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: | \(30\) |
Twist minimal: | no (minimal twist has level 43) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.9 | ||
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.89826 | −1.02469 | −0.512346 | − | 0.858779i | \(-0.671223\pi\) | ||||
−0.512346 | + | 0.858779i | \(0.671223\pi\) | |||||||
\(3\) | 6.20542 | 1.19423 | 0.597117 | − | 0.802154i | \(-0.296313\pi\) | ||||
0.597117 | + | 0.802154i | \(0.296313\pi\) | |||||||
\(4\) | 0.399940 | 0.0499925 | ||||||||
\(5\) | −21.5042 | −1.92339 | −0.961697 | − | 0.274113i | \(-0.911616\pi\) | ||||
−0.961697 | + | 0.274113i | \(0.911616\pi\) | |||||||
\(6\) | −17.9850 | −1.22372 | ||||||||
\(7\) | −25.5918 | −1.38183 | −0.690913 | − | 0.722938i | \(-0.742791\pi\) | ||||
−0.690913 | + | 0.722938i | \(0.742791\pi\) | |||||||
\(8\) | 22.0270 | 0.973465 | ||||||||
\(9\) | 11.5073 | 0.426195 | ||||||||
\(10\) | 62.3249 | 1.97089 | ||||||||
\(11\) | −44.3020 | −1.21432 | −0.607161 | − | 0.794579i | \(-0.707692\pi\) | ||||
−0.607161 | + | 0.794579i | \(0.707692\pi\) | |||||||
\(12\) | 2.48179 | 0.0597027 | ||||||||
\(13\) | 22.5787 | 0.481708 | 0.240854 | − | 0.970561i | \(-0.422573\pi\) | ||||
0.240854 | + | 0.970561i | \(0.422573\pi\) | |||||||
\(14\) | 74.1718 | 1.41595 | ||||||||
\(15\) | −133.443 | −2.29698 | ||||||||
\(16\) | −67.0396 | −1.04749 | ||||||||
\(17\) | −32.0183 | −0.456799 | −0.228400 | − | 0.973567i | \(-0.573349\pi\) | ||||
−0.228400 | + | 0.973567i | \(0.573349\pi\) | |||||||
\(18\) | −33.3511 | −0.436718 | ||||||||
\(19\) | 76.6633 | 0.925673 | 0.462836 | − | 0.886444i | \(-0.346832\pi\) | ||||
0.462836 | + | 0.886444i | \(0.346832\pi\) | |||||||
\(20\) | −8.60039 | −0.0961552 | ||||||||
\(21\) | −158.808 | −1.65022 | ||||||||
\(22\) | 128.399 | 1.24431 | ||||||||
\(23\) | 50.4034 | 0.456949 | 0.228475 | − | 0.973550i | \(-0.426626\pi\) | ||||
0.228475 | + | 0.973550i | \(0.426626\pi\) | |||||||
\(24\) | 136.687 | 1.16254 | ||||||||
\(25\) | 337.431 | 2.69945 | ||||||||
\(26\) | −65.4390 | −0.493602 | ||||||||
\(27\) | −96.1390 | −0.685258 | ||||||||
\(28\) | −10.2352 | −0.0690809 | ||||||||
\(29\) | 52.0400 | 0.333227 | 0.166614 | − | 0.986022i | \(-0.446717\pi\) | ||||
0.166614 | + | 0.986022i | \(0.446717\pi\) | |||||||
\(30\) | 386.752 | 2.35370 | ||||||||
\(31\) | 267.978 | 1.55259 | 0.776296 | − | 0.630369i | \(-0.217096\pi\) | ||||
0.776296 | + | 0.630369i | \(0.217096\pi\) | |||||||
\(32\) | 18.0825 | 0.0998927 | ||||||||
\(33\) | −274.912 | −1.45019 | ||||||||
\(34\) | 92.7976 | 0.468078 | ||||||||
\(35\) | 550.331 | 2.65780 | ||||||||
\(36\) | 4.60221 | 0.0213065 | ||||||||
\(37\) | −73.1460 | −0.325004 | −0.162502 | − | 0.986708i | \(-0.551956\pi\) | ||||
−0.162502 | + | 0.986708i | \(0.551956\pi\) | |||||||
\(38\) | −222.191 | −0.948529 | ||||||||
\(39\) | 140.110 | 0.575272 | ||||||||
\(40\) | −473.673 | −1.87236 | ||||||||
\(41\) | 128.420 | 0.489167 | 0.244584 | − | 0.969628i | \(-0.421349\pi\) | ||||
0.244584 | + | 0.969628i | \(0.421349\pi\) | |||||||
\(42\) | 460.267 | 1.69097 | ||||||||
\(43\) | 0 | 0 | ||||||||
\(44\) | −17.7181 | −0.0607070 | ||||||||
\(45\) | −247.454 | −0.819740 | ||||||||
\(46\) | −146.082 | −0.468232 | ||||||||
\(47\) | 158.149 | 0.490816 | 0.245408 | − | 0.969420i | \(-0.421078\pi\) | ||||
0.245408 | + | 0.969420i | \(0.421078\pi\) | |||||||
\(48\) | −416.009 | −1.25095 | ||||||||
\(49\) | 311.939 | 0.909443 | ||||||||
\(50\) | −977.964 | −2.76610 | ||||||||
\(51\) | −198.687 | −0.545525 | ||||||||
\(52\) | 9.03011 | 0.0240818 | ||||||||
\(53\) | −419.186 | −1.08641 | −0.543204 | − | 0.839601i | \(-0.682789\pi\) | ||||
−0.543204 | + | 0.839601i | \(0.682789\pi\) | |||||||
\(54\) | 278.636 | 0.702178 | ||||||||
\(55\) | 952.679 | 2.33562 | ||||||||
\(56\) | −563.710 | −1.34516 | ||||||||
\(57\) | 475.728 | 1.10547 | ||||||||
\(58\) | −150.826 | −0.341455 | ||||||||
\(59\) | 208.681 | 0.460474 | 0.230237 | − | 0.973135i | \(-0.426050\pi\) | ||||
0.230237 | + | 0.973135i | \(0.426050\pi\) | |||||||
\(60\) | −53.3690 | −0.114832 | ||||||||
\(61\) | −307.109 | −0.644610 | −0.322305 | − | 0.946636i | \(-0.604458\pi\) | ||||
−0.322305 | + | 0.946636i | \(0.604458\pi\) | |||||||
\(62\) | −776.672 | −1.59093 | ||||||||
\(63\) | −294.491 | −0.588927 | ||||||||
\(64\) | 483.909 | 0.945134 | ||||||||
\(65\) | −485.537 | −0.926514 | ||||||||
\(66\) | 796.769 | 1.48599 | ||||||||
\(67\) | 345.123 | 0.629305 | 0.314653 | − | 0.949207i | \(-0.398112\pi\) | ||||
0.314653 | + | 0.949207i | \(0.398112\pi\) | |||||||
\(68\) | −12.8054 | −0.0228365 | ||||||||
\(69\) | 312.774 | 0.545704 | ||||||||
\(70\) | −1595.00 | −2.72342 | ||||||||
\(71\) | 399.163 | 0.667210 | 0.333605 | − | 0.942713i | \(-0.391735\pi\) | ||||
0.333605 | + | 0.942713i | \(0.391735\pi\) | |||||||
\(72\) | 253.470 | 0.414885 | ||||||||
\(73\) | 87.7114 | 0.140628 | 0.0703140 | − | 0.997525i | \(-0.477600\pi\) | ||||
0.0703140 | + | 0.997525i | \(0.477600\pi\) | |||||||
\(74\) | 211.997 | 0.333028 | ||||||||
\(75\) | 2093.90 | 3.22377 | ||||||||
\(76\) | 30.6607 | 0.0462766 | ||||||||
\(77\) | 1133.77 | 1.67798 | ||||||||
\(78\) | −406.077 | −0.589476 | ||||||||
\(79\) | 221.031 | 0.314783 | 0.157392 | − | 0.987536i | \(-0.449692\pi\) | ||||
0.157392 | + | 0.987536i | \(0.449692\pi\) | |||||||
\(80\) | 1441.63 | 2.01474 | ||||||||
\(81\) | −907.279 | −1.24455 | ||||||||
\(82\) | −372.196 | −0.501246 | ||||||||
\(83\) | 433.834 | 0.573729 | 0.286864 | − | 0.957971i | \(-0.407387\pi\) | ||||
0.286864 | + | 0.957971i | \(0.407387\pi\) | |||||||
\(84\) | −63.5135 | −0.0824987 | ||||||||
\(85\) | 688.529 | 0.878605 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 322.930 | 0.397951 | ||||||||
\(88\) | −975.839 | −1.18210 | ||||||||
\(89\) | 18.7214 | 0.0222973 | 0.0111487 | − | 0.999938i | \(-0.496451\pi\) | ||||
0.0111487 | + | 0.999938i | \(0.496451\pi\) | |||||||
\(90\) | 717.188 | 0.839981 | ||||||||
\(91\) | −577.829 | −0.665636 | ||||||||
\(92\) | 20.1583 | 0.0228440 | ||||||||
\(93\) | 1662.92 | 1.85416 | ||||||||
\(94\) | −458.357 | −0.502935 | ||||||||
\(95\) | −1648.58 | −1.78043 | ||||||||
\(96\) | 112.210 | 0.119295 | ||||||||
\(97\) | 334.287 | 0.349914 | 0.174957 | − | 0.984576i | \(-0.444021\pi\) | ||||
0.174957 | + | 0.984576i | \(0.444021\pi\) | |||||||
\(98\) | −904.082 | −0.931899 | ||||||||
\(99\) | −509.794 | −0.517538 | ||||||||
\(100\) | 134.952 | 0.134952 | ||||||||
\(101\) | −1303.49 | −1.28418 | −0.642091 | − | 0.766629i | \(-0.721933\pi\) | ||||
−0.642091 | + | 0.766629i | \(0.721933\pi\) | |||||||
\(102\) | 575.848 | 0.558995 | ||||||||
\(103\) | 2084.38 | 1.99398 | 0.996992 | − | 0.0775103i | \(-0.0246971\pi\) | ||||
0.996992 | + | 0.0775103i | \(0.0246971\pi\) | |||||||
\(104\) | 497.340 | 0.468925 | ||||||||
\(105\) | 3415.04 | 3.17403 | ||||||||
\(106\) | 1214.91 | 1.11323 | ||||||||
\(107\) | 824.744 | 0.745150 | 0.372575 | − | 0.928002i | \(-0.378475\pi\) | ||||
0.372575 | + | 0.928002i | \(0.378475\pi\) | |||||||
\(108\) | −38.4498 | −0.0342577 | ||||||||
\(109\) | −1574.34 | −1.38344 | −0.691719 | − | 0.722166i | \(-0.743146\pi\) | ||||
−0.691719 | + | 0.722166i | \(0.743146\pi\) | |||||||
\(110\) | −2761.12 | −2.39329 | ||||||||
\(111\) | −453.902 | −0.388130 | ||||||||
\(112\) | 1715.66 | 1.44745 | ||||||||
\(113\) | −1504.81 | −1.25275 | −0.626374 | − | 0.779523i | \(-0.715462\pi\) | ||||
−0.626374 | + | 0.779523i | \(0.715462\pi\) | |||||||
\(114\) | −1378.79 | −1.13277 | ||||||||
\(115\) | −1083.89 | −0.878894 | ||||||||
\(116\) | 20.8129 | 0.0166588 | ||||||||
\(117\) | 259.819 | 0.205301 | ||||||||
\(118\) | −604.813 | −0.471844 | ||||||||
\(119\) | 819.406 | 0.631217 | ||||||||
\(120\) | −2939.34 | −2.23603 | ||||||||
\(121\) | 631.665 | 0.474579 | ||||||||
\(122\) | 890.082 | 0.660527 | ||||||||
\(123\) | 796.901 | 0.584180 | ||||||||
\(124\) | 107.175 | 0.0776179 | ||||||||
\(125\) | −4568.16 | −3.26871 | ||||||||
\(126\) | 853.513 | 0.603468 | ||||||||
\(127\) | 228.899 | 0.159933 | 0.0799667 | − | 0.996798i | \(-0.474519\pi\) | ||||
0.0799667 | + | 0.996798i | \(0.474519\pi\) | |||||||
\(128\) | −1547.16 | −1.06836 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 1407.21 | 0.949391 | ||||||||
\(131\) | −398.299 | −0.265646 | −0.132823 | − | 0.991140i | \(-0.542404\pi\) | ||||
−0.132823 | + | 0.991140i | \(0.542404\pi\) | |||||||
\(132\) | −109.948 | −0.0724983 | ||||||||
\(133\) | −1961.95 | −1.27912 | ||||||||
\(134\) | −1000.26 | −0.644844 | ||||||||
\(135\) | 2067.39 | 1.31802 | ||||||||
\(136\) | −705.268 | −0.444678 | ||||||||
\(137\) | −1309.27 | −0.816488 | −0.408244 | − | 0.912873i | \(-0.633859\pi\) | ||||
−0.408244 | + | 0.912873i | \(0.633859\pi\) | |||||||
\(138\) | −906.503 | −0.559179 | ||||||||
\(139\) | 1333.29 | 0.813583 | 0.406791 | − | 0.913521i | \(-0.366648\pi\) | ||||
0.406791 | + | 0.913521i | \(0.366648\pi\) | |||||||
\(140\) | 220.099 | 0.132870 | ||||||||
\(141\) | 981.379 | 0.586149 | ||||||||
\(142\) | −1156.88 | −0.683684 | ||||||||
\(143\) | −1000.28 | −0.584949 | ||||||||
\(144\) | −771.441 | −0.446436 | ||||||||
\(145\) | −1119.08 | −0.640927 | ||||||||
\(146\) | −254.211 | −0.144100 | ||||||||
\(147\) | 1935.71 | 1.08609 | ||||||||
\(148\) | −29.2540 | −0.0162477 | ||||||||
\(149\) | −1890.48 | −1.03943 | −0.519713 | − | 0.854341i | \(-0.673961\pi\) | ||||
−0.519713 | + | 0.854341i | \(0.673961\pi\) | |||||||
\(150\) | −6068.68 | −3.30337 | ||||||||
\(151\) | −2113.98 | −1.13929 | −0.569647 | − | 0.821889i | \(-0.692920\pi\) | ||||
−0.569647 | + | 0.821889i | \(0.692920\pi\) | |||||||
\(152\) | 1688.66 | 0.901109 | ||||||||
\(153\) | −368.443 | −0.194685 | ||||||||
\(154\) | −3285.96 | −1.71941 | ||||||||
\(155\) | −5762.66 | −2.98625 | ||||||||
\(156\) | 56.0356 | 0.0287592 | ||||||||
\(157\) | 1264.21 | 0.642643 | 0.321322 | − | 0.946970i | \(-0.395873\pi\) | ||||
0.321322 | + | 0.946970i | \(0.395873\pi\) | |||||||
\(158\) | −640.605 | −0.322556 | ||||||||
\(159\) | −2601.22 | −1.29742 | ||||||||
\(160\) | −388.850 | −0.192133 | ||||||||
\(161\) | −1289.91 | −0.631425 | ||||||||
\(162\) | 2629.53 | 1.27528 | ||||||||
\(163\) | 42.9125 | 0.0206206 | 0.0103103 | − | 0.999947i | \(-0.496718\pi\) | ||||
0.0103103 | + | 0.999947i | \(0.496718\pi\) | |||||||
\(164\) | 51.3603 | 0.0244547 | ||||||||
\(165\) | 5911.77 | 2.78928 | ||||||||
\(166\) | −1257.37 | −0.587895 | ||||||||
\(167\) | 2337.25 | 1.08301 | 0.541503 | − | 0.840699i | \(-0.317855\pi\) | ||||
0.541503 | + | 0.840699i | \(0.317855\pi\) | |||||||
\(168\) | −3498.06 | −1.60643 | ||||||||
\(169\) | −1687.20 | −0.767958 | ||||||||
\(170\) | −1995.54 | −0.900299 | ||||||||
\(171\) | 882.185 | 0.394517 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 3506.24 | 1.54089 | 0.770446 | − | 0.637506i | \(-0.220034\pi\) | ||||
0.770446 | + | 0.637506i | \(0.220034\pi\) | |||||||
\(174\) | −935.937 | −0.407777 | ||||||||
\(175\) | −8635.46 | −3.73017 | ||||||||
\(176\) | 2969.99 | 1.27199 | ||||||||
\(177\) | 1294.95 | 0.549913 | ||||||||
\(178\) | −54.2595 | −0.0228479 | ||||||||
\(179\) | 210.751 | 0.0880017 | 0.0440009 | − | 0.999031i | \(-0.485990\pi\) | ||||
0.0440009 | + | 0.999031i | \(0.485990\pi\) | |||||||
\(180\) | −98.9668 | −0.0409808 | ||||||||
\(181\) | −1984.99 | −0.815155 | −0.407577 | − | 0.913171i | \(-0.633626\pi\) | ||||
−0.407577 | + | 0.913171i | \(0.633626\pi\) | |||||||
\(182\) | 1674.70 | 0.682072 | ||||||||
\(183\) | −1905.74 | −0.769815 | ||||||||
\(184\) | 1110.24 | 0.444824 | ||||||||
\(185\) | 1572.95 | 0.625110 | ||||||||
\(186\) | −4819.58 | −1.89994 | ||||||||
\(187\) | 1418.48 | 0.554702 | ||||||||
\(188\) | 63.2499 | 0.0245371 | ||||||||
\(189\) | 2460.37 | 0.946907 | ||||||||
\(190\) | 4778.03 | 1.82440 | ||||||||
\(191\) | −3624.62 | −1.37313 | −0.686566 | − | 0.727068i | \(-0.740883\pi\) | ||||
−0.686566 | + | 0.727068i | \(0.740883\pi\) | |||||||
\(192\) | 3002.86 | 1.12871 | ||||||||
\(193\) | −2385.96 | −0.889872 | −0.444936 | − | 0.895562i | \(-0.646774\pi\) | ||||
−0.444936 | + | 0.895562i | \(0.646774\pi\) | |||||||
\(194\) | −968.852 | −0.358554 | ||||||||
\(195\) | −3012.96 | −1.10647 | ||||||||
\(196\) | 124.757 | 0.0454653 | ||||||||
\(197\) | −879.761 | −0.318175 | −0.159087 | − | 0.987265i | \(-0.550855\pi\) | ||||
−0.159087 | + | 0.987265i | \(0.550855\pi\) | |||||||
\(198\) | 1477.52 | 0.530316 | ||||||||
\(199\) | 409.595 | 0.145907 | 0.0729533 | − | 0.997335i | \(-0.476758\pi\) | ||||
0.0729533 | + | 0.997335i | \(0.476758\pi\) | |||||||
\(200\) | 7432.59 | 2.62782 | ||||||||
\(201\) | 2141.63 | 0.751538 | ||||||||
\(202\) | 3777.87 | 1.31589 | ||||||||
\(203\) | −1331.80 | −0.460462 | ||||||||
\(204\) | −79.4629 | −0.0272721 | ||||||||
\(205\) | −2761.57 | −0.940862 | ||||||||
\(206\) | −6041.09 | −2.04322 | ||||||||
\(207\) | 580.005 | 0.194749 | ||||||||
\(208\) | −1513.67 | −0.504586 | ||||||||
\(209\) | −3396.34 | −1.12407 | ||||||||
\(210\) | −9897.68 | −3.25240 | ||||||||
\(211\) | 4857.26 | 1.58477 | 0.792387 | − | 0.610018i | \(-0.208838\pi\) | ||||
0.792387 | + | 0.610018i | \(0.208838\pi\) | |||||||
\(212\) | −167.649 | −0.0543122 | ||||||||
\(213\) | 2476.97 | 0.796805 | ||||||||
\(214\) | −2390.33 | −0.763549 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −2117.65 | −0.667074 | ||||||||
\(217\) | −6858.04 | −2.14541 | ||||||||
\(218\) | 4562.87 | 1.41760 | ||||||||
\(219\) | 544.286 | 0.167943 | ||||||||
\(220\) | 381.014 | 0.116763 | ||||||||
\(221\) | −722.932 | −0.220044 | ||||||||
\(222\) | 1315.53 | 0.397714 | ||||||||
\(223\) | −117.917 | −0.0354095 | −0.0177048 | − | 0.999843i | \(-0.505636\pi\) | ||||
−0.0177048 | + | 0.999843i | \(0.505636\pi\) | |||||||
\(224\) | −462.764 | −0.138034 | ||||||||
\(225\) | 3882.90 | 1.15049 | ||||||||
\(226\) | 4361.34 | 1.28368 | ||||||||
\(227\) | 4470.82 | 1.30722 | 0.653610 | − | 0.756832i | \(-0.273254\pi\) | ||||
0.653610 | + | 0.756832i | \(0.273254\pi\) | |||||||
\(228\) | 190.263 | 0.0552651 | ||||||||
\(229\) | 5589.76 | 1.61302 | 0.806510 | − | 0.591220i | \(-0.201354\pi\) | ||||
0.806510 | + | 0.591220i | \(0.201354\pi\) | |||||||
\(230\) | 3141.39 | 0.900595 | ||||||||
\(231\) | 7035.50 | 2.00390 | ||||||||
\(232\) | 1146.28 | 0.324385 | ||||||||
\(233\) | −4104.15 | −1.15396 | −0.576978 | − | 0.816759i | \(-0.695768\pi\) | ||||
−0.576978 | + | 0.816759i | \(0.695768\pi\) | |||||||
\(234\) | −753.023 | −0.210370 | ||||||||
\(235\) | −3400.86 | −0.944033 | ||||||||
\(236\) | 83.4598 | 0.0230202 | ||||||||
\(237\) | 1371.59 | 0.375925 | ||||||||
\(238\) | −2374.86 | −0.646803 | ||||||||
\(239\) | 3722.43 | 1.00746 | 0.503732 | − | 0.863860i | \(-0.331960\pi\) | ||||
0.503732 | + | 0.863860i | \(0.331960\pi\) | |||||||
\(240\) | 8945.94 | 2.40607 | ||||||||
\(241\) | 4626.46 | 1.23658 | 0.618291 | − | 0.785949i | \(-0.287825\pi\) | ||||
0.618291 | + | 0.785949i | \(0.287825\pi\) | |||||||
\(242\) | −1830.73 | −0.486297 | ||||||||
\(243\) | −3034.29 | −0.801029 | ||||||||
\(244\) | −122.825 | −0.0322256 | ||||||||
\(245\) | −6708.00 | −1.74922 | ||||||||
\(246\) | −2309.63 | −0.598604 | ||||||||
\(247\) | 1730.96 | 0.445904 | ||||||||
\(248\) | 5902.76 | 1.51139 | ||||||||
\(249\) | 2692.12 | 0.685166 | ||||||||
\(250\) | 13239.7 | 3.34942 | ||||||||
\(251\) | 1136.12 | 0.285702 | 0.142851 | − | 0.989744i | \(-0.454373\pi\) | ||||
0.142851 | + | 0.989744i | \(0.454373\pi\) | |||||||
\(252\) | −117.779 | −0.0294419 | ||||||||
\(253\) | −2232.97 | −0.554884 | ||||||||
\(254\) | −663.411 | −0.163882 | ||||||||
\(255\) | 4272.61 | 1.04926 | ||||||||
\(256\) | 612.798 | 0.149609 | ||||||||
\(257\) | 6235.33 | 1.51342 | 0.756710 | − | 0.653750i | \(-0.226805\pi\) | ||||
0.756710 | + | 0.653750i | \(0.226805\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1871.94 | 0.449099 | ||||||||
\(260\) | −194.185 | −0.0463187 | ||||||||
\(261\) | 598.838 | 0.142020 | ||||||||
\(262\) | 1154.38 | 0.272205 | ||||||||
\(263\) | −7120.70 | −1.66951 | −0.834755 | − | 0.550622i | \(-0.814391\pi\) | ||||
−0.834755 | + | 0.550622i | \(0.814391\pi\) | |||||||
\(264\) | −6055.49 | −1.41170 | ||||||||
\(265\) | 9014.26 | 2.08959 | ||||||||
\(266\) | 5686.25 | 1.31070 | ||||||||
\(267\) | 116.174 | 0.0266282 | ||||||||
\(268\) | 138.028 | 0.0314605 | ||||||||
\(269\) | 4139.98 | 0.938360 | 0.469180 | − | 0.883102i | \(-0.344550\pi\) | ||||
0.469180 | + | 0.883102i | \(0.344550\pi\) | |||||||
\(270\) | −5991.85 | −1.35057 | ||||||||
\(271\) | −2761.65 | −0.619033 | −0.309517 | − | 0.950894i | \(-0.600167\pi\) | ||||
−0.309517 | + | 0.950894i | \(0.600167\pi\) | |||||||
\(272\) | 2146.50 | 0.478494 | ||||||||
\(273\) | −3585.67 | −0.794925 | ||||||||
\(274\) | 3794.62 | 0.836648 | ||||||||
\(275\) | −14948.9 | −3.27800 | ||||||||
\(276\) | 125.091 | 0.0272811 | ||||||||
\(277\) | −6788.15 | −1.47242 | −0.736211 | − | 0.676753i | \(-0.763387\pi\) | ||||
−0.736211 | + | 0.676753i | \(0.763387\pi\) | |||||||
\(278\) | −3864.22 | −0.833671 | ||||||||
\(279\) | 3083.70 | 0.661706 | ||||||||
\(280\) | 12122.1 | 2.58727 | ||||||||
\(281\) | 2258.93 | 0.479560 | 0.239780 | − | 0.970827i | \(-0.422925\pi\) | ||||
0.239780 | + | 0.970827i | \(0.422925\pi\) | |||||||
\(282\) | −2844.30 | −0.600622 | ||||||||
\(283\) | 2447.93 | 0.514185 | 0.257093 | − | 0.966387i | \(-0.417235\pi\) | ||||
0.257093 | + | 0.966387i | \(0.417235\pi\) | |||||||
\(284\) | 159.641 | 0.0333555 | ||||||||
\(285\) | −10230.2 | −2.12625 | ||||||||
\(286\) | 2899.08 | 0.599392 | ||||||||
\(287\) | −3286.50 | −0.675944 | ||||||||
\(288\) | 208.080 | 0.0425737 | ||||||||
\(289\) | −3887.83 | −0.791334 | ||||||||
\(290\) | 3243.39 | 0.656753 | ||||||||
\(291\) | 2074.39 | 0.417880 | ||||||||
\(292\) | 35.0793 | 0.00703034 | ||||||||
\(293\) | −7628.90 | −1.52111 | −0.760555 | − | 0.649274i | \(-0.775073\pi\) | ||||
−0.760555 | + | 0.649274i | \(0.775073\pi\) | |||||||
\(294\) | −5610.21 | −1.11291 | ||||||||
\(295\) | −4487.52 | −0.885673 | ||||||||
\(296\) | −1611.19 | −0.316380 | ||||||||
\(297\) | 4259.15 | 0.832124 | ||||||||
\(298\) | 5479.12 | 1.06509 | ||||||||
\(299\) | 1138.04 | 0.220116 | ||||||||
\(300\) | 837.434 | 0.161164 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 6126.88 | 1.16742 | ||||||||
\(303\) | −8088.72 | −1.53361 | ||||||||
\(304\) | −5139.48 | −0.969636 | ||||||||
\(305\) | 6604.13 | 1.23984 | ||||||||
\(306\) | 1067.85 | 0.199492 | ||||||||
\(307\) | −4363.26 | −0.811154 | −0.405577 | − | 0.914061i | \(-0.632929\pi\) | ||||
−0.405577 | + | 0.914061i | \(0.632929\pi\) | |||||||
\(308\) | 453.438 | 0.0838865 | ||||||||
\(309\) | 12934.5 | 2.38128 | ||||||||
\(310\) | 16701.7 | 3.05998 | ||||||||
\(311\) | −1370.87 | −0.249951 | −0.124975 | − | 0.992160i | \(-0.539885\pi\) | ||||
−0.124975 | + | 0.992160i | \(0.539885\pi\) | |||||||
\(312\) | 3086.21 | 0.560007 | ||||||||
\(313\) | 3305.03 | 0.596841 | 0.298421 | − | 0.954434i | \(-0.403540\pi\) | ||||
0.298421 | + | 0.954434i | \(0.403540\pi\) | |||||||
\(314\) | −3664.02 | −0.658511 | ||||||||
\(315\) | 6332.80 | 1.13274 | ||||||||
\(316\) | 88.3989 | 0.0157368 | ||||||||
\(317\) | 4457.62 | 0.789794 | 0.394897 | − | 0.918725i | \(-0.370780\pi\) | ||||
0.394897 | + | 0.918725i | \(0.370780\pi\) | |||||||
\(318\) | 7539.04 | 1.32946 | ||||||||
\(319\) | −2305.48 | −0.404645 | ||||||||
\(320\) | −10406.1 | −1.81787 | ||||||||
\(321\) | 5117.89 | 0.889883 | ||||||||
\(322\) | 3738.51 | 0.647015 | ||||||||
\(323\) | −2454.63 | −0.422847 | ||||||||
\(324\) | −362.857 | −0.0622183 | ||||||||
\(325\) | 7618.75 | 1.30034 | ||||||||
\(326\) | −124.372 | −0.0211298 | ||||||||
\(327\) | −9769.47 | −1.65215 | ||||||||
\(328\) | 2828.71 | 0.476187 | ||||||||
\(329\) | −4047.30 | −0.678222 | ||||||||
\(330\) | −17133.9 | −2.85815 | ||||||||
\(331\) | 1446.18 | 0.240149 | 0.120074 | − | 0.992765i | \(-0.461687\pi\) | ||||
0.120074 | + | 0.992765i | \(0.461687\pi\) | |||||||
\(332\) | 173.508 | 0.0286821 | ||||||||
\(333\) | −841.710 | −0.138515 | ||||||||
\(334\) | −6773.98 | −1.10975 | ||||||||
\(335\) | −7421.59 | −1.21040 | ||||||||
\(336\) | 10646.4 | 1.72860 | ||||||||
\(337\) | −957.005 | −0.154692 | −0.0773462 | − | 0.997004i | \(-0.524645\pi\) | ||||
−0.0773462 | + | 0.997004i | \(0.524645\pi\) | |||||||
\(338\) | 4889.96 | 0.786920 | ||||||||
\(339\) | −9337.97 | −1.49607 | ||||||||
\(340\) | 275.370 | 0.0439236 | ||||||||
\(341\) | −11872.0 | −1.88535 | ||||||||
\(342\) | −2556.80 | −0.404258 | ||||||||
\(343\) | 794.905 | 0.125134 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −6725.96 | −1.04961 | ||||||||
\(346\) | −10162.0 | −1.57894 | ||||||||
\(347\) | −5663.55 | −0.876183 | −0.438092 | − | 0.898930i | \(-0.644345\pi\) | ||||
−0.438092 | + | 0.898930i | \(0.644345\pi\) | |||||||
\(348\) | 129.153 | 0.0198946 | ||||||||
\(349\) | 8397.53 | 1.28799 | 0.643996 | − | 0.765029i | \(-0.277275\pi\) | ||||
0.643996 | + | 0.765029i | \(0.277275\pi\) | |||||||
\(350\) | 25027.8 | 3.82227 | ||||||||
\(351\) | −2170.69 | −0.330094 | ||||||||
\(352\) | −801.091 | −0.121302 | ||||||||
\(353\) | 11111.3 | 1.67534 | 0.837669 | − | 0.546178i | \(-0.183918\pi\) | ||||
0.837669 | + | 0.546178i | \(0.183918\pi\) | |||||||
\(354\) | −3753.12 | −0.563492 | ||||||||
\(355\) | −8583.68 | −1.28331 | ||||||||
\(356\) | 7.48742 | 0.00111470 | ||||||||
\(357\) | 5084.76 | 0.753821 | ||||||||
\(358\) | −610.814 | −0.0901746 | ||||||||
\(359\) | −1277.78 | −0.187851 | −0.0939255 | − | 0.995579i | \(-0.529942\pi\) | ||||
−0.0939255 | + | 0.995579i | \(0.529942\pi\) | |||||||
\(360\) | −5450.67 | −0.797988 | ||||||||
\(361\) | −981.731 | −0.143130 | ||||||||
\(362\) | 5753.02 | 0.835282 | ||||||||
\(363\) | 3919.75 | 0.566759 | ||||||||
\(364\) | −231.097 | −0.0332768 | ||||||||
\(365\) | −1886.16 | −0.270483 | ||||||||
\(366\) | 5523.33 | 0.788823 | ||||||||
\(367\) | −4649.71 | −0.661343 | −0.330671 | − | 0.943746i | \(-0.607275\pi\) | ||||
−0.330671 | + | 0.943746i | \(0.607275\pi\) | |||||||
\(368\) | −3379.02 | −0.478651 | ||||||||
\(369\) | 1477.76 | 0.208480 | ||||||||
\(370\) | −4558.82 | −0.640545 | ||||||||
\(371\) | 10727.7 | 1.50123 | ||||||||
\(372\) | 665.067 | 0.0926939 | ||||||||
\(373\) | −8278.57 | −1.14919 | −0.574595 | − | 0.818438i | \(-0.694840\pi\) | ||||
−0.574595 | + | 0.818438i | \(0.694840\pi\) | |||||||
\(374\) | −4111.12 | −0.568398 | ||||||||
\(375\) | −28347.4 | −3.90360 | ||||||||
\(376\) | 3483.54 | 0.477792 | ||||||||
\(377\) | 1174.99 | 0.160518 | ||||||||
\(378\) | −7130.80 | −0.970288 | ||||||||
\(379\) | 6040.29 | 0.818651 | 0.409326 | − | 0.912388i | \(-0.365764\pi\) | ||||
0.409326 | + | 0.912388i | \(0.365764\pi\) | |||||||
\(380\) | −659.334 | −0.0890083 | ||||||||
\(381\) | 1420.42 | 0.190998 | ||||||||
\(382\) | 10505.1 | 1.40704 | ||||||||
\(383\) | −7225.42 | −0.963973 | −0.481986 | − | 0.876179i | \(-0.660085\pi\) | ||||
−0.481986 | + | 0.876179i | \(0.660085\pi\) | |||||||
\(384\) | −9600.75 | −1.27588 | ||||||||
\(385\) | −24380.7 | −3.22742 | ||||||||
\(386\) | 6915.15 | 0.911844 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 133.695 | 0.0174931 | ||||||||
\(389\) | 5861.61 | 0.763998 | 0.381999 | − | 0.924163i | \(-0.375236\pi\) | ||||
0.381999 | + | 0.924163i | \(0.375236\pi\) | |||||||
\(390\) | 8732.36 | 1.13379 | ||||||||
\(391\) | −1613.83 | −0.208734 | ||||||||
\(392\) | 6871.08 | 0.885311 | ||||||||
\(393\) | −2471.62 | −0.317243 | ||||||||
\(394\) | 2549.78 | 0.326031 | ||||||||
\(395\) | −4753.09 | −0.605452 | ||||||||
\(396\) | −203.887 | −0.0258730 | ||||||||
\(397\) | −10532.9 | −1.33156 | −0.665782 | − | 0.746146i | \(-0.731902\pi\) | ||||
−0.665782 | + | 0.746146i | \(0.731902\pi\) | |||||||
\(398\) | −1187.12 | −0.149509 | ||||||||
\(399\) | −12174.7 | −1.52757 | ||||||||
\(400\) | −22621.2 | −2.82765 | ||||||||
\(401\) | 5013.05 | 0.624289 | 0.312144 | − | 0.950035i | \(-0.398953\pi\) | ||||
0.312144 | + | 0.950035i | \(0.398953\pi\) | |||||||
\(402\) | −6207.02 | −0.770094 | ||||||||
\(403\) | 6050.60 | 0.747895 | ||||||||
\(404\) | −521.318 | −0.0641994 | ||||||||
\(405\) | 19510.3 | 2.39377 | ||||||||
\(406\) | 3859.90 | 0.471831 | ||||||||
\(407\) | 3240.51 | 0.394659 | ||||||||
\(408\) | −4376.48 | −0.531049 | ||||||||
\(409\) | −12564.0 | −1.51895 | −0.759473 | − | 0.650539i | \(-0.774543\pi\) | ||||
−0.759473 | + | 0.650539i | \(0.774543\pi\) | |||||||
\(410\) | 8003.77 | 0.964093 | ||||||||
\(411\) | −8124.59 | −0.975077 | ||||||||
\(412\) | 833.627 | 0.0996841 | ||||||||
\(413\) | −5340.52 | −0.636295 | ||||||||
\(414\) | −1681.01 | −0.199558 | ||||||||
\(415\) | −9329.26 | −1.10351 | ||||||||
\(416\) | 408.279 | 0.0481191 | ||||||||
\(417\) | 8273.61 | 0.971608 | ||||||||
\(418\) | 9843.49 | 1.15182 | ||||||||
\(419\) | −13524.0 | −1.57683 | −0.788413 | − | 0.615146i | \(-0.789097\pi\) | ||||
−0.788413 | + | 0.615146i | \(0.789097\pi\) | |||||||
\(420\) | 1365.81 | 0.158678 | ||||||||
\(421\) | 16298.4 | 1.88678 | 0.943389 | − | 0.331688i | \(-0.107618\pi\) | ||||
0.943389 | + | 0.331688i | \(0.107618\pi\) | |||||||
\(422\) | −14077.6 | −1.62391 | ||||||||
\(423\) | 1819.86 | 0.209183 | ||||||||
\(424\) | −9233.40 | −1.05758 | ||||||||
\(425\) | −10804.0 | −1.23311 | ||||||||
\(426\) | −7178.92 | −0.816479 | ||||||||
\(427\) | 7859.45 | 0.890739 | ||||||||
\(428\) | 329.848 | 0.0372519 | ||||||||
\(429\) | −6207.16 | −0.698565 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 1648.67 | 0.184255 | 0.0921274 | − | 0.995747i | \(-0.470633\pi\) | ||||
0.0921274 | + | 0.995747i | \(0.470633\pi\) | |||||||
\(432\) | 6445.12 | 0.717803 | ||||||||
\(433\) | −4180.27 | −0.463952 | −0.231976 | − | 0.972722i | \(-0.574519\pi\) | ||||
−0.231976 | + | 0.972722i | \(0.574519\pi\) | |||||||
\(434\) | 19876.4 | 2.19838 | ||||||||
\(435\) | −6944.36 | −0.765417 | ||||||||
\(436\) | −629.643 | −0.0691615 | ||||||||
\(437\) | 3864.09 | 0.422985 | ||||||||
\(438\) | −1577.49 | −0.172089 | ||||||||
\(439\) | 6108.96 | 0.664157 | 0.332078 | − | 0.943252i | \(-0.392250\pi\) | ||||
0.332078 | + | 0.943252i | \(0.392250\pi\) | |||||||
\(440\) | 20984.6 | 2.27365 | ||||||||
\(441\) | 3589.56 | 0.387600 | ||||||||
\(442\) | 2095.25 | 0.225477 | ||||||||
\(443\) | 14676.2 | 1.57401 | 0.787004 | − | 0.616948i | \(-0.211631\pi\) | ||||
0.787004 | + | 0.616948i | \(0.211631\pi\) | |||||||
\(444\) | −181.533 | −0.0194036 | ||||||||
\(445\) | −402.588 | −0.0428866 | ||||||||
\(446\) | 341.755 | 0.0362838 | ||||||||
\(447\) | −11731.2 | −1.24132 | ||||||||
\(448\) | −12384.1 | −1.30601 | ||||||||
\(449\) | −9548.52 | −1.00361 | −0.501807 | − | 0.864980i | \(-0.667331\pi\) | ||||
−0.501807 | + | 0.864980i | \(0.667331\pi\) | |||||||
\(450\) | −11253.7 | −1.17890 | ||||||||
\(451\) | −5689.27 | −0.594007 | ||||||||
\(452\) | −601.833 | −0.0626280 | ||||||||
\(453\) | −13118.1 | −1.36058 | ||||||||
\(454\) | −12957.6 | −1.33950 | ||||||||
\(455\) | 12425.7 | 1.28028 | ||||||||
\(456\) | 10478.9 | 1.07614 | ||||||||
\(457\) | −11740.0 | −1.20170 | −0.600849 | − | 0.799363i | \(-0.705171\pi\) | ||||
−0.600849 | + | 0.799363i | \(0.705171\pi\) | |||||||
\(458\) | −16200.6 | −1.65285 | ||||||||
\(459\) | 3078.21 | 0.313025 | ||||||||
\(460\) | −433.489 | −0.0439381 | ||||||||
\(461\) | 8505.48 | 0.859305 | 0.429652 | − | 0.902994i | \(-0.358636\pi\) | ||||
0.429652 | + | 0.902994i | \(0.358636\pi\) | |||||||
\(462\) | −20390.7 | −2.05338 | ||||||||
\(463\) | −15636.9 | −1.56957 | −0.784784 | − | 0.619769i | \(-0.787226\pi\) | ||||
−0.784784 | + | 0.619769i | \(0.787226\pi\) | |||||||
\(464\) | −3488.74 | −0.349053 | ||||||||
\(465\) | −35759.8 | −3.56628 | ||||||||
\(466\) | 11894.9 | 1.18245 | ||||||||
\(467\) | 1591.28 | 0.157678 | 0.0788392 | − | 0.996887i | \(-0.474879\pi\) | ||||
0.0788392 | + | 0.996887i | \(0.474879\pi\) | |||||||
\(468\) | 103.912 | 0.0102635 | ||||||||
\(469\) | −8832.31 | −0.869591 | ||||||||
\(470\) | 9856.59 | 0.967342 | ||||||||
\(471\) | 7844.96 | 0.767467 | ||||||||
\(472\) | 4596.61 | 0.448255 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | −3975.22 | −0.385207 | ||||||||
\(475\) | 25868.6 | 2.49880 | ||||||||
\(476\) | 327.713 | 0.0315561 | ||||||||
\(477\) | −4823.68 | −0.463021 | ||||||||
\(478\) | −10788.6 | −1.03234 | ||||||||
\(479\) | −9244.11 | −0.881783 | −0.440891 | − | 0.897560i | \(-0.645338\pi\) | ||||
−0.440891 | + | 0.897560i | \(0.645338\pi\) | |||||||
\(480\) | −2412.98 | −0.229452 | ||||||||
\(481\) | −1651.54 | −0.156557 | ||||||||
\(482\) | −13408.7 | −1.26712 | ||||||||
\(483\) | −8004.45 | −0.754069 | ||||||||
\(484\) | 252.628 | 0.0237254 | ||||||||
\(485\) | −7188.58 | −0.673024 | ||||||||
\(486\) | 8794.19 | 0.820808 | ||||||||
\(487\) | 2684.94 | 0.249828 | 0.124914 | − | 0.992168i | \(-0.460135\pi\) | ||||
0.124914 | + | 0.992168i | \(0.460135\pi\) | |||||||
\(488\) | −6764.68 | −0.627505 | ||||||||
\(489\) | 266.290 | 0.0246259 | ||||||||
\(490\) | 19441.6 | 1.79241 | ||||||||
\(491\) | 10476.7 | 0.962947 | 0.481473 | − | 0.876461i | \(-0.340102\pi\) | ||||
0.481473 | + | 0.876461i | \(0.340102\pi\) | |||||||
\(492\) | 318.712 | 0.0292046 | ||||||||
\(493\) | −1666.23 | −0.152218 | ||||||||
\(494\) | −5016.77 | −0.456914 | ||||||||
\(495\) | 10962.7 | 0.995429 | ||||||||
\(496\) | −17965.2 | −1.62633 | ||||||||
\(497\) | −10215.3 | −0.921968 | ||||||||
\(498\) | −7802.49 | −0.702084 | ||||||||
\(499\) | 14762.9 | 1.32440 | 0.662201 | − | 0.749326i | \(-0.269623\pi\) | ||||
0.662201 | + | 0.749326i | \(0.269623\pi\) | |||||||
\(500\) | −1826.99 | −0.163411 | ||||||||
\(501\) | 14503.6 | 1.29336 | ||||||||
\(502\) | −3292.78 | −0.292757 | ||||||||
\(503\) | −11354.1 | −1.00647 | −0.503237 | − | 0.864149i | \(-0.667858\pi\) | ||||
−0.503237 | + | 0.864149i | \(0.667858\pi\) | |||||||
\(504\) | −6486.75 | −0.573299 | ||||||||
\(505\) | 28030.6 | 2.46999 | ||||||||
\(506\) | 6471.74 | 0.568585 | ||||||||
\(507\) | −10469.8 | −0.917121 | ||||||||
\(508\) | 91.5459 | 0.00799546 | ||||||||
\(509\) | −17946.4 | −1.56279 | −0.781396 | − | 0.624036i | \(-0.785492\pi\) | ||||
−0.781396 | + | 0.624036i | \(0.785492\pi\) | |||||||
\(510\) | −12383.2 | −1.07517 | ||||||||
\(511\) | −2244.69 | −0.194323 | ||||||||
\(512\) | 10601.2 | 0.915061 | ||||||||
\(513\) | −7370.34 | −0.634324 | ||||||||
\(514\) | −18071.6 | −1.55079 | ||||||||
\(515\) | −44823.0 | −3.83522 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −7006.30 | −0.596009 | ||||||||
\(518\) | −5425.37 | −0.460187 | ||||||||
\(519\) | 21757.7 | 1.84018 | ||||||||
\(520\) | −10694.9 | −0.901929 | ||||||||
\(521\) | 3271.82 | 0.275127 | 0.137564 | − | 0.990493i | \(-0.456073\pi\) | ||||
0.137564 | + | 0.990493i | \(0.456073\pi\) | |||||||
\(522\) | −1735.59 | −0.145526 | ||||||||
\(523\) | 4629.62 | 0.387073 | 0.193536 | − | 0.981093i | \(-0.438004\pi\) | ||||
0.193536 | + | 0.981093i | \(0.438004\pi\) | |||||||
\(524\) | −159.296 | −0.0132803 | ||||||||
\(525\) | −53586.7 | −4.45469 | ||||||||
\(526\) | 20637.7 | 1.71073 | ||||||||
\(527\) | −8580.22 | −0.709223 | ||||||||
\(528\) | 18430.0 | 1.51906 | ||||||||
\(529\) | −9626.50 | −0.791197 | ||||||||
\(530\) | −26125.7 | −2.14119 | ||||||||
\(531\) | 2401.35 | 0.196251 | ||||||||
\(532\) | −784.662 | −0.0639463 | ||||||||
\(533\) | 2899.56 | 0.235636 | ||||||||
\(534\) | −336.703 | −0.0272857 | ||||||||
\(535\) | −17735.5 | −1.43322 | ||||||||
\(536\) | 7602.02 | 0.612607 | ||||||||
\(537\) | 1307.80 | 0.105095 | ||||||||
\(538\) | −11998.8 | −0.961530 | ||||||||
\(539\) | −13819.5 | −1.10436 | ||||||||
\(540\) | 826.833 | 0.0658911 | ||||||||
\(541\) | −11418.8 | −0.907452 | −0.453726 | − | 0.891141i | \(-0.649906\pi\) | ||||
−0.453726 | + | 0.891141i | \(0.649906\pi\) | |||||||
\(542\) | 8003.98 | 0.634318 | ||||||||
\(543\) | −12317.7 | −0.973485 | ||||||||
\(544\) | −578.972 | −0.0456309 | ||||||||
\(545\) | 33855.0 | 2.66090 | ||||||||
\(546\) | 10392.2 | 0.814553 | ||||||||
\(547\) | 6243.35 | 0.488019 | 0.244009 | − | 0.969773i | \(-0.421537\pi\) | ||||
0.244009 | + | 0.969773i | \(0.421537\pi\) | |||||||
\(548\) | −523.630 | −0.0408182 | ||||||||
\(549\) | −3533.98 | −0.274729 | ||||||||
\(550\) | 43325.8 | 3.35894 | ||||||||
\(551\) | 3989.56 | 0.308459 | ||||||||
\(552\) | 6889.48 | 0.531224 | ||||||||
\(553\) | −5656.56 | −0.434976 | ||||||||
\(554\) | 19673.9 | 1.50878 | ||||||||
\(555\) | 9760.80 | 0.746528 | ||||||||
\(556\) | 533.235 | 0.0406730 | ||||||||
\(557\) | −1313.79 | −0.0999412 | −0.0499706 | − | 0.998751i | \(-0.515913\pi\) | ||||
−0.0499706 | + | 0.998751i | \(0.515913\pi\) | |||||||
\(558\) | −8937.37 | −0.678045 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | −36893.9 | −2.78402 | ||||||||
\(561\) | 8802.24 | 0.662444 | ||||||||
\(562\) | −6546.98 | −0.491401 | ||||||||
\(563\) | −12978.3 | −0.971525 | −0.485763 | − | 0.874091i | \(-0.661458\pi\) | ||||
−0.485763 | + | 0.874091i | \(0.661458\pi\) | |||||||
\(564\) | 392.492 | 0.0293030 | ||||||||
\(565\) | 32359.7 | 2.40953 | ||||||||
\(566\) | −7094.75 | −0.526881 | ||||||||
\(567\) | 23218.9 | 1.71976 | ||||||||
\(568\) | 8792.35 | 0.649505 | ||||||||
\(569\) | −19149.9 | −1.41091 | −0.705454 | − | 0.708756i | \(-0.749257\pi\) | ||||
−0.705454 | + | 0.708756i | \(0.749257\pi\) | |||||||
\(570\) | 29649.7 | 2.17875 | ||||||||
\(571\) | 3603.81 | 0.264124 | 0.132062 | − | 0.991241i | \(-0.457840\pi\) | ||||
0.132062 | + | 0.991241i | \(0.457840\pi\) | |||||||
\(572\) | −400.052 | −0.0292430 | ||||||||
\(573\) | −22492.3 | −1.63984 | ||||||||
\(574\) | 9525.15 | 0.692634 | ||||||||
\(575\) | 17007.7 | 1.23351 | ||||||||
\(576\) | 5568.46 | 0.402811 | ||||||||
\(577\) | 11668.0 | 0.841843 | 0.420921 | − | 0.907097i | \(-0.361707\pi\) | ||||
0.420921 | + | 0.907097i | \(0.361707\pi\) | |||||||
\(578\) | 11267.9 | 0.810874 | ||||||||
\(579\) | −14805.9 | −1.06271 | ||||||||
\(580\) | −447.564 | −0.0320415 | ||||||||
\(581\) | −11102.6 | −0.792793 | ||||||||
\(582\) | −6012.14 | −0.428198 | ||||||||
\(583\) | 18570.8 | 1.31925 | ||||||||
\(584\) | 1932.02 | 0.136896 | ||||||||
\(585\) | −5587.19 | −0.394875 | ||||||||
\(586\) | 22110.6 | 1.55867 | ||||||||
\(587\) | 21935.6 | 1.54238 | 0.771191 | − | 0.636603i | \(-0.219661\pi\) | ||||
0.771191 | + | 0.636603i | \(0.219661\pi\) | |||||||
\(588\) | 774.168 | 0.0542962 | ||||||||
\(589\) | 20544.1 | 1.43719 | ||||||||
\(590\) | 13006.0 | 0.907542 | ||||||||
\(591\) | −5459.29 | −0.379975 | ||||||||
\(592\) | 4903.68 | 0.340439 | ||||||||
\(593\) | −10763.9 | −0.745396 | −0.372698 | − | 0.927953i | \(-0.621567\pi\) | ||||
−0.372698 | + | 0.927953i | \(0.621567\pi\) | |||||||
\(594\) | −12344.1 | −0.852670 | ||||||||
\(595\) | −17620.7 | −1.21408 | ||||||||
\(596\) | −756.079 | −0.0519634 | ||||||||
\(597\) | 2541.71 | 0.174247 | ||||||||
\(598\) | −3298.35 | −0.225551 | ||||||||
\(599\) | −16831.8 | −1.14813 | −0.574064 | − | 0.818810i | \(-0.694634\pi\) | ||||
−0.574064 | + | 0.818810i | \(0.694634\pi\) | |||||||
\(600\) | 46122.3 | 3.13823 | ||||||||
\(601\) | 21858.0 | 1.48354 | 0.741770 | − | 0.670654i | \(-0.233987\pi\) | ||||
0.741770 | + | 0.670654i | \(0.233987\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 3971.42 | 0.268207 | ||||||||
\(604\) | −845.465 | −0.0569561 | ||||||||
\(605\) | −13583.5 | −0.912804 | ||||||||
\(606\) | 23443.2 | 1.57148 | ||||||||
\(607\) | 16133.2 | 1.07879 | 0.539396 | − | 0.842052i | \(-0.318653\pi\) | ||||
0.539396 | + | 0.842052i | \(0.318653\pi\) | |||||||
\(608\) | 1386.27 | 0.0924680 | ||||||||
\(609\) | −8264.36 | −0.549899 | ||||||||
\(610\) | −19140.5 | −1.27045 | ||||||||
\(611\) | 3570.79 | 0.236430 | ||||||||
\(612\) | −147.355 | −0.00973280 | ||||||||
\(613\) | 14424.6 | 0.950415 | 0.475208 | − | 0.879874i | \(-0.342373\pi\) | ||||
0.475208 | + | 0.879874i | \(0.342373\pi\) | |||||||
\(614\) | 12645.9 | 0.831182 | ||||||||
\(615\) | −17136.7 | −1.12361 | ||||||||
\(616\) | 24973.5 | 1.63346 | ||||||||
\(617\) | −12177.9 | −0.794592 | −0.397296 | − | 0.917691i | \(-0.630051\pi\) | ||||
−0.397296 | + | 0.917691i | \(0.630051\pi\) | |||||||
\(618\) | −37487.5 | −2.44008 | ||||||||
\(619\) | −9555.90 | −0.620491 | −0.310246 | − | 0.950656i | \(-0.600411\pi\) | ||||
−0.310246 | + | 0.950656i | \(0.600411\pi\) | |||||||
\(620\) | −2304.72 | −0.149290 | ||||||||
\(621\) | −4845.73 | −0.313128 | ||||||||
\(622\) | 3973.13 | 0.256122 | ||||||||
\(623\) | −479.113 | −0.0308110 | ||||||||
\(624\) | −9392.93 | −0.602593 | ||||||||
\(625\) | 56055.8 | 3.58757 | ||||||||
\(626\) | −9578.85 | −0.611578 | ||||||||
\(627\) | −21075.7 | −1.34240 | ||||||||
\(628\) | 505.608 | 0.0321273 | ||||||||
\(629\) | 2342.01 | 0.148461 | ||||||||
\(630\) | −18354.1 | −1.16071 | ||||||||
\(631\) | 14800.3 | 0.933740 | 0.466870 | − | 0.884326i | \(-0.345382\pi\) | ||||
0.466870 | + | 0.884326i | \(0.345382\pi\) | |||||||
\(632\) | 4868.64 | 0.306430 | ||||||||
\(633\) | 30141.3 | 1.89259 | ||||||||
\(634\) | −12919.4 | −0.809295 | ||||||||
\(635\) | −4922.30 | −0.307615 | ||||||||
\(636\) | −1040.33 | −0.0648614 | ||||||||
\(637\) | 7043.17 | 0.438086 | ||||||||
\(638\) | 6681.88 | 0.414637 | ||||||||
\(639\) | 4593.27 | 0.284361 | ||||||||
\(640\) | 33270.4 | 2.05488 | ||||||||
\(641\) | −12808.0 | −0.789214 | −0.394607 | − | 0.918850i | \(-0.629119\pi\) | ||||
−0.394607 | + | 0.918850i | \(0.629119\pi\) | |||||||
\(642\) | −14833.0 | −0.911856 | ||||||||
\(643\) | 3164.25 | 0.194068 | 0.0970342 | − | 0.995281i | \(-0.469064\pi\) | ||||
0.0970342 | + | 0.995281i | \(0.469064\pi\) | |||||||
\(644\) | −515.887 | −0.0315665 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 7114.18 | 0.433287 | ||||||||
\(647\) | −18517.4 | −1.12519 | −0.562593 | − | 0.826734i | \(-0.690196\pi\) | ||||
−0.562593 | + | 0.826734i | \(0.690196\pi\) | |||||||
\(648\) | −19984.6 | −1.21153 | ||||||||
\(649\) | −9244.98 | −0.559164 | ||||||||
\(650\) | −22081.1 | −1.33245 | ||||||||
\(651\) | −42557.0 | −2.56212 | ||||||||
\(652\) | 17.1624 | 0.00103088 | ||||||||
\(653\) | −21579.1 | −1.29319 | −0.646596 | − | 0.762833i | \(-0.723808\pi\) | ||||
−0.646596 | + | 0.762833i | \(0.723808\pi\) | |||||||
\(654\) | 28314.5 | 1.69294 | ||||||||
\(655\) | 8565.11 | 0.510941 | ||||||||
\(656\) | −8609.23 | −0.512399 | ||||||||
\(657\) | 1009.32 | 0.0599349 | ||||||||
\(658\) | 11730.2 | 0.694968 | ||||||||
\(659\) | 2264.45 | 0.133855 | 0.0669274 | − | 0.997758i | \(-0.478680\pi\) | ||||
0.0669274 | + | 0.997758i | \(0.478680\pi\) | |||||||
\(660\) | 2364.35 | 0.139443 | ||||||||
\(661\) | −14720.0 | −0.866174 | −0.433087 | − | 0.901352i | \(-0.642576\pi\) | ||||
−0.433087 | + | 0.901352i | \(0.642576\pi\) | |||||||
\(662\) | −4191.41 | −0.246078 | ||||||||
\(663\) | −4486.10 | −0.262784 | ||||||||
\(664\) | 9556.06 | 0.558505 | ||||||||
\(665\) | 42190.2 | 2.46025 | ||||||||
\(666\) | 2439.50 | 0.141935 | ||||||||
\(667\) | 2622.99 | 0.152268 | ||||||||
\(668\) | 934.760 | 0.0541422 | ||||||||
\(669\) | −731.726 | −0.0422872 | ||||||||
\(670\) | 21509.7 | 1.24029 | ||||||||
\(671\) | 13605.5 | 0.782765 | ||||||||
\(672\) | −2871.64 | −0.164845 | ||||||||
\(673\) | 5130.48 | 0.293857 | 0.146928 | − | 0.989147i | \(-0.453061\pi\) | ||||
0.146928 | + | 0.989147i | \(0.453061\pi\) | |||||||
\(674\) | 2773.65 | 0.158512 | ||||||||
\(675\) | −32440.3 | −1.84982 | ||||||||
\(676\) | −674.779 | −0.0383921 | ||||||||
\(677\) | −339.763 | −0.0192883 | −0.00964413 | − | 0.999953i | \(-0.503070\pi\) | ||||
−0.00964413 | + | 0.999953i | \(0.503070\pi\) | |||||||
\(678\) | 27063.9 | 1.53301 | ||||||||
\(679\) | −8555.00 | −0.483521 | ||||||||
\(680\) | 15166.2 | 0.855291 | ||||||||
\(681\) | 27743.3 | 1.56113 | ||||||||
\(682\) | 34408.1 | 1.93190 | ||||||||
\(683\) | 10488.8 | 0.587616 | 0.293808 | − | 0.955864i | \(-0.405077\pi\) | ||||
0.293808 | + | 0.955864i | \(0.405077\pi\) | |||||||
\(684\) | 352.821 | 0.0197229 | ||||||||
\(685\) | 28154.9 | 1.57043 | ||||||||
\(686\) | −2303.84 | −0.128223 | ||||||||
\(687\) | 34686.8 | 1.92632 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −9464.66 | −0.523331 | ||||||||
\(690\) | 19493.6 | 1.07552 | ||||||||
\(691\) | 30039.5 | 1.65377 | 0.826887 | − | 0.562368i | \(-0.190109\pi\) | ||||
0.826887 | + | 0.562368i | \(0.190109\pi\) | |||||||
\(692\) | 1402.28 | 0.0770329 | ||||||||
\(693\) | 13046.5 | 0.715147 | ||||||||
\(694\) | 16414.5 | 0.897817 | ||||||||
\(695\) | −28671.3 | −1.56484 | ||||||||
\(696\) | 7113.18 | 0.387391 | ||||||||
\(697\) | −4111.80 | −0.223451 | ||||||||
\(698\) | −24338.3 | −1.31980 | ||||||||
\(699\) | −25468.0 | −1.37809 | ||||||||
\(700\) | −3453.66 | −0.186480 | ||||||||
\(701\) | −21987.7 | −1.18468 | −0.592342 | − | 0.805687i | \(-0.701797\pi\) | ||||
−0.592342 | + | 0.805687i | \(0.701797\pi\) | |||||||
\(702\) | 6291.24 | 0.338244 | ||||||||
\(703\) | −5607.62 | −0.300847 | ||||||||
\(704\) | −21438.1 | −1.14770 | ||||||||
\(705\) | −21103.8 | −1.12740 | ||||||||
\(706\) | −32203.5 | −1.71670 | ||||||||
\(707\) | 33358.7 | 1.77452 | ||||||||
\(708\) | 517.903 | 0.0274915 | ||||||||
\(709\) | 18478.4 | 0.978805 | 0.489402 | − | 0.872058i | \(-0.337215\pi\) | ||||
0.489402 | + | 0.872058i | \(0.337215\pi\) | |||||||
\(710\) | 24877.8 | 1.31499 | ||||||||
\(711\) | 2543.45 | 0.134159 | ||||||||
\(712\) | 412.375 | 0.0217057 | ||||||||
\(713\) | 13507.0 | 0.709456 | ||||||||
\(714\) | −14737.0 | −0.772434 | ||||||||
\(715\) | 21510.2 | 1.12509 | ||||||||
\(716\) | 84.2879 | 0.00439942 | ||||||||
\(717\) | 23099.2 | 1.20315 | ||||||||
\(718\) | 3703.34 | 0.192489 | ||||||||
\(719\) | −26993.9 | −1.40014 | −0.700071 | − | 0.714073i | \(-0.746848\pi\) | ||||
−0.700071 | + | 0.714073i | \(0.746848\pi\) | |||||||
\(720\) | 16589.2 | 0.858673 | ||||||||
\(721\) | −53343.0 | −2.75534 | ||||||||
\(722\) | 2845.32 | 0.146664 | ||||||||
\(723\) | 28709.1 | 1.47677 | ||||||||
\(724\) | −793.875 | −0.0407516 | ||||||||
\(725\) | 17559.9 | 0.899529 | ||||||||
\(726\) | −11360.5 | −0.580753 | ||||||||
\(727\) | −2671.91 | −0.136308 | −0.0681539 | − | 0.997675i | \(-0.521711\pi\) | ||||
−0.0681539 | + | 0.997675i | \(0.521711\pi\) | |||||||
\(728\) | −12727.8 | −0.647973 | ||||||||
\(729\) | 5667.46 | 0.287937 | ||||||||
\(730\) | 5466.60 | 0.277162 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | −762.180 | −0.0384850 | ||||||||
\(733\) | −6471.71 | −0.326109 | −0.163055 | − | 0.986617i | \(-0.552135\pi\) | ||||
−0.163055 | + | 0.986617i | \(0.552135\pi\) | |||||||
\(734\) | 13476.1 | 0.677672 | ||||||||
\(735\) | −41626.0 | −2.08898 | ||||||||
\(736\) | 911.420 | 0.0456459 | ||||||||
\(737\) | −15289.6 | −0.764180 | ||||||||
\(738\) | −4282.95 | −0.213628 | ||||||||
\(739\) | 7029.25 | 0.349899 | 0.174949 | − | 0.984577i | \(-0.444024\pi\) | ||||
0.174949 | + | 0.984577i | \(0.444024\pi\) | |||||||
\(740\) | 629.084 | 0.0312508 | ||||||||
\(741\) | 10741.3 | 0.532513 | ||||||||
\(742\) | −31091.7 | −1.53829 | ||||||||
\(743\) | −23560.5 | −1.16332 | −0.581662 | − | 0.813431i | \(-0.697597\pi\) | ||||
−0.581662 | + | 0.813431i | \(0.697597\pi\) | |||||||
\(744\) | 36629.1 | 1.80496 | ||||||||
\(745\) | 40653.3 | 1.99923 | ||||||||
\(746\) | 23993.5 | 1.17757 | ||||||||
\(747\) | 4992.24 | 0.244520 | ||||||||
\(748\) | 567.305 | 0.0277309 | ||||||||
\(749\) | −21106.7 | −1.02967 | ||||||||
\(750\) | 82158.2 | 3.99999 | ||||||||
\(751\) | −20853.5 | −1.01326 | −0.506629 | − | 0.862164i | \(-0.669108\pi\) | ||||
−0.506629 | + | 0.862164i | \(0.669108\pi\) | |||||||
\(752\) | −10602.2 | −0.514126 | ||||||||
\(753\) | 7050.11 | 0.341195 | ||||||||
\(754\) | −3405.45 | −0.164481 | ||||||||
\(755\) | 45459.5 | 2.19131 | ||||||||
\(756\) | 983.999 | 0.0473382 | ||||||||
\(757\) | −18722.3 | −0.898910 | −0.449455 | − | 0.893303i | \(-0.648382\pi\) | ||||
−0.449455 | + | 0.893303i | \(0.648382\pi\) | |||||||
\(758\) | −17506.4 | −0.838865 | ||||||||
\(759\) | −13856.5 | −0.662661 | ||||||||
\(760\) | −36313.4 | −1.73319 | ||||||||
\(761\) | 16358.5 | 0.779233 | 0.389616 | − | 0.920977i | \(-0.372608\pi\) | ||||
0.389616 | + | 0.920977i | \(0.372608\pi\) | |||||||
\(762\) | −4116.74 | −0.195714 | ||||||||
\(763\) | 40290.3 | 1.91167 | ||||||||
\(764\) | −1449.63 | −0.0686462 | ||||||||
\(765\) | 7923.08 | 0.374457 | ||||||||
\(766\) | 20941.2 | 0.987775 | ||||||||
\(767\) | 4711.74 | 0.221814 | ||||||||
\(768\) | 3802.67 | 0.178668 | ||||||||
\(769\) | −10838.7 | −0.508263 | −0.254131 | − | 0.967170i | \(-0.581790\pi\) | ||||
−0.254131 | + | 0.967170i | \(0.581790\pi\) | |||||||
\(770\) | 70661.9 | 3.30711 | ||||||||
\(771\) | 38692.8 | 1.80738 | ||||||||
\(772\) | −954.240 | −0.0444869 | ||||||||
\(773\) | −7220.23 | −0.335955 | −0.167978 | − | 0.985791i | \(-0.553724\pi\) | ||||
−0.167978 | + | 0.985791i | \(0.553724\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 90424.2 | 4.19114 | ||||||||
\(776\) | 7363.34 | 0.340629 | ||||||||
\(777\) | 11616.2 | 0.536329 | ||||||||
\(778\) | −16988.5 | −0.782862 | ||||||||
\(779\) | 9845.12 | 0.452809 | ||||||||
\(780\) | −1205.00 | −0.0553154 | ||||||||
\(781\) | −17683.7 | −0.810208 | ||||||||
\(782\) | 4677.32 | 0.213888 | ||||||||
\(783\) | −5003.08 | −0.228347 | ||||||||
\(784\) | −20912.3 | −0.952636 | ||||||||
\(785\) | −27185.9 | −1.23606 | ||||||||
\(786\) | 7163.40 | 0.325076 | ||||||||
\(787\) | 30348.7 | 1.37460 | 0.687302 | − | 0.726372i | \(-0.258795\pi\) | ||||
0.687302 | + | 0.726372i | \(0.258795\pi\) | |||||||
\(788\) | −351.851 | −0.0159063 | ||||||||
\(789\) | −44186.9 | −1.99379 | ||||||||
\(790\) | 13775.7 | 0.620402 | ||||||||
\(791\) | 38510.7 | 1.73108 | ||||||||
\(792\) | −11229.2 | −0.503805 | ||||||||
\(793\) | −6934.11 | −0.310514 | ||||||||
\(794\) | 30527.1 | 1.36444 | ||||||||
\(795\) | 55937.3 | 2.49546 | ||||||||
\(796\) | 163.813 | 0.00729423 | ||||||||
\(797\) | −1900.17 | −0.0844509 | −0.0422254 | − | 0.999108i | \(-0.513445\pi\) | ||||
−0.0422254 | + | 0.999108i | \(0.513445\pi\) | |||||||
\(798\) | 35285.6 | 1.56528 | ||||||||
\(799\) | −5063.66 | −0.224204 | ||||||||
\(800\) | 6101.60 | 0.269655 | ||||||||
\(801\) | 215.432 | 0.00950300 | ||||||||
\(802\) | −14529.1 | −0.639703 | ||||||||
\(803\) | −3885.79 | −0.170768 | ||||||||
\(804\) | 856.524 | 0.0375712 | ||||||||
\(805\) | 27738.6 | 1.21448 | ||||||||
\(806\) | −17536.2 | −0.766362 | ||||||||
\(807\) | 25690.3 | 1.12062 | ||||||||
\(808\) | −28712.0 | −1.25011 | ||||||||
\(809\) | −18024.2 | −0.783309 | −0.391654 | − | 0.920112i | \(-0.628097\pi\) | ||||
−0.391654 | + | 0.920112i | \(0.628097\pi\) | |||||||
\(810\) | −56546.1 | −2.45287 | ||||||||
\(811\) | 28590.6 | 1.23792 | 0.618958 | − | 0.785424i | \(-0.287555\pi\) | ||||
0.618958 | + | 0.785424i | \(0.287555\pi\) | |||||||
\(812\) | −532.638 | −0.0230196 | ||||||||
\(813\) | −17137.2 | −0.739271 | ||||||||
\(814\) | −9391.87 | −0.404404 | ||||||||
\(815\) | −922.799 | −0.0396616 | ||||||||
\(816\) | 13319.9 | 0.571434 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 36413.7 | 1.55645 | ||||||||
\(819\) | −6649.22 | −0.283691 | ||||||||
\(820\) | −1104.46 | −0.0470360 | ||||||||
\(821\) | 9514.04 | 0.404436 | 0.202218 | − | 0.979340i | \(-0.435185\pi\) | ||||
0.202218 | + | 0.979340i | \(0.435185\pi\) | |||||||
\(822\) | 23547.2 | 0.999153 | ||||||||
\(823\) | −44795.5 | −1.89729 | −0.948646 | − | 0.316338i | \(-0.897546\pi\) | ||||
−0.948646 | + | 0.316338i | \(0.897546\pi\) | |||||||
\(824\) | 45912.7 | 1.94107 | ||||||||
\(825\) | −92764.0 | −3.91470 | ||||||||
\(826\) | 15478.2 | 0.652006 | ||||||||
\(827\) | −36045.1 | −1.51561 | −0.757806 | − | 0.652480i | \(-0.773729\pi\) | ||||
−0.757806 | + | 0.652480i | \(0.773729\pi\) | |||||||
\(828\) | 231.967 | 0.00973600 | ||||||||
\(829\) | −37164.1 | −1.55701 | −0.778506 | − | 0.627637i | \(-0.784022\pi\) | ||||
−0.778506 | + | 0.627637i | \(0.784022\pi\) | |||||||
\(830\) | 27038.7 | 1.13075 | ||||||||
\(831\) | −42123.4 | −1.75842 | ||||||||
\(832\) | 10926.0 | 0.455278 | ||||||||
\(833\) | −9987.77 | −0.415433 | ||||||||
\(834\) | −23979.1 | −0.995598 | ||||||||
\(835\) | −50260.8 | −2.08305 | ||||||||
\(836\) | −1358.33 | −0.0561948 | ||||||||
\(837\) | −25763.2 | −1.06393 | ||||||||
\(838\) | 39196.1 | 1.61576 | ||||||||
\(839\) | −2120.52 | −0.0872567 | −0.0436284 | − | 0.999048i | \(-0.513892\pi\) | ||||
−0.0436284 | + | 0.999048i | \(0.513892\pi\) | |||||||
\(840\) | 75222.9 | 3.08981 | ||||||||
\(841\) | −21680.8 | −0.888960 | ||||||||
\(842\) | −47237.0 | −1.93337 | ||||||||
\(843\) | 14017.6 | 0.572707 | ||||||||
\(844\) | 1942.61 | 0.0792268 | ||||||||
\(845\) | 36282.0 | 1.47709 | ||||||||
\(846\) | −5274.43 | −0.214348 | ||||||||
\(847\) | −16165.4 | −0.655786 | ||||||||
\(848\) | 28102.0 | 1.13800 | ||||||||
\(849\) | 15190.4 | 0.614057 | ||||||||
\(850\) | 31312.8 | 1.26355 | ||||||||
\(851\) | −3686.81 | −0.148510 | ||||||||
\(852\) | 990.640 | 0.0398342 | ||||||||
\(853\) | −30242.2 | −1.21392 | −0.606960 | − | 0.794732i | \(-0.707611\pi\) | ||||
−0.606960 | + | 0.794732i | \(0.707611\pi\) | |||||||
\(854\) | −22778.8 | −0.912733 | ||||||||
\(855\) | −18970.7 | −0.758811 | ||||||||
\(856\) | 18166.6 | 0.725377 | ||||||||
\(857\) | 19083.9 | 0.760668 | 0.380334 | − | 0.924849i | \(-0.375809\pi\) | ||||
0.380334 | + | 0.924849i | \(0.375809\pi\) | |||||||
\(858\) | 17990.0 | 0.715814 | ||||||||
\(859\) | 25660.8 | 1.01925 | 0.509625 | − | 0.860397i | \(-0.329784\pi\) | ||||
0.509625 | + | 0.860397i | \(0.329784\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −20394.1 | −0.807235 | ||||||||
\(862\) | −4778.29 | −0.188804 | ||||||||
\(863\) | −26806.1 | −1.05735 | −0.528674 | − | 0.848825i | \(-0.677310\pi\) | ||||
−0.528674 | + | 0.848825i | \(0.677310\pi\) | |||||||
\(864\) | −1738.44 | −0.0684523 | ||||||||
\(865\) | −75398.8 | −2.96374 | ||||||||
\(866\) | 12115.5 | 0.475407 | ||||||||
\(867\) | −24125.6 | −0.945038 | ||||||||
\(868\) | −2742.80 | −0.107254 | ||||||||
\(869\) | −9792.09 | −0.382248 | ||||||||
\(870\) | 20126.6 | 0.784316 | ||||||||
\(871\) | 7792.42 | 0.303141 | ||||||||
\(872\) | −34678.1 | −1.34673 | ||||||||
\(873\) | 3846.72 | 0.149132 | ||||||||
\(874\) | −11199.2 | −0.433430 | ||||||||
\(875\) | 116907. | 4.51679 | ||||||||
\(876\) | 217.682 | 0.00839587 | ||||||||
\(877\) | 37676.2 | 1.45067 | 0.725333 | − | 0.688398i | \(-0.241686\pi\) | ||||
0.725333 | + | 0.688398i | \(0.241686\pi\) | |||||||
\(878\) | −17705.4 | −0.680556 | ||||||||
\(879\) | −47340.5 | −1.81656 | ||||||||
\(880\) | −63867.2 | −2.44655 | ||||||||
\(881\) | −10062.6 | −0.384810 | −0.192405 | − | 0.981316i | \(-0.561629\pi\) | ||||
−0.192405 | + | 0.981316i | \(0.561629\pi\) | |||||||
\(882\) | −10403.5 | −0.397170 | ||||||||
\(883\) | 4862.49 | 0.185318 | 0.0926591 | − | 0.995698i | \(-0.470463\pi\) | ||||
0.0926591 | + | 0.995698i | \(0.470463\pi\) | |||||||
\(884\) | −289.129 | −0.0110005 | ||||||||
\(885\) | −27847.0 | −1.05770 | ||||||||
\(886\) | −42535.4 | −1.61287 | ||||||||
\(887\) | 27243.1 | 1.03127 | 0.515634 | − | 0.856809i | \(-0.327557\pi\) | ||||
0.515634 | + | 0.856809i | \(0.327557\pi\) | |||||||
\(888\) | −9998.09 | −0.377831 | ||||||||
\(889\) | −5857.94 | −0.221000 | ||||||||
\(890\) | 1166.81 | 0.0439455 | ||||||||
\(891\) | 40194.3 | 1.51129 | ||||||||
\(892\) | −47.1598 | −0.00177021 | ||||||||
\(893\) | 12124.2 | 0.454335 | ||||||||
\(894\) | 34000.3 | 1.27197 | ||||||||
\(895\) | −4532.04 | −0.169262 | ||||||||
\(896\) | 39594.5 | 1.47629 | ||||||||
\(897\) | 7062.03 | 0.262870 | ||||||||
\(898\) | 27674.1 | 1.02839 | ||||||||
\(899\) | 13945.6 | 0.517366 | ||||||||
\(900\) | 1552.93 | 0.0575158 | ||||||||
\(901\) | 13421.6 | 0.496270 | ||||||||
\(902\) | 16489.0 | 0.608674 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −33146.4 | −1.21951 | ||||||||
\(905\) | 42685.6 | 1.56786 | ||||||||
\(906\) | 38019.9 | 1.39418 | ||||||||
\(907\) | −2391.74 | −0.0875596 | −0.0437798 | − | 0.999041i | \(-0.513940\pi\) | ||||
−0.0437798 | + | 0.999041i | \(0.513940\pi\) | |||||||
\(908\) | 1788.06 | 0.0653511 | ||||||||
\(909\) | −14999.6 | −0.547311 | ||||||||
\(910\) | −36013.1 | −1.31189 | ||||||||
\(911\) | 14501.2 | 0.527385 | 0.263692 | − | 0.964607i | \(-0.415060\pi\) | ||||
0.263692 | + | 0.964607i | \(0.415060\pi\) | |||||||
\(912\) | −31892.6 | −1.15797 | ||||||||
\(913\) | −19219.7 | −0.696692 | ||||||||
\(914\) | 34025.7 | 1.23137 | ||||||||
\(915\) | 40981.4 | 1.48066 | ||||||||
\(916\) | 2235.57 | 0.0806389 | ||||||||
\(917\) | 10193.2 | 0.367076 | ||||||||
\(918\) | −8921.47 | −0.320754 | ||||||||
\(919\) | 26321.1 | 0.944779 | 0.472389 | − | 0.881390i | \(-0.343392\pi\) | ||||
0.472389 | + | 0.881390i | \(0.343392\pi\) | |||||||
\(920\) | −23874.7 | −0.855572 | ||||||||
\(921\) | −27075.8 | −0.968707 | ||||||||
\(922\) | −24651.1 | −0.880522 | ||||||||
\(923\) | 9012.57 | 0.321400 | ||||||||
\(924\) | 2813.77 | 0.100180 | ||||||||
\(925\) | −24681.7 | −0.877330 | ||||||||
\(926\) | 45320.0 | 1.60832 | ||||||||
\(927\) | 23985.5 | 0.849825 | ||||||||
\(928\) | 941.014 | 0.0332870 | ||||||||
\(929\) | 5321.18 | 0.187925 | 0.0939625 | − | 0.995576i | \(-0.470047\pi\) | ||||
0.0939625 | + | 0.995576i | \(0.470047\pi\) | |||||||
\(930\) | 103641. | 3.65433 | ||||||||
\(931\) | 23914.3 | 0.841847 | ||||||||
\(932\) | −1641.41 | −0.0576891 | ||||||||
\(933\) | −8506.80 | −0.298500 | ||||||||
\(934\) | −4611.96 | −0.161572 | ||||||||
\(935\) | −30503.2 | −1.06691 | ||||||||
\(936\) | 5723.02 | 0.199853 | ||||||||
\(937\) | 45519.2 | 1.58703 | 0.793515 | − | 0.608551i | \(-0.208249\pi\) | ||||
0.793515 | + | 0.608551i | \(0.208249\pi\) | |||||||
\(938\) | 25598.4 | 0.891062 | ||||||||
\(939\) | 20509.1 | 0.712768 | ||||||||
\(940\) | −1360.14 | −0.0471945 | ||||||||
\(941\) | −22898.3 | −0.793264 | −0.396632 | − | 0.917978i | \(-0.629821\pi\) | ||||
−0.396632 | + | 0.917978i | \(0.629821\pi\) | |||||||
\(942\) | −22736.8 | −0.786416 | ||||||||
\(943\) | 6472.81 | 0.223525 | ||||||||
\(944\) | −13989.9 | −0.482343 | ||||||||
\(945\) | −52908.3 | −1.82128 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 7576.46 | 0.259981 | 0.129990 | − | 0.991515i | \(-0.458505\pi\) | ||||
0.129990 | + | 0.991515i | \(0.458505\pi\) | |||||||
\(948\) | 548.552 | 0.0187934 | ||||||||
\(949\) | 1980.41 | 0.0677416 | ||||||||
\(950\) | −74974.0 | −2.56050 | ||||||||
\(951\) | 27661.4 | 0.943199 | ||||||||
\(952\) | 18049.1 | 0.614468 | ||||||||
\(953\) | 10070.1 | 0.342289 | 0.171144 | − | 0.985246i | \(-0.445254\pi\) | ||||
0.171144 | + | 0.985246i | \(0.445254\pi\) | |||||||
\(954\) | 13980.3 | 0.474454 | ||||||||
\(955\) | 77944.5 | 2.64107 | ||||||||
\(956\) | 1488.75 | 0.0503656 | ||||||||
\(957\) | −14306.4 | −0.483241 | ||||||||
\(958\) | 26791.9 | 0.903555 | ||||||||
\(959\) | 33506.6 | 1.12824 | ||||||||
\(960\) | −64574.1 | −2.17096 | ||||||||
\(961\) | 42021.4 | 1.41054 | ||||||||
\(962\) | 4786.60 | 0.160422 | ||||||||
\(963\) | 9490.54 | 0.317579 | ||||||||
\(964\) | 1850.30 | 0.0618198 | ||||||||
\(965\) | 51308.2 | 1.71157 | ||||||||
\(966\) | 23199.0 | 0.772688 | ||||||||
\(967\) | 12667.8 | 0.421271 | 0.210636 | − | 0.977565i | \(-0.432447\pi\) | ||||
0.210636 | + | 0.977565i | \(0.432447\pi\) | |||||||
\(968\) | 13913.7 | 0.461986 | ||||||||
\(969\) | −15232.0 | −0.504978 | ||||||||
\(970\) | 20834.4 | 0.689642 | ||||||||
\(971\) | −57726.9 | −1.90787 | −0.953936 | − | 0.300011i | \(-0.903010\pi\) | ||||
−0.953936 | + | 0.300011i | \(0.903010\pi\) | |||||||
\(972\) | −1213.53 | −0.0400454 | ||||||||
\(973\) | −34121.2 | −1.12423 | ||||||||
\(974\) | −7781.66 | −0.255996 | ||||||||
\(975\) | 47277.5 | 1.55292 | ||||||||
\(976\) | 20588.4 | 0.675225 | ||||||||
\(977\) | −35376.7 | −1.15844 | −0.579222 | − | 0.815170i | \(-0.696644\pi\) | ||||
−0.579222 | + | 0.815170i | \(0.696644\pi\) | |||||||
\(978\) | −771.779 | −0.0252339 | ||||||||
\(979\) | −829.394 | −0.0270761 | ||||||||
\(980\) | −2682.80 | −0.0874477 | ||||||||
\(981\) | −18116.4 | −0.589614 | ||||||||
\(982\) | −30364.2 | −0.986723 | ||||||||
\(983\) | −9770.00 | −0.317004 | −0.158502 | − | 0.987359i | \(-0.550666\pi\) | ||||
−0.158502 | + | 0.987359i | \(0.550666\pi\) | |||||||
\(984\) | 17553.3 | 0.568679 | ||||||||
\(985\) | 18918.6 | 0.611975 | ||||||||
\(986\) | 4829.19 | 0.155976 | ||||||||
\(987\) | −25115.2 | −0.809956 | ||||||||
\(988\) | 692.278 | 0.0222918 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | −31772.9 | −1.02001 | ||||||||
\(991\) | −16535.4 | −0.530036 | −0.265018 | − | 0.964244i | \(-0.585378\pi\) | ||||
−0.265018 | + | 0.964244i | \(0.585378\pi\) | |||||||
\(992\) | 4845.72 | 0.155093 | ||||||||
\(993\) | 8974.16 | 0.286794 | ||||||||
\(994\) | 29606.6 | 0.944733 | ||||||||
\(995\) | −8808.02 | −0.280636 | ||||||||
\(996\) | 1076.69 | 0.0342532 | ||||||||
\(997\) | 16753.6 | 0.532187 | 0.266094 | − | 0.963947i | \(-0.414267\pi\) | ||||
0.266094 | + | 0.963947i | \(0.414267\pi\) | |||||||
\(998\) | −42786.7 | −1.35710 | ||||||||
\(999\) | 7032.19 | 0.222711 |
(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.g.1.9 | 30 | ||
43.2 | odd | 14 | 43.4.e.a.4.8 | ✓ | 60 | ||
43.22 | odd | 14 | 43.4.e.a.11.8 | yes | 60 | ||
43.42 | odd | 2 | 1849.4.a.h.1.22 | 30 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
43.4.e.a.4.8 | ✓ | 60 | 43.2 | odd | 14 | ||
43.4.e.a.11.8 | yes | 60 | 43.22 | odd | 14 | ||
1849.4.a.g.1.9 | 30 | 1.1 | even | 1 | trivial | ||
1849.4.a.h.1.22 | 30 | 43.42 | odd | 2 |