Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6160,2,Mod(1,6160)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6160, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6160.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6160 = 2^{4} \cdot 5 \cdot 7 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6160.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: | \(49.1878476451\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{8})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - 2 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 3080) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(1.41421\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6160.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 1.41421 | 0.816497 | 0.408248 | − | 0.912871i | \(-0.366140\pi\) | ||||
0.408248 | + | 0.912871i | \(0.366140\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.00000 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.00000 | −0.301511 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.585786 | −0.162468 | −0.0812340 | − | 0.996695i | \(-0.525886\pi\) | ||||
−0.0812340 | + | 0.996695i | \(0.525886\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.41421 | 0.365148 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −0.585786 | −0.142074 | −0.0710370 | − | 0.997474i | \(-0.522631\pi\) | ||||
−0.0710370 | + | 0.997474i | \(0.522631\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.41421 | 0.308607 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −3.65685 | −0.762507 | −0.381253 | − | 0.924471i | \(-0.624507\pi\) | ||||
−0.381253 | + | 0.924471i | \(0.624507\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −5.65685 | −1.08866 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −0.828427 | −0.153835 | −0.0769175 | − | 0.997037i | \(-0.524508\pi\) | ||||
−0.0769175 | + | 0.997037i | \(0.524508\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.41421 | −0.613211 | −0.306605 | − | 0.951837i | \(-0.599193\pi\) | ||||
−0.306605 | + | 0.951837i | \(0.599193\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −1.41421 | −0.246183 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1.00000 | 0.169031 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −10.8284 | −1.78018 | −0.890091 | − | 0.455782i | \(-0.849360\pi\) | ||||
−0.890091 | + | 0.455782i | \(0.849360\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −0.828427 | −0.132655 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −8.24264 | −1.28728 | −0.643642 | − | 0.765327i | \(-0.722577\pi\) | ||||
−0.643642 | + | 0.765327i | \(0.722577\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −7.65685 | −1.16766 | −0.583830 | − | 0.811876i | \(-0.698446\pi\) | ||||
−0.583830 | + | 0.811876i | \(0.698446\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.00000 | −0.149071 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 2.58579 | 0.377176 | 0.188588 | − | 0.982056i | \(-0.439609\pi\) | ||||
0.188588 | + | 0.982056i | \(0.439609\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −0.828427 | −0.116003 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −1.17157 | −0.160928 | −0.0804640 | − | 0.996758i | \(-0.525640\pi\) | ||||
−0.0804640 | + | 0.996758i | \(0.525640\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1.00000 | −0.134840 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −10.2426 | −1.33348 | −0.666739 | − | 0.745291i | \(-0.732310\pi\) | ||||
−0.666739 | + | 0.745291i | \(0.732310\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −5.41421 | −0.693219 | −0.346610 | − | 0.938010i | \(-0.612667\pi\) | ||||
−0.346610 | + | 0.938010i | \(0.612667\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −1.00000 | −0.125988 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −0.585786 | −0.0726579 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 15.6569 | 1.91279 | 0.956395 | − | 0.292078i | \(-0.0943466\pi\) | ||||
0.956395 | + | 0.292078i | \(0.0943466\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −5.17157 | −0.622584 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 12.4853 | 1.48173 | 0.740865 | − | 0.671654i | \(-0.234416\pi\) | ||||
0.740865 | + | 0.671654i | \(0.234416\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 0.585786 | 0.0685611 | 0.0342806 | − | 0.999412i | \(-0.489086\pi\) | ||||
0.0342806 | + | 0.999412i | \(0.489086\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 1.41421 | 0.163299 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −1.00000 | −0.113961 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −14.4853 | −1.62972 | −0.814861 | − | 0.579657i | \(-0.803187\pi\) | ||||
−0.814861 | + | 0.579657i | \(0.803187\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −5.00000 | −0.555556 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 15.3137 | 1.68090 | 0.840449 | − | 0.541891i | \(-0.182291\pi\) | ||||
0.840449 | + | 0.541891i | \(0.182291\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.585786 | −0.0635375 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −1.17157 | −0.125606 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 4.82843 | 0.511812 | 0.255906 | − | 0.966702i | \(-0.417626\pi\) | ||||
0.255906 | + | 0.966702i | \(0.417626\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −0.585786 | −0.0614071 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −4.82843 | −0.500685 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −0.343146 | −0.0348412 | −0.0174206 | − | 0.999848i | \(-0.505545\pi\) | ||||
−0.0174206 | + | 0.999848i | \(0.505545\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1.00000 | 0.100504 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 0.242641 | 0.0241437 | 0.0120718 | − | 0.999927i | \(-0.496157\pi\) | ||||
0.0120718 | + | 0.999927i | \(0.496157\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 3.07107 | 0.302601 | 0.151301 | − | 0.988488i | \(-0.451654\pi\) | ||||
0.151301 | + | 0.988488i | \(0.451654\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 1.41421 | 0.138013 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 0.828427 | 0.0793489 | 0.0396745 | − | 0.999213i | \(-0.487368\pi\) | ||||
0.0396745 | + | 0.999213i | \(0.487368\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −15.3137 | −1.45351 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −17.3137 | −1.62874 | −0.814368 | − | 0.580348i | \(-0.802916\pi\) | ||||
−0.814368 | + | 0.580348i | \(0.802916\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −3.65685 | −0.341003 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0.585786 | 0.0541560 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −0.585786 | −0.0536990 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −11.6569 | −1.05106 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −9.65685 | −0.856907 | −0.428454 | − | 0.903564i | \(-0.640941\pi\) | ||||
−0.428454 | + | 0.903564i | \(0.640941\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −10.8284 | −0.953390 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −15.3137 | −1.33796 | −0.668982 | − | 0.743278i | \(-0.733270\pi\) | ||||
−0.668982 | + | 0.743278i | \(0.733270\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −5.65685 | −0.486864 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −14.8284 | −1.26688 | −0.633439 | − | 0.773793i | \(-0.718357\pi\) | ||||
−0.633439 | + | 0.773793i | \(0.718357\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 14.1421 | 1.19952 | 0.599760 | − | 0.800180i | \(-0.295263\pi\) | ||||
0.599760 | + | 0.800180i | \(0.295263\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 3.65685 | 0.307963 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0.585786 | 0.0489859 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −0.828427 | −0.0687971 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 1.41421 | 0.116642 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 9.31371 | 0.763009 | 0.381504 | − | 0.924367i | \(-0.375406\pi\) | ||||
0.381504 | + | 0.924367i | \(0.375406\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 21.7990 | 1.77398 | 0.886988 | − | 0.461792i | \(-0.152793\pi\) | ||||
0.886988 | + | 0.461792i | \(0.152793\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0.585786 | 0.0473580 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −3.41421 | −0.274236 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1.51472 | −0.120888 | −0.0604439 | − | 0.998172i | \(-0.519252\pi\) | ||||
−0.0604439 | + | 0.998172i | \(0.519252\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −1.65685 | −0.131397 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −3.65685 | −0.288200 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 11.6569 | 0.913035 | 0.456518 | − | 0.889714i | \(-0.349097\pi\) | ||||
0.456518 | + | 0.889714i | \(0.349097\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −1.41421 | −0.110096 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 16.4853 | 1.27567 | 0.637835 | − | 0.770173i | \(-0.279830\pi\) | ||||
0.637835 | + | 0.770173i | \(0.279830\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.6569 | −0.973604 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −14.7279 | −1.11974 | −0.559872 | − | 0.828579i | \(-0.689150\pi\) | ||||
−0.559872 | + | 0.828579i | \(0.689150\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1.00000 | 0.0755929 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −14.4853 | −1.08878 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −19.3137 | −1.44357 | −0.721787 | − | 0.692115i | \(-0.756679\pi\) | ||||
−0.721787 | + | 0.692115i | \(0.756679\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −11.6569 | −0.866447 | −0.433224 | − | 0.901286i | \(-0.642624\pi\) | ||||
−0.433224 | + | 0.901286i | \(0.642624\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −7.65685 | −0.566011 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −10.8284 | −0.796122 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0.585786 | 0.0428369 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −5.65685 | −0.411476 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 17.6569 | 1.27761 | 0.638803 | − | 0.769371i | \(-0.279430\pi\) | ||||
0.638803 | + | 0.769371i | \(0.279430\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −0.485281 | −0.0349313 | −0.0174657 | − | 0.999847i | \(-0.505560\pi\) | ||||
−0.0174657 | + | 0.999847i | \(0.505560\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −0.828427 | −0.0593249 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −18.1421 | −1.29257 | −0.646287 | − | 0.763095i | \(-0.723679\pi\) | ||||
−0.646287 | + | 0.763095i | \(0.723679\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 2.24264 | 0.158977 | 0.0794883 | − | 0.996836i | \(-0.474671\pi\) | ||||
0.0794883 | + | 0.996836i | \(0.474671\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 22.1421 | 1.56179 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −0.828427 | −0.0581442 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −8.24264 | −0.575691 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 3.65685 | 0.254169 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 7.31371 | 0.503496 | 0.251748 | − | 0.967793i | \(-0.418995\pi\) | ||||
0.251748 | + | 0.967793i | \(0.418995\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 17.6569 | 1.20983 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −7.65685 | −0.522193 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −3.41421 | −0.231772 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0.828427 | 0.0559799 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0.343146 | 0.0230825 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −9.89949 | −0.662919 | −0.331460 | − | 0.943469i | \(-0.607541\pi\) | ||||
−0.331460 | + | 0.943469i | \(0.607541\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −1.00000 | −0.0666667 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −17.6569 | −1.17193 | −0.585963 | − | 0.810338i | \(-0.699284\pi\) | ||||
−0.585963 | + | 0.810338i | \(0.699284\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 14.4853 | 0.957214 | 0.478607 | − | 0.878029i | \(-0.341142\pi\) | ||||
0.478607 | + | 0.878029i | \(0.341142\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −1.41421 | −0.0930484 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −16.9706 | −1.11178 | −0.555889 | − | 0.831256i | \(-0.687622\pi\) | ||||
−0.555889 | + | 0.831256i | \(0.687622\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 2.58579 | 0.168678 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −20.4853 | −1.33066 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −8.97056 | −0.580257 | −0.290129 | − | 0.956988i | \(-0.593698\pi\) | ||||
−0.290129 | + | 0.956988i | \(0.593698\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 13.4142 | 0.864085 | 0.432043 | − | 0.901853i | \(-0.357793\pi\) | ||||
0.432043 | + | 0.901853i | \(0.357793\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 9.89949 | 0.635053 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 1.00000 | 0.0638877 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 21.6569 | 1.37245 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 23.2132 | 1.46520 | 0.732602 | − | 0.680657i | \(-0.238306\pi\) | ||||
0.732602 | + | 0.680657i | \(0.238306\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 3.65685 | 0.229904 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −0.828427 | −0.0518781 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 4.14214 | 0.258379 | 0.129190 | − | 0.991620i | \(-0.458762\pi\) | ||||
0.129190 | + | 0.991620i | \(0.458762\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −10.8284 | −0.672846 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0.828427 | 0.0512784 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 20.9706 | 1.29310 | 0.646550 | − | 0.762871i | \(-0.276211\pi\) | ||||
0.646550 | + | 0.762871i | \(0.276211\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1.17157 | −0.0719691 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 6.82843 | 0.417893 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 2.97056 | 0.181118 | 0.0905592 | − | 0.995891i | \(-0.471135\pi\) | ||||
0.0905592 | + | 0.995891i | \(0.471135\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 14.8284 | 0.900763 | 0.450381 | − | 0.892836i | \(-0.351288\pi\) | ||||
0.450381 | + | 0.892836i | \(0.351288\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −0.828427 | −0.0501387 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −1.00000 | −0.0603023 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −2.82843 | −0.169944 | −0.0849719 | − | 0.996383i | \(-0.527080\pi\) | ||||
−0.0849719 | + | 0.996383i | \(0.527080\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 3.41421 | 0.204404 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 4.82843 | 0.288040 | 0.144020 | − | 0.989575i | \(-0.453997\pi\) | ||||
0.144020 | + | 0.989575i | \(0.453997\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −7.31371 | −0.434755 | −0.217377 | − | 0.976088i | \(-0.569750\pi\) | ||||
−0.217377 | + | 0.976088i | \(0.569750\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −8.24264 | −0.486548 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.6569 | −0.979815 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −0.485281 | −0.0284477 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −11.8995 | −0.695176 | −0.347588 | − | 0.937647i | \(-0.612999\pi\) | ||||
−0.347588 | + | 0.937647i | \(0.612999\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −10.2426 | −0.596350 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 5.65685 | 0.328244 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 2.14214 | 0.123883 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −7.65685 | −0.441334 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0.343146 | 0.0197132 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −5.41421 | −0.310017 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −0.485281 | −0.0276965 | −0.0138482 | − | 0.999904i | \(-0.504408\pi\) | ||||
−0.0138482 | + | 0.999904i | \(0.504408\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 4.34315 | 0.247073 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −15.4142 | −0.874060 | −0.437030 | − | 0.899447i | \(-0.643970\pi\) | ||||
−0.437030 | + | 0.899447i | \(0.643970\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −20.6274 | −1.16593 | −0.582965 | − | 0.812497i | \(-0.698108\pi\) | ||||
−0.582965 | + | 0.812497i | \(0.698108\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −1.00000 | −0.0563436 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −1.02944 | −0.0578190 | −0.0289095 | − | 0.999582i | \(-0.509203\pi\) | ||||
−0.0289095 | + | 0.999582i | \(0.509203\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0.828427 | 0.0463830 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −0.585786 | −0.0324936 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 1.17157 | 0.0647881 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 2.58579 | 0.142559 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 4.00000 | 0.219860 | 0.109930 | − | 0.993939i | \(-0.464937\pi\) | ||||
0.109930 | + | 0.993939i | \(0.464937\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 10.8284 | 0.593394 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 15.6569 | 0.855425 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −9.65685 | −0.526042 | −0.263021 | − | 0.964790i | \(-0.584719\pi\) | ||||
−0.263021 | + | 0.964790i | \(0.584719\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −24.4853 | −1.32986 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 3.41421 | 0.184890 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −5.17157 | −0.278428 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 6.97056 | 0.374199 | 0.187100 | − | 0.982341i | \(-0.440091\pi\) | ||||
0.187100 | + | 0.982341i | \(0.440091\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 9.21320 | 0.493171 | 0.246586 | − | 0.969121i | \(-0.420691\pi\) | ||||
0.246586 | + | 0.969121i | \(0.420691\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 3.31371 | 0.176873 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 28.6274 | 1.52368 | 0.761842 | − | 0.647763i | \(-0.224295\pi\) | ||||
0.761842 | + | 0.647763i | \(0.224295\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 12.4853 | 0.662650 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −0.828427 | −0.0438450 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 17.7990 | 0.939395 | 0.469697 | − | 0.882827i | \(-0.344363\pi\) | ||||
0.469697 | + | 0.882827i | \(0.344363\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −19.0000 | −1.00000 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 1.41421 | 0.0742270 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0.585786 | 0.0306615 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 30.8701 | 1.61140 | 0.805702 | − | 0.592321i | \(-0.201788\pi\) | ||||
0.805702 | + | 0.592321i | \(0.201788\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 8.24264 | 0.429095 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −1.17157 | −0.0608250 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 27.7990 | 1.43938 | 0.719689 | − | 0.694297i | \(-0.244285\pi\) | ||||
0.719689 | + | 0.694297i | \(0.244285\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 1.41421 | 0.0730297 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0.485281 | 0.0249933 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −5.17157 | −0.265646 | −0.132823 | − | 0.991140i | \(-0.542404\pi\) | ||||
−0.132823 | + | 0.991140i | \(0.542404\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −13.6569 | −0.699662 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −26.3848 | −1.34820 | −0.674100 | − | 0.738641i | \(-0.735468\pi\) | ||||
−0.674100 | + | 0.738641i | \(0.735468\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1.00000 | −0.0509647 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 7.65685 | 0.389220 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 7.65685 | 0.388218 | 0.194109 | − | 0.980980i | \(-0.437818\pi\) | ||||
0.194109 | + | 0.980980i | \(0.437818\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2.14214 | 0.108332 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −21.6569 | −1.09244 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −14.4853 | −0.728834 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 8.82843 | 0.443086 | 0.221543 | − | 0.975151i | \(-0.428891\pi\) | ||||
0.221543 | + | 0.975151i | \(0.428891\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −6.00000 | −0.299626 | −0.149813 | − | 0.988714i | \(-0.547867\pi\) | ||||
−0.149813 | + | 0.988714i | \(0.547867\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 2.00000 | 0.0996271 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −5.00000 | −0.248452 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 10.8284 | 0.536745 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −0.242641 | −0.0119978 | −0.00599890 | − | 0.999982i | \(-0.501910\pi\) | ||||
−0.00599890 | + | 0.999982i | \(0.501910\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −20.9706 | −1.03440 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −10.2426 | −0.504007 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 15.3137 | 0.751720 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 20.0000 | 0.979404 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −31.4142 | −1.53468 | −0.767342 | − | 0.641238i | \(-0.778421\pi\) | ||||
−0.767342 | + | 0.641238i | \(0.778421\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −12.0000 | −0.584844 | −0.292422 | − | 0.956289i | \(-0.594461\pi\) | ||||
−0.292422 | + | 0.956289i | \(0.594461\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −2.58579 | −0.125725 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −0.585786 | −0.0284148 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −5.41421 | −0.262012 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0.828427 | 0.0399968 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −24.8284 | −1.19594 | −0.597972 | − | 0.801517i | \(-0.704026\pi\) | ||||
−0.597972 | + | 0.801517i | \(0.704026\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −39.4558 | −1.89613 | −0.948063 | − | 0.318081i | \(-0.896961\pi\) | ||||
−0.948063 | + | 0.318081i | \(0.896961\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −1.17157 | −0.0561726 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −27.7990 | −1.32677 | −0.663387 | − | 0.748277i | \(-0.730882\pi\) | ||||
−0.663387 | + | 0.748277i | \(0.730882\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −1.00000 | −0.0476190 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −29.7990 | −1.41579 | −0.707896 | − | 0.706316i | \(-0.750356\pi\) | ||||
−0.707896 | + | 0.706316i | \(0.750356\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 4.82843 | 0.228889 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 13.1716 | 0.622994 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −13.6569 | −0.644507 | −0.322253 | − | 0.946653i | \(-0.604440\pi\) | ||||
−0.322253 | + | 0.946653i | \(0.604440\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 8.24264 | 0.388131 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 30.8284 | 1.44845 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −0.585786 | −0.0274621 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 11.7990 | 0.551933 | 0.275967 | − | 0.961167i | \(-0.411002\pi\) | ||||
0.275967 | + | 0.961167i | \(0.411002\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 3.31371 | 0.154671 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 37.6985 | 1.75579 | 0.877897 | − | 0.478850i | \(-0.158946\pi\) | ||||
0.877897 | + | 0.478850i | \(0.158946\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 22.9706 | 1.06753 | 0.533766 | − | 0.845632i | \(-0.320776\pi\) | ||||
0.533766 | + | 0.845632i | \(0.320776\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −4.82843 | −0.223913 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 8.24264 | 0.381424 | 0.190712 | − | 0.981646i | \(-0.438920\pi\) | ||||
0.190712 | + | 0.981646i | \(0.438920\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 15.6569 | 0.722966 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −2.14214 | −0.0987044 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 7.65685 | 0.352063 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 1.17157 | 0.0536426 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 5.65685 | 0.258468 | 0.129234 | − | 0.991614i | \(-0.458748\pi\) | ||||
0.129234 | + | 0.991614i | \(0.458748\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 6.34315 | 0.289223 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −5.17157 | −0.235315 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −0.343146 | −0.0155814 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −12.6274 | −0.572203 | −0.286101 | − | 0.958199i | \(-0.592359\pi\) | ||||
−0.286101 | + | 0.958199i | \(0.592359\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 16.4853 | 0.745490 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 8.14214 | 0.367449 | 0.183725 | − | 0.982978i | \(-0.441185\pi\) | ||||
0.183725 | + | 0.982978i | \(0.441185\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0.485281 | 0.0218560 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 1.00000 | 0.0449467 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 12.4853 | 0.560041 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −37.4558 | −1.67675 | −0.838377 | − | 0.545091i | \(-0.816495\pi\) | ||||
−0.838377 | + | 0.545091i | \(0.816495\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 23.3137 | 1.04158 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 12.0000 | 0.535054 | 0.267527 | − | 0.963550i | \(-0.413794\pi\) | ||||
0.267527 | + | 0.963550i | \(0.413794\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0.242641 | 0.0107974 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −17.8995 | −0.794944 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −4.82843 | −0.214016 | −0.107008 | − | 0.994258i | \(-0.534127\pi\) | ||||
−0.107008 | + | 0.994258i | \(0.534127\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0.585786 | 0.0259137 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 3.07107 | 0.135327 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −2.58579 | −0.113723 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −20.8284 | −0.914266 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −6.97056 | −0.305386 | −0.152693 | − | 0.988274i | \(-0.548795\pi\) | ||||
−0.152693 | + | 0.988274i | \(0.548795\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −1.17157 | −0.0512293 | −0.0256147 | − | 0.999672i | \(-0.508154\pi\) | ||||
−0.0256147 | + | 0.999672i | \(0.508154\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 1.41421 | 0.0617213 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 2.00000 | 0.0871214 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −9.62742 | −0.418583 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 10.2426 | 0.444493 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 4.82843 | 0.209142 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −27.3137 | −1.17867 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −1.00000 | −0.0430730 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 9.31371 | 0.400428 | 0.200214 | − | 0.979752i | \(-0.435836\pi\) | ||||
0.200214 | + | 0.979752i | \(0.435836\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −16.4853 | −0.707451 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0.828427 | 0.0354859 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 36.0000 | 1.53925 | 0.769624 | − | 0.638497i | \(-0.220443\pi\) | ||||
0.769624 | + | 0.638497i | \(0.220443\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 5.41421 | 0.231073 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −14.4853 | −0.615977 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −15.3137 | −0.650031 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 1.17157 | 0.0496411 | 0.0248206 | − | 0.999692i | \(-0.492099\pi\) | ||||
0.0248206 | + | 0.999692i | \(0.492099\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 4.48528 | 0.189707 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0.828427 | 0.0349762 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −44.4853 | −1.87483 | −0.937416 | − | 0.348213i | \(-0.886789\pi\) | ||||
−0.937416 | + | 0.348213i | \(0.886789\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −17.3137 | −0.728393 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −5.00000 | −0.209980 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −28.1421 | −1.17978 | −0.589890 | − | 0.807484i | \(-0.700829\pi\) | ||||
−0.589890 | + | 0.807484i | \(0.700829\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 0.686292 | 0.0287204 | 0.0143602 | − | 0.999897i | \(-0.495429\pi\) | ||||
0.0143602 | + | 0.999897i | \(0.495429\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 24.9706 | 1.04316 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −3.65685 | −0.152501 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 23.6569 | 0.984848 | 0.492424 | − | 0.870356i | \(-0.336111\pi\) | ||||
0.492424 | + | 0.870356i | \(0.336111\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −0.686292 | −0.0285213 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 15.3137 | 0.635320 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1.17157 | 0.0485216 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0.585786 | 0.0242193 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −18.1005 | −0.747088 | −0.373544 | − | 0.927613i | \(-0.621857\pi\) | ||||
−0.373544 | + | 0.927613i | \(0.621857\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −25.6569 | −1.05538 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 37.0711 | 1.52233 | 0.761163 | − | 0.648560i | \(-0.224629\pi\) | ||||
0.761163 | + | 0.648560i | \(0.224629\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −0.585786 | −0.0240149 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 3.17157 | 0.129804 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −5.17157 | −0.211305 | −0.105652 | − | 0.994403i | \(-0.533693\pi\) | ||||
−0.105652 | + | 0.994403i | \(0.533693\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 31.3553 | 1.27901 | 0.639505 | − | 0.768787i | \(-0.279139\pi\) | ||||
0.639505 | + | 0.768787i | \(0.279139\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −15.6569 | −0.637596 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 1.00000 | 0.0406558 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −2.82843 | −0.114802 | −0.0574012 | − | 0.998351i | \(-0.518281\pi\) | ||||
−0.0574012 | + | 0.998351i | \(0.518281\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −1.17157 | −0.0474745 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −1.51472 | −0.0612790 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 6.34315 | 0.256197 | 0.128099 | − | 0.991761i | \(-0.459113\pi\) | ||||
0.128099 | + | 0.991761i | \(0.459113\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −11.6569 | −0.470050 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −14.8284 | −0.596970 | −0.298485 | − | 0.954414i | \(-0.596481\pi\) | ||||
−0.298485 | + | 0.954414i | \(0.596481\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −39.2132 | −1.57611 | −0.788056 | − | 0.615604i | \(-0.788912\pi\) | ||||
−0.788056 | + | 0.615604i | \(0.788912\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 20.6863 | 0.830112 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 4.82843 | 0.193447 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 6.34315 | 0.252918 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −8.00000 | −0.318475 | −0.159237 | − | 0.987240i | \(-0.550904\pi\) | ||||
−0.159237 | + | 0.987240i | \(0.550904\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 10.3431 | 0.411103 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −9.65685 | −0.383221 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −0.585786 | −0.0232097 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −12.4853 | −0.493910 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 23.3137 | 0.920836 | 0.460418 | − | 0.887702i | \(-0.347700\pi\) | ||||
0.460418 | + | 0.887702i | \(0.347700\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 12.0416 | 0.474876 | 0.237438 | − | 0.971403i | \(-0.423692\pi\) | ||||
0.237438 | + | 0.971403i | \(0.423692\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −10.8284 | −0.426369 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 24.7279 | 0.972155 | 0.486077 | − | 0.873916i | \(-0.338427\pi\) | ||||
0.486077 | + | 0.873916i | \(0.338427\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 10.2426 | 0.402059 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −4.82843 | −0.189241 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −47.2548 | −1.84922 | −0.924612 | − | 0.380910i | \(-0.875611\pi\) | ||||
−0.924612 | + | 0.380910i | \(0.875611\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −15.3137 | −0.598356 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −0.585786 | −0.0228537 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −46.4853 | −1.81081 | −0.905405 | − | 0.424549i | \(-0.860432\pi\) | ||||
−0.905405 | + | 0.424549i | \(0.860432\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 19.1716 | 0.745688 | 0.372844 | − | 0.927894i | \(-0.378383\pi\) | ||||
0.372844 | + | 0.927894i | \(0.378383\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0.485281 | 0.0188468 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 3.02944 | 0.117300 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −14.0000 | −0.541271 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 5.41421 | 0.209013 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 4.97056 | 0.191601 | 0.0958006 | − | 0.995401i | \(-0.469459\pi\) | ||||
0.0958006 | + | 0.995401i | \(0.469459\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −5.65685 | −0.217732 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 16.3848 | 0.629718 | 0.314859 | − | 0.949138i | \(-0.398043\pi\) | ||||
0.314859 | + | 0.949138i | \(0.398043\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −0.343146 | −0.0131687 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −24.9706 | −0.956874 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −11.1716 | −0.427468 | −0.213734 | − | 0.976892i | \(-0.568563\pi\) | ||||
−0.213734 | + | 0.976892i | \(0.568563\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −14.8284 | −0.566565 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 20.4853 | 0.781562 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0.686292 | 0.0261456 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −2.72792 | −0.103775 | −0.0518875 | − | 0.998653i | \(-0.516524\pi\) | ||||
−0.0518875 | + | 0.998653i | \(0.516524\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 1.00000 | 0.0379869 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 14.1421 | 0.536442 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 4.82843 | 0.182890 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −24.0000 | −0.907763 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −12.1421 | −0.458602 | −0.229301 | − | 0.973356i | \(-0.573644\pi\) | ||||
−0.229301 | + | 0.973356i | \(0.573644\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 3.65685 | 0.137725 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0.242641 | 0.00912544 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −18.0000 | −0.676004 | −0.338002 | − | 0.941145i | \(-0.609751\pi\) | ||||
−0.338002 | + | 0.941145i | \(0.609751\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 14.4853 | 0.543240 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 12.4853 | 0.467577 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0.585786 | 0.0219072 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −12.6863 | −0.473778 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −25.5563 | −0.953091 | −0.476545 | − | 0.879150i | \(-0.658111\pi\) | ||||
−0.476545 | + | 0.879150i | \(0.658111\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 3.07107 | 0.114373 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 18.9706 | 0.705523 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −0.828427 | −0.0307670 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 30.3848 | 1.12691 | 0.563454 | − | 0.826147i | \(-0.309472\pi\) | ||||
0.563454 | + | 0.826147i | \(0.309472\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 29.0000 | 1.07407 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 4.48528 | 0.165894 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 45.3553 | 1.67524 | 0.837619 | − | 0.546255i | \(-0.183947\pi\) | ||||
0.837619 | + | 0.546255i | \(0.183947\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 1.41421 | 0.0521641 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −15.6569 | −0.576728 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 51.5980 | 1.89806 | 0.949031 | − | 0.315182i | \(-0.102066\pi\) | ||||
0.949031 | + | 0.315182i | \(0.102066\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 11.0294 | 0.404631 | 0.202315 | − | 0.979320i | \(-0.435153\pi\) | ||||
0.202315 | + | 0.979320i | \(0.435153\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 9.31371 | 0.341228 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −15.3137 | −0.560299 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 26.8284 | 0.978983 | 0.489492 | − | 0.872008i | \(-0.337182\pi\) | ||||
0.489492 | + | 0.872008i | \(0.337182\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 32.8284 | 1.19633 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 21.7990 | 0.793346 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −11.6569 | −0.423676 | −0.211838 | − | 0.977305i | \(-0.567945\pi\) | ||||
−0.211838 | + | 0.977305i | \(0.567945\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 5.17157 | 0.187716 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 12.4437 | 0.451082 | 0.225541 | − | 0.974234i | \(-0.427585\pi\) | ||||
0.225541 | + | 0.974234i | \(0.427585\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0.828427 | 0.0299911 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0.585786 | 0.0211792 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 6.00000 | 0.216647 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −39.0711 | −1.40894 | −0.704469 | − | 0.709734i | \(-0.748815\pi\) | ||||
−0.704469 | + | 0.709734i | \(0.748815\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 5.85786 | 0.210966 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 30.0000 | 1.07903 | 0.539513 | − | 0.841978i | \(-0.318609\pi\) | ||||
0.539513 | + | 0.841978i | \(0.318609\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −3.41421 | −0.122642 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −15.3137 | −0.549376 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −12.4853 | −0.446758 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 4.68629 | 0.167474 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −1.51472 | −0.0540626 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −17.8579 | −0.636564 | −0.318282 | − | 0.947996i | \(-0.603106\pi\) | ||||
−0.318282 | + | 0.947996i | \(0.603106\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 29.6569 | 1.05581 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −17.3137 | −0.615605 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 3.17157 | 0.112626 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −1.65685 | −0.0587626 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −32.1421 | −1.13853 | −0.569266 | − | 0.822153i | \(-0.692773\pi\) | ||||
−0.569266 | + | 0.822153i | \(0.692773\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −1.51472 | −0.0535869 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −4.82843 | −0.170604 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −0.585786 | −0.0206720 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −3.65685 | −0.128887 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 4.20101 | 0.147883 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 46.0000 | 1.61727 | 0.808637 | − | 0.588308i | \(-0.200206\pi\) | ||||
0.808637 | + | 0.588308i | \(0.200206\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −2.82843 | −0.0993195 | −0.0496598 | − | 0.998766i | \(-0.515814\pi\) | ||||
−0.0496598 | + | 0.998766i | \(0.515814\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 20.9706 | 0.735470 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 11.6569 | 0.408322 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0.585786 | 0.0204690 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 42.9706 | 1.49968 | 0.749841 | − | 0.661618i | \(-0.230130\pi\) | ||||
0.749841 | + | 0.661618i | \(0.230130\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 33.5147 | 1.16825 | 0.584125 | − | 0.811664i | \(-0.301438\pi\) | ||||
0.584125 | + | 0.811664i | \(0.301438\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −1.41421 | −0.0492366 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −14.0000 | −0.486828 | −0.243414 | − | 0.969923i | \(-0.578267\pi\) | ||||
−0.243414 | + | 0.969923i | \(0.578267\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 11.6569 | 0.404859 | 0.202430 | − | 0.979297i | \(-0.435116\pi\) | ||||
0.202430 | + | 0.979297i | \(0.435116\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −4.00000 | −0.138758 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −0.585786 | −0.0202963 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 16.4853 | 0.570497 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 19.3137 | 0.667579 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −22.9289 | −0.791595 | −0.395797 | − | 0.918338i | \(-0.629532\pi\) | ||||
−0.395797 | + | 0.918338i | \(0.629532\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.3137 | −0.976335 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 6.82843 | 0.235184 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −12.6569 | −0.435409 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1.00000 | 0.0343604 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −10.3431 | −0.354976 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 39.5980 | 1.35740 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 13.7574 | 0.471043 | 0.235522 | − | 0.971869i | \(-0.424320\pi\) | ||||
0.235522 | + | 0.971869i | \(0.424320\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 41.5563 | 1.41954 | 0.709769 | − | 0.704435i | \(-0.248799\pi\) | ||||
0.709769 | + | 0.704435i | \(0.248799\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −31.4142 | −1.07184 | −0.535920 | − | 0.844269i | \(-0.680035\pi\) | ||||
−0.535920 | + | 0.844269i | \(0.680035\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −11.6569 | −0.397265 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 9.51472 | 0.323885 | 0.161942 | − | 0.986800i | \(-0.448224\pi\) | ||||
0.161942 | + | 0.986800i | \(0.448224\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −14.7279 | −0.500764 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −23.5563 | −0.800016 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 14.4853 | 0.491380 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −9.17157 | −0.310767 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0.343146 | 0.0116137 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 1.00000 | 0.0338062 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −51.5980 | −1.74234 | −0.871170 | − | 0.490982i | \(-0.836638\pi\) | ||||
−0.871170 | + | 0.490982i | \(0.836638\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −16.8284 | −0.567609 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −14.9706 | −0.504371 | −0.252186 | − | 0.967679i | \(-0.581149\pi\) | ||||
−0.252186 | + | 0.967679i | \(0.581149\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −50.0833 | −1.68544 | −0.842718 | − | 0.538355i | \(-0.819046\pi\) | ||||
−0.842718 | + | 0.538355i | \(0.819046\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −14.4853 | −0.486917 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 45.4558 | 1.52626 | 0.763129 | − | 0.646246i | \(-0.223662\pi\) | ||||
0.763129 | + | 0.646246i | \(0.223662\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −9.65685 | −0.323880 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 5.00000 | 0.167506 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −19.3137 | −0.645586 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 3.02944 | 0.101150 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 2.82843 | 0.0943333 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0.686292 | 0.0228637 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −10.8284 | −0.360347 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −11.6569 | −0.387487 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 24.3431 | 0.808301 | 0.404150 | − | 0.914693i | \(-0.367567\pi\) | ||||
0.404150 | + | 0.914693i | \(0.367567\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −0.242641 | −0.00804788 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 26.1421 | 0.866128 | 0.433064 | − | 0.901363i | \(-0.357432\pi\) | ||||
0.433064 | + | 0.901363i | \(0.357432\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −15.3137 | −0.506810 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −7.65685 | −0.253128 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −15.3137 | −0.505703 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 48.9706 | 1.61539 | 0.807695 | − | 0.589601i | \(-0.200715\pi\) | ||||
0.807695 | + | 0.589601i | \(0.200715\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −0.686292 | −0.0226141 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −7.31371 | −0.240734 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −10.8284 | −0.356036 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −3.07107 | −0.100867 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −57.5980 | −1.88973 | −0.944864 | − | 0.327462i | \(-0.893807\pi\) | ||||
−0.944864 | + | 0.327462i | \(0.893807\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −21.7990 | −0.713667 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0.585786 | 0.0191573 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −4.58579 | −0.149811 | −0.0749056 | − | 0.997191i | \(-0.523866\pi\) | ||||
−0.0749056 | + | 0.997191i | \(0.523866\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −29.1716 | −0.951978 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −6.10051 | −0.198871 | −0.0994354 | − | 0.995044i | \(-0.531704\pi\) | ||||
−0.0994354 | + | 0.995044i | \(0.531704\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 30.1421 | 0.981563 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −5.65685 | −0.184017 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −1.79899 | −0.0584593 | −0.0292297 | − | 0.999573i | \(-0.509305\pi\) | ||||
−0.0292297 | + | 0.999573i | \(0.509305\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −0.343146 | −0.0111390 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −1.45584 | −0.0472090 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 37.4558 | 1.21331 | 0.606657 | − | 0.794964i | \(-0.292510\pi\) | ||||
0.606657 | + | 0.794964i | \(0.292510\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 17.6569 | 0.571362 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 1.17157 | 0.0378716 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −14.8284 | −0.478835 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −19.3431 | −0.623972 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −0.485281 | −0.0156218 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1.02944 | 0.0331045 | 0.0165522 | − | 0.999863i | \(-0.494731\pi\) | ||||
0.0165522 | + | 0.999863i | \(0.494731\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −6.92893 | −0.222360 | −0.111180 | − | 0.993800i | \(-0.535463\pi\) | ||||
−0.111180 | + | 0.993800i | \(0.535463\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 14.1421 | 0.453376 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −0.828427 | −0.0265309 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 54.2843 | 1.73671 | 0.868354 | − | 0.495945i | \(-0.165178\pi\) | ||||
0.868354 | + | 0.495945i | \(0.165178\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −4.82843 | −0.154317 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −0.828427 | −0.0264496 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −32.7279 | −1.04386 | −0.521929 | − | 0.852989i | \(-0.674788\pi\) | ||||
−0.521929 | + | 0.852989i | \(0.674788\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −18.1421 | −0.578057 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 3.65685 | 0.116399 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 28.0000 | 0.890348 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −18.1421 | −0.576304 | −0.288152 | − | 0.957585i | \(-0.593041\pi\) | ||||
−0.288152 | + | 0.957585i | \(0.593041\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 5.65685 | 0.179515 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 2.24264 | 0.0710965 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −37.3553 | −1.18306 | −0.591528 | − | 0.806285i | \(-0.701475\pi\) | ||||
−0.591528 | + | 0.806285i | \(0.701475\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 61.2548 | 1.93802 |
(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 | 6160.2.a.bc.1.2 | 2 | ||
4.3 | odd | 2 | 3080.2.a.h.1.1 | ✓ | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3080.2.a.h.1.1 | ✓ | 2 | 4.3 | odd | 2 | ||
6160.2.a.bc.1.2 | 2 | 1.1 | even | 1 | trivial |