Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [280,2,Mod(1,280)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(280, 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("280.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 280 = 2^{3} \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 280.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: | \(2.23581125660\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{17}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 4 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(2.56155\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 280.1 |
$q$-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 | ||||||||
\(3\) | 2.56155 | 1.47891 | 0.739457 | − | 0.673204i | \(-0.235083\pi\) | ||||
0.739457 | + | 0.673204i | \(0.235083\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 3.56155 | 1.18718 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.56155 | −0.772337 | −0.386169 | − | 0.922428i | \(-0.626202\pi\) | ||||
−0.386169 | + | 0.922428i | \(0.626202\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −5.68466 | −1.57664 | −0.788320 | − | 0.615265i | \(-0.789049\pi\) | ||||
−0.788320 | + | 0.615265i | \(0.789049\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 2.56155 | 0.661390 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 3.43845 | 0.833946 | 0.416973 | − | 0.908919i | \(-0.363091\pi\) | ||||
0.416973 | + | 0.908919i | \(0.363091\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.12311 | 0.257658 | 0.128829 | − | 0.991667i | \(-0.458878\pi\) | ||||
0.128829 | + | 0.991667i | \(0.458878\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 2.56155 | 0.558977 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −5.12311 | −1.06824 | −0.534121 | − | 0.845408i | \(-0.679357\pi\) | ||||
−0.534121 | + | 0.845408i | \(0.679357\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.43845 | 0.276829 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 4.56155 | 0.847059 | 0.423530 | − | 0.905882i | \(-0.360791\pi\) | ||||
0.423530 | + | 0.905882i | \(0.360791\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −10.2462 | −1.84027 | −0.920137 | − | 0.391597i | \(-0.871923\pi\) | ||||
−0.920137 | + | 0.391597i | \(0.871923\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −6.56155 | −1.14222 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1.00000 | 0.169031 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 8.24621 | 1.35567 | 0.677834 | − | 0.735215i | \(-0.262919\pi\) | ||||
0.677834 | + | 0.735215i | \(0.262919\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −14.5616 | −2.33171 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 7.12311 | 1.11244 | 0.556221 | − | 0.831034i | \(-0.312251\pi\) | ||||
0.556221 | + | 0.831034i | \(0.312251\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.12311 | 0.171272 | 0.0856360 | − | 0.996326i | \(-0.472708\pi\) | ||||
0.0856360 | + | 0.996326i | \(0.472708\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 3.56155 | 0.530925 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 6.56155 | 0.957101 | 0.478550 | − | 0.878060i | \(-0.341162\pi\) | ||||
0.478550 | + | 0.878060i | \(0.341162\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 8.80776 | 1.23333 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −4.87689 | −0.669893 | −0.334946 | − | 0.942237i | \(-0.608718\pi\) | ||||
−0.334946 | + | 0.942237i | \(0.608718\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −2.56155 | −0.345400 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 2.87689 | 0.381054 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −4.00000 | −0.520756 | −0.260378 | − | 0.965507i | \(-0.583847\pi\) | ||||
−0.260378 | + | 0.965507i | \(0.583847\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −15.1231 | −1.93632 | −0.968158 | − | 0.250341i | \(-0.919457\pi\) | ||||
−0.968158 | + | 0.250341i | \(0.919457\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 3.56155 | 0.448713 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −5.68466 | −0.705095 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −14.2462 | −1.74045 | −0.870226 | − | 0.492653i | \(-0.836027\pi\) | ||||
−0.870226 | + | 0.492653i | \(0.836027\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −13.1231 | −1.57984 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 12.2462 | 1.43331 | 0.716655 | − | 0.697428i | \(-0.245672\pi\) | ||||
0.716655 | + | 0.697428i | \(0.245672\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 2.56155 | 0.295783 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −2.56155 | −0.291916 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −11.6847 | −1.31463 | −0.657313 | − | 0.753617i | \(-0.728307\pi\) | ||||
−0.657313 | + | 0.753617i | \(0.728307\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −7.00000 | −0.777778 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 12.0000 | 1.31717 | 0.658586 | − | 0.752506i | \(-0.271155\pi\) | ||||
0.658586 | + | 0.752506i | \(0.271155\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 3.43845 | 0.372952 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 11.6847 | 1.25273 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −3.12311 | −0.331049 | −0.165524 | − | 0.986206i | \(-0.552932\pi\) | ||||
−0.165524 | + | 0.986206i | \(0.552932\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −5.68466 | −0.595914 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −26.2462 | −2.72161 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 1.12311 | 0.115228 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 13.6847 | 1.38947 | 0.694733 | − | 0.719267i | \(-0.255522\pi\) | ||||
0.694733 | + | 0.719267i | \(0.255522\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −9.12311 | −0.916907 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 6.00000 | 0.597022 | 0.298511 | − | 0.954406i | \(-0.403510\pi\) | ||||
0.298511 | + | 0.954406i | \(0.403510\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 8.80776 | 0.867855 | 0.433927 | − | 0.900948i | \(-0.357127\pi\) | ||||
0.433927 | + | 0.900948i | \(0.357127\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 2.56155 | 0.249982 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 6.87689 | 0.664814 | 0.332407 | − | 0.943136i | \(-0.392139\pi\) | ||||
0.332407 | + | 0.943136i | \(0.392139\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −8.56155 | −0.820048 | −0.410024 | − | 0.912075i | \(-0.634480\pi\) | ||||
−0.410024 | + | 0.912075i | \(0.634480\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 21.1231 | 2.00492 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −8.24621 | −0.775738 | −0.387869 | − | 0.921714i | \(-0.626789\pi\) | ||||
−0.387869 | + | 0.921714i | \(0.626789\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −5.12311 | −0.477732 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −20.2462 | −1.87176 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 3.43845 | 0.315202 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −4.43845 | −0.403495 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 18.2462 | 1.64521 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 10.2462 | 0.909204 | 0.454602 | − | 0.890695i | \(-0.349781\pi\) | ||||
0.454602 | + | 0.890695i | \(0.349781\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 2.87689 | 0.253296 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 6.87689 | 0.600837 | 0.300419 | − | 0.953807i | \(-0.402874\pi\) | ||||
0.300419 | + | 0.953807i | \(0.402874\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.12311 | 0.0973856 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 1.43845 | 0.123802 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 17.3693 | 1.48396 | 0.741980 | − | 0.670422i | \(-0.233887\pi\) | ||||
0.741980 | + | 0.670422i | \(0.233887\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 3.36932 | 0.285782 | 0.142891 | − | 0.989738i | \(-0.454360\pi\) | ||||
0.142891 | + | 0.989738i | \(0.454360\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 16.8078 | 1.41547 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 14.5616 | 1.21770 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 4.56155 | 0.378816 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 2.56155 | 0.211273 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 16.2462 | 1.33094 | 0.665471 | − | 0.746424i | \(-0.268231\pi\) | ||||
0.665471 | + | 0.746424i | \(0.268231\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 0.807764 | 0.0657349 | 0.0328675 | − | 0.999460i | \(-0.489536\pi\) | ||||
0.0328675 | + | 0.999460i | \(0.489536\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 12.2462 | 0.990048 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −10.2462 | −0.822995 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −12.2462 | −0.977354 | −0.488677 | − | 0.872465i | \(-0.662520\pi\) | ||||
−0.488677 | + | 0.872465i | \(0.662520\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −12.4924 | −0.990714 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −5.12311 | −0.403757 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −21.6155 | −1.69306 | −0.846529 | − | 0.532342i | \(-0.821312\pi\) | ||||
−0.846529 | + | 0.532342i | \(0.821312\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −6.56155 | −0.510816 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 24.8078 | 1.91968 | 0.959841 | − | 0.280544i | \(-0.0905148\pi\) | ||||
0.959841 | + | 0.280544i | \(0.0905148\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 19.3153 | 1.48580 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 4.00000 | 0.305888 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 22.1771 | 1.68609 | 0.843046 | − | 0.537841i | \(-0.180760\pi\) | ||||
0.843046 | + | 0.537841i | \(0.180760\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1.00000 | 0.0755929 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −10.2462 | −0.770152 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −4.00000 | −0.298974 | −0.149487 | − | 0.988764i | \(-0.547762\pi\) | ||||
−0.149487 | + | 0.988764i | \(0.547762\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 3.12311 | 0.232139 | 0.116069 | − | 0.993241i | \(-0.462971\pi\) | ||||
0.116069 | + | 0.993241i | \(0.462971\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −38.7386 | −2.86364 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 8.24621 | 0.606274 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −8.80776 | −0.644087 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 1.43845 | 0.104632 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 11.6847 | 0.845472 | 0.422736 | − | 0.906253i | \(-0.361070\pi\) | ||||
0.422736 | + | 0.906253i | \(0.361070\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 4.87689 | 0.351047 | 0.175523 | − | 0.984475i | \(-0.443838\pi\) | ||||
0.175523 | + | 0.984475i | \(0.443838\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −14.5616 | −1.04277 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −4.87689 | −0.347464 | −0.173732 | − | 0.984793i | \(-0.555583\pi\) | ||||
−0.173732 | + | 0.984793i | \(0.555583\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 2.24621 | 0.159230 | 0.0796148 | − | 0.996826i | \(-0.474631\pi\) | ||||
0.0796148 | + | 0.996826i | \(0.474631\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −36.4924 | −2.57398 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 4.56155 | 0.320158 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 7.12311 | 0.497499 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −18.2462 | −1.26820 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −2.87689 | −0.198999 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −13.4384 | −0.925141 | −0.462570 | − | 0.886583i | \(-0.653073\pi\) | ||||
−0.462570 | + | 0.886583i | \(0.653073\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 1.12311 | 0.0765952 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −10.2462 | −0.695558 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 31.3693 | 2.11974 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −19.5464 | −1.31483 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 12.3153 | 0.824696 | 0.412348 | − | 0.911026i | \(-0.364709\pi\) | ||||
0.412348 | + | 0.911026i | \(0.364709\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 3.56155 | 0.237437 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −23.6847 | −1.57201 | −0.786003 | − | 0.618223i | \(-0.787853\pi\) | ||||
−0.786003 | + | 0.618223i | \(0.787853\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 13.3693 | 0.883469 | 0.441735 | − | 0.897146i | \(-0.354363\pi\) | ||||
0.441735 | + | 0.897146i | \(0.354363\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −6.56155 | −0.431718 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −19.1231 | −1.25280 | −0.626398 | − | 0.779503i | \(-0.715472\pi\) | ||||
−0.626398 | + | 0.779503i | \(0.715472\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 6.56155 | 0.428029 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −29.9309 | −1.94422 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 19.0540 | 1.23250 | 0.616250 | − | 0.787551i | \(-0.288651\pi\) | ||||
0.616250 | + | 0.787551i | \(0.288651\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 2.00000 | 0.128831 | 0.0644157 | − | 0.997923i | \(-0.479482\pi\) | ||||
0.0644157 | + | 0.997923i | \(0.479482\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −22.2462 | −1.42710 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 1.00000 | 0.0638877 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −6.38447 | −0.406234 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 30.7386 | 1.94798 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −11.3693 | −0.717625 | −0.358812 | − | 0.933410i | \(-0.616818\pi\) | ||||
−0.358812 | + | 0.933410i | \(0.616818\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 13.1231 | 0.825043 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 8.80776 | 0.551564 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 14.4924 | 0.904012 | 0.452006 | − | 0.892015i | \(-0.350708\pi\) | ||||
0.452006 | + | 0.892015i | \(0.350708\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 8.24621 | 0.512395 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 16.2462 | 1.00562 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −15.3693 | −0.947713 | −0.473856 | − | 0.880602i | \(-0.657138\pi\) | ||||
−0.473856 | + | 0.880602i | \(0.657138\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −4.87689 | −0.299585 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −8.00000 | −0.489592 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −12.2462 | −0.746665 | −0.373332 | − | 0.927698i | \(-0.621785\pi\) | ||||
−0.373332 | + | 0.927698i | \(0.621785\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 10.2462 | 0.622413 | 0.311207 | − | 0.950342i | \(-0.399267\pi\) | ||||
0.311207 | + | 0.950342i | \(0.399267\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −14.5616 | −0.881305 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −2.56155 | −0.154467 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 8.24621 | 0.495467 | 0.247733 | − | 0.968828i | \(-0.420314\pi\) | ||||
0.247733 | + | 0.968828i | \(0.420314\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −36.4924 | −2.18474 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −15.4384 | −0.920981 | −0.460490 | − | 0.887665i | \(-0.652326\pi\) | ||||
−0.460490 | + | 0.887665i | \(0.652326\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 7.68466 | 0.456806 | 0.228403 | − | 0.973567i | \(-0.426650\pi\) | ||||
0.228403 | + | 0.973567i | \(0.426650\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 2.87689 | 0.170413 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 7.12311 | 0.420464 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −5.17708 | −0.304534 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 35.0540 | 2.05490 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −5.05398 | −0.295256 | −0.147628 | − | 0.989043i | \(-0.547164\pi\) | ||||
−0.147628 | + | 0.989043i | \(0.547164\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −4.00000 | −0.232889 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −3.68466 | −0.213806 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 29.1231 | 1.68423 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.12311 | 0.0647347 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 15.3693 | 0.882944 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −15.1231 | −0.865947 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −16.3153 | −0.931166 | −0.465583 | − | 0.885004i | \(-0.654155\pi\) | ||||
−0.465583 | + | 0.885004i | \(0.654155\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 22.5616 | 1.28348 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −21.1231 | −1.19778 | −0.598891 | − | 0.800831i | \(-0.704392\pi\) | ||||
−0.598891 | + | 0.800831i | \(0.704392\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 14.3153 | 0.809151 | 0.404575 | − | 0.914505i | \(-0.367419\pi\) | ||||
0.404575 | + | 0.914505i | \(0.367419\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 3.56155 | 0.200671 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −10.0000 | −0.561656 | −0.280828 | − | 0.959758i | \(-0.590609\pi\) | ||||
−0.280828 | + | 0.959758i | \(0.590609\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −11.6847 | −0.654215 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 17.6155 | 0.983203 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 3.86174 | 0.214873 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −5.68466 | −0.315328 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −21.9309 | −1.21278 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 6.56155 | 0.361750 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −12.0000 | −0.659580 | −0.329790 | − | 0.944054i | \(-0.606978\pi\) | ||||
−0.329790 | + | 0.944054i | \(0.606978\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 29.3693 | 1.60943 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −14.2462 | −0.778354 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 2.00000 | 0.108947 | 0.0544735 | − | 0.998515i | \(-0.482652\pi\) | ||||
0.0544735 | + | 0.998515i | \(0.482652\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −21.1231 | −1.14725 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 26.2462 | 1.42131 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −13.1231 | −0.706524 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 6.87689 | 0.369171 | 0.184586 | − | 0.982816i | \(-0.440906\pi\) | ||||
0.184586 | + | 0.982816i | \(0.440906\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −28.2462 | −1.51199 | −0.755993 | − | 0.654580i | \(-0.772845\pi\) | ||||
−0.755993 | + | 0.654580i | \(0.772845\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −8.17708 | −0.436460 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −22.8078 | −1.21393 | −0.606967 | − | 0.794727i | \(-0.707614\pi\) | ||||
−0.606967 | + | 0.794727i | \(0.707614\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 8.80776 | 0.466156 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 32.0000 | 1.68890 | 0.844448 | − | 0.535638i | \(-0.179929\pi\) | ||||
0.844448 | + | 0.535638i | \(0.179929\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −17.7386 | −0.933612 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −11.3693 | −0.596734 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 12.2462 | 0.640996 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −13.9309 | −0.727185 | −0.363593 | − | 0.931558i | \(-0.618450\pi\) | ||||
−0.363593 | + | 0.931558i | \(0.618450\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 25.3693 | 1.32067 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −4.87689 | −0.253196 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −9.36932 | −0.485125 | −0.242562 | − | 0.970136i | \(-0.577988\pi\) | ||||
−0.242562 | + | 0.970136i | \(0.577988\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 2.56155 | 0.132278 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −25.9309 | −1.33551 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −0.492423 | −0.0252940 | −0.0126470 | − | 0.999920i | \(-0.504026\pi\) | ||||
−0.0126470 | + | 0.999920i | \(0.504026\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 26.2462 | 1.34463 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −26.2462 | −1.34112 | −0.670559 | − | 0.741856i | \(-0.733946\pi\) | ||||
−0.670559 | + | 0.741856i | \(0.733946\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −2.56155 | −0.130549 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 4.00000 | 0.203331 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −31.3002 | −1.58698 | −0.793491 | − | 0.608582i | \(-0.791739\pi\) | ||||
−0.793491 | + | 0.608582i | \(0.791739\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −17.6155 | −0.890856 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 17.6155 | 0.888586 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −11.6847 | −0.587919 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 22.1771 | 1.11304 | 0.556518 | − | 0.830836i | \(-0.312137\pi\) | ||||
0.556518 | + | 0.830836i | \(0.312137\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 2.87689 | 0.144025 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 15.9309 | 0.795550 | 0.397775 | − | 0.917483i | \(-0.369783\pi\) | ||||
0.397775 | + | 0.917483i | \(0.369783\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 58.2462 | 2.90145 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −7.00000 | −0.347833 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −21.1231 | −1.04703 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 14.4924 | 0.716604 | 0.358302 | − | 0.933606i | \(-0.383356\pi\) | ||||
0.358302 | + | 0.933606i | \(0.383356\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 44.4924 | 2.19465 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −4.00000 | −0.196827 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 12.0000 | 0.589057 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 8.63068 | 0.422646 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −1.75379 | −0.0856782 | −0.0428391 | − | 0.999082i | \(-0.513640\pi\) | ||||
−0.0428391 | + | 0.999082i | \(0.513640\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −0.561553 | −0.0273684 | −0.0136842 | − | 0.999906i | \(-0.504356\pi\) | ||||
−0.0136842 | + | 0.999906i | \(0.504356\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 23.3693 | 1.13626 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 3.43845 | 0.166789 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −15.1231 | −0.731858 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 37.3002 | 1.80087 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 5.93087 | 0.285680 | 0.142840 | − | 0.989746i | \(-0.454377\pi\) | ||||
0.142840 | + | 0.989746i | \(0.454377\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 36.2462 | 1.74188 | 0.870941 | − | 0.491388i | \(-0.163510\pi\) | ||||
0.870941 | + | 0.491388i | \(0.163510\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 11.6847 | 0.560236 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −5.75379 | −0.275241 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 10.8769 | 0.519126 | 0.259563 | − | 0.965726i | \(-0.416422\pi\) | ||||
0.259563 | + | 0.965726i | \(0.416422\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 3.56155 | 0.169598 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 21.6155 | 1.02698 | 0.513492 | − | 0.858094i | \(-0.328351\pi\) | ||||
0.513492 | + | 0.858094i | \(0.328351\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −3.12311 | −0.148049 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 41.6155 | 1.96835 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −33.6847 | −1.58968 | −0.794839 | − | 0.606821i | \(-0.792445\pi\) | ||||
−0.794839 | + | 0.606821i | \(0.792445\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −18.2462 | −0.859181 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 2.06913 | 0.0972162 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −5.68466 | −0.266501 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 33.3693 | 1.56095 | 0.780475 | − | 0.625186i | \(-0.214977\pi\) | ||||
0.780475 | + | 0.625186i | \(0.214977\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 4.94602 | 0.230861 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 27.1231 | 1.26325 | 0.631624 | − | 0.775274i | \(-0.282388\pi\) | ||||
0.631624 | + | 0.775274i | \(0.282388\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 10.2462 | 0.476182 | 0.238091 | − | 0.971243i | \(-0.423478\pi\) | ||||
0.238091 | + | 0.971243i | \(0.423478\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −26.2462 | −1.21714 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 21.4384 | 0.992053 | 0.496027 | − | 0.868307i | \(-0.334792\pi\) | ||||
0.496027 | + | 0.868307i | \(0.334792\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −14.2462 | −0.657829 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −31.3693 | −1.44542 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −2.87689 | −0.132280 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1.12311 | 0.0515316 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −17.3693 | −0.795286 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −7.36932 | −0.336713 | −0.168356 | − | 0.985726i | \(-0.553846\pi\) | ||||
−0.168356 | + | 0.985726i | \(0.553846\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −46.8769 | −2.13740 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −13.1231 | −0.597122 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 13.6847 | 0.621388 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −5.12311 | −0.232150 | −0.116075 | − | 0.993240i | \(-0.537031\pi\) | ||||
−0.116075 | + | 0.993240i | \(0.537031\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −55.3693 | −2.50389 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −15.6847 | −0.707839 | −0.353919 | − | 0.935276i | \(-0.615151\pi\) | ||||
−0.353919 | + | 0.935276i | \(0.615151\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 15.6847 | 0.706401 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −9.12311 | −0.410053 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −20.8078 | −0.931483 | −0.465742 | − | 0.884921i | \(-0.654212\pi\) | ||||
−0.465742 | + | 0.884921i | \(0.654212\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 63.5464 | 2.83904 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 16.1771 | 0.721300 | 0.360650 | − | 0.932701i | \(-0.382555\pi\) | ||||
0.360650 | + | 0.932701i | \(0.382555\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 6.00000 | 0.266996 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 49.4773 | 2.19736 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −16.7386 | −0.741927 | −0.370963 | − | 0.928647i | \(-0.620972\pi\) | ||||
−0.370963 | + | 0.928647i | \(0.620972\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 12.2462 | 0.541740 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 1.61553 | 0.0713273 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 8.80776 | 0.388116 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −16.8078 | −0.739205 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 56.8078 | 2.49358 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 4.24621 | 0.186030 | 0.0930149 | − | 0.995665i | \(-0.470350\pi\) | ||||
0.0930149 | + | 0.995665i | \(0.470350\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −12.0000 | −0.524723 | −0.262362 | − | 0.964970i | \(-0.584501\pi\) | ||||
−0.262362 | + | 0.964970i | \(0.584501\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 2.56155 | 0.111795 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −35.2311 | −1.53469 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 3.24621 | 0.141140 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −14.2462 | −0.618233 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −40.4924 | −1.75392 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 6.87689 | 0.297314 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −10.2462 | −0.442157 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −2.56155 | −0.110334 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −20.4233 | −0.878066 | −0.439033 | − | 0.898471i | \(-0.644679\pi\) | ||||
−0.439033 | + | 0.898471i | \(0.644679\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 8.00000 | 0.343313 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −8.56155 | −0.366737 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 12.0000 | 0.513083 | 0.256541 | − | 0.966533i | \(-0.417417\pi\) | ||||
0.256541 | + | 0.966533i | \(0.417417\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −53.8617 | −2.29876 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 5.12311 | 0.218252 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −11.6847 | −0.496882 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 21.1231 | 0.896626 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 23.6155 | 1.00062 | 0.500311 | − | 0.865846i | \(-0.333219\pi\) | ||||
0.500311 | + | 0.865846i | \(0.333219\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −6.38447 | −0.270034 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −22.5616 | −0.952550 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −40.4924 | −1.70655 | −0.853276 | − | 0.521459i | \(-0.825388\pi\) | ||||
−0.853276 | + | 0.521459i | \(0.825388\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −8.24621 | −0.346921 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −7.00000 | −0.293972 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −46.9848 | −1.96971 | −0.984854 | − | 0.173388i | \(-0.944529\pi\) | ||||
−0.984854 | + | 0.173388i | \(0.944529\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 20.0000 | 0.836974 | 0.418487 | − | 0.908223i | \(-0.362561\pi\) | ||||
0.418487 | + | 0.908223i | \(0.362561\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 29.9309 | 1.25038 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −5.12311 | −0.213648 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 0.561553 | 0.0233777 | 0.0116889 | − | 0.999932i | \(-0.496279\pi\) | ||||
0.0116889 | + | 0.999932i | \(0.496279\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 12.4924 | 0.519167 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 12.0000 | 0.497844 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 12.4924 | 0.517383 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −20.2462 | −0.837078 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −6.24621 | −0.257809 | −0.128904 | − | 0.991657i | \(-0.541146\pi\) | ||||
−0.128904 | + | 0.991657i | \(0.541146\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −11.5076 | −0.474161 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −12.4924 | −0.513870 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −24.4233 | −1.00294 | −0.501472 | − | 0.865174i | \(-0.667208\pi\) | ||||
−0.501472 | + | 0.865174i | \(0.667208\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 3.43845 | 0.140963 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 5.75379 | 0.235487 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −18.0691 | −0.738285 | −0.369142 | − | 0.929373i | \(-0.620349\pi\) | ||||
−0.369142 | + | 0.929373i | \(0.620349\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −22.0000 | −0.897399 | −0.448699 | − | 0.893683i | \(-0.648113\pi\) | ||||
−0.448699 | + | 0.893683i | \(0.648113\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −50.7386 | −2.06624 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −4.43845 | −0.180449 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 3.68466 | 0.149556 | 0.0747778 | − | 0.997200i | \(-0.476175\pi\) | ||||
0.0747778 | + | 0.997200i | \(0.476175\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 11.6847 | 0.473486 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −37.3002 | −1.50900 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −32.7386 | −1.32230 | −0.661150 | − | 0.750253i | \(-0.729932\pi\) | ||||
−0.661150 | + | 0.750253i | \(0.729932\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 18.2462 | 0.735758 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −32.2462 | −1.29818 | −0.649092 | − | 0.760710i | \(-0.724851\pi\) | ||||
−0.649092 | + | 0.760710i | \(0.724851\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 35.3693 | 1.42161 | 0.710806 | − | 0.703388i | \(-0.248330\pi\) | ||||
0.710806 | + | 0.703388i | \(0.248330\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −7.36932 | −0.295720 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −3.12311 | −0.125125 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −7.36932 | −0.294302 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 28.3542 | 1.13055 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 34.4233 | 1.37037 | 0.685185 | − | 0.728369i | \(-0.259721\pi\) | ||||
0.685185 | + | 0.728369i | \(0.259721\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −34.4233 | −1.36820 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 10.2462 | 0.406608 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −5.68466 | −0.225234 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 42.9848 | 1.69780 | 0.848900 | − | 0.528554i | \(-0.177266\pi\) | ||||
0.848900 | + | 0.528554i | \(0.177266\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 7.05398 | 0.278182 | 0.139091 | − | 0.990280i | \(-0.455582\pi\) | ||||
0.139091 | + | 0.990280i | \(0.455582\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 2.87689 | 0.113278 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 8.00000 | 0.314512 | 0.157256 | − | 0.987558i | \(-0.449735\pi\) | ||||
0.157256 | + | 0.987558i | \(0.449735\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 10.2462 | 0.402199 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −26.2462 | −1.02867 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −5.50758 | −0.215528 | −0.107764 | − | 0.994176i | \(-0.534369\pi\) | ||||
−0.107764 | + | 0.994176i | \(0.534369\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 6.87689 | 0.268702 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 43.6155 | 1.70160 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −20.8078 | −0.810555 | −0.405278 | − | 0.914194i | \(-0.632825\pi\) | ||||
−0.405278 | + | 0.914194i | \(0.632825\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 23.6155 | 0.918538 | 0.459269 | − | 0.888297i | \(-0.348111\pi\) | ||||
0.459269 | + | 0.888297i | \(0.348111\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −50.0691 | −1.94452 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 1.12311 | 0.0435522 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −23.3693 | −0.904864 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 31.5464 | 1.21965 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 38.7386 | 1.49549 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 0.384472 | 0.0148203 | 0.00741015 | − | 0.999973i | \(-0.497641\pi\) | ||||
0.00741015 | + | 0.999973i | \(0.497641\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 1.43845 | 0.0553659 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −13.6847 | −0.525944 | −0.262972 | − | 0.964803i | \(-0.584703\pi\) | ||||
−0.262972 | + | 0.964803i | \(0.584703\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 13.6847 | 0.525169 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −60.6695 | −2.32486 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −20.9848 | −0.802963 | −0.401481 | − | 0.915867i | \(-0.631505\pi\) | ||||
−0.401481 | + | 0.915867i | \(0.631505\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 17.3693 | 0.663647 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 34.2462 | 1.30657 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 27.7235 | 1.05618 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −16.4924 | −0.627401 | −0.313701 | − | 0.949522i | \(-0.601569\pi\) | ||||
−0.313701 | + | 0.949522i | \(0.601569\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −9.12311 | −0.346558 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 3.36932 | 0.127805 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 24.4924 | 0.927717 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −48.9848 | −1.85278 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −21.6847 | −0.819018 | −0.409509 | − | 0.912306i | \(-0.634300\pi\) | ||||
−0.409509 | + | 0.912306i | \(0.634300\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 9.26137 | 0.349299 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 16.8078 | 0.633017 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 6.00000 | 0.225653 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 33.0540 | 1.24137 | 0.620684 | − | 0.784061i | \(-0.286855\pi\) | ||||
0.620684 | + | 0.784061i | \(0.286855\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −41.6155 | −1.56070 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 52.4924 | 1.96586 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 14.5616 | 0.544571 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 48.8078 | 1.82276 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 17.6155 | 0.656948 | 0.328474 | − | 0.944513i | \(-0.393466\pi\) | ||||
0.328474 | + | 0.944513i | \(0.393466\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 8.80776 | 0.328018 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 5.12311 | 0.190530 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 4.56155 | 0.169412 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −16.9848 | −0.629933 | −0.314967 | − | 0.949103i | \(-0.601993\pi\) | ||||
−0.314967 | + | 0.949103i | \(0.601993\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −35.9848 | −1.33277 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 3.86174 | 0.142832 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 20.5616 | 0.759458 | 0.379729 | − | 0.925098i | \(-0.376017\pi\) | ||||
0.379729 | + | 0.925098i | \(0.376017\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 2.56155 | 0.0944843 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 36.4924 | 1.34422 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −10.5616 | −0.388513 | −0.194257 | − | 0.980951i | \(-0.562229\pi\) | ||||
−0.194257 | + | 0.980951i | \(0.562229\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −16.3542 | −0.600785 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −24.0000 | −0.880475 | −0.440237 | − | 0.897881i | \(-0.645106\pi\) | ||||
−0.440237 | + | 0.897881i | \(0.645106\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 16.2462 | 0.595215 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 42.7386 | 1.56372 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 6.87689 | 0.251276 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −43.6847 | −1.59408 | −0.797038 | − | 0.603929i | \(-0.793601\pi\) | ||||
−0.797038 | + | 0.603929i | \(0.793601\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −29.1231 | −1.06130 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0.807764 | 0.0293975 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −9.36932 | −0.340534 | −0.170267 | − | 0.985398i | \(-0.554463\pi\) | ||||
−0.170267 | + | 0.985398i | \(0.554463\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 33.6155 | 1.22017 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 26.0000 | 0.942499 | 0.471250 | − | 0.882000i | \(-0.343803\pi\) | ||||
0.471250 | + | 0.882000i | \(0.343803\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −8.56155 | −0.309949 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 12.2462 | 0.442763 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 22.7386 | 0.821044 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −22.9848 | −0.828855 | −0.414427 | − | 0.910082i | \(-0.636018\pi\) | ||||
−0.414427 | + | 0.910082i | \(0.636018\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 37.1231 | 1.33696 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −9.19224 | −0.330622 | −0.165311 | − | 0.986242i | \(-0.552863\pi\) | ||||
−0.165311 | + | 0.986242i | \(0.552863\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −10.2462 | −0.368055 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 21.1231 | 0.757787 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 8.00000 | 0.286630 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 6.56155 | 0.234491 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −12.2462 | −0.437086 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −12.1771 | −0.434066 | −0.217033 | − | 0.976164i | \(-0.569638\pi\) | ||||
−0.217033 | + | 0.976164i | \(0.569638\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −39.3693 | −1.40158 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −8.24621 | −0.293202 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 85.9697 | 3.05287 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −12.4924 | −0.443061 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −2.80776 | −0.0994561 | −0.0497281 | − | 0.998763i | \(-0.515835\pi\) | ||||
−0.0497281 | + | 0.998763i | \(0.515835\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 22.5616 | 0.798170 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −11.1231 | −0.393016 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −31.3693 | −1.10700 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −5.12311 | −0.180566 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −31.3693 | −1.10425 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −33.0540 | −1.16212 | −0.581058 | − | 0.813862i | \(-0.697361\pi\) | ||||
−0.581058 | + | 0.813862i | \(0.697361\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 13.6155 | 0.478106 | 0.239053 | − | 0.971007i | \(-0.423163\pi\) | ||||
0.239053 | + | 0.971007i | \(0.423163\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 26.2462 | 0.920495 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −21.6155 | −0.757159 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1.26137 | 0.0441296 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −20.2462 | −0.707460 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 0.699813 | 0.0244237 | 0.0122118 | − | 0.999925i | \(-0.496113\pi\) | ||||
0.0122118 | + | 0.999925i | \(0.496113\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −34.2462 | −1.19375 | −0.596874 | − | 0.802335i | \(-0.703591\pi\) | ||||
−0.596874 | + | 0.802335i | \(0.703591\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −6.56155 | −0.228444 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 33.1231 | 1.15180 | 0.575902 | − | 0.817519i | \(-0.304651\pi\) | ||||
0.575902 | + | 0.817519i | \(0.304651\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −35.6155 | −1.23698 | −0.618489 | − | 0.785793i | \(-0.712255\pi\) | ||||
−0.618489 | + | 0.785793i | \(0.712255\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 21.1231 | 0.732752 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 3.43845 | 0.119135 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 24.8078 | 0.858508 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −14.7386 | −0.509442 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 10.8769 | 0.375512 | 0.187756 | − | 0.982216i | \(-0.439879\pi\) | ||||
0.187756 | + | 0.982216i | \(0.439879\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −8.19224 | −0.282491 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −39.5464 | −1.36205 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 19.3153 | 0.664468 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −4.43845 | −0.152507 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 19.6847 | 0.675576 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −42.2462 | −1.44818 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 32.2462 | 1.10409 | 0.552045 | − | 0.833815i | \(-0.313848\pi\) | ||||
0.552045 | + | 0.833815i | \(0.313848\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 4.00000 | 0.136797 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 3.26137 | 0.111406 | 0.0557031 | − | 0.998447i | \(-0.482260\pi\) | ||||
0.0557031 | + | 0.998447i | \(0.482260\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −28.9848 | −0.988950 | −0.494475 | − | 0.869192i | \(-0.664640\pi\) | ||||
−0.494475 | + | 0.869192i | \(0.664640\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 18.2462 | 0.621829 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −4.49242 | −0.152924 | −0.0764619 | − | 0.997073i | \(-0.524362\pi\) | ||||
−0.0764619 | + | 0.997073i | \(0.524362\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 22.1771 | 0.754043 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −13.2614 | −0.450380 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 29.9309 | 1.01534 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 80.9848 | 2.74407 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 48.7386 | 1.64955 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 1.00000 | 0.0338062 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −46.4924 | −1.56994 | −0.784969 | − | 0.619535i | \(-0.787321\pi\) | ||||
−0.784969 | + | 0.619535i | \(0.787321\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −12.9460 | −0.436659 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −20.1080 | −0.677454 | −0.338727 | − | 0.940885i | \(-0.609996\pi\) | ||||
−0.338727 | + | 0.940885i | \(0.609996\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 38.2462 | 1.28709 | 0.643544 | − | 0.765409i | \(-0.277463\pi\) | ||||
0.643544 | + | 0.765409i | \(0.277463\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −10.2462 | −0.344423 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −3.50758 | −0.117773 | −0.0588865 | − | 0.998265i | \(-0.518755\pi\) | ||||
−0.0588865 | + | 0.998265i | \(0.518755\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 10.2462 | 0.343647 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 17.9309 | 0.600707 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 7.36932 | 0.246605 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −4.00000 | −0.133705 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 74.6004 | 2.49083 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −46.7386 | −1.55882 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −16.7689 | −0.558655 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 2.87689 | 0.0957371 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 3.12311 | 0.103816 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 26.1080 | 0.866900 | 0.433450 | − | 0.901178i | \(-0.357296\pi\) | ||||
0.433450 | + | 0.901178i | \(0.357296\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 21.3693 | 0.708776 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 8.00000 | 0.265052 | 0.132526 | − | 0.991180i | \(-0.457691\pi\) | ||||
0.132526 | + | 0.991180i | \(0.457691\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −30.7386 | −1.01730 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −38.7386 | −1.28066 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 6.87689 | 0.227095 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 6.56155 | 0.216446 | 0.108223 | − | 0.994127i | \(-0.465484\pi\) | ||||
0.108223 | + | 0.994127i | \(0.465484\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −41.7926 | −1.37711 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 8.24621 | 0.271134 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 31.3693 | 1.03030 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −11.1231 | −0.364937 | −0.182469 | − | 0.983212i | \(-0.558409\pi\) | ||||
−0.182469 | + | 0.983212i | \(0.558409\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1.12311 | 0.0368083 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −54.1080 | −1.77141 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −8.80776 | −0.288045 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 17.1922 | 0.561646 | 0.280823 | − | 0.959760i | \(-0.409393\pi\) | ||||
0.280823 | + | 0.959760i | \(0.409393\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 36.6695 | 1.19666 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 53.3693 | 1.73979 | 0.869895 | − | 0.493237i | \(-0.164186\pi\) | ||||
0.869895 | + | 0.493237i | \(0.164186\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −36.4924 | −1.18836 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 1.43845 | 0.0467927 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 47.2311 | 1.53480 | 0.767402 | − | 0.641167i | \(-0.221549\pi\) | ||||
0.767402 | + | 0.641167i | \(0.221549\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −69.6155 | −2.25982 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −25.6155 | −0.830640 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 5.86174 | 0.189880 | 0.0949402 | − | 0.995483i | \(-0.469734\pi\) | ||||
0.0949402 | + | 0.995483i | \(0.469734\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 11.6847 | 0.378107 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −29.9309 | −0.967528 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 17.3693 | 0.560884 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 73.9848 | 2.38661 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 24.4924 | 0.789257 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 4.87689 | 0.156993 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −30.1080 | −0.968206 | −0.484103 | − | 0.875011i | \(-0.660854\pi\) | ||||
−0.484103 | + | 0.875011i | \(0.660854\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 9.89205 | 0.317778 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 26.7386 | 0.858084 | 0.429042 | − | 0.903285i | \(-0.358851\pi\) | ||||
0.429042 | + | 0.903285i | \(0.358851\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 3.36932 | 0.108015 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −14.5616 | −0.466343 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −54.9848 | −1.75912 | −0.879561 | − | 0.475787i | \(-0.842163\pi\) | ||||
−0.879561 | + | 0.475787i | \(0.842163\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 8.00000 | 0.255681 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −30.4924 | −0.973548 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 16.1771 | 0.515969 | 0.257984 | − | 0.966149i | \(-0.416942\pi\) | ||||
0.257984 | + | 0.966149i | \(0.416942\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −4.87689 | −0.155391 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 16.8078 | 0.534997 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −5.75379 | −0.182960 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 12.4924 | 0.396835 | 0.198417 | − | 0.980118i | \(-0.436420\pi\) | ||||
0.198417 | + | 0.980118i | \(0.436420\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −30.7386 | −0.975461 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 2.24621 | 0.0712097 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −28.0691 | −0.888958 | −0.444479 | − | 0.895789i | \(-0.646611\pi\) | ||||
−0.444479 | + | 0.895789i | \(0.646611\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 11.8617 | 0.375289 |
(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 | 280.2.a.d.1.2 | ✓ | 2 | |
3.2 | odd | 2 | 2520.2.a.w.1.2 | 2 | |||
4.3 | odd | 2 | 560.2.a.g.1.1 | 2 | |||
5.2 | odd | 4 | 1400.2.g.k.449.1 | 4 | |||
5.3 | odd | 4 | 1400.2.g.k.449.4 | 4 | |||
5.4 | even | 2 | 1400.2.a.p.1.1 | 2 | |||
7.2 | even | 3 | 1960.2.q.s.361.1 | 4 | |||
7.3 | odd | 6 | 1960.2.q.u.961.2 | 4 | |||
7.4 | even | 3 | 1960.2.q.s.961.1 | 4 | |||
7.5 | odd | 6 | 1960.2.q.u.361.2 | 4 | |||
7.6 | odd | 2 | 1960.2.a.r.1.1 | 2 | |||
8.3 | odd | 2 | 2240.2.a.bi.1.2 | 2 | |||
8.5 | even | 2 | 2240.2.a.be.1.1 | 2 | |||
12.11 | even | 2 | 5040.2.a.bq.1.1 | 2 | |||
20.3 | even | 4 | 2800.2.g.u.449.1 | 4 | |||
20.7 | even | 4 | 2800.2.g.u.449.4 | 4 | |||
20.19 | odd | 2 | 2800.2.a.bn.1.2 | 2 | |||
28.27 | even | 2 | 3920.2.a.bu.1.2 | 2 | |||
35.34 | odd | 2 | 9800.2.a.by.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
280.2.a.d.1.2 | ✓ | 2 | 1.1 | even | 1 | trivial | |
560.2.a.g.1.1 | 2 | 4.3 | odd | 2 | |||
1400.2.a.p.1.1 | 2 | 5.4 | even | 2 | |||
1400.2.g.k.449.1 | 4 | 5.2 | odd | 4 | |||
1400.2.g.k.449.4 | 4 | 5.3 | odd | 4 | |||
1960.2.a.r.1.1 | 2 | 7.6 | odd | 2 | |||
1960.2.q.s.361.1 | 4 | 7.2 | even | 3 | |||
1960.2.q.s.961.1 | 4 | 7.4 | even | 3 | |||
1960.2.q.u.361.2 | 4 | 7.5 | odd | 6 | |||
1960.2.q.u.961.2 | 4 | 7.3 | odd | 6 | |||
2240.2.a.be.1.1 | 2 | 8.5 | even | 2 | |||
2240.2.a.bi.1.2 | 2 | 8.3 | odd | 2 | |||
2520.2.a.w.1.2 | 2 | 3.2 | odd | 2 | |||
2800.2.a.bn.1.2 | 2 | 20.19 | odd | 2 | |||
2800.2.g.u.449.1 | 4 | 20.3 | even | 4 | |||
2800.2.g.u.449.4 | 4 | 20.7 | even | 4 | |||
3920.2.a.bu.1.2 | 2 | 28.27 | even | 2 | |||
5040.2.a.bq.1.1 | 2 | 12.11 | even | 2 | |||
9800.2.a.by.1.2 | 2 | 35.34 | odd | 2 |