Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [7800,2,Mod(1,7800)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(7800, 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("7800.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 7800 = 2^{3} \cdot 3 \cdot 5^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 7800.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: | \(62.2833135766\) |
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: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-1.41421\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 7800.1 |
$q$-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 | ||||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.41421 | −0.912487 | −0.456243 | − | 0.889855i | \(-0.650805\pi\) | ||||
−0.456243 | + | 0.889855i | \(0.650805\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.414214 | 0.124890 | 0.0624450 | − | 0.998048i | \(-0.480110\pi\) | ||||
0.0624450 | + | 0.998048i | \(0.480110\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.00000 | 0.277350 | ||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −3.82843 | −0.928530 | −0.464265 | − | 0.885696i | \(-0.653681\pi\) | ||||
−0.464265 | + | 0.885696i | \(0.653681\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.00000 | −0.458831 | −0.229416 | − | 0.973329i | \(-0.573682\pi\) | ||||
−0.229416 | + | 0.973329i | \(0.573682\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −2.41421 | −0.526825 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0.828427 | 0.172739 | 0.0863695 | − | 0.996263i | \(-0.472473\pi\) | ||||
0.0863695 | + | 0.996263i | \(0.472473\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −8.65685 | −1.60754 | −0.803769 | − | 0.594942i | \(-0.797175\pi\) | ||||
−0.803769 | + | 0.594942i | \(0.797175\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.41421 | 0.792816 | 0.396408 | − | 0.918074i | \(-0.370257\pi\) | ||||
0.396408 | + | 0.918074i | \(0.370257\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0.414214 | 0.0721053 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 7.65685 | 1.25878 | 0.629390 | − | 0.777090i | \(-0.283305\pi\) | ||||
0.629390 | + | 0.777090i | \(0.283305\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 1.00000 | 0.160128 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 5.65685 | 0.883452 | 0.441726 | − | 0.897150i | \(-0.354366\pi\) | ||||
0.441726 | + | 0.897150i | \(0.354366\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 10.4853 | 1.59899 | 0.799495 | − | 0.600672i | \(-0.205100\pi\) | ||||
0.799495 | + | 0.600672i | \(0.205100\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 2.07107 | 0.302096 | 0.151048 | − | 0.988526i | \(-0.451735\pi\) | ||||
0.151048 | + | 0.988526i | \(0.451735\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.17157 | −0.167368 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −3.82843 | −0.536087 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 5.82843 | 0.800596 | 0.400298 | − | 0.916385i | \(-0.368907\pi\) | ||||
0.400298 | + | 0.916385i | \(0.368907\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −2.00000 | −0.264906 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −6.41421 | −0.835059 | −0.417530 | − | 0.908663i | \(-0.637104\pi\) | ||||
−0.417530 | + | 0.908663i | \(0.637104\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.82843 | −0.234106 | −0.117053 | − | 0.993126i | \(-0.537345\pi\) | ||||
−0.117053 | + | 0.993126i | \(0.537345\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −2.41421 | −0.304162 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −0.757359 | −0.0925262 | −0.0462631 | − | 0.998929i | \(-0.514731\pi\) | ||||
−0.0462631 | + | 0.998929i | \(0.514731\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0.828427 | 0.0997309 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −7.65685 | −0.908701 | −0.454351 | − | 0.890823i | \(-0.650129\pi\) | ||||
−0.454351 | + | 0.890823i | \(0.650129\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −9.31371 | −1.09009 | −0.545044 | − | 0.838408i | \(-0.683487\pi\) | ||||
−0.545044 | + | 0.838408i | \(0.683487\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −1.00000 | −0.113961 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −8.82843 | −0.993276 | −0.496638 | − | 0.867958i | \(-0.665432\pi\) | ||||
−0.496638 | + | 0.867958i | \(0.665432\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −13.7279 | −1.50684 | −0.753418 | − | 0.657542i | \(-0.771596\pi\) | ||||
−0.753418 | + | 0.657542i | \(0.771596\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −8.65685 | −0.928112 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.41421 | −0.253078 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 4.41421 | 0.457733 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −14.9706 | −1.52003 | −0.760015 | − | 0.649905i | \(-0.774809\pi\) | ||||
−0.760015 | + | 0.649905i | \(0.774809\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0.414214 | 0.0416300 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −6.17157 | −0.614094 | −0.307047 | − | 0.951694i | \(-0.599341\pi\) | ||||
−0.307047 | + | 0.951694i | \(0.599341\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −18.4853 | −1.78704 | −0.893520 | − | 0.449024i | \(-0.851772\pi\) | ||||
−0.893520 | + | 0.449024i | \(0.851772\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −19.3137 | −1.84992 | −0.924959 | − | 0.380067i | \(-0.875901\pi\) | ||||
−0.924959 | + | 0.380067i | \(0.875901\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 7.65685 | 0.726756 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 13.3137 | 1.25245 | 0.626224 | − | 0.779643i | \(-0.284599\pi\) | ||||
0.626224 | + | 0.779643i | \(0.284599\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 1.00000 | 0.0924500 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 9.24264 | 0.847271 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.8284 | −0.984402 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 5.65685 | 0.510061 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −11.1716 | −0.991317 | −0.495658 | − | 0.868518i | \(-0.665073\pi\) | ||||
−0.495658 | + | 0.868518i | \(0.665073\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 10.4853 | 0.923178 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −17.6569 | −1.54269 | −0.771343 | − | 0.636419i | \(-0.780415\pi\) | ||||
−0.771343 | + | 0.636419i | \(0.780415\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 4.82843 | 0.418678 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 16.9706 | 1.44989 | 0.724947 | − | 0.688805i | \(-0.241864\pi\) | ||||
0.724947 | + | 0.688805i | \(0.241864\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −3.17157 | −0.269009 | −0.134505 | − | 0.990913i | \(-0.542944\pi\) | ||||
−0.134505 | + | 0.990913i | \(0.542944\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 2.07107 | 0.174415 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0.414214 | 0.0346383 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −1.17157 | −0.0966297 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 17.3137 | 1.41839 | 0.709197 | − | 0.705010i | \(-0.249058\pi\) | ||||
0.709197 | + | 0.705010i | \(0.249058\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −7.24264 | −0.589398 | −0.294699 | − | 0.955590i | \(-0.595219\pi\) | ||||
−0.294699 | + | 0.955590i | \(0.595219\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −3.82843 | −0.309510 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 18.3137 | 1.46159 | 0.730797 | − | 0.682595i | \(-0.239149\pi\) | ||||
0.730797 | + | 0.682595i | \(0.239149\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 5.82843 | 0.462224 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −2.00000 | −0.157622 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 2.68629 | 0.210407 | 0.105203 | − | 0.994451i | \(-0.466451\pi\) | ||||
0.105203 | + | 0.994451i | \(0.466451\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −25.3137 | −1.95883 | −0.979417 | − | 0.201848i | \(-0.935305\pi\) | ||||
−0.979417 | + | 0.201848i | \(0.935305\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −2.00000 | −0.152944 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −3.48528 | −0.264981 | −0.132491 | − | 0.991184i | \(-0.542297\pi\) | ||||
−0.132491 | + | 0.991184i | \(0.542297\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −6.41421 | −0.482122 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −4.00000 | −0.298974 | −0.149487 | − | 0.988764i | \(-0.547762\pi\) | ||||
−0.149487 | + | 0.988764i | \(0.547762\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −3.34315 | −0.248494 | −0.124247 | − | 0.992251i | \(-0.539652\pi\) | ||||
−0.124247 | + | 0.992251i | \(0.539652\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −1.82843 | −0.135161 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1.58579 | −0.115964 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −2.41421 | −0.175608 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 14.4853 | 1.04812 | 0.524059 | − | 0.851682i | \(-0.324417\pi\) | ||||
0.524059 | + | 0.851682i | \(0.324417\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −4.00000 | −0.287926 | −0.143963 | − | 0.989583i | \(-0.545985\pi\) | ||||
−0.143963 | + | 0.989583i | \(0.545985\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 4.00000 | 0.284988 | 0.142494 | − | 0.989796i | \(-0.454488\pi\) | ||||
0.142494 | + | 0.989796i | \(0.454488\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −0.828427 | −0.0587256 | −0.0293628 | − | 0.999569i | \(-0.509348\pi\) | ||||
−0.0293628 | + | 0.999569i | \(0.509348\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −0.757359 | −0.0534200 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 20.8995 | 1.46686 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0.828427 | 0.0575797 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −0.828427 | −0.0573035 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 10.4853 | 0.721837 | 0.360918 | − | 0.932597i | \(-0.382463\pi\) | ||||
0.360918 | + | 0.932597i | \(0.382463\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −7.65685 | −0.524639 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −10.6569 | −0.723434 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −9.31371 | −0.629362 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −3.82843 | −0.257528 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 23.6569 | 1.58418 | 0.792090 | − | 0.610404i | \(-0.208993\pi\) | ||||
0.792090 | + | 0.610404i | \(0.208993\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −11.5858 | −0.768976 | −0.384488 | − | 0.923130i | \(-0.625622\pi\) | ||||
−0.384488 | + | 0.923130i | \(0.625622\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −4.34315 | −0.287003 | −0.143502 | − | 0.989650i | \(-0.545836\pi\) | ||||
−0.143502 | + | 0.989650i | \(0.545836\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −1.00000 | −0.0657952 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −10.0000 | −0.655122 | −0.327561 | − | 0.944830i | \(-0.606227\pi\) | ||||
−0.327561 | + | 0.944830i | \(0.606227\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −8.82843 | −0.573468 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −5.24264 | −0.339118 | −0.169559 | − | 0.985520i | \(-0.554234\pi\) | ||||
−0.169559 | + | 0.985520i | \(0.554234\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −4.00000 | −0.257663 | −0.128831 | − | 0.991667i | \(-0.541123\pi\) | ||||
−0.128831 | + | 0.991667i | \(0.541123\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −2.00000 | −0.127257 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −13.7279 | −0.869972 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −8.00000 | −0.504956 | −0.252478 | − | 0.967603i | \(-0.581245\pi\) | ||||
−0.252478 | + | 0.967603i | \(0.581245\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0.343146 | 0.0215734 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −1.00000 | −0.0623783 | −0.0311891 | − | 0.999514i | \(-0.509929\pi\) | ||||
−0.0311891 | + | 0.999514i | \(0.509929\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −18.4853 | −1.14862 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −8.65685 | −0.535846 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 3.31371 | 0.204332 | 0.102166 | − | 0.994767i | \(-0.467423\pi\) | ||||
0.102166 | + | 0.994767i | \(0.467423\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 12.3137 | 0.750780 | 0.375390 | − | 0.926867i | \(-0.377509\pi\) | ||||
0.375390 | + | 0.926867i | \(0.377509\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −4.89949 | −0.297623 | −0.148812 | − | 0.988866i | \(-0.547545\pi\) | ||||
−0.148812 | + | 0.988866i | \(0.547545\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −2.41421 | −0.146115 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 9.31371 | 0.559607 | 0.279803 | − | 0.960057i | \(-0.409731\pi\) | ||||
0.279803 | + | 0.960057i | \(0.409731\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 4.41421 | 0.264272 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −14.0000 | −0.835170 | −0.417585 | − | 0.908638i | \(-0.637123\pi\) | ||||
−0.417585 | + | 0.908638i | \(0.637123\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −27.4558 | −1.63208 | −0.816040 | − | 0.577995i | \(-0.803835\pi\) | ||||
−0.816040 | + | 0.577995i | \(0.803835\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −13.6569 | −0.806139 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −2.34315 | −0.137832 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −14.9706 | −0.877590 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −5.31371 | −0.310430 | −0.155215 | − | 0.987881i | \(-0.549607\pi\) | ||||
−0.155215 | + | 0.987881i | \(0.549607\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0.414214 | 0.0240351 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0.828427 | 0.0479092 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −25.3137 | −1.45906 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −6.17157 | −0.354548 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −2.00000 | −0.114146 | −0.0570730 | − | 0.998370i | \(-0.518177\pi\) | ||||
−0.0570730 | + | 0.998370i | \(0.518177\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −18.4853 | −1.04820 | −0.524102 | − | 0.851655i | \(-0.675599\pi\) | ||||
−0.524102 | + | 0.851655i | \(0.675599\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 19.8284 | 1.12077 | 0.560384 | − | 0.828233i | \(-0.310653\pi\) | ||||
0.560384 | + | 0.828233i | \(0.310653\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −2.97056 | −0.166843 | −0.0834217 | − | 0.996514i | \(-0.526585\pi\) | ||||
−0.0834217 | + | 0.996514i | \(0.526585\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −3.58579 | −0.200765 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −18.4853 | −1.03175 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 7.65685 | 0.426039 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −19.3137 | −1.06805 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −5.00000 | −0.275659 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 18.9706 | 1.04272 | 0.521358 | − | 0.853338i | \(-0.325426\pi\) | ||||
0.521358 | + | 0.853338i | \(0.325426\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 7.65685 | 0.419593 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 7.48528 | 0.407749 | 0.203875 | − | 0.978997i | \(-0.434647\pi\) | ||||
0.203875 | + | 0.978997i | \(0.434647\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 13.3137 | 0.723101 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1.82843 | 0.0990149 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 19.7279 | 1.06521 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −13.5147 | −0.725508 | −0.362754 | − | 0.931885i | \(-0.618163\pi\) | ||||
−0.362754 | + | 0.931885i | \(0.618163\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −3.65685 | −0.195747 | −0.0978735 | − | 0.995199i | \(-0.531204\pi\) | ||||
−0.0978735 | + | 0.995199i | \(0.531204\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.00000 | 0.0533761 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −0.686292 | −0.0365276 | −0.0182638 | − | 0.999833i | \(-0.505814\pi\) | ||||
−0.0182638 | + | 0.999833i | \(0.505814\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 9.24264 | 0.489172 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −1.10051 | −0.0580824 | −0.0290412 | − | 0.999578i | \(-0.509245\pi\) | ||||
−0.0290412 | + | 0.999578i | \(0.509245\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −15.0000 | −0.789474 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −10.8284 | −0.568345 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 9.65685 | 0.504084 | 0.252042 | − | 0.967716i | \(-0.418898\pi\) | ||||
0.252042 | + | 0.967716i | \(0.418898\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 5.65685 | 0.294484 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −14.0711 | −0.730533 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 32.6569 | 1.69091 | 0.845454 | − | 0.534048i | \(-0.179330\pi\) | ||||
0.845454 | + | 0.534048i | \(0.179330\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −8.65685 | −0.445851 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 0.0710678 | 0.00365051 | 0.00182525 | − | 0.999998i | \(-0.499419\pi\) | ||||
0.00182525 | + | 0.999998i | \(0.499419\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −11.1716 | −0.572337 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −3.65685 | −0.186857 | −0.0934283 | − | 0.995626i | \(-0.529783\pi\) | ||||
−0.0934283 | + | 0.995626i | \(0.529783\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 10.4853 | 0.532997 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −16.6274 | −0.843044 | −0.421522 | − | 0.906818i | \(-0.638504\pi\) | ||||
−0.421522 | + | 0.906818i | \(0.638504\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −3.17157 | −0.160393 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −17.6569 | −0.890670 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −34.2843 | −1.72068 | −0.860339 | − | 0.509722i | \(-0.829748\pi\) | ||||
−0.860339 | + | 0.509722i | \(0.829748\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 4.82843 | 0.241724 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −29.3137 | −1.46386 | −0.731928 | − | 0.681382i | \(-0.761379\pi\) | ||||
−0.731928 | + | 0.681382i | \(0.761379\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 4.41421 | 0.219888 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 3.17157 | 0.157209 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 19.3137 | 0.955001 | 0.477501 | − | 0.878631i | \(-0.341543\pi\) | ||||
0.477501 | + | 0.878631i | \(0.341543\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 16.9706 | 0.837096 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 15.4853 | 0.761981 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −3.17157 | −0.155313 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 2.34315 | 0.114470 | 0.0572351 | − | 0.998361i | \(-0.481772\pi\) | ||||
0.0572351 | + | 0.998361i | \(0.481772\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −11.3137 | −0.551396 | −0.275698 | − | 0.961244i | \(-0.588909\pi\) | ||||
−0.275698 | + | 0.961244i | \(0.588909\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 2.07107 | 0.100699 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 4.41421 | 0.213619 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0.414214 | 0.0199984 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 6.97056 | 0.335760 | 0.167880 | − | 0.985807i | \(-0.446308\pi\) | ||||
0.167880 | + | 0.985807i | \(0.446308\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 25.3137 | 1.21650 | 0.608250 | − | 0.793746i | \(-0.291872\pi\) | ||||
0.608250 | + | 0.793746i | \(0.291872\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −1.65685 | −0.0792581 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −18.4853 | −0.882254 | −0.441127 | − | 0.897445i | \(-0.645421\pi\) | ||||
−0.441127 | + | 0.897445i | \(0.645421\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −1.17157 | −0.0557892 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −23.4558 | −1.11442 | −0.557210 | − | 0.830371i | \(-0.688128\pi\) | ||||
−0.557210 | + | 0.830371i | \(0.688128\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 17.3137 | 0.818910 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 2.34315 | 0.110334 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −7.24264 | −0.340289 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 29.6569 | 1.38729 | 0.693645 | − | 0.720317i | \(-0.256004\pi\) | ||||
0.693645 | + | 0.720317i | \(0.256004\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −3.82843 | −0.178696 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −2.00000 | −0.0931493 | −0.0465746 | − | 0.998915i | \(-0.514831\pi\) | ||||
−0.0465746 | + | 0.998915i | \(0.514831\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 23.7279 | 1.10273 | 0.551365 | − | 0.834264i | \(-0.314107\pi\) | ||||
0.551365 | + | 0.834264i | \(0.314107\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −28.0000 | −1.29569 | −0.647843 | − | 0.761774i | \(-0.724329\pi\) | ||||
−0.647843 | + | 0.761774i | \(0.724329\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1.82843 | 0.0844289 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 18.3137 | 0.843851 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 4.34315 | 0.199698 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 5.82843 | 0.266865 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 21.0416 | 0.961417 | 0.480708 | − | 0.876881i | \(-0.340380\pi\) | ||||
0.480708 | + | 0.876881i | \(0.340380\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 7.65685 | 0.349123 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −2.00000 | −0.0910032 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 1.24264 | 0.0563094 | 0.0281547 | − | 0.999604i | \(-0.491037\pi\) | ||||
0.0281547 | + | 0.999604i | \(0.491037\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 2.68629 | 0.121478 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −22.4853 | −1.01475 | −0.507373 | − | 0.861726i | \(-0.669383\pi\) | ||||
−0.507373 | + | 0.861726i | \(0.669383\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 33.1421 | 1.49265 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 18.4853 | 0.829178 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −24.4142 | −1.09293 | −0.546465 | − | 0.837482i | \(-0.684027\pi\) | ||||
−0.546465 | + | 0.837482i | \(0.684027\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −25.3137 | −1.13093 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −20.2843 | −0.904431 | −0.452215 | − | 0.891909i | \(-0.649366\pi\) | ||||
−0.452215 | + | 0.891909i | \(0.649366\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 1.00000 | 0.0444116 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −8.00000 | −0.354594 | −0.177297 | − | 0.984157i | \(-0.556735\pi\) | ||||
−0.177297 | + | 0.984157i | \(0.556735\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 22.4853 | 0.994690 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −2.00000 | −0.0883022 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0.857864 | 0.0377288 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −3.48528 | −0.152987 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −18.0000 | −0.788594 | −0.394297 | − | 0.918983i | \(-0.629012\pi\) | ||||
−0.394297 | + | 0.918983i | \(0.629012\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −10.4853 | −0.458489 | −0.229245 | − | 0.973369i | \(-0.573626\pi\) | ||||
−0.229245 | + | 0.973369i | \(0.573626\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −16.8995 | −0.736154 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −22.3137 | −0.970161 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −6.41421 | −0.278353 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 5.65685 | 0.245026 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −4.00000 | −0.172613 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −0.485281 | −0.0209025 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −18.0000 | −0.773880 | −0.386940 | − | 0.922105i | \(-0.626468\pi\) | ||||
−0.386940 | + | 0.922105i | \(0.626468\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −3.34315 | −0.143468 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −22.6274 | −0.967478 | −0.483739 | − | 0.875212i | \(-0.660722\pi\) | ||||
−0.483739 | + | 0.875212i | \(0.660722\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −1.82843 | −0.0780354 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 17.3137 | 0.737589 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 21.3137 | 0.906351 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 16.0000 | 0.677942 | 0.338971 | − | 0.940797i | \(-0.389921\pi\) | ||||
0.338971 | + | 0.940797i | \(0.389921\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 10.4853 | 0.443480 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −1.58579 | −0.0669520 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −10.4853 | −0.441902 | −0.220951 | − | 0.975285i | \(-0.570916\pi\) | ||||
−0.220951 | + | 0.975285i | \(0.570916\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −2.41421 | −0.101387 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 21.6863 | 0.909137 | 0.454568 | − | 0.890712i | \(-0.349794\pi\) | ||||
0.454568 | + | 0.890712i | \(0.349794\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −18.4853 | −0.773585 | −0.386792 | − | 0.922167i | \(-0.626417\pi\) | ||||
−0.386792 | + | 0.922167i | \(0.626417\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 14.4853 | 0.605131 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 42.2843 | 1.76032 | 0.880159 | − | 0.474680i | \(-0.157436\pi\) | ||||
0.880159 | + | 0.474680i | \(0.157436\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −4.00000 | −0.166234 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 33.1421 | 1.37497 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 2.41421 | 0.0999865 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 11.7279 | 0.484063 | 0.242032 | − | 0.970268i | \(-0.422186\pi\) | ||||
0.242032 | + | 0.970268i | \(0.422186\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −8.82843 | −0.363769 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 4.00000 | 0.164538 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −16.6274 | −0.682806 | −0.341403 | − | 0.939917i | \(-0.610902\pi\) | ||||
−0.341403 | + | 0.939917i | \(0.610902\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −0.828427 | −0.0339053 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −5.65685 | −0.231133 | −0.115566 | − | 0.993300i | \(-0.536868\pi\) | ||||
−0.115566 | + | 0.993300i | \(0.536868\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −27.1421 | −1.10715 | −0.553575 | − | 0.832799i | \(-0.686737\pi\) | ||||
−0.553575 | + | 0.832799i | \(0.686737\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −0.757359 | −0.0308421 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −16.1421 | −0.655189 | −0.327595 | − | 0.944818i | \(-0.606238\pi\) | ||||
−0.327595 | + | 0.944818i | \(0.606238\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 20.8995 | 0.846890 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 2.07107 | 0.0837864 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 24.3431 | 0.983210 | 0.491605 | − | 0.870818i | \(-0.336410\pi\) | ||||
0.491605 | + | 0.870818i | \(0.336410\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 38.9706 | 1.56890 | 0.784448 | − | 0.620195i | \(-0.212946\pi\) | ||||
0.784448 | + | 0.620195i | \(0.212946\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −44.6274 | −1.79373 | −0.896864 | − | 0.442307i | \(-0.854160\pi\) | ||||
−0.896864 | + | 0.442307i | \(0.854160\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0.828427 | 0.0332436 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −0.828427 | −0.0330842 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −29.3137 | −1.16881 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 14.0000 | 0.557331 | 0.278666 | − | 0.960388i | \(-0.410108\pi\) | ||||
0.278666 | + | 0.960388i | \(0.410108\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 10.4853 | 0.416753 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.17157 | −0.0464194 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −7.65685 | −0.302900 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −18.5147 | −0.731287 | −0.365644 | − | 0.930755i | \(-0.619151\pi\) | ||||
−0.365644 | + | 0.930755i | \(0.619151\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 40.6274 | 1.60219 | 0.801094 | − | 0.598538i | \(-0.204251\pi\) | ||||
0.801094 | + | 0.598538i | \(0.204251\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 21.9411 | 0.862595 | 0.431297 | − | 0.902210i | \(-0.358056\pi\) | ||||
0.431297 | + | 0.902210i | \(0.358056\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −2.65685 | −0.104291 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −10.6569 | −0.417675 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −23.3431 | −0.913488 | −0.456744 | − | 0.889598i | \(-0.650984\pi\) | ||||
−0.456744 | + | 0.889598i | \(0.650984\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −9.31371 | −0.363362 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −3.85786 | −0.150281 | −0.0751405 | − | 0.997173i | \(-0.523941\pi\) | ||||
−0.0751405 | + | 0.997173i | \(0.523941\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 45.9411 | 1.78690 | 0.893451 | − | 0.449160i | \(-0.148277\pi\) | ||||
0.893451 | + | 0.449160i | \(0.148277\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −3.82843 | −0.148684 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −7.17157 | −0.277684 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 23.6569 | 0.914627 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −0.757359 | −0.0292375 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −7.14214 | −0.275309 | −0.137655 | − | 0.990480i | \(-0.543956\pi\) | ||||
−0.137655 | + | 0.990480i | \(0.543956\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 2.00000 | 0.0768662 | 0.0384331 | − | 0.999261i | \(-0.487763\pi\) | ||||
0.0384331 | + | 0.999261i | \(0.487763\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 36.1421 | 1.38701 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −11.5858 | −0.443968 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 43.1838 | 1.65238 | 0.826190 | − | 0.563391i | \(-0.190503\pi\) | ||||
0.826190 | + | 0.563391i | \(0.190503\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −4.34315 | −0.165701 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 5.82843 | 0.222045 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 9.24264 | 0.351607 | 0.175803 | − | 0.984425i | \(-0.443748\pi\) | ||||
0.175803 | + | 0.984425i | \(0.443748\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −1.00000 | −0.0379869 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −21.6569 | −0.820312 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −10.0000 | −0.378235 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −32.3137 | −1.22047 | −0.610236 | − | 0.792220i | \(-0.708925\pi\) | ||||
−0.610236 | + | 0.792220i | \(0.708925\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −15.3137 | −0.577567 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 14.8995 | 0.560353 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 34.6274 | 1.30046 | 0.650230 | − | 0.759737i | \(-0.274673\pi\) | ||||
0.650230 | + | 0.759737i | \(0.274673\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −8.82843 | −0.331092 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 3.65685 | 0.136950 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −5.24264 | −0.195790 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −42.6274 | −1.58973 | −0.794867 | − | 0.606783i | \(-0.792460\pi\) | ||||
−0.794867 | + | 0.606783i | \(0.792460\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −4.00000 | −0.148762 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −0.686292 | −0.0254531 | −0.0127266 | − | 0.999919i | \(-0.504051\pi\) | ||||
−0.0127266 | + | 0.999919i | \(0.504051\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −40.1421 | −1.48471 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 28.6863 | 1.05955 | 0.529776 | − | 0.848137i | \(-0.322276\pi\) | ||||
0.529776 | + | 0.848137i | \(0.322276\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −0.313708 | −0.0115556 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 34.5563 | 1.27118 | 0.635588 | − | 0.772028i | \(-0.280758\pi\) | ||||
0.635588 | + | 0.772028i | \(0.280758\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −2.00000 | −0.0734718 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 18.4142 | 0.675552 | 0.337776 | − | 0.941227i | \(-0.390325\pi\) | ||||
0.337776 | + | 0.941227i | \(0.390325\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −13.7279 | −0.502278 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 44.6274 | 1.63065 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 50.4853 | 1.84223 | 0.921117 | − | 0.389286i | \(-0.127278\pi\) | ||||
0.921117 | + | 0.389286i | \(0.127278\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −8.00000 | −0.291536 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 30.7990 | 1.11941 | 0.559704 | − | 0.828692i | \(-0.310915\pi\) | ||||
0.559704 | + | 0.828692i | \(0.310915\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0.343146 | 0.0124554 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 14.0000 | 0.507500 | 0.253750 | − | 0.967270i | \(-0.418336\pi\) | ||||
0.253750 | + | 0.967270i | \(0.418336\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 46.6274 | 1.68803 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −6.41421 | −0.231604 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −17.6569 | −0.636722 | −0.318361 | − | 0.947969i | \(-0.603132\pi\) | ||||
−0.318361 | + | 0.947969i | \(0.603132\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −1.00000 | −0.0360141 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 28.6274 | 1.02966 | 0.514828 | − | 0.857293i | \(-0.327856\pi\) | ||||
0.514828 | + | 0.857293i | \(0.327856\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −18.4853 | −0.663156 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −11.3137 | −0.405356 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −3.17157 | −0.113488 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −8.65685 | −0.309371 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 3.38478 | 0.120654 | 0.0603271 | − | 0.998179i | \(-0.480786\pi\) | ||||
0.0603271 | + | 0.998179i | \(0.480786\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 3.31371 | 0.117971 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −32.1421 | −1.14284 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −1.82843 | −0.0649294 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −5.34315 | −0.189264 | −0.0946320 | − | 0.995512i | \(-0.530167\pi\) | ||||
−0.0946320 | + | 0.995512i | \(0.530167\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −7.92893 | −0.280505 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −3.85786 | −0.136141 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 12.3137 | 0.433463 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 41.3137 | 1.45251 | 0.726256 | − | 0.687424i | \(-0.241259\pi\) | ||||
0.726256 | + | 0.687424i | \(0.241259\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 28.2721 | 0.992767 | 0.496383 | − | 0.868103i | \(-0.334661\pi\) | ||||
0.496383 | + | 0.868103i | \(0.334661\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −4.89949 | −0.171833 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −20.9706 | −0.733667 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −2.41421 | −0.0843594 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 33.3137 | 1.16266 | 0.581328 | − | 0.813669i | \(-0.302533\pi\) | ||||
0.581328 | + | 0.813669i | \(0.302533\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −49.9411 | −1.74084 | −0.870419 | − | 0.492311i | \(-0.836152\pi\) | ||||
−0.870419 | + | 0.492311i | \(0.836152\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −17.3848 | −0.604528 | −0.302264 | − | 0.953224i | \(-0.597742\pi\) | ||||
−0.302264 | + | 0.953224i | \(0.597742\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −3.82843 | −0.132967 | −0.0664834 | − | 0.997788i | \(-0.521178\pi\) | ||||
−0.0664834 | + | 0.997788i | \(0.521178\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 9.31371 | 0.323089 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 4.48528 | 0.155406 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 4.41421 | 0.152578 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 7.65685 | 0.264344 | 0.132172 | − | 0.991227i | \(-0.457805\pi\) | ||||
0.132172 | + | 0.991227i | \(0.457805\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 45.9411 | 1.58418 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −14.0000 | −0.482186 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 26.1421 | 0.898254 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −27.4558 | −0.942282 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 6.34315 | 0.217440 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 18.3431 | 0.628057 | 0.314029 | − | 0.949413i | \(-0.398321\pi\) | ||||
0.314029 | + | 0.949413i | \(0.398321\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −12.6274 | −0.431344 | −0.215672 | − | 0.976466i | \(-0.569194\pi\) | ||||
−0.215672 | + | 0.976466i | \(0.569194\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −39.1716 | −1.33652 | −0.668258 | − | 0.743929i | \(-0.732960\pi\) | ||||
−0.668258 | + | 0.743929i | \(0.732960\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −13.6569 | −0.465424 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −29.5858 | −1.00711 | −0.503556 | − | 0.863963i | \(-0.667975\pi\) | ||||
−0.503556 | + | 0.863963i | \(0.667975\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −2.34315 | −0.0795774 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −3.65685 | −0.124050 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −0.757359 | −0.0256621 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −14.9706 | −0.506677 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 14.3431 | 0.484334 | 0.242167 | − | 0.970235i | \(-0.422142\pi\) | ||||
0.242167 | + | 0.970235i | \(0.422142\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −5.31371 | −0.179227 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −54.5980 | −1.83945 | −0.919726 | − | 0.392560i | \(-0.871589\pi\) | ||||
−0.919726 | + | 0.392560i | \(0.871589\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 3.31371 | 0.111515 | 0.0557576 | − | 0.998444i | \(-0.482243\pi\) | ||||
0.0557576 | + | 0.998444i | \(0.482243\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −3.17157 | −0.106491 | −0.0532455 | − | 0.998581i | \(-0.516957\pi\) | ||||
−0.0532455 | + | 0.998581i | \(0.516957\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 26.9706 | 0.904564 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0.414214 | 0.0138767 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −4.14214 | −0.138611 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0.828427 | 0.0276604 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −38.2132 | −1.27448 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −22.3137 | −0.743377 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −25.3137 | −0.842387 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −33.9411 | −1.12700 | −0.563498 | − | 0.826117i | \(-0.690545\pi\) | ||||
−0.563498 | + | 0.826117i | \(0.690545\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −6.17157 | −0.204698 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −20.8284 | −0.690077 | −0.345038 | − | 0.938589i | \(-0.612134\pi\) | ||||
−0.345038 | + | 0.938589i | \(0.612134\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −5.68629 | −0.188189 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 42.6274 | 1.40768 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 17.7990 | 0.587135 | 0.293567 | − | 0.955938i | \(-0.405158\pi\) | ||||
0.293567 | + | 0.955938i | \(0.405158\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −2.00000 | −0.0659022 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −7.65685 | −0.252028 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 42.0000 | 1.37798 | 0.688988 | − | 0.724773i | \(-0.258055\pi\) | ||||
0.688988 | + | 0.724773i | \(0.258055\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 2.34315 | 0.0767935 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −18.4853 | −0.605181 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −46.5980 | −1.52229 | −0.761145 | − | 0.648582i | \(-0.775362\pi\) | ||||
−0.761145 | + | 0.648582i | \(0.775362\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 19.8284 | 0.647076 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 45.3137 | 1.47718 | 0.738592 | − | 0.674152i | \(-0.235491\pi\) | ||||
0.738592 | + | 0.674152i | \(0.235491\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 4.68629 | 0.152607 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −20.4142 | −0.663373 | −0.331686 | − | 0.943390i | \(-0.607618\pi\) | ||||
−0.331686 | + | 0.943390i | \(0.607618\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −9.31371 | −0.302336 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −2.97056 | −0.0963271 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −34.6569 | −1.12265 | −0.561323 | − | 0.827597i | \(-0.689707\pi\) | ||||
−0.561323 | + | 0.827597i | \(0.689707\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −3.58579 | −0.115912 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −40.9706 | −1.32301 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −11.5147 | −0.371443 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −18.4853 | −0.595680 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −24.0122 | −0.772180 | −0.386090 | − | 0.922461i | \(-0.626175\pi\) | ||||
−0.386090 | + | 0.922461i | \(0.626175\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 7.65685 | 0.245974 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −28.8284 | −0.925148 | −0.462574 | − | 0.886581i | \(-0.653074\pi\) | ||||
−0.462574 | + | 0.886581i | \(0.653074\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 7.65685 | 0.245467 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −32.9706 | −1.05482 | −0.527411 | − | 0.849610i | \(-0.676837\pi\) | ||||
−0.527411 | + | 0.849610i | \(0.676837\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −19.3137 | −0.616639 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −8.75736 | −0.279316 | −0.139658 | − | 0.990200i | \(-0.544600\pi\) | ||||
−0.139658 | + | 0.990200i | \(0.544600\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −5.00000 | −0.159152 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 8.68629 | 0.276208 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 15.8579 | 0.503742 | 0.251871 | − | 0.967761i | \(-0.418954\pi\) | ||||
0.251871 | + | 0.967761i | \(0.418954\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 18.9706 | 0.602013 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 58.7990 | 1.86218 | 0.931091 | − | 0.364786i | \(-0.118858\pi\) | ||||
0.931091 | + | 0.364786i | \(0.118858\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 7.65685 | 0.242252 |
(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 | 7800.2.a.ba.1.1 | yes | 2 | |
5.4 | even | 2 | 7800.2.a.z.1.2 | ✓ | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
7800.2.a.z.1.2 | ✓ | 2 | 5.4 | even | 2 | ||
7800.2.a.ba.1.1 | yes | 2 | 1.1 | even | 1 | trivial |