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: | \(1\) |
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 | 1.5 | ||
Root | \(1.07125\) 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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.07125 | −0.378742 | −0.189371 | − | 0.981906i | \(-0.560645\pi\) | ||||
−0.189371 | + | 0.981906i | \(0.560645\pi\) | |||||||
\(3\) | 5.02012 | 0.966123 | 0.483061 | − | 0.875586i | \(-0.339525\pi\) | ||||
0.483061 | + | 0.875586i | \(0.339525\pi\) | |||||||
\(4\) | −6.85243 | −0.856554 | ||||||||
\(5\) | −4.32398 | −0.386749 | −0.193374 | − | 0.981125i | \(-0.561943\pi\) | ||||
−0.193374 | + | 0.981125i | \(0.561943\pi\) | |||||||
\(6\) | −5.37778 | −0.365912 | ||||||||
\(7\) | −4.44673 | −0.240101 | −0.120050 | − | 0.992768i | \(-0.538306\pi\) | ||||
−0.120050 | + | 0.992768i | \(0.538306\pi\) | |||||||
\(8\) | 15.9106 | 0.703156 | ||||||||
\(9\) | −1.79838 | −0.0666068 | ||||||||
\(10\) | 4.63204 | 0.146478 | ||||||||
\(11\) | 68.9570 | 1.89012 | 0.945059 | − | 0.326899i | \(-0.106004\pi\) | ||||
0.945059 | + | 0.326899i | \(0.106004\pi\) | |||||||
\(12\) | −34.4000 | −0.827536 | ||||||||
\(13\) | −27.1960 | −0.580217 | −0.290108 | − | 0.956994i | \(-0.593691\pi\) | ||||
−0.290108 | + | 0.956994i | \(0.593691\pi\) | |||||||
\(14\) | 4.76354 | 0.0909363 | ||||||||
\(15\) | −21.7069 | −0.373647 | ||||||||
\(16\) | 37.7753 | 0.590239 | ||||||||
\(17\) | 0 | 0 | ||||||||
\(18\) | 1.92651 | 0.0252268 | ||||||||
\(19\) | −123.839 | −1.49529 | −0.747646 | − | 0.664098i | \(-0.768816\pi\) | ||||
−0.747646 | + | 0.664098i | \(0.768816\pi\) | |||||||
\(20\) | 29.6298 | 0.331271 | ||||||||
\(21\) | −22.3231 | −0.231967 | ||||||||
\(22\) | −73.8698 | −0.715868 | ||||||||
\(23\) | −98.6310 | −0.894173 | −0.447086 | − | 0.894491i | \(-0.647538\pi\) | ||||
−0.447086 | + | 0.894491i | \(0.647538\pi\) | |||||||
\(24\) | 79.8731 | 0.679335 | ||||||||
\(25\) | −106.303 | −0.850426 | ||||||||
\(26\) | 29.1336 | 0.219753 | ||||||||
\(27\) | −144.571 | −1.03047 | ||||||||
\(28\) | 30.4709 | 0.205659 | ||||||||
\(29\) | −21.9952 | −0.140842 | −0.0704209 | − | 0.997517i | \(-0.522434\pi\) | ||||
−0.0704209 | + | 0.997517i | \(0.522434\pi\) | |||||||
\(30\) | 23.2534 | 0.141516 | ||||||||
\(31\) | −241.893 | −1.40146 | −0.700730 | − | 0.713426i | \(-0.747142\pi\) | ||||
−0.700730 | + | 0.713426i | \(0.747142\pi\) | |||||||
\(32\) | −167.751 | −0.926705 | ||||||||
\(33\) | 346.172 | 1.82609 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 19.2276 | 0.0928586 | ||||||||
\(36\) | 12.3233 | 0.0570524 | ||||||||
\(37\) | −324.851 | −1.44338 | −0.721692 | − | 0.692214i | \(-0.756636\pi\) | ||||
−0.721692 | + | 0.692214i | \(0.756636\pi\) | |||||||
\(38\) | 132.662 | 0.566330 | ||||||||
\(39\) | −136.527 | −0.560561 | ||||||||
\(40\) | −68.7971 | −0.271945 | ||||||||
\(41\) | 164.148 | 0.625260 | 0.312630 | − | 0.949875i | \(-0.398790\pi\) | ||||
0.312630 | + | 0.949875i | \(0.398790\pi\) | |||||||
\(42\) | 23.9135 | 0.0878557 | ||||||||
\(43\) | 383.332 | 1.35948 | 0.679739 | − | 0.733454i | \(-0.262093\pi\) | ||||
0.679739 | + | 0.733454i | \(0.262093\pi\) | |||||||
\(44\) | −472.523 | −1.61899 | ||||||||
\(45\) | 7.77618 | 0.0257601 | ||||||||
\(46\) | 105.658 | 0.338661 | ||||||||
\(47\) | 411.060 | 1.27573 | 0.637865 | − | 0.770148i | \(-0.279818\pi\) | ||||
0.637865 | + | 0.770148i | \(0.279818\pi\) | |||||||
\(48\) | 189.637 | 0.570243 | ||||||||
\(49\) | −323.227 | −0.942352 | ||||||||
\(50\) | 113.877 | 0.322092 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 186.359 | 0.496987 | ||||||||
\(53\) | −380.053 | −0.984987 | −0.492493 | − | 0.870316i | \(-0.663914\pi\) | ||||
−0.492493 | + | 0.870316i | \(0.663914\pi\) | |||||||
\(54\) | 154.871 | 0.390284 | ||||||||
\(55\) | −298.169 | −0.731001 | ||||||||
\(56\) | −70.7501 | −0.168828 | ||||||||
\(57\) | −621.685 | −1.44464 | ||||||||
\(58\) | 23.5623 | 0.0533428 | ||||||||
\(59\) | 63.3150 | 0.139710 | 0.0698552 | − | 0.997557i | \(-0.477746\pi\) | ||||
0.0698552 | + | 0.997557i | \(0.477746\pi\) | |||||||
\(60\) | 148.745 | 0.320049 | ||||||||
\(61\) | 37.1265 | 0.0779272 | 0.0389636 | − | 0.999241i | \(-0.487594\pi\) | ||||
0.0389636 | + | 0.999241i | \(0.487594\pi\) | |||||||
\(62\) | 259.127 | 0.530793 | ||||||||
\(63\) | 7.99693 | 0.0159924 | ||||||||
\(64\) | −122.499 | −0.239257 | ||||||||
\(65\) | 117.595 | 0.224398 | ||||||||
\(66\) | −370.836 | −0.691617 | ||||||||
\(67\) | −48.2971 | −0.0880660 | −0.0440330 | − | 0.999030i | \(-0.514021\pi\) | ||||
−0.0440330 | + | 0.999030i | \(0.514021\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −495.139 | −0.863881 | ||||||||
\(70\) | −20.5974 | −0.0351695 | ||||||||
\(71\) | −672.362 | −1.12387 | −0.561934 | − | 0.827182i | \(-0.689943\pi\) | ||||
−0.561934 | + | 0.827182i | \(0.689943\pi\) | |||||||
\(72\) | −28.6134 | −0.0468350 | ||||||||
\(73\) | −562.892 | −0.902486 | −0.451243 | − | 0.892401i | \(-0.649019\pi\) | ||||
−0.451243 | + | 0.892401i | \(0.649019\pi\) | |||||||
\(74\) | 347.996 | 0.546671 | ||||||||
\(75\) | −533.655 | −0.821615 | ||||||||
\(76\) | 848.596 | 1.28080 | ||||||||
\(77\) | −306.633 | −0.453819 | ||||||||
\(78\) | 146.254 | 0.212308 | ||||||||
\(79\) | 461.229 | 0.656864 | 0.328432 | − | 0.944528i | \(-0.393480\pi\) | ||||
0.328432 | + | 0.944528i | \(0.393480\pi\) | |||||||
\(80\) | −163.340 | −0.228274 | ||||||||
\(81\) | −677.209 | −0.928957 | ||||||||
\(82\) | −175.843 | −0.236812 | ||||||||
\(83\) | 972.576 | 1.28619 | 0.643097 | − | 0.765785i | \(-0.277649\pi\) | ||||
0.643097 | + | 0.765785i | \(0.277649\pi\) | |||||||
\(84\) | 152.968 | 0.198692 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −410.643 | −0.514892 | ||||||||
\(87\) | −110.419 | −0.136071 | ||||||||
\(88\) | 1097.15 | 1.32905 | ||||||||
\(89\) | 16.0131 | 0.0190717 | 0.00953587 | − | 0.999955i | \(-0.496965\pi\) | ||||
0.00953587 | + | 0.999955i | \(0.496965\pi\) | |||||||
\(90\) | −8.33020 | −0.00975645 | ||||||||
\(91\) | 120.933 | 0.139311 | ||||||||
\(92\) | 675.862 | 0.765907 | ||||||||
\(93\) | −1214.33 | −1.35398 | ||||||||
\(94\) | −440.346 | −0.483173 | ||||||||
\(95\) | 535.476 | 0.578302 | ||||||||
\(96\) | −842.133 | −0.895310 | ||||||||
\(97\) | −598.704 | −0.626693 | −0.313346 | − | 0.949639i | \(-0.601450\pi\) | ||||
−0.313346 | + | 0.949639i | \(0.601450\pi\) | |||||||
\(98\) | 346.255 | 0.356909 | ||||||||
\(99\) | −124.011 | −0.125895 | ||||||||
\(100\) | 728.436 | 0.728436 | ||||||||
\(101\) | −1545.14 | −1.52225 | −0.761124 | − | 0.648607i | \(-0.775352\pi\) | ||||
−0.761124 | + | 0.648607i | \(0.775352\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1045.57 | 1.00022 | 0.500111 | − | 0.865961i | \(-0.333292\pi\) | ||||
0.500111 | + | 0.865961i | \(0.333292\pi\) | |||||||
\(104\) | −432.705 | −0.407983 | ||||||||
\(105\) | 96.5247 | 0.0897128 | ||||||||
\(106\) | 407.130 | 0.373056 | ||||||||
\(107\) | 815.729 | 0.737005 | 0.368502 | − | 0.929627i | \(-0.379871\pi\) | ||||
0.368502 | + | 0.929627i | \(0.379871\pi\) | |||||||
\(108\) | 990.666 | 0.882656 | ||||||||
\(109\) | −438.510 | −0.385336 | −0.192668 | − | 0.981264i | \(-0.561714\pi\) | ||||
−0.192668 | + | 0.981264i | \(0.561714\pi\) | |||||||
\(110\) | 319.412 | 0.276861 | ||||||||
\(111\) | −1630.79 | −1.39449 | ||||||||
\(112\) | −167.977 | −0.141717 | ||||||||
\(113\) | −665.416 | −0.553956 | −0.276978 | − | 0.960876i | \(-0.589333\pi\) | ||||
−0.276978 | + | 0.960876i | \(0.589333\pi\) | |||||||
\(114\) | 665.977 | 0.547145 | ||||||||
\(115\) | 426.478 | 0.345820 | ||||||||
\(116\) | 150.721 | 0.120639 | ||||||||
\(117\) | 48.9089 | 0.0386464 | ||||||||
\(118\) | −67.8259 | −0.0529143 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −345.370 | −0.262732 | ||||||||
\(121\) | 3424.06 | 2.57255 | ||||||||
\(122\) | −39.7716 | −0.0295143 | ||||||||
\(123\) | 824.044 | 0.604077 | ||||||||
\(124\) | 1657.56 | 1.20043 | ||||||||
\(125\) | 1000.15 | 0.715649 | ||||||||
\(126\) | −8.56667 | −0.00605698 | ||||||||
\(127\) | −524.835 | −0.366706 | −0.183353 | − | 0.983047i | \(-0.558695\pi\) | ||||
−0.183353 | + | 0.983047i | \(0.558695\pi\) | |||||||
\(128\) | 1473.24 | 1.01732 | ||||||||
\(129\) | 1924.37 | 1.31342 | ||||||||
\(130\) | −125.973 | −0.0849891 | ||||||||
\(131\) | 129.359 | 0.0862760 | 0.0431380 | − | 0.999069i | \(-0.486264\pi\) | ||||
0.0431380 | + | 0.999069i | \(0.486264\pi\) | |||||||
\(132\) | −2372.12 | −1.56414 | ||||||||
\(133\) | 550.677 | 0.359021 | ||||||||
\(134\) | 51.7380 | 0.0333543 | ||||||||
\(135\) | 625.124 | 0.398534 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 760.804 | 0.474452 | 0.237226 | − | 0.971455i | \(-0.423762\pi\) | ||||
0.237226 | + | 0.971455i | \(0.423762\pi\) | |||||||
\(138\) | 530.416 | 0.327188 | ||||||||
\(139\) | 859.570 | 0.524516 | 0.262258 | − | 0.964998i | \(-0.415533\pi\) | ||||
0.262258 | + | 0.964998i | \(0.415533\pi\) | |||||||
\(140\) | −131.756 | −0.0795384 | ||||||||
\(141\) | 2063.57 | 1.23251 | ||||||||
\(142\) | 720.265 | 0.425657 | ||||||||
\(143\) | −1875.36 | −1.09668 | ||||||||
\(144\) | −67.9345 | −0.0393140 | ||||||||
\(145\) | 95.1070 | 0.0544704 | ||||||||
\(146\) | 602.995 | 0.341810 | ||||||||
\(147\) | −1622.64 | −0.910427 | ||||||||
\(148\) | 2226.02 | 1.23634 | ||||||||
\(149\) | 2709.00 | 1.48946 | 0.744730 | − | 0.667366i | \(-0.232578\pi\) | ||||
0.744730 | + | 0.667366i | \(0.232578\pi\) | |||||||
\(150\) | 571.675 | 0.311181 | ||||||||
\(151\) | 406.811 | 0.219244 | 0.109622 | − | 0.993973i | \(-0.465036\pi\) | ||||
0.109622 | + | 0.993973i | \(0.465036\pi\) | |||||||
\(152\) | −1970.35 | −1.05142 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 328.479 | 0.171881 | ||||||||
\(155\) | 1045.94 | 0.542013 | ||||||||
\(156\) | 935.544 | 0.480151 | ||||||||
\(157\) | −2314.18 | −1.17638 | −0.588191 | − | 0.808722i | \(-0.700160\pi\) | ||||
−0.588191 | + | 0.808722i | \(0.700160\pi\) | |||||||
\(158\) | −494.089 | −0.248782 | ||||||||
\(159\) | −1907.91 | −0.951618 | ||||||||
\(160\) | 725.354 | 0.358402 | ||||||||
\(161\) | 438.585 | 0.214692 | ||||||||
\(162\) | 725.457 | 0.351835 | ||||||||
\(163\) | 2046.67 | 0.983481 | 0.491741 | − | 0.870742i | \(-0.336361\pi\) | ||||
0.491741 | + | 0.870742i | \(0.336361\pi\) | |||||||
\(164\) | −1124.81 | −0.535569 | ||||||||
\(165\) | −1496.84 | −0.706237 | ||||||||
\(166\) | −1041.87 | −0.487136 | ||||||||
\(167\) | 821.932 | 0.380856 | 0.190428 | − | 0.981701i | \(-0.439012\pi\) | ||||
0.190428 | + | 0.981701i | \(0.439012\pi\) | |||||||
\(168\) | −355.174 | −0.163109 | ||||||||
\(169\) | −1457.38 | −0.663348 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 222.710 | 0.0995967 | ||||||||
\(172\) | −2626.76 | −1.16447 | ||||||||
\(173\) | −1450.84 | −0.637603 | −0.318802 | − | 0.947821i | \(-0.603280\pi\) | ||||
−0.318802 | + | 0.947821i | \(0.603280\pi\) | |||||||
\(174\) | 118.286 | 0.0515357 | ||||||||
\(175\) | 472.701 | 0.204188 | ||||||||
\(176\) | 2604.87 | 1.11562 | ||||||||
\(177\) | 317.849 | 0.134977 | ||||||||
\(178\) | −17.1539 | −0.00722327 | ||||||||
\(179\) | −2841.91 | −1.18667 | −0.593337 | − | 0.804954i | \(-0.702190\pi\) | ||||
−0.593337 | + | 0.804954i | \(0.702190\pi\) | |||||||
\(180\) | −53.2858 | −0.0220649 | ||||||||
\(181\) | 4019.94 | 1.65083 | 0.825414 | − | 0.564528i | \(-0.190942\pi\) | ||||
0.825414 | + | 0.564528i | \(0.190942\pi\) | |||||||
\(182\) | −129.549 | −0.0527628 | ||||||||
\(183\) | 186.379 | 0.0752872 | ||||||||
\(184\) | −1569.28 | −0.628743 | ||||||||
\(185\) | 1404.65 | 0.558227 | ||||||||
\(186\) | 1300.85 | 0.512811 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | −2816.76 | −1.09273 | ||||||||
\(189\) | 642.870 | 0.247417 | ||||||||
\(190\) | −573.626 | −0.219027 | ||||||||
\(191\) | 3374.10 | 1.27823 | 0.639113 | − | 0.769113i | \(-0.279301\pi\) | ||||
0.639113 | + | 0.769113i | \(0.279301\pi\) | |||||||
\(192\) | −614.962 | −0.231151 | ||||||||
\(193\) | −343.680 | −0.128179 | −0.0640897 | − | 0.997944i | \(-0.520414\pi\) | ||||
−0.0640897 | + | 0.997944i | \(0.520414\pi\) | |||||||
\(194\) | 641.359 | 0.237355 | ||||||||
\(195\) | 590.342 | 0.216796 | ||||||||
\(196\) | 2214.89 | 0.807175 | ||||||||
\(197\) | −4600.65 | −1.66387 | −0.831935 | − | 0.554873i | \(-0.812767\pi\) | ||||
−0.831935 | + | 0.554873i | \(0.812767\pi\) | |||||||
\(198\) | 132.846 | 0.0476817 | ||||||||
\(199\) | −1018.79 | −0.362914 | −0.181457 | − | 0.983399i | \(-0.558081\pi\) | ||||
−0.181457 | + | 0.983399i | \(0.558081\pi\) | |||||||
\(200\) | −1691.35 | −0.597982 | ||||||||
\(201\) | −242.457 | −0.0850826 | ||||||||
\(202\) | 1655.22 | 0.576540 | ||||||||
\(203\) | 97.8069 | 0.0338162 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −709.774 | −0.241818 | ||||||||
\(206\) | −1120.06 | −0.378827 | ||||||||
\(207\) | 177.376 | 0.0595580 | ||||||||
\(208\) | −1027.34 | −0.342467 | ||||||||
\(209\) | −8539.54 | −2.82628 | ||||||||
\(210\) | −103.402 | −0.0339781 | ||||||||
\(211\) | −2498.29 | −0.815115 | −0.407557 | − | 0.913180i | \(-0.633619\pi\) | ||||
−0.407557 | + | 0.913180i | \(0.633619\pi\) | |||||||
\(212\) | 2604.29 | 0.843694 | ||||||||
\(213\) | −3375.34 | −1.08580 | ||||||||
\(214\) | −873.846 | −0.279135 | ||||||||
\(215\) | −1657.52 | −0.525776 | ||||||||
\(216\) | −2300.22 | −0.724583 | ||||||||
\(217\) | 1075.63 | 0.336492 | ||||||||
\(218\) | 469.752 | 0.145943 | ||||||||
\(219\) | −2825.78 | −0.871912 | ||||||||
\(220\) | 2043.18 | 0.626142 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 1746.98 | 0.528151 | ||||||||
\(223\) | −4252.54 | −1.27700 | −0.638500 | − | 0.769622i | \(-0.720445\pi\) | ||||
−0.638500 | + | 0.769622i | \(0.720445\pi\) | |||||||
\(224\) | 745.945 | 0.222502 | ||||||||
\(225\) | 191.174 | 0.0566442 | ||||||||
\(226\) | 712.823 | 0.209807 | ||||||||
\(227\) | −6652.94 | −1.94525 | −0.972623 | − | 0.232387i | \(-0.925347\pi\) | ||||
−0.972623 | + | 0.232387i | \(0.925347\pi\) | |||||||
\(228\) | 4260.06 | 1.23741 | ||||||||
\(229\) | −3364.85 | −0.970984 | −0.485492 | − | 0.874241i | \(-0.661359\pi\) | ||||
−0.485492 | + | 0.874241i | \(0.661359\pi\) | |||||||
\(230\) | −456.863 | −0.130977 | ||||||||
\(231\) | −1539.33 | −0.438445 | ||||||||
\(232\) | −349.958 | −0.0990338 | ||||||||
\(233\) | 1944.15 | 0.546634 | 0.273317 | − | 0.961924i | \(-0.411879\pi\) | ||||
0.273317 | + | 0.961924i | \(0.411879\pi\) | |||||||
\(234\) | −52.3935 | −0.0146370 | ||||||||
\(235\) | −1777.42 | −0.493387 | ||||||||
\(236\) | −433.862 | −0.119670 | ||||||||
\(237\) | 2315.42 | 0.634612 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −392.233 | −0.106157 | −0.0530783 | − | 0.998590i | \(-0.516903\pi\) | ||||
−0.0530783 | + | 0.998590i | \(0.516903\pi\) | |||||||
\(240\) | −819.985 | −0.220541 | ||||||||
\(241\) | −1163.20 | −0.310905 | −0.155453 | − | 0.987843i | \(-0.549684\pi\) | ||||
−0.155453 | + | 0.987843i | \(0.549684\pi\) | |||||||
\(242\) | −3668.01 | −0.974334 | ||||||||
\(243\) | 503.754 | 0.132987 | ||||||||
\(244\) | −254.407 | −0.0667488 | ||||||||
\(245\) | 1397.63 | 0.364453 | ||||||||
\(246\) | −882.753 | −0.228790 | ||||||||
\(247\) | 3367.92 | 0.867594 | ||||||||
\(248\) | −3848.66 | −0.985445 | ||||||||
\(249\) | 4882.45 | 1.24262 | ||||||||
\(250\) | −1071.41 | −0.271047 | ||||||||
\(251\) | 2743.17 | 0.689831 | 0.344915 | − | 0.938634i | \(-0.387908\pi\) | ||||
0.344915 | + | 0.938634i | \(0.387908\pi\) | |||||||
\(252\) | −54.7984 | −0.0136983 | ||||||||
\(253\) | −6801.29 | −1.69009 | ||||||||
\(254\) | 562.227 | 0.138887 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −598.204 | −0.146046 | ||||||||
\(257\) | 689.924 | 0.167456 | 0.0837282 | − | 0.996489i | \(-0.473317\pi\) | ||||
0.0837282 | + | 0.996489i | \(0.473317\pi\) | |||||||
\(258\) | −2061.48 | −0.497449 | ||||||||
\(259\) | 1444.53 | 0.346558 | ||||||||
\(260\) | −805.813 | −0.192209 | ||||||||
\(261\) | 39.5559 | 0.00938103 | ||||||||
\(262\) | −138.575 | −0.0326764 | ||||||||
\(263\) | 4670.18 | 1.09497 | 0.547483 | − | 0.836817i | \(-0.315586\pi\) | ||||
0.547483 | + | 0.836817i | \(0.315586\pi\) | |||||||
\(264\) | 5507.81 | 1.28402 | ||||||||
\(265\) | 1643.34 | 0.380942 | ||||||||
\(266\) | −589.910 | −0.135976 | ||||||||
\(267\) | 80.3876 | 0.0184256 | ||||||||
\(268\) | 330.952 | 0.0754333 | ||||||||
\(269\) | 868.931 | 0.196951 | 0.0984753 | − | 0.995140i | \(-0.468603\pi\) | ||||
0.0984753 | + | 0.995140i | \(0.468603\pi\) | |||||||
\(270\) | −669.661 | −0.150942 | ||||||||
\(271\) | 6730.27 | 1.50862 | 0.754308 | − | 0.656521i | \(-0.227973\pi\) | ||||
0.754308 | + | 0.656521i | \(0.227973\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 607.100 | 0.134591 | ||||||||
\(274\) | −815.008 | −0.179695 | ||||||||
\(275\) | −7330.35 | −1.60741 | ||||||||
\(276\) | 3392.91 | 0.739961 | ||||||||
\(277\) | 3264.04 | 0.708005 | 0.354003 | − | 0.935244i | \(-0.384820\pi\) | ||||
0.354003 | + | 0.935244i | \(0.384820\pi\) | |||||||
\(278\) | −920.810 | −0.198657 | ||||||||
\(279\) | 435.017 | 0.0933469 | ||||||||
\(280\) | 305.922 | 0.0652941 | ||||||||
\(281\) | 8205.96 | 1.74209 | 0.871044 | − | 0.491205i | \(-0.163443\pi\) | ||||
0.871044 | + | 0.491205i | \(0.163443\pi\) | |||||||
\(282\) | −2210.59 | −0.466805 | ||||||||
\(283\) | 2958.69 | 0.621469 | 0.310734 | − | 0.950497i | \(-0.399425\pi\) | ||||
0.310734 | + | 0.950497i | \(0.399425\pi\) | |||||||
\(284\) | 4607.32 | 0.962654 | ||||||||
\(285\) | 2688.15 | 0.558711 | ||||||||
\(286\) | 2008.97 | 0.415359 | ||||||||
\(287\) | −729.922 | −0.150125 | ||||||||
\(288\) | 301.682 | 0.0617249 | ||||||||
\(289\) | 0 | 0 | ||||||||
\(290\) | −101.883 | −0.0206303 | ||||||||
\(291\) | −3005.57 | −0.605462 | ||||||||
\(292\) | 3857.18 | 0.773028 | ||||||||
\(293\) | −5413.44 | −1.07937 | −0.539687 | − | 0.841866i | \(-0.681457\pi\) | ||||
−0.539687 | + | 0.841866i | \(0.681457\pi\) | |||||||
\(294\) | 1738.24 | 0.344817 | ||||||||
\(295\) | −273.773 | −0.0540328 | ||||||||
\(296\) | −5168.58 | −1.01492 | ||||||||
\(297\) | −9969.20 | −1.94772 | ||||||||
\(298\) | −2902.00 | −0.564122 | ||||||||
\(299\) | 2682.37 | 0.518814 | ||||||||
\(300\) | 3656.83 | 0.703758 | ||||||||
\(301\) | −1704.57 | −0.326412 | ||||||||
\(302\) | −435.795 | −0.0830370 | ||||||||
\(303\) | −7756.78 | −1.47068 | ||||||||
\(304\) | −4678.04 | −0.882580 | ||||||||
\(305\) | −160.534 | −0.0301382 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 7347.01 | 1.36585 | 0.682925 | − | 0.730488i | \(-0.260707\pi\) | ||||
0.682925 | + | 0.730488i | \(0.260707\pi\) | |||||||
\(308\) | 2101.18 | 0.388721 | ||||||||
\(309\) | 5248.88 | 0.966338 | ||||||||
\(310\) | −1120.46 | −0.205283 | ||||||||
\(311\) | −4971.09 | −0.906381 | −0.453190 | − | 0.891414i | \(-0.649714\pi\) | ||||
−0.453190 | + | 0.891414i | \(0.649714\pi\) | |||||||
\(312\) | −2172.23 | −0.394162 | ||||||||
\(313\) | 6935.73 | 1.25249 | 0.626247 | − | 0.779625i | \(-0.284590\pi\) | ||||
0.626247 | + | 0.779625i | \(0.284590\pi\) | |||||||
\(314\) | 2479.06 | 0.445546 | ||||||||
\(315\) | −34.5786 | −0.00618502 | ||||||||
\(316\) | −3160.54 | −0.562640 | ||||||||
\(317\) | −7667.25 | −1.35847 | −0.679236 | − | 0.733920i | \(-0.737689\pi\) | ||||
−0.679236 | + | 0.733920i | \(0.737689\pi\) | |||||||
\(318\) | 2043.84 | 0.360418 | ||||||||
\(319\) | −1516.73 | −0.266208 | ||||||||
\(320\) | 529.685 | 0.0925322 | ||||||||
\(321\) | 4095.06 | 0.712037 | ||||||||
\(322\) | −469.832 | −0.0813128 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 4640.53 | 0.795702 | ||||||||
\(325\) | 2891.02 | 0.493431 | ||||||||
\(326\) | −2192.48 | −0.372486 | ||||||||
\(327\) | −2201.37 | −0.372282 | ||||||||
\(328\) | 2611.70 | 0.439655 | ||||||||
\(329\) | −1827.87 | −0.306304 | ||||||||
\(330\) | 1603.49 | 0.267482 | ||||||||
\(331\) | 1425.58 | 0.236728 | 0.118364 | − | 0.992970i | \(-0.462235\pi\) | ||||
0.118364 | + | 0.992970i | \(0.462235\pi\) | |||||||
\(332\) | −6664.51 | −1.10169 | ||||||||
\(333\) | 584.208 | 0.0961393 | ||||||||
\(334\) | −880.491 | −0.144246 | ||||||||
\(335\) | 208.836 | 0.0340594 | ||||||||
\(336\) | −843.262 | −0.136916 | ||||||||
\(337\) | 2472.94 | 0.399732 | 0.199866 | − | 0.979823i | \(-0.435949\pi\) | ||||
0.199866 | + | 0.979823i | \(0.435949\pi\) | |||||||
\(338\) | 1561.21 | 0.251238 | ||||||||
\(339\) | −3340.47 | −0.535190 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −16680.2 | −2.64893 | ||||||||
\(342\) | −238.577 | −0.0377215 | ||||||||
\(343\) | 2962.53 | 0.466360 | ||||||||
\(344\) | 6099.04 | 0.955925 | ||||||||
\(345\) | 2140.97 | 0.334105 | ||||||||
\(346\) | 1554.21 | 0.241487 | ||||||||
\(347\) | −3930.28 | −0.608036 | −0.304018 | − | 0.952666i | \(-0.598328\pi\) | ||||
−0.304018 | + | 0.952666i | \(0.598328\pi\) | |||||||
\(348\) | 756.637 | 0.116552 | ||||||||
\(349\) | −6606.93 | −1.01336 | −0.506678 | − | 0.862136i | \(-0.669127\pi\) | ||||
−0.506678 | + | 0.862136i | \(0.669127\pi\) | |||||||
\(350\) | −506.379 | −0.0773346 | ||||||||
\(351\) | 3931.77 | 0.597898 | ||||||||
\(352\) | −11567.6 | −1.75158 | ||||||||
\(353\) | −6336.87 | −0.955461 | −0.477731 | − | 0.878506i | \(-0.658541\pi\) | ||||
−0.477731 | + | 0.878506i | \(0.658541\pi\) | |||||||
\(354\) | −340.494 | −0.0511217 | ||||||||
\(355\) | 2907.28 | 0.434655 | ||||||||
\(356\) | −109.729 | −0.0163360 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 3044.39 | 0.449444 | ||||||||
\(359\) | −3060.68 | −0.449963 | −0.224982 | − | 0.974363i | \(-0.572232\pi\) | ||||
−0.224982 | + | 0.974363i | \(0.572232\pi\) | |||||||
\(360\) | 123.724 | 0.0181134 | ||||||||
\(361\) | 8477.02 | 1.23590 | ||||||||
\(362\) | −4306.34 | −0.625238 | ||||||||
\(363\) | 17189.2 | 2.48540 | ||||||||
\(364\) | −828.688 | −0.119327 | ||||||||
\(365\) | 2433.93 | 0.349035 | ||||||||
\(366\) | −199.658 | −0.0285145 | ||||||||
\(367\) | 5391.79 | 0.766892 | 0.383446 | − | 0.923563i | \(-0.374737\pi\) | ||||
0.383446 | + | 0.923563i | \(0.374737\pi\) | |||||||
\(368\) | −3725.81 | −0.527776 | ||||||||
\(369\) | −295.202 | −0.0416466 | ||||||||
\(370\) | −1504.73 | −0.211424 | ||||||||
\(371\) | 1689.99 | 0.236496 | ||||||||
\(372\) | 8321.13 | 1.15976 | ||||||||
\(373\) | −1509.56 | −0.209550 | −0.104775 | − | 0.994496i | \(-0.533412\pi\) | ||||
−0.104775 | + | 0.994496i | \(0.533412\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 5020.88 | 0.691405 | ||||||||
\(376\) | 6540.22 | 0.897037 | ||||||||
\(377\) | 598.183 | 0.0817189 | ||||||||
\(378\) | −688.671 | −0.0937075 | ||||||||
\(379\) | 4111.54 | 0.557244 | 0.278622 | − | 0.960401i | \(-0.410122\pi\) | ||||
0.278622 | + | 0.960401i | \(0.410122\pi\) | |||||||
\(380\) | −3669.31 | −0.495347 | ||||||||
\(381\) | −2634.74 | −0.354283 | ||||||||
\(382\) | −3614.49 | −0.484119 | ||||||||
\(383\) | −6538.64 | −0.872347 | −0.436173 | − | 0.899863i | \(-0.643667\pi\) | ||||
−0.436173 | + | 0.899863i | \(0.643667\pi\) | |||||||
\(384\) | 7395.84 | 0.982857 | ||||||||
\(385\) | 1325.87 | 0.175514 | ||||||||
\(386\) | 368.166 | 0.0485470 | ||||||||
\(387\) | −689.378 | −0.0905506 | ||||||||
\(388\) | 4102.58 | 0.536796 | ||||||||
\(389\) | 7955.67 | 1.03694 | 0.518468 | − | 0.855097i | \(-0.326502\pi\) | ||||
0.518468 | + | 0.855097i | \(0.326502\pi\) | |||||||
\(390\) | −632.401 | −0.0821099 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | −5142.73 | −0.662620 | ||||||||
\(393\) | 649.398 | 0.0833532 | ||||||||
\(394\) | 4928.42 | 0.630178 | ||||||||
\(395\) | −1994.34 | −0.254041 | ||||||||
\(396\) | 849.778 | 0.107836 | ||||||||
\(397\) | −2375.20 | −0.300271 | −0.150136 | − | 0.988665i | \(-0.547971\pi\) | ||||
−0.150136 | + | 0.988665i | \(0.547971\pi\) | |||||||
\(398\) | 1091.37 | 0.137451 | ||||||||
\(399\) | 2764.46 | 0.346858 | ||||||||
\(400\) | −4015.64 | −0.501954 | ||||||||
\(401\) | −434.525 | −0.0541125 | −0.0270563 | − | 0.999634i | \(-0.508613\pi\) | ||||
−0.0270563 | + | 0.999634i | \(0.508613\pi\) | |||||||
\(402\) | 259.731 | 0.0322244 | ||||||||
\(403\) | 6578.53 | 0.813151 | ||||||||
\(404\) | 10588.0 | 1.30389 | ||||||||
\(405\) | 2928.24 | 0.359273 | ||||||||
\(406\) | −104.775 | −0.0128076 | ||||||||
\(407\) | −22400.8 | −2.72817 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −3564.54 | −0.430942 | −0.215471 | − | 0.976510i | \(-0.569129\pi\) | ||||
−0.215471 | + | 0.976510i | \(0.569129\pi\) | |||||||
\(410\) | 760.342 | 0.0915868 | ||||||||
\(411\) | 3819.33 | 0.458378 | ||||||||
\(412\) | −7164.69 | −0.856745 | ||||||||
\(413\) | −281.545 | −0.0335446 | ||||||||
\(414\) | −190.014 | −0.0225572 | ||||||||
\(415\) | −4205.40 | −0.497434 | ||||||||
\(416\) | 4562.17 | 0.537690 | ||||||||
\(417\) | 4315.14 | 0.506747 | ||||||||
\(418\) | 9147.94 | 1.07043 | ||||||||
\(419\) | −16502.8 | −1.92414 | −0.962072 | − | 0.272797i | \(-0.912051\pi\) | ||||
−0.962072 | + | 0.272797i | \(0.912051\pi\) | |||||||
\(420\) | −661.429 | −0.0768439 | ||||||||
\(421\) | −11424.1 | −1.32251 | −0.661255 | − | 0.750161i | \(-0.729976\pi\) | ||||
−0.661255 | + | 0.750161i | \(0.729976\pi\) | |||||||
\(422\) | 2676.28 | 0.308718 | ||||||||
\(423\) | −739.245 | −0.0849724 | ||||||||
\(424\) | −6046.87 | −0.692599 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 3615.82 | 0.411237 | ||||||||
\(427\) | −165.091 | −0.0187104 | ||||||||
\(428\) | −5589.73 | −0.631284 | ||||||||
\(429\) | −9414.51 | −1.05953 | ||||||||
\(430\) | 1775.61 | 0.199134 | ||||||||
\(431\) | 7929.24 | 0.886167 | 0.443083 | − | 0.896480i | \(-0.353885\pi\) | ||||
0.443083 | + | 0.896480i | \(0.353885\pi\) | |||||||
\(432\) | −5461.23 | −0.608226 | ||||||||
\(433\) | −377.380 | −0.0418839 | −0.0209419 | − | 0.999781i | \(-0.506667\pi\) | ||||
−0.0209419 | + | 0.999781i | \(0.506667\pi\) | |||||||
\(434\) | −1152.27 | −0.127444 | ||||||||
\(435\) | 477.449 | 0.0526251 | ||||||||
\(436\) | 3004.86 | 0.330061 | ||||||||
\(437\) | 12214.3 | 1.33705 | ||||||||
\(438\) | 3027.11 | 0.330230 | ||||||||
\(439\) | −4049.99 | −0.440308 | −0.220154 | − | 0.975465i | \(-0.570656\pi\) | ||||
−0.220154 | + | 0.975465i | \(0.570656\pi\) | |||||||
\(440\) | −4744.04 | −0.514008 | ||||||||
\(441\) | 581.286 | 0.0627671 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 3944.38 | 0.423032 | 0.211516 | − | 0.977374i | \(-0.432160\pi\) | ||||
0.211516 | + | 0.977374i | \(0.432160\pi\) | |||||||
\(444\) | 11174.9 | 1.19445 | ||||||||
\(445\) | −69.2403 | −0.00737596 | ||||||||
\(446\) | 4555.51 | 0.483654 | ||||||||
\(447\) | 13599.5 | 1.43900 | ||||||||
\(448\) | 544.722 | 0.0574457 | ||||||||
\(449\) | −2830.17 | −0.297470 | −0.148735 | − | 0.988877i | \(-0.547520\pi\) | ||||
−0.148735 | + | 0.988877i | \(0.547520\pi\) | |||||||
\(450\) | −204.794 | −0.0214535 | ||||||||
\(451\) | 11319.2 | 1.18181 | ||||||||
\(452\) | 4559.72 | 0.474493 | ||||||||
\(453\) | 2042.24 | 0.211817 | ||||||||
\(454\) | 7126.93 | 0.736748 | ||||||||
\(455\) | −522.913 | −0.0538781 | ||||||||
\(456\) | −9891.38 | −1.01580 | ||||||||
\(457\) | 8796.64 | 0.900414 | 0.450207 | − | 0.892924i | \(-0.351350\pi\) | ||||
0.450207 | + | 0.892924i | \(0.351350\pi\) | |||||||
\(458\) | 3604.58 | 0.367753 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −2922.41 | −0.296214 | ||||||||
\(461\) | 10424.8 | 1.05321 | 0.526606 | − | 0.850110i | \(-0.323464\pi\) | ||||
0.526606 | + | 0.850110i | \(0.323464\pi\) | |||||||
\(462\) | 1649.00 | 0.166058 | ||||||||
\(463\) | 6847.90 | 0.687362 | 0.343681 | − | 0.939086i | \(-0.388326\pi\) | ||||
0.343681 | + | 0.939086i | \(0.388326\pi\) | |||||||
\(464\) | −830.877 | −0.0831304 | ||||||||
\(465\) | 5250.75 | 0.523651 | ||||||||
\(466\) | −2082.67 | −0.207033 | ||||||||
\(467\) | 14390.7 | 1.42596 | 0.712979 | − | 0.701186i | \(-0.247346\pi\) | ||||
0.712979 | + | 0.701186i | \(0.247346\pi\) | |||||||
\(468\) | −335.145 | −0.0331028 | ||||||||
\(469\) | 214.764 | 0.0211447 | ||||||||
\(470\) | 1904.05 | 0.186867 | ||||||||
\(471\) | −11617.5 | −1.13653 | ||||||||
\(472\) | 1007.38 | 0.0982382 | ||||||||
\(473\) | 26433.4 | 2.56958 | ||||||||
\(474\) | −2480.39 | −0.240354 | ||||||||
\(475\) | 13164.4 | 1.27163 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 683.482 | 0.0656069 | ||||||||
\(478\) | 420.178 | 0.0402060 | ||||||||
\(479\) | −7163.29 | −0.683296 | −0.341648 | − | 0.939828i | \(-0.610985\pi\) | ||||
−0.341648 | + | 0.939828i | \(0.610985\pi\) | |||||||
\(480\) | 3641.36 | 0.346260 | ||||||||
\(481\) | 8834.67 | 0.837476 | ||||||||
\(482\) | 1246.07 | 0.117753 | ||||||||
\(483\) | 2201.75 | 0.207418 | ||||||||
\(484\) | −23463.2 | −2.20353 | ||||||||
\(485\) | 2588.79 | 0.242373 | ||||||||
\(486\) | −539.644 | −0.0503678 | ||||||||
\(487\) | −14830.1 | −1.37991 | −0.689957 | − | 0.723850i | \(-0.742371\pi\) | ||||
−0.689957 | + | 0.723850i | \(0.742371\pi\) | |||||||
\(488\) | 590.704 | 0.0547949 | ||||||||
\(489\) | 10274.5 | 0.950164 | ||||||||
\(490\) | −1497.20 | −0.138034 | ||||||||
\(491\) | −9634.41 | −0.885529 | −0.442765 | − | 0.896638i | \(-0.646002\pi\) | ||||
−0.442765 | + | 0.896638i | \(0.646002\pi\) | |||||||
\(492\) | −5646.71 | −0.517425 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | −3607.87 | −0.328595 | ||||||||
\(495\) | 536.222 | 0.0486897 | ||||||||
\(496\) | −9137.59 | −0.827197 | ||||||||
\(497\) | 2989.81 | 0.269842 | ||||||||
\(498\) | −5230.30 | −0.470633 | ||||||||
\(499\) | −2033.72 | −0.182449 | −0.0912244 | − | 0.995830i | \(-0.529078\pi\) | ||||
−0.0912244 | + | 0.995830i | \(0.529078\pi\) | |||||||
\(500\) | −6853.46 | −0.612993 | ||||||||
\(501\) | 4126.20 | 0.367954 | ||||||||
\(502\) | −2938.61 | −0.261268 | ||||||||
\(503\) | −6715.07 | −0.595249 | −0.297625 | − | 0.954683i | \(-0.596194\pi\) | ||||
−0.297625 | + | 0.954683i | \(0.596194\pi\) | |||||||
\(504\) | 127.236 | 0.0112451 | ||||||||
\(505\) | 6681.15 | 0.588727 | ||||||||
\(506\) | 7285.85 | 0.640110 | ||||||||
\(507\) | −7316.20 | −0.640876 | ||||||||
\(508\) | 3596.40 | 0.314103 | ||||||||
\(509\) | −1060.04 | −0.0923096 | −0.0461548 | − | 0.998934i | \(-0.514697\pi\) | ||||
−0.0461548 | + | 0.998934i | \(0.514697\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 2503.03 | 0.216688 | ||||||||
\(512\) | −11145.1 | −0.962007 | ||||||||
\(513\) | 17903.5 | 1.54086 | ||||||||
\(514\) | −739.078 | −0.0634228 | ||||||||
\(515\) | −4521.02 | −0.386835 | ||||||||
\(516\) | −13186.6 | −1.12502 | ||||||||
\(517\) | 28345.5 | 2.41128 | ||||||||
\(518\) | −1547.44 | −0.131256 | ||||||||
\(519\) | −7283.39 | −0.616003 | ||||||||
\(520\) | 1871.01 | 0.157787 | ||||||||
\(521\) | 3742.36 | 0.314694 | 0.157347 | − | 0.987543i | \(-0.449706\pi\) | ||||
0.157347 | + | 0.987543i | \(0.449706\pi\) | |||||||
\(522\) | −42.3741 | −0.00355300 | ||||||||
\(523\) | −11603.1 | −0.970113 | −0.485057 | − | 0.874483i | \(-0.661201\pi\) | ||||
−0.485057 | + | 0.874483i | \(0.661201\pi\) | |||||||
\(524\) | −886.425 | −0.0739001 | ||||||||
\(525\) | 2373.02 | 0.197270 | ||||||||
\(526\) | −5002.91 | −0.414710 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 13076.8 | 1.07783 | ||||||||
\(529\) | −2438.93 | −0.200455 | ||||||||
\(530\) | −1760.42 | −0.144279 | ||||||||
\(531\) | −113.865 | −0.00930567 | ||||||||
\(532\) | −3773.48 | −0.307521 | ||||||||
\(533\) | −4464.18 | −0.362786 | ||||||||
\(534\) | −86.1149 | −0.00697857 | ||||||||
\(535\) | −3527.20 | −0.285035 | ||||||||
\(536\) | −768.435 | −0.0619242 | ||||||||
\(537\) | −14266.8 | −1.14647 | ||||||||
\(538\) | −930.839 | −0.0745935 | ||||||||
\(539\) | −22288.7 | −1.78116 | ||||||||
\(540\) | −4283.62 | −0.341366 | ||||||||
\(541\) | −24094.9 | −1.91483 | −0.957415 | − | 0.288717i | \(-0.906771\pi\) | ||||
−0.957415 | + | 0.288717i | \(0.906771\pi\) | |||||||
\(542\) | −7209.77 | −0.571377 | ||||||||
\(543\) | 20180.6 | 1.59490 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 1896.11 | 0.149028 | ||||||||
\(546\) | −650.353 | −0.0509754 | ||||||||
\(547\) | 11145.9 | 0.871234 | 0.435617 | − | 0.900132i | \(-0.356530\pi\) | ||||
0.435617 | + | 0.900132i | \(0.356530\pi\) | |||||||
\(548\) | −5213.36 | −0.406393 | ||||||||
\(549\) | −66.7677 | −0.00519048 | ||||||||
\(550\) | 7852.60 | 0.608793 | ||||||||
\(551\) | 2723.86 | 0.210600 | ||||||||
\(552\) | −7877.96 | −0.607443 | ||||||||
\(553\) | −2050.96 | −0.157714 | ||||||||
\(554\) | −3496.59 | −0.268152 | ||||||||
\(555\) | 7051.52 | 0.539316 | ||||||||
\(556\) | −5890.14 | −0.449276 | ||||||||
\(557\) | −1634.29 | −0.124322 | −0.0621609 | − | 0.998066i | \(-0.519799\pi\) | ||||
−0.0621609 | + | 0.998066i | \(0.519799\pi\) | |||||||
\(558\) | −466.010 | −0.0353544 | ||||||||
\(559\) | −10425.1 | −0.788793 | ||||||||
\(560\) | 726.327 | 0.0548088 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −8790.60 | −0.659803 | ||||||||
\(563\) | −17760.1 | −1.32948 | −0.664741 | − | 0.747074i | \(-0.731458\pi\) | ||||
−0.664741 | + | 0.747074i | \(0.731458\pi\) | |||||||
\(564\) | −14140.5 | −1.05571 | ||||||||
\(565\) | 2877.24 | 0.214242 | ||||||||
\(566\) | −3169.48 | −0.235377 | ||||||||
\(567\) | 3011.37 | 0.223043 | ||||||||
\(568\) | −10697.7 | −0.790255 | ||||||||
\(569\) | 7497.30 | 0.552378 | 0.276189 | − | 0.961103i | \(-0.410928\pi\) | ||||
0.276189 | + | 0.961103i | \(0.410928\pi\) | |||||||
\(570\) | −2879.67 | −0.211607 | ||||||||
\(571\) | −11381.8 | −0.834172 | −0.417086 | − | 0.908867i | \(-0.636949\pi\) | ||||
−0.417086 | + | 0.908867i | \(0.636949\pi\) | |||||||
\(572\) | 12850.7 | 0.939365 | ||||||||
\(573\) | 16938.4 | 1.23492 | ||||||||
\(574\) | 781.926 | 0.0568588 | ||||||||
\(575\) | 10484.8 | 0.760427 | ||||||||
\(576\) | 220.301 | 0.0159361 | ||||||||
\(577\) | 14264.6 | 1.02919 | 0.514596 | − | 0.857433i | \(-0.327942\pi\) | ||||
0.514596 | + | 0.857433i | \(0.327942\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −1725.32 | −0.123837 | ||||||||
\(580\) | −651.715 | −0.0466569 | ||||||||
\(581\) | −4324.78 | −0.308816 | ||||||||
\(582\) | 3219.70 | 0.229314 | ||||||||
\(583\) | −26207.3 | −1.86174 | ||||||||
\(584\) | −8955.94 | −0.634588 | ||||||||
\(585\) | −211.481 | −0.0149464 | ||||||||
\(586\) | 5799.12 | 0.408805 | ||||||||
\(587\) | 15284.6 | 1.07472 | 0.537361 | − | 0.843353i | \(-0.319421\pi\) | ||||
0.537361 | + | 0.843353i | \(0.319421\pi\) | |||||||
\(588\) | 11119.0 | 0.779830 | ||||||||
\(589\) | 29955.7 | 2.09559 | ||||||||
\(590\) | 293.278 | 0.0204645 | ||||||||
\(591\) | −23095.8 | −1.60750 | ||||||||
\(592\) | −12271.4 | −0.851942 | ||||||||
\(593\) | 22175.8 | 1.53566 | 0.767832 | − | 0.640651i | \(-0.221335\pi\) | ||||
0.767832 | + | 0.640651i | \(0.221335\pi\) | |||||||
\(594\) | 10679.5 | 0.737683 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −18563.2 | −1.27580 | ||||||||
\(597\) | −5114.43 | −0.350619 | ||||||||
\(598\) | −2873.48 | −0.196497 | ||||||||
\(599\) | −5573.44 | −0.380175 | −0.190087 | − | 0.981767i | \(-0.560877\pi\) | ||||
−0.190087 | + | 0.981767i | \(0.560877\pi\) | |||||||
\(600\) | −8490.77 | −0.577724 | ||||||||
\(601\) | −11936.4 | −0.810144 | −0.405072 | − | 0.914285i | \(-0.632754\pi\) | ||||
−0.405072 | + | 0.914285i | \(0.632754\pi\) | |||||||
\(602\) | 1826.02 | 0.123626 | ||||||||
\(603\) | 86.8567 | 0.00586580 | ||||||||
\(604\) | −2787.65 | −0.187794 | ||||||||
\(605\) | −14805.6 | −0.994930 | ||||||||
\(606\) | 8309.41 | 0.557008 | ||||||||
\(607\) | −18129.9 | −1.21230 | −0.606152 | − | 0.795349i | \(-0.707288\pi\) | ||||
−0.606152 | + | 0.795349i | \(0.707288\pi\) | |||||||
\(608\) | 20774.1 | 1.38569 | ||||||||
\(609\) | 491.002 | 0.0326706 | ||||||||
\(610\) | 171.971 | 0.0114146 | ||||||||
\(611\) | −11179.2 | −0.740200 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 14680.7 | 0.967289 | 0.483644 | − | 0.875265i | \(-0.339313\pi\) | ||||
0.483644 | + | 0.875265i | \(0.339313\pi\) | |||||||
\(614\) | −7870.45 | −0.517306 | ||||||||
\(615\) | −3563.15 | −0.233626 | ||||||||
\(616\) | −4878.71 | −0.319105 | ||||||||
\(617\) | 1056.15 | 0.0689123 | 0.0344561 | − | 0.999406i | \(-0.489030\pi\) | ||||
0.0344561 | + | 0.999406i | \(0.489030\pi\) | |||||||
\(618\) | −5622.84 | −0.365993 | ||||||||
\(619\) | −11068.5 | −0.718707 | −0.359353 | − | 0.933202i | \(-0.617003\pi\) | ||||
−0.359353 | + | 0.933202i | \(0.617003\pi\) | |||||||
\(620\) | −7167.24 | −0.464263 | ||||||||
\(621\) | 14259.2 | 0.921421 | ||||||||
\(622\) | 5325.25 | 0.343285 | ||||||||
\(623\) | −71.2059 | −0.00457914 | ||||||||
\(624\) | −5157.36 | −0.330865 | ||||||||
\(625\) | 8963.27 | 0.573649 | ||||||||
\(626\) | −7429.86 | −0.474372 | ||||||||
\(627\) | −42869.5 | −2.73053 | ||||||||
\(628\) | 15857.8 | 1.00763 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 37.0421 | 0.00234253 | ||||||||
\(631\) | −15903.0 | −1.00331 | −0.501655 | − | 0.865068i | \(-0.667275\pi\) | ||||
−0.501655 | + | 0.865068i | \(0.667275\pi\) | |||||||
\(632\) | 7338.43 | 0.461878 | ||||||||
\(633\) | −12541.7 | −0.787501 | ||||||||
\(634\) | 8213.50 | 0.514511 | ||||||||
\(635\) | 2269.38 | 0.141823 | ||||||||
\(636\) | 13073.8 | 0.815112 | ||||||||
\(637\) | 8790.48 | 0.546768 | ||||||||
\(638\) | 1624.79 | 0.100824 | ||||||||
\(639\) | 1209.17 | 0.0748574 | ||||||||
\(640\) | −6370.25 | −0.393448 | ||||||||
\(641\) | 3380.02 | 0.208272 | 0.104136 | − | 0.994563i | \(-0.466792\pi\) | ||||
0.104136 | + | 0.994563i | \(0.466792\pi\) | |||||||
\(642\) | −4386.81 | −0.269679 | ||||||||
\(643\) | 19441.2 | 1.19236 | 0.596178 | − | 0.802852i | \(-0.296685\pi\) | ||||
0.596178 | + | 0.802852i | \(0.296685\pi\) | |||||||
\(644\) | −3005.37 | −0.183895 | ||||||||
\(645\) | −8320.95 | −0.507965 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 4778.18 | 0.290339 | 0.145170 | − | 0.989407i | \(-0.453627\pi\) | ||||
0.145170 | + | 0.989407i | \(0.453627\pi\) | |||||||
\(648\) | −10774.8 | −0.653201 | ||||||||
\(649\) | 4366.01 | 0.264069 | ||||||||
\(650\) | −3097.00 | −0.186883 | ||||||||
\(651\) | 5399.81 | 0.325092 | ||||||||
\(652\) | −14024.7 | −0.842405 | ||||||||
\(653\) | 24415.5 | 1.46317 | 0.731587 | − | 0.681749i | \(-0.238780\pi\) | ||||
0.731587 | + | 0.681749i | \(0.238780\pi\) | |||||||
\(654\) | 2358.21 | 0.140999 | ||||||||
\(655\) | −559.346 | −0.0333671 | ||||||||
\(656\) | 6200.75 | 0.369053 | ||||||||
\(657\) | 1012.30 | 0.0601118 | ||||||||
\(658\) | 1958.10 | 0.116010 | ||||||||
\(659\) | 3212.43 | 0.189891 | 0.0949457 | − | 0.995482i | \(-0.469732\pi\) | ||||
0.0949457 | + | 0.995482i | \(0.469732\pi\) | |||||||
\(660\) | 10257.0 | 0.604930 | ||||||||
\(661\) | −6486.27 | −0.381674 | −0.190837 | − | 0.981622i | \(-0.561120\pi\) | ||||
−0.190837 | + | 0.981622i | \(0.561120\pi\) | |||||||
\(662\) | −1527.15 | −0.0896591 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 15474.3 | 0.904395 | ||||||||
\(665\) | −2381.12 | −0.138851 | ||||||||
\(666\) | −625.830 | −0.0364120 | ||||||||
\(667\) | 2169.41 | 0.125937 | ||||||||
\(668\) | −5632.23 | −0.326224 | ||||||||
\(669\) | −21348.2 | −1.23374 | ||||||||
\(670\) | −223.714 | −0.0128997 | ||||||||
\(671\) | 2560.13 | 0.147292 | ||||||||
\(672\) | 3744.73 | 0.214965 | ||||||||
\(673\) | −25244.2 | −1.44590 | −0.722952 | − | 0.690898i | \(-0.757215\pi\) | ||||
−0.722952 | + | 0.690898i | \(0.757215\pi\) | |||||||
\(674\) | −2649.13 | −0.151396 | ||||||||
\(675\) | 15368.4 | 0.876341 | ||||||||
\(676\) | 9986.57 | 0.568194 | ||||||||
\(677\) | −9817.09 | −0.557314 | −0.278657 | − | 0.960391i | \(-0.589889\pi\) | ||||
−0.278657 | + | 0.960391i | \(0.589889\pi\) | |||||||
\(678\) | 3578.46 | 0.202699 | ||||||||
\(679\) | 2662.28 | 0.150469 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −33398.6 | −1.87935 | ||||||||
\(682\) | 17868.6 | 1.00326 | ||||||||
\(683\) | −26082.8 | −1.46125 | −0.730624 | − | 0.682780i | \(-0.760771\pi\) | ||||
−0.730624 | + | 0.682780i | \(0.760771\pi\) | |||||||
\(684\) | −1526.10 | −0.0853099 | ||||||||
\(685\) | −3289.70 | −0.183493 | ||||||||
\(686\) | −3173.60 | −0.176630 | ||||||||
\(687\) | −16891.9 | −0.938090 | ||||||||
\(688\) | 14480.5 | 0.802417 | ||||||||
\(689\) | 10335.9 | 0.571506 | ||||||||
\(690\) | −2293.51 | −0.126540 | ||||||||
\(691\) | −23259.6 | −1.28052 | −0.640258 | − | 0.768160i | \(-0.721173\pi\) | ||||
−0.640258 | + | 0.768160i | \(0.721173\pi\) | |||||||
\(692\) | 9941.79 | 0.546142 | ||||||||
\(693\) | 551.444 | 0.0302275 | ||||||||
\(694\) | 4210.29 | 0.230289 | ||||||||
\(695\) | −3716.76 | −0.202856 | ||||||||
\(696\) | −1756.83 | −0.0956788 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 7077.64 | 0.383801 | ||||||||
\(699\) | 9759.88 | 0.528115 | ||||||||
\(700\) | −3239.15 | −0.174898 | ||||||||
\(701\) | 17022.9 | 0.917183 | 0.458592 | − | 0.888647i | \(-0.348354\pi\) | ||||
0.458592 | + | 0.888647i | \(0.348354\pi\) | |||||||
\(702\) | −4211.89 | −0.226449 | ||||||||
\(703\) | 40229.2 | 2.15828 | ||||||||
\(704\) | −8447.19 | −0.452224 | ||||||||
\(705\) | −8922.85 | −0.476672 | ||||||||
\(706\) | 6788.35 | 0.361874 | ||||||||
\(707\) | 6870.81 | 0.365493 | ||||||||
\(708\) | −2178.04 | −0.115615 | ||||||||
\(709\) | 4322.81 | 0.228980 | 0.114490 | − | 0.993424i | \(-0.463477\pi\) | ||||
0.114490 | + | 0.993424i | \(0.463477\pi\) | |||||||
\(710\) | −3114.41 | −0.164622 | ||||||||
\(711\) | −829.467 | −0.0437517 | ||||||||
\(712\) | 254.778 | 0.0134104 | ||||||||
\(713\) | 23858.1 | 1.25315 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 8109.00 | 0.424139 | ||||||||
\(716\) | 19474.0 | 1.01645 | ||||||||
\(717\) | −1969.06 | −0.102560 | ||||||||
\(718\) | 3278.74 | 0.170420 | ||||||||
\(719\) | −6228.36 | −0.323058 | −0.161529 | − | 0.986868i | \(-0.551642\pi\) | ||||
−0.161529 | + | 0.986868i | \(0.551642\pi\) | |||||||
\(720\) | 293.748 | 0.0152046 | ||||||||
\(721\) | −4649.36 | −0.240154 | ||||||||
\(722\) | −9080.97 | −0.468087 | ||||||||
\(723\) | −5839.39 | −0.300373 | ||||||||
\(724\) | −27546.4 | −1.41402 | ||||||||
\(725\) | 2338.16 | 0.119776 | ||||||||
\(726\) | −18413.9 | −0.941326 | ||||||||
\(727\) | 24426.4 | 1.24611 | 0.623057 | − | 0.782176i | \(-0.285890\pi\) | ||||
0.623057 | + | 0.782176i | \(0.285890\pi\) | |||||||
\(728\) | 1924.12 | 0.0979570 | ||||||||
\(729\) | 20813.6 | 1.05744 | ||||||||
\(730\) | −2607.34 | −0.132194 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | −1277.15 | −0.0644876 | ||||||||
\(733\) | 16963.6 | 0.854793 | 0.427396 | − | 0.904064i | \(-0.359431\pi\) | ||||
0.427396 | + | 0.904064i | \(0.359431\pi\) | |||||||
\(734\) | −5775.93 | −0.290455 | ||||||||
\(735\) | 7016.25 | 0.352106 | ||||||||
\(736\) | 16545.5 | 0.828634 | ||||||||
\(737\) | −3330.42 | −0.166455 | ||||||||
\(738\) | 316.233 | 0.0157733 | ||||||||
\(739\) | −8021.02 | −0.399266 | −0.199633 | − | 0.979871i | \(-0.563975\pi\) | ||||
−0.199633 | + | 0.979871i | \(0.563975\pi\) | |||||||
\(740\) | −9625.28 | −0.478152 | ||||||||
\(741\) | 16907.4 | 0.838202 | ||||||||
\(742\) | −1810.40 | −0.0895711 | ||||||||
\(743\) | 9925.69 | 0.490092 | 0.245046 | − | 0.969511i | \(-0.421197\pi\) | ||||
0.245046 | + | 0.969511i | \(0.421197\pi\) | |||||||
\(744\) | −19320.8 | −0.952061 | ||||||||
\(745\) | −11713.6 | −0.576047 | ||||||||
\(746\) | 1617.11 | 0.0793655 | ||||||||
\(747\) | −1749.07 | −0.0856693 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −3627.32 | −0.176955 | ||||||||
\(750\) | −5378.59 | −0.261865 | ||||||||
\(751\) | 16444.3 | 0.799018 | 0.399509 | − | 0.916729i | \(-0.369181\pi\) | ||||
0.399509 | + | 0.916729i | \(0.369181\pi\) | |||||||
\(752\) | 15527.9 | 0.752986 | ||||||||
\(753\) | 13771.1 | 0.666461 | ||||||||
\(754\) | −640.801 | −0.0309504 | ||||||||
\(755\) | −1759.04 | −0.0847923 | ||||||||
\(756\) | −4405.22 | −0.211926 | ||||||||
\(757\) | −10727.3 | −0.515047 | −0.257523 | − | 0.966272i | \(-0.582906\pi\) | ||||
−0.257523 | + | 0.966272i | \(0.582906\pi\) | |||||||
\(758\) | −4404.47 | −0.211052 | ||||||||
\(759\) | −34143.3 | −1.63284 | ||||||||
\(760\) | 8519.75 | 0.406636 | ||||||||
\(761\) | 2379.78 | 0.113360 | 0.0566801 | − | 0.998392i | \(-0.481948\pi\) | ||||
0.0566801 | + | 0.998392i | \(0.481948\pi\) | |||||||
\(762\) | 2822.45 | 0.134182 | ||||||||
\(763\) | 1949.93 | 0.0925194 | ||||||||
\(764\) | −23120.8 | −1.09487 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 7004.49 | 0.330395 | ||||||||
\(767\) | −1721.92 | −0.0810623 | ||||||||
\(768\) | −3003.06 | −0.141098 | ||||||||
\(769\) | −7698.01 | −0.360985 | −0.180492 | − | 0.983576i | \(-0.557769\pi\) | ||||
−0.180492 | + | 0.983576i | \(0.557769\pi\) | |||||||
\(770\) | −1420.34 | −0.0664745 | ||||||||
\(771\) | 3463.50 | 0.161783 | ||||||||
\(772\) | 2355.05 | 0.109793 | ||||||||
\(773\) | 217.026 | 0.0100981 | 0.00504907 | − | 0.999987i | \(-0.498393\pi\) | ||||
0.00504907 | + | 0.999987i | \(0.498393\pi\) | |||||||
\(774\) | 738.493 | 0.0342953 | ||||||||
\(775\) | 25714.0 | 1.19184 | ||||||||
\(776\) | −9525.75 | −0.440663 | ||||||||
\(777\) | 7251.69 | 0.334817 | ||||||||
\(778\) | −8522.47 | −0.392732 | ||||||||
\(779\) | −20327.9 | −0.934945 | ||||||||
\(780\) | −4045.28 | −0.185698 | ||||||||
\(781\) | −46364.0 | −2.12425 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 3179.88 | 0.145134 | ||||||||
\(784\) | −12210.0 | −0.556213 | ||||||||
\(785\) | 10006.5 | 0.454964 | ||||||||
\(786\) | −695.665 | −0.0315694 | ||||||||
\(787\) | −14718.5 | −0.666657 | −0.333329 | − | 0.942811i | \(-0.608172\pi\) | ||||
−0.333329 | + | 0.942811i | \(0.608172\pi\) | |||||||
\(788\) | 31525.6 | 1.42520 | ||||||||
\(789\) | 23444.9 | 1.05787 | ||||||||
\(790\) | 2136.43 | 0.0962162 | ||||||||
\(791\) | 2958.92 | 0.133005 | ||||||||
\(792\) | −1973.09 | −0.0885237 | ||||||||
\(793\) | −1009.69 | −0.0452147 | ||||||||
\(794\) | 2544.42 | 0.113725 | ||||||||
\(795\) | 8249.78 | 0.368037 | ||||||||
\(796\) | 6981.17 | 0.310855 | ||||||||
\(797\) | 24288.0 | 1.07945 | 0.539727 | − | 0.841840i | \(-0.318527\pi\) | ||||
0.539727 | + | 0.841840i | \(0.318527\pi\) | |||||||
\(798\) | −2961.42 | −0.131370 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 17832.5 | 0.788093 | ||||||||
\(801\) | −28.7977 | −0.00127031 | ||||||||
\(802\) | 465.483 | 0.0204947 | ||||||||
\(803\) | −38815.3 | −1.70581 | ||||||||
\(804\) | 1661.42 | 0.0728779 | ||||||||
\(805\) | −1896.43 | −0.0830317 | ||||||||
\(806\) | −7047.22 | −0.307975 | ||||||||
\(807\) | 4362.14 | 0.190278 | ||||||||
\(808\) | −24584.1 | −1.07038 | ||||||||
\(809\) | 29816.7 | 1.29580 | 0.647898 | − | 0.761727i | \(-0.275648\pi\) | ||||
0.647898 | + | 0.761727i | \(0.275648\pi\) | |||||||
\(810\) | −3136.86 | −0.136072 | ||||||||
\(811\) | −27414.4 | −1.18699 | −0.593495 | − | 0.804838i | \(-0.702252\pi\) | ||||
−0.593495 | + | 0.804838i | \(0.702252\pi\) | |||||||
\(812\) | −670.215 | −0.0289654 | ||||||||
\(813\) | 33786.8 | 1.45751 | ||||||||
\(814\) | 23996.7 | 1.03327 | ||||||||
\(815\) | −8849.76 | −0.380360 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −47471.3 | −2.03282 | ||||||||
\(818\) | 3818.50 | 0.163216 | ||||||||
\(819\) | −217.485 | −0.00927904 | ||||||||
\(820\) | 4863.68 | 0.207130 | ||||||||
\(821\) | 36258.7 | 1.54134 | 0.770668 | − | 0.637236i | \(-0.219922\pi\) | ||||
0.770668 | + | 0.637236i | \(0.219922\pi\) | |||||||
\(822\) | −4091.44 | −0.173607 | ||||||||
\(823\) | −4167.25 | −0.176502 | −0.0882511 | − | 0.996098i | \(-0.528128\pi\) | ||||
−0.0882511 | + | 0.996098i | \(0.528128\pi\) | |||||||
\(824\) | 16635.6 | 0.703312 | ||||||||
\(825\) | −36799.2 | −1.55295 | ||||||||
\(826\) | 301.603 | 0.0127048 | ||||||||
\(827\) | 32608.4 | 1.37111 | 0.685553 | − | 0.728023i | \(-0.259561\pi\) | ||||
0.685553 | + | 0.728023i | \(0.259561\pi\) | |||||||
\(828\) | −1215.46 | −0.0510147 | ||||||||
\(829\) | −23614.7 | −0.989351 | −0.494676 | − | 0.869078i | \(-0.664713\pi\) | ||||
−0.494676 | + | 0.869078i | \(0.664713\pi\) | |||||||
\(830\) | 4505.01 | 0.188399 | ||||||||
\(831\) | 16385.9 | 0.684020 | ||||||||
\(832\) | 3331.50 | 0.138821 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −4622.58 | −0.191927 | ||||||||
\(835\) | −3554.02 | −0.147296 | ||||||||
\(836\) | 58516.6 | 2.42086 | ||||||||
\(837\) | 34970.8 | 1.44417 | ||||||||
\(838\) | 17678.6 | 0.728755 | ||||||||
\(839\) | 13162.0 | 0.541600 | 0.270800 | − | 0.962636i | \(-0.412712\pi\) | ||||
0.270800 | + | 0.962636i | \(0.412712\pi\) | |||||||
\(840\) | 1535.77 | 0.0630821 | ||||||||
\(841\) | −23905.2 | −0.980164 | ||||||||
\(842\) | 12238.0 | 0.500891 | ||||||||
\(843\) | 41194.9 | 1.68307 | ||||||||
\(844\) | 17119.3 | 0.698190 | ||||||||
\(845\) | 6301.67 | 0.256549 | ||||||||
\(846\) | 791.912 | 0.0321826 | ||||||||
\(847\) | −15225.9 | −0.617671 | ||||||||
\(848\) | −14356.6 | −0.581378 | ||||||||
\(849\) | 14853.0 | 0.600415 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 32040.4 | 1.29064 | ||||||||
\(852\) | 23129.3 | 0.930042 | ||||||||
\(853\) | −27360.7 | −1.09826 | −0.549129 | − | 0.835738i | \(-0.685040\pi\) | ||||
−0.549129 | + | 0.835738i | \(0.685040\pi\) | |||||||
\(854\) | 176.853 | 0.00708641 | ||||||||
\(855\) | −962.992 | −0.0385189 | ||||||||
\(856\) | 12978.7 | 0.518229 | ||||||||
\(857\) | −46845.7 | −1.86723 | −0.933617 | − | 0.358272i | \(-0.883366\pi\) | ||||
−0.933617 | + | 0.358272i | \(0.883366\pi\) | |||||||
\(858\) | 10085.3 | 0.401288 | ||||||||
\(859\) | 15314.6 | 0.608299 | 0.304149 | − | 0.952624i | \(-0.401628\pi\) | ||||
0.304149 | + | 0.952624i | \(0.401628\pi\) | |||||||
\(860\) | 11358.0 | 0.450356 | ||||||||
\(861\) | −3664.30 | −0.145039 | ||||||||
\(862\) | −8494.16 | −0.335629 | ||||||||
\(863\) | −39481.1 | −1.55730 | −0.778651 | − | 0.627458i | \(-0.784096\pi\) | ||||
−0.778651 | + | 0.627458i | \(0.784096\pi\) | |||||||
\(864\) | 24252.1 | 0.954944 | ||||||||
\(865\) | 6273.41 | 0.246592 | ||||||||
\(866\) | 404.266 | 0.0158632 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −7370.70 | −0.288223 | ||||||||
\(869\) | 31804.9 | 1.24155 | ||||||||
\(870\) | −511.465 | −0.0199314 | ||||||||
\(871\) | 1313.49 | 0.0510974 | ||||||||
\(872\) | −6976.95 | −0.270951 | ||||||||
\(873\) | 1076.70 | 0.0417420 | ||||||||
\(874\) | −13084.5 | −0.506397 | ||||||||
\(875\) | −4447.40 | −0.171828 | ||||||||
\(876\) | 19363.5 | 0.746840 | ||||||||
\(877\) | 30914.9 | 1.19033 | 0.595166 | − | 0.803603i | \(-0.297086\pi\) | ||||
0.595166 | + | 0.803603i | \(0.297086\pi\) | |||||||
\(878\) | 4338.53 | 0.166763 | ||||||||
\(879\) | −27176.1 | −1.04281 | ||||||||
\(880\) | −11263.4 | −0.431465 | ||||||||
\(881\) | −5477.01 | −0.209450 | −0.104725 | − | 0.994501i | \(-0.533396\pi\) | ||||
−0.104725 | + | 0.994501i | \(0.533396\pi\) | |||||||
\(882\) | −622.700 | −0.0237726 | ||||||||
\(883\) | −24324.0 | −0.927029 | −0.463515 | − | 0.886089i | \(-0.653412\pi\) | ||||
−0.463515 | + | 0.886089i | \(0.653412\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −1374.37 | −0.0522023 | ||||||||
\(886\) | −4225.40 | −0.160220 | ||||||||
\(887\) | 22552.0 | 0.853688 | 0.426844 | − | 0.904325i | \(-0.359625\pi\) | ||||
0.426844 | + | 0.904325i | \(0.359625\pi\) | |||||||
\(888\) | −25946.9 | −0.980542 | ||||||||
\(889\) | 2333.80 | 0.0880463 | ||||||||
\(890\) | 74.1733 | 0.00279359 | ||||||||
\(891\) | −46698.3 | −1.75584 | ||||||||
\(892\) | 29140.2 | 1.09382 | ||||||||
\(893\) | −50905.2 | −1.90759 | ||||||||
\(894\) | −14568.4 | −0.545011 | ||||||||
\(895\) | 12288.4 | 0.458944 | ||||||||
\(896\) | −6551.09 | −0.244260 | ||||||||
\(897\) | 13465.8 | 0.501238 | ||||||||
\(898\) | 3031.80 | 0.112664 | ||||||||
\(899\) | 5320.50 | 0.197384 | ||||||||
\(900\) | −1310.01 | −0.0485188 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | −12125.6 | −0.447603 | ||||||||
\(903\) | −8557.16 | −0.315354 | ||||||||
\(904\) | −10587.2 | −0.389517 | ||||||||
\(905\) | −17382.1 | −0.638455 | ||||||||
\(906\) | −2187.74 | −0.0802239 | ||||||||
\(907\) | 8057.54 | 0.294979 | 0.147490 | − | 0.989064i | \(-0.452881\pi\) | ||||
0.147490 | + | 0.989064i | \(0.452881\pi\) | |||||||
\(908\) | 45588.8 | 1.66621 | ||||||||
\(909\) | 2778.75 | 0.101392 | ||||||||
\(910\) | 560.169 | 0.0204059 | ||||||||
\(911\) | −22191.3 | −0.807058 | −0.403529 | − | 0.914967i | \(-0.632217\pi\) | ||||
−0.403529 | + | 0.914967i | \(0.632217\pi\) | |||||||
\(912\) | −23484.3 | −0.852680 | ||||||||
\(913\) | 67065.9 | 2.43106 | ||||||||
\(914\) | −9423.36 | −0.341025 | ||||||||
\(915\) | −805.901 | −0.0291172 | ||||||||
\(916\) | 23057.4 | 0.831700 | ||||||||
\(917\) | −575.225 | −0.0207149 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 18688.4 | 0.670810 | 0.335405 | − | 0.942074i | \(-0.391127\pi\) | ||||
0.335405 | + | 0.942074i | \(0.391127\pi\) | |||||||
\(920\) | 6785.53 | 0.243165 | ||||||||
\(921\) | 36882.9 | 1.31958 | ||||||||
\(922\) | −11167.5 | −0.398896 | ||||||||
\(923\) | 18285.6 | 0.652088 | ||||||||
\(924\) | 10548.2 | 0.375552 | ||||||||
\(925\) | 34532.7 | 1.22749 | ||||||||
\(926\) | −7335.78 | −0.260333 | ||||||||
\(927\) | −1880.33 | −0.0666217 | ||||||||
\(928\) | 3689.73 | 0.130519 | ||||||||
\(929\) | 46.6711 | 0.00164826 | 0.000824128 | − | 1.00000i | \(-0.499738\pi\) | ||||
0.000824128 | 1.00000i | \(0.499738\pi\) | ||||||||
\(930\) | −5624.84 | −0.198329 | ||||||||
\(931\) | 40028.0 | 1.40909 | ||||||||
\(932\) | −13322.2 | −0.468222 | ||||||||
\(933\) | −24955.5 | −0.875675 | ||||||||
\(934\) | −15416.0 | −0.540071 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 778.170 | 0.0271745 | ||||||||
\(937\) | −1778.92 | −0.0620222 | −0.0310111 | − | 0.999519i | \(-0.509873\pi\) | ||||
−0.0310111 | + | 0.999519i | \(0.509873\pi\) | |||||||
\(938\) | −230.065 | −0.00800840 | ||||||||
\(939\) | 34818.2 | 1.21006 | ||||||||
\(940\) | 12179.6 | 0.422612 | ||||||||
\(941\) | −47634.0 | −1.65018 | −0.825092 | − | 0.564998i | \(-0.808877\pi\) | ||||
−0.825092 | + | 0.564998i | \(0.808877\pi\) | |||||||
\(942\) | 12445.2 | 0.430452 | ||||||||
\(943\) | −16190.1 | −0.559090 | ||||||||
\(944\) | 2391.74 | 0.0824625 | ||||||||
\(945\) | −2779.76 | −0.0956883 | ||||||||
\(946\) | −28316.7 | −0.973208 | ||||||||
\(947\) | −21092.5 | −0.723776 | −0.361888 | − | 0.932222i | \(-0.617868\pi\) | ||||
−0.361888 | + | 0.932222i | \(0.617868\pi\) | |||||||
\(948\) | −15866.3 | −0.543579 | ||||||||
\(949\) | 15308.4 | 0.523638 | ||||||||
\(950\) | −14102.4 | −0.481622 | ||||||||
\(951\) | −38490.5 | −1.31245 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 45019.9 | 1.53026 | 0.765130 | − | 0.643876i | \(-0.222675\pi\) | ||||
0.765130 | + | 0.643876i | \(0.222675\pi\) | |||||||
\(954\) | −732.177 | −0.0248481 | ||||||||
\(955\) | −14589.5 | −0.494352 | ||||||||
\(956\) | 2687.75 | 0.0909289 | ||||||||
\(957\) | −7614.15 | −0.257190 | ||||||||
\(958\) | 7673.64 | 0.258793 | ||||||||
\(959\) | −3383.09 | −0.113916 | ||||||||
\(960\) | 2659.09 | 0.0893975 | ||||||||
\(961\) | 28721.3 | 0.964092 | ||||||||
\(962\) | −9464.10 | −0.317188 | ||||||||
\(963\) | −1466.99 | −0.0490896 | ||||||||
\(964\) | 7970.74 | 0.266307 | ||||||||
\(965\) | 1486.07 | 0.0495732 | ||||||||
\(966\) | −2358.61 | −0.0785582 | ||||||||
\(967\) | −16583.3 | −0.551482 | −0.275741 | − | 0.961232i | \(-0.588923\pi\) | ||||
−0.275741 | + | 0.961232i | \(0.588923\pi\) | |||||||
\(968\) | 54478.9 | 1.80890 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −2773.23 | −0.0917968 | ||||||||
\(971\) | 19060.7 | 0.629957 | 0.314978 | − | 0.949099i | \(-0.398003\pi\) | ||||
0.314978 | + | 0.949099i | \(0.398003\pi\) | |||||||
\(972\) | −3451.94 | −0.113911 | ||||||||
\(973\) | −3822.27 | −0.125937 | ||||||||
\(974\) | 15886.7 | 0.522632 | ||||||||
\(975\) | 14513.3 | 0.476715 | ||||||||
\(976\) | 1402.46 | 0.0459957 | ||||||||
\(977\) | −44082.8 | −1.44353 | −0.721767 | − | 0.692136i | \(-0.756670\pi\) | ||||
−0.721767 | + | 0.692136i | \(0.756670\pi\) | |||||||
\(978\) | −11006.5 | −0.359867 | ||||||||
\(979\) | 1104.21 | 0.0360478 | ||||||||
\(980\) | −9577.14 | −0.312174 | ||||||||
\(981\) | 788.609 | 0.0256660 | ||||||||
\(982\) | 10320.8 | 0.335388 | ||||||||
\(983\) | −39309.6 | −1.27546 | −0.637732 | − | 0.770258i | \(-0.720127\pi\) | ||||
−0.637732 | + | 0.770258i | \(0.720127\pi\) | |||||||
\(984\) | 13111.0 | 0.424761 | ||||||||
\(985\) | 19893.1 | 0.643500 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −9176.15 | −0.295927 | ||||||||
\(988\) | −23078.4 | −0.743141 | ||||||||
\(989\) | −37808.4 | −1.21561 | ||||||||
\(990\) | −574.425 | −0.0184408 | ||||||||
\(991\) | −24889.9 | −0.797834 | −0.398917 | − | 0.916987i | \(-0.630614\pi\) | ||||
−0.398917 | + | 0.916987i | \(0.630614\pi\) | |||||||
\(992\) | 40577.9 | 1.29874 | ||||||||
\(993\) | 7156.59 | 0.228709 | ||||||||
\(994\) | −3202.82 | −0.102201 | ||||||||
\(995\) | 4405.21 | 0.140356 | ||||||||
\(996\) | −33456.7 | −1.06437 | ||||||||
\(997\) | 10612.3 | 0.337105 | 0.168552 | − | 0.985693i | \(-0.446091\pi\) | ||||
0.168552 | + | 0.985693i | \(0.446091\pi\) | |||||||
\(998\) | 2178.62 | 0.0691011 | ||||||||
\(999\) | 46964.2 | 1.48737 |
(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.h.1.5 | ✓ | 12 | |
17.4 | even | 4 | 289.4.b.f.288.16 | 24 | |||
17.13 | even | 4 | 289.4.b.f.288.15 | 24 | |||
17.16 | even | 2 | 289.4.a.i.1.5 | yes | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
289.4.a.h.1.5 | ✓ | 12 | 1.1 | even | 1 | trivial | |
289.4.a.i.1.5 | yes | 12 | 17.16 | even | 2 | ||
289.4.b.f.288.15 | 24 | 17.13 | even | 4 | |||
289.4.b.f.288.16 | 24 | 17.4 | even | 4 |