Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [864,2,Mod(433,864)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(864, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("864.433");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 864 = 2^{5} \cdot 3^{3} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 864.d (of order \(2\), degree \(1\), 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: | \(6.89907473464\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.0.629407744.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 2x^{6} + 2x^{4} - 8x^{2} + 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{6}\cdot 3^{2} \) |
Twist minimal: | no (minimal twist has level 216) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 433.7 | ||
Root | \(-1.38255 + 0.297594i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 864.433 |
Dual form | 864.2.d.c.433.2 |
$q$-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 \(\left(\mathbb{Z}/864\mathbb{Z}\right)^\times\).
\(n\) | \(325\) | \(353\) | \(703\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 3.36028i | 1.50276i | 0.659867 | + | 0.751382i | \(0.270612\pi\) | ||||
−0.659867 | + | 0.751382i | \(0.729388\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.64575 | 1.00000 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.16991i | 0.654252i | 0.944981 | + | 0.327126i | \(0.106080\pi\) | ||||
−0.944981 | + | 0.327126i | \(0.893920\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − 4.64575i | − 1.28850i | −0.764815 | − | 0.644250i | \(-0.777170\pi\) | ||||
0.764815 | − | 0.644250i | \(-0.222830\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 4.55066 | 1.10370 | 0.551848 | − | 0.833944i | \(-0.313923\pi\) | ||||
0.551848 | + | 0.833944i | \(0.313923\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 6.29150i | 1.44337i | 0.692222 | + | 0.721685i | \(0.256632\pi\) | ||||
−0.692222 | + | 0.721685i | \(0.743368\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −0.979531 | −0.204246 | −0.102123 | − | 0.994772i | \(-0.532564\pi\) | ||||
−0.102123 | + | 0.994772i | \(0.532564\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −6.29150 | −1.25830 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 4.33981i | 0.805883i | 0.915226 | + | 0.402942i | \(0.132012\pi\) | ||||
−0.915226 | + | 0.402942i | \(0.867988\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.00000 | −0.359211 | −0.179605 | − | 0.983739i | \(-0.557482\pi\) | ||||
−0.179605 | + | 0.983739i | \(0.557482\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 8.89047i | 1.50276i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.35425i | 0.222637i | 0.993785 | + | 0.111319i | \(0.0355074\pi\) | ||||
−0.993785 | + | 0.111319i | \(0.964493\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −11.0604 | −1.72734 | −0.863671 | − | 0.504057i | \(-0.831840\pi\) | ||||
−0.863671 | + | 0.504057i | \(0.831840\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − 3.29150i | − 0.501949i | −0.967994 | − | 0.250975i | \(-0.919249\pi\) | ||||
0.967994 | − | 0.250975i | \(-0.0807511\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 10.0808 | 1.47044 | 0.735222 | − | 0.677827i | \(-0.237078\pi\) | ||||
0.735222 | + | 0.677827i | \(0.237078\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 4.33981i | 0.596119i | 0.954547 | + | 0.298060i | \(0.0963394\pi\) | ||||
−0.954547 | + | 0.298060i | \(0.903661\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −7.29150 | −0.983186 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 11.2712i | 1.46739i | 0.679480 | + | 0.733694i | \(0.262206\pi\) | ||||
−0.679480 | + | 0.733694i | \(0.737794\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.93725i | 0.248040i | 0.992280 | + | 0.124020i | \(0.0395787\pi\) | ||||
−0.992280 | + | 0.124020i | \(0.960421\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 15.6110 | 1.93631 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − 3.00000i | − 0.366508i | −0.983066 | − | 0.183254i | \(-0.941337\pi\) | ||||
0.983066 | − | 0.183254i | \(-0.0586631\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 11.5830 | 1.35569 | 0.677844 | − | 0.735206i | \(-0.262914\pi\) | ||||
0.677844 | + | 0.735206i | \(0.262914\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 5.74103i | 0.654252i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 8.64575 | 0.972723 | 0.486362 | − | 0.873758i | \(-0.338324\pi\) | ||||
0.486362 | + | 0.873758i | \(0.338324\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − 2.38075i | − 0.261321i | −0.991427 | − | 0.130661i | \(-0.958290\pi\) | ||||
0.991427 | − | 0.130661i | \(-0.0417099\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 15.2915i | 1.65860i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −4.55066 | −0.482369 | −0.241184 | − | 0.970479i | \(-0.577536\pi\) | ||||
−0.241184 | + | 0.970479i | \(0.577536\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − 12.2915i | − 1.28850i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −21.1412 | −2.16904 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 2.29150 | 0.232667 | 0.116333 | − | 0.993210i | \(-0.462886\pi\) | ||||
0.116333 | + | 0.993210i | \(0.462886\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − 6.72057i | − 0.668721i | −0.942445 | − | 0.334361i | \(-0.891480\pi\) | ||||
0.942445 | − | 0.334361i | \(-0.108520\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 5.35425 | 0.527570 | 0.263785 | − | 0.964582i | \(-0.415029\pi\) | ||||
0.263785 | + | 0.964582i | \(0.415029\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − 17.9918i | − 1.73933i | −0.493640 | − | 0.869666i | \(-0.664334\pi\) | ||||
0.493640 | − | 0.869666i | \(-0.335666\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − 15.2915i | − 1.46466i | −0.680950 | − | 0.732330i | \(-0.738433\pi\) | ||||
0.680950 | − | 0.732330i | \(-0.261567\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −6.50972 | −0.612383 | −0.306192 | − | 0.951970i | \(-0.599055\pi\) | ||||
−0.306192 | + | 0.951970i | \(0.599055\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − 3.29150i | − 0.306934i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 12.0399 | 1.10370 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 6.29150 | 0.571955 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − 4.33981i | − 0.388165i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −5.29150 | −0.469545 | −0.234772 | − | 0.972050i | \(-0.575435\pi\) | ||||
−0.234772 | + | 0.972050i | \(0.575435\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − 15.4002i | − 1.34552i | −0.739860 | − | 0.672761i | \(-0.765108\pi\) | ||||
0.739860 | − | 0.672761i | \(-0.234892\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 16.6458i | 1.44337i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 6.50972 | 0.556163 | 0.278082 | − | 0.960557i | \(-0.410301\pi\) | ||||
0.278082 | + | 0.960557i | \(0.410301\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 12.2915i | 1.04255i | 0.853388 | + | 0.521276i | \(0.174544\pi\) | ||||
−0.853388 | + | 0.521276i | \(0.825456\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 10.0808 | 0.843003 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −14.5830 | −1.21105 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − 8.67963i | − 0.711063i | −0.934664 | − | 0.355531i | \(-0.884300\pi\) | ||||
0.934664 | − | 0.355531i | \(-0.115700\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −12.6458 | −1.02910 | −0.514548 | − | 0.857461i | \(-0.672040\pi\) | ||||
−0.514548 | + | 0.857461i | \(0.672040\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − 6.72057i | − 0.539809i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − 8.70850i | − 0.695014i | −0.937677 | − | 0.347507i | \(-0.887028\pi\) | ||||
0.937677 | − | 0.347507i | \(-0.112972\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −2.59160 | −0.204246 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − 6.29150i | − 0.492789i | −0.969170 | − | 0.246394i | \(-0.920754\pi\) | ||||
0.969170 | − | 0.246394i | \(-0.0792458\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −19.1822 | −1.48436 | −0.742180 | − | 0.670200i | \(-0.766208\pi\) | ||||
−0.742180 | + | 0.670200i | \(0.766208\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −8.58301 | −0.660231 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − 15.8219i | − 1.20292i | −0.798905 | − | 0.601458i | \(-0.794587\pi\) | ||||
0.798905 | − | 0.601458i | \(-0.205413\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −16.6458 | −1.25830 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 4.76150i | 0.355891i | 0.984040 | + | 0.177946i | \(0.0569452\pi\) | ||||
−0.984040 | + | 0.177946i | \(0.943055\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 16.6458i | 1.23727i | 0.785679 | + | 0.618634i | \(0.212314\pi\) | ||||
−0.785679 | + | 0.618634i | \(0.787686\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −4.55066 | −0.334571 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 9.87451i | 0.722096i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −8.12179 | −0.587672 | −0.293836 | − | 0.955856i | \(-0.594932\pi\) | ||||
−0.293836 | + | 0.955856i | \(0.594932\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −4.29150 | −0.308909 | −0.154455 | − | 0.988000i | \(-0.549362\pi\) | ||||
−0.154455 | + | 0.988000i | \(0.549362\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − 7.70010i | − 0.548609i | −0.961643 | − | 0.274305i | \(-0.911552\pi\) | ||||
0.961643 | − | 0.274305i | \(-0.0884477\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 18.5203 | 1.31287 | 0.656433 | − | 0.754384i | \(-0.272064\pi\) | ||||
0.656433 | + | 0.754384i | \(0.272064\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 11.4821i | 0.805883i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − 37.1660i | − 2.59579i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −13.6520 | −0.944327 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − 0.291503i | − 0.0200679i | −0.999950 | − | 0.0100339i | \(-0.996806\pi\) | ||||
0.999950 | − | 0.0100339i | \(-0.00319395\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 11.0604 | 0.754312 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −5.29150 | −0.359211 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − 21.1412i | − 1.42211i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 10.0000 | 0.669650 | 0.334825 | − | 0.942280i | \(-0.391323\pi\) | ||||
0.334825 | + | 0.942280i | \(0.391323\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − 13.4411i | − 0.892119i | −0.895003 | − | 0.446060i | \(-0.852827\pi\) | ||||
0.895003 | − | 0.446060i | \(-0.147173\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − 13.1660i | − 0.870034i | −0.900422 | − | 0.435017i | \(-0.856742\pi\) | ||||
0.900422 | − | 0.435017i | \(-0.143258\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 9.10132 | 0.596247 | 0.298124 | − | 0.954527i | \(-0.403639\pi\) | ||||
0.298124 | + | 0.954527i | \(0.403639\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 33.8745i | 2.20973i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 20.1617 | 1.30415 | 0.652076 | − | 0.758154i | \(-0.273898\pi\) | ||||
0.652076 | + | 0.758154i | \(0.273898\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 26.8745 | 1.73114 | 0.865570 | − | 0.500789i | \(-0.166957\pi\) | ||||
0.865570 | + | 0.500789i | \(0.166957\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 29.2288 | 1.85978 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − 24.5015i | − 1.54652i | −0.634088 | − | 0.773261i | \(-0.718624\pi\) | ||||
0.634088 | − | 0.773261i | \(-0.281376\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − 2.12549i | − 0.133629i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −20.1617 | −1.25765 | −0.628826 | − | 0.777546i | \(-0.716464\pi\) | ||||
−0.628826 | + | 0.777546i | \(0.716464\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 3.58301i | 0.222637i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −1.95906 | −0.120801 | −0.0604005 | − | 0.998174i | \(-0.519238\pi\) | ||||
−0.0604005 | + | 0.998174i | \(0.519238\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −14.5830 | −0.895827 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − 5.74103i | − 0.350037i | −0.984565 | − | 0.175019i | \(-0.944001\pi\) | ||||
0.984565 | − | 0.175019i | \(-0.0559985\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 21.2288 | 1.28956 | 0.644778 | − | 0.764370i | \(-0.276950\pi\) | ||||
0.644778 | + | 0.764370i | \(0.276950\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | − 13.6520i | − 0.823245i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 8.70850i | 0.523243i | 0.965171 | + | 0.261621i | \(0.0842572\pi\) | ||||
−0.965171 | + | 0.261621i | \(0.915743\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 20.1617 | 1.20275 | 0.601373 | − | 0.798968i | \(-0.294621\pi\) | ||||
0.601373 | + | 0.798968i | \(0.294621\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − 27.2915i | − 1.62231i | −0.584830 | − | 0.811156i | \(-0.698839\pi\) | ||||
0.584830 | − | 0.811156i | \(-0.301161\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −29.2630 | −1.72734 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 3.70850 | 0.218147 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 14.4207i | 0.842464i | 0.906953 | + | 0.421232i | \(0.138402\pi\) | ||||
−0.906953 | + | 0.421232i | \(0.861598\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −37.8745 | −2.20514 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 4.55066i | 0.263171i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | − 8.70850i | − 0.501949i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −6.50972 | −0.372746 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − 9.87451i | − 0.563568i | −0.959478 | − | 0.281784i | \(-0.909074\pi\) | ||||
0.959478 | − | 0.281784i | \(-0.0909261\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −0.979531 | −0.0555441 | −0.0277721 | − | 0.999614i | \(-0.508841\pi\) | ||||
−0.0277721 | + | 0.999614i | \(0.508841\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 14.8745 | 0.840757 | 0.420378 | − | 0.907349i | \(-0.361897\pi\) | ||||
0.420378 | + | 0.907349i | \(0.361897\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 20.5834i | 1.15608i | 0.816009 | + | 0.578039i | \(0.196182\pi\) | ||||
−0.816009 | + | 0.578039i | \(0.803818\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −9.41699 | −0.527250 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 28.6305i | 1.59304i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 29.2288i | 1.62132i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 26.6714 | 1.47044 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 5.70850i | 0.313767i | 0.987617 | + | 0.156884i | \(0.0501448\pi\) | ||||
−0.987617 | + | 0.156884i | \(0.949855\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 10.0808 | 0.550776 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 2.29150 | 0.124826 | 0.0624131 | − | 0.998050i | \(-0.480120\pi\) | ||||
0.0624131 | + | 0.998050i | \(0.480120\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − 4.33981i | − 0.235014i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −18.5203 | −1.00000 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − 0.421689i | − 0.0226375i | −0.999936 | − | 0.0113187i | \(-0.996397\pi\) | ||||
0.999936 | − | 0.0113187i | \(-0.00360294\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − 10.6458i | − 0.569854i | −0.958549 | − | 0.284927i | \(-0.908031\pi\) | ||||
0.958549 | − | 0.284927i | \(-0.0919694\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −13.0194 | −0.692955 | −0.346478 | − | 0.938058i | \(-0.612622\pi\) | ||||
−0.346478 | + | 0.938058i | \(0.612622\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −21.1412 | −1.11579 | −0.557896 | − | 0.829911i | \(-0.688391\pi\) | ||||
−0.557896 | + | 0.829911i | \(0.688391\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −20.5830 | −1.08332 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 38.9222i | 2.03728i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −4.52026 | −0.235956 | −0.117978 | − | 0.993016i | \(-0.537641\pi\) | ||||
−0.117978 | + | 0.993016i | \(0.537641\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 11.4821i | 0.596119i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 38.5203i | 1.99450i | 0.0740880 | + | 0.997252i | \(0.476395\pi\) | ||||
−0.0740880 | + | 0.997252i | \(0.523605\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 20.1617 | 1.03838 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − 21.5830i | − 1.10864i | −0.832302 | − | 0.554322i | \(-0.812978\pi\) | ||||
0.832302 | − | 0.554322i | \(-0.187022\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 20.1617 | 1.03021 | 0.515107 | − | 0.857126i | \(-0.327752\pi\) | ||||
0.515107 | + | 0.857126i | \(0.327752\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −19.2915 | −0.983186 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 5.31935i | 0.269702i | 0.990866 | + | 0.134851i | \(0.0430555\pi\) | ||||
−0.990866 | + | 0.134851i | \(0.956944\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −4.45751 | −0.225426 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 29.0522i | 1.46177i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − 15.2915i | − 0.767459i | −0.923446 | − | 0.383729i | \(-0.874640\pi\) | ||||
0.923446 | − | 0.383729i | \(-0.125360\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 13.0194 | 0.650160 | 0.325080 | − | 0.945687i | \(-0.394609\pi\) | ||||
0.325080 | + | 0.945687i | \(0.394609\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 9.29150i | 0.462843i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −2.93859 | −0.145661 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 8.29150 | 0.409988 | 0.204994 | − | 0.978763i | \(-0.434282\pi\) | ||||
0.204994 | + | 0.978763i | \(0.434282\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 29.8209i | 1.46739i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 8.00000 | 0.392705 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 2.16991i | 0.106007i | 0.998594 | + | 0.0530035i | \(0.0168794\pi\) | ||||
−0.998594 | + | 0.0530035i | \(0.983121\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 22.6458i | 1.10369i | 0.833948 | + | 0.551843i | \(0.186075\pi\) | ||||
−0.833948 | + | 0.551843i | \(0.813925\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −28.6305 | −1.38878 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 5.12549i | 0.248040i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 30.2425 | 1.45673 | 0.728366 | − | 0.685188i | \(-0.240280\pi\) | ||||
0.728366 | + | 0.685188i | \(0.240280\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −0.125492 | −0.00603077 | −0.00301538 | − | 0.999995i | \(-0.500960\pi\) | ||||
−0.00301538 | + | 0.999995i | \(0.500960\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − 6.16272i | − 0.294803i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 11.1660 | 0.532925 | 0.266462 | − | 0.963845i | \(-0.414145\pi\) | ||||
0.266462 | + | 0.963845i | \(0.414145\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 28.8413i | 1.37029i | 0.728405 | + | 0.685146i | \(0.240262\pi\) | ||||
−0.728405 | + | 0.685146i | \(0.759738\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − 15.2915i | − 0.724887i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −19.5292 | −0.921638 | −0.460819 | − | 0.887494i | \(-0.652444\pi\) | ||||
−0.460819 | + | 0.887494i | \(0.652444\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − 24.0000i | − 1.13012i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 41.3029 | 1.93631 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 23.8745 | 1.11680 | 0.558401 | − | 0.829571i | \(-0.311415\pi\) | ||||
0.558401 | + | 0.829571i | \(0.311415\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − 18.7605i | − 0.873763i | −0.899519 | − | 0.436881i | \(-0.856083\pi\) | ||||
0.899519 | − | 0.436881i | \(-0.143917\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −31.2288 | −1.45132 | −0.725662 | − | 0.688052i | \(-0.758466\pi\) | ||||
−0.725662 | + | 0.688052i | \(0.758466\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 0.210845i | 0.00975672i | 0.999988 | + | 0.00487836i | \(0.00155284\pi\) | ||||
−0.999988 | + | 0.00487836i | \(0.998447\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − 7.93725i | − 0.366508i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 7.14226 | 0.328401 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − 39.5830i | − 1.81619i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −35.1402 | −1.60560 | −0.802798 | − | 0.596250i | \(-0.796657\pi\) | ||||
−0.802798 | + | 0.596250i | \(0.796657\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 6.29150 | 0.286868 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 7.70010i | 0.349643i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −6.06275 | −0.274729 | −0.137365 | − | 0.990521i | \(-0.543863\pi\) | ||||
−0.137365 | + | 0.990521i | \(0.543863\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 4.12897i | 0.186338i | 0.995650 | + | 0.0931689i | \(0.0296997\pi\) | ||||
−0.995650 | + | 0.0931689i | \(0.970300\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 19.7490i | 0.889451i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 43.7490i | 1.95847i | 0.202717 | + | 0.979237i | \(0.435023\pi\) | ||||
−0.202717 | + | 0.979237i | \(0.564977\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −2.93859 | −0.131025 | −0.0655127 | − | 0.997852i | \(-0.520868\pi\) | ||||
−0.0655127 | + | 0.997852i | \(0.520868\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 22.5830 | 1.00493 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − 33.0450i | − 1.46469i | −0.680932 | − | 0.732347i | \(-0.738425\pi\) | ||||
0.680932 | − | 0.732347i | \(-0.261575\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 30.6458 | 1.35569 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 17.9918i | 0.792813i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 21.8745i | 0.962040i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −13.6520 | −0.598104 | −0.299052 | − | 0.954237i | \(-0.596670\pi\) | ||||
−0.299052 | + | 0.954237i | \(0.596670\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − 0.874508i | − 0.0382396i | −0.999817 | − | 0.0191198i | \(-0.993914\pi\) | ||||
0.999817 | − | 0.0191198i | \(-0.00608639\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −9.10132 | −0.396460 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −22.0405 | −0.958283 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 51.3838i | 2.22568i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 60.4575 | 2.61381 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − 26.5203i | − 1.14019i | −0.821577 | − | 0.570097i | \(-0.806905\pi\) | ||||
0.821577 | − | 0.570097i | \(-0.193095\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 51.3838 | 2.20104 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − 9.58301i | − 0.409740i | −0.978789 | − | 0.204870i | \(-0.934323\pi\) | ||||
0.978789 | − | 0.204870i | \(-0.0656771\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −27.3040 | −1.16319 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 22.8745 | 0.972723 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 1.40122i | 0.0593716i | 0.999559 | + | 0.0296858i | \(0.00945067\pi\) | ||||
−0.999559 | + | 0.0296858i | \(0.990549\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −15.2915 | −0.646762 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 41.8608i | 1.76422i | 0.471042 | + | 0.882111i | \(0.343878\pi\) | ||||
−0.471042 | + | 0.882111i | \(0.656122\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − 21.8745i | − 0.920267i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −26.6714 | −1.11812 | −0.559062 | − | 0.829126i | \(-0.688839\pi\) | ||||
−0.559062 | + | 0.829126i | \(0.688839\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − 5.70850i | − 0.238893i | −0.992841 | − | 0.119447i | \(-0.961888\pi\) | ||||
0.992841 | − | 0.119447i | \(-0.0381120\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 6.16272 | 0.257003 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 23.5830 | 0.981773 | 0.490887 | − | 0.871223i | \(-0.336673\pi\) | ||||
0.490887 | + | 0.871223i | \(0.336673\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − 6.29888i | − 0.261321i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −9.41699 | −0.390012 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − 21.9099i | − 0.904319i | −0.891937 | − | 0.452160i | \(-0.850654\pi\) | ||||
0.891937 | − | 0.452160i | \(-0.149346\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − 12.5830i | − 0.518474i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 33.1811 | 1.36259 | 0.681293 | − | 0.732011i | \(-0.261418\pi\) | ||||
0.681293 | + | 0.732011i | \(0.261418\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 40.4575i | 1.65860i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 35.1402 | 1.43579 | 0.717895 | − | 0.696151i | \(-0.245106\pi\) | ||||
0.717895 | + | 0.696151i | \(0.245106\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −31.8745 | −1.30019 | −0.650094 | − | 0.759854i | \(-0.725271\pi\) | ||||
−0.650094 | + | 0.759854i | \(0.725271\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 21.1412i | 0.859513i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −33.3542 | −1.35381 | −0.676904 | − | 0.736072i | \(-0.736679\pi\) | ||||
−0.676904 | + | 0.736072i | \(0.736679\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − 46.8331i | − 1.89467i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − 21.1033i | − 0.852353i | −0.904640 | − | 0.426176i | \(-0.859860\pi\) | ||||
0.904640 | − | 0.426176i | \(-0.140140\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 17.5701 | 0.707346 | 0.353673 | − | 0.935369i | \(-0.384933\pi\) | ||||
0.353673 | + | 0.935369i | \(0.384933\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 39.0000i | 1.56754i | 0.621050 | + | 0.783771i | \(0.286706\pi\) | ||||
−0.621050 | + | 0.783771i | \(0.713294\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −12.0399 | −0.482369 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −16.8745 | −0.674980 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 6.16272i | 0.245724i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −19.2288 | −0.765485 | −0.382742 | − | 0.923855i | \(-0.625020\pi\) | ||||
−0.382742 | + | 0.923855i | \(0.625020\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | − 17.7809i | − 0.705615i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −22.1208 | −0.873718 | −0.436859 | − | 0.899530i | \(-0.643909\pi\) | ||||
−0.436859 | + | 0.899530i | \(0.643909\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − 27.2915i | − 1.07627i | −0.842858 | − | 0.538136i | \(-0.819129\pi\) | ||||
0.842858 | − | 0.538136i | \(-0.180871\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 33.1811 | 1.30449 | 0.652243 | − | 0.758010i | \(-0.273828\pi\) | ||||
0.652243 | + | 0.758010i | \(0.273828\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −24.4575 | −0.960041 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 24.5015i | 0.958818i | 0.877592 | + | 0.479409i | \(0.159149\pi\) | ||||
−0.877592 | + | 0.479409i | \(0.840851\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 51.7490 | 2.02200 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − 11.4821i | − 0.447278i | −0.974672 | − | 0.223639i | \(-0.928206\pi\) | ||||
0.974672 | − | 0.223639i | \(-0.0717937\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − 14.5203i | − 0.564773i | −0.959301 | − | 0.282386i | \(-0.908874\pi\) | ||||
0.959301 | − | 0.282386i | \(-0.0911260\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −55.9344 | −2.16904 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − 4.25098i | − 0.164599i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −4.20366 | −0.162281 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −40.8745 | −1.57560 | −0.787798 | − | 0.615933i | \(-0.788779\pi\) | ||||
−0.787798 | + | 0.615933i | \(0.788779\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − 31.7799i | − 1.22140i | −0.791861 | − | 0.610701i | \(-0.790888\pi\) | ||||
0.791861 | − | 0.610701i | \(-0.209112\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 6.06275 | 0.232667 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 17.7809i | 0.680369i | 0.940359 | + | 0.340185i | \(0.110490\pi\) | ||||
−0.940359 | + | 0.340185i | \(0.889510\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 21.8745i | 0.835782i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 20.1617 | 0.768100 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 27.2915i | 1.03822i | 0.854708 | + | 0.519109i | \(0.173736\pi\) | ||||
−0.854708 | + | 0.519109i | \(0.826264\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −41.3029 | −1.56671 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −50.3320 | −1.90646 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − 16.8014i | − 0.634581i | −0.948328 | − | 0.317290i | \(-0.897227\pi\) | ||||
0.948328 | − | 0.317290i | \(-0.102773\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −8.52026 | −0.321348 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − 17.7809i | − 0.668721i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − 3.47974i | − 0.130684i | −0.997863 | − | 0.0653422i | \(-0.979186\pi\) | ||||
0.997863 | − | 0.0653422i | \(-0.0208139\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 1.95906 | 0.0733675 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 33.8745i | 1.26683i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −51.3838 | −1.91629 | −0.958146 | − | 0.286281i | \(-0.907581\pi\) | ||||
−0.958146 | + | 0.286281i | \(0.907581\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 14.1660 | 0.527570 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − 27.3040i | − 1.01404i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −44.5830 | −1.65349 | −0.826746 | − | 0.562575i | \(-0.809811\pi\) | ||||
−0.826746 | + | 0.562575i | \(0.809811\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − 14.9785i | − 0.554000i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − 28.4575i | − 1.05110i | −0.850762 | − | 0.525551i | \(-0.823859\pi\) | ||||
0.850762 | − | 0.525551i | \(-0.176141\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 6.50972 | 0.239789 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 40.4575i | 1.48825i | 0.668038 | + | 0.744127i | \(0.267134\pi\) | ||||
−0.668038 | + | 0.744127i | \(0.732866\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −25.0594 | −0.919339 | −0.459669 | − | 0.888090i | \(-0.652032\pi\) | ||||
−0.459669 | + | 0.888090i | \(0.652032\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 29.1660 | 1.06856 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − 47.6018i | − 1.73933i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −24.0627 | −0.878062 | −0.439031 | − | 0.898472i | \(-0.644678\pi\) | ||||
−0.439031 | + | 0.898472i | \(0.644678\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − 42.4933i | − 1.54649i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 13.9373i | 0.506558i | 0.967393 | + | 0.253279i | \(0.0815091\pi\) | ||||
−0.967393 | + | 0.253279i | \(0.918491\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −9.73385 | −0.352852 | −0.176426 | − | 0.984314i | \(-0.556454\pi\) | ||||
−0.176426 | + | 0.984314i | \(0.556454\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − 40.4575i | − 1.46466i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 52.3633 | 1.89073 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 36.1660 | 1.30418 | 0.652090 | − | 0.758142i | \(-0.273892\pi\) | ||||
0.652090 | + | 0.758142i | \(0.273892\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 6.29888i | 0.226555i | 0.993563 | + | 0.113277i | \(0.0361349\pi\) | ||||
−0.993563 | + | 0.113277i | \(0.963865\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 12.5830 | 0.451995 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − 69.5864i | − 2.49319i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 29.2630 | 1.04444 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − 50.6235i | − 1.80453i | −0.431178 | − | 0.902267i | \(-0.641902\pi\) | ||||
0.431178 | − | 0.902267i | \(-0.358098\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −17.2231 | −0.612383 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 9.00000 | 0.319599 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − 50.9621i | − 1.80517i | −0.430512 | − | 0.902585i | \(-0.641667\pi\) | ||||
0.430512 | − | 0.902585i | \(-0.358333\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 45.8745 | 1.62292 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 25.1340i | 0.886961i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | − 8.70850i | − 0.306934i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 20.7085i | 0.727174i | 0.931560 | + | 0.363587i | \(0.118448\pi\) | ||||
−0.931560 | + | 0.363587i | \(0.881552\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 21.1412 | 0.740545 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 20.7085 | 0.724499 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − 49.9826i | − 1.74440i | −0.489146 | − | 0.872202i | \(-0.662692\pi\) | ||||
0.489146 | − | 0.872202i | \(-0.337308\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 20.0627 | 0.699343 | 0.349672 | − | 0.936872i | \(-0.386293\pi\) | ||||
0.349672 | + | 0.936872i | \(0.386293\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 49.6356i | 1.72600i | 0.505206 | + | 0.862999i | \(0.331417\pi\) | ||||
−0.505206 | + | 0.862999i | \(0.668583\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 6.77124i | 0.235175i | 0.993063 | + | 0.117588i | \(0.0375161\pi\) | ||||
−0.993063 | + | 0.117588i | \(0.962484\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − 64.4575i | − 2.23064i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 31.2221 | 1.07791 | 0.538953 | − | 0.842336i | \(-0.318820\pi\) | ||||
0.538953 | + | 0.842336i | \(0.318820\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 10.1660 | 0.350552 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − 28.8413i | − 0.992172i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 16.6458 | 0.571955 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − 1.32653i | − 0.0454728i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 29.8118i | 1.02074i | 0.859956 | + | 0.510368i | \(0.170491\pi\) | ||||
−0.859956 | + | 0.510368i | \(0.829509\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −40.3234 | −1.37742 | −0.688711 | − | 0.725036i | \(-0.741823\pi\) | ||||
−0.688711 | + | 0.725036i | \(0.741823\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − 26.4170i | − 0.901336i | −0.892692 | − | 0.450668i | \(-0.851186\pi\) | ||||
0.892692 | − | 0.450668i | \(-0.148814\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 36.1197 | 1.22953 | 0.614765 | − | 0.788710i | \(-0.289251\pi\) | ||||
0.614765 | + | 0.788710i | \(0.289251\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 53.1660 | 1.80770 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 18.7605i | 0.636406i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −13.9373 | −0.472246 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | − 11.4821i | − 0.388165i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 48.3948i | 1.63418i | 0.576514 | + | 0.817088i | \(0.304413\pi\) | ||||
−0.576514 | + | 0.817088i | \(0.695587\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −31.8546 | −1.07321 | −0.536605 | − | 0.843834i | \(-0.680293\pi\) | ||||
−0.536605 | + | 0.843834i | \(0.680293\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − 16.1660i | − 0.544030i | −0.962293 | − | 0.272015i | \(-0.912310\pi\) | ||||
0.962293 | − | 0.272015i | \(-0.0876900\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −7.14226 | −0.239813 | −0.119907 | − | 0.992785i | \(-0.538260\pi\) | ||||
−0.119907 | + | 0.992785i | \(0.538260\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −14.0000 | −0.469545 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 63.4237i | 2.12239i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −16.0000 | −0.534821 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − 8.67963i | − 0.289482i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 19.7490i | 0.657935i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −55.9344 | −1.85932 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 56.0405i | 1.86079i | 0.366552 | + | 0.930397i | \(0.380538\pi\) | ||||
−0.366552 | + | 0.930397i | \(0.619462\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −47.4657 | −1.57261 | −0.786304 | − | 0.617840i | \(-0.788008\pi\) | ||||
−0.786304 | + | 0.617840i | \(0.788008\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 5.16601 | 0.170970 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − 40.7451i | − 1.34552i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −20.5830 | −0.678971 | −0.339485 | − | 0.940611i | \(-0.610253\pi\) | ||||
−0.339485 | + | 0.940611i | \(0.610253\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − 8.52026i | − 0.280144i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 16.9376 | 0.555704 | 0.277852 | − | 0.960624i | \(-0.410378\pi\) | ||||
0.277852 | + | 0.960624i | \(0.410378\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −33.1811 | −1.08514 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −9.12549 | −0.298117 | −0.149058 | − | 0.988828i | \(-0.547624\pi\) | ||||
−0.149058 | + | 0.988828i | \(0.547624\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 21.5629i | 0.702931i | 0.936201 | + | 0.351466i | \(0.114317\pi\) | ||||
−0.936201 | + | 0.351466i | \(0.885683\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 10.8340 | 0.352803 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − 31.0112i | − 1.00773i | −0.863782 | − | 0.503865i | \(-0.831911\pi\) | ||||
0.863782 | − | 0.503865i | \(-0.168089\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − 53.8118i | − 1.74680i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 40.9559 | 1.32669 | 0.663346 | − | 0.748312i | \(-0.269136\pi\) | ||||
0.663346 | + | 0.748312i | \(0.269136\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − 27.2915i | − 0.883132i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 17.2231 | 0.556163 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −27.0000 | −0.870968 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − 14.4207i | − 0.464218i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 38.0627 | 1.22402 | 0.612008 | − | 0.790852i | \(-0.290362\pi\) | ||||
0.612008 | + | 0.790852i | \(0.290362\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − 17.9918i | − 0.577384i | −0.957422 | − | 0.288692i | \(-0.906780\pi\) | ||||
0.957422 | − | 0.288692i | \(-0.0932204\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 32.5203i | 1.04255i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −29.2630 | −0.936207 | −0.468103 | − | 0.883674i | \(-0.655063\pi\) | ||||
−0.468103 | + | 0.883674i | \(0.655063\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − 9.87451i | − 0.315591i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 28.2835 | 0.902103 | 0.451052 | − | 0.892498i | \(-0.351049\pi\) | ||||
0.451052 | + | 0.892498i | \(0.351049\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 25.8745 | 0.824430 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 3.22413i | 0.102521i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −21.9373 | −0.696860 | −0.348430 | − | 0.937335i | \(-0.613285\pi\) | ||||
−0.348430 | + | 0.937335i | \(0.613285\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 62.2333i | 1.97293i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − 21.8745i | − 0.692773i | −0.938092 | − | 0.346386i | \(-0.887409\pi\) | ||||
0.938092 | − | 0.346386i | \(-0.112591\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))