Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [289,4,Mod(1,289)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(289, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("289.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 289 = 17^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 289.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(17.0515519917\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 54x^{6} - 20x^{5} + 677x^{4} + 380x^{3} - 2216x^{2} - 1000x + 476 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 17) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(2.06321\) 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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.351005 | 0.124099 | 0.0620496 | − | 0.998073i | \(-0.480236\pi\) | ||||
0.0620496 | + | 0.998073i | \(0.480236\pi\) | |||||||
\(3\) | −3.22714 | −0.621063 | −0.310532 | − | 0.950563i | \(-0.600507\pi\) | ||||
−0.310532 | + | 0.950563i | \(0.600507\pi\) | |||||||
\(4\) | −7.87680 | −0.984599 | ||||||||
\(5\) | −13.1900 | −1.17975 | −0.589876 | − | 0.807494i | \(-0.700823\pi\) | ||||
−0.589876 | + | 0.807494i | \(0.700823\pi\) | |||||||
\(6\) | −1.13274 | −0.0770735 | ||||||||
\(7\) | −33.2885 | −1.79741 | −0.898704 | − | 0.438555i | \(-0.855490\pi\) | ||||
−0.898704 | + | 0.438555i | \(0.855490\pi\) | |||||||
\(8\) | −5.57284 | −0.246287 | ||||||||
\(9\) | −16.5856 | −0.614280 | ||||||||
\(10\) | −4.62977 | −0.146406 | ||||||||
\(11\) | −13.6294 | −0.373584 | −0.186792 | − | 0.982399i | \(-0.559809\pi\) | ||||
−0.186792 | + | 0.982399i | \(0.559809\pi\) | |||||||
\(12\) | 25.4195 | 0.611499 | ||||||||
\(13\) | 5.12996 | 0.109446 | 0.0547229 | − | 0.998502i | \(-0.482572\pi\) | ||||
0.0547229 | + | 0.998502i | \(0.482572\pi\) | |||||||
\(14\) | −11.6844 | −0.223057 | ||||||||
\(15\) | 42.5661 | 0.732701 | ||||||||
\(16\) | 61.0583 | 0.954035 | ||||||||
\(17\) | 0 | 0 | ||||||||
\(18\) | −5.82162 | −0.0762317 | ||||||||
\(19\) | −38.4093 | −0.463774 | −0.231887 | − | 0.972743i | \(-0.574490\pi\) | ||||
−0.231887 | + | 0.972743i | \(0.574490\pi\) | |||||||
\(20\) | 103.895 | 1.16158 | ||||||||
\(21\) | 107.427 | 1.11630 | ||||||||
\(22\) | −4.78401 | −0.0463615 | ||||||||
\(23\) | −18.7334 | −0.169834 | −0.0849168 | − | 0.996388i | \(-0.527062\pi\) | ||||
−0.0849168 | + | 0.996388i | \(0.527062\pi\) | |||||||
\(24\) | 17.9843 | 0.152960 | ||||||||
\(25\) | 48.9769 | 0.391815 | ||||||||
\(26\) | 1.80065 | 0.0135821 | ||||||||
\(27\) | 140.657 | 1.00257 | ||||||||
\(28\) | 262.206 | 1.76973 | ||||||||
\(29\) | −211.179 | −1.35224 | −0.676121 | − | 0.736791i | \(-0.736340\pi\) | ||||
−0.676121 | + | 0.736791i | \(0.736340\pi\) | |||||||
\(30\) | 14.9409 | 0.0909276 | ||||||||
\(31\) | −234.411 | −1.35811 | −0.679056 | − | 0.734086i | \(-0.737611\pi\) | ||||
−0.679056 | + | 0.734086i | \(0.737611\pi\) | |||||||
\(32\) | 66.0145 | 0.364682 | ||||||||
\(33\) | 43.9841 | 0.232020 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 439.076 | 2.12050 | ||||||||
\(36\) | 130.641 | 0.604820 | ||||||||
\(37\) | −2.77851 | −0.0123455 | −0.00617275 | − | 0.999981i | \(-0.501965\pi\) | ||||
−0.00617275 | + | 0.999981i | \(0.501965\pi\) | |||||||
\(38\) | −13.4819 | −0.0575540 | ||||||||
\(39\) | −16.5551 | −0.0679728 | ||||||||
\(40\) | 73.5060 | 0.290558 | ||||||||
\(41\) | −303.782 | −1.15714 | −0.578570 | − | 0.815633i | \(-0.696389\pi\) | ||||
−0.578570 | + | 0.815633i | \(0.696389\pi\) | |||||||
\(42\) | 37.7073 | 0.138533 | ||||||||
\(43\) | −149.494 | −0.530179 | −0.265089 | − | 0.964224i | \(-0.585401\pi\) | ||||
−0.265089 | + | 0.964224i | \(0.585401\pi\) | |||||||
\(44\) | 107.356 | 0.367831 | ||||||||
\(45\) | 218.764 | 0.724698 | ||||||||
\(46\) | −6.57551 | −0.0210762 | ||||||||
\(47\) | 366.525 | 1.13751 | 0.568757 | − | 0.822506i | \(-0.307424\pi\) | ||||
0.568757 | + | 0.822506i | \(0.307424\pi\) | |||||||
\(48\) | −197.044 | −0.592517 | ||||||||
\(49\) | 765.122 | 2.23068 | ||||||||
\(50\) | 17.1912 | 0.0486240 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −40.4077 | −0.107760 | ||||||||
\(53\) | −499.269 | −1.29396 | −0.646981 | − | 0.762507i | \(-0.723969\pi\) | ||||
−0.646981 | + | 0.762507i | \(0.723969\pi\) | |||||||
\(54\) | 49.3713 | 0.124418 | ||||||||
\(55\) | 179.773 | 0.440737 | ||||||||
\(56\) | 185.511 | 0.442679 | ||||||||
\(57\) | 123.952 | 0.288033 | ||||||||
\(58\) | −74.1251 | −0.167812 | ||||||||
\(59\) | −507.289 | −1.11938 | −0.559690 | − | 0.828702i | \(-0.689080\pi\) | ||||
−0.559690 | + | 0.828702i | \(0.689080\pi\) | |||||||
\(60\) | −335.284 | −0.721417 | ||||||||
\(61\) | −33.0645 | −0.0694013 | −0.0347006 | − | 0.999398i | \(-0.511048\pi\) | ||||
−0.0347006 | + | 0.999398i | \(0.511048\pi\) | |||||||
\(62\) | −82.2796 | −0.168541 | ||||||||
\(63\) | 552.108 | 1.10411 | ||||||||
\(64\) | −465.295 | −0.908779 | ||||||||
\(65\) | −67.6644 | −0.129119 | ||||||||
\(66\) | 15.4387 | 0.0287934 | ||||||||
\(67\) | 442.124 | 0.806180 | 0.403090 | − | 0.915160i | \(-0.367936\pi\) | ||||
0.403090 | + | 0.915160i | \(0.367936\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 60.4552 | 0.105477 | ||||||||
\(70\) | 154.118 | 0.263152 | ||||||||
\(71\) | 475.863 | 0.795416 | 0.397708 | − | 0.917512i | \(-0.369806\pi\) | ||||
0.397708 | + | 0.917512i | \(0.369806\pi\) | |||||||
\(72\) | 92.4287 | 0.151289 | ||||||||
\(73\) | −735.977 | −1.17999 | −0.589997 | − | 0.807405i | \(-0.700871\pi\) | ||||
−0.589997 | + | 0.807405i | \(0.700871\pi\) | |||||||
\(74\) | −0.975271 | −0.00153207 | ||||||||
\(75\) | −158.055 | −0.243342 | ||||||||
\(76\) | 302.543 | 0.456632 | ||||||||
\(77\) | 453.703 | 0.671484 | ||||||||
\(78\) | −5.81094 | −0.00843537 | ||||||||
\(79\) | 214.438 | 0.305395 | 0.152697 | − | 0.988273i | \(-0.451204\pi\) | ||||
0.152697 | + | 0.988273i | \(0.451204\pi\) | |||||||
\(80\) | −805.360 | −1.12553 | ||||||||
\(81\) | −6.10881 | −0.00837971 | ||||||||
\(82\) | −106.629 | −0.143600 | ||||||||
\(83\) | −1187.18 | −1.57000 | −0.784999 | − | 0.619497i | \(-0.787336\pi\) | ||||
−0.784999 | + | 0.619497i | \(0.787336\pi\) | |||||||
\(84\) | −846.177 | −1.09911 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −52.4734 | −0.0657948 | ||||||||
\(87\) | 681.505 | 0.839828 | ||||||||
\(88\) | 75.9547 | 0.0920091 | ||||||||
\(89\) | −325.436 | −0.387598 | −0.193799 | − | 0.981041i | \(-0.562081\pi\) | ||||
−0.193799 | + | 0.981041i | \(0.562081\pi\) | |||||||
\(90\) | 76.7874 | 0.0899345 | ||||||||
\(91\) | −170.769 | −0.196719 | ||||||||
\(92\) | 147.559 | 0.167218 | ||||||||
\(93\) | 756.478 | 0.843474 | ||||||||
\(94\) | 128.652 | 0.141165 | ||||||||
\(95\) | 506.620 | 0.547139 | ||||||||
\(96\) | −213.038 | −0.226491 | ||||||||
\(97\) | 240.025 | 0.251245 | 0.125623 | − | 0.992078i | \(-0.459907\pi\) | ||||
0.125623 | + | 0.992078i | \(0.459907\pi\) | |||||||
\(98\) | 268.562 | 0.276825 | ||||||||
\(99\) | 226.052 | 0.229486 | ||||||||
\(100\) | −385.781 | −0.385781 | ||||||||
\(101\) | 718.617 | 0.707971 | 0.353986 | − | 0.935251i | \(-0.384826\pi\) | ||||
0.353986 | + | 0.935251i | \(0.384826\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −797.855 | −0.763252 | −0.381626 | − | 0.924317i | \(-0.624636\pi\) | ||||
−0.381626 | + | 0.924317i | \(0.624636\pi\) | |||||||
\(104\) | −28.5885 | −0.0269551 | ||||||||
\(105\) | −1416.96 | −1.31696 | ||||||||
\(106\) | −175.246 | −0.160580 | ||||||||
\(107\) | 461.001 | 0.416511 | 0.208256 | − | 0.978074i | \(-0.433221\pi\) | ||||
0.208256 | + | 0.978074i | \(0.433221\pi\) | |||||||
\(108\) | −1107.92 | −0.987130 | ||||||||
\(109\) | 1566.72 | 1.37674 | 0.688368 | − | 0.725362i | \(-0.258328\pi\) | ||||
0.688368 | + | 0.725362i | \(0.258328\pi\) | |||||||
\(110\) | 63.1012 | 0.0546951 | ||||||||
\(111\) | 8.96663 | 0.00766734 | ||||||||
\(112\) | −2032.54 | −1.71479 | ||||||||
\(113\) | −1596.67 | −1.32922 | −0.664611 | − | 0.747189i | \(-0.731403\pi\) | ||||
−0.664611 | + | 0.747189i | \(0.731403\pi\) | |||||||
\(114\) | 43.5080 | 0.0357447 | ||||||||
\(115\) | 247.093 | 0.200362 | ||||||||
\(116\) | 1663.42 | 1.33142 | ||||||||
\(117\) | −85.0833 | −0.0672304 | ||||||||
\(118\) | −178.061 | −0.138914 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −237.214 | −0.180455 | ||||||||
\(121\) | −1145.24 | −0.860435 | ||||||||
\(122\) | −11.6058 | −0.00861264 | ||||||||
\(123\) | 980.346 | 0.718657 | ||||||||
\(124\) | 1846.41 | 1.33720 | ||||||||
\(125\) | 1002.75 | 0.717507 | ||||||||
\(126\) | 193.793 | 0.137019 | ||||||||
\(127\) | −834.122 | −0.582806 | −0.291403 | − | 0.956600i | \(-0.594122\pi\) | ||||
−0.291403 | + | 0.956600i | \(0.594122\pi\) | |||||||
\(128\) | −691.437 | −0.477461 | ||||||||
\(129\) | 482.440 | 0.329275 | ||||||||
\(130\) | −23.7506 | −0.0160236 | ||||||||
\(131\) | 1215.93 | 0.810967 | 0.405484 | − | 0.914102i | \(-0.367103\pi\) | ||||
0.405484 | + | 0.914102i | \(0.367103\pi\) | |||||||
\(132\) | −346.454 | −0.228446 | ||||||||
\(133\) | 1278.59 | 0.833592 | ||||||||
\(134\) | 155.188 | 0.100046 | ||||||||
\(135\) | −1855.27 | −1.18278 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −1665.56 | −1.03867 | −0.519337 | − | 0.854569i | \(-0.673821\pi\) | ||||
−0.519337 | + | 0.854569i | \(0.673821\pi\) | |||||||
\(138\) | 21.2201 | 0.0130897 | ||||||||
\(139\) | −1375.96 | −0.839619 | −0.419810 | − | 0.907612i | \(-0.637903\pi\) | ||||
−0.419810 | + | 0.907612i | \(0.637903\pi\) | |||||||
\(140\) | −3458.51 | −2.08784 | ||||||||
\(141\) | −1182.83 | −0.706469 | ||||||||
\(142\) | 167.030 | 0.0987104 | ||||||||
\(143\) | −69.9185 | −0.0408873 | ||||||||
\(144\) | −1012.69 | −0.586045 | ||||||||
\(145\) | 2785.46 | 1.59531 | ||||||||
\(146\) | −258.332 | −0.146436 | ||||||||
\(147\) | −2469.16 | −1.38539 | ||||||||
\(148\) | 21.8857 | 0.0121554 | ||||||||
\(149\) | −1917.84 | −1.05447 | −0.527234 | − | 0.849720i | \(-0.676771\pi\) | ||||
−0.527234 | + | 0.849720i | \(0.676771\pi\) | |||||||
\(150\) | −55.4783 | −0.0301986 | ||||||||
\(151\) | −1878.30 | −1.01228 | −0.506138 | − | 0.862452i | \(-0.668927\pi\) | ||||
−0.506138 | + | 0.862452i | \(0.668927\pi\) | |||||||
\(152\) | 214.049 | 0.114222 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 159.252 | 0.0833306 | ||||||||
\(155\) | 3091.89 | 1.60224 | ||||||||
\(156\) | 130.401 | 0.0669260 | ||||||||
\(157\) | −98.6939 | −0.0501696 | −0.0250848 | − | 0.999685i | \(-0.507986\pi\) | ||||
−0.0250848 | + | 0.999685i | \(0.507986\pi\) | |||||||
\(158\) | 75.2690 | 0.0378992 | ||||||||
\(159\) | 1611.21 | 0.803632 | ||||||||
\(160\) | −870.734 | −0.430235 | ||||||||
\(161\) | 623.605 | 0.305260 | ||||||||
\(162\) | −2.14423 | −0.00103992 | ||||||||
\(163\) | 629.733 | 0.302604 | 0.151302 | − | 0.988488i | \(-0.451653\pi\) | ||||
0.151302 | + | 0.988488i | \(0.451653\pi\) | |||||||
\(164\) | 2392.83 | 1.13932 | ||||||||
\(165\) | −580.152 | −0.273726 | ||||||||
\(166\) | −416.706 | −0.194835 | ||||||||
\(167\) | −182.302 | −0.0844728 | −0.0422364 | − | 0.999108i | \(-0.513448\pi\) | ||||
−0.0422364 | + | 0.999108i | \(0.513448\pi\) | |||||||
\(168\) | −598.671 | −0.274932 | ||||||||
\(169\) | −2170.68 | −0.988022 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 637.041 | 0.284887 | ||||||||
\(172\) | 1177.54 | 0.522014 | ||||||||
\(173\) | 1589.91 | 0.698720 | 0.349360 | − | 0.936989i | \(-0.386399\pi\) | ||||
0.349360 | + | 0.936989i | \(0.386399\pi\) | |||||||
\(174\) | 239.212 | 0.104222 | ||||||||
\(175\) | −1630.37 | −0.704252 | ||||||||
\(176\) | −832.190 | −0.356413 | ||||||||
\(177\) | 1637.09 | 0.695206 | ||||||||
\(178\) | −114.230 | −0.0481006 | ||||||||
\(179\) | 2471.01 | 1.03180 | 0.515898 | − | 0.856650i | \(-0.327458\pi\) | ||||
0.515898 | + | 0.856650i | \(0.327458\pi\) | |||||||
\(180\) | −1723.16 | −0.713538 | ||||||||
\(181\) | −1116.02 | −0.458303 | −0.229151 | − | 0.973391i | \(-0.573595\pi\) | ||||
−0.229151 | + | 0.973391i | \(0.573595\pi\) | |||||||
\(182\) | −59.9407 | −0.0244127 | ||||||||
\(183\) | 106.704 | 0.0431026 | ||||||||
\(184\) | 104.398 | 0.0418278 | ||||||||
\(185\) | 36.6486 | 0.0145646 | ||||||||
\(186\) | 265.528 | 0.104674 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | −2887.04 | −1.12000 | ||||||||
\(189\) | −4682.25 | −1.80203 | ||||||||
\(190\) | 177.827 | 0.0678994 | ||||||||
\(191\) | 3850.07 | 1.45854 | 0.729271 | − | 0.684225i | \(-0.239859\pi\) | ||||
0.729271 | + | 0.684225i | \(0.239859\pi\) | |||||||
\(192\) | 1501.57 | 0.564409 | ||||||||
\(193\) | −2224.43 | −0.829626 | −0.414813 | − | 0.909907i | \(-0.636153\pi\) | ||||
−0.414813 | + | 0.909907i | \(0.636153\pi\) | |||||||
\(194\) | 84.2500 | 0.0311794 | ||||||||
\(195\) | 218.362 | 0.0801911 | ||||||||
\(196\) | −6026.71 | −2.19632 | ||||||||
\(197\) | 1870.67 | 0.676545 | 0.338273 | − | 0.941048i | \(-0.390157\pi\) | ||||
0.338273 | + | 0.941048i | \(0.390157\pi\) | |||||||
\(198\) | 79.3454 | 0.0284790 | ||||||||
\(199\) | 873.475 | 0.311151 | 0.155575 | − | 0.987824i | \(-0.450277\pi\) | ||||
0.155575 | + | 0.987824i | \(0.450277\pi\) | |||||||
\(200\) | −272.941 | −0.0964991 | ||||||||
\(201\) | −1426.80 | −0.500689 | ||||||||
\(202\) | 252.239 | 0.0878586 | ||||||||
\(203\) | 7029.83 | 2.43053 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 4006.89 | 1.36514 | ||||||||
\(206\) | −280.052 | −0.0947190 | ||||||||
\(207\) | 310.703 | 0.104325 | ||||||||
\(208\) | 313.227 | 0.104415 | ||||||||
\(209\) | 523.498 | 0.173259 | ||||||||
\(210\) | −497.361 | −0.163434 | ||||||||
\(211\) | 828.392 | 0.270279 | 0.135139 | − | 0.990827i | \(-0.456852\pi\) | ||||
0.135139 | + | 0.990827i | \(0.456852\pi\) | |||||||
\(212\) | 3932.64 | 1.27403 | ||||||||
\(213\) | −1535.68 | −0.494004 | ||||||||
\(214\) | 161.814 | 0.0516887 | ||||||||
\(215\) | 1971.84 | 0.625480 | ||||||||
\(216\) | −783.858 | −0.246920 | ||||||||
\(217\) | 7803.19 | 2.44108 | ||||||||
\(218\) | 549.926 | 0.170852 | ||||||||
\(219\) | 2375.10 | 0.732851 | ||||||||
\(220\) | −1416.03 | −0.433949 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 3.14734 | 0.000951511 0 | ||||||||
\(223\) | −1381.60 | −0.414882 | −0.207441 | − | 0.978248i | \(-0.566513\pi\) | ||||
−0.207441 | + | 0.978248i | \(0.566513\pi\) | |||||||
\(224\) | −2197.52 | −0.655483 | ||||||||
\(225\) | −812.310 | −0.240684 | ||||||||
\(226\) | −560.440 | −0.164955 | ||||||||
\(227\) | −169.477 | −0.0495531 | −0.0247766 | − | 0.999693i | \(-0.507887\pi\) | ||||
−0.0247766 | + | 0.999693i | \(0.507887\pi\) | |||||||
\(228\) | −976.347 | −0.283597 | ||||||||
\(229\) | −2463.08 | −0.710764 | −0.355382 | − | 0.934721i | \(-0.615649\pi\) | ||||
−0.355382 | + | 0.934721i | \(0.615649\pi\) | |||||||
\(230\) | 86.7312 | 0.0248647 | ||||||||
\(231\) | −1464.16 | −0.417034 | ||||||||
\(232\) | 1176.87 | 0.333040 | ||||||||
\(233\) | −2514.37 | −0.706960 | −0.353480 | − | 0.935442i | \(-0.615002\pi\) | ||||
−0.353480 | + | 0.935442i | \(0.615002\pi\) | |||||||
\(234\) | −29.8647 | −0.00834324 | ||||||||
\(235\) | −4834.48 | −1.34199 | ||||||||
\(236\) | 3995.81 | 1.10214 | ||||||||
\(237\) | −692.022 | −0.189669 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 3438.63 | 0.930656 | 0.465328 | − | 0.885138i | \(-0.345936\pi\) | ||||
0.465328 | + | 0.885138i | \(0.345936\pi\) | |||||||
\(240\) | 2599.01 | 0.699023 | ||||||||
\(241\) | 4093.41 | 1.09411 | 0.547054 | − | 0.837097i | \(-0.315749\pi\) | ||||
0.547054 | + | 0.837097i | \(0.315749\pi\) | |||||||
\(242\) | −401.985 | −0.106779 | ||||||||
\(243\) | −3778.02 | −0.997366 | ||||||||
\(244\) | 260.442 | 0.0683325 | ||||||||
\(245\) | −10092.0 | −2.63165 | ||||||||
\(246\) | 344.107 | 0.0891848 | ||||||||
\(247\) | −197.039 | −0.0507581 | ||||||||
\(248\) | 1306.34 | 0.334486 | ||||||||
\(249\) | 3831.19 | 0.975068 | ||||||||
\(250\) | 351.970 | 0.0890420 | ||||||||
\(251\) | −2927.86 | −0.736274 | −0.368137 | − | 0.929772i | \(-0.620004\pi\) | ||||
−0.368137 | + | 0.929772i | \(0.620004\pi\) | |||||||
\(252\) | −4348.84 | −1.08711 | ||||||||
\(253\) | 255.325 | 0.0634472 | ||||||||
\(254\) | −292.781 | −0.0723258 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 3479.66 | 0.849526 | ||||||||
\(257\) | 1139.92 | 0.276677 | 0.138338 | − | 0.990385i | \(-0.455824\pi\) | ||||
0.138338 | + | 0.990385i | \(0.455824\pi\) | |||||||
\(258\) | 169.339 | 0.0408627 | ||||||||
\(259\) | 92.4923 | 0.0221899 | ||||||||
\(260\) | 532.978 | 0.127130 | ||||||||
\(261\) | 3502.53 | 0.830655 | ||||||||
\(262\) | 426.800 | 0.100640 | ||||||||
\(263\) | −1853.52 | −0.434573 | −0.217287 | − | 0.976108i | \(-0.569721\pi\) | ||||
−0.217287 | + | 0.976108i | \(0.569721\pi\) | |||||||
\(264\) | −245.116 | −0.0571435 | ||||||||
\(265\) | 6585.38 | 1.52655 | ||||||||
\(266\) | 448.792 | 0.103448 | ||||||||
\(267\) | 1050.23 | 0.240723 | ||||||||
\(268\) | −3482.52 | −0.793765 | ||||||||
\(269\) | 2224.97 | 0.504307 | 0.252153 | − | 0.967687i | \(-0.418861\pi\) | ||||
0.252153 | + | 0.967687i | \(0.418861\pi\) | |||||||
\(270\) | −651.209 | −0.146783 | ||||||||
\(271\) | 737.207 | 0.165248 | 0.0826238 | − | 0.996581i | \(-0.473670\pi\) | ||||
0.0826238 | + | 0.996581i | \(0.473670\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 551.094 | 0.122175 | ||||||||
\(274\) | −584.621 | −0.128899 | ||||||||
\(275\) | −667.528 | −0.146376 | ||||||||
\(276\) | −476.193 | −0.103853 | ||||||||
\(277\) | 1500.24 | 0.325418 | 0.162709 | − | 0.986674i | \(-0.447977\pi\) | ||||
0.162709 | + | 0.986674i | \(0.447977\pi\) | |||||||
\(278\) | −482.968 | −0.104196 | ||||||||
\(279\) | 3887.84 | 0.834262 | ||||||||
\(280\) | −2446.90 | −0.522251 | ||||||||
\(281\) | 5367.39 | 1.13947 | 0.569736 | − | 0.821828i | \(-0.307046\pi\) | ||||
0.569736 | + | 0.821828i | \(0.307046\pi\) | |||||||
\(282\) | −415.179 | −0.0876722 | ||||||||
\(283\) | 4967.98 | 1.04352 | 0.521759 | − | 0.853093i | \(-0.325276\pi\) | ||||
0.521759 | + | 0.853093i | \(0.325276\pi\) | |||||||
\(284\) | −3748.27 | −0.783166 | ||||||||
\(285\) | −1634.94 | −0.339808 | ||||||||
\(286\) | −24.5418 | −0.00507408 | ||||||||
\(287\) | 10112.4 | 2.07985 | ||||||||
\(288\) | −1094.89 | −0.224017 | ||||||||
\(289\) | 0 | 0 | ||||||||
\(290\) | 977.712 | 0.197977 | ||||||||
\(291\) | −774.593 | −0.156039 | ||||||||
\(292\) | 5797.14 | 1.16182 | ||||||||
\(293\) | 6477.52 | 1.29154 | 0.645769 | − | 0.763533i | \(-0.276537\pi\) | ||||
0.645769 | + | 0.763533i | \(0.276537\pi\) | |||||||
\(294\) | −866.688 | −0.171926 | ||||||||
\(295\) | 6691.16 | 1.32059 | ||||||||
\(296\) | 15.4842 | 0.00304054 | ||||||||
\(297\) | −1917.07 | −0.374545 | ||||||||
\(298\) | −673.172 | −0.130858 | ||||||||
\(299\) | −96.1014 | −0.0185876 | ||||||||
\(300\) | 1244.97 | 0.239595 | ||||||||
\(301\) | 4976.44 | 0.952948 | ||||||||
\(302\) | −659.293 | −0.125623 | ||||||||
\(303\) | −2319.08 | −0.439695 | ||||||||
\(304\) | −2345.21 | −0.442457 | ||||||||
\(305\) | 436.122 | 0.0818763 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −5348.77 | −0.994366 | −0.497183 | − | 0.867646i | \(-0.665632\pi\) | ||||
−0.497183 | + | 0.867646i | \(0.665632\pi\) | |||||||
\(308\) | −3573.73 | −0.661143 | ||||||||
\(309\) | 2574.79 | 0.474028 | ||||||||
\(310\) | 1085.27 | 0.198836 | ||||||||
\(311\) | 3620.42 | 0.660113 | 0.330057 | − | 0.943961i | \(-0.392932\pi\) | ||||
0.330057 | + | 0.943961i | \(0.392932\pi\) | |||||||
\(312\) | 92.2590 | 0.0167408 | ||||||||
\(313\) | 2073.00 | 0.374355 | 0.187177 | − | 0.982326i | \(-0.440066\pi\) | ||||
0.187177 | + | 0.982326i | \(0.440066\pi\) | |||||||
\(314\) | −34.6421 | −0.00622601 | ||||||||
\(315\) | −7282.32 | −1.30258 | ||||||||
\(316\) | −1689.09 | −0.300691 | ||||||||
\(317\) | −7965.83 | −1.41137 | −0.705687 | − | 0.708524i | \(-0.749361\pi\) | ||||
−0.705687 | + | 0.708524i | \(0.749361\pi\) | |||||||
\(318\) | 565.544 | 0.0997301 | ||||||||
\(319\) | 2878.25 | 0.505176 | ||||||||
\(320\) | 6137.25 | 1.07213 | ||||||||
\(321\) | −1487.72 | −0.258680 | ||||||||
\(322\) | 218.889 | 0.0378826 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 48.1178 | 0.00825066 | ||||||||
\(325\) | 251.250 | 0.0428826 | ||||||||
\(326\) | 221.040 | 0.0375530 | ||||||||
\(327\) | −5056.01 | −0.855040 | ||||||||
\(328\) | 1692.93 | 0.284989 | ||||||||
\(329\) | −12201.1 | −2.04458 | ||||||||
\(330\) | −203.636 | −0.0339691 | ||||||||
\(331\) | 8062.01 | 1.33875 | 0.669377 | − | 0.742922i | \(-0.266561\pi\) | ||||
0.669377 | + | 0.742922i | \(0.266561\pi\) | |||||||
\(332\) | 9351.16 | 1.54582 | ||||||||
\(333\) | 46.0831 | 0.00758360 | ||||||||
\(334\) | −63.9891 | −0.0104830 | ||||||||
\(335\) | −5831.63 | −0.951093 | ||||||||
\(336\) | 6559.28 | 1.06499 | ||||||||
\(337\) | −7837.81 | −1.26692 | −0.633461 | − | 0.773774i | \(-0.718366\pi\) | ||||
−0.633461 | + | 0.773774i | \(0.718366\pi\) | |||||||
\(338\) | −761.922 | −0.122613 | ||||||||
\(339\) | 5152.68 | 0.825532 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 3194.89 | 0.507370 | ||||||||
\(342\) | 223.605 | 0.0353543 | ||||||||
\(343\) | −14051.8 | −2.21203 | ||||||||
\(344\) | 833.109 | 0.130576 | ||||||||
\(345\) | −797.405 | −0.124437 | ||||||||
\(346\) | 558.067 | 0.0867106 | ||||||||
\(347\) | −4664.53 | −0.721628 | −0.360814 | − | 0.932638i | \(-0.617501\pi\) | ||||
−0.360814 | + | 0.932638i | \(0.617501\pi\) | |||||||
\(348\) | −5368.07 | −0.826894 | ||||||||
\(349\) | −9868.72 | −1.51364 | −0.756820 | − | 0.653623i | \(-0.773248\pi\) | ||||
−0.756820 | + | 0.653623i | \(0.773248\pi\) | |||||||
\(350\) | −572.268 | −0.0873971 | ||||||||
\(351\) | 721.564 | 0.109727 | ||||||||
\(352\) | −899.741 | −0.136240 | ||||||||
\(353\) | −955.958 | −0.144137 | −0.0720687 | − | 0.997400i | \(-0.522960\pi\) | ||||
−0.0720687 | + | 0.997400i | \(0.522960\pi\) | |||||||
\(354\) | 574.629 | 0.0862745 | ||||||||
\(355\) | −6276.64 | −0.938393 | ||||||||
\(356\) | 2563.40 | 0.381628 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 867.337 | 0.128045 | ||||||||
\(359\) | 8341.26 | 1.22628 | 0.613141 | − | 0.789974i | \(-0.289906\pi\) | ||||
0.613141 | + | 0.789974i | \(0.289906\pi\) | |||||||
\(360\) | −1219.14 | −0.178484 | ||||||||
\(361\) | −5383.72 | −0.784914 | ||||||||
\(362\) | −391.728 | −0.0568750 | ||||||||
\(363\) | 3695.85 | 0.534385 | ||||||||
\(364\) | 1345.11 | 0.193689 | ||||||||
\(365\) | 9707.56 | 1.39210 | ||||||||
\(366\) | 37.4536 | 0.00534900 | ||||||||
\(367\) | −8335.18 | −1.18554 | −0.592770 | − | 0.805372i | \(-0.701965\pi\) | ||||
−0.592770 | + | 0.805372i | \(0.701965\pi\) | |||||||
\(368\) | −1143.83 | −0.162027 | ||||||||
\(369\) | 5038.39 | 0.710808 | ||||||||
\(370\) | 12.8639 | 0.00180746 | ||||||||
\(371\) | 16619.9 | 2.32578 | ||||||||
\(372\) | −5958.62 | −0.830484 | ||||||||
\(373\) | −11406.4 | −1.58338 | −0.791689 | − | 0.610924i | \(-0.790798\pi\) | ||||
−0.791689 | + | 0.610924i | \(0.790798\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −3236.00 | −0.445617 | ||||||||
\(376\) | −2042.59 | −0.280155 | ||||||||
\(377\) | −1083.34 | −0.147997 | ||||||||
\(378\) | −1643.49 | −0.223630 | ||||||||
\(379\) | −11663.1 | −1.58072 | −0.790361 | − | 0.612641i | \(-0.790107\pi\) | ||||
−0.790361 | + | 0.612641i | \(0.790107\pi\) | |||||||
\(380\) | −3990.55 | −0.538712 | ||||||||
\(381\) | 2691.83 | 0.361960 | ||||||||
\(382\) | 1351.40 | 0.181004 | ||||||||
\(383\) | 4091.40 | 0.545851 | 0.272925 | − | 0.962035i | \(-0.412009\pi\) | ||||
0.272925 | + | 0.962035i | \(0.412009\pi\) | |||||||
\(384\) | 2231.36 | 0.296533 | ||||||||
\(385\) | −5984.36 | −0.792185 | ||||||||
\(386\) | −780.786 | −0.102956 | ||||||||
\(387\) | 2479.45 | 0.325678 | ||||||||
\(388\) | −1890.62 | −0.247376 | ||||||||
\(389\) | −9245.70 | −1.20508 | −0.602539 | − | 0.798089i | \(-0.705844\pi\) | ||||
−0.602539 | + | 0.798089i | \(0.705844\pi\) | |||||||
\(390\) | 76.6464 | 0.00995165 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | −4263.91 | −0.549387 | ||||||||
\(393\) | −3923.99 | −0.503662 | ||||||||
\(394\) | 656.614 | 0.0839587 | ||||||||
\(395\) | −2828.45 | −0.360290 | ||||||||
\(396\) | −1780.56 | −0.225951 | ||||||||
\(397\) | −6436.28 | −0.813671 | −0.406836 | − | 0.913501i | \(-0.633368\pi\) | ||||
−0.406836 | + | 0.913501i | \(0.633368\pi\) | |||||||
\(398\) | 306.594 | 0.0386135 | ||||||||
\(399\) | −4126.18 | −0.517713 | ||||||||
\(400\) | 2990.45 | 0.373806 | ||||||||
\(401\) | −1379.54 | −0.171798 | −0.0858989 | − | 0.996304i | \(-0.527376\pi\) | ||||
−0.0858989 | + | 0.996304i | \(0.527376\pi\) | |||||||
\(402\) | −500.814 | −0.0621351 | ||||||||
\(403\) | −1202.52 | −0.148640 | ||||||||
\(404\) | −5660.40 | −0.697068 | ||||||||
\(405\) | 80.5754 | 0.00988598 | ||||||||
\(406\) | 2467.51 | 0.301627 | ||||||||
\(407\) | 37.8695 | 0.00461209 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −13063.3 | −1.57931 | −0.789654 | − | 0.613552i | \(-0.789740\pi\) | ||||
−0.789654 | + | 0.613552i | \(0.789740\pi\) | |||||||
\(410\) | 1406.44 | 0.169412 | ||||||||
\(411\) | 5375.00 | 0.645083 | ||||||||
\(412\) | 6284.54 | 0.751498 | ||||||||
\(413\) | 16886.9 | 2.01198 | ||||||||
\(414\) | 109.059 | 0.0129467 | ||||||||
\(415\) | 15658.9 | 1.85221 | ||||||||
\(416\) | 338.652 | 0.0399129 | ||||||||
\(417\) | 4440.40 | 0.521457 | ||||||||
\(418\) | 183.751 | 0.0215013 | ||||||||
\(419\) | −7651.38 | −0.892111 | −0.446056 | − | 0.895005i | \(-0.647172\pi\) | ||||
−0.446056 | + | 0.895005i | \(0.647172\pi\) | |||||||
\(420\) | 11161.1 | 1.29668 | ||||||||
\(421\) | −15634.9 | −1.80997 | −0.904985 | − | 0.425443i | \(-0.860118\pi\) | ||||
−0.904985 | + | 0.425443i | \(0.860118\pi\) | |||||||
\(422\) | 290.770 | 0.0335414 | ||||||||
\(423\) | −6079.02 | −0.698752 | ||||||||
\(424\) | 2782.35 | 0.318686 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −539.031 | −0.0613054 | ||||||||
\(427\) | 1100.67 | 0.124742 | ||||||||
\(428\) | −3631.21 | −0.410097 | ||||||||
\(429\) | 225.637 | 0.0253936 | ||||||||
\(430\) | 692.125 | 0.0776215 | ||||||||
\(431\) | 11099.0 | 1.24042 | 0.620211 | − | 0.784435i | \(-0.287047\pi\) | ||||
0.620211 | + | 0.784435i | \(0.287047\pi\) | |||||||
\(432\) | 8588.26 | 0.956488 | ||||||||
\(433\) | −14696.8 | −1.63114 | −0.815569 | − | 0.578660i | \(-0.803576\pi\) | ||||
−0.815569 | + | 0.578660i | \(0.803576\pi\) | |||||||
\(434\) | 2738.96 | 0.302936 | ||||||||
\(435\) | −8989.07 | −0.990788 | ||||||||
\(436\) | −12340.7 | −1.35553 | ||||||||
\(437\) | 719.536 | 0.0787644 | ||||||||
\(438\) | 833.673 | 0.0909463 | ||||||||
\(439\) | 9402.11 | 1.02218 | 0.511091 | − | 0.859526i | \(-0.329241\pi\) | ||||
0.511091 | + | 0.859526i | \(0.329241\pi\) | |||||||
\(440\) | −1001.84 | −0.108548 | ||||||||
\(441\) | −12690.0 | −1.37026 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −7550.22 | −0.809756 | −0.404878 | − | 0.914371i | \(-0.632686\pi\) | ||||
−0.404878 | + | 0.914371i | \(0.632686\pi\) | |||||||
\(444\) | −70.6283 | −0.00754926 | ||||||||
\(445\) | 4292.52 | 0.457269 | ||||||||
\(446\) | −484.948 | −0.0514865 | ||||||||
\(447\) | 6189.14 | 0.654891 | ||||||||
\(448\) | 15488.9 | 1.63345 | ||||||||
\(449\) | −7228.02 | −0.759714 | −0.379857 | − | 0.925045i | \(-0.624027\pi\) | ||||
−0.379857 | + | 0.925045i | \(0.624027\pi\) | |||||||
\(450\) | −285.125 | −0.0298687 | ||||||||
\(451\) | 4140.37 | 0.432289 | ||||||||
\(452\) | 12576.6 | 1.30875 | ||||||||
\(453\) | 6061.53 | 0.628688 | ||||||||
\(454\) | −59.4872 | −0.00614950 | ||||||||
\(455\) | 2252.44 | 0.232080 | ||||||||
\(456\) | −690.767 | −0.0709389 | ||||||||
\(457\) | 6030.84 | 0.617311 | 0.308655 | − | 0.951174i | \(-0.400121\pi\) | ||||
0.308655 | + | 0.951174i | \(0.400121\pi\) | |||||||
\(458\) | −864.555 | −0.0882053 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −1946.30 | −0.197276 | ||||||||
\(461\) | 3790.02 | 0.382904 | 0.191452 | − | 0.981502i | \(-0.438680\pi\) | ||||
0.191452 | + | 0.981502i | \(0.438680\pi\) | |||||||
\(462\) | −513.929 | −0.0517536 | ||||||||
\(463\) | −9287.18 | −0.932207 | −0.466103 | − | 0.884730i | \(-0.654343\pi\) | ||||
−0.466103 | + | 0.884730i | \(0.654343\pi\) | |||||||
\(464\) | −12894.2 | −1.29009 | ||||||||
\(465\) | −9977.97 | −0.995091 | ||||||||
\(466\) | −882.557 | −0.0877332 | ||||||||
\(467\) | 596.896 | 0.0591458 | 0.0295729 | − | 0.999563i | \(-0.490585\pi\) | ||||
0.0295729 | + | 0.999563i | \(0.490585\pi\) | |||||||
\(468\) | 670.184 | 0.0661950 | ||||||||
\(469\) | −14717.6 | −1.44904 | ||||||||
\(470\) | −1696.93 | −0.166539 | ||||||||
\(471\) | 318.499 | 0.0311585 | ||||||||
\(472\) | 2827.04 | 0.275689 | ||||||||
\(473\) | 2037.52 | 0.198067 | ||||||||
\(474\) | −242.903 | −0.0235378 | ||||||||
\(475\) | −1881.17 | −0.181714 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 8280.67 | 0.794855 | ||||||||
\(478\) | 1206.98 | 0.115494 | ||||||||
\(479\) | −4436.73 | −0.423214 | −0.211607 | − | 0.977355i | \(-0.567870\pi\) | ||||
−0.211607 | + | 0.977355i | \(0.567870\pi\) | |||||||
\(480\) | 2809.98 | 0.267203 | ||||||||
\(481\) | −14.2536 | −0.00135116 | ||||||||
\(482\) | 1436.81 | 0.135778 | ||||||||
\(483\) | −2012.46 | −0.189586 | ||||||||
\(484\) | 9020.81 | 0.847183 | ||||||||
\(485\) | −3165.93 | −0.296407 | ||||||||
\(486\) | −1326.11 | −0.123772 | ||||||||
\(487\) | 8654.25 | 0.805260 | 0.402630 | − | 0.915363i | \(-0.368096\pi\) | ||||
0.402630 | + | 0.915363i | \(0.368096\pi\) | |||||||
\(488\) | 184.263 | 0.0170926 | ||||||||
\(489\) | −2032.24 | −0.187937 | ||||||||
\(490\) | −3542.34 | −0.326585 | ||||||||
\(491\) | −5160.59 | −0.474326 | −0.237163 | − | 0.971470i | \(-0.576218\pi\) | ||||
−0.237163 | + | 0.971470i | \(0.576218\pi\) | |||||||
\(492\) | −7721.98 | −0.707589 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | −69.1616 | −0.00629904 | ||||||||
\(495\) | −2981.63 | −0.270736 | ||||||||
\(496\) | −14312.7 | −1.29569 | ||||||||
\(497\) | −15840.7 | −1.42969 | ||||||||
\(498\) | 1344.77 | 0.121005 | ||||||||
\(499\) | −8724.42 | −0.782683 | −0.391341 | − | 0.920246i | \(-0.627989\pi\) | ||||
−0.391341 | + | 0.920246i | \(0.627989\pi\) | |||||||
\(500\) | −7898.43 | −0.706457 | ||||||||
\(501\) | 588.315 | 0.0524630 | ||||||||
\(502\) | −1027.69 | −0.0913710 | ||||||||
\(503\) | 16908.0 | 1.49879 | 0.749395 | − | 0.662124i | \(-0.230345\pi\) | ||||
0.749395 | + | 0.662124i | \(0.230345\pi\) | |||||||
\(504\) | −3076.81 | −0.271929 | ||||||||
\(505\) | −9478.58 | −0.835230 | ||||||||
\(506\) | 89.6205 | 0.00787375 | ||||||||
\(507\) | 7005.10 | 0.613624 | ||||||||
\(508\) | 6570.21 | 0.573831 | ||||||||
\(509\) | 11762.9 | 1.02433 | 0.512163 | − | 0.858888i | \(-0.328844\pi\) | ||||
0.512163 | + | 0.858888i | \(0.328844\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 24499.5 | 2.12093 | ||||||||
\(512\) | 6752.88 | 0.582886 | ||||||||
\(513\) | −5402.53 | −0.464966 | ||||||||
\(514\) | 400.117 | 0.0343354 | ||||||||
\(515\) | 10523.7 | 0.900449 | ||||||||
\(516\) | −3800.08 | −0.324204 | ||||||||
\(517\) | −4995.53 | −0.424958 | ||||||||
\(518\) | 32.4653 | 0.00275375 | ||||||||
\(519\) | −5130.86 | −0.433949 | ||||||||
\(520\) | 377.083 | 0.0318003 | ||||||||
\(521\) | 11346.9 | 0.954159 | 0.477080 | − | 0.878860i | \(-0.341695\pi\) | ||||
0.477080 | + | 0.878860i | \(0.341695\pi\) | |||||||
\(522\) | 1229.41 | 0.103084 | ||||||||
\(523\) | 11430.3 | 0.955661 | 0.477831 | − | 0.878452i | \(-0.341423\pi\) | ||||
0.477831 | + | 0.878452i | \(0.341423\pi\) | |||||||
\(524\) | −9577.67 | −0.798478 | ||||||||
\(525\) | 5261.42 | 0.437385 | ||||||||
\(526\) | −650.595 | −0.0539302 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 2685.59 | 0.221355 | ||||||||
\(529\) | −11816.1 | −0.971157 | ||||||||
\(530\) | 2311.50 | 0.189444 | ||||||||
\(531\) | 8413.68 | 0.687613 | ||||||||
\(532\) | −10071.2 | −0.820754 | ||||||||
\(533\) | −1558.39 | −0.126644 | ||||||||
\(534\) | 368.636 | 0.0298735 | ||||||||
\(535\) | −6080.62 | −0.491380 | ||||||||
\(536\) | −2463.89 | −0.198552 | ||||||||
\(537\) | −7974.28 | −0.640811 | ||||||||
\(538\) | 780.975 | 0.0625841 | ||||||||
\(539\) | −10428.2 | −0.833346 | ||||||||
\(540\) | 14613.6 | 1.16457 | ||||||||
\(541\) | −12526.0 | −0.995445 | −0.497722 | − | 0.867336i | \(-0.665830\pi\) | ||||
−0.497722 | + | 0.867336i | \(0.665830\pi\) | |||||||
\(542\) | 258.764 | 0.0205071 | ||||||||
\(543\) | 3601.54 | 0.284635 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −20665.0 | −1.62421 | ||||||||
\(546\) | 193.437 | 0.0151618 | ||||||||
\(547\) | 5126.09 | 0.400687 | 0.200344 | − | 0.979726i | \(-0.435794\pi\) | ||||
0.200344 | + | 0.979726i | \(0.435794\pi\) | |||||||
\(548\) | 13119.3 | 1.02268 | ||||||||
\(549\) | 548.394 | 0.0426318 | ||||||||
\(550\) | −234.306 | −0.0181652 | ||||||||
\(551\) | 8111.25 | 0.627134 | ||||||||
\(552\) | −336.907 | −0.0259777 | ||||||||
\(553\) | −7138.32 | −0.548919 | ||||||||
\(554\) | 526.593 | 0.0403841 | ||||||||
\(555\) | −118.270 | −0.00904557 | ||||||||
\(556\) | 10838.1 | 0.826688 | ||||||||
\(557\) | −7368.19 | −0.560503 | −0.280251 | − | 0.959927i | \(-0.590418\pi\) | ||||
−0.280251 | + | 0.959927i | \(0.590418\pi\) | |||||||
\(558\) | 1364.65 | 0.103531 | ||||||||
\(559\) | −766.901 | −0.0580259 | ||||||||
\(560\) | 26809.2 | 2.02303 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 1883.98 | 0.141408 | ||||||||
\(563\) | 11247.6 | 0.841969 | 0.420984 | − | 0.907068i | \(-0.361685\pi\) | ||||
0.420984 | + | 0.907068i | \(0.361685\pi\) | |||||||
\(564\) | 9316.89 | 0.695589 | ||||||||
\(565\) | 21060.1 | 1.56815 | ||||||||
\(566\) | 1743.79 | 0.129500 | ||||||||
\(567\) | 203.353 | 0.0150618 | ||||||||
\(568\) | −2651.91 | −0.195901 | ||||||||
\(569\) | 25878.6 | 1.90666 | 0.953329 | − | 0.301935i | \(-0.0976324\pi\) | ||||
0.953329 | + | 0.301935i | \(0.0976324\pi\) | |||||||
\(570\) | −573.871 | −0.0421699 | ||||||||
\(571\) | −5352.07 | −0.392255 | −0.196127 | − | 0.980578i | \(-0.562837\pi\) | ||||
−0.196127 | + | 0.980578i | \(0.562837\pi\) | |||||||
\(572\) | 550.734 | 0.0402576 | ||||||||
\(573\) | −12424.7 | −0.905847 | ||||||||
\(574\) | 3549.52 | 0.258108 | ||||||||
\(575\) | −917.502 | −0.0665434 | ||||||||
\(576\) | 7717.17 | 0.558245 | ||||||||
\(577\) | −3052.95 | −0.220270 | −0.110135 | − | 0.993917i | \(-0.535128\pi\) | ||||
−0.110135 | + | 0.993917i | \(0.535128\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 7178.54 | 0.515250 | ||||||||
\(580\) | −21940.5 | −1.57074 | ||||||||
\(581\) | 39519.4 | 2.82193 | ||||||||
\(582\) | −271.886 | −0.0193644 | ||||||||
\(583\) | 6804.76 | 0.483404 | ||||||||
\(584\) | 4101.48 | 0.290617 | ||||||||
\(585\) | 1122.25 | 0.0793152 | ||||||||
\(586\) | 2273.65 | 0.160279 | ||||||||
\(587\) | −6669.73 | −0.468977 | −0.234488 | − | 0.972119i | \(-0.575341\pi\) | ||||
−0.234488 | + | 0.972119i | \(0.575341\pi\) | |||||||
\(588\) | 19449.0 | 1.36406 | ||||||||
\(589\) | 9003.58 | 0.629857 | ||||||||
\(590\) | 2348.63 | 0.163884 | ||||||||
\(591\) | −6036.90 | −0.420178 | ||||||||
\(592\) | −169.651 | −0.0117781 | ||||||||
\(593\) | 13962.7 | 0.966914 | 0.483457 | − | 0.875368i | \(-0.339381\pi\) | ||||
0.483457 | + | 0.875368i | \(0.339381\pi\) | |||||||
\(594\) | −672.903 | −0.0464807 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 15106.4 | 1.03823 | ||||||||
\(597\) | −2818.83 | −0.193244 | ||||||||
\(598\) | −33.7321 | −0.00230670 | ||||||||
\(599\) | −3286.64 | −0.224188 | −0.112094 | − | 0.993698i | \(-0.535756\pi\) | ||||
−0.112094 | + | 0.993698i | \(0.535756\pi\) | |||||||
\(600\) | 880.818 | 0.0599321 | ||||||||
\(601\) | −1510.08 | −0.102491 | −0.0512456 | − | 0.998686i | \(-0.516319\pi\) | ||||
−0.0512456 | + | 0.998686i | \(0.516319\pi\) | |||||||
\(602\) | 1746.76 | 0.118260 | ||||||||
\(603\) | −7332.88 | −0.495221 | ||||||||
\(604\) | 14795.0 | 0.996687 | ||||||||
\(605\) | 15105.7 | 1.01510 | ||||||||
\(606\) | −814.009 | −0.0545658 | ||||||||
\(607\) | 5665.96 | 0.378870 | 0.189435 | − | 0.981893i | \(-0.439334\pi\) | ||||
0.189435 | + | 0.981893i | \(0.439334\pi\) | |||||||
\(608\) | −2535.57 | −0.169130 | ||||||||
\(609\) | −22686.3 | −1.50951 | ||||||||
\(610\) | 153.081 | 0.0101608 | ||||||||
\(611\) | 1880.26 | 0.124496 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −11074.1 | −0.729653 | −0.364827 | − | 0.931076i | \(-0.618872\pi\) | ||||
−0.364827 | + | 0.931076i | \(0.618872\pi\) | |||||||
\(614\) | −1877.45 | −0.123400 | ||||||||
\(615\) | −12930.8 | −0.847837 | ||||||||
\(616\) | −2528.42 | −0.165378 | ||||||||
\(617\) | −22059.5 | −1.43936 | −0.719678 | − | 0.694308i | \(-0.755710\pi\) | ||||
−0.719678 | + | 0.694308i | \(0.755710\pi\) | |||||||
\(618\) | 903.766 | 0.0588265 | ||||||||
\(619\) | −19314.4 | −1.25414 | −0.627068 | − | 0.778964i | \(-0.715745\pi\) | ||||
−0.627068 | + | 0.778964i | \(0.715745\pi\) | |||||||
\(620\) | −24354.2 | −1.57756 | ||||||||
\(621\) | −2634.97 | −0.170270 | ||||||||
\(622\) | 1270.79 | 0.0819195 | ||||||||
\(623\) | 10833.3 | 0.696671 | ||||||||
\(624\) | −1010.83 | −0.0648485 | ||||||||
\(625\) | −19348.4 | −1.23830 | ||||||||
\(626\) | 727.635 | 0.0464571 | ||||||||
\(627\) | −1689.40 | −0.107605 | ||||||||
\(628\) | 777.391 | 0.0493970 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | −2556.14 | −0.161649 | ||||||||
\(631\) | 29548.0 | 1.86417 | 0.932083 | − | 0.362245i | \(-0.117990\pi\) | ||||
0.932083 | + | 0.362245i | \(0.117990\pi\) | |||||||
\(632\) | −1195.03 | −0.0752148 | ||||||||
\(633\) | −2673.34 | −0.167860 | ||||||||
\(634\) | −2796.05 | −0.175150 | ||||||||
\(635\) | 11002.1 | 0.687567 | ||||||||
\(636\) | −12691.2 | −0.791255 | ||||||||
\(637\) | 3925.05 | 0.244138 | ||||||||
\(638\) | 1010.28 | 0.0626920 | ||||||||
\(639\) | −7892.45 | −0.488608 | ||||||||
\(640\) | 9120.08 | 0.563286 | ||||||||
\(641\) | −1917.21 | −0.118136 | −0.0590679 | − | 0.998254i | \(-0.518813\pi\) | ||||
−0.0590679 | + | 0.998254i | \(0.518813\pi\) | |||||||
\(642\) | −522.197 | −0.0321020 | ||||||||
\(643\) | −4764.36 | −0.292205 | −0.146103 | − | 0.989269i | \(-0.546673\pi\) | ||||
−0.146103 | + | 0.989269i | \(0.546673\pi\) | |||||||
\(644\) | −4912.01 | −0.300559 | ||||||||
\(645\) | −6363.39 | −0.388463 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 26374.3 | 1.60260 | 0.801299 | − | 0.598264i | \(-0.204143\pi\) | ||||
0.801299 | + | 0.598264i | \(0.204143\pi\) | |||||||
\(648\) | 34.0434 | 0.00206382 | ||||||||
\(649\) | 6914.06 | 0.418183 | ||||||||
\(650\) | 88.1901 | 0.00532169 | ||||||||
\(651\) | −25182.0 | −1.51607 | ||||||||
\(652\) | −4960.28 | −0.297944 | ||||||||
\(653\) | −25117.5 | −1.50524 | −0.752620 | − | 0.658455i | \(-0.771210\pi\) | ||||
−0.752620 | + | 0.658455i | \(0.771210\pi\) | |||||||
\(654\) | −1774.69 | −0.106110 | ||||||||
\(655\) | −16038.2 | −0.956741 | ||||||||
\(656\) | −18548.4 | −1.10395 | ||||||||
\(657\) | 12206.6 | 0.724847 | ||||||||
\(658\) | −4282.64 | −0.253730 | ||||||||
\(659\) | 16035.4 | 0.947878 | 0.473939 | − | 0.880558i | \(-0.342832\pi\) | ||||
0.473939 | + | 0.880558i | \(0.342832\pi\) | |||||||
\(660\) | 4569.74 | 0.269510 | ||||||||
\(661\) | 15871.5 | 0.933932 | 0.466966 | − | 0.884275i | \(-0.345347\pi\) | ||||
0.466966 | + | 0.884275i | \(0.345347\pi\) | |||||||
\(662\) | 2829.81 | 0.166138 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 6615.96 | 0.386670 | ||||||||
\(665\) | −16864.6 | −0.983432 | ||||||||
\(666\) | 16.1754 | 0.000941119 0 | ||||||||
\(667\) | 3956.09 | 0.229656 | ||||||||
\(668\) | 1435.96 | 0.0831719 | ||||||||
\(669\) | 4458.61 | 0.257668 | ||||||||
\(670\) | −2046.94 | −0.118030 | ||||||||
\(671\) | 450.651 | 0.0259272 | ||||||||
\(672\) | 7091.71 | 0.407096 | ||||||||
\(673\) | 28425.6 | 1.62812 | 0.814062 | − | 0.580779i | \(-0.197252\pi\) | ||||
0.814062 | + | 0.580779i | \(0.197252\pi\) | |||||||
\(674\) | −2751.12 | −0.157224 | ||||||||
\(675\) | 6888.93 | 0.392823 | ||||||||
\(676\) | 17098.0 | 0.972805 | ||||||||
\(677\) | −6162.76 | −0.349858 | −0.174929 | − | 0.984581i | \(-0.555970\pi\) | ||||
−0.174929 | + | 0.984581i | \(0.555970\pi\) | |||||||
\(678\) | 1808.62 | 0.102448 | ||||||||
\(679\) | −7990.05 | −0.451591 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 546.925 | 0.0307756 | ||||||||
\(682\) | 1121.42 | 0.0629642 | ||||||||
\(683\) | −23399.7 | −1.31093 | −0.655464 | − | 0.755227i | \(-0.727527\pi\) | ||||
−0.655464 | + | 0.755227i | \(0.727527\pi\) | |||||||
\(684\) | −5017.84 | −0.280500 | ||||||||
\(685\) | 21968.8 | 1.22538 | ||||||||
\(686\) | −4932.26 | −0.274511 | ||||||||
\(687\) | 7948.71 | 0.441430 | ||||||||
\(688\) | −9127.87 | −0.505809 | ||||||||
\(689\) | −2561.23 | −0.141619 | ||||||||
\(690\) | −279.894 | −0.0154426 | ||||||||
\(691\) | −2684.02 | −0.147764 | −0.0738821 | − | 0.997267i | \(-0.523539\pi\) | ||||
−0.0738821 | + | 0.997267i | \(0.523539\pi\) | |||||||
\(692\) | −12523.4 | −0.687959 | ||||||||
\(693\) | −7524.92 | −0.412479 | ||||||||
\(694\) | −1637.28 | −0.0895535 | ||||||||
\(695\) | 18148.9 | 0.990542 | ||||||||
\(696\) | −3797.92 | −0.206839 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | −3463.98 | −0.187842 | ||||||||
\(699\) | 8114.22 | 0.439067 | ||||||||
\(700\) | 12842.1 | 0.693406 | ||||||||
\(701\) | −29195.5 | −1.57304 | −0.786519 | − | 0.617566i | \(-0.788119\pi\) | ||||
−0.786519 | + | 0.617566i | \(0.788119\pi\) | |||||||
\(702\) | 253.273 | 0.0136170 | ||||||||
\(703\) | 106.721 | 0.00572553 | ||||||||
\(704\) | 6341.70 | 0.339506 | ||||||||
\(705\) | 15601.5 | 0.833458 | ||||||||
\(706\) | −335.546 | −0.0178873 | ||||||||
\(707\) | −23921.7 | −1.27251 | ||||||||
\(708\) | −12895.0 | −0.684499 | ||||||||
\(709\) | 25492.2 | 1.35032 | 0.675161 | − | 0.737670i | \(-0.264074\pi\) | ||||
0.675161 | + | 0.737670i | \(0.264074\pi\) | |||||||
\(710\) | −2203.14 | −0.116454 | ||||||||
\(711\) | −3556.58 | −0.187598 | ||||||||
\(712\) | 1813.61 | 0.0954603 | ||||||||
\(713\) | 4391.31 | 0.230653 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 922.227 | 0.0482368 | ||||||||
\(716\) | −19463.6 | −1.01591 | ||||||||
\(717\) | −11097.0 | −0.577996 | ||||||||
\(718\) | 2927.83 | 0.152181 | ||||||||
\(719\) | 36699.3 | 1.90355 | 0.951776 | − | 0.306794i | \(-0.0992563\pi\) | ||||
0.951776 | + | 0.306794i | \(0.0992563\pi\) | |||||||
\(720\) | 13357.4 | 0.691388 | ||||||||
\(721\) | 26559.4 | 1.37188 | ||||||||
\(722\) | −1889.72 | −0.0974071 | ||||||||
\(723\) | −13210.0 | −0.679510 | ||||||||
\(724\) | 8790.63 | 0.451245 | ||||||||
\(725\) | −10342.9 | −0.529829 | ||||||||
\(726\) | 1297.26 | 0.0663167 | ||||||||
\(727\) | 12123.1 | 0.618462 | 0.309231 | − | 0.950987i | \(-0.399928\pi\) | ||||
0.309231 | + | 0.950987i | \(0.399928\pi\) | |||||||
\(728\) | 951.667 | 0.0484493 | ||||||||
\(729\) | 12357.1 | 0.627807 | ||||||||
\(730\) | 3407.41 | 0.172759 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | −840.484 | −0.0424388 | ||||||||
\(733\) | −14071.9 | −0.709080 | −0.354540 | − | 0.935041i | \(-0.615363\pi\) | ||||
−0.354540 | + | 0.935041i | \(0.615363\pi\) | |||||||
\(734\) | −2925.69 | −0.147124 | ||||||||
\(735\) | 32568.3 | 1.63442 | ||||||||
\(736\) | −1236.67 | −0.0619353 | ||||||||
\(737\) | −6025.90 | −0.301176 | ||||||||
\(738\) | 1768.50 | 0.0882107 | ||||||||
\(739\) | −19170.8 | −0.954276 | −0.477138 | − | 0.878828i | \(-0.658326\pi\) | ||||
−0.477138 | + | 0.878828i | \(0.658326\pi\) | |||||||
\(740\) | −288.673 | −0.0143403 | ||||||||
\(741\) | 635.871 | 0.0315240 | ||||||||
\(742\) | 5833.68 | 0.288627 | ||||||||
\(743\) | −23171.1 | −1.14410 | −0.572050 | − | 0.820219i | \(-0.693852\pi\) | ||||
−0.572050 | + | 0.820219i | \(0.693852\pi\) | |||||||
\(744\) | −4215.73 | −0.207737 | ||||||||
\(745\) | 25296.4 | 1.24401 | ||||||||
\(746\) | −4003.70 | −0.196496 | ||||||||
\(747\) | 19690.0 | 0.964418 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −15346.0 | −0.748641 | ||||||||
\(750\) | −1135.86 | −0.0553008 | ||||||||
\(751\) | 7719.44 | 0.375082 | 0.187541 | − | 0.982257i | \(-0.439948\pi\) | ||||
0.187541 | + | 0.982257i | \(0.439948\pi\) | |||||||
\(752\) | 22379.4 | 1.08523 | ||||||||
\(753\) | 9448.61 | 0.457273 | ||||||||
\(754\) | −380.259 | −0.0183663 | ||||||||
\(755\) | 24774.8 | 1.19424 | ||||||||
\(756\) | 36881.1 | 1.77428 | ||||||||
\(757\) | −200.163 | −0.00961038 | −0.00480519 | − | 0.999988i | \(-0.501530\pi\) | ||||
−0.00480519 | + | 0.999988i | \(0.501530\pi\) | |||||||
\(758\) | −4093.82 | −0.196166 | ||||||||
\(759\) | −823.970 | −0.0394047 | ||||||||
\(760\) | −2823.32 | −0.134753 | ||||||||
\(761\) | 21047.7 | 1.00260 | 0.501300 | − | 0.865274i | \(-0.332855\pi\) | ||||
0.501300 | + | 0.865274i | \(0.332855\pi\) | |||||||
\(762\) | 944.847 | 0.0449189 | ||||||||
\(763\) | −52153.6 | −2.47456 | ||||||||
\(764\) | −30326.2 | −1.43608 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 1436.10 | 0.0677396 | ||||||||
\(767\) | −2602.37 | −0.122511 | ||||||||
\(768\) | −11229.3 | −0.527610 | ||||||||
\(769\) | −21670.0 | −1.01618 | −0.508089 | − | 0.861305i | \(-0.669648\pi\) | ||||
−0.508089 | + | 0.861305i | \(0.669648\pi\) | |||||||
\(770\) | −2100.54 | −0.0983095 | ||||||||
\(771\) | −3678.67 | −0.171834 | ||||||||
\(772\) | 17521.4 | 0.816849 | ||||||||
\(773\) | −9286.93 | −0.432118 | −0.216059 | − | 0.976380i | \(-0.569320\pi\) | ||||
−0.216059 | + | 0.976380i | \(0.569320\pi\) | |||||||
\(774\) | 870.301 | 0.0404164 | ||||||||
\(775\) | −11480.7 | −0.532129 | ||||||||
\(776\) | −1337.62 | −0.0618785 | ||||||||
\(777\) | −298.486 | −0.0137813 | ||||||||
\(778\) | −3245.29 | −0.149549 | ||||||||
\(779\) | 11668.1 | 0.536651 | ||||||||
\(780\) | −1720.00 | −0.0789561 | ||||||||
\(781\) | −6485.74 | −0.297155 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −29703.8 | −1.35572 | ||||||||
\(784\) | 46717.0 | 2.12815 | ||||||||
\(785\) | 1301.78 | 0.0591877 | ||||||||
\(786\) | −1377.34 | −0.0625041 | ||||||||
\(787\) | −23483.9 | −1.06368 | −0.531838 | − | 0.846846i | \(-0.678498\pi\) | ||||
−0.531838 | + | 0.846846i | \(0.678498\pi\) | |||||||
\(788\) | −14734.9 | −0.666126 | ||||||||
\(789\) | 5981.56 | 0.269898 | ||||||||
\(790\) | −992.800 | −0.0447117 | ||||||||
\(791\) | 53150.7 | 2.38916 | ||||||||
\(792\) | −1259.75 | −0.0565193 | ||||||||
\(793\) | −169.620 | −0.00759568 | ||||||||
\(794\) | −2259.17 | −0.100976 | ||||||||
\(795\) | −21251.9 | −0.948087 | ||||||||
\(796\) | −6880.18 | −0.306359 | ||||||||
\(797\) | −28764.0 | −1.27839 | −0.639193 | − | 0.769046i | \(-0.720731\pi\) | ||||
−0.639193 | + | 0.769046i | \(0.720731\pi\) | |||||||
\(798\) | −1448.31 | −0.0642478 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 3233.19 | 0.142888 | ||||||||
\(801\) | 5397.55 | 0.238094 | ||||||||
\(802\) | −484.226 | −0.0213200 | ||||||||
\(803\) | 10030.9 | 0.440828 | ||||||||
\(804\) | 11238.6 | 0.492978 | ||||||||
\(805\) | −8225.37 | −0.360132 | ||||||||
\(806\) | −422.091 | −0.0184461 | ||||||||
\(807\) | −7180.28 | −0.313207 | ||||||||
\(808\) | −4004.74 | −0.174364 | ||||||||
\(809\) | 9148.76 | 0.397594 | 0.198797 | − | 0.980041i | \(-0.436297\pi\) | ||||
0.198797 | + | 0.980041i | \(0.436297\pi\) | |||||||
\(810\) | 28.2824 | 0.00122684 | ||||||||
\(811\) | 9227.06 | 0.399514 | 0.199757 | − | 0.979845i | \(-0.435985\pi\) | ||||
0.199757 | + | 0.979845i | \(0.435985\pi\) | |||||||
\(812\) | −55372.6 | −2.39310 | ||||||||
\(813\) | −2379.07 | −0.102629 | ||||||||
\(814\) | 13.2924 | 0.000572357 0 | ||||||||
\(815\) | −8306.20 | −0.356998 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 5741.98 | 0.245883 | ||||||||
\(818\) | −4585.28 | −0.195991 | ||||||||
\(819\) | 2832.29 | 0.120841 | ||||||||
\(820\) | −31561.4 | −1.34411 | ||||||||
\(821\) | −26834.5 | −1.14072 | −0.570360 | − | 0.821395i | \(-0.693196\pi\) | ||||
−0.570360 | + | 0.821395i | \(0.693196\pi\) | |||||||
\(822\) | 1886.65 | 0.0800543 | ||||||||
\(823\) | −33089.0 | −1.40147 | −0.700735 | − | 0.713421i | \(-0.747145\pi\) | ||||
−0.700735 | + | 0.713421i | \(0.747145\pi\) | |||||||
\(824\) | 4446.32 | 0.187979 | ||||||||
\(825\) | 2154.21 | 0.0909089 | ||||||||
\(826\) | 5927.39 | 0.249685 | ||||||||
\(827\) | −25987.6 | −1.09272 | −0.546360 | − | 0.837551i | \(-0.683987\pi\) | ||||
−0.546360 | + | 0.837551i | \(0.683987\pi\) | |||||||
\(828\) | −2447.35 | −0.102719 | ||||||||
\(829\) | 4089.38 | 0.171327 | 0.0856635 | − | 0.996324i | \(-0.472699\pi\) | ||||
0.0856635 | + | 0.996324i | \(0.472699\pi\) | |||||||
\(830\) | 5496.37 | 0.229857 | ||||||||
\(831\) | −4841.49 | −0.202105 | ||||||||
\(832\) | −2386.94 | −0.0994620 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 1558.61 | 0.0647124 | ||||||||
\(835\) | 2404.57 | 0.0996570 | ||||||||
\(836\) | −4123.48 | −0.170590 | ||||||||
\(837\) | −32971.5 | −1.36160 | ||||||||
\(838\) | −2685.68 | −0.110710 | ||||||||
\(839\) | 14215.0 | 0.584932 | 0.292466 | − | 0.956276i | \(-0.405524\pi\) | ||||
0.292466 | + | 0.956276i | \(0.405524\pi\) | |||||||
\(840\) | 7896.49 | 0.324351 | ||||||||
\(841\) | 20207.7 | 0.828556 | ||||||||
\(842\) | −5487.93 | −0.224616 | ||||||||
\(843\) | −17321.3 | −0.707684 | ||||||||
\(844\) | −6525.07 | −0.266116 | ||||||||
\(845\) | 28631.4 | 1.16562 | ||||||||
\(846\) | −2133.77 | −0.0867146 | ||||||||
\(847\) | 38123.2 | 1.54655 | ||||||||
\(848\) | −30484.5 | −1.23448 | ||||||||
\(849\) | −16032.4 | −0.648091 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 52.0508 | 0.00209668 | ||||||||
\(852\) | 12096.2 | 0.486396 | ||||||||
\(853\) | −9233.05 | −0.370614 | −0.185307 | − | 0.982681i | \(-0.559328\pi\) | ||||
−0.185307 | + | 0.982681i | \(0.559328\pi\) | |||||||
\(854\) | 386.340 | 0.0154804 | ||||||||
\(855\) | −8402.59 | −0.336096 | ||||||||
\(856\) | −2569.09 | −0.102581 | ||||||||
\(857\) | −8309.78 | −0.331221 | −0.165611 | − | 0.986191i | \(-0.552960\pi\) | ||||
−0.165611 | + | 0.986191i | \(0.552960\pi\) | |||||||
\(858\) | 79.1998 | 0.00315132 | ||||||||
\(859\) | 19105.7 | 0.758880 | 0.379440 | − | 0.925216i | \(-0.376117\pi\) | ||||
0.379440 | + | 0.925216i | \(0.376117\pi\) | |||||||
\(860\) | −15531.8 | −0.615847 | ||||||||
\(861\) | −32634.2 | −1.29172 | ||||||||
\(862\) | 3895.82 | 0.153935 | ||||||||
\(863\) | 24172.0 | 0.953447 | 0.476724 | − | 0.879053i | \(-0.341824\pi\) | ||||
0.476724 | + | 0.879053i | \(0.341824\pi\) | |||||||
\(864\) | 9285.39 | 0.365620 | ||||||||
\(865\) | −20970.9 | −0.824316 | ||||||||
\(866\) | −5158.65 | −0.202423 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −61464.1 | −2.40349 | ||||||||
\(869\) | −2922.67 | −0.114091 | ||||||||
\(870\) | −3155.21 | −0.122956 | ||||||||
\(871\) | 2268.08 | 0.0882331 | ||||||||
\(872\) | −8731.06 | −0.339072 | ||||||||
\(873\) | −3980.94 | −0.154335 | ||||||||
\(874\) | 252.561 | 0.00977460 | ||||||||
\(875\) | −33379.9 | −1.28965 | ||||||||
\(876\) | −18708.2 | −0.721565 | ||||||||
\(877\) | 2782.43 | 0.107133 | 0.0535666 | − | 0.998564i | \(-0.482941\pi\) | ||||
0.0535666 | + | 0.998564i | \(0.482941\pi\) | |||||||
\(878\) | 3300.19 | 0.126852 | ||||||||
\(879\) | −20903.9 | −0.802127 | ||||||||
\(880\) | 10976.6 | 0.420479 | ||||||||
\(881\) | 10940.4 | 0.418377 | 0.209189 | − | 0.977875i | \(-0.432918\pi\) | ||||
0.209189 | + | 0.977875i | \(0.432918\pi\) | |||||||
\(882\) | −4454.26 | −0.170048 | ||||||||
\(883\) | 47442.1 | 1.80810 | 0.904052 | − | 0.427423i | \(-0.140579\pi\) | ||||
0.904052 | + | 0.427423i | \(0.140579\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −21593.3 | −0.820171 | ||||||||
\(886\) | −2650.17 | −0.100490 | ||||||||
\(887\) | −19641.2 | −0.743501 | −0.371751 | − | 0.928333i | \(-0.621242\pi\) | ||||
−0.371751 | + | 0.928333i | \(0.621242\pi\) | |||||||
\(888\) | −49.9696 | −0.00188837 | ||||||||
\(889\) | 27766.7 | 1.04754 | ||||||||
\(890\) | 1506.70 | 0.0567467 | ||||||||
\(891\) | 83.2596 | 0.00313053 | ||||||||
\(892\) | 10882.6 | 0.408492 | ||||||||
\(893\) | −14078.0 | −0.527550 | ||||||||
\(894\) | 2172.42 | 0.0812714 | ||||||||
\(895\) | −32592.6 | −1.21726 | ||||||||
\(896\) | 23016.9 | 0.858192 | ||||||||
\(897\) | 310.133 | 0.0115441 | ||||||||
\(898\) | −2537.08 | −0.0942799 | ||||||||
\(899\) | 49502.8 | 1.83650 | ||||||||
\(900\) | 6398.40 | 0.236978 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 1453.29 | 0.0536467 | ||||||||
\(903\) | −16059.7 | −0.591841 | ||||||||
\(904\) | 8897.99 | 0.327370 | ||||||||
\(905\) | 14720.3 | 0.540684 | ||||||||
\(906\) | 2127.63 | 0.0780197 | ||||||||
\(907\) | 16516.5 | 0.604653 | 0.302327 | − | 0.953204i | \(-0.402237\pi\) | ||||
0.302327 | + | 0.953204i | \(0.402237\pi\) | |||||||
\(908\) | 1334.93 | 0.0487900 | ||||||||
\(909\) | −11918.7 | −0.434893 | ||||||||
\(910\) | 790.620 | 0.0288009 | ||||||||
\(911\) | −48493.4 | −1.76362 | −0.881810 | − | 0.471606i | \(-0.843675\pi\) | ||||
−0.881810 | + | 0.471606i | \(0.843675\pi\) | |||||||
\(912\) | 7568.31 | 0.274794 | ||||||||
\(913\) | 16180.6 | 0.586527 | ||||||||
\(914\) | 2116.86 | 0.0766078 | ||||||||
\(915\) | −1407.43 | −0.0508504 | ||||||||
\(916\) | 19401.2 | 0.699818 | ||||||||
\(917\) | −40476.6 | −1.45764 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 24953.8 | 0.895703 | 0.447851 | − | 0.894108i | \(-0.352189\pi\) | ||||
0.447851 | + | 0.894108i | \(0.352189\pi\) | |||||||
\(920\) | −1377.01 | −0.0493465 | ||||||||
\(921\) | 17261.2 | 0.617565 | ||||||||
\(922\) | 1330.32 | 0.0475181 | ||||||||
\(923\) | 2441.16 | 0.0870549 | ||||||||
\(924\) | 11532.9 | 0.410612 | ||||||||
\(925\) | −136.083 | −0.00483716 | ||||||||
\(926\) | −3259.85 | −0.115686 | ||||||||
\(927\) | 13232.9 | 0.468851 | ||||||||
\(928\) | −13940.9 | −0.493138 | ||||||||
\(929\) | −19392.6 | −0.684878 | −0.342439 | − | 0.939540i | \(-0.611253\pi\) | ||||
−0.342439 | + | 0.939540i | \(0.611253\pi\) | |||||||
\(930\) | −3502.32 | −0.123490 | ||||||||
\(931\) | −29387.9 | −1.03453 | ||||||||
\(932\) | 19805.2 | 0.696073 | ||||||||
\(933\) | −11683.6 | −0.409972 | ||||||||
\(934\) | 209.514 | 0.00733994 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 474.156 | 0.0165580 | ||||||||
\(937\) | −41919.9 | −1.46154 | −0.730770 | − | 0.682624i | \(-0.760839\pi\) | ||||
−0.730770 | + | 0.682624i | \(0.760839\pi\) | |||||||
\(938\) | −5165.97 | −0.179824 | ||||||||
\(939\) | −6689.87 | −0.232498 | ||||||||
\(940\) | 38080.2 | 1.32132 | ||||||||
\(941\) | −48057.2 | −1.66484 | −0.832422 | − | 0.554142i | \(-0.813046\pi\) | ||||
−0.832422 | + | 0.554142i | \(0.813046\pi\) | |||||||
\(942\) | 111.795 | 0.00386674 | ||||||||
\(943\) | 5690.85 | 0.196521 | ||||||||
\(944\) | −30974.2 | −1.06793 | ||||||||
\(945\) | 61759.0 | 2.12595 | ||||||||
\(946\) | 715.182 | 0.0245799 | ||||||||
\(947\) | 38890.6 | 1.33450 | 0.667252 | − | 0.744832i | \(-0.267470\pi\) | ||||
0.667252 | + | 0.744832i | \(0.267470\pi\) | |||||||
\(948\) | 5450.91 | 0.186748 | ||||||||
\(949\) | −3775.53 | −0.129145 | ||||||||
\(950\) | −660.302 | −0.0225505 | ||||||||
\(951\) | 25706.8 | 0.876553 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −6364.48 | −0.216333 | −0.108167 | − | 0.994133i | \(-0.534498\pi\) | ||||
−0.108167 | + | 0.994133i | \(0.534498\pi\) | |||||||
\(954\) | 2906.56 | 0.0986408 | ||||||||
\(955\) | −50782.6 | −1.72072 | ||||||||
\(956\) | −27085.4 | −0.916323 | ||||||||
\(957\) | −9288.53 | −0.313747 | ||||||||
\(958\) | −1557.32 | −0.0525205 | ||||||||
\(959\) | 55444.0 | 1.86692 | ||||||||
\(960\) | −19805.8 | −0.665863 | ||||||||
\(961\) | 25157.6 | 0.844470 | ||||||||
\(962\) | −5.00311 | −0.000167678 0 | ||||||||
\(963\) | −7645.97 | −0.255854 | ||||||||
\(964\) | −32243.0 | −1.07726 | ||||||||
\(965\) | 29340.3 | 0.978753 | ||||||||
\(966\) | −706.384 | −0.0235275 | ||||||||
\(967\) | −1031.78 | −0.0343121 | −0.0171560 | − | 0.999853i | \(-0.505461\pi\) | ||||
−0.0171560 | + | 0.999853i | \(0.505461\pi\) | |||||||
\(968\) | 6382.23 | 0.211914 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −1111.26 | −0.0367839 | ||||||||
\(971\) | 30980.7 | 1.02391 | 0.511956 | − | 0.859012i | \(-0.328921\pi\) | ||||
0.511956 | + | 0.859012i | \(0.328921\pi\) | |||||||
\(972\) | 29758.7 | 0.982006 | ||||||||
\(973\) | 45803.5 | 1.50914 | ||||||||
\(974\) | 3037.69 | 0.0999321 | ||||||||
\(975\) | −810.819 | −0.0266328 | ||||||||
\(976\) | −2018.86 | −0.0662113 | ||||||||
\(977\) | 37987.7 | 1.24394 | 0.621972 | − | 0.783040i | \(-0.286332\pi\) | ||||
0.621972 | + | 0.783040i | \(0.286332\pi\) | |||||||
\(978\) | −713.327 | −0.0233228 | ||||||||
\(979\) | 4435.51 | 0.144800 | ||||||||
\(980\) | 79492.5 | 2.59112 | ||||||||
\(981\) | −25984.9 | −0.845701 | ||||||||
\(982\) | −1811.40 | −0.0588635 | ||||||||
\(983\) | −54835.9 | −1.77924 | −0.889620 | − | 0.456702i | \(-0.849030\pi\) | ||||
−0.889620 | + | 0.456702i | \(0.849030\pi\) | |||||||
\(984\) | −5463.31 | −0.176996 | ||||||||
\(985\) | −24674.1 | −0.798156 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 39374.5 | 1.26981 | ||||||||
\(988\) | 1552.03 | 0.0499764 | ||||||||
\(989\) | 2800.53 | 0.0900422 | ||||||||
\(990\) | −1046.57 | −0.0335981 | ||||||||
\(991\) | −39381.6 | −1.26236 | −0.631180 | − | 0.775636i | \(-0.717429\pi\) | ||||
−0.631180 | + | 0.775636i | \(0.717429\pi\) | |||||||
\(992\) | −15474.5 | −0.495279 | ||||||||
\(993\) | −26017.2 | −0.831452 | ||||||||
\(994\) | −5560.19 | −0.177423 | ||||||||
\(995\) | −11521.2 | −0.367081 | ||||||||
\(996\) | −30177.5 | −0.960051 | ||||||||
\(997\) | 22509.1 | 0.715014 | 0.357507 | − | 0.933910i | \(-0.383627\pi\) | ||||
0.357507 | + | 0.933910i | \(0.383627\pi\) | |||||||
\(998\) | −3062.32 | −0.0971303 | ||||||||
\(999\) | −390.816 | −0.0123772 |
(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.f.1.3 | 8 | ||
17.4 | even | 4 | 289.4.b.c.288.6 | 8 | |||
17.8 | even | 8 | 17.4.c.a.13.3 | yes | 8 | ||
17.13 | even | 4 | 289.4.b.c.288.5 | 8 | |||
17.15 | even | 8 | 17.4.c.a.4.2 | ✓ | 8 | ||
17.16 | even | 2 | inner | 289.4.a.f.1.4 | 8 | ||
51.8 | odd | 8 | 153.4.f.a.64.2 | 8 | |||
51.32 | odd | 8 | 153.4.f.a.55.3 | 8 | |||
68.15 | odd | 8 | 272.4.o.e.225.2 | 8 | |||
68.59 | odd | 8 | 272.4.o.e.81.2 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
17.4.c.a.4.2 | ✓ | 8 | 17.15 | even | 8 | ||
17.4.c.a.13.3 | yes | 8 | 17.8 | even | 8 | ||
153.4.f.a.55.3 | 8 | 51.32 | odd | 8 | |||
153.4.f.a.64.2 | 8 | 51.8 | odd | 8 | |||
272.4.o.e.81.2 | 8 | 68.59 | odd | 8 | |||
272.4.o.e.225.2 | 8 | 68.15 | odd | 8 | |||
289.4.a.f.1.3 | 8 | 1.1 | even | 1 | trivial | ||
289.4.a.f.1.4 | 8 | 17.16 | even | 2 | inner | ||
289.4.b.c.288.5 | 8 | 17.13 | even | 4 | |||
289.4.b.c.288.6 | 8 | 17.4 | even | 4 |