Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [690,2,Mod(1,690)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(690, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("690.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 690.a (trivial) |
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: | yes |
Analytic conductor: | \(5.50967773947\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{17}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-1.56155\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 690.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
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 | ||||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | −1.00000 | −0.408248 | ||||||||
\(7\) | 3.12311 | 1.18042 | 0.590211 | − | 0.807249i | \(-0.299044\pi\) | ||||
0.590211 | + | 0.807249i | \(0.299044\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 1.00000 | 0.316228 | ||||||||
\(11\) | −3.12311 | −0.941652 | −0.470826 | − | 0.882226i | \(-0.656044\pi\) | ||||
−0.470826 | + | 0.882226i | \(0.656044\pi\) | |||||||
\(12\) | −1.00000 | −0.288675 | ||||||||
\(13\) | 2.00000 | 0.554700 | 0.277350 | − | 0.960769i | \(-0.410544\pi\) | ||||
0.277350 | + | 0.960769i | \(0.410544\pi\) | |||||||
\(14\) | 3.12311 | 0.834685 | ||||||||
\(15\) | −1.00000 | −0.258199 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −1.12311 | −0.272393 | −0.136197 | − | 0.990682i | \(-0.543488\pi\) | ||||
−0.136197 | + | 0.990682i | \(0.543488\pi\) | |||||||
\(18\) | 1.00000 | 0.235702 | ||||||||
\(19\) | 4.00000 | 0.917663 | 0.458831 | − | 0.888523i | \(-0.348268\pi\) | ||||
0.458831 | + | 0.888523i | \(0.348268\pi\) | |||||||
\(20\) | 1.00000 | 0.223607 | ||||||||
\(21\) | −3.12311 | −0.681518 | ||||||||
\(22\) | −3.12311 | −0.665848 | ||||||||
\(23\) | 1.00000 | 0.208514 | ||||||||
\(24\) | −1.00000 | −0.204124 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 2.00000 | 0.392232 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 3.12311 | 0.590211 | ||||||||
\(29\) | 2.00000 | 0.371391 | 0.185695 | − | 0.982607i | \(-0.440546\pi\) | ||||
0.185695 | + | 0.982607i | \(0.440546\pi\) | |||||||
\(30\) | −1.00000 | −0.182574 | ||||||||
\(31\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 3.12311 | 0.543663 | ||||||||
\(34\) | −1.12311 | −0.192611 | ||||||||
\(35\) | 3.12311 | 0.527901 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | 1.12311 | 0.184637 | 0.0923187 | − | 0.995730i | \(-0.470572\pi\) | ||||
0.0923187 | + | 0.995730i | \(0.470572\pi\) | |||||||
\(38\) | 4.00000 | 0.648886 | ||||||||
\(39\) | −2.00000 | −0.320256 | ||||||||
\(40\) | 1.00000 | 0.158114 | ||||||||
\(41\) | 2.00000 | 0.312348 | 0.156174 | − | 0.987730i | \(-0.450084\pi\) | ||||
0.156174 | + | 0.987730i | \(0.450084\pi\) | |||||||
\(42\) | −3.12311 | −0.481906 | ||||||||
\(43\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(44\) | −3.12311 | −0.470826 | ||||||||
\(45\) | 1.00000 | 0.149071 | ||||||||
\(46\) | 1.00000 | 0.147442 | ||||||||
\(47\) | −8.00000 | −1.16692 | −0.583460 | − | 0.812142i | \(-0.698301\pi\) | ||||
−0.583460 | + | 0.812142i | \(0.698301\pi\) | |||||||
\(48\) | −1.00000 | −0.144338 | ||||||||
\(49\) | 2.75379 | 0.393398 | ||||||||
\(50\) | 1.00000 | 0.141421 | ||||||||
\(51\) | 1.12311 | 0.157266 | ||||||||
\(52\) | 2.00000 | 0.277350 | ||||||||
\(53\) | 12.2462 | 1.68215 | 0.841073 | − | 0.540921i | \(-0.181924\pi\) | ||||
0.841073 | + | 0.540921i | \(0.181924\pi\) | |||||||
\(54\) | −1.00000 | −0.136083 | ||||||||
\(55\) | −3.12311 | −0.421119 | ||||||||
\(56\) | 3.12311 | 0.417343 | ||||||||
\(57\) | −4.00000 | −0.529813 | ||||||||
\(58\) | 2.00000 | 0.262613 | ||||||||
\(59\) | 2.24621 | 0.292432 | 0.146216 | − | 0.989253i | \(-0.453291\pi\) | ||||
0.146216 | + | 0.989253i | \(0.453291\pi\) | |||||||
\(60\) | −1.00000 | −0.129099 | ||||||||
\(61\) | 9.12311 | 1.16809 | 0.584047 | − | 0.811720i | \(-0.301468\pi\) | ||||
0.584047 | + | 0.811720i | \(0.301468\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 3.12311 | 0.393474 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 2.00000 | 0.248069 | ||||||||
\(66\) | 3.12311 | 0.384428 | ||||||||
\(67\) | −8.00000 | −0.977356 | −0.488678 | − | 0.872464i | \(-0.662521\pi\) | ||||
−0.488678 | + | 0.872464i | \(0.662521\pi\) | |||||||
\(68\) | −1.12311 | −0.136197 | ||||||||
\(69\) | −1.00000 | −0.120386 | ||||||||
\(70\) | 3.12311 | 0.373283 | ||||||||
\(71\) | −10.2462 | −1.21600 | −0.608001 | − | 0.793936i | \(-0.708028\pi\) | ||||
−0.608001 | + | 0.793936i | \(0.708028\pi\) | |||||||
\(72\) | 1.00000 | 0.117851 | ||||||||
\(73\) | −4.24621 | −0.496981 | −0.248491 | − | 0.968634i | \(-0.579935\pi\) | ||||
−0.248491 | + | 0.968634i | \(0.579935\pi\) | |||||||
\(74\) | 1.12311 | 0.130558 | ||||||||
\(75\) | −1.00000 | −0.115470 | ||||||||
\(76\) | 4.00000 | 0.458831 | ||||||||
\(77\) | −9.75379 | −1.11155 | ||||||||
\(78\) | −2.00000 | −0.226455 | ||||||||
\(79\) | 3.12311 | 0.351377 | 0.175688 | − | 0.984446i | \(-0.443785\pi\) | ||||
0.175688 | + | 0.984446i | \(0.443785\pi\) | |||||||
\(80\) | 1.00000 | 0.111803 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 2.00000 | 0.220863 | ||||||||
\(83\) | −13.3693 | −1.46747 | −0.733737 | − | 0.679434i | \(-0.762225\pi\) | ||||
−0.733737 | + | 0.679434i | \(0.762225\pi\) | |||||||
\(84\) | −3.12311 | −0.340759 | ||||||||
\(85\) | −1.12311 | −0.121818 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −2.00000 | −0.214423 | ||||||||
\(88\) | −3.12311 | −0.332924 | ||||||||
\(89\) | −5.12311 | −0.543048 | −0.271524 | − | 0.962432i | \(-0.587528\pi\) | ||||
−0.271524 | + | 0.962432i | \(0.587528\pi\) | |||||||
\(90\) | 1.00000 | 0.105409 | ||||||||
\(91\) | 6.24621 | 0.654781 | ||||||||
\(92\) | 1.00000 | 0.104257 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −8.00000 | −0.825137 | ||||||||
\(95\) | 4.00000 | 0.410391 | ||||||||
\(96\) | −1.00000 | −0.102062 | ||||||||
\(97\) | −16.2462 | −1.64955 | −0.824776 | − | 0.565459i | \(-0.808699\pi\) | ||||
−0.824776 | + | 0.565459i | \(0.808699\pi\) | |||||||
\(98\) | 2.75379 | 0.278175 | ||||||||
\(99\) | −3.12311 | −0.313884 | ||||||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | 0.246211 | 0.0244989 | 0.0122495 | − | 0.999925i | \(-0.496101\pi\) | ||||
0.0122495 | + | 0.999925i | \(0.496101\pi\) | |||||||
\(102\) | 1.12311 | 0.111204 | ||||||||
\(103\) | −9.36932 | −0.923186 | −0.461593 | − | 0.887092i | \(-0.652722\pi\) | ||||
−0.461593 | + | 0.887092i | \(0.652722\pi\) | |||||||
\(104\) | 2.00000 | 0.196116 | ||||||||
\(105\) | −3.12311 | −0.304784 | ||||||||
\(106\) | 12.2462 | 1.18946 | ||||||||
\(107\) | −13.3693 | −1.29246 | −0.646230 | − | 0.763142i | \(-0.723655\pi\) | ||||
−0.646230 | + | 0.763142i | \(0.723655\pi\) | |||||||
\(108\) | −1.00000 | −0.0962250 | ||||||||
\(109\) | 2.87689 | 0.275557 | 0.137778 | − | 0.990463i | \(-0.456004\pi\) | ||||
0.137778 | + | 0.990463i | \(0.456004\pi\) | |||||||
\(110\) | −3.12311 | −0.297776 | ||||||||
\(111\) | −1.12311 | −0.106600 | ||||||||
\(112\) | 3.12311 | 0.295106 | ||||||||
\(113\) | −9.12311 | −0.858230 | −0.429115 | − | 0.903250i | \(-0.641174\pi\) | ||||
−0.429115 | + | 0.903250i | \(0.641174\pi\) | |||||||
\(114\) | −4.00000 | −0.374634 | ||||||||
\(115\) | 1.00000 | 0.0932505 | ||||||||
\(116\) | 2.00000 | 0.185695 | ||||||||
\(117\) | 2.00000 | 0.184900 | ||||||||
\(118\) | 2.24621 | 0.206781 | ||||||||
\(119\) | −3.50758 | −0.321539 | ||||||||
\(120\) | −1.00000 | −0.0912871 | ||||||||
\(121\) | −1.24621 | −0.113292 | ||||||||
\(122\) | 9.12311 | 0.825967 | ||||||||
\(123\) | −2.00000 | −0.180334 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 3.12311 | 0.278228 | ||||||||
\(127\) | −5.75379 | −0.510566 | −0.255283 | − | 0.966866i | \(-0.582169\pi\) | ||||
−0.255283 | + | 0.966866i | \(0.582169\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 2.00000 | 0.175412 | ||||||||
\(131\) | −4.00000 | −0.349482 | −0.174741 | − | 0.984614i | \(-0.555909\pi\) | ||||
−0.174741 | + | 0.984614i | \(0.555909\pi\) | |||||||
\(132\) | 3.12311 | 0.271831 | ||||||||
\(133\) | 12.4924 | 1.08323 | ||||||||
\(134\) | −8.00000 | −0.691095 | ||||||||
\(135\) | −1.00000 | −0.0860663 | ||||||||
\(136\) | −1.12311 | −0.0963055 | ||||||||
\(137\) | −10.8769 | −0.929276 | −0.464638 | − | 0.885501i | \(-0.653816\pi\) | ||||
−0.464638 | + | 0.885501i | \(0.653816\pi\) | |||||||
\(138\) | −1.00000 | −0.0851257 | ||||||||
\(139\) | 16.4924 | 1.39887 | 0.699435 | − | 0.714697i | \(-0.253435\pi\) | ||||
0.699435 | + | 0.714697i | \(0.253435\pi\) | |||||||
\(140\) | 3.12311 | 0.263951 | ||||||||
\(141\) | 8.00000 | 0.673722 | ||||||||
\(142\) | −10.2462 | −0.859843 | ||||||||
\(143\) | −6.24621 | −0.522334 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | 2.00000 | 0.166091 | ||||||||
\(146\) | −4.24621 | −0.351419 | ||||||||
\(147\) | −2.75379 | −0.227129 | ||||||||
\(148\) | 1.12311 | 0.0923187 | ||||||||
\(149\) | −10.0000 | −0.819232 | −0.409616 | − | 0.912258i | \(-0.634337\pi\) | ||||
−0.409616 | + | 0.912258i | \(0.634337\pi\) | |||||||
\(150\) | −1.00000 | −0.0816497 | ||||||||
\(151\) | 6.24621 | 0.508309 | 0.254155 | − | 0.967164i | \(-0.418203\pi\) | ||||
0.254155 | + | 0.967164i | \(0.418203\pi\) | |||||||
\(152\) | 4.00000 | 0.324443 | ||||||||
\(153\) | −1.12311 | −0.0907977 | ||||||||
\(154\) | −9.75379 | −0.785983 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −2.00000 | −0.160128 | ||||||||
\(157\) | 9.12311 | 0.728103 | 0.364052 | − | 0.931379i | \(-0.381393\pi\) | ||||
0.364052 | + | 0.931379i | \(0.381393\pi\) | |||||||
\(158\) | 3.12311 | 0.248461 | ||||||||
\(159\) | −12.2462 | −0.971188 | ||||||||
\(160\) | 1.00000 | 0.0790569 | ||||||||
\(161\) | 3.12311 | 0.246135 | ||||||||
\(162\) | 1.00000 | 0.0785674 | ||||||||
\(163\) | −12.0000 | −0.939913 | −0.469956 | − | 0.882690i | \(-0.655730\pi\) | ||||
−0.469956 | + | 0.882690i | \(0.655730\pi\) | |||||||
\(164\) | 2.00000 | 0.156174 | ||||||||
\(165\) | 3.12311 | 0.243133 | ||||||||
\(166\) | −13.3693 | −1.03766 | ||||||||
\(167\) | −8.00000 | −0.619059 | −0.309529 | − | 0.950890i | \(-0.600171\pi\) | ||||
−0.309529 | + | 0.950890i | \(0.600171\pi\) | |||||||
\(168\) | −3.12311 | −0.240953 | ||||||||
\(169\) | −9.00000 | −0.692308 | ||||||||
\(170\) | −1.12311 | −0.0861383 | ||||||||
\(171\) | 4.00000 | 0.305888 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 20.2462 | 1.53929 | 0.769645 | − | 0.638471i | \(-0.220433\pi\) | ||||
0.769645 | + | 0.638471i | \(0.220433\pi\) | |||||||
\(174\) | −2.00000 | −0.151620 | ||||||||
\(175\) | 3.12311 | 0.236085 | ||||||||
\(176\) | −3.12311 | −0.235413 | ||||||||
\(177\) | −2.24621 | −0.168836 | ||||||||
\(178\) | −5.12311 | −0.383993 | ||||||||
\(179\) | −8.49242 | −0.634753 | −0.317377 | − | 0.948300i | \(-0.602802\pi\) | ||||
−0.317377 | + | 0.948300i | \(0.602802\pi\) | |||||||
\(180\) | 1.00000 | 0.0745356 | ||||||||
\(181\) | 10.8769 | 0.808473 | 0.404237 | − | 0.914654i | \(-0.367537\pi\) | ||||
0.404237 | + | 0.914654i | \(0.367537\pi\) | |||||||
\(182\) | 6.24621 | 0.463000 | ||||||||
\(183\) | −9.12311 | −0.674399 | ||||||||
\(184\) | 1.00000 | 0.0737210 | ||||||||
\(185\) | 1.12311 | 0.0825724 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 3.50758 | 0.256499 | ||||||||
\(188\) | −8.00000 | −0.583460 | ||||||||
\(189\) | −3.12311 | −0.227173 | ||||||||
\(190\) | 4.00000 | 0.290191 | ||||||||
\(191\) | 12.4924 | 0.903920 | 0.451960 | − | 0.892038i | \(-0.350725\pi\) | ||||
0.451960 | + | 0.892038i | \(0.350725\pi\) | |||||||
\(192\) | −1.00000 | −0.0721688 | ||||||||
\(193\) | 8.24621 | 0.593575 | 0.296788 | − | 0.954944i | \(-0.404085\pi\) | ||||
0.296788 | + | 0.954944i | \(0.404085\pi\) | |||||||
\(194\) | −16.2462 | −1.16641 | ||||||||
\(195\) | −2.00000 | −0.143223 | ||||||||
\(196\) | 2.75379 | 0.196699 | ||||||||
\(197\) | −10.0000 | −0.712470 | −0.356235 | − | 0.934396i | \(-0.615940\pi\) | ||||
−0.356235 | + | 0.934396i | \(0.615940\pi\) | |||||||
\(198\) | −3.12311 | −0.221949 | ||||||||
\(199\) | 19.1231 | 1.35560 | 0.677801 | − | 0.735246i | \(-0.262933\pi\) | ||||
0.677801 | + | 0.735246i | \(0.262933\pi\) | |||||||
\(200\) | 1.00000 | 0.0707107 | ||||||||
\(201\) | 8.00000 | 0.564276 | ||||||||
\(202\) | 0.246211 | 0.0173234 | ||||||||
\(203\) | 6.24621 | 0.438398 | ||||||||
\(204\) | 1.12311 | 0.0786331 | ||||||||
\(205\) | 2.00000 | 0.139686 | ||||||||
\(206\) | −9.36932 | −0.652791 | ||||||||
\(207\) | 1.00000 | 0.0695048 | ||||||||
\(208\) | 2.00000 | 0.138675 | ||||||||
\(209\) | −12.4924 | −0.864119 | ||||||||
\(210\) | −3.12311 | −0.215515 | ||||||||
\(211\) | −16.4924 | −1.13539 | −0.567693 | − | 0.823241i | \(-0.692164\pi\) | ||||
−0.567693 | + | 0.823241i | \(0.692164\pi\) | |||||||
\(212\) | 12.2462 | 0.841073 | ||||||||
\(213\) | 10.2462 | 0.702059 | ||||||||
\(214\) | −13.3693 | −0.913908 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −1.00000 | −0.0680414 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 2.87689 | 0.194848 | ||||||||
\(219\) | 4.24621 | 0.286932 | ||||||||
\(220\) | −3.12311 | −0.210560 | ||||||||
\(221\) | −2.24621 | −0.151097 | ||||||||
\(222\) | −1.12311 | −0.0753779 | ||||||||
\(223\) | −10.2462 | −0.686137 | −0.343069 | − | 0.939310i | \(-0.611466\pi\) | ||||
−0.343069 | + | 0.939310i | \(0.611466\pi\) | |||||||
\(224\) | 3.12311 | 0.208671 | ||||||||
\(225\) | 1.00000 | 0.0666667 | ||||||||
\(226\) | −9.12311 | −0.606860 | ||||||||
\(227\) | −5.36932 | −0.356374 | −0.178187 | − | 0.983997i | \(-0.557023\pi\) | ||||
−0.178187 | + | 0.983997i | \(0.557023\pi\) | |||||||
\(228\) | −4.00000 | −0.264906 | ||||||||
\(229\) | 23.3693 | 1.54429 | 0.772144 | − | 0.635448i | \(-0.219184\pi\) | ||||
0.772144 | + | 0.635448i | \(0.219184\pi\) | |||||||
\(230\) | 1.00000 | 0.0659380 | ||||||||
\(231\) | 9.75379 | 0.641752 | ||||||||
\(232\) | 2.00000 | 0.131306 | ||||||||
\(233\) | 28.7386 | 1.88273 | 0.941365 | − | 0.337389i | \(-0.109544\pi\) | ||||
0.941365 | + | 0.337389i | \(0.109544\pi\) | |||||||
\(234\) | 2.00000 | 0.130744 | ||||||||
\(235\) | −8.00000 | −0.521862 | ||||||||
\(236\) | 2.24621 | 0.146216 | ||||||||
\(237\) | −3.12311 | −0.202868 | ||||||||
\(238\) | −3.50758 | −0.227362 | ||||||||
\(239\) | −18.2462 | −1.18025 | −0.590125 | − | 0.807312i | \(-0.700921\pi\) | ||||
−0.590125 | + | 0.807312i | \(0.700921\pi\) | |||||||
\(240\) | −1.00000 | −0.0645497 | ||||||||
\(241\) | 30.4924 | 1.96419 | 0.982095 | − | 0.188387i | \(-0.0603260\pi\) | ||||
0.982095 | + | 0.188387i | \(0.0603260\pi\) | |||||||
\(242\) | −1.24621 | −0.0801095 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 9.12311 | 0.584047 | ||||||||
\(245\) | 2.75379 | 0.175933 | ||||||||
\(246\) | −2.00000 | −0.127515 | ||||||||
\(247\) | 8.00000 | 0.509028 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 13.3693 | 0.847246 | ||||||||
\(250\) | 1.00000 | 0.0632456 | ||||||||
\(251\) | 17.3693 | 1.09634 | 0.548171 | − | 0.836366i | \(-0.315324\pi\) | ||||
0.548171 | + | 0.836366i | \(0.315324\pi\) | |||||||
\(252\) | 3.12311 | 0.196737 | ||||||||
\(253\) | −3.12311 | −0.196348 | ||||||||
\(254\) | −5.75379 | −0.361025 | ||||||||
\(255\) | 1.12311 | 0.0703316 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 8.24621 | 0.514385 | 0.257192 | − | 0.966360i | \(-0.417203\pi\) | ||||
0.257192 | + | 0.966360i | \(0.417203\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 3.50758 | 0.217950 | ||||||||
\(260\) | 2.00000 | 0.124035 | ||||||||
\(261\) | 2.00000 | 0.123797 | ||||||||
\(262\) | −4.00000 | −0.247121 | ||||||||
\(263\) | −6.24621 | −0.385158 | −0.192579 | − | 0.981281i | \(-0.561685\pi\) | ||||
−0.192579 | + | 0.981281i | \(0.561685\pi\) | |||||||
\(264\) | 3.12311 | 0.192214 | ||||||||
\(265\) | 12.2462 | 0.752279 | ||||||||
\(266\) | 12.4924 | 0.765960 | ||||||||
\(267\) | 5.12311 | 0.313529 | ||||||||
\(268\) | −8.00000 | −0.488678 | ||||||||
\(269\) | 0.246211 | 0.0150118 | 0.00750588 | − | 0.999972i | \(-0.497611\pi\) | ||||
0.00750588 | + | 0.999972i | \(0.497611\pi\) | |||||||
\(270\) | −1.00000 | −0.0608581 | ||||||||
\(271\) | −6.24621 | −0.379430 | −0.189715 | − | 0.981839i | \(-0.560756\pi\) | ||||
−0.189715 | + | 0.981839i | \(0.560756\pi\) | |||||||
\(272\) | −1.12311 | −0.0680983 | ||||||||
\(273\) | −6.24621 | −0.378038 | ||||||||
\(274\) | −10.8769 | −0.657097 | ||||||||
\(275\) | −3.12311 | −0.188330 | ||||||||
\(276\) | −1.00000 | −0.0601929 | ||||||||
\(277\) | 3.75379 | 0.225543 | 0.112772 | − | 0.993621i | \(-0.464027\pi\) | ||||
0.112772 | + | 0.993621i | \(0.464027\pi\) | |||||||
\(278\) | 16.4924 | 0.989150 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 3.12311 | 0.186641 | ||||||||
\(281\) | −21.1231 | −1.26010 | −0.630049 | − | 0.776555i | \(-0.716965\pi\) | ||||
−0.630049 | + | 0.776555i | \(0.716965\pi\) | |||||||
\(282\) | 8.00000 | 0.476393 | ||||||||
\(283\) | 14.2462 | 0.846849 | 0.423425 | − | 0.905931i | \(-0.360828\pi\) | ||||
0.423425 | + | 0.905931i | \(0.360828\pi\) | |||||||
\(284\) | −10.2462 | −0.608001 | ||||||||
\(285\) | −4.00000 | −0.236940 | ||||||||
\(286\) | −6.24621 | −0.369346 | ||||||||
\(287\) | 6.24621 | 0.368702 | ||||||||
\(288\) | 1.00000 | 0.0589256 | ||||||||
\(289\) | −15.7386 | −0.925802 | ||||||||
\(290\) | 2.00000 | 0.117444 | ||||||||
\(291\) | 16.2462 | 0.952370 | ||||||||
\(292\) | −4.24621 | −0.248491 | ||||||||
\(293\) | 28.2462 | 1.65016 | 0.825081 | − | 0.565015i | \(-0.191130\pi\) | ||||
0.825081 | + | 0.565015i | \(0.191130\pi\) | |||||||
\(294\) | −2.75379 | −0.160604 | ||||||||
\(295\) | 2.24621 | 0.130779 | ||||||||
\(296\) | 1.12311 | 0.0652792 | ||||||||
\(297\) | 3.12311 | 0.181221 | ||||||||
\(298\) | −10.0000 | −0.579284 | ||||||||
\(299\) | 2.00000 | 0.115663 | ||||||||
\(300\) | −1.00000 | −0.0577350 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 6.24621 | 0.359429 | ||||||||
\(303\) | −0.246211 | −0.0141445 | ||||||||
\(304\) | 4.00000 | 0.229416 | ||||||||
\(305\) | 9.12311 | 0.522388 | ||||||||
\(306\) | −1.12311 | −0.0642037 | ||||||||
\(307\) | −32.4924 | −1.85444 | −0.927220 | − | 0.374516i | \(-0.877809\pi\) | ||||
−0.927220 | + | 0.374516i | \(0.877809\pi\) | |||||||
\(308\) | −9.75379 | −0.555774 | ||||||||
\(309\) | 9.36932 | 0.533002 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −22.7386 | −1.28939 | −0.644695 | − | 0.764440i | \(-0.723016\pi\) | ||||
−0.644695 | + | 0.764440i | \(0.723016\pi\) | |||||||
\(312\) | −2.00000 | −0.113228 | ||||||||
\(313\) | −22.4924 | −1.27135 | −0.635673 | − | 0.771958i | \(-0.719278\pi\) | ||||
−0.635673 | + | 0.771958i | \(0.719278\pi\) | |||||||
\(314\) | 9.12311 | 0.514847 | ||||||||
\(315\) | 3.12311 | 0.175967 | ||||||||
\(316\) | 3.12311 | 0.175688 | ||||||||
\(317\) | −28.7386 | −1.61412 | −0.807061 | − | 0.590468i | \(-0.798943\pi\) | ||||
−0.807061 | + | 0.590468i | \(0.798943\pi\) | |||||||
\(318\) | −12.2462 | −0.686733 | ||||||||
\(319\) | −6.24621 | −0.349721 | ||||||||
\(320\) | 1.00000 | 0.0559017 | ||||||||
\(321\) | 13.3693 | 0.746203 | ||||||||
\(322\) | 3.12311 | 0.174044 | ||||||||
\(323\) | −4.49242 | −0.249965 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | 2.00000 | 0.110940 | ||||||||
\(326\) | −12.0000 | −0.664619 | ||||||||
\(327\) | −2.87689 | −0.159093 | ||||||||
\(328\) | 2.00000 | 0.110432 | ||||||||
\(329\) | −24.9848 | −1.37746 | ||||||||
\(330\) | 3.12311 | 0.171921 | ||||||||
\(331\) | 0.492423 | 0.0270660 | 0.0135330 | − | 0.999908i | \(-0.495692\pi\) | ||||
0.0135330 | + | 0.999908i | \(0.495692\pi\) | |||||||
\(332\) | −13.3693 | −0.733737 | ||||||||
\(333\) | 1.12311 | 0.0615458 | ||||||||
\(334\) | −8.00000 | −0.437741 | ||||||||
\(335\) | −8.00000 | −0.437087 | ||||||||
\(336\) | −3.12311 | −0.170379 | ||||||||
\(337\) | 26.4924 | 1.44313 | 0.721567 | − | 0.692345i | \(-0.243422\pi\) | ||||
0.721567 | + | 0.692345i | \(0.243422\pi\) | |||||||
\(338\) | −9.00000 | −0.489535 | ||||||||
\(339\) | 9.12311 | 0.495499 | ||||||||
\(340\) | −1.12311 | −0.0609090 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 4.00000 | 0.216295 | ||||||||
\(343\) | −13.2614 | −0.716046 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −1.00000 | −0.0538382 | ||||||||
\(346\) | 20.2462 | 1.08844 | ||||||||
\(347\) | 14.7386 | 0.791211 | 0.395606 | − | 0.918420i | \(-0.370535\pi\) | ||||
0.395606 | + | 0.918420i | \(0.370535\pi\) | |||||||
\(348\) | −2.00000 | −0.107211 | ||||||||
\(349\) | 24.7386 | 1.32423 | 0.662114 | − | 0.749403i | \(-0.269659\pi\) | ||||
0.662114 | + | 0.749403i | \(0.269659\pi\) | |||||||
\(350\) | 3.12311 | 0.166937 | ||||||||
\(351\) | −2.00000 | −0.106752 | ||||||||
\(352\) | −3.12311 | −0.166462 | ||||||||
\(353\) | −14.0000 | −0.745145 | −0.372572 | − | 0.928003i | \(-0.621524\pi\) | ||||
−0.372572 | + | 0.928003i | \(0.621524\pi\) | |||||||
\(354\) | −2.24621 | −0.119385 | ||||||||
\(355\) | −10.2462 | −0.543812 | ||||||||
\(356\) | −5.12311 | −0.271524 | ||||||||
\(357\) | 3.50758 | 0.185641 | ||||||||
\(358\) | −8.49242 | −0.448838 | ||||||||
\(359\) | 20.4924 | 1.08155 | 0.540774 | − | 0.841168i | \(-0.318131\pi\) | ||||
0.540774 | + | 0.841168i | \(0.318131\pi\) | |||||||
\(360\) | 1.00000 | 0.0527046 | ||||||||
\(361\) | −3.00000 | −0.157895 | ||||||||
\(362\) | 10.8769 | 0.571677 | ||||||||
\(363\) | 1.24621 | 0.0654091 | ||||||||
\(364\) | 6.24621 | 0.327390 | ||||||||
\(365\) | −4.24621 | −0.222257 | ||||||||
\(366\) | −9.12311 | −0.476872 | ||||||||
\(367\) | 4.87689 | 0.254572 | 0.127286 | − | 0.991866i | \(-0.459373\pi\) | ||||
0.127286 | + | 0.991866i | \(0.459373\pi\) | |||||||
\(368\) | 1.00000 | 0.0521286 | ||||||||
\(369\) | 2.00000 | 0.104116 | ||||||||
\(370\) | 1.12311 | 0.0583875 | ||||||||
\(371\) | 38.2462 | 1.98564 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −11.3693 | −0.588681 | −0.294340 | − | 0.955701i | \(-0.595100\pi\) | ||||
−0.294340 | + | 0.955701i | \(0.595100\pi\) | |||||||
\(374\) | 3.50758 | 0.181373 | ||||||||
\(375\) | −1.00000 | −0.0516398 | ||||||||
\(376\) | −8.00000 | −0.412568 | ||||||||
\(377\) | 4.00000 | 0.206010 | ||||||||
\(378\) | −3.12311 | −0.160635 | ||||||||
\(379\) | 4.00000 | 0.205466 | 0.102733 | − | 0.994709i | \(-0.467241\pi\) | ||||
0.102733 | + | 0.994709i | \(0.467241\pi\) | |||||||
\(380\) | 4.00000 | 0.205196 | ||||||||
\(381\) | 5.75379 | 0.294776 | ||||||||
\(382\) | 12.4924 | 0.639168 | ||||||||
\(383\) | 30.2462 | 1.54551 | 0.772755 | − | 0.634705i | \(-0.218878\pi\) | ||||
0.772755 | + | 0.634705i | \(0.218878\pi\) | |||||||
\(384\) | −1.00000 | −0.0510310 | ||||||||
\(385\) | −9.75379 | −0.497099 | ||||||||
\(386\) | 8.24621 | 0.419721 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −16.2462 | −0.824776 | ||||||||
\(389\) | −18.0000 | −0.912636 | −0.456318 | − | 0.889817i | \(-0.650832\pi\) | ||||
−0.456318 | + | 0.889817i | \(0.650832\pi\) | |||||||
\(390\) | −2.00000 | −0.101274 | ||||||||
\(391\) | −1.12311 | −0.0567979 | ||||||||
\(392\) | 2.75379 | 0.139087 | ||||||||
\(393\) | 4.00000 | 0.201773 | ||||||||
\(394\) | −10.0000 | −0.503793 | ||||||||
\(395\) | 3.12311 | 0.157140 | ||||||||
\(396\) | −3.12311 | −0.156942 | ||||||||
\(397\) | −1.50758 | −0.0756631 | −0.0378316 | − | 0.999284i | \(-0.512045\pi\) | ||||
−0.0378316 | + | 0.999284i | \(0.512045\pi\) | |||||||
\(398\) | 19.1231 | 0.958555 | ||||||||
\(399\) | −12.4924 | −0.625403 | ||||||||
\(400\) | 1.00000 | 0.0500000 | ||||||||
\(401\) | 7.36932 | 0.368006 | 0.184003 | − | 0.982926i | \(-0.441094\pi\) | ||||
0.184003 | + | 0.982926i | \(0.441094\pi\) | |||||||
\(402\) | 8.00000 | 0.399004 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 0.246211 | 0.0122495 | ||||||||
\(405\) | 1.00000 | 0.0496904 | ||||||||
\(406\) | 6.24621 | 0.309994 | ||||||||
\(407\) | −3.50758 | −0.173864 | ||||||||
\(408\) | 1.12311 | 0.0556020 | ||||||||
\(409\) | 0.246211 | 0.0121744 | 0.00608718 | − | 0.999981i | \(-0.498062\pi\) | ||||
0.00608718 | + | 0.999981i | \(0.498062\pi\) | |||||||
\(410\) | 2.00000 | 0.0987730 | ||||||||
\(411\) | 10.8769 | 0.536518 | ||||||||
\(412\) | −9.36932 | −0.461593 | ||||||||
\(413\) | 7.01515 | 0.345193 | ||||||||
\(414\) | 1.00000 | 0.0491473 | ||||||||
\(415\) | −13.3693 | −0.656274 | ||||||||
\(416\) | 2.00000 | 0.0980581 | ||||||||
\(417\) | −16.4924 | −0.807637 | ||||||||
\(418\) | −12.4924 | −0.611024 | ||||||||
\(419\) | 39.6155 | 1.93535 | 0.967673 | − | 0.252210i | \(-0.0811573\pi\) | ||||
0.967673 | + | 0.252210i | \(0.0811573\pi\) | |||||||
\(420\) | −3.12311 | −0.152392 | ||||||||
\(421\) | −11.3693 | −0.554107 | −0.277053 | − | 0.960855i | \(-0.589358\pi\) | ||||
−0.277053 | + | 0.960855i | \(0.589358\pi\) | |||||||
\(422\) | −16.4924 | −0.802839 | ||||||||
\(423\) | −8.00000 | −0.388973 | ||||||||
\(424\) | 12.2462 | 0.594729 | ||||||||
\(425\) | −1.12311 | −0.0544786 | ||||||||
\(426\) | 10.2462 | 0.496431 | ||||||||
\(427\) | 28.4924 | 1.37884 | ||||||||
\(428\) | −13.3693 | −0.646230 | ||||||||
\(429\) | 6.24621 | 0.301570 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 9.75379 | 0.469823 | 0.234912 | − | 0.972017i | \(-0.424520\pi\) | ||||
0.234912 | + | 0.972017i | \(0.424520\pi\) | |||||||
\(432\) | −1.00000 | −0.0481125 | ||||||||
\(433\) | −22.4924 | −1.08092 | −0.540458 | − | 0.841371i | \(-0.681749\pi\) | ||||
−0.540458 | + | 0.841371i | \(0.681749\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −2.00000 | −0.0958927 | ||||||||
\(436\) | 2.87689 | 0.137778 | ||||||||
\(437\) | 4.00000 | 0.191346 | ||||||||
\(438\) | 4.24621 | 0.202892 | ||||||||
\(439\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(440\) | −3.12311 | −0.148888 | ||||||||
\(441\) | 2.75379 | 0.131133 | ||||||||
\(442\) | −2.24621 | −0.106841 | ||||||||
\(443\) | 8.49242 | 0.403487 | 0.201744 | − | 0.979438i | \(-0.435339\pi\) | ||||
0.201744 | + | 0.979438i | \(0.435339\pi\) | |||||||
\(444\) | −1.12311 | −0.0533002 | ||||||||
\(445\) | −5.12311 | −0.242858 | ||||||||
\(446\) | −10.2462 | −0.485172 | ||||||||
\(447\) | 10.0000 | 0.472984 | ||||||||
\(448\) | 3.12311 | 0.147553 | ||||||||
\(449\) | 22.4924 | 1.06148 | 0.530742 | − | 0.847534i | \(-0.321913\pi\) | ||||
0.530742 | + | 0.847534i | \(0.321913\pi\) | |||||||
\(450\) | 1.00000 | 0.0471405 | ||||||||
\(451\) | −6.24621 | −0.294123 | ||||||||
\(452\) | −9.12311 | −0.429115 | ||||||||
\(453\) | −6.24621 | −0.293473 | ||||||||
\(454\) | −5.36932 | −0.251995 | ||||||||
\(455\) | 6.24621 | 0.292827 | ||||||||
\(456\) | −4.00000 | −0.187317 | ||||||||
\(457\) | 16.7386 | 0.783000 | 0.391500 | − | 0.920178i | \(-0.371956\pi\) | ||||
0.391500 | + | 0.920178i | \(0.371956\pi\) | |||||||
\(458\) | 23.3693 | 1.09198 | ||||||||
\(459\) | 1.12311 | 0.0524221 | ||||||||
\(460\) | 1.00000 | 0.0466252 | ||||||||
\(461\) | −16.7386 | −0.779596 | −0.389798 | − | 0.920900i | \(-0.627455\pi\) | ||||
−0.389798 | + | 0.920900i | \(0.627455\pi\) | |||||||
\(462\) | 9.75379 | 0.453787 | ||||||||
\(463\) | −36.0000 | −1.67306 | −0.836531 | − | 0.547920i | \(-0.815420\pi\) | ||||
−0.836531 | + | 0.547920i | \(0.815420\pi\) | |||||||
\(464\) | 2.00000 | 0.0928477 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 28.7386 | 1.33129 | ||||||||
\(467\) | 21.3693 | 0.988854 | 0.494427 | − | 0.869219i | \(-0.335378\pi\) | ||||
0.494427 | + | 0.869219i | \(0.335378\pi\) | |||||||
\(468\) | 2.00000 | 0.0924500 | ||||||||
\(469\) | −24.9848 | −1.15369 | ||||||||
\(470\) | −8.00000 | −0.369012 | ||||||||
\(471\) | −9.12311 | −0.420371 | ||||||||
\(472\) | 2.24621 | 0.103390 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | −3.12311 | −0.143449 | ||||||||
\(475\) | 4.00000 | 0.183533 | ||||||||
\(476\) | −3.50758 | −0.160770 | ||||||||
\(477\) | 12.2462 | 0.560715 | ||||||||
\(478\) | −18.2462 | −0.834562 | ||||||||
\(479\) | 12.4924 | 0.570793 | 0.285397 | − | 0.958409i | \(-0.407875\pi\) | ||||
0.285397 | + | 0.958409i | \(0.407875\pi\) | |||||||
\(480\) | −1.00000 | −0.0456435 | ||||||||
\(481\) | 2.24621 | 0.102418 | ||||||||
\(482\) | 30.4924 | 1.38889 | ||||||||
\(483\) | −3.12311 | −0.142106 | ||||||||
\(484\) | −1.24621 | −0.0566460 | ||||||||
\(485\) | −16.2462 | −0.737702 | ||||||||
\(486\) | −1.00000 | −0.0453609 | ||||||||
\(487\) | 7.50758 | 0.340201 | 0.170100 | − | 0.985427i | \(-0.445591\pi\) | ||||
0.170100 | + | 0.985427i | \(0.445591\pi\) | |||||||
\(488\) | 9.12311 | 0.412984 | ||||||||
\(489\) | 12.0000 | 0.542659 | ||||||||
\(490\) | 2.75379 | 0.124403 | ||||||||
\(491\) | −12.0000 | −0.541552 | −0.270776 | − | 0.962642i | \(-0.587280\pi\) | ||||
−0.270776 | + | 0.962642i | \(0.587280\pi\) | |||||||
\(492\) | −2.00000 | −0.0901670 | ||||||||
\(493\) | −2.24621 | −0.101164 | ||||||||
\(494\) | 8.00000 | 0.359937 | ||||||||
\(495\) | −3.12311 | −0.140373 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −32.0000 | −1.43540 | ||||||||
\(498\) | 13.3693 | 0.599093 | ||||||||
\(499\) | 36.9848 | 1.65567 | 0.827835 | − | 0.560972i | \(-0.189573\pi\) | ||||
0.827835 | + | 0.560972i | \(0.189573\pi\) | |||||||
\(500\) | 1.00000 | 0.0447214 | ||||||||
\(501\) | 8.00000 | 0.357414 | ||||||||
\(502\) | 17.3693 | 0.775231 | ||||||||
\(503\) | 42.7386 | 1.90562 | 0.952811 | − | 0.303565i | \(-0.0981769\pi\) | ||||
0.952811 | + | 0.303565i | \(0.0981769\pi\) | |||||||
\(504\) | 3.12311 | 0.139114 | ||||||||
\(505\) | 0.246211 | 0.0109563 | ||||||||
\(506\) | −3.12311 | −0.138839 | ||||||||
\(507\) | 9.00000 | 0.399704 | ||||||||
\(508\) | −5.75379 | −0.255283 | ||||||||
\(509\) | 34.0000 | 1.50702 | 0.753512 | − | 0.657434i | \(-0.228358\pi\) | ||||
0.753512 | + | 0.657434i | \(0.228358\pi\) | |||||||
\(510\) | 1.12311 | 0.0497320 | ||||||||
\(511\) | −13.2614 | −0.586648 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | −4.00000 | −0.176604 | ||||||||
\(514\) | 8.24621 | 0.363725 | ||||||||
\(515\) | −9.36932 | −0.412861 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 24.9848 | 1.09883 | ||||||||
\(518\) | 3.50758 | 0.154114 | ||||||||
\(519\) | −20.2462 | −0.888710 | ||||||||
\(520\) | 2.00000 | 0.0877058 | ||||||||
\(521\) | 17.1231 | 0.750177 | 0.375088 | − | 0.926989i | \(-0.377612\pi\) | ||||
0.375088 | + | 0.926989i | \(0.377612\pi\) | |||||||
\(522\) | 2.00000 | 0.0875376 | ||||||||
\(523\) | 4.49242 | 0.196440 | 0.0982200 | − | 0.995165i | \(-0.468685\pi\) | ||||
0.0982200 | + | 0.995165i | \(0.468685\pi\) | |||||||
\(524\) | −4.00000 | −0.174741 | ||||||||
\(525\) | −3.12311 | −0.136304 | ||||||||
\(526\) | −6.24621 | −0.272348 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 3.12311 | 0.135916 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 12.2462 | 0.531941 | ||||||||
\(531\) | 2.24621 | 0.0974773 | ||||||||
\(532\) | 12.4924 | 0.541615 | ||||||||
\(533\) | 4.00000 | 0.173259 | ||||||||
\(534\) | 5.12311 | 0.221698 | ||||||||
\(535\) | −13.3693 | −0.578006 | ||||||||
\(536\) | −8.00000 | −0.345547 | ||||||||
\(537\) | 8.49242 | 0.366475 | ||||||||
\(538\) | 0.246211 | 0.0106149 | ||||||||
\(539\) | −8.60037 | −0.370444 | ||||||||
\(540\) | −1.00000 | −0.0430331 | ||||||||
\(541\) | −32.2462 | −1.38637 | −0.693186 | − | 0.720758i | \(-0.743794\pi\) | ||||
−0.693186 | + | 0.720758i | \(0.743794\pi\) | |||||||
\(542\) | −6.24621 | −0.268298 | ||||||||
\(543\) | −10.8769 | −0.466772 | ||||||||
\(544\) | −1.12311 | −0.0481528 | ||||||||
\(545\) | 2.87689 | 0.123233 | ||||||||
\(546\) | −6.24621 | −0.267313 | ||||||||
\(547\) | −32.4924 | −1.38928 | −0.694638 | − | 0.719360i | \(-0.744435\pi\) | ||||
−0.694638 | + | 0.719360i | \(0.744435\pi\) | |||||||
\(548\) | −10.8769 | −0.464638 | ||||||||
\(549\) | 9.12311 | 0.389365 | ||||||||
\(550\) | −3.12311 | −0.133170 | ||||||||
\(551\) | 8.00000 | 0.340811 | ||||||||
\(552\) | −1.00000 | −0.0425628 | ||||||||
\(553\) | 9.75379 | 0.414773 | ||||||||
\(554\) | 3.75379 | 0.159483 | ||||||||
\(555\) | −1.12311 | −0.0476732 | ||||||||
\(556\) | 16.4924 | 0.699435 | ||||||||
\(557\) | −2.00000 | −0.0847427 | −0.0423714 | − | 0.999102i | \(-0.513491\pi\) | ||||
−0.0423714 | + | 0.999102i | \(0.513491\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 3.12311 | 0.131975 | ||||||||
\(561\) | −3.50758 | −0.148090 | ||||||||
\(562\) | −21.1231 | −0.891024 | ||||||||
\(563\) | −13.3693 | −0.563450 | −0.281725 | − | 0.959495i | \(-0.590907\pi\) | ||||
−0.281725 | + | 0.959495i | \(0.590907\pi\) | |||||||
\(564\) | 8.00000 | 0.336861 | ||||||||
\(565\) | −9.12311 | −0.383812 | ||||||||
\(566\) | 14.2462 | 0.598813 | ||||||||
\(567\) | 3.12311 | 0.131158 | ||||||||
\(568\) | −10.2462 | −0.429921 | ||||||||
\(569\) | 18.8769 | 0.791361 | 0.395680 | − | 0.918388i | \(-0.370509\pi\) | ||||
0.395680 | + | 0.918388i | \(0.370509\pi\) | |||||||
\(570\) | −4.00000 | −0.167542 | ||||||||
\(571\) | −14.7386 | −0.616793 | −0.308396 | − | 0.951258i | \(-0.599792\pi\) | ||||
−0.308396 | + | 0.951258i | \(0.599792\pi\) | |||||||
\(572\) | −6.24621 | −0.261167 | ||||||||
\(573\) | −12.4924 | −0.521878 | ||||||||
\(574\) | 6.24621 | 0.260712 | ||||||||
\(575\) | 1.00000 | 0.0417029 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | −18.4924 | −0.769850 | −0.384925 | − | 0.922948i | \(-0.625773\pi\) | ||||
−0.384925 | + | 0.922948i | \(0.625773\pi\) | |||||||
\(578\) | −15.7386 | −0.654641 | ||||||||
\(579\) | −8.24621 | −0.342701 | ||||||||
\(580\) | 2.00000 | 0.0830455 | ||||||||
\(581\) | −41.7538 | −1.73224 | ||||||||
\(582\) | 16.2462 | 0.673427 | ||||||||
\(583\) | −38.2462 | −1.58400 | ||||||||
\(584\) | −4.24621 | −0.175709 | ||||||||
\(585\) | 2.00000 | 0.0826898 | ||||||||
\(586\) | 28.2462 | 1.16684 | ||||||||
\(587\) | −26.2462 | −1.08330 | −0.541649 | − | 0.840605i | \(-0.682200\pi\) | ||||
−0.541649 | + | 0.840605i | \(0.682200\pi\) | |||||||
\(588\) | −2.75379 | −0.113564 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 2.24621 | 0.0924751 | ||||||||
\(591\) | 10.0000 | 0.411345 | ||||||||
\(592\) | 1.12311 | 0.0461594 | ||||||||
\(593\) | 24.2462 | 0.995673 | 0.497836 | − | 0.867271i | \(-0.334128\pi\) | ||||
0.497836 | + | 0.867271i | \(0.334128\pi\) | |||||||
\(594\) | 3.12311 | 0.128143 | ||||||||
\(595\) | −3.50758 | −0.143797 | ||||||||
\(596\) | −10.0000 | −0.409616 | ||||||||
\(597\) | −19.1231 | −0.782657 | ||||||||
\(598\) | 2.00000 | 0.0817861 | ||||||||
\(599\) | 10.2462 | 0.418649 | 0.209324 | − | 0.977846i | \(-0.432874\pi\) | ||||
0.209324 | + | 0.977846i | \(0.432874\pi\) | |||||||
\(600\) | −1.00000 | −0.0408248 | ||||||||
\(601\) | −6.00000 | −0.244745 | −0.122373 | − | 0.992484i | \(-0.539050\pi\) | ||||
−0.122373 | + | 0.992484i | \(0.539050\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −8.00000 | −0.325785 | ||||||||
\(604\) | 6.24621 | 0.254155 | ||||||||
\(605\) | −1.24621 | −0.0506657 | ||||||||
\(606\) | −0.246211 | −0.0100016 | ||||||||
\(607\) | −22.7386 | −0.922933 | −0.461466 | − | 0.887158i | \(-0.652676\pi\) | ||||
−0.461466 | + | 0.887158i | \(0.652676\pi\) | |||||||
\(608\) | 4.00000 | 0.162221 | ||||||||
\(609\) | −6.24621 | −0.253109 | ||||||||
\(610\) | 9.12311 | 0.369384 | ||||||||
\(611\) | −16.0000 | −0.647291 | ||||||||
\(612\) | −1.12311 | −0.0453989 | ||||||||
\(613\) | 34.8769 | 1.40866 | 0.704332 | − | 0.709870i | \(-0.251247\pi\) | ||||
0.704332 | + | 0.709870i | \(0.251247\pi\) | |||||||
\(614\) | −32.4924 | −1.31129 | ||||||||
\(615\) | −2.00000 | −0.0806478 | ||||||||
\(616\) | −9.75379 | −0.392991 | ||||||||
\(617\) | −34.1080 | −1.37313 | −0.686567 | − | 0.727066i | \(-0.740883\pi\) | ||||
−0.686567 | + | 0.727066i | \(0.740883\pi\) | |||||||
\(618\) | 9.36932 | 0.376889 | ||||||||
\(619\) | −36.0000 | −1.44696 | −0.723481 | − | 0.690344i | \(-0.757459\pi\) | ||||
−0.723481 | + | 0.690344i | \(0.757459\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1.00000 | −0.0401286 | ||||||||
\(622\) | −22.7386 | −0.911736 | ||||||||
\(623\) | −16.0000 | −0.641026 | ||||||||
\(624\) | −2.00000 | −0.0800641 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −22.4924 | −0.898978 | ||||||||
\(627\) | 12.4924 | 0.498899 | ||||||||
\(628\) | 9.12311 | 0.364052 | ||||||||
\(629\) | −1.26137 | −0.0502940 | ||||||||
\(630\) | 3.12311 | 0.124428 | ||||||||
\(631\) | −14.6307 | −0.582438 | −0.291219 | − | 0.956656i | \(-0.594061\pi\) | ||||
−0.291219 | + | 0.956656i | \(0.594061\pi\) | |||||||
\(632\) | 3.12311 | 0.124230 | ||||||||
\(633\) | 16.4924 | 0.655515 | ||||||||
\(634\) | −28.7386 | −1.14136 | ||||||||
\(635\) | −5.75379 | −0.228332 | ||||||||
\(636\) | −12.2462 | −0.485594 | ||||||||
\(637\) | 5.50758 | 0.218218 | ||||||||
\(638\) | −6.24621 | −0.247290 | ||||||||
\(639\) | −10.2462 | −0.405334 | ||||||||
\(640\) | 1.00000 | 0.0395285 | ||||||||
\(641\) | 15.3693 | 0.607052 | 0.303526 | − | 0.952823i | \(-0.401836\pi\) | ||||
0.303526 | + | 0.952823i | \(0.401836\pi\) | |||||||
\(642\) | 13.3693 | 0.527645 | ||||||||
\(643\) | 3.50758 | 0.138325 | 0.0691627 | − | 0.997605i | \(-0.477967\pi\) | ||||
0.0691627 | + | 0.997605i | \(0.477967\pi\) | |||||||
\(644\) | 3.12311 | 0.123068 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −4.49242 | −0.176752 | ||||||||
\(647\) | 44.4924 | 1.74918 | 0.874589 | − | 0.484865i | \(-0.161131\pi\) | ||||
0.874589 | + | 0.484865i | \(0.161131\pi\) | |||||||
\(648\) | 1.00000 | 0.0392837 | ||||||||
\(649\) | −7.01515 | −0.275369 | ||||||||
\(650\) | 2.00000 | 0.0784465 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −12.0000 | −0.469956 | ||||||||
\(653\) | −22.4924 | −0.880197 | −0.440098 | − | 0.897950i | \(-0.645056\pi\) | ||||
−0.440098 | + | 0.897950i | \(0.645056\pi\) | |||||||
\(654\) | −2.87689 | −0.112495 | ||||||||
\(655\) | −4.00000 | −0.156293 | ||||||||
\(656\) | 2.00000 | 0.0780869 | ||||||||
\(657\) | −4.24621 | −0.165660 | ||||||||
\(658\) | −24.9848 | −0.974011 | ||||||||
\(659\) | 17.3693 | 0.676613 | 0.338306 | − | 0.941036i | \(-0.390146\pi\) | ||||
0.338306 | + | 0.941036i | \(0.390146\pi\) | |||||||
\(660\) | 3.12311 | 0.121567 | ||||||||
\(661\) | −23.8617 | −0.928114 | −0.464057 | − | 0.885805i | \(-0.653607\pi\) | ||||
−0.464057 | + | 0.885805i | \(0.653607\pi\) | |||||||
\(662\) | 0.492423 | 0.0191385 | ||||||||
\(663\) | 2.24621 | 0.0872356 | ||||||||
\(664\) | −13.3693 | −0.518830 | ||||||||
\(665\) | 12.4924 | 0.484435 | ||||||||
\(666\) | 1.12311 | 0.0435195 | ||||||||
\(667\) | 2.00000 | 0.0774403 | ||||||||
\(668\) | −8.00000 | −0.309529 | ||||||||
\(669\) | 10.2462 | 0.396141 | ||||||||
\(670\) | −8.00000 | −0.309067 | ||||||||
\(671\) | −28.4924 | −1.09994 | ||||||||
\(672\) | −3.12311 | −0.120476 | ||||||||
\(673\) | 18.9848 | 0.731812 | 0.365906 | − | 0.930652i | \(-0.380759\pi\) | ||||
0.365906 | + | 0.930652i | \(0.380759\pi\) | |||||||
\(674\) | 26.4924 | 1.02045 | ||||||||
\(675\) | −1.00000 | −0.0384900 | ||||||||
\(676\) | −9.00000 | −0.346154 | ||||||||
\(677\) | −13.5076 | −0.519138 | −0.259569 | − | 0.965725i | \(-0.583581\pi\) | ||||
−0.259569 | + | 0.965725i | \(0.583581\pi\) | |||||||
\(678\) | 9.12311 | 0.350371 | ||||||||
\(679\) | −50.7386 | −1.94717 | ||||||||
\(680\) | −1.12311 | −0.0430691 | ||||||||
\(681\) | 5.36932 | 0.205753 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 34.2462 | 1.31039 | 0.655197 | − | 0.755458i | \(-0.272585\pi\) | ||||
0.655197 | + | 0.755458i | \(0.272585\pi\) | |||||||
\(684\) | 4.00000 | 0.152944 | ||||||||
\(685\) | −10.8769 | −0.415585 | ||||||||
\(686\) | −13.2614 | −0.506321 | ||||||||
\(687\) | −23.3693 | −0.891595 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 24.4924 | 0.933087 | ||||||||
\(690\) | −1.00000 | −0.0380693 | ||||||||
\(691\) | 20.0000 | 0.760836 | 0.380418 | − | 0.924815i | \(-0.375780\pi\) | ||||
0.380418 | + | 0.924815i | \(0.375780\pi\) | |||||||
\(692\) | 20.2462 | 0.769645 | ||||||||
\(693\) | −9.75379 | −0.370516 | ||||||||
\(694\) | 14.7386 | 0.559471 | ||||||||
\(695\) | 16.4924 | 0.625593 | ||||||||
\(696\) | −2.00000 | −0.0758098 | ||||||||
\(697\) | −2.24621 | −0.0850813 | ||||||||
\(698\) | 24.7386 | 0.936371 | ||||||||
\(699\) | −28.7386 | −1.08699 | ||||||||
\(700\) | 3.12311 | 0.118042 | ||||||||
\(701\) | −19.7538 | −0.746090 | −0.373045 | − | 0.927813i | \(-0.621686\pi\) | ||||
−0.373045 | + | 0.927813i | \(0.621686\pi\) | |||||||
\(702\) | −2.00000 | −0.0754851 | ||||||||
\(703\) | 4.49242 | 0.169435 | ||||||||
\(704\) | −3.12311 | −0.117706 | ||||||||
\(705\) | 8.00000 | 0.301297 | ||||||||
\(706\) | −14.0000 | −0.526897 | ||||||||
\(707\) | 0.768944 | 0.0289191 | ||||||||
\(708\) | −2.24621 | −0.0844178 | ||||||||
\(709\) | −11.3693 | −0.426984 | −0.213492 | − | 0.976945i | \(-0.568484\pi\) | ||||
−0.213492 | + | 0.976945i | \(0.568484\pi\) | |||||||
\(710\) | −10.2462 | −0.384533 | ||||||||
\(711\) | 3.12311 | 0.117126 | ||||||||
\(712\) | −5.12311 | −0.191997 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 3.50758 | 0.131268 | ||||||||
\(715\) | −6.24621 | −0.233595 | ||||||||
\(716\) | −8.49242 | −0.317377 | ||||||||
\(717\) | 18.2462 | 0.681417 | ||||||||
\(718\) | 20.4924 | 0.764770 | ||||||||
\(719\) | −26.2462 | −0.978819 | −0.489409 | − | 0.872054i | \(-0.662788\pi\) | ||||
−0.489409 | + | 0.872054i | \(0.662788\pi\) | |||||||
\(720\) | 1.00000 | 0.0372678 | ||||||||
\(721\) | −29.2614 | −1.08975 | ||||||||
\(722\) | −3.00000 | −0.111648 | ||||||||
\(723\) | −30.4924 | −1.13403 | ||||||||
\(724\) | 10.8769 | 0.404237 | ||||||||
\(725\) | 2.00000 | 0.0742781 | ||||||||
\(726\) | 1.24621 | 0.0462512 | ||||||||
\(727\) | −29.8617 | −1.10751 | −0.553755 | − | 0.832679i | \(-0.686806\pi\) | ||||
−0.553755 | + | 0.832679i | \(0.686806\pi\) | |||||||
\(728\) | 6.24621 | 0.231500 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −4.24621 | −0.157159 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | −9.12311 | −0.337200 | ||||||||
\(733\) | 43.8617 | 1.62007 | 0.810035 | − | 0.586381i | \(-0.199448\pi\) | ||||
0.810035 | + | 0.586381i | \(0.199448\pi\) | |||||||
\(734\) | 4.87689 | 0.180009 | ||||||||
\(735\) | −2.75379 | −0.101575 | ||||||||
\(736\) | 1.00000 | 0.0368605 | ||||||||
\(737\) | 24.9848 | 0.920329 | ||||||||
\(738\) | 2.00000 | 0.0736210 | ||||||||
\(739\) | 7.50758 | 0.276171 | 0.138085 | − | 0.990420i | \(-0.455905\pi\) | ||||
0.138085 | + | 0.990420i | \(0.455905\pi\) | |||||||
\(740\) | 1.12311 | 0.0412862 | ||||||||
\(741\) | −8.00000 | −0.293887 | ||||||||
\(742\) | 38.2462 | 1.40406 | ||||||||
\(743\) | 34.7386 | 1.27444 | 0.637218 | − | 0.770683i | \(-0.280085\pi\) | ||||
0.637218 | + | 0.770683i | \(0.280085\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −10.0000 | −0.366372 | ||||||||
\(746\) | −11.3693 | −0.416260 | ||||||||
\(747\) | −13.3693 | −0.489158 | ||||||||
\(748\) | 3.50758 | 0.128250 | ||||||||
\(749\) | −41.7538 | −1.52565 | ||||||||
\(750\) | −1.00000 | −0.0365148 | ||||||||
\(751\) | −13.8617 | −0.505822 | −0.252911 | − | 0.967490i | \(-0.581388\pi\) | ||||
−0.252911 | + | 0.967490i | \(0.581388\pi\) | |||||||
\(752\) | −8.00000 | −0.291730 | ||||||||
\(753\) | −17.3693 | −0.632973 | ||||||||
\(754\) | 4.00000 | 0.145671 | ||||||||
\(755\) | 6.24621 | 0.227323 | ||||||||
\(756\) | −3.12311 | −0.113586 | ||||||||
\(757\) | −47.8617 | −1.73956 | −0.869782 | − | 0.493436i | \(-0.835741\pi\) | ||||
−0.869782 | + | 0.493436i | \(0.835741\pi\) | |||||||
\(758\) | 4.00000 | 0.145287 | ||||||||
\(759\) | 3.12311 | 0.113362 | ||||||||
\(760\) | 4.00000 | 0.145095 | ||||||||
\(761\) | −31.7538 | −1.15107 | −0.575537 | − | 0.817776i | \(-0.695207\pi\) | ||||
−0.575537 | + | 0.817776i | \(0.695207\pi\) | |||||||
\(762\) | 5.75379 | 0.208438 | ||||||||
\(763\) | 8.98485 | 0.325273 | ||||||||
\(764\) | 12.4924 | 0.451960 | ||||||||
\(765\) | −1.12311 | −0.0406060 | ||||||||
\(766\) | 30.2462 | 1.09284 | ||||||||
\(767\) | 4.49242 | 0.162212 | ||||||||
\(768\) | −1.00000 | −0.0360844 | ||||||||
\(769\) | 28.7386 | 1.03634 | 0.518171 | − | 0.855277i | \(-0.326613\pi\) | ||||
0.518171 | + | 0.855277i | \(0.326613\pi\) | |||||||
\(770\) | −9.75379 | −0.351502 | ||||||||
\(771\) | −8.24621 | −0.296980 | ||||||||
\(772\) | 8.24621 | 0.296788 | ||||||||
\(773\) | −19.7538 | −0.710494 | −0.355247 | − | 0.934772i | \(-0.615603\pi\) | ||||
−0.355247 | + | 0.934772i | \(0.615603\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −16.2462 | −0.583205 | ||||||||
\(777\) | −3.50758 | −0.125834 | ||||||||
\(778\) | −18.0000 | −0.645331 | ||||||||
\(779\) | 8.00000 | 0.286630 | ||||||||
\(780\) | −2.00000 | −0.0716115 | ||||||||
\(781\) | 32.0000 | 1.14505 | ||||||||
\(782\) | −1.12311 | −0.0401622 | ||||||||
\(783\) | −2.00000 | −0.0714742 | ||||||||
\(784\) | 2.75379 | 0.0983496 | ||||||||
\(785\) | 9.12311 | 0.325618 | ||||||||
\(786\) | 4.00000 | 0.142675 | ||||||||
\(787\) | 48.0000 | 1.71102 | 0.855508 | − | 0.517790i | \(-0.173245\pi\) | ||||
0.855508 | + | 0.517790i | \(0.173245\pi\) | |||||||
\(788\) | −10.0000 | −0.356235 | ||||||||
\(789\) | 6.24621 | 0.222371 | ||||||||
\(790\) | 3.12311 | 0.111115 | ||||||||
\(791\) | −28.4924 | −1.01307 | ||||||||
\(792\) | −3.12311 | −0.110975 | ||||||||
\(793\) | 18.2462 | 0.647942 | ||||||||
\(794\) | −1.50758 | −0.0535019 | ||||||||
\(795\) | −12.2462 | −0.434328 | ||||||||
\(796\) | 19.1231 | 0.677801 | ||||||||
\(797\) | 10.4924 | 0.371661 | 0.185830 | − | 0.982582i | \(-0.440503\pi\) | ||||
0.185830 | + | 0.982582i | \(0.440503\pi\) | |||||||
\(798\) | −12.4924 | −0.442227 | ||||||||
\(799\) | 8.98485 | 0.317861 | ||||||||
\(800\) | 1.00000 | 0.0353553 | ||||||||
\(801\) | −5.12311 | −0.181016 | ||||||||
\(802\) | 7.36932 | 0.260220 | ||||||||
\(803\) | 13.2614 | 0.467983 | ||||||||
\(804\) | 8.00000 | 0.282138 | ||||||||
\(805\) | 3.12311 | 0.110075 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −0.246211 | −0.00866705 | ||||||||
\(808\) | 0.246211 | 0.00866168 | ||||||||
\(809\) | −12.2462 | −0.430554 | −0.215277 | − | 0.976553i | \(-0.569065\pi\) | ||||
−0.215277 | + | 0.976553i | \(0.569065\pi\) | |||||||
\(810\) | 1.00000 | 0.0351364 | ||||||||
\(811\) | −36.0000 | −1.26413 | −0.632065 | − | 0.774915i | \(-0.717793\pi\) | ||||
−0.632065 | + | 0.774915i | \(0.717793\pi\) | |||||||
\(812\) | 6.24621 | 0.219199 | ||||||||
\(813\) | 6.24621 | 0.219064 | ||||||||
\(814\) | −3.50758 | −0.122941 | ||||||||
\(815\) | −12.0000 | −0.420342 | ||||||||
\(816\) | 1.12311 | 0.0393166 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 0.246211 | 0.00860857 | ||||||||
\(819\) | 6.24621 | 0.218260 | ||||||||
\(820\) | 2.00000 | 0.0698430 | ||||||||
\(821\) | −36.2462 | −1.26500 | −0.632501 | − | 0.774560i | \(-0.717971\pi\) | ||||
−0.632501 | + | 0.774560i | \(0.717971\pi\) | |||||||
\(822\) | 10.8769 | 0.379375 | ||||||||
\(823\) | −4.00000 | −0.139431 | −0.0697156 | − | 0.997567i | \(-0.522209\pi\) | ||||
−0.0697156 | + | 0.997567i | \(0.522209\pi\) | |||||||
\(824\) | −9.36932 | −0.326396 | ||||||||
\(825\) | 3.12311 | 0.108733 | ||||||||
\(826\) | 7.01515 | 0.244088 | ||||||||
\(827\) | 8.87689 | 0.308680 | 0.154340 | − | 0.988018i | \(-0.450675\pi\) | ||||
0.154340 | + | 0.988018i | \(0.450675\pi\) | |||||||
\(828\) | 1.00000 | 0.0347524 | ||||||||
\(829\) | 15.7538 | 0.547152 | 0.273576 | − | 0.961850i | \(-0.411794\pi\) | ||||
0.273576 | + | 0.961850i | \(0.411794\pi\) | |||||||
\(830\) | −13.3693 | −0.464056 | ||||||||
\(831\) | −3.75379 | −0.130217 | ||||||||
\(832\) | 2.00000 | 0.0693375 | ||||||||
\(833\) | −3.09280 | −0.107159 | ||||||||
\(834\) | −16.4924 | −0.571086 | ||||||||
\(835\) | −8.00000 | −0.276851 | ||||||||
\(836\) | −12.4924 | −0.432059 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 39.6155 | 1.36850 | ||||||||
\(839\) | −9.75379 | −0.336738 | −0.168369 | − | 0.985724i | \(-0.553850\pi\) | ||||
−0.168369 | + | 0.985724i | \(0.553850\pi\) | |||||||
\(840\) | −3.12311 | −0.107757 | ||||||||
\(841\) | −25.0000 | −0.862069 | ||||||||
\(842\) | −11.3693 | −0.391813 | ||||||||
\(843\) | 21.1231 | 0.727518 | ||||||||
\(844\) | −16.4924 | −0.567693 | ||||||||
\(845\) | −9.00000 | −0.309609 | ||||||||
\(846\) | −8.00000 | −0.275046 | ||||||||
\(847\) | −3.89205 | −0.133732 | ||||||||
\(848\) | 12.2462 | 0.420537 | ||||||||
\(849\) | −14.2462 | −0.488929 | ||||||||
\(850\) | −1.12311 | −0.0385222 | ||||||||
\(851\) | 1.12311 | 0.0384996 | ||||||||
\(852\) | 10.2462 | 0.351029 | ||||||||
\(853\) | −6.00000 | −0.205436 | −0.102718 | − | 0.994711i | \(-0.532754\pi\) | ||||
−0.102718 | + | 0.994711i | \(0.532754\pi\) | |||||||
\(854\) | 28.4924 | 0.974991 | ||||||||
\(855\) | 4.00000 | 0.136797 | ||||||||
\(856\) | −13.3693 | −0.456954 | ||||||||
\(857\) | −24.7386 | −0.845056 | −0.422528 | − | 0.906350i | \(-0.638857\pi\) | ||||
−0.422528 | + | 0.906350i | \(0.638857\pi\) | |||||||
\(858\) | 6.24621 | 0.213242 | ||||||||
\(859\) | 15.5076 | 0.529112 | 0.264556 | − | 0.964370i | \(-0.414775\pi\) | ||||
0.264556 | + | 0.964370i | \(0.414775\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −6.24621 | −0.212870 | ||||||||
\(862\) | 9.75379 | 0.332215 | ||||||||
\(863\) | −16.9848 | −0.578171 | −0.289085 | − | 0.957303i | \(-0.593351\pi\) | ||||
−0.289085 | + | 0.957303i | \(0.593351\pi\) | |||||||
\(864\) | −1.00000 | −0.0340207 | ||||||||
\(865\) | 20.2462 | 0.688392 | ||||||||
\(866\) | −22.4924 | −0.764324 | ||||||||
\(867\) | 15.7386 | 0.534512 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −9.75379 | −0.330875 | ||||||||
\(870\) | −2.00000 | −0.0678064 | ||||||||
\(871\) | −16.0000 | −0.542139 | ||||||||
\(872\) | 2.87689 | 0.0974239 | ||||||||
\(873\) | −16.2462 | −0.549851 | ||||||||
\(874\) | 4.00000 | 0.135302 | ||||||||
\(875\) | 3.12311 | 0.105580 | ||||||||
\(876\) | 4.24621 | 0.143466 | ||||||||
\(877\) | 52.7386 | 1.78086 | 0.890429 | − | 0.455123i | \(-0.150405\pi\) | ||||
0.890429 | + | 0.455123i | \(0.150405\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −28.2462 | −0.952721 | ||||||||
\(880\) | −3.12311 | −0.105280 | ||||||||
\(881\) | −9.61553 | −0.323955 | −0.161978 | − | 0.986794i | \(-0.551787\pi\) | ||||
−0.161978 | + | 0.986794i | \(0.551787\pi\) | |||||||
\(882\) | 2.75379 | 0.0927249 | ||||||||
\(883\) | 44.9848 | 1.51386 | 0.756930 | − | 0.653496i | \(-0.226698\pi\) | ||||
0.756930 | + | 0.653496i | \(0.226698\pi\) | |||||||
\(884\) | −2.24621 | −0.0755483 | ||||||||
\(885\) | −2.24621 | −0.0755056 | ||||||||
\(886\) | 8.49242 | 0.285309 | ||||||||
\(887\) | 19.5076 | 0.655000 | 0.327500 | − | 0.944851i | \(-0.393794\pi\) | ||||
0.327500 | + | 0.944851i | \(0.393794\pi\) | |||||||
\(888\) | −1.12311 | −0.0376890 | ||||||||
\(889\) | −17.9697 | −0.602684 | ||||||||
\(890\) | −5.12311 | −0.171727 | ||||||||
\(891\) | −3.12311 | −0.104628 | ||||||||
\(892\) | −10.2462 | −0.343069 | ||||||||
\(893\) | −32.0000 | −1.07084 | ||||||||
\(894\) | 10.0000 | 0.334450 | ||||||||
\(895\) | −8.49242 | −0.283870 | ||||||||
\(896\) | 3.12311 | 0.104336 | ||||||||
\(897\) | −2.00000 | −0.0667781 | ||||||||
\(898\) | 22.4924 | 0.750582 | ||||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 1.00000 | 0.0333333 | ||||||||
\(901\) | −13.7538 | −0.458205 | ||||||||
\(902\) | −6.24621 | −0.207976 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −9.12311 | −0.303430 | ||||||||
\(905\) | 10.8769 | 0.361560 | ||||||||
\(906\) | −6.24621 | −0.207516 | ||||||||
\(907\) | 54.2462 | 1.80122 | 0.900608 | − | 0.434632i | \(-0.143122\pi\) | ||||
0.900608 | + | 0.434632i | \(0.143122\pi\) | |||||||
\(908\) | −5.36932 | −0.178187 | ||||||||
\(909\) | 0.246211 | 0.00816631 | ||||||||
\(910\) | 6.24621 | 0.207060 | ||||||||
\(911\) | −30.2462 | −1.00210 | −0.501051 | − | 0.865418i | \(-0.667053\pi\) | ||||
−0.501051 | + | 0.865418i | \(0.667053\pi\) | |||||||
\(912\) | −4.00000 | −0.132453 | ||||||||
\(913\) | 41.7538 | 1.38185 | ||||||||
\(914\) | 16.7386 | 0.553665 | ||||||||
\(915\) | −9.12311 | −0.301601 | ||||||||
\(916\) | 23.3693 | 0.772144 | ||||||||
\(917\) | −12.4924 | −0.412536 | ||||||||
\(918\) | 1.12311 | 0.0370680 | ||||||||
\(919\) | 19.1231 | 0.630813 | 0.315407 | − | 0.948957i | \(-0.397859\pi\) | ||||
0.315407 | + | 0.948957i | \(0.397859\pi\) | |||||||
\(920\) | 1.00000 | 0.0329690 | ||||||||
\(921\) | 32.4924 | 1.07066 | ||||||||
\(922\) | −16.7386 | −0.551258 | ||||||||
\(923\) | −20.4924 | −0.674516 | ||||||||
\(924\) | 9.75379 | 0.320876 | ||||||||
\(925\) | 1.12311 | 0.0369275 | ||||||||
\(926\) | −36.0000 | −1.18303 | ||||||||
\(927\) | −9.36932 | −0.307729 | ||||||||
\(928\) | 2.00000 | 0.0656532 | ||||||||
\(929\) | 34.9848 | 1.14782 | 0.573908 | − | 0.818920i | \(-0.305427\pi\) | ||||
0.573908 | + | 0.818920i | \(0.305427\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 11.0152 | 0.361007 | ||||||||
\(932\) | 28.7386 | 0.941365 | ||||||||
\(933\) | 22.7386 | 0.744429 | ||||||||
\(934\) | 21.3693 | 0.699225 | ||||||||
\(935\) | 3.50758 | 0.114710 | ||||||||
\(936\) | 2.00000 | 0.0653720 | ||||||||
\(937\) | 32.7386 | 1.06952 | 0.534762 | − | 0.845003i | \(-0.320401\pi\) | ||||
0.534762 | + | 0.845003i | \(0.320401\pi\) | |||||||
\(938\) | −24.9848 | −0.815784 | ||||||||
\(939\) | 22.4924 | 0.734012 | ||||||||
\(940\) | −8.00000 | −0.260931 | ||||||||
\(941\) | 26.4924 | 0.863628 | 0.431814 | − | 0.901963i | \(-0.357874\pi\) | ||||
0.431814 | + | 0.901963i | \(0.357874\pi\) | |||||||
\(942\) | −9.12311 | −0.297247 | ||||||||
\(943\) | 2.00000 | 0.0651290 | ||||||||
\(944\) | 2.24621 | 0.0731079 | ||||||||
\(945\) | −3.12311 | −0.101595 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 5.75379 | 0.186973 | 0.0934865 | − | 0.995621i | \(-0.470199\pi\) | ||||
0.0934865 | + | 0.995621i | \(0.470199\pi\) | |||||||
\(948\) | −3.12311 | −0.101434 | ||||||||
\(949\) | −8.49242 | −0.275676 | ||||||||
\(950\) | 4.00000 | 0.129777 | ||||||||
\(951\) | 28.7386 | 0.931914 | ||||||||
\(952\) | −3.50758 | −0.113681 | ||||||||
\(953\) | 23.8617 | 0.772958 | 0.386479 | − | 0.922298i | \(-0.373691\pi\) | ||||
0.386479 | + | 0.922298i | \(0.373691\pi\) | |||||||
\(954\) | 12.2462 | 0.396486 | ||||||||
\(955\) | 12.4924 | 0.404245 | ||||||||
\(956\) | −18.2462 | −0.590125 | ||||||||
\(957\) | 6.24621 | 0.201911 | ||||||||
\(958\) | 12.4924 | 0.403612 | ||||||||
\(959\) | −33.9697 | −1.09694 | ||||||||
\(960\) | −1.00000 | −0.0322749 | ||||||||
\(961\) | −31.0000 | −1.00000 | ||||||||
\(962\) | 2.24621 | 0.0724208 | ||||||||
\(963\) | −13.3693 | −0.430820 | ||||||||
\(964\) | 30.4924 | 0.982095 | ||||||||
\(965\) | 8.24621 | 0.265455 | ||||||||
\(966\) | −3.12311 | −0.100484 | ||||||||
\(967\) | 60.9848 | 1.96114 | 0.980570 | − | 0.196168i | \(-0.0628500\pi\) | ||||
0.980570 | + | 0.196168i | \(0.0628500\pi\) | |||||||
\(968\) | −1.24621 | −0.0400547 | ||||||||
\(969\) | 4.49242 | 0.144317 | ||||||||
\(970\) | −16.2462 | −0.521634 | ||||||||
\(971\) | 43.1231 | 1.38389 | 0.691943 | − | 0.721952i | \(-0.256755\pi\) | ||||
0.691943 | + | 0.721952i | \(0.256755\pi\) | |||||||
\(972\) | −1.00000 | −0.0320750 | ||||||||
\(973\) | 51.5076 | 1.65126 | ||||||||
\(974\) | 7.50758 | 0.240558 | ||||||||
\(975\) | −2.00000 | −0.0640513 | ||||||||
\(976\) | 9.12311 | 0.292023 | ||||||||
\(977\) | −35.8617 | −1.14732 | −0.573659 | − | 0.819094i | \(-0.694477\pi\) | ||||
−0.573659 | + | 0.819094i | \(0.694477\pi\) | |||||||
\(978\) | 12.0000 | 0.383718 | ||||||||
\(979\) | 16.0000 | 0.511362 | ||||||||
\(980\) | 2.75379 | 0.0879666 | ||||||||
\(981\) | 2.87689 | 0.0918522 | ||||||||
\(982\) | −12.0000 | −0.382935 | ||||||||
\(983\) | −9.75379 | −0.311098 | −0.155549 | − | 0.987828i | \(-0.549715\pi\) | ||||
−0.155549 | + | 0.987828i | \(0.549715\pi\) | |||||||
\(984\) | −2.00000 | −0.0637577 | ||||||||
\(985\) | −10.0000 | −0.318626 | ||||||||
\(986\) | −2.24621 | −0.0715339 | ||||||||
\(987\) | 24.9848 | 0.795276 | ||||||||
\(988\) | 8.00000 | 0.254514 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | −3.12311 | −0.0992588 | ||||||||
\(991\) | 61.4773 | 1.95289 | 0.976445 | − | 0.215767i | \(-0.0692252\pi\) | ||||
0.976445 | + | 0.215767i | \(0.0692252\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −0.492423 | −0.0156266 | ||||||||
\(994\) | −32.0000 | −1.01498 | ||||||||
\(995\) | 19.1231 | 0.606243 | ||||||||
\(996\) | 13.3693 | 0.423623 | ||||||||
\(997\) | 3.75379 | 0.118884 | 0.0594418 | − | 0.998232i | \(-0.481068\pi\) | ||||
0.0594418 | + | 0.998232i | \(0.481068\pi\) | |||||||
\(998\) | 36.9848 | 1.17073 | ||||||||
\(999\) | −1.12311 | −0.0355335 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 690.2.a.l.1.2 | ✓ | 2 | |
3.2 | odd | 2 | 2070.2.a.t.1.2 | 2 | |||
4.3 | odd | 2 | 5520.2.a.bs.1.1 | 2 | |||
5.2 | odd | 4 | 3450.2.d.v.2899.4 | 4 | |||
5.3 | odd | 4 | 3450.2.d.v.2899.1 | 4 | |||
5.4 | even | 2 | 3450.2.a.bi.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
690.2.a.l.1.2 | ✓ | 2 | 1.1 | even | 1 | trivial | |
2070.2.a.t.1.2 | 2 | 3.2 | odd | 2 | |||
3450.2.a.bi.1.1 | 2 | 5.4 | even | 2 | |||
3450.2.d.v.2899.1 | 4 | 5.3 | odd | 4 | |||
3450.2.d.v.2899.4 | 4 | 5.2 | odd | 4 | |||
5520.2.a.bs.1.1 | 2 | 4.3 | odd | 2 |