Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [315,4,Mod(1,315)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(315, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("315.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 315 = 3^{2} \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 315.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: | \(18.5856016518\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{17}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 4 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(2.56155\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 315.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.56155 | −0.905646 | −0.452823 | − | 0.891601i | \(-0.649583\pi\) | ||||
−0.452823 | + | 0.891601i | \(0.649583\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.43845 | −0.179806 | ||||||||
\(5\) | −5.00000 | −0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −7.00000 | −0.377964 | ||||||||
\(8\) | 24.1771 | 1.06849 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 12.8078 | 0.405017 | ||||||||
\(11\) | −6.24621 | −0.171209 | −0.0856047 | − | 0.996329i | \(-0.527282\pi\) | ||||
−0.0856047 | + | 0.996329i | \(0.527282\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −56.3542 | −1.20229 | −0.601147 | − | 0.799138i | \(-0.705290\pi\) | ||||
−0.601147 | + | 0.799138i | \(0.705290\pi\) | |||||||
\(14\) | 17.9309 | 0.342302 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −50.4233 | −0.787864 | ||||||||
\(17\) | −24.6004 | −0.350969 | −0.175484 | − | 0.984482i | \(-0.556149\pi\) | ||||
−0.175484 | + | 0.984482i | \(0.556149\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −90.7083 | −1.09526 | −0.547629 | − | 0.836721i | \(-0.684470\pi\) | ||||
−0.547629 | + | 0.836721i | \(0.684470\pi\) | |||||||
\(20\) | 7.19224 | 0.0804116 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 16.0000 | 0.155055 | ||||||||
\(23\) | 69.8617 | 0.633356 | 0.316678 | − | 0.948533i | \(-0.397433\pi\) | ||||
0.316678 | + | 0.948533i | \(0.397433\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 25.0000 | 0.200000 | ||||||||
\(26\) | 144.354 | 1.08885 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 10.0691 | 0.0679602 | ||||||||
\(29\) | 228.847 | 1.46537 | 0.732685 | − | 0.680568i | \(-0.238267\pi\) | ||||
0.732685 | + | 0.680568i | \(0.238267\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −67.8920 | −0.393347 | −0.196674 | − | 0.980469i | \(-0.563014\pi\) | ||||
−0.196674 | + | 0.980469i | \(0.563014\pi\) | |||||||
\(32\) | −64.2547 | −0.354961 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 63.0152 | 0.317853 | ||||||||
\(35\) | 35.0000 | 0.169031 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −58.8466 | −0.261468 | −0.130734 | − | 0.991417i | \(-0.541733\pi\) | ||||
−0.130734 | + | 0.991417i | \(0.541733\pi\) | |||||||
\(38\) | 232.354 | 0.991916 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −120.885 | −0.477842 | ||||||||
\(41\) | −19.2007 | −0.0731379 | −0.0365689 | − | 0.999331i | \(-0.511643\pi\) | ||||
−0.0365689 | + | 0.999331i | \(0.511643\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 365.218 | 1.29524 | 0.647618 | − | 0.761965i | \(-0.275765\pi\) | ||||
0.647618 | + | 0.761965i | \(0.275765\pi\) | |||||||
\(44\) | 8.98485 | 0.0307845 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −178.955 | −0.573596 | ||||||||
\(47\) | 195.153 | 0.605661 | 0.302830 | − | 0.953044i | \(-0.402068\pi\) | ||||
0.302830 | + | 0.953044i | \(0.402068\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 49.0000 | 0.142857 | ||||||||
\(50\) | −64.0388 | −0.181129 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 81.0625 | 0.216180 | ||||||||
\(53\) | 511.201 | 1.32488 | 0.662442 | − | 0.749113i | \(-0.269520\pi\) | ||||
0.662442 | + | 0.749113i | \(0.269520\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 31.2311 | 0.0765672 | ||||||||
\(56\) | −169.240 | −0.403850 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −586.203 | −1.32711 | ||||||||
\(59\) | 284.000 | 0.626672 | 0.313336 | − | 0.949642i | \(-0.398553\pi\) | ||||
0.313336 | + | 0.949642i | \(0.398553\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −123.460 | −0.259139 | −0.129569 | − | 0.991570i | \(-0.541359\pi\) | ||||
−0.129569 | + | 0.991570i | \(0.541359\pi\) | |||||||
\(62\) | 173.909 | 0.356233 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 567.978 | 1.10933 | ||||||||
\(65\) | 281.771 | 0.537683 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 144.968 | 0.264338 | 0.132169 | − | 0.991227i | \(-0.457806\pi\) | ||||
0.132169 | + | 0.991227i | \(0.457806\pi\) | |||||||
\(68\) | 35.3863 | 0.0631062 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −89.6543 | −0.153082 | ||||||||
\(71\) | 73.0284 | 0.122069 | 0.0610344 | − | 0.998136i | \(-0.480560\pi\) | ||||
0.0610344 | + | 0.998136i | \(0.480560\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 638.850 | 1.02427 | 0.512135 | − | 0.858905i | \(-0.328855\pi\) | ||||
0.512135 | + | 0.858905i | \(0.328855\pi\) | |||||||
\(74\) | 150.739 | 0.236797 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 130.479 | 0.196934 | ||||||||
\(77\) | 43.7235 | 0.0647111 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 976.189 | 1.39025 | 0.695126 | − | 0.718888i | \(-0.255349\pi\) | ||||
0.695126 | + | 0.718888i | \(0.255349\pi\) | |||||||
\(80\) | 252.116 | 0.352343 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 49.1837 | 0.0662370 | ||||||||
\(83\) | 484.466 | 0.640687 | 0.320344 | − | 0.947301i | \(-0.396202\pi\) | ||||
0.320344 | + | 0.947301i | \(0.396202\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 123.002 | 0.156958 | ||||||||
\(86\) | −935.525 | −1.17303 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −151.015 | −0.182935 | ||||||||
\(89\) | −1017.30 | −1.21161 | −0.605806 | − | 0.795612i | \(-0.707149\pi\) | ||||
−0.605806 | + | 0.795612i | \(0.707149\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 394.479 | 0.454425 | ||||||||
\(92\) | −100.492 | −0.113881 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −499.896 | −0.548514 | ||||||||
\(95\) | 453.542 | 0.489815 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1806.67 | 1.89113 | 0.945564 | − | 0.325437i | \(-0.105511\pi\) | ||||
0.945564 | + | 0.325437i | \(0.105511\pi\) | |||||||
\(98\) | −125.516 | −0.129378 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −35.9612 | −0.0359612 | ||||||||
\(101\) | −483.053 | −0.475897 | −0.237948 | − | 0.971278i | \(-0.576475\pi\) | ||||
−0.237948 | + | 0.971278i | \(0.576475\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −339.049 | −0.324345 | −0.162172 | − | 0.986762i | \(-0.551850\pi\) | ||||
−0.162172 | + | 0.986762i | \(0.551850\pi\) | |||||||
\(104\) | −1362.48 | −1.28464 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −1309.47 | −1.19987 | ||||||||
\(107\) | −450.847 | −0.407336 | −0.203668 | − | 0.979040i | \(-0.565286\pi\) | ||||
−0.203668 | + | 0.979040i | \(0.565286\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1841.70 | −1.61838 | −0.809189 | − | 0.587548i | \(-0.800093\pi\) | ||||
−0.809189 | + | 0.587548i | \(0.800093\pi\) | |||||||
\(110\) | −80.0000 | −0.0693427 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 352.963 | 0.297785 | ||||||||
\(113\) | 1874.72 | 1.56069 | 0.780347 | − | 0.625347i | \(-0.215042\pi\) | ||||
0.780347 | + | 0.625347i | \(0.215042\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −349.309 | −0.283245 | ||||||||
\(116\) | −329.184 | −0.263482 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −727.481 | −0.567543 | ||||||||
\(119\) | 172.203 | 0.132654 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1291.98 | −0.970687 | ||||||||
\(122\) | 316.250 | 0.234688 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 97.6591 | 0.0707262 | ||||||||
\(125\) | −125.000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −38.0984 | −0.0266196 | −0.0133098 | − | 0.999911i | \(-0.504237\pi\) | ||||
−0.0133098 | + | 0.999911i | \(0.504237\pi\) | |||||||
\(128\) | −940.868 | −0.649702 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −721.771 | −0.486950 | ||||||||
\(131\) | −1551.51 | −1.03478 | −0.517389 | − | 0.855750i | \(-0.673096\pi\) | ||||
−0.517389 | + | 0.855750i | \(0.673096\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 634.958 | 0.413969 | ||||||||
\(134\) | −371.343 | −0.239396 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −594.765 | −0.375005 | ||||||||
\(137\) | −1203.24 | −0.750364 | −0.375182 | − | 0.926951i | \(-0.622420\pi\) | ||||
−0.375182 | + | 0.926951i | \(0.622420\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1897.00 | 1.15756 | 0.578781 | − | 0.815483i | \(-0.303529\pi\) | ||||
0.578781 | + | 0.815483i | \(0.303529\pi\) | |||||||
\(140\) | −50.3457 | −0.0303927 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −187.066 | −0.110551 | ||||||||
\(143\) | 352.000 | 0.205844 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1144.23 | −0.655334 | ||||||||
\(146\) | −1636.45 | −0.927626 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 84.6477 | 0.0470135 | ||||||||
\(149\) | 704.888 | 0.387562 | 0.193781 | − | 0.981045i | \(-0.437925\pi\) | ||||
0.193781 | + | 0.981045i | \(0.437925\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −3035.21 | −1.63578 | −0.817888 | − | 0.575378i | \(-0.804855\pi\) | ||||
−0.817888 | + | 0.575378i | \(0.804855\pi\) | |||||||
\(152\) | −2193.06 | −1.17027 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −112.000 | −0.0586053 | ||||||||
\(155\) | 339.460 | 0.175910 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2713.65 | 1.37944 | 0.689722 | − | 0.724074i | \(-0.257733\pi\) | ||||
0.689722 | + | 0.724074i | \(0.257733\pi\) | |||||||
\(158\) | −2500.56 | −1.25908 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 321.274 | 0.158743 | ||||||||
\(161\) | −489.032 | −0.239386 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −465.259 | −0.223570 | −0.111785 | − | 0.993732i | \(-0.535657\pi\) | ||||
−0.111785 | + | 0.993732i | \(0.535657\pi\) | |||||||
\(164\) | 27.6193 | 0.0131506 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −1240.98 | −0.580236 | ||||||||
\(167\) | −4156.06 | −1.92578 | −0.962891 | − | 0.269892i | \(-0.913012\pi\) | ||||
−0.962891 | + | 0.269892i | \(0.913012\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 978.792 | 0.445513 | ||||||||
\(170\) | −315.076 | −0.142148 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −525.346 | −0.232891 | ||||||||
\(173\) | 4241.17 | 1.86387 | 0.931936 | − | 0.362622i | \(-0.118119\pi\) | ||||
0.931936 | + | 0.362622i | \(0.118119\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −175.000 | −0.0755929 | ||||||||
\(176\) | 314.955 | 0.134890 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 2605.87 | 1.09729 | ||||||||
\(179\) | 2940.35 | 1.22778 | 0.613889 | − | 0.789392i | \(-0.289604\pi\) | ||||
0.613889 | + | 0.789392i | \(0.289604\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1986.35 | −0.815716 | −0.407858 | − | 0.913045i | \(-0.633724\pi\) | ||||
−0.407858 | + | 0.913045i | \(0.633724\pi\) | |||||||
\(182\) | −1010.48 | −0.411548 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 1689.05 | 0.676732 | ||||||||
\(185\) | 294.233 | 0.116932 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 153.659 | 0.0600891 | ||||||||
\(188\) | −280.718 | −0.108901 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −1161.77 | −0.443598 | ||||||||
\(191\) | −1615.88 | −0.612150 | −0.306075 | − | 0.952007i | \(-0.599016\pi\) | ||||
−0.306075 | + | 0.952007i | \(0.599016\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −2052.44 | −0.765482 | −0.382741 | − | 0.923856i | \(-0.625020\pi\) | ||||
−0.382741 | + | 0.923856i | \(0.625020\pi\) | |||||||
\(194\) | −4627.88 | −1.71269 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −70.4839 | −0.0256866 | ||||||||
\(197\) | 4468.58 | 1.61611 | 0.808054 | − | 0.589108i | \(-0.200521\pi\) | ||||
0.808054 | + | 0.589108i | \(0.200521\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1543.07 | 0.549675 | 0.274838 | − | 0.961491i | \(-0.411376\pi\) | ||||
0.274838 | + | 0.961491i | \(0.411376\pi\) | |||||||
\(200\) | 604.427 | 0.213697 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 1237.37 | 0.430994 | ||||||||
\(203\) | −1601.93 | −0.553858 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 96.0037 | 0.0327083 | ||||||||
\(206\) | 868.492 | 0.293741 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 2841.56 | 0.947245 | ||||||||
\(209\) | 566.583 | 0.187519 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1284.02 | 0.418937 | 0.209469 | − | 0.977815i | \(-0.432827\pi\) | ||||
0.209469 | + | 0.977815i | \(0.432827\pi\) | |||||||
\(212\) | −735.335 | −0.238222 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 1154.87 | 0.368902 | ||||||||
\(215\) | −1826.09 | −0.579248 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 475.244 | 0.148671 | ||||||||
\(218\) | 4717.62 | 1.46568 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −44.9242 | −0.0137672 | ||||||||
\(221\) | 1386.33 | 0.421968 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 3815.31 | 1.14571 | 0.572853 | − | 0.819658i | \(-0.305837\pi\) | ||||
0.572853 | + | 0.819658i | \(0.305837\pi\) | |||||||
\(224\) | 449.783 | 0.134162 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −4802.18 | −1.41344 | ||||||||
\(227\) | 2271.53 | 0.664172 | 0.332086 | − | 0.943249i | \(-0.392248\pi\) | ||||
0.332086 | + | 0.943249i | \(0.392248\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −2367.54 | −0.683195 | −0.341598 | − | 0.939846i | \(-0.610968\pi\) | ||||
−0.341598 | + | 0.939846i | \(0.610968\pi\) | |||||||
\(230\) | 894.773 | 0.256520 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 5532.84 | 1.56573 | ||||||||
\(233\) | −1617.71 | −0.454849 | −0.227425 | − | 0.973796i | \(-0.573030\pi\) | ||||
−0.227425 | + | 0.973796i | \(0.573030\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −975.767 | −0.270860 | ||||||||
\(236\) | −408.519 | −0.112679 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −441.106 | −0.120137 | ||||||||
\(239\) | 1935.29 | 0.523781 | 0.261891 | − | 0.965098i | \(-0.415654\pi\) | ||||
0.261891 | + | 0.965098i | \(0.415654\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 477.901 | 0.127736 | 0.0638679 | − | 0.997958i | \(-0.479656\pi\) | ||||
0.0638679 | + | 0.997958i | \(0.479656\pi\) | |||||||
\(242\) | 3309.49 | 0.879099 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 177.591 | 0.0465947 | ||||||||
\(245\) | −245.000 | −0.0638877 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 5111.79 | 1.31682 | ||||||||
\(248\) | −1641.43 | −0.420286 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 320.194 | 0.0810034 | ||||||||
\(251\) | 4769.70 | 1.19944 | 0.599722 | − | 0.800208i | \(-0.295278\pi\) | ||||
0.599722 | + | 0.800208i | \(0.295278\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −436.371 | −0.108436 | ||||||||
\(254\) | 97.5910 | 0.0241079 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −2133.74 | −0.520933 | ||||||||
\(257\) | 682.524 | 0.165660 | 0.0828302 | − | 0.996564i | \(-0.473604\pi\) | ||||
0.0828302 | + | 0.996564i | \(0.473604\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 411.926 | 0.0988256 | ||||||||
\(260\) | −405.312 | −0.0966785 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 3974.27 | 0.937142 | ||||||||
\(263\) | 3029.11 | 0.710202 | 0.355101 | − | 0.934828i | \(-0.384447\pi\) | ||||
0.355101 | + | 0.934828i | \(0.384447\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −2556.00 | −0.592506 | ||||||||
\(266\) | −1626.48 | −0.374909 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −208.529 | −0.0475295 | ||||||||
\(269\) | 6187.33 | 1.40241 | 0.701205 | − | 0.712960i | \(-0.252646\pi\) | ||||
0.701205 | + | 0.712960i | \(0.252646\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −7558.90 | −1.69436 | −0.847178 | − | 0.531309i | \(-0.821700\pi\) | ||||
−0.847178 | + | 0.531309i | \(0.821700\pi\) | |||||||
\(272\) | 1240.43 | 0.276516 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 3082.17 | 0.679564 | ||||||||
\(275\) | −156.155 | −0.0342419 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 3685.36 | 0.799393 | 0.399697 | − | 0.916647i | \(-0.369115\pi\) | ||||
0.399697 | + | 0.916647i | \(0.369115\pi\) | |||||||
\(278\) | −4859.26 | −1.04834 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 846.198 | 0.180607 | ||||||||
\(281\) | 7969.11 | 1.69180 | 0.845902 | − | 0.533338i | \(-0.179063\pi\) | ||||
0.845902 | + | 0.533338i | \(0.179063\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −2479.73 | −0.520864 | −0.260432 | − | 0.965492i | \(-0.583865\pi\) | ||||
−0.260432 | + | 0.965492i | \(0.583865\pi\) | |||||||
\(284\) | −105.048 | −0.0219487 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −901.667 | −0.186422 | ||||||||
\(287\) | 134.405 | 0.0276435 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −4307.82 | −0.876821 | ||||||||
\(290\) | 2931.01 | 0.593500 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −918.952 | −0.184170 | ||||||||
\(293\) | −5950.02 | −1.18636 | −0.593181 | − | 0.805069i | \(-0.702128\pi\) | ||||
−0.593181 | + | 0.805069i | \(0.702128\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1420.00 | −0.280256 | ||||||||
\(296\) | −1422.74 | −0.279375 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −1805.61 | −0.350994 | ||||||||
\(299\) | −3937.00 | −0.761480 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2556.52 | −0.489554 | ||||||||
\(302\) | 7774.86 | 1.48143 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 4573.81 | 0.862915 | ||||||||
\(305\) | 617.301 | 0.115890 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −3129.90 | −0.581865 | −0.290933 | − | 0.956744i | \(-0.593966\pi\) | ||||
−0.290933 | + | 0.956744i | \(0.593966\pi\) | |||||||
\(308\) | −62.8939 | −0.0116354 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −869.545 | −0.159312 | ||||||||
\(311\) | 7261.25 | 1.32395 | 0.661973 | − | 0.749527i | \(-0.269719\pi\) | ||||
0.661973 | + | 0.749527i | \(0.269719\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −2310.83 | −0.417303 | −0.208652 | − | 0.977990i | \(-0.566907\pi\) | ||||
−0.208652 | + | 0.977990i | \(0.566907\pi\) | |||||||
\(314\) | −6951.16 | −1.24929 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −1404.20 | −0.249975 | ||||||||
\(317\) | 4701.40 | 0.832987 | 0.416494 | − | 0.909139i | \(-0.363259\pi\) | ||||
0.416494 | + | 0.909139i | \(0.363259\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1429.42 | −0.250885 | ||||||||
\(320\) | −2839.89 | −0.496109 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 1252.68 | 0.216799 | ||||||||
\(323\) | 2231.46 | 0.384401 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1408.85 | −0.240459 | ||||||||
\(326\) | 1191.79 | 0.202475 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −464.218 | −0.0781468 | ||||||||
\(329\) | −1366.07 | −0.228918 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1366.18 | 0.226864 | 0.113432 | − | 0.993546i | \(-0.463816\pi\) | ||||
0.113432 | + | 0.993546i | \(0.463816\pi\) | |||||||
\(332\) | −696.879 | −0.115199 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 10646.0 | 1.74408 | ||||||||
\(335\) | −724.839 | −0.118215 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −740.632 | −0.119718 | −0.0598588 | − | 0.998207i | \(-0.519065\pi\) | ||||
−0.0598588 | + | 0.998207i | \(0.519065\pi\) | |||||||
\(338\) | −2507.23 | −0.403477 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −176.932 | −0.0282220 | ||||||||
\(341\) | 424.068 | 0.0673448 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −343.000 | −0.0539949 | ||||||||
\(344\) | 8829.90 | 1.38394 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −10864.0 | −1.68801 | ||||||||
\(347\) | −2605.56 | −0.403094 | −0.201547 | − | 0.979479i | \(-0.564597\pi\) | ||||
−0.201547 | + | 0.979479i | \(0.564597\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 4665.07 | 0.715517 | 0.357758 | − | 0.933814i | \(-0.383541\pi\) | ||||
0.357758 | + | 0.933814i | \(0.383541\pi\) | |||||||
\(350\) | 448.272 | 0.0684604 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 401.349 | 0.0607726 | ||||||||
\(353\) | 2964.75 | 0.447019 | 0.223509 | − | 0.974702i | \(-0.428249\pi\) | ||||
0.223509 | + | 0.974702i | \(0.428249\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −365.142 | −0.0545908 | ||||||||
\(356\) | 1463.33 | 0.217855 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −7531.87 | −1.11193 | ||||||||
\(359\) | 4267.55 | 0.627389 | 0.313695 | − | 0.949524i | \(-0.398433\pi\) | ||||
0.313695 | + | 0.949524i | \(0.398433\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1369.00 | 0.199592 | ||||||||
\(362\) | 5088.15 | 0.738749 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −567.437 | −0.0817082 | ||||||||
\(365\) | −3194.25 | −0.458068 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −9280.33 | −1.31997 | −0.659985 | − | 0.751279i | \(-0.729438\pi\) | ||||
−0.659985 | + | 0.751279i | \(0.729438\pi\) | |||||||
\(368\) | −3522.66 | −0.498998 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −753.693 | −0.105899 | ||||||||
\(371\) | −3578.41 | −0.500759 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 10781.1 | 1.49657 | 0.748286 | − | 0.663376i | \(-0.230877\pi\) | ||||
0.748286 | + | 0.663376i | \(0.230877\pi\) | |||||||
\(374\) | −393.606 | −0.0544195 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 4718.24 | 0.647140 | ||||||||
\(377\) | −12896.5 | −1.76181 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −5914.16 | −0.801557 | −0.400779 | − | 0.916175i | \(-0.631260\pi\) | ||||
−0.400779 | + | 0.916175i | \(0.631260\pi\) | |||||||
\(380\) | −652.396 | −0.0880716 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 4139.15 | 0.554391 | ||||||||
\(383\) | −11513.9 | −1.53612 | −0.768059 | − | 0.640379i | \(-0.778777\pi\) | ||||
−0.768059 | + | 0.640379i | \(0.778777\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −218.617 | −0.0289397 | ||||||||
\(386\) | 5257.44 | 0.693256 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −2598.80 | −0.340036 | ||||||||
\(389\) | 5399.73 | 0.703797 | 0.351898 | − | 0.936038i | \(-0.385536\pi\) | ||||
0.351898 | + | 0.936038i | \(0.385536\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1718.62 | −0.222288 | ||||||||
\(392\) | 1184.68 | 0.152641 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −11446.5 | −1.46362 | ||||||||
\(395\) | −4880.95 | −0.621739 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 2622.13 | 0.331488 | 0.165744 | − | 0.986169i | \(-0.446997\pi\) | ||||
0.165744 | + | 0.986169i | \(0.446997\pi\) | |||||||
\(398\) | −3952.66 | −0.497811 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −1260.58 | −0.157573 | ||||||||
\(401\) | −11119.1 | −1.38469 | −0.692344 | − | 0.721568i | \(-0.743422\pi\) | ||||
−0.692344 | + | 0.721568i | \(0.743422\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 3826.00 | 0.472920 | ||||||||
\(404\) | 694.846 | 0.0855690 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 4103.42 | 0.501599 | ||||||||
\(407\) | 367.568 | 0.0447658 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −6589.18 | −0.796611 | −0.398305 | − | 0.917253i | \(-0.630402\pi\) | ||||
−0.398305 | + | 0.917253i | \(0.630402\pi\) | |||||||
\(410\) | −245.919 | −0.0296221 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 487.704 | 0.0583191 | ||||||||
\(413\) | −1988.00 | −0.236860 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −2422.33 | −0.286524 | ||||||||
\(416\) | 3621.02 | 0.426767 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −1451.33 | −0.169825 | ||||||||
\(419\) | −11871.6 | −1.38416 | −0.692081 | − | 0.721820i | \(-0.743306\pi\) | ||||
−0.692081 | + | 0.721820i | \(0.743306\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −1731.57 | −0.200455 | −0.100227 | − | 0.994965i | \(-0.531957\pi\) | ||||
−0.100227 | + | 0.994965i | \(0.531957\pi\) | |||||||
\(422\) | −3289.09 | −0.379409 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 12359.3 | 1.41562 | ||||||||
\(425\) | −615.009 | −0.0701937 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 864.222 | 0.0979452 | ||||||||
\(428\) | 648.519 | 0.0732415 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 4677.62 | 0.524593 | ||||||||
\(431\) | 10653.8 | 1.19066 | 0.595330 | − | 0.803481i | \(-0.297021\pi\) | ||||
0.595330 | + | 0.803481i | \(0.297021\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 2642.01 | 0.293226 | 0.146613 | − | 0.989194i | \(-0.453163\pi\) | ||||
0.146613 | + | 0.989194i | \(0.453163\pi\) | |||||||
\(434\) | −1217.36 | −0.134644 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 2649.19 | 0.290994 | ||||||||
\(437\) | −6337.04 | −0.693688 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 8858.21 | 0.963051 | 0.481525 | − | 0.876432i | \(-0.340083\pi\) | ||||
0.481525 | + | 0.876432i | \(0.340083\pi\) | |||||||
\(440\) | 755.076 | 0.0818110 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −3551.17 | −0.382153 | ||||||||
\(443\) | −6621.73 | −0.710176 | −0.355088 | − | 0.934833i | \(-0.615549\pi\) | ||||
−0.355088 | + | 0.934833i | \(0.615549\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 5086.50 | 0.541849 | ||||||||
\(446\) | −9773.13 | −1.03760 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −3975.85 | −0.419288 | ||||||||
\(449\) | 13081.7 | 1.37497 | 0.687487 | − | 0.726196i | \(-0.258714\pi\) | ||||
0.687487 | + | 0.726196i | \(0.258714\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 119.932 | 0.0125219 | ||||||||
\(452\) | −2696.68 | −0.280622 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −5818.65 | −0.601504 | ||||||||
\(455\) | −1972.40 | −0.203225 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 12167.0 | 1.24540 | 0.622699 | − | 0.782461i | \(-0.286036\pi\) | ||||
0.622699 | + | 0.782461i | \(0.286036\pi\) | |||||||
\(458\) | 6064.59 | 0.618733 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 502.462 | 0.0509292 | ||||||||
\(461\) | 11283.8 | 1.14000 | 0.570000 | − | 0.821645i | \(-0.306943\pi\) | ||||
0.570000 | + | 0.821645i | \(0.306943\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 16542.9 | 1.66051 | 0.830254 | − | 0.557385i | \(-0.188195\pi\) | ||||
0.830254 | + | 0.557385i | \(0.188195\pi\) | |||||||
\(464\) | −11539.2 | −1.15451 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 4143.85 | 0.411932 | ||||||||
\(467\) | −10266.9 | −1.01734 | −0.508668 | − | 0.860963i | \(-0.669862\pi\) | ||||
−0.508668 | + | 0.860963i | \(0.669862\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −1014.77 | −0.0999103 | ||||||||
\(470\) | 2499.48 | 0.245303 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 6866.29 | 0.669590 | ||||||||
\(473\) | −2281.23 | −0.221757 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −2267.71 | −0.219052 | ||||||||
\(476\) | −247.704 | −0.0238519 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −4957.36 | −0.474360 | ||||||||
\(479\) | −7967.98 | −0.760055 | −0.380027 | − | 0.924975i | \(-0.624085\pi\) | ||||
−0.380027 | + | 0.924975i | \(0.624085\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 3316.25 | 0.314362 | ||||||||
\(482\) | −1224.17 | −0.115683 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 1858.45 | 0.174535 | ||||||||
\(485\) | −9033.34 | −0.845738 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 9956.62 | 0.926443 | 0.463221 | − | 0.886243i | \(-0.346694\pi\) | ||||
0.463221 | + | 0.886243i | \(0.346694\pi\) | |||||||
\(488\) | −2984.91 | −0.276886 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 627.580 | 0.0578596 | ||||||||
\(491\) | −18660.8 | −1.71518 | −0.857589 | − | 0.514336i | \(-0.828038\pi\) | ||||
−0.857589 | + | 0.514336i | \(0.828038\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −5629.71 | −0.514299 | ||||||||
\(494\) | −13094.1 | −1.19258 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 3423.34 | 0.309904 | ||||||||
\(497\) | −511.199 | −0.0461377 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 4074.21 | 0.365504 | 0.182752 | − | 0.983159i | \(-0.441499\pi\) | ||||
0.182752 | + | 0.983159i | \(0.441499\pi\) | |||||||
\(500\) | 179.806 | 0.0160823 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −12217.8 | −1.08627 | ||||||||
\(503\) | −4255.51 | −0.377224 | −0.188612 | − | 0.982052i | \(-0.560399\pi\) | ||||
−0.188612 | + | 0.982052i | \(0.560399\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 2415.26 | 0.212827 | ||||||||
\(506\) | 1117.79 | 0.0982050 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 54.8025 | 0.00478636 | ||||||||
\(509\) | 10171.8 | 0.885771 | 0.442885 | − | 0.896578i | \(-0.353955\pi\) | ||||
0.442885 | + | 0.896578i | \(0.353955\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −4471.95 | −0.387138 | ||||||||
\(512\) | 12992.6 | 1.12148 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −1748.32 | −0.150030 | ||||||||
\(515\) | 1695.25 | 0.145051 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −1218.97 | −0.103695 | ||||||||
\(518\) | −1055.17 | −0.0895010 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 6812.40 | 0.574506 | ||||||||
\(521\) | 1680.39 | 0.141303 | 0.0706517 | − | 0.997501i | \(-0.477492\pi\) | ||||
0.0706517 | + | 0.997501i | \(0.477492\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 13211.8 | 1.10461 | 0.552305 | − | 0.833642i | \(-0.313749\pi\) | ||||
0.552305 | + | 0.833642i | \(0.313749\pi\) | |||||||
\(524\) | 2231.76 | 0.186059 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −7759.23 | −0.643191 | ||||||||
\(527\) | 1670.17 | 0.138053 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −7286.34 | −0.598861 | ||||||||
\(530\) | 6547.34 | 0.536600 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −913.354 | −0.0744341 | ||||||||
\(533\) | 1082.04 | 0.0879333 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 2254.23 | 0.182166 | ||||||||
\(536\) | 3504.90 | 0.282441 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −15849.2 | −1.27009 | ||||||||
\(539\) | −306.064 | −0.0244585 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 9650.84 | 0.766954 | 0.383477 | − | 0.923551i | \(-0.374727\pi\) | ||||
0.383477 | + | 0.923551i | \(0.374727\pi\) | |||||||
\(542\) | 19362.5 | 1.53449 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 1580.69 | 0.124580 | ||||||||
\(545\) | 9208.52 | 0.723761 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −23864.3 | −1.86538 | −0.932689 | − | 0.360682i | \(-0.882544\pi\) | ||||
−0.932689 | + | 0.360682i | \(0.882544\pi\) | |||||||
\(548\) | 1730.80 | 0.134920 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 400.000 | 0.0310110 | ||||||||
\(551\) | −20758.3 | −1.60496 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −6833.33 | −0.525466 | ||||||||
\(554\) | −9440.25 | −0.723967 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −2728.73 | −0.208136 | ||||||||
\(557\) | −2314.22 | −0.176044 | −0.0880221 | − | 0.996119i | \(-0.528055\pi\) | ||||
−0.0880221 | + | 0.996119i | \(0.528055\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −20581.5 | −1.55726 | ||||||||
\(560\) | −1764.82 | −0.133173 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −20413.3 | −1.53218 | ||||||||
\(563\) | −7017.86 | −0.525342 | −0.262671 | − | 0.964885i | \(-0.584603\pi\) | ||||
−0.262671 | + | 0.964885i | \(0.584603\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −9373.58 | −0.697964 | ||||||||
\(566\) | 6351.95 | 0.471718 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 1765.61 | 0.130429 | ||||||||
\(569\) | 5302.37 | 0.390662 | 0.195331 | − | 0.980737i | \(-0.437422\pi\) | ||||
0.195331 | + | 0.980737i | \(0.437422\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 17767.2 | 1.30216 | 0.651082 | − | 0.759008i | \(-0.274315\pi\) | ||||
0.651082 | + | 0.759008i | \(0.274315\pi\) | |||||||
\(572\) | −506.333 | −0.0370120 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −344.286 | −0.0250352 | ||||||||
\(575\) | 1746.54 | 0.126671 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −6089.57 | −0.439363 | −0.219681 | − | 0.975572i | \(-0.570502\pi\) | ||||
−0.219681 | + | 0.975572i | \(0.570502\pi\) | |||||||
\(578\) | 11034.7 | 0.794089 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 1645.92 | 0.117833 | ||||||||
\(581\) | −3391.26 | −0.242157 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −3193.07 | −0.226833 | ||||||||
\(584\) | 15445.5 | 1.09442 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 15241.3 | 1.07442 | ||||||||
\(587\) | −26543.9 | −1.86641 | −0.933205 | − | 0.359344i | \(-0.883000\pi\) | ||||
−0.933205 | + | 0.359344i | \(0.883000\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 6158.37 | 0.430817 | ||||||||
\(590\) | 3637.40 | 0.253813 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 2967.24 | 0.206001 | ||||||||
\(593\) | 16365.0 | 1.13327 | 0.566635 | − | 0.823969i | \(-0.308245\pi\) | ||||
0.566635 | + | 0.823969i | \(0.308245\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −861.013 | −0.0593245 | ||||||||
\(596\) | −1013.94 | −0.0696859 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 10084.8 | 0.689631 | ||||||||
\(599\) | −17516.3 | −1.19482 | −0.597411 | − | 0.801935i | \(-0.703804\pi\) | ||||
−0.597411 | + | 0.801935i | \(0.703804\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 8693.80 | 0.590062 | 0.295031 | − | 0.955488i | \(-0.404670\pi\) | ||||
0.295031 | + | 0.955488i | \(0.404670\pi\) | |||||||
\(602\) | 6548.67 | 0.443362 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 4365.99 | 0.294122 | ||||||||
\(605\) | 6459.92 | 0.434105 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −18096.9 | −1.21010 | −0.605051 | − | 0.796186i | \(-0.706847\pi\) | ||||
−0.605051 | + | 0.796186i | \(0.706847\pi\) | |||||||
\(608\) | 5828.44 | 0.388774 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −1581.25 | −0.104956 | ||||||||
\(611\) | −10997.7 | −0.728183 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 4641.61 | 0.305828 | 0.152914 | − | 0.988239i | \(-0.451134\pi\) | ||||
0.152914 | + | 0.988239i | \(0.451134\pi\) | |||||||
\(614\) | 8017.40 | 0.526964 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 1057.11 | 0.0691429 | ||||||||
\(617\) | 14676.1 | 0.957600 | 0.478800 | − | 0.877924i | \(-0.341072\pi\) | ||||
0.478800 | + | 0.877924i | \(0.341072\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −19645.3 | −1.27563 | −0.637813 | − | 0.770192i | \(-0.720161\pi\) | ||||
−0.637813 | + | 0.770192i | \(0.720161\pi\) | |||||||
\(620\) | −488.296 | −0.0316297 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −18600.1 | −1.19903 | ||||||||
\(623\) | 7121.09 | 0.457946 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 625.000 | 0.0400000 | ||||||||
\(626\) | 5919.32 | 0.377929 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −3903.44 | −0.248032 | ||||||||
\(629\) | 1447.65 | 0.0917671 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 26231.2 | 1.65491 | 0.827456 | − | 0.561531i | \(-0.189788\pi\) | ||||
0.827456 | + | 0.561531i | \(0.189788\pi\) | |||||||
\(632\) | 23601.4 | 1.48546 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −12042.9 | −0.754391 | ||||||||
\(635\) | 190.492 | 0.0119046 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −2761.35 | −0.171756 | ||||||||
\(638\) | 3661.55 | 0.227213 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 4704.34 | 0.290555 | ||||||||
\(641\) | 30882.4 | 1.90293 | 0.951466 | − | 0.307754i | \(-0.0995773\pi\) | ||||
0.951466 | + | 0.307754i | \(0.0995773\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −6216.88 | −0.381290 | −0.190645 | − | 0.981659i | \(-0.561058\pi\) | ||||
−0.190645 | + | 0.981659i | \(0.561058\pi\) | |||||||
\(644\) | 703.447 | 0.0430430 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −5716.00 | −0.348132 | ||||||||
\(647\) | −21210.4 | −1.28882 | −0.644410 | − | 0.764680i | \(-0.722897\pi\) | ||||
−0.644410 | + | 0.764680i | \(0.722897\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −1773.92 | −0.107292 | ||||||||
\(650\) | 3608.85 | 0.217771 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 669.251 | 0.0401992 | ||||||||
\(653\) | 32938.7 | 1.97395 | 0.986977 | − | 0.160864i | \(-0.0514281\pi\) | ||||
0.986977 | + | 0.160864i | \(0.0514281\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 7757.54 | 0.462767 | ||||||||
\(656\) | 968.165 | 0.0576227 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 3499.27 | 0.207319 | ||||||||
\(659\) | 9543.51 | 0.564131 | 0.282066 | − | 0.959395i | \(-0.408980\pi\) | ||||
0.282066 | + | 0.959395i | \(0.408980\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 13274.5 | 0.781116 | 0.390558 | − | 0.920578i | \(-0.372282\pi\) | ||||
0.390558 | + | 0.920578i | \(0.372282\pi\) | |||||||
\(662\) | −3499.55 | −0.205459 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 11713.0 | 0.684565 | ||||||||
\(665\) | −3174.79 | −0.185133 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 15987.6 | 0.928101 | ||||||||
\(668\) | 5978.27 | 0.346267 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 1856.71 | 0.107061 | ||||||||
\(671\) | 771.159 | 0.0443670 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −13575.3 | −0.777545 | −0.388772 | − | 0.921334i | \(-0.627101\pi\) | ||||
−0.388772 | + | 0.921334i | \(0.627101\pi\) | |||||||
\(674\) | 1897.17 | 0.108422 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −1407.94 | −0.0801058 | ||||||||
\(677\) | 12020.7 | 0.682414 | 0.341207 | − | 0.939988i | \(-0.389164\pi\) | ||||
0.341207 | + | 0.939988i | \(0.389164\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −12646.7 | −0.714779 | ||||||||
\(680\) | 2973.83 | 0.167707 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −1086.27 | −0.0609905 | ||||||||
\(683\) | 18391.9 | 1.03038 | 0.515188 | − | 0.857077i | \(-0.327722\pi\) | ||||
0.515188 | + | 0.857077i | \(0.327722\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 6016.21 | 0.335573 | ||||||||
\(686\) | 878.613 | 0.0489003 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −18415.5 | −1.02047 | ||||||||
\(689\) | −28808.3 | −1.59290 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 15594.1 | 0.858508 | 0.429254 | − | 0.903184i | \(-0.358777\pi\) | ||||
0.429254 | + | 0.903184i | \(0.358777\pi\) | |||||||
\(692\) | −6100.69 | −0.335135 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 6674.28 | 0.365061 | ||||||||
\(695\) | −9484.98 | −0.517677 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 472.346 | 0.0256691 | ||||||||
\(698\) | −11949.8 | −0.648004 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 251.728 | 0.0135920 | ||||||||
\(701\) | −31093.7 | −1.67531 | −0.837656 | − | 0.546198i | \(-0.816075\pi\) | ||||
−0.837656 | + | 0.546198i | \(0.816075\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 5337.88 | 0.286375 | ||||||||
\(704\) | −3547.71 | −0.189928 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −7594.36 | −0.404841 | ||||||||
\(707\) | 3381.37 | 0.179872 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −2494.67 | −0.132143 | −0.0660714 | − | 0.997815i | \(-0.521047\pi\) | ||||
−0.0660714 | + | 0.997815i | \(0.521047\pi\) | |||||||
\(710\) | 935.331 | 0.0494399 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −24595.3 | −1.29459 | ||||||||
\(713\) | −4743.06 | −0.249129 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1760.00 | −0.0920563 | ||||||||
\(716\) | −4229.54 | −0.220762 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −10931.6 | −0.568192 | ||||||||
\(719\) | 34467.1 | 1.78777 | 0.893885 | − | 0.448295i | \(-0.147969\pi\) | ||||
0.893885 | + | 0.448295i | \(0.147969\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 2373.34 | 0.122591 | ||||||||
\(722\) | −3506.77 | −0.180759 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 2857.27 | 0.146670 | ||||||||
\(725\) | 5721.16 | 0.293074 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 9314.97 | 0.475204 | 0.237602 | − | 0.971363i | \(-0.423639\pi\) | ||||
0.237602 | + | 0.971363i | \(0.423639\pi\) | |||||||
\(728\) | 9537.35 | 0.485547 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 8182.24 | 0.414847 | ||||||||
\(731\) | −8984.49 | −0.454588 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 16146.3 | 0.813611 | 0.406805 | − | 0.913515i | \(-0.366643\pi\) | ||||
0.406805 | + | 0.913515i | \(0.366643\pi\) | |||||||
\(734\) | 23772.1 | 1.19543 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −4488.95 | −0.224816 | ||||||||
\(737\) | −905.500 | −0.0452571 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −36749.1 | −1.82928 | −0.914640 | − | 0.404268i | \(-0.867526\pi\) | ||||
−0.914640 | + | 0.404268i | \(0.867526\pi\) | |||||||
\(740\) | −423.239 | −0.0210251 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 9166.27 | 0.453510 | ||||||||
\(743\) | −2527.09 | −0.124778 | −0.0623890 | − | 0.998052i | \(-0.519872\pi\) | ||||
−0.0623890 | + | 0.998052i | \(0.519872\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −3524.44 | −0.173323 | ||||||||
\(746\) | −27616.2 | −1.35536 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −221.031 | −0.0108044 | ||||||||
\(749\) | 3155.93 | 0.153959 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 15828.0 | 0.769070 | 0.384535 | − | 0.923111i | \(-0.374362\pi\) | ||||
0.384535 | + | 0.923111i | \(0.374362\pi\) | |||||||
\(752\) | −9840.28 | −0.477178 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 33035.0 | 1.59557 | ||||||||
\(755\) | 15176.1 | 0.731541 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −20845.9 | −1.00087 | −0.500435 | − | 0.865774i | \(-0.666826\pi\) | ||||
−0.500435 | + | 0.865774i | \(0.666826\pi\) | |||||||
\(758\) | 15149.4 | 0.725927 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 10965.3 | 0.523360 | ||||||||
\(761\) | 2420.55 | 0.115302 | 0.0576511 | − | 0.998337i | \(-0.481639\pi\) | ||||
0.0576511 | + | 0.998337i | \(0.481639\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 12891.9 | 0.611690 | ||||||||
\(764\) | 2324.35 | 0.110068 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 29493.5 | 1.39118 | ||||||||
\(767\) | −16004.6 | −0.753445 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 22646.3 | 1.06196 | 0.530980 | − | 0.847384i | \(-0.321824\pi\) | ||||
0.530980 | + | 0.847384i | \(0.321824\pi\) | |||||||
\(770\) | 560.000 | 0.0262091 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 2952.33 | 0.137638 | ||||||||
\(773\) | 27620.2 | 1.28516 | 0.642580 | − | 0.766219i | \(-0.277864\pi\) | ||||
0.642580 | + | 0.766219i | \(0.277864\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −1697.30 | −0.0786695 | ||||||||
\(776\) | 43680.0 | 2.02064 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −13831.7 | −0.637391 | ||||||||
\(779\) | 1741.67 | 0.0801049 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −456.151 | −0.0208993 | ||||||||
\(782\) | 4402.35 | 0.201314 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −2470.74 | −0.112552 | ||||||||
\(785\) | −13568.2 | −0.616906 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 14767.1 | 0.668859 | 0.334429 | − | 0.942421i | \(-0.391456\pi\) | ||||
0.334429 | + | 0.942421i | \(0.391456\pi\) | |||||||
\(788\) | −6427.82 | −0.290586 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 12502.8 | 0.563076 | ||||||||
\(791\) | −13123.0 | −0.589887 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 6957.50 | 0.311561 | ||||||||
\(794\) | −6716.71 | −0.300211 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −2219.62 | −0.0988348 | ||||||||
\(797\) | −7549.97 | −0.335551 | −0.167775 | − | 0.985825i | \(-0.553658\pi\) | ||||
−0.167775 | + | 0.985825i | \(0.553658\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −4800.85 | −0.212568 | ||||||||
\(800\) | −1606.37 | −0.0709921 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 28482.1 | 1.25404 | ||||||||
\(803\) | −3990.39 | −0.175365 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 2445.16 | 0.107057 | ||||||||
\(806\) | −9800.50 | −0.428298 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −11678.8 | −0.508489 | ||||||||
\(809\) | 17920.0 | 0.778783 | 0.389391 | − | 0.921072i | \(-0.372685\pi\) | ||||
0.389391 | + | 0.921072i | \(0.372685\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 25536.6 | 1.10569 | 0.552843 | − | 0.833285i | \(-0.313543\pi\) | ||||
0.552843 | + | 0.833285i | \(0.313543\pi\) | |||||||
\(812\) | 2304.29 | 0.0995869 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −941.545 | −0.0405420 | ||||||||
\(815\) | 2326.30 | 0.0999836 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −33128.3 | −1.41862 | ||||||||
\(818\) | 16878.5 | 0.721447 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −138.096 | −0.00588114 | ||||||||
\(821\) | −13688.8 | −0.581904 | −0.290952 | − | 0.956738i | \(-0.593972\pi\) | ||||
−0.290952 | + | 0.956738i | \(0.593972\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −15102.9 | −0.639678 | −0.319839 | − | 0.947472i | \(-0.603629\pi\) | ||||
−0.319839 | + | 0.947472i | \(0.603629\pi\) | |||||||
\(824\) | −8197.22 | −0.346558 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 5092.37 | 0.214511 | ||||||||
\(827\) | −36290.3 | −1.52592 | −0.762961 | − | 0.646445i | \(-0.776255\pi\) | ||||
−0.762961 | + | 0.646445i | \(0.776255\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −39405.1 | −1.65090 | −0.825449 | − | 0.564477i | \(-0.809078\pi\) | ||||
−0.825449 | + | 0.564477i | \(0.809078\pi\) | |||||||
\(830\) | 6204.92 | 0.259489 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −32007.9 | −1.33374 | ||||||||
\(833\) | −1205.42 | −0.0501384 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 20780.3 | 0.861236 | ||||||||
\(836\) | −815.000 | −0.0337170 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 30409.6 | 1.25356 | ||||||||
\(839\) | −33093.9 | −1.36177 | −0.680886 | − | 0.732389i | \(-0.738405\pi\) | ||||
−0.680886 | + | 0.732389i | \(0.738405\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 27981.8 | 1.14731 | ||||||||
\(842\) | 4435.50 | 0.181541 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −1847.00 | −0.0753274 | ||||||||
\(845\) | −4893.96 | −0.199239 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 9043.89 | 0.366885 | ||||||||
\(848\) | −25776.4 | −1.04383 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 1575.38 | 0.0635706 | ||||||||
\(851\) | −4111.12 | −0.165602 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 29441.6 | 1.18178 | 0.590892 | − | 0.806750i | \(-0.298776\pi\) | ||||
0.590892 | + | 0.806750i | \(0.298776\pi\) | |||||||
\(854\) | −2213.75 | −0.0887037 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −10900.2 | −0.435233 | ||||||||
\(857\) | −16012.9 | −0.638260 | −0.319130 | − | 0.947711i | \(-0.603391\pi\) | ||||
−0.319130 | + | 0.947711i | \(0.603391\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −13404.3 | −0.532421 | −0.266211 | − | 0.963915i | \(-0.585772\pi\) | ||||
−0.266211 | + | 0.963915i | \(0.585772\pi\) | |||||||
\(860\) | 2626.73 | 0.104152 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −27290.2 | −1.07832 | ||||||||
\(863\) | 2058.73 | 0.0812050 | 0.0406025 | − | 0.999175i | \(-0.487072\pi\) | ||||
0.0406025 | + | 0.999175i | \(0.487072\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −21205.8 | −0.833549 | ||||||||
\(866\) | −6767.66 | −0.265559 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −683.614 | −0.0267320 | ||||||||
\(869\) | −6097.48 | −0.238024 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −8169.54 | −0.317812 | ||||||||
\(872\) | −44527.0 | −1.72922 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 16232.7 | 0.628236 | ||||||||
\(875\) | 875.000 | 0.0338062 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −16477.0 | −0.634422 | −0.317211 | − | 0.948355i | \(-0.602746\pi\) | ||||
−0.317211 | + | 0.948355i | \(0.602746\pi\) | |||||||
\(878\) | −22690.8 | −0.872183 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −1574.77 | −0.0603245 | ||||||||
\(881\) | 43307.7 | 1.65616 | 0.828079 | − | 0.560612i | \(-0.189434\pi\) | ||||
0.828079 | + | 0.560612i | \(0.189434\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 15197.9 | 0.579217 | 0.289608 | − | 0.957145i | \(-0.406475\pi\) | ||||
0.289608 | + | 0.957145i | \(0.406475\pi\) | |||||||
\(884\) | −1994.17 | −0.0758723 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 16961.9 | 0.643168 | ||||||||
\(887\) | 44953.6 | 1.70168 | 0.850842 | − | 0.525422i | \(-0.176093\pi\) | ||||
0.850842 | + | 0.525422i | \(0.176093\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 266.689 | 0.0100613 | ||||||||
\(890\) | −13029.3 | −0.490724 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −5488.13 | −0.206005 | ||||||||
\(893\) | −17702.0 | −0.663355 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −14701.8 | −0.549079 | ||||||||
\(896\) | 6586.08 | 0.245564 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −33509.5 | −1.24524 | ||||||||
\(899\) | −15536.9 | −0.576400 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −12575.7 | −0.464993 | ||||||||
\(902\) | −307.212 | −0.0113404 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 45325.2 | 1.66758 | ||||||||
\(905\) | 9931.77 | 0.364799 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −38388.7 | −1.40537 | −0.702687 | − | 0.711499i | \(-0.748017\pi\) | ||||
−0.702687 | + | 0.711499i | \(0.748017\pi\) | |||||||
\(908\) | −3267.48 | −0.119422 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 5052.40 | 0.184050 | ||||||||
\(911\) | −46222.1 | −1.68102 | −0.840508 | − | 0.541799i | \(-0.817743\pi\) | ||||
−0.840508 | + | 0.541799i | \(0.817743\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −3026.08 | −0.109692 | ||||||||
\(914\) | −31166.3 | −1.12789 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 3405.59 | 0.122842 | ||||||||
\(917\) | 10860.6 | 0.391109 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −30946.4 | −1.11080 | −0.555402 | − | 0.831582i | \(-0.687436\pi\) | ||||
−0.555402 | + | 0.831582i | \(0.687436\pi\) | |||||||
\(920\) | −8445.26 | −0.302644 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −28904.1 | −1.03244 | ||||||||
\(923\) | −4115.46 | −0.146763 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1471.16 | −0.0522936 | ||||||||
\(926\) | −42375.6 | −1.50383 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −14704.5 | −0.520149 | ||||||||
\(929\) | −1907.48 | −0.0673652 | −0.0336826 | − | 0.999433i | \(-0.510724\pi\) | ||||
−0.0336826 | + | 0.999433i | \(0.510724\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −4444.71 | −0.156466 | ||||||||
\(932\) | 2326.99 | 0.0817845 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 26299.2 | 0.921347 | ||||||||
\(935\) | −768.296 | −0.0268727 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −3334.99 | −0.116275 | −0.0581374 | − | 0.998309i | \(-0.518516\pi\) | ||||
−0.0581374 | + | 0.998309i | \(0.518516\pi\) | |||||||
\(938\) | 2599.40 | 0.0904834 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 1403.59 | 0.0487022 | ||||||||
\(941\) | 9632.00 | 0.333681 | 0.166841 | − | 0.985984i | \(-0.446643\pi\) | ||||
0.166841 | + | 0.985984i | \(0.446643\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −1341.40 | −0.0463223 | ||||||||
\(944\) | −14320.2 | −0.493732 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 5843.48 | 0.200833 | ||||||||
\(947\) | 53606.0 | 1.83945 | 0.919727 | − | 0.392559i | \(-0.128410\pi\) | ||||
0.919727 | + | 0.392559i | \(0.128410\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −36001.9 | −1.23148 | ||||||||
\(950\) | 5808.85 | 0.198383 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 4163.36 | 0.141739 | ||||||||
\(953\) | −28433.6 | −0.966481 | −0.483240 | − | 0.875488i | \(-0.660540\pi\) | ||||
−0.483240 | + | 0.875488i | \(0.660540\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 8079.38 | 0.273762 | ||||||||
\(956\) | −2783.82 | −0.0941790 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 20410.4 | 0.688341 | ||||||||
\(959\) | 8422.70 | 0.283611 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −25181.7 | −0.845278 | ||||||||
\(962\) | −8494.75 | −0.284700 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −687.436 | −0.0229676 | ||||||||
\(965\) | 10262.2 | 0.342334 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 33877.6 | 1.12661 | 0.563304 | − | 0.826250i | \(-0.309530\pi\) | ||||
0.563304 | + | 0.826250i | \(0.309530\pi\) | |||||||
\(968\) | −31236.4 | −1.03717 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 23139.4 | 0.765939 | ||||||||
\(971\) | 10208.6 | 0.337394 | 0.168697 | − | 0.985668i | \(-0.446044\pi\) | ||||
0.168697 | + | 0.985668i | \(0.446044\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −13279.0 | −0.437517 | ||||||||
\(974\) | −25504.4 | −0.839029 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 6225.27 | 0.204166 | ||||||||
\(977\) | 35478.1 | 1.16177 | 0.580883 | − | 0.813987i | \(-0.302707\pi\) | ||||
0.580883 | + | 0.813987i | \(0.302707\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 6354.27 | 0.207439 | ||||||||
\(980\) | 352.420 | 0.0114874 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 47800.7 | 1.55334 | ||||||||
\(983\) | −54435.8 | −1.76626 | −0.883130 | − | 0.469128i | \(-0.844568\pi\) | ||||
−0.883130 | + | 0.469128i | \(0.844568\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −22342.9 | −0.722746 | ||||||||
\(986\) | 14420.8 | 0.465773 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −7353.04 | −0.236773 | ||||||||
\(989\) | 25514.7 | 0.820346 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −47319.6 | −1.51681 | −0.758404 | − | 0.651784i | \(-0.774021\pi\) | ||||
−0.758404 | + | 0.651784i | \(0.774021\pi\) | |||||||
\(992\) | 4362.38 | 0.139623 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 1309.46 | 0.0417844 | ||||||||
\(995\) | −7715.35 | −0.245822 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 26273.1 | 0.834580 | 0.417290 | − | 0.908773i | \(-0.362980\pi\) | ||||
0.417290 | + | 0.908773i | \(0.362980\pi\) | |||||||
\(998\) | −10436.3 | −0.331017 | ||||||||
\(999\) | 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 | 315.4.a.h.1.1 | ✓ | 2 | |
3.2 | odd | 2 | 315.4.a.j.1.2 | yes | 2 | ||
5.4 | even | 2 | 1575.4.a.u.1.2 | 2 | |||
7.6 | odd | 2 | 2205.4.a.y.1.1 | 2 | |||
15.14 | odd | 2 | 1575.4.a.r.1.1 | 2 | |||
21.20 | even | 2 | 2205.4.a.ba.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
315.4.a.h.1.1 | ✓ | 2 | 1.1 | even | 1 | trivial | |
315.4.a.j.1.2 | yes | 2 | 3.2 | odd | 2 | ||
1575.4.a.r.1.1 | 2 | 15.14 | odd | 2 | |||
1575.4.a.u.1.2 | 2 | 5.4 | even | 2 | |||
2205.4.a.y.1.1 | 2 | 7.6 | odd | 2 | |||
2205.4.a.ba.1.2 | 2 | 21.20 | even | 2 |