Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8280,2,Mod(1,8280)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8280, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("8280.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8280 = 2^{3} \cdot 3^{2} \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8280.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: | \(66.1161328736\) |
Analytic rank: | \(1\) |
Dimension: | \(6\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{6} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 2x^{5} - 16x^{4} + 26x^{3} + 52x^{2} - 48x + 9 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(0.287750\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8280.1 |
$q$-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 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.73629 | −1.03422 | −0.517109 | − | 0.855919i | \(-0.672992\pi\) | ||||
−0.517109 | + | 0.855919i | \(0.672992\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 5.97718 | 1.80219 | 0.901094 | − | 0.433624i | \(-0.142765\pi\) | ||||
0.901094 | + | 0.433624i | \(0.142765\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −5.40168 | −1.49816 | −0.749078 | − | 0.662482i | \(-0.769503\pi\) | ||||
−0.749078 | + | 0.662482i | \(0.769503\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 6.94546 | 1.68452 | 0.842261 | − | 0.539070i | \(-0.181224\pi\) | ||||
0.842261 | + | 0.539070i | \(0.181224\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −3.97718 | −0.912428 | −0.456214 | − | 0.889870i | \(-0.650795\pi\) | ||||
−0.456214 | + | 0.889870i | \(0.650795\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.00000 | −0.208514 | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −9.29741 | −1.72649 | −0.863243 | − | 0.504788i | \(-0.831571\pi\) | ||||
−0.863243 | + | 0.504788i | \(0.831571\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.54378 | −0.636482 | −0.318241 | − | 0.948010i | \(-0.603092\pi\) | ||||
−0.318241 | + | 0.948010i | \(0.603092\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 2.73629 | 0.462517 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 7.17782 | 1.18003 | 0.590013 | − | 0.807394i | \(-0.299123\pi\) | ||||
0.590013 | + | 0.807394i | \(0.299123\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 10.1945 | 1.59211 | 0.796056 | − | 0.605223i | \(-0.206916\pi\) | ||||
0.796056 | + | 0.605223i | \(0.206916\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.42450 | 0.217234 | 0.108617 | − | 0.994084i | \(-0.465358\pi\) | ||||
0.108617 | + | 0.994084i | \(0.465358\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 10.4187 | 1.51973 | 0.759863 | − | 0.650084i | \(-0.225266\pi\) | ||||
0.759863 | + | 0.650084i | \(0.225266\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0.487260 | 0.0696085 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −4.04839 | −0.556089 | −0.278044 | − | 0.960568i | \(-0.589686\pi\) | ||||
−0.278044 | + | 0.960568i | \(0.589686\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −5.97718 | −0.805963 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −8.13797 | −1.05947 | −0.529736 | − | 0.848162i | \(-0.677709\pi\) | ||||
−0.529736 | + | 0.848162i | \(0.677709\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −3.34516 | −0.428304 | −0.214152 | − | 0.976800i | \(-0.568699\pi\) | ||||
−0.214152 | + | 0.976800i | \(0.568699\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 5.40168 | 0.669996 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1.70525 | −0.208329 | −0.104164 | − | 0.994560i | \(-0.533217\pi\) | ||||
−0.104164 | + | 0.994560i | \(0.533217\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 7.56247 | 0.897500 | 0.448750 | − | 0.893657i | \(-0.351869\pi\) | ||||
0.448750 | + | 0.893657i | \(0.351869\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 7.85722 | 0.919618 | 0.459809 | − | 0.888018i | \(-0.347918\pi\) | ||||
0.459809 | + | 0.888018i | \(0.347918\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −16.3553 | −1.86386 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1.36798 | −0.153910 | −0.0769548 | − | 0.997035i | \(-0.524520\pi\) | ||||
−0.0769548 | + | 0.997035i | \(0.524520\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −13.9709 | −1.53351 | −0.766755 | − | 0.641940i | \(-0.778130\pi\) | ||||
−0.766755 | + | 0.641940i | \(0.778130\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −6.94546 | −0.753341 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 6.49805 | 0.688792 | 0.344396 | − | 0.938824i | \(-0.388084\pi\) | ||||
0.344396 | + | 0.938824i | \(0.388084\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 14.7805 | 1.54942 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 3.97718 | 0.408050 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −13.8769 | −1.40899 | −0.704493 | − | 0.709710i | \(-0.748826\pi\) | ||||
−0.704493 | + | 0.709710i | \(0.748826\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −18.4293 | −1.83378 | −0.916890 | − | 0.399140i | \(-0.869309\pi\) | ||||
−0.916890 | + | 0.399140i | \(0.869309\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 8.29130 | 0.816966 | 0.408483 | − | 0.912766i | \(-0.366058\pi\) | ||||
0.408483 | + | 0.912766i | \(0.366058\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 0.583632 | 0.0564218 | 0.0282109 | − | 0.999602i | \(-0.491019\pi\) | ||||
0.0282109 | + | 0.999602i | \(0.491019\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −4.37064 | −0.418631 | −0.209316 | − | 0.977848i | \(-0.567124\pi\) | ||||
−0.209316 | + | 0.977848i | \(0.567124\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −11.4504 | −1.07717 | −0.538583 | − | 0.842572i | \(-0.681040\pi\) | ||||
−0.538583 | + | 0.842572i | \(0.681040\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.00000 | 0.0932505 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −19.0048 | −1.74216 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 24.7267 | 2.24788 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 16.9710 | 1.50594 | 0.752968 | − | 0.658058i | \(-0.228622\pi\) | ||||
0.752968 | + | 0.658058i | \(0.228622\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 18.3727 | 1.60523 | 0.802616 | − | 0.596497i | \(-0.203441\pi\) | ||||
0.802616 | + | 0.596497i | \(0.203441\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 10.8827 | 0.943650 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −7.74607 | −0.661792 | −0.330896 | − | 0.943667i | \(-0.607351\pi\) | ||||
−0.330896 | + | 0.943667i | \(0.607351\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −10.2906 | −0.872839 | −0.436419 | − | 0.899743i | \(-0.643754\pi\) | ||||
−0.436419 | + | 0.899743i | \(0.643754\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −32.2868 | −2.69996 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 9.29741 | 0.772108 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −17.0647 | −1.39800 | −0.698999 | − | 0.715123i | \(-0.746371\pi\) | ||||
−0.698999 | + | 0.715123i | \(0.746371\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −15.9141 | −1.29507 | −0.647536 | − | 0.762035i | \(-0.724200\pi\) | ||||
−0.647536 | + | 0.762035i | \(0.724200\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 3.54378 | 0.284643 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 24.5482 | 1.95916 | 0.979581 | − | 0.201050i | \(-0.0644355\pi\) | ||||
0.979581 | + | 0.201050i | \(0.0644355\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 2.73629 | 0.215650 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −7.71580 | −0.604348 | −0.302174 | − | 0.953253i | \(-0.597712\pi\) | ||||
−0.302174 | + | 0.953253i | \(0.597712\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −0.0793410 | −0.00613959 | −0.00306979 | − | 0.999995i | \(-0.500977\pi\) | ||||
−0.00306979 | + | 0.999995i | \(0.500977\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 16.1781 | 1.24447 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 19.1590 | 1.45663 | 0.728316 | − | 0.685242i | \(-0.240303\pi\) | ||||
0.728316 | + | 0.685242i | \(0.240303\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −2.73629 | −0.206844 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −4.68009 | −0.349807 | −0.174903 | − | 0.984586i | \(-0.555961\pi\) | ||||
−0.174903 | + | 0.984586i | \(0.555961\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 7.46476 | 0.554851 | 0.277426 | − | 0.960747i | \(-0.410519\pi\) | ||||
0.277426 | + | 0.960747i | \(0.410519\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −7.17782 | −0.527724 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 41.5143 | 3.03582 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −26.7805 | −1.93777 | −0.968886 | − | 0.247508i | \(-0.920388\pi\) | ||||
−0.968886 | + | 0.247508i | \(0.920388\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 12.8196 | 0.922777 | 0.461388 | − | 0.887198i | \(-0.347351\pi\) | ||||
0.461388 | + | 0.887198i | \(0.347351\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −2.60577 | −0.185654 | −0.0928268 | − | 0.995682i | \(-0.529590\pi\) | ||||
−0.0928268 | + | 0.995682i | \(0.529590\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −12.5686 | −0.890963 | −0.445482 | − | 0.895291i | \(-0.646968\pi\) | ||||
−0.445482 | + | 0.895291i | \(0.646968\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 25.4404 | 1.78556 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −10.1945 | −0.712014 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −23.7723 | −1.64437 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −25.1102 | −1.72866 | −0.864330 | − | 0.502925i | \(-0.832257\pi\) | ||||
−0.864330 | + | 0.502925i | \(0.832257\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −1.42450 | −0.0971501 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 9.69680 | 0.658261 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −37.5172 | −2.52368 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −10.4718 | −0.701244 | −0.350622 | − | 0.936517i | \(-0.614030\pi\) | ||||
−0.350622 | + | 0.936517i | \(0.614030\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 17.2767 | 1.14669 | 0.573347 | − | 0.819312i | \(-0.305645\pi\) | ||||
0.573347 | + | 0.819312i | \(0.305645\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −12.5065 | −0.826453 | −0.413226 | − | 0.910628i | \(-0.635598\pi\) | ||||
−0.413226 | + | 0.910628i | \(0.635598\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 6.09678 | 0.399413 | 0.199707 | − | 0.979856i | \(-0.436001\pi\) | ||||
0.199707 | + | 0.979856i | \(0.436001\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −10.4187 | −0.679642 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 4.57168 | 0.295718 | 0.147859 | − | 0.989008i | \(-0.452762\pi\) | ||||
0.147859 | + | 0.989008i | \(0.452762\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −25.9022 | −1.66851 | −0.834253 | − | 0.551383i | \(-0.814100\pi\) | ||||
−0.834253 | + | 0.551383i | \(0.814100\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −0.487260 | −0.0311299 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 21.4835 | 1.36696 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 0.803360 | 0.0507076 | 0.0253538 | − | 0.999679i | \(-0.491929\pi\) | ||||
0.0253538 | + | 0.999679i | \(0.491929\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −5.97718 | −0.375782 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −6.20486 | −0.387049 | −0.193524 | − | 0.981095i | \(-0.561992\pi\) | ||||
−0.193524 | + | 0.981095i | \(0.561992\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −19.6406 | −1.22040 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −20.8348 | −1.28473 | −0.642366 | − | 0.766398i | \(-0.722047\pi\) | ||||
−0.642366 | + | 0.766398i | \(0.722047\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 4.04839 | 0.248691 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 22.8374 | 1.39242 | 0.696210 | − | 0.717838i | \(-0.254868\pi\) | ||||
0.696210 | + | 0.717838i | \(0.254868\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −28.5632 | −1.73509 | −0.867547 | − | 0.497356i | \(-0.834304\pi\) | ||||
−0.867547 | + | 0.497356i | \(0.834304\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 5.97718 | 0.360438 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −26.2565 | −1.57760 | −0.788801 | − | 0.614648i | \(-0.789298\pi\) | ||||
−0.788801 | + | 0.614648i | \(0.789298\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 3.27463 | 0.195348 | 0.0976740 | − | 0.995218i | \(-0.468860\pi\) | ||||
0.0976740 | + | 0.995218i | \(0.468860\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −8.87870 | −0.527784 | −0.263892 | − | 0.964552i | \(-0.585006\pi\) | ||||
−0.263892 | + | 0.964552i | \(0.585006\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −27.8950 | −1.64659 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 31.2394 | 1.83761 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 16.3646 | 0.956029 | 0.478014 | − | 0.878352i | \(-0.341357\pi\) | ||||
0.478014 | + | 0.878352i | \(0.341357\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 8.13797 | 0.473811 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 5.40168 | 0.312387 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −3.89784 | −0.224668 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 3.34516 | 0.191543 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −21.0803 | −1.20312 | −0.601558 | − | 0.798829i | \(-0.705453\pi\) | ||||
−0.601558 | + | 0.798829i | \(0.705453\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −24.9877 | −1.41692 | −0.708460 | − | 0.705751i | \(-0.750610\pi\) | ||||
−0.708460 | + | 0.705751i | \(0.750610\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −26.8602 | −1.51823 | −0.759114 | − | 0.650957i | \(-0.774368\pi\) | ||||
−0.759114 | + | 0.650957i | \(0.774368\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −25.0456 | −1.40670 | −0.703350 | − | 0.710843i | \(-0.748313\pi\) | ||||
−0.703350 | + | 0.710843i | \(0.748313\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −55.5723 | −3.11145 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −27.6233 | −1.53700 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −5.40168 | −0.299631 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −28.5086 | −1.57173 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −13.4803 | −0.740947 | −0.370473 | − | 0.928843i | \(-0.620804\pi\) | ||||
−0.370473 | + | 0.928843i | \(0.620804\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 1.70525 | 0.0931675 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 24.3478 | 1.32631 | 0.663155 | − | 0.748482i | \(-0.269217\pi\) | ||||
0.663155 | + | 0.748482i | \(0.269217\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −21.1818 | −1.14706 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 17.8207 | 0.962228 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −5.15100 | −0.276520 | −0.138260 | − | 0.990396i | \(-0.544151\pi\) | ||||
−0.138260 | + | 0.990396i | \(0.544151\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 23.0646 | 1.23462 | 0.617310 | − | 0.786720i | \(-0.288222\pi\) | ||||
0.617310 | + | 0.786720i | \(0.288222\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −2.62321 | −0.139619 | −0.0698097 | − | 0.997560i | \(-0.522239\pi\) | ||||
−0.0698097 | + | 0.997560i | \(0.522239\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −7.56247 | −0.401374 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 1.36987 | 0.0722991 | 0.0361495 | − | 0.999346i | \(-0.488491\pi\) | ||||
0.0361495 | + | 0.999346i | \(0.488491\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −3.18204 | −0.167476 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −7.85722 | −0.411266 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −8.01055 | −0.418147 | −0.209074 | − | 0.977900i | \(-0.567045\pi\) | ||||
−0.209074 | + | 0.977900i | \(0.567045\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 11.0775 | 0.575118 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −7.80815 | −0.404291 | −0.202145 | − | 0.979356i | \(-0.564791\pi\) | ||||
−0.202145 | + | 0.979356i | \(0.564791\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 50.2217 | 2.58655 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −23.8126 | −1.22317 | −0.611585 | − | 0.791179i | \(-0.709468\pi\) | ||||
−0.611585 | + | 0.791179i | \(0.709468\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −16.4730 | −0.841732 | −0.420866 | − | 0.907123i | \(-0.638274\pi\) | ||||
−0.420866 | + | 0.907123i | \(0.638274\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 16.3553 | 0.833542 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 5.71444 | 0.289734 | 0.144867 | − | 0.989451i | \(-0.453725\pi\) | ||||
0.144867 | + | 0.989451i | \(0.453725\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −6.94546 | −0.351247 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 1.36798 | 0.0688305 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −14.6525 | −0.735388 | −0.367694 | − | 0.929947i | \(-0.619853\pi\) | ||||
−0.367694 | + | 0.929947i | \(0.619853\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −21.2851 | −1.06293 | −0.531465 | − | 0.847080i | \(-0.678358\pi\) | ||||
−0.531465 | + | 0.847080i | \(0.678358\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 19.1424 | 0.953549 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 42.9031 | 2.12663 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 31.1908 | 1.54228 | 0.771142 | − | 0.636663i | \(-0.219686\pi\) | ||||
0.771142 | + | 0.636663i | \(0.219686\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 22.2678 | 1.09573 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 13.9709 | 0.685807 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −36.4950 | −1.78290 | −0.891448 | − | 0.453123i | \(-0.850310\pi\) | ||||
−0.891448 | + | 0.453123i | \(0.850310\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −2.94307 | −0.143437 | −0.0717183 | − | 0.997425i | \(-0.522848\pi\) | ||||
−0.0717183 | + | 0.997425i | \(0.522848\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 6.94546 | 0.336904 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 9.15331 | 0.442960 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −3.53529 | −0.170289 | −0.0851444 | − | 0.996369i | \(-0.527135\pi\) | ||||
−0.0851444 | + | 0.996369i | \(0.527135\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 38.5181 | 1.85106 | 0.925532 | − | 0.378671i | \(-0.123619\pi\) | ||||
0.925532 | + | 0.378671i | \(0.123619\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 3.97718 | 0.190254 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −13.3043 | −0.634980 | −0.317490 | − | 0.948262i | \(-0.602840\pi\) | ||||
−0.317490 | + | 0.948262i | \(0.602840\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −21.1259 | −1.00372 | −0.501862 | − | 0.864948i | \(-0.667351\pi\) | ||||
−0.501862 | + | 0.864948i | \(0.667351\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −6.49805 | −0.308037 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −2.13932 | −0.100961 | −0.0504805 | − | 0.998725i | \(-0.516075\pi\) | ||||
−0.0504805 | + | 0.998725i | \(0.516075\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 60.9343 | 2.86928 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −14.7805 | −0.692922 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 0.0350873 | 0.00164131 | 0.000820657 | − | 1.00000i | \(-0.499739\pi\) | ||||
0.000820657 | 1.00000i | \(0.499739\pi\) | ||||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 30.2381 | 1.40833 | 0.704164 | − | 0.710037i | \(-0.251322\pi\) | ||||
0.704164 | + | 0.710037i | \(0.251322\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −4.31412 | −0.200494 | −0.100247 | − | 0.994963i | \(-0.531963\pi\) | ||||
−0.100247 | + | 0.994963i | \(0.531963\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −19.7680 | −0.914753 | −0.457376 | − | 0.889273i | \(-0.651211\pi\) | ||||
−0.457376 | + | 0.889273i | \(0.651211\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 4.66604 | 0.215458 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 8.51449 | 0.391497 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −3.97718 | −0.182486 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −18.5883 | −0.849320 | −0.424660 | − | 0.905353i | \(-0.639606\pi\) | ||||
−0.424660 | + | 0.905353i | \(0.639606\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −38.7723 | −1.76786 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 13.8769 | 0.630118 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 15.1337 | 0.685775 | 0.342888 | − | 0.939376i | \(-0.388595\pi\) | ||||
0.342888 | + | 0.939376i | \(0.388595\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −29.0762 | −1.31219 | −0.656095 | − | 0.754678i | \(-0.727793\pi\) | ||||
−0.656095 | + | 0.754678i | \(0.727793\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −64.5748 | −2.90830 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −20.6931 | −0.928211 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 13.4060 | 0.600133 | 0.300067 | − | 0.953918i | \(-0.402991\pi\) | ||||
0.300067 | + | 0.953918i | \(0.402991\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 13.2143 | 0.589197 | 0.294598 | − | 0.955621i | \(-0.404814\pi\) | ||||
0.294598 | + | 0.955621i | \(0.404814\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 18.4293 | 0.820091 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −8.41682 | −0.373069 | −0.186534 | − | 0.982448i | \(-0.559726\pi\) | ||||
−0.186534 | + | 0.982448i | \(0.559726\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −21.4996 | −0.951086 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −8.29130 | −0.365358 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 62.2745 | 2.73883 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 4.03908 | 0.176955 | 0.0884777 | − | 0.996078i | \(-0.471800\pi\) | ||||
0.0884777 | + | 0.996078i | \(0.471800\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 8.85699 | 0.387289 | 0.193645 | − | 0.981072i | \(-0.437969\pi\) | ||||
0.193645 | + | 0.981072i | \(0.437969\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −24.6132 | −1.07217 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −55.0674 | −2.38523 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −0.583632 | −0.0252326 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 2.91244 | 0.125448 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −28.1566 | −1.21055 | −0.605274 | − | 0.796017i | \(-0.706936\pi\) | ||||
−0.605274 | + | 0.796017i | \(0.706936\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 4.37064 | 0.187218 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −19.4765 | −0.832756 | −0.416378 | − | 0.909191i | \(-0.636701\pi\) | ||||
−0.416378 | + | 0.909191i | \(0.636701\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 36.9775 | 1.57529 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 3.74318 | 0.159176 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −6.88185 | −0.291593 | −0.145797 | − | 0.989315i | \(-0.546575\pi\) | ||||
−0.145797 | + | 0.989315i | \(0.546575\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −7.69469 | −0.325451 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 9.30665 | 0.392229 | 0.196114 | − | 0.980581i | \(-0.437168\pi\) | ||||
0.196114 | + | 0.980581i | \(0.437168\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 11.4504 | 0.481723 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 18.5779 | 0.778827 | 0.389414 | − | 0.921063i | \(-0.372678\pi\) | ||||
0.389414 | + | 0.921063i | \(0.372678\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 39.5512 | 1.65517 | 0.827583 | − | 0.561343i | \(-0.189715\pi\) | ||||
0.827583 | + | 0.561343i | \(0.189715\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −1.00000 | −0.0417029 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −13.1923 | −0.549204 | −0.274602 | − | 0.961558i | \(-0.588546\pi\) | ||||
−0.274602 | + | 0.961558i | \(0.588546\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 38.2285 | 1.58598 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −24.1979 | −1.00218 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −10.7066 | −0.441908 | −0.220954 | − | 0.975284i | \(-0.570917\pi\) | ||||
−0.220954 | + | 0.975284i | \(0.570917\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 14.0943 | 0.580744 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 3.98410 | 0.163607 | 0.0818036 | − | 0.996648i | \(-0.473932\pi\) | ||||
0.0818036 | + | 0.996648i | \(0.473932\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 19.0048 | 0.779119 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 25.9056 | 1.05847 | 0.529237 | − | 0.848474i | \(-0.322478\pi\) | ||||
0.529237 | + | 0.848474i | \(0.322478\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 12.3935 | 0.505542 | 0.252771 | − | 0.967526i | \(-0.418658\pi\) | ||||
0.252771 | + | 0.967526i | \(0.418658\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −24.7267 | −1.00528 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −22.4768 | −0.912304 | −0.456152 | − | 0.889902i | \(-0.650773\pi\) | ||||
−0.456152 | + | 0.889902i | \(0.650773\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −56.2785 | −2.27679 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −23.9995 | −0.969332 | −0.484666 | − | 0.874699i | \(-0.661059\pi\) | ||||
−0.484666 | + | 0.874699i | \(0.661059\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −30.7574 | −1.23825 | −0.619123 | − | 0.785294i | \(-0.712512\pi\) | ||||
−0.619123 | + | 0.785294i | \(0.712512\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −34.4693 | −1.38544 | −0.692719 | − | 0.721207i | \(-0.743588\pi\) | ||||
−0.692719 | + | 0.721207i | \(0.743588\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −17.7805 | −0.712362 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 49.8532 | 1.98778 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −8.22555 | −0.327454 | −0.163727 | − | 0.986506i | \(-0.552352\pi\) | ||||
−0.163727 | + | 0.986506i | \(0.552352\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −16.9710 | −0.673475 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −2.63202 | −0.104284 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −40.5166 | −1.60031 | −0.800154 | − | 0.599795i | \(-0.795249\pi\) | ||||
−0.800154 | + | 0.599795i | \(0.795249\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 0.890308 | 0.0351103 | 0.0175552 | − | 0.999846i | \(-0.494412\pi\) | ||||
0.0175552 | + | 0.999846i | \(0.494412\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −31.0168 | −1.21940 | −0.609699 | − | 0.792633i | \(-0.708710\pi\) | ||||
−0.609699 | + | 0.792633i | \(0.708710\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −48.6421 | −1.90937 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 11.8735 | 0.464645 | 0.232323 | − | 0.972639i | \(-0.425367\pi\) | ||||
0.232323 | + | 0.972639i | \(0.425367\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −18.3727 | −0.717881 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 33.0551 | 1.28764 | 0.643822 | − | 0.765175i | \(-0.277348\pi\) | ||||
0.643822 | + | 0.765175i | \(0.277348\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −4.71253 | −0.183296 | −0.0916482 | − | 0.995791i | \(-0.529214\pi\) | ||||
−0.0916482 | + | 0.995791i | \(0.529214\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −10.8827 | −0.422013 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 9.29741 | 0.359997 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −19.9946 | −0.771884 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −13.0906 | −0.504605 | −0.252303 | − | 0.967648i | \(-0.581188\pi\) | ||||
−0.252303 | + | 0.967648i | \(0.581188\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −0.915188 | −0.0351735 | −0.0175868 | − | 0.999845i | \(-0.505598\pi\) | ||||
−0.0175868 | + | 0.999845i | \(0.505598\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 37.9712 | 1.45720 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 30.1856 | 1.15502 | 0.577511 | − | 0.816383i | \(-0.304024\pi\) | ||||
0.577511 | + | 0.816383i | \(0.304024\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 7.74607 | 0.295962 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 21.8681 | 0.833108 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −38.8018 | −1.47609 | −0.738044 | − | 0.674752i | \(-0.764250\pi\) | ||||
−0.738044 | + | 0.674752i | \(0.764250\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 10.2906 | 0.390345 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 70.8054 | 2.68195 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −14.6348 | −0.552749 | −0.276375 | − | 0.961050i | \(-0.589133\pi\) | ||||
−0.276375 | + | 0.961050i | \(0.589133\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −28.5475 | −1.07669 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 50.4277 | 1.89653 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −6.89807 | −0.259062 | −0.129531 | − | 0.991575i | \(-0.541347\pi\) | ||||
−0.129531 | + | 0.991575i | \(0.541347\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 3.54378 | 0.132716 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 32.2868 | 1.20746 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 21.9504 | 0.818610 | 0.409305 | − | 0.912398i | \(-0.365771\pi\) | ||||
0.409305 | + | 0.912398i | \(0.365771\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −22.6874 | −0.844922 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −9.29741 | −0.345297 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 39.8620 | 1.47840 | 0.739200 | − | 0.673486i | \(-0.235204\pi\) | ||||
0.739200 | + | 0.673486i | \(0.235204\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 9.89381 | 0.365936 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 50.6101 | 1.86933 | 0.934663 | − | 0.355536i | \(-0.115701\pi\) | ||||
0.934663 | + | 0.355536i | \(0.115701\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −10.1926 | −0.375448 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 11.1158 | 0.408901 | 0.204451 | − | 0.978877i | \(-0.434459\pi\) | ||||
0.204451 | + | 0.978877i | \(0.434459\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −40.8523 | −1.49873 | −0.749363 | − | 0.662159i | \(-0.769640\pi\) | ||||
−0.749363 | + | 0.662159i | \(0.769640\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 17.0647 | 0.625204 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −1.59698 | −0.0583525 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −5.21900 | −0.190444 | −0.0952221 | − | 0.995456i | \(-0.530356\pi\) | ||||
−0.0952221 | + | 0.995456i | \(0.530356\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 15.9141 | 0.579173 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 3.27998 | 0.119213 | 0.0596064 | − | 0.998222i | \(-0.481015\pi\) | ||||
0.0596064 | + | 0.998222i | \(0.481015\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −25.5191 | −0.925066 | −0.462533 | − | 0.886602i | \(-0.653059\pi\) | ||||
−0.462533 | + | 0.886602i | \(0.653059\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 11.9593 | 0.432956 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 43.9587 | 1.58726 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 34.5086 | 1.24441 | 0.622205 | − | 0.782854i | \(-0.286237\pi\) | ||||
0.622205 | + | 0.782854i | \(0.286237\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 50.8067 | 1.82739 | 0.913695 | − | 0.406401i | \(-0.133216\pi\) | ||||
0.913695 | + | 0.406401i | \(0.133216\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −3.54378 | −0.127296 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −40.5453 | −1.45269 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 45.2022 | 1.61746 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −24.5482 | −0.876164 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −28.9087 | −1.03048 | −0.515242 | − | 0.857045i | \(-0.672298\pi\) | ||||
−0.515242 | + | 0.857045i | \(0.672298\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 31.3317 | 1.11403 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 18.0695 | 0.641666 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −41.7056 | −1.47729 | −0.738644 | − | 0.674095i | \(-0.764534\pi\) | ||||
−0.738644 | + | 0.674095i | \(0.764534\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 72.3627 | 2.56001 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 46.9640 | 1.65732 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −2.73629 | −0.0964414 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −39.2397 | −1.37959 | −0.689797 | − | 0.724002i | \(-0.742300\pi\) | ||||
−0.689797 | + | 0.724002i | \(0.742300\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 32.2340 | 1.13189 | 0.565945 | − | 0.824443i | \(-0.308511\pi\) | ||||
0.565945 | + | 0.824443i | \(0.308511\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 7.71580 | 0.270273 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −5.66549 | −0.198210 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 26.1197 | 0.911583 | 0.455792 | − | 0.890087i | \(-0.349356\pi\) | ||||
0.455792 | + | 0.890087i | \(0.349356\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 14.6734 | 0.511481 | 0.255740 | − | 0.966745i | \(-0.417681\pi\) | ||||
0.255740 | + | 0.966745i | \(0.417681\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 14.3498 | 0.498990 | 0.249495 | − | 0.968376i | \(-0.419735\pi\) | ||||
0.249495 | + | 0.968376i | \(0.419735\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −14.9407 | −0.518911 | −0.259456 | − | 0.965755i | \(-0.583543\pi\) | ||||
−0.259456 | + | 0.965755i | \(0.583543\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 3.38424 | 0.117257 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0.0793410 | 0.00274571 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 38.1982 | 1.31875 | 0.659375 | − | 0.751814i | \(-0.270821\pi\) | ||||
0.659375 | + | 0.751814i | \(0.270821\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 57.4419 | 1.98076 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −16.1781 | −0.556545 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −67.6593 | −2.32480 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −7.17782 | −0.246052 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −13.0969 | −0.448430 | −0.224215 | − | 0.974540i | \(-0.571982\pi\) | ||||
−0.224215 | + | 0.974540i | \(0.571982\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 44.6533 | 1.52533 | 0.762664 | − | 0.646795i | \(-0.223891\pi\) | ||||
0.762664 | + | 0.646795i | \(0.223891\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −23.6964 | −0.808512 | −0.404256 | − | 0.914646i | \(-0.632470\pi\) | ||||
−0.404256 | + | 0.914646i | \(0.632470\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 28.5825 | 0.972961 | 0.486480 | − | 0.873692i | \(-0.338281\pi\) | ||||
0.486480 | + | 0.873692i | \(0.338281\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −19.1590 | −0.651425 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −8.17666 | −0.277374 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 9.21119 | 0.312109 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 2.73629 | 0.0925033 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 29.4797 | 0.995457 | 0.497729 | − | 0.867333i | \(-0.334168\pi\) | ||||
0.497729 | + | 0.867333i | \(0.334168\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 20.1078 | 0.677450 | 0.338725 | − | 0.940885i | \(-0.390004\pi\) | ||||
0.338725 | + | 0.940885i | \(0.390004\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −50.7789 | −1.70885 | −0.854424 | − | 0.519577i | \(-0.826090\pi\) | ||||
−0.854424 | + | 0.519577i | \(0.826090\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −0.365439 | −0.0122703 | −0.00613513 | − | 0.999981i | \(-0.501953\pi\) | ||||
−0.00613513 | + | 0.999981i | \(0.501953\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −46.4376 | −1.55747 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −41.4371 | −1.38664 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 4.68009 | 0.156438 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 32.9480 | 1.09888 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −28.1179 | −0.936744 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −7.46476 | −0.248137 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 16.9221 | 0.561890 | 0.280945 | − | 0.959724i | \(-0.409352\pi\) | ||||
0.280945 | + | 0.959724i | \(0.409352\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −12.0149 | −0.398072 | −0.199036 | − | 0.979992i | \(-0.563781\pi\) | ||||
−0.199036 | + | 0.979992i | \(0.563781\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −83.5068 | −2.76367 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −50.2730 | −1.66016 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −12.1340 | −0.400263 | −0.200131 | − | 0.979769i | \(-0.564137\pi\) | ||||
−0.200131 | + | 0.979769i | \(0.564137\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −40.8500 | −1.34459 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 7.17782 | 0.236005 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −1.70399 | −0.0559060 | −0.0279530 | − | 0.999609i | \(-0.508899\pi\) | ||||
−0.0279530 | + | 0.999609i | \(0.508899\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.93792 | −0.0635127 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −41.5143 | −1.35766 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 20.1572 | 0.658505 | 0.329253 | − | 0.944242i | \(-0.393203\pi\) | ||||
0.329253 | + | 0.944242i | \(0.393203\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −0.934801 | −0.0304736 | −0.0152368 | − | 0.999884i | \(-0.504850\pi\) | ||||
−0.0152368 | + | 0.999884i | \(0.504850\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −10.1945 | −0.331978 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 0.0830101 | 0.00269747 | 0.00134873 | − | 0.999999i | \(-0.499571\pi\) | ||||
0.00134873 | + | 0.999999i | \(0.499571\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −42.4422 | −1.37773 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −27.0754 | −0.877059 | −0.438530 | − | 0.898717i | \(-0.644501\pi\) | ||||
−0.438530 | + | 0.898717i | \(0.644501\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 26.7805 | 0.866598 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 21.1955 | 0.684437 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −18.4416 | −0.594891 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −12.8196 | −0.412678 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 2.18529 | 0.0702743 | 0.0351371 | − | 0.999383i | \(-0.488813\pi\) | ||||
0.0351371 | + | 0.999383i | \(0.488813\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −10.0519 | −0.322580 | −0.161290 | − | 0.986907i | \(-0.551565\pi\) | ||||
−0.161290 | + | 0.986907i | \(0.551565\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 28.1581 | 0.902706 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −3.22903 | −0.103306 | −0.0516529 | − | 0.998665i | \(-0.516449\pi\) | ||||
−0.0516529 | + | 0.998665i | \(0.516449\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 38.8400 | 1.24133 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −39.6353 | −1.26417 | −0.632085 | − | 0.774899i | \(-0.717801\pi\) | ||||
−0.632085 | + | 0.774899i | \(0.717801\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 2.60577 | 0.0830268 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −1.42450 | −0.0452965 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 5.77615 | 0.183485 | 0.0917427 | − | 0.995783i | \(-0.470756\pi\) | ||||
0.0917427 | + | 0.995783i | \(0.470756\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 12.5686 | 0.398451 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 57.5757 | 1.82344 | 0.911721 | − | 0.410810i | \(-0.134754\pi\) | ||||
0.911721 | + | 0.410810i | \(0.134754\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 8280.2.a.bt.1.2 | ✓ | 6 | |
3.2 | odd | 2 | 8280.2.a.bu.1.2 | yes | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8280.2.a.bt.1.2 | ✓ | 6 | 1.1 | even | 1 | trivial | |
8280.2.a.bu.1.2 | yes | 6 | 3.2 | odd | 2 |