Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8004,2,Mod(1,8004)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8004, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("8004.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8004 = 2^{2} \cdot 3 \cdot 23 \cdot 29 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8004.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: | \(63.9122617778\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 3 x^{15} - 49 x^{14} + 130 x^{13} + 932 x^{12} - 2028 x^{11} - 8965 x^{10} + 14400 x^{9} + 46229 x^{8} - 47547 x^{7} - 122604 x^{6} + 65278 x^{5} + 151028 x^{4} + \cdots + 3888 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.13 | ||
Root | \(2.96949\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8004.1 |
$q$-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 | ||||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 2.96949 | 1.32800 | 0.663998 | − | 0.747734i | \(-0.268858\pi\) | ||||
0.663998 | + | 0.747734i | \(0.268858\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −3.61534 | −1.36647 | −0.683236 | − | 0.730198i | \(-0.739428\pi\) | ||||
−0.683236 | + | 0.730198i | \(0.739428\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.51788 | −0.457658 | −0.228829 | − | 0.973467i | \(-0.573490\pi\) | ||||
−0.228829 | + | 0.973467i | \(0.573490\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.595774 | 0.165238 | 0.0826191 | − | 0.996581i | \(-0.473672\pi\) | ||||
0.0826191 | + | 0.996581i | \(0.473672\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 2.96949 | 0.766719 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0.748243 | 0.181476 | 0.0907378 | − | 0.995875i | \(-0.471077\pi\) | ||||
0.0907378 | + | 0.995875i | \(0.471077\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −3.13742 | −0.719773 | −0.359886 | − | 0.932996i | \(-0.617185\pi\) | ||||
−0.359886 | + | 0.932996i | \(0.617185\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −3.61534 | −0.788933 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.00000 | 0.208514 | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 3.81787 | 0.763574 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −1.00000 | −0.185695 | ||||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.50532 | 0.270363 | 0.135182 | − | 0.990821i | \(-0.456838\pi\) | ||||
0.135182 | + | 0.990821i | \(0.456838\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −1.51788 | −0.264229 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −10.7357 | −1.81467 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 3.65707 | 0.601218 | 0.300609 | − | 0.953747i | \(-0.402810\pi\) | ||||
0.300609 | + | 0.953747i | \(0.402810\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0.595774 | 0.0954003 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −0.901553 | −0.140799 | −0.0703995 | − | 0.997519i | \(-0.522427\pi\) | ||||
−0.0703995 | + | 0.997519i | \(0.522427\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −7.23898 | −1.10393 | −0.551967 | − | 0.833866i | \(-0.686123\pi\) | ||||
−0.551967 | + | 0.833866i | \(0.686123\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 2.96949 | 0.442665 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 6.53719 | 0.953547 | 0.476774 | − | 0.879026i | \(-0.341806\pi\) | ||||
0.476774 | + | 0.879026i | \(0.341806\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 6.07071 | 0.867244 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0.748243 | 0.104775 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 11.1195 | 1.52738 | 0.763688 | − | 0.645585i | \(-0.223386\pi\) | ||||
0.763688 | + | 0.645585i | \(0.223386\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −4.50733 | −0.607768 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −3.13742 | −0.415561 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 14.9523 | 1.94662 | 0.973310 | − | 0.229495i | \(-0.0737073\pi\) | ||||
0.973310 | + | 0.229495i | \(0.0737073\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 4.00415 | 0.512679 | 0.256340 | − | 0.966587i | \(-0.417483\pi\) | ||||
0.256340 | + | 0.966587i | \(0.417483\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −3.61534 | −0.455490 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 1.76915 | 0.219436 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 7.19360 | 0.878838 | 0.439419 | − | 0.898282i | \(-0.355184\pi\) | ||||
0.439419 | + | 0.898282i | \(0.355184\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 1.00000 | 0.120386 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 7.23527 | 0.858668 | 0.429334 | − | 0.903146i | \(-0.358748\pi\) | ||||
0.429334 | + | 0.903146i | \(0.358748\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 8.91700 | 1.04366 | 0.521828 | − | 0.853051i | \(-0.325250\pi\) | ||||
0.521828 | + | 0.853051i | \(0.325250\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 3.81787 | 0.440850 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 5.48765 | 0.625376 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 8.63438 | 0.971444 | 0.485722 | − | 0.874113i | \(-0.338557\pi\) | ||||
0.485722 | + | 0.874113i | \(0.338557\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −7.09135 | −0.778377 | −0.389188 | − | 0.921158i | \(-0.627244\pi\) | ||||
−0.389188 | + | 0.921158i | \(0.627244\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 2.22190 | 0.240999 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −1.00000 | −0.107211 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 14.5972 | 1.54730 | 0.773650 | − | 0.633613i | \(-0.218429\pi\) | ||||
0.773650 | + | 0.633613i | \(0.218429\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.15393 | −0.225793 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 1.50532 | 0.156094 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −9.31653 | −0.955856 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −7.05569 | −0.716397 | −0.358199 | − | 0.933645i | \(-0.616609\pi\) | ||||
−0.358199 | + | 0.933645i | \(0.616609\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −1.51788 | −0.152553 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 0.489092 | 0.0486665 | 0.0243332 | − | 0.999704i | \(-0.492254\pi\) | ||||
0.0243332 | + | 0.999704i | \(0.492254\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −7.56907 | −0.745802 | −0.372901 | − | 0.927871i | \(-0.621637\pi\) | ||||
−0.372901 | + | 0.927871i | \(0.621637\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −10.7357 | −1.04770 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −15.9910 | −1.54591 | −0.772956 | − | 0.634460i | \(-0.781223\pi\) | ||||
−0.772956 | + | 0.634460i | \(0.781223\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −5.98769 | −0.573516 | −0.286758 | − | 0.958003i | \(-0.592578\pi\) | ||||
−0.286758 | + | 0.958003i | \(0.592578\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 3.65707 | 0.347114 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 19.5955 | 1.84339 | 0.921696 | − | 0.387912i | \(-0.126804\pi\) | ||||
0.921696 | + | 0.387912i | \(0.126804\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 2.96949 | 0.276906 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0.595774 | 0.0550794 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −2.70516 | −0.247981 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −8.69604 | −0.790549 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −0.901553 | −0.0812903 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −3.51032 | −0.313973 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −0.522271 | −0.0463440 | −0.0231720 | − | 0.999731i | \(-0.507377\pi\) | ||||
−0.0231720 | + | 0.999731i | \(0.507377\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −7.23898 | −0.637357 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 2.62958 | 0.229747 | 0.114874 | − | 0.993380i | \(-0.463354\pi\) | ||||
0.114874 | + | 0.993380i | \(0.463354\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 11.3428 | 0.983549 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 2.96949 | 0.255573 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −6.98816 | −0.597039 | −0.298519 | − | 0.954404i | \(-0.596493\pi\) | ||||
−0.298519 | + | 0.954404i | \(0.596493\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 13.6556 | 1.15825 | 0.579125 | − | 0.815239i | \(-0.303394\pi\) | ||||
0.579125 | + | 0.815239i | \(0.303394\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 6.53719 | 0.550531 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −0.904314 | −0.0756225 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −2.96949 | −0.246603 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 6.07071 | 0.500704 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 22.8048 | 1.86824 | 0.934122 | − | 0.356953i | \(-0.116184\pi\) | ||||
0.934122 | + | 0.356953i | \(0.116184\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 10.8986 | 0.886915 | 0.443458 | − | 0.896295i | \(-0.353752\pi\) | ||||
0.443458 | + | 0.896295i | \(0.353752\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0.748243 | 0.0604919 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 4.47003 | 0.359042 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −11.3841 | −0.908553 | −0.454277 | − | 0.890861i | \(-0.650102\pi\) | ||||
−0.454277 | + | 0.890861i | \(0.650102\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 11.1195 | 0.881831 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −3.61534 | −0.284929 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 9.05790 | 0.709469 | 0.354735 | − | 0.934967i | \(-0.384571\pi\) | ||||
0.354735 | + | 0.934967i | \(0.384571\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −4.50733 | −0.350895 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −0.683362 | −0.0528802 | −0.0264401 | − | 0.999650i | \(-0.508417\pi\) | ||||
−0.0264401 | + | 0.999650i | \(0.508417\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.6451 | −0.972696 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −3.13742 | −0.239924 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 18.5209 | 1.40812 | 0.704058 | − | 0.710142i | \(-0.251369\pi\) | ||||
0.704058 | + | 0.710142i | \(0.251369\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −13.8029 | −1.04340 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 14.9523 | 1.12388 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 15.3322 | 1.14598 | 0.572990 | − | 0.819562i | \(-0.305783\pi\) | ||||
0.572990 | + | 0.819562i | \(0.305783\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 17.8648 | 1.32788 | 0.663940 | − | 0.747786i | \(-0.268883\pi\) | ||||
0.663940 | + | 0.747786i | \(0.268883\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 4.00415 | 0.295996 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 10.8596 | 0.798416 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1.13574 | −0.0830537 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −3.61534 | −0.262978 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 11.9148 | 0.862127 | 0.431063 | − | 0.902322i | \(-0.358139\pi\) | ||||
0.431063 | + | 0.902322i | \(0.358139\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 2.56622 | 0.184721 | 0.0923603 | − | 0.995726i | \(-0.470559\pi\) | ||||
0.0923603 | + | 0.995726i | \(0.470559\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 1.76915 | 0.126691 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 24.1492 | 1.72056 | 0.860280 | − | 0.509823i | \(-0.170289\pi\) | ||||
0.860280 | + | 0.509823i | \(0.170289\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −18.0349 | −1.27846 | −0.639231 | − | 0.769015i | \(-0.720747\pi\) | ||||
−0.639231 | + | 0.769015i | \(0.720747\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 7.19360 | 0.507397 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 3.61534 | 0.253747 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −2.67715 | −0.186981 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 1.00000 | 0.0695048 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 4.76222 | 0.329410 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −24.7157 | −1.70150 | −0.850751 | − | 0.525569i | \(-0.823852\pi\) | ||||
−0.850751 | + | 0.525569i | \(0.823852\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 7.23527 | 0.495752 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −21.4961 | −1.46602 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −5.44225 | −0.369444 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 8.91700 | 0.602555 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0.445784 | 0.0299867 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −18.6236 | −1.24713 | −0.623563 | − | 0.781773i | \(-0.714315\pi\) | ||||
−0.623563 | + | 0.781773i | \(0.714315\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 3.81787 | 0.254525 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −19.2355 | −1.27671 | −0.638354 | − | 0.769743i | \(-0.720384\pi\) | ||||
−0.638354 | + | 0.769743i | \(0.720384\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 19.3237 | 1.27694 | 0.638472 | − | 0.769645i | \(-0.279567\pi\) | ||||
0.638472 | + | 0.769645i | \(0.279567\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 5.48765 | 0.361061 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 6.70768 | 0.439435 | 0.219718 | − | 0.975564i | \(-0.429486\pi\) | ||||
0.219718 | + | 0.975564i | \(0.429486\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 19.4121 | 1.26631 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 8.63438 | 0.560863 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −8.25440 | −0.533933 | −0.266966 | − | 0.963706i | \(-0.586021\pi\) | ||||
−0.266966 | + | 0.963706i | \(0.586021\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 2.59131 | 0.166921 | 0.0834604 | − | 0.996511i | \(-0.473403\pi\) | ||||
0.0834604 | + | 0.996511i | \(0.473403\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 18.0269 | 1.15170 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1.86919 | −0.118934 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −7.09135 | −0.449396 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 13.2452 | 0.836028 | 0.418014 | − | 0.908441i | \(-0.362726\pi\) | ||||
0.418014 | + | 0.908441i | \(0.362726\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1.51788 | −0.0954282 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 2.22190 | 0.139141 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 18.4842 | 1.15301 | 0.576505 | − | 0.817094i | \(-0.304416\pi\) | ||||
0.576505 | + | 0.817094i | \(0.304416\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −13.2216 | −0.821548 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1.00000 | −0.0618984 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −17.5161 | −1.08009 | −0.540044 | − | 0.841637i | \(-0.681592\pi\) | ||||
−0.540044 | + | 0.841637i | \(0.681592\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 33.0192 | 2.02835 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 14.5972 | 0.893334 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −12.9857 | −0.791754 | −0.395877 | − | 0.918303i | \(-0.629559\pi\) | ||||
−0.395877 | + | 0.918303i | \(0.629559\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −3.97009 | −0.241166 | −0.120583 | − | 0.992703i | \(-0.538476\pi\) | ||||
−0.120583 | + | 0.992703i | \(0.538476\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −2.15393 | −0.130362 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −5.79507 | −0.349456 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −23.8848 | −1.43510 | −0.717549 | − | 0.696508i | \(-0.754736\pi\) | ||||
−0.717549 | + | 0.696508i | \(0.754736\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 1.50532 | 0.0901211 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −26.7422 | −1.59531 | −0.797654 | − | 0.603115i | \(-0.793926\pi\) | ||||
−0.797654 | + | 0.603115i | \(0.793926\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 16.1073 | 0.957480 | 0.478740 | − | 0.877957i | \(-0.341094\pi\) | ||||
0.478740 | + | 0.877957i | \(0.341094\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −9.31653 | −0.551863 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 3.25943 | 0.192398 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.4401 | −0.967067 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −7.05569 | −0.413612 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −16.4362 | −0.960215 | −0.480107 | − | 0.877210i | \(-0.659402\pi\) | ||||
−0.480107 | + | 0.877210i | \(0.659402\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 44.4006 | 2.58510 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −1.51788 | −0.0880763 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0.595774 | 0.0344545 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 26.1714 | 1.50849 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0.489092 | 0.0280976 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 11.8903 | 0.680836 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −11.2107 | −0.639827 | −0.319914 | − | 0.947447i | \(-0.603654\pi\) | ||||
−0.319914 | + | 0.947447i | \(0.603654\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −7.56907 | −0.430589 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 25.7748 | 1.46156 | 0.730779 | − | 0.682614i | \(-0.239157\pi\) | ||||
0.730779 | + | 0.682614i | \(0.239157\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 14.0344 | 0.793272 | 0.396636 | − | 0.917976i | \(-0.370178\pi\) | ||||
0.396636 | + | 0.917976i | \(0.370178\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −10.7357 | −0.604890 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 23.8531 | 1.33972 | 0.669862 | − | 0.742485i | \(-0.266353\pi\) | ||||
0.669862 | + | 0.742485i | \(0.266353\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1.51788 | 0.0849849 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −15.9910 | −0.892533 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −2.34755 | −0.130621 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 2.27459 | 0.126172 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −5.98769 | −0.331120 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −23.6342 | −1.30299 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −18.1473 | −0.997463 | −0.498732 | − | 0.866756i | \(-0.666201\pi\) | ||||
−0.498732 | + | 0.866756i | \(0.666201\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 3.65707 | 0.200406 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 21.3613 | 1.16709 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 10.9981 | 0.599107 | 0.299554 | − | 0.954079i | \(-0.403162\pi\) | ||||
0.299554 | + | 0.954079i | \(0.403162\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 19.5955 | 1.06428 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −2.28489 | −0.123734 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 3.35971 | 0.181407 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 2.96949 | 0.159872 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −13.9639 | −0.749621 | −0.374810 | − | 0.927101i | \(-0.622292\pi\) | ||||
−0.374810 | + | 0.927101i | \(0.622292\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −32.6420 | −1.74729 | −0.873643 | − | 0.486568i | \(-0.838249\pi\) | ||||
−0.873643 | + | 0.486568i | \(0.838249\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0.595774 | 0.0318001 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 9.20185 | 0.489765 | 0.244883 | − | 0.969553i | \(-0.421251\pi\) | ||||
0.244883 | + | 0.969553i | \(0.421251\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 21.4851 | 1.14031 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −2.70516 | −0.143172 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 19.7939 | 1.04468 | 0.522340 | − | 0.852737i | \(-0.325059\pi\) | ||||
0.522340 | + | 0.852737i | \(0.325059\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −9.15662 | −0.481927 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −8.69604 | −0.456424 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 26.4789 | 1.38597 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −37.4361 | −1.95415 | −0.977074 | − | 0.212900i | \(-0.931709\pi\) | ||||
−0.977074 | + | 0.212900i | \(0.931709\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −0.901553 | −0.0469330 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −40.2007 | −2.08712 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 5.28532 | 0.273664 | 0.136832 | − | 0.990594i | \(-0.456308\pi\) | ||||
0.136832 | + | 0.990594i | \(0.456308\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −3.51032 | −0.181272 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −0.595774 | −0.0306839 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −8.48940 | −0.436071 | −0.218036 | − | 0.975941i | \(-0.569965\pi\) | ||||
−0.218036 | + | 0.975941i | \(0.569965\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −0.522271 | −0.0267567 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −30.8141 | −1.57453 | −0.787263 | − | 0.616618i | \(-0.788502\pi\) | ||||
−0.787263 | + | 0.616618i | \(0.788502\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 16.2955 | 0.830497 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −7.23898 | −0.367978 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −25.1893 | −1.27715 | −0.638573 | − | 0.769561i | \(-0.720475\pi\) | ||||
−0.638573 | + | 0.769561i | \(0.720475\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0.748243 | 0.0378403 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 2.62958 | 0.132645 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 25.6397 | 1.29007 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 3.19320 | 0.160262 | 0.0801311 | − | 0.996784i | \(-0.474466\pi\) | ||||
0.0801311 | + | 0.996784i | \(0.474466\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 11.3428 | 0.567852 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 21.8365 | 1.09047 | 0.545233 | − | 0.838285i | \(-0.316441\pi\) | ||||
0.545233 | + | 0.838285i | \(0.316441\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0.896831 | 0.0446743 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 2.96949 | 0.147555 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −5.55099 | −0.275152 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 27.4123 | 1.35545 | 0.677726 | − | 0.735315i | \(-0.262966\pi\) | ||||
0.677726 | + | 0.735315i | \(0.262966\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −6.98816 | −0.344700 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −54.0576 | −2.66000 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −21.0577 | −1.03368 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 13.6556 | 0.668716 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −35.6782 | −1.74299 | −0.871497 | − | 0.490400i | \(-0.836851\pi\) | ||||
−0.871497 | + | 0.490400i | \(0.836851\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 35.1282 | 1.71205 | 0.856023 | − | 0.516939i | \(-0.172928\pi\) | ||||
0.856023 | + | 0.516939i | \(0.172928\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 6.53719 | 0.317849 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 2.85670 | 0.138570 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −14.4764 | −0.700562 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −0.904314 | −0.0436607 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −31.1086 | −1.49845 | −0.749224 | − | 0.662317i | \(-0.769573\pi\) | ||||
−0.749224 | + | 0.662317i | \(0.769573\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 26.3963 | 1.26852 | 0.634262 | − | 0.773118i | \(-0.281304\pi\) | ||||
0.634262 | + | 0.773118i | \(0.281304\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −2.96949 | −0.142376 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −3.13742 | −0.150083 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 10.4597 | 0.499212 | 0.249606 | − | 0.968347i | \(-0.419699\pi\) | ||||
0.249606 | + | 0.968347i | \(0.419699\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 6.07071 | 0.289081 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 10.5558 | 0.501521 | 0.250760 | − | 0.968049i | \(-0.419319\pi\) | ||||
0.250760 | + | 0.968049i | \(0.419319\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 43.3462 | 2.05481 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 22.8048 | 1.07863 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −20.8975 | −0.986212 | −0.493106 | − | 0.869969i | \(-0.664139\pi\) | ||||
−0.493106 | + | 0.869969i | \(0.664139\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.36845 | 0.0644378 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 10.8986 | 0.512061 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −6.39607 | −0.299852 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 31.4248 | 1.46999 | 0.734996 | − | 0.678071i | \(-0.237184\pi\) | ||||
0.734996 | + | 0.678071i | \(0.237184\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0.748243 | 0.0349250 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 33.5817 | 1.56406 | 0.782028 | − | 0.623243i | \(-0.214185\pi\) | ||||
0.782028 | + | 0.623243i | \(0.214185\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −7.03132 | −0.326773 | −0.163387 | − | 0.986562i | \(-0.552242\pi\) | ||||
−0.163387 | + | 0.986562i | \(0.552242\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 4.47003 | 0.207293 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 28.1474 | 1.30250 | 0.651252 | − | 0.758861i | \(-0.274244\pi\) | ||||
0.651252 | + | 0.758861i | \(0.274244\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −26.0073 | −1.20091 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −11.3841 | −0.524554 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 10.9879 | 0.505224 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −11.9783 | −0.549600 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 11.1195 | 0.509126 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −0.674384 | −0.0308134 | −0.0154067 | − | 0.999881i | \(-0.504904\pi\) | ||||
−0.0154067 | + | 0.999881i | \(0.504904\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 2.17879 | 0.0993442 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −3.61534 | −0.164504 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −20.9518 | −0.951373 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 3.35339 | 0.151957 | 0.0759783 | − | 0.997109i | \(-0.475792\pi\) | ||||
0.0759783 | + | 0.997109i | \(0.475792\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 9.05790 | 0.409612 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −8.13220 | −0.367001 | −0.183501 | − | 0.983020i | \(-0.558743\pi\) | ||||
−0.183501 | + | 0.983020i | \(0.558743\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −0.748243 | −0.0336992 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −4.50733 | −0.202589 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −26.1580 | −1.17335 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 20.1591 | 0.902447 | 0.451224 | − | 0.892411i | \(-0.350988\pi\) | ||||
0.451224 | + | 0.892411i | \(0.350988\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −0.683362 | −0.0305304 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −7.03823 | −0.313819 | −0.156910 | − | 0.987613i | \(-0.550153\pi\) | ||||
−0.156910 | + | 0.987613i | \(0.550153\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 1.45235 | 0.0646289 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −12.6451 | −0.561587 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 1.35598 | 0.0601029 | 0.0300514 | − | 0.999548i | \(-0.490433\pi\) | ||||
0.0300514 | + | 0.999548i | \(0.490433\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −32.2380 | −1.42613 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −3.13742 | −0.138520 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −22.4763 | −0.990423 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −9.92266 | −0.436398 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 18.5209 | 0.812977 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −38.3386 | −1.67964 | −0.839821 | − | 0.542863i | \(-0.817340\pi\) | ||||
−0.839821 | + | 0.542863i | \(0.817340\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 41.8322 | 1.82919 | 0.914597 | − | 0.404367i | \(-0.132508\pi\) | ||||
0.914597 | + | 0.404367i | \(0.132508\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −13.8029 | −0.602409 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 1.12635 | 0.0490644 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 14.9523 | 0.648873 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −0.537123 | −0.0232654 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −47.4852 | −2.05297 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 15.3322 | 0.661632 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −9.21460 | −0.396901 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −1.04015 | −0.0447197 | −0.0223599 | − | 0.999750i | \(-0.507118\pi\) | ||||
−0.0223599 | + | 0.999750i | \(0.507118\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 17.8648 | 0.766652 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −17.7804 | −0.761628 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 14.0370 | 0.600178 | 0.300089 | − | 0.953911i | \(-0.402984\pi\) | ||||
0.300089 | + | 0.953911i | \(0.402984\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 4.00415 | 0.170893 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 3.13742 | 0.133658 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −31.2163 | −1.32745 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 10.8596 | 0.460966 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 5.83425 | 0.247205 | 0.123603 | − | 0.992332i | \(-0.460555\pi\) | ||||
0.123603 | + | 0.992332i | \(0.460555\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −4.31280 | −0.182412 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −1.13574 | −0.0479511 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −1.56991 | −0.0661639 | −0.0330820 | − | 0.999453i | \(-0.510532\pi\) | ||||
−0.0330820 | + | 0.999453i | \(0.510532\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 58.1887 | 2.44802 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −3.61534 | −0.151830 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −3.71444 | −0.155717 | −0.0778587 | − | 0.996964i | \(-0.524808\pi\) | ||||
−0.0778587 | + | 0.996964i | \(0.524808\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −17.2059 | −0.720044 | −0.360022 | − | 0.932944i | \(-0.617231\pi\) | ||||
−0.360022 | + | 0.932944i | \(0.617231\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 11.9148 | 0.497749 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 3.81787 | 0.159216 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −14.4600 | −0.601979 | −0.300990 | − | 0.953627i | \(-0.597317\pi\) | ||||
−0.300990 | + | 0.953627i | \(0.597317\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 2.56622 | 0.106649 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 25.6377 | 1.06363 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −16.8780 | −0.699016 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 1.76915 | 0.0731452 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −12.2038 | −0.503704 | −0.251852 | − | 0.967766i | \(-0.581040\pi\) | ||||
−0.251852 | + | 0.967766i | \(0.581040\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −4.72281 | −0.194600 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 24.1492 | 0.993365 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 4.93531 | 0.202669 | 0.101334 | − | 0.994852i | \(-0.467689\pi\) | ||||
0.101334 | + | 0.994852i | \(0.467689\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −8.03294 | −0.329318 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −18.0349 | −0.738121 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −7.75551 | −0.316881 | −0.158441 | − | 0.987368i | \(-0.550647\pi\) | ||||
−0.158441 | + | 0.987368i | \(0.550647\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 2.38433 | 0.0972589 | 0.0486295 | − | 0.998817i | \(-0.484515\pi\) | ||||
0.0486295 | + | 0.998817i | \(0.484515\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 7.19360 | 0.292946 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −25.8228 | −1.04985 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 37.4722 | 1.52095 | 0.760475 | − | 0.649367i | \(-0.224966\pi\) | ||||
0.760475 | + | 0.649367i | \(0.224966\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 3.61534 | 0.146501 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 3.89469 | 0.157562 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −36.0966 | −1.45793 | −0.728965 | − | 0.684551i | \(-0.759998\pi\) | ||||
−0.728965 | + | 0.684551i | \(0.759998\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −2.67715 | −0.107953 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 19.7814 | 0.796370 | 0.398185 | − | 0.917305i | \(-0.369640\pi\) | ||||
0.398185 | + | 0.917305i | \(0.369640\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 3.42660 | 0.137727 | 0.0688633 | − | 0.997626i | \(-0.478063\pi\) | ||||
0.0688633 | + | 0.997626i | \(0.478063\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.00000 | 0.0401286 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −52.7739 | −2.11434 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −29.5132 | −1.18053 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 4.76222 | 0.190185 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 2.73638 | 0.109107 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −6.82247 | −0.271598 | −0.135799 | − | 0.990736i | \(-0.543360\pi\) | ||||
−0.135799 | + | 0.990736i | \(0.543360\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −24.7157 | −0.982363 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −1.55088 | −0.0615447 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 3.61677 | 0.143302 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 7.23527 | 0.286223 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −47.5579 | −1.87842 | −0.939212 | − | 0.343337i | \(-0.888443\pi\) | ||||
−0.939212 | + | 0.343337i | \(0.888443\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −4.07286 | −0.160618 | −0.0803090 | − | 0.996770i | \(-0.525591\pi\) | ||||
−0.0803090 | + | 0.996770i | \(0.525591\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −21.4961 | −0.846407 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 6.44068 | 0.253209 | 0.126605 | − | 0.991953i | \(-0.459592\pi\) | ||||
0.126605 | + | 0.991953i | \(0.459592\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −22.6957 | −0.890886 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −5.44225 | −0.213298 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 19.4753 | 0.762128 | 0.381064 | − | 0.924549i | \(-0.375558\pi\) | ||||
0.381064 | + | 0.924549i | \(0.375558\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 7.80851 | 0.305104 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 8.91700 | 0.347885 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −2.19761 | −0.0856068 | −0.0428034 | − | 0.999084i | \(-0.513629\pi\) | ||||
−0.0428034 | + | 0.999084i | \(0.513629\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −49.2488 | −1.91556 | −0.957778 | − | 0.287509i | \(-0.907173\pi\) | ||||
−0.957778 | + | 0.287509i | \(0.907173\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0.445784 | 0.0173128 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 33.6824 | 1.30615 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1.00000 | −0.0387202 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −18.6236 | −0.720028 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −6.07782 | −0.234632 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 10.9216 | 0.420999 | 0.210499 | − | 0.977594i | \(-0.432491\pi\) | ||||
0.210499 | + | 0.977594i | \(0.432491\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 3.81787 | 0.146950 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −38.2241 | −1.46907 | −0.734535 | − | 0.678571i | \(-0.762600\pi\) | ||||
−0.734535 | + | 0.678571i | \(0.762600\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 25.5088 | 0.978936 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −19.2355 | −0.737108 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 5.44797 | 0.208461 | 0.104230 | − | 0.994553i | \(-0.466762\pi\) | ||||
0.104230 | + | 0.994553i | \(0.466762\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −20.7513 | −0.792865 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 19.3237 | 0.737244 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 6.62470 | 0.252381 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −37.7948 | −1.43778 | −0.718890 | − | 0.695123i | \(-0.755350\pi\) | ||||
−0.718890 | + | 0.695123i | \(0.755350\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 5.48765 | 0.208459 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 40.5501 | 1.53815 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −0.674581 | −0.0255516 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 6.70768 | 0.253708 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 26.7296 | 1.00956 | 0.504782 | − | 0.863247i | \(-0.331573\pi\) | ||||
0.504782 | + | 0.863247i | \(0.331573\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −11.4737 | −0.432741 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 19.4121 | 0.731103 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −1.76824 | −0.0665013 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −11.5893 | −0.435244 | −0.217622 | − | 0.976033i | \(-0.569830\pi\) | ||||
−0.217622 | + | 0.976033i | \(0.569830\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 8.63438 | 0.323815 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 1.50532 | 0.0563747 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −2.68535 | −0.100426 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −8.25440 | −0.308266 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 26.3213 | 0.981618 | 0.490809 | − | 0.871267i | \(-0.336701\pi\) | ||||
0.490809 | + | 0.871267i | \(0.336701\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 27.3648 | 1.01912 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 2.59131 | 0.0963718 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −3.81787 | −0.141792 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 26.5364 | 0.984179 | 0.492090 | − | 0.870545i | \(-0.336233\pi\) | ||||
0.492090 | + | 0.870545i | \(0.336233\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −5.41652 | −0.200337 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −33.8396 | −1.24989 | −0.624946 | − | 0.780668i | \(-0.714879\pi\) | ||||
−0.624946 | + | 0.780668i | \(0.714879\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 18.0269 | 0.664932 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −10.9190 | −0.402207 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 9.65004 | 0.354983 | 0.177491 | − | 0.984122i | \(-0.443202\pi\) | ||||
0.177491 | + | 0.984122i | \(0.443202\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −1.86919 | −0.0686665 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −33.3923 | −1.22505 | −0.612523 | − | 0.790453i | \(-0.709845\pi\) | ||||
−0.612523 | + | 0.790453i | \(0.709845\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 67.7187 | 2.48102 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −7.09135 | −0.259459 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 57.8131 | 2.11244 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −13.0629 | −0.476673 | −0.238336 | − | 0.971183i | \(-0.576602\pi\) | ||||
−0.238336 | + | 0.971183i | \(0.576602\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 13.2452 | 0.482681 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 32.3633 | 1.17782 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 12.7202 | 0.462323 | 0.231162 | − | 0.972915i | \(-0.425747\pi\) | ||||
0.231162 | + | 0.972915i | \(0.425747\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −1.51788 | −0.0550955 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 8.96963 | 0.325149 | 0.162574 | − | 0.986696i | \(-0.448020\pi\) | ||||
0.162574 | + | 0.986696i | \(0.448020\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 21.6475 | 0.783694 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 2.22190 | 0.0803330 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 8.90818 | 0.321656 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 46.1450 | 1.66403 | 0.832015 | − | 0.554753i | \(-0.187187\pi\) | ||||
0.832015 | + | 0.554753i | \(0.187187\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 18.4842 | 0.665690 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −12.9246 | −0.464866 | −0.232433 | − | 0.972612i | \(-0.574669\pi\) | ||||
−0.232433 | + | 0.972612i | \(0.574669\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 5.74712 | 0.206443 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −13.2216 | −0.474321 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 2.82855 | 0.101343 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −10.9823 | −0.392976 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −1.00000 | −0.0357371 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −33.8051 | −1.20656 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 34.2016 | 1.21916 | 0.609578 | − | 0.792726i | \(-0.291339\pi\) | ||||
0.609578 | + | 0.792726i | \(0.291339\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −17.5161 | −0.623589 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −70.8446 | −2.51894 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 2.38557 | 0.0847142 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 33.0192 | 1.17107 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −2.29771 | −0.0813892 | −0.0406946 | − | 0.999172i | \(-0.512957\pi\) | ||||
−0.0406946 | + | 0.999172i | \(0.512957\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 4.89141 | 0.173046 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 14.5972 | 0.515767 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −13.5349 | −0.477637 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −10.7357 | −0.378385 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −12.9857 | −0.457120 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 25.8336 | 0.908263 | 0.454131 | − | 0.890935i | \(-0.349950\pi\) | ||||
0.454131 | + | 0.890935i | \(0.349950\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 47.3390 | 1.66230 | 0.831148 | − | 0.556051i | \(-0.187684\pi\) | ||||
0.831148 | + | 0.556051i | \(0.187684\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −3.97009 | −0.139237 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 26.8973 | 0.942173 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 22.7117 | 0.794582 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −2.15393 | −0.0752644 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −26.8013 | −0.935370 | −0.467685 | − | 0.883895i | \(-0.654912\pi\) | ||||
−0.467685 | + | 0.883895i | \(0.654912\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 39.6268 | 1.38130 | 0.690651 | − | 0.723188i | \(-0.257324\pi\) | ||||
0.690651 | + | 0.723188i | \(0.257324\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −5.79507 | −0.201758 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 11.2693 | 0.391873 | 0.195936 | − | 0.980617i | \(-0.437225\pi\) | ||||
0.195936 | + | 0.980617i | \(0.437225\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −16.4640 | −0.571818 | −0.285909 | − | 0.958257i | \(-0.592295\pi\) | ||||
−0.285909 | + | 0.958257i | \(0.592295\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −23.8848 | −0.828555 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 4.54237 | 0.157384 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −2.02924 | −0.0702246 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 1.50532 | 0.0520315 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −9.94977 | −0.343504 | −0.171752 | − | 0.985140i | \(-0.554943\pi\) | ||||
−0.171752 | + | 0.985140i | \(0.554943\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.00000 | 0.0344828 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −26.7422 | −0.921051 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −37.5494 | −1.29174 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 31.4392 | 1.08026 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 16.1073 | 0.552801 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 3.65707 | 0.125363 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −26.2812 | −0.899850 | −0.449925 | − | 0.893066i | \(-0.648549\pi\) | ||||
−0.449925 | + | 0.893066i | \(0.648549\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −9.31653 | −0.318619 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −28.6513 | −0.978708 | −0.489354 | − | 0.872085i | \(-0.662767\pi\) | ||||
−0.489354 | + | 0.872085i | \(0.662767\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 32.0376 | 1.09311 | 0.546555 | − | 0.837423i | \(-0.315939\pi\) | ||||
0.546555 | + | 0.837423i | \(0.315939\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 3.25943 | 0.111081 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 2.20860 | 0.0751816 | 0.0375908 | − | 0.999293i | \(-0.488032\pi\) | ||||
0.0375908 | + | 0.999293i | \(0.488032\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 54.9976 | 1.86997 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −16.4401 | −0.558336 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −13.1059 | −0.444589 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 4.28576 | 0.145218 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −7.05569 | −0.238799 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 12.6910 | 0.429035 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 4.99989 | 0.168834 | 0.0844172 | − | 0.996430i | \(-0.473097\pi\) | ||||
0.0844172 | + | 0.996430i | \(0.473097\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −16.4362 | −0.554380 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −16.5006 | −0.555921 | −0.277960 | − | 0.960593i | \(-0.589658\pi\) | ||||
−0.277960 | + | 0.960593i | \(0.589658\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 5.44352 | 0.183189 | 0.0915944 | − | 0.995796i | \(-0.470804\pi\) | ||||
0.0915944 | + | 0.995796i | \(0.470804\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 44.4006 | 1.49251 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −28.3234 | −0.951007 | −0.475503 | − | 0.879714i | \(-0.657734\pi\) | ||||
−0.475503 | + | 0.879714i | \(0.657734\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.88819 | 0.0633278 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1.51788 | −0.0508509 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −20.5099 | −0.686337 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 45.5288 | 1.52186 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0.595774 | 0.0198923 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −1.50532 | −0.0502052 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 8.32007 | 0.277182 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 26.1714 | 0.870930 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 53.0493 | 1.76342 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 56.7963 | 1.88589 | 0.942945 | − | 0.332947i | \(-0.108043\pi\) | ||||
0.942945 | + | 0.332947i | \(0.108043\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0.489092 | 0.0162222 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −5.50129 | −0.182266 | −0.0911329 | − | 0.995839i | \(-0.529049\pi\) | ||||
−0.0911329 | + | 0.995839i | \(0.529049\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 10.7638 | 0.356230 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 11.8903 | 0.393081 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −9.50683 | −0.313943 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −13.7290 | −0.452878 | −0.226439 | − | 0.974025i | \(-0.572708\pi\) | ||||
−0.226439 | + | 0.974025i | \(0.572708\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −11.2107 | −0.369404 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 4.31059 | 0.141885 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 13.9622 | 0.459075 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −7.56907 | −0.248601 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 49.5234 | 1.62481 | 0.812406 | − | 0.583093i | \(-0.198158\pi\) | ||||
0.812406 | + | 0.583093i | \(0.198158\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −19.0463 | −0.624219 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 25.7748 | 0.843831 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −3.37258 | −0.110295 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −11.2506 | −0.367541 | −0.183771 | − | 0.982969i | \(-0.558830\pi\) | ||||
−0.183771 | + | 0.982969i | \(0.558830\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 14.0344 | 0.457996 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −26.2221 | −0.854816 | −0.427408 | − | 0.904059i | \(-0.640573\pi\) | ||||
−0.427408 | + | 0.904059i | \(0.640573\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −0.901553 | −0.0293586 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −10.7357 | −0.349233 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −17.2120 | −0.559315 | −0.279657 | − | 0.960100i | \(-0.590221\pi\) | ||||
−0.279657 | + | 0.960100i | \(0.590221\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 5.31252 | 0.172452 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 23.8531 | 0.773490 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −9.18539 | −0.297544 | −0.148772 | − | 0.988872i | \(-0.547532\pi\) | ||||
−0.148772 | + | 0.988872i | \(0.547532\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 35.3810 | 1.14490 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 1.51788 | 0.0490661 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 25.2646 | 0.815836 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −28.7340 | −0.926904 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −15.9910 | −0.515304 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 7.62037 | 0.245308 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1.33968 | 0.0430813 | 0.0215407 | − | 0.999768i | \(-0.493143\pi\) | ||||
0.0215407 | + | 0.999768i | \(0.493143\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −2.34755 | −0.0754142 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −22.3694 | −0.717868 | −0.358934 | − | 0.933363i | \(-0.616860\pi\) | ||||
−0.358934 | + | 0.933363i | \(0.616860\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −49.3696 | −1.58272 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 2.27459 | 0.0728452 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 16.4507 | 0.526303 | 0.263151 | − | 0.964755i | \(-0.415238\pi\) | ||||
0.263151 | + | 0.964755i | \(0.415238\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −22.1568 | −0.708134 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −5.98769 | −0.191172 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −4.90684 | −0.156504 | −0.0782519 | − | 0.996934i | \(-0.524934\pi\) | ||||
−0.0782519 | + | 0.996934i | \(0.524934\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 71.7108 | 2.28490 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −23.6342 | −0.752284 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −7.23898 | −0.230186 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 34.4570 | 1.09456 | 0.547282 | − | 0.836948i | \(-0.315663\pi\) | ||||
0.547282 | + | 0.836948i | \(0.315663\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −18.1473 | −0.575886 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −53.5546 | −1.69779 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 41.1311 | 1.30264 | 0.651318 | − | 0.758805i | \(-0.274217\pi\) | ||||
0.651318 | + | 0.758805i | \(0.274217\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 3.65707 | 0.115705 |
(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 | 8004.2.a.j.1.13 | ✓ | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8004.2.a.j.1.13 | ✓ | 16 | 1.1 | even | 1 | trivial |