Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [768,2,Mod(383,768)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(768, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("768.383");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 768 = 2^{8} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 768.f (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: | \(6.13251087523\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\zeta_{8})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{3} \) |
Twist minimal: | no (minimal twist has level 96) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 383.3 | ||
Root | \(0.707107 + 0.707107i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 768.383 |
Dual form | 768.2.f.g.383.1 |
$q$-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 \(\left(\mathbb{Z}/768\mathbb{Z}\right)^\times\).
\(n\) | \(257\) | \(511\) | \(517\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(-1\) |
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 | ||||||||
\(3\) | 1.00000 | + | 1.41421i | 0.577350 | + | 0.816497i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −2.82843 | −1.26491 | −0.632456 | − | 0.774597i | \(-0.717953\pi\) | ||||
−0.632456 | + | 0.774597i | \(0.717953\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 2.00000i | − | 0.755929i | −0.925820 | − | 0.377964i | \(-0.876624\pi\) | ||
0.925820 | − | 0.377964i | \(-0.123376\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.00000 | + | 2.82843i | −0.333333 | + | 0.942809i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.82843i | 0.852803i | 0.904534 | + | 0.426401i | \(0.140219\pi\) | ||||
−0.904534 | + | 0.426401i | \(0.859781\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.00000i | 0.554700i | 0.960769 | + | 0.277350i | \(0.0894562\pi\) | ||||
−0.960769 | + | 0.277350i | \(0.910544\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −2.82843 | − | 4.00000i | −0.730297 | − | 1.03280i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −6.00000 | −1.37649 | −0.688247 | − | 0.725476i | \(-0.741620\pi\) | ||||
−0.688247 | + | 0.725476i | \(0.741620\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 2.82843 | − | 2.00000i | 0.617213 | − | 0.436436i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −5.65685 | −1.17954 | −0.589768 | − | 0.807573i | \(-0.700781\pi\) | ||||
−0.589768 | + | 0.807573i | \(0.700781\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 3.00000 | 0.600000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −5.00000 | + | 1.41421i | −0.962250 | + | 0.272166i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −2.82843 | −0.525226 | −0.262613 | − | 0.964901i | \(-0.584584\pi\) | ||||
−0.262613 | + | 0.964901i | \(0.584584\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.00000i | 0.359211i | 0.983739 | + | 0.179605i | \(0.0574821\pi\) | ||||
−0.983739 | + | 0.179605i | \(0.942518\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −4.00000 | + | 2.82843i | −0.696311 | + | 0.492366i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 5.65685i | 0.956183i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 6.00000i | 0.986394i | 0.869918 | + | 0.493197i | \(0.164172\pi\) | ||||
−0.869918 | + | 0.493197i | \(0.835828\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −2.82843 | + | 2.00000i | −0.452911 | + | 0.320256i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 5.65685i | − | 0.883452i | −0.897150 | − | 0.441726i | \(-0.854366\pi\) | ||
0.897150 | − | 0.441726i | \(-0.145634\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −2.00000 | −0.304997 | −0.152499 | − | 0.988304i | \(-0.548732\pi\) | ||||
−0.152499 | + | 0.988304i | \(0.548732\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 2.82843 | − | 8.00000i | 0.421637 | − | 1.19257i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −11.3137 | −1.65027 | −0.825137 | − | 0.564933i | \(-0.808902\pi\) | ||||
−0.825137 | + | 0.564933i | \(0.808902\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 3.00000 | 0.428571 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 8.48528 | 1.16554 | 0.582772 | − | 0.812636i | \(-0.301968\pi\) | ||||
0.582772 | + | 0.812636i | \(0.301968\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 8.00000i | − | 1.07872i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −6.00000 | − | 8.48528i | −0.794719 | − | 1.12390i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 2.82843i | 0.368230i | 0.982905 | + | 0.184115i | \(0.0589419\pi\) | ||||
−0.982905 | + | 0.184115i | \(0.941058\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.00000i | 0.256074i | 0.991769 | + | 0.128037i | \(0.0408676\pi\) | ||||
−0.991769 | + | 0.128037i | \(0.959132\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 5.65685 | + | 2.00000i | 0.712697 | + | 0.251976i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | − | 5.65685i | − | 0.701646i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2.00000 | 0.244339 | 0.122169 | − | 0.992509i | \(-0.461015\pi\) | ||||
0.122169 | + | 0.992509i | \(0.461015\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −5.65685 | − | 8.00000i | −0.681005 | − | 0.963087i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 5.65685 | 0.671345 | 0.335673 | − | 0.941979i | \(-0.391036\pi\) | ||||
0.335673 | + | 0.941979i | \(0.391036\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 6.00000 | 0.702247 | 0.351123 | − | 0.936329i | \(-0.385800\pi\) | ||||
0.351123 | + | 0.936329i | \(0.385800\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 3.00000 | + | 4.24264i | 0.346410 | + | 0.489898i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 5.65685 | 0.644658 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 14.0000i | − | 1.57512i | −0.616236 | − | 0.787562i | \(-0.711343\pi\) | ||
0.616236 | − | 0.787562i | \(-0.288657\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −7.00000 | − | 5.65685i | −0.777778 | − | 0.628539i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 2.82843i | 0.310460i | 0.987878 | + | 0.155230i | \(0.0496119\pi\) | ||||
−0.987878 | + | 0.155230i | \(0.950388\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −2.82843 | − | 4.00000i | −0.303239 | − | 0.428845i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 16.9706i | 1.79888i | 0.437048 | + | 0.899438i | \(0.356024\pi\) | ||||
−0.437048 | + | 0.899438i | \(0.643976\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 4.00000 | 0.419314 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −2.82843 | + | 2.00000i | −0.293294 | + | 0.207390i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 16.9706 | 1.74114 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 10.0000 | 1.01535 | 0.507673 | − | 0.861550i | \(-0.330506\pi\) | ||||
0.507673 | + | 0.861550i | \(0.330506\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −8.00000 | − | 2.82843i | −0.804030 | − | 0.284268i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −2.82843 | −0.281439 | −0.140720 | − | 0.990050i | \(-0.544942\pi\) | ||||
−0.140720 | + | 0.990050i | \(0.544942\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 14.0000i | 1.37946i | 0.724066 | + | 0.689730i | \(0.242271\pi\) | ||||
−0.724066 | + | 0.689730i | \(0.757729\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −8.00000 | + | 5.65685i | −0.780720 | + | 0.552052i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 8.48528i | − | 0.820303i | −0.912017 | − | 0.410152i | \(-0.865476\pi\) | ||
0.912017 | − | 0.410152i | \(-0.134524\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 18.0000i | 1.72409i | 0.506834 | + | 0.862044i | \(0.330816\pi\) | ||||
−0.506834 | + | 0.862044i | \(0.669184\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −8.48528 | + | 6.00000i | −0.805387 | + | 0.569495i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 11.3137i | 1.06430i | 0.846649 | + | 0.532152i | \(0.178617\pi\) | ||||
−0.846649 | + | 0.532152i | \(0.821383\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 16.0000 | 1.49201 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −5.65685 | − | 2.00000i | −0.522976 | − | 0.184900i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 3.00000 | 0.272727 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 8.00000 | − | 5.65685i | 0.721336 | − | 0.510061i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 5.65685 | 0.505964 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 18.0000i | 1.59724i | 0.601834 | + | 0.798621i | \(0.294437\pi\) | ||||
−0.601834 | + | 0.798621i | \(0.705563\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −2.00000 | − | 2.82843i | −0.176090 | − | 0.249029i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 19.7990i | − | 1.72985i | −0.501905 | − | 0.864923i | \(-0.667367\pi\) | ||
0.501905 | − | 0.864923i | \(-0.332633\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 12.0000i | 1.04053i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 14.1421 | − | 4.00000i | 1.21716 | − | 0.344265i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 5.65685i | − | 0.483298i | −0.970364 | − | 0.241649i | \(-0.922312\pi\) | ||
0.970364 | − | 0.241649i | \(-0.0776882\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −10.0000 | −0.848189 | −0.424094 | − | 0.905618i | \(-0.639408\pi\) | ||||
−0.424094 | + | 0.905618i | \(0.639408\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −11.3137 | − | 16.0000i | −0.952786 | − | 1.34744i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −5.65685 | −0.473050 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 8.00000 | 0.664364 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 3.00000 | + | 4.24264i | 0.247436 | + | 0.349927i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −14.1421 | −1.15857 | −0.579284 | − | 0.815125i | \(-0.696668\pi\) | ||||
−0.579284 | + | 0.815125i | \(0.696668\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 14.0000i | 1.13930i | 0.821886 | + | 0.569652i | \(0.192922\pi\) | ||||
−0.821886 | + | 0.569652i | \(0.807078\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − | 5.65685i | − | 0.454369i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 14.0000i | − | 1.11732i | −0.829396 | − | 0.558661i | \(-0.811315\pi\) | ||
0.829396 | − | 0.558661i | \(-0.188685\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 8.48528 | + | 12.0000i | 0.672927 | + | 0.951662i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 11.3137i | 0.891645i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −6.00000 | −0.469956 | −0.234978 | − | 0.972001i | \(-0.575502\pi\) | ||||
−0.234978 | + | 0.972001i | \(0.575502\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 11.3137 | − | 8.00000i | 0.880771 | − | 0.622799i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 5.65685 | 0.437741 | 0.218870 | − | 0.975754i | \(-0.429763\pi\) | ||||
0.218870 | + | 0.975754i | \(0.429763\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 9.00000 | 0.692308 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 6.00000 | − | 16.9706i | 0.458831 | − | 1.29777i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −14.1421 | −1.07521 | −0.537603 | − | 0.843198i | \(-0.680670\pi\) | ||||
−0.537603 | + | 0.843198i | \(0.680670\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − | 6.00000i | − | 0.453557i | ||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −4.00000 | + | 2.82843i | −0.300658 | + | 0.212598i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 8.48528i | − | 0.634220i | −0.948389 | − | 0.317110i | \(-0.897288\pi\) | ||
0.948389 | − | 0.317110i | \(-0.102712\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 6.00000i | 0.445976i | 0.974821 | + | 0.222988i | \(0.0715812\pi\) | ||||
−0.974821 | + | 0.222988i | \(0.928419\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −2.82843 | + | 2.00000i | −0.209083 | + | 0.147844i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − | 16.9706i | − | 1.24770i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 2.82843 | + | 10.0000i | 0.205738 | + | 0.727393i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 22.6274 | 1.63726 | 0.818631 | − | 0.574320i | \(-0.194733\pi\) | ||||
0.818631 | + | 0.574320i | \(0.194733\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −14.0000 | −1.00774 | −0.503871 | − | 0.863779i | \(-0.668091\pi\) | ||||
−0.503871 | + | 0.863779i | \(0.668091\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 8.00000 | − | 5.65685i | 0.572892 | − | 0.405096i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 19.7990 | 1.41062 | 0.705310 | − | 0.708899i | \(-0.250808\pi\) | ||||
0.705310 | + | 0.708899i | \(0.250808\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 2.00000i | − | 0.141776i | −0.997484 | − | 0.0708881i | \(-0.977417\pi\) | ||
0.997484 | − | 0.0708881i | \(-0.0225833\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 2.00000 | + | 2.82843i | 0.141069 | + | 0.199502i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 5.65685i | 0.397033i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 16.0000i | 1.11749i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 5.65685 | − | 16.0000i | 0.393179 | − | 1.11208i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 16.9706i | − | 1.17388i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2.00000 | 0.137686 | 0.0688428 | − | 0.997628i | \(-0.478069\pi\) | ||||
0.0688428 | + | 0.997628i | \(0.478069\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 5.65685 | + | 8.00000i | 0.387601 | + | 0.548151i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 5.65685 | 0.385794 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 4.00000 | 0.271538 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 6.00000 | + | 8.48528i | 0.405442 | + | 0.573382i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 2.00000i | 0.133930i | 0.997755 | + | 0.0669650i | \(0.0213316\pi\) | ||||
−0.997755 | + | 0.0669650i | \(0.978668\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −3.00000 | + | 8.48528i | −0.200000 | + | 0.565685i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 14.1421i | 0.938647i | 0.883026 | + | 0.469323i | \(0.155502\pi\) | ||||
−0.883026 | + | 0.469323i | \(0.844498\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 10.0000i | − | 0.660819i | −0.943838 | − | 0.330409i | \(-0.892813\pi\) | ||
0.943838 | − | 0.330409i | \(-0.107187\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 5.65685 | + | 8.00000i | 0.372194 | + | 0.526361i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 5.65685i | 0.370593i | 0.982683 | + | 0.185296i | \(0.0593245\pi\) | ||||
−0.982683 | + | 0.185296i | \(0.940675\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 32.0000 | 2.08745 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 19.7990 | − | 14.0000i | 1.28608 | − | 0.909398i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −11.3137 | −0.731823 | −0.365911 | − | 0.930650i | \(-0.619243\pi\) | ||||
−0.365911 | + | 0.930650i | \(0.619243\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 2.00000 | 0.128831 | 0.0644157 | − | 0.997923i | \(-0.479482\pi\) | ||||
0.0644157 | + | 0.997923i | \(0.479482\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000 | − | 15.5563i | 0.0641500 | − | 0.997940i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −8.48528 | −0.542105 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 12.0000i | − | 0.763542i | ||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −4.00000 | + | 2.82843i | −0.253490 | + | 0.179244i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 8.48528i | − | 0.535586i | −0.963476 | − | 0.267793i | \(-0.913706\pi\) | ||
0.963476 | − | 0.267793i | \(-0.0862944\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 16.0000i | − | 1.00591i | ||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 22.6274i | − | 1.41146i | −0.708481 | − | 0.705730i | \(-0.750619\pi\) | ||
0.708481 | − | 0.705730i | \(-0.249381\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 12.0000 | 0.745644 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 2.82843 | − | 8.00000i | 0.175075 | − | 0.495188i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 5.65685 | 0.348817 | 0.174408 | − | 0.984673i | \(-0.444199\pi\) | ||||
0.174408 | + | 0.984673i | \(0.444199\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −24.0000 | −1.47431 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −24.0000 | + | 16.9706i | −1.46878 | + | 1.03858i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 8.48528 | 0.517357 | 0.258678 | − | 0.965964i | \(-0.416713\pi\) | ||||
0.258678 | + | 0.965964i | \(0.416713\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 18.0000i | 1.09342i | 0.837321 | + | 0.546711i | \(0.184120\pi\) | ||||
−0.837321 | + | 0.546711i | \(0.815880\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 4.00000 | + | 5.65685i | 0.242091 | + | 0.342368i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 8.48528i | 0.511682i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 10.0000i | − | 0.600842i | −0.953807 | − | 0.300421i | \(-0.902873\pi\) | ||
0.953807 | − | 0.300421i | \(-0.0971271\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −5.65685 | − | 2.00000i | −0.338667 | − | 0.119737i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 5.65685i | − | 0.337460i | −0.985662 | − | 0.168730i | \(-0.946033\pi\) | ||
0.985662 | − | 0.168730i | \(-0.0539665\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −10.0000 | −0.594438 | −0.297219 | − | 0.954809i | \(-0.596059\pi\) | ||||
−0.297219 | + | 0.954809i | \(0.596059\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 16.9706 | + | 24.0000i | 1.00525 | + | 1.42164i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −11.3137 | −0.667827 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 17.0000 | 1.00000 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 10.0000 | + | 14.1421i | 0.586210 | + | 0.829027i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −2.82843 | −0.165238 | −0.0826192 | − | 0.996581i | \(-0.526329\pi\) | ||||
−0.0826192 | + | 0.996581i | \(0.526329\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 8.00000i | − | 0.465778i | ||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −4.00000 | − | 14.1421i | −0.232104 | − | 0.820610i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − | 11.3137i | − | 0.654289i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 4.00000i | 0.230556i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −2.82843 | − | 4.00000i | −0.162489 | − | 0.229794i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − | 5.65685i | − | 0.323911i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −30.0000 | −1.71219 | −0.856095 | − | 0.516818i | \(-0.827116\pi\) | ||||
−0.856095 | + | 0.516818i | \(0.827116\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −19.7990 | + | 14.0000i | −1.12633 | + | 0.796432i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −5.65685 | −0.320771 | −0.160385 | − | 0.987054i | \(-0.551274\pi\) | ||||
−0.160385 | + | 0.987054i | \(0.551274\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −2.00000 | −0.113047 | −0.0565233 | − | 0.998401i | \(-0.518002\pi\) | ||||
−0.0565233 | + | 0.998401i | \(0.518002\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −16.0000 | − | 5.65685i | −0.901498 | − | 0.318728i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −2.82843 | −0.158860 | −0.0794301 | − | 0.996840i | \(-0.525310\pi\) | ||||
−0.0794301 | + | 0.996840i | \(0.525310\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 8.00000i | − | 0.447914i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 12.0000 | − | 8.48528i | 0.669775 | − | 0.473602i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 6.00000i | 0.332820i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −25.4558 | + | 18.0000i | −1.40771 | + | 0.995402i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 22.6274i | 1.24749i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −10.0000 | −0.549650 | −0.274825 | − | 0.961494i | \(-0.588620\pi\) | ||||
−0.274825 | + | 0.961494i | \(0.588620\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −16.9706 | − | 6.00000i | −0.929981 | − | 0.328798i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −5.65685 | −0.309067 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −22.0000 | −1.19842 | −0.599208 | − | 0.800593i | \(-0.704518\pi\) | ||||
−0.599208 | + | 0.800593i | \(0.704518\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −16.0000 | + | 11.3137i | −0.869001 | + | 0.614476i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −5.65685 | −0.306336 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 20.0000i | − | 1.07990i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 16.0000 | + | 22.6274i | 0.861411 | + | 1.21822i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 14.1421i | 0.759190i | 0.925153 | + | 0.379595i | \(0.123937\pi\) | ||||
−0.925153 | + | 0.379595i | \(0.876063\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 14.0000i | − | 0.749403i | −0.927146 | − | 0.374701i | \(-0.877745\pi\) | ||
0.927146 | − | 0.374701i | \(-0.122255\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −2.82843 | − | 10.0000i | −0.150970 | − | 0.533761i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 22.6274i | 1.20434i | 0.798369 | + | 0.602168i | \(0.205696\pi\) | ||||
−0.798369 | + | 0.602168i | \(0.794304\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −16.0000 | −0.849192 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −16.9706 | −0.895672 | −0.447836 | − | 0.894116i | \(-0.647805\pi\) | ||||
−0.447836 | + | 0.894116i | \(0.647805\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 17.0000 | 0.894737 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 3.00000 | + | 4.24264i | 0.157459 | + | 0.222681i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −16.9706 | −0.888280 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 14.0000i | − | 0.730794i | −0.930852 | − | 0.365397i | \(-0.880933\pi\) | ||
0.930852 | − | 0.365397i | \(-0.119067\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 16.0000 | + | 5.65685i | 0.832927 | + | 0.294484i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − | 16.9706i | − | 0.881068i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 26.0000i | − | 1.34623i | −0.739538 | − | 0.673114i | \(-0.764956\pi\) | ||
0.739538 | − | 0.673114i | \(-0.235044\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 5.65685 | + | 8.00000i | 0.292119 | + | 0.413118i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 5.65685i | − | 0.291343i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −2.00000 | −0.102733 | −0.0513665 | − | 0.998680i | \(-0.516358\pi\) | ||||
−0.0513665 | + | 0.998680i | \(0.516358\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −25.4558 | + | 18.0000i | −1.30414 | + | 0.922168i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −22.6274 | −1.15621 | −0.578103 | − | 0.815963i | \(-0.696207\pi\) | ||||
−0.578103 | + | 0.815963i | \(0.696207\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −16.0000 | −0.815436 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 2.00000 | − | 5.65685i | 0.101666 | − | 0.287554i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −2.82843 | −0.143407 | −0.0717035 | − | 0.997426i | \(-0.522844\pi\) | ||||
−0.0717035 | + | 0.997426i | \(0.522844\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 28.0000 | − | 19.7990i | 1.41241 | − | 0.998727i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 39.5980i | 1.99239i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 18.0000i | 0.903394i | 0.892171 | + | 0.451697i | \(0.149181\pi\) | ||||
−0.892171 | + | 0.451697i | \(0.850819\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −16.9706 | + | 12.0000i | −0.849591 | + | 0.600751i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 22.6274i | 1.12996i | 0.825105 | + | 0.564980i | \(0.191116\pi\) | ||||
−0.825105 | + | 0.564980i | \(0.808884\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −4.00000 | −0.199254 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 19.7990 | + | 16.0000i | 0.983820 | + | 0.795046i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −16.9706 | −0.841200 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −26.0000 | −1.28562 | −0.642809 | − | 0.766027i | \(-0.722231\pi\) | ||||
−0.642809 | + | 0.766027i | \(0.722231\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 8.00000 | − | 5.65685i | 0.394611 | − | 0.279032i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 5.65685 | 0.278356 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 8.00000i | − | 0.392705i | ||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −10.0000 | − | 14.1421i | −0.489702 | − | 0.692543i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 36.7696i | 1.79631i | 0.439679 | + | 0.898155i | \(0.355092\pi\) | ||||
−0.439679 | + | 0.898155i | \(0.644908\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 22.0000i | 1.07221i | 0.844150 | + | 0.536107i | \(0.180106\pi\) | ||||
−0.844150 | + | 0.536107i | \(0.819894\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 11.3137 | − | 32.0000i | 0.550091 | − | 1.55589i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 4.00000 | 0.193574 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −5.65685 | − | 8.00000i | −0.273115 | − | 0.386244i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 33.9411 | 1.63489 | 0.817443 | − | 0.576009i | \(-0.195391\pi\) | ||||
0.817443 | + | 0.576009i | \(0.195391\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −6.00000 | −0.288342 | −0.144171 | − | 0.989553i | \(-0.546051\pi\) | ||||
−0.144171 | + | 0.989553i | \(0.546051\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 8.00000 | + | 11.3137i | 0.383571 | + | 0.542451i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 33.9411 | 1.62362 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 14.0000i | 0.668184i | 0.942541 | + | 0.334092i | \(0.108430\pi\) | ||||
−0.942541 | + | 0.334092i | \(0.891570\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −3.00000 | + | 8.48528i | −0.142857 | + | 0.404061i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 14.1421i | 0.671913i | 0.941877 | + | 0.335957i | \(0.109060\pi\) | ||||
−0.941877 | + | 0.335957i | \(0.890940\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − | 48.0000i | − | 2.27542i | ||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −14.1421 | − | 20.0000i | −0.668900 | − | 0.945968i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 33.9411i | 1.60178i | 0.598811 | + | 0.800890i | \(0.295640\pi\) | ||||
−0.598811 | + | 0.800890i | \(0.704360\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 16.0000 | 0.753411 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −19.7990 | + | 14.0000i | −0.930238 | + | 0.657777i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −11.3137 | −0.530395 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −10.0000 | −0.467780 | −0.233890 | − | 0.972263i | \(-0.575146\pi\) | ||||
−0.233890 | + | 0.972263i | \(0.575146\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 31.1127 | 1.44906 | 0.724531 | − | 0.689242i | \(-0.242056\pi\) | ||||
0.724531 | + | 0.689242i | \(0.242056\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 2.00000i | 0.0929479i | 0.998920 | + | 0.0464739i | \(0.0147984\pi\) | ||||
−0.998920 | + | 0.0464739i | \(0.985202\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 8.00000 | − | 5.65685i | 0.370991 | − | 0.262330i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 25.4558i | 1.17796i | 0.808149 | + | 0.588978i | \(0.200470\pi\) | ||||
−0.808149 | + | 0.588978i | \(0.799530\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 4.00000i | − | 0.184703i | ||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 19.7990 | − | 14.0000i | 0.912289 | − | 0.645086i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 5.65685i | − | 0.260102i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −18.0000 | −0.825897 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −8.48528 | + | 24.0000i | −0.388514 | + | 1.09888i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −22.6274 | −1.03387 | −0.516937 | − | 0.856024i | \(-0.672928\pi\) | ||||
−0.516937 | + | 0.856024i | \(0.672928\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −12.0000 | −0.547153 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −16.0000 | + | 11.3137i | −0.728025 | + | 0.514792i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −28.2843 | −1.28432 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 18.0000i | − | 0.815658i | −0.913058 | − | 0.407829i | \(-0.866286\pi\) | ||
0.913058 | − | 0.407829i | \(-0.133714\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −6.00000 | − | 8.48528i | −0.271329 | − | 0.383718i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 31.1127i | − | 1.40410i | −0.712129 | − | 0.702048i | \(-0.752269\pi\) | ||
0.712129 | − | 0.702048i | \(-0.247731\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 22.6274 | + | 8.00000i | 1.01703 | + | 0.359573i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − | 11.3137i | − | 0.507489i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 34.0000 | 1.52205 | 0.761025 | − | 0.648723i | \(-0.224697\pi\) | ||||
0.761025 | + | 0.648723i | \(0.224697\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 5.65685 | + | 8.00000i | 0.252730 | + | 0.357414i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −5.65685 | −0.252227 | −0.126113 | − | 0.992016i | \(-0.540250\pi\) | ||||
−0.126113 | + | 0.992016i | \(0.540250\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 8.00000 | 0.355995 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 9.00000 | + | 12.7279i | 0.399704 | + | 0.565267i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −2.82843 | −0.125368 | −0.0626839 | − | 0.998033i | \(-0.519966\pi\) | ||||
−0.0626839 | + | 0.998033i | \(0.519966\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 12.0000i | − | 0.530849i | ||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 30.0000 | − | 8.48528i | 1.32453 | − | 0.374634i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − | 39.5980i | − | 1.74490i | ||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 32.0000i | − | 1.40736i | ||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −14.1421 | − | 20.0000i | −0.620771 | − | 0.877903i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 5.65685i | − | 0.247831i | −0.992293 | − | 0.123916i | \(-0.960455\pi\) | ||
0.992293 | − | 0.123916i | \(-0.0395452\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −34.0000 | −1.48672 | −0.743358 | − | 0.668894i | \(-0.766768\pi\) | ||||
−0.743358 | + | 0.668894i | \(0.766768\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 8.48528 | − | 6.00000i | 0.370328 | − | 0.261861i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 9.00000 | 0.391304 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −8.00000 | − | 2.82843i | −0.347170 | − | 0.122743i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 11.3137 | 0.490051 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 24.0000i | 1.03761i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 12.0000 | − | 8.48528i | 0.517838 | − | 0.366167i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 8.48528i | 0.365487i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 2.00000i | 0.0859867i | 0.999075 | + | 0.0429934i | \(0.0136894\pi\) | ||||
−0.999075 | + | 0.0429934i | \(0.986311\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −8.48528 | + | 6.00000i | −0.364138 | + | 0.257485i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − | 50.9117i | − | 2.18082i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −38.0000 | −1.62476 | −0.812381 | − | 0.583127i | \(-0.801829\pi\) | ||||
−0.812381 | + | 0.583127i | \(0.801829\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −5.65685 | − | 2.00000i | −0.241429 | − | 0.0853579i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 16.9706 | 0.722970 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −28.0000 | −1.19068 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 24.0000 | − | 16.9706i | 1.01874 | − | 0.720360i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 8.48528 | 0.359533 | 0.179766 | − | 0.983709i | \(-0.442466\pi\) | ||||
0.179766 | + | 0.983709i | \(0.442466\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 4.00000i | − | 0.169182i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 2.82843i | 0.119204i | 0.998222 | + | 0.0596020i | \(0.0189832\pi\) | ||||
−0.998222 | + | 0.0596020i | \(0.981017\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − | 32.0000i | − | 1.34625i | ||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −11.3137 | + | 14.0000i | −0.475131 | + | 0.587945i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 5.65685i | 0.237148i | 0.992945 | + | 0.118574i | \(0.0378322\pi\) | ||||
−0.992945 | + | 0.118574i | \(0.962168\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 22.0000 | 0.920671 | 0.460336 | − | 0.887745i | \(-0.347729\pi\) | ||||
0.460336 | + | 0.887745i | \(0.347729\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 22.6274 | + | 32.0000i | 0.945274 | + | 1.33682i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −16.9706 | −0.707721 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −6.00000 | −0.249783 | −0.124892 | − | 0.992170i | \(-0.539858\pi\) | ||||
−0.124892 | + | 0.992170i | \(0.539858\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −14.0000 | − | 19.7990i | −0.581820 | − | 0.822818i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 5.65685 | 0.234686 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 24.0000i | 0.993978i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 16.0000 | + | 5.65685i | 0.661519 | + | 0.233882i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 14.1421i | 0.583708i | 0.956463 | + | 0.291854i | \(0.0942722\pi\) | ||||
−0.956463 | + | 0.291854i | \(0.905728\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 12.0000i | − | 0.494451i | ||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 19.7990 | + | 28.0000i | 0.814422 | + | 1.15177i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 33.9411i | − | 1.39379i | −0.717171 | − | 0.696897i | \(-0.754563\pi\) | ||
0.717171 | − | 0.696897i | \(-0.245437\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 2.82843 | − | 2.00000i | 0.115760 | − | 0.0818546i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 39.5980 | 1.61793 | 0.808965 | − | 0.587857i | \(-0.200028\pi\) | ||||
0.808965 | + | 0.587857i | \(0.200028\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −10.0000 | −0.407909 | −0.203954 | − | 0.978980i | \(-0.565379\pi\) | ||||
−0.203954 | + | 0.978980i | \(0.565379\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −2.00000 | + | 5.65685i | −0.0814463 | + | 0.230365i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −8.48528 | −0.344976 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 14.0000i | − | 0.568242i | −0.958788 | − | 0.284121i | \(-0.908298\pi\) | ||
0.958788 | − | 0.284121i | \(-0.0917018\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −8.00000 | + | 5.65685i | −0.324176 | + | 0.229227i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 22.6274i | − | 0.915407i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 6.00000i | 0.242338i | 0.992632 | + | 0.121169i | \(0.0386643\pi\) | ||||
−0.992632 | + | 0.121169i | \(0.961336\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −22.6274 | + | 16.0000i | −0.912426 | + | 0.645182i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 28.2843i | 1.13868i | 0.822102 | + | 0.569341i | \(0.192802\pi\) | ||||
−0.822102 | + | 0.569341i | \(0.807198\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −10.0000 | −0.401934 | −0.200967 | − | 0.979598i | \(-0.564408\pi\) | ||||
−0.200967 | + | 0.979598i | \(0.564408\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 28.2843 | − | 8.00000i | 1.13501 | − | 0.321029i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 33.9411 | 1.35982 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −31.0000 | −1.24000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 24.0000 | − | 16.9706i | 0.958468 | − | 0.677739i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 30.0000i | 1.19428i | 0.802137 | + | 0.597141i | \(0.203697\pi\) | ||||
−0.802137 | + | 0.597141i | \(0.796303\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 2.00000 | + | 2.82843i | 0.0794929 | + | 0.112420i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | − | 50.9117i | − | 2.02037i | ||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 6.00000i | 0.237729i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −5.65685 | + | 16.0000i | −0.223782 | + | 0.632950i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 11.3137i | 0.446865i | 0.974719 | + | 0.223432i | \(0.0717262\pi\) | ||||
−0.974719 | + | 0.223432i | \(0.928274\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 26.0000 | 1.02534 | 0.512670 | − | 0.858586i | \(-0.328656\pi\) | ||||
0.512670 | + | 0.858586i | \(0.328656\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 5.65685 | + | 8.00000i | 0.222738 | + | 0.315000i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −16.9706 | −0.667182 | −0.333591 | − | 0.942718i | \(-0.608260\pi\) | ||||
−0.333591 | + | 0.942718i | \(0.608260\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −8.00000 | −0.314027 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 4.00000 | + | 5.65685i | 0.156772 | + | 0.221710i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −14.1421 | −0.553425 | −0.276712 | − | 0.960953i | \(-0.589245\pi\) | ||||
−0.276712 | + | 0.960953i | \(0.589245\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 56.0000i | 2.18810i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −6.00000 | + | 16.9706i | −0.234082 | + | 0.662085i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 14.1421i | 0.550899i | 0.961315 | + | 0.275450i | \(0.0888267\pi\) | ||||
−0.961315 | + | 0.275450i | \(0.911173\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 10.0000i | − | 0.388955i | −0.980907 | − | 0.194477i | \(-0.937699\pi\) | ||
0.980907 | − | 0.194477i | \(-0.0623011\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | − | 33.9411i | − | 1.31618i | ||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 16.0000 | 0.619522 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −2.82843 | + | 2.00000i | −0.109353 | + | 0.0773245i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −5.65685 | −0.218380 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 10.0000 | 0.385472 | 0.192736 | − | 0.981251i | \(-0.438264\pi\) | ||||
0.192736 | + | 0.981251i | \(0.438264\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −15.0000 | + | 4.24264i | −0.577350 | + | 0.163299i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −2.82843 | −0.108705 | −0.0543526 | − | 0.998522i | \(-0.517310\pi\) | ||||
−0.0543526 | + | 0.998522i | \(0.517310\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 20.0000i | − | 0.767530i | ||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −20.0000 | + | 14.1421i | −0.766402 | + | 0.541928i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 42.4264i | − | 1.62340i | −0.584074 | − | 0.811701i | \(-0.698542\pi\) | ||
0.584074 | − | 0.811701i | \(-0.301458\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 16.0000i | 0.611329i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 14.1421 | − | 10.0000i | 0.539556 | − | 0.381524i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 16.9706i | 0.646527i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 26.0000 | 0.989087 | 0.494543 | − | 0.869153i | \(-0.335335\pi\) | ||||
0.494543 | + | 0.869153i | \(0.335335\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −5.65685 | + | 16.0000i | −0.214886 | + | 0.607790i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 28.2843 | 1.07288 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −8.00000 | + | 5.65685i | −0.302588 | + | 0.213962i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −25.4558 | −0.961454 | −0.480727 | − | 0.876870i | \(-0.659627\pi\) | ||||
−0.480727 | + | 0.876870i | \(0.659627\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 36.0000i | − | 1.35777i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 32.0000 | + | 45.2548i | 1.20519 | + | 1.70440i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 5.65685i | 0.212748i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 38.0000i | 1.42712i | 0.700594 | + | 0.713560i | \(0.252918\pi\) | ||||
−0.700594 | + | 0.713560i | \(0.747082\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 39.5980 | + | 14.0000i | 1.48504 | + | 0.525041i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 11.3137i | − | 0.423702i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 16.0000 | 0.598366 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −11.3137 | − | 16.0000i | −0.422518 | − | 0.597531i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 33.9411 | 1.26579 | 0.632895 | − | 0.774237i | \(-0.281866\pi\) | ||||
0.632895 | + | 0.774237i | \(0.281866\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 28.0000 | 1.04277 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 2.00000 | + | 2.82843i | 0.0743808 | + | 0.105190i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −8.48528 | −0.315135 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 34.0000i | − | 1.26099i | −0.776193 | − | 0.630495i | \(-0.782852\pi\) | ||
0.776193 | − | 0.630495i | \(-0.217148\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 23.0000 | − | 14.1421i | 0.851852 | − | 0.523783i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 46.0000i | − | 1.69905i | −0.527549 | − | 0.849524i | \(-0.676889\pi\) | ||
0.527549 | − | 0.849524i | \(-0.323111\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −8.48528 | − | 12.0000i | −0.312984 | − | 0.442627i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 5.65685i | 0.208373i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 34.0000 | 1.25071 | 0.625355 | − | 0.780340i | \(-0.284954\pi\) | ||||
0.625355 | + | 0.780340i | \(0.284954\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 16.9706 | − | 12.0000i | 0.623429 | − | 0.440831i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 5.65685 | 0.207530 | 0.103765 | − | 0.994602i | \(-0.466911\pi\) | ||||
0.103765 | + | 0.994602i | \(0.466911\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 40.0000 | 1.46549 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −8.00000 | − | 2.82843i | −0.292705 | − | 0.103487i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −16.9706 | −0.620091 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 34.0000i | 1.24068i | 0.784334 | + | 0.620339i | \(0.213005\pi\) | ||||
−0.784334 | + | 0.620339i | \(0.786995\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 12.0000 | − | 8.48528i | 0.437304 | − | 0.309221i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − | 39.5980i | − | 1.44112i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 38.0000i | 1.38113i | 0.723269 | + | 0.690567i | \(0.242639\pi\) | ||||
−0.723269 | + | 0.690567i | \(0.757361\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 22.6274 | − | 16.0000i | 0.821323 | − | 0.580763i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 28.2843i | 1.02530i | 0.858596 | + | 0.512652i | \(0.171337\pi\) | ||||
−0.858596 | + | 0.512652i | \(0.828663\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 36.0000 | 1.30329 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −5.65685 | −0.204257 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −46.0000 | −1.65880 | −0.829401 | − | 0.558653i | \(-0.811318\pi\) | ||||
−0.829401 | + | 0.558653i | \(0.811318\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 32.0000 | − | 22.6274i | 1.15245 | − | 0.814907i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −25.4558 | −0.915583 | −0.457792 | − | 0.889060i | \(-0.651359\pi\) | ||||
−0.457792 | + | 0.889060i | \(0.651359\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 6.00000i | 0.215526i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 12.0000 | + | 16.9706i | 0.430498 | + | 0.608816i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 33.9411i | 1.21607i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 16.0000i | 0.572525i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 14.1421 | − | 4.00000i | 0.505399 | − | 0.142948i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 39.5980i | 1.41331i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −38.0000 | −1.35455 | −0.677277 | − | 0.735728i | \(-0.736840\pi\) | ||||
−0.677277 | + | 0.735728i | \(0.736840\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 5.65685 | + | 8.00000i | 0.201389 | + | 0.284808i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 22.6274 | 0.804538 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −4.00000 | −0.142044 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −24.0000 | − | 33.9411i | −0.851192 | − | 1.20377i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −2.82843 | −0.100188 | −0.0500940 | − | 0.998745i | \(-0.515952\pi\) | ||||
−0.0500940 | + | 0.998745i | \(0.515952\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −48.0000 | − | 16.9706i | −1.69600 | − | 0.599625i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 16.9706i | 0.598878i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | − | 32.0000i | − | 1.12785i | ||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 8.48528 | + | 12.0000i | 0.298696 | + | 0.422420i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 50.9117i | − | 1.78996i | −0.446107 | − | 0.894980i | \(-0.647190\pi\) | ||
0.446107 | − | 0.894980i | \(-0.352810\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 30.0000 | 1.05344 | 0.526721 | − | 0.850038i | \(-0.323421\pi\) | ||||
0.526721 | + | 0.850038i | \(0.323421\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −25.4558 | + | 18.0000i | −0.892775 | + | 0.631288i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 16.9706 | 0.594453 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 12.0000 | 0.419827 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −4.00000 | + | 11.3137i | −0.139771 | + | 0.395333i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −14.1421 | −0.493564 | −0.246782 | − | 0.969071i | \(-0.579373\pi\) | ||||
−0.246782 | + | 0.969071i | \(0.579373\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 2.00000i | − | 0.0697156i | −0.999392 | − | 0.0348578i | \(-0.988902\pi\) | ||
0.999392 | − | 0.0348578i | \(-0.0110978\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −12.0000 | + | 8.48528i | −0.417786 | + | 0.295420i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 25.4558i | 0.885186i | 0.896723 | + | 0.442593i | \(0.145941\pi\) | ||||
−0.896723 | + | 0.442593i | \(0.854059\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 18.0000i | 0.625166i | 0.949890 | + | 0.312583i | \(0.101194\pi\) | ||||
−0.949890 | + | 0.312583i | \(0.898806\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 14.1421 | − | 10.0000i | 0.490585 | − | 0.346896i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −16.0000 | −0.553703 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −2.82843 | − | 10.0000i | −0.0977647 | − | 0.345651i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −39.5980 | −1.36707 | −0.683537 | − | 0.729916i | \(-0.739559\pi\) | ||||
−0.683537 | + | 0.729916i | \(0.739559\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −21.0000 | −0.724138 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 8.00000 | − | 5.65685i | 0.275535 | − | 0.194832i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −25.4558 | −0.875708 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 6.00000i | − | 0.206162i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −10.0000 | − | 14.1421i | −0.343199 | − | 0.485357i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 33.9411i | − | 1.16349i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 26.0000i | − | 0.890223i | −0.895475 | − | 0.445112i | \(-0.853164\pi\) | ||
0.895475 | − | 0.445112i | \(-0.146836\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −16.9706 | + | 48.0000i | −0.580381 | + | 1.64157i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 28.2843i | 0.966172i | 0.875573 | + | 0.483086i | \(0.160484\pi\) | ||||
−0.875573 | + | 0.483086i | \(0.839516\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −2.00000 | −0.0682391 | −0.0341196 | − | 0.999418i | \(-0.510863\pi\) | ||||
−0.0341196 | + | 0.999418i | \(0.510863\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −11.3137 | − | 16.0000i | −0.385570 | − | 0.545279i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 40.0000 | 1.36004 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 17.0000 | + | 24.0416i | 0.577350 | + | 0.816497i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 39.5980 | 1.34327 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 4.00000i | 0.135535i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −10.0000 | + | 28.2843i | −0.338449 | + | 0.957278i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | − | 11.3137i | − | 0.382473i | ||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 2.00000i | 0.0675352i | 0.999430 | + | 0.0337676i | \(0.0107506\pi\) | ||||
−0.999430 | + | 0.0337676i | \(0.989249\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −2.82843 | − | 4.00000i | −0.0954005 | − | 0.134917i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 33.9411i | − | 1.14351i | −0.820426 | − | 0.571753i | \(-0.806264\pi\) | ||
0.820426 | − | 0.571753i | \(-0.193736\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −6.00000 | −0.201916 | −0.100958 | − | 0.994891i | \(-0.532191\pi\) | ||||
−0.100958 | + | 0.994891i | \(0.532191\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 11.3137 | − | 8.00000i | 0.380306 | − | 0.268917i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −5.65685 | −0.189939 | −0.0949693 | − | 0.995480i | \(-0.530275\pi\) | ||||
−0.0949693 | + | 0.995480i | \(0.530275\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 36.0000 | 1.20740 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 16.0000 | − | 19.7990i | 0.536020 | − | 0.663291i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 67.8823 | 2.27159 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 24.0000i | 0.802232i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 16.0000 | − | 11.3137i | 0.534224 | − | 0.377754i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − | 5.65685i | − | 0.188667i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −5.65685 | + | 4.00000i | −0.188248 | + | 0.133112i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − | 16.9706i | − | 0.564121i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −2.00000 | −0.0664089 | −0.0332045 | − | 0.999449i | \(-0.510571\pi\) | ||||
−0.0332045 | + | 0.999449i | \(0.510571\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 2.82843 | − | 8.00000i | 0.0938130 | − | 0.265343i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 11.3137 | 0.374840 | 0.187420 | − | 0.982280i | \(-0.439987\pi\) | ||||
0.187420 | + | 0.982280i | \(0.439987\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −8.00000 | −0.264761 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 8.00000 | − | 5.65685i | 0.264472 | − | 0.187010i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −39.5980 | −1.30764 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 30.0000i | 0.989609i | 0.869004 | + | 0.494804i | \(0.164760\pi\) | ||||
−0.869004 | + | 0.494804i | \(0.835240\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −30.0000 | − | 42.4264i | −0.988534 | − | 1.39800i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 11.3137i | 0.372395i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 18.0000i | 0.591836i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −39.5980 | − | 14.0000i | −1.30057 | − | 0.459820i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − | 11.3137i | − | 0.371191i | −0.982626 | − | 0.185595i | \(-0.940579\pi\) | ||
0.982626 | − | 0.185595i | \(-0.0594214\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −18.0000 | −0.589926 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −5.65685 | − | 8.00000i | −0.185197 | − | 0.261908i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 30.0000 | 0.980057 | 0.490029 | − | 0.871706i | \(-0.336986\pi\) | ||||
0.490029 | + | 0.871706i | \(0.336986\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −2.00000 | − | 2.82843i | −0.0652675 | − | 0.0923022i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 53.7401 | 1.75188 | 0.875939 | − | 0.482422i | \(-0.160243\pi\) | ||||
0.875939 | + | 0.482422i | \(0.160243\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 32.0000i | 1.04206i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −8.00000 | − | 28.2843i | −0.260240 | − | 0.920087i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 14.1421i | 0.459558i | 0.973243 | + | 0.229779i | \(0.0738003\pi\) | ||||
−0.973243 | + | 0.229779i | \(0.926200\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 12.0000i | 0.389536i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −2.82843 | − | 4.00000i | −0.0917180 | − | 0.129709i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 50.9117i | 1.64919i | 0.565723 | + | 0.824596i | \(0.308597\pi\) | ||||
−0.565723 | + | 0.824596i | \(0.691403\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −64.0000 | −2.07099 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 11.3137 | − | 8.00000i | 0.365720 | − | 0.258603i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −11.3137 | −0.365339 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 27.0000 | 0.870968 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 24.0000 | + | 8.48528i | 0.773389 | + | 0.273434i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 39.5980 | 1.27470 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 50.0000i | − | 1.60789i | −0.594703 | − | 0.803946i | \(-0.702730\pi\) | ||
0.594703 | − | 0.803946i | \(-0.297270\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 19.7990i | − | 0.635380i | −0.948195 | − | 0.317690i | \(-0.897093\pi\) | ||
0.948195 | − | 0.317690i | \(-0.102907\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 20.0000i | 0.641171i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −8.48528 | + | 6.00000i | −0.271746 | + | 0.192154i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 45.2548i | 1.44783i | 0.689889 | + | 0.723915i | \(0.257659\pi\) | ||||
−0.689889 | + | 0.723915i | \(0.742341\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −48.0000 | −1.53409 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −50.9117 | − | 18.0000i | −1.62549 | − | 0.574696i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −28.2843 | −0.902128 | −0.451064 | − | 0.892492i | \(-0.648955\pi\) | ||||
−0.451064 | + | 0.892492i | \(0.648955\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −56.0000 | −1.78431 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −32.0000 | + | 22.6274i | −1.01857 | + | 0.720239i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 11.3137 | 0.359755 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 18.0000i | 0.571789i | 0.958261 | + | 0.285894i | \(0.0922907\pi\) | ||||
−0.958261 | + | 0.285894i | \(0.907709\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −10.0000 | − | 14.1421i | −0.317340 | − | 0.448787i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 5.65685i | 0.179334i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 38.0000i | 1.20347i | 0.798695 | + | 0.601736i | \(0.205524\pi\) | ||||
−0.798695 | + | 0.601736i | \(0.794476\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −8.48528 | − | 30.0000i | −0.268462 | − | 0.949158i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))