Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3360,2,Mod(1,3360)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3360, 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("3360.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3360 = 2^{5} \cdot 3 \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3360.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(26.8297350792\) |
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: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2 \) |
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 | \(\chi\) | \(=\) | 3360.1 |
$q$-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 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.82843 | −0.852803 | −0.426401 | − | 0.904534i | \(-0.640219\pi\) | ||||
−0.426401 | + | 0.904534i | \(0.640219\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.828427 | 0.229764 | 0.114882 | − | 0.993379i | \(-0.463351\pi\) | ||||
0.114882 | + | 0.993379i | \(0.463351\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.00000 | −0.258199 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 7.65685 | 1.85706 | 0.928530 | − | 0.371257i | \(-0.121073\pi\) | ||||
0.928530 | + | 0.371257i | \(0.121073\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.82843 | −0.648886 | −0.324443 | − | 0.945905i | \(-0.605177\pi\) | ||||
−0.324443 | + | 0.945905i | \(0.605177\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.00000 | −0.218218 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −4.00000 | −0.834058 | −0.417029 | − | 0.908893i | \(-0.636929\pi\) | ||||
−0.417029 | + | 0.908893i | \(0.636929\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −7.65685 | −1.42184 | −0.710921 | − | 0.703272i | \(-0.751722\pi\) | ||||
−0.710921 | + | 0.703272i | \(0.751722\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.82843 | −0.508001 | −0.254000 | − | 0.967204i | \(-0.581746\pi\) | ||||
−0.254000 | + | 0.967204i | \(0.581746\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −2.82843 | −0.492366 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1.00000 | 0.169031 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −11.6569 | −1.91638 | −0.958188 | − | 0.286141i | \(-0.907627\pi\) | ||||
−0.958188 | + | 0.286141i | \(0.907627\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0.828427 | 0.132655 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −7.65685 | −1.19580 | −0.597900 | − | 0.801571i | \(-0.703998\pi\) | ||||
−0.597900 | + | 0.801571i | \(0.703998\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.65685 | 0.252668 | 0.126334 | − | 0.991988i | \(-0.459679\pi\) | ||||
0.126334 | + | 0.991988i | \(0.459679\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.00000 | −0.149071 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 11.3137 | 1.65027 | 0.825137 | − | 0.564933i | \(-0.191098\pi\) | ||||
0.825137 | + | 0.564933i | \(0.191098\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 7.65685 | 1.07217 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 10.4853 | 1.44026 | 0.720132 | − | 0.693837i | \(-0.244081\pi\) | ||||
0.720132 | + | 0.693837i | \(0.244081\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 2.82843 | 0.381385 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −2.82843 | −0.374634 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 9.31371 | 1.19250 | 0.596249 | − | 0.802799i | \(-0.296657\pi\) | ||||
0.596249 | + | 0.802799i | \(0.296657\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −1.00000 | −0.125988 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −0.828427 | −0.102754 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −4.00000 | −0.488678 | −0.244339 | − | 0.969690i | \(-0.578571\pi\) | ||||
−0.244339 | + | 0.969690i | \(0.578571\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −4.00000 | −0.481543 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −10.8284 | −1.28510 | −0.642549 | − | 0.766245i | \(-0.722123\pi\) | ||||
−0.642549 | + | 0.766245i | \(0.722123\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −4.82843 | −0.565125 | −0.282562 | − | 0.959249i | \(-0.591184\pi\) | ||||
−0.282562 | + | 0.959249i | \(0.591184\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 1.00000 | 0.115470 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 2.82843 | 0.322329 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −15.3137 | −1.72293 | −0.861463 | − | 0.507820i | \(-0.830452\pi\) | ||||
−0.861463 | + | 0.507820i | \(0.830452\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −17.6569 | −1.93809 | −0.969046 | − | 0.246881i | \(-0.920594\pi\) | ||||
−0.969046 | + | 0.246881i | \(0.920594\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −7.65685 | −0.830502 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −7.65685 | −0.820901 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 11.6569 | 1.23562 | 0.617812 | − | 0.786326i | \(-0.288019\pi\) | ||||
0.617812 | + | 0.786326i | \(0.288019\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −0.828427 | −0.0868428 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −2.82843 | −0.293294 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 2.82843 | 0.290191 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −7.17157 | −0.728163 | −0.364081 | − | 0.931367i | \(-0.618617\pi\) | ||||
−0.364081 | + | 0.931367i | \(0.618617\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −2.82843 | −0.284268 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −17.3137 | −1.72278 | −0.861389 | − | 0.507946i | \(-0.830405\pi\) | ||||
−0.861389 | + | 0.507946i | \(0.830405\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −8.00000 | −0.788263 | −0.394132 | − | 0.919054i | \(-0.628955\pi\) | ||||
−0.394132 | + | 0.919054i | \(0.628955\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 1.00000 | 0.0975900 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −8.00000 | −0.773389 | −0.386695 | − | 0.922208i | \(-0.626383\pi\) | ||||
−0.386695 | + | 0.922208i | \(0.626383\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −13.3137 | −1.27522 | −0.637611 | − | 0.770358i | \(-0.720077\pi\) | ||||
−0.637611 | + | 0.770358i | \(0.720077\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −11.6569 | −1.10642 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 20.8284 | 1.95937 | 0.979687 | − | 0.200534i | \(-0.0642676\pi\) | ||||
0.979687 | + | 0.200534i | \(0.0642676\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 4.00000 | 0.373002 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0.828427 | 0.0765881 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −7.65685 | −0.701903 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −3.00000 | −0.272727 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −7.65685 | −0.690395 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −5.65685 | −0.501965 | −0.250982 | − | 0.967992i | \(-0.580754\pi\) | ||||
−0.250982 | + | 0.967992i | \(0.580754\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 1.65685 | 0.145878 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 5.65685 | 0.494242 | 0.247121 | − | 0.968985i | \(-0.420516\pi\) | ||||
0.247121 | + | 0.968985i | \(0.420516\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2.82843 | 0.245256 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −1.00000 | −0.0860663 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −0.828427 | −0.0707773 | −0.0353887 | − | 0.999374i | \(-0.511267\pi\) | ||||
−0.0353887 | + | 0.999374i | \(0.511267\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 19.7990 | 1.67933 | 0.839664 | − | 0.543106i | \(-0.182752\pi\) | ||||
0.839664 | + | 0.543106i | \(0.182752\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 11.3137 | 0.952786 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −2.34315 | −0.195944 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 7.65685 | 0.635867 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 1.00000 | 0.0824786 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 17.3137 | 1.41839 | 0.709197 | − | 0.705010i | \(-0.249058\pi\) | ||||
0.709197 | + | 0.705010i | \(0.249058\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1.65685 | 0.134833 | 0.0674164 | − | 0.997725i | \(-0.478524\pi\) | ||||
0.0674164 | + | 0.997725i | \(0.478524\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 7.65685 | 0.619020 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 2.82843 | 0.227185 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −12.8284 | −1.02382 | −0.511910 | − | 0.859039i | \(-0.671062\pi\) | ||||
−0.511910 | + | 0.859039i | \(0.671062\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 10.4853 | 0.831537 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 4.00000 | 0.315244 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −17.6569 | −1.38299 | −0.691496 | − | 0.722380i | \(-0.743048\pi\) | ||||
−0.691496 | + | 0.722380i | \(0.743048\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 2.82843 | 0.220193 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −24.9706 | −1.93228 | −0.966140 | − | 0.258018i | \(-0.916931\pi\) | ||||
−0.966140 | + | 0.258018i | \(0.916931\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.3137 | −0.947208 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −2.82843 | −0.216295 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −14.9706 | −1.13819 | −0.569095 | − | 0.822272i | \(-0.692706\pi\) | ||||
−0.569095 | + | 0.822272i | \(0.692706\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1.00000 | −0.0755929 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 5.17157 | 0.386542 | 0.193271 | − | 0.981145i | \(-0.438090\pi\) | ||||
0.193271 | + | 0.981145i | \(0.438090\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −12.3431 | −0.917459 | −0.458729 | − | 0.888576i | \(-0.651695\pi\) | ||||
−0.458729 | + | 0.888576i | \(0.651695\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 9.31371 | 0.688489 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 11.6569 | 0.857029 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −21.6569 | −1.58371 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −1.00000 | −0.0727393 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −13.1716 | −0.953062 | −0.476531 | − | 0.879158i | \(-0.658106\pi\) | ||||
−0.476531 | + | 0.879158i | \(0.658106\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 10.0000 | 0.719816 | 0.359908 | − | 0.932988i | \(-0.382808\pi\) | ||||
0.359908 | + | 0.932988i | \(0.382808\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −0.828427 | −0.0593249 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 12.8284 | 0.913988 | 0.456994 | − | 0.889470i | \(-0.348926\pi\) | ||||
0.456994 | + | 0.889470i | \(0.348926\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 8.48528 | 0.601506 | 0.300753 | − | 0.953702i | \(-0.402762\pi\) | ||||
0.300753 | + | 0.953702i | \(0.402762\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −4.00000 | −0.282138 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 7.65685 | 0.537406 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 7.65685 | 0.534778 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −4.00000 | −0.278019 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 8.00000 | 0.553372 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −20.0000 | −1.37686 | −0.688428 | − | 0.725304i | \(-0.741699\pi\) | ||||
−0.688428 | + | 0.725304i | \(0.741699\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −10.8284 | −0.741952 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −1.65685 | −0.112997 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 2.82843 | 0.192006 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −4.82843 | −0.326275 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 6.34315 | 0.426686 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 16.9706 | 1.13643 | 0.568216 | − | 0.822879i | \(-0.307634\pi\) | ||||
0.568216 | + | 0.822879i | \(0.307634\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.00000 | 0.0666667 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −6.34315 | −0.421009 | −0.210505 | − | 0.977593i | \(-0.567511\pi\) | ||||
−0.210505 | + | 0.977593i | \(0.567511\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 2.68629 | 0.177515 | 0.0887576 | − | 0.996053i | \(-0.471710\pi\) | ||||
0.0887576 | + | 0.996053i | \(0.471710\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 2.82843 | 0.186097 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 28.8284 | 1.88861 | 0.944307 | − | 0.329067i | \(-0.106734\pi\) | ||||
0.944307 | + | 0.329067i | \(0.106734\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −11.3137 | −0.738025 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −15.3137 | −0.994732 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 13.1716 | 0.851998 | 0.425999 | − | 0.904724i | \(-0.359923\pi\) | ||||
0.425999 | + | 0.904724i | \(0.359923\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −3.65685 | −0.235559 | −0.117779 | − | 0.993040i | \(-0.537578\pi\) | ||||
−0.117779 | + | 0.993040i | \(0.537578\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −1.00000 | −0.0638877 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −2.34315 | −0.149091 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −17.6569 | −1.11896 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 11.3137 | 0.714115 | 0.357057 | − | 0.934082i | \(-0.383780\pi\) | ||||
0.357057 | + | 0.934082i | \(0.383780\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 11.3137 | 0.711287 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −7.65685 | −0.479491 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 6.68629 | 0.417079 | 0.208540 | − | 0.978014i | \(-0.433129\pi\) | ||||
0.208540 | + | 0.978014i | \(0.433129\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 11.6569 | 0.724322 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −7.65685 | −0.473947 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −20.9706 | −1.29310 | −0.646550 | − | 0.762871i | \(-0.723789\pi\) | ||||
−0.646550 | + | 0.762871i | \(0.723789\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −10.4853 | −0.644106 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 11.6569 | 0.713388 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 5.31371 | 0.323983 | 0.161991 | − | 0.986792i | \(-0.448208\pi\) | ||||
0.161991 | + | 0.986792i | \(0.448208\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 10.8284 | 0.657780 | 0.328890 | − | 0.944368i | \(-0.393325\pi\) | ||||
0.328890 | + | 0.944368i | \(0.393325\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −0.828427 | −0.0501387 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −2.82843 | −0.170561 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 2.97056 | 0.178484 | 0.0892419 | − | 0.996010i | \(-0.471556\pi\) | ||||
0.0892419 | + | 0.996010i | \(0.471556\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −2.82843 | −0.169334 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 18.9706 | 1.13169 | 0.565844 | − | 0.824512i | \(-0.308550\pi\) | ||||
0.565844 | + | 0.824512i | \(0.308550\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −15.3137 | −0.910305 | −0.455153 | − | 0.890413i | \(-0.650415\pi\) | ||||
−0.455153 | + | 0.890413i | \(0.650415\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 2.82843 | 0.167542 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 7.65685 | 0.451970 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 41.6274 | 2.44867 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −7.17157 | −0.420405 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −19.6569 | −1.14837 | −0.574183 | − | 0.818727i | \(-0.694680\pi\) | ||||
−0.574183 | + | 0.818727i | \(0.694680\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −2.82843 | −0.164122 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −3.31371 | −0.191637 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1.65685 | −0.0954995 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −17.3137 | −0.994647 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −9.31371 | −0.533301 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −17.6569 | −1.00773 | −0.503865 | − | 0.863782i | \(-0.668089\pi\) | ||||
−0.503865 | + | 0.863782i | \(0.668089\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −8.00000 | −0.455104 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −8.00000 | −0.453638 | −0.226819 | − | 0.973937i | \(-0.572833\pi\) | ||||
−0.226819 | + | 0.973937i | \(0.572833\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 0.828427 | 0.0468255 | 0.0234127 | − | 0.999726i | \(-0.492547\pi\) | ||||
0.0234127 | + | 0.999726i | \(0.492547\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 1.00000 | 0.0563436 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 7.17157 | 0.402796 | 0.201398 | − | 0.979510i | \(-0.435452\pi\) | ||||
0.201398 | + | 0.979510i | \(0.435452\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 21.6569 | 1.21255 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −8.00000 | −0.446516 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −21.6569 | −1.20502 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0.828427 | 0.0459529 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −13.3137 | −0.736250 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −11.3137 | −0.623745 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −4.00000 | −0.219860 | −0.109930 | − | 0.993939i | \(-0.535063\pi\) | ||||
−0.109930 | + | 0.993939i | \(0.535063\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −11.6569 | −0.638792 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 4.00000 | 0.218543 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −1.31371 | −0.0715623 | −0.0357811 | − | 0.999360i | \(-0.511392\pi\) | ||||
−0.0357811 | + | 0.999360i | \(0.511392\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 20.8284 | 1.13124 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 8.00000 | 0.433224 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 4.00000 | 0.215353 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 29.6569 | 1.59206 | 0.796032 | − | 0.605255i | \(-0.206929\pi\) | ||||
0.796032 | + | 0.605255i | \(0.206929\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −6.68629 | −0.357909 | −0.178954 | − | 0.983857i | \(-0.557271\pi\) | ||||
−0.178954 | + | 0.983857i | \(0.557271\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0.828427 | 0.0442182 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −6.97056 | −0.371006 | −0.185503 | − | 0.982644i | \(-0.559391\pi\) | ||||
−0.185503 | + | 0.982644i | \(0.559391\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 10.8284 | 0.574713 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −7.65685 | −0.405244 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 33.4558 | 1.76573 | 0.882866 | − | 0.469625i | \(-0.155611\pi\) | ||||
0.882866 | + | 0.469625i | \(0.155611\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −11.0000 | −0.578947 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −3.00000 | −0.157459 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 4.82843 | 0.252731 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 29.6569 | 1.54808 | 0.774038 | − | 0.633140i | \(-0.218234\pi\) | ||||
0.774038 | + | 0.633140i | \(0.218234\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −7.65685 | −0.398600 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −10.4853 | −0.544369 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 10.0000 | 0.517780 | 0.258890 | − | 0.965907i | \(-0.416643\pi\) | ||||
0.258890 | + | 0.965907i | \(0.416643\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −1.00000 | −0.0516398 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −6.34315 | −0.326689 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −1.65685 | −0.0851069 | −0.0425534 | − | 0.999094i | \(-0.513549\pi\) | ||||
−0.0425534 | + | 0.999094i | \(0.513549\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −5.65685 | −0.289809 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −28.2843 | −1.44526 | −0.722629 | − | 0.691236i | \(-0.757067\pi\) | ||||
−0.722629 | + | 0.691236i | \(0.757067\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −2.82843 | −0.144150 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 1.65685 | 0.0842226 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 9.31371 | 0.472224 | 0.236112 | − | 0.971726i | \(-0.424127\pi\) | ||||
0.236112 | + | 0.971726i | \(0.424127\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −30.6274 | −1.54890 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 5.65685 | 0.285351 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 15.3137 | 0.770516 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −2.48528 | −0.124733 | −0.0623663 | − | 0.998053i | \(-0.519865\pi\) | ||||
−0.0623663 | + | 0.998053i | \(0.519865\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 2.82843 | 0.141598 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −1.31371 | −0.0656035 | −0.0328017 | − | 0.999462i | \(-0.510443\pi\) | ||||
−0.0328017 | + | 0.999462i | \(0.510443\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −2.34315 | −0.116720 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −1.00000 | −0.0496904 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 32.9706 | 1.63429 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 13.3137 | 0.658321 | 0.329160 | − | 0.944274i | \(-0.393234\pi\) | ||||
0.329160 | + | 0.944274i | \(0.393234\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −0.828427 | −0.0408633 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 17.6569 | 0.866741 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 19.7990 | 0.969561 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −16.9706 | −0.829066 | −0.414533 | − | 0.910034i | \(-0.636055\pi\) | ||||
−0.414533 | + | 0.910034i | \(0.636055\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −21.3137 | −1.03877 | −0.519383 | − | 0.854541i | \(-0.673838\pi\) | ||||
−0.519383 | + | 0.854541i | \(0.673838\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 11.3137 | 0.550091 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 7.65685 | 0.371412 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −9.31371 | −0.450722 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −2.34315 | −0.113128 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 0.485281 | 0.0233752 | 0.0116876 | − | 0.999932i | \(-0.496280\pi\) | ||||
0.0116876 | + | 0.999932i | \(0.496280\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 13.5147 | 0.649476 | 0.324738 | − | 0.945804i | \(-0.394724\pi\) | ||||
0.324738 | + | 0.945804i | \(0.394724\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 7.65685 | 0.367118 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 11.3137 | 0.541208 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 13.1716 | 0.628645 | 0.314322 | − | 0.949316i | \(-0.398223\pi\) | ||||
0.314322 | + | 0.949316i | \(0.398223\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.00000 | 0.0476190 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 24.9706 | 1.18639 | 0.593194 | − | 0.805060i | \(-0.297867\pi\) | ||||
0.593194 | + | 0.805060i | \(0.297867\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −11.6569 | −0.552588 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 17.3137 | 0.818910 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 2.00000 | 0.0943858 | 0.0471929 | − | 0.998886i | \(-0.484972\pi\) | ||||
0.0471929 | + | 0.998886i | \(0.484972\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 21.6569 | 1.01978 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 1.65685 | 0.0778458 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0.828427 | 0.0388373 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −8.34315 | −0.390276 | −0.195138 | − | 0.980776i | \(-0.562515\pi\) | ||||
−0.195138 | + | 0.980776i | \(0.562515\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 7.65685 | 0.357391 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 16.6274 | 0.774416 | 0.387208 | − | 0.921992i | \(-0.373440\pi\) | ||||
0.387208 | + | 0.921992i | \(0.373440\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −20.2843 | −0.942690 | −0.471345 | − | 0.881949i | \(-0.656231\pi\) | ||||
−0.471345 | + | 0.881949i | \(0.656231\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 2.82843 | 0.131165 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 28.9706 | 1.34060 | 0.670299 | − | 0.742091i | \(-0.266166\pi\) | ||||
0.670299 | + | 0.742091i | \(0.266166\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 4.00000 | 0.184703 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −12.8284 | −0.591103 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −4.68629 | −0.215476 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −2.82843 | −0.129777 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 10.4853 | 0.480088 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −3.31371 | −0.151407 | −0.0757036 | − | 0.997130i | \(-0.524120\pi\) | ||||
−0.0757036 | + | 0.997130i | \(0.524120\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −9.65685 | −0.440315 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 4.00000 | 0.182006 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 7.17157 | 0.325644 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 5.65685 | 0.256337 | 0.128168 | − | 0.991752i | \(-0.459090\pi\) | ||||
0.128168 | + | 0.991752i | \(0.459090\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −17.6569 | −0.798471 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −33.4558 | −1.50984 | −0.754921 | − | 0.655816i | \(-0.772325\pi\) | ||||
−0.754921 | + | 0.655816i | \(0.772325\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −58.6274 | −2.64045 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 2.82843 | 0.127128 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 10.8284 | 0.485721 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 6.34315 | 0.283958 | 0.141979 | − | 0.989870i | \(-0.454653\pi\) | ||||
0.141979 | + | 0.989870i | \(0.454653\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −24.9706 | −1.11560 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 39.5980 | 1.76559 | 0.882793 | − | 0.469762i | \(-0.155660\pi\) | ||||
0.882793 | + | 0.469762i | \(0.155660\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 17.3137 | 0.770450 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −12.3137 | −0.546871 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 21.3137 | 0.944714 | 0.472357 | − | 0.881407i | \(-0.343403\pi\) | ||||
0.472357 | + | 0.881407i | \(0.343403\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 4.82843 | 0.213597 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −2.82843 | −0.124878 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 8.00000 | 0.352522 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −32.0000 | −1.40736 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −14.9706 | −0.657135 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 14.9706 | 0.655872 | 0.327936 | − | 0.944700i | \(-0.393647\pi\) | ||||
0.327936 | + | 0.944700i | \(0.393647\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −22.3431 | −0.976998 | −0.488499 | − | 0.872565i | \(-0.662455\pi\) | ||||
−0.488499 | + | 0.872565i | \(0.662455\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −1.00000 | −0.0436436 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −21.6569 | −0.943387 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −7.00000 | −0.304348 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −6.34315 | −0.274752 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 8.00000 | 0.345870 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 5.17157 | 0.223170 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −2.82843 | −0.121829 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −0.627417 | −0.0269748 | −0.0134874 | − | 0.999909i | \(-0.504293\pi\) | ||||
−0.0134874 | + | 0.999909i | \(0.504293\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −12.3431 | −0.529695 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 13.3137 | 0.570297 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −20.0000 | −0.855138 | −0.427569 | − | 0.903983i | \(-0.640630\pi\) | ||||
−0.427569 | + | 0.903983i | \(0.640630\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 9.31371 | 0.397499 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 21.6569 | 0.922613 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 15.3137 | 0.651205 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 11.6569 | 0.494806 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 15.1716 | 0.642840 | 0.321420 | − | 0.946937i | \(-0.395840\pi\) | ||||
0.321420 | + | 0.946937i | \(0.395840\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1.37258 | 0.0580541 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −21.6569 | −0.914353 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −0.686292 | −0.0289237 | −0.0144619 | − | 0.999895i | \(-0.504604\pi\) | ||||
−0.0144619 | + | 0.999895i | \(0.504604\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −20.8284 | −0.876259 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −1.00000 | −0.0419961 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −20.6274 | −0.864746 | −0.432373 | − | 0.901695i | \(-0.642324\pi\) | ||||
−0.432373 | + | 0.901695i | \(0.642324\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 35.5980 | 1.48973 | 0.744865 | − | 0.667216i | \(-0.232514\pi\) | ||||
0.744865 | + | 0.667216i | \(0.232514\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −13.1716 | −0.550250 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −4.00000 | −0.166812 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 0.828427 | 0.0344879 | 0.0172439 | − | 0.999851i | \(-0.494511\pi\) | ||||
0.0172439 | + | 0.999851i | \(0.494511\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 10.0000 | 0.415586 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 17.6569 | 0.732530 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −29.6569 | −1.22826 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −0.828427 | −0.0342512 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −15.3137 | −0.632064 | −0.316032 | − | 0.948748i | \(-0.602351\pi\) | ||||
−0.316032 | + | 0.948748i | \(0.602351\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 8.00000 | 0.329634 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 12.8284 | 0.527691 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 39.6569 | 1.62851 | 0.814256 | − | 0.580506i | \(-0.197145\pi\) | ||||
0.814256 | + | 0.580506i | \(0.197145\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 7.65685 | 0.313900 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 8.48528 | 0.347279 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 15.5147 | 0.633914 | 0.316957 | − | 0.948440i | \(-0.397339\pi\) | ||||
0.316957 | + | 0.948440i | \(0.397339\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −24.3431 | −0.992978 | −0.496489 | − | 0.868043i | \(-0.665378\pi\) | ||||
−0.496489 | + | 0.868043i | \(0.665378\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −4.00000 | −0.162893 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 3.00000 | 0.121967 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 18.3431 | 0.744525 | 0.372263 | − | 0.928127i | \(-0.378582\pi\) | ||||
0.372263 | + | 0.928127i | \(0.378582\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 7.65685 | 0.310271 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 9.37258 | 0.379174 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −27.6569 | −1.11705 | −0.558525 | − | 0.829488i | \(-0.688632\pi\) | ||||
−0.558525 | + | 0.829488i | \(0.688632\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 7.65685 | 0.308754 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 17.5147 | 0.705116 | 0.352558 | − | 0.935790i | \(-0.385312\pi\) | ||||
0.352558 | + | 0.935790i | \(0.385312\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −9.45584 | −0.380062 | −0.190031 | − | 0.981778i | \(-0.560859\pi\) | ||||
−0.190031 | + | 0.981778i | \(0.560859\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −4.00000 | −0.160514 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −11.6569 | −0.467022 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 8.00000 | 0.319489 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −89.2548 | −3.55882 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 26.6274 | 1.06002 | 0.530010 | − | 0.847991i | \(-0.322188\pi\) | ||||
0.530010 | + | 0.847991i | \(0.322188\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −20.0000 | −0.794929 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 5.65685 | 0.224485 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0.828427 | 0.0328235 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −10.8284 | −0.428366 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −0.343146 | −0.0135534 | −0.00677672 | − | 0.999977i | \(-0.502157\pi\) | ||||
−0.00677672 | + | 0.999977i | \(0.502157\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −33.6569 | −1.32730 | −0.663648 | − | 0.748045i | \(-0.730993\pi\) | ||||
−0.663648 | + | 0.748045i | \(0.730993\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −1.65685 | −0.0652386 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −24.9706 | −0.981694 | −0.490847 | − | 0.871246i | \(-0.663313\pi\) | ||||
−0.490847 | + | 0.871246i | \(0.663313\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 2.82843 | 0.110855 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 9.51472 | 0.372340 | 0.186170 | − | 0.982518i | \(-0.440393\pi\) | ||||
0.186170 | + | 0.982518i | \(0.440393\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −5.65685 | −0.221032 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −4.82843 | −0.188375 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 36.7696 | 1.43234 | 0.716169 | − | 0.697927i | \(-0.245894\pi\) | ||||
0.716169 | + | 0.697927i | \(0.245894\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 6.00000 | 0.233373 | 0.116686 | − | 0.993169i | \(-0.462773\pi\) | ||||
0.116686 | + | 0.993169i | \(0.462773\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 6.34315 | 0.246347 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −2.82843 | −0.109682 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 30.6274 | 1.18590 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 16.9706 | 0.656120 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −26.3431 | −1.01697 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 28.3431 | 1.09255 | 0.546274 | − | 0.837607i | \(-0.316046\pi\) | ||||
0.546274 | + | 0.837607i | \(0.316046\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 1.00000 | 0.0384900 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −6.97056 | −0.267900 | −0.133950 | − | 0.990988i | \(-0.542766\pi\) | ||||
−0.133950 | + | 0.990988i | \(0.542766\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 7.17157 | 0.275220 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −6.34315 | −0.243070 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 10.3431 | 0.395769 | 0.197885 | − | 0.980225i | \(-0.436593\pi\) | ||||
0.197885 | + | 0.980225i | \(0.436593\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0.828427 | 0.0316526 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 2.68629 | 0.102488 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 8.68629 | 0.330921 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −51.7990 | −1.97053 | −0.985263 | − | 0.171045i | \(-0.945286\pi\) | ||||
−0.985263 | + | 0.171045i | \(0.945286\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 2.82843 | 0.107443 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −19.7990 | −0.751018 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −58.6274 | −2.22067 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 28.8284 | 1.09039 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 13.0294 | 0.492115 | 0.246058 | − | 0.969255i | \(-0.420865\pi\) | ||||
0.246058 | + | 0.969255i | \(0.420865\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 32.9706 | 1.24351 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −11.3137 | −0.426099 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 17.3137 | 0.651149 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −5.31371 | −0.199561 | −0.0997803 | − | 0.995009i | \(-0.531814\pi\) | ||||
−0.0997803 | + | 0.995009i | \(0.531814\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −15.3137 | −0.574309 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 11.3137 | 0.423702 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 2.34315 | 0.0876287 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 13.1716 | 0.491901 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 37.6569 | 1.40436 | 0.702182 | − | 0.711998i | \(-0.252209\pi\) | ||||
0.702182 | + | 0.711998i | \(0.252209\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 8.00000 | 0.297936 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −3.65685 | −0.136000 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −7.65685 | −0.284368 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 37.6569 | 1.39662 | 0.698308 | − | 0.715798i | \(-0.253937\pi\) | ||||
0.698308 | + | 0.715798i | \(0.253937\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 12.6863 | 0.469219 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 42.7696 | 1.57973 | 0.789865 | − | 0.613281i | \(-0.210151\pi\) | ||||
0.789865 | + | 0.613281i | \(0.210151\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −1.00000 | −0.0368856 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 11.3137 | 0.416746 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 25.6569 | 0.943803 | 0.471901 | − | 0.881651i | \(-0.343568\pi\) | ||||
0.471901 | + | 0.881651i | \(0.343568\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −2.34315 | −0.0860776 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −14.3431 | −0.526199 | −0.263099 | − | 0.964769i | \(-0.584745\pi\) | ||||
−0.263099 | + | 0.964769i | \(0.584745\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −17.3137 | −0.634325 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −17.6569 | −0.646031 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 8.00000 | 0.292314 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 20.0000 | 0.729810 | 0.364905 | − | 0.931045i | \(-0.381101\pi\) | ||||
0.364905 | + | 0.931045i | \(0.381101\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 11.3137 | 0.412294 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −1.65685 | −0.0602991 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −22.0000 | −0.799604 | −0.399802 | − | 0.916602i | \(-0.630921\pi\) | ||||
−0.399802 | + | 0.916602i | \(0.630921\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 11.3137 | 0.410662 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 3.65685 | 0.132561 | 0.0662804 | − | 0.997801i | \(-0.478887\pi\) | ||||
0.0662804 | + | 0.997801i | \(0.478887\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 13.3137 | 0.481989 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −7.65685 | −0.276834 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −22.9706 | −0.828340 | −0.414170 | − | 0.910200i | \(-0.635928\pi\) | ||||
−0.414170 | + | 0.910200i | \(0.635928\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 6.68629 | 0.240801 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 2.97056 | 0.106844 | 0.0534219 | − | 0.998572i | \(-0.482987\pi\) | ||||
0.0534219 | + | 0.998572i | \(0.482987\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −2.82843 | −0.101600 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 11.6569 | 0.418187 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 21.6569 | 0.775937 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 30.6274 | 1.09594 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −7.65685 | −0.273634 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 12.8284 | 0.457866 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −30.3431 | −1.08162 | −0.540808 | − | 0.841146i | \(-0.681882\pi\) | ||||
−0.540808 | + | 0.841146i | \(0.681882\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −20.9706 | −0.746572 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −20.8284 | −0.740574 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 7.71573 | 0.273994 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −10.4853 | −0.371875 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 1.02944 | 0.0364645 | 0.0182323 | − | 0.999834i | \(-0.494196\pi\) | ||||
0.0182323 | + | 0.999834i | \(0.494196\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 86.6274 | 3.06466 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 11.6569 | 0.411875 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 13.6569 | 0.481940 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −4.00000 | −0.140981 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 5.31371 | 0.187051 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −38.9706 | −1.37013 | −0.685066 | − | 0.728481i | \(-0.740227\pi\) | ||||
−0.685066 | + | 0.728481i | \(0.740227\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −1.45584 | −0.0511216 | −0.0255608 | − | 0.999673i | \(-0.508137\pi\) | ||||
−0.0255608 | + | 0.999673i | \(0.508137\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 10.8284 | 0.379770 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 17.6569 | 0.618493 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −4.68629 | −0.163953 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −0.828427 | −0.0289476 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 10.2843 | 0.358924 | 0.179462 | − | 0.983765i | \(-0.442564\pi\) | ||||
0.179462 | + | 0.983765i | \(0.442564\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −20.2843 | −0.707065 | −0.353533 | − | 0.935422i | \(-0.615020\pi\) | ||||
−0.353533 | + | 0.935422i | \(0.615020\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −2.82843 | −0.0984732 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −45.2548 | −1.57366 | −0.786832 | − | 0.617167i | \(-0.788280\pi\) | ||||
−0.786832 | + | 0.617167i | \(0.788280\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 34.2843 | 1.19074 | 0.595371 | − | 0.803451i | \(-0.297005\pi\) | ||||
0.595371 | + | 0.803451i | \(0.297005\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 2.97056 | 0.103048 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 7.65685 | 0.265294 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 24.9706 | 0.864142 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −2.82843 | −0.0977647 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 48.9706 | 1.69065 | 0.845326 | − | 0.534251i | \(-0.179406\pi\) | ||||
0.845326 | + | 0.534251i | \(0.179406\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 29.6274 | 1.02164 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 18.9706 | 0.653381 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 12.3137 | 0.423604 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 3.00000 | 0.103081 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −15.3137 | −0.525565 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 46.6274 | 1.59837 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −31.1716 | −1.06729 | −0.533647 | − | 0.845707i | \(-0.679179\pi\) | ||||
−0.533647 | + | 0.845707i | \(0.679179\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 2.82843 | 0.0967302 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −23.9411 | −0.817813 | −0.408907 | − | 0.912576i | \(-0.634090\pi\) | ||||
−0.408907 | + | 0.912576i | \(0.634090\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 17.4558 | 0.595586 | 0.297793 | − | 0.954631i | \(-0.403750\pi\) | ||||
0.297793 | + | 0.954631i | \(0.403750\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 7.65685 | 0.260945 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −36.0000 | −1.22545 | −0.612727 | − | 0.790295i | \(-0.709928\pi\) | ||||
−0.612727 | + | 0.790295i | \(0.709928\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 14.9706 | 0.509014 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 41.6274 | 1.41374 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 43.3137 | 1.46932 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −3.31371 | −0.112281 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −7.17157 | −0.242721 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 1.00000 | 0.0338062 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 54.2843 | 1.83305 | 0.916525 | − | 0.399978i | \(-0.130982\pi\) | ||||
0.916525 | + | 0.399978i | \(0.130982\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −19.6569 | −0.663009 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −42.9706 | −1.44772 | −0.723858 | − | 0.689949i | \(-0.757633\pi\) | ||||
−0.723858 | + | 0.689949i | \(0.757633\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 18.6274 | 0.626862 | 0.313431 | − | 0.949611i | \(-0.398521\pi\) | ||||
0.313431 | + | 0.949611i | \(0.398521\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 12.6863 | 0.425964 | 0.212982 | − | 0.977056i | \(-0.431682\pi\) | ||||
0.212982 | + | 0.977056i | \(0.431682\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 5.65685 | 0.189725 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −2.82843 | −0.0947559 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −32.0000 | −1.07084 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −5.17157 | −0.172867 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −3.31371 | −0.110642 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 21.6569 | 0.722297 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 80.2843 | 2.67466 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −1.65685 | −0.0551367 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 12.3431 | 0.410300 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −10.6274 | −0.352878 | −0.176439 | − | 0.984312i | \(-0.556458\pi\) | ||||
−0.176439 | + | 0.984312i | \(0.556458\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −17.3137 | −0.574259 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −16.4853 | −0.546182 | −0.273091 | − | 0.961988i | \(-0.588046\pi\) | ||||
−0.273091 | + | 0.961988i | \(0.588046\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 49.9411 | 1.65281 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −9.31371 | −0.307902 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −5.65685 | −0.186806 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 23.3137 | 0.769048 | 0.384524 | − | 0.923115i | \(-0.374366\pi\) | ||||
0.384524 | + | 0.923115i | \(0.374366\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −17.6569 | −0.581813 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −8.97056 | −0.295270 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −11.6569 | −0.383275 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −8.00000 | −0.262754 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 34.2843 | 1.12483 | 0.562415 | − | 0.826855i | \(-0.309872\pi\) | ||||
0.562415 | + | 0.826855i | \(0.309872\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −2.82843 | −0.0926980 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −8.00000 | −0.261908 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 21.6569 | 0.708255 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −41.5147 | −1.35623 | −0.678113 | − | 0.734957i | \(-0.737202\pi\) | ||||
−0.678113 | + | 0.734957i | \(0.737202\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0.828427 | 0.0270347 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 34.0000 | 1.10837 | 0.554184 | − | 0.832394i | \(-0.313030\pi\) | ||||
0.554184 | + | 0.832394i | \(0.313030\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 30.6274 | 0.997366 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 1.00000 | 0.0325300 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −50.9117 | −1.65441 | −0.827204 | − | 0.561902i | \(-0.810070\pi\) | ||||
−0.827204 | + | 0.561902i | \(0.810070\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −4.00000 | −0.129845 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 7.17157 | 0.232554 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −56.4264 | −1.82783 | −0.913915 | − | 0.405905i | \(-0.866956\pi\) | ||||
−0.913915 | + | 0.405905i | \(0.866956\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 13.1716 | 0.426222 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 21.6569 | 0.700067 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0.828427 | 0.0267513 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −23.0000 | −0.741935 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −8.00000 | −0.257796 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −10.0000 | −0.321911 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 41.9411 | 1.34874 | 0.674368 | − | 0.738396i | \(-0.264416\pi\) | ||||
0.674368 | + | 0.738396i | \(0.264416\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −21.6569 | −0.695718 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −8.00000 | −0.256732 | −0.128366 | − | 0.991727i | \(-0.540973\pi\) | ||||
−0.128366 | + | 0.991727i | \(0.540973\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −19.7990 | −0.634726 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0.828427 | 0.0265309 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −7.85786 | −0.251395 | −0.125698 | − | 0.992069i | \(-0.540117\pi\) | ||||
−0.125698 | + | 0.992069i | \(0.540117\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −32.9706 | −1.05374 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −13.3137 | −0.425074 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −51.3137 | −1.63665 | −0.818327 | − | 0.574754i | \(-0.805098\pi\) | ||||
−0.818327 | + | 0.574754i | \(0.805098\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −12.8284 | −0.408748 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −11.3137 | −0.360119 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −6.62742 | −0.210740 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −53.9411 | −1.71350 | −0.856748 | − | 0.515735i | \(-0.827519\pi\) | ||||
−0.856748 | + | 0.515735i | \(0.827519\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −4.00000 | −0.126936 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −8.48528 | −0.269002 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 4.14214 | 0.131183 | 0.0655914 | − | 0.997847i | \(-0.479107\pi\) | ||||
0.0655914 | + | 0.997847i | \(0.479107\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −11.6569 | −0.368807 |
(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 | 3360.2.a.be.1.1 | yes | 2 | |
4.3 | odd | 2 | 3360.2.a.bc.1.2 | ✓ | 2 | ||
8.3 | odd | 2 | 6720.2.a.cy.1.1 | 2 | |||
8.5 | even | 2 | 6720.2.a.cr.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3360.2.a.bc.1.2 | ✓ | 2 | 4.3 | odd | 2 | ||
3360.2.a.be.1.1 | yes | 2 | 1.1 | even | 1 | trivial | |
6720.2.a.cr.1.2 | 2 | 8.5 | even | 2 | |||
6720.2.a.cy.1.1 | 2 | 8.3 | odd | 2 |