Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6422,2,Mod(1,6422)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6422, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("6422.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6422 = 2 \cdot 13^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6422.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: | \(51.2799281781\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | \(\Q(\zeta_{14})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 2x + 1 \) |
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 | 1.1 | ||
Root | \(1.80194\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6422.1 |
$q$-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 | ||||||||
\(3\) | −1.80194 | −1.04035 | −0.520175 | − | 0.854060i | \(-0.674133\pi\) | ||||
−0.520175 | + | 0.854060i | \(0.674133\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 2.44504 | 1.09346 | 0.546728 | − | 0.837310i | \(-0.315873\pi\) | ||||
0.546728 | + | 0.837310i | \(0.315873\pi\) | |||||||
\(6\) | 1.80194 | 0.735638 | ||||||||
\(7\) | 4.49396 | 1.69856 | 0.849278 | − | 0.527945i | \(-0.177037\pi\) | ||||
0.849278 | + | 0.527945i | \(0.177037\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 0.246980 | 0.0823265 | ||||||||
\(10\) | −2.44504 | −0.773190 | ||||||||
\(11\) | 2.49396 | 0.751957 | 0.375978 | − | 0.926628i | \(-0.377307\pi\) | ||||
0.375978 | + | 0.926628i | \(0.377307\pi\) | |||||||
\(12\) | −1.80194 | −0.520175 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | −4.49396 | −1.20106 | ||||||||
\(15\) | −4.40581 | −1.13758 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 7.74094 | 1.87745 | 0.938727 | − | 0.344662i | \(-0.112007\pi\) | ||||
0.938727 | + | 0.344662i | \(0.112007\pi\) | |||||||
\(18\) | −0.246980 | −0.0582137 | ||||||||
\(19\) | −1.00000 | −0.229416 | ||||||||
\(20\) | 2.44504 | 0.546728 | ||||||||
\(21\) | −8.09783 | −1.76709 | ||||||||
\(22\) | −2.49396 | −0.531714 | ||||||||
\(23\) | 4.27413 | 0.891217 | 0.445609 | − | 0.895228i | \(-0.352987\pi\) | ||||
0.445609 | + | 0.895228i | \(0.352987\pi\) | |||||||
\(24\) | 1.80194 | 0.367819 | ||||||||
\(25\) | 0.978230 | 0.195646 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 4.96077 | 0.954701 | ||||||||
\(28\) | 4.49396 | 0.849278 | ||||||||
\(29\) | −0.713792 | −0.132548 | −0.0662739 | − | 0.997801i | \(-0.521111\pi\) | ||||
−0.0662739 | + | 0.997801i | \(0.521111\pi\) | |||||||
\(30\) | 4.40581 | 0.804388 | ||||||||
\(31\) | 0.911854 | 0.163774 | 0.0818869 | − | 0.996642i | \(-0.473905\pi\) | ||||
0.0818869 | + | 0.996642i | \(0.473905\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | −4.49396 | −0.782298 | ||||||||
\(34\) | −7.74094 | −1.32756 | ||||||||
\(35\) | 10.9879 | 1.85730 | ||||||||
\(36\) | 0.246980 | 0.0411633 | ||||||||
\(37\) | −6.81163 | −1.11982 | −0.559912 | − | 0.828552i | \(-0.689165\pi\) | ||||
−0.559912 | + | 0.828552i | \(0.689165\pi\) | |||||||
\(38\) | 1.00000 | 0.162221 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −2.44504 | −0.386595 | ||||||||
\(41\) | 3.28621 | 0.513220 | 0.256610 | − | 0.966515i | \(-0.417394\pi\) | ||||
0.256610 | + | 0.966515i | \(0.417394\pi\) | |||||||
\(42\) | 8.09783 | 1.24952 | ||||||||
\(43\) | 7.20775 | 1.09917 | 0.549586 | − | 0.835437i | \(-0.314786\pi\) | ||||
0.549586 | + | 0.835437i | \(0.314786\pi\) | |||||||
\(44\) | 2.49396 | 0.375978 | ||||||||
\(45\) | 0.603875 | 0.0900204 | ||||||||
\(46\) | −4.27413 | −0.630186 | ||||||||
\(47\) | −5.20775 | −0.759629 | −0.379814 | − | 0.925063i | \(-0.624012\pi\) | ||||
−0.379814 | + | 0.925063i | \(0.624012\pi\) | |||||||
\(48\) | −1.80194 | −0.260087 | ||||||||
\(49\) | 13.1957 | 1.88510 | ||||||||
\(50\) | −0.978230 | −0.138343 | ||||||||
\(51\) | −13.9487 | −1.95321 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −8.89008 | −1.22115 | −0.610573 | − | 0.791960i | \(-0.709061\pi\) | ||||
−0.610573 | + | 0.791960i | \(0.709061\pi\) | |||||||
\(54\) | −4.96077 | −0.675075 | ||||||||
\(55\) | 6.09783 | 0.822232 | ||||||||
\(56\) | −4.49396 | −0.600531 | ||||||||
\(57\) | 1.80194 | 0.238672 | ||||||||
\(58\) | 0.713792 | 0.0937254 | ||||||||
\(59\) | 11.2567 | 1.46549 | 0.732747 | − | 0.680501i | \(-0.238238\pi\) | ||||
0.732747 | + | 0.680501i | \(0.238238\pi\) | |||||||
\(60\) | −4.40581 | −0.568788 | ||||||||
\(61\) | 3.43296 | 0.439546 | 0.219773 | − | 0.975551i | \(-0.429468\pi\) | ||||
0.219773 | + | 0.975551i | \(0.429468\pi\) | |||||||
\(62\) | −0.911854 | −0.115806 | ||||||||
\(63\) | 1.10992 | 0.139836 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 4.49396 | 0.553168 | ||||||||
\(67\) | 1.40581 | 0.171747 | 0.0858737 | − | 0.996306i | \(-0.472632\pi\) | ||||
0.0858737 | + | 0.996306i | \(0.472632\pi\) | |||||||
\(68\) | 7.74094 | 0.938727 | ||||||||
\(69\) | −7.70171 | −0.927177 | ||||||||
\(70\) | −10.9879 | −1.31331 | ||||||||
\(71\) | −3.86294 | −0.458446 | −0.229223 | − | 0.973374i | \(-0.573619\pi\) | ||||
−0.229223 | + | 0.973374i | \(0.573619\pi\) | |||||||
\(72\) | −0.246980 | −0.0291068 | ||||||||
\(73\) | 7.74094 | 0.906008 | 0.453004 | − | 0.891508i | \(-0.350352\pi\) | ||||
0.453004 | + | 0.891508i | \(0.350352\pi\) | |||||||
\(74\) | 6.81163 | 0.791835 | ||||||||
\(75\) | −1.76271 | −0.203540 | ||||||||
\(76\) | −1.00000 | −0.114708 | ||||||||
\(77\) | 11.2078 | 1.27724 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1.91723 | −0.215705 | −0.107853 | − | 0.994167i | \(-0.534397\pi\) | ||||
−0.107853 | + | 0.994167i | \(0.534397\pi\) | |||||||
\(80\) | 2.44504 | 0.273364 | ||||||||
\(81\) | −9.67994 | −1.07555 | ||||||||
\(82\) | −3.28621 | −0.362901 | ||||||||
\(83\) | 0.396125 | 0.0434803 | 0.0217402 | − | 0.999764i | \(-0.493079\pi\) | ||||
0.0217402 | + | 0.999764i | \(0.493079\pi\) | |||||||
\(84\) | −8.09783 | −0.883546 | ||||||||
\(85\) | 18.9269 | 2.05291 | ||||||||
\(86\) | −7.20775 | −0.777232 | ||||||||
\(87\) | 1.28621 | 0.137896 | ||||||||
\(88\) | −2.49396 | −0.265857 | ||||||||
\(89\) | 16.7681 | 1.77741 | 0.888707 | − | 0.458476i | \(-0.151605\pi\) | ||||
0.888707 | + | 0.458476i | \(0.151605\pi\) | |||||||
\(90\) | −0.603875 | −0.0636541 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 4.27413 | 0.445609 | ||||||||
\(93\) | −1.64310 | −0.170382 | ||||||||
\(94\) | 5.20775 | 0.537138 | ||||||||
\(95\) | −2.44504 | −0.250856 | ||||||||
\(96\) | 1.80194 | 0.183910 | ||||||||
\(97\) | −3.16421 | −0.321277 | −0.160638 | − | 0.987013i | \(-0.551355\pi\) | ||||
−0.160638 | + | 0.987013i | \(0.551355\pi\) | |||||||
\(98\) | −13.1957 | −1.33296 | ||||||||
\(99\) | 0.615957 | 0.0619060 | ||||||||
\(100\) | 0.978230 | 0.0978230 | ||||||||
\(101\) | 15.5308 | 1.54537 | 0.772686 | − | 0.634789i | \(-0.218913\pi\) | ||||
0.772686 | + | 0.634789i | \(0.218913\pi\) | |||||||
\(102\) | 13.9487 | 1.38113 | ||||||||
\(103\) | −3.03684 | −0.299228 | −0.149614 | − | 0.988744i | \(-0.547803\pi\) | ||||
−0.149614 | + | 0.988744i | \(0.547803\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −19.7995 | −1.93224 | ||||||||
\(106\) | 8.89008 | 0.863481 | ||||||||
\(107\) | −2.53319 | −0.244893 | −0.122446 | − | 0.992475i | \(-0.539074\pi\) | ||||
−0.122446 | + | 0.992475i | \(0.539074\pi\) | |||||||
\(108\) | 4.96077 | 0.477350 | ||||||||
\(109\) | 10.2198 | 0.978882 | 0.489441 | − | 0.872036i | \(-0.337201\pi\) | ||||
0.489441 | + | 0.872036i | \(0.337201\pi\) | |||||||
\(110\) | −6.09783 | −0.581406 | ||||||||
\(111\) | 12.2741 | 1.16501 | ||||||||
\(112\) | 4.49396 | 0.424639 | ||||||||
\(113\) | 7.60388 | 0.715312 | 0.357656 | − | 0.933853i | \(-0.383576\pi\) | ||||
0.357656 | + | 0.933853i | \(0.383576\pi\) | |||||||
\(114\) | −1.80194 | −0.168767 | ||||||||
\(115\) | 10.4504 | 0.974507 | ||||||||
\(116\) | −0.713792 | −0.0662739 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −11.2567 | −1.03626 | ||||||||
\(119\) | 34.7875 | 3.18896 | ||||||||
\(120\) | 4.40581 | 0.402194 | ||||||||
\(121\) | −4.78017 | −0.434561 | ||||||||
\(122\) | −3.43296 | −0.310806 | ||||||||
\(123\) | −5.92154 | −0.533928 | ||||||||
\(124\) | 0.911854 | 0.0818869 | ||||||||
\(125\) | −9.83340 | −0.879526 | ||||||||
\(126\) | −1.10992 | −0.0988792 | ||||||||
\(127\) | −18.6920 | −1.65865 | −0.829324 | − | 0.558768i | \(-0.811274\pi\) | ||||
−0.829324 | + | 0.558768i | \(0.811274\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | −12.9879 | −1.14352 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −8.49396 | −0.742121 | −0.371060 | − | 0.928609i | \(-0.621006\pi\) | ||||
−0.371060 | + | 0.928609i | \(0.621006\pi\) | |||||||
\(132\) | −4.49396 | −0.391149 | ||||||||
\(133\) | −4.49396 | −0.389676 | ||||||||
\(134\) | −1.40581 | −0.121444 | ||||||||
\(135\) | 12.1293 | 1.04392 | ||||||||
\(136\) | −7.74094 | −0.663780 | ||||||||
\(137\) | −19.7506 | −1.68741 | −0.843705 | − | 0.536807i | \(-0.819630\pi\) | ||||
−0.843705 | + | 0.536807i | \(0.819630\pi\) | |||||||
\(138\) | 7.70171 | 0.655613 | ||||||||
\(139\) | 8.15213 | 0.691455 | 0.345727 | − | 0.938335i | \(-0.387632\pi\) | ||||
0.345727 | + | 0.938335i | \(0.387632\pi\) | |||||||
\(140\) | 10.9879 | 0.928649 | ||||||||
\(141\) | 9.38404 | 0.790279 | ||||||||
\(142\) | 3.86294 | 0.324170 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0.246980 | 0.0205816 | ||||||||
\(145\) | −1.74525 | −0.144935 | ||||||||
\(146\) | −7.74094 | −0.640645 | ||||||||
\(147\) | −23.7778 | −1.96116 | ||||||||
\(148\) | −6.81163 | −0.559912 | ||||||||
\(149\) | −8.11290 | −0.664635 | −0.332317 | − | 0.943168i | \(-0.607830\pi\) | ||||
−0.332317 | + | 0.943168i | \(0.607830\pi\) | |||||||
\(150\) | 1.76271 | 0.143925 | ||||||||
\(151\) | −5.56465 | −0.452845 | −0.226422 | − | 0.974029i | \(-0.572703\pi\) | ||||
−0.226422 | + | 0.974029i | \(0.572703\pi\) | |||||||
\(152\) | 1.00000 | 0.0811107 | ||||||||
\(153\) | 1.91185 | 0.154564 | ||||||||
\(154\) | −11.2078 | −0.903146 | ||||||||
\(155\) | 2.22952 | 0.179079 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −6.77240 | −0.540496 | −0.270248 | − | 0.962791i | \(-0.587106\pi\) | ||||
−0.270248 | + | 0.962791i | \(0.587106\pi\) | |||||||
\(158\) | 1.91723 | 0.152527 | ||||||||
\(159\) | 16.0194 | 1.27042 | ||||||||
\(160\) | −2.44504 | −0.193298 | ||||||||
\(161\) | 19.2078 | 1.51378 | ||||||||
\(162\) | 9.67994 | 0.760528 | ||||||||
\(163\) | 8.27413 | 0.648080 | 0.324040 | − | 0.946043i | \(-0.394959\pi\) | ||||
0.324040 | + | 0.946043i | \(0.394959\pi\) | |||||||
\(164\) | 3.28621 | 0.256610 | ||||||||
\(165\) | −10.9879 | −0.855408 | ||||||||
\(166\) | −0.396125 | −0.0307452 | ||||||||
\(167\) | 6.25236 | 0.483822 | 0.241911 | − | 0.970298i | \(-0.422226\pi\) | ||||
0.241911 | + | 0.970298i | \(0.422226\pi\) | |||||||
\(168\) | 8.09783 | 0.624762 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | −18.9269 | −1.45163 | ||||||||
\(171\) | −0.246980 | −0.0188870 | ||||||||
\(172\) | 7.20775 | 0.549586 | ||||||||
\(173\) | 24.5133 | 1.86371 | 0.931857 | − | 0.362825i | \(-0.118188\pi\) | ||||
0.931857 | + | 0.362825i | \(0.118188\pi\) | |||||||
\(174\) | −1.28621 | −0.0975072 | ||||||||
\(175\) | 4.39612 | 0.332316 | ||||||||
\(176\) | 2.49396 | 0.187989 | ||||||||
\(177\) | −20.2838 | −1.52462 | ||||||||
\(178\) | −16.7681 | −1.25682 | ||||||||
\(179\) | −25.9366 | −1.93859 | −0.969297 | − | 0.245895i | \(-0.920918\pi\) | ||||
−0.969297 | + | 0.245895i | \(0.920918\pi\) | |||||||
\(180\) | 0.603875 | 0.0450102 | ||||||||
\(181\) | 5.23191 | 0.388885 | 0.194443 | − | 0.980914i | \(-0.437710\pi\) | ||||
0.194443 | + | 0.980914i | \(0.437710\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −6.18598 | −0.457281 | ||||||||
\(184\) | −4.27413 | −0.315093 | ||||||||
\(185\) | −16.6547 | −1.22448 | ||||||||
\(186\) | 1.64310 | 0.120478 | ||||||||
\(187\) | 19.3056 | 1.41176 | ||||||||
\(188\) | −5.20775 | −0.379814 | ||||||||
\(189\) | 22.2935 | 1.62161 | ||||||||
\(190\) | 2.44504 | 0.177382 | ||||||||
\(191\) | −17.4819 | −1.26494 | −0.632472 | − | 0.774583i | \(-0.717960\pi\) | ||||
−0.632472 | + | 0.774583i | \(0.717960\pi\) | |||||||
\(192\) | −1.80194 | −0.130044 | ||||||||
\(193\) | −23.7754 | −1.71139 | −0.855695 | − | 0.517481i | \(-0.826870\pi\) | ||||
−0.855695 | + | 0.517481i | \(0.826870\pi\) | |||||||
\(194\) | 3.16421 | 0.227177 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 13.1957 | 0.942548 | ||||||||
\(197\) | −22.6069 | −1.61067 | −0.805336 | − | 0.592819i | \(-0.798015\pi\) | ||||
−0.805336 | + | 0.592819i | \(0.798015\pi\) | |||||||
\(198\) | −0.615957 | −0.0437742 | ||||||||
\(199\) | −16.7332 | −1.18618 | −0.593091 | − | 0.805135i | \(-0.702093\pi\) | ||||
−0.593091 | + | 0.805135i | \(0.702093\pi\) | |||||||
\(200\) | −0.978230 | −0.0691713 | ||||||||
\(201\) | −2.53319 | −0.178677 | ||||||||
\(202\) | −15.5308 | −1.09274 | ||||||||
\(203\) | −3.20775 | −0.225140 | ||||||||
\(204\) | −13.9487 | −0.976604 | ||||||||
\(205\) | 8.03492 | 0.561183 | ||||||||
\(206\) | 3.03684 | 0.211586 | ||||||||
\(207\) | 1.05562 | 0.0733708 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −2.49396 | −0.172511 | ||||||||
\(210\) | 19.7995 | 1.36630 | ||||||||
\(211\) | 15.3817 | 1.05892 | 0.529458 | − | 0.848336i | \(-0.322395\pi\) | ||||
0.529458 | + | 0.848336i | \(0.322395\pi\) | |||||||
\(212\) | −8.89008 | −0.610573 | ||||||||
\(213\) | 6.96077 | 0.476944 | ||||||||
\(214\) | 2.53319 | 0.173165 | ||||||||
\(215\) | 17.6233 | 1.20190 | ||||||||
\(216\) | −4.96077 | −0.337538 | ||||||||
\(217\) | 4.09783 | 0.278179 | ||||||||
\(218\) | −10.2198 | −0.692174 | ||||||||
\(219\) | −13.9487 | −0.942565 | ||||||||
\(220\) | 6.09783 | 0.411116 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | −12.2741 | −0.823785 | ||||||||
\(223\) | 28.4198 | 1.90313 | 0.951566 | − | 0.307445i | \(-0.0994741\pi\) | ||||
0.951566 | + | 0.307445i | \(0.0994741\pi\) | |||||||
\(224\) | −4.49396 | −0.300265 | ||||||||
\(225\) | 0.241603 | 0.0161069 | ||||||||
\(226\) | −7.60388 | −0.505802 | ||||||||
\(227\) | 10.1981 | 0.676869 | 0.338435 | − | 0.940990i | \(-0.390103\pi\) | ||||
0.338435 | + | 0.940990i | \(0.390103\pi\) | |||||||
\(228\) | 1.80194 | 0.119336 | ||||||||
\(229\) | 14.5429 | 0.961020 | 0.480510 | − | 0.876989i | \(-0.340452\pi\) | ||||
0.480510 | + | 0.876989i | \(0.340452\pi\) | |||||||
\(230\) | −10.4504 | −0.689080 | ||||||||
\(231\) | −20.1957 | −1.32878 | ||||||||
\(232\) | 0.713792 | 0.0468627 | ||||||||
\(233\) | −26.0683 | −1.70779 | −0.853895 | − | 0.520445i | \(-0.825766\pi\) | ||||
−0.853895 | + | 0.520445i | \(0.825766\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −12.7332 | −0.830620 | ||||||||
\(236\) | 11.2567 | 0.732747 | ||||||||
\(237\) | 3.45473 | 0.224409 | ||||||||
\(238\) | −34.7875 | −2.25494 | ||||||||
\(239\) | −16.2198 | −1.04917 | −0.524587 | − | 0.851357i | \(-0.675780\pi\) | ||||
−0.524587 | + | 0.851357i | \(0.675780\pi\) | |||||||
\(240\) | −4.40581 | −0.284394 | ||||||||
\(241\) | −27.3250 | −1.76016 | −0.880078 | − | 0.474830i | \(-0.842510\pi\) | ||||
−0.880078 | + | 0.474830i | \(0.842510\pi\) | |||||||
\(242\) | 4.78017 | 0.307281 | ||||||||
\(243\) | 2.56033 | 0.164246 | ||||||||
\(244\) | 3.43296 | 0.219773 | ||||||||
\(245\) | 32.2640 | 2.06127 | ||||||||
\(246\) | 5.92154 | 0.377544 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −0.911854 | −0.0579028 | ||||||||
\(249\) | −0.713792 | −0.0452347 | ||||||||
\(250\) | 9.83340 | 0.621919 | ||||||||
\(251\) | 14.7922 | 0.933678 | 0.466839 | − | 0.884342i | \(-0.345393\pi\) | ||||
0.466839 | + | 0.884342i | \(0.345393\pi\) | |||||||
\(252\) | 1.10992 | 0.0699182 | ||||||||
\(253\) | 10.6595 | 0.670157 | ||||||||
\(254\) | 18.6920 | 1.17284 | ||||||||
\(255\) | −34.1051 | −2.13575 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −26.5918 | −1.65875 | −0.829375 | − | 0.558692i | \(-0.811303\pi\) | ||||
−0.829375 | + | 0.558692i | \(0.811303\pi\) | |||||||
\(258\) | 12.9879 | 0.808592 | ||||||||
\(259\) | −30.6112 | −1.90209 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −0.176292 | −0.0109122 | ||||||||
\(262\) | 8.49396 | 0.524759 | ||||||||
\(263\) | −24.7332 | −1.52511 | −0.762556 | − | 0.646922i | \(-0.776056\pi\) | ||||
−0.762556 | + | 0.646922i | \(0.776056\pi\) | |||||||
\(264\) | 4.49396 | 0.276584 | ||||||||
\(265\) | −21.7366 | −1.33527 | ||||||||
\(266\) | 4.49396 | 0.275542 | ||||||||
\(267\) | −30.2150 | −1.84913 | ||||||||
\(268\) | 1.40581 | 0.0858737 | ||||||||
\(269\) | 16.2935 | 0.993432 | 0.496716 | − | 0.867913i | \(-0.334539\pi\) | ||||
0.496716 | + | 0.867913i | \(0.334539\pi\) | |||||||
\(270\) | −12.1293 | −0.738165 | ||||||||
\(271\) | −25.7560 | −1.56457 | −0.782283 | − | 0.622923i | \(-0.785945\pi\) | ||||
−0.782283 | + | 0.622923i | \(0.785945\pi\) | |||||||
\(272\) | 7.74094 | 0.469363 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 19.7506 | 1.19318 | ||||||||
\(275\) | 2.43967 | 0.147117 | ||||||||
\(276\) | −7.70171 | −0.463588 | ||||||||
\(277\) | 2.19029 | 0.131602 | 0.0658010 | − | 0.997833i | \(-0.479040\pi\) | ||||
0.0658010 | + | 0.997833i | \(0.479040\pi\) | |||||||
\(278\) | −8.15213 | −0.488932 | ||||||||
\(279\) | 0.225209 | 0.0134829 | ||||||||
\(280\) | −10.9879 | −0.656654 | ||||||||
\(281\) | 24.6353 | 1.46962 | 0.734810 | − | 0.678273i | \(-0.237271\pi\) | ||||
0.734810 | + | 0.678273i | \(0.237271\pi\) | |||||||
\(282\) | −9.38404 | −0.558812 | ||||||||
\(283\) | −4.48321 | −0.266499 | −0.133249 | − | 0.991083i | \(-0.542541\pi\) | ||||
−0.133249 | + | 0.991083i | \(0.542541\pi\) | |||||||
\(284\) | −3.86294 | −0.229223 | ||||||||
\(285\) | 4.40581 | 0.260978 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 14.7681 | 0.871733 | ||||||||
\(288\) | −0.246980 | −0.0145534 | ||||||||
\(289\) | 42.9221 | 2.52483 | ||||||||
\(290\) | 1.74525 | 0.102485 | ||||||||
\(291\) | 5.70171 | 0.334240 | ||||||||
\(292\) | 7.74094 | 0.453004 | ||||||||
\(293\) | 3.32975 | 0.194526 | 0.0972630 | − | 0.995259i | \(-0.468991\pi\) | ||||
0.0972630 | + | 0.995259i | \(0.468991\pi\) | |||||||
\(294\) | 23.7778 | 1.38675 | ||||||||
\(295\) | 27.5230 | 1.60245 | ||||||||
\(296\) | 6.81163 | 0.395918 | ||||||||
\(297\) | 12.3720 | 0.717894 | ||||||||
\(298\) | 8.11290 | 0.469968 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | −1.76271 | −0.101770 | ||||||||
\(301\) | 32.3913 | 1.86701 | ||||||||
\(302\) | 5.56465 | 0.320209 | ||||||||
\(303\) | −27.9855 | −1.60773 | ||||||||
\(304\) | −1.00000 | −0.0573539 | ||||||||
\(305\) | 8.39373 | 0.480624 | ||||||||
\(306\) | −1.91185 | −0.109293 | ||||||||
\(307\) | 2.74632 | 0.156741 | 0.0783703 | − | 0.996924i | \(-0.475028\pi\) | ||||
0.0783703 | + | 0.996924i | \(0.475028\pi\) | |||||||
\(308\) | 11.2078 | 0.638621 | ||||||||
\(309\) | 5.47219 | 0.311302 | ||||||||
\(310\) | −2.22952 | −0.126628 | ||||||||
\(311\) | −13.6775 | −0.775583 | −0.387791 | − | 0.921747i | \(-0.626762\pi\) | ||||
−0.387791 | + | 0.921747i | \(0.626762\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 16.1903 | 0.915129 | 0.457565 | − | 0.889176i | \(-0.348722\pi\) | ||||
0.457565 | + | 0.889176i | \(0.348722\pi\) | |||||||
\(314\) | 6.77240 | 0.382189 | ||||||||
\(315\) | 2.71379 | 0.152905 | ||||||||
\(316\) | −1.91723 | −0.107853 | ||||||||
\(317\) | 19.8538 | 1.11510 | 0.557551 | − | 0.830142i | \(-0.311741\pi\) | ||||
0.557551 | + | 0.830142i | \(0.311741\pi\) | |||||||
\(318\) | −16.0194 | −0.898322 | ||||||||
\(319\) | −1.78017 | −0.0996702 | ||||||||
\(320\) | 2.44504 | 0.136682 | ||||||||
\(321\) | 4.56465 | 0.254774 | ||||||||
\(322\) | −19.2078 | −1.07041 | ||||||||
\(323\) | −7.74094 | −0.430717 | ||||||||
\(324\) | −9.67994 | −0.537774 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −8.27413 | −0.458261 | ||||||||
\(327\) | −18.4155 | −1.01838 | ||||||||
\(328\) | −3.28621 | −0.181450 | ||||||||
\(329\) | −23.4034 | −1.29027 | ||||||||
\(330\) | 10.9879 | 0.604865 | ||||||||
\(331\) | −19.2295 | −1.05695 | −0.528475 | − | 0.848949i | \(-0.677236\pi\) | ||||
−0.528475 | + | 0.848949i | \(0.677236\pi\) | |||||||
\(332\) | 0.396125 | 0.0217402 | ||||||||
\(333\) | −1.68233 | −0.0921913 | ||||||||
\(334\) | −6.25236 | −0.342114 | ||||||||
\(335\) | 3.43727 | 0.187798 | ||||||||
\(336\) | −8.09783 | −0.441773 | ||||||||
\(337\) | −10.8465 | −0.590849 | −0.295424 | − | 0.955366i | \(-0.595461\pi\) | ||||
−0.295424 | + | 0.955366i | \(0.595461\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −13.7017 | −0.744175 | ||||||||
\(340\) | 18.9269 | 1.02646 | ||||||||
\(341\) | 2.27413 | 0.123151 | ||||||||
\(342\) | 0.246980 | 0.0133551 | ||||||||
\(343\) | 27.8431 | 1.50339 | ||||||||
\(344\) | −7.20775 | −0.388616 | ||||||||
\(345\) | −18.8310 | −1.01383 | ||||||||
\(346\) | −24.5133 | −1.31785 | ||||||||
\(347\) | 13.8974 | 0.746050 | 0.373025 | − | 0.927821i | \(-0.378320\pi\) | ||||
0.373025 | + | 0.927821i | \(0.378320\pi\) | |||||||
\(348\) | 1.28621 | 0.0689480 | ||||||||
\(349\) | −1.89977 | −0.101692 | −0.0508462 | − | 0.998706i | \(-0.516192\pi\) | ||||
−0.0508462 | + | 0.998706i | \(0.516192\pi\) | |||||||
\(350\) | −4.39612 | −0.234983 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −2.49396 | −0.132928 | ||||||||
\(353\) | −17.1618 | −0.913431 | −0.456716 | − | 0.889613i | \(-0.650974\pi\) | ||||
−0.456716 | + | 0.889613i | \(0.650974\pi\) | |||||||
\(354\) | 20.2838 | 1.07807 | ||||||||
\(355\) | −9.44504 | −0.501291 | ||||||||
\(356\) | 16.7681 | 0.888707 | ||||||||
\(357\) | −62.6848 | −3.31763 | ||||||||
\(358\) | 25.9366 | 1.37079 | ||||||||
\(359\) | −18.5181 | −0.977349 | −0.488675 | − | 0.872466i | \(-0.662519\pi\) | ||||
−0.488675 | + | 0.872466i | \(0.662519\pi\) | |||||||
\(360\) | −0.603875 | −0.0318270 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | −5.23191 | −0.274983 | ||||||||
\(363\) | 8.61356 | 0.452095 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 18.9269 | 0.990680 | ||||||||
\(366\) | 6.18598 | 0.323346 | ||||||||
\(367\) | 8.39612 | 0.438274 | 0.219137 | − | 0.975694i | \(-0.429676\pi\) | ||||
0.219137 | + | 0.975694i | \(0.429676\pi\) | |||||||
\(368\) | 4.27413 | 0.222804 | ||||||||
\(369\) | 0.811626 | 0.0422516 | ||||||||
\(370\) | 16.6547 | 0.865837 | ||||||||
\(371\) | −39.9517 | −2.07419 | ||||||||
\(372\) | −1.64310 | −0.0851910 | ||||||||
\(373\) | 29.5991 | 1.53258 | 0.766291 | − | 0.642493i | \(-0.222100\pi\) | ||||
0.766291 | + | 0.642493i | \(0.222100\pi\) | |||||||
\(374\) | −19.3056 | −0.998268 | ||||||||
\(375\) | 17.7192 | 0.915014 | ||||||||
\(376\) | 5.20775 | 0.268569 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | −22.2935 | −1.14665 | ||||||||
\(379\) | −18.9638 | −0.974103 | −0.487051 | − | 0.873373i | \(-0.661928\pi\) | ||||
−0.487051 | + | 0.873373i | \(0.661928\pi\) | |||||||
\(380\) | −2.44504 | −0.125428 | ||||||||
\(381\) | 33.6819 | 1.72557 | ||||||||
\(382\) | 17.4819 | 0.894451 | ||||||||
\(383\) | 28.4644 | 1.45446 | 0.727232 | − | 0.686392i | \(-0.240806\pi\) | ||||
0.727232 | + | 0.686392i | \(0.240806\pi\) | |||||||
\(384\) | 1.80194 | 0.0919548 | ||||||||
\(385\) | 27.4034 | 1.39661 | ||||||||
\(386\) | 23.7754 | 1.21014 | ||||||||
\(387\) | 1.78017 | 0.0904910 | ||||||||
\(388\) | −3.16421 | −0.160638 | ||||||||
\(389\) | 6.90084 | 0.349886 | 0.174943 | − | 0.984579i | \(-0.444026\pi\) | ||||
0.174943 | + | 0.984579i | \(0.444026\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 33.0858 | 1.67322 | ||||||||
\(392\) | −13.1957 | −0.666482 | ||||||||
\(393\) | 15.3056 | 0.772065 | ||||||||
\(394\) | 22.6069 | 1.13892 | ||||||||
\(395\) | −4.68771 | −0.235864 | ||||||||
\(396\) | 0.615957 | 0.0309530 | ||||||||
\(397\) | −27.8726 | −1.39889 | −0.699443 | − | 0.714688i | \(-0.746569\pi\) | ||||
−0.699443 | + | 0.714688i | \(0.746569\pi\) | |||||||
\(398\) | 16.7332 | 0.838758 | ||||||||
\(399\) | 8.09783 | 0.405399 | ||||||||
\(400\) | 0.978230 | 0.0489115 | ||||||||
\(401\) | 27.5120 | 1.37388 | 0.686942 | − | 0.726712i | \(-0.258953\pi\) | ||||
0.686942 | + | 0.726712i | \(0.258953\pi\) | |||||||
\(402\) | 2.53319 | 0.126344 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 15.5308 | 0.772686 | ||||||||
\(405\) | −23.6679 | −1.17607 | ||||||||
\(406\) | 3.20775 | 0.159198 | ||||||||
\(407\) | −16.9879 | −0.842060 | ||||||||
\(408\) | 13.9487 | 0.690563 | ||||||||
\(409\) | 10.8358 | 0.535795 | 0.267898 | − | 0.963447i | \(-0.413671\pi\) | ||||
0.267898 | + | 0.963447i | \(0.413671\pi\) | |||||||
\(410\) | −8.03492 | −0.396816 | ||||||||
\(411\) | 35.5894 | 1.75550 | ||||||||
\(412\) | −3.03684 | −0.149614 | ||||||||
\(413\) | 50.5870 | 2.48922 | ||||||||
\(414\) | −1.05562 | −0.0518810 | ||||||||
\(415\) | 0.968541 | 0.0475438 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −14.6896 | −0.719354 | ||||||||
\(418\) | 2.49396 | 0.121984 | ||||||||
\(419\) | −28.4892 | −1.39179 | −0.695894 | − | 0.718145i | \(-0.744991\pi\) | ||||
−0.695894 | + | 0.718145i | \(0.744991\pi\) | |||||||
\(420\) | −19.7995 | −0.966119 | ||||||||
\(421\) | 28.1957 | 1.37417 | 0.687086 | − | 0.726576i | \(-0.258889\pi\) | ||||
0.687086 | + | 0.726576i | \(0.258889\pi\) | |||||||
\(422\) | −15.3817 | −0.748767 | ||||||||
\(423\) | −1.28621 | −0.0625376 | ||||||||
\(424\) | 8.89008 | 0.431741 | ||||||||
\(425\) | 7.57242 | 0.367316 | ||||||||
\(426\) | −6.96077 | −0.337250 | ||||||||
\(427\) | 15.4276 | 0.746593 | ||||||||
\(428\) | −2.53319 | −0.122446 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −17.6233 | −0.849869 | ||||||||
\(431\) | −20.4722 | −0.986111 | −0.493055 | − | 0.869998i | \(-0.664120\pi\) | ||||
−0.493055 | + | 0.869998i | \(0.664120\pi\) | |||||||
\(432\) | 4.96077 | 0.238675 | ||||||||
\(433\) | 9.69096 | 0.465718 | 0.232859 | − | 0.972511i | \(-0.425192\pi\) | ||||
0.232859 | + | 0.972511i | \(0.425192\pi\) | |||||||
\(434\) | −4.09783 | −0.196702 | ||||||||
\(435\) | 3.14483 | 0.150783 | ||||||||
\(436\) | 10.2198 | 0.489441 | ||||||||
\(437\) | −4.27413 | −0.204459 | ||||||||
\(438\) | 13.9487 | 0.666494 | ||||||||
\(439\) | −7.67994 | −0.366544 | −0.183272 | − | 0.983062i | \(-0.558669\pi\) | ||||
−0.183272 | + | 0.983062i | \(0.558669\pi\) | |||||||
\(440\) | −6.09783 | −0.290703 | ||||||||
\(441\) | 3.25906 | 0.155193 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −11.5168 | −0.547179 | −0.273590 | − | 0.961846i | \(-0.588211\pi\) | ||||
−0.273590 | + | 0.961846i | \(0.588211\pi\) | |||||||
\(444\) | 12.2741 | 0.582504 | ||||||||
\(445\) | 40.9987 | 1.94352 | ||||||||
\(446\) | −28.4198 | −1.34572 | ||||||||
\(447\) | 14.6189 | 0.691452 | ||||||||
\(448\) | 4.49396 | 0.212320 | ||||||||
\(449\) | −1.16421 | −0.0549425 | −0.0274712 | − | 0.999623i | \(-0.508745\pi\) | ||||
−0.0274712 | + | 0.999623i | \(0.508745\pi\) | |||||||
\(450\) | −0.241603 | −0.0113893 | ||||||||
\(451\) | 8.19567 | 0.385919 | ||||||||
\(452\) | 7.60388 | 0.357656 | ||||||||
\(453\) | 10.0271 | 0.471116 | ||||||||
\(454\) | −10.1981 | −0.478619 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −1.80194 | −0.0843835 | ||||||||
\(457\) | 30.3230 | 1.41845 | 0.709226 | − | 0.704981i | \(-0.249045\pi\) | ||||
0.709226 | + | 0.704981i | \(0.249045\pi\) | |||||||
\(458\) | −14.5429 | −0.679544 | ||||||||
\(459\) | 38.4010 | 1.79241 | ||||||||
\(460\) | 10.4504 | 0.487253 | ||||||||
\(461\) | −0.992230 | −0.0462128 | −0.0231064 | − | 0.999733i | \(-0.507356\pi\) | ||||
−0.0231064 | + | 0.999733i | \(0.507356\pi\) | |||||||
\(462\) | 20.1957 | 0.939588 | ||||||||
\(463\) | 28.8767 | 1.34201 | 0.671006 | − | 0.741452i | \(-0.265862\pi\) | ||||
0.671006 | + | 0.741452i | \(0.265862\pi\) | |||||||
\(464\) | −0.713792 | −0.0331369 | ||||||||
\(465\) | −4.01746 | −0.186305 | ||||||||
\(466\) | 26.0683 | 1.20759 | ||||||||
\(467\) | −19.8189 | −0.917110 | −0.458555 | − | 0.888666i | \(-0.651633\pi\) | ||||
−0.458555 | + | 0.888666i | \(0.651633\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 6.31767 | 0.291723 | ||||||||
\(470\) | 12.7332 | 0.587337 | ||||||||
\(471\) | 12.2034 | 0.562305 | ||||||||
\(472\) | −11.2567 | −0.518130 | ||||||||
\(473\) | 17.9758 | 0.826530 | ||||||||
\(474\) | −3.45473 | −0.158681 | ||||||||
\(475\) | −0.978230 | −0.0448843 | ||||||||
\(476\) | 34.7875 | 1.59448 | ||||||||
\(477\) | −2.19567 | −0.100533 | ||||||||
\(478\) | 16.2198 | 0.741878 | ||||||||
\(479\) | −21.9758 | −1.00410 | −0.502051 | − | 0.864838i | \(-0.667421\pi\) | ||||
−0.502051 | + | 0.864838i | \(0.667421\pi\) | |||||||
\(480\) | 4.40581 | 0.201097 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 27.3250 | 1.24462 | ||||||||
\(483\) | −34.6112 | −1.57486 | ||||||||
\(484\) | −4.78017 | −0.217280 | ||||||||
\(485\) | −7.73663 | −0.351302 | ||||||||
\(486\) | −2.56033 | −0.116139 | ||||||||
\(487\) | 36.1148 | 1.63652 | 0.818259 | − | 0.574849i | \(-0.194939\pi\) | ||||
0.818259 | + | 0.574849i | \(0.194939\pi\) | |||||||
\(488\) | −3.43296 | −0.155403 | ||||||||
\(489\) | −14.9095 | −0.674229 | ||||||||
\(490\) | −32.2640 | −1.45754 | ||||||||
\(491\) | −21.2814 | −0.960417 | −0.480209 | − | 0.877154i | \(-0.659439\pi\) | ||||
−0.480209 | + | 0.877154i | \(0.659439\pi\) | |||||||
\(492\) | −5.92154 | −0.266964 | ||||||||
\(493\) | −5.52542 | −0.248852 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 1.50604 | 0.0676915 | ||||||||
\(496\) | 0.911854 | 0.0409435 | ||||||||
\(497\) | −17.3599 | −0.778697 | ||||||||
\(498\) | 0.713792 | 0.0319858 | ||||||||
\(499\) | 5.00730 | 0.224157 | 0.112079 | − | 0.993699i | \(-0.464249\pi\) | ||||
0.112079 | + | 0.993699i | \(0.464249\pi\) | |||||||
\(500\) | −9.83340 | −0.439763 | ||||||||
\(501\) | −11.2664 | −0.503344 | ||||||||
\(502\) | −14.7922 | −0.660210 | ||||||||
\(503\) | 44.0930 | 1.96601 | 0.983006 | − | 0.183574i | \(-0.0587666\pi\) | ||||
0.983006 | + | 0.183574i | \(0.0587666\pi\) | |||||||
\(504\) | −1.10992 | −0.0494396 | ||||||||
\(505\) | 37.9734 | 1.68980 | ||||||||
\(506\) | −10.6595 | −0.473872 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −18.6920 | −0.829324 | ||||||||
\(509\) | −24.8901 | −1.10323 | −0.551617 | − | 0.834098i | \(-0.685989\pi\) | ||||
−0.551617 | + | 0.834098i | \(0.685989\pi\) | |||||||
\(510\) | 34.1051 | 1.51020 | ||||||||
\(511\) | 34.7875 | 1.53891 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | −4.96077 | −0.219023 | ||||||||
\(514\) | 26.5918 | 1.17291 | ||||||||
\(515\) | −7.42519 | −0.327193 | ||||||||
\(516\) | −12.9879 | −0.571761 | ||||||||
\(517\) | −12.9879 | −0.571208 | ||||||||
\(518\) | 30.6112 | 1.34498 | ||||||||
\(519\) | −44.1715 | −1.93891 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −13.8974 | −0.608855 | −0.304428 | − | 0.952535i | \(-0.598465\pi\) | ||||
−0.304428 | + | 0.952535i | \(0.598465\pi\) | |||||||
\(522\) | 0.176292 | 0.00771609 | ||||||||
\(523\) | 1.78017 | 0.0778413 | 0.0389206 | − | 0.999242i | \(-0.487608\pi\) | ||||
0.0389206 | + | 0.999242i | \(0.487608\pi\) | |||||||
\(524\) | −8.49396 | −0.371060 | ||||||||
\(525\) | −7.92154 | −0.345724 | ||||||||
\(526\) | 24.7332 | 1.07842 | ||||||||
\(527\) | 7.05861 | 0.307478 | ||||||||
\(528\) | −4.49396 | −0.195574 | ||||||||
\(529\) | −4.73184 | −0.205732 | ||||||||
\(530\) | 21.7366 | 0.944179 | ||||||||
\(531\) | 2.78017 | 0.120649 | ||||||||
\(532\) | −4.49396 | −0.194838 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 30.2150 | 1.30753 | ||||||||
\(535\) | −6.19375 | −0.267779 | ||||||||
\(536\) | −1.40581 | −0.0607219 | ||||||||
\(537\) | 46.7362 | 2.01681 | ||||||||
\(538\) | −16.2935 | −0.702463 | ||||||||
\(539\) | 32.9095 | 1.41751 | ||||||||
\(540\) | 12.1293 | 0.521962 | ||||||||
\(541\) | 38.7308 | 1.66517 | 0.832583 | − | 0.553900i | \(-0.186861\pi\) | ||||
0.832583 | + | 0.553900i | \(0.186861\pi\) | |||||||
\(542\) | 25.7560 | 1.10632 | ||||||||
\(543\) | −9.42758 | −0.404576 | ||||||||
\(544\) | −7.74094 | −0.331890 | ||||||||
\(545\) | 24.9879 | 1.07036 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −6.25906 | −0.267618 | −0.133809 | − | 0.991007i | \(-0.542721\pi\) | ||||
−0.133809 | + | 0.991007i | \(0.542721\pi\) | |||||||
\(548\) | −19.7506 | −0.843705 | ||||||||
\(549\) | 0.847871 | 0.0361863 | ||||||||
\(550\) | −2.43967 | −0.104028 | ||||||||
\(551\) | 0.713792 | 0.0304086 | ||||||||
\(552\) | 7.70171 | 0.327807 | ||||||||
\(553\) | −8.61596 | −0.366388 | ||||||||
\(554\) | −2.19029 | −0.0930566 | ||||||||
\(555\) | 30.0108 | 1.27389 | ||||||||
\(556\) | 8.15213 | 0.345727 | ||||||||
\(557\) | 25.3980 | 1.07615 | 0.538075 | − | 0.842897i | \(-0.319152\pi\) | ||||
0.538075 | + | 0.842897i | \(0.319152\pi\) | |||||||
\(558\) | −0.225209 | −0.00953387 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 10.9879 | 0.464324 | ||||||||
\(561\) | −34.7875 | −1.46873 | ||||||||
\(562\) | −24.6353 | −1.03918 | ||||||||
\(563\) | 8.61835 | 0.363220 | 0.181610 | − | 0.983371i | \(-0.441869\pi\) | ||||
0.181610 | + | 0.983371i | \(0.441869\pi\) | |||||||
\(564\) | 9.38404 | 0.395139 | ||||||||
\(565\) | 18.5918 | 0.782163 | ||||||||
\(566\) | 4.48321 | 0.188443 | ||||||||
\(567\) | −43.5013 | −1.82688 | ||||||||
\(568\) | 3.86294 | 0.162085 | ||||||||
\(569\) | −3.10992 | −0.130374 | −0.0651872 | − | 0.997873i | \(-0.520764\pi\) | ||||
−0.0651872 | + | 0.997873i | \(0.520764\pi\) | |||||||
\(570\) | −4.40581 | −0.184539 | ||||||||
\(571\) | −44.6741 | −1.86955 | −0.934776 | − | 0.355237i | \(-0.884400\pi\) | ||||
−0.934776 | + | 0.355237i | \(0.884400\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 31.5013 | 1.31598 | ||||||||
\(574\) | −14.7681 | −0.616408 | ||||||||
\(575\) | 4.18108 | 0.174363 | ||||||||
\(576\) | 0.246980 | 0.0102908 | ||||||||
\(577\) | 35.3817 | 1.47296 | 0.736479 | − | 0.676461i | \(-0.236487\pi\) | ||||
0.736479 | + | 0.676461i | \(0.236487\pi\) | |||||||
\(578\) | −42.9221 | −1.78533 | ||||||||
\(579\) | 42.8418 | 1.78044 | ||||||||
\(580\) | −1.74525 | −0.0724676 | ||||||||
\(581\) | 1.78017 | 0.0738538 | ||||||||
\(582\) | −5.70171 | −0.236343 | ||||||||
\(583\) | −22.1715 | −0.918250 | ||||||||
\(584\) | −7.74094 | −0.320322 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −3.32975 | −0.137551 | ||||||||
\(587\) | 19.4711 | 0.803659 | 0.401830 | − | 0.915714i | \(-0.368374\pi\) | ||||
0.401830 | + | 0.915714i | \(0.368374\pi\) | |||||||
\(588\) | −23.7778 | −0.980579 | ||||||||
\(589\) | −0.911854 | −0.0375723 | ||||||||
\(590\) | −27.5230 | −1.13311 | ||||||||
\(591\) | 40.7362 | 1.67566 | ||||||||
\(592\) | −6.81163 | −0.279956 | ||||||||
\(593\) | −5.31634 | −0.218316 | −0.109158 | − | 0.994024i | \(-0.534815\pi\) | ||||
−0.109158 | + | 0.994024i | \(0.534815\pi\) | |||||||
\(594\) | −12.3720 | −0.507628 | ||||||||
\(595\) | 85.0568 | 3.48699 | ||||||||
\(596\) | −8.11290 | −0.332317 | ||||||||
\(597\) | 30.1521 | 1.23404 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −13.2644 | −0.541970 | −0.270985 | − | 0.962584i | \(-0.587349\pi\) | ||||
−0.270985 | + | 0.962584i | \(0.587349\pi\) | |||||||
\(600\) | 1.76271 | 0.0719623 | ||||||||
\(601\) | 32.0388 | 1.30689 | 0.653444 | − | 0.756975i | \(-0.273323\pi\) | ||||
0.653444 | + | 0.756975i | \(0.273323\pi\) | |||||||
\(602\) | −32.3913 | −1.32017 | ||||||||
\(603\) | 0.347207 | 0.0141394 | ||||||||
\(604\) | −5.56465 | −0.226422 | ||||||||
\(605\) | −11.6877 | −0.475173 | ||||||||
\(606\) | 27.9855 | 1.13683 | ||||||||
\(607\) | −24.0355 | −0.975571 | −0.487786 | − | 0.872963i | \(-0.662195\pi\) | ||||
−0.487786 | + | 0.872963i | \(0.662195\pi\) | |||||||
\(608\) | 1.00000 | 0.0405554 | ||||||||
\(609\) | 5.78017 | 0.234224 | ||||||||
\(610\) | −8.39373 | −0.339852 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 1.91185 | 0.0772821 | ||||||||
\(613\) | 41.6122 | 1.68070 | 0.840351 | − | 0.542042i | \(-0.182349\pi\) | ||||
0.840351 | + | 0.542042i | \(0.182349\pi\) | |||||||
\(614\) | −2.74632 | −0.110832 | ||||||||
\(615\) | −14.4784 | −0.583826 | ||||||||
\(616\) | −11.2078 | −0.451573 | ||||||||
\(617\) | 2.20477 | 0.0887606 | 0.0443803 | − | 0.999015i | \(-0.485869\pi\) | ||||
0.0443803 | + | 0.999015i | \(0.485869\pi\) | |||||||
\(618\) | −5.47219 | −0.220124 | ||||||||
\(619\) | −19.1207 | −0.768525 | −0.384262 | − | 0.923224i | \(-0.625544\pi\) | ||||
−0.384262 | + | 0.923224i | \(0.625544\pi\) | |||||||
\(620\) | 2.22952 | 0.0895397 | ||||||||
\(621\) | 21.2030 | 0.850846 | ||||||||
\(622\) | 13.6775 | 0.548420 | ||||||||
\(623\) | 75.3551 | 3.01904 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −28.9342 | −1.15737 | ||||||||
\(626\) | −16.1903 | −0.647094 | ||||||||
\(627\) | 4.49396 | 0.179471 | ||||||||
\(628\) | −6.77240 | −0.270248 | ||||||||
\(629\) | −52.7284 | −2.10242 | ||||||||
\(630\) | −2.71379 | −0.108120 | ||||||||
\(631\) | 40.7332 | 1.62156 | 0.810781 | − | 0.585350i | \(-0.199043\pi\) | ||||
0.810781 | + | 0.585350i | \(0.199043\pi\) | |||||||
\(632\) | 1.91723 | 0.0762633 | ||||||||
\(633\) | −27.7168 | −1.10164 | ||||||||
\(634\) | −19.8538 | −0.788497 | ||||||||
\(635\) | −45.7028 | −1.81366 | ||||||||
\(636\) | 16.0194 | 0.635210 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 1.78017 | 0.0704775 | ||||||||
\(639\) | −0.954067 | −0.0377423 | ||||||||
\(640\) | −2.44504 | −0.0966488 | ||||||||
\(641\) | 11.3491 | 0.448264 | 0.224132 | − | 0.974559i | \(-0.428045\pi\) | ||||
0.224132 | + | 0.974559i | \(0.428045\pi\) | |||||||
\(642\) | −4.56465 | −0.180152 | ||||||||
\(643\) | 35.9409 | 1.41737 | 0.708686 | − | 0.705524i | \(-0.249288\pi\) | ||||
0.708686 | + | 0.705524i | \(0.249288\pi\) | |||||||
\(644\) | 19.2078 | 0.756891 | ||||||||
\(645\) | −31.7560 | −1.25039 | ||||||||
\(646\) | 7.74094 | 0.304563 | ||||||||
\(647\) | −22.7788 | −0.895529 | −0.447764 | − | 0.894152i | \(-0.647780\pi\) | ||||
−0.447764 | + | 0.894152i | \(0.647780\pi\) | |||||||
\(648\) | 9.67994 | 0.380264 | ||||||||
\(649\) | 28.0737 | 1.10199 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −7.38404 | −0.289403 | ||||||||
\(652\) | 8.27413 | 0.324040 | ||||||||
\(653\) | 22.2543 | 0.870877 | 0.435439 | − | 0.900218i | \(-0.356593\pi\) | ||||
0.435439 | + | 0.900218i | \(0.356593\pi\) | |||||||
\(654\) | 18.4155 | 0.720103 | ||||||||
\(655\) | −20.7681 | −0.811476 | ||||||||
\(656\) | 3.28621 | 0.128305 | ||||||||
\(657\) | 1.91185 | 0.0745885 | ||||||||
\(658\) | 23.4034 | 0.912360 | ||||||||
\(659\) | −46.3666 | −1.80619 | −0.903093 | − | 0.429445i | \(-0.858709\pi\) | ||||
−0.903093 | + | 0.429445i | \(0.858709\pi\) | |||||||
\(660\) | −10.9879 | −0.427704 | ||||||||
\(661\) | 31.0315 | 1.20698 | 0.603492 | − | 0.797369i | \(-0.293776\pi\) | ||||
0.603492 | + | 0.797369i | \(0.293776\pi\) | |||||||
\(662\) | 19.2295 | 0.747377 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −0.396125 | −0.0153726 | ||||||||
\(665\) | −10.9879 | −0.426093 | ||||||||
\(666\) | 1.68233 | 0.0651891 | ||||||||
\(667\) | −3.05084 | −0.118129 | ||||||||
\(668\) | 6.25236 | 0.241911 | ||||||||
\(669\) | −51.2107 | −1.97992 | ||||||||
\(670\) | −3.43727 | −0.132793 | ||||||||
\(671\) | 8.56166 | 0.330519 | ||||||||
\(672\) | 8.09783 | 0.312381 | ||||||||
\(673\) | −22.6461 | −0.872943 | −0.436471 | − | 0.899718i | \(-0.643772\pi\) | ||||
−0.436471 | + | 0.899718i | \(0.643772\pi\) | |||||||
\(674\) | 10.8465 | 0.417793 | ||||||||
\(675\) | 4.85277 | 0.186783 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 24.7138 | 0.949828 | 0.474914 | − | 0.880032i | \(-0.342479\pi\) | ||||
0.474914 | + | 0.880032i | \(0.342479\pi\) | |||||||
\(678\) | 13.7017 | 0.526211 | ||||||||
\(679\) | −14.2198 | −0.545707 | ||||||||
\(680\) | −18.9269 | −0.725814 | ||||||||
\(681\) | −18.3763 | −0.704180 | ||||||||
\(682\) | −2.27413 | −0.0870808 | ||||||||
\(683\) | 30.9536 | 1.18441 | 0.592203 | − | 0.805789i | \(-0.298258\pi\) | ||||
0.592203 | + | 0.805789i | \(0.298258\pi\) | |||||||
\(684\) | −0.246980 | −0.00944350 | ||||||||
\(685\) | −48.2911 | −1.84511 | ||||||||
\(686\) | −27.8431 | −1.06305 | ||||||||
\(687\) | −26.2054 | −0.999797 | ||||||||
\(688\) | 7.20775 | 0.274793 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 18.8310 | 0.716884 | ||||||||
\(691\) | −5.94092 | −0.226003 | −0.113002 | − | 0.993595i | \(-0.536047\pi\) | ||||
−0.113002 | + | 0.993595i | \(0.536047\pi\) | |||||||
\(692\) | 24.5133 | 0.931857 | ||||||||
\(693\) | 2.76809 | 0.105151 | ||||||||
\(694\) | −13.8974 | −0.527537 | ||||||||
\(695\) | 19.9323 | 0.756075 | ||||||||
\(696\) | −1.28621 | −0.0487536 | ||||||||
\(697\) | 25.4383 | 0.963546 | ||||||||
\(698\) | 1.89977 | 0.0719074 | ||||||||
\(699\) | 46.9734 | 1.77670 | ||||||||
\(700\) | 4.39612 | 0.166158 | ||||||||
\(701\) | −7.48427 | −0.282677 | −0.141338 | − | 0.989961i | \(-0.545141\pi\) | ||||
−0.141338 | + | 0.989961i | \(0.545141\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 6.81163 | 0.256905 | ||||||||
\(704\) | 2.49396 | 0.0939946 | ||||||||
\(705\) | 22.9444 | 0.864135 | ||||||||
\(706\) | 17.1618 | 0.645894 | ||||||||
\(707\) | 69.7948 | 2.62490 | ||||||||
\(708\) | −20.2838 | −0.762312 | ||||||||
\(709\) | −20.7966 | −0.781031 | −0.390516 | − | 0.920596i | \(-0.627703\pi\) | ||||
−0.390516 | + | 0.920596i | \(0.627703\pi\) | |||||||
\(710\) | 9.44504 | 0.354466 | ||||||||
\(711\) | −0.473517 | −0.0177583 | ||||||||
\(712\) | −16.7681 | −0.628411 | ||||||||
\(713\) | 3.89738 | 0.145958 | ||||||||
\(714\) | 62.6848 | 2.34592 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −25.9366 | −0.969297 | ||||||||
\(717\) | 29.2271 | 1.09151 | ||||||||
\(718\) | 18.5181 | 0.691090 | ||||||||
\(719\) | −36.3913 | −1.35717 | −0.678584 | − | 0.734523i | \(-0.737406\pi\) | ||||
−0.678584 | + | 0.734523i | \(0.737406\pi\) | |||||||
\(720\) | 0.603875 | 0.0225051 | ||||||||
\(721\) | −13.6474 | −0.508256 | ||||||||
\(722\) | −1.00000 | −0.0372161 | ||||||||
\(723\) | 49.2379 | 1.83118 | ||||||||
\(724\) | 5.23191 | 0.194443 | ||||||||
\(725\) | −0.698252 | −0.0259324 | ||||||||
\(726\) | −8.61356 | −0.319679 | ||||||||
\(727\) | 34.4698 | 1.27841 | 0.639207 | − | 0.769035i | \(-0.279263\pi\) | ||||
0.639207 | + | 0.769035i | \(0.279263\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 24.4263 | 0.904676 | ||||||||
\(730\) | −18.9269 | −0.700517 | ||||||||
\(731\) | 55.7948 | 2.06364 | ||||||||
\(732\) | −6.18598 | −0.228640 | ||||||||
\(733\) | 15.6732 | 0.578904 | 0.289452 | − | 0.957193i | \(-0.406527\pi\) | ||||
0.289452 | + | 0.957193i | \(0.406527\pi\) | |||||||
\(734\) | −8.39612 | −0.309907 | ||||||||
\(735\) | −58.1377 | −2.14444 | ||||||||
\(736\) | −4.27413 | −0.157546 | ||||||||
\(737\) | 3.50604 | 0.129147 | ||||||||
\(738\) | −0.811626 | −0.0298764 | ||||||||
\(739\) | 31.7861 | 1.16927 | 0.584636 | − | 0.811296i | \(-0.301237\pi\) | ||||
0.584636 | + | 0.811296i | \(0.301237\pi\) | |||||||
\(740\) | −16.6547 | −0.612239 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 39.9517 | 1.46667 | ||||||||
\(743\) | −26.7308 | −0.980657 | −0.490329 | − | 0.871538i | \(-0.663123\pi\) | ||||
−0.490329 | + | 0.871538i | \(0.663123\pi\) | |||||||
\(744\) | 1.64310 | 0.0602391 | ||||||||
\(745\) | −19.8364 | −0.726749 | ||||||||
\(746\) | −29.5991 | −1.08370 | ||||||||
\(747\) | 0.0978347 | 0.00357958 | ||||||||
\(748\) | 19.3056 | 0.705882 | ||||||||
\(749\) | −11.3840 | −0.415964 | ||||||||
\(750\) | −17.7192 | −0.647013 | ||||||||
\(751\) | 3.09916 | 0.113090 | 0.0565450 | − | 0.998400i | \(-0.481992\pi\) | ||||
0.0565450 | + | 0.998400i | \(0.481992\pi\) | |||||||
\(752\) | −5.20775 | −0.189907 | ||||||||
\(753\) | −26.6547 | −0.971352 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −13.6058 | −0.495166 | ||||||||
\(756\) | 22.2935 | 0.810807 | ||||||||
\(757\) | −25.0670 | −0.911074 | −0.455537 | − | 0.890217i | \(-0.650553\pi\) | ||||
−0.455537 | + | 0.890217i | \(0.650553\pi\) | |||||||
\(758\) | 18.9638 | 0.688795 | ||||||||
\(759\) | −19.2078 | −0.697197 | ||||||||
\(760\) | 2.44504 | 0.0886910 | ||||||||
\(761\) | −32.7375 | −1.18673 | −0.593366 | − | 0.804933i | \(-0.702201\pi\) | ||||
−0.593366 | + | 0.804933i | \(0.702201\pi\) | |||||||
\(762\) | −33.6819 | −1.22017 | ||||||||
\(763\) | 45.9275 | 1.66269 | ||||||||
\(764\) | −17.4819 | −0.632472 | ||||||||
\(765\) | 4.67456 | 0.169009 | ||||||||
\(766\) | −28.4644 | −1.02846 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −1.80194 | −0.0650218 | ||||||||
\(769\) | −0.836381 | −0.0301607 | −0.0150803 | − | 0.999886i | \(-0.504800\pi\) | ||||
−0.0150803 | + | 0.999886i | \(0.504800\pi\) | |||||||
\(770\) | −27.4034 | −0.987551 | ||||||||
\(771\) | 47.9168 | 1.72568 | ||||||||
\(772\) | −23.7754 | −0.855695 | ||||||||
\(773\) | 9.52542 | 0.342605 | 0.171303 | − | 0.985218i | \(-0.445202\pi\) | ||||
0.171303 | + | 0.985218i | \(0.445202\pi\) | |||||||
\(774\) | −1.78017 | −0.0639868 | ||||||||
\(775\) | 0.892003 | 0.0320417 | ||||||||
\(776\) | 3.16421 | 0.113589 | ||||||||
\(777\) | 55.1594 | 1.97883 | ||||||||
\(778\) | −6.90084 | −0.247407 | ||||||||
\(779\) | −3.28621 | −0.117741 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −9.63401 | −0.344732 | ||||||||
\(782\) | −33.0858 | −1.18314 | ||||||||
\(783\) | −3.54096 | −0.126544 | ||||||||
\(784\) | 13.1957 | 0.471274 | ||||||||
\(785\) | −16.5588 | −0.591009 | ||||||||
\(786\) | −15.3056 | −0.545932 | ||||||||
\(787\) | −27.4040 | −0.976848 | −0.488424 | − | 0.872607i | \(-0.662428\pi\) | ||||
−0.488424 | + | 0.872607i | \(0.662428\pi\) | |||||||
\(788\) | −22.6069 | −0.805336 | ||||||||
\(789\) | 44.5676 | 1.58665 | ||||||||
\(790\) | 4.68771 | 0.166781 | ||||||||
\(791\) | 34.1715 | 1.21500 | ||||||||
\(792\) | −0.615957 | −0.0218871 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 27.8726 | 0.989162 | ||||||||
\(795\) | 39.1680 | 1.38915 | ||||||||
\(796\) | −16.7332 | −0.593091 | ||||||||
\(797\) | −28.4241 | −1.00683 | −0.503417 | − | 0.864044i | \(-0.667924\pi\) | ||||
−0.503417 | + | 0.864044i | \(0.667924\pi\) | |||||||
\(798\) | −8.09783 | −0.286660 | ||||||||
\(799\) | −40.3129 | −1.42617 | ||||||||
\(800\) | −0.978230 | −0.0345856 | ||||||||
\(801\) | 4.14138 | 0.146328 | ||||||||
\(802\) | −27.5120 | −0.971483 | ||||||||
\(803\) | 19.3056 | 0.681279 | ||||||||
\(804\) | −2.53319 | −0.0893386 | ||||||||
\(805\) | 46.9638 | 1.65525 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −29.3599 | −1.03352 | ||||||||
\(808\) | −15.5308 | −0.546371 | ||||||||
\(809\) | −34.9855 | −1.23003 | −0.615013 | − | 0.788517i | \(-0.710849\pi\) | ||||
−0.615013 | + | 0.788517i | \(0.710849\pi\) | |||||||
\(810\) | 23.6679 | 0.831604 | ||||||||
\(811\) | 6.08383 | 0.213632 | 0.106816 | − | 0.994279i | \(-0.465934\pi\) | ||||
0.106816 | + | 0.994279i | \(0.465934\pi\) | |||||||
\(812\) | −3.20775 | −0.112570 | ||||||||
\(813\) | 46.4107 | 1.62769 | ||||||||
\(814\) | 16.9879 | 0.595426 | ||||||||
\(815\) | 20.2306 | 0.708647 | ||||||||
\(816\) | −13.9487 | −0.488302 | ||||||||
\(817\) | −7.20775 | −0.252167 | ||||||||
\(818\) | −10.8358 | −0.378864 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 8.03492 | 0.280591 | ||||||||
\(821\) | −15.0804 | −0.526309 | −0.263154 | − | 0.964754i | \(-0.584763\pi\) | ||||
−0.263154 | + | 0.964754i | \(0.584763\pi\) | |||||||
\(822\) | −35.5894 | −1.24132 | ||||||||
\(823\) | 9.20297 | 0.320795 | 0.160398 | − | 0.987052i | \(-0.448722\pi\) | ||||
0.160398 | + | 0.987052i | \(0.448722\pi\) | |||||||
\(824\) | 3.03684 | 0.105793 | ||||||||
\(825\) | −4.39612 | −0.153053 | ||||||||
\(826\) | −50.5870 | −1.76015 | ||||||||
\(827\) | −38.4849 | −1.33825 | −0.669125 | − | 0.743150i | \(-0.733331\pi\) | ||||
−0.669125 | + | 0.743150i | \(0.733331\pi\) | |||||||
\(828\) | 1.05562 | 0.0366854 | ||||||||
\(829\) | 46.1366 | 1.60239 | 0.801195 | − | 0.598403i | \(-0.204198\pi\) | ||||
0.801195 | + | 0.598403i | \(0.204198\pi\) | |||||||
\(830\) | −0.968541 | −0.0336186 | ||||||||
\(831\) | −3.94677 | −0.136912 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 102.147 | 3.53918 | ||||||||
\(834\) | 14.6896 | 0.508660 | ||||||||
\(835\) | 15.2873 | 0.529038 | ||||||||
\(836\) | −2.49396 | −0.0862554 | ||||||||
\(837\) | 4.52350 | 0.156355 | ||||||||
\(838\) | 28.4892 | 0.984142 | ||||||||
\(839\) | 27.7808 | 0.959098 | 0.479549 | − | 0.877515i | \(-0.340800\pi\) | ||||
0.479549 | + | 0.877515i | \(0.340800\pi\) | |||||||
\(840\) | 19.7995 | 0.683149 | ||||||||
\(841\) | −28.4905 | −0.982431 | ||||||||
\(842\) | −28.1957 | −0.971687 | ||||||||
\(843\) | −44.3913 | −1.52892 | ||||||||
\(844\) | 15.3817 | 0.529458 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 1.28621 | 0.0442208 | ||||||||
\(847\) | −21.4819 | −0.738126 | ||||||||
\(848\) | −8.89008 | −0.305287 | ||||||||
\(849\) | 8.07846 | 0.277252 | ||||||||
\(850\) | −7.57242 | −0.259732 | ||||||||
\(851\) | −29.1138 | −0.998007 | ||||||||
\(852\) | 6.96077 | 0.238472 | ||||||||
\(853\) | 7.16746 | 0.245409 | 0.122705 | − | 0.992443i | \(-0.460843\pi\) | ||||
0.122705 | + | 0.992443i | \(0.460843\pi\) | |||||||
\(854\) | −15.4276 | −0.527921 | ||||||||
\(855\) | −0.603875 | −0.0206521 | ||||||||
\(856\) | 2.53319 | 0.0865826 | ||||||||
\(857\) | 6.47458 | 0.221168 | 0.110584 | − | 0.993867i | \(-0.464728\pi\) | ||||
0.110584 | + | 0.993867i | \(0.464728\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 4.64874 | 0.158613 | 0.0793065 | − | 0.996850i | \(-0.474729\pi\) | ||||
0.0793065 | + | 0.996850i | \(0.474729\pi\) | |||||||
\(860\) | 17.6233 | 0.600948 | ||||||||
\(861\) | −26.6112 | −0.906906 | ||||||||
\(862\) | 20.4722 | 0.697286 | ||||||||
\(863\) | −3.16900 | −0.107874 | −0.0539369 | − | 0.998544i | \(-0.517177\pi\) | ||||
−0.0539369 | + | 0.998544i | \(0.517177\pi\) | |||||||
\(864\) | −4.96077 | −0.168769 | ||||||||
\(865\) | 59.9361 | 2.03789 | ||||||||
\(866\) | −9.69096 | −0.329312 | ||||||||
\(867\) | −77.3430 | −2.62671 | ||||||||
\(868\) | 4.09783 | 0.139090 | ||||||||
\(869\) | −4.78150 | −0.162201 | ||||||||
\(870\) | −3.14483 | −0.106620 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | −10.2198 | −0.346087 | ||||||||
\(873\) | −0.781495 | −0.0264496 | ||||||||
\(874\) | 4.27413 | 0.144574 | ||||||||
\(875\) | −44.1909 | −1.49392 | ||||||||
\(876\) | −13.9487 | −0.471283 | ||||||||
\(877\) | 12.1763 | 0.411164 | 0.205582 | − | 0.978640i | \(-0.434091\pi\) | ||||
0.205582 | + | 0.978640i | \(0.434091\pi\) | |||||||
\(878\) | 7.67994 | 0.259185 | ||||||||
\(879\) | −6.00000 | −0.202375 | ||||||||
\(880\) | 6.09783 | 0.205558 | ||||||||
\(881\) | −21.2704 | −0.716618 | −0.358309 | − | 0.933603i | \(-0.616647\pi\) | ||||
−0.358309 | + | 0.933603i | \(0.616647\pi\) | |||||||
\(882\) | −3.25906 | −0.109738 | ||||||||
\(883\) | −36.0978 | −1.21479 | −0.607394 | − | 0.794400i | \(-0.707785\pi\) | ||||
−0.607394 | + | 0.794400i | \(0.707785\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −49.5948 | −1.66711 | ||||||||
\(886\) | 11.5168 | 0.386914 | ||||||||
\(887\) | −2.97956 | −0.100044 | −0.0500219 | − | 0.998748i | \(-0.515929\pi\) | ||||
−0.0500219 | + | 0.998748i | \(0.515929\pi\) | |||||||
\(888\) | −12.2741 | −0.411893 | ||||||||
\(889\) | −84.0012 | −2.81731 | ||||||||
\(890\) | −40.9987 | −1.37428 | ||||||||
\(891\) | −24.1414 | −0.808766 | ||||||||
\(892\) | 28.4198 | 0.951566 | ||||||||
\(893\) | 5.20775 | 0.174271 | ||||||||
\(894\) | −14.6189 | −0.488931 | ||||||||
\(895\) | −63.4161 | −2.11977 | ||||||||
\(896\) | −4.49396 | −0.150133 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 1.16421 | 0.0388502 | ||||||||
\(899\) | −0.650874 | −0.0217079 | ||||||||
\(900\) | 0.241603 | 0.00805343 | ||||||||
\(901\) | −68.8176 | −2.29265 | ||||||||
\(902\) | −8.19567 | −0.272886 | ||||||||
\(903\) | −58.3672 | −1.94234 | ||||||||
\(904\) | −7.60388 | −0.252901 | ||||||||
\(905\) | 12.7922 | 0.425229 | ||||||||
\(906\) | −10.0271 | −0.333130 | ||||||||
\(907\) | −11.1594 | −0.370543 | −0.185271 | − | 0.982687i | \(-0.559316\pi\) | ||||
−0.185271 | + | 0.982687i | \(0.559316\pi\) | |||||||
\(908\) | 10.1981 | 0.338435 | ||||||||
\(909\) | 3.83579 | 0.127225 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −19.3787 | −0.642044 | −0.321022 | − | 0.947072i | \(-0.604026\pi\) | ||||
−0.321022 | + | 0.947072i | \(0.604026\pi\) | |||||||
\(912\) | 1.80194 | 0.0596681 | ||||||||
\(913\) | 0.987918 | 0.0326953 | ||||||||
\(914\) | −30.3230 | −1.00300 | ||||||||
\(915\) | −15.1250 | −0.500016 | ||||||||
\(916\) | 14.5429 | 0.480510 | ||||||||
\(917\) | −38.1715 | −1.26053 | ||||||||
\(918\) | −38.4010 | −1.26742 | ||||||||
\(919\) | 16.1763 | 0.533607 | 0.266803 | − | 0.963751i | \(-0.414033\pi\) | ||||
0.266803 | + | 0.963751i | \(0.414033\pi\) | |||||||
\(920\) | −10.4504 | −0.344540 | ||||||||
\(921\) | −4.94869 | −0.163065 | ||||||||
\(922\) | 0.992230 | 0.0326774 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | −20.1957 | −0.664389 | ||||||||
\(925\) | −6.66334 | −0.219089 | ||||||||
\(926\) | −28.8767 | −0.948946 | ||||||||
\(927\) | −0.750036 | −0.0246344 | ||||||||
\(928\) | 0.713792 | 0.0234314 | ||||||||
\(929\) | 20.2127 | 0.663156 | 0.331578 | − | 0.943428i | \(-0.392419\pi\) | ||||
0.331578 | + | 0.943428i | \(0.392419\pi\) | |||||||
\(930\) | 4.01746 | 0.131738 | ||||||||
\(931\) | −13.1957 | −0.432471 | ||||||||
\(932\) | −26.0683 | −0.853895 | ||||||||
\(933\) | 24.6461 | 0.806877 | ||||||||
\(934\) | 19.8189 | 0.648495 | ||||||||
\(935\) | 47.2030 | 1.54370 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 30.8769 | 1.00871 | 0.504353 | − | 0.863498i | \(-0.331731\pi\) | ||||
0.504353 | + | 0.863498i | \(0.331731\pi\) | |||||||
\(938\) | −6.31767 | −0.206279 | ||||||||
\(939\) | −29.1739 | −0.952054 | ||||||||
\(940\) | −12.7332 | −0.415310 | ||||||||
\(941\) | 17.5749 | 0.572926 | 0.286463 | − | 0.958091i | \(-0.407520\pi\) | ||||
0.286463 | + | 0.958091i | \(0.407520\pi\) | |||||||
\(942\) | −12.2034 | −0.397610 | ||||||||
\(943\) | 14.0457 | 0.457390 | ||||||||
\(944\) | 11.2567 | 0.366373 | ||||||||
\(945\) | 54.5086 | 1.77316 | ||||||||
\(946\) | −17.9758 | −0.584445 | ||||||||
\(947\) | 20.0435 | 0.651328 | 0.325664 | − | 0.945486i | \(-0.394412\pi\) | ||||
0.325664 | + | 0.945486i | \(0.394412\pi\) | |||||||
\(948\) | 3.45473 | 0.112204 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 0.978230 | 0.0317380 | ||||||||
\(951\) | −35.7754 | −1.16010 | ||||||||
\(952\) | −34.7875 | −1.12747 | ||||||||
\(953\) | −11.3685 | −0.368262 | −0.184131 | − | 0.982902i | \(-0.558947\pi\) | ||||
−0.184131 | + | 0.982902i | \(0.558947\pi\) | |||||||
\(954\) | 2.19567 | 0.0710874 | ||||||||
\(955\) | −42.7439 | −1.38316 | ||||||||
\(956\) | −16.2198 | −0.524587 | ||||||||
\(957\) | 3.20775 | 0.103692 | ||||||||
\(958\) | 21.9758 | 0.710007 | ||||||||
\(959\) | −88.7585 | −2.86616 | ||||||||
\(960\) | −4.40581 | −0.142197 | ||||||||
\(961\) | −30.1685 | −0.973178 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −0.625646 | −0.0201612 | ||||||||
\(964\) | −27.3250 | −0.880078 | ||||||||
\(965\) | −58.1318 | −1.87133 | ||||||||
\(966\) | 34.6112 | 1.11360 | ||||||||
\(967\) | −20.2741 | −0.651972 | −0.325986 | − | 0.945375i | \(-0.605696\pi\) | ||||
−0.325986 | + | 0.945375i | \(0.605696\pi\) | |||||||
\(968\) | 4.78017 | 0.153640 | ||||||||
\(969\) | 13.9487 | 0.448096 | ||||||||
\(970\) | 7.73663 | 0.248408 | ||||||||
\(971\) | 20.8528 | 0.669197 | 0.334599 | − | 0.942361i | \(-0.391399\pi\) | ||||
0.334599 | + | 0.942361i | \(0.391399\pi\) | |||||||
\(972\) | 2.56033 | 0.0821228 | ||||||||
\(973\) | 36.6353 | 1.17447 | ||||||||
\(974\) | −36.1148 | −1.15719 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 3.43296 | 0.109886 | ||||||||
\(977\) | 16.2452 | 0.519729 | 0.259865 | − | 0.965645i | \(-0.416322\pi\) | ||||
0.259865 | + | 0.965645i | \(0.416322\pi\) | |||||||
\(978\) | 14.9095 | 0.476752 | ||||||||
\(979\) | 41.8189 | 1.33654 | ||||||||
\(980\) | 32.2640 | 1.03063 | ||||||||
\(981\) | 2.52409 | 0.0805880 | ||||||||
\(982\) | 21.2814 | 0.679117 | ||||||||
\(983\) | −6.02582 | −0.192194 | −0.0960969 | − | 0.995372i | \(-0.530636\pi\) | ||||
−0.0960969 | + | 0.995372i | \(0.530636\pi\) | |||||||
\(984\) | 5.92154 | 0.188772 | ||||||||
\(985\) | −55.2747 | −1.76120 | ||||||||
\(986\) | 5.52542 | 0.175965 | ||||||||
\(987\) | 42.1715 | 1.34233 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 30.8068 | 0.979601 | ||||||||
\(990\) | −1.50604 | −0.0478651 | ||||||||
\(991\) | −39.6334 | −1.25900 | −0.629498 | − | 0.777002i | \(-0.716740\pi\) | ||||
−0.629498 | + | 0.777002i | \(0.716740\pi\) | |||||||
\(992\) | −0.911854 | −0.0289514 | ||||||||
\(993\) | 34.6504 | 1.09960 | ||||||||
\(994\) | 17.3599 | 0.550622 | ||||||||
\(995\) | −40.9133 | −1.29704 | ||||||||
\(996\) | −0.713792 | −0.0226174 | ||||||||
\(997\) | −15.9627 | −0.505543 | −0.252772 | − | 0.967526i | \(-0.581342\pi\) | ||||
−0.252772 | + | 0.967526i | \(0.581342\pi\) | |||||||
\(998\) | −5.00730 | −0.158503 | ||||||||
\(999\) | −33.7909 | −1.06910 |
(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 | 6422.2.a.n.1.1 | ✓ | 3 | |
13.12 | even | 2 | 6422.2.a.v.1.1 | yes | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6422.2.a.n.1.1 | ✓ | 3 | 1.1 | even | 1 | trivial | |
6422.2.a.v.1.1 | yes | 3 | 13.12 | even | 2 |