Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1520,2,Mod(1,1520)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1520, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("1520.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1520 = 2^{4} \cdot 5 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1520.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: | \(12.1372611072\) |
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: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 760) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-1.41421\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1520.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −1.41421 | −0.816497 | −0.408248 | − | 0.912871i | \(-0.633860\pi\) | ||||
−0.408248 | + | 0.912871i | \(0.633860\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.82843 | −1.06904 | −0.534522 | − | 0.845154i | \(-0.679509\pi\) | ||||
−0.534522 | + | 0.845154i | \(0.679509\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.00000 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −4.82843 | −1.45583 | −0.727913 | − | 0.685670i | \(-0.759509\pi\) | ||||
−0.727913 | + | 0.685670i | \(0.759509\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.585786 | 0.162468 | 0.0812340 | − | 0.996695i | \(-0.474114\pi\) | ||||
0.0812340 | + | 0.996695i | \(0.474114\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.41421 | 0.365148 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −0.828427 | −0.200923 | −0.100462 | − | 0.994941i | \(-0.532032\pi\) | ||||
−0.100462 | + | 0.994941i | \(0.532032\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.00000 | 0.229416 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 4.00000 | 0.872872 | ||||||||
\(22\) | 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 | ||||||||
\(27\) | 5.65685 | 1.08866 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 4.82843 | 0.896616 | 0.448308 | − | 0.893879i | \(-0.352027\pi\) | ||||
0.448308 | + | 0.893879i | \(0.352027\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 6.82843 | 1.18868 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 2.82843 | 0.478091 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.75736 | 0.288908 | 0.144454 | − | 0.989512i | \(-0.453857\pi\) | ||||
0.144454 | + | 0.989512i | \(0.453857\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −0.828427 | −0.132655 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 4.82843 | 0.754074 | 0.377037 | − | 0.926198i | \(-0.376943\pi\) | ||||
0.377037 | + | 0.926198i | \(0.376943\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.82843 | 0.431331 | 0.215666 | − | 0.976467i | \(-0.430808\pi\) | ||||
0.215666 | + | 0.976467i | \(0.430808\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1.00000 | 0.149071 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −8.48528 | −1.23771 | −0.618853 | − | 0.785507i | \(-0.712402\pi\) | ||||
−0.618853 | + | 0.785507i | \(0.712402\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 1.17157 | 0.164053 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −1.07107 | −0.147122 | −0.0735612 | − | 0.997291i | \(-0.523436\pi\) | ||||
−0.0735612 | + | 0.997291i | \(0.523436\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 4.82843 | 0.651065 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −1.41421 | −0.187317 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 2.82843 | 0.368230 | 0.184115 | − | 0.982905i | \(-0.441058\pi\) | ||||
0.184115 | + | 0.982905i | \(0.441058\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 9.65685 | 1.23643 | 0.618217 | − | 0.786008i | \(-0.287855\pi\) | ||||
0.618217 | + | 0.786008i | \(0.287855\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 2.82843 | 0.356348 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −0.585786 | −0.0726579 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 6.58579 | 0.804582 | 0.402291 | − | 0.915512i | \(-0.368214\pi\) | ||||
0.402291 | + | 0.915512i | \(0.368214\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 5.65685 | 0.681005 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 7.31371 | 0.867978 | 0.433989 | − | 0.900918i | \(-0.357106\pi\) | ||||
0.433989 | + | 0.900918i | \(0.357106\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −16.1421 | −1.88929 | −0.944647 | − | 0.328088i | \(-0.893596\pi\) | ||||
−0.944647 | + | 0.328088i | \(0.893596\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −1.41421 | −0.163299 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 13.6569 | 1.55634 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 14.8284 | 1.66833 | 0.834164 | − | 0.551516i | \(-0.185951\pi\) | ||||
0.834164 | + | 0.551516i | \(0.185951\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −5.00000 | −0.555556 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −8.00000 | −0.878114 | −0.439057 | − | 0.898459i | \(-0.644687\pi\) | ||||
−0.439057 | + | 0.898459i | \(0.644687\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0.828427 | 0.0898555 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −6.82843 | −0.732084 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −8.82843 | −0.935811 | −0.467906 | − | 0.883778i | \(-0.654991\pi\) | ||||
−0.467906 | + | 0.883778i | \(0.654991\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.65685 | −0.173686 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −1.00000 | −0.102598 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 6.24264 | 0.633844 | 0.316922 | − | 0.948452i | \(-0.397351\pi\) | ||||
0.316922 | + | 0.948452i | \(0.397351\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 4.82843 | 0.485275 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 6.34315 | 0.631167 | 0.315583 | − | 0.948898i | \(-0.397800\pi\) | ||||
0.315583 | + | 0.948898i | \(0.397800\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0.242641 | 0.0239081 | 0.0119540 | − | 0.999929i | \(-0.496195\pi\) | ||||
0.0119540 | + | 0.999929i | \(0.496195\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −4.00000 | −0.390360 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 1.41421 | 0.136717 | 0.0683586 | − | 0.997661i | \(-0.478224\pi\) | ||||
0.0683586 | + | 0.997661i | \(0.478224\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −7.65685 | −0.733394 | −0.366697 | − | 0.930341i | \(-0.619511\pi\) | ||||
−0.366697 | + | 0.930341i | \(0.619511\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −2.48528 | −0.235892 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 10.7279 | 1.00920 | 0.504599 | − | 0.863354i | \(-0.331640\pi\) | ||||
0.504599 | + | 0.863354i | \(0.331640\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 4.00000 | 0.373002 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −0.585786 | −0.0541560 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 2.34315 | 0.214796 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 12.3137 | 1.11943 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −6.82843 | −0.615699 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 10.5858 | 0.939337 | 0.469668 | − | 0.882843i | \(-0.344374\pi\) | ||||
0.469668 | + | 0.882843i | \(0.344374\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −4.00000 | −0.352180 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 15.3137 | 1.33796 | 0.668982 | − | 0.743278i | \(-0.266730\pi\) | ||||
0.668982 | + | 0.743278i | \(0.266730\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −2.82843 | −0.245256 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −5.65685 | −0.486864 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −12.8284 | −1.09601 | −0.548003 | − | 0.836476i | \(-0.684612\pi\) | ||||
−0.548003 | + | 0.836476i | \(0.684612\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 8.82843 | 0.748817 | 0.374409 | − | 0.927264i | \(-0.377846\pi\) | ||||
0.374409 | + | 0.927264i | \(0.377846\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 12.0000 | 1.01058 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −2.82843 | −0.236525 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −4.82843 | −0.400979 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −1.41421 | −0.116642 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −9.65685 | −0.791120 | −0.395560 | − | 0.918440i | \(-0.629450\pi\) | ||||
−0.395560 | + | 0.918440i | \(0.629450\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 22.1421 | 1.80190 | 0.900951 | − | 0.433921i | \(-0.142870\pi\) | ||||
0.900951 | + | 0.433921i | \(0.142870\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0.828427 | 0.0669744 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 6.48528 | 0.517582 | 0.258791 | − | 0.965933i | \(-0.416676\pi\) | ||||
0.258791 | + | 0.965933i | \(0.416676\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 1.51472 | 0.120125 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 11.3137 | 0.891645 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −9.17157 | −0.718373 | −0.359187 | − | 0.933266i | \(-0.616946\pi\) | ||||
−0.359187 | + | 0.933266i | \(0.616946\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −6.82843 | −0.531592 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −21.8995 | −1.69463 | −0.847317 | − | 0.531088i | \(-0.821783\pi\) | ||||
−0.847317 | + | 0.531088i | \(0.821783\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.6569 | −0.973604 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1.00000 | −0.0764719 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 14.7279 | 1.11974 | 0.559872 | − | 0.828579i | \(-0.310850\pi\) | ||||
0.559872 | + | 0.828579i | \(0.310850\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −2.82843 | −0.213809 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −4.00000 | −0.300658 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 8.48528 | 0.634220 | 0.317110 | − | 0.948389i | \(-0.397288\pi\) | ||||
0.317110 | + | 0.948389i | \(0.397288\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 17.3137 | 1.28692 | 0.643459 | − | 0.765481i | \(-0.277499\pi\) | ||||
0.643459 | + | 0.765481i | \(0.277499\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −13.6569 | −1.00954 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −1.75736 | −0.129204 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 4.00000 | 0.292509 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −16.0000 | −1.16383 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 19.3137 | 1.39749 | 0.698745 | − | 0.715370i | \(-0.253742\pi\) | ||||
0.698745 | + | 0.715370i | \(0.253742\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −21.0711 | −1.51673 | −0.758364 | − | 0.651831i | \(-0.774001\pi\) | ||||
−0.758364 | + | 0.651831i | \(0.774001\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0.828427 | 0.0593249 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 2.68629 | 0.191390 | 0.0956952 | − | 0.995411i | \(-0.469493\pi\) | ||||
0.0956952 | + | 0.995411i | \(0.469493\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −5.65685 | −0.401004 | −0.200502 | − | 0.979693i | \(-0.564257\pi\) | ||||
−0.200502 | + | 0.979693i | \(0.564257\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −9.31371 | −0.656938 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −13.6569 | −0.958523 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −4.82843 | −0.337232 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 4.00000 | 0.278019 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −4.82843 | −0.333989 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −0.485281 | −0.0334081 | −0.0167041 | − | 0.999860i | \(-0.505317\pi\) | ||||
−0.0167041 | + | 0.999860i | \(0.505317\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −10.3431 | −0.708701 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −2.82843 | −0.192897 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 22.8284 | 1.54260 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −0.485281 | −0.0326436 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −10.5858 | −0.708877 | −0.354438 | − | 0.935079i | \(-0.615328\pi\) | ||||
−0.354438 | + | 0.935079i | \(0.615328\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −1.00000 | −0.0666667 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 24.0416 | 1.59570 | 0.797850 | − | 0.602857i | \(-0.205971\pi\) | ||||
0.797850 | + | 0.602857i | \(0.205971\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −11.3137 | −0.747631 | −0.373815 | − | 0.927503i | \(-0.621951\pi\) | ||||
−0.373815 | + | 0.927503i | \(0.621951\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −19.3137 | −1.27075 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −10.0000 | −0.655122 | −0.327561 | − | 0.944830i | \(-0.606227\pi\) | ||||
−0.327561 | + | 0.944830i | \(0.606227\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 8.48528 | 0.553519 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −20.9706 | −1.36218 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −8.00000 | −0.517477 | −0.258738 | − | 0.965947i | \(-0.583307\pi\) | ||||
−0.258738 | + | 0.965947i | \(0.583307\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −20.1421 | −1.29747 | −0.648735 | − | 0.761015i | \(-0.724701\pi\) | ||||
−0.648735 | + | 0.761015i | \(0.724701\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −9.89949 | −0.635053 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −1.00000 | −0.0638877 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0.585786 | 0.0372727 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 11.3137 | 0.716977 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 4.97056 | 0.313739 | 0.156870 | − | 0.987619i | \(-0.449860\pi\) | ||||
0.156870 | + | 0.987619i | \(0.449860\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 19.3137 | 1.21424 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −1.17157 | −0.0733667 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −23.8995 | −1.49081 | −0.745405 | − | 0.666612i | \(-0.767744\pi\) | ||||
−0.745405 | + | 0.666612i | \(0.767744\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −4.97056 | −0.308856 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −4.82843 | −0.298872 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −4.68629 | −0.288969 | −0.144485 | − | 0.989507i | \(-0.546152\pi\) | ||||
−0.144485 | + | 0.989507i | \(0.546152\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1.07107 | 0.0657952 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 12.4853 | 0.764087 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −6.68629 | −0.407670 | −0.203835 | − | 0.979005i | \(-0.565341\pi\) | ||||
−0.203835 | + | 0.979005i | \(0.565341\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 26.4853 | 1.60887 | 0.804433 | − | 0.594043i | \(-0.202469\pi\) | ||||
0.804433 | + | 0.594043i | \(0.202469\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 2.34315 | 0.141814 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −4.82843 | −0.291165 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 24.8284 | 1.49180 | 0.745898 | − | 0.666060i | \(-0.232021\pi\) | ||||
0.745898 | + | 0.666060i | \(0.232021\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 16.8284 | 1.00390 | 0.501950 | − | 0.864897i | \(-0.332616\pi\) | ||||
0.501950 | + | 0.864897i | \(0.332616\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −17.6569 | −1.04959 | −0.524796 | − | 0.851228i | \(-0.675858\pi\) | ||||
−0.524796 | + | 0.851228i | \(0.675858\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 1.41421 | 0.0837708 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −13.6569 | −0.806139 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.3137 | −0.959630 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −8.82843 | −0.517532 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −4.38478 | −0.256161 | −0.128081 | − | 0.991764i | \(-0.540882\pi\) | ||||
−0.128081 | + | 0.991764i | \(0.540882\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −2.82843 | −0.164677 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −27.3137 | −1.58490 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −2.34315 | −0.135508 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −8.00000 | −0.461112 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −8.97056 | −0.515345 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −9.65685 | −0.552950 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 1.41421 | 0.0807134 | 0.0403567 | − | 0.999185i | \(-0.487151\pi\) | ||||
0.0403567 | + | 0.999185i | \(0.487151\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −0.343146 | −0.0195209 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −24.8284 | −1.40789 | −0.703945 | − | 0.710254i | \(-0.748580\pi\) | ||||
−0.703945 | + | 0.710254i | \(0.748580\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 17.3137 | 0.978629 | 0.489314 | − | 0.872107i | \(-0.337247\pi\) | ||||
0.489314 | + | 0.872107i | \(0.337247\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −2.82843 | −0.159364 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 19.8995 | 1.11767 | 0.558833 | − | 0.829280i | \(-0.311249\pi\) | ||||
0.558833 | + | 0.829280i | \(0.311249\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −23.3137 | −1.30532 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −2.00000 | −0.111629 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −0.828427 | −0.0460949 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0.585786 | 0.0324936 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 10.8284 | 0.598813 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 24.0000 | 1.32316 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −33.4558 | −1.83890 | −0.919450 | − | 0.393208i | \(-0.871365\pi\) | ||||
−0.919450 | + | 0.393208i | \(0.871365\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −1.75736 | −0.0963027 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −6.58579 | −0.359820 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 16.3848 | 0.892536 | 0.446268 | − | 0.894899i | \(-0.352753\pi\) | ||||
0.446268 | + | 0.894899i | \(0.352753\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −15.1716 | −0.824007 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 16.9706 | 0.916324 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −5.65685 | −0.304555 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −36.2843 | −1.94784 | −0.973921 | − | 0.226888i | \(-0.927145\pi\) | ||||
−0.973921 | + | 0.226888i | \(0.927145\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 23.6569 | 1.26632 | 0.633161 | − | 0.774020i | \(-0.281757\pi\) | ||||
0.633161 | + | 0.774020i | \(0.281757\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 3.31371 | 0.176873 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 16.1421 | 0.859159 | 0.429580 | − | 0.903029i | \(-0.358662\pi\) | ||||
0.429580 | + | 0.903029i | \(0.358662\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −7.31371 | −0.388171 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −3.31371 | −0.175380 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −31.4558 | −1.66018 | −0.830088 | − | 0.557632i | \(-0.811710\pi\) | ||||
−0.830088 | + | 0.557632i | \(0.811710\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −17.4142 | −0.914009 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 16.1421 | 0.844918 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 31.1127 | 1.62407 | 0.812035 | − | 0.583609i | \(-0.198360\pi\) | ||||
0.812035 | + | 0.583609i | \(0.198360\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −4.82843 | −0.251358 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 3.02944 | 0.157281 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −2.44365 | −0.126527 | −0.0632637 | − | 0.997997i | \(-0.520151\pi\) | ||||
−0.0632637 | + | 0.997997i | \(0.520151\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 1.41421 | 0.0730297 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 2.82843 | 0.145671 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 1.65685 | 0.0851069 | 0.0425534 | − | 0.999094i | \(-0.486451\pi\) | ||||
0.0425534 | + | 0.999094i | \(0.486451\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −14.9706 | −0.766965 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −7.27208 | −0.371586 | −0.185793 | − | 0.982589i | \(-0.559485\pi\) | ||||
−0.185793 | + | 0.982589i | \(0.559485\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −13.6569 | −0.696018 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −2.82843 | −0.143777 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −13.3137 | −0.675032 | −0.337516 | − | 0.941320i | \(-0.609587\pi\) | ||||
−0.337516 | + | 0.941320i | \(0.609587\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 3.31371 | 0.167581 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −21.6569 | −1.09244 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −14.8284 | −0.746099 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 31.1716 | 1.56446 | 0.782228 | − | 0.622992i | \(-0.214083\pi\) | ||||
0.782228 | + | 0.622992i | \(0.214083\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 4.00000 | 0.200250 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −18.9706 | −0.947345 | −0.473672 | − | 0.880701i | \(-0.657072\pi\) | ||||
−0.473672 | + | 0.880701i | \(0.657072\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 5.00000 | 0.248452 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −8.48528 | −0.420600 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 26.2843 | 1.29967 | 0.649837 | − | 0.760074i | \(-0.274837\pi\) | ||||
0.649837 | + | 0.760074i | \(0.274837\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 18.1421 | 0.894886 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −8.00000 | −0.393654 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 8.00000 | 0.392705 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −12.4853 | −0.611407 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 9.65685 | 0.471768 | 0.235884 | − | 0.971781i | \(-0.424201\pi\) | ||||
0.235884 | + | 0.971781i | \(0.424201\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −15.1716 | −0.739417 | −0.369709 | − | 0.929148i | \(-0.620542\pi\) | ||||
−0.369709 | + | 0.929148i | \(0.620542\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 8.48528 | 0.412568 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −0.828427 | −0.0401846 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −27.3137 | −1.32180 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 4.00000 | 0.193122 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 9.17157 | 0.441779 | 0.220890 | − | 0.975299i | \(-0.429104\pi\) | ||||
0.220890 | + | 0.975299i | \(0.429104\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 30.0416 | 1.44371 | 0.721854 | − | 0.692045i | \(-0.243290\pi\) | ||||
0.721854 | + | 0.692045i | \(0.243290\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 6.82843 | 0.327398 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −4.00000 | −0.191346 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 14.1421 | 0.674967 | 0.337484 | − | 0.941331i | \(-0.390424\pi\) | ||||
0.337484 | + | 0.941331i | \(0.390424\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −1.00000 | −0.0476190 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −23.3137 | −1.10767 | −0.553834 | − | 0.832627i | \(-0.686836\pi\) | ||||
−0.553834 | + | 0.832627i | \(0.686836\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 8.82843 | 0.418508 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 13.6569 | 0.645947 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −30.2843 | −1.42920 | −0.714602 | − | 0.699532i | \(-0.753392\pi\) | ||||
−0.714602 | + | 0.699532i | \(0.753392\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −23.3137 | −1.09780 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −31.3137 | −1.47125 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 1.65685 | 0.0776745 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 22.2843 | 1.04241 | 0.521207 | − | 0.853430i | \(-0.325482\pi\) | ||||
0.521207 | + | 0.853430i | \(0.325482\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −4.68629 | −0.218737 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 36.6274 | 1.70591 | 0.852954 | − | 0.521985i | \(-0.174808\pi\) | ||||
0.852954 | + | 0.521985i | \(0.174808\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 18.6274 | 0.865689 | 0.432845 | − | 0.901468i | \(-0.357510\pi\) | ||||
0.432845 | + | 0.901468i | \(0.357510\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −24.0000 | −1.11059 | −0.555294 | − | 0.831654i | \(-0.687394\pi\) | ||||
−0.555294 | + | 0.831654i | \(0.687394\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −18.6274 | −0.860134 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −9.17157 | −0.422604 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −13.6569 | −0.627943 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1.00000 | 0.0458831 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 1.07107 | 0.0490408 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 27.4558 | 1.25449 | 0.627245 | − | 0.778822i | \(-0.284183\pi\) | ||||
0.627245 | + | 0.778822i | \(0.284183\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.02944 | 0.0469383 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −16.0000 | −0.728025 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −6.24264 | −0.283464 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 3.55635 | 0.161154 | 0.0805768 | − | 0.996748i | \(-0.474324\pi\) | ||||
0.0805768 | + | 0.996748i | \(0.474324\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 12.9706 | 0.586549 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −20.9706 | −0.946388 | −0.473194 | − | 0.880958i | \(-0.656899\pi\) | ||||
−0.473194 | + | 0.880958i | \(0.656899\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −4.00000 | −0.180151 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −4.82843 | −0.217022 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −20.6863 | −0.927907 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 24.1421 | 1.08075 | 0.540375 | − | 0.841424i | \(-0.318282\pi\) | ||||
0.540375 | + | 0.841424i | \(0.318282\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 30.9706 | 1.38366 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −9.65685 | −0.430578 | −0.215289 | − | 0.976550i | \(-0.569069\pi\) | ||||
−0.215289 | + | 0.976550i | \(0.569069\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −6.34315 | −0.282266 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 17.8995 | 0.794944 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 35.4558 | 1.57155 | 0.785776 | − | 0.618511i | \(-0.212264\pi\) | ||||
0.785776 | + | 0.618511i | \(0.212264\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 45.6569 | 2.01974 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 5.65685 | 0.249756 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −0.242641 | −0.0106920 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 40.9706 | 1.80188 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −20.8284 | −0.914266 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 37.3137 | 1.63474 | 0.817372 | − | 0.576111i | \(-0.195430\pi\) | ||||
0.817372 | + | 0.576111i | \(0.195430\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 27.7574 | 1.21374 | 0.606872 | − | 0.794799i | \(-0.292424\pi\) | ||||
0.606872 | + | 0.794799i | \(0.292424\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 4.00000 | 0.174574 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −7.00000 | −0.304348 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −2.82843 | −0.122743 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 2.82843 | 0.122513 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −1.41421 | −0.0611418 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −12.0000 | −0.517838 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −4.82843 | −0.207975 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −20.2843 | −0.872089 | −0.436044 | − | 0.899925i | \(-0.643621\pi\) | ||||
−0.436044 | + | 0.899925i | \(0.643621\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −24.4853 | −1.05076 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 7.65685 | 0.327984 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 24.9289 | 1.06588 | 0.532942 | − | 0.846152i | \(-0.321086\pi\) | ||||
0.532942 | + | 0.846152i | \(0.321086\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −9.65685 | −0.412144 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 4.82843 | 0.205698 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −41.9411 | −1.78352 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 2.48528 | 0.105494 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 33.7990 | 1.43211 | 0.716055 | − | 0.698044i | \(-0.245946\pi\) | ||||
0.716055 | + | 0.698044i | \(0.245946\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1.65685 | 0.0700775 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −5.65685 | −0.238833 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −4.24264 | −0.178806 | −0.0894030 | − | 0.995996i | \(-0.528496\pi\) | ||||
−0.0894030 | + | 0.995996i | \(0.528496\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −10.7279 | −0.451327 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 14.1421 | 0.593914 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 35.9411 | 1.50673 | 0.753365 | − | 0.657602i | \(-0.228429\pi\) | ||||
0.753365 | + | 0.657602i | \(0.228429\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 13.5147 | 0.565573 | 0.282787 | − | 0.959183i | \(-0.408741\pi\) | ||||
0.282787 | + | 0.959183i | \(0.408741\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −27.3137 | −1.14105 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −4.00000 | −0.166812 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −0.627417 | −0.0261197 | −0.0130599 | − | 0.999915i | \(-0.504157\pi\) | ||||
−0.0130599 | + | 0.999915i | \(0.504157\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 29.7990 | 1.23840 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 22.6274 | 0.938743 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 5.17157 | 0.214185 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0.585786 | 0.0242193 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −5.65685 | −0.233483 | −0.116742 | − | 0.993162i | \(-0.537245\pi\) | ||||
−0.116742 | + | 0.993162i | \(0.537245\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −3.79899 | −0.156270 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −28.6274 | −1.17559 | −0.587794 | − | 0.809011i | \(-0.700003\pi\) | ||||
−0.587794 | + | 0.809011i | \(0.700003\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −2.34315 | −0.0960596 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 8.00000 | 0.327418 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 22.1421 | 0.904703 | 0.452352 | − | 0.891840i | \(-0.350585\pi\) | ||||
0.452352 | + | 0.891840i | \(0.350585\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 2.48528 | 0.101377 | 0.0506884 | − | 0.998715i | \(-0.483858\pi\) | ||||
0.0506884 | + | 0.998715i | \(0.483858\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −6.58579 | −0.268194 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −12.3137 | −0.500623 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 16.2426 | 0.659268 | 0.329634 | − | 0.944109i | \(-0.393075\pi\) | ||||
0.329634 | + | 0.944109i | \(0.393075\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 19.3137 | 0.782631 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −4.97056 | −0.201087 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −21.7990 | −0.880453 | −0.440226 | − | 0.897887i | \(-0.645102\pi\) | ||||
−0.440226 | + | 0.897887i | \(0.645102\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 6.82843 | 0.275349 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 1.79899 | 0.0724246 | 0.0362123 | − | 0.999344i | \(-0.488471\pi\) | ||||
0.0362123 | + | 0.999344i | \(0.488471\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −11.8579 | −0.476608 | −0.238304 | − | 0.971191i | \(-0.576591\pi\) | ||||
−0.238304 | + | 0.971191i | \(0.576591\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −22.6274 | −0.908007 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 24.9706 | 1.00042 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 6.82843 | 0.272701 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −1.45584 | −0.0580483 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 17.5147 | 0.697250 | 0.348625 | − | 0.937262i | \(-0.386649\pi\) | ||||
0.348625 | + | 0.937262i | \(0.386649\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0.686292 | 0.0272776 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −10.5858 | −0.420084 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0.585786 | 0.0232097 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −7.31371 | −0.289326 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −23.4558 | −0.926450 | −0.463225 | − | 0.886241i | \(-0.653308\pi\) | ||||
−0.463225 | + | 0.886241i | \(0.653308\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 12.6863 | 0.500298 | 0.250149 | − | 0.968207i | \(-0.419520\pi\) | ||||
0.250149 | + | 0.968207i | \(0.419520\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 4.00000 | 0.157500 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 39.3137 | 1.54558 | 0.772791 | − | 0.634661i | \(-0.218860\pi\) | ||||
0.772791 | + | 0.634661i | \(0.218860\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −13.6569 | −0.536078 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −16.1421 | −0.631691 | −0.315845 | − | 0.948811i | \(-0.602288\pi\) | ||||
−0.315845 | + | 0.948811i | \(0.602288\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −15.3137 | −0.598356 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 16.1421 | 0.629765 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 11.5147 | 0.448550 | 0.224275 | − | 0.974526i | \(-0.427999\pi\) | ||||
0.224275 | + | 0.974526i | \(0.427999\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 3.17157 | 0.123360 | 0.0616799 | − | 0.998096i | \(-0.480354\pi\) | ||||
0.0616799 | + | 0.998096i | \(0.480354\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0.686292 | 0.0266534 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 2.82843 | 0.109682 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −19.3137 | −0.747830 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 14.9706 | 0.578795 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −46.6274 | −1.80003 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −28.3848 | −1.09415 | −0.547076 | − | 0.837083i | \(-0.684259\pi\) | ||||
−0.547076 | + | 0.837083i | \(0.684259\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 5.65685 | 0.217732 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −44.3848 | −1.70585 | −0.852923 | − | 0.522037i | \(-0.825172\pi\) | ||||
−0.852923 | + | 0.522037i | \(0.825172\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −17.6569 | −0.677608 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −34.0000 | −1.30288 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −9.89949 | −0.378794 | −0.189397 | − | 0.981901i | \(-0.560653\pi\) | ||||
−0.189397 | + | 0.981901i | \(0.560653\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 12.8284 | 0.490149 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 16.0000 | 0.610438 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −0.627417 | −0.0239027 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 40.8284 | 1.55319 | 0.776593 | − | 0.630002i | \(-0.216946\pi\) | ||||
0.776593 | + | 0.630002i | \(0.216946\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −13.6569 | −0.518781 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −8.82843 | −0.334881 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −4.00000 | −0.151511 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 14.1421 | 0.534905 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −24.0000 | −0.906467 | −0.453234 | − | 0.891392i | \(-0.649730\pi\) | ||||
−0.453234 | + | 0.891392i | \(0.649730\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1.75736 | 0.0662801 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −12.0000 | −0.451946 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −17.9411 | −0.674745 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 38.2843 | 1.43780 | 0.718898 | − | 0.695116i | \(-0.244647\pi\) | ||||
0.718898 | + | 0.695116i | \(0.244647\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −14.8284 | −0.556109 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 2.82843 | 0.105777 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 11.3137 | 0.422518 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −19.4558 | −0.725581 | −0.362790 | − | 0.931871i | \(-0.618176\pi\) | ||||
−0.362790 | + | 0.931871i | \(0.618176\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −0.686292 | −0.0255588 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 28.4853 | 1.05938 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 4.82843 | 0.179323 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −9.45584 | −0.350698 | −0.175349 | − | 0.984506i | \(-0.556105\pi\) | ||||
−0.175349 | + | 0.984506i | \(0.556105\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 29.0000 | 1.07407 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −2.34315 | −0.0866644 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 15.6569 | 0.578299 | 0.289150 | − | 0.957284i | \(-0.406628\pi\) | ||||
0.289150 | + | 0.957284i | \(0.406628\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 1.41421 | 0.0521641 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −31.7990 | −1.17133 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −23.3137 | −0.857609 | −0.428804 | − | 0.903397i | \(-0.641065\pi\) | ||||
−0.428804 | + | 0.903397i | \(0.641065\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −0.828427 | −0.0304330 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 24.2426 | 0.889376 | 0.444688 | − | 0.895685i | \(-0.353315\pi\) | ||||
0.444688 | + | 0.895685i | \(0.353315\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 9.65685 | 0.353800 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 8.00000 | 0.292705 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −4.00000 | −0.146157 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 27.5147 | 1.00403 | 0.502013 | − | 0.864860i | \(-0.332593\pi\) | ||||
0.502013 | + | 0.864860i | \(0.332593\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −7.02944 | −0.256167 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −22.1421 | −0.805835 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 34.2843 | 1.24608 | 0.623042 | − | 0.782189i | \(-0.285897\pi\) | ||||
0.623042 | + | 0.782189i | \(0.285897\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −27.3137 | −0.991425 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 46.6274 | 1.69024 | 0.845121 | − | 0.534575i | \(-0.179528\pi\) | ||||
0.845121 | + | 0.534575i | \(0.179528\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 21.6569 | 0.784031 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −0.828427 | −0.0299518 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 1.65685 | 0.0598255 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 40.0000 | 1.44244 | 0.721218 | − | 0.692708i | \(-0.243582\pi\) | ||||
0.721218 | + | 0.692708i | \(0.243582\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 33.7990 | 1.21724 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 4.87006 | 0.175164 | 0.0875819 | − | 0.996157i | \(-0.472086\pi\) | ||||
0.0875819 | + | 0.996157i | \(0.472086\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 7.02944 | 0.252180 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 4.82843 | 0.172996 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −35.3137 | −1.26362 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 27.3137 | 0.976112 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −6.48528 | −0.231470 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −1.41421 | −0.0504113 | −0.0252056 | − | 0.999682i | \(-0.508024\pi\) | ||||
−0.0252056 | + | 0.999682i | \(0.508024\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 6.62742 | 0.235942 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −30.3431 | −1.07888 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 5.65685 | 0.200881 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −1.51472 | −0.0537215 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −31.6985 | −1.12282 | −0.561409 | − | 0.827538i | \(-0.689741\pi\) | ||||
−0.561409 | + | 0.827538i | \(0.689741\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 7.02944 | 0.248684 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 8.82843 | 0.311937 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 77.9411 | 2.75048 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −11.3137 | −0.398756 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 9.45584 | 0.332861 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 38.0000 | 1.33601 | 0.668004 | − | 0.744157i | \(-0.267149\pi\) | ||||
0.668004 | + | 0.744157i | \(0.267149\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 23.3137 | 0.818655 | 0.409328 | − | 0.912388i | \(-0.365763\pi\) | ||||
0.409328 | + | 0.912388i | \(0.365763\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −37.4558 | −1.31363 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 9.17157 | 0.321266 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 2.82843 | 0.0989541 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 1.65685 | 0.0578952 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 29.5980 | 1.03298 | 0.516488 | − | 0.856294i | \(-0.327239\pi\) | ||||
0.516488 | + | 0.856294i | \(0.327239\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −0.485281 | −0.0169158 | −0.00845792 | − | 0.999964i | \(-0.502692\pi\) | ||||
−0.00845792 | + | 0.999964i | \(0.502692\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 6.82843 | 0.237735 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 45.6985 | 1.58909 | 0.794546 | − | 0.607204i | \(-0.207709\pi\) | ||||
0.794546 | + | 0.607204i | \(0.207709\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 29.5980 | 1.02798 | 0.513990 | − | 0.857796i | \(-0.328167\pi\) | ||||
0.513990 | + | 0.857796i | \(0.328167\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −35.1127 | −1.21805 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −0.828427 | −0.0287033 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 21.8995 | 0.757863 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −39.7990 | −1.37401 | −0.687007 | − | 0.726651i | \(-0.741076\pi\) | ||||
−0.687007 | + | 0.726651i | \(0.741076\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −5.68629 | −0.196079 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −23.7990 | −0.819681 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 12.6569 | 0.435409 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −34.8284 | −1.19672 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 24.9706 | 0.856987 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −7.02944 | −0.240966 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 39.9411 | 1.36756 | 0.683779 | − | 0.729689i | \(-0.260335\pi\) | ||||
0.683779 | + | 0.729689i | \(0.260335\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 1.00000 | 0.0341993 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −11.2132 | −0.383036 | −0.191518 | − | 0.981489i | \(-0.561341\pi\) | ||||
−0.191518 | + | 0.981489i | \(0.561341\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −17.6569 | −0.602444 | −0.301222 | − | 0.953554i | \(-0.597395\pi\) | ||||
−0.301222 | + | 0.953554i | \(0.597395\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 19.3137 | 0.658209 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −4.04163 | −0.137579 | −0.0687894 | − | 0.997631i | \(-0.521914\pi\) | ||||
−0.0687894 | + | 0.997631i | \(0.521914\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −14.7279 | −0.500764 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 23.0711 | 0.783535 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −71.5980 | −2.42880 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 3.85786 | 0.130719 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −6.24264 | −0.211281 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 2.82843 | 0.0956183 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −6.72792 | −0.227186 | −0.113593 | − | 0.993527i | \(-0.536236\pi\) | ||||
−0.113593 | + | 0.993527i | \(0.536236\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 6.20101 | 0.209155 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 9.65685 | 0.325348 | 0.162674 | − | 0.986680i | \(-0.447988\pi\) | ||||
0.162674 | + | 0.986680i | \(0.447988\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 5.17157 | 0.174037 | 0.0870186 | − | 0.996207i | \(-0.472266\pi\) | ||||
0.0870186 | + | 0.996207i | \(0.472266\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 4.00000 | 0.134459 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 40.7279 | 1.36751 | 0.683755 | − | 0.729712i | \(-0.260346\pi\) | ||||
0.683755 | + | 0.729712i | \(0.260346\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −29.9411 | −1.00419 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 24.1421 | 0.808792 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −8.48528 | −0.283949 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −8.48528 | −0.283632 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 3.31371 | 0.110642 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0.887302 | 0.0295603 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 11.3137 | 0.376497 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −17.3137 | −0.575527 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 0.0416306 | 0.00138232 | 0.000691160 | − | 1.00000i | \(-0.499780\pi\) | ||||
0.000691160 | 1.00000i | \(0.499780\pi\) | ||||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −6.34315 | −0.210389 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 14.8284 | 0.491288 | 0.245644 | − | 0.969360i | \(-0.421001\pi\) | ||||
0.245644 | + | 0.969360i | \(0.421001\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 38.6274 | 1.27838 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 13.6569 | 0.451482 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −43.3137 | −1.43034 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −49.9411 | −1.64741 | −0.823703 | − | 0.567022i | \(-0.808096\pi\) | ||||
−0.823703 | + | 0.567022i | \(0.808096\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −2.00000 | −0.0659022 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 4.28427 | 0.141019 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1.75736 | 0.0577816 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −0.242641 | −0.00796937 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 18.6863 | 0.613077 | 0.306539 | − | 0.951858i | \(-0.400829\pi\) | ||||
0.306539 | + | 0.951858i | \(0.400829\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1.00000 | 0.0327737 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 35.1127 | 1.14954 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −4.00000 | −0.130814 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 4.54416 | 0.148451 | 0.0742256 | − | 0.997241i | \(-0.476352\pi\) | ||||
0.0742256 | + | 0.997241i | \(0.476352\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −24.4853 | −0.799047 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −57.5980 | −1.87764 | −0.938820 | − | 0.344408i | \(-0.888080\pi\) | ||||
−0.938820 | + | 0.344408i | \(0.888080\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −19.3137 | −0.628941 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 16.0000 | 0.520480 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −24.6863 | −0.802197 | −0.401098 | − | 0.916035i | \(-0.631371\pi\) | ||||
−0.401098 | + | 0.916035i | \(0.631371\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −9.45584 | −0.306950 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −28.1421 | −0.912571 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −9.27208 | −0.300352 | −0.150176 | − | 0.988659i | \(-0.547984\pi\) | ||||
−0.150176 | + | 0.988659i | \(0.547984\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −19.3137 | −0.624977 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 32.9706 | 1.06579 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 36.2843 | 1.17168 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −31.0000 | −1.00000 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −1.41421 | −0.0455724 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 21.0711 | 0.678302 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −26.3431 | −0.847138 | −0.423569 | − | 0.905864i | \(-0.639223\pi\) | ||||
−0.423569 | + | 0.905864i | \(0.639223\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 1.17157 | 0.0376363 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 41.9411 | 1.34595 | 0.672977 | − | 0.739663i | \(-0.265015\pi\) | ||||
0.672977 | + | 0.739663i | \(0.265015\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −24.9706 | −0.800519 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −0.828427 | −0.0265309 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 33.8406 | 1.08266 | 0.541329 | − | 0.840811i | \(-0.317921\pi\) | ||||
0.541329 | + | 0.840811i | \(0.317921\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 42.6274 | 1.36238 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 7.65685 | 0.244465 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 44.0416 | 1.40471 | 0.702355 | − | 0.711827i | \(-0.252132\pi\) | ||||
0.702355 | + | 0.711827i | \(0.252132\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −2.68629 | −0.0855924 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −33.9411 | −1.08036 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −11.3137 | −0.359755 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 28.7696 | 0.913895 | 0.456947 | − | 0.889494i | \(-0.348943\pi\) | ||||
0.456947 | + | 0.889494i | \(0.348943\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 47.3137 | 1.50146 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 5.65685 | 0.179334 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 7.17157 | 0.227126 | 0.113563 | − | 0.993531i | \(-0.463774\pi\) | ||||
0.113563 | + | 0.993531i | \(0.463774\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 9.94113 | 0.314523 |
(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 | 1520.2.a.m.1.1 | 2 | ||
4.3 | odd | 2 | 760.2.a.f.1.2 | ✓ | 2 | ||
5.4 | even | 2 | 7600.2.a.ba.1.2 | 2 | |||
8.3 | odd | 2 | 6080.2.a.bf.1.1 | 2 | |||
8.5 | even | 2 | 6080.2.a.bg.1.2 | 2 | |||
12.11 | even | 2 | 6840.2.a.z.1.2 | 2 | |||
20.3 | even | 4 | 3800.2.d.i.3649.4 | 4 | |||
20.7 | even | 4 | 3800.2.d.i.3649.2 | 4 | |||
20.19 | odd | 2 | 3800.2.a.n.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
760.2.a.f.1.2 | ✓ | 2 | 4.3 | odd | 2 | ||
1520.2.a.m.1.1 | 2 | 1.1 | even | 1 | trivial | ||
3800.2.a.n.1.1 | 2 | 20.19 | odd | 2 | |||
3800.2.d.i.3649.2 | 4 | 20.7 | even | 4 | |||
3800.2.d.i.3649.4 | 4 | 20.3 | even | 4 | |||
6080.2.a.bf.1.1 | 2 | 8.3 | odd | 2 | |||
6080.2.a.bg.1.2 | 2 | 8.5 | even | 2 | |||
6840.2.a.z.1.2 | 2 | 12.11 | even | 2 | |||
7600.2.a.ba.1.2 | 2 | 5.4 | even | 2 |