Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8046,2,Mod(1,8046)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8046, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("8046.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8046 = 2 \cdot 3^{3} \cdot 149 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8046.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: | \(64.2476334663\) |
Analytic rank: | \(1\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 3 x^{11} - 31 x^{10} + 82 x^{9} + 334 x^{8} - 684 x^{7} - 1561 x^{6} + 1551 x^{5} + 3573 x^{4} + \cdots - 3 \) |
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 | 1.12 | ||
Root | \(-3.46379\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8046.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 3.46379 | 1.54905 | 0.774527 | − | 0.632541i | \(-0.217988\pi\) | ||||
0.774527 | + | 0.632541i | \(0.217988\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −3.72396 | −1.40752 | −0.703762 | − | 0.710436i | \(-0.748498\pi\) | ||||
−0.703762 | + | 0.710436i | \(0.748498\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 3.46379 | 1.09535 | ||||||||
\(11\) | −5.41125 | −1.63155 | −0.815777 | − | 0.578367i | \(-0.803690\pi\) | ||||
−0.815777 | + | 0.578367i | \(0.803690\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 5.45430 | 1.51275 | 0.756375 | − | 0.654138i | \(-0.226968\pi\) | ||||
0.756375 | + | 0.654138i | \(0.226968\pi\) | |||||||
\(14\) | −3.72396 | −0.995270 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −5.94735 | −1.44245 | −0.721223 | − | 0.692703i | \(-0.756420\pi\) | ||||
−0.721223 | + | 0.692703i | \(0.756420\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 5.41154 | 1.24149 | 0.620746 | − | 0.784012i | \(-0.286830\pi\) | ||||
0.620746 | + | 0.784012i | \(0.286830\pi\) | |||||||
\(20\) | 3.46379 | 0.774527 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −5.41125 | −1.15368 | ||||||||
\(23\) | −4.72212 | −0.984631 | −0.492316 | − | 0.870417i | \(-0.663849\pi\) | ||||
−0.492316 | + | 0.870417i | \(0.663849\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 6.99784 | 1.39957 | ||||||||
\(26\) | 5.45430 | 1.06968 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −3.72396 | −0.703762 | ||||||||
\(29\) | −5.68434 | −1.05556 | −0.527778 | − | 0.849382i | \(-0.676975\pi\) | ||||
−0.527778 | + | 0.849382i | \(0.676975\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.89421 | 0.879026 | 0.439513 | − | 0.898236i | \(-0.355151\pi\) | ||||
0.439513 | + | 0.898236i | \(0.355151\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −5.94735 | −1.01996 | ||||||||
\(35\) | −12.8990 | −2.18033 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −10.8128 | −1.77761 | −0.888807 | − | 0.458281i | \(-0.848465\pi\) | ||||
−0.888807 | + | 0.458281i | \(0.848465\pi\) | |||||||
\(38\) | 5.41154 | 0.877868 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 3.46379 | 0.547673 | ||||||||
\(41\) | −10.6945 | −1.67020 | −0.835101 | − | 0.550097i | \(-0.814591\pi\) | ||||
−0.835101 | + | 0.550097i | \(0.814591\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −12.8009 | −1.95211 | −0.976057 | − | 0.217514i | \(-0.930205\pi\) | ||||
−0.976057 | + | 0.217514i | \(0.930205\pi\) | |||||||
\(44\) | −5.41125 | −0.815777 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −4.72212 | −0.696239 | ||||||||
\(47\) | −8.22990 | −1.20045 | −0.600227 | − | 0.799829i | \(-0.704923\pi\) | ||||
−0.600227 | + | 0.799829i | \(0.704923\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 6.86788 | 0.981125 | ||||||||
\(50\) | 6.99784 | 0.989645 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 5.45430 | 0.756375 | ||||||||
\(53\) | 11.8187 | 1.62343 | 0.811714 | − | 0.584055i | \(-0.198535\pi\) | ||||
0.811714 | + | 0.584055i | \(0.198535\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −18.7434 | −2.52737 | ||||||||
\(56\) | −3.72396 | −0.497635 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −5.68434 | −0.746391 | ||||||||
\(59\) | −6.31276 | −0.821851 | −0.410926 | − | 0.911669i | \(-0.634794\pi\) | ||||
−0.410926 | + | 0.911669i | \(0.634794\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 10.9822 | 1.40613 | 0.703063 | − | 0.711127i | \(-0.251815\pi\) | ||||
0.703063 | + | 0.711127i | \(0.251815\pi\) | |||||||
\(62\) | 4.89421 | 0.621565 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 18.8926 | 2.34333 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −8.30144 | −1.01418 | −0.507091 | − | 0.861892i | \(-0.669279\pi\) | ||||
−0.507091 | + | 0.861892i | \(0.669279\pi\) | |||||||
\(68\) | −5.94735 | −0.721223 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −12.8990 | −1.54173 | ||||||||
\(71\) | −0.883937 | −0.104904 | −0.0524520 | − | 0.998623i | \(-0.516704\pi\) | ||||
−0.0524520 | + | 0.998623i | \(0.516704\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 6.87933 | 0.805164 | 0.402582 | − | 0.915384i | \(-0.368113\pi\) | ||||
0.402582 | + | 0.915384i | \(0.368113\pi\) | |||||||
\(74\) | −10.8128 | −1.25696 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 5.41154 | 0.620746 | ||||||||
\(77\) | 20.1513 | 2.29645 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 2.27886 | 0.256392 | 0.128196 | − | 0.991749i | \(-0.459081\pi\) | ||||
0.128196 | + | 0.991749i | \(0.459081\pi\) | |||||||
\(80\) | 3.46379 | 0.387264 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −10.6945 | −1.18101 | ||||||||
\(83\) | −4.53459 | −0.497736 | −0.248868 | − | 0.968537i | \(-0.580059\pi\) | ||||
−0.248868 | + | 0.968537i | \(0.580059\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −20.6004 | −2.23443 | ||||||||
\(86\) | −12.8009 | −1.38035 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −5.41125 | −0.576841 | ||||||||
\(89\) | −1.46095 | −0.154860 | −0.0774301 | − | 0.996998i | \(-0.524671\pi\) | ||||
−0.0774301 | + | 0.996998i | \(0.524671\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −20.3116 | −2.12923 | ||||||||
\(92\) | −4.72212 | −0.492316 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −8.22990 | −0.848850 | ||||||||
\(95\) | 18.7444 | 1.92314 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 18.1261 | 1.84043 | 0.920213 | − | 0.391419i | \(-0.128016\pi\) | ||||
0.920213 | + | 0.391419i | \(0.128016\pi\) | |||||||
\(98\) | 6.86788 | 0.693760 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 6.99784 | 0.699784 | ||||||||
\(101\) | −7.96826 | −0.792871 | −0.396436 | − | 0.918063i | \(-0.629753\pi\) | ||||
−0.396436 | + | 0.918063i | \(0.629753\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 11.8574 | 1.16835 | 0.584174 | − | 0.811628i | \(-0.301419\pi\) | ||||
0.584174 | + | 0.811628i | \(0.301419\pi\) | |||||||
\(104\) | 5.45430 | 0.534838 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 11.8187 | 1.14794 | ||||||||
\(107\) | −4.13345 | −0.399596 | −0.199798 | − | 0.979837i | \(-0.564029\pi\) | ||||
−0.199798 | + | 0.979837i | \(0.564029\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −16.8105 | −1.61015 | −0.805077 | − | 0.593170i | \(-0.797876\pi\) | ||||
−0.805077 | + | 0.593170i | \(0.797876\pi\) | |||||||
\(110\) | −18.7434 | −1.78712 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −3.72396 | −0.351881 | ||||||||
\(113\) | 9.43021 | 0.887120 | 0.443560 | − | 0.896245i | \(-0.353715\pi\) | ||||
0.443560 | + | 0.896245i | \(0.353715\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −16.3564 | −1.52525 | ||||||||
\(116\) | −5.68434 | −0.527778 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −6.31276 | −0.581137 | ||||||||
\(119\) | 22.1477 | 2.03028 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 18.2816 | 1.66197 | ||||||||
\(122\) | 10.9822 | 0.994282 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 4.89421 | 0.439513 | ||||||||
\(125\) | 6.92011 | 0.618954 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −0.238039 | −0.0211225 | −0.0105613 | − | 0.999944i | \(-0.503362\pi\) | ||||
−0.0105613 | + | 0.999944i | \(0.503362\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 18.8926 | 1.65699 | ||||||||
\(131\) | −0.0242757 | −0.00212098 | −0.00106049 | − | 0.999999i | \(-0.500338\pi\) | ||||
−0.00106049 | + | 0.999999i | \(0.500338\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −20.1524 | −1.74743 | ||||||||
\(134\) | −8.30144 | −0.717135 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −5.94735 | −0.509981 | ||||||||
\(137\) | 2.19280 | 0.187344 | 0.0936718 | − | 0.995603i | \(-0.470140\pi\) | ||||
0.0936718 | + | 0.995603i | \(0.470140\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −7.61095 | −0.645552 | −0.322776 | − | 0.946475i | \(-0.604616\pi\) | ||||
−0.322776 | + | 0.946475i | \(0.604616\pi\) | |||||||
\(140\) | −12.8990 | −1.09017 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −0.883937 | −0.0741784 | ||||||||
\(143\) | −29.5146 | −2.46813 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −19.6894 | −1.63511 | ||||||||
\(146\) | 6.87933 | 0.569337 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −10.8128 | −0.888807 | ||||||||
\(149\) | 1.00000 | 0.0819232 | ||||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2.74712 | 0.223558 | 0.111779 | − | 0.993733i | \(-0.464345\pi\) | ||||
0.111779 | + | 0.993733i | \(0.464345\pi\) | |||||||
\(152\) | 5.41154 | 0.438934 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 20.1513 | 1.62384 | ||||||||
\(155\) | 16.9525 | 1.36166 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −11.6087 | −0.926478 | −0.463239 | − | 0.886233i | \(-0.653313\pi\) | ||||
−0.463239 | + | 0.886233i | \(0.653313\pi\) | |||||||
\(158\) | 2.27886 | 0.181296 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 3.46379 | 0.273837 | ||||||||
\(161\) | 17.5850 | 1.38589 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −23.2573 | −1.82165 | −0.910826 | − | 0.412790i | \(-0.864554\pi\) | ||||
−0.910826 | + | 0.412790i | \(0.864554\pi\) | |||||||
\(164\) | −10.6945 | −0.835101 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −4.53459 | −0.351952 | ||||||||
\(167\) | 20.1860 | 1.56204 | 0.781021 | − | 0.624504i | \(-0.214699\pi\) | ||||
0.781021 | + | 0.624504i | \(0.214699\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 16.7494 | 1.28841 | ||||||||
\(170\) | −20.6004 | −1.57998 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −12.8009 | −0.976057 | ||||||||
\(173\) | −2.95800 | −0.224893 | −0.112446 | − | 0.993658i | \(-0.535869\pi\) | ||||
−0.112446 | + | 0.993658i | \(0.535869\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −26.0597 | −1.96993 | ||||||||
\(176\) | −5.41125 | −0.407888 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −1.46095 | −0.109503 | ||||||||
\(179\) | −11.9473 | −0.892986 | −0.446493 | − | 0.894787i | \(-0.647327\pi\) | ||||
−0.446493 | + | 0.894787i | \(0.647327\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −20.7182 | −1.53997 | −0.769986 | − | 0.638060i | \(-0.779737\pi\) | ||||
−0.769986 | + | 0.638060i | \(0.779737\pi\) | |||||||
\(182\) | −20.3116 | −1.50560 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −4.72212 | −0.348120 | ||||||||
\(185\) | −37.4533 | −2.75362 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 32.1826 | 2.35343 | ||||||||
\(188\) | −8.22990 | −0.600227 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 18.7444 | 1.35986 | ||||||||
\(191\) | −17.1850 | −1.24346 | −0.621731 | − | 0.783231i | \(-0.713570\pi\) | ||||
−0.621731 | + | 0.783231i | \(0.713570\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 0.843776 | 0.0607364 | 0.0303682 | − | 0.999539i | \(-0.490332\pi\) | ||||
0.0303682 | + | 0.999539i | \(0.490332\pi\) | |||||||
\(194\) | 18.1261 | 1.30138 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 6.86788 | 0.490563 | ||||||||
\(197\) | 9.38954 | 0.668977 | 0.334489 | − | 0.942400i | \(-0.391436\pi\) | ||||
0.334489 | + | 0.942400i | \(0.391436\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 4.08274 | 0.289418 | 0.144709 | − | 0.989474i | \(-0.453775\pi\) | ||||
0.144709 | + | 0.989474i | \(0.453775\pi\) | |||||||
\(200\) | 6.99784 | 0.494822 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −7.96826 | −0.560645 | ||||||||
\(203\) | 21.1683 | 1.48572 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −37.0435 | −2.58723 | ||||||||
\(206\) | 11.8574 | 0.826147 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 5.45430 | 0.378188 | ||||||||
\(209\) | −29.2832 | −2.02556 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 12.4094 | 0.854298 | 0.427149 | − | 0.904181i | \(-0.359518\pi\) | ||||
0.427149 | + | 0.904181i | \(0.359518\pi\) | |||||||
\(212\) | 11.8187 | 0.811714 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −4.13345 | −0.282557 | ||||||||
\(215\) | −44.3395 | −3.02393 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −18.2258 | −1.23725 | ||||||||
\(218\) | −16.8105 | −1.13855 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −18.7434 | −1.26368 | ||||||||
\(221\) | −32.4387 | −2.18206 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −2.60836 | −0.174669 | −0.0873345 | − | 0.996179i | \(-0.527835\pi\) | ||||
−0.0873345 | + | 0.996179i | \(0.527835\pi\) | |||||||
\(224\) | −3.72396 | −0.248818 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 9.43021 | 0.627289 | ||||||||
\(227\) | −1.09859 | −0.0729158 | −0.0364579 | − | 0.999335i | \(-0.511607\pi\) | ||||
−0.0364579 | + | 0.999335i | \(0.511607\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 19.5454 | 1.29160 | 0.645799 | − | 0.763508i | \(-0.276524\pi\) | ||||
0.645799 | + | 0.763508i | \(0.276524\pi\) | |||||||
\(230\) | −16.3564 | −1.07851 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −5.68434 | −0.373196 | ||||||||
\(233\) | −22.8074 | −1.49416 | −0.747081 | − | 0.664733i | \(-0.768545\pi\) | ||||
−0.747081 | + | 0.664733i | \(0.768545\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −28.5067 | −1.85957 | ||||||||
\(236\) | −6.31276 | −0.410926 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 22.1477 | 1.43562 | ||||||||
\(239\) | 1.17661 | 0.0761086 | 0.0380543 | − | 0.999276i | \(-0.487884\pi\) | ||||
0.0380543 | + | 0.999276i | \(0.487884\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −22.0093 | −1.41774 | −0.708870 | − | 0.705339i | \(-0.750795\pi\) | ||||
−0.708870 | + | 0.705339i | \(0.750795\pi\) | |||||||
\(242\) | 18.2816 | 1.17519 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 10.9822 | 0.703063 | ||||||||
\(245\) | 23.7889 | 1.51982 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 29.5162 | 1.87807 | ||||||||
\(248\) | 4.89421 | 0.310783 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 6.92011 | 0.437666 | ||||||||
\(251\) | 0.340199 | 0.0214732 | 0.0107366 | − | 0.999942i | \(-0.496582\pi\) | ||||
0.0107366 | + | 0.999942i | \(0.496582\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 25.5526 | 1.60648 | ||||||||
\(254\) | −0.238039 | −0.0149359 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −5.40682 | −0.337268 | −0.168634 | − | 0.985679i | \(-0.553936\pi\) | ||||
−0.168634 | + | 0.985679i | \(0.553936\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 40.2665 | 2.50204 | ||||||||
\(260\) | 18.8926 | 1.17167 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −0.0242757 | −0.00149976 | ||||||||
\(263\) | 18.4228 | 1.13600 | 0.567999 | − | 0.823029i | \(-0.307718\pi\) | ||||
0.567999 | + | 0.823029i | \(0.307718\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 40.9376 | 2.51478 | ||||||||
\(266\) | −20.1524 | −1.23562 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −8.30144 | −0.507091 | ||||||||
\(269\) | 6.50417 | 0.396566 | 0.198283 | − | 0.980145i | \(-0.436463\pi\) | ||||
0.198283 | + | 0.980145i | \(0.436463\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −22.0203 | −1.33764 | −0.668818 | − | 0.743427i | \(-0.733199\pi\) | ||||
−0.668818 | + | 0.743427i | \(0.733199\pi\) | |||||||
\(272\) | −5.94735 | −0.360611 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 2.19280 | 0.132472 | ||||||||
\(275\) | −37.8671 | −2.28347 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 30.3999 | 1.82655 | 0.913276 | − | 0.407340i | \(-0.133544\pi\) | ||||
0.913276 | + | 0.407340i | \(0.133544\pi\) | |||||||
\(278\) | −7.61095 | −0.456474 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −12.8990 | −0.770864 | ||||||||
\(281\) | −4.00120 | −0.238691 | −0.119346 | − | 0.992853i | \(-0.538080\pi\) | ||||
−0.119346 | + | 0.992853i | \(0.538080\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 5.09021 | 0.302581 | 0.151291 | − | 0.988489i | \(-0.451657\pi\) | ||||
0.151291 | + | 0.988489i | \(0.451657\pi\) | |||||||
\(284\) | −0.883937 | −0.0524520 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −29.5146 | −1.74523 | ||||||||
\(287\) | 39.8259 | 2.35085 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 18.3710 | 1.08065 | ||||||||
\(290\) | −19.6894 | −1.15620 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 6.87933 | 0.402582 | ||||||||
\(293\) | 2.56800 | 0.150024 | 0.0750121 | − | 0.997183i | \(-0.476100\pi\) | ||||
0.0750121 | + | 0.997183i | \(0.476100\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −21.8661 | −1.27309 | ||||||||
\(296\) | −10.8128 | −0.628482 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 1.00000 | 0.0579284 | ||||||||
\(299\) | −25.7559 | −1.48950 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 47.6699 | 2.74765 | ||||||||
\(302\) | 2.74712 | 0.158079 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 5.41154 | 0.310373 | ||||||||
\(305\) | 38.0400 | 2.17817 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 0.252021 | 0.0143836 | 0.00719181 | − | 0.999974i | \(-0.497711\pi\) | ||||
0.00719181 | + | 0.999974i | \(0.497711\pi\) | |||||||
\(308\) | 20.1513 | 1.14823 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 16.9525 | 0.962838 | ||||||||
\(311\) | 3.21065 | 0.182059 | 0.0910295 | − | 0.995848i | \(-0.470984\pi\) | ||||
0.0910295 | + | 0.995848i | \(0.470984\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −17.6474 | −0.997489 | −0.498745 | − | 0.866749i | \(-0.666205\pi\) | ||||
−0.498745 | + | 0.866749i | \(0.666205\pi\) | |||||||
\(314\) | −11.6087 | −0.655119 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 2.27886 | 0.128196 | ||||||||
\(317\) | −9.68734 | −0.544095 | −0.272048 | − | 0.962284i | \(-0.587701\pi\) | ||||
−0.272048 | + | 0.962284i | \(0.587701\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 30.7594 | 1.72220 | ||||||||
\(320\) | 3.46379 | 0.193632 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 17.5850 | 0.979974 | ||||||||
\(323\) | −32.1843 | −1.79078 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 38.1683 | 2.11720 | ||||||||
\(326\) | −23.2573 | −1.28810 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −10.6945 | −0.590506 | ||||||||
\(329\) | 30.6478 | 1.68967 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 23.3524 | 1.28356 | 0.641781 | − | 0.766888i | \(-0.278196\pi\) | ||||
0.641781 | + | 0.766888i | \(0.278196\pi\) | |||||||
\(332\) | −4.53459 | −0.248868 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 20.1860 | 1.10453 | ||||||||
\(335\) | −28.7544 | −1.57102 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 11.1102 | 0.605213 | 0.302607 | − | 0.953116i | \(-0.402143\pi\) | ||||
0.302607 | + | 0.953116i | \(0.402143\pi\) | |||||||
\(338\) | 16.7494 | 0.911047 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −20.6004 | −1.11721 | ||||||||
\(341\) | −26.4838 | −1.43418 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0.492021 | 0.0265666 | ||||||||
\(344\) | −12.8009 | −0.690177 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −2.95800 | −0.159023 | ||||||||
\(347\) | −13.1429 | −0.705549 | −0.352774 | − | 0.935708i | \(-0.614762\pi\) | ||||
−0.352774 | + | 0.935708i | \(0.614762\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −10.0265 | −0.536708 | −0.268354 | − | 0.963320i | \(-0.586480\pi\) | ||||
−0.268354 | + | 0.963320i | \(0.586480\pi\) | |||||||
\(350\) | −26.0597 | −1.39295 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −5.41125 | −0.288421 | ||||||||
\(353\) | −22.1184 | −1.17724 | −0.588621 | − | 0.808409i | \(-0.700329\pi\) | ||||
−0.588621 | + | 0.808409i | \(0.700329\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −3.06177 | −0.162502 | ||||||||
\(356\) | −1.46095 | −0.0774301 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −11.9473 | −0.631437 | ||||||||
\(359\) | 19.5158 | 1.03000 | 0.515002 | − | 0.857189i | \(-0.327791\pi\) | ||||
0.515002 | + | 0.857189i | \(0.327791\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 10.2848 | 0.541303 | ||||||||
\(362\) | −20.7182 | −1.08893 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −20.3116 | −1.06462 | ||||||||
\(365\) | 23.8285 | 1.24724 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 3.06129 | 0.159798 | 0.0798991 | − | 0.996803i | \(-0.474540\pi\) | ||||
0.0798991 | + | 0.996803i | \(0.474540\pi\) | |||||||
\(368\) | −4.72212 | −0.246158 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −37.4533 | −1.94710 | ||||||||
\(371\) | −44.0125 | −2.28501 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −16.5213 | −0.855442 | −0.427721 | − | 0.903911i | \(-0.640683\pi\) | ||||
−0.427721 | + | 0.903911i | \(0.640683\pi\) | |||||||
\(374\) | 32.1826 | 1.66412 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −8.22990 | −0.424425 | ||||||||
\(377\) | −31.0041 | −1.59679 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −24.7081 | −1.26917 | −0.634584 | − | 0.772854i | \(-0.718829\pi\) | ||||
−0.634584 | + | 0.772854i | \(0.718829\pi\) | |||||||
\(380\) | 18.7444 | 0.961569 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −17.1850 | −0.879260 | ||||||||
\(383\) | 4.53673 | 0.231816 | 0.115908 | − | 0.993260i | \(-0.463022\pi\) | ||||
0.115908 | + | 0.993260i | \(0.463022\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 69.7998 | 3.55733 | ||||||||
\(386\) | 0.843776 | 0.0429471 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 18.1261 | 0.920213 | ||||||||
\(389\) | 31.1647 | 1.58011 | 0.790056 | − | 0.613035i | \(-0.210052\pi\) | ||||
0.790056 | + | 0.613035i | \(0.210052\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 28.0841 | 1.42028 | ||||||||
\(392\) | 6.86788 | 0.346880 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 9.38954 | 0.473038 | ||||||||
\(395\) | 7.89350 | 0.397165 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 14.0089 | 0.703088 | 0.351544 | − | 0.936171i | \(-0.385657\pi\) | ||||
0.351544 | + | 0.936171i | \(0.385657\pi\) | |||||||
\(398\) | 4.08274 | 0.204649 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 6.99784 | 0.349892 | ||||||||
\(401\) | −19.7883 | −0.988178 | −0.494089 | − | 0.869411i | \(-0.664498\pi\) | ||||
−0.494089 | + | 0.869411i | \(0.664498\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 26.6945 | 1.32975 | ||||||||
\(404\) | −7.96826 | −0.396436 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 21.1683 | 1.05056 | ||||||||
\(407\) | 58.5108 | 2.90027 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −12.8739 | −0.636575 | −0.318288 | − | 0.947994i | \(-0.603108\pi\) | ||||
−0.318288 | + | 0.947994i | \(0.603108\pi\) | |||||||
\(410\) | −37.0435 | −1.82945 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 11.8574 | 0.584174 | ||||||||
\(413\) | 23.5085 | 1.15678 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −15.7069 | −0.771020 | ||||||||
\(416\) | 5.45430 | 0.267419 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −29.2832 | −1.43229 | ||||||||
\(419\) | −17.4280 | −0.851412 | −0.425706 | − | 0.904862i | \(-0.639974\pi\) | ||||
−0.425706 | + | 0.904862i | \(0.639974\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 26.0347 | 1.26885 | 0.634427 | − | 0.772983i | \(-0.281236\pi\) | ||||
0.634427 | + | 0.772983i | \(0.281236\pi\) | |||||||
\(422\) | 12.4094 | 0.604080 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 11.8187 | 0.573968 | ||||||||
\(425\) | −41.6187 | −2.01880 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −40.8973 | −1.97916 | ||||||||
\(428\) | −4.13345 | −0.199798 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −44.3395 | −2.13824 | ||||||||
\(431\) | −4.09204 | −0.197107 | −0.0985533 | − | 0.995132i | \(-0.531421\pi\) | ||||
−0.0985533 | + | 0.995132i | \(0.531421\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 21.9423 | 1.05448 | 0.527241 | − | 0.849716i | \(-0.323227\pi\) | ||||
0.527241 | + | 0.849716i | \(0.323227\pi\) | |||||||
\(434\) | −18.2258 | −0.874868 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −16.8105 | −0.805077 | ||||||||
\(437\) | −25.5540 | −1.22241 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −26.8522 | −1.28158 | −0.640792 | − | 0.767715i | \(-0.721394\pi\) | ||||
−0.640792 | + | 0.767715i | \(0.721394\pi\) | |||||||
\(440\) | −18.7434 | −0.893559 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −32.4387 | −1.54295 | ||||||||
\(443\) | −1.31682 | −0.0625639 | −0.0312819 | − | 0.999511i | \(-0.509959\pi\) | ||||
−0.0312819 | + | 0.999511i | \(0.509959\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −5.06042 | −0.239887 | ||||||||
\(446\) | −2.60836 | −0.123510 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −3.72396 | −0.175941 | ||||||||
\(449\) | 9.00217 | 0.424838 | 0.212419 | − | 0.977179i | \(-0.431866\pi\) | ||||
0.212419 | + | 0.977179i | \(0.431866\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 57.8707 | 2.72502 | ||||||||
\(452\) | 9.43021 | 0.443560 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −1.09859 | −0.0515592 | ||||||||
\(455\) | −70.3551 | −3.29830 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 0.899724 | 0.0420873 | 0.0210437 | − | 0.999779i | \(-0.493301\pi\) | ||||
0.0210437 | + | 0.999779i | \(0.493301\pi\) | |||||||
\(458\) | 19.5454 | 0.913298 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −16.3564 | −0.762623 | ||||||||
\(461\) | 2.41367 | 0.112416 | 0.0562079 | − | 0.998419i | \(-0.482099\pi\) | ||||
0.0562079 | + | 0.998419i | \(0.482099\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −10.3255 | −0.479869 | −0.239934 | − | 0.970789i | \(-0.577126\pi\) | ||||
−0.239934 | + | 0.970789i | \(0.577126\pi\) | |||||||
\(464\) | −5.68434 | −0.263889 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −22.8074 | −1.05653 | ||||||||
\(467\) | −11.2771 | −0.521844 | −0.260922 | − | 0.965360i | \(-0.584027\pi\) | ||||
−0.260922 | + | 0.965360i | \(0.584027\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 30.9142 | 1.42749 | ||||||||
\(470\) | −28.5067 | −1.31491 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −6.31276 | −0.290568 | ||||||||
\(473\) | 69.2687 | 3.18498 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 37.8691 | 1.73755 | ||||||||
\(476\) | 22.1477 | 1.01514 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 1.17661 | 0.0538169 | ||||||||
\(479\) | 14.2371 | 0.650509 | 0.325254 | − | 0.945627i | \(-0.394550\pi\) | ||||
0.325254 | + | 0.945627i | \(0.394550\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −58.9763 | −2.68909 | ||||||||
\(482\) | −22.0093 | −1.00249 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 18.2816 | 0.830984 | ||||||||
\(485\) | 62.7850 | 2.85092 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 7.25573 | 0.328789 | 0.164394 | − | 0.986395i | \(-0.447433\pi\) | ||||
0.164394 | + | 0.986395i | \(0.447433\pi\) | |||||||
\(488\) | 10.9822 | 0.497141 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 23.7889 | 1.07467 | ||||||||
\(491\) | −9.21094 | −0.415684 | −0.207842 | − | 0.978162i | \(-0.566644\pi\) | ||||
−0.207842 | + | 0.978162i | \(0.566644\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 33.8068 | 1.52258 | ||||||||
\(494\) | 29.5162 | 1.32799 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 4.89421 | 0.219756 | ||||||||
\(497\) | 3.29175 | 0.147655 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −34.1216 | −1.52749 | −0.763747 | − | 0.645516i | \(-0.776642\pi\) | ||||
−0.763747 | + | 0.645516i | \(0.776642\pi\) | |||||||
\(500\) | 6.92011 | 0.309477 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0.340199 | 0.0151838 | ||||||||
\(503\) | −2.34544 | −0.104578 | −0.0522890 | − | 0.998632i | \(-0.516652\pi\) | ||||
−0.0522890 | + | 0.998632i | \(0.516652\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −27.6004 | −1.22820 | ||||||||
\(506\) | 25.5526 | 1.13595 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −0.238039 | −0.0105613 | ||||||||
\(509\) | −1.10156 | −0.0488258 | −0.0244129 | − | 0.999702i | \(-0.507772\pi\) | ||||
−0.0244129 | + | 0.999702i | \(0.507772\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −25.6183 | −1.13329 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −5.40682 | −0.238485 | ||||||||
\(515\) | 41.0717 | 1.80983 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 44.5341 | 1.95861 | ||||||||
\(518\) | 40.2665 | 1.76921 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 18.8926 | 0.828493 | ||||||||
\(521\) | 8.55087 | 0.374620 | 0.187310 | − | 0.982301i | \(-0.440023\pi\) | ||||
0.187310 | + | 0.982301i | \(0.440023\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −18.3580 | −0.802740 | −0.401370 | − | 0.915916i | \(-0.631466\pi\) | ||||
−0.401370 | + | 0.915916i | \(0.631466\pi\) | |||||||
\(524\) | −0.0242757 | −0.00106049 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 18.4228 | 0.803272 | ||||||||
\(527\) | −29.1076 | −1.26795 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −0.701541 | −0.0305018 | ||||||||
\(530\) | 40.9376 | 1.77822 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −20.1524 | −0.873715 | ||||||||
\(533\) | −58.3311 | −2.52660 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −14.3174 | −0.618995 | ||||||||
\(536\) | −8.30144 | −0.358568 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 6.50417 | 0.280415 | ||||||||
\(539\) | −37.1638 | −1.60076 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −37.9301 | −1.63074 | −0.815372 | − | 0.578937i | \(-0.803468\pi\) | ||||
−0.815372 | + | 0.578937i | \(0.803468\pi\) | |||||||
\(542\) | −22.0203 | −0.945851 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −5.94735 | −0.254991 | ||||||||
\(545\) | −58.2281 | −2.49422 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 28.1125 | 1.20200 | 0.601001 | − | 0.799248i | \(-0.294769\pi\) | ||||
0.601001 | + | 0.799248i | \(0.294769\pi\) | |||||||
\(548\) | 2.19280 | 0.0936718 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −37.8671 | −1.61466 | ||||||||
\(551\) | −30.7611 | −1.31046 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −8.48639 | −0.360878 | ||||||||
\(554\) | 30.3999 | 1.29157 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −7.61095 | −0.322776 | ||||||||
\(557\) | 30.8310 | 1.30635 | 0.653175 | − | 0.757207i | \(-0.273436\pi\) | ||||
0.653175 | + | 0.757207i | \(0.273436\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −69.8198 | −2.95306 | ||||||||
\(560\) | −12.8990 | −0.545083 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −4.00120 | −0.168780 | ||||||||
\(563\) | −6.47841 | −0.273033 | −0.136516 | − | 0.990638i | \(-0.543591\pi\) | ||||
−0.136516 | + | 0.990638i | \(0.543591\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 32.6643 | 1.37420 | ||||||||
\(566\) | 5.09021 | 0.213957 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −0.883937 | −0.0370892 | ||||||||
\(569\) | 10.7510 | 0.450707 | 0.225354 | − | 0.974277i | \(-0.427646\pi\) | ||||
0.225354 | + | 0.974277i | \(0.427646\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −32.2527 | −1.34973 | −0.674867 | − | 0.737940i | \(-0.735799\pi\) | ||||
−0.674867 | + | 0.737940i | \(0.735799\pi\) | |||||||
\(572\) | −29.5146 | −1.23407 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 39.8259 | 1.66230 | ||||||||
\(575\) | −33.0447 | −1.37806 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 29.0518 | 1.20944 | 0.604721 | − | 0.796438i | \(-0.293285\pi\) | ||||
0.604721 | + | 0.796438i | \(0.293285\pi\) | |||||||
\(578\) | 18.3710 | 0.764134 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −19.6894 | −0.817557 | ||||||||
\(581\) | 16.8866 | 0.700576 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −63.9541 | −2.64871 | ||||||||
\(584\) | 6.87933 | 0.284669 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 2.56800 | 0.106083 | ||||||||
\(587\) | 37.6130 | 1.55245 | 0.776227 | − | 0.630454i | \(-0.217131\pi\) | ||||
0.776227 | + | 0.630454i | \(0.217131\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 26.4852 | 1.09130 | ||||||||
\(590\) | −21.8661 | −0.900212 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −10.8128 | −0.444404 | ||||||||
\(593\) | −25.5257 | −1.04821 | −0.524106 | − | 0.851653i | \(-0.675601\pi\) | ||||
−0.524106 | + | 0.851653i | \(0.675601\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 76.7150 | 3.14501 | ||||||||
\(596\) | 1.00000 | 0.0409616 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −25.7559 | −1.05324 | ||||||||
\(599\) | −21.1821 | −0.865478 | −0.432739 | − | 0.901519i | \(-0.642453\pi\) | ||||
−0.432739 | + | 0.901519i | \(0.642453\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 29.6931 | 1.21120 | 0.605602 | − | 0.795767i | \(-0.292932\pi\) | ||||
0.605602 | + | 0.795767i | \(0.292932\pi\) | |||||||
\(602\) | 47.6699 | 1.94288 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 2.74712 | 0.111779 | ||||||||
\(605\) | 63.3238 | 2.57448 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 6.32992 | 0.256923 | 0.128462 | − | 0.991714i | \(-0.458996\pi\) | ||||
0.128462 | + | 0.991714i | \(0.458996\pi\) | |||||||
\(608\) | 5.41154 | 0.219467 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 38.0400 | 1.54020 | ||||||||
\(611\) | −44.8884 | −1.81599 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 8.36343 | 0.337796 | 0.168898 | − | 0.985634i | \(-0.445979\pi\) | ||||
0.168898 | + | 0.985634i | \(0.445979\pi\) | |||||||
\(614\) | 0.252021 | 0.0101708 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 20.1513 | 0.811918 | ||||||||
\(617\) | 47.7212 | 1.92118 | 0.960592 | − | 0.277963i | \(-0.0896593\pi\) | ||||
0.960592 | + | 0.277963i | \(0.0896593\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −29.7786 | −1.19690 | −0.598451 | − | 0.801159i | \(-0.704217\pi\) | ||||
−0.598451 | + | 0.801159i | \(0.704217\pi\) | |||||||
\(620\) | 16.9525 | 0.680829 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 3.21065 | 0.128735 | ||||||||
\(623\) | 5.44051 | 0.217969 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −11.0194 | −0.440776 | ||||||||
\(626\) | −17.6474 | −0.705332 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −11.6087 | −0.463239 | ||||||||
\(629\) | 64.3076 | 2.56411 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 27.3209 | 1.08763 | 0.543815 | − | 0.839205i | \(-0.316979\pi\) | ||||
0.543815 | + | 0.839205i | \(0.316979\pi\) | |||||||
\(632\) | 2.27886 | 0.0906482 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −9.68734 | −0.384733 | ||||||||
\(635\) | −0.824516 | −0.0327199 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 37.4595 | 1.48420 | ||||||||
\(638\) | 30.7594 | 1.21778 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 3.46379 | 0.136918 | ||||||||
\(641\) | 26.6147 | 1.05122 | 0.525610 | − | 0.850726i | \(-0.323837\pi\) | ||||
0.525610 | + | 0.850726i | \(0.323837\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 25.3467 | 0.999577 | 0.499789 | − | 0.866147i | \(-0.333411\pi\) | ||||
0.499789 | + | 0.866147i | \(0.333411\pi\) | |||||||
\(644\) | 17.5850 | 0.692946 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −32.1843 | −1.26628 | ||||||||
\(647\) | 4.22827 | 0.166230 | 0.0831151 | − | 0.996540i | \(-0.473513\pi\) | ||||
0.0831151 | + | 0.996540i | \(0.473513\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 34.1599 | 1.34089 | ||||||||
\(650\) | 38.1683 | 1.49709 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −23.2573 | −0.910826 | ||||||||
\(653\) | −11.3973 | −0.446010 | −0.223005 | − | 0.974817i | \(-0.571587\pi\) | ||||
−0.223005 | + | 0.974817i | \(0.571587\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −0.0840858 | −0.00328551 | ||||||||
\(656\) | −10.6945 | −0.417551 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 30.6478 | 1.19478 | ||||||||
\(659\) | −22.0121 | −0.857471 | −0.428735 | − | 0.903430i | \(-0.641041\pi\) | ||||
−0.428735 | + | 0.903430i | \(0.641041\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −35.6587 | −1.38696 | −0.693481 | − | 0.720475i | \(-0.743924\pi\) | ||||
−0.693481 | + | 0.720475i | \(0.743924\pi\) | |||||||
\(662\) | 23.3524 | 0.907616 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −4.53459 | −0.175976 | ||||||||
\(665\) | −69.8035 | −2.70686 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 26.8422 | 1.03933 | ||||||||
\(668\) | 20.1860 | 0.781021 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −28.7544 | −1.11088 | ||||||||
\(671\) | −59.4275 | −2.29417 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −36.5338 | −1.40827 | −0.704137 | − | 0.710064i | \(-0.748666\pi\) | ||||
−0.704137 | + | 0.710064i | \(0.748666\pi\) | |||||||
\(674\) | 11.1102 | 0.427950 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 16.7494 | 0.644207 | ||||||||
\(677\) | 20.0748 | 0.771539 | 0.385770 | − | 0.922595i | \(-0.373936\pi\) | ||||
0.385770 | + | 0.922595i | \(0.373936\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −67.5008 | −2.59044 | ||||||||
\(680\) | −20.6004 | −0.789989 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −26.4838 | −1.01412 | ||||||||
\(683\) | 21.0937 | 0.807129 | 0.403565 | − | 0.914951i | \(-0.367771\pi\) | ||||
0.403565 | + | 0.914951i | \(0.367771\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 7.59541 | 0.290206 | ||||||||
\(686\) | 0.492021 | 0.0187855 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −12.8009 | −0.488029 | ||||||||
\(689\) | 64.4629 | 2.45584 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 22.4326 | 0.853377 | 0.426689 | − | 0.904399i | \(-0.359680\pi\) | ||||
0.426689 | + | 0.904399i | \(0.359680\pi\) | |||||||
\(692\) | −2.95800 | −0.112446 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −13.1429 | −0.498898 | ||||||||
\(695\) | −26.3627 | −0.999996 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 63.6041 | 2.40918 | ||||||||
\(698\) | −10.0265 | −0.379510 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −26.0597 | −0.984964 | ||||||||
\(701\) | 31.3649 | 1.18464 | 0.592318 | − | 0.805704i | \(-0.298213\pi\) | ||||
0.592318 | + | 0.805704i | \(0.298213\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −58.5139 | −2.20689 | ||||||||
\(704\) | −5.41125 | −0.203944 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −22.1184 | −0.832436 | ||||||||
\(707\) | 29.6735 | 1.11599 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 19.4658 | 0.731055 | 0.365528 | − | 0.930801i | \(-0.380889\pi\) | ||||
0.365528 | + | 0.930801i | \(0.380889\pi\) | |||||||
\(710\) | −3.06177 | −0.114906 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −1.46095 | −0.0547513 | ||||||||
\(713\) | −23.1111 | −0.865516 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −102.232 | −3.82327 | ||||||||
\(716\) | −11.9473 | −0.446493 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 19.5158 | 0.728323 | ||||||||
\(719\) | 8.77430 | 0.327226 | 0.163613 | − | 0.986525i | \(-0.447685\pi\) | ||||
0.163613 | + | 0.986525i | \(0.447685\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −44.1566 | −1.64448 | ||||||||
\(722\) | 10.2848 | 0.382759 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −20.7182 | −0.769986 | ||||||||
\(725\) | −39.7782 | −1.47732 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 4.57286 | 0.169598 | 0.0847990 | − | 0.996398i | \(-0.472975\pi\) | ||||
0.0847990 | + | 0.996398i | \(0.472975\pi\) | |||||||
\(728\) | −20.3116 | −0.752798 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 23.8285 | 0.881934 | ||||||||
\(731\) | 76.1313 | 2.81582 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 22.0022 | 0.812670 | 0.406335 | − | 0.913724i | \(-0.366807\pi\) | ||||
0.406335 | + | 0.913724i | \(0.366807\pi\) | |||||||
\(734\) | 3.06129 | 0.112994 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −4.72212 | −0.174060 | ||||||||
\(737\) | 44.9212 | 1.65469 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −31.4305 | −1.15619 | −0.578095 | − | 0.815969i | \(-0.696204\pi\) | ||||
−0.578095 | + | 0.815969i | \(0.696204\pi\) | |||||||
\(740\) | −37.4533 | −1.37681 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −44.0125 | −1.61575 | ||||||||
\(743\) | 37.2913 | 1.36809 | 0.684043 | − | 0.729441i | \(-0.260220\pi\) | ||||
0.684043 | + | 0.729441i | \(0.260220\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 3.46379 | 0.126903 | ||||||||
\(746\) | −16.5213 | −0.604889 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 32.1826 | 1.17671 | ||||||||
\(749\) | 15.3928 | 0.562441 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 20.7149 | 0.755898 | 0.377949 | − | 0.925826i | \(-0.376630\pi\) | ||||
0.377949 | + | 0.925826i | \(0.376630\pi\) | |||||||
\(752\) | −8.22990 | −0.300114 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −31.0041 | −1.12910 | ||||||||
\(755\) | 9.51546 | 0.346303 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1.38254 | 0.0502492 | 0.0251246 | − | 0.999684i | \(-0.492002\pi\) | ||||
0.0251246 | + | 0.999684i | \(0.492002\pi\) | |||||||
\(758\) | −24.7081 | −0.897438 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 18.7444 | 0.679932 | ||||||||
\(761\) | −40.2126 | −1.45771 | −0.728853 | − | 0.684670i | \(-0.759946\pi\) | ||||
−0.728853 | + | 0.684670i | \(0.759946\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 62.6017 | 2.26633 | ||||||||
\(764\) | −17.1850 | −0.621731 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 4.53673 | 0.163919 | ||||||||
\(767\) | −34.4317 | −1.24326 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 4.72751 | 0.170478 | 0.0852391 | − | 0.996361i | \(-0.472835\pi\) | ||||
0.0852391 | + | 0.996361i | \(0.472835\pi\) | |||||||
\(770\) | 69.7998 | 2.51541 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0.843776 | 0.0303682 | ||||||||
\(773\) | −0.478036 | −0.0171937 | −0.00859687 | − | 0.999963i | \(-0.502737\pi\) | ||||
−0.00859687 | + | 0.999963i | \(0.502737\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 34.2489 | 1.23026 | ||||||||
\(776\) | 18.1261 | 0.650689 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 31.1647 | 1.11731 | ||||||||
\(779\) | −57.8738 | −2.07354 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 4.78321 | 0.171157 | ||||||||
\(782\) | 28.0841 | 1.00429 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 6.86788 | 0.245281 | ||||||||
\(785\) | −40.2103 | −1.43517 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 8.16119 | 0.290915 | 0.145457 | − | 0.989365i | \(-0.453535\pi\) | ||||
0.145457 | + | 0.989365i | \(0.453535\pi\) | |||||||
\(788\) | 9.38954 | 0.334489 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 7.89350 | 0.280838 | ||||||||
\(791\) | −35.1177 | −1.24864 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 59.9002 | 2.12712 | ||||||||
\(794\) | 14.0089 | 0.497159 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 4.08274 | 0.144709 | ||||||||
\(797\) | −53.1778 | −1.88365 | −0.941827 | − | 0.336098i | \(-0.890893\pi\) | ||||
−0.941827 | + | 0.336098i | \(0.890893\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 48.9461 | 1.73159 | ||||||||
\(800\) | 6.99784 | 0.247411 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −19.7883 | −0.698747 | ||||||||
\(803\) | −37.2258 | −1.31367 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 60.9108 | 2.14682 | ||||||||
\(806\) | 26.6945 | 0.940273 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −7.96826 | −0.280322 | ||||||||
\(809\) | −5.56478 | −0.195647 | −0.0978236 | − | 0.995204i | \(-0.531188\pi\) | ||||
−0.0978236 | + | 0.995204i | \(0.531188\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −18.6131 | −0.653594 | −0.326797 | − | 0.945094i | \(-0.605969\pi\) | ||||
−0.326797 | + | 0.945094i | \(0.605969\pi\) | |||||||
\(812\) | 21.1683 | 0.742861 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 58.5108 | 2.05080 | ||||||||
\(815\) | −80.5584 | −2.82184 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −69.2724 | −2.42353 | ||||||||
\(818\) | −12.8739 | −0.450127 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −37.0435 | −1.29362 | ||||||||
\(821\) | −52.9148 | −1.84674 | −0.923370 | − | 0.383912i | \(-0.874577\pi\) | ||||
−0.923370 | + | 0.383912i | \(0.874577\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 37.9567 | 1.32309 | 0.661543 | − | 0.749907i | \(-0.269902\pi\) | ||||
0.661543 | + | 0.749907i | \(0.269902\pi\) | |||||||
\(824\) | 11.8574 | 0.413073 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 23.5085 | 0.817964 | ||||||||
\(827\) | 38.1529 | 1.32670 | 0.663352 | − | 0.748307i | \(-0.269133\pi\) | ||||
0.663352 | + | 0.748307i | \(0.269133\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −13.0479 | −0.453173 | −0.226587 | − | 0.973991i | \(-0.572757\pi\) | ||||
−0.226587 | + | 0.973991i | \(0.572757\pi\) | |||||||
\(830\) | −15.7069 | −0.545193 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 5.45430 | 0.189094 | ||||||||
\(833\) | −40.8457 | −1.41522 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 69.9202 | 2.41969 | ||||||||
\(836\) | −29.2832 | −1.01278 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −17.4280 | −0.602039 | ||||||||
\(839\) | 31.5390 | 1.08885 | 0.544424 | − | 0.838810i | \(-0.316748\pi\) | ||||
0.544424 | + | 0.838810i | \(0.316748\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 3.31178 | 0.114199 | ||||||||
\(842\) | 26.0347 | 0.897215 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 12.4094 | 0.427149 | ||||||||
\(845\) | 58.0164 | 1.99582 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −68.0801 | −2.33926 | ||||||||
\(848\) | 11.8187 | 0.405857 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −41.6187 | −1.42751 | ||||||||
\(851\) | 51.0594 | 1.75029 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −30.8429 | −1.05604 | −0.528021 | − | 0.849232i | \(-0.677066\pi\) | ||||
−0.528021 | + | 0.849232i | \(0.677066\pi\) | |||||||
\(854\) | −40.8973 | −1.39948 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −4.13345 | −0.141278 | ||||||||
\(857\) | −15.4634 | −0.528219 | −0.264110 | − | 0.964493i | \(-0.585078\pi\) | ||||
−0.264110 | + | 0.964493i | \(0.585078\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 31.4288 | 1.07234 | 0.536168 | − | 0.844112i | \(-0.319871\pi\) | ||||
0.536168 | + | 0.844112i | \(0.319871\pi\) | |||||||
\(860\) | −44.3395 | −1.51197 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −4.09204 | −0.139375 | ||||||||
\(863\) | 31.7402 | 1.08045 | 0.540224 | − | 0.841521i | \(-0.318340\pi\) | ||||
0.540224 | + | 0.841521i | \(0.318340\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −10.2459 | −0.348371 | ||||||||
\(866\) | 21.9423 | 0.745631 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −18.2258 | −0.618625 | ||||||||
\(869\) | −12.3315 | −0.418317 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −45.2785 | −1.53420 | ||||||||
\(872\) | −16.8105 | −0.569276 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −25.5540 | −0.864376 | ||||||||
\(875\) | −25.7702 | −0.871193 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −29.5509 | −0.997863 | −0.498931 | − | 0.866642i | \(-0.666274\pi\) | ||||
−0.498931 | + | 0.866642i | \(0.666274\pi\) | |||||||
\(878\) | −26.8522 | −0.906216 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −18.7434 | −0.631841 | ||||||||
\(881\) | −16.4745 | −0.555040 | −0.277520 | − | 0.960720i | \(-0.589512\pi\) | ||||
−0.277520 | + | 0.960720i | \(0.589512\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 5.97164 | 0.200962 | 0.100481 | − | 0.994939i | \(-0.467962\pi\) | ||||
0.100481 | + | 0.994939i | \(0.467962\pi\) | |||||||
\(884\) | −32.4387 | −1.09103 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −1.31682 | −0.0442393 | ||||||||
\(887\) | 21.7725 | 0.731048 | 0.365524 | − | 0.930802i | \(-0.380890\pi\) | ||||
0.365524 | + | 0.930802i | \(0.380890\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0.886447 | 0.0297305 | ||||||||
\(890\) | −5.06042 | −0.169626 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −2.60836 | −0.0873345 | ||||||||
\(893\) | −44.5364 | −1.49036 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −41.3831 | −1.38328 | ||||||||
\(896\) | −3.72396 | −0.124409 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 9.00217 | 0.300406 | ||||||||
\(899\) | −27.8204 | −0.927861 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −70.2902 | −2.34171 | ||||||||
\(902\) | 57.8707 | 1.92688 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 9.43021 | 0.313644 | ||||||||
\(905\) | −71.7635 | −2.38550 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 33.1641 | 1.10120 | 0.550598 | − | 0.834771i | \(-0.314400\pi\) | ||||
0.550598 | + | 0.834771i | \(0.314400\pi\) | |||||||
\(908\) | −1.09859 | −0.0364579 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −70.3551 | −2.33225 | ||||||||
\(911\) | −18.7236 | −0.620342 | −0.310171 | − | 0.950681i | \(-0.600386\pi\) | ||||
−0.310171 | + | 0.950681i | \(0.600386\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 24.5378 | 0.812083 | ||||||||
\(914\) | 0.899724 | 0.0297602 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 19.5454 | 0.645799 | ||||||||
\(917\) | 0.0904016 | 0.00298532 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −5.10012 | −0.168237 | −0.0841187 | − | 0.996456i | \(-0.526807\pi\) | ||||
−0.0841187 | + | 0.996456i | \(0.526807\pi\) | |||||||
\(920\) | −16.3564 | −0.539256 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 2.41367 | 0.0794900 | ||||||||
\(923\) | −4.82126 | −0.158694 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −75.6664 | −2.48789 | ||||||||
\(926\) | −10.3255 | −0.339318 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −5.68434 | −0.186598 | ||||||||
\(929\) | −22.0558 | −0.723627 | −0.361813 | − | 0.932251i | \(-0.617842\pi\) | ||||
−0.361813 | + | 0.932251i | \(0.617842\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 37.1658 | 1.21806 | ||||||||
\(932\) | −22.8074 | −0.747081 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −11.2771 | −0.369000 | ||||||||
\(935\) | 111.474 | 3.64559 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 43.4294 | 1.41878 | 0.709388 | − | 0.704818i | \(-0.248971\pi\) | ||||
0.709388 | + | 0.704818i | \(0.248971\pi\) | |||||||
\(938\) | 30.9142 | 1.00939 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −28.5067 | −0.929785 | ||||||||
\(941\) | 4.85491 | 0.158265 | 0.0791327 | − | 0.996864i | \(-0.474785\pi\) | ||||
0.0791327 | + | 0.996864i | \(0.474785\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 50.5008 | 1.64453 | ||||||||
\(944\) | −6.31276 | −0.205463 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 69.2687 | 2.25212 | ||||||||
\(947\) | −3.91485 | −0.127215 | −0.0636077 | − | 0.997975i | \(-0.520261\pi\) | ||||
−0.0636077 | + | 0.997975i | \(0.520261\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 37.5219 | 1.21801 | ||||||||
\(950\) | 37.8691 | 1.22864 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 22.1477 | 0.717811 | ||||||||
\(953\) | 14.1503 | 0.458375 | 0.229187 | − | 0.973382i | \(-0.426393\pi\) | ||||
0.229187 | + | 0.973382i | \(0.426393\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −59.5252 | −1.92619 | ||||||||
\(956\) | 1.17661 | 0.0380543 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 14.2371 | 0.459979 | ||||||||
\(959\) | −8.16591 | −0.263691 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −7.04673 | −0.227314 | ||||||||
\(962\) | −58.9763 | −1.90147 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −22.0093 | −0.708870 | ||||||||
\(965\) | 2.92266 | 0.0940839 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 57.0322 | 1.83403 | 0.917016 | − | 0.398850i | \(-0.130591\pi\) | ||||
0.917016 | + | 0.398850i | \(0.130591\pi\) | |||||||
\(968\) | 18.2816 | 0.587594 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 62.7850 | 2.01590 | ||||||||
\(971\) | −13.2501 | −0.425216 | −0.212608 | − | 0.977138i | \(-0.568196\pi\) | ||||
−0.212608 | + | 0.977138i | \(0.568196\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 28.3429 | 0.908631 | ||||||||
\(974\) | 7.25573 | 0.232489 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 10.9822 | 0.351532 | ||||||||
\(977\) | 25.1158 | 0.803526 | 0.401763 | − | 0.915744i | \(-0.368398\pi\) | ||||
0.401763 | + | 0.915744i | \(0.368398\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 7.90556 | 0.252663 | ||||||||
\(980\) | 23.7889 | 0.759908 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −9.21094 | −0.293933 | ||||||||
\(983\) | −30.8442 | −0.983778 | −0.491889 | − | 0.870658i | \(-0.663694\pi\) | ||||
−0.491889 | + | 0.870658i | \(0.663694\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 32.5234 | 1.03628 | ||||||||
\(986\) | 33.8068 | 1.07663 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 29.5162 | 0.939034 | ||||||||
\(989\) | 60.4473 | 1.92211 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −11.8688 | −0.377025 | −0.188512 | − | 0.982071i | \(-0.560367\pi\) | ||||
−0.188512 | + | 0.982071i | \(0.560367\pi\) | |||||||
\(992\) | 4.89421 | 0.155391 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 3.29175 | 0.104408 | ||||||||
\(995\) | 14.1418 | 0.448324 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −42.8911 | −1.35838 | −0.679188 | − | 0.733964i | \(-0.737668\pi\) | ||||
−0.679188 | + | 0.733964i | \(0.737668\pi\) | |||||||
\(998\) | −34.1216 | −1.08010 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 8046.2.a.n.1.12 | yes | 12 | |
3.2 | odd | 2 | 8046.2.a.k.1.1 | ✓ | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8046.2.a.k.1.1 | ✓ | 12 | 3.2 | odd | 2 | ||
8046.2.a.n.1.12 | yes | 12 | 1.1 | even | 1 | trivial |