Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2205,4,Mod(1,2205)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2205, 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("2205.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2205 = 3^{2} \cdot 5 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 2205.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: | \(130.099211563\) |
Analytic rank: | \(1\) |
Dimension: | \(6\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{6} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 34x^{4} + 241x^{2} - 64 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{9} \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-3.09945\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2205.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −3.09945 | −1.09582 | −0.547911 | − | 0.836536i | \(-0.684577\pi\) | ||||
−0.547911 | + | 0.836536i | \(0.684577\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.60662 | 0.200827 | ||||||||
\(5\) | −5.00000 | −0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 19.8160 | 0.875751 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 15.4973 | 0.490067 | ||||||||
\(11\) | 31.1878 | 0.854861 | 0.427430 | − | 0.904048i | \(-0.359419\pi\) | ||||
0.427430 | + | 0.904048i | \(0.359419\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −54.1032 | −1.15427 | −0.577136 | − | 0.816648i | \(-0.695830\pi\) | ||||
−0.577136 | + | 0.816648i | \(0.695830\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −74.2717 | −1.16050 | ||||||||
\(17\) | 81.8784 | 1.16814 | 0.584071 | − | 0.811703i | \(-0.301459\pi\) | ||||
0.584071 | + | 0.811703i | \(0.301459\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 37.3653 | 0.451168 | 0.225584 | − | 0.974224i | \(-0.427571\pi\) | ||||
0.225584 | + | 0.974224i | \(0.427571\pi\) | |||||||
\(20\) | −8.03310 | −0.0898128 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −96.6651 | −0.936776 | ||||||||
\(23\) | −116.264 | −1.05403 | −0.527017 | − | 0.849855i | \(-0.676689\pi\) | ||||
−0.527017 | + | 0.849855i | \(0.676689\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 25.0000 | 0.200000 | ||||||||
\(26\) | 167.691 | 1.26488 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −22.5290 | −0.144260 | −0.0721298 | − | 0.997395i | \(-0.522980\pi\) | ||||
−0.0721298 | + | 0.997395i | \(0.522980\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −89.9535 | −0.521165 | −0.260583 | − | 0.965452i | \(-0.583915\pi\) | ||||
−0.260583 | + | 0.965452i | \(0.583915\pi\) | |||||||
\(32\) | 71.6739 | 0.395946 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −253.778 | −1.28008 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 344.782 | 1.53194 | 0.765971 | − | 0.642876i | \(-0.222259\pi\) | ||||
0.765971 | + | 0.642876i | \(0.222259\pi\) | |||||||
\(38\) | −115.812 | −0.494400 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −99.0800 | −0.391648 | ||||||||
\(41\) | −245.889 | −0.936620 | −0.468310 | − | 0.883564i | \(-0.655137\pi\) | ||||
−0.468310 | + | 0.883564i | \(0.655137\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 41.4519 | 0.147008 | 0.0735041 | − | 0.997295i | \(-0.476582\pi\) | ||||
0.0735041 | + | 0.997295i | \(0.476582\pi\) | |||||||
\(44\) | 50.1069 | 0.171680 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 360.356 | 1.15503 | ||||||||
\(47\) | −431.524 | −1.33924 | −0.669620 | − | 0.742704i | \(-0.733543\pi\) | ||||
−0.669620 | + | 0.742704i | \(0.733543\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −77.4864 | −0.219165 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −86.9233 | −0.231810 | ||||||||
\(53\) | 263.673 | 0.683365 | 0.341682 | − | 0.939815i | \(-0.389003\pi\) | ||||
0.341682 | + | 0.939815i | \(0.389003\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −155.939 | −0.382305 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 69.8276 | 0.158083 | ||||||||
\(59\) | −627.005 | −1.38354 | −0.691772 | − | 0.722116i | \(-0.743170\pi\) | ||||
−0.691772 | + | 0.722116i | \(0.743170\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 715.666 | 1.50216 | 0.751079 | − | 0.660212i | \(-0.229534\pi\) | ||||
0.751079 | + | 0.660212i | \(0.229534\pi\) | |||||||
\(62\) | 278.807 | 0.571105 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 372.024 | 0.726609 | ||||||||
\(65\) | 270.516 | 0.516206 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −809.809 | −1.47663 | −0.738313 | − | 0.674459i | \(-0.764377\pi\) | ||||
−0.738313 | + | 0.674459i | \(0.764377\pi\) | |||||||
\(68\) | 131.547 | 0.234595 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −54.8762 | −0.0917268 | −0.0458634 | − | 0.998948i | \(-0.514604\pi\) | ||||
−0.0458634 | + | 0.998948i | \(0.514604\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 508.548 | 0.815356 | 0.407678 | − | 0.913126i | \(-0.366339\pi\) | ||||
0.407678 | + | 0.913126i | \(0.366339\pi\) | |||||||
\(74\) | −1068.64 | −1.67874 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 60.0319 | 0.0906070 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 61.8168 | 0.0880372 | 0.0440186 | − | 0.999031i | \(-0.485984\pi\) | ||||
0.0440186 | + | 0.999031i | \(0.485984\pi\) | |||||||
\(80\) | 371.359 | 0.518989 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 762.122 | 1.02637 | ||||||||
\(83\) | −560.154 | −0.740782 | −0.370391 | − | 0.928876i | \(-0.620776\pi\) | ||||
−0.370391 | + | 0.928876i | \(0.620776\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −409.392 | −0.522409 | ||||||||
\(86\) | −128.478 | −0.161095 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 618.017 | 0.748646 | ||||||||
\(89\) | −102.286 | −0.121824 | −0.0609119 | − | 0.998143i | \(-0.519401\pi\) | ||||
−0.0609119 | + | 0.998143i | \(0.519401\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −186.792 | −0.211679 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 1337.49 | 1.46757 | ||||||||
\(95\) | −186.827 | −0.201769 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −253.910 | −0.265780 | −0.132890 | − | 0.991131i | \(-0.542426\pi\) | ||||
−0.132890 | + | 0.991131i | \(0.542426\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 40.1655 | 0.0401655 | ||||||||
\(101\) | 612.694 | 0.603617 | 0.301809 | − | 0.953369i | \(-0.402410\pi\) | ||||
0.301809 | + | 0.953369i | \(0.402410\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1865.47 | 1.78457 | 0.892283 | − | 0.451477i | \(-0.149103\pi\) | ||||
0.892283 | + | 0.451477i | \(0.149103\pi\) | |||||||
\(104\) | −1072.11 | −1.01086 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −817.244 | −0.748847 | ||||||||
\(107\) | 997.858 | 0.901557 | 0.450779 | − | 0.892636i | \(-0.351146\pi\) | ||||
0.450779 | + | 0.892636i | \(0.351146\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1553.97 | 1.36554 | 0.682768 | − | 0.730635i | \(-0.260776\pi\) | ||||
0.682768 | + | 0.730635i | \(0.260776\pi\) | |||||||
\(110\) | 483.326 | 0.418939 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −268.484 | −0.223512 | −0.111756 | − | 0.993736i | \(-0.535647\pi\) | ||||
−0.111756 | + | 0.993736i | \(0.535647\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 581.321 | 0.471378 | ||||||||
\(116\) | −36.1955 | −0.0289713 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 1943.37 | 1.51612 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −358.322 | −0.269213 | ||||||||
\(122\) | −2218.18 | −1.64610 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −144.521 | −0.104664 | ||||||||
\(125\) | −125.000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −43.7474 | −0.0305665 | −0.0152833 | − | 0.999883i | \(-0.504865\pi\) | ||||
−0.0152833 | + | 0.999883i | \(0.504865\pi\) | |||||||
\(128\) | −1726.46 | −1.19218 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −838.453 | −0.565670 | ||||||||
\(131\) | 1641.52 | 1.09481 | 0.547407 | − | 0.836867i | \(-0.315615\pi\) | ||||
0.547407 | + | 0.836867i | \(0.315615\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 2509.97 | 1.61812 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 1622.50 | 1.02300 | ||||||||
\(137\) | 2465.15 | 1.53731 | 0.768656 | − | 0.639662i | \(-0.220926\pi\) | ||||
0.768656 | + | 0.639662i | \(0.220926\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −2954.45 | −1.80283 | −0.901416 | − | 0.432955i | \(-0.857471\pi\) | ||||
−0.901416 | + | 0.432955i | \(0.857471\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 170.086 | 0.100516 | ||||||||
\(143\) | −1687.36 | −0.986742 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 112.645 | 0.0645148 | ||||||||
\(146\) | −1576.22 | −0.893486 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 553.934 | 0.307656 | ||||||||
\(149\) | 16.8760 | 0.00927875 | 0.00463938 | − | 0.999989i | \(-0.498523\pi\) | ||||
0.00463938 | + | 0.999989i | \(0.498523\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1792.06 | −0.965797 | −0.482899 | − | 0.875676i | \(-0.660416\pi\) | ||||
−0.482899 | + | 0.875676i | \(0.660416\pi\) | |||||||
\(152\) | 740.431 | 0.395111 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 449.767 | 0.233072 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 3543.34 | 1.80121 | 0.900603 | − | 0.434643i | \(-0.143125\pi\) | ||||
0.900603 | + | 0.434643i | \(0.143125\pi\) | |||||||
\(158\) | −191.598 | −0.0964731 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −358.370 | −0.177073 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −70.4005 | −0.0338294 | −0.0169147 | − | 0.999857i | \(-0.505384\pi\) | ||||
−0.0169147 | + | 0.999857i | \(0.505384\pi\) | |||||||
\(164\) | −395.050 | −0.188099 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 1736.17 | 0.811765 | ||||||||
\(167\) | −2493.09 | −1.15522 | −0.577609 | − | 0.816313i | \(-0.696014\pi\) | ||||
−0.577609 | + | 0.816313i | \(0.696014\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 730.159 | 0.332344 | ||||||||
\(170\) | 1268.89 | 0.572468 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 66.5974 | 0.0295233 | ||||||||
\(173\) | −487.259 | −0.214137 | −0.107068 | − | 0.994252i | \(-0.534146\pi\) | ||||
−0.107068 | + | 0.994252i | \(0.534146\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −2316.37 | −0.992062 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 317.032 | 0.133497 | ||||||||
\(179\) | 340.024 | 0.141981 | 0.0709904 | − | 0.997477i | \(-0.477384\pi\) | ||||
0.0709904 | + | 0.997477i | \(0.477384\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1863.23 | −0.765152 | −0.382576 | − | 0.923924i | \(-0.624963\pi\) | ||||
−0.382576 | + | 0.923924i | \(0.624963\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −2303.89 | −0.923071 | ||||||||
\(185\) | −1723.91 | −0.685105 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 2553.60 | 0.998599 | ||||||||
\(188\) | −693.295 | −0.268956 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 579.061 | 0.221103 | ||||||||
\(191\) | −1557.97 | −0.590214 | −0.295107 | − | 0.955464i | \(-0.595355\pi\) | ||||
−0.295107 | + | 0.955464i | \(0.595355\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −338.441 | −0.126225 | −0.0631127 | − | 0.998006i | \(-0.520103\pi\) | ||||
−0.0631127 | + | 0.998006i | \(0.520103\pi\) | |||||||
\(194\) | 786.982 | 0.291248 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −903.950 | −0.326923 | −0.163461 | − | 0.986550i | \(-0.552266\pi\) | ||||
−0.163461 | + | 0.986550i | \(0.552266\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1987.44 | 0.707971 | 0.353985 | − | 0.935251i | \(-0.384826\pi\) | ||||
0.353985 | + | 0.935251i | \(0.384826\pi\) | |||||||
\(200\) | 495.400 | 0.175150 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −1899.02 | −0.661457 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1229.45 | 0.418869 | ||||||||
\(206\) | −5781.94 | −1.95557 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 4018.34 | 1.33953 | ||||||||
\(209\) | 1165.34 | 0.385686 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 3749.01 | 1.22319 | 0.611594 | − | 0.791172i | \(-0.290529\pi\) | ||||
0.611594 | + | 0.791172i | \(0.290529\pi\) | |||||||
\(212\) | 423.623 | 0.137238 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −3092.82 | −0.987947 | ||||||||
\(215\) | −207.259 | −0.0657441 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −4816.47 | −1.49639 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −250.534 | −0.0767774 | ||||||||
\(221\) | −4429.88 | −1.34835 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −3939.34 | −1.18295 | −0.591475 | − | 0.806324i | \(-0.701454\pi\) | ||||
−0.591475 | + | 0.806324i | \(0.701454\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 832.154 | 0.244929 | ||||||||
\(227\) | −2808.27 | −0.821107 | −0.410554 | − | 0.911836i | \(-0.634665\pi\) | ||||
−0.410554 | + | 0.911836i | \(0.634665\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1809.85 | 0.522264 | 0.261132 | − | 0.965303i | \(-0.415904\pi\) | ||||
0.261132 | + | 0.965303i | \(0.415904\pi\) | |||||||
\(230\) | −1801.78 | −0.516547 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −446.434 | −0.126336 | ||||||||
\(233\) | −973.995 | −0.273856 | −0.136928 | − | 0.990581i | \(-0.543723\pi\) | ||||
−0.136928 | + | 0.990581i | \(0.543723\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 2157.62 | 0.598926 | ||||||||
\(236\) | −1007.36 | −0.277854 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 6015.41 | 1.62805 | 0.814027 | − | 0.580828i | \(-0.197271\pi\) | ||||
0.814027 | + | 0.580828i | \(0.197271\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 384.989 | 0.102902 | 0.0514509 | − | 0.998676i | \(-0.483615\pi\) | ||||
0.0514509 | + | 0.998676i | \(0.483615\pi\) | |||||||
\(242\) | 1110.60 | 0.295010 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 1149.80 | 0.301675 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −2021.59 | −0.520771 | ||||||||
\(248\) | −1782.52 | −0.456411 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 387.432 | 0.0980134 | ||||||||
\(251\) | −1857.04 | −0.466994 | −0.233497 | − | 0.972357i | \(-0.575017\pi\) | ||||
−0.233497 | + | 0.972357i | \(0.575017\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −3626.02 | −0.901052 | ||||||||
\(254\) | 135.593 | 0.0334955 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 2374.90 | 0.579810 | ||||||||
\(257\) | 4825.03 | 1.17112 | 0.585559 | − | 0.810630i | \(-0.300875\pi\) | ||||
0.585559 | + | 0.810630i | \(0.300875\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 434.617 | 0.103668 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −5087.83 | −1.19972 | ||||||||
\(263\) | −836.796 | −0.196194 | −0.0980971 | − | 0.995177i | \(-0.531276\pi\) | ||||
−0.0980971 | + | 0.995177i | \(0.531276\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1318.37 | −0.305610 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −1301.05 | −0.296547 | ||||||||
\(269\) | −5454.11 | −1.23622 | −0.618110 | − | 0.786092i | \(-0.712101\pi\) | ||||
−0.618110 | + | 0.786092i | \(0.712101\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2580.16 | 0.578352 | 0.289176 | − | 0.957276i | \(-0.406619\pi\) | ||||
0.289176 | + | 0.957276i | \(0.406619\pi\) | |||||||
\(272\) | −6081.25 | −1.35562 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −7640.61 | −1.68462 | ||||||||
\(275\) | 779.694 | 0.170972 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 591.932 | 0.128396 | 0.0641981 | − | 0.997937i | \(-0.479551\pi\) | ||||
0.0641981 | + | 0.997937i | \(0.479551\pi\) | |||||||
\(278\) | 9157.20 | 1.97558 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −6365.13 | −1.35129 | −0.675644 | − | 0.737228i | \(-0.736134\pi\) | ||||
−0.675644 | + | 0.737228i | \(0.736134\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1074.93 | 0.225787 | 0.112894 | − | 0.993607i | \(-0.463988\pi\) | ||||
0.112894 | + | 0.993607i | \(0.463988\pi\) | |||||||
\(284\) | −88.1651 | −0.0184213 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 5229.89 | 1.08129 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1791.06 | 0.364556 | ||||||||
\(290\) | −349.138 | −0.0706968 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 817.042 | 0.163746 | ||||||||
\(293\) | −5914.66 | −1.17931 | −0.589656 | − | 0.807655i | \(-0.700737\pi\) | ||||
−0.589656 | + | 0.807655i | \(0.700737\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 3135.03 | 0.618740 | ||||||||
\(296\) | 6832.20 | 1.34160 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −52.3063 | −0.0101679 | ||||||||
\(299\) | 6290.27 | 1.21664 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 5554.39 | 1.05834 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −2775.19 | −0.523579 | ||||||||
\(305\) | −3578.33 | −0.671786 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 3162.52 | 0.587929 | 0.293965 | − | 0.955816i | \(-0.405025\pi\) | ||||
0.293965 | + | 0.955816i | \(0.405025\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −1394.03 | −0.255406 | ||||||||
\(311\) | −6941.22 | −1.26560 | −0.632798 | − | 0.774317i | \(-0.718094\pi\) | ||||
−0.632798 | + | 0.774317i | \(0.718094\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −8789.17 | −1.58720 | −0.793600 | − | 0.608440i | \(-0.791795\pi\) | ||||
−0.793600 | + | 0.608440i | \(0.791795\pi\) | |||||||
\(314\) | −10982.4 | −1.97380 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 99.3161 | 0.0176803 | ||||||||
\(317\) | −4837.69 | −0.857135 | −0.428568 | − | 0.903510i | \(-0.640982\pi\) | ||||
−0.428568 | + | 0.903510i | \(0.640982\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −702.629 | −0.123322 | ||||||||
\(320\) | −1860.12 | −0.324949 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 3059.41 | 0.527029 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1352.58 | −0.230854 | ||||||||
\(326\) | 218.203 | 0.0370710 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −4872.54 | −0.820246 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −4122.43 | −0.684560 | −0.342280 | − | 0.939598i | \(-0.611199\pi\) | ||||
−0.342280 | + | 0.939598i | \(0.611199\pi\) | |||||||
\(332\) | −899.954 | −0.148769 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 7727.23 | 1.26591 | ||||||||
\(335\) | 4049.04 | 0.660367 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 9671.74 | 1.56336 | 0.781681 | − | 0.623678i | \(-0.214362\pi\) | ||||
0.781681 | + | 0.623678i | \(0.214362\pi\) | |||||||
\(338\) | −2263.10 | −0.364190 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −657.737 | −0.104914 | ||||||||
\(341\) | −2805.45 | −0.445524 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 821.410 | 0.128743 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 1510.24 | 0.234656 | ||||||||
\(347\) | 6169.21 | 0.954411 | 0.477205 | − | 0.878792i | \(-0.341650\pi\) | ||||
0.477205 | + | 0.878792i | \(0.341650\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 7346.44 | 1.12678 | 0.563390 | − | 0.826191i | \(-0.309497\pi\) | ||||
0.563390 | + | 0.826191i | \(0.309497\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 2235.35 | 0.338479 | ||||||||
\(353\) | −10850.5 | −1.63602 | −0.818008 | − | 0.575206i | \(-0.804922\pi\) | ||||
−0.818008 | + | 0.575206i | \(0.804922\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 274.381 | 0.0410215 | ||||||||
\(356\) | −164.335 | −0.0244656 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −1053.89 | −0.155586 | ||||||||
\(359\) | 4365.52 | 0.641792 | 0.320896 | − | 0.947114i | \(-0.396016\pi\) | ||||
0.320896 | + | 0.947114i | \(0.396016\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −5462.83 | −0.796447 | ||||||||
\(362\) | 5774.99 | 0.838471 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −2542.74 | −0.364638 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 7197.13 | 1.02367 | 0.511835 | − | 0.859084i | \(-0.328966\pi\) | ||||
0.511835 | + | 0.859084i | \(0.328966\pi\) | |||||||
\(368\) | 8635.14 | 1.22320 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 5343.18 | 0.750754 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 12300.6 | 1.70751 | 0.853753 | − | 0.520678i | \(-0.174321\pi\) | ||||
0.853753 | + | 0.520678i | \(0.174321\pi\) | |||||||
\(374\) | −7914.78 | −1.09429 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −8551.08 | −1.17284 | ||||||||
\(377\) | 1218.89 | 0.166515 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −888.207 | −0.120380 | −0.0601901 | − | 0.998187i | \(-0.519171\pi\) | ||||
−0.0601901 | + | 0.998187i | \(0.519171\pi\) | |||||||
\(380\) | −300.159 | −0.0405207 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 4828.86 | 0.646770 | ||||||||
\(383\) | −10524.1 | −1.40406 | −0.702031 | − | 0.712147i | \(-0.747723\pi\) | ||||
−0.702031 | + | 0.712147i | \(0.747723\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 1048.98 | 0.138321 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −407.937 | −0.0533759 | ||||||||
\(389\) | 6006.81 | 0.782924 | 0.391462 | − | 0.920194i | \(-0.371970\pi\) | ||||
0.391462 | + | 0.920194i | \(0.371970\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −9519.52 | −1.23126 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 2801.75 | 0.358249 | ||||||||
\(395\) | −309.084 | −0.0393714 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −14706.6 | −1.85920 | −0.929602 | − | 0.368565i | \(-0.879849\pi\) | ||||
−0.929602 | + | 0.368565i | \(0.879849\pi\) | |||||||
\(398\) | −6159.99 | −0.775810 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −1856.79 | −0.232099 | ||||||||
\(401\) | −2513.22 | −0.312978 | −0.156489 | − | 0.987680i | \(-0.550018\pi\) | ||||
−0.156489 | + | 0.987680i | \(0.550018\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 4866.77 | 0.601566 | ||||||||
\(404\) | 984.366 | 0.121223 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 10753.0 | 1.30960 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −4288.99 | −0.518526 | −0.259263 | − | 0.965807i | \(-0.583480\pi\) | ||||
−0.259263 | + | 0.965807i | \(0.583480\pi\) | |||||||
\(410\) | −3810.61 | −0.459006 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 2997.10 | 0.358390 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 2800.77 | 0.331288 | ||||||||
\(416\) | −3877.79 | −0.457030 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −3611.92 | −0.422643 | ||||||||
\(419\) | −6467.11 | −0.754031 | −0.377016 | − | 0.926207i | \(-0.623050\pi\) | ||||
−0.377016 | + | 0.926207i | \(0.623050\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −13647.0 | −1.57984 | −0.789921 | − | 0.613209i | \(-0.789878\pi\) | ||||
−0.789921 | + | 0.613209i | \(0.789878\pi\) | |||||||
\(422\) | −11619.9 | −1.34040 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 5224.95 | 0.598458 | ||||||||
\(425\) | 2046.96 | 0.233628 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 1603.18 | 0.181057 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 642.391 | 0.0720438 | ||||||||
\(431\) | −17252.7 | −1.92815 | −0.964074 | − | 0.265634i | \(-0.914419\pi\) | ||||
−0.964074 | + | 0.265634i | \(0.914419\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 4033.03 | 0.447610 | 0.223805 | − | 0.974634i | \(-0.428152\pi\) | ||||
0.223805 | + | 0.974634i | \(0.428152\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 2496.64 | 0.274237 | ||||||||
\(437\) | −4344.25 | −0.475546 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −16593.8 | −1.80405 | −0.902025 | − | 0.431684i | \(-0.857920\pi\) | ||||
−0.902025 | + | 0.431684i | \(0.857920\pi\) | |||||||
\(440\) | −3090.08 | −0.334804 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 13730.2 | 1.47756 | ||||||||
\(443\) | 5587.14 | 0.599216 | 0.299608 | − | 0.954062i | \(-0.403144\pi\) | ||||
0.299608 | + | 0.954062i | \(0.403144\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 511.431 | 0.0544813 | ||||||||
\(446\) | 12209.8 | 1.29630 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −13090.2 | −1.37587 | −0.687935 | − | 0.725772i | \(-0.741483\pi\) | ||||
−0.687935 | + | 0.725772i | \(0.741483\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −7668.73 | −0.800680 | ||||||||
\(452\) | −431.352 | −0.0448873 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 8704.10 | 0.899788 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 7594.11 | 0.777324 | 0.388662 | − | 0.921380i | \(-0.372937\pi\) | ||||
0.388662 | + | 0.921380i | \(0.372937\pi\) | |||||||
\(458\) | −5609.55 | −0.572308 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 933.962 | 0.0946656 | ||||||||
\(461\) | −15260.2 | −1.54173 | −0.770865 | − | 0.636998i | \(-0.780176\pi\) | ||||
−0.770865 | + | 0.636998i | \(0.780176\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −4278.64 | −0.429472 | −0.214736 | − | 0.976672i | \(-0.568889\pi\) | ||||
−0.214736 | + | 0.976672i | \(0.568889\pi\) | |||||||
\(464\) | 1673.27 | 0.167413 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 3018.85 | 0.300098 | ||||||||
\(467\) | −9102.32 | −0.901938 | −0.450969 | − | 0.892540i | \(-0.648922\pi\) | ||||
−0.450969 | + | 0.892540i | \(0.648922\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −6687.45 | −0.656317 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −12424.7 | −1.21164 | ||||||||
\(473\) | 1292.79 | 0.125672 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 934.133 | 0.0902336 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −18644.5 | −1.78406 | ||||||||
\(479\) | −4226.58 | −0.403167 | −0.201584 | − | 0.979471i | \(-0.564609\pi\) | ||||
−0.201584 | + | 0.979471i | \(0.564609\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −18653.8 | −1.76828 | ||||||||
\(482\) | −1193.26 | −0.112762 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −575.688 | −0.0540653 | ||||||||
\(485\) | 1269.55 | 0.118860 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −9576.48 | −0.891071 | −0.445536 | − | 0.895264i | \(-0.646987\pi\) | ||||
−0.445536 | + | 0.895264i | \(0.646987\pi\) | |||||||
\(488\) | 14181.6 | 1.31552 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −21412.2 | −1.96806 | −0.984030 | − | 0.178000i | \(-0.943037\pi\) | ||||
−0.984030 | + | 0.178000i | \(0.943037\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −1844.64 | −0.168516 | ||||||||
\(494\) | 6265.81 | 0.570672 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 6681.00 | 0.604810 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −19706.9 | −1.76794 | −0.883970 | − | 0.467543i | \(-0.845139\pi\) | ||||
−0.883970 | + | 0.467543i | \(0.845139\pi\) | |||||||
\(500\) | −200.827 | −0.0179626 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 5755.82 | 0.511743 | ||||||||
\(503\) | −176.759 | −0.0156685 | −0.00783427 | − | 0.999969i | \(-0.502494\pi\) | ||||
−0.00783427 | + | 0.999969i | \(0.502494\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −3063.47 | −0.269946 | ||||||||
\(506\) | 11238.7 | 0.987393 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −70.2854 | −0.00613860 | ||||||||
\(509\) | −776.451 | −0.0676142 | −0.0338071 | − | 0.999428i | \(-0.510763\pi\) | ||||
−0.0338071 | + | 0.999428i | \(0.510763\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 6450.80 | 0.556812 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −14955.0 | −1.28334 | ||||||||
\(515\) | −9327.35 | −0.798082 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −13458.3 | −1.14486 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 5360.55 | 0.452068 | ||||||||
\(521\) | −4248.01 | −0.357215 | −0.178607 | − | 0.983920i | \(-0.557159\pi\) | ||||
−0.178607 | + | 0.983920i | \(0.557159\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −13490.8 | −1.12794 | −0.563968 | − | 0.825797i | \(-0.690726\pi\) | ||||
−0.563968 | + | 0.825797i | \(0.690726\pi\) | |||||||
\(524\) | 2637.30 | 0.219869 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 2593.61 | 0.214994 | ||||||||
\(527\) | −7365.24 | −0.608795 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1350.36 | 0.110986 | ||||||||
\(530\) | 4086.22 | 0.334894 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 13303.4 | 1.08111 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −4989.29 | −0.403189 | ||||||||
\(536\) | −16047.2 | −1.29316 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 16904.8 | 1.35468 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −10582.4 | −0.840984 | −0.420492 | − | 0.907296i | \(-0.638143\pi\) | ||||
−0.420492 | + | 0.907296i | \(0.638143\pi\) | |||||||
\(542\) | −7997.08 | −0.633771 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 5868.54 | 0.462521 | ||||||||
\(545\) | −7769.86 | −0.610687 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −6182.43 | −0.483257 | −0.241629 | − | 0.970369i | \(-0.577682\pi\) | ||||
−0.241629 | + | 0.970369i | \(0.577682\pi\) | |||||||
\(548\) | 3960.56 | 0.308735 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −2416.63 | −0.187355 | ||||||||
\(551\) | −841.803 | −0.0650853 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −1834.67 | −0.140699 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −4746.68 | −0.362058 | ||||||||
\(557\) | 20848.5 | 1.58596 | 0.792979 | − | 0.609249i | \(-0.208529\pi\) | ||||
0.792979 | + | 0.609249i | \(0.208529\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −2242.68 | −0.169687 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 19728.4 | 1.48077 | ||||||||
\(563\) | 13326.0 | 0.997557 | 0.498779 | − | 0.866729i | \(-0.333782\pi\) | ||||
0.498779 | + | 0.866729i | \(0.333782\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 1342.42 | 0.0999576 | ||||||||
\(566\) | −3331.69 | −0.247423 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −1087.43 | −0.0803299 | ||||||||
\(569\) | −11592.9 | −0.854126 | −0.427063 | − | 0.904222i | \(-0.640452\pi\) | ||||
−0.427063 | + | 0.904222i | \(0.640452\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1603.77 | 0.117541 | 0.0587704 | − | 0.998272i | \(-0.481282\pi\) | ||||
0.0587704 | + | 0.998272i | \(0.481282\pi\) | |||||||
\(572\) | −2710.94 | −0.198165 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −2906.60 | −0.210807 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −12475.4 | −0.900097 | −0.450048 | − | 0.893004i | \(-0.648593\pi\) | ||||
−0.450048 | + | 0.893004i | \(0.648593\pi\) | |||||||
\(578\) | −5551.32 | −0.399489 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 180.978 | 0.0129564 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 8223.39 | 0.584182 | ||||||||
\(584\) | 10077.4 | 0.714049 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 18332.2 | 1.29232 | ||||||||
\(587\) | −11367.0 | −0.799264 | −0.399632 | − | 0.916676i | \(-0.630862\pi\) | ||||
−0.399632 | + | 0.916676i | \(0.630862\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −3361.14 | −0.235133 | ||||||||
\(590\) | −9716.87 | −0.678029 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −25607.6 | −1.77781 | ||||||||
\(593\) | −2463.42 | −0.170591 | −0.0852955 | − | 0.996356i | \(-0.527183\pi\) | ||||
−0.0852955 | + | 0.996356i | \(0.527183\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 27.1133 | 0.00186343 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −19496.4 | −1.33322 | ||||||||
\(599\) | 26493.7 | 1.80719 | 0.903593 | − | 0.428393i | \(-0.140920\pi\) | ||||
0.903593 | + | 0.428393i | \(0.140920\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −5703.89 | −0.387132 | −0.193566 | − | 0.981087i | \(-0.562005\pi\) | ||||
−0.193566 | + | 0.981087i | \(0.562005\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −2879.15 | −0.193959 | ||||||||
\(605\) | 1791.61 | 0.120396 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −6111.92 | −0.408691 | −0.204345 | − | 0.978899i | \(-0.565507\pi\) | ||||
−0.204345 | + | 0.978899i | \(0.565507\pi\) | |||||||
\(608\) | 2678.12 | 0.178638 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 11090.9 | 0.736158 | ||||||||
\(611\) | 23346.8 | 1.54585 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 15496.0 | 1.02101 | 0.510504 | − | 0.859875i | \(-0.329459\pi\) | ||||
0.510504 | + | 0.859875i | \(0.329459\pi\) | |||||||
\(614\) | −9802.08 | −0.644266 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 23071.0 | 1.50535 | 0.752676 | − | 0.658391i | \(-0.228763\pi\) | ||||
0.752676 | + | 0.658391i | \(0.228763\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 9160.95 | 0.594846 | 0.297423 | − | 0.954746i | \(-0.403873\pi\) | ||||
0.297423 | + | 0.954746i | \(0.403873\pi\) | |||||||
\(620\) | 722.605 | 0.0468073 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 21514.0 | 1.38687 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 625.000 | 0.0400000 | ||||||||
\(626\) | 27241.6 | 1.73929 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 5692.80 | 0.361732 | ||||||||
\(629\) | 28230.2 | 1.78953 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 26685.9 | 1.68360 | 0.841798 | − | 0.539793i | \(-0.181497\pi\) | ||||
0.841798 | + | 0.539793i | \(0.181497\pi\) | |||||||
\(632\) | 1224.96 | 0.0770987 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 14994.2 | 0.939268 | ||||||||
\(635\) | 218.737 | 0.0136698 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 2177.77 | 0.135139 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 8632.31 | 0.533159 | ||||||||
\(641\) | −22763.0 | −1.40263 | −0.701314 | − | 0.712852i | \(-0.747403\pi\) | ||||
−0.701314 | + | 0.712852i | \(0.747403\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −13560.1 | −0.831660 | −0.415830 | − | 0.909442i | \(-0.636509\pi\) | ||||
−0.415830 | + | 0.909442i | \(0.636509\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −9482.51 | −0.577530 | ||||||||
\(647\) | −24534.7 | −1.49082 | −0.745408 | − | 0.666609i | \(-0.767745\pi\) | ||||
−0.745408 | + | 0.666609i | \(0.767745\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −19554.9 | −1.18274 | ||||||||
\(650\) | 4192.26 | 0.252975 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −113.107 | −0.00679388 | ||||||||
\(653\) | 14176.0 | 0.849539 | 0.424769 | − | 0.905302i | \(-0.360355\pi\) | ||||
0.424769 | + | 0.905302i | \(0.360355\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −8207.62 | −0.489616 | ||||||||
\(656\) | 18262.6 | 1.08694 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 20212.3 | 1.19478 | 0.597391 | − | 0.801950i | \(-0.296204\pi\) | ||||
0.597391 | + | 0.801950i | \(0.296204\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −23850.7 | −1.40346 | −0.701728 | − | 0.712445i | \(-0.747588\pi\) | ||||
−0.701728 | + | 0.712445i | \(0.747588\pi\) | |||||||
\(662\) | 12777.3 | 0.750156 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −11100.0 | −0.648741 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 2619.31 | 0.152054 | ||||||||
\(668\) | −4005.45 | −0.232000 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −12549.8 | −0.723645 | ||||||||
\(671\) | 22320.0 | 1.28414 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 395.817 | 0.0226711 | 0.0113355 | − | 0.999936i | \(-0.496392\pi\) | ||||
0.0113355 | + | 0.999936i | \(0.496392\pi\) | |||||||
\(674\) | −29977.1 | −1.71317 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 1173.09 | 0.0667437 | ||||||||
\(677\) | −8729.25 | −0.495557 | −0.247779 | − | 0.968817i | \(-0.579701\pi\) | ||||
−0.247779 | + | 0.968817i | \(0.579701\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −8112.50 | −0.457500 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 8695.36 | 0.488215 | ||||||||
\(683\) | −7531.85 | −0.421959 | −0.210980 | − | 0.977490i | \(-0.567665\pi\) | ||||
−0.210980 | + | 0.977490i | \(0.567665\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −12325.7 | −0.687507 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −3078.70 | −0.170602 | ||||||||
\(689\) | −14265.6 | −0.788789 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −163.381 | −0.00899465 | −0.00449732 | − | 0.999990i | \(-0.501432\pi\) | ||||
−0.00449732 | + | 0.999990i | \(0.501432\pi\) | |||||||
\(692\) | −782.840 | −0.0430045 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −19121.2 | −1.04587 | ||||||||
\(695\) | 14772.3 | 0.806251 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −20133.0 | −1.09411 | ||||||||
\(698\) | −22770.0 | −1.23475 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −29759.6 | −1.60343 | −0.801716 | − | 0.597705i | \(-0.796079\pi\) | ||||
−0.801716 | + | 0.597705i | \(0.796079\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 12882.9 | 0.691163 | ||||||||
\(704\) | 11602.6 | 0.621150 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 33630.6 | 1.79278 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −15454.6 | −0.818633 | −0.409316 | − | 0.912393i | \(-0.634233\pi\) | ||||
−0.409316 | + | 0.912393i | \(0.634233\pi\) | |||||||
\(710\) | −850.431 | −0.0449523 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −2026.90 | −0.106687 | ||||||||
\(713\) | 10458.4 | 0.549325 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 8436.80 | 0.441284 | ||||||||
\(716\) | 546.289 | 0.0285136 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −13530.7 | −0.703290 | ||||||||
\(719\) | −13452.1 | −0.697744 | −0.348872 | − | 0.937170i | \(-0.613435\pi\) | ||||
−0.348872 | + | 0.937170i | \(0.613435\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 16931.8 | 0.872765 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −2993.50 | −0.153664 | ||||||||
\(725\) | −563.225 | −0.0288519 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 6644.23 | 0.338956 | 0.169478 | − | 0.985534i | \(-0.445792\pi\) | ||||
0.169478 | + | 0.985534i | \(0.445792\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 7881.10 | 0.399579 | ||||||||
\(731\) | 3394.01 | 0.171726 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 12532.8 | 0.631525 | 0.315762 | − | 0.948838i | \(-0.397740\pi\) | ||||
0.315762 | + | 0.948838i | \(0.397740\pi\) | |||||||
\(734\) | −22307.2 | −1.12176 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −8333.11 | −0.417340 | ||||||||
\(737\) | −25256.1 | −1.26231 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 16509.4 | 0.821799 | 0.410900 | − | 0.911681i | \(-0.365215\pi\) | ||||
0.410900 | + | 0.911681i | \(0.365215\pi\) | |||||||
\(740\) | −2769.67 | −0.137588 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 11768.9 | 0.581102 | 0.290551 | − | 0.956859i | \(-0.406161\pi\) | ||||
0.290551 | + | 0.956859i | \(0.406161\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −84.3799 | −0.00414958 | ||||||||
\(746\) | −38125.1 | −1.87112 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 4102.67 | 0.200546 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 18336.1 | 0.890938 | 0.445469 | − | 0.895297i | \(-0.353037\pi\) | ||||
0.445469 | + | 0.895297i | \(0.353037\pi\) | |||||||
\(752\) | 32050.0 | 1.55418 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −3777.90 | −0.182471 | ||||||||
\(755\) | 8960.28 | 0.431918 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 24340.5 | 1.16865 | 0.584326 | − | 0.811519i | \(-0.301359\pi\) | ||||
0.584326 | + | 0.811519i | \(0.301359\pi\) | |||||||
\(758\) | 2752.96 | 0.131915 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −3702.16 | −0.176699 | ||||||||
\(761\) | −28022.5 | −1.33484 | −0.667421 | − | 0.744681i | \(-0.732602\pi\) | ||||
−0.667421 | + | 0.744681i | \(0.732602\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −2503.07 | −0.118531 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 32618.9 | 1.53860 | ||||||||
\(767\) | 33923.0 | 1.59699 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −33595.9 | −1.57542 | −0.787712 | − | 0.616044i | \(-0.788734\pi\) | ||||
−0.787712 | + | 0.616044i | \(0.788734\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −543.745 | −0.0253495 | ||||||||
\(773\) | −668.213 | −0.0310918 | −0.0155459 | − | 0.999879i | \(-0.504949\pi\) | ||||
−0.0155459 | + | 0.999879i | \(0.504949\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −2248.84 | −0.104233 | ||||||||
\(776\) | −5031.48 | −0.232757 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −18617.8 | −0.857945 | ||||||||
\(779\) | −9187.73 | −0.422573 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1711.47 | −0.0784136 | ||||||||
\(782\) | 29505.3 | 1.34924 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −17716.7 | −0.805524 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 16719.9 | 0.757305 | 0.378653 | − | 0.925539i | \(-0.376388\pi\) | ||||
0.378653 | + | 0.925539i | \(0.376388\pi\) | |||||||
\(788\) | −1452.30 | −0.0656550 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 957.992 | 0.0431441 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −38719.9 | −1.73390 | ||||||||
\(794\) | 45582.5 | 2.03736 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 3193.07 | 0.142180 | ||||||||
\(797\) | 40821.1 | 1.81425 | 0.907126 | − | 0.420860i | \(-0.138272\pi\) | ||||
0.907126 | + | 0.420860i | \(0.138272\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −35332.5 | −1.56442 | ||||||||
\(800\) | 1791.85 | 0.0791892 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 7789.60 | 0.342968 | ||||||||
\(803\) | 15860.5 | 0.697016 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −15084.3 | −0.659210 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 12141.1 | 0.528619 | ||||||||
\(809\) | 10822.7 | 0.470340 | 0.235170 | − | 0.971954i | \(-0.424435\pi\) | ||||
0.235170 | + | 0.971954i | \(0.424435\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −19650.6 | −0.850833 | −0.425417 | − | 0.904998i | \(-0.639872\pi\) | ||||
−0.425417 | + | 0.904998i | \(0.639872\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −33328.4 | −1.43509 | ||||||||
\(815\) | 352.003 | 0.0151290 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1548.86 | 0.0663254 | ||||||||
\(818\) | 13293.5 | 0.568212 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 1975.25 | 0.0841204 | ||||||||
\(821\) | 24495.9 | 1.04130 | 0.520652 | − | 0.853769i | \(-0.325689\pi\) | ||||
0.520652 | + | 0.853769i | \(0.325689\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 21651.7 | 0.917048 | 0.458524 | − | 0.888682i | \(-0.348378\pi\) | ||||
0.458524 | + | 0.888682i | \(0.348378\pi\) | |||||||
\(824\) | 36966.1 | 1.56284 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 4550.97 | 0.191358 | 0.0956788 | − | 0.995412i | \(-0.469498\pi\) | ||||
0.0956788 | + | 0.995412i | \(0.469498\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 43235.4 | 1.81137 | 0.905686 | − | 0.423949i | \(-0.139356\pi\) | ||||
0.905686 | + | 0.423949i | \(0.139356\pi\) | |||||||
\(830\) | −8680.86 | −0.363033 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −20127.7 | −0.838704 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 12465.5 | 0.516629 | ||||||||
\(836\) | 1872.26 | 0.0774563 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 20044.5 | 0.826285 | ||||||||
\(839\) | 139.264 | 0.00573053 | 0.00286527 | − | 0.999996i | \(-0.499088\pi\) | ||||
0.00286527 | + | 0.999996i | \(0.499088\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −23881.4 | −0.979189 | ||||||||
\(842\) | 42298.2 | 1.73123 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 6023.24 | 0.245650 | ||||||||
\(845\) | −3650.80 | −0.148629 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −19583.5 | −0.793042 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −6344.46 | −0.256015 | ||||||||
\(851\) | −40085.8 | −1.61472 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 13239.6 | 0.531437 | 0.265718 | − | 0.964051i | \(-0.414391\pi\) | ||||
0.265718 | + | 0.964051i | \(0.414391\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 19773.6 | 0.789540 | ||||||||
\(857\) | 44722.7 | 1.78261 | 0.891305 | − | 0.453404i | \(-0.149791\pi\) | ||||
0.891305 | + | 0.453404i | \(0.149791\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 19350.8 | 0.768617 | 0.384308 | − | 0.923205i | \(-0.374440\pi\) | ||||
0.384308 | + | 0.923205i | \(0.374440\pi\) | |||||||
\(860\) | −332.987 | −0.0132032 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 53473.9 | 2.11291 | ||||||||
\(863\) | −34706.8 | −1.36899 | −0.684493 | − | 0.729020i | \(-0.739976\pi\) | ||||
−0.684493 | + | 0.729020i | \(0.739976\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 2436.30 | 0.0957648 | ||||||||
\(866\) | −12500.2 | −0.490501 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 1927.93 | 0.0752595 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 43813.3 | 1.70443 | ||||||||
\(872\) | 30793.5 | 1.19587 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 13464.8 | 0.521114 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 33566.2 | 1.29242 | 0.646209 | − | 0.763160i | \(-0.276353\pi\) | ||||
0.646209 | + | 0.763160i | \(0.276353\pi\) | |||||||
\(878\) | 51431.7 | 1.97692 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 11581.9 | 0.443664 | ||||||||
\(881\) | 32706.1 | 1.25074 | 0.625368 | − | 0.780330i | \(-0.284949\pi\) | ||||
0.625368 | + | 0.780330i | \(0.284949\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −19854.3 | −0.756683 | −0.378342 | − | 0.925666i | \(-0.623506\pi\) | ||||
−0.378342 | + | 0.925666i | \(0.623506\pi\) | |||||||
\(884\) | −7117.14 | −0.270786 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −17317.1 | −0.656635 | ||||||||
\(887\) | −29902.1 | −1.13192 | −0.565960 | − | 0.824433i | \(-0.691494\pi\) | ||||
−0.565960 | + | 0.824433i | \(0.691494\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −1585.16 | −0.0597018 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −6329.02 | −0.237569 | ||||||||
\(893\) | −16124.0 | −0.604222 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −1700.12 | −0.0634957 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 40572.5 | 1.50771 | ||||||||
\(899\) | 2026.56 | 0.0751831 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 21589.1 | 0.798267 | ||||||||
\(902\) | 23768.9 | 0.877403 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −5320.28 | −0.195741 | ||||||||
\(905\) | 9316.14 | 0.342187 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 38973.5 | 1.42679 | 0.713393 | − | 0.700764i | \(-0.247158\pi\) | ||||
0.713393 | + | 0.700764i | \(0.247158\pi\) | |||||||
\(908\) | −4511.82 | −0.164901 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −41356.0 | −1.50404 | −0.752022 | − | 0.659138i | \(-0.770922\pi\) | ||||
−0.752022 | + | 0.659138i | \(0.770922\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −17470.0 | −0.633265 | ||||||||
\(914\) | −23537.6 | −0.851810 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 2907.74 | 0.104885 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 14009.2 | 0.502852 | 0.251426 | − | 0.967876i | \(-0.419100\pi\) | ||||
0.251426 | + | 0.967876i | \(0.419100\pi\) | |||||||
\(920\) | 11519.5 | 0.412810 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 47298.3 | 1.68946 | ||||||||
\(923\) | 2968.98 | 0.105878 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 8619.55 | 0.306388 | ||||||||
\(926\) | 13261.5 | 0.470625 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −1614.74 | −0.0571190 | ||||||||
\(929\) | −39996.1 | −1.41252 | −0.706259 | − | 0.707954i | \(-0.749619\pi\) | ||||
−0.706259 | + | 0.707954i | \(0.749619\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −1564.84 | −0.0549979 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 28212.2 | 0.988365 | ||||||||
\(935\) | −12768.0 | −0.446587 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −14964.6 | −0.521743 | −0.260872 | − | 0.965374i | \(-0.584010\pi\) | ||||
−0.260872 | + | 0.965374i | \(0.584010\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 3466.48 | 0.120281 | ||||||||
\(941\) | −31615.3 | −1.09525 | −0.547624 | − | 0.836725i | \(-0.684468\pi\) | ||||
−0.547624 | + | 0.836725i | \(0.684468\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 28588.1 | 0.987229 | ||||||||
\(944\) | 46568.8 | 1.60560 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −4006.95 | −0.137714 | ||||||||
\(947\) | −29872.2 | −1.02504 | −0.512522 | − | 0.858674i | \(-0.671289\pi\) | ||||
−0.512522 | + | 0.858674i | \(0.671289\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −27514.1 | −0.941143 | ||||||||
\(950\) | −2895.30 | −0.0988801 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 41530.2 | 1.41164 | 0.705821 | − | 0.708390i | \(-0.250578\pi\) | ||||
0.705821 | + | 0.708390i | \(0.250578\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 7789.85 | 0.263952 | ||||||||
\(956\) | 9664.48 | 0.326958 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 13100.1 | 0.441800 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −21699.4 | −0.728387 | ||||||||
\(962\) | 57816.7 | 1.93772 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 618.531 | 0.0206655 | ||||||||
\(965\) | 1692.20 | 0.0564497 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 53414.9 | 1.77633 | 0.888164 | − | 0.459527i | \(-0.151981\pi\) | ||||
0.888164 | + | 0.459527i | \(0.151981\pi\) | |||||||
\(968\) | −7100.51 | −0.235764 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −3934.91 | −0.130250 | ||||||||
\(971\) | −38471.8 | −1.27149 | −0.635747 | − | 0.771898i | \(-0.719308\pi\) | ||||
−0.635747 | + | 0.771898i | \(0.719308\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 29681.9 | 0.976456 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −53153.8 | −1.74325 | ||||||||
\(977\) | 53414.8 | 1.74912 | 0.874561 | − | 0.484916i | \(-0.161150\pi\) | ||||
0.874561 | + | 0.484916i | \(0.161150\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −3190.08 | −0.104142 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 66366.1 | 2.15665 | ||||||||
\(983\) | −13893.2 | −0.450788 | −0.225394 | − | 0.974268i | \(-0.572367\pi\) | ||||
−0.225394 | + | 0.974268i | \(0.572367\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 4519.75 | 0.146204 | ||||||||
\(986\) | 5717.37 | 0.184663 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −3247.92 | −0.104585 | ||||||||
\(989\) | −4819.37 | −0.154951 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 10389.5 | 0.333031 | 0.166516 | − | 0.986039i | \(-0.446748\pi\) | ||||
0.166516 | + | 0.986039i | \(0.446748\pi\) | |||||||
\(992\) | −6447.32 | −0.206353 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −9937.22 | −0.316614 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 36396.7 | 1.15616 | 0.578082 | − | 0.815979i | \(-0.303801\pi\) | ||||
0.578082 | + | 0.815979i | \(0.303801\pi\) | |||||||
\(998\) | 61080.7 | 1.93735 | ||||||||
\(999\) | 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 | 2205.4.a.bx.1.2 | ✓ | 6 | |
3.2 | odd | 2 | 2205.4.a.by.1.5 | yes | 6 | ||
7.6 | odd | 2 | 2205.4.a.by.1.2 | yes | 6 | ||
21.20 | even | 2 | inner | 2205.4.a.bx.1.5 | yes | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2205.4.a.bx.1.2 | ✓ | 6 | 1.1 | even | 1 | trivial | |
2205.4.a.bx.1.5 | yes | 6 | 21.20 | even | 2 | inner | |
2205.4.a.by.1.2 | yes | 6 | 7.6 | odd | 2 | ||
2205.4.a.by.1.5 | yes | 6 | 3.2 | odd | 2 |