Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [798,4,Mod(1,798)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(798, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("798.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 798 = 2 \cdot 3 \cdot 7 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 798.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: | \(47.0835241846\) |
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: | \( x^{4} - 310x^{2} - 1444x - 1712 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Fricke sign: | \(+1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(-2.35201\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 798.1 |
$q$-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 | ||||||||
\(3\) | −3.00000 | −0.577350 | ||||||||
\(4\) | 4.00000 | 0.500000 | ||||||||
\(5\) | −2.35201 | −0.210370 | −0.105185 | − | 0.994453i | \(-0.533543\pi\) | ||||
−0.105185 | + | 0.994453i | \(0.533543\pi\) | |||||||
\(6\) | 6.00000 | 0.408248 | ||||||||
\(7\) | −7.00000 | −0.377964 | ||||||||
\(8\) | −8.00000 | −0.353553 | ||||||||
\(9\) | 9.00000 | 0.333333 | ||||||||
\(10\) | 4.70401 | 0.148754 | ||||||||
\(11\) | −65.1379 | −1.78544 | −0.892719 | − | 0.450613i | \(-0.851205\pi\) | ||||
−0.892719 | + | 0.450613i | \(0.851205\pi\) | |||||||
\(12\) | −12.0000 | −0.288675 | ||||||||
\(13\) | −31.4764 | −0.671537 | −0.335768 | − | 0.941945i | \(-0.608996\pi\) | ||||
−0.335768 | + | 0.941945i | \(0.608996\pi\) | |||||||
\(14\) | 14.0000 | 0.267261 | ||||||||
\(15\) | 7.05602 | 0.121457 | ||||||||
\(16\) | 16.0000 | 0.250000 | ||||||||
\(17\) | −43.0831 | −0.614658 | −0.307329 | − | 0.951603i | \(-0.599435\pi\) | ||||
−0.307329 | + | 0.951603i | \(0.599435\pi\) | |||||||
\(18\) | −18.0000 | −0.235702 | ||||||||
\(19\) | −19.0000 | −0.229416 | ||||||||
\(20\) | −9.40803 | −0.105185 | ||||||||
\(21\) | 21.0000 | 0.218218 | ||||||||
\(22\) | 130.276 | 1.26250 | ||||||||
\(23\) | 92.8218 | 0.841508 | 0.420754 | − | 0.907175i | \(-0.361766\pi\) | ||||
0.420754 | + | 0.907175i | \(0.361766\pi\) | |||||||
\(24\) | 24.0000 | 0.204124 | ||||||||
\(25\) | −119.468 | −0.955744 | ||||||||
\(26\) | 62.9528 | 0.474848 | ||||||||
\(27\) | −27.0000 | −0.192450 | ||||||||
\(28\) | −28.0000 | −0.188982 | ||||||||
\(29\) | −95.7140 | −0.612884 | −0.306442 | − | 0.951889i | \(-0.599139\pi\) | ||||
−0.306442 | + | 0.951889i | \(0.599139\pi\) | |||||||
\(30\) | −14.1120 | −0.0858832 | ||||||||
\(31\) | 161.087 | 0.933294 | 0.466647 | − | 0.884444i | \(-0.345462\pi\) | ||||
0.466647 | + | 0.884444i | \(0.345462\pi\) | |||||||
\(32\) | −32.0000 | −0.176777 | ||||||||
\(33\) | 195.414 | 1.03082 | ||||||||
\(34\) | 86.1662 | 0.434629 | ||||||||
\(35\) | 16.4641 | 0.0795124 | ||||||||
\(36\) | 36.0000 | 0.166667 | ||||||||
\(37\) | 5.04480 | 0.0224151 | 0.0112076 | − | 0.999937i | \(-0.496432\pi\) | ||||
0.0112076 | + | 0.999937i | \(0.496432\pi\) | |||||||
\(38\) | 38.0000 | 0.162221 | ||||||||
\(39\) | 94.4291 | 0.387712 | ||||||||
\(40\) | 18.8161 | 0.0743770 | ||||||||
\(41\) | −434.908 | −1.65661 | −0.828307 | − | 0.560274i | \(-0.810696\pi\) | ||||
−0.828307 | + | 0.560274i | \(0.810696\pi\) | |||||||
\(42\) | −42.0000 | −0.154303 | ||||||||
\(43\) | 54.7476 | 0.194161 | 0.0970805 | − | 0.995277i | \(-0.469050\pi\) | ||||
0.0970805 | + | 0.995277i | \(0.469050\pi\) | |||||||
\(44\) | −260.552 | −0.892719 | ||||||||
\(45\) | −21.1681 | −0.0701233 | ||||||||
\(46\) | −185.644 | −0.595036 | ||||||||
\(47\) | −220.621 | −0.684698 | −0.342349 | − | 0.939573i | \(-0.611223\pi\) | ||||
−0.342349 | + | 0.939573i | \(0.611223\pi\) | |||||||
\(48\) | −48.0000 | −0.144338 | ||||||||
\(49\) | 49.0000 | 0.142857 | ||||||||
\(50\) | 238.936 | 0.675813 | ||||||||
\(51\) | 129.249 | 0.354873 | ||||||||
\(52\) | −125.906 | −0.335768 | ||||||||
\(53\) | 175.142 | 0.453917 | 0.226959 | − | 0.973904i | \(-0.427122\pi\) | ||||
0.226959 | + | 0.973904i | \(0.427122\pi\) | |||||||
\(54\) | 54.0000 | 0.136083 | ||||||||
\(55\) | 153.205 | 0.375603 | ||||||||
\(56\) | 56.0000 | 0.133631 | ||||||||
\(57\) | 57.0000 | 0.132453 | ||||||||
\(58\) | 191.428 | 0.433375 | ||||||||
\(59\) | −383.026 | −0.845181 | −0.422591 | − | 0.906321i | \(-0.638879\pi\) | ||||
−0.422591 | + | 0.906321i | \(0.638879\pi\) | |||||||
\(60\) | 28.2241 | 0.0607286 | ||||||||
\(61\) | 431.625 | 0.905965 | 0.452983 | − | 0.891519i | \(-0.350360\pi\) | ||||
0.452983 | + | 0.891519i | \(0.350360\pi\) | |||||||
\(62\) | −322.174 | −0.659938 | ||||||||
\(63\) | −63.0000 | −0.125988 | ||||||||
\(64\) | 64.0000 | 0.125000 | ||||||||
\(65\) | 74.0327 | 0.141271 | ||||||||
\(66\) | −390.828 | −0.728902 | ||||||||
\(67\) | −989.711 | −1.80466 | −0.902332 | − | 0.431042i | \(-0.858146\pi\) | ||||
−0.902332 | + | 0.431042i | \(0.858146\pi\) | |||||||
\(68\) | −172.332 | −0.307329 | ||||||||
\(69\) | −278.465 | −0.485845 | ||||||||
\(70\) | −32.9281 | −0.0562237 | ||||||||
\(71\) | −456.366 | −0.762827 | −0.381413 | − | 0.924405i | \(-0.624563\pi\) | ||||
−0.381413 | + | 0.924405i | \(0.624563\pi\) | |||||||
\(72\) | −72.0000 | −0.117851 | ||||||||
\(73\) | 92.3693 | 0.148096 | 0.0740480 | − | 0.997255i | \(-0.476408\pi\) | ||||
0.0740480 | + | 0.997255i | \(0.476408\pi\) | |||||||
\(74\) | −10.0896 | −0.0158499 | ||||||||
\(75\) | 358.404 | 0.551799 | ||||||||
\(76\) | −76.0000 | −0.114708 | ||||||||
\(77\) | 455.965 | 0.674832 | ||||||||
\(78\) | −188.858 | −0.274154 | ||||||||
\(79\) | 620.873 | 0.884224 | 0.442112 | − | 0.896960i | \(-0.354229\pi\) | ||||
0.442112 | + | 0.896960i | \(0.354229\pi\) | |||||||
\(80\) | −37.6321 | −0.0525925 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | 869.816 | 1.17140 | ||||||||
\(83\) | 519.728 | 0.687320 | 0.343660 | − | 0.939094i | \(-0.388333\pi\) | ||||
0.343660 | + | 0.939094i | \(0.388333\pi\) | |||||||
\(84\) | 84.0000 | 0.109109 | ||||||||
\(85\) | 101.332 | 0.129306 | ||||||||
\(86\) | −109.495 | −0.137293 | ||||||||
\(87\) | 287.142 | 0.353849 | ||||||||
\(88\) | 521.103 | 0.631248 | ||||||||
\(89\) | 1049.89 | 1.25042 | 0.625212 | − | 0.780455i | \(-0.285013\pi\) | ||||
0.625212 | + | 0.780455i | \(0.285013\pi\) | |||||||
\(90\) | 42.3361 | 0.0495847 | ||||||||
\(91\) | 220.335 | 0.253817 | ||||||||
\(92\) | 371.287 | 0.420754 | ||||||||
\(93\) | −483.261 | −0.538837 | ||||||||
\(94\) | 441.241 | 0.484155 | ||||||||
\(95\) | 44.6881 | 0.0482622 | ||||||||
\(96\) | 96.0000 | 0.102062 | ||||||||
\(97\) | −166.305 | −0.174079 | −0.0870396 | − | 0.996205i | \(-0.527741\pi\) | ||||
−0.0870396 | + | 0.996205i | \(0.527741\pi\) | |||||||
\(98\) | −98.0000 | −0.101015 | ||||||||
\(99\) | −586.241 | −0.595146 | ||||||||
\(100\) | −477.872 | −0.477872 | ||||||||
\(101\) | 1504.58 | 1.48229 | 0.741147 | − | 0.671343i | \(-0.234282\pi\) | ||||
0.741147 | + | 0.671343i | \(0.234282\pi\) | |||||||
\(102\) | −258.499 | −0.250933 | ||||||||
\(103\) | −1145.68 | −1.09599 | −0.547994 | − | 0.836482i | \(-0.684608\pi\) | ||||
−0.547994 | + | 0.836482i | \(0.684608\pi\) | |||||||
\(104\) | 251.811 | 0.237424 | ||||||||
\(105\) | −49.3922 | −0.0459065 | ||||||||
\(106\) | −350.284 | −0.320968 | ||||||||
\(107\) | −804.550 | −0.726905 | −0.363452 | − | 0.931613i | \(-0.618402\pi\) | ||||
−0.363452 | + | 0.931613i | \(0.618402\pi\) | |||||||
\(108\) | −108.000 | −0.0962250 | ||||||||
\(109\) | 2146.46 | 1.88618 | 0.943089 | − | 0.332541i | \(-0.107906\pi\) | ||||
0.943089 | + | 0.332541i | \(0.107906\pi\) | |||||||
\(110\) | −306.410 | −0.265591 | ||||||||
\(111\) | −15.1344 | −0.0129414 | ||||||||
\(112\) | −112.000 | −0.0944911 | ||||||||
\(113\) | −456.239 | −0.379818 | −0.189909 | − | 0.981802i | \(-0.560819\pi\) | ||||
−0.189909 | + | 0.981802i | \(0.560819\pi\) | |||||||
\(114\) | −114.000 | −0.0936586 | ||||||||
\(115\) | −218.318 | −0.177028 | ||||||||
\(116\) | −382.856 | −0.306442 | ||||||||
\(117\) | −283.287 | −0.223846 | ||||||||
\(118\) | 766.051 | 0.597633 | ||||||||
\(119\) | 301.582 | 0.232319 | ||||||||
\(120\) | −56.4482 | −0.0429416 | ||||||||
\(121\) | 2911.95 | 2.18779 | ||||||||
\(122\) | −863.250 | −0.640614 | ||||||||
\(123\) | 1304.72 | 0.956447 | ||||||||
\(124\) | 644.349 | 0.466647 | ||||||||
\(125\) | 574.991 | 0.411430 | ||||||||
\(126\) | 126.000 | 0.0890871 | ||||||||
\(127\) | 1257.44 | 0.878582 | 0.439291 | − | 0.898345i | \(-0.355230\pi\) | ||||
0.439291 | + | 0.898345i | \(0.355230\pi\) | |||||||
\(128\) | −128.000 | −0.0883883 | ||||||||
\(129\) | −164.243 | −0.112099 | ||||||||
\(130\) | −148.065 | −0.0998938 | ||||||||
\(131\) | −2329.46 | −1.55363 | −0.776817 | − | 0.629726i | \(-0.783167\pi\) | ||||
−0.776817 | + | 0.629726i | \(0.783167\pi\) | |||||||
\(132\) | 781.655 | 0.515412 | ||||||||
\(133\) | 133.000 | 0.0867110 | ||||||||
\(134\) | 1979.42 | 1.27609 | ||||||||
\(135\) | 63.5042 | 0.0404857 | ||||||||
\(136\) | 344.665 | 0.217315 | ||||||||
\(137\) | 1728.59 | 1.07798 | 0.538990 | − | 0.842312i | \(-0.318806\pi\) | ||||
0.538990 | + | 0.842312i | \(0.318806\pi\) | |||||||
\(138\) | 556.931 | 0.343544 | ||||||||
\(139\) | −691.205 | −0.421779 | −0.210889 | − | 0.977510i | \(-0.567636\pi\) | ||||
−0.210889 | + | 0.977510i | \(0.567636\pi\) | |||||||
\(140\) | 65.8562 | 0.0397562 | ||||||||
\(141\) | 661.862 | 0.395311 | ||||||||
\(142\) | 912.733 | 0.539400 | ||||||||
\(143\) | 2050.31 | 1.19899 | ||||||||
\(144\) | 144.000 | 0.0833333 | ||||||||
\(145\) | 225.120 | 0.128932 | ||||||||
\(146\) | −184.739 | −0.104720 | ||||||||
\(147\) | −147.000 | −0.0824786 | ||||||||
\(148\) | 20.1792 | 0.0112076 | ||||||||
\(149\) | −2337.76 | −1.28535 | −0.642674 | − | 0.766140i | \(-0.722175\pi\) | ||||
−0.642674 | + | 0.766140i | \(0.722175\pi\) | |||||||
\(150\) | −716.808 | −0.390181 | ||||||||
\(151\) | 2681.77 | 1.44529 | 0.722646 | − | 0.691218i | \(-0.242926\pi\) | ||||
0.722646 | + | 0.691218i | \(0.242926\pi\) | |||||||
\(152\) | 152.000 | 0.0811107 | ||||||||
\(153\) | −387.748 | −0.204886 | ||||||||
\(154\) | −911.931 | −0.477178 | ||||||||
\(155\) | −378.878 | −0.196337 | ||||||||
\(156\) | 377.717 | 0.193856 | ||||||||
\(157\) | 762.000 | 0.387352 | 0.193676 | − | 0.981066i | \(-0.437959\pi\) | ||||
0.193676 | + | 0.981066i | \(0.437959\pi\) | |||||||
\(158\) | −1241.75 | −0.625241 | ||||||||
\(159\) | −525.426 | −0.262069 | ||||||||
\(160\) | 75.2642 | 0.0371885 | ||||||||
\(161\) | −649.752 | −0.318060 | ||||||||
\(162\) | −162.000 | −0.0785674 | ||||||||
\(163\) | 3452.06 | 1.65881 | 0.829406 | − | 0.558647i | \(-0.188679\pi\) | ||||
0.829406 | + | 0.558647i | \(0.188679\pi\) | |||||||
\(164\) | −1739.63 | −0.828307 | ||||||||
\(165\) | −459.615 | −0.216854 | ||||||||
\(166\) | −1039.46 | −0.486009 | ||||||||
\(167\) | 3589.50 | 1.66326 | 0.831628 | − | 0.555333i | \(-0.187409\pi\) | ||||
0.831628 | + | 0.555333i | \(0.187409\pi\) | |||||||
\(168\) | −168.000 | −0.0771517 | ||||||||
\(169\) | −1206.24 | −0.549039 | ||||||||
\(170\) | −202.664 | −0.0914329 | ||||||||
\(171\) | −171.000 | −0.0764719 | ||||||||
\(172\) | 218.990 | 0.0970805 | ||||||||
\(173\) | 1795.76 | 0.789187 | 0.394593 | − | 0.918856i | \(-0.370885\pi\) | ||||
0.394593 | + | 0.918856i | \(0.370885\pi\) | |||||||
\(174\) | −574.284 | −0.250209 | ||||||||
\(175\) | 836.276 | 0.361237 | ||||||||
\(176\) | −1042.21 | −0.446360 | ||||||||
\(177\) | 1149.08 | 0.487966 | ||||||||
\(178\) | −2099.77 | −0.884183 | ||||||||
\(179\) | −2476.29 | −1.03400 | −0.517002 | − | 0.855984i | \(-0.672952\pi\) | ||||
−0.517002 | + | 0.855984i | \(0.672952\pi\) | |||||||
\(180\) | −84.6723 | −0.0350617 | ||||||||
\(181\) | 2402.09 | 0.986441 | 0.493220 | − | 0.869904i | \(-0.335820\pi\) | ||||
0.493220 | + | 0.869904i | \(0.335820\pi\) | |||||||
\(182\) | −440.669 | −0.179476 | ||||||||
\(183\) | −1294.87 | −0.523059 | ||||||||
\(184\) | −742.574 | −0.297518 | ||||||||
\(185\) | −11.8654 | −0.00471547 | ||||||||
\(186\) | 966.523 | 0.381016 | ||||||||
\(187\) | 2806.34 | 1.09743 | ||||||||
\(188\) | −882.482 | −0.342349 | ||||||||
\(189\) | 189.000 | 0.0727393 | ||||||||
\(190\) | −89.3763 | −0.0341265 | ||||||||
\(191\) | −1635.57 | −0.619610 | −0.309805 | − | 0.950800i | \(-0.600264\pi\) | ||||
−0.309805 | + | 0.950800i | \(0.600264\pi\) | |||||||
\(192\) | −192.000 | −0.0721688 | ||||||||
\(193\) | 4432.79 | 1.65326 | 0.826630 | − | 0.562746i | \(-0.190255\pi\) | ||||
0.826630 | + | 0.562746i | \(0.190255\pi\) | |||||||
\(194\) | 332.609 | 0.123093 | ||||||||
\(195\) | −222.098 | −0.0815629 | ||||||||
\(196\) | 196.000 | 0.0714286 | ||||||||
\(197\) | 2601.65 | 0.940914 | 0.470457 | − | 0.882423i | \(-0.344089\pi\) | ||||
0.470457 | + | 0.882423i | \(0.344089\pi\) | |||||||
\(198\) | 1172.48 | 0.420832 | ||||||||
\(199\) | 1975.71 | 0.703791 | 0.351895 | − | 0.936039i | \(-0.385537\pi\) | ||||
0.351895 | + | 0.936039i | \(0.385537\pi\) | |||||||
\(200\) | 955.744 | 0.337907 | ||||||||
\(201\) | 2969.13 | 1.04192 | ||||||||
\(202\) | −3009.17 | −1.04814 | ||||||||
\(203\) | 669.998 | 0.231649 | ||||||||
\(204\) | 516.997 | 0.177437 | ||||||||
\(205\) | 1022.91 | 0.348502 | ||||||||
\(206\) | 2291.35 | 0.774980 | ||||||||
\(207\) | 835.396 | 0.280503 | ||||||||
\(208\) | −503.622 | −0.167884 | ||||||||
\(209\) | 1237.62 | 0.409608 | ||||||||
\(210\) | 98.7843 | 0.0324608 | ||||||||
\(211\) | −3735.55 | −1.21880 | −0.609398 | − | 0.792864i | \(-0.708589\pi\) | ||||
−0.609398 | + | 0.792864i | \(0.708589\pi\) | |||||||
\(212\) | 700.568 | 0.226959 | ||||||||
\(213\) | 1369.10 | 0.440418 | ||||||||
\(214\) | 1609.10 | 0.513999 | ||||||||
\(215\) | −128.767 | −0.0408456 | ||||||||
\(216\) | 216.000 | 0.0680414 | ||||||||
\(217\) | −1127.61 | −0.352752 | ||||||||
\(218\) | −4292.91 | −1.33373 | ||||||||
\(219\) | −277.108 | −0.0855033 | ||||||||
\(220\) | 612.819 | 0.187801 | ||||||||
\(221\) | 1356.10 | 0.412766 | ||||||||
\(222\) | 30.2688 | 0.00915094 | ||||||||
\(223\) | 5621.09 | 1.68796 | 0.843982 | − | 0.536372i | \(-0.180205\pi\) | ||||
0.843982 | + | 0.536372i | \(0.180205\pi\) | |||||||
\(224\) | 224.000 | 0.0668153 | ||||||||
\(225\) | −1075.21 | −0.318581 | ||||||||
\(226\) | 912.479 | 0.268572 | ||||||||
\(227\) | −88.9122 | −0.0259970 | −0.0129985 | − | 0.999916i | \(-0.504138\pi\) | ||||
−0.0129985 | + | 0.999916i | \(0.504138\pi\) | |||||||
\(228\) | 228.000 | 0.0662266 | ||||||||
\(229\) | −3591.62 | −1.03642 | −0.518211 | − | 0.855253i | \(-0.673402\pi\) | ||||
−0.518211 | + | 0.855253i | \(0.673402\pi\) | |||||||
\(230\) | 436.635 | 0.125178 | ||||||||
\(231\) | −1367.90 | −0.389615 | ||||||||
\(232\) | 765.712 | 0.216687 | ||||||||
\(233\) | −1783.34 | −0.501417 | −0.250709 | − | 0.968063i | \(-0.580664\pi\) | ||||
−0.250709 | + | 0.968063i | \(0.580664\pi\) | |||||||
\(234\) | 566.575 | 0.158283 | ||||||||
\(235\) | 518.901 | 0.144040 | ||||||||
\(236\) | −1532.10 | −0.422591 | ||||||||
\(237\) | −1862.62 | −0.510507 | ||||||||
\(238\) | −603.164 | −0.164274 | ||||||||
\(239\) | −5280.63 | −1.42919 | −0.714594 | − | 0.699540i | \(-0.753388\pi\) | ||||
−0.714594 | + | 0.699540i | \(0.753388\pi\) | |||||||
\(240\) | 112.896 | 0.0303643 | ||||||||
\(241\) | 7111.18 | 1.90071 | 0.950355 | − | 0.311167i | \(-0.100720\pi\) | ||||
0.950355 | + | 0.311167i | \(0.100720\pi\) | |||||||
\(242\) | −5823.90 | −1.54700 | ||||||||
\(243\) | −243.000 | −0.0641500 | ||||||||
\(244\) | 1726.50 | 0.452983 | ||||||||
\(245\) | −115.248 | −0.0300528 | ||||||||
\(246\) | −2609.45 | −0.676310 | ||||||||
\(247\) | 598.051 | 0.154061 | ||||||||
\(248\) | −1288.70 | −0.329969 | ||||||||
\(249\) | −1559.18 | −0.396824 | ||||||||
\(250\) | −1149.98 | −0.290925 | ||||||||
\(251\) | −2522.95 | −0.634450 | −0.317225 | − | 0.948350i | \(-0.602751\pi\) | ||||
−0.317225 | + | 0.948350i | \(0.602751\pi\) | |||||||
\(252\) | −252.000 | −0.0629941 | ||||||||
\(253\) | −6046.22 | −1.50246 | ||||||||
\(254\) | −2514.88 | −0.621251 | ||||||||
\(255\) | −303.995 | −0.0746546 | ||||||||
\(256\) | 256.000 | 0.0625000 | ||||||||
\(257\) | −2126.61 | −0.516165 | −0.258082 | − | 0.966123i | \(-0.583091\pi\) | ||||
−0.258082 | + | 0.966123i | \(0.583091\pi\) | |||||||
\(258\) | 328.485 | 0.0792659 | ||||||||
\(259\) | −35.3136 | −0.00847213 | ||||||||
\(260\) | 296.131 | 0.0706356 | ||||||||
\(261\) | −861.426 | −0.204295 | ||||||||
\(262\) | 4658.92 | 1.09859 | ||||||||
\(263\) | −2709.59 | −0.635287 | −0.317644 | − | 0.948210i | \(-0.602892\pi\) | ||||
−0.317644 | + | 0.948210i | \(0.602892\pi\) | |||||||
\(264\) | −1563.31 | −0.364451 | ||||||||
\(265\) | −411.935 | −0.0954905 | ||||||||
\(266\) | −266.000 | −0.0613139 | ||||||||
\(267\) | −3149.66 | −0.721932 | ||||||||
\(268\) | −3958.84 | −0.902332 | ||||||||
\(269\) | −1063.61 | −0.241076 | −0.120538 | − | 0.992709i | \(-0.538462\pi\) | ||||
−0.120538 | + | 0.992709i | \(0.538462\pi\) | |||||||
\(270\) | −127.008 | −0.0286277 | ||||||||
\(271\) | 2415.84 | 0.541519 | 0.270759 | − | 0.962647i | \(-0.412725\pi\) | ||||
0.270759 | + | 0.962647i | \(0.412725\pi\) | |||||||
\(272\) | −689.330 | −0.153665 | ||||||||
\(273\) | −661.004 | −0.146541 | ||||||||
\(274\) | −3457.18 | −0.762247 | ||||||||
\(275\) | 7781.90 | 1.70642 | ||||||||
\(276\) | −1113.86 | −0.242922 | ||||||||
\(277\) | −2923.91 | −0.634226 | −0.317113 | − | 0.948388i | \(-0.602713\pi\) | ||||
−0.317113 | + | 0.948388i | \(0.602713\pi\) | |||||||
\(278\) | 1382.41 | 0.298243 | ||||||||
\(279\) | 1449.78 | 0.311098 | ||||||||
\(280\) | −131.712 | −0.0281119 | ||||||||
\(281\) | −7064.52 | −1.49976 | −0.749882 | − | 0.661571i | \(-0.769890\pi\) | ||||
−0.749882 | + | 0.661571i | \(0.769890\pi\) | |||||||
\(282\) | −1323.72 | −0.279527 | ||||||||
\(283\) | −7199.32 | −1.51221 | −0.756104 | − | 0.654451i | \(-0.772900\pi\) | ||||
−0.756104 | + | 0.654451i | \(0.772900\pi\) | |||||||
\(284\) | −1825.47 | −0.381413 | ||||||||
\(285\) | −134.064 | −0.0278642 | ||||||||
\(286\) | −4100.61 | −0.847812 | ||||||||
\(287\) | 3044.35 | 0.626141 | ||||||||
\(288\) | −288.000 | −0.0589256 | ||||||||
\(289\) | −3056.85 | −0.622195 | ||||||||
\(290\) | −450.240 | −0.0911690 | ||||||||
\(291\) | 498.914 | 0.100505 | ||||||||
\(292\) | 369.477 | 0.0740480 | ||||||||
\(293\) | 3001.16 | 0.598395 | 0.299198 | − | 0.954191i | \(-0.403281\pi\) | ||||
0.299198 | + | 0.954191i | \(0.403281\pi\) | |||||||
\(294\) | 294.000 | 0.0583212 | ||||||||
\(295\) | 900.879 | 0.177801 | ||||||||
\(296\) | −40.3584 | −0.00792495 | ||||||||
\(297\) | 1758.72 | 0.343608 | ||||||||
\(298\) | 4675.52 | 0.908878 | ||||||||
\(299\) | −2921.69 | −0.565103 | ||||||||
\(300\) | 1433.62 | 0.275900 | ||||||||
\(301\) | −383.233 | −0.0733860 | ||||||||
\(302\) | −5363.54 | −1.02198 | ||||||||
\(303\) | −4513.75 | −0.855803 | ||||||||
\(304\) | −304.000 | −0.0573539 | ||||||||
\(305\) | −1015.18 | −0.190588 | ||||||||
\(306\) | 775.496 | 0.144876 | ||||||||
\(307\) | 1737.38 | 0.322988 | 0.161494 | − | 0.986874i | \(-0.448369\pi\) | ||||
0.161494 | + | 0.986874i | \(0.448369\pi\) | |||||||
\(308\) | 1823.86 | 0.337416 | ||||||||
\(309\) | 3437.03 | 0.632769 | ||||||||
\(310\) | 757.756 | 0.138831 | ||||||||
\(311\) | 3951.77 | 0.720529 | 0.360264 | − | 0.932850i | \(-0.382686\pi\) | ||||
0.360264 | + | 0.932850i | \(0.382686\pi\) | |||||||
\(312\) | −755.433 | −0.137077 | ||||||||
\(313\) | 2496.86 | 0.450898 | 0.225449 | − | 0.974255i | \(-0.427615\pi\) | ||||
0.225449 | + | 0.974255i | \(0.427615\pi\) | |||||||
\(314\) | −1524.00 | −0.273899 | ||||||||
\(315\) | 148.176 | 0.0265041 | ||||||||
\(316\) | 2483.49 | 0.442112 | ||||||||
\(317\) | 2515.69 | 0.445725 | 0.222863 | − | 0.974850i | \(-0.428460\pi\) | ||||
0.222863 | + | 0.974850i | \(0.428460\pi\) | |||||||
\(318\) | 1050.85 | 0.185311 | ||||||||
\(319\) | 6234.61 | 1.09427 | ||||||||
\(320\) | −150.528 | −0.0262962 | ||||||||
\(321\) | 2413.65 | 0.419679 | ||||||||
\(322\) | 1299.50 | 0.224902 | ||||||||
\(323\) | 818.579 | 0.141012 | ||||||||
\(324\) | 324.000 | 0.0555556 | ||||||||
\(325\) | 3760.42 | 0.641817 | ||||||||
\(326\) | −6904.12 | −1.17296 | ||||||||
\(327\) | −6439.37 | −1.08898 | ||||||||
\(328\) | 3479.26 | 0.585702 | ||||||||
\(329\) | 1544.34 | 0.258792 | ||||||||
\(330\) | 919.229 | 0.153339 | ||||||||
\(331\) | 980.008 | 0.162738 | 0.0813688 | − | 0.996684i | \(-0.474071\pi\) | ||||
0.0813688 | + | 0.996684i | \(0.474071\pi\) | |||||||
\(332\) | 2078.91 | 0.343660 | ||||||||
\(333\) | 45.4032 | 0.00747171 | ||||||||
\(334\) | −7179.00 | −1.17610 | ||||||||
\(335\) | 2327.81 | 0.379647 | ||||||||
\(336\) | 336.000 | 0.0545545 | ||||||||
\(337\) | −8806.36 | −1.42348 | −0.711740 | − | 0.702443i | \(-0.752093\pi\) | ||||
−0.711740 | + | 0.702443i | \(0.752093\pi\) | |||||||
\(338\) | 2412.48 | 0.388229 | ||||||||
\(339\) | 1368.72 | 0.219288 | ||||||||
\(340\) | 405.327 | 0.0646528 | ||||||||
\(341\) | −10492.9 | −1.66634 | ||||||||
\(342\) | 342.000 | 0.0540738 | ||||||||
\(343\) | −343.000 | −0.0539949 | ||||||||
\(344\) | −437.980 | −0.0686463 | ||||||||
\(345\) | 654.953 | 0.102207 | ||||||||
\(346\) | −3591.53 | −0.558039 | ||||||||
\(347\) | −4506.05 | −0.697110 | −0.348555 | − | 0.937288i | \(-0.613328\pi\) | ||||
−0.348555 | + | 0.937288i | \(0.613328\pi\) | |||||||
\(348\) | 1148.57 | 0.176924 | ||||||||
\(349\) | −11683.9 | −1.79204 | −0.896021 | − | 0.444011i | \(-0.853555\pi\) | ||||
−0.896021 | + | 0.444011i | \(0.853555\pi\) | |||||||
\(350\) | −1672.55 | −0.255433 | ||||||||
\(351\) | 849.862 | 0.129237 | ||||||||
\(352\) | 2084.41 | 0.315624 | ||||||||
\(353\) | 10542.7 | 1.58960 | 0.794802 | − | 0.606868i | \(-0.207574\pi\) | ||||
0.794802 | + | 0.606868i | \(0.207574\pi\) | |||||||
\(354\) | −2298.15 | −0.345044 | ||||||||
\(355\) | 1073.38 | 0.160476 | ||||||||
\(356\) | 4199.54 | 0.625212 | ||||||||
\(357\) | −904.745 | −0.134129 | ||||||||
\(358\) | 4952.58 | 0.731151 | ||||||||
\(359\) | −365.565 | −0.0537432 | −0.0268716 | − | 0.999639i | \(-0.508555\pi\) | ||||
−0.0268716 | + | 0.999639i | \(0.508555\pi\) | |||||||
\(360\) | 169.345 | 0.0247923 | ||||||||
\(361\) | 361.000 | 0.0526316 | ||||||||
\(362\) | −4804.18 | −0.697519 | ||||||||
\(363\) | −8735.85 | −1.26312 | ||||||||
\(364\) | 881.339 | 0.126909 | ||||||||
\(365\) | −217.253 | −0.0311550 | ||||||||
\(366\) | 2589.75 | 0.369859 | ||||||||
\(367\) | −3287.08 | −0.467532 | −0.233766 | − | 0.972293i | \(-0.575105\pi\) | ||||
−0.233766 | + | 0.972293i | \(0.575105\pi\) | |||||||
\(368\) | 1485.15 | 0.210377 | ||||||||
\(369\) | −3914.17 | −0.552205 | ||||||||
\(370\) | 23.7308 | 0.00333434 | ||||||||
\(371\) | −1225.99 | −0.171565 | ||||||||
\(372\) | −1933.05 | −0.269419 | ||||||||
\(373\) | 8899.17 | 1.23534 | 0.617669 | − | 0.786438i | \(-0.288077\pi\) | ||||
0.617669 | + | 0.786438i | \(0.288077\pi\) | |||||||
\(374\) | −5612.69 | −0.776003 | ||||||||
\(375\) | −1724.97 | −0.237539 | ||||||||
\(376\) | 1764.96 | 0.242077 | ||||||||
\(377\) | 3012.73 | 0.411574 | ||||||||
\(378\) | −378.000 | −0.0514344 | ||||||||
\(379\) | −11650.9 | −1.57907 | −0.789536 | − | 0.613705i | \(-0.789679\pi\) | ||||
−0.789536 | + | 0.613705i | \(0.789679\pi\) | |||||||
\(380\) | 178.753 | 0.0241311 | ||||||||
\(381\) | −3772.32 | −0.507249 | ||||||||
\(382\) | 3271.14 | 0.438131 | ||||||||
\(383\) | 3378.50 | 0.450739 | 0.225370 | − | 0.974273i | \(-0.427641\pi\) | ||||
0.225370 | + | 0.974273i | \(0.427641\pi\) | |||||||
\(384\) | 384.000 | 0.0510310 | ||||||||
\(385\) | −1072.43 | −0.141964 | ||||||||
\(386\) | −8865.58 | −1.16903 | ||||||||
\(387\) | 492.728 | 0.0647203 | ||||||||
\(388\) | −665.219 | −0.0870396 | ||||||||
\(389\) | −4069.59 | −0.530428 | −0.265214 | − | 0.964190i | \(-0.585443\pi\) | ||||
−0.265214 | + | 0.964190i | \(0.585443\pi\) | |||||||
\(390\) | 444.196 | 0.0576737 | ||||||||
\(391\) | −3999.05 | −0.517240 | ||||||||
\(392\) | −392.000 | −0.0505076 | ||||||||
\(393\) | 6988.39 | 0.896991 | ||||||||
\(394\) | −5203.30 | −0.665327 | ||||||||
\(395\) | −1460.30 | −0.186014 | ||||||||
\(396\) | −2344.97 | −0.297573 | ||||||||
\(397\) | 9273.75 | 1.17238 | 0.586191 | − | 0.810173i | \(-0.300627\pi\) | ||||
0.586191 | + | 0.810173i | \(0.300627\pi\) | |||||||
\(398\) | −3951.42 | −0.497655 | ||||||||
\(399\) | −399.000 | −0.0500626 | ||||||||
\(400\) | −1911.49 | −0.238936 | ||||||||
\(401\) | 5544.49 | 0.690471 | 0.345235 | − | 0.938516i | \(-0.387799\pi\) | ||||
0.345235 | + | 0.938516i | \(0.387799\pi\) | |||||||
\(402\) | −5938.27 | −0.736751 | ||||||||
\(403\) | −5070.44 | −0.626741 | ||||||||
\(404\) | 6018.34 | 0.741147 | ||||||||
\(405\) | −190.513 | −0.0233744 | ||||||||
\(406\) | −1340.00 | −0.163800 | ||||||||
\(407\) | −328.608 | −0.0400209 | ||||||||
\(408\) | −1033.99 | −0.125467 | ||||||||
\(409\) | −4863.21 | −0.587947 | −0.293973 | − | 0.955814i | \(-0.594978\pi\) | ||||
−0.293973 | + | 0.955814i | \(0.594978\pi\) | |||||||
\(410\) | −2045.81 | −0.246428 | ||||||||
\(411\) | −5185.77 | −0.622372 | ||||||||
\(412\) | −4582.70 | −0.547994 | ||||||||
\(413\) | 2681.18 | 0.319449 | ||||||||
\(414\) | −1670.79 | −0.198345 | ||||||||
\(415\) | −1222.40 | −0.144591 | ||||||||
\(416\) | 1007.24 | 0.118712 | ||||||||
\(417\) | 2073.61 | 0.243514 | ||||||||
\(418\) | −2475.24 | −0.289636 | ||||||||
\(419\) | −2633.77 | −0.307084 | −0.153542 | − | 0.988142i | \(-0.549068\pi\) | ||||
−0.153542 | + | 0.988142i | \(0.549068\pi\) | |||||||
\(420\) | −197.569 | −0.0229532 | ||||||||
\(421\) | 12763.2 | 1.47753 | 0.738767 | − | 0.673961i | \(-0.235409\pi\) | ||||
0.738767 | + | 0.673961i | \(0.235409\pi\) | |||||||
\(422\) | 7471.10 | 0.861819 | ||||||||
\(423\) | −1985.59 | −0.228233 | ||||||||
\(424\) | −1401.14 | −0.160484 | ||||||||
\(425\) | 5147.06 | 0.587456 | ||||||||
\(426\) | −2738.20 | −0.311423 | ||||||||
\(427\) | −3021.37 | −0.342423 | ||||||||
\(428\) | −3218.20 | −0.363452 | ||||||||
\(429\) | −6150.92 | −0.692236 | ||||||||
\(430\) | 257.533 | 0.0288822 | ||||||||
\(431\) | −3351.91 | −0.374607 | −0.187304 | − | 0.982302i | \(-0.559975\pi\) | ||||
−0.187304 | + | 0.982302i | \(0.559975\pi\) | |||||||
\(432\) | −432.000 | −0.0481125 | ||||||||
\(433\) | −3364.43 | −0.373405 | −0.186702 | − | 0.982417i | \(-0.559780\pi\) | ||||
−0.186702 | + | 0.982417i | \(0.559780\pi\) | |||||||
\(434\) | 2255.22 | 0.249433 | ||||||||
\(435\) | −675.360 | −0.0744392 | ||||||||
\(436\) | 8585.83 | 0.943089 | ||||||||
\(437\) | −1763.61 | −0.193055 | ||||||||
\(438\) | 554.216 | 0.0604600 | ||||||||
\(439\) | −4991.62 | −0.542682 | −0.271341 | − | 0.962483i | \(-0.587467\pi\) | ||||
−0.271341 | + | 0.962483i | \(0.587467\pi\) | |||||||
\(440\) | −1225.64 | −0.132796 | ||||||||
\(441\) | 441.000 | 0.0476190 | ||||||||
\(442\) | −2712.20 | −0.291869 | ||||||||
\(443\) | −13437.4 | −1.44115 | −0.720574 | − | 0.693378i | \(-0.756122\pi\) | ||||
−0.720574 | + | 0.693378i | \(0.756122\pi\) | |||||||
\(444\) | −60.5376 | −0.00647069 | ||||||||
\(445\) | −2469.34 | −0.263051 | ||||||||
\(446\) | −11242.2 | −1.19357 | ||||||||
\(447\) | 7013.28 | 0.742096 | ||||||||
\(448\) | −448.000 | −0.0472456 | ||||||||
\(449\) | 3090.05 | 0.324785 | 0.162392 | − | 0.986726i | \(-0.448079\pi\) | ||||
0.162392 | + | 0.986726i | \(0.448079\pi\) | |||||||
\(450\) | 2150.43 | 0.225271 | ||||||||
\(451\) | 28329.0 | 2.95778 | ||||||||
\(452\) | −1824.96 | −0.189909 | ||||||||
\(453\) | −8045.30 | −0.834440 | ||||||||
\(454\) | 177.824 | 0.0183826 | ||||||||
\(455\) | −518.229 | −0.0533955 | ||||||||
\(456\) | −456.000 | −0.0468293 | ||||||||
\(457\) | 9282.31 | 0.950127 | 0.475063 | − | 0.879952i | \(-0.342425\pi\) | ||||
0.475063 | + | 0.879952i | \(0.342425\pi\) | |||||||
\(458\) | 7183.23 | 0.732861 | ||||||||
\(459\) | 1163.24 | 0.118291 | ||||||||
\(460\) | −873.270 | −0.0885140 | ||||||||
\(461\) | −14936.7 | −1.50904 | −0.754522 | − | 0.656275i | \(-0.772131\pi\) | ||||
−0.754522 | + | 0.656275i | \(0.772131\pi\) | |||||||
\(462\) | 2735.79 | 0.275499 | ||||||||
\(463\) | 7024.39 | 0.705078 | 0.352539 | − | 0.935797i | \(-0.385318\pi\) | ||||
0.352539 | + | 0.935797i | \(0.385318\pi\) | |||||||
\(464\) | −1531.42 | −0.153221 | ||||||||
\(465\) | 1136.63 | 0.113355 | ||||||||
\(466\) | 3566.67 | 0.354556 | ||||||||
\(467\) | 800.205 | 0.0792914 | 0.0396457 | − | 0.999214i | \(-0.487377\pi\) | ||||
0.0396457 | + | 0.999214i | \(0.487377\pi\) | |||||||
\(468\) | −1133.15 | −0.111923 | ||||||||
\(469\) | 6927.98 | 0.682099 | ||||||||
\(470\) | −1037.80 | −0.101852 | ||||||||
\(471\) | −2286.00 | −0.223638 | ||||||||
\(472\) | 3064.21 | 0.298817 | ||||||||
\(473\) | −3566.14 | −0.346663 | ||||||||
\(474\) | 3725.24 | 0.360983 | ||||||||
\(475\) | 2269.89 | 0.219263 | ||||||||
\(476\) | 1206.33 | 0.116159 | ||||||||
\(477\) | 1576.28 | 0.151306 | ||||||||
\(478\) | 10561.3 | 1.01059 | ||||||||
\(479\) | 3573.45 | 0.340867 | 0.170433 | − | 0.985369i | \(-0.445483\pi\) | ||||
0.170433 | + | 0.985369i | \(0.445483\pi\) | |||||||
\(480\) | −225.793 | −0.0214708 | ||||||||
\(481\) | −158.792 | −0.0150526 | ||||||||
\(482\) | −14222.4 | −1.34401 | ||||||||
\(483\) | 1949.26 | 0.183632 | ||||||||
\(484\) | 11647.8 | 1.09389 | ||||||||
\(485\) | 391.150 | 0.0366210 | ||||||||
\(486\) | 486.000 | 0.0453609 | ||||||||
\(487\) | −13085.1 | −1.21755 | −0.608773 | − | 0.793345i | \(-0.708338\pi\) | ||||
−0.608773 | + | 0.793345i | \(0.708338\pi\) | |||||||
\(488\) | −3453.00 | −0.320307 | ||||||||
\(489\) | −10356.2 | −0.957715 | ||||||||
\(490\) | 230.497 | 0.0212506 | ||||||||
\(491\) | −9072.15 | −0.833850 | −0.416925 | − | 0.908941i | \(-0.636892\pi\) | ||||
−0.416925 | + | 0.908941i | \(0.636892\pi\) | |||||||
\(492\) | 5218.89 | 0.478223 | ||||||||
\(493\) | 4123.66 | 0.376714 | ||||||||
\(494\) | −1196.10 | −0.108938 | ||||||||
\(495\) | 1378.84 | 0.125201 | ||||||||
\(496\) | 2577.39 | 0.233323 | ||||||||
\(497\) | 3194.56 | 0.288321 | ||||||||
\(498\) | 3118.37 | 0.280597 | ||||||||
\(499\) | −1920.38 | −0.172281 | −0.0861403 | − | 0.996283i | \(-0.527453\pi\) | ||||
−0.0861403 | + | 0.996283i | \(0.527453\pi\) | |||||||
\(500\) | 2299.96 | 0.205715 | ||||||||
\(501\) | −10768.5 | −0.960281 | ||||||||
\(502\) | 5045.89 | 0.448624 | ||||||||
\(503\) | −14852.4 | −1.31657 | −0.658285 | − | 0.752769i | \(-0.728718\pi\) | ||||
−0.658285 | + | 0.752769i | \(0.728718\pi\) | |||||||
\(504\) | 504.000 | 0.0445435 | ||||||||
\(505\) | −3538.79 | −0.311830 | ||||||||
\(506\) | 12092.4 | 1.06240 | ||||||||
\(507\) | 3618.71 | 0.316988 | ||||||||
\(508\) | 5029.76 | 0.439291 | ||||||||
\(509\) | 14779.7 | 1.28703 | 0.643514 | − | 0.765434i | \(-0.277476\pi\) | ||||
0.643514 | + | 0.765434i | \(0.277476\pi\) | |||||||
\(510\) | 607.991 | 0.0527888 | ||||||||
\(511\) | −646.585 | −0.0559751 | ||||||||
\(512\) | −512.000 | −0.0441942 | ||||||||
\(513\) | 513.000 | 0.0441511 | ||||||||
\(514\) | 4253.22 | 0.364983 | ||||||||
\(515\) | 2694.64 | 0.230563 | ||||||||
\(516\) | −656.971 | −0.0560495 | ||||||||
\(517\) | 14370.8 | 1.22249 | ||||||||
\(518\) | 70.6272 | 0.00599070 | ||||||||
\(519\) | −5387.29 | −0.455637 | ||||||||
\(520\) | −592.261 | −0.0499469 | ||||||||
\(521\) | 6548.34 | 0.550648 | 0.275324 | − | 0.961351i | \(-0.411215\pi\) | ||||
0.275324 | + | 0.961351i | \(0.411215\pi\) | |||||||
\(522\) | 1722.85 | 0.144458 | ||||||||
\(523\) | 783.385 | 0.0654972 | 0.0327486 | − | 0.999464i | \(-0.489574\pi\) | ||||
0.0327486 | + | 0.999464i | \(0.489574\pi\) | |||||||
\(524\) | −9317.85 | −0.776817 | ||||||||
\(525\) | −2508.83 | −0.208561 | ||||||||
\(526\) | 5419.18 | 0.449216 | ||||||||
\(527\) | −6940.14 | −0.573657 | ||||||||
\(528\) | 3126.62 | 0.257706 | ||||||||
\(529\) | −3551.12 | −0.291865 | ||||||||
\(530\) | 823.871 | 0.0675220 | ||||||||
\(531\) | −3447.23 | −0.281727 | ||||||||
\(532\) | 532.000 | 0.0433555 | ||||||||
\(533\) | 13689.3 | 1.11248 | ||||||||
\(534\) | 6299.32 | 0.510483 | ||||||||
\(535\) | 1892.31 | 0.152919 | ||||||||
\(536\) | 7917.69 | 0.638045 | ||||||||
\(537\) | 7428.88 | 0.596983 | ||||||||
\(538\) | 2127.22 | 0.170466 | ||||||||
\(539\) | −3191.76 | −0.255063 | ||||||||
\(540\) | 254.017 | 0.0202429 | ||||||||
\(541\) | 11120.2 | 0.883720 | 0.441860 | − | 0.897084i | \(-0.354319\pi\) | ||||
0.441860 | + | 0.897084i | \(0.354319\pi\) | |||||||
\(542\) | −4831.67 | −0.382912 | ||||||||
\(543\) | −7206.26 | −0.569522 | ||||||||
\(544\) | 1378.66 | 0.108657 | ||||||||
\(545\) | −5048.48 | −0.396795 | ||||||||
\(546\) | 1322.01 | 0.103620 | ||||||||
\(547\) | −16006.1 | −1.25114 | −0.625569 | − | 0.780169i | \(-0.715133\pi\) | ||||
−0.625569 | + | 0.780169i | \(0.715133\pi\) | |||||||
\(548\) | 6914.36 | 0.538990 | ||||||||
\(549\) | 3884.62 | 0.301988 | ||||||||
\(550\) | −15563.8 | −1.20662 | ||||||||
\(551\) | 1818.57 | 0.140605 | ||||||||
\(552\) | 2227.72 | 0.171772 | ||||||||
\(553\) | −4346.11 | −0.334205 | ||||||||
\(554\) | 5847.82 | 0.448466 | ||||||||
\(555\) | 35.5962 | 0.00272248 | ||||||||
\(556\) | −2764.82 | −0.210889 | ||||||||
\(557\) | −13422.4 | −1.02105 | −0.510524 | − | 0.859863i | \(-0.670549\pi\) | ||||
−0.510524 | + | 0.859863i | \(0.670549\pi\) | |||||||
\(558\) | −2899.57 | −0.219979 | ||||||||
\(559\) | −1723.25 | −0.130386 | ||||||||
\(560\) | 263.425 | 0.0198781 | ||||||||
\(561\) | −8419.03 | −0.633604 | ||||||||
\(562\) | 14129.0 | 1.06049 | ||||||||
\(563\) | 18317.0 | 1.37117 | 0.685586 | − | 0.727991i | \(-0.259546\pi\) | ||||
0.685586 | + | 0.727991i | \(0.259546\pi\) | |||||||
\(564\) | 2647.45 | 0.197655 | ||||||||
\(565\) | 1073.08 | 0.0799022 | ||||||||
\(566\) | 14398.6 | 1.06929 | ||||||||
\(567\) | −567.000 | −0.0419961 | ||||||||
\(568\) | 3650.93 | 0.269700 | ||||||||
\(569\) | 10513.3 | 0.774589 | 0.387295 | − | 0.921956i | \(-0.373410\pi\) | ||||
0.387295 | + | 0.921956i | \(0.373410\pi\) | |||||||
\(570\) | 268.129 | 0.0197029 | ||||||||
\(571\) | −12420.2 | −0.910277 | −0.455138 | − | 0.890421i | \(-0.650410\pi\) | ||||
−0.455138 | + | 0.890421i | \(0.650410\pi\) | |||||||
\(572\) | 8201.22 | 0.599494 | ||||||||
\(573\) | 4906.70 | 0.357732 | ||||||||
\(574\) | −6088.71 | −0.442749 | ||||||||
\(575\) | −11089.2 | −0.804266 | ||||||||
\(576\) | 576.000 | 0.0416667 | ||||||||
\(577\) | 7149.46 | 0.515833 | 0.257917 | − | 0.966167i | \(-0.416964\pi\) | ||||
0.257917 | + | 0.966167i | \(0.416964\pi\) | |||||||
\(578\) | 6113.69 | 0.439958 | ||||||||
\(579\) | −13298.4 | −0.954510 | ||||||||
\(580\) | 900.480 | 0.0644662 | ||||||||
\(581\) | −3638.10 | −0.259782 | ||||||||
\(582\) | −997.828 | −0.0710675 | ||||||||
\(583\) | −11408.4 | −0.810441 | ||||||||
\(584\) | −738.955 | −0.0523599 | ||||||||
\(585\) | 666.294 | 0.0470904 | ||||||||
\(586\) | −6002.32 | −0.423129 | ||||||||
\(587\) | 25413.4 | 1.78692 | 0.893461 | − | 0.449140i | \(-0.148270\pi\) | ||||
0.893461 | + | 0.449140i | \(0.148270\pi\) | |||||||
\(588\) | −588.000 | −0.0412393 | ||||||||
\(589\) | −3060.66 | −0.214112 | ||||||||
\(590\) | −1801.76 | −0.125724 | ||||||||
\(591\) | −7804.96 | −0.543237 | ||||||||
\(592\) | 80.7168 | 0.00560379 | ||||||||
\(593\) | 11905.5 | 0.824452 | 0.412226 | − | 0.911082i | \(-0.364751\pi\) | ||||
0.412226 | + | 0.911082i | \(0.364751\pi\) | |||||||
\(594\) | −3517.45 | −0.242967 | ||||||||
\(595\) | −709.323 | −0.0488729 | ||||||||
\(596\) | −9351.04 | −0.642674 | ||||||||
\(597\) | −5927.13 | −0.406334 | ||||||||
\(598\) | 5843.39 | 0.399588 | ||||||||
\(599\) | 22430.9 | 1.53005 | 0.765027 | − | 0.643998i | \(-0.222725\pi\) | ||||
0.765027 | + | 0.643998i | \(0.222725\pi\) | |||||||
\(600\) | −2867.23 | −0.195091 | ||||||||
\(601\) | −9645.59 | −0.654662 | −0.327331 | − | 0.944910i | \(-0.606149\pi\) | ||||
−0.327331 | + | 0.944910i | \(0.606149\pi\) | |||||||
\(602\) | 766.466 | 0.0518917 | ||||||||
\(603\) | −8907.40 | −0.601555 | ||||||||
\(604\) | 10727.1 | 0.722646 | ||||||||
\(605\) | −6848.92 | −0.460245 | ||||||||
\(606\) | 9027.51 | 0.605144 | ||||||||
\(607\) | −2535.39 | −0.169536 | −0.0847679 | − | 0.996401i | \(-0.527015\pi\) | ||||
−0.0847679 | + | 0.996401i | \(0.527015\pi\) | |||||||
\(608\) | 608.000 | 0.0405554 | ||||||||
\(609\) | −2009.99 | −0.133742 | ||||||||
\(610\) | 2030.37 | 0.134766 | ||||||||
\(611\) | 6944.34 | 0.459800 | ||||||||
\(612\) | −1550.99 | −0.102443 | ||||||||
\(613\) | 17163.0 | 1.13084 | 0.565421 | − | 0.824802i | \(-0.308714\pi\) | ||||
0.565421 | + | 0.824802i | \(0.308714\pi\) | |||||||
\(614\) | −3474.75 | −0.228387 | ||||||||
\(615\) | −3068.72 | −0.201208 | ||||||||
\(616\) | −3647.72 | −0.238589 | ||||||||
\(617\) | 2852.64 | 0.186131 | 0.0930656 | − | 0.995660i | \(-0.470333\pi\) | ||||
0.0930656 | + | 0.995660i | \(0.470333\pi\) | |||||||
\(618\) | −6874.05 | −0.447435 | ||||||||
\(619\) | −15912.1 | −1.03322 | −0.516608 | − | 0.856222i | \(-0.672805\pi\) | ||||
−0.516608 | + | 0.856222i | \(0.672805\pi\) | |||||||
\(620\) | −1515.51 | −0.0981685 | ||||||||
\(621\) | −2506.19 | −0.161948 | ||||||||
\(622\) | −7903.54 | −0.509491 | ||||||||
\(623\) | −7349.20 | −0.472616 | ||||||||
\(624\) | 1510.87 | 0.0969280 | ||||||||
\(625\) | 13581.1 | 0.869192 | ||||||||
\(626\) | −4993.73 | −0.318833 | ||||||||
\(627\) | −3712.86 | −0.236487 | ||||||||
\(628\) | 3048.00 | 0.193676 | ||||||||
\(629\) | −217.346 | −0.0137777 | ||||||||
\(630\) | −296.353 | −0.0187412 | ||||||||
\(631\) | −6717.70 | −0.423815 | −0.211908 | − | 0.977290i | \(-0.567968\pi\) | ||||
−0.211908 | + | 0.977290i | \(0.567968\pi\) | |||||||
\(632\) | −4966.98 | −0.312620 | ||||||||
\(633\) | 11206.7 | 0.703672 | ||||||||
\(634\) | −5031.37 | −0.315175 | ||||||||
\(635\) | −2957.51 | −0.184827 | ||||||||
\(636\) | −2101.70 | −0.131035 | ||||||||
\(637\) | −1542.34 | −0.0959338 | ||||||||
\(638\) | −12469.2 | −0.773764 | ||||||||
\(639\) | −4107.30 | −0.254276 | ||||||||
\(640\) | 301.057 | 0.0185943 | ||||||||
\(641\) | 23563.0 | 1.45192 | 0.725961 | − | 0.687736i | \(-0.241395\pi\) | ||||
0.725961 | + | 0.687736i | \(0.241395\pi\) | |||||||
\(642\) | −4827.30 | −0.296758 | ||||||||
\(643\) | 12722.7 | 0.780303 | 0.390152 | − | 0.920751i | \(-0.372423\pi\) | ||||
0.390152 | + | 0.920751i | \(0.372423\pi\) | |||||||
\(644\) | −2599.01 | −0.159030 | ||||||||
\(645\) | 386.300 | 0.0235822 | ||||||||
\(646\) | −1637.16 | −0.0997107 | ||||||||
\(647\) | 20322.2 | 1.23485 | 0.617424 | − | 0.786631i | \(-0.288176\pi\) | ||||
0.617424 | + | 0.786631i | \(0.288176\pi\) | |||||||
\(648\) | −648.000 | −0.0392837 | ||||||||
\(649\) | 24949.5 | 1.50902 | ||||||||
\(650\) | −7520.84 | −0.453833 | ||||||||
\(651\) | 3382.83 | 0.203661 | ||||||||
\(652\) | 13808.2 | 0.829406 | ||||||||
\(653\) | −19287.3 | −1.15585 | −0.577924 | − | 0.816091i | \(-0.696137\pi\) | ||||
−0.577924 | + | 0.816091i | \(0.696137\pi\) | |||||||
\(654\) | 12878.7 | 0.770029 | ||||||||
\(655\) | 5478.91 | 0.326838 | ||||||||
\(656\) | −6958.52 | −0.414154 | ||||||||
\(657\) | 831.324 | 0.0493654 | ||||||||
\(658\) | −3088.69 | −0.182993 | ||||||||
\(659\) | −7186.76 | −0.424820 | −0.212410 | − | 0.977181i | \(-0.568131\pi\) | ||||
−0.212410 | + | 0.977181i | \(0.568131\pi\) | |||||||
\(660\) | −1838.46 | −0.108427 | ||||||||
\(661\) | −23799.5 | −1.40044 | −0.700220 | − | 0.713927i | \(-0.746915\pi\) | ||||
−0.700220 | + | 0.713927i | \(0.746915\pi\) | |||||||
\(662\) | −1960.02 | −0.115073 | ||||||||
\(663\) | −4068.30 | −0.238310 | ||||||||
\(664\) | −4157.82 | −0.243004 | ||||||||
\(665\) | −312.817 | −0.0182414 | ||||||||
\(666\) | −90.8064 | −0.00528330 | ||||||||
\(667\) | −8884.35 | −0.515747 | ||||||||
\(668\) | 14358.0 | 0.831628 | ||||||||
\(669\) | −16863.3 | −0.974546 | ||||||||
\(670\) | −4655.62 | −0.268451 | ||||||||
\(671\) | −28115.1 | −1.61755 | ||||||||
\(672\) | −672.000 | −0.0385758 | ||||||||
\(673\) | −6426.09 | −0.368065 | −0.184032 | − | 0.982920i | \(-0.558915\pi\) | ||||
−0.184032 | + | 0.982920i | \(0.558915\pi\) | |||||||
\(674\) | 17612.7 | 1.00655 | ||||||||
\(675\) | 3225.64 | 0.183933 | ||||||||
\(676\) | −4824.95 | −0.274519 | ||||||||
\(677\) | 5295.09 | 0.300601 | 0.150301 | − | 0.988640i | \(-0.451976\pi\) | ||||
0.150301 | + | 0.988640i | \(0.451976\pi\) | |||||||
\(678\) | −2737.44 | −0.155060 | ||||||||
\(679\) | 1164.13 | 0.0657958 | ||||||||
\(680\) | −810.654 | −0.0457164 | ||||||||
\(681\) | 266.737 | 0.0150094 | ||||||||
\(682\) | 20985.8 | 1.17828 | ||||||||
\(683\) | 27838.6 | 1.55961 | 0.779807 | − | 0.626020i | \(-0.215317\pi\) | ||||
0.779807 | + | 0.626020i | \(0.215317\pi\) | |||||||
\(684\) | −684.000 | −0.0382360 | ||||||||
\(685\) | −4065.65 | −0.226775 | ||||||||
\(686\) | 686.000 | 0.0381802 | ||||||||
\(687\) | 10774.9 | 0.598379 | ||||||||
\(688\) | 875.961 | 0.0485403 | ||||||||
\(689\) | −5512.84 | −0.304822 | ||||||||
\(690\) | −1309.91 | −0.0722714 | ||||||||
\(691\) | −19503.3 | −1.07372 | −0.536859 | − | 0.843672i | \(-0.680389\pi\) | ||||
−0.536859 | + | 0.843672i | \(0.680389\pi\) | |||||||
\(692\) | 7183.05 | 0.394593 | ||||||||
\(693\) | 4103.69 | 0.224944 | ||||||||
\(694\) | 9012.10 | 0.492932 | ||||||||
\(695\) | 1625.72 | 0.0887296 | ||||||||
\(696\) | −2297.14 | −0.125104 | ||||||||
\(697\) | 18737.2 | 1.01825 | ||||||||
\(698\) | 23367.7 | 1.26717 | ||||||||
\(699\) | 5350.01 | 0.289494 | ||||||||
\(700\) | 3345.11 | 0.180619 | ||||||||
\(701\) | 6387.15 | 0.344136 | 0.172068 | − | 0.985085i | \(-0.444955\pi\) | ||||
0.172068 | + | 0.985085i | \(0.444955\pi\) | |||||||
\(702\) | −1699.72 | −0.0913846 | ||||||||
\(703\) | −95.8512 | −0.00514239 | ||||||||
\(704\) | −4168.83 | −0.223180 | ||||||||
\(705\) | −1556.70 | −0.0831615 | ||||||||
\(706\) | −21085.4 | −1.12402 | ||||||||
\(707\) | −10532.1 | −0.560255 | ||||||||
\(708\) | 4596.31 | 0.243983 | ||||||||
\(709\) | 24946.9 | 1.32144 | 0.660720 | − | 0.750632i | \(-0.270251\pi\) | ||||
0.660720 | + | 0.750632i | \(0.270251\pi\) | |||||||
\(710\) | −2146.75 | −0.113474 | ||||||||
\(711\) | 5587.86 | 0.294741 | ||||||||
\(712\) | −8399.09 | −0.442091 | ||||||||
\(713\) | 14952.4 | 0.785374 | ||||||||
\(714\) | 1809.49 | 0.0948438 | ||||||||
\(715\) | −4822.33 | −0.252231 | ||||||||
\(716\) | −9905.17 | −0.517002 | ||||||||
\(717\) | 15841.9 | 0.825142 | ||||||||
\(718\) | 731.130 | 0.0380022 | ||||||||
\(719\) | 32315.2 | 1.67615 | 0.838077 | − | 0.545552i | \(-0.183680\pi\) | ||||
0.838077 | + | 0.545552i | \(0.183680\pi\) | |||||||
\(720\) | −338.689 | −0.0175308 | ||||||||
\(721\) | 8019.73 | 0.414244 | ||||||||
\(722\) | −722.000 | −0.0372161 | ||||||||
\(723\) | −21333.5 | −1.09738 | ||||||||
\(724\) | 9608.35 | 0.493220 | ||||||||
\(725\) | 11434.8 | 0.585761 | ||||||||
\(726\) | 17471.7 | 0.893162 | ||||||||
\(727\) | 21195.9 | 1.08131 | 0.540656 | − | 0.841244i | \(-0.318176\pi\) | ||||
0.540656 | + | 0.841244i | \(0.318176\pi\) | |||||||
\(728\) | −1762.68 | −0.0897379 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | 434.507 | 0.0220299 | ||||||||
\(731\) | −2358.70 | −0.119343 | ||||||||
\(732\) | −5179.50 | −0.261530 | ||||||||
\(733\) | −11952.5 | −0.602287 | −0.301144 | − | 0.953579i | \(-0.597368\pi\) | ||||
−0.301144 | + | 0.953579i | \(0.597368\pi\) | |||||||
\(734\) | 6574.16 | 0.330595 | ||||||||
\(735\) | 345.745 | 0.0173510 | ||||||||
\(736\) | −2970.30 | −0.148759 | ||||||||
\(737\) | 64467.7 | 3.22212 | ||||||||
\(738\) | 7828.34 | 0.390468 | ||||||||
\(739\) | −12355.2 | −0.615010 | −0.307505 | − | 0.951546i | \(-0.599494\pi\) | ||||
−0.307505 | + | 0.951546i | \(0.599494\pi\) | |||||||
\(740\) | −47.4616 | −0.00235774 | ||||||||
\(741\) | −1794.15 | −0.0889472 | ||||||||
\(742\) | 2451.99 | 0.121314 | ||||||||
\(743\) | 545.630 | 0.0269411 | 0.0134705 | − | 0.999909i | \(-0.495712\pi\) | ||||
0.0134705 | + | 0.999909i | \(0.495712\pi\) | |||||||
\(744\) | 3866.09 | 0.190508 | ||||||||
\(745\) | 5498.43 | 0.270399 | ||||||||
\(746\) | −17798.3 | −0.873516 | ||||||||
\(747\) | 4677.55 | 0.229107 | ||||||||
\(748\) | 11225.4 | 0.548717 | ||||||||
\(749\) | 5631.85 | 0.274744 | ||||||||
\(750\) | 3449.94 | 0.167966 | ||||||||
\(751\) | −24657.5 | −1.19809 | −0.599044 | − | 0.800716i | \(-0.704453\pi\) | ||||
−0.599044 | + | 0.800716i | \(0.704453\pi\) | |||||||
\(752\) | −3529.93 | −0.171175 | ||||||||
\(753\) | 7568.84 | 0.366300 | ||||||||
\(754\) | −6025.46 | −0.291027 | ||||||||
\(755\) | −6307.54 | −0.304046 | ||||||||
\(756\) | 756.000 | 0.0363696 | ||||||||
\(757\) | −9802.82 | −0.470660 | −0.235330 | − | 0.971916i | \(-0.575617\pi\) | ||||
−0.235330 | + | 0.971916i | \(0.575617\pi\) | |||||||
\(758\) | 23301.9 | 1.11657 | ||||||||
\(759\) | 18138.7 | 0.867446 | ||||||||
\(760\) | −357.505 | −0.0170633 | ||||||||
\(761\) | −38995.6 | −1.85754 | −0.928770 | − | 0.370656i | \(-0.879133\pi\) | ||||
−0.928770 | + | 0.370656i | \(0.879133\pi\) | |||||||
\(762\) | 7544.65 | 0.358679 | ||||||||
\(763\) | −15025.2 | −0.712908 | ||||||||
\(764\) | −6542.27 | −0.309805 | ||||||||
\(765\) | 911.986 | 0.0431019 | ||||||||
\(766\) | −6756.99 | −0.318721 | ||||||||
\(767\) | 12056.3 | 0.567570 | ||||||||
\(768\) | −768.000 | −0.0360844 | ||||||||
\(769\) | 11656.9 | 0.546631 | 0.273315 | − | 0.961924i | \(-0.411880\pi\) | ||||
0.273315 | + | 0.961924i | \(0.411880\pi\) | |||||||
\(770\) | 2144.87 | 0.100384 | ||||||||
\(771\) | 6379.83 | 0.298008 | ||||||||
\(772\) | 17731.2 | 0.826630 | ||||||||
\(773\) | 18534.7 | 0.862414 | 0.431207 | − | 0.902253i | \(-0.358088\pi\) | ||||
0.431207 | + | 0.902253i | \(0.358088\pi\) | |||||||
\(774\) | −985.456 | −0.0457642 | ||||||||
\(775\) | −19244.8 | −0.891990 | ||||||||
\(776\) | 1330.44 | 0.0615463 | ||||||||
\(777\) | 105.941 | 0.00489139 | ||||||||
\(778\) | 8139.19 | 0.375069 | ||||||||
\(779\) | 8263.25 | 0.380053 | ||||||||
\(780\) | −888.392 | −0.0407815 | ||||||||
\(781\) | 29726.7 | 1.36198 | ||||||||
\(782\) | 7998.10 | 0.365744 | ||||||||
\(783\) | 2584.28 | 0.117950 | ||||||||
\(784\) | 784.000 | 0.0357143 | ||||||||
\(785\) | −1792.23 | −0.0814872 | ||||||||
\(786\) | −13976.8 | −0.634268 | ||||||||
\(787\) | 21029.9 | 0.952521 | 0.476261 | − | 0.879304i | \(-0.341992\pi\) | ||||
0.476261 | + | 0.879304i | \(0.341992\pi\) | |||||||
\(788\) | 10406.6 | 0.470457 | ||||||||
\(789\) | 8128.77 | 0.366783 | ||||||||
\(790\) | 2920.60 | 0.131532 | ||||||||
\(791\) | 3193.68 | 0.143558 | ||||||||
\(792\) | 4689.93 | 0.210416 | ||||||||
\(793\) | −13586.0 | −0.608389 | ||||||||
\(794\) | −18547.5 | −0.829000 | ||||||||
\(795\) | 1235.81 | 0.0551315 | ||||||||
\(796\) | 7902.84 | 0.351895 | ||||||||
\(797\) | −16890.1 | −0.750661 | −0.375330 | − | 0.926891i | \(-0.622471\pi\) | ||||
−0.375330 | + | 0.926891i | \(0.622471\pi\) | |||||||
\(798\) | 798.000 | 0.0353996 | ||||||||
\(799\) | 9505.02 | 0.420856 | ||||||||
\(800\) | 3822.98 | 0.168953 | ||||||||
\(801\) | 9448.97 | 0.416808 | ||||||||
\(802\) | −11089.0 | −0.488237 | ||||||||
\(803\) | −6016.75 | −0.264416 | ||||||||
\(804\) | 11876.5 | 0.520962 | ||||||||
\(805\) | 1528.22 | 0.0669103 | ||||||||
\(806\) | 10140.9 | 0.443173 | ||||||||
\(807\) | 3190.83 | 0.139185 | ||||||||
\(808\) | −12036.7 | −0.524070 | ||||||||
\(809\) | −26270.6 | −1.14169 | −0.570843 | − | 0.821059i | \(-0.693384\pi\) | ||||
−0.570843 | + | 0.821059i | \(0.693384\pi\) | |||||||
\(810\) | 381.025 | 0.0165282 | ||||||||
\(811\) | −886.827 | −0.0383979 | −0.0191990 | − | 0.999816i | \(-0.506112\pi\) | ||||
−0.0191990 | + | 0.999816i | \(0.506112\pi\) | |||||||
\(812\) | 2679.99 | 0.115824 | ||||||||
\(813\) | −7247.51 | −0.312646 | ||||||||
\(814\) | 657.216 | 0.0282990 | ||||||||
\(815\) | −8119.27 | −0.348964 | ||||||||
\(816\) | 2067.99 | 0.0887183 | ||||||||
\(817\) | −1040.20 | −0.0445436 | ||||||||
\(818\) | 9726.42 | 0.415741 | ||||||||
\(819\) | 1983.01 | 0.0846057 | ||||||||
\(820\) | 4091.63 | 0.174251 | ||||||||
\(821\) | −16810.5 | −0.714605 | −0.357303 | − | 0.933989i | \(-0.616304\pi\) | ||||
−0.357303 | + | 0.933989i | \(0.616304\pi\) | |||||||
\(822\) | 10371.5 | 0.440084 | ||||||||
\(823\) | −40374.7 | −1.71005 | −0.855027 | − | 0.518583i | \(-0.826460\pi\) | ||||
−0.855027 | + | 0.518583i | \(0.826460\pi\) | |||||||
\(824\) | 9165.40 | 0.387490 | ||||||||
\(825\) | −23345.7 | −0.985204 | ||||||||
\(826\) | −5362.36 | −0.225884 | ||||||||
\(827\) | −21653.2 | −0.910468 | −0.455234 | − | 0.890372i | \(-0.650444\pi\) | ||||
−0.455234 | + | 0.890372i | \(0.650444\pi\) | |||||||
\(828\) | 3341.58 | 0.140251 | ||||||||
\(829\) | 9284.49 | 0.388979 | 0.194490 | − | 0.980905i | \(-0.437695\pi\) | ||||
0.194490 | + | 0.980905i | \(0.437695\pi\) | |||||||
\(830\) | 2444.81 | 0.102242 | ||||||||
\(831\) | 8771.73 | 0.366171 | ||||||||
\(832\) | −2014.49 | −0.0839421 | ||||||||
\(833\) | −2111.07 | −0.0878083 | ||||||||
\(834\) | −4147.23 | −0.172190 | ||||||||
\(835\) | −8442.53 | −0.349899 | ||||||||
\(836\) | 4950.48 | 0.204804 | ||||||||
\(837\) | −4349.35 | −0.179612 | ||||||||
\(838\) | 5267.54 | 0.217141 | ||||||||
\(839\) | 30110.7 | 1.23902 | 0.619509 | − | 0.784989i | \(-0.287332\pi\) | ||||
0.619509 | + | 0.784989i | \(0.287332\pi\) | |||||||
\(840\) | 395.137 | 0.0162304 | ||||||||
\(841\) | −15227.8 | −0.624373 | ||||||||
\(842\) | −25526.4 | −1.04477 | ||||||||
\(843\) | 21193.6 | 0.865890 | ||||||||
\(844\) | −14942.2 | −0.609398 | ||||||||
\(845\) | 2837.08 | 0.115501 | ||||||||
\(846\) | 3971.17 | 0.161385 | ||||||||
\(847\) | −20383.6 | −0.826907 | ||||||||
\(848\) | 2802.27 | 0.113479 | ||||||||
\(849\) | 21598.0 | 0.873074 | ||||||||
\(850\) | −10294.1 | −0.415394 | ||||||||
\(851\) | 468.268 | 0.0188625 | ||||||||
\(852\) | 5476.40 | 0.220209 | ||||||||
\(853\) | −28220.7 | −1.13278 | −0.566389 | − | 0.824138i | \(-0.691660\pi\) | ||||
−0.566389 | + | 0.824138i | \(0.691660\pi\) | |||||||
\(854\) | 6042.75 | 0.242129 | ||||||||
\(855\) | 402.193 | 0.0160874 | ||||||||
\(856\) | 6436.40 | 0.257000 | ||||||||
\(857\) | 37317.9 | 1.48746 | 0.743731 | − | 0.668479i | \(-0.233054\pi\) | ||||
0.743731 | + | 0.668479i | \(0.233054\pi\) | |||||||
\(858\) | 12301.8 | 0.489485 | ||||||||
\(859\) | −15643.5 | −0.621363 | −0.310681 | − | 0.950514i | \(-0.600557\pi\) | ||||
−0.310681 | + | 0.950514i | \(0.600557\pi\) | |||||||
\(860\) | −515.067 | −0.0204228 | ||||||||
\(861\) | −9133.06 | −0.361503 | ||||||||
\(862\) | 6703.82 | 0.264887 | ||||||||
\(863\) | −17616.3 | −0.694860 | −0.347430 | − | 0.937706i | \(-0.612946\pi\) | ||||
−0.347430 | + | 0.937706i | \(0.612946\pi\) | |||||||
\(864\) | 864.000 | 0.0340207 | ||||||||
\(865\) | −4223.65 | −0.166021 | ||||||||
\(866\) | 6728.87 | 0.264037 | ||||||||
\(867\) | 9170.54 | 0.359225 | ||||||||
\(868\) | −4510.44 | −0.176376 | ||||||||
\(869\) | −40442.4 | −1.57873 | ||||||||
\(870\) | 1350.72 | 0.0526364 | ||||||||
\(871\) | 31152.5 | 1.21190 | ||||||||
\(872\) | −17171.7 | −0.666864 | ||||||||
\(873\) | −1496.74 | −0.0580264 | ||||||||
\(874\) | 3527.23 | 0.136511 | ||||||||
\(875\) | −4024.93 | −0.155506 | ||||||||
\(876\) | −1108.43 | −0.0427517 | ||||||||
\(877\) | 12573.4 | 0.484121 | 0.242060 | − | 0.970261i | \(-0.422177\pi\) | ||||
0.242060 | + | 0.970261i | \(0.422177\pi\) | |||||||
\(878\) | 9983.25 | 0.383734 | ||||||||
\(879\) | −9003.49 | −0.345484 | ||||||||
\(880\) | 2451.28 | 0.0939006 | ||||||||
\(881\) | −9079.75 | −0.347224 | −0.173612 | − | 0.984814i | \(-0.555544\pi\) | ||||
−0.173612 | + | 0.984814i | \(0.555544\pi\) | |||||||
\(882\) | −882.000 | −0.0336718 | ||||||||
\(883\) | 30666.4 | 1.16875 | 0.584376 | − | 0.811483i | \(-0.301340\pi\) | ||||
0.584376 | + | 0.811483i | \(0.301340\pi\) | |||||||
\(884\) | 5424.40 | 0.206383 | ||||||||
\(885\) | −2702.64 | −0.102653 | ||||||||
\(886\) | 26874.7 | 1.01905 | ||||||||
\(887\) | 24420.8 | 0.924431 | 0.462216 | − | 0.886768i | \(-0.347055\pi\) | ||||
0.462216 | + | 0.886768i | \(0.347055\pi\) | |||||||
\(888\) | 121.075 | 0.00457547 | ||||||||
\(889\) | −8802.09 | −0.332073 | ||||||||
\(890\) | 4938.68 | 0.186005 | ||||||||
\(891\) | −5276.17 | −0.198382 | ||||||||
\(892\) | 22484.4 | 0.843982 | ||||||||
\(893\) | 4191.79 | 0.157081 | ||||||||
\(894\) | −14026.6 | −0.524741 | ||||||||
\(895\) | 5824.26 | 0.217523 | ||||||||
\(896\) | 896.000 | 0.0334077 | ||||||||
\(897\) | 8765.08 | 0.326263 | ||||||||
\(898\) | −6180.09 | −0.229657 | ||||||||
\(899\) | −15418.3 | −0.572001 | ||||||||
\(900\) | −4300.85 | −0.159291 | ||||||||
\(901\) | −7545.67 | −0.279004 | ||||||||
\(902\) | −56658.0 | −2.09147 | ||||||||
\(903\) | 1149.70 | 0.0423694 | ||||||||
\(904\) | 3649.92 | 0.134286 | ||||||||
\(905\) | −5649.73 | −0.207517 | ||||||||
\(906\) | 16090.6 | 0.590038 | ||||||||
\(907\) | −23548.1 | −0.862075 | −0.431037 | − | 0.902334i | \(-0.641852\pi\) | ||||
−0.431037 | + | 0.902334i | \(0.641852\pi\) | |||||||
\(908\) | −355.649 | −0.0129985 | ||||||||
\(909\) | 13541.3 | 0.494098 | ||||||||
\(910\) | 1036.46 | 0.0377563 | ||||||||
\(911\) | −26956.7 | −0.980368 | −0.490184 | − | 0.871619i | \(-0.663070\pi\) | ||||
−0.490184 | + | 0.871619i | \(0.663070\pi\) | |||||||
\(912\) | 912.000 | 0.0331133 | ||||||||
\(913\) | −33854.0 | −1.22717 | ||||||||
\(914\) | −18564.6 | −0.671841 | ||||||||
\(915\) | 3045.55 | 0.110036 | ||||||||
\(916\) | −14366.5 | −0.518211 | ||||||||
\(917\) | 16306.2 | 0.587218 | ||||||||
\(918\) | −2326.49 | −0.0836444 | ||||||||
\(919\) | −8314.91 | −0.298459 | −0.149229 | − | 0.988803i | \(-0.547679\pi\) | ||||
−0.149229 | + | 0.988803i | \(0.547679\pi\) | |||||||
\(920\) | 1746.54 | 0.0625888 | ||||||||
\(921\) | −5212.13 | −0.186477 | ||||||||
\(922\) | 29873.3 | 1.06706 | ||||||||
\(923\) | 14364.8 | 0.512266 | ||||||||
\(924\) | −5471.59 | −0.194807 | ||||||||
\(925\) | −602.693 | −0.0214231 | ||||||||
\(926\) | −14048.8 | −0.498566 | ||||||||
\(927\) | −10311.1 | −0.365329 | ||||||||
\(928\) | 3062.85 | 0.108344 | ||||||||
\(929\) | −716.122 | −0.0252908 | −0.0126454 | − | 0.999920i | \(-0.504025\pi\) | ||||
−0.0126454 | + | 0.999920i | \(0.504025\pi\) | |||||||
\(930\) | −2273.27 | −0.0801542 | ||||||||
\(931\) | −931.000 | −0.0327737 | ||||||||
\(932\) | −7133.35 | −0.250709 | ||||||||
\(933\) | −11855.3 | −0.415997 | ||||||||
\(934\) | −1600.41 | −0.0560675 | ||||||||
\(935\) | −6600.54 | −0.230867 | ||||||||
\(936\) | 2266.30 | 0.0791414 | ||||||||
\(937\) | −29545.2 | −1.03010 | −0.515048 | − | 0.857161i | \(-0.672226\pi\) | ||||
−0.515048 | + | 0.857161i | \(0.672226\pi\) | |||||||
\(938\) | −13856.0 | −0.482317 | ||||||||
\(939\) | −7490.59 | −0.260326 | ||||||||
\(940\) | 2075.61 | 0.0720200 | ||||||||
\(941\) | −12021.2 | −0.416452 | −0.208226 | − | 0.978081i | \(-0.566769\pi\) | ||||
−0.208226 | + | 0.978081i | \(0.566769\pi\) | |||||||
\(942\) | 4572.00 | 0.158136 | ||||||||
\(943\) | −40368.9 | −1.39405 | ||||||||
\(944\) | −6128.41 | −0.211295 | ||||||||
\(945\) | −444.529 | −0.0153022 | ||||||||
\(946\) | 7132.28 | 0.245127 | ||||||||
\(947\) | 32892.4 | 1.12868 | 0.564340 | − | 0.825542i | \(-0.309131\pi\) | ||||
0.564340 | + | 0.825542i | \(0.309131\pi\) | |||||||
\(948\) | −7450.48 | −0.255253 | ||||||||
\(949\) | −2907.45 | −0.0994519 | ||||||||
\(950\) | −4539.79 | −0.155042 | ||||||||
\(951\) | −7547.06 | −0.257340 | ||||||||
\(952\) | −2412.65 | −0.0821372 | ||||||||
\(953\) | −25757.2 | −0.875505 | −0.437752 | − | 0.899096i | \(-0.644225\pi\) | ||||
−0.437752 | + | 0.899096i | \(0.644225\pi\) | |||||||
\(954\) | −3152.56 | −0.106989 | ||||||||
\(955\) | 3846.87 | 0.130347 | ||||||||
\(956\) | −21122.5 | −0.714594 | ||||||||
\(957\) | −18703.8 | −0.631775 | ||||||||
\(958\) | −7146.91 | −0.241029 | ||||||||
\(959\) | −12100.1 | −0.407438 | ||||||||
\(960\) | 451.585 | 0.0151821 | ||||||||
\(961\) | −3841.94 | −0.128963 | ||||||||
\(962\) | 317.584 | 0.0106438 | ||||||||
\(963\) | −7240.95 | −0.242302 | ||||||||
\(964\) | 28444.7 | 0.950355 | ||||||||
\(965\) | −10426.0 | −0.347796 | ||||||||
\(966\) | −3898.51 | −0.129847 | ||||||||
\(967\) | −18681.0 | −0.621243 | −0.310621 | − | 0.950534i | \(-0.600537\pi\) | ||||
−0.310621 | + | 0.950534i | \(0.600537\pi\) | |||||||
\(968\) | −23295.6 | −0.773501 | ||||||||
\(969\) | −2455.74 | −0.0814135 | ||||||||
\(970\) | −782.300 | −0.0258950 | ||||||||
\(971\) | 20470.4 | 0.676546 | 0.338273 | − | 0.941048i | \(-0.390157\pi\) | ||||
0.338273 | + | 0.941048i | \(0.390157\pi\) | |||||||
\(972\) | −972.000 | −0.0320750 | ||||||||
\(973\) | 4838.43 | 0.159417 | ||||||||
\(974\) | 26170.3 | 0.860934 | ||||||||
\(975\) | −11281.3 | −0.370553 | ||||||||
\(976\) | 6906.00 | 0.226491 | ||||||||
\(977\) | −57784.2 | −1.89220 | −0.946100 | − | 0.323874i | \(-0.895015\pi\) | ||||
−0.946100 | + | 0.323874i | \(0.895015\pi\) | |||||||
\(978\) | 20712.4 | 0.677207 | ||||||||
\(979\) | −68387.4 | −2.23255 | ||||||||
\(980\) | −460.993 | −0.0150264 | ||||||||
\(981\) | 19318.1 | 0.628726 | ||||||||
\(982\) | 18144.3 | 0.589621 | ||||||||
\(983\) | 37476.2 | 1.21598 | 0.607989 | − | 0.793945i | \(-0.291976\pi\) | ||||
0.607989 | + | 0.793945i | \(0.291976\pi\) | |||||||
\(984\) | −10437.8 | −0.338155 | ||||||||
\(985\) | −6119.10 | −0.197940 | ||||||||
\(986\) | −8247.32 | −0.266377 | ||||||||
\(987\) | −4633.03 | −0.149413 | ||||||||
\(988\) | 2392.20 | 0.0770305 | ||||||||
\(989\) | 5081.77 | 0.163388 | ||||||||
\(990\) | −2757.69 | −0.0885304 | ||||||||
\(991\) | −20663.9 | −0.662373 | −0.331186 | − | 0.943565i | \(-0.607449\pi\) | ||||
−0.331186 | + | 0.943565i | \(0.607449\pi\) | |||||||
\(992\) | −5154.79 | −0.164985 | ||||||||
\(993\) | −2940.02 | −0.0939566 | ||||||||
\(994\) | −6389.13 | −0.203874 | ||||||||
\(995\) | −4646.88 | −0.148056 | ||||||||
\(996\) | −6236.73 | −0.198412 | ||||||||
\(997\) | 41487.0 | 1.31786 | 0.658930 | − | 0.752205i | \(-0.271009\pi\) | ||||
0.658930 | + | 0.752205i | \(0.271009\pi\) | |||||||
\(998\) | 3840.76 | 0.121821 | ||||||||
\(999\) | −136.210 | −0.00431380 |
(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 | 798.4.a.k.1.3 | ✓ | 4 | |
3.2 | odd | 2 | 2394.4.a.x.1.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
798.4.a.k.1.3 | ✓ | 4 | 1.1 | even | 1 | trivial | |
2394.4.a.x.1.2 | 4 | 3.2 | odd | 2 |