Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1849,4,Mod(1,1849)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1849, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1849.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1849 = 43^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1849.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(109.094531601\) |
Analytic rank: | \(1\) |
Dimension: | \(50\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Character | \(\chi\) | \(=\) | 1849.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −4.80413 | −1.69852 | −0.849258 | − | 0.527977i | \(-0.822951\pi\) | ||||
−0.849258 | + | 0.527977i | \(0.822951\pi\) | |||||||
\(3\) | 2.56623 | 0.493871 | 0.246936 | − | 0.969032i | \(-0.420576\pi\) | ||||
0.246936 | + | 0.969032i | \(0.420576\pi\) | |||||||
\(4\) | 15.0797 | 1.88496 | ||||||||
\(5\) | 6.34124 | 0.567178 | 0.283589 | − | 0.958946i | \(-0.408475\pi\) | ||||
0.283589 | + | 0.958946i | \(0.408475\pi\) | |||||||
\(6\) | −12.3285 | −0.838849 | ||||||||
\(7\) | −6.17767 | −0.333563 | −0.166782 | − | 0.985994i | \(-0.553337\pi\) | ||||
−0.166782 | + | 0.985994i | \(0.553337\pi\) | |||||||
\(8\) | −34.0117 | −1.50312 | ||||||||
\(9\) | −20.4145 | −0.756091 | ||||||||
\(10\) | −30.4642 | −0.963361 | ||||||||
\(11\) | 33.6300 | 0.921803 | 0.460902 | − | 0.887451i | \(-0.347526\pi\) | ||||
0.460902 | + | 0.887451i | \(0.347526\pi\) | |||||||
\(12\) | 38.6979 | 0.930928 | ||||||||
\(13\) | −34.3998 | −0.733906 | −0.366953 | − | 0.930239i | \(-0.619599\pi\) | ||||
−0.366953 | + | 0.930239i | \(0.619599\pi\) | |||||||
\(14\) | 29.6784 | 0.566562 | ||||||||
\(15\) | 16.2731 | 0.280113 | ||||||||
\(16\) | 42.7593 | 0.668114 | ||||||||
\(17\) | 105.843 | 1.51004 | 0.755020 | − | 0.655702i | \(-0.227627\pi\) | ||||
0.755020 | + | 0.655702i | \(0.227627\pi\) | |||||||
\(18\) | 98.0737 | 1.28423 | ||||||||
\(19\) | −14.3178 | −0.172880 | −0.0864400 | − | 0.996257i | \(-0.527549\pi\) | ||||
−0.0864400 | + | 0.996257i | \(0.527549\pi\) | |||||||
\(20\) | 95.6239 | 1.06911 | ||||||||
\(21\) | −15.8533 | −0.164737 | ||||||||
\(22\) | −161.563 | −1.56570 | ||||||||
\(23\) | −160.517 | −1.45522 | −0.727612 | − | 0.685988i | \(-0.759370\pi\) | ||||
−0.727612 | + | 0.685988i | \(0.759370\pi\) | |||||||
\(24\) | −87.2819 | −0.742348 | ||||||||
\(25\) | −84.7886 | −0.678309 | ||||||||
\(26\) | 165.261 | 1.24655 | ||||||||
\(27\) | −121.676 | −0.867283 | ||||||||
\(28\) | −93.1573 | −0.628753 | ||||||||
\(29\) | 42.2224 | 0.270362 | 0.135181 | − | 0.990821i | \(-0.456838\pi\) | ||||
0.135181 | + | 0.990821i | \(0.456838\pi\) | |||||||
\(30\) | −78.1781 | −0.475777 | ||||||||
\(31\) | 0.100791 | 0.000583952 0 | 0.000291976 | − | 1.00000i | \(-0.499907\pi\) | ||||
0.000291976 | 1.00000i | \(0.499907\pi\) | ||||||||
\(32\) | 66.6725 | 0.368317 | ||||||||
\(33\) | 86.3024 | 0.455252 | ||||||||
\(34\) | −508.483 | −2.56483 | ||||||||
\(35\) | −39.1741 | −0.189190 | ||||||||
\(36\) | −307.843 | −1.42520 | ||||||||
\(37\) | 369.747 | 1.64287 | 0.821433 | − | 0.570305i | \(-0.193175\pi\) | ||||
0.821433 | + | 0.570305i | \(0.193175\pi\) | |||||||
\(38\) | 68.7844 | 0.293640 | ||||||||
\(39\) | −88.2778 | −0.362455 | ||||||||
\(40\) | −215.676 | −0.852536 | ||||||||
\(41\) | 450.083 | 1.71442 | 0.857210 | − | 0.514967i | \(-0.172196\pi\) | ||||
0.857210 | + | 0.514967i | \(0.172196\pi\) | |||||||
\(42\) | 76.1615 | 0.279809 | ||||||||
\(43\) | 0 | 0 | ||||||||
\(44\) | 507.130 | 1.73756 | ||||||||
\(45\) | −129.453 | −0.428838 | ||||||||
\(46\) | 771.146 | 2.47172 | ||||||||
\(47\) | −288.931 | −0.896700 | −0.448350 | − | 0.893858i | \(-0.647988\pi\) | ||||
−0.448350 | + | 0.893858i | \(0.647988\pi\) | |||||||
\(48\) | 109.730 | 0.329962 | ||||||||
\(49\) | −304.836 | −0.888736 | ||||||||
\(50\) | 407.336 | 1.15212 | ||||||||
\(51\) | 271.617 | 0.745765 | ||||||||
\(52\) | −518.738 | −1.38338 | ||||||||
\(53\) | 439.646 | 1.13943 | 0.569717 | − | 0.821841i | \(-0.307053\pi\) | ||||
0.569717 | + | 0.821841i | \(0.307053\pi\) | |||||||
\(54\) | 584.550 | 1.47310 | ||||||||
\(55\) | 213.256 | 0.522826 | ||||||||
\(56\) | 210.113 | 0.501385 | ||||||||
\(57\) | −36.7427 | −0.0853805 | ||||||||
\(58\) | −202.842 | −0.459215 | ||||||||
\(59\) | −16.1085 | −0.0355450 | −0.0177725 | − | 0.999842i | \(-0.505657\pi\) | ||||
−0.0177725 | + | 0.999842i | \(0.505657\pi\) | |||||||
\(60\) | 245.393 | 0.528002 | ||||||||
\(61\) | 764.542 | 1.60475 | 0.802374 | − | 0.596822i | \(-0.203570\pi\) | ||||
0.802374 | + | 0.596822i | \(0.203570\pi\) | |||||||
\(62\) | −0.484211 | −0.000991853 0 | ||||||||
\(63\) | 126.114 | 0.252204 | ||||||||
\(64\) | −662.378 | −1.29371 | ||||||||
\(65\) | −218.137 | −0.416256 | ||||||||
\(66\) | −414.608 | −0.773254 | ||||||||
\(67\) | −415.572 | −0.757764 | −0.378882 | − | 0.925445i | \(-0.623691\pi\) | ||||
−0.378882 | + | 0.925445i | \(0.623691\pi\) | |||||||
\(68\) | 1596.08 | 2.84636 | ||||||||
\(69\) | −411.925 | −0.718694 | ||||||||
\(70\) | 188.198 | 0.321342 | ||||||||
\(71\) | −998.578 | −1.66915 | −0.834573 | − | 0.550897i | \(-0.814286\pi\) | ||||
−0.834573 | + | 0.550897i | \(0.814286\pi\) | |||||||
\(72\) | 694.330 | 1.13649 | ||||||||
\(73\) | −160.169 | −0.256799 | −0.128400 | − | 0.991723i | \(-0.540984\pi\) | ||||
−0.128400 | + | 0.991723i | \(0.540984\pi\) | |||||||
\(74\) | −1776.31 | −2.79044 | ||||||||
\(75\) | −217.587 | −0.334998 | ||||||||
\(76\) | −215.907 | −0.325872 | ||||||||
\(77\) | −207.755 | −0.307479 | ||||||||
\(78\) | 424.098 | 0.615637 | ||||||||
\(79\) | −1319.53 | −1.87922 | −0.939609 | − | 0.342251i | \(-0.888811\pi\) | ||||
−0.939609 | + | 0.342251i | \(0.888811\pi\) | |||||||
\(80\) | 271.147 | 0.378939 | ||||||||
\(81\) | 238.940 | 0.327765 | ||||||||
\(82\) | −2162.26 | −2.91197 | ||||||||
\(83\) | −374.027 | −0.494636 | −0.247318 | − | 0.968934i | \(-0.579549\pi\) | ||||
−0.247318 | + | 0.968934i | \(0.579549\pi\) | |||||||
\(84\) | −239.063 | −0.310523 | ||||||||
\(85\) | 671.175 | 0.856461 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 108.352 | 0.133524 | ||||||||
\(88\) | −1143.81 | −1.38558 | ||||||||
\(89\) | 706.315 | 0.841227 | 0.420614 | − | 0.907240i | \(-0.361815\pi\) | ||||
0.420614 | + | 0.907240i | \(0.361815\pi\) | |||||||
\(90\) | 621.909 | 0.728389 | ||||||||
\(91\) | 212.511 | 0.244804 | ||||||||
\(92\) | −2420.55 | −2.74304 | ||||||||
\(93\) | 0.258652 | 0.000288397 0 | ||||||||
\(94\) | 1388.06 | 1.52306 | ||||||||
\(95\) | −90.7924 | −0.0980538 | ||||||||
\(96\) | 171.097 | 0.181901 | ||||||||
\(97\) | −1260.72 | −1.31966 | −0.659829 | − | 0.751416i | \(-0.729371\pi\) | ||||
−0.659829 | + | 0.751416i | \(0.729371\pi\) | |||||||
\(98\) | 1464.47 | 1.50953 | ||||||||
\(99\) | −686.539 | −0.696967 | ||||||||
\(100\) | −1278.59 | −1.27859 | ||||||||
\(101\) | −617.433 | −0.608286 | −0.304143 | − | 0.952626i | \(-0.598370\pi\) | ||||
−0.304143 | + | 0.952626i | \(0.598370\pi\) | |||||||
\(102\) | −1304.89 | −1.26669 | ||||||||
\(103\) | −217.291 | −0.207867 | −0.103934 | − | 0.994584i | \(-0.533143\pi\) | ||||
−0.103934 | + | 0.994584i | \(0.533143\pi\) | |||||||
\(104\) | 1170.00 | 1.10315 | ||||||||
\(105\) | −100.530 | −0.0934353 | ||||||||
\(106\) | −2112.12 | −1.93535 | ||||||||
\(107\) | 322.466 | 0.291346 | 0.145673 | − | 0.989333i | \(-0.453465\pi\) | ||||
0.145673 | + | 0.989333i | \(0.453465\pi\) | |||||||
\(108\) | −1834.84 | −1.63479 | ||||||||
\(109\) | 74.8798 | 0.0657999 | 0.0328999 | − | 0.999459i | \(-0.489526\pi\) | ||||
0.0328999 | + | 0.999459i | \(0.489526\pi\) | |||||||
\(110\) | −1024.51 | −0.888030 | ||||||||
\(111\) | 948.856 | 0.811365 | ||||||||
\(112\) | −264.153 | −0.222858 | ||||||||
\(113\) | 1937.66 | 1.61309 | 0.806545 | − | 0.591172i | \(-0.201335\pi\) | ||||
0.806545 | + | 0.591172i | \(0.201335\pi\) | |||||||
\(114\) | 176.517 | 0.145020 | ||||||||
\(115\) | −1017.88 | −0.825371 | ||||||||
\(116\) | 636.700 | 0.509622 | ||||||||
\(117\) | 702.253 | 0.554900 | ||||||||
\(118\) | 77.3876 | 0.0603737 | ||||||||
\(119\) | −653.863 | −0.503693 | ||||||||
\(120\) | −553.476 | −0.421043 | ||||||||
\(121\) | −200.021 | −0.150279 | ||||||||
\(122\) | −3672.96 | −2.72569 | ||||||||
\(123\) | 1155.02 | 0.846703 | ||||||||
\(124\) | 1.51989 | 0.00110073 | ||||||||
\(125\) | −1330.32 | −0.951900 | ||||||||
\(126\) | −605.867 | −0.428373 | ||||||||
\(127\) | −85.5015 | −0.0597404 | −0.0298702 | − | 0.999554i | \(-0.509509\pi\) | ||||
−0.0298702 | + | 0.999554i | \(0.509509\pi\) | |||||||
\(128\) | 2648.77 | 1.82906 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 1047.96 | 0.707017 | ||||||||
\(131\) | 1370.38 | 0.913975 | 0.456988 | − | 0.889473i | \(-0.348928\pi\) | ||||
0.456988 | + | 0.889473i | \(0.348928\pi\) | |||||||
\(132\) | 1301.41 | 0.858132 | ||||||||
\(133\) | 88.4505 | 0.0576664 | ||||||||
\(134\) | 1996.46 | 1.28708 | ||||||||
\(135\) | −771.580 | −0.491904 | ||||||||
\(136\) | −3599.90 | −2.26977 | ||||||||
\(137\) | 355.929 | 0.221964 | 0.110982 | − | 0.993822i | \(-0.464600\pi\) | ||||
0.110982 | + | 0.993822i | \(0.464600\pi\) | |||||||
\(138\) | 1978.94 | 1.22071 | ||||||||
\(139\) | −2301.37 | −1.40431 | −0.702156 | − | 0.712024i | \(-0.747779\pi\) | ||||
−0.702156 | + | 0.712024i | \(0.747779\pi\) | |||||||
\(140\) | −590.733 | −0.356615 | ||||||||
\(141\) | −741.463 | −0.442855 | ||||||||
\(142\) | 4797.30 | 2.83507 | ||||||||
\(143\) | −1156.87 | −0.676517 | ||||||||
\(144\) | −872.907 | −0.505155 | ||||||||
\(145\) | 267.743 | 0.153343 | ||||||||
\(146\) | 769.472 | 0.436178 | ||||||||
\(147\) | −782.281 | −0.438921 | ||||||||
\(148\) | 5575.67 | 3.09674 | ||||||||
\(149\) | −1231.68 | −0.677202 | −0.338601 | − | 0.940930i | \(-0.609954\pi\) | ||||
−0.338601 | + | 0.940930i | \(0.609954\pi\) | |||||||
\(150\) | 1045.32 | 0.568999 | ||||||||
\(151\) | −1504.88 | −0.811032 | −0.405516 | − | 0.914088i | \(-0.632908\pi\) | ||||
−0.405516 | + | 0.914088i | \(0.632908\pi\) | |||||||
\(152\) | 486.972 | 0.259859 | ||||||||
\(153\) | −2160.72 | −1.14173 | ||||||||
\(154\) | 998.084 | 0.522259 | ||||||||
\(155\) | 0.639138 | 0.000331205 0 | ||||||||
\(156\) | −1331.20 | −0.683214 | ||||||||
\(157\) | 1740.89 | 0.884955 | 0.442477 | − | 0.896780i | \(-0.354100\pi\) | ||||
0.442477 | + | 0.896780i | \(0.354100\pi\) | |||||||
\(158\) | 6339.17 | 3.19188 | ||||||||
\(159\) | 1128.23 | 0.562734 | ||||||||
\(160\) | 422.786 | 0.208901 | ||||||||
\(161\) | 991.623 | 0.485409 | ||||||||
\(162\) | −1147.90 | −0.556714 | ||||||||
\(163\) | −1171.60 | −0.562986 | −0.281493 | − | 0.959563i | \(-0.590830\pi\) | ||||
−0.281493 | + | 0.959563i | \(0.590830\pi\) | |||||||
\(164\) | 6787.11 | 3.23161 | ||||||||
\(165\) | 547.265 | 0.258209 | ||||||||
\(166\) | 1796.88 | 0.840148 | ||||||||
\(167\) | 1555.44 | 0.720741 | 0.360370 | − | 0.932809i | \(-0.382650\pi\) | ||||
0.360370 | + | 0.932809i | \(0.382650\pi\) | |||||||
\(168\) | 539.199 | 0.247620 | ||||||||
\(169\) | −1013.65 | −0.461381 | ||||||||
\(170\) | −3224.41 | −1.45471 | ||||||||
\(171\) | 292.289 | 0.130713 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 2048.52 | 0.900268 | 0.450134 | − | 0.892961i | \(-0.351376\pi\) | ||||
0.450134 | + | 0.892961i | \(0.351376\pi\) | |||||||
\(174\) | −520.539 | −0.226793 | ||||||||
\(175\) | 523.797 | 0.226259 | ||||||||
\(176\) | 1438.00 | 0.615869 | ||||||||
\(177\) | −41.3382 | −0.0175547 | ||||||||
\(178\) | −3393.23 | −1.42884 | ||||||||
\(179\) | −4392.22 | −1.83402 | −0.917011 | − | 0.398863i | \(-0.869405\pi\) | ||||
−0.917011 | + | 0.398863i | \(0.869405\pi\) | |||||||
\(180\) | −1952.11 | −0.808343 | ||||||||
\(181\) | 2563.35 | 1.05266 | 0.526332 | − | 0.850279i | \(-0.323567\pi\) | ||||
0.526332 | + | 0.850279i | \(0.323567\pi\) | |||||||
\(182\) | −1020.93 | −0.415804 | ||||||||
\(183\) | 1961.99 | 0.792539 | ||||||||
\(184\) | 5459.47 | 2.18738 | ||||||||
\(185\) | 2344.66 | 0.931797 | ||||||||
\(186\) | −1.24260 | −0.000489848 0 | ||||||||
\(187\) | 3559.50 | 1.39196 | ||||||||
\(188\) | −4356.98 | −1.69024 | ||||||||
\(189\) | 751.677 | 0.289294 | ||||||||
\(190\) | 436.179 | 0.166546 | ||||||||
\(191\) | −1139.09 | −0.431528 | −0.215764 | − | 0.976446i | \(-0.569224\pi\) | ||||
−0.215764 | + | 0.976446i | \(0.569224\pi\) | |||||||
\(192\) | −1699.81 | −0.638924 | ||||||||
\(193\) | 2118.90 | 0.790267 | 0.395133 | − | 0.918624i | \(-0.370698\pi\) | ||||
0.395133 | + | 0.918624i | \(0.370698\pi\) | |||||||
\(194\) | 6056.67 | 2.24146 | ||||||||
\(195\) | −559.791 | −0.205577 | ||||||||
\(196\) | −4596.83 | −1.67523 | ||||||||
\(197\) | −4044.27 | −1.46265 | −0.731326 | − | 0.682028i | \(-0.761098\pi\) | ||||
−0.731326 | + | 0.682028i | \(0.761098\pi\) | |||||||
\(198\) | 3298.22 | 1.18381 | ||||||||
\(199\) | 1717.52 | 0.611817 | 0.305908 | − | 0.952061i | \(-0.401040\pi\) | ||||
0.305908 | + | 0.952061i | \(0.401040\pi\) | |||||||
\(200\) | 2883.81 | 1.01958 | ||||||||
\(201\) | −1066.45 | −0.374238 | ||||||||
\(202\) | 2966.23 | 1.03318 | ||||||||
\(203\) | −260.836 | −0.0901828 | ||||||||
\(204\) | 4095.90 | 1.40574 | ||||||||
\(205\) | 2854.09 | 0.972381 | ||||||||
\(206\) | 1043.90 | 0.353066 | ||||||||
\(207\) | 3276.87 | 1.10028 | ||||||||
\(208\) | −1470.91 | −0.490333 | ||||||||
\(209\) | −481.507 | −0.159361 | ||||||||
\(210\) | 482.959 | 0.158702 | ||||||||
\(211\) | 3943.80 | 1.28674 | 0.643370 | − | 0.765555i | \(-0.277536\pi\) | ||||
0.643370 | + | 0.765555i | \(0.277536\pi\) | |||||||
\(212\) | 6629.71 | 2.14779 | ||||||||
\(213\) | −2562.58 | −0.824344 | ||||||||
\(214\) | −1549.17 | −0.494856 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 4138.42 | 1.30363 | ||||||||
\(217\) | −0.622651 | −0.000194785 0 | ||||||||
\(218\) | −359.732 | −0.111762 | ||||||||
\(219\) | −411.030 | −0.126826 | ||||||||
\(220\) | 3215.83 | 0.985507 | ||||||||
\(221\) | −3640.97 | −1.10823 | ||||||||
\(222\) | −4558.43 | −1.37812 | ||||||||
\(223\) | −1798.16 | −0.539971 | −0.269985 | − | 0.962864i | \(-0.587019\pi\) | ||||
−0.269985 | + | 0.962864i | \(0.587019\pi\) | |||||||
\(224\) | −411.881 | −0.122857 | ||||||||
\(225\) | 1730.91 | 0.512863 | ||||||||
\(226\) | −9308.75 | −2.73986 | ||||||||
\(227\) | −6340.20 | −1.85381 | −0.926903 | − | 0.375301i | \(-0.877539\pi\) | ||||
−0.926903 | + | 0.375301i | \(0.877539\pi\) | |||||||
\(228\) | −554.068 | −0.160939 | ||||||||
\(229\) | −1568.74 | −0.452686 | −0.226343 | − | 0.974048i | \(-0.572677\pi\) | ||||
−0.226343 | + | 0.974048i | \(0.572677\pi\) | |||||||
\(230\) | 4890.03 | 1.40191 | ||||||||
\(231\) | −533.148 | −0.151855 | ||||||||
\(232\) | −1436.06 | −0.406387 | ||||||||
\(233\) | −2409.61 | −0.677505 | −0.338752 | − | 0.940876i | \(-0.610005\pi\) | ||||
−0.338752 | + | 0.940876i | \(0.610005\pi\) | |||||||
\(234\) | −3373.72 | −0.942507 | ||||||||
\(235\) | −1832.18 | −0.508588 | ||||||||
\(236\) | −242.912 | −0.0670009 | ||||||||
\(237\) | −3386.21 | −0.928092 | ||||||||
\(238\) | 3141.24 | 0.855531 | ||||||||
\(239\) | 2111.13 | 0.571371 | 0.285685 | − | 0.958324i | \(-0.407779\pi\) | ||||
0.285685 | + | 0.958324i | \(0.407779\pi\) | |||||||
\(240\) | 695.826 | 0.187147 | ||||||||
\(241\) | 3837.49 | 1.02570 | 0.512852 | − | 0.858477i | \(-0.328589\pi\) | ||||
0.512852 | + | 0.858477i | \(0.328589\pi\) | |||||||
\(242\) | 960.929 | 0.255252 | ||||||||
\(243\) | 3898.44 | 1.02916 | ||||||||
\(244\) | 11529.0 | 3.02488 | ||||||||
\(245\) | −1933.04 | −0.504071 | ||||||||
\(246\) | −5548.86 | −1.43814 | ||||||||
\(247\) | 492.528 | 0.126878 | ||||||||
\(248\) | −3.42806 | −0.000877750 0 | ||||||||
\(249\) | −959.840 | −0.244287 | ||||||||
\(250\) | 6391.04 | 1.61682 | ||||||||
\(251\) | −7394.81 | −1.85959 | −0.929793 | − | 0.368083i | \(-0.880014\pi\) | ||||
−0.929793 | + | 0.368083i | \(0.880014\pi\) | |||||||
\(252\) | 1901.76 | 0.475394 | ||||||||
\(253\) | −5398.20 | −1.34143 | ||||||||
\(254\) | 410.760 | 0.101470 | ||||||||
\(255\) | 1722.39 | 0.422982 | ||||||||
\(256\) | −7426.01 | −1.81299 | ||||||||
\(257\) | −2496.57 | −0.605959 | −0.302980 | − | 0.952997i | \(-0.597981\pi\) | ||||
−0.302980 | + | 0.952997i | \(0.597981\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −2284.18 | −0.547999 | ||||||||
\(260\) | −3289.44 | −0.784625 | ||||||||
\(261\) | −861.947 | −0.204418 | ||||||||
\(262\) | −6583.49 | −1.55240 | ||||||||
\(263\) | −1815.08 | −0.425562 | −0.212781 | − | 0.977100i | \(-0.568252\pi\) | ||||
−0.212781 | + | 0.977100i | \(0.568252\pi\) | |||||||
\(264\) | −2935.29 | −0.684298 | ||||||||
\(265\) | 2787.90 | 0.646261 | ||||||||
\(266\) | −424.928 | −0.0979473 | ||||||||
\(267\) | 1812.57 | 0.415458 | ||||||||
\(268\) | −6266.69 | −1.42836 | ||||||||
\(269\) | −673.864 | −0.152737 | −0.0763684 | − | 0.997080i | \(-0.524333\pi\) | ||||
−0.0763684 | + | 0.997080i | \(0.524333\pi\) | |||||||
\(270\) | 3706.77 | 0.835507 | ||||||||
\(271\) | 2582.80 | 0.578944 | 0.289472 | − | 0.957186i | \(-0.406520\pi\) | ||||
0.289472 | + | 0.957186i | \(0.406520\pi\) | |||||||
\(272\) | 4525.76 | 1.00888 | ||||||||
\(273\) | 545.351 | 0.120902 | ||||||||
\(274\) | −1709.93 | −0.377009 | ||||||||
\(275\) | −2851.44 | −0.625267 | ||||||||
\(276\) | −6211.69 | −1.35471 | ||||||||
\(277\) | 2042.43 | 0.443024 | 0.221512 | − | 0.975158i | \(-0.428901\pi\) | ||||
0.221512 | + | 0.975158i | \(0.428901\pi\) | |||||||
\(278\) | 11056.1 | 2.38525 | ||||||||
\(279\) | −2.05759 | −0.000441521 0 | ||||||||
\(280\) | 1332.38 | 0.284375 | ||||||||
\(281\) | 5529.75 | 1.17394 | 0.586970 | − | 0.809608i | \(-0.300321\pi\) | ||||
0.586970 | + | 0.809608i | \(0.300321\pi\) | |||||||
\(282\) | 3562.09 | 0.752196 | ||||||||
\(283\) | 213.594 | 0.0448653 | 0.0224326 | − | 0.999748i | \(-0.492859\pi\) | ||||
0.0224326 | + | 0.999748i | \(0.492859\pi\) | |||||||
\(284\) | −15058.2 | −3.14627 | ||||||||
\(285\) | −232.994 | −0.0484260 | ||||||||
\(286\) | 5557.73 | 1.14908 | ||||||||
\(287\) | −2780.47 | −0.571867 | ||||||||
\(288\) | −1361.08 | −0.278481 | ||||||||
\(289\) | 6289.71 | 1.28022 | ||||||||
\(290\) | −1286.27 | −0.260456 | ||||||||
\(291\) | −3235.30 | −0.651741 | ||||||||
\(292\) | −2415.29 | −0.484056 | ||||||||
\(293\) | −6029.67 | −1.20224 | −0.601121 | − | 0.799158i | \(-0.705279\pi\) | ||||
−0.601121 | + | 0.799158i | \(0.705279\pi\) | |||||||
\(294\) | 3758.18 | 0.745515 | ||||||||
\(295\) | −102.148 | −0.0201603 | ||||||||
\(296\) | −12575.7 | −2.46942 | ||||||||
\(297\) | −4091.98 | −0.799464 | ||||||||
\(298\) | 5917.15 | 1.15024 | ||||||||
\(299\) | 5521.76 | 1.06800 | ||||||||
\(300\) | −3281.15 | −0.631457 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 7229.66 | 1.37755 | ||||||||
\(303\) | −1584.47 | −0.300415 | ||||||||
\(304\) | −612.217 | −0.115504 | ||||||||
\(305\) | 4848.15 | 0.910177 | ||||||||
\(306\) | 10380.4 | 1.93924 | ||||||||
\(307\) | 9957.66 | 1.85118 | 0.925592 | − | 0.378523i | \(-0.123568\pi\) | ||||
0.925592 | + | 0.378523i | \(0.123568\pi\) | |||||||
\(308\) | −3132.88 | −0.579586 | ||||||||
\(309\) | −557.619 | −0.102660 | ||||||||
\(310\) | −3.07050 | −0.000562557 0 | ||||||||
\(311\) | 9950.53 | 1.81429 | 0.907143 | − | 0.420824i | \(-0.138259\pi\) | ||||
0.907143 | + | 0.420824i | \(0.138259\pi\) | |||||||
\(312\) | 3002.48 | 0.544814 | ||||||||
\(313\) | 1906.47 | 0.344281 | 0.172140 | − | 0.985072i | \(-0.444932\pi\) | ||||
0.172140 | + | 0.985072i | \(0.444932\pi\) | |||||||
\(314\) | −8363.45 | −1.50311 | ||||||||
\(315\) | 799.718 | 0.143045 | ||||||||
\(316\) | −19898.0 | −3.54225 | ||||||||
\(317\) | −2985.80 | −0.529019 | −0.264510 | − | 0.964383i | \(-0.585210\pi\) | ||||
−0.264510 | + | 0.964383i | \(0.585210\pi\) | |||||||
\(318\) | −5420.18 | −0.955812 | ||||||||
\(319\) | 1419.94 | 0.249221 | ||||||||
\(320\) | −4200.30 | −0.733762 | ||||||||
\(321\) | 827.523 | 0.143887 | ||||||||
\(322\) | −4763.89 | −0.824476 | ||||||||
\(323\) | −1515.43 | −0.261056 | ||||||||
\(324\) | 3603.14 | 0.617823 | ||||||||
\(325\) | 2916.71 | 0.497815 | ||||||||
\(326\) | 5628.52 | 0.956242 | ||||||||
\(327\) | 192.159 | 0.0324967 | ||||||||
\(328\) | −15308.1 | −2.57698 | ||||||||
\(329\) | 1784.92 | 0.299106 | ||||||||
\(330\) | −2629.13 | −0.438572 | ||||||||
\(331\) | −842.438 | −0.139893 | −0.0699465 | − | 0.997551i | \(-0.522283\pi\) | ||||
−0.0699465 | + | 0.997551i | \(0.522283\pi\) | |||||||
\(332\) | −5640.21 | −0.932370 | ||||||||
\(333\) | −7548.18 | −1.24216 | ||||||||
\(334\) | −7472.55 | −1.22419 | ||||||||
\(335\) | −2635.24 | −0.429787 | ||||||||
\(336\) | −677.877 | −0.110063 | ||||||||
\(337\) | −3058.48 | −0.494380 | −0.247190 | − | 0.968967i | \(-0.579507\pi\) | ||||
−0.247190 | + | 0.968967i | \(0.579507\pi\) | |||||||
\(338\) | 4869.73 | 0.783664 | ||||||||
\(339\) | 4972.47 | 0.796659 | ||||||||
\(340\) | 10121.1 | 1.61439 | ||||||||
\(341\) | 3.38959 | 0.000538289 0 | ||||||||
\(342\) | −1404.20 | −0.222018 | ||||||||
\(343\) | 4002.12 | 0.630012 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −2612.11 | −0.407627 | ||||||||
\(346\) | −9841.37 | −1.52912 | ||||||||
\(347\) | −11415.0 | −1.76597 | −0.882985 | − | 0.469402i | \(-0.844470\pi\) | ||||
−0.882985 | + | 0.469402i | \(0.844470\pi\) | |||||||
\(348\) | 1633.92 | 0.251688 | ||||||||
\(349\) | 2729.17 | 0.418594 | 0.209297 | − | 0.977852i | \(-0.432882\pi\) | ||||
0.209297 | + | 0.977852i | \(0.432882\pi\) | |||||||
\(350\) | −2516.39 | −0.384304 | ||||||||
\(351\) | 4185.64 | 0.636505 | ||||||||
\(352\) | 2242.20 | 0.339516 | ||||||||
\(353\) | −11443.4 | −1.72541 | −0.862703 | − | 0.505710i | \(-0.831230\pi\) | ||||
−0.862703 | + | 0.505710i | \(0.831230\pi\) | |||||||
\(354\) | 198.594 | 0.0298169 | ||||||||
\(355\) | −6332.23 | −0.946703 | ||||||||
\(356\) | 10651.0 | 1.58568 | ||||||||
\(357\) | −1677.96 | −0.248760 | ||||||||
\(358\) | 21100.8 | 3.11512 | ||||||||
\(359\) | −3938.99 | −0.579086 | −0.289543 | − | 0.957165i | \(-0.593503\pi\) | ||||
−0.289543 | + | 0.957165i | \(0.593503\pi\) | |||||||
\(360\) | 4402.92 | 0.644595 | ||||||||
\(361\) | −6654.00 | −0.970112 | ||||||||
\(362\) | −12314.7 | −1.78797 | ||||||||
\(363\) | −513.301 | −0.0742185 | ||||||||
\(364\) | 3204.59 | 0.461446 | ||||||||
\(365\) | −1015.67 | −0.145651 | ||||||||
\(366\) | −9425.67 | −1.34614 | ||||||||
\(367\) | −7300.33 | −1.03835 | −0.519175 | − | 0.854668i | \(-0.673761\pi\) | ||||
−0.519175 | + | 0.854668i | \(0.673761\pi\) | |||||||
\(368\) | −6863.60 | −0.972256 | ||||||||
\(369\) | −9188.21 | −1.29626 | ||||||||
\(370\) | −11264.0 | −1.58267 | ||||||||
\(371\) | −2715.99 | −0.380073 | ||||||||
\(372\) | 3.90039 | 0.000543618 0 | ||||||||
\(373\) | −9652.92 | −1.33997 | −0.669985 | − | 0.742374i | \(-0.733700\pi\) | ||||
−0.669985 | + | 0.742374i | \(0.733700\pi\) | |||||||
\(374\) | −17100.3 | −2.36427 | ||||||||
\(375\) | −3413.91 | −0.470116 | ||||||||
\(376\) | 9827.03 | 1.34785 | ||||||||
\(377\) | −1452.44 | −0.198421 | ||||||||
\(378\) | −3611.16 | −0.491370 | ||||||||
\(379\) | −1436.71 | −0.194720 | −0.0973601 | − | 0.995249i | \(-0.531040\pi\) | ||||
−0.0973601 | + | 0.995249i | \(0.531040\pi\) | |||||||
\(380\) | −1369.12 | −0.184827 | ||||||||
\(381\) | −219.417 | −0.0295041 | ||||||||
\(382\) | 5472.35 | 0.732958 | ||||||||
\(383\) | −9742.88 | −1.29984 | −0.649919 | − | 0.760003i | \(-0.725197\pi\) | ||||
−0.649919 | + | 0.760003i | \(0.725197\pi\) | |||||||
\(384\) | 6797.35 | 0.903323 | ||||||||
\(385\) | −1317.43 | −0.174396 | ||||||||
\(386\) | −10179.5 | −1.34228 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −19011.3 | −2.48750 | ||||||||
\(389\) | −853.522 | −0.111248 | −0.0556238 | − | 0.998452i | \(-0.517715\pi\) | ||||
−0.0556238 | + | 0.998452i | \(0.517715\pi\) | |||||||
\(390\) | 2689.31 | 0.349176 | ||||||||
\(391\) | −16989.6 | −2.19745 | ||||||||
\(392\) | 10368.0 | 1.33588 | ||||||||
\(393\) | 3516.71 | 0.451386 | ||||||||
\(394\) | 19429.2 | 2.48434 | ||||||||
\(395\) | −8367.43 | −1.06585 | ||||||||
\(396\) | −10352.8 | −1.31375 | ||||||||
\(397\) | 7093.70 | 0.896782 | 0.448391 | − | 0.893837i | \(-0.351997\pi\) | ||||
0.448391 | + | 0.893837i | \(0.351997\pi\) | |||||||
\(398\) | −8251.18 | −1.03918 | ||||||||
\(399\) | 226.984 | 0.0284798 | ||||||||
\(400\) | −3625.50 | −0.453188 | ||||||||
\(401\) | −2816.61 | −0.350761 | −0.175380 | − | 0.984501i | \(-0.556115\pi\) | ||||
−0.175380 | + | 0.984501i | \(0.556115\pi\) | |||||||
\(402\) | 5123.38 | 0.635650 | ||||||||
\(403\) | −3.46718 | −0.000428567 0 | ||||||||
\(404\) | −9310.69 | −1.14659 | ||||||||
\(405\) | 1515.18 | 0.185901 | ||||||||
\(406\) | 1253.09 | 0.153177 | ||||||||
\(407\) | 12434.6 | 1.51440 | ||||||||
\(408\) | −9238.17 | −1.12097 | ||||||||
\(409\) | −11950.0 | −1.44472 | −0.722358 | − | 0.691520i | \(-0.756942\pi\) | ||||
−0.722358 | + | 0.691520i | \(0.756942\pi\) | |||||||
\(410\) | −13711.4 | −1.65161 | ||||||||
\(411\) | 913.395 | 0.109622 | ||||||||
\(412\) | −3276.68 | −0.391822 | ||||||||
\(413\) | 99.5133 | 0.0118565 | ||||||||
\(414\) | −15742.5 | −1.86885 | ||||||||
\(415\) | −2371.80 | −0.280547 | ||||||||
\(416\) | −2293.52 | −0.270310 | ||||||||
\(417\) | −5905.84 | −0.693549 | ||||||||
\(418\) | 2313.22 | 0.270678 | ||||||||
\(419\) | 2847.25 | 0.331974 | 0.165987 | − | 0.986128i | \(-0.446919\pi\) | ||||
0.165987 | + | 0.986128i | \(0.446919\pi\) | |||||||
\(420\) | −1515.96 | −0.176122 | ||||||||
\(421\) | −10205.8 | −1.18147 | −0.590737 | − | 0.806864i | \(-0.701163\pi\) | ||||
−0.590737 | + | 0.806864i | \(0.701163\pi\) | |||||||
\(422\) | −18946.5 | −2.18555 | ||||||||
\(423\) | 5898.37 | 0.677987 | ||||||||
\(424\) | −14953.1 | −1.71270 | ||||||||
\(425\) | −8974.27 | −1.02427 | ||||||||
\(426\) | 12311.0 | 1.40016 | ||||||||
\(427\) | −4723.09 | −0.535284 | ||||||||
\(428\) | 4862.69 | 0.549175 | ||||||||
\(429\) | −2968.78 | −0.334113 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −13829.3 | −1.54555 | −0.772775 | − | 0.634680i | \(-0.781132\pi\) | ||||
−0.772775 | + | 0.634680i | \(0.781132\pi\) | |||||||
\(432\) | −5202.80 | −0.579444 | ||||||||
\(433\) | 8717.43 | 0.967512 | 0.483756 | − | 0.875203i | \(-0.339272\pi\) | ||||
0.483756 | + | 0.875203i | \(0.339272\pi\) | |||||||
\(434\) | 2.99130 | 0.000330846 0 | ||||||||
\(435\) | 687.089 | 0.0757320 | ||||||||
\(436\) | 1129.16 | 0.124030 | ||||||||
\(437\) | 2298.25 | 0.251579 | ||||||||
\(438\) | 1974.64 | 0.215416 | ||||||||
\(439\) | −14904.6 | −1.62041 | −0.810203 | − | 0.586149i | \(-0.800643\pi\) | ||||
−0.810203 | + | 0.586149i | \(0.800643\pi\) | |||||||
\(440\) | −7253.21 | −0.785870 | ||||||||
\(441\) | 6223.07 | 0.671965 | ||||||||
\(442\) | 17491.7 | 1.88234 | ||||||||
\(443\) | 16289.2 | 1.74700 | 0.873502 | − | 0.486820i | \(-0.161843\pi\) | ||||
0.873502 | + | 0.486820i | \(0.161843\pi\) | |||||||
\(444\) | 14308.4 | 1.52939 | ||||||||
\(445\) | 4478.91 | 0.477126 | ||||||||
\(446\) | 8638.58 | 0.917149 | ||||||||
\(447\) | −3160.77 | −0.334451 | ||||||||
\(448\) | 4091.95 | 0.431532 | ||||||||
\(449\) | −12947.9 | −1.36092 | −0.680458 | − | 0.732787i | \(-0.738219\pi\) | ||||
−0.680458 | + | 0.732787i | \(0.738219\pi\) | |||||||
\(450\) | −8315.54 | −0.871107 | ||||||||
\(451\) | 15136.3 | 1.58036 | ||||||||
\(452\) | 29219.2 | 3.04061 | ||||||||
\(453\) | −3861.88 | −0.400545 | ||||||||
\(454\) | 30459.2 | 3.14872 | ||||||||
\(455\) | 1347.58 | 0.138847 | ||||||||
\(456\) | 1249.68 | 0.128337 | ||||||||
\(457\) | −1521.06 | −0.155694 | −0.0778469 | − | 0.996965i | \(-0.524805\pi\) | ||||
−0.0778469 | + | 0.996965i | \(0.524805\pi\) | |||||||
\(458\) | 7536.42 | 0.768895 | ||||||||
\(459\) | −12878.6 | −1.30963 | ||||||||
\(460\) | −15349.3 | −1.55579 | ||||||||
\(461\) | −4500.11 | −0.454644 | −0.227322 | − | 0.973820i | \(-0.572997\pi\) | ||||
−0.227322 | + | 0.973820i | \(0.572997\pi\) | |||||||
\(462\) | 2561.31 | 0.257929 | ||||||||
\(463\) | 5096.27 | 0.511542 | 0.255771 | − | 0.966737i | \(-0.417671\pi\) | ||||
0.255771 | + | 0.966737i | \(0.417671\pi\) | |||||||
\(464\) | 1805.40 | 0.180633 | ||||||||
\(465\) | 1.64018 | 0.000163573 0 | ||||||||
\(466\) | 11576.1 | 1.15075 | ||||||||
\(467\) | 5931.03 | 0.587699 | 0.293850 | − | 0.955852i | \(-0.405064\pi\) | ||||
0.293850 | + | 0.955852i | \(0.405064\pi\) | |||||||
\(468\) | 10589.7 | 1.04596 | ||||||||
\(469\) | 2567.27 | 0.252762 | ||||||||
\(470\) | 8802.04 | 0.863846 | ||||||||
\(471\) | 4467.52 | 0.437054 | ||||||||
\(472\) | 547.879 | 0.0534283 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 16267.8 | 1.57638 | ||||||||
\(475\) | 1213.98 | 0.117266 | ||||||||
\(476\) | −9860.04 | −0.949441 | ||||||||
\(477\) | −8975.13 | −0.861515 | ||||||||
\(478\) | −10142.1 | −0.970482 | ||||||||
\(479\) | −13403.9 | −1.27858 | −0.639292 | − | 0.768964i | \(-0.720772\pi\) | ||||
−0.639292 | + | 0.768964i | \(0.720772\pi\) | |||||||
\(480\) | 1084.97 | 0.103170 | ||||||||
\(481\) | −12719.2 | −1.20571 | ||||||||
\(482\) | −18435.8 | −1.74218 | ||||||||
\(483\) | 2544.74 | 0.239730 | ||||||||
\(484\) | −3016.26 | −0.283270 | ||||||||
\(485\) | −7994.54 | −0.748481 | ||||||||
\(486\) | −18728.6 | −1.74804 | ||||||||
\(487\) | 9526.78 | 0.886447 | 0.443223 | − | 0.896411i | \(-0.353835\pi\) | ||||
0.443223 | + | 0.896411i | \(0.353835\pi\) | |||||||
\(488\) | −26003.4 | −2.41213 | ||||||||
\(489\) | −3006.60 | −0.278043 | ||||||||
\(490\) | 9286.58 | 0.856174 | ||||||||
\(491\) | −6851.57 | −0.629750 | −0.314875 | − | 0.949133i | \(-0.601963\pi\) | ||||
−0.314875 | + | 0.949133i | \(0.601963\pi\) | |||||||
\(492\) | 17417.3 | 1.59600 | ||||||||
\(493\) | 4468.94 | 0.408257 | ||||||||
\(494\) | −2366.17 | −0.215504 | ||||||||
\(495\) | −4353.51 | −0.395304 | ||||||||
\(496\) | 4.30973 | 0.000390147 0 | ||||||||
\(497\) | 6168.89 | 0.556766 | ||||||||
\(498\) | 4611.20 | 0.414925 | ||||||||
\(499\) | 3033.89 | 0.272176 | 0.136088 | − | 0.990697i | \(-0.456547\pi\) | ||||
0.136088 | + | 0.990697i | \(0.456547\pi\) | |||||||
\(500\) | −20060.8 | −1.79429 | ||||||||
\(501\) | 3991.62 | 0.355953 | ||||||||
\(502\) | 35525.6 | 3.15854 | ||||||||
\(503\) | 6789.54 | 0.601850 | 0.300925 | − | 0.953648i | \(-0.402705\pi\) | ||||
0.300925 | + | 0.953648i | \(0.402705\pi\) | |||||||
\(504\) | −4289.35 | −0.379093 | ||||||||
\(505\) | −3915.29 | −0.345006 | ||||||||
\(506\) | 25933.7 | 2.27844 | ||||||||
\(507\) | −2601.27 | −0.227863 | ||||||||
\(508\) | −1289.33 | −0.112608 | ||||||||
\(509\) | −2197.89 | −0.191395 | −0.0956974 | − | 0.995410i | \(-0.530508\pi\) | ||||
−0.0956974 | + | 0.995410i | \(0.530508\pi\) | |||||||
\(510\) | −8274.59 | −0.718441 | ||||||||
\(511\) | 989.470 | 0.0856587 | ||||||||
\(512\) | 14485.4 | 1.25033 | ||||||||
\(513\) | 1742.14 | 0.149936 | ||||||||
\(514\) | 11993.8 | 1.02923 | ||||||||
\(515\) | −1377.90 | −0.117898 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −9716.75 | −0.826581 | ||||||||
\(518\) | 10973.5 | 0.930786 | ||||||||
\(519\) | 5256.98 | 0.444617 | ||||||||
\(520\) | 7419.22 | 0.625682 | ||||||||
\(521\) | −17320.1 | −1.45644 | −0.728222 | − | 0.685341i | \(-0.759653\pi\) | ||||
−0.728222 | + | 0.685341i | \(0.759653\pi\) | |||||||
\(522\) | 4140.91 | 0.347208 | ||||||||
\(523\) | −11154.5 | −0.932601 | −0.466300 | − | 0.884626i | \(-0.654413\pi\) | ||||
−0.466300 | + | 0.884626i | \(0.654413\pi\) | |||||||
\(524\) | 20664.9 | 1.72281 | ||||||||
\(525\) | 1344.18 | 0.111743 | ||||||||
\(526\) | 8719.90 | 0.722824 | ||||||||
\(527\) | 10.6680 | 0.000881791 0 | ||||||||
\(528\) | 3690.23 | 0.304160 | ||||||||
\(529\) | 13598.8 | 1.11768 | ||||||||
\(530\) | −13393.4 | −1.09769 | ||||||||
\(531\) | 328.847 | 0.0268752 | ||||||||
\(532\) | 1333.80 | 0.108699 | ||||||||
\(533\) | −15482.8 | −1.25822 | ||||||||
\(534\) | −8707.81 | −0.705663 | ||||||||
\(535\) | 2044.84 | 0.165245 | ||||||||
\(536\) | 14134.3 | 1.13901 | ||||||||
\(537\) | −11271.4 | −0.905771 | ||||||||
\(538\) | 3237.33 | 0.259426 | ||||||||
\(539\) | −10251.7 | −0.819239 | ||||||||
\(540\) | −11635.2 | −0.927219 | ||||||||
\(541\) | −18613.0 | −1.47918 | −0.739591 | − | 0.673057i | \(-0.764981\pi\) | ||||
−0.739591 | + | 0.673057i | \(0.764981\pi\) | |||||||
\(542\) | −12408.1 | −0.983347 | ||||||||
\(543\) | 6578.14 | 0.519881 | ||||||||
\(544\) | 7056.81 | 0.556173 | ||||||||
\(545\) | 474.831 | 0.0373202 | ||||||||
\(546\) | −2619.94 | −0.205354 | ||||||||
\(547\) | 19378.5 | 1.51474 | 0.757371 | − | 0.652985i | \(-0.226484\pi\) | ||||
0.757371 | + | 0.652985i | \(0.226484\pi\) | |||||||
\(548\) | 5367.29 | 0.418393 | ||||||||
\(549\) | −15607.7 | −1.21333 | ||||||||
\(550\) | 13698.7 | 1.06203 | ||||||||
\(551\) | −604.531 | −0.0467402 | ||||||||
\(552\) | 14010.3 | 1.08028 | ||||||||
\(553\) | 8151.59 | 0.626837 | ||||||||
\(554\) | −9812.11 | −0.752485 | ||||||||
\(555\) | 6016.93 | 0.460188 | ||||||||
\(556\) | −34703.8 | −2.64707 | ||||||||
\(557\) | −8962.10 | −0.681753 | −0.340877 | − | 0.940108i | \(-0.610724\pi\) | ||||
−0.340877 | + | 0.940108i | \(0.610724\pi\) | |||||||
\(558\) | 9.88491 | 0.000749931 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | −1675.06 | −0.126400 | ||||||||
\(561\) | 9134.50 | 0.687449 | ||||||||
\(562\) | −26565.7 | −1.99396 | ||||||||
\(563\) | 12298.5 | 0.920640 | 0.460320 | − | 0.887753i | \(-0.347735\pi\) | ||||
0.460320 | + | 0.887753i | \(0.347735\pi\) | |||||||
\(564\) | −11181.0 | −0.834763 | ||||||||
\(565\) | 12287.1 | 0.914910 | ||||||||
\(566\) | −1026.14 | −0.0762044 | ||||||||
\(567\) | −1476.10 | −0.109330 | ||||||||
\(568\) | 33963.3 | 2.50893 | ||||||||
\(569\) | 5282.29 | 0.389183 | 0.194592 | − | 0.980884i | \(-0.437662\pi\) | ||||
0.194592 | + | 0.980884i | \(0.437662\pi\) | |||||||
\(570\) | 1119.34 | 0.0822523 | ||||||||
\(571\) | −20315.8 | −1.48895 | −0.744475 | − | 0.667650i | \(-0.767300\pi\) | ||||
−0.744475 | + | 0.667650i | \(0.767300\pi\) | |||||||
\(572\) | −17445.2 | −1.27521 | ||||||||
\(573\) | −2923.18 | −0.213119 | ||||||||
\(574\) | 13357.7 | 0.971326 | ||||||||
\(575\) | 13610.0 | 0.987092 | ||||||||
\(576\) | 13522.1 | 0.978160 | ||||||||
\(577\) | −12757.9 | −0.920484 | −0.460242 | − | 0.887793i | \(-0.652237\pi\) | ||||
−0.460242 | + | 0.887793i | \(0.652237\pi\) | |||||||
\(578\) | −30216.6 | −2.17447 | ||||||||
\(579\) | 5437.58 | 0.390290 | ||||||||
\(580\) | 4037.47 | 0.289046 | ||||||||
\(581\) | 2310.62 | 0.164992 | ||||||||
\(582\) | 15542.8 | 1.10699 | ||||||||
\(583\) | 14785.3 | 1.05033 | ||||||||
\(584\) | 5447.61 | 0.386000 | ||||||||
\(585\) | 4453.16 | 0.314727 | ||||||||
\(586\) | 28967.3 | 2.04203 | ||||||||
\(587\) | −10685.7 | −0.751354 | −0.375677 | − | 0.926751i | \(-0.622590\pi\) | ||||
−0.375677 | + | 0.926751i | \(0.622590\pi\) | |||||||
\(588\) | −11796.5 | −0.827349 | ||||||||
\(589\) | −1.44310 | −0.000100954 0 | ||||||||
\(590\) | 490.733 | 0.0342427 | ||||||||
\(591\) | −10378.5 | −0.722362 | ||||||||
\(592\) | 15810.1 | 1.09762 | ||||||||
\(593\) | −2637.21 | −0.182626 | −0.0913130 | − | 0.995822i | \(-0.529106\pi\) | ||||
−0.0913130 | + | 0.995822i | \(0.529106\pi\) | |||||||
\(594\) | 19658.4 | 1.35790 | ||||||||
\(595\) | −4146.30 | −0.285684 | ||||||||
\(596\) | −18573.3 | −1.27650 | ||||||||
\(597\) | 4407.55 | 0.302159 | ||||||||
\(598\) | −26527.3 | −1.81401 | ||||||||
\(599\) | 20472.5 | 1.39647 | 0.698234 | − | 0.715869i | \(-0.253969\pi\) | ||||
0.698234 | + | 0.715869i | \(0.253969\pi\) | |||||||
\(600\) | 7400.51 | 0.503541 | ||||||||
\(601\) | 848.655 | 0.0575996 | 0.0287998 | − | 0.999585i | \(-0.490831\pi\) | ||||
0.0287998 | + | 0.999585i | \(0.490831\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 8483.68 | 0.572939 | ||||||||
\(604\) | −22693.2 | −1.52876 | ||||||||
\(605\) | −1268.38 | −0.0852350 | ||||||||
\(606\) | 7612.03 | 0.510260 | ||||||||
\(607\) | 19963.6 | 1.33492 | 0.667461 | − | 0.744645i | \(-0.267381\pi\) | ||||
0.667461 | + | 0.744645i | \(0.267381\pi\) | |||||||
\(608\) | −954.601 | −0.0636746 | ||||||||
\(609\) | −669.366 | −0.0445387 | ||||||||
\(610\) | −23291.1 | −1.54595 | ||||||||
\(611\) | 9939.16 | 0.658094 | ||||||||
\(612\) | −32583.0 | −2.15211 | ||||||||
\(613\) | −7530.10 | −0.496147 | −0.248073 | − | 0.968741i | \(-0.579797\pi\) | ||||
−0.248073 | + | 0.968741i | \(0.579797\pi\) | |||||||
\(614\) | −47837.9 | −3.14427 | ||||||||
\(615\) | 7324.25 | 0.480231 | ||||||||
\(616\) | 7066.11 | 0.462178 | ||||||||
\(617\) | 10468.8 | 0.683075 | 0.341538 | − | 0.939868i | \(-0.389052\pi\) | ||||
0.341538 | + | 0.939868i | \(0.389052\pi\) | |||||||
\(618\) | 2678.88 | 0.174369 | ||||||||
\(619\) | 5756.07 | 0.373757 | 0.186879 | − | 0.982383i | \(-0.440163\pi\) | ||||
0.186879 | + | 0.982383i | \(0.440163\pi\) | |||||||
\(620\) | 9.63799 | 0.000624308 0 | ||||||||
\(621\) | 19531.2 | 1.26209 | ||||||||
\(622\) | −47803.6 | −3.08159 | ||||||||
\(623\) | −4363.38 | −0.280602 | ||||||||
\(624\) | −3774.69 | −0.242161 | ||||||||
\(625\) | 2162.69 | 0.138412 | ||||||||
\(626\) | −9158.91 | −0.584766 | ||||||||
\(627\) | −1235.66 | −0.0787040 | ||||||||
\(628\) | 26252.0 | 1.66810 | ||||||||
\(629\) | 39135.1 | 2.48079 | ||||||||
\(630\) | −3841.95 | −0.242964 | ||||||||
\(631\) | −27752.2 | −1.75087 | −0.875433 | − | 0.483339i | \(-0.839424\pi\) | ||||
−0.875433 | + | 0.483339i | \(0.839424\pi\) | |||||||
\(632\) | 44879.3 | 2.82469 | ||||||||
\(633\) | 10120.7 | 0.635484 | ||||||||
\(634\) | 14344.2 | 0.898548 | ||||||||
\(635\) | −542.186 | −0.0338834 | ||||||||
\(636\) | 17013.4 | 1.06073 | ||||||||
\(637\) | 10486.3 | 0.652249 | ||||||||
\(638\) | −6821.58 | −0.423306 | ||||||||
\(639\) | 20385.4 | 1.26203 | ||||||||
\(640\) | 16796.5 | 1.03741 | ||||||||
\(641\) | 2219.51 | 0.136763 | 0.0683816 | − | 0.997659i | \(-0.478216\pi\) | ||||
0.0683816 | + | 0.997659i | \(0.478216\pi\) | |||||||
\(642\) | −3975.53 | −0.244395 | ||||||||
\(643\) | −20580.1 | −1.26221 | −0.631104 | − | 0.775698i | \(-0.717398\pi\) | ||||
−0.631104 | + | 0.775698i | \(0.717398\pi\) | |||||||
\(644\) | 14953.4 | 0.914977 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 7280.34 | 0.443407 | ||||||||
\(647\) | −16963.7 | −1.03078 | −0.515389 | − | 0.856957i | \(-0.672352\pi\) | ||||
−0.515389 | + | 0.856957i | \(0.672352\pi\) | |||||||
\(648\) | −8126.77 | −0.492669 | ||||||||
\(649\) | −541.731 | −0.0327655 | ||||||||
\(650\) | −14012.3 | −0.845548 | ||||||||
\(651\) | −1.59787 | −9.61987e−5 0 | ||||||||
\(652\) | −17667.3 | −1.06121 | ||||||||
\(653\) | −5184.83 | −0.310717 | −0.155358 | − | 0.987858i | \(-0.549653\pi\) | ||||
−0.155358 | + | 0.987858i | \(0.549653\pi\) | |||||||
\(654\) | −923.157 | −0.0551961 | ||||||||
\(655\) | 8689.92 | 0.518387 | ||||||||
\(656\) | 19245.2 | 1.14543 | ||||||||
\(657\) | 3269.76 | 0.194163 | ||||||||
\(658\) | −8574.99 | −0.508037 | ||||||||
\(659\) | −30887.9 | −1.82583 | −0.912915 | − | 0.408149i | \(-0.866174\pi\) | ||||
−0.912915 | + | 0.408149i | \(0.866174\pi\) | |||||||
\(660\) | 8252.57 | 0.486714 | ||||||||
\(661\) | −5445.52 | −0.320433 | −0.160216 | − | 0.987082i | \(-0.551219\pi\) | ||||
−0.160216 | + | 0.987082i | \(0.551219\pi\) | |||||||
\(662\) | 4047.18 | 0.237611 | ||||||||
\(663\) | −9343.58 | −0.547322 | ||||||||
\(664\) | 12721.3 | 0.743497 | ||||||||
\(665\) | 560.886 | 0.0327071 | ||||||||
\(666\) | 36262.5 | 2.10982 | ||||||||
\(667\) | −6777.43 | −0.393438 | ||||||||
\(668\) | 23455.6 | 1.35857 | ||||||||
\(669\) | −4614.48 | −0.266676 | ||||||||
\(670\) | 12660.1 | 0.730001 | ||||||||
\(671\) | 25711.6 | 1.47926 | ||||||||
\(672\) | −1056.98 | −0.0606755 | ||||||||
\(673\) | 12480.7 | 0.714850 | 0.357425 | − | 0.933942i | \(-0.383655\pi\) | ||||
0.357425 | + | 0.933942i | \(0.383655\pi\) | |||||||
\(674\) | 14693.3 | 0.839712 | ||||||||
\(675\) | 10316.8 | 0.588286 | ||||||||
\(676\) | −15285.6 | −0.869685 | ||||||||
\(677\) | −30422.7 | −1.72709 | −0.863546 | − | 0.504270i | \(-0.831762\pi\) | ||||
−0.863546 | + | 0.504270i | \(0.831762\pi\) | |||||||
\(678\) | −23888.4 | −1.35314 | ||||||||
\(679\) | 7788.32 | 0.440189 | ||||||||
\(680\) | −22827.8 | −1.28736 | ||||||||
\(681\) | −16270.4 | −0.915542 | ||||||||
\(682\) | −16.2840 | −0.000914293 0 | ||||||||
\(683\) | −9567.17 | −0.535985 | −0.267992 | − | 0.963421i | \(-0.586360\pi\) | ||||
−0.267992 | + | 0.963421i | \(0.586360\pi\) | |||||||
\(684\) | 4407.63 | 0.246389 | ||||||||
\(685\) | 2257.03 | 0.125893 | ||||||||
\(686\) | −19226.7 | −1.07009 | ||||||||
\(687\) | −4025.74 | −0.223569 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −15123.7 | −0.836237 | ||||||||
\(690\) | 12548.9 | 0.692362 | ||||||||
\(691\) | 14041.5 | 0.773031 | 0.386516 | − | 0.922283i | \(-0.373679\pi\) | ||||
0.386516 | + | 0.922283i | \(0.373679\pi\) | |||||||
\(692\) | 30891.1 | 1.69697 | ||||||||
\(693\) | 4241.21 | 0.232482 | ||||||||
\(694\) | 54839.3 | 2.99953 | ||||||||
\(695\) | −14593.5 | −0.796494 | ||||||||
\(696\) | −3685.25 | −0.200703 | ||||||||
\(697\) | 47638.1 | 2.58884 | ||||||||
\(698\) | −13111.3 | −0.710989 | ||||||||
\(699\) | −6183.61 | −0.334600 | ||||||||
\(700\) | 7898.68 | 0.426489 | ||||||||
\(701\) | 4386.14 | 0.236323 | 0.118161 | − | 0.992994i | \(-0.462300\pi\) | ||||
0.118161 | + | 0.992994i | \(0.462300\pi\) | |||||||
\(702\) | −20108.4 | −1.08111 | ||||||||
\(703\) | −5293.95 | −0.284019 | ||||||||
\(704\) | −22275.8 | −1.19254 | ||||||||
\(705\) | −4701.80 | −0.251177 | ||||||||
\(706\) | 54975.4 | 2.93063 | ||||||||
\(707\) | 3814.30 | 0.202902 | ||||||||
\(708\) | −623.368 | −0.0330898 | ||||||||
\(709\) | −2852.53 | −0.151099 | −0.0755494 | − | 0.997142i | \(-0.524071\pi\) | ||||
−0.0755494 | + | 0.997142i | \(0.524071\pi\) | |||||||
\(710\) | 30420.8 | 1.60799 | ||||||||
\(711\) | 26937.4 | 1.42086 | ||||||||
\(712\) | −24023.0 | −1.26447 | ||||||||
\(713\) | −16.1786 | −0.000849782 0 | ||||||||
\(714\) | 8061.15 | 0.422523 | ||||||||
\(715\) | −7335.97 | −0.383706 | ||||||||
\(716\) | −66233.2 | −3.45706 | ||||||||
\(717\) | 5417.64 | 0.282184 | ||||||||
\(718\) | 18923.4 | 0.983588 | ||||||||
\(719\) | 608.604 | 0.0315676 | 0.0157838 | − | 0.999875i | \(-0.494976\pi\) | ||||
0.0157838 | + | 0.999875i | \(0.494976\pi\) | |||||||
\(720\) | −5535.32 | −0.286513 | ||||||||
\(721\) | 1342.35 | 0.0693369 | ||||||||
\(722\) | 31966.7 | 1.64775 | ||||||||
\(723\) | 9847.90 | 0.506566 | ||||||||
\(724\) | 38654.5 | 1.98423 | ||||||||
\(725\) | −3579.98 | −0.183389 | ||||||||
\(726\) | 2465.97 | 0.126061 | ||||||||
\(727\) | −38172.7 | −1.94738 | −0.973691 | − | 0.227872i | \(-0.926823\pi\) | ||||
−0.973691 | + | 0.227872i | \(0.926823\pi\) | |||||||
\(728\) | −7227.85 | −0.367970 | ||||||||
\(729\) | 3552.91 | 0.180507 | ||||||||
\(730\) | 4879.41 | 0.247390 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 29586.2 | 1.49390 | ||||||||
\(733\) | 31896.8 | 1.60728 | 0.803639 | − | 0.595117i | \(-0.202894\pi\) | ||||
0.803639 | + | 0.595117i | \(0.202894\pi\) | |||||||
\(734\) | 35071.8 | 1.76365 | ||||||||
\(735\) | −4960.63 | −0.248946 | ||||||||
\(736\) | −10702.1 | −0.535984 | ||||||||
\(737\) | −13975.7 | −0.698509 | ||||||||
\(738\) | 44141.4 | 2.20172 | ||||||||
\(739\) | −3826.00 | −0.190449 | −0.0952245 | − | 0.995456i | \(-0.530357\pi\) | ||||
−0.0952245 | + | 0.995456i | \(0.530357\pi\) | |||||||
\(740\) | 35356.7 | 1.75640 | ||||||||
\(741\) | 1263.94 | 0.0626613 | ||||||||
\(742\) | 13048.0 | 0.645560 | ||||||||
\(743\) | −17425.8 | −0.860418 | −0.430209 | − | 0.902729i | \(-0.641560\pi\) | ||||
−0.430209 | + | 0.902729i | \(0.641560\pi\) | |||||||
\(744\) | −8.79720 | −0.000433496 0 | ||||||||
\(745\) | −7810.38 | −0.384094 | ||||||||
\(746\) | 46373.9 | 2.27596 | ||||||||
\(747\) | 7635.56 | 0.373990 | ||||||||
\(748\) | 53676.1 | 2.62379 | ||||||||
\(749\) | −1992.09 | −0.0971822 | ||||||||
\(750\) | 16400.9 | 0.798500 | ||||||||
\(751\) | −15398.9 | −0.748223 | −0.374112 | − | 0.927384i | \(-0.622052\pi\) | ||||
−0.374112 | + | 0.927384i | \(0.622052\pi\) | |||||||
\(752\) | −12354.5 | −0.599097 | ||||||||
\(753\) | −18976.8 | −0.918396 | ||||||||
\(754\) | 6977.72 | 0.337021 | ||||||||
\(755\) | −9542.84 | −0.459999 | ||||||||
\(756\) | 11335.1 | 0.545307 | ||||||||
\(757\) | 15476.4 | 0.743065 | 0.371532 | − | 0.928420i | \(-0.378832\pi\) | ||||
0.371532 | + | 0.928420i | \(0.378832\pi\) | |||||||
\(758\) | 6902.16 | 0.330736 | ||||||||
\(759\) | −13853.0 | −0.662494 | ||||||||
\(760\) | 3088.01 | 0.147386 | ||||||||
\(761\) | 19666.4 | 0.936802 | 0.468401 | − | 0.883516i | \(-0.344830\pi\) | ||||
0.468401 | + | 0.883516i | \(0.344830\pi\) | |||||||
\(762\) | 1054.11 | 0.0501132 | ||||||||
\(763\) | −462.583 | −0.0219484 | ||||||||
\(764\) | −17177.2 | −0.813413 | ||||||||
\(765\) | −13701.7 | −0.647562 | ||||||||
\(766\) | 46806.1 | 2.20780 | ||||||||
\(767\) | 554.130 | 0.0260867 | ||||||||
\(768\) | −19056.9 | −0.895385 | ||||||||
\(769\) | 18122.5 | 0.849821 | 0.424911 | − | 0.905235i | \(-0.360306\pi\) | ||||
0.424911 | + | 0.905235i | \(0.360306\pi\) | |||||||
\(770\) | 6329.09 | 0.296214 | ||||||||
\(771\) | −6406.77 | −0.299266 | ||||||||
\(772\) | 31952.3 | 1.48962 | ||||||||
\(773\) | 20770.5 | 0.966444 | 0.483222 | − | 0.875498i | \(-0.339466\pi\) | ||||
0.483222 | + | 0.875498i | \(0.339466\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −8.54590 | −0.000396100 0 | ||||||||
\(776\) | 42879.3 | 1.98360 | ||||||||
\(777\) | −5861.72 | −0.270641 | ||||||||
\(778\) | 4100.43 | 0.188956 | ||||||||
\(779\) | −6444.19 | −0.296389 | ||||||||
\(780\) | −8441.47 | −0.387504 | ||||||||
\(781\) | −33582.2 | −1.53862 | ||||||||
\(782\) | 81620.3 | 3.73240 | ||||||||
\(783\) | −5137.47 | −0.234481 | ||||||||
\(784\) | −13034.6 | −0.593776 | ||||||||
\(785\) | 11039.4 | 0.501927 | ||||||||
\(786\) | −16894.8 | −0.766687 | ||||||||
\(787\) | 10239.3 | 0.463776 | 0.231888 | − | 0.972743i | \(-0.425510\pi\) | ||||
0.231888 | + | 0.972743i | \(0.425510\pi\) | |||||||
\(788\) | −60986.3 | −2.75704 | ||||||||
\(789\) | −4657.92 | −0.210173 | ||||||||
\(790\) | 40198.2 | 1.81037 | ||||||||
\(791\) | −11970.2 | −0.538067 | ||||||||
\(792\) | 23350.4 | 1.04762 | ||||||||
\(793\) | −26300.1 | −1.17773 | ||||||||
\(794\) | −34079.1 | −1.52320 | ||||||||
\(795\) | 7154.39 | 0.319170 | ||||||||
\(796\) | 25899.6 | 1.15325 | ||||||||
\(797\) | −25982.1 | −1.15475 | −0.577373 | − | 0.816481i | \(-0.695922\pi\) | ||||
−0.577373 | + | 0.816481i | \(0.695922\pi\) | |||||||
\(798\) | −1090.46 | −0.0483734 | ||||||||
\(799\) | −30581.3 | −1.35405 | ||||||||
\(800\) | −5653.07 | −0.249833 | ||||||||
\(801\) | −14419.0 | −0.636044 | ||||||||
\(802\) | 13531.4 | 0.595773 | ||||||||
\(803\) | −5386.48 | −0.236718 | ||||||||
\(804\) | −16081.8 | −0.705424 | ||||||||
\(805\) | 6288.12 | 0.275313 | ||||||||
\(806\) | 16.6568 | 0.000727927 0 | ||||||||
\(807\) | −1729.29 | −0.0754324 | ||||||||
\(808\) | 20999.9 | 0.914326 | ||||||||
\(809\) | −22187.4 | −0.964236 | −0.482118 | − | 0.876106i | \(-0.660132\pi\) | ||||
−0.482118 | + | 0.876106i | \(0.660132\pi\) | |||||||
\(810\) | −7279.12 | −0.315756 | ||||||||
\(811\) | 8163.38 | 0.353459 | 0.176729 | − | 0.984259i | \(-0.443448\pi\) | ||||
0.176729 | + | 0.984259i | \(0.443448\pi\) | |||||||
\(812\) | −3933.33 | −0.169991 | ||||||||
\(813\) | 6628.06 | 0.285924 | ||||||||
\(814\) | −59737.5 | −2.57223 | ||||||||
\(815\) | −7429.40 | −0.319313 | ||||||||
\(816\) | 11614.2 | 0.498256 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 57409.3 | 2.45387 | ||||||||
\(819\) | −4338.29 | −0.185094 | ||||||||
\(820\) | 43038.7 | 1.83290 | ||||||||
\(821\) | −1562.98 | −0.0664415 | −0.0332208 | − | 0.999448i | \(-0.510576\pi\) | ||||
−0.0332208 | + | 0.999448i | \(0.510576\pi\) | |||||||
\(822\) | −4388.07 | −0.186194 | ||||||||
\(823\) | −35023.3 | −1.48340 | −0.741699 | − | 0.670733i | \(-0.765980\pi\) | ||||
−0.741699 | + | 0.670733i | \(0.765980\pi\) | |||||||
\(824\) | 7390.44 | 0.312449 | ||||||||
\(825\) | −7317.47 | −0.308802 | ||||||||
\(826\) | −478.075 | −0.0201384 | ||||||||
\(827\) | 19516.9 | 0.820638 | 0.410319 | − | 0.911942i | \(-0.365417\pi\) | ||||
0.410319 | + | 0.911942i | \(0.365417\pi\) | |||||||
\(828\) | 49414.2 | 2.07399 | ||||||||
\(829\) | 17033.7 | 0.713635 | 0.356818 | − | 0.934174i | \(-0.383862\pi\) | ||||
0.356818 | + | 0.934174i | \(0.383862\pi\) | |||||||
\(830\) | 11394.4 | 0.476514 | ||||||||
\(831\) | 5241.35 | 0.218797 | ||||||||
\(832\) | 22785.6 | 0.949459 | ||||||||
\(833\) | −32264.8 | −1.34203 | ||||||||
\(834\) | 28372.4 | 1.17800 | ||||||||
\(835\) | 9863.43 | 0.408788 | ||||||||
\(836\) | −7260.97 | −0.300390 | ||||||||
\(837\) | −12.2638 | −0.000506452 0 | ||||||||
\(838\) | −13678.6 | −0.563864 | ||||||||
\(839\) | −7296.99 | −0.300262 | −0.150131 | − | 0.988666i | \(-0.547970\pi\) | ||||
−0.150131 | + | 0.988666i | \(0.547970\pi\) | |||||||
\(840\) | 3419.19 | 0.140444 | ||||||||
\(841\) | −22606.3 | −0.926904 | ||||||||
\(842\) | 49030.1 | 2.00675 | ||||||||
\(843\) | 14190.6 | 0.579776 | ||||||||
\(844\) | 59471.2 | 2.42545 | ||||||||
\(845\) | −6427.83 | −0.261685 | ||||||||
\(846\) | −28336.5 | −1.15157 | ||||||||
\(847\) | 1235.67 | 0.0501275 | ||||||||
\(848\) | 18798.9 | 0.761271 | ||||||||
\(849\) | 548.133 | 0.0221577 | ||||||||
\(850\) | 43113.6 | 1.73975 | ||||||||
\(851\) | −59350.8 | −2.39074 | ||||||||
\(852\) | −38642.9 | −1.55386 | ||||||||
\(853\) | −9689.81 | −0.388948 | −0.194474 | − | 0.980908i | \(-0.562300\pi\) | ||||
−0.194474 | + | 0.980908i | \(0.562300\pi\) | |||||||
\(854\) | 22690.4 | 0.909189 | ||||||||
\(855\) | 1853.48 | 0.0741376 | ||||||||
\(856\) | −10967.6 | −0.437927 | ||||||||
\(857\) | 25619.7 | 1.02118 | 0.510590 | − | 0.859824i | \(-0.329427\pi\) | ||||
0.510590 | + | 0.859824i | \(0.329427\pi\) | |||||||
\(858\) | 14262.4 | 0.567496 | ||||||||
\(859\) | 33986.1 | 1.34993 | 0.674966 | − | 0.737849i | \(-0.264158\pi\) | ||||
0.674966 | + | 0.737849i | \(0.264158\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −7135.32 | −0.282429 | ||||||||
\(862\) | 66437.6 | 2.62514 | ||||||||
\(863\) | −10162.6 | −0.400855 | −0.200427 | − | 0.979709i | \(-0.564233\pi\) | ||||
−0.200427 | + | 0.979709i | \(0.564233\pi\) | |||||||
\(864\) | −8112.47 | −0.319435 | ||||||||
\(865\) | 12990.2 | 0.510612 | ||||||||
\(866\) | −41879.7 | −1.64334 | ||||||||
\(867\) | 16140.9 | 0.632263 | ||||||||
\(868\) | −9.38938 | −0.000367162 0 | ||||||||
\(869\) | −44375.7 | −1.73227 | ||||||||
\(870\) | −3300.87 | −0.128632 | ||||||||
\(871\) | 14295.6 | 0.556128 | ||||||||
\(872\) | −2546.79 | −0.0989050 | ||||||||
\(873\) | 25736.9 | 0.997781 | ||||||||
\(874\) | −11041.1 | −0.427312 | ||||||||
\(875\) | 8218.29 | 0.317519 | ||||||||
\(876\) | −6198.20 | −0.239061 | ||||||||
\(877\) | 33751.4 | 1.29955 | 0.649774 | − | 0.760127i | \(-0.274863\pi\) | ||||
0.649774 | + | 0.760127i | \(0.274863\pi\) | |||||||
\(878\) | 71603.7 | 2.75229 | ||||||||
\(879\) | −15473.5 | −0.593753 | ||||||||
\(880\) | 9118.68 | 0.349307 | ||||||||
\(881\) | 18540.8 | 0.709030 | 0.354515 | − | 0.935050i | \(-0.384646\pi\) | ||||
0.354515 | + | 0.935050i | \(0.384646\pi\) | |||||||
\(882\) | −29896.4 | −1.14134 | ||||||||
\(883\) | −33606.6 | −1.28081 | −0.640403 | − | 0.768039i | \(-0.721233\pi\) | ||||
−0.640403 | + | 0.768039i | \(0.721233\pi\) | |||||||
\(884\) | −54904.7 | −2.08896 | ||||||||
\(885\) | −262.136 | −0.00995661 | ||||||||
\(886\) | −78255.4 | −2.96732 | ||||||||
\(887\) | 36259.0 | 1.37256 | 0.686279 | − | 0.727339i | \(-0.259243\pi\) | ||||
0.686279 | + | 0.727339i | \(0.259243\pi\) | |||||||
\(888\) | −32272.2 | −1.21958 | ||||||||
\(889\) | 528.200 | 0.0199272 | ||||||||
\(890\) | −21517.3 | −0.810406 | ||||||||
\(891\) | 8035.57 | 0.302134 | ||||||||
\(892\) | −27115.6 | −1.01782 | ||||||||
\(893\) | 4136.84 | 0.155022 | ||||||||
\(894\) | 15184.8 | 0.568070 | ||||||||
\(895\) | −27852.1 | −1.04022 | ||||||||
\(896\) | −16363.2 | −0.610108 | ||||||||
\(897\) | 14170.1 | 0.527454 | ||||||||
\(898\) | 62203.6 | 2.31154 | ||||||||
\(899\) | 4.25562 | 0.000157879 0 | ||||||||
\(900\) | 26101.6 | 0.966727 | ||||||||
\(901\) | 46533.3 | 1.72059 | ||||||||
\(902\) | −72716.8 | −2.68426 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −65903.0 | −2.42467 | ||||||||
\(905\) | 16254.8 | 0.597048 | ||||||||
\(906\) | 18553.0 | 0.680333 | ||||||||
\(907\) | 2435.81 | 0.0891730 | 0.0445865 | − | 0.999006i | \(-0.485803\pi\) | ||||
0.0445865 | + | 0.999006i | \(0.485803\pi\) | |||||||
\(908\) | −95608.2 | −3.49435 | ||||||||
\(909\) | 12604.6 | 0.459919 | ||||||||
\(910\) | −6473.96 | −0.235835 | ||||||||
\(911\) | 26035.1 | 0.946851 | 0.473426 | − | 0.880834i | \(-0.343017\pi\) | ||||
0.473426 | + | 0.880834i | \(0.343017\pi\) | |||||||
\(912\) | −1571.09 | −0.0570439 | ||||||||
\(913\) | −12578.5 | −0.455957 | ||||||||
\(914\) | 7307.36 | 0.264449 | ||||||||
\(915\) | 12441.5 | 0.449511 | ||||||||
\(916\) | −23656.1 | −0.853295 | ||||||||
\(917\) | −8465.76 | −0.304868 | ||||||||
\(918\) | 61870.4 | 2.22443 | ||||||||
\(919\) | −37812.0 | −1.35724 | −0.678620 | − | 0.734490i | \(-0.737422\pi\) | ||||
−0.678620 | + | 0.734490i | \(0.737422\pi\) | |||||||
\(920\) | 34619.8 | 1.24063 | ||||||||
\(921\) | 25553.7 | 0.914247 | ||||||||
\(922\) | 21619.1 | 0.772221 | ||||||||
\(923\) | 34350.9 | 1.22500 | ||||||||
\(924\) | −8039.70 | −0.286241 | ||||||||
\(925\) | −31350.3 | −1.11437 | ||||||||
\(926\) | −24483.2 | −0.868862 | ||||||||
\(927\) | 4435.88 | 0.157167 | ||||||||
\(928\) | 2815.07 | 0.0995790 | ||||||||
\(929\) | 27043.9 | 0.955093 | 0.477546 | − | 0.878607i | \(-0.341526\pi\) | ||||
0.477546 | + | 0.878607i | \(0.341526\pi\) | |||||||
\(930\) | −7.87962 | −0.000277831 0 | ||||||||
\(931\) | 4364.58 | 0.153645 | ||||||||
\(932\) | −36336.1 | −1.27707 | ||||||||
\(933\) | 25535.4 | 0.896024 | ||||||||
\(934\) | −28493.5 | −0.998217 | ||||||||
\(935\) | 22571.6 | 0.789488 | ||||||||
\(936\) | −23884.8 | −0.834081 | ||||||||
\(937\) | 35620.5 | 1.24191 | 0.620956 | − | 0.783845i | \(-0.286745\pi\) | ||||
0.620956 | + | 0.783845i | \(0.286745\pi\) | |||||||
\(938\) | −12333.5 | −0.429321 | ||||||||
\(939\) | 4892.43 | 0.170030 | ||||||||
\(940\) | −27628.7 | −0.958669 | ||||||||
\(941\) | −54098.1 | −1.87412 | −0.937060 | − | 0.349168i | \(-0.886464\pi\) | ||||
−0.937060 | + | 0.349168i | \(0.886464\pi\) | |||||||
\(942\) | −21462.5 | −0.742343 | ||||||||
\(943\) | −72246.2 | −2.49487 | ||||||||
\(944\) | −688.790 | −0.0237481 | ||||||||
\(945\) | 4766.57 | 0.164081 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −1896.92 | −0.0650914 | −0.0325457 | − | 0.999470i | \(-0.510361\pi\) | ||||
−0.0325457 | + | 0.999470i | \(0.510361\pi\) | |||||||
\(948\) | −51062.9 | −1.74942 | ||||||||
\(949\) | 5509.77 | 0.188467 | ||||||||
\(950\) | −5832.14 | −0.199178 | ||||||||
\(951\) | −7662.25 | −0.261268 | ||||||||
\(952\) | 22239.0 | 0.757111 | ||||||||
\(953\) | 38430.6 | 1.30629 | 0.653143 | − | 0.757235i | \(-0.273450\pi\) | ||||
0.653143 | + | 0.757235i | \(0.273450\pi\) | |||||||
\(954\) | 43117.7 | 1.46330 | ||||||||
\(955\) | −7223.27 | −0.244753 | ||||||||
\(956\) | 31835.1 | 1.07701 | ||||||||
\(957\) | 3643.90 | 0.123083 | ||||||||
\(958\) | 64394.3 | 2.17170 | ||||||||
\(959\) | −2198.81 | −0.0740389 | ||||||||
\(960\) | −10778.9 | −0.362384 | ||||||||
\(961\) | −29791.0 | −1.00000 | ||||||||
\(962\) | 61104.8 | 2.04792 | ||||||||
\(963\) | −6582.98 | −0.220284 | ||||||||
\(964\) | 57868.2 | 1.93341 | ||||||||
\(965\) | 13436.4 | 0.448222 | ||||||||
\(966\) | −12225.2 | −0.407185 | ||||||||
\(967\) | −43807.6 | −1.45683 | −0.728417 | − | 0.685135i | \(-0.759743\pi\) | ||||
−0.728417 | + | 0.685135i | \(0.759743\pi\) | |||||||
\(968\) | 6803.07 | 0.225887 | ||||||||
\(969\) | −3888.95 | −0.128928 | ||||||||
\(970\) | 38406.8 | 1.27131 | ||||||||
\(971\) | 13880.3 | 0.458742 | 0.229371 | − | 0.973339i | \(-0.426333\pi\) | ||||
0.229371 | + | 0.973339i | \(0.426333\pi\) | |||||||
\(972\) | 58787.2 | 1.93992 | ||||||||
\(973\) | 14217.1 | 0.468426 | ||||||||
\(974\) | −45767.9 | −1.50564 | ||||||||
\(975\) | 7484.96 | 0.245857 | ||||||||
\(976\) | 32691.3 | 1.07215 | ||||||||
\(977\) | 16948.3 | 0.554990 | 0.277495 | − | 0.960727i | \(-0.410496\pi\) | ||||
0.277495 | + | 0.960727i | \(0.410496\pi\) | |||||||
\(978\) | 14444.1 | 0.472260 | ||||||||
\(979\) | 23753.4 | 0.775446 | ||||||||
\(980\) | −29149.6 | −0.950154 | ||||||||
\(981\) | −1528.63 | −0.0497507 | ||||||||
\(982\) | 32915.8 | 1.06964 | ||||||||
\(983\) | 6232.10 | 0.202211 | 0.101105 | − | 0.994876i | \(-0.467762\pi\) | ||||
0.101105 | + | 0.994876i | \(0.467762\pi\) | |||||||
\(984\) | −39284.1 | −1.27270 | ||||||||
\(985\) | −25645.7 | −0.829584 | ||||||||
\(986\) | −21469.4 | −0.693432 | ||||||||
\(987\) | 4580.52 | 0.147720 | ||||||||
\(988\) | 7427.17 | 0.239160 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 20914.8 | 0.671431 | ||||||||
\(991\) | −41002.7 | −1.31432 | −0.657161 | − | 0.753751i | \(-0.728243\pi\) | ||||
−0.657161 | + | 0.753751i | \(0.728243\pi\) | |||||||
\(992\) | 6.71996 | 0.000215080 0 | ||||||||
\(993\) | −2161.89 | −0.0690892 | ||||||||
\(994\) | −29636.2 | −0.945676 | ||||||||
\(995\) | 10891.2 | 0.347009 | ||||||||
\(996\) | −14474.1 | −0.460471 | ||||||||
\(997\) | −4141.03 | −0.131542 | −0.0657712 | − | 0.997835i | \(-0.520951\pi\) | ||||
−0.0657712 | + | 0.997835i | \(0.520951\pi\) | |||||||
\(998\) | −14575.2 | −0.462295 | ||||||||
\(999\) | −44989.5 | −1.42483 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 1849.4.a.j.1.3 | yes | 50 | |
43.42 | odd | 2 | 1849.4.a.i.1.48 | ✓ | 50 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1849.4.a.i.1.48 | ✓ | 50 | 43.42 | odd | 2 | ||
1849.4.a.j.1.3 | yes | 50 | 1.1 | even | 1 | trivial |