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: | \(1\) |
Dimension: | \(9\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{9} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{9} - 3x^{8} - 13x^{7} + 32x^{6} + 40x^{5} - 79x^{4} - 39x^{3} + 58x^{2} + 9x - 11 \) |
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 | 1.6 | ||
Root | \(-0.975163\) 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 | ||||||||
\(5\) | 0.900888 | 0.402889 | 0.201445 | − | 0.979500i | \(-0.435436\pi\) | ||||
0.201445 | + | 0.979500i | \(0.435436\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.90501 | 1.47595 | 0.737977 | − | 0.674826i | \(-0.235781\pi\) | ||||
0.737977 | + | 0.674826i | \(0.235781\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −5.39807 | −1.62758 | −0.813790 | − | 0.581159i | \(-0.802600\pi\) | ||||
−0.813790 | + | 0.581159i | \(0.802600\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.18514 | −0.606050 | −0.303025 | − | 0.952983i | \(-0.597997\pi\) | ||||
−0.303025 | + | 0.952983i | \(0.597997\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −0.900888 | −0.232608 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −2.64370 | −0.641191 | −0.320595 | − | 0.947216i | \(-0.603883\pi\) | ||||
−0.320595 | + | 0.947216i | \(0.603883\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.37158 | 0.773494 | 0.386747 | − | 0.922186i | \(-0.373599\pi\) | ||||
0.386747 | + | 0.922186i | \(0.373599\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −3.90501 | −0.852142 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.00000 | −0.208514 | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.18840 | −0.837680 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.00000 | 0.185695 | ||||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 5.08447 | 0.913197 | 0.456599 | − | 0.889673i | \(-0.349068\pi\) | ||||
0.456599 | + | 0.889673i | \(0.349068\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 5.39807 | 0.939684 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 3.51798 | 0.594646 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −3.79035 | −0.623130 | −0.311565 | − | 0.950225i | \(-0.600853\pi\) | ||||
−0.311565 | + | 0.950225i | \(0.600853\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 2.18514 | 0.349903 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 8.82974 | 1.37897 | 0.689487 | − | 0.724298i | \(-0.257836\pi\) | ||||
0.689487 | + | 0.724298i | \(0.257836\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0.613535 | 0.0935632 | 0.0467816 | − | 0.998905i | \(-0.485104\pi\) | ||||
0.0467816 | + | 0.998905i | \(0.485104\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0.900888 | 0.134296 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 1.02676 | 0.149768 | 0.0748839 | − | 0.997192i | \(-0.476141\pi\) | ||||
0.0748839 | + | 0.997192i | \(0.476141\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 8.24908 | 1.17844 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 2.64370 | 0.370192 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 5.94186 | 0.816177 | 0.408088 | − | 0.912942i | \(-0.366196\pi\) | ||||
0.408088 | + | 0.912942i | \(0.366196\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −4.86306 | −0.655735 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −3.37158 | −0.446577 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −10.0058 | −1.30265 | −0.651323 | − | 0.758800i | \(-0.725786\pi\) | ||||
−0.651323 | + | 0.758800i | \(0.725786\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −3.09826 | −0.396692 | −0.198346 | − | 0.980132i | \(-0.563557\pi\) | ||||
−0.198346 | + | 0.980132i | \(0.563557\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 3.90501 | 0.491985 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −1.96857 | −0.244171 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −12.6836 | −1.54954 | −0.774771 | − | 0.632242i | \(-0.782135\pi\) | ||||
−0.774771 | + | 0.632242i | \(0.782135\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 1.00000 | 0.120386 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −4.69605 | −0.557318 | −0.278659 | − | 0.960390i | \(-0.589890\pi\) | ||||
−0.278659 | + | 0.960390i | \(0.589890\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 9.03175 | 1.05709 | 0.528543 | − | 0.848906i | \(-0.322738\pi\) | ||||
0.528543 | + | 0.848906i | \(0.322738\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 4.18840 | 0.483635 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −21.0795 | −2.40223 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −3.30647 | −0.372007 | −0.186004 | − | 0.982549i | \(-0.559554\pi\) | ||||
−0.186004 | + | 0.982549i | \(0.559554\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −1.01449 | −0.111354 | −0.0556772 | − | 0.998449i | \(-0.517732\pi\) | ||||
−0.0556772 | + | 0.998449i | \(0.517732\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −2.38168 | −0.258329 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −1.00000 | −0.107211 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −17.4884 | −1.85376 | −0.926882 | − | 0.375352i | \(-0.877522\pi\) | ||||
−0.926882 | + | 0.375352i | \(0.877522\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −8.53300 | −0.894501 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −5.08447 | −0.527235 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 3.03742 | 0.311632 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 4.91409 | 0.498950 | 0.249475 | − | 0.968381i | \(-0.419742\pi\) | ||||
0.249475 | + | 0.968381i | \(0.419742\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −5.39807 | −0.542527 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −12.7246 | −1.26615 | −0.633074 | − | 0.774091i | \(-0.718207\pi\) | ||||
−0.633074 | + | 0.774091i | \(0.718207\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −8.55800 | −0.843245 | −0.421622 | − | 0.906772i | \(-0.638539\pi\) | ||||
−0.421622 | + | 0.906772i | \(0.638539\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −3.51798 | −0.343319 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −14.5746 | −1.40898 | −0.704489 | − | 0.709715i | \(-0.748824\pi\) | ||||
−0.704489 | + | 0.709715i | \(0.748824\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 8.01651 | 0.767842 | 0.383921 | − | 0.923366i | \(-0.374573\pi\) | ||||
0.383921 | + | 0.923366i | \(0.374573\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 3.79035 | 0.359764 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −14.3051 | −1.34571 | −0.672856 | − | 0.739774i | \(-0.734933\pi\) | ||||
−0.672856 | + | 0.739774i | \(0.734933\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −0.900888 | −0.0840083 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −2.18514 | −0.202017 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −10.3237 | −0.946368 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 18.1392 | 1.64902 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −8.82974 | −0.796151 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −8.27772 | −0.740382 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 14.7786 | 1.31139 | 0.655696 | − | 0.755025i | \(-0.272375\pi\) | ||||
0.655696 | + | 0.755025i | \(0.272375\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −0.613535 | −0.0540187 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0.115094 | 0.0100558 | 0.00502789 | − | 0.999987i | \(-0.498400\pi\) | ||||
0.00502789 | + | 0.999987i | \(0.498400\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 13.1660 | 1.14164 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −0.900888 | −0.0775361 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 7.19790 | 0.614958 | 0.307479 | − | 0.951555i | \(-0.400515\pi\) | ||||
0.307479 | + | 0.951555i | \(0.400515\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −4.33778 | −0.367925 | −0.183963 | − | 0.982933i | \(-0.558893\pi\) | ||||
−0.183963 | + | 0.982933i | \(0.558893\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −1.02676 | −0.0864684 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 11.7956 | 0.986395 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0.900888 | 0.0748147 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −8.24908 | −0.680373 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −11.5364 | −0.945099 | −0.472550 | − | 0.881304i | \(-0.656666\pi\) | ||||
−0.472550 | + | 0.881304i | \(0.656666\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 13.6790 | 1.11318 | 0.556592 | − | 0.830786i | \(-0.312109\pi\) | ||||
0.556592 | + | 0.830786i | \(0.312109\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −2.64370 | −0.213730 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 4.58054 | 0.367918 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 0.0214029 | 0.00170814 | 0.000854068 | − | 1.00000i | \(-0.499728\pi\) | ||||
0.000854068 | 1.00000i | \(0.499728\pi\) | ||||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −5.94186 | −0.471220 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −3.90501 | −0.307758 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −0.555776 | −0.0435318 | −0.0217659 | − | 0.999763i | \(-0.506929\pi\) | ||||
−0.0217659 | + | 0.999763i | \(0.506929\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 4.86306 | 0.378589 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 6.90544 | 0.534359 | 0.267179 | − | 0.963647i | \(-0.413908\pi\) | ||||
0.267179 | + | 0.963647i | \(0.413908\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −8.22515 | −0.632704 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 3.37158 | 0.257831 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 5.27785 | 0.401267 | 0.200634 | − | 0.979666i | \(-0.435700\pi\) | ||||
0.200634 | + | 0.979666i | \(0.435700\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −16.3557 | −1.23638 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 10.0058 | 0.752083 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −6.77665 | −0.506511 | −0.253255 | − | 0.967399i | \(-0.581501\pi\) | ||||
−0.253255 | + | 0.967399i | \(0.581501\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −22.0103 | −1.63601 | −0.818005 | − | 0.575211i | \(-0.804920\pi\) | ||||
−0.818005 | + | 0.575211i | \(0.804920\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 3.09826 | 0.229030 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −3.41469 | −0.251053 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 14.2709 | 1.04359 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −3.90501 | −0.284047 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 11.7210 | 0.848103 | 0.424051 | − | 0.905638i | \(-0.360608\pi\) | ||||
0.424051 | + | 0.905638i | \(0.360608\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 8.21648 | 0.591435 | 0.295717 | − | 0.955275i | \(-0.404441\pi\) | ||||
0.295717 | + | 0.955275i | \(0.404441\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 1.96857 | 0.140972 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 0.510756 | 0.0363899 | 0.0181949 | − | 0.999834i | \(-0.494208\pi\) | ||||
0.0181949 | + | 0.999834i | \(0.494208\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −9.23340 | −0.654538 | −0.327269 | − | 0.944931i | \(-0.606128\pi\) | ||||
−0.327269 | + | 0.944931i | \(0.606128\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 12.6836 | 0.894629 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 3.90501 | 0.274078 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 7.95461 | 0.555574 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −1.00000 | −0.0695048 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −18.2000 | −1.25892 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 13.8507 | 0.953520 | 0.476760 | − | 0.879033i | \(-0.341811\pi\) | ||||
0.476760 | + | 0.879033i | \(0.341811\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 4.69605 | 0.321768 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0.552726 | 0.0376956 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 19.8549 | 1.34784 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −9.03175 | −0.610309 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 5.77686 | 0.388593 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 0.400408 | 0.0268133 | 0.0134066 | − | 0.999910i | \(-0.495732\pi\) | ||||
0.0134066 | + | 0.999910i | \(0.495732\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −4.18840 | −0.279227 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 6.20230 | 0.411661 | 0.205830 | − | 0.978588i | \(-0.434010\pi\) | ||||
0.205830 | + | 0.978588i | \(0.434010\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 7.12470 | 0.470813 | 0.235407 | − | 0.971897i | \(-0.424358\pi\) | ||||
0.235407 | + | 0.971897i | \(0.424358\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 21.0795 | 1.38693 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −8.64191 | −0.566150 | −0.283075 | − | 0.959098i | \(-0.591355\pi\) | ||||
−0.283075 | + | 0.959098i | \(0.591355\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0.924992 | 0.0603398 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 3.30647 | 0.214778 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 15.2043 | 0.983486 | 0.491743 | − | 0.870741i | \(-0.336360\pi\) | ||||
0.491743 | + | 0.870741i | \(0.336360\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −23.0248 | −1.48316 | −0.741580 | − | 0.670865i | \(-0.765923\pi\) | ||||
−0.741580 | + | 0.670865i | \(0.765923\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 7.43150 | 0.474781 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −7.36739 | −0.468776 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 1.01449 | 0.0642905 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 18.5440 | 1.17049 | 0.585245 | − | 0.810857i | \(-0.300998\pi\) | ||||
0.585245 | + | 0.810857i | \(0.300998\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 5.39807 | 0.339374 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 2.38168 | 0.149146 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −12.8335 | −0.800531 | −0.400265 | − | 0.916399i | \(-0.631082\pi\) | ||||
−0.400265 | + | 0.916399i | \(0.631082\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −14.8014 | −0.919712 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1.00000 | 0.0618984 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −14.8682 | −0.916812 | −0.458406 | − | 0.888743i | \(-0.651579\pi\) | ||||
−0.458406 | + | 0.888743i | \(0.651579\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 5.35295 | 0.328829 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 17.4884 | 1.07027 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −15.3258 | −0.934430 | −0.467215 | − | 0.884144i | \(-0.654743\pi\) | ||||
−0.467215 | + | 0.884144i | \(0.654743\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −25.3597 | −1.54049 | −0.770246 | − | 0.637747i | \(-0.779867\pi\) | ||||
−0.770246 | + | 0.637747i | \(0.779867\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 8.53300 | 0.516441 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 22.6093 | 1.36339 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −14.5368 | −0.873430 | −0.436715 | − | 0.899600i | \(-0.643858\pi\) | ||||
−0.436715 | + | 0.899600i | \(0.643858\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 5.08447 | 0.304399 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −27.7945 | −1.65808 | −0.829040 | − | 0.559189i | \(-0.811113\pi\) | ||||
−0.829040 | + | 0.559189i | \(0.811113\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −4.01747 | −0.238814 | −0.119407 | − | 0.992845i | \(-0.538099\pi\) | ||||
−0.119407 | + | 0.992845i | \(0.538099\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −3.03742 | −0.179921 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 34.4802 | 2.03530 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −10.0109 | −0.588875 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −4.91409 | −0.288069 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −32.9948 | −1.92757 | −0.963787 | − | 0.266673i | \(-0.914076\pi\) | ||||
−0.963787 | + | 0.266673i | \(0.914076\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −9.01412 | −0.524823 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 5.39807 | 0.313228 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 2.18514 | 0.126370 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2.39586 | 0.138095 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 12.7246 | 0.731011 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −2.79119 | −0.159823 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −9.56599 | −0.545960 | −0.272980 | − | 0.962020i | \(-0.588009\pi\) | ||||
−0.272980 | + | 0.962020i | \(0.588009\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 8.55800 | 0.486848 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 4.28315 | 0.242875 | 0.121438 | − | 0.992599i | \(-0.461250\pi\) | ||||
0.121438 | + | 0.992599i | \(0.461250\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 0.673397 | 0.0380626 | 0.0190313 | − | 0.999819i | \(-0.493942\pi\) | ||||
0.0190313 | + | 0.999819i | \(0.493942\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 3.51798 | 0.198215 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −17.0792 | −0.959263 | −0.479632 | − | 0.877470i | \(-0.659230\pi\) | ||||
−0.479632 | + | 0.877470i | \(0.659230\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −5.39807 | −0.302234 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 14.5746 | 0.813474 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −8.91344 | −0.495957 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 9.15225 | 0.507676 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −8.01651 | −0.443314 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 4.00949 | 0.221050 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 7.39283 | 0.406347 | 0.203173 | − | 0.979143i | \(-0.434875\pi\) | ||||
0.203173 | + | 0.979143i | \(0.434875\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −3.79035 | −0.207710 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −11.4265 | −0.624294 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 14.4508 | 0.787186 | 0.393593 | − | 0.919285i | \(-0.371232\pi\) | ||||
0.393593 | + | 0.919285i | \(0.371232\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 14.3051 | 0.776947 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −27.4463 | −1.48630 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 4.87767 | 0.263369 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0.900888 | 0.0485022 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 16.0698 | 0.862669 | 0.431335 | − | 0.902192i | \(-0.358043\pi\) | ||||
0.431335 | + | 0.902192i | \(0.358043\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 17.8796 | 0.957075 | 0.478537 | − | 0.878067i | \(-0.341167\pi\) | ||||
0.478537 | + | 0.878067i | \(0.341167\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 2.18514 | 0.116634 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −31.2236 | −1.66187 | −0.830933 | − | 0.556373i | \(-0.812193\pi\) | ||||
−0.830933 | + | 0.556373i | \(0.812193\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −4.23061 | −0.224538 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 10.3237 | 0.546386 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −23.6558 | −1.24851 | −0.624253 | − | 0.781222i | \(-0.714596\pi\) | ||||
−0.624253 | + | 0.781222i | \(0.714596\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −7.63244 | −0.401708 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −18.1392 | −0.952062 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 8.13660 | 0.425889 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 30.1044 | 1.57144 | 0.785719 | − | 0.618583i | \(-0.212293\pi\) | ||||
0.785719 | + | 0.618583i | \(0.212293\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 8.82974 | 0.459658 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 23.2030 | 1.20464 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −25.6816 | −1.32974 | −0.664871 | − | 0.746958i | \(-0.731513\pi\) | ||||
−0.664871 | + | 0.746958i | \(0.731513\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 8.27772 | 0.427460 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −2.18514 | −0.112541 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 24.8901 | 1.27852 | 0.639260 | − | 0.768991i | \(-0.279241\pi\) | ||||
0.639260 | + | 0.768991i | \(0.279241\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −14.7786 | −0.757133 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 5.32682 | 0.272188 | 0.136094 | − | 0.990696i | \(-0.456545\pi\) | ||||
0.136094 | + | 0.990696i | \(0.456545\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −18.9903 | −0.967835 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0.613535 | 0.0311877 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 31.6443 | 1.60443 | 0.802216 | − | 0.597034i | \(-0.203654\pi\) | ||||
0.802216 | + | 0.597034i | \(0.203654\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2.64370 | 0.133697 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −0.115094 | −0.00580571 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −2.97876 | −0.149878 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −1.70334 | −0.0854881 | −0.0427441 | − | 0.999086i | \(-0.513610\pi\) | ||||
−0.0427441 | + | 0.999086i | \(0.513610\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −13.1660 | −0.659127 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 24.1375 | 1.20537 | 0.602684 | − | 0.797980i | \(-0.294098\pi\) | ||||
0.602684 | + | 0.797980i | \(0.294098\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −11.1103 | −0.553443 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0.900888 | 0.0447655 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 20.4606 | 1.01419 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −24.7975 | −1.22616 | −0.613078 | − | 0.790022i | \(-0.710069\pi\) | ||||
−0.613078 | + | 0.790022i | \(0.710069\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −7.19790 | −0.355046 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −39.0728 | −1.92265 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −0.913939 | −0.0448635 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 4.33778 | 0.212422 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 23.5959 | 1.15274 | 0.576368 | − | 0.817190i | \(-0.304470\pi\) | ||||
0.576368 | + | 0.817190i | \(0.304470\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −34.6655 | −1.68949 | −0.844746 | − | 0.535167i | \(-0.820249\pi\) | ||||
−0.844746 | + | 0.535167i | \(0.820249\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 1.02676 | 0.0499226 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 11.0729 | 0.537113 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −12.0987 | −0.585499 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −11.7956 | −0.569495 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −2.67396 | −0.128800 | −0.0644001 | − | 0.997924i | \(-0.520513\pi\) | ||||
−0.0644001 | + | 0.997924i | \(0.520513\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 26.4396 | 1.27061 | 0.635304 | − | 0.772262i | \(-0.280875\pi\) | ||||
0.635304 | + | 0.772262i | \(0.280875\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −0.900888 | −0.0431943 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −3.37158 | −0.161285 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −6.00149 | −0.286436 | −0.143218 | − | 0.989691i | \(-0.545745\pi\) | ||||
−0.143218 | + | 0.989691i | \(0.545745\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 8.24908 | 0.392813 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 22.8584 | 1.08604 | 0.543019 | − | 0.839721i | \(-0.317281\pi\) | ||||
0.543019 | + | 0.839721i | \(0.317281\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −15.7551 | −0.746862 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 11.5364 | 0.545653 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 9.28471 | 0.438173 | 0.219086 | − | 0.975705i | \(-0.429692\pi\) | ||||
0.219086 | + | 0.975705i | \(0.429692\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −47.6636 | −2.24439 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −13.6790 | −0.642697 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −7.68728 | −0.360385 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 11.6566 | 0.545275 | 0.272637 | − | 0.962117i | \(-0.412104\pi\) | ||||
0.272637 | + | 0.962117i | \(0.412104\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 2.64370 | 0.123397 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 14.0282 | 0.653359 | 0.326680 | − | 0.945135i | \(-0.394070\pi\) | ||||
0.326680 | + | 0.945135i | \(0.394070\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 37.9064 | 1.76166 | 0.880829 | − | 0.473434i | \(-0.156986\pi\) | ||||
0.880829 | + | 0.473434i | \(0.156986\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −4.58054 | −0.212417 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −25.5002 | −1.18001 | −0.590004 | − | 0.807400i | \(-0.700874\pi\) | ||||
−0.590004 | + | 0.807400i | \(0.700874\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −49.5294 | −2.28705 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −0.0214029 | −0.000986192 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −3.31191 | −0.152282 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −14.1215 | −0.647940 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 5.94186 | 0.272059 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −36.0071 | −1.64521 | −0.822603 | − | 0.568616i | \(-0.807479\pi\) | ||||
−0.822603 | + | 0.568616i | \(0.807479\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 8.28247 | 0.377648 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 3.90501 | 0.177684 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 4.42704 | 0.201022 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −20.6281 | −0.934747 | −0.467373 | − | 0.884060i | \(-0.654800\pi\) | ||||
−0.467373 | + | 0.884060i | \(0.654800\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0.555776 | 0.0251331 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −16.8265 | −0.759370 | −0.379685 | − | 0.925116i | \(-0.623968\pi\) | ||||
−0.379685 | + | 0.925116i | \(0.623968\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −2.64370 | −0.119066 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −4.86306 | −0.218578 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −18.3381 | −0.822576 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 39.1885 | 1.75432 | 0.877160 | − | 0.480198i | \(-0.159435\pi\) | ||||
0.877160 | + | 0.480198i | \(0.159435\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −6.90544 | −0.308512 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −33.7518 | −1.50492 | −0.752458 | − | 0.658640i | \(-0.771132\pi\) | ||||
−0.752458 | + | 0.658640i | \(0.771132\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −11.4635 | −0.510118 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 8.22515 | 0.365292 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 17.6294 | 0.781407 | 0.390704 | − | 0.920517i | \(-0.372232\pi\) | ||||
0.390704 | + | 0.920517i | \(0.372232\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 35.2690 | 1.56021 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −3.37158 | −0.148859 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −7.70980 | −0.339734 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −5.54250 | −0.243759 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −5.27785 | −0.231672 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −17.1971 | −0.753418 | −0.376709 | − | 0.926332i | \(-0.622944\pi\) | ||||
−0.376709 | + | 0.926332i | \(0.622944\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 18.5539 | 0.811304 | 0.405652 | − | 0.914028i | \(-0.367044\pi\) | ||||
0.405652 | + | 0.914028i | \(0.367044\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 16.3557 | 0.713823 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −13.4418 | −0.585534 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −10.0058 | −0.434215 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −19.2942 | −0.835726 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −13.1301 | −0.567662 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 6.77665 | 0.292434 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −44.5292 | −1.91801 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 3.64277 | 0.156615 | 0.0783074 | − | 0.996929i | \(-0.475048\pi\) | ||||
0.0783074 | + | 0.996929i | \(0.475048\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 22.0103 | 0.944551 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 7.22198 | 0.309355 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −0.827186 | −0.0353679 | −0.0176840 | − | 0.999844i | \(-0.505629\pi\) | ||||
−0.0176840 | + | 0.999844i | \(0.505629\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −3.09826 | −0.132231 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 3.37158 | 0.143634 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −12.9118 | −0.549065 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 3.41469 | 0.144945 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −31.7654 | −1.34594 | −0.672972 | − | 0.739668i | \(-0.734983\pi\) | ||||
−0.672972 | + | 0.739668i | \(0.734983\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −1.34066 | −0.0567039 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −14.2709 | −0.602517 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −21.1838 | −0.892789 | −0.446395 | − | 0.894836i | \(-0.647292\pi\) | ||||
−0.446395 | + | 0.894836i | \(0.647292\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −12.8873 | −0.542173 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 3.90501 | 0.163995 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 11.4066 | 0.478188 | 0.239094 | − | 0.970996i | \(-0.423150\pi\) | ||||
0.239094 | + | 0.970996i | \(0.423150\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −20.0422 | −0.838740 | −0.419370 | − | 0.907815i | \(-0.637749\pi\) | ||||
−0.419370 | + | 0.907815i | \(0.637749\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −11.7210 | −0.489652 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 4.18840 | 0.174668 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 35.4444 | 1.47557 | 0.737785 | − | 0.675036i | \(-0.235872\pi\) | ||||
0.737785 | + | 0.675036i | \(0.235872\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −8.21648 | −0.341465 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −3.96158 | −0.164354 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −32.0746 | −1.32839 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −1.96857 | −0.0813904 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −18.2013 | −0.751249 | −0.375625 | − | 0.926772i | \(-0.622572\pi\) | ||||
−0.375625 | + | 0.926772i | \(0.622572\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 17.1427 | 0.706352 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −0.510756 | −0.0210097 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 32.2026 | 1.32240 | 0.661200 | − | 0.750209i | \(-0.270047\pi\) | ||||
0.661200 | + | 0.750209i | \(0.270047\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −9.30046 | −0.381282 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 9.23340 | 0.377898 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 9.58646 | 0.391692 | 0.195846 | − | 0.980635i | \(-0.437255\pi\) | ||||
0.195846 | + | 0.980635i | \(0.437255\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −11.3781 | −0.464122 | −0.232061 | − | 0.972701i | \(-0.574547\pi\) | ||||
−0.232061 | + | 0.972701i | \(0.574547\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −12.6836 | −0.516514 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 16.3414 | 0.664372 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −42.0701 | −1.70757 | −0.853787 | − | 0.520623i | \(-0.825700\pi\) | ||||
−0.853787 | + | 0.520623i | \(0.825700\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −3.90501 | −0.158239 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −2.24361 | −0.0907667 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −25.5846 | −1.03335 | −0.516676 | − | 0.856181i | \(-0.672831\pi\) | ||||
−0.516676 | + | 0.856181i | \(0.672831\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −7.95461 | −0.320761 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −21.8215 | −0.878502 | −0.439251 | − | 0.898364i | \(-0.644756\pi\) | ||||
−0.439251 | + | 0.898364i | \(0.644756\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 23.7623 | 0.955087 | 0.477544 | − | 0.878608i | \(-0.341527\pi\) | ||||
0.477544 | + | 0.878608i | \(0.341527\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.00000 | 0.0401286 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −68.2922 | −2.73607 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 13.4847 | 0.539388 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 18.2000 | 0.726840 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 10.0205 | 0.399545 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 19.0191 | 0.757138 | 0.378569 | − | 0.925573i | \(-0.376416\pi\) | ||||
0.378569 | + | 0.925573i | \(0.376416\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −13.8507 | −0.550515 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 13.3139 | 0.528346 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −18.0254 | −0.714193 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −4.69605 | −0.185773 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −11.2100 | −0.442767 | −0.221383 | − | 0.975187i | \(-0.571057\pi\) | ||||
−0.221383 | + | 0.975187i | \(0.571057\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −22.7058 | −0.895430 | −0.447715 | − | 0.894176i | \(-0.647762\pi\) | ||||
−0.447715 | + | 0.894176i | \(0.647762\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −0.552726 | −0.0217636 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −13.7388 | −0.540127 | −0.270064 | − | 0.962842i | \(-0.587045\pi\) | ||||
−0.270064 | + | 0.962842i | \(0.587045\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 54.0121 | 2.12016 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −19.8549 | −0.778174 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −3.31245 | −0.129626 | −0.0648130 | − | 0.997897i | \(-0.520645\pi\) | ||||
−0.0648130 | + | 0.997897i | \(0.520645\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0.103687 | 0.00405137 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 9.03175 | 0.352362 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 4.02358 | 0.156736 | 0.0783681 | − | 0.996924i | \(-0.475029\pi\) | ||||
0.0783681 | + | 0.996924i | \(0.475029\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −15.0724 | −0.586249 | −0.293125 | − | 0.956074i | \(-0.594695\pi\) | ||||
−0.293125 | + | 0.956074i | \(0.594695\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −5.77686 | −0.224355 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 11.8611 | 0.459955 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1.00000 | −0.0387202 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −0.400408 | −0.0154807 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 16.7246 | 0.645648 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −15.0200 | −0.578978 | −0.289489 | − | 0.957181i | \(-0.593485\pi\) | ||||
−0.289489 | + | 0.957181i | \(0.593485\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 4.18840 | 0.161212 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −20.0315 | −0.769872 | −0.384936 | − | 0.922943i | \(-0.625776\pi\) | ||||
−0.384936 | + | 0.922943i | \(0.625776\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 19.1895 | 0.736427 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −6.20230 | −0.237673 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 32.3988 | 1.23971 | 0.619853 | − | 0.784718i | \(-0.287192\pi\) | ||||
0.619853 | + | 0.784718i | \(0.287192\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 6.48450 | 0.247760 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −7.12470 | −0.271824 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −12.9838 | −0.494644 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −31.9042 | −1.21369 | −0.606847 | − | 0.794818i | \(-0.707566\pi\) | ||||
−0.606847 | + | 0.794818i | \(0.707566\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −21.0795 | −0.800745 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −3.90785 | −0.148233 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −23.3432 | −0.884185 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 8.64191 | 0.326867 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −41.2753 | −1.55894 | −0.779472 | − | 0.626437i | \(-0.784513\pi\) | ||||
−0.779472 | + | 0.626437i | \(0.784513\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −12.7795 | −0.481987 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −0.924992 | −0.0348372 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −49.6898 | −1.86878 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −11.4863 | −0.431379 | −0.215689 | − | 0.976462i | \(-0.569200\pi\) | ||||
−0.215689 | + | 0.976462i | \(0.569200\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −3.30647 | −0.124002 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −5.08447 | −0.190415 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 10.6265 | 0.397408 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −15.2043 | −0.567816 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 45.5003 | 1.69687 | 0.848437 | − | 0.529297i | \(-0.177544\pi\) | ||||
0.848437 | + | 0.529297i | \(0.177544\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −33.4190 | −1.24459 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 23.0248 | 0.856302 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −4.18840 | −0.155553 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 2.52414 | 0.0936152 | 0.0468076 | − | 0.998904i | \(-0.485095\pi\) | ||||
0.0468076 | + | 0.998904i | \(0.485095\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −1.62200 | −0.0599918 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −22.9871 | −0.849049 | −0.424524 | − | 0.905417i | \(-0.639559\pi\) | ||||
−0.424524 | + | 0.905417i | \(0.639559\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −7.43150 | −0.274115 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 68.4668 | 2.52201 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 28.4478 | 1.04647 | 0.523234 | − | 0.852189i | \(-0.324725\pi\) | ||||
0.523234 | + | 0.852189i | \(0.324725\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 7.36739 | 0.270648 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 9.46727 | 0.347321 | 0.173660 | − | 0.984806i | \(-0.444441\pi\) | ||||
0.173660 | + | 0.984806i | \(0.444441\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −10.3930 | −0.380771 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −1.01449 | −0.0371181 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −56.9138 | −2.07959 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −11.2455 | −0.410355 | −0.205177 | − | 0.978725i | \(-0.565777\pi\) | ||||
−0.205177 | + | 0.978725i | \(0.565777\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −18.5440 | −0.675782 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 12.3233 | 0.448490 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 5.68039 | 0.206457 | 0.103229 | − | 0.994658i | \(-0.467083\pi\) | ||||
0.103229 | + | 0.994658i | \(0.467083\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −5.39807 | −0.195938 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −14.1168 | −0.511734 | −0.255867 | − | 0.966712i | \(-0.582361\pi\) | ||||
−0.255867 | + | 0.966712i | \(0.582361\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 31.3045 | 1.13330 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −2.38168 | −0.0861097 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 21.8641 | 0.789469 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −1.36141 | −0.0490938 | −0.0245469 | − | 0.999699i | \(-0.507814\pi\) | ||||
−0.0245469 | + | 0.999699i | \(0.507814\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 12.8335 | 0.462187 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −36.4036 | −1.30935 | −0.654673 | − | 0.755912i | \(-0.727194\pi\) | ||||
−0.654673 | + | 0.755912i | \(0.727194\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −21.2958 | −0.764967 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 14.8014 | 0.530996 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 29.7702 | 1.06663 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 25.3496 | 0.907080 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −1.00000 | −0.0357371 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0.0192816 | 0.000688190 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −53.5148 | −1.90760 | −0.953799 | − | 0.300447i | \(-0.902864\pi\) | ||||
−0.953799 | + | 0.300447i | \(0.902864\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 14.8682 | 0.529322 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −55.8616 | −1.98621 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 6.77015 | 0.240415 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −5.35295 | −0.189850 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 43.8576 | 1.55351 | 0.776757 | − | 0.629800i | \(-0.216863\pi\) | ||||
0.776757 | + | 0.629800i | \(0.216863\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −2.71443 | −0.0960297 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −17.4884 | −0.617921 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −48.7541 | −1.72049 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −3.51798 | −0.123992 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 15.3258 | 0.539493 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −20.4766 | −0.719920 | −0.359960 | − | 0.932968i | \(-0.617210\pi\) | ||||
−0.359960 | + | 0.932968i | \(0.617210\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 41.0750 | 1.44234 | 0.721170 | − | 0.692758i | \(-0.243605\pi\) | ||||
0.721170 | + | 0.692758i | \(0.243605\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 25.3597 | 0.889403 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −0.500692 | −0.0175385 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 2.06858 | 0.0723705 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −8.53300 | −0.298167 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −34.0314 | −1.18770 | −0.593852 | − | 0.804574i | \(-0.702393\pi\) | ||||
−0.593852 | + | 0.804574i | \(0.702393\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −54.7566 | −1.90870 | −0.954348 | − | 0.298698i | \(-0.903448\pi\) | ||||
−0.954348 | + | 0.298698i | \(0.903448\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −22.6093 | −0.787155 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 4.40663 | 0.153233 | 0.0766167 | − | 0.997061i | \(-0.475588\pi\) | ||||
0.0766167 | + | 0.997061i | \(0.475588\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −27.7917 | −0.965244 | −0.482622 | − | 0.875829i | \(-0.660315\pi\) | ||||
−0.482622 | + | 0.875829i | \(0.660315\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 14.5368 | 0.504275 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −21.8081 | −0.755605 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 6.22103 | 0.215287 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −5.08447 | −0.175745 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 35.7491 | 1.23420 | 0.617098 | − | 0.786886i | \(-0.288308\pi\) | ||||
0.617098 | + | 0.786886i | \(0.288308\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.00000 | 0.0344828 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 27.7945 | 0.957293 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −7.40994 | −0.254910 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 70.8337 | 2.43388 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 4.01747 | 0.137879 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 3.79035 | 0.129932 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 20.2840 | 0.694509 | 0.347255 | − | 0.937771i | \(-0.387114\pi\) | ||||
0.347255 | + | 0.937771i | \(0.387114\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 3.03742 | 0.103877 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 11.5100 | 0.393175 | 0.196588 | − | 0.980486i | \(-0.437014\pi\) | ||||
0.196588 | + | 0.980486i | \(0.437014\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −44.2221 | −1.50884 | −0.754419 | − | 0.656393i | \(-0.772081\pi\) | ||||
−0.754419 | + | 0.656393i | \(0.772081\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −34.4802 | −1.17508 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −26.5666 | −0.904337 | −0.452169 | − | 0.891932i | \(-0.649349\pi\) | ||||
−0.452169 | + | 0.891932i | \(0.649349\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 4.75475 | 0.161666 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 10.0109 | 0.339987 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 17.8486 | 0.605471 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 27.7154 | 0.939100 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 4.91409 | 0.166317 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −32.3246 | −1.09277 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 23.1214 | 0.780754 | 0.390377 | − | 0.920655i | \(-0.372345\pi\) | ||||
0.390377 | + | 0.920655i | \(0.372345\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 32.9948 | 1.11289 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 21.4796 | 0.723666 | 0.361833 | − | 0.932243i | \(-0.382151\pi\) | ||||
0.361833 | + | 0.932243i | \(0.382151\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −11.9649 | −0.402650 | −0.201325 | − | 0.979525i | \(-0.564525\pi\) | ||||
−0.201325 | + | 0.979525i | \(0.564525\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 9.01412 | 0.303006 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 43.8213 | 1.47138 | 0.735688 | − | 0.677320i | \(-0.236859\pi\) | ||||
0.735688 | + | 0.677320i | \(0.236859\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 57.7107 | 1.93556 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −5.39807 | −0.180842 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 3.46179 | 0.115844 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −6.10501 | −0.204068 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −2.18514 | −0.0729598 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 5.08447 | 0.169576 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −15.7085 | −0.523325 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −2.39586 | −0.0797291 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −19.8288 | −0.659131 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 37.5669 | 1.24739 | 0.623694 | − | 0.781668i | \(-0.285631\pi\) | ||||
0.623694 | + | 0.781668i | \(0.285631\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −12.7246 | −0.422050 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −6.78171 | −0.224688 | −0.112344 | − | 0.993669i | \(-0.535836\pi\) | ||||
−0.112344 | + | 0.993669i | \(0.535836\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 5.47627 | 0.181238 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 2.79119 | 0.0922738 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0.449442 | 0.0148419 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −35.3208 | −1.16513 | −0.582563 | − | 0.812786i | \(-0.697950\pi\) | ||||
−0.582563 | + | 0.812786i | \(0.697950\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 9.56599 | 0.315210 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 10.2615 | 0.337762 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 15.8755 | 0.521984 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −8.55800 | −0.281082 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −25.8804 | −0.849108 | −0.424554 | − | 0.905403i | \(-0.639569\pi\) | ||||
−0.424554 | + | 0.905403i | \(0.639569\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 27.8124 | 0.911516 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −4.28315 | −0.140224 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 12.8565 | 0.420451 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 29.1283 | 0.951582 | 0.475791 | − | 0.879558i | \(-0.342162\pi\) | ||||
0.475791 | + | 0.879558i | \(0.342162\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −0.673397 | −0.0219755 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −2.68696 | −0.0875925 | −0.0437963 | − | 0.999040i | \(-0.513945\pi\) | ||||
−0.0437963 | + | 0.999040i | \(0.513945\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −8.82974 | −0.287536 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −3.51798 | −0.114440 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 39.4768 | 1.28282 | 0.641412 | − | 0.767197i | \(-0.278349\pi\) | ||||
0.641412 | + | 0.767197i | \(0.278349\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −19.7357 | −0.640647 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 17.0792 | 0.553831 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 19.7605 | 0.640106 | 0.320053 | − | 0.947400i | \(-0.396299\pi\) | ||||
0.320053 | + | 0.947400i | \(0.396299\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 10.5593 | 0.341692 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 5.39807 | 0.174495 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 28.1078 | 0.907649 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −5.14819 | −0.166071 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −14.5746 | −0.469659 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 7.40213 | 0.238283 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 55.6598 | 1.78990 | 0.894949 | − | 0.446169i | \(-0.147212\pi\) | ||||
0.894949 | + | 0.446169i | \(0.147212\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 8.91344 | 0.286341 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −21.7277 | −0.697276 | −0.348638 | − | 0.937257i | \(-0.613356\pi\) | ||||
−0.348638 | + | 0.937257i | \(0.613356\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −16.9390 | −0.543041 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −9.15225 | −0.293107 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 8.02371 | 0.256701 | 0.128351 | − | 0.991729i | \(-0.459032\pi\) | ||||
0.128351 | + | 0.991729i | \(0.459032\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 94.4036 | 3.01715 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 8.01651 | 0.255947 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 35.6083 | 1.13573 | 0.567865 | − | 0.823122i | \(-0.307770\pi\) | ||||
0.567865 | + | 0.823122i | \(0.307770\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0.460134 | 0.0146611 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −4.00949 | −0.127623 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −0.613535 | −0.0195093 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 27.9781 | 0.888755 | 0.444377 | − | 0.895840i | \(-0.353425\pi\) | ||||
0.444377 | + | 0.895840i | \(0.353425\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −7.39283 | −0.234604 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −8.31826 | −0.263707 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 57.5748 | 1.82341 | 0.911707 | − | 0.410842i | \(-0.134765\pi\) | ||||
0.911707 | + | 0.410842i | \(0.134765\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 3.79035 | 0.119921 |
(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.e.1.6 | ✓ | 9 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8004.2.a.e.1.6 | ✓ | 9 | 1.1 | even | 1 | trivial |