Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6039,2,Mod(1,6039)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6039, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6039.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6039 = 3^{2} \cdot 11 \cdot 61 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6039.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: | \(48.2216577807\) |
Analytic rank: | \(1\) |
Dimension: | \(25\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.19 | ||
Character | \(\chi\) | \(=\) | 6039.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.07776 | 0.762091 | 0.381045 | − | 0.924556i | \(-0.375564\pi\) | ||||
0.381045 | + | 0.924556i | \(0.375564\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −0.838436 | −0.419218 | ||||||||
\(5\) | −3.04682 | −1.36258 | −0.681290 | − | 0.732013i | \(-0.738581\pi\) | ||||
−0.681290 | + | 0.732013i | \(0.738581\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.44893 | 1.30357 | 0.651787 | − | 0.758402i | \(-0.274019\pi\) | ||||
0.651787 | + | 0.758402i | \(0.274019\pi\) | |||||||
\(8\) | −3.05915 | −1.08157 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −3.28374 | −1.03841 | ||||||||
\(11\) | −1.00000 | −0.301511 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.71326 | 0.752523 | 0.376261 | − | 0.926514i | \(-0.377209\pi\) | ||||
0.376261 | + | 0.926514i | \(0.377209\pi\) | |||||||
\(14\) | 3.71712 | 0.993442 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −1.62015 | −0.405038 | ||||||||
\(17\) | −3.42003 | −0.829480 | −0.414740 | − | 0.909940i | \(-0.636127\pi\) | ||||
−0.414740 | + | 0.909940i | \(0.636127\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.81606 | −0.416632 | −0.208316 | − | 0.978062i | \(-0.566798\pi\) | ||||
−0.208316 | + | 0.978062i | \(0.566798\pi\) | |||||||
\(20\) | 2.55457 | 0.571218 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −1.07776 | −0.229779 | ||||||||
\(23\) | 6.08551 | 1.26892 | 0.634459 | − | 0.772957i | \(-0.281223\pi\) | ||||
0.634459 | + | 0.772957i | \(0.281223\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 4.28313 | 0.856626 | ||||||||
\(26\) | 2.92424 | 0.573491 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −2.89171 | −0.546482 | ||||||||
\(29\) | −0.376637 | −0.0699397 | −0.0349699 | − | 0.999388i | \(-0.511134\pi\) | ||||
−0.0349699 | + | 0.999388i | \(0.511134\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.93900 | 0.887071 | 0.443536 | − | 0.896257i | \(-0.353724\pi\) | ||||
0.443536 | + | 0.896257i | \(0.353724\pi\) | |||||||
\(32\) | 4.37216 | 0.772897 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −3.68597 | −0.632139 | ||||||||
\(35\) | −10.5083 | −1.77623 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 3.50288 | 0.575870 | 0.287935 | − | 0.957650i | \(-0.407031\pi\) | ||||
0.287935 | + | 0.957650i | \(0.407031\pi\) | |||||||
\(38\) | −1.95727 | −0.317511 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 9.32069 | 1.47373 | ||||||||
\(41\) | −5.87719 | −0.917862 | −0.458931 | − | 0.888472i | \(-0.651768\pi\) | ||||
−0.458931 | + | 0.888472i | \(0.651768\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −8.07962 | −1.23213 | −0.616065 | − | 0.787695i | \(-0.711274\pi\) | ||||
−0.616065 | + | 0.787695i | \(0.711274\pi\) | |||||||
\(44\) | 0.838436 | 0.126399 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 6.55872 | 0.967030 | ||||||||
\(47\) | −6.22226 | −0.907609 | −0.453805 | − | 0.891101i | \(-0.649934\pi\) | ||||
−0.453805 | + | 0.891101i | \(0.649934\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 4.89515 | 0.699307 | ||||||||
\(50\) | 4.61618 | 0.652827 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −2.27489 | −0.315471 | ||||||||
\(53\) | −2.61126 | −0.358684 | −0.179342 | − | 0.983787i | \(-0.557397\pi\) | ||||
−0.179342 | + | 0.983787i | \(0.557397\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 3.04682 | 0.410834 | ||||||||
\(56\) | −10.5508 | −1.40991 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −0.405924 | −0.0533004 | ||||||||
\(59\) | 2.54527 | 0.331365 | 0.165683 | − | 0.986179i | \(-0.447017\pi\) | ||||
0.165683 | + | 0.986179i | \(0.447017\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.00000 | −0.128037 | ||||||||
\(62\) | 5.32305 | 0.676028 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 7.95245 | 0.994056 | ||||||||
\(65\) | −8.26682 | −1.02537 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 7.44820 | 0.909942 | 0.454971 | − | 0.890506i | \(-0.349650\pi\) | ||||
0.454971 | + | 0.890506i | \(0.349650\pi\) | |||||||
\(68\) | 2.86748 | 0.347733 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −11.3254 | −1.35364 | ||||||||
\(71\) | −4.42352 | −0.524975 | −0.262488 | − | 0.964935i | \(-0.584543\pi\) | ||||
−0.262488 | + | 0.964935i | \(0.584543\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 9.20943 | 1.07788 | 0.538941 | − | 0.842344i | \(-0.318825\pi\) | ||||
0.538941 | + | 0.842344i | \(0.318825\pi\) | |||||||
\(74\) | 3.77526 | 0.438865 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 1.52265 | 0.174660 | ||||||||
\(77\) | −3.44893 | −0.393043 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 5.23667 | 0.589171 | 0.294585 | − | 0.955625i | \(-0.404818\pi\) | ||||
0.294585 | + | 0.955625i | \(0.404818\pi\) | |||||||
\(80\) | 4.93632 | 0.551898 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −6.33419 | −0.699494 | ||||||||
\(83\) | 8.81625 | 0.967710 | 0.483855 | − | 0.875148i | \(-0.339236\pi\) | ||||
0.483855 | + | 0.875148i | \(0.339236\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 10.4202 | 1.13023 | ||||||||
\(86\) | −8.70788 | −0.938995 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 3.05915 | 0.326106 | ||||||||
\(89\) | −8.15358 | −0.864278 | −0.432139 | − | 0.901807i | \(-0.642241\pi\) | ||||
−0.432139 | + | 0.901807i | \(0.642241\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 9.35785 | 0.980970 | ||||||||
\(92\) | −5.10231 | −0.531953 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −6.70609 | −0.691681 | ||||||||
\(95\) | 5.53320 | 0.567695 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1.34982 | 0.137054 | 0.0685269 | − | 0.997649i | \(-0.478170\pi\) | ||||
0.0685269 | + | 0.997649i | \(0.478170\pi\) | |||||||
\(98\) | 5.27579 | 0.532935 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −3.59113 | −0.359113 | ||||||||
\(101\) | −4.97047 | −0.494580 | −0.247290 | − | 0.968942i | \(-0.579540\pi\) | ||||
−0.247290 | + | 0.968942i | \(0.579540\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −18.1042 | −1.78386 | −0.891929 | − | 0.452176i | \(-0.850648\pi\) | ||||
−0.891929 | + | 0.452176i | \(0.850648\pi\) | |||||||
\(104\) | −8.30027 | −0.813908 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −2.81431 | −0.273350 | ||||||||
\(107\) | −1.38867 | −0.134247 | −0.0671237 | − | 0.997745i | \(-0.521382\pi\) | ||||
−0.0671237 | + | 0.997745i | \(0.521382\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −11.4775 | −1.09935 | −0.549673 | − | 0.835380i | \(-0.685248\pi\) | ||||
−0.549673 | + | 0.835380i | \(0.685248\pi\) | |||||||
\(110\) | 3.28374 | 0.313092 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −5.58780 | −0.527998 | ||||||||
\(113\) | −8.65339 | −0.814042 | −0.407021 | − | 0.913419i | \(-0.633432\pi\) | ||||
−0.407021 | + | 0.913419i | \(0.633432\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −18.5415 | −1.72900 | ||||||||
\(116\) | 0.315786 | 0.0293200 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 2.74318 | 0.252530 | ||||||||
\(119\) | −11.7955 | −1.08129 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | −1.07776 | −0.0975757 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −4.14104 | −0.371876 | ||||||||
\(125\) | 2.18417 | 0.195358 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −8.67839 | −0.770082 | −0.385041 | − | 0.922899i | \(-0.625813\pi\) | ||||
−0.385041 | + | 0.922899i | \(0.625813\pi\) | |||||||
\(128\) | −0.173509 | −0.0153362 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −8.90964 | −0.781427 | ||||||||
\(131\) | −3.54246 | −0.309506 | −0.154753 | − | 0.987953i | \(-0.549458\pi\) | ||||
−0.154753 | + | 0.987953i | \(0.549458\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −6.26346 | −0.543111 | ||||||||
\(134\) | 8.02736 | 0.693458 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 10.4624 | 0.897143 | ||||||||
\(137\) | −18.0703 | −1.54385 | −0.771924 | − | 0.635715i | \(-0.780705\pi\) | ||||
−0.771924 | + | 0.635715i | \(0.780705\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −3.32448 | −0.281979 | −0.140989 | − | 0.990011i | \(-0.545028\pi\) | ||||
−0.140989 | + | 0.990011i | \(0.545028\pi\) | |||||||
\(140\) | 8.81053 | 0.744626 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −4.76749 | −0.400079 | ||||||||
\(143\) | −2.71326 | −0.226894 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1.14755 | 0.0952986 | ||||||||
\(146\) | 9.92554 | 0.821444 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −2.93694 | −0.241415 | ||||||||
\(149\) | 1.93908 | 0.158856 | 0.0794278 | − | 0.996841i | \(-0.474691\pi\) | ||||
0.0794278 | + | 0.996841i | \(0.474691\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −8.63107 | −0.702386 | −0.351193 | − | 0.936303i | \(-0.614224\pi\) | ||||
−0.351193 | + | 0.936303i | \(0.614224\pi\) | |||||||
\(152\) | 5.55559 | 0.450618 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −3.71712 | −0.299534 | ||||||||
\(155\) | −15.0483 | −1.20871 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −7.40501 | −0.590984 | −0.295492 | − | 0.955345i | \(-0.595484\pi\) | ||||
−0.295492 | + | 0.955345i | \(0.595484\pi\) | |||||||
\(158\) | 5.64386 | 0.449002 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −13.3212 | −1.05313 | ||||||||
\(161\) | 20.9885 | 1.65413 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −4.33911 | −0.339865 | −0.169933 | − | 0.985456i | \(-0.554355\pi\) | ||||
−0.169933 | + | 0.985456i | \(0.554355\pi\) | |||||||
\(164\) | 4.92764 | 0.384784 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 9.50180 | 0.737482 | ||||||||
\(167\) | −12.1403 | −0.939441 | −0.469721 | − | 0.882815i | \(-0.655645\pi\) | ||||
−0.469721 | + | 0.882815i | \(0.655645\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −5.63822 | −0.433709 | ||||||||
\(170\) | 11.2305 | 0.861340 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 6.77424 | 0.516531 | ||||||||
\(173\) | 4.34300 | 0.330192 | 0.165096 | − | 0.986278i | \(-0.447207\pi\) | ||||
0.165096 | + | 0.986278i | \(0.447207\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 14.7722 | 1.11668 | ||||||||
\(176\) | 1.62015 | 0.122124 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −8.78759 | −0.658658 | ||||||||
\(179\) | −6.46245 | −0.483026 | −0.241513 | − | 0.970398i | \(-0.577644\pi\) | ||||
−0.241513 | + | 0.970398i | \(0.577644\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −14.7017 | −1.09277 | −0.546385 | − | 0.837534i | \(-0.683996\pi\) | ||||
−0.546385 | + | 0.837534i | \(0.683996\pi\) | |||||||
\(182\) | 10.0855 | 0.747588 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −18.6165 | −1.37243 | ||||||||
\(185\) | −10.6727 | −0.784669 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 3.42003 | 0.250098 | ||||||||
\(188\) | 5.21696 | 0.380486 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 5.96346 | 0.432635 | ||||||||
\(191\) | −24.4638 | −1.77014 | −0.885070 | − | 0.465459i | \(-0.845889\pi\) | ||||
−0.885070 | + | 0.465459i | \(0.845889\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −2.45063 | −0.176400 | −0.0882001 | − | 0.996103i | \(-0.528111\pi\) | ||||
−0.0882001 | + | 0.996103i | \(0.528111\pi\) | |||||||
\(194\) | 1.45478 | 0.104447 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −4.10427 | −0.293162 | ||||||||
\(197\) | −9.82650 | −0.700109 | −0.350055 | − | 0.936729i | \(-0.613837\pi\) | ||||
−0.350055 | + | 0.936729i | \(0.613837\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −18.7230 | −1.32724 | −0.663619 | − | 0.748071i | \(-0.730980\pi\) | ||||
−0.663619 | + | 0.748071i | \(0.730980\pi\) | |||||||
\(200\) | −13.1027 | −0.926503 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −5.35697 | −0.376915 | ||||||||
\(203\) | −1.29900 | −0.0911717 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 17.9067 | 1.25066 | ||||||||
\(206\) | −19.5119 | −1.35946 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −4.39590 | −0.304801 | ||||||||
\(209\) | 1.81606 | 0.125619 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −12.2966 | −0.846531 | −0.423265 | − | 0.906006i | \(-0.639116\pi\) | ||||
−0.423265 | + | 0.906006i | \(0.639116\pi\) | |||||||
\(212\) | 2.18938 | 0.150367 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −1.49665 | −0.102309 | ||||||||
\(215\) | 24.6172 | 1.67888 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 17.0343 | 1.15636 | ||||||||
\(218\) | −12.3700 | −0.837801 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −2.55457 | −0.172229 | ||||||||
\(221\) | −9.27944 | −0.624203 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −0.629713 | −0.0421687 | −0.0210844 | − | 0.999778i | \(-0.506712\pi\) | ||||
−0.0210844 | + | 0.999778i | \(0.506712\pi\) | |||||||
\(224\) | 15.0793 | 1.00753 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −9.32627 | −0.620374 | ||||||||
\(227\) | 21.8544 | 1.45053 | 0.725264 | − | 0.688471i | \(-0.241718\pi\) | ||||
0.725264 | + | 0.688471i | \(0.241718\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 21.6849 | 1.43298 | 0.716489 | − | 0.697598i | \(-0.245748\pi\) | ||||
0.716489 | + | 0.697598i | \(0.245748\pi\) | |||||||
\(230\) | −19.9832 | −1.31766 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 1.15219 | 0.0756449 | ||||||||
\(233\) | −13.8094 | −0.904681 | −0.452341 | − | 0.891845i | \(-0.649411\pi\) | ||||
−0.452341 | + | 0.891845i | \(0.649411\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 18.9581 | 1.23669 | ||||||||
\(236\) | −2.13404 | −0.138914 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −12.7127 | −0.824040 | ||||||||
\(239\) | −8.10196 | −0.524072 | −0.262036 | − | 0.965058i | \(-0.584394\pi\) | ||||
−0.262036 | + | 0.965058i | \(0.584394\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −5.88395 | −0.379018 | −0.189509 | − | 0.981879i | \(-0.560690\pi\) | ||||
−0.189509 | + | 0.981879i | \(0.560690\pi\) | |||||||
\(242\) | 1.07776 | 0.0692810 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0.838436 | 0.0536754 | ||||||||
\(245\) | −14.9147 | −0.952862 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −4.92743 | −0.313525 | ||||||||
\(248\) | −15.1091 | −0.959432 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 2.35401 | 0.148881 | ||||||||
\(251\) | 18.2741 | 1.15345 | 0.576726 | − | 0.816938i | \(-0.304330\pi\) | ||||
0.576726 | + | 0.816938i | \(0.304330\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −6.08551 | −0.382593 | ||||||||
\(254\) | −9.35321 | −0.586872 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −16.0919 | −1.00574 | ||||||||
\(257\) | 3.47117 | 0.216526 | 0.108263 | − | 0.994122i | \(-0.465471\pi\) | ||||
0.108263 | + | 0.994122i | \(0.465471\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 12.0812 | 0.750689 | ||||||||
\(260\) | 6.93120 | 0.429855 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −3.81791 | −0.235871 | ||||||||
\(263\) | −1.56304 | −0.0963814 | −0.0481907 | − | 0.998838i | \(-0.515346\pi\) | ||||
−0.0481907 | + | 0.998838i | \(0.515346\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 7.95605 | 0.488737 | ||||||||
\(266\) | −6.75050 | −0.413900 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −6.24483 | −0.381464 | ||||||||
\(269\) | 11.7725 | 0.717782 | 0.358891 | − | 0.933379i | \(-0.383155\pi\) | ||||
0.358891 | + | 0.933379i | \(0.383155\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 20.5162 | 1.24627 | 0.623135 | − | 0.782114i | \(-0.285859\pi\) | ||||
0.623135 | + | 0.782114i | \(0.285859\pi\) | |||||||
\(272\) | 5.54098 | 0.335971 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −19.4754 | −1.17655 | ||||||||
\(275\) | −4.28313 | −0.258283 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −0.101873 | −0.00612094 | −0.00306047 | − | 0.999995i | \(-0.500974\pi\) | ||||
−0.00306047 | + | 0.999995i | \(0.500974\pi\) | |||||||
\(278\) | −3.58299 | −0.214893 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 32.1464 | 1.92112 | ||||||||
\(281\) | 14.3249 | 0.854552 | 0.427276 | − | 0.904121i | \(-0.359473\pi\) | ||||
0.427276 | + | 0.904121i | \(0.359473\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −26.4737 | −1.57370 | −0.786850 | − | 0.617144i | \(-0.788290\pi\) | ||||
−0.786850 | + | 0.617144i | \(0.788290\pi\) | |||||||
\(284\) | 3.70884 | 0.220079 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −2.92424 | −0.172914 | ||||||||
\(287\) | −20.2700 | −1.19650 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −5.30336 | −0.311963 | ||||||||
\(290\) | 1.23678 | 0.0726261 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −7.72151 | −0.451867 | ||||||||
\(293\) | −7.46832 | −0.436304 | −0.218152 | − | 0.975915i | \(-0.570003\pi\) | ||||
−0.218152 | + | 0.975915i | \(0.570003\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −7.75498 | −0.451512 | ||||||||
\(296\) | −10.7158 | −0.622845 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 2.08986 | 0.121062 | ||||||||
\(299\) | 16.5116 | 0.954889 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −27.8661 | −1.60617 | ||||||||
\(302\) | −9.30221 | −0.535282 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 2.94229 | 0.168752 | ||||||||
\(305\) | 3.04682 | 0.174461 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 23.2988 | 1.32973 | 0.664867 | − | 0.746962i | \(-0.268488\pi\) | ||||
0.664867 | + | 0.746962i | \(0.268488\pi\) | |||||||
\(308\) | 2.89171 | 0.164770 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −16.2184 | −0.921143 | ||||||||
\(311\) | −17.3926 | −0.986244 | −0.493122 | − | 0.869960i | \(-0.664144\pi\) | ||||
−0.493122 | + | 0.869960i | \(0.664144\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −1.69958 | −0.0960659 | −0.0480330 | − | 0.998846i | \(-0.515295\pi\) | ||||
−0.0480330 | + | 0.998846i | \(0.515295\pi\) | |||||||
\(314\) | −7.98081 | −0.450383 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −4.39061 | −0.246991 | ||||||||
\(317\) | 29.6094 | 1.66303 | 0.831515 | − | 0.555502i | \(-0.187474\pi\) | ||||
0.831515 | + | 0.555502i | \(0.187474\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0.376637 | 0.0210876 | ||||||||
\(320\) | −24.2297 | −1.35448 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 22.6206 | 1.26060 | ||||||||
\(323\) | 6.21098 | 0.345588 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 11.6212 | 0.644631 | ||||||||
\(326\) | −4.67651 | −0.259008 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 17.9792 | 0.992735 | ||||||||
\(329\) | −21.4602 | −1.18314 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −4.47943 | −0.246211 | −0.123106 | − | 0.992394i | \(-0.539285\pi\) | ||||
−0.123106 | + | 0.992394i | \(0.539285\pi\) | |||||||
\(332\) | −7.39186 | −0.405681 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −13.0843 | −0.715939 | ||||||||
\(335\) | −22.6933 | −1.23987 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 6.91513 | 0.376691 | 0.188345 | − | 0.982103i | \(-0.439688\pi\) | ||||
0.188345 | + | 0.982103i | \(0.439688\pi\) | |||||||
\(338\) | −6.07664 | −0.330526 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −8.73670 | −0.473814 | ||||||||
\(341\) | −4.93900 | −0.267462 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −7.25949 | −0.391976 | ||||||||
\(344\) | 24.7168 | 1.33264 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 4.68070 | 0.251636 | ||||||||
\(347\) | −18.5560 | −0.996140 | −0.498070 | − | 0.867137i | \(-0.665958\pi\) | ||||
−0.498070 | + | 0.867137i | \(0.665958\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −6.98021 | −0.373642 | −0.186821 | − | 0.982394i | \(-0.559818\pi\) | ||||
−0.186821 | + | 0.982394i | \(0.559818\pi\) | |||||||
\(350\) | 15.9209 | 0.851008 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −4.37216 | −0.233037 | ||||||||
\(353\) | −25.0961 | −1.33573 | −0.667867 | − | 0.744281i | \(-0.732792\pi\) | ||||
−0.667867 | + | 0.744281i | \(0.732792\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 13.4777 | 0.715321 | ||||||||
\(356\) | 6.83625 | 0.362321 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −6.96496 | −0.368110 | ||||||||
\(359\) | 26.6233 | 1.40513 | 0.702563 | − | 0.711621i | \(-0.252039\pi\) | ||||
0.702563 | + | 0.711621i | \(0.252039\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −15.7019 | −0.826418 | ||||||||
\(362\) | −15.8449 | −0.832790 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −7.84596 | −0.411240 | ||||||||
\(365\) | −28.0595 | −1.46870 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 2.88012 | 0.150341 | 0.0751705 | − | 0.997171i | \(-0.476050\pi\) | ||||
0.0751705 | + | 0.997171i | \(0.476050\pi\) | |||||||
\(368\) | −9.85947 | −0.513960 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −11.5025 | −0.597989 | ||||||||
\(371\) | −9.00607 | −0.467572 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −5.86690 | −0.303777 | −0.151888 | − | 0.988398i | \(-0.548535\pi\) | ||||
−0.151888 | + | 0.988398i | \(0.548535\pi\) | |||||||
\(374\) | 3.68597 | 0.190597 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 19.0348 | 0.981646 | ||||||||
\(377\) | −1.02191 | −0.0526313 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 25.8822 | 1.32948 | 0.664739 | − | 0.747076i | \(-0.268543\pi\) | ||||
0.664739 | + | 0.747076i | \(0.268543\pi\) | |||||||
\(380\) | −4.63924 | −0.237988 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −26.3661 | −1.34901 | ||||||||
\(383\) | 18.2813 | 0.934133 | 0.467066 | − | 0.884222i | \(-0.345311\pi\) | ||||
0.467066 | + | 0.884222i | \(0.345311\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 10.5083 | 0.535552 | ||||||||
\(386\) | −2.64119 | −0.134433 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −1.13174 | −0.0574554 | ||||||||
\(389\) | −6.60365 | −0.334818 | −0.167409 | − | 0.985887i | \(-0.553540\pi\) | ||||
−0.167409 | + | 0.985887i | \(0.553540\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −20.8127 | −1.05254 | ||||||||
\(392\) | −14.9750 | −0.756351 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −10.5906 | −0.533547 | ||||||||
\(395\) | −15.9552 | −0.802793 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 5.31584 | 0.266795 | 0.133397 | − | 0.991063i | \(-0.457411\pi\) | ||||
0.133397 | + | 0.991063i | \(0.457411\pi\) | |||||||
\(398\) | −20.1789 | −1.01148 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −6.93933 | −0.346967 | ||||||||
\(401\) | 23.5518 | 1.17612 | 0.588060 | − | 0.808817i | \(-0.299892\pi\) | ||||
0.588060 | + | 0.808817i | \(0.299892\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 13.4008 | 0.667541 | ||||||||
\(404\) | 4.16742 | 0.207337 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −1.40001 | −0.0694811 | ||||||||
\(407\) | −3.50288 | −0.173631 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 29.8085 | 1.47393 | 0.736967 | − | 0.675929i | \(-0.236258\pi\) | ||||
0.736967 | + | 0.675929i | \(0.236258\pi\) | |||||||
\(410\) | 19.2992 | 0.953117 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 15.1792 | 0.747825 | ||||||||
\(413\) | 8.77846 | 0.431960 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −26.8616 | −1.31858 | ||||||||
\(416\) | 11.8628 | 0.581622 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 1.95727 | 0.0957333 | ||||||||
\(419\) | 22.0112 | 1.07532 | 0.537660 | − | 0.843162i | \(-0.319309\pi\) | ||||
0.537660 | + | 0.843162i | \(0.319309\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −2.64031 | −0.128681 | −0.0643404 | − | 0.997928i | \(-0.520494\pi\) | ||||
−0.0643404 | + | 0.997928i | \(0.520494\pi\) | |||||||
\(422\) | −13.2527 | −0.645133 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 7.98824 | 0.387943 | ||||||||
\(425\) | −14.6485 | −0.710554 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −3.44893 | −0.166906 | ||||||||
\(428\) | 1.16431 | 0.0562790 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 26.5314 | 1.27946 | ||||||||
\(431\) | −11.5029 | −0.554076 | −0.277038 | − | 0.960859i | \(-0.589353\pi\) | ||||
−0.277038 | + | 0.960859i | \(0.589353\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 19.3604 | 0.930403 | 0.465201 | − | 0.885205i | \(-0.345982\pi\) | ||||
0.465201 | + | 0.885205i | \(0.345982\pi\) | |||||||
\(434\) | 18.3589 | 0.881254 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 9.62316 | 0.460866 | ||||||||
\(437\) | −11.0516 | −0.528671 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −13.8560 | −0.661312 | −0.330656 | − | 0.943751i | \(-0.607270\pi\) | ||||
−0.330656 | + | 0.943751i | \(0.607270\pi\) | |||||||
\(440\) | −9.32069 | −0.444346 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −10.0010 | −0.475699 | ||||||||
\(443\) | −13.1908 | −0.626714 | −0.313357 | − | 0.949635i | \(-0.601454\pi\) | ||||
−0.313357 | + | 0.949635i | \(0.601454\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 24.8425 | 1.17765 | ||||||||
\(446\) | −0.678679 | −0.0321364 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 27.4275 | 1.29583 | ||||||||
\(449\) | −10.4842 | −0.494782 | −0.247391 | − | 0.968916i | \(-0.579573\pi\) | ||||
−0.247391 | + | 0.968916i | \(0.579573\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 5.87719 | 0.276746 | ||||||||
\(452\) | 7.25531 | 0.341261 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 23.5538 | 1.10543 | ||||||||
\(455\) | −28.5117 | −1.33665 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 5.55221 | 0.259722 | 0.129861 | − | 0.991532i | \(-0.458547\pi\) | ||||
0.129861 | + | 0.991532i | \(0.458547\pi\) | |||||||
\(458\) | 23.3711 | 1.09206 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 15.5458 | 0.724829 | ||||||||
\(461\) | 14.2444 | 0.663430 | 0.331715 | − | 0.943380i | \(-0.392373\pi\) | ||||
0.331715 | + | 0.943380i | \(0.392373\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 5.17058 | 0.240297 | 0.120149 | − | 0.992756i | \(-0.461663\pi\) | ||||
0.120149 | + | 0.992756i | \(0.461663\pi\) | |||||||
\(464\) | 0.610210 | 0.0283283 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −14.8832 | −0.689449 | ||||||||
\(467\) | −36.3845 | −1.68368 | −0.841838 | − | 0.539731i | \(-0.818526\pi\) | ||||
−0.841838 | + | 0.539731i | \(0.818526\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 25.6883 | 1.18618 | ||||||||
\(470\) | 20.4323 | 0.942471 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −7.78635 | −0.358396 | ||||||||
\(473\) | 8.07962 | 0.371501 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −7.77841 | −0.356898 | ||||||||
\(476\) | 9.88975 | 0.453296 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −8.73196 | −0.399390 | ||||||||
\(479\) | −37.5482 | −1.71562 | −0.857810 | − | 0.513967i | \(-0.828175\pi\) | ||||
−0.857810 | + | 0.513967i | \(0.828175\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 9.50422 | 0.433355 | ||||||||
\(482\) | −6.34148 | −0.288846 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −0.838436 | −0.0381107 | ||||||||
\(485\) | −4.11267 | −0.186747 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 11.4763 | 0.520042 | 0.260021 | − | 0.965603i | \(-0.416270\pi\) | ||||
0.260021 | + | 0.965603i | \(0.416270\pi\) | |||||||
\(488\) | 3.05915 | 0.138481 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −16.0744 | −0.726167 | ||||||||
\(491\) | −15.7233 | −0.709581 | −0.354791 | − | 0.934946i | \(-0.615448\pi\) | ||||
−0.354791 | + | 0.934946i | \(0.615448\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1.28811 | 0.0580136 | ||||||||
\(494\) | −5.31058 | −0.238934 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −8.00194 | −0.359298 | ||||||||
\(497\) | −15.2564 | −0.684345 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −31.2829 | −1.40041 | −0.700207 | − | 0.713940i | \(-0.746909\pi\) | ||||
−0.700207 | + | 0.713940i | \(0.746909\pi\) | |||||||
\(500\) | −1.83129 | −0.0818977 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 19.6951 | 0.879035 | ||||||||
\(503\) | −22.4470 | −1.00086 | −0.500431 | − | 0.865777i | \(-0.666825\pi\) | ||||
−0.500431 | + | 0.865777i | \(0.666825\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 15.1441 | 0.673905 | ||||||||
\(506\) | −6.55872 | −0.291570 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 7.27627 | 0.322832 | ||||||||
\(509\) | −7.38076 | −0.327146 | −0.163573 | − | 0.986531i | \(-0.552302\pi\) | ||||
−0.163573 | + | 0.986531i | \(0.552302\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 31.7627 | 1.40510 | ||||||||
\(512\) | −16.9962 | −0.751131 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 3.74108 | 0.165012 | ||||||||
\(515\) | 55.1602 | 2.43065 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 6.22226 | 0.273655 | ||||||||
\(518\) | 13.0206 | 0.572093 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 25.2894 | 1.10902 | ||||||||
\(521\) | −27.5979 | −1.20909 | −0.604543 | − | 0.796572i | \(-0.706644\pi\) | ||||
−0.604543 | + | 0.796572i | \(0.706644\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 21.3348 | 0.932904 | 0.466452 | − | 0.884547i | \(-0.345532\pi\) | ||||
0.466452 | + | 0.884547i | \(0.345532\pi\) | |||||||
\(524\) | 2.97012 | 0.129750 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −1.68458 | −0.0734513 | ||||||||
\(527\) | −16.8916 | −0.735808 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 14.0335 | 0.610151 | ||||||||
\(530\) | 8.57471 | 0.372462 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 5.25151 | 0.227682 | ||||||||
\(533\) | −15.9463 | −0.690712 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 4.23102 | 0.182923 | ||||||||
\(536\) | −22.7851 | −0.984168 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 12.6879 | 0.547015 | ||||||||
\(539\) | −4.89515 | −0.210849 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 2.69913 | 0.116045 | 0.0580224 | − | 0.998315i | \(-0.481521\pi\) | ||||
0.0580224 | + | 0.998315i | \(0.481521\pi\) | |||||||
\(542\) | 22.1115 | 0.949770 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −14.9530 | −0.641102 | ||||||||
\(545\) | 34.9699 | 1.49795 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 6.51857 | 0.278714 | 0.139357 | − | 0.990242i | \(-0.455496\pi\) | ||||
0.139357 | + | 0.990242i | \(0.455496\pi\) | |||||||
\(548\) | 15.1508 | 0.647208 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −4.61618 | −0.196835 | ||||||||
\(551\) | 0.683994 | 0.0291391 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 18.0609 | 0.768028 | ||||||||
\(554\) | −0.109794 | −0.00466471 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 2.78736 | 0.118210 | ||||||||
\(557\) | 1.33512 | 0.0565708 | 0.0282854 | − | 0.999600i | \(-0.490995\pi\) | ||||
0.0282854 | + | 0.999600i | \(0.490995\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −21.9221 | −0.927206 | ||||||||
\(560\) | 17.0250 | 0.719440 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 15.4388 | 0.651246 | ||||||||
\(563\) | 9.26909 | 0.390646 | 0.195323 | − | 0.980739i | \(-0.437425\pi\) | ||||
0.195323 | + | 0.980739i | \(0.437425\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 26.3653 | 1.10920 | ||||||||
\(566\) | −28.5323 | −1.19930 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 13.5322 | 0.567799 | ||||||||
\(569\) | 24.4489 | 1.02495 | 0.512475 | − | 0.858702i | \(-0.328729\pi\) | ||||
0.512475 | + | 0.858702i | \(0.328729\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −13.5222 | −0.565888 | −0.282944 | − | 0.959136i | \(-0.591311\pi\) | ||||
−0.282944 | + | 0.959136i | \(0.591311\pi\) | |||||||
\(572\) | 2.27489 | 0.0951181 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −21.8462 | −0.911843 | ||||||||
\(575\) | 26.0651 | 1.08699 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 14.4217 | 0.600383 | 0.300192 | − | 0.953879i | \(-0.402949\pi\) | ||||
0.300192 | + | 0.953879i | \(0.402949\pi\) | |||||||
\(578\) | −5.71575 | −0.237744 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −0.962144 | −0.0399509 | ||||||||
\(581\) | 30.4067 | 1.26148 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 2.61126 | 0.108147 | ||||||||
\(584\) | −28.1730 | −1.16581 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −8.04905 | −0.332503 | ||||||||
\(587\) | 32.9640 | 1.36057 | 0.680285 | − | 0.732947i | \(-0.261856\pi\) | ||||
0.680285 | + | 0.732947i | \(0.261856\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −8.96951 | −0.369582 | ||||||||
\(590\) | −8.35799 | −0.344093 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −5.67520 | −0.233249 | ||||||||
\(593\) | −44.9564 | −1.84614 | −0.923069 | − | 0.384633i | \(-0.874328\pi\) | ||||
−0.923069 | + | 0.384633i | \(0.874328\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 35.9387 | 1.47334 | ||||||||
\(596\) | −1.62579 | −0.0665951 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 17.7955 | 0.727712 | ||||||||
\(599\) | 10.6539 | 0.435306 | 0.217653 | − | 0.976026i | \(-0.430160\pi\) | ||||
0.217653 | + | 0.976026i | \(0.430160\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 0.426911 | 0.0174140 | 0.00870702 | − | 0.999962i | \(-0.497228\pi\) | ||||
0.00870702 | + | 0.999962i | \(0.497228\pi\) | |||||||
\(602\) | −30.0329 | −1.22405 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 7.23659 | 0.294453 | ||||||||
\(605\) | −3.04682 | −0.123871 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −37.0498 | −1.50381 | −0.751903 | − | 0.659274i | \(-0.770864\pi\) | ||||
−0.751903 | + | 0.659274i | \(0.770864\pi\) | |||||||
\(608\) | −7.94010 | −0.322013 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 3.28374 | 0.132955 | ||||||||
\(611\) | −16.8826 | −0.682997 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 1.90829 | 0.0770750 | 0.0385375 | − | 0.999257i | \(-0.487730\pi\) | ||||
0.0385375 | + | 0.999257i | \(0.487730\pi\) | |||||||
\(614\) | 25.1105 | 1.01338 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 10.5508 | 0.425104 | ||||||||
\(617\) | −36.7736 | −1.48045 | −0.740226 | − | 0.672359i | \(-0.765281\pi\) | ||||
−0.740226 | + | 0.672359i | \(0.765281\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −25.8507 | −1.03903 | −0.519513 | − | 0.854462i | \(-0.673887\pi\) | ||||
−0.519513 | + | 0.854462i | \(0.673887\pi\) | |||||||
\(620\) | 12.6170 | 0.506711 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −18.7450 | −0.751608 | ||||||||
\(623\) | −28.1212 | −1.12665 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −28.0704 | −1.12282 | ||||||||
\(626\) | −1.83174 | −0.0732110 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 6.20862 | 0.247751 | ||||||||
\(629\) | −11.9800 | −0.477673 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −44.0002 | −1.75162 | −0.875810 | − | 0.482657i | \(-0.839672\pi\) | ||||
−0.875810 | + | 0.482657i | \(0.839672\pi\) | |||||||
\(632\) | −16.0197 | −0.637231 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 31.9118 | 1.26738 | ||||||||
\(635\) | 26.4415 | 1.04930 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 13.2818 | 0.526244 | ||||||||
\(638\) | 0.405924 | 0.0160707 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0.528651 | 0.0208968 | ||||||||
\(641\) | 45.9375 | 1.81442 | 0.907211 | − | 0.420677i | \(-0.138207\pi\) | ||||
0.907211 | + | 0.420677i | \(0.138207\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −10.9831 | −0.433132 | −0.216566 | − | 0.976268i | \(-0.569486\pi\) | ||||
−0.216566 | + | 0.976268i | \(0.569486\pi\) | |||||||
\(644\) | −17.5975 | −0.693440 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 6.69393 | 0.263369 | ||||||||
\(647\) | 9.24470 | 0.363447 | 0.181723 | − | 0.983350i | \(-0.441832\pi\) | ||||
0.181723 | + | 0.983350i | \(0.441832\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −2.54527 | −0.0999104 | ||||||||
\(650\) | 12.5249 | 0.491267 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 3.63806 | 0.142478 | ||||||||
\(653\) | 36.3448 | 1.42228 | 0.711140 | − | 0.703050i | \(-0.248179\pi\) | ||||
0.711140 | + | 0.703050i | \(0.248179\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 10.7932 | 0.421727 | ||||||||
\(656\) | 9.52194 | 0.371769 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −23.1289 | −0.901657 | ||||||||
\(659\) | −12.8729 | −0.501458 | −0.250729 | − | 0.968057i | \(-0.580670\pi\) | ||||
−0.250729 | + | 0.968057i | \(0.580670\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 24.6328 | 0.958105 | 0.479053 | − | 0.877786i | \(-0.340980\pi\) | ||||
0.479053 | + | 0.877786i | \(0.340980\pi\) | |||||||
\(662\) | −4.82774 | −0.187635 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −26.9702 | −1.04665 | ||||||||
\(665\) | 19.0837 | 0.740032 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −2.29203 | −0.0887478 | ||||||||
\(668\) | 10.1788 | 0.393831 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −24.4579 | −0.944893 | ||||||||
\(671\) | 1.00000 | 0.0386046 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 28.8608 | 1.11250 | 0.556250 | − | 0.831015i | \(-0.312240\pi\) | ||||
0.556250 | + | 0.831015i | \(0.312240\pi\) | |||||||
\(674\) | 7.45284 | 0.287073 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 4.72729 | 0.181819 | ||||||||
\(677\) | −27.3298 | −1.05037 | −0.525184 | − | 0.850989i | \(-0.676004\pi\) | ||||
−0.525184 | + | 0.850989i | \(0.676004\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 4.65545 | 0.178660 | ||||||||
\(680\) | −31.8771 | −1.22243 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −5.32305 | −0.203830 | ||||||||
\(683\) | 4.55326 | 0.174226 | 0.0871128 | − | 0.996198i | \(-0.472236\pi\) | ||||
0.0871128 | + | 0.996198i | \(0.472236\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 55.0569 | 2.10362 | ||||||||
\(686\) | −7.82398 | −0.298721 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 13.0902 | 0.499060 | ||||||||
\(689\) | −7.08503 | −0.269918 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 6.69036 | 0.254513 | 0.127257 | − | 0.991870i | \(-0.459383\pi\) | ||||
0.127257 | + | 0.991870i | \(0.459383\pi\) | |||||||
\(692\) | −3.64132 | −0.138422 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −19.9989 | −0.759149 | ||||||||
\(695\) | 10.1291 | 0.384219 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 20.1002 | 0.761348 | ||||||||
\(698\) | −7.52298 | −0.284749 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −12.3856 | −0.468131 | ||||||||
\(701\) | 3.64599 | 0.137707 | 0.0688536 | − | 0.997627i | \(-0.478066\pi\) | ||||
0.0688536 | + | 0.997627i | \(0.478066\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −6.36143 | −0.239926 | ||||||||
\(704\) | −7.95245 | −0.299719 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −27.0476 | −1.01795 | ||||||||
\(707\) | −17.1428 | −0.644722 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 8.31591 | 0.312310 | 0.156155 | − | 0.987733i | \(-0.450090\pi\) | ||||
0.156155 | + | 0.987733i | \(0.450090\pi\) | |||||||
\(710\) | 14.5257 | 0.545140 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 24.9430 | 0.934779 | ||||||||
\(713\) | 30.0564 | 1.12562 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 8.26682 | 0.309162 | ||||||||
\(716\) | 5.41835 | 0.202493 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 28.6935 | 1.07083 | ||||||||
\(719\) | 10.6667 | 0.397800 | 0.198900 | − | 0.980020i | \(-0.436263\pi\) | ||||
0.198900 | + | 0.980020i | \(0.436263\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −62.4401 | −2.32539 | ||||||||
\(722\) | −16.9229 | −0.629805 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 12.3264 | 0.458109 | ||||||||
\(725\) | −1.61319 | −0.0599122 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −8.80084 | −0.326405 | −0.163203 | − | 0.986593i | \(-0.552182\pi\) | ||||
−0.163203 | + | 0.986593i | \(0.552182\pi\) | |||||||
\(728\) | −28.6271 | −1.06099 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −30.2414 | −1.11928 | ||||||||
\(731\) | 27.6326 | 1.02203 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −4.17577 | −0.154236 | −0.0771179 | − | 0.997022i | \(-0.524572\pi\) | ||||
−0.0771179 | + | 0.997022i | \(0.524572\pi\) | |||||||
\(734\) | 3.10407 | 0.114573 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 26.6069 | 0.980742 | ||||||||
\(737\) | −7.44820 | −0.274358 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 54.2009 | 1.99381 | 0.996906 | − | 0.0786054i | \(-0.0250467\pi\) | ||||
0.996906 | + | 0.0786054i | \(0.0250467\pi\) | |||||||
\(740\) | 8.94834 | 0.328947 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −9.70637 | −0.356332 | ||||||||
\(743\) | −22.4243 | −0.822666 | −0.411333 | − | 0.911485i | \(-0.634937\pi\) | ||||
−0.411333 | + | 0.911485i | \(0.634937\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −5.90803 | −0.216453 | ||||||||
\(746\) | −6.32310 | −0.231505 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −2.86748 | −0.104845 | ||||||||
\(749\) | −4.78942 | −0.175002 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −46.3856 | −1.69263 | −0.846316 | − | 0.532681i | \(-0.821185\pi\) | ||||
−0.846316 | + | 0.532681i | \(0.821185\pi\) | |||||||
\(752\) | 10.0810 | 0.367617 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −1.10138 | −0.0401098 | ||||||||
\(755\) | 26.2973 | 0.957058 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −2.80886 | −0.102090 | −0.0510448 | − | 0.998696i | \(-0.516255\pi\) | ||||
−0.0510448 | + | 0.998696i | \(0.516255\pi\) | |||||||
\(758\) | 27.8947 | 1.01318 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −16.9269 | −0.614003 | ||||||||
\(761\) | −18.9731 | −0.687773 | −0.343887 | − | 0.939011i | \(-0.611744\pi\) | ||||
−0.343887 | + | 0.939011i | \(0.611744\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −39.5852 | −1.43308 | ||||||||
\(764\) | 20.5113 | 0.742074 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 19.7029 | 0.711894 | ||||||||
\(767\) | 6.90597 | 0.249360 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 27.9821 | 1.00906 | 0.504530 | − | 0.863394i | \(-0.331666\pi\) | ||||
0.504530 | + | 0.863394i | \(0.331666\pi\) | |||||||
\(770\) | 11.3254 | 0.408139 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 2.05470 | 0.0739501 | ||||||||
\(773\) | 17.6472 | 0.634727 | 0.317363 | − | 0.948304i | \(-0.397203\pi\) | ||||
0.317363 | + | 0.948304i | \(0.397203\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 21.1544 | 0.759888 | ||||||||
\(776\) | −4.12931 | −0.148234 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −7.11714 | −0.255162 | ||||||||
\(779\) | 10.6733 | 0.382411 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 4.42352 | 0.158286 | ||||||||
\(782\) | −22.4310 | −0.802132 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −7.93089 | −0.283246 | ||||||||
\(785\) | 22.5617 | 0.805263 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −50.6943 | −1.80706 | −0.903528 | − | 0.428528i | \(-0.859032\pi\) | ||||
−0.903528 | + | 0.428528i | \(0.859032\pi\) | |||||||
\(788\) | 8.23889 | 0.293498 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −17.1959 | −0.611801 | ||||||||
\(791\) | −29.8450 | −1.06116 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −2.71326 | −0.0963507 | ||||||||
\(794\) | 5.72920 | 0.203322 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 15.6980 | 0.556402 | ||||||||
\(797\) | 13.5778 | 0.480951 | 0.240476 | − | 0.970655i | \(-0.422697\pi\) | ||||
0.240476 | + | 0.970655i | \(0.422697\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 21.2803 | 0.752844 | ||||||||
\(800\) | 18.7266 | 0.662084 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 25.3831 | 0.896310 | ||||||||
\(803\) | −9.20943 | −0.324994 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −63.9484 | −2.25388 | ||||||||
\(806\) | 14.4428 | 0.508727 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 15.2054 | 0.534924 | ||||||||
\(809\) | 44.4156 | 1.56157 | 0.780785 | − | 0.624799i | \(-0.214819\pi\) | ||||
0.780785 | + | 0.624799i | \(0.214819\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 41.7978 | 1.46772 | 0.733859 | − | 0.679301i | \(-0.237717\pi\) | ||||
0.733859 | + | 0.679301i | \(0.237717\pi\) | |||||||
\(812\) | 1.08913 | 0.0382208 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −3.77526 | −0.132323 | ||||||||
\(815\) | 13.2205 | 0.463094 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 14.6730 | 0.513345 | ||||||||
\(818\) | 32.1263 | 1.12327 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −15.0137 | −0.524300 | ||||||||
\(821\) | −6.14459 | −0.214448 | −0.107224 | − | 0.994235i | \(-0.534196\pi\) | ||||
−0.107224 | + | 0.994235i | \(0.534196\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −10.4844 | −0.365464 | −0.182732 | − | 0.983163i | \(-0.558494\pi\) | ||||
−0.182732 | + | 0.983163i | \(0.558494\pi\) | |||||||
\(824\) | 55.3834 | 1.92937 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 9.46106 | 0.329192 | ||||||||
\(827\) | 1.30033 | 0.0452168 | 0.0226084 | − | 0.999744i | \(-0.492803\pi\) | ||||
0.0226084 | + | 0.999744i | \(0.492803\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 51.8433 | 1.80059 | 0.900296 | − | 0.435279i | \(-0.143350\pi\) | ||||
0.900296 | + | 0.435279i | \(0.143350\pi\) | |||||||
\(830\) | −28.9503 | −1.00488 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 21.5770 | 0.748050 | ||||||||
\(833\) | −16.7416 | −0.580061 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 36.9892 | 1.28006 | ||||||||
\(836\) | −1.52265 | −0.0526618 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 23.7228 | 0.819491 | ||||||||
\(839\) | 8.55057 | 0.295198 | 0.147599 | − | 0.989047i | \(-0.452845\pi\) | ||||
0.147599 | + | 0.989047i | \(0.452845\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.8581 | −0.995108 | ||||||||
\(842\) | −2.84562 | −0.0980665 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 10.3099 | 0.354881 | ||||||||
\(845\) | 17.1787 | 0.590964 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 3.44893 | 0.118507 | ||||||||
\(848\) | 4.23065 | 0.145281 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −15.7875 | −0.541507 | ||||||||
\(851\) | 21.3168 | 0.730731 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −3.34288 | −0.114458 | −0.0572289 | − | 0.998361i | \(-0.518226\pi\) | ||||
−0.0572289 | + | 0.998361i | \(0.518226\pi\) | |||||||
\(854\) | −3.71712 | −0.127197 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 4.24814 | 0.145198 | ||||||||
\(857\) | 39.8478 | 1.36117 | 0.680587 | − | 0.732667i | \(-0.261725\pi\) | ||||
0.680587 | + | 0.732667i | \(0.261725\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −9.75337 | −0.332781 | −0.166390 | − | 0.986060i | \(-0.553211\pi\) | ||||
−0.166390 | + | 0.986060i | \(0.553211\pi\) | |||||||
\(860\) | −20.6399 | −0.703815 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −12.3974 | −0.422256 | ||||||||
\(863\) | −13.2225 | −0.450098 | −0.225049 | − | 0.974347i | \(-0.572254\pi\) | ||||
−0.225049 | + | 0.974347i | \(0.572254\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −13.2323 | −0.449913 | ||||||||
\(866\) | 20.8659 | 0.709051 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −14.2822 | −0.484768 | ||||||||
\(869\) | −5.23667 | −0.177642 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 20.2089 | 0.684752 | ||||||||
\(872\) | 35.1114 | 1.18902 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −11.9110 | −0.402896 | ||||||||
\(875\) | 7.53307 | 0.254664 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −13.0314 | −0.440039 | −0.220020 | − | 0.975495i | \(-0.570612\pi\) | ||||
−0.220020 | + | 0.975495i | \(0.570612\pi\) | |||||||
\(878\) | −14.9335 | −0.503980 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −4.93632 | −0.166403 | ||||||||
\(881\) | 16.8445 | 0.567507 | 0.283753 | − | 0.958897i | \(-0.408420\pi\) | ||||
0.283753 | + | 0.958897i | \(0.408420\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −11.2257 | −0.377775 | −0.188888 | − | 0.981999i | \(-0.560488\pi\) | ||||
−0.188888 | + | 0.981999i | \(0.560488\pi\) | |||||||
\(884\) | 7.78022 | 0.261677 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −14.2165 | −0.477613 | ||||||||
\(887\) | −18.9067 | −0.634823 | −0.317412 | − | 0.948288i | \(-0.602814\pi\) | ||||
−0.317412 | + | 0.948288i | \(0.602814\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −29.9312 | −1.00386 | ||||||||
\(890\) | 26.7742 | 0.897475 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0.527974 | 0.0176779 | ||||||||
\(893\) | 11.3000 | 0.378139 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 19.6899 | 0.658162 | ||||||||
\(896\) | −0.598421 | −0.0199918 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −11.2995 | −0.377068 | ||||||||
\(899\) | −1.86021 | −0.0620415 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 8.93061 | 0.297522 | ||||||||
\(902\) | 6.33419 | 0.210905 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 26.4720 | 0.880446 | ||||||||
\(905\) | 44.7935 | 1.48899 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 27.4334 | 0.910911 | 0.455456 | − | 0.890259i | \(-0.349476\pi\) | ||||
0.455456 | + | 0.890259i | \(0.349476\pi\) | |||||||
\(908\) | −18.3235 | −0.608088 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −30.7288 | −1.01865 | ||||||||
\(911\) | −15.5416 | −0.514916 | −0.257458 | − | 0.966289i | \(-0.582885\pi\) | ||||
−0.257458 | + | 0.966289i | \(0.582885\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −8.81625 | −0.291775 | ||||||||
\(914\) | 5.98395 | 0.197931 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −18.1814 | −0.600730 | ||||||||
\(917\) | −12.2177 | −0.403464 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 50.8268 | 1.67662 | 0.838310 | − | 0.545193i | \(-0.183544\pi\) | ||||
0.838310 | + | 0.545193i | \(0.183544\pi\) | |||||||
\(920\) | 56.7212 | 1.87004 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 15.3521 | 0.505593 | ||||||||
\(923\) | −12.0022 | −0.395056 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 15.0033 | 0.493305 | ||||||||
\(926\) | 5.57264 | 0.183128 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −1.64672 | −0.0540562 | ||||||||
\(929\) | 8.78485 | 0.288221 | 0.144111 | − | 0.989562i | \(-0.453968\pi\) | ||||
0.144111 | + | 0.989562i | \(0.453968\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −8.88987 | −0.291354 | ||||||||
\(932\) | 11.5783 | 0.379259 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −39.2138 | −1.28311 | ||||||||
\(935\) | −10.4202 | −0.340778 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 56.6855 | 1.85184 | 0.925918 | − | 0.377725i | \(-0.123293\pi\) | ||||
0.925918 | + | 0.377725i | \(0.123293\pi\) | |||||||
\(938\) | 27.6858 | 0.903975 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −15.8952 | −0.518443 | ||||||||
\(941\) | 41.0121 | 1.33696 | 0.668479 | − | 0.743731i | \(-0.266946\pi\) | ||||
0.668479 | + | 0.743731i | \(0.266946\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −35.7657 | −1.16469 | ||||||||
\(944\) | −4.12372 | −0.134216 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 8.70788 | 0.283118 | ||||||||
\(947\) | 9.18122 | 0.298349 | 0.149175 | − | 0.988811i | \(-0.452338\pi\) | ||||
0.149175 | + | 0.988811i | \(0.452338\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 24.9876 | 0.811131 | ||||||||
\(950\) | −8.38325 | −0.271988 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 36.0841 | 1.16949 | ||||||||
\(953\) | 17.0299 | 0.551653 | 0.275826 | − | 0.961207i | \(-0.411049\pi\) | ||||
0.275826 | + | 0.961207i | \(0.411049\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 74.5369 | 2.41196 | ||||||||
\(956\) | 6.79297 | 0.219700 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −40.4679 | −1.30746 | ||||||||
\(959\) | −62.3232 | −2.01252 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −6.60625 | −0.213105 | ||||||||
\(962\) | 10.2433 | 0.330256 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 4.93331 | 0.158891 | ||||||||
\(965\) | 7.46663 | 0.240359 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −16.5606 | −0.532555 | −0.266277 | − | 0.963896i | \(-0.585794\pi\) | ||||
−0.266277 | + | 0.963896i | \(0.585794\pi\) | |||||||
\(968\) | −3.05915 | −0.0983248 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −4.43247 | −0.142318 | ||||||||
\(971\) | 12.9086 | 0.414256 | 0.207128 | − | 0.978314i | \(-0.433588\pi\) | ||||
0.207128 | + | 0.978314i | \(0.433588\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −11.4659 | −0.367580 | ||||||||
\(974\) | 12.3687 | 0.396319 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 1.62015 | 0.0518599 | ||||||||
\(977\) | −6.73089 | −0.215340 | −0.107670 | − | 0.994187i | \(-0.534339\pi\) | ||||
−0.107670 | + | 0.994187i | \(0.534339\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 8.15358 | 0.260590 | ||||||||
\(980\) | 12.5050 | 0.399457 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −16.9459 | −0.540765 | ||||||||
\(983\) | 3.89460 | 0.124219 | 0.0621093 | − | 0.998069i | \(-0.480217\pi\) | ||||
0.0621093 | + | 0.998069i | \(0.480217\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 29.9396 | 0.953955 | ||||||||
\(986\) | 1.38827 | 0.0442116 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 4.13134 | 0.131435 | ||||||||
\(989\) | −49.1686 | −1.56347 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 47.0696 | 1.49522 | 0.747608 | − | 0.664141i | \(-0.231202\pi\) | ||||
0.747608 | + | 0.664141i | \(0.231202\pi\) | |||||||
\(992\) | 21.5941 | 0.685614 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −16.4428 | −0.521533 | ||||||||
\(995\) | 57.0457 | 1.80847 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −35.0684 | −1.11063 | −0.555314 | − | 0.831641i | \(-0.687402\pi\) | ||||
−0.555314 | + | 0.831641i | \(0.687402\pi\) | |||||||
\(998\) | −33.7154 | −1.06724 | ||||||||
\(999\) | 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 | 6039.2.a.n.1.19 | ✓ | 25 | |
3.2 | odd | 2 | 6039.2.a.o.1.7 | yes | 25 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6039.2.a.n.1.19 | ✓ | 25 | 1.1 | even | 1 | trivial | |
6039.2.a.o.1.7 | yes | 25 | 3.2 | odd | 2 |