Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6032,2,Mod(1,6032)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6032, 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("6032.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6032 = 2^{4} \cdot 13 \cdot 29 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6032.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: | \(48.1657624992\) |
Analytic rank: | \(1\) |
Dimension: | \(10\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} - 3x^{9} - 17x^{8} + 47x^{7} + 104x^{6} - 235x^{5} - 283x^{4} + 364x^{3} + 330x^{2} + 12x - 8 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 3016) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.8 | ||
Root | \(-1.58994\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6032.1 |
$q$-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 | ||||||||
\(3\) | 1.58994 | 0.917953 | 0.458976 | − | 0.888448i | \(-0.348216\pi\) | ||||
0.458976 | + | 0.888448i | \(0.348216\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 3.10645 | 1.38925 | 0.694623 | − | 0.719374i | \(-0.255571\pi\) | ||||
0.694623 | + | 0.719374i | \(0.255571\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.36044 | −0.892163 | −0.446081 | − | 0.894992i | \(-0.647181\pi\) | ||||
−0.446081 | + | 0.894992i | \(0.647181\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −0.472088 | −0.157363 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.816398 | 0.246153 | 0.123077 | − | 0.992397i | \(-0.460724\pi\) | ||||
0.123077 | + | 0.992397i | \(0.460724\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.00000 | −0.277350 | ||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 4.93907 | 1.27526 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −3.91558 | −0.949667 | −0.474834 | − | 0.880076i | \(-0.657492\pi\) | ||||
−0.474834 | + | 0.880076i | \(0.657492\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −3.83032 | −0.878736 | −0.439368 | − | 0.898307i | \(-0.644798\pi\) | ||||
−0.439368 | + | 0.898307i | \(0.644798\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −3.75296 | −0.818963 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0.187045 | 0.0390016 | 0.0195008 | − | 0.999810i | \(-0.493792\pi\) | ||||
0.0195008 | + | 0.999810i | \(0.493792\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 4.65003 | 0.930006 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −5.52041 | −1.06240 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −1.00000 | −0.185695 | ||||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −5.86942 | −1.05418 | −0.527089 | − | 0.849810i | \(-0.676717\pi\) | ||||
−0.527089 | + | 0.849810i | \(0.676717\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 1.29802 | 0.225957 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −7.33259 | −1.23943 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −3.70681 | −0.609395 | −0.304698 | − | 0.952449i | \(-0.598555\pi\) | ||||
−0.304698 | + | 0.952449i | \(0.598555\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −1.58994 | −0.254594 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 6.03084 | 0.941859 | 0.470929 | − | 0.882171i | \(-0.343919\pi\) | ||||
0.470929 | + | 0.882171i | \(0.343919\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −7.79773 | −1.18914 | −0.594571 | − | 0.804043i | \(-0.702678\pi\) | ||||
−0.594571 | + | 0.804043i | \(0.702678\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.46652 | −0.218616 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −12.8759 | −1.87815 | −0.939075 | − | 0.343714i | \(-0.888315\pi\) | ||||
−0.939075 | + | 0.343714i | \(0.888315\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.42832 | −0.204046 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −6.22554 | −0.871750 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0.553149 | 0.0759808 | 0.0379904 | − | 0.999278i | \(-0.487904\pi\) | ||||
0.0379904 | + | 0.999278i | \(0.487904\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 2.53610 | 0.341968 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −6.08998 | −0.806638 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −1.22849 | −0.159936 | −0.0799679 | − | 0.996797i | \(-0.525482\pi\) | ||||
−0.0799679 | + | 0.996797i | \(0.525482\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0.251767 | 0.0322354 | 0.0161177 | − | 0.999870i | \(-0.494869\pi\) | ||||
0.0161177 | + | 0.999870i | \(0.494869\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 1.11434 | 0.140393 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −3.10645 | −0.385308 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 12.9180 | 1.57818 | 0.789091 | − | 0.614276i | \(-0.210552\pi\) | ||||
0.789091 | + | 0.614276i | \(0.210552\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0.297391 | 0.0358016 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −4.57668 | −0.543151 | −0.271576 | − | 0.962417i | \(-0.587545\pi\) | ||||
−0.271576 | + | 0.962417i | \(0.587545\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 3.62147 | 0.423861 | 0.211931 | − | 0.977285i | \(-0.432025\pi\) | ||||
0.211931 | + | 0.977285i | \(0.432025\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 7.39327 | 0.853701 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −1.92706 | −0.219609 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 7.07472 | 0.795968 | 0.397984 | − | 0.917392i | \(-0.369710\pi\) | ||||
0.397984 | + | 0.917392i | \(0.369710\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −7.36087 | −0.817874 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −12.6738 | −1.39113 | −0.695564 | − | 0.718464i | \(-0.744845\pi\) | ||||
−0.695564 | + | 0.718464i | \(0.744845\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −12.1635 | −1.31932 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −1.58994 | −0.170460 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 7.27356 | 0.770996 | 0.385498 | − | 0.922709i | \(-0.374030\pi\) | ||||
0.385498 | + | 0.922709i | \(0.374030\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.36044 | 0.247441 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −9.33202 | −0.967686 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −11.8987 | −1.22078 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −7.35022 | −0.746302 | −0.373151 | − | 0.927771i | \(-0.621723\pi\) | ||||
−0.373151 | + | 0.927771i | \(0.621723\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −0.385412 | −0.0387353 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 10.5242 | 1.04720 | 0.523598 | − | 0.851965i | \(-0.324589\pi\) | ||||
0.523598 | + | 0.851965i | \(0.324589\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −0.249989 | −0.0246322 | −0.0123161 | − | 0.999924i | \(-0.503920\pi\) | ||||
−0.0123161 | + | 0.999924i | \(0.503920\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −11.6584 | −1.13774 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 8.88422 | 0.858870 | 0.429435 | − | 0.903098i | \(-0.358713\pi\) | ||||
0.429435 | + | 0.903098i | \(0.358713\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 6.40079 | 0.613085 | 0.306542 | − | 0.951857i | \(-0.400828\pi\) | ||||
0.306542 | + | 0.951857i | \(0.400828\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −5.89360 | −0.559396 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 3.52842 | 0.331925 | 0.165963 | − | 0.986132i | \(-0.446927\pi\) | ||||
0.165963 | + | 0.986132i | \(0.446927\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0.581046 | 0.0541828 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0.472088 | 0.0436446 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 9.24249 | 0.847258 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.3335 | −0.939409 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 9.58867 | 0.864582 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1.08717 | −0.0972391 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −13.4823 | −1.19636 | −0.598178 | − | 0.801363i | \(-0.704108\pi\) | ||||
−0.598178 | + | 0.801363i | \(0.704108\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −12.3979 | −1.09158 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 10.4241 | 0.910760 | 0.455380 | − | 0.890297i | \(-0.349503\pi\) | ||||
0.455380 | + | 0.890297i | \(0.349503\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 9.04125 | 0.783975 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −17.1489 | −1.47594 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −11.3018 | −0.965575 | −0.482788 | − | 0.875737i | \(-0.660376\pi\) | ||||
−0.482788 | + | 0.875737i | \(0.660376\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −22.4425 | −1.90355 | −0.951774 | − | 0.306799i | \(-0.900742\pi\) | ||||
−0.951774 | + | 0.306799i | \(0.900742\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −20.4720 | −1.72405 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −0.816398 | −0.0682706 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −3.10645 | −0.257977 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −2.27095 | −0.187304 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 17.7352 | 1.45293 | 0.726463 | − | 0.687206i | \(-0.241163\pi\) | ||||
0.726463 | + | 0.687206i | \(0.241163\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 5.73675 | 0.466850 | 0.233425 | − | 0.972375i | \(-0.425007\pi\) | ||||
0.233425 | + | 0.972375i | \(0.425007\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 1.84850 | 0.149442 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −18.2330 | −1.46451 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 11.6950 | 0.933364 | 0.466682 | − | 0.884425i | \(-0.345449\pi\) | ||||
0.466682 | + | 0.884425i | \(0.345449\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0.879474 | 0.0697468 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −0.441509 | −0.0347958 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 10.7803 | 0.844376 | 0.422188 | − | 0.906508i | \(-0.361262\pi\) | ||||
0.422188 | + | 0.906508i | \(0.361262\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 4.03225 | 0.313910 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −22.0165 | −1.70369 | −0.851845 | − | 0.523794i | \(-0.824516\pi\) | ||||
−0.851845 | + | 0.523794i | \(0.824516\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1.80825 | 0.138280 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −11.0552 | −0.840510 | −0.420255 | − | 0.907406i | \(-0.638059\pi\) | ||||
−0.420255 | + | 0.907406i | \(0.638059\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −10.9761 | −0.829716 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −1.95323 | −0.146813 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −8.83680 | −0.660493 | −0.330247 | − | 0.943895i | \(-0.607132\pi\) | ||||
−0.330247 | + | 0.943895i | \(0.607132\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 22.6553 | 1.68395 | 0.841976 | − | 0.539515i | \(-0.181392\pi\) | ||||
0.841976 | + | 0.539515i | \(0.181392\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0.400294 | 0.0295906 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −11.5150 | −0.846600 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −3.19667 | −0.233764 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 13.0306 | 0.947837 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 10.8841 | 0.787546 | 0.393773 | − | 0.919208i | \(-0.371170\pi\) | ||||
0.393773 | + | 0.919208i | \(0.371170\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 17.1059 | 1.23131 | 0.615654 | − | 0.788017i | \(-0.288892\pi\) | ||||
0.615654 | + | 0.788017i | \(0.288892\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −4.93907 | −0.353694 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −6.58584 | −0.469222 | −0.234611 | − | 0.972089i | \(-0.575382\pi\) | ||||
−0.234611 | + | 0.972089i | \(0.575382\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −10.2648 | −0.727653 | −0.363826 | − | 0.931467i | \(-0.618530\pi\) | ||||
−0.363826 | + | 0.931467i | \(0.618530\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 20.5388 | 1.44870 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 2.36044 | 0.165670 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 18.7345 | 1.30847 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −0.0883018 | −0.00613740 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −3.12707 | −0.216304 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 3.19865 | 0.220204 | 0.110102 | − | 0.993920i | \(-0.464882\pi\) | ||||
0.110102 | + | 0.993920i | \(0.464882\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −7.27664 | −0.498587 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −24.2232 | −1.65201 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 13.8544 | 0.940498 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 5.75793 | 0.389085 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 3.91558 | 0.263390 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 23.7923 | 1.59325 | 0.796624 | − | 0.604476i | \(-0.206617\pi\) | ||||
0.796624 | + | 0.604476i | \(0.206617\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −2.19522 | −0.146348 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −5.44160 | −0.361171 | −0.180586 | − | 0.983559i | \(-0.557799\pi\) | ||||
−0.180586 | + | 0.983559i | \(0.557799\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 2.31309 | 0.152853 | 0.0764265 | − | 0.997075i | \(-0.475649\pi\) | ||||
0.0764265 | + | 0.997075i | \(0.475649\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −3.06391 | −0.201590 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −3.59167 | −0.235298 | −0.117649 | − | 0.993055i | \(-0.537536\pi\) | ||||
−0.117649 | + | 0.993055i | \(0.537536\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −39.9985 | −2.60921 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 11.2484 | 0.730661 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −4.14058 | −0.267832 | −0.133916 | − | 0.990993i | \(-0.542755\pi\) | ||||
−0.133916 | + | 0.990993i | \(0.542755\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −23.4205 | −1.50865 | −0.754324 | − | 0.656502i | \(-0.772035\pi\) | ||||
−0.754324 | + | 0.656502i | \(0.772035\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 4.85790 | 0.311634 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −4.43701 | −0.283470 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 3.83032 | 0.243718 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −20.1505 | −1.27699 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 10.9924 | 0.693835 | 0.346917 | − | 0.937896i | \(-0.387228\pi\) | ||||
0.346917 | + | 0.937896i | \(0.387228\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0.152703 | 0.00960037 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −19.3393 | −1.21108 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −9.69758 | −0.604918 | −0.302459 | − | 0.953162i | \(-0.597808\pi\) | ||||
−0.302459 | + | 0.953162i | \(0.597808\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 8.74969 | 0.543680 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0.472088 | 0.0292215 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −28.5062 | −1.75777 | −0.878883 | − | 0.477037i | \(-0.841711\pi\) | ||||
−0.878883 | + | 0.477037i | \(0.841711\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1.71833 | 0.105556 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 11.5645 | 0.707738 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 27.1593 | 1.65593 | 0.827967 | − | 0.560777i | \(-0.189498\pi\) | ||||
0.827967 | + | 0.560777i | \(0.189498\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1.29120 | −0.0784349 | −0.0392174 | − | 0.999231i | \(-0.512486\pi\) | ||||
−0.0392174 | + | 0.999231i | \(0.512486\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 3.75296 | 0.227140 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 3.79628 | 0.228924 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 28.1612 | 1.69204 | 0.846020 | − | 0.533151i | \(-0.178992\pi\) | ||||
0.846020 | + | 0.533151i | \(0.178992\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 2.77088 | 0.165888 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −23.4881 | −1.40118 | −0.700591 | − | 0.713563i | \(-0.747080\pi\) | ||||
−0.700591 | + | 0.713563i | \(0.747080\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 2.88422 | 0.171449 | 0.0857244 | − | 0.996319i | \(-0.472680\pi\) | ||||
0.0857244 | + | 0.996319i | \(0.472680\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −18.9182 | −1.12062 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −14.2354 | −0.840291 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1.66824 | −0.0981320 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −11.6864 | −0.685070 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −17.7155 | −1.03495 | −0.517475 | − | 0.855698i | \(-0.673128\pi\) | ||||
−0.517475 | + | 0.855698i | \(0.673128\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −3.81624 | −0.222190 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −4.50686 | −0.261514 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −0.187045 | −0.0108171 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 18.4061 | 1.06091 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 16.7328 | 0.961277 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0.782100 | 0.0447829 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −21.5927 | −1.23236 | −0.616181 | − | 0.787604i | \(-0.711321\pi\) | ||||
−0.616181 | + | 0.787604i | \(0.711321\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −0.397468 | −0.0226112 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −29.4332 | −1.66901 | −0.834503 | − | 0.551004i | \(-0.814245\pi\) | ||||
−0.834503 | + | 0.551004i | \(0.814245\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 9.18393 | 0.519106 | 0.259553 | − | 0.965729i | \(-0.416425\pi\) | ||||
0.259553 | + | 0.965729i | \(0.416425\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 3.46163 | 0.195041 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 15.2241 | 0.855068 | 0.427534 | − | 0.903999i | \(-0.359382\pi\) | ||||
0.427534 | + | 0.903999i | \(0.359382\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −0.816398 | −0.0457095 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 14.1254 | 0.788402 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 14.9979 | 0.834507 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −4.65003 | −0.257937 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 10.1769 | 0.562783 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 30.3929 | 1.67561 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 8.50024 | 0.467215 | 0.233608 | − | 0.972331i | \(-0.424947\pi\) | ||||
0.233608 | + | 0.972331i | \(0.424947\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 1.74994 | 0.0958961 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 40.1290 | 2.19248 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −11.4735 | −0.625000 | −0.312500 | − | 0.949918i | \(-0.601166\pi\) | ||||
−0.312500 | + | 0.949918i | \(0.601166\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 5.60997 | 0.304692 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −4.79178 | −0.259489 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 19.8945 | 1.07420 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0.923829 | 0.0497373 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −25.5955 | −1.37404 | −0.687020 | − | 0.726639i | \(-0.741081\pi\) | ||||
−0.687020 | + | 0.726639i | \(0.741081\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 19.4461 | 1.04093 | 0.520464 | − | 0.853884i | \(-0.325759\pi\) | ||||
0.520464 | + | 0.853884i | \(0.325759\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 5.52041 | 0.294658 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 3.02630 | 0.161074 | 0.0805368 | − | 0.996752i | \(-0.474337\pi\) | ||||
0.0805368 | + | 0.996752i | \(0.474337\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −14.2172 | −0.754571 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 14.6950 | 0.777743 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 25.2742 | 1.33392 | 0.666962 | − | 0.745092i | \(-0.267594\pi\) | ||||
0.666962 | + | 0.745092i | \(0.267594\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −4.32864 | −0.227823 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −16.4296 | −0.862333 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 11.2499 | 0.588848 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 24.7174 | 1.29024 | 0.645120 | − | 0.764082i | \(-0.276808\pi\) | ||||
0.645120 | + | 0.764082i | \(0.276808\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −2.84709 | −0.148213 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −1.30567 | −0.0677873 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −27.7618 | −1.43745 | −0.718726 | − | 0.695293i | \(-0.755274\pi\) | ||||
−0.718726 | + | 0.695293i | \(0.755274\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −1.72853 | −0.0892609 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 1.00000 | 0.0515026 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −11.8263 | −0.607474 | −0.303737 | − | 0.952756i | \(-0.598234\pi\) | ||||
−0.303737 | + | 0.952756i | \(0.598234\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −21.4360 | −1.09820 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 8.17709 | 0.417830 | 0.208915 | − | 0.977934i | \(-0.433007\pi\) | ||||
0.208915 | + | 0.977934i | \(0.433007\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −5.98631 | −0.305091 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 3.68121 | 0.187127 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 21.6722 | 1.09882 | 0.549412 | − | 0.835552i | \(-0.314852\pi\) | ||||
0.549412 | + | 0.835552i | \(0.314852\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −0.732390 | −0.0370386 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 16.5738 | 0.836035 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 21.9773 | 1.10580 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −9.24134 | −0.463809 | −0.231905 | − | 0.972739i | \(-0.574496\pi\) | ||||
−0.231905 | + | 0.972739i | \(0.574496\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 14.3750 | 0.719652 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −36.5336 | −1.82440 | −0.912200 | − | 0.409746i | \(-0.865617\pi\) | ||||
−0.912200 | + | 0.409746i | \(0.865617\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 5.86942 | 0.292376 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −22.8662 | −1.13623 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −3.02623 | −0.150005 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 2.39512 | 0.118431 | 0.0592154 | − | 0.998245i | \(-0.481140\pi\) | ||||
0.0592154 | + | 0.998245i | \(0.481140\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −17.9691 | −0.886353 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 2.89978 | 0.142689 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −39.3704 | −1.93262 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −35.6823 | −1.74737 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 10.4109 | 0.508605 | 0.254302 | − | 0.967125i | \(-0.418154\pi\) | ||||
0.254302 | + | 0.967125i | \(0.418154\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −6.38045 | −0.310964 | −0.155482 | − | 0.987839i | \(-0.549693\pi\) | ||||
−0.155482 | + | 0.987839i | \(0.549693\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 6.07858 | 0.295551 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −18.2076 | −0.883196 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −0.594280 | −0.0287592 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −1.29802 | −0.0626692 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 2.42218 | 0.116673 | 0.0583363 | − | 0.998297i | \(-0.481420\pi\) | ||||
0.0583363 | + | 0.998297i | \(0.481420\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 15.8771 | 0.763006 | 0.381503 | − | 0.924368i | \(-0.375407\pi\) | ||||
0.381503 | + | 0.924368i | \(0.375407\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −4.93907 | −0.236810 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −0.716443 | −0.0342721 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 22.9516 | 1.09542 | 0.547709 | − | 0.836669i | \(-0.315500\pi\) | ||||
0.547709 | + | 0.836669i | \(0.315500\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0.674293 | 0.0321092 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −2.76948 | −0.131582 | −0.0657911 | − | 0.997833i | \(-0.520957\pi\) | ||||
−0.0657911 | + | 0.997833i | \(0.520957\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 22.5950 | 1.07110 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 28.1979 | 1.33372 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 27.1512 | 1.28135 | 0.640673 | − | 0.767814i | \(-0.278656\pi\) | ||||
0.640673 | + | 0.767814i | \(0.278656\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 4.92356 | 0.231842 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 9.12109 | 0.428546 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 7.33259 | 0.343757 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −12.4511 | −0.582440 | −0.291220 | − | 0.956656i | \(-0.594061\pi\) | ||||
−0.291220 | + | 0.956656i | \(0.594061\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 21.6156 | 1.00893 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 37.5424 | 1.74853 | 0.874263 | − | 0.485453i | \(-0.161345\pi\) | ||||
0.874263 | + | 0.485453i | \(0.161345\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 21.0931 | 0.980279 | 0.490140 | − | 0.871644i | \(-0.336946\pi\) | ||||
0.490140 | + | 0.871644i | \(0.336946\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −28.9895 | −1.34435 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 7.35843 | 0.340508 | 0.170254 | − | 0.985400i | \(-0.445541\pi\) | ||||
0.170254 | + | 0.985400i | \(0.445541\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −30.4921 | −1.40800 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 18.5944 | 0.856784 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −6.36605 | −0.292711 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −17.8111 | −0.817230 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −0.261135 | −0.0119565 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 12.9261 | 0.590607 | 0.295304 | − | 0.955403i | \(-0.404579\pi\) | ||||
0.295304 | + | 0.955403i | \(0.404579\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 3.70681 | 0.169016 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −0.701973 | −0.0319409 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −22.8331 | −1.03680 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 4.88214 | 0.221231 | 0.110615 | − | 0.993863i | \(-0.464718\pi\) | ||||
0.110615 | + | 0.993863i | \(0.464718\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 17.1400 | 0.775097 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 4.86864 | 0.219719 | 0.109859 | − | 0.993947i | \(-0.464960\pi\) | ||||
0.109859 | + | 0.993947i | \(0.464960\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 3.91558 | 0.176349 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −1.19726 | −0.0538129 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 10.8030 | 0.484579 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −3.00575 | −0.134556 | −0.0672780 | − | 0.997734i | \(-0.521431\pi\) | ||||
−0.0672780 | + | 0.997734i | \(0.521431\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −35.0050 | −1.56391 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −11.1121 | −0.495463 | −0.247732 | − | 0.968829i | \(-0.579685\pi\) | ||||
−0.247732 | + | 0.968829i | \(0.579685\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 32.6929 | 1.45481 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 1.58994 | 0.0706118 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −6.51993 | −0.288991 | −0.144495 | − | 0.989505i | \(-0.546156\pi\) | ||||
−0.144495 | + | 0.989505i | \(0.546156\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −8.54827 | −0.378153 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 21.1450 | 0.933573 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −0.776580 | −0.0342202 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −10.5119 | −0.462313 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −17.5771 | −0.771549 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −23.3042 | −1.02098 | −0.510488 | − | 0.859885i | \(-0.670535\pi\) | ||||
−0.510488 | + | 0.859885i | \(0.670535\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 14.0635 | 0.614955 | 0.307477 | − | 0.951555i | \(-0.400515\pi\) | ||||
0.307477 | + | 0.951555i | \(0.400515\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −17.4514 | −0.761641 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 22.9822 | 1.00112 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −22.9650 | −0.998479 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0.579955 | 0.0251679 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −6.03084 | −0.261225 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 27.5984 | 1.19318 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −14.0500 | −0.606301 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −1.16608 | −0.0502266 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −28.7461 | −1.23589 | −0.617945 | − | 0.786222i | \(-0.712034\pi\) | ||||
−0.617945 | + | 0.786222i | \(0.712034\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 36.0205 | 1.54579 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 19.8837 | 0.851726 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 5.19168 | 0.221980 | 0.110990 | − | 0.993822i | \(-0.464598\pi\) | ||||
0.110990 | + | 0.993822i | \(0.464598\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −0.118856 | −0.00507265 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 3.83032 | 0.163177 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −16.6994 | −0.710133 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −18.3082 | −0.777139 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −23.8076 | −1.00876 | −0.504380 | − | 0.863482i | \(-0.668279\pi\) | ||||
−0.504380 | + | 0.863482i | \(0.668279\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 7.79773 | 0.329809 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −5.08252 | −0.214584 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 13.9175 | 0.586552 | 0.293276 | − | 0.956028i | \(-0.405254\pi\) | ||||
0.293276 | + | 0.956028i | \(0.405254\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 10.9608 | 0.461126 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 17.3749 | 0.729677 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −8.89659 | −0.372964 | −0.186482 | − | 0.982458i | \(-0.559709\pi\) | ||||
−0.186482 | + | 0.982458i | \(0.559709\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −20.6817 | −0.865502 | −0.432751 | − | 0.901513i | \(-0.642457\pi\) | ||||
−0.432751 | + | 0.901513i | \(0.642457\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 17.3051 | 0.722930 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0.869765 | 0.0362717 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −3.79935 | −0.158169 | −0.0790844 | − | 0.996868i | \(-0.525200\pi\) | ||||
−0.0790844 | + | 0.996868i | \(0.525200\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 27.1973 | 1.13028 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 29.9157 | 1.24111 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0.451590 | 0.0187029 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 1.46652 | 0.0606331 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −6.91359 | −0.285354 | −0.142677 | − | 0.989769i | \(-0.545571\pi\) | ||||
−0.142677 | + | 0.989769i | \(0.545571\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 22.4818 | 0.926344 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −10.4711 | −0.430724 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −21.6513 | −0.889114 | −0.444557 | − | 0.895751i | \(-0.646639\pi\) | ||||
−0.444557 | + | 0.895751i | \(0.646639\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 28.7113 | 1.17705 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −16.3204 | −0.667951 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −46.8921 | −1.91596 | −0.957979 | − | 0.286838i | \(-0.907396\pi\) | ||||
−0.957979 | + | 0.286838i | \(0.907396\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −32.4501 | −1.32367 | −0.661833 | − | 0.749651i | \(-0.730221\pi\) | ||||
−0.661833 | + | 0.749651i | \(0.730221\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −6.09842 | −0.248347 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −32.1005 | −1.30507 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −0.745772 | −0.0302700 | −0.0151350 | − | 0.999885i | \(-0.504818\pi\) | ||||
−0.0151350 | + | 0.999885i | \(0.504818\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 3.75296 | 0.152078 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 12.8759 | 0.520905 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −15.6677 | −0.632814 | −0.316407 | − | 0.948623i | \(-0.602477\pi\) | ||||
−0.316407 | + | 0.948623i | \(0.602477\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 29.7867 | 1.20112 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −30.7252 | −1.23695 | −0.618474 | − | 0.785805i | \(-0.712249\pi\) | ||||
−0.618474 | + | 0.785805i | \(0.712249\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 4.49750 | 0.180770 | 0.0903849 | − | 0.995907i | \(-0.471190\pi\) | ||||
0.0903849 | + | 0.995907i | \(0.471190\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1.03257 | −0.0414355 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −17.1688 | −0.687854 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −26.6274 | −1.06509 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −4.97185 | −0.198557 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 14.5143 | 0.578723 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 19.5314 | 0.777534 | 0.388767 | − | 0.921336i | \(-0.372901\pi\) | ||||
0.388767 | + | 0.921336i | \(0.372901\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 5.08567 | 0.202137 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −41.8819 | −1.66203 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1.42832 | 0.0565921 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 2.16059 | 0.0854718 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 40.6112 | 1.60405 | 0.802024 | − | 0.597292i | \(-0.203757\pi\) | ||||
0.802024 | + | 0.597292i | \(0.203757\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 34.9483 | 1.37823 | 0.689113 | − | 0.724654i | \(-0.258000\pi\) | ||||
0.689113 | + | 0.724654i | \(0.258000\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −38.5135 | −1.51647 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −23.8896 | −0.939198 | −0.469599 | − | 0.882880i | \(-0.655602\pi\) | ||||
−0.469599 | + | 0.882880i | \(0.655602\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −1.00294 | −0.0393687 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 22.0277 | 0.863333 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −14.8680 | −0.581830 | −0.290915 | − | 0.956749i | \(-0.593960\pi\) | ||||
−0.290915 | + | 0.956749i | \(0.593960\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 32.3820 | 1.26527 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −1.70965 | −0.0666999 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −21.4462 | −0.835427 | −0.417714 | − | 0.908579i | \(-0.637168\pi\) | ||||
−0.417714 | + | 0.908579i | \(0.637168\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 2.63100 | 0.102334 | 0.0511669 | − | 0.998690i | \(-0.483706\pi\) | ||||
0.0511669 | + | 0.998690i | \(0.483706\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 6.22554 | 0.241780 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 28.0862 | 1.08914 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −0.187045 | −0.00724242 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 37.8283 | 1.46253 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0.205542 | 0.00793485 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −20.1979 | −0.778573 | −0.389287 | − | 0.921117i | \(-0.627278\pi\) | ||||
−0.389287 | + | 0.921117i | \(0.627278\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −25.6701 | −0.988042 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −1.10452 | −0.0424502 | −0.0212251 | − | 0.999775i | \(-0.506757\pi\) | ||||
−0.0212251 | + | 0.999775i | \(0.506757\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 17.3498 | 0.665823 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −8.65182 | −0.331538 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −17.5799 | −0.672678 | −0.336339 | − | 0.941741i | \(-0.609189\pi\) | ||||
−0.336339 | + | 0.941741i | \(0.609189\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −35.1084 | −1.34142 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 3.67767 | 0.140312 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −0.553149 | −0.0210733 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 15.7339 | 0.598547 | 0.299273 | − | 0.954167i | \(-0.403256\pi\) | ||||
0.299273 | + | 0.954167i | \(0.403256\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0.909742 | 0.0345582 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −69.7165 | −2.64450 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −23.6142 | −0.894452 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −5.71054 | −0.215992 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −48.7119 | −1.83982 | −0.919912 | − | 0.392126i | \(-0.871740\pi\) | ||||
−0.919912 | + | 0.392126i | \(0.871740\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 14.1983 | 0.535497 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −63.5952 | −2.39513 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −24.8417 | −0.934269 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −12.0483 | −0.452483 | −0.226241 | − | 0.974071i | \(-0.572644\pi\) | ||||
−0.226241 | + | 0.974071i | \(0.572644\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −3.33989 | −0.125256 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −1.09785 | −0.0411146 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −2.53610 | −0.0948447 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −6.58328 | −0.245857 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −39.8103 | −1.48467 | −0.742337 | − | 0.670027i | \(-0.766283\pi\) | ||||
−0.742337 | + | 0.670027i | \(0.766283\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0.590085 | 0.0219759 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −37.2372 | −1.38487 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −4.65003 | −0.172698 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −4.08086 | −0.151351 | −0.0756754 | − | 0.997133i | \(-0.524111\pi\) | ||||
−0.0756754 | + | 0.997133i | \(0.524111\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 29.8064 | 1.10394 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 30.5326 | 1.12929 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 25.6048 | 0.945735 | 0.472867 | − | 0.881134i | \(-0.343219\pi\) | ||||
0.472867 | + | 0.881134i | \(0.343219\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −7.05458 | −0.260212 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 10.5462 | 0.388475 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −10.9915 | −0.404328 | −0.202164 | − | 0.979352i | \(-0.564797\pi\) | ||||
−0.202164 | + | 0.979352i | \(0.564797\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 6.08998 | 0.223721 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 8.42606 | 0.309122 | 0.154561 | − | 0.987983i | \(-0.450604\pi\) | ||||
0.154561 | + | 0.987983i | \(0.450604\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 55.0935 | 2.01847 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 5.98314 | 0.218912 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −20.9707 | −0.766252 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 15.8856 | 0.579674 | 0.289837 | − | 0.957076i | \(-0.406399\pi\) | ||||
0.289837 | + | 0.957076i | \(0.406399\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 17.4773 | 0.636907 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 17.8209 | 0.648570 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −32.8803 | −1.19506 | −0.597528 | − | 0.801848i | \(-0.703850\pi\) | ||||
−0.597528 | + | 0.801848i | \(0.703850\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0.242789 | 0.00881269 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 19.4632 | 0.705541 | 0.352770 | − | 0.935710i | \(-0.385240\pi\) | ||||
0.352770 | + | 0.935710i | \(0.385240\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −15.1087 | −0.546971 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 5.74227 | 0.207612 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 1.22849 | 0.0443582 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 6.22888 | 0.224619 | 0.112310 | − | 0.993673i | \(-0.464175\pi\) | ||||
0.112310 | + | 0.993673i | \(0.464175\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −15.4186 | −0.555286 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −13.4007 | −0.481990 | −0.240995 | − | 0.970526i | \(-0.577474\pi\) | ||||
−0.240995 | + | 0.970526i | \(0.577474\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −27.2930 | −0.980392 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 13.9115 | 0.499072 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −23.1000 | −0.827645 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −3.73639 | −0.133699 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 5.52041 | 0.197284 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 36.3300 | 1.29667 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −6.05665 | −0.215896 | −0.107948 | − | 0.994157i | \(-0.534428\pi\) | ||||
−0.107948 | + | 0.994157i | \(0.534428\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −45.3231 | −1.61355 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −8.32862 | −0.296131 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −0.251767 | −0.00894050 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 2.73204 | 0.0968955 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 29.0664 | 1.02959 | 0.514793 | − | 0.857314i | \(-0.327869\pi\) | ||||
0.514793 | + | 0.857314i | \(0.327869\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 50.4168 | 1.78362 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −3.43376 | −0.121326 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 2.95656 | 0.104335 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −1.37153 | −0.0483399 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 43.1817 | 1.52007 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −40.9128 | −1.43842 | −0.719209 | − | 0.694794i | \(-0.755495\pi\) | ||||
−0.719209 | + | 0.694794i | \(0.755495\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −19.8842 | −0.698228 | −0.349114 | − | 0.937080i | \(-0.613517\pi\) | ||||
−0.349114 | + | 0.937080i | \(0.613517\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −2.05293 | −0.0719995 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 33.4884 | 1.17305 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 29.8678 | 1.04494 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −1.11434 | −0.0389380 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −47.7971 | −1.66813 | −0.834064 | − | 0.551667i | \(-0.813992\pi\) | ||||
−0.834064 | + | 0.551667i | \(0.813992\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −6.16596 | −0.214932 | −0.107466 | − | 0.994209i | \(-0.534274\pi\) | ||||
−0.107466 | + | 0.994209i | \(0.534274\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 6.03585 | 0.210141 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −1.87980 | −0.0653671 | −0.0326836 | − | 0.999466i | \(-0.510405\pi\) | ||||
−0.0326836 | + | 0.999466i | \(0.510405\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 28.0363 | 0.973742 | 0.486871 | − | 0.873474i | \(-0.338138\pi\) | ||||
0.486871 | + | 0.873474i | \(0.338138\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 44.7746 | 1.55321 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 5.59270 | 0.193776 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −68.3932 | −2.36684 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 32.4016 | 1.11996 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −40.4393 | −1.39612 | −0.698059 | − | 0.716040i | \(-0.745953\pi\) | ||||
−0.698059 | + | 0.716040i | \(0.745953\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.00000 | 0.0344828 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −37.3447 | −1.28622 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 3.10645 | 0.106865 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 24.3916 | 0.838105 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 4.58573 | 0.157382 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −0.693340 | −0.0237674 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −6.55069 | −0.224291 | −0.112146 | − | 0.993692i | \(-0.535772\pi\) | ||||
−0.112146 | + | 0.993692i | \(0.535772\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 5.61723 | 0.192105 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −19.0739 | −0.651553 | −0.325777 | − | 0.945447i | \(-0.605626\pi\) | ||||
−0.325777 | + | 0.945447i | \(0.605626\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −23.0570 | −0.786695 | −0.393348 | − | 0.919390i | \(-0.628683\pi\) | ||||
−0.393348 | + | 0.919390i | \(0.628683\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −22.6335 | −0.771347 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 49.2810 | 1.67754 | 0.838772 | − | 0.544484i | \(-0.183274\pi\) | ||||
0.838772 | + | 0.544484i | \(0.183274\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −34.3424 | −1.16768 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −2.65241 | −0.0900805 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 5.77579 | 0.195930 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −12.9180 | −0.437709 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 3.46995 | 0.117440 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 2.56619 | 0.0867531 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 36.6539 | 1.23771 | 0.618856 | − | 0.785504i | \(-0.287596\pi\) | ||||
0.618856 | + | 0.785504i | \(0.287596\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −28.1666 | −0.950036 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 30.6245 | 1.03177 | 0.515883 | − | 0.856659i | \(-0.327464\pi\) | ||||
0.515883 | + | 0.856659i | \(0.327464\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −51.5865 | −1.73603 | −0.868013 | − | 0.496542i | \(-0.834603\pi\) | ||||
−0.868013 | + | 0.496542i | \(0.834603\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −6.06760 | −0.203960 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 9.52716 | 0.319891 | 0.159945 | − | 0.987126i | \(-0.448868\pi\) | ||||
0.159945 | + | 0.987126i | \(0.448868\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 31.8240 | 1.06734 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −6.00940 | −0.201322 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 49.3190 | 1.65040 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −27.4511 | −0.917588 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −0.297391 | −0.00992959 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 5.86942 | 0.195756 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −2.16590 | −0.0721565 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 29.2646 | 0.973864 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 70.3774 | 2.33942 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 9.17351 | 0.304601 | 0.152301 | − | 0.988334i | \(-0.451332\pi\) | ||||
0.152301 | + | 0.988334i | \(0.451332\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −4.96834 | −0.164790 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 31.1004 | 1.03040 | 0.515201 | − | 0.857069i | \(-0.327717\pi\) | ||||
0.515201 | + | 0.857069i | \(0.327717\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −10.3468 | −0.342431 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 1.24349 | 0.0411086 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −24.6055 | −0.812546 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 9.60301 | 0.316774 | 0.158387 | − | 0.987377i | \(-0.449371\pi\) | ||||
0.158387 | + | 0.987377i | \(0.449371\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −34.3312 | −1.13125 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 4.57668 | 0.150643 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −17.2368 | −0.566741 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0.118017 | 0.00387619 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −0.204374 | −0.00670530 | −0.00335265 | − | 0.999994i | \(-0.501067\pi\) | ||||
−0.00335265 | + | 0.999994i | \(0.501067\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 5.47093 | 0.179302 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −46.7971 | −1.53207 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −9.93030 | −0.324755 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −4.79992 | −0.156807 | −0.0784033 | − | 0.996922i | \(-0.524982\pi\) | ||||
−0.0784033 | + | 0.996922i | \(0.524982\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 14.6019 | 0.476515 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 60.2934 | 1.96551 | 0.982754 | − | 0.184916i | \(-0.0592014\pi\) | ||||
0.982754 | + | 0.184916i | \(0.0592014\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1.12804 | 0.0367340 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 40.4789 | 1.31678 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 36.5730 | 1.18846 | 0.594232 | − | 0.804294i | \(-0.297456\pi\) | ||||
0.594232 | + | 0.804294i | \(0.297456\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −3.62147 | −0.117558 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 24.2053 | 0.784912 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 5.90927 | 0.191420 | 0.0957100 | − | 0.995409i | \(-0.469488\pi\) | ||||
0.0957100 | + | 0.995409i | \(0.469488\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 33.8109 | 1.09409 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −1.29802 | −0.0419592 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 26.6772 | 0.861450 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 3.45005 | 0.111292 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −4.19414 | −0.135154 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 53.1386 | 1.71059 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −4.57062 | −0.146981 | −0.0734906 | − | 0.997296i | \(-0.523414\pi\) | ||||
−0.0734906 | + | 0.997296i | \(0.523414\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 23.8458 | 0.766038 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 29.0080 | 0.930912 | 0.465456 | − | 0.885071i | \(-0.345890\pi\) | ||||
0.465456 | + | 0.885071i | \(0.345890\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 52.9742 | 1.69827 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −7.39327 | −0.236774 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 14.8889 | 0.476338 | 0.238169 | − | 0.971224i | \(-0.423453\pi\) | ||||
0.238169 | + | 0.971224i | \(0.423453\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 5.93812 | 0.189783 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −3.02174 | −0.0964767 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 15.9148 | 0.507602 | 0.253801 | − | 0.967256i | \(-0.418319\pi\) | ||||
0.253801 | + | 0.967256i | \(0.418319\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −20.4586 | −0.651865 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 48.3229 | 1.53813 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −1.45853 | −0.0463785 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −10.4040 | −0.330495 | −0.165247 | − | 0.986252i | \(-0.552842\pi\) | ||||
−0.165247 | + | 0.986252i | \(0.552842\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 13.5149 | 0.428882 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −31.8871 | −1.01089 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −24.4556 | −0.774517 | −0.387259 | − | 0.921971i | \(-0.626578\pi\) | ||||
−0.387259 | + | 0.921971i | \(0.626578\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 20.4631 | 0.647424 |
(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 | 6032.2.a.z.1.8 | 10 | ||
4.3 | odd | 2 | 3016.2.a.h.1.3 | ✓ | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3016.2.a.h.1.3 | ✓ | 10 | 4.3 | odd | 2 | ||
6032.2.a.z.1.8 | 10 | 1.1 | even | 1 | trivial |