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: | \(0\) |
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: | \( x^{12} - 5 x^{11} - 21 x^{10} + 116 x^{9} + 106 x^{8} - 774 x^{7} - 63 x^{6} + 2013 x^{5} - 417 x^{4} - 2249 x^{3} + 761 x^{2} + 910 x - 375 \) |
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 | 1.11 | ||
Root | \(4.11015\) 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 | ||||||||
\(5\) | 4.11015 | 1.83812 | 0.919058 | − | 0.394123i | \(-0.128951\pi\) | ||||
0.919058 | + | 0.394123i | \(0.128951\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −3.78475 | −1.43050 | −0.715250 | − | 0.698869i | \(-0.753687\pi\) | ||||
−0.715250 | + | 0.698869i | \(0.753687\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −4.11015 | −1.29974 | ||||||||
\(11\) | 2.15275 | 0.649079 | 0.324539 | − | 0.945872i | \(-0.394791\pi\) | ||||
0.324539 | + | 0.945872i | \(0.394791\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 5.55753 | 1.54138 | 0.770690 | − | 0.637210i | \(-0.219912\pi\) | ||||
0.770690 | + | 0.637210i | \(0.219912\pi\) | |||||||
\(14\) | 3.78475 | 1.01152 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −2.24829 | −0.545292 | −0.272646 | − | 0.962114i | \(-0.587899\pi\) | ||||
−0.272646 | + | 0.962114i | \(0.587899\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.44233 | 0.560308 | 0.280154 | − | 0.959955i | \(-0.409614\pi\) | ||||
0.280154 | + | 0.959955i | \(0.409614\pi\) | |||||||
\(20\) | 4.11015 | 0.919058 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −2.15275 | −0.458968 | ||||||||
\(23\) | −0.398673 | −0.0831291 | −0.0415645 | − | 0.999136i | \(-0.513234\pi\) | ||||
−0.0415645 | + | 0.999136i | \(0.513234\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 11.8933 | 2.37867 | ||||||||
\(26\) | −5.55753 | −1.08992 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −3.78475 | −0.715250 | ||||||||
\(29\) | 8.12942 | 1.50959 | 0.754797 | − | 0.655958i | \(-0.227735\pi\) | ||||
0.754797 | + | 0.655958i | \(0.227735\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.810327 | 0.145539 | 0.0727695 | − | 0.997349i | \(-0.476816\pi\) | ||||
0.0727695 | + | 0.997349i | \(0.476816\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 2.24829 | 0.385579 | ||||||||
\(35\) | −15.5559 | −2.62942 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 8.17817 | 1.34448 | 0.672241 | − | 0.740332i | \(-0.265332\pi\) | ||||
0.672241 | + | 0.740332i | \(0.265332\pi\) | |||||||
\(38\) | −2.44233 | −0.396198 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −4.11015 | −0.649872 | ||||||||
\(41\) | 0.726269 | 0.113424 | 0.0567121 | − | 0.998391i | \(-0.481938\pi\) | ||||
0.0567121 | + | 0.998391i | \(0.481938\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −3.96985 | −0.605396 | −0.302698 | − | 0.953087i | \(-0.597887\pi\) | ||||
−0.302698 | + | 0.953087i | \(0.597887\pi\) | |||||||
\(44\) | 2.15275 | 0.324539 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0.398673 | 0.0587811 | ||||||||
\(47\) | 7.08367 | 1.03326 | 0.516630 | − | 0.856209i | \(-0.327186\pi\) | ||||
0.516630 | + | 0.856209i | \(0.327186\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 7.32431 | 1.04633 | ||||||||
\(50\) | −11.8933 | −1.68197 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 5.55753 | 0.770690 | ||||||||
\(53\) | −9.53601 | −1.30987 | −0.654936 | − | 0.755685i | \(-0.727304\pi\) | ||||
−0.654936 | + | 0.755685i | \(0.727304\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 8.84813 | 1.19308 | ||||||||
\(56\) | 3.78475 | 0.505758 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −8.12942 | −1.06744 | ||||||||
\(59\) | −11.4244 | −1.48733 | −0.743664 | − | 0.668553i | \(-0.766914\pi\) | ||||
−0.743664 | + | 0.668553i | \(0.766914\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 5.54958 | 0.710551 | 0.355276 | − | 0.934762i | \(-0.384387\pi\) | ||||
0.355276 | + | 0.934762i | \(0.384387\pi\) | |||||||
\(62\) | −0.810327 | −0.102912 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 22.8423 | 2.83324 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 3.37901 | 0.412812 | 0.206406 | − | 0.978466i | \(-0.433823\pi\) | ||||
0.206406 | + | 0.978466i | \(0.433823\pi\) | |||||||
\(68\) | −2.24829 | −0.272646 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 15.5559 | 1.85928 | ||||||||
\(71\) | 8.38502 | 0.995119 | 0.497559 | − | 0.867430i | \(-0.334230\pi\) | ||||
0.497559 | + | 0.867430i | \(0.334230\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −5.85256 | −0.684991 | −0.342495 | − | 0.939520i | \(-0.611272\pi\) | ||||
−0.342495 | + | 0.939520i | \(0.611272\pi\) | |||||||
\(74\) | −8.17817 | −0.950693 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 2.44233 | 0.280154 | ||||||||
\(77\) | −8.14762 | −0.928507 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −10.4633 | −1.17721 | −0.588604 | − | 0.808422i | \(-0.700322\pi\) | ||||
−0.588604 | + | 0.808422i | \(0.700322\pi\) | |||||||
\(80\) | 4.11015 | 0.459529 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −0.726269 | −0.0802030 | ||||||||
\(83\) | −1.42102 | −0.155977 | −0.0779886 | − | 0.996954i | \(-0.524850\pi\) | ||||
−0.0779886 | + | 0.996954i | \(0.524850\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −9.24083 | −1.00231 | ||||||||
\(86\) | 3.96985 | 0.428079 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −2.15275 | −0.229484 | ||||||||
\(89\) | 15.6438 | 1.65824 | 0.829119 | − | 0.559072i | \(-0.188842\pi\) | ||||
0.829119 | + | 0.559072i | \(0.188842\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −21.0338 | −2.20494 | ||||||||
\(92\) | −0.398673 | −0.0415645 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −7.08367 | −0.730625 | ||||||||
\(95\) | 10.0383 | 1.02991 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −10.0228 | −1.01766 | −0.508829 | − | 0.860868i | \(-0.669922\pi\) | ||||
−0.508829 | + | 0.860868i | \(0.669922\pi\) | |||||||
\(98\) | −7.32431 | −0.739867 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 11.8933 | 1.18933 | ||||||||
\(101\) | 6.69423 | 0.666101 | 0.333050 | − | 0.942909i | \(-0.391922\pi\) | ||||
0.333050 | + | 0.942909i | \(0.391922\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −12.2037 | −1.20247 | −0.601233 | − | 0.799074i | \(-0.705323\pi\) | ||||
−0.601233 | + | 0.799074i | \(0.705323\pi\) | |||||||
\(104\) | −5.55753 | −0.544960 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 9.53601 | 0.926219 | ||||||||
\(107\) | −1.15590 | −0.111745 | −0.0558726 | − | 0.998438i | \(-0.517794\pi\) | ||||
−0.0558726 | + | 0.998438i | \(0.517794\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 10.3304 | 0.989476 | 0.494738 | − | 0.869042i | \(-0.335264\pi\) | ||||
0.494738 | + | 0.869042i | \(0.335264\pi\) | |||||||
\(110\) | −8.84813 | −0.843636 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −3.78475 | −0.357625 | ||||||||
\(113\) | −14.7374 | −1.38638 | −0.693190 | − | 0.720755i | \(-0.743795\pi\) | ||||
−0.693190 | + | 0.720755i | \(0.743795\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1.63861 | −0.152801 | ||||||||
\(116\) | 8.12942 | 0.754797 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 11.4244 | 1.05170 | ||||||||
\(119\) | 8.50923 | 0.780039 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −6.36566 | −0.578697 | ||||||||
\(122\) | −5.54958 | −0.502435 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0.810327 | 0.0727695 | ||||||||
\(125\) | 28.3327 | 2.53415 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −15.4737 | −1.37307 | −0.686535 | − | 0.727097i | \(-0.740869\pi\) | ||||
−0.686535 | + | 0.727097i | \(0.740869\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −22.8423 | −2.00340 | ||||||||
\(131\) | −17.0676 | −1.49120 | −0.745600 | − | 0.666394i | \(-0.767837\pi\) | ||||
−0.745600 | + | 0.666394i | \(0.767837\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −9.24359 | −0.801521 | ||||||||
\(134\) | −3.37901 | −0.291902 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 2.24829 | 0.192790 | ||||||||
\(137\) | −12.0167 | −1.02665 | −0.513327 | − | 0.858193i | \(-0.671587\pi\) | ||||
−0.513327 | + | 0.858193i | \(0.671587\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 8.26244 | 0.700811 | 0.350406 | − | 0.936598i | \(-0.386044\pi\) | ||||
0.350406 | + | 0.936598i | \(0.386044\pi\) | |||||||
\(140\) | −15.5559 | −1.31471 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −8.38502 | −0.703655 | ||||||||
\(143\) | 11.9640 | 1.00048 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 33.4131 | 2.77481 | ||||||||
\(146\) | 5.85256 | 0.484361 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 8.17817 | 0.672241 | ||||||||
\(149\) | 1.00000 | 0.0819232 | ||||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 23.5649 | 1.91769 | 0.958843 | − | 0.283938i | \(-0.0916410\pi\) | ||||
0.958843 | + | 0.283938i | \(0.0916410\pi\) | |||||||
\(152\) | −2.44233 | −0.198099 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 8.14762 | 0.656554 | ||||||||
\(155\) | 3.33057 | 0.267517 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 3.01390 | 0.240535 | 0.120268 | − | 0.992741i | \(-0.461625\pi\) | ||||
0.120268 | + | 0.992741i | \(0.461625\pi\) | |||||||
\(158\) | 10.4633 | 0.832412 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −4.11015 | −0.324936 | ||||||||
\(161\) | 1.50888 | 0.118916 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −15.9593 | −1.25003 | −0.625016 | − | 0.780612i | \(-0.714908\pi\) | ||||
−0.625016 | + | 0.780612i | \(0.714908\pi\) | |||||||
\(164\) | 0.726269 | 0.0567121 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 1.42102 | 0.110292 | ||||||||
\(167\) | 25.5613 | 1.97799 | 0.988997 | − | 0.147939i | \(-0.0472639\pi\) | ||||
0.988997 | + | 0.147939i | \(0.0472639\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 17.8861 | 1.37585 | ||||||||
\(170\) | 9.24083 | 0.708740 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −3.96985 | −0.302698 | ||||||||
\(173\) | 17.7637 | 1.35055 | 0.675274 | − | 0.737567i | \(-0.264025\pi\) | ||||
0.675274 | + | 0.737567i | \(0.264025\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −45.0133 | −3.40269 | ||||||||
\(176\) | 2.15275 | 0.162270 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −15.6438 | −1.17255 | ||||||||
\(179\) | 15.5056 | 1.15895 | 0.579473 | − | 0.814992i | \(-0.303259\pi\) | ||||
0.579473 | + | 0.814992i | \(0.303259\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −14.7689 | −1.09777 | −0.548883 | − | 0.835899i | \(-0.684947\pi\) | ||||
−0.548883 | + | 0.835899i | \(0.684947\pi\) | |||||||
\(182\) | 21.0338 | 1.55913 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0.398673 | 0.0293906 | ||||||||
\(185\) | 33.6135 | 2.47131 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −4.84002 | −0.353937 | ||||||||
\(188\) | 7.08367 | 0.516630 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −10.0383 | −0.728257 | ||||||||
\(191\) | 4.50124 | 0.325699 | 0.162849 | − | 0.986651i | \(-0.447932\pi\) | ||||
0.162849 | + | 0.986651i | \(0.447932\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 11.3824 | 0.819325 | 0.409663 | − | 0.912237i | \(-0.365646\pi\) | ||||
0.409663 | + | 0.912237i | \(0.365646\pi\) | |||||||
\(194\) | 10.0228 | 0.719593 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 7.32431 | 0.523165 | ||||||||
\(197\) | 12.9512 | 0.922734 | 0.461367 | − | 0.887209i | \(-0.347359\pi\) | ||||
0.461367 | + | 0.887209i | \(0.347359\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1.67614 | 0.118818 | 0.0594092 | − | 0.998234i | \(-0.481078\pi\) | ||||
0.0594092 | + | 0.998234i | \(0.481078\pi\) | |||||||
\(200\) | −11.8933 | −0.840987 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −6.69423 | −0.471004 | ||||||||
\(203\) | −30.7678 | −2.15947 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 2.98508 | 0.208487 | ||||||||
\(206\) | 12.2037 | 0.850271 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 5.55753 | 0.385345 | ||||||||
\(209\) | 5.25772 | 0.363684 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −23.0409 | −1.58620 | −0.793101 | − | 0.609091i | \(-0.791535\pi\) | ||||
−0.793101 | + | 0.609091i | \(0.791535\pi\) | |||||||
\(212\) | −9.53601 | −0.654936 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 1.15590 | 0.0790158 | ||||||||
\(215\) | −16.3167 | −1.11279 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −3.06688 | −0.208193 | ||||||||
\(218\) | −10.3304 | −0.699665 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 8.84813 | 0.596541 | ||||||||
\(221\) | −12.4950 | −0.840502 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 4.24071 | 0.283979 | 0.141990 | − | 0.989868i | \(-0.454650\pi\) | ||||
0.141990 | + | 0.989868i | \(0.454650\pi\) | |||||||
\(224\) | 3.78475 | 0.252879 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 14.7374 | 0.980318 | ||||||||
\(227\) | 21.1581 | 1.40431 | 0.702156 | − | 0.712023i | \(-0.252221\pi\) | ||||
0.702156 | + | 0.712023i | \(0.252221\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 9.81055 | 0.648299 | 0.324150 | − | 0.946006i | \(-0.394922\pi\) | ||||
0.324150 | + | 0.946006i | \(0.394922\pi\) | |||||||
\(230\) | 1.63861 | 0.108047 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −8.12942 | −0.533722 | ||||||||
\(233\) | 27.6563 | 1.81183 | 0.905914 | − | 0.423462i | \(-0.139185\pi\) | ||||
0.905914 | + | 0.423462i | \(0.139185\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 29.1150 | 1.89925 | ||||||||
\(236\) | −11.4244 | −0.743664 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −8.50923 | −0.551571 | ||||||||
\(239\) | 20.9751 | 1.35676 | 0.678382 | − | 0.734710i | \(-0.262682\pi\) | ||||
0.678382 | + | 0.734710i | \(0.262682\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 16.3880 | 1.05565 | 0.527823 | − | 0.849355i | \(-0.323009\pi\) | ||||
0.527823 | + | 0.849355i | \(0.323009\pi\) | |||||||
\(242\) | 6.36566 | 0.409200 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 5.54958 | 0.355276 | ||||||||
\(245\) | 30.1040 | 1.92327 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 13.5733 | 0.863648 | ||||||||
\(248\) | −0.810327 | −0.0514558 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −28.3327 | −1.79192 | ||||||||
\(251\) | −1.25604 | −0.0792806 | −0.0396403 | − | 0.999214i | \(-0.512621\pi\) | ||||
−0.0396403 | + | 0.999214i | \(0.512621\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −0.858243 | −0.0539573 | ||||||||
\(254\) | 15.4737 | 0.970907 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −18.7145 | −1.16738 | −0.583688 | − | 0.811978i | \(-0.698391\pi\) | ||||
−0.583688 | + | 0.811978i | \(0.698391\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −30.9523 | −1.92328 | ||||||||
\(260\) | 22.8423 | 1.41662 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 17.0676 | 1.05444 | ||||||||
\(263\) | 24.6171 | 1.51796 | 0.758978 | − | 0.651116i | \(-0.225699\pi\) | ||||
0.758978 | + | 0.651116i | \(0.225699\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −39.1944 | −2.40769 | ||||||||
\(266\) | 9.24359 | 0.566761 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 3.37901 | 0.206406 | ||||||||
\(269\) | −16.4410 | −1.00242 | −0.501211 | − | 0.865325i | \(-0.667112\pi\) | ||||
−0.501211 | + | 0.865325i | \(0.667112\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −7.32917 | −0.445215 | −0.222608 | − | 0.974908i | \(-0.571457\pi\) | ||||
−0.222608 | + | 0.974908i | \(0.571457\pi\) | |||||||
\(272\) | −2.24829 | −0.136323 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 12.0167 | 0.725954 | ||||||||
\(275\) | 25.6034 | 1.54394 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −20.8558 | −1.25310 | −0.626551 | − | 0.779381i | \(-0.715534\pi\) | ||||
−0.626551 | + | 0.779381i | \(0.715534\pi\) | |||||||
\(278\) | −8.26244 | −0.495548 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 15.5559 | 0.929642 | ||||||||
\(281\) | −17.8130 | −1.06264 | −0.531318 | − | 0.847172i | \(-0.678303\pi\) | ||||
−0.531318 | + | 0.847172i | \(0.678303\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −27.8399 | −1.65491 | −0.827456 | − | 0.561531i | \(-0.810213\pi\) | ||||
−0.827456 | + | 0.561531i | \(0.810213\pi\) | |||||||
\(284\) | 8.38502 | 0.497559 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −11.9640 | −0.707444 | ||||||||
\(287\) | −2.74874 | −0.162253 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −11.9452 | −0.702657 | ||||||||
\(290\) | −33.4131 | −1.96209 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −5.85256 | −0.342495 | ||||||||
\(293\) | 11.6167 | 0.678656 | 0.339328 | − | 0.940668i | \(-0.389800\pi\) | ||||
0.339328 | + | 0.940668i | \(0.389800\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −46.9560 | −2.73388 | ||||||||
\(296\) | −8.17817 | −0.475346 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −1.00000 | −0.0579284 | ||||||||
\(299\) | −2.21564 | −0.128133 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 15.0249 | 0.866018 | ||||||||
\(302\) | −23.5649 | −1.35601 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 2.44233 | 0.140077 | ||||||||
\(305\) | 22.8096 | 1.30608 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 15.6923 | 0.895607 | 0.447804 | − | 0.894132i | \(-0.352206\pi\) | ||||
0.447804 | + | 0.894132i | \(0.352206\pi\) | |||||||
\(308\) | −8.14762 | −0.464253 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −3.33057 | −0.189163 | ||||||||
\(311\) | 4.04112 | 0.229151 | 0.114576 | − | 0.993415i | \(-0.463449\pi\) | ||||
0.114576 | + | 0.993415i | \(0.463449\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 4.56731 | 0.258160 | 0.129080 | − | 0.991634i | \(-0.458798\pi\) | ||||
0.129080 | + | 0.991634i | \(0.458798\pi\) | |||||||
\(314\) | −3.01390 | −0.170084 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −10.4633 | −0.588604 | ||||||||
\(317\) | −24.3298 | −1.36650 | −0.683249 | − | 0.730185i | \(-0.739434\pi\) | ||||
−0.683249 | + | 0.730185i | \(0.739434\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 17.5006 | 0.979846 | ||||||||
\(320\) | 4.11015 | 0.229764 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −1.50888 | −0.0840864 | ||||||||
\(323\) | −5.49107 | −0.305531 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 66.0976 | 3.66643 | ||||||||
\(326\) | 15.9593 | 0.883906 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −0.726269 | −0.0401015 | ||||||||
\(329\) | −26.8099 | −1.47808 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 15.2814 | 0.839942 | 0.419971 | − | 0.907538i | \(-0.362040\pi\) | ||||
0.419971 | + | 0.907538i | \(0.362040\pi\) | |||||||
\(332\) | −1.42102 | −0.0779886 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −25.5613 | −1.39865 | ||||||||
\(335\) | 13.8883 | 0.758796 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 16.3455 | 0.890398 | 0.445199 | − | 0.895432i | \(-0.353133\pi\) | ||||
0.445199 | + | 0.895432i | \(0.353133\pi\) | |||||||
\(338\) | −17.8861 | −0.972875 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −9.24083 | −0.501155 | ||||||||
\(341\) | 1.74443 | 0.0944663 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.22742 | −0.0662742 | ||||||||
\(344\) | 3.96985 | 0.214040 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −17.7637 | −0.954981 | ||||||||
\(347\) | 18.2895 | 0.981830 | 0.490915 | − | 0.871207i | \(-0.336663\pi\) | ||||
0.490915 | + | 0.871207i | \(0.336663\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 5.35471 | 0.286631 | 0.143316 | − | 0.989677i | \(-0.454224\pi\) | ||||
0.143316 | + | 0.989677i | \(0.454224\pi\) | |||||||
\(350\) | 45.0133 | 2.40606 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −2.15275 | −0.114742 | ||||||||
\(353\) | 26.9483 | 1.43431 | 0.717157 | − | 0.696912i | \(-0.245443\pi\) | ||||
0.717157 | + | 0.696912i | \(0.245443\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 34.4637 | 1.82914 | ||||||||
\(356\) | 15.6438 | 0.829119 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −15.5056 | −0.819498 | ||||||||
\(359\) | −10.2380 | −0.540342 | −0.270171 | − | 0.962812i | \(-0.587080\pi\) | ||||
−0.270171 | + | 0.962812i | \(0.587080\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −13.0350 | −0.686055 | ||||||||
\(362\) | 14.7689 | 0.776238 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −21.0338 | −1.10247 | ||||||||
\(365\) | −24.0549 | −1.25909 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 6.92125 | 0.361287 | 0.180643 | − | 0.983549i | \(-0.442182\pi\) | ||||
0.180643 | + | 0.983549i | \(0.442182\pi\) | |||||||
\(368\) | −0.398673 | −0.0207823 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −33.6135 | −1.74748 | ||||||||
\(371\) | 36.0914 | 1.87377 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 6.70601 | 0.347224 | 0.173612 | − | 0.984814i | \(-0.444456\pi\) | ||||
0.173612 | + | 0.984814i | \(0.444456\pi\) | |||||||
\(374\) | 4.84002 | 0.250271 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −7.08367 | −0.365312 | ||||||||
\(377\) | 45.1794 | 2.32686 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −8.87420 | −0.455837 | −0.227918 | − | 0.973680i | \(-0.573192\pi\) | ||||
−0.227918 | + | 0.973680i | \(0.573192\pi\) | |||||||
\(380\) | 10.0383 | 0.514956 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −4.50124 | −0.230304 | ||||||||
\(383\) | −15.6017 | −0.797212 | −0.398606 | − | 0.917122i | \(-0.630506\pi\) | ||||
−0.398606 | + | 0.917122i | \(0.630506\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −33.4879 | −1.70670 | ||||||||
\(386\) | −11.3824 | −0.579350 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −10.0228 | −0.508829 | ||||||||
\(389\) | −1.71896 | −0.0871546 | −0.0435773 | − | 0.999050i | \(-0.513875\pi\) | ||||
−0.0435773 | + | 0.999050i | \(0.513875\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0.896334 | 0.0453296 | ||||||||
\(392\) | −7.32431 | −0.369933 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −12.9512 | −0.652472 | ||||||||
\(395\) | −43.0055 | −2.16384 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −11.2415 | −0.564196 | −0.282098 | − | 0.959386i | \(-0.591030\pi\) | ||||
−0.282098 | + | 0.959386i | \(0.591030\pi\) | |||||||
\(398\) | −1.67614 | −0.0840172 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 11.8933 | 0.594667 | ||||||||
\(401\) | −20.2914 | −1.01330 | −0.506651 | − | 0.862151i | \(-0.669117\pi\) | ||||
−0.506651 | + | 0.862151i | \(0.669117\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 4.50341 | 0.224331 | ||||||||
\(404\) | 6.69423 | 0.333050 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 30.7678 | 1.52698 | ||||||||
\(407\) | 17.6056 | 0.872675 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −17.9113 | −0.885659 | −0.442829 | − | 0.896606i | \(-0.646025\pi\) | ||||
−0.442829 | + | 0.896606i | \(0.646025\pi\) | |||||||
\(410\) | −2.98508 | −0.147422 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −12.2037 | −0.601233 | ||||||||
\(413\) | 43.2384 | 2.12762 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −5.84061 | −0.286704 | ||||||||
\(416\) | −5.55753 | −0.272480 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −5.25772 | −0.257164 | ||||||||
\(419\) | −15.7447 | −0.769180 | −0.384590 | − | 0.923087i | \(-0.625657\pi\) | ||||
−0.384590 | + | 0.923087i | \(0.625657\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −6.80219 | −0.331518 | −0.165759 | − | 0.986166i | \(-0.553007\pi\) | ||||
−0.165759 | + | 0.986166i | \(0.553007\pi\) | |||||||
\(422\) | 23.0409 | 1.12161 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 9.53601 | 0.463109 | ||||||||
\(425\) | −26.7398 | −1.29707 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −21.0038 | −1.01644 | ||||||||
\(428\) | −1.15590 | −0.0558726 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 16.3167 | 0.786860 | ||||||||
\(431\) | 4.88102 | 0.235111 | 0.117555 | − | 0.993066i | \(-0.462494\pi\) | ||||
0.117555 | + | 0.993066i | \(0.462494\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −33.8020 | −1.62442 | −0.812211 | − | 0.583364i | \(-0.801736\pi\) | ||||
−0.812211 | + | 0.583364i | \(0.801736\pi\) | |||||||
\(434\) | 3.06688 | 0.147215 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 10.3304 | 0.494738 | ||||||||
\(437\) | −0.973690 | −0.0465779 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 0.322206 | 0.0153780 | 0.00768902 | − | 0.999970i | \(-0.497552\pi\) | ||||
0.00768902 | + | 0.999970i | \(0.497552\pi\) | |||||||
\(440\) | −8.84813 | −0.421818 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 12.4950 | 0.594324 | ||||||||
\(443\) | 25.6552 | 1.21891 | 0.609457 | − | 0.792819i | \(-0.291387\pi\) | ||||
0.609457 | + | 0.792819i | \(0.291387\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 64.2984 | 3.04803 | ||||||||
\(446\) | −4.24071 | −0.200804 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −3.78475 | −0.178812 | ||||||||
\(449\) | −14.1446 | −0.667527 | −0.333764 | − | 0.942657i | \(-0.608319\pi\) | ||||
−0.333764 | + | 0.942657i | \(0.608319\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.56348 | 0.0736212 | ||||||||
\(452\) | −14.7374 | −0.693190 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −21.1581 | −0.992998 | ||||||||
\(455\) | −86.4522 | −4.05294 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 8.82093 | 0.412626 | 0.206313 | − | 0.978486i | \(-0.433854\pi\) | ||||
0.206313 | + | 0.978486i | \(0.433854\pi\) | |||||||
\(458\) | −9.81055 | −0.458417 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −1.63861 | −0.0764004 | ||||||||
\(461\) | 26.3264 | 1.22614 | 0.613072 | − | 0.790027i | \(-0.289934\pi\) | ||||
0.613072 | + | 0.790027i | \(0.289934\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −2.95723 | −0.137434 | −0.0687171 | − | 0.997636i | \(-0.521891\pi\) | ||||
−0.0687171 | + | 0.997636i | \(0.521891\pi\) | |||||||
\(464\) | 8.12942 | 0.377399 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −27.6563 | −1.28116 | ||||||||
\(467\) | −31.9881 | −1.48023 | −0.740116 | − | 0.672480i | \(-0.765229\pi\) | ||||
−0.740116 | + | 0.672480i | \(0.765229\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −12.7887 | −0.590528 | ||||||||
\(470\) | −29.1150 | −1.34297 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 11.4244 | 0.525850 | ||||||||
\(473\) | −8.54609 | −0.392950 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 29.0474 | 1.33279 | ||||||||
\(476\) | 8.50923 | 0.390020 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −20.9751 | −0.959377 | ||||||||
\(479\) | 1.09806 | 0.0501719 | 0.0250859 | − | 0.999685i | \(-0.492014\pi\) | ||||
0.0250859 | + | 0.999685i | \(0.492014\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 45.4504 | 2.07236 | ||||||||
\(482\) | −16.3880 | −0.746454 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −6.36566 | −0.289348 | ||||||||
\(485\) | −41.1951 | −1.87057 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 15.0374 | 0.681409 | 0.340704 | − | 0.940170i | \(-0.389334\pi\) | ||||
0.340704 | + | 0.940170i | \(0.389334\pi\) | |||||||
\(488\) | −5.54958 | −0.251218 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −30.1040 | −1.35996 | ||||||||
\(491\) | 35.2574 | 1.59114 | 0.795571 | − | 0.605860i | \(-0.207171\pi\) | ||||
0.795571 | + | 0.605860i | \(0.207171\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −18.2773 | −0.823169 | ||||||||
\(494\) | −13.5733 | −0.610691 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0.810327 | 0.0363847 | ||||||||
\(497\) | −31.7352 | −1.42352 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 25.6838 | 1.14977 | 0.574883 | − | 0.818235i | \(-0.305047\pi\) | ||||
0.574883 | + | 0.818235i | \(0.305047\pi\) | |||||||
\(500\) | 28.3327 | 1.26708 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 1.25604 | 0.0560599 | ||||||||
\(503\) | −15.5146 | −0.691763 | −0.345882 | − | 0.938278i | \(-0.612420\pi\) | ||||
−0.345882 | + | 0.938278i | \(0.612420\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 27.5143 | 1.22437 | ||||||||
\(506\) | 0.858243 | 0.0381536 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −15.4737 | −0.686535 | ||||||||
\(509\) | 23.9031 | 1.05949 | 0.529743 | − | 0.848158i | \(-0.322289\pi\) | ||||
0.529743 | + | 0.848158i | \(0.322289\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 22.1505 | 0.979879 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 18.7145 | 0.825460 | ||||||||
\(515\) | −50.1590 | −2.21027 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 15.2494 | 0.670667 | ||||||||
\(518\) | 30.9523 | 1.35997 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −22.8423 | −1.00170 | ||||||||
\(521\) | 16.3759 | 0.717442 | 0.358721 | − | 0.933445i | \(-0.383213\pi\) | ||||
0.358721 | + | 0.933445i | \(0.383213\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −35.5618 | −1.55501 | −0.777505 | − | 0.628877i | \(-0.783515\pi\) | ||||
−0.777505 | + | 0.628877i | \(0.783515\pi\) | |||||||
\(524\) | −17.0676 | −0.745600 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −24.6171 | −1.07336 | ||||||||
\(527\) | −1.82185 | −0.0793612 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −22.8411 | −0.993090 | ||||||||
\(530\) | 39.1944 | 1.70250 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −9.24359 | −0.400760 | ||||||||
\(533\) | 4.03626 | 0.174830 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −4.75093 | −0.205401 | ||||||||
\(536\) | −3.37901 | −0.145951 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 16.4410 | 0.708820 | ||||||||
\(539\) | 15.7674 | 0.679150 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −8.19214 | −0.352208 | −0.176104 | − | 0.984372i | \(-0.556349\pi\) | ||||
−0.176104 | + | 0.984372i | \(0.556349\pi\) | |||||||
\(542\) | 7.32917 | 0.314815 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 2.24829 | 0.0963948 | ||||||||
\(545\) | 42.4596 | 1.81877 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −1.42337 | −0.0608588 | −0.0304294 | − | 0.999537i | \(-0.509687\pi\) | ||||
−0.0304294 | + | 0.999537i | \(0.509687\pi\) | |||||||
\(548\) | −12.0167 | −0.513327 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −25.6034 | −1.09173 | ||||||||
\(551\) | 19.8547 | 0.845838 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 39.6008 | 1.68400 | ||||||||
\(554\) | 20.8558 | 0.886076 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 8.26244 | 0.350406 | ||||||||
\(557\) | 12.5490 | 0.531716 | 0.265858 | − | 0.964012i | \(-0.414345\pi\) | ||||
0.265858 | + | 0.964012i | \(0.414345\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −22.0625 | −0.933145 | ||||||||
\(560\) | −15.5559 | −0.657356 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 17.8130 | 0.751397 | ||||||||
\(563\) | −30.0087 | −1.26472 | −0.632359 | − | 0.774676i | \(-0.717913\pi\) | ||||
−0.632359 | + | 0.774676i | \(0.717913\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −60.5730 | −2.54833 | ||||||||
\(566\) | 27.8399 | 1.17020 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −8.38502 | −0.351828 | ||||||||
\(569\) | −33.4950 | −1.40418 | −0.702092 | − | 0.712087i | \(-0.747750\pi\) | ||||
−0.702092 | + | 0.712087i | \(0.747750\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 2.65000 | 0.110899 | 0.0554495 | − | 0.998461i | \(-0.482341\pi\) | ||||
0.0554495 | + | 0.998461i | \(0.482341\pi\) | |||||||
\(572\) | 11.9640 | 0.500239 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 2.74874 | 0.114730 | ||||||||
\(575\) | −4.74156 | −0.197737 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 29.1798 | 1.21477 | 0.607386 | − | 0.794407i | \(-0.292218\pi\) | ||||
0.607386 | + | 0.794407i | \(0.292218\pi\) | |||||||
\(578\) | 11.9452 | 0.496854 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 33.4131 | 1.38741 | ||||||||
\(581\) | 5.37820 | 0.223125 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −20.5286 | −0.850210 | ||||||||
\(584\) | 5.85256 | 0.242181 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −11.6167 | −0.479883 | ||||||||
\(587\) | −3.91577 | −0.161621 | −0.0808106 | − | 0.996729i | \(-0.525751\pi\) | ||||
−0.0808106 | + | 0.996729i | \(0.525751\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1.97908 | 0.0815467 | ||||||||
\(590\) | 46.9560 | 1.93315 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 8.17817 | 0.336121 | ||||||||
\(593\) | −33.1199 | −1.36007 | −0.680035 | − | 0.733180i | \(-0.738035\pi\) | ||||
−0.680035 | + | 0.733180i | \(0.738035\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 34.9742 | 1.43380 | ||||||||
\(596\) | 1.00000 | 0.0409616 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 2.21564 | 0.0906041 | ||||||||
\(599\) | 22.2847 | 0.910527 | 0.455263 | − | 0.890357i | \(-0.349545\pi\) | ||||
0.455263 | + | 0.890357i | \(0.349545\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 30.2514 | 1.23398 | 0.616991 | − | 0.786971i | \(-0.288352\pi\) | ||||
0.616991 | + | 0.786971i | \(0.288352\pi\) | |||||||
\(602\) | −15.0249 | −0.612368 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 23.5649 | 0.958843 | ||||||||
\(605\) | −26.1638 | −1.06371 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −0.504778 | −0.0204883 | −0.0102442 | − | 0.999948i | \(-0.503261\pi\) | ||||
−0.0102442 | + | 0.999948i | \(0.503261\pi\) | |||||||
\(608\) | −2.44233 | −0.0990494 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −22.8096 | −0.923535 | ||||||||
\(611\) | 39.3677 | 1.59265 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −2.30487 | −0.0930928 | −0.0465464 | − | 0.998916i | \(-0.514822\pi\) | ||||
−0.0465464 | + | 0.998916i | \(0.514822\pi\) | |||||||
\(614\) | −15.6923 | −0.633290 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 8.14762 | 0.328277 | ||||||||
\(617\) | −43.7493 | −1.76128 | −0.880640 | − | 0.473785i | \(-0.842887\pi\) | ||||
−0.880640 | + | 0.473785i | \(0.842887\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 3.25992 | 0.131027 | 0.0655136 | − | 0.997852i | \(-0.479131\pi\) | ||||
0.0655136 | + | 0.997852i | \(0.479131\pi\) | |||||||
\(620\) | 3.33057 | 0.133759 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −4.04112 | −0.162034 | ||||||||
\(623\) | −59.2078 | −2.37211 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 56.9850 | 2.27940 | ||||||||
\(626\) | −4.56731 | −0.182547 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 3.01390 | 0.120268 | ||||||||
\(629\) | −18.3869 | −0.733135 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 29.2273 | 1.16352 | 0.581761 | − | 0.813360i | \(-0.302364\pi\) | ||||
0.581761 | + | 0.813360i | \(0.302364\pi\) | |||||||
\(632\) | 10.4633 | 0.416206 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 24.3298 | 0.966260 | ||||||||
\(635\) | −63.5993 | −2.52386 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 40.7050 | 1.61279 | ||||||||
\(638\) | −17.5006 | −0.692856 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −4.11015 | −0.162468 | ||||||||
\(641\) | 26.1571 | 1.03314 | 0.516571 | − | 0.856244i | \(-0.327208\pi\) | ||||
0.516571 | + | 0.856244i | \(0.327208\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −18.9542 | −0.747482 | −0.373741 | − | 0.927533i | \(-0.621925\pi\) | ||||
−0.373741 | + | 0.927533i | \(0.621925\pi\) | |||||||
\(644\) | 1.50888 | 0.0594580 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 5.49107 | 0.216043 | ||||||||
\(647\) | −28.1286 | −1.10585 | −0.552925 | − | 0.833231i | \(-0.686488\pi\) | ||||
−0.552925 | + | 0.833231i | \(0.686488\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −24.5939 | −0.965394 | ||||||||
\(650\) | −66.0976 | −2.59256 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −15.9593 | −0.625016 | ||||||||
\(653\) | 25.8434 | 1.01133 | 0.505665 | − | 0.862730i | \(-0.331247\pi\) | ||||
0.505665 | + | 0.862730i | \(0.331247\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −70.1502 | −2.74100 | ||||||||
\(656\) | 0.726269 | 0.0283560 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 26.8099 | 1.04516 | ||||||||
\(659\) | 11.1184 | 0.433112 | 0.216556 | − | 0.976270i | \(-0.430518\pi\) | ||||
0.216556 | + | 0.976270i | \(0.430518\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 10.6871 | 0.415680 | 0.207840 | − | 0.978163i | \(-0.433357\pi\) | ||||
0.207840 | + | 0.978163i | \(0.433357\pi\) | |||||||
\(662\) | −15.2814 | −0.593929 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 1.42102 | 0.0551462 | ||||||||
\(665\) | −37.9926 | −1.47329 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −3.24098 | −0.125491 | ||||||||
\(668\) | 25.5613 | 0.988997 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −13.8883 | −0.536550 | ||||||||
\(671\) | 11.9469 | 0.461204 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −8.75317 | −0.337410 | −0.168705 | − | 0.985667i | \(-0.553959\pi\) | ||||
−0.168705 | + | 0.985667i | \(0.553959\pi\) | |||||||
\(674\) | −16.3455 | −0.629607 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 17.8861 | 0.687927 | ||||||||
\(677\) | 30.0676 | 1.15559 | 0.577797 | − | 0.816181i | \(-0.303913\pi\) | ||||
0.577797 | + | 0.816181i | \(0.303913\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 37.9336 | 1.45576 | ||||||||
\(680\) | 9.24083 | 0.354370 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −1.74443 | −0.0667977 | ||||||||
\(683\) | 26.4002 | 1.01018 | 0.505088 | − | 0.863068i | \(-0.331460\pi\) | ||||
0.505088 | + | 0.863068i | \(0.331460\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −49.3904 | −1.88711 | ||||||||
\(686\) | 1.22742 | 0.0468629 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −3.96985 | −0.151349 | ||||||||
\(689\) | −52.9966 | −2.01901 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −0.519830 | −0.0197752 | −0.00988762 | − | 0.999951i | \(-0.503147\pi\) | ||||
−0.00988762 | + | 0.999951i | \(0.503147\pi\) | |||||||
\(692\) | 17.7637 | 0.675274 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −18.2895 | −0.694259 | ||||||||
\(695\) | 33.9599 | 1.28817 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1.63287 | −0.0618492 | ||||||||
\(698\) | −5.35471 | −0.202679 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −45.0133 | −1.70134 | ||||||||
\(701\) | −7.56304 | −0.285652 | −0.142826 | − | 0.989748i | \(-0.545619\pi\) | ||||
−0.142826 | + | 0.989748i | \(0.545619\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 19.9738 | 0.753325 | ||||||||
\(704\) | 2.15275 | 0.0811348 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −26.9483 | −1.01421 | ||||||||
\(707\) | −25.3360 | −0.952857 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −6.02154 | −0.226144 | −0.113072 | − | 0.993587i | \(-0.536069\pi\) | ||||
−0.113072 | + | 0.993587i | \(0.536069\pi\) | |||||||
\(710\) | −34.4637 | −1.29340 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −15.6438 | −0.586276 | ||||||||
\(713\) | −0.323055 | −0.0120985 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 49.1737 | 1.83899 | ||||||||
\(716\) | 15.5056 | 0.579473 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 10.2380 | 0.382079 | ||||||||
\(719\) | −31.8340 | −1.18721 | −0.593604 | − | 0.804757i | \(-0.702296\pi\) | ||||
−0.593604 | + | 0.804757i | \(0.702296\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 46.1879 | 1.72013 | ||||||||
\(722\) | 13.0350 | 0.485114 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −14.7689 | −0.548883 | ||||||||
\(725\) | 96.6860 | 3.59083 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 44.3884 | 1.64627 | 0.823137 | − | 0.567843i | \(-0.192222\pi\) | ||||
0.823137 | + | 0.567843i | \(0.192222\pi\) | |||||||
\(728\) | 21.0338 | 0.779565 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 24.0549 | 0.890312 | ||||||||
\(731\) | 8.92538 | 0.330117 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 51.3963 | 1.89837 | 0.949183 | − | 0.314724i | \(-0.101912\pi\) | ||||
0.949183 | + | 0.314724i | \(0.101912\pi\) | |||||||
\(734\) | −6.92125 | −0.255468 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0.398673 | 0.0146953 | ||||||||
\(737\) | 7.27417 | 0.267948 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 39.8302 | 1.46518 | 0.732589 | − | 0.680671i | \(-0.238312\pi\) | ||||
0.732589 | + | 0.680671i | \(0.238312\pi\) | |||||||
\(740\) | 33.6135 | 1.23566 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −36.0914 | −1.32496 | ||||||||
\(743\) | 27.0929 | 0.993941 | 0.496971 | − | 0.867767i | \(-0.334446\pi\) | ||||
0.496971 | + | 0.867767i | \(0.334446\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 4.11015 | 0.150584 | ||||||||
\(746\) | −6.70601 | −0.245525 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −4.84002 | −0.176969 | ||||||||
\(749\) | 4.37479 | 0.159851 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −38.4389 | −1.40265 | −0.701327 | − | 0.712840i | \(-0.747409\pi\) | ||||
−0.701327 | + | 0.712840i | \(0.747409\pi\) | |||||||
\(752\) | 7.08367 | 0.258315 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −45.1794 | −1.64534 | ||||||||
\(755\) | 96.8554 | 3.52493 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −36.7309 | −1.33501 | −0.667503 | − | 0.744607i | \(-0.732637\pi\) | ||||
−0.667503 | + | 0.744607i | \(0.732637\pi\) | |||||||
\(758\) | 8.87420 | 0.322325 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −10.0383 | −0.364129 | ||||||||
\(761\) | −7.93102 | −0.287499 | −0.143750 | − | 0.989614i | \(-0.545916\pi\) | ||||
−0.143750 | + | 0.989614i | \(0.545916\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −39.0981 | −1.41545 | ||||||||
\(764\) | 4.50124 | 0.162849 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 15.6017 | 0.563714 | ||||||||
\(767\) | −63.4913 | −2.29254 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −10.4124 | −0.375482 | −0.187741 | − | 0.982219i | \(-0.560117\pi\) | ||||
−0.187741 | + | 0.982219i | \(0.560117\pi\) | |||||||
\(770\) | 33.4879 | 1.20682 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 11.3824 | 0.409663 | ||||||||
\(773\) | 28.1383 | 1.01206 | 0.506031 | − | 0.862515i | \(-0.331112\pi\) | ||||
0.506031 | + | 0.862515i | \(0.331112\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 9.63750 | 0.346189 | ||||||||
\(776\) | 10.0228 | 0.359797 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 1.71896 | 0.0616276 | ||||||||
\(779\) | 1.77379 | 0.0635525 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 18.0509 | 0.645911 | ||||||||
\(782\) | −0.896334 | −0.0320528 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 7.32431 | 0.261582 | ||||||||
\(785\) | 12.3876 | 0.442132 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −20.5218 | −0.731524 | −0.365762 | − | 0.930708i | \(-0.619192\pi\) | ||||
−0.365762 | + | 0.930708i | \(0.619192\pi\) | |||||||
\(788\) | 12.9512 | 0.461367 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 43.0055 | 1.53007 | ||||||||
\(791\) | 55.7774 | 1.98322 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 30.8419 | 1.09523 | ||||||||
\(794\) | 11.2415 | 0.398947 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 1.67614 | 0.0594092 | ||||||||
\(797\) | −11.5545 | −0.409282 | −0.204641 | − | 0.978837i | \(-0.565603\pi\) | ||||
−0.204641 | + | 0.978837i | \(0.565603\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −15.9262 | −0.563428 | ||||||||
\(800\) | −11.8933 | −0.420493 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 20.2914 | 0.716513 | ||||||||
\(803\) | −12.5991 | −0.444613 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 6.20171 | 0.218582 | ||||||||
\(806\) | −4.50341 | −0.158626 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −6.69423 | −0.235502 | ||||||||
\(809\) | −0.554547 | −0.0194968 | −0.00974842 | − | 0.999952i | \(-0.503103\pi\) | ||||
−0.00974842 | + | 0.999952i | \(0.503103\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 15.8752 | 0.557454 | 0.278727 | − | 0.960370i | \(-0.410088\pi\) | ||||
0.278727 | + | 0.960370i | \(0.410088\pi\) | |||||||
\(812\) | −30.7678 | −1.07974 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −17.6056 | −0.617074 | ||||||||
\(815\) | −65.5953 | −2.29770 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −9.69566 | −0.339208 | ||||||||
\(818\) | 17.9113 | 0.626255 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 2.98508 | 0.104243 | ||||||||
\(821\) | 49.0204 | 1.71082 | 0.855411 | − | 0.517949i | \(-0.173304\pi\) | ||||
0.855411 | + | 0.517949i | \(0.173304\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −0.949756 | −0.0331064 | −0.0165532 | − | 0.999863i | \(-0.505269\pi\) | ||||
−0.0165532 | + | 0.999863i | \(0.505269\pi\) | |||||||
\(824\) | 12.2037 | 0.425136 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −43.2384 | −1.50446 | ||||||||
\(827\) | −20.9351 | −0.727986 | −0.363993 | − | 0.931402i | \(-0.618587\pi\) | ||||
−0.363993 | + | 0.931402i | \(0.618587\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −0.932727 | −0.0323950 | −0.0161975 | − | 0.999869i | \(-0.505156\pi\) | ||||
−0.0161975 | + | 0.999869i | \(0.505156\pi\) | |||||||
\(830\) | 5.84061 | 0.202730 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 5.55753 | 0.192673 | ||||||||
\(833\) | −16.4672 | −0.570555 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 105.061 | 3.63578 | ||||||||
\(836\) | 5.25772 | 0.181842 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 15.7447 | 0.543893 | ||||||||
\(839\) | −28.0932 | −0.969884 | −0.484942 | − | 0.874546i | \(-0.661159\pi\) | ||||
−0.484942 | + | 0.874546i | \(0.661159\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 37.0874 | 1.27888 | ||||||||
\(842\) | 6.80219 | 0.234419 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −23.0409 | −0.793101 | ||||||||
\(845\) | 73.5146 | 2.52898 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 24.0924 | 0.827826 | ||||||||
\(848\) | −9.53601 | −0.327468 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 26.7398 | 0.917166 | ||||||||
\(851\) | −3.26041 | −0.111766 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −30.7394 | −1.05250 | −0.526249 | − | 0.850330i | \(-0.676402\pi\) | ||||
−0.526249 | + | 0.850330i | \(0.676402\pi\) | |||||||
\(854\) | 21.0038 | 0.718734 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 1.15590 | 0.0395079 | ||||||||
\(857\) | −11.2952 | −0.385837 | −0.192918 | − | 0.981215i | \(-0.561795\pi\) | ||||
−0.192918 | + | 0.981215i | \(0.561795\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −6.02701 | −0.205639 | −0.102819 | − | 0.994700i | \(-0.532786\pi\) | ||||
−0.102819 | + | 0.994700i | \(0.532786\pi\) | |||||||
\(860\) | −16.3167 | −0.556394 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −4.88102 | −0.166248 | ||||||||
\(863\) | 14.2444 | 0.484884 | 0.242442 | − | 0.970166i | \(-0.422052\pi\) | ||||
0.242442 | + | 0.970166i | \(0.422052\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 73.0114 | 2.48246 | ||||||||
\(866\) | 33.8020 | 1.14864 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −3.06688 | −0.104097 | ||||||||
\(869\) | −22.5248 | −0.764101 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 18.7790 | 0.636300 | ||||||||
\(872\) | −10.3304 | −0.349833 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0.973690 | 0.0329355 | ||||||||
\(875\) | −107.232 | −3.62511 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 7.36741 | 0.248780 | 0.124390 | − | 0.992233i | \(-0.460303\pi\) | ||||
0.124390 | + | 0.992233i | \(0.460303\pi\) | |||||||
\(878\) | −0.322206 | −0.0108739 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 8.84813 | 0.298270 | ||||||||
\(881\) | 39.8625 | 1.34300 | 0.671501 | − | 0.741004i | \(-0.265650\pi\) | ||||
0.671501 | + | 0.741004i | \(0.265650\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 43.3786 | 1.45980 | 0.729902 | − | 0.683551i | \(-0.239565\pi\) | ||||
0.729902 | + | 0.683551i | \(0.239565\pi\) | |||||||
\(884\) | −12.4950 | −0.420251 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −25.6552 | −0.861903 | ||||||||
\(887\) | 18.0823 | 0.607144 | 0.303572 | − | 0.952808i | \(-0.401821\pi\) | ||||
0.303572 | + | 0.952808i | \(0.401821\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 58.5641 | 1.96418 | ||||||||
\(890\) | −64.2984 | −2.15529 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 4.24071 | 0.141990 | ||||||||
\(893\) | 17.3006 | 0.578944 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 63.7305 | 2.13028 | ||||||||
\(896\) | 3.78475 | 0.126440 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 14.1446 | 0.472013 | ||||||||
\(899\) | 6.58748 | 0.219705 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 21.4398 | 0.714262 | ||||||||
\(902\) | −1.56348 | −0.0520580 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 14.7374 | 0.490159 | ||||||||
\(905\) | −60.7025 | −2.01782 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −5.55440 | −0.184431 | −0.0922155 | − | 0.995739i | \(-0.529395\pi\) | ||||
−0.0922155 | + | 0.995739i | \(0.529395\pi\) | |||||||
\(908\) | 21.1581 | 0.702156 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 86.4522 | 2.86586 | ||||||||
\(911\) | 17.6798 | 0.585757 | 0.292878 | − | 0.956150i | \(-0.405387\pi\) | ||||
0.292878 | + | 0.956150i | \(0.405387\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −3.05910 | −0.101241 | ||||||||
\(914\) | −8.82093 | −0.291770 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 9.81055 | 0.324150 | ||||||||
\(917\) | 64.5964 | 2.13316 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −50.7230 | −1.67320 | −0.836598 | − | 0.547817i | \(-0.815459\pi\) | ||||
−0.836598 | + | 0.547817i | \(0.815459\pi\) | |||||||
\(920\) | 1.63861 | 0.0540233 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −26.3264 | −0.867014 | ||||||||
\(923\) | 46.6000 | 1.53386 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 97.2658 | 3.19808 | ||||||||
\(926\) | 2.95723 | 0.0971806 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −8.12942 | −0.266861 | ||||||||
\(929\) | 1.25154 | 0.0410616 | 0.0205308 | − | 0.999789i | \(-0.493464\pi\) | ||||
0.0205308 | + | 0.999789i | \(0.493464\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 17.8883 | 0.586267 | ||||||||
\(932\) | 27.6563 | 0.905914 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 31.9881 | 1.04668 | ||||||||
\(935\) | −19.8932 | −0.650578 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 37.2661 | 1.21743 | 0.608714 | − | 0.793389i | \(-0.291686\pi\) | ||||
0.608714 | + | 0.793389i | \(0.291686\pi\) | |||||||
\(938\) | 12.7887 | 0.417566 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 29.1150 | 0.949625 | ||||||||
\(941\) | 60.3111 | 1.96608 | 0.983042 | − | 0.183380i | \(-0.0587039\pi\) | ||||
0.983042 | + | 0.183380i | \(0.0587039\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −0.289544 | −0.00942884 | ||||||||
\(944\) | −11.4244 | −0.371832 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 8.54609 | 0.277857 | ||||||||
\(947\) | 20.2775 | 0.658930 | 0.329465 | − | 0.944168i | \(-0.393132\pi\) | ||||
0.329465 | + | 0.944168i | \(0.393132\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −32.5258 | −1.05583 | ||||||||
\(950\) | −29.0474 | −0.942424 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −8.50923 | −0.275786 | ||||||||
\(953\) | 15.2560 | 0.494191 | 0.247095 | − | 0.968991i | \(-0.420524\pi\) | ||||
0.247095 | + | 0.968991i | \(0.420524\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 18.5008 | 0.598672 | ||||||||
\(956\) | 20.9751 | 0.678382 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −1.09806 | −0.0354769 | ||||||||
\(959\) | 45.4801 | 1.46863 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.3434 | −0.978818 | ||||||||
\(962\) | −45.4504 | −1.46538 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 16.3880 | 0.527823 | ||||||||
\(965\) | 46.7835 | 1.50601 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −61.0089 | −1.96192 | −0.980958 | − | 0.194222i | \(-0.937782\pi\) | ||||
−0.980958 | + | 0.194222i | \(0.937782\pi\) | |||||||
\(968\) | 6.36566 | 0.204600 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 41.1951 | 1.32270 | ||||||||
\(971\) | 5.18080 | 0.166260 | 0.0831300 | − | 0.996539i | \(-0.473508\pi\) | ||||
0.0831300 | + | 0.996539i | \(0.473508\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −31.2712 | −1.00251 | ||||||||
\(974\) | −15.0374 | −0.481829 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 5.54958 | 0.177638 | ||||||||
\(977\) | 39.1613 | 1.25288 | 0.626441 | − | 0.779469i | \(-0.284511\pi\) | ||||
0.626441 | + | 0.779469i | \(0.284511\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 33.6772 | 1.07633 | ||||||||
\(980\) | 30.1040 | 0.961637 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −35.2574 | −1.12511 | ||||||||
\(983\) | −47.3920 | −1.51157 | −0.755785 | − | 0.654820i | \(-0.772744\pi\) | ||||
−0.755785 | + | 0.654820i | \(0.772744\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 53.2314 | 1.69609 | ||||||||
\(986\) | 18.2773 | 0.582069 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 13.5733 | 0.431824 | ||||||||
\(989\) | 1.58267 | 0.0503260 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 48.4544 | 1.53920 | 0.769602 | − | 0.638524i | \(-0.220455\pi\) | ||||
0.769602 | + | 0.638524i | \(0.220455\pi\) | |||||||
\(992\) | −0.810327 | −0.0257279 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 31.7352 | 1.00658 | ||||||||
\(995\) | 6.88918 | 0.218402 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 29.6563 | 0.939224 | 0.469612 | − | 0.882873i | \(-0.344394\pi\) | ||||
0.469612 | + | 0.882873i | \(0.344394\pi\) | |||||||
\(998\) | −25.6838 | −0.813008 | ||||||||
\(999\) | 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.l.1.11 | ✓ | 12 | |
3.2 | odd | 2 | 8046.2.a.m.1.2 | yes | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8046.2.a.l.1.11 | ✓ | 12 | 1.1 | even | 1 | trivial | |
8046.2.a.m.1.2 | yes | 12 | 3.2 | odd | 2 |