Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [34,2,Mod(33,34)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(34, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("34.33");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 34 = 2 \cdot 17 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 34.b (of order \(2\), degree \(1\), 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: | \(0.271491366872\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{-2}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} + 2 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 33.2 | ||
Root | \(1.41421i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 34.33 |
Dual form | 34.2.b.a.33.1 |
$q$-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 \(\left(\mathbb{Z}/34\mathbb{Z}\right)^\times\).
\(n\) | \(3\) |
\(\chi(n)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | 2.82843i | 1.63299i | 0.577350 | + | 0.816497i | \(0.304087\pi\) | ||||
−0.577350 | + | 0.816497i | \(0.695913\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | − | 2.82843i | − | 1.26491i | −0.774597 | − | 0.632456i | \(-0.782047\pi\) | ||
0.774597 | − | 0.632456i | \(-0.217953\pi\) | |||||||
\(6\) | − | 2.82843i | − | 1.15470i | ||||||
\(7\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | −5.00000 | −1.66667 | ||||||||
\(10\) | 2.82843i | 0.894427i | ||||||||
\(11\) | − | 2.82843i | − | 0.852803i | −0.904534 | − | 0.426401i | \(-0.859781\pi\) | ||
0.904534 | − | 0.426401i | \(-0.140219\pi\) | |||||||
\(12\) | 2.82843i | 0.816497i | ||||||||
\(13\) | 2.00000 | 0.554700 | 0.277350 | − | 0.960769i | \(-0.410544\pi\) | ||||
0.277350 | + | 0.960769i | \(0.410544\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 8.00000 | 2.06559 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −3.00000 | + | 2.82843i | −0.727607 | + | 0.685994i | ||||
\(18\) | 5.00000 | 1.17851 | ||||||||
\(19\) | −4.00000 | −0.917663 | −0.458831 | − | 0.888523i | \(-0.651732\pi\) | ||||
−0.458831 | + | 0.888523i | \(0.651732\pi\) | |||||||
\(20\) | − | 2.82843i | − | 0.632456i | ||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 2.82843i | 0.603023i | ||||||||
\(23\) | 5.65685i | 1.17954i | 0.807573 | + | 0.589768i | \(0.200781\pi\) | ||||
−0.807573 | + | 0.589768i | \(0.799219\pi\) | |||||||
\(24\) | − | 2.82843i | − | 0.577350i | ||||||
\(25\) | −3.00000 | −0.600000 | ||||||||
\(26\) | −2.00000 | −0.392232 | ||||||||
\(27\) | − | 5.65685i | − | 1.08866i | ||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 2.82843i | − | 0.525226i | −0.964901 | − | 0.262613i | \(-0.915416\pi\) | ||
0.964901 | − | 0.262613i | \(-0.0845842\pi\) | |||||||
\(30\) | −8.00000 | −1.46059 | ||||||||
\(31\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 8.00000 | 1.39262 | ||||||||
\(34\) | 3.00000 | − | 2.82843i | 0.514496 | − | 0.485071i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −5.00000 | −0.833333 | ||||||||
\(37\) | − | 8.48528i | − | 1.39497i | −0.716599 | − | 0.697486i | \(-0.754302\pi\) | ||
0.716599 | − | 0.697486i | \(-0.245698\pi\) | |||||||
\(38\) | 4.00000 | 0.648886 | ||||||||
\(39\) | 5.65685i | 0.905822i | ||||||||
\(40\) | 2.82843i | 0.447214i | ||||||||
\(41\) | 5.65685i | 0.883452i | 0.897150 | + | 0.441726i | \(0.145634\pi\) | ||||
−0.897150 | + | 0.441726i | \(0.854366\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −4.00000 | −0.609994 | −0.304997 | − | 0.952353i | \(-0.598656\pi\) | ||||
−0.304997 | + | 0.952353i | \(0.598656\pi\) | |||||||
\(44\) | − | 2.82843i | − | 0.426401i | ||||||
\(45\) | 14.1421i | 2.10819i | ||||||||
\(46\) | − | 5.65685i | − | 0.834058i | ||||||
\(47\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(48\) | 2.82843i | 0.408248i | ||||||||
\(49\) | 7.00000 | 1.00000 | ||||||||
\(50\) | 3.00000 | 0.424264 | ||||||||
\(51\) | −8.00000 | − | 8.48528i | −1.12022 | − | 1.18818i | ||||
\(52\) | 2.00000 | 0.277350 | ||||||||
\(53\) | 6.00000 | 0.824163 | 0.412082 | − | 0.911147i | \(-0.364802\pi\) | ||||
0.412082 | + | 0.911147i | \(0.364802\pi\) | |||||||
\(54\) | 5.65685i | 0.769800i | ||||||||
\(55\) | −8.00000 | −1.07872 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − | 11.3137i | − | 1.49854i | ||||||
\(58\) | 2.82843i | 0.371391i | ||||||||
\(59\) | 12.0000 | 1.56227 | 0.781133 | − | 0.624364i | \(-0.214642\pi\) | ||||
0.781133 | + | 0.624364i | \(0.214642\pi\) | |||||||
\(60\) | 8.00000 | 1.03280 | ||||||||
\(61\) | 8.48528i | 1.08643i | 0.839594 | + | 0.543214i | \(0.182793\pi\) | ||||
−0.839594 | + | 0.543214i | \(0.817207\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | − | 5.65685i | − | 0.701646i | ||||||
\(66\) | −8.00000 | −0.984732 | ||||||||
\(67\) | −4.00000 | −0.488678 | −0.244339 | − | 0.969690i | \(-0.578571\pi\) | ||||
−0.244339 | + | 0.969690i | \(0.578571\pi\) | |||||||
\(68\) | −3.00000 | + | 2.82843i | −0.363803 | + | 0.342997i | ||||
\(69\) | −16.0000 | −1.92617 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 5.65685i | 0.671345i | 0.941979 | + | 0.335673i | \(0.108964\pi\) | ||||
−0.941979 | + | 0.335673i | \(0.891036\pi\) | |||||||
\(72\) | 5.00000 | 0.589256 | ||||||||
\(73\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(74\) | 8.48528i | 0.986394i | ||||||||
\(75\) | − | 8.48528i | − | 0.979796i | ||||||
\(76\) | −4.00000 | −0.458831 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | − | 5.65685i | − | 0.640513i | ||||||
\(79\) | − | 16.9706i | − | 1.90934i | −0.297670 | − | 0.954669i | \(-0.596210\pi\) | ||
0.297670 | − | 0.954669i | \(-0.403790\pi\) | |||||||
\(80\) | − | 2.82843i | − | 0.316228i | ||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | − | 5.65685i | − | 0.624695i | ||||||
\(83\) | −12.0000 | −1.31717 | −0.658586 | − | 0.752506i | \(-0.728845\pi\) | ||||
−0.658586 | + | 0.752506i | \(0.728845\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 8.00000 | + | 8.48528i | 0.867722 | + | 0.920358i | ||||
\(86\) | 4.00000 | 0.431331 | ||||||||
\(87\) | 8.00000 | 0.857690 | ||||||||
\(88\) | 2.82843i | 0.301511i | ||||||||
\(89\) | 6.00000 | 0.635999 | 0.317999 | − | 0.948091i | \(-0.396989\pi\) | ||||
0.317999 | + | 0.948091i | \(0.396989\pi\) | |||||||
\(90\) | − | 14.1421i | − | 1.49071i | ||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 5.65685i | 0.589768i | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 11.3137i | 1.16076i | ||||||||
\(96\) | − | 2.82843i | − | 0.288675i | ||||||
\(97\) | 16.9706i | 1.72310i | 0.507673 | + | 0.861550i | \(0.330506\pi\) | ||||
−0.507673 | + | 0.861550i | \(0.669494\pi\) | |||||||
\(98\) | −7.00000 | −0.707107 | ||||||||
\(99\) | 14.1421i | 1.42134i | ||||||||
\(100\) | −3.00000 | −0.300000 | ||||||||
\(101\) | −6.00000 | −0.597022 | −0.298511 | − | 0.954406i | \(-0.596490\pi\) | ||||
−0.298511 | + | 0.954406i | \(0.596490\pi\) | |||||||
\(102\) | 8.00000 | + | 8.48528i | 0.792118 | + | 0.840168i | ||||
\(103\) | 8.00000 | 0.788263 | 0.394132 | − | 0.919054i | \(-0.371045\pi\) | ||||
0.394132 | + | 0.919054i | \(0.371045\pi\) | |||||||
\(104\) | −2.00000 | −0.196116 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −6.00000 | −0.582772 | ||||||||
\(107\) | − | 2.82843i | − | 0.273434i | −0.990610 | − | 0.136717i | \(-0.956345\pi\) | ||
0.990610 | − | 0.136717i | \(-0.0436552\pi\) | |||||||
\(108\) | − | 5.65685i | − | 0.544331i | ||||||
\(109\) | − | 8.48528i | − | 0.812743i | −0.913708 | − | 0.406371i | \(-0.866794\pi\) | ||
0.913708 | − | 0.406371i | \(-0.133206\pi\) | |||||||
\(110\) | 8.00000 | 0.762770 | ||||||||
\(111\) | 24.0000 | 2.27798 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 11.3137i | − | 1.06430i | −0.846649 | − | 0.532152i | \(-0.821383\pi\) | ||
0.846649 | − | 0.532152i | \(-0.178617\pi\) | |||||||
\(114\) | 11.3137i | 1.05963i | ||||||||
\(115\) | 16.0000 | 1.49201 | ||||||||
\(116\) | − | 2.82843i | − | 0.262613i | ||||||
\(117\) | −10.0000 | −0.924500 | ||||||||
\(118\) | −12.0000 | −1.10469 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −8.00000 | −0.730297 | ||||||||
\(121\) | 3.00000 | 0.272727 | ||||||||
\(122\) | − | 8.48528i | − | 0.768221i | ||||||
\(123\) | −16.0000 | −1.44267 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − | 5.65685i | − | 0.505964i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −16.0000 | −1.41977 | −0.709885 | − | 0.704317i | \(-0.751253\pi\) | ||||
−0.709885 | + | 0.704317i | \(0.751253\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | − | 11.3137i | − | 0.996116i | ||||||
\(130\) | 5.65685i | 0.496139i | ||||||||
\(131\) | − | 2.82843i | − | 0.247121i | −0.992337 | − | 0.123560i | \(-0.960569\pi\) | ||
0.992337 | − | 0.123560i | \(-0.0394313\pi\) | |||||||
\(132\) | 8.00000 | 0.696311 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 4.00000 | 0.345547 | ||||||||
\(135\) | −16.0000 | −1.37706 | ||||||||
\(136\) | 3.00000 | − | 2.82843i | 0.257248 | − | 0.242536i | ||||
\(137\) | −18.0000 | −1.53784 | −0.768922 | − | 0.639343i | \(-0.779207\pi\) | ||||
−0.768922 | + | 0.639343i | \(0.779207\pi\) | |||||||
\(138\) | 16.0000 | 1.36201 | ||||||||
\(139\) | 8.48528i | 0.719712i | 0.933008 | + | 0.359856i | \(0.117174\pi\) | ||||
−0.933008 | + | 0.359856i | \(0.882826\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | − | 5.65685i | − | 0.474713i | ||||||
\(143\) | − | 5.65685i | − | 0.473050i | ||||||
\(144\) | −5.00000 | −0.416667 | ||||||||
\(145\) | −8.00000 | −0.664364 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 19.7990i | 1.63299i | ||||||||
\(148\) | − | 8.48528i | − | 0.697486i | ||||||
\(149\) | 6.00000 | 0.491539 | 0.245770 | − | 0.969328i | \(-0.420959\pi\) | ||||
0.245770 | + | 0.969328i | \(0.420959\pi\) | |||||||
\(150\) | 8.48528i | 0.692820i | ||||||||
\(151\) | 8.00000 | 0.651031 | 0.325515 | − | 0.945537i | \(-0.394462\pi\) | ||||
0.325515 | + | 0.945537i | \(0.394462\pi\) | |||||||
\(152\) | 4.00000 | 0.324443 | ||||||||
\(153\) | 15.0000 | − | 14.1421i | 1.21268 | − | 1.14332i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 5.65685i | 0.452911i | ||||||||
\(157\) | 14.0000 | 1.11732 | 0.558661 | − | 0.829396i | \(-0.311315\pi\) | ||||
0.558661 | + | 0.829396i | \(0.311315\pi\) | |||||||
\(158\) | 16.9706i | 1.35011i | ||||||||
\(159\) | 16.9706i | 1.34585i | ||||||||
\(160\) | 2.82843i | 0.223607i | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −1.00000 | −0.0785674 | ||||||||
\(163\) | − | 8.48528i | − | 0.664619i | −0.943170 | − | 0.332309i | \(-0.892172\pi\) | ||
0.943170 | − | 0.332309i | \(-0.107828\pi\) | |||||||
\(164\) | 5.65685i | 0.441726i | ||||||||
\(165\) | − | 22.6274i | − | 1.76154i | ||||||
\(166\) | 12.0000 | 0.931381 | ||||||||
\(167\) | − | 11.3137i | − | 0.875481i | −0.899101 | − | 0.437741i | \(-0.855779\pi\) | ||
0.899101 | − | 0.437741i | \(-0.144221\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −9.00000 | −0.692308 | ||||||||
\(170\) | −8.00000 | − | 8.48528i | −0.613572 | − | 0.650791i | ||||
\(171\) | 20.0000 | 1.52944 | ||||||||
\(172\) | −4.00000 | −0.304997 | ||||||||
\(173\) | − | 2.82843i | − | 0.215041i | −0.994203 | − | 0.107521i | \(-0.965709\pi\) | ||
0.994203 | − | 0.107521i | \(-0.0342912\pi\) | |||||||
\(174\) | −8.00000 | −0.606478 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | − | 2.82843i | − | 0.213201i | ||||||
\(177\) | 33.9411i | 2.55117i | ||||||||
\(178\) | −6.00000 | −0.449719 | ||||||||
\(179\) | 12.0000 | 0.896922 | 0.448461 | − | 0.893802i | \(-0.351972\pi\) | ||||
0.448461 | + | 0.893802i | \(0.351972\pi\) | |||||||
\(180\) | 14.1421i | 1.05409i | ||||||||
\(181\) | 8.48528i | 0.630706i | 0.948974 | + | 0.315353i | \(0.102123\pi\) | ||||
−0.948974 | + | 0.315353i | \(0.897877\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −24.0000 | −1.77413 | ||||||||
\(184\) | − | 5.65685i | − | 0.417029i | ||||||
\(185\) | −24.0000 | −1.76452 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 8.00000 | + | 8.48528i | 0.585018 | + | 0.620505i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | − | 11.3137i | − | 0.820783i | ||||||
\(191\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(192\) | 2.82843i | 0.204124i | ||||||||
\(193\) | 16.9706i | 1.22157i | 0.791797 | + | 0.610784i | \(0.209146\pi\) | ||||
−0.791797 | + | 0.610784i | \(0.790854\pi\) | |||||||
\(194\) | − | 16.9706i | − | 1.21842i | ||||||
\(195\) | 16.0000 | 1.14578 | ||||||||
\(196\) | 7.00000 | 0.500000 | ||||||||
\(197\) | − | 2.82843i | − | 0.201517i | −0.994911 | − | 0.100759i | \(-0.967873\pi\) | ||
0.994911 | − | 0.100759i | \(-0.0321270\pi\) | |||||||
\(198\) | − | 14.1421i | − | 1.00504i | ||||||
\(199\) | − | 16.9706i | − | 1.20301i | −0.798869 | − | 0.601506i | \(-0.794568\pi\) | ||
0.798869 | − | 0.601506i | \(-0.205432\pi\) | |||||||
\(200\) | 3.00000 | 0.212132 | ||||||||
\(201\) | − | 11.3137i | − | 0.798007i | ||||||
\(202\) | 6.00000 | 0.422159 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −8.00000 | − | 8.48528i | −0.560112 | − | 0.594089i | ||||
\(205\) | 16.0000 | 1.11749 | ||||||||
\(206\) | −8.00000 | −0.557386 | ||||||||
\(207\) | − | 28.2843i | − | 1.96589i | ||||||
\(208\) | 2.00000 | 0.138675 | ||||||||
\(209\) | 11.3137i | 0.782586i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 8.48528i | 0.584151i | 0.956395 | + | 0.292075i | \(0.0943458\pi\) | ||||
−0.956395 | + | 0.292075i | \(0.905654\pi\) | |||||||
\(212\) | 6.00000 | 0.412082 | ||||||||
\(213\) | −16.0000 | −1.09630 | ||||||||
\(214\) | 2.82843i | 0.193347i | ||||||||
\(215\) | 11.3137i | 0.771589i | ||||||||
\(216\) | 5.65685i | 0.384900i | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 8.48528i | 0.574696i | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −8.00000 | −0.539360 | ||||||||
\(221\) | −6.00000 | + | 5.65685i | −0.403604 | + | 0.380521i | ||||
\(222\) | −24.0000 | −1.61077 | ||||||||
\(223\) | −16.0000 | −1.07144 | −0.535720 | − | 0.844396i | \(-0.679960\pi\) | ||||
−0.535720 | + | 0.844396i | \(0.679960\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 15.0000 | 1.00000 | ||||||||
\(226\) | 11.3137i | 0.752577i | ||||||||
\(227\) | − | 19.7990i | − | 1.31411i | −0.753845 | − | 0.657053i | \(-0.771803\pi\) | ||
0.753845 | − | 0.657053i | \(-0.228197\pi\) | |||||||
\(228\) | − | 11.3137i | − | 0.749269i | ||||||
\(229\) | −22.0000 | −1.45380 | −0.726900 | − | 0.686743i | \(-0.759040\pi\) | ||||
−0.726900 | + | 0.686743i | \(0.759040\pi\) | |||||||
\(230\) | −16.0000 | −1.05501 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 2.82843i | 0.185695i | ||||||||
\(233\) | 22.6274i | 1.48237i | 0.671300 | + | 0.741186i | \(0.265736\pi\) | ||||
−0.671300 | + | 0.741186i | \(0.734264\pi\) | |||||||
\(234\) | 10.0000 | 0.653720 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 12.0000 | 0.781133 | ||||||||
\(237\) | 48.0000 | 3.11794 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(240\) | 8.00000 | 0.516398 | ||||||||
\(241\) | 16.9706i | 1.09317i | 0.837404 | + | 0.546585i | \(0.184072\pi\) | ||||
−0.837404 | + | 0.546585i | \(0.815928\pi\) | |||||||
\(242\) | −3.00000 | −0.192847 | ||||||||
\(243\) | − | 14.1421i | − | 0.907218i | ||||||
\(244\) | 8.48528i | 0.543214i | ||||||||
\(245\) | − | 19.7990i | − | 1.26491i | ||||||
\(246\) | 16.0000 | 1.02012 | ||||||||
\(247\) | −8.00000 | −0.509028 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | − | 33.9411i | − | 2.15093i | ||||||
\(250\) | 5.65685i | 0.357771i | ||||||||
\(251\) | −12.0000 | −0.757433 | −0.378717 | − | 0.925513i | \(-0.623635\pi\) | ||||
−0.378717 | + | 0.925513i | \(0.623635\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 16.0000 | 1.00591 | ||||||||
\(254\) | 16.0000 | 1.00393 | ||||||||
\(255\) | −24.0000 | + | 22.6274i | −1.50294 | + | 1.41698i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 6.00000 | 0.374270 | 0.187135 | − | 0.982334i | \(-0.440080\pi\) | ||||
0.187135 | + | 0.982334i | \(0.440080\pi\) | |||||||
\(258\) | 11.3137i | 0.704361i | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | − | 5.65685i | − | 0.350823i | ||||||
\(261\) | 14.1421i | 0.875376i | ||||||||
\(262\) | 2.82843i | 0.174741i | ||||||||
\(263\) | 24.0000 | 1.47990 | 0.739952 | − | 0.672660i | \(-0.234848\pi\) | ||||
0.739952 | + | 0.672660i | \(0.234848\pi\) | |||||||
\(264\) | −8.00000 | −0.492366 | ||||||||
\(265\) | − | 16.9706i | − | 1.04249i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 16.9706i | 1.03858i | ||||||||
\(268\) | −4.00000 | −0.244339 | ||||||||
\(269\) | 31.1127i | 1.89697i | 0.316815 | + | 0.948487i | \(0.397387\pi\) | ||||
−0.316815 | + | 0.948487i | \(0.602613\pi\) | |||||||
\(270\) | 16.0000 | 0.973729 | ||||||||
\(271\) | −16.0000 | −0.971931 | −0.485965 | − | 0.873978i | \(-0.661532\pi\) | ||||
−0.485965 | + | 0.873978i | \(0.661532\pi\) | |||||||
\(272\) | −3.00000 | + | 2.82843i | −0.181902 | + | 0.171499i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 18.0000 | 1.08742 | ||||||||
\(275\) | 8.48528i | 0.511682i | ||||||||
\(276\) | −16.0000 | −0.963087 | ||||||||
\(277\) | − | 25.4558i | − | 1.52949i | −0.644331 | − | 0.764747i | \(-0.722864\pi\) | ||
0.644331 | − | 0.764747i | \(-0.277136\pi\) | |||||||
\(278\) | − | 8.48528i | − | 0.508913i | ||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 18.0000 | 1.07379 | 0.536895 | − | 0.843649i | \(-0.319597\pi\) | ||||
0.536895 | + | 0.843649i | \(0.319597\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 8.48528i | 0.504398i | 0.967675 | + | 0.252199i | \(0.0811537\pi\) | ||||
−0.967675 | + | 0.252199i | \(0.918846\pi\) | |||||||
\(284\) | 5.65685i | 0.335673i | ||||||||
\(285\) | −32.0000 | −1.89552 | ||||||||
\(286\) | 5.65685i | 0.334497i | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 5.00000 | 0.294628 | ||||||||
\(289\) | 1.00000 | − | 16.9706i | 0.0588235 | − | 0.998268i | ||||
\(290\) | 8.00000 | 0.469776 | ||||||||
\(291\) | −48.0000 | −2.81381 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 6.00000 | 0.350524 | 0.175262 | − | 0.984522i | \(-0.443923\pi\) | ||||
0.175262 | + | 0.984522i | \(0.443923\pi\) | |||||||
\(294\) | − | 19.7990i | − | 1.15470i | ||||||
\(295\) | − | 33.9411i | − | 1.97613i | ||||||
\(296\) | 8.48528i | 0.493197i | ||||||||
\(297\) | −16.0000 | −0.928414 | ||||||||
\(298\) | −6.00000 | −0.347571 | ||||||||
\(299\) | 11.3137i | 0.654289i | ||||||||
\(300\) | − | 8.48528i | − | 0.489898i | ||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −8.00000 | −0.460348 | ||||||||
\(303\) | − | 16.9706i | − | 0.974933i | ||||||
\(304\) | −4.00000 | −0.229416 | ||||||||
\(305\) | 24.0000 | 1.37424 | ||||||||
\(306\) | −15.0000 | + | 14.1421i | −0.857493 | + | 0.808452i | ||||
\(307\) | 20.0000 | 1.14146 | 0.570730 | − | 0.821138i | \(-0.306660\pi\) | ||||
0.570730 | + | 0.821138i | \(0.306660\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 22.6274i | 1.28723i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 11.3137i | − | 0.641542i | −0.947157 | − | 0.320771i | \(-0.896058\pi\) | ||
0.947157 | − | 0.320771i | \(-0.103942\pi\) | |||||||
\(312\) | − | 5.65685i | − | 0.320256i | ||||||
\(313\) | − | 16.9706i | − | 0.959233i | −0.877478 | − | 0.479616i | \(-0.840776\pi\) | ||
0.877478 | − | 0.479616i | \(-0.159224\pi\) | |||||||
\(314\) | −14.0000 | −0.790066 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | − | 16.9706i | − | 0.954669i | ||||||
\(317\) | − | 2.82843i | − | 0.158860i | −0.996840 | − | 0.0794301i | \(-0.974690\pi\) | ||
0.996840 | − | 0.0794301i | \(-0.0253101\pi\) | |||||||
\(318\) | − | 16.9706i | − | 0.951662i | ||||||
\(319\) | −8.00000 | −0.447914 | ||||||||
\(320\) | − | 2.82843i | − | 0.158114i | ||||||
\(321\) | 8.00000 | 0.446516 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 12.0000 | − | 11.3137i | 0.667698 | − | 0.629512i | ||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | −6.00000 | −0.332820 | ||||||||
\(326\) | 8.48528i | 0.469956i | ||||||||
\(327\) | 24.0000 | 1.32720 | ||||||||
\(328\) | − | 5.65685i | − | 0.312348i | ||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 22.6274i | 1.24560i | ||||||||
\(331\) | −4.00000 | −0.219860 | −0.109930 | − | 0.993939i | \(-0.535063\pi\) | ||||
−0.109930 | + | 0.993939i | \(0.535063\pi\) | |||||||
\(332\) | −12.0000 | −0.658586 | ||||||||
\(333\) | 42.4264i | 2.32495i | ||||||||
\(334\) | 11.3137i | 0.619059i | ||||||||
\(335\) | 11.3137i | 0.618134i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(338\) | 9.00000 | 0.489535 | ||||||||
\(339\) | 32.0000 | 1.73800 | ||||||||
\(340\) | 8.00000 | + | 8.48528i | 0.433861 | + | 0.460179i | ||||
\(341\) | 0 | 0 | ||||||||
\(342\) | −20.0000 | −1.08148 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 4.00000 | 0.215666 | ||||||||
\(345\) | 45.2548i | 2.43644i | ||||||||
\(346\) | 2.82843i | 0.152057i | ||||||||
\(347\) | 14.1421i | 0.759190i | 0.925153 | + | 0.379595i | \(0.123937\pi\) | ||||
−0.925153 | + | 0.379595i | \(0.876063\pi\) | |||||||
\(348\) | 8.00000 | 0.428845 | ||||||||
\(349\) | −34.0000 | −1.81998 | −0.909989 | − | 0.414632i | \(-0.863910\pi\) | ||||
−0.909989 | + | 0.414632i | \(0.863910\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | − | 11.3137i | − | 0.603881i | ||||||
\(352\) | 2.82843i | 0.150756i | ||||||||
\(353\) | −6.00000 | −0.319348 | −0.159674 | − | 0.987170i | \(-0.551044\pi\) | ||||
−0.159674 | + | 0.987170i | \(0.551044\pi\) | |||||||
\(354\) | − | 33.9411i | − | 1.80395i | ||||||
\(355\) | 16.0000 | 0.849192 | ||||||||
\(356\) | 6.00000 | 0.317999 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −12.0000 | −0.634220 | ||||||||
\(359\) | 24.0000 | 1.26667 | 0.633336 | − | 0.773877i | \(-0.281685\pi\) | ||||
0.633336 | + | 0.773877i | \(0.281685\pi\) | |||||||
\(360\) | − | 14.1421i | − | 0.745356i | ||||||
\(361\) | −3.00000 | −0.157895 | ||||||||
\(362\) | − | 8.48528i | − | 0.445976i | ||||||
\(363\) | 8.48528i | 0.445362i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 24.0000 | 1.25450 | ||||||||
\(367\) | 16.9706i | 0.885856i | 0.896557 | + | 0.442928i | \(0.146060\pi\) | ||||
−0.896557 | + | 0.442928i | \(0.853940\pi\) | |||||||
\(368\) | 5.65685i | 0.294884i | ||||||||
\(369\) | − | 28.2843i | − | 1.47242i | ||||||
\(370\) | 24.0000 | 1.24770 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −22.0000 | −1.13912 | −0.569558 | − | 0.821951i | \(-0.692886\pi\) | ||||
−0.569558 | + | 0.821951i | \(0.692886\pi\) | |||||||
\(374\) | −8.00000 | − | 8.48528i | −0.413670 | − | 0.438763i | ||||
\(375\) | 16.0000 | 0.826236 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 5.65685i | − | 0.291343i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 25.4558i | 1.30758i | 0.756677 | + | 0.653789i | \(0.226822\pi\) | ||||
−0.756677 | + | 0.653789i | \(0.773178\pi\) | |||||||
\(380\) | 11.3137i | 0.580381i | ||||||||
\(381\) | − | 45.2548i | − | 2.31848i | ||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(384\) | − | 2.82843i | − | 0.144338i | ||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | − | 16.9706i | − | 0.863779i | ||||||
\(387\) | 20.0000 | 1.01666 | ||||||||
\(388\) | 16.9706i | 0.861550i | ||||||||
\(389\) | −6.00000 | −0.304212 | −0.152106 | − | 0.988364i | \(-0.548606\pi\) | ||||
−0.152106 | + | 0.988364i | \(0.548606\pi\) | |||||||
\(390\) | −16.0000 | −0.810191 | ||||||||
\(391\) | −16.0000 | − | 16.9706i | −0.809155 | − | 0.858238i | ||||
\(392\) | −7.00000 | −0.353553 | ||||||||
\(393\) | 8.00000 | 0.403547 | ||||||||
\(394\) | 2.82843i | 0.142494i | ||||||||
\(395\) | −48.0000 | −2.41514 | ||||||||
\(396\) | 14.1421i | 0.710669i | ||||||||
\(397\) | 8.48528i | 0.425864i | 0.977067 | + | 0.212932i | \(0.0683013\pi\) | ||||
−0.977067 | + | 0.212932i | \(0.931699\pi\) | |||||||
\(398\) | 16.9706i | 0.850657i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −3.00000 | −0.150000 | ||||||||
\(401\) | − | 28.2843i | − | 1.41245i | −0.707988 | − | 0.706225i | \(-0.750397\pi\) | ||
0.707988 | − | 0.706225i | \(-0.249603\pi\) | |||||||
\(402\) | 11.3137i | 0.564276i | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | −6.00000 | −0.298511 | ||||||||
\(405\) | − | 2.82843i | − | 0.140546i | ||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −24.0000 | −1.18964 | ||||||||
\(408\) | 8.00000 | + | 8.48528i | 0.396059 | + | 0.420084i | ||||
\(409\) | 2.00000 | 0.0988936 | 0.0494468 | − | 0.998777i | \(-0.484254\pi\) | ||||
0.0494468 | + | 0.998777i | \(0.484254\pi\) | |||||||
\(410\) | −16.0000 | −0.790184 | ||||||||
\(411\) | − | 50.9117i | − | 2.51129i | ||||||
\(412\) | 8.00000 | 0.394132 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 28.2843i | 1.39010i | ||||||||
\(415\) | 33.9411i | 1.66610i | ||||||||
\(416\) | −2.00000 | −0.0980581 | ||||||||
\(417\) | −24.0000 | −1.17529 | ||||||||
\(418\) | − | 11.3137i | − | 0.553372i | ||||||
\(419\) | 14.1421i | 0.690889i | 0.938439 | + | 0.345444i | \(0.112272\pi\) | ||||
−0.938439 | + | 0.345444i | \(0.887728\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 26.0000 | 1.26716 | 0.633581 | − | 0.773676i | \(-0.281584\pi\) | ||||
0.633581 | + | 0.773676i | \(0.281584\pi\) | |||||||
\(422\) | − | 8.48528i | − | 0.413057i | ||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −6.00000 | −0.291386 | ||||||||
\(425\) | 9.00000 | − | 8.48528i | 0.436564 | − | 0.411597i | ||||
\(426\) | 16.0000 | 0.775203 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | − | 2.82843i | − | 0.136717i | ||||||
\(429\) | 16.0000 | 0.772487 | ||||||||
\(430\) | − | 11.3137i | − | 0.545595i | ||||||
\(431\) | 5.65685i | 0.272481i | 0.990676 | + | 0.136241i | \(0.0435020\pi\) | ||||
−0.990676 | + | 0.136241i | \(0.956498\pi\) | |||||||
\(432\) | − | 5.65685i | − | 0.272166i | ||||||
\(433\) | 14.0000 | 0.672797 | 0.336399 | − | 0.941720i | \(-0.390791\pi\) | ||||
0.336399 | + | 0.941720i | \(0.390791\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | − | 22.6274i | − | 1.08490i | ||||||
\(436\) | − | 8.48528i | − | 0.406371i | ||||||
\(437\) | − | 22.6274i | − | 1.08242i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 16.9706i | 0.809961i | 0.914325 | + | 0.404980i | \(0.132722\pi\) | ||||
−0.914325 | + | 0.404980i | \(0.867278\pi\) | |||||||
\(440\) | 8.00000 | 0.381385 | ||||||||
\(441\) | −35.0000 | −1.66667 | ||||||||
\(442\) | 6.00000 | − | 5.65685i | 0.285391 | − | 0.269069i | ||||
\(443\) | −12.0000 | −0.570137 | −0.285069 | − | 0.958507i | \(-0.592016\pi\) | ||||
−0.285069 | + | 0.958507i | \(0.592016\pi\) | |||||||
\(444\) | 24.0000 | 1.13899 | ||||||||
\(445\) | − | 16.9706i | − | 0.804482i | ||||||
\(446\) | 16.0000 | 0.757622 | ||||||||
\(447\) | 16.9706i | 0.802680i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 5.65685i | 0.266963i | 0.991051 | + | 0.133482i | \(0.0426157\pi\) | ||||
−0.991051 | + | 0.133482i | \(0.957384\pi\) | |||||||
\(450\) | −15.0000 | −0.707107 | ||||||||
\(451\) | 16.0000 | 0.753411 | ||||||||
\(452\) | − | 11.3137i | − | 0.532152i | ||||||
\(453\) | 22.6274i | 1.06313i | ||||||||
\(454\) | 19.7990i | 0.929213i | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 11.3137i | 0.529813i | ||||||||
\(457\) | −10.0000 | −0.467780 | −0.233890 | − | 0.972263i | \(-0.575146\pi\) | ||||
−0.233890 | + | 0.972263i | \(0.575146\pi\) | |||||||
\(458\) | 22.0000 | 1.02799 | ||||||||
\(459\) | 16.0000 | + | 16.9706i | 0.746816 | + | 0.792118i | ||||
\(460\) | 16.0000 | 0.746004 | ||||||||
\(461\) | −18.0000 | −0.838344 | −0.419172 | − | 0.907907i | \(-0.637680\pi\) | ||||
−0.419172 | + | 0.907907i | \(0.637680\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 32.0000 | 1.48717 | 0.743583 | − | 0.668644i | \(-0.233125\pi\) | ||||
0.743583 | + | 0.668644i | \(0.233125\pi\) | |||||||
\(464\) | − | 2.82843i | − | 0.131306i | ||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | − | 22.6274i | − | 1.04819i | ||||||
\(467\) | −36.0000 | −1.66588 | −0.832941 | − | 0.553362i | \(-0.813345\pi\) | ||||
−0.832941 | + | 0.553362i | \(0.813345\pi\) | |||||||
\(468\) | −10.0000 | −0.462250 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 39.5980i | 1.82458i | ||||||||
\(472\) | −12.0000 | −0.552345 | ||||||||
\(473\) | 11.3137i | 0.520205i | ||||||||
\(474\) | −48.0000 | −2.20471 | ||||||||
\(475\) | 12.0000 | 0.550598 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −30.0000 | −1.37361 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 5.65685i | 0.258468i | 0.991614 | + | 0.129234i | \(0.0412519\pi\) | ||||
−0.991614 | + | 0.129234i | \(0.958748\pi\) | |||||||
\(480\) | −8.00000 | −0.365148 | ||||||||
\(481\) | − | 16.9706i | − | 0.773791i | ||||||
\(482\) | − | 16.9706i | − | 0.772988i | ||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 3.00000 | 0.136364 | ||||||||
\(485\) | 48.0000 | 2.17957 | ||||||||
\(486\) | 14.1421i | 0.641500i | ||||||||
\(487\) | 16.9706i | 0.769010i | 0.923123 | + | 0.384505i | \(0.125628\pi\) | ||||
−0.923123 | + | 0.384505i | \(0.874372\pi\) | |||||||
\(488\) | − | 8.48528i | − | 0.384111i | ||||||
\(489\) | 24.0000 | 1.08532 | ||||||||
\(490\) | 19.7990i | 0.894427i | ||||||||
\(491\) | −12.0000 | −0.541552 | −0.270776 | − | 0.962642i | \(-0.587280\pi\) | ||||
−0.270776 | + | 0.962642i | \(0.587280\pi\) | |||||||
\(492\) | −16.0000 | −0.721336 | ||||||||
\(493\) | 8.00000 | + | 8.48528i | 0.360302 | + | 0.382158i | ||||
\(494\) | 8.00000 | 0.359937 | ||||||||
\(495\) | 40.0000 | 1.79787 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 33.9411i | 1.52094i | ||||||||
\(499\) | − | 25.4558i | − | 1.13956i | −0.821797 | − | 0.569780i | \(-0.807028\pi\) | ||
0.821797 | − | 0.569780i | \(-0.192972\pi\) | |||||||
\(500\) | − | 5.65685i | − | 0.252982i | ||||||
\(501\) | 32.0000 | 1.42965 | ||||||||
\(502\) | 12.0000 | 0.535586 | ||||||||
\(503\) | − | 28.2843i | − | 1.26113i | −0.776135 | − | 0.630567i | \(-0.782823\pi\) | ||
0.776135 | − | 0.630567i | \(-0.217177\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 16.9706i | 0.755180i | ||||||||
\(506\) | −16.0000 | −0.711287 | ||||||||
\(507\) | − | 25.4558i | − | 1.13053i | ||||||
\(508\) | −16.0000 | −0.709885 | ||||||||
\(509\) | −18.0000 | −0.797836 | −0.398918 | − | 0.916987i | \(-0.630614\pi\) | ||||
−0.398918 | + | 0.916987i | \(0.630614\pi\) | |||||||
\(510\) | 24.0000 | − | 22.6274i | 1.06274 | − | 1.00196i | ||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 22.6274i | 0.999025i | ||||||||
\(514\) | −6.00000 | −0.264649 | ||||||||
\(515\) | − | 22.6274i | − | 0.997083i | ||||||
\(516\) | − | 11.3137i | − | 0.498058i | ||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 8.00000 | 0.351161 | ||||||||
\(520\) | 5.65685i | 0.248069i | ||||||||
\(521\) | 5.65685i | 0.247831i | 0.992293 | + | 0.123916i | \(0.0395452\pi\) | ||||
−0.992293 | + | 0.123916i | \(0.960455\pi\) | |||||||
\(522\) | − | 14.1421i | − | 0.618984i | ||||||
\(523\) | 20.0000 | 0.874539 | 0.437269 | − | 0.899331i | \(-0.355946\pi\) | ||||
0.437269 | + | 0.899331i | \(0.355946\pi\) | |||||||
\(524\) | − | 2.82843i | − | 0.123560i | ||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −24.0000 | −1.04645 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 8.00000 | 0.348155 | ||||||||
\(529\) | −9.00000 | −0.391304 | ||||||||
\(530\) | 16.9706i | 0.737154i | ||||||||
\(531\) | −60.0000 | −2.60378 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 11.3137i | 0.490051i | ||||||||
\(534\) | − | 16.9706i | − | 0.734388i | ||||||
\(535\) | −8.00000 | −0.345870 | ||||||||
\(536\) | 4.00000 | 0.172774 | ||||||||
\(537\) | 33.9411i | 1.46467i | ||||||||
\(538\) | − | 31.1127i | − | 1.34136i | ||||||
\(539\) | − | 19.7990i | − | 0.852803i | ||||||
\(540\) | −16.0000 | −0.688530 | ||||||||
\(541\) | − | 8.48528i | − | 0.364811i | −0.983223 | − | 0.182405i | \(-0.941612\pi\) | ||
0.983223 | − | 0.182405i | \(-0.0583883\pi\) | |||||||
\(542\) | 16.0000 | 0.687259 | ||||||||
\(543\) | −24.0000 | −1.02994 | ||||||||
\(544\) | 3.00000 | − | 2.82843i | 0.128624 | − | 0.121268i | ||||
\(545\) | −24.0000 | −1.02805 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 42.4264i | 1.81402i | 0.421107 | + | 0.907011i | \(0.361642\pi\) | ||||
−0.421107 | + | 0.907011i | \(0.638358\pi\) | |||||||
\(548\) | −18.0000 | −0.768922 | ||||||||
\(549\) | − | 42.4264i | − | 1.81071i | ||||||
\(550\) | − | 8.48528i | − | 0.361814i | ||||||
\(551\) | 11.3137i | 0.481980i | ||||||||
\(552\) | 16.0000 | 0.681005 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 25.4558i | 1.08152i | ||||||||
\(555\) | − | 67.8823i | − | 2.88144i | ||||||
\(556\) | 8.48528i | 0.359856i | ||||||||
\(557\) | 18.0000 | 0.762684 | 0.381342 | − | 0.924434i | \(-0.375462\pi\) | ||||
0.381342 | + | 0.924434i | \(0.375462\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −8.00000 | −0.338364 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −24.0000 | + | 22.6274i | −1.01328 | + | 0.955330i | ||||
\(562\) | −18.0000 | −0.759284 | ||||||||
\(563\) | 36.0000 | 1.51722 | 0.758610 | − | 0.651546i | \(-0.225879\pi\) | ||||
0.758610 | + | 0.651546i | \(0.225879\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −32.0000 | −1.34625 | ||||||||
\(566\) | − | 8.48528i | − | 0.356663i | ||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | − | 5.65685i | − | 0.237356i | ||||||
\(569\) | −6.00000 | −0.251533 | −0.125767 | − | 0.992060i | \(-0.540139\pi\) | ||||
−0.125767 | + | 0.992060i | \(0.540139\pi\) | |||||||
\(570\) | 32.0000 | 1.34033 | ||||||||
\(571\) | 25.4558i | 1.06529i | 0.846338 | + | 0.532647i | \(0.178803\pi\) | ||||
−0.846338 | + | 0.532647i | \(0.821197\pi\) | |||||||
\(572\) | − | 5.65685i | − | 0.236525i | ||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 16.9706i | − | 0.707721i | ||||||
\(576\) | −5.00000 | −0.208333 | ||||||||
\(577\) | 38.0000 | 1.58196 | 0.790980 | − | 0.611842i | \(-0.209571\pi\) | ||||
0.790980 | + | 0.611842i | \(0.209571\pi\) | |||||||
\(578\) | −1.00000 | + | 16.9706i | −0.0415945 | + | 0.705882i | ||||
\(579\) | −48.0000 | −1.99481 | ||||||||
\(580\) | −8.00000 | −0.332182 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 48.0000 | 1.98966 | ||||||||
\(583\) | − | 16.9706i | − | 0.702849i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 28.2843i | 1.16941i | ||||||||
\(586\) | −6.00000 | −0.247858 | ||||||||
\(587\) | −12.0000 | −0.495293 | −0.247647 | − | 0.968850i | \(-0.579657\pi\) | ||||
−0.247647 | + | 0.968850i | \(0.579657\pi\) | |||||||
\(588\) | 19.7990i | 0.816497i | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 33.9411i | 1.39733i | ||||||||
\(591\) | 8.00000 | 0.329076 | ||||||||
\(592\) | − | 8.48528i | − | 0.348743i | ||||||
\(593\) | 18.0000 | 0.739171 | 0.369586 | − | 0.929197i | \(-0.379500\pi\) | ||||
0.369586 | + | 0.929197i | \(0.379500\pi\) | |||||||
\(594\) | 16.0000 | 0.656488 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 6.00000 | 0.245770 | ||||||||
\(597\) | 48.0000 | 1.96451 | ||||||||
\(598\) | − | 11.3137i | − | 0.462652i | ||||||
\(599\) | 24.0000 | 0.980613 | 0.490307 | − | 0.871550i | \(-0.336885\pi\) | ||||
0.490307 | + | 0.871550i | \(0.336885\pi\) | |||||||
\(600\) | 8.48528i | 0.346410i | ||||||||
\(601\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 20.0000 | 0.814463 | ||||||||
\(604\) | 8.00000 | 0.325515 | ||||||||
\(605\) | − | 8.48528i | − | 0.344976i | ||||||
\(606\) | 16.9706i | 0.689382i | ||||||||
\(607\) | − | 33.9411i | − | 1.37763i | −0.724938 | − | 0.688814i | \(-0.758132\pi\) | ||
0.724938 | − | 0.688814i | \(-0.241868\pi\) | |||||||
\(608\) | 4.00000 | 0.162221 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −24.0000 | −0.971732 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 15.0000 | − | 14.1421i | 0.606339 | − | 0.571662i | ||||
\(613\) | −10.0000 | −0.403896 | −0.201948 | − | 0.979396i | \(-0.564727\pi\) | ||||
−0.201948 | + | 0.979396i | \(0.564727\pi\) | |||||||
\(614\) | −20.0000 | −0.807134 | ||||||||
\(615\) | 45.2548i | 1.82485i | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 11.3137i | − | 0.455473i | −0.973723 | − | 0.227736i | \(-0.926868\pi\) | ||
0.973723 | − | 0.227736i | \(-0.0731324\pi\) | |||||||
\(618\) | − | 22.6274i | − | 0.910208i | ||||||
\(619\) | − | 8.48528i | − | 0.341052i | −0.985353 | − | 0.170526i | \(-0.945453\pi\) | ||
0.985353 | − | 0.170526i | \(-0.0545467\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 32.0000 | 1.28412 | ||||||||
\(622\) | 11.3137i | 0.453638i | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 5.65685i | 0.226455i | ||||||||
\(625\) | −31.0000 | −1.24000 | ||||||||
\(626\) | 16.9706i | 0.678280i | ||||||||
\(627\) | −32.0000 | −1.27796 | ||||||||
\(628\) | 14.0000 | 0.558661 | ||||||||
\(629\) | 24.0000 | + | 25.4558i | 0.956943 | + | 1.01499i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 8.00000 | 0.318475 | 0.159237 | − | 0.987240i | \(-0.449096\pi\) | ||||
0.159237 | + | 0.987240i | \(0.449096\pi\) | |||||||
\(632\) | 16.9706i | 0.675053i | ||||||||
\(633\) | −24.0000 | −0.953914 | ||||||||
\(634\) | 2.82843i | 0.112331i | ||||||||
\(635\) | 45.2548i | 1.79588i | ||||||||
\(636\) | 16.9706i | 0.672927i | ||||||||
\(637\) | 14.0000 | 0.554700 | ||||||||
\(638\) | 8.00000 | 0.316723 | ||||||||
\(639\) | − | 28.2843i | − | 1.11891i | ||||||
\(640\) | 2.82843i | 0.111803i | ||||||||
\(641\) | 5.65685i | 0.223432i | 0.993740 | + | 0.111716i | \(0.0356347\pi\) | ||||
−0.993740 | + | 0.111716i | \(0.964365\pi\) | |||||||
\(642\) | −8.00000 | −0.315735 | ||||||||
\(643\) | − | 8.48528i | − | 0.334627i | −0.985904 | − | 0.167313i | \(-0.946491\pi\) | ||
0.985904 | − | 0.167313i | \(-0.0535092\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −32.0000 | −1.26000 | ||||||||
\(646\) | −12.0000 | + | 11.3137i | −0.472134 | + | 0.445132i | ||||
\(647\) | −24.0000 | −0.943537 | −0.471769 | − | 0.881722i | \(-0.656384\pi\) | ||||
−0.471769 | + | 0.881722i | \(0.656384\pi\) | |||||||
\(648\) | −1.00000 | −0.0392837 | ||||||||
\(649\) | − | 33.9411i | − | 1.33231i | ||||||
\(650\) | 6.00000 | 0.235339 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | − | 8.48528i | − | 0.332309i | ||||||
\(653\) | 14.1421i | 0.553425i | 0.960953 | + | 0.276712i | \(0.0892449\pi\) | ||||
−0.960953 | + | 0.276712i | \(0.910755\pi\) | |||||||
\(654\) | −24.0000 | −0.938474 | ||||||||
\(655\) | −8.00000 | −0.312586 | ||||||||
\(656\) | 5.65685i | 0.220863i | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −12.0000 | −0.467454 | −0.233727 | − | 0.972302i | \(-0.575092\pi\) | ||||
−0.233727 | + | 0.972302i | \(0.575092\pi\) | |||||||
\(660\) | − | 22.6274i | − | 0.880771i | ||||||
\(661\) | −10.0000 | −0.388955 | −0.194477 | − | 0.980907i | \(-0.562301\pi\) | ||||
−0.194477 | + | 0.980907i | \(0.562301\pi\) | |||||||
\(662\) | 4.00000 | 0.155464 | ||||||||
\(663\) | −16.0000 | − | 16.9706i | −0.621389 | − | 0.659082i | ||||
\(664\) | 12.0000 | 0.465690 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | − | 42.4264i | − | 1.64399i | ||||||
\(667\) | 16.0000 | 0.619522 | ||||||||
\(668\) | − | 11.3137i | − | 0.437741i | ||||||
\(669\) | − | 45.2548i | − | 1.74965i | ||||||
\(670\) | − | 11.3137i | − | 0.437087i | ||||||
\(671\) | 24.0000 | 0.926510 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 16.9706i | − | 0.654167i | −0.944995 | − | 0.327084i | \(-0.893934\pi\) | ||
0.944995 | − | 0.327084i | \(-0.106066\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 16.9706i | 0.653197i | ||||||||
\(676\) | −9.00000 | −0.346154 | ||||||||
\(677\) | 14.1421i | 0.543526i | 0.962364 | + | 0.271763i | \(0.0876068\pi\) | ||||
−0.962364 | + | 0.271763i | \(0.912393\pi\) | |||||||
\(678\) | −32.0000 | −1.22895 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −8.00000 | − | 8.48528i | −0.306786 | − | 0.325396i | ||||
\(681\) | 56.0000 | 2.14592 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 19.7990i | − | 0.757587i | −0.925481 | − | 0.378794i | \(-0.876339\pi\) | ||
0.925481 | − | 0.378794i | \(-0.123661\pi\) | |||||||
\(684\) | 20.0000 | 0.764719 | ||||||||
\(685\) | 50.9117i | 1.94524i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − | 62.2254i | − | 2.37405i | ||||||
\(688\) | −4.00000 | −0.152499 | ||||||||
\(689\) | 12.0000 | 0.457164 | ||||||||
\(690\) | − | 45.2548i | − | 1.72282i | ||||||
\(691\) | 8.48528i | 0.322795i | 0.986889 | + | 0.161398i | \(0.0516002\pi\) | ||||
−0.986889 | + | 0.161398i | \(0.948400\pi\) | |||||||
\(692\) | − | 2.82843i | − | 0.107521i | ||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | − | 14.1421i | − | 0.536828i | ||||||
\(695\) | 24.0000 | 0.910372 | ||||||||
\(696\) | −8.00000 | −0.303239 | ||||||||
\(697\) | −16.0000 | − | 16.9706i | −0.606043 | − | 0.642806i | ||||
\(698\) | 34.0000 | 1.28692 | ||||||||
\(699\) | −64.0000 | −2.42070 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −30.0000 | −1.13308 | −0.566542 | − | 0.824033i | \(-0.691719\pi\) | ||||
−0.566542 | + | 0.824033i | \(0.691719\pi\) | |||||||
\(702\) | 11.3137i | 0.427008i | ||||||||
\(703\) | 33.9411i | 1.28011i | ||||||||
\(704\) | − | 2.82843i | − | 0.106600i | ||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 6.00000 | 0.225813 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 33.9411i | 1.27559i | ||||||||
\(709\) | 8.48528i | 0.318671i | 0.987224 | + | 0.159336i | \(0.0509352\pi\) | ||||
−0.987224 | + | 0.159336i | \(0.949065\pi\) | |||||||
\(710\) | −16.0000 | −0.600469 | ||||||||
\(711\) | 84.8528i | 3.18223i | ||||||||
\(712\) | −6.00000 | −0.224860 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −16.0000 | −0.598366 | ||||||||
\(716\) | 12.0000 | 0.448461 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −24.0000 | −0.895672 | ||||||||
\(719\) | 39.5980i | 1.47676i | 0.674387 | + | 0.738378i | \(0.264408\pi\) | ||||
−0.674387 | + | 0.738378i | \(0.735592\pi\) | |||||||
\(720\) | 14.1421i | 0.527046i | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 3.00000 | 0.111648 | ||||||||
\(723\) | −48.0000 | −1.78514 | ||||||||
\(724\) | 8.48528i | 0.315353i | ||||||||
\(725\) | 8.48528i | 0.315135i | ||||||||
\(726\) | − | 8.48528i | − | 0.314918i | ||||||
\(727\) | 8.00000 | 0.296704 | 0.148352 | − | 0.988935i | \(-0.452603\pi\) | ||||
0.148352 | + | 0.988935i | \(0.452603\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 43.0000 | 1.59259 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 12.0000 | − | 11.3137i | 0.443836 | − | 0.418453i | ||||
\(732\) | −24.0000 | −0.887066 | ||||||||
\(733\) | 14.0000 | 0.517102 | 0.258551 | − | 0.965998i | \(-0.416755\pi\) | ||||
0.258551 | + | 0.965998i | \(0.416755\pi\) | |||||||
\(734\) | − | 16.9706i | − | 0.626395i | ||||||
\(735\) | 56.0000 | 2.06559 | ||||||||
\(736\) | − | 5.65685i | − | 0.208514i | ||||||
\(737\) | 11.3137i | 0.416746i | ||||||||
\(738\) | 28.2843i | 1.04116i | ||||||||
\(739\) | 44.0000 | 1.61857 | 0.809283 | − | 0.587419i | \(-0.199856\pi\) | ||||
0.809283 | + | 0.587419i | \(0.199856\pi\) | |||||||
\(740\) | −24.0000 | −0.882258 | ||||||||
\(741\) | − | 22.6274i | − | 0.831239i | ||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 11.3137i | − | 0.415060i | −0.978229 | − | 0.207530i | \(-0.933458\pi\) | ||
0.978229 | − | 0.207530i | \(-0.0665424\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | − | 16.9706i | − | 0.621753i | ||||||
\(746\) | 22.0000 | 0.805477 | ||||||||
\(747\) | 60.0000 | 2.19529 | ||||||||
\(748\) | 8.00000 | + | 8.48528i | 0.292509 | + | 0.310253i | ||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −16.0000 | −0.584237 | ||||||||
\(751\) | − | 16.9706i | − | 0.619265i | −0.950856 | − | 0.309632i | \(-0.899794\pi\) | ||
0.950856 | − | 0.309632i | \(-0.100206\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | − | 33.9411i | − | 1.23688i | ||||||
\(754\) | 5.65685i | 0.206010i | ||||||||
\(755\) | − | 22.6274i | − | 0.823496i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −22.0000 | −0.799604 | −0.399802 | − | 0.916602i | \(-0.630921\pi\) | ||||
−0.399802 | + | 0.916602i | \(0.630921\pi\) | |||||||
\(758\) | − | 25.4558i | − | 0.924598i | ||||||
\(759\) | 45.2548i | 1.64265i | ||||||||
\(760\) | − | 11.3137i | − | 0.410391i | ||||||
\(761\) | 30.0000 | 1.08750 | 0.543750 | − | 0.839248i | \(-0.317004\pi\) | ||||
0.543750 | + | 0.839248i | \(0.317004\pi\) | |||||||
\(762\) | 45.2548i | 1.63941i | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −40.0000 | − | 42.4264i | −1.44620 | − | 1.53393i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 24.0000 | 0.866590 | ||||||||
\(768\) | 2.82843i | 0.102062i | ||||||||
\(769\) | −10.0000 | −0.360609 | −0.180305 | − | 0.983611i | \(-0.557708\pi\) | ||||
−0.180305 | + | 0.983611i | \(0.557708\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 16.9706i | 0.611180i | ||||||||
\(772\) | 16.9706i | 0.610784i | ||||||||
\(773\) | −54.0000 | −1.94225 | −0.971123 | − | 0.238581i | \(-0.923318\pi\) | ||||
−0.971123 | + | 0.238581i | \(0.923318\pi\) | |||||||
\(774\) | −20.0000 | −0.718885 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | − | 16.9706i | − | 0.609208i | ||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 6.00000 | 0.215110 | ||||||||
\(779\) | − | 22.6274i | − | 0.810711i | ||||||
\(780\) | 16.0000 | 0.572892 | ||||||||
\(781\) | 16.0000 | 0.572525 | ||||||||
\(782\) | 16.0000 | + | 16.9706i | 0.572159 | + | 0.606866i | ||||
\(783\) | −16.0000 | −0.571793 | ||||||||
\(784\) | 7.00000 | 0.250000 | ||||||||
\(785\) | − | 39.5980i | − | 1.41331i | ||||||
\(786\) | −8.00000 | −0.285351 | ||||||||
\(787\) | 42.4264i | 1.51234i | 0.654376 | + | 0.756169i | \(0.272931\pi\) | ||||
−0.654376 | + | 0.756169i | \(0.727069\pi\) | |||||||
\(788\) | − | 2.82843i | − | 0.100759i | ||||||
\(789\) | 67.8823i | 2.41667i | ||||||||
\(790\) | 48.0000 | 1.70776 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | − | 14.1421i | − | 0.502519i | ||||||
\(793\) | 16.9706i | 0.602642i | ||||||||
\(794\) | − | 8.48528i | − | 0.301131i | ||||||
\(795\) | 48.0000 | 1.70238 | ||||||||
\(796\) | − | 16.9706i | − | 0.601506i | ||||||
\(797\) | −18.0000 | −0.637593 | −0.318796 | − | 0.947823i | \(-0.603279\pi\) | ||||
−0.318796 | + | 0.947823i | \(0.603279\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 3.00000 | 0.106066 | ||||||||
\(801\) | −30.0000 | −1.06000 | ||||||||
\(802\) | 28.2843i | 0.998752i | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | − | 11.3137i | − | 0.399004i | ||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −88.0000 | −3.09775 | ||||||||
\(808\) | 6.00000 | 0.211079 | ||||||||
\(809\) | 39.5980i | 1.39219i | 0.717949 | + | 0.696095i | \(0.245081\pi\) | ||||
−0.717949 | + | 0.696095i | \(0.754919\pi\) | |||||||
\(810\) | 2.82843i | 0.0993808i | ||||||||
\(811\) | − | 42.4264i | − | 1.48979i | −0.667180 | − | 0.744896i | \(-0.732499\pi\) | ||
0.667180 | − | 0.744896i | \(-0.267501\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − | 45.2548i | − | 1.58716i | ||||||
\(814\) | 24.0000 | 0.841200 | ||||||||
\(815\) | −24.0000 | −0.840683 | ||||||||
\(816\) | −8.00000 | − | 8.48528i | −0.280056 | − | 0.297044i | ||||
\(817\) | 16.0000 | 0.559769 | ||||||||
\(818\) | −2.00000 | −0.0699284 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 16.0000 | 0.558744 | ||||||||
\(821\) | 48.0833i | 1.67812i | 0.544041 | + | 0.839059i | \(0.316894\pi\) | ||||
−0.544041 | + | 0.839059i | \(0.683106\pi\) | |||||||
\(822\) | 50.9117i | 1.77575i | ||||||||
\(823\) | − | 16.9706i | − | 0.591557i | −0.955257 | − | 0.295778i | \(-0.904421\pi\) | ||
0.955257 | − | 0.295778i | \(-0.0955790\pi\) | |||||||
\(824\) | −8.00000 | −0.278693 | ||||||||
\(825\) | −24.0000 | −0.835573 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 36.7696i | − | 1.27860i | −0.768956 | − | 0.639301i | \(-0.779224\pi\) | ||
0.768956 | − | 0.639301i | \(-0.220776\pi\) | |||||||
\(828\) | − | 28.2843i | − | 0.982946i | ||||||
\(829\) | −34.0000 | −1.18087 | −0.590434 | − | 0.807086i | \(-0.701044\pi\) | ||||
−0.590434 | + | 0.807086i | \(0.701044\pi\) | |||||||
\(830\) | − | 33.9411i | − | 1.17811i | ||||||
\(831\) | 72.0000 | 2.49765 | ||||||||
\(832\) | 2.00000 | 0.0693375 | ||||||||
\(833\) | −21.0000 | + | 19.7990i | −0.727607 | + | 0.685994i | ||||
\(834\) | 24.0000 | 0.831052 | ||||||||
\(835\) | −32.0000 | −1.10741 | ||||||||
\(836\) | 11.3137i | 0.391293i | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | − | 14.1421i | − | 0.488532i | ||||||
\(839\) | − | 45.2548i | − | 1.56237i | −0.624299 | − | 0.781185i | \(-0.714615\pi\) | ||
0.624299 | − | 0.781185i | \(-0.285385\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 21.0000 | 0.724138 | ||||||||
\(842\) | −26.0000 | −0.896019 | ||||||||
\(843\) | 50.9117i | 1.75349i | ||||||||
\(844\) | 8.48528i | 0.292075i | ||||||||
\(845\) | 25.4558i | 0.875708i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 6.00000 | 0.206041 | ||||||||
\(849\) | −24.0000 | −0.823678 | ||||||||
\(850\) | −9.00000 | + | 8.48528i | −0.308697 | + | 0.291043i | ||||
\(851\) | 48.0000 | 1.64542 | ||||||||
\(852\) | −16.0000 | −0.548151 | ||||||||
\(853\) | − | 25.4558i | − | 0.871592i | −0.900046 | − | 0.435796i | \(-0.856467\pi\) | ||
0.900046 | − | 0.435796i | \(-0.143533\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | − | 56.5685i | − | 1.93460i | ||||||
\(856\) | 2.82843i | 0.0966736i | ||||||||
\(857\) | − | 28.2843i | − | 0.966172i | −0.875573 | − | 0.483086i | \(-0.839516\pi\) | ||
0.875573 | − | 0.483086i | \(-0.160484\pi\) | |||||||
\(858\) | −16.0000 | −0.546231 | ||||||||
\(859\) | −4.00000 | −0.136478 | −0.0682391 | − | 0.997669i | \(-0.521738\pi\) | ||||
−0.0682391 | + | 0.997669i | \(0.521738\pi\) | |||||||
\(860\) | 11.3137i | 0.385794i | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | − | 5.65685i | − | 0.192673i | ||||||
\(863\) | −48.0000 | −1.63394 | −0.816970 | − | 0.576681i | \(-0.804348\pi\) | ||||
−0.816970 | + | 0.576681i | \(0.804348\pi\) | |||||||
\(864\) | 5.65685i | 0.192450i | ||||||||
\(865\) | −8.00000 | −0.272008 | ||||||||
\(866\) | −14.0000 | −0.475739 | ||||||||
\(867\) | 48.0000 | + | 2.82843i | 1.63017 | + | 0.0960584i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −48.0000 | −1.62829 | ||||||||
\(870\) | 22.6274i | 0.767141i | ||||||||
\(871\) | −8.00000 | −0.271070 | ||||||||
\(872\) | 8.48528i | 0.287348i | ||||||||
\(873\) | − | 84.8528i | − | 2.87183i | ||||||
\(874\) | 22.6274i | 0.765384i | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − | 8.48528i | − | 0.286528i | −0.989685 | − | 0.143264i | \(-0.954240\pi\) | ||
0.989685 | − | 0.143264i | \(-0.0457597\pi\) | |||||||
\(878\) | − | 16.9706i | − | 0.572729i | ||||||
\(879\) | 16.9706i | 0.572403i | ||||||||
\(880\) | −8.00000 | −0.269680 | ||||||||
\(881\) | − | 45.2548i | − | 1.52467i | −0.647180 | − | 0.762337i | \(-0.724052\pi\) | ||
0.647180 | − | 0.762337i | \(-0.275948\pi\) | |||||||
\(882\) | 35.0000 | 1.17851 | ||||||||
\(883\) | 44.0000 | 1.48072 | 0.740359 | − | 0.672212i | \(-0.234656\pi\) | ||||
0.740359 | + | 0.672212i | \(0.234656\pi\) | |||||||
\(884\) | −6.00000 | + | 5.65685i | −0.201802 | + | 0.190261i | ||||
\(885\) | 96.0000 | 3.22700 | ||||||||
\(886\) | 12.0000 | 0.403148 | ||||||||
\(887\) | 39.5980i | 1.32957i | 0.747035 | + | 0.664785i | \(0.231477\pi\) | ||||
−0.747035 | + | 0.664785i | \(0.768523\pi\) | |||||||
\(888\) | −24.0000 | −0.805387 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 16.9706i | 0.568855i | ||||||||
\(891\) | − | 2.82843i | − | 0.0947559i | ||||||
\(892\) | −16.0000 | −0.535720 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | − | 16.9706i | − | 0.567581i | ||||||
\(895\) | − | 33.9411i | − | 1.13453i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −32.0000 | −1.06845 | ||||||||
\(898\) | − | 5.65685i | − | 0.188772i | ||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 15.0000 | 0.500000 | ||||||||
\(901\) | −18.0000 | + | 16.9706i | −0.599667 | + | 0.565371i | ||||
\(902\) | −16.0000 | −0.532742 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 11.3137i | 0.376288i | ||||||||
\(905\) | 24.0000 | 0.797787 | ||||||||
\(906\) | − | 22.6274i | − | 0.751746i | ||||||
\(907\) | 42.4264i | 1.40875i | 0.709830 | + | 0.704373i | \(0.248772\pi\) | ||||
−0.709830 | + | 0.704373i | \(0.751228\pi\) | |||||||
\(908\) | − | 19.7990i | − | 0.657053i | ||||||
\(909\) | 30.0000 | 0.995037 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 56.5685i | 1.87420i | 0.349062 | + | 0.937100i | \(0.386500\pi\) | ||||
−0.349062 | + | 0.937100i | \(0.613500\pi\) | |||||||
\(912\) | − | 11.3137i | − | 0.374634i | ||||||
\(913\) | 33.9411i | 1.12329i | ||||||||
\(914\) | 10.0000 | 0.330771 | ||||||||
\(915\) | 67.8823i | 2.24412i | ||||||||
\(916\) | −22.0000 | −0.726900 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −16.0000 | − | 16.9706i | −0.528079 | − | 0.560112i | ||||
\(919\) | −40.0000 | −1.31948 | −0.659739 | − | 0.751495i | \(-0.729333\pi\) | ||||
−0.659739 | + | 0.751495i | \(0.729333\pi\) | |||||||
\(920\) | −16.0000 | −0.527504 | ||||||||
\(921\) | 56.5685i | 1.86400i | ||||||||
\(922\) | 18.0000 | 0.592798 | ||||||||
\(923\) | 11.3137i | 0.372395i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 25.4558i | 0.836983i | ||||||||
\(926\) | −32.0000 | −1.05159 | ||||||||
\(927\) | −40.0000 | −1.31377 | ||||||||
\(928\) | 2.82843i | 0.0928477i | ||||||||
\(929\) | 5.65685i | 0.185595i | 0.995685 | + | 0.0927977i | \(0.0295810\pi\) | ||||
−0.995685 | + | 0.0927977i | \(0.970419\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −28.0000 | −0.917663 | ||||||||
\(932\) | 22.6274i | 0.741186i | ||||||||
\(933\) | 32.0000 | 1.04763 | ||||||||
\(934\) | 36.0000 | 1.17796 | ||||||||
\(935\) | 24.0000 | − | 22.6274i | 0.784884 | − | 0.739996i | ||||
\(936\) | 10.0000 | 0.326860 | ||||||||
\(937\) | 2.00000 | 0.0653372 | 0.0326686 | − | 0.999466i | \(-0.489599\pi\) | ||||
0.0326686 | + | 0.999466i | \(0.489599\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 48.0000 | 1.56642 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 36.7696i | − | 1.19865i | −0.800505 | − | 0.599327i | \(-0.795435\pi\) | ||
0.800505 | − | 0.599327i | \(-0.204565\pi\) | |||||||
\(942\) | − | 39.5980i | − | 1.29017i | ||||||
\(943\) | −32.0000 | −1.04206 | ||||||||
\(944\) | 12.0000 | 0.390567 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | − | 11.3137i | − | 0.367840i | ||||||
\(947\) | − | 2.82843i | − | 0.0919115i | −0.998943 | − | 0.0459558i | \(-0.985367\pi\) | ||
0.998943 | − | 0.0459558i | \(-0.0146333\pi\) | |||||||
\(948\) | 48.0000 | 1.55897 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | −12.0000 | −0.389331 | ||||||||
\(951\) | 8.00000 | 0.259418 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 6.00000 | 0.194359 | 0.0971795 | − | 0.995267i | \(-0.469018\pi\) | ||||
0.0971795 | + | 0.995267i | \(0.469018\pi\) | |||||||
\(954\) | 30.0000 | 0.971286 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − | 22.6274i | − | 0.731441i | ||||||
\(958\) | − | 5.65685i | − | 0.182765i | ||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 8.00000 | 0.258199 | ||||||||
\(961\) | 31.0000 | 1.00000 | ||||||||
\(962\) | 16.9706i | 0.547153i | ||||||||
\(963\) | 14.1421i | 0.455724i | ||||||||
\(964\) | 16.9706i | 0.546585i | ||||||||
\(965\) | 48.0000 | 1.54517 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 8.00000 | 0.257263 | 0.128631 | − | 0.991692i | \(-0.458942\pi\) | ||||
0.128631 | + | 0.991692i | \(0.458942\pi\) | |||||||
\(968\) | −3.00000 | −0.0964237 | ||||||||
\(969\) | 32.0000 | + | 33.9411i | 1.02799 | + | 1.09035i | ||||
\(970\) | −48.0000 | −1.54119 | ||||||||
\(971\) | 12.0000 | 0.385098 | 0.192549 | − | 0.981287i | \(-0.438325\pi\) | ||||
0.192549 | + | 0.981287i | \(0.438325\pi\) | |||||||
\(972\) | − | 14.1421i | − | 0.453609i | ||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | − | 16.9706i | − | 0.543772i | ||||||
\(975\) | − | 16.9706i | − | 0.543493i | ||||||
\(976\) | 8.48528i | 0.271607i | ||||||||
\(977\) | 18.0000 | 0.575871 | 0.287936 | − | 0.957650i | \(-0.407031\pi\) | ||||
0.287936 | + | 0.957650i | \(0.407031\pi\) | |||||||
\(978\) | −24.0000 | −0.767435 | ||||||||
\(979\) | − | 16.9706i | − | 0.542382i | ||||||
\(980\) | − | 19.7990i | − | 0.632456i | ||||||
\(981\) | 42.4264i | 1.35457i | ||||||||
\(982\) | 12.0000 | 0.382935 | ||||||||
\(983\) | 5.65685i | 0.180426i | 0.995923 | + | 0.0902128i | \(0.0287547\pi\) | ||||
−0.995923 | + | 0.0902128i | \(0.971245\pi\) | |||||||
\(984\) | 16.0000 | 0.510061 | ||||||||
\(985\) | −8.00000 | −0.254901 | ||||||||
\(986\) | −8.00000 | − | 8.48528i | −0.254772 | − | 0.270226i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −8.00000 | −0.254514 | ||||||||
\(989\) | − | 22.6274i | − | 0.719510i | ||||||
\(990\) | −40.0000 | −1.27128 | ||||||||
\(991\) | − | 50.9117i | − | 1.61726i | −0.588315 | − | 0.808632i | \(-0.700209\pi\) | ||
0.588315 | − | 0.808632i | \(-0.299791\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − | 11.3137i | − | 0.359030i | ||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −48.0000 | −1.52170 | ||||||||
\(996\) | − | 33.9411i | − | 1.07547i | ||||||
\(997\) | − | 59.3970i | − | 1.88112i | −0.339626 | − | 0.940560i | \(-0.610301\pi\) | ||
0.339626 | − | 0.940560i | \(-0.389699\pi\) | |||||||
\(998\) | 25.4558i | 0.805791i | ||||||||
\(999\) | −48.0000 | −1.51865 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))