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: | \(1\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 4 x^{11} - 58 x^{10} + 204 x^{9} + 1191 x^{8} - 3456 x^{7} - 10364 x^{6} + 21448 x^{5} + 38476 x^{4} - 32336 x^{3} - 57024 x^{2} - 15776 x + 1156 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 17) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.5 | ||
Root | \(-1.47083\) 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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.70547 | −0.602974 | −0.301487 | − | 0.953470i | \(-0.597483\pi\) | ||||
−0.301487 | + | 0.953470i | \(0.597483\pi\) | |||||||
\(3\) | −4.44379 | −0.855209 | −0.427604 | − | 0.903966i | \(-0.640642\pi\) | ||||
−0.427604 | + | 0.903966i | \(0.640642\pi\) | |||||||
\(4\) | −5.09138 | −0.636422 | ||||||||
\(5\) | 6.80983 | 0.609090 | 0.304545 | − | 0.952498i | \(-0.401496\pi\) | ||||
0.304545 | + | 0.952498i | \(0.401496\pi\) | |||||||
\(6\) | 7.57875 | 0.515668 | ||||||||
\(7\) | −13.8760 | −0.749235 | −0.374618 | − | 0.927179i | \(-0.622226\pi\) | ||||
−0.374618 | + | 0.927179i | \(0.622226\pi\) | |||||||
\(8\) | 22.3269 | 0.986720 | ||||||||
\(9\) | −7.25269 | −0.268618 | ||||||||
\(10\) | −11.6140 | −0.367265 | ||||||||
\(11\) | 30.8361 | 0.845221 | 0.422610 | − | 0.906311i | \(-0.361114\pi\) | ||||
0.422610 | + | 0.906311i | \(0.361114\pi\) | |||||||
\(12\) | 22.6250 | 0.544274 | ||||||||
\(13\) | 66.0130 | 1.40836 | 0.704181 | − | 0.710021i | \(-0.251314\pi\) | ||||
0.704181 | + | 0.710021i | \(0.251314\pi\) | |||||||
\(14\) | 23.6651 | 0.451769 | ||||||||
\(15\) | −30.2615 | −0.520899 | ||||||||
\(16\) | 2.65318 | 0.0414559 | ||||||||
\(17\) | 0 | 0 | ||||||||
\(18\) | 12.3692 | 0.161970 | ||||||||
\(19\) | −79.7150 | −0.962520 | −0.481260 | − | 0.876578i | \(-0.659821\pi\) | ||||
−0.481260 | + | 0.876578i | \(0.659821\pi\) | |||||||
\(20\) | −34.6714 | −0.387639 | ||||||||
\(21\) | 61.6622 | 0.640752 | ||||||||
\(22\) | −52.5899 | −0.509646 | ||||||||
\(23\) | 28.8986 | 0.261990 | 0.130995 | − | 0.991383i | \(-0.458183\pi\) | ||||
0.130995 | + | 0.991383i | \(0.458183\pi\) | |||||||
\(24\) | −99.2163 | −0.843851 | ||||||||
\(25\) | −78.6262 | −0.629009 | ||||||||
\(26\) | −112.583 | −0.849205 | ||||||||
\(27\) | 152.212 | 1.08493 | ||||||||
\(28\) | 70.6481 | 0.476830 | ||||||||
\(29\) | 266.201 | 1.70456 | 0.852281 | − | 0.523084i | \(-0.175219\pi\) | ||||
0.852281 | + | 0.523084i | \(0.175219\pi\) | |||||||
\(30\) | 51.6100 | 0.314089 | ||||||||
\(31\) | −35.7906 | −0.207361 | −0.103680 | − | 0.994611i | \(-0.533062\pi\) | ||||
−0.103680 | + | 0.994611i | \(0.533062\pi\) | |||||||
\(32\) | −183.140 | −1.01172 | ||||||||
\(33\) | −137.029 | −0.722840 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −94.4935 | −0.456352 | ||||||||
\(36\) | 36.9262 | 0.170955 | ||||||||
\(37\) | −357.875 | −1.59011 | −0.795057 | − | 0.606535i | \(-0.792559\pi\) | ||||
−0.795057 | + | 0.606535i | \(0.792559\pi\) | |||||||
\(38\) | 135.951 | 0.580374 | ||||||||
\(39\) | −293.348 | −1.20444 | ||||||||
\(40\) | 152.043 | 0.601001 | ||||||||
\(41\) | 32.7452 | 0.124730 | 0.0623652 | − | 0.998053i | \(-0.480136\pi\) | ||||
0.0623652 | + | 0.998053i | \(0.480136\pi\) | |||||||
\(42\) | −105.163 | −0.386357 | ||||||||
\(43\) | −516.157 | −1.83054 | −0.915270 | − | 0.402841i | \(-0.868023\pi\) | ||||
−0.915270 | + | 0.402841i | \(0.868023\pi\) | |||||||
\(44\) | −156.998 | −0.537917 | ||||||||
\(45\) | −49.3896 | −0.163613 | ||||||||
\(46\) | −49.2857 | −0.157973 | ||||||||
\(47\) | −210.602 | −0.653606 | −0.326803 | − | 0.945093i | \(-0.605971\pi\) | ||||
−0.326803 | + | 0.945093i | \(0.605971\pi\) | |||||||
\(48\) | −11.7902 | −0.0354534 | ||||||||
\(49\) | −150.456 | −0.438647 | ||||||||
\(50\) | 134.094 | 0.379276 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −336.097 | −0.896313 | ||||||||
\(53\) | 87.2324 | 0.226081 | 0.113040 | − | 0.993590i | \(-0.463941\pi\) | ||||
0.113040 | + | 0.993590i | \(0.463941\pi\) | |||||||
\(54\) | −259.593 | −0.654186 | ||||||||
\(55\) | 209.989 | 0.514815 | ||||||||
\(56\) | −309.809 | −0.739285 | ||||||||
\(57\) | 354.237 | 0.823155 | ||||||||
\(58\) | −453.997 | −1.02781 | ||||||||
\(59\) | −310.728 | −0.685651 | −0.342825 | − | 0.939399i | \(-0.611384\pi\) | ||||
−0.342825 | + | 0.939399i | \(0.611384\pi\) | |||||||
\(60\) | 154.073 | 0.331512 | ||||||||
\(61\) | −365.247 | −0.766641 | −0.383321 | − | 0.923615i | \(-0.625220\pi\) | ||||
−0.383321 | + | 0.923615i | \(0.625220\pi\) | |||||||
\(62\) | 61.0397 | 0.125033 | ||||||||
\(63\) | 100.639 | 0.201258 | ||||||||
\(64\) | 291.115 | 0.568583 | ||||||||
\(65\) | 449.537 | 0.857819 | ||||||||
\(66\) | 233.699 | 0.435854 | ||||||||
\(67\) | −660.131 | −1.20370 | −0.601850 | − | 0.798609i | \(-0.705569\pi\) | ||||
−0.601850 | + | 0.798609i | \(0.705569\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −128.420 | −0.224056 | ||||||||
\(70\) | 161.156 | 0.275168 | ||||||||
\(71\) | 398.030 | 0.665316 | 0.332658 | − | 0.943047i | \(-0.392054\pi\) | ||||
0.332658 | + | 0.943047i | \(0.392054\pi\) | |||||||
\(72\) | −161.930 | −0.265051 | ||||||||
\(73\) | 643.443 | 1.03163 | 0.515817 | − | 0.856699i | \(-0.327489\pi\) | ||||
0.515817 | + | 0.856699i | \(0.327489\pi\) | |||||||
\(74\) | 610.344 | 0.958797 | ||||||||
\(75\) | 349.399 | 0.537934 | ||||||||
\(76\) | 405.859 | 0.612569 | ||||||||
\(77\) | −427.882 | −0.633269 | ||||||||
\(78\) | 500.296 | 0.726248 | ||||||||
\(79\) | −384.511 | −0.547605 | −0.273803 | − | 0.961786i | \(-0.588282\pi\) | ||||
−0.273803 | + | 0.961786i | \(0.588282\pi\) | |||||||
\(80\) | 18.0677 | 0.0252504 | ||||||||
\(81\) | −480.576 | −0.659226 | ||||||||
\(82\) | −55.8460 | −0.0752092 | ||||||||
\(83\) | −153.488 | −0.202983 | −0.101491 | − | 0.994836i | \(-0.532361\pi\) | ||||
−0.101491 | + | 0.994836i | \(0.532361\pi\) | |||||||
\(84\) | −313.946 | −0.407789 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 880.289 | 1.10377 | ||||||||
\(87\) | −1182.94 | −1.45776 | ||||||||
\(88\) | 688.475 | 0.833996 | ||||||||
\(89\) | −599.053 | −0.713477 | −0.356738 | − | 0.934204i | \(-0.616111\pi\) | ||||
−0.356738 | + | 0.934204i | \(0.616111\pi\) | |||||||
\(90\) | 84.2324 | 0.0986542 | ||||||||
\(91\) | −915.998 | −1.05519 | ||||||||
\(92\) | −147.134 | −0.166737 | ||||||||
\(93\) | 159.046 | 0.177336 | ||||||||
\(94\) | 359.175 | 0.394107 | ||||||||
\(95\) | −542.846 | −0.586261 | ||||||||
\(96\) | 813.838 | 0.865229 | ||||||||
\(97\) | 44.5693 | 0.0466529 | 0.0233265 | − | 0.999728i | \(-0.492574\pi\) | ||||
0.0233265 | + | 0.999728i | \(0.492574\pi\) | |||||||
\(98\) | 256.598 | 0.264492 | ||||||||
\(99\) | −223.645 | −0.227042 | ||||||||
\(100\) | 400.316 | 0.400316 | ||||||||
\(101\) | 1478.33 | 1.45643 | 0.728215 | − | 0.685348i | \(-0.240350\pi\) | ||||
0.728215 | + | 0.685348i | \(0.240350\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 618.133 | 0.591325 | 0.295662 | − | 0.955293i | \(-0.404460\pi\) | ||||
0.295662 | + | 0.955293i | \(0.404460\pi\) | |||||||
\(104\) | 1473.87 | 1.38966 | ||||||||
\(105\) | 419.909 | 0.390276 | ||||||||
\(106\) | −148.772 | −0.136321 | ||||||||
\(107\) | 138.979 | 0.125567 | 0.0627833 | − | 0.998027i | \(-0.480002\pi\) | ||||
0.0627833 | + | 0.998027i | \(0.480002\pi\) | |||||||
\(108\) | −774.969 | −0.690476 | ||||||||
\(109\) | 823.466 | 0.723612 | 0.361806 | − | 0.932253i | \(-0.382160\pi\) | ||||
0.361806 | + | 0.932253i | \(0.382160\pi\) | |||||||
\(110\) | −358.129 | −0.310420 | ||||||||
\(111\) | 1590.32 | 1.35988 | ||||||||
\(112\) | −36.8156 | −0.0310602 | ||||||||
\(113\) | −602.474 | −0.501558 | −0.250779 | − | 0.968044i | \(-0.580687\pi\) | ||||
−0.250779 | + | 0.968044i | \(0.580687\pi\) | |||||||
\(114\) | −604.140 | −0.496341 | ||||||||
\(115\) | 196.795 | 0.159576 | ||||||||
\(116\) | −1355.33 | −1.08482 | ||||||||
\(117\) | −478.772 | −0.378312 | ||||||||
\(118\) | 529.937 | 0.413430 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −675.646 | −0.513982 | ||||||||
\(121\) | −380.136 | −0.285602 | ||||||||
\(122\) | 622.917 | 0.462265 | ||||||||
\(123\) | −145.513 | −0.106671 | ||||||||
\(124\) | 182.223 | 0.131969 | ||||||||
\(125\) | −1386.66 | −0.992213 | ||||||||
\(126\) | −171.636 | −0.121354 | ||||||||
\(127\) | 1506.98 | 1.05294 | 0.526468 | − | 0.850195i | \(-0.323516\pi\) | ||||
0.526468 | + | 0.850195i | \(0.323516\pi\) | |||||||
\(128\) | 968.636 | 0.668876 | ||||||||
\(129\) | 2293.70 | 1.56549 | ||||||||
\(130\) | −766.671 | −0.517243 | ||||||||
\(131\) | −2783.58 | −1.85651 | −0.928254 | − | 0.371946i | \(-0.878691\pi\) | ||||
−0.928254 | + | 0.371946i | \(0.878691\pi\) | |||||||
\(132\) | 697.667 | 0.460032 | ||||||||
\(133\) | 1106.13 | 0.721154 | ||||||||
\(134\) | 1125.83 | 0.725799 | ||||||||
\(135\) | 1036.54 | 0.660822 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −629.783 | −0.392744 | −0.196372 | − | 0.980529i | \(-0.562916\pi\) | ||||
−0.196372 | + | 0.980529i | \(0.562916\pi\) | |||||||
\(138\) | 219.015 | 0.135100 | ||||||||
\(139\) | −2654.10 | −1.61955 | −0.809775 | − | 0.586740i | \(-0.800411\pi\) | ||||
−0.809775 | + | 0.586740i | \(0.800411\pi\) | |||||||
\(140\) | 481.102 | 0.290432 | ||||||||
\(141\) | 935.872 | 0.558969 | ||||||||
\(142\) | −678.827 | −0.401168 | ||||||||
\(143\) | 2035.58 | 1.19038 | ||||||||
\(144\) | −19.2427 | −0.0111358 | ||||||||
\(145\) | 1812.78 | 1.03823 | ||||||||
\(146\) | −1097.37 | −0.622048 | ||||||||
\(147\) | 668.595 | 0.375134 | ||||||||
\(148\) | 1822.08 | 1.01198 | ||||||||
\(149\) | −2216.30 | −1.21857 | −0.609283 | − | 0.792953i | \(-0.708543\pi\) | ||||
−0.609283 | + | 0.792953i | \(0.708543\pi\) | |||||||
\(150\) | −595.888 | −0.324360 | ||||||||
\(151\) | 2133.15 | 1.14963 | 0.574813 | − | 0.818285i | \(-0.305075\pi\) | ||||
0.574813 | + | 0.818285i | \(0.305075\pi\) | |||||||
\(152\) | −1779.79 | −0.949737 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 729.740 | 0.381845 | ||||||||
\(155\) | −243.728 | −0.126301 | ||||||||
\(156\) | 1493.55 | 0.766534 | ||||||||
\(157\) | −345.107 | −0.175430 | −0.0877152 | − | 0.996146i | \(-0.527957\pi\) | ||||
−0.0877152 | + | 0.996146i | \(0.527957\pi\) | |||||||
\(158\) | 655.770 | 0.330192 | ||||||||
\(159\) | −387.643 | −0.193346 | ||||||||
\(160\) | −1247.16 | −0.616227 | ||||||||
\(161\) | −400.998 | −0.196292 | ||||||||
\(162\) | 819.606 | 0.397496 | ||||||||
\(163\) | −678.526 | −0.326050 | −0.163025 | − | 0.986622i | \(-0.552125\pi\) | ||||
−0.163025 | + | 0.986622i | \(0.552125\pi\) | |||||||
\(164\) | −166.718 | −0.0793812 | ||||||||
\(165\) | −933.146 | −0.440275 | ||||||||
\(166\) | 261.770 | 0.122393 | ||||||||
\(167\) | −799.790 | −0.370596 | −0.185298 | − | 0.982682i | \(-0.559325\pi\) | ||||
−0.185298 | + | 0.982682i | \(0.559325\pi\) | |||||||
\(168\) | 1376.73 | 0.632243 | ||||||||
\(169\) | 2160.71 | 0.983483 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 578.148 | 0.258550 | ||||||||
\(172\) | 2627.95 | 1.16500 | ||||||||
\(173\) | 1885.48 | 0.828615 | 0.414307 | − | 0.910137i | \(-0.364024\pi\) | ||||
0.414307 | + | 0.910137i | \(0.364024\pi\) | |||||||
\(174\) | 2017.47 | 0.878989 | ||||||||
\(175\) | 1091.02 | 0.471276 | ||||||||
\(176\) | 81.8136 | 0.0350394 | ||||||||
\(177\) | 1380.81 | 0.586374 | ||||||||
\(178\) | 1021.66 | 0.430208 | ||||||||
\(179\) | −3588.86 | −1.49857 | −0.749286 | − | 0.662247i | \(-0.769603\pi\) | ||||
−0.749286 | + | 0.662247i | \(0.769603\pi\) | |||||||
\(180\) | 251.461 | 0.104127 | ||||||||
\(181\) | −461.347 | −0.189457 | −0.0947284 | − | 0.995503i | \(-0.530198\pi\) | ||||
−0.0947284 | + | 0.995503i | \(0.530198\pi\) | |||||||
\(182\) | 1562.20 | 0.636255 | ||||||||
\(183\) | 1623.08 | 0.655638 | ||||||||
\(184\) | 645.218 | 0.258511 | ||||||||
\(185\) | −2437.07 | −0.968522 | ||||||||
\(186\) | −271.248 | −0.106929 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 1072.26 | 0.415969 | ||||||||
\(189\) | −2112.10 | −0.812870 | ||||||||
\(190\) | 925.806 | 0.353500 | ||||||||
\(191\) | −4519.91 | −1.71230 | −0.856149 | − | 0.516728i | \(-0.827150\pi\) | ||||
−0.856149 | + | 0.516728i | \(0.827150\pi\) | |||||||
\(192\) | −1293.65 | −0.486257 | ||||||||
\(193\) | 2928.92 | 1.09238 | 0.546188 | − | 0.837663i | \(-0.316078\pi\) | ||||
0.546188 | + | 0.837663i | \(0.316078\pi\) | |||||||
\(194\) | −76.0116 | −0.0281305 | ||||||||
\(195\) | −1997.65 | −0.733614 | ||||||||
\(196\) | 766.027 | 0.279165 | ||||||||
\(197\) | −1926.13 | −0.696606 | −0.348303 | − | 0.937382i | \(-0.613242\pi\) | ||||
−0.348303 | + | 0.937382i | \(0.613242\pi\) | |||||||
\(198\) | 381.419 | 0.136900 | ||||||||
\(199\) | −3086.61 | −1.09952 | −0.549759 | − | 0.835323i | \(-0.685280\pi\) | ||||
−0.549759 | + | 0.835323i | \(0.685280\pi\) | |||||||
\(200\) | −1755.48 | −0.620656 | ||||||||
\(201\) | 2933.49 | 1.02941 | ||||||||
\(202\) | −2521.25 | −0.878190 | ||||||||
\(203\) | −3693.81 | −1.27712 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 222.990 | 0.0759721 | ||||||||
\(206\) | −1054.21 | −0.356553 | ||||||||
\(207\) | −209.593 | −0.0703754 | ||||||||
\(208\) | 175.144 | 0.0583849 | ||||||||
\(209\) | −2458.10 | −0.813541 | ||||||||
\(210\) | −716.142 | −0.235326 | ||||||||
\(211\) | −3602.40 | −1.17535 | −0.587676 | − | 0.809097i | \(-0.699957\pi\) | ||||
−0.587676 | + | 0.809097i | \(0.699957\pi\) | |||||||
\(212\) | −444.133 | −0.143883 | ||||||||
\(213\) | −1768.76 | −0.568984 | ||||||||
\(214\) | −237.024 | −0.0757133 | ||||||||
\(215\) | −3514.94 | −1.11496 | ||||||||
\(216\) | 3398.42 | 1.07053 | ||||||||
\(217\) | 496.631 | 0.155362 | ||||||||
\(218\) | −1404.39 | −0.436319 | ||||||||
\(219\) | −2859.33 | −0.882262 | ||||||||
\(220\) | −1069.13 | −0.327640 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | −2712.24 | −0.819972 | ||||||||
\(223\) | −1577.43 | −0.473688 | −0.236844 | − | 0.971548i | \(-0.576113\pi\) | ||||
−0.236844 | + | 0.971548i | \(0.576113\pi\) | |||||||
\(224\) | 2541.26 | 0.758014 | ||||||||
\(225\) | 570.252 | 0.168963 | ||||||||
\(226\) | 1027.50 | 0.302426 | ||||||||
\(227\) | 4292.90 | 1.25520 | 0.627599 | − | 0.778537i | \(-0.284038\pi\) | ||||
0.627599 | + | 0.778537i | \(0.284038\pi\) | |||||||
\(228\) | −1803.55 | −0.523874 | ||||||||
\(229\) | 580.893 | 0.167627 | 0.0838133 | − | 0.996481i | \(-0.473290\pi\) | ||||
0.0838133 | + | 0.996481i | \(0.473290\pi\) | |||||||
\(230\) | −335.627 | −0.0962200 | ||||||||
\(231\) | 1901.42 | 0.541577 | ||||||||
\(232\) | 5943.45 | 1.68193 | ||||||||
\(233\) | 671.778 | 0.188883 | 0.0944413 | − | 0.995530i | \(-0.469894\pi\) | ||||
0.0944413 | + | 0.995530i | \(0.469894\pi\) | |||||||
\(234\) | 816.530 | 0.228112 | ||||||||
\(235\) | −1434.16 | −0.398105 | ||||||||
\(236\) | 1582.04 | 0.436363 | ||||||||
\(237\) | 1708.69 | 0.468317 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −273.635 | −0.0740584 | −0.0370292 | − | 0.999314i | \(-0.511789\pi\) | ||||
−0.0370292 | + | 0.999314i | \(0.511789\pi\) | |||||||
\(240\) | −80.2891 | −0.0215943 | ||||||||
\(241\) | −6486.56 | −1.73376 | −0.866879 | − | 0.498518i | \(-0.833878\pi\) | ||||
−0.866879 | + | 0.498518i | \(0.833878\pi\) | |||||||
\(242\) | 648.310 | 0.172211 | ||||||||
\(243\) | −1974.14 | −0.521158 | ||||||||
\(244\) | 1859.61 | 0.487908 | ||||||||
\(245\) | −1024.58 | −0.267175 | ||||||||
\(246\) | 248.168 | 0.0643195 | ||||||||
\(247\) | −5262.22 | −1.35558 | ||||||||
\(248\) | −799.093 | −0.204607 | ||||||||
\(249\) | 682.071 | 0.173592 | ||||||||
\(250\) | 2364.90 | 0.598279 | ||||||||
\(251\) | −2527.58 | −0.635615 | −0.317808 | − | 0.948155i | \(-0.602947\pi\) | ||||
−0.317808 | + | 0.948155i | \(0.602947\pi\) | |||||||
\(252\) | −512.389 | −0.128085 | ||||||||
\(253\) | 891.120 | 0.221440 | ||||||||
\(254\) | −2570.11 | −0.634893 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −3980.89 | −0.971898 | ||||||||
\(257\) | 1702.44 | 0.413211 | 0.206605 | − | 0.978424i | \(-0.433758\pi\) | ||||
0.206605 | + | 0.978424i | \(0.433758\pi\) | |||||||
\(258\) | −3911.82 | −0.943952 | ||||||||
\(259\) | 4965.88 | 1.19137 | ||||||||
\(260\) | −2288.76 | −0.545935 | ||||||||
\(261\) | −1930.67 | −0.457877 | ||||||||
\(262\) | 4747.31 | 1.11943 | ||||||||
\(263\) | −4274.40 | −1.00217 | −0.501085 | − | 0.865398i | \(-0.667066\pi\) | ||||
−0.501085 | + | 0.865398i | \(0.667066\pi\) | |||||||
\(264\) | −3059.44 | −0.713241 | ||||||||
\(265\) | 594.038 | 0.137704 | ||||||||
\(266\) | −1886.46 | −0.434837 | ||||||||
\(267\) | 2662.07 | 0.610172 | ||||||||
\(268\) | 3360.98 | 0.766061 | ||||||||
\(269\) | 7996.34 | 1.81244 | 0.906218 | − | 0.422810i | \(-0.138956\pi\) | ||||
0.906218 | + | 0.422810i | \(0.138956\pi\) | |||||||
\(270\) | −1767.78 | −0.398458 | ||||||||
\(271\) | 474.268 | 0.106309 | 0.0531545 | − | 0.998586i | \(-0.483072\pi\) | ||||
0.0531545 | + | 0.998586i | \(0.483072\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 4070.51 | 0.902411 | ||||||||
\(274\) | 1074.07 | 0.236815 | ||||||||
\(275\) | −2424.52 | −0.531652 | ||||||||
\(276\) | 653.833 | 0.142595 | ||||||||
\(277\) | −2826.25 | −0.613043 | −0.306521 | − | 0.951864i | \(-0.599165\pi\) | ||||
−0.306521 | + | 0.951864i | \(0.599165\pi\) | |||||||
\(278\) | 4526.48 | 0.976547 | ||||||||
\(279\) | 259.578 | 0.0557008 | ||||||||
\(280\) | −2109.75 | −0.450291 | ||||||||
\(281\) | −2498.15 | −0.530346 | −0.265173 | − | 0.964201i | \(-0.585429\pi\) | ||||
−0.265173 | + | 0.964201i | \(0.585429\pi\) | |||||||
\(282\) | −1596.10 | −0.337044 | ||||||||
\(283\) | 2417.07 | 0.507704 | 0.253852 | − | 0.967243i | \(-0.418302\pi\) | ||||
0.253852 | + | 0.967243i | \(0.418302\pi\) | |||||||
\(284\) | −2026.52 | −0.423422 | ||||||||
\(285\) | 2412.29 | 0.501375 | ||||||||
\(286\) | −3471.62 | −0.717766 | ||||||||
\(287\) | −454.374 | −0.0934524 | ||||||||
\(288\) | 1328.26 | 0.271766 | ||||||||
\(289\) | 0 | 0 | ||||||||
\(290\) | −3091.65 | −0.626027 | ||||||||
\(291\) | −198.057 | −0.0398980 | ||||||||
\(292\) | −3276.01 | −0.656555 | ||||||||
\(293\) | 6652.17 | 1.32636 | 0.663181 | − | 0.748459i | \(-0.269206\pi\) | ||||
0.663181 | + | 0.748459i | \(0.269206\pi\) | |||||||
\(294\) | −1140.27 | −0.226196 | ||||||||
\(295\) | −2116.01 | −0.417623 | ||||||||
\(296\) | −7990.24 | −1.56900 | ||||||||
\(297\) | 4693.62 | 0.917008 | ||||||||
\(298\) | 3779.83 | 0.734764 | ||||||||
\(299\) | 1907.68 | 0.368977 | ||||||||
\(300\) | −1778.92 | −0.342353 | ||||||||
\(301\) | 7162.21 | 1.37150 | ||||||||
\(302\) | −3638.02 | −0.693194 | ||||||||
\(303\) | −6569.40 | −1.24555 | ||||||||
\(304\) | −211.498 | −0.0399021 | ||||||||
\(305\) | −2487.27 | −0.466954 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −2511.18 | −0.466842 | −0.233421 | − | 0.972376i | \(-0.574992\pi\) | ||||
−0.233421 | + | 0.972376i | \(0.574992\pi\) | |||||||
\(308\) | 2178.51 | 0.403027 | ||||||||
\(309\) | −2746.85 | −0.505706 | ||||||||
\(310\) | 415.670 | 0.0761563 | ||||||||
\(311\) | 3585.10 | 0.653674 | 0.326837 | − | 0.945081i | \(-0.394017\pi\) | ||||
0.326837 | + | 0.945081i | \(0.394017\pi\) | |||||||
\(312\) | −6549.56 | −1.18845 | ||||||||
\(313\) | −2612.32 | −0.471747 | −0.235874 | − | 0.971784i | \(-0.575795\pi\) | ||||
−0.235874 | + | 0.971784i | \(0.575795\pi\) | |||||||
\(314\) | 588.570 | 0.105780 | ||||||||
\(315\) | 685.332 | 0.122584 | ||||||||
\(316\) | 1957.69 | 0.348508 | ||||||||
\(317\) | −3903.80 | −0.691669 | −0.345834 | − | 0.938296i | \(-0.612404\pi\) | ||||
−0.345834 | + | 0.938296i | \(0.612404\pi\) | |||||||
\(318\) | 661.112 | 0.116583 | ||||||||
\(319\) | 8208.60 | 1.44073 | ||||||||
\(320\) | 1982.44 | 0.346318 | ||||||||
\(321\) | −617.594 | −0.107386 | ||||||||
\(322\) | 683.890 | 0.118359 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 2446.79 | 0.419546 | ||||||||
\(325\) | −5190.35 | −0.885873 | ||||||||
\(326\) | 1157.20 | 0.196600 | ||||||||
\(327\) | −3659.31 | −0.618839 | ||||||||
\(328\) | 731.101 | 0.123074 | ||||||||
\(329\) | 2922.32 | 0.489704 | ||||||||
\(330\) | 1591.45 | 0.265474 | ||||||||
\(331\) | −6236.03 | −1.03554 | −0.517769 | − | 0.855520i | \(-0.673237\pi\) | ||||
−0.517769 | + | 0.855520i | \(0.673237\pi\) | |||||||
\(332\) | 781.468 | 0.129183 | ||||||||
\(333\) | 2595.55 | 0.427134 | ||||||||
\(334\) | 1364.02 | 0.223460 | ||||||||
\(335\) | −4495.38 | −0.733161 | ||||||||
\(336\) | 163.601 | 0.0265630 | ||||||||
\(337\) | 3842.08 | 0.621043 | 0.310521 | − | 0.950566i | \(-0.399496\pi\) | ||||
0.310521 | + | 0.950566i | \(0.399496\pi\) | |||||||
\(338\) | −3685.02 | −0.593014 | ||||||||
\(339\) | 2677.27 | 0.428936 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −1103.64 | −0.175265 | ||||||||
\(342\) | −986.014 | −0.155899 | ||||||||
\(343\) | 6847.21 | 1.07788 | ||||||||
\(344\) | −11524.2 | −1.80623 | ||||||||
\(345\) | −874.516 | −0.136471 | ||||||||
\(346\) | −3215.62 | −0.499633 | ||||||||
\(347\) | 8301.86 | 1.28434 | 0.642172 | − | 0.766561i | \(-0.278034\pi\) | ||||
0.642172 | + | 0.766561i | \(0.278034\pi\) | |||||||
\(348\) | 6022.81 | 0.927748 | ||||||||
\(349\) | 4929.17 | 0.756024 | 0.378012 | − | 0.925801i | \(-0.376608\pi\) | ||||
0.378012 | + | 0.925801i | \(0.376608\pi\) | |||||||
\(350\) | −1860.70 | −0.284167 | ||||||||
\(351\) | 10048.0 | 1.52798 | ||||||||
\(352\) | −5647.33 | −0.855124 | ||||||||
\(353\) | −9607.54 | −1.44861 | −0.724303 | − | 0.689482i | \(-0.757838\pi\) | ||||
−0.724303 | + | 0.689482i | \(0.757838\pi\) | |||||||
\(354\) | −2354.93 | −0.353568 | ||||||||
\(355\) | 2710.52 | 0.405237 | ||||||||
\(356\) | 3050.00 | 0.454073 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 6120.69 | 0.903600 | ||||||||
\(359\) | −1962.76 | −0.288553 | −0.144277 | − | 0.989537i | \(-0.546085\pi\) | ||||
−0.144277 | + | 0.989537i | \(0.546085\pi\) | |||||||
\(360\) | −1102.72 | −0.161440 | ||||||||
\(361\) | −504.522 | −0.0735561 | ||||||||
\(362\) | 786.813 | 0.114238 | ||||||||
\(363\) | 1689.25 | 0.244249 | ||||||||
\(364\) | 4663.69 | 0.671549 | ||||||||
\(365\) | 4381.74 | 0.628358 | ||||||||
\(366\) | −2768.12 | −0.395333 | ||||||||
\(367\) | 3458.29 | 0.491883 | 0.245941 | − | 0.969285i | \(-0.420903\pi\) | ||||
0.245941 | + | 0.969285i | \(0.420903\pi\) | |||||||
\(368\) | 76.6732 | 0.0108610 | ||||||||
\(369\) | −237.491 | −0.0335049 | ||||||||
\(370\) | 4156.34 | 0.583994 | ||||||||
\(371\) | −1210.44 | −0.169388 | ||||||||
\(372\) | −809.763 | −0.112861 | ||||||||
\(373\) | 2661.22 | 0.369418 | 0.184709 | − | 0.982793i | \(-0.440866\pi\) | ||||
0.184709 | + | 0.982793i | \(0.440866\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 6162.03 | 0.848549 | ||||||||
\(376\) | −4702.10 | −0.644926 | ||||||||
\(377\) | 17572.7 | 2.40064 | ||||||||
\(378\) | 3602.11 | 0.490140 | ||||||||
\(379\) | 5583.03 | 0.756677 | 0.378339 | − | 0.925667i | \(-0.376495\pi\) | ||||
0.378339 | + | 0.925667i | \(0.376495\pi\) | |||||||
\(380\) | 2763.83 | 0.373110 | ||||||||
\(381\) | −6696.71 | −0.900480 | ||||||||
\(382\) | 7708.56 | 1.03247 | ||||||||
\(383\) | 7832.13 | 1.04492 | 0.522459 | − | 0.852665i | \(-0.325015\pi\) | ||||
0.522459 | + | 0.852665i | \(0.325015\pi\) | |||||||
\(384\) | −4304.42 | −0.572029 | ||||||||
\(385\) | −2913.81 | −0.385718 | ||||||||
\(386\) | −4995.18 | −0.658674 | ||||||||
\(387\) | 3743.53 | 0.491717 | ||||||||
\(388\) | −226.919 | −0.0296910 | ||||||||
\(389\) | 7432.95 | 0.968807 | 0.484403 | − | 0.874845i | \(-0.339037\pi\) | ||||
0.484403 | + | 0.874845i | \(0.339037\pi\) | |||||||
\(390\) | 3406.93 | 0.442350 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | −3359.22 | −0.432821 | ||||||||
\(393\) | 12369.7 | 1.58770 | ||||||||
\(394\) | 3284.96 | 0.420035 | ||||||||
\(395\) | −2618.45 | −0.333541 | ||||||||
\(396\) | 1138.66 | 0.144494 | ||||||||
\(397\) | −9540.26 | −1.20608 | −0.603038 | − | 0.797713i | \(-0.706043\pi\) | ||||
−0.603038 | + | 0.797713i | \(0.706043\pi\) | |||||||
\(398\) | 5264.12 | 0.662981 | ||||||||
\(399\) | −4915.40 | −0.616737 | ||||||||
\(400\) | −208.609 | −0.0260761 | ||||||||
\(401\) | −8663.30 | −1.07886 | −0.539432 | − | 0.842029i | \(-0.681361\pi\) | ||||
−0.539432 | + | 0.842029i | \(0.681361\pi\) | |||||||
\(402\) | −5002.97 | −0.620710 | ||||||||
\(403\) | −2362.64 | −0.292039 | ||||||||
\(404\) | −7526.75 | −0.926905 | ||||||||
\(405\) | −3272.64 | −0.401528 | ||||||||
\(406\) | 6299.68 | 0.770069 | ||||||||
\(407\) | −11035.4 | −1.34400 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 5279.17 | 0.638235 | 0.319117 | − | 0.947715i | \(-0.396614\pi\) | ||||
0.319117 | + | 0.947715i | \(0.396614\pi\) | |||||||
\(410\) | −380.302 | −0.0458092 | ||||||||
\(411\) | 2798.62 | 0.335878 | ||||||||
\(412\) | −3147.15 | −0.376332 | ||||||||
\(413\) | 4311.68 | 0.513714 | ||||||||
\(414\) | 357.454 | 0.0424346 | ||||||||
\(415\) | −1045.23 | −0.123635 | ||||||||
\(416\) | −12089.6 | −1.42486 | ||||||||
\(417\) | 11794.3 | 1.38505 | ||||||||
\(418\) | 4192.21 | 0.490544 | ||||||||
\(419\) | −9408.24 | −1.09695 | −0.548476 | − | 0.836166i | \(-0.684792\pi\) | ||||
−0.548476 | + | 0.836166i | \(0.684792\pi\) | |||||||
\(420\) | −2137.92 | −0.248380 | ||||||||
\(421\) | −8191.97 | −0.948343 | −0.474171 | − | 0.880433i | \(-0.657252\pi\) | ||||
−0.474171 | + | 0.880433i | \(0.657252\pi\) | |||||||
\(422\) | 6143.77 | 0.708706 | ||||||||
\(423\) | 1527.43 | 0.175570 | ||||||||
\(424\) | 1947.63 | 0.223079 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 3016.57 | 0.343083 | ||||||||
\(427\) | 5068.18 | 0.574395 | ||||||||
\(428\) | −707.595 | −0.0799133 | ||||||||
\(429\) | −9045.70 | −1.01802 | ||||||||
\(430\) | 5994.62 | 0.672294 | ||||||||
\(431\) | −1950.29 | −0.217964 | −0.108982 | − | 0.994044i | \(-0.534759\pi\) | ||||
−0.108982 | + | 0.994044i | \(0.534759\pi\) | |||||||
\(432\) | 403.845 | 0.0449769 | ||||||||
\(433\) | 11152.3 | 1.23775 | 0.618876 | − | 0.785489i | \(-0.287588\pi\) | ||||
0.618876 | + | 0.785489i | \(0.287588\pi\) | |||||||
\(434\) | −846.988 | −0.0936791 | ||||||||
\(435\) | −8055.64 | −0.887905 | ||||||||
\(436\) | −4192.58 | −0.460523 | ||||||||
\(437\) | −2303.65 | −0.252171 | ||||||||
\(438\) | 4876.49 | 0.531981 | ||||||||
\(439\) | −470.158 | −0.0511149 | −0.0255574 | − | 0.999673i | \(-0.508136\pi\) | ||||
−0.0255574 | + | 0.999673i | \(0.508136\pi\) | |||||||
\(440\) | 4688.40 | 0.507979 | ||||||||
\(441\) | 1091.21 | 0.117829 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −13132.9 | −1.40849 | −0.704246 | − | 0.709956i | \(-0.748715\pi\) | ||||
−0.704246 | + | 0.709956i | \(0.748715\pi\) | |||||||
\(444\) | −8096.93 | −0.865457 | ||||||||
\(445\) | −4079.45 | −0.434572 | ||||||||
\(446\) | 2690.25 | 0.285621 | ||||||||
\(447\) | 9848.78 | 1.04213 | ||||||||
\(448\) | −4039.51 | −0.426002 | ||||||||
\(449\) | 10433.0 | 1.09658 | 0.548291 | − | 0.836288i | \(-0.315279\pi\) | ||||
0.548291 | + | 0.836288i | \(0.315279\pi\) | |||||||
\(450\) | −972.546 | −0.101881 | ||||||||
\(451\) | 1009.73 | 0.105425 | ||||||||
\(452\) | 3067.43 | 0.319203 | ||||||||
\(453\) | −9479.28 | −0.983169 | ||||||||
\(454\) | −7321.40 | −0.756851 | ||||||||
\(455\) | −6237.79 | −0.642708 | ||||||||
\(456\) | 7909.02 | 0.812224 | ||||||||
\(457\) | −253.385 | −0.0259362 | −0.0129681 | − | 0.999916i | \(-0.504128\pi\) | ||||
−0.0129681 | + | 0.999916i | \(0.504128\pi\) | |||||||
\(458\) | −990.694 | −0.101074 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −1001.96 | −0.101558 | ||||||||
\(461\) | 15560.2 | 1.57204 | 0.786019 | − | 0.618202i | \(-0.212139\pi\) | ||||
0.786019 | + | 0.618202i | \(0.212139\pi\) | |||||||
\(462\) | −3242.81 | −0.326557 | ||||||||
\(463\) | 10727.9 | 1.07682 | 0.538409 | − | 0.842684i | \(-0.319026\pi\) | ||||
0.538409 | + | 0.842684i | \(0.319026\pi\) | |||||||
\(464\) | 706.279 | 0.0706641 | ||||||||
\(465\) | 1083.08 | 0.108014 | ||||||||
\(466\) | −1145.70 | −0.113891 | ||||||||
\(467\) | −1960.48 | −0.194262 | −0.0971308 | − | 0.995272i | \(-0.530967\pi\) | ||||
−0.0971308 | + | 0.995272i | \(0.530967\pi\) | |||||||
\(468\) | 2437.61 | 0.240766 | ||||||||
\(469\) | 9160.00 | 0.901854 | ||||||||
\(470\) | 2445.92 | 0.240047 | ||||||||
\(471\) | 1533.59 | 0.150030 | ||||||||
\(472\) | −6937.61 | −0.676545 | ||||||||
\(473\) | −15916.3 | −1.54721 | ||||||||
\(474\) | −2914.11 | −0.282383 | ||||||||
\(475\) | 6267.68 | 0.605434 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −632.670 | −0.0607295 | ||||||||
\(478\) | 466.675 | 0.0446553 | ||||||||
\(479\) | 4294.19 | 0.409617 | 0.204808 | − | 0.978802i | \(-0.434343\pi\) | ||||
0.204808 | + | 0.978802i | \(0.434343\pi\) | |||||||
\(480\) | 5542.10 | 0.527002 | ||||||||
\(481\) | −23624.4 | −2.23946 | ||||||||
\(482\) | 11062.6 | 1.04541 | ||||||||
\(483\) | 1781.95 | 0.167871 | ||||||||
\(484\) | 1935.42 | 0.181764 | ||||||||
\(485\) | 303.510 | 0.0284158 | ||||||||
\(486\) | 3366.84 | 0.314244 | ||||||||
\(487\) | 18013.5 | 1.67612 | 0.838060 | − | 0.545578i | \(-0.183690\pi\) | ||||
0.838060 | + | 0.545578i | \(0.183690\pi\) | |||||||
\(488\) | −8154.85 | −0.756460 | ||||||||
\(489\) | 3015.23 | 0.278841 | ||||||||
\(490\) | 1747.39 | 0.161100 | ||||||||
\(491\) | 13733.2 | 1.26226 | 0.631129 | − | 0.775678i | \(-0.282592\pi\) | ||||
0.631129 | + | 0.775678i | \(0.282592\pi\) | |||||||
\(492\) | 740.862 | 0.0678875 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 8974.55 | 0.817377 | ||||||||
\(495\) | −1522.98 | −0.138289 | ||||||||
\(496\) | −94.9587 | −0.00859632 | ||||||||
\(497\) | −5523.07 | −0.498478 | ||||||||
\(498\) | −1163.25 | −0.104672 | ||||||||
\(499\) | −7747.71 | −0.695060 | −0.347530 | − | 0.937669i | \(-0.612980\pi\) | ||||
−0.347530 | + | 0.937669i | \(0.612980\pi\) | |||||||
\(500\) | 7060.01 | 0.631467 | ||||||||
\(501\) | 3554.10 | 0.316937 | ||||||||
\(502\) | 4310.71 | 0.383259 | ||||||||
\(503\) | −19203.7 | −1.70229 | −0.851143 | − | 0.524934i | \(-0.824090\pi\) | ||||
−0.851143 | + | 0.524934i | \(0.824090\pi\) | |||||||
\(504\) | 2246.95 | 0.198586 | ||||||||
\(505\) | 10067.2 | 0.887098 | ||||||||
\(506\) | −1519.78 | −0.133522 | ||||||||
\(507\) | −9601.76 | −0.841083 | ||||||||
\(508\) | −7672.61 | −0.670112 | ||||||||
\(509\) | 151.325 | 0.0131775 | 0.00658876 | − | 0.999978i | \(-0.497903\pi\) | ||||
0.00658876 | + | 0.999978i | \(0.497903\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −8928.43 | −0.772936 | ||||||||
\(512\) | −959.802 | −0.0828470 | ||||||||
\(513\) | −12133.6 | −1.04427 | ||||||||
\(514\) | −2903.45 | −0.249155 | ||||||||
\(515\) | 4209.38 | 0.360170 | ||||||||
\(516\) | −11678.1 | −0.996315 | ||||||||
\(517\) | −6494.14 | −0.552441 | ||||||||
\(518\) | −8469.15 | −0.718365 | ||||||||
\(519\) | −8378.68 | −0.708638 | ||||||||
\(520\) | 10036.8 | 0.846427 | ||||||||
\(521\) | 8548.62 | 0.718852 | 0.359426 | − | 0.933174i | \(-0.382973\pi\) | ||||
0.359426 | + | 0.933174i | \(0.382973\pi\) | |||||||
\(522\) | 3292.70 | 0.276088 | ||||||||
\(523\) | 17874.0 | 1.49441 | 0.747205 | − | 0.664593i | \(-0.231395\pi\) | ||||
0.747205 | + | 0.664593i | \(0.231395\pi\) | |||||||
\(524\) | 14172.3 | 1.18152 | ||||||||
\(525\) | −4848.26 | −0.403039 | ||||||||
\(526\) | 7289.85 | 0.604283 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | −363.563 | −0.0299660 | ||||||||
\(529\) | −11331.9 | −0.931361 | ||||||||
\(530\) | −1013.11 | −0.0830317 | ||||||||
\(531\) | 2253.62 | 0.184178 | ||||||||
\(532\) | −5631.71 | −0.458958 | ||||||||
\(533\) | 2161.61 | 0.175666 | ||||||||
\(534\) | −4540.07 | −0.367918 | ||||||||
\(535\) | 946.425 | 0.0764813 | ||||||||
\(536\) | −14738.7 | −1.18771 | ||||||||
\(537\) | 15948.2 | 1.28159 | ||||||||
\(538\) | −13637.5 | −1.09285 | ||||||||
\(539\) | −4639.47 | −0.370753 | ||||||||
\(540\) | −5277.41 | −0.420562 | ||||||||
\(541\) | −2122.24 | −0.168655 | −0.0843273 | − | 0.996438i | \(-0.526874\pi\) | ||||
−0.0843273 | + | 0.996438i | \(0.526874\pi\) | |||||||
\(542\) | −808.849 | −0.0641015 | ||||||||
\(543\) | 2050.13 | 0.162025 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 5607.67 | 0.440745 | ||||||||
\(546\) | −6942.12 | −0.544130 | ||||||||
\(547\) | −284.066 | −0.0222044 | −0.0111022 | − | 0.999938i | \(-0.503534\pi\) | ||||
−0.0111022 | + | 0.999938i | \(0.503534\pi\) | |||||||
\(548\) | 3206.46 | 0.249951 | ||||||||
\(549\) | 2649.03 | 0.205934 | ||||||||
\(550\) | 4134.95 | 0.320572 | ||||||||
\(551\) | −21220.2 | −1.64067 | ||||||||
\(552\) | −2867.21 | −0.221081 | ||||||||
\(553\) | 5335.48 | 0.410285 | ||||||||
\(554\) | 4820.08 | 0.369649 | ||||||||
\(555\) | 10829.8 | 0.828289 | ||||||||
\(556\) | 13513.0 | 1.03072 | ||||||||
\(557\) | 9915.36 | 0.754268 | 0.377134 | − | 0.926159i | \(-0.376910\pi\) | ||||
0.377134 | + | 0.926159i | \(0.376910\pi\) | |||||||
\(558\) | −442.702 | −0.0335862 | ||||||||
\(559\) | −34073.1 | −2.57806 | ||||||||
\(560\) | −250.708 | −0.0189185 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 4260.52 | 0.319785 | ||||||||
\(563\) | −5048.52 | −0.377922 | −0.188961 | − | 0.981985i | \(-0.560512\pi\) | ||||
−0.188961 | + | 0.981985i | \(0.560512\pi\) | |||||||
\(564\) | −4764.88 | −0.355741 | ||||||||
\(565\) | −4102.75 | −0.305494 | ||||||||
\(566\) | −4122.24 | −0.306132 | ||||||||
\(567\) | 6668.48 | 0.493915 | ||||||||
\(568\) | 8886.78 | 0.656481 | ||||||||
\(569\) | 10964.5 | 0.807828 | 0.403914 | − | 0.914797i | \(-0.367650\pi\) | ||||
0.403914 | + | 0.914797i | \(0.367650\pi\) | |||||||
\(570\) | −4114.09 | −0.302316 | ||||||||
\(571\) | −6757.57 | −0.495263 | −0.247632 | − | 0.968854i | \(-0.579652\pi\) | ||||
−0.247632 | + | 0.968854i | \(0.579652\pi\) | |||||||
\(572\) | −10363.9 | −0.757582 | ||||||||
\(573\) | 20085.5 | 1.46437 | ||||||||
\(574\) | 774.920 | 0.0563494 | ||||||||
\(575\) | −2272.19 | −0.164794 | ||||||||
\(576\) | −2111.36 | −0.152732 | ||||||||
\(577\) | −18050.9 | −1.30237 | −0.651187 | − | 0.758917i | \(-0.725729\pi\) | ||||
−0.651187 | + | 0.758917i | \(0.725729\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −13015.5 | −0.934209 | ||||||||
\(580\) | −9229.57 | −0.660754 | ||||||||
\(581\) | 2129.81 | 0.152082 | ||||||||
\(582\) | 337.780 | 0.0240574 | ||||||||
\(583\) | 2689.90 | 0.191088 | ||||||||
\(584\) | 14366.1 | 1.01793 | ||||||||
\(585\) | −3260.36 | −0.230426 | ||||||||
\(586\) | −11345.1 | −0.799762 | ||||||||
\(587\) | −7447.06 | −0.523634 | −0.261817 | − | 0.965118i | \(-0.584322\pi\) | ||||
−0.261817 | + | 0.965118i | \(0.584322\pi\) | |||||||
\(588\) | −3404.07 | −0.238744 | ||||||||
\(589\) | 2853.04 | 0.199589 | ||||||||
\(590\) | 3608.78 | 0.251816 | ||||||||
\(591\) | 8559.34 | 0.595743 | ||||||||
\(592\) | −949.505 | −0.0659196 | ||||||||
\(593\) | −1229.32 | −0.0851298 | −0.0425649 | − | 0.999094i | \(-0.513553\pi\) | ||||
−0.0425649 | + | 0.999094i | \(0.513553\pi\) | |||||||
\(594\) | −8004.82 | −0.552932 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 11284.0 | 0.775523 | ||||||||
\(597\) | 13716.3 | 0.940317 | ||||||||
\(598\) | −3253.49 | −0.222484 | ||||||||
\(599\) | 10655.6 | 0.726840 | 0.363420 | − | 0.931625i | \(-0.381609\pi\) | ||||
0.363420 | + | 0.931625i | \(0.381609\pi\) | |||||||
\(600\) | 7800.99 | 0.530790 | ||||||||
\(601\) | −2134.49 | −0.144871 | −0.0724356 | − | 0.997373i | \(-0.523077\pi\) | ||||
−0.0724356 | + | 0.997373i | \(0.523077\pi\) | |||||||
\(602\) | −12214.9 | −0.826982 | ||||||||
\(603\) | 4787.73 | 0.323336 | ||||||||
\(604\) | −10860.7 | −0.731647 | ||||||||
\(605\) | −2588.67 | −0.173957 | ||||||||
\(606\) | 11203.9 | 0.751036 | ||||||||
\(607\) | 12364.9 | 0.826812 | 0.413406 | − | 0.910547i | \(-0.364339\pi\) | ||||
0.413406 | + | 0.910547i | \(0.364339\pi\) | |||||||
\(608\) | 14599.0 | 0.973797 | ||||||||
\(609\) | 16414.5 | 1.09220 | ||||||||
\(610\) | 4241.96 | 0.281561 | ||||||||
\(611\) | −13902.5 | −0.920513 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 4888.87 | 0.322120 | 0.161060 | − | 0.986945i | \(-0.448509\pi\) | ||||
0.161060 | + | 0.986945i | \(0.448509\pi\) | |||||||
\(614\) | 4282.73 | 0.281493 | ||||||||
\(615\) | −990.920 | −0.0649720 | ||||||||
\(616\) | −9553.30 | −0.624859 | ||||||||
\(617\) | −24750.0 | −1.61491 | −0.807453 | − | 0.589932i | \(-0.799155\pi\) | ||||
−0.807453 | + | 0.589932i | \(0.799155\pi\) | |||||||
\(618\) | 4684.67 | 0.304927 | ||||||||
\(619\) | −10794.8 | −0.700937 | −0.350469 | − | 0.936574i | \(-0.613978\pi\) | ||||
−0.350469 | + | 0.936574i | \(0.613978\pi\) | |||||||
\(620\) | 1240.91 | 0.0803809 | ||||||||
\(621\) | 4398.72 | 0.284242 | ||||||||
\(622\) | −6114.28 | −0.394148 | ||||||||
\(623\) | 8312.47 | 0.534562 | ||||||||
\(624\) | −778.304 | −0.0499313 | ||||||||
\(625\) | 385.346 | 0.0246621 | ||||||||
\(626\) | 4455.22 | 0.284451 | ||||||||
\(627\) | 10923.3 | 0.695748 | ||||||||
\(628\) | 1757.07 | 0.111648 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | −1168.81 | −0.0739152 | ||||||||
\(631\) | −7579.90 | −0.478211 | −0.239106 | − | 0.970994i | \(-0.576854\pi\) | ||||
−0.239106 | + | 0.970994i | \(0.576854\pi\) | |||||||
\(632\) | −8584.94 | −0.540333 | ||||||||
\(633\) | 16008.3 | 1.00517 | ||||||||
\(634\) | 6657.80 | 0.417058 | ||||||||
\(635\) | 10262.3 | 0.641333 | ||||||||
\(636\) | 1973.64 | 0.123050 | ||||||||
\(637\) | −9932.03 | −0.617773 | ||||||||
\(638\) | −13999.5 | −0.868723 | ||||||||
\(639\) | −2886.79 | −0.178716 | ||||||||
\(640\) | 6596.25 | 0.407406 | ||||||||
\(641\) | 3181.53 | 0.196042 | 0.0980208 | − | 0.995184i | \(-0.468749\pi\) | ||||
0.0980208 | + | 0.995184i | \(0.468749\pi\) | |||||||
\(642\) | 1053.29 | 0.0647507 | ||||||||
\(643\) | −10552.8 | −0.647219 | −0.323609 | − | 0.946191i | \(-0.604896\pi\) | ||||
−0.323609 | + | 0.946191i | \(0.604896\pi\) | |||||||
\(644\) | 2041.63 | 0.124925 | ||||||||
\(645\) | 15619.7 | 0.953526 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −10952.0 | −0.665483 | −0.332742 | − | 0.943018i | \(-0.607974\pi\) | ||||
−0.332742 | + | 0.943018i | \(0.607974\pi\) | |||||||
\(648\) | −10729.8 | −0.650471 | ||||||||
\(649\) | −9581.64 | −0.579526 | ||||||||
\(650\) | 8851.97 | 0.534158 | ||||||||
\(651\) | −2206.93 | −0.132867 | ||||||||
\(652\) | 3454.63 | 0.207506 | ||||||||
\(653\) | 6526.76 | 0.391136 | 0.195568 | − | 0.980690i | \(-0.437345\pi\) | ||||
0.195568 | + | 0.980690i | \(0.437345\pi\) | |||||||
\(654\) | 6240.84 | 0.373144 | ||||||||
\(655\) | −18955.7 | −1.13078 | ||||||||
\(656\) | 86.8789 | 0.00517081 | ||||||||
\(657\) | −4666.69 | −0.277116 | ||||||||
\(658\) | −4983.92 | −0.295279 | ||||||||
\(659\) | −25717.9 | −1.52022 | −0.760111 | − | 0.649793i | \(-0.774855\pi\) | ||||
−0.760111 | + | 0.649793i | \(0.774855\pi\) | |||||||
\(660\) | 4751.00 | 0.280201 | ||||||||
\(661\) | 11808.9 | 0.694878 | 0.347439 | − | 0.937703i | \(-0.387051\pi\) | ||||
0.347439 | + | 0.937703i | \(0.387051\pi\) | |||||||
\(662\) | 10635.3 | 0.624403 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −3426.93 | −0.200287 | ||||||||
\(665\) | 7532.54 | 0.439247 | ||||||||
\(666\) | −4426.64 | −0.257550 | ||||||||
\(667\) | 7692.85 | 0.446579 | ||||||||
\(668\) | 4072.03 | 0.235856 | ||||||||
\(669\) | 7009.76 | 0.405102 | ||||||||
\(670\) | 7666.73 | 0.442077 | ||||||||
\(671\) | −11262.8 | −0.647981 | ||||||||
\(672\) | −11292.8 | −0.648260 | ||||||||
\(673\) | 6282.85 | 0.359860 | 0.179930 | − | 0.983679i | \(-0.442413\pi\) | ||||
0.179930 | + | 0.983679i | \(0.442413\pi\) | |||||||
\(674\) | −6552.54 | −0.374472 | ||||||||
\(675\) | −11967.8 | −0.682433 | ||||||||
\(676\) | −11001.0 | −0.625910 | ||||||||
\(677\) | 18502.8 | 1.05040 | 0.525200 | − | 0.850979i | \(-0.323991\pi\) | ||||
0.525200 | + | 0.850979i | \(0.323991\pi\) | |||||||
\(678\) | −4566.00 | −0.258638 | ||||||||
\(679\) | −618.446 | −0.0349540 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −19076.8 | −1.07346 | ||||||||
\(682\) | 1882.22 | 0.105680 | ||||||||
\(683\) | −137.518 | −0.00770424 | −0.00385212 | − | 0.999993i | \(-0.501226\pi\) | ||||
−0.00385212 | + | 0.999993i | \(0.501226\pi\) | |||||||
\(684\) | −2943.57 | −0.164547 | ||||||||
\(685\) | −4288.71 | −0.239217 | ||||||||
\(686\) | −11677.7 | −0.649936 | ||||||||
\(687\) | −2581.37 | −0.143356 | ||||||||
\(688\) | −1369.46 | −0.0758867 | ||||||||
\(689\) | 5758.47 | 0.318404 | ||||||||
\(690\) | 1491.46 | 0.0822882 | ||||||||
\(691\) | −303.235 | −0.0166940 | −0.00834702 | − | 0.999965i | \(-0.502657\pi\) | ||||
−0.00834702 | + | 0.999965i | \(0.502657\pi\) | |||||||
\(692\) | −9599.69 | −0.527349 | ||||||||
\(693\) | 3103.30 | 0.170108 | ||||||||
\(694\) | −14158.6 | −0.774426 | ||||||||
\(695\) | −18074.0 | −0.986452 | ||||||||
\(696\) | −26411.5 | −1.43840 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | −8406.54 | −0.455863 | ||||||||
\(699\) | −2985.24 | −0.161534 | ||||||||
\(700\) | −5554.79 | −0.299931 | ||||||||
\(701\) | −23434.3 | −1.26263 | −0.631313 | − | 0.775528i | \(-0.717484\pi\) | ||||
−0.631313 | + | 0.775528i | \(0.717484\pi\) | |||||||
\(702\) | −17136.5 | −0.921331 | ||||||||
\(703\) | 28528.0 | 1.53052 | ||||||||
\(704\) | 8976.83 | 0.480578 | ||||||||
\(705\) | 6373.13 | 0.340463 | ||||||||
\(706\) | 16385.4 | 0.873472 | ||||||||
\(707\) | −20513.4 | −1.09121 | ||||||||
\(708\) | −7030.24 | −0.373182 | ||||||||
\(709\) | −52.1860 | −0.00276430 | −0.00138215 | − | 0.999999i | \(-0.500440\pi\) | ||||
−0.00138215 | + | 0.999999i | \(0.500440\pi\) | |||||||
\(710\) | −4622.70 | −0.244348 | ||||||||
\(711\) | 2788.74 | 0.147097 | ||||||||
\(712\) | −13375.0 | −0.704002 | ||||||||
\(713\) | −1034.30 | −0.0543265 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 13862.0 | 0.725046 | ||||||||
\(716\) | 18272.3 | 0.953725 | ||||||||
\(717\) | 1215.98 | 0.0633354 | ||||||||
\(718\) | 3347.43 | 0.173990 | ||||||||
\(719\) | −2244.80 | −0.116435 | −0.0582175 | − | 0.998304i | \(-0.518542\pi\) | ||||
−0.0582175 | + | 0.998304i | \(0.518542\pi\) | |||||||
\(720\) | −131.039 | −0.00678271 | ||||||||
\(721\) | −8577.23 | −0.443041 | ||||||||
\(722\) | 860.445 | 0.0443524 | ||||||||
\(723\) | 28824.9 | 1.48272 | ||||||||
\(724\) | 2348.89 | 0.120575 | ||||||||
\(725\) | −20930.4 | −1.07219 | ||||||||
\(726\) | −2880.96 | −0.147276 | ||||||||
\(727\) | −2971.90 | −0.151612 | −0.0758059 | − | 0.997123i | \(-0.524153\pi\) | ||||
−0.0758059 | + | 0.997123i | \(0.524153\pi\) | |||||||
\(728\) | −20451.4 | −1.04118 | ||||||||
\(729\) | 21748.2 | 1.10492 | ||||||||
\(730\) | −7472.91 | −0.378883 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | −8263.73 | −0.417263 | ||||||||
\(733\) | 31704.8 | 1.59760 | 0.798802 | − | 0.601594i | \(-0.205468\pi\) | ||||
0.798802 | + | 0.601594i | \(0.205468\pi\) | |||||||
\(734\) | −5898.00 | −0.296593 | ||||||||
\(735\) | 4553.02 | 0.228491 | ||||||||
\(736\) | −5292.50 | −0.265060 | ||||||||
\(737\) | −20355.9 | −1.01739 | ||||||||
\(738\) | 405.034 | 0.0202026 | ||||||||
\(739\) | −36985.6 | −1.84105 | −0.920526 | − | 0.390681i | \(-0.872240\pi\) | ||||
−0.920526 | + | 0.390681i | \(0.872240\pi\) | |||||||
\(740\) | 12408.0 | 0.616389 | ||||||||
\(741\) | 23384.2 | 1.15930 | ||||||||
\(742\) | 2064.36 | 0.102136 | ||||||||
\(743\) | 10601.9 | 0.523481 | 0.261741 | − | 0.965138i | \(-0.415704\pi\) | ||||
0.261741 | + | 0.965138i | \(0.415704\pi\) | |||||||
\(744\) | 3551.01 | 0.174981 | ||||||||
\(745\) | −15092.6 | −0.742217 | ||||||||
\(746\) | −4538.63 | −0.222750 | ||||||||
\(747\) | 1113.21 | 0.0545248 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −1928.48 | −0.0940789 | ||||||||
\(750\) | −10509.1 | −0.511653 | ||||||||
\(751\) | 29161.5 | 1.41694 | 0.708468 | − | 0.705743i | \(-0.249387\pi\) | ||||
0.708468 | + | 0.705743i | \(0.249387\pi\) | |||||||
\(752\) | −558.765 | −0.0270958 | ||||||||
\(753\) | 11232.0 | 0.543583 | ||||||||
\(754\) | −29969.7 | −1.44752 | ||||||||
\(755\) | 14526.4 | 0.700225 | ||||||||
\(756\) | 10753.5 | 0.517329 | ||||||||
\(757\) | −34447.9 | −1.65394 | −0.826969 | − | 0.562248i | \(-0.809937\pi\) | ||||
−0.826969 | + | 0.562248i | \(0.809937\pi\) | |||||||
\(758\) | −9521.67 | −0.456257 | ||||||||
\(759\) | −3959.96 | −0.189377 | ||||||||
\(760\) | −12120.1 | −0.578476 | ||||||||
\(761\) | −14414.5 | −0.686632 | −0.343316 | − | 0.939220i | \(-0.611550\pi\) | ||||
−0.343316 | + | 0.939220i | \(0.611550\pi\) | |||||||
\(762\) | 11421.0 | 0.542966 | ||||||||
\(763\) | −11426.4 | −0.542156 | ||||||||
\(764\) | 23012.6 | 1.08975 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −13357.5 | −0.630058 | ||||||||
\(767\) | −20512.1 | −0.965644 | ||||||||
\(768\) | 17690.3 | 0.831175 | ||||||||
\(769\) | −7049.33 | −0.330566 | −0.165283 | − | 0.986246i | \(-0.552854\pi\) | ||||
−0.165283 | + | 0.986246i | \(0.552854\pi\) | |||||||
\(770\) | 4969.40 | 0.232578 | ||||||||
\(771\) | −7565.28 | −0.353381 | ||||||||
\(772\) | −14912.3 | −0.695212 | ||||||||
\(773\) | 26768.3 | 1.24552 | 0.622760 | − | 0.782413i | \(-0.286011\pi\) | ||||
0.622760 | + | 0.782413i | \(0.286011\pi\) | |||||||
\(774\) | −6384.47 | −0.296492 | ||||||||
\(775\) | 2814.08 | 0.130432 | ||||||||
\(776\) | 995.097 | 0.0460334 | ||||||||
\(777\) | −22067.3 | −1.01887 | ||||||||
\(778\) | −12676.7 | −0.584165 | ||||||||
\(779\) | −2610.29 | −0.120055 | ||||||||
\(780\) | 10170.8 | 0.466889 | ||||||||
\(781\) | 12273.7 | 0.562339 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 40519.0 | 1.84934 | ||||||||
\(784\) | −399.186 | −0.0181845 | ||||||||
\(785\) | −2350.12 | −0.106853 | ||||||||
\(786\) | −21096.1 | −0.957343 | ||||||||
\(787\) | 26085.5 | 1.18151 | 0.590755 | − | 0.806851i | \(-0.298830\pi\) | ||||
0.590755 | + | 0.806851i | \(0.298830\pi\) | |||||||
\(788\) | 9806.68 | 0.443336 | ||||||||
\(789\) | 18994.6 | 0.857065 | ||||||||
\(790\) | 4465.69 | 0.201116 | ||||||||
\(791\) | 8359.95 | 0.375785 | ||||||||
\(792\) | −4993.30 | −0.224027 | ||||||||
\(793\) | −24111.1 | −1.07971 | ||||||||
\(794\) | 16270.6 | 0.727232 | ||||||||
\(795\) | −2639.78 | −0.117765 | ||||||||
\(796\) | 15715.1 | 0.699758 | ||||||||
\(797\) | 18108.6 | 0.804818 | 0.402409 | − | 0.915460i | \(-0.368173\pi\) | ||||
0.402409 | + | 0.915460i | \(0.368173\pi\) | |||||||
\(798\) | 8383.06 | 0.371876 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 14399.6 | 0.636379 | ||||||||
\(801\) | 4344.75 | 0.191653 | ||||||||
\(802\) | 14775.0 | 0.650527 | ||||||||
\(803\) | 19841.2 | 0.871958 | ||||||||
\(804\) | −14935.5 | −0.655142 | ||||||||
\(805\) | −2730.73 | −0.119560 | ||||||||
\(806\) | 4029.41 | 0.176092 | ||||||||
\(807\) | −35534.1 | −1.55001 | ||||||||
\(808\) | 33006.6 | 1.43709 | ||||||||
\(809\) | −7304.62 | −0.317450 | −0.158725 | − | 0.987323i | \(-0.550738\pi\) | ||||
−0.158725 | + | 0.987323i | \(0.550738\pi\) | |||||||
\(810\) | 5581.38 | 0.242111 | ||||||||
\(811\) | −19511.7 | −0.844817 | −0.422409 | − | 0.906405i | \(-0.638815\pi\) | ||||
−0.422409 | + | 0.906405i | \(0.638815\pi\) | |||||||
\(812\) | 18806.6 | 0.812786 | ||||||||
\(813\) | −2107.55 | −0.0909163 | ||||||||
\(814\) | 18820.6 | 0.810395 | ||||||||
\(815\) | −4620.65 | −0.198594 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 41145.5 | 1.76193 | ||||||||
\(818\) | −9003.45 | −0.384839 | ||||||||
\(819\) | 6643.45 | 0.283444 | ||||||||
\(820\) | −1135.32 | −0.0483503 | ||||||||
\(821\) | 29364.3 | 1.24826 | 0.624131 | − | 0.781320i | \(-0.285453\pi\) | ||||
0.624131 | + | 0.781320i | \(0.285453\pi\) | |||||||
\(822\) | −4772.96 | −0.202526 | ||||||||
\(823\) | 28112.4 | 1.19069 | 0.595345 | − | 0.803470i | \(-0.297015\pi\) | ||||
0.595345 | + | 0.803470i | \(0.297015\pi\) | |||||||
\(824\) | 13801.0 | 0.583472 | ||||||||
\(825\) | 10774.1 | 0.454673 | ||||||||
\(826\) | −7353.43 | −0.309756 | ||||||||
\(827\) | 39360.5 | 1.65502 | 0.827509 | − | 0.561453i | \(-0.189757\pi\) | ||||
0.827509 | + | 0.561453i | \(0.189757\pi\) | |||||||
\(828\) | 1067.12 | 0.0447885 | ||||||||
\(829\) | 15525.3 | 0.650443 | 0.325221 | − | 0.945638i | \(-0.394561\pi\) | ||||
0.325221 | + | 0.945638i | \(0.394561\pi\) | |||||||
\(830\) | 1782.61 | 0.0745485 | ||||||||
\(831\) | 12559.3 | 0.524280 | ||||||||
\(832\) | 19217.3 | 0.800771 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −20114.7 | −0.835151 | ||||||||
\(835\) | −5446.44 | −0.225727 | ||||||||
\(836\) | 12515.1 | 0.517756 | ||||||||
\(837\) | −5447.75 | −0.224972 | ||||||||
\(838\) | 16045.5 | 0.661433 | ||||||||
\(839\) | −30007.9 | −1.23479 | −0.617394 | − | 0.786654i | \(-0.711811\pi\) | ||||
−0.617394 | + | 0.786654i | \(0.711811\pi\) | |||||||
\(840\) | 9375.29 | 0.385093 | ||||||||
\(841\) | 46474.0 | 1.90553 | ||||||||
\(842\) | 13971.1 | 0.571826 | ||||||||
\(843\) | 11101.3 | 0.453556 | ||||||||
\(844\) | 18341.2 | 0.748020 | ||||||||
\(845\) | 14714.1 | 0.599029 | ||||||||
\(846\) | −2604.99 | −0.105864 | ||||||||
\(847\) | 5274.78 | 0.213983 | ||||||||
\(848\) | 231.443 | 0.00937239 | ||||||||
\(849\) | −10741.0 | −0.434193 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −10342.1 | −0.416595 | ||||||||
\(852\) | 9005.44 | 0.362114 | ||||||||
\(853\) | 4351.43 | 0.174666 | 0.0873331 | − | 0.996179i | \(-0.472166\pi\) | ||||
0.0873331 | + | 0.996179i | \(0.472166\pi\) | |||||||
\(854\) | −8643.62 | −0.346345 | ||||||||
\(855\) | 3937.09 | 0.157480 | ||||||||
\(856\) | 3102.98 | 0.123899 | ||||||||
\(857\) | −25861.5 | −1.03082 | −0.515410 | − | 0.856944i | \(-0.672360\pi\) | ||||
−0.515410 | + | 0.856944i | \(0.672360\pi\) | |||||||
\(858\) | 15427.2 | 0.613840 | ||||||||
\(859\) | 19084.0 | 0.758017 | 0.379009 | − | 0.925393i | \(-0.376265\pi\) | ||||
0.379009 | + | 0.925393i | \(0.376265\pi\) | |||||||
\(860\) | 17895.9 | 0.709588 | ||||||||
\(861\) | 2019.14 | 0.0799213 | ||||||||
\(862\) | 3326.16 | 0.131426 | ||||||||
\(863\) | 24790.2 | 0.977831 | 0.488916 | − | 0.872331i | \(-0.337393\pi\) | ||||
0.488916 | + | 0.872331i | \(0.337393\pi\) | |||||||
\(864\) | −27876.1 | −1.09765 | ||||||||
\(865\) | 12839.8 | 0.504701 | ||||||||
\(866\) | −19019.9 | −0.746332 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −2528.54 | −0.0988757 | ||||||||
\(869\) | −11856.8 | −0.462847 | ||||||||
\(870\) | 13738.6 | 0.535383 | ||||||||
\(871\) | −43577.2 | −1.69524 | ||||||||
\(872\) | 18385.5 | 0.714003 | ||||||||
\(873\) | −323.248 | −0.0125318 | ||||||||
\(874\) | 3928.81 | 0.152053 | ||||||||
\(875\) | 19241.3 | 0.743401 | ||||||||
\(876\) | 14557.9 | 0.561491 | ||||||||
\(877\) | 14394.0 | 0.554219 | 0.277109 | − | 0.960838i | \(-0.410624\pi\) | ||||
0.277109 | + | 0.960838i | \(0.410624\pi\) | |||||||
\(878\) | 801.839 | 0.0308209 | ||||||||
\(879\) | −29560.9 | −1.13432 | ||||||||
\(880\) | 557.137 | 0.0213421 | ||||||||
\(881\) | 15328.6 | 0.586190 | 0.293095 | − | 0.956083i | \(-0.405315\pi\) | ||||
0.293095 | + | 0.956083i | \(0.405315\pi\) | |||||||
\(882\) | −1861.02 | −0.0710475 | ||||||||
\(883\) | 8385.90 | 0.319602 | 0.159801 | − | 0.987149i | \(-0.448915\pi\) | ||||
0.159801 | + | 0.987149i | \(0.448915\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 9403.11 | 0.357155 | ||||||||
\(886\) | 22397.7 | 0.849283 | ||||||||
\(887\) | −9215.90 | −0.348861 | −0.174430 | − | 0.984669i | \(-0.555808\pi\) | ||||
−0.174430 | + | 0.984669i | \(0.555808\pi\) | |||||||
\(888\) | 35507.0 | 1.34182 | ||||||||
\(889\) | −20910.9 | −0.788897 | ||||||||
\(890\) | 6957.37 | 0.262035 | ||||||||
\(891\) | −14819.1 | −0.557191 | ||||||||
\(892\) | 8031.28 | 0.301465 | ||||||||
\(893\) | 16788.1 | 0.629108 | ||||||||
\(894\) | −16796.8 | −0.628376 | ||||||||
\(895\) | −24439.6 | −0.912765 | ||||||||
\(896\) | −13440.8 | −0.501146 | ||||||||
\(897\) | −8477.36 | −0.315553 | ||||||||
\(898\) | −17793.2 | −0.661211 | ||||||||
\(899\) | −9527.49 | −0.353459 | ||||||||
\(900\) | −2903.37 | −0.107532 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | −1722.07 | −0.0635684 | ||||||||
\(903\) | −31827.4 | −1.17292 | ||||||||
\(904\) | −13451.4 | −0.494897 | ||||||||
\(905\) | −3141.70 | −0.115396 | ||||||||
\(906\) | 16166.6 | 0.592825 | ||||||||
\(907\) | 7468.98 | 0.273433 | 0.136716 | − | 0.990610i | \(-0.456345\pi\) | ||||
0.136716 | + | 0.990610i | \(0.456345\pi\) | |||||||
\(908\) | −21856.8 | −0.798836 | ||||||||
\(909\) | −10721.9 | −0.391224 | ||||||||
\(910\) | 10638.4 | 0.387536 | ||||||||
\(911\) | 30698.3 | 1.11644 | 0.558222 | − | 0.829692i | \(-0.311484\pi\) | ||||
0.558222 | + | 0.829692i | \(0.311484\pi\) | |||||||
\(912\) | 939.854 | 0.0341246 | ||||||||
\(913\) | −4732.98 | −0.171565 | ||||||||
\(914\) | 432.140 | 0.0156389 | ||||||||
\(915\) | 11052.9 | 0.399343 | ||||||||
\(916\) | −2957.55 | −0.106681 | ||||||||
\(917\) | 38625.1 | 1.39096 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −24550.8 | −0.881237 | −0.440619 | − | 0.897694i | \(-0.645241\pi\) | ||||
−0.440619 | + | 0.897694i | \(0.645241\pi\) | |||||||
\(920\) | 4393.82 | 0.157457 | ||||||||
\(921\) | 11159.2 | 0.399247 | ||||||||
\(922\) | −26537.4 | −0.947898 | ||||||||
\(923\) | 26275.1 | 0.937006 | ||||||||
\(924\) | −9680.86 | −0.344672 | ||||||||
\(925\) | 28138.3 | 1.00020 | ||||||||
\(926\) | −18296.0 | −0.649293 | ||||||||
\(927\) | −4483.13 | −0.158841 | ||||||||
\(928\) | −48752.1 | −1.72453 | ||||||||
\(929\) | −41655.0 | −1.47110 | −0.735552 | − | 0.677468i | \(-0.763077\pi\) | ||||
−0.735552 | + | 0.677468i | \(0.763077\pi\) | |||||||
\(930\) | −1847.15 | −0.0651296 | ||||||||
\(931\) | 11993.6 | 0.422206 | ||||||||
\(932\) | −3420.28 | −0.120209 | ||||||||
\(933\) | −15931.5 | −0.559027 | ||||||||
\(934\) | 3343.54 | 0.117135 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −10689.5 | −0.373288 | ||||||||
\(937\) | 83.7368 | 0.00291949 | 0.00145975 | − | 0.999999i | \(-0.499535\pi\) | ||||
0.00145975 | + | 0.999999i | \(0.499535\pi\) | |||||||
\(938\) | −15622.1 | −0.543795 | ||||||||
\(939\) | 11608.6 | 0.403442 | ||||||||
\(940\) | 7301.88 | 0.253363 | ||||||||
\(941\) | −49294.1 | −1.70770 | −0.853848 | − | 0.520523i | \(-0.825737\pi\) | ||||
−0.853848 | + | 0.520523i | \(0.825737\pi\) | |||||||
\(942\) | −2615.48 | −0.0904639 | ||||||||
\(943\) | 946.293 | 0.0326782 | ||||||||
\(944\) | −824.418 | −0.0284243 | ||||||||
\(945\) | −14383.0 | −0.495111 | ||||||||
\(946\) | 27144.7 | 0.932927 | ||||||||
\(947\) | −9445.27 | −0.324108 | −0.162054 | − | 0.986782i | \(-0.551812\pi\) | ||||
−0.162054 | + | 0.986782i | \(0.551812\pi\) | |||||||
\(948\) | −8699.57 | −0.298047 | ||||||||
\(949\) | 42475.5 | 1.45291 | ||||||||
\(950\) | −10689.3 | −0.365061 | ||||||||
\(951\) | 17347.7 | 0.591521 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 41693.4 | 1.41719 | 0.708595 | − | 0.705616i | \(-0.249329\pi\) | ||||
0.708595 | + | 0.705616i | \(0.249329\pi\) | |||||||
\(954\) | 1079.00 | 0.0366183 | ||||||||
\(955\) | −30779.8 | −1.04294 | ||||||||
\(956\) | 1393.18 | 0.0471324 | ||||||||
\(957\) | −36477.3 | −1.23213 | ||||||||
\(958\) | −7323.60 | −0.246988 | ||||||||
\(959\) | 8738.88 | 0.294258 | ||||||||
\(960\) | −8809.56 | −0.296174 | ||||||||
\(961\) | −28510.0 | −0.957002 | ||||||||
\(962\) | 40290.6 | 1.35033 | ||||||||
\(963\) | −1007.97 | −0.0337295 | ||||||||
\(964\) | 33025.5 | 1.10340 | ||||||||
\(965\) | 19945.5 | 0.665355 | ||||||||
\(966\) | −3039.06 | −0.101222 | ||||||||
\(967\) | 32380.0 | 1.07681 | 0.538403 | − | 0.842688i | \(-0.319028\pi\) | ||||
0.538403 | + | 0.842688i | \(0.319028\pi\) | |||||||
\(968\) | −8487.28 | −0.281809 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −517.626 | −0.0171340 | ||||||||
\(971\) | 5401.25 | 0.178511 | 0.0892556 | − | 0.996009i | \(-0.471551\pi\) | ||||
0.0892556 | + | 0.996009i | \(0.471551\pi\) | |||||||
\(972\) | 10051.1 | 0.331676 | ||||||||
\(973\) | 36828.3 | 1.21342 | ||||||||
\(974\) | −30721.5 | −1.01066 | ||||||||
\(975\) | 23064.8 | 0.757606 | ||||||||
\(976\) | −969.066 | −0.0317818 | ||||||||
\(977\) | −25086.2 | −0.821473 | −0.410737 | − | 0.911754i | \(-0.634728\pi\) | ||||
−0.410737 | + | 0.911754i | \(0.634728\pi\) | |||||||
\(978\) | −5142.37 | −0.168134 | ||||||||
\(979\) | −18472.4 | −0.603045 | ||||||||
\(980\) | 5216.52 | 0.170036 | ||||||||
\(981\) | −5972.35 | −0.194375 | ||||||||
\(982\) | −23421.4 | −0.761108 | ||||||||
\(983\) | −59631.6 | −1.93485 | −0.967423 | − | 0.253166i | \(-0.918528\pi\) | ||||
−0.967423 | + | 0.253166i | \(0.918528\pi\) | |||||||
\(984\) | −3248.86 | −0.105254 | ||||||||
\(985\) | −13116.7 | −0.424296 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −12986.2 | −0.418799 | ||||||||
\(988\) | 26792.0 | 0.862719 | ||||||||
\(989\) | −14916.2 | −0.479584 | ||||||||
\(990\) | 2597.40 | 0.0833846 | ||||||||
\(991\) | −40063.8 | −1.28423 | −0.642114 | − | 0.766609i | \(-0.721942\pi\) | ||||
−0.642114 | + | 0.766609i | \(0.721942\pi\) | |||||||
\(992\) | 6554.70 | 0.209790 | ||||||||
\(993\) | 27711.6 | 0.885601 | ||||||||
\(994\) | 9419.43 | 0.300569 | ||||||||
\(995\) | −21019.3 | −0.669706 | ||||||||
\(996\) | −3472.68 | −0.110478 | ||||||||
\(997\) | −10818.4 | −0.343652 | −0.171826 | − | 0.985127i | \(-0.554967\pi\) | ||||
−0.171826 | + | 0.985127i | \(0.554967\pi\) | |||||||
\(998\) | 13213.5 | 0.419103 | ||||||||
\(999\) | −54472.8 | −1.72517 |
(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.g.1.5 | 12 | ||
17.4 | even | 4 | 289.4.b.e.288.8 | 12 | |||
17.11 | odd | 16 | 17.4.d.a.2.2 | ✓ | 12 | ||
17.13 | even | 4 | 289.4.b.e.288.7 | 12 | |||
17.14 | odd | 16 | 17.4.d.a.9.2 | yes | 12 | ||
17.16 | even | 2 | inner | 289.4.a.g.1.6 | 12 | ||
51.11 | even | 16 | 153.4.l.a.19.2 | 12 | |||
51.14 | even | 16 | 153.4.l.a.145.2 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
17.4.d.a.2.2 | ✓ | 12 | 17.11 | odd | 16 | ||
17.4.d.a.9.2 | yes | 12 | 17.14 | odd | 16 | ||
153.4.l.a.19.2 | 12 | 51.11 | even | 16 | |||
153.4.l.a.145.2 | 12 | 51.14 | even | 16 | |||
289.4.a.g.1.5 | 12 | 1.1 | even | 1 | trivial | ||
289.4.a.g.1.6 | 12 | 17.16 | even | 2 | inner | ||
289.4.b.e.288.7 | 12 | 17.13 | even | 4 | |||
289.4.b.e.288.8 | 12 | 17.4 | even | 4 |