Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2760,2,Mod(1,2760)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2760, 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("2760.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2760 = 2^{3} \cdot 3 \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2760.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: | \(22.0387109579\) |
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: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(1.41421\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2760.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.82843 | 0.691080 | 0.345540 | − | 0.938404i | \(-0.387696\pi\) | ||||
0.345540 | + | 0.938404i | \(0.387696\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.41421 | −0.426401 | −0.213201 | − | 0.977008i | \(-0.568389\pi\) | ||||
−0.213201 | + | 0.977008i | \(0.568389\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.585786 | 0.162468 | 0.0812340 | − | 0.996695i | \(-0.474114\pi\) | ||||
0.0812340 | + | 0.996695i | \(0.474114\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.00000 | −0.258199 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −2.41421 | −0.585533 | −0.292766 | − | 0.956184i | \(-0.594576\pi\) | ||||
−0.292766 | + | 0.956184i | \(0.594576\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −7.41421 | −1.70094 | −0.850469 | − | 0.526026i | \(-0.823682\pi\) | ||||
−0.850469 | + | 0.526026i | \(0.823682\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.82843 | −0.398996 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.00000 | −0.208514 | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −3.58579 | −0.665864 | −0.332932 | − | 0.942951i | \(-0.608038\pi\) | ||||
−0.332932 | + | 0.942951i | \(0.608038\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.00000 | −0.179605 | −0.0898027 | − | 0.995960i | \(-0.528624\pi\) | ||||
−0.0898027 | + | 0.995960i | \(0.528624\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 1.41421 | 0.246183 | ||||||||
\(34\) | 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 | ||||||||
\(39\) | −0.585786 | −0.0938009 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 7.24264 | 1.13111 | 0.565555 | − | 0.824710i | \(-0.308662\pi\) | ||||
0.565555 | + | 0.824710i | \(0.308662\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −7.65685 | −1.16766 | −0.583830 | − | 0.811876i | \(-0.698446\pi\) | ||||
−0.583830 | + | 0.811876i | \(0.698446\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1.00000 | 0.149071 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −6.24264 | −0.910583 | −0.455291 | − | 0.890343i | \(-0.650465\pi\) | ||||
−0.455291 | + | 0.890343i | \(0.650465\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −3.65685 | −0.522408 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 2.41421 | 0.338058 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 5.24264 | 0.720132 | 0.360066 | − | 0.932927i | \(-0.382754\pi\) | ||||
0.360066 | + | 0.932927i | \(0.382754\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1.41421 | −0.190693 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 7.41421 | 0.982037 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 13.7279 | 1.78722 | 0.893612 | − | 0.448841i | \(-0.148163\pi\) | ||||
0.893612 | + | 0.448841i | \(0.148163\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.41421 | 0.181071 | 0.0905357 | − | 0.995893i | \(-0.471142\pi\) | ||||
0.0905357 | + | 0.995893i | \(0.471142\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 1.82843 | 0.230360 | ||||||||
\(64\) | 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 | ||||||||
\(69\) | 1.00000 | 0.120386 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −14.0711 | −1.66993 | −0.834964 | − | 0.550304i | \(-0.814512\pi\) | ||||
−0.834964 | + | 0.550304i | \(0.814512\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 2.24264 | 0.262481 | 0.131241 | − | 0.991351i | \(-0.458104\pi\) | ||||
0.131241 | + | 0.991351i | \(0.458104\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −1.00000 | −0.115470 | ||||||||
\(76\) | 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 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 2.75736 | 0.302660 | 0.151330 | − | 0.988483i | \(-0.451644\pi\) | ||||
0.151330 | + | 0.988483i | \(0.451644\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −2.41421 | −0.261858 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 3.58579 | 0.384437 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −9.17157 | −0.972185 | −0.486092 | − | 0.873907i | \(-0.661578\pi\) | ||||
−0.486092 | + | 0.873907i | \(0.661578\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.07107 | 0.112278 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 1.00000 | 0.103695 | ||||||||
\(94\) | 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 | ||||||||
\(99\) | −1.41421 | −0.142134 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −10.0711 | −1.00211 | −0.501054 | − | 0.865416i | \(-0.667054\pi\) | ||||
−0.501054 | + | 0.865416i | \(0.667054\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1.51472 | −0.149250 | −0.0746248 | − | 0.997212i | \(-0.523776\pi\) | ||||
−0.0746248 | + | 0.997212i | \(0.523776\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −1.82843 | −0.178436 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 3.58579 | 0.346651 | 0.173326 | − | 0.984865i | \(-0.444549\pi\) | ||||
0.173326 | + | 0.984865i | \(0.444549\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −7.41421 | −0.710153 | −0.355076 | − | 0.934837i | \(-0.615545\pi\) | ||||
−0.355076 | + | 0.934837i | \(0.615545\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 7.48528 | 0.710471 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 18.8995 | 1.77791 | 0.888957 | − | 0.457990i | \(-0.151430\pi\) | ||||
0.888957 | + | 0.457990i | \(0.151430\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1.00000 | −0.0932505 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0.585786 | 0.0541560 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −4.41421 | −0.404650 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −9.00000 | −0.818182 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −7.24264 | −0.653047 | ||||||||
\(124\) | 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 | ||||||||
\(129\) | 7.65685 | 0.674148 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −16.0000 | −1.39793 | −0.698963 | − | 0.715158i | \(-0.746355\pi\) | ||||
−0.698963 | + | 0.715158i | \(0.746355\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −13.5563 | −1.17548 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −1.00000 | −0.0860663 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 2.82843 | 0.241649 | 0.120824 | − | 0.992674i | \(-0.461446\pi\) | ||||
0.120824 | + | 0.992674i | \(0.461446\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −17.4853 | −1.48308 | −0.741541 | − | 0.670907i | \(-0.765905\pi\) | ||||
−0.741541 | + | 0.670907i | \(0.765905\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 6.24264 | 0.525725 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −0.828427 | −0.0692766 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −3.58579 | −0.297783 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 3.65685 | 0.301612 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −2.24264 | −0.183724 | −0.0918621 | − | 0.995772i | \(-0.529282\pi\) | ||||
−0.0918621 | + | 0.995772i | \(0.529282\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −21.3137 | −1.73448 | −0.867242 | − | 0.497886i | \(-0.834110\pi\) | ||||
−0.867242 | + | 0.497886i | \(0.834110\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −2.41421 | −0.195178 | ||||||||
\(154\) | 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 | ||||||||
\(159\) | −5.24264 | −0.415768 | ||||||||
\(160\) | 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 | ||||||||
\(165\) | 1.41421 | 0.110096 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −1.75736 | −0.135989 | −0.0679943 | − | 0.997686i | \(-0.521660\pi\) | ||||
−0.0679943 | + | 0.997686i | \(0.521660\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.6569 | −0.973604 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −7.41421 | −0.566979 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 21.6569 | 1.64654 | 0.823270 | − | 0.567650i | \(-0.192147\pi\) | ||||
0.823270 | + | 0.567650i | \(0.192147\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1.82843 | 0.138216 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −13.7279 | −1.03185 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −19.6569 | −1.46922 | −0.734611 | − | 0.678488i | \(-0.762635\pi\) | ||||
−0.734611 | + | 0.678488i | \(0.762635\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −3.51472 | −0.261247 | −0.130623 | − | 0.991432i | \(-0.541698\pi\) | ||||
−0.130623 | + | 0.991432i | \(0.541698\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −1.41421 | −0.104542 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −7.48528 | −0.550329 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 3.41421 | 0.249672 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −1.82843 | −0.132999 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 5.75736 | 0.416588 | 0.208294 | − | 0.978066i | \(-0.433209\pi\) | ||||
0.208294 | + | 0.978066i | \(0.433209\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 18.1421 | 1.30590 | 0.652950 | − | 0.757401i | \(-0.273531\pi\) | ||||
0.652950 | + | 0.757401i | \(0.273531\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −0.585786 | −0.0419490 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −7.17157 | −0.510953 | −0.255477 | − | 0.966815i | \(-0.582232\pi\) | ||||
−0.255477 | + | 0.966815i | \(0.582232\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −14.4853 | −1.02683 | −0.513417 | − | 0.858139i | \(-0.671621\pi\) | ||||
−0.513417 | + | 0.858139i | \(0.671621\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 15.4853 | 1.09225 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −6.55635 | −0.460166 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 7.24264 | 0.505848 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −1.00000 | −0.0695048 | ||||||||
\(208\) | 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 | ||||||||
\(213\) | 14.0711 | 0.964134 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −7.65685 | −0.522193 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1.82843 | −0.124122 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −2.24264 | −0.151544 | ||||||||
\(220\) | 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 | ||||||||
\(225\) | 1.00000 | 0.0666667 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −0.686292 | −0.0455508 | −0.0227754 | − | 0.999741i | \(-0.507250\pi\) | ||||
−0.0227754 | + | 0.999741i | \(0.507250\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −16.4853 | −1.08938 | −0.544689 | − | 0.838638i | \(-0.683352\pi\) | ||||
−0.544689 | + | 0.838638i | \(0.683352\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 2.58579 | 0.170132 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −5.65685 | −0.370593 | −0.185296 | − | 0.982683i | \(-0.559325\pi\) | ||||
−0.185296 | + | 0.982683i | \(0.559325\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −6.24264 | −0.407225 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −16.9706 | −1.10236 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 4.41421 | 0.285532 | 0.142766 | − | 0.989756i | \(-0.454400\pi\) | ||||
0.142766 | + | 0.989756i | \(0.454400\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −15.2132 | −0.979969 | −0.489984 | − | 0.871731i | \(-0.662997\pi\) | ||||
−0.489984 | + | 0.871731i | \(0.662997\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −3.65685 | −0.233628 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −4.34315 | −0.276348 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −2.75736 | −0.174741 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −14.9706 | −0.944934 | −0.472467 | − | 0.881348i | \(-0.656636\pi\) | ||||
−0.472467 | + | 0.881348i | \(0.656636\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.41421 | 0.0889108 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 2.41421 | 0.151184 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −11.4142 | −0.711999 | −0.356000 | − | 0.934486i | \(-0.615860\pi\) | ||||
−0.356000 | + | 0.934486i | \(0.615860\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −13.6863 | −0.850425 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −3.58579 | −0.221955 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 12.4142 | 0.765493 | 0.382747 | − | 0.923853i | \(-0.374978\pi\) | ||||
0.382747 | + | 0.923853i | \(0.374978\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 5.24264 | 0.322053 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 9.17157 | 0.561291 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 12.0711 | 0.735986 | 0.367993 | − | 0.929829i | \(-0.380045\pi\) | ||||
0.367993 | + | 0.929829i | \(0.380045\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 18.3137 | 1.11248 | 0.556239 | − | 0.831022i | \(-0.312244\pi\) | ||||
0.556239 | + | 0.831022i | \(0.312244\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −1.07107 | −0.0648240 | ||||||||
\(274\) | 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 | ||||||||
\(279\) | −1.00000 | −0.0598684 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 3.75736 | 0.224145 | 0.112073 | − | 0.993700i | \(-0.464251\pi\) | ||||
0.112073 | + | 0.993700i | \(0.464251\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −25.6274 | −1.52339 | −0.761696 | − | 0.647935i | \(-0.775633\pi\) | ||||
−0.761696 | + | 0.647935i | \(0.775633\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 7.41421 | 0.439180 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 13.2426 | 0.781688 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −11.1716 | −0.657151 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −18.1421 | −1.06351 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 10.8995 | 0.636755 | 0.318378 | − | 0.947964i | \(-0.396862\pi\) | ||||
0.318378 | + | 0.947964i | \(0.396862\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 13.7279 | 0.799271 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 1.41421 | 0.0820610 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −0.585786 | −0.0338769 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −14.0000 | −0.806947 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 10.0711 | 0.578568 | ||||||||
\(304\) | 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 | ||||||||
\(309\) | 1.51472 | 0.0861693 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 31.3137 | 1.77564 | 0.887819 | − | 0.460193i | \(-0.152220\pi\) | ||||
0.887819 | + | 0.460193i | \(0.152220\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 21.1421 | 1.19502 | 0.597512 | − | 0.801860i | \(-0.296156\pi\) | ||||
0.597512 | + | 0.801860i | \(0.296156\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 1.82843 | 0.103020 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −7.41421 | −0.416424 | −0.208212 | − | 0.978084i | \(-0.566764\pi\) | ||||
−0.208212 | + | 0.978084i | \(0.566764\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 5.07107 | 0.283925 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −3.58579 | −0.200139 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 17.8995 | 0.995955 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0.585786 | 0.0324936 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 7.41421 | 0.410007 | ||||||||
\(328\) | 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 | ||||||||
\(333\) | −7.48528 | −0.410191 | ||||||||
\(334\) | 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 | ||||||||
\(339\) | −18.8995 | −1.02648 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1.41421 | 0.0765840 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −19.4853 | −1.05211 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 1.00000 | 0.0538382 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 4.48528 | 0.240783 | 0.120391 | − | 0.992727i | \(-0.461585\pi\) | ||||
0.120391 | + | 0.992727i | \(0.461585\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −15.8284 | −0.847276 | −0.423638 | − | 0.905832i | \(-0.639247\pi\) | ||||
−0.423638 | + | 0.905832i | \(0.639247\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −0.585786 | −0.0312670 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −22.0416 | −1.17316 | −0.586579 | − | 0.809892i | \(-0.699526\pi\) | ||||
−0.586579 | + | 0.809892i | \(0.699526\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −14.0711 | −0.746815 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 4.41421 | 0.233625 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −5.07107 | −0.267641 | −0.133820 | − | 0.991006i | \(-0.542725\pi\) | ||||
−0.133820 | + | 0.991006i | \(0.542725\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 35.9706 | 1.89319 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 9.00000 | 0.472377 | ||||||||
\(364\) | 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 | ||||||||
\(369\) | 7.24264 | 0.377037 | ||||||||
\(370\) | 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 | ||||||||
\(375\) | −1.00000 | −0.0516398 | ||||||||
\(376\) | 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 | ||||||||
\(381\) | 19.5563 | 1.00190 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 13.7279 | 0.701464 | 0.350732 | − | 0.936476i | \(-0.385933\pi\) | ||||
0.350732 | + | 0.936476i | \(0.385933\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −2.58579 | −0.131784 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −7.65685 | −0.389220 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −19.4558 | −0.986450 | −0.493225 | − | 0.869902i | \(-0.664182\pi\) | ||||
−0.493225 | + | 0.869902i | \(0.664182\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2.41421 | 0.122092 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 16.0000 | 0.807093 | ||||||||
\(394\) | 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 | ||||||||
\(399\) | 13.5563 | 0.678666 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 38.4853 | 1.92186 | 0.960932 | − | 0.276786i | \(-0.0892693\pi\) | ||||
0.960932 | + | 0.276786i | \(0.0892693\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −0.585786 | −0.0291801 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 1.00000 | 0.0496904 | ||||||||
\(406\) | 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 | ||||||||
\(411\) | −2.82843 | −0.139516 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 25.1005 | 1.23512 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 2.75736 | 0.135353 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 17.4853 | 0.856258 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 35.3553 | 1.72722 | 0.863611 | − | 0.504159i | \(-0.168198\pi\) | ||||
0.863611 | + | 0.504159i | \(0.168198\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 32.8701 | 1.60199 | 0.800994 | − | 0.598672i | \(-0.204305\pi\) | ||||
0.800994 | + | 0.598672i | \(0.204305\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −6.24264 | −0.303528 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −2.41421 | −0.117107 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 2.58579 | 0.125135 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0.828427 | 0.0399968 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 28.4853 | 1.37209 | 0.686044 | − | 0.727560i | \(-0.259346\pi\) | ||||
0.686044 | + | 0.727560i | \(0.259346\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 3.68629 | 0.177152 | 0.0885759 | − | 0.996069i | \(-0.471768\pi\) | ||||
0.0885759 | + | 0.996069i | \(0.471768\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 3.58579 | 0.171925 | ||||||||
\(436\) | 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 | ||||||||
\(441\) | −3.65685 | −0.174136 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 15.8995 | 0.755408 | 0.377704 | − | 0.925926i | \(-0.376714\pi\) | ||||
0.377704 | + | 0.925926i | \(0.376714\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −9.17157 | −0.434774 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 2.24264 | 0.106073 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 1.10051 | 0.0519360 | 0.0259680 | − | 0.999663i | \(-0.491733\pi\) | ||||
0.0259680 | + | 0.999663i | \(0.491733\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −10.2426 | −0.482307 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 21.3137 | 1.00141 | ||||||||
\(454\) | 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 | ||||||||
\(459\) | 2.41421 | 0.112686 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −27.4558 | −1.27875 | −0.639373 | − | 0.768897i | \(-0.720806\pi\) | ||||
−0.639373 | + | 0.768897i | \(0.720806\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 22.0416 | 1.02436 | 0.512181 | − | 0.858878i | \(-0.328838\pi\) | ||||
0.512181 | + | 0.858878i | \(0.328838\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 1.00000 | 0.0463739 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 11.5858 | 0.536126 | 0.268063 | − | 0.963401i | \(-0.413616\pi\) | ||||
0.268063 | + | 0.963401i | \(0.413616\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −28.3137 | −1.30741 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 3.00000 | 0.138233 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 10.8284 | 0.497892 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −7.41421 | −0.340187 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 5.24264 | 0.240044 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 20.1005 | 0.918416 | 0.459208 | − | 0.888329i | \(-0.348133\pi\) | ||||
0.459208 | + | 0.888329i | \(0.348133\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −4.38478 | −0.199929 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 1.82843 | 0.0831963 | ||||||||
\(484\) | 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 | ||||||||
\(489\) | −18.9706 | −0.857879 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 23.1005 | 1.04251 | 0.521256 | − | 0.853401i | \(-0.325464\pi\) | ||||
0.521256 | + | 0.853401i | \(0.325464\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 8.65685 | 0.389885 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −1.41421 | −0.0635642 | ||||||||
\(496\) | 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 | ||||||||
\(501\) | 1.75736 | 0.0785130 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 20.7574 | 0.925525 | 0.462762 | − | 0.886482i | \(-0.346858\pi\) | ||||
0.462762 | + | 0.886482i | \(0.346858\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −10.0711 | −0.448157 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 12.6569 | 0.562111 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −20.4853 | −0.907994 | −0.453997 | − | 0.891003i | \(-0.650002\pi\) | ||||
−0.453997 | + | 0.891003i | \(0.650002\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 4.10051 | 0.181396 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 7.41421 | 0.327346 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −1.51472 | −0.0667465 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 8.82843 | 0.388274 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −21.6569 | −0.950630 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −24.7279 | −1.08335 | −0.541675 | − | 0.840588i | \(-0.682210\pi\) | ||||
−0.541675 | + | 0.840588i | \(0.682210\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −20.0000 | −0.874539 | −0.437269 | − | 0.899331i | \(-0.644054\pi\) | ||||
−0.437269 | + | 0.899331i | \(0.644054\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −1.82843 | −0.0797991 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 2.41421 | 0.105165 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 13.7279 | 0.595741 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 4.24264 | 0.183769 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 3.58579 | 0.155027 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 19.6569 | 0.848256 | ||||||||
\(538\) | 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 | ||||||||
\(543\) | 3.51472 | 0.150831 | ||||||||
\(544\) | 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 | ||||||||
\(549\) | 1.41421 | 0.0603572 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 26.5858 | 1.13259 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 31.0294 | 1.31951 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 7.48528 | 0.317732 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 33.5269 | 1.42058 | 0.710290 | − | 0.703909i | \(-0.248564\pi\) | ||||
0.710290 | + | 0.703909i | \(0.248564\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −4.48528 | −0.189707 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −3.41421 | −0.144148 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −43.5858 | −1.83692 | −0.918461 | − | 0.395512i | \(-0.870567\pi\) | ||||
−0.918461 | + | 0.395512i | \(0.870567\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 18.8995 | 0.795108 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 1.82843 | 0.0767867 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 18.4853 | 0.774943 | 0.387472 | − | 0.921882i | \(-0.373349\pi\) | ||||
0.387472 | + | 0.921882i | \(0.373349\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −1.89949 | −0.0794914 | −0.0397457 | − | 0.999210i | \(-0.512655\pi\) | ||||
−0.0397457 | + | 0.999210i | \(0.512655\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −5.75736 | −0.240517 | ||||||||
\(574\) | 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 | ||||||||
\(579\) | −18.1421 | −0.753961 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 5.04163 | 0.209162 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −7.41421 | −0.307065 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0.585786 | 0.0242193 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 36.6274 | 1.51178 | 0.755888 | − | 0.654701i | \(-0.227206\pi\) | ||||
0.755888 | + | 0.654701i | \(0.227206\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 7.41421 | 0.305497 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 7.17157 | 0.294999 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −6.92893 | −0.284537 | −0.142269 | − | 0.989828i | \(-0.545440\pi\) | ||||
−0.142269 | + | 0.989828i | \(0.545440\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −4.41421 | −0.180965 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 14.4853 | 0.592843 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −18.1421 | −0.741268 | −0.370634 | − | 0.928779i | \(-0.620859\pi\) | ||||
−0.370634 | + | 0.928779i | \(0.620859\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 22.6569 | 0.924192 | 0.462096 | − | 0.886830i | \(-0.347097\pi\) | ||||
0.462096 | + | 0.886830i | \(0.347097\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −15.4853 | −0.630609 | ||||||||
\(604\) | 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 | ||||||||
\(609\) | 6.55635 | 0.265677 | ||||||||
\(610\) | 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 | ||||||||
\(615\) | −7.24264 | −0.292051 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 17.2426 | 0.694163 | 0.347081 | − | 0.937835i | \(-0.387173\pi\) | ||||
0.347081 | + | 0.937835i | \(0.387173\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 16.2843 | 0.654520 | 0.327260 | − | 0.944934i | \(-0.393875\pi\) | ||||
0.327260 | + | 0.944934i | \(0.393875\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.00000 | 0.0401286 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −16.7696 | −0.671858 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −10.4853 | −0.418742 | ||||||||
\(628\) | 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 | ||||||||
\(633\) | −20.7990 | −0.826686 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −19.5563 | −0.776070 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −2.14214 | −0.0848745 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −14.0711 | −0.556643 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −21.4142 | −0.845811 | −0.422905 | − | 0.906174i | \(-0.638990\pi\) | ||||
−0.422905 | + | 0.906174i | \(0.638990\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 31.3431 | 1.23605 | 0.618027 | − | 0.786157i | \(-0.287932\pi\) | ||||
0.618027 | + | 0.786157i | \(0.287932\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 7.65685 | 0.301488 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −2.38478 | −0.0937552 | −0.0468776 | − | 0.998901i | \(-0.514927\pi\) | ||||
−0.0468776 | + | 0.998901i | \(0.514927\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −19.4142 | −0.762075 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 1.82843 | 0.0716617 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −16.7279 | −0.654614 | −0.327307 | − | 0.944918i | \(-0.606141\pi\) | ||||
−0.327307 | + | 0.944918i | \(0.606141\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −16.0000 | −0.625172 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 2.24264 | 0.0874937 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −6.38478 | −0.248716 | −0.124358 | − | 0.992237i | \(-0.539687\pi\) | ||||
−0.124358 | + | 0.992237i | \(0.539687\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 13.1127 | 0.510025 | 0.255012 | − | 0.966938i | \(-0.417920\pi\) | ||||
0.255012 | + | 0.966938i | \(0.417920\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 1.41421 | 0.0549235 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −13.5563 | −0.525693 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 3.58579 | 0.138842 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 18.9706 | 0.733444 | ||||||||
\(670\) | 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 | ||||||||
\(675\) | −1.00000 | −0.0384900 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −43.1838 | −1.65969 | −0.829843 | − | 0.557996i | \(-0.811570\pi\) | ||||
−0.829843 | + | 0.557996i | \(0.811570\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 33.1716 | 1.27301 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0.686292 | 0.0262987 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 43.0122 | 1.64582 | 0.822908 | − | 0.568175i | \(-0.192350\pi\) | ||||
0.822908 | + | 0.568175i | \(0.192350\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 2.82843 | 0.108069 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 16.4853 | 0.628953 | ||||||||
\(688\) | 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 | ||||||||
\(693\) | −2.58579 | −0.0982259 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −17.4853 | −0.663255 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −17.4853 | −0.662302 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 5.65685 | 0.213962 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 49.5563 | 1.87172 | 0.935859 | − | 0.352375i | \(-0.114626\pi\) | ||||
0.935859 | + | 0.352375i | \(0.114626\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 55.4975 | 2.09313 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 6.24264 | 0.235111 | ||||||||
\(706\) | 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 | ||||||||
\(711\) | 16.9706 | 0.636446 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 1.00000 | 0.0374503 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −0.828427 | −0.0309814 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −4.41421 | −0.164852 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 32.5563 | 1.21415 | 0.607073 | − | 0.794646i | \(-0.292343\pi\) | ||||
0.607073 | + | 0.794646i | \(0.292343\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −2.76955 | −0.103144 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 15.2132 | 0.565785 | ||||||||
\(724\) | 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 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 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 | ||||||||
\(735\) | 3.65685 | 0.134885 | ||||||||
\(736\) | 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 | ||||||||
\(741\) | 4.34315 | 0.159549 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 4.00000 | 0.146746 | 0.0733729 | − | 0.997305i | \(-0.476624\pi\) | ||||
0.0733729 | + | 0.997305i | \(0.476624\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −2.24264 | −0.0821640 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 2.75736 | 0.100887 | ||||||||
\(748\) | 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 | ||||||||
\(753\) | 14.9706 | 0.545558 | ||||||||
\(754\) | 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 | ||||||||
\(759\) | −1.41421 | −0.0513327 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −23.9289 | −0.867423 | −0.433712 | − | 0.901052i | \(-0.642796\pi\) | ||||
−0.433712 | + | 0.901052i | \(0.642796\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −13.5563 | −0.490773 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −2.41421 | −0.0872861 | ||||||||
\(766\) | 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 | ||||||||
\(771\) | 11.4142 | 0.411073 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −13.7990 | −0.496315 | −0.248158 | − | 0.968720i | \(-0.579825\pi\) | ||||
−0.248158 | + | 0.968720i | \(0.579825\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −1.00000 | −0.0359211 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 13.6863 | 0.490993 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −53.6985 | −1.92395 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 19.8995 | 0.712060 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 3.58579 | 0.128146 | ||||||||
\(784\) | 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 | ||||||||
\(789\) | −12.4142 | −0.441958 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 34.5563 | 1.22868 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0.828427 | 0.0294183 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −5.24264 | −0.185937 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −34.8995 | −1.23620 | −0.618102 | − | 0.786098i | \(-0.712098\pi\) | ||||
−0.618102 | + | 0.786098i | \(0.712098\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 15.0711 | 0.533176 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −9.17157 | −0.324062 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −3.17157 | −0.111922 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −1.82843 | −0.0644436 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −12.0711 | −0.424922 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 29.7279 | 1.04518 | 0.522589 | − | 0.852585i | \(-0.324966\pi\) | ||||
0.522589 | + | 0.852585i | \(0.324966\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −5.14214 | −0.180565 | −0.0902824 | − | 0.995916i | \(-0.528777\pi\) | ||||
−0.0902824 | + | 0.995916i | \(0.528777\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −18.3137 | −0.642290 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 18.9706 | 0.664510 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 56.7696 | 1.98612 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 1.07107 | 0.0374261 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 33.4558 | 1.16762 | 0.583809 | − | 0.811891i | \(-0.301562\pi\) | ||||
0.583809 | + | 0.811891i | \(0.301562\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −53.6569 | −1.87036 | −0.935180 | − | 0.354172i | \(-0.884763\pi\) | ||||
−0.935180 | + | 0.354172i | \(0.884763\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 1.41421 | 0.0492366 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 2.27208 | 0.0790079 | 0.0395039 | − | 0.999219i | \(-0.487422\pi\) | ||||
0.0395039 | + | 0.999219i | \(0.487422\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −7.82843 | −0.271893 | −0.135946 | − | 0.990716i | \(-0.543407\pi\) | ||||
−0.135946 | + | 0.990716i | \(0.543407\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −18.9706 | −0.658082 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 8.82843 | 0.305887 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −1.75736 | −0.0608159 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 1.00000 | 0.0345651 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 28.3431 | 0.978514 | 0.489257 | − | 0.872140i | \(-0.337268\pi\) | ||||
0.489257 | + | 0.872140i | \(0.337268\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −16.1421 | −0.556625 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −3.75736 | −0.129410 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −12.6569 | −0.435409 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −16.4558 | −0.565429 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 25.6274 | 0.879531 | ||||||||
\(850\) | 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 | ||||||||
\(855\) | −7.41421 | −0.253561 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −30.6863 | −1.04822 | −0.524112 | − | 0.851649i | \(-0.675603\pi\) | ||||
−0.524112 | + | 0.851649i | \(0.675603\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −53.8284 | −1.83660 | −0.918301 | − | 0.395883i | \(-0.870439\pi\) | ||||
−0.918301 | + | 0.395883i | \(0.870439\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −13.2426 | −0.451308 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 46.4853 | 1.58238 | 0.791189 | − | 0.611572i | \(-0.209463\pi\) | ||||
0.791189 | + | 0.611572i | \(0.209463\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 21.6569 | 0.736355 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 11.1716 | 0.379407 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −24.0000 | −0.814144 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −9.07107 | −0.307361 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 18.1421 | 0.614018 | ||||||||
\(874\) | 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 | ||||||||
\(879\) | −10.8995 | −0.367631 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −10.9289 | −0.368205 | −0.184103 | − | 0.982907i | \(-0.558938\pi\) | ||||
−0.184103 | + | 0.982907i | \(0.558938\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −32.9289 | −1.10815 | −0.554073 | − | 0.832468i | \(-0.686927\pi\) | ||||
−0.554073 | + | 0.832468i | \(0.686927\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −13.7279 | −0.461459 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −4.82843 | −0.162123 | −0.0810614 | − | 0.996709i | \(-0.525831\pi\) | ||||
−0.0810614 | + | 0.996709i | \(0.525831\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −35.7574 | −1.19926 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1.41421 | −0.0473779 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 46.2843 | 1.54884 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −19.6569 | −0.657056 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0.585786 | 0.0195588 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 3.58579 | 0.119593 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −12.6569 | −0.421661 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 14.0000 | 0.465891 | ||||||||
\(904\) | 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 | ||||||||
\(909\) | −10.0711 | −0.334036 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 28.9706 | 0.959838 | 0.479919 | − | 0.877313i | \(-0.340666\pi\) | ||||
0.479919 | + | 0.877313i | \(0.340666\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −3.89949 | −0.129054 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −1.41421 | −0.0467525 | ||||||||
\(916\) | 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 | ||||||||
\(921\) | −3.89949 | −0.128493 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −8.24264 | −0.271310 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −7.48528 | −0.246115 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −1.51472 | −0.0497499 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −32.7574 | −1.07473 | −0.537367 | − | 0.843348i | \(-0.680581\pi\) | ||||
−0.537367 | + | 0.843348i | \(0.680581\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 27.1127 | 0.888583 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −31.3137 | −1.02516 | ||||||||
\(934\) | 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 | ||||||||
\(939\) | −21.1421 | −0.689948 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 6.52691 | 0.212771 | 0.106386 | − | 0.994325i | \(-0.466072\pi\) | ||||
0.106386 | + | 0.994325i | \(0.466072\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −7.24264 | −0.235853 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −1.82843 | −0.0594787 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −28.4853 | −0.925647 | −0.462824 | − | 0.886450i | \(-0.653164\pi\) | ||||
−0.462824 | + | 0.886450i | \(0.653164\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1.31371 | 0.0426448 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 7.41421 | 0.240422 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −4.62742 | −0.149897 | −0.0749484 | − | 0.997187i | \(-0.523879\pi\) | ||||
−0.0749484 | + | 0.997187i | \(0.523879\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 5.75736 | 0.186304 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −5.07107 | −0.163924 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 5.17157 | 0.166999 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.0000 | −0.967742 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 3.58579 | 0.115550 | ||||||||
\(964\) | 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 | ||||||||
\(969\) | −17.8995 | −0.575015 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −34.4264 | −1.10480 | −0.552398 | − | 0.833581i | \(-0.686287\pi\) | ||||
−0.552398 | + | 0.833581i | \(0.686287\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −31.9706 | −1.02493 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −0.585786 | −0.0187602 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −49.8701 | −1.59548 | −0.797742 | − | 0.602999i | \(-0.793972\pi\) | ||||
−0.797742 | + | 0.602999i | \(0.793972\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 12.9706 | 0.414541 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −7.41421 | −0.236718 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −37.5269 | −1.19692 | −0.598461 | − | 0.801152i | \(-0.704221\pi\) | ||||
−0.598461 | + | 0.801152i | \(0.704221\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −7.17157 | −0.228505 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 11.4142 | 0.363318 | ||||||||
\(988\) | 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 | ||||||||
\(993\) | 23.8284 | 0.756172 | ||||||||
\(994\) | 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 | ||||||||
\(999\) | 7.48528 | 0.236824 |
(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 | 2760.2.a.n.1.2 | ✓ | 2 | |
3.2 | odd | 2 | 8280.2.a.x.1.2 | 2 | |||
4.3 | odd | 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 | 1.1 | even | 1 | trivial | |
5520.2.a.bt.1.1 | 2 | 4.3 | odd | 2 | |||
8280.2.a.x.1.2 | 2 | 3.2 | odd | 2 |