Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1150,4,Mod(1,1150)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1150, 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("1150.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1150 = 2 \cdot 5^{2} \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1150.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: | \(67.8521965066\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{4} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 68x^{2} - 111x + 342 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 230) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(8.73081\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1150.1 |
$q$-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 | ||||||||
\(3\) | −7.73081 | −1.48779 | −0.743897 | − | 0.668294i | \(-0.767025\pi\) | ||||
−0.743897 | + | 0.668294i | \(0.767025\pi\) | |||||||
\(4\) | 4.00000 | 0.500000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −15.4616 | −1.05203 | ||||||||
\(7\) | −23.5622 | −1.27224 | −0.636121 | − | 0.771589i | \(-0.719462\pi\) | ||||
−0.636121 | + | 0.771589i | \(0.719462\pi\) | |||||||
\(8\) | 8.00000 | 0.353553 | ||||||||
\(9\) | 32.7654 | 1.21353 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −32.1352 | −0.880830 | −0.440415 | − | 0.897794i | \(-0.645169\pi\) | ||||
−0.440415 | + | 0.897794i | \(0.645169\pi\) | |||||||
\(12\) | −30.9232 | −0.743897 | ||||||||
\(13\) | −40.0811 | −0.855115 | −0.427557 | − | 0.903988i | \(-0.640626\pi\) | ||||
−0.427557 | + | 0.903988i | \(0.640626\pi\) | |||||||
\(14\) | −47.1245 | −0.899611 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 16.0000 | 0.250000 | ||||||||
\(17\) | −126.165 | −1.79997 | −0.899987 | − | 0.435916i | \(-0.856424\pi\) | ||||
−0.899987 | + | 0.435916i | \(0.856424\pi\) | |||||||
\(18\) | 65.5308 | 0.858097 | ||||||||
\(19\) | 0.232742 | 0.00281024 | 0.00140512 | − | 0.999999i | \(-0.499553\pi\) | ||||
0.00140512 | + | 0.999999i | \(0.499553\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 182.155 | 1.89283 | ||||||||
\(22\) | −64.2704 | −0.622841 | ||||||||
\(23\) | 23.0000 | 0.208514 | ||||||||
\(24\) | −61.8465 | −0.526015 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −80.1621 | −0.604657 | ||||||||
\(27\) | −44.5711 | −0.317693 | ||||||||
\(28\) | −94.2490 | −0.636121 | ||||||||
\(29\) | −137.226 | −0.878695 | −0.439347 | − | 0.898317i | \(-0.644790\pi\) | ||||
−0.439347 | + | 0.898317i | \(0.644790\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 112.866 | 0.653914 | 0.326957 | − | 0.945039i | \(-0.393977\pi\) | ||||
0.326957 | + | 0.945039i | \(0.393977\pi\) | |||||||
\(32\) | 32.0000 | 0.176777 | ||||||||
\(33\) | 248.431 | 1.31049 | ||||||||
\(34\) | −252.331 | −1.27277 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 131.062 | 0.606766 | ||||||||
\(37\) | −45.7057 | −0.203080 | −0.101540 | − | 0.994831i | \(-0.532377\pi\) | ||||
−0.101540 | + | 0.994831i | \(0.532377\pi\) | |||||||
\(38\) | 0.465483 | 0.00198714 | ||||||||
\(39\) | 309.859 | 1.27223 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −135.385 | −0.515696 | −0.257848 | − | 0.966186i | \(-0.583013\pi\) | ||||
−0.257848 | + | 0.966186i | \(0.583013\pi\) | |||||||
\(42\) | 364.310 | 1.33844 | ||||||||
\(43\) | −543.528 | −1.92761 | −0.963805 | − | 0.266608i | \(-0.914097\pi\) | ||||
−0.963805 | + | 0.266608i | \(0.914097\pi\) | |||||||
\(44\) | −128.541 | −0.440415 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 46.0000 | 0.147442 | ||||||||
\(47\) | −26.4344 | −0.0820394 | −0.0410197 | − | 0.999158i | \(-0.513061\pi\) | ||||
−0.0410197 | + | 0.999158i | \(0.513061\pi\) | |||||||
\(48\) | −123.693 | −0.371949 | ||||||||
\(49\) | 212.180 | 0.618599 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 975.359 | 2.67799 | ||||||||
\(52\) | −160.324 | −0.427557 | ||||||||
\(53\) | −43.6958 | −0.113247 | −0.0566235 | − | 0.998396i | \(-0.518033\pi\) | ||||
−0.0566235 | + | 0.998396i | \(0.518033\pi\) | |||||||
\(54\) | −89.1422 | −0.224643 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −188.498 | −0.449805 | ||||||||
\(57\) | −1.79928 | −0.00418106 | ||||||||
\(58\) | −274.451 | −0.621331 | ||||||||
\(59\) | 202.248 | 0.446278 | 0.223139 | − | 0.974787i | \(-0.428370\pi\) | ||||
0.223139 | + | 0.974787i | \(0.428370\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 150.279 | 0.315430 | 0.157715 | − | 0.987485i | \(-0.449587\pi\) | ||||
0.157715 | + | 0.987485i | \(0.449587\pi\) | |||||||
\(62\) | 225.732 | 0.462387 | ||||||||
\(63\) | −772.026 | −1.54391 | ||||||||
\(64\) | 64.0000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 496.862 | 0.926659 | ||||||||
\(67\) | 420.722 | 0.767155 | 0.383577 | − | 0.923509i | \(-0.374692\pi\) | ||||
0.383577 | + | 0.923509i | \(0.374692\pi\) | |||||||
\(68\) | −504.661 | −0.899987 | ||||||||
\(69\) | −177.809 | −0.310227 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 667.381 | 1.11554 | 0.557771 | − | 0.829995i | \(-0.311657\pi\) | ||||
0.557771 | + | 0.829995i | \(0.311657\pi\) | |||||||
\(72\) | 262.123 | 0.429049 | ||||||||
\(73\) | −602.960 | −0.966728 | −0.483364 | − | 0.875420i | \(-0.660585\pi\) | ||||
−0.483364 | + | 0.875420i | \(0.660585\pi\) | |||||||
\(74\) | −91.4115 | −0.143600 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0.930966 | 0.00140512 | ||||||||
\(77\) | 757.178 | 1.12063 | ||||||||
\(78\) | 619.718 | 0.899606 | ||||||||
\(79\) | −1378.88 | −1.96374 | −0.981872 | − | 0.189545i | \(-0.939299\pi\) | ||||
−0.981872 | + | 0.189545i | \(0.939299\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −540.095 | −0.740871 | ||||||||
\(82\) | −270.769 | −0.364652 | ||||||||
\(83\) | 485.178 | 0.641629 | 0.320815 | − | 0.947142i | \(-0.396043\pi\) | ||||
0.320815 | + | 0.947142i | \(0.396043\pi\) | |||||||
\(84\) | 728.621 | 0.946417 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −1087.06 | −1.36303 | ||||||||
\(87\) | 1060.86 | 1.30732 | ||||||||
\(88\) | −257.082 | −0.311420 | ||||||||
\(89\) | −1127.71 | −1.34311 | −0.671556 | − | 0.740954i | \(-0.734374\pi\) | ||||
−0.671556 | + | 0.740954i | \(0.734374\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 944.400 | 1.08791 | ||||||||
\(92\) | 92.0000 | 0.104257 | ||||||||
\(93\) | −872.545 | −0.972890 | ||||||||
\(94\) | −52.8688 | −0.0580106 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −247.386 | −0.263007 | ||||||||
\(97\) | 1486.24 | 1.55572 | 0.777858 | − | 0.628441i | \(-0.216306\pi\) | ||||
0.777858 | + | 0.628441i | \(0.216306\pi\) | |||||||
\(98\) | 424.359 | 0.437416 | ||||||||
\(99\) | −1052.92 | −1.06892 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1888.86 | 1.86087 | 0.930437 | − | 0.366451i | \(-0.119427\pi\) | ||||
0.930437 | + | 0.366451i | \(0.119427\pi\) | |||||||
\(102\) | 1950.72 | 1.89363 | ||||||||
\(103\) | 1497.17 | 1.43224 | 0.716118 | − | 0.697979i | \(-0.245917\pi\) | ||||
0.716118 | + | 0.697979i | \(0.245917\pi\) | |||||||
\(104\) | −320.649 | −0.302329 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −87.3917 | −0.0800777 | ||||||||
\(107\) | 585.150 | 0.528678 | 0.264339 | − | 0.964430i | \(-0.414846\pi\) | ||||
0.264339 | + | 0.964430i | \(0.414846\pi\) | |||||||
\(108\) | −178.284 | −0.158846 | ||||||||
\(109\) | −139.166 | −0.122290 | −0.0611452 | − | 0.998129i | \(-0.519475\pi\) | ||||
−0.0611452 | + | 0.998129i | \(0.519475\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 353.342 | 0.302142 | ||||||||
\(112\) | −376.996 | −0.318060 | ||||||||
\(113\) | 1293.18 | 1.07656 | 0.538282 | − | 0.842765i | \(-0.319073\pi\) | ||||
0.538282 | + | 0.842765i | \(0.319073\pi\) | |||||||
\(114\) | −3.59856 | −0.00295646 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −548.902 | −0.439347 | ||||||||
\(117\) | −1313.27 | −1.03771 | ||||||||
\(118\) | 404.495 | 0.315566 | ||||||||
\(119\) | 2972.74 | 2.29000 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −298.328 | −0.224138 | ||||||||
\(122\) | 300.557 | 0.223043 | ||||||||
\(123\) | 1046.63 | 0.767250 | ||||||||
\(124\) | 451.464 | 0.326957 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −1544.05 | −1.09171 | ||||||||
\(127\) | 1298.43 | 0.907221 | 0.453610 | − | 0.891200i | \(-0.350136\pi\) | ||||
0.453610 | + | 0.891200i | \(0.350136\pi\) | |||||||
\(128\) | 128.000 | 0.0883883 | ||||||||
\(129\) | 4201.91 | 2.86789 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −525.247 | −0.350313 | −0.175157 | − | 0.984541i | \(-0.556043\pi\) | ||||
−0.175157 | + | 0.984541i | \(0.556043\pi\) | |||||||
\(132\) | 993.725 | 0.655247 | ||||||||
\(133\) | −5.48392 | −0.00357531 | ||||||||
\(134\) | 841.444 | 0.542460 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −1009.32 | −0.636387 | ||||||||
\(137\) | 2428.12 | 1.51422 | 0.757109 | − | 0.653288i | \(-0.226611\pi\) | ||||
0.757109 | + | 0.653288i | \(0.226611\pi\) | |||||||
\(138\) | −355.617 | −0.219363 | ||||||||
\(139\) | 2456.46 | 1.49895 | 0.749476 | − | 0.662031i | \(-0.230305\pi\) | ||||
0.749476 | + | 0.662031i | \(0.230305\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 204.359 | 0.122058 | ||||||||
\(142\) | 1334.76 | 0.788808 | ||||||||
\(143\) | 1288.01 | 0.753211 | ||||||||
\(144\) | 524.246 | 0.303383 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −1205.92 | −0.683580 | ||||||||
\(147\) | −1640.32 | −0.920349 | ||||||||
\(148\) | −182.823 | −0.101540 | ||||||||
\(149\) | −2405.39 | −1.32253 | −0.661266 | − | 0.750151i | \(-0.729981\pi\) | ||||
−0.661266 | + | 0.750151i | \(0.729981\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −649.276 | −0.349916 | −0.174958 | − | 0.984576i | \(-0.555979\pi\) | ||||
−0.174958 | + | 0.984576i | \(0.555979\pi\) | |||||||
\(152\) | 1.86193 | 0.000993570 0 | ||||||||
\(153\) | −4133.85 | −2.18433 | ||||||||
\(154\) | 1514.36 | 0.792404 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 1239.44 | 0.636117 | ||||||||
\(157\) | −3665.04 | −1.86307 | −0.931536 | − | 0.363650i | \(-0.881530\pi\) | ||||
−0.931536 | + | 0.363650i | \(0.881530\pi\) | |||||||
\(158\) | −2757.75 | −1.38858 | ||||||||
\(159\) | 337.804 | 0.168488 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −541.932 | −0.265281 | ||||||||
\(162\) | −1080.19 | −0.523875 | ||||||||
\(163\) | 1055.27 | 0.507088 | 0.253544 | − | 0.967324i | \(-0.418404\pi\) | ||||
0.253544 | + | 0.967324i | \(0.418404\pi\) | |||||||
\(164\) | −541.539 | −0.257848 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 970.356 | 0.453700 | ||||||||
\(167\) | 731.805 | 0.339095 | 0.169547 | − | 0.985522i | \(-0.445769\pi\) | ||||
0.169547 | + | 0.985522i | \(0.445769\pi\) | |||||||
\(168\) | 1457.24 | 0.669218 | ||||||||
\(169\) | −590.507 | −0.268779 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 7.62587 | 0.00341032 | ||||||||
\(172\) | −2174.11 | −0.963805 | ||||||||
\(173\) | 521.773 | 0.229304 | 0.114652 | − | 0.993406i | \(-0.463425\pi\) | ||||
0.114652 | + | 0.993406i | \(0.463425\pi\) | |||||||
\(174\) | 2121.73 | 0.924413 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −514.163 | −0.220208 | ||||||||
\(177\) | −1563.54 | −0.663970 | ||||||||
\(178\) | −2255.42 | −0.949723 | ||||||||
\(179\) | −1183.07 | −0.494005 | −0.247002 | − | 0.969015i | \(-0.579446\pi\) | ||||
−0.247002 | + | 0.969015i | \(0.579446\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1723.92 | 0.707946 | 0.353973 | − | 0.935256i | \(-0.384830\pi\) | ||||
0.353973 | + | 0.935256i | \(0.384830\pi\) | |||||||
\(182\) | 1888.80 | 0.769270 | ||||||||
\(183\) | −1161.78 | −0.469295 | ||||||||
\(184\) | 184.000 | 0.0737210 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −1745.09 | −0.687937 | ||||||||
\(187\) | 4054.35 | 1.58547 | ||||||||
\(188\) | −105.738 | −0.0410197 | ||||||||
\(189\) | 1050.20 | 0.404182 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −2798.12 | −1.06002 | −0.530012 | − | 0.847990i | \(-0.677813\pi\) | ||||
−0.530012 | + | 0.847990i | \(0.677813\pi\) | |||||||
\(192\) | −494.772 | −0.185974 | ||||||||
\(193\) | 497.686 | 0.185618 | 0.0928089 | − | 0.995684i | \(-0.470415\pi\) | ||||
0.0928089 | + | 0.995684i | \(0.470415\pi\) | |||||||
\(194\) | 2972.47 | 1.10006 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 848.718 | 0.309300 | ||||||||
\(197\) | −296.489 | −0.107228 | −0.0536141 | − | 0.998562i | \(-0.517074\pi\) | ||||
−0.0536141 | + | 0.998562i | \(0.517074\pi\) | |||||||
\(198\) | −2105.85 | −0.755838 | ||||||||
\(199\) | 2347.43 | 0.836207 | 0.418103 | − | 0.908399i | \(-0.362695\pi\) | ||||
0.418103 | + | 0.908399i | \(0.362695\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −3252.52 | −1.14137 | ||||||||
\(202\) | 3777.71 | 1.31584 | ||||||||
\(203\) | 3233.34 | 1.11791 | ||||||||
\(204\) | 3901.44 | 1.33900 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 2994.34 | 1.01274 | ||||||||
\(207\) | 753.604 | 0.253039 | ||||||||
\(208\) | −641.297 | −0.213779 | ||||||||
\(209\) | −7.47920 | −0.00247535 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2838.61 | 0.926153 | 0.463076 | − | 0.886318i | \(-0.346746\pi\) | ||||
0.463076 | + | 0.886318i | \(0.346746\pi\) | |||||||
\(212\) | −174.783 | −0.0566235 | ||||||||
\(213\) | −5159.39 | −1.65970 | ||||||||
\(214\) | 1170.30 | 0.373832 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −356.569 | −0.112321 | ||||||||
\(217\) | −2659.38 | −0.831937 | ||||||||
\(218\) | −278.331 | −0.0864723 | ||||||||
\(219\) | 4661.37 | 1.43829 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 5056.84 | 1.53918 | ||||||||
\(222\) | 706.685 | 0.213647 | ||||||||
\(223\) | 2124.68 | 0.638024 | 0.319012 | − | 0.947751i | \(-0.396649\pi\) | ||||
0.319012 | + | 0.947751i | \(0.396649\pi\) | |||||||
\(224\) | −753.992 | −0.224903 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 2586.35 | 0.761246 | ||||||||
\(227\) | −1551.97 | −0.453780 | −0.226890 | − | 0.973920i | \(-0.572856\pi\) | ||||
−0.226890 | + | 0.973920i | \(0.572856\pi\) | |||||||
\(228\) | −7.19712 | −0.00209053 | ||||||||
\(229\) | −158.531 | −0.0457469 | −0.0228735 | − | 0.999738i | \(-0.507281\pi\) | ||||
−0.0228735 | + | 0.999738i | \(0.507281\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −5853.60 | −1.66727 | ||||||||
\(232\) | −1097.80 | −0.310666 | ||||||||
\(233\) | 728.999 | 0.204971 | 0.102486 | − | 0.994734i | \(-0.467320\pi\) | ||||
0.102486 | + | 0.994734i | \(0.467320\pi\) | |||||||
\(234\) | −2626.54 | −0.733772 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 808.991 | 0.223139 | ||||||||
\(237\) | 10659.8 | 2.92165 | ||||||||
\(238\) | 5945.47 | 1.61928 | ||||||||
\(239\) | −6201.60 | −1.67844 | −0.839222 | − | 0.543789i | \(-0.816989\pi\) | ||||
−0.839222 | + | 0.543789i | \(0.816989\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −7223.04 | −1.93061 | −0.965305 | − | 0.261126i | \(-0.915906\pi\) | ||||
−0.965305 | + | 0.261126i | \(0.915906\pi\) | |||||||
\(242\) | −596.656 | −0.158490 | ||||||||
\(243\) | 5378.79 | 1.41996 | ||||||||
\(244\) | 601.115 | 0.157715 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 2093.27 | 0.542527 | ||||||||
\(247\) | −9.32853 | −0.00240308 | ||||||||
\(248\) | 902.928 | 0.231193 | ||||||||
\(249\) | −3750.82 | −0.954612 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 5042.78 | 1.26812 | 0.634059 | − | 0.773285i | \(-0.281388\pi\) | ||||
0.634059 | + | 0.773285i | \(0.281388\pi\) | |||||||
\(252\) | −3088.10 | −0.771954 | ||||||||
\(253\) | −739.110 | −0.183666 | ||||||||
\(254\) | 2596.86 | 0.641502 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 256.000 | 0.0625000 | ||||||||
\(257\) | −2981.15 | −0.723577 | −0.361788 | − | 0.932260i | \(-0.617834\pi\) | ||||
−0.361788 | + | 0.932260i | \(0.617834\pi\) | |||||||
\(258\) | 8403.82 | 2.02790 | ||||||||
\(259\) | 1076.93 | 0.258367 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −4496.25 | −1.06632 | ||||||||
\(262\) | −1050.49 | −0.247709 | ||||||||
\(263\) | −7242.86 | −1.69815 | −0.849076 | − | 0.528271i | \(-0.822841\pi\) | ||||
−0.849076 | + | 0.528271i | \(0.822841\pi\) | |||||||
\(264\) | 1987.45 | 0.463330 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −10.9678 | −0.00252812 | ||||||||
\(267\) | 8718.10 | 1.99827 | ||||||||
\(268\) | 1682.89 | 0.383577 | ||||||||
\(269\) | −2567.58 | −0.581962 | −0.290981 | − | 0.956729i | \(-0.593982\pi\) | ||||
−0.290981 | + | 0.956729i | \(0.593982\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 8066.27 | 1.80808 | 0.904042 | − | 0.427443i | \(-0.140586\pi\) | ||||
0.904042 | + | 0.427443i | \(0.140586\pi\) | |||||||
\(272\) | −2018.64 | −0.449994 | ||||||||
\(273\) | −7300.98 | −1.61859 | ||||||||
\(274\) | 4856.23 | 1.07071 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −711.234 | −0.155113 | ||||||||
\(277\) | −8991.54 | −1.95036 | −0.975179 | − | 0.221418i | \(-0.928932\pi\) | ||||
−0.975179 | + | 0.221418i | \(0.928932\pi\) | |||||||
\(278\) | 4912.92 | 1.05992 | ||||||||
\(279\) | 3698.10 | 0.793546 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 968.130 | 0.205529 | 0.102765 | − | 0.994706i | \(-0.467231\pi\) | ||||
0.102765 | + | 0.994706i | \(0.467231\pi\) | |||||||
\(282\) | 408.718 | 0.0863079 | ||||||||
\(283\) | 2252.65 | 0.473167 | 0.236583 | − | 0.971611i | \(-0.423972\pi\) | ||||
0.236583 | + | 0.971611i | \(0.423972\pi\) | |||||||
\(284\) | 2669.52 | 0.557771 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 2576.03 | 0.532600 | ||||||||
\(287\) | 3189.97 | 0.656090 | ||||||||
\(288\) | 1048.49 | 0.214524 | ||||||||
\(289\) | 11004.7 | 2.23991 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −11489.8 | −2.31458 | ||||||||
\(292\) | −2411.84 | −0.483364 | ||||||||
\(293\) | −2734.35 | −0.545196 | −0.272598 | − | 0.962128i | \(-0.587883\pi\) | ||||
−0.272598 | + | 0.962128i | \(0.587883\pi\) | |||||||
\(294\) | −3280.64 | −0.650785 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −365.646 | −0.0717998 | ||||||||
\(297\) | 1432.30 | 0.279834 | ||||||||
\(298\) | −4810.78 | −0.935172 | ||||||||
\(299\) | −921.865 | −0.178304 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 12806.7 | 2.45239 | ||||||||
\(302\) | −1298.55 | −0.247428 | ||||||||
\(303\) | −14602.4 | −2.76860 | ||||||||
\(304\) | 3.72387 | 0.000702560 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −8267.71 | −1.54455 | ||||||||
\(307\) | 7977.09 | 1.48299 | 0.741493 | − | 0.670961i | \(-0.234118\pi\) | ||||
0.741493 | + | 0.670961i | \(0.234118\pi\) | |||||||
\(308\) | 3028.71 | 0.560314 | ||||||||
\(309\) | −11574.3 | −2.13087 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 7729.43 | 1.40931 | 0.704655 | − | 0.709550i | \(-0.251102\pi\) | ||||
0.704655 | + | 0.709550i | \(0.251102\pi\) | |||||||
\(312\) | 2478.87 | 0.449803 | ||||||||
\(313\) | −5506.25 | −0.994350 | −0.497175 | − | 0.867650i | \(-0.665629\pi\) | ||||
−0.497175 | + | 0.867650i | \(0.665629\pi\) | |||||||
\(314\) | −7330.08 | −1.31739 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −5515.51 | −0.981872 | ||||||||
\(317\) | −5231.37 | −0.926887 | −0.463443 | − | 0.886126i | \(-0.653386\pi\) | ||||
−0.463443 | + | 0.886126i | \(0.653386\pi\) | |||||||
\(318\) | 675.608 | 0.119139 | ||||||||
\(319\) | 4409.77 | 0.773981 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −4523.68 | −0.786565 | ||||||||
\(322\) | −1083.86 | −0.187582 | ||||||||
\(323\) | −29.3639 | −0.00505836 | ||||||||
\(324\) | −2160.38 | −0.370435 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 2110.55 | 0.358566 | ||||||||
\(327\) | 1075.86 | 0.181943 | ||||||||
\(328\) | −1083.08 | −0.182326 | ||||||||
\(329\) | 622.854 | 0.104374 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −3551.61 | −0.589771 | −0.294885 | − | 0.955533i | \(-0.595281\pi\) | ||||
−0.294885 | + | 0.955533i | \(0.595281\pi\) | |||||||
\(332\) | 1940.71 | 0.320815 | ||||||||
\(333\) | −1497.57 | −0.246445 | ||||||||
\(334\) | 1463.61 | 0.239776 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 2914.48 | 0.473209 | ||||||||
\(337\) | 7002.99 | 1.13198 | 0.565990 | − | 0.824412i | \(-0.308494\pi\) | ||||
0.565990 | + | 0.824412i | \(0.308494\pi\) | |||||||
\(338\) | −1181.01 | −0.190055 | ||||||||
\(339\) | −9997.29 | −1.60171 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −3626.97 | −0.575987 | ||||||||
\(342\) | 15.2517 | 0.00241146 | ||||||||
\(343\) | 3082.42 | 0.485234 | ||||||||
\(344\) | −4348.22 | −0.681513 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 1043.55 | 0.162143 | ||||||||
\(347\) | 10268.2 | 1.58854 | 0.794272 | − | 0.607562i | \(-0.207852\pi\) | ||||
0.794272 | + | 0.607562i | \(0.207852\pi\) | |||||||
\(348\) | 4243.46 | 0.653659 | ||||||||
\(349\) | 4515.58 | 0.692588 | 0.346294 | − | 0.938126i | \(-0.387440\pi\) | ||||
0.346294 | + | 0.938126i | \(0.387440\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1786.46 | 0.271664 | ||||||||
\(352\) | −1028.33 | −0.155710 | ||||||||
\(353\) | −7838.63 | −1.18189 | −0.590947 | − | 0.806711i | \(-0.701246\pi\) | ||||
−0.590947 | + | 0.806711i | \(0.701246\pi\) | |||||||
\(354\) | −3127.08 | −0.469498 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −4510.84 | −0.671556 | ||||||||
\(357\) | −22981.7 | −3.40705 | ||||||||
\(358\) | −2366.14 | −0.349314 | ||||||||
\(359\) | −12464.8 | −1.83250 | −0.916250 | − | 0.400606i | \(-0.868799\pi\) | ||||
−0.916250 | + | 0.400606i | \(0.868799\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −6858.95 | −0.999992 | ||||||||
\(362\) | 3447.85 | 0.500594 | ||||||||
\(363\) | 2306.32 | 0.333472 | ||||||||
\(364\) | 3777.60 | 0.543956 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −2323.55 | −0.331842 | ||||||||
\(367\) | −3936.14 | −0.559850 | −0.279925 | − | 0.960022i | \(-0.590310\pi\) | ||||
−0.279925 | + | 0.960022i | \(0.590310\pi\) | |||||||
\(368\) | 368.000 | 0.0521286 | ||||||||
\(369\) | −4435.93 | −0.625814 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1029.57 | 0.144077 | ||||||||
\(372\) | −3490.18 | −0.486445 | ||||||||
\(373\) | −1920.72 | −0.266625 | −0.133313 | − | 0.991074i | \(-0.542561\pi\) | ||||
−0.133313 | + | 0.991074i | \(0.542561\pi\) | |||||||
\(374\) | 8108.69 | 1.12110 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −211.475 | −0.0290053 | ||||||||
\(377\) | 5500.15 | 0.751385 | ||||||||
\(378\) | 2100.39 | 0.285800 | ||||||||
\(379\) | −13074.5 | −1.77201 | −0.886004 | − | 0.463678i | \(-0.846530\pi\) | ||||
−0.886004 | + | 0.463678i | \(0.846530\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −10037.9 | −1.34976 | ||||||||
\(382\) | −5596.23 | −0.749550 | ||||||||
\(383\) | −8838.22 | −1.17914 | −0.589571 | − | 0.807716i | \(-0.700703\pi\) | ||||
−0.589571 | + | 0.807716i | \(0.700703\pi\) | |||||||
\(384\) | −989.543 | −0.131504 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 995.372 | 0.131252 | ||||||||
\(387\) | −17808.9 | −2.33922 | ||||||||
\(388\) | 5944.94 | 0.777858 | ||||||||
\(389\) | −12687.3 | −1.65365 | −0.826827 | − | 0.562456i | \(-0.809856\pi\) | ||||
−0.826827 | + | 0.562456i | \(0.809856\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −2901.80 | −0.375321 | ||||||||
\(392\) | 1697.44 | 0.218708 | ||||||||
\(393\) | 4060.58 | 0.521194 | ||||||||
\(394\) | −592.977 | −0.0758218 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −4211.69 | −0.534458 | ||||||||
\(397\) | −8060.49 | −1.01900 | −0.509501 | − | 0.860470i | \(-0.670170\pi\) | ||||
−0.509501 | + | 0.860470i | \(0.670170\pi\) | |||||||
\(398\) | 4694.87 | 0.591287 | ||||||||
\(399\) | 42.3951 | 0.00531932 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 12325.1 | 1.53488 | 0.767440 | − | 0.641121i | \(-0.221530\pi\) | ||||
0.767440 | + | 0.641121i | \(0.221530\pi\) | |||||||
\(402\) | −6505.04 | −0.807070 | ||||||||
\(403\) | −4523.79 | −0.559171 | ||||||||
\(404\) | 7555.43 | 0.930437 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 6466.69 | 0.790483 | ||||||||
\(407\) | 1468.76 | 0.178879 | ||||||||
\(408\) | 7802.87 | 0.946813 | ||||||||
\(409\) | −10806.7 | −1.30650 | −0.653250 | − | 0.757143i | \(-0.726595\pi\) | ||||
−0.653250 | + | 0.757143i | \(0.726595\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −18771.3 | −2.25285 | ||||||||
\(412\) | 5988.67 | 0.716118 | ||||||||
\(413\) | −4765.41 | −0.567774 | ||||||||
\(414\) | 1507.21 | 0.178926 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −1282.59 | −0.151164 | ||||||||
\(417\) | −18990.4 | −2.23013 | ||||||||
\(418\) | −14.9584 | −0.00175033 | ||||||||
\(419\) | −1823.74 | −0.212639 | −0.106319 | − | 0.994332i | \(-0.533907\pi\) | ||||
−0.106319 | + | 0.994332i | \(0.533907\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 5995.43 | 0.694060 | 0.347030 | − | 0.937854i | \(-0.387190\pi\) | ||||
0.347030 | + | 0.937854i | \(0.387190\pi\) | |||||||
\(422\) | 5677.23 | 0.654889 | ||||||||
\(423\) | −866.133 | −0.0995575 | ||||||||
\(424\) | −349.567 | −0.0400388 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −10318.8 | −1.17358 | ||||||||
\(427\) | −3540.91 | −0.401303 | ||||||||
\(428\) | 2340.60 | 0.264339 | ||||||||
\(429\) | −9957.39 | −1.12062 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 3887.80 | 0.434499 | 0.217249 | − | 0.976116i | \(-0.430292\pi\) | ||||
0.217249 | + | 0.976116i | \(0.430292\pi\) | |||||||
\(432\) | −713.137 | −0.0794232 | ||||||||
\(433\) | 4422.93 | 0.490884 | 0.245442 | − | 0.969411i | \(-0.421067\pi\) | ||||
0.245442 | + | 0.969411i | \(0.421067\pi\) | |||||||
\(434\) | −5318.75 | −0.588268 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −556.662 | −0.0611452 | ||||||||
\(437\) | 5.35306 | 0.000585976 0 | ||||||||
\(438\) | 9322.74 | 1.01703 | ||||||||
\(439\) | −1748.08 | −0.190048 | −0.0950242 | − | 0.995475i | \(-0.530293\pi\) | ||||
−0.0950242 | + | 0.995475i | \(0.530293\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 6952.14 | 0.750690 | ||||||||
\(442\) | 10113.7 | 1.08837 | ||||||||
\(443\) | −3371.31 | −0.361571 | −0.180785 | − | 0.983523i | \(-0.557864\pi\) | ||||
−0.180785 | + | 0.983523i | \(0.557864\pi\) | |||||||
\(444\) | 1413.37 | 0.151071 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 4249.37 | 0.451151 | ||||||||
\(447\) | 18595.6 | 1.96766 | ||||||||
\(448\) | −1507.98 | −0.159030 | ||||||||
\(449\) | 13314.7 | 1.39947 | 0.699734 | − | 0.714404i | \(-0.253302\pi\) | ||||
0.699734 | + | 0.714404i | \(0.253302\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 4350.61 | 0.454240 | ||||||||
\(452\) | 5172.70 | 0.538282 | ||||||||
\(453\) | 5019.43 | 0.520603 | ||||||||
\(454\) | −3103.94 | −0.320871 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −14.3942 | −0.00147823 | ||||||||
\(457\) | −3767.20 | −0.385607 | −0.192803 | − | 0.981237i | \(-0.561758\pi\) | ||||
−0.192803 | + | 0.981237i | \(0.561758\pi\) | |||||||
\(458\) | −317.063 | −0.0323480 | ||||||||
\(459\) | 5623.32 | 0.571839 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 9674.06 | 0.977366 | 0.488683 | − | 0.872461i | \(-0.337477\pi\) | ||||
0.488683 | + | 0.872461i | \(0.337477\pi\) | |||||||
\(462\) | −11707.2 | −1.17893 | ||||||||
\(463\) | −2977.73 | −0.298892 | −0.149446 | − | 0.988770i | \(-0.547749\pi\) | ||||
−0.149446 | + | 0.988770i | \(0.547749\pi\) | |||||||
\(464\) | −2195.61 | −0.219674 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 1458.00 | 0.144937 | ||||||||
\(467\) | 10701.0 | 1.06035 | 0.530176 | − | 0.847888i | \(-0.322126\pi\) | ||||
0.530176 | + | 0.847888i | \(0.322126\pi\) | |||||||
\(468\) | −5253.09 | −0.518855 | ||||||||
\(469\) | −9913.16 | −0.976006 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 28333.7 | 2.77187 | ||||||||
\(472\) | 1617.98 | 0.157783 | ||||||||
\(473\) | 17466.4 | 1.69790 | ||||||||
\(474\) | 21319.7 | 2.06592 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 11890.9 | 1.14500 | ||||||||
\(477\) | −1431.71 | −0.137429 | ||||||||
\(478\) | −12403.2 | −1.18684 | ||||||||
\(479\) | 2337.15 | 0.222937 | 0.111469 | − | 0.993768i | \(-0.464445\pi\) | ||||
0.111469 | + | 0.993768i | \(0.464445\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1831.94 | 0.173657 | ||||||||
\(482\) | −14446.1 | −1.36515 | ||||||||
\(483\) | 4189.57 | 0.394683 | ||||||||
\(484\) | −1193.31 | −0.112069 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 10757.6 | 1.00406 | ||||||||
\(487\) | 7183.85 | 0.668442 | 0.334221 | − | 0.942495i | \(-0.391527\pi\) | ||||
0.334221 | + | 0.942495i | \(0.391527\pi\) | |||||||
\(488\) | 1202.23 | 0.111521 | ||||||||
\(489\) | −8158.12 | −0.754443 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −12084.2 | −1.11070 | −0.555350 | − | 0.831617i | \(-0.687416\pi\) | ||||
−0.555350 | + | 0.831617i | \(0.687416\pi\) | |||||||
\(492\) | 4186.53 | 0.383625 | ||||||||
\(493\) | 17313.1 | 1.58163 | ||||||||
\(494\) | −18.6571 | −0.00169923 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 1805.86 | 0.163478 | ||||||||
\(497\) | −15725.0 | −1.41924 | ||||||||
\(498\) | −7501.64 | −0.675013 | ||||||||
\(499\) | 7145.78 | 0.641060 | 0.320530 | − | 0.947238i | \(-0.396139\pi\) | ||||
0.320530 | + | 0.947238i | \(0.396139\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −5657.45 | −0.504503 | ||||||||
\(502\) | 10085.6 | 0.896695 | ||||||||
\(503\) | −20436.2 | −1.81154 | −0.905770 | − | 0.423771i | \(-0.860706\pi\) | ||||
−0.905770 | + | 0.423771i | \(0.860706\pi\) | |||||||
\(504\) | −6176.21 | −0.545854 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −1478.22 | −0.129871 | ||||||||
\(507\) | 4565.10 | 0.399888 | ||||||||
\(508\) | 5193.72 | 0.453610 | ||||||||
\(509\) | 19721.7 | 1.71738 | 0.858690 | − | 0.512495i | \(-0.171279\pi\) | ||||
0.858690 | + | 0.512495i | \(0.171279\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 14207.1 | 1.22991 | ||||||||
\(512\) | 512.000 | 0.0441942 | ||||||||
\(513\) | −10.3735 | −0.000892794 0 | ||||||||
\(514\) | −5962.30 | −0.511646 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 16807.6 | 1.43394 | ||||||||
\(517\) | 849.475 | 0.0722628 | ||||||||
\(518\) | 2153.86 | 0.182693 | ||||||||
\(519\) | −4033.73 | −0.341158 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 3483.23 | 0.292904 | 0.146452 | − | 0.989218i | \(-0.453215\pi\) | ||||
0.146452 | + | 0.989218i | \(0.453215\pi\) | |||||||
\(522\) | −8992.50 | −0.754006 | ||||||||
\(523\) | −15689.0 | −1.31172 | −0.655862 | − | 0.754881i | \(-0.727695\pi\) | ||||
−0.655862 | + | 0.754881i | \(0.727695\pi\) | |||||||
\(524\) | −2100.99 | −0.175157 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −14485.7 | −1.20077 | ||||||||
\(527\) | −14239.8 | −1.17703 | ||||||||
\(528\) | 3974.90 | 0.327624 | ||||||||
\(529\) | 529.000 | 0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 6626.72 | 0.541573 | ||||||||
\(532\) | −21.9357 | −0.00178765 | ||||||||
\(533\) | 5426.36 | 0.440979 | ||||||||
\(534\) | 17436.2 | 1.41299 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 3365.78 | 0.271230 | ||||||||
\(537\) | 9146.09 | 0.734977 | ||||||||
\(538\) | −5135.15 | −0.411510 | ||||||||
\(539\) | −6818.43 | −0.544881 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 7620.73 | 0.605621 | 0.302810 | − | 0.953051i | \(-0.402075\pi\) | ||||
0.302810 | + | 0.953051i | \(0.402075\pi\) | |||||||
\(542\) | 16132.5 | 1.27851 | ||||||||
\(543\) | −13327.3 | −1.05328 | ||||||||
\(544\) | −4037.29 | −0.318194 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −14602.0 | −1.14452 | ||||||||
\(547\) | −5925.62 | −0.463183 | −0.231592 | − | 0.972813i | \(-0.574393\pi\) | ||||
−0.231592 | + | 0.972813i | \(0.574393\pi\) | |||||||
\(548\) | 9712.47 | 0.757109 | ||||||||
\(549\) | 4923.94 | 0.382784 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −31.9381 | −0.00246934 | ||||||||
\(552\) | −1422.47 | −0.109682 | ||||||||
\(553\) | 32489.4 | 2.49836 | ||||||||
\(554\) | −17983.1 | −1.37911 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 9825.85 | 0.749476 | ||||||||
\(557\) | 5456.16 | 0.415054 | 0.207527 | − | 0.978229i | \(-0.433459\pi\) | ||||
0.207527 | + | 0.978229i | \(0.433459\pi\) | |||||||
\(558\) | 7396.20 | 0.561122 | ||||||||
\(559\) | 21785.2 | 1.64833 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −31343.4 | −2.35886 | ||||||||
\(562\) | 1936.26 | 0.145331 | ||||||||
\(563\) | 9194.29 | 0.688265 | 0.344132 | − | 0.938921i | \(-0.388173\pi\) | ||||
0.344132 | + | 0.938921i | \(0.388173\pi\) | |||||||
\(564\) | 817.437 | 0.0610289 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 4505.30 | 0.334580 | ||||||||
\(567\) | 12725.8 | 0.942567 | ||||||||
\(568\) | 5339.05 | 0.394404 | ||||||||
\(569\) | 338.831 | 0.0249640 | 0.0124820 | − | 0.999922i | \(-0.496027\pi\) | ||||
0.0124820 | + | 0.999922i | \(0.496027\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −1725.34 | −0.126451 | −0.0632254 | − | 0.997999i | \(-0.520139\pi\) | ||||
−0.0632254 | + | 0.997999i | \(0.520139\pi\) | |||||||
\(572\) | 5152.06 | 0.376605 | ||||||||
\(573\) | 21631.7 | 1.57710 | ||||||||
\(574\) | 6379.93 | 0.463926 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 2096.98 | 0.151692 | ||||||||
\(577\) | −23300.0 | −1.68109 | −0.840547 | − | 0.541738i | \(-0.817766\pi\) | ||||
−0.840547 | + | 0.541738i | \(0.817766\pi\) | |||||||
\(578\) | 22009.3 | 1.58385 | ||||||||
\(579\) | −3847.52 | −0.276161 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −11431.9 | −0.816307 | ||||||||
\(582\) | −22979.6 | −1.63666 | ||||||||
\(583\) | 1404.18 | 0.0997513 | ||||||||
\(584\) | −4823.68 | −0.341790 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −5468.70 | −0.385512 | ||||||||
\(587\) | −15653.3 | −1.10065 | −0.550325 | − | 0.834950i | \(-0.685496\pi\) | ||||
−0.550325 | + | 0.834950i | \(0.685496\pi\) | |||||||
\(588\) | −6561.28 | −0.460174 | ||||||||
\(589\) | 26.2686 | 0.00183766 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 2292.10 | 0.159533 | ||||||||
\(592\) | −731.292 | −0.0507701 | ||||||||
\(593\) | 2658.08 | 0.184072 | 0.0920358 | − | 0.995756i | \(-0.470663\pi\) | ||||
0.0920358 | + | 0.995756i | \(0.470663\pi\) | |||||||
\(594\) | 2864.60 | 0.197872 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −9621.57 | −0.661266 | ||||||||
\(597\) | −18147.6 | −1.24410 | ||||||||
\(598\) | −1843.73 | −0.126080 | ||||||||
\(599\) | 19417.6 | 1.32451 | 0.662256 | − | 0.749278i | \(-0.269599\pi\) | ||||
0.662256 | + | 0.749278i | \(0.269599\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −18469.0 | −1.25352 | −0.626760 | − | 0.779213i | \(-0.715619\pi\) | ||||
−0.626760 | + | 0.779213i | \(0.715619\pi\) | |||||||
\(602\) | 25613.5 | 1.73410 | ||||||||
\(603\) | 13785.1 | 0.930968 | ||||||||
\(604\) | −2597.10 | −0.174958 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −29204.8 | −1.95770 | ||||||||
\(607\) | −3968.56 | −0.265369 | −0.132684 | − | 0.991158i | \(-0.542360\pi\) | ||||
−0.132684 | + | 0.991158i | \(0.542360\pi\) | |||||||
\(608\) | 7.44773 | 0.000496785 0 | ||||||||
\(609\) | −24996.4 | −1.66322 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1059.52 | 0.0701531 | ||||||||
\(612\) | −16535.4 | −1.09216 | ||||||||
\(613\) | 11478.7 | 0.756311 | 0.378156 | − | 0.925742i | \(-0.376558\pi\) | ||||
0.378156 | + | 0.925742i | \(0.376558\pi\) | |||||||
\(614\) | 15954.2 | 1.04863 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 6057.42 | 0.396202 | ||||||||
\(617\) | 15691.1 | 1.02382 | 0.511911 | − | 0.859039i | \(-0.328938\pi\) | ||||
0.511911 | + | 0.859039i | \(0.328938\pi\) | |||||||
\(618\) | −23148.6 | −1.50676 | ||||||||
\(619\) | −18249.4 | −1.18499 | −0.592494 | − | 0.805575i | \(-0.701856\pi\) | ||||
−0.592494 | + | 0.805575i | \(0.701856\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1025.14 | −0.0662436 | ||||||||
\(622\) | 15458.9 | 0.996533 | ||||||||
\(623\) | 26571.4 | 1.70876 | ||||||||
\(624\) | 4957.75 | 0.318059 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −11012.5 | −0.703111 | ||||||||
\(627\) | 57.8203 | 0.00368281 | ||||||||
\(628\) | −14660.2 | −0.931536 | ||||||||
\(629\) | 5766.48 | 0.365540 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −23528.8 | −1.48442 | −0.742208 | − | 0.670169i | \(-0.766222\pi\) | ||||
−0.742208 | + | 0.670169i | \(0.766222\pi\) | |||||||
\(632\) | −11031.0 | −0.694288 | ||||||||
\(633\) | −21944.8 | −1.37793 | ||||||||
\(634\) | −10462.7 | −0.655408 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 1351.22 | 0.0842441 | ||||||||
\(637\) | −8504.38 | −0.528973 | ||||||||
\(638\) | 8819.55 | 0.547287 | ||||||||
\(639\) | 21867.0 | 1.35375 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 3748.79 | 0.230996 | 0.115498 | − | 0.993308i | \(-0.463154\pi\) | ||||
0.115498 | + | 0.993308i | \(0.463154\pi\) | |||||||
\(642\) | −9047.36 | −0.556185 | ||||||||
\(643\) | −15924.3 | −0.976660 | −0.488330 | − | 0.872659i | \(-0.662394\pi\) | ||||
−0.488330 | + | 0.872659i | \(0.662394\pi\) | |||||||
\(644\) | −2167.73 | −0.132640 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −58.7278 | −0.00357680 | ||||||||
\(647\) | 2854.11 | 0.173426 | 0.0867129 | − | 0.996233i | \(-0.472364\pi\) | ||||
0.0867129 | + | 0.996233i | \(0.472364\pi\) | |||||||
\(648\) | −4320.76 | −0.261937 | ||||||||
\(649\) | −6499.27 | −0.393095 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 20559.1 | 1.23775 | ||||||||
\(652\) | 4221.09 | 0.253544 | ||||||||
\(653\) | −7925.97 | −0.474988 | −0.237494 | − | 0.971389i | \(-0.576326\pi\) | ||||
−0.237494 | + | 0.971389i | \(0.576326\pi\) | |||||||
\(654\) | 2151.72 | 0.128653 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −2166.15 | −0.128924 | ||||||||
\(657\) | −19756.2 | −1.17316 | ||||||||
\(658\) | 1245.71 | 0.0738035 | ||||||||
\(659\) | −5799.43 | −0.342813 | −0.171406 | − | 0.985200i | \(-0.554831\pi\) | ||||
−0.171406 | + | 0.985200i | \(0.554831\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 22324.8 | 1.31367 | 0.656833 | − | 0.754036i | \(-0.271896\pi\) | ||||
0.656833 | + | 0.754036i | \(0.271896\pi\) | |||||||
\(662\) | −7103.22 | −0.417031 | ||||||||
\(663\) | −39093.4 | −2.28999 | ||||||||
\(664\) | 3881.42 | 0.226850 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −2995.13 | −0.174263 | ||||||||
\(667\) | −3156.19 | −0.183221 | ||||||||
\(668\) | 2927.22 | 0.169547 | ||||||||
\(669\) | −16425.5 | −0.949249 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −4829.24 | −0.277840 | ||||||||
\(672\) | 5828.97 | 0.334609 | ||||||||
\(673\) | 23253.5 | 1.33188 | 0.665940 | − | 0.746005i | \(-0.268031\pi\) | ||||
0.665940 | + | 0.746005i | \(0.268031\pi\) | |||||||
\(674\) | 14006.0 | 0.800430 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −2362.03 | −0.134389 | ||||||||
\(677\) | 19003.7 | 1.07884 | 0.539419 | − | 0.842038i | \(-0.318644\pi\) | ||||
0.539419 | + | 0.842038i | \(0.318644\pi\) | |||||||
\(678\) | −19994.6 | −1.13258 | ||||||||
\(679\) | −35019.1 | −1.97925 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 11998.0 | 0.675131 | ||||||||
\(682\) | −7253.94 | −0.407284 | ||||||||
\(683\) | 11222.5 | 0.628722 | 0.314361 | − | 0.949304i | \(-0.398210\pi\) | ||||
0.314361 | + | 0.949304i | \(0.398210\pi\) | |||||||
\(684\) | 30.5035 | 0.00170516 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 6164.85 | 0.343112 | ||||||||
\(687\) | 1225.58 | 0.0680620 | ||||||||
\(688\) | −8696.45 | −0.481902 | ||||||||
\(689\) | 1751.38 | 0.0968391 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 4297.68 | 0.236601 | 0.118301 | − | 0.992978i | \(-0.462255\pi\) | ||||
0.118301 | + | 0.992978i | \(0.462255\pi\) | |||||||
\(692\) | 2087.09 | 0.114652 | ||||||||
\(693\) | 24809.2 | 1.35992 | ||||||||
\(694\) | 20536.4 | 1.12327 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 8486.92 | 0.462206 | ||||||||
\(697\) | 17080.8 | 0.928240 | ||||||||
\(698\) | 9031.15 | 0.489734 | ||||||||
\(699\) | −5635.75 | −0.304955 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 25769.6 | 1.38845 | 0.694225 | − | 0.719758i | \(-0.255747\pi\) | ||||
0.694225 | + | 0.719758i | \(0.255747\pi\) | |||||||
\(702\) | 3572.91 | 0.192095 | ||||||||
\(703\) | −10.6376 | −0.000570705 0 | ||||||||
\(704\) | −2056.65 | −0.110104 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −15677.3 | −0.835725 | ||||||||
\(707\) | −44505.7 | −2.36748 | ||||||||
\(708\) | −6254.15 | −0.331985 | ||||||||
\(709\) | −4900.01 | −0.259554 | −0.129777 | − | 0.991543i | \(-0.541426\pi\) | ||||
−0.129777 | + | 0.991543i | \(0.541426\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −45179.4 | −2.38307 | ||||||||
\(712\) | −9021.67 | −0.474862 | ||||||||
\(713\) | 2595.92 | 0.136350 | ||||||||
\(714\) | −45963.3 | −2.40915 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −4732.28 | −0.247002 | ||||||||
\(717\) | 47943.4 | 2.49718 | ||||||||
\(718\) | −24929.6 | −1.29577 | ||||||||
\(719\) | 7631.85 | 0.395855 | 0.197928 | − | 0.980217i | \(-0.436579\pi\) | ||||
0.197928 | + | 0.980217i | \(0.436579\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −35276.6 | −1.82215 | ||||||||
\(722\) | −13717.9 | −0.707101 | ||||||||
\(723\) | 55839.9 | 2.87235 | ||||||||
\(724\) | 6895.70 | 0.353973 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 4612.64 | 0.235800 | ||||||||
\(727\) | 36985.6 | 1.88682 | 0.943410 | − | 0.331628i | \(-0.107598\pi\) | ||||
0.943410 | + | 0.331628i | \(0.107598\pi\) | |||||||
\(728\) | 7555.20 | 0.384635 | ||||||||
\(729\) | −26999.8 | −1.37173 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 68574.3 | 3.46965 | ||||||||
\(732\) | −4647.10 | −0.234647 | ||||||||
\(733\) | 22227.3 | 1.12003 | 0.560015 | − | 0.828482i | \(-0.310795\pi\) | ||||
0.560015 | + | 0.828482i | \(0.310795\pi\) | |||||||
\(734\) | −7872.29 | −0.395874 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 736.000 | 0.0368605 | ||||||||
\(737\) | −13520.0 | −0.675733 | ||||||||
\(738\) | −8871.86 | −0.442517 | ||||||||
\(739\) | −17899.1 | −0.890974 | −0.445487 | − | 0.895288i | \(-0.646970\pi\) | ||||
−0.445487 | + | 0.895288i | \(0.646970\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 72.1171 | 0.00357529 | ||||||||
\(742\) | 2059.14 | 0.101878 | ||||||||
\(743\) | 29843.4 | 1.47355 | 0.736776 | − | 0.676137i | \(-0.236347\pi\) | ||||
0.736776 | + | 0.676137i | \(0.236347\pi\) | |||||||
\(744\) | −6980.36 | −0.343968 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −3841.44 | −0.188532 | ||||||||
\(747\) | 15897.0 | 0.778638 | ||||||||
\(748\) | 16217.4 | 0.792736 | ||||||||
\(749\) | −13787.4 | −0.672606 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −9399.65 | −0.456722 | −0.228361 | − | 0.973577i | \(-0.573337\pi\) | ||||
−0.228361 | + | 0.973577i | \(0.573337\pi\) | |||||||
\(752\) | −422.950 | −0.0205098 | ||||||||
\(753\) | −38984.8 | −1.88670 | ||||||||
\(754\) | 11000.3 | 0.531309 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 4200.78 | 0.202091 | ||||||||
\(757\) | −29871.6 | −1.43422 | −0.717109 | − | 0.696961i | \(-0.754535\pi\) | ||||
−0.717109 | + | 0.696961i | \(0.754535\pi\) | |||||||
\(758\) | −26149.0 | −1.25300 | ||||||||
\(759\) | 5713.92 | 0.273257 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −273.955 | −0.0130497 | −0.00652487 | − | 0.999979i | \(-0.502077\pi\) | ||||
−0.00652487 | + | 0.999979i | \(0.502077\pi\) | |||||||
\(762\) | −20075.8 | −0.954423 | ||||||||
\(763\) | 3279.05 | 0.155583 | ||||||||
\(764\) | −11192.5 | −0.530012 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −17676.4 | −0.833780 | ||||||||
\(767\) | −8106.31 | −0.381619 | ||||||||
\(768\) | −1979.09 | −0.0929872 | ||||||||
\(769\) | −13273.8 | −0.622450 | −0.311225 | − | 0.950336i | \(-0.600739\pi\) | ||||
−0.311225 | + | 0.950336i | \(0.600739\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 23046.7 | 1.07653 | ||||||||
\(772\) | 1990.74 | 0.0928089 | ||||||||
\(773\) | −34161.1 | −1.58951 | −0.794753 | − | 0.606933i | \(-0.792400\pi\) | ||||
−0.794753 | + | 0.606933i | \(0.792400\pi\) | |||||||
\(774\) | −35617.8 | −1.65408 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 11889.9 | 0.550028 | ||||||||
\(777\) | −8325.54 | −0.384398 | ||||||||
\(778\) | −25374.6 | −1.16931 | ||||||||
\(779\) | −31.5096 | −0.00144923 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −21446.4 | −0.982603 | ||||||||
\(782\) | −5803.60 | −0.265392 | ||||||||
\(783\) | 6116.29 | 0.279155 | ||||||||
\(784\) | 3394.87 | 0.154650 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 8121.17 | 0.368540 | ||||||||
\(787\) | 38489.6 | 1.74334 | 0.871669 | − | 0.490095i | \(-0.163038\pi\) | ||||
0.871669 | + | 0.490095i | \(0.163038\pi\) | |||||||
\(788\) | −1185.95 | −0.0536141 | ||||||||
\(789\) | 55993.2 | 2.52650 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −30470.1 | −1.36965 | ||||||||
\(792\) | −8423.38 | −0.377919 | ||||||||
\(793\) | −6023.33 | −0.269729 | ||||||||
\(794\) | −16121.0 | −0.720544 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 9389.73 | 0.418103 | ||||||||
\(797\) | −17176.8 | −0.763405 | −0.381702 | − | 0.924285i | \(-0.624662\pi\) | ||||
−0.381702 | + | 0.924285i | \(0.624662\pi\) | |||||||
\(798\) | 84.7902 | 0.00376133 | ||||||||
\(799\) | 3335.10 | 0.147669 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −36949.8 | −1.62991 | ||||||||
\(802\) | 24650.2 | 1.08532 | ||||||||
\(803\) | 19376.2 | 0.851523 | ||||||||
\(804\) | −13010.1 | −0.570684 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −9047.58 | −0.395394 | ||||||||
\(807\) | 19849.4 | 0.865841 | ||||||||
\(808\) | 15110.9 | 0.657918 | ||||||||
\(809\) | 8226.61 | 0.357518 | 0.178759 | − | 0.983893i | \(-0.442792\pi\) | ||||
0.178759 | + | 0.983893i | \(0.442792\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 27867.9 | 1.20662 | 0.603312 | − | 0.797505i | \(-0.293847\pi\) | ||||
0.603312 | + | 0.797505i | \(0.293847\pi\) | |||||||
\(812\) | 12933.4 | 0.558956 | ||||||||
\(813\) | −62358.8 | −2.69006 | ||||||||
\(814\) | 2937.53 | 0.126487 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 15605.7 | 0.669498 | ||||||||
\(817\) | −126.502 | −0.00541705 | ||||||||
\(818\) | −21613.5 | −0.923835 | ||||||||
\(819\) | 30943.6 | 1.32022 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −17637.5 | −0.749761 | −0.374880 | − | 0.927073i | \(-0.622316\pi\) | ||||
−0.374880 | + | 0.927073i | \(0.622316\pi\) | |||||||
\(822\) | −37542.6 | −1.59300 | ||||||||
\(823\) | −28048.6 | −1.18799 | −0.593993 | − | 0.804470i | \(-0.702449\pi\) | ||||
−0.593993 | + | 0.804470i | \(0.702449\pi\) | |||||||
\(824\) | 11977.3 | 0.506372 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −9530.82 | −0.401477 | ||||||||
\(827\) | 32592.9 | 1.37046 | 0.685228 | − | 0.728329i | \(-0.259703\pi\) | ||||
0.685228 | + | 0.728329i | \(0.259703\pi\) | |||||||
\(828\) | 3014.42 | 0.126520 | ||||||||
\(829\) | 18815.9 | 0.788303 | 0.394152 | − | 0.919045i | \(-0.371038\pi\) | ||||
0.394152 | + | 0.919045i | \(0.371038\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 69511.9 | 2.90173 | ||||||||
\(832\) | −2565.19 | −0.106889 | ||||||||
\(833\) | −26769.7 | −1.11346 | ||||||||
\(834\) | −37980.9 | −1.57694 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −29.9168 | −0.00123767 | ||||||||
\(837\) | −5030.56 | −0.207744 | ||||||||
\(838\) | −3647.48 | −0.150358 | ||||||||
\(839\) | 7612.72 | 0.313254 | 0.156627 | − | 0.987658i | \(-0.449938\pi\) | ||||
0.156627 | + | 0.987658i | \(0.449938\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −5558.14 | −0.227896 | ||||||||
\(842\) | 11990.9 | 0.490775 | ||||||||
\(843\) | −7484.43 | −0.305786 | ||||||||
\(844\) | 11354.5 | 0.463076 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −1732.27 | −0.0703978 | ||||||||
\(847\) | 7029.28 | 0.285158 | ||||||||
\(848\) | −699.134 | −0.0283117 | ||||||||
\(849\) | −17414.8 | −0.703975 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −1051.23 | −0.0423452 | ||||||||
\(852\) | −20637.6 | −0.829849 | ||||||||
\(853\) | 31421.4 | 1.26125 | 0.630627 | − | 0.776086i | \(-0.282798\pi\) | ||||
0.630627 | + | 0.776086i | \(0.282798\pi\) | |||||||
\(854\) | −7081.81 | −0.283764 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 4681.20 | 0.186916 | ||||||||
\(857\) | −20909.5 | −0.833435 | −0.416718 | − | 0.909036i | \(-0.636820\pi\) | ||||
−0.416718 | + | 0.909036i | \(0.636820\pi\) | |||||||
\(858\) | −19914.8 | −0.792400 | ||||||||
\(859\) | 23304.5 | 0.925655 | 0.462828 | − | 0.886448i | \(-0.346835\pi\) | ||||
0.462828 | + | 0.886448i | \(0.346835\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −24661.0 | −0.976127 | ||||||||
\(862\) | 7775.61 | 0.307237 | ||||||||
\(863\) | 19146.3 | 0.755211 | 0.377606 | − | 0.925966i | \(-0.376747\pi\) | ||||
0.377606 | + | 0.925966i | \(0.376747\pi\) | |||||||
\(864\) | −1426.27 | −0.0561607 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 8845.87 | 0.347107 | ||||||||
\(867\) | −85075.0 | −3.33252 | ||||||||
\(868\) | −10637.5 | −0.415968 | ||||||||
\(869\) | 44310.5 | 1.72972 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −16863.0 | −0.656005 | ||||||||
\(872\) | −1113.32 | −0.0432362 | ||||||||
\(873\) | 48697.1 | 1.88791 | ||||||||
\(874\) | 10.7061 | 0.000414347 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 18645.5 | 0.719146 | ||||||||
\(877\) | −31389.0 | −1.20859 | −0.604293 | − | 0.796762i | \(-0.706544\pi\) | ||||
−0.604293 | + | 0.796762i | \(0.706544\pi\) | |||||||
\(878\) | −3496.16 | −0.134384 | ||||||||
\(879\) | 21138.7 | 0.811139 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 44496.3 | 1.70161 | 0.850806 | − | 0.525480i | \(-0.176114\pi\) | ||||
0.850806 | + | 0.525480i | \(0.176114\pi\) | |||||||
\(882\) | 13904.3 | 0.530818 | ||||||||
\(883\) | −8906.65 | −0.339448 | −0.169724 | − | 0.985492i | \(-0.554288\pi\) | ||||
−0.169724 | + | 0.985492i | \(0.554288\pi\) | |||||||
\(884\) | 20227.4 | 0.769592 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −6742.62 | −0.255669 | ||||||||
\(887\) | 36584.7 | 1.38489 | 0.692444 | − | 0.721472i | \(-0.256534\pi\) | ||||
0.692444 | + | 0.721472i | \(0.256534\pi\) | |||||||
\(888\) | 2826.74 | 0.106823 | ||||||||
\(889\) | −30593.9 | −1.15420 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 17356.1 | 0.652581 | ||||||||
\(892\) | 8498.74 | 0.319012 | ||||||||
\(893\) | −6.15238 | −0.000230551 0 | ||||||||
\(894\) | 37191.2 | 1.39134 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −3015.97 | −0.112451 | ||||||||
\(897\) | 7126.76 | 0.265279 | ||||||||
\(898\) | 26629.5 | 0.989573 | ||||||||
\(899\) | −15488.1 | −0.574591 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 5512.90 | 0.203842 | ||||||||
\(902\) | 8701.23 | 0.321197 | ||||||||
\(903\) | −99006.4 | −3.64865 | ||||||||
\(904\) | 10345.4 | 0.380623 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 10038.9 | 0.368122 | ||||||||
\(907\) | 21346.1 | 0.781463 | 0.390731 | − | 0.920505i | \(-0.372222\pi\) | ||||
0.390731 | + | 0.920505i | \(0.372222\pi\) | |||||||
\(908\) | −6207.89 | −0.226890 | ||||||||
\(909\) | 61889.1 | 2.25823 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −10208.0 | −0.371246 | −0.185623 | − | 0.982621i | \(-0.559430\pi\) | ||||
−0.185623 | + | 0.982621i | \(0.559430\pi\) | |||||||
\(912\) | −28.7885 | −0.00104527 | ||||||||
\(913\) | −15591.3 | −0.565166 | ||||||||
\(914\) | −7534.40 | −0.272665 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −634.125 | −0.0228735 | ||||||||
\(917\) | 12376.0 | 0.445683 | ||||||||
\(918\) | 11246.6 | 0.404351 | ||||||||
\(919\) | 1758.00 | 0.0631025 | 0.0315513 | − | 0.999502i | \(-0.489955\pi\) | ||||
0.0315513 | + | 0.999502i | \(0.489955\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −61669.3 | −2.20638 | ||||||||
\(922\) | 19348.1 | 0.691102 | ||||||||
\(923\) | −26749.3 | −0.953917 | ||||||||
\(924\) | −23414.4 | −0.833633 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −5955.46 | −0.211348 | ||||||||
\(927\) | 49055.3 | 1.73807 | ||||||||
\(928\) | −4391.22 | −0.155333 | ||||||||
\(929\) | −845.008 | −0.0298426 | −0.0149213 | − | 0.999889i | \(-0.504750\pi\) | ||||
−0.0149213 | + | 0.999889i | \(0.504750\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 49.3830 | 0.00173841 | ||||||||
\(932\) | 2915.99 | 0.102486 | ||||||||
\(933\) | −59754.7 | −2.09676 | ||||||||
\(934\) | 21402.0 | 0.749782 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −10506.2 | −0.366886 | ||||||||
\(937\) | −3851.61 | −0.134287 | −0.0671433 | − | 0.997743i | \(-0.521388\pi\) | ||||
−0.0671433 | + | 0.997743i | \(0.521388\pi\) | |||||||
\(938\) | −19826.3 | −0.690141 | ||||||||
\(939\) | 42567.7 | 1.47939 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −4379.36 | −0.151714 | −0.0758571 | − | 0.997119i | \(-0.524169\pi\) | ||||
−0.0758571 | + | 0.997119i | \(0.524169\pi\) | |||||||
\(942\) | 56667.5 | 1.96001 | ||||||||
\(943\) | −3113.85 | −0.107530 | ||||||||
\(944\) | 3235.96 | 0.111570 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 34932.8 | 1.20059 | ||||||||
\(947\) | −29746.9 | −1.02074 | −0.510371 | − | 0.859954i | \(-0.670492\pi\) | ||||
−0.510371 | + | 0.859954i | \(0.670492\pi\) | |||||||
\(948\) | 42639.3 | 1.46082 | ||||||||
\(949\) | 24167.3 | 0.826663 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 40442.7 | 1.37902 | ||||||||
\(952\) | 23781.9 | 0.809638 | ||||||||
\(953\) | −4306.61 | −0.146385 | −0.0731924 | − | 0.997318i | \(-0.523319\pi\) | ||||
−0.0731924 | + | 0.997318i | \(0.523319\pi\) | |||||||
\(954\) | −2863.42 | −0.0971769 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −24806.4 | −0.839222 | ||||||||
\(957\) | −34091.1 | −1.15152 | ||||||||
\(958\) | 4674.29 | 0.157640 | ||||||||
\(959\) | −57211.9 | −1.92645 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −17052.3 | −0.572397 | ||||||||
\(962\) | 3663.87 | 0.122794 | ||||||||
\(963\) | 19172.7 | 0.641568 | ||||||||
\(964\) | −28892.2 | −0.965305 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 8379.14 | 0.279083 | ||||||||
\(967\) | 12233.4 | 0.406824 | 0.203412 | − | 0.979093i | \(-0.434797\pi\) | ||||
0.203412 | + | 0.979093i | \(0.434797\pi\) | |||||||
\(968\) | −2386.63 | −0.0792449 | ||||||||
\(969\) | 227.007 | 0.00752581 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 48207.7 | 1.59326 | 0.796631 | − | 0.604465i | \(-0.206613\pi\) | ||||
0.796631 | + | 0.604465i | \(0.206613\pi\) | |||||||
\(972\) | 21515.2 | 0.709978 | ||||||||
\(973\) | −57879.8 | −1.90703 | ||||||||
\(974\) | 14367.7 | 0.472660 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 2404.46 | 0.0788575 | ||||||||
\(977\) | −28662.9 | −0.938595 | −0.469298 | − | 0.883040i | \(-0.655493\pi\) | ||||
−0.469298 | + | 0.883040i | \(0.655493\pi\) | |||||||
\(978\) | −16316.2 | −0.533472 | ||||||||
\(979\) | 36239.2 | 1.18305 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −4559.81 | −0.148403 | ||||||||
\(982\) | −24168.4 | −0.785383 | ||||||||
\(983\) | 20944.1 | 0.679567 | 0.339783 | − | 0.940504i | \(-0.389646\pi\) | ||||
0.339783 | + | 0.940504i | \(0.389646\pi\) | |||||||
\(984\) | 8373.06 | 0.271264 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 34626.2 | 1.11838 | ||||||||
\(987\) | −4815.16 | −0.155287 | ||||||||
\(988\) | −37.3141 | −0.00120154 | ||||||||
\(989\) | −12501.1 | −0.401934 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −36440.2 | −1.16808 | −0.584038 | − | 0.811727i | \(-0.698528\pi\) | ||||
−0.584038 | + | 0.811727i | \(0.698528\pi\) | |||||||
\(992\) | 3611.71 | 0.115597 | ||||||||
\(993\) | 27456.8 | 0.877458 | ||||||||
\(994\) | −31450.0 | −1.00355 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −15003.3 | −0.477306 | ||||||||
\(997\) | 11945.0 | 0.379439 | 0.189720 | − | 0.981838i | \(-0.439242\pi\) | ||||
0.189720 | + | 0.981838i | \(0.439242\pi\) | |||||||
\(998\) | 14291.6 | 0.453298 | ||||||||
\(999\) | 2037.15 | 0.0645172 |
(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 | 1150.4.a.p.1.1 | 4 | ||
5.2 | odd | 4 | 1150.4.b.n.599.8 | 8 | |||
5.3 | odd | 4 | 1150.4.b.n.599.1 | 8 | |||
5.4 | even | 2 | 230.4.a.h.1.4 | ✓ | 4 | ||
15.14 | odd | 2 | 2070.4.a.bj.1.3 | 4 | |||
20.19 | odd | 2 | 1840.4.a.m.1.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
230.4.a.h.1.4 | ✓ | 4 | 5.4 | even | 2 | ||
1150.4.a.p.1.1 | 4 | 1.1 | even | 1 | trivial | ||
1150.4.b.n.599.1 | 8 | 5.3 | odd | 4 | |||
1150.4.b.n.599.8 | 8 | 5.2 | odd | 4 | |||
1840.4.a.m.1.1 | 4 | 20.19 | odd | 2 | |||
2070.4.a.bj.1.3 | 4 | 15.14 | odd | 2 |