Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [207,4,Mod(1,207)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(207, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("207.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 207 = 3^{2} \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 207.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: | \(12.2133953712\) |
Analytic rank: | \(0\) |
Dimension: | \(5\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{5} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{5} - x^{4} - 26x^{3} + 10x^{2} + 144x + 56 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.5 | ||
Root | \(-4.06335\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 207.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 5.06335 | 1.79017 | 0.895083 | − | 0.445900i | \(-0.147116\pi\) | ||||
0.895083 | + | 0.445900i | \(0.147116\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 17.6375 | 2.20469 | ||||||||
\(5\) | 2.15617 | 0.192853 | 0.0964267 | − | 0.995340i | \(-0.469259\pi\) | ||||
0.0964267 | + | 0.995340i | \(0.469259\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.11437 | 0.114165 | 0.0570827 | − | 0.998369i | \(-0.481820\pi\) | ||||
0.0570827 | + | 0.998369i | \(0.481820\pi\) | |||||||
\(8\) | 48.7982 | 2.15660 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 10.9174 | 0.345239 | ||||||||
\(11\) | 33.1380 | 0.908317 | 0.454159 | − | 0.890921i | \(-0.349940\pi\) | ||||
0.454159 | + | 0.890921i | \(0.349940\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 6.68057 | 0.142527 | 0.0712637 | − | 0.997458i | \(-0.477297\pi\) | ||||
0.0712637 | + | 0.997458i | \(0.477297\pi\) | |||||||
\(14\) | 10.7058 | 0.204375 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 105.982 | 1.65597 | ||||||||
\(17\) | −55.3297 | −0.789378 | −0.394689 | − | 0.918815i | \(-0.629148\pi\) | ||||
−0.394689 | + | 0.918815i | \(0.629148\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 77.1072 | 0.931032 | 0.465516 | − | 0.885040i | \(-0.345869\pi\) | ||||
0.465516 | + | 0.885040i | \(0.345869\pi\) | |||||||
\(20\) | 38.0295 | 0.425182 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 167.789 | 1.62604 | ||||||||
\(23\) | −23.0000 | −0.208514 | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −120.351 | −0.962808 | ||||||||
\(26\) | 33.8261 | 0.255148 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 37.2923 | 0.251700 | ||||||||
\(29\) | −14.9375 | −0.0956488 | −0.0478244 | − | 0.998856i | \(-0.515229\pi\) | ||||
−0.0478244 | + | 0.998856i | \(0.515229\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −40.4477 | −0.234342 | −0.117171 | − | 0.993112i | \(-0.537383\pi\) | ||||
−0.117171 | + | 0.993112i | \(0.537383\pi\) | |||||||
\(32\) | 146.240 | 0.807870 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −280.154 | −1.41312 | ||||||||
\(35\) | 4.55894 | 0.0220172 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −223.461 | −0.992884 | −0.496442 | − | 0.868070i | \(-0.665360\pi\) | ||||
−0.496442 | + | 0.868070i | \(0.665360\pi\) | |||||||
\(38\) | 390.421 | 1.66670 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 105.217 | 0.415907 | ||||||||
\(41\) | 29.5816 | 0.112680 | 0.0563399 | − | 0.998412i | \(-0.482057\pi\) | ||||
0.0563399 | + | 0.998412i | \(0.482057\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −430.366 | −1.52628 | −0.763141 | − | 0.646232i | \(-0.776344\pi\) | ||||
−0.763141 | + | 0.646232i | \(0.776344\pi\) | |||||||
\(44\) | 584.473 | 2.00256 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −116.457 | −0.373275 | ||||||||
\(47\) | 498.856 | 1.54820 | 0.774102 | − | 0.633061i | \(-0.218202\pi\) | ||||
0.774102 | + | 0.633061i | \(0.218202\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −338.529 | −0.986966 | ||||||||
\(50\) | −609.379 | −1.72358 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 117.829 | 0.314229 | ||||||||
\(53\) | 485.561 | 1.25843 | 0.629216 | − | 0.777231i | \(-0.283376\pi\) | ||||
0.629216 | + | 0.777231i | \(0.283376\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 71.4511 | 0.175172 | ||||||||
\(56\) | 103.178 | 0.246209 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −75.6336 | −0.171227 | ||||||||
\(59\) | −425.760 | −0.939478 | −0.469739 | − | 0.882805i | \(-0.655652\pi\) | ||||
−0.469739 | + | 0.882805i | \(0.655652\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 185.041 | 0.388394 | 0.194197 | − | 0.980963i | \(-0.437790\pi\) | ||||
0.194197 | + | 0.980963i | \(0.437790\pi\) | |||||||
\(62\) | −204.801 | −0.419512 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −107.394 | −0.209753 | ||||||||
\(65\) | 14.4044 | 0.0274869 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 20.9209 | 0.0381477 | 0.0190738 | − | 0.999818i | \(-0.493928\pi\) | ||||
0.0190738 | + | 0.999818i | \(0.493928\pi\) | |||||||
\(68\) | −975.879 | −1.74033 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 23.0835 | 0.0394144 | ||||||||
\(71\) | −839.195 | −1.40273 | −0.701367 | − | 0.712800i | \(-0.747427\pi\) | ||||
−0.701367 | + | 0.712800i | \(0.747427\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −830.042 | −1.33081 | −0.665404 | − | 0.746483i | \(-0.731741\pi\) | ||||
−0.665404 | + | 0.746483i | \(0.731741\pi\) | |||||||
\(74\) | −1131.46 | −1.77743 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 1359.98 | 2.05264 | ||||||||
\(77\) | 70.0661 | 0.103698 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −392.651 | −0.559198 | −0.279599 | − | 0.960117i | \(-0.590202\pi\) | ||||
−0.279599 | + | 0.960117i | \(0.590202\pi\) | |||||||
\(80\) | 228.516 | 0.319360 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 149.782 | 0.201716 | ||||||||
\(83\) | 932.749 | 1.23352 | 0.616762 | − | 0.787150i | \(-0.288444\pi\) | ||||
0.616762 | + | 0.787150i | \(0.288444\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −119.300 | −0.152234 | ||||||||
\(86\) | −2179.09 | −2.73230 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 1617.08 | 1.95887 | ||||||||
\(89\) | 411.955 | 0.490642 | 0.245321 | − | 0.969442i | \(-0.421107\pi\) | ||||
0.245321 | + | 0.969442i | \(0.421107\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 14.1252 | 0.0162717 | ||||||||
\(92\) | −405.663 | −0.459710 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 2525.88 | 2.77154 | ||||||||
\(95\) | 166.256 | 0.179553 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1608.89 | 1.68411 | 0.842054 | − | 0.539393i | \(-0.181346\pi\) | ||||
0.842054 | + | 0.539393i | \(0.181346\pi\) | |||||||
\(98\) | −1714.09 | −1.76683 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −2122.69 | −2.12269 | ||||||||
\(101\) | 487.980 | 0.480751 | 0.240376 | − | 0.970680i | \(-0.422729\pi\) | ||||
0.240376 | + | 0.970680i | \(0.422729\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −865.083 | −0.827565 | −0.413782 | − | 0.910376i | \(-0.635793\pi\) | ||||
−0.413782 | + | 0.910376i | \(0.635793\pi\) | |||||||
\(104\) | 326.000 | 0.307374 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 2458.56 | 2.25280 | ||||||||
\(107\) | 1776.61 | 1.60516 | 0.802578 | − | 0.596547i | \(-0.203461\pi\) | ||||
0.802578 | + | 0.596547i | \(0.203461\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 127.044 | 0.111639 | 0.0558193 | − | 0.998441i | \(-0.482223\pi\) | ||||
0.0558193 | + | 0.998441i | \(0.482223\pi\) | |||||||
\(110\) | 361.782 | 0.313587 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 224.086 | 0.189055 | ||||||||
\(113\) | 1384.34 | 1.15246 | 0.576229 | − | 0.817288i | \(-0.304523\pi\) | ||||
0.576229 | + | 0.817288i | \(0.304523\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −49.5918 | −0.0402127 | ||||||||
\(116\) | −263.460 | −0.210876 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −2155.77 | −1.68182 | ||||||||
\(119\) | −116.988 | −0.0901196 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −232.872 | −0.174960 | ||||||||
\(122\) | 936.925 | 0.695289 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −713.397 | −0.516653 | ||||||||
\(125\) | −529.018 | −0.378534 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −2433.91 | −1.70058 | −0.850292 | − | 0.526311i | \(-0.823575\pi\) | ||||
−0.850292 | + | 0.526311i | \(0.823575\pi\) | |||||||
\(128\) | −1713.69 | −1.18336 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 72.9347 | 0.0492061 | ||||||||
\(131\) | −739.866 | −0.493453 | −0.246727 | − | 0.969085i | \(-0.579355\pi\) | ||||
−0.246727 | + | 0.969085i | \(0.579355\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 163.033 | 0.106292 | ||||||||
\(134\) | 105.930 | 0.0682907 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −2699.99 | −1.70237 | ||||||||
\(137\) | −749.250 | −0.467246 | −0.233623 | − | 0.972327i | \(-0.575058\pi\) | ||||
−0.233623 | + | 0.972327i | \(0.575058\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2693.60 | 1.64365 | 0.821827 | − | 0.569737i | \(-0.192955\pi\) | ||||
0.821827 | + | 0.569737i | \(0.192955\pi\) | |||||||
\(140\) | 80.4085 | 0.0485411 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −4249.14 | −2.51113 | ||||||||
\(143\) | 221.381 | 0.129460 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −32.2076 | −0.0184462 | ||||||||
\(146\) | −4202.79 | −2.38237 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −3941.30 | −2.18900 | ||||||||
\(149\) | 1253.10 | 0.688978 | 0.344489 | − | 0.938790i | \(-0.388052\pi\) | ||||
0.344489 | + | 0.938790i | \(0.388052\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 696.459 | 0.375344 | 0.187672 | − | 0.982232i | \(-0.439906\pi\) | ||||
0.187672 | + | 0.982232i | \(0.439906\pi\) | |||||||
\(152\) | 3762.69 | 2.00786 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 354.770 | 0.185637 | ||||||||
\(155\) | −87.2119 | −0.0451937 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 3144.36 | 1.59839 | 0.799195 | − | 0.601071i | \(-0.205259\pi\) | ||||
0.799195 | + | 0.601071i | \(0.205259\pi\) | |||||||
\(158\) | −1988.13 | −1.00106 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 315.318 | 0.155800 | ||||||||
\(161\) | −48.6306 | −0.0238051 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 2733.73 | 1.31363 | 0.656816 | − | 0.754051i | \(-0.271903\pi\) | ||||
0.656816 | + | 0.754051i | \(0.271903\pi\) | |||||||
\(164\) | 521.747 | 0.248424 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 4722.83 | 2.20821 | ||||||||
\(167\) | −341.032 | −0.158023 | −0.0790115 | − | 0.996874i | \(-0.525176\pi\) | ||||
−0.0790115 | + | 0.996874i | \(0.525176\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −2152.37 | −0.979686 | ||||||||
\(170\) | −604.058 | −0.272524 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −7590.59 | −3.36498 | ||||||||
\(173\) | 1277.25 | 0.561314 | 0.280657 | − | 0.959808i | \(-0.409448\pi\) | ||||
0.280657 | + | 0.959808i | \(0.409448\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −254.467 | −0.109919 | ||||||||
\(176\) | 3512.04 | 1.50415 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 2085.87 | 0.878331 | ||||||||
\(179\) | 1177.28 | 0.491588 | 0.245794 | − | 0.969322i | \(-0.420951\pi\) | ||||
0.245794 | + | 0.969322i | \(0.420951\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −367.909 | −0.151085 | −0.0755427 | − | 0.997143i | \(-0.524069\pi\) | ||||
−0.0755427 | + | 0.997143i | \(0.524069\pi\) | |||||||
\(182\) | 71.5210 | 0.0291290 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −1122.36 | −0.449682 | ||||||||
\(185\) | −481.818 | −0.191481 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1833.52 | −0.717005 | ||||||||
\(188\) | 8798.58 | 3.41331 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 841.812 | 0.321429 | ||||||||
\(191\) | −1892.89 | −0.717091 | −0.358546 | − | 0.933512i | \(-0.616727\pi\) | ||||
−0.358546 | + | 0.933512i | \(0.616727\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 3305.10 | 1.23268 | 0.616338 | − | 0.787481i | \(-0.288615\pi\) | ||||
0.616338 | + | 0.787481i | \(0.288615\pi\) | |||||||
\(194\) | 8146.40 | 3.01483 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −5970.82 | −2.17596 | ||||||||
\(197\) | 4083.31 | 1.47677 | 0.738385 | − | 0.674380i | \(-0.235589\pi\) | ||||
0.738385 | + | 0.674380i | \(0.235589\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 2885.38 | 1.02783 | 0.513917 | − | 0.857840i | \(-0.328194\pi\) | ||||
0.513917 | + | 0.857840i | \(0.328194\pi\) | |||||||
\(200\) | −5872.91 | −2.07639 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 2470.82 | 0.860624 | ||||||||
\(203\) | −31.5834 | −0.0109198 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 63.7829 | 0.0217307 | ||||||||
\(206\) | −4380.22 | −1.48148 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 708.023 | 0.236022 | ||||||||
\(209\) | 2555.18 | 0.845672 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −898.025 | −0.292998 | −0.146499 | − | 0.989211i | \(-0.546801\pi\) | ||||
−0.146499 | + | 0.989211i | \(0.546801\pi\) | |||||||
\(212\) | 8564.09 | 2.77445 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 8995.62 | 2.87349 | ||||||||
\(215\) | −927.940 | −0.294349 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −85.5214 | −0.0267538 | ||||||||
\(218\) | 643.268 | 0.199851 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 1260.22 | 0.386200 | ||||||||
\(221\) | −369.634 | −0.112508 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 3934.09 | 1.18137 | 0.590686 | − | 0.806901i | \(-0.298857\pi\) | ||||
0.590686 | + | 0.806901i | \(0.298857\pi\) | |||||||
\(224\) | 309.206 | 0.0922308 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 7009.41 | 2.06309 | ||||||||
\(227\) | −5362.67 | −1.56799 | −0.783993 | − | 0.620770i | \(-0.786820\pi\) | ||||
−0.783993 | + | 0.620770i | \(0.786820\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 3830.28 | 1.10529 | 0.552646 | − | 0.833416i | \(-0.313618\pi\) | ||||
0.552646 | + | 0.833416i | \(0.313618\pi\) | |||||||
\(230\) | −251.101 | −0.0719874 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −728.921 | −0.206276 | ||||||||
\(233\) | −1997.73 | −0.561697 | −0.280848 | − | 0.959752i | \(-0.590616\pi\) | ||||
−0.280848 | + | 0.959752i | \(0.590616\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1075.62 | 0.298576 | ||||||||
\(236\) | −7509.36 | −2.07126 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −592.349 | −0.161329 | ||||||||
\(239\) | 3145.12 | 0.851217 | 0.425609 | − | 0.904907i | \(-0.360060\pi\) | ||||
0.425609 | + | 0.904907i | \(0.360060\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −3189.67 | −0.852552 | −0.426276 | − | 0.904593i | \(-0.640175\pi\) | ||||
−0.426276 | + | 0.904593i | \(0.640175\pi\) | |||||||
\(242\) | −1179.11 | −0.313207 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 3263.66 | 0.856288 | ||||||||
\(245\) | −729.926 | −0.190340 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 515.120 | 0.132698 | ||||||||
\(248\) | −1973.77 | −0.505382 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −2678.60 | −0.677639 | ||||||||
\(251\) | −4270.59 | −1.07393 | −0.536967 | − | 0.843603i | \(-0.680430\pi\) | ||||
−0.536967 | + | 0.843603i | \(0.680430\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −762.174 | −0.189397 | ||||||||
\(254\) | −12323.7 | −3.04433 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −7817.88 | −1.90866 | ||||||||
\(257\) | 7585.83 | 1.84121 | 0.920606 | − | 0.390493i | \(-0.127696\pi\) | ||||
0.920606 | + | 0.390493i | \(0.127696\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −472.479 | −0.113353 | ||||||||
\(260\) | 254.059 | 0.0606002 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −3746.20 | −0.883363 | ||||||||
\(263\) | 961.653 | 0.225468 | 0.112734 | − | 0.993625i | \(-0.464039\pi\) | ||||
0.112734 | + | 0.993625i | \(0.464039\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1046.95 | 0.242693 | ||||||||
\(266\) | 825.495 | 0.190280 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 368.993 | 0.0841039 | ||||||||
\(269\) | −7770.51 | −1.76125 | −0.880625 | − | 0.473814i | \(-0.842877\pi\) | ||||
−0.880625 | + | 0.473814i | \(0.842877\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −3812.06 | −0.854487 | −0.427243 | − | 0.904137i | \(-0.640515\pi\) | ||||
−0.427243 | + | 0.904137i | \(0.640515\pi\) | |||||||
\(272\) | −5863.97 | −1.30719 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −3793.72 | −0.836448 | ||||||||
\(275\) | −3988.19 | −0.874535 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −6781.71 | −1.47102 | −0.735512 | − | 0.677512i | \(-0.763058\pi\) | ||||
−0.735512 | + | 0.677512i | \(0.763058\pi\) | |||||||
\(278\) | 13638.6 | 2.94241 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 222.468 | 0.0474822 | ||||||||
\(281\) | 5389.07 | 1.14408 | 0.572038 | − | 0.820227i | \(-0.306153\pi\) | ||||
0.572038 | + | 0.820227i | \(0.306153\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 3747.11 | 0.787076 | 0.393538 | − | 0.919308i | \(-0.371251\pi\) | ||||
0.393538 | + | 0.919308i | \(0.371251\pi\) | |||||||
\(284\) | −14801.3 | −3.09260 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 1120.93 | 0.231755 | ||||||||
\(287\) | 62.5466 | 0.0128641 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1851.63 | −0.376883 | ||||||||
\(290\) | −163.079 | −0.0330217 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −14639.9 | −2.93402 | ||||||||
\(293\) | 2580.83 | 0.514585 | 0.257293 | − | 0.966334i | \(-0.417170\pi\) | ||||
0.257293 | + | 0.966334i | \(0.417170\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −918.009 | −0.181182 | ||||||||
\(296\) | −10904.5 | −2.14125 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 6344.87 | 1.23338 | ||||||||
\(299\) | −153.653 | −0.0297190 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −909.954 | −0.174249 | ||||||||
\(302\) | 3526.42 | 0.671929 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 8172.00 | 1.54176 | ||||||||
\(305\) | 398.978 | 0.0749030 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −2665.09 | −0.495455 | −0.247727 | − | 0.968830i | \(-0.579684\pi\) | ||||
−0.247727 | + | 0.968830i | \(0.579684\pi\) | |||||||
\(308\) | 1235.79 | 0.228623 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −441.584 | −0.0809042 | ||||||||
\(311\) | −5643.13 | −1.02892 | −0.514458 | − | 0.857516i | \(-0.672007\pi\) | ||||
−0.514458 | + | 0.857516i | \(0.672007\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 4589.28 | 0.828759 | 0.414380 | − | 0.910104i | \(-0.363999\pi\) | ||||
0.414380 | + | 0.910104i | \(0.363999\pi\) | |||||||
\(314\) | 15921.0 | 2.86138 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −6925.39 | −1.23286 | ||||||||
\(317\) | 1268.43 | 0.224738 | 0.112369 | − | 0.993667i | \(-0.464156\pi\) | ||||
0.112369 | + | 0.993667i | \(0.464156\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −494.998 | −0.0868794 | ||||||||
\(320\) | −231.559 | −0.0404516 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −246.234 | −0.0426151 | ||||||||
\(323\) | −4266.32 | −0.734936 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −804.013 | −0.137227 | ||||||||
\(326\) | 13841.8 | 2.35162 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 1443.53 | 0.243005 | ||||||||
\(329\) | 1054.77 | 0.176751 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −5744.29 | −0.953881 | −0.476940 | − | 0.878936i | \(-0.658254\pi\) | ||||
−0.476940 | + | 0.878936i | \(0.658254\pi\) | |||||||
\(332\) | 16451.4 | 2.71954 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −1726.76 | −0.282887 | ||||||||
\(335\) | 45.1090 | 0.00735691 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −5584.45 | −0.902684 | −0.451342 | − | 0.892351i | \(-0.649055\pi\) | ||||
−0.451342 | + | 0.892351i | \(0.649055\pi\) | |||||||
\(338\) | −10898.2 | −1.75380 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −2104.16 | −0.335629 | ||||||||
\(341\) | −1340.36 | −0.212857 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1441.01 | −0.226843 | ||||||||
\(344\) | −21001.1 | −3.29158 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 6467.15 | 1.00484 | ||||||||
\(347\) | −4329.48 | −0.669795 | −0.334897 | − | 0.942255i | \(-0.608702\pi\) | ||||
−0.334897 | + | 0.942255i | \(0.608702\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −1605.98 | −0.246322 | −0.123161 | − | 0.992387i | \(-0.539303\pi\) | ||||
−0.123161 | + | 0.992387i | \(0.539303\pi\) | |||||||
\(350\) | −1288.46 | −0.196774 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 4846.11 | 0.733802 | ||||||||
\(353\) | −5975.48 | −0.900970 | −0.450485 | − | 0.892784i | \(-0.648749\pi\) | ||||
−0.450485 | + | 0.892784i | \(0.648749\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −1809.44 | −0.270522 | ||||||||
\(356\) | 7265.88 | 1.08172 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 5961.00 | 0.880024 | ||||||||
\(359\) | −1513.76 | −0.222544 | −0.111272 | − | 0.993790i | \(-0.535492\pi\) | ||||
−0.111272 | + | 0.993790i | \(0.535492\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −913.481 | −0.133180 | ||||||||
\(362\) | −1862.85 | −0.270468 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 249.134 | 0.0358741 | ||||||||
\(365\) | −1789.71 | −0.256651 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −9072.68 | −1.29044 | −0.645218 | − | 0.763999i | \(-0.723233\pi\) | ||||
−0.645218 | + | 0.763999i | \(0.723233\pi\) | |||||||
\(368\) | −2437.59 | −0.345294 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −2439.62 | −0.342783 | ||||||||
\(371\) | 1026.66 | 0.143669 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −5292.60 | −0.734693 | −0.367347 | − | 0.930084i | \(-0.619734\pi\) | ||||
−0.367347 | + | 0.930084i | \(0.619734\pi\) | |||||||
\(374\) | −9283.74 | −1.28356 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 24343.3 | 3.33885 | ||||||||
\(377\) | −99.7907 | −0.0136326 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 7061.29 | 0.957029 | 0.478515 | − | 0.878080i | \(-0.341175\pi\) | ||||
0.478515 | + | 0.878080i | \(0.341175\pi\) | |||||||
\(380\) | 2932.34 | 0.395858 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −9584.35 | −1.28371 | ||||||||
\(383\) | −1213.73 | −0.161929 | −0.0809644 | − | 0.996717i | \(-0.525800\pi\) | ||||
−0.0809644 | + | 0.996717i | \(0.525800\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 151.074 | 0.0199986 | ||||||||
\(386\) | 16734.9 | 2.20670 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 28376.9 | 3.71294 | ||||||||
\(389\) | 1193.72 | 0.155588 | 0.0777942 | − | 0.996969i | \(-0.475212\pi\) | ||||
0.0777942 | + | 0.996969i | \(0.475212\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1272.58 | 0.164597 | ||||||||
\(392\) | −16519.6 | −2.12849 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 20675.2 | 2.64366 | ||||||||
\(395\) | −846.620 | −0.107843 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 3390.50 | 0.428625 | 0.214312 | − | 0.976765i | \(-0.431249\pi\) | ||||
0.214312 | + | 0.976765i | \(0.431249\pi\) | |||||||
\(398\) | 14609.7 | 1.83999 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −12755.1 | −1.59438 | ||||||||
\(401\) | 2342.79 | 0.291754 | 0.145877 | − | 0.989303i | \(-0.453400\pi\) | ||||
0.145877 | + | 0.989303i | \(0.453400\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −270.213 | −0.0334002 | ||||||||
\(404\) | 8606.77 | 1.05991 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −159.918 | −0.0195482 | ||||||||
\(407\) | −7405.04 | −0.901854 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 12070.1 | 1.45923 | 0.729617 | − | 0.683856i | \(-0.239698\pi\) | ||||
0.729617 | + | 0.683856i | \(0.239698\pi\) | |||||||
\(410\) | 322.955 | 0.0389015 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −15257.9 | −1.82453 | ||||||||
\(413\) | −900.216 | −0.107256 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 2011.16 | 0.237889 | ||||||||
\(416\) | 976.967 | 0.115144 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 12937.8 | 1.51389 | ||||||||
\(419\) | −1561.32 | −0.182042 | −0.0910211 | − | 0.995849i | \(-0.529013\pi\) | ||||
−0.0910211 | + | 0.995849i | \(0.529013\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −7096.40 | −0.821514 | −0.410757 | − | 0.911745i | \(-0.634736\pi\) | ||||
−0.410757 | + | 0.911745i | \(0.634736\pi\) | |||||||
\(422\) | −4547.02 | −0.524515 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 23694.5 | 2.71393 | ||||||||
\(425\) | 6658.98 | 0.760019 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 391.245 | 0.0443411 | ||||||||
\(428\) | 31335.1 | 3.53887 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −4698.49 | −0.526933 | ||||||||
\(431\) | −14072.8 | −1.57277 | −0.786386 | − | 0.617736i | \(-0.788050\pi\) | ||||
−0.786386 | + | 0.617736i | \(0.788050\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −12446.4 | −1.38138 | −0.690690 | − | 0.723151i | \(-0.742693\pi\) | ||||
−0.690690 | + | 0.723151i | \(0.742693\pi\) | |||||||
\(434\) | −433.025 | −0.0478937 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 2240.74 | 0.246129 | ||||||||
\(437\) | −1773.47 | −0.194134 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −9441.14 | −1.02643 | −0.513213 | − | 0.858261i | \(-0.671545\pi\) | ||||
−0.513213 | + | 0.858261i | \(0.671545\pi\) | |||||||
\(440\) | 3486.69 | 0.377776 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −1871.59 | −0.201408 | ||||||||
\(443\) | −8932.41 | −0.957994 | −0.478997 | − | 0.877817i | \(-0.659000\pi\) | ||||
−0.478997 | + | 0.877817i | \(0.659000\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 888.244 | 0.0946221 | ||||||||
\(446\) | 19919.7 | 2.11485 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −227.070 | −0.0239466 | ||||||||
\(449\) | 8402.96 | 0.883208 | 0.441604 | − | 0.897210i | \(-0.354410\pi\) | ||||
0.441604 | + | 0.897210i | \(0.354410\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 980.276 | 0.102349 | ||||||||
\(452\) | 24416.4 | 2.54082 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −27153.1 | −2.80695 | ||||||||
\(455\) | 30.4563 | 0.00313805 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 3059.29 | 0.313146 | 0.156573 | − | 0.987666i | \(-0.449955\pi\) | ||||
0.156573 | + | 0.987666i | \(0.449955\pi\) | |||||||
\(458\) | 19394.0 | 1.97866 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −874.678 | −0.0886566 | ||||||||
\(461\) | 18346.1 | 1.85350 | 0.926751 | − | 0.375677i | \(-0.122590\pi\) | ||||
0.926751 | + | 0.375677i | \(0.122590\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 11616.6 | 1.16602 | 0.583010 | − | 0.812465i | \(-0.301875\pi\) | ||||
0.583010 | + | 0.812465i | \(0.301875\pi\) | |||||||
\(464\) | −1583.11 | −0.158392 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −10115.2 | −1.00553 | ||||||||
\(467\) | 5595.70 | 0.554471 | 0.277236 | − | 0.960802i | \(-0.410582\pi\) | ||||
0.277236 | + | 0.960802i | \(0.410582\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 44.2346 | 0.00435515 | ||||||||
\(470\) | 5446.22 | 0.534501 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −20776.3 | −2.02608 | ||||||||
\(473\) | −14261.5 | −1.38635 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −9279.92 | −0.896404 | ||||||||
\(476\) | −2063.37 | −0.198686 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 15924.9 | 1.52382 | ||||||||
\(479\) | 2323.55 | 0.221640 | 0.110820 | − | 0.993840i | \(-0.464652\pi\) | ||||
0.110820 | + | 0.993840i | \(0.464652\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1492.85 | −0.141513 | ||||||||
\(482\) | −16150.4 | −1.52621 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −4107.28 | −0.385733 | ||||||||
\(485\) | 3469.04 | 0.324786 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 8265.12 | 0.769052 | 0.384526 | − | 0.923114i | \(-0.374365\pi\) | ||||
0.384526 | + | 0.923114i | \(0.374365\pi\) | |||||||
\(488\) | 9029.65 | 0.837609 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −3695.87 | −0.340740 | ||||||||
\(491\) | −10618.1 | −0.975947 | −0.487973 | − | 0.872859i | \(-0.662264\pi\) | ||||
−0.487973 | + | 0.872859i | \(0.662264\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 826.485 | 0.0755030 | ||||||||
\(494\) | 2608.23 | 0.237551 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −4286.74 | −0.388065 | ||||||||
\(497\) | −1774.37 | −0.160144 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −5503.12 | −0.493695 | −0.246847 | − | 0.969054i | \(-0.579395\pi\) | ||||
−0.246847 | + | 0.969054i | \(0.579395\pi\) | |||||||
\(500\) | −9330.56 | −0.834551 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −21623.5 | −1.92252 | ||||||||
\(503\) | −15861.1 | −1.40599 | −0.702993 | − | 0.711197i | \(-0.748154\pi\) | ||||
−0.702993 | + | 0.711197i | \(0.748154\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 1052.17 | 0.0927145 | ||||||||
\(506\) | −3859.16 | −0.339052 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −42928.1 | −3.74926 | ||||||||
\(509\) | 7085.11 | 0.616979 | 0.308489 | − | 0.951228i | \(-0.400177\pi\) | ||||
0.308489 | + | 0.951228i | \(0.400177\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1755.02 | −0.151932 | ||||||||
\(512\) | −25875.1 | −2.23346 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 38409.8 | 3.29607 | ||||||||
\(515\) | −1865.26 | −0.159599 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 16531.1 | 1.40626 | ||||||||
\(518\) | −2392.33 | −0.202921 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 702.910 | 0.0592782 | ||||||||
\(521\) | 22508.5 | 1.89273 | 0.946367 | − | 0.323093i | \(-0.104723\pi\) | ||||
0.946367 | + | 0.323093i | \(0.104723\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 722.225 | 0.0603838 | 0.0301919 | − | 0.999544i | \(-0.490388\pi\) | ||||
0.0301919 | + | 0.999544i | \(0.490388\pi\) | |||||||
\(524\) | −13049.4 | −1.08791 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 4869.19 | 0.403625 | ||||||||
\(527\) | 2237.96 | 0.184985 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 529.000 | 0.0434783 | ||||||||
\(530\) | 5301.08 | 0.434460 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 2875.51 | 0.234340 | ||||||||
\(533\) | 197.622 | 0.0160600 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 3830.67 | 0.309560 | ||||||||
\(536\) | 1020.90 | 0.0822692 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −39344.8 | −3.15293 | ||||||||
\(539\) | −11218.2 | −0.896478 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 16933.0 | 1.34566 | 0.672832 | − | 0.739795i | \(-0.265077\pi\) | ||||
0.672832 | + | 0.739795i | \(0.265077\pi\) | |||||||
\(542\) | −19301.8 | −1.52967 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −8091.42 | −0.637714 | ||||||||
\(545\) | 273.928 | 0.0215299 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −19402.6 | −1.51663 | −0.758316 | − | 0.651888i | \(-0.773977\pi\) | ||||
−0.758316 | + | 0.651888i | \(0.773977\pi\) | |||||||
\(548\) | −13214.9 | −1.03013 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −20193.6 | −1.56556 | ||||||||
\(551\) | −1151.79 | −0.0890521 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −830.210 | −0.0638411 | ||||||||
\(554\) | −34338.2 | −2.63337 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 47508.4 | 3.62375 | ||||||||
\(557\) | −19903.5 | −1.51408 | −0.757038 | − | 0.653371i | \(-0.773354\pi\) | ||||
−0.757038 | + | 0.653371i | \(0.773354\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −2875.09 | −0.217537 | ||||||||
\(560\) | 483.167 | 0.0364599 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 27286.8 | 2.04808 | ||||||||
\(563\) | 20255.6 | 1.51629 | 0.758147 | − | 0.652084i | \(-0.226105\pi\) | ||||
0.758147 | + | 0.652084i | \(0.226105\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 2984.87 | 0.222256 | ||||||||
\(566\) | 18972.9 | 1.40900 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −40951.2 | −3.02513 | ||||||||
\(569\) | −17124.4 | −1.26167 | −0.630835 | − | 0.775917i | \(-0.717288\pi\) | ||||
−0.630835 | + | 0.775917i | \(0.717288\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −2476.48 | −0.181502 | −0.0907508 | − | 0.995874i | \(-0.528927\pi\) | ||||
−0.0907508 | + | 0.995874i | \(0.528927\pi\) | |||||||
\(572\) | 3904.61 | 0.285420 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 316.695 | 0.0230289 | ||||||||
\(575\) | 2768.07 | 0.200759 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −5158.81 | −0.372208 | −0.186104 | − | 0.982530i | \(-0.559586\pi\) | ||||
−0.186104 | + | 0.982530i | \(0.559586\pi\) | |||||||
\(578\) | −9375.44 | −0.674683 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −568.063 | −0.0406682 | ||||||||
\(581\) | 1972.18 | 0.140826 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 16090.5 | 1.14306 | ||||||||
\(584\) | −40504.6 | −2.87002 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 13067.6 | 0.921192 | ||||||||
\(587\) | −1429.09 | −0.100485 | −0.0502425 | − | 0.998737i | \(-0.515999\pi\) | ||||
−0.0502425 | + | 0.998737i | \(0.515999\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −3118.80 | −0.218180 | ||||||||
\(590\) | −4648.21 | −0.324345 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −23682.9 | −1.64419 | ||||||||
\(593\) | 19207.1 | 1.33008 | 0.665041 | − | 0.746807i | \(-0.268414\pi\) | ||||
0.665041 | + | 0.746807i | \(0.268414\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −252.245 | −0.0173799 | ||||||||
\(596\) | 22101.5 | 1.51898 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −778.000 | −0.0532020 | ||||||||
\(599\) | 4323.19 | 0.294893 | 0.147447 | − | 0.989070i | \(-0.452895\pi\) | ||||
0.147447 | + | 0.989070i | \(0.452895\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 5603.82 | 0.380340 | 0.190170 | − | 0.981751i | \(-0.439096\pi\) | ||||
0.190170 | + | 0.981751i | \(0.439096\pi\) | |||||||
\(602\) | −4607.42 | −0.311934 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 12283.8 | 0.827519 | ||||||||
\(605\) | −502.110 | −0.0337416 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 15551.9 | 1.03992 | 0.519961 | − | 0.854190i | \(-0.325947\pi\) | ||||
0.519961 | + | 0.854190i | \(0.325947\pi\) | |||||||
\(608\) | 11276.2 | 0.752153 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 2020.17 | 0.134089 | ||||||||
\(611\) | 3332.64 | 0.220662 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 1211.55 | 0.0798275 | 0.0399137 | − | 0.999203i | \(-0.487292\pi\) | ||||
0.0399137 | + | 0.999203i | \(0.487292\pi\) | |||||||
\(614\) | −13494.3 | −0.886946 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 3419.10 | 0.223636 | ||||||||
\(617\) | 29762.6 | 1.94197 | 0.970987 | − | 0.239131i | \(-0.0768624\pi\) | ||||
0.970987 | + | 0.239131i | \(0.0768624\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 28628.5 | 1.85893 | 0.929464 | − | 0.368912i | \(-0.120270\pi\) | ||||
0.929464 | + | 0.368912i | \(0.120270\pi\) | |||||||
\(620\) | −1538.20 | −0.0996382 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −28573.2 | −1.84193 | ||||||||
\(623\) | 871.027 | 0.0560144 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 13903.2 | 0.889806 | ||||||||
\(626\) | 23237.2 | 1.48362 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 55458.8 | 3.52396 | ||||||||
\(629\) | 12364.0 | 0.783760 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 18457.5 | 1.16447 | 0.582234 | − | 0.813021i | \(-0.302179\pi\) | ||||
0.582234 | + | 0.813021i | \(0.302179\pi\) | |||||||
\(632\) | −19160.7 | −1.20596 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 6422.50 | 0.402319 | ||||||||
\(635\) | −5247.90 | −0.327963 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −2261.57 | −0.140670 | ||||||||
\(638\) | −2506.35 | −0.155529 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −3695.01 | −0.228216 | ||||||||
\(641\) | 12136.0 | 0.747808 | 0.373904 | − | 0.927467i | \(-0.378019\pi\) | ||||
0.373904 | + | 0.927467i | \(0.378019\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 10954.8 | 0.671877 | 0.335939 | − | 0.941884i | \(-0.390947\pi\) | ||||
0.335939 | + | 0.941884i | \(0.390947\pi\) | |||||||
\(644\) | −857.724 | −0.0524830 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −21601.9 | −1.31566 | ||||||||
\(647\) | −22621.7 | −1.37457 | −0.687287 | − | 0.726386i | \(-0.741199\pi\) | ||||
−0.687287 | + | 0.726386i | \(0.741199\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −14108.8 | −0.853344 | ||||||||
\(650\) | −4071.00 | −0.245658 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 48216.2 | 2.89615 | ||||||||
\(653\) | 29747.8 | 1.78273 | 0.891363 | − | 0.453291i | \(-0.149750\pi\) | ||||
0.891363 | + | 0.453291i | \(0.149750\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −1595.27 | −0.0951642 | ||||||||
\(656\) | 3135.13 | 0.186595 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 5340.66 | 0.316414 | ||||||||
\(659\) | −19334.4 | −1.14289 | −0.571443 | − | 0.820642i | \(-0.693616\pi\) | ||||
−0.571443 | + | 0.820642i | \(0.693616\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 2973.50 | 0.174971 | 0.0874854 | − | 0.996166i | \(-0.472117\pi\) | ||||
0.0874854 | + | 0.996166i | \(0.472117\pi\) | |||||||
\(662\) | −29085.3 | −1.70760 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 45516.5 | 2.66021 | ||||||||
\(665\) | 351.527 | 0.0204987 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 343.561 | 0.0199442 | ||||||||
\(668\) | −6014.96 | −0.348392 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 228.403 | 0.0131701 | ||||||||
\(671\) | 6131.88 | 0.352785 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 5190.74 | 0.297308 | 0.148654 | − | 0.988889i | \(-0.452506\pi\) | ||||
0.148654 | + | 0.988889i | \(0.452506\pi\) | |||||||
\(674\) | −28276.1 | −1.61595 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −37962.5 | −2.15991 | ||||||||
\(677\) | 4033.92 | 0.229005 | 0.114502 | − | 0.993423i | \(-0.463473\pi\) | ||||
0.114502 | + | 0.993423i | \(0.463473\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 3401.80 | 0.192267 | ||||||||
\(680\) | −5821.63 | −0.328308 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −6786.69 | −0.381050 | ||||||||
\(683\) | −443.990 | −0.0248738 | −0.0124369 | − | 0.999923i | \(-0.503959\pi\) | ||||
−0.0124369 | + | 0.999923i | \(0.503959\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −1615.51 | −0.0901101 | ||||||||
\(686\) | −7296.33 | −0.406086 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −45611.2 | −2.52748 | ||||||||
\(689\) | 3243.82 | 0.179361 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1305.21 | 0.0718562 | 0.0359281 | − | 0.999354i | \(-0.488561\pi\) | ||||
0.0359281 | + | 0.999354i | \(0.488561\pi\) | |||||||
\(692\) | 22527.5 | 1.23752 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −21921.7 | −1.19904 | ||||||||
\(695\) | 5807.84 | 0.316984 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1636.74 | −0.0889470 | ||||||||
\(698\) | −8131.66 | −0.440957 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −4488.17 | −0.242338 | ||||||||
\(701\) | −21638.2 | −1.16585 | −0.582926 | − | 0.812525i | \(-0.698092\pi\) | ||||
−0.582926 | + | 0.812525i | \(0.698092\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −17230.4 | −0.924407 | ||||||||
\(704\) | −3558.81 | −0.190523 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −30255.9 | −1.61289 | ||||||||
\(707\) | 1031.77 | 0.0548852 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 11914.6 | 0.631116 | 0.315558 | − | 0.948906i | \(-0.397808\pi\) | ||||
0.315558 | + | 0.948906i | \(0.397808\pi\) | |||||||
\(710\) | −9161.86 | −0.484279 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 20102.7 | 1.05812 | ||||||||
\(713\) | 930.296 | 0.0488638 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 477.334 | 0.0249668 | ||||||||
\(716\) | 20764.4 | 1.08380 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −7664.70 | −0.398390 | ||||||||
\(719\) | −10462.6 | −0.542683 | −0.271341 | − | 0.962483i | \(-0.587467\pi\) | ||||
−0.271341 | + | 0.962483i | \(0.587467\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1829.11 | −0.0944793 | ||||||||
\(722\) | −4625.28 | −0.238414 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −6489.01 | −0.333097 | ||||||||
\(725\) | 1797.74 | 0.0920914 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −31769.4 | −1.62072 | −0.810358 | − | 0.585935i | \(-0.800727\pi\) | ||||
−0.810358 | + | 0.585935i | \(0.800727\pi\) | |||||||
\(728\) | 689.286 | 0.0350915 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −9061.92 | −0.459448 | ||||||||
\(731\) | 23812.0 | 1.20481 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 9298.69 | 0.468561 | 0.234280 | − | 0.972169i | \(-0.424727\pi\) | ||||
0.234280 | + | 0.972169i | \(0.424727\pi\) | |||||||
\(734\) | −45938.2 | −2.31009 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −3363.52 | −0.168453 | ||||||||
\(737\) | 693.277 | 0.0346502 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −19146.9 | −0.953084 | −0.476542 | − | 0.879152i | \(-0.658110\pi\) | ||||
−0.476542 | + | 0.879152i | \(0.658110\pi\) | |||||||
\(740\) | −8498.09 | −0.422157 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 5198.32 | 0.257192 | ||||||||
\(743\) | 14937.9 | 0.737574 | 0.368787 | − | 0.929514i | \(-0.379773\pi\) | ||||
0.368787 | + | 0.929514i | \(0.379773\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 2701.89 | 0.132872 | ||||||||
\(746\) | −26798.3 | −1.31522 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −32338.7 | −1.58078 | ||||||||
\(749\) | 3756.42 | 0.183253 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 6447.80 | 0.313294 | 0.156647 | − | 0.987655i | \(-0.449932\pi\) | ||||
0.156647 | + | 0.987655i | \(0.449932\pi\) | |||||||
\(752\) | 52869.9 | 2.56378 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −505.276 | −0.0244046 | ||||||||
\(755\) | 1501.68 | 0.0723865 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −39280.8 | −1.88598 | −0.942989 | − | 0.332824i | \(-0.891998\pi\) | ||||
−0.942989 | + | 0.332824i | \(0.891998\pi\) | |||||||
\(758\) | 35753.8 | 1.71324 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 8113.00 | 0.387223 | ||||||||
\(761\) | 16581.0 | 0.789830 | 0.394915 | − | 0.918718i | \(-0.370774\pi\) | ||||
0.394915 | + | 0.918718i | \(0.370774\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 268.618 | 0.0127453 | ||||||||
\(764\) | −33385.8 | −1.58097 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −6145.55 | −0.289879 | ||||||||
\(767\) | −2844.32 | −0.133901 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −2007.30 | −0.0941289 | −0.0470645 | − | 0.998892i | \(-0.514987\pi\) | ||||
−0.0470645 | + | 0.998892i | \(0.514987\pi\) | |||||||
\(770\) | 764.942 | 0.0358008 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 58293.9 | 2.71767 | ||||||||
\(773\) | −27280.6 | −1.26936 | −0.634679 | − | 0.772776i | \(-0.718868\pi\) | ||||
−0.634679 | + | 0.772776i | \(0.718868\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 4867.91 | 0.225627 | ||||||||
\(776\) | 78511.2 | 3.63194 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 6044.21 | 0.278529 | ||||||||
\(779\) | 2280.96 | 0.104909 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −27809.3 | −1.27413 | ||||||||
\(782\) | 6443.53 | 0.294655 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −35878.1 | −1.63439 | ||||||||
\(785\) | 6779.77 | 0.308255 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 31184.4 | 1.41246 | 0.706228 | − | 0.707984i | \(-0.250395\pi\) | ||||
0.706228 | + | 0.707984i | \(0.250395\pi\) | |||||||
\(788\) | 72019.5 | 3.25582 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −4286.73 | −0.193057 | ||||||||
\(791\) | 2927.01 | 0.131571 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1236.18 | 0.0553568 | ||||||||
\(794\) | 17167.3 | 0.767309 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 50891.0 | 2.26606 | ||||||||
\(797\) | −32389.4 | −1.43951 | −0.719756 | − | 0.694228i | \(-0.755746\pi\) | ||||
−0.719756 | + | 0.694228i | \(0.755746\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −27601.5 | −1.22212 | ||||||||
\(800\) | −17600.1 | −0.777823 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 11862.4 | 0.522288 | ||||||||
\(803\) | −27505.9 | −1.20880 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −104.856 | −0.00459090 | ||||||||
\(806\) | −1368.19 | −0.0597919 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 23812.6 | 1.03679 | ||||||||
\(809\) | 43432.4 | 1.88752 | 0.943759 | − | 0.330634i | \(-0.107262\pi\) | ||||
0.943759 | + | 0.330634i | \(0.107262\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −34577.5 | −1.49714 | −0.748570 | − | 0.663055i | \(-0.769259\pi\) | ||||
−0.748570 | + | 0.663055i | \(0.769259\pi\) | |||||||
\(812\) | −557.052 | −0.0240748 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −37494.3 | −1.61447 | ||||||||
\(815\) | 5894.37 | 0.253338 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −33184.3 | −1.42102 | ||||||||
\(818\) | 61115.1 | 2.61227 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 1124.97 | 0.0479095 | ||||||||
\(821\) | −11403.8 | −0.484769 | −0.242384 | − | 0.970180i | \(-0.577929\pi\) | ||||
−0.242384 | + | 0.970180i | \(0.577929\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 9128.97 | 0.386654 | 0.193327 | − | 0.981134i | \(-0.438072\pi\) | ||||
0.193327 | + | 0.981134i | \(0.438072\pi\) | |||||||
\(824\) | −42214.5 | −1.78472 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −4558.11 | −0.192006 | ||||||||
\(827\) | 35646.9 | 1.49887 | 0.749434 | − | 0.662079i | \(-0.230326\pi\) | ||||
0.749434 | + | 0.662079i | \(0.230326\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 27340.1 | 1.14543 | 0.572714 | − | 0.819755i | \(-0.305891\pi\) | ||||
0.572714 | + | 0.819755i | \(0.305891\pi\) | |||||||
\(830\) | 10183.2 | 0.425861 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −717.451 | −0.0298956 | ||||||||
\(833\) | 18730.7 | 0.779089 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −735.321 | −0.0304753 | ||||||||
\(836\) | 45067.1 | 1.86445 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −7905.53 | −0.325886 | ||||||||
\(839\) | 36805.4 | 1.51450 | 0.757248 | − | 0.653127i | \(-0.226543\pi\) | ||||
0.757248 | + | 0.653127i | \(0.226543\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −24165.9 | −0.990851 | ||||||||
\(842\) | −35931.6 | −1.47065 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −15839.0 | −0.645971 | ||||||||
\(845\) | −4640.87 | −0.188936 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −492.378 | −0.0199744 | ||||||||
\(848\) | 51460.9 | 2.08393 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 33716.8 | 1.36056 | ||||||||
\(851\) | 5139.60 | 0.207031 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 9553.72 | 0.383485 | 0.191743 | − | 0.981445i | \(-0.438586\pi\) | ||||
0.191743 | + | 0.981445i | \(0.438586\pi\) | |||||||
\(854\) | 1981.01 | 0.0793779 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 86695.6 | 3.46167 | ||||||||
\(857\) | 37407.4 | 1.49103 | 0.745515 | − | 0.666489i | \(-0.232204\pi\) | ||||
0.745515 | + | 0.666489i | \(0.232204\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −10460.8 | −0.415506 | −0.207753 | − | 0.978181i | \(-0.566615\pi\) | ||||
−0.207753 | + | 0.978181i | \(0.566615\pi\) | |||||||
\(860\) | −16366.6 | −0.648948 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −71255.7 | −2.81552 | ||||||||
\(863\) | −28475.5 | −1.12319 | −0.561597 | − | 0.827411i | \(-0.689813\pi\) | ||||
−0.561597 | + | 0.827411i | \(0.689813\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 2753.96 | 0.108251 | ||||||||
\(866\) | −63020.7 | −2.47290 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −1508.39 | −0.0589839 | ||||||||
\(869\) | −13011.7 | −0.507929 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 139.764 | 0.00543709 | ||||||||
\(872\) | 6199.52 | 0.240759 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −8979.68 | −0.347531 | ||||||||
\(875\) | −1118.54 | −0.0432155 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 9710.29 | 0.373880 | 0.186940 | − | 0.982371i | \(-0.440143\pi\) | ||||
0.186940 | + | 0.982371i | \(0.440143\pi\) | |||||||
\(878\) | −47803.8 | −1.83747 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 7572.55 | 0.290080 | ||||||||
\(881\) | −14335.7 | −0.548220 | −0.274110 | − | 0.961698i | \(-0.588383\pi\) | ||||
−0.274110 | + | 0.961698i | \(0.588383\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 12712.0 | 0.484475 | 0.242238 | − | 0.970217i | \(-0.422119\pi\) | ||||
0.242238 | + | 0.970217i | \(0.422119\pi\) | |||||||
\(884\) | −6519.43 | −0.248045 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −45227.9 | −1.71497 | ||||||||
\(887\) | −14044.4 | −0.531640 | −0.265820 | − | 0.964023i | \(-0.585643\pi\) | ||||
−0.265820 | + | 0.964023i | \(0.585643\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −5146.18 | −0.194148 | ||||||||
\(890\) | 4497.49 | 0.169389 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 69387.6 | 2.60456 | ||||||||
\(893\) | 38465.3 | 1.44143 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 2538.42 | 0.0948044 | ||||||||
\(896\) | −3623.39 | −0.135099 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 42547.2 | 1.58109 | ||||||||
\(899\) | 604.185 | 0.0224146 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −26865.9 | −0.993378 | ||||||||
\(902\) | 4963.49 | 0.183222 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 67553.4 | 2.48539 | ||||||||
\(905\) | −793.273 | −0.0291373 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −21352.9 | −0.781710 | −0.390855 | − | 0.920452i | \(-0.627821\pi\) | ||||
−0.390855 | + | 0.920452i | \(0.627821\pi\) | |||||||
\(908\) | −94584.2 | −3.45692 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 154.211 | 0.00561764 | ||||||||
\(911\) | −51282.0 | −1.86504 | −0.932519 | − | 0.361121i | \(-0.882394\pi\) | ||||
−0.932519 | + | 0.361121i | \(0.882394\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 30909.4 | 1.12043 | ||||||||
\(914\) | 15490.3 | 0.560583 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 67556.6 | 2.43683 | ||||||||
\(917\) | −1564.35 | −0.0563353 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −10026.8 | −0.359905 | −0.179953 | − | 0.983675i | \(-0.557594\pi\) | ||||
−0.179953 | + | 0.983675i | \(0.557594\pi\) | |||||||
\(920\) | −2419.99 | −0.0867226 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 92892.9 | 3.31807 | ||||||||
\(923\) | −5606.30 | −0.199928 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 26893.7 | 0.955956 | ||||||||
\(926\) | 58818.7 | 2.08737 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −2184.45 | −0.0772718 | ||||||||
\(929\) | 12614.6 | 0.445501 | 0.222750 | − | 0.974875i | \(-0.428496\pi\) | ||||
0.222750 | + | 0.974875i | \(0.428496\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −26103.1 | −0.918897 | ||||||||
\(932\) | −35235.0 | −1.23837 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 28333.0 | 0.992595 | ||||||||
\(935\) | −3953.37 | −0.138277 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 47032.5 | 1.63979 | 0.819896 | − | 0.572513i | \(-0.194031\pi\) | ||||
0.819896 | + | 0.572513i | \(0.194031\pi\) | |||||||
\(938\) | 223.975 | 0.00779643 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 18971.2 | 0.658269 | ||||||||
\(941\) | −40313.9 | −1.39660 | −0.698298 | − | 0.715807i | \(-0.746059\pi\) | ||||
−0.698298 | + | 0.715807i | \(0.746059\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −680.377 | −0.0234954 | ||||||||
\(944\) | −45123.0 | −1.55575 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −72210.8 | −2.48179 | ||||||||
\(947\) | −2843.88 | −0.0975857 | −0.0487928 | − | 0.998809i | \(-0.515537\pi\) | ||||
−0.0487928 | + | 0.998809i | \(0.515537\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −5545.15 | −0.189677 | ||||||||
\(950\) | −46987.5 | −1.60471 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −5708.79 | −0.194352 | ||||||||
\(953\) | −47683.6 | −1.62080 | −0.810401 | − | 0.585876i | \(-0.800751\pi\) | ||||
−0.810401 | + | 0.585876i | \(0.800751\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −4081.38 | −0.138294 | ||||||||
\(956\) | 55472.2 | 1.87667 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 11765.0 | 0.396773 | ||||||||
\(959\) | −1584.19 | −0.0533434 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −28155.0 | −0.945084 | ||||||||
\(962\) | −7558.80 | −0.253332 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −56258.0 | −1.87961 | ||||||||
\(965\) | 7126.36 | 0.237726 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −29531.0 | −0.982061 | −0.491031 | − | 0.871142i | \(-0.663380\pi\) | ||||
−0.491031 | + | 0.871142i | \(0.663380\pi\) | |||||||
\(968\) | −11363.7 | −0.377318 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 17565.0 | 0.581420 | ||||||||
\(971\) | −36965.3 | −1.22170 | −0.610851 | − | 0.791746i | \(-0.709172\pi\) | ||||
−0.610851 | + | 0.791746i | \(0.709172\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 5695.27 | 0.187648 | ||||||||
\(974\) | 41849.2 | 1.37673 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 19611.0 | 0.643170 | ||||||||
\(977\) | 7366.55 | 0.241225 | 0.120612 | − | 0.992700i | \(-0.461514\pi\) | ||||
0.120612 | + | 0.992700i | \(0.461514\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 13651.4 | 0.445659 | ||||||||
\(980\) | −12874.1 | −0.419641 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −53763.4 | −1.74711 | ||||||||
\(983\) | 16255.6 | 0.527440 | 0.263720 | − | 0.964599i | \(-0.415051\pi\) | ||||
0.263720 | + | 0.964599i | \(0.415051\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 8804.29 | 0.284800 | ||||||||
\(986\) | 4184.78 | 0.135163 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 9085.45 | 0.292557 | ||||||||
\(989\) | 9898.41 | 0.318252 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 13730.4 | 0.440121 | 0.220061 | − | 0.975486i | \(-0.429374\pi\) | ||||
0.220061 | + | 0.975486i | \(0.429374\pi\) | |||||||
\(992\) | −5915.07 | −0.189318 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −8984.27 | −0.286684 | ||||||||
\(995\) | 6221.36 | 0.198221 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −49655.8 | −1.57735 | −0.788673 | − | 0.614813i | \(-0.789232\pi\) | ||||
−0.788673 | + | 0.614813i | \(0.789232\pi\) | |||||||
\(998\) | −27864.3 | −0.883795 | ||||||||
\(999\) | 0 | 0 |
(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 | 207.4.a.h.1.5 | yes | 5 | |
3.2 | odd | 2 | 207.4.a.g.1.1 | ✓ | 5 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
207.4.a.g.1.1 | ✓ | 5 | 3.2 | odd | 2 | ||
207.4.a.h.1.5 | yes | 5 | 1.1 | even | 1 | trivial |