Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [7728,2,Mod(1,7728)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(7728, 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("7728.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 7728 = 2^{4} \cdot 3 \cdot 7 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 7728.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: | \(61.7083906820\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{10})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 483) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(1.61803\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 7728.1 |
$q$-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 | ||||||||
\(5\) | −2.61803 | −1.17082 | −0.585410 | − | 0.810737i | \(-0.699067\pi\) | ||||
−0.585410 | + | 0.810737i | \(0.699067\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.23607 | 0.674200 | 0.337100 | − | 0.941469i | \(-0.390554\pi\) | ||||
0.337100 | + | 0.941469i | \(0.390554\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −6.85410 | −1.90099 | −0.950493 | − | 0.310746i | \(-0.899421\pi\) | ||||
−0.950493 | + | 0.310746i | \(0.899421\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −2.61803 | −0.675973 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 3.47214 | 0.842117 | 0.421058 | − | 0.907034i | \(-0.361659\pi\) | ||||
0.421058 | + | 0.907034i | \(0.361659\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.76393 | 0.863505 | 0.431753 | − | 0.901992i | \(-0.357895\pi\) | ||||
0.431753 | + | 0.901992i | \(0.357895\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.00000 | −0.218218 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.00000 | −0.208514 | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.85410 | 0.370820 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 10.7082 | 1.98846 | 0.994232 | − | 0.107253i | \(-0.0342054\pi\) | ||||
0.994232 | + | 0.107253i | \(0.0342054\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 5.00000 | 0.898027 | 0.449013 | − | 0.893525i | \(-0.351776\pi\) | ||||
0.449013 | + | 0.893525i | \(0.351776\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 2.23607 | 0.389249 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 2.61803 | 0.442529 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −9.47214 | −1.55721 | −0.778605 | − | 0.627515i | \(-0.784072\pi\) | ||||
−0.778605 | + | 0.627515i | \(0.784072\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −6.85410 | −1.09753 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −4.70820 | −0.735298 | −0.367649 | − | 0.929965i | \(-0.619837\pi\) | ||||
−0.367649 | + | 0.929965i | \(0.619837\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −7.32624 | −1.11724 | −0.558620 | − | 0.829423i | \(-0.688669\pi\) | ||||
−0.558620 | + | 0.829423i | \(0.688669\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −2.61803 | −0.390273 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −0.763932 | −0.111431 | −0.0557155 | − | 0.998447i | \(-0.517744\pi\) | ||||
−0.0557155 | + | 0.998447i | \(0.517744\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 3.47214 | 0.486196 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −1.38197 | −0.189828 | −0.0949138 | − | 0.995485i | \(-0.530258\pi\) | ||||
−0.0949138 | + | 0.995485i | \(0.530258\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −5.85410 | −0.789367 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 3.76393 | 0.498545 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −1.85410 | −0.241384 | −0.120692 | − | 0.992690i | \(-0.538511\pi\) | ||||
−0.120692 | + | 0.992690i | \(0.538511\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.09017 | 0.267619 | 0.133809 | − | 0.991007i | \(-0.457279\pi\) | ||||
0.133809 | + | 0.991007i | \(0.457279\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −1.00000 | −0.125988 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 17.9443 | 2.22571 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0.145898 | 0.0178243 | 0.00891214 | − | 0.999960i | \(-0.497163\pi\) | ||||
0.00891214 | + | 0.999960i | \(0.497163\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −1.00000 | −0.120386 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −11.6180 | −1.37881 | −0.689403 | − | 0.724378i | \(-0.742127\pi\) | ||||
−0.689403 | + | 0.724378i | \(0.742127\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 5.47214 | 0.640465 | 0.320233 | − | 0.947339i | \(-0.396239\pi\) | ||||
0.320233 | + | 0.947339i | \(0.396239\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 1.85410 | 0.214093 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −2.23607 | −0.254824 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 11.9443 | 1.34384 | 0.671918 | − | 0.740626i | \(-0.265471\pi\) | ||||
0.671918 | + | 0.740626i | \(0.265471\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 9.94427 | 1.09153 | 0.545763 | − | 0.837940i | \(-0.316240\pi\) | ||||
0.545763 | + | 0.837940i | \(0.316240\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −9.09017 | −0.985967 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 10.7082 | 1.14804 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −0.673762 | −0.0714186 | −0.0357093 | − | 0.999362i | \(-0.511369\pi\) | ||||
−0.0357093 | + | 0.999362i | \(0.511369\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 6.85410 | 0.718505 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 5.00000 | 0.518476 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −9.85410 | −1.01101 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 5.18034 | 0.525984 | 0.262992 | − | 0.964798i | \(-0.415291\pi\) | ||||
0.262992 | + | 0.964798i | \(0.415291\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 2.23607 | 0.224733 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −4.90983 | −0.488546 | −0.244273 | − | 0.969706i | \(-0.578549\pi\) | ||||
−0.244273 | + | 0.969706i | \(0.578549\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 6.47214 | 0.637719 | 0.318859 | − | 0.947802i | \(-0.396700\pi\) | ||||
0.318859 | + | 0.947802i | \(0.396700\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 2.61803 | 0.255494 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 0.854102 | 0.0825692 | 0.0412846 | − | 0.999147i | \(-0.486855\pi\) | ||||
0.0412846 | + | 0.999147i | \(0.486855\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −14.0344 | −1.34426 | −0.672128 | − | 0.740435i | \(-0.734619\pi\) | ||||
−0.672128 | + | 0.740435i | \(0.734619\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −9.47214 | −0.899055 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −7.09017 | −0.666987 | −0.333494 | − | 0.942752i | \(-0.608228\pi\) | ||||
−0.333494 | + | 0.942752i | \(0.608228\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 2.61803 | 0.244133 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −6.85410 | −0.633662 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −3.47214 | −0.318290 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −6.00000 | −0.545455 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −4.70820 | −0.424524 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 8.23607 | 0.736656 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 2.67376 | 0.237258 | 0.118629 | − | 0.992939i | \(-0.462150\pi\) | ||||
0.118629 | + | 0.992939i | \(0.462150\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −7.32624 | −0.645039 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 12.4164 | 1.08483 | 0.542413 | − | 0.840112i | \(-0.317511\pi\) | ||||
0.542413 | + | 0.840112i | \(0.317511\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −3.76393 | −0.326374 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −2.61803 | −0.225324 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −19.9443 | −1.70395 | −0.851977 | − | 0.523579i | \(-0.824596\pi\) | ||||
−0.851977 | + | 0.523579i | \(0.824596\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −19.8541 | −1.68400 | −0.842001 | − | 0.539475i | \(-0.818623\pi\) | ||||
−0.842001 | + | 0.539475i | \(0.818623\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −0.763932 | −0.0643347 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −15.3262 | −1.28164 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −28.0344 | −2.32813 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 1.00000 | 0.0824786 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −14.6525 | −1.20038 | −0.600189 | − | 0.799858i | \(-0.704908\pi\) | ||||
−0.600189 | + | 0.799858i | \(0.704908\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1.70820 | 0.139012 | 0.0695058 | − | 0.997582i | \(-0.477858\pi\) | ||||
0.0695058 | + | 0.997582i | \(0.477858\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 3.47214 | 0.280706 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −13.0902 | −1.05143 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −14.1803 | −1.13171 | −0.565857 | − | 0.824503i | \(-0.691455\pi\) | ||||
−0.565857 | + | 0.824503i | \(0.691455\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −1.38197 | −0.109597 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1.00000 | 0.0788110 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 22.5066 | 1.76285 | 0.881426 | − | 0.472323i | \(-0.156584\pi\) | ||||
0.881426 | + | 0.472323i | \(0.156584\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −5.85410 | −0.455741 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −11.4721 | −0.887741 | −0.443870 | − | 0.896091i | \(-0.646395\pi\) | ||||
−0.443870 | + | 0.896091i | \(0.646395\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 33.9787 | 2.61375 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 3.76393 | 0.287835 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −11.2918 | −0.858499 | −0.429250 | − | 0.903186i | \(-0.641222\pi\) | ||||
−0.429250 | + | 0.903186i | \(0.641222\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1.85410 | −0.140157 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −1.85410 | −0.139363 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −20.0344 | −1.49744 | −0.748722 | − | 0.662884i | \(-0.769332\pi\) | ||||
−0.748722 | + | 0.662884i | \(0.769332\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −15.1803 | −1.12835 | −0.564173 | − | 0.825657i | \(-0.690805\pi\) | ||||
−0.564173 | + | 0.825657i | \(0.690805\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 2.09017 | 0.154510 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 24.7984 | 1.82321 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 7.76393 | 0.567755 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −1.00000 | −0.0727393 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −21.7082 | −1.57075 | −0.785375 | − | 0.619020i | \(-0.787530\pi\) | ||||
−0.785375 | + | 0.619020i | \(0.787530\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −18.1803 | −1.30865 | −0.654325 | − | 0.756214i | \(-0.727047\pi\) | ||||
−0.654325 | + | 0.756214i | \(0.727047\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 17.9443 | 1.28502 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −25.3262 | −1.80442 | −0.902210 | − | 0.431297i | \(-0.858056\pi\) | ||||
−0.902210 | + | 0.431297i | \(0.858056\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 9.56231 | 0.677854 | 0.338927 | − | 0.940813i | \(-0.389936\pi\) | ||||
0.338927 | + | 0.940813i | \(0.389936\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0.145898 | 0.0102909 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −10.7082 | −0.751569 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 12.3262 | 0.860902 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −1.00000 | −0.0695048 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 8.41641 | 0.582175 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −15.0000 | −1.03264 | −0.516321 | − | 0.856395i | \(-0.672699\pi\) | ||||
−0.516321 | + | 0.856395i | \(0.672699\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −11.6180 | −0.796055 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 19.1803 | 1.30809 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −5.00000 | −0.339422 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 5.47214 | 0.369773 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −23.7984 | −1.60085 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −18.3262 | −1.22722 | −0.613608 | − | 0.789611i | \(-0.710282\pi\) | ||||
−0.613608 | + | 0.789611i | \(0.710282\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.85410 | 0.123607 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −15.2705 | −1.01354 | −0.506770 | − | 0.862081i | \(-0.669161\pi\) | ||||
−0.506770 | + | 0.862081i | \(0.669161\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −5.67376 | −0.374933 | −0.187466 | − | 0.982271i | \(-0.560028\pi\) | ||||
−0.187466 | + | 0.982271i | \(0.560028\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −2.23607 | −0.147122 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 7.09017 | 0.464492 | 0.232246 | − | 0.972657i | \(-0.425392\pi\) | ||||
0.232246 | + | 0.972657i | \(0.425392\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 2.00000 | 0.130466 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 11.9443 | 0.775864 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 6.61803 | 0.428085 | 0.214043 | − | 0.976824i | \(-0.431337\pi\) | ||||
0.214043 | + | 0.976824i | \(0.431337\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 28.7082 | 1.84926 | 0.924629 | − | 0.380869i | \(-0.124375\pi\) | ||||
0.924629 | + | 0.380869i | \(0.124375\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −2.61803 | −0.167260 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −25.7984 | −1.64151 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 9.94427 | 0.630193 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 12.2918 | 0.775851 | 0.387926 | − | 0.921691i | \(-0.373192\pi\) | ||||
0.387926 | + | 0.921691i | \(0.373192\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2.23607 | −0.140580 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −9.09017 | −0.569249 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 29.7082 | 1.85315 | 0.926573 | − | 0.376114i | \(-0.122740\pi\) | ||||
0.926573 | + | 0.376114i | \(0.122740\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 9.47214 | 0.588570 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 10.7082 | 0.662821 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −5.00000 | −0.308313 | −0.154157 | − | 0.988046i | \(-0.549266\pi\) | ||||
−0.154157 | + | 0.988046i | \(0.549266\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 3.61803 | 0.222254 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −0.673762 | −0.0412336 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −2.85410 | −0.174018 | −0.0870088 | − | 0.996208i | \(-0.527731\pi\) | ||||
−0.0870088 | + | 0.996208i | \(0.527731\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 17.1803 | 1.04363 | 0.521816 | − | 0.853058i | \(-0.325255\pi\) | ||||
0.521816 | + | 0.853058i | \(0.325255\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 6.85410 | 0.414829 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 4.14590 | 0.250007 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 21.2148 | 1.27467 | 0.637336 | − | 0.770586i | \(-0.280036\pi\) | ||||
0.637336 | + | 0.770586i | \(0.280036\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 5.00000 | 0.299342 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −21.5967 | −1.28835 | −0.644177 | − | 0.764876i | \(-0.722800\pi\) | ||||
−0.644177 | + | 0.764876i | \(0.722800\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −14.3262 | −0.851606 | −0.425803 | − | 0.904816i | \(-0.640008\pi\) | ||||
−0.425803 | + | 0.904816i | \(0.640008\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −9.85410 | −0.583707 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 4.70820 | 0.277916 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −4.94427 | −0.290840 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 5.18034 | 0.303677 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −9.52786 | −0.556624 | −0.278312 | − | 0.960491i | \(-0.589775\pi\) | ||||
−0.278312 | + | 0.960491i | \(0.589775\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 4.85410 | 0.282617 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 2.23607 | 0.129750 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 6.85410 | 0.396383 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 7.32624 | 0.422277 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −4.90983 | −0.282062 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −5.47214 | −0.313334 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −25.9443 | −1.48072 | −0.740359 | − | 0.672212i | \(-0.765344\pi\) | ||||
−0.740359 | + | 0.672212i | \(0.765344\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 6.47214 | 0.368187 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −7.61803 | −0.431979 | −0.215990 | − | 0.976396i | \(-0.569298\pi\) | ||||
−0.215990 | + | 0.976396i | \(0.569298\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −1.52786 | −0.0863600 | −0.0431800 | − | 0.999067i | \(-0.513749\pi\) | ||||
−0.0431800 | + | 0.999067i | \(0.513749\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 2.61803 | 0.147510 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −22.1459 | −1.24384 | −0.621919 | − | 0.783082i | \(-0.713647\pi\) | ||||
−0.621919 | + | 0.783082i | \(0.713647\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 23.9443 | 1.34062 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0.854102 | 0.0476713 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 13.0689 | 0.727172 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −12.7082 | −0.704924 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −14.0344 | −0.776106 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0.763932 | 0.0421169 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −10.9443 | −0.601552 | −0.300776 | − | 0.953695i | \(-0.597246\pi\) | ||||
−0.300776 | + | 0.953695i | \(0.597246\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −9.47214 | −0.519070 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −0.381966 | −0.0208690 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −18.5623 | −1.01115 | −0.505577 | − | 0.862782i | \(-0.668720\pi\) | ||||
−0.505577 | + | 0.862782i | \(0.668720\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −7.09017 | −0.385085 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 11.1803 | 0.605449 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 2.61803 | 0.140950 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 3.65248 | 0.196075 | 0.0980376 | − | 0.995183i | \(-0.468743\pi\) | ||||
0.0980376 | + | 0.995183i | \(0.468743\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −6.50658 | −0.348289 | −0.174145 | − | 0.984720i | \(-0.555716\pi\) | ||||
−0.174145 | + | 0.984720i | \(0.555716\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −6.85410 | −0.365845 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −26.5967 | −1.41560 | −0.707801 | − | 0.706412i | \(-0.750313\pi\) | ||||
−0.707801 | + | 0.706412i | \(0.750313\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 30.4164 | 1.61434 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −3.47214 | −0.183765 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −22.7984 | −1.20325 | −0.601626 | − | 0.798778i | \(-0.705480\pi\) | ||||
−0.601626 | + | 0.798778i | \(0.705480\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −4.83282 | −0.254359 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −6.00000 | −0.314918 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −14.3262 | −0.749870 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 32.4508 | 1.69392 | 0.846960 | − | 0.531656i | \(-0.178430\pi\) | ||||
0.846960 | + | 0.531656i | \(0.178430\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −4.70820 | −0.245099 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1.38197 | 0.0717481 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 2.88854 | 0.149563 | 0.0747816 | − | 0.997200i | \(-0.476174\pi\) | ||||
0.0747816 | + | 0.997200i | \(0.476174\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 8.23607 | 0.425309 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −73.3951 | −3.78004 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 20.9443 | 1.07583 | 0.537917 | − | 0.842997i | \(-0.319211\pi\) | ||||
0.537917 | + | 0.842997i | \(0.319211\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 2.67376 | 0.136981 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 4.52786 | 0.231363 | 0.115682 | − | 0.993286i | \(-0.463095\pi\) | ||||
0.115682 | + | 0.993286i | \(0.463095\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 5.85410 | 0.298353 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −7.32624 | −0.372414 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 22.1246 | 1.12176 | 0.560881 | − | 0.827896i | \(-0.310462\pi\) | ||||
0.560881 | + | 0.827896i | \(0.310462\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −3.47214 | −0.175593 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 12.4164 | 0.626325 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −31.2705 | −1.57339 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 15.2361 | 0.764676 | 0.382338 | − | 0.924022i | \(-0.375119\pi\) | ||||
0.382338 | + | 0.924022i | \(0.375119\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −3.76393 | −0.188432 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 6.81966 | 0.340558 | 0.170279 | − | 0.985396i | \(-0.445533\pi\) | ||||
0.170279 | + | 0.985396i | \(0.445533\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −34.2705 | −1.70714 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −2.61803 | −0.130091 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −21.1803 | −1.04987 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 23.6525 | 1.16954 | 0.584770 | − | 0.811199i | \(-0.301185\pi\) | ||||
0.584770 | + | 0.811199i | \(0.301185\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −19.9443 | −0.983778 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 1.85410 | 0.0912344 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −26.0344 | −1.27798 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −19.8541 | −0.972260 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −19.5623 | −0.955681 | −0.477841 | − | 0.878447i | \(-0.658580\pi\) | ||||
−0.477841 | + | 0.878447i | \(0.658580\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 10.6738 | 0.520207 | 0.260104 | − | 0.965581i | \(-0.416243\pi\) | ||||
0.260104 | + | 0.965581i | \(0.416243\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −0.763932 | −0.0371436 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 6.43769 | 0.312274 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −2.09017 | −0.101150 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −15.3262 | −0.739958 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −19.9098 | −0.959023 | −0.479511 | − | 0.877536i | \(-0.659186\pi\) | ||||
−0.479511 | + | 0.877536i | \(0.659186\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 23.1246 | 1.11130 | 0.555649 | − | 0.831417i | \(-0.312470\pi\) | ||||
0.555649 | + | 0.831417i | \(0.312470\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −28.0344 | −1.34415 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −3.76393 | −0.180053 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 17.9443 | 0.856433 | 0.428217 | − | 0.903676i | \(-0.359142\pi\) | ||||
0.428217 | + | 0.903676i | \(0.359142\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.00000 | 0.0476190 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 4.00000 | 0.190046 | 0.0950229 | − | 0.995475i | \(-0.469708\pi\) | ||||
0.0950229 | + | 0.995475i | \(0.469708\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1.76393 | 0.0836184 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −14.6525 | −0.693038 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 12.9098 | 0.609253 | 0.304626 | − | 0.952472i | \(-0.401468\pi\) | ||||
0.304626 | + | 0.952472i | \(0.401468\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −10.5279 | −0.495738 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 1.70820 | 0.0802584 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −17.9443 | −0.841240 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −32.7984 | −1.53424 | −0.767122 | − | 0.641502i | \(-0.778312\pi\) | ||||
−0.767122 | + | 0.641502i | \(0.778312\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 3.47214 | 0.162065 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 6.14590 | 0.286243 | 0.143122 | − | 0.989705i | \(-0.454286\pi\) | ||||
0.143122 | + | 0.989705i | \(0.454286\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −14.5967 | −0.678368 | −0.339184 | − | 0.940720i | \(-0.610151\pi\) | ||||
−0.339184 | + | 0.940720i | \(0.610151\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −13.0902 | −0.607042 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −18.8885 | −0.874058 | −0.437029 | − | 0.899448i | \(-0.643969\pi\) | ||||
−0.437029 | + | 0.899448i | \(0.643969\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −0.145898 | −0.00673695 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −14.1803 | −0.653396 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −16.3820 | −0.753244 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 6.97871 | 0.320205 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −1.38197 | −0.0632759 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 5.65248 | 0.258268 | 0.129134 | − | 0.991627i | \(-0.458780\pi\) | ||||
0.129134 | + | 0.991627i | \(0.458780\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 64.9230 | 2.96023 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 1.00000 | 0.0455016 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −13.5623 | −0.615833 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −17.7639 | −0.804961 | −0.402480 | − | 0.915429i | \(-0.631852\pi\) | ||||
−0.402480 | + | 0.915429i | \(0.631852\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 22.5066 | 1.01778 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −28.0902 | −1.26769 | −0.633846 | − | 0.773459i | \(-0.718525\pi\) | ||||
−0.633846 | + | 0.773459i | \(0.718525\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 37.1803 | 1.67452 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −5.85410 | −0.263122 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 11.6180 | 0.521140 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −12.7984 | −0.572934 | −0.286467 | − | 0.958090i | \(-0.592481\pi\) | ||||
−0.286467 | + | 0.958090i | \(0.592481\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −11.4721 | −0.512537 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 21.0902 | 0.940364 | 0.470182 | − | 0.882569i | \(-0.344188\pi\) | ||||
0.470182 | + | 0.882569i | \(0.344188\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 12.8541 | 0.572000 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 33.9787 | 1.50905 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 25.7082 | 1.13950 | 0.569748 | − | 0.821819i | \(-0.307041\pi\) | ||||
0.569748 | + | 0.821819i | \(0.307041\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −5.47214 | −0.242073 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 3.76393 | 0.166182 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −16.9443 | −0.746654 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −1.70820 | −0.0751267 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −11.2918 | −0.495655 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −3.52786 | −0.154559 | −0.0772793 | − | 0.997009i | \(-0.524623\pi\) | ||||
−0.0772793 | + | 0.997009i | \(0.524623\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −32.8328 | −1.43568 | −0.717839 | − | 0.696209i | \(-0.754869\pi\) | ||||
−0.717839 | + | 0.696209i | \(0.754869\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −1.85410 | −0.0809196 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 17.3607 | 0.756243 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −1.85410 | −0.0804612 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 32.2705 | 1.39779 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −2.23607 | −0.0966736 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −20.0344 | −0.864550 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 2.23607 | 0.0963143 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −23.2361 | −0.998997 | −0.499498 | − | 0.866315i | \(-0.666482\pi\) | ||||
−0.499498 | + | 0.866315i | \(0.666482\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −15.1803 | −0.651451 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 36.7426 | 1.57388 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 26.6180 | 1.13810 | 0.569052 | − | 0.822301i | \(-0.307310\pi\) | ||||
0.569052 | + | 0.822301i | \(0.307310\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 2.09017 | 0.0892063 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 40.3050 | 1.71705 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −11.9443 | −0.507922 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 24.7984 | 1.05263 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −17.2361 | −0.730316 | −0.365158 | − | 0.930946i | \(-0.618985\pi\) | ||||
−0.365158 | + | 0.930946i | \(0.618985\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 50.2148 | 2.12386 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 7.76393 | 0.327793 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −8.56231 | −0.360858 | −0.180429 | − | 0.983588i | \(-0.557749\pi\) | ||||
−0.180429 | + | 0.983588i | \(0.557749\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 18.5623 | 0.780922 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −1.00000 | −0.0419961 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 27.7771 | 1.16448 | 0.582238 | − | 0.813018i | \(-0.302177\pi\) | ||||
0.582238 | + | 0.813018i | \(0.302177\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 44.7771 | 1.87386 | 0.936931 | − | 0.349513i | \(-0.113653\pi\) | ||||
0.936931 | + | 0.349513i | \(0.113653\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −21.7082 | −0.906873 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −1.85410 | −0.0773214 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −17.4164 | −0.725055 | −0.362527 | − | 0.931973i | \(-0.618086\pi\) | ||||
−0.362527 | + | 0.931973i | \(0.618086\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −18.1803 | −0.755549 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −9.94427 | −0.412558 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −3.09017 | −0.127982 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 17.9443 | 0.741904 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −2.56231 | −0.105758 | −0.0528788 | − | 0.998601i | \(-0.516840\pi\) | ||||
−0.0528788 | + | 0.998601i | \(0.516840\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 18.8197 | 0.775451 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −25.3262 | −1.04178 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −24.2918 | −0.997545 | −0.498772 | − | 0.866733i | \(-0.666216\pi\) | ||||
−0.498772 | + | 0.866733i | \(0.666216\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 9.09017 | 0.372661 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 9.56231 | 0.391359 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −7.72949 | −0.315818 | −0.157909 | − | 0.987454i | \(-0.550475\pi\) | ||||
−0.157909 | + | 0.987454i | \(0.550475\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 12.5066 | 0.510154 | 0.255077 | − | 0.966921i | \(-0.417899\pi\) | ||||
0.255077 | + | 0.966921i | \(0.417899\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0.145898 | 0.00594143 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 15.7082 | 0.638629 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 8.38197 | 0.340214 | 0.170107 | − | 0.985426i | \(-0.445589\pi\) | ||||
0.170107 | + | 0.985426i | \(0.445589\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −10.7082 | −0.433918 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 5.23607 | 0.211829 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −6.34752 | −0.256374 | −0.128187 | − | 0.991750i | \(-0.540916\pi\) | ||||
−0.128187 | + | 0.991750i | \(0.540916\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 12.3262 | 0.497042 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −4.74265 | −0.190932 | −0.0954659 | − | 0.995433i | \(-0.530434\pi\) | ||||
−0.0954659 | + | 0.995433i | \(0.530434\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −0.270510 | −0.0108727 | −0.00543635 | − | 0.999985i | \(-0.501730\pi\) | ||||
−0.00543635 | + | 0.999985i | \(0.501730\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1.00000 | −0.0401286 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0.673762 | 0.0269937 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −30.8328 | −1.23331 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 8.41641 | 0.336119 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −32.8885 | −1.31135 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 33.7639 | 1.34412 | 0.672060 | − | 0.740496i | \(-0.265409\pi\) | ||||
0.672060 | + | 0.740496i | \(0.265409\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −15.0000 | −0.596196 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −7.00000 | −0.277787 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −6.85410 | −0.271569 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −11.6180 | −0.459602 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −26.3820 | −1.04203 | −0.521013 | − | 0.853549i | \(-0.674446\pi\) | ||||
−0.521013 | + | 0.853549i | \(0.674446\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 35.5066 | 1.40024 | 0.700121 | − | 0.714024i | \(-0.253129\pi\) | ||||
0.700121 | + | 0.714024i | \(0.253129\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 19.1803 | 0.755225 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 9.09017 | 0.357371 | 0.178686 | − | 0.983906i | \(-0.442815\pi\) | ||||
0.178686 | + | 0.983906i | \(0.442815\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −4.14590 | −0.162741 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −5.00000 | −0.195965 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −20.9098 | −0.818265 | −0.409132 | − | 0.912475i | \(-0.634169\pi\) | ||||
−0.409132 | + | 0.912475i | \(0.634169\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −32.5066 | −1.27014 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 5.47214 | 0.213488 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −20.5967 | −0.802335 | −0.401168 | − | 0.916005i | \(-0.631396\pi\) | ||||
−0.401168 | + | 0.916005i | \(0.631396\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 29.1803 | 1.13498 | 0.567492 | − | 0.823379i | \(-0.307914\pi\) | ||||
0.567492 | + | 0.823379i | \(0.307914\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −23.7984 | −0.924252 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 9.85410 | 0.382126 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −10.7082 | −0.414623 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −18.3262 | −0.708533 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 4.67376 | 0.180429 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 4.05573 | 0.156337 | 0.0781684 | − | 0.996940i | \(-0.475093\pi\) | ||||
0.0781684 | + | 0.996940i | \(0.475093\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 1.85410 | 0.0713644 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −23.7984 | −0.914646 | −0.457323 | − | 0.889301i | \(-0.651192\pi\) | ||||
−0.457323 | + | 0.889301i | \(0.651192\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −5.18034 | −0.198803 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −15.2705 | −0.585167 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −27.2918 | −1.04429 | −0.522146 | − | 0.852856i | \(-0.674868\pi\) | ||||
−0.522146 | + | 0.852856i | \(0.674868\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 52.2148 | 1.99502 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −5.67376 | −0.216468 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 9.47214 | 0.360860 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −3.79837 | −0.144497 | −0.0722485 | − | 0.997387i | \(-0.523017\pi\) | ||||
−0.0722485 | + | 0.997387i | \(0.523017\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −2.23607 | −0.0849412 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 51.9787 | 1.97166 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −16.3475 | −0.619207 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 7.09017 | 0.268175 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −7.20163 | −0.272002 | −0.136001 | − | 0.990709i | \(-0.543425\pi\) | ||||
−0.136001 | + | 0.990709i | \(0.543425\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −35.6525 | −1.34466 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 2.00000 | 0.0753244 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 4.90983 | 0.184653 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 3.32624 | 0.124919 | 0.0624597 | − | 0.998047i | \(-0.480105\pi\) | ||||
0.0624597 | + | 0.998047i | \(0.480105\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 11.9443 | 0.447945 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −5.00000 | −0.187251 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 40.1246 | 1.50058 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 6.61803 | 0.247155 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −22.7082 | −0.846873 | −0.423437 | − | 0.905926i | \(-0.639176\pi\) | ||||
−0.423437 | + | 0.905926i | \(0.639176\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −6.47214 | −0.241035 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 28.7082 | 1.06767 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 19.8541 | 0.737363 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 25.7639 | 0.955531 | 0.477766 | − | 0.878487i | \(-0.341447\pi\) | ||||
0.477766 | + | 0.878487i | \(0.341447\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −25.4377 | −0.940847 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −38.5410 | −1.42355 | −0.711773 | − | 0.702410i | \(-0.752107\pi\) | ||||
−0.711773 | + | 0.702410i | \(0.752107\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −2.61803 | −0.0965676 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0.326238 | 0.0120171 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 13.5836 | 0.499681 | 0.249840 | − | 0.968287i | \(-0.419622\pi\) | ||||
0.249840 | + | 0.968287i | \(0.419622\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −25.7984 | −0.947727 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 48.3951 | 1.77544 | 0.887722 | − | 0.460379i | \(-0.152287\pi\) | ||||
0.887722 | + | 0.460379i | \(0.152287\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 38.3607 | 1.40543 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 9.94427 | 0.363842 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −0.854102 | −0.0312082 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 20.9098 | 0.763011 | 0.381505 | − | 0.924367i | \(-0.375406\pi\) | ||||
0.381505 | + | 0.924367i | \(0.375406\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 12.2918 | 0.447938 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −4.47214 | −0.162758 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −5.58359 | −0.202939 | −0.101470 | − | 0.994839i | \(-0.532354\pi\) | ||||
−0.101470 | + | 0.994839i | \(0.532354\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −2.23607 | −0.0811641 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 18.1115 | 0.656540 | 0.328270 | − | 0.944584i | \(-0.393534\pi\) | ||||
0.328270 | + | 0.944584i | \(0.393534\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 14.0344 | 0.508081 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −9.09017 | −0.328656 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 12.7082 | 0.458867 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −45.9574 | −1.65727 | −0.828634 | − | 0.559791i | \(-0.810881\pi\) | ||||
−0.828634 | + | 0.559791i | \(0.810881\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 29.7082 | 1.06991 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 40.0132 | 1.43917 | 0.719587 | − | 0.694403i | \(-0.244331\pi\) | ||||
0.719587 | + | 0.694403i | \(0.244331\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 9.27051 | 0.333007 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 9.47214 | 0.339811 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −17.7214 | −0.634934 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −25.9787 | −0.929591 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 10.7082 | 0.382680 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 37.1246 | 1.32503 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −22.7984 | −0.812674 | −0.406337 | − | 0.913723i | \(-0.633194\pi\) | ||||
−0.406337 | + | 0.913723i | \(0.633194\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −5.00000 | −0.178005 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 7.09017 | 0.252097 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −14.3262 | −0.508740 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 3.61803 | 0.128318 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 9.70820 | 0.343882 | 0.171941 | − | 0.985107i | \(-0.444996\pi\) | ||||
0.171941 | + | 0.985107i | \(0.444996\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −2.65248 | −0.0938378 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −0.673762 | −0.0238062 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 12.2361 | 0.431801 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −2.61803 | −0.0922736 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −2.85410 | −0.100469 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −22.5623 | −0.793248 | −0.396624 | − | 0.917981i | \(-0.629818\pi\) | ||||
−0.396624 | + | 0.917981i | \(0.629818\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −41.5410 | −1.45870 | −0.729351 | − | 0.684139i | \(-0.760178\pi\) | ||||
−0.729351 | + | 0.684139i | \(0.760178\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 17.1803 | 0.602541 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −58.9230 | −2.06398 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −27.5755 | −0.964743 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 6.85410 | 0.239502 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 25.7082 | 0.897223 | 0.448611 | − | 0.893727i | \(-0.351919\pi\) | ||||
0.448611 | + | 0.893727i | \(0.351919\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −54.9787 | −1.91644 | −0.958219 | − | 0.286036i | \(-0.907662\pi\) | ||||
−0.958219 | + | 0.286036i | \(0.907662\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 4.14590 | 0.144342 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 16.1459 | 0.561448 | 0.280724 | − | 0.959789i | \(-0.409425\pi\) | ||||
0.280724 | + | 0.959789i | \(0.409425\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −23.0689 | −0.801215 | −0.400608 | − | 0.916250i | \(-0.631201\pi\) | ||||
−0.400608 | + | 0.916250i | \(0.631201\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 21.2148 | 0.735933 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 3.47214 | 0.120302 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 30.0344 | 1.03938 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 5.00000 | 0.172825 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 36.2705 | 1.25220 | 0.626099 | − | 0.779744i | \(-0.284651\pi\) | ||||
0.626099 | + | 0.779744i | \(0.284651\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 85.6656 | 2.95399 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −21.5967 | −0.743832 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −88.9574 | −3.06023 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 6.00000 | 0.206162 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −14.3262 | −0.491675 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 9.47214 | 0.324701 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −11.3475 | −0.388532 | −0.194266 | − | 0.980949i | \(-0.562232\pi\) | ||||
−0.194266 | + | 0.980949i | \(0.562232\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −9.85410 | −0.337003 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −49.9574 | −1.70651 | −0.853257 | − | 0.521491i | \(-0.825376\pi\) | ||||
−0.853257 | + | 0.521491i | \(0.825376\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 25.4164 | 0.867197 | 0.433598 | − | 0.901106i | \(-0.357244\pi\) | ||||
0.433598 | + | 0.901106i | \(0.357244\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 4.70820 | 0.160455 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 17.5967 | 0.599000 | 0.299500 | − | 0.954096i | \(-0.403180\pi\) | ||||
0.299500 | + | 0.954096i | \(0.403180\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 29.5623 | 1.00515 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −4.94427 | −0.167916 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 26.7082 | 0.906014 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1.00000 | −0.0338837 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 5.18034 | 0.175328 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −8.23607 | −0.278430 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −17.5279 | −0.591874 | −0.295937 | − | 0.955207i | \(-0.595632\pi\) | ||||
−0.295937 | + | 0.955207i | \(0.595632\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −9.52786 | −0.321367 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 26.5410 | 0.894190 | 0.447095 | − | 0.894487i | \(-0.352459\pi\) | ||||
0.447095 | + | 0.894487i | \(0.352459\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 34.7426 | 1.16918 | 0.584592 | − | 0.811328i | \(-0.301255\pi\) | ||||
0.584592 | + | 0.811328i | \(0.301255\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 4.85410 | 0.163169 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −6.67376 | −0.224083 | −0.112041 | − | 0.993704i | \(-0.535739\pi\) | ||||
−0.112041 | + | 0.993704i | \(0.535739\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −2.67376 | −0.0896751 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 2.23607 | 0.0749111 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −2.87539 | −0.0962212 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 52.4508 | 1.75324 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 6.85410 | 0.228852 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 53.5410 | 1.78569 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −4.79837 | −0.159857 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 7.32624 | 0.243802 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 39.7426 | 1.32109 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 16.3262 | 0.542104 | 0.271052 | − | 0.962565i | \(-0.412628\pi\) | ||||
0.271052 | + | 0.962565i | \(0.412628\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −4.90983 | −0.162849 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 18.2918 | 0.606034 | 0.303017 | − | 0.952985i | \(-0.402006\pi\) | ||||
0.303017 | + | 0.952985i | \(0.402006\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 22.2361 | 0.735906 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −5.47214 | −0.180903 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −12.4164 | −0.410026 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −36.4853 | −1.20354 | −0.601769 | − | 0.798670i | \(-0.705537\pi\) | ||||
−0.601769 | + | 0.798670i | \(0.705537\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −25.9443 | −0.854893 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 79.6312 | 2.62109 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −17.5623 | −0.577445 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 6.47214 | 0.212573 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 33.7426 | 1.10706 | 0.553530 | − | 0.832829i | \(-0.313280\pi\) | ||||
0.553530 | + | 0.832829i | \(0.313280\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 3.76393 | 0.123358 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −7.61803 | −0.249403 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −20.3262 | −0.664739 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −33.3607 | −1.08985 | −0.544923 | − | 0.838486i | \(-0.683441\pi\) | ||||
−0.544923 | + | 0.838486i | \(0.683441\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −1.52786 | −0.0498600 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −34.8328 | −1.13552 | −0.567759 | − | 0.823195i | \(-0.692189\pi\) | ||||
−0.567759 | + | 0.823195i | \(0.692189\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 4.70820 | 0.153320 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 2.61803 | 0.0851647 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 46.7214 | 1.51824 | 0.759120 | − | 0.650951i | \(-0.225630\pi\) | ||||
0.759120 | + | 0.650951i | \(0.225630\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −37.5066 | −1.21752 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −22.1459 | −0.718130 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 48.9230 | 1.58477 | 0.792385 | − | 0.610021i | \(-0.208839\pi\) | ||||
0.792385 | + | 0.610021i | \(0.208839\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 56.8328 | 1.83907 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 23.9443 | 0.774008 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 19.9443 | 0.644034 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −6.00000 | −0.193548 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0.854102 | 0.0275231 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 47.5967 | 1.53219 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 16.4721 | 0.529708 | 0.264854 | − | 0.964288i | \(-0.414676\pi\) | ||||
0.264854 | + | 0.964288i | \(0.414676\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 13.0689 | 0.419833 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 14.0902 | 0.452175 | 0.226088 | − | 0.974107i | \(-0.427406\pi\) | ||||
0.226088 | + | 0.974107i | \(0.427406\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 19.8541 | 0.636493 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −12.7082 | −0.406988 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 53.9787 | 1.72693 | 0.863466 | − | 0.504407i | \(-0.168289\pi\) | ||||
0.863466 | + | 0.504407i | \(0.168289\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −1.50658 | −0.0481504 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −14.0344 | −0.448085 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 59.3607 | 1.89331 | 0.946656 | − | 0.322246i | \(-0.104438\pi\) | ||||
0.946656 | + | 0.322246i | \(0.104438\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 66.3050 | 2.11265 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0.763932 | 0.0243162 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 7.32624 | 0.232961 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −2.67376 | −0.0849349 | −0.0424674 | − | 0.999098i | \(-0.513522\pi\) | ||||
−0.0424674 | + | 0.999098i | \(0.513522\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −10.9443 | −0.347306 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −25.0344 | −0.793645 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −25.5410 | −0.808892 | −0.404446 | − | 0.914562i | \(-0.632536\pi\) | ||||
−0.404446 | + | 0.914562i | \(0.632536\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −9.47214 | −0.299685 |
(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 | 7728.2.a.bg.1.1 | 2 | ||
4.3 | odd | 2 | 483.2.a.g.1.2 | ✓ | 2 | ||
12.11 | even | 2 | 1449.2.a.f.1.1 | 2 | |||
28.27 | even | 2 | 3381.2.a.u.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
483.2.a.g.1.2 | ✓ | 2 | 4.3 | odd | 2 | ||
1449.2.a.f.1.1 | 2 | 12.11 | even | 2 | |||
3381.2.a.u.1.2 | 2 | 28.27 | even | 2 | |||
7728.2.a.bg.1.1 | 2 | 1.1 | even | 1 | trivial |