Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1024,4,Mod(1,1024)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1024, 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("1024.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1024 = 2^{10} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1024.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: | \(60.4179558459\) |
Analytic rank: | \(0\) |
Dimension: | \(10\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} - 36x^{8} + 405x^{6} - 1380x^{4} + 420x^{2} - 32 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{22} \) |
Twist minimal: | no (minimal twist has level 16) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.8 | ||
Root | \(-0.446984\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1024.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 4.62644 | 0.890358 | 0.445179 | − | 0.895441i | \(-0.353140\pi\) | ||||
0.445179 | + | 0.895441i | \(0.353140\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −17.8826 | −1.59947 | −0.799733 | − | 0.600356i | \(-0.795026\pi\) | ||||
−0.799733 | + | 0.600356i | \(0.795026\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 13.8754 | 0.749200 | 0.374600 | − | 0.927187i | \(-0.377780\pi\) | ||||
0.374600 | + | 0.927187i | \(0.377780\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −5.59607 | −0.207262 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.18771 | −0.0599653 | −0.0299827 | − | 0.999550i | \(-0.509545\pi\) | ||||
−0.0299827 | + | 0.999550i | \(0.509545\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 46.3685 | 0.989255 | 0.494627 | − | 0.869105i | \(-0.335305\pi\) | ||||
0.494627 | + | 0.869105i | \(0.335305\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −82.7326 | −1.42410 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −18.6531 | −0.266119 | −0.133060 | − | 0.991108i | \(-0.542480\pi\) | ||||
−0.133060 | + | 0.991108i | \(0.542480\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −122.194 | −1.47543 | −0.737716 | − | 0.675111i | \(-0.764096\pi\) | ||||
−0.737716 | + | 0.675111i | \(0.764096\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 64.1936 | 0.667057 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 134.006 | 1.21488 | 0.607438 | − | 0.794367i | \(-0.292197\pi\) | ||||
0.607438 | + | 0.794367i | \(0.292197\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 194.786 | 1.55829 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −150.804 | −1.07490 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 84.5628 | 0.541480 | 0.270740 | − | 0.962653i | \(-0.412732\pi\) | ||||
0.270740 | + | 0.962653i | \(0.412732\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −31.5391 | −0.182729 | −0.0913645 | − | 0.995818i | \(-0.529123\pi\) | ||||
−0.0913645 | + | 0.995818i | \(0.529123\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −10.1213 | −0.0533906 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −248.128 | −1.19832 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 126.129 | 0.560418 | 0.280209 | − | 0.959939i | \(-0.409596\pi\) | ||||
0.280209 | + | 0.959939i | \(0.409596\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 214.521 | 0.880791 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 210.504 | 0.801834 | 0.400917 | − | 0.916114i | \(-0.368692\pi\) | ||||
0.400917 | + | 0.916114i | \(0.368692\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −168.860 | −0.598857 | −0.299429 | − | 0.954119i | \(-0.596796\pi\) | ||||
−0.299429 | + | 0.954119i | \(0.596796\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 100.072 | 0.331508 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 182.902 | 0.567638 | 0.283819 | − | 0.958878i | \(-0.408398\pi\) | ||||
0.283819 | + | 0.958878i | \(0.408398\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −150.474 | −0.438699 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −86.2972 | −0.236942 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 37.0020 | 0.0958984 | 0.0479492 | − | 0.998850i | \(-0.484731\pi\) | ||||
0.0479492 | + | 0.998850i | \(0.484731\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 39.1219 | 0.0959125 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −565.323 | −1.31366 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 624.494 | 1.37800 | 0.689001 | − | 0.724760i | \(-0.258050\pi\) | ||||
0.689001 | + | 0.724760i | \(0.258050\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 246.759 | 0.517938 | 0.258969 | − | 0.965886i | \(-0.416617\pi\) | ||||
0.258969 | + | 0.965886i | \(0.416617\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −77.6476 | −0.155281 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −829.188 | −1.58228 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −129.763 | −0.236613 | −0.118306 | − | 0.992977i | \(-0.537747\pi\) | ||||
−0.118306 | + | 0.992977i | \(0.537747\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 619.970 | 1.08168 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 348.360 | 0.582291 | 0.291146 | − | 0.956679i | \(-0.405964\pi\) | ||||
0.291146 | + | 0.956679i | \(0.405964\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 299.436 | 0.480087 | 0.240043 | − | 0.970762i | \(-0.422838\pi\) | ||||
0.240043 | + | 0.970762i | \(0.422838\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 901.168 | 1.38744 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −30.3553 | −0.0449260 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 943.487 | 1.34368 | 0.671839 | − | 0.740697i | \(-0.265505\pi\) | ||||
0.671839 | + | 0.740697i | \(0.265505\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −546.590 | −0.749781 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 443.034 | 0.585895 | 0.292947 | − | 0.956129i | \(-0.405364\pi\) | ||||
0.292947 | + | 0.956129i | \(0.405364\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 333.565 | 0.425649 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 391.224 | 0.482111 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 1412.35 | 1.68212 | 0.841060 | − | 0.540942i | \(-0.181932\pi\) | ||||
0.841060 | + | 0.540942i | \(0.181932\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 643.381 | 0.741150 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −145.914 | −0.162694 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 2185.14 | 2.35990 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1515.29 | 1.58613 | 0.793063 | − | 0.609140i | \(-0.208485\pi\) | ||||
0.793063 | + | 0.609140i | \(0.208485\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 12.2426 | 0.0124285 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −810.631 | −0.798621 | −0.399311 | − | 0.916816i | \(-0.630751\pi\) | ||||
−0.399311 | + | 0.916816i | \(0.630751\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1021.00 | −0.976717 | −0.488359 | − | 0.872643i | \(-0.662404\pi\) | ||||
−0.488359 | + | 0.872643i | \(0.662404\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −1147.95 | −1.06693 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 1754.75 | 1.58540 | 0.792700 | − | 0.609612i | \(-0.208675\pi\) | ||||
0.792700 | + | 0.609612i | \(0.208675\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −153.624 | −0.134996 | −0.0674980 | − | 0.997719i | \(-0.521502\pi\) | ||||
−0.0674980 | + | 0.997719i | \(0.521502\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 583.528 | 0.498973 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1722.22 | 1.43374 | 0.716870 | − | 0.697207i | \(-0.245574\pi\) | ||||
0.716870 | + | 0.697207i | \(0.245574\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −2396.37 | −1.94315 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −259.481 | −0.205035 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −258.818 | −0.199377 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1326.21 | −0.996404 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 973.883 | 0.713919 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1247.96 | −0.892969 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 699.127 | 0.488484 | 0.244242 | − | 0.969714i | \(-0.421461\pi\) | ||||
0.244242 | + | 0.969714i | \(0.421461\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −781.219 | −0.533198 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −279.972 | −0.186727 | −0.0933636 | − | 0.995632i | \(-0.529762\pi\) | ||||
−0.0933636 | + | 0.995632i | \(0.529762\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1695.49 | −1.10539 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 2696.76 | 1.71926 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 271.386 | 0.169242 | 0.0846209 | − | 0.996413i | \(-0.473032\pi\) | ||||
0.0846209 | + | 0.996413i | \(0.473032\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −650.449 | −0.396909 | −0.198455 | − | 0.980110i | \(-0.563592\pi\) | ||||
−0.198455 | + | 0.980110i | \(0.563592\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 846.185 | 0.505402 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −101.441 | −0.0593210 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1512.20 | −0.866079 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −696.158 | −0.390600 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −856.692 | −0.471026 | −0.235513 | − | 0.971871i | \(-0.575677\pi\) | ||||
−0.235513 | + | 0.971871i | \(0.575677\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 3534.47 | 1.90484 | 0.952421 | − | 0.304785i | \(-0.0985848\pi\) | ||||
0.952421 | + | 0.304785i | \(0.0985848\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 104.384 | 0.0551564 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 564.001 | 0.292269 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1744.48 | 0.886784 | 0.443392 | − | 0.896328i | \(-0.353775\pi\) | ||||
0.443392 | + | 0.896328i | \(0.353775\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 171.187 | 0.0853839 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1859.38 | 0.910186 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −3633.63 | −1.74606 | −0.873030 | − | 0.487666i | \(-0.837848\pi\) | ||||
−0.873030 | + | 0.487666i | \(0.837848\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 180.995 | 0.0853965 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 3048.39 | 1.41252 | 0.706262 | − | 0.707950i | \(-0.250380\pi\) | ||||
0.706262 | + | 0.707950i | \(0.250380\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −46.9618 | −0.0213754 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 683.806 | 0.305801 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −2152.51 | −0.945965 | −0.472983 | − | 0.881072i | \(-0.656823\pi\) | ||||
−0.472983 | + | 0.881072i | \(0.656823\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 2702.74 | 1.16747 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 2889.18 | 1.22692 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 427.457 | 0.178489 | 0.0892447 | − | 0.996010i | \(-0.471555\pi\) | ||||
0.0892447 | + | 0.996010i | \(0.471555\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −2399.83 | −0.985515 | −0.492758 | − | 0.870167i | \(-0.664011\pi\) | ||||
−0.492758 | + | 0.870167i | \(0.664011\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 1141.62 | 0.461151 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −2255.51 | −0.896370 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 40.8074 | 0.0159579 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −2092.46 | −0.805312 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −4035.31 | −1.52872 | −0.764358 | − | 0.644792i | \(-0.776944\pi\) | ||||
−0.764358 | + | 0.644792i | \(0.776944\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −886.172 | −0.330508 | −0.165254 | − | 0.986251i | \(-0.552844\pi\) | ||||
−0.165254 | + | 0.986251i | \(0.552844\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −3836.19 | −1.40880 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 4624.65 | 1.67255 | 0.836276 | − | 0.548308i | \(-0.184728\pi\) | ||||
0.836276 | + | 0.548308i | \(0.184728\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 222.513 | 0.0792639 | 0.0396319 | − | 0.999214i | \(-0.487381\pi\) | ||||
0.0396319 | + | 0.999214i | \(0.487381\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −600.340 | −0.210670 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 1173.34 | 0.405677 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −3764.35 | −1.28251 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −749.907 | −0.251798 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 267.325 | 0.0884748 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −4988.58 | −1.62762 | −0.813810 | − | 0.581131i | \(-0.802610\pi\) | ||||
−0.813810 | + | 0.581131i | \(0.802610\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 1611.66 | 0.518448 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 3019.65 | 0.957852 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −437.618 | −0.136901 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 1385.32 | 0.427449 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −864.914 | −0.263260 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 5841.90 | 1.75427 | 0.877136 | − | 0.480242i | \(-0.159451\pi\) | ||||
0.877136 | + | 0.480242i | \(0.159451\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −1090.04 | −0.322975 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 1597.41 | 0.467065 | 0.233533 | − | 0.972349i | \(-0.424971\pi\) | ||||
0.233533 | + | 0.972349i | \(0.424971\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −4108.86 | −1.18568 | −0.592840 | − | 0.805320i | \(-0.701994\pi\) | ||||
−0.592840 | + | 0.805320i | \(0.701994\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −140.437 | −0.0400003 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 734.054 | 0.206393 | 0.103196 | − | 0.994661i | \(-0.467093\pi\) | ||||
0.103196 | + | 0.994661i | \(0.467093\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −3270.76 | −0.907918 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 4364.98 | 1.19635 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 511.807 | 0.138519 | 0.0692595 | − | 0.997599i | \(-0.477936\pi\) | ||||
0.0692595 | + | 0.997599i | \(0.477936\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −5920.31 | −1.58241 | −0.791204 | − | 0.611552i | \(-0.790545\pi\) | ||||
−0.791204 | + | 0.611552i | \(0.790545\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1542.93 | 0.407322 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 2690.86 | 0.701685 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −5665.95 | −1.45958 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 2049.67 | 0.521656 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −437.462 | −0.110009 | −0.0550046 | − | 0.998486i | \(-0.517517\pi\) | ||||
−0.0550046 | + | 0.998486i | \(0.517517\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −293.166 | −0.0728505 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 1543.22 | 0.378980 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 323.723 | 0.0785730 | 0.0392865 | − | 0.999228i | \(-0.487491\pi\) | ||||
0.0392865 | + | 0.999228i | \(0.487491\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1750.09 | 0.419865 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −473.219 | −0.112228 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 2689.15 | 0.630495 | 0.315248 | − | 0.949009i | \(-0.397912\pi\) | ||||
0.315248 | + | 0.949009i | \(0.397912\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −661.691 | −0.153386 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 6534.14 | 1.49769 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 6652.15 | 1.50776 | 0.753882 | − | 0.657009i | \(-0.228179\pi\) | ||||
0.753882 | + | 0.657009i | \(0.228179\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2018.97 | 0.452561 | 0.226280 | − | 0.974062i | \(-0.427343\pi\) | ||||
0.226280 | + | 0.974062i | \(0.427343\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 2976.56 | 0.659889 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −426.136 | −0.0934435 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 4356.63 | 0.944999 | 0.472499 | − | 0.881331i | \(-0.343352\pi\) | ||||
0.472499 | + | 0.881331i | \(0.343352\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 176.495 | 0.0378728 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 3893.51 | 0.826575 | 0.413287 | − | 0.910601i | \(-0.364381\pi\) | ||||
0.413287 | + | 0.910601i | \(0.364381\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 2865.74 | 0.601945 | 0.300972 | − | 0.953633i | \(-0.402689\pi\) | ||||
0.300972 | + | 0.953633i | \(0.402689\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 10109.4 | 2.10116 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 2920.82 | 0.600734 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −4565.06 | −0.929180 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 7010.39 | 1.41222 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −1416.60 | −0.282452 | −0.141226 | − | 0.989977i | \(-0.545104\pi\) | ||||
−0.141226 | + | 0.989977i | \(0.545104\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −11167.6 | −2.20407 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 329.914 | 0.0644565 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 6213.65 | 1.20182 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2342.99 | −0.448664 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −3750.33 | −0.711059 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −4412.69 | −0.828425 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 4195.32 | 0.779934 | 0.389967 | − | 0.920829i | \(-0.372486\pi\) | ||||
0.389967 | + | 0.920829i | \(0.372486\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −4723.58 | −0.869628 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 2911.18 | 0.530797 | 0.265399 | − | 0.964139i | \(-0.414496\pi\) | ||||
0.265399 | + | 0.964139i | \(0.414496\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 8287.74 | 1.49665 | 0.748324 | − | 0.663333i | \(-0.230859\pi\) | ||||
0.748324 | + | 0.663333i | \(0.230859\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 1388.54 | 0.248366 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −8120.67 | −1.43881 | −0.719404 | − | 0.694592i | \(-0.755585\pi\) | ||||
−0.719404 | + | 0.694592i | \(0.755585\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −184.999 | −0.0324700 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 8118.23 | 1.41157 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 2279.29 | 0.392641 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 9031.96 | 1.54155 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −710.734 | −0.120195 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 2537.84 | 0.425275 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −6362.92 | −1.05661 | −0.528305 | − | 0.849055i | \(-0.677172\pi\) | ||||
−0.528305 | + | 0.849055i | \(0.677172\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −705.827 | −0.116153 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 2320.50 | 0.378454 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 5860.06 | 0.947234 | 0.473617 | − | 0.880731i | \(-0.342948\pi\) | ||||
0.473617 | + | 0.880731i | \(0.342948\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 7967.73 | 1.27654 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 68.9984 | 0.0109574 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −6847.14 | −1.07787 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −11086.7 | −1.73010 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −2869.60 | −0.443942 | −0.221971 | − | 0.975053i | \(-0.571249\pi\) | ||||
−0.221971 | + | 0.975053i | \(0.571249\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 2748.19 | 0.421511 | 0.210755 | − | 0.977539i | \(-0.432408\pi\) | ||||
0.210755 | + | 0.977539i | \(0.432408\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −6992.54 | −1.06335 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −7548.63 | −1.13817 | −0.569084 | − | 0.822280i | \(-0.692702\pi\) | ||||
−0.569084 | + | 0.822280i | \(0.692702\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −6229.57 | −0.931355 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −1197.41 | −0.177517 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 5554.15 | 0.816537 | 0.408269 | − | 0.912862i | \(-0.366133\pi\) | ||||
0.408269 | + | 0.912862i | \(0.366133\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 8072.37 | 1.17690 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −6135.65 | −0.887157 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −5354.69 | −0.767883 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 3610.98 | 0.513601 | 0.256800 | − | 0.966464i | \(-0.417332\pi\) | ||||
0.256800 | + | 0.966464i | \(0.417332\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −1177.99 | −0.166190 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 513.417 | 0.0718471 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −1718.96 | −0.238618 | −0.119309 | − | 0.992857i | \(-0.538068\pi\) | ||||
−0.119309 | + | 0.992857i | \(0.538068\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −5773.62 | −0.795062 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 3921.05 | 0.535661 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −10391.4 | −1.40836 | −0.704180 | − | 0.710021i | \(-0.748685\pi\) | ||||
−0.704180 | + | 0.710021i | \(0.748685\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 3234.47 | 0.434926 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −7668.98 | −1.02315 | −0.511575 | − | 0.859238i | \(-0.670938\pi\) | ||||
−0.511575 | + | 0.859238i | \(0.670938\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 542.831 | 0.0718577 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 944.951 | 0.124120 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −284.150 | −0.0370359 | −0.0185180 | − | 0.999829i | \(-0.505895\pi\) | ||||
−0.0185180 | + | 0.999829i | \(0.505895\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −2499.62 | −0.323302 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −1295.27 | −0.166254 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −16872.0 | −2.14917 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 9209.66 | 1.16428 | 0.582141 | − | 0.813088i | \(-0.302215\pi\) | ||||
0.582141 | + | 0.813088i | \(0.302215\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −7844.07 | −0.984197 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −5565.10 | −0.693036 | −0.346518 | − | 0.938043i | \(-0.612636\pi\) | ||||
−0.346518 | + | 0.938043i | \(0.612636\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1462.42 | −0.180765 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 9774.44 | 1.19925 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −275.933 | −0.0336057 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −12077.6 | −1.46014 | −0.730072 | − | 0.683370i | \(-0.760514\pi\) | ||||
−0.730072 | + | 0.683370i | \(0.760514\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 1255.55 | 0.150686 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 8665.08 | 1.03240 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −7922.58 | −0.937119 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −3009.26 | −0.353391 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 2054.89 | 0.239590 | 0.119795 | − | 0.992799i | \(-0.461776\pi\) | ||||
0.119795 | + | 0.992799i | \(0.461776\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −6819.69 | −0.789480 | −0.394740 | − | 0.918793i | \(-0.629165\pi\) | ||||
−0.394740 | + | 0.918793i | \(0.629165\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −1023.53 | −0.117650 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −3633.36 | −0.414692 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 3423.87 | 0.388040 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −469.309 | −0.0528169 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −12519.2 | −1.39914 | −0.699571 | − | 0.714563i | \(-0.746626\pi\) | ||||
−0.699571 | + | 0.714563i | \(0.746626\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 2921.40 | 0.324235 | 0.162117 | − | 0.986771i | \(-0.448168\pi\) | ||||
0.162117 | + | 0.986771i | \(0.448168\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −6996.10 | −0.771120 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −16374.7 | −1.79247 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −1140.50 | −0.123993 | −0.0619967 | − | 0.998076i | \(-0.519747\pi\) | ||||
−0.0619967 | + | 0.998076i | \(0.519747\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 842.062 | 0.0909256 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −2606.46 | −0.279541 | −0.139771 | − | 0.990184i | \(-0.544637\pi\) | ||||
−0.139771 | + | 0.990184i | \(0.544637\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −25256.4 | −2.69049 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −3963.43 | −0.419382 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 1752.13 | 0.184161 | 0.0920805 | − | 0.995752i | \(-0.470648\pi\) | ||||
0.0920805 | + | 0.995752i | \(0.470648\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −460.521 | −0.0480822 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 16352.0 | 1.69599 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −11505.3 | −1.18544 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −12875.6 | −1.31794 | −0.658968 | − | 0.752171i | \(-0.729007\pi\) | ||||
−0.658968 | + | 0.752171i | \(0.729007\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 2812.95 | 0.286051 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −19346.0 | −1.95452 | −0.977259 | − | 0.212050i | \(-0.931986\pi\) | ||||
−0.977259 | + | 0.212050i | \(0.931986\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −15002.4 | −1.50588 | −0.752938 | − | 0.658091i | \(-0.771364\pi\) | ||||
−0.752938 | + | 0.658091i | \(0.771364\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 2609.32 | 0.260224 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 13674.6 | 1.35500 | 0.677501 | − | 0.735522i | \(-0.263063\pi\) | ||||
0.677501 | + | 0.735522i | \(0.263063\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −1800.51 | −0.177270 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 8070.75 | 0.789555 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 369.416 | 0.0359107 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −23801.7 | −2.29915 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −207.066 | −0.0198761 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −3072.68 | −0.293099 | −0.146550 | − | 0.989203i | \(-0.546817\pi\) | ||||
−0.146550 | + | 0.989203i | \(0.546817\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 5848.41 | 0.554396 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 8602.32 | 0.810392 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −27097.3 | −2.53695 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 8689.64 | 0.808553 | 0.404276 | − | 0.914637i | \(-0.367523\pi\) | ||||
0.404276 | + | 0.914637i | \(0.367523\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −16810.8 | −1.55462 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −15831.2 | −1.45509 | −0.727547 | − | 0.686057i | \(-0.759340\pi\) | ||||
−0.727547 | + | 0.686057i | \(0.759340\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −1577.35 | −0.144098 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −218.929 | −0.0198790 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 4833.62 | 0.436253 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −2309.01 | −0.207146 | −0.103573 | − | 0.994622i | \(-0.533027\pi\) | ||||
−0.103573 | + | 0.994622i | \(0.533027\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 14103.2 | 1.25765 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 6901.81 | 0.611802 | 0.305901 | − | 0.952063i | \(-0.401042\pi\) | ||||
0.305901 | + | 0.952063i | \(0.401042\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 14496.2 | 1.27737 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −217.266 | −0.0190318 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −131.481 | −0.0114495 | −0.00572475 | − | 0.999984i | \(-0.501822\pi\) | ||||
−0.00572475 | + | 0.999984i | \(0.501822\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 4154.79 | 0.359681 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 18427.3 | 1.58594 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 18258.1 | 1.56223 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −400.136 | −0.0340386 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −9958.43 | −0.842248 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 11931.3 | 1.00330 | 0.501649 | − | 0.865071i | \(-0.332727\pi\) | ||||
0.501649 | + | 0.865071i | \(0.332727\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 13721.4 | 1.14721 | 0.573607 | − | 0.819131i | \(-0.305544\pi\) | ||||
0.573607 | + | 0.819131i | \(0.305544\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 12504.0 | 1.03947 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 588.301 | 0.0486277 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 5790.59 | 0.475926 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −3494.71 | −0.285607 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 9760.75 | 0.793218 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −31379.4 | −2.53579 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 1977.60 | 0.158920 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 329.193 | 0.0263067 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 12101.0 | 0.961665 | 0.480833 | − | 0.876812i | \(-0.340334\pi\) | ||||
0.480833 | + | 0.876812i | \(0.340334\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −11102.7 | −0.877462 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 2747.20 | 0.215921 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 63.9157 | 0.00499605 | 0.00249803 | − | 0.999997i | \(-0.499205\pi\) | ||||
0.00249803 | + | 0.999997i | \(0.499205\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −1380.88 | −0.107349 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −10333.1 | −0.798917 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 13091.2 | 1.00668 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −10435.0 | −0.798090 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 6052.26 | 0.460400 | 0.230200 | − | 0.973143i | \(-0.426062\pi\) | ||||
0.230200 | + | 0.973143i | \(0.426062\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −7829.77 | −0.592422 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 188.793 | 0.0142083 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 20638.9 | 1.54498 | 0.772491 | − | 0.635026i | \(-0.219011\pi\) | ||||
0.772491 | + | 0.635026i | \(0.219011\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −30797.7 | −2.29322 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −7584.14 | −0.561736 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −21728.1 | −1.60086 | −0.800431 | − | 0.599425i | \(-0.795396\pi\) | ||||
−0.800431 | + | 0.599425i | \(0.795396\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 22737.8 | 1.66646 | 0.833229 | − | 0.552929i | \(-0.186490\pi\) | ||||
0.833229 | + | 0.552929i | \(0.186490\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −18669.1 | −1.36110 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 26102.5 | 1.89313 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −26648.2 | −1.92267 | −0.961335 | − | 0.275383i | \(-0.911195\pi\) | ||||
−0.961335 | + | 0.275383i | \(0.911195\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −4099.82 | −0.294270 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 6147.26 | 0.438952 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −80.9495 | −0.00575058 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 4640.20 | 0.327946 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −1898.75 | −0.133509 | −0.0667544 | − | 0.997769i | \(-0.521264\pi\) | ||||
−0.0667544 | + | 0.997769i | \(0.521264\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 3853.89 | 0.269604 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 21395.7 | 1.48917 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −4474.79 | −0.309878 | −0.154939 | − | 0.987924i | \(-0.549518\pi\) | ||||
−0.154939 | + | 0.987924i | \(0.549518\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 4628.34 | 0.318896 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 1029.44 | 0.0705733 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −12603.8 | −0.859725 | −0.429863 | − | 0.902894i | \(-0.641438\pi\) | ||||
−0.429863 | + | 0.902894i | \(0.641438\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 7220.64 | 0.490077 | 0.245038 | − | 0.969513i | \(-0.421199\pi\) | ||||
0.245038 | + | 0.969513i | \(0.421199\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 726.163 | 0.0490408 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 23716.1 | 1.59371 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −13695.6 | −0.915796 | −0.457898 | − | 0.889005i | \(-0.651397\pi\) | ||||
−0.457898 | + | 0.889005i | \(0.651397\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 5428.39 | 0.361198 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 8480.89 | 0.561539 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −3335.20 | −0.219751 | −0.109876 | − | 0.993945i | \(-0.535045\pi\) | ||||
−0.109876 | + | 0.993945i | \(0.535045\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −17415.5 | −1.14189 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −4186.39 | −0.273157 | −0.136579 | − | 0.990629i | \(-0.543611\pi\) | ||||
−0.136579 | + | 0.990629i | \(0.543611\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 6788.94 | 0.440825 | 0.220412 | − | 0.975407i | \(-0.429260\pi\) | ||||
0.220412 | + | 0.975407i | \(0.429260\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −20208.6 | −1.30587 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 19596.9 | 1.26024 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −2031.54 | −0.130018 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 1236.76 | 0.0787743 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −2352.69 | −0.149138 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 16106.3 | 1.01614 | 0.508069 | − | 0.861316i | \(-0.330360\pi\) | ||||
0.508069 | + | 0.861316i | \(0.330360\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −23079.3 | −1.44917 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −12502.2 | −0.781314 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −6977.25 | −0.433985 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −1949.45 | −0.120687 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −6682.21 | −0.411749 | −0.205875 | − | 0.978578i | \(-0.566004\pi\) | ||||
−0.205875 | + | 0.978578i | \(0.566004\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 7047.69 | 0.432245 | 0.216123 | − | 0.976366i | \(-0.430659\pi\) | ||||
0.216123 | + | 0.976366i | \(0.430659\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 13970.2 | 0.852832 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 5078.45 | 0.308585 | 0.154292 | − | 0.988025i | \(-0.450690\pi\) | ||||
0.154292 | + | 0.988025i | \(0.450690\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −1366.21 | −0.0826324 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −2024.61 | −0.121891 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 8753.86 | 0.524602 | 0.262301 | − | 0.964986i | \(-0.415519\pi\) | ||||
0.262301 | + | 0.964986i | \(0.415519\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 5006.62 | 0.298664 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −1675.67 | −0.0995037 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 8133.42 | 0.480778 | 0.240389 | − | 0.970677i | \(-0.422725\pi\) | ||||
0.240389 | + | 0.970677i | \(0.422725\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 8917.15 | 0.524716 | 0.262358 | − | 0.964971i | \(-0.415500\pi\) | ||||
0.262358 | + | 0.964971i | \(0.415500\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −4001.47 | −0.234396 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 30319.7 | 1.76804 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 11331.9 | 0.657831 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 27027.2 | 1.56193 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −539.837 | −0.0310584 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 14664.4 | 0.839925 | 0.419963 | − | 0.907541i | \(-0.362043\pi\) | ||||
0.419963 | + | 0.907541i | \(0.362043\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −29374.5 | −1.67500 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 8195.60 | 0.465262 | 0.232631 | − | 0.972565i | \(-0.425267\pi\) | ||||
0.232631 | + | 0.972565i | \(0.425267\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 21025.2 | 1.18833 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 7390.32 | 0.415855 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 18574.4 | 1.04060 | 0.520300 | − | 0.853983i | \(-0.325820\pi\) | ||||
0.520300 | + | 0.853983i | \(0.325820\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −4853.09 | −0.270696 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −19009.4 | −1.05568 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 1715.73 | 0.0948679 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 20257.2 | 1.11523 | 0.557613 | − | 0.830101i | \(-0.311718\pi\) | ||||
0.557613 | + | 0.830101i | \(0.311718\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 169.870 | 0.00931146 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 11631.7 | 0.634843 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −3926.54 | −0.213383 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 3396.06 | 0.183763 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −22609.3 | −1.21818 | −0.609089 | − | 0.793102i | \(-0.708465\pi\) | ||||
−0.609089 | + | 0.793102i | \(0.708465\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −15412.2 | −0.826859 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −15132.0 | −0.808373 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −11247.8 | −0.598327 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 27690.9 | 1.46679 | 0.733395 | − | 0.679802i | \(-0.237934\pi\) | ||||
0.733395 | + | 0.679802i | \(0.237934\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −5279.82 | −0.278493 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −4226.43 | −0.221993 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1814.02 | 0.0948819 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 2367.84 | 0.123331 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 2111.24 | 0.109507 | 0.0547537 | − | 0.998500i | \(-0.482563\pi\) | ||||
0.0547537 | + | 0.998500i | \(0.482563\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −14166.7 | −0.731757 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −27389.9 | −1.40891 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 16471.7 | 0.843784 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 14763.6 | 0.753164 | 0.376582 | − | 0.926383i | \(-0.377099\pi\) | ||||
0.376582 | + | 0.926383i | \(0.377099\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 21896.2 | 1.11244 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 3149.75 | 0.159368 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −4836.29 | −0.243700 | −0.121850 | − | 0.992549i | \(-0.538883\pi\) | ||||
−0.121850 | + | 0.992549i | \(0.538883\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 12449.1 | 0.624751 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 283.883 | 0.0141886 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 16015.7 | 0.797224 | 0.398612 | − | 0.917120i | \(-0.369492\pi\) | ||||
0.398612 | + | 0.917120i | \(0.369492\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −26213.2 | −1.29955 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 20313.3 | 1.00299 | 0.501495 | − | 0.865160i | \(-0.332783\pi\) | ||||
0.501495 | + | 0.865160i | \(0.332783\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 15319.9 | 0.753391 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −2479.25 | −0.121434 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 24347.8 | 1.18778 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −28755.3 | −1.39720 | −0.698598 | − | 0.715514i | \(-0.746192\pi\) | ||||
−0.698598 | + | 0.715514i | \(0.746192\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −2023.89 | −0.0979477 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −63205.4 | −3.04673 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 32535.4 | 1.56211 | 0.781057 | − | 0.624460i | \(-0.214681\pi\) | ||||
0.781057 | + | 0.624460i | \(0.214681\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −1356.31 | −0.0648631 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −9298.53 | −0.442932 | −0.221466 | − | 0.975168i | \(-0.571084\pi\) | ||||
−0.221466 | + | 0.975168i | \(0.571084\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −2131.60 | −0.101139 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −1866.65 | −0.0882208 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 28956.8 | 1.36319 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −20402.0 | −0.956717 | −0.478358 | − | 0.878165i | \(-0.658768\pi\) | ||||
−0.478358 | + | 0.878165i | \(0.658768\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1497.68 | 0.0699582 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 10376.1 | 0.482798 | 0.241399 | − | 0.970426i | \(-0.422394\pi\) | ||||
0.241399 | + | 0.970426i | \(0.422394\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −6143.40 | −0.284745 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 8096.67 | 0.373831 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −25722.3 | −1.18305 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −762.109 | −0.0349173 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −12752.4 | −0.582034 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −31195.9 | −1.41838 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −16869.6 | −0.764088 | −0.382044 | − | 0.924144i | \(-0.624780\pi\) | ||||
−0.382044 | + | 0.924144i | \(0.624780\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 12441.2 | 0.561367 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 23896.4 | 1.07416 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 11441.8 | 0.512373 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −3061.27 | −0.136569 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 9300.12 | 0.413334 | 0.206667 | − | 0.978411i | \(-0.433738\pi\) | ||||
0.206667 | + | 0.978411i | \(0.433738\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −3411.68 | −0.151060 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −7903.61 | −0.348639 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −655.079 | −0.0287886 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −33250.6 | −1.45581 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 30775.8 | 1.34245 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −29320.9 | −1.27425 | −0.637126 | − | 0.770760i | \(-0.719877\pi\) | ||||
−0.637126 | + | 0.770760i | \(0.719877\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 20488.9 | 0.887132 | 0.443566 | − | 0.896242i | \(-0.353713\pi\) | ||||
0.443566 | + | 0.896242i | \(0.353713\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 9340.66 | 0.402941 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 64978.7 | 2.79276 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 20633.6 | 0.883574 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −3600.40 | −0.153612 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −28650.9 | −1.21793 | −0.608966 | − | 0.793196i | \(-0.708415\pi\) | ||||
−0.608966 | + | 0.793196i | \(0.708415\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 24605.9 | 1.04217 | 0.521086 | − | 0.853504i | \(-0.325527\pi\) | ||||
0.521086 | + | 0.853504i | \(0.325527\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −1971.49 | −0.0831982 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −34076.6 | −1.43284 | −0.716421 | − | 0.697668i | \(-0.754221\pi\) | ||||
−0.716421 | + | 0.697668i | \(0.754221\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 1293.46 | 0.0541904 | 0.0270952 | − | 0.999633i | \(-0.491374\pi\) | ||||
0.0270952 | + | 0.999633i | \(0.491374\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 20155.7 | 0.841388 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 2806.80 | 0.116746 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −54513.1 | −2.25929 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 4756.22 | 0.196415 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 28847.5 | 1.18704 | 0.593521 | − | 0.804819i | \(-0.297737\pi\) | ||||
0.593521 | + | 0.804819i | \(0.297737\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −17238.1 | −0.706800 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 18013.1 | 0.735948 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 839.798 | 0.0341893 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −18401.7 | −0.746506 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 13258.2 | 0.535947 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 16902.0 | 0.680839 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −58.7693 | −0.00235900 | −0.00117950 | − | 0.999999i | \(-0.500375\pi\) | ||||
−0.00117950 | + | 0.999999i | \(0.500375\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −12228.2 | −0.489118 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −20953.6 | −0.835194 | −0.417597 | − | 0.908632i | \(-0.637128\pi\) | ||||
−0.417597 | + | 0.908632i | \(0.637128\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 41459.5 | 1.64677 | 0.823387 | − | 0.567481i | \(-0.192082\pi\) | ||||
0.823387 | + | 0.567481i | \(0.192082\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 13513.0 | 0.534868 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −3389.59 | −0.133700 | −0.0668499 | − | 0.997763i | \(-0.521295\pi\) | ||||
−0.0668499 | + | 0.997763i | \(0.521295\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 38492.3 | 1.51304 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −21120.0 | −0.827304 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −2064.07 | −0.0805741 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −6016.91 | −0.234070 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −8479.66 | −0.328743 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −17315.9 | −0.669012 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −19675.3 | −0.757568 | −0.378784 | − | 0.925485i | \(-0.623658\pi\) | ||||
−0.378784 | + | 0.925485i | \(0.623658\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −6553.79 | −0.251484 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 1497.48 | 0.0572660 | 0.0286330 | − | 0.999590i | \(-0.490885\pi\) | ||||
0.0286330 | + | 0.999590i | \(0.490885\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −5860.23 | −0.223344 | −0.111672 | − | 0.993745i | \(-0.535621\pi\) | ||||
−0.111672 | + | 0.993745i | \(0.535621\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −51666.0 | −1.96241 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 18058.0 | 0.683573 | 0.341787 | − | 0.939778i | \(-0.388968\pi\) | ||||
0.341787 | + | 0.939778i | \(0.388968\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 9700.66 | 0.365973 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1195.78 | 0.0449609 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −22349.5 | −0.837512 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −7644.03 | −0.285488 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 28747.1 | 1.07005 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −2667.04 | −0.0989441 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −690.200 | −0.0255204 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −10839.7 | −0.399472 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 42915.2 | 1.57630 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 30297.4 | 1.10916 | 0.554580 | − | 0.832130i | \(-0.312879\pi\) | ||||
0.554580 | + | 0.832130i | \(0.312879\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 4536.35 | 0.165524 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 31977.7 | 1.16297 | 0.581487 | − | 0.813556i | \(-0.302471\pi\) | ||||
0.581487 | + | 0.813556i | \(0.302471\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −969.228 | −0.0351334 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −20415.0 | −0.737595 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −3884.72 | −0.139896 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 40696.7 | 1.46078 | 0.730391 | − | 0.683029i | \(-0.239338\pi\) | ||||
0.730391 | + | 0.683029i | \(0.239338\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 19409.4 | 0.694421 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 16152.9 | 0.576034 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 24568.2 | 0.873295 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 5713.57 | 0.202436 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −11467.5 | −0.404989 | −0.202495 | − | 0.979283i | \(-0.564905\pi\) | ||||
−0.202495 | + | 0.979283i | \(0.564905\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 18387.0 | 0.647271 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 13468.4 | 0.472600 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −729.742 | −0.0255242 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 14100.2 | 0.491603 | 0.245802 | − | 0.969320i | \(-0.420949\pi\) | ||||
0.245802 | + | 0.969320i | \(0.420949\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 38342.7 | 1.33255 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −29781.6 | −1.03172 | −0.515862 | − | 0.856672i | \(-0.672528\pi\) | ||||
−0.515862 | + | 0.856672i | \(0.672528\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 28208.8 | 0.974129 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 37418.5 | 1.28807 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 35353.8 | 1.21314 | 0.606571 | − | 0.795030i | \(-0.292545\pi\) | ||||
0.606571 | + | 0.795030i | \(0.292545\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 13884.4 | 0.474928 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −37569.8 | −1.28106 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 6456.01 | 0.219445 | 0.109722 | − | 0.993962i | \(-0.465004\pi\) | ||||
0.109722 | + | 0.993962i | \(0.465004\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 72161.7 | 2.44513 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −855.885 | −0.0289100 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 3765.59 | 0.126796 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −28796.3 | −0.966610 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −9819.69 | −0.328593 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 15847.0 | 0.528636 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 15099.9 | 0.502153 | 0.251076 | − | 0.967967i | \(-0.419215\pi\) | ||||
0.251076 | + | 0.967967i | \(0.419215\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 10545.0 | 0.349591 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 8800.82 | 0.290867 | 0.145433 | − | 0.989368i | \(-0.453542\pi\) | ||||
0.145433 | + | 0.989368i | \(0.453542\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −9025.23 | −0.297364 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 41785.8 | 1.37253 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 34900.0 | 1.14284 | 0.571418 | − | 0.820659i | \(-0.306393\pi\) | ||||
0.571418 | + | 0.820659i | \(0.306393\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −3089.81 | −0.100869 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 859.693 | 0.0279795 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −21221.5 | −0.688567 | −0.344283 | − | 0.938866i | \(-0.611878\pi\) | ||||
−0.344283 | + | 0.938866i | \(0.611878\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −82700.7 | −2.67519 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 11741.1 | 0.378647 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −22628.2 | −0.727538 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 23985.3 | 0.768838 | 0.384419 | − | 0.923159i | \(-0.374402\pi\) | ||||
0.384419 | + | 0.923159i | \(0.374402\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −29437.7 | −0.940761 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −3979.10 | −0.126780 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 15222.3 | 0.483547 | 0.241773 | − | 0.970333i | \(-0.422271\pi\) | ||||
0.241773 | + | 0.970333i | \(0.422271\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −19020.7 | −0.602391 |
(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 | 1024.4.a.n.1.8 | 10 | ||
4.3 | odd | 2 | 1024.4.a.m.1.3 | 10 | |||
8.3 | odd | 2 | 1024.4.a.m.1.8 | 10 | |||
8.5 | even | 2 | inner | 1024.4.a.n.1.3 | 10 | ||
16.3 | odd | 4 | 1024.4.b.k.513.3 | 10 | |||
16.5 | even | 4 | 1024.4.b.j.513.3 | 10 | |||
16.11 | odd | 4 | 1024.4.b.k.513.8 | 10 | |||
16.13 | even | 4 | 1024.4.b.j.513.8 | 10 | |||
32.3 | odd | 8 | 128.4.e.a.33.2 | 10 | |||
32.5 | even | 8 | 16.4.e.a.5.5 | ✓ | 10 | ||
32.11 | odd | 8 | 128.4.e.a.97.2 | 10 | |||
32.13 | even | 8 | 16.4.e.a.13.5 | yes | 10 | ||
32.19 | odd | 8 | 64.4.e.a.17.4 | 10 | |||
32.21 | even | 8 | 128.4.e.b.97.4 | 10 | |||
32.27 | odd | 8 | 64.4.e.a.49.4 | 10 | |||
32.29 | even | 8 | 128.4.e.b.33.4 | 10 | |||
96.5 | odd | 8 | 144.4.k.a.37.1 | 10 | |||
96.59 | even | 8 | 576.4.k.a.433.5 | 10 | |||
96.77 | odd | 8 | 144.4.k.a.109.1 | 10 | |||
96.83 | even | 8 | 576.4.k.a.145.5 | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
16.4.e.a.5.5 | ✓ | 10 | 32.5 | even | 8 | ||
16.4.e.a.13.5 | yes | 10 | 32.13 | even | 8 | ||
64.4.e.a.17.4 | 10 | 32.19 | odd | 8 | |||
64.4.e.a.49.4 | 10 | 32.27 | odd | 8 | |||
128.4.e.a.33.2 | 10 | 32.3 | odd | 8 | |||
128.4.e.a.97.2 | 10 | 32.11 | odd | 8 | |||
128.4.e.b.33.4 | 10 | 32.29 | even | 8 | |||
128.4.e.b.97.4 | 10 | 32.21 | even | 8 | |||
144.4.k.a.37.1 | 10 | 96.5 | odd | 8 | |||
144.4.k.a.109.1 | 10 | 96.77 | odd | 8 | |||
576.4.k.a.145.5 | 10 | 96.83 | even | 8 | |||
576.4.k.a.433.5 | 10 | 96.59 | even | 8 | |||
1024.4.a.m.1.3 | 10 | 4.3 | odd | 2 | |||
1024.4.a.m.1.8 | 10 | 8.3 | odd | 2 | |||
1024.4.a.n.1.3 | 10 | 8.5 | even | 2 | inner | ||
1024.4.a.n.1.8 | 10 | 1.1 | even | 1 | trivial | ||
1024.4.b.j.513.3 | 10 | 16.5 | even | 4 | |||
1024.4.b.j.513.8 | 10 | 16.13 | even | 4 | |||
1024.4.b.k.513.3 | 10 | 16.3 | odd | 4 | |||
1024.4.b.k.513.8 | 10 | 16.11 | odd | 4 |