Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1840,4,Mod(1,1840)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1840, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 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("1840.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1840 = 2^{4} \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1840.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: | \(108.563514411\) |
Analytic rank: | \(1\) |
Dimension: | \(4\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{4} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 2x^{3} - 60x^{2} - 45x + 108 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 3 \) |
Twist minimal: | no (minimal twist has level 230) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(1.01192\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1840.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −2.98808 | −0.575055 | −0.287528 | − | 0.957772i | \(-0.592833\pi\) | ||||
−0.287528 | + | 0.957772i | \(0.592833\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 5.00000 | 0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.98517 | −0.161184 | −0.0805921 | − | 0.996747i | \(-0.525681\pi\) | ||||
−0.0805921 | + | 0.996747i | \(0.525681\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −18.0714 | −0.669311 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −68.6262 | −1.88105 | −0.940527 | − | 0.339720i | \(-0.889668\pi\) | ||||
−0.940527 | + | 0.339720i | \(0.889668\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −12.0028 | −0.256074 | −0.128037 | − | 0.991769i | \(-0.540868\pi\) | ||||
−0.128037 | + | 0.991769i | \(0.540868\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −14.9404 | −0.257173 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 106.208 | 1.51525 | 0.757623 | − | 0.652693i | \(-0.226361\pi\) | ||||
0.757623 | + | 0.652693i | \(0.226361\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 48.4891 | 0.585482 | 0.292741 | − | 0.956192i | \(-0.405433\pi\) | ||||
0.292741 | + | 0.956192i | \(0.405433\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 8.91992 | 0.0926898 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 23.0000 | 0.208514 | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 25.0000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 134.677 | 0.959946 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 135.226 | 0.865890 | 0.432945 | − | 0.901420i | \(-0.357474\pi\) | ||||
0.432945 | + | 0.901420i | \(0.357474\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 230.782 | 1.33709 | 0.668544 | − | 0.743673i | \(-0.266918\pi\) | ||||
0.668544 | + | 0.743673i | \(0.266918\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 205.060 | 1.08171 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −14.9259 | −0.0720838 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −107.956 | −0.479672 | −0.239836 | − | 0.970813i | \(-0.577094\pi\) | ||||
−0.239836 | + | 0.970813i | \(0.577094\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 35.8651 | 0.147257 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 394.637 | 1.50322 | 0.751610 | − | 0.659608i | \(-0.229278\pi\) | ||||
0.751610 | + | 0.659608i | \(0.229278\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −136.063 | −0.482543 | −0.241272 | − | 0.970458i | \(-0.577564\pi\) | ||||
−0.241272 | + | 0.970458i | \(0.577564\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −90.3570 | −0.299325 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 50.4512 | 0.156576 | 0.0782880 | − | 0.996931i | \(-0.475055\pi\) | ||||
0.0782880 | + | 0.996931i | \(0.475055\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −334.089 | −0.974020 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −317.357 | −0.871350 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −414.707 | −1.07480 | −0.537400 | − | 0.843327i | \(-0.680594\pi\) | ||||
−0.537400 | + | 0.843327i | \(0.680594\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −343.131 | −0.841232 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −144.889 | −0.336685 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 183.586 | 0.405100 | 0.202550 | − | 0.979272i | \(-0.435077\pi\) | ||||
0.202550 | + | 0.979272i | \(0.435077\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −98.4751 | −0.206696 | −0.103348 | − | 0.994645i | \(-0.532956\pi\) | ||||
−0.103348 | + | 0.994645i | \(0.532956\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 53.9463 | 0.107882 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −60.0138 | −0.114520 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −136.925 | −0.249672 | −0.124836 | − | 0.992177i | \(-0.539840\pi\) | ||||
−0.124836 | + | 0.992177i | \(0.539840\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −68.7257 | −0.119907 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 708.800 | 1.18478 | 0.592388 | − | 0.805653i | \(-0.298185\pi\) | ||||
0.592388 | + | 0.805653i | \(0.298185\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −689.605 | −1.10565 | −0.552823 | − | 0.833299i | \(-0.686449\pi\) | ||||
−0.552823 | + | 0.833299i | \(0.686449\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −74.7019 | −0.115011 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 204.861 | 0.303196 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −546.583 | −0.778423 | −0.389212 | − | 0.921148i | \(-0.627252\pi\) | ||||
−0.389212 | + | 0.921148i | \(0.627252\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 85.5038 | 0.117289 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 20.2622 | 0.0267959 | 0.0133980 | − | 0.999910i | \(-0.495735\pi\) | ||||
0.0133980 | + | 0.999910i | \(0.495735\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 531.039 | 0.677638 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −404.065 | −0.497935 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −1087.31 | −1.29499 | −0.647495 | − | 0.762069i | \(-0.724183\pi\) | ||||
−0.647495 | + | 0.762069i | \(0.724183\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 35.8303 | 0.0412751 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −689.595 | −0.768900 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 242.445 | 0.261836 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1115.90 | −1.16807 | −0.584036 | − | 0.811728i | \(-0.698527\pi\) | ||||
−0.584036 | + | 0.811728i | \(0.698527\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1240.17 | 1.25901 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −134.565 | −0.132572 | −0.0662859 | − | 0.997801i | \(-0.521115\pi\) | ||||
−0.0662859 | + | 0.997801i | \(0.521115\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 925.953 | 0.885795 | 0.442898 | − | 0.896572i | \(-0.353951\pi\) | ||||
0.442898 | + | 0.896572i | \(0.353951\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 44.5996 | 0.0414522 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −1871.13 | −1.69055 | −0.845273 | − | 0.534334i | \(-0.820562\pi\) | ||||
−0.845273 | + | 0.534334i | \(0.820562\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −978.242 | −0.859620 | −0.429810 | − | 0.902919i | \(-0.641419\pi\) | ||||
−0.429810 | + | 0.902919i | \(0.641419\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 322.581 | 0.275838 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −1760.45 | −1.46557 | −0.732786 | − | 0.680459i | \(-0.761780\pi\) | ||||
−0.732786 | + | 0.680459i | \(0.761780\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 115.000 | 0.0932505 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 216.907 | 0.171393 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −317.049 | −0.244234 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 3378.56 | 2.53836 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −1179.21 | −0.864434 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 125.000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1260.87 | 0.880980 | 0.440490 | − | 0.897758i | \(-0.354805\pi\) | ||||
0.440490 | + | 0.897758i | \(0.354805\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 406.566 | 0.277489 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −444.283 | −0.296314 | −0.148157 | − | 0.988964i | \(-0.547334\pi\) | ||||
−0.148157 | + | 0.988964i | \(0.547334\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −144.748 | −0.0943705 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 673.384 | 0.429301 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 429.072 | 0.267577 | 0.133789 | − | 0.991010i | \(-0.457286\pi\) | ||||
0.133789 | + | 0.991010i | \(0.457286\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 249.755 | 0.152402 | 0.0762012 | − | 0.997092i | \(-0.475721\pi\) | ||||
0.0762012 | + | 0.997092i | \(0.475721\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −150.752 | −0.0900398 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 823.704 | 0.481689 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 676.129 | 0.387238 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 998.282 | 0.560115 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −1564.18 | −0.860020 | −0.430010 | − | 0.902824i | \(-0.641490\pi\) | ||||
−0.430010 | + | 0.902824i | \(0.641490\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1860.04 | 1.00244 | 0.501219 | − | 0.865321i | \(-0.332885\pi\) | ||||
0.501219 | + | 0.865321i | \(0.332885\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −1919.32 | −1.01417 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1153.91 | 0.597964 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2834.52 | 1.44089 | 0.720445 | − | 0.693512i | \(-0.243938\pi\) | ||||
0.720445 | + | 0.693512i | \(0.243938\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 1239.18 | 0.618070 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −68.6590 | −0.0336092 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −2114.51 | −1.01608 | −0.508041 | − | 0.861333i | \(-0.669630\pi\) | ||||
−0.508041 | + | 0.861333i | \(0.669630\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 1025.30 | 0.483755 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −2487.41 | −1.15258 | −0.576291 | − | 0.817244i | \(-0.695501\pi\) | ||||
−0.576291 | + | 0.817244i | \(0.695501\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −2052.93 | −0.934426 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −876.266 | −0.391870 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 3672.32 | 1.61388 | 0.806939 | − | 0.590634i | \(-0.201122\pi\) | ||||
0.806939 | + | 0.590634i | \(0.201122\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −74.6293 | −0.0322368 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −548.569 | −0.232955 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 3224.63 | 1.34648 | 0.673240 | − | 0.739424i | \(-0.264902\pi\) | ||||
0.673240 | + | 0.739424i | \(0.264902\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −2224.23 | −0.913401 | −0.456700 | − | 0.889621i | \(-0.650969\pi\) | ||||
−0.456700 | + | 0.889621i | \(0.650969\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 294.251 | 0.118862 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −539.780 | −0.214516 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −7288.64 | −2.85026 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −402.033 | −0.154728 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −3273.53 | −1.24013 | −0.620063 | − | 0.784552i | \(-0.712893\pi\) | ||||
−0.620063 | + | 0.784552i | \(0.712893\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 5126.86 | 1.91212 | 0.956062 | − | 0.293166i | \(-0.0947089\pi\) | ||||
0.956062 | + | 0.293166i | \(0.0947089\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 179.326 | 0.0658553 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 3262.57 | 1.17994 | 0.589971 | − | 0.807425i | \(-0.299139\pi\) | ||||
0.589971 | + | 0.807425i | \(0.299139\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 168.282 | 0.0599457 | 0.0299728 | − | 0.999551i | \(-0.490458\pi\) | ||||
0.0299728 | + | 0.999551i | \(0.490458\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 409.141 | 0.143575 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −403.673 | −0.139568 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1973.19 | 0.672260 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −415.642 | −0.139561 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −3327.62 | −1.10132 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −4197.01 | −1.36936 | −0.684678 | − | 0.728846i | \(-0.740057\pi\) | ||||
−0.684678 | + | 0.728846i | \(0.740057\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −2117.95 | −0.681312 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −680.313 | −0.215800 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −688.925 | −0.215518 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 2060.59 | 0.635807 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1274.79 | −0.388015 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −5192.66 | −1.55931 | −0.779656 | − | 0.626208i | \(-0.784606\pi\) | ||||
−0.779656 | + | 0.626208i | \(0.784606\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −451.785 | −0.133862 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −4701.24 | −1.37459 | −0.687295 | − | 0.726378i | \(-0.741202\pi\) | ||||
−0.687295 | + | 0.726378i | \(0.741202\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −2125.17 | −0.613255 | −0.306628 | − | 0.951830i | \(-0.599201\pi\) | ||||
−0.306628 | + | 0.951830i | \(0.599201\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −612.141 | −0.174355 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −1646.67 | −0.462992 | −0.231496 | − | 0.972836i | \(-0.574362\pi\) | ||||
−0.231496 | + | 0.972836i | \(0.574362\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 252.256 | 0.0700229 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 1633.23 | 0.447636 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −2877.88 | −0.778888 | −0.389444 | − | 0.921050i | \(-0.627333\pi\) | ||||
−0.389444 | + | 0.921050i | \(0.627333\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −4244.54 | −1.13450 | −0.567251 | − | 0.823545i | \(-0.691993\pi\) | ||||
−0.567251 | + | 0.823545i | \(0.691993\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −3891.76 | −1.02739 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −1670.44 | −0.435595 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −582.003 | −0.149927 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −60.5449 | −0.0154092 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −4401.99 | −1.10698 | −0.553488 | − | 0.832857i | \(-0.686704\pi\) | ||||
−0.553488 | + | 0.832857i | \(0.686704\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1578.40 | −0.392227 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −1586.78 | −0.389680 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 1694.78 | 0.411352 | 0.205676 | − | 0.978620i | \(-0.434061\pi\) | ||||
0.205676 | + | 0.978620i | \(0.434061\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 322.268 | 0.0773156 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −2443.72 | −0.579550 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 727.462 | 0.170560 | 0.0852799 | − | 0.996357i | \(-0.472822\pi\) | ||||
0.0852799 | + | 0.996357i | \(0.472822\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −2073.54 | −0.480666 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 3248.95 | 0.744691 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 94.9937 | 0.0215311 | 0.0107656 | − | 0.999942i | \(-0.496573\pi\) | ||||
0.0107656 | + | 0.999942i | \(0.496573\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −5321.54 | −1.19284 | −0.596422 | − | 0.802671i | \(-0.703411\pi\) | ||||
−0.596422 | + | 0.802671i | \(0.703411\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −107.064 | −0.0237355 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −1715.66 | −0.376211 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 2561.25 | 0.555562 | 0.277781 | − | 0.960644i | \(-0.410401\pi\) | ||||
0.277781 | + | 0.960644i | \(0.410401\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −4170.56 | −0.894928 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −8753.73 | −1.85838 | −0.929188 | − | 0.369606i | \(-0.879493\pi\) | ||||
−0.929188 | + | 0.369606i | \(0.879493\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 2400.14 | 0.504147 | 0.252073 | − | 0.967708i | \(-0.418888\pi\) | ||||
0.252073 | + | 0.967708i | \(0.418888\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −724.445 | −0.150570 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −1178.06 | −0.242295 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 6367.09 | 1.29597 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 3334.41 | 0.671706 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 1045.56 | 0.208472 | 0.104236 | − | 0.994553i | \(-0.466760\pi\) | ||||
0.104236 | + | 0.994553i | \(0.466760\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 917.931 | 0.181166 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −9242.36 | −1.80571 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −276.063 | −0.0533952 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 406.171 | 0.0777784 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 402.091 | 0.0762361 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −492.376 | −0.0924372 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 7905.84 | 1.46974 | 0.734870 | − | 0.678208i | \(-0.237243\pi\) | ||||
0.734870 | + | 0.678208i | \(0.237243\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −2766.82 | −0.509381 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 9227.63 | 1.68248 | 0.841240 | − | 0.540662i | \(-0.181826\pi\) | ||||
0.841240 | + | 0.540662i | \(0.181826\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 2712.57 | 0.489852 | 0.244926 | − | 0.969542i | \(-0.421236\pi\) | ||||
0.244926 | + | 0.969542i | \(0.421236\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 269.731 | 0.0482465 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −3440.29 | −0.609546 | −0.304773 | − | 0.952425i | \(-0.598581\pi\) | ||||
−0.304773 | + | 0.952425i | \(0.598581\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −9280.04 | −1.62879 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 5591.06 | 0.972158 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 5149.92 | 0.887149 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −300.069 | −0.0512149 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 2923.06 | 0.494329 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −150.606 | −0.0252376 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −3259.75 | −0.541305 | −0.270652 | − | 0.962677i | \(-0.587239\pi\) | ||||
−0.270652 | + | 0.962677i | \(0.587239\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 1950.92 | 0.321050 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −684.623 | −0.111657 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 7163.38 | 1.15790 | 0.578952 | − | 0.815361i | \(-0.303462\pi\) | ||||
0.578952 | + | 0.815361i | \(0.303462\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 5260.37 | 0.842785 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −15837.7 | −2.51513 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 2021.23 | 0.318181 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −343.629 | −0.0536242 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 1833.45 | 0.283645 | 0.141822 | − | 0.989892i | \(-0.454704\pi\) | ||||
0.141822 | + | 0.989892i | \(0.454704\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −10400.3 | −1.59517 | −0.797583 | − | 0.603209i | \(-0.793888\pi\) | ||||
−0.797583 | + | 0.603209i | \(0.793888\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1616.49 | −0.245818 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −3156.48 | −0.475928 | −0.237964 | − | 0.971274i | \(-0.576480\pi\) | ||||
−0.237964 | + | 0.971274i | \(0.576480\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 3544.00 | 0.529848 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 947.365 | 0.140448 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 9324.16 | 1.37078 | 0.685390 | − | 0.728176i | \(-0.259632\pi\) | ||||
0.685390 | + | 0.728176i | \(0.259632\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −4507.81 | −0.657211 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −10095.4 | −1.45970 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −3448.02 | −0.494460 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −3802.68 | −0.540867 | −0.270434 | − | 0.962739i | \(-0.587167\pi\) | ||||
−0.270434 | + | 0.962739i | \(0.587167\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −7131.65 | −1.00612 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1237.97 | 0.173241 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −8928.03 | −1.23935 | −0.619673 | − | 0.784860i | \(-0.712735\pi\) | ||||
−0.619673 | + | 0.784860i | \(0.712735\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −373.509 | −0.0514345 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −1623.08 | −0.221732 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −3798.13 | −0.514768 | −0.257384 | − | 0.966309i | \(-0.582860\pi\) | ||||
−0.257384 | + | 0.966309i | \(0.582860\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −3767.58 | −0.506612 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −1456.41 | −0.194306 | −0.0971530 | − | 0.995269i | \(-0.530974\pi\) | ||||
−0.0971530 | + | 0.995269i | \(0.530974\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1024.31 | 0.135593 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 2458.84 | 0.322972 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −8211.34 | −1.07026 | −0.535130 | − | 0.844769i | \(-0.679738\pi\) | ||||
−0.535130 | + | 0.844769i | \(0.679738\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2442.78 | 0.315950 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 1327.55 | 0.170397 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −2732.92 | −0.348121 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 914.365 | 0.115594 | 0.0577968 | − | 0.998328i | \(-0.481592\pi\) | ||||
0.0577968 | + | 0.998328i | \(0.481592\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 432.519 | 0.0542683 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 9414.97 | 1.17247 | 0.586236 | − | 0.810140i | \(-0.300609\pi\) | ||||
0.586236 | + | 0.810140i | \(0.300609\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −2770.02 | −0.342394 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 427.519 | 0.0524533 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 7408.62 | 0.902289 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 3299.41 | 0.398889 | 0.199444 | − | 0.979909i | \(-0.436086\pi\) | ||||
0.199444 | + | 0.979909i | \(0.436086\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −1282.10 | −0.153872 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −548.037 | −0.0652957 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 101.311 | 0.0119835 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −746.286 | −0.0876398 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 3554.64 | 0.414452 | 0.207226 | − | 0.978293i | \(-0.433556\pi\) | ||||
0.207226 | + | 0.978293i | \(0.433556\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 11655.5 | 1.34930 | 0.674649 | − | 0.738139i | \(-0.264295\pi\) | ||||
0.674649 | + | 0.738139i | \(0.264295\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −911.725 | −0.104798 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 2655.19 | 0.303049 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 293.965 | 0.0333161 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −2461.29 | −0.276998 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −4727.38 | −0.528330 | −0.264165 | − | 0.964478i | \(-0.585096\pi\) | ||||
−0.264165 | + | 0.964478i | \(0.585096\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 3936.24 | 0.436868 | 0.218434 | − | 0.975852i | \(-0.429905\pi\) | ||||
0.218434 | + | 0.975852i | \(0.429905\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −2020.33 | −0.222683 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 1115.25 | 0.122081 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −6859.77 | −0.745784 | −0.372892 | − | 0.927875i | \(-0.621634\pi\) | ||||
−0.372892 | + | 0.927875i | \(0.621634\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 6037.45 | 0.651922 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −16814.4 | −1.80334 | −0.901668 | − | 0.432430i | \(-0.857656\pi\) | ||||
−0.901668 | + | 0.432430i | \(0.857656\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −5436.53 | −0.579137 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 4673.90 | 0.494559 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 10673.8 | 1.12189 | 0.560943 | − | 0.827855i | \(-0.310439\pi\) | ||||
0.560943 | + | 0.827855i | \(0.310439\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −27082.5 | −2.82764 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −5557.94 | −0.576457 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 179.152 | 0.0184588 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 15493.0 | 1.58585 | 0.792926 | − | 0.609318i | \(-0.208557\pi\) | ||||
0.792926 | + | 0.609318i | \(0.208557\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 14303.7 | 1.45455 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −10793.0 | −1.09041 | −0.545207 | − | 0.838302i | \(-0.683549\pi\) | ||||
−0.545207 | + | 0.838302i | \(0.683549\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 6165.87 | 0.618904 | 0.309452 | − | 0.950915i | \(-0.399854\pi\) | ||||
0.309452 | + | 0.950915i | \(0.399854\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −3447.97 | −0.343862 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 10736.4 | 1.06386 | 0.531929 | − | 0.846789i | \(-0.321467\pi\) | ||||
0.531929 | + | 0.846789i | \(0.321467\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 408.744 | 0.0402431 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −8469.77 | −0.828591 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 9337.47 | 0.907690 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1212.23 | 0.117096 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 7494.35 | 0.719377 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −6333.30 | −0.604125 | −0.302062 | − | 0.953288i | \(-0.597675\pi\) | ||||
−0.302062 | + | 0.953288i | \(0.597675\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1295.77 | 0.122832 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 205.158 | 0.0193272 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −5579.52 | −0.522377 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 16833.3 | 1.56630 | 0.783149 | − | 0.621834i | \(-0.213612\pi\) | ||||
0.783149 | + | 0.621834i | \(0.213612\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 6318.33 | 0.584304 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 4.80428 | 0.000441577 0 | 0.000220788 | − | 1.00000i | \(-0.499930\pi\) | ||||
0.000220788 | 1.00000i | \(0.499930\pi\) | ||||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 14362.0 | 1.31204 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 6200.86 | 0.563046 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −2115.89 | −0.190967 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −21206.9 | −1.90251 | −0.951253 | − | 0.308412i | \(-0.900203\pi\) | ||||
−0.951253 | + | 0.308412i | \(0.900203\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 7432.56 | 0.662799 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −14513.7 | −1.28655 | −0.643275 | − | 0.765635i | \(-0.722425\pi\) | ||||
−0.643275 | + | 0.765635i | \(0.722425\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −672.827 | −0.0592879 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 6134.32 | 0.537347 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −2545.77 | −0.221689 | −0.110844 | − | 0.993838i | \(-0.535355\pi\) | ||||
−0.110844 | + | 0.993838i | \(0.535355\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 2058.59 | 0.178213 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 6530.35 | 0.562032 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 4629.77 | 0.396140 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −3462.28 | −0.294528 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −10973.2 | −0.928070 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −21343.1 | −1.79473 | −0.897367 | − | 0.441285i | \(-0.854523\pi\) | ||||
−0.897367 | + | 0.441285i | \(0.854523\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 789.191 | 0.0659827 | 0.0329913 | − | 0.999456i | \(-0.489497\pi\) | ||||
0.0329913 | + | 0.999456i | \(0.489497\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 222.998 | 0.0185380 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 24510.9 | 2.02602 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 529.000 | 0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −3317.66 | −0.271138 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −4736.74 | −0.384936 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −9355.63 | −0.756036 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −9635.42 | −0.774300 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 22927.2 | 1.83218 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 13405.1 | 1.06531 | 0.532653 | − | 0.846334i | \(-0.321195\pi\) | ||||
0.532653 | + | 0.846334i | \(0.321195\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 6646.16 | 0.525256 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −4891.21 | −0.384434 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −10088.8 | −0.788605 | −0.394303 | − | 0.918981i | \(-0.629014\pi\) | ||||
−0.394303 | + | 0.918981i | \(0.629014\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 1779.58 | 0.138344 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 6556.98 | 0.506963 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 1631.65 | 0.125470 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 1612.90 | 0.123359 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −11657.7 | −0.886809 | −0.443405 | − | 0.896322i | \(-0.646230\pi\) | ||||
−0.443405 | + | 0.896322i | \(0.646230\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1633.13 | 0.123567 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 21779.0 | 1.63906 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −4839.43 | −0.362270 | −0.181135 | − | 0.983458i | \(-0.557977\pi\) | ||||
−0.181135 | + | 0.983458i | \(0.557977\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −8802.27 | −0.655424 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −255.244 | −0.0189052 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −646.680 | −0.0476454 | −0.0238227 | − | 0.999716i | \(-0.507584\pi\) | ||||
−0.0238227 | + | 0.999716i | \(0.507584\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −3263.66 | −0.239194 | −0.119597 | − | 0.992822i | \(-0.538160\pi\) | ||||
−0.119597 | + | 0.992822i | \(0.538160\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 9781.54 | 0.713141 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 575.000 | 0.0417029 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −8980.46 | −0.647940 | −0.323970 | − | 0.946067i | \(-0.605018\pi\) | ||||
−0.323970 | + | 0.946067i | \(0.605018\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −15319.5 | −1.09958 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −60.4861 | −0.00431908 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 28459.8 | 2.02176 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 1084.53 | 0.0766495 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 6538.05 | 0.459718 | 0.229859 | − | 0.973224i | \(-0.426174\pi\) | ||||
0.229859 | + | 0.973224i | \(0.426174\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 11190.4 | 0.782841 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −9748.80 | −0.678532 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 7803.41 | 0.540384 | 0.270192 | − | 0.962806i | \(-0.412913\pi\) | ||||
0.270192 | + | 0.962806i | \(0.412913\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −1585.24 | −0.109225 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −502.839 | −0.0344721 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 27812.0 | 1.89711 | 0.948555 | − | 0.316613i | \(-0.102546\pi\) | ||||
0.948555 | + | 0.316613i | \(0.102546\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 483.216 | 0.0327966 | 0.0163983 | − | 0.999866i | \(-0.494780\pi\) | ||||
0.0163983 | + | 0.999866i | \(0.494780\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 2474.42 | 0.167108 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 16892.8 | 1.13519 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 18104.0 | 1.21058 | 0.605289 | − | 0.796006i | \(-0.293058\pi\) | ||||
0.605289 | + | 0.796006i | \(0.293058\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 1206.20 | 0.0802592 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −605.554 | −0.0400951 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 2191.19 | 0.144374 | 0.0721870 | − | 0.997391i | \(-0.477002\pi\) | ||||
0.0721870 | + | 0.997391i | \(0.477002\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −5896.03 | −0.386587 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −8243.06 | −0.537849 | −0.268925 | − | 0.963161i | \(-0.586668\pi\) | ||||
−0.268925 | + | 0.963161i | \(0.586668\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −18298.0 | −1.18814 | −0.594069 | − | 0.804414i | \(-0.702479\pi\) | ||||
−0.594069 | + | 0.804414i | \(0.702479\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 3097.57 | 0.200163 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 3245.80 | 0.208732 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 625.000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 9943.19 | 0.633322 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −11465.8 | −0.726821 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 26472.0 | 1.67010 | 0.835051 | − | 0.550172i | \(-0.185438\pi\) | ||||
0.835051 | + | 0.550172i | \(0.185438\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 12541.0 | 0.787455 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 6304.37 | 0.393986 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 4009.99 | 0.249421 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −12809.0 | −0.792984 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 7411.93 | 0.456714 | 0.228357 | − | 0.973577i | \(-0.426665\pi\) | ||||
0.228357 | + | 0.973577i | \(0.426665\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −8405.96 | −0.515550 | −0.257775 | − | 0.966205i | \(-0.582989\pi\) | ||||
−0.257775 | + | 0.966205i | \(0.582989\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 2032.83 | 0.124097 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −27878.3 | −1.69398 | −0.846992 | − | 0.531605i | \(-0.821589\pi\) | ||||
−0.846992 | + | 0.531605i | \(0.821589\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −12598.8 | −0.762014 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 2058.56 | 0.123934 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −18871.1 | −1.13091 | −0.565455 | − | 0.824779i | \(-0.691299\pi\) | ||||
−0.565455 | + | 0.824779i | \(0.691299\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −2221.42 | −0.132516 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 12462.1 | 0.740021 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 12144.4 | 0.717872 | 0.358936 | − | 0.933362i | \(-0.383140\pi\) | ||||
0.358936 | + | 0.933362i | \(0.383140\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −32504.2 | −1.91266 | −0.956328 | − | 0.292295i | \(-0.905581\pi\) | ||||
−0.956328 | + | 0.292295i | \(0.905581\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 3809.16 | 0.223130 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −723.742 | −0.0422038 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 3110.19 | 0.180551 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 15516.1 | 0.896690 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 6757.98 | 0.388806 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −21387.8 | −1.22502 | −0.612511 | − | 0.790462i | \(-0.709840\pi\) | ||||
−0.612511 | + | 0.790462i | \(0.709840\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 3366.92 | 0.191989 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 10494.6 | 0.595776 | 0.297888 | − | 0.954601i | \(-0.403718\pi\) | ||||
0.297888 | + | 0.954601i | \(0.403718\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 3331.17 | 0.188275 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 14047.6 | 0.790466 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −24014.2 | −1.34535 | −0.672677 | − | 0.739937i | \(-0.734855\pi\) | ||||
−0.672677 | + | 0.739937i | \(0.734855\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 2145.36 | 0.119664 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 6350.18 | 0.352656 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 4977.63 | 0.275229 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 10825.8 | 0.595995 | 0.297997 | − | 0.954567i | \(-0.403681\pi\) | ||||
0.297997 | + | 0.954567i | \(0.403681\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −3702.13 | −0.202933 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 1248.77 | 0.0681564 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 41913.6 | 2.27775 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 4920.38 | 0.266246 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −171.021 | −0.00921451 | −0.00460726 | − | 0.999989i | \(-0.501467\pi\) | ||||
−0.00460726 | + | 0.999989i | \(0.501467\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −5234.69 | −0.280840 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −753.760 | −0.0402670 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 401.701 | 0.0213685 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 28732.7 | 1.52197 | 0.760987 | − | 0.648767i | \(-0.224715\pi\) | ||||
0.760987 | + | 0.648767i | \(0.224715\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 9877.53 | 0.521007 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 5307.99 | 0.278802 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 4118.52 | 0.215418 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 8599.31 | 0.447904 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −6976.22 | −0.361849 | −0.180924 | − | 0.983497i | \(-0.557909\pi\) | ||||
−0.180924 | + | 0.983497i | \(0.557909\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −2764.13 | −0.142776 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 12683.0 | 0.652401 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 3380.65 | 0.173178 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −13114.6 | −0.669042 | −0.334521 | − | 0.942388i | \(-0.608574\pi\) | ||||
−0.334521 | + | 0.942388i | \(0.608574\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 9320.28 | 0.473519 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −14450.9 | −0.731172 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −22681.7 | −1.14293 | −0.571466 | − | 0.820626i | \(-0.693625\pi\) | ||||
−0.571466 | + | 0.820626i | \(0.693625\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 4991.41 | 0.250491 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 9396.62 | 0.469646 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −24237.8 | −1.20650 | −0.603249 | − | 0.797553i | \(-0.706127\pi\) | ||||
−0.603249 | + | 0.797553i | \(0.706127\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 1739.07 | 0.0862163 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −27356.7 | −1.35077 | −0.675384 | − | 0.737466i | \(-0.736022\pi\) | ||||
−0.675384 | + | 0.737466i | \(0.736022\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −7820.92 | −0.384612 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −366.166 | −0.0179348 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 5585.63 | 0.272489 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −22297.8 | −1.08343 | −0.541716 | − | 0.840561i | \(-0.682225\pi\) | ||||
−0.541716 | + | 0.840561i | \(0.682225\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 13153.5 | 0.636573 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 9300.21 | 0.448304 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −16088.4 | −0.772447 | −0.386224 | − | 0.922405i | \(-0.626221\pi\) | ||||
−0.386224 | + | 0.922405i | \(0.626221\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 4716.39 | 0.225552 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 22500.2 | 1.07179 | 0.535894 | − | 0.844285i | \(-0.319975\pi\) | ||||
0.535894 | + | 0.844285i | \(0.319975\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 2920.22 | 0.138557 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −9596.62 | −0.453551 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −2203.54 | −0.103736 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −22677.7 | −1.06343 | −0.531716 | − | 0.846923i | \(-0.678453\pi\) | ||||
−0.531716 | + | 0.846923i | \(0.678453\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −5064.13 | −0.236550 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 20465.1 | 0.952235 | 0.476118 | − | 0.879382i | \(-0.342044\pi\) | ||||
0.476118 | + | 0.879382i | \(0.342044\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 5769.56 | 0.267418 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −962.960 | −0.0444607 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 19135.6 | 0.880108 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −48642.3 | −2.22863 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 18211.8 | 0.831208 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 14172.6 | 0.644386 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 28850.8 | 1.30676 | 0.653379 | − | 0.757031i | \(-0.273351\pi\) | ||||
0.653379 | + | 0.757031i | \(0.273351\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −2173.71 | −0.0980813 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 5255.26 | 0.236227 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1181.97 | 0.0529295 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 6195.88 | 0.276409 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −39332.9 | −1.74811 | −0.874054 | − | 0.485828i | \(-0.838518\pi\) | ||||
−0.874054 | + | 0.485828i | \(0.838518\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 5358.31 | 0.237251 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 19649.1 | 0.866752 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 47325.0 | 2.07978 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −343.295 | −0.0150305 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −283.848 | −0.0123816 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 33946.5 | 1.47527 | 0.737637 | − | 0.675198i | \(-0.235942\pi\) | ||||
0.737637 | + | 0.675198i | \(0.235942\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 20772.2 | 0.899398 | 0.449699 | − | 0.893180i | \(-0.351531\pi\) | ||||
0.449699 | + | 0.893180i | \(0.351531\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 15901.2 | 0.685951 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −10572.6 | −0.454406 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −6597.56 | −0.282521 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −647.504 | −0.0276259 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 6466.37 | 0.274882 | 0.137441 | − | 0.990510i | \(-0.456112\pi\) | ||||
0.137441 | + | 0.990510i | \(0.456112\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 16503.7 | 0.699008 | 0.349504 | − | 0.936935i | \(-0.386350\pi\) | ||||
0.349504 | + | 0.936935i | \(0.386350\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 5126.51 | 0.216342 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −36540.8 | −1.53645 | −0.768227 | − | 0.640177i | \(-0.778861\pi\) | ||||
−0.768227 | + | 0.640177i | \(0.778861\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −24874.5 | −1.04213 | −0.521066 | − | 0.853516i | \(-0.674465\pi\) | ||||
−0.521066 | + | 0.853516i | \(0.674465\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −7653.21 | −0.319479 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −35482.8 | −1.47588 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −12437.0 | −0.515450 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 31081.0 | 1.28353 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −15814.3 | −0.650741 | −0.325370 | − | 0.945587i | \(-0.605489\pi\) | ||||
−0.325370 | + | 0.945587i | \(0.605489\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −6102.97 | −0.250234 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 26156.8 | 1.06867 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −10264.7 | −0.417888 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −10085.6 | −0.409144 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −7171.80 | −0.289912 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −2482.99 | −0.100019 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −31093.2 | −1.24808 | −0.624039 | − | 0.781394i | \(-0.714509\pi\) | ||||
−0.624039 | + | 0.781394i | \(0.714509\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −4381.33 | −0.175250 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 34212.4 | 1.36368 | 0.681840 | − | 0.731501i | \(-0.261180\pi\) | ||||
0.681840 | + | 0.731501i | \(0.261180\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −4821.57 | −0.191513 | −0.0957567 | − | 0.995405i | \(-0.530527\pi\) | ||||
−0.0957567 | + | 0.995405i | \(0.530527\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 3520.13 | 0.139333 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −19145.6 | −0.755185 | −0.377593 | − | 0.925972i | \(-0.623248\pi\) | ||||
−0.377593 | + | 0.925972i | \(0.623248\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 18361.6 | 0.721748 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −19025.4 | −0.745254 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 37509.9 | 1.46426 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1643.47 | 0.0639345 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 20166.0 | 0.781804 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −373.147 | −0.0144168 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 16890.8 | 0.650354 | 0.325177 | − | 0.945653i | \(-0.394576\pi\) | ||||
0.325177 | + | 0.945653i | \(0.394576\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −3124.21 | −0.119883 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −27802.3 | −1.06321 | −0.531603 | − | 0.846994i | \(-0.678410\pi\) | ||||
−0.531603 | + | 0.846994i | \(0.678410\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −9794.15 | −0.373272 | −0.186636 | − | 0.982429i | \(-0.559759\pi\) | ||||
−0.186636 | + | 0.982429i | \(0.559759\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −2742.85 | −0.104181 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 41652.4 | 1.57672 | 0.788360 | − | 0.615214i | \(-0.210930\pi\) | ||||
0.788360 | + | 0.615214i | \(0.210930\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −3763.93 | −0.142000 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −5867.80 | −0.220627 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 2446.34 | 0.0916724 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 16123.1 | 0.602164 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 824.898 | 0.0307052 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 31207.7 | 1.15777 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −44045.2 | −1.62859 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −1213.67 | −0.0447269 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −11121.1 | −0.408485 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −5467.21 | −0.200150 | −0.100075 | − | 0.994980i | \(-0.531908\pi\) | ||||
−0.100075 | + | 0.994980i | \(0.531908\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 2431.79 | 0.0887318 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −33520.9 | −1.21910 | −0.609549 | − | 0.792749i | \(-0.708649\pi\) | ||||
−0.609549 | + | 0.792749i | \(0.708649\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −1390.52 | −0.0504046 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 1471.26 | 0.0531565 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 1326.26 | 0.0477612 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −21423.9 | −0.768996 | −0.384498 | − | 0.923126i | \(-0.625625\pi\) | ||||
−0.384498 | + | 0.923126i | \(0.625625\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −23623.2 | −0.845182 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −8507.56 | −0.303391 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −2698.90 | −0.0959344 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −16733.3 | −0.592873 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 25838.9 | 0.912538 | 0.456269 | − | 0.889842i | \(-0.349186\pi\) | ||||
0.456269 | + | 0.889842i | \(0.349186\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −16199.7 | −0.570271 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −27572.9 | −0.967519 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −36443.2 | −1.27467 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 48095.9 | 1.67687 | 0.838434 | − | 0.545003i | \(-0.183472\pi\) | ||||
0.838434 | + | 0.545003i | \(0.183472\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −8105.38 | −0.281692 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −32450.4 | −1.12418 | −0.562089 | − | 0.827077i | \(-0.690002\pi\) | ||||
−0.562089 | + | 0.827077i | \(0.690002\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 9076.66 | 0.313443 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −2010.17 | −0.0691966 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −39067.9 | −1.34059 | −0.670294 | − | 0.742096i | \(-0.733832\pi\) | ||||
−0.670294 | + | 0.742096i | \(0.733832\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 8277.16 | 0.283127 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 10279.8 | 0.350522 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 17756.2 | 0.603546 | 0.301773 | − | 0.953380i | \(-0.402422\pi\) | ||||
0.301773 | + | 0.953380i | \(0.402422\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −16367.6 | −0.554601 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 27729.5 | 0.936642 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −1280.85 | −0.0431292 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 23469.5 | 0.787805 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 33813.9 | 1.13150 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 25634.3 | 0.855127 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 10696.2 | 0.355705 | 0.177853 | − | 0.984057i | \(-0.443085\pi\) | ||||
0.177853 | + | 0.984057i | \(0.443085\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −15388.3 | −0.510160 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 53635.1 | 1.77264 | 0.886320 | − | 0.463074i | \(-0.153254\pi\) | ||||
0.886320 | + | 0.463074i | \(0.153254\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −745.561 | −0.0245649 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 896.629 | 0.0294514 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −21627.7 | −0.708220 | −0.354110 | − | 0.935204i | \(-0.615216\pi\) | ||||
−0.354110 | + | 0.935204i | \(0.615216\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 74617.7 | 2.43595 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 17678.2 | 0.575353 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −12031.4 | −0.390378 | −0.195189 | − | 0.980766i | \(-0.562532\pi\) | ||||
−0.195189 | + | 0.980766i | \(0.562532\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 16312.8 | 0.527686 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 450.021 | 0.0145130 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −3129.44 | −0.100617 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 24573.0 | 0.787675 | 0.393838 | − | 0.919180i | \(-0.371147\pi\) | ||||
0.393838 | + | 0.919180i | \(0.371147\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 9740.36 | 0.311280 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 841.410 | 0.0268085 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −14209.7 | −0.451379 | −0.225690 | − | 0.974199i | \(-0.572464\pi\) | ||||
−0.225690 | + | 0.974199i | \(0.572464\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −14539.2 | −0.460460 |
(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 | 1840.4.a.k.1.3 | 4 | ||
4.3 | odd | 2 | 230.4.a.j.1.2 | ✓ | 4 | ||
12.11 | even | 2 | 2070.4.a.bg.1.2 | 4 | |||
20.3 | even | 4 | 1150.4.b.o.599.2 | 8 | |||
20.7 | even | 4 | 1150.4.b.o.599.7 | 8 | |||
20.19 | odd | 2 | 1150.4.a.n.1.3 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
230.4.a.j.1.2 | ✓ | 4 | 4.3 | odd | 2 | ||
1150.4.a.n.1.3 | 4 | 20.19 | odd | 2 | |||
1150.4.b.o.599.2 | 8 | 20.3 | even | 4 | |||
1150.4.b.o.599.7 | 8 | 20.7 | even | 4 | |||
1840.4.a.k.1.3 | 4 | 1.1 | even | 1 | trivial | ||
2070.4.a.bg.1.2 | 4 | 12.11 | even | 2 |