Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [138,4,Mod(137,138)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(138, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("138.137");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 138 = 2 \cdot 3 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 138.d (of order \(2\), degree \(1\), minimal) |
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: | no |
Analytic conductor: | \(8.14226358079\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 137.8 | ||
Character | \(\chi\) | \(=\) | 138.137 |
Dual form | 138.4.d.a.137.20 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/138\mathbb{Z}\right)^\times\).
\(n\) | \(47\) | \(97\) |
\(\chi(n)\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 2.00000i | − | 0.707107i | ||||||
\(3\) | 2.34341 | + | 4.63772i | 0.450989 | + | 0.892530i | ||||
\(4\) | −4.00000 | −0.500000 | ||||||||
\(5\) | 10.8839 | 0.973487 | 0.486744 | − | 0.873545i | \(-0.338185\pi\) | ||||
0.486744 | + | 0.873545i | \(0.338185\pi\) | |||||||
\(6\) | 9.27544 | − | 4.68682i | 0.631114 | − | 0.318897i | ||||
\(7\) | 21.8179i | 1.17806i | 0.808112 | + | 0.589028i | \(0.200489\pi\) | ||||
−0.808112 | + | 0.589028i | \(0.799511\pi\) | |||||||
\(8\) | 8.00000i | 0.353553i | ||||||||
\(9\) | −16.0169 | + | 21.7361i | −0.593218 | + | 0.805042i | ||||
\(10\) | − | 21.7678i | − | 0.688359i | ||||||
\(11\) | −10.5986 | −0.290508 | −0.145254 | − | 0.989394i | \(-0.546400\pi\) | ||||
−0.145254 | + | 0.989394i | \(0.546400\pi\) | |||||||
\(12\) | −9.37363 | − | 18.5509i | −0.225494 | − | 0.446265i | ||||
\(13\) | −57.2594 | −1.22161 | −0.610804 | − | 0.791782i | \(-0.709154\pi\) | ||||
−0.610804 | + | 0.791782i | \(0.709154\pi\) | |||||||
\(14\) | 43.6358 | 0.833012 | ||||||||
\(15\) | 25.5055 | + | 50.4766i | 0.439032 | + | 0.868866i | ||||
\(16\) | 16.0000 | 0.250000 | ||||||||
\(17\) | 114.219 | 1.62955 | 0.814773 | − | 0.579780i | \(-0.196861\pi\) | ||||
0.814773 | + | 0.579780i | \(0.196861\pi\) | |||||||
\(18\) | 43.4723 | + | 32.0338i | 0.569251 | + | 0.419468i | ||||
\(19\) | 113.444i | 1.36978i | 0.728648 | + | 0.684888i | \(0.240149\pi\) | ||||
−0.728648 | + | 0.684888i | \(0.759851\pi\) | |||||||
\(20\) | −43.5357 | −0.486744 | ||||||||
\(21\) | −101.185 | + | 51.1283i | −1.05145 | + | 0.531291i | ||||
\(22\) | 21.1971i | 0.205420i | ||||||||
\(23\) | 99.6450 | − | 47.3062i | 0.903366 | − | 0.428870i | ||||
\(24\) | −37.1018 | + | 18.7473i | −0.315557 | + | 0.159449i | ||||
\(25\) | −6.54035 | −0.0523228 | ||||||||
\(26\) | 114.519i | 0.863807i | ||||||||
\(27\) | −138.340 | − | 23.3452i | −0.986058 | − | 0.166399i | ||||
\(28\) | − | 87.2717i | − | 0.589028i | ||||||
\(29\) | 126.097i | 0.807433i | 0.914884 | + | 0.403717i | \(0.132282\pi\) | ||||
−0.914884 | + | 0.403717i | \(0.867718\pi\) | |||||||
\(30\) | 100.953 | − | 51.0109i | 0.614381 | − | 0.310442i | ||||
\(31\) | 289.289 | 1.67606 | 0.838030 | − | 0.545624i | \(-0.183707\pi\) | ||||
0.838030 | + | 0.545624i | \(0.183707\pi\) | |||||||
\(32\) | − | 32.0000i | − | 0.176777i | ||||||
\(33\) | −24.8368 | − | 49.1532i | −0.131016 | − | 0.259287i | ||||
\(34\) | − | 228.439i | − | 1.15226i | ||||||
\(35\) | 237.464i | 1.14682i | ||||||||
\(36\) | 64.0675 | − | 86.9445i | 0.296609 | − | 0.402521i | ||||
\(37\) | − | 84.7151i | − | 0.376408i | −0.982130 | − | 0.188204i | \(-0.939733\pi\) | ||
0.982130 | − | 0.188204i | \(-0.0602665\pi\) | |||||||
\(38\) | 226.887 | 0.968578 | ||||||||
\(39\) | −134.182 | − | 265.553i | −0.550932 | − | 1.09032i | ||||
\(40\) | 87.0713i | 0.344180i | ||||||||
\(41\) | − | 299.551i | − | 1.14102i | −0.821290 | − | 0.570511i | \(-0.806745\pi\) | ||
0.821290 | − | 0.570511i | \(-0.193255\pi\) | |||||||
\(42\) | 102.257 | + | 202.371i | 0.375679 | + | 0.743488i | ||||
\(43\) | − | 365.488i | − | 1.29619i | −0.761558 | − | 0.648097i | \(-0.775565\pi\) | ||
0.761558 | − | 0.648097i | \(-0.224435\pi\) | |||||||
\(44\) | 42.3943 | 0.145254 | ||||||||
\(45\) | −174.326 | + | 236.574i | −0.577490 | + | 0.783698i | ||||
\(46\) | −94.6123 | − | 199.290i | −0.303257 | − | 0.638776i | ||||
\(47\) | 254.505i | 0.789859i | 0.918712 | + | 0.394929i | \(0.129231\pi\) | ||||
−0.918712 | + | 0.394929i | \(0.870769\pi\) | |||||||
\(48\) | 37.4945 | + | 74.2035i | 0.112747 | + | 0.223132i | ||||
\(49\) | −133.021 | −0.387817 | ||||||||
\(50\) | 13.0807i | 0.0369978i | ||||||||
\(51\) | 267.663 | + | 529.718i | 0.734908 | + | 1.45442i | ||||
\(52\) | 229.038 | 0.610804 | ||||||||
\(53\) | −467.085 | −1.21055 | −0.605274 | − | 0.796017i | \(-0.706936\pi\) | ||||
−0.605274 | + | 0.796017i | \(0.706936\pi\) | |||||||
\(54\) | −46.6904 | + | 276.680i | −0.117662 | + | 0.697249i | ||||
\(55\) | −115.354 | −0.282806 | ||||||||
\(56\) | −174.543 | −0.416506 | ||||||||
\(57\) | −526.120 | + | 265.845i | −1.22257 | + | 0.617754i | ||||
\(58\) | 252.193 | 0.570941 | ||||||||
\(59\) | − | 304.305i | − | 0.671476i | −0.941955 | − | 0.335738i | \(-0.891014\pi\) | ||
0.941955 | − | 0.335738i | \(-0.108986\pi\) | |||||||
\(60\) | −102.022 | − | 201.906i | −0.219516 | − | 0.434433i | ||||
\(61\) | − | 697.918i | − | 1.46491i | −0.680818 | − | 0.732453i | \(-0.738375\pi\) | ||
0.680818 | − | 0.732453i | \(-0.261625\pi\) | |||||||
\(62\) | − | 578.578i | − | 1.18515i | ||||||
\(63\) | −474.237 | − | 349.455i | −0.948385 | − | 0.698844i | ||||
\(64\) | −64.0000 | −0.125000 | ||||||||
\(65\) | −623.206 | −1.18922 | ||||||||
\(66\) | −98.3063 | + | 49.6735i | −0.183344 | + | 0.0926422i | ||||
\(67\) | 671.692i | 1.22478i | 0.790556 | + | 0.612389i | \(0.209792\pi\) | ||||
−0.790556 | + | 0.612389i | \(0.790208\pi\) | |||||||
\(68\) | −456.878 | −0.814773 | ||||||||
\(69\) | 452.902 | + | 351.268i | 0.790188 | + | 0.612865i | ||||
\(70\) | 474.929 | 0.810926 | ||||||||
\(71\) | − | 354.578i | − | 0.592685i | −0.955082 | − | 0.296343i | \(-0.904233\pi\) | ||
0.955082 | − | 0.296343i | \(-0.0957670\pi\) | |||||||
\(72\) | −173.889 | − | 128.135i | −0.284625 | − | 0.209734i | ||||
\(73\) | −321.406 | −0.515311 | −0.257656 | − | 0.966237i | \(-0.582950\pi\) | ||||
−0.257656 | + | 0.966237i | \(0.582950\pi\) | |||||||
\(74\) | −169.430 | −0.266160 | ||||||||
\(75\) | −15.3267 | − | 30.3323i | −0.0235970 | − | 0.0466996i | ||||
\(76\) | − | 453.774i | − | 0.684888i | ||||||
\(77\) | − | 231.239i | − | 0.342235i | ||||||
\(78\) | −531.106 | + | 268.364i | −0.770973 | + | 0.389567i | ||||
\(79\) | − | 78.6582i | − | 0.112022i | −0.998430 | − | 0.0560110i | \(-0.982162\pi\) | ||
0.998430 | − | 0.0560110i | \(-0.0178382\pi\) | |||||||
\(80\) | 174.143 | 0.243372 | ||||||||
\(81\) | −215.919 | − | 696.290i | −0.296185 | − | 0.955131i | ||||
\(82\) | −599.101 | −0.806825 | ||||||||
\(83\) | 506.936 | 0.670404 | 0.335202 | − | 0.942146i | \(-0.391195\pi\) | ||||
0.335202 | + | 0.942146i | \(0.391195\pi\) | |||||||
\(84\) | 404.741 | − | 204.513i | 0.525725 | − | 0.265645i | ||||
\(85\) | 1243.16 | 1.58634 | ||||||||
\(86\) | −730.976 | −0.916548 | ||||||||
\(87\) | −584.801 | + | 295.496i | −0.720658 | + | 0.364143i | ||||
\(88\) | − | 84.7885i | − | 0.102710i | ||||||
\(89\) | 1122.44 | 1.33683 | 0.668416 | − | 0.743788i | \(-0.266973\pi\) | ||||
0.668416 | + | 0.743788i | \(0.266973\pi\) | |||||||
\(90\) | 473.149 | + | 348.653i | 0.554158 | + | 0.408347i | ||||
\(91\) | − | 1249.28i | − | 1.43912i | ||||||
\(92\) | −398.580 | + | 189.225i | −0.451683 | + | 0.214435i | ||||
\(93\) | 677.922 | + | 1341.64i | 0.755885 | + | 1.49593i | ||||
\(94\) | 509.010 | 0.558514 | ||||||||
\(95\) | 1234.71i | 1.33346i | ||||||||
\(96\) | 148.407 | − | 74.9890i | 0.157778 | − | 0.0797243i | ||||
\(97\) | 553.523i | 0.579399i | 0.957118 | + | 0.289700i | \(0.0935554\pi\) | ||||
−0.957118 | + | 0.289700i | \(0.906445\pi\) | |||||||
\(98\) | 266.043i | 0.274228i | ||||||||
\(99\) | 169.756 | − | 230.372i | 0.172334 | − | 0.233871i | ||||
\(100\) | 26.1614 | 0.0261614 | ||||||||
\(101\) | − | 619.354i | − | 0.610179i | −0.952324 | − | 0.305089i | \(-0.901314\pi\) | ||
0.952324 | − | 0.305089i | \(-0.0986863\pi\) | |||||||
\(102\) | 1059.44 | − | 535.326i | 1.02843 | − | 0.519658i | ||||
\(103\) | − | 1232.74i | − | 1.17928i | −0.807667 | − | 0.589639i | \(-0.799270\pi\) | ||
0.807667 | − | 0.589639i | \(-0.200730\pi\) | |||||||
\(104\) | − | 458.075i | − | 0.431903i | ||||||
\(105\) | −1101.29 | + | 556.476i | −1.02357 | + | 0.517205i | ||||
\(106\) | 934.169i | 0.855986i | ||||||||
\(107\) | 998.586 | 0.902215 | 0.451107 | − | 0.892470i | \(-0.351029\pi\) | ||||
0.451107 | + | 0.892470i | \(0.351029\pi\) | |||||||
\(108\) | 553.361 | + | 93.3808i | 0.493029 | + | 0.0831997i | ||||
\(109\) | 1042.56i | 0.916140i | 0.888916 | + | 0.458070i | \(0.151459\pi\) | ||||
−0.888916 | + | 0.458070i | \(0.848541\pi\) | |||||||
\(110\) | 230.708i | 0.199974i | ||||||||
\(111\) | 392.885 | − | 198.522i | 0.335955 | − | 0.169756i | ||||
\(112\) | 349.087i | 0.294514i | ||||||||
\(113\) | 1720.22 | 1.43208 | 0.716039 | − | 0.698060i | \(-0.245953\pi\) | ||||
0.716039 | + | 0.698060i | \(0.245953\pi\) | |||||||
\(114\) | 531.689 | + | 1052.24i | 0.436818 | + | 0.864484i | ||||
\(115\) | 1084.53 | − | 514.876i | 0.879415 | − | 0.417500i | ||||
\(116\) | − | 504.387i | − | 0.403717i | ||||||
\(117\) | 917.117 | − | 1244.60i | 0.724679 | − | 0.983445i | ||||
\(118\) | −608.609 | −0.474805 | ||||||||
\(119\) | 2492.03i | 1.91970i | ||||||||
\(120\) | −403.812 | + | 204.044i | −0.307191 | + | 0.155221i | ||||
\(121\) | −1218.67 | −0.915605 | ||||||||
\(122\) | −1395.84 | −1.03584 | ||||||||
\(123\) | 1389.23 | − | 701.969i | 1.01840 | − | 0.514589i | ||||
\(124\) | −1157.16 | −0.838030 | ||||||||
\(125\) | −1431.67 | −1.02442 | ||||||||
\(126\) | −698.910 | + | 948.474i | −0.494157 | + | 0.670609i | ||||
\(127\) | −417.436 | −0.291665 | −0.145833 | − | 0.989309i | \(-0.546586\pi\) | ||||
−0.145833 | + | 0.989309i | \(0.546586\pi\) | |||||||
\(128\) | 128.000i | 0.0883883i | ||||||||
\(129\) | 1695.03 | − | 856.487i | 1.15689 | − | 0.584570i | ||||
\(130\) | 1246.41i | 0.840905i | ||||||||
\(131\) | − | 994.475i | − | 0.663265i | −0.943409 | − | 0.331633i | \(-0.892401\pi\) | ||
0.943409 | − | 0.331633i | \(-0.107599\pi\) | |||||||
\(132\) | 99.3470 | + | 196.613i | 0.0655079 | + | 0.129643i | ||||
\(133\) | −2475.10 | −1.61367 | ||||||||
\(134\) | 1343.38 | 0.866049 | ||||||||
\(135\) | −1505.68 | − | 254.087i | −0.959915 | − | 0.161988i | ||||
\(136\) | 913.756i | 0.576132i | ||||||||
\(137\) | −1322.32 | −0.824624 | −0.412312 | − | 0.911043i | \(-0.635279\pi\) | ||||
−0.412312 | + | 0.911043i | \(0.635279\pi\) | |||||||
\(138\) | 702.536 | − | 905.803i | 0.433361 | − | 0.558747i | ||||
\(139\) | 642.320 | 0.391949 | 0.195974 | − | 0.980609i | \(-0.437213\pi\) | ||||
0.195974 | + | 0.980609i | \(0.437213\pi\) | |||||||
\(140\) | − | 949.857i | − | 0.573411i | ||||||
\(141\) | −1180.32 | + | 596.409i | −0.704972 | + | 0.356217i | ||||
\(142\) | −709.156 | −0.419092 | ||||||||
\(143\) | 606.867 | 0.354887 | ||||||||
\(144\) | −256.270 | + | 347.778i | −0.148304 | + | 0.201260i | ||||
\(145\) | 1372.43i | 0.786026i | ||||||||
\(146\) | 642.812i | 0.364380i | ||||||||
\(147\) | −311.723 | − | 616.916i | −0.174901 | − | 0.346138i | ||||
\(148\) | 338.860i | 0.188204i | ||||||||
\(149\) | 69.6174 | 0.0382770 | 0.0191385 | − | 0.999817i | \(-0.493908\pi\) | ||||
0.0191385 | + | 0.999817i | \(0.493908\pi\) | |||||||
\(150\) | −60.6646 | + | 30.6534i | −0.0330216 | + | 0.0166856i | ||||
\(151\) | 1839.55 | 0.991394 | 0.495697 | − | 0.868496i | \(-0.334913\pi\) | ||||
0.495697 | + | 0.868496i | \(0.334913\pi\) | |||||||
\(152\) | −907.549 | −0.484289 | ||||||||
\(153\) | −1829.44 | + | 2482.69i | −0.966676 | + | 1.31185i | ||||
\(154\) | −462.477 | −0.241997 | ||||||||
\(155\) | 3148.60 | 1.63162 | ||||||||
\(156\) | 536.728 | + | 1062.21i | 0.275466 | + | 0.545160i | ||||
\(157\) | 686.113i | 0.348776i | 0.984677 | + | 0.174388i | \(0.0557947\pi\) | ||||
−0.984677 | + | 0.174388i | \(0.944205\pi\) | |||||||
\(158\) | −157.316 | −0.0792115 | ||||||||
\(159\) | −1094.57 | − | 2166.21i | −0.545943 | − | 1.08045i | ||||
\(160\) | − | 348.285i | − | 0.172090i | ||||||
\(161\) | 1032.12 | + | 2174.05i | 0.505234 | + | 1.06422i | ||||
\(162\) | −1392.58 | + | 431.838i | −0.675379 | + | 0.209435i | ||||
\(163\) | 2558.16 | 1.22927 | 0.614633 | − | 0.788813i | \(-0.289304\pi\) | ||||
0.614633 | + | 0.788813i | \(0.289304\pi\) | |||||||
\(164\) | 1198.20i | 0.570511i | ||||||||
\(165\) | −270.321 | − | 534.979i | −0.127542 | − | 0.252412i | ||||
\(166\) | − | 1013.87i | − | 0.474047i | ||||||
\(167\) | − | 722.148i | − | 0.334620i | −0.985904 | − | 0.167310i | \(-0.946492\pi\) | ||
0.985904 | − | 0.167310i | \(-0.0535080\pi\) | |||||||
\(168\) | −409.026 | − | 809.483i | −0.187840 | − | 0.371744i | ||||
\(169\) | 1081.64 | 0.492325 | ||||||||
\(170\) | − | 2486.31i | − | 1.12171i | ||||||
\(171\) | −2465.83 | − | 1817.01i | −1.10273 | − | 0.812576i | ||||
\(172\) | 1461.95i | 0.648097i | ||||||||
\(173\) | − | 2672.05i | − | 1.17429i | −0.809482 | − | 0.587145i | \(-0.800252\pi\) | ||
0.809482 | − | 0.587145i | \(-0.199748\pi\) | |||||||
\(174\) | 590.992 | + | 1169.60i | 0.257488 | + | 0.509582i | ||||
\(175\) | − | 142.697i | − | 0.0616392i | ||||||
\(176\) | −169.577 | −0.0726270 | ||||||||
\(177\) | 1411.28 | − | 713.109i | 0.599312 | − | 0.302828i | ||||
\(178\) | − | 2244.87i | − | 0.945283i | ||||||
\(179\) | 1537.45i | 0.641982i | 0.947082 | + | 0.320991i | \(0.104016\pi\) | ||||
−0.947082 | + | 0.320991i | \(0.895984\pi\) | |||||||
\(180\) | 697.306 | − | 946.297i | 0.288745 | − | 0.391849i | ||||
\(181\) | 2480.61i | 1.01869i | 0.860563 | + | 0.509344i | \(0.170112\pi\) | ||||
−0.860563 | + | 0.509344i | \(0.829888\pi\) | |||||||
\(182\) | −2498.56 | −1.01761 | ||||||||
\(183\) | 3236.75 | − | 1635.51i | 1.30747 | − | 0.660656i | ||||
\(184\) | 378.449 | + | 797.160i | 0.151629 | + | 0.319388i | ||||
\(185\) | − | 922.032i | − | 0.366428i | ||||||
\(186\) | 2683.28 | − | 1355.84i | 1.05778 | − | 0.534491i | ||||
\(187\) | −1210.56 | −0.473396 | ||||||||
\(188\) | − | 1018.02i | − | 0.394929i | ||||||
\(189\) | 509.343 | − | 3018.29i | 0.196028 | − | 1.16163i | ||||
\(190\) | 2469.42 | 0.942898 | ||||||||
\(191\) | 2283.68 | 0.865139 | 0.432570 | − | 0.901601i | \(-0.357607\pi\) | ||||
0.432570 | + | 0.901601i | \(0.357607\pi\) | |||||||
\(192\) | −149.978 | − | 296.814i | −0.0563736 | − | 0.111566i | ||||
\(193\) | −3711.80 | −1.38436 | −0.692179 | − | 0.721726i | \(-0.743349\pi\) | ||||
−0.692179 | + | 0.721726i | \(0.743349\pi\) | |||||||
\(194\) | 1107.05 | 0.409697 | ||||||||
\(195\) | −1460.43 | − | 2890.26i | −0.536325 | − | 1.06141i | ||||
\(196\) | 532.085 | 0.193909 | ||||||||
\(197\) | 3550.99i | 1.28425i | 0.766600 | + | 0.642125i | \(0.221947\pi\) | ||||
−0.766600 | + | 0.642125i | \(0.778053\pi\) | |||||||
\(198\) | −460.744 | − | 339.512i | −0.165372 | − | 0.121859i | ||||
\(199\) | − | 501.412i | − | 0.178614i | −0.996004 | − | 0.0893070i | \(-0.971535\pi\) | ||
0.996004 | − | 0.0893070i | \(-0.0284652\pi\) | |||||||
\(200\) | − | 52.3228i | − | 0.0184989i | ||||||
\(201\) | −3115.12 | + | 1574.05i | −1.09315 | + | 0.552362i | ||||
\(202\) | −1238.71 | −0.431462 | ||||||||
\(203\) | −2751.17 | −0.951202 | ||||||||
\(204\) | −1070.65 | − | 2118.87i | −0.367454 | − | 0.727209i | ||||
\(205\) | − | 3260.28i | − | 1.11077i | ||||||
\(206\) | −2465.48 | −0.833875 | ||||||||
\(207\) | −567.749 | + | 2923.59i | −0.190634 | + | 0.981661i | ||||
\(208\) | −916.150 | −0.305402 | ||||||||
\(209\) | − | 1202.34i | − | 0.397931i | ||||||
\(210\) | 1112.95 | + | 2202.59i | 0.365719 | + | 0.723776i | ||||
\(211\) | −5985.97 | −1.95304 | −0.976520 | − | 0.215429i | \(-0.930885\pi\) | ||||
−0.976520 | + | 0.215429i | \(0.930885\pi\) | |||||||
\(212\) | 1868.34 | 0.605274 | ||||||||
\(213\) | 1644.43 | − | 830.920i | 0.528989 | − | 0.267294i | ||||
\(214\) | − | 1997.17i | − | 0.637962i | ||||||
\(215\) | − | 3977.94i | − | 1.26183i | ||||||
\(216\) | 186.762 | − | 1106.72i | 0.0588311 | − | 0.348624i | ||||
\(217\) | 6311.68i | 1.97449i | ||||||||
\(218\) | 2085.12 | 0.647809 | ||||||||
\(219\) | −753.185 | − | 1490.59i | −0.232400 | − | 0.459930i | ||||
\(220\) | 461.416 | 0.141403 | ||||||||
\(221\) | −6540.14 | −1.99067 | ||||||||
\(222\) | −397.044 | − | 785.770i | −0.120035 | − | 0.237556i | ||||
\(223\) | 3360.05 | 1.00899 | 0.504496 | − | 0.863414i | \(-0.331678\pi\) | ||||
0.504496 | + | 0.863414i | \(0.331678\pi\) | |||||||
\(224\) | 698.173 | 0.208253 | ||||||||
\(225\) | 104.756 | − | 142.162i | 0.0310388 | − | 0.0421220i | ||||
\(226\) | − | 3440.44i | − | 1.01263i | ||||||
\(227\) | −864.868 | −0.252878 | −0.126439 | − | 0.991974i | \(-0.540355\pi\) | ||||
−0.126439 | + | 0.991974i | \(0.540355\pi\) | |||||||
\(228\) | 2104.48 | − | 1063.38i | 0.611283 | − | 0.308877i | ||||
\(229\) | 644.141i | 0.185878i | 0.995672 | + | 0.0929390i | \(0.0296262\pi\) | ||||
−0.995672 | + | 0.0929390i | \(0.970374\pi\) | |||||||
\(230\) | −1029.75 | − | 2169.06i | −0.295217 | − | 0.621840i | ||||
\(231\) | 1072.42 | − | 541.886i | 0.305455 | − | 0.154344i | ||||
\(232\) | −1008.77 | −0.285471 | ||||||||
\(233\) | 5314.43i | 1.49425i | 0.664685 | + | 0.747124i | \(0.268566\pi\) | ||||
−0.664685 | + | 0.747124i | \(0.731434\pi\) | |||||||
\(234\) | −2489.20 | − | 1834.23i | −0.695401 | − | 0.512426i | ||||
\(235\) | 2770.01i | 0.768917i | ||||||||
\(236\) | 1217.22i | 0.335738i | ||||||||
\(237\) | 364.795 | − | 184.328i | 0.0999830 | − | 0.0505207i | ||||
\(238\) | 4984.06 | 1.35743 | ||||||||
\(239\) | − | 3518.25i | − | 0.952204i | −0.879390 | − | 0.476102i | \(-0.842049\pi\) | ||
0.879390 | − | 0.476102i | \(-0.157951\pi\) | |||||||
\(240\) | 408.087 | + | 807.625i | 0.109758 | + | 0.217217i | ||||
\(241\) | 4742.64i | 1.26763i | 0.773483 | + | 0.633817i | \(0.218513\pi\) | ||||
−0.773483 | + | 0.633817i | \(0.781487\pi\) | |||||||
\(242\) | 2437.34i | 0.647431i | ||||||||
\(243\) | 2723.21 | − | 2633.06i | 0.718906 | − | 0.695107i | ||||
\(244\) | 2791.67i | 0.732453i | ||||||||
\(245\) | −1447.79 | −0.377535 | ||||||||
\(246\) | −1403.94 | − | 2778.46i | −0.363869 | − | 0.720115i | ||||
\(247\) | − | 6495.71i | − | 1.67333i | ||||||
\(248\) | 2314.31i | 0.592577i | ||||||||
\(249\) | 1187.96 | + | 2351.03i | 0.302345 | + | 0.598355i | ||||
\(250\) | 2863.35i | 0.724376i | ||||||||
\(251\) | −930.257 | −0.233933 | −0.116967 | − | 0.993136i | \(-0.537317\pi\) | ||||
−0.116967 | + | 0.993136i | \(0.537317\pi\) | |||||||
\(252\) | 1896.95 | + | 1397.82i | 0.474193 | + | 0.349422i | ||||
\(253\) | −1056.09 | + | 501.377i | −0.262435 | + | 0.124590i | ||||
\(254\) | 834.873i | 0.206238i | ||||||||
\(255\) | 2913.22 | + | 5765.41i | 0.715423 | + | 1.41586i | ||||
\(256\) | 256.000 | 0.0625000 | ||||||||
\(257\) | 1399.11i | 0.339588i | 0.985480 | + | 0.169794i | \(0.0543102\pi\) | ||||
−0.985480 | + | 0.169794i | \(0.945690\pi\) | |||||||
\(258\) | −1712.97 | − | 3390.06i | −0.413353 | − | 0.818046i | ||||
\(259\) | 1848.31 | 0.443429 | ||||||||
\(260\) | 2492.83 | 0.594610 | ||||||||
\(261\) | −2740.85 | − | 2019.68i | −0.650017 | − | 0.478984i | ||||
\(262\) | −1988.95 | −0.468999 | ||||||||
\(263\) | 4854.60 | 1.13820 | 0.569101 | − | 0.822267i | \(-0.307291\pi\) | ||||
0.569101 | + | 0.822267i | \(0.307291\pi\) | |||||||
\(264\) | 393.225 | − | 198.694i | 0.0916718 | − | 0.0463211i | ||||
\(265\) | −5083.71 | −1.17845 | ||||||||
\(266\) | 4950.21i | 1.14104i | ||||||||
\(267\) | 2630.33 | + | 5205.55i | 0.602896 | + | 1.19316i | ||||
\(268\) | − | 2686.77i | − | 0.612389i | ||||||
\(269\) | − | 4990.97i | − | 1.13124i | −0.824665 | − | 0.565622i | \(-0.808636\pi\) | ||
0.824665 | − | 0.565622i | \(-0.191364\pi\) | |||||||
\(270\) | −508.174 | + | 3011.37i | −0.114543 | + | 0.678763i | ||||
\(271\) | −5973.67 | −1.33902 | −0.669510 | − | 0.742803i | \(-0.733496\pi\) | ||||
−0.669510 | + | 0.742803i | \(0.733496\pi\) | |||||||
\(272\) | 1827.51 | 0.407387 | ||||||||
\(273\) | 5793.81 | − | 2927.57i | 1.28446 | − | 0.649029i | ||||
\(274\) | 2644.64i | 0.583097i | ||||||||
\(275\) | 69.3183 | 0.0152002 | ||||||||
\(276\) | −1811.61 | − | 1405.07i | −0.395094 | − | 0.306433i | ||||
\(277\) | 2759.86 | 0.598642 | 0.299321 | − | 0.954152i | \(-0.403240\pi\) | ||||
0.299321 | + | 0.954152i | \(0.403240\pi\) | |||||||
\(278\) | − | 1284.64i | − | 0.277150i | ||||||
\(279\) | −4633.51 | + | 6288.03i | −0.994269 | + | 1.34930i | ||||
\(280\) | −1899.71 | −0.405463 | ||||||||
\(281\) | −902.764 | −0.191653 | −0.0958263 | − | 0.995398i | \(-0.530549\pi\) | ||||
−0.0958263 | + | 0.995398i | \(0.530549\pi\) | |||||||
\(282\) | 1192.82 | + | 2360.64i | 0.251884 | + | 0.498491i | ||||
\(283\) | 7168.41i | 1.50572i | 0.658183 | + | 0.752858i | \(0.271325\pi\) | ||||
−0.658183 | + | 0.752858i | \(0.728675\pi\) | |||||||
\(284\) | 1418.31i | 0.296343i | ||||||||
\(285\) | −5726.24 | + | 2893.43i | −1.19015 | + | 0.601376i | ||||
\(286\) | − | 1213.73i | − | 0.250943i | ||||||
\(287\) | 6535.57 | 1.34419 | ||||||||
\(288\) | 695.556 | + | 512.540i | 0.142313 | + | 0.104867i | ||||
\(289\) | 8133.09 | 1.65542 | ||||||||
\(290\) | 2744.85 | 0.555804 | ||||||||
\(291\) | −2567.08 | + | 1297.13i | −0.517131 | + | 0.261303i | ||||
\(292\) | 1285.62 | 0.257656 | ||||||||
\(293\) | 601.951 | 0.120022 | 0.0600109 | − | 0.998198i | \(-0.480886\pi\) | ||||
0.0600109 | + | 0.998198i | \(0.480886\pi\) | |||||||
\(294\) | −1233.83 | + | 623.447i | −0.244757 | + | 0.123674i | ||||
\(295\) | − | 3312.03i | − | 0.653673i | ||||||
\(296\) | 677.721 | 0.133080 | ||||||||
\(297\) | 1466.21 | + | 247.425i | 0.286458 | + | 0.0483403i | ||||
\(298\) | − | 139.235i | − | 0.0270660i | ||||||
\(299\) | −5705.61 | + | 2708.72i | −1.10356 | + | 0.523911i | ||||
\(300\) | 61.3068 | + | 121.329i | 0.0117985 | + | 0.0233498i | ||||
\(301\) | 7974.18 | 1.52699 | ||||||||
\(302\) | − | 3679.10i | − | 0.701021i | ||||||
\(303\) | 2872.39 | − | 1451.40i | 0.544603 | − | 0.275184i | ||||
\(304\) | 1815.10i | 0.342444i | ||||||||
\(305\) | − | 7596.08i | − | 1.42607i | ||||||
\(306\) | 4965.38 | + | 3658.88i | 0.927620 | + | 0.683543i | ||||
\(307\) | −9095.26 | −1.69086 | −0.845429 | − | 0.534087i | \(-0.820655\pi\) | ||||
−0.845429 | + | 0.534087i | \(0.820655\pi\) | |||||||
\(308\) | 924.954i | 0.171117i | ||||||||
\(309\) | 5717.11 | − | 2888.82i | 1.05254 | − | 0.531841i | ||||
\(310\) | − | 6297.20i | − | 1.15373i | ||||||
\(311\) | − | 2085.16i | − | 0.380188i | −0.981766 | − | 0.190094i | \(-0.939121\pi\) | ||
0.981766 | − | 0.190094i | \(-0.0608793\pi\) | |||||||
\(312\) | 2124.42 | − | 1073.46i | 0.385487 | − | 0.194784i | ||||
\(313\) | − | 7530.75i | − | 1.35995i | −0.733237 | − | 0.679973i | \(-0.761992\pi\) | ||
0.733237 | − | 0.679973i | \(-0.238008\pi\) | |||||||
\(314\) | 1372.23 | 0.246622 | ||||||||
\(315\) | −5161.56 | − | 3803.44i | −0.923241 | − | 0.680316i | ||||
\(316\) | 314.633i | 0.0560110i | ||||||||
\(317\) | − | 5822.34i | − | 1.03159i | −0.856711 | − | 0.515797i | \(-0.827496\pi\) | ||
0.856711 | − | 0.515797i | \(-0.172504\pi\) | |||||||
\(318\) | −4332.41 | + | 2189.14i | −0.763993 | + | 0.386040i | ||||
\(319\) | − | 1336.44i | − | 0.234566i | ||||||
\(320\) | −696.571 | −0.121686 | ||||||||
\(321\) | 2340.09 | + | 4631.16i | 0.406889 | + | 0.805253i | ||||
\(322\) | 4348.09 | − | 2064.24i | 0.752515 | − | 0.357254i | ||||
\(323\) | 12957.5i | 2.23211i | ||||||||
\(324\) | 863.676 | + | 2785.16i | 0.148093 | + | 0.477565i | ||||
\(325\) | 374.496 | 0.0639179 | ||||||||
\(326\) | − | 5116.31i | − | 0.869222i | ||||||
\(327\) | −4835.11 | + | 2443.15i | −0.817682 | + | 0.413169i | ||||
\(328\) | 2396.40 | 0.403413 | ||||||||
\(329\) | −5552.77 | −0.930498 | ||||||||
\(330\) | −1069.96 | + | 540.642i | −0.178483 | + | 0.0901860i | ||||
\(331\) | 9020.57 | 1.49793 | 0.748965 | − | 0.662609i | \(-0.230551\pi\) | ||||
0.748965 | + | 0.662609i | \(0.230551\pi\) | |||||||
\(332\) | −2027.75 | −0.335202 | ||||||||
\(333\) | 1841.38 | + | 1356.87i | 0.303024 | + | 0.223292i | ||||
\(334\) | −1444.30 | −0.236612 | ||||||||
\(335\) | 7310.64i | 1.19231i | ||||||||
\(336\) | −1618.97 | + | 818.052i | −0.262863 | + | 0.132823i | ||||
\(337\) | − | 7456.58i | − | 1.20530i | −0.798006 | − | 0.602649i | \(-0.794112\pi\) | ||
0.798006 | − | 0.602649i | \(-0.205888\pi\) | |||||||
\(338\) | − | 2163.28i | − | 0.348126i | ||||||
\(339\) | 4031.18 | + | 7977.90i | 0.645851 | + | 1.27817i | ||||
\(340\) | −4972.62 | −0.793171 | ||||||||
\(341\) | −3066.05 | −0.486909 | ||||||||
\(342\) | −3634.03 | + | 4931.65i | −0.574578 | + | 0.779746i | ||||
\(343\) | 4581.30i | 0.721186i | ||||||||
\(344\) | 2923.90 | 0.458274 | ||||||||
\(345\) | 4929.34 | + | 3823.17i | 0.769237 | + | 0.596616i | ||||
\(346\) | −5344.10 | −0.830348 | ||||||||
\(347\) | 4527.76i | 0.700469i | 0.936662 | + | 0.350235i | \(0.113898\pi\) | ||||
−0.936662 | + | 0.350235i | \(0.886102\pi\) | |||||||
\(348\) | 2339.20 | − | 1181.98i | 0.360329 | − | 0.182072i | ||||
\(349\) | 1114.89 | 0.170999 | 0.0854993 | − | 0.996338i | \(-0.472751\pi\) | ||||
0.0854993 | + | 0.996338i | \(0.472751\pi\) | |||||||
\(350\) | −285.393 | −0.0435855 | ||||||||
\(351\) | 7921.27 | + | 1336.73i | 1.20458 | + | 0.203275i | ||||
\(352\) | 339.154i | 0.0513550i | ||||||||
\(353\) | − | 817.597i | − | 0.123276i | −0.998099 | − | 0.0616378i | \(-0.980368\pi\) | ||
0.998099 | − | 0.0616378i | \(-0.0196324\pi\) | |||||||
\(354\) | −1426.22 | − | 2822.56i | −0.214132 | − | 0.423778i | ||||
\(355\) | − | 3859.20i | − | 0.576971i | ||||||
\(356\) | −4489.75 | −0.668416 | ||||||||
\(357\) | −11557.3 | + | 5839.84i | −1.71339 | + | 0.865763i | ||||
\(358\) | 3074.91 | 0.453950 | ||||||||
\(359\) | 5448.72 | 0.801038 | 0.400519 | − | 0.916288i | \(-0.368830\pi\) | ||||
0.400519 | + | 0.916288i | \(0.368830\pi\) | |||||||
\(360\) | −1892.59 | − | 1394.61i | −0.277079 | − | 0.204174i | ||||
\(361\) | −6010.45 | −0.876287 | ||||||||
\(362\) | 4961.22 | 0.720321 | ||||||||
\(363\) | −2855.84 | − | 5651.85i | −0.412928 | − | 0.817205i | ||||
\(364\) | 4997.12i | 0.719561i | ||||||||
\(365\) | −3498.15 | −0.501649 | ||||||||
\(366\) | −3271.01 | − | 6473.50i | −0.467155 | − | 0.924522i | ||||
\(367\) | 168.276i | 0.0239345i | 0.999928 | + | 0.0119672i | \(0.00380938\pi\) | ||||
−0.999928 | + | 0.0119672i | \(0.996191\pi\) | |||||||
\(368\) | 1594.32 | − | 756.899i | 0.225842 | − | 0.107218i | ||||
\(369\) | 6511.07 | + | 4797.87i | 0.918571 | + | 0.676875i | ||||
\(370\) | −1844.06 | −0.259104 | ||||||||
\(371\) | − | 10190.8i | − | 1.42609i | ||||||
\(372\) | −2711.69 | − | 5366.57i | −0.377942 | − | 0.747966i | ||||
\(373\) | − | 8526.68i | − | 1.18363i | −0.806073 | − | 0.591816i | \(-0.798411\pi\) | ||
0.806073 | − | 0.591816i | \(-0.201589\pi\) | |||||||
\(374\) | 2421.12i | 0.334742i | ||||||||
\(375\) | −3355.00 | − | 6639.70i | −0.462003 | − | 0.914327i | ||||
\(376\) | −2036.04 | −0.279257 | ||||||||
\(377\) | − | 7220.22i | − | 0.986366i | ||||||
\(378\) | −6036.59 | − | 1018.69i | −0.821398 | − | 0.138613i | ||||
\(379\) | 1545.20i | 0.209423i | 0.994503 | + | 0.104712i | \(0.0333920\pi\) | ||||
−0.994503 | + | 0.104712i | \(0.966608\pi\) | |||||||
\(380\) | − | 4938.84i | − | 0.666730i | ||||||
\(381\) | −978.223 | − | 1935.95i | −0.131538 | − | 0.260320i | ||||
\(382\) | − | 4567.37i | − | 0.611746i | ||||||
\(383\) | 5941.15 | 0.792633 | 0.396316 | − | 0.918114i | \(-0.370288\pi\) | ||||
0.396316 | + | 0.918114i | \(0.370288\pi\) | |||||||
\(384\) | −593.628 | + | 299.956i | −0.0788892 | + | 0.0398622i | ||||
\(385\) | − | 2516.78i | − | 0.333161i | ||||||
\(386\) | 7423.60i | 0.978889i | ||||||||
\(387\) | 7944.29 | + | 5853.98i | 1.04349 | + | 0.768926i | ||||
\(388\) | − | 2214.09i | − | 0.289700i | ||||||
\(389\) | −8342.65 | −1.08738 | −0.543688 | − | 0.839288i | \(-0.682972\pi\) | ||||
−0.543688 | + | 0.839288i | \(0.682972\pi\) | |||||||
\(390\) | −5780.51 | + | 2920.85i | −0.750532 | + | 0.379239i | ||||
\(391\) | 11381.4 | − | 5403.29i | 1.47208 | − | 0.698864i | ||||
\(392\) | − | 1064.17i | − | 0.137114i | ||||||
\(393\) | 4612.10 | − | 2330.46i | 0.591984 | − | 0.299125i | ||||
\(394\) | 7101.97 | 0.908102 | ||||||||
\(395\) | − | 856.110i | − | 0.109052i | ||||||
\(396\) | −679.024 | + | 921.487i | −0.0861672 | + | 0.116936i | ||||
\(397\) | 12254.3 | 1.54918 | 0.774591 | − | 0.632462i | \(-0.217956\pi\) | ||||
0.774591 | + | 0.632462i | \(0.217956\pi\) | |||||||
\(398\) | −1002.82 | −0.126299 | ||||||||
\(399\) | −5800.17 | − | 11478.8i | −0.727749 | − | 1.44025i | ||||
\(400\) | −104.646 | −0.0130807 | ||||||||
\(401\) | −5605.08 | −0.698016 | −0.349008 | − | 0.937120i | \(-0.613481\pi\) | ||||
−0.349008 | + | 0.937120i | \(0.613481\pi\) | |||||||
\(402\) | 3148.09 | + | 6230.23i | 0.390579 | + | 0.772975i | ||||
\(403\) | −16564.5 | −2.04749 | ||||||||
\(404\) | 2477.42i | 0.305089i | ||||||||
\(405\) | −2350.04 | − | 7578.36i | −0.288332 | − | 0.929807i | ||||
\(406\) | 5502.33i | 0.672601i | ||||||||
\(407\) | 897.859i | 0.109349i | ||||||||
\(408\) | −4237.74 | + | 2141.30i | −0.514215 | + | 0.259829i | ||||
\(409\) | −5378.51 | −0.650245 | −0.325123 | − | 0.945672i | \(-0.605406\pi\) | ||||
−0.325123 | + | 0.945672i | \(0.605406\pi\) | |||||||
\(410\) | −6520.57 | −0.785434 | ||||||||
\(411\) | −3098.74 | − | 6132.55i | −0.371896 | − | 0.736001i | ||||
\(412\) | 4930.97i | 0.589639i | ||||||||
\(413\) | 6639.29 | 0.791037 | ||||||||
\(414\) | 5847.19 | + | 1135.50i | 0.694139 | + | 0.134799i | ||||
\(415\) | 5517.45 | 0.652629 | ||||||||
\(416\) | 1832.30i | 0.215952i | ||||||||
\(417\) | 1505.22 | + | 2978.90i | 0.176765 | + | 0.349826i | ||||
\(418\) | −2404.68 | −0.281380 | ||||||||
\(419\) | −8349.36 | −0.973491 | −0.486746 | − | 0.873544i | \(-0.661816\pi\) | ||||
−0.486746 | + | 0.873544i | \(0.661816\pi\) | |||||||
\(420\) | 4405.17 | − | 2225.90i | 0.511787 | − | 0.258602i | ||||
\(421\) | − | 9197.86i | − | 1.06479i | −0.846496 | − | 0.532395i | \(-0.821292\pi\) | ||
0.846496 | − | 0.532395i | \(-0.178708\pi\) | |||||||
\(422\) | 11971.9i | 1.38101i | ||||||||
\(423\) | −5531.95 | − | 4076.37i | −0.635869 | − | 0.468558i | ||||
\(424\) | − | 3736.68i | − | 0.427993i | ||||||
\(425\) | −747.035 | −0.0852624 | ||||||||
\(426\) | −1661.84 | − | 3288.87i | −0.189006 | − | 0.374052i | ||||
\(427\) | 15227.1 | 1.72574 | ||||||||
\(428\) | −3994.34 | −0.451107 | ||||||||
\(429\) | 1422.14 | + | 2814.48i | 0.160050 | + | 0.316747i | ||||
\(430\) | −7955.88 | −0.892248 | ||||||||
\(431\) | −14207.2 | −1.58779 | −0.793896 | − | 0.608053i | \(-0.791951\pi\) | ||||
−0.793896 | + | 0.608053i | \(0.791951\pi\) | |||||||
\(432\) | −2213.44 | − | 373.523i | −0.246515 | − | 0.0415999i | ||||
\(433\) | − | 3114.44i | − | 0.345659i | −0.984952 | − | 0.172829i | \(-0.944709\pi\) | ||
0.984952 | − | 0.172829i | \(-0.0552910\pi\) | |||||||
\(434\) | 12623.4 | 1.39618 | ||||||||
\(435\) | −6364.92 | + | 3216.15i | −0.701551 | + | 0.354489i | ||||
\(436\) | − | 4170.25i | − | 0.458070i | ||||||
\(437\) | 5366.58 | + | 11304.1i | 0.587456 | + | 1.23741i | ||||
\(438\) | −2981.18 | + | 1506.37i | −0.325220 | + | 0.164331i | ||||
\(439\) | −8269.58 | −0.899055 | −0.449528 | − | 0.893266i | \(-0.648408\pi\) | ||||
−0.449528 | + | 0.893266i | \(0.648408\pi\) | |||||||
\(440\) | − | 922.831i | − | 0.0999869i | ||||||
\(441\) | 2130.59 | − | 2891.37i | 0.230060 | − | 0.312209i | ||||
\(442\) | 13080.3i | 1.40761i | ||||||||
\(443\) | 5073.97i | 0.544179i | 0.962272 | + | 0.272090i | \(0.0877147\pi\) | ||||
−0.962272 | + | 0.272090i | \(0.912285\pi\) | |||||||
\(444\) | −1571.54 | + | 794.088i | −0.167977 | + | 0.0848778i | ||||
\(445\) | 12216.5 | 1.30139 | ||||||||
\(446\) | − | 6720.09i | − | 0.713466i | ||||||
\(447\) | 163.142 | + | 322.866i | 0.0172625 | + | 0.0341634i | ||||
\(448\) | − | 1396.35i | − | 0.147257i | ||||||
\(449\) | 3625.22i | 0.381035i | 0.981684 | + | 0.190518i | \(0.0610166\pi\) | ||||
−0.981684 | + | 0.190518i | \(0.938983\pi\) | |||||||
\(450\) | −284.324 | − | 209.512i | −0.0297848 | − | 0.0219477i | ||||
\(451\) | 3174.81i | 0.331476i | ||||||||
\(452\) | −6880.89 | −0.716039 | ||||||||
\(453\) | 4310.81 | + | 8531.32i | 0.447108 | + | 0.884848i | ||||
\(454\) | 1729.74i | 0.178812i | ||||||||
\(455\) | − | 13597.1i | − | 1.40097i | ||||||
\(456\) | −2126.76 | − | 4208.96i | −0.218409 | − | 0.432242i | ||||
\(457\) | − | 2136.11i | − | 0.218650i | −0.994006 | − | 0.109325i | \(-0.965131\pi\) | ||
0.994006 | − | 0.109325i | \(-0.0348689\pi\) | |||||||
\(458\) | 1288.28 | 0.131436 | ||||||||
\(459\) | −15801.1 | − | 2666.48i | −1.60683 | − | 0.271156i | ||||
\(460\) | −4338.11 | + | 2059.51i | −0.439708 | + | 0.208750i | ||||
\(461\) | − | 16072.6i | − | 1.62381i | −0.583789 | − | 0.811905i | \(-0.698430\pi\) | ||
0.583789 | − | 0.811905i | \(-0.301570\pi\) | |||||||
\(462\) | −1083.77 | − | 2144.84i | −0.109138 | − | 0.215989i | ||||
\(463\) | 5419.34 | 0.543970 | 0.271985 | − | 0.962302i | \(-0.412320\pi\) | ||||
0.271985 | + | 0.962302i | \(0.412320\pi\) | |||||||
\(464\) | 2017.55i | 0.201858i | ||||||||
\(465\) | 7378.45 | + | 14602.3i | 0.735844 | + | 1.45627i | ||||
\(466\) | 10628.9 | 1.05659 | ||||||||
\(467\) | 11598.4 | 1.14927 | 0.574635 | − | 0.818410i | \(-0.305144\pi\) | ||||
0.574635 | + | 0.818410i | \(0.305144\pi\) | |||||||
\(468\) | −3668.47 | + | 4978.39i | −0.362340 | + | 0.491723i | ||||
\(469\) | −14654.9 | −1.44286 | ||||||||
\(470\) | 5540.02 | 0.543707 | ||||||||
\(471\) | −3182.00 | + | 1607.84i | −0.311293 | + | 0.157294i | ||||
\(472\) | 2434.44 | 0.237403 | ||||||||
\(473\) | 3873.65i | 0.376555i | ||||||||
\(474\) | −368.657 | − | 729.590i | −0.0357235 | − | 0.0706986i | ||||
\(475\) | − | 741.960i | − | 0.0716705i | ||||||
\(476\) | − | 9968.12i | − | 0.959849i | ||||||
\(477\) | 7481.24 | − | 10152.6i | 0.718118 | − | 0.974541i | ||||
\(478\) | −7036.51 | −0.673310 | ||||||||
\(479\) | 5374.35 | 0.512652 | 0.256326 | − | 0.966590i | \(-0.417488\pi\) | ||||
0.256326 | + | 0.966590i | \(0.417488\pi\) | |||||||
\(480\) | 1615.25 | − | 816.175i | 0.153595 | − | 0.0776106i | ||||
\(481\) | 4850.74i | 0.459822i | ||||||||
\(482\) | 9485.27 | 0.896353 | ||||||||
\(483\) | −7663.93 | + | 9881.37i | −0.721990 | + | 0.930886i | ||||
\(484\) | 4874.68 | 0.457803 | ||||||||
\(485\) | 6024.50i | 0.564038i | ||||||||
\(486\) | −5266.13 | − | 5446.42i | −0.491515 | − | 0.508343i | ||||
\(487\) | −6983.42 | −0.649792 | −0.324896 | − | 0.945750i | \(-0.605329\pi\) | ||||
−0.324896 | + | 0.945750i | \(0.605329\pi\) | |||||||
\(488\) | 5583.34 | 0.517922 | ||||||||
\(489\) | 5994.80 | + | 11864.0i | 0.554385 | + | 1.09716i | ||||
\(490\) | 2895.59i | 0.266958i | ||||||||
\(491\) | 8559.41i | 0.786723i | 0.919384 | + | 0.393361i | \(0.128688\pi\) | ||||
−0.919384 | + | 0.393361i | \(0.871312\pi\) | |||||||
\(492\) | −5556.93 | + | 2807.88i | −0.509198 | + | 0.257294i | ||||
\(493\) | 14402.7i | 1.31575i | ||||||||
\(494\) | −12991.4 | −1.18322 | ||||||||
\(495\) | 1847.61 | − | 2507.35i | 0.167765 | − | 0.227670i | ||||
\(496\) | 4628.63 | 0.419015 | ||||||||
\(497\) | 7736.15 | 0.698217 | ||||||||
\(498\) | 4702.06 | − | 2375.92i | 0.423101 | − | 0.213790i | ||||
\(499\) | −18995.8 | −1.70415 | −0.852073 | − | 0.523423i | \(-0.824655\pi\) | ||||
−0.852073 | + | 0.523423i | \(0.824655\pi\) | |||||||
\(500\) | 5726.70 | 0.512211 | ||||||||
\(501\) | 3349.12 | − | 1692.29i | 0.298658 | − | 0.150910i | ||||
\(502\) | 1860.51i | 0.165416i | ||||||||
\(503\) | −11330.9 | −1.00441 | −0.502206 | − | 0.864748i | \(-0.667478\pi\) | ||||
−0.502206 | + | 0.864748i | \(0.667478\pi\) | |||||||
\(504\) | 2795.64 | − | 3793.90i | 0.247079 | − | 0.335305i | ||||
\(505\) | − | 6741.00i | − | 0.594001i | ||||||
\(506\) | 1002.75 | + | 2112.19i | 0.0880986 | + | 0.185570i | ||||
\(507\) | 2534.72 | + | 5016.33i | 0.222033 | + | 0.439414i | ||||
\(508\) | 1669.75 | 0.145833 | ||||||||
\(509\) | − | 8569.51i | − | 0.746242i | −0.927783 | − | 0.373121i | \(-0.878288\pi\) | ||
0.927783 | − | 0.373121i | \(-0.121712\pi\) | |||||||
\(510\) | 11530.8 | − | 5826.44i | 1.00116 | − | 0.505881i | ||||
\(511\) | − | 7012.40i | − | 0.607066i | ||||||
\(512\) | − | 512.000i | − | 0.0441942i | ||||||
\(513\) | 2648.36 | − | 15693.8i | 0.227930 | − | 1.35068i | ||||
\(514\) | 2798.22 | 0.240125 | ||||||||
\(515\) | − | 13417.1i | − | 1.14801i | ||||||
\(516\) | −6780.12 | + | 3425.95i | −0.578446 | + | 0.292285i | ||||
\(517\) | − | 2697.39i | − | 0.229460i | ||||||
\(518\) | − | 3696.61i | − | 0.313552i | ||||||
\(519\) | 12392.2 | − | 6261.70i | 1.04809 | − | 0.529592i | ||||
\(520\) | − | 4985.65i | − | 0.420452i | ||||||
\(521\) | 4048.12 | 0.340405 | 0.170203 | − | 0.985409i | \(-0.445558\pi\) | ||||
0.170203 | + | 0.985409i | \(0.445558\pi\) | |||||||
\(522\) | −4039.35 | + | 5481.71i | −0.338693 | + | 0.459632i | ||||
\(523\) | 23230.1i | 1.94222i | 0.238631 | + | 0.971110i | \(0.423301\pi\) | ||||
−0.238631 | + | 0.971110i | \(0.576699\pi\) | |||||||
\(524\) | 3977.90i | 0.331633i | ||||||||
\(525\) | 661.787 | − | 334.397i | 0.0550148 | − | 0.0277986i | ||||
\(526\) | − | 9709.19i | − | 0.804831i | ||||||
\(527\) | 33042.5 | 2.73122 | ||||||||
\(528\) | −397.388 | − | 786.451i | −0.0327540 | − | 0.0648217i | ||||
\(529\) | 7691.25 | − | 9427.65i | 0.632140 | − | 0.774854i | ||||
\(530\) | 10167.4i | 0.833292i | ||||||||
\(531\) | 6614.40 | + | 4874.01i | 0.540566 | + | 0.398331i | ||||
\(532\) | 9900.41 | 0.806837 | ||||||||
\(533\) | 17152.1i | 1.39388i | ||||||||
\(534\) | 10411.1 | − | 5260.65i | 0.843693 | − | 0.426312i | ||||
\(535\) | 10868.5 | 0.878294 | ||||||||
\(536\) | −5373.53 | −0.433025 | ||||||||
\(537\) | −7130.28 | + | 3602.88i | −0.572988 | + | 0.289527i | ||||
\(538\) | −9981.93 | −0.799910 | ||||||||
\(539\) | 1409.84 | 0.112664 | ||||||||
\(540\) | 6022.73 | + | 1016.35i | 0.479958 | + | 0.0809938i | ||||
\(541\) | −24127.3 | −1.91740 | −0.958699 | − | 0.284423i | \(-0.908198\pi\) | ||||
−0.958699 | + | 0.284423i | \(0.908198\pi\) | |||||||
\(542\) | 11947.3i | 0.946831i | ||||||||
\(543\) | −11504.4 | + | 5813.08i | −0.909208 | + | 0.459417i | ||||
\(544\) | − | 3655.02i | − | 0.288066i | ||||||
\(545\) | 11347.2i | 0.891851i | ||||||||
\(546\) | −5855.15 | − | 11587.6i | −0.458932 | − | 0.908250i | ||||
\(547\) | −13147.0 | −1.02765 | −0.513825 | − | 0.857895i | \(-0.671772\pi\) | ||||
−0.513825 | + | 0.857895i | \(0.671772\pi\) | |||||||
\(548\) | 5289.28 | 0.412312 | ||||||||
\(549\) | 15170.0 | + | 11178.5i | 1.17931 | + | 0.869008i | ||||
\(550\) | − | 138.637i | − | 0.0107482i | ||||||
\(551\) | −14304.9 | −1.10600 | ||||||||
\(552\) | −2810.14 | + | 3623.21i | −0.216681 | + | 0.279374i | ||||
\(553\) | 1716.16 | 0.131968 | ||||||||
\(554\) | − | 5519.72i | − | 0.423304i | ||||||
\(555\) | 4276.13 | − | 2160.70i | 0.327048 | − | 0.165255i | ||||
\(556\) | −2569.28 | −0.195974 | ||||||||
\(557\) | 17149.8 | 1.30460 | 0.652299 | − | 0.757962i | \(-0.273805\pi\) | ||||
0.652299 | + | 0.757962i | \(0.273805\pi\) | |||||||
\(558\) | 12576.1 | + | 9267.02i | 0.954098 | + | 0.703054i | ||||
\(559\) | 20927.6i | 1.58344i | ||||||||
\(560\) | 3799.43i | 0.286706i | ||||||||
\(561\) | −2836.84 | − | 5614.25i | −0.213496 | − | 0.422520i | ||||
\(562\) | 1805.53i | 0.135519i | ||||||||
\(563\) | −11494.3 | −0.860439 | −0.430220 | − | 0.902724i | \(-0.641564\pi\) | ||||
−0.430220 | + | 0.902724i | \(0.641564\pi\) | |||||||
\(564\) | 4721.29 | − | 2385.63i | 0.352486 | − | 0.178109i | ||||
\(565\) | 18722.7 | 1.39411 | ||||||||
\(566\) | 14336.8 | 1.06470 | ||||||||
\(567\) | 15191.6 | − | 4710.90i | 1.12520 | − | 0.348923i | ||||
\(568\) | 2836.62 | 0.209546 | ||||||||
\(569\) | −17741.2 | −1.30712 | −0.653559 | − | 0.756876i | \(-0.726725\pi\) | ||||
−0.653559 | + | 0.756876i | \(0.726725\pi\) | |||||||
\(570\) | 5786.86 | + | 11452.5i | 0.425237 | + | 0.841565i | ||||
\(571\) | 4401.50i | 0.322587i | 0.986906 | + | 0.161293i | \(0.0515665\pi\) | ||||
−0.986906 | + | 0.161293i | \(0.948433\pi\) | |||||||
\(572\) | −2427.47 | −0.177443 | ||||||||
\(573\) | 5351.60 | + | 10591.1i | 0.390168 | + | 0.772162i | ||||
\(574\) | − | 13071.1i | − | 0.950486i | ||||||
\(575\) | −651.713 | + | 309.399i | −0.0472666 | + | 0.0224397i | ||||
\(576\) | 1025.08 | − | 1391.11i | 0.0741522 | − | 0.100630i | ||||
\(577\) | −19288.4 | −1.39165 | −0.695827 | − | 0.718209i | \(-0.744962\pi\) | ||||
−0.695827 | + | 0.718209i | \(0.744962\pi\) | |||||||
\(578\) | − | 16266.2i | − | 1.17056i | ||||||
\(579\) | −8698.25 | − | 17214.3i | −0.624330 | − | 1.23558i | ||||
\(580\) | − | 5489.70i | − | 0.393013i | ||||||
\(581\) | 11060.3i | 0.789773i | ||||||||
\(582\) | 2594.26 | + | 5134.17i | 0.184769 | + | 0.365667i | ||||
\(583\) | 4950.43 | 0.351674 | ||||||||
\(584\) | − | 2571.25i | − | 0.182190i | ||||||
\(585\) | 9981.82 | − | 13546.1i | 0.705466 | − | 0.957371i | ||||
\(586\) | − | 1203.90i | − | 0.0848682i | ||||||
\(587\) | 15199.2i | 1.06872i | 0.845258 | + | 0.534359i | \(0.179447\pi\) | ||||
−0.845258 | + | 0.534359i | \(0.820553\pi\) | |||||||
\(588\) | 1246.89 | + | 2467.66i | 0.0874507 | + | 0.173069i | ||||
\(589\) | 32818.0i | 2.29583i | ||||||||
\(590\) | −6624.05 | −0.462217 | ||||||||
\(591\) | −16468.5 | + | 8321.41i | −1.14623 | + | 0.579183i | ||||
\(592\) | − | 1355.44i | − | 0.0941019i | ||||||
\(593\) | − | 28258.0i | − | 1.95686i | −0.206582 | − | 0.978429i | \(-0.566234\pi\) | ||
0.206582 | − | 0.978429i | \(-0.433766\pi\) | |||||||
\(594\) | 494.851 | − | 2932.41i | 0.0341818 | − | 0.202556i | ||||
\(595\) | 27123.1i | 1.86880i | ||||||||
\(596\) | −278.470 | −0.0191385 | ||||||||
\(597\) | 2325.41 | − | 1175.01i | 0.159418 | − | 0.0805529i | ||||
\(598\) | 5417.45 | + | 11411.2i | 0.370461 | + | 0.780334i | ||||
\(599\) | − | 12584.5i | − | 0.858413i | −0.903206 | − | 0.429207i | \(-0.858793\pi\) | ||
0.903206 | − | 0.429207i | \(-0.141207\pi\) | |||||||
\(600\) | 242.658 | − | 122.614i | 0.0165108 | − | 0.00834280i | ||||
\(601\) | 11623.5 | 0.788907 | 0.394453 | − | 0.918916i | \(-0.370934\pi\) | ||||
0.394453 | + | 0.918916i | \(0.370934\pi\) | |||||||
\(602\) | − | 15948.4i | − | 1.07975i | ||||||
\(603\) | −14600.0 | − | 10758.4i | −0.985998 | − | 0.726561i | ||||
\(604\) | −7358.20 | −0.495697 | ||||||||
\(605\) | −13263.9 | −0.891330 | ||||||||
\(606\) | −2902.80 | − | 5744.78i | −0.194584 | − | 0.385092i | ||||
\(607\) | −356.633 | −0.0238473 | −0.0119236 | − | 0.999929i | \(-0.503796\pi\) | ||||
−0.0119236 | + | 0.999929i | \(0.503796\pi\) | |||||||
\(608\) | 3630.20 | 0.242145 | ||||||||
\(609\) | −6447.10 | − | 12759.1i | −0.428982 | − | 0.848976i | ||||
\(610\) | −15192.2 | −1.00838 | ||||||||
\(611\) | − | 14572.8i | − | 0.964897i | ||||||
\(612\) | 7317.76 | − | 9930.76i | 0.483338 | − | 0.655927i | ||||
\(613\) | 27137.1i | 1.78802i | 0.448047 | + | 0.894010i | \(0.352120\pi\) | ||||
−0.448047 | + | 0.894010i | \(0.647880\pi\) | |||||||
\(614\) | 18190.5i | 1.19562i | ||||||||
\(615\) | 15120.3 | − | 7640.17i | 0.991396 | − | 0.500946i | ||||
\(616\) | 1849.91 | 0.120998 | ||||||||
\(617\) | 4164.50 | 0.271728 | 0.135864 | − | 0.990727i | \(-0.456619\pi\) | ||||
0.135864 | + | 0.990727i | \(0.456619\pi\) | |||||||
\(618\) | −5777.63 | − | 11434.2i | −0.376069 | − | 0.744258i | ||||
\(619\) | − | 15299.4i | − | 0.993434i | −0.867913 | − | 0.496717i | \(-0.834539\pi\) | ||
0.867913 | − | 0.496717i | \(-0.165461\pi\) | |||||||
\(620\) | −12594.4 | −0.815811 | ||||||||
\(621\) | −14889.3 | + | 4218.11i | −0.962135 | + | 0.272572i | ||||
\(622\) | −4170.32 | −0.268834 | ||||||||
\(623\) | 24489.2i | 1.57486i | ||||||||
\(624\) | −2146.91 | − | 4248.85i | −0.137733 | − | 0.272580i | ||||
\(625\) | −14764.7 | −0.944940 | ||||||||
\(626\) | −15061.5 | −0.961627 | ||||||||
\(627\) | 5576.11 | − | 2817.57i | 0.355165 | − | 0.179462i | ||||
\(628\) | − | 2744.45i | − | 0.174388i | ||||||
\(629\) | − | 9676.12i | − | 0.613374i | ||||||
\(630\) | −7606.88 | + | 10323.1i | −0.481056 | + | 0.652830i | ||||
\(631\) | − | 19697.8i | − | 1.24272i | −0.783524 | − | 0.621361i | \(-0.786580\pi\) | ||
0.783524 | − | 0.621361i | \(-0.213420\pi\) | |||||||
\(632\) | 629.266 | 0.0396058 | ||||||||
\(633\) | −14027.6 | − | 27761.3i | −0.880799 | − | 1.74315i | ||||
\(634\) | −11644.7 | −0.729447 | ||||||||
\(635\) | −4543.34 | −0.283932 | ||||||||
\(636\) | 4378.28 | + | 8664.83i | 0.272972 | + | 0.540225i | ||||
\(637\) | 7616.72 | 0.473761 | ||||||||
\(638\) | −2672.89 | −0.165863 | ||||||||
\(639\) | 7707.15 | + | 5679.23i | 0.477136 | + | 0.351591i | ||||
\(640\) | 1393.14i | 0.0860449i | ||||||||
\(641\) | −16305.2 | −1.00471 | −0.502353 | − | 0.864663i | \(-0.667532\pi\) | ||||
−0.502353 | + | 0.864663i | \(0.667532\pi\) | |||||||
\(642\) | 9262.32 | − | 4680.19i | 0.569400 | − | 0.287714i | ||||
\(643\) | 27798.7i | 1.70494i | 0.522777 | + | 0.852469i | \(0.324896\pi\) | ||||
−0.522777 | + | 0.852469i | \(0.675104\pi\) | |||||||
\(644\) | −4128.49 | − | 8696.18i | −0.252617 | − | 0.532108i | ||||
\(645\) | 18448.6 | − | 9321.93i | 1.12622 | − | 0.569071i | ||||
\(646\) | 25914.9 | 1.57834 | ||||||||
\(647\) | 27022.7i | 1.64200i | 0.570929 | + | 0.820999i | \(0.306583\pi\) | ||||
−0.570929 | + | 0.820999i | \(0.693417\pi\) | |||||||
\(648\) | 5570.32 | − | 1727.35i | 0.337690 | − | 0.104717i | ||||
\(649\) | 3225.19i | 0.195069i | ||||||||
\(650\) | − | 748.992i | − | 0.0451968i | ||||||
\(651\) | −29271.8 | + | 14790.8i | −1.76229 | + | 0.890475i | ||||
\(652\) | −10232.6 | −0.614633 | ||||||||
\(653\) | − | 10675.4i | − | 0.639757i | −0.947459 | − | 0.319878i | \(-0.896358\pi\) | ||
0.947459 | − | 0.319878i | \(-0.103642\pi\) | |||||||
\(654\) | 4886.29 | + | 9670.21i | 0.292155 | + | 0.578188i | ||||
\(655\) | − | 10823.8i | − | 0.645680i | ||||||
\(656\) | − | 4792.81i | − | 0.285256i | ||||||
\(657\) | 5147.92 | − | 6986.12i | 0.305692 | − | 0.414847i | ||||
\(658\) | 11105.5i | 0.657961i | ||||||||
\(659\) | −11027.6 | −0.651856 | −0.325928 | − | 0.945395i | \(-0.605677\pi\) | ||||
−0.325928 | + | 0.945395i | \(0.605677\pi\) | |||||||
\(660\) | 1081.28 | + | 2139.92i | 0.0637711 | + | 0.126206i | ||||
\(661\) | − | 32451.1i | − | 1.90953i | −0.297361 | − | 0.954765i | \(-0.596106\pi\) | ||
0.297361 | − | 0.954765i | \(-0.403894\pi\) | |||||||
\(662\) | − | 18041.1i | − | 1.05920i | ||||||
\(663\) | −15326.2 | − | 30331.3i | −0.897769 | − | 1.77673i | ||||
\(664\) | 4055.49i | 0.237023i | ||||||||
\(665\) | −26938.8 | −1.57089 | ||||||||
\(666\) | 2713.74 | − | 3682.76i | 0.157891 | − | 0.214270i | ||||
\(667\) | 5965.15 | + | 12564.9i | 0.346284 | + | 0.729408i | ||||
\(668\) | 2888.59i | 0.167310i | ||||||||
\(669\) | 7873.96 | + | 15583.0i | 0.455045 | + | 0.900556i | ||||
\(670\) | 14621.3 | 0.843088 | ||||||||
\(671\) | 7396.93i | 0.425567i | ||||||||
\(672\) | 1636.10 | + | 3237.93i | 0.0939198 | + | 0.185872i | ||||
\(673\) | −11825.2 | −0.677306 | −0.338653 | − | 0.940911i | \(-0.609971\pi\) | ||||
−0.338653 | + | 0.940911i | \(0.609971\pi\) | |||||||
\(674\) | −14913.2 | −0.852275 | ||||||||
\(675\) | 904.793 | + | 152.686i | 0.0515933 | + | 0.00870648i | ||||
\(676\) | −4326.55 | −0.246162 | ||||||||
\(677\) | −20118.7 | −1.14213 | −0.571066 | − | 0.820904i | \(-0.693470\pi\) | ||||
−0.571066 | + | 0.820904i | \(0.693470\pi\) | |||||||
\(678\) | 15955.8 | − | 8062.36i | 0.903804 | − | 0.456686i | ||||
\(679\) | −12076.7 | −0.682565 | ||||||||
\(680\) | 9945.24i | 0.560857i | ||||||||
\(681\) | −2026.74 | − | 4011.01i | −0.114045 | − | 0.225701i | ||||
\(682\) | 6132.10i | 0.344296i | ||||||||
\(683\) | − | 21040.7i | − | 1.17877i | −0.807852 | − | 0.589386i | \(-0.799370\pi\) | ||
0.807852 | − | 0.589386i | \(-0.200630\pi\) | |||||||
\(684\) | 9863.30 | + | 7268.05i | 0.551364 | + | 0.406288i | ||||
\(685\) | −14392.0 | −0.802761 | ||||||||
\(686\) | 9162.59 | 0.509955 | ||||||||
\(687\) | −2987.35 | + | 1509.49i | −0.165902 | + | 0.0838289i | ||||
\(688\) | − | 5847.81i | − | 0.324049i | ||||||
\(689\) | 26745.0 | 1.47881 | ||||||||
\(690\) | 7646.34 | − | 9858.69i | 0.421871 | − | 0.543933i | ||||
\(691\) | 18617.3 | 1.02495 | 0.512473 | − | 0.858703i | \(-0.328730\pi\) | ||||
0.512473 | + | 0.858703i | \(0.328730\pi\) | |||||||
\(692\) | 10688.2i | 0.587145i | ||||||||
\(693\) | 5026.23 | + | 3703.72i | 0.275513 | + | 0.203020i | ||||
\(694\) | 9055.52 | 0.495307 | ||||||||
\(695\) | 6990.96 | 0.381557 | ||||||||
\(696\) | −2363.97 | − | 4678.41i | −0.128744 | − | 0.254791i | ||||
\(697\) | − | 34214.5i | − | 1.85935i | ||||||
\(698\) | − | 2229.77i | − | 0.120914i | ||||||
\(699\) | −24646.8 | + | 12453.9i | −1.33366 | + | 0.673889i | ||||
\(700\) | 570.787i | 0.0308196i | ||||||||
\(701\) | 9866.96 | 0.531626 | 0.265813 | − | 0.964025i | \(-0.414360\pi\) | ||||
0.265813 | + | 0.964025i | \(0.414360\pi\) | |||||||
\(702\) | 2673.46 | − | 15842.5i | 0.143737 | − | 0.851764i | ||||
\(703\) | 9610.39 | 0.515594 | ||||||||
\(704\) | 678.308 | 0.0363135 | ||||||||
\(705\) | −12846.5 | + | 6491.26i | −0.686281 | + | 0.346773i | ||||
\(706\) | −1635.19 | −0.0871690 | ||||||||
\(707\) | 13513.0 | 0.718825 | ||||||||
\(708\) | −5645.12 | + | 2852.44i | −0.299656 | + | 0.151414i | ||||
\(709\) | 33.7969i | 0.00179022i | 1.00000 | 0.000895112i | \(0.000284923\pi\) | |||||
−1.00000 | 0.000895112i | \(0.999715\pi\) | ||||||||
\(710\) | −7718.39 | −0.407980 | ||||||||
\(711\) | 1709.73 | + | 1259.86i | 0.0901824 | + | 0.0664535i | ||||
\(712\) | 8979.49i | 0.472641i | ||||||||
\(713\) | 28826.2 | − | 13685.2i | 1.51410 | − | 0.718812i | ||||
\(714\) | 11679.7 | + | 23114.7i | 0.612187 | + | 1.21155i | ||||
\(715\) | 6605.09 | 0.345478 | ||||||||
\(716\) | − | 6149.82i | − | 0.320991i | ||||||
\(717\) | 16316.7 | − | 8244.70i | 0.849871 | − | 0.429434i | ||||
\(718\) | − | 10897.4i | − | 0.566419i | ||||||
\(719\) | 899.131i | 0.0466369i | 0.999728 | + | 0.0233184i | \(0.00742316\pi\) | ||||
−0.999728 | + | 0.0233184i | \(0.992577\pi\) | |||||||
\(720\) | −2789.22 | + | 3785.19i | −0.144372 | + | 0.195925i | ||||
\(721\) | 26895.8 | 1.38926 | ||||||||
\(722\) | 12020.9i | 0.619628i | ||||||||
\(723\) | −21995.0 | + | 11113.9i | −1.13140 | + | 0.571689i | ||||
\(724\) | − | 9922.44i | − | 0.509344i | ||||||
\(725\) | − | 824.716i | − | 0.0422471i | ||||||
\(726\) | −11303.7 | + | 5711.68i | −0.577851 | + | 0.291984i | ||||
\(727\) | − | 21188.1i | − | 1.08091i | −0.841372 | − | 0.540456i | \(-0.818252\pi\) | ||
0.841372 | − | 0.540456i | \(-0.181748\pi\) | |||||||
\(728\) | 9994.24 | 0.508807 | ||||||||
\(729\) | 18593.0 | + | 6459.15i | 0.944622 | + | 0.328159i | ||||
\(730\) | 6996.31i | 0.354719i | ||||||||
\(731\) | − | 41745.8i | − | 2.11221i | ||||||
\(732\) | −12947.0 | + | 6542.03i | −0.653736 | + | 0.330328i | ||||
\(733\) | − | 22353.8i | − | 1.12641i | −0.826318 | − | 0.563204i | \(-0.809569\pi\) | ||
0.826318 | − | 0.563204i | \(-0.190431\pi\) | |||||||
\(734\) | 336.553 | 0.0169242 | ||||||||
\(735\) | −3392.77 | − | 6714.46i | −0.170264 | − | 0.336961i | ||||
\(736\) | −1513.80 | − | 3188.64i | −0.0758143 | − | 0.159694i | ||||
\(737\) | − | 7118.97i | − | 0.355808i | ||||||
\(738\) | 9595.73 | − | 13022.1i | 0.478623 | − | 0.649528i | ||||
\(739\) | 923.698 | 0.0459794 | 0.0229897 | − | 0.999736i | \(-0.492682\pi\) | ||||
0.0229897 | + | 0.999736i | \(0.492682\pi\) | |||||||
\(740\) | 3688.13i | 0.183214i | ||||||||
\(741\) | 30125.3 | − | 15222.1i | 1.49350 | − | 0.754653i | ||||
\(742\) | −20381.6 | −1.00840 | ||||||||
\(743\) | 33416.4 | 1.64997 | 0.824986 | − | 0.565153i | \(-0.191183\pi\) | ||||
0.824986 | + | 0.565153i | \(0.191183\pi\) | |||||||
\(744\) | −10733.1 | + | 5423.38i | −0.528892 | + | 0.267246i | ||||
\(745\) | 757.710 | 0.0372622 | ||||||||
\(746\) | −17053.4 | −0.836954 | ||||||||
\(747\) | −8119.54 | + | 11018.8i | −0.397695 | + | 0.539703i | ||||
\(748\) | 4842.25 | 0.236698 | ||||||||
\(749\) | 21787.1i | 1.06286i | ||||||||
\(750\) | −13279.4 | + | 6709.99i | −0.646527 | + | 0.326686i | ||||
\(751\) | − | 29846.4i | − | 1.45022i | −0.688635 | − | 0.725108i | \(-0.741790\pi\) | ||
0.688635 | − | 0.725108i | \(-0.258210\pi\) | |||||||
\(752\) | 4072.08i | 0.197465i | ||||||||
\(753\) | −2179.97 | − | 4314.27i | −0.105501 | − | 0.208792i | ||||
\(754\) | −14440.4 | −0.697466 | ||||||||
\(755\) | 20021.5 | 0.965109 | ||||||||
\(756\) | −2037.37 | + | 12073.2i | −0.0980140 | + | 0.580816i | ||||
\(757\) | − | 18544.8i | − | 0.890387i | −0.895434 | − | 0.445194i | \(-0.853135\pi\) | ||
0.895434 | − | 0.445194i | \(-0.146865\pi\) | |||||||
\(758\) | 3090.39 | 0.148085 | ||||||||
\(759\) | −4800.11 | − | 3722.94i | −0.229556 | − | 0.178042i | ||||
\(760\) | −9877.69 | −0.471449 | ||||||||
\(761\) | 19671.3i | 0.937035i | 0.883454 | + | 0.468518i | \(0.155212\pi\) | ||||
−0.883454 | + | 0.468518i | \(0.844788\pi\) | |||||||
\(762\) | −3871.90 | + | 1956.45i | −0.184074 | + | 0.0930113i | ||||
\(763\) | −22746.5 | −1.07926 | ||||||||
\(764\) | −9134.74 | −0.432570 | ||||||||
\(765\) | −19911.5 | + | 27021.4i | −0.941047 | + | 1.27707i | ||||
\(766\) | − | 11882.3i | − | 0.560476i | ||||||
\(767\) | 17424.3i | 0.820280i | ||||||||
\(768\) | 599.912 | + | 1187.26i | 0.0281868 | + | 0.0557831i | ||||
\(769\) | − | 5569.11i | − | 0.261154i | −0.991438 | − | 0.130577i | \(-0.958317\pi\) | ||
0.991438 | − | 0.130577i | \(-0.0416829\pi\) | |||||||
\(770\) | −5033.56 | −0.235581 | ||||||||
\(771\) | −6488.68 | + | 3278.69i | −0.303092 | + | 0.153150i | ||||
\(772\) | 14847.2 | 0.692179 | ||||||||
\(773\) | −22579.3 | −1.05061 | −0.525304 | − | 0.850914i | \(-0.676049\pi\) | ||||
−0.525304 | + | 0.850914i | \(0.676049\pi\) | |||||||
\(774\) | 11708.0 | − | 15888.6i | 0.543713 | − | 0.737860i | ||||
\(775\) | −1892.05 | −0.0876961 | ||||||||
\(776\) | −4428.18 | −0.204849 | ||||||||
\(777\) | 4331.34 | + | 8571.93i | 0.199982 | + | 0.395774i | ||||
\(778\) | 16685.3i | 0.768890i | ||||||||
\(779\) | 33982.1 | 1.56295 | ||||||||
\(780\) | 5841.71 | + | 11561.0i | 0.268162 | + | 0.530707i | ||||
\(781\) | 3758.02i | 0.172180i | ||||||||
\(782\) | −10806.6 | − | 22762.8i | −0.494172 | − | 1.04092i | ||||
\(783\) | 2943.75 | − | 17444.2i | 0.134356 | − | 0.796176i | ||||
\(784\) | −2128.34 | −0.0969543 | ||||||||
\(785\) | 7467.60i | 0.339529i | ||||||||
\(786\) | −4660.92 | − | 9224.20i | −0.211513 | − | 0.418596i | ||||
\(787\) | 12325.7i | 0.558279i | 0.960251 | + | 0.279139i | \(0.0900491\pi\) | ||||
−0.960251 | + | 0.279139i | \(0.909951\pi\) | |||||||
\(788\) | − | 14203.9i | − | 0.642125i | ||||||
\(789\) | 11376.3 | + | 22514.3i | 0.513317 | + | 1.01588i | ||||
\(790\) | −1712.22 | −0.0771114 | ||||||||
\(791\) | 37531.6i | 1.68707i | ||||||||
\(792\) | 1842.97 | + | 1358.05i | 0.0826859 | + | 0.0609294i | ||||
\(793\) | 39962.4i | 1.78954i | ||||||||
\(794\) | − | 24508.6i | − | 1.09544i | ||||||
\(795\) | −11913.2 | − | 23576.8i | −0.531469 | − | 1.05180i | ||||
\(796\) | 2005.65i | 0.0893070i | ||||||||
\(797\) | −10368.6 | −0.460820 | −0.230410 | − | 0.973094i | \(-0.574007\pi\) | ||||
−0.230410 | + | 0.973094i | \(0.574007\pi\) | |||||||
\(798\) | −22957.7 | + | 11600.3i | −1.01841 | + | 0.514596i | ||||
\(799\) | 29069.4i | 1.28711i | ||||||||
\(800\) | 209.291i | 0.00924945i | ||||||||
\(801\) | −17977.9 | + | 24397.4i | −0.793033 | + | 1.07621i | ||||
\(802\) | 11210.2i | 0.493572i | ||||||||
\(803\) | 3406.44 | 0.149702 | ||||||||
\(804\) | 12460.5 | − | 6296.19i | 0.546576 | − | 0.276181i | ||||
\(805\) | 11233.5 | + | 23662.1i | 0.491838 | + | 1.03600i | ||||
\(806\) | 33129.0i | 1.44779i | ||||||||
\(807\) | 23146.7 | − | 11695.9i | 1.00967 | − | 0.510179i | ||||
\(808\) | 4954.83 | 0.215731 | ||||||||
\(809\) | 29964.1i | 1.30220i | 0.758991 | + | 0.651102i | \(0.225693\pi\) | ||||
−0.758991 | + | 0.651102i | \(0.774307\pi\) | |||||||
\(810\) | −15156.7 | + | 4700.09i | −0.657473 | + | 0.203882i | ||||
\(811\) | −13277.9 | −0.574906 | −0.287453 | − | 0.957795i | \(-0.592809\pi\) | ||||
−0.287453 | + | 0.957795i | \(0.592809\pi\) | |||||||
\(812\) | 11004.7 | 0.475601 | ||||||||
\(813\) | −13998.7 | − | 27704.2i | −0.603884 | − | 1.19512i | ||||
\(814\) | 1795.72 | 0.0773217 | ||||||||
\(815\) | 27842.8 | 1.19667 | ||||||||
\(816\) | 4282.60 | + | 8475.49i | 0.183727 | + | 0.363605i | ||||
\(817\) | 41462.3 | 1.77550 | ||||||||
\(818\) | 10757.0i | 0.459793i | ||||||||
\(819\) | 27154.5 | + | 20009.6i | 1.15855 | + | 0.853713i | ||||
\(820\) | 13041.1i | 0.555386i | ||||||||
\(821\) | − | 23294.6i | − | 0.990238i | −0.868825 | − | 0.495119i | \(-0.835124\pi\) | ||
0.868825 | − | 0.495119i | \(-0.164876\pi\) | |||||||
\(822\) | −12265.1 | + | 6197.47i | −0.520431 | + | 0.262970i | ||||
\(823\) | 11000.7 | 0.465928 | 0.232964 | − | 0.972485i | \(-0.425158\pi\) | ||||
0.232964 | + | 0.972485i | \(0.425158\pi\) | |||||||
\(824\) | 9861.93 | 0.416938 | ||||||||
\(825\) | 162.441 | + | 321.479i | 0.00685511 | + | 0.0135666i | ||||
\(826\) | − | 13278.6i | − | 0.559347i | ||||||
\(827\) | −259.872 | −0.0109270 | −0.00546350 | − | 0.999985i | \(-0.501739\pi\) | ||||
−0.00546350 | + | 0.999985i | \(0.501739\pi\) | |||||||
\(828\) | 2271.00 | − | 11694.4i | 0.0953171 | − | 0.490831i | ||||
\(829\) | −10639.1 | −0.445732 | −0.222866 | − | 0.974849i | \(-0.571541\pi\) | ||||
−0.222866 | + | 0.974849i | \(0.571541\pi\) | |||||||
\(830\) | − | 11034.9i | − | 0.461479i | ||||||
\(831\) | 6467.47 | + | 12799.5i | 0.269981 | + | 0.534306i | ||||
\(832\) | 3664.60 | 0.152701 | ||||||||
\(833\) | −15193.6 | −0.631966 | ||||||||
\(834\) | 5957.80 | − | 3010.43i | 0.247364 | − | 0.124991i | ||||
\(835\) | − | 7859.80i | − | 0.325748i | ||||||
\(836\) | 4809.36i | 0.198965i | ||||||||
\(837\) | −40020.3 | − | 6753.51i | −1.65269 | − | 0.278895i | ||||
\(838\) | 16698.7i | 0.688362i | ||||||||
\(839\) | 11414.8 | 0.469706 | 0.234853 | − | 0.972031i | \(-0.424539\pi\) | ||||
0.234853 | + | 0.972031i | \(0.424539\pi\) | |||||||
\(840\) | −4451.81 | − | 8810.34i | −0.182859 | − | 0.361888i | ||||
\(841\) | 8488.64 | 0.348052 | ||||||||
\(842\) | −18395.7 | −0.752920 | ||||||||
\(843\) | −2115.54 | − | 4186.76i | −0.0864332 | − | 0.171056i | ||||
\(844\) | 23943.9 | 0.976520 | ||||||||
\(845\) | 11772.5 | 0.479272 | ||||||||
\(846\) | −8152.75 | + | 11063.9i | −0.331321 | + | 0.449627i | ||||
\(847\) | − | 26588.8i | − | 1.07863i | ||||||
\(848\) | −7473.35 | −0.302637 | ||||||||
\(849\) | −33245.1 | + | 16798.5i | −1.34390 | + | 0.679062i | ||||
\(850\) | 1494.07i | 0.0602896i | ||||||||
\(851\) | −4007.55 | − | 8441.44i | −0.161430 | − | 0.340034i | ||||
\(852\) | −6577.73 | + | 3323.68i | −0.264495 | + | 0.133647i | ||||
\(853\) | −15505.0 | −0.622369 | −0.311185 | − | 0.950349i | \(-0.600726\pi\) | ||||
−0.311185 | + | 0.950349i | \(0.600726\pi\) | |||||||
\(854\) | − | 30454.2i | − | 1.22028i | ||||||
\(855\) | −26837.8 | − | 19776.2i | −1.07349 | − | 0.791032i | ||||
\(856\) | 7988.69i | 0.318981i | ||||||||
\(857\) | 12174.6i | 0.485270i | 0.970118 | + | 0.242635i | \(0.0780118\pi\) | ||||
−0.970118 | + | 0.242635i | \(0.921988\pi\) | |||||||
\(858\) | 5628.96 | − | 2844.27i | 0.223974 | − | 0.113172i | ||||
\(859\) | −389.206 | −0.0154593 | −0.00772966 | − | 0.999970i | \(-0.502460\pi\) | ||||
−0.00772966 | + | 0.999970i | \(0.502460\pi\) | |||||||
\(860\) | 15911.8i | 0.630914i | ||||||||
\(861\) | 15315.5 | + | 30310.1i | 0.606215 | + | 1.19973i | ||||
\(862\) | 28414.5i | 1.12274i | ||||||||
\(863\) | 23693.5i | 0.934574i | 0.884106 | + | 0.467287i | \(0.154769\pi\) | ||||
−0.884106 | + | 0.467287i | \(0.845231\pi\) | |||||||
\(864\) | −747.046 | + | 4426.89i | −0.0294155 | + | 0.174312i | ||||
\(865\) | − | 29082.3i | − | 1.14316i | ||||||
\(866\) | −6228.88 | −0.244418 | ||||||||
\(867\) | 19059.1 | + | 37719.0i | 0.746577 | + | 1.47751i | ||||
\(868\) | − | 25246.7i | − | 0.987247i | ||||||
\(869\) | 833.664i | 0.0325433i | ||||||||
\(870\) | 6432.30 | + | 12729.8i | 0.250662 | + | 0.496072i | ||||
\(871\) | − | 38460.6i | − | 1.49620i | ||||||
\(872\) | −8340.49 | −0.323904 | ||||||||
\(873\) | −12031.4 | − | 8865.71i | −0.466441 | − | 0.343710i | ||||
\(874\) | 22608.2 | − | 10733.2i | 0.874980 | − | 0.415394i | ||||
\(875\) | − | 31236.1i | − | 1.20683i | ||||||
\(876\) | 3012.74 | + | 5962.36i | 0.116200 | + | 0.229965i | ||||
\(877\) | −13683.0 | −0.526843 | −0.263422 | − | 0.964681i | \(-0.584851\pi\) | ||||
−0.263422 | + | 0.964681i | \(0.584851\pi\) | |||||||
\(878\) | 16539.2i | 0.635728i | ||||||||
\(879\) | 1410.62 | + | 2791.68i | 0.0541285 | + | 0.107123i | ||||
\(880\) | −1845.66 | −0.0707014 | ||||||||
\(881\) | 36403.5 | 1.39213 | 0.696065 | − | 0.717979i | \(-0.254933\pi\) | ||||
0.696065 | + | 0.717979i | \(0.254933\pi\) | |||||||
\(882\) | −5782.74 | − | 4261.17i | −0.220765 | − | 0.162677i | ||||
\(883\) | 13924.0 | 0.530669 | 0.265335 | − | 0.964156i | \(-0.414518\pi\) | ||||
0.265335 | + | 0.964156i | \(0.414518\pi\) | |||||||
\(884\) | 26160.5 | 0.995333 | ||||||||
\(885\) | 15360.2 | − | 7761.42i | 0.583423 | − | 0.294799i | ||||
\(886\) | 10147.9 | 0.384793 | ||||||||
\(887\) | 3666.91i | 0.138808i | 0.997589 | + | 0.0694041i | \(0.0221098\pi\) | ||||
−0.997589 | + | 0.0694041i | \(0.977890\pi\) | |||||||
\(888\) | 1588.18 | + | 3143.08i | 0.0600177 | + | 0.118778i | ||||
\(889\) | − | 9107.59i | − | 0.343598i | ||||||
\(890\) | − | 24433.0i | − | 0.920221i | ||||||
\(891\) | 2288.43 | + | 7379.68i | 0.0860441 | + | 0.277473i | ||||
\(892\) | −13440.2 | −0.504496 | ||||||||
\(893\) | −28871.9 | −1.08193 | ||||||||
\(894\) | 645.732 | − | 326.284i | 0.0241572 | − | 0.0122064i | ||||
\(895\) | 16733.5i | 0.624961i | ||||||||
\(896\) | −2792.69 | −0.104126 | ||||||||
\(897\) | −25932.9 | − | 20113.4i | −0.965299 | − | 0.748680i | ||||
\(898\) | 7250.44 | 0.269432 | ||||||||
\(899\) | 36478.4i | 1.35331i | ||||||||
\(900\) | −419.024 | + | 568.647i | −0.0155194 | + | 0.0210610i | ||||
\(901\) | −53350.2 | −1.97264 | ||||||||
\(902\) | 6349.61 | 0.234389 | ||||||||
\(903\) | 18686.8 | + | 36982.0i | 0.688656 | + | 1.36288i | ||||
\(904\) | 13761.8i | 0.506316i | ||||||||
\(905\) | 26998.8i | 0.991679i | ||||||||
\(906\) | 17062.6 | − | 8621.63i | 0.625682 | − | 0.316153i | ||||
\(907\) | − | 20915.3i | − | 0.765691i | −0.923812 | − | 0.382845i | \(-0.874944\pi\) | ||
0.923812 | − | 0.382845i | \(-0.125056\pi\) | |||||||
\(908\) | 3459.47 | 0.126439 | ||||||||
\(909\) | 13462.4 | + | 9920.12i | 0.491220 | + | 0.361969i | ||||
\(910\) | −27194.1 | −0.990634 | ||||||||
\(911\) | 18080.6 | 0.657561 | 0.328781 | − | 0.944406i | \(-0.393362\pi\) | ||||
0.328781 | + | 0.944406i | \(0.393362\pi\) | |||||||
\(912\) | −8417.91 | + | 4253.51i | −0.305641 | + | 0.154438i | ||||
\(913\) | −5372.80 | −0.194758 | ||||||||
\(914\) | −4272.22 | −0.154609 | ||||||||
\(915\) | 35228.5 | − | 17800.7i | 1.27281 | − | 0.643140i | ||||
\(916\) | − | 2576.57i | − | 0.0929390i | ||||||
\(917\) | 21697.4 | 0.781364 | ||||||||
\(918\) | −5332.95 | + | 31602.3i | −0.191736 | + | 1.13620i | ||||
\(919\) | − | 21465.5i | − | 0.770491i | −0.922814 | − | 0.385245i | \(-0.874117\pi\) | ||
0.922814 | − | 0.385245i | \(-0.125883\pi\) | |||||||
\(920\) | 4119.01 | + | 8676.22i | 0.147608 | + | 0.310920i | ||||
\(921\) | −21313.9 | − | 42181.2i | −0.762559 | − | 1.50914i | ||||
\(922\) | −32145.2 | −1.14821 | ||||||||
\(923\) | 20302.9i | 0.724029i | ||||||||
\(924\) | −4289.68 | + | 2167.54i | −0.152727 | + | 0.0771721i | ||||
\(925\) | 554.066i | 0.0196947i | ||||||||
\(926\) | − | 10838.7i | − | 0.384645i | ||||||
\(927\) | 26795.0 | + | 19744.7i | 0.949368 | + | 0.699569i | ||||
\(928\) | 4035.09 | 0.142735 | ||||||||
\(929\) | − | 44128.4i | − | 1.55846i | −0.626740 | − | 0.779229i | \(-0.715611\pi\) | ||
0.626740 | − | 0.779229i | \(-0.284389\pi\) | |||||||
\(930\) | 29204.6 | − | 14756.9i | 1.02974 | − | 0.520320i | ||||
\(931\) | − | 15090.4i | − | 0.531223i | ||||||
\(932\) | − | 21257.7i | − | 0.747124i | ||||||
\(933\) | 9670.38 | − | 4886.38i | 0.339329 | − | 0.171461i | ||||
\(934\) | − | 23196.8i | − | 0.812656i | ||||||
\(935\) | −13175.7 | −0.460845 | ||||||||
\(936\) | 9956.78 | + | 7336.94i | 0.347700 | + | 0.256213i | ||||
\(937\) | 27758.5i | 0.967803i | 0.875122 | + | 0.483902i | \(0.160781\pi\) | ||||
−0.875122 | + | 0.483902i | \(0.839219\pi\) | |||||||
\(938\) | 29309.8i | 1.02026i | ||||||||
\(939\) | 34925.5 | − | 17647.6i | 1.21379 | − | 0.613321i | ||||
\(940\) | − | 11080.0i | − | 0.384459i | ||||||
\(941\) | 18461.1 | 0.639549 | 0.319774 | − | 0.947494i | \(-0.396393\pi\) | ||||
0.319774 | + | 0.947494i | \(0.396393\pi\) | |||||||
\(942\) | 3215.69 | + | 6364.00i | 0.111224 | + | 0.220117i | ||||
\(943\) | −14170.6 | − | 29848.7i | −0.489351 | − | 1.03076i | ||||
\(944\) | − | 4868.87i | − | 0.167869i | ||||||
\(945\) | 5543.65 | − | 32850.9i | 0.190831 | − | 1.13083i | ||||
\(946\) | 7747.29 | 0.266264 | ||||||||
\(947\) | 3695.82i | 0.126819i | 0.997988 | + | 0.0634097i | \(0.0201975\pi\) | ||||
−0.997988 | + | 0.0634097i | \(0.979803\pi\) | |||||||
\(948\) | −1459.18 | + | 737.313i | −0.0499915 | + | 0.0252604i | ||||
\(949\) | 18403.5 | 0.629508 | ||||||||
\(950\) | −1483.92 | −0.0506787 | ||||||||
\(951\) | 27002.4 | − | 13644.1i | 0.920728 | − | 0.465237i | ||||
\(952\) | −19936.2 | −0.678716 | ||||||||
\(953\) | −10904.7 | −0.370658 | −0.185329 | − | 0.982677i | \(-0.559335\pi\) | ||||
−0.185329 | + | 0.982677i | \(0.559335\pi\) | |||||||
\(954\) | −20305.2 | − | 14962.5i | −0.689105 | − | 0.507786i | ||||
\(955\) | 24855.4 | 0.842202 | ||||||||
\(956\) | 14073.0i | 0.476102i | ||||||||
\(957\) | 6198.05 | − | 3131.83i | 0.209357 | − | 0.105787i | ||||
\(958\) | − | 10748.7i | − | 0.362500i | ||||||
\(959\) | − | 28850.3i | − | 0.971454i | ||||||
\(960\) | −1632.35 | − | 3230.50i | −0.0548790 | − | 0.108608i | ||||
\(961\) | 53897.2 | 1.80918 | ||||||||
\(962\) | 9701.47 | 0.325143 | ||||||||
\(963\) | −15994.2 | + | 21705.4i | −0.535210 | + | 0.726321i | ||||
\(964\) | − | 18970.5i | − | 0.633817i | ||||||
\(965\) | −40398.9 | −1.34765 | ||||||||
\(966\) | 19762.7 | + | 15327.9i | 0.658236 | + | 0.510524i | ||||
\(967\) | 34528.8 | 1.14827 | 0.574133 | − | 0.818762i | \(-0.305339\pi\) | ||||
0.574133 | + | 0.818762i | \(0.305339\pi\) | |||||||
\(968\) | − | 9749.36i | − | 0.323715i | ||||||
\(969\) | −60093.1 | + | 30364.6i | −1.99223 | + | 1.00666i | ||||
\(970\) | 12049.0 | 0.398835 | ||||||||
\(971\) | −41579.1 | −1.37419 | −0.687094 | − | 0.726568i | \(-0.741114\pi\) | ||||
−0.687094 | + | 0.726568i | \(0.741114\pi\) | |||||||
\(972\) | −10892.8 | + | 10532.3i | −0.359453 | + | 0.347554i | ||||
\(973\) | 14014.1i | 0.461738i | ||||||||
\(974\) | 13966.8i | 0.459473i | ||||||||
\(975\) | 877.597 | + | 1736.81i | 0.0288263 | + | 0.0570486i | ||||
\(976\) | − | 11166.7i | − | 0.366226i | ||||||
\(977\) | −4631.39 | −0.151660 | −0.0758298 | − | 0.997121i | \(-0.524161\pi\) | ||||
−0.0758298 | + | 0.997121i | \(0.524161\pi\) | |||||||
\(978\) | 23728.0 | − | 11989.6i | 0.775806 | − | 0.392009i | ||||
\(979\) | −11896.2 | −0.388360 | ||||||||
\(980\) | 5791.17 | 0.188768 | ||||||||
\(981\) | −22661.3 | − | 16698.6i | −0.737531 | − | 0.543471i | ||||
\(982\) | 17118.8 | 0.556297 | ||||||||
\(983\) | −11223.2 | −0.364155 | −0.182077 | − | 0.983284i | \(-0.558282\pi\) | ||||
−0.182077 | + | 0.983284i | \(0.558282\pi\) | |||||||
\(984\) | 5615.75 | + | 11113.9i | 0.181935 | + | 0.360058i | ||||
\(985\) | 38648.6i | 1.25020i | ||||||||
\(986\) | 28805.4 | 0.930376 | ||||||||
\(987\) | −13012.4 | − | 25752.2i | −0.419644 | − | 0.830497i | ||||
\(988\) | 25982.8i | 0.836664i | ||||||||
\(989\) | −17289.8 | − | 36419.0i | −0.555900 | − | 1.17094i | ||||
\(990\) | −5014.69 | − | 3695.22i | −0.160987 | − | 0.118628i | ||||
\(991\) | 19975.4 | 0.640304 | 0.320152 | − | 0.947366i | \(-0.396266\pi\) | ||||
0.320152 | + | 0.947366i | \(0.396266\pi\) | |||||||
\(992\) | − | 9257.25i | − | 0.296288i | ||||||
\(993\) | 21138.9 | + | 41834.9i | 0.675550 | + | 1.33695i | ||||
\(994\) | − | 15472.3i | − | 0.493714i | ||||||
\(995\) | − | 5457.33i | − | 0.173878i | ||||||
\(996\) | −4751.83 | − | 9404.12i | −0.151172 | − | 0.299178i | ||||
\(997\) | 22337.7 | 0.709571 | 0.354785 | − | 0.934948i | \(-0.384554\pi\) | ||||
0.354785 | + | 0.934948i | \(0.384554\pi\) | |||||||
\(998\) | 37991.6i | 1.20501i | ||||||||
\(999\) | −1977.69 | + | 11719.5i | −0.0626340 | + | 0.371160i |
(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 | 138.4.d.a.137.8 | yes | 24 | |
3.2 | odd | 2 | inner | 138.4.d.a.137.19 | yes | 24 | |
23.22 | odd | 2 | inner | 138.4.d.a.137.7 | ✓ | 24 | |
69.68 | even | 2 | inner | 138.4.d.a.137.20 | yes | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
138.4.d.a.137.7 | ✓ | 24 | 23.22 | odd | 2 | inner | |
138.4.d.a.137.8 | yes | 24 | 1.1 | even | 1 | trivial | |
138.4.d.a.137.19 | yes | 24 | 3.2 | odd | 2 | inner | |
138.4.d.a.137.20 | yes | 24 | 69.68 | even | 2 | inner |