Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2646,2,Mod(1979,2646)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2646, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([1, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2646.1979");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2646 = 2 \cdot 3^{3} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2646.t (of order \(6\), degree \(2\), not minimal) |
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: | no |
Analytic conductor: | \(21.1284163748\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 6x^{14} + 9x^{12} + 54x^{10} - 288x^{8} + 486x^{6} + 729x^{4} - 4374x^{2} + 6561 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 2^{2}\cdot 3^{4} \) |
Twist minimal: | no (minimal twist has level 126) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 1979.5 | ||
Root | \(-1.69547 - 0.354107i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2646.1979 |
Dual form | 2646.2.t.a.2285.5 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/2646\mathbb{Z}\right)^\times\).
\(n\) | \(785\) | \(1081\) |
\(\chi(n)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{5}{6}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.866025 | − | 0.500000i | 0.612372 | − | 0.353553i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0.500000 | − | 0.866025i | 0.250000 | − | 0.433013i | ||||
\(5\) | −1.79035 | −0.800669 | −0.400334 | − | 0.916369i | \(-0.631106\pi\) | ||||
−0.400334 | + | 0.916369i | \(0.631106\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | − | 1.00000i | − | 0.353553i | ||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −1.55049 | + | 0.895175i | −0.490307 | + | 0.283079i | ||||
\(11\) | − | 2.40150i | − | 0.724081i | −0.932162 | − | 0.362040i | \(-0.882080\pi\) | ||
0.932162 | − | 0.362040i | \(-0.117920\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −4.23601 | + | 2.44566i | −1.17486 | + | 0.678305i | −0.954820 | − | 0.297186i | \(-0.903952\pi\) |
−0.220039 | + | 0.975491i | \(0.570618\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.500000 | − | 0.866025i | −0.125000 | − | 0.216506i | ||||
\(17\) | 1.83233 | + | 3.17369i | 0.444406 | + | 0.769734i | 0.998011 | − | 0.0630460i | \(-0.0200815\pi\) |
−0.553605 | + | 0.832780i | \(0.686748\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.61281 | − | 1.50851i | −0.599419 | − | 0.346075i | 0.169394 | − | 0.985548i | \(-0.445819\pi\) |
−0.768813 | + | 0.639474i | \(0.779152\pi\) | |||||||
\(20\) | −0.895175 | + | 1.55049i | −0.200167 | + | 0.346700i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −1.20075 | − | 2.07976i | −0.256001 | − | 0.443407i | ||||
\(23\) | − | 3.76638i | − | 0.785345i | −0.919678 | − | 0.392673i | \(-0.871551\pi\) | ||
0.919678 | − | 0.392673i | \(-0.128449\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.79465 | −0.358930 | ||||||||
\(26\) | −2.44566 | + | 4.23601i | −0.479634 | + | 0.830750i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 5.68202 | + | 3.28052i | 1.05512 | + | 0.609176i | 0.924080 | − | 0.382200i | \(-0.124833\pi\) |
0.131045 | + | 0.991376i | \(0.458167\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.02408 | + | 2.32330i | 0.722746 | + | 0.417278i | 0.815763 | − | 0.578387i | \(-0.196318\pi\) |
−0.0930163 | + | 0.995665i | \(0.529651\pi\) | |||||||
\(32\) | −0.866025 | − | 0.500000i | −0.153093 | − | 0.0883883i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 3.17369 | + | 1.83233i | 0.544284 | + | 0.314242i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −4.68202 | + | 8.10950i | −0.769719 | + | 1.33319i | 0.167996 | + | 0.985788i | \(0.446271\pi\) |
−0.937715 | + | 0.347405i | \(0.887063\pi\) | |||||||
\(38\) | −3.01701 | −0.489424 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 1.79035i | 0.283079i | ||||||||
\(41\) | 4.04094 | + | 6.99911i | 0.631088 | + | 1.09308i | 0.987330 | + | 0.158683i | \(0.0507248\pi\) |
−0.356241 | + | 0.934394i | \(0.615942\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −3.48127 | + | 6.02973i | −0.530888 | + | 0.919526i | 0.468462 | + | 0.883484i | \(0.344808\pi\) |
−0.999350 | + | 0.0360419i | \(0.988525\pi\) | |||||||
\(44\) | −2.07976 | − | 1.20075i | −0.313536 | − | 0.181020i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −1.88319 | − | 3.26178i | −0.277661 | − | 0.480924i | ||||
\(47\) | −2.56802 | − | 4.44794i | −0.374584 | − | 0.648799i | 0.615680 | − | 0.787996i | \(-0.288881\pi\) |
−0.990265 | + | 0.139197i | \(0.955548\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −1.55421 | + | 0.897324i | −0.219799 | + | 0.126901i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 4.89133i | 0.678305i | ||||||||
\(53\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 4.29953i | 0.579749i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 6.56103 | 0.861506 | ||||||||
\(59\) | −7.29501 | + | 12.6353i | −0.949729 | + | 1.64498i | −0.203735 | + | 0.979026i | \(0.565308\pi\) |
−0.745994 | + | 0.665953i | \(0.768025\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −9.81058 | + | 5.66414i | −1.25612 | + | 0.725219i | −0.972317 | − | 0.233665i | \(-0.924928\pi\) |
−0.283799 | + | 0.958884i | \(0.591595\pi\) | |||||||
\(62\) | 4.64661 | 0.590120 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 7.58394 | − | 4.37859i | 0.940672 | − | 0.543097i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −0.285115 | + | 0.493834i | −0.0348324 | + | 0.0603315i | −0.882916 | − | 0.469531i | \(-0.844423\pi\) |
0.848084 | + | 0.529862i | \(0.177756\pi\) | |||||||
\(68\) | 3.66466 | 0.444406 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 5.96254i | − | 0.707623i | −0.935317 | − | 0.353811i | \(-0.884885\pi\) | ||
0.935317 | − | 0.353811i | \(-0.115115\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −10.7226 | + | 6.19070i | −1.25499 | + | 0.724567i | −0.972096 | − | 0.234585i | \(-0.924627\pi\) |
−0.282891 | + | 0.959152i | \(0.591294\pi\) | |||||||
\(74\) | 9.36404i | 1.08855i | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −2.61281 | + | 1.50851i | −0.299710 | + | 0.173037i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1.51831 | − | 2.62979i | −0.170824 | − | 0.295875i | 0.767884 | − | 0.640588i | \(-0.221309\pi\) |
−0.938708 | + | 0.344713i | \(0.887976\pi\) | |||||||
\(80\) | 0.895175 | + | 1.55049i | 0.100084 | + | 0.173350i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 6.99911 | + | 4.04094i | 0.772922 | + | 0.446247i | ||||
\(83\) | 7.00270 | − | 12.1290i | 0.768646 | − | 1.33133i | −0.169651 | − | 0.985504i | \(-0.554264\pi\) |
0.938297 | − | 0.345830i | \(-0.112403\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −3.28052 | − | 5.68202i | −0.355822 | − | 0.616302i | ||||
\(86\) | 6.96254i | 0.750790i | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −2.40150 | −0.256001 | ||||||||
\(89\) | −1.87432 | + | 3.24641i | −0.198677 | + | 0.344119i | −0.948100 | − | 0.317973i | \(-0.896998\pi\) |
0.749423 | + | 0.662092i | \(0.230331\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −3.26178 | − | 1.88319i | −0.340064 | − | 0.196336i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −4.44794 | − | 2.56802i | −0.458770 | − | 0.264871i | ||||
\(95\) | 4.67784 | + | 2.70075i | 0.479936 | + | 0.277091i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 4.77256 | + | 2.75544i | 0.484580 | + | 0.279772i | 0.722323 | − | 0.691556i | \(-0.243074\pi\) |
−0.237743 | + | 0.971328i | \(0.576408\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −0.897324 | + | 1.55421i | −0.0897324 | + | 0.155421i | ||||
\(101\) | −0.250324 | −0.0249082 | −0.0124541 | − | 0.999922i | \(-0.503964\pi\) | ||||
−0.0124541 | + | 0.999922i | \(0.503964\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0.167931i | 0.0165468i | 0.999966 | + | 0.00827339i | \(0.00263353\pi\) | ||||
−0.999966 | + | 0.00827339i | \(0.997366\pi\) | |||||||
\(104\) | 2.44566 | + | 4.23601i | 0.239817 | + | 0.415375i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −6.92024 | − | 3.99540i | −0.669004 | − | 0.386250i | 0.126695 | − | 0.991942i | \(-0.459563\pi\) |
−0.795699 | + | 0.605692i | \(0.792896\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 9.47667 | + | 16.4141i | 0.907700 | + | 1.57218i | 0.817251 | + | 0.576282i | \(0.195497\pi\) |
0.0904491 | + | 0.995901i | \(0.471170\pi\) | |||||||
\(110\) | 2.14977 | + | 3.72350i | 0.204972 | + | 0.355022i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1.00418 | − | 0.579764i | 0.0944653 | − | 0.0545396i | −0.452023 | − | 0.892006i | \(-0.649298\pi\) |
0.546488 | + | 0.837467i | \(0.315964\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 6.74314i | 0.628801i | ||||||||
\(116\) | 5.68202 | − | 3.28052i | 0.527562 | − | 0.304588i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 14.5900i | 1.34312i | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 5.23278 | 0.475707 | ||||||||
\(122\) | −5.66414 | + | 9.81058i | −0.512807 | + | 0.888208i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 4.02408 | − | 2.32330i | 0.361373 | − | 0.208639i | ||||
\(125\) | 12.1648 | 1.08805 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1.40150 | 0.124363 | 0.0621817 | − | 0.998065i | \(-0.480194\pi\) | ||||
0.0621817 | + | 0.998065i | \(0.480194\pi\) | |||||||
\(128\) | −0.866025 | + | 0.500000i | −0.0765466 | + | 0.0441942i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 4.37859 | − | 7.58394i | 0.384028 | − | 0.665156i | ||||
\(131\) | −10.4918 | −0.916671 | −0.458335 | − | 0.888779i | \(-0.651554\pi\) | ||||
−0.458335 | + | 0.888779i | \(0.651554\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0.570231i | 0.0492604i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 3.17369 | − | 1.83233i | 0.272142 | − | 0.157121i | ||||
\(137\) | − | 4.72056i | − | 0.403305i | −0.979457 | − | 0.201652i | \(-0.935369\pi\) | ||
0.979457 | − | 0.201652i | \(-0.0646311\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −2.04707 | + | 1.18187i | −0.173630 | + | 0.100245i | −0.584296 | − | 0.811540i | \(-0.698629\pi\) |
0.410666 | + | 0.911786i | \(0.365296\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −2.98127 | − | 5.16371i | −0.250182 | − | 0.433329i | ||||
\(143\) | 5.87327 | + | 10.1728i | 0.491148 | + | 0.850692i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −10.1728 | − | 5.87327i | −0.844805 | − | 0.487749i | ||||
\(146\) | −6.19070 | + | 10.7226i | −0.512346 | + | 0.887410i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 4.68202 | + | 8.10950i | 0.384860 | + | 0.666597i | ||||
\(149\) | 17.3640i | 1.42252i | 0.702930 | + | 0.711259i | \(0.251875\pi\) | ||||
−0.702930 | + | 0.711259i | \(0.748125\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −11.2328 | −0.914110 | −0.457055 | − | 0.889438i | \(-0.651096\pi\) | ||||
−0.457055 | + | 0.889438i | \(0.651096\pi\) | |||||||
\(152\) | −1.50851 | + | 2.61281i | −0.122356 | + | 0.211927i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −7.20451 | − | 4.15953i | −0.578680 | − | 0.334101i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −11.9885 | − | 6.92154i | −0.956783 | − | 0.552399i | −0.0616014 | − | 0.998101i | \(-0.519621\pi\) |
−0.895181 | + | 0.445702i | \(0.852954\pi\) | |||||||
\(158\) | −2.62979 | − | 1.51831i | −0.209215 | − | 0.120790i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 1.55049 | + | 0.895175i | 0.122577 | + | 0.0707698i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 2.16789 | − | 3.75489i | 0.169802 | − | 0.294106i | −0.768548 | − | 0.639792i | \(-0.779020\pi\) |
0.938350 | + | 0.345686i | \(0.112354\pi\) | |||||||
\(164\) | 8.08188 | 0.631088 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | − | 14.0054i | − | 1.08703i | ||||||
\(167\) | 6.20756 | + | 10.7518i | 0.480355 | + | 0.832000i | 0.999746 | − | 0.0225370i | \(-0.00717435\pi\) |
−0.519391 | + | 0.854537i | \(0.673841\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 5.46254 | − | 9.46139i | 0.420195 | − | 0.727799i | ||||
\(170\) | −5.68202 | − | 3.28052i | −0.435791 | − | 0.251604i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 3.48127 | + | 6.02973i | 0.265444 | + | 0.459763i | ||||
\(173\) | −8.70908 | − | 15.0846i | −0.662139 | − | 1.14686i | −0.980052 | − | 0.198739i | \(-0.936315\pi\) |
0.317913 | − | 0.948120i | \(-0.397018\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −2.07976 | + | 1.20075i | −0.156768 | + | 0.0905101i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 3.74863i | 0.280972i | ||||||||
\(179\) | −11.3640 | + | 6.56103i | −0.849388 | + | 0.490395i | −0.860444 | − | 0.509544i | \(-0.829814\pi\) |
0.0110562 | + | 0.999939i | \(0.496481\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 13.3577i | 0.992873i | 0.868073 | + | 0.496437i | \(0.165359\pi\) | ||||
−0.868073 | + | 0.496437i | \(0.834641\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −3.76638 | −0.277661 | ||||||||
\(185\) | 8.38245 | − | 14.5188i | 0.616290 | − | 1.06745i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 7.62164 | − | 4.40035i | 0.557349 | − | 0.321786i | ||||
\(188\) | −5.13604 | −0.374584 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 5.40150 | 0.391866 | ||||||||
\(191\) | −8.01361 | + | 4.62666i | −0.579845 | + | 0.334774i | −0.761072 | − | 0.648668i | \(-0.775326\pi\) |
0.181227 | + | 0.983441i | \(0.441993\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 12.2801 | − | 21.2698i | 0.883941 | − | 1.53103i | 0.0370176 | − | 0.999315i | \(-0.488214\pi\) |
0.846923 | − | 0.531716i | \(-0.178452\pi\) | |||||||
\(194\) | 5.51087 | 0.395658 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 12.4861i | 0.889598i | 0.895630 | + | 0.444799i | \(0.146725\pi\) | ||||
−0.895630 | + | 0.444799i | \(0.853275\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 0.155144 | − | 0.0895727i | 0.0109979 | − | 0.00634964i | −0.494491 | − | 0.869183i | \(-0.664645\pi\) |
0.505489 | + | 0.862833i | \(0.331312\pi\) | |||||||
\(200\) | 1.79465i | 0.126901i | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −0.216787 | + | 0.125162i | −0.0152531 | + | 0.00880637i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −7.23469 | − | 12.5309i | −0.505293 | − | 0.875193i | ||||
\(206\) | 0.0839657 | + | 0.145433i | 0.00585017 | + | 0.0101328i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 4.23601 | + | 2.44566i | 0.293715 | + | 0.169576i | ||||
\(209\) | −3.62268 | + | 6.27467i | −0.250586 | + | 0.434028i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 7.56103 | + | 13.0961i | 0.520523 | + | 0.901572i | 0.999715 | + | 0.0238622i | \(0.00759629\pi\) |
−0.479192 | + | 0.877710i | \(0.659070\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −7.99080 | −0.546240 | ||||||||
\(215\) | 6.23269 | − | 10.7953i | 0.425066 | − | 0.736235i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 16.4141 | + | 9.47667i | 1.11170 | + | 0.641841i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 3.72350 | + | 2.14977i | 0.251039 | + | 0.144937i | ||||
\(221\) | −15.5236 | − | 8.96254i | −1.04423 | − | 0.602885i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −7.27049 | − | 4.19762i | −0.486868 | − | 0.281093i | 0.236406 | − | 0.971654i | \(-0.424030\pi\) |
−0.723274 | + | 0.690561i | \(0.757364\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0.579764 | − | 1.00418i | 0.0385653 | − | 0.0667971i | ||||
\(227\) | 2.42522 | 0.160967 | 0.0804836 | − | 0.996756i | \(-0.474354\pi\) | ||||
0.0804836 | + | 0.996756i | \(0.474354\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 2.01975i | 0.133469i | 0.997771 | + | 0.0667344i | \(0.0212580\pi\) | ||||
−0.997771 | + | 0.0667344i | \(0.978742\pi\) | |||||||
\(230\) | 3.37157 | + | 5.83973i | 0.222315 | + | 0.385061i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 3.28052 | − | 5.68202i | 0.215376 | − | 0.373043i | ||||
\(233\) | 11.0236 | + | 6.36446i | 0.722178 | + | 0.416950i | 0.815554 | − | 0.578681i | \(-0.196432\pi\) |
−0.0933759 | + | 0.995631i | \(0.529766\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 4.59766 | + | 7.96337i | 0.299918 | + | 0.519473i | ||||
\(236\) | 7.29501 | + | 12.6353i | 0.474864 | + | 0.822489i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −15.1117 | + | 8.72474i | −0.977494 | + | 0.564356i | −0.901513 | − | 0.432753i | \(-0.857542\pi\) |
−0.0759814 | + | 0.997109i | \(0.524209\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 11.4332i | − | 0.736476i | −0.929732 | − | 0.368238i | \(-0.879961\pi\) | ||
0.929732 | − | 0.368238i | \(-0.120039\pi\) | |||||||
\(242\) | 4.53172 | − | 2.61639i | 0.291310 | − | 0.168188i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 11.3283i | 0.725219i | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 14.7572 | 0.938977 | ||||||||
\(248\) | 2.32330 | − | 4.02408i | 0.147530 | − | 0.255529i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 10.5350 | − | 6.08240i | 0.666293 | − | 0.384685i | ||||
\(251\) | 27.3560 | 1.72669 | 0.863347 | − | 0.504611i | \(-0.168364\pi\) | ||||
0.863347 | + | 0.504611i | \(0.168364\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −9.04499 | −0.568653 | ||||||||
\(254\) | 1.21374 | − | 0.700752i | 0.0761567 | − | 0.0439691i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.500000 | + | 0.866025i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | 3.49673 | 0.218120 | 0.109060 | − | 0.994035i | \(-0.465216\pi\) | ||||
0.109060 | + | 0.994035i | \(0.465216\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | − | 8.75718i | − | 0.543097i | ||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −9.08614 | + | 5.24589i | −0.561344 | + | 0.324092i | ||||
\(263\) | − | 9.64348i | − | 0.594643i | −0.954777 | − | 0.297321i | \(-0.903907\pi\) | ||
0.954777 | − | 0.297321i | \(-0.0960932\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0.285115 | + | 0.493834i | 0.0174162 | + | 0.0301657i | ||||
\(269\) | −3.45554 | − | 5.98517i | −0.210688 | − | 0.364922i | 0.741242 | − | 0.671238i | \(-0.234237\pi\) |
−0.951930 | + | 0.306316i | \(0.900904\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −17.8672 | − | 10.3156i | −1.08535 | − | 0.626629i | −0.153017 | − | 0.988224i | \(-0.548899\pi\) |
−0.932335 | + | 0.361595i | \(0.882232\pi\) | |||||||
\(272\) | 1.83233 | − | 3.17369i | 0.111101 | − | 0.192433i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −2.36028 | − | 4.08812i | −0.142590 | − | 0.246973i | ||||
\(275\) | 4.30986i | 0.259894i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −15.5144 | −0.932168 | −0.466084 | − | 0.884740i | \(-0.654336\pi\) | ||||
−0.466084 | + | 0.884740i | \(0.654336\pi\) | |||||||
\(278\) | −1.18187 | + | 2.04707i | −0.0708841 | + | 0.122775i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −11.7759 | − | 6.79883i | −0.702492 | − | 0.405584i | 0.105783 | − | 0.994389i | \(-0.466265\pi\) |
−0.808275 | + | 0.588805i | \(0.799599\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 4.71796 | + | 2.72392i | 0.280454 | + | 0.161920i | 0.633629 | − | 0.773637i | \(-0.281565\pi\) |
−0.353175 | + | 0.935557i | \(0.614898\pi\) | |||||||
\(284\) | −5.16371 | − | 2.98127i | −0.306410 | − | 0.176906i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 10.1728 | + | 5.87327i | 0.601530 | + | 0.347294i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1.78512 | − | 3.09191i | 0.105007 | − | 0.181877i | ||||
\(290\) | −11.7465 | −0.689781 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 12.3814i | 0.724567i | ||||||||
\(293\) | −12.2311 | − | 21.1849i | −0.714550 | − | 1.23764i | −0.963133 | − | 0.269026i | \(-0.913298\pi\) |
0.248583 | − | 0.968610i | \(-0.420035\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 13.0606 | − | 22.6216i | 0.760418 | − | 1.31708i | ||||
\(296\) | 8.10950 | + | 4.68202i | 0.471355 | + | 0.272137i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 8.68202 | + | 15.0377i | 0.502936 | + | 0.871111i | ||||
\(299\) | 9.21130 | + | 15.9544i | 0.532703 | + | 0.922670i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −9.72787 | + | 5.61639i | −0.559776 | + | 0.323187i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 3.01701i | 0.173037i | ||||||||
\(305\) | 17.5644 | − | 10.1408i | 1.00573 | − | 0.580660i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 31.2223i | − | 1.78195i | −0.454053 | − | 0.890975i | \(-0.650022\pi\) | ||
0.454053 | − | 0.890975i | \(-0.349978\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −8.31905 | −0.472491 | ||||||||
\(311\) | 5.45501 | − | 9.44836i | 0.309325 | − | 0.535767i | −0.668889 | − | 0.743362i | \(-0.733230\pi\) |
0.978215 | + | 0.207594i | \(0.0665634\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −2.96532 | + | 1.71203i | −0.167610 | + | 0.0967694i | −0.581458 | − | 0.813576i | \(-0.697518\pi\) |
0.413849 | + | 0.910346i | \(0.364184\pi\) | |||||||
\(314\) | −13.8431 | −0.781210 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −3.03663 | −0.170824 | ||||||||
\(317\) | 16.4953 | − | 9.52357i | 0.926468 | − | 0.534897i | 0.0407755 | − | 0.999168i | \(-0.487017\pi\) |
0.885693 | + | 0.464272i | \(0.153684\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 7.87817 | − | 13.6454i | 0.441093 | − | 0.763995i | ||||
\(320\) | 1.79035 | 0.100084 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 11.0563i | − | 0.615191i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 7.60215 | − | 4.38910i | 0.421692 | − | 0.243464i | ||||
\(326\) | − | 4.33577i | − | 0.240136i | ||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 6.99911 | − | 4.04094i | 0.386461 | − | 0.223123i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −0.0366251 | − | 0.0634366i | −0.00201310 | − | 0.00348679i | 0.865017 | − | 0.501742i | \(-0.167307\pi\) |
−0.867030 | + | 0.498256i | \(0.833974\pi\) | |||||||
\(332\) | −7.00270 | − | 12.1290i | −0.384323 | − | 0.665667i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 10.7518 | + | 6.20756i | 0.588313 | + | 0.339663i | ||||
\(335\) | 0.510456 | − | 0.884136i | 0.0278892 | − | 0.0483055i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1.11639 | + | 1.93364i | 0.0608136 | + | 0.105332i | 0.894829 | − | 0.446408i | \(-0.147297\pi\) |
−0.834016 | + | 0.551741i | \(0.813964\pi\) | |||||||
\(338\) | − | 10.9251i | − | 0.594246i | ||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −6.56103 | −0.355822 | ||||||||
\(341\) | 5.57943 | − | 9.66385i | 0.302143 | − | 0.523327i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 6.02973 | + | 3.48127i | 0.325101 | + | 0.187697i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −15.0846 | − | 8.70908i | −0.810952 | − | 0.468203i | ||||
\(347\) | 27.5751 | + | 15.9205i | 1.48031 | + | 0.854656i | 0.999751 | − | 0.0223084i | \(-0.00710156\pi\) |
0.480556 | + | 0.876964i | \(0.340435\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −12.7613 | − | 7.36772i | −0.683095 | − | 0.394385i | 0.117925 | − | 0.993022i | \(-0.462376\pi\) |
−0.801020 | + | 0.598637i | \(0.795709\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −1.20075 | + | 2.07976i | −0.0640003 | + | 0.110852i | ||||
\(353\) | −2.15957 | −0.114943 | −0.0574713 | − | 0.998347i | \(-0.518304\pi\) | ||||
−0.0574713 | + | 0.998347i | \(0.518304\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 10.6750i | 0.566571i | ||||||||
\(356\) | 1.87432 | + | 3.24641i | 0.0993385 | + | 0.172059i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −6.56103 | + | 11.3640i | −0.346761 | + | 0.600608i | ||||
\(359\) | −28.2712 | − | 16.3224i | −1.49210 | − | 0.861463i | −0.492139 | − | 0.870517i | \(-0.663785\pi\) |
−0.999959 | + | 0.00905364i | \(0.997118\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −4.94882 | − | 8.57161i | −0.260464 | − | 0.451138i | ||||
\(362\) | 6.67887 | + | 11.5681i | 0.351034 | + | 0.608008i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 19.1972 | − | 11.0835i | 1.00483 | − | 0.580138i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 29.7003i | − | 1.55034i | −0.631751 | − | 0.775171i | \(-0.717664\pi\) | ||
0.631751 | − | 0.775171i | \(-0.282336\pi\) | |||||||
\(368\) | −3.26178 | + | 1.88319i | −0.170032 | + | 0.0981682i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | − | 16.7649i | − | 0.871566i | ||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −2.01672 | −0.104422 | −0.0522109 | − | 0.998636i | \(-0.516627\pi\) | ||||
−0.0522109 | + | 0.998636i | \(0.516627\pi\) | |||||||
\(374\) | 4.40035 | − | 7.62164i | 0.227537 | − | 0.394105i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −4.44794 | + | 2.56802i | −0.229385 | + | 0.132436i | ||||
\(377\) | −32.0921 | −1.65283 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −18.8709 | −0.969332 | −0.484666 | − | 0.874699i | \(-0.661059\pi\) | ||||
−0.484666 | + | 0.874699i | \(0.661059\pi\) | |||||||
\(380\) | 4.67784 | − | 2.70075i | 0.239968 | − | 0.138546i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −4.62666 | + | 8.01361i | −0.236721 | + | 0.410012i | ||||
\(383\) | −0.836511 | −0.0427437 | −0.0213719 | − | 0.999772i | \(-0.506803\pi\) | ||||
−0.0213719 | + | 0.999772i | \(0.506803\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | − | 24.5602i | − | 1.25008i | ||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 4.77256 | − | 2.75544i | 0.242290 | − | 0.139886i | ||||
\(389\) | 24.8219i | 1.25852i | 0.777195 | + | 0.629260i | \(0.216642\pi\) | ||||
−0.777195 | + | 0.629260i | \(0.783358\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 11.9533 | − | 6.90127i | 0.604507 | − | 0.349012i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 6.24305 | + | 10.8133i | 0.314520 | + | 0.544765i | ||||
\(395\) | 2.71831 | + | 4.70825i | 0.136773 | + | 0.236898i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 2.62744 | + | 1.51695i | 0.131867 | + | 0.0761336i | 0.564482 | − | 0.825445i | \(-0.309076\pi\) |
−0.432615 | + | 0.901579i | \(0.642409\pi\) | |||||||
\(398\) | 0.0895727 | − | 0.155144i | 0.00448987 | − | 0.00777669i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0.897324 | + | 1.55421i | 0.0448662 | + | 0.0777105i | ||||
\(401\) | − | 13.0771i | − | 0.653038i | −0.945191 | − | 0.326519i | \(-0.894124\pi\) | ||
0.945191 | − | 0.326519i | \(-0.105876\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −22.7281 | −1.13217 | ||||||||
\(404\) | −0.125162 | + | 0.216787i | −0.00622705 | + | 0.0107856i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 19.4750 | + | 11.2439i | 0.965339 | + | 0.557339i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −4.82124 | − | 2.78354i | −0.238395 | − | 0.137637i | 0.376044 | − | 0.926602i | \(-0.377284\pi\) |
−0.614439 | + | 0.788965i | \(0.710618\pi\) | |||||||
\(410\) | −12.5309 | − | 7.23469i | −0.618855 | − | 0.357296i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0.145433 | + | 0.0839657i | 0.00716496 | + | 0.00413669i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −12.5373 | + | 21.7152i | −0.615431 | + | 1.06596i | ||||
\(416\) | 4.89133 | 0.239817 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 7.24536i | 0.354382i | ||||||||
\(419\) | −8.19938 | − | 14.2017i | −0.400566 | − | 0.693800i | 0.593228 | − | 0.805034i | \(-0.297853\pi\) |
−0.993794 | + | 0.111234i | \(0.964520\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −7.72892 | + | 13.3869i | −0.376684 | + | 0.652437i | −0.990578 | − | 0.136952i | \(-0.956269\pi\) |
0.613893 | + | 0.789389i | \(0.289603\pi\) | |||||||
\(422\) | 13.0961 | + | 7.56103i | 0.637508 | + | 0.368065i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −3.28839 | − | 5.69566i | −0.159510 | − | 0.276280i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −6.92024 | + | 3.99540i | −0.334502 | + | 0.193125i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | − | 12.4654i | − | 0.601134i | ||||||
\(431\) | −21.6737 | + | 12.5133i | −1.04398 | + | 0.602744i | −0.920959 | − | 0.389660i | \(-0.872593\pi\) |
−0.123024 | + | 0.992404i | \(0.539259\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 2.25168i | − | 0.108209i | −0.998535 | − | 0.0541044i | \(-0.982770\pi\) | ||
0.998535 | − | 0.0541044i | \(-0.0172304\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 18.9533 | 0.907700 | ||||||||
\(437\) | −5.68161 | + | 9.84084i | −0.271788 | + | 0.470751i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −16.2293 | + | 9.37000i | −0.774583 | + | 0.447206i | −0.834507 | − | 0.550997i | \(-0.814248\pi\) |
0.0599239 | + | 0.998203i | \(0.480914\pi\) | |||||||
\(440\) | 4.29953 | 0.204972 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −17.9251 | −0.852609 | ||||||||
\(443\) | −1.04314 | + | 0.602256i | −0.0495610 | + | 0.0286141i | −0.524576 | − | 0.851364i | \(-0.675776\pi\) |
0.475015 | + | 0.879978i | \(0.342443\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 3.35568 | − | 5.81221i | 0.159074 | − | 0.275525i | ||||
\(446\) | −8.39524 | −0.397526 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 26.8022i | 1.26487i | 0.774612 | + | 0.632436i | \(0.217945\pi\) | ||||
−0.774612 | + | 0.632436i | \(0.782055\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 16.8084 | − | 9.70433i | 0.791476 | − | 0.456959i | ||||
\(452\) | − | 1.15953i | − | 0.0545396i | ||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 2.10030 | − | 1.21261i | 0.0985719 | − | 0.0569105i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −6.92442 | − | 11.9934i | −0.323911 | − | 0.561030i | 0.657381 | − | 0.753559i | \(-0.271664\pi\) |
−0.981291 | + | 0.192529i | \(0.938331\pi\) | |||||||
\(458\) | 1.00987 | + | 1.74915i | 0.0471883 | + | 0.0817326i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 5.83973 | + | 3.37157i | 0.272279 | + | 0.157200i | ||||
\(461\) | −2.40241 | + | 4.16110i | −0.111892 | + | 0.193802i | −0.916533 | − | 0.399959i | \(-0.869024\pi\) |
0.804641 | + | 0.593761i | \(0.202358\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 10.5194 | + | 18.2201i | 0.488877 | + | 0.846760i | 0.999918 | − | 0.0127960i | \(-0.00407321\pi\) |
−0.511041 | + | 0.859556i | \(0.670740\pi\) | |||||||
\(464\) | − | 6.56103i | − | 0.304588i | ||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 12.7289 | 0.589656 | ||||||||
\(467\) | 2.91151 | − | 5.04288i | 0.134729 | − | 0.233357i | −0.790765 | − | 0.612120i | \(-0.790317\pi\) |
0.925494 | + | 0.378763i | \(0.123650\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 7.96337 | + | 4.59766i | 0.367323 | + | 0.212074i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 12.6353 | + | 7.29501i | 0.581588 | + | 0.335780i | ||||
\(473\) | 14.4804 | + | 8.36028i | 0.665811 | + | 0.384406i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 4.68907 | + | 2.70724i | 0.215149 | + | 0.124217i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −8.72474 | + | 15.1117i | −0.399060 | + | 0.691193i | ||||
\(479\) | 26.9561 | 1.23166 | 0.615828 | − | 0.787881i | \(-0.288822\pi\) | ||||
0.615828 | + | 0.787881i | \(0.288822\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | − | 45.8026i | − | 2.08842i | ||||||
\(482\) | −5.71659 | − | 9.90142i | −0.260383 | − | 0.450997i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 2.61639 | − | 4.53172i | 0.118927 | − | 0.205987i | ||||
\(485\) | −8.54455 | − | 4.93320i | −0.387988 | − | 0.224005i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 6.81338 | + | 11.8011i | 0.308744 | + | 0.534760i | 0.978088 | − | 0.208193i | \(-0.0667581\pi\) |
−0.669344 | + | 0.742953i | \(0.733425\pi\) | |||||||
\(488\) | 5.66414 | + | 9.81058i | 0.256404 | + | 0.444104i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 33.7430 | − | 19.4815i | 1.52280 | − | 0.879188i | 0.523162 | − | 0.852234i | \(-0.324752\pi\) |
0.999637 | − | 0.0269544i | \(-0.00858088\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 24.0440i | 1.08289i | ||||||||
\(494\) | 12.7801 | − | 7.37859i | 0.575004 | − | 0.331979i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | − | 4.64661i | − | 0.208639i | ||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 26.0097 | 1.16435 | 0.582176 | − | 0.813063i | \(-0.302201\pi\) | ||||
0.582176 | + | 0.813063i | \(0.302201\pi\) | |||||||
\(500\) | 6.08240 | − | 10.5350i | 0.272013 | − | 0.471141i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 23.6910 | − | 13.6780i | 1.05738 | − | 0.610478i | ||||
\(503\) | −10.5271 | −0.469378 | −0.234689 | − | 0.972070i | \(-0.575407\pi\) | ||||
−0.234689 | + | 0.972070i | \(0.575407\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0.448168 | 0.0199432 | ||||||||
\(506\) | −7.83319 | + | 4.52249i | −0.348228 | + | 0.201049i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0.700752 | − | 1.21374i | 0.0310908 | − | 0.0538509i | ||||
\(509\) | 0.938871 | 0.0416147 | 0.0208074 | − | 0.999784i | \(-0.493376\pi\) | ||||
0.0208074 | + | 0.999784i | \(0.493376\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 1.00000i | 0.0441942i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 3.02826 | − | 1.74837i | 0.133571 | − | 0.0771172i | ||||
\(515\) | − | 0.300656i | − | 0.0132485i | ||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −10.6818 | + | 6.16711i | −0.469783 | + | 0.271229i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −4.37859 | − | 7.58394i | −0.192014 | − | 0.332578i | ||||
\(521\) | −19.7527 | − | 34.2127i | −0.865382 | − | 1.49889i | −0.866667 | − | 0.498887i | \(-0.833742\pi\) |
0.00128461 | − | 0.999999i | \(-0.499591\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 21.0697 | + | 12.1646i | 0.921315 | + | 0.531922i | 0.884054 | − | 0.467384i | \(-0.154803\pi\) |
0.0372609 | + | 0.999306i | \(0.488137\pi\) | |||||||
\(524\) | −5.24589 | + | 9.08614i | −0.229168 | + | 0.396930i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −4.82174 | − | 8.35150i | −0.210238 | − | 0.364143i | ||||
\(527\) | 17.0283i | 0.741763i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 8.81436 | 0.383233 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −34.2349 | − | 19.7655i | −1.48288 | − | 0.856141i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 12.3896 | + | 7.15316i | 0.535651 | + | 0.309258i | ||||
\(536\) | 0.493834 | + | 0.285115i | 0.0213304 | + | 0.0123151i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −5.98517 | − | 3.45554i | −0.258039 | − | 0.148979i | ||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −21.3640 | + | 37.0036i | −0.918512 | + | 1.59091i | −0.116835 | + | 0.993151i | \(0.537275\pi\) |
−0.801677 | + | 0.597758i | \(0.796058\pi\) | |||||||
\(542\) | −20.6312 | −0.886187 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | − | 3.66466i | − | 0.157121i | ||||||
\(545\) | −16.9665 | − | 29.3869i | −0.726767 | − | 1.25880i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −12.2477 | + | 21.2136i | −0.523672 | + | 0.907026i | 0.475949 | + | 0.879473i | \(0.342105\pi\) |
−0.999620 | + | 0.0275530i | \(0.991229\pi\) | |||||||
\(548\) | −4.08812 | − | 2.36028i | −0.174636 | − | 0.100826i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 2.15493 | + | 3.73244i | 0.0918864 | + | 0.159152i | ||||
\(551\) | −9.89735 | − | 17.1427i | −0.421641 | − | 0.730304i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −13.4358 | + | 7.75718i | −0.570834 | + | 0.329571i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 2.36375i | 0.100245i | ||||||||
\(557\) | −2.20344 | + | 1.27216i | −0.0933627 | + | 0.0539030i | −0.545954 | − | 0.837815i | \(-0.683833\pi\) |
0.452592 | + | 0.891718i | \(0.350499\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 34.0560i | − | 1.44042i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −13.5977 | −0.573583 | ||||||||
\(563\) | 7.90707 | − | 13.6954i | 0.333243 | − | 0.577194i | −0.649902 | − | 0.760018i | \(-0.725190\pi\) |
0.983146 | + | 0.182823i | \(0.0585236\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −1.79783 | + | 1.03798i | −0.0756354 | + | 0.0436681i | ||||
\(566\) | 5.44783 | 0.228990 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −5.96254 | −0.250182 | ||||||||
\(569\) | −5.52793 | + | 3.19155i | −0.231743 | + | 0.133797i | −0.611376 | − | 0.791340i | \(-0.709384\pi\) |
0.379633 | + | 0.925137i | \(0.376050\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 3.91188 | − | 6.77557i | 0.163707 | − | 0.283549i | −0.772488 | − | 0.635029i | \(-0.780988\pi\) |
0.936195 | + | 0.351480i | \(0.114322\pi\) | |||||||
\(572\) | 11.7465 | 0.491148 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 6.75933i | 0.281884i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 12.4012 | − | 7.15986i | 0.516270 | − | 0.298069i | −0.219137 | − | 0.975694i | \(-0.570324\pi\) |
0.735407 | + | 0.677625i | \(0.236991\pi\) | |||||||
\(578\) | − | 3.57023i | − | 0.148502i | ||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −10.1728 | + | 5.87327i | −0.422403 | + | 0.243874i | ||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 6.19070 | + | 10.7226i | 0.256173 | + | 0.443705i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −21.1849 | − | 12.2311i | −0.875141 | − | 0.505263i | ||||
\(587\) | 2.37575 | − | 4.11492i | 0.0980577 | − | 0.169841i | −0.812823 | − | 0.582511i | \(-0.802070\pi\) |
0.910881 | + | 0.412670i | \(0.135404\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −7.00943 | − | 12.1407i | −0.288819 | − | 0.500249i | ||||
\(590\) | − | 26.1212i | − | 1.07539i | ||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 9.36404 | 0.384860 | ||||||||
\(593\) | 1.79035 | − | 3.10098i | 0.0735208 | − | 0.127342i | −0.826921 | − | 0.562318i | \(-0.809910\pi\) |
0.900442 | + | 0.434976i | \(0.143243\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 15.0377 | + | 8.68202i | 0.615968 | + | 0.355629i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 15.9544 | + | 9.21130i | 0.652426 | + | 0.376678i | ||||
\(599\) | −13.0471 | − | 7.53277i | −0.533091 | − | 0.307780i | 0.209183 | − | 0.977877i | \(-0.432920\pi\) |
−0.742274 | + | 0.670096i | \(0.766253\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −19.8704 | − | 11.4722i | −0.810530 | − | 0.467960i | 0.0366096 | − | 0.999330i | \(-0.488344\pi\) |
−0.847140 | + | 0.531370i | \(0.821678\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −5.61639 | + | 9.72787i | −0.228528 | + | 0.395821i | ||||
\(605\) | −9.36850 | −0.380884 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 24.4832i | 0.993741i | 0.867825 | + | 0.496870i | \(0.165518\pi\) | ||||
−0.867825 | + | 0.496870i | \(0.834482\pi\) | |||||||
\(608\) | 1.50851 | + | 2.61281i | 0.0611780 | + | 0.105963i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 10.1408 | − | 17.5644i | 0.410589 | − | 0.711161i | ||||
\(611\) | 21.7563 | + | 12.5610i | 0.880167 | + | 0.508165i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 0.440043 | + | 0.762177i | 0.0177732 | + | 0.0307840i | 0.874775 | − | 0.484529i | \(-0.161009\pi\) |
−0.857002 | + | 0.515313i | \(0.827676\pi\) | |||||||
\(614\) | −15.6111 | − | 27.0393i | −0.630014 | − | 1.09122i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 11.7607 | − | 6.79005i | 0.473468 | − | 0.273357i | −0.244222 | − | 0.969719i | \(-0.578533\pi\) |
0.717690 | + | 0.696362i | \(0.245199\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 35.4869i | 1.42634i | 0.700992 | + | 0.713169i | \(0.252741\pi\) | ||||
−0.700992 | + | 0.713169i | \(0.747259\pi\) | |||||||
\(620\) | −7.20451 | + | 4.15953i | −0.289340 | + | 0.167051i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | − | 10.9100i | − | 0.437452i | ||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −12.8060 | −0.512240 | ||||||||
\(626\) | −1.71203 | + | 2.96532i | −0.0684263 | + | 0.118518i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −11.9885 | + | 6.92154i | −0.478391 | + | 0.276199i | ||||
\(629\) | −34.3161 | −1.36827 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 26.9822 | 1.07415 | 0.537073 | − | 0.843536i | \(-0.319530\pi\) | ||||
0.537073 | + | 0.843536i | \(0.319530\pi\) | |||||||
\(632\) | −2.62979 | + | 1.51831i | −0.104608 | + | 0.0603952i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 9.52357 | − | 16.4953i | 0.378229 | − | 0.655112i | ||||
\(635\) | −2.50918 | −0.0995739 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | − | 15.7563i | − | 0.623800i | ||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 1.55049 | − | 0.895175i | 0.0612884 | − | 0.0353849i | ||||
\(641\) | 1.07708i | 0.0425420i | 0.999774 | + | 0.0212710i | \(0.00677128\pi\) | ||||
−0.999774 | + | 0.0212710i | \(0.993229\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 33.3126 | − | 19.2330i | 1.31372 | − | 0.758477i | 0.331010 | − | 0.943627i | \(-0.392611\pi\) |
0.982710 | + | 0.185150i | \(0.0592773\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −5.52817 | − | 9.57507i | −0.217503 | − | 0.376726i | ||||
\(647\) | −4.47605 | − | 7.75275i | −0.175972 | − | 0.304792i | 0.764525 | − | 0.644594i | \(-0.222973\pi\) |
−0.940497 | + | 0.339802i | \(0.889640\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 30.3438 | + | 17.5190i | 1.19110 | + | 0.687680i | ||||
\(650\) | 4.38910 | − | 7.60215i | 0.172155 | − | 0.298181i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −2.16789 | − | 3.75489i | −0.0849010 | − | 0.147053i | ||||
\(653\) | 11.3846i | 0.445513i | 0.974874 | + | 0.222757i | \(0.0715055\pi\) | ||||
−0.974874 | + | 0.222757i | \(0.928494\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 18.7839 | 0.733949 | ||||||||
\(656\) | 4.04094 | − | 6.99911i | 0.157772 | − | 0.273269i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −31.4373 | − | 18.1503i | −1.22462 | − | 0.707036i | −0.258723 | − | 0.965952i | \(-0.583302\pi\) |
−0.965900 | + | 0.258915i | \(0.916635\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 31.2425 | + | 18.0379i | 1.21519 | + | 0.701593i | 0.963886 | − | 0.266315i | \(-0.0858060\pi\) |
0.251308 | + | 0.967907i | \(0.419139\pi\) | |||||||
\(662\) | −0.0634366 | − | 0.0366251i | −0.00246553 | − | 0.00142348i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −12.1290 | − | 7.00270i | −0.470698 | − | 0.271757i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 12.3557 | − | 21.4007i | 0.478414 | − | 0.828637i | ||||
\(668\) | 12.4151 | 0.480355 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | − | 1.02091i | − | 0.0394413i | ||||||
\(671\) | 13.6025 | + | 23.5602i | 0.525117 | + | 0.909530i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 4.78512 | − | 8.28806i | 0.184453 | − | 0.319481i | −0.758939 | − | 0.651161i | \(-0.774282\pi\) |
0.943392 | + | 0.331680i | \(0.107615\pi\) | |||||||
\(674\) | 1.93364 | + | 1.11639i | 0.0744811 | + | 0.0430017i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −5.46254 | − | 9.46139i | −0.210098 | − | 0.363900i | ||||
\(677\) | −7.81408 | − | 13.5344i | −0.300320 | − | 0.520169i | 0.675889 | − | 0.737004i | \(-0.263760\pi\) |
−0.976208 | + | 0.216835i | \(0.930427\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −5.68202 | + | 3.28052i | −0.217896 | + | 0.125802i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | − | 11.1589i | − | 0.427294i | ||||||
\(683\) | 9.63996 | − | 5.56563i | 0.368863 | − | 0.212963i | −0.304099 | − | 0.952640i | \(-0.598355\pi\) |
0.672961 | + | 0.739678i | \(0.265022\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 8.45145i | 0.322913i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 6.96254 | 0.265444 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −2.61903 | + | 1.51210i | −0.0996324 | + | 0.0575228i | −0.548988 | − | 0.835830i | \(-0.684987\pi\) |
0.449356 | + | 0.893353i | \(0.351654\pi\) | |||||||
\(692\) | −17.4182 | −0.662139 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 31.8409 | 1.20867 | ||||||||
\(695\) | 3.66497 | − | 2.11597i | 0.139020 | − | 0.0802633i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −14.8087 | + | 25.6494i | −0.560919 | + | 0.971540i | ||||
\(698\) | −14.7354 | −0.557745 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 50.1486i | 1.89409i | 0.321103 | + | 0.947044i | \(0.395946\pi\) | ||||
−0.321103 | + | 0.947044i | \(0.604054\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 24.4664 | − | 14.1257i | 0.922769 | − | 0.532761i | ||||
\(704\) | 2.40150i | 0.0905101i | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −1.87025 | + | 1.07979i | −0.0703876 | + | 0.0406383i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 1.80385 | + | 3.12436i | 0.0677449 | + | 0.117338i | 0.897908 | − | 0.440183i | \(-0.145086\pi\) |
−0.830163 | + | 0.557520i | \(0.811753\pi\) | |||||||
\(710\) | 5.33751 | + | 9.24484i | 0.200313 | + | 0.346953i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 3.24641 | + | 1.87432i | 0.121664 | + | 0.0702429i | ||||
\(713\) | 8.75046 | − | 15.1562i | 0.327707 | − | 0.567605i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −10.5152 | − | 18.2129i | −0.393246 | − | 0.681123i | ||||
\(716\) | 13.1221i | 0.490395i | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −32.6448 | −1.21829 | ||||||||
\(719\) | −17.1580 | + | 29.7186i | −0.639887 | + | 1.10832i | 0.345571 | + | 0.938393i | \(0.387685\pi\) |
−0.985457 | + | 0.169924i | \(0.945648\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −8.57161 | − | 4.94882i | −0.319002 | − | 0.184176i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 11.5681 | + | 6.67887i | 0.429927 | + | 0.248218i | ||||
\(725\) | −10.1972 | − | 5.88737i | −0.378716 | − | 0.218651i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 19.4757 | + | 11.2443i | 0.722315 | + | 0.417029i | 0.815604 | − | 0.578610i | \(-0.196405\pi\) |
−0.0932892 | + | 0.995639i | \(0.529738\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 11.0835 | − | 19.1972i | 0.410220 | − | 0.710521i | ||||
\(731\) | −25.5154 | −0.943720 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 31.1845i | 1.15182i | 0.817512 | + | 0.575912i | \(0.195353\pi\) | ||||
−0.817512 | + | 0.575912i | \(0.804647\pi\) | |||||||
\(734\) | −14.8501 | − | 25.7212i | −0.548129 | − | 0.949387i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −1.88319 | + | 3.26178i | −0.0694154 | + | 0.120231i | ||||
\(737\) | 1.18595 | + | 0.684706i | 0.0436849 | + | 0.0252215i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −2.04314 | − | 3.53882i | −0.0751581 | − | 0.130178i | 0.825997 | − | 0.563675i | \(-0.190613\pi\) |
−0.901155 | + | 0.433497i | \(0.857279\pi\) | |||||||
\(740\) | −8.38245 | − | 14.5188i | −0.308145 | − | 0.533723i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 1.78246 | − | 1.02910i | 0.0653921 | − | 0.0377542i | −0.466947 | − | 0.884285i | \(-0.654646\pi\) |
0.532340 | + | 0.846531i | \(0.321313\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | − | 31.0877i | − | 1.13897i | ||||||
\(746\) | −1.74653 | + | 1.00836i | −0.0639450 | + | 0.0369187i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | − | 8.80071i | − | 0.321786i | ||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 23.8105 | 0.868859 | 0.434429 | − | 0.900706i | \(-0.356950\pi\) | ||||
0.434429 | + | 0.900706i | \(0.356950\pi\) | |||||||
\(752\) | −2.56802 | + | 4.44794i | −0.0936461 | + | 0.162200i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −27.7926 | + | 16.0461i | −1.01215 | + | 0.584363i | ||||
\(755\) | 20.1106 | 0.731900 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 10.0754 | 0.366197 | 0.183098 | − | 0.983095i | \(-0.441387\pi\) | ||||
0.183098 | + | 0.983095i | \(0.441387\pi\) | |||||||
\(758\) | −16.3427 | + | 9.43544i | −0.593592 | + | 0.342711i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 2.70075 | − | 4.67784i | 0.0979666 | − | 0.169683i | ||||
\(761\) | 27.8735 | 1.01041 | 0.505207 | − | 0.862998i | \(-0.331416\pi\) | ||||
0.505207 | + | 0.862998i | \(0.331416\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 9.25333i | 0.334774i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −0.724440 | + | 0.418256i | −0.0261751 | + | 0.0151122i | ||||
\(767\) | − | 71.3645i | − | 2.57682i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −6.21166 | + | 3.58631i | −0.223998 | + | 0.129326i | −0.607800 | − | 0.794090i | \(-0.707948\pi\) |
0.383802 | + | 0.923415i | \(0.374615\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −12.2801 | − | 21.2698i | −0.441970 | − | 0.765515i | ||||
\(773\) | −1.07077 | − | 1.85462i | −0.0385128 | − | 0.0667061i | 0.846127 | − | 0.532982i | \(-0.178929\pi\) |
−0.884639 | + | 0.466276i | \(0.845595\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −7.22181 | − | 4.16951i | −0.259415 | − | 0.149773i | ||||
\(776\) | 2.75544 | − | 4.77256i | 0.0989144 | − | 0.171325i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 12.4109 | + | 21.4964i | 0.444954 | + | 0.770682i | ||||
\(779\) | − | 24.3831i | − | 0.873615i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −14.3191 | −0.512376 | ||||||||
\(782\) | 6.90127 | − | 11.9533i | 0.246789 | − | 0.427451i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 21.4635 | + | 12.3920i | 0.766066 | + | 0.442288i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −15.8961 | − | 9.17759i | −0.566633 | − | 0.327146i | 0.189170 | − | 0.981944i | \(-0.439420\pi\) |
−0.755804 | + | 0.654798i | \(0.772753\pi\) | |||||||
\(788\) | 10.8133 | + | 6.24305i | 0.385207 | + | 0.222400i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 4.70825 | + | 2.71831i | 0.167512 | + | 0.0967131i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 27.7052 | − | 47.9868i | 0.983839 | − | 1.70406i | ||||
\(794\) | 3.03390 | 0.107669 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | − | 0.179145i | − | 0.00634964i | ||||||
\(797\) | −12.4226 | − | 21.5166i | −0.440031 | − | 0.762156i | 0.557660 | − | 0.830069i | \(-0.311699\pi\) |
−0.997691 | + | 0.0679130i | \(0.978366\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 9.41094 | − | 16.3002i | 0.332935 | − | 0.576660i | ||||
\(800\) | 1.55421 | + | 0.897324i | 0.0549497 | + | 0.0317252i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −6.53854 | − | 11.3251i | −0.230884 | − | 0.399903i | ||||
\(803\) | 14.8670 | + | 25.7504i | 0.524645 | + | 0.908712i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −19.6831 | + | 11.3640i | −0.693307 | + | 0.400281i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0.250324i | 0.00880637i | ||||||||
\(809\) | −32.7237 | + | 18.8930i | −1.15050 | + | 0.664244i | −0.949010 | − | 0.315246i | \(-0.897913\pi\) |
−0.201494 | + | 0.979490i | \(0.564580\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 36.5165i | − | 1.28227i | −0.767429 | − | 0.641134i | \(-0.778464\pi\) | ||
0.767429 | − | 0.641134i | \(-0.221536\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 22.4878 | 0.788196 | ||||||||
\(815\) | −3.88128 | + | 6.72257i | −0.135955 | + | 0.235481i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 18.1918 | − | 10.5030i | 0.636449 | − | 0.367454i | ||||
\(818\) | −5.56709 | −0.194649 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −14.4694 | −0.505293 | ||||||||
\(821\) | −5.52142 | + | 3.18779i | −0.192699 | + | 0.111255i | −0.593245 | − | 0.805022i | \(-0.702154\pi\) |
0.400547 | + | 0.916276i | \(0.368820\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −14.0293 | + | 24.2995i | −0.489032 | + | 0.847028i | −0.999920 | − | 0.0126187i | \(-0.995983\pi\) |
0.510888 | + | 0.859647i | \(0.329317\pi\) | |||||||
\(824\) | 0.167931 | 0.00585017 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 0.581579i | − | 0.0202235i | −0.999949 | − | 0.0101117i | \(-0.996781\pi\) | ||
0.999949 | − | 0.0101117i | \(-0.00321872\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −44.9680 | + | 25.9623i | −1.56180 | + | 0.901708i | −0.564729 | + | 0.825276i | \(0.691019\pi\) |
−0.997075 | + | 0.0764314i | \(0.975647\pi\) | |||||||
\(830\) | 25.0746i | 0.870351i | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 4.23601 | − | 2.44566i | 0.146857 | − | 0.0847881i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −11.1137 | − | 19.2495i | −0.384606 | − | 0.666156i | ||||
\(836\) | 3.62268 | + | 6.27467i | 0.125293 | + | 0.217014i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −14.2017 | − | 8.19938i | −0.490591 | − | 0.283243i | ||||
\(839\) | 3.33038 | − | 5.76838i | 0.114977 | − | 0.199147i | −0.802793 | − | 0.596257i | \(-0.796654\pi\) |
0.917771 | + | 0.397111i | \(0.129987\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 7.02357 | + | 12.1652i | 0.242192 | + | 0.419489i | ||||
\(842\) | 15.4578i | 0.532712i | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 15.1221 | 0.520523 | ||||||||
\(845\) | −9.77985 | + | 16.9392i | −0.336437 | + | 0.582726i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −5.69566 | − | 3.28839i | −0.195360 | − | 0.112791i | ||||
\(851\) | 30.5435 | + | 17.6343i | 1.04702 | + | 0.604495i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −19.2287 | − | 11.1017i | −0.658378 | − | 0.380115i | 0.133281 | − | 0.991078i | \(-0.457449\pi\) |
−0.791659 | + | 0.610964i | \(0.790782\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −3.99540 | + | 6.92024i | −0.136560 | + | 0.236529i | ||||
\(857\) | −15.2966 | −0.522522 | −0.261261 | − | 0.965268i | \(-0.584138\pi\) | ||||
−0.261261 | + | 0.965268i | \(0.584138\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 4.25646i | 0.145229i | 0.997360 | + | 0.0726143i | \(0.0231342\pi\) | ||||
−0.997360 | + | 0.0726143i | \(0.976866\pi\) | |||||||
\(860\) | −6.23269 | − | 10.7953i | −0.212533 | − | 0.368118i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −12.5133 | + | 21.6737i | −0.426204 | + | 0.738208i | ||||
\(863\) | 20.4922 | + | 11.8312i | 0.697562 | + | 0.402738i | 0.806439 | − | 0.591317i | \(-0.201392\pi\) |
−0.108876 | + | 0.994055i | \(0.534725\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 15.5923 | + | 27.0067i | 0.530154 | + | 0.918254i | ||||
\(866\) | −1.12584 | − | 1.95001i | −0.0382576 | − | 0.0662641i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −6.31546 | + | 3.64623i | −0.214237 | + | 0.123690i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 2.78919i | − | 0.0945079i | ||||||
\(872\) | 16.4141 | − | 9.47667i | 0.555851 | − | 0.320920i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 11.3632i | 0.384367i | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −20.3923 | −0.688599 | −0.344300 | − | 0.938860i | \(-0.611884\pi\) | ||||
−0.344300 | + | 0.938860i | \(0.611884\pi\) | |||||||
\(878\) | −9.37000 | + | 16.2293i | −0.316222 | + | 0.547713i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 3.72350 | − | 2.14977i | 0.125519 | − | 0.0724686i | ||||
\(881\) | −32.4586 | −1.09356 | −0.546780 | − | 0.837276i | \(-0.684147\pi\) | ||||
−0.546780 | + | 0.837276i | \(0.684147\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −24.8311 | −0.835632 | −0.417816 | − | 0.908532i | \(-0.637204\pi\) | ||||
−0.417816 | + | 0.908532i | \(0.637204\pi\) | |||||||
\(884\) | −15.5236 | + | 8.96254i | −0.522114 | + | 0.301443i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −0.602256 | + | 1.04314i | −0.0202332 | + | 0.0350449i | ||||
\(887\) | −9.72119 | −0.326405 | −0.163203 | − | 0.986593i | \(-0.552182\pi\) | ||||
−0.163203 | + | 0.986593i | \(0.552182\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | − | 6.71136i | − | 0.224965i | ||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −7.27049 | + | 4.19762i | −0.243434 | + | 0.140547i | ||||
\(893\) | 15.4955i | 0.518537i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 20.3456 | − | 11.7465i | 0.680079 | − | 0.392644i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 13.4011 | + | 23.2114i | 0.447200 | + | 0.774573i | ||||
\(899\) | 15.2433 | + | 26.4021i | 0.508392 | + | 0.880560i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 9.70433 | − | 16.8084i | 0.323119 | − | 0.559658i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −0.579764 | − | 1.00418i | −0.0192827 | − | 0.0333985i | ||||
\(905\) | − | 23.9150i | − | 0.794963i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −16.0863 | −0.534136 | −0.267068 | − | 0.963678i | \(-0.586055\pi\) | ||||
−0.267068 | + | 0.963678i | \(0.586055\pi\) | |||||||
\(908\) | 1.21261 | − | 2.10030i | 0.0402418 | − | 0.0697009i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −27.0087 | − | 15.5935i | −0.894838 | − | 0.516635i | −0.0193161 | − | 0.999813i | \(-0.506149\pi\) |
−0.875522 | + | 0.483179i | \(0.839482\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −29.1279 | − | 16.8170i | −0.963993 | − | 0.556562i | ||||
\(914\) | −11.9934 | − | 6.92442i | −0.396708 | − | 0.229039i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 1.74915 | + | 1.00987i | 0.0577936 | + | 0.0333672i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −12.8832 | + | 22.3143i | −0.424977 | + | 0.736082i | −0.996418 | − | 0.0845609i | \(-0.973051\pi\) |
0.571441 | + | 0.820643i | \(0.306385\pi\) | |||||||
\(920\) | 6.74314 | 0.222315 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 4.80483i | 0.158239i | ||||||||
\(923\) | 14.5824 | + | 25.2574i | 0.479984 | + | 0.831357i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 8.40258 | − | 14.5537i | 0.276275 | − | 0.478522i | ||||
\(926\) | 18.2201 | + | 10.5194i | 0.598750 | + | 0.345689i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −3.28052 | − | 5.68202i | −0.107688 | − | 0.186521i | ||||
\(929\) | 27.3744 | + | 47.4138i | 0.898124 | + | 1.55560i | 0.829891 | + | 0.557926i | \(0.188403\pi\) |
0.0682329 | + | 0.997669i | \(0.478264\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 11.0236 | − | 6.36446i | 0.361089 | − | 0.208475i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | − | 5.82302i | − | 0.190535i | ||||||
\(935\) | −13.6454 | + | 7.87817i | −0.446252 | + | 0.257644i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 58.2065i | 1.90152i | 0.309924 | + | 0.950761i | \(0.399696\pi\) | ||||
−0.309924 | + | 0.950761i | \(0.600304\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 9.19531 | 0.299918 | ||||||||
\(941\) | −16.6658 | + | 28.8660i | −0.543289 | + | 0.941005i | 0.455423 | + | 0.890275i | \(0.349488\pi\) |
−0.998712 | + | 0.0507297i | \(0.983845\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 26.3613 | − | 15.2197i | 0.858443 | − | 0.495622i | ||||
\(944\) | 14.5900 | 0.474864 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 16.7206 | 0.543632 | ||||||||
\(947\) | −6.59497 | + | 3.80761i | −0.214308 | + | 0.123731i | −0.603312 | − | 0.797505i | \(-0.706153\pi\) |
0.389004 | + | 0.921236i | \(0.372819\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 30.2808 | − | 52.4478i | 0.982955 | − | 1.70253i | ||||
\(950\) | 5.41447 | 0.175669 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 55.7861i | − | 1.80709i | −0.428495 | − | 0.903544i | \(-0.640956\pi\) | ||
0.428495 | − | 0.903544i | \(-0.359044\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 14.3472 | − | 8.28334i | 0.464264 | − | 0.268043i | ||||
\(956\) | 17.4495i | 0.564356i | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 23.3447 | − | 13.4781i | 0.754232 | − | 0.435456i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −4.70451 | − | 8.14845i | −0.151758 | − | 0.262853i | ||||
\(962\) | −22.9013 | − | 39.6662i | −0.738367 | − | 1.27889i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −9.90142 | − | 5.71659i | −0.318903 | − | 0.184119i | ||||
\(965\) | −21.9857 | + | 38.0803i | −0.707744 | + | 1.22585i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −13.3369 | − | 23.1003i | −0.428887 | − | 0.742855i | 0.567887 | − | 0.823106i | \(-0.307761\pi\) |
−0.996775 | + | 0.0802517i | \(0.974428\pi\) | |||||||
\(968\) | − | 5.23278i | − | 0.168188i | ||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −9.86639 | −0.316791 | ||||||||
\(971\) | −4.29971 | + | 7.44731i | −0.137984 | + | 0.238996i | −0.926733 | − | 0.375719i | \(-0.877396\pi\) |
0.788749 | + | 0.614715i | \(0.210729\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 11.8011 | + | 6.81338i | 0.378132 | + | 0.218315i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 9.81058 | + | 5.66414i | 0.314029 | + | 0.181305i | ||||
\(977\) | −12.7973 | − | 7.38854i | −0.409423 | − | 0.236380i | 0.281119 | − | 0.959673i | \(-0.409295\pi\) |
−0.690542 | + | 0.723293i | \(0.742628\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 7.79627 | + | 4.50118i | 0.249170 | + | 0.143858i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 19.4815 | − | 33.7430i | 0.621680 | − | 1.07678i | ||||
\(983\) | 20.5135 | 0.654280 | 0.327140 | − | 0.944976i | \(-0.393915\pi\) | ||||
0.327140 | + | 0.944976i | \(0.393915\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | − | 22.3545i | − | 0.712273i | ||||||
\(986\) | 12.0220 | + | 20.8227i | 0.382858 | + | 0.663130i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 7.37859 | − | 12.7801i | 0.234744 | − | 0.406589i | ||||
\(989\) | 22.7103 | + | 13.1118i | 0.722145 | + | 0.416931i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 4.64647 | + | 8.04792i | 0.147600 | + | 0.255651i | 0.930340 | − | 0.366698i | \(-0.119512\pi\) |
−0.782740 | + | 0.622349i | \(0.786179\pi\) | |||||||
\(992\) | −2.32330 | − | 4.02408i | −0.0737650 | − | 0.127765i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −0.277763 | + | 0.160366i | −0.00880567 | + | 0.00508396i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 0.0199668i | 0.000632354i | 1.00000 | 0.000316177i | \(0.000100642\pi\) | |||||
−1.00000 | 0.000316177i | \(0.999899\pi\) | ||||||||
\(998\) | 22.5250 | − | 13.0048i | 0.713018 | − | 0.411661i | ||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))