Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [289,4,Mod(1,289)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(289, 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("289.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 289 = 17^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 289.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: | \(17.0515519917\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.2636.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - 14x - 4 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 17) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(3.87707\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 289.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.36122 | 0.481264 | 0.240632 | − | 0.970616i | \(-0.422645\pi\) | ||||
0.240632 | + | 0.970616i | \(0.422645\pi\) | |||||||
\(3\) | −3.15463 | −0.607109 | −0.303555 | − | 0.952814i | \(-0.598173\pi\) | ||||
−0.303555 | + | 0.952814i | \(0.598173\pi\) | |||||||
\(4\) | −6.14708 | −0.768385 | ||||||||
\(5\) | −3.03171 | −0.271164 | −0.135582 | − | 0.990766i | \(-0.543290\pi\) | ||||
−0.135582 | + | 0.990766i | \(0.543290\pi\) | |||||||
\(6\) | −4.29415 | −0.292180 | ||||||||
\(7\) | 7.94049 | 0.428746 | 0.214373 | − | 0.976752i | \(-0.431229\pi\) | ||||
0.214373 | + | 0.976752i | \(0.431229\pi\) | |||||||
\(8\) | −19.2573 | −0.851061 | ||||||||
\(9\) | −17.0483 | −0.631419 | ||||||||
\(10\) | −4.12682 | −0.130502 | ||||||||
\(11\) | −27.6161 | −0.756961 | −0.378481 | − | 0.925609i | \(-0.623553\pi\) | ||||
−0.378481 | + | 0.925609i | \(0.623553\pi\) | |||||||
\(12\) | 19.3918 | 0.466493 | ||||||||
\(13\) | 58.1117 | 1.23979 | 0.619896 | − | 0.784684i | \(-0.287175\pi\) | ||||
0.619896 | + | 0.784684i | \(0.287175\pi\) | |||||||
\(14\) | 10.8088 | 0.206340 | ||||||||
\(15\) | 9.56391 | 0.164626 | ||||||||
\(16\) | 22.9632 | 0.358799 | ||||||||
\(17\) | 0 | 0 | ||||||||
\(18\) | −23.2065 | −0.303879 | ||||||||
\(19\) | 89.1688 | 1.07667 | 0.538335 | − | 0.842731i | \(-0.319054\pi\) | ||||
0.538335 | + | 0.842731i | \(0.319054\pi\) | |||||||
\(20\) | 18.6361 | 0.208358 | ||||||||
\(21\) | −25.0493 | −0.260296 | ||||||||
\(22\) | −37.5916 | −0.364298 | ||||||||
\(23\) | 115.269 | 1.04501 | 0.522507 | − | 0.852635i | \(-0.324997\pi\) | ||||
0.522507 | + | 0.852635i | \(0.324997\pi\) | |||||||
\(24\) | 60.7497 | 0.516687 | ||||||||
\(25\) | −115.809 | −0.926470 | ||||||||
\(26\) | 79.1029 | 0.596668 | ||||||||
\(27\) | 138.956 | 0.990449 | ||||||||
\(28\) | −48.8108 | −0.329442 | ||||||||
\(29\) | 128.558 | 0.823191 | 0.411596 | − | 0.911367i | \(-0.364972\pi\) | ||||
0.411596 | + | 0.911367i | \(0.364972\pi\) | |||||||
\(30\) | 13.0186 | 0.0792287 | ||||||||
\(31\) | −273.460 | −1.58435 | −0.792174 | − | 0.610295i | \(-0.791051\pi\) | ||||
−0.792174 | + | 0.610295i | \(0.791051\pi\) | |||||||
\(32\) | 185.316 | 1.02374 | ||||||||
\(33\) | 87.1187 | 0.459558 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −24.0732 | −0.116260 | ||||||||
\(36\) | 104.797 | 0.485172 | ||||||||
\(37\) | 132.351 | 0.588063 | 0.294031 | − | 0.955796i | \(-0.405003\pi\) | ||||
0.294031 | + | 0.955796i | \(0.405003\pi\) | |||||||
\(38\) | 121.379 | 0.518163 | ||||||||
\(39\) | −183.321 | −0.752689 | ||||||||
\(40\) | 58.3825 | 0.230777 | ||||||||
\(41\) | 470.559 | 1.79241 | 0.896207 | − | 0.443636i | \(-0.146312\pi\) | ||||
0.896207 | + | 0.443636i | \(0.146312\pi\) | |||||||
\(42\) | −34.0977 | −0.125271 | ||||||||
\(43\) | 352.642 | 1.25064 | 0.625318 | − | 0.780370i | \(-0.284969\pi\) | ||||
0.625318 | + | 0.780370i | \(0.284969\pi\) | |||||||
\(44\) | 169.758 | 0.581637 | ||||||||
\(45\) | 51.6854 | 0.171218 | ||||||||
\(46\) | 156.907 | 0.502928 | ||||||||
\(47\) | 152.598 | 0.473589 | 0.236795 | − | 0.971560i | \(-0.423903\pi\) | ||||
0.236795 | + | 0.971560i | \(0.423903\pi\) | |||||||
\(48\) | −72.4403 | −0.217830 | ||||||||
\(49\) | −279.949 | −0.816177 | ||||||||
\(50\) | −157.641 | −0.445877 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −357.217 | −0.952637 | ||||||||
\(53\) | 527.614 | 1.36742 | 0.683711 | − | 0.729753i | \(-0.260365\pi\) | ||||
0.683711 | + | 0.729753i | \(0.260365\pi\) | |||||||
\(54\) | 189.150 | 0.476668 | ||||||||
\(55\) | 83.7239 | 0.205261 | ||||||||
\(56\) | −152.912 | −0.364889 | ||||||||
\(57\) | −281.295 | −0.653656 | ||||||||
\(58\) | 174.995 | 0.396173 | ||||||||
\(59\) | −292.020 | −0.644368 | −0.322184 | − | 0.946677i | \(-0.604417\pi\) | ||||
−0.322184 | + | 0.946677i | \(0.604417\pi\) | |||||||
\(60\) | −58.7901 | −0.126496 | ||||||||
\(61\) | 53.8962 | 0.113126 | 0.0565632 | − | 0.998399i | \(-0.481986\pi\) | ||||
0.0565632 | + | 0.998399i | \(0.481986\pi\) | |||||||
\(62\) | −372.239 | −0.762490 | ||||||||
\(63\) | −135.372 | −0.270718 | ||||||||
\(64\) | 68.5514 | 0.133889 | ||||||||
\(65\) | −176.178 | −0.336187 | ||||||||
\(66\) | 118.588 | 0.221169 | ||||||||
\(67\) | 52.9572 | 0.0965635 | 0.0482817 | − | 0.998834i | \(-0.484625\pi\) | ||||
0.0482817 | + | 0.998834i | \(0.484625\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −363.632 | −0.634437 | ||||||||
\(70\) | −32.7690 | −0.0559520 | ||||||||
\(71\) | −788.400 | −1.31783 | −0.658915 | − | 0.752218i | \(-0.728984\pi\) | ||||
−0.658915 | + | 0.752218i | \(0.728984\pi\) | |||||||
\(72\) | 328.304 | 0.537375 | ||||||||
\(73\) | −295.780 | −0.474224 | −0.237112 | − | 0.971482i | \(-0.576201\pi\) | ||||
−0.237112 | + | 0.971482i | \(0.576201\pi\) | |||||||
\(74\) | 180.159 | 0.283014 | ||||||||
\(75\) | 365.334 | 0.562468 | ||||||||
\(76\) | −548.127 | −0.827296 | ||||||||
\(77\) | −219.285 | −0.324544 | ||||||||
\(78\) | −249.541 | −0.362242 | ||||||||
\(79\) | 720.325 | 1.02586 | 0.512930 | − | 0.858430i | \(-0.328560\pi\) | ||||
0.512930 | + | 0.858430i | \(0.328560\pi\) | |||||||
\(80\) | −69.6175 | −0.0972934 | ||||||||
\(81\) | 21.9487 | 0.0301079 | ||||||||
\(82\) | 640.535 | 0.862625 | ||||||||
\(83\) | −116.051 | −0.153473 | −0.0767363 | − | 0.997051i | \(-0.524450\pi\) | ||||
−0.0767363 | + | 0.997051i | \(0.524450\pi\) | |||||||
\(84\) | 153.980 | 0.200007 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 480.024 | 0.601887 | ||||||||
\(87\) | −405.552 | −0.499767 | ||||||||
\(88\) | 531.812 | 0.644220 | ||||||||
\(89\) | −813.329 | −0.968682 | −0.484341 | − | 0.874879i | \(-0.660941\pi\) | ||||
−0.484341 | + | 0.874879i | \(0.660941\pi\) | |||||||
\(90\) | 70.3553 | 0.0824011 | ||||||||
\(91\) | 461.435 | 0.531556 | ||||||||
\(92\) | −708.569 | −0.802972 | ||||||||
\(93\) | 862.664 | 0.961872 | ||||||||
\(94\) | 207.720 | 0.227922 | ||||||||
\(95\) | −270.334 | −0.291954 | ||||||||
\(96\) | −584.605 | −0.621521 | ||||||||
\(97\) | −794.693 | −0.831844 | −0.415922 | − | 0.909400i | \(-0.636541\pi\) | ||||
−0.415922 | + | 0.909400i | \(0.636541\pi\) | |||||||
\(98\) | −381.072 | −0.392797 | ||||||||
\(99\) | 470.808 | 0.477959 | ||||||||
\(100\) | 711.885 | 0.711885 | ||||||||
\(101\) | 265.513 | 0.261579 | 0.130790 | − | 0.991410i | \(-0.458249\pi\) | ||||
0.130790 | + | 0.991410i | \(0.458249\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 523.107 | 0.500420 | 0.250210 | − | 0.968192i | \(-0.419500\pi\) | ||||
0.250210 | + | 0.968192i | \(0.419500\pi\) | |||||||
\(104\) | −1119.07 | −1.05514 | ||||||||
\(105\) | 75.9421 | 0.0705828 | ||||||||
\(106\) | 718.199 | 0.658091 | ||||||||
\(107\) | 986.039 | 0.890878 | 0.445439 | − | 0.895312i | \(-0.353048\pi\) | ||||
0.445439 | + | 0.895312i | \(0.353048\pi\) | |||||||
\(108\) | −854.174 | −0.761046 | ||||||||
\(109\) | −1814.39 | −1.59438 | −0.797188 | − | 0.603732i | \(-0.793680\pi\) | ||||
−0.797188 | + | 0.603732i | \(0.793680\pi\) | |||||||
\(110\) | 113.967 | 0.0987846 | ||||||||
\(111\) | −417.518 | −0.357018 | ||||||||
\(112\) | 182.339 | 0.153834 | ||||||||
\(113\) | 707.339 | 0.588857 | 0.294429 | − | 0.955673i | \(-0.404871\pi\) | ||||
0.294429 | + | 0.955673i | \(0.404871\pi\) | |||||||
\(114\) | −382.904 | −0.314581 | ||||||||
\(115\) | −349.463 | −0.283370 | ||||||||
\(116\) | −790.253 | −0.632527 | ||||||||
\(117\) | −990.706 | −0.782827 | ||||||||
\(118\) | −397.503 | −0.310112 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −184.175 | −0.140107 | ||||||||
\(121\) | −568.350 | −0.427010 | ||||||||
\(122\) | 73.3647 | 0.0544437 | ||||||||
\(123\) | −1484.44 | −1.08819 | ||||||||
\(124\) | 1680.98 | 1.21739 | ||||||||
\(125\) | 730.061 | 0.522389 | ||||||||
\(126\) | −184.271 | −0.130287 | ||||||||
\(127\) | 2648.18 | 1.85030 | 0.925151 | − | 0.379600i | \(-0.123938\pi\) | ||||
0.925151 | + | 0.379600i | \(0.123938\pi\) | |||||||
\(128\) | −1389.22 | −0.959302 | ||||||||
\(129\) | −1112.46 | −0.759273 | ||||||||
\(130\) | −239.817 | −0.161795 | ||||||||
\(131\) | 1979.08 | 1.31995 | 0.659974 | − | 0.751289i | \(-0.270567\pi\) | ||||
0.659974 | + | 0.751289i | \(0.270567\pi\) | |||||||
\(132\) | −535.525 | −0.353117 | ||||||||
\(133\) | 708.044 | 0.461618 | ||||||||
\(134\) | 72.0865 | 0.0464726 | ||||||||
\(135\) | −421.274 | −0.268574 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 3141.92 | 1.95936 | 0.979679 | − | 0.200570i | \(-0.0642794\pi\) | ||||
0.979679 | + | 0.200570i | \(0.0642794\pi\) | |||||||
\(138\) | −494.984 | −0.305332 | ||||||||
\(139\) | −1468.07 | −0.895830 | −0.447915 | − | 0.894076i | \(-0.647833\pi\) | ||||
−0.447915 | + | 0.894076i | \(0.647833\pi\) | |||||||
\(140\) | 147.980 | 0.0893327 | ||||||||
\(141\) | −481.390 | −0.287520 | ||||||||
\(142\) | −1073.19 | −0.634224 | ||||||||
\(143\) | −1604.82 | −0.938474 | ||||||||
\(144\) | −391.483 | −0.226553 | ||||||||
\(145\) | −389.749 | −0.223220 | ||||||||
\(146\) | −402.621 | −0.228227 | ||||||||
\(147\) | 883.135 | 0.495508 | ||||||||
\(148\) | −813.570 | −0.451858 | ||||||||
\(149\) | −286.027 | −0.157263 | −0.0786316 | − | 0.996904i | \(-0.525055\pi\) | ||||
−0.0786316 | + | 0.996904i | \(0.525055\pi\) | |||||||
\(150\) | 497.300 | 0.270696 | ||||||||
\(151\) | −669.626 | −0.360883 | −0.180442 | − | 0.983586i | \(-0.557753\pi\) | ||||
−0.180442 | + | 0.983586i | \(0.557753\pi\) | |||||||
\(152\) | −1717.15 | −0.916311 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −298.496 | −0.156191 | ||||||||
\(155\) | 829.049 | 0.429618 | ||||||||
\(156\) | 1126.89 | 0.578354 | ||||||||
\(157\) | 720.809 | 0.366413 | 0.183206 | − | 0.983074i | \(-0.441352\pi\) | ||||
0.183206 | + | 0.983074i | \(0.441352\pi\) | |||||||
\(158\) | 980.522 | 0.493710 | ||||||||
\(159\) | −1664.43 | −0.830174 | ||||||||
\(160\) | −561.825 | −0.277601 | ||||||||
\(161\) | 915.294 | 0.448045 | ||||||||
\(162\) | 29.8770 | 0.0144899 | ||||||||
\(163\) | 676.599 | 0.325125 | 0.162562 | − | 0.986698i | \(-0.448024\pi\) | ||||
0.162562 | + | 0.986698i | \(0.448024\pi\) | |||||||
\(164\) | −2892.56 | −1.37726 | ||||||||
\(165\) | −264.118 | −0.124616 | ||||||||
\(166\) | −157.971 | −0.0738609 | ||||||||
\(167\) | 2835.67 | 1.31396 | 0.656979 | − | 0.753909i | \(-0.271834\pi\) | ||||
0.656979 | + | 0.753909i | \(0.271834\pi\) | |||||||
\(168\) | 482.382 | 0.221527 | ||||||||
\(169\) | 1179.97 | 0.537083 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1520.18 | −0.679829 | ||||||||
\(172\) | −2167.72 | −0.960970 | ||||||||
\(173\) | 177.314 | 0.0779243 | 0.0389621 | − | 0.999241i | \(-0.487595\pi\) | ||||
0.0389621 | + | 0.999241i | \(0.487595\pi\) | |||||||
\(174\) | −552.046 | −0.240520 | ||||||||
\(175\) | −919.578 | −0.397220 | ||||||||
\(176\) | −634.153 | −0.271597 | ||||||||
\(177\) | 921.214 | 0.391202 | ||||||||
\(178\) | −1107.12 | −0.466192 | ||||||||
\(179\) | −1023.76 | −0.427483 | −0.213741 | − | 0.976890i | \(-0.568565\pi\) | ||||
−0.213741 | + | 0.976890i | \(0.568565\pi\) | |||||||
\(180\) | −317.714 | −0.131561 | ||||||||
\(181\) | 3450.21 | 1.41686 | 0.708432 | − | 0.705779i | \(-0.249403\pi\) | ||||
0.708432 | + | 0.705779i | \(0.249403\pi\) | |||||||
\(182\) | 628.116 | 0.255819 | ||||||||
\(183\) | −170.023 | −0.0686800 | ||||||||
\(184\) | −2219.78 | −0.889370 | ||||||||
\(185\) | −401.248 | −0.159461 | ||||||||
\(186\) | 1174.28 | 0.462915 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | −938.031 | −0.363899 | ||||||||
\(189\) | 1103.38 | 0.424651 | ||||||||
\(190\) | −367.984 | −0.140507 | ||||||||
\(191\) | −490.894 | −0.185968 | −0.0929839 | − | 0.995668i | \(-0.529640\pi\) | ||||
−0.0929839 | + | 0.995668i | \(0.529640\pi\) | |||||||
\(192\) | −216.254 | −0.0812855 | ||||||||
\(193\) | 3548.80 | 1.32357 | 0.661783 | − | 0.749696i | \(-0.269800\pi\) | ||||
0.661783 | + | 0.749696i | \(0.269800\pi\) | |||||||
\(194\) | −1081.75 | −0.400337 | ||||||||
\(195\) | 555.775 | 0.204102 | ||||||||
\(196\) | 1720.87 | 0.627138 | ||||||||
\(197\) | −1363.15 | −0.492996 | −0.246498 | − | 0.969143i | \(-0.579280\pi\) | ||||
−0.246498 | + | 0.969143i | \(0.579280\pi\) | |||||||
\(198\) | 640.874 | 0.230025 | ||||||||
\(199\) | −3737.46 | −1.33137 | −0.665683 | − | 0.746235i | \(-0.731860\pi\) | ||||
−0.665683 | + | 0.746235i | \(0.731860\pi\) | |||||||
\(200\) | 2230.16 | 0.788482 | ||||||||
\(201\) | −167.060 | −0.0586246 | ||||||||
\(202\) | 361.422 | 0.125889 | ||||||||
\(203\) | 1020.81 | 0.352940 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1426.60 | −0.486038 | ||||||||
\(206\) | 712.064 | 0.240834 | ||||||||
\(207\) | −1965.15 | −0.659841 | ||||||||
\(208\) | 1334.43 | 0.444836 | ||||||||
\(209\) | −2462.50 | −0.814997 | ||||||||
\(210\) | 103.374 | 0.0339690 | ||||||||
\(211\) | 5266.12 | 1.71817 | 0.859087 | − | 0.511829i | \(-0.171032\pi\) | ||||
0.859087 | + | 0.511829i | \(0.171032\pi\) | |||||||
\(212\) | −3243.28 | −1.05071 | ||||||||
\(213\) | 2487.11 | 0.800066 | ||||||||
\(214\) | 1342.22 | 0.428748 | ||||||||
\(215\) | −1069.11 | −0.339128 | ||||||||
\(216\) | −2675.92 | −0.842932 | ||||||||
\(217\) | −2171.40 | −0.679283 | ||||||||
\(218\) | −2469.78 | −0.767316 | ||||||||
\(219\) | 933.075 | 0.287906 | ||||||||
\(220\) | −514.657 | −0.157719 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | −568.334 | −0.171820 | ||||||||
\(223\) | 704.546 | 0.211569 | 0.105785 | − | 0.994389i | \(-0.466265\pi\) | ||||
0.105785 | + | 0.994389i | \(0.466265\pi\) | |||||||
\(224\) | 1471.50 | 0.438923 | ||||||||
\(225\) | 1974.34 | 0.584990 | ||||||||
\(226\) | 962.845 | 0.283396 | ||||||||
\(227\) | 2151.26 | 0.629006 | 0.314503 | − | 0.949256i | \(-0.398162\pi\) | ||||
0.314503 | + | 0.949256i | \(0.398162\pi\) | |||||||
\(228\) | 1729.14 | 0.502259 | ||||||||
\(229\) | −3916.94 | −1.13030 | −0.565149 | − | 0.824989i | \(-0.691181\pi\) | ||||
−0.565149 | + | 0.824989i | \(0.691181\pi\) | |||||||
\(230\) | −475.696 | −0.136376 | ||||||||
\(231\) | 691.764 | 0.197034 | ||||||||
\(232\) | −2475.67 | −0.700586 | ||||||||
\(233\) | 5192.74 | 1.46003 | 0.730017 | − | 0.683429i | \(-0.239512\pi\) | ||||
0.730017 | + | 0.683429i | \(0.239512\pi\) | |||||||
\(234\) | −1348.57 | −0.376747 | ||||||||
\(235\) | −462.632 | −0.128420 | ||||||||
\(236\) | 1795.07 | 0.495123 | ||||||||
\(237\) | −2272.36 | −0.622809 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 334.305 | 0.0904786 | 0.0452393 | − | 0.998976i | \(-0.485595\pi\) | ||||
0.0452393 | + | 0.998976i | \(0.485595\pi\) | |||||||
\(240\) | 219.618 | 0.0590677 | ||||||||
\(241\) | 1918.45 | 0.512773 | 0.256386 | − | 0.966574i | \(-0.417468\pi\) | ||||
0.256386 | + | 0.966574i | \(0.417468\pi\) | |||||||
\(242\) | −773.651 | −0.205505 | ||||||||
\(243\) | −3821.06 | −1.00873 | ||||||||
\(244\) | −331.304 | −0.0869245 | ||||||||
\(245\) | 848.722 | 0.221318 | ||||||||
\(246\) | −2020.65 | −0.523708 | ||||||||
\(247\) | 5181.75 | 1.33485 | ||||||||
\(248\) | 5266.09 | 1.34838 | ||||||||
\(249\) | 366.097 | 0.0931746 | ||||||||
\(250\) | 993.775 | 0.251407 | ||||||||
\(251\) | 7695.71 | 1.93525 | 0.967627 | − | 0.252385i | \(-0.0812148\pi\) | ||||
0.967627 | + | 0.252385i | \(0.0812148\pi\) | |||||||
\(252\) | 832.141 | 0.208016 | ||||||||
\(253\) | −3183.29 | −0.791035 | ||||||||
\(254\) | 3604.76 | 0.890484 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −2439.44 | −0.595567 | ||||||||
\(257\) | 5335.10 | 1.29492 | 0.647460 | − | 0.762099i | \(-0.275831\pi\) | ||||
0.647460 | + | 0.762099i | \(0.275831\pi\) | |||||||
\(258\) | −1514.30 | −0.365411 | ||||||||
\(259\) | 1050.93 | 0.252130 | ||||||||
\(260\) | 1082.98 | 0.258321 | ||||||||
\(261\) | −2191.69 | −0.519778 | ||||||||
\(262\) | 2693.97 | 0.635244 | ||||||||
\(263\) | 3934.15 | 0.922396 | 0.461198 | − | 0.887297i | \(-0.347420\pi\) | ||||
0.461198 | + | 0.887297i | \(0.347420\pi\) | |||||||
\(264\) | −1677.67 | −0.391112 | ||||||||
\(265\) | −1599.57 | −0.370795 | ||||||||
\(266\) | 963.804 | 0.222160 | ||||||||
\(267\) | 2565.75 | 0.588095 | ||||||||
\(268\) | −325.532 | −0.0741979 | ||||||||
\(269\) | −3424.04 | −0.776088 | −0.388044 | − | 0.921641i | \(-0.626849\pi\) | ||||
−0.388044 | + | 0.921641i | \(0.626849\pi\) | |||||||
\(270\) | −573.447 | −0.129255 | ||||||||
\(271\) | 549.034 | 0.123068 | 0.0615340 | − | 0.998105i | \(-0.480401\pi\) | ||||
0.0615340 | + | 0.998105i | \(0.480401\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −1455.66 | −0.322712 | ||||||||
\(274\) | 4276.85 | 0.942970 | ||||||||
\(275\) | 3198.19 | 0.701302 | ||||||||
\(276\) | 2235.27 | 0.487492 | ||||||||
\(277\) | −5203.65 | −1.12873 | −0.564363 | − | 0.825527i | \(-0.690878\pi\) | ||||
−0.564363 | + | 0.825527i | \(0.690878\pi\) | |||||||
\(278\) | −1998.37 | −0.431131 | ||||||||
\(279\) | 4662.02 | 1.00039 | ||||||||
\(280\) | 463.585 | 0.0989447 | ||||||||
\(281\) | −1986.73 | −0.421774 | −0.210887 | − | 0.977510i | \(-0.567635\pi\) | ||||
−0.210887 | + | 0.977510i | \(0.567635\pi\) | |||||||
\(282\) | −655.279 | −0.138373 | ||||||||
\(283\) | −753.696 | −0.158313 | −0.0791565 | − | 0.996862i | \(-0.525223\pi\) | ||||
−0.0791565 | + | 0.996862i | \(0.525223\pi\) | |||||||
\(284\) | 4846.36 | 1.01260 | ||||||||
\(285\) | 852.803 | 0.177248 | ||||||||
\(286\) | −2184.51 | −0.451654 | ||||||||
\(287\) | 3736.47 | 0.768490 | ||||||||
\(288\) | −3159.33 | −0.646407 | ||||||||
\(289\) | 0 | 0 | ||||||||
\(290\) | −530.534 | −0.107428 | ||||||||
\(291\) | 2506.96 | 0.505020 | ||||||||
\(292\) | 1818.18 | 0.364387 | ||||||||
\(293\) | −7202.22 | −1.43603 | −0.718017 | − | 0.696025i | \(-0.754950\pi\) | ||||
−0.718017 | + | 0.696025i | \(0.754950\pi\) | |||||||
\(294\) | 1202.14 | 0.238471 | ||||||||
\(295\) | 885.318 | 0.174729 | ||||||||
\(296\) | −2548.72 | −0.500477 | ||||||||
\(297\) | −3837.43 | −0.749731 | ||||||||
\(298\) | −389.345 | −0.0756852 | ||||||||
\(299\) | 6698.50 | 1.29560 | ||||||||
\(300\) | −2245.74 | −0.432192 | ||||||||
\(301\) | 2800.15 | 0.536205 | ||||||||
\(302\) | −911.509 | −0.173680 | ||||||||
\(303\) | −837.595 | −0.158807 | ||||||||
\(304\) | 2047.60 | 0.386308 | ||||||||
\(305\) | −163.398 | −0.0306758 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 2425.71 | 0.450953 | 0.225477 | − | 0.974249i | \(-0.427606\pi\) | ||||
0.225477 | + | 0.974249i | \(0.427606\pi\) | |||||||
\(308\) | 1347.96 | 0.249375 | ||||||||
\(309\) | −1650.21 | −0.303809 | ||||||||
\(310\) | 1128.52 | 0.206760 | ||||||||
\(311\) | 9544.94 | 1.74033 | 0.870167 | − | 0.492757i | \(-0.164011\pi\) | ||||
0.870167 | + | 0.492757i | \(0.164011\pi\) | |||||||
\(312\) | 3530.27 | 0.640584 | ||||||||
\(313\) | −588.379 | −0.106253 | −0.0531264 | − | 0.998588i | \(-0.516919\pi\) | ||||
−0.0531264 | + | 0.998588i | \(0.516919\pi\) | |||||||
\(314\) | 981.180 | 0.176341 | ||||||||
\(315\) | 410.407 | 0.0734090 | ||||||||
\(316\) | −4427.89 | −0.788255 | ||||||||
\(317\) | −7653.31 | −1.35600 | −0.678001 | − | 0.735061i | \(-0.737154\pi\) | ||||
−0.678001 | + | 0.735061i | \(0.737154\pi\) | |||||||
\(318\) | −2265.65 | −0.399533 | ||||||||
\(319\) | −3550.26 | −0.623124 | ||||||||
\(320\) | −207.828 | −0.0363060 | ||||||||
\(321\) | −3110.59 | −0.540860 | ||||||||
\(322\) | 1245.92 | 0.215628 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | −134.920 | −0.0231345 | ||||||||
\(325\) | −6729.85 | −1.14863 | ||||||||
\(326\) | 921.001 | 0.156471 | ||||||||
\(327\) | 5723.73 | 0.967960 | ||||||||
\(328\) | −9061.70 | −1.52545 | ||||||||
\(329\) | 1211.70 | 0.203050 | ||||||||
\(330\) | −359.523 | −0.0599730 | ||||||||
\(331\) | 752.266 | 0.124919 | 0.0624597 | − | 0.998047i | \(-0.480106\pi\) | ||||
0.0624597 | + | 0.998047i | \(0.480106\pi\) | |||||||
\(332\) | 713.373 | 0.117926 | ||||||||
\(333\) | −2256.36 | −0.371314 | ||||||||
\(334\) | 3859.98 | 0.632361 | ||||||||
\(335\) | −160.551 | −0.0261845 | ||||||||
\(336\) | −575.211 | −0.0933939 | ||||||||
\(337\) | 1968.57 | 0.318204 | 0.159102 | − | 0.987262i | \(-0.449140\pi\) | ||||
0.159102 | + | 0.987262i | \(0.449140\pi\) | |||||||
\(338\) | 1606.20 | 0.258479 | ||||||||
\(339\) | −2231.39 | −0.357501 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 7551.89 | 1.19929 | ||||||||
\(342\) | −2069.30 | −0.327178 | ||||||||
\(343\) | −4946.52 | −0.778678 | ||||||||
\(344\) | −6790.93 | −1.06437 | ||||||||
\(345\) | 1102.43 | 0.172037 | ||||||||
\(346\) | 241.363 | 0.0375022 | ||||||||
\(347\) | −3983.10 | −0.616207 | −0.308104 | − | 0.951353i | \(-0.599694\pi\) | ||||
−0.308104 | + | 0.951353i | \(0.599694\pi\) | |||||||
\(348\) | 2492.96 | 0.384013 | ||||||||
\(349\) | 1495.61 | 0.229393 | 0.114697 | − | 0.993401i | \(-0.463410\pi\) | ||||
0.114697 | + | 0.993401i | \(0.463410\pi\) | |||||||
\(350\) | −1251.75 | −0.191168 | ||||||||
\(351\) | 8074.98 | 1.22795 | ||||||||
\(352\) | −5117.72 | −0.774930 | ||||||||
\(353\) | 6482.49 | 0.977417 | 0.488708 | − | 0.872447i | \(-0.337468\pi\) | ||||
0.488708 | + | 0.872447i | \(0.337468\pi\) | |||||||
\(354\) | 1253.98 | 0.188272 | ||||||||
\(355\) | 2390.20 | 0.357348 | ||||||||
\(356\) | 4999.59 | 0.744320 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −1393.56 | −0.205732 | ||||||||
\(359\) | −4943.42 | −0.726751 | −0.363376 | − | 0.931643i | \(-0.618376\pi\) | ||||
−0.363376 | + | 0.931643i | \(0.618376\pi\) | |||||||
\(360\) | −995.322 | −0.145717 | ||||||||
\(361\) | 1092.08 | 0.159218 | ||||||||
\(362\) | 4696.50 | 0.681886 | ||||||||
\(363\) | 1792.94 | 0.259242 | ||||||||
\(364\) | −2836.48 | −0.408439 | ||||||||
\(365\) | 896.717 | 0.128593 | ||||||||
\(366\) | −231.439 | −0.0330533 | ||||||||
\(367\) | 14.8871 | 0.00211743 | 0.00105872 | − | 0.999999i | \(-0.499663\pi\) | ||||
0.00105872 | + | 0.999999i | \(0.499663\pi\) | |||||||
\(368\) | 2646.95 | 0.374950 | ||||||||
\(369\) | −8022.23 | −1.13176 | ||||||||
\(370\) | −546.188 | −0.0767431 | ||||||||
\(371\) | 4189.51 | 0.586276 | ||||||||
\(372\) | −5302.86 | −0.739088 | ||||||||
\(373\) | 1923.18 | 0.266966 | 0.133483 | − | 0.991051i | \(-0.457384\pi\) | ||||
0.133483 | + | 0.991051i | \(0.457384\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −2303.07 | −0.317147 | ||||||||
\(376\) | −2938.63 | −0.403053 | ||||||||
\(377\) | 7470.70 | 1.02059 | ||||||||
\(378\) | 1501.94 | 0.204369 | ||||||||
\(379\) | 9592.87 | 1.30014 | 0.650069 | − | 0.759875i | \(-0.274740\pi\) | ||||
0.650069 | + | 0.759875i | \(0.274740\pi\) | |||||||
\(380\) | 1661.76 | 0.224333 | ||||||||
\(381\) | −8354.04 | −1.12333 | ||||||||
\(382\) | −668.215 | −0.0894996 | ||||||||
\(383\) | −9083.77 | −1.21190 | −0.605951 | − | 0.795502i | \(-0.707207\pi\) | ||||
−0.605951 | + | 0.795502i | \(0.707207\pi\) | |||||||
\(384\) | 4382.47 | 0.582401 | ||||||||
\(385\) | 664.809 | 0.0880046 | ||||||||
\(386\) | 4830.70 | 0.636985 | ||||||||
\(387\) | −6011.95 | −0.789675 | ||||||||
\(388\) | 4885.04 | 0.639176 | ||||||||
\(389\) | −1143.78 | −0.149079 | −0.0745396 | − | 0.997218i | \(-0.523749\pi\) | ||||
−0.0745396 | + | 0.997218i | \(0.523749\pi\) | |||||||
\(390\) | 756.533 | 0.0982271 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 5391.06 | 0.694616 | ||||||||
\(393\) | −6243.27 | −0.801352 | ||||||||
\(394\) | −1855.55 | −0.237262 | ||||||||
\(395\) | −2183.81 | −0.278176 | ||||||||
\(396\) | −2894.09 | −0.367256 | ||||||||
\(397\) | −10604.5 | −1.34061 | −0.670307 | − | 0.742084i | \(-0.733838\pi\) | ||||
−0.670307 | + | 0.742084i | \(0.733838\pi\) | |||||||
\(398\) | −5087.51 | −0.640739 | ||||||||
\(399\) | −2233.62 | −0.280252 | ||||||||
\(400\) | −2659.33 | −0.332417 | ||||||||
\(401\) | −13785.4 | −1.71674 | −0.858368 | − | 0.513035i | \(-0.828521\pi\) | ||||
−0.858368 | + | 0.513035i | \(0.828521\pi\) | |||||||
\(402\) | −227.406 | −0.0282139 | ||||||||
\(403\) | −15891.2 | −1.96426 | ||||||||
\(404\) | −1632.13 | −0.200993 | ||||||||
\(405\) | −66.5420 | −0.00816419 | ||||||||
\(406\) | 1389.55 | 0.169857 | ||||||||
\(407\) | −3655.01 | −0.445141 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −9505.94 | −1.14924 | −0.574619 | − | 0.818421i | \(-0.694850\pi\) | ||||
−0.574619 | + | 0.818421i | \(0.694850\pi\) | |||||||
\(410\) | −1941.91 | −0.233913 | ||||||||
\(411\) | −9911.59 | −1.18954 | ||||||||
\(412\) | −3215.58 | −0.384515 | ||||||||
\(413\) | −2318.78 | −0.276270 | ||||||||
\(414\) | −2675.00 | −0.317558 | ||||||||
\(415\) | 351.832 | 0.0416162 | ||||||||
\(416\) | 10769.1 | 1.26922 | ||||||||
\(417\) | 4631.23 | 0.543866 | ||||||||
\(418\) | −3352.00 | −0.392229 | ||||||||
\(419\) | −9680.86 | −1.12874 | −0.564369 | − | 0.825523i | \(-0.690880\pi\) | ||||
−0.564369 | + | 0.825523i | \(0.690880\pi\) | |||||||
\(420\) | −466.822 | −0.0542347 | ||||||||
\(421\) | −12360.3 | −1.43089 | −0.715444 | − | 0.698671i | \(-0.753775\pi\) | ||||
−0.715444 | + | 0.698671i | \(0.753775\pi\) | |||||||
\(422\) | 7168.36 | 0.826897 | ||||||||
\(423\) | −2601.54 | −0.299033 | ||||||||
\(424\) | −10160.4 | −1.16376 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 3385.51 | 0.385043 | ||||||||
\(427\) | 427.962 | 0.0485025 | ||||||||
\(428\) | −6061.25 | −0.684537 | ||||||||
\(429\) | 5062.61 | 0.569756 | ||||||||
\(430\) | −1455.29 | −0.163210 | ||||||||
\(431\) | −2970.58 | −0.331990 | −0.165995 | − | 0.986127i | \(-0.553084\pi\) | ||||
−0.165995 | + | 0.986127i | \(0.553084\pi\) | |||||||
\(432\) | 3190.87 | 0.355372 | ||||||||
\(433\) | 6131.50 | 0.680510 | 0.340255 | − | 0.940333i | \(-0.389487\pi\) | ||||
0.340255 | + | 0.940333i | \(0.389487\pi\) | |||||||
\(434\) | −2955.76 | −0.326915 | ||||||||
\(435\) | 1229.51 | 0.135519 | ||||||||
\(436\) | 11153.2 | 1.22509 | ||||||||
\(437\) | 10278.4 | 1.12513 | ||||||||
\(438\) | 1270.12 | 0.138559 | ||||||||
\(439\) | 2544.91 | 0.276679 | 0.138339 | − | 0.990385i | \(-0.455824\pi\) | ||||
0.138339 | + | 0.990385i | \(0.455824\pi\) | |||||||
\(440\) | −1612.30 | −0.174689 | ||||||||
\(441\) | 4772.65 | 0.515349 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 8529.82 | 0.914817 | 0.457408 | − | 0.889257i | \(-0.348778\pi\) | ||||
0.457408 | + | 0.889257i | \(0.348778\pi\) | |||||||
\(444\) | 2566.51 | 0.274327 | ||||||||
\(445\) | 2465.77 | 0.262672 | ||||||||
\(446\) | 959.043 | 0.101821 | ||||||||
\(447\) | 902.308 | 0.0954759 | ||||||||
\(448\) | 544.331 | 0.0574046 | ||||||||
\(449\) | −8855.74 | −0.930798 | −0.465399 | − | 0.885101i | \(-0.654089\pi\) | ||||
−0.465399 | + | 0.885101i | \(0.654089\pi\) | |||||||
\(450\) | 2687.52 | 0.281535 | ||||||||
\(451\) | −12995.0 | −1.35679 | ||||||||
\(452\) | −4348.07 | −0.452469 | ||||||||
\(453\) | 2112.42 | 0.219095 | ||||||||
\(454\) | 2928.35 | 0.302718 | ||||||||
\(455\) | −1398.94 | −0.144139 | ||||||||
\(456\) | 5416.98 | 0.556301 | ||||||||
\(457\) | −7154.78 | −0.732356 | −0.366178 | − | 0.930545i | \(-0.619334\pi\) | ||||
−0.366178 | + | 0.930545i | \(0.619334\pi\) | |||||||
\(458\) | −5331.82 | −0.543973 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 2148.17 | 0.217737 | ||||||||
\(461\) | −7263.06 | −0.733784 | −0.366892 | − | 0.930264i | \(-0.619578\pi\) | ||||
−0.366892 | + | 0.930264i | \(0.619578\pi\) | |||||||
\(462\) | 941.645 | 0.0948253 | ||||||||
\(463\) | 352.898 | 0.0354224 | 0.0177112 | − | 0.999843i | \(-0.494362\pi\) | ||||
0.0177112 | + | 0.999843i | \(0.494362\pi\) | |||||||
\(464\) | 2952.09 | 0.295360 | ||||||||
\(465\) | −2615.34 | −0.260825 | ||||||||
\(466\) | 7068.47 | 0.702662 | ||||||||
\(467\) | 1483.02 | 0.146951 | 0.0734753 | − | 0.997297i | \(-0.476591\pi\) | ||||
0.0734753 | + | 0.997297i | \(0.476591\pi\) | |||||||
\(468\) | 6089.94 | 0.601512 | ||||||||
\(469\) | 420.506 | 0.0414012 | ||||||||
\(470\) | −629.745 | −0.0618042 | ||||||||
\(471\) | −2273.89 | −0.222452 | ||||||||
\(472\) | 5623.51 | 0.548396 | ||||||||
\(473\) | −9738.60 | −0.946683 | ||||||||
\(474\) | −3093.19 | −0.299736 | ||||||||
\(475\) | −10326.5 | −0.997502 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −8994.92 | −0.863415 | ||||||||
\(478\) | 455.063 | 0.0435441 | ||||||||
\(479\) | 9990.10 | 0.952942 | 0.476471 | − | 0.879190i | \(-0.341916\pi\) | ||||
0.476471 | + | 0.879190i | \(0.341916\pi\) | |||||||
\(480\) | 1772.35 | 0.168534 | ||||||||
\(481\) | 7691.13 | 0.729075 | ||||||||
\(482\) | 2611.44 | 0.246779 | ||||||||
\(483\) | −2887.42 | −0.272012 | ||||||||
\(484\) | 3493.69 | 0.328108 | ||||||||
\(485\) | 2409.27 | 0.225566 | ||||||||
\(486\) | −5201.30 | −0.485465 | ||||||||
\(487\) | 1129.88 | 0.105133 | 0.0525663 | − | 0.998617i | \(-0.483260\pi\) | ||||
0.0525663 | + | 0.998617i | \(0.483260\pi\) | |||||||
\(488\) | −1037.90 | −0.0962774 | ||||||||
\(489\) | −2134.42 | −0.197386 | ||||||||
\(490\) | 1155.30 | 0.106512 | ||||||||
\(491\) | 18774.9 | 1.72566 | 0.862832 | − | 0.505491i | \(-0.168689\pi\) | ||||
0.862832 | + | 0.505491i | \(0.168689\pi\) | |||||||
\(492\) | 9124.97 | 0.836149 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 7053.51 | 0.642414 | ||||||||
\(495\) | −1427.35 | −0.129605 | ||||||||
\(496\) | −6279.49 | −0.568463 | ||||||||
\(497\) | −6260.28 | −0.565014 | ||||||||
\(498\) | 498.339 | 0.0448416 | ||||||||
\(499\) | −17329.1 | −1.55462 | −0.777310 | − | 0.629118i | \(-0.783416\pi\) | ||||
−0.777310 | + | 0.629118i | \(0.783416\pi\) | |||||||
\(500\) | −4487.74 | −0.401396 | ||||||||
\(501\) | −8945.50 | −0.797716 | ||||||||
\(502\) | 10475.6 | 0.931369 | ||||||||
\(503\) | 20837.0 | 1.84707 | 0.923533 | − | 0.383518i | \(-0.125288\pi\) | ||||
0.923533 | + | 0.383518i | \(0.125288\pi\) | |||||||
\(504\) | 2606.90 | 0.230398 | ||||||||
\(505\) | −804.957 | −0.0709309 | ||||||||
\(506\) | −4333.16 | −0.380697 | ||||||||
\(507\) | −3722.37 | −0.326068 | ||||||||
\(508\) | −16278.6 | −1.42174 | ||||||||
\(509\) | 11835.0 | 1.03060 | 0.515301 | − | 0.857009i | \(-0.327680\pi\) | ||||
0.515301 | + | 0.857009i | \(0.327680\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −2348.63 | −0.203322 | ||||||||
\(512\) | 7793.12 | 0.672676 | ||||||||
\(513\) | 12390.6 | 1.06639 | ||||||||
\(514\) | 7262.26 | 0.623199 | ||||||||
\(515\) | −1585.91 | −0.135696 | ||||||||
\(516\) | 6838.35 | 0.583414 | ||||||||
\(517\) | −4214.16 | −0.358489 | ||||||||
\(518\) | 1430.55 | 0.121341 | ||||||||
\(519\) | −559.359 | −0.0473086 | ||||||||
\(520\) | 3392.71 | 0.286115 | ||||||||
\(521\) | −7686.37 | −0.646346 | −0.323173 | − | 0.946340i | \(-0.604750\pi\) | ||||
−0.323173 | + | 0.946340i | \(0.604750\pi\) | |||||||
\(522\) | −2983.37 | −0.250151 | ||||||||
\(523\) | 11476.4 | 0.959518 | 0.479759 | − | 0.877400i | \(-0.340724\pi\) | ||||
0.479759 | + | 0.877400i | \(0.340724\pi\) | |||||||
\(524\) | −12165.6 | −1.01423 | ||||||||
\(525\) | 2900.93 | 0.241156 | ||||||||
\(526\) | 5355.25 | 0.443916 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 2000.52 | 0.164889 | ||||||||
\(529\) | 1120.01 | 0.0920535 | ||||||||
\(530\) | −2177.37 | −0.178451 | ||||||||
\(531\) | 4978.44 | 0.406866 | ||||||||
\(532\) | −4352.40 | −0.354700 | ||||||||
\(533\) | 27345.0 | 2.22222 | ||||||||
\(534\) | 3492.56 | 0.283029 | ||||||||
\(535\) | −2989.38 | −0.241574 | ||||||||
\(536\) | −1019.81 | −0.0821814 | ||||||||
\(537\) | 3229.59 | 0.259529 | ||||||||
\(538\) | −4660.88 | −0.373504 | ||||||||
\(539\) | 7731.09 | 0.617814 | ||||||||
\(540\) | 2589.60 | 0.206368 | ||||||||
\(541\) | 546.481 | 0.0434289 | 0.0217145 | − | 0.999764i | \(-0.493088\pi\) | ||||
0.0217145 | + | 0.999764i | \(0.493088\pi\) | |||||||
\(542\) | 747.357 | 0.0592283 | ||||||||
\(543\) | −10884.1 | −0.860191 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 5500.69 | 0.432337 | ||||||||
\(546\) | −1981.47 | −0.155310 | ||||||||
\(547\) | −8397.33 | −0.656388 | −0.328194 | − | 0.944610i | \(-0.606440\pi\) | ||||
−0.328194 | + | 0.944610i | \(0.606440\pi\) | |||||||
\(548\) | −19313.6 | −1.50554 | ||||||||
\(549\) | −918.839 | −0.0714301 | ||||||||
\(550\) | 4353.44 | 0.337512 | ||||||||
\(551\) | 11463.3 | 0.886305 | ||||||||
\(552\) | 7002.58 | 0.539945 | ||||||||
\(553\) | 5719.73 | 0.439833 | ||||||||
\(554\) | −7083.32 | −0.543215 | ||||||||
\(555\) | 1265.79 | 0.0968105 | ||||||||
\(556\) | 9024.36 | 0.688342 | ||||||||
\(557\) | −4881.65 | −0.371350 | −0.185675 | − | 0.982611i | \(-0.559447\pi\) | ||||
−0.185675 | + | 0.982611i | \(0.559447\pi\) | |||||||
\(558\) | 6346.04 | 0.481451 | ||||||||
\(559\) | 20492.6 | 1.55053 | ||||||||
\(560\) | −552.797 | −0.0417142 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −2704.38 | −0.202985 | ||||||||
\(563\) | 7198.57 | 0.538870 | 0.269435 | − | 0.963019i | \(-0.413163\pi\) | ||||
0.269435 | + | 0.963019i | \(0.413163\pi\) | |||||||
\(564\) | 2959.14 | 0.220926 | ||||||||
\(565\) | −2144.44 | −0.159677 | ||||||||
\(566\) | −1025.95 | −0.0761904 | ||||||||
\(567\) | 174.283 | 0.0129087 | ||||||||
\(568\) | 15182.5 | 1.12155 | ||||||||
\(569\) | −23946.9 | −1.76433 | −0.882167 | − | 0.470937i | \(-0.843916\pi\) | ||||
−0.882167 | + | 0.470937i | \(0.843916\pi\) | |||||||
\(570\) | 1160.85 | 0.0853032 | ||||||||
\(571\) | −1593.15 | −0.116763 | −0.0583813 | − | 0.998294i | \(-0.518594\pi\) | ||||
−0.0583813 | + | 0.998294i | \(0.518594\pi\) | |||||||
\(572\) | 9864.95 | 0.721109 | ||||||||
\(573\) | 1548.59 | 0.112903 | ||||||||
\(574\) | 5086.16 | 0.369847 | ||||||||
\(575\) | −13349.2 | −0.968174 | ||||||||
\(576\) | −1168.69 | −0.0845403 | ||||||||
\(577\) | 12937.4 | 0.933435 | 0.466717 | − | 0.884406i | \(-0.345436\pi\) | ||||
0.466717 | + | 0.884406i | \(0.345436\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −11195.2 | −0.803549 | ||||||||
\(580\) | 2395.82 | 0.171519 | ||||||||
\(581\) | −921.499 | −0.0658007 | ||||||||
\(582\) | 3412.53 | 0.243048 | ||||||||
\(583\) | −14570.6 | −1.03508 | ||||||||
\(584\) | 5695.92 | 0.403594 | ||||||||
\(585\) | 3003.53 | 0.212275 | ||||||||
\(586\) | −9803.82 | −0.691112 | ||||||||
\(587\) | −12899.2 | −0.906998 | −0.453499 | − | 0.891257i | \(-0.649824\pi\) | ||||
−0.453499 | + | 0.891257i | \(0.649824\pi\) | |||||||
\(588\) | −5428.70 | −0.380741 | ||||||||
\(589\) | −24384.1 | −1.70582 | ||||||||
\(590\) | 1205.11 | 0.0840911 | ||||||||
\(591\) | 4300.23 | 0.299302 | ||||||||
\(592\) | 3039.19 | 0.210997 | ||||||||
\(593\) | 4357.13 | 0.301730 | 0.150865 | − | 0.988554i | \(-0.451794\pi\) | ||||
0.150865 | + | 0.988554i | \(0.451794\pi\) | |||||||
\(594\) | −5223.59 | −0.360819 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 1758.23 | 0.120839 | ||||||||
\(597\) | 11790.3 | 0.808284 | ||||||||
\(598\) | 9118.14 | 0.623526 | ||||||||
\(599\) | 13726.8 | 0.936328 | 0.468164 | − | 0.883642i | \(-0.344916\pi\) | ||||
0.468164 | + | 0.883642i | \(0.344916\pi\) | |||||||
\(600\) | −7035.35 | −0.478695 | ||||||||
\(601\) | −2531.41 | −0.171811 | −0.0859056 | − | 0.996303i | \(-0.527378\pi\) | ||||
−0.0859056 | + | 0.996303i | \(0.527378\pi\) | |||||||
\(602\) | 3811.62 | 0.258057 | ||||||||
\(603\) | −902.830 | −0.0609720 | ||||||||
\(604\) | 4116.24 | 0.277297 | ||||||||
\(605\) | 1723.07 | 0.115790 | ||||||||
\(606\) | −1140.15 | −0.0764283 | ||||||||
\(607\) | −185.004 | −0.0123708 | −0.00618540 | − | 0.999981i | \(-0.501969\pi\) | ||||
−0.00618540 | + | 0.999981i | \(0.501969\pi\) | |||||||
\(608\) | 16524.4 | 1.10223 | ||||||||
\(609\) | −3220.28 | −0.214273 | ||||||||
\(610\) | −222.420 | −0.0147632 | ||||||||
\(611\) | 8867.73 | 0.587152 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −17706.9 | −1.16668 | −0.583339 | − | 0.812228i | \(-0.698254\pi\) | ||||
−0.583339 | + | 0.812228i | \(0.698254\pi\) | |||||||
\(614\) | 3301.93 | 0.217028 | ||||||||
\(615\) | 4500.39 | 0.295078 | ||||||||
\(616\) | 4222.84 | 0.276207 | ||||||||
\(617\) | 6183.89 | 0.403491 | 0.201746 | − | 0.979438i | \(-0.435339\pi\) | ||||
0.201746 | + | 0.979438i | \(0.435339\pi\) | |||||||
\(618\) | −2246.30 | −0.146213 | ||||||||
\(619\) | 1247.51 | 0.0810046 | 0.0405023 | − | 0.999179i | \(-0.487104\pi\) | ||||
0.0405023 | + | 0.999179i | \(0.487104\pi\) | |||||||
\(620\) | −5096.23 | −0.330112 | ||||||||
\(621\) | 16017.4 | 1.03503 | ||||||||
\(622\) | 12992.8 | 0.837561 | ||||||||
\(623\) | −6458.23 | −0.415318 | ||||||||
\(624\) | −4209.63 | −0.270064 | ||||||||
\(625\) | 12262.8 | 0.784817 | ||||||||
\(626\) | −800.914 | −0.0511357 | ||||||||
\(627\) | 7768.27 | 0.494792 | ||||||||
\(628\) | −4430.87 | −0.281546 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 558.655 | 0.0353292 | ||||||||
\(631\) | 24053.3 | 1.51750 | 0.758752 | − | 0.651379i | \(-0.225809\pi\) | ||||
0.758752 | + | 0.651379i | \(0.225809\pi\) | |||||||
\(632\) | −13871.5 | −0.873069 | ||||||||
\(633\) | −16612.7 | −1.04312 | ||||||||
\(634\) | −10417.8 | −0.652596 | ||||||||
\(635\) | −8028.51 | −0.501735 | ||||||||
\(636\) | 10231.4 | 0.637893 | ||||||||
\(637\) | −16268.3 | −1.01189 | ||||||||
\(638\) | −4832.69 | −0.299887 | ||||||||
\(639\) | 13440.9 | 0.832102 | ||||||||
\(640\) | 4211.70 | 0.260128 | ||||||||
\(641\) | 21286.8 | 1.31167 | 0.655834 | − | 0.754905i | \(-0.272317\pi\) | ||||
0.655834 | + | 0.754905i | \(0.272317\pi\) | |||||||
\(642\) | −4234.20 | −0.260297 | ||||||||
\(643\) | 1789.41 | 0.109747 | 0.0548736 | − | 0.998493i | \(-0.482524\pi\) | ||||
0.0548736 | + | 0.998493i | \(0.482524\pi\) | |||||||
\(644\) | −5626.38 | −0.344271 | ||||||||
\(645\) | 3372.64 | 0.205888 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −4378.61 | −0.266060 | −0.133030 | − | 0.991112i | \(-0.542471\pi\) | ||||
−0.133030 | + | 0.991112i | \(0.542471\pi\) | |||||||
\(648\) | −422.672 | −0.0256237 | ||||||||
\(649\) | 8064.45 | 0.487762 | ||||||||
\(650\) | −9160.81 | −0.552795 | ||||||||
\(651\) | 6849.97 | 0.412399 | ||||||||
\(652\) | −4159.11 | −0.249821 | ||||||||
\(653\) | 7665.15 | 0.459358 | 0.229679 | − | 0.973266i | \(-0.426232\pi\) | ||||
0.229679 | + | 0.973266i | \(0.426232\pi\) | |||||||
\(654\) | 7791.26 | 0.465845 | ||||||||
\(655\) | −5999.99 | −0.357922 | ||||||||
\(656\) | 10805.5 | 0.643117 | ||||||||
\(657\) | 5042.54 | 0.299434 | ||||||||
\(658\) | 1649.39 | 0.0977205 | ||||||||
\(659\) | −4710.22 | −0.278428 | −0.139214 | − | 0.990262i | \(-0.544458\pi\) | ||||
−0.139214 | + | 0.990262i | \(0.544458\pi\) | |||||||
\(660\) | 1623.55 | 0.0957527 | ||||||||
\(661\) | −31266.6 | −1.83983 | −0.919916 | − | 0.392116i | \(-0.871743\pi\) | ||||
−0.919916 | + | 0.392116i | \(0.871743\pi\) | |||||||
\(662\) | 1024.00 | 0.0601192 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 2234.82 | 0.130614 | ||||||||
\(665\) | −2146.58 | −0.125174 | ||||||||
\(666\) | −3071.40 | −0.178700 | ||||||||
\(667\) | 14818.7 | 0.860246 | ||||||||
\(668\) | −17431.1 | −1.00962 | ||||||||
\(669\) | −2222.58 | −0.128446 | ||||||||
\(670\) | −218.545 | −0.0126017 | ||||||||
\(671\) | −1488.40 | −0.0856322 | ||||||||
\(672\) | −4642.05 | −0.266474 | ||||||||
\(673\) | −11723.0 | −0.671454 | −0.335727 | − | 0.941959i | \(-0.608982\pi\) | ||||
−0.335727 | + | 0.941959i | \(0.608982\pi\) | |||||||
\(674\) | 2679.65 | 0.153140 | ||||||||
\(675\) | −16092.3 | −0.917621 | ||||||||
\(676\) | −7253.37 | −0.412686 | ||||||||
\(677\) | 289.531 | 0.0164366 | 0.00821829 | − | 0.999966i | \(-0.497384\pi\) | ||||
0.00821829 | + | 0.999966i | \(0.497384\pi\) | |||||||
\(678\) | −3037.42 | −0.172052 | ||||||||
\(679\) | −6310.25 | −0.356650 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −6786.45 | −0.381875 | ||||||||
\(682\) | 10279.8 | 0.577175 | ||||||||
\(683\) | −1720.10 | −0.0963660 | −0.0481830 | − | 0.998839i | \(-0.515343\pi\) | ||||
−0.0481830 | + | 0.998839i | \(0.515343\pi\) | |||||||
\(684\) | 9344.64 | 0.522370 | ||||||||
\(685\) | −9525.37 | −0.531308 | ||||||||
\(686\) | −6733.30 | −0.374750 | ||||||||
\(687\) | 12356.5 | 0.686215 | ||||||||
\(688\) | 8097.77 | 0.448728 | ||||||||
\(689\) | 30660.5 | 1.69532 | ||||||||
\(690\) | 1500.65 | 0.0827951 | ||||||||
\(691\) | 16777.7 | 0.923665 | 0.461832 | − | 0.886967i | \(-0.347192\pi\) | ||||
0.461832 | + | 0.886967i | \(0.347192\pi\) | |||||||
\(692\) | −1089.96 | −0.0598758 | ||||||||
\(693\) | 3738.44 | 0.204923 | ||||||||
\(694\) | −5421.88 | −0.296559 | ||||||||
\(695\) | 4450.77 | 0.242917 | ||||||||
\(696\) | 7809.84 | 0.425332 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 2035.86 | 0.110399 | ||||||||
\(699\) | −16381.2 | −0.886400 | ||||||||
\(700\) | 5652.71 | 0.305218 | ||||||||
\(701\) | 23981.1 | 1.29209 | 0.646043 | − | 0.763301i | \(-0.276423\pi\) | ||||
0.646043 | + | 0.763301i | \(0.276423\pi\) | |||||||
\(702\) | 10991.8 | 0.590969 | ||||||||
\(703\) | 11801.6 | 0.633150 | ||||||||
\(704\) | −1893.12 | −0.101349 | ||||||||
\(705\) | 1459.43 | 0.0779652 | ||||||||
\(706\) | 8824.10 | 0.470396 | ||||||||
\(707\) | 2108.30 | 0.112151 | ||||||||
\(708\) | −5662.78 | −0.300593 | ||||||||
\(709\) | 7709.28 | 0.408361 | 0.204181 | − | 0.978933i | \(-0.434547\pi\) | ||||
0.204181 | + | 0.978933i | \(0.434547\pi\) | |||||||
\(710\) | 3253.59 | 0.171979 | ||||||||
\(711\) | −12280.3 | −0.647747 | ||||||||
\(712\) | 15662.5 | 0.824407 | ||||||||
\(713\) | −31521.5 | −1.65567 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 4865.34 | 0.254480 | ||||||||
\(716\) | 6293.13 | 0.328471 | ||||||||
\(717\) | −1054.61 | −0.0549304 | ||||||||
\(718\) | −6729.09 | −0.349760 | ||||||||
\(719\) | 11976.5 | 0.621209 | 0.310605 | − | 0.950539i | \(-0.399468\pi\) | ||||
0.310605 | + | 0.950539i | \(0.399468\pi\) | |||||||
\(720\) | 1186.86 | 0.0614329 | ||||||||
\(721\) | 4153.72 | 0.214553 | ||||||||
\(722\) | 1486.56 | 0.0766260 | ||||||||
\(723\) | −6052.00 | −0.311309 | ||||||||
\(724\) | −21208.7 | −1.08870 | ||||||||
\(725\) | −14888.1 | −0.762662 | ||||||||
\(726\) | 2440.58 | 0.124764 | ||||||||
\(727\) | −18597.3 | −0.948745 | −0.474372 | − | 0.880324i | \(-0.657325\pi\) | ||||
−0.474372 | + | 0.880324i | \(0.657325\pi\) | |||||||
\(728\) | −8886.00 | −0.452386 | ||||||||
\(729\) | 11461.4 | 0.582300 | ||||||||
\(730\) | 1220.63 | 0.0618870 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 1045.14 | 0.0527727 | ||||||||
\(733\) | −23569.5 | −1.18767 | −0.593833 | − | 0.804588i | \(-0.702386\pi\) | ||||
−0.593833 | + | 0.804588i | \(0.702386\pi\) | |||||||
\(734\) | 20.2646 | 0.00101905 | ||||||||
\(735\) | −2677.41 | −0.134364 | ||||||||
\(736\) | 21361.3 | 1.06982 | ||||||||
\(737\) | −1462.47 | −0.0730948 | ||||||||
\(738\) | −10920.0 | −0.544678 | ||||||||
\(739\) | 10149.1 | 0.505199 | 0.252599 | − | 0.967571i | \(-0.418715\pi\) | ||||
0.252599 | + | 0.967571i | \(0.418715\pi\) | |||||||
\(740\) | 2466.50 | 0.122528 | ||||||||
\(741\) | −16346.5 | −0.810397 | ||||||||
\(742\) | 5702.85 | 0.282154 | ||||||||
\(743\) | −27758.0 | −1.37058 | −0.685291 | − | 0.728269i | \(-0.740325\pi\) | ||||
−0.685291 | + | 0.728269i | \(0.740325\pi\) | |||||||
\(744\) | −16612.6 | −0.818611 | ||||||||
\(745\) | 867.148 | 0.0426441 | ||||||||
\(746\) | 2617.87 | 0.128481 | ||||||||
\(747\) | 1978.47 | 0.0969054 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 7829.63 | 0.381960 | ||||||||
\(750\) | −3134.99 | −0.152632 | ||||||||
\(751\) | 815.225 | 0.0396112 | 0.0198056 | − | 0.999804i | \(-0.493695\pi\) | ||||
0.0198056 | + | 0.999804i | \(0.493695\pi\) | |||||||
\(752\) | 3504.13 | 0.169924 | ||||||||
\(753\) | −24277.1 | −1.17491 | ||||||||
\(754\) | 10169.3 | 0.491172 | ||||||||
\(755\) | 2030.11 | 0.0978585 | ||||||||
\(756\) | −6782.56 | −0.326295 | ||||||||
\(757\) | −13239.4 | −0.635659 | −0.317829 | − | 0.948148i | \(-0.602954\pi\) | ||||
−0.317829 | + | 0.948148i | \(0.602954\pi\) | |||||||
\(758\) | 13058.0 | 0.625710 | ||||||||
\(759\) | 10042.1 | 0.480244 | ||||||||
\(760\) | 5205.90 | 0.248471 | ||||||||
\(761\) | −11028.2 | −0.525324 | −0.262662 | − | 0.964888i | \(-0.584600\pi\) | ||||
−0.262662 | + | 0.964888i | \(0.584600\pi\) | |||||||
\(762\) | −11371.7 | −0.540621 | ||||||||
\(763\) | −14407.1 | −0.683582 | ||||||||
\(764\) | 3017.56 | 0.142895 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −12365.0 | −0.583246 | ||||||||
\(767\) | −16969.8 | −0.798882 | ||||||||
\(768\) | 7695.55 | 0.361574 | ||||||||
\(769\) | −18921.2 | −0.887277 | −0.443639 | − | 0.896206i | \(-0.646313\pi\) | ||||
−0.443639 | + | 0.896206i | \(0.646313\pi\) | |||||||
\(770\) | 904.952 | 0.0423535 | ||||||||
\(771\) | −16830.3 | −0.786158 | ||||||||
\(772\) | −21814.7 | −1.01701 | ||||||||
\(773\) | 38728.6 | 1.80203 | 0.901016 | − | 0.433786i | \(-0.142823\pi\) | ||||
0.901016 | + | 0.433786i | \(0.142823\pi\) | |||||||
\(774\) | −8183.59 | −0.380043 | ||||||||
\(775\) | 31669.0 | 1.46785 | ||||||||
\(776\) | 15303.6 | 0.707949 | ||||||||
\(777\) | −3315.29 | −0.153070 | ||||||||
\(778\) | −1556.93 | −0.0717465 | ||||||||
\(779\) | 41959.2 | 1.92984 | ||||||||
\(780\) | −3416.39 | −0.156829 | ||||||||
\(781\) | 21772.5 | 0.997545 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 17863.9 | 0.815329 | ||||||||
\(784\) | −6428.50 | −0.292844 | ||||||||
\(785\) | −2185.28 | −0.0993579 | ||||||||
\(786\) | −8498.47 | −0.385662 | ||||||||
\(787\) | 20587.3 | 0.932477 | 0.466239 | − | 0.884659i | \(-0.345609\pi\) | ||||
0.466239 | + | 0.884659i | \(0.345609\pi\) | |||||||
\(788\) | 8379.37 | 0.378811 | ||||||||
\(789\) | −12410.8 | −0.559995 | ||||||||
\(790\) | −2972.66 | −0.133876 | ||||||||
\(791\) | 5616.62 | 0.252470 | ||||||||
\(792\) | −9066.49 | −0.406772 | ||||||||
\(793\) | 3132.00 | 0.140253 | ||||||||
\(794\) | −14435.0 | −0.645190 | ||||||||
\(795\) | 5046.05 | 0.225113 | ||||||||
\(796\) | 22974.5 | 1.02300 | ||||||||
\(797\) | −15871.4 | −0.705385 | −0.352693 | − | 0.935739i | \(-0.614734\pi\) | ||||
−0.352693 | + | 0.935739i | \(0.614734\pi\) | |||||||
\(798\) | −3040.45 | −0.134876 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | −21461.3 | −0.948463 | ||||||||
\(801\) | 13865.9 | 0.611644 | ||||||||
\(802\) | −18765.0 | −0.826204 | ||||||||
\(803\) | 8168.28 | 0.358969 | ||||||||
\(804\) | 1026.93 | 0.0450462 | ||||||||
\(805\) | −2774.90 | −0.121494 | ||||||||
\(806\) | −21631.4 | −0.945329 | ||||||||
\(807\) | 10801.6 | 0.471170 | ||||||||
\(808\) | −5113.06 | −0.222620 | ||||||||
\(809\) | −39667.1 | −1.72388 | −0.861942 | − | 0.507007i | \(-0.830752\pi\) | ||||
−0.861942 | + | 0.507007i | \(0.830752\pi\) | |||||||
\(810\) | −90.5783 | −0.00392913 | ||||||||
\(811\) | −8003.87 | −0.346552 | −0.173276 | − | 0.984873i | \(-0.555435\pi\) | ||||
−0.173276 | + | 0.984873i | \(0.555435\pi\) | |||||||
\(812\) | −6275.00 | −0.271194 | ||||||||
\(813\) | −1732.00 | −0.0747157 | ||||||||
\(814\) | −4975.28 | −0.214230 | ||||||||
\(815\) | −2051.25 | −0.0881621 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 31444.7 | 1.34652 | ||||||||
\(818\) | −12939.7 | −0.553088 | ||||||||
\(819\) | −7866.69 | −0.335634 | ||||||||
\(820\) | 8769.40 | 0.373464 | ||||||||
\(821\) | 13279.1 | 0.564489 | 0.282244 | − | 0.959343i | \(-0.408921\pi\) | ||||
0.282244 | + | 0.959343i | \(0.408921\pi\) | |||||||
\(822\) | −13491.9 | −0.572486 | ||||||||
\(823\) | −28934.0 | −1.22549 | −0.612745 | − | 0.790281i | \(-0.709935\pi\) | ||||
−0.612745 | + | 0.790281i | \(0.709935\pi\) | |||||||
\(824\) | −10073.6 | −0.425887 | ||||||||
\(825\) | −10089.1 | −0.425767 | ||||||||
\(826\) | −3156.37 | −0.132959 | ||||||||
\(827\) | 13679.6 | 0.575193 | 0.287597 | − | 0.957752i | \(-0.407144\pi\) | ||||
0.287597 | + | 0.957752i | \(0.407144\pi\) | |||||||
\(828\) | 12079.9 | 0.507012 | ||||||||
\(829\) | 16514.5 | 0.691886 | 0.345943 | − | 0.938256i | \(-0.387559\pi\) | ||||
0.345943 | + | 0.938256i | \(0.387559\pi\) | |||||||
\(830\) | 478.921 | 0.0200284 | ||||||||
\(831\) | 16415.6 | 0.685260 | ||||||||
\(832\) | 3983.64 | 0.165995 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 6304.13 | 0.261744 | ||||||||
\(835\) | −8596.93 | −0.356298 | ||||||||
\(836\) | 15137.1 | 0.626231 | ||||||||
\(837\) | −37998.9 | −1.56922 | ||||||||
\(838\) | −13177.8 | −0.543221 | ||||||||
\(839\) | 87.9839 | 0.00362043 | 0.00181022 | − | 0.999998i | \(-0.499424\pi\) | ||||
0.00181022 | + | 0.999998i | \(0.499424\pi\) | |||||||
\(840\) | −1462.44 | −0.0600702 | ||||||||
\(841\) | −7861.94 | −0.322356 | ||||||||
\(842\) | −16825.1 | −0.688635 | ||||||||
\(843\) | 6267.41 | 0.256063 | ||||||||
\(844\) | −32371.3 | −1.32022 | ||||||||
\(845\) | −3577.33 | −0.145638 | ||||||||
\(846\) | −3541.27 | −0.143914 | ||||||||
\(847\) | −4512.98 | −0.183079 | ||||||||
\(848\) | 12115.7 | 0.490630 | ||||||||
\(849\) | 2377.63 | 0.0961133 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 15256.0 | 0.614534 | ||||||||
\(852\) | −15288.5 | −0.614758 | ||||||||
\(853\) | −8162.96 | −0.327660 | −0.163830 | − | 0.986489i | \(-0.552385\pi\) | ||||
−0.163830 | + | 0.986489i | \(0.552385\pi\) | |||||||
\(854\) | 582.551 | 0.0233425 | ||||||||
\(855\) | 4608.73 | 0.184345 | ||||||||
\(856\) | −18988.4 | −0.758191 | ||||||||
\(857\) | −18724.9 | −0.746361 | −0.373181 | − | 0.927759i | \(-0.621733\pi\) | ||||
−0.373181 | + | 0.927759i | \(0.621733\pi\) | |||||||
\(858\) | 6891.34 | 0.274203 | ||||||||
\(859\) | −46422.5 | −1.84391 | −0.921953 | − | 0.387301i | \(-0.873407\pi\) | ||||
−0.921953 | + | 0.387301i | \(0.873407\pi\) | |||||||
\(860\) | 6571.88 | 0.260580 | ||||||||
\(861\) | −11787.2 | −0.466557 | ||||||||
\(862\) | −4043.61 | −0.159775 | ||||||||
\(863\) | 29112.3 | 1.14831 | 0.574157 | − | 0.818746i | \(-0.305330\pi\) | ||||
0.574157 | + | 0.818746i | \(0.305330\pi\) | |||||||
\(864\) | 25750.8 | 1.01396 | ||||||||
\(865\) | −537.563 | −0.0211303 | ||||||||
\(866\) | 8346.33 | 0.327505 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 13347.8 | 0.521950 | ||||||||
\(869\) | −19892.6 | −0.776536 | ||||||||
\(870\) | 1673.64 | 0.0652204 | ||||||||
\(871\) | 3077.43 | 0.119719 | ||||||||
\(872\) | 34940.2 | 1.35691 | ||||||||
\(873\) | 13548.2 | 0.525241 | ||||||||
\(874\) | 13991.2 | 0.541487 | ||||||||
\(875\) | 5797.04 | 0.223972 | ||||||||
\(876\) | −5735.69 | −0.221222 | ||||||||
\(877\) | −39163.0 | −1.50791 | −0.753957 | − | 0.656924i | \(-0.771857\pi\) | ||||
−0.753957 | + | 0.656924i | \(0.771857\pi\) | |||||||
\(878\) | 3464.19 | 0.133156 | ||||||||
\(879\) | 22720.3 | 0.871830 | ||||||||
\(880\) | 1922.57 | 0.0736473 | ||||||||
\(881\) | 35073.2 | 1.34125 | 0.670627 | − | 0.741795i | \(-0.266025\pi\) | ||||
0.670627 | + | 0.741795i | \(0.266025\pi\) | |||||||
\(882\) | 6496.63 | 0.248019 | ||||||||
\(883\) | −48775.7 | −1.85893 | −0.929463 | − | 0.368915i | \(-0.879729\pi\) | ||||
−0.929463 | + | 0.368915i | \(0.879729\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −2792.85 | −0.106080 | ||||||||
\(886\) | 11611.0 | 0.440269 | ||||||||
\(887\) | −13296.0 | −0.503309 | −0.251654 | − | 0.967817i | \(-0.580975\pi\) | ||||
−0.251654 | + | 0.967817i | \(0.580975\pi\) | |||||||
\(888\) | 8040.27 | 0.303844 | ||||||||
\(889\) | 21027.9 | 0.793309 | ||||||||
\(890\) | 3356.46 | 0.126415 | ||||||||
\(891\) | −606.137 | −0.0227905 | ||||||||
\(892\) | −4330.90 | −0.162566 | ||||||||
\(893\) | 13607.0 | 0.509899 | ||||||||
\(894\) | 1228.24 | 0.0459492 | ||||||||
\(895\) | 3103.74 | 0.115918 | ||||||||
\(896\) | −11031.1 | −0.411297 | ||||||||
\(897\) | −21131.3 | −0.786570 | ||||||||
\(898\) | −12054.6 | −0.447960 | ||||||||
\(899\) | −35155.3 | −1.30422 | ||||||||
\(900\) | −12136.4 | −0.449498 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | −17689.1 | −0.652974 | ||||||||
\(903\) | −8833.44 | −0.325535 | ||||||||
\(904\) | −13621.4 | −0.501153 | ||||||||
\(905\) | −10460.0 | −0.384202 | ||||||||
\(906\) | 2875.47 | 0.105443 | ||||||||
\(907\) | 11675.0 | 0.427410 | 0.213705 | − | 0.976898i | \(-0.431447\pi\) | ||||
0.213705 | + | 0.976898i | \(0.431447\pi\) | |||||||
\(908\) | −13224.0 | −0.483319 | ||||||||
\(909\) | −4526.54 | −0.165166 | ||||||||
\(910\) | −1904.26 | −0.0693689 | ||||||||
\(911\) | −18552.9 | −0.674738 | −0.337369 | − | 0.941372i | \(-0.609537\pi\) | ||||
−0.337369 | + | 0.941372i | \(0.609537\pi\) | |||||||
\(912\) | −6459.41 | −0.234531 | ||||||||
\(913\) | 3204.87 | 0.116173 | ||||||||
\(914\) | −9739.24 | −0.352457 | ||||||||
\(915\) | 515.459 | 0.0186235 | ||||||||
\(916\) | 24077.7 | 0.868504 | ||||||||
\(917\) | 15714.9 | 0.565922 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 33956.8 | 1.21886 | 0.609429 | − | 0.792841i | \(-0.291399\pi\) | ||||
0.609429 | + | 0.792841i | \(0.291399\pi\) | |||||||
\(920\) | 6729.71 | 0.241165 | ||||||||
\(921\) | −7652.23 | −0.273778 | ||||||||
\(922\) | −9886.63 | −0.353144 | ||||||||
\(923\) | −45815.3 | −1.63383 | ||||||||
\(924\) | −4252.33 | −0.151398 | ||||||||
\(925\) | −15327.4 | −0.544823 | ||||||||
\(926\) | 480.372 | 0.0170475 | ||||||||
\(927\) | −8918.08 | −0.315974 | ||||||||
\(928\) | 23823.8 | 0.842732 | ||||||||
\(929\) | 23695.3 | 0.836832 | 0.418416 | − | 0.908256i | \(-0.362585\pi\) | ||||
0.418416 | + | 0.908256i | \(0.362585\pi\) | |||||||
\(930\) | −3560.06 | −0.125526 | ||||||||
\(931\) | −24962.7 | −0.878753 | ||||||||
\(932\) | −31920.2 | −1.12187 | ||||||||
\(933\) | −30110.8 | −1.05657 | ||||||||
\(934\) | 2018.72 | 0.0707221 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 19078.3 | 0.666234 | ||||||||
\(937\) | 7990.62 | 0.278593 | 0.139297 | − | 0.990251i | \(-0.455516\pi\) | ||||
0.139297 | + | 0.990251i | \(0.455516\pi\) | |||||||
\(938\) | 572.402 | 0.0199249 | ||||||||
\(939\) | 1856.12 | 0.0645071 | ||||||||
\(940\) | 2843.83 | 0.0986762 | ||||||||
\(941\) | −24385.9 | −0.844799 | −0.422400 | − | 0.906410i | \(-0.638812\pi\) | ||||
−0.422400 | + | 0.906410i | \(0.638812\pi\) | |||||||
\(942\) | −3095.26 | −0.107058 | ||||||||
\(943\) | 54241.0 | 1.87310 | ||||||||
\(944\) | −6705.69 | −0.231199 | ||||||||
\(945\) | −3345.12 | −0.115150 | ||||||||
\(946\) | −13256.4 | −0.455605 | ||||||||
\(947\) | 1174.62 | 0.0403064 | 0.0201532 | − | 0.999797i | \(-0.493585\pi\) | ||||
0.0201532 | + | 0.999797i | \(0.493585\pi\) | |||||||
\(948\) | 13968.4 | 0.478557 | ||||||||
\(949\) | −17188.3 | −0.587939 | ||||||||
\(950\) | −14056.7 | −0.480063 | ||||||||
\(951\) | 24143.4 | 0.823241 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −33546.9 | −1.14029 | −0.570143 | − | 0.821546i | \(-0.693112\pi\) | ||||
−0.570143 | + | 0.821546i | \(0.693112\pi\) | |||||||
\(954\) | −12244.1 | −0.415531 | ||||||||
\(955\) | 1488.25 | 0.0504277 | ||||||||
\(956\) | −2055.00 | −0.0695224 | ||||||||
\(957\) | 11199.8 | 0.378304 | ||||||||
\(958\) | 13598.7 | 0.458617 | ||||||||
\(959\) | 24948.4 | 0.840067 | ||||||||
\(960\) | 655.620 | 0.0220417 | ||||||||
\(961\) | 44989.1 | 1.51016 | ||||||||
\(962\) | 10469.3 | 0.350878 | ||||||||
\(963\) | −16810.3 | −0.562517 | ||||||||
\(964\) | −11792.9 | −0.394007 | ||||||||
\(965\) | −10758.9 | −0.358903 | ||||||||
\(966\) | −3930.41 | −0.130910 | ||||||||
\(967\) | 24766.8 | 0.823625 | 0.411813 | − | 0.911269i | \(-0.364896\pi\) | ||||
0.411813 | + | 0.911269i | \(0.364896\pi\) | |||||||
\(968\) | 10944.9 | 0.363411 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 3279.56 | 0.108557 | ||||||||
\(971\) | 42324.3 | 1.39882 | 0.699409 | − | 0.714721i | \(-0.253447\pi\) | ||||
0.699409 | + | 0.714721i | \(0.253447\pi\) | |||||||
\(972\) | 23488.3 | 0.775091 | ||||||||
\(973\) | −11657.2 | −0.384083 | ||||||||
\(974\) | 1538.01 | 0.0505966 | ||||||||
\(975\) | 21230.2 | 0.697344 | ||||||||
\(976\) | 1237.63 | 0.0405896 | ||||||||
\(977\) | −11320.4 | −0.370698 | −0.185349 | − | 0.982673i | \(-0.559342\pi\) | ||||
−0.185349 | + | 0.982673i | \(0.559342\pi\) | |||||||
\(978\) | −2905.42 | −0.0949949 | ||||||||
\(979\) | 22461.0 | 0.733254 | ||||||||
\(980\) | −5217.16 | −0.170057 | ||||||||
\(981\) | 30932.2 | 1.00672 | ||||||||
\(982\) | 25556.8 | 0.830500 | ||||||||
\(983\) | 11311.9 | 0.367032 | 0.183516 | − | 0.983017i | \(-0.441252\pi\) | ||||
0.183516 | + | 0.983017i | \(0.441252\pi\) | |||||||
\(984\) | 28586.3 | 0.926116 | ||||||||
\(985\) | 4132.66 | 0.133683 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −3822.47 | −0.123273 | ||||||||
\(988\) | −31852.6 | −1.02568 | ||||||||
\(989\) | 40648.8 | 1.30693 | ||||||||
\(990\) | −1942.94 | −0.0623744 | ||||||||
\(991\) | 29405.5 | 0.942580 | 0.471290 | − | 0.881978i | \(-0.343788\pi\) | ||||
0.471290 | + | 0.881978i | \(0.343788\pi\) | |||||||
\(992\) | −50676.5 | −1.62196 | ||||||||
\(993\) | −2373.12 | −0.0758397 | ||||||||
\(994\) | −8521.63 | −0.271921 | ||||||||
\(995\) | 11330.9 | 0.361018 | ||||||||
\(996\) | −2250.43 | −0.0715939 | ||||||||
\(997\) | 54905.9 | 1.74412 | 0.872060 | − | 0.489398i | \(-0.162784\pi\) | ||||
0.872060 | + | 0.489398i | \(0.162784\pi\) | |||||||
\(998\) | −23588.7 | −0.748183 | ||||||||
\(999\) | 18390.9 | 0.582446 |
(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 | 289.4.a.b.1.2 | 3 | ||
17.4 | even | 4 | 289.4.b.b.288.4 | 6 | |||
17.13 | even | 4 | 289.4.b.b.288.3 | 6 | |||
17.16 | even | 2 | 17.4.a.b.1.2 | ✓ | 3 | ||
51.50 | odd | 2 | 153.4.a.g.1.2 | 3 | |||
68.67 | odd | 2 | 272.4.a.h.1.2 | 3 | |||
85.33 | odd | 4 | 425.4.b.f.324.3 | 6 | |||
85.67 | odd | 4 | 425.4.b.f.324.4 | 6 | |||
85.84 | even | 2 | 425.4.a.g.1.2 | 3 | |||
119.118 | odd | 2 | 833.4.a.d.1.2 | 3 | |||
136.67 | odd | 2 | 1088.4.a.x.1.2 | 3 | |||
136.101 | even | 2 | 1088.4.a.v.1.2 | 3 | |||
187.186 | odd | 2 | 2057.4.a.e.1.2 | 3 | |||
204.203 | even | 2 | 2448.4.a.bi.1.1 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
17.4.a.b.1.2 | ✓ | 3 | 17.16 | even | 2 | ||
153.4.a.g.1.2 | 3 | 51.50 | odd | 2 | |||
272.4.a.h.1.2 | 3 | 68.67 | odd | 2 | |||
289.4.a.b.1.2 | 3 | 1.1 | even | 1 | trivial | ||
289.4.b.b.288.3 | 6 | 17.13 | even | 4 | |||
289.4.b.b.288.4 | 6 | 17.4 | even | 4 | |||
425.4.a.g.1.2 | 3 | 85.84 | even | 2 | |||
425.4.b.f.324.3 | 6 | 85.33 | odd | 4 | |||
425.4.b.f.324.4 | 6 | 85.67 | odd | 4 | |||
833.4.a.d.1.2 | 3 | 119.118 | odd | 2 | |||
1088.4.a.v.1.2 | 3 | 136.101 | even | 2 | |||
1088.4.a.x.1.2 | 3 | 136.67 | odd | 2 | |||
2057.4.a.e.1.2 | 3 | 187.186 | odd | 2 | |||
2448.4.a.bi.1.1 | 3 | 204.203 | even | 2 |