.559512i | \(0.810989\pi\) | |||||||
\(992\) | 50593.9 | 1.61931 | ||||||||
\(993\) | 15629.7 | 0.499490 | ||||||||
\(994\) | 698.272 | 0.0222815 | ||||||||
\(995\) | 3709.59 | 0.118193 | ||||||||
\(996\) | 27394.1 | 0.871500 | ||||||||
\(997\) | −3230.85 | −0.102630 | −0.0513150 | − | 0.998683i | \(-0.516341\pi\) | ||||
−0.0513150 | + | 0.998683i | \(0.516341\pi\) | |||||||
\(998\) | 16663.0 | 0.528515 | ||||||||
\(999\) | −25126.3 | −0.795756 |
(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 | 1859.4.a.o.1.6 | yes | 39 | |
13.12 | even | 2 | 1859.4.a.n.1.34 | ✓ | 39 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1859.4.a.n.1.34 | ✓ | 39 | 13.12 | even | 2 | ||
1859.4.a.o.1.6 | yes | 39 | 1.1 | even | 1 | trivial |