Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2240,2,Mod(1791,2240)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2240, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2240.1791");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2240 = 2^{6} \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2240.k (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: | \(17.8864900528\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.0.342102016.5 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + x^{6} + 4x^{4} + 4x^{2} + 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | no (minimal twist has level 140) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1791.7 | ||
Root | \(-1.17915 - 0.780776i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2240.1791 |
Dual form | 2240.2.k.e.1791.8 |
$q$-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 \(\left(\mathbb{Z}/2240\mathbb{Z}\right)^\times\).
\(n\) | \(897\) | \(1471\) | \(1541\) | \(1921\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) | \(-1\) |
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 | ||||||||
\(3\) | 3.02045 | 1.74386 | 0.871928 | − | 0.489634i | \(-0.162870\pi\) | ||||
0.871928 | + | 0.489634i | \(0.162870\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | − | 1.00000i | − | 0.447214i | ||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.17238 | − | 1.51022i | 0.821081 | − | 0.570811i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 6.12311 | 2.04104 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 4.71659i | − | 1.42211i | −0.703139 | − | 0.711053i | \(-0.748219\pi\) | ||
0.703139 | − | 0.711053i | \(-0.251781\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 2.00000i | − | 0.554700i | −0.960769 | − | 0.277350i | \(-0.910544\pi\) | ||
0.960769 | − | 0.277350i | \(-0.0894562\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | − | 3.02045i | − | 0.779876i | ||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.12311i | 0.272393i | 0.990682 | + | 0.136197i | \(0.0434879\pi\) | ||||
−0.990682 | + | 0.136197i | \(0.956512\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −4.71659 | −1.08206 | −0.541030 | − | 0.841003i | \(-0.681965\pi\) | ||||
−0.541030 | + | 0.841003i | \(0.681965\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 6.56155 | − | 4.56155i | 1.43185 | − | 0.995412i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 6.41273i | 1.33715i | 0.743646 | + | 0.668573i | \(0.233095\pi\) | ||||
−0.743646 | + | 0.668573i | \(0.766905\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.00000 | −0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 9.43318 | 1.81542 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.00000 | 0.371391 | 0.185695 | − | 0.982607i | \(-0.440546\pi\) | ||||
0.185695 | + | 0.982607i | \(0.440546\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.39228 | 0.609272 | 0.304636 | − | 0.952469i | \(-0.401465\pi\) | ||||
0.304636 | + | 0.952469i | \(0.401465\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | − | 14.2462i | − | 2.47995i | ||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −1.51022 | − | 2.17238i | −0.255274 | − | 0.367199i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −2.00000 | −0.328798 | −0.164399 | − | 0.986394i | \(-0.552568\pi\) | ||||
−0.164399 | + | 0.986394i | \(0.552568\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | − | 6.04090i | − | 0.967317i | ||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 1.12311i | − | 0.175400i | −0.996147 | − | 0.0876998i | \(-0.972048\pi\) | ||
0.996147 | − | 0.0876998i | \(-0.0279516\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0.371834i | 0.0567042i | 0.999598 | + | 0.0283521i | \(0.00902596\pi\) | ||||
−0.999598 | + | 0.0283521i | \(0.990974\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | − | 6.12311i | − | 0.912779i | ||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −5.08842 | −0.742223 | −0.371111 | − | 0.928588i | \(-0.621023\pi\) | ||||
−0.371111 | + | 0.928588i | \(0.621023\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 2.43845 | − | 6.56155i | 0.348350 | − | 0.937365i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 3.39228i | 0.475014i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −2.00000 | −0.274721 | −0.137361 | − | 0.990521i | \(-0.543862\pi\) | ||||
−0.137361 | + | 0.990521i | \(0.543862\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −4.71659 | −0.635985 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −14.2462 | −1.88696 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −2.06798 | −0.269227 | −0.134614 | − | 0.990898i | \(-0.542979\pi\) | ||||
−0.134614 | + | 0.990898i | \(0.542979\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 2.00000i | − | 0.256074i | −0.991769 | − | 0.128037i | \(-0.959132\pi\) | ||
0.991769 | − | 0.128037i | \(-0.0408676\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 13.3017 | − | 9.24726i | 1.67586 | − | 1.16505i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −2.00000 | −0.248069 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 3.76412i | 0.459860i | 0.973207 | + | 0.229930i | \(0.0738497\pi\) | ||||
−0.973207 | + | 0.229930i | \(0.926150\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 19.3693i | 2.33179i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 7.36520i | − | 0.874089i | −0.899440 | − | 0.437044i | \(-0.856025\pi\) | ||
0.899440 | − | 0.437044i | \(-0.143975\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 15.3693i | 1.79884i | 0.437083 | + | 0.899421i | \(0.356012\pi\) | ||||
−0.437083 | + | 0.899421i | \(0.643988\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −3.02045 | −0.348771 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −7.12311 | − | 10.2462i | −0.811753 | − | 1.16766i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1.32431i | 0.148996i | 0.997221 | + | 0.0744981i | \(0.0237355\pi\) | ||||
−0.997221 | + | 0.0744981i | \(0.976265\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 10.1231 | 1.12479 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 3.02045 | 0.331537 | 0.165769 | − | 0.986165i | \(-0.446990\pi\) | ||||
0.165769 | + | 0.986165i | \(0.446990\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.12311 | 0.121818 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 6.04090 | 0.647652 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 12.0000i | 1.27200i | 0.771690 | + | 0.635999i | \(0.219412\pi\) | ||||
−0.771690 | + | 0.635999i | \(0.780588\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −3.02045 | − | 4.34475i | −0.316629 | − | 0.455454i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 10.2462 | 1.06248 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 4.71659i | 0.483912i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 1.12311i | − | 0.114034i | −0.998373 | − | 0.0570170i | \(-0.981841\pi\) | ||
0.998373 | − | 0.0570170i | \(-0.0181589\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | − | 28.8802i | − | 2.90257i | ||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 15.1231i | 1.50481i | 0.658703 | + | 0.752403i | \(0.271105\pi\) | ||||
−0.658703 | + | 0.752403i | \(0.728895\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 7.73704 | 0.762353 | 0.381176 | − | 0.924502i | \(-0.375519\pi\) | ||||
0.381176 | + | 0.924502i | \(0.375519\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −4.56155 | − | 6.56155i | −0.445162 | − | 0.640342i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 5.66906i | 0.548049i | 0.961723 | + | 0.274024i | \(0.0883549\pi\) | ||||
−0.961723 | + | 0.274024i | \(0.911645\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 7.12311 | 0.682270 | 0.341135 | − | 0.940014i | \(-0.389189\pi\) | ||||
0.341135 | + | 0.940014i | \(0.389189\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −6.04090 | −0.573376 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 18.4924 | 1.73962 | 0.869810 | − | 0.493386i | \(-0.164241\pi\) | ||||
0.869810 | + | 0.493386i | \(0.164241\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 6.41273 | 0.597990 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | − | 12.2462i | − | 1.13216i | ||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 1.69614 | + | 2.43981i | 0.155485 | + | 0.223657i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −11.2462 | −1.02238 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − | 3.39228i | − | 0.305872i | ||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.00000i | 0.0894427i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 17.7509i | − | 1.57513i | −0.616229 | − | 0.787567i | \(-0.711341\pi\) | ||
0.616229 | − | 0.787567i | \(-0.288659\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 1.12311i | 0.0988839i | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 17.5420 | 1.53266 | 0.766328 | − | 0.642450i | \(-0.222082\pi\) | ||||
0.766328 | + | 0.642450i | \(0.222082\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −10.2462 | + | 7.12311i | −0.888459 | + | 0.617652i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | − | 9.43318i | − | 0.811879i | ||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −14.0000 | −1.19610 | −0.598050 | − | 0.801459i | \(-0.704058\pi\) | ||||
−0.598050 | + | 0.801459i | \(0.704058\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 16.7984 | 1.42482 | 0.712410 | − | 0.701763i | \(-0.247604\pi\) | ||||
0.712410 | + | 0.701763i | \(0.247604\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −15.3693 | −1.29433 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −9.43318 | −0.788842 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 2.00000i | − | 0.166091i | ||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 7.36520 | − | 19.8188i | 0.607472 | − | 1.63463i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −5.36932 | −0.439872 | −0.219936 | − | 0.975514i | \(-0.570585\pi\) | ||||
−0.219936 | + | 0.975514i | \(0.570585\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 10.0138i | − | 0.814913i | −0.913225 | − | 0.407456i | \(-0.866416\pi\) | ||
0.913225 | − | 0.407456i | \(-0.133584\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 6.87689i | 0.555964i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − | 3.39228i | − | 0.272475i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 0.246211i | 0.0196498i | 0.999952 | + | 0.00982490i | \(0.00312741\pi\) | ||||
−0.999952 | + | 0.00982490i | \(0.996873\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −6.04090 | −0.479074 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 9.68466 | + | 13.9309i | 0.763258 | + | 1.09791i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 3.02045i | − | 0.236580i | −0.992979 | − | 0.118290i | \(-0.962259\pi\) | ||
0.992979 | − | 0.118290i | \(-0.0377412\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −14.2462 | −1.10907 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 19.8188 | 1.53363 | 0.766813 | − | 0.641870i | \(-0.221841\pi\) | ||||
0.766813 | + | 0.641870i | \(0.221841\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 9.00000 | 0.692308 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −28.8802 | −2.20852 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 16.2462i | 1.23518i | 0.786502 | + | 0.617588i | \(0.211890\pi\) | ||||
−0.786502 | + | 0.617588i | \(0.788110\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −2.17238 | + | 1.51022i | −0.164216 | + | 0.114162i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −6.24621 | −0.469494 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 10.7575i | 0.804052i | 0.915628 | + | 0.402026i | \(0.131694\pi\) | ||||
−0.915628 | + | 0.402026i | \(0.868306\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 15.1231i | 1.12409i | 0.827106 | + | 0.562046i | \(0.189986\pi\) | ||||
−0.827106 | + | 0.562046i | \(0.810014\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − | 6.04090i | − | 0.446556i | ||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 2.00000i | 0.147043i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 5.29723 | 0.387372 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 20.4924 | − | 14.2462i | 1.49060 | − | 1.03626i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 16.7984i | 1.21549i | 0.794133 | + | 0.607744i | \(0.207925\pi\) | ||||
−0.794133 | + | 0.607744i | \(0.792075\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −22.4924 | −1.61904 | −0.809520 | − | 0.587092i | \(-0.800273\pi\) | ||||
−0.809520 | + | 0.587092i | \(0.800273\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −6.04090 | −0.432598 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −18.0000 | −1.28245 | −0.641223 | − | 0.767354i | \(-0.721573\pi\) | ||||
−0.641223 | + | 0.767354i | \(0.721573\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 26.8122 | 1.90067 | 0.950333 | − | 0.311235i | \(-0.100742\pi\) | ||||
0.950333 | + | 0.311235i | \(0.100742\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 11.3693i | 0.801930i | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 4.34475 | − | 3.02045i | 0.304942 | − | 0.211994i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1.12311 | −0.0784411 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 39.2658i | 2.72916i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 22.2462i | 1.53880i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 22.0956i | − | 1.52112i | −0.649265 | − | 0.760562i | \(-0.724923\pi\) | ||
0.649265 | − | 0.760562i | \(-0.275077\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − | 22.2462i | − | 1.52429i | ||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0.371834 | 0.0253589 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 7.36932 | − | 5.12311i | 0.500262 | − | 0.347779i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 46.4222i | 3.13692i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 2.24621 | 0.151097 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −20.5625 | −1.37697 | −0.688483 | − | 0.725252i | \(-0.741723\pi\) | ||||
−0.688483 | + | 0.725252i | \(0.741723\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −6.12311 | −0.408207 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −3.76412 | −0.249833 | −0.124917 | − | 0.992167i | \(-0.539866\pi\) | ||||
−0.124917 | + | 0.992167i | \(0.539866\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 12.8769i | 0.850929i | 0.904975 | + | 0.425465i | \(0.139889\pi\) | ||||
−0.904975 | + | 0.425465i | \(0.860111\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −21.5150 | − | 30.9481i | −1.41558 | − | 2.03624i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 7.75379 | 0.507968 | 0.253984 | − | 0.967208i | \(-0.418259\pi\) | ||||
0.253984 | + | 0.967208i | \(0.418259\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 5.08842i | 0.331932i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 4.00000i | 0.259828i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 3.97292i | 0.256987i | 0.991710 | + | 0.128493i | \(0.0410141\pi\) | ||||
−0.991710 | + | 0.128493i | \(0.958986\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 25.6155i | − | 1.65004i | −0.565103 | − | 0.825021i | \(-0.691163\pi\) | ||
0.565103 | − | 0.825021i | \(-0.308837\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 2.27678 | 0.146055 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −6.56155 | − | 2.43845i | −0.419202 | − | 0.155787i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 9.43318i | 0.600219i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 9.12311 | 0.578153 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −16.0547 | −1.01336 | −0.506682 | − | 0.862133i | \(-0.669128\pi\) | ||||
−0.506682 | + | 0.862133i | \(0.669128\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 30.2462 | 1.90156 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 3.39228 | 0.212433 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 11.3693i | − | 0.709199i | −0.935018 | − | 0.354599i | \(-0.884617\pi\) | ||
0.935018 | − | 0.354599i | \(-0.115383\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −4.34475 | + | 3.02045i | −0.269970 | + | 0.187682i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 12.2462 | 0.758021 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 18.4945i | − | 1.14042i | −0.821499 | − | 0.570211i | \(-0.806862\pi\) | ||
0.821499 | − | 0.570211i | \(-0.193138\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 2.00000i | 0.122859i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 36.2454i | 2.21818i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 0.246211i | 0.0150118i | 0.999972 | + | 0.00750588i | \(0.00238922\pi\) | ||||
−0.999972 | + | 0.00750588i | \(0.997611\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1.90495 | −0.115717 | −0.0578586 | − | 0.998325i | \(-0.518427\pi\) | ||||
−0.0578586 | + | 0.998325i | \(0.518427\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −9.12311 | − | 13.1231i | −0.552155 | − | 0.794246i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 4.71659i | 0.284421i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −12.2462 | −0.735804 | −0.367902 | − | 0.929865i | \(-0.619924\pi\) | ||||
−0.367902 | + | 0.929865i | \(0.619924\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 20.7713 | 1.24355 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −29.3693 | −1.75203 | −0.876013 | − | 0.482287i | \(-0.839806\pi\) | ||||
−0.876013 | + | 0.482287i | \(0.839806\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −4.92539 | −0.292784 | −0.146392 | − | 0.989227i | \(-0.546766\pi\) | ||||
−0.146392 | + | 0.989227i | \(0.546766\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 14.2462i | 0.843873i | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −1.69614 | − | 2.43981i | −0.100120 | − | 0.144017i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 15.7386 | 0.925802 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | − | 3.39228i | − | 0.198859i | ||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 15.7538i | 0.920346i | 0.887829 | + | 0.460173i | \(0.152213\pi\) | ||||
−0.887829 | + | 0.460173i | \(0.847787\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 2.06798i | 0.120402i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − | 44.4924i | − | 2.58171i | ||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 12.8255 | 0.741715 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0.561553 | + | 0.807764i | 0.0323674 | + | 0.0465587i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 45.6786i | 2.62416i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −2.00000 | −0.114520 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 1.53311 | 0.0874993 | 0.0437496 | − | 0.999043i | \(-0.486070\pi\) | ||||
0.0437496 | + | 0.999043i | \(0.486070\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 23.3693 | 1.32943 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −30.2045 | −1.71274 | −0.856369 | − | 0.516364i | \(-0.827285\pi\) | ||||
−0.856369 | + | 0.516364i | \(0.827285\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 33.6155i | 1.90006i | 0.312156 | + | 0.950031i | \(0.398949\pi\) | ||||
−0.312156 | + | 0.950031i | \(0.601051\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −9.24726 | − | 13.3017i | −0.521024 | − | 0.749466i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −12.2462 | −0.687816 | −0.343908 | − | 0.939003i | \(-0.611751\pi\) | ||||
−0.343908 | + | 0.939003i | \(0.611751\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 9.43318i | − | 0.528157i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 17.1231i | 0.955719i | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 5.29723i | − | 0.294746i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 2.00000i | 0.110940i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 21.5150 | 1.18978 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −11.0540 | + | 7.68466i | −0.609425 | + | 0.423669i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 18.2857i | − | 1.00507i | −0.864556 | − | 0.502537i | \(-0.832400\pi\) | ||
0.864556 | − | 0.502537i | \(-0.167600\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −12.2462 | −0.671088 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 3.76412 | 0.205656 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −12.2462 | −0.667094 | −0.333547 | − | 0.942734i | \(-0.608246\pi\) | ||||
−0.333547 | + | 0.942734i | \(0.608246\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 55.8554 | 3.03365 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 16.0000i | − | 0.866449i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −4.61219 | − | 17.9368i | −0.249035 | − | 0.968495i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 19.3693 | 1.04281 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 5.66906i | 0.304331i | 0.988355 | + | 0.152166i | \(0.0486247\pi\) | ||||
−0.988355 | + | 0.152166i | \(0.951375\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 29.8617i | − | 1.59846i | −0.601024 | − | 0.799231i | \(-0.705240\pi\) | ||
0.601024 | − | 0.799231i | \(-0.294760\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | − | 18.8664i | − | 1.00701i | ||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 19.3693i | − | 1.03092i | −0.856912 | − | 0.515462i | \(-0.827620\pi\) | ||
0.856912 | − | 0.515462i | \(-0.172380\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −7.36520 | −0.390904 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 5.12311 | + | 7.36932i | 0.271144 | + | 0.390026i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 16.0547i | 0.847335i | 0.905818 | + | 0.423668i | \(0.139258\pi\) | ||||
−0.905818 | + | 0.423668i | \(0.860742\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 3.24621 | 0.170853 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −33.9686 | −1.78289 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 15.3693 | 0.804467 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 10.3857 | 0.542127 | 0.271063 | − | 0.962562i | \(-0.412625\pi\) | ||||
0.271063 | + | 0.962562i | \(0.412625\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | − | 6.87689i | − | 0.357997i | ||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −4.34475 | + | 3.02045i | −0.225568 | + | 0.156814i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 10.4924 | 0.543277 | 0.271639 | − | 0.962399i | \(-0.412434\pi\) | ||||
0.271639 | + | 0.962399i | \(0.412434\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 3.02045i | 0.155975i | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 4.00000i | − | 0.206010i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 14.8934i | − | 0.765024i | −0.923950 | − | 0.382512i | \(-0.875059\pi\) | ||
0.923950 | − | 0.382512i | \(-0.124941\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | − | 53.6155i | − | 2.74681i | ||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 19.0752 | 0.974695 | 0.487348 | − | 0.873208i | \(-0.337964\pi\) | ||||
0.487348 | + | 0.873208i | \(0.337964\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −10.2462 | + | 7.12311i | −0.522195 | + | 0.363027i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 2.27678i | 0.115735i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 7.12311 | 0.361156 | 0.180578 | − | 0.983561i | \(-0.442203\pi\) | ||||
0.180578 | + | 0.983561i | \(0.442203\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −7.20217 | −0.364230 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 52.9848 | 2.67273 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 1.32431 | 0.0666331 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 14.0000i | 0.702640i | 0.936255 | + | 0.351320i | \(0.114267\pi\) | ||||
−0.936255 | + | 0.351320i | \(0.885733\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −30.9481 | + | 21.5150i | −1.54935 | + | 1.07710i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 6.00000 | 0.299626 | 0.149813 | − | 0.988714i | \(-0.452133\pi\) | ||||
0.149813 | + | 0.988714i | \(0.452133\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 6.78456i | − | 0.337963i | ||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | − | 10.1231i | − | 0.503021i | ||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 9.43318i | 0.467585i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 17.1231i | − | 0.846683i | −0.905970 | − | 0.423342i | \(-0.860857\pi\) | ||
0.905970 | − | 0.423342i | \(-0.139143\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −42.2863 | −2.08583 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −4.49242 | + | 3.12311i | −0.221058 | + | 0.153678i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 3.02045i | − | 0.148268i | ||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 50.7386 | 2.48468 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −23.5829 | −1.15210 | −0.576051 | − | 0.817414i | \(-0.695407\pi\) | ||||
−0.576051 | + | 0.817414i | \(0.695407\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −23.6155 | −1.15095 | −0.575475 | − | 0.817819i | \(-0.695183\pi\) | ||||
−0.575475 | + | 0.817819i | \(0.695183\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −31.1570 | −1.51490 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | − | 1.12311i | − | 0.0544786i | ||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −3.02045 | − | 4.34475i | −0.146170 | − | 0.210257i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −28.4924 | −1.37563 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 5.87787i | 0.283127i | 0.989929 | + | 0.141563i | \(0.0452129\pi\) | ||||
−0.989929 | + | 0.141563i | \(0.954787\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 29.6155i | 1.42323i | 0.702569 | + | 0.711616i | \(0.252036\pi\) | ||||
−0.702569 | + | 0.711616i | \(0.747964\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | − | 6.04090i | − | 0.289639i | ||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − | 30.2462i | − | 1.44687i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −16.2177 | −0.774031 | −0.387015 | − | 0.922073i | \(-0.626494\pi\) | ||||
−0.387015 | + | 0.922073i | \(0.626494\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 14.9309 | − | 40.1771i | 0.710994 | − | 1.91319i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 23.0481i | 1.09505i | 0.836790 | + | 0.547524i | \(0.184429\pi\) | ||||
−0.836790 | + | 0.547524i | \(0.815571\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 12.0000 | 0.568855 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −16.2177 | −0.767073 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −15.6155 | −0.736942 | −0.368471 | − | 0.929639i | \(-0.620119\pi\) | ||||
−0.368471 | + | 0.929639i | \(0.620119\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −5.29723 | −0.249437 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | − | 30.2462i | − | 1.42109i | ||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −4.34475 | + | 3.02045i | −0.203685 | + | 0.141601i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 6.00000 | 0.280668 | 0.140334 | − | 0.990104i | \(-0.455182\pi\) | ||||
0.140334 | + | 0.990104i | \(0.455182\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 10.5945i | 0.494507i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 3.61553i | − | 0.168392i | −0.996449 | − | 0.0841960i | \(-0.973168\pi\) | ||
0.996449 | − | 0.0841960i | \(-0.0268322\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 28.6714i | − | 1.33247i | −0.745741 | − | 0.666236i | \(-0.767904\pi\) | ||
0.745741 | − | 0.666236i | \(-0.232096\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | − | 10.2462i | − | 0.475157i | ||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 18.4945 | 0.855824 | 0.427912 | − | 0.903820i | \(-0.359249\pi\) | ||||
0.427912 | + | 0.903820i | \(0.359249\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 5.68466 | + | 8.17708i | 0.262493 | + | 0.377583i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0.743668i | 0.0342664i | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 1.75379 | 0.0806393 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 4.71659 | 0.216412 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −12.2462 | −0.560715 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 4.00000i | 0.182384i | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 29.2520 | + | 42.0775i | 1.33101 | + | 1.91459i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −1.12311 | −0.0509976 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 13.1973i | 0.598026i | 0.954249 | + | 0.299013i | \(0.0966575\pi\) | ||||
−0.954249 | + | 0.299013i | \(0.903343\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | − | 9.12311i | − | 0.412561i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 31.5288i | 1.42287i | 0.702750 | + | 0.711437i | \(0.251955\pi\) | ||||
−0.702750 | + | 0.711437i | \(0.748045\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 2.24621i | 0.101164i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −28.8802 | −1.29807 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −11.1231 | − | 16.0000i | −0.498939 | − | 0.717698i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 24.3266i | 1.08901i | 0.838758 | + | 0.544504i | \(0.183282\pi\) | ||||
−0.838758 | + | 0.544504i | \(0.816718\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 59.8617 | 2.67443 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 17.9139 | 0.798741 | 0.399370 | − | 0.916790i | \(-0.369229\pi\) | ||||
0.399370 | + | 0.916790i | \(0.369229\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 15.1231 | 0.672969 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 27.1840 | 1.20729 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 23.6155i | 1.04674i | 0.852106 | + | 0.523370i | \(0.175325\pi\) | ||||
−0.852106 | + | 0.523370i | \(0.824675\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 23.2111 | + | 33.3880i | 1.02680 | + | 1.47700i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −44.4924 | −1.96439 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − | 7.73704i | − | 0.340935i | ||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 24.0000i | 1.05552i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 49.0708i | 2.15397i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 9.75379i | − | 0.427321i | −0.976908 | − | 0.213661i | \(-0.931461\pi\) | ||
0.976908 | − | 0.213661i | \(-0.0685387\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 19.2382 | 0.841227 | 0.420614 | − | 0.907240i | \(-0.361815\pi\) | ||||
0.420614 | + | 0.907240i | \(0.361815\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −6.56155 | + | 4.56155i | −0.286370 | + | 0.199082i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 3.80989i | 0.165961i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −18.1231 | −0.787961 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −12.6624 | −0.549503 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −2.24621 | −0.0972942 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 5.66906 | 0.245095 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 32.4924i | 1.40215i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −30.9481 | − | 11.5012i | −1.33303 | − | 0.495390i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −30.0000 | −1.28980 | −0.644900 | − | 0.764267i | \(-0.723101\pi\) | ||||
−0.644900 | + | 0.764267i | \(0.723101\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 45.6786i | 1.96025i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − | 7.12311i | − | 0.305120i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 30.5763i | − | 1.30735i | −0.756776 | − | 0.653674i | \(-0.773227\pi\) | ||
0.756776 | − | 0.653674i | \(-0.226773\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | − | 12.2462i | − | 0.522656i | ||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −9.43318 | −0.401867 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 2.00000 | + | 2.87689i | 0.0850487 | + | 0.122338i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 6.04090i | 0.256422i | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 26.4924 | 1.12252 | 0.561260 | − | 0.827640i | \(-0.310317\pi\) | ||||
0.561260 | + | 0.827640i | \(0.310317\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0.743668 | 0.0314538 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 16.0000 | 0.675521 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −38.1045 | −1.60592 | −0.802958 | − | 0.596036i | \(-0.796741\pi\) | ||||
−0.802958 | + | 0.596036i | \(0.796741\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − | 18.4924i | − | 0.777982i | ||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 21.9912 | − | 15.2882i | 0.923544 | − | 0.642042i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −28.8769 | −1.21058 | −0.605291 | − | 0.796004i | \(-0.706943\pi\) | ||||
−0.605291 | + | 0.796004i | \(0.706943\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 3.22925i | − | 0.135140i | −0.997715 | − | 0.0675700i | \(-0.978475\pi\) | ||
0.997715 | − | 0.0675700i | \(-0.0215246\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 50.7386i | 2.11964i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 6.41273i | − | 0.267429i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 45.6155i | 1.89900i | 0.313768 | + | 0.949500i | \(0.398409\pi\) | ||||
−0.313768 | + | 0.949500i | \(0.601591\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −67.9372 | −2.82337 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 6.56155 | − | 4.56155i | 0.272219 | − | 0.189245i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 9.43318i | 0.390682i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −12.2462 | −0.506319 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −21.8868 | −0.903365 | −0.451683 | − | 0.892179i | \(-0.649176\pi\) | ||||
−0.451683 | + | 0.892179i | \(0.649176\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −16.0000 | −0.659269 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −54.3681 | −2.23640 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 11.3693i | − | 0.466882i | −0.972371 | − | 0.233441i | \(-0.925001\pi\) | ||
0.972371 | − | 0.233441i | \(-0.0749986\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 2.43981 | − | 1.69614i | 0.100022 | − | 0.0695350i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 80.9848 | 3.31449 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 29.6238i | − | 1.21040i | −0.796074 | − | 0.605199i | \(-0.793094\pi\) | ||
0.796074 | − | 0.605199i | \(-0.206906\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 17.1231i | 0.698466i | 0.937036 | + | 0.349233i | \(0.113558\pi\) | ||||
−0.937036 | + | 0.349233i | \(0.886442\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 23.0481i | 0.938590i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 11.2462i | 0.457224i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 37.9415 | 1.54000 | 0.769999 | − | 0.638045i | \(-0.220257\pi\) | ||||
0.769999 | + | 0.638045i | \(0.220257\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 13.1231 | − | 9.12311i | 0.531775 | − | 0.369687i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 10.1768i | 0.411711i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −28.2462 | −1.14085 | −0.570427 | − | 0.821348i | \(-0.693222\pi\) | ||||
−0.570427 | + | 0.821348i | \(0.693222\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −3.39228 | −0.136790 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −26.0000 | −1.04672 | −0.523360 | − | 0.852111i | \(-0.675322\pi\) | ||||
−0.523360 | + | 0.852111i | \(0.675322\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 20.6083 | 0.828316 | 0.414158 | − | 0.910205i | \(-0.364076\pi\) | ||||
0.414158 | + | 0.910205i | \(0.364076\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 60.4924i | 2.42748i | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 18.1227 | + | 26.0685i | 0.726070 | + | 1.04441i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 67.1935i | 2.68345i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 2.24621i | − | 0.0895623i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 14.1498i | − | 0.563293i | −0.959518 | − | 0.281647i | \(-0.909119\pi\) | ||
0.959518 | − | 0.281647i | \(-0.0908806\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | − | 66.7386i | − | 2.65262i | ||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −17.7509 | −0.704421 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −13.1231 | − | 4.87689i | −0.519956 | − | 0.193230i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | − | 45.0979i | − | 1.78405i | ||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −7.12311 | −0.281346 | −0.140673 | − | 0.990056i | \(-0.544927\pi\) | ||||
−0.140673 | + | 0.990056i | \(0.544927\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 33.9686 | 1.33959 | 0.669795 | − | 0.742546i | \(-0.266382\pi\) | ||||
0.669795 | + | 0.742546i | \(0.266382\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 1.12311 | 0.0442222 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −40.1725 | −1.57934 | −0.789672 | − | 0.613529i | \(-0.789749\pi\) | ||||
−0.789672 | + | 0.613529i | \(0.789749\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 9.75379i | 0.382870i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 22.2586 | − | 15.4741i | 0.872385 | − | 0.606477i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 22.9848 | 0.899466 | 0.449733 | − | 0.893163i | \(-0.351519\pi\) | ||||
0.449733 | + | 0.893163i | \(0.351519\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − | 17.5420i | − | 0.685425i | ||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 94.1080i | 3.67150i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 1.32431i | − | 0.0515877i | −0.999667 | − | 0.0257938i | \(-0.991789\pi\) | ||
0.999667 | − | 0.0257938i | \(-0.00821134\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 12.2462i | 0.476322i | 0.971226 | + | 0.238161i | \(0.0765447\pi\) | ||||
−0.971226 | + | 0.238161i | \(0.923455\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 6.78456 | 0.263491 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 7.12311 | + | 10.2462i | 0.276222 | + | 0.397331i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 12.8255i | 0.496604i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −62.1080 | −2.40123 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −9.43318 | −0.364164 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −14.0000 | −0.539660 | −0.269830 | − | 0.962908i | \(-0.586968\pi\) | ||||
−0.269830 | + | 0.962908i | \(0.586968\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −9.43318 | −0.363083 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 32.7386i | 1.25825i | 0.777305 | + | 0.629124i | \(0.216586\pi\) | ||||
−0.777305 | + | 0.629124i | \(0.783414\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −1.69614 | − | 2.43981i | −0.0650919 | − | 0.0936313i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −11.3693 | −0.435673 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 0.371834i | 0.0142278i | 0.999975 | + | 0.00711392i | \(0.00226445\pi\) | ||||
−0.999975 | + | 0.00711392i | \(0.997736\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 14.0000i | 0.534913i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 38.8940i | 1.48390i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 4.00000i | 0.152388i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −14.8934 | −0.566573 | −0.283286 | − | 0.959035i | \(-0.591425\pi\) | ||||
−0.283286 | + | 0.959035i | \(0.591425\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −43.6155 | − | 62.7386i | −1.65682 | − | 2.38324i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − | 16.7984i | − | 0.637199i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1.26137 | 0.0477777 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 23.4199 | 0.885823 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −11.1231 | −0.420114 | −0.210057 | − | 0.977689i | \(-0.567365\pi\) | ||||
−0.210057 | + | 0.977689i | \(0.567365\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 9.43318 | 0.355779 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 15.3693i | 0.578842i | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 22.8393 | + | 32.8531i | 0.858959 | + | 1.23557i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −44.7386 | −1.68019 | −0.840097 | − | 0.542436i | \(-0.817502\pi\) | ||||
−0.840097 | + | 0.542436i | \(0.817502\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 8.10887i | 0.304106i | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 21.7538i | 0.814686i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 9.43318i | 0.352781i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 12.0000i | 0.448148i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −22.6762 | −0.845681 | −0.422841 | − | 0.906204i | \(-0.638967\pi\) | ||||
−0.422841 | + | 0.906204i | \(0.638967\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 16.8078 | − | 11.6847i | 0.625954 | − | 0.435159i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − | 77.3704i | − | 2.87743i | ||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −2.00000 | −0.0742781 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 9.64198 | 0.357601 | 0.178801 | − | 0.983885i | \(-0.442778\pi\) | ||||
0.178801 | + | 0.983885i | \(0.442778\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −23.4924 | −0.870090 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −0.417609 | −0.0154458 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 0.738634i | − | 0.0272821i | −0.999907 | − | 0.0136410i | \(-0.995658\pi\) | ||
0.999907 | − | 0.0136410i | \(-0.00434221\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −19.8188 | − | 7.36520i | −0.731029 | − | 0.271670i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 17.7538 | 0.653969 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 37.5697i | − | 1.38202i | −0.722844 | − | 0.691012i | \(-0.757165\pi\) | ||
0.722844 | − | 0.691012i | \(-0.242835\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 28.4924i | 1.04670i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 23.7917i | 0.872835i | 0.899744 | + | 0.436417i | \(0.143753\pi\) | ||||
−0.899744 | + | 0.436417i | \(0.856247\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 5.36932i | 0.196717i | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 18.4945 | 0.676679 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 8.56155 | + | 12.3153i | 0.312832 | + | 0.449993i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 28.8802i | − | 1.05385i | −0.849911 | − | 0.526926i | \(-0.823344\pi\) | ||
0.849911 | − | 0.526926i | \(-0.176656\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −48.4924 | −1.76716 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −10.0138 | −0.364440 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −4.24621 | −0.154331 | −0.0771656 | − | 0.997018i | \(-0.524587\pi\) | ||||
−0.0771656 | + | 0.997018i | \(0.524587\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 91.3571 | 3.31605 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 47.2311i | − | 1.71212i | −0.516873 | − | 0.856062i | \(-0.672904\pi\) | ||
0.516873 | − | 0.856062i | \(-0.327096\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 15.4741 | − | 10.7575i | 0.560199 | − | 0.389447i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 6.87689 | 0.248635 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 4.13595i | 0.149341i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 27.2311i | − | 0.981977i | −0.871166 | − | 0.490989i | \(-0.836636\pi\) | ||
0.871166 | − | 0.490989i | \(-0.163364\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | − | 34.3404i | − | 1.23674i | ||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 32.7386i | 1.17753i | 0.808305 | + | 0.588763i | \(0.200385\pi\) | ||||
−0.808305 | + | 0.588763i | \(0.799615\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −3.39228 | −0.121854 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −13.1231 | + | 9.12311i | −0.470789 | + | 0.327290i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 5.29723i | 0.189793i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −34.7386 | −1.24305 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 18.8664 | 0.674229 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0.246211 | 0.00878766 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 3.02045 | 0.107667 | 0.0538337 | − | 0.998550i | \(-0.482856\pi\) | ||||
0.0538337 | + | 0.998550i | \(0.482856\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | − | 55.8617i | − | 1.98873i | ||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 40.1725 | − | 27.9277i | 1.42837 | − | 0.992995i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −4.00000 | −0.142044 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 6.04090i | 0.214248i | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 3.75379i | 0.132966i | 0.997788 | + | 0.0664830i | \(0.0211778\pi\) | ||||
−0.997788 | + | 0.0664830i | \(0.978822\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 5.71484i | − | 0.202176i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 73.4773i | 2.59619i | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 72.4908 | 2.55814 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 13.9309 | − | 9.68466i | 0.490999 | − | 0.341339i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0.743668i | 0.0261784i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 46.9848 | 1.65190 | 0.825950 | − | 0.563744i | \(-0.190640\pi\) | ||||
0.825950 | + | 0.563744i | \(0.190640\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 8.10887 | 0.284741 | 0.142370 | − | 0.989813i | \(-0.454528\pi\) | ||||
0.142370 | + | 0.989813i | \(0.454528\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −5.75379 | −0.201794 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −3.02045 | −0.105802 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 1.75379i | − | 0.0613573i | ||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −18.4945 | − | 26.6034i | −0.646251 | − | 0.929598i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −15.6155 | −0.544986 | −0.272493 | − | 0.962158i | \(-0.587848\pi\) | ||||
−0.272493 | + | 0.962158i | \(0.587848\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 29.0890i | − | 1.01398i | −0.861953 | − | 0.506989i | \(-0.830758\pi\) | ||
0.861953 | − | 0.506989i | \(-0.169242\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 14.2462i | 0.495989i | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 24.5354i | 0.853180i | 0.904445 | + | 0.426590i | \(0.140285\pi\) | ||||
−0.904445 | + | 0.426590i | \(0.859715\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 15.7538i | − | 0.547152i | −0.961850 | − | 0.273576i | \(-0.911794\pi\) | ||
0.961850 | − | 0.273576i | \(-0.0882065\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −36.9890 | −1.28314 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 7.36932 | + | 2.73863i | 0.255332 | + | 0.0948880i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − | 19.8188i | − | 0.685859i | ||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 32.0000 | 1.10608 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −10.9205 | −0.377018 | −0.188509 | − | 0.982071i | \(-0.560365\pi\) | ||||
−0.188509 | + | 0.982071i | \(0.560365\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −25.0000 | −0.862069 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −88.7085 | −3.05528 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − | 9.00000i | − | 0.309609i | ||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −24.4310 | + | 16.9843i | −0.839460 | + | 0.583587i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −14.8769 | −0.510574 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 12.8255i | − | 0.439651i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 24.2462i | − | 0.830174i | −0.909782 | − | 0.415087i | \(-0.863751\pi\) | ||
0.909782 | − | 0.415087i | \(-0.136249\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 28.8802i | 0.987681i | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 25.6155i | 0.875010i | 0.899216 | + | 0.437505i | \(0.144138\pi\) | ||||
−0.899216 | + | 0.437505i | \(0.855862\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −3.55531 | −0.121306 | −0.0606528 | − | 0.998159i | \(-0.519318\pi\) | ||||
−0.0606528 | + | 0.998159i | \(0.519318\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −5.12311 | − | 7.36932i | −0.174595 | − | 0.251146i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 10.2226i | − | 0.347982i | −0.984747 | − | 0.173991i | \(-0.944334\pi\) | ||
0.984747 | − | 0.173991i | \(-0.0556664\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 16.2462 | 0.552388 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 47.5377 | 1.61447 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 6.24621 | 0.211888 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 7.52823 | 0.255084 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − | 6.87689i | − | 0.232748i | ||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 1.51022 | + | 2.17238i | 0.0510549 | + | 0.0734398i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −0.738634 | −0.0249419 | −0.0124709 | − | 0.999922i | \(-0.503970\pi\) | ||||
−0.0124709 | + | 0.999922i | \(0.503970\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 47.5835i | 1.60495i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 31.3693i | 1.05686i | 0.848977 | + | 0.528430i | \(0.177219\pi\) | ||||
−0.848977 | + | 0.528430i | \(0.822781\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 31.3200i | 1.05400i | 0.849865 | + | 0.527001i | \(0.176683\pi\) | ||||
−0.849865 | + | 0.527001i | \(0.823317\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 6.24621i | 0.209964i | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −29.9957 | −1.00716 | −0.503578 | − | 0.863950i | \(-0.667983\pi\) | ||||
−0.503578 | + | 0.863950i | \(0.667983\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −26.8078 | − | 38.5616i | −0.899104 | − | 1.29331i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | − | 47.7465i | − | 1.59957i | ||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 24.0000 | 0.803129 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 10.7575 | 0.359583 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 38.7386 | 1.29345 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 6.78456 | 0.226278 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 2.24621i | − | 0.0748321i | ||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 1.69614 | + | 2.43981i | 0.0564440 | + | 0.0811918i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 15.1231 | 0.502709 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 52.8350i | − | 1.75436i | −0.480166 | − | 0.877178i | \(-0.659423\pi\) | ||
0.480166 | − | 0.877178i | \(-0.340577\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 92.6004i | 3.07136i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 2.06798i | 0.0685151i | 0.999413 | + | 0.0342575i | \(0.0109066\pi\) | ||||
−0.999413 | + | 0.0342575i | \(0.989093\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 14.2462i | − | 0.471481i | ||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −6.04090 | −0.199706 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 38.1080 | − | 26.4924i | 1.25844 | − | 0.874857i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 9.27015i | − | 0.305794i | −0.988242 | − | 0.152897i | \(-0.951140\pi\) | ||
0.988242 | − | 0.152897i | \(-0.0488603\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 4.63068 | 0.152586 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −14.7304 | −0.484857 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 2.00000 | 0.0657596 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 47.3747 | 1.55599 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − | 21.1231i | − | 0.693027i | −0.938045 | − | 0.346513i | \(-0.887366\pi\) | ||
0.938045 | − | 0.346513i | \(-0.112634\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −11.5012 | + | 30.9481i | −0.376935 | + | 1.01428i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −91.2311 | −2.98677 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − | 5.29723i | − | 0.173238i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 38.1080i | − | 1.24493i | −0.782647 | − | 0.622466i | \(-0.786131\pi\) | ||
0.782647 | − | 0.622466i | \(-0.213869\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 101.534i | 3.31344i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 26.6307i | − | 0.868135i | −0.900880 | − | 0.434068i | \(-0.857078\pi\) | ||
0.900880 | − | 0.434068i | \(-0.142922\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 7.20217 | 0.234535 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −14.2462 | − | 20.4924i | −0.463429 | − | 0.666619i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − | 35.8735i | − | 1.16573i | −0.812568 | − | 0.582867i | \(-0.801931\pi\) | ||
0.812568 | − | 0.582867i | \(-0.198069\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 30.7386 | 0.997818 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −36.9890 | −1.19945 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 28.2462 | 0.914985 | 0.457492 | − | 0.889214i | \(-0.348748\pi\) | ||||
0.457492 | + | 0.889214i | \(0.348748\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 16.7984 | 0.543583 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − | 28.4924i | − | 0.921029i | ||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −30.4133 | + | 21.1431i | −0.982096 | + | 0.682747i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −19.4924 | −0.628788 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 34.7123i | 1.11859i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 22.4924i | 0.724057i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 3.43806i | 0.110560i | 0.998471 | + | 0.0552802i | \(0.0176052\pi\) | ||||
−0.998471 | + | 0.0552802i | \(0.982395\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | − | 16.0000i | − | 0.513994i | ||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −10.7575 | −0.345224 | −0.172612 | − | 0.984990i | \(-0.555221\pi\) | ||||
−0.172612 | + | 0.984990i | \(0.555221\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 36.4924 | − | 25.3693i | 1.16989 | − | 0.813303i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 6.04090i | 0.193463i | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 22.4924 | 0.719596 | 0.359798 | − | 0.933030i | \(-0.382846\pi\) | ||||
0.359798 | + | 0.933030i | \(0.382846\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 56.5991 | 1.80891 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 43.6155 | 1.39254 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −28.5083 | −0.909275 | −0.454637 | − | 0.890677i | \(-0.650231\pi\) | ||||
−0.454637 | + | 0.890677i | \(0.650231\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 18.0000i | 0.573528i | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −33.3880 | + | 23.2111i | −1.06275 | + | 0.738818i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −2.38447 | −0.0758218 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 48.9078i | − | 1.55361i | −0.629743 | − | 0.776804i | \(-0.716840\pi\) | ||
0.629743 | − | 0.776804i | \(-0.283160\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − | 55.2311i | − | 1.75270i | ||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − | 26.8122i | − | 0.850004i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 5.50758i | 0.174427i | 0.996190 | + | 0.0872134i | \(0.0277962\pi\) | ||||
−0.996190 | + | 0.0872134i | \(0.972204\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −18.8664 | −0.596905 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))