Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1521,4,Mod(1,1521)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1521, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1521.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1521 = 3^{2} \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1521.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: | \(89.7419051187\) |
Analytic rank: | \(0\) |
Dimension: | \(9\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{9} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{9} - 4x^{8} - 46x^{7} + 145x^{6} + 680x^{5} - 1501x^{4} - 3203x^{3} + 4784x^{2} + 3584x - 4096 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 13^{2} \) |
Twist minimal: | no (minimal twist has level 169) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.8 | ||
Root | \(-3.82555\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1521.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 4.82555 | 1.70609 | 0.853046 | − | 0.521836i | \(-0.174753\pi\) | ||||
0.853046 | + | 0.521836i | \(0.174753\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 15.2860 | 1.91075 | ||||||||
\(5\) | −12.7712 | −1.14229 | −0.571145 | − | 0.820849i | \(-0.693501\pi\) | ||||
−0.571145 | + | 0.820849i | \(0.693501\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −26.1871 | −1.41397 | −0.706986 | − | 0.707228i | \(-0.749945\pi\) | ||||
−0.706986 | + | 0.707228i | \(0.749945\pi\) | |||||||
\(8\) | 35.1589 | 1.55382 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −61.6281 | −1.94885 | ||||||||
\(11\) | 42.3430 | 1.16063 | 0.580314 | − | 0.814393i | \(-0.302930\pi\) | ||||
0.580314 | + | 0.814393i | \(0.302930\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | −126.367 | −2.41236 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 47.3733 | 0.740208 | ||||||||
\(17\) | 27.3331 | 0.389955 | 0.194978 | − | 0.980808i | \(-0.437537\pi\) | ||||
0.194978 | + | 0.980808i | \(0.437537\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 13.1196 | 0.158413 | 0.0792065 | − | 0.996858i | \(-0.474761\pi\) | ||||
0.0792065 | + | 0.996858i | \(0.474761\pi\) | |||||||
\(20\) | −195.220 | −2.18263 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 204.329 | 1.98014 | ||||||||
\(23\) | 28.7976 | 0.261074 | 0.130537 | − | 0.991443i | \(-0.458330\pi\) | ||||
0.130537 | + | 0.991443i | \(0.458330\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 38.1033 | 0.304826 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −400.296 | −2.70174 | ||||||||
\(29\) | 141.628 | 0.906882 | 0.453441 | − | 0.891286i | \(-0.350196\pi\) | ||||
0.453441 | + | 0.891286i | \(0.350196\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 56.0144 | 0.324532 | 0.162266 | − | 0.986747i | \(-0.448120\pi\) | ||||
0.162266 | + | 0.986747i | \(0.448120\pi\) | |||||||
\(32\) | −52.6687 | −0.290956 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 131.897 | 0.665300 | ||||||||
\(35\) | 334.441 | 1.61516 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 313.982 | 1.39509 | 0.697545 | − | 0.716541i | \(-0.254276\pi\) | ||||
0.697545 | + | 0.716541i | \(0.254276\pi\) | |||||||
\(38\) | 63.3095 | 0.270267 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −449.021 | −1.77491 | ||||||||
\(41\) | 352.375 | 1.34224 | 0.671118 | − | 0.741351i | \(-0.265814\pi\) | ||||
0.671118 | + | 0.741351i | \(0.265814\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −320.676 | −1.13727 | −0.568636 | − | 0.822589i | \(-0.692529\pi\) | ||||
−0.568636 | + | 0.822589i | \(0.692529\pi\) | |||||||
\(44\) | 647.255 | 2.21767 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 138.964 | 0.445417 | ||||||||
\(47\) | 339.339 | 1.05314 | 0.526571 | − | 0.850131i | \(-0.323477\pi\) | ||||
0.526571 | + | 0.850131i | \(0.323477\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 342.765 | 0.999315 | ||||||||
\(50\) | 183.869 | 0.520061 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −349.461 | −0.905701 | −0.452851 | − | 0.891586i | \(-0.649593\pi\) | ||||
−0.452851 | + | 0.891586i | \(0.649593\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −540.771 | −1.32577 | ||||||||
\(56\) | −920.710 | −2.19705 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 683.432 | 1.54722 | ||||||||
\(59\) | 258.742 | 0.570937 | 0.285469 | − | 0.958388i | \(-0.407851\pi\) | ||||
0.285469 | + | 0.958388i | \(0.407851\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 650.732 | 1.36586 | 0.682932 | − | 0.730482i | \(-0.260705\pi\) | ||||
0.682932 | + | 0.730482i | \(0.260705\pi\) | |||||||
\(62\) | 270.301 | 0.553681 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −633.142 | −1.23661 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 894.996 | 1.63196 | 0.815979 | − | 0.578082i | \(-0.196199\pi\) | ||||
0.815979 | + | 0.578082i | \(0.196199\pi\) | |||||||
\(68\) | 417.813 | 0.745106 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 1613.86 | 2.75562 | ||||||||
\(71\) | 741.469 | 1.23938 | 0.619691 | − | 0.784846i | \(-0.287258\pi\) | ||||
0.619691 | + | 0.784846i | \(0.287258\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −820.643 | −1.31574 | −0.657870 | − | 0.753131i | \(-0.728542\pi\) | ||||
−0.657870 | + | 0.753131i | \(0.728542\pi\) | |||||||
\(74\) | 1515.14 | 2.38015 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 200.546 | 0.302687 | ||||||||
\(77\) | −1108.84 | −1.64109 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −199.372 | −0.283938 | −0.141969 | − | 0.989871i | \(-0.545343\pi\) | ||||
−0.141969 | + | 0.989871i | \(0.545343\pi\) | |||||||
\(80\) | −605.013 | −0.845532 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 1700.40 | 2.28998 | ||||||||
\(83\) | 541.696 | 0.716372 | 0.358186 | − | 0.933650i | \(-0.383395\pi\) | ||||
0.358186 | + | 0.933650i | \(0.383395\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −349.076 | −0.445442 | ||||||||
\(86\) | −1547.44 | −1.94029 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 1488.73 | 1.80340 | ||||||||
\(89\) | 380.615 | 0.453315 | 0.226658 | − | 0.973974i | \(-0.427220\pi\) | ||||
0.226658 | + | 0.973974i | \(0.427220\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 440.199 | 0.498847 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 1637.50 | 1.79676 | ||||||||
\(95\) | −167.553 | −0.180954 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1430.50 | 1.49737 | 0.748687 | − | 0.662924i | \(-0.230685\pi\) | ||||
0.748687 | + | 0.662924i | \(0.230685\pi\) | |||||||
\(98\) | 1654.03 | 1.70492 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 582.446 | 0.582446 | ||||||||
\(101\) | 801.195 | 0.789326 | 0.394663 | − | 0.918826i | \(-0.370861\pi\) | ||||
0.394663 | + | 0.918826i | \(0.370861\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −745.805 | −0.713459 | −0.356730 | − | 0.934208i | \(-0.616108\pi\) | ||||
−0.356730 | + | 0.934208i | \(0.616108\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −1686.34 | −1.54521 | ||||||||
\(107\) | 134.546 | 0.121561 | 0.0607806 | − | 0.998151i | \(-0.480641\pi\) | ||||
0.0607806 | + | 0.998151i | \(0.480641\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −293.245 | −0.257686 | −0.128843 | − | 0.991665i | \(-0.541126\pi\) | ||||
−0.128843 | + | 0.991665i | \(0.541126\pi\) | |||||||
\(110\) | −2609.52 | −2.26189 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −1240.57 | −1.04663 | ||||||||
\(113\) | −1705.38 | −1.41972 | −0.709861 | − | 0.704342i | \(-0.751242\pi\) | ||||
−0.709861 | + | 0.704342i | \(0.751242\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −367.779 | −0.298223 | ||||||||
\(116\) | 2164.92 | 1.73282 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 1248.57 | 0.974071 | ||||||||
\(119\) | −715.774 | −0.551386 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 461.932 | 0.347056 | ||||||||
\(122\) | 3140.14 | 2.33029 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 856.235 | 0.620098 | ||||||||
\(125\) | 1109.77 | 0.794090 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1493.18 | 1.04329 | 0.521646 | − | 0.853162i | \(-0.325318\pi\) | ||||
0.521646 | + | 0.853162i | \(0.325318\pi\) | |||||||
\(128\) | −2633.91 | −1.81881 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 459.112 | 0.306205 | 0.153102 | − | 0.988210i | \(-0.451074\pi\) | ||||
0.153102 | + | 0.988210i | \(0.451074\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −343.565 | −0.223991 | ||||||||
\(134\) | 4318.85 | 2.78427 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 961.000 | 0.605920 | ||||||||
\(137\) | −2503.06 | −1.56096 | −0.780478 | − | 0.625183i | \(-0.785024\pi\) | ||||
−0.780478 | + | 0.625183i | \(0.785024\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1803.73 | 1.10065 | 0.550326 | − | 0.834950i | \(-0.314503\pi\) | ||||
0.550326 | + | 0.834950i | \(0.314503\pi\) | |||||||
\(140\) | 5112.25 | 3.08617 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 3578.00 | 2.11450 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1808.75 | −1.03592 | ||||||||
\(146\) | −3960.06 | −2.24477 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 4799.52 | 2.66566 | ||||||||
\(149\) | 2925.44 | 1.60846 | 0.804232 | − | 0.594316i | \(-0.202577\pi\) | ||||
0.804232 | + | 0.594316i | \(0.202577\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1769.28 | 0.953524 | 0.476762 | − | 0.879032i | \(-0.341810\pi\) | ||||
0.476762 | + | 0.879032i | \(0.341810\pi\) | |||||||
\(152\) | 461.271 | 0.246145 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −5350.78 | −2.79986 | ||||||||
\(155\) | −715.371 | −0.370709 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1157.24 | −0.588265 | −0.294132 | − | 0.955765i | \(-0.595031\pi\) | ||||
−0.294132 | + | 0.955765i | \(0.595031\pi\) | |||||||
\(158\) | −962.079 | −0.484423 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 672.641 | 0.332356 | ||||||||
\(161\) | −754.126 | −0.369152 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −2909.21 | −1.39795 | −0.698977 | − | 0.715144i | \(-0.746361\pi\) | ||||
−0.698977 | + | 0.715144i | \(0.746361\pi\) | |||||||
\(164\) | 5386.39 | 2.56467 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 2613.98 | 1.22220 | ||||||||
\(167\) | −1272.16 | −0.589476 | −0.294738 | − | 0.955578i | \(-0.595232\pi\) | ||||
−0.294738 | + | 0.955578i | \(0.595232\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | −1684.48 | −0.759965 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −4901.85 | −2.17304 | ||||||||
\(173\) | −2371.80 | −1.04234 | −0.521169 | − | 0.853453i | \(-0.674504\pi\) | ||||
−0.521169 | + | 0.853453i | \(0.674504\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −997.815 | −0.431015 | ||||||||
\(176\) | 2005.93 | 0.859105 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 1836.68 | 0.773397 | ||||||||
\(179\) | −727.183 | −0.303643 | −0.151822 | − | 0.988408i | \(-0.548514\pi\) | ||||
−0.151822 | + | 0.988408i | \(0.548514\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 3874.20 | 1.59098 | 0.795488 | − | 0.605969i | \(-0.207215\pi\) | ||||
0.795488 | + | 0.605969i | \(0.207215\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 1012.49 | 0.405662 | ||||||||
\(185\) | −4009.92 | −1.59360 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1157.36 | 0.452593 | ||||||||
\(188\) | 5187.13 | 2.01229 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −808.537 | −0.308723 | ||||||||
\(191\) | −2003.77 | −0.759098 | −0.379549 | − | 0.925172i | \(-0.623921\pi\) | ||||
−0.379549 | + | 0.925172i | \(0.623921\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1026.25 | 0.382751 | 0.191376 | − | 0.981517i | \(-0.438705\pi\) | ||||
0.191376 | + | 0.981517i | \(0.438705\pi\) | |||||||
\(194\) | 6902.96 | 2.55466 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 5239.50 | 1.90944 | ||||||||
\(197\) | −1308.19 | −0.473120 | −0.236560 | − | 0.971617i | \(-0.576020\pi\) | ||||
−0.236560 | + | 0.971617i | \(0.576020\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −285.120 | −0.101566 | −0.0507830 | − | 0.998710i | \(-0.516172\pi\) | ||||
−0.0507830 | + | 0.998710i | \(0.516172\pi\) | |||||||
\(200\) | 1339.67 | 0.473644 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 3866.21 | 1.34666 | ||||||||
\(203\) | −3708.82 | −1.28231 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −4500.24 | −1.53322 | ||||||||
\(206\) | −3598.92 | −1.21723 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 555.525 | 0.183859 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −2813.91 | −0.918092 | −0.459046 | − | 0.888412i | \(-0.651809\pi\) | ||||
−0.459046 | + | 0.888412i | \(0.651809\pi\) | |||||||
\(212\) | −5341.86 | −1.73057 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 649.259 | 0.207395 | ||||||||
\(215\) | 4095.42 | 1.29909 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1466.86 | −0.458879 | ||||||||
\(218\) | −1415.07 | −0.439635 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −8266.21 | −2.53322 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1509.86 | −0.453399 | −0.226699 | − | 0.973965i | \(-0.572794\pi\) | ||||
−0.226699 | + | 0.973965i | \(0.572794\pi\) | |||||||
\(224\) | 1379.24 | 0.411403 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −8229.40 | −2.42217 | ||||||||
\(227\) | −643.122 | −0.188042 | −0.0940209 | − | 0.995570i | \(-0.529972\pi\) | ||||
−0.0940209 | + | 0.995570i | \(0.529972\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −154.009 | −0.0444420 | −0.0222210 | − | 0.999753i | \(-0.507074\pi\) | ||||
−0.0222210 | + | 0.999753i | \(0.507074\pi\) | |||||||
\(230\) | −1774.74 | −0.508795 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 4979.47 | 1.40913 | ||||||||
\(233\) | 261.668 | 0.0735726 | 0.0367863 | − | 0.999323i | \(-0.488288\pi\) | ||||
0.0367863 | + | 0.999323i | \(0.488288\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −4333.76 | −1.20299 | ||||||||
\(236\) | 3955.12 | 1.09092 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −3454.01 | −0.940714 | ||||||||
\(239\) | −2495.09 | −0.675288 | −0.337644 | − | 0.941274i | \(-0.609630\pi\) | ||||
−0.337644 | + | 0.941274i | \(0.609630\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −3835.70 | −1.02522 | −0.512612 | − | 0.858620i | \(-0.671322\pi\) | ||||
−0.512612 | + | 0.858620i | \(0.671322\pi\) | |||||||
\(242\) | 2229.08 | 0.592110 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 9947.07 | 2.60982 | ||||||||
\(245\) | −4377.52 | −1.14151 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 1969.40 | 0.504263 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 5355.28 | 1.35479 | ||||||||
\(251\) | 3977.59 | 1.00025 | 0.500126 | − | 0.865953i | \(-0.333287\pi\) | ||||
0.500126 | + | 0.865953i | \(0.333287\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1219.38 | 0.303010 | ||||||||
\(254\) | 7205.41 | 1.77995 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −7644.95 | −1.86644 | ||||||||
\(257\) | 121.486 | 0.0294868 | 0.0147434 | − | 0.999891i | \(-0.495307\pi\) | ||||
0.0147434 | + | 0.999891i | \(0.495307\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −8222.29 | −1.97262 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 2215.47 | 0.522413 | ||||||||
\(263\) | −1175.42 | −0.275586 | −0.137793 | − | 0.990461i | \(-0.544001\pi\) | ||||
−0.137793 | + | 0.990461i | \(0.544001\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 4463.03 | 1.03457 | ||||||||
\(266\) | −1657.89 | −0.382150 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 13680.9 | 3.11826 | ||||||||
\(269\) | 8319.66 | 1.88572 | 0.942860 | − | 0.333190i | \(-0.108125\pi\) | ||||
0.942860 | + | 0.333190i | \(0.108125\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −3928.56 | −0.880602 | −0.440301 | − | 0.897850i | \(-0.645128\pi\) | ||||
−0.440301 | + | 0.897850i | \(0.645128\pi\) | |||||||
\(272\) | 1294.86 | 0.288648 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −12078.7 | −2.66313 | ||||||||
\(275\) | 1613.41 | 0.353790 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −6022.61 | −1.30637 | −0.653183 | − | 0.757200i | \(-0.726567\pi\) | ||||
−0.653183 | + | 0.757200i | \(0.726567\pi\) | |||||||
\(278\) | 8704.01 | 1.87781 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 11758.6 | 2.50967 | ||||||||
\(281\) | −2183.71 | −0.463592 | −0.231796 | − | 0.972764i | \(-0.574460\pi\) | ||||
−0.231796 | + | 0.972764i | \(0.574460\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −8133.25 | −1.70838 | −0.854190 | − | 0.519961i | \(-0.825946\pi\) | ||||
−0.854190 | + | 0.519961i | \(0.825946\pi\) | |||||||
\(284\) | 11334.1 | 2.36815 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −9227.67 | −1.89788 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −4165.90 | −0.847935 | ||||||||
\(290\) | −8728.24 | −1.76738 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −12544.3 | −2.51405 | ||||||||
\(293\) | −3182.55 | −0.634562 | −0.317281 | − | 0.948332i | \(-0.602770\pi\) | ||||
−0.317281 | + | 0.948332i | \(0.602770\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −3304.44 | −0.652176 | ||||||||
\(296\) | 11039.3 | 2.16772 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 14116.9 | 2.74419 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 8397.59 | 1.60807 | ||||||||
\(302\) | 8537.77 | 1.62680 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 621.520 | 0.117259 | ||||||||
\(305\) | −8310.62 | −1.56021 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −1230.21 | −0.228703 | −0.114352 | − | 0.993440i | \(-0.536479\pi\) | ||||
−0.114352 | + | 0.993440i | \(0.536479\pi\) | |||||||
\(308\) | −16949.7 | −3.13572 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −3452.06 | −0.632464 | ||||||||
\(311\) | 5881.49 | 1.07237 | 0.536187 | − | 0.844099i | \(-0.319864\pi\) | ||||
0.536187 | + | 0.844099i | \(0.319864\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 6800.24 | 1.22803 | 0.614013 | − | 0.789296i | \(-0.289554\pi\) | ||||
0.614013 | + | 0.789296i | \(0.289554\pi\) | |||||||
\(314\) | −5584.31 | −1.00363 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −3047.59 | −0.542533 | ||||||||
\(317\) | 2212.50 | 0.392008 | 0.196004 | − | 0.980603i | \(-0.437204\pi\) | ||||
0.196004 | + | 0.980603i | \(0.437204\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 5996.94 | 1.05255 | ||||||||
\(320\) | 8085.97 | 1.41256 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −3639.07 | −0.629807 | ||||||||
\(323\) | 358.600 | 0.0617740 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −14038.5 | −2.38504 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 12389.1 | 2.08559 | ||||||||
\(329\) | −8886.31 | −1.48911 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1744.14 | 0.289627 | 0.144814 | − | 0.989459i | \(-0.453742\pi\) | ||||
0.144814 | + | 0.989459i | \(0.453742\pi\) | |||||||
\(332\) | 8280.35 | 1.36881 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −6138.87 | −1.00570 | ||||||||
\(335\) | −11430.2 | −1.86417 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 8805.54 | 1.42335 | 0.711674 | − | 0.702510i | \(-0.247937\pi\) | ||||
0.711674 | + | 0.702510i | \(0.247937\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −5335.96 | −0.851127 | ||||||||
\(341\) | 2371.82 | 0.376661 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 6.15700 | 0.000969232 0 | ||||||||
\(344\) | −11274.6 | −1.76711 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −11445.2 | −1.77832 | ||||||||
\(347\) | 1943.15 | 0.300616 | 0.150308 | − | 0.988639i | \(-0.451973\pi\) | ||||
0.150308 | + | 0.988639i | \(0.451973\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 5316.91 | 0.815495 | 0.407748 | − | 0.913095i | \(-0.366314\pi\) | ||||
0.407748 | + | 0.913095i | \(0.366314\pi\) | |||||||
\(350\) | −4815.01 | −0.735352 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −2230.15 | −0.337692 | ||||||||
\(353\) | 5013.67 | 0.755951 | 0.377976 | − | 0.925816i | \(-0.376620\pi\) | ||||
0.377976 | + | 0.925816i | \(0.376620\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −9469.44 | −1.41573 | ||||||||
\(356\) | 5818.07 | 0.866171 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −3509.06 | −0.518043 | ||||||||
\(359\) | 8143.55 | 1.19722 | 0.598608 | − | 0.801042i | \(-0.295721\pi\) | ||||
0.598608 | + | 0.801042i | \(0.295721\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −6686.88 | −0.974905 | ||||||||
\(362\) | 18695.1 | 2.71435 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 10480.6 | 1.50296 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 6517.85 | 0.927054 | 0.463527 | − | 0.886083i | \(-0.346584\pi\) | ||||
0.463527 | + | 0.886083i | \(0.346584\pi\) | |||||||
\(368\) | 1364.24 | 0.193249 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −19350.1 | −2.71882 | ||||||||
\(371\) | 9151.38 | 1.28064 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 7247.57 | 1.00607 | 0.503036 | − | 0.864266i | \(-0.332216\pi\) | ||||
0.503036 | + | 0.864266i | \(0.332216\pi\) | |||||||
\(374\) | 5584.93 | 0.772165 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 11930.8 | 1.63639 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 6549.25 | 0.887632 | 0.443816 | − | 0.896118i | \(-0.353624\pi\) | ||||
0.443816 | + | 0.896118i | \(0.353624\pi\) | |||||||
\(380\) | −2561.21 | −0.345757 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −9669.31 | −1.29509 | ||||||||
\(383\) | 8030.33 | 1.07136 | 0.535679 | − | 0.844421i | \(-0.320056\pi\) | ||||
0.535679 | + | 0.844421i | \(0.320056\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 14161.2 | 1.87460 | ||||||||
\(386\) | 4952.22 | 0.653009 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 21866.6 | 2.86110 | ||||||||
\(389\) | −481.389 | −0.0627440 | −0.0313720 | − | 0.999508i | \(-0.509988\pi\) | ||||
−0.0313720 | + | 0.999508i | \(0.509988\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 787.126 | 0.101807 | ||||||||
\(392\) | 12051.2 | 1.55275 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −6312.74 | −0.807186 | ||||||||
\(395\) | 2546.21 | 0.324339 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −2802.07 | −0.354237 | −0.177118 | − | 0.984190i | \(-0.556678\pi\) | ||||
−0.177118 | + | 0.984190i | \(0.556678\pi\) | |||||||
\(398\) | −1375.86 | −0.173281 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 1805.08 | 0.225635 | ||||||||
\(401\) | −4376.79 | −0.545053 | −0.272527 | − | 0.962148i | \(-0.587859\pi\) | ||||
−0.272527 | + | 0.962148i | \(0.587859\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 12247.1 | 1.50820 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −17897.1 | −2.18773 | ||||||||
\(407\) | 13295.0 | 1.61918 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 12969.0 | 1.56791 | 0.783954 | − | 0.620819i | \(-0.213200\pi\) | ||||
0.783954 | + | 0.620819i | \(0.213200\pi\) | |||||||
\(410\) | −21716.2 | −2.61582 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −11400.4 | −1.36324 | ||||||||
\(413\) | −6775.70 | −0.807289 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −6918.10 | −0.818304 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 2680.71 | 0.313679 | ||||||||
\(419\) | −7679.05 | −0.895336 | −0.447668 | − | 0.894200i | \(-0.647745\pi\) | ||||
−0.447668 | + | 0.894200i | \(0.647745\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −2963.10 | −0.343022 | −0.171511 | − | 0.985182i | \(-0.554865\pi\) | ||||
−0.171511 | + | 0.985182i | \(0.554865\pi\) | |||||||
\(422\) | −13578.7 | −1.56635 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −12286.7 | −1.40730 | ||||||||
\(425\) | 1041.48 | 0.118869 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −17040.8 | −1.93129 | ||||||||
\(428\) | 2056.67 | 0.232273 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 19762.7 | 2.21637 | ||||||||
\(431\) | 14202.6 | 1.58728 | 0.793639 | − | 0.608389i | \(-0.208184\pi\) | ||||
0.793639 | + | 0.608389i | \(0.208184\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 10118.2 | 1.12298 | 0.561488 | − | 0.827485i | \(-0.310229\pi\) | ||||
0.561488 | + | 0.827485i | \(0.310229\pi\) | |||||||
\(434\) | −7078.39 | −0.782889 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −4482.53 | −0.492372 | ||||||||
\(437\) | 377.814 | 0.0413576 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −16184.3 | −1.75954 | −0.879768 | − | 0.475404i | \(-0.842302\pi\) | ||||
−0.879768 | + | 0.475404i | \(0.842302\pi\) | |||||||
\(440\) | −19012.9 | −2.06001 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 10025.2 | 1.07519 | 0.537596 | − | 0.843203i | \(-0.319333\pi\) | ||||
0.537596 | + | 0.843203i | \(0.319333\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −4860.90 | −0.517818 | ||||||||
\(446\) | −7285.93 | −0.773540 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 16580.2 | 1.74852 | ||||||||
\(449\) | −10428.3 | −1.09608 | −0.548041 | − | 0.836451i | \(-0.684626\pi\) | ||||
−0.548041 | + | 0.836451i | \(0.684626\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 14920.6 | 1.55784 | ||||||||
\(452\) | −26068.4 | −2.71273 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −3103.42 | −0.320816 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 12263.8 | 1.25531 | 0.627656 | − | 0.778491i | \(-0.284015\pi\) | ||||
0.627656 | + | 0.778491i | \(0.284015\pi\) | |||||||
\(458\) | −743.180 | −0.0758221 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −5621.87 | −0.569828 | ||||||||
\(461\) | 4047.98 | 0.408966 | 0.204483 | − | 0.978870i | \(-0.434449\pi\) | ||||
0.204483 | + | 0.978870i | \(0.434449\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 10473.9 | 1.05133 | 0.525663 | − | 0.850693i | \(-0.323817\pi\) | ||||
0.525663 | + | 0.850693i | \(0.323817\pi\) | |||||||
\(464\) | 6709.37 | 0.671281 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 1262.69 | 0.125522 | ||||||||
\(467\) | −4906.17 | −0.486146 | −0.243073 | − | 0.970008i | \(-0.578155\pi\) | ||||
−0.243073 | + | 0.970008i | \(0.578155\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −23437.4 | −2.30754 | ||||||||
\(470\) | −20912.8 | −2.05242 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 9097.07 | 0.887132 | ||||||||
\(473\) | −13578.4 | −1.31995 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 499.901 | 0.0482884 | ||||||||
\(476\) | −10941.3 | −1.05356 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −12040.2 | −1.15210 | ||||||||
\(479\) | −1249.42 | −0.119180 | −0.0595902 | − | 0.998223i | \(-0.518979\pi\) | ||||
−0.0595902 | + | 0.998223i | \(0.518979\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | −18509.4 | −1.74913 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 7061.08 | 0.663137 | ||||||||
\(485\) | −18269.2 | −1.71044 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −19290.2 | −1.79492 | −0.897458 | − | 0.441100i | \(-0.854588\pi\) | ||||
−0.897458 | + | 0.441100i | \(0.854588\pi\) | |||||||
\(488\) | 22879.0 | 2.12230 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −21123.9 | −1.94751 | ||||||||
\(491\) | 8381.17 | 0.770339 | 0.385170 | − | 0.922846i | \(-0.374143\pi\) | ||||
0.385170 | + | 0.922846i | \(0.374143\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 3871.12 | 0.353644 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 2653.59 | 0.240221 | ||||||||
\(497\) | −19416.9 | −1.75245 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −199.025 | −0.0178549 | −0.00892743 | − | 0.999960i | \(-0.502842\pi\) | ||||
−0.00892743 | + | 0.999960i | \(0.502842\pi\) | |||||||
\(500\) | 16964.0 | 1.51731 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 19194.1 | 1.70652 | ||||||||
\(503\) | 7567.90 | 0.670847 | 0.335424 | − | 0.942067i | \(-0.391121\pi\) | ||||
0.335424 | + | 0.942067i | \(0.391121\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −10232.2 | −0.901639 | ||||||||
\(506\) | 5884.17 | 0.516963 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 22824.7 | 1.99347 | ||||||||
\(509\) | 5998.22 | 0.522331 | 0.261166 | − | 0.965294i | \(-0.415893\pi\) | ||||
0.261166 | + | 0.965294i | \(0.415893\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 21490.3 | 1.86042 | ||||||||
\(512\) | −15819.8 | −1.36552 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 586.238 | 0.0503071 | ||||||||
\(515\) | 9524.81 | 0.814977 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 14368.6 | 1.22231 | ||||||||
\(518\) | −39677.1 | −3.36547 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 2863.99 | 0.240833 | 0.120416 | − | 0.992723i | \(-0.461577\pi\) | ||||
0.120416 | + | 0.992723i | \(0.461577\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −2529.09 | −0.211452 | −0.105726 | − | 0.994395i | \(-0.533717\pi\) | ||||
−0.105726 | + | 0.994395i | \(0.533717\pi\) | |||||||
\(524\) | 7017.98 | 0.585080 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −5672.03 | −0.470176 | ||||||||
\(527\) | 1531.05 | 0.126553 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −11337.7 | −0.931840 | ||||||||
\(530\) | 21536.6 | 1.76508 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −5251.73 | −0.427991 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −1718.31 | −0.138858 | ||||||||
\(536\) | 31467.0 | 2.53576 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 40147.0 | 3.21721 | ||||||||
\(539\) | 14513.7 | 1.15983 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −22053.6 | −1.75260 | −0.876302 | − | 0.481762i | \(-0.839997\pi\) | ||||
−0.876302 | + | 0.481762i | \(0.839997\pi\) | |||||||
\(542\) | −18957.5 | −1.50239 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −1439.60 | −0.113460 | ||||||||
\(545\) | 3745.08 | 0.294352 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −2821.80 | −0.220569 | −0.110285 | − | 0.993900i | \(-0.535176\pi\) | ||||
−0.110285 | + | 0.993900i | \(0.535176\pi\) | |||||||
\(548\) | −38261.8 | −2.98259 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 7785.59 | 0.603597 | ||||||||
\(551\) | 1858.10 | 0.143662 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 5220.97 | 0.401479 | ||||||||
\(554\) | −29062.4 | −2.22878 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 27571.8 | 2.10307 | ||||||||
\(557\) | 1837.17 | 0.139754 | 0.0698772 | − | 0.997556i | \(-0.477739\pi\) | ||||
0.0698772 | + | 0.997556i | \(0.477739\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 15843.6 | 1.19556 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −10537.6 | −0.790930 | ||||||||
\(563\) | 24877.9 | 1.86230 | 0.931152 | − | 0.364631i | \(-0.118805\pi\) | ||||
0.931152 | + | 0.364631i | \(0.118805\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 21779.7 | 1.62173 | ||||||||
\(566\) | −39247.4 | −2.91465 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 26069.2 | 1.92577 | ||||||||
\(569\) | 7111.72 | 0.523969 | 0.261985 | − | 0.965072i | \(-0.415623\pi\) | ||||
0.261985 | + | 0.965072i | \(0.415623\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −11919.4 | −0.873578 | −0.436789 | − | 0.899564i | \(-0.643884\pi\) | ||||
−0.436789 | + | 0.899564i | \(0.643884\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −44528.6 | −3.23796 | ||||||||
\(575\) | 1097.28 | 0.0795823 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −11600.6 | −0.836984 | −0.418492 | − | 0.908220i | \(-0.637441\pi\) | ||||
−0.418492 | + | 0.908220i | \(0.637441\pi\) | |||||||
\(578\) | −20102.8 | −1.44665 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −27648.6 | −1.97939 | ||||||||
\(581\) | −14185.5 | −1.01293 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −14797.2 | −1.05118 | ||||||||
\(584\) | −28852.9 | −2.04442 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −15357.6 | −1.08262 | ||||||||
\(587\) | −10341.7 | −0.727167 | −0.363583 | − | 0.931562i | \(-0.618447\pi\) | ||||
−0.363583 | + | 0.931562i | \(0.618447\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 734.888 | 0.0514101 | ||||||||
\(590\) | −15945.8 | −1.11267 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 14874.4 | 1.03266 | ||||||||
\(593\) | −2782.21 | −0.192668 | −0.0963338 | − | 0.995349i | \(-0.530712\pi\) | ||||
−0.0963338 | + | 0.995349i | \(0.530712\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 9141.29 | 0.629842 | ||||||||
\(596\) | 44718.2 | 3.07337 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −10560.6 | −0.720359 | −0.360179 | − | 0.932883i | \(-0.617285\pi\) | ||||
−0.360179 | + | 0.932883i | \(0.617285\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 3846.85 | 0.261092 | 0.130546 | − | 0.991442i | \(-0.458327\pi\) | ||||
0.130546 | + | 0.991442i | \(0.458327\pi\) | |||||||
\(602\) | 40523.0 | 2.74351 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 27045.2 | 1.82194 | ||||||||
\(605\) | −5899.42 | −0.396439 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 6495.50 | 0.434340 | 0.217170 | − | 0.976134i | \(-0.430317\pi\) | ||||
0.217170 | + | 0.976134i | \(0.430317\pi\) | |||||||
\(608\) | −690.993 | −0.0460912 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −40103.4 | −2.66186 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 3532.60 | 0.232758 | 0.116379 | − | 0.993205i | \(-0.462871\pi\) | ||||
0.116379 | + | 0.993205i | \(0.462871\pi\) | |||||||
\(614\) | −5936.46 | −0.390189 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −38985.6 | −2.54996 | ||||||||
\(617\) | 16297.9 | 1.06342 | 0.531710 | − | 0.846926i | \(-0.321549\pi\) | ||||
0.531710 | + | 0.846926i | \(0.321549\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 9123.86 | 0.592438 | 0.296219 | − | 0.955120i | \(-0.404274\pi\) | ||||
0.296219 | + | 0.955120i | \(0.404274\pi\) | |||||||
\(620\) | −10935.1 | −0.708332 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 28381.4 | 1.82957 | ||||||||
\(623\) | −9967.20 | −0.640975 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −18936.0 | −1.21191 | ||||||||
\(626\) | 32814.9 | 2.09512 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −17689.5 | −1.12402 | ||||||||
\(629\) | 8582.09 | 0.544023 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −23250.8 | −1.46688 | −0.733438 | − | 0.679756i | \(-0.762086\pi\) | ||||
−0.733438 | + | 0.679756i | \(0.762086\pi\) | |||||||
\(632\) | −7009.68 | −0.441187 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 10676.5 | 0.668801 | ||||||||
\(635\) | −19069.7 | −1.19174 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 28938.6 | 1.79575 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 33638.2 | 2.07760 | ||||||||
\(641\) | 7478.44 | 0.460812 | 0.230406 | − | 0.973095i | \(-0.425995\pi\) | ||||
0.230406 | + | 0.973095i | \(0.425995\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −8327.98 | −0.510768 | −0.255384 | − | 0.966840i | \(-0.582202\pi\) | ||||
−0.255384 | + | 0.966840i | \(0.582202\pi\) | |||||||
\(644\) | −11527.5 | −0.705356 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 1730.44 | 0.105392 | ||||||||
\(647\) | −6278.75 | −0.381519 | −0.190760 | − | 0.981637i | \(-0.561095\pi\) | ||||
−0.190760 | + | 0.981637i | \(0.561095\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 10955.9 | 0.662645 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −44470.1 | −2.67114 | ||||||||
\(653\) | 27163.5 | 1.62786 | 0.813928 | − | 0.580966i | \(-0.197325\pi\) | ||||
0.813928 | + | 0.580966i | \(0.197325\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −5863.41 | −0.349774 | ||||||||
\(656\) | 16693.1 | 0.993533 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −42881.4 | −2.54056 | ||||||||
\(659\) | 10352.0 | 0.611921 | 0.305961 | − | 0.952044i | \(-0.401022\pi\) | ||||
0.305961 | + | 0.952044i | \(0.401022\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −6270.46 | −0.368975 | −0.184487 | − | 0.982835i | \(-0.559063\pi\) | ||||
−0.184487 | + | 0.982835i | \(0.559063\pi\) | |||||||
\(662\) | 8416.44 | 0.494130 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 19045.4 | 1.11311 | ||||||||
\(665\) | 4387.73 | 0.255863 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 4078.53 | 0.236764 | ||||||||
\(668\) | −19446.2 | −1.12634 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −55156.9 | −3.18044 | ||||||||
\(671\) | 27554.0 | 1.58526 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −30301.9 | −1.73559 | −0.867794 | − | 0.496923i | \(-0.834463\pi\) | ||||
−0.867794 | + | 0.496923i | \(0.834463\pi\) | |||||||
\(674\) | 42491.6 | 2.42836 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 10223.3 | 0.580375 | 0.290188 | − | 0.956970i | \(-0.406282\pi\) | ||||
0.290188 | + | 0.956970i | \(0.406282\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −37460.7 | −2.11724 | ||||||||
\(680\) | −12273.1 | −0.692136 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 11445.3 | 0.642617 | ||||||||
\(683\) | 16978.0 | 0.951163 | 0.475582 | − | 0.879672i | \(-0.342238\pi\) | ||||
0.475582 | + | 0.879672i | \(0.342238\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 31967.1 | 1.78307 | ||||||||
\(686\) | 29.7109 | 0.00165360 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −15191.5 | −0.841818 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −7935.33 | −0.436866 | −0.218433 | − | 0.975852i | \(-0.570094\pi\) | ||||
−0.218433 | + | 0.975852i | \(0.570094\pi\) | |||||||
\(692\) | −36255.3 | −1.99165 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 9376.79 | 0.512879 | ||||||||
\(695\) | −23035.8 | −1.25726 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 9631.48 | 0.523412 | ||||||||
\(698\) | 25657.1 | 1.39131 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −15252.6 | −0.823562 | ||||||||
\(701\) | −18557.3 | −0.999857 | −0.499928 | − | 0.866067i | \(-0.666640\pi\) | ||||
−0.499928 | + | 0.866067i | \(0.666640\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 4119.33 | 0.221001 | ||||||||
\(704\) | −26809.1 | −1.43524 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 24193.7 | 1.28972 | ||||||||
\(707\) | −20981.0 | −1.11608 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −14163.7 | −0.750253 | −0.375127 | − | 0.926974i | \(-0.622401\pi\) | ||||
−0.375127 | + | 0.926974i | \(0.622401\pi\) | |||||||
\(710\) | −45695.3 | −2.41537 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 13382.0 | 0.704370 | ||||||||
\(713\) | 1613.08 | 0.0847270 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −11115.7 | −0.580186 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 39297.2 | 2.04256 | ||||||||
\(719\) | −24836.7 | −1.28825 | −0.644125 | − | 0.764920i | \(-0.722778\pi\) | ||||
−0.644125 | + | 0.764920i | \(0.722778\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 19530.5 | 1.00881 | ||||||||
\(722\) | −32267.9 | −1.66328 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 59220.9 | 3.03995 | ||||||||
\(725\) | 5396.48 | 0.276441 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −10641.0 | −0.542852 | −0.271426 | − | 0.962459i | \(-0.587495\pi\) | ||||
−0.271426 | + | 0.962459i | \(0.587495\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 50574.7 | 2.56418 | ||||||||
\(731\) | −8765.07 | −0.443486 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 22429.1 | 1.13020 | 0.565102 | − | 0.825021i | \(-0.308837\pi\) | ||||
0.565102 | + | 0.825021i | \(0.308837\pi\) | |||||||
\(734\) | 31452.2 | 1.58164 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −1516.73 | −0.0759612 | ||||||||
\(737\) | 37896.8 | 1.89409 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 33425.8 | 1.66386 | 0.831928 | − | 0.554884i | \(-0.187237\pi\) | ||||
0.831928 | + | 0.554884i | \(0.187237\pi\) | |||||||
\(740\) | −61295.6 | −3.04496 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 44160.5 | 2.18488 | ||||||||
\(743\) | −13136.3 | −0.648619 | −0.324309 | − | 0.945951i | \(-0.605132\pi\) | ||||
−0.324309 | + | 0.945951i | \(0.605132\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −37361.3 | −1.83733 | ||||||||
\(746\) | 34973.5 | 1.71645 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 17691.5 | 0.864791 | ||||||||
\(749\) | −3523.37 | −0.171884 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 20688.2 | 1.00522 | 0.502612 | − | 0.864512i | \(-0.332373\pi\) | ||||
0.502612 | + | 0.864512i | \(0.332373\pi\) | |||||||
\(752\) | 16075.6 | 0.779544 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −22595.8 | −1.08920 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −6145.85 | −0.295079 | −0.147539 | − | 0.989056i | \(-0.547135\pi\) | ||||
−0.147539 | + | 0.989056i | \(0.547135\pi\) | |||||||
\(758\) | 31603.8 | 1.51438 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −5890.98 | −0.281169 | ||||||||
\(761\) | 16488.5 | 0.785424 | 0.392712 | − | 0.919662i | \(-0.371537\pi\) | ||||
0.392712 | + | 0.919662i | \(0.371537\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 7679.23 | 0.364360 | ||||||||
\(764\) | −30629.6 | −1.45045 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 38750.8 | 1.82784 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −7801.71 | −0.365848 | −0.182924 | − | 0.983127i | \(-0.558556\pi\) | ||||
−0.182924 | + | 0.983127i | \(0.558556\pi\) | |||||||
\(770\) | 68335.8 | 3.19825 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 15687.2 | 0.731341 | ||||||||
\(773\) | 27301.3 | 1.27032 | 0.635161 | − | 0.772380i | \(-0.280934\pi\) | ||||
0.635161 | + | 0.772380i | \(0.280934\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 2134.33 | 0.0989258 | ||||||||
\(776\) | 50294.8 | 2.32665 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −2322.97 | −0.107047 | ||||||||
\(779\) | 4623.02 | 0.212628 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 31396.0 | 1.43846 | ||||||||
\(782\) | 3798.32 | 0.173693 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 16237.9 | 0.739700 | ||||||||
\(785\) | 14779.3 | 0.671969 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 26016.0 | 1.17836 | 0.589181 | − | 0.808001i | \(-0.299450\pi\) | ||||
0.589181 | + | 0.808001i | \(0.299450\pi\) | |||||||
\(788\) | −19997.0 | −0.904013 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 12286.9 | 0.553352 | ||||||||
\(791\) | 44658.9 | 2.00745 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | −13521.5 | −0.604360 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −4358.34 | −0.194067 | ||||||||
\(797\) | −8178.16 | −0.363470 | −0.181735 | − | 0.983348i | \(-0.558171\pi\) | ||||
−0.181735 | + | 0.983348i | \(0.558171\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 9275.18 | 0.410678 | ||||||||
\(800\) | −2006.85 | −0.0886910 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −21120.4 | −0.929911 | ||||||||
\(803\) | −34748.5 | −1.52708 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 9631.08 | 0.421678 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 28169.1 | 1.22647 | ||||||||
\(809\) | −16162.0 | −0.702380 | −0.351190 | − | 0.936304i | \(-0.614223\pi\) | ||||
−0.351190 | + | 0.936304i | \(0.614223\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 24714.6 | 1.07009 | 0.535046 | − | 0.844823i | \(-0.320294\pi\) | ||||
0.535046 | + | 0.844823i | \(0.320294\pi\) | |||||||
\(812\) | −56692.9 | −2.45016 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 64155.5 | 2.76247 | ||||||||
\(815\) | 37154.0 | 1.59687 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −4207.15 | −0.180159 | ||||||||
\(818\) | 62582.5 | 2.67499 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −68790.6 | −2.92960 | ||||||||
\(821\) | 28565.3 | 1.21429 | 0.607147 | − | 0.794589i | \(-0.292314\pi\) | ||||
0.607147 | + | 0.794589i | \(0.292314\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 9276.01 | 0.392881 | 0.196441 | − | 0.980516i | \(-0.437062\pi\) | ||||
0.196441 | + | 0.980516i | \(0.437062\pi\) | |||||||
\(824\) | −26221.7 | −1.10859 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −32696.5 | −1.37731 | ||||||||
\(827\) | 36.2767 | 0.00152535 | 0.000762676 | − | 1.00000i | \(-0.499757\pi\) | ||||
0.000762676 | 1.00000i | \(0.499757\pi\) | ||||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 16764.4 | 0.702355 | 0.351177 | − | 0.936309i | \(-0.385781\pi\) | ||||
0.351177 | + | 0.936309i | \(0.385781\pi\) | |||||||
\(830\) | −33383.7 | −1.39610 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 9368.82 | 0.389688 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 16247.0 | 0.673353 | ||||||||
\(836\) | 8491.74 | 0.351307 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −37055.7 | −1.52753 | ||||||||
\(839\) | 45316.6 | 1.86473 | 0.932363 | − | 0.361525i | \(-0.117744\pi\) | ||||
0.932363 | + | 0.361525i | \(0.117744\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −4330.61 | −0.177564 | ||||||||
\(842\) | −14298.6 | −0.585227 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −43013.3 | −1.75424 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −12096.7 | −0.490728 | ||||||||
\(848\) | −16555.1 | −0.670407 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 5025.72 | 0.202801 | ||||||||
\(851\) | 9041.93 | 0.364222 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −17557.7 | −0.704766 | −0.352383 | − | 0.935856i | \(-0.614629\pi\) | ||||
−0.352383 | + | 0.935856i | \(0.614629\pi\) | |||||||
\(854\) | −82231.3 | −3.29496 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 4730.49 | 0.188884 | ||||||||
\(857\) | −37943.6 | −1.51240 | −0.756201 | − | 0.654339i | \(-0.772947\pi\) | ||||
−0.756201 | + | 0.654339i | \(0.772947\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −12833.2 | −0.509735 | −0.254867 | − | 0.966976i | \(-0.582032\pi\) | ||||
−0.254867 | + | 0.966976i | \(0.582032\pi\) | |||||||
\(860\) | 62602.5 | 2.48224 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 68535.6 | 2.70804 | ||||||||
\(863\) | 24264.0 | 0.957076 | 0.478538 | − | 0.878067i | \(-0.341167\pi\) | ||||
0.478538 | + | 0.878067i | \(0.341167\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 30290.7 | 1.19065 | ||||||||
\(866\) | 48825.8 | 1.91590 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −22422.3 | −0.876801 | ||||||||
\(869\) | −8442.00 | −0.329546 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | −10310.2 | −0.400397 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 1823.16 | 0.0705598 | ||||||||
\(875\) | −29061.8 | −1.12282 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −4098.68 | −0.157814 | −0.0789069 | − | 0.996882i | \(-0.525143\pi\) | ||||
−0.0789069 | + | 0.996882i | \(0.525143\pi\) | |||||||
\(878\) | −78098.4 | −3.00193 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −25618.1 | −0.981347 | ||||||||
\(881\) | −46763.9 | −1.78833 | −0.894164 | − | 0.447740i | \(-0.852229\pi\) | ||||
−0.894164 | + | 0.447740i | \(0.852229\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −27183.9 | −1.03603 | −0.518013 | − | 0.855373i | \(-0.673328\pi\) | ||||
−0.518013 | + | 0.855373i | \(0.673328\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 48377.0 | 1.83438 | ||||||||
\(887\) | 21182.0 | 0.801827 | 0.400914 | − | 0.916116i | \(-0.368693\pi\) | ||||
0.400914 | + | 0.916116i | \(0.368693\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −39102.0 | −1.47518 | ||||||||
\(890\) | −23456.5 | −0.883444 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −23079.7 | −0.866331 | ||||||||
\(893\) | 4452.00 | 0.166831 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 9286.99 | 0.346849 | ||||||||
\(896\) | 68974.5 | 2.57174 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −50322.3 | −1.87002 | ||||||||
\(899\) | 7933.19 | 0.294312 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −9551.85 | −0.353183 | ||||||||
\(902\) | 72000.2 | 2.65781 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −59959.2 | −2.20599 | ||||||||
\(905\) | −49478.1 | −1.81736 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −50810.3 | −1.86012 | −0.930060 | − | 0.367409i | \(-0.880245\pi\) | ||||
−0.930060 | + | 0.367409i | \(0.880245\pi\) | |||||||
\(908\) | −9830.75 | −0.359300 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 7309.10 | 0.265819 | 0.132910 | − | 0.991128i | \(-0.457568\pi\) | ||||
0.132910 | + | 0.991128i | \(0.457568\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 22937.1 | 0.831441 | ||||||||
\(914\) | 59179.7 | 2.14168 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −2354.18 | −0.0849174 | ||||||||
\(917\) | −12022.8 | −0.432964 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 3509.95 | 0.125988 | 0.0629939 | − | 0.998014i | \(-0.479935\pi\) | ||||
0.0629939 | + | 0.998014i | \(0.479935\pi\) | |||||||
\(920\) | −12930.7 | −0.463384 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 19533.8 | 0.697733 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 11963.7 | 0.425260 | ||||||||
\(926\) | 50542.4 | 1.79366 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −7459.34 | −0.263863 | ||||||||
\(929\) | −6624.68 | −0.233960 | −0.116980 | − | 0.993134i | \(-0.537321\pi\) | ||||
−0.116980 | + | 0.993134i | \(0.537321\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 4496.95 | 0.158304 | ||||||||
\(932\) | 3999.84 | 0.140579 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −23675.0 | −0.829410 | ||||||||
\(935\) | −14780.9 | −0.516992 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 36109.1 | 1.25895 | 0.629473 | − | 0.777022i | \(-0.283271\pi\) | ||||
0.629473 | + | 0.777022i | \(0.283271\pi\) | |||||||
\(938\) | −113098. | −3.93687 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −66245.8 | −2.29862 | ||||||||
\(941\) | −47894.5 | −1.65921 | −0.829604 | − | 0.558352i | \(-0.811434\pi\) | ||||
−0.829604 | + | 0.558352i | \(0.811434\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 10147.5 | 0.350423 | ||||||||
\(944\) | 12257.4 | 0.422612 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −65523.4 | −2.25195 | ||||||||
\(947\) | −34541.3 | −1.18526 | −0.592631 | − | 0.805474i | \(-0.701911\pi\) | ||||
−0.592631 | + | 0.805474i | \(0.701911\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 2412.30 | 0.0823845 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −25165.8 | −0.856753 | ||||||||
\(953\) | −37217.0 | −1.26503 | −0.632517 | − | 0.774546i | \(-0.717978\pi\) | ||||
−0.632517 | + | 0.774546i | \(0.717978\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 25590.5 | 0.867110 | ||||||||
\(956\) | −38139.9 | −1.29030 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −6029.14 | −0.203332 | ||||||||
\(959\) | 65548.0 | 2.20715 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −26653.4 | −0.894679 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −58632.4 | −1.95894 | ||||||||
\(965\) | −13106.4 | −0.437213 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −19683.1 | −0.654567 | −0.327283 | − | 0.944926i | \(-0.606133\pi\) | ||||
−0.327283 | + | 0.944926i | \(0.606133\pi\) | |||||||
\(968\) | 16241.0 | 0.539262 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −88159.0 | −2.91816 | ||||||||
\(971\) | −33750.5 | −1.11545 | −0.557726 | − | 0.830025i | \(-0.688326\pi\) | ||||
−0.557726 | + | 0.830025i | \(0.688326\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −47234.6 | −1.55629 | ||||||||
\(974\) | −93086.1 | −3.06229 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 30827.3 | 1.01102 | ||||||||
\(977\) | 23945.2 | 0.784110 | 0.392055 | − | 0.919942i | \(-0.371764\pi\) | ||||
0.392055 | + | 0.919942i | \(0.371764\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 16116.4 | 0.526130 | ||||||||
\(980\) | −66914.6 | −2.18113 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 40443.8 | 1.31427 | ||||||||
\(983\) | −53283.1 | −1.72886 | −0.864429 | − | 0.502756i | \(-0.832320\pi\) | ||||
−0.864429 | + | 0.502756i | \(0.832320\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 16707.1 | 0.540440 | ||||||||
\(986\) | 18680.3 | 0.603348 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −9234.71 | −0.296913 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −46669.4 | −1.49597 | −0.747983 | − | 0.663717i | \(-0.768978\pi\) | ||||
−0.747983 | + | 0.663717i | \(0.768978\pi\) | |||||||
\(992\) | −2950.20 | −0.0944245 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −93697.4 | −2.98984 | ||||||||
\(995\) | 3641.32 | 0.116018 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −28293.1 | −0.898748 | −0.449374 | − | 0.893344i | \(-0.648353\pi\) | ||||
−0.449374 | + | 0.893344i | \(0.648353\pi\) | |||||||
\(998\) | −960.405 | −0.0304620 | ||||||||
\(999\) | 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 | 1521.4.a.bh.1.8 | 9 | ||
3.2 | odd | 2 | 169.4.a.k.1.2 | ✓ | 9 | ||
13.12 | even | 2 | 1521.4.a.bg.1.2 | 9 | |||
39.2 | even | 12 | 169.4.e.h.147.3 | 36 | |||
39.5 | even | 4 | 169.4.b.g.168.16 | 18 | |||
39.8 | even | 4 | 169.4.b.g.168.3 | 18 | |||
39.11 | even | 12 | 169.4.e.h.147.16 | 36 | |||
39.17 | odd | 6 | 169.4.c.k.146.2 | 18 | |||
39.20 | even | 12 | 169.4.e.h.23.3 | 36 | |||
39.23 | odd | 6 | 169.4.c.k.22.2 | 18 | |||
39.29 | odd | 6 | 169.4.c.l.22.8 | 18 | |||
39.32 | even | 12 | 169.4.e.h.23.16 | 36 | |||
39.35 | odd | 6 | 169.4.c.l.146.8 | 18 | |||
39.38 | odd | 2 | 169.4.a.l.1.8 | yes | 9 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
169.4.a.k.1.2 | ✓ | 9 | 3.2 | odd | 2 | ||
169.4.a.l.1.8 | yes | 9 | 39.38 | odd | 2 | ||
169.4.b.g.168.3 | 18 | 39.8 | even | 4 | |||
169.4.b.g.168.16 | 18 | 39.5 | even | 4 | |||
169.4.c.k.22.2 | 18 | 39.23 | odd | 6 | |||
169.4.c.k.146.2 | 18 | 39.17 | odd | 6 | |||
169.4.c.l.22.8 | 18 | 39.29 | odd | 6 | |||
169.4.c.l.146.8 | 18 | 39.35 | odd | 6 | |||
169.4.e.h.23.3 | 36 | 39.20 | even | 12 | |||
169.4.e.h.23.16 | 36 | 39.32 | even | 12 | |||
169.4.e.h.147.3 | 36 | 39.2 | even | 12 | |||
169.4.e.h.147.16 | 36 | 39.11 | even | 12 | |||
1521.4.a.bg.1.2 | 9 | 13.12 | even | 2 | |||
1521.4.a.bh.1.8 | 9 | 1.1 | even | 1 | trivial |