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: | \(1\) |
Dimension: | \(4\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{4} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 2x^{3} - 25x^{2} + 24x + 78 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 39) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(5.33039\) 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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 5.33039 | 1.88458 | 0.942289 | − | 0.334800i | \(-0.108669\pi\) | ||||
0.942289 | + | 0.334800i | \(0.108669\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 20.4131 | 2.55164 | ||||||||
\(5\) | −16.4131 | −1.46803 | −0.734016 | − | 0.679132i | \(-0.762356\pi\) | ||||
−0.734016 | + | 0.679132i | \(0.762356\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −9.67968 | −0.522654 | −0.261327 | − | 0.965250i | \(-0.584160\pi\) | ||||
−0.261327 | + | 0.965250i | \(0.584160\pi\) | |||||||
\(8\) | 66.1667 | 2.92418 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −87.4882 | −2.76662 | ||||||||
\(11\) | 27.5882 | 0.756195 | 0.378098 | − | 0.925766i | \(-0.376578\pi\) | ||||
0.378098 | + | 0.925766i | \(0.376578\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | −51.5965 | −0.984982 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 189.390 | 2.95921 | ||||||||
\(17\) | −107.928 | −1.53979 | −0.769895 | − | 0.638171i | \(-0.779691\pi\) | ||||
−0.769895 | + | 0.638171i | \(0.779691\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.24723 | 0.0271342 | 0.0135671 | − | 0.999908i | \(-0.495681\pi\) | ||||
0.0135671 | + | 0.999908i | \(0.495681\pi\) | |||||||
\(20\) | −335.042 | −3.74588 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 147.056 | 1.42511 | ||||||||
\(23\) | −41.8090 | −0.379034 | −0.189517 | − | 0.981877i | \(-0.560692\pi\) | ||||
−0.189517 | + | 0.981877i | \(0.560692\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 144.390 | 1.15512 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −197.592 | −1.33362 | ||||||||
\(29\) | −61.6213 | −0.394579 | −0.197289 | − | 0.980345i | \(-0.563214\pi\) | ||||
−0.197289 | + | 0.980345i | \(0.563214\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −191.932 | −1.11200 | −0.556000 | − | 0.831182i | \(-0.687665\pi\) | ||||
−0.556000 | + | 0.831182i | \(0.687665\pi\) | |||||||
\(32\) | 480.187 | 2.65269 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −575.300 | −2.90185 | ||||||||
\(35\) | 158.874 | 0.767272 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −98.4236 | −0.437317 | −0.218659 | − | 0.975801i | \(-0.570168\pi\) | ||||
−0.218659 | + | 0.975801i | \(0.570168\pi\) | |||||||
\(38\) | 11.9786 | 0.0511366 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −1086.00 | −4.29279 | ||||||||
\(41\) | −30.7452 | −0.117112 | −0.0585561 | − | 0.998284i | \(-0.518650\pi\) | ||||
−0.0585561 | + | 0.998284i | \(0.518650\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 238.325 | 0.845216 | 0.422608 | − | 0.906313i | \(-0.361115\pi\) | ||||
0.422608 | + | 0.906313i | \(0.361115\pi\) | |||||||
\(44\) | 563.160 | 1.92953 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −222.858 | −0.714319 | ||||||||
\(47\) | −511.482 | −1.58739 | −0.793695 | − | 0.608316i | \(-0.791845\pi\) | ||||
−0.793695 | + | 0.608316i | \(0.791845\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −249.304 | −0.726833 | ||||||||
\(50\) | 769.653 | 2.17691 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −492.825 | −1.27726 | −0.638630 | − | 0.769514i | \(-0.720498\pi\) | ||||
−0.638630 | + | 0.769514i | \(0.720498\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −452.807 | −1.11012 | ||||||||
\(56\) | −640.472 | −1.52833 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −328.466 | −0.743615 | ||||||||
\(59\) | 484.179 | 1.06838 | 0.534192 | − | 0.845363i | \(-0.320616\pi\) | ||||
0.534192 | + | 0.845363i | \(0.320616\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −444.021 | −0.931985 | −0.465993 | − | 0.884789i | \(-0.654303\pi\) | ||||
−0.465993 | + | 0.884789i | \(0.654303\pi\) | |||||||
\(62\) | −1023.07 | −2.09565 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1044.47 | 2.03998 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −190.114 | −0.346658 | −0.173329 | − | 0.984864i | \(-0.555452\pi\) | ||||
−0.173329 | + | 0.984864i | \(0.555452\pi\) | |||||||
\(68\) | −2203.15 | −3.92898 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 846.858 | 1.44598 | ||||||||
\(71\) | 484.785 | 0.810329 | 0.405164 | − | 0.914244i | \(-0.367214\pi\) | ||||
0.405164 | + | 0.914244i | \(0.367214\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 957.780 | 1.53561 | 0.767806 | − | 0.640683i | \(-0.221349\pi\) | ||||
0.767806 | + | 0.640683i | \(0.221349\pi\) | |||||||
\(74\) | −524.636 | −0.824159 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 45.8729 | 0.0692367 | ||||||||
\(77\) | −267.045 | −0.395228 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −375.216 | −0.534368 | −0.267184 | − | 0.963646i | \(-0.586093\pi\) | ||||
−0.267184 | + | 0.963646i | \(0.586093\pi\) | |||||||
\(80\) | −3108.47 | −4.34422 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −163.884 | −0.220707 | ||||||||
\(83\) | −715.765 | −0.946571 | −0.473286 | − | 0.880909i | \(-0.656932\pi\) | ||||
−0.473286 | + | 0.880909i | \(0.656932\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1771.43 | 2.26046 | ||||||||
\(86\) | 1270.37 | 1.59288 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 1825.42 | 2.21125 | ||||||||
\(89\) | −1038.15 | −1.23645 | −0.618224 | − | 0.786002i | \(-0.712148\pi\) | ||||
−0.618224 | + | 0.786002i | \(0.712148\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −853.451 | −0.967157 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −2726.40 | −2.99156 | ||||||||
\(95\) | −36.8840 | −0.0398339 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −65.5636 | −0.0686286 | −0.0343143 | − | 0.999411i | \(-0.510925\pi\) | ||||
−0.0343143 | + | 0.999411i | \(0.510925\pi\) | |||||||
\(98\) | −1328.89 | −1.36977 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 2947.44 | 2.94744 | ||||||||
\(101\) | −531.798 | −0.523920 | −0.261960 | − | 0.965079i | \(-0.584369\pi\) | ||||
−0.261960 | + | 0.965079i | \(0.584369\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −735.984 | −0.704064 | −0.352032 | − | 0.935988i | \(-0.614509\pi\) | ||||
−0.352032 | + | 0.935988i | \(0.614509\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −2626.95 | −2.40710 | ||||||||
\(107\) | 783.265 | 0.707673 | 0.353837 | − | 0.935307i | \(-0.384877\pi\) | ||||
0.353837 | + | 0.935307i | \(0.384877\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 532.339 | 0.467788 | 0.233894 | − | 0.972262i | \(-0.424853\pi\) | ||||
0.233894 | + | 0.972262i | \(0.424853\pi\) | |||||||
\(110\) | −2413.64 | −2.09210 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −1833.23 | −1.54664 | ||||||||
\(113\) | 180.589 | 0.150340 | 0.0751699 | − | 0.997171i | \(-0.476050\pi\) | ||||
0.0751699 | + | 0.997171i | \(0.476050\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 686.215 | 0.556434 | ||||||||
\(116\) | −1257.88 | −1.00682 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 2580.86 | 2.01346 | ||||||||
\(119\) | 1044.71 | 0.804777 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −569.893 | −0.428169 | ||||||||
\(122\) | −2366.81 | −1.75640 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −3917.92 | −2.83742 | ||||||||
\(125\) | −318.242 | −0.227716 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1431.63 | 1.00029 | 0.500146 | − | 0.865941i | \(-0.333280\pi\) | ||||
0.500146 | + | 0.865941i | \(0.333280\pi\) | |||||||
\(128\) | 1725.94 | 1.19182 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −2067.32 | −1.37880 | −0.689400 | − | 0.724381i | \(-0.742126\pi\) | ||||
−0.689400 | + | 0.724381i | \(0.742126\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −21.7525 | −0.0141818 | ||||||||
\(134\) | −1013.38 | −0.653304 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −7141.25 | −4.50262 | ||||||||
\(137\) | −387.512 | −0.241660 | −0.120830 | − | 0.992673i | \(-0.538556\pi\) | ||||
−0.120830 | + | 0.992673i | \(0.538556\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 752.568 | 0.459223 | 0.229611 | − | 0.973282i | \(-0.426254\pi\) | ||||
0.229611 | + | 0.973282i | \(0.426254\pi\) | |||||||
\(140\) | 3243.10 | 1.95780 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 2584.09 | 1.52713 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1011.40 | 0.579254 | ||||||||
\(146\) | 5105.34 | 2.89398 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −2009.13 | −1.11587 | ||||||||
\(149\) | −2636.72 | −1.44972 | −0.724862 | − | 0.688895i | \(-0.758096\pi\) | ||||
−0.724862 | + | 0.688895i | \(0.758096\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 3332.42 | 1.79595 | 0.897975 | − | 0.440046i | \(-0.145038\pi\) | ||||
0.897975 | + | 0.440046i | \(0.145038\pi\) | |||||||
\(152\) | 148.692 | 0.0793454 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −1423.45 | −0.744839 | ||||||||
\(155\) | 3150.20 | 1.63245 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1625.26 | −0.826179 | −0.413089 | − | 0.910690i | \(-0.635550\pi\) | ||||
−0.413089 | + | 0.910690i | \(0.635550\pi\) | |||||||
\(158\) | −2000.05 | −1.00706 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −7881.36 | −3.89423 | ||||||||
\(161\) | 404.698 | 0.198104 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1835.37 | 0.881944 | 0.440972 | − | 0.897521i | \(-0.354634\pi\) | ||||
0.440972 | + | 0.897521i | \(0.354634\pi\) | |||||||
\(164\) | −627.605 | −0.298828 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −3815.31 | −1.78389 | ||||||||
\(167\) | 1945.00 | 0.901248 | 0.450624 | − | 0.892714i | \(-0.351202\pi\) | ||||
0.450624 | + | 0.892714i | \(0.351202\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | 9442.44 | 4.26001 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 4864.96 | 2.15668 | ||||||||
\(173\) | −2531.63 | −1.11258 | −0.556289 | − | 0.830989i | \(-0.687775\pi\) | ||||
−0.556289 | + | 0.830989i | \(0.687775\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1397.65 | −0.603726 | ||||||||
\(176\) | 5224.91 | 2.23774 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −5533.76 | −2.33018 | ||||||||
\(179\) | −4263.01 | −1.78007 | −0.890035 | − | 0.455892i | \(-0.849320\pi\) | ||||
−0.890035 | + | 0.455892i | \(0.849320\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 3944.61 | 1.61989 | 0.809946 | − | 0.586504i | \(-0.199496\pi\) | ||||
0.809946 | + | 0.586504i | \(0.199496\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −2766.36 | −1.10836 | ||||||||
\(185\) | 1615.43 | 0.641995 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −2977.54 | −1.16438 | ||||||||
\(188\) | −10440.9 | −4.05044 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −196.606 | −0.0750701 | ||||||||
\(191\) | 214.109 | 0.0811119 | 0.0405559 | − | 0.999177i | \(-0.487087\pi\) | ||||
0.0405559 | + | 0.999177i | \(0.487087\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1207.19 | 0.450234 | 0.225117 | − | 0.974332i | \(-0.427724\pi\) | ||||
0.225117 | + | 0.974332i | \(0.427724\pi\) | |||||||
\(194\) | −349.480 | −0.129336 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −5089.06 | −1.85461 | ||||||||
\(197\) | −927.631 | −0.335487 | −0.167744 | − | 0.985831i | \(-0.553648\pi\) | ||||
−0.167744 | + | 0.985831i | \(0.553648\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 478.951 | 0.170613 | 0.0853064 | − | 0.996355i | \(-0.472813\pi\) | ||||
0.0853064 | + | 0.996355i | \(0.472813\pi\) | |||||||
\(200\) | 9553.77 | 3.37777 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −2834.69 | −0.987368 | ||||||||
\(203\) | 596.474 | 0.206228 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 504.624 | 0.171924 | ||||||||
\(206\) | −3923.08 | −1.32686 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 61.9970 | 0.0205188 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1450.95 | −0.473402 | −0.236701 | − | 0.971583i | \(-0.576066\pi\) | ||||
−0.236701 | + | 0.971583i | \(0.576066\pi\) | |||||||
\(212\) | −10060.1 | −3.25910 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 4175.11 | 1.33367 | ||||||||
\(215\) | −3911.66 | −1.24080 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1857.84 | 0.581191 | ||||||||
\(218\) | 2837.58 | 0.881583 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −9243.19 | −2.83262 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 2059.79 | 0.618536 | 0.309268 | − | 0.950975i | \(-0.399916\pi\) | ||||
0.309268 | + | 0.950975i | \(0.399916\pi\) | |||||||
\(224\) | −4648.06 | −1.38644 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 962.612 | 0.283327 | ||||||||
\(227\) | 4482.46 | 1.31062 | 0.655311 | − | 0.755359i | \(-0.272537\pi\) | ||||
0.655311 | + | 0.755359i | \(0.272537\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1630.39 | 0.470477 | 0.235239 | − | 0.971938i | \(-0.424413\pi\) | ||||
0.235239 | + | 0.971938i | \(0.424413\pi\) | |||||||
\(230\) | 3657.80 | 1.04864 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −4077.27 | −1.15382 | ||||||||
\(233\) | 1903.69 | 0.535258 | 0.267629 | − | 0.963522i | \(-0.413760\pi\) | ||||
0.267629 | + | 0.963522i | \(0.413760\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 8395.00 | 2.33034 | ||||||||
\(236\) | 9883.58 | 2.72613 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 5568.72 | 1.51667 | ||||||||
\(239\) | 3763.79 | 1.01866 | 0.509328 | − | 0.860572i | \(-0.329894\pi\) | ||||
0.509328 | + | 0.860572i | \(0.329894\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 3614.74 | 0.966166 | 0.483083 | − | 0.875575i | \(-0.339517\pi\) | ||||
0.483083 | + | 0.875575i | \(0.339517\pi\) | |||||||
\(242\) | −3037.75 | −0.806918 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −9063.85 | −2.37809 | ||||||||
\(245\) | 4091.84 | 1.06701 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −12699.5 | −3.25169 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −1696.36 | −0.429148 | ||||||||
\(251\) | 5729.77 | 1.44088 | 0.720438 | − | 0.693520i | \(-0.243941\pi\) | ||||
0.720438 | + | 0.693520i | \(0.243941\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1153.43 | −0.286624 | ||||||||
\(254\) | 7631.18 | 1.88513 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 844.191 | 0.206101 | ||||||||
\(257\) | 5525.79 | 1.34120 | 0.670602 | − | 0.741818i | \(-0.266036\pi\) | ||||
0.670602 | + | 0.741818i | \(0.266036\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 952.709 | 0.228565 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −11019.6 | −2.59846 | ||||||||
\(263\) | −5223.21 | −1.22463 | −0.612313 | − | 0.790615i | \(-0.709761\pi\) | ||||
−0.612313 | + | 0.790615i | \(0.709761\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 8088.78 | 1.87506 | ||||||||
\(266\) | −115.949 | −0.0267267 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −3880.81 | −0.884545 | ||||||||
\(269\) | −7203.88 | −1.63282 | −0.816410 | − | 0.577473i | \(-0.804039\pi\) | ||||
−0.816410 | + | 0.577473i | \(0.804039\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 8577.69 | 1.92272 | 0.961360 | − | 0.275293i | \(-0.0887750\pi\) | ||||
0.961360 | + | 0.275293i | \(0.0887750\pi\) | |||||||
\(272\) | −20440.5 | −4.55656 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −2065.59 | −0.455427 | ||||||||
\(275\) | 3983.44 | 0.873493 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 7169.19 | 1.55507 | 0.777536 | − | 0.628838i | \(-0.216469\pi\) | ||||
0.777536 | + | 0.628838i | \(0.216469\pi\) | |||||||
\(278\) | 4011.48 | 0.865442 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 10512.1 | 2.24364 | ||||||||
\(281\) | 849.157 | 0.180272 | 0.0901360 | − | 0.995929i | \(-0.471270\pi\) | ||||
0.0901360 | + | 0.995929i | \(0.471270\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1115.37 | 0.234283 | 0.117141 | − | 0.993115i | \(-0.462627\pi\) | ||||
0.117141 | + | 0.993115i | \(0.462627\pi\) | |||||||
\(284\) | 9895.95 | 2.06766 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 297.604 | 0.0612091 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 6735.49 | 1.37095 | ||||||||
\(290\) | 5391.14 | 1.09165 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 19551.2 | 3.91832 | ||||||||
\(293\) | −1863.53 | −0.371565 | −0.185782 | − | 0.982591i | \(-0.559482\pi\) | ||||
−0.185782 | + | 0.982591i | \(0.559482\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −7946.87 | −1.56842 | ||||||||
\(296\) | −6512.36 | −1.27879 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −14054.8 | −2.73212 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2306.91 | −0.441755 | ||||||||
\(302\) | 17763.1 | 3.38461 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 425.602 | 0.0802959 | ||||||||
\(305\) | 7287.76 | 1.36818 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 6387.50 | 1.18747 | 0.593736 | − | 0.804660i | \(-0.297652\pi\) | ||||
0.593736 | + | 0.804660i | \(0.297652\pi\) | |||||||
\(308\) | −5451.21 | −1.00848 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 16791.8 | 3.07648 | ||||||||
\(311\) | 3492.59 | 0.636806 | 0.318403 | − | 0.947955i | \(-0.396853\pi\) | ||||
0.318403 | + | 0.947955i | \(0.396853\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −5912.01 | −1.06762 | −0.533812 | − | 0.845603i | \(-0.679241\pi\) | ||||
−0.533812 | + | 0.845603i | \(0.679241\pi\) | |||||||
\(314\) | −8663.29 | −1.55700 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −7659.31 | −1.36351 | ||||||||
\(317\) | −1677.54 | −0.297224 | −0.148612 | − | 0.988896i | \(-0.547481\pi\) | ||||
−0.148612 | + | 0.988896i | \(0.547481\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1700.02 | −0.298378 | ||||||||
\(320\) | −17143.0 | −2.99476 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 2157.20 | 0.373342 | ||||||||
\(323\) | −242.540 | −0.0417810 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 9783.22 | 1.66209 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −2034.31 | −0.342457 | ||||||||
\(329\) | 4950.98 | 0.829655 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −2010.31 | −0.333827 | −0.166913 | − | 0.985972i | \(-0.553380\pi\) | ||||
−0.166913 | + | 0.985972i | \(0.553380\pi\) | |||||||
\(332\) | −14611.0 | −2.41531 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 10367.6 | 1.69847 | ||||||||
\(335\) | 3120.35 | 0.508905 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 7139.24 | 1.15400 | 0.577002 | − | 0.816743i | \(-0.304222\pi\) | ||||
0.577002 | + | 0.816743i | \(0.304222\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 36160.5 | 5.76787 | ||||||||
\(341\) | −5295.05 | −0.840889 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 5733.31 | 0.902536 | ||||||||
\(344\) | 15769.2 | 2.47156 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −13494.6 | −2.09674 | ||||||||
\(347\) | −1.13990 | −0.000176349 0 | −8.81743e−5 | − | 1.00000i | \(-0.500028\pi\) | ||||
−8.81743e−5 | 1.00000i | \(0.500028\pi\) | ||||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −12199.1 | −1.87107 | −0.935535 | − | 0.353235i | \(-0.885082\pi\) | ||||
−0.935535 | + | 0.353235i | \(0.885082\pi\) | |||||||
\(350\) | −7450.00 | −1.13777 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 13247.5 | 2.00595 | ||||||||
\(353\) | −10892.3 | −1.64232 | −0.821160 | − | 0.570698i | \(-0.806673\pi\) | ||||
−0.821160 | + | 0.570698i | \(0.806673\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −7956.81 | −1.18959 | ||||||||
\(356\) | −21191.9 | −3.15497 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −22723.5 | −3.35468 | ||||||||
\(359\) | −3525.78 | −0.518339 | −0.259169 | − | 0.965832i | \(-0.583449\pi\) | ||||
−0.259169 | + | 0.965832i | \(0.583449\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −6853.95 | −0.999264 | ||||||||
\(362\) | 21026.3 | 3.05281 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −15720.1 | −2.25433 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 2383.75 | 0.339049 | 0.169525 | − | 0.985526i | \(-0.445777\pi\) | ||||
0.169525 | + | 0.985526i | \(0.445777\pi\) | |||||||
\(368\) | −7918.19 | −1.12164 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 8610.90 | 1.20989 | ||||||||
\(371\) | 4770.39 | 0.667564 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −13282.2 | −1.84377 | −0.921885 | − | 0.387463i | \(-0.873352\pi\) | ||||
−0.921885 | + | 0.387463i | \(0.873352\pi\) | |||||||
\(374\) | −15871.5 | −2.19437 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −33843.1 | −4.64181 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 4436.73 | 0.601318 | 0.300659 | − | 0.953732i | \(-0.402793\pi\) | ||||
0.300659 | + | 0.953732i | \(0.402793\pi\) | |||||||
\(380\) | −752.917 | −0.101642 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 1141.28 | 0.152862 | ||||||||
\(383\) | −810.412 | −0.108120 | −0.0540602 | − | 0.998538i | \(-0.517216\pi\) | ||||
−0.0540602 | + | 0.998538i | \(0.517216\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 4383.03 | 0.580207 | ||||||||
\(386\) | 6434.78 | 0.848501 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −1338.35 | −0.175115 | ||||||||
\(389\) | −3463.79 | −0.451469 | −0.225734 | − | 0.974189i | \(-0.572478\pi\) | ||||
−0.225734 | + | 0.974189i | \(0.572478\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 4512.37 | 0.583633 | ||||||||
\(392\) | −16495.6 | −2.12539 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −4944.64 | −0.632252 | ||||||||
\(395\) | 6158.45 | 0.784469 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −425.405 | −0.0537796 | −0.0268898 | − | 0.999638i | \(-0.508560\pi\) | ||||
−0.0268898 | + | 0.999638i | \(0.508560\pi\) | |||||||
\(398\) | 2553.00 | 0.321533 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 27345.9 | 3.41823 | ||||||||
\(401\) | −1186.85 | −0.147801 | −0.0739007 | − | 0.997266i | \(-0.523545\pi\) | ||||
−0.0739007 | + | 0.997266i | \(0.523545\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | −10855.6 | −1.33685 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 3179.44 | 0.388653 | ||||||||
\(407\) | −2715.33 | −0.330697 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −8007.42 | −0.968071 | −0.484036 | − | 0.875048i | \(-0.660830\pi\) | ||||
−0.484036 | + | 0.875048i | \(0.660830\pi\) | |||||||
\(410\) | 2689.84 | 0.324005 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −15023.7 | −1.79652 | ||||||||
\(413\) | −4686.70 | −0.558395 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 11747.9 | 1.38960 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 330.468 | 0.0386692 | ||||||||
\(419\) | −6832.46 | −0.796629 | −0.398314 | − | 0.917249i | \(-0.630405\pi\) | ||||
−0.398314 | + | 0.917249i | \(0.630405\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −10739.6 | −1.24326 | −0.621632 | − | 0.783309i | \(-0.713530\pi\) | ||||
−0.621632 | + | 0.783309i | \(0.713530\pi\) | |||||||
\(422\) | −7734.16 | −0.892163 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −32608.6 | −3.73494 | ||||||||
\(425\) | −15583.7 | −1.77864 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 4297.99 | 0.487106 | ||||||||
\(428\) | 15988.9 | 1.80573 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −20850.7 | −2.33839 | ||||||||
\(431\) | 5214.45 | 0.582763 | 0.291382 | − | 0.956607i | \(-0.405885\pi\) | ||||
0.291382 | + | 0.956607i | \(0.405885\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 8642.24 | 0.959168 | 0.479584 | − | 0.877496i | \(-0.340788\pi\) | ||||
0.479584 | + | 0.877496i | \(0.340788\pi\) | |||||||
\(434\) | 9903.02 | 1.09530 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 10866.7 | 1.19362 | ||||||||
\(437\) | −93.9545 | −0.0102848 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −13026.2 | −1.41619 | −0.708097 | − | 0.706116i | \(-0.750446\pi\) | ||||
−0.708097 | + | 0.706116i | \(0.750446\pi\) | |||||||
\(440\) | −29960.7 | −3.24619 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 11533.0 | 1.23690 | 0.618450 | − | 0.785824i | \(-0.287761\pi\) | ||||
0.618450 | + | 0.785824i | \(0.287761\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 17039.3 | 1.81515 | ||||||||
\(446\) | 10979.5 | 1.16568 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −10110.2 | −1.06621 | ||||||||
\(449\) | 9882.75 | 1.03874 | 0.519372 | − | 0.854548i | \(-0.326166\pi\) | ||||
0.519372 | + | 0.854548i | \(0.326166\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −848.204 | −0.0885596 | ||||||||
\(452\) | 3686.38 | 0.383613 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 23893.3 | 2.46997 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 15628.1 | 1.59967 | 0.799836 | − | 0.600218i | \(-0.204920\pi\) | ||||
0.799836 | + | 0.600218i | \(0.204920\pi\) | |||||||
\(458\) | 8690.63 | 0.886652 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 14007.8 | 1.41982 | ||||||||
\(461\) | −7747.46 | −0.782723 | −0.391361 | − | 0.920237i | \(-0.627996\pi\) | ||||
−0.391361 | + | 0.920237i | \(0.627996\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 333.422 | 0.0334675 | 0.0167337 | − | 0.999860i | \(-0.494673\pi\) | ||||
0.0167337 | + | 0.999860i | \(0.494673\pi\) | |||||||
\(464\) | −11670.4 | −1.16764 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 10147.4 | 1.00874 | ||||||||
\(467\) | −8198.33 | −0.812363 | −0.406182 | − | 0.913792i | \(-0.633140\pi\) | ||||
−0.406182 | + | 0.913792i | \(0.633140\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1840.24 | 0.181182 | ||||||||
\(470\) | 44748.7 | 4.39171 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 32036.5 | 3.12415 | ||||||||
\(473\) | 6574.96 | 0.639148 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 324.477 | 0.0313432 | ||||||||
\(476\) | 21325.8 | 2.05350 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 20062.5 | 1.91974 | ||||||||
\(479\) | −6435.88 | −0.613910 | −0.306955 | − | 0.951724i | \(-0.599310\pi\) | ||||
−0.306955 | + | 0.951724i | \(0.599310\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 19268.0 | 1.82082 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −11633.3 | −1.09253 | ||||||||
\(485\) | 1076.10 | 0.100749 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −8095.37 | −0.753257 | −0.376629 | − | 0.926364i | \(-0.622917\pi\) | ||||
−0.376629 | + | 0.926364i | \(0.622917\pi\) | |||||||
\(488\) | −29379.4 | −2.72529 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 21811.1 | 2.01087 | ||||||||
\(491\) | −5116.46 | −0.470270 | −0.235135 | − | 0.971963i | \(-0.575553\pi\) | ||||
−0.235135 | + | 0.971963i | \(0.575553\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 6650.67 | 0.607568 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −36349.9 | −3.29064 | ||||||||
\(497\) | −4692.56 | −0.423521 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 18050.7 | 1.61936 | 0.809682 | − | 0.586870i | \(-0.199640\pi\) | ||||
0.809682 | + | 0.586870i | \(0.199640\pi\) | |||||||
\(500\) | −6496.31 | −0.581047 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 30541.9 | 2.71544 | ||||||||
\(503\) | −10531.1 | −0.933512 | −0.466756 | − | 0.884386i | \(-0.654577\pi\) | ||||
−0.466756 | + | 0.884386i | \(0.654577\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 8728.45 | 0.769131 | ||||||||
\(506\) | −6148.25 | −0.540165 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 29224.1 | 2.55238 | ||||||||
\(509\) | −1963.31 | −0.170967 | −0.0854834 | − | 0.996340i | \(-0.527243\pi\) | ||||
−0.0854834 | + | 0.996340i | \(0.527243\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −9271.00 | −0.802593 | ||||||||
\(512\) | −9307.69 | −0.803409 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 29454.6 | 2.52760 | ||||||||
\(515\) | 12079.8 | 1.03359 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −14110.9 | −1.20038 | ||||||||
\(518\) | 5078.31 | 0.430750 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 7044.93 | 0.592407 | 0.296203 | − | 0.955125i | \(-0.404279\pi\) | ||||
0.296203 | + | 0.955125i | \(0.404279\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −3213.29 | −0.268657 | −0.134328 | − | 0.990937i | \(-0.542888\pi\) | ||||
−0.134328 | + | 0.990937i | \(0.542888\pi\) | |||||||
\(524\) | −42200.4 | −3.51819 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −27841.7 | −2.30790 | ||||||||
\(527\) | 20714.9 | 1.71225 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −10419.0 | −0.856333 | ||||||||
\(530\) | 43116.4 | 3.53369 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −444.036 | −0.0361868 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −12855.8 | −1.03889 | ||||||||
\(536\) | −12579.2 | −1.01369 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −38399.5 | −3.07718 | ||||||||
\(539\) | −6877.83 | −0.549627 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −11251.4 | −0.894150 | −0.447075 | − | 0.894497i | \(-0.647534\pi\) | ||||
−0.447075 | + | 0.894497i | \(0.647534\pi\) | |||||||
\(542\) | 45722.4 | 3.62352 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −51825.8 | −4.08458 | ||||||||
\(545\) | −8737.33 | −0.686727 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 1533.54 | 0.119871 | 0.0599353 | − | 0.998202i | \(-0.480911\pi\) | ||||
0.0599353 | + | 0.998202i | \(0.480911\pi\) | |||||||
\(548\) | −7910.31 | −0.616628 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 21233.3 | 1.64617 | ||||||||
\(551\) | −138.477 | −0.0107066 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 3631.97 | 0.279289 | ||||||||
\(554\) | 38214.6 | 2.93066 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 15362.2 | 1.17177 | ||||||||
\(557\) | 16845.7 | 1.28146 | 0.640731 | − | 0.767766i | \(-0.278631\pi\) | ||||
0.640731 | + | 0.767766i | \(0.278631\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 30089.0 | 2.27052 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 4526.34 | 0.339737 | ||||||||
\(563\) | 20820.1 | 1.55855 | 0.779273 | − | 0.626685i | \(-0.215589\pi\) | ||||
0.779273 | + | 0.626685i | \(0.215589\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −2964.03 | −0.220704 | ||||||||
\(566\) | 5945.37 | 0.441524 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 32076.6 | 2.36955 | ||||||||
\(569\) | −23636.6 | −1.74147 | −0.870735 | − | 0.491752i | \(-0.836357\pi\) | ||||
−0.870735 | + | 0.491752i | \(0.836357\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −26955.1 | −1.97554 | −0.987771 | − | 0.155913i | \(-0.950168\pi\) | ||||
−0.987771 | + | 0.155913i | \(0.950168\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 1586.35 | 0.115353 | ||||||||
\(575\) | −6036.78 | −0.437828 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −23499.8 | −1.69551 | −0.847755 | − | 0.530388i | \(-0.822046\pi\) | ||||
−0.847755 | + | 0.530388i | \(0.822046\pi\) | |||||||
\(578\) | 35902.8 | 2.58367 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 20645.7 | 1.47805 | ||||||||
\(581\) | 6928.38 | 0.494729 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −13596.1 | −0.965857 | ||||||||
\(584\) | 63373.1 | 4.49040 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −9933.33 | −0.700243 | ||||||||
\(587\) | 4637.50 | 0.326082 | 0.163041 | − | 0.986619i | \(-0.447870\pi\) | ||||
0.163041 | + | 0.986619i | \(0.447870\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −431.316 | −0.0301733 | ||||||||
\(590\) | −42359.9 | −2.95582 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −18640.4 | −1.29411 | ||||||||
\(593\) | 12633.5 | 0.874869 | 0.437434 | − | 0.899250i | \(-0.355887\pi\) | ||||
0.437434 | + | 0.899250i | \(0.355887\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −17146.9 | −1.18144 | ||||||||
\(596\) | −53823.7 | −3.69917 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 18757.1 | 1.27946 | 0.639730 | − | 0.768600i | \(-0.279046\pi\) | ||||
0.639730 | + | 0.768600i | \(0.279046\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −3632.98 | −0.246576 | −0.123288 | − | 0.992371i | \(-0.539344\pi\) | ||||
−0.123288 | + | 0.992371i | \(0.539344\pi\) | |||||||
\(602\) | −12296.8 | −0.832522 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 68025.0 | 4.58261 | ||||||||
\(605\) | 9353.71 | 0.628566 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −12700.0 | −0.849219 | −0.424610 | − | 0.905377i | \(-0.639589\pi\) | ||||
−0.424610 | + | 0.905377i | \(0.639589\pi\) | |||||||
\(608\) | 1079.09 | 0.0719786 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 38846.6 | 2.57845 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −21640.1 | −1.42584 | −0.712918 | − | 0.701248i | \(-0.752627\pi\) | ||||
−0.712918 | + | 0.701248i | \(0.752627\pi\) | |||||||
\(614\) | 34047.9 | 2.23788 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −17669.5 | −1.15572 | ||||||||
\(617\) | −16541.7 | −1.07933 | −0.539663 | − | 0.841881i | \(-0.681448\pi\) | ||||
−0.539663 | + | 0.841881i | \(0.681448\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 21138.9 | 1.37261 | 0.686303 | − | 0.727316i | \(-0.259233\pi\) | ||||
0.686303 | + | 0.727316i | \(0.259233\pi\) | |||||||
\(620\) | 64305.2 | 4.16542 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 18616.9 | 1.20011 | ||||||||
\(623\) | 10049.0 | 0.646235 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −12825.4 | −0.820823 | ||||||||
\(626\) | −31513.3 | −2.01202 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −33176.6 | −2.10811 | ||||||||
\(629\) | 10622.7 | 0.673377 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −5489.80 | −0.346348 | −0.173174 | − | 0.984891i | \(-0.555402\pi\) | ||||
−0.173174 | + | 0.984891i | \(0.555402\pi\) | |||||||
\(632\) | −24826.8 | −1.56259 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −8941.94 | −0.560141 | ||||||||
\(635\) | −23497.5 | −1.46846 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −9061.76 | −0.562318 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −28328.1 | −1.74963 | ||||||||
\(641\) | −4297.04 | −0.264778 | −0.132389 | − | 0.991198i | \(-0.542265\pi\) | ||||
−0.132389 | + | 0.991198i | \(0.542265\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −25696.9 | −1.57603 | −0.788016 | − | 0.615655i | \(-0.788892\pi\) | ||||
−0.788016 | + | 0.615655i | \(0.788892\pi\) | |||||||
\(644\) | 8261.14 | 0.505488 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −1292.83 | −0.0787396 | ||||||||
\(647\) | −2174.98 | −0.132160 | −0.0660798 | − | 0.997814i | \(-0.521049\pi\) | ||||
−0.0660798 | + | 0.997814i | \(0.521049\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 13357.6 | 0.807907 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 37465.5 | 2.25040 | ||||||||
\(653\) | 15454.5 | 0.926160 | 0.463080 | − | 0.886316i | \(-0.346744\pi\) | ||||
0.463080 | + | 0.886316i | \(0.346744\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 33931.1 | 2.02412 | ||||||||
\(656\) | −5822.82 | −0.346560 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 26390.7 | 1.56355 | ||||||||
\(659\) | 3148.77 | 0.186129 | 0.0930643 | − | 0.995660i | \(-0.470334\pi\) | ||||
0.0930643 | + | 0.995660i | \(0.470334\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 2099.70 | 0.123553 | 0.0617767 | − | 0.998090i | \(-0.480323\pi\) | ||||
0.0617767 | + | 0.998090i | \(0.480323\pi\) | |||||||
\(662\) | −10715.7 | −0.629122 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −47359.8 | −2.76795 | ||||||||
\(665\) | 357.026 | 0.0208193 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 2576.32 | 0.149559 | ||||||||
\(668\) | 39703.4 | 2.29966 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 16632.7 | 0.959071 | ||||||||
\(671\) | −12249.7 | −0.704763 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 30970.8 | 1.77390 | 0.886950 | − | 0.461865i | \(-0.152819\pi\) | ||||
0.886950 | + | 0.461865i | \(0.152819\pi\) | |||||||
\(674\) | 38055.0 | 2.17481 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −14640.6 | −0.831141 | −0.415570 | − | 0.909561i | \(-0.636418\pi\) | ||||
−0.415570 | + | 0.909561i | \(0.636418\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 634.635 | 0.0358690 | ||||||||
\(680\) | 117210. | 6.60999 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −28224.7 | −1.58472 | ||||||||
\(683\) | −6685.83 | −0.374563 | −0.187281 | − | 0.982306i | \(-0.559968\pi\) | ||||
−0.187281 | + | 0.982306i | \(0.559968\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 6360.27 | 0.354764 | ||||||||
\(686\) | 30560.8 | 1.70090 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 45136.3 | 2.50117 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 30194.1 | 1.66228 | 0.831141 | − | 0.556062i | \(-0.187688\pi\) | ||||
0.831141 | + | 0.556062i | \(0.187688\pi\) | |||||||
\(692\) | −51678.4 | −2.83890 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −6.07611 | −0.000332343 0 | ||||||||
\(695\) | −12352.0 | −0.674154 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 3318.28 | 0.180328 | ||||||||
\(698\) | −65026.0 | −3.52618 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −28530.3 | −1.54049 | ||||||||
\(701\) | 30300.9 | 1.63260 | 0.816298 | − | 0.577631i | \(-0.196023\pi\) | ||||
0.816298 | + | 0.577631i | \(0.196023\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −221.181 | −0.0118663 | ||||||||
\(704\) | 28815.1 | 1.54263 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −58060.3 | −3.09508 | ||||||||
\(707\) | 5147.64 | 0.273829 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −26123.2 | −1.38375 | −0.691875 | − | 0.722017i | \(-0.743215\pi\) | ||||
−0.691875 | + | 0.722017i | \(0.743215\pi\) | |||||||
\(710\) | −42412.9 | −2.24187 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −68691.1 | −3.61560 | ||||||||
\(713\) | 8024.48 | 0.421486 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −87021.3 | −4.54209 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −18793.8 | −0.976850 | ||||||||
\(719\) | −19325.7 | −1.00240 | −0.501200 | − | 0.865331i | \(-0.667108\pi\) | ||||
−0.501200 | + | 0.865331i | \(0.667108\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 7124.09 | 0.367982 | ||||||||
\(722\) | −36534.2 | −1.88319 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 80521.7 | 4.13338 | ||||||||
\(725\) | −8897.47 | −0.455784 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 26065.8 | 1.32975 | 0.664875 | − | 0.746954i | \(-0.268485\pi\) | ||||
0.664875 | + | 0.746954i | \(0.268485\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −83794.4 | −4.24845 | ||||||||
\(731\) | −25722.0 | −1.30145 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −1055.45 | −0.0531843 | −0.0265921 | − | 0.999646i | \(-0.508466\pi\) | ||||
−0.0265921 | + | 0.999646i | \(0.508466\pi\) | |||||||
\(734\) | 12706.4 | 0.638965 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −20076.2 | −1.00546 | ||||||||
\(737\) | −5244.89 | −0.262141 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −9410.40 | −0.468426 | −0.234213 | − | 0.972185i | \(-0.575251\pi\) | ||||
−0.234213 | + | 0.972185i | \(0.575251\pi\) | |||||||
\(740\) | 32976.0 | 1.63814 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 25428.1 | 1.25808 | ||||||||
\(743\) | −7523.70 | −0.371491 | −0.185746 | − | 0.982598i | \(-0.559470\pi\) | ||||
−0.185746 | + | 0.982598i | \(0.559470\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 43276.8 | 2.12824 | ||||||||
\(746\) | −70799.4 | −3.47473 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −60780.8 | −2.97108 | ||||||||
\(749\) | −7581.76 | −0.369868 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −12984.1 | −0.630886 | −0.315443 | − | 0.948945i | \(-0.602153\pi\) | ||||
−0.315443 | + | 0.948945i | \(0.602153\pi\) | |||||||
\(752\) | −96869.3 | −4.69742 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −54695.3 | −2.63651 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −27934.6 | −1.34122 | −0.670609 | − | 0.741811i | \(-0.733967\pi\) | ||||
−0.670609 | + | 0.741811i | \(0.733967\pi\) | |||||||
\(758\) | 23649.5 | 1.13323 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −2440.49 | −0.116482 | ||||||||
\(761\) | −15519.3 | −0.739255 | −0.369627 | − | 0.929180i | \(-0.620515\pi\) | ||||
−0.369627 | + | 0.929180i | \(0.620515\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −5152.88 | −0.244491 | ||||||||
\(764\) | 4370.62 | 0.206968 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −4319.82 | −0.203761 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −12885.2 | −0.604228 | −0.302114 | − | 0.953272i | \(-0.597692\pi\) | ||||
−0.302114 | + | 0.953272i | \(0.597692\pi\) | |||||||
\(770\) | 23363.3 | 1.09345 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 24642.4 | 1.14883 | ||||||||
\(773\) | 5892.04 | 0.274155 | 0.137078 | − | 0.990560i | \(-0.456229\pi\) | ||||
0.137078 | + | 0.990560i | \(0.456229\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −27713.0 | −1.28449 | ||||||||
\(776\) | −4338.12 | −0.200682 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −18463.4 | −0.850828 | ||||||||
\(779\) | −69.0916 | −0.00317775 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 13374.3 | 0.612766 | ||||||||
\(782\) | 24052.7 | 1.09990 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −47215.5 | −2.15085 | ||||||||
\(785\) | 26675.6 | 1.21286 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 21020.4 | 0.952091 | 0.476045 | − | 0.879421i | \(-0.342070\pi\) | ||||
0.476045 | + | 0.879421i | \(0.342070\pi\) | |||||||
\(788\) | −18935.8 | −0.856042 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 32827.0 | 1.47839 | ||||||||
\(791\) | −1748.05 | −0.0785757 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | −2267.58 | −0.101352 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 9776.87 | 0.435342 | ||||||||
\(797\) | −31355.6 | −1.39356 | −0.696782 | − | 0.717283i | \(-0.745386\pi\) | ||||
−0.696782 | + | 0.717283i | \(0.745386\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 55203.3 | 2.44425 | ||||||||
\(800\) | 69334.0 | 3.06416 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −6326.37 | −0.278543 | ||||||||
\(803\) | 26423.4 | 1.16122 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −6642.34 | −0.290822 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −35187.3 | −1.53204 | ||||||||
\(809\) | 18132.5 | 0.788017 | 0.394009 | − | 0.919107i | \(-0.371088\pi\) | ||||
0.394009 | + | 0.919107i | \(0.371088\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 24755.3 | 1.07186 | 0.535928 | − | 0.844263i | \(-0.319962\pi\) | ||||
0.535928 | + | 0.844263i | \(0.319962\pi\) | |||||||
\(812\) | 12175.9 | 0.526219 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −14473.8 | −0.623225 | ||||||||
\(815\) | −30124.0 | −1.29472 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 535.572 | 0.0229343 | ||||||||
\(818\) | −42682.7 | −1.82441 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 10300.9 | 0.438688 | ||||||||
\(821\) | 4082.65 | 0.173551 | 0.0867755 | − | 0.996228i | \(-0.472344\pi\) | ||||
0.0867755 | + | 0.996228i | \(0.472344\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −34327.0 | −1.45391 | −0.726954 | − | 0.686687i | \(-0.759065\pi\) | ||||
−0.726954 | + | 0.686687i | \(0.759065\pi\) | |||||||
\(824\) | −48697.6 | −2.05881 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −24981.9 | −1.05234 | ||||||||
\(827\) | 3228.87 | 0.135767 | 0.0678833 | − | 0.997693i | \(-0.478375\pi\) | ||||
0.0678833 | + | 0.997693i | \(0.478375\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −10452.4 | −0.437908 | −0.218954 | − | 0.975735i | \(-0.570265\pi\) | ||||
−0.218954 | + | 0.975735i | \(0.570265\pi\) | |||||||
\(830\) | 62621.0 | 2.61880 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 26906.9 | 1.11917 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −31923.4 | −1.32306 | ||||||||
\(836\) | 1265.55 | 0.0523564 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −36419.7 | −1.50131 | ||||||||
\(839\) | −28289.0 | −1.16406 | −0.582028 | − | 0.813169i | \(-0.697741\pi\) | ||||
−0.582028 | + | 0.813169i | \(0.697741\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −20591.8 | −0.844308 | ||||||||
\(842\) | −57246.1 | −2.34303 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −29618.5 | −1.20795 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 5516.39 | 0.223784 | ||||||||
\(848\) | −93335.9 | −3.77968 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −83067.2 | −3.35198 | ||||||||
\(851\) | 4114.99 | 0.165758 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 26631.8 | 1.06900 | 0.534498 | − | 0.845170i | \(-0.320501\pi\) | ||||
0.534498 | + | 0.845170i | \(0.320501\pi\) | |||||||
\(854\) | 22910.0 | 0.917989 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 51826.0 | 2.06936 | ||||||||
\(857\) | −11796.7 | −0.470209 | −0.235104 | − | 0.971970i | \(-0.575543\pi\) | ||||
−0.235104 | + | 0.971970i | \(0.575543\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −22672.8 | −0.900567 | −0.450283 | − | 0.892886i | \(-0.648677\pi\) | ||||
−0.450283 | + | 0.892886i | \(0.648677\pi\) | |||||||
\(860\) | −79849.0 | −3.16608 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 27795.0 | 1.09826 | ||||||||
\(863\) | 21421.1 | 0.844940 | 0.422470 | − | 0.906377i | \(-0.361163\pi\) | ||||
0.422470 | + | 0.906377i | \(0.361163\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 41551.9 | 1.63330 | ||||||||
\(866\) | 46066.6 | 1.80763 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 37924.3 | 1.48299 | ||||||||
\(869\) | −10351.5 | −0.404086 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 35223.1 | 1.36790 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −500.814 | −0.0193825 | ||||||||
\(875\) | 3080.48 | 0.119016 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 5155.20 | 0.198493 | 0.0992466 | − | 0.995063i | \(-0.468357\pi\) | ||||
0.0992466 | + | 0.995063i | \(0.468357\pi\) | |||||||
\(878\) | −69435.0 | −2.66893 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −85756.9 | −3.28507 | ||||||||
\(881\) | −23692.2 | −0.906027 | −0.453013 | − | 0.891504i | \(-0.649651\pi\) | ||||
−0.453013 | + | 0.891504i | \(0.649651\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −14591.5 | −0.556108 | −0.278054 | − | 0.960565i | \(-0.589689\pi\) | ||||
−0.278054 | + | 0.960565i | \(0.589689\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 61475.2 | 2.33104 | ||||||||
\(887\) | 9722.26 | 0.368029 | 0.184014 | − | 0.982924i | \(-0.441091\pi\) | ||||
0.184014 | + | 0.982924i | \(0.441091\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −13857.8 | −0.522806 | ||||||||
\(890\) | 90826.1 | 3.42078 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 42046.6 | 1.57828 | ||||||||
\(893\) | −1149.42 | −0.0430726 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 69969.2 | 2.61320 | ||||||||
\(896\) | −16706.6 | −0.622911 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 52678.9 | 1.95759 | ||||||||
\(899\) | 11827.1 | 0.438771 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 53189.7 | 1.96671 | ||||||||
\(902\) | −4521.26 | −0.166898 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 11949.0 | 0.439621 | ||||||||
\(905\) | −64743.2 | −2.37805 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 11799.0 | 0.431951 | 0.215975 | − | 0.976399i | \(-0.430707\pi\) | ||||
0.215975 | + | 0.976399i | \(0.430707\pi\) | |||||||
\(908\) | 91500.9 | 3.34423 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 43012.4 | 1.56429 | 0.782143 | − | 0.623099i | \(-0.214127\pi\) | ||||
0.782143 | + | 0.623099i | \(0.214127\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −19746.6 | −0.715793 | ||||||||
\(914\) | 83303.8 | 3.01471 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 33281.3 | 1.20049 | ||||||||
\(917\) | 20011.0 | 0.720635 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −4951.41 | −0.177728 | −0.0888639 | − | 0.996044i | \(-0.528324\pi\) | ||||
−0.0888639 | + | 0.996044i | \(0.528324\pi\) | |||||||
\(920\) | 45404.5 | 1.62711 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −41297.0 | −1.47510 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −14211.3 | −0.505152 | ||||||||
\(926\) | 1777.27 | 0.0630721 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −29589.8 | −1.04669 | ||||||||
\(929\) | −8934.86 | −0.315547 | −0.157774 | − | 0.987475i | \(-0.550432\pi\) | ||||
−0.157774 | + | 0.987475i | \(0.550432\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −560.243 | −0.0197221 | ||||||||
\(932\) | 38860.2 | 1.36578 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −43700.3 | −1.53096 | ||||||||
\(935\) | 48870.6 | 1.70935 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −13182.8 | −0.459620 | −0.229810 | − | 0.973235i | \(-0.573811\pi\) | ||||
−0.229810 | + | 0.973235i | \(0.573811\pi\) | |||||||
\(938\) | 9809.20 | 0.341452 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 171368. | 5.94618 | ||||||||
\(941\) | −21693.7 | −0.751536 | −0.375768 | − | 0.926714i | \(-0.622621\pi\) | ||||
−0.375768 | + | 0.926714i | \(0.622621\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1285.43 | 0.0443895 | ||||||||
\(944\) | 91698.4 | 3.16158 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 35047.1 | 1.20452 | ||||||||
\(947\) | −49790.0 | −1.70851 | −0.854254 | − | 0.519856i | \(-0.825986\pi\) | ||||
−0.854254 | + | 0.519856i | \(0.825986\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 1729.59 | 0.0590687 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 69125.0 | 2.35331 | ||||||||
\(953\) | −4217.93 | −0.143371 | −0.0716853 | − | 0.997427i | \(-0.522838\pi\) | ||||
−0.0716853 | + | 0.997427i | \(0.522838\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −3514.19 | −0.119075 | ||||||||
\(956\) | 76830.5 | 2.59924 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −34305.8 | −1.15696 | ||||||||
\(959\) | 3750.99 | 0.126304 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 7046.87 | 0.236544 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 73788.1 | 2.46530 | ||||||||
\(965\) | −19813.7 | −0.660958 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 40927.9 | 1.36107 | 0.680534 | − | 0.732717i | \(-0.261748\pi\) | ||||
0.680534 | + | 0.732717i | \(0.261748\pi\) | |||||||
\(968\) | −37707.9 | −1.25204 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 5736.04 | 0.189869 | ||||||||
\(971\) | 17114.8 | 0.565645 | 0.282822 | − | 0.959172i | \(-0.408729\pi\) | ||||
0.282822 | + | 0.959172i | \(0.408729\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −7284.62 | −0.240015 | ||||||||
\(974\) | −43151.5 | −1.41957 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −84093.0 | −2.75794 | ||||||||
\(977\) | −118.470 | −0.00387940 | −0.00193970 | − | 0.999998i | \(-0.500617\pi\) | ||||
−0.00193970 | + | 0.999998i | \(0.500617\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −28640.7 | −0.934996 | ||||||||
\(980\) | 83527.2 | 2.72263 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −27272.8 | −0.886261 | ||||||||
\(983\) | 26002.8 | 0.843705 | 0.421852 | − | 0.906665i | \(-0.361380\pi\) | ||||
0.421852 | + | 0.906665i | \(0.361380\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 15225.3 | 0.492506 | ||||||||
\(986\) | 35450.7 | 1.14501 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −9964.14 | −0.320365 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −16062.0 | −0.514860 | −0.257430 | − | 0.966297i | \(-0.582876\pi\) | ||||
−0.257430 | + | 0.966297i | \(0.582876\pi\) | |||||||
\(992\) | −92163.3 | −2.94979 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −25013.2 | −0.798159 | ||||||||
\(995\) | −7861.07 | −0.250465 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1361.54 | 0.0432503 | 0.0216251 | − | 0.999766i | \(-0.493116\pi\) | ||||
0.0216251 | + | 0.999766i | \(0.493116\pi\) | |||||||
\(998\) | 96217.5 | 3.05182 | ||||||||
\(999\) | 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.bb.1.4 | 4 | ||
3.2 | odd | 2 | 507.4.a.i.1.1 | 4 | |||
13.4 | even | 6 | 117.4.g.e.55.4 | 8 | |||
13.10 | even | 6 | 117.4.g.e.100.4 | 8 | |||
13.12 | even | 2 | 1521.4.a.v.1.1 | 4 | |||
39.5 | even | 4 | 507.4.b.h.337.8 | 8 | |||
39.8 | even | 4 | 507.4.b.h.337.1 | 8 | |||
39.17 | odd | 6 | 39.4.e.c.16.1 | ✓ | 8 | ||
39.23 | odd | 6 | 39.4.e.c.22.1 | yes | 8 | ||
39.38 | odd | 2 | 507.4.a.m.1.4 | 4 | |||
156.23 | even | 6 | 624.4.q.i.529.1 | 8 | |||
156.95 | even | 6 | 624.4.q.i.289.1 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
39.4.e.c.16.1 | ✓ | 8 | 39.17 | odd | 6 | ||
39.4.e.c.22.1 | yes | 8 | 39.23 | odd | 6 | ||
117.4.g.e.55.4 | 8 | 13.4 | even | 6 | |||
117.4.g.e.100.4 | 8 | 13.10 | even | 6 | |||
507.4.a.i.1.1 | 4 | 3.2 | odd | 2 | |||
507.4.a.m.1.4 | 4 | 39.38 | odd | 2 | |||
507.4.b.h.337.1 | 8 | 39.8 | even | 4 | |||
507.4.b.h.337.8 | 8 | 39.5 | even | 4 | |||
624.4.q.i.289.1 | 8 | 156.95 | even | 6 | |||
624.4.q.i.529.1 | 8 | 156.23 | even | 6 | |||
1521.4.a.v.1.1 | 4 | 13.12 | even | 2 | |||
1521.4.a.bb.1.4 | 4 | 1.1 | even | 1 | trivial |