Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3330,2,Mod(1,3330)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3330, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("3330.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3330 = 2 \cdot 3^{2} \cdot 5 \cdot 37 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3330.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: | \(26.5901838731\) |
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: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 1110) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-1.56155\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3330.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.00000 | −0.377964 | −0.188982 | − | 0.981981i | \(-0.560519\pi\) | ||||
−0.188982 | + | 0.981981i | \(0.560519\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −1.00000 | −0.316228 | ||||||||
\(11\) | −2.12311 | −0.640140 | −0.320070 | − | 0.947394i | \(-0.603707\pi\) | ||||
−0.320070 | + | 0.947394i | \(0.603707\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −6.68466 | −1.85399 | −0.926995 | − | 0.375073i | \(-0.877618\pi\) | ||||
−0.926995 | + | 0.375073i | \(0.877618\pi\) | |||||||
\(14\) | 1.00000 | 0.267261 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 5.00000 | 1.21268 | 0.606339 | − | 0.795206i | \(-0.292637\pi\) | ||||
0.606339 | + | 0.795206i | \(0.292637\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −3.56155 | −0.817076 | −0.408538 | − | 0.912741i | \(-0.633961\pi\) | ||||
−0.408538 | + | 0.912741i | \(0.633961\pi\) | |||||||
\(20\) | 1.00000 | 0.223607 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 2.12311 | 0.452648 | ||||||||
\(23\) | 2.43845 | 0.508451 | 0.254226 | − | 0.967145i | \(-0.418179\pi\) | ||||
0.254226 | + | 0.967145i | \(0.418179\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 6.68466 | 1.31097 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −1.00000 | −0.188982 | ||||||||
\(29\) | −5.68466 | −1.05561 | −0.527807 | − | 0.849364i | \(-0.676986\pi\) | ||||
−0.527807 | + | 0.849364i | \(0.676986\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.561553 | 0.100858 | 0.0504289 | − | 0.998728i | \(-0.483941\pi\) | ||||
0.0504289 | + | 0.998728i | \(0.483941\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −5.00000 | −0.857493 | ||||||||
\(35\) | −1.00000 | −0.169031 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.00000 | 0.164399 | ||||||||
\(38\) | 3.56155 | 0.577760 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −1.00000 | −0.158114 | ||||||||
\(41\) | 3.68466 | 0.575447 | 0.287723 | − | 0.957714i | \(-0.407102\pi\) | ||||
0.287723 | + | 0.957714i | \(0.407102\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −0.315342 | −0.0480891 | −0.0240446 | − | 0.999711i | \(-0.507654\pi\) | ||||
−0.0240446 | + | 0.999711i | \(0.507654\pi\) | |||||||
\(44\) | −2.12311 | −0.320070 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −2.43845 | −0.359529 | ||||||||
\(47\) | 8.00000 | 1.16692 | 0.583460 | − | 0.812142i | \(-0.301699\pi\) | ||||
0.583460 | + | 0.812142i | \(0.301699\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.00000 | −0.857143 | ||||||||
\(50\) | −1.00000 | −0.141421 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −6.68466 | −0.926995 | ||||||||
\(53\) | 11.2462 | 1.54479 | 0.772393 | − | 0.635145i | \(-0.219060\pi\) | ||||
0.772393 | + | 0.635145i | \(0.219060\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −2.12311 | −0.286280 | ||||||||
\(56\) | 1.00000 | 0.133631 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 5.68466 | 0.746432 | ||||||||
\(59\) | 12.2462 | 1.59432 | 0.797160 | − | 0.603768i | \(-0.206334\pi\) | ||||
0.797160 | + | 0.603768i | \(0.206334\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 6.80776 | 0.871645 | 0.435822 | − | 0.900033i | \(-0.356458\pi\) | ||||
0.435822 | + | 0.900033i | \(0.356458\pi\) | |||||||
\(62\) | −0.561553 | −0.0713173 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −6.68466 | −0.829130 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 4.87689 | 0.595807 | 0.297904 | − | 0.954596i | \(-0.403713\pi\) | ||||
0.297904 | + | 0.954596i | \(0.403713\pi\) | |||||||
\(68\) | 5.00000 | 0.606339 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 1.00000 | 0.119523 | ||||||||
\(71\) | 7.12311 | 0.845357 | 0.422679 | − | 0.906280i | \(-0.361090\pi\) | ||||
0.422679 | + | 0.906280i | \(0.361090\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −2.43845 | −0.285399 | −0.142699 | − | 0.989766i | \(-0.545578\pi\) | ||||
−0.142699 | + | 0.989766i | \(0.545578\pi\) | |||||||
\(74\) | −1.00000 | −0.116248 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −3.56155 | −0.408538 | ||||||||
\(77\) | 2.12311 | 0.241950 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −2.24621 | −0.252719 | −0.126359 | − | 0.991985i | \(-0.540329\pi\) | ||||
−0.126359 | + | 0.991985i | \(0.540329\pi\) | |||||||
\(80\) | 1.00000 | 0.111803 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −3.68466 | −0.406902 | ||||||||
\(83\) | 11.5616 | 1.26905 | 0.634523 | − | 0.772904i | \(-0.281197\pi\) | ||||
0.634523 | + | 0.772904i | \(0.281197\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 5.00000 | 0.542326 | ||||||||
\(86\) | 0.315342 | 0.0340042 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 2.12311 | 0.226324 | ||||||||
\(89\) | 6.68466 | 0.708572 | 0.354286 | − | 0.935137i | \(-0.384724\pi\) | ||||
0.354286 | + | 0.935137i | \(0.384724\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 6.68466 | 0.700743 | ||||||||
\(92\) | 2.43845 | 0.254226 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −8.00000 | −0.825137 | ||||||||
\(95\) | −3.56155 | −0.365408 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 15.6847 | 1.59254 | 0.796268 | − | 0.604944i | \(-0.206805\pi\) | ||||
0.796268 | + | 0.604944i | \(0.206805\pi\) | |||||||
\(98\) | 6.00000 | 0.606092 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | −19.1231 | −1.90282 | −0.951410 | − | 0.307927i | \(-0.900365\pi\) | ||||
−0.951410 | + | 0.307927i | \(0.900365\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 16.4924 | 1.62505 | 0.812523 | − | 0.582929i | \(-0.198093\pi\) | ||||
0.812523 | + | 0.582929i | \(0.198093\pi\) | |||||||
\(104\) | 6.68466 | 0.655485 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −11.2462 | −1.09233 | ||||||||
\(107\) | −9.80776 | −0.948152 | −0.474076 | − | 0.880484i | \(-0.657218\pi\) | ||||
−0.474076 | + | 0.880484i | \(0.657218\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 6.12311 | 0.586487 | 0.293244 | − | 0.956038i | \(-0.405265\pi\) | ||||
0.293244 | + | 0.956038i | \(0.405265\pi\) | |||||||
\(110\) | 2.12311 | 0.202430 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −1.00000 | −0.0944911 | ||||||||
\(113\) | −1.68466 | −0.158479 | −0.0792397 | − | 0.996856i | \(-0.525249\pi\) | ||||
−0.0792397 | + | 0.996856i | \(0.525249\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 2.43845 | 0.227386 | ||||||||
\(116\) | −5.68466 | −0.527807 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −12.2462 | −1.12736 | ||||||||
\(119\) | −5.00000 | −0.458349 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −6.49242 | −0.590220 | ||||||||
\(122\) | −6.80776 | −0.616346 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0.561553 | 0.0504289 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 10.4384 | 0.926262 | 0.463131 | − | 0.886290i | \(-0.346726\pi\) | ||||
0.463131 | + | 0.886290i | \(0.346726\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 6.68466 | 0.586283 | ||||||||
\(131\) | 1.12311 | 0.0981262 | 0.0490631 | − | 0.998796i | \(-0.484376\pi\) | ||||
0.0490631 | + | 0.998796i | \(0.484376\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 3.56155 | 0.308826 | ||||||||
\(134\) | −4.87689 | −0.421300 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −5.00000 | −0.428746 | ||||||||
\(137\) | −12.2462 | −1.04626 | −0.523132 | − | 0.852252i | \(-0.675237\pi\) | ||||
−0.523132 | + | 0.852252i | \(0.675237\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −6.80776 | −0.577427 | −0.288714 | − | 0.957416i | \(-0.593228\pi\) | ||||
−0.288714 | + | 0.957416i | \(0.593228\pi\) | |||||||
\(140\) | −1.00000 | −0.0845154 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −7.12311 | −0.597758 | ||||||||
\(143\) | 14.1922 | 1.18681 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −5.68466 | −0.472085 | ||||||||
\(146\) | 2.43845 | 0.201807 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 1.00000 | 0.0821995 | ||||||||
\(149\) | −24.2462 | −1.98633 | −0.993164 | − | 0.116731i | \(-0.962758\pi\) | ||||
−0.993164 | + | 0.116731i | \(0.962758\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −19.5616 | −1.59190 | −0.795948 | − | 0.605365i | \(-0.793027\pi\) | ||||
−0.795948 | + | 0.605365i | \(0.793027\pi\) | |||||||
\(152\) | 3.56155 | 0.288880 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −2.12311 | −0.171085 | ||||||||
\(155\) | 0.561553 | 0.0451050 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 19.0540 | 1.52067 | 0.760336 | − | 0.649530i | \(-0.225034\pi\) | ||||
0.760336 | + | 0.649530i | \(0.225034\pi\) | |||||||
\(158\) | 2.24621 | 0.178699 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −1.00000 | −0.0790569 | ||||||||
\(161\) | −2.43845 | −0.192177 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −13.4924 | −1.05681 | −0.528404 | − | 0.848993i | \(-0.677209\pi\) | ||||
−0.528404 | + | 0.848993i | \(0.677209\pi\) | |||||||
\(164\) | 3.68466 | 0.287723 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −11.5616 | −0.897351 | ||||||||
\(167\) | 18.0540 | 1.39706 | 0.698529 | − | 0.715581i | \(-0.253838\pi\) | ||||
0.698529 | + | 0.715581i | \(0.253838\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 31.6847 | 2.43728 | ||||||||
\(170\) | −5.00000 | −0.383482 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −0.315342 | −0.0240446 | ||||||||
\(173\) | −6.12311 | −0.465531 | −0.232766 | − | 0.972533i | \(-0.574777\pi\) | ||||
−0.232766 | + | 0.972533i | \(0.574777\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1.00000 | −0.0755929 | ||||||||
\(176\) | −2.12311 | −0.160035 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −6.68466 | −0.501036 | ||||||||
\(179\) | 4.00000 | 0.298974 | 0.149487 | − | 0.988764i | \(-0.452238\pi\) | ||||
0.149487 | + | 0.988764i | \(0.452238\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 3.75379 | 0.279017 | 0.139508 | − | 0.990221i | \(-0.455448\pi\) | ||||
0.139508 | + | 0.990221i | \(0.455448\pi\) | |||||||
\(182\) | −6.68466 | −0.495500 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −2.43845 | −0.179765 | ||||||||
\(185\) | 1.00000 | 0.0735215 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −10.6155 | −0.776284 | ||||||||
\(188\) | 8.00000 | 0.583460 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 3.56155 | 0.258382 | ||||||||
\(191\) | 10.3693 | 0.750297 | 0.375149 | − | 0.926965i | \(-0.377592\pi\) | ||||
0.375149 | + | 0.926965i | \(0.377592\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −14.0000 | −1.00774 | −0.503871 | − | 0.863779i | \(-0.668091\pi\) | ||||
−0.503871 | + | 0.863779i | \(0.668091\pi\) | |||||||
\(194\) | −15.6847 | −1.12609 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −6.00000 | −0.428571 | ||||||||
\(197\) | 14.6847 | 1.04624 | 0.523119 | − | 0.852259i | \(-0.324768\pi\) | ||||
0.523119 | + | 0.852259i | \(0.324768\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 16.4924 | 1.16912 | 0.584558 | − | 0.811352i | \(-0.301268\pi\) | ||||
0.584558 | + | 0.811352i | \(0.301268\pi\) | |||||||
\(200\) | −1.00000 | −0.0707107 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 19.1231 | 1.34550 | ||||||||
\(203\) | 5.68466 | 0.398985 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 3.68466 | 0.257348 | ||||||||
\(206\) | −16.4924 | −1.14908 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −6.68466 | −0.463498 | ||||||||
\(209\) | 7.56155 | 0.523044 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 8.56155 | 0.589402 | 0.294701 | − | 0.955590i | \(-0.404780\pi\) | ||||
0.294701 | + | 0.955590i | \(0.404780\pi\) | |||||||
\(212\) | 11.2462 | 0.772393 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 9.80776 | 0.670445 | ||||||||
\(215\) | −0.315342 | −0.0215061 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −0.561553 | −0.0381207 | ||||||||
\(218\) | −6.12311 | −0.414709 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −2.12311 | −0.143140 | ||||||||
\(221\) | −33.4233 | −2.24829 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 0.807764 | 0.0540919 | 0.0270459 | − | 0.999634i | \(-0.491390\pi\) | ||||
0.0270459 | + | 0.999634i | \(0.491390\pi\) | |||||||
\(224\) | 1.00000 | 0.0668153 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 1.68466 | 0.112062 | ||||||||
\(227\) | −17.9309 | −1.19011 | −0.595057 | − | 0.803684i | \(-0.702870\pi\) | ||||
−0.595057 | + | 0.803684i | \(0.702870\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 3.12311 | 0.206381 | 0.103190 | − | 0.994662i | \(-0.467095\pi\) | ||||
0.103190 | + | 0.994662i | \(0.467095\pi\) | |||||||
\(230\) | −2.43845 | −0.160786 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 5.68466 | 0.373216 | ||||||||
\(233\) | 13.3693 | 0.875853 | 0.437927 | − | 0.899011i | \(-0.355713\pi\) | ||||
0.437927 | + | 0.899011i | \(0.355713\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 8.00000 | 0.521862 | ||||||||
\(236\) | 12.2462 | 0.797160 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 5.00000 | 0.324102 | ||||||||
\(239\) | 12.8078 | 0.828465 | 0.414233 | − | 0.910171i | \(-0.364050\pi\) | ||||
0.414233 | + | 0.910171i | \(0.364050\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −2.00000 | −0.128831 | −0.0644157 | − | 0.997923i | \(-0.520518\pi\) | ||||
−0.0644157 | + | 0.997923i | \(0.520518\pi\) | |||||||
\(242\) | 6.49242 | 0.417349 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 6.80776 | 0.435822 | ||||||||
\(245\) | −6.00000 | −0.383326 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 23.8078 | 1.51485 | ||||||||
\(248\) | −0.561553 | −0.0356586 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −1.00000 | −0.0632456 | ||||||||
\(251\) | 15.6155 | 0.985643 | 0.492822 | − | 0.870130i | \(-0.335965\pi\) | ||||
0.492822 | + | 0.870130i | \(0.335965\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −5.17708 | −0.325480 | ||||||||
\(254\) | −10.4384 | −0.654966 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 9.80776 | 0.611792 | 0.305896 | − | 0.952065i | \(-0.401044\pi\) | ||||
0.305896 | + | 0.952065i | \(0.401044\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1.00000 | −0.0621370 | ||||||||
\(260\) | −6.68466 | −0.414565 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −1.12311 | −0.0693857 | ||||||||
\(263\) | 10.5616 | 0.651253 | 0.325627 | − | 0.945498i | \(-0.394425\pi\) | ||||
0.325627 | + | 0.945498i | \(0.394425\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 11.2462 | 0.690849 | ||||||||
\(266\) | −3.56155 | −0.218373 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 4.87689 | 0.297904 | ||||||||
\(269\) | −3.80776 | −0.232163 | −0.116082 | − | 0.993240i | \(-0.537033\pi\) | ||||
−0.116082 | + | 0.993240i | \(0.537033\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 16.4924 | 1.00184 | 0.500922 | − | 0.865493i | \(-0.332994\pi\) | ||||
0.500922 | + | 0.865493i | \(0.332994\pi\) | |||||||
\(272\) | 5.00000 | 0.303170 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 12.2462 | 0.739821 | ||||||||
\(275\) | −2.12311 | −0.128028 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 15.3153 | 0.920210 | 0.460105 | − | 0.887865i | \(-0.347812\pi\) | ||||
0.460105 | + | 0.887865i | \(0.347812\pi\) | |||||||
\(278\) | 6.80776 | 0.408303 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 1.00000 | 0.0597614 | ||||||||
\(281\) | 23.1771 | 1.38263 | 0.691314 | − | 0.722554i | \(-0.257032\pi\) | ||||
0.691314 | + | 0.722554i | \(0.257032\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −18.9309 | −1.12532 | −0.562662 | − | 0.826687i | \(-0.690223\pi\) | ||||
−0.562662 | + | 0.826687i | \(0.690223\pi\) | |||||||
\(284\) | 7.12311 | 0.422679 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −14.1922 | −0.839205 | ||||||||
\(287\) | −3.68466 | −0.217499 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 8.00000 | 0.470588 | ||||||||
\(290\) | 5.68466 | 0.333815 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −2.43845 | −0.142699 | ||||||||
\(293\) | −24.6155 | −1.43805 | −0.719027 | − | 0.694982i | \(-0.755412\pi\) | ||||
−0.719027 | + | 0.694982i | \(0.755412\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 12.2462 | 0.713002 | ||||||||
\(296\) | −1.00000 | −0.0581238 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 24.2462 | 1.40455 | ||||||||
\(299\) | −16.3002 | −0.942664 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0.315342 | 0.0181760 | ||||||||
\(302\) | 19.5616 | 1.12564 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −3.56155 | −0.204269 | ||||||||
\(305\) | 6.80776 | 0.389811 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 16.2462 | 0.927220 | 0.463610 | − | 0.886039i | \(-0.346554\pi\) | ||||
0.463610 | + | 0.886039i | \(0.346554\pi\) | |||||||
\(308\) | 2.12311 | 0.120975 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −0.561553 | −0.0318941 | ||||||||
\(311\) | −24.1771 | −1.37096 | −0.685478 | − | 0.728093i | \(-0.740407\pi\) | ||||
−0.685478 | + | 0.728093i | \(0.740407\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −33.1231 | −1.87223 | −0.936114 | − | 0.351696i | \(-0.885605\pi\) | ||||
−0.936114 | + | 0.351696i | \(0.885605\pi\) | |||||||
\(314\) | −19.0540 | −1.07528 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −2.24621 | −0.126359 | ||||||||
\(317\) | 11.9309 | 0.670104 | 0.335052 | − | 0.942200i | \(-0.391246\pi\) | ||||
0.335052 | + | 0.942200i | \(0.391246\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 12.0691 | 0.675742 | ||||||||
\(320\) | 1.00000 | 0.0559017 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 2.43845 | 0.135889 | ||||||||
\(323\) | −17.8078 | −0.990850 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −6.68466 | −0.370798 | ||||||||
\(326\) | 13.4924 | 0.747276 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −3.68466 | −0.203451 | ||||||||
\(329\) | −8.00000 | −0.441054 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −12.0000 | −0.659580 | −0.329790 | − | 0.944054i | \(-0.606978\pi\) | ||||
−0.329790 | + | 0.944054i | \(0.606978\pi\) | |||||||
\(332\) | 11.5616 | 0.634523 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −18.0540 | −0.987870 | ||||||||
\(335\) | 4.87689 | 0.266453 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 0.438447 | 0.0238837 | 0.0119419 | − | 0.999929i | \(-0.496199\pi\) | ||||
0.0119419 | + | 0.999929i | \(0.496199\pi\) | |||||||
\(338\) | −31.6847 | −1.72342 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 5.00000 | 0.271163 | ||||||||
\(341\) | −1.19224 | −0.0645632 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 13.0000 | 0.701934 | ||||||||
\(344\) | 0.315342 | 0.0170021 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 6.12311 | 0.329180 | ||||||||
\(347\) | 28.0000 | 1.50312 | 0.751559 | − | 0.659665i | \(-0.229302\pi\) | ||||
0.751559 | + | 0.659665i | \(0.229302\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −2.24621 | −0.120237 | −0.0601185 | − | 0.998191i | \(-0.519148\pi\) | ||||
−0.0601185 | + | 0.998191i | \(0.519148\pi\) | |||||||
\(350\) | 1.00000 | 0.0534522 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 2.12311 | 0.113162 | ||||||||
\(353\) | 9.19224 | 0.489253 | 0.244627 | − | 0.969617i | \(-0.421335\pi\) | ||||
0.244627 | + | 0.969617i | \(0.421335\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 7.12311 | 0.378055 | ||||||||
\(356\) | 6.68466 | 0.354286 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −4.00000 | −0.211407 | ||||||||
\(359\) | 29.1231 | 1.53706 | 0.768529 | − | 0.639815i | \(-0.220989\pi\) | ||||
0.768529 | + | 0.639815i | \(0.220989\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −6.31534 | −0.332386 | ||||||||
\(362\) | −3.75379 | −0.197295 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 6.68466 | 0.350371 | ||||||||
\(365\) | −2.43845 | −0.127634 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −17.0000 | −0.887393 | −0.443696 | − | 0.896177i | \(-0.646333\pi\) | ||||
−0.443696 | + | 0.896177i | \(0.646333\pi\) | |||||||
\(368\) | 2.43845 | 0.127113 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −1.00000 | −0.0519875 | ||||||||
\(371\) | −11.2462 | −0.583874 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 2.49242 | 0.129053 | 0.0645264 | − | 0.997916i | \(-0.479446\pi\) | ||||
0.0645264 | + | 0.997916i | \(0.479446\pi\) | |||||||
\(374\) | 10.6155 | 0.548916 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −8.00000 | −0.412568 | ||||||||
\(377\) | 38.0000 | 1.95710 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −11.1231 | −0.571356 | −0.285678 | − | 0.958326i | \(-0.592219\pi\) | ||||
−0.285678 | + | 0.958326i | \(0.592219\pi\) | |||||||
\(380\) | −3.56155 | −0.182704 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −10.3693 | −0.530540 | ||||||||
\(383\) | 15.3153 | 0.782577 | 0.391289 | − | 0.920268i | \(-0.372029\pi\) | ||||
0.391289 | + | 0.920268i | \(0.372029\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 2.12311 | 0.108203 | ||||||||
\(386\) | 14.0000 | 0.712581 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 15.6847 | 0.796268 | ||||||||
\(389\) | 7.93087 | 0.402111 | 0.201056 | − | 0.979580i | \(-0.435563\pi\) | ||||
0.201056 | + | 0.979580i | \(0.435563\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 12.1922 | 0.616588 | ||||||||
\(392\) | 6.00000 | 0.303046 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −14.6847 | −0.739802 | ||||||||
\(395\) | −2.24621 | −0.113019 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 18.8769 | 0.947404 | 0.473702 | − | 0.880685i | \(-0.342917\pi\) | ||||
0.473702 | + | 0.880685i | \(0.342917\pi\) | |||||||
\(398\) | −16.4924 | −0.826690 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 1.00000 | 0.0500000 | ||||||||
\(401\) | −5.80776 | −0.290026 | −0.145013 | − | 0.989430i | \(-0.546322\pi\) | ||||
−0.145013 | + | 0.989430i | \(0.546322\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −3.75379 | −0.186990 | ||||||||
\(404\) | −19.1231 | −0.951410 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −5.68466 | −0.282125 | ||||||||
\(407\) | −2.12311 | −0.105238 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −9.12311 | −0.451109 | −0.225554 | − | 0.974231i | \(-0.572419\pi\) | ||||
−0.225554 | + | 0.974231i | \(0.572419\pi\) | |||||||
\(410\) | −3.68466 | −0.181972 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 16.4924 | 0.812523 | ||||||||
\(413\) | −12.2462 | −0.602597 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 11.5616 | 0.567534 | ||||||||
\(416\) | 6.68466 | 0.327742 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −7.56155 | −0.369848 | ||||||||
\(419\) | 6.43845 | 0.314539 | 0.157269 | − | 0.987556i | \(-0.449731\pi\) | ||||
0.157269 | + | 0.987556i | \(0.449731\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −34.9848 | −1.70506 | −0.852529 | − | 0.522681i | \(-0.824932\pi\) | ||||
−0.852529 | + | 0.522681i | \(0.824932\pi\) | |||||||
\(422\) | −8.56155 | −0.416770 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −11.2462 | −0.546164 | ||||||||
\(425\) | 5.00000 | 0.242536 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −6.80776 | −0.329451 | ||||||||
\(428\) | −9.80776 | −0.474076 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0.315342 | 0.0152071 | ||||||||
\(431\) | 29.0000 | 1.39688 | 0.698440 | − | 0.715668i | \(-0.253878\pi\) | ||||
0.698440 | + | 0.715668i | \(0.253878\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 31.4233 | 1.51011 | 0.755054 | − | 0.655663i | \(-0.227611\pi\) | ||||
0.755054 | + | 0.655663i | \(0.227611\pi\) | |||||||
\(434\) | 0.561553 | 0.0269554 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 6.12311 | 0.293244 | ||||||||
\(437\) | −8.68466 | −0.415444 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 23.0540 | 1.10031 | 0.550153 | − | 0.835064i | \(-0.314569\pi\) | ||||
0.550153 | + | 0.835064i | \(0.314569\pi\) | |||||||
\(440\) | 2.12311 | 0.101215 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 33.4233 | 1.58978 | ||||||||
\(443\) | 23.8617 | 1.13371 | 0.566853 | − | 0.823819i | \(-0.308161\pi\) | ||||
0.566853 | + | 0.823819i | \(0.308161\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 6.68466 | 0.316883 | ||||||||
\(446\) | −0.807764 | −0.0382487 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −1.00000 | −0.0472456 | ||||||||
\(449\) | −39.6155 | −1.86957 | −0.934786 | − | 0.355211i | \(-0.884409\pi\) | ||||
−0.934786 | + | 0.355211i | \(0.884409\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −7.82292 | −0.368367 | ||||||||
\(452\) | −1.68466 | −0.0792397 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 17.9309 | 0.841537 | ||||||||
\(455\) | 6.68466 | 0.313382 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −2.06913 | −0.0967898 | −0.0483949 | − | 0.998828i | \(-0.515411\pi\) | ||||
−0.0483949 | + | 0.998828i | \(0.515411\pi\) | |||||||
\(458\) | −3.12311 | −0.145933 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 2.43845 | 0.113693 | ||||||||
\(461\) | −4.56155 | −0.212453 | −0.106226 | − | 0.994342i | \(-0.533877\pi\) | ||||
−0.106226 | + | 0.994342i | \(0.533877\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 13.1231 | 0.609882 | 0.304941 | − | 0.952371i | \(-0.401363\pi\) | ||||
0.304941 | + | 0.952371i | \(0.401363\pi\) | |||||||
\(464\) | −5.68466 | −0.263904 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −13.3693 | −0.619322 | ||||||||
\(467\) | −6.56155 | −0.303632 | −0.151816 | − | 0.988409i | \(-0.548512\pi\) | ||||
−0.151816 | + | 0.988409i | \(0.548512\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −4.87689 | −0.225194 | ||||||||
\(470\) | −8.00000 | −0.369012 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −12.2462 | −0.563678 | ||||||||
\(473\) | 0.669503 | 0.0307838 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −3.56155 | −0.163415 | ||||||||
\(476\) | −5.00000 | −0.229175 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −12.8078 | −0.585813 | ||||||||
\(479\) | 2.43845 | 0.111415 | 0.0557077 | − | 0.998447i | \(-0.482258\pi\) | ||||
0.0557077 | + | 0.998447i | \(0.482258\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −6.68466 | −0.304794 | ||||||||
\(482\) | 2.00000 | 0.0910975 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −6.49242 | −0.295110 | ||||||||
\(485\) | 15.6847 | 0.712204 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −32.7386 | −1.48353 | −0.741765 | − | 0.670660i | \(-0.766011\pi\) | ||||
−0.741765 | + | 0.670660i | \(0.766011\pi\) | |||||||
\(488\) | −6.80776 | −0.308173 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 6.00000 | 0.271052 | ||||||||
\(491\) | −33.1771 | −1.49726 | −0.748630 | − | 0.662988i | \(-0.769288\pi\) | ||||
−0.748630 | + | 0.662988i | \(0.769288\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −28.4233 | −1.28012 | ||||||||
\(494\) | −23.8078 | −1.07116 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0.561553 | 0.0252145 | ||||||||
\(497\) | −7.12311 | −0.319515 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 12.1922 | 0.545799 | 0.272900 | − | 0.962042i | \(-0.412017\pi\) | ||||
0.272900 | + | 0.962042i | \(0.412017\pi\) | |||||||
\(500\) | 1.00000 | 0.0447214 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −15.6155 | −0.696955 | ||||||||
\(503\) | 1.75379 | 0.0781976 | 0.0390988 | − | 0.999235i | \(-0.487551\pi\) | ||||
0.0390988 | + | 0.999235i | \(0.487551\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −19.1231 | −0.850967 | ||||||||
\(506\) | 5.17708 | 0.230149 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 10.4384 | 0.463131 | ||||||||
\(509\) | 14.0540 | 0.622932 | 0.311466 | − | 0.950257i | \(-0.399180\pi\) | ||||
0.311466 | + | 0.950257i | \(0.399180\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 2.43845 | 0.107871 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −9.80776 | −0.432602 | ||||||||
\(515\) | 16.4924 | 0.726743 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −16.9848 | −0.746993 | ||||||||
\(518\) | 1.00000 | 0.0439375 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 6.68466 | 0.293142 | ||||||||
\(521\) | 22.5616 | 0.988440 | 0.494220 | − | 0.869337i | \(-0.335454\pi\) | ||||
0.494220 | + | 0.869337i | \(0.335454\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −18.7386 | −0.819383 | −0.409692 | − | 0.912224i | \(-0.634364\pi\) | ||||
−0.409692 | + | 0.912224i | \(0.634364\pi\) | |||||||
\(524\) | 1.12311 | 0.0490631 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −10.5616 | −0.460506 | ||||||||
\(527\) | 2.80776 | 0.122308 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −17.0540 | −0.741477 | ||||||||
\(530\) | −11.2462 | −0.488504 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 3.56155 | 0.154413 | ||||||||
\(533\) | −24.6307 | −1.06687 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −9.80776 | −0.424027 | ||||||||
\(536\) | −4.87689 | −0.210650 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 3.80776 | 0.164164 | ||||||||
\(539\) | 12.7386 | 0.548692 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 41.4233 | 1.78093 | 0.890463 | − | 0.455055i | \(-0.150380\pi\) | ||||
0.890463 | + | 0.455055i | \(0.150380\pi\) | |||||||
\(542\) | −16.4924 | −0.708410 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −5.00000 | −0.214373 | ||||||||
\(545\) | 6.12311 | 0.262285 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 9.73863 | 0.416394 | 0.208197 | − | 0.978087i | \(-0.433240\pi\) | ||||
0.208197 | + | 0.978087i | \(0.433240\pi\) | |||||||
\(548\) | −12.2462 | −0.523132 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 2.12311 | 0.0905295 | ||||||||
\(551\) | 20.2462 | 0.862518 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 2.24621 | 0.0955186 | ||||||||
\(554\) | −15.3153 | −0.650687 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −6.80776 | −0.288714 | ||||||||
\(557\) | 33.6155 | 1.42434 | 0.712168 | − | 0.702009i | \(-0.247714\pi\) | ||||
0.712168 | + | 0.702009i | \(0.247714\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 2.10795 | 0.0891568 | ||||||||
\(560\) | −1.00000 | −0.0422577 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −23.1771 | −0.977666 | ||||||||
\(563\) | 23.9309 | 1.00857 | 0.504283 | − | 0.863538i | \(-0.331757\pi\) | ||||
0.504283 | + | 0.863538i | \(0.331757\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −1.68466 | −0.0708741 | ||||||||
\(566\) | 18.9309 | 0.795724 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −7.12311 | −0.298879 | ||||||||
\(569\) | −14.6847 | −0.615613 | −0.307806 | − | 0.951449i | \(-0.599595\pi\) | ||||
−0.307806 | + | 0.951449i | \(0.599595\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 14.8078 | 0.619686 | 0.309843 | − | 0.950788i | \(-0.399724\pi\) | ||||
0.309843 | + | 0.950788i | \(0.399724\pi\) | |||||||
\(572\) | 14.1922 | 0.593407 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 3.68466 | 0.153795 | ||||||||
\(575\) | 2.43845 | 0.101690 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 18.4924 | 0.769850 | 0.384925 | − | 0.922948i | \(-0.374227\pi\) | ||||
0.384925 | + | 0.922948i | \(0.374227\pi\) | |||||||
\(578\) | −8.00000 | −0.332756 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −5.68466 | −0.236043 | ||||||||
\(581\) | −11.5616 | −0.479654 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −23.8769 | −0.988880 | ||||||||
\(584\) | 2.43845 | 0.100904 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 24.6155 | 1.01686 | ||||||||
\(587\) | −41.3002 | −1.70464 | −0.852321 | − | 0.523020i | \(-0.824805\pi\) | ||||
−0.852321 | + | 0.523020i | \(0.824805\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −2.00000 | −0.0824086 | ||||||||
\(590\) | −12.2462 | −0.504169 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 1.00000 | 0.0410997 | ||||||||
\(593\) | −13.1231 | −0.538901 | −0.269451 | − | 0.963014i | \(-0.586842\pi\) | ||||
−0.269451 | + | 0.963014i | \(0.586842\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −5.00000 | −0.204980 | ||||||||
\(596\) | −24.2462 | −0.993164 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 16.3002 | 0.666564 | ||||||||
\(599\) | 22.7386 | 0.929075 | 0.464538 | − | 0.885553i | \(-0.346221\pi\) | ||||
0.464538 | + | 0.885553i | \(0.346221\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 14.8617 | 0.606223 | 0.303111 | − | 0.952955i | \(-0.401975\pi\) | ||||
0.303111 | + | 0.952955i | \(0.401975\pi\) | |||||||
\(602\) | −0.315342 | −0.0128524 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −19.5616 | −0.795948 | ||||||||
\(605\) | −6.49242 | −0.263955 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 6.49242 | 0.263519 | 0.131760 | − | 0.991282i | \(-0.457937\pi\) | ||||
0.131760 | + | 0.991282i | \(0.457937\pi\) | |||||||
\(608\) | 3.56155 | 0.144440 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −6.80776 | −0.275638 | ||||||||
\(611\) | −53.4773 | −2.16346 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 12.5616 | 0.507356 | 0.253678 | − | 0.967289i | \(-0.418360\pi\) | ||||
0.253678 | + | 0.967289i | \(0.418360\pi\) | |||||||
\(614\) | −16.2462 | −0.655644 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −2.12311 | −0.0855424 | ||||||||
\(617\) | 18.4924 | 0.744477 | 0.372238 | − | 0.928137i | \(-0.378590\pi\) | ||||
0.372238 | + | 0.928137i | \(0.378590\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −15.1922 | −0.610628 | −0.305314 | − | 0.952252i | \(-0.598761\pi\) | ||||
−0.305314 | + | 0.952252i | \(0.598761\pi\) | |||||||
\(620\) | 0.561553 | 0.0225525 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 24.1771 | 0.969413 | ||||||||
\(623\) | −6.68466 | −0.267815 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 33.1231 | 1.32387 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 19.0540 | 0.760336 | ||||||||
\(629\) | 5.00000 | 0.199363 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 27.6847 | 1.10211 | 0.551054 | − | 0.834469i | \(-0.314226\pi\) | ||||
0.551054 | + | 0.834469i | \(0.314226\pi\) | |||||||
\(632\) | 2.24621 | 0.0893495 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −11.9309 | −0.473835 | ||||||||
\(635\) | 10.4384 | 0.414237 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 40.1080 | 1.58913 | ||||||||
\(638\) | −12.0691 | −0.477821 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −1.00000 | −0.0395285 | ||||||||
\(641\) | −39.0540 | −1.54254 | −0.771270 | − | 0.636509i | \(-0.780378\pi\) | ||||
−0.771270 | + | 0.636509i | \(0.780378\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −25.8769 | −1.02049 | −0.510243 | − | 0.860031i | \(-0.670444\pi\) | ||||
−0.510243 | + | 0.860031i | \(0.670444\pi\) | |||||||
\(644\) | −2.43845 | −0.0960883 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 17.8078 | 0.700637 | ||||||||
\(647\) | 16.1922 | 0.636582 | 0.318291 | − | 0.947993i | \(-0.396891\pi\) | ||||
0.318291 | + | 0.947993i | \(0.396891\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −26.0000 | −1.02059 | ||||||||
\(650\) | 6.68466 | 0.262194 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −13.4924 | −0.528404 | ||||||||
\(653\) | −4.49242 | −0.175802 | −0.0879010 | − | 0.996129i | \(-0.528016\pi\) | ||||
−0.0879010 | + | 0.996129i | \(0.528016\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 1.12311 | 0.0438834 | ||||||||
\(656\) | 3.68466 | 0.143862 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 8.00000 | 0.311872 | ||||||||
\(659\) | 1.75379 | 0.0683179 | 0.0341590 | − | 0.999416i | \(-0.489125\pi\) | ||||
0.0341590 | + | 0.999416i | \(0.489125\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −24.8617 | −0.967010 | −0.483505 | − | 0.875342i | \(-0.660636\pi\) | ||||
−0.483505 | + | 0.875342i | \(0.660636\pi\) | |||||||
\(662\) | 12.0000 | 0.466393 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −11.5616 | −0.448675 | ||||||||
\(665\) | 3.56155 | 0.138111 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −13.8617 | −0.536729 | ||||||||
\(668\) | 18.0540 | 0.698529 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −4.87689 | −0.188411 | ||||||||
\(671\) | −14.4536 | −0.557975 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −14.4384 | −0.556561 | −0.278281 | − | 0.960500i | \(-0.589765\pi\) | ||||
−0.278281 | + | 0.960500i | \(0.589765\pi\) | |||||||
\(674\) | −0.438447 | −0.0168884 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 31.6847 | 1.21864 | ||||||||
\(677\) | −7.06913 | −0.271689 | −0.135844 | − | 0.990730i | \(-0.543375\pi\) | ||||
−0.135844 | + | 0.990730i | \(0.543375\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −15.6847 | −0.601922 | ||||||||
\(680\) | −5.00000 | −0.191741 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 1.19224 | 0.0456531 | ||||||||
\(683\) | 34.5616 | 1.32246 | 0.661231 | − | 0.750183i | \(-0.270035\pi\) | ||||
0.661231 | + | 0.750183i | \(0.270035\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −12.2462 | −0.467904 | ||||||||
\(686\) | −13.0000 | −0.496342 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −0.315342 | −0.0120223 | ||||||||
\(689\) | −75.1771 | −2.86402 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −17.6847 | −0.672756 | −0.336378 | − | 0.941727i | \(-0.609202\pi\) | ||||
−0.336378 | + | 0.941727i | \(0.609202\pi\) | |||||||
\(692\) | −6.12311 | −0.232766 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −28.0000 | −1.06287 | ||||||||
\(695\) | −6.80776 | −0.258233 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 18.4233 | 0.697832 | ||||||||
\(698\) | 2.24621 | 0.0850203 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −1.00000 | −0.0377964 | ||||||||
\(701\) | 15.3693 | 0.580491 | 0.290246 | − | 0.956952i | \(-0.406263\pi\) | ||||
0.290246 | + | 0.956952i | \(0.406263\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −3.56155 | −0.134327 | ||||||||
\(704\) | −2.12311 | −0.0800176 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −9.19224 | −0.345954 | ||||||||
\(707\) | 19.1231 | 0.719198 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −37.4924 | −1.40806 | −0.704029 | − | 0.710171i | \(-0.748617\pi\) | ||||
−0.704029 | + | 0.710171i | \(0.748617\pi\) | |||||||
\(710\) | −7.12311 | −0.267325 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −6.68466 | −0.250518 | ||||||||
\(713\) | 1.36932 | 0.0512813 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 14.1922 | 0.530760 | ||||||||
\(716\) | 4.00000 | 0.149487 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −29.1231 | −1.08686 | ||||||||
\(719\) | 2.00000 | 0.0745874 | 0.0372937 | − | 0.999304i | \(-0.488126\pi\) | ||||
0.0372937 | + | 0.999304i | \(0.488126\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −16.4924 | −0.614210 | ||||||||
\(722\) | 6.31534 | 0.235033 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 3.75379 | 0.139508 | ||||||||
\(725\) | −5.68466 | −0.211123 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −14.9848 | −0.555757 | −0.277879 | − | 0.960616i | \(-0.589631\pi\) | ||||
−0.277879 | + | 0.960616i | \(0.589631\pi\) | |||||||
\(728\) | −6.68466 | −0.247750 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 2.43845 | 0.0902510 | ||||||||
\(731\) | −1.57671 | −0.0583166 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 31.3002 | 1.15610 | 0.578049 | − | 0.816002i | \(-0.303814\pi\) | ||||
0.578049 | + | 0.816002i | \(0.303814\pi\) | |||||||
\(734\) | 17.0000 | 0.627481 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −2.43845 | −0.0898824 | ||||||||
\(737\) | −10.3542 | −0.381400 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 6.17708 | 0.227228 | 0.113614 | − | 0.993525i | \(-0.463757\pi\) | ||||
0.113614 | + | 0.993525i | \(0.463757\pi\) | |||||||
\(740\) | 1.00000 | 0.0367607 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 11.2462 | 0.412861 | ||||||||
\(743\) | 40.4233 | 1.48299 | 0.741493 | − | 0.670960i | \(-0.234118\pi\) | ||||
0.741493 | + | 0.670960i | \(0.234118\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −24.2462 | −0.888312 | ||||||||
\(746\) | −2.49242 | −0.0912541 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −10.6155 | −0.388142 | ||||||||
\(749\) | 9.80776 | 0.358368 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −26.7386 | −0.975707 | −0.487853 | − | 0.872926i | \(-0.662220\pi\) | ||||
−0.487853 | + | 0.872926i | \(0.662220\pi\) | |||||||
\(752\) | 8.00000 | 0.291730 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −38.0000 | −1.38388 | ||||||||
\(755\) | −19.5616 | −0.711918 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −52.0540 | −1.89193 | −0.945967 | − | 0.324263i | \(-0.894884\pi\) | ||||
−0.945967 | + | 0.324263i | \(0.894884\pi\) | |||||||
\(758\) | 11.1231 | 0.404009 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 3.56155 | 0.129191 | ||||||||
\(761\) | −29.6847 | −1.07607 | −0.538034 | − | 0.842923i | \(-0.680833\pi\) | ||||
−0.538034 | + | 0.842923i | \(0.680833\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −6.12311 | −0.221671 | ||||||||
\(764\) | 10.3693 | 0.375149 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −15.3153 | −0.553366 | ||||||||
\(767\) | −81.8617 | −2.95586 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −42.4924 | −1.53232 | −0.766158 | − | 0.642652i | \(-0.777834\pi\) | ||||
−0.766158 | + | 0.642652i | \(0.777834\pi\) | |||||||
\(770\) | −2.12311 | −0.0765114 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −14.0000 | −0.503871 | ||||||||
\(773\) | −29.4924 | −1.06077 | −0.530384 | − | 0.847757i | \(-0.677952\pi\) | ||||
−0.530384 | + | 0.847757i | \(0.677952\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0.561553 | 0.0201716 | ||||||||
\(776\) | −15.6847 | −0.563046 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −7.93087 | −0.284335 | ||||||||
\(779\) | −13.1231 | −0.470184 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −15.1231 | −0.541147 | ||||||||
\(782\) | −12.1922 | −0.435993 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −6.00000 | −0.214286 | ||||||||
\(785\) | 19.0540 | 0.680066 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 35.1231 | 1.25200 | 0.626002 | − | 0.779822i | \(-0.284690\pi\) | ||||
0.626002 | + | 0.779822i | \(0.284690\pi\) | |||||||
\(788\) | 14.6847 | 0.523119 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 2.24621 | 0.0799166 | ||||||||
\(791\) | 1.68466 | 0.0598996 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −45.5076 | −1.61602 | ||||||||
\(794\) | −18.8769 | −0.669916 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 16.4924 | 0.584558 | ||||||||
\(797\) | −15.6155 | −0.553130 | −0.276565 | − | 0.960995i | \(-0.589196\pi\) | ||||
−0.276565 | + | 0.960995i | \(0.589196\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 40.0000 | 1.41510 | ||||||||
\(800\) | −1.00000 | −0.0353553 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 5.80776 | 0.205079 | ||||||||
\(803\) | 5.17708 | 0.182695 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −2.43845 | −0.0859440 | ||||||||
\(806\) | 3.75379 | 0.132222 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 19.1231 | 0.672749 | ||||||||
\(809\) | 29.5616 | 1.03933 | 0.519664 | − | 0.854370i | \(-0.326057\pi\) | ||||
0.519664 | + | 0.854370i | \(0.326057\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −46.7386 | −1.64122 | −0.820608 | − | 0.571492i | \(-0.806365\pi\) | ||||
−0.820608 | + | 0.571492i | \(0.806365\pi\) | |||||||
\(812\) | 5.68466 | 0.199492 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 2.12311 | 0.0744148 | ||||||||
\(815\) | −13.4924 | −0.472619 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1.12311 | 0.0392925 | ||||||||
\(818\) | 9.12311 | 0.318982 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 3.68466 | 0.128674 | ||||||||
\(821\) | −27.5616 | −0.961905 | −0.480952 | − | 0.876747i | \(-0.659709\pi\) | ||||
−0.480952 | + | 0.876747i | \(0.659709\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −38.5464 | −1.34364 | −0.671821 | − | 0.740713i | \(-0.734488\pi\) | ||||
−0.671821 | + | 0.740713i | \(0.734488\pi\) | |||||||
\(824\) | −16.4924 | −0.574541 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 12.2462 | 0.426100 | ||||||||
\(827\) | 14.5616 | 0.506355 | 0.253177 | − | 0.967420i | \(-0.418524\pi\) | ||||
0.253177 | + | 0.967420i | \(0.418524\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −13.8769 | −0.481964 | −0.240982 | − | 0.970530i | \(-0.577470\pi\) | ||||
−0.240982 | + | 0.970530i | \(0.577470\pi\) | |||||||
\(830\) | −11.5616 | −0.401307 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −6.68466 | −0.231749 | ||||||||
\(833\) | −30.0000 | −1.03944 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 18.0540 | 0.624784 | ||||||||
\(836\) | 7.56155 | 0.261522 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −6.43845 | −0.222412 | ||||||||
\(839\) | −11.7538 | −0.405786 | −0.202893 | − | 0.979201i | \(-0.565034\pi\) | ||||
−0.202893 | + | 0.979201i | \(0.565034\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 3.31534 | 0.114322 | ||||||||
\(842\) | 34.9848 | 1.20566 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 8.56155 | 0.294701 | ||||||||
\(845\) | 31.6847 | 1.08999 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 6.49242 | 0.223082 | ||||||||
\(848\) | 11.2462 | 0.386196 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −5.00000 | −0.171499 | ||||||||
\(851\) | 2.43845 | 0.0835889 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −20.9309 | −0.716659 | −0.358330 | − | 0.933595i | \(-0.616654\pi\) | ||||
−0.358330 | + | 0.933595i | \(0.616654\pi\) | |||||||
\(854\) | 6.80776 | 0.232957 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 9.80776 | 0.335222 | ||||||||
\(857\) | 25.2462 | 0.862394 | 0.431197 | − | 0.902258i | \(-0.358091\pi\) | ||||
0.431197 | + | 0.902258i | \(0.358091\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 17.8078 | 0.607593 | 0.303797 | − | 0.952737i | \(-0.401746\pi\) | ||||
0.303797 | + | 0.952737i | \(0.401746\pi\) | |||||||
\(860\) | −0.315342 | −0.0107531 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −29.0000 | −0.987744 | ||||||||
\(863\) | −40.8078 | −1.38911 | −0.694556 | − | 0.719438i | \(-0.744399\pi\) | ||||
−0.694556 | + | 0.719438i | \(0.744399\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −6.12311 | −0.208192 | ||||||||
\(866\) | −31.4233 | −1.06781 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −0.561553 | −0.0190603 | ||||||||
\(869\) | 4.76894 | 0.161775 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −32.6004 | −1.10462 | ||||||||
\(872\) | −6.12311 | −0.207355 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 8.68466 | 0.293763 | ||||||||
\(875\) | −1.00000 | −0.0338062 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 18.0691 | 0.610151 | 0.305076 | − | 0.952328i | \(-0.401318\pi\) | ||||
0.305076 | + | 0.952328i | \(0.401318\pi\) | |||||||
\(878\) | −23.0540 | −0.778034 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −2.12311 | −0.0715699 | ||||||||
\(881\) | −6.06913 | −0.204474 | −0.102237 | − | 0.994760i | \(-0.532600\pi\) | ||||
−0.102237 | + | 0.994760i | \(0.532600\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 10.3693 | 0.348955 | 0.174478 | − | 0.984661i | \(-0.444176\pi\) | ||||
0.174478 | + | 0.984661i | \(0.444176\pi\) | |||||||
\(884\) | −33.4233 | −1.12415 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −23.8617 | −0.801651 | ||||||||
\(887\) | −2.80776 | −0.0942755 | −0.0471377 | − | 0.998888i | \(-0.515010\pi\) | ||||
−0.0471377 | + | 0.998888i | \(0.515010\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −10.4384 | −0.350094 | ||||||||
\(890\) | −6.68466 | −0.224070 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0.807764 | 0.0270459 | ||||||||
\(893\) | −28.4924 | −0.953463 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 4.00000 | 0.133705 | ||||||||
\(896\) | 1.00000 | 0.0334077 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 39.6155 | 1.32199 | ||||||||
\(899\) | −3.19224 | −0.106467 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 56.2311 | 1.87333 | ||||||||
\(902\) | 7.82292 | 0.260475 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 1.68466 | 0.0560309 | ||||||||
\(905\) | 3.75379 | 0.124780 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 49.5616 | 1.64566 | 0.822832 | − | 0.568284i | \(-0.192393\pi\) | ||||
0.822832 | + | 0.568284i | \(0.192393\pi\) | |||||||
\(908\) | −17.9309 | −0.595057 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −6.68466 | −0.221594 | ||||||||
\(911\) | 12.4924 | 0.413892 | 0.206946 | − | 0.978352i | \(-0.433647\pi\) | ||||
0.206946 | + | 0.978352i | \(0.433647\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −24.5464 | −0.812367 | ||||||||
\(914\) | 2.06913 | 0.0684407 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 3.12311 | 0.103190 | ||||||||
\(917\) | −1.12311 | −0.0370882 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −42.7386 | −1.40982 | −0.704909 | − | 0.709298i | \(-0.749012\pi\) | ||||
−0.704909 | + | 0.709298i | \(0.749012\pi\) | |||||||
\(920\) | −2.43845 | −0.0803932 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 4.56155 | 0.150227 | ||||||||
\(923\) | −47.6155 | −1.56728 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1.00000 | 0.0328798 | ||||||||
\(926\) | −13.1231 | −0.431252 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 5.68466 | 0.186608 | ||||||||
\(929\) | −14.8078 | −0.485827 | −0.242913 | − | 0.970048i | \(-0.578103\pi\) | ||||
−0.242913 | + | 0.970048i | \(0.578103\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 21.3693 | 0.700351 | ||||||||
\(932\) | 13.3693 | 0.437927 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 6.56155 | 0.214701 | ||||||||
\(935\) | −10.6155 | −0.347165 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −25.3693 | −0.828779 | −0.414390 | − | 0.910100i | \(-0.636005\pi\) | ||||
−0.414390 | + | 0.910100i | \(0.636005\pi\) | |||||||
\(938\) | 4.87689 | 0.159236 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 8.00000 | 0.260931 | ||||||||
\(941\) | −8.24621 | −0.268819 | −0.134409 | − | 0.990926i | \(-0.542914\pi\) | ||||
−0.134409 | + | 0.990926i | \(0.542914\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 8.98485 | 0.292587 | ||||||||
\(944\) | 12.2462 | 0.398580 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −0.669503 | −0.0217674 | ||||||||
\(947\) | 37.3002 | 1.21209 | 0.606047 | − | 0.795429i | \(-0.292754\pi\) | ||||
0.606047 | + | 0.795429i | \(0.292754\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 16.3002 | 0.529126 | ||||||||
\(950\) | 3.56155 | 0.115552 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 5.00000 | 0.162051 | ||||||||
\(953\) | −39.6155 | −1.28327 | −0.641636 | − | 0.767009i | \(-0.721744\pi\) | ||||
−0.641636 | + | 0.767009i | \(0.721744\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 10.3693 | 0.335543 | ||||||||
\(956\) | 12.8078 | 0.414233 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −2.43845 | −0.0787827 | ||||||||
\(959\) | 12.2462 | 0.395451 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.6847 | −0.989828 | ||||||||
\(962\) | 6.68466 | 0.215522 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −2.00000 | −0.0644157 | ||||||||
\(965\) | −14.0000 | −0.450676 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 57.3693 | 1.84487 | 0.922436 | − | 0.386149i | \(-0.126195\pi\) | ||||
0.922436 | + | 0.386149i | \(0.126195\pi\) | |||||||
\(968\) | 6.49242 | 0.208674 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −15.6847 | −0.503604 | ||||||||
\(971\) | −4.80776 | −0.154288 | −0.0771442 | − | 0.997020i | \(-0.524580\pi\) | ||||
−0.0771442 | + | 0.997020i | \(0.524580\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 6.80776 | 0.218247 | ||||||||
\(974\) | 32.7386 | 1.04901 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 6.80776 | 0.217911 | ||||||||
\(977\) | 45.4924 | 1.45543 | 0.727716 | − | 0.685879i | \(-0.240582\pi\) | ||||
0.727716 | + | 0.685879i | \(0.240582\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −14.1922 | −0.453586 | ||||||||
\(980\) | −6.00000 | −0.191663 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 33.1771 | 1.05872 | ||||||||
\(983\) | −3.93087 | −0.125375 | −0.0626876 | − | 0.998033i | \(-0.519967\pi\) | ||||
−0.0626876 | + | 0.998033i | \(0.519967\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 14.6847 | 0.467892 | ||||||||
\(986\) | 28.4233 | 0.905182 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 23.8078 | 0.757426 | ||||||||
\(989\) | −0.768944 | −0.0244510 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −58.4233 | −1.85588 | −0.927939 | − | 0.372733i | \(-0.878421\pi\) | ||||
−0.927939 | + | 0.372733i | \(0.878421\pi\) | |||||||
\(992\) | −0.561553 | −0.0178293 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 7.12311 | 0.225931 | ||||||||
\(995\) | 16.4924 | 0.522845 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −34.3002 | −1.08630 | −0.543149 | − | 0.839636i | \(-0.682768\pi\) | ||||
−0.543149 | + | 0.839636i | \(0.682768\pi\) | |||||||
\(998\) | −12.1922 | −0.385938 | ||||||||
\(999\) | 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 | 3330.2.a.bc.1.1 | 2 | ||
3.2 | odd | 2 | 1110.2.a.r.1.2 | ✓ | 2 | ||
12.11 | even | 2 | 8880.2.a.bp.1.1 | 2 | |||
15.14 | odd | 2 | 5550.2.a.bw.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1110.2.a.r.1.2 | ✓ | 2 | 3.2 | odd | 2 | ||
3330.2.a.bc.1.1 | 2 | 1.1 | even | 1 | trivial | ||
5550.2.a.bw.1.2 | 2 | 15.14 | odd | 2 | |||
8880.2.a.bp.1.1 | 2 | 12.11 | even | 2 |