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: | \( x^{12} - 72 x^{10} - 17 x^{9} + 1872 x^{8} + 627 x^{7} - 20922 x^{6} - 5163 x^{5} + 93255 x^{4} + \cdots + 29352 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{3}\cdot 17^{2} \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(2.16473\) 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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.16473 | −0.765347 | −0.382673 | − | 0.923884i | \(-0.624997\pi\) | ||||
−0.382673 | + | 0.923884i | \(0.624997\pi\) | |||||||
\(3\) | −9.14133 | −1.75925 | −0.879625 | − | 0.475668i | \(-0.842206\pi\) | ||||
−0.879625 | + | 0.475668i | \(0.842206\pi\) | |||||||
\(4\) | −3.31395 | −0.414244 | ||||||||
\(5\) | −16.2298 | −1.45164 | −0.725819 | − | 0.687886i | \(-0.758539\pi\) | ||||
−0.725819 | + | 0.687886i | \(0.758539\pi\) | |||||||
\(6\) | 19.7885 | 1.34644 | ||||||||
\(7\) | −12.2246 | −0.660065 | −0.330032 | − | 0.943970i | \(-0.607060\pi\) | ||||
−0.330032 | + | 0.943970i | \(0.607060\pi\) | |||||||
\(8\) | 24.4916 | 1.08239 | ||||||||
\(9\) | 56.5639 | 2.09496 | ||||||||
\(10\) | 35.1331 | 1.11101 | ||||||||
\(11\) | 11.1761 | 0.306338 | 0.153169 | − | 0.988200i | \(-0.451052\pi\) | ||||
0.153169 | + | 0.988200i | \(0.451052\pi\) | |||||||
\(12\) | 30.2939 | 0.728759 | ||||||||
\(13\) | 28.9000 | 0.616570 | 0.308285 | − | 0.951294i | \(-0.400245\pi\) | ||||
0.308285 | + | 0.951294i | \(0.400245\pi\) | |||||||
\(14\) | 26.4629 | 0.505178 | ||||||||
\(15\) | 148.362 | 2.55379 | ||||||||
\(16\) | −26.5061 | −0.414158 | ||||||||
\(17\) | 0 | 0 | ||||||||
\(18\) | −122.445 | −1.60337 | ||||||||
\(19\) | −79.5850 | −0.960950 | −0.480475 | − | 0.877009i | \(-0.659536\pi\) | ||||
−0.480475 | + | 0.877009i | \(0.659536\pi\) | |||||||
\(20\) | 53.7848 | 0.601332 | ||||||||
\(21\) | 111.749 | 1.16122 | ||||||||
\(22\) | −24.1932 | −0.234455 | ||||||||
\(23\) | 45.0447 | 0.408368 | 0.204184 | − | 0.978933i | \(-0.434546\pi\) | ||||
0.204184 | + | 0.978933i | \(0.434546\pi\) | |||||||
\(24\) | −223.886 | −1.90419 | ||||||||
\(25\) | 138.406 | 1.10725 | ||||||||
\(26\) | −62.5606 | −0.471890 | ||||||||
\(27\) | −270.253 | −1.92631 | ||||||||
\(28\) | 40.5117 | 0.273428 | ||||||||
\(29\) | −20.3774 | −0.130482 | −0.0652411 | − | 0.997870i | \(-0.520782\pi\) | ||||
−0.0652411 | + | 0.997870i | \(0.520782\pi\) | |||||||
\(30\) | −321.163 | −1.95454 | ||||||||
\(31\) | −1.03839 | −0.00601613 | −0.00300806 | − | 0.999995i | \(-0.500957\pi\) | ||||
−0.00300806 | + | 0.999995i | \(0.500957\pi\) | |||||||
\(32\) | −138.555 | −0.765413 | ||||||||
\(33\) | −102.164 | −0.538926 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 198.402 | 0.958175 | ||||||||
\(36\) | −187.450 | −0.867824 | ||||||||
\(37\) | 219.921 | 0.977159 | 0.488579 | − | 0.872520i | \(-0.337515\pi\) | ||||
0.488579 | + | 0.872520i | \(0.337515\pi\) | |||||||
\(38\) | 172.280 | 0.735460 | ||||||||
\(39\) | −264.184 | −1.08470 | ||||||||
\(40\) | −397.494 | −1.57123 | ||||||||
\(41\) | 310.992 | 1.18460 | 0.592302 | − | 0.805716i | \(-0.298219\pi\) | ||||
0.592302 | + | 0.805716i | \(0.298219\pi\) | |||||||
\(42\) | −241.906 | −0.888735 | ||||||||
\(43\) | 483.760 | 1.71564 | 0.857822 | − | 0.513947i | \(-0.171817\pi\) | ||||
0.857822 | + | 0.513947i | \(0.171817\pi\) | |||||||
\(44\) | −37.0371 | −0.126899 | ||||||||
\(45\) | −918.020 | −3.04112 | ||||||||
\(46\) | −97.5095 | −0.312543 | ||||||||
\(47\) | −632.422 | −1.96273 | −0.981364 | − | 0.192156i | \(-0.938452\pi\) | ||||
−0.981364 | + | 0.192156i | \(0.938452\pi\) | |||||||
\(48\) | 242.301 | 0.728606 | ||||||||
\(49\) | −193.560 | −0.564315 | ||||||||
\(50\) | −299.612 | −0.847431 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −95.7732 | −0.255411 | ||||||||
\(53\) | 490.172 | 1.27038 | 0.635192 | − | 0.772354i | \(-0.280921\pi\) | ||||
0.635192 | + | 0.772354i | \(0.280921\pi\) | |||||||
\(54\) | 585.024 | 1.47429 | ||||||||
\(55\) | −181.386 | −0.444692 | ||||||||
\(56\) | −299.400 | −0.714446 | ||||||||
\(57\) | 727.512 | 1.69055 | ||||||||
\(58\) | 44.1115 | 0.0998642 | ||||||||
\(59\) | 147.956 | 0.326478 | 0.163239 | − | 0.986587i | \(-0.447806\pi\) | ||||
0.163239 | + | 0.986587i | \(0.447806\pi\) | |||||||
\(60\) | −491.665 | −1.05789 | ||||||||
\(61\) | −176.395 | −0.370246 | −0.185123 | − | 0.982715i | \(-0.559268\pi\) | ||||
−0.185123 | + | 0.982715i | \(0.559268\pi\) | |||||||
\(62\) | 2.24783 | 0.00460442 | ||||||||
\(63\) | −691.469 | −1.38281 | ||||||||
\(64\) | 511.982 | 0.999964 | ||||||||
\(65\) | −469.041 | −0.895037 | ||||||||
\(66\) | 221.158 | 0.412465 | ||||||||
\(67\) | 809.312 | 1.47572 | 0.737860 | − | 0.674954i | \(-0.235836\pi\) | ||||
0.737860 | + | 0.674954i | \(0.235836\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −411.768 | −0.718421 | ||||||||
\(70\) | −429.487 | −0.733336 | ||||||||
\(71\) | −714.189 | −1.19378 | −0.596892 | − | 0.802322i | \(-0.703598\pi\) | ||||
−0.596892 | + | 0.802322i | \(0.703598\pi\) | |||||||
\(72\) | 1385.34 | 2.26756 | ||||||||
\(73\) | −780.184 | −1.25087 | −0.625436 | − | 0.780276i | \(-0.715079\pi\) | ||||
−0.625436 | + | 0.780276i | \(0.715079\pi\) | |||||||
\(74\) | −476.070 | −0.747865 | ||||||||
\(75\) | −1265.22 | −1.94793 | ||||||||
\(76\) | 263.741 | 0.398068 | ||||||||
\(77\) | −136.623 | −0.202203 | ||||||||
\(78\) | 571.887 | 0.830172 | ||||||||
\(79\) | 230.265 | 0.327935 | 0.163968 | − | 0.986466i | \(-0.447571\pi\) | ||||
0.163968 | + | 0.986466i | \(0.447571\pi\) | |||||||
\(80\) | 430.188 | 0.601207 | ||||||||
\(81\) | 943.248 | 1.29389 | ||||||||
\(82\) | −673.213 | −0.906633 | ||||||||
\(83\) | 236.046 | 0.312161 | 0.156080 | − | 0.987744i | \(-0.450114\pi\) | ||||
0.156080 | + | 0.987744i | \(0.450114\pi\) | |||||||
\(84\) | −370.330 | −0.481028 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −1047.21 | −1.31306 | ||||||||
\(87\) | 186.276 | 0.229551 | ||||||||
\(88\) | 273.721 | 0.331577 | ||||||||
\(89\) | −688.557 | −0.820078 | −0.410039 | − | 0.912068i | \(-0.634485\pi\) | ||||
−0.410039 | + | 0.912068i | \(0.634485\pi\) | |||||||
\(90\) | 1987.26 | 2.32751 | ||||||||
\(91\) | −353.290 | −0.406976 | ||||||||
\(92\) | −149.276 | −0.169164 | ||||||||
\(93\) | 9.49224 | 0.0105839 | ||||||||
\(94\) | 1369.02 | 1.50217 | ||||||||
\(95\) | 1291.65 | 1.39495 | ||||||||
\(96\) | 1266.57 | 1.34655 | ||||||||
\(97\) | 1846.11 | 1.93241 | 0.966205 | − | 0.257775i | \(-0.0829893\pi\) | ||||
0.966205 | + | 0.257775i | \(0.0829893\pi\) | |||||||
\(98\) | 419.004 | 0.431896 | ||||||||
\(99\) | 632.164 | 0.641766 | ||||||||
\(100\) | −458.672 | −0.458672 | ||||||||
\(101\) | −735.748 | −0.724848 | −0.362424 | − | 0.932013i | \(-0.618051\pi\) | ||||
−0.362424 | + | 0.932013i | \(0.618051\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 387.334 | 0.370535 | 0.185268 | − | 0.982688i | \(-0.440685\pi\) | ||||
0.185268 | + | 0.982688i | \(0.440685\pi\) | |||||||
\(104\) | 707.808 | 0.667368 | ||||||||
\(105\) | −1813.66 | −1.68567 | ||||||||
\(106\) | −1061.09 | −0.972284 | ||||||||
\(107\) | −793.424 | −0.716852 | −0.358426 | − | 0.933558i | \(-0.616686\pi\) | ||||
−0.358426 | + | 0.933558i | \(0.616686\pi\) | |||||||
\(108\) | 895.606 | 0.797961 | ||||||||
\(109\) | 1709.67 | 1.50236 | 0.751178 | − | 0.660100i | \(-0.229486\pi\) | ||||
0.751178 | + | 0.660100i | \(0.229486\pi\) | |||||||
\(110\) | 392.651 | 0.340344 | ||||||||
\(111\) | −2010.37 | −1.71907 | ||||||||
\(112\) | 324.025 | 0.273371 | ||||||||
\(113\) | −42.1279 | −0.0350713 | −0.0175357 | − | 0.999846i | \(-0.505582\pi\) | ||||
−0.0175357 | + | 0.999846i | \(0.505582\pi\) | |||||||
\(114\) | −1574.87 | −1.29386 | ||||||||
\(115\) | −731.066 | −0.592802 | ||||||||
\(116\) | 67.5297 | 0.0540515 | ||||||||
\(117\) | 1634.70 | 1.29169 | ||||||||
\(118\) | −320.284 | −0.249869 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 3633.63 | 2.76419 | ||||||||
\(121\) | −1206.09 | −0.906157 | ||||||||
\(122\) | 381.846 | 0.283367 | ||||||||
\(123\) | −2842.88 | −2.08401 | ||||||||
\(124\) | 3.44117 | 0.00249215 | ||||||||
\(125\) | −217.583 | −0.155690 | ||||||||
\(126\) | 1496.84 | 1.05833 | ||||||||
\(127\) | −1536.78 | −1.07376 | −0.536878 | − | 0.843660i | \(-0.680397\pi\) | ||||
−0.536878 | + | 0.843660i | \(0.680397\pi\) | |||||||
\(128\) | 0.135867 | 9.38207e−5 0 | ||||||||
\(129\) | −4422.21 | −3.01825 | ||||||||
\(130\) | 1015.35 | 0.685013 | ||||||||
\(131\) | 264.718 | 0.176554 | 0.0882768 | − | 0.996096i | \(-0.471864\pi\) | ||||
0.0882768 | + | 0.996096i | \(0.471864\pi\) | |||||||
\(132\) | 338.568 | 0.223247 | ||||||||
\(133\) | 972.892 | 0.634289 | ||||||||
\(134\) | −1751.94 | −1.12944 | ||||||||
\(135\) | 4386.15 | 2.79630 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 686.450 | 0.428083 | 0.214042 | − | 0.976825i | \(-0.431337\pi\) | ||||
0.214042 | + | 0.976825i | \(0.431337\pi\) | |||||||
\(138\) | 891.366 | 0.549841 | ||||||||
\(139\) | 43.2364 | 0.0263832 | 0.0131916 | − | 0.999913i | \(-0.495801\pi\) | ||||
0.0131916 | + | 0.999913i | \(0.495801\pi\) | |||||||
\(140\) | −657.496 | −0.396918 | ||||||||
\(141\) | 5781.18 | 3.45293 | ||||||||
\(142\) | 1546.02 | 0.913659 | ||||||||
\(143\) | 322.989 | 0.188879 | ||||||||
\(144\) | −1499.29 | −0.867643 | ||||||||
\(145\) | 330.721 | 0.189413 | ||||||||
\(146\) | 1688.89 | 0.957350 | ||||||||
\(147\) | 1769.39 | 0.992770 | ||||||||
\(148\) | −728.810 | −0.404782 | ||||||||
\(149\) | 335.407 | 0.184413 | 0.0922067 | − | 0.995740i | \(-0.470608\pi\) | ||||
0.0922067 | + | 0.995740i | \(0.470608\pi\) | |||||||
\(150\) | 2738.85 | 1.49084 | ||||||||
\(151\) | −2432.29 | −1.31084 | −0.655421 | − | 0.755264i | \(-0.727509\pi\) | ||||
−0.655421 | + | 0.755264i | \(0.727509\pi\) | |||||||
\(152\) | −1949.17 | −1.04012 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 295.752 | 0.154756 | ||||||||
\(155\) | 16.8528 | 0.00873324 | ||||||||
\(156\) | 875.494 | 0.449331 | ||||||||
\(157\) | 2706.98 | 1.37605 | 0.688026 | − | 0.725686i | \(-0.258477\pi\) | ||||
0.688026 | + | 0.725686i | \(0.258477\pi\) | |||||||
\(158\) | −498.462 | −0.250984 | ||||||||
\(159\) | −4480.83 | −2.23492 | ||||||||
\(160\) | 2248.71 | 1.11110 | ||||||||
\(161\) | −550.652 | −0.269549 | ||||||||
\(162\) | −2041.87 | −0.990277 | ||||||||
\(163\) | 190.765 | 0.0916678 | 0.0458339 | − | 0.998949i | \(-0.485405\pi\) | ||||
0.0458339 | + | 0.998949i | \(0.485405\pi\) | |||||||
\(164\) | −1030.61 | −0.490715 | ||||||||
\(165\) | 1658.11 | 0.782325 | ||||||||
\(166\) | −510.974 | −0.238911 | ||||||||
\(167\) | −2757.18 | −1.27759 | −0.638793 | − | 0.769379i | \(-0.720566\pi\) | ||||
−0.638793 | + | 0.769379i | \(0.720566\pi\) | |||||||
\(168\) | 2736.91 | 1.25689 | ||||||||
\(169\) | −1361.79 | −0.619841 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −4501.63 | −2.01315 | ||||||||
\(172\) | −1603.16 | −0.710696 | ||||||||
\(173\) | −1453.00 | −0.638554 | −0.319277 | − | 0.947661i | \(-0.603440\pi\) | ||||
−0.319277 | + | 0.947661i | \(0.603440\pi\) | |||||||
\(174\) | −403.238 | −0.175686 | ||||||||
\(175\) | −1691.96 | −0.730858 | ||||||||
\(176\) | −296.235 | −0.126872 | ||||||||
\(177\) | −1352.51 | −0.574356 | ||||||||
\(178\) | 1490.54 | 0.627644 | ||||||||
\(179\) | −1171.47 | −0.489160 | −0.244580 | − | 0.969629i | \(-0.578650\pi\) | ||||
−0.244580 | + | 0.969629i | \(0.578650\pi\) | |||||||
\(180\) | 3042.28 | 1.25977 | ||||||||
\(181\) | 2737.41 | 1.12414 | 0.562072 | − | 0.827089i | \(-0.310005\pi\) | ||||
0.562072 | + | 0.827089i | \(0.310005\pi\) | |||||||
\(182\) | 764.776 | 0.311478 | ||||||||
\(183\) | 1612.48 | 0.651355 | ||||||||
\(184\) | 1103.22 | 0.442012 | ||||||||
\(185\) | −3569.28 | −1.41848 | ||||||||
\(186\) | −20.5481 | −0.00810033 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 2095.82 | 0.813049 | ||||||||
\(189\) | 3303.73 | 1.27149 | ||||||||
\(190\) | −2796.07 | −1.06762 | ||||||||
\(191\) | −1345.56 | −0.509744 | −0.254872 | − | 0.966975i | \(-0.582033\pi\) | ||||
−0.254872 | + | 0.966975i | \(0.582033\pi\) | |||||||
\(192\) | −4680.19 | −1.75919 | ||||||||
\(193\) | 3787.61 | 1.41263 | 0.706317 | − | 0.707896i | \(-0.250355\pi\) | ||||
0.706317 | + | 0.707896i | \(0.250355\pi\) | |||||||
\(194\) | −3996.32 | −1.47896 | ||||||||
\(195\) | 4287.66 | 1.57459 | ||||||||
\(196\) | 641.448 | 0.233764 | ||||||||
\(197\) | 72.4095 | 0.0261876 | 0.0130938 | − | 0.999914i | \(-0.495832\pi\) | ||||
0.0130938 | + | 0.999914i | \(0.495832\pi\) | |||||||
\(198\) | −1368.46 | −0.491174 | ||||||||
\(199\) | 2703.59 | 0.963077 | 0.481539 | − | 0.876425i | \(-0.340078\pi\) | ||||
0.481539 | + | 0.876425i | \(0.340078\pi\) | |||||||
\(200\) | 3389.80 | 1.19847 | ||||||||
\(201\) | −7398.19 | −2.59616 | ||||||||
\(202\) | 1592.69 | 0.554760 | ||||||||
\(203\) | 249.105 | 0.0861267 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −5047.33 | −1.71962 | ||||||||
\(206\) | −838.472 | −0.283588 | ||||||||
\(207\) | 2547.90 | 0.855514 | ||||||||
\(208\) | −766.025 | −0.255357 | ||||||||
\(209\) | −889.450 | −0.294376 | ||||||||
\(210\) | 3926.08 | 1.29012 | ||||||||
\(211\) | −2338.29 | −0.762911 | −0.381456 | − | 0.924387i | \(-0.624577\pi\) | ||||
−0.381456 | + | 0.924387i | \(0.624577\pi\) | |||||||
\(212\) | −1624.41 | −0.526249 | ||||||||
\(213\) | 6528.64 | 2.10016 | ||||||||
\(214\) | 1717.55 | 0.548640 | ||||||||
\(215\) | −7851.33 | −2.49049 | ||||||||
\(216\) | −6618.94 | −2.08501 | ||||||||
\(217\) | 12.6938 | 0.00397103 | ||||||||
\(218\) | −3700.97 | −1.14982 | ||||||||
\(219\) | 7131.91 | 2.20059 | ||||||||
\(220\) | 601.105 | 0.184211 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 4351.91 | 1.31568 | ||||||||
\(223\) | 1737.70 | 0.521815 | 0.260908 | − | 0.965364i | \(-0.415978\pi\) | ||||
0.260908 | + | 0.965364i | \(0.415978\pi\) | |||||||
\(224\) | 1693.77 | 0.505222 | ||||||||
\(225\) | 7828.80 | 2.31965 | ||||||||
\(226\) | 91.1954 | 0.0268417 | ||||||||
\(227\) | −4480.83 | −1.31015 | −0.655073 | − | 0.755565i | \(-0.727362\pi\) | ||||
−0.655073 | + | 0.755565i | \(0.727362\pi\) | |||||||
\(228\) | −2410.94 | −0.700301 | ||||||||
\(229\) | −3917.73 | −1.13053 | −0.565264 | − | 0.824910i | \(-0.691226\pi\) | ||||
−0.565264 | + | 0.824910i | \(0.691226\pi\) | |||||||
\(230\) | 1582.56 | 0.453699 | ||||||||
\(231\) | 1248.92 | 0.355726 | ||||||||
\(232\) | −499.075 | −0.141232 | ||||||||
\(233\) | −4166.02 | −1.17135 | −0.585675 | − | 0.810546i | \(-0.699171\pi\) | ||||
−0.585675 | + | 0.810546i | \(0.699171\pi\) | |||||||
\(234\) | −3538.67 | −0.988590 | ||||||||
\(235\) | 10264.1 | 2.84917 | ||||||||
\(236\) | −490.318 | −0.135242 | ||||||||
\(237\) | −2104.93 | −0.576920 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −1780.06 | −0.481768 | −0.240884 | − | 0.970554i | \(-0.577437\pi\) | ||||
−0.240884 | + | 0.970554i | \(0.577437\pi\) | |||||||
\(240\) | −3932.49 | −1.05767 | ||||||||
\(241\) | −2469.12 | −0.659958 | −0.329979 | − | 0.943988i | \(-0.607042\pi\) | ||||
−0.329979 | + | 0.943988i | \(0.607042\pi\) | |||||||
\(242\) | 2610.87 | 0.693524 | ||||||||
\(243\) | −1325.70 | −0.349975 | ||||||||
\(244\) | 584.563 | 0.153372 | ||||||||
\(245\) | 3141.44 | 0.819180 | ||||||||
\(246\) | 6154.06 | 1.59499 | ||||||||
\(247\) | −2300.00 | −0.592493 | ||||||||
\(248\) | −25.4318 | −0.00651178 | ||||||||
\(249\) | −2157.77 | −0.549169 | ||||||||
\(250\) | 471.009 | 0.119157 | ||||||||
\(251\) | −4824.05 | −1.21311 | −0.606557 | − | 0.795040i | \(-0.707450\pi\) | ||||
−0.606557 | + | 0.795040i | \(0.707450\pi\) | |||||||
\(252\) | 2291.50 | 0.572820 | ||||||||
\(253\) | 503.424 | 0.125099 | ||||||||
\(254\) | 3326.71 | 0.821796 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −4096.15 | −1.00004 | ||||||||
\(257\) | 5558.77 | 1.34921 | 0.674604 | − | 0.738180i | \(-0.264314\pi\) | ||||
0.674604 | + | 0.738180i | \(0.264314\pi\) | |||||||
\(258\) | 9572.88 | 2.31000 | ||||||||
\(259\) | −2688.45 | −0.644988 | ||||||||
\(260\) | 1554.38 | 0.370764 | ||||||||
\(261\) | −1152.62 | −0.273355 | ||||||||
\(262\) | −573.043 | −0.135125 | ||||||||
\(263\) | −3172.23 | −0.743757 | −0.371878 | − | 0.928281i | \(-0.621286\pi\) | ||||
−0.371878 | + | 0.928281i | \(0.621286\pi\) | |||||||
\(264\) | −2502.17 | −0.583326 | ||||||||
\(265\) | −7955.40 | −1.84414 | ||||||||
\(266\) | −2106.05 | −0.485451 | ||||||||
\(267\) | 6294.33 | 1.44272 | ||||||||
\(268\) | −2682.02 | −0.611309 | ||||||||
\(269\) | −2849.92 | −0.645959 | −0.322979 | − | 0.946406i | \(-0.604684\pi\) | ||||
−0.322979 | + | 0.946406i | \(0.604684\pi\) | |||||||
\(270\) | −9494.83 | −2.14014 | ||||||||
\(271\) | −2565.11 | −0.574980 | −0.287490 | − | 0.957784i | \(-0.592821\pi\) | ||||
−0.287490 | + | 0.957784i | \(0.592821\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 3229.54 | 0.715973 | ||||||||
\(274\) | −1485.98 | −0.327632 | ||||||||
\(275\) | 1546.84 | 0.339194 | ||||||||
\(276\) | 1364.58 | 0.297602 | ||||||||
\(277\) | −6260.95 | −1.35806 | −0.679032 | − | 0.734108i | \(-0.737600\pi\) | ||||
−0.679032 | + | 0.734108i | \(0.737600\pi\) | |||||||
\(278\) | −93.5951 | −0.0201923 | ||||||||
\(279\) | −58.7352 | −0.0126035 | ||||||||
\(280\) | 4859.20 | 1.03712 | ||||||||
\(281\) | −1807.59 | −0.383744 | −0.191872 | − | 0.981420i | \(-0.561456\pi\) | ||||
−0.191872 | + | 0.981420i | \(0.561456\pi\) | |||||||
\(282\) | −12514.7 | −2.64269 | ||||||||
\(283\) | 1264.09 | 0.265521 | 0.132761 | − | 0.991148i | \(-0.457616\pi\) | ||||
0.132761 | + | 0.991148i | \(0.457616\pi\) | |||||||
\(284\) | 2366.79 | 0.494518 | ||||||||
\(285\) | −11807.4 | −2.45407 | ||||||||
\(286\) | −699.184 | −0.144558 | ||||||||
\(287\) | −3801.74 | −0.781915 | ||||||||
\(288\) | −7837.18 | −1.60351 | ||||||||
\(289\) | 0 | 0 | ||||||||
\(290\) | −715.921 | −0.144967 | ||||||||
\(291\) | −16875.9 | −3.39959 | ||||||||
\(292\) | 2585.49 | 0.518166 | ||||||||
\(293\) | 3708.40 | 0.739410 | 0.369705 | − | 0.929149i | \(-0.379459\pi\) | ||||
0.369705 | + | 0.929149i | \(0.379459\pi\) | |||||||
\(294\) | −3830.26 | −0.759813 | ||||||||
\(295\) | −2401.29 | −0.473927 | ||||||||
\(296\) | 5386.24 | 1.05766 | ||||||||
\(297\) | −3020.38 | −0.590101 | ||||||||
\(298\) | −726.065 | −0.141140 | ||||||||
\(299\) | 1301.79 | 0.251788 | ||||||||
\(300\) | 4192.88 | 0.806919 | ||||||||
\(301\) | −5913.76 | −1.13244 | ||||||||
\(302\) | 5265.25 | 1.00325 | ||||||||
\(303\) | 6725.71 | 1.27519 | ||||||||
\(304\) | 2109.49 | 0.397985 | ||||||||
\(305\) | 2862.85 | 0.537463 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 4689.47 | 0.871799 | 0.435899 | − | 0.899995i | \(-0.356430\pi\) | ||||
0.435899 | + | 0.899995i | \(0.356430\pi\) | |||||||
\(308\) | 452.763 | 0.0837615 | ||||||||
\(309\) | −3540.75 | −0.651864 | ||||||||
\(310\) | −36.4818 | −0.00668396 | ||||||||
\(311\) | 2725.79 | 0.496995 | 0.248497 | − | 0.968633i | \(-0.420063\pi\) | ||||
0.248497 | + | 0.968633i | \(0.420063\pi\) | |||||||
\(312\) | −6470.30 | −1.17407 | ||||||||
\(313\) | 1406.42 | 0.253980 | 0.126990 | − | 0.991904i | \(-0.459468\pi\) | ||||
0.126990 | + | 0.991904i | \(0.459468\pi\) | |||||||
\(314\) | −5859.87 | −1.05316 | ||||||||
\(315\) | 11222.4 | 2.00734 | ||||||||
\(316\) | −763.089 | −0.135845 | ||||||||
\(317\) | 836.717 | 0.148248 | 0.0741241 | − | 0.997249i | \(-0.476384\pi\) | ||||
0.0741241 | + | 0.997249i | \(0.476384\pi\) | |||||||
\(318\) | 9699.77 | 1.71049 | ||||||||
\(319\) | −227.740 | −0.0399717 | ||||||||
\(320\) | −8309.36 | −1.45159 | ||||||||
\(321\) | 7252.95 | 1.26112 | ||||||||
\(322\) | 1192.01 | 0.206299 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | −3125.88 | −0.535987 | ||||||||
\(325\) | 3999.94 | 0.682698 | ||||||||
\(326\) | −412.954 | −0.0701577 | ||||||||
\(327\) | −15628.7 | −2.64302 | ||||||||
\(328\) | 7616.70 | 1.28220 | ||||||||
\(329\) | 7731.09 | 1.29553 | ||||||||
\(330\) | −3589.35 | −0.598750 | ||||||||
\(331\) | 2544.99 | 0.422614 | 0.211307 | − | 0.977420i | \(-0.432228\pi\) | ||||
0.211307 | + | 0.977420i | \(0.432228\pi\) | |||||||
\(332\) | −782.244 | −0.129311 | ||||||||
\(333\) | 12439.6 | 2.04711 | ||||||||
\(334\) | 5968.54 | 0.977796 | ||||||||
\(335\) | −13135.0 | −2.14221 | ||||||||
\(336\) | −2962.02 | −0.480927 | ||||||||
\(337\) | 9258.04 | 1.49649 | 0.748246 | − | 0.663422i | \(-0.230896\pi\) | ||||
0.748246 | + | 0.663422i | \(0.230896\pi\) | |||||||
\(338\) | 2947.91 | 0.474393 | ||||||||
\(339\) | 385.105 | 0.0616992 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −11.6051 | −0.00184297 | ||||||||
\(342\) | 9744.81 | 1.54076 | ||||||||
\(343\) | 6559.21 | 1.03255 | ||||||||
\(344\) | 11848.1 | 1.85699 | ||||||||
\(345\) | 6682.92 | 1.04289 | ||||||||
\(346\) | 3145.36 | 0.488716 | ||||||||
\(347\) | −11972.3 | −1.85217 | −0.926087 | − | 0.377310i | \(-0.876849\pi\) | ||||
−0.926087 | + | 0.377310i | \(0.876849\pi\) | |||||||
\(348\) | −617.311 | −0.0950901 | ||||||||
\(349\) | 1887.57 | 0.289511 | 0.144755 | − | 0.989467i | \(-0.453760\pi\) | ||||
0.144755 | + | 0.989467i | \(0.453760\pi\) | |||||||
\(350\) | 3662.63 | 0.559360 | ||||||||
\(351\) | −7810.31 | −1.18770 | ||||||||
\(352\) | −1548.50 | −0.234475 | ||||||||
\(353\) | 7441.02 | 1.12194 | 0.560971 | − | 0.827836i | \(-0.310428\pi\) | ||||
0.560971 | + | 0.827836i | \(0.310428\pi\) | |||||||
\(354\) | 2927.82 | 0.439581 | ||||||||
\(355\) | 11591.1 | 1.73294 | ||||||||
\(356\) | 2281.85 | 0.339712 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 2535.91 | 0.374377 | ||||||||
\(359\) | 11518.8 | 1.69342 | 0.846711 | − | 0.532052i | \(-0.178579\pi\) | ||||
0.846711 | + | 0.532052i | \(0.178579\pi\) | |||||||
\(360\) | −22483.8 | −3.29167 | ||||||||
\(361\) | −525.233 | −0.0765757 | ||||||||
\(362\) | −5925.74 | −0.860359 | ||||||||
\(363\) | 11025.3 | 1.59416 | ||||||||
\(364\) | 1170.79 | 0.168588 | ||||||||
\(365\) | 12662.2 | 1.81581 | ||||||||
\(366\) | −3490.58 | −0.498513 | ||||||||
\(367\) | 702.580 | 0.0999302 | 0.0499651 | − | 0.998751i | \(-0.484089\pi\) | ||||
0.0499651 | + | 0.998751i | \(0.484089\pi\) | |||||||
\(368\) | −1193.96 | −0.169129 | ||||||||
\(369\) | 17590.9 | 2.48170 | ||||||||
\(370\) | 7726.52 | 1.08563 | ||||||||
\(371\) | −5992.15 | −0.838536 | ||||||||
\(372\) | −31.4569 | −0.00438431 | ||||||||
\(373\) | 8797.32 | 1.22120 | 0.610600 | − | 0.791939i | \(-0.290928\pi\) | ||||
0.610600 | + | 0.791939i | \(0.290928\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 1989.00 | 0.273897 | ||||||||
\(376\) | −15489.0 | −2.12443 | ||||||||
\(377\) | −588.906 | −0.0804515 | ||||||||
\(378\) | −7151.67 | −0.973128 | ||||||||
\(379\) | 3113.75 | 0.422012 | 0.211006 | − | 0.977485i | \(-0.432326\pi\) | ||||
0.211006 | + | 0.977485i | \(0.432326\pi\) | |||||||
\(380\) | −4280.46 | −0.577850 | ||||||||
\(381\) | 14048.2 | 1.88901 | ||||||||
\(382\) | 2912.77 | 0.390131 | ||||||||
\(383\) | −9735.60 | −1.29887 | −0.649434 | − | 0.760418i | \(-0.724994\pi\) | ||||
−0.649434 | + | 0.760418i | \(0.724994\pi\) | |||||||
\(384\) | −1.24200 | −0.000165054 0 | ||||||||
\(385\) | 2217.37 | 0.293526 | ||||||||
\(386\) | −8199.15 | −1.08115 | ||||||||
\(387\) | 27363.3 | 3.59420 | ||||||||
\(388\) | −6117.91 | −0.800490 | ||||||||
\(389\) | −1772.22 | −0.230990 | −0.115495 | − | 0.993308i | \(-0.536845\pi\) | ||||
−0.115495 | + | 0.993308i | \(0.536845\pi\) | |||||||
\(390\) | −9281.61 | −1.20511 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | −4740.60 | −0.610807 | ||||||||
\(393\) | −2419.88 | −0.310602 | ||||||||
\(394\) | −156.747 | −0.0200426 | ||||||||
\(395\) | −3737.16 | −0.476043 | ||||||||
\(396\) | −2094.96 | −0.265848 | ||||||||
\(397\) | −1201.80 | −0.151931 | −0.0759653 | − | 0.997110i | \(-0.524204\pi\) | ||||
−0.0759653 | + | 0.997110i | \(0.524204\pi\) | |||||||
\(398\) | −5852.54 | −0.737088 | ||||||||
\(399\) | −8893.53 | −1.11587 | ||||||||
\(400\) | −3668.61 | −0.458576 | ||||||||
\(401\) | 13633.2 | 1.69778 | 0.848892 | − | 0.528566i | \(-0.177270\pi\) | ||||
0.848892 | + | 0.528566i | \(0.177270\pi\) | |||||||
\(402\) | 16015.1 | 1.98696 | ||||||||
\(403\) | −30.0094 | −0.00370937 | ||||||||
\(404\) | 2438.23 | 0.300264 | ||||||||
\(405\) | −15308.7 | −1.87826 | ||||||||
\(406\) | −539.244 | −0.0659168 | ||||||||
\(407\) | 2457.87 | 0.299341 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 7345.95 | 0.888103 | 0.444051 | − | 0.896001i | \(-0.353541\pi\) | ||||
0.444051 | + | 0.896001i | \(0.353541\pi\) | |||||||
\(410\) | 10926.1 | 1.31610 | ||||||||
\(411\) | −6275.07 | −0.753105 | ||||||||
\(412\) | −1283.61 | −0.153492 | ||||||||
\(413\) | −1808.69 | −0.215496 | ||||||||
\(414\) | −5515.51 | −0.654765 | ||||||||
\(415\) | −3830.97 | −0.453145 | ||||||||
\(416\) | −4004.23 | −0.471931 | ||||||||
\(417\) | −395.238 | −0.0464146 | ||||||||
\(418\) | 1925.42 | 0.225300 | ||||||||
\(419\) | 3293.55 | 0.384011 | 0.192005 | − | 0.981394i | \(-0.438501\pi\) | ||||
0.192005 | + | 0.981394i | \(0.438501\pi\) | |||||||
\(420\) | 6010.39 | 0.698278 | ||||||||
\(421\) | −9775.57 | −1.13167 | −0.565834 | − | 0.824519i | \(-0.691446\pi\) | ||||
−0.565834 | + | 0.824519i | \(0.691446\pi\) | |||||||
\(422\) | 5061.75 | 0.583892 | ||||||||
\(423\) | −35772.2 | −4.11184 | ||||||||
\(424\) | 12005.1 | 1.37505 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −14132.7 | −1.60735 | ||||||||
\(427\) | 2156.35 | 0.244386 | ||||||||
\(428\) | 2629.37 | 0.296952 | ||||||||
\(429\) | −2952.55 | −0.332286 | ||||||||
\(430\) | 16996.0 | 1.90609 | ||||||||
\(431\) | −7842.98 | −0.876527 | −0.438263 | − | 0.898847i | \(-0.644406\pi\) | ||||
−0.438263 | + | 0.898847i | \(0.644406\pi\) | |||||||
\(432\) | 7163.35 | 0.797794 | ||||||||
\(433\) | −5178.49 | −0.574740 | −0.287370 | − | 0.957820i | \(-0.592781\pi\) | ||||
−0.287370 | + | 0.957820i | \(0.592781\pi\) | |||||||
\(434\) | −27.4787 | −0.00303922 | ||||||||
\(435\) | −3023.23 | −0.333225 | ||||||||
\(436\) | −5665.77 | −0.622342 | ||||||||
\(437\) | −3584.88 | −0.392421 | ||||||||
\(438\) | −15438.7 | −1.68422 | ||||||||
\(439\) | −5661.88 | −0.615550 | −0.307775 | − | 0.951459i | \(-0.599584\pi\) | ||||
−0.307775 | + | 0.951459i | \(0.599584\pi\) | |||||||
\(440\) | −4442.44 | −0.481329 | ||||||||
\(441\) | −10948.5 | −1.18222 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −3020.29 | −0.323924 | −0.161962 | − | 0.986797i | \(-0.551782\pi\) | ||||
−0.161962 | + | 0.986797i | \(0.551782\pi\) | |||||||
\(444\) | 6662.29 | 0.712113 | ||||||||
\(445\) | 11175.1 | 1.19046 | ||||||||
\(446\) | −3761.64 | −0.399370 | ||||||||
\(447\) | −3066.06 | −0.324429 | ||||||||
\(448\) | −6258.76 | −0.660041 | ||||||||
\(449\) | 13308.6 | 1.39883 | 0.699413 | − | 0.714718i | \(-0.253445\pi\) | ||||
0.699413 | + | 0.714718i | \(0.253445\pi\) | |||||||
\(450\) | −16947.2 | −1.77533 | ||||||||
\(451\) | 3475.68 | 0.362890 | ||||||||
\(452\) | 139.610 | 0.0145281 | ||||||||
\(453\) | 22234.4 | 2.30610 | ||||||||
\(454\) | 9699.78 | 1.00272 | ||||||||
\(455\) | 5733.82 | 0.590782 | ||||||||
\(456\) | 17818.0 | 1.82983 | ||||||||
\(457\) | 7260.23 | 0.743150 | 0.371575 | − | 0.928403i | \(-0.378818\pi\) | ||||
0.371575 | + | 0.928403i | \(0.378818\pi\) | |||||||
\(458\) | 8480.83 | 0.865247 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 2422.72 | 0.245565 | ||||||||
\(461\) | −2580.20 | −0.260677 | −0.130338 | − | 0.991470i | \(-0.541606\pi\) | ||||
−0.130338 | + | 0.991470i | \(0.541606\pi\) | |||||||
\(462\) | −2703.56 | −0.272254 | ||||||||
\(463\) | 14392.8 | 1.44469 | 0.722345 | − | 0.691533i | \(-0.243064\pi\) | ||||
0.722345 | + | 0.691533i | \(0.243064\pi\) | |||||||
\(464\) | 540.125 | 0.0540402 | ||||||||
\(465\) | −154.057 | −0.0153639 | ||||||||
\(466\) | 9018.29 | 0.896490 | ||||||||
\(467\) | −11696.0 | −1.15894 | −0.579471 | − | 0.814993i | \(-0.696741\pi\) | ||||
−0.579471 | + | 0.814993i | \(0.696741\pi\) | |||||||
\(468\) | −5417.30 | −0.535075 | ||||||||
\(469\) | −9893.50 | −0.974071 | ||||||||
\(470\) | −22218.9 | −2.18060 | ||||||||
\(471\) | −24745.4 | −2.42082 | ||||||||
\(472\) | 3623.68 | 0.353375 | ||||||||
\(473\) | 5406.55 | 0.525568 | ||||||||
\(474\) | 4556.61 | 0.441544 | ||||||||
\(475\) | −11015.1 | −1.06401 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 27726.0 | 2.66140 | ||||||||
\(478\) | 3853.35 | 0.368720 | ||||||||
\(479\) | −13997.5 | −1.33520 | −0.667599 | − | 0.744521i | \(-0.732678\pi\) | ||||
−0.667599 | + | 0.744521i | \(0.732678\pi\) | |||||||
\(480\) | −20556.2 | −1.95471 | ||||||||
\(481\) | 6355.73 | 0.602487 | ||||||||
\(482\) | 5344.97 | 0.505097 | ||||||||
\(483\) | 5033.69 | 0.474205 | ||||||||
\(484\) | 3996.94 | 0.375370 | ||||||||
\(485\) | −29961.9 | −2.80516 | ||||||||
\(486\) | 2869.78 | 0.267852 | ||||||||
\(487\) | −2888.42 | −0.268761 | −0.134381 | − | 0.990930i | \(-0.542905\pi\) | ||||
−0.134381 | + | 0.990930i | \(0.542905\pi\) | |||||||
\(488\) | −4320.19 | −0.400750 | ||||||||
\(489\) | −1743.84 | −0.161267 | ||||||||
\(490\) | −6800.36 | −0.626957 | ||||||||
\(491\) | −9420.11 | −0.865832 | −0.432916 | − | 0.901434i | \(-0.642515\pi\) | ||||
−0.432916 | + | 0.901434i | \(0.642515\pi\) | |||||||
\(492\) | 9421.17 | 0.863291 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 4978.88 | 0.453463 | ||||||||
\(495\) | −10259.9 | −0.931612 | ||||||||
\(496\) | 27.5236 | 0.00249162 | ||||||||
\(497\) | 8730.65 | 0.787975 | ||||||||
\(498\) | 4670.98 | 0.420305 | ||||||||
\(499\) | −713.936 | −0.0640484 | −0.0320242 | − | 0.999487i | \(-0.510195\pi\) | ||||
−0.0320242 | + | 0.999487i | \(0.510195\pi\) | |||||||
\(500\) | 721.061 | 0.0644937 | ||||||||
\(501\) | 25204.3 | 2.24759 | ||||||||
\(502\) | 10442.8 | 0.928453 | ||||||||
\(503\) | −17604.4 | −1.56052 | −0.780260 | − | 0.625456i | \(-0.784913\pi\) | ||||
−0.780260 | + | 0.625456i | \(0.784913\pi\) | |||||||
\(504\) | −16935.2 | −1.49673 | ||||||||
\(505\) | 11941.0 | 1.05222 | ||||||||
\(506\) | −1089.78 | −0.0957440 | ||||||||
\(507\) | 12448.6 | 1.09046 | ||||||||
\(508\) | 5092.81 | 0.444797 | ||||||||
\(509\) | 12291.2 | 1.07033 | 0.535165 | − | 0.844748i | \(-0.320249\pi\) | ||||
0.535165 | + | 0.844748i | \(0.320249\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 9537.41 | 0.825656 | ||||||||
\(512\) | 8865.96 | 0.765280 | ||||||||
\(513\) | 21508.1 | 1.85108 | ||||||||
\(514\) | −12033.2 | −1.03261 | ||||||||
\(515\) | −6286.35 | −0.537883 | ||||||||
\(516\) | 14655.0 | 1.25029 | ||||||||
\(517\) | −7068.02 | −0.601259 | ||||||||
\(518\) | 5819.75 | 0.493639 | ||||||||
\(519\) | 13282.4 | 1.12338 | ||||||||
\(520\) | −11487.6 | −0.968776 | ||||||||
\(521\) | −8736.73 | −0.734670 | −0.367335 | − | 0.930089i | \(-0.619730\pi\) | ||||
−0.367335 | + | 0.930089i | \(0.619730\pi\) | |||||||
\(522\) | 2495.12 | 0.209211 | ||||||||
\(523\) | −2513.00 | −0.210107 | −0.105053 | − | 0.994467i | \(-0.533501\pi\) | ||||
−0.105053 | + | 0.994467i | \(0.533501\pi\) | |||||||
\(524\) | −877.264 | −0.0731363 | ||||||||
\(525\) | 15466.8 | 1.28576 | ||||||||
\(526\) | 6867.01 | 0.569232 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 2707.98 | 0.223200 | ||||||||
\(529\) | −10138.0 | −0.833236 | ||||||||
\(530\) | 17221.3 | 1.41140 | ||||||||
\(531\) | 8368.95 | 0.683957 | ||||||||
\(532\) | −3224.12 | −0.262751 | ||||||||
\(533\) | 8987.66 | 0.730392 | ||||||||
\(534\) | −13625.5 | −1.10418 | ||||||||
\(535\) | 12877.1 | 1.04061 | ||||||||
\(536\) | 19821.4 | 1.59730 | ||||||||
\(537\) | 10708.8 | 0.860554 | ||||||||
\(538\) | 6169.31 | 0.494383 | ||||||||
\(539\) | −2163.25 | −0.172871 | ||||||||
\(540\) | −14535.5 | −1.15835 | ||||||||
\(541\) | −9702.15 | −0.771031 | −0.385516 | − | 0.922701i | \(-0.625976\pi\) | ||||
−0.385516 | + | 0.922701i | \(0.625976\pi\) | |||||||
\(542\) | 5552.77 | 0.440059 | ||||||||
\(543\) | −25023.5 | −1.97765 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −27747.6 | −2.18088 | ||||||||
\(546\) | −6991.07 | −0.547968 | ||||||||
\(547\) | −16198.6 | −1.26618 | −0.633092 | − | 0.774077i | \(-0.718215\pi\) | ||||
−0.633092 | + | 0.774077i | \(0.718215\pi\) | |||||||
\(548\) | −2274.86 | −0.177331 | ||||||||
\(549\) | −9977.56 | −0.775650 | ||||||||
\(550\) | −3348.50 | −0.259601 | ||||||||
\(551\) | 1621.73 | 0.125387 | ||||||||
\(552\) | −10084.9 | −0.777610 | ||||||||
\(553\) | −2814.90 | −0.216459 | ||||||||
\(554\) | 13553.2 | 1.03939 | ||||||||
\(555\) | 32628.0 | 2.49546 | ||||||||
\(556\) | −143.283 | −0.0109291 | ||||||||
\(557\) | −9873.27 | −0.751066 | −0.375533 | − | 0.926809i | \(-0.622540\pi\) | ||||
−0.375533 | + | 0.926809i | \(0.622540\pi\) | |||||||
\(558\) | 127.146 | 0.00964608 | ||||||||
\(559\) | 13980.7 | 1.05782 | ||||||||
\(560\) | −5258.87 | −0.396835 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 3912.95 | 0.293697 | ||||||||
\(563\) | 3283.56 | 0.245801 | 0.122900 | − | 0.992419i | \(-0.460780\pi\) | ||||
0.122900 | + | 0.992419i | \(0.460780\pi\) | |||||||
\(564\) | −19158.6 | −1.43036 | ||||||||
\(565\) | 683.727 | 0.0509108 | ||||||||
\(566\) | −2736.42 | −0.203216 | ||||||||
\(567\) | −11530.8 | −0.854053 | ||||||||
\(568\) | −17491.7 | −1.29214 | ||||||||
\(569\) | −15065.3 | −1.10996 | −0.554982 | − | 0.831862i | \(-0.687275\pi\) | ||||
−0.554982 | + | 0.831862i | \(0.687275\pi\) | |||||||
\(570\) | 25559.8 | 1.87821 | ||||||||
\(571\) | 2567.87 | 0.188200 | 0.0941000 | − | 0.995563i | \(-0.470003\pi\) | ||||
0.0941000 | + | 0.995563i | \(0.470003\pi\) | |||||||
\(572\) | −1070.37 | −0.0782421 | ||||||||
\(573\) | 12300.2 | 0.896767 | ||||||||
\(574\) | 8229.73 | 0.598436 | ||||||||
\(575\) | 6234.47 | 0.452166 | ||||||||
\(576\) | 28959.7 | 2.09488 | ||||||||
\(577\) | −23042.3 | −1.66250 | −0.831249 | − | 0.555900i | \(-0.812374\pi\) | ||||
−0.831249 | + | 0.555900i | \(0.812374\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −34623.8 | −2.48517 | ||||||||
\(580\) | −1095.99 | −0.0784632 | ||||||||
\(581\) | −2885.56 | −0.206046 | ||||||||
\(582\) | 36531.7 | 2.60187 | ||||||||
\(583\) | 5478.22 | 0.389167 | ||||||||
\(584\) | −19108.0 | −1.35393 | ||||||||
\(585\) | −26530.8 | −1.87506 | ||||||||
\(586\) | −8027.68 | −0.565905 | ||||||||
\(587\) | −4094.68 | −0.287914 | −0.143957 | − | 0.989584i | \(-0.545983\pi\) | ||||
−0.143957 | + | 0.989584i | \(0.545983\pi\) | |||||||
\(588\) | −5863.69 | −0.411249 | ||||||||
\(589\) | 82.6401 | 0.00578120 | ||||||||
\(590\) | 5198.14 | 0.362719 | ||||||||
\(591\) | −661.919 | −0.0460706 | ||||||||
\(592\) | −5829.26 | −0.404698 | ||||||||
\(593\) | −25698.4 | −1.77961 | −0.889803 | − | 0.456344i | \(-0.849159\pi\) | ||||
−0.889803 | + | 0.456344i | \(0.849159\pi\) | |||||||
\(594\) | 6538.30 | 0.451632 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −1111.52 | −0.0763922 | ||||||||
\(597\) | −24714.4 | −1.69429 | ||||||||
\(598\) | −2818.02 | −0.192705 | ||||||||
\(599\) | 1085.55 | 0.0740472 | 0.0370236 | − | 0.999314i | \(-0.488212\pi\) | ||||
0.0370236 | + | 0.999314i | \(0.488212\pi\) | |||||||
\(600\) | −30987.3 | −2.10842 | ||||||||
\(601\) | 11163.9 | 0.757713 | 0.378857 | − | 0.925455i | \(-0.376317\pi\) | ||||
0.378857 | + | 0.925455i | \(0.376317\pi\) | |||||||
\(602\) | 12801.7 | 0.866706 | ||||||||
\(603\) | 45777.8 | 3.09157 | ||||||||
\(604\) | 8060.50 | 0.543008 | ||||||||
\(605\) | 19574.7 | 1.31541 | ||||||||
\(606\) | −14559.3 | −0.975961 | ||||||||
\(607\) | 167.486 | 0.0111994 | 0.00559971 | − | 0.999984i | \(-0.498218\pi\) | ||||
0.00559971 | + | 0.999984i | \(0.498218\pi\) | |||||||
\(608\) | 11026.9 | 0.735524 | ||||||||
\(609\) | −2277.15 | −0.151518 | ||||||||
\(610\) | −6197.29 | −0.411346 | ||||||||
\(611\) | −18277.0 | −1.21016 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −6533.58 | −0.430487 | −0.215244 | − | 0.976560i | \(-0.569055\pi\) | ||||
−0.215244 | + | 0.976560i | \(0.569055\pi\) | |||||||
\(614\) | −10151.4 | −0.667228 | ||||||||
\(615\) | 46139.3 | 3.02523 | ||||||||
\(616\) | −3346.12 | −0.218862 | ||||||||
\(617\) | −9073.82 | −0.592056 | −0.296028 | − | 0.955179i | \(-0.595662\pi\) | ||||
−0.296028 | + | 0.955179i | \(0.595662\pi\) | |||||||
\(618\) | 7664.75 | 0.498902 | ||||||||
\(619\) | −26617.2 | −1.72833 | −0.864163 | − | 0.503212i | \(-0.832151\pi\) | ||||
−0.864163 | + | 0.503212i | \(0.832151\pi\) | |||||||
\(620\) | −55.8495 | −0.00361769 | ||||||||
\(621\) | −12173.5 | −0.786641 | ||||||||
\(622\) | −5900.60 | −0.380374 | ||||||||
\(623\) | 8417.32 | 0.541304 | ||||||||
\(624\) | 7002.49 | 0.449237 | ||||||||
\(625\) | −13769.5 | −0.881246 | ||||||||
\(626\) | −3044.52 | −0.194383 | ||||||||
\(627\) | 8130.76 | 0.517881 | ||||||||
\(628\) | −8970.79 | −0.570022 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | −24293.5 | −1.53631 | ||||||||
\(631\) | 5977.98 | 0.377147 | 0.188573 | − | 0.982059i | \(-0.439614\pi\) | ||||
0.188573 | + | 0.982059i | \(0.439614\pi\) | |||||||
\(632\) | 5639.58 | 0.354953 | ||||||||
\(633\) | 21375.0 | 1.34215 | ||||||||
\(634\) | −1811.26 | −0.113461 | ||||||||
\(635\) | 24941.6 | 1.55870 | ||||||||
\(636\) | 14849.2 | 0.925803 | ||||||||
\(637\) | −5593.88 | −0.347940 | ||||||||
\(638\) | 492.995 | 0.0305922 | ||||||||
\(639\) | −40397.3 | −2.50093 | ||||||||
\(640\) | −2.20509 | −0.000136194 0 | ||||||||
\(641\) | 7927.25 | 0.488467 | 0.244234 | − | 0.969716i | \(-0.421464\pi\) | ||||
0.244234 | + | 0.969716i | \(0.421464\pi\) | |||||||
\(642\) | −15700.7 | −0.965195 | ||||||||
\(643\) | 9197.33 | 0.564086 | 0.282043 | − | 0.959402i | \(-0.408988\pi\) | ||||
0.282043 | + | 0.959402i | \(0.408988\pi\) | |||||||
\(644\) | 1824.83 | 0.111659 | ||||||||
\(645\) | 71771.5 | 4.38140 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 19035.8 | 1.15669 | 0.578343 | − | 0.815794i | \(-0.303700\pi\) | ||||
0.578343 | + | 0.815794i | \(0.303700\pi\) | |||||||
\(648\) | 23101.7 | 1.40049 | ||||||||
\(649\) | 1653.57 | 0.100013 | ||||||||
\(650\) | −8658.79 | −0.522501 | ||||||||
\(651\) | −116.039 | −0.00698604 | ||||||||
\(652\) | −632.186 | −0.0379729 | ||||||||
\(653\) | −19349.6 | −1.15958 | −0.579792 | − | 0.814764i | \(-0.696866\pi\) | ||||
−0.579792 | + | 0.814764i | \(0.696866\pi\) | |||||||
\(654\) | 33831.8 | 2.02283 | ||||||||
\(655\) | −4296.32 | −0.256292 | ||||||||
\(656\) | −8243.17 | −0.490613 | ||||||||
\(657\) | −44130.2 | −2.62052 | ||||||||
\(658\) | −16735.7 | −0.991528 | ||||||||
\(659\) | 16666.8 | 0.985201 | 0.492600 | − | 0.870256i | \(-0.336046\pi\) | ||||
0.492600 | + | 0.870256i | \(0.336046\pi\) | |||||||
\(660\) | −5494.90 | −0.324074 | ||||||||
\(661\) | −6024.30 | −0.354490 | −0.177245 | − | 0.984167i | \(-0.556719\pi\) | ||||
−0.177245 | + | 0.984167i | \(0.556719\pi\) | |||||||
\(662\) | −5509.21 | −0.323446 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 5781.14 | 0.337879 | ||||||||
\(665\) | −15789.8 | −0.920758 | ||||||||
\(666\) | −26928.4 | −1.56675 | ||||||||
\(667\) | −917.893 | −0.0532848 | ||||||||
\(668\) | 9137.16 | 0.529232 | ||||||||
\(669\) | −15884.9 | −0.918003 | ||||||||
\(670\) | 28433.7 | 1.63953 | ||||||||
\(671\) | −1971.40 | −0.113421 | ||||||||
\(672\) | −15483.3 | −0.888812 | ||||||||
\(673\) | 27296.1 | 1.56343 | 0.781714 | − | 0.623637i | \(-0.214346\pi\) | ||||
0.781714 | + | 0.623637i | \(0.214346\pi\) | |||||||
\(674\) | −20041.1 | −1.14534 | ||||||||
\(675\) | −37404.8 | −2.13290 | ||||||||
\(676\) | 4512.91 | 0.256766 | ||||||||
\(677\) | −13081.5 | −0.742632 | −0.371316 | − | 0.928507i | \(-0.621093\pi\) | ||||
−0.371316 | + | 0.928507i | \(0.621093\pi\) | |||||||
\(678\) | −833.647 | −0.0472213 | ||||||||
\(679\) | −22567.9 | −1.27552 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 40960.8 | 2.30487 | ||||||||
\(682\) | 25.1220 | 0.00141051 | ||||||||
\(683\) | 15698.0 | 0.879452 | 0.439726 | − | 0.898132i | \(-0.355075\pi\) | ||||
0.439726 | + | 0.898132i | \(0.355075\pi\) | |||||||
\(684\) | 14918.2 | 0.833936 | ||||||||
\(685\) | −11140.9 | −0.621422 | ||||||||
\(686\) | −14198.9 | −0.790258 | ||||||||
\(687\) | 35813.3 | 1.98888 | ||||||||
\(688\) | −12822.6 | −0.710547 | ||||||||
\(689\) | 14166.0 | 0.783281 | ||||||||
\(690\) | −14466.7 | −0.798170 | ||||||||
\(691\) | −13621.7 | −0.749919 | −0.374959 | − | 0.927041i | \(-0.622343\pi\) | ||||
−0.374959 | + | 0.927041i | \(0.622343\pi\) | |||||||
\(692\) | 4815.19 | 0.264517 | ||||||||
\(693\) | −7727.93 | −0.423607 | ||||||||
\(694\) | 25916.7 | 1.41756 | ||||||||
\(695\) | −701.718 | −0.0382988 | ||||||||
\(696\) | 4562.21 | 0.248463 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | −4086.08 | −0.221576 | ||||||||
\(699\) | 38082.9 | 2.06070 | ||||||||
\(700\) | 5607.07 | 0.302753 | ||||||||
\(701\) | 5733.01 | 0.308892 | 0.154446 | − | 0.988001i | \(-0.450641\pi\) | ||||
0.154446 | + | 0.988001i | \(0.450641\pi\) | |||||||
\(702\) | 16907.2 | 0.909004 | ||||||||
\(703\) | −17502.4 | −0.939000 | ||||||||
\(704\) | 5721.96 | 0.306327 | ||||||||
\(705\) | −93827.4 | −5.01240 | ||||||||
\(706\) | −16107.8 | −0.858674 | ||||||||
\(707\) | 8994.20 | 0.478447 | ||||||||
\(708\) | 4482.16 | 0.237924 | ||||||||
\(709\) | −25474.5 | −1.34939 | −0.674694 | − | 0.738097i | \(-0.735725\pi\) | ||||
−0.674694 | + | 0.738097i | \(0.735725\pi\) | |||||||
\(710\) | −25091.7 | −1.32630 | ||||||||
\(711\) | 13024.7 | 0.687011 | ||||||||
\(712\) | −16863.9 | −0.887642 | ||||||||
\(713\) | −46.7739 | −0.00245679 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −5242.05 | −0.274184 | ||||||||
\(716\) | 3882.19 | 0.202632 | ||||||||
\(717\) | 16272.1 | 0.847551 | ||||||||
\(718\) | −24935.1 | −1.29606 | ||||||||
\(719\) | −15508.0 | −0.804380 | −0.402190 | − | 0.915556i | \(-0.631751\pi\) | ||||
−0.402190 | + | 0.915556i | \(0.631751\pi\) | |||||||
\(720\) | 24333.1 | 1.25950 | ||||||||
\(721\) | −4734.99 | −0.244577 | ||||||||
\(722\) | 1136.99 | 0.0586070 | ||||||||
\(723\) | 22571.0 | 1.16103 | ||||||||
\(724\) | −9071.64 | −0.465670 | ||||||||
\(725\) | −2820.36 | −0.144477 | ||||||||
\(726\) | −23866.8 | −1.22008 | ||||||||
\(727\) | −32127.0 | −1.63896 | −0.819481 | − | 0.573106i | \(-0.805738\pi\) | ||||
−0.819481 | + | 0.573106i | \(0.805738\pi\) | |||||||
\(728\) | −8652.65 | −0.440506 | ||||||||
\(729\) | −13349.0 | −0.678200 | ||||||||
\(730\) | −27410.3 | −1.38973 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | −5343.68 | −0.269820 | ||||||||
\(733\) | 1723.27 | 0.0868353 | 0.0434177 | − | 0.999057i | \(-0.486175\pi\) | ||||
0.0434177 | + | 0.999057i | \(0.486175\pi\) | |||||||
\(734\) | −1520.89 | −0.0764812 | ||||||||
\(735\) | −28716.9 | −1.44114 | ||||||||
\(736\) | −6241.15 | −0.312570 | ||||||||
\(737\) | 9044.96 | 0.452070 | ||||||||
\(738\) | −38079.5 | −1.89936 | ||||||||
\(739\) | 22411.5 | 1.11559 | 0.557796 | − | 0.829978i | \(-0.311647\pi\) | ||||
0.557796 | + | 0.829978i | \(0.311647\pi\) | |||||||
\(740\) | 11828.4 | 0.587597 | ||||||||
\(741\) | 21025.1 | 1.04234 | ||||||||
\(742\) | 12971.4 | 0.641771 | ||||||||
\(743\) | 23971.3 | 1.18361 | 0.591804 | − | 0.806082i | \(-0.298416\pi\) | ||||
0.591804 | + | 0.806082i | \(0.298416\pi\) | |||||||
\(744\) | 232.481 | 0.0114558 | ||||||||
\(745\) | −5443.59 | −0.267701 | ||||||||
\(746\) | −19043.8 | −0.934642 | ||||||||
\(747\) | 13351.7 | 0.653964 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 9699.26 | 0.473169 | ||||||||
\(750\) | −4305.64 | −0.209627 | ||||||||
\(751\) | −26268.1 | −1.27635 | −0.638175 | − | 0.769892i | \(-0.720310\pi\) | ||||
−0.638175 | + | 0.769892i | \(0.720310\pi\) | |||||||
\(752\) | 16763.0 | 0.812879 | ||||||||
\(753\) | 44098.3 | 2.13417 | ||||||||
\(754\) | 1274.82 | 0.0615733 | ||||||||
\(755\) | 39475.6 | 1.90287 | ||||||||
\(756\) | −10948.4 | −0.526706 | ||||||||
\(757\) | −345.842 | −0.0166048 | −0.00830239 | − | 0.999966i | \(-0.502643\pi\) | ||||
−0.00830239 | + | 0.999966i | \(0.502643\pi\) | |||||||
\(758\) | −6740.42 | −0.322986 | ||||||||
\(759\) | −4601.97 | −0.220080 | ||||||||
\(760\) | 31634.6 | 1.50988 | ||||||||
\(761\) | 28929.2 | 1.37803 | 0.689015 | − | 0.724747i | \(-0.258043\pi\) | ||||
0.689015 | + | 0.724747i | \(0.258043\pi\) | |||||||
\(762\) | −30410.5 | −1.44574 | ||||||||
\(763\) | −20900.0 | −0.991652 | ||||||||
\(764\) | 4459.11 | 0.211159 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 21074.9 | 0.994084 | ||||||||
\(767\) | 4275.92 | 0.201297 | ||||||||
\(768\) | 37444.2 | 1.75931 | ||||||||
\(769\) | −29320.3 | −1.37492 | −0.687462 | − | 0.726221i | \(-0.741275\pi\) | ||||
−0.687462 | + | 0.726221i | \(0.741275\pi\) | |||||||
\(770\) | −4799.99 | −0.224649 | ||||||||
\(771\) | −50814.6 | −2.37359 | ||||||||
\(772\) | −12552.0 | −0.585175 | ||||||||
\(773\) | 25830.3 | 1.20188 | 0.600938 | − | 0.799296i | \(-0.294794\pi\) | ||||
0.600938 | + | 0.799296i | \(0.294794\pi\) | |||||||
\(774\) | −59234.2 | −2.75081 | ||||||||
\(775\) | −143.720 | −0.00666137 | ||||||||
\(776\) | 45214.2 | 2.09162 | ||||||||
\(777\) | 24576.0 | 1.13469 | ||||||||
\(778\) | 3836.37 | 0.176787 | ||||||||
\(779\) | −24750.3 | −1.13834 | ||||||||
\(780\) | −14209.1 | −0.652266 | ||||||||
\(781\) | −7981.85 | −0.365702 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 5507.05 | 0.251349 | ||||||||
\(784\) | 5130.51 | 0.233715 | ||||||||
\(785\) | −43933.7 | −1.99753 | ||||||||
\(786\) | 5238.37 | 0.237718 | ||||||||
\(787\) | −13639.9 | −0.617801 | −0.308900 | − | 0.951094i | \(-0.599961\pi\) | ||||
−0.308900 | + | 0.951094i | \(0.599961\pi\) | |||||||
\(788\) | −239.962 | −0.0108481 | ||||||||
\(789\) | 28998.4 | 1.30845 | ||||||||
\(790\) | 8089.94 | 0.364338 | ||||||||
\(791\) | 514.995 | 0.0231493 | ||||||||
\(792\) | 15482.7 | 0.694640 | ||||||||
\(793\) | −5097.80 | −0.228283 | ||||||||
\(794\) | 2601.56 | 0.116280 | ||||||||
\(795\) | 72722.9 | 3.24430 | ||||||||
\(796\) | −8959.57 | −0.398949 | ||||||||
\(797\) | 35932.1 | 1.59697 | 0.798483 | − | 0.602017i | \(-0.205636\pi\) | ||||
0.798483 | + | 0.602017i | \(0.205636\pi\) | |||||||
\(798\) | 19252.1 | 0.854030 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | −19176.8 | −0.847505 | ||||||||
\(801\) | −38947.5 | −1.71803 | ||||||||
\(802\) | −29512.3 | −1.29939 | ||||||||
\(803\) | −8719.42 | −0.383190 | ||||||||
\(804\) | 24517.3 | 1.07544 | ||||||||
\(805\) | 8936.97 | 0.391288 | ||||||||
\(806\) | 64.9622 | 0.00283895 | ||||||||
\(807\) | 26052.1 | 1.13640 | ||||||||
\(808\) | −18019.7 | −0.784566 | ||||||||
\(809\) | −19296.4 | −0.838598 | −0.419299 | − | 0.907848i | \(-0.637724\pi\) | ||||
−0.419299 | + | 0.907848i | \(0.637724\pi\) | |||||||
\(810\) | 33139.2 | 1.43752 | ||||||||
\(811\) | 5464.45 | 0.236600 | 0.118300 | − | 0.992978i | \(-0.462256\pi\) | ||||
0.118300 | + | 0.992978i | \(0.462256\pi\) | |||||||
\(812\) | −825.522 | −0.0356775 | ||||||||
\(813\) | 23448.6 | 1.01153 | ||||||||
\(814\) | −5320.61 | −0.229100 | ||||||||
\(815\) | −3096.08 | −0.133068 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −38500.0 | −1.64865 | ||||||||
\(818\) | −15902.0 | −0.679707 | ||||||||
\(819\) | −19983.4 | −0.852598 | ||||||||
\(820\) | 16726.6 | 0.712341 | ||||||||
\(821\) | −16693.5 | −0.709631 | −0.354816 | − | 0.934936i | \(-0.615456\pi\) | ||||
−0.354816 | + | 0.934936i | \(0.615456\pi\) | |||||||
\(822\) | 13583.8 | 0.576387 | ||||||||
\(823\) | 5833.41 | 0.247072 | 0.123536 | − | 0.992340i | \(-0.460577\pi\) | ||||
0.123536 | + | 0.992340i | \(0.460577\pi\) | |||||||
\(824\) | 9486.44 | 0.401063 | ||||||||
\(825\) | −14140.2 | −0.596726 | ||||||||
\(826\) | 3915.33 | 0.164930 | ||||||||
\(827\) | 11048.3 | 0.464556 | 0.232278 | − | 0.972649i | \(-0.425382\pi\) | ||||
0.232278 | + | 0.972649i | \(0.425382\pi\) | |||||||
\(828\) | −8443.63 | −0.354392 | ||||||||
\(829\) | −26287.1 | −1.10131 | −0.550657 | − | 0.834732i | \(-0.685623\pi\) | ||||
−0.550657 | + | 0.834732i | \(0.685623\pi\) | |||||||
\(830\) | 8293.01 | 0.346813 | ||||||||
\(831\) | 57233.4 | 2.38917 | ||||||||
\(832\) | 14796.3 | 0.616548 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 855.583 | 0.0355233 | ||||||||
\(835\) | 44748.4 | 1.85459 | ||||||||
\(836\) | 2947.60 | 0.121943 | ||||||||
\(837\) | 280.628 | 0.0115889 | ||||||||
\(838\) | −7129.64 | −0.293901 | ||||||||
\(839\) | 8311.95 | 0.342027 | 0.171013 | − | 0.985269i | \(-0.445296\pi\) | ||||
0.171013 | + | 0.985269i | \(0.445296\pi\) | |||||||
\(840\) | −44419.5 | −1.82455 | ||||||||
\(841\) | −23973.8 | −0.982974 | ||||||||
\(842\) | 21161.5 | 0.866119 | ||||||||
\(843\) | 16523.8 | 0.675101 | ||||||||
\(844\) | 7748.97 | 0.316032 | ||||||||
\(845\) | 22101.6 | 0.899785 | ||||||||
\(846\) | 77437.2 | 3.14698 | ||||||||
\(847\) | 14744.0 | 0.598122 | ||||||||
\(848\) | −12992.5 | −0.526139 | ||||||||
\(849\) | −11555.5 | −0.467118 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 9906.29 | 0.399040 | ||||||||
\(852\) | −21635.6 | −0.869981 | ||||||||
\(853\) | 3875.16 | 0.155549 | 0.0777743 | − | 0.996971i | \(-0.475219\pi\) | ||||
0.0777743 | + | 0.996971i | \(0.475219\pi\) | |||||||
\(854\) | −4667.91 | −0.187040 | ||||||||
\(855\) | 73060.6 | 2.92236 | ||||||||
\(856\) | −19432.2 | −0.775912 | ||||||||
\(857\) | −31317.9 | −1.24831 | −0.624154 | − | 0.781301i | \(-0.714556\pi\) | ||||
−0.624154 | + | 0.781301i | \(0.714556\pi\) | |||||||
\(858\) | 6391.47 | 0.254314 | ||||||||
\(859\) | 35801.6 | 1.42204 | 0.711021 | − | 0.703171i | \(-0.248233\pi\) | ||||
0.711021 | + | 0.703171i | \(0.248233\pi\) | |||||||
\(860\) | 26018.9 | 1.03167 | ||||||||
\(861\) | 34753.0 | 1.37558 | ||||||||
\(862\) | 16977.9 | 0.670847 | ||||||||
\(863\) | −5935.67 | −0.234128 | −0.117064 | − | 0.993124i | \(-0.537348\pi\) | ||||
−0.117064 | + | 0.993124i | \(0.537348\pi\) | |||||||
\(864\) | 37444.8 | 1.47442 | ||||||||
\(865\) | 23582.0 | 0.926950 | ||||||||
\(866\) | 11210.0 | 0.439875 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −42.0668 | −0.00164498 | ||||||||
\(869\) | 2573.47 | 0.100459 | ||||||||
\(870\) | 6544.46 | 0.255032 | ||||||||
\(871\) | 23389.1 | 0.909885 | ||||||||
\(872\) | 41872.6 | 1.62613 | ||||||||
\(873\) | 104423. | 4.04832 | ||||||||
\(874\) | 7760.29 | 0.300338 | ||||||||
\(875\) | 2659.86 | 0.102765 | ||||||||
\(876\) | −23634.8 | −0.911583 | ||||||||
\(877\) | 43699.3 | 1.68258 | 0.841290 | − | 0.540585i | \(-0.181797\pi\) | ||||
0.841290 | + | 0.540585i | \(0.181797\pi\) | |||||||
\(878\) | 12256.4 | 0.471110 | ||||||||
\(879\) | −33899.7 | −1.30081 | ||||||||
\(880\) | 4807.83 | 0.184173 | ||||||||
\(881\) | 30329.5 | 1.15985 | 0.579924 | − | 0.814671i | \(-0.303082\pi\) | ||||
0.579924 | + | 0.814671i | \(0.303082\pi\) | |||||||
\(882\) | 23700.5 | 0.904805 | ||||||||
\(883\) | 35558.7 | 1.35521 | 0.677603 | − | 0.735428i | \(-0.263019\pi\) | ||||
0.677603 | + | 0.735428i | \(0.263019\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 21951.0 | 0.833757 | ||||||||
\(886\) | 6538.11 | 0.247914 | ||||||||
\(887\) | −23689.6 | −0.896752 | −0.448376 | − | 0.893845i | \(-0.647997\pi\) | ||||
−0.448376 | + | 0.893845i | \(0.647997\pi\) | |||||||
\(888\) | −49237.3 | −1.86069 | ||||||||
\(889\) | 18786.5 | 0.708749 | ||||||||
\(890\) | −24191.1 | −0.911111 | ||||||||
\(891\) | 10541.8 | 0.396369 | ||||||||
\(892\) | −5758.65 | −0.216159 | ||||||||
\(893\) | 50331.3 | 1.88608 | ||||||||
\(894\) | 6637.19 | 0.248301 | ||||||||
\(895\) | 19012.7 | 0.710083 | ||||||||
\(896\) | −1.66091 | −6.19277e−5 0 | ||||||||
\(897\) | −11900.1 | −0.442957 | ||||||||
\(898\) | −28809.6 | −1.07059 | ||||||||
\(899\) | 21.1596 | 0.000784998 0 | ||||||||
\(900\) | −25944.3 | −0.960900 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | −7523.90 | −0.277737 | ||||||||
\(903\) | 54059.6 | 1.99224 | ||||||||
\(904\) | −1031.78 | −0.0379608 | ||||||||
\(905\) | −44427.6 | −1.63185 | ||||||||
\(906\) | −48131.4 | −1.76496 | ||||||||
\(907\) | −12176.0 | −0.445752 | −0.222876 | − | 0.974847i | \(-0.571544\pi\) | ||||
−0.222876 | + | 0.974847i | \(0.571544\pi\) | |||||||
\(908\) | 14849.3 | 0.542721 | ||||||||
\(909\) | −41616.8 | −1.51853 | ||||||||
\(910\) | −12412.2 | −0.452153 | ||||||||
\(911\) | −34830.5 | −1.26673 | −0.633363 | − | 0.773855i | \(-0.718326\pi\) | ||||
−0.633363 | + | 0.773855i | \(0.718326\pi\) | |||||||
\(912\) | −19283.5 | −0.700154 | ||||||||
\(913\) | 2638.07 | 0.0956269 | ||||||||
\(914\) | −15716.4 | −0.568767 | ||||||||
\(915\) | −26170.2 | −0.945531 | ||||||||
\(916\) | 12983.2 | 0.468315 | ||||||||
\(917\) | −3236.07 | −0.116537 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −15886.7 | −0.570244 | −0.285122 | − | 0.958491i | \(-0.592034\pi\) | ||||
−0.285122 | + | 0.958491i | \(0.592034\pi\) | |||||||
\(920\) | −17905.0 | −0.641642 | ||||||||
\(921\) | −42868.0 | −1.53371 | ||||||||
\(922\) | 5585.44 | 0.199508 | ||||||||
\(923\) | −20640.1 | −0.736052 | ||||||||
\(924\) | −4138.85 | −0.147357 | ||||||||
\(925\) | 30438.5 | 1.08196 | ||||||||
\(926\) | −31156.6 | −1.10569 | ||||||||
\(927\) | 21909.1 | 0.776256 | ||||||||
\(928\) | 2823.38 | 0.0998728 | ||||||||
\(929\) | 14115.7 | 0.498514 | 0.249257 | − | 0.968437i | \(-0.419814\pi\) | ||||
0.249257 | + | 0.968437i | \(0.419814\pi\) | |||||||
\(930\) | 333.492 | 0.0117587 | ||||||||
\(931\) | 15404.5 | 0.542278 | ||||||||
\(932\) | 13806.0 | 0.485225 | ||||||||
\(933\) | −24917.4 | −0.874338 | ||||||||
\(934\) | 25318.6 | 0.886993 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 40036.4 | 1.39811 | ||||||||
\(937\) | −39312.3 | −1.37063 | −0.685314 | − | 0.728248i | \(-0.740335\pi\) | ||||
−0.685314 | + | 0.728248i | \(0.740335\pi\) | |||||||
\(938\) | 21416.7 | 0.745502 | ||||||||
\(939\) | −12856.6 | −0.446814 | ||||||||
\(940\) | −34014.7 | −1.18025 | ||||||||
\(941\) | −30478.0 | −1.05585 | −0.527924 | − | 0.849291i | \(-0.677030\pi\) | ||||
−0.527924 | + | 0.849291i | \(0.677030\pi\) | |||||||
\(942\) | 53567.0 | 1.85277 | ||||||||
\(943\) | 14008.5 | 0.483754 | ||||||||
\(944\) | −3921.73 | −0.135213 | ||||||||
\(945\) | −53618.8 | −1.84574 | ||||||||
\(946\) | −11703.7 | −0.402242 | ||||||||
\(947\) | −45331.1 | −1.55551 | −0.777753 | − | 0.628570i | \(-0.783640\pi\) | ||||
−0.777753 | + | 0.628570i | \(0.783640\pi\) | |||||||
\(948\) | 6975.65 | 0.238986 | ||||||||
\(949\) | −22547.3 | −0.771250 | ||||||||
\(950\) | 23844.6 | 0.814339 | ||||||||
\(951\) | −7648.70 | −0.260806 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 33782.9 | 1.14830 | 0.574152 | − | 0.818748i | \(-0.305332\pi\) | ||||
0.574152 | + | 0.818748i | \(0.305332\pi\) | |||||||
\(954\) | −60019.3 | −2.03690 | ||||||||
\(955\) | 21838.1 | 0.739964 | ||||||||
\(956\) | 5899.04 | 0.199570 | ||||||||
\(957\) | 2081.84 | 0.0703202 | ||||||||
\(958\) | 30300.7 | 1.02189 | ||||||||
\(959\) | −8391.56 | −0.282563 | ||||||||
\(960\) | 75958.6 | 2.55370 | ||||||||
\(961\) | −29789.9 | −0.999964 | ||||||||
\(962\) | −13758.4 | −0.461111 | ||||||||
\(963\) | −44879.1 | −1.50178 | ||||||||
\(964\) | 8182.55 | 0.273384 | ||||||||
\(965\) | −61472.2 | −2.05063 | ||||||||
\(966\) | −10896.6 | −0.362931 | ||||||||
\(967\) | −45742.7 | −1.52119 | −0.760593 | − | 0.649229i | \(-0.775092\pi\) | ||||
−0.760593 | + | 0.649229i | \(0.775092\pi\) | |||||||
\(968\) | −29539.2 | −0.980813 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 64859.5 | 2.14692 | ||||||||
\(971\) | 7001.98 | 0.231415 | 0.115708 | − | 0.993283i | \(-0.463086\pi\) | ||||
0.115708 | + | 0.993283i | \(0.463086\pi\) | |||||||
\(972\) | 4393.31 | 0.144975 | ||||||||
\(973\) | −528.547 | −0.0174146 | ||||||||
\(974\) | 6252.64 | 0.205696 | ||||||||
\(975\) | −36564.8 | −1.20104 | ||||||||
\(976\) | 4675.53 | 0.153340 | ||||||||
\(977\) | 36142.8 | 1.18353 | 0.591767 | − | 0.806109i | \(-0.298431\pi\) | ||||
0.591767 | + | 0.806109i | \(0.298431\pi\) | |||||||
\(978\) | 3774.95 | 0.123425 | ||||||||
\(979\) | −7695.39 | −0.251221 | ||||||||
\(980\) | −10410.6 | −0.339341 | ||||||||
\(981\) | 96705.6 | 3.14737 | ||||||||
\(982\) | 20392.0 | 0.662662 | ||||||||
\(983\) | 21919.3 | 0.711207 | 0.355603 | − | 0.934637i | \(-0.384275\pi\) | ||||
0.355603 | + | 0.934637i | \(0.384275\pi\) | |||||||
\(984\) | −69626.7 | −2.25571 | ||||||||
\(985\) | −1175.19 | −0.0380150 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −70672.4 | −2.27916 | ||||||||
\(988\) | 7622.11 | 0.245437 | ||||||||
\(989\) | 21790.8 | 0.700614 | ||||||||
\(990\) | 22209.9 | 0.713006 | ||||||||
\(991\) | −19931.0 | −0.638880 | −0.319440 | − | 0.947607i | \(-0.603495\pi\) | ||||
−0.319440 | + | 0.947607i | \(0.603495\pi\) | |||||||
\(992\) | 143.873 | 0.00460482 | ||||||||
\(993\) | −23264.6 | −0.743483 | ||||||||
\(994\) | −18899.5 | −0.603074 | ||||||||
\(995\) | −43878.7 | −1.39804 | ||||||||
\(996\) | 7150.75 | 0.227490 | ||||||||
\(997\) | −18298.2 | −0.581253 | −0.290626 | − | 0.956837i | \(-0.593864\pi\) | ||||
−0.290626 | + | 0.956837i | \(0.593864\pi\) | |||||||
\(998\) | 1545.48 | 0.0490193 | ||||||||
\(999\) | −59434.5 | −1.88231 |
(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.h.1.4 | ✓ | 12 | |
17.4 | even | 4 | 289.4.b.f.288.18 | 24 | |||
17.13 | even | 4 | 289.4.b.f.288.17 | 24 | |||
17.16 | even | 2 | 289.4.a.i.1.4 | yes | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
289.4.a.h.1.4 | ✓ | 12 | 1.1 | even | 1 | trivial | |
289.4.a.i.1.4 | yes | 12 | 17.16 | even | 2 | ||
289.4.b.f.288.17 | 24 | 17.13 | even | 4 | |||
289.4.b.f.288.18 | 24 | 17.4 | even | 4 |