Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2254,4,Mod(1,2254)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2254, 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("2254.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2254 = 2 \cdot 7^{2} \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 2254.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: | \(132.990305153\) |
Analytic rank: | \(0\) |
Dimension: | \(11\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{11} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{11} - 234 x^{9} - 105 x^{8} + 18997 x^{7} + 16513 x^{6} - 621598 x^{5} - 743169 x^{4} + \cdots - 12103441 \)
|
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 7 \) |
Twist minimal: | no (minimal twist has level 322) |
Fricke sign: | \(+1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.6 | ||
Root | \(-0.423740\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2254.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.00000 | −0.707107 | ||||||||
\(3\) | −0.423740 | −0.0815489 | −0.0407744 | − | 0.999168i | \(-0.512983\pi\) | ||||
−0.0407744 | + | 0.999168i | \(0.512983\pi\) | |||||||
\(4\) | 4.00000 | 0.500000 | ||||||||
\(5\) | 18.0271 | 1.61239 | 0.806197 | − | 0.591648i | \(-0.201522\pi\) | ||||
0.806197 | + | 0.591648i | \(0.201522\pi\) | |||||||
\(6\) | 0.847481 | 0.0576637 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −8.00000 | −0.353553 | ||||||||
\(9\) | −26.8204 | −0.993350 | ||||||||
\(10\) | −36.0542 | −1.14013 | ||||||||
\(11\) | 10.8276 | 0.296787 | 0.148394 | − | 0.988928i | \(-0.452590\pi\) | ||||
0.148394 | + | 0.988928i | \(0.452590\pi\) | |||||||
\(12\) | −1.69496 | −0.0407744 | ||||||||
\(13\) | 20.0082 | 0.426867 | 0.213433 | − | 0.976958i | \(-0.431535\pi\) | ||||
0.213433 | + | 0.976958i | \(0.431535\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −7.63881 | −0.131489 | ||||||||
\(16\) | 16.0000 | 0.250000 | ||||||||
\(17\) | 109.597 | 1.56360 | 0.781802 | − | 0.623527i | \(-0.214301\pi\) | ||||
0.781802 | + | 0.623527i | \(0.214301\pi\) | |||||||
\(18\) | 53.6409 | 0.702404 | ||||||||
\(19\) | −16.0076 | −0.193284 | −0.0966421 | − | 0.995319i | \(-0.530810\pi\) | ||||
−0.0966421 | + | 0.995319i | \(0.530810\pi\) | |||||||
\(20\) | 72.1084 | 0.806197 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −21.6553 | −0.209860 | ||||||||
\(23\) | 23.0000 | 0.208514 | ||||||||
\(24\) | 3.38992 | 0.0288319 | ||||||||
\(25\) | 199.976 | 1.59981 | ||||||||
\(26\) | −40.0163 | −0.301840 | ||||||||
\(27\) | 22.8059 | 0.162555 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 174.550 | 1.11769 | 0.558847 | − | 0.829271i | \(-0.311244\pi\) | ||||
0.558847 | + | 0.829271i | \(0.311244\pi\) | |||||||
\(30\) | 15.2776 | 0.0929766 | ||||||||
\(31\) | −285.169 | −1.65219 | −0.826093 | − | 0.563533i | \(-0.809442\pi\) | ||||
−0.826093 | + | 0.563533i | \(0.809442\pi\) | |||||||
\(32\) | −32.0000 | −0.176777 | ||||||||
\(33\) | −4.58811 | −0.0242026 | ||||||||
\(34\) | −219.195 | −1.10564 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −107.282 | −0.496675 | ||||||||
\(37\) | 201.953 | 0.897319 | 0.448659 | − | 0.893703i | \(-0.351902\pi\) | ||||
0.448659 | + | 0.893703i | \(0.351902\pi\) | |||||||
\(38\) | 32.0152 | 0.136673 | ||||||||
\(39\) | −8.47827 | −0.0348105 | ||||||||
\(40\) | −144.217 | −0.570067 | ||||||||
\(41\) | 72.7492 | 0.277110 | 0.138555 | − | 0.990355i | \(-0.455754\pi\) | ||||
0.138555 | + | 0.990355i | \(0.455754\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −22.4963 | −0.0797827 | −0.0398914 | − | 0.999204i | \(-0.512701\pi\) | ||||
−0.0398914 | + | 0.999204i | \(0.512701\pi\) | |||||||
\(44\) | 43.3106 | 0.148394 | ||||||||
\(45\) | −483.495 | −1.60167 | ||||||||
\(46\) | −46.0000 | −0.147442 | ||||||||
\(47\) | 26.1314 | 0.0810992 | 0.0405496 | − | 0.999178i | \(-0.487089\pi\) | ||||
0.0405496 | + | 0.999178i | \(0.487089\pi\) | |||||||
\(48\) | −6.77984 | −0.0203872 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −399.953 | −1.13124 | ||||||||
\(51\) | −46.4408 | −0.127510 | ||||||||
\(52\) | 80.0327 | 0.213433 | ||||||||
\(53\) | −299.634 | −0.776565 | −0.388282 | − | 0.921540i | \(-0.626931\pi\) | ||||
−0.388282 | + | 0.921540i | \(0.626931\pi\) | |||||||
\(54\) | −45.6118 | −0.114944 | ||||||||
\(55\) | 195.191 | 0.478537 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 6.78307 | 0.0157621 | ||||||||
\(58\) | −349.100 | −0.790330 | ||||||||
\(59\) | −571.609 | −1.26131 | −0.630654 | − | 0.776064i | \(-0.717213\pi\) | ||||
−0.630654 | + | 0.776064i | \(0.717213\pi\) | |||||||
\(60\) | −30.5552 | −0.0657444 | ||||||||
\(61\) | 493.219 | 1.03525 | 0.517625 | − | 0.855608i | \(-0.326816\pi\) | ||||
0.517625 | + | 0.855608i | \(0.326816\pi\) | |||||||
\(62\) | 570.337 | 1.16827 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 64.0000 | 0.125000 | ||||||||
\(65\) | 360.689 | 0.688277 | ||||||||
\(66\) | 9.17622 | 0.0171139 | ||||||||
\(67\) | 853.087 | 1.55554 | 0.777770 | − | 0.628550i | \(-0.216351\pi\) | ||||
0.777770 | + | 0.628550i | \(0.216351\pi\) | |||||||
\(68\) | 438.390 | 0.781802 | ||||||||
\(69\) | −9.74603 | −0.0170041 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −275.485 | −0.460480 | −0.230240 | − | 0.973134i | \(-0.573951\pi\) | ||||
−0.230240 | + | 0.973134i | \(0.573951\pi\) | |||||||
\(72\) | 214.564 | 0.351202 | ||||||||
\(73\) | 405.694 | 0.650451 | 0.325225 | − | 0.945637i | \(-0.394560\pi\) | ||||
0.325225 | + | 0.945637i | \(0.394560\pi\) | |||||||
\(74\) | −403.905 | −0.634500 | ||||||||
\(75\) | −84.7381 | −0.130463 | ||||||||
\(76\) | −64.0305 | −0.0966421 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 16.9565 | 0.0246147 | ||||||||
\(79\) | −49.0626 | −0.0698731 | −0.0349365 | − | 0.999390i | \(-0.511123\pi\) | ||||
−0.0349365 | + | 0.999390i | \(0.511123\pi\) | |||||||
\(80\) | 288.434 | 0.403098 | ||||||||
\(81\) | 714.488 | 0.980094 | ||||||||
\(82\) | −145.498 | −0.195946 | ||||||||
\(83\) | −537.134 | −0.710339 | −0.355170 | − | 0.934802i | \(-0.615577\pi\) | ||||
−0.355170 | + | 0.934802i | \(0.615577\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1975.72 | 2.52114 | ||||||||
\(86\) | 44.9927 | 0.0564149 | ||||||||
\(87\) | −73.9639 | −0.0911467 | ||||||||
\(88\) | −86.6212 | −0.104930 | ||||||||
\(89\) | −408.857 | −0.486952 | −0.243476 | − | 0.969907i | \(-0.578288\pi\) | ||||
−0.243476 | + | 0.969907i | \(0.578288\pi\) | |||||||
\(90\) | 966.990 | 1.13255 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 92.0000 | 0.104257 | ||||||||
\(93\) | 120.837 | 0.134734 | ||||||||
\(94\) | −52.2629 | −0.0573458 | ||||||||
\(95\) | −288.571 | −0.311650 | ||||||||
\(96\) | 13.5597 | 0.0144159 | ||||||||
\(97\) | −1164.89 | −1.21935 | −0.609675 | − | 0.792651i | \(-0.708700\pi\) | ||||
−0.609675 | + | 0.792651i | \(0.708700\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −290.402 | −0.294813 | ||||||||
\(100\) | 799.906 | 0.799906 | ||||||||
\(101\) | 1888.04 | 1.86006 | 0.930032 | − | 0.367478i | \(-0.119779\pi\) | ||||
0.930032 | + | 0.367478i | \(0.119779\pi\) | |||||||
\(102\) | 92.8817 | 0.0901633 | ||||||||
\(103\) | 732.800 | 0.701019 | 0.350510 | − | 0.936559i | \(-0.386008\pi\) | ||||
0.350510 | + | 0.936559i | \(0.386008\pi\) | |||||||
\(104\) | −160.065 | −0.150920 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 599.269 | 0.549114 | ||||||||
\(107\) | 29.3551 | 0.0265221 | 0.0132610 | − | 0.999912i | \(-0.495779\pi\) | ||||
0.0132610 | + | 0.999912i | \(0.495779\pi\) | |||||||
\(108\) | 91.2236 | 0.0812777 | ||||||||
\(109\) | 1504.64 | 1.32219 | 0.661094 | − | 0.750303i | \(-0.270092\pi\) | ||||
0.661094 | + | 0.750303i | \(0.270092\pi\) | |||||||
\(110\) | −390.382 | −0.338377 | ||||||||
\(111\) | −85.5754 | −0.0731753 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −215.494 | −0.179398 | −0.0896990 | − | 0.995969i | \(-0.528591\pi\) | ||||
−0.0896990 | + | 0.995969i | \(0.528591\pi\) | |||||||
\(114\) | −13.5661 | −0.0111455 | ||||||||
\(115\) | 414.623 | 0.336207 | ||||||||
\(116\) | 698.201 | 0.558847 | ||||||||
\(117\) | −536.628 | −0.424028 | ||||||||
\(118\) | 1143.22 | 0.891880 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 61.1105 | 0.0464883 | ||||||||
\(121\) | −1213.76 | −0.911917 | ||||||||
\(122\) | −986.439 | −0.732032 | ||||||||
\(123\) | −30.8268 | −0.0225980 | ||||||||
\(124\) | −1140.67 | −0.826093 | ||||||||
\(125\) | 1351.61 | 0.967132 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1680.34 | 1.17406 | 0.587032 | − | 0.809564i | \(-0.300296\pi\) | ||||
0.587032 | + | 0.809564i | \(0.300296\pi\) | |||||||
\(128\) | −128.000 | −0.0883883 | ||||||||
\(129\) | 9.53260 | 0.00650619 | ||||||||
\(130\) | −721.378 | −0.486685 | ||||||||
\(131\) | 1838.25 | 1.22602 | 0.613009 | − | 0.790076i | \(-0.289959\pi\) | ||||
0.613009 | + | 0.790076i | \(0.289959\pi\) | |||||||
\(132\) | −18.3524 | −0.0121013 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −1706.17 | −1.09993 | ||||||||
\(135\) | 411.124 | 0.262103 | ||||||||
\(136\) | −876.779 | −0.552818 | ||||||||
\(137\) | 2530.78 | 1.57824 | 0.789120 | − | 0.614239i | \(-0.210537\pi\) | ||||
0.789120 | + | 0.614239i | \(0.210537\pi\) | |||||||
\(138\) | 19.4921 | 0.0120237 | ||||||||
\(139\) | 235.342 | 0.143607 | 0.0718037 | − | 0.997419i | \(-0.477124\pi\) | ||||
0.0718037 | + | 0.997419i | \(0.477124\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −11.0729 | −0.00661354 | ||||||||
\(142\) | 550.970 | 0.325608 | ||||||||
\(143\) | 216.641 | 0.126688 | ||||||||
\(144\) | −429.127 | −0.248337 | ||||||||
\(145\) | 3146.63 | 1.80216 | ||||||||
\(146\) | −811.388 | −0.459938 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 807.810 | 0.448659 | ||||||||
\(149\) | −1681.29 | −0.924406 | −0.462203 | − | 0.886774i | \(-0.652941\pi\) | ||||
−0.462203 | + | 0.886774i | \(0.652941\pi\) | |||||||
\(150\) | 169.476 | 0.0922511 | ||||||||
\(151\) | −539.920 | −0.290980 | −0.145490 | − | 0.989360i | \(-0.546476\pi\) | ||||
−0.145490 | + | 0.989360i | \(0.546476\pi\) | |||||||
\(152\) | 128.061 | 0.0683363 | ||||||||
\(153\) | −2939.45 | −1.55321 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −5140.76 | −2.66397 | ||||||||
\(156\) | −33.9131 | −0.0174052 | ||||||||
\(157\) | 1042.01 | 0.529692 | 0.264846 | − | 0.964291i | \(-0.414679\pi\) | ||||
0.264846 | + | 0.964291i | \(0.414679\pi\) | |||||||
\(158\) | 98.1252 | 0.0494077 | ||||||||
\(159\) | 126.967 | 0.0633280 | ||||||||
\(160\) | −576.867 | −0.285034 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −1428.98 | −0.693031 | ||||||||
\(163\) | 851.681 | 0.409257 | 0.204628 | − | 0.978840i | \(-0.434401\pi\) | ||||
0.204628 | + | 0.978840i | \(0.434401\pi\) | |||||||
\(164\) | 290.997 | 0.138555 | ||||||||
\(165\) | −82.7103 | −0.0390242 | ||||||||
\(166\) | 1074.27 | 0.502286 | ||||||||
\(167\) | −3658.62 | −1.69528 | −0.847642 | − | 0.530568i | \(-0.821979\pi\) | ||||
−0.847642 | + | 0.530568i | \(0.821979\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1796.67 | −0.817785 | ||||||||
\(170\) | −3951.45 | −1.78272 | ||||||||
\(171\) | 429.331 | 0.191999 | ||||||||
\(172\) | −89.9853 | −0.0398914 | ||||||||
\(173\) | 46.2925 | 0.0203442 | 0.0101721 | − | 0.999948i | \(-0.496762\pi\) | ||||
0.0101721 | + | 0.999948i | \(0.496762\pi\) | |||||||
\(174\) | 147.928 | 0.0644505 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 173.242 | 0.0741968 | ||||||||
\(177\) | 242.214 | 0.102858 | ||||||||
\(178\) | 817.714 | 0.344327 | ||||||||
\(179\) | −2996.72 | −1.25131 | −0.625657 | − | 0.780098i | \(-0.715169\pi\) | ||||
−0.625657 | + | 0.780098i | \(0.715169\pi\) | |||||||
\(180\) | −1933.98 | −0.800835 | ||||||||
\(181\) | −1333.04 | −0.547426 | −0.273713 | − | 0.961811i | \(-0.588252\pi\) | ||||
−0.273713 | + | 0.961811i | \(0.588252\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −208.997 | −0.0844235 | ||||||||
\(184\) | −184.000 | −0.0737210 | ||||||||
\(185\) | 3640.62 | 1.44683 | ||||||||
\(186\) | −241.675 | −0.0952713 | ||||||||
\(187\) | 1186.68 | 0.464058 | ||||||||
\(188\) | 104.526 | 0.0405496 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 577.142 | 0.220370 | ||||||||
\(191\) | −3098.01 | −1.17363 | −0.586816 | − | 0.809720i | \(-0.699619\pi\) | ||||
−0.586816 | + | 0.809720i | \(0.699619\pi\) | |||||||
\(192\) | −27.1194 | −0.0101936 | ||||||||
\(193\) | 3065.90 | 1.14346 | 0.571732 | − | 0.820440i | \(-0.306272\pi\) | ||||
0.571732 | + | 0.820440i | \(0.306272\pi\) | |||||||
\(194\) | 2329.79 | 0.862211 | ||||||||
\(195\) | −152.839 | −0.0561282 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 503.114 | 0.181956 | 0.0909781 | − | 0.995853i | \(-0.471001\pi\) | ||||
0.0909781 | + | 0.995853i | \(0.471001\pi\) | |||||||
\(198\) | 580.804 | 0.208465 | ||||||||
\(199\) | 1269.09 | 0.452078 | 0.226039 | − | 0.974118i | \(-0.427422\pi\) | ||||
0.226039 | + | 0.974118i | \(0.427422\pi\) | |||||||
\(200\) | −1599.81 | −0.565619 | ||||||||
\(201\) | −361.487 | −0.126852 | ||||||||
\(202\) | −3776.07 | −1.31526 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −185.763 | −0.0637551 | ||||||||
\(205\) | 1311.46 | 0.446810 | ||||||||
\(206\) | −1465.60 | −0.495695 | ||||||||
\(207\) | −616.870 | −0.207128 | ||||||||
\(208\) | 320.131 | 0.106717 | ||||||||
\(209\) | −173.325 | −0.0573642 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −3149.06 | −1.02744 | −0.513722 | − | 0.857957i | \(-0.671734\pi\) | ||||
−0.513722 | + | 0.857957i | \(0.671734\pi\) | |||||||
\(212\) | −1198.54 | −0.388282 | ||||||||
\(213\) | 116.734 | 0.0375516 | ||||||||
\(214\) | −58.7102 | −0.0187539 | ||||||||
\(215\) | −405.544 | −0.128641 | ||||||||
\(216\) | −182.447 | −0.0574720 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −3009.28 | −0.934928 | ||||||||
\(219\) | −171.909 | −0.0530435 | ||||||||
\(220\) | 780.764 | 0.239269 | ||||||||
\(221\) | 2192.84 | 0.667451 | ||||||||
\(222\) | 171.151 | 0.0517428 | ||||||||
\(223\) | −475.283 | −0.142723 | −0.0713617 | − | 0.997451i | \(-0.522734\pi\) | ||||
−0.0713617 | + | 0.997451i | \(0.522734\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −5363.46 | −1.58917 | ||||||||
\(226\) | 430.988 | 0.126854 | ||||||||
\(227\) | 4923.88 | 1.43969 | 0.719845 | − | 0.694135i | \(-0.244213\pi\) | ||||
0.719845 | + | 0.694135i | \(0.244213\pi\) | |||||||
\(228\) | 27.1323 | 0.00788105 | ||||||||
\(229\) | −3098.75 | −0.894198 | −0.447099 | − | 0.894484i | \(-0.647543\pi\) | ||||
−0.447099 | + | 0.894484i | \(0.647543\pi\) | |||||||
\(230\) | −829.247 | −0.237734 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −1396.40 | −0.395165 | ||||||||
\(233\) | 6838.24 | 1.92270 | 0.961348 | − | 0.275335i | \(-0.0887889\pi\) | ||||
0.961348 | + | 0.275335i | \(0.0887889\pi\) | |||||||
\(234\) | 1073.26 | 0.299833 | ||||||||
\(235\) | 471.074 | 0.130764 | ||||||||
\(236\) | −2286.44 | −0.630654 | ||||||||
\(237\) | 20.7898 | 0.00569807 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −4248.98 | −1.14997 | −0.574987 | − | 0.818163i | \(-0.694993\pi\) | ||||
−0.574987 | + | 0.818163i | \(0.694993\pi\) | |||||||
\(240\) | −122.221 | −0.0328722 | ||||||||
\(241\) | −4234.73 | −1.13188 | −0.565939 | − | 0.824447i | \(-0.691486\pi\) | ||||
−0.565939 | + | 0.824447i | \(0.691486\pi\) | |||||||
\(242\) | 2427.52 | 0.644823 | ||||||||
\(243\) | −918.516 | −0.242481 | ||||||||
\(244\) | 1972.88 | 0.517625 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 61.6535 | 0.0159792 | ||||||||
\(247\) | −320.283 | −0.0825066 | ||||||||
\(248\) | 2281.35 | 0.584136 | ||||||||
\(249\) | 227.605 | 0.0579273 | ||||||||
\(250\) | −2703.22 | −0.683866 | ||||||||
\(251\) | 2246.31 | 0.564885 | 0.282442 | − | 0.959284i | \(-0.408855\pi\) | ||||
0.282442 | + | 0.959284i | \(0.408855\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 249.036 | 0.0618844 | ||||||||
\(254\) | −3360.68 | −0.830188 | ||||||||
\(255\) | −837.194 | −0.205596 | ||||||||
\(256\) | 256.000 | 0.0625000 | ||||||||
\(257\) | 3129.11 | 0.759489 | 0.379744 | − | 0.925091i | \(-0.376012\pi\) | ||||
0.379744 | + | 0.925091i | \(0.376012\pi\) | |||||||
\(258\) | −19.0652 | −0.00460057 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 1442.76 | 0.344138 | ||||||||
\(261\) | −4681.51 | −1.11026 | ||||||||
\(262\) | −3676.49 | −0.866925 | ||||||||
\(263\) | 5978.66 | 1.40175 | 0.700875 | − | 0.713284i | \(-0.252793\pi\) | ||||
0.700875 | + | 0.713284i | \(0.252793\pi\) | |||||||
\(264\) | 36.7049 | 0.00855693 | ||||||||
\(265\) | −5401.54 | −1.25213 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 173.249 | 0.0397104 | ||||||||
\(268\) | 3412.35 | 0.777770 | ||||||||
\(269\) | −6190.03 | −1.40302 | −0.701511 | − | 0.712659i | \(-0.747491\pi\) | ||||
−0.701511 | + | 0.712659i | \(0.747491\pi\) | |||||||
\(270\) | −822.248 | −0.185335 | ||||||||
\(271\) | −2570.30 | −0.576142 | −0.288071 | − | 0.957609i | \(-0.593014\pi\) | ||||
−0.288071 | + | 0.957609i | \(0.593014\pi\) | |||||||
\(272\) | 1753.56 | 0.390901 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −5061.55 | −1.11598 | ||||||||
\(275\) | 2165.27 | 0.474803 | ||||||||
\(276\) | −38.9841 | −0.00850206 | ||||||||
\(277\) | −3305.91 | −0.717086 | −0.358543 | − | 0.933513i | \(-0.616726\pi\) | ||||
−0.358543 | + | 0.933513i | \(0.616726\pi\) | |||||||
\(278\) | −470.684 | −0.101546 | ||||||||
\(279\) | 7648.35 | 1.64120 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 4740.20 | 1.00632 | 0.503162 | − | 0.864192i | \(-0.332170\pi\) | ||||
0.503162 | + | 0.864192i | \(0.332170\pi\) | |||||||
\(282\) | 22.1459 | 0.00467648 | ||||||||
\(283\) | 8775.14 | 1.84321 | 0.921605 | − | 0.388130i | \(-0.126879\pi\) | ||||
0.921605 | + | 0.388130i | \(0.126879\pi\) | |||||||
\(284\) | −1101.94 | −0.230240 | ||||||||
\(285\) | 122.279 | 0.0254147 | ||||||||
\(286\) | −433.283 | −0.0895823 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 858.254 | 0.175601 | ||||||||
\(289\) | 7098.59 | 1.44486 | ||||||||
\(290\) | −6293.27 | −1.27432 | ||||||||
\(291\) | 493.612 | 0.0994366 | ||||||||
\(292\) | 1622.78 | 0.325225 | ||||||||
\(293\) | −2717.70 | −0.541875 | −0.270938 | − | 0.962597i | \(-0.587334\pi\) | ||||
−0.270938 | + | 0.962597i | \(0.587334\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −10304.5 | −2.03372 | ||||||||
\(296\) | −1615.62 | −0.317250 | ||||||||
\(297\) | 246.934 | 0.0482443 | ||||||||
\(298\) | 3362.57 | 0.653653 | ||||||||
\(299\) | 460.188 | 0.0890078 | ||||||||
\(300\) | −338.952 | −0.0652314 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 1079.84 | 0.205754 | ||||||||
\(303\) | −800.037 | −0.151686 | ||||||||
\(304\) | −256.122 | −0.0483210 | ||||||||
\(305\) | 8891.32 | 1.66923 | ||||||||
\(306\) | 5878.90 | 1.09828 | ||||||||
\(307\) | 7532.14 | 1.40027 | 0.700133 | − | 0.714012i | \(-0.253124\pi\) | ||||
0.700133 | + | 0.714012i | \(0.253124\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −310.517 | −0.0571673 | ||||||||
\(310\) | 10281.5 | 1.88371 | ||||||||
\(311\) | 10918.9 | 1.99085 | 0.995425 | − | 0.0955425i | \(-0.0304586\pi\) | ||||
0.995425 | + | 0.0955425i | \(0.0304586\pi\) | |||||||
\(312\) | 67.8261 | 0.0123074 | ||||||||
\(313\) | 7687.50 | 1.38825 | 0.694126 | − | 0.719853i | \(-0.255791\pi\) | ||||
0.694126 | + | 0.719853i | \(0.255791\pi\) | |||||||
\(314\) | −2084.03 | −0.374549 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −196.250 | −0.0349365 | ||||||||
\(317\) | −9269.22 | −1.64231 | −0.821153 | − | 0.570708i | \(-0.806669\pi\) | ||||
−0.821153 | + | 0.570708i | \(0.806669\pi\) | |||||||
\(318\) | −253.934 | −0.0447796 | ||||||||
\(319\) | 1889.97 | 0.331717 | ||||||||
\(320\) | 1153.73 | 0.201549 | ||||||||
\(321\) | −12.4389 | −0.00216285 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −1754.39 | −0.302220 | ||||||||
\(324\) | 2857.95 | 0.490047 | ||||||||
\(325\) | 4001.16 | 0.682906 | ||||||||
\(326\) | −1703.36 | −0.289388 | ||||||||
\(327\) | −637.577 | −0.107823 | ||||||||
\(328\) | −581.993 | −0.0979732 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 165.421 | 0.0275943 | ||||||||
\(331\) | 9939.55 | 1.65054 | 0.825268 | − | 0.564742i | \(-0.191024\pi\) | ||||
0.825268 | + | 0.564742i | \(0.191024\pi\) | |||||||
\(332\) | −2148.54 | −0.355170 | ||||||||
\(333\) | −5416.46 | −0.891351 | ||||||||
\(334\) | 7317.24 | 1.19875 | ||||||||
\(335\) | 15378.7 | 2.50814 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −921.909 | −0.149020 | −0.0745098 | − | 0.997220i | \(-0.523739\pi\) | ||||
−0.0745098 | + | 0.997220i | \(0.523739\pi\) | |||||||
\(338\) | 3593.35 | 0.578261 | ||||||||
\(339\) | 91.3135 | 0.0146297 | ||||||||
\(340\) | 7902.89 | 1.26057 | ||||||||
\(341\) | −3087.70 | −0.490348 | ||||||||
\(342\) | −858.663 | −0.135764 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 179.971 | 0.0282075 | ||||||||
\(345\) | −175.693 | −0.0274173 | ||||||||
\(346\) | −92.5850 | −0.0143855 | ||||||||
\(347\) | 7343.80 | 1.13613 | 0.568063 | − | 0.822985i | \(-0.307693\pi\) | ||||
0.568063 | + | 0.822985i | \(0.307693\pi\) | |||||||
\(348\) | −295.856 | −0.0455734 | ||||||||
\(349\) | 7623.29 | 1.16924 | 0.584621 | − | 0.811306i | \(-0.301243\pi\) | ||||
0.584621 | + | 0.811306i | \(0.301243\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 456.304 | 0.0693895 | ||||||||
\(352\) | −346.485 | −0.0524650 | ||||||||
\(353\) | −1935.30 | −0.291801 | −0.145900 | − | 0.989299i | \(-0.546608\pi\) | ||||
−0.145900 | + | 0.989299i | \(0.546608\pi\) | |||||||
\(354\) | −484.428 | −0.0727318 | ||||||||
\(355\) | −4966.20 | −0.742475 | ||||||||
\(356\) | −1635.43 | −0.243476 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 5993.44 | 0.884813 | ||||||||
\(359\) | −1420.86 | −0.208887 | −0.104443 | − | 0.994531i | \(-0.533306\pi\) | ||||
−0.104443 | + | 0.994531i | \(0.533306\pi\) | |||||||
\(360\) | 3867.96 | 0.566276 | ||||||||
\(361\) | −6602.76 | −0.962641 | ||||||||
\(362\) | 2666.08 | 0.387089 | ||||||||
\(363\) | 514.320 | 0.0743658 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 7313.49 | 1.04878 | ||||||||
\(366\) | 417.994 | 0.0596964 | ||||||||
\(367\) | −6740.90 | −0.958779 | −0.479390 | − | 0.877602i | \(-0.659142\pi\) | ||||
−0.479390 | + | 0.877602i | \(0.659142\pi\) | |||||||
\(368\) | 368.000 | 0.0521286 | ||||||||
\(369\) | −1951.17 | −0.275267 | ||||||||
\(370\) | −7281.24 | −1.02306 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 483.350 | 0.0673670 | ||||||||
\(373\) | 5369.88 | 0.745420 | 0.372710 | − | 0.927948i | \(-0.378429\pi\) | ||||
0.372710 | + | 0.927948i | \(0.378429\pi\) | |||||||
\(374\) | −2373.36 | −0.328138 | ||||||||
\(375\) | −572.731 | −0.0788685 | ||||||||
\(376\) | −209.051 | −0.0286729 | ||||||||
\(377\) | 3492.43 | 0.477107 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 2510.75 | 0.340286 | 0.170143 | − | 0.985419i | \(-0.445577\pi\) | ||||
0.170143 | + | 0.985419i | \(0.445577\pi\) | |||||||
\(380\) | −1154.28 | −0.155825 | ||||||||
\(381\) | −712.028 | −0.0957435 | ||||||||
\(382\) | 6196.01 | 0.829884 | ||||||||
\(383\) | 9436.92 | 1.25902 | 0.629509 | − | 0.776993i | \(-0.283256\pi\) | ||||
0.629509 | + | 0.776993i | \(0.283256\pi\) | |||||||
\(384\) | 54.2388 | 0.00720797 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −6131.81 | −0.808551 | ||||||||
\(387\) | 603.361 | 0.0792522 | ||||||||
\(388\) | −4659.57 | −0.609675 | ||||||||
\(389\) | −3025.19 | −0.394301 | −0.197151 | − | 0.980373i | \(-0.563169\pi\) | ||||
−0.197151 | + | 0.980373i | \(0.563169\pi\) | |||||||
\(390\) | 305.677 | 0.0396886 | ||||||||
\(391\) | 2520.74 | 0.326034 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −778.939 | −0.0999803 | ||||||||
\(394\) | −1006.23 | −0.128662 | ||||||||
\(395\) | −884.456 | −0.112663 | ||||||||
\(396\) | −1161.61 | −0.147407 | ||||||||
\(397\) | 13999.3 | 1.76979 | 0.884895 | − | 0.465791i | \(-0.154230\pi\) | ||||
0.884895 | + | 0.465791i | \(0.154230\pi\) | |||||||
\(398\) | −2538.18 | −0.319668 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 3199.62 | 0.399953 | ||||||||
\(401\) | 3017.67 | 0.375799 | 0.187900 | − | 0.982188i | \(-0.439832\pi\) | ||||
0.187900 | + | 0.982188i | \(0.439832\pi\) | |||||||
\(402\) | 722.974 | 0.0896982 | ||||||||
\(403\) | −5705.70 | −0.705263 | ||||||||
\(404\) | 7552.14 | 0.930032 | ||||||||
\(405\) | 12880.2 | 1.58030 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 2186.67 | 0.266313 | ||||||||
\(408\) | 371.527 | 0.0450816 | ||||||||
\(409\) | 6741.78 | 0.815060 | 0.407530 | − | 0.913192i | \(-0.366390\pi\) | ||||
0.407530 | + | 0.913192i | \(0.366390\pi\) | |||||||
\(410\) | −2622.91 | −0.315943 | ||||||||
\(411\) | −1072.39 | −0.128704 | ||||||||
\(412\) | 2931.20 | 0.350510 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 1233.74 | 0.146461 | ||||||||
\(415\) | −9682.98 | −1.14535 | ||||||||
\(416\) | −640.261 | −0.0754601 | ||||||||
\(417\) | −99.7238 | −0.0117110 | ||||||||
\(418\) | 346.650 | 0.0405626 | ||||||||
\(419\) | 2505.65 | 0.292146 | 0.146073 | − | 0.989274i | \(-0.453337\pi\) | ||||
0.146073 | + | 0.989274i | \(0.453337\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 7665.96 | 0.887449 | 0.443724 | − | 0.896163i | \(-0.353657\pi\) | ||||
0.443724 | + | 0.896163i | \(0.353657\pi\) | |||||||
\(422\) | 6298.13 | 0.726512 | ||||||||
\(423\) | −700.856 | −0.0805598 | ||||||||
\(424\) | 2397.07 | 0.274557 | ||||||||
\(425\) | 21916.9 | 2.50147 | ||||||||
\(426\) | −233.468 | −0.0265530 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 117.420 | 0.0132610 | ||||||||
\(429\) | −91.7996 | −0.0103313 | ||||||||
\(430\) | 811.087 | 0.0909630 | ||||||||
\(431\) | −3735.71 | −0.417501 | −0.208751 | − | 0.977969i | \(-0.566940\pi\) | ||||
−0.208751 | + | 0.977969i | \(0.566940\pi\) | |||||||
\(432\) | 364.894 | 0.0406388 | ||||||||
\(433\) | −13124.0 | −1.45658 | −0.728289 | − | 0.685270i | \(-0.759684\pi\) | ||||
−0.728289 | + | 0.685270i | \(0.759684\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −1333.36 | −0.146964 | ||||||||
\(436\) | 6018.57 | 0.661094 | ||||||||
\(437\) | −368.175 | −0.0403025 | ||||||||
\(438\) | 343.818 | 0.0375074 | ||||||||
\(439\) | 10836.5 | 1.17813 | 0.589066 | − | 0.808085i | \(-0.299496\pi\) | ||||
0.589066 | + | 0.808085i | \(0.299496\pi\) | |||||||
\(440\) | −1561.53 | −0.169189 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −4385.69 | −0.471959 | ||||||||
\(443\) | −8521.87 | −0.913964 | −0.456982 | − | 0.889476i | \(-0.651070\pi\) | ||||
−0.456982 | + | 0.889476i | \(0.651070\pi\) | |||||||
\(444\) | −342.302 | −0.0365877 | ||||||||
\(445\) | −7370.51 | −0.785159 | ||||||||
\(446\) | 950.567 | 0.100921 | ||||||||
\(447\) | 712.429 | 0.0753842 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −12286.0 | −1.29134 | −0.645671 | − | 0.763616i | \(-0.723422\pi\) | ||||
−0.645671 | + | 0.763616i | \(0.723422\pi\) | |||||||
\(450\) | 10726.9 | 1.12371 | ||||||||
\(451\) | 787.702 | 0.0822427 | ||||||||
\(452\) | −861.977 | −0.0896990 | ||||||||
\(453\) | 228.786 | 0.0237291 | ||||||||
\(454\) | −9847.77 | −1.01801 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −54.2646 | −0.00557275 | ||||||||
\(457\) | 6936.85 | 0.710049 | 0.355024 | − | 0.934857i | \(-0.384473\pi\) | ||||
0.355024 | + | 0.934857i | \(0.384473\pi\) | |||||||
\(458\) | 6197.51 | 0.632293 | ||||||||
\(459\) | 2499.47 | 0.254172 | ||||||||
\(460\) | 1658.49 | 0.168104 | ||||||||
\(461\) | −6741.05 | −0.681045 | −0.340523 | − | 0.940236i | \(-0.610604\pi\) | ||||
−0.340523 | + | 0.940236i | \(0.610604\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 5242.34 | 0.526203 | 0.263102 | − | 0.964768i | \(-0.415255\pi\) | ||||
0.263102 | + | 0.964768i | \(0.415255\pi\) | |||||||
\(464\) | 2792.80 | 0.279424 | ||||||||
\(465\) | 2178.35 | 0.217244 | ||||||||
\(466\) | −13676.5 | −1.35955 | ||||||||
\(467\) | 825.259 | 0.0817740 | 0.0408870 | − | 0.999164i | \(-0.486982\pi\) | ||||
0.0408870 | + | 0.999164i | \(0.486982\pi\) | |||||||
\(468\) | −2146.51 | −0.212014 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −942.148 | −0.0924639 | ||||||||
\(471\) | −441.543 | −0.0431958 | ||||||||
\(472\) | 4572.87 | 0.445940 | ||||||||
\(473\) | −243.582 | −0.0236785 | ||||||||
\(474\) | −41.5796 | −0.00402914 | ||||||||
\(475\) | −3201.15 | −0.309218 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 8036.32 | 0.771400 | ||||||||
\(478\) | 8497.96 | 0.813154 | ||||||||
\(479\) | 10998.2 | 1.04911 | 0.524553 | − | 0.851378i | \(-0.324233\pi\) | ||||
0.524553 | + | 0.851378i | \(0.324233\pi\) | |||||||
\(480\) | 244.442 | 0.0232442 | ||||||||
\(481\) | 4040.70 | 0.383035 | ||||||||
\(482\) | 8469.46 | 0.800359 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −4855.05 | −0.455959 | ||||||||
\(485\) | −20999.7 | −1.96607 | ||||||||
\(486\) | 1837.03 | 0.171460 | ||||||||
\(487\) | −5976.46 | −0.556097 | −0.278048 | − | 0.960567i | \(-0.589688\pi\) | ||||
−0.278048 | + | 0.960567i | \(0.589688\pi\) | |||||||
\(488\) | −3945.75 | −0.366016 | ||||||||
\(489\) | −360.892 | −0.0333744 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −1119.29 | −0.102878 | −0.0514389 | − | 0.998676i | \(-0.516381\pi\) | ||||
−0.0514389 | + | 0.998676i | \(0.516381\pi\) | |||||||
\(492\) | −123.307 | −0.0112990 | ||||||||
\(493\) | 19130.2 | 1.74763 | ||||||||
\(494\) | 640.566 | 0.0583410 | ||||||||
\(495\) | −5235.11 | −0.475355 | ||||||||
\(496\) | −4562.70 | −0.413047 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −455.211 | −0.0409608 | ||||||||
\(499\) | 7057.72 | 0.633160 | 0.316580 | − | 0.948566i | \(-0.397465\pi\) | ||||
0.316580 | + | 0.948566i | \(0.397465\pi\) | |||||||
\(500\) | 5406.43 | 0.483566 | ||||||||
\(501\) | 1550.31 | 0.138249 | ||||||||
\(502\) | −4492.63 | −0.399434 | ||||||||
\(503\) | −9822.07 | −0.870665 | −0.435332 | − | 0.900270i | \(-0.643369\pi\) | ||||
−0.435332 | + | 0.900270i | \(0.643369\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 34035.8 | 2.99916 | ||||||||
\(506\) | −498.072 | −0.0437589 | ||||||||
\(507\) | 761.323 | 0.0666894 | ||||||||
\(508\) | 6721.36 | 0.587032 | ||||||||
\(509\) | 10971.9 | 0.955445 | 0.477722 | − | 0.878511i | \(-0.341462\pi\) | ||||
0.477722 | + | 0.878511i | \(0.341462\pi\) | |||||||
\(510\) | 1674.39 | 0.145379 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −512.000 | −0.0441942 | ||||||||
\(513\) | −365.068 | −0.0314194 | ||||||||
\(514\) | −6258.22 | −0.537040 | ||||||||
\(515\) | 13210.3 | 1.13032 | ||||||||
\(516\) | 38.1304 | 0.00325310 | ||||||||
\(517\) | 282.942 | 0.0240692 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −19.6160 | −0.00165905 | ||||||||
\(520\) | −2885.51 | −0.243343 | ||||||||
\(521\) | 11404.8 | 0.959027 | 0.479514 | − | 0.877534i | \(-0.340813\pi\) | ||||
0.479514 | + | 0.877534i | \(0.340813\pi\) | |||||||
\(522\) | 9363.03 | 0.785074 | ||||||||
\(523\) | −8931.53 | −0.746747 | −0.373373 | − | 0.927681i | \(-0.621799\pi\) | ||||
−0.373373 | + | 0.927681i | \(0.621799\pi\) | |||||||
\(524\) | 7352.99 | 0.613009 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −11957.3 | −0.991186 | ||||||||
\(527\) | −31253.7 | −2.58337 | ||||||||
\(528\) | −73.4097 | −0.00605066 | ||||||||
\(529\) | 529.000 | 0.0434783 | ||||||||
\(530\) | 10803.1 | 0.885388 | ||||||||
\(531\) | 15330.8 | 1.25292 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 1455.58 | 0.118289 | ||||||||
\(534\) | −346.498 | −0.0280795 | ||||||||
\(535\) | 529.187 | 0.0427640 | ||||||||
\(536\) | −6824.69 | −0.549966 | ||||||||
\(537\) | 1269.83 | 0.102043 | ||||||||
\(538\) | 12380.1 | 0.992086 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 1644.50 | 0.131052 | ||||||||
\(541\) | 6503.89 | 0.516865 | 0.258433 | − | 0.966029i | \(-0.416794\pi\) | ||||
0.258433 | + | 0.966029i | \(0.416794\pi\) | |||||||
\(542\) | 5140.59 | 0.407394 | ||||||||
\(543\) | 564.863 | 0.0446420 | ||||||||
\(544\) | −3507.12 | −0.276409 | ||||||||
\(545\) | 27124.3 | 2.13189 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −14483.9 | −1.13215 | −0.566077 | − | 0.824352i | \(-0.691540\pi\) | ||||
−0.566077 | + | 0.824352i | \(0.691540\pi\) | |||||||
\(548\) | 10123.1 | 0.789120 | ||||||||
\(549\) | −13228.4 | −1.02837 | ||||||||
\(550\) | −4330.55 | −0.335737 | ||||||||
\(551\) | −2794.13 | −0.216033 | ||||||||
\(552\) | 77.9682 | 0.00601186 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 6611.82 | 0.507056 | ||||||||
\(555\) | −1542.68 | −0.117987 | ||||||||
\(556\) | 941.367 | 0.0718037 | ||||||||
\(557\) | 19776.6 | 1.50442 | 0.752210 | − | 0.658924i | \(-0.228988\pi\) | ||||
0.752210 | + | 0.658924i | \(0.228988\pi\) | |||||||
\(558\) | −15296.7 | −1.16050 | ||||||||
\(559\) | −450.110 | −0.0340566 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −502.845 | −0.0378434 | ||||||||
\(562\) | −9480.41 | −0.711578 | ||||||||
\(563\) | −11618.4 | −0.869727 | −0.434863 | − | 0.900496i | \(-0.643203\pi\) | ||||
−0.434863 | + | 0.900496i | \(0.643203\pi\) | |||||||
\(564\) | −44.2918 | −0.00330677 | ||||||||
\(565\) | −3884.74 | −0.289260 | ||||||||
\(566\) | −17550.3 | −1.30335 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 2203.88 | 0.162804 | ||||||||
\(569\) | −21913.2 | −1.61449 | −0.807247 | − | 0.590213i | \(-0.799044\pi\) | ||||
−0.807247 | + | 0.590213i | \(0.799044\pi\) | |||||||
\(570\) | −244.558 | −0.0179709 | ||||||||
\(571\) | 7580.99 | 0.555612 | 0.277806 | − | 0.960637i | \(-0.410393\pi\) | ||||
0.277806 | + | 0.960637i | \(0.410393\pi\) | |||||||
\(572\) | 866.565 | 0.0633442 | ||||||||
\(573\) | 1312.75 | 0.0957084 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 4599.46 | 0.333584 | ||||||||
\(576\) | −1716.51 | −0.124169 | ||||||||
\(577\) | 5057.21 | 0.364877 | 0.182439 | − | 0.983217i | \(-0.441601\pi\) | ||||
0.182439 | + | 0.983217i | \(0.441601\pi\) | |||||||
\(578\) | −14197.2 | −1.02167 | ||||||||
\(579\) | −1299.15 | −0.0932482 | ||||||||
\(580\) | 12586.5 | 0.901082 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −987.225 | −0.0703123 | ||||||||
\(583\) | −3244.33 | −0.230474 | ||||||||
\(584\) | −3245.55 | −0.229969 | ||||||||
\(585\) | −9673.85 | −0.683700 | ||||||||
\(586\) | 5435.39 | 0.383164 | ||||||||
\(587\) | 9108.51 | 0.640457 | 0.320229 | − | 0.947340i | \(-0.396240\pi\) | ||||
0.320229 | + | 0.947340i | \(0.396240\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 4564.87 | 0.319342 | ||||||||
\(590\) | 20608.9 | 1.43806 | ||||||||
\(591\) | −213.190 | −0.0148383 | ||||||||
\(592\) | 3231.24 | 0.224330 | ||||||||
\(593\) | −11793.9 | −0.816721 | −0.408361 | − | 0.912821i | \(-0.633899\pi\) | ||||
−0.408361 | + | 0.912821i | \(0.633899\pi\) | |||||||
\(594\) | −493.868 | −0.0341139 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −6725.15 | −0.462203 | ||||||||
\(597\) | −537.766 | −0.0368665 | ||||||||
\(598\) | −920.376 | −0.0629381 | ||||||||
\(599\) | −27046.3 | −1.84488 | −0.922440 | − | 0.386140i | \(-0.873808\pi\) | ||||
−0.922440 | + | 0.386140i | \(0.873808\pi\) | |||||||
\(600\) | 677.905 | 0.0461256 | ||||||||
\(601\) | −19013.2 | −1.29046 | −0.645230 | − | 0.763989i | \(-0.723238\pi\) | ||||
−0.645230 | + | 0.763989i | \(0.723238\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −22880.2 | −1.54519 | ||||||||
\(604\) | −2159.68 | −0.145490 | ||||||||
\(605\) | −21880.6 | −1.47037 | ||||||||
\(606\) | 1600.07 | 0.107258 | ||||||||
\(607\) | 1868.60 | 0.124949 | 0.0624745 | − | 0.998047i | \(-0.480101\pi\) | ||||
0.0624745 | + | 0.998047i | \(0.480101\pi\) | |||||||
\(608\) | 512.244 | 0.0341681 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −17782.6 | −1.18032 | ||||||||
\(611\) | 522.842 | 0.0346185 | ||||||||
\(612\) | −11757.8 | −0.776603 | ||||||||
\(613\) | −735.324 | −0.0484493 | −0.0242247 | − | 0.999707i | \(-0.507712\pi\) | ||||
−0.0242247 | + | 0.999707i | \(0.507712\pi\) | |||||||
\(614\) | −15064.3 | −0.990138 | ||||||||
\(615\) | −555.717 | −0.0364369 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −10128.6 | −0.660876 | −0.330438 | − | 0.943828i | \(-0.607196\pi\) | ||||
−0.330438 | + | 0.943828i | \(0.607196\pi\) | |||||||
\(618\) | 621.034 | 0.0404234 | ||||||||
\(619\) | 6555.19 | 0.425647 | 0.212823 | − | 0.977091i | \(-0.431734\pi\) | ||||
0.212823 | + | 0.977091i | \(0.431734\pi\) | |||||||
\(620\) | −20563.1 | −1.33199 | ||||||||
\(621\) | 524.535 | 0.0338951 | ||||||||
\(622\) | −21837.8 | −1.40774 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −135.652 | −0.00870262 | ||||||||
\(625\) | −631.476 | −0.0404144 | ||||||||
\(626\) | −15375.0 | −0.981643 | ||||||||
\(627\) | 73.4447 | 0.00467799 | ||||||||
\(628\) | 4168.05 | 0.264846 | ||||||||
\(629\) | 22133.5 | 1.40305 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −26053.0 | −1.64367 | −0.821833 | − | 0.569728i | \(-0.807049\pi\) | ||||
−0.821833 | + | 0.569728i | \(0.807049\pi\) | |||||||
\(632\) | 392.501 | 0.0247039 | ||||||||
\(633\) | 1334.39 | 0.0837868 | ||||||||
\(634\) | 18538.4 | 1.16129 | ||||||||
\(635\) | 30291.7 | 1.89305 | ||||||||
\(636\) | 507.868 | 0.0316640 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −3779.93 | −0.234560 | ||||||||
\(639\) | 7388.63 | 0.457418 | ||||||||
\(640\) | −2307.47 | −0.142517 | ||||||||
\(641\) | 7834.67 | 0.482763 | 0.241381 | − | 0.970430i | \(-0.422400\pi\) | ||||
0.241381 | + | 0.970430i | \(0.422400\pi\) | |||||||
\(642\) | 24.8779 | 0.00152936 | ||||||||
\(643\) | −22205.5 | −1.36190 | −0.680949 | − | 0.732331i | \(-0.738433\pi\) | ||||
−0.680949 | + | 0.732331i | \(0.738433\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 171.845 | 0.0104905 | ||||||||
\(646\) | 3508.79 | 0.213702 | ||||||||
\(647\) | 28757.5 | 1.74741 | 0.873704 | − | 0.486458i | \(-0.161711\pi\) | ||||
0.873704 | + | 0.486458i | \(0.161711\pi\) | |||||||
\(648\) | −5715.91 | −0.346515 | ||||||||
\(649\) | −6189.18 | −0.374340 | ||||||||
\(650\) | −8002.32 | −0.482888 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 3406.73 | 0.204628 | ||||||||
\(653\) | 23477.2 | 1.40694 | 0.703471 | − | 0.710724i | \(-0.251633\pi\) | ||||
0.703471 | + | 0.710724i | \(0.251633\pi\) | |||||||
\(654\) | 1275.15 | 0.0762423 | ||||||||
\(655\) | 33138.3 | 1.97682 | ||||||||
\(656\) | 1163.99 | 0.0692775 | ||||||||
\(657\) | −10880.9 | −0.646125 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −82.2052 | −0.00485927 | −0.00242964 | − | 0.999997i | \(-0.500773\pi\) | ||||
−0.00242964 | + | 0.999997i | \(0.500773\pi\) | |||||||
\(660\) | −330.841 | −0.0195121 | ||||||||
\(661\) | 32371.0 | 1.90482 | 0.952411 | − | 0.304818i | \(-0.0985957\pi\) | ||||
0.952411 | + | 0.304818i | \(0.0985957\pi\) | |||||||
\(662\) | −19879.1 | −1.16710 | ||||||||
\(663\) | −929.196 | −0.0544298 | ||||||||
\(664\) | 4297.07 | 0.251143 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 10832.9 | 0.630280 | ||||||||
\(667\) | 4014.65 | 0.233055 | ||||||||
\(668\) | −14634.5 | −0.847642 | ||||||||
\(669\) | 201.397 | 0.0116389 | ||||||||
\(670\) | −30757.4 | −1.77352 | ||||||||
\(671\) | 5340.40 | 0.307249 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −10946.9 | −0.627001 | −0.313501 | − | 0.949588i | \(-0.601502\pi\) | ||||
−0.313501 | + | 0.949588i | \(0.601502\pi\) | |||||||
\(674\) | 1843.82 | 0.105373 | ||||||||
\(675\) | 4560.64 | 0.260058 | ||||||||
\(676\) | −7186.69 | −0.408892 | ||||||||
\(677\) | 17975.5 | 1.02046 | 0.510232 | − | 0.860037i | \(-0.329559\pi\) | ||||
0.510232 | + | 0.860037i | \(0.329559\pi\) | |||||||
\(678\) | −182.627 | −0.0103448 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −15805.8 | −0.891359 | ||||||||
\(681\) | −2086.45 | −0.117405 | ||||||||
\(682\) | 6175.41 | 0.346728 | ||||||||
\(683\) | −24747.0 | −1.38641 | −0.693204 | − | 0.720741i | \(-0.743801\pi\) | ||||
−0.693204 | + | 0.720741i | \(0.743801\pi\) | |||||||
\(684\) | 1717.33 | 0.0959994 | ||||||||
\(685\) | 45622.6 | 2.54474 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 1313.07 | 0.0729208 | ||||||||
\(688\) | −359.941 | −0.0199457 | ||||||||
\(689\) | −5995.13 | −0.331490 | ||||||||
\(690\) | 351.385 | 0.0193870 | ||||||||
\(691\) | −22534.5 | −1.24060 | −0.620299 | − | 0.784365i | \(-0.712989\pi\) | ||||
−0.620299 | + | 0.784365i | \(0.712989\pi\) | |||||||
\(692\) | 185.170 | 0.0101721 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −14687.6 | −0.803362 | ||||||||
\(695\) | 4242.53 | 0.231552 | ||||||||
\(696\) | 591.711 | 0.0322252 | ||||||||
\(697\) | 7973.12 | 0.433290 | ||||||||
\(698\) | −15246.6 | −0.826779 | ||||||||
\(699\) | −2897.64 | −0.156794 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 33521.9 | 1.80614 | 0.903069 | − | 0.429495i | \(-0.141308\pi\) | ||||
0.903069 | + | 0.429495i | \(0.141308\pi\) | |||||||
\(702\) | −912.608 | −0.0490658 | ||||||||
\(703\) | −3232.78 | −0.173437 | ||||||||
\(704\) | 692.969 | 0.0370984 | ||||||||
\(705\) | −199.613 | −0.0106636 | ||||||||
\(706\) | 3870.60 | 0.206334 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 968.856 | 0.0514291 | ||||||||
\(709\) | 6358.64 | 0.336818 | 0.168409 | − | 0.985717i | \(-0.446137\pi\) | ||||
0.168409 | + | 0.985717i | \(0.446137\pi\) | |||||||
\(710\) | 9932.40 | 0.525009 | ||||||||
\(711\) | 1315.88 | 0.0694084 | ||||||||
\(712\) | 3270.86 | 0.172164 | ||||||||
\(713\) | −6558.88 | −0.344505 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 3905.41 | 0.204272 | ||||||||
\(716\) | −11986.9 | −0.625657 | ||||||||
\(717\) | 1800.46 | 0.0937790 | ||||||||
\(718\) | 2841.73 | 0.147705 | ||||||||
\(719\) | −23439.4 | −1.21577 | −0.607887 | − | 0.794024i | \(-0.707983\pi\) | ||||
−0.607887 | + | 0.794024i | \(0.707983\pi\) | |||||||
\(720\) | −7735.92 | −0.400418 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 13205.5 | 0.680690 | ||||||||
\(723\) | 1794.42 | 0.0923034 | ||||||||
\(724\) | −5332.16 | −0.273713 | ||||||||
\(725\) | 34905.9 | 1.78810 | ||||||||
\(726\) | −1028.64 | −0.0525846 | ||||||||
\(727\) | −19080.9 | −0.973415 | −0.486708 | − | 0.873565i | \(-0.661802\pi\) | ||||
−0.486708 | + | 0.873565i | \(0.661802\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −18902.0 | −0.960320 | ||||||||
\(730\) | −14627.0 | −0.741601 | ||||||||
\(731\) | −2465.54 | −0.124749 | ||||||||
\(732\) | −835.988 | −0.0422117 | ||||||||
\(733\) | 7975.41 | 0.401881 | 0.200940 | − | 0.979603i | \(-0.435600\pi\) | ||||
0.200940 | + | 0.979603i | \(0.435600\pi\) | |||||||
\(734\) | 13481.8 | 0.677959 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −736.000 | −0.0368605 | ||||||||
\(737\) | 9236.92 | 0.461664 | ||||||||
\(738\) | 3902.33 | 0.194643 | ||||||||
\(739\) | 12646.3 | 0.629502 | 0.314751 | − | 0.949174i | \(-0.398079\pi\) | ||||
0.314751 | + | 0.949174i | \(0.398079\pi\) | |||||||
\(740\) | 14562.5 | 0.723415 | ||||||||
\(741\) | 135.717 | 0.00672832 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 21893.7 | 1.08103 | 0.540514 | − | 0.841335i | \(-0.318230\pi\) | ||||
0.540514 | + | 0.841335i | \(0.318230\pi\) | |||||||
\(744\) | −966.699 | −0.0476356 | ||||||||
\(745\) | −30308.7 | −1.49051 | ||||||||
\(746\) | −10739.8 | −0.527092 | ||||||||
\(747\) | 14406.2 | 0.705615 | ||||||||
\(748\) | 4746.73 | 0.232029 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 1145.46 | 0.0557685 | ||||||||
\(751\) | 29541.1 | 1.43538 | 0.717689 | − | 0.696363i | \(-0.245200\pi\) | ||||
0.717689 | + | 0.696363i | \(0.245200\pi\) | |||||||
\(752\) | 418.103 | 0.0202748 | ||||||||
\(753\) | −951.853 | −0.0460657 | ||||||||
\(754\) | −6984.86 | −0.337365 | ||||||||
\(755\) | −9733.19 | −0.469175 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −18772.7 | −0.901326 | −0.450663 | − | 0.892694i | \(-0.648812\pi\) | ||||
−0.450663 | + | 0.892694i | \(0.648812\pi\) | |||||||
\(758\) | −5021.49 | −0.240618 | ||||||||
\(759\) | −105.527 | −0.00504660 | ||||||||
\(760\) | 2308.57 | 0.110185 | ||||||||
\(761\) | 27796.9 | 1.32410 | 0.662049 | − | 0.749461i | \(-0.269687\pi\) | ||||
0.662049 | + | 0.749461i | \(0.269687\pi\) | |||||||
\(762\) | 1424.06 | 0.0677009 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −12392.0 | −0.586816 | ||||||||
\(765\) | −52989.8 | −2.50438 | ||||||||
\(766\) | −18873.8 | −0.890260 | ||||||||
\(767\) | −11436.9 | −0.538410 | ||||||||
\(768\) | −108.478 | −0.00509680 | ||||||||
\(769\) | 3876.68 | 0.181790 | 0.0908950 | − | 0.995860i | \(-0.471027\pi\) | ||||
0.0908950 | + | 0.995860i | \(0.471027\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −1325.93 | −0.0619354 | ||||||||
\(772\) | 12263.6 | 0.571732 | ||||||||
\(773\) | 25970.4 | 1.20840 | 0.604198 | − | 0.796834i | \(-0.293493\pi\) | ||||
0.604198 | + | 0.796834i | \(0.293493\pi\) | |||||||
\(774\) | −1206.72 | −0.0560397 | ||||||||
\(775\) | −57027.0 | −2.64319 | ||||||||
\(776\) | 9319.15 | 0.431106 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 6050.38 | 0.278813 | ||||||||
\(779\) | −1164.54 | −0.0535610 | ||||||||
\(780\) | −611.354 | −0.0280641 | ||||||||
\(781\) | −2982.85 | −0.136664 | ||||||||
\(782\) | −5041.48 | −0.230541 | ||||||||
\(783\) | 3980.77 | 0.181687 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 18784.5 | 0.854072 | ||||||||
\(786\) | 1557.88 | 0.0706968 | ||||||||
\(787\) | 38804.8 | 1.75761 | 0.878806 | − | 0.477180i | \(-0.158341\pi\) | ||||
0.878806 | + | 0.477180i | \(0.158341\pi\) | |||||||
\(788\) | 2012.46 | 0.0909781 | ||||||||
\(789\) | −2533.40 | −0.114311 | ||||||||
\(790\) | 1768.91 | 0.0796647 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 2323.22 | 0.104232 | ||||||||
\(793\) | 9868.41 | 0.441914 | ||||||||
\(794\) | −27998.7 | −1.25143 | ||||||||
\(795\) | 2288.85 | 0.102110 | ||||||||
\(796\) | 5076.37 | 0.226039 | ||||||||
\(797\) | 28345.3 | 1.25978 | 0.629888 | − | 0.776686i | \(-0.283101\pi\) | ||||
0.629888 | + | 0.776686i | \(0.283101\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 2863.94 | 0.126807 | ||||||||
\(800\) | −6399.25 | −0.282809 | ||||||||
\(801\) | 10965.7 | 0.483714 | ||||||||
\(802\) | −6035.35 | −0.265730 | ||||||||
\(803\) | 4392.71 | 0.193045 | ||||||||
\(804\) | −1445.95 | −0.0634262 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 11411.4 | 0.498696 | ||||||||
\(807\) | 2622.97 | 0.114415 | ||||||||
\(808\) | −15104.3 | −0.657632 | ||||||||
\(809\) | −20784.8 | −0.903282 | −0.451641 | − | 0.892200i | \(-0.649161\pi\) | ||||
−0.451641 | + | 0.892200i | \(0.649161\pi\) | |||||||
\(810\) | −25760.3 | −1.11744 | ||||||||
\(811\) | 10577.0 | 0.457963 | 0.228981 | − | 0.973431i | \(-0.426461\pi\) | ||||
0.228981 | + | 0.973431i | \(0.426461\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 1089.14 | 0.0469837 | ||||||||
\(814\) | −4373.34 | −0.188311 | ||||||||
\(815\) | 15353.3 | 0.659883 | ||||||||
\(816\) | −743.053 | −0.0318775 | ||||||||
\(817\) | 360.113 | 0.0154207 | ||||||||
\(818\) | −13483.6 | −0.576335 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 5245.83 | 0.223405 | ||||||||
\(821\) | 1446.68 | 0.0614975 | 0.0307488 | − | 0.999527i | \(-0.490211\pi\) | ||||
0.0307488 | + | 0.999527i | \(0.490211\pi\) | |||||||
\(822\) | 2144.78 | 0.0910072 | ||||||||
\(823\) | −37849.9 | −1.60311 | −0.801557 | − | 0.597918i | \(-0.795995\pi\) | ||||
−0.801557 | + | 0.597918i | \(0.795995\pi\) | |||||||
\(824\) | −5862.40 | −0.247848 | ||||||||
\(825\) | −917.514 | −0.0387197 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 24988.6 | 1.05071 | 0.525355 | − | 0.850883i | \(-0.323932\pi\) | ||||
0.525355 | + | 0.850883i | \(0.323932\pi\) | |||||||
\(828\) | −2467.48 | −0.103564 | ||||||||
\(829\) | −25002.4 | −1.04749 | −0.523744 | − | 0.851876i | \(-0.675465\pi\) | ||||
−0.523744 | + | 0.851876i | \(0.675465\pi\) | |||||||
\(830\) | 19366.0 | 0.809882 | ||||||||
\(831\) | 1400.85 | 0.0584776 | ||||||||
\(832\) | 1280.52 | 0.0533583 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 199.448 | 0.00828094 | ||||||||
\(835\) | −65954.3 | −2.73347 | ||||||||
\(836\) | −693.299 | −0.0286821 | ||||||||
\(837\) | −6503.52 | −0.268572 | ||||||||
\(838\) | −5011.30 | −0.206578 | ||||||||
\(839\) | −12191.6 | −0.501671 | −0.250836 | − | 0.968030i | \(-0.580705\pi\) | ||||
−0.250836 | + | 0.968030i | \(0.580705\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 6078.75 | 0.249242 | ||||||||
\(842\) | −15331.9 | −0.627521 | ||||||||
\(843\) | −2008.61 | −0.0820645 | ||||||||
\(844\) | −12596.3 | −0.513722 | ||||||||
\(845\) | −32388.8 | −1.31859 | ||||||||
\(846\) | 1401.71 | 0.0569644 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −4794.15 | −0.194141 | ||||||||
\(849\) | −3718.38 | −0.150312 | ||||||||
\(850\) | −43833.8 | −1.76881 | ||||||||
\(851\) | 4644.91 | 0.187104 | ||||||||
\(852\) | 466.937 | 0.0187758 | ||||||||
\(853\) | −27618.4 | −1.10860 | −0.554300 | − | 0.832317i | \(-0.687014\pi\) | ||||
−0.554300 | + | 0.832317i | \(0.687014\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 7739.60 | 0.309578 | ||||||||
\(856\) | −234.841 | −0.00937697 | ||||||||
\(857\) | 12648.6 | 0.504164 | 0.252082 | − | 0.967706i | \(-0.418885\pi\) | ||||
0.252082 | + | 0.967706i | \(0.418885\pi\) | |||||||
\(858\) | 183.599 | 0.00730533 | ||||||||
\(859\) | 5293.51 | 0.210259 | 0.105129 | − | 0.994459i | \(-0.466474\pi\) | ||||
0.105129 | + | 0.994459i | \(0.466474\pi\) | |||||||
\(860\) | −1622.17 | −0.0643206 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 7471.43 | 0.295218 | ||||||||
\(863\) | 40972.6 | 1.61614 | 0.808068 | − | 0.589089i | \(-0.200513\pi\) | ||||
0.808068 | + | 0.589089i | \(0.200513\pi\) | |||||||
\(864\) | −729.789 | −0.0287360 | ||||||||
\(865\) | 834.520 | 0.0328029 | ||||||||
\(866\) | 26248.0 | 1.02996 | ||||||||
\(867\) | −3007.96 | −0.117827 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −531.232 | −0.0207374 | ||||||||
\(870\) | 2666.71 | 0.103919 | ||||||||
\(871\) | 17068.7 | 0.664008 | ||||||||
\(872\) | −12037.1 | −0.467464 | ||||||||
\(873\) | 31243.0 | 1.21124 | ||||||||
\(874\) | 736.350 | 0.0284982 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −687.636 | −0.0265217 | ||||||||
\(877\) | 50035.4 | 1.92654 | 0.963269 | − | 0.268537i | \(-0.0865403\pi\) | ||||
0.963269 | + | 0.268537i | \(0.0865403\pi\) | |||||||
\(878\) | −21673.1 | −0.833066 | ||||||||
\(879\) | 1151.60 | 0.0441893 | ||||||||
\(880\) | 3123.06 | 0.119634 | ||||||||
\(881\) | −11129.7 | −0.425618 | −0.212809 | − | 0.977094i | \(-0.568261\pi\) | ||||
−0.212809 | + | 0.977094i | \(0.568261\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 10184.5 | 0.388149 | 0.194074 | − | 0.980987i | \(-0.437830\pi\) | ||||
0.194074 | + | 0.980987i | \(0.437830\pi\) | |||||||
\(884\) | 8771.37 | 0.333725 | ||||||||
\(885\) | 4366.41 | 0.165848 | ||||||||
\(886\) | 17043.7 | 0.646270 | ||||||||
\(887\) | −36749.2 | −1.39111 | −0.695556 | − | 0.718472i | \(-0.744842\pi\) | ||||
−0.695556 | + | 0.718472i | \(0.744842\pi\) | |||||||
\(888\) | 684.603 | 0.0258714 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 14741.0 | 0.555191 | ||||||||
\(891\) | 7736.22 | 0.290879 | ||||||||
\(892\) | −1901.13 | −0.0713617 | ||||||||
\(893\) | −418.302 | −0.0156752 | ||||||||
\(894\) | −1424.86 | −0.0533047 | ||||||||
\(895\) | −54022.2 | −2.01761 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −195.000 | −0.00725849 | ||||||||
\(898\) | 24572.0 | 0.913117 | ||||||||
\(899\) | −49776.2 | −1.84664 | ||||||||
\(900\) | −21453.8 | −0.794586 | ||||||||
\(901\) | −32839.1 | −1.21424 | ||||||||
\(902\) | −1575.40 | −0.0581544 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 1723.95 | 0.0634268 | ||||||||
\(905\) | −24030.9 | −0.882666 | ||||||||
\(906\) | −457.571 | −0.0167790 | ||||||||
\(907\) | −3161.83 | −0.115752 | −0.0578759 | − | 0.998324i | \(-0.518433\pi\) | ||||
−0.0578759 | + | 0.998324i | \(0.518433\pi\) | |||||||
\(908\) | 19695.5 | 0.719845 | ||||||||
\(909\) | −50637.9 | −1.84769 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −7515.86 | −0.273339 | −0.136669 | − | 0.990617i | \(-0.543640\pi\) | ||||
−0.136669 | + | 0.990617i | \(0.543640\pi\) | |||||||
\(912\) | 108.529 | 0.00394053 | ||||||||
\(913\) | −5815.90 | −0.210819 | ||||||||
\(914\) | −13873.7 | −0.502080 | ||||||||
\(915\) | −3767.61 | −0.136124 | ||||||||
\(916\) | −12395.0 | −0.447099 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −4998.93 | −0.179727 | ||||||||
\(919\) | −3072.55 | −0.110287 | −0.0551437 | − | 0.998478i | \(-0.517562\pi\) | ||||
−0.0551437 | + | 0.998478i | \(0.517562\pi\) | |||||||
\(920\) | −3316.99 | −0.118867 | ||||||||
\(921\) | −3191.67 | −0.114190 | ||||||||
\(922\) | 13482.1 | 0.481572 | ||||||||
\(923\) | −5511.95 | −0.196563 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 40385.7 | 1.43554 | ||||||||
\(926\) | −10484.7 | −0.372082 | ||||||||
\(927\) | −19654.0 | −0.696357 | ||||||||
\(928\) | −5585.60 | −0.197582 | ||||||||
\(929\) | 12994.6 | 0.458924 | 0.229462 | − | 0.973318i | \(-0.426303\pi\) | ||||
0.229462 | + | 0.973318i | \(0.426303\pi\) | |||||||
\(930\) | −4356.70 | −0.153615 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 27353.0 | 0.961348 | ||||||||
\(933\) | −4626.78 | −0.162352 | ||||||||
\(934\) | −1650.52 | −0.0578229 | ||||||||
\(935\) | 21392.4 | 0.748243 | ||||||||
\(936\) | 4293.02 | 0.149916 | ||||||||
\(937\) | −28457.1 | −0.992161 | −0.496080 | − | 0.868277i | \(-0.665228\pi\) | ||||
−0.496080 | + | 0.868277i | \(0.665228\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −3257.50 | −0.113210 | ||||||||
\(940\) | 1884.30 | 0.0653819 | ||||||||
\(941\) | −38435.1 | −1.33151 | −0.665754 | − | 0.746172i | \(-0.731890\pi\) | ||||
−0.665754 | + | 0.746172i | \(0.731890\pi\) | |||||||
\(942\) | 883.086 | 0.0305440 | ||||||||
\(943\) | 1673.23 | 0.0577814 | ||||||||
\(944\) | −9145.75 | −0.315327 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 487.164 | 0.0167432 | ||||||||
\(947\) | −50283.5 | −1.72544 | −0.862722 | − | 0.505679i | \(-0.831242\pi\) | ||||
−0.862722 | + | 0.505679i | \(0.831242\pi\) | |||||||
\(948\) | 83.1592 | 0.00284903 | ||||||||
\(949\) | 8117.19 | 0.277656 | ||||||||
\(950\) | 6402.29 | 0.218650 | ||||||||
\(951\) | 3927.74 | 0.133928 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −3339.05 | −0.113497 | −0.0567483 | − | 0.998389i | \(-0.518073\pi\) | ||||
−0.0567483 | + | 0.998389i | \(0.518073\pi\) | |||||||
\(954\) | −16072.6 | −0.545462 | ||||||||
\(955\) | −55848.1 | −1.89236 | ||||||||
\(956\) | −16995.9 | −0.574987 | ||||||||
\(957\) | −800.855 | −0.0270512 | ||||||||
\(958\) | −21996.4 | −0.741830 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −488.884 | −0.0164361 | ||||||||
\(961\) | 51530.1 | 1.72972 | ||||||||
\(962\) | −8081.40 | −0.270847 | ||||||||
\(963\) | −787.316 | −0.0263457 | ||||||||
\(964\) | −16938.9 | −0.565939 | ||||||||
\(965\) | 55269.4 | 1.84371 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 44743.8 | 1.48797 | 0.743983 | − | 0.668198i | \(-0.232934\pi\) | ||||
0.743983 | + | 0.668198i | \(0.232934\pi\) | |||||||
\(968\) | 9710.10 | 0.322412 | ||||||||
\(969\) | 743.407 | 0.0246457 | ||||||||
\(970\) | 41999.3 | 1.39022 | ||||||||
\(971\) | 592.085 | 0.0195684 | 0.00978420 | − | 0.999952i | \(-0.496886\pi\) | ||||
0.00978420 | + | 0.999952i | \(0.496886\pi\) | |||||||
\(972\) | −3674.07 | −0.121240 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 11952.9 | 0.393220 | ||||||||
\(975\) | −1695.45 | −0.0556902 | ||||||||
\(976\) | 7891.51 | 0.258813 | ||||||||
\(977\) | 7513.33 | 0.246031 | 0.123016 | − | 0.992405i | \(-0.460743\pi\) | ||||
0.123016 | + | 0.992405i | \(0.460743\pi\) | |||||||
\(978\) | 721.783 | 0.0235993 | ||||||||
\(979\) | −4426.96 | −0.144521 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −40355.1 | −1.31340 | ||||||||
\(982\) | 2238.59 | 0.0727456 | ||||||||
\(983\) | 12122.1 | 0.393321 | 0.196660 | − | 0.980472i | \(-0.436990\pi\) | ||||
0.196660 | + | 0.980472i | \(0.436990\pi\) | |||||||
\(984\) | 246.614 | 0.00798960 | ||||||||
\(985\) | 9069.69 | 0.293385 | ||||||||
\(986\) | −38260.5 | −1.23576 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −1281.13 | −0.0412533 | ||||||||
\(989\) | −517.415 | −0.0166358 | ||||||||
\(990\) | 10470.2 | 0.336127 | ||||||||
\(991\) | −1562.94 | −0.0500995 | −0.0250497 | − | 0.999686i | \(-0.507974\pi\) | ||||
−0.0250497 | + | 0.999686i | \(0.507974\pi\) | |||||||
\(992\) | 9125.39 | 0.292068 | ||||||||
\(993\) | −4211.79 | −0.134599 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 22878.1 | 0.728928 | ||||||||
\(996\) | 910.422 | 0.0289637 | ||||||||
\(997\) | −58687.6 | −1.86425 | −0.932124 | − | 0.362138i | \(-0.882047\pi\) | ||||
−0.932124 | + | 0.362138i | \(0.882047\pi\) | |||||||
\(998\) | −14115.4 | −0.447712 | ||||||||
\(999\) | 4605.71 | 0.145864 |
(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 | 2254.4.a.u.1.6 | 11 | ||
7.3 | odd | 6 | 322.4.e.d.93.6 | ✓ | 22 | ||
7.5 | odd | 6 | 322.4.e.d.277.6 | yes | 22 | ||
7.6 | odd | 2 | 2254.4.a.r.1.6 | 11 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
322.4.e.d.93.6 | ✓ | 22 | 7.3 | odd | 6 | ||
322.4.e.d.277.6 | yes | 22 | 7.5 | odd | 6 | ||
2254.4.a.r.1.6 | 11 | 7.6 | odd | 2 | |||
2254.4.a.u.1.6 | 11 | 1.1 | even | 1 | trivial |