Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8280,2,Mod(1,8280)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8280, 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("8280.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8280 = 2^{3} \cdot 3^{2} \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8280.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: | \(66.1161328736\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{8})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 2760) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(1.41421\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8280.1 |
$q$-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 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.82843 | 0.691080 | 0.345540 | − | 0.938404i | \(-0.387696\pi\) | ||||
0.345540 | + | 0.938404i | \(0.387696\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.41421 | 0.426401 | 0.213201 | − | 0.977008i | \(-0.431611\pi\) | ||||
0.213201 | + | 0.977008i | \(0.431611\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.585786 | 0.162468 | 0.0812340 | − | 0.996695i | \(-0.474114\pi\) | ||||
0.0812340 | + | 0.996695i | \(0.474114\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 2.41421 | 0.585533 | 0.292766 | − | 0.956184i | \(-0.405424\pi\) | ||||
0.292766 | + | 0.956184i | \(0.405424\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −7.41421 | −1.70094 | −0.850469 | − | 0.526026i | \(-0.823682\pi\) | ||||
−0.850469 | + | 0.526026i | \(0.823682\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.00000 | 0.208514 | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 3.58579 | 0.665864 | 0.332932 | − | 0.942951i | \(-0.391962\pi\) | ||||
0.332932 | + | 0.942951i | \(0.391962\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.00000 | −0.179605 | −0.0898027 | − | 0.995960i | \(-0.528624\pi\) | ||||
−0.0898027 | + | 0.995960i | \(0.528624\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −1.82843 | −0.309061 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −7.48528 | −1.23057 | −0.615286 | − | 0.788304i | \(-0.710960\pi\) | ||||
−0.615286 | + | 0.788304i | \(0.710960\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −7.24264 | −1.13111 | −0.565555 | − | 0.824710i | \(-0.691338\pi\) | ||||
−0.565555 | + | 0.824710i | \(0.691338\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −7.65685 | −1.16766 | −0.583830 | − | 0.811876i | \(-0.698446\pi\) | ||||
−0.583830 | + | 0.811876i | \(0.698446\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 6.24264 | 0.910583 | 0.455291 | − | 0.890343i | \(-0.349535\pi\) | ||||
0.455291 | + | 0.890343i | \(0.349535\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −3.65685 | −0.522408 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −5.24264 | −0.720132 | −0.360066 | − | 0.932927i | \(-0.617246\pi\) | ||||
−0.360066 | + | 0.932927i | \(0.617246\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1.41421 | −0.190693 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −13.7279 | −1.78722 | −0.893612 | − | 0.448841i | \(-0.851837\pi\) | ||||
−0.893612 | + | 0.448841i | \(0.851837\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.41421 | 0.181071 | 0.0905357 | − | 0.995893i | \(-0.471142\pi\) | ||||
0.0905357 | + | 0.995893i | \(0.471142\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −0.585786 | −0.0726579 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −15.4853 | −1.89183 | −0.945914 | − | 0.324417i | \(-0.894832\pi\) | ||||
−0.945914 | + | 0.324417i | \(0.894832\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 14.0711 | 1.66993 | 0.834964 | − | 0.550304i | \(-0.185488\pi\) | ||||
0.834964 | + | 0.550304i | \(0.185488\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 2.24264 | 0.262481 | 0.131241 | − | 0.991351i | \(-0.458104\pi\) | ||||
0.131241 | + | 0.991351i | \(0.458104\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 2.58579 | 0.294678 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 16.9706 | 1.90934 | 0.954669 | − | 0.297670i | \(-0.0962096\pi\) | ||||
0.954669 | + | 0.297670i | \(0.0962096\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −2.75736 | −0.302660 | −0.151330 | − | 0.988483i | \(-0.548356\pi\) | ||||
−0.151330 | + | 0.988483i | \(0.548356\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −2.41421 | −0.261858 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 9.17157 | 0.972185 | 0.486092 | − | 0.873907i | \(-0.338422\pi\) | ||||
0.486092 | + | 0.873907i | \(0.338422\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.07107 | 0.112278 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 7.41421 | 0.760682 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 18.1421 | 1.84205 | 0.921027 | − | 0.389498i | \(-0.127351\pi\) | ||||
0.921027 | + | 0.389498i | \(0.127351\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 10.0711 | 1.00211 | 0.501054 | − | 0.865416i | \(-0.332946\pi\) | ||||
0.501054 | + | 0.865416i | \(0.332946\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1.51472 | −0.149250 | −0.0746248 | − | 0.997212i | \(-0.523776\pi\) | ||||
−0.0746248 | + | 0.997212i | \(0.523776\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −3.58579 | −0.346651 | −0.173326 | − | 0.984865i | \(-0.555451\pi\) | ||||
−0.173326 | + | 0.984865i | \(0.555451\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −7.41421 | −0.710153 | −0.355076 | − | 0.934837i | \(-0.615545\pi\) | ||||
−0.355076 | + | 0.934837i | \(0.615545\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −18.8995 | −1.77791 | −0.888957 | − | 0.457990i | \(-0.848570\pi\) | ||||
−0.888957 | + | 0.457990i | \(0.848570\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1.00000 | −0.0932505 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 4.41421 | 0.404650 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −9.00000 | −0.818182 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −19.5563 | −1.73535 | −0.867673 | − | 0.497136i | \(-0.834385\pi\) | ||||
−0.867673 | + | 0.497136i | \(0.834385\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 16.0000 | 1.39793 | 0.698963 | − | 0.715158i | \(-0.253645\pi\) | ||||
0.698963 | + | 0.715158i | \(0.253645\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −13.5563 | −1.17548 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −2.82843 | −0.241649 | −0.120824 | − | 0.992674i | \(-0.538554\pi\) | ||||
−0.120824 | + | 0.992674i | \(0.538554\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −17.4853 | −1.48308 | −0.741541 | − | 0.670907i | \(-0.765905\pi\) | ||||
−0.741541 | + | 0.670907i | \(0.765905\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0.828427 | 0.0692766 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −3.58579 | −0.297783 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 2.24264 | 0.183724 | 0.0918621 | − | 0.995772i | \(-0.470718\pi\) | ||||
0.0918621 | + | 0.995772i | \(0.470718\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −21.3137 | −1.73448 | −0.867242 | − | 0.497886i | \(-0.834110\pi\) | ||||
−0.867242 | + | 0.497886i | \(0.834110\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1.00000 | 0.0803219 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −3.00000 | −0.239426 | −0.119713 | − | 0.992809i | \(-0.538197\pi\) | ||||
−0.119713 | + | 0.992809i | \(0.538197\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1.82843 | 0.144100 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 18.9706 | 1.48589 | 0.742945 | − | 0.669353i | \(-0.233429\pi\) | ||||
0.742945 | + | 0.669353i | \(0.233429\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 1.75736 | 0.135989 | 0.0679943 | − | 0.997686i | \(-0.478340\pi\) | ||||
0.0679943 | + | 0.997686i | \(0.478340\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.6569 | −0.973604 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −21.6569 | −1.64654 | −0.823270 | − | 0.567650i | \(-0.807853\pi\) | ||||
−0.823270 | + | 0.567650i | \(0.807853\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1.82843 | 0.138216 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 19.6569 | 1.46922 | 0.734611 | − | 0.678488i | \(-0.237365\pi\) | ||||
0.734611 | + | 0.678488i | \(0.237365\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −3.51472 | −0.261247 | −0.130623 | − | 0.991432i | \(-0.541698\pi\) | ||||
−0.130623 | + | 0.991432i | \(0.541698\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 7.48528 | 0.550329 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 3.41421 | 0.249672 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −5.75736 | −0.416588 | −0.208294 | − | 0.978066i | \(-0.566791\pi\) | ||||
−0.208294 | + | 0.978066i | \(0.566791\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 18.1421 | 1.30590 | 0.652950 | − | 0.757401i | \(-0.273531\pi\) | ||||
0.652950 | + | 0.757401i | \(0.273531\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 7.17157 | 0.510953 | 0.255477 | − | 0.966815i | \(-0.417768\pi\) | ||||
0.255477 | + | 0.966815i | \(0.417768\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −14.4853 | −1.02683 | −0.513417 | − | 0.858139i | \(-0.671621\pi\) | ||||
−0.513417 | + | 0.858139i | \(0.671621\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 6.55635 | 0.460166 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 7.24264 | 0.505848 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −10.4853 | −0.725282 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 20.7990 | 1.43186 | 0.715931 | − | 0.698171i | \(-0.246003\pi\) | ||||
0.715931 | + | 0.698171i | \(0.246003\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 7.65685 | 0.522193 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1.82843 | −0.124122 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1.41421 | 0.0951303 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −18.9706 | −1.27036 | −0.635181 | − | 0.772363i | \(-0.719075\pi\) | ||||
−0.635181 | + | 0.772363i | \(0.719075\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 0.686292 | 0.0455508 | 0.0227754 | − | 0.999741i | \(-0.492750\pi\) | ||||
0.0227754 | + | 0.999741i | \(0.492750\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −16.4853 | −1.08938 | −0.544689 | − | 0.838638i | \(-0.683352\pi\) | ||||
−0.544689 | + | 0.838638i | \(0.683352\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 5.65685 | 0.370593 | 0.185296 | − | 0.982683i | \(-0.440675\pi\) | ||||
0.185296 | + | 0.982683i | \(0.440675\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −6.24264 | −0.407225 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −4.41421 | −0.285532 | −0.142766 | − | 0.989756i | \(-0.545600\pi\) | ||||
−0.142766 | + | 0.989756i | \(0.545600\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −15.2132 | −0.979969 | −0.489984 | − | 0.871731i | \(-0.662997\pi\) | ||||
−0.489984 | + | 0.871731i | \(0.662997\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 3.65685 | 0.233628 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −4.34315 | −0.276348 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 14.9706 | 0.944934 | 0.472467 | − | 0.881348i | \(-0.343364\pi\) | ||||
0.472467 | + | 0.881348i | \(0.343364\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.41421 | 0.0889108 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 11.4142 | 0.711999 | 0.356000 | − | 0.934486i | \(-0.384140\pi\) | ||||
0.356000 | + | 0.934486i | \(0.384140\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −13.6863 | −0.850425 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −12.4142 | −0.765493 | −0.382747 | − | 0.923853i | \(-0.625022\pi\) | ||||
−0.382747 | + | 0.923853i | \(0.625022\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 5.24264 | 0.322053 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −12.0711 | −0.735986 | −0.367993 | − | 0.929829i | \(-0.619955\pi\) | ||||
−0.367993 | + | 0.929829i | \(0.619955\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 18.3137 | 1.11248 | 0.556239 | − | 0.831022i | \(-0.312244\pi\) | ||||
0.556239 | + | 0.831022i | \(0.312244\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 1.41421 | 0.0852803 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 18.9706 | 1.13983 | 0.569915 | − | 0.821703i | \(-0.306976\pi\) | ||||
0.569915 | + | 0.821703i | \(0.306976\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −3.75736 | −0.224145 | −0.112073 | − | 0.993700i | \(-0.535749\pi\) | ||||
−0.112073 | + | 0.993700i | \(0.535749\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −25.6274 | −1.52339 | −0.761696 | − | 0.647935i | \(-0.775633\pi\) | ||||
−0.761696 | + | 0.647935i | \(0.775633\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −13.2426 | −0.781688 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −11.1716 | −0.657151 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −10.8995 | −0.636755 | −0.318378 | − | 0.947964i | \(-0.603138\pi\) | ||||
−0.318378 | + | 0.947964i | \(0.603138\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 13.7279 | 0.799271 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0.585786 | 0.0338769 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −14.0000 | −0.806947 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −1.41421 | −0.0809776 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 3.89949 | 0.222556 | 0.111278 | − | 0.993789i | \(-0.464506\pi\) | ||||
0.111278 | + | 0.993789i | \(0.464506\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −31.3137 | −1.77564 | −0.887819 | − | 0.460193i | \(-0.847780\pi\) | ||||
−0.887819 | + | 0.460193i | \(0.847780\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 21.1421 | 1.19502 | 0.597512 | − | 0.801860i | \(-0.296156\pi\) | ||||
0.597512 | + | 0.801860i | \(0.296156\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 7.41421 | 0.416424 | 0.208212 | − | 0.978084i | \(-0.433236\pi\) | ||||
0.208212 | + | 0.978084i | \(0.433236\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 5.07107 | 0.283925 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −17.8995 | −0.995955 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0.585786 | 0.0324936 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 11.4142 | 0.629286 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −23.8284 | −1.30973 | −0.654864 | − | 0.755746i | \(-0.727274\pi\) | ||||
−0.654864 | + | 0.755746i | \(0.727274\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 15.4853 | 0.846051 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −8.34315 | −0.454480 | −0.227240 | − | 0.973839i | \(-0.572970\pi\) | ||||
−0.227240 | + | 0.973839i | \(0.572970\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −1.41421 | −0.0765840 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −19.4853 | −1.05211 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −4.48528 | −0.240783 | −0.120391 | − | 0.992727i | \(-0.538415\pi\) | ||||
−0.120391 | + | 0.992727i | \(0.538415\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −15.8284 | −0.847276 | −0.423638 | − | 0.905832i | \(-0.639247\pi\) | ||||
−0.423638 | + | 0.905832i | \(0.639247\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 22.0416 | 1.17316 | 0.586579 | − | 0.809892i | \(-0.300474\pi\) | ||||
0.586579 | + | 0.809892i | \(0.300474\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −14.0711 | −0.746815 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 5.07107 | 0.267641 | 0.133820 | − | 0.991006i | \(-0.457275\pi\) | ||||
0.133820 | + | 0.991006i | \(0.457275\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 35.9706 | 1.89319 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −2.24264 | −0.117385 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 3.00000 | 0.156599 | 0.0782994 | − | 0.996930i | \(-0.475051\pi\) | ||||
0.0782994 | + | 0.996930i | \(0.475051\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −9.58579 | −0.497669 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 17.6569 | 0.914237 | 0.457119 | − | 0.889406i | \(-0.348881\pi\) | ||||
0.457119 | + | 0.889406i | \(0.348881\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 2.10051 | 0.108182 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −14.3431 | −0.736758 | −0.368379 | − | 0.929676i | \(-0.620087\pi\) | ||||
−0.368379 | + | 0.929676i | \(0.620087\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −13.7279 | −0.701464 | −0.350732 | − | 0.936476i | \(-0.614067\pi\) | ||||
−0.350732 | + | 0.936476i | \(0.614067\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −2.58579 | −0.131784 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 19.4558 | 0.986450 | 0.493225 | − | 0.869902i | \(-0.335818\pi\) | ||||
0.493225 | + | 0.869902i | \(0.335818\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2.41421 | 0.122092 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −16.9706 | −0.853882 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −21.6569 | −1.08693 | −0.543463 | − | 0.839433i | \(-0.682887\pi\) | ||||
−0.543463 | + | 0.839433i | \(0.682887\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −38.4853 | −1.92186 | −0.960932 | − | 0.276786i | \(-0.910731\pi\) | ||||
−0.960932 | + | 0.276786i | \(0.910731\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −0.585786 | −0.0291801 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −10.5858 | −0.524718 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 19.8284 | 0.980453 | 0.490226 | − | 0.871595i | \(-0.336914\pi\) | ||||
0.490226 | + | 0.871595i | \(0.336914\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −25.1005 | −1.23512 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 2.75736 | 0.135353 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −35.3553 | −1.72722 | −0.863611 | − | 0.504159i | \(-0.831802\pi\) | ||||
−0.863611 | + | 0.504159i | \(0.831802\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 32.8701 | 1.60199 | 0.800994 | − | 0.598672i | \(-0.204305\pi\) | ||||
0.800994 | + | 0.598672i | \(0.204305\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 2.41421 | 0.117107 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 2.58579 | 0.125135 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −28.4853 | −1.37209 | −0.686044 | − | 0.727560i | \(-0.740654\pi\) | ||||
−0.686044 | + | 0.727560i | \(0.740654\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 3.68629 | 0.177152 | 0.0885759 | − | 0.996069i | \(-0.471768\pi\) | ||||
0.0885759 | + | 0.996069i | \(0.471768\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −7.41421 | −0.354670 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −33.7990 | −1.61314 | −0.806569 | − | 0.591140i | \(-0.798678\pi\) | ||||
−0.806569 | + | 0.591140i | \(0.798678\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −15.8995 | −0.755408 | −0.377704 | − | 0.925926i | \(-0.623286\pi\) | ||||
−0.377704 | + | 0.925926i | \(0.623286\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −9.17157 | −0.434774 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −1.10051 | −0.0519360 | −0.0259680 | − | 0.999663i | \(-0.508267\pi\) | ||||
−0.0259680 | + | 0.999663i | \(0.508267\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −10.2426 | −0.482307 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −1.07107 | −0.0502124 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −10.4558 | −0.489104 | −0.244552 | − | 0.969636i | \(-0.578641\pi\) | ||||
−0.244552 | + | 0.969636i | \(0.578641\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 27.4558 | 1.27875 | 0.639373 | − | 0.768897i | \(-0.279194\pi\) | ||||
0.639373 | + | 0.768897i | \(0.279194\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 22.0416 | 1.02436 | 0.512181 | − | 0.858878i | \(-0.328838\pi\) | ||||
0.512181 | + | 0.858878i | \(0.328838\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −11.5858 | −0.536126 | −0.268063 | − | 0.963401i | \(-0.586384\pi\) | ||||
−0.268063 | + | 0.963401i | \(0.586384\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −28.3137 | −1.30741 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −10.8284 | −0.497892 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −7.41421 | −0.340187 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −20.1005 | −0.918416 | −0.459208 | − | 0.888329i | \(-0.651867\pi\) | ||||
−0.459208 | + | 0.888329i | \(0.651867\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −4.38478 | −0.199929 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −18.1421 | −0.823792 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 31.0711 | 1.40796 | 0.703982 | − | 0.710218i | \(-0.251403\pi\) | ||||
0.703982 | + | 0.710218i | \(0.251403\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −23.1005 | −1.04251 | −0.521256 | − | 0.853401i | \(-0.674536\pi\) | ||||
−0.521256 | + | 0.853401i | \(0.674536\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 8.65685 | 0.389885 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 25.7279 | 1.15406 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −24.4558 | −1.09479 | −0.547397 | − | 0.836873i | \(-0.684381\pi\) | ||||
−0.547397 | + | 0.836873i | \(0.684381\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −20.7574 | −0.925525 | −0.462762 | − | 0.886482i | \(-0.653142\pi\) | ||||
−0.462762 | + | 0.886482i | \(0.653142\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −10.0711 | −0.448157 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 20.4853 | 0.907994 | 0.453997 | − | 0.891003i | \(-0.349998\pi\) | ||||
0.453997 | + | 0.891003i | \(0.349998\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 4.10051 | 0.181396 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 1.51472 | 0.0667465 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 8.82843 | 0.388274 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 24.7279 | 1.08335 | 0.541675 | − | 0.840588i | \(-0.317790\pi\) | ||||
0.541675 | + | 0.840588i | \(0.317790\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −20.0000 | −0.874539 | −0.437269 | − | 0.899331i | \(-0.644054\pi\) | ||||
−0.437269 | + | 0.899331i | \(0.644054\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −2.41421 | −0.105165 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −4.24264 | −0.183769 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 3.58579 | 0.155027 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −5.17157 | −0.222755 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −43.1127 | −1.85356 | −0.926780 | − | 0.375605i | \(-0.877435\pi\) | ||||
−0.926780 | + | 0.375605i | \(0.877435\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 7.41421 | 0.317590 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 6.34315 | 0.271213 | 0.135607 | − | 0.990763i | \(-0.456702\pi\) | ||||
0.135607 | + | 0.990763i | \(0.456702\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −26.5858 | −1.13259 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 31.0294 | 1.31951 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −33.5269 | −1.42058 | −0.710290 | − | 0.703909i | \(-0.751436\pi\) | ||||
−0.710290 | + | 0.703909i | \(0.751436\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −4.48528 | −0.189707 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 43.5858 | 1.83692 | 0.918461 | − | 0.395512i | \(-0.129433\pi\) | ||||
0.918461 | + | 0.395512i | \(0.129433\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 18.8995 | 0.795108 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −18.4853 | −0.774943 | −0.387472 | − | 0.921882i | \(-0.626651\pi\) | ||||
−0.387472 | + | 0.921882i | \(0.626651\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −1.89949 | −0.0794914 | −0.0397457 | − | 0.999210i | \(-0.512655\pi\) | ||||
−0.0397457 | + | 0.999210i | \(0.512655\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1.00000 | 0.0417029 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 24.2843 | 1.01097 | 0.505484 | − | 0.862836i | \(-0.331314\pi\) | ||||
0.505484 | + | 0.862836i | \(0.331314\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −5.04163 | −0.209162 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −7.41421 | −0.307065 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −36.6274 | −1.51178 | −0.755888 | − | 0.654701i | \(-0.772794\pi\) | ||||
−0.755888 | + | 0.654701i | \(0.772794\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 7.41421 | 0.305497 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 6.92893 | 0.284537 | 0.142269 | − | 0.989828i | \(-0.454560\pi\) | ||||
0.142269 | + | 0.989828i | \(0.454560\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −4.41421 | −0.180965 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 18.1421 | 0.741268 | 0.370634 | − | 0.928779i | \(-0.379141\pi\) | ||||
0.370634 | + | 0.928779i | \(0.379141\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 22.6569 | 0.924192 | 0.462096 | − | 0.886830i | \(-0.347097\pi\) | ||||
0.462096 | + | 0.886830i | \(0.347097\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 9.00000 | 0.365902 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −12.7279 | −0.516610 | −0.258305 | − | 0.966063i | \(-0.583164\pi\) | ||||
−0.258305 | + | 0.966063i | \(0.583164\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 3.65685 | 0.147940 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −4.62742 | −0.186900 | −0.0934498 | − | 0.995624i | \(-0.529789\pi\) | ||||
−0.0934498 | + | 0.995624i | \(0.529789\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −17.2426 | −0.694163 | −0.347081 | − | 0.937835i | \(-0.612827\pi\) | ||||
−0.347081 | + | 0.937835i | \(0.612827\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 16.2843 | 0.654520 | 0.327260 | − | 0.944934i | \(-0.393875\pi\) | ||||
0.327260 | + | 0.944934i | \(0.393875\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 16.7696 | 0.671858 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −18.0711 | −0.720541 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1.41421 | 0.0562990 | 0.0281495 | − | 0.999604i | \(-0.491039\pi\) | ||||
0.0281495 | + | 0.999604i | \(0.491039\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 19.5563 | 0.776070 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −2.14214 | −0.0848745 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 21.4142 | 0.845811 | 0.422905 | − | 0.906174i | \(-0.361010\pi\) | ||||
0.422905 | + | 0.906174i | \(0.361010\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 31.3431 | 1.23605 | 0.618027 | − | 0.786157i | \(-0.287932\pi\) | ||||
0.618027 | + | 0.786157i | \(0.287932\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 2.38478 | 0.0937552 | 0.0468776 | − | 0.998901i | \(-0.485073\pi\) | ||||
0.0468776 | + | 0.998901i | \(0.485073\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −19.4142 | −0.762075 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 16.7279 | 0.654614 | 0.327307 | − | 0.944918i | \(-0.393859\pi\) | ||||
0.327307 | + | 0.944918i | \(0.393859\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −16.0000 | −0.625172 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 6.38478 | 0.248716 | 0.124358 | − | 0.992237i | \(-0.460313\pi\) | ||||
0.124358 | + | 0.992237i | \(0.460313\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 13.1127 | 0.510025 | 0.255012 | − | 0.966938i | \(-0.417920\pi\) | ||||
0.255012 | + | 0.966938i | \(0.417920\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 13.5563 | 0.525693 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 3.58579 | 0.138842 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 2.00000 | 0.0772091 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 7.27208 | 0.280318 | 0.140159 | − | 0.990129i | \(-0.455239\pi\) | ||||
0.140159 | + | 0.990129i | \(0.455239\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 43.1838 | 1.65969 | 0.829843 | − | 0.557996i | \(-0.188430\pi\) | ||||
0.829843 | + | 0.557996i | \(0.188430\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 33.1716 | 1.27301 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −43.0122 | −1.64582 | −0.822908 | − | 0.568175i | \(-0.807650\pi\) | ||||
−0.822908 | + | 0.568175i | \(0.807650\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 2.82843 | 0.108069 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −3.07107 | −0.116998 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −14.9706 | −0.569507 | −0.284754 | − | 0.958601i | \(-0.591912\pi\) | ||||
−0.284754 | + | 0.958601i | \(0.591912\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 17.4853 | 0.663255 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −17.4853 | −0.662302 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −49.5563 | −1.87172 | −0.935859 | − | 0.352375i | \(-0.885374\pi\) | ||||
−0.935859 | + | 0.352375i | \(0.885374\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 55.4975 | 2.09313 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 18.4142 | 0.692538 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 17.6985 | 0.664681 | 0.332340 | − | 0.943160i | \(-0.392162\pi\) | ||||
0.332340 | + | 0.943160i | \(0.392162\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −1.00000 | −0.0374503 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −0.828427 | −0.0309814 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −32.5563 | −1.21415 | −0.607073 | − | 0.794646i | \(-0.707657\pi\) | ||||
−0.607073 | + | 0.794646i | \(0.707657\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −2.76955 | −0.103144 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 3.58579 | 0.133173 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 9.00000 | 0.333792 | 0.166896 | − | 0.985975i | \(-0.446626\pi\) | ||||
0.166896 | + | 0.985975i | \(0.446626\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −18.4853 | −0.683703 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 16.3137 | 0.602561 | 0.301280 | − | 0.953536i | \(-0.402586\pi\) | ||||
0.301280 | + | 0.953536i | \(0.402586\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −21.8995 | −0.806678 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 17.1421 | 0.630584 | 0.315292 | − | 0.948995i | \(-0.397898\pi\) | ||||
0.315292 | + | 0.948995i | \(0.397898\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −4.00000 | −0.146746 | −0.0733729 | − | 0.997305i | \(-0.523376\pi\) | ||||
−0.0733729 | + | 0.997305i | \(0.523376\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −2.24264 | −0.0821640 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −6.55635 | −0.239564 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −45.0711 | −1.64467 | −0.822333 | − | 0.569006i | \(-0.807328\pi\) | ||||
−0.822333 | + | 0.569006i | \(0.807328\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 21.3137 | 0.775685 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −1.82843 | −0.0664553 | −0.0332277 | − | 0.999448i | \(-0.510579\pi\) | ||||
−0.0332277 | + | 0.999448i | \(0.510579\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 23.9289 | 0.867423 | 0.433712 | − | 0.901052i | \(-0.357204\pi\) | ||||
0.433712 | + | 0.901052i | \(0.357204\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −13.5563 | −0.490773 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −8.04163 | −0.290366 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −15.2721 | −0.550725 | −0.275363 | − | 0.961340i | \(-0.588798\pi\) | ||||
−0.275363 | + | 0.961340i | \(0.588798\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 13.7990 | 0.496315 | 0.248158 | − | 0.968720i | \(-0.420175\pi\) | ||||
0.248158 | + | 0.968720i | \(0.420175\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −1.00000 | −0.0359211 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 53.6985 | 1.92395 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 19.8995 | 0.712060 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 3.00000 | 0.107075 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −19.2843 | −0.687410 | −0.343705 | − | 0.939078i | \(-0.611682\pi\) | ||||
−0.343705 | + | 0.939078i | \(0.611682\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −34.5563 | −1.22868 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0.828427 | 0.0294183 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 34.8995 | 1.23620 | 0.618102 | − | 0.786098i | \(-0.287902\pi\) | ||||
0.618102 | + | 0.786098i | \(0.287902\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 15.0711 | 0.533176 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 3.17157 | 0.111922 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −1.82843 | −0.0644436 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −29.7279 | −1.04518 | −0.522589 | − | 0.852585i | \(-0.675034\pi\) | ||||
−0.522589 | + | 0.852585i | \(0.675034\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −5.14214 | −0.180565 | −0.0902824 | − | 0.995916i | \(-0.528777\pi\) | ||||
−0.0902824 | + | 0.995916i | \(0.528777\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −18.9706 | −0.664510 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 56.7696 | 1.98612 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −33.4558 | −1.16762 | −0.583809 | − | 0.811891i | \(-0.698438\pi\) | ||||
−0.583809 | + | 0.811891i | \(0.698438\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −53.6569 | −1.87036 | −0.935180 | − | 0.354172i | \(-0.884763\pi\) | ||||
−0.935180 | + | 0.354172i | \(0.884763\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −2.27208 | −0.0790079 | −0.0395039 | − | 0.999219i | \(-0.512578\pi\) | ||||
−0.0395039 | + | 0.999219i | \(0.512578\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −7.82843 | −0.271893 | −0.135946 | − | 0.990716i | \(-0.543407\pi\) | ||||
−0.135946 | + | 0.990716i | \(0.543407\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −8.82843 | −0.305887 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −1.75736 | −0.0608159 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −28.3431 | −0.978514 | −0.489257 | − | 0.872140i | \(-0.662732\pi\) | ||||
−0.489257 | + | 0.872140i | \(0.662732\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −16.1421 | −0.556625 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 12.6569 | 0.435409 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −16.4558 | −0.565429 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −7.48528 | −0.256592 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 6.48528 | 0.222052 | 0.111026 | − | 0.993818i | \(-0.464586\pi\) | ||||
0.111026 | + | 0.993818i | \(0.464586\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 30.6863 | 1.04822 | 0.524112 | − | 0.851649i | \(-0.324397\pi\) | ||||
0.524112 | + | 0.851649i | \(0.324397\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −53.8284 | −1.83660 | −0.918301 | − | 0.395883i | \(-0.870439\pi\) | ||||
−0.918301 | + | 0.395883i | \(0.870439\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −46.4853 | −1.58238 | −0.791189 | − | 0.611572i | \(-0.790537\pi\) | ||||
−0.791189 | + | 0.611572i | \(0.790537\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 21.6569 | 0.736355 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 24.0000 | 0.814144 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −9.07107 | −0.307361 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −1.82843 | −0.0618121 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −7.17157 | −0.242167 | −0.121083 | − | 0.992642i | \(-0.538637\pi\) | ||||
−0.121083 | + | 0.992642i | \(0.538637\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 10.9289 | 0.368205 | 0.184103 | − | 0.982907i | \(-0.441062\pi\) | ||||
0.184103 | + | 0.982907i | \(0.441062\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −32.9289 | −1.10815 | −0.554073 | − | 0.832468i | \(-0.686927\pi\) | ||||
−0.554073 | + | 0.832468i | \(0.686927\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 4.82843 | 0.162123 | 0.0810614 | − | 0.996709i | \(-0.474169\pi\) | ||||
0.0810614 | + | 0.996709i | \(0.474169\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −35.7574 | −1.19926 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −46.2843 | −1.54884 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −19.6569 | −0.657056 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −3.58579 | −0.119593 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −12.6569 | −0.421661 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 3.51472 | 0.116833 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 18.1716 | 0.603377 | 0.301689 | − | 0.953407i | \(-0.402450\pi\) | ||||
0.301689 | + | 0.953407i | \(0.402450\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −28.9706 | −0.959838 | −0.479919 | − | 0.877313i | \(-0.659334\pi\) | ||||
−0.479919 | + | 0.877313i | \(0.659334\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −3.89949 | −0.129054 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 29.2548 | 0.966080 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 24.2843 | 0.801064 | 0.400532 | − | 0.916283i | \(-0.368825\pi\) | ||||
0.400532 | + | 0.916283i | \(0.368825\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 8.24264 | 0.271310 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −7.48528 | −0.246115 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 32.7574 | 1.07473 | 0.537367 | − | 0.843348i | \(-0.319419\pi\) | ||||
0.537367 | + | 0.843348i | \(0.319419\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 27.1127 | 0.888583 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −3.41421 | −0.111657 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 16.4853 | 0.538551 | 0.269275 | − | 0.963063i | \(-0.413216\pi\) | ||||
0.269275 | + | 0.963063i | \(0.413216\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −6.52691 | −0.212771 | −0.106386 | − | 0.994325i | \(-0.533928\pi\) | ||||
−0.106386 | + | 0.994325i | \(0.533928\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −7.24264 | −0.235853 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 28.4853 | 0.925647 | 0.462824 | − | 0.886450i | \(-0.346836\pi\) | ||||
0.462824 | + | 0.886450i | \(0.346836\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1.31371 | 0.0426448 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 4.62742 | 0.149897 | 0.0749484 | − | 0.997187i | \(-0.476121\pi\) | ||||
0.0749484 | + | 0.997187i | \(0.476121\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 5.75736 | 0.186304 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −5.17157 | −0.166999 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.0000 | −0.967742 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −18.1421 | −0.584016 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 42.3848 | 1.36300 | 0.681501 | − | 0.731817i | \(-0.261327\pi\) | ||||
0.681501 | + | 0.731817i | \(0.261327\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 34.4264 | 1.10480 | 0.552398 | − | 0.833581i | \(-0.313713\pi\) | ||||
0.552398 | + | 0.833581i | \(0.313713\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −31.9706 | −1.02493 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 49.8701 | 1.59548 | 0.797742 | − | 0.602999i | \(-0.206028\pi\) | ||||
0.797742 | + | 0.602999i | \(0.206028\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 12.9706 | 0.414541 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 37.5269 | 1.19692 | 0.598461 | − | 0.801152i | \(-0.295779\pi\) | ||||
0.598461 | + | 0.801152i | \(0.295779\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −7.17157 | −0.228505 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −7.65685 | −0.243474 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 50.4558 | 1.60278 | 0.801391 | − | 0.598140i | \(-0.204093\pi\) | ||||
0.801391 | + | 0.598140i | \(0.204093\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 14.4853 | 0.459214 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 19.5147 | 0.618037 | 0.309019 | − | 0.951056i | \(-0.399999\pi\) | ||||
0.309019 | + | 0.951056i | \(0.399999\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(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 | 8280.2.a.x.1.2 | 2 | ||
3.2 | odd | 2 | 2760.2.a.n.1.2 | ✓ | 2 | ||
12.11 | even | 2 | 5520.2.a.bt.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2760.2.a.n.1.2 | ✓ | 2 | 3.2 | odd | 2 | ||
5520.2.a.bt.1.1 | 2 | 12.11 | even | 2 | |||
8280.2.a.x.1.2 | 2 | 1.1 | even | 1 | trivial |