Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6720,2,Mod(1,6720)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6720, 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("6720.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6720 = 2^{6} \cdot 3 \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6720.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: | \(53.6594701583\) |
Analytic rank: | \(0\) |
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: | no (minimal twist has level 3360) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(1.41421\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6720.1 |
$q$-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 | \(-0.359781\pi\) | ||||
0.426401 | + | 0.904534i | \(0.359781\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.82843 | 1.33916 | 0.669582 | − | 0.742738i | \(-0.266473\pi\) | ||||
0.669582 | + | 0.742738i | \(0.266473\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.00000 | 0.258199 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −3.65685 | −0.886917 | −0.443459 | − | 0.896295i | \(-0.646249\pi\) | ||||
−0.443459 | + | 0.896295i | \(0.646249\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.82843 | 0.648886 | 0.324443 | − | 0.945905i | \(-0.394823\pi\) | ||||
0.324443 | + | 0.945905i | \(0.394823\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.00000 | 0.218218 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 4.00000 | 0.834058 | 0.417029 | − | 0.908893i | \(-0.363071\pi\) | ||||
0.417029 | + | 0.908893i | \(0.363071\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −3.65685 | −0.679061 | −0.339530 | − | 0.940595i | \(-0.610268\pi\) | ||||
−0.339530 | + | 0.940595i | \(0.610268\pi\) | |||||||
\(30\) | 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 | ||||||||
\(37\) | 0.343146 | 0.0564128 | 0.0282064 | − | 0.999602i | \(-0.491020\pi\) | ||||
0.0282064 | + | 0.999602i | \(0.491020\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 4.82843 | 0.773167 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 3.65685 | 0.571105 | 0.285552 | − | 0.958363i | \(-0.407823\pi\) | ||||
0.285552 | + | 0.958363i | \(0.407823\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −9.65685 | −1.47266 | −0.736328 | − | 0.676625i | \(-0.763442\pi\) | ||||
−0.736328 | + | 0.676625i | \(0.763442\pi\) | |||||||
\(44\) | 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 | ||||||||
\(51\) | −3.65685 | −0.512062 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 6.48528 | 0.890822 | 0.445411 | − | 0.895326i | \(-0.353058\pi\) | ||||
0.445411 | + | 0.895326i | \(0.353058\pi\) | |||||||
\(54\) | 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 | ||||||||
\(61\) | 13.3137 | 1.70465 | 0.852323 | − | 0.523016i | \(-0.175193\pi\) | ||||
0.852323 | + | 0.523016i | \(0.175193\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 1.00000 | 0.125988 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 4.82843 | 0.598893 | ||||||||
\(66\) | 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 | ||||||||
\(71\) | 5.17157 | 0.613753 | 0.306876 | − | 0.951749i | \(-0.400716\pi\) | ||||
0.306876 | + | 0.951749i | \(0.400716\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 0.828427 | 0.0969601 | 0.0484800 | − | 0.998824i | \(-0.484562\pi\) | ||||
0.0484800 | + | 0.998824i | \(0.484562\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 1.00000 | 0.115470 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 2.82843 | 0.322329 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −7.31371 | −0.822856 | −0.411428 | − | 0.911442i | \(-0.634970\pi\) | ||||
−0.411428 | + | 0.911442i | \(0.634970\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −6.34315 | −0.696251 | −0.348125 | − | 0.937448i | \(-0.613182\pi\) | ||||
−0.348125 | + | 0.937448i | \(0.613182\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −3.65685 | −0.396642 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −3.65685 | −0.392056 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 0.343146 | 0.0363734 | 0.0181867 | − | 0.999835i | \(-0.494211\pi\) | ||||
0.0181867 | + | 0.999835i | \(0.494211\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 4.82843 | 0.506157 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −2.82843 | −0.293294 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 2.82843 | 0.290191 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −12.8284 | −1.30253 | −0.651265 | − | 0.758851i | \(-0.725761\pi\) | ||||
−0.651265 | + | 0.758851i | \(0.725761\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 2.82843 | 0.284268 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −5.31371 | −0.528734 | −0.264367 | − | 0.964422i | \(-0.585163\pi\) | ||||
−0.264367 | + | 0.964422i | \(0.585163\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 8.00000 | 0.788263 | 0.394132 | − | 0.919054i | \(-0.371045\pi\) | ||||
0.394132 | + | 0.919054i | \(0.371045\pi\) | |||||||
\(104\) | 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 | ||||||||
\(109\) | −9.31371 | −0.892091 | −0.446046 | − | 0.895010i | \(-0.647168\pi\) | ||||
−0.446046 | + | 0.895010i | \(0.647168\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0.343146 | 0.0325700 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 15.1716 | 1.42722 | 0.713611 | − | 0.700542i | \(-0.247059\pi\) | ||||
0.713611 | + | 0.700542i | \(0.247059\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 4.00000 | 0.373002 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 4.82843 | 0.446388 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −3.65685 | −0.335223 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −3.00000 | −0.272727 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 3.65685 | 0.329727 | ||||||||
\(124\) | 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 | ||||||||
\(129\) | −9.65685 | −0.850239 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −5.65685 | −0.494242 | −0.247121 | − | 0.968985i | \(-0.579484\pi\) | ||||
−0.247121 | + | 0.968985i | \(0.579484\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2.82843 | 0.245256 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 1.00000 | 0.0860663 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 4.82843 | 0.412520 | 0.206260 | − | 0.978497i | \(-0.433871\pi\) | ||||
0.206260 | + | 0.978497i | \(0.433871\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −19.7990 | −1.67933 | −0.839664 | − | 0.543106i | \(-0.817248\pi\) | ||||
−0.839664 | + | 0.543106i | \(0.817248\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 11.3137 | 0.952786 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 13.6569 | 1.14204 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −3.65685 | −0.303685 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 1.00000 | 0.0824786 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 5.31371 | 0.435316 | 0.217658 | − | 0.976025i | \(-0.430158\pi\) | ||||
0.217658 | + | 0.976025i | \(0.430158\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 9.65685 | 0.785864 | 0.392932 | − | 0.919568i | \(-0.371461\pi\) | ||||
0.392932 | + | 0.919568i | \(0.371461\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −3.65685 | −0.295639 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −2.82843 | −0.227185 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 7.17157 | 0.572354 | 0.286177 | − | 0.958177i | \(-0.407615\pi\) | ||||
0.286177 | + | 0.958177i | \(0.407615\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 6.48528 | 0.514316 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 4.00000 | 0.315244 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −6.34315 | −0.496834 | −0.248417 | − | 0.968653i | \(-0.579910\pi\) | ||||
−0.248417 | + | 0.968653i | \(0.579910\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 2.82843 | 0.220193 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −8.97056 | −0.694163 | −0.347081 | − | 0.937835i | \(-0.612827\pi\) | ||||
−0.347081 | + | 0.937835i | \(0.612827\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 10.3137 | 0.793362 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 2.82843 | 0.216295 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −18.9706 | −1.44231 | −0.721153 | − | 0.692776i | \(-0.756387\pi\) | ||||
−0.721153 | + | 0.692776i | \(0.756387\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1.00000 | 0.0755929 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 10.8284 | 0.809355 | 0.404677 | − | 0.914460i | \(-0.367384\pi\) | ||||
0.404677 | + | 0.914460i | \(0.367384\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 23.6569 | 1.75840 | 0.879200 | − | 0.476453i | \(-0.158078\pi\) | ||||
0.879200 | + | 0.476453i | \(0.158078\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 13.3137 | 0.984178 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0.343146 | 0.0252286 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −10.3431 | −0.756366 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 1.00000 | 0.0727393 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 18.8284 | 1.36238 | 0.681189 | − | 0.732108i | \(-0.261463\pi\) | ||||
0.681189 | + | 0.732108i | \(0.261463\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 10.0000 | 0.719816 | 0.359908 | − | 0.932988i | \(-0.382808\pi\) | ||||
0.359908 | + | 0.932988i | \(0.382808\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 4.82843 | 0.345771 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −7.17157 | −0.510953 | −0.255477 | − | 0.966815i | \(-0.582232\pi\) | ||||
−0.255477 | + | 0.966815i | \(0.582232\pi\) | |||||||
\(198\) | 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 | ||||||||
\(203\) | −3.65685 | −0.256661 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 3.65685 | 0.255406 | ||||||||
\(206\) | 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 | ||||||||
\(213\) | 5.17157 | 0.354350 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −9.65685 | −0.658592 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −2.82843 | −0.192006 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0.828427 | 0.0559799 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −17.6569 | −1.18773 | ||||||||
\(222\) | 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 | ||||||||
\(227\) | −17.6569 | −1.17193 | −0.585963 | − | 0.810338i | \(-0.699284\pi\) | ||||
−0.585963 | + | 0.810338i | \(0.699284\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −25.3137 | −1.67278 | −0.836388 | − | 0.548137i | \(-0.815337\pi\) | ||||
−0.836388 | + | 0.548137i | \(0.815337\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 2.82843 | 0.186097 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 23.1716 | 1.51802 | 0.759010 | − | 0.651079i | \(-0.225683\pi\) | ||||
0.759010 | + | 0.651079i | \(0.225683\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 11.3137 | 0.738025 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −7.31371 | −0.475076 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −18.8284 | −1.21791 | −0.608955 | − | 0.793205i | \(-0.708411\pi\) | ||||
−0.608955 | + | 0.793205i | \(0.708411\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 7.65685 | 0.493221 | 0.246611 | − | 0.969115i | \(-0.420683\pi\) | ||||
0.246611 | + | 0.969115i | \(0.420683\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 1.00000 | 0.0638877 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 13.6569 | 0.868965 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −6.34315 | −0.401981 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −11.3137 | −0.714115 | −0.357057 | − | 0.934082i | \(-0.616220\pi\) | ||||
−0.357057 | + | 0.934082i | \(0.616220\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 11.3137 | 0.711287 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −3.65685 | −0.229001 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 29.3137 | 1.82854 | 0.914269 | − | 0.405107i | \(-0.132766\pi\) | ||||
0.914269 | + | 0.405107i | \(0.132766\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0.343146 | 0.0213220 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −3.65685 | −0.226354 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −12.9706 | −0.799799 | −0.399900 | − | 0.916559i | \(-0.630955\pi\) | ||||
−0.399900 | + | 0.916559i | \(0.630955\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 6.48528 | 0.398388 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0.343146 | 0.0210002 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 17.3137 | 1.05564 | 0.527818 | − | 0.849358i | \(-0.323010\pi\) | ||||
0.527818 | + | 0.849358i | \(0.323010\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −5.17157 | −0.314151 | −0.157075 | − | 0.987587i | \(-0.550207\pi\) | ||||
−0.157075 | + | 0.987587i | \(0.550207\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 4.82843 | 0.292230 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 2.82843 | 0.170561 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 30.9706 | 1.86084 | 0.930420 | − | 0.366494i | \(-0.119442\pi\) | ||||
0.930420 | + | 0.366494i | \(0.119442\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −2.82843 | −0.169334 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −14.9706 | −0.893069 | −0.446534 | − | 0.894766i | \(-0.647342\pi\) | ||||
−0.446534 | + | 0.894766i | \(0.647342\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 7.31371 | 0.434755 | 0.217377 | − | 0.976088i | \(-0.430250\pi\) | ||||
0.217377 | + | 0.976088i | \(0.430250\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 2.82843 | 0.167542 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 3.65685 | 0.215857 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −3.62742 | −0.213377 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −12.8284 | −0.752016 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 8.34315 | 0.487412 | 0.243706 | − | 0.969849i | \(-0.421637\pi\) | ||||
0.243706 | + | 0.969849i | \(0.421637\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 2.82843 | 0.164122 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 19.3137 | 1.11694 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −9.65685 | −0.556612 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −5.31371 | −0.305265 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 13.3137 | 0.762341 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −6.34315 | −0.362022 | −0.181011 | − | 0.983481i | \(-0.557937\pi\) | ||||
−0.181011 | + | 0.983481i | \(0.557937\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 8.00000 | 0.455104 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 8.00000 | 0.453638 | 0.226819 | − | 0.973937i | \(-0.427167\pi\) | ||||
0.226819 | + | 0.973937i | \(0.427167\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −4.82843 | −0.272919 | −0.136459 | − | 0.990646i | \(-0.543572\pi\) | ||||
−0.136459 | + | 0.990646i | \(0.543572\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 1.00000 | 0.0563436 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −12.8284 | −0.720516 | −0.360258 | − | 0.932853i | \(-0.617311\pi\) | ||||
−0.360258 | + | 0.932853i | \(0.617311\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −10.3431 | −0.579105 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −8.00000 | −0.446516 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −10.3431 | −0.575508 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 4.82843 | 0.267833 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −9.31371 | −0.515049 | ||||||||
\(328\) | 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 | ||||||||
\(333\) | 0.343146 | 0.0188043 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −4.00000 | −0.218543 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 21.3137 | 1.16103 | 0.580516 | − | 0.814249i | \(-0.302851\pi\) | ||||
0.580516 | + | 0.814249i | \(0.302851\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 15.1716 | 0.824007 | ||||||||
\(340\) | 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 | ||||||||
\(347\) | 18.3431 | 0.984712 | 0.492356 | − | 0.870394i | \(-0.336136\pi\) | ||||
0.492356 | + | 0.870394i | \(0.336136\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 29.3137 | 1.56913 | 0.784563 | − | 0.620049i | \(-0.212887\pi\) | ||||
0.784563 | + | 0.620049i | \(0.212887\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 4.82843 | 0.257722 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 26.9706 | 1.43550 | 0.717749 | − | 0.696302i | \(-0.245172\pi\) | ||||
0.717749 | + | 0.696302i | \(0.245172\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 5.17157 | 0.274479 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −3.65685 | −0.193541 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 17.4558 | 0.921284 | 0.460642 | − | 0.887586i | \(-0.347619\pi\) | ||||
0.460642 | + | 0.887586i | \(0.347619\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −11.0000 | −0.578947 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −3.00000 | −0.157459 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0.828427 | 0.0433619 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −18.3431 | −0.957504 | −0.478752 | − | 0.877950i | \(-0.658911\pi\) | ||||
−0.478752 | + | 0.877950i | \(0.658911\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 3.65685 | 0.190368 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 6.48528 | 0.336699 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −10.0000 | −0.517780 | −0.258890 | − | 0.965907i | \(-0.583357\pi\) | ||||
−0.258890 | + | 0.965907i | \(0.583357\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 1.00000 | 0.0516398 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −17.6569 | −0.909374 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 9.65685 | 0.496039 | 0.248020 | − | 0.968755i | \(-0.420220\pi\) | ||||
0.248020 | + | 0.968755i | \(0.420220\pi\) | |||||||
\(380\) | 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 | ||||||||
\(387\) | −9.65685 | −0.490885 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 13.3137 | 0.675032 | 0.337516 | − | 0.941320i | \(-0.390413\pi\) | ||||
0.337516 | + | 0.941320i | \(0.390413\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −14.6274 | −0.739740 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −5.65685 | −0.285351 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −7.31371 | −0.367993 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −14.4853 | −0.726995 | −0.363498 | − | 0.931595i | \(-0.618418\pi\) | ||||
−0.363498 | + | 0.931595i | \(0.618418\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 2.82843 | 0.141598 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 21.3137 | 1.06436 | 0.532178 | − | 0.846633i | \(-0.321374\pi\) | ||||
0.532178 | + | 0.846633i | \(0.321374\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −13.6569 | −0.680296 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 1.00000 | 0.0496904 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0.970563 | 0.0481090 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −9.31371 | −0.460533 | −0.230267 | − | 0.973128i | \(-0.573960\pi\) | ||||
−0.230267 | + | 0.973128i | \(0.573960\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 4.82843 | 0.238169 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −6.34315 | −0.311373 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −19.7990 | −0.969561 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 16.9706 | 0.829066 | 0.414533 | − | 0.910034i | \(-0.363945\pi\) | ||||
0.414533 | + | 0.910034i | \(0.363945\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −1.31371 | −0.0640262 | −0.0320131 | − | 0.999487i | \(-0.510192\pi\) | ||||
−0.0320131 | + | 0.999487i | \(0.510192\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 11.3137 | 0.550091 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −3.65685 | −0.177383 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 13.3137 | 0.644296 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 13.6569 | 0.659359 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 16.4853 | 0.794068 | 0.397034 | − | 0.917804i | \(-0.370039\pi\) | ||||
0.397034 | + | 0.917804i | \(0.370039\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 30.4853 | 1.46503 | 0.732515 | − | 0.680751i | \(-0.238347\pi\) | ||||
0.732515 | + | 0.680751i | \(0.238347\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −3.65685 | −0.175333 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 11.3137 | 0.541208 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −18.8284 | −0.898632 | −0.449316 | − | 0.893373i | \(-0.648332\pi\) | ||||
−0.449316 | + | 0.893373i | \(0.648332\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.00000 | 0.0476190 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −8.97056 | −0.426204 | −0.213102 | − | 0.977030i | \(-0.568357\pi\) | ||||
−0.213102 | + | 0.977030i | \(0.568357\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0.343146 | 0.0162667 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 5.31371 | 0.251330 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 2.00000 | 0.0943858 | 0.0471929 | − | 0.998886i | \(-0.484972\pi\) | ||||
0.0471929 | + | 0.998886i | \(0.484972\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 10.3431 | 0.487040 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 9.65685 | 0.453719 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 4.82843 | 0.226360 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −19.6569 | −0.919509 | −0.459754 | − | 0.888046i | \(-0.652063\pi\) | ||||
−0.459754 | + | 0.888046i | \(0.652063\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −3.65685 | −0.170687 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 28.6274 | 1.33331 | 0.666656 | − | 0.745366i | \(-0.267725\pi\) | ||||
0.666656 | + | 0.745366i | \(0.267725\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −36.2843 | −1.68627 | −0.843137 | − | 0.537700i | \(-0.819293\pi\) | ||||
−0.843137 | + | 0.537700i | \(0.819293\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −2.82843 | −0.131165 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −4.97056 | −0.230010 | −0.115005 | − | 0.993365i | \(-0.536688\pi\) | ||||
−0.115005 | + | 0.993365i | \(0.536688\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −4.00000 | −0.184703 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 7.17157 | 0.330449 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −27.3137 | −1.25589 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 2.82843 | 0.129777 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 6.48528 | 0.296941 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −19.3137 | −0.882466 | −0.441233 | − | 0.897393i | \(-0.645459\pi\) | ||||
−0.441233 | + | 0.897393i | \(0.645459\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.65685 | 0.0755461 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 4.00000 | 0.182006 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −12.8284 | −0.582509 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 5.65685 | 0.256337 | 0.128168 | − | 0.991752i | \(-0.459090\pi\) | ||||
0.128168 | + | 0.991752i | \(0.459090\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −6.34315 | −0.286847 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 17.4558 | 0.787771 | 0.393886 | − | 0.919159i | \(-0.371131\pi\) | ||||
0.393886 | + | 0.919159i | \(0.371131\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 13.3726 | 0.602271 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 2.82843 | 0.127128 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 5.17157 | 0.231977 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 17.6569 | 0.790429 | 0.395215 | − | 0.918589i | \(-0.370670\pi\) | ||||
0.395215 | + | 0.918589i | \(0.370670\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −8.97056 | −0.400775 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 39.5980 | 1.76559 | 0.882793 | − | 0.469762i | \(-0.155660\pi\) | ||||
0.882793 | + | 0.469762i | \(0.155660\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −5.31371 | −0.236457 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 10.3137 | 0.458048 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 1.31371 | 0.0582291 | 0.0291146 | − | 0.999576i | \(-0.490731\pi\) | ||||
0.0291146 | + | 0.999576i | \(0.490731\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0.828427 | 0.0366475 | ||||||||
\(512\) | 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 | ||||||||
\(519\) | −18.9706 | −0.832715 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −18.9706 | −0.831115 | −0.415558 | − | 0.909567i | \(-0.636414\pi\) | ||||
−0.415558 | + | 0.909567i | \(0.636414\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −33.6569 | −1.47171 | −0.735856 | − | 0.677138i | \(-0.763220\pi\) | ||||
−0.735856 | + | 0.677138i | \(0.763220\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 1.00000 | 0.0436436 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 10.3431 | 0.450555 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −7.00000 | −0.304348 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 17.6569 | 0.764803 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −8.00000 | −0.345870 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 10.8284 | 0.467281 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 2.82843 | 0.121829 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −44.6274 | −1.91868 | −0.959341 | − | 0.282249i | \(-0.908920\pi\) | ||||
−0.959341 | + | 0.282249i | \(0.908920\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 23.6569 | 1.01521 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −9.31371 | −0.398955 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −20.0000 | −0.855138 | −0.427569 | − | 0.903983i | \(-0.640630\pi\) | ||||
−0.427569 | + | 0.903983i | \(0.640630\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 13.3137 | 0.568215 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −10.3431 | −0.440633 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −7.31371 | −0.311011 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0.343146 | 0.0145657 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −20.8284 | −0.882529 | −0.441264 | − | 0.897377i | \(-0.645470\pi\) | ||||
−0.441264 | + | 0.897377i | \(0.645470\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −46.6274 | −1.97213 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −10.3431 | −0.436688 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −23.3137 | −0.982556 | −0.491278 | − | 0.871003i | \(-0.663470\pi\) | ||||
−0.491278 | + | 0.871003i | \(0.663470\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 15.1716 | 0.638273 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 1.00000 | 0.0419961 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 24.6274 | 1.03244 | 0.516218 | − | 0.856458i | \(-0.327340\pi\) | ||||
0.516218 | + | 0.856458i | \(0.327340\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −43.5980 | −1.82452 | −0.912259 | − | 0.409613i | \(-0.865664\pi\) | ||||
−0.912259 | + | 0.409613i | \(0.865664\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 18.8284 | 0.786569 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 4.00000 | 0.166812 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −4.82843 | −0.201010 | −0.100505 | − | 0.994937i | \(-0.532046\pi\) | ||||
−0.100505 | + | 0.994937i | \(0.532046\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 10.0000 | 0.415586 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −6.34315 | −0.263158 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 18.3431 | 0.759695 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 4.82843 | 0.199631 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 7.31371 | 0.301869 | 0.150935 | − | 0.988544i | \(-0.451772\pi\) | ||||
0.150935 | + | 0.988544i | \(0.451772\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −8.00000 | −0.329634 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −7.17157 | −0.294999 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 28.3431 | 1.16391 | 0.581957 | − | 0.813220i | \(-0.302287\pi\) | ||||
0.581957 | + | 0.813220i | \(0.302287\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −3.65685 | −0.149916 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 8.48528 | 0.347279 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −32.4853 | −1.32731 | −0.663656 | − | 0.748038i | \(-0.730996\pi\) | ||||
−0.663656 | + | 0.748038i | \(0.730996\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −35.6569 | −1.45447 | −0.727237 | − | 0.686387i | \(-0.759196\pi\) | ||||
−0.727237 | + | 0.686387i | \(0.759196\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −4.00000 | −0.162893 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −3.00000 | −0.121967 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −29.6569 | −1.20373 | −0.601867 | − | 0.798596i | \(-0.705576\pi\) | ||||
−0.601867 | + | 0.798596i | \(0.705576\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −3.65685 | −0.148183 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 54.6274 | 2.20999 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 16.3431 | 0.660093 | 0.330047 | − | 0.943965i | \(-0.392935\pi\) | ||||
0.330047 | + | 0.943965i | \(0.392935\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 3.65685 | 0.147459 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 34.4853 | 1.38833 | 0.694163 | − | 0.719818i | \(-0.255775\pi\) | ||||
0.694163 | + | 0.719818i | \(0.255775\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 41.4558 | 1.66625 | 0.833126 | − | 0.553084i | \(-0.186549\pi\) | ||||
0.833126 | + | 0.553084i | \(0.186549\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 4.00000 | 0.160514 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0.343146 | 0.0137478 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 8.00000 | 0.319489 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −1.25483 | −0.0500335 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 18.6274 | 0.741546 | 0.370773 | − | 0.928724i | \(-0.379093\pi\) | ||||
0.370773 | + | 0.928724i | \(0.379093\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −20.0000 | −0.794929 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −5.65685 | −0.224485 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 4.82843 | 0.191309 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 5.17157 | 0.204584 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −11.6569 | −0.460418 | −0.230209 | − | 0.973141i | \(-0.573941\pi\) | ||||
−0.230209 | + | 0.973141i | \(0.573941\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −22.3431 | −0.881128 | −0.440564 | − | 0.897721i | \(-0.645221\pi\) | ||||
−0.440564 | + | 0.897721i | \(0.645221\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −9.65685 | −0.380238 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −8.97056 | −0.352669 | −0.176335 | − | 0.984330i | \(-0.556424\pi\) | ||||
−0.176335 | + | 0.984330i | \(0.556424\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −2.82843 | −0.110855 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −26.4853 | −1.03645 | −0.518225 | − | 0.855245i | \(-0.673407\pi\) | ||||
−0.518225 | + | 0.855245i | \(0.673407\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −5.65685 | −0.221032 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0.828427 | 0.0323200 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −36.7696 | −1.43234 | −0.716169 | − | 0.697927i | \(-0.754106\pi\) | ||||
−0.716169 | + | 0.697927i | \(0.754106\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −6.00000 | −0.233373 | −0.116686 | − | 0.993169i | \(-0.537227\pi\) | ||||
−0.116686 | + | 0.993169i | \(0.537227\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −17.6569 | −0.685735 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 2.82843 | 0.109682 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −14.6274 | −0.566376 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 16.9706 | 0.656120 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 37.6569 | 1.45373 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 39.6569 | 1.52866 | 0.764330 | − | 0.644826i | \(-0.223070\pi\) | ||||
0.764330 | + | 0.644826i | \(0.223070\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 1.00000 | 0.0384900 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −26.9706 | −1.03656 | −0.518281 | − | 0.855210i | \(-0.673428\pi\) | ||||
−0.518281 | + | 0.855210i | \(0.673428\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −12.8284 | −0.492310 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −17.6569 | −0.676612 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 21.6569 | 0.828676 | 0.414338 | − | 0.910123i | \(-0.364013\pi\) | ||||
0.414338 | + | 0.910123i | \(0.364013\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 4.82843 | 0.184485 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −25.3137 | −0.965778 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 31.3137 | 1.19296 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −12.2010 | −0.464148 | −0.232074 | − | 0.972698i | \(-0.574551\pi\) | ||||
−0.232074 | + | 0.972698i | \(0.574551\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 2.82843 | 0.107443 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −19.7990 | −0.751018 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −13.3726 | −0.506523 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 23.1716 | 0.876429 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −46.9706 | −1.77405 | −0.887027 | − | 0.461718i | \(-0.847233\pi\) | ||||
−0.887027 | + | 0.461718i | \(0.847233\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0.970563 | 0.0366055 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 11.3137 | 0.426099 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −5.31371 | −0.199843 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −17.3137 | −0.650230 | −0.325115 | − | 0.945674i | \(-0.605403\pi\) | ||||
−0.325115 | + | 0.945674i | \(0.605403\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −7.31371 | −0.274285 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −11.3137 | −0.423702 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 13.6569 | 0.510737 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −18.8284 | −0.703160 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −26.3431 | −0.982434 | −0.491217 | − | 0.871037i | \(-0.663448\pi\) | ||||
−0.491217 | + | 0.871037i | \(0.663448\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 8.00000 | 0.297936 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 7.65685 | 0.284761 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −3.65685 | −0.135812 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −26.3431 | −0.977013 | −0.488507 | − | 0.872560i | \(-0.662458\pi\) | ||||
−0.488507 | + | 0.872560i | \(0.662458\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 35.3137 | 1.30612 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 30.7696 | 1.13650 | 0.568250 | − | 0.822856i | \(-0.307621\pi\) | ||||
0.568250 | + | 0.822856i | \(0.307621\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 1.00000 | 0.0368856 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −11.3137 | −0.416746 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 14.3431 | 0.527621 | 0.263811 | − | 0.964575i | \(-0.415021\pi\) | ||||
0.263811 | + | 0.964575i | \(0.415021\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 13.6569 | 0.501697 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 25.6569 | 0.941259 | 0.470629 | − | 0.882331i | \(-0.344027\pi\) | ||||
0.470629 | + | 0.882331i | \(0.344027\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 5.31371 | 0.194679 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −6.34315 | −0.232084 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −8.00000 | −0.292314 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −20.0000 | −0.729810 | −0.364905 | − | 0.931045i | \(-0.618899\pi\) | ||||
−0.364905 | + | 0.931045i | \(0.618899\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −11.3137 | −0.412294 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 9.65685 | 0.351449 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 22.0000 | 0.799604 | 0.399802 | − | 0.916602i | \(-0.369079\pi\) | ||||
0.399802 | + | 0.916602i | \(0.369079\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 11.3137 | 0.410662 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −7.65685 | −0.277561 | −0.138780 | − | 0.990323i | \(-0.544318\pi\) | ||||
−0.138780 | + | 0.990323i | \(0.544318\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −9.31371 | −0.337179 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −3.65685 | −0.132214 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 10.9706 | 0.395609 | 0.197804 | − | 0.980242i | \(-0.436619\pi\) | ||||
0.197804 | + | 0.980242i | \(0.436619\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 29.3137 | 1.05571 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 30.9706 | 1.11393 | 0.556967 | − | 0.830535i | \(-0.311965\pi\) | ||||
0.556967 | + | 0.830535i | \(0.311965\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −2.82843 | −0.101600 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0.343146 | 0.0123103 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 10.3431 | 0.370582 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 14.6274 | 0.523410 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −3.65685 | −0.130685 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 7.17157 | 0.255964 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −41.6569 | −1.48491 | −0.742453 | − | 0.669898i | \(-0.766338\pi\) | ||||
−0.742453 | + | 0.669898i | \(0.766338\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −12.9706 | −0.461764 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 15.1716 | 0.539439 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 64.2843 | 2.28280 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 6.48528 | 0.230009 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −34.9706 | −1.23872 | −0.619360 | − | 0.785107i | \(-0.712608\pi\) | ||||
−0.619360 | + | 0.785107i | \(0.712608\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −41.3726 | −1.46366 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0.343146 | 0.0121245 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 2.34315 | 0.0826878 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 4.00000 | 0.140981 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 17.3137 | 0.609471 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −5.02944 | −0.176826 | −0.0884128 | − | 0.996084i | \(-0.528179\pi\) | ||||
−0.0884128 | + | 0.996084i | \(0.528179\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 49.4558 | 1.73663 | 0.868315 | − | 0.496014i | \(-0.165203\pi\) | ||||
0.868315 | + | 0.496014i | \(0.165203\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −5.17157 | −0.181375 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −6.34315 | −0.222191 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −27.3137 | −0.955586 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 4.82843 | 0.168719 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 46.2843 | 1.61533 | 0.807666 | − | 0.589640i | \(-0.200730\pi\) | ||||
0.807666 | + | 0.589640i | \(0.200730\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −36.2843 | −1.26479 | −0.632395 | − | 0.774646i | \(-0.717928\pi\) | ||||
−0.632395 | + | 0.774646i | \(0.717928\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 2.82843 | 0.0984732 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 45.2548 | 1.57366 | 0.786832 | − | 0.617167i | \(-0.211720\pi\) | ||||
0.786832 | + | 0.617167i | \(0.211720\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 22.2843 | 0.773965 | 0.386982 | − | 0.922087i | \(-0.373517\pi\) | ||||
0.386982 | + | 0.922087i | \(0.373517\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 30.9706 | 1.07436 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −3.65685 | −0.126702 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −8.97056 | −0.310439 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −2.82843 | −0.0977647 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −15.0294 | −0.518874 | −0.259437 | − | 0.965760i | \(-0.583537\pi\) | ||||
−0.259437 | + | 0.965760i | \(0.583537\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −15.6274 | −0.538876 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −14.9706 | −0.515614 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 10.3137 | 0.354802 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −3.00000 | −0.103081 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 7.31371 | 0.251006 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1.37258 | 0.0470515 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 36.8284 | 1.26098 | 0.630491 | − | 0.776197i | \(-0.282854\pi\) | ||||
0.630491 | + | 0.776197i | \(0.282854\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 2.82843 | 0.0967302 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 43.9411 | 1.50100 | 0.750500 | − | 0.660870i | \(-0.229813\pi\) | ||||
0.750500 | + | 0.660870i | \(0.229813\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −33.4558 | −1.14150 | −0.570749 | − | 0.821124i | \(-0.693347\pi\) | ||||
−0.570749 | + | 0.821124i | \(0.693347\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 3.65685 | 0.124625 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 36.0000 | 1.22545 | 0.612727 | − | 0.790295i | \(-0.290072\pi\) | ||||
0.612727 | + | 0.790295i | \(0.290072\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −18.9706 | −0.645018 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −3.62742 | −0.123194 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −20.6863 | −0.701734 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −19.3137 | −0.654420 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −12.8284 | −0.434176 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 1.00000 | 0.0338062 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 2.28427 | 0.0771344 | 0.0385672 | − | 0.999256i | \(-0.487721\pi\) | ||||
0.0385672 | + | 0.999256i | \(0.487721\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 8.34315 | 0.281407 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −9.02944 | −0.304209 | −0.152105 | − | 0.988364i | \(-0.548605\pi\) | ||||
−0.152105 | + | 0.988364i | \(0.548605\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −26.6274 | −0.896084 | −0.448042 | − | 0.894013i | \(-0.647878\pi\) | ||||
−0.448042 | + | 0.894013i | \(0.647878\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −35.3137 | −1.18572 | −0.592859 | − | 0.805306i | \(-0.702001\pi\) | ||||
−0.592859 | + | 0.805306i | \(0.702001\pi\) | |||||||
\(888\) | 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 | ||||||||
\(895\) | 10.8284 | 0.361954 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 19.3137 | 0.644866 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 10.3431 | 0.344963 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −23.7157 | −0.790085 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −9.65685 | −0.321360 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 23.6569 | 0.786380 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 34.6274 | 1.14978 | 0.574892 | − | 0.818229i | \(-0.305044\pi\) | ||||
0.574892 | + | 0.818229i | \(0.305044\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −5.31371 | −0.176245 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −0.485281 | −0.0160781 | −0.00803904 | − | 0.999968i | \(-0.502559\pi\) | ||||
−0.00803904 | + | 0.999968i | \(0.502559\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −17.9411 | −0.593765 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 13.3137 | 0.440138 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −5.65685 | −0.186806 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −0.686292 | −0.0226387 | −0.0113193 | − | 0.999936i | \(-0.503603\pi\) | ||||
−0.0113193 | + | 0.999936i | \(0.503603\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −6.34315 | −0.209014 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 24.9706 | 0.821916 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0.343146 | 0.0112826 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 8.00000 | 0.262754 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −22.2843 | −0.731123 | −0.365562 | − | 0.930787i | \(-0.619123\pi\) | ||||
−0.365562 | + | 0.930787i | \(0.619123\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 2.82843 | 0.0926980 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 8.00000 | 0.261908 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −10.3431 | −0.338257 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −58.4853 | −1.91063 | −0.955315 | − | 0.295588i | \(-0.904484\pi\) | ||||
−0.955315 | + | 0.295588i | \(0.904484\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −4.82843 | −0.157570 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −34.0000 | −1.10837 | −0.554184 | − | 0.832394i | \(-0.686970\pi\) | ||||
−0.554184 | + | 0.832394i | \(0.686970\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 14.6274 | 0.476334 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 1.00000 | 0.0325300 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 50.9117 | 1.65441 | 0.827204 | − | 0.561902i | \(-0.189930\pi\) | ||||
0.827204 | + | 0.561902i | \(0.189930\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 4.00000 | 0.129845 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −12.8284 | −0.415990 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 28.4264 | 0.920822 | 0.460411 | − | 0.887706i | \(-0.347702\pi\) | ||||
0.460411 | + | 0.887706i | \(0.347702\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 18.8284 | 0.609274 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −10.3431 | −0.334346 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 4.82843 | 0.155918 | ||||||||
\(960\) | 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 | ||||||||
\(967\) | 25.9411 | 0.834210 | 0.417105 | − | 0.908858i | \(-0.363045\pi\) | ||||
0.417105 | + | 0.908858i | \(0.363045\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −10.3431 | −0.332270 | ||||||||
\(970\) | 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 | ||||||||
\(975\) | 4.82843 | 0.154633 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −36.1421 | −1.15629 | −0.578145 | − | 0.815934i | \(-0.696223\pi\) | ||||
−0.578145 | + | 0.815934i | \(0.696223\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0.970563 | 0.0310193 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −9.31371 | −0.297364 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 28.6863 | 0.914951 | 0.457475 | − | 0.889222i | \(-0.348754\pi\) | ||||
0.457475 | + | 0.889222i | \(0.348754\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −7.17157 | −0.228505 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 11.3137 | 0.360119 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −38.6274 | −1.22828 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −13.9411 | −0.442854 | −0.221427 | − | 0.975177i | \(-0.571072\pi\) | ||||
−0.221427 | + | 0.975177i | \(0.571072\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −4.00000 | −0.126936 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 8.48528 | 0.269002 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 24.1421 | 0.764589 | 0.382295 | − | 0.924041i | \(-0.375134\pi\) | ||||
0.382295 | + | 0.924041i | \(0.375134\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0.343146 | 0.0108567 |
(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 | 6720.2.a.cy.1.2 | 2 | ||
4.3 | odd | 2 | 6720.2.a.cr.1.1 | 2 | |||
8.3 | odd | 2 | 3360.2.a.be.1.2 | yes | 2 | ||
8.5 | even | 2 | 3360.2.a.bc.1.1 | ✓ | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3360.2.a.bc.1.1 | ✓ | 2 | 8.5 | even | 2 | ||
3360.2.a.be.1.2 | yes | 2 | 8.3 | odd | 2 | ||
6720.2.a.cr.1.1 | 2 | 4.3 | odd | 2 | |||
6720.2.a.cy.1.2 | 2 | 1.1 | even | 1 | trivial |