Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2166,4,Mod(1,2166)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2166, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2166.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2166 = 2 \cdot 3 \cdot 19^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 2166.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: | \(127.798137072\) |
Analytic rank: | \(1\) |
Dimension: | \(8\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 2x^{7} - 350x^{6} + 948x^{5} + 37019x^{4} - 115308x^{3} - 1098530x^{2} + 2724222x + 7883581 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 19 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(12.0376\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2166.1 |
$q$-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 | ||||||||
\(5\) | −8.38845 | −0.750286 | −0.375143 | − | 0.926967i | \(-0.622406\pi\) | ||||
−0.375143 | + | 0.926967i | \(0.622406\pi\) | |||||||
\(6\) | −6.00000 | −0.408248 | ||||||||
\(7\) | 16.0395 | 0.866054 | 0.433027 | − | 0.901381i | \(-0.357445\pi\) | ||||
0.433027 | + | 0.901381i | \(0.357445\pi\) | |||||||
\(8\) | −8.00000 | −0.353553 | ||||||||
\(9\) | 9.00000 | 0.333333 | ||||||||
\(10\) | 16.7769 | 0.530532 | ||||||||
\(11\) | −27.9688 | −0.766627 | −0.383314 | − | 0.923618i | \(-0.625217\pi\) | ||||
−0.383314 | + | 0.923618i | \(0.625217\pi\) | |||||||
\(12\) | 12.0000 | 0.288675 | ||||||||
\(13\) | −32.6032 | −0.695577 | −0.347788 | − | 0.937573i | \(-0.613067\pi\) | ||||
−0.347788 | + | 0.937573i | \(0.613067\pi\) | |||||||
\(14\) | −32.0791 | −0.612393 | ||||||||
\(15\) | −25.1654 | −0.433178 | ||||||||
\(16\) | 16.0000 | 0.250000 | ||||||||
\(17\) | −19.2640 | −0.274835 | −0.137418 | − | 0.990513i | \(-0.543880\pi\) | ||||
−0.137418 | + | 0.990513i | \(0.543880\pi\) | |||||||
\(18\) | −18.0000 | −0.235702 | ||||||||
\(19\) | 0 | 0 | ||||||||
\(20\) | −33.5538 | −0.375143 | ||||||||
\(21\) | 48.1186 | 0.500017 | ||||||||
\(22\) | 55.9375 | 0.542087 | ||||||||
\(23\) | 79.7464 | 0.722969 | 0.361484 | − | 0.932378i | \(-0.382270\pi\) | ||||
0.361484 | + | 0.932378i | \(0.382270\pi\) | |||||||
\(24\) | −24.0000 | −0.204124 | ||||||||
\(25\) | −54.6339 | −0.437071 | ||||||||
\(26\) | 65.2064 | 0.491847 | ||||||||
\(27\) | 27.0000 | 0.192450 | ||||||||
\(28\) | 64.1582 | 0.433027 | ||||||||
\(29\) | 141.470 | 0.905876 | 0.452938 | − | 0.891542i | \(-0.350376\pi\) | ||||
0.452938 | + | 0.891542i | \(0.350376\pi\) | |||||||
\(30\) | 50.3307 | 0.306303 | ||||||||
\(31\) | 167.373 | 0.969715 | 0.484858 | − | 0.874593i | \(-0.338871\pi\) | ||||
0.484858 | + | 0.874593i | \(0.338871\pi\) | |||||||
\(32\) | −32.0000 | −0.176777 | ||||||||
\(33\) | −83.9063 | −0.442612 | ||||||||
\(34\) | 38.5279 | 0.194338 | ||||||||
\(35\) | −134.547 | −0.649788 | ||||||||
\(36\) | 36.0000 | 0.166667 | ||||||||
\(37\) | 55.2319 | 0.245407 | 0.122704 | − | 0.992443i | \(-0.460844\pi\) | ||||
0.122704 | + | 0.992443i | \(0.460844\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −97.8096 | −0.401591 | ||||||||
\(40\) | 67.1076 | 0.265266 | ||||||||
\(41\) | 42.0654 | 0.160232 | 0.0801161 | − | 0.996786i | \(-0.474471\pi\) | ||||
0.0801161 | + | 0.996786i | \(0.474471\pi\) | |||||||
\(42\) | −96.2373 | −0.353565 | ||||||||
\(43\) | 110.445 | 0.391690 | 0.195845 | − | 0.980635i | \(-0.437255\pi\) | ||||
0.195845 | + | 0.980635i | \(0.437255\pi\) | |||||||
\(44\) | −111.875 | −0.383314 | ||||||||
\(45\) | −75.4961 | −0.250095 | ||||||||
\(46\) | −159.493 | −0.511216 | ||||||||
\(47\) | 268.524 | 0.833367 | 0.416684 | − | 0.909052i | \(-0.363192\pi\) | ||||
0.416684 | + | 0.909052i | \(0.363192\pi\) | |||||||
\(48\) | 48.0000 | 0.144338 | ||||||||
\(49\) | −85.7330 | −0.249950 | ||||||||
\(50\) | 109.268 | 0.309056 | ||||||||
\(51\) | −57.7919 | −0.158676 | ||||||||
\(52\) | −130.413 | −0.347788 | ||||||||
\(53\) | −111.653 | −0.289371 | −0.144685 | − | 0.989478i | \(-0.546217\pi\) | ||||
−0.144685 | + | 0.989478i | \(0.546217\pi\) | |||||||
\(54\) | −54.0000 | −0.136083 | ||||||||
\(55\) | 234.615 | 0.575189 | ||||||||
\(56\) | −128.316 | −0.306196 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −282.941 | −0.640551 | ||||||||
\(59\) | −644.590 | −1.42235 | −0.711174 | − | 0.703016i | \(-0.751836\pi\) | ||||
−0.711174 | + | 0.703016i | \(0.751836\pi\) | |||||||
\(60\) | −100.661 | −0.216589 | ||||||||
\(61\) | 360.293 | 0.756242 | 0.378121 | − | 0.925756i | \(-0.376570\pi\) | ||||
0.378121 | + | 0.925756i | \(0.376570\pi\) | |||||||
\(62\) | −334.747 | −0.685692 | ||||||||
\(63\) | 144.356 | 0.288685 | ||||||||
\(64\) | 64.0000 | 0.125000 | ||||||||
\(65\) | 273.490 | 0.521881 | ||||||||
\(66\) | 167.813 | 0.312974 | ||||||||
\(67\) | −94.7662 | −0.172799 | −0.0863995 | − | 0.996261i | \(-0.527536\pi\) | ||||
−0.0863995 | + | 0.996261i | \(0.527536\pi\) | |||||||
\(68\) | −77.0559 | −0.137418 | ||||||||
\(69\) | 239.239 | 0.417406 | ||||||||
\(70\) | 269.094 | 0.459470 | ||||||||
\(71\) | −1185.73 | −1.98198 | −0.990991 | − | 0.133925i | \(-0.957242\pi\) | ||||
−0.990991 | + | 0.133925i | \(0.957242\pi\) | |||||||
\(72\) | −72.0000 | −0.117851 | ||||||||
\(73\) | −817.058 | −1.30999 | −0.654996 | − | 0.755632i | \(-0.727330\pi\) | ||||
−0.654996 | + | 0.755632i | \(0.727330\pi\) | |||||||
\(74\) | −110.464 | −0.173529 | ||||||||
\(75\) | −163.902 | −0.252343 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −448.606 | −0.663941 | ||||||||
\(78\) | 195.619 | 0.283968 | ||||||||
\(79\) | 970.784 | 1.38255 | 0.691277 | − | 0.722590i | \(-0.257048\pi\) | ||||
0.691277 | + | 0.722590i | \(0.257048\pi\) | |||||||
\(80\) | −134.215 | −0.187571 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | −84.1309 | −0.113301 | ||||||||
\(83\) | −1136.70 | −1.50324 | −0.751618 | − | 0.659598i | \(-0.770726\pi\) | ||||
−0.751618 | + | 0.659598i | \(0.770726\pi\) | |||||||
\(84\) | 192.475 | 0.250008 | ||||||||
\(85\) | 161.595 | 0.206205 | ||||||||
\(86\) | −220.889 | −0.276966 | ||||||||
\(87\) | 424.411 | 0.523008 | ||||||||
\(88\) | 223.750 | 0.271044 | ||||||||
\(89\) | 93.7280 | 0.111631 | 0.0558154 | − | 0.998441i | \(-0.482224\pi\) | ||||
0.0558154 | + | 0.998441i | \(0.482224\pi\) | |||||||
\(90\) | 150.992 | 0.176844 | ||||||||
\(91\) | −522.940 | −0.602407 | ||||||||
\(92\) | 318.986 | 0.361484 | ||||||||
\(93\) | 502.120 | 0.559865 | ||||||||
\(94\) | −537.048 | −0.589280 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −96.0000 | −0.102062 | ||||||||
\(97\) | −554.985 | −0.580930 | −0.290465 | − | 0.956886i | \(-0.593810\pi\) | ||||
−0.290465 | + | 0.956886i | \(0.593810\pi\) | |||||||
\(98\) | 171.466 | 0.176742 | ||||||||
\(99\) | −251.719 | −0.255542 | ||||||||
\(100\) | −218.536 | −0.218536 | ||||||||
\(101\) | −101.877 | −0.100367 | −0.0501837 | − | 0.998740i | \(-0.515981\pi\) | ||||
−0.0501837 | + | 0.998740i | \(0.515981\pi\) | |||||||
\(102\) | 115.584 | 0.112201 | ||||||||
\(103\) | 1885.45 | 1.80368 | 0.901841 | − | 0.432067i | \(-0.142216\pi\) | ||||
0.901841 | + | 0.432067i | \(0.142216\pi\) | |||||||
\(104\) | 260.825 | 0.245923 | ||||||||
\(105\) | −403.641 | −0.375155 | ||||||||
\(106\) | 223.305 | 0.204616 | ||||||||
\(107\) | −644.911 | −0.582672 | −0.291336 | − | 0.956621i | \(-0.594100\pi\) | ||||
−0.291336 | + | 0.956621i | \(0.594100\pi\) | |||||||
\(108\) | 108.000 | 0.0962250 | ||||||||
\(109\) | 1232.86 | 1.08336 | 0.541680 | − | 0.840584i | \(-0.317788\pi\) | ||||
0.541680 | + | 0.840584i | \(0.317788\pi\) | |||||||
\(110\) | −469.229 | −0.406720 | ||||||||
\(111\) | 165.696 | 0.141686 | ||||||||
\(112\) | 256.633 | 0.216514 | ||||||||
\(113\) | −261.847 | −0.217987 | −0.108993 | − | 0.994042i | \(-0.534763\pi\) | ||||
−0.108993 | + | 0.994042i | \(0.534763\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −668.949 | −0.542433 | ||||||||
\(116\) | 565.882 | 0.452938 | ||||||||
\(117\) | −293.429 | −0.231859 | ||||||||
\(118\) | 1289.18 | 1.00575 | ||||||||
\(119\) | −308.985 | −0.238022 | ||||||||
\(120\) | 201.323 | 0.153151 | ||||||||
\(121\) | −548.749 | −0.412283 | ||||||||
\(122\) | −720.586 | −0.534744 | ||||||||
\(123\) | 126.196 | 0.0925101 | ||||||||
\(124\) | 669.494 | 0.484858 | ||||||||
\(125\) | 1506.85 | 1.07821 | ||||||||
\(126\) | −288.712 | −0.204131 | ||||||||
\(127\) | 2696.16 | 1.88383 | 0.941913 | − | 0.335858i | \(-0.109026\pi\) | ||||
0.941913 | + | 0.335858i | \(0.109026\pi\) | |||||||
\(128\) | −128.000 | −0.0883883 | ||||||||
\(129\) | 331.334 | 0.226142 | ||||||||
\(130\) | −546.980 | −0.369026 | ||||||||
\(131\) | −1389.43 | −0.926682 | −0.463341 | − | 0.886180i | \(-0.653349\pi\) | ||||
−0.463341 | + | 0.886180i | \(0.653349\pi\) | |||||||
\(132\) | −335.625 | −0.221306 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 189.532 | 0.122187 | ||||||||
\(135\) | −226.488 | −0.144393 | ||||||||
\(136\) | 154.112 | 0.0971689 | ||||||||
\(137\) | −784.529 | −0.489247 | −0.244624 | − | 0.969618i | \(-0.578664\pi\) | ||||
−0.244624 | + | 0.969618i | \(0.578664\pi\) | |||||||
\(138\) | −478.479 | −0.295151 | ||||||||
\(139\) | −2714.27 | −1.65627 | −0.828134 | − | 0.560530i | \(-0.810598\pi\) | ||||
−0.828134 | + | 0.560530i | \(0.810598\pi\) | |||||||
\(140\) | −538.188 | −0.324894 | ||||||||
\(141\) | 805.572 | 0.481145 | ||||||||
\(142\) | 2371.47 | 1.40147 | ||||||||
\(143\) | 911.871 | 0.533248 | ||||||||
\(144\) | 144.000 | 0.0833333 | ||||||||
\(145\) | −1186.72 | −0.679666 | ||||||||
\(146\) | 1634.12 | 0.926305 | ||||||||
\(147\) | −257.199 | −0.144309 | ||||||||
\(148\) | 220.927 | 0.122704 | ||||||||
\(149\) | −503.598 | −0.276888 | −0.138444 | − | 0.990370i | \(-0.544210\pi\) | ||||
−0.138444 | + | 0.990370i | \(0.544210\pi\) | |||||||
\(150\) | 327.803 | 0.178434 | ||||||||
\(151\) | −308.359 | −0.166185 | −0.0830924 | − | 0.996542i | \(-0.526480\pi\) | ||||
−0.0830924 | + | 0.996542i | \(0.526480\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −173.376 | −0.0916117 | ||||||||
\(154\) | 897.212 | 0.469477 | ||||||||
\(155\) | −1404.00 | −0.727563 | ||||||||
\(156\) | −391.238 | −0.200796 | ||||||||
\(157\) | 2.02349 | 0.00102861 | 0.000514307 | − | 1.00000i | \(-0.499836\pi\) | ||||
0.000514307 | 1.00000i | \(0.499836\pi\) | ||||||||
\(158\) | −1941.57 | −0.977613 | ||||||||
\(159\) | −334.958 | −0.167068 | ||||||||
\(160\) | 268.430 | 0.132633 | ||||||||
\(161\) | 1279.10 | 0.626130 | ||||||||
\(162\) | −162.000 | −0.0785674 | ||||||||
\(163\) | −530.326 | −0.254836 | −0.127418 | − | 0.991849i | \(-0.540669\pi\) | ||||
−0.127418 | + | 0.991849i | \(0.540669\pi\) | |||||||
\(164\) | 168.262 | 0.0801161 | ||||||||
\(165\) | 703.844 | 0.332086 | ||||||||
\(166\) | 2273.39 | 1.06295 | ||||||||
\(167\) | −3066.43 | −1.42088 | −0.710441 | − | 0.703756i | \(-0.751505\pi\) | ||||
−0.710441 | + | 0.703756i | \(0.751505\pi\) | |||||||
\(168\) | −384.949 | −0.176783 | ||||||||
\(169\) | −1134.03 | −0.516173 | ||||||||
\(170\) | −323.190 | −0.145809 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 441.779 | 0.195845 | ||||||||
\(173\) | −1561.41 | −0.686194 | −0.343097 | − | 0.939300i | \(-0.611476\pi\) | ||||
−0.343097 | + | 0.939300i | \(0.611476\pi\) | |||||||
\(174\) | −848.823 | −0.369822 | ||||||||
\(175\) | −876.303 | −0.378527 | ||||||||
\(176\) | −447.500 | −0.191657 | ||||||||
\(177\) | −1933.77 | −0.821193 | ||||||||
\(178\) | −187.456 | −0.0789350 | ||||||||
\(179\) | −1476.69 | −0.616610 | −0.308305 | − | 0.951287i | \(-0.599762\pi\) | ||||
−0.308305 | + | 0.951287i | \(0.599762\pi\) | |||||||
\(180\) | −301.984 | −0.125048 | ||||||||
\(181\) | 3585.47 | 1.47241 | 0.736205 | − | 0.676759i | \(-0.236616\pi\) | ||||
0.736205 | + | 0.676759i | \(0.236616\pi\) | |||||||
\(182\) | 1045.88 | 0.425966 | ||||||||
\(183\) | 1080.88 | 0.436617 | ||||||||
\(184\) | −637.971 | −0.255608 | ||||||||
\(185\) | −463.310 | −0.184125 | ||||||||
\(186\) | −1004.24 | −0.395884 | ||||||||
\(187\) | 538.789 | 0.210696 | ||||||||
\(188\) | 1074.10 | 0.416684 | ||||||||
\(189\) | 433.068 | 0.166672 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −2164.90 | −0.820139 | −0.410069 | − | 0.912054i | \(-0.634496\pi\) | ||||
−0.410069 | + | 0.912054i | \(0.634496\pi\) | |||||||
\(192\) | 192.000 | 0.0721688 | ||||||||
\(193\) | −2977.28 | −1.11041 | −0.555206 | − | 0.831713i | \(-0.687361\pi\) | ||||
−0.555206 | + | 0.831713i | \(0.687361\pi\) | |||||||
\(194\) | 1109.97 | 0.410780 | ||||||||
\(195\) | 820.471 | 0.301308 | ||||||||
\(196\) | −342.932 | −0.124975 | ||||||||
\(197\) | −4423.90 | −1.59995 | −0.799974 | − | 0.600035i | \(-0.795153\pi\) | ||||
−0.799974 | + | 0.600035i | \(0.795153\pi\) | |||||||
\(198\) | 503.438 | 0.180696 | ||||||||
\(199\) | 1471.38 | 0.524138 | 0.262069 | − | 0.965049i | \(-0.415595\pi\) | ||||
0.262069 | + | 0.965049i | \(0.415595\pi\) | |||||||
\(200\) | 437.071 | 0.154528 | ||||||||
\(201\) | −284.299 | −0.0997656 | ||||||||
\(202\) | 203.753 | 0.0709704 | ||||||||
\(203\) | 2269.12 | 0.784537 | ||||||||
\(204\) | −231.168 | −0.0793381 | ||||||||
\(205\) | −352.864 | −0.120220 | ||||||||
\(206\) | −3770.91 | −1.27540 | ||||||||
\(207\) | 717.718 | 0.240990 | ||||||||
\(208\) | −521.651 | −0.173894 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 807.282 | 0.265275 | ||||||||
\(211\) | 59.8544 | 0.0195287 | 0.00976433 | − | 0.999952i | \(-0.496892\pi\) | ||||
0.00976433 | + | 0.999952i | \(0.496892\pi\) | |||||||
\(212\) | −446.610 | −0.144685 | ||||||||
\(213\) | −3557.20 | −1.14430 | ||||||||
\(214\) | 1289.82 | 0.412011 | ||||||||
\(215\) | −926.459 | −0.293879 | ||||||||
\(216\) | −216.000 | −0.0680414 | ||||||||
\(217\) | 2684.59 | 0.839826 | ||||||||
\(218\) | −2465.72 | −0.766052 | ||||||||
\(219\) | −2451.18 | −0.756325 | ||||||||
\(220\) | 938.458 | 0.287595 | ||||||||
\(221\) | 628.067 | 0.191169 | ||||||||
\(222\) | −331.391 | −0.100187 | ||||||||
\(223\) | 483.339 | 0.145143 | 0.0725713 | − | 0.997363i | \(-0.476880\pi\) | ||||
0.0725713 | + | 0.997363i | \(0.476880\pi\) | |||||||
\(224\) | −513.265 | −0.153098 | ||||||||
\(225\) | −491.705 | −0.145690 | ||||||||
\(226\) | 523.694 | 0.154140 | ||||||||
\(227\) | 1711.16 | 0.500324 | 0.250162 | − | 0.968204i | \(-0.419516\pi\) | ||||
0.250162 | + | 0.968204i | \(0.419516\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −2137.54 | −0.616823 | −0.308412 | − | 0.951253i | \(-0.599797\pi\) | ||||
−0.308412 | + | 0.951253i | \(0.599797\pi\) | |||||||
\(230\) | 1337.90 | 0.383558 | ||||||||
\(231\) | −1345.82 | −0.383326 | ||||||||
\(232\) | −1131.76 | −0.320275 | ||||||||
\(233\) | 937.852 | 0.263694 | 0.131847 | − | 0.991270i | \(-0.457909\pi\) | ||||
0.131847 | + | 0.991270i | \(0.457909\pi\) | |||||||
\(234\) | 586.857 | 0.163949 | ||||||||
\(235\) | −2252.50 | −0.625263 | ||||||||
\(236\) | −2578.36 | −0.711174 | ||||||||
\(237\) | 2912.35 | 0.798218 | ||||||||
\(238\) | 617.971 | 0.168307 | ||||||||
\(239\) | −1841.70 | −0.498449 | −0.249225 | − | 0.968446i | \(-0.580176\pi\) | ||||
−0.249225 | + | 0.968446i | \(0.580176\pi\) | |||||||
\(240\) | −402.646 | −0.108294 | ||||||||
\(241\) | 2972.53 | 0.794513 | 0.397257 | − | 0.917708i | \(-0.369962\pi\) | ||||
0.397257 | + | 0.917708i | \(0.369962\pi\) | |||||||
\(242\) | 1097.50 | 0.291528 | ||||||||
\(243\) | 243.000 | 0.0641500 | ||||||||
\(244\) | 1441.17 | 0.378121 | ||||||||
\(245\) | 719.167 | 0.187534 | ||||||||
\(246\) | −252.393 | −0.0654145 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −1338.99 | −0.342846 | ||||||||
\(249\) | −3410.09 | −0.867894 | ||||||||
\(250\) | −3013.70 | −0.762413 | ||||||||
\(251\) | 4249.17 | 1.06855 | 0.534273 | − | 0.845312i | \(-0.320585\pi\) | ||||
0.534273 | + | 0.845312i | \(0.320585\pi\) | |||||||
\(252\) | 577.424 | 0.144342 | ||||||||
\(253\) | −2230.41 | −0.554247 | ||||||||
\(254\) | −5392.33 | −1.33207 | ||||||||
\(255\) | 484.784 | 0.119052 | ||||||||
\(256\) | 256.000 | 0.0625000 | ||||||||
\(257\) | 5987.38 | 1.45324 | 0.726620 | − | 0.687039i | \(-0.241090\pi\) | ||||
0.726620 | + | 0.687039i | \(0.241090\pi\) | |||||||
\(258\) | −662.668 | −0.159907 | ||||||||
\(259\) | 885.894 | 0.212536 | ||||||||
\(260\) | 1093.96 | 0.260941 | ||||||||
\(261\) | 1273.23 | 0.301959 | ||||||||
\(262\) | 2778.87 | 0.655263 | ||||||||
\(263\) | −320.368 | −0.0751132 | −0.0375566 | − | 0.999295i | \(-0.511957\pi\) | ||||
−0.0375566 | + | 0.999295i | \(0.511957\pi\) | |||||||
\(264\) | 671.250 | 0.156487 | ||||||||
\(265\) | 936.592 | 0.217111 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 281.184 | 0.0644501 | ||||||||
\(268\) | −379.065 | −0.0863995 | ||||||||
\(269\) | −7577.76 | −1.71756 | −0.858781 | − | 0.512342i | \(-0.828778\pi\) | ||||
−0.858781 | + | 0.512342i | \(0.828778\pi\) | |||||||
\(270\) | 452.976 | 0.102101 | ||||||||
\(271\) | −1701.46 | −0.381389 | −0.190694 | − | 0.981649i | \(-0.561074\pi\) | ||||
−0.190694 | + | 0.981649i | \(0.561074\pi\) | |||||||
\(272\) | −308.223 | −0.0687088 | ||||||||
\(273\) | −1568.82 | −0.347800 | ||||||||
\(274\) | 1569.06 | 0.345950 | ||||||||
\(275\) | 1528.04 | 0.335071 | ||||||||
\(276\) | 956.957 | 0.208703 | ||||||||
\(277\) | −7967.33 | −1.72820 | −0.864098 | − | 0.503324i | \(-0.832110\pi\) | ||||
−0.864098 | + | 0.503324i | \(0.832110\pi\) | |||||||
\(278\) | 5428.54 | 1.17116 | ||||||||
\(279\) | 1506.36 | 0.323238 | ||||||||
\(280\) | 1076.38 | 0.229735 | ||||||||
\(281\) | 6285.85 | 1.33446 | 0.667228 | − | 0.744854i | \(-0.267481\pi\) | ||||
0.667228 | + | 0.744854i | \(0.267481\pi\) | |||||||
\(282\) | −1611.14 | −0.340221 | ||||||||
\(283\) | −6592.08 | −1.38466 | −0.692329 | − | 0.721582i | \(-0.743415\pi\) | ||||
−0.692329 | + | 0.721582i | \(0.743415\pi\) | |||||||
\(284\) | −4742.94 | −0.990991 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −1823.74 | −0.377063 | ||||||||
\(287\) | 674.711 | 0.138770 | ||||||||
\(288\) | −288.000 | −0.0589256 | ||||||||
\(289\) | −4541.90 | −0.924466 | ||||||||
\(290\) | 2373.44 | 0.480596 | ||||||||
\(291\) | −1664.96 | −0.335400 | ||||||||
\(292\) | −3268.23 | −0.654996 | ||||||||
\(293\) | −1051.46 | −0.209649 | −0.104824 | − | 0.994491i | \(-0.533428\pi\) | ||||
−0.104824 | + | 0.994491i | \(0.533428\pi\) | |||||||
\(294\) | 514.398 | 0.102042 | ||||||||
\(295\) | 5407.11 | 1.06717 | ||||||||
\(296\) | −441.855 | −0.0867645 | ||||||||
\(297\) | −755.156 | −0.147537 | ||||||||
\(298\) | 1007.20 | 0.195790 | ||||||||
\(299\) | −2599.99 | −0.502880 | ||||||||
\(300\) | −655.607 | −0.126172 | ||||||||
\(301\) | 1771.48 | 0.339224 | ||||||||
\(302\) | 616.718 | 0.117510 | ||||||||
\(303\) | −305.630 | −0.0579471 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −3022.30 | −0.567398 | ||||||||
\(306\) | 346.751 | 0.0647793 | ||||||||
\(307\) | 2096.61 | 0.389771 | 0.194886 | − | 0.980826i | \(-0.437566\pi\) | ||||
0.194886 | + | 0.980826i | \(0.437566\pi\) | |||||||
\(308\) | −1794.42 | −0.331970 | ||||||||
\(309\) | 5656.36 | 1.04136 | ||||||||
\(310\) | 2808.01 | 0.514465 | ||||||||
\(311\) | −9812.04 | −1.78903 | −0.894517 | − | 0.447034i | \(-0.852480\pi\) | ||||
−0.894517 | + | 0.447034i | \(0.852480\pi\) | |||||||
\(312\) | 782.476 | 0.141984 | ||||||||
\(313\) | 7508.78 | 1.35598 | 0.677990 | − | 0.735071i | \(-0.262851\pi\) | ||||
0.677990 | + | 0.735071i | \(0.262851\pi\) | |||||||
\(314\) | −4.04699 | −0.000727340 0 | ||||||||
\(315\) | −1210.92 | −0.216596 | ||||||||
\(316\) | 3883.14 | 0.691277 | ||||||||
\(317\) | 3638.34 | 0.644636 | 0.322318 | − | 0.946632i | \(-0.395538\pi\) | ||||
0.322318 | + | 0.946632i | \(0.395538\pi\) | |||||||
\(318\) | 669.915 | 0.118135 | ||||||||
\(319\) | −3956.75 | −0.694469 | ||||||||
\(320\) | −536.861 | −0.0937857 | ||||||||
\(321\) | −1934.73 | −0.336406 | ||||||||
\(322\) | −2558.19 | −0.442741 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 324.000 | 0.0555556 | ||||||||
\(325\) | 1781.24 | 0.304017 | ||||||||
\(326\) | 1060.65 | 0.180197 | ||||||||
\(327\) | 3698.57 | 0.625479 | ||||||||
\(328\) | −336.524 | −0.0566506 | ||||||||
\(329\) | 4307.00 | 0.721741 | ||||||||
\(330\) | −1407.69 | −0.234820 | ||||||||
\(331\) | −1992.93 | −0.330940 | −0.165470 | − | 0.986215i | \(-0.552914\pi\) | ||||
−0.165470 | + | 0.986215i | \(0.552914\pi\) | |||||||
\(332\) | −4546.79 | −0.751618 | ||||||||
\(333\) | 497.087 | 0.0818024 | ||||||||
\(334\) | 6132.86 | 1.00472 | ||||||||
\(335\) | 794.942 | 0.129649 | ||||||||
\(336\) | 769.898 | 0.125004 | ||||||||
\(337\) | 598.670 | 0.0967705 | 0.0483852 | − | 0.998829i | \(-0.484592\pi\) | ||||
0.0483852 | + | 0.998829i | \(0.484592\pi\) | |||||||
\(338\) | 2268.06 | 0.364989 | ||||||||
\(339\) | −785.542 | −0.125855 | ||||||||
\(340\) | 646.379 | 0.103102 | ||||||||
\(341\) | −4681.23 | −0.743410 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −6876.68 | −1.08252 | ||||||||
\(344\) | −883.557 | −0.138483 | ||||||||
\(345\) | −2006.85 | −0.313174 | ||||||||
\(346\) | 3122.81 | 0.485213 | ||||||||
\(347\) | 5326.79 | 0.824084 | 0.412042 | − | 0.911165i | \(-0.364816\pi\) | ||||
0.412042 | + | 0.911165i | \(0.364816\pi\) | |||||||
\(348\) | 1697.65 | 0.261504 | ||||||||
\(349\) | 8069.88 | 1.23774 | 0.618869 | − | 0.785494i | \(-0.287591\pi\) | ||||
0.618869 | + | 0.785494i | \(0.287591\pi\) | |||||||
\(350\) | 1752.61 | 0.267659 | ||||||||
\(351\) | −880.286 | −0.133864 | ||||||||
\(352\) | 895.000 | 0.135522 | ||||||||
\(353\) | −11595.5 | −1.74835 | −0.874177 | − | 0.485608i | \(-0.838598\pi\) | ||||
−0.874177 | + | 0.485608i | \(0.838598\pi\) | |||||||
\(354\) | 3867.54 | 0.580671 | ||||||||
\(355\) | 9946.47 | 1.48705 | ||||||||
\(356\) | 374.912 | 0.0558154 | ||||||||
\(357\) | −926.956 | −0.137422 | ||||||||
\(358\) | 2953.39 | 0.436009 | ||||||||
\(359\) | −5015.77 | −0.737388 | −0.368694 | − | 0.929551i | \(-0.620195\pi\) | ||||
−0.368694 | + | 0.929551i | \(0.620195\pi\) | |||||||
\(360\) | 603.968 | 0.0884220 | ||||||||
\(361\) | 0 | 0 | ||||||||
\(362\) | −7170.95 | −1.04115 | ||||||||
\(363\) | −1646.25 | −0.238032 | ||||||||
\(364\) | −2091.76 | −0.301204 | ||||||||
\(365\) | 6853.85 | 0.982869 | ||||||||
\(366\) | −2161.76 | −0.308735 | ||||||||
\(367\) | −3854.86 | −0.548289 | −0.274145 | − | 0.961688i | \(-0.588395\pi\) | ||||
−0.274145 | + | 0.961688i | \(0.588395\pi\) | |||||||
\(368\) | 1275.94 | 0.180742 | ||||||||
\(369\) | 378.589 | 0.0534107 | ||||||||
\(370\) | 926.620 | 0.130196 | ||||||||
\(371\) | −1790.86 | −0.250611 | ||||||||
\(372\) | 2008.48 | 0.279933 | ||||||||
\(373\) | 11951.8 | 1.65909 | 0.829543 | − | 0.558443i | \(-0.188601\pi\) | ||||
0.829543 | + | 0.558443i | \(0.188601\pi\) | |||||||
\(374\) | −1077.58 | −0.148985 | ||||||||
\(375\) | 4520.55 | 0.622507 | ||||||||
\(376\) | −2148.19 | −0.294640 | ||||||||
\(377\) | −4612.39 | −0.630106 | ||||||||
\(378\) | −866.135 | −0.117855 | ||||||||
\(379\) | −14300.6 | −1.93818 | −0.969090 | − | 0.246706i | \(-0.920652\pi\) | ||||
−0.969090 | + | 0.246706i | \(0.920652\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 8088.49 | 1.08763 | ||||||||
\(382\) | 4329.80 | 0.579926 | ||||||||
\(383\) | −5827.22 | −0.777434 | −0.388717 | − | 0.921357i | \(-0.627082\pi\) | ||||
−0.388717 | + | 0.921357i | \(0.627082\pi\) | |||||||
\(384\) | −384.000 | −0.0510310 | ||||||||
\(385\) | 3763.11 | 0.498145 | ||||||||
\(386\) | 5954.57 | 0.785180 | ||||||||
\(387\) | 994.002 | 0.130563 | ||||||||
\(388\) | −2219.94 | −0.290465 | ||||||||
\(389\) | 7130.95 | 0.929443 | 0.464722 | − | 0.885457i | \(-0.346154\pi\) | ||||
0.464722 | + | 0.885457i | \(0.346154\pi\) | |||||||
\(390\) | −1640.94 | −0.213057 | ||||||||
\(391\) | −1536.23 | −0.198697 | ||||||||
\(392\) | 685.864 | 0.0883708 | ||||||||
\(393\) | −4168.30 | −0.535020 | ||||||||
\(394\) | 8847.79 | 1.13133 | ||||||||
\(395\) | −8143.37 | −1.03731 | ||||||||
\(396\) | −1006.88 | −0.127771 | ||||||||
\(397\) | −13937.1 | −1.76192 | −0.880962 | − | 0.473187i | \(-0.843103\pi\) | ||||
−0.880962 | + | 0.473187i | \(0.843103\pi\) | |||||||
\(398\) | −2942.77 | −0.370622 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −874.142 | −0.109268 | ||||||||
\(401\) | 251.101 | 0.0312703 | 0.0156352 | − | 0.999878i | \(-0.495023\pi\) | ||||
0.0156352 | + | 0.999878i | \(0.495023\pi\) | |||||||
\(402\) | 568.597 | 0.0705449 | ||||||||
\(403\) | −5456.91 | −0.674511 | ||||||||
\(404\) | −407.506 | −0.0501837 | ||||||||
\(405\) | −679.464 | −0.0833651 | ||||||||
\(406\) | −4538.24 | −0.554752 | ||||||||
\(407\) | −1544.77 | −0.188136 | ||||||||
\(408\) | 462.335 | 0.0561005 | ||||||||
\(409\) | −9956.74 | −1.20374 | −0.601869 | − | 0.798595i | \(-0.705577\pi\) | ||||
−0.601869 | + | 0.798595i | \(0.705577\pi\) | |||||||
\(410\) | 705.728 | 0.0850083 | ||||||||
\(411\) | −2353.59 | −0.282467 | ||||||||
\(412\) | 7541.82 | 0.901841 | ||||||||
\(413\) | −10338.9 | −1.23183 | ||||||||
\(414\) | −1435.44 | −0.170405 | ||||||||
\(415\) | 9535.12 | 1.12786 | ||||||||
\(416\) | 1043.30 | 0.122962 | ||||||||
\(417\) | −8142.81 | −0.956247 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 1055.61 | 0.123079 | 0.0615393 | − | 0.998105i | \(-0.480399\pi\) | ||||
0.0615393 | + | 0.998105i | \(0.480399\pi\) | |||||||
\(420\) | −1614.56 | −0.187578 | ||||||||
\(421\) | −10960.6 | −1.26885 | −0.634427 | − | 0.772983i | \(-0.718764\pi\) | ||||
−0.634427 | + | 0.772983i | \(0.718764\pi\) | |||||||
\(422\) | −119.709 | −0.0138088 | ||||||||
\(423\) | 2416.72 | 0.277789 | ||||||||
\(424\) | 893.220 | 0.102308 | ||||||||
\(425\) | 1052.47 | 0.120123 | ||||||||
\(426\) | 7114.41 | 0.809141 | ||||||||
\(427\) | 5778.93 | 0.654947 | ||||||||
\(428\) | −2579.64 | −0.291336 | ||||||||
\(429\) | 2735.61 | 0.307871 | ||||||||
\(430\) | 1852.92 | 0.207804 | ||||||||
\(431\) | −8433.76 | −0.942552 | −0.471276 | − | 0.881986i | \(-0.656206\pi\) | ||||
−0.471276 | + | 0.881986i | \(0.656206\pi\) | |||||||
\(432\) | 432.000 | 0.0481125 | ||||||||
\(433\) | −6816.97 | −0.756588 | −0.378294 | − | 0.925686i | \(-0.623489\pi\) | ||||
−0.378294 | + | 0.925686i | \(0.623489\pi\) | |||||||
\(434\) | −5369.19 | −0.593846 | ||||||||
\(435\) | −3560.15 | −0.392405 | ||||||||
\(436\) | 4931.43 | 0.541680 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 4902.35 | 0.534802 | ||||||||
\(439\) | −6648.82 | −0.722849 | −0.361424 | − | 0.932401i | \(-0.617709\pi\) | ||||
−0.361424 | + | 0.932401i | \(0.617709\pi\) | |||||||
\(440\) | −1876.92 | −0.203360 | ||||||||
\(441\) | −771.597 | −0.0833168 | ||||||||
\(442\) | −1256.13 | −0.135177 | ||||||||
\(443\) | −12248.2 | −1.31361 | −0.656804 | − | 0.754062i | \(-0.728092\pi\) | ||||
−0.656804 | + | 0.754062i | \(0.728092\pi\) | |||||||
\(444\) | 662.782 | 0.0708429 | ||||||||
\(445\) | −786.233 | −0.0837551 | ||||||||
\(446\) | −966.678 | −0.102631 | ||||||||
\(447\) | −1510.79 | −0.159862 | ||||||||
\(448\) | 1026.53 | 0.108257 | ||||||||
\(449\) | 4396.26 | 0.462076 | 0.231038 | − | 0.972945i | \(-0.425788\pi\) | ||||
0.231038 | + | 0.972945i | \(0.425788\pi\) | |||||||
\(450\) | 983.410 | 0.103019 | ||||||||
\(451\) | −1176.52 | −0.122838 | ||||||||
\(452\) | −1047.39 | −0.108993 | ||||||||
\(453\) | −925.078 | −0.0959469 | ||||||||
\(454\) | −3422.32 | −0.353782 | ||||||||
\(455\) | 4386.66 | 0.451977 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 4307.95 | 0.440957 | 0.220478 | − | 0.975392i | \(-0.429238\pi\) | ||||
0.220478 | + | 0.975392i | \(0.429238\pi\) | |||||||
\(458\) | 4275.08 | 0.436160 | ||||||||
\(459\) | −520.127 | −0.0528921 | ||||||||
\(460\) | −2675.80 | −0.271217 | ||||||||
\(461\) | 8592.47 | 0.868094 | 0.434047 | − | 0.900890i | \(-0.357085\pi\) | ||||
0.434047 | + | 0.900890i | \(0.357085\pi\) | |||||||
\(462\) | 2691.64 | 0.271053 | ||||||||
\(463\) | 3188.27 | 0.320025 | 0.160012 | − | 0.987115i | \(-0.448847\pi\) | ||||
0.160012 | + | 0.987115i | \(0.448847\pi\) | |||||||
\(464\) | 2263.53 | 0.226469 | ||||||||
\(465\) | −4212.01 | −0.420059 | ||||||||
\(466\) | −1875.70 | −0.186460 | ||||||||
\(467\) | −11923.6 | −1.18149 | −0.590745 | − | 0.806858i | \(-0.701166\pi\) | ||||
−0.590745 | + | 0.806858i | \(0.701166\pi\) | |||||||
\(468\) | −1173.71 | −0.115929 | ||||||||
\(469\) | −1520.01 | −0.149653 | ||||||||
\(470\) | 4505.00 | 0.442128 | ||||||||
\(471\) | 6.07048 | 0.000593871 0 | ||||||||
\(472\) | 5156.72 | 0.502876 | ||||||||
\(473\) | −3089.00 | −0.300280 | ||||||||
\(474\) | −5824.70 | −0.564425 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −1235.94 | −0.119011 | ||||||||
\(477\) | −1004.87 | −0.0964570 | ||||||||
\(478\) | 3683.39 | 0.352457 | ||||||||
\(479\) | 2874.54 | 0.274199 | 0.137099 | − | 0.990557i | \(-0.456222\pi\) | ||||
0.137099 | + | 0.990557i | \(0.456222\pi\) | |||||||
\(480\) | 805.291 | 0.0765757 | ||||||||
\(481\) | −1800.74 | −0.170699 | ||||||||
\(482\) | −5945.06 | −0.561806 | ||||||||
\(483\) | 3837.29 | 0.361496 | ||||||||
\(484\) | −2194.99 | −0.206141 | ||||||||
\(485\) | 4655.47 | 0.435864 | ||||||||
\(486\) | −486.000 | −0.0453609 | ||||||||
\(487\) | −261.803 | −0.0243602 | −0.0121801 | − | 0.999926i | \(-0.503877\pi\) | ||||
−0.0121801 | + | 0.999926i | \(0.503877\pi\) | |||||||
\(488\) | −2882.34 | −0.267372 | ||||||||
\(489\) | −1590.98 | −0.147130 | ||||||||
\(490\) | −1438.33 | −0.132607 | ||||||||
\(491\) | −3367.59 | −0.309526 | −0.154763 | − | 0.987952i | \(-0.549461\pi\) | ||||
−0.154763 | + | 0.987952i | \(0.549461\pi\) | |||||||
\(492\) | 504.785 | 0.0462550 | ||||||||
\(493\) | −2725.28 | −0.248967 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 2111.53 | 0.191730 | ||||||||
\(496\) | 2677.98 | 0.242429 | ||||||||
\(497\) | −19018.6 | −1.71650 | ||||||||
\(498\) | 6820.18 | 0.613694 | ||||||||
\(499\) | 2959.52 | 0.265504 | 0.132752 | − | 0.991149i | \(-0.457619\pi\) | ||||
0.132752 | + | 0.991149i | \(0.457619\pi\) | |||||||
\(500\) | 6027.40 | 0.539107 | ||||||||
\(501\) | −9199.29 | −0.820347 | ||||||||
\(502\) | −8498.34 | −0.755577 | ||||||||
\(503\) | −8431.54 | −0.747404 | −0.373702 | − | 0.927549i | \(-0.621912\pi\) | ||||
−0.373702 | + | 0.927549i | \(0.621912\pi\) | |||||||
\(504\) | −1154.85 | −0.102065 | ||||||||
\(505\) | 854.587 | 0.0753042 | ||||||||
\(506\) | 4460.82 | 0.391912 | ||||||||
\(507\) | −3402.10 | −0.298013 | ||||||||
\(508\) | 10784.7 | 0.941913 | ||||||||
\(509\) | −5152.39 | −0.448675 | −0.224338 | − | 0.974512i | \(-0.572022\pi\) | ||||
−0.224338 | + | 0.974512i | \(0.572022\pi\) | |||||||
\(510\) | −969.569 | −0.0841828 | ||||||||
\(511\) | −13105.2 | −1.13452 | ||||||||
\(512\) | −512.000 | −0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −11974.8 | −1.02760 | ||||||||
\(515\) | −15816.0 | −1.35328 | ||||||||
\(516\) | 1325.34 | 0.113071 | ||||||||
\(517\) | −7510.28 | −0.638882 | ||||||||
\(518\) | −1771.79 | −0.150286 | ||||||||
\(519\) | −4684.22 | −0.396174 | ||||||||
\(520\) | −2187.92 | −0.184513 | ||||||||
\(521\) | 21068.9 | 1.77168 | 0.885841 | − | 0.463989i | \(-0.153582\pi\) | ||||
0.885841 | + | 0.463989i | \(0.153582\pi\) | |||||||
\(522\) | −2546.47 | −0.213517 | ||||||||
\(523\) | −7615.04 | −0.636678 | −0.318339 | − | 0.947977i | \(-0.603125\pi\) | ||||
−0.318339 | + | 0.947977i | \(0.603125\pi\) | |||||||
\(524\) | −5557.73 | −0.463341 | ||||||||
\(525\) | −2628.91 | −0.218543 | ||||||||
\(526\) | 640.737 | 0.0531130 | ||||||||
\(527\) | −3224.28 | −0.266512 | ||||||||
\(528\) | −1342.50 | −0.110653 | ||||||||
\(529\) | −5807.51 | −0.477316 | ||||||||
\(530\) | −1873.18 | −0.153521 | ||||||||
\(531\) | −5801.31 | −0.474116 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −1371.47 | −0.111454 | ||||||||
\(534\) | −562.368 | −0.0455731 | ||||||||
\(535\) | 5409.80 | 0.437170 | ||||||||
\(536\) | 758.130 | 0.0610937 | ||||||||
\(537\) | −4430.08 | −0.356000 | ||||||||
\(538\) | 15155.5 | 1.21450 | ||||||||
\(539\) | 2397.84 | 0.191619 | ||||||||
\(540\) | −905.953 | −0.0721963 | ||||||||
\(541\) | 6088.48 | 0.483853 | 0.241926 | − | 0.970295i | \(-0.422221\pi\) | ||||
0.241926 | + | 0.970295i | \(0.422221\pi\) | |||||||
\(542\) | 3402.92 | 0.269683 | ||||||||
\(543\) | 10756.4 | 0.850096 | ||||||||
\(544\) | 616.447 | 0.0485845 | ||||||||
\(545\) | −10341.8 | −0.812830 | ||||||||
\(546\) | 3137.64 | 0.245932 | ||||||||
\(547\) | −23451.4 | −1.83311 | −0.916554 | − | 0.399910i | \(-0.869041\pi\) | ||||
−0.916554 | + | 0.399910i | \(0.869041\pi\) | |||||||
\(548\) | −3138.12 | −0.244624 | ||||||||
\(549\) | 3242.64 | 0.252081 | ||||||||
\(550\) | −3056.08 | −0.236931 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | −1913.91 | −0.147575 | ||||||||
\(553\) | 15570.9 | 1.19737 | ||||||||
\(554\) | 15934.7 | 1.22202 | ||||||||
\(555\) | −1389.93 | −0.106305 | ||||||||
\(556\) | −10857.1 | −0.828134 | ||||||||
\(557\) | −14161.3 | −1.07726 | −0.538631 | − | 0.842542i | \(-0.681058\pi\) | ||||
−0.538631 | + | 0.842542i | \(0.681058\pi\) | |||||||
\(558\) | −3012.72 | −0.228564 | ||||||||
\(559\) | −3600.85 | −0.272450 | ||||||||
\(560\) | −2152.75 | −0.162447 | ||||||||
\(561\) | 1616.37 | 0.121645 | ||||||||
\(562\) | −12571.7 | −0.943603 | ||||||||
\(563\) | 4782.00 | 0.357970 | 0.178985 | − | 0.983852i | \(-0.442719\pi\) | ||||
0.178985 | + | 0.983852i | \(0.442719\pi\) | |||||||
\(564\) | 3222.29 | 0.240572 | ||||||||
\(565\) | 2196.49 | 0.163552 | ||||||||
\(566\) | 13184.2 | 0.979102 | ||||||||
\(567\) | 1299.20 | 0.0962282 | ||||||||
\(568\) | 9485.88 | 0.700737 | ||||||||
\(569\) | 9926.67 | 0.731367 | 0.365683 | − | 0.930739i | \(-0.380835\pi\) | ||||
0.365683 | + | 0.930739i | \(0.380835\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −13656.1 | −1.00086 | −0.500430 | − | 0.865777i | \(-0.666825\pi\) | ||||
−0.500430 | + | 0.865777i | \(0.666825\pi\) | |||||||
\(572\) | 3647.48 | 0.266624 | ||||||||
\(573\) | −6494.69 | −0.473507 | ||||||||
\(574\) | −1349.42 | −0.0981250 | ||||||||
\(575\) | −4356.86 | −0.315989 | ||||||||
\(576\) | 576.000 | 0.0416667 | ||||||||
\(577\) | 14811.1 | 1.06862 | 0.534311 | − | 0.845288i | \(-0.320571\pi\) | ||||
0.534311 | + | 0.845288i | \(0.320571\pi\) | |||||||
\(578\) | 9083.80 | 0.653696 | ||||||||
\(579\) | −8931.85 | −0.641097 | ||||||||
\(580\) | −4746.87 | −0.339833 | ||||||||
\(581\) | −18232.1 | −1.30188 | ||||||||
\(582\) | 3329.91 | 0.237164 | ||||||||
\(583\) | 3122.78 | 0.221840 | ||||||||
\(584\) | 6536.47 | 0.463152 | ||||||||
\(585\) | 2461.41 | 0.173960 | ||||||||
\(586\) | 2102.92 | 0.148244 | ||||||||
\(587\) | 14292.4 | 1.00496 | 0.502478 | − | 0.864590i | \(-0.332422\pi\) | ||||
0.502478 | + | 0.864590i | \(0.332422\pi\) | |||||||
\(588\) | −1028.80 | −0.0721544 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | −10814.2 | −0.754601 | ||||||||
\(591\) | −13271.7 | −0.923730 | ||||||||
\(592\) | 883.710 | 0.0613518 | ||||||||
\(593\) | 9657.63 | 0.668788 | 0.334394 | − | 0.942433i | \(-0.391468\pi\) | ||||
0.334394 | + | 0.942433i | \(0.391468\pi\) | |||||||
\(594\) | 1510.31 | 0.104325 | ||||||||
\(595\) | 2591.91 | 0.178585 | ||||||||
\(596\) | −2014.39 | −0.138444 | ||||||||
\(597\) | 4414.15 | 0.302611 | ||||||||
\(598\) | 5199.98 | 0.355590 | ||||||||
\(599\) | 9217.95 | 0.628773 | 0.314387 | − | 0.949295i | \(-0.398201\pi\) | ||||
0.314387 | + | 0.949295i | \(0.398201\pi\) | |||||||
\(600\) | 1311.21 | 0.0892168 | ||||||||
\(601\) | −18966.6 | −1.28730 | −0.643649 | − | 0.765321i | \(-0.722580\pi\) | ||||
−0.643649 | + | 0.765321i | \(0.722580\pi\) | |||||||
\(602\) | −3542.96 | −0.239868 | ||||||||
\(603\) | −852.896 | −0.0575997 | ||||||||
\(604\) | −1233.44 | −0.0830924 | ||||||||
\(605\) | 4603.15 | 0.309330 | ||||||||
\(606\) | 611.260 | 0.0409748 | ||||||||
\(607\) | 9556.83 | 0.639044 | 0.319522 | − | 0.947579i | \(-0.396478\pi\) | ||||
0.319522 | + | 0.947579i | \(0.396478\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 6807.36 | 0.452953 | ||||||||
\(610\) | 6044.60 | 0.401211 | ||||||||
\(611\) | −8754.74 | −0.579671 | ||||||||
\(612\) | −693.503 | −0.0458059 | ||||||||
\(613\) | −14958.7 | −0.985606 | −0.492803 | − | 0.870141i | \(-0.664028\pi\) | ||||
−0.492803 | + | 0.870141i | \(0.664028\pi\) | |||||||
\(614\) | −4193.22 | −0.275610 | ||||||||
\(615\) | −1058.59 | −0.0694090 | ||||||||
\(616\) | 3588.85 | 0.234738 | ||||||||
\(617\) | −25766.3 | −1.68122 | −0.840610 | − | 0.541641i | \(-0.817803\pi\) | ||||
−0.840610 | + | 0.541641i | \(0.817803\pi\) | |||||||
\(618\) | −11312.7 | −0.736350 | ||||||||
\(619\) | −9724.16 | −0.631417 | −0.315708 | − | 0.948856i | \(-0.602242\pi\) | ||||
−0.315708 | + | 0.948856i | \(0.602242\pi\) | |||||||
\(620\) | −5616.02 | −0.363782 | ||||||||
\(621\) | 2153.15 | 0.139135 | ||||||||
\(622\) | 19624.1 | 1.26504 | ||||||||
\(623\) | 1503.35 | 0.0966784 | ||||||||
\(624\) | −1564.95 | −0.100398 | ||||||||
\(625\) | −5810.90 | −0.371898 | ||||||||
\(626\) | −15017.6 | −0.958822 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 8.09398 | 0.000514307 0 | ||||||||
\(629\) | −1063.98 | −0.0674465 | ||||||||
\(630\) | 2421.84 | 0.153157 | ||||||||
\(631\) | 4792.37 | 0.302348 | 0.151174 | − | 0.988507i | \(-0.451695\pi\) | ||||
0.151174 | + | 0.988507i | \(0.451695\pi\) | |||||||
\(632\) | −7766.27 | −0.488807 | ||||||||
\(633\) | 179.563 | 0.0112749 | ||||||||
\(634\) | −7276.68 | −0.455826 | ||||||||
\(635\) | −22616.6 | −1.41341 | ||||||||
\(636\) | −1339.83 | −0.0835342 | ||||||||
\(637\) | 2795.17 | 0.173860 | ||||||||
\(638\) | 7913.50 | 0.491064 | ||||||||
\(639\) | −10671.6 | −0.660661 | ||||||||
\(640\) | 1073.72 | 0.0663165 | ||||||||
\(641\) | −7757.10 | −0.477983 | −0.238992 | − | 0.971022i | \(-0.576817\pi\) | ||||
−0.238992 | + | 0.971022i | \(0.576817\pi\) | |||||||
\(642\) | 3869.46 | 0.237875 | ||||||||
\(643\) | 25559.8 | 1.56762 | 0.783810 | − | 0.621001i | \(-0.213274\pi\) | ||||
0.783810 | + | 0.621001i | \(0.213274\pi\) | |||||||
\(644\) | 5116.39 | 0.313065 | ||||||||
\(645\) | −2779.38 | −0.169671 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −16384.6 | −0.995585 | −0.497793 | − | 0.867296i | \(-0.665856\pi\) | ||||
−0.497793 | + | 0.867296i | \(0.665856\pi\) | |||||||
\(648\) | −648.000 | −0.0392837 | ||||||||
\(649\) | 18028.4 | 1.09041 | ||||||||
\(650\) | −3562.48 | −0.214972 | ||||||||
\(651\) | 8053.78 | 0.484874 | ||||||||
\(652\) | −2121.30 | −0.127418 | ||||||||
\(653\) | 15643.0 | 0.937455 | 0.468727 | − | 0.883343i | \(-0.344713\pi\) | ||||
0.468727 | + | 0.883343i | \(0.344713\pi\) | |||||||
\(654\) | −7397.15 | −0.442280 | ||||||||
\(655\) | 11655.2 | 0.695276 | ||||||||
\(656\) | 673.047 | 0.0400580 | ||||||||
\(657\) | −7353.53 | −0.436664 | ||||||||
\(658\) | −8614.01 | −0.510348 | ||||||||
\(659\) | −32774.1 | −1.93733 | −0.968663 | − | 0.248378i | \(-0.920102\pi\) | ||||
−0.968663 | + | 0.248378i | \(0.920102\pi\) | |||||||
\(660\) | 2815.37 | 0.166043 | ||||||||
\(661\) | −13644.5 | −0.802887 | −0.401443 | − | 0.915884i | \(-0.631491\pi\) | ||||
−0.401443 | + | 0.915884i | \(0.631491\pi\) | |||||||
\(662\) | 3985.85 | 0.234010 | ||||||||
\(663\) | 1884.20 | 0.110371 | ||||||||
\(664\) | 9093.57 | 0.531474 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −994.174 | −0.0578430 | ||||||||
\(667\) | 11281.8 | 0.654920 | ||||||||
\(668\) | −12265.7 | −0.710441 | ||||||||
\(669\) | 1450.02 | 0.0837981 | ||||||||
\(670\) | −1589.88 | −0.0916755 | ||||||||
\(671\) | −10076.9 | −0.579756 | ||||||||
\(672\) | −1539.80 | −0.0883913 | ||||||||
\(673\) | −14135.4 | −0.809631 | −0.404815 | − | 0.914398i | \(-0.632664\pi\) | ||||
−0.404815 | + | 0.914398i | \(0.632664\pi\) | |||||||
\(674\) | −1197.34 | −0.0684271 | ||||||||
\(675\) | −1475.12 | −0.0841144 | ||||||||
\(676\) | −4536.13 | −0.258087 | ||||||||
\(677\) | 8604.23 | 0.488460 | 0.244230 | − | 0.969717i | \(-0.421465\pi\) | ||||
0.244230 | + | 0.969717i | \(0.421465\pi\) | |||||||
\(678\) | 1571.08 | 0.0889928 | ||||||||
\(679\) | −8901.71 | −0.503117 | ||||||||
\(680\) | −1292.76 | −0.0729045 | ||||||||
\(681\) | 5133.47 | 0.288862 | ||||||||
\(682\) | 9362.46 | 0.525670 | ||||||||
\(683\) | 17472.7 | 0.978881 | 0.489440 | − | 0.872037i | \(-0.337201\pi\) | ||||
0.489440 | + | 0.872037i | \(0.337201\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 6580.99 | 0.367075 | ||||||||
\(686\) | 13753.4 | 0.765460 | ||||||||
\(687\) | −6412.62 | −0.356123 | ||||||||
\(688\) | 1767.11 | 0.0979224 | ||||||||
\(689\) | 3640.23 | 0.201280 | ||||||||
\(690\) | 4013.69 | 0.221447 | ||||||||
\(691\) | 9660.63 | 0.531849 | 0.265925 | − | 0.963994i | \(-0.414323\pi\) | ||||
0.265925 | + | 0.963994i | \(0.414323\pi\) | |||||||
\(692\) | −6245.63 | −0.343097 | ||||||||
\(693\) | −4037.46 | −0.221314 | ||||||||
\(694\) | −10653.6 | −0.582716 | ||||||||
\(695\) | 22768.5 | 1.24267 | ||||||||
\(696\) | −3395.29 | −0.184911 | ||||||||
\(697\) | −810.347 | −0.0440374 | ||||||||
\(698\) | −16139.8 | −0.875214 | ||||||||
\(699\) | 2813.56 | 0.152244 | ||||||||
\(700\) | −3505.21 | −0.189264 | ||||||||
\(701\) | 22673.6 | 1.22164 | 0.610819 | − | 0.791770i | \(-0.290840\pi\) | ||||
0.610819 | + | 0.791770i | \(0.290840\pi\) | |||||||
\(702\) | 1760.57 | 0.0946560 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | −1790.00 | −0.0958284 | ||||||||
\(705\) | −6757.50 | −0.360996 | ||||||||
\(706\) | 23191.1 | 1.23627 | ||||||||
\(707\) | −1634.05 | −0.0869235 | ||||||||
\(708\) | −7735.08 | −0.410596 | ||||||||
\(709\) | 13285.1 | 0.703711 | 0.351855 | − | 0.936054i | \(-0.385551\pi\) | ||||
0.351855 | + | 0.936054i | \(0.385551\pi\) | |||||||
\(710\) | −19892.9 | −1.05151 | ||||||||
\(711\) | 8737.06 | 0.460851 | ||||||||
\(712\) | −749.824 | −0.0394675 | ||||||||
\(713\) | 13347.4 | 0.701074 | ||||||||
\(714\) | 1853.91 | 0.0971721 | ||||||||
\(715\) | −7649.18 | −0.400088 | ||||||||
\(716\) | −5906.77 | −0.308305 | ||||||||
\(717\) | −5525.09 | −0.287780 | ||||||||
\(718\) | 10031.5 | 0.521412 | ||||||||
\(719\) | −28752.4 | −1.49136 | −0.745678 | − | 0.666306i | \(-0.767874\pi\) | ||||
−0.745678 | + | 0.666306i | \(0.767874\pi\) | |||||||
\(720\) | −1207.94 | −0.0625238 | ||||||||
\(721\) | 30241.8 | 1.56209 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 8917.60 | 0.458712 | ||||||||
\(724\) | 14341.9 | 0.736205 | ||||||||
\(725\) | −7729.08 | −0.395932 | ||||||||
\(726\) | 3292.49 | 0.168314 | ||||||||
\(727\) | 28931.3 | 1.47593 | 0.737967 | − | 0.674837i | \(-0.235786\pi\) | ||||
0.737967 | + | 0.674837i | \(0.235786\pi\) | |||||||
\(728\) | 4183.52 | 0.212983 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | −13707.7 | −0.694993 | ||||||||
\(731\) | −2127.60 | −0.107650 | ||||||||
\(732\) | 4323.51 | 0.218308 | ||||||||
\(733\) | 10740.6 | 0.541219 | 0.270609 | − | 0.962689i | \(-0.412775\pi\) | ||||
0.270609 | + | 0.962689i | \(0.412775\pi\) | |||||||
\(734\) | 7709.73 | 0.387699 | ||||||||
\(735\) | 2157.50 | 0.108273 | ||||||||
\(736\) | −2551.89 | −0.127804 | ||||||||
\(737\) | 2650.49 | 0.132472 | ||||||||
\(738\) | −757.178 | −0.0377671 | ||||||||
\(739\) | −936.700 | −0.0466266 | −0.0233133 | − | 0.999728i | \(-0.507422\pi\) | ||||
−0.0233133 | + | 0.999728i | \(0.507422\pi\) | |||||||
\(740\) | −1853.24 | −0.0920627 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 3581.71 | 0.177209 | ||||||||
\(743\) | −31780.2 | −1.56918 | −0.784591 | − | 0.620014i | \(-0.787127\pi\) | ||||
−0.784591 | + | 0.620014i | \(0.787127\pi\) | |||||||
\(744\) | −4016.96 | −0.197942 | ||||||||
\(745\) | 4224.41 | 0.207745 | ||||||||
\(746\) | −23903.5 | −1.17315 | ||||||||
\(747\) | −10230.3 | −0.501079 | ||||||||
\(748\) | 2155.16 | 0.105348 | ||||||||
\(749\) | −10344.1 | −0.504625 | ||||||||
\(750\) | −9041.10 | −0.440179 | ||||||||
\(751\) | 25394.4 | 1.23389 | 0.616947 | − | 0.787005i | \(-0.288369\pi\) | ||||
0.616947 | + | 0.787005i | \(0.288369\pi\) | |||||||
\(752\) | 4296.38 | 0.208342 | ||||||||
\(753\) | 12747.5 | 0.616926 | ||||||||
\(754\) | 9224.77 | 0.445552 | ||||||||
\(755\) | 2586.66 | 0.124686 | ||||||||
\(756\) | 1732.27 | 0.0833361 | ||||||||
\(757\) | 26773.4 | 1.28546 | 0.642732 | − | 0.766091i | \(-0.277801\pi\) | ||||
0.642732 | + | 0.766091i | \(0.277801\pi\) | |||||||
\(758\) | 28601.1 | 1.37050 | ||||||||
\(759\) | −6691.23 | −0.319995 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 26354.6 | 1.25539 | 0.627696 | − | 0.778459i | \(-0.283998\pi\) | ||||
0.627696 | + | 0.778459i | \(0.283998\pi\) | |||||||
\(762\) | −16177.0 | −0.769068 | ||||||||
\(763\) | 19774.5 | 0.938249 | ||||||||
\(764\) | −8659.59 | −0.410069 | ||||||||
\(765\) | 1454.35 | 0.0687350 | ||||||||
\(766\) | 11654.4 | 0.549729 | ||||||||
\(767\) | 21015.7 | 0.989352 | ||||||||
\(768\) | 768.000 | 0.0360844 | ||||||||
\(769\) | 37499.2 | 1.75846 | 0.879230 | − | 0.476397i | \(-0.158058\pi\) | ||||
0.879230 | + | 0.476397i | \(0.158058\pi\) | |||||||
\(770\) | −7526.22 | −0.352242 | ||||||||
\(771\) | 17962.2 | 0.839029 | ||||||||
\(772\) | −11909.1 | −0.555206 | ||||||||
\(773\) | 17461.2 | 0.812464 | 0.406232 | − | 0.913770i | \(-0.366843\pi\) | ||||
0.406232 | + | 0.913770i | \(0.366843\pi\) | |||||||
\(774\) | −1988.00 | −0.0923221 | ||||||||
\(775\) | −9144.27 | −0.423834 | ||||||||
\(776\) | 4439.88 | 0.205390 | ||||||||
\(777\) | 2657.68 | 0.122708 | ||||||||
\(778\) | −14261.9 | −0.657216 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 3281.88 | 0.150654 | ||||||||
\(781\) | 33163.5 | 1.51944 | ||||||||
\(782\) | 3072.46 | 0.140500 | ||||||||
\(783\) | 3819.70 | 0.174336 | ||||||||
\(784\) | −1371.73 | −0.0624876 | ||||||||
\(785\) | −16.9740 | −0.000771755 0 | ||||||||
\(786\) | 8336.60 | 0.378316 | ||||||||
\(787\) | −3251.22 | −0.147260 | −0.0736299 | − | 0.997286i | \(-0.523458\pi\) | ||||
−0.0736299 | + | 0.997286i | \(0.523458\pi\) | |||||||
\(788\) | −17695.6 | −0.799974 | ||||||||
\(789\) | −961.105 | −0.0433666 | ||||||||
\(790\) | 16286.7 | 0.733489 | ||||||||
\(791\) | −4199.91 | −0.188788 | ||||||||
\(792\) | 2013.75 | 0.0903479 | ||||||||
\(793\) | −11746.7 | −0.526024 | ||||||||
\(794\) | 27874.2 | 1.24587 | ||||||||
\(795\) | 2809.78 | 0.125349 | ||||||||
\(796\) | 5885.53 | 0.262069 | ||||||||
\(797\) | −3246.61 | −0.144292 | −0.0721460 | − | 0.997394i | \(-0.522985\pi\) | ||||
−0.0721460 | + | 0.997394i | \(0.522985\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −5172.84 | −0.229039 | ||||||||
\(800\) | 1748.28 | 0.0772640 | ||||||||
\(801\) | 843.552 | 0.0372103 | ||||||||
\(802\) | −502.202 | −0.0221114 | ||||||||
\(803\) | 22852.1 | 1.00428 | ||||||||
\(804\) | −1137.19 | −0.0498828 | ||||||||
\(805\) | −10729.6 | −0.469776 | ||||||||
\(806\) | 10913.8 | 0.476951 | ||||||||
\(807\) | −22733.3 | −0.991635 | ||||||||
\(808\) | 815.013 | 0.0354852 | ||||||||
\(809\) | 7901.78 | 0.343401 | 0.171701 | − | 0.985149i | \(-0.445074\pi\) | ||||
0.171701 | + | 0.985149i | \(0.445074\pi\) | |||||||
\(810\) | 1358.93 | 0.0589480 | ||||||||
\(811\) | −22332.4 | −0.966952 | −0.483476 | − | 0.875358i | \(-0.660626\pi\) | ||||
−0.483476 | + | 0.875358i | \(0.660626\pi\) | |||||||
\(812\) | 9076.49 | 0.392269 | ||||||||
\(813\) | −5104.38 | −0.220195 | ||||||||
\(814\) | 3089.53 | 0.133032 | ||||||||
\(815\) | 4448.61 | 0.191200 | ||||||||
\(816\) | −924.670 | −0.0396690 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 19913.5 | 0.851172 | ||||||||
\(819\) | −4706.46 | −0.200802 | ||||||||
\(820\) | −1411.46 | −0.0601100 | ||||||||
\(821\) | 10068.8 | 0.428021 | 0.214010 | − | 0.976831i | \(-0.431347\pi\) | ||||
0.214010 | + | 0.976831i | \(0.431347\pi\) | |||||||
\(822\) | 4707.18 | 0.199734 | ||||||||
\(823\) | −35561.9 | −1.50621 | −0.753104 | − | 0.657902i | \(-0.771444\pi\) | ||||
−0.753104 | + | 0.657902i | \(0.771444\pi\) | |||||||
\(824\) | −15083.6 | −0.637698 | ||||||||
\(825\) | 4584.13 | 0.193453 | ||||||||
\(826\) | 20677.9 | 0.871035 | ||||||||
\(827\) | −35425.4 | −1.48955 | −0.744777 | − | 0.667313i | \(-0.767444\pi\) | ||||
−0.744777 | + | 0.667313i | \(0.767444\pi\) | |||||||
\(828\) | 2870.87 | 0.120495 | ||||||||
\(829\) | −31632.8 | −1.32528 | −0.662638 | − | 0.748940i | \(-0.730563\pi\) | ||||
−0.662638 | + | 0.748940i | \(0.730563\pi\) | |||||||
\(830\) | −19070.2 | −0.797515 | ||||||||
\(831\) | −23902.0 | −0.997774 | ||||||||
\(832\) | −2086.60 | −0.0869471 | ||||||||
\(833\) | 1651.56 | 0.0686951 | ||||||||
\(834\) | 16285.6 | 0.676169 | ||||||||
\(835\) | 25722.6 | 1.06607 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 4519.08 | 0.186622 | ||||||||
\(838\) | −2111.22 | −0.0870297 | ||||||||
\(839\) | 35877.6 | 1.47632 | 0.738160 | − | 0.674625i | \(-0.235695\pi\) | ||||
0.738160 | + | 0.674625i | \(0.235695\pi\) | |||||||
\(840\) | 3229.13 | 0.132637 | ||||||||
\(841\) | −4375.12 | −0.179389 | ||||||||
\(842\) | 21921.2 | 0.897215 | ||||||||
\(843\) | 18857.5 | 0.770448 | ||||||||
\(844\) | 239.418 | 0.00976433 | ||||||||
\(845\) | 9512.77 | 0.387277 | ||||||||
\(846\) | −4833.43 | −0.196427 | ||||||||
\(847\) | −8801.68 | −0.357059 | ||||||||
\(848\) | −1786.44 | −0.0723427 | ||||||||
\(849\) | −19776.2 | −0.799433 | ||||||||
\(850\) | −2104.93 | −0.0849395 | ||||||||
\(851\) | 4404.54 | 0.177422 | ||||||||
\(852\) | −14228.8 | −0.572149 | ||||||||
\(853\) | −41382.1 | −1.66107 | −0.830537 | − | 0.556964i | \(-0.811966\pi\) | ||||
−0.830537 | + | 0.556964i | \(0.811966\pi\) | |||||||
\(854\) | −11557.9 | −0.463117 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 5159.29 | 0.206006 | ||||||||
\(857\) | −22106.8 | −0.881159 | −0.440580 | − | 0.897714i | \(-0.645227\pi\) | ||||
−0.440580 | + | 0.897714i | \(0.645227\pi\) | |||||||
\(858\) | −5471.22 | −0.217698 | ||||||||
\(859\) | −20872.2 | −0.829047 | −0.414524 | − | 0.910038i | \(-0.636052\pi\) | ||||
−0.414524 | + | 0.910038i | \(0.636052\pi\) | |||||||
\(860\) | −3705.84 | −0.146940 | ||||||||
\(861\) | 2024.13 | 0.0801187 | ||||||||
\(862\) | 16867.5 | 0.666485 | ||||||||
\(863\) | 2076.93 | 0.0819231 | 0.0409616 | − | 0.999161i | \(-0.486958\pi\) | ||||
0.0409616 | + | 0.999161i | \(0.486958\pi\) | |||||||
\(864\) | −864.000 | −0.0340207 | ||||||||
\(865\) | 13097.8 | 0.514842 | ||||||||
\(866\) | 13633.9 | 0.534988 | ||||||||
\(867\) | −13625.7 | −0.533740 | ||||||||
\(868\) | 10738.4 | 0.419913 | ||||||||
\(869\) | −27151.6 | −1.05990 | ||||||||
\(870\) | 7120.31 | 0.277472 | ||||||||
\(871\) | 3089.68 | 0.120195 | ||||||||
\(872\) | −9862.86 | −0.383026 | ||||||||
\(873\) | −4994.87 | −0.193643 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 24169.2 | 0.933792 | ||||||||
\(876\) | −9804.70 | −0.378162 | ||||||||
\(877\) | 43101.3 | 1.65955 | 0.829776 | − | 0.558097i | \(-0.188468\pi\) | ||||
0.829776 | + | 0.558097i | \(0.188468\pi\) | |||||||
\(878\) | 13297.6 | 0.511131 | ||||||||
\(879\) | −3154.39 | −0.121041 | ||||||||
\(880\) | 3753.83 | 0.143797 | ||||||||
\(881\) | 27654.6 | 1.05756 | 0.528778 | − | 0.848760i | \(-0.322650\pi\) | ||||
0.528778 | + | 0.848760i | \(0.322650\pi\) | |||||||
\(882\) | 1543.19 | 0.0589139 | ||||||||
\(883\) | 14726.2 | 0.561243 | 0.280622 | − | 0.959818i | \(-0.409459\pi\) | ||||
0.280622 | + | 0.959818i | \(0.409459\pi\) | |||||||
\(884\) | 2512.27 | 0.0955845 | ||||||||
\(885\) | 16221.3 | 0.616129 | ||||||||
\(886\) | 24496.3 | 0.928861 | ||||||||
\(887\) | 19781.1 | 0.748800 | 0.374400 | − | 0.927267i | \(-0.377849\pi\) | ||||
0.374400 | + | 0.927267i | \(0.377849\pi\) | |||||||
\(888\) | −1325.56 | −0.0500935 | ||||||||
\(889\) | 43245.2 | 1.63149 | ||||||||
\(890\) | 1572.47 | 0.0592238 | ||||||||
\(891\) | −2265.47 | −0.0851808 | ||||||||
\(892\) | 1933.36 | 0.0725713 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 3021.59 | 0.113039 | ||||||||
\(895\) | 12387.2 | 0.462634 | ||||||||
\(896\) | −2053.06 | −0.0765491 | ||||||||
\(897\) | −7799.96 | −0.290338 | ||||||||
\(898\) | −8792.52 | −0.326737 | ||||||||
\(899\) | 23678.4 | 0.878441 | ||||||||
\(900\) | −1966.82 | −0.0728452 | ||||||||
\(901\) | 2150.87 | 0.0795293 | ||||||||
\(902\) | 2353.04 | 0.0868598 | ||||||||
\(903\) | 5314.45 | 0.195851 | ||||||||
\(904\) | 2094.78 | 0.0770700 | ||||||||
\(905\) | −30076.6 | −1.10473 | ||||||||
\(906\) | 1850.16 | 0.0678447 | ||||||||
\(907\) | 25912.0 | 0.948614 | 0.474307 | − | 0.880360i | \(-0.342699\pi\) | ||||
0.474307 | + | 0.880360i | \(0.342699\pi\) | |||||||
\(908\) | 6844.63 | 0.250162 | ||||||||
\(909\) | −916.889 | −0.0334558 | ||||||||
\(910\) | −8773.32 | −0.319596 | ||||||||
\(911\) | 46653.3 | 1.69670 | 0.848350 | − | 0.529437i | \(-0.177597\pi\) | ||||
0.848350 | + | 0.529437i | \(0.177597\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 31792.0 | 1.15242 | ||||||||
\(914\) | −8615.90 | −0.311804 | ||||||||
\(915\) | −9066.89 | −0.327587 | ||||||||
\(916\) | −8550.15 | −0.308412 | ||||||||
\(917\) | −22285.9 | −0.802556 | ||||||||
\(918\) | 1040.25 | 0.0374003 | ||||||||
\(919\) | 44547.1 | 1.59899 | 0.799495 | − | 0.600673i | \(-0.205101\pi\) | ||||
0.799495 | + | 0.600673i | \(0.205101\pi\) | |||||||
\(920\) | 5351.59 | 0.191779 | ||||||||
\(921\) | 6289.83 | 0.225035 | ||||||||
\(922\) | −17184.9 | −0.613835 | ||||||||
\(923\) | 38658.7 | 1.37862 | ||||||||
\(924\) | −5383.27 | −0.191663 | ||||||||
\(925\) | −3017.53 | −0.107260 | ||||||||
\(926\) | −6376.54 | −0.226292 | ||||||||
\(927\) | 16969.1 | 0.601228 | ||||||||
\(928\) | −4527.05 | −0.160138 | ||||||||
\(929\) | 3524.10 | 0.124458 | 0.0622292 | − | 0.998062i | \(-0.480179\pi\) | ||||
0.0622292 | + | 0.998062i | \(0.480179\pi\) | |||||||
\(930\) | 8424.03 | 0.297027 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 3751.41 | 0.131847 | ||||||||
\(933\) | −29436.1 | −1.03290 | ||||||||
\(934\) | 23847.1 | 0.835440 | ||||||||
\(935\) | −4519.61 | −0.158082 | ||||||||
\(936\) | 2347.43 | 0.0819745 | ||||||||
\(937\) | −19144.8 | −0.667486 | −0.333743 | − | 0.942664i | \(-0.608312\pi\) | ||||
−0.333743 | + | 0.942664i | \(0.608312\pi\) | |||||||
\(938\) | 3040.02 | 0.105821 | ||||||||
\(939\) | 22526.4 | 0.782875 | ||||||||
\(940\) | −9010.00 | −0.312632 | ||||||||
\(941\) | 2110.74 | 0.0731224 | 0.0365612 | − | 0.999331i | \(-0.488360\pi\) | ||||
0.0365612 | + | 0.999331i | \(0.488360\pi\) | |||||||
\(942\) | −12.1410 | −0.000419930 0 | ||||||||
\(943\) | 3354.57 | 0.115843 | ||||||||
\(944\) | −10313.4 | −0.355587 | ||||||||
\(945\) | −3632.77 | −0.125052 | ||||||||
\(946\) | 6178.00 | 0.212330 | ||||||||
\(947\) | −18860.7 | −0.647192 | −0.323596 | − | 0.946195i | \(-0.604892\pi\) | ||||
−0.323596 | + | 0.946195i | \(0.604892\pi\) | |||||||
\(948\) | 11649.4 | 0.399109 | ||||||||
\(949\) | 26638.7 | 0.911200 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 10915.0 | 0.372181 | ||||||||
\(952\) | 2471.88 | 0.0841535 | ||||||||
\(953\) | 20352.1 | 0.691784 | 0.345892 | − | 0.938274i | \(-0.387576\pi\) | ||||
0.345892 | + | 0.938274i | \(0.387576\pi\) | |||||||
\(954\) | 2009.75 | 0.0682054 | ||||||||
\(955\) | 18160.1 | 0.615338 | ||||||||
\(956\) | −7366.78 | −0.249225 | ||||||||
\(957\) | −11870.3 | −0.400952 | ||||||||
\(958\) | −5749.08 | −0.193888 | ||||||||
\(959\) | −12583.5 | −0.423714 | ||||||||
\(960\) | −1610.58 | −0.0541472 | ||||||||
\(961\) | −1777.12 | −0.0596528 | ||||||||
\(962\) | 3601.47 | 0.120703 | ||||||||
\(963\) | −5804.20 | −0.194224 | ||||||||
\(964\) | 11890.1 | 0.397257 | ||||||||
\(965\) | 24974.8 | 0.833126 | ||||||||
\(966\) | −7674.58 | −0.255616 | ||||||||
\(967\) | 4107.74 | 0.136604 | 0.0683020 | − | 0.997665i | \(-0.478242\pi\) | ||||
0.0683020 | + | 0.997665i | \(0.478242\pi\) | |||||||
\(968\) | 4389.99 | 0.145764 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −9310.93 | −0.308202 | ||||||||
\(971\) | −15720.4 | −0.519560 | −0.259780 | − | 0.965668i | \(-0.583650\pi\) | ||||
−0.259780 | + | 0.965668i | \(0.583650\pi\) | |||||||
\(972\) | 972.000 | 0.0320750 | ||||||||
\(973\) | −43535.6 | −1.43442 | ||||||||
\(974\) | 523.607 | 0.0172253 | ||||||||
\(975\) | 5343.72 | 0.175524 | ||||||||
\(976\) | 5764.68 | 0.189061 | ||||||||
\(977\) | −21779.1 | −0.713179 | −0.356590 | − | 0.934261i | \(-0.616061\pi\) | ||||
−0.356590 | + | 0.934261i | \(0.616061\pi\) | |||||||
\(978\) | 3181.96 | 0.104037 | ||||||||
\(979\) | −2621.46 | −0.0855793 | ||||||||
\(980\) | 2876.67 | 0.0937671 | ||||||||
\(981\) | 11095.7 | 0.361120 | ||||||||
\(982\) | 6735.19 | 0.218868 | ||||||||
\(983\) | −2370.66 | −0.0769201 | −0.0384600 | − | 0.999260i | \(-0.512245\pi\) | ||||
−0.0384600 | + | 0.999260i | \(0.512245\pi\) | |||||||
\(984\) | −1009.57 | −0.0327073 | ||||||||
\(985\) | 37109.6 | 1.20042 | ||||||||
\(986\) | 5450.56 | 0.176046 | ||||||||
\(987\) | 12921.0 | 0.416697 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 8807.57 | 0.283179 | ||||||||
\(990\) | −4223.06 | −0.135573 | ||||||||
\(991\) | 46028.0 | 1.47541 | 0.737703 | − | 0.675125i | \(-0.235910\pi\) | ||||
0.737703 | + | 0.675125i | \(0.235910\pi\) | |||||||
\(992\) | −5355.95 | −0.171423 | ||||||||
\(993\) | −5978.78 | −0.191068 | ||||||||
\(994\) | 38037.3 | 1.21375 | ||||||||
\(995\) | −12342.6 | −0.393254 | ||||||||
\(996\) | −13640.4 | −0.433947 | ||||||||
\(997\) | 14463.3 | 0.459436 | 0.229718 | − | 0.973257i | \(-0.426220\pi\) | ||||
0.229718 | + | 0.973257i | \(0.426220\pi\) | |||||||
\(998\) | −5919.04 | −0.187739 | ||||||||
\(999\) | 1491.26 | 0.0472286 |
(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 | 2166.4.a.bh.1.4 | ✓ | 8 | |
19.18 | odd | 2 | 2166.4.a.bi.1.4 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2166.4.a.bh.1.4 | ✓ | 8 | 1.1 | even | 1 | trivial | |
2166.4.a.bi.1.4 | yes | 8 | 19.18 | odd | 2 |