Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [882,2,Mod(361,882)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(882, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("882.361");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 882 = 2 \cdot 3^{2} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 882.g (of order \(3\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(7.04280545828\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 42) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 361.1 | ||
Root | \(0.500000 + 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 882.361 |
Dual form | 882.2.g.h.667.1 |
$q$-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 \(\left(\mathbb{Z}/882\mathbb{Z}\right)^\times\).
\(n\) | \(199\) | \(785\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.500000 | + | 0.866025i | 0.353553 | + | 0.612372i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −0.500000 | + | 0.866025i | −0.250000 | + | 0.433013i | ||||
\(5\) | −1.00000 | − | 1.73205i | −0.447214 | − | 0.774597i | 0.550990 | − | 0.834512i | \(-0.314250\pi\) |
−0.998203 | + | 0.0599153i | \(0.980917\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 1.00000 | − | 1.73205i | 0.316228 | − | 0.547723i | ||||
\(11\) | −2.00000 | + | 3.46410i | −0.603023 | + | 1.04447i | 0.389338 | + | 0.921095i | \(0.372704\pi\) |
−0.992361 | + | 0.123371i | \(0.960630\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 6.00000 | 1.66410 | 0.832050 | − | 0.554700i | \(-0.187167\pi\) | ||||
0.832050 | + | 0.554700i | \(0.187167\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.500000 | − | 0.866025i | −0.125000 | − | 0.216506i | ||||
\(17\) | 1.00000 | − | 1.73205i | 0.242536 | − | 0.420084i | −0.718900 | − | 0.695113i | \(-0.755354\pi\) |
0.961436 | + | 0.275029i | \(0.0886875\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.00000 | + | 3.46410i | 0.458831 | + | 0.794719i | 0.998899 | − | 0.0469020i | \(-0.0149348\pi\) |
−0.540068 | + | 0.841621i | \(0.681602\pi\) | |||||||
\(20\) | 2.00000 | 0.447214 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −4.00000 | −0.852803 | ||||||||
\(23\) | 4.00000 | + | 6.92820i | 0.834058 | + | 1.44463i | 0.894795 | + | 0.446476i | \(0.147321\pi\) |
−0.0607377 | + | 0.998154i | \(0.519345\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0.500000 | − | 0.866025i | 0.100000 | − | 0.173205i | ||||
\(26\) | 3.00000 | + | 5.19615i | 0.588348 | + | 1.01905i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.00000 | 0.371391 | 0.185695 | − | 0.982607i | \(-0.440546\pi\) | ||||
0.185695 | + | 0.982607i | \(0.440546\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(32\) | 0.500000 | − | 0.866025i | 0.0883883 | − | 0.153093i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 2.00000 | 0.342997 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 5.00000 | + | 8.66025i | 0.821995 | + | 1.42374i | 0.904194 | + | 0.427121i | \(0.140472\pi\) |
−0.0821995 | + | 0.996616i | \(0.526194\pi\) | |||||||
\(38\) | −2.00000 | + | 3.46410i | −0.324443 | + | 0.561951i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 1.00000 | + | 1.73205i | 0.158114 | + | 0.273861i | ||||
\(41\) | 6.00000 | 0.937043 | 0.468521 | − | 0.883452i | \(-0.344787\pi\) | ||||
0.468521 | + | 0.883452i | \(0.344787\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −4.00000 | −0.609994 | −0.304997 | − | 0.952353i | \(-0.598656\pi\) | ||||
−0.304997 | + | 0.952353i | \(0.598656\pi\) | |||||||
\(44\) | −2.00000 | − | 3.46410i | −0.301511 | − | 0.522233i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −4.00000 | + | 6.92820i | −0.589768 | + | 1.02151i | ||||
\(47\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 1.00000 | 0.141421 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −3.00000 | + | 5.19615i | −0.416025 | + | 0.720577i | ||||
\(53\) | 3.00000 | − | 5.19615i | 0.412082 | − | 0.713746i | −0.583036 | − | 0.812447i | \(-0.698135\pi\) |
0.995117 | + | 0.0987002i | \(0.0314685\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 8.00000 | 1.07872 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 1.00000 | + | 1.73205i | 0.131306 | + | 0.227429i | ||||
\(59\) | 2.00000 | − | 3.46410i | 0.260378 | − | 0.450988i | −0.705965 | − | 0.708247i | \(-0.749486\pi\) |
0.966342 | + | 0.257260i | \(0.0828195\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −3.00000 | − | 5.19615i | −0.384111 | − | 0.665299i | 0.607535 | − | 0.794293i | \(-0.292159\pi\) |
−0.991645 | + | 0.128994i | \(0.958825\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −6.00000 | − | 10.3923i | −0.744208 | − | 1.28901i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −2.00000 | + | 3.46410i | −0.244339 | + | 0.423207i | −0.961946 | − | 0.273241i | \(-0.911904\pi\) |
0.717607 | + | 0.696449i | \(0.245238\pi\) | |||||||
\(68\) | 1.00000 | + | 1.73205i | 0.121268 | + | 0.210042i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −8.00000 | −0.949425 | −0.474713 | − | 0.880141i | \(-0.657448\pi\) | ||||
−0.474713 | + | 0.880141i | \(0.657448\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −5.00000 | + | 8.66025i | −0.585206 | + | 1.01361i | 0.409644 | + | 0.912245i | \(0.365653\pi\) |
−0.994850 | + | 0.101361i | \(0.967680\pi\) | |||||||
\(74\) | −5.00000 | + | 8.66025i | −0.581238 | + | 1.00673i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −4.00000 | −0.458831 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(80\) | −1.00000 | + | 1.73205i | −0.111803 | + | 0.193649i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 3.00000 | + | 5.19615i | 0.331295 | + | 0.573819i | ||||
\(83\) | 4.00000 | 0.439057 | 0.219529 | − | 0.975606i | \(-0.429548\pi\) | ||||
0.219529 | + | 0.975606i | \(0.429548\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −4.00000 | −0.433861 | ||||||||
\(86\) | −2.00000 | − | 3.46410i | −0.215666 | − | 0.373544i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 2.00000 | − | 3.46410i | 0.213201 | − | 0.369274i | ||||
\(89\) | −3.00000 | − | 5.19615i | −0.317999 | − | 0.550791i | 0.662071 | − | 0.749441i | \(-0.269678\pi\) |
−0.980071 | + | 0.198650i | \(0.936344\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −8.00000 | −0.834058 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 4.00000 | − | 6.92820i | 0.410391 | − | 0.710819i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −14.0000 | −1.42148 | −0.710742 | − | 0.703452i | \(-0.751641\pi\) | ||||
−0.710742 | + | 0.703452i | \(0.751641\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0.500000 | + | 0.866025i | 0.0500000 | + | 0.0866025i | ||||
\(101\) | −1.00000 | + | 1.73205i | −0.0995037 | + | 0.172345i | −0.911479 | − | 0.411346i | \(-0.865059\pi\) |
0.811976 | + | 0.583691i | \(0.198392\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −4.00000 | − | 6.92820i | −0.394132 | − | 0.682656i | 0.598858 | − | 0.800855i | \(-0.295621\pi\) |
−0.992990 | + | 0.118199i | \(0.962288\pi\) | |||||||
\(104\) | −6.00000 | −0.588348 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 6.00000 | 0.582772 | ||||||||
\(107\) | 6.00000 | + | 10.3923i | 0.580042 | + | 1.00466i | 0.995474 | + | 0.0950377i | \(0.0302972\pi\) |
−0.415432 | + | 0.909624i | \(0.636370\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1.00000 | − | 1.73205i | 0.0957826 | − | 0.165900i | −0.814152 | − | 0.580651i | \(-0.802798\pi\) |
0.909935 | + | 0.414751i | \(0.136131\pi\) | |||||||
\(110\) | 4.00000 | + | 6.92820i | 0.381385 | + | 0.660578i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 14.0000 | 1.31701 | 0.658505 | − | 0.752577i | \(-0.271189\pi\) | ||||
0.658505 | + | 0.752577i | \(0.271189\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 8.00000 | − | 13.8564i | 0.746004 | − | 1.29212i | ||||
\(116\) | −1.00000 | + | 1.73205i | −0.0928477 | + | 0.160817i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 4.00000 | 0.368230 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −2.50000 | − | 4.33013i | −0.227273 | − | 0.393648i | ||||
\(122\) | 3.00000 | − | 5.19615i | 0.271607 | − | 0.470438i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −12.0000 | −1.07331 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(128\) | 0.500000 | + | 0.866025i | 0.0441942 | + | 0.0765466i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 6.00000 | − | 10.3923i | 0.526235 | − | 0.911465i | ||||
\(131\) | −10.0000 | − | 17.3205i | −0.873704 | − | 1.51330i | −0.858137 | − | 0.513421i | \(-0.828378\pi\) |
−0.0155672 | − | 0.999879i | \(-0.504955\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −4.00000 | −0.345547 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −1.00000 | + | 1.73205i | −0.0857493 | + | 0.148522i | ||||
\(137\) | 5.00000 | − | 8.66025i | 0.427179 | − | 0.739895i | −0.569442 | − | 0.822031i | \(-0.692841\pi\) |
0.996621 | + | 0.0821359i | \(0.0261741\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 4.00000 | 0.339276 | 0.169638 | − | 0.985506i | \(-0.445740\pi\) | ||||
0.169638 | + | 0.985506i | \(0.445740\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −4.00000 | − | 6.92820i | −0.335673 | − | 0.581402i | ||||
\(143\) | −12.0000 | + | 20.7846i | −1.00349 | + | 1.73810i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −2.00000 | − | 3.46410i | −0.166091 | − | 0.287678i | ||||
\(146\) | −10.0000 | −0.827606 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −10.0000 | −0.821995 | ||||||||
\(149\) | 3.00000 | + | 5.19615i | 0.245770 | + | 0.425685i | 0.962348 | − | 0.271821i | \(-0.0876260\pi\) |
−0.716578 | + | 0.697507i | \(0.754293\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 4.00000 | − | 6.92820i | 0.325515 | − | 0.563809i | −0.656101 | − | 0.754673i | \(-0.727796\pi\) |
0.981617 | + | 0.190864i | \(0.0611289\pi\) | |||||||
\(152\) | −2.00000 | − | 3.46410i | −0.162221 | − | 0.280976i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 5.00000 | − | 8.66025i | 0.399043 | − | 0.691164i | −0.594565 | − | 0.804048i | \(-0.702676\pi\) |
0.993608 | + | 0.112884i | \(0.0360089\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −2.00000 | −0.158114 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −10.0000 | − | 17.3205i | −0.783260 | − | 1.35665i | −0.930033 | − | 0.367477i | \(-0.880222\pi\) |
0.146772 | − | 0.989170i | \(-0.453112\pi\) | |||||||
\(164\) | −3.00000 | + | 5.19615i | −0.234261 | + | 0.405751i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 2.00000 | + | 3.46410i | 0.155230 | + | 0.268866i | ||||
\(167\) | 8.00000 | 0.619059 | 0.309529 | − | 0.950890i | \(-0.399829\pi\) | ||||
0.309529 | + | 0.950890i | \(0.399829\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 23.0000 | 1.76923 | ||||||||
\(170\) | −2.00000 | − | 3.46410i | −0.153393 | − | 0.265684i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 2.00000 | − | 3.46410i | 0.152499 | − | 0.264135i | ||||
\(173\) | 11.0000 | + | 19.0526i | 0.836315 | + | 1.44854i | 0.892956 | + | 0.450145i | \(0.148628\pi\) |
−0.0566411 | + | 0.998395i | \(0.518039\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 4.00000 | 0.301511 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 3.00000 | − | 5.19615i | 0.224860 | − | 0.389468i | ||||
\(179\) | −6.00000 | + | 10.3923i | −0.448461 | + | 0.776757i | −0.998286 | − | 0.0585225i | \(-0.981361\pi\) |
0.549825 | + | 0.835280i | \(0.314694\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −18.0000 | −1.33793 | −0.668965 | − | 0.743294i | \(-0.733262\pi\) | ||||
−0.668965 | + | 0.743294i | \(0.733262\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −4.00000 | − | 6.92820i | −0.294884 | − | 0.510754i | ||||
\(185\) | 10.0000 | − | 17.3205i | 0.735215 | − | 1.27343i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 4.00000 | + | 6.92820i | 0.292509 | + | 0.506640i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 8.00000 | 0.580381 | ||||||||
\(191\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1.00000 | + | 1.73205i | −0.0719816 | + | 0.124676i | −0.899770 | − | 0.436365i | \(-0.856266\pi\) |
0.827788 | + | 0.561041i | \(0.189599\pi\) | |||||||
\(194\) | −7.00000 | − | 12.1244i | −0.502571 | − | 0.870478i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 10.0000 | 0.712470 | 0.356235 | − | 0.934396i | \(-0.384060\pi\) | ||||
0.356235 | + | 0.934396i | \(0.384060\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −4.00000 | + | 6.92820i | −0.283552 | + | 0.491127i | −0.972257 | − | 0.233915i | \(-0.924846\pi\) |
0.688705 | + | 0.725042i | \(0.258180\pi\) | |||||||
\(200\) | −0.500000 | + | 0.866025i | −0.0353553 | + | 0.0612372i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −2.00000 | −0.140720 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −6.00000 | − | 10.3923i | −0.419058 | − | 0.725830i | ||||
\(206\) | 4.00000 | − | 6.92820i | 0.278693 | − | 0.482711i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −3.00000 | − | 5.19615i | −0.208013 | − | 0.360288i | ||||
\(209\) | −16.0000 | −1.10674 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 20.0000 | 1.37686 | 0.688428 | − | 0.725304i | \(-0.258301\pi\) | ||||
0.688428 | + | 0.725304i | \(0.258301\pi\) | |||||||
\(212\) | 3.00000 | + | 5.19615i | 0.206041 | + | 0.356873i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −6.00000 | + | 10.3923i | −0.410152 | + | 0.710403i | ||||
\(215\) | 4.00000 | + | 6.92820i | 0.272798 | + | 0.472500i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 2.00000 | 0.135457 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −4.00000 | + | 6.92820i | −0.269680 | + | 0.467099i | ||||
\(221\) | 6.00000 | − | 10.3923i | 0.403604 | − | 0.699062i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −16.0000 | −1.07144 | −0.535720 | − | 0.844396i | \(-0.679960\pi\) | ||||
−0.535720 | + | 0.844396i | \(0.679960\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 7.00000 | + | 12.1244i | 0.465633 | + | 0.806500i | ||||
\(227\) | 6.00000 | − | 10.3923i | 0.398234 | − | 0.689761i | −0.595274 | − | 0.803523i | \(-0.702957\pi\) |
0.993508 | + | 0.113761i | \(0.0362899\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1.00000 | + | 1.73205i | 0.0660819 | + | 0.114457i | 0.897173 | − | 0.441679i | \(-0.145617\pi\) |
−0.831092 | + | 0.556136i | \(0.812283\pi\) | |||||||
\(230\) | 16.0000 | 1.05501 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −2.00000 | −0.131306 | ||||||||
\(233\) | −11.0000 | − | 19.0526i | −0.720634 | − | 1.24817i | −0.960746 | − | 0.277429i | \(-0.910518\pi\) |
0.240112 | − | 0.970745i | \(-0.422816\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 2.00000 | + | 3.46410i | 0.130189 | + | 0.225494i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1.00000 | + | 1.73205i | −0.0644157 | + | 0.111571i | −0.896435 | − | 0.443176i | \(-0.853852\pi\) |
0.832019 | + | 0.554747i | \(0.187185\pi\) | |||||||
\(242\) | 2.50000 | − | 4.33013i | 0.160706 | − | 0.278351i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 6.00000 | 0.384111 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 12.0000 | + | 20.7846i | 0.763542 | + | 1.32249i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −6.00000 | − | 10.3923i | −0.379473 | − | 0.657267i | ||||
\(251\) | 12.0000 | 0.757433 | 0.378717 | − | 0.925513i | \(-0.376365\pi\) | ||||
0.378717 | + | 0.925513i | \(0.376365\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −32.0000 | −2.01182 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.500000 | + | 0.866025i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | −15.0000 | − | 25.9808i | −0.935674 | − | 1.62064i | −0.773427 | − | 0.633885i | \(-0.781459\pi\) |
−0.162247 | − | 0.986750i | \(-0.551874\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 12.0000 | 0.744208 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 10.0000 | − | 17.3205i | 0.617802 | − | 1.07006i | ||||
\(263\) | −12.0000 | + | 20.7846i | −0.739952 | + | 1.28163i | 0.212565 | + | 0.977147i | \(0.431818\pi\) |
−0.952517 | + | 0.304487i | \(0.901515\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −12.0000 | −0.737154 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −2.00000 | − | 3.46410i | −0.122169 | − | 0.211604i | ||||
\(269\) | 11.0000 | − | 19.0526i | 0.670682 | − | 1.16166i | −0.307029 | − | 0.951700i | \(-0.599335\pi\) |
0.977711 | − | 0.209955i | \(-0.0673317\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(272\) | −2.00000 | −0.121268 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 10.0000 | 0.604122 | ||||||||
\(275\) | 2.00000 | + | 3.46410i | 0.120605 | + | 0.208893i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 5.00000 | − | 8.66025i | 0.300421 | − | 0.520344i | −0.675810 | − | 0.737075i | \(-0.736206\pi\) |
0.976231 | + | 0.216731i | \(0.0695395\pi\) | |||||||
\(278\) | 2.00000 | + | 3.46410i | 0.119952 | + | 0.207763i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −26.0000 | −1.55103 | −0.775515 | − | 0.631329i | \(-0.782510\pi\) | ||||
−0.775515 | + | 0.631329i | \(0.782510\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −2.00000 | + | 3.46410i | −0.118888 | + | 0.205919i | −0.919327 | − | 0.393494i | \(-0.871266\pi\) |
0.800439 | + | 0.599414i | \(0.204600\pi\) | |||||||
\(284\) | 4.00000 | − | 6.92820i | 0.237356 | − | 0.411113i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −24.0000 | −1.41915 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 6.50000 | + | 11.2583i | 0.382353 | + | 0.662255i | ||||
\(290\) | 2.00000 | − | 3.46410i | 0.117444 | − | 0.203419i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −5.00000 | − | 8.66025i | −0.292603 | − | 0.506803i | ||||
\(293\) | −30.0000 | −1.75262 | −0.876309 | − | 0.481749i | \(-0.840002\pi\) | ||||
−0.876309 | + | 0.481749i | \(0.840002\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −8.00000 | −0.465778 | ||||||||
\(296\) | −5.00000 | − | 8.66025i | −0.290619 | − | 0.503367i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −3.00000 | + | 5.19615i | −0.173785 | + | 0.301005i | ||||
\(299\) | 24.0000 | + | 41.5692i | 1.38796 | + | 2.40401i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 8.00000 | 0.460348 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 2.00000 | − | 3.46410i | 0.114708 | − | 0.198680i | ||||
\(305\) | −6.00000 | + | 10.3923i | −0.343559 | + | 0.595062i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 28.0000 | 1.59804 | 0.799022 | − | 0.601302i | \(-0.205351\pi\) | ||||
0.799022 | + | 0.601302i | \(0.205351\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −4.00000 | + | 6.92820i | −0.226819 | + | 0.392862i | −0.956864 | − | 0.290537i | \(-0.906166\pi\) |
0.730044 | + | 0.683400i | \(0.239499\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −5.00000 | − | 8.66025i | −0.282617 | − | 0.489506i | 0.689412 | − | 0.724370i | \(-0.257869\pi\) |
−0.972028 | + | 0.234863i | \(0.924536\pi\) | |||||||
\(314\) | 10.0000 | 0.564333 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −9.00000 | − | 15.5885i | −0.505490 | − | 0.875535i | −0.999980 | − | 0.00635137i | \(-0.997978\pi\) |
0.494489 | − | 0.869184i | \(-0.335355\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −4.00000 | + | 6.92820i | −0.223957 | + | 0.387905i | ||||
\(320\) | −1.00000 | − | 1.73205i | −0.0559017 | − | 0.0968246i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 8.00000 | 0.445132 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 3.00000 | − | 5.19615i | 0.166410 | − | 0.288231i | ||||
\(326\) | 10.0000 | − | 17.3205i | 0.553849 | − | 0.959294i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −6.00000 | −0.331295 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 2.00000 | + | 3.46410i | 0.109930 | + | 0.190404i | 0.915742 | − | 0.401768i | \(-0.131604\pi\) |
−0.805812 | + | 0.592172i | \(0.798271\pi\) | |||||||
\(332\) | −2.00000 | + | 3.46410i | −0.109764 | + | 0.190117i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 4.00000 | + | 6.92820i | 0.218870 | + | 0.379094i | ||||
\(335\) | 8.00000 | 0.437087 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 18.0000 | 0.980522 | 0.490261 | − | 0.871576i | \(-0.336901\pi\) | ||||
0.490261 | + | 0.871576i | \(0.336901\pi\) | |||||||
\(338\) | 11.5000 | + | 19.9186i | 0.625518 | + | 1.08343i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 2.00000 | − | 3.46410i | 0.108465 | − | 0.187867i | ||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 4.00000 | 0.215666 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −11.0000 | + | 19.0526i | −0.591364 | + | 1.02427i | ||||
\(347\) | 6.00000 | − | 10.3923i | 0.322097 | − | 0.557888i | −0.658824 | − | 0.752297i | \(-0.728946\pi\) |
0.980921 | + | 0.194409i | \(0.0622790\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 22.0000 | 1.17763 | 0.588817 | − | 0.808267i | \(-0.299594\pi\) | ||||
0.588817 | + | 0.808267i | \(0.299594\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 2.00000 | + | 3.46410i | 0.106600 | + | 0.184637i | ||||
\(353\) | −15.0000 | + | 25.9808i | −0.798369 | + | 1.38282i | 0.122308 | + | 0.992492i | \(0.460970\pi\) |
−0.920677 | + | 0.390324i | \(0.872363\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 8.00000 | + | 13.8564i | 0.424596 | + | 0.735422i | ||||
\(356\) | 6.00000 | 0.317999 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −12.0000 | −0.634220 | ||||||||
\(359\) | −4.00000 | − | 6.92820i | −0.211112 | − | 0.365657i | 0.740951 | − | 0.671559i | \(-0.234375\pi\) |
−0.952063 | + | 0.305903i | \(0.901042\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.50000 | − | 2.59808i | 0.0789474 | − | 0.136741i | ||||
\(362\) | −9.00000 | − | 15.5885i | −0.473029 | − | 0.819311i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 20.0000 | 1.04685 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −16.0000 | + | 27.7128i | −0.835193 | + | 1.44660i | 0.0586798 | + | 0.998277i | \(0.481311\pi\) |
−0.893873 | + | 0.448320i | \(0.852022\pi\) | |||||||
\(368\) | 4.00000 | − | 6.92820i | 0.208514 | − | 0.361158i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 20.0000 | 1.03975 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −11.0000 | − | 19.0526i | −0.569558 | − | 0.986504i | −0.996610 | − | 0.0822766i | \(-0.973781\pi\) |
0.427051 | − | 0.904227i | \(-0.359552\pi\) | |||||||
\(374\) | −4.00000 | + | 6.92820i | −0.206835 | + | 0.358249i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 12.0000 | 0.618031 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −20.0000 | −1.02733 | −0.513665 | − | 0.857991i | \(-0.671713\pi\) | ||||
−0.513665 | + | 0.857991i | \(0.671713\pi\) | |||||||
\(380\) | 4.00000 | + | 6.92820i | 0.205196 | + | 0.355409i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −8.00000 | − | 13.8564i | −0.408781 | − | 0.708029i | 0.585973 | − | 0.810331i | \(-0.300713\pi\) |
−0.994753 | + | 0.102302i | \(0.967379\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −2.00000 | −0.101797 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 7.00000 | − | 12.1244i | 0.355371 | − | 0.615521i | ||||
\(389\) | −13.0000 | + | 22.5167i | −0.659126 | + | 1.14164i | 0.321716 | + | 0.946836i | \(0.395740\pi\) |
−0.980842 | + | 0.194804i | \(0.937593\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 16.0000 | 0.809155 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 5.00000 | + | 8.66025i | 0.251896 | + | 0.436297i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −3.00000 | − | 5.19615i | −0.150566 | − | 0.260787i | 0.780870 | − | 0.624694i | \(-0.214776\pi\) |
−0.931436 | + | 0.363906i | \(0.881443\pi\) | |||||||
\(398\) | −8.00000 | −0.401004 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −1.00000 | −0.0500000 | ||||||||
\(401\) | 9.00000 | + | 15.5885i | 0.449439 | + | 0.778450i | 0.998350 | − | 0.0574304i | \(-0.0182907\pi\) |
−0.548911 | + | 0.835881i | \(0.684957\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | −1.00000 | − | 1.73205i | −0.0497519 | − | 0.0861727i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −40.0000 | −1.98273 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 11.0000 | − | 19.0526i | 0.543915 | − | 0.942088i | −0.454759 | − | 0.890614i | \(-0.650275\pi\) |
0.998674 | − | 0.0514740i | \(-0.0163919\pi\) | |||||||
\(410\) | 6.00000 | − | 10.3923i | 0.296319 | − | 0.513239i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 8.00000 | 0.394132 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −4.00000 | − | 6.92820i | −0.196352 | − | 0.340092i | ||||
\(416\) | 3.00000 | − | 5.19615i | 0.147087 | − | 0.254762i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −8.00000 | − | 13.8564i | −0.391293 | − | 0.677739i | ||||
\(419\) | 36.0000 | 1.75872 | 0.879358 | − | 0.476162i | \(-0.157972\pi\) | ||||
0.879358 | + | 0.476162i | \(0.157972\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 6.00000 | 0.292422 | 0.146211 | − | 0.989253i | \(-0.453292\pi\) | ||||
0.146211 | + | 0.989253i | \(0.453292\pi\) | |||||||
\(422\) | 10.0000 | + | 17.3205i | 0.486792 | + | 0.843149i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −3.00000 | + | 5.19615i | −0.145693 | + | 0.252347i | ||||
\(425\) | −1.00000 | − | 1.73205i | −0.0485071 | − | 0.0840168i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −12.0000 | −0.580042 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −4.00000 | + | 6.92820i | −0.192897 | + | 0.334108i | ||||
\(431\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 2.00000 | 0.0961139 | 0.0480569 | − | 0.998845i | \(-0.484697\pi\) | ||||
0.0480569 | + | 0.998845i | \(0.484697\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 1.00000 | + | 1.73205i | 0.0478913 | + | 0.0829502i | ||||
\(437\) | −16.0000 | + | 27.7128i | −0.765384 | + | 1.32568i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 12.0000 | + | 20.7846i | 0.572729 | + | 0.991995i | 0.996284 | + | 0.0861252i | \(0.0274485\pi\) |
−0.423556 | + | 0.905870i | \(0.639218\pi\) | |||||||
\(440\) | −8.00000 | −0.381385 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 12.0000 | 0.570782 | ||||||||
\(443\) | −2.00000 | − | 3.46410i | −0.0950229 | − | 0.164584i | 0.814595 | − | 0.580030i | \(-0.196959\pi\) |
−0.909618 | + | 0.415445i | \(0.863626\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −6.00000 | + | 10.3923i | −0.284427 | + | 0.492642i | ||||
\(446\) | −8.00000 | − | 13.8564i | −0.378811 | − | 0.656120i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −34.0000 | −1.60456 | −0.802280 | − | 0.596948i | \(-0.796380\pi\) | ||||
−0.802280 | + | 0.596948i | \(0.796380\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −12.0000 | + | 20.7846i | −0.565058 | + | 0.978709i | ||||
\(452\) | −7.00000 | + | 12.1244i | −0.329252 | + | 0.570282i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 12.0000 | 0.563188 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −5.00000 | − | 8.66025i | −0.233890 | − | 0.405110i | 0.725059 | − | 0.688686i | \(-0.241812\pi\) |
−0.958950 | + | 0.283577i | \(0.908479\pi\) | |||||||
\(458\) | −1.00000 | + | 1.73205i | −0.0467269 | + | 0.0809334i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 8.00000 | + | 13.8564i | 0.373002 | + | 0.646058i | ||||
\(461\) | −22.0000 | −1.02464 | −0.512321 | − | 0.858794i | \(-0.671214\pi\) | ||||
−0.512321 | + | 0.858794i | \(0.671214\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −32.0000 | −1.48717 | −0.743583 | − | 0.668644i | \(-0.766875\pi\) | ||||
−0.743583 | + | 0.668644i | \(0.766875\pi\) | |||||||
\(464\) | −1.00000 | − | 1.73205i | −0.0464238 | − | 0.0804084i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 11.0000 | − | 19.0526i | 0.509565 | − | 0.882593i | ||||
\(467\) | 14.0000 | + | 24.2487i | 0.647843 | + | 1.12210i | 0.983637 | + | 0.180161i | \(0.0576619\pi\) |
−0.335794 | + | 0.941935i | \(0.609005\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −2.00000 | + | 3.46410i | −0.0920575 | + | 0.159448i | ||||
\(473\) | 8.00000 | − | 13.8564i | 0.367840 | − | 0.637118i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 4.00000 | 0.183533 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −8.00000 | + | 13.8564i | −0.365529 | + | 0.633115i | −0.988861 | − | 0.148842i | \(-0.952445\pi\) |
0.623332 | + | 0.781958i | \(0.285779\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 30.0000 | + | 51.9615i | 1.36788 | + | 2.36924i | ||||
\(482\) | −2.00000 | −0.0910975 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 5.00000 | 0.227273 | ||||||||
\(485\) | 14.0000 | + | 24.2487i | 0.635707 | + | 1.10108i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −4.00000 | + | 6.92820i | −0.181257 | + | 0.313947i | −0.942309 | − | 0.334744i | \(-0.891350\pi\) |
0.761052 | + | 0.648691i | \(0.224683\pi\) | |||||||
\(488\) | 3.00000 | + | 5.19615i | 0.135804 | + | 0.235219i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −12.0000 | −0.541552 | −0.270776 | − | 0.962642i | \(-0.587280\pi\) | ||||
−0.270776 | + | 0.962642i | \(0.587280\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 2.00000 | − | 3.46410i | 0.0900755 | − | 0.156015i | ||||
\(494\) | −12.0000 | + | 20.7846i | −0.539906 | + | 0.935144i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 22.0000 | + | 38.1051i | 0.984855 | + | 1.70582i | 0.642578 | + | 0.766220i | \(0.277865\pi\) |
0.342277 | + | 0.939599i | \(0.388802\pi\) | |||||||
\(500\) | 6.00000 | − | 10.3923i | 0.268328 | − | 0.464758i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 6.00000 | + | 10.3923i | 0.267793 | + | 0.463831i | ||||
\(503\) | −24.0000 | −1.07011 | −0.535054 | − | 0.844818i | \(-0.679709\pi\) | ||||
−0.535054 | + | 0.844818i | \(0.679709\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 4.00000 | 0.177998 | ||||||||
\(506\) | −16.0000 | − | 27.7128i | −0.711287 | − | 1.23198i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 3.00000 | + | 5.19615i | 0.132973 | + | 0.230315i | 0.924821 | − | 0.380402i | \(-0.124214\pi\) |
−0.791849 | + | 0.610718i | \(0.790881\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 15.0000 | − | 25.9808i | 0.661622 | − | 1.14596i | ||||
\(515\) | −8.00000 | + | 13.8564i | −0.352522 | + | 0.610586i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 6.00000 | + | 10.3923i | 0.263117 | + | 0.455733i | ||||
\(521\) | −3.00000 | + | 5.19615i | −0.131432 | + | 0.227648i | −0.924229 | − | 0.381839i | \(-0.875291\pi\) |
0.792797 | + | 0.609486i | \(0.208624\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −10.0000 | − | 17.3205i | −0.437269 | − | 0.757373i | 0.560208 | − | 0.828352i | \(-0.310721\pi\) |
−0.997478 | + | 0.0709788i | \(0.977388\pi\) | |||||||
\(524\) | 20.0000 | 0.873704 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −24.0000 | −1.04645 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −20.5000 | + | 35.5070i | −0.891304 | + | 1.54378i | ||||
\(530\) | −6.00000 | − | 10.3923i | −0.260623 | − | 0.451413i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 36.0000 | 1.55933 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 12.0000 | − | 20.7846i | 0.518805 | − | 0.898597i | ||||
\(536\) | 2.00000 | − | 3.46410i | 0.0863868 | − | 0.149626i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 22.0000 | 0.948487 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −15.0000 | − | 25.9808i | −0.644900 | − | 1.11700i | −0.984325 | − | 0.176367i | \(-0.943566\pi\) |
0.339424 | − | 0.940633i | \(-0.389768\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −1.00000 | − | 1.73205i | −0.0428746 | − | 0.0742611i | ||||
\(545\) | −4.00000 | −0.171341 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −12.0000 | −0.513083 | −0.256541 | − | 0.966533i | \(-0.582583\pi\) | ||||
−0.256541 | + | 0.966533i | \(0.582583\pi\) | |||||||
\(548\) | 5.00000 | + | 8.66025i | 0.213589 | + | 0.369948i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −2.00000 | + | 3.46410i | −0.0852803 | + | 0.147710i | ||||
\(551\) | 4.00000 | + | 6.92820i | 0.170406 | + | 0.295151i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 10.0000 | 0.424859 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −2.00000 | + | 3.46410i | −0.0848189 | + | 0.146911i | ||||
\(557\) | −1.00000 | + | 1.73205i | −0.0423714 | + | 0.0733893i | −0.886433 | − | 0.462856i | \(-0.846825\pi\) |
0.844062 | + | 0.536246i | \(0.180158\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −24.0000 | −1.01509 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −13.0000 | − | 22.5167i | −0.548372 | − | 0.949808i | ||||
\(563\) | 22.0000 | − | 38.1051i | 0.927189 | − | 1.60594i | 0.139188 | − | 0.990266i | \(-0.455551\pi\) |
0.788002 | − | 0.615673i | \(-0.211116\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −14.0000 | − | 24.2487i | −0.588984 | − | 1.02015i | ||||
\(566\) | −4.00000 | −0.168133 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 8.00000 | 0.335673 | ||||||||
\(569\) | −3.00000 | − | 5.19615i | −0.125767 | − | 0.217834i | 0.796266 | − | 0.604947i | \(-0.206806\pi\) |
−0.922032 | + | 0.387113i | \(0.873472\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −6.00000 | + | 10.3923i | −0.251092 | + | 0.434904i | −0.963827 | − | 0.266529i | \(-0.914123\pi\) |
0.712735 | + | 0.701434i | \(0.247456\pi\) | |||||||
\(572\) | −12.0000 | − | 20.7846i | −0.501745 | − | 0.869048i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 8.00000 | 0.333623 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −17.0000 | + | 29.4449i | −0.707719 | + | 1.22581i | 0.257982 | + | 0.966150i | \(0.416942\pi\) |
−0.965701 | + | 0.259656i | \(0.916391\pi\) | |||||||
\(578\) | −6.50000 | + | 11.2583i | −0.270364 | + | 0.468285i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 4.00000 | 0.166091 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 12.0000 | + | 20.7846i | 0.496989 | + | 0.860811i | ||||
\(584\) | 5.00000 | − | 8.66025i | 0.206901 | − | 0.358364i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −15.0000 | − | 25.9808i | −0.619644 | − | 1.07326i | ||||
\(587\) | 28.0000 | 1.15568 | 0.577842 | − | 0.816149i | \(-0.303895\pi\) | ||||
0.577842 | + | 0.816149i | \(0.303895\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | −4.00000 | − | 6.92820i | −0.164677 | − | 0.285230i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 5.00000 | − | 8.66025i | 0.205499 | − | 0.355934i | ||||
\(593\) | 9.00000 | + | 15.5885i | 0.369586 | + | 0.640141i | 0.989501 | − | 0.144528i | \(-0.0461663\pi\) |
−0.619915 | + | 0.784669i | \(0.712833\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −6.00000 | −0.245770 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −24.0000 | + | 41.5692i | −0.981433 | + | 1.69989i | ||||
\(599\) | 12.0000 | − | 20.7846i | 0.490307 | − | 0.849236i | −0.509631 | − | 0.860393i | \(-0.670218\pi\) |
0.999938 | + | 0.0111569i | \(0.00355143\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 26.0000 | 1.06056 | 0.530281 | − | 0.847822i | \(-0.322086\pi\) | ||||
0.530281 | + | 0.847822i | \(0.322086\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 4.00000 | + | 6.92820i | 0.162758 | + | 0.281905i | ||||
\(605\) | −5.00000 | + | 8.66025i | −0.203279 | + | 0.352089i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −24.0000 | − | 41.5692i | −0.974130 | − | 1.68724i | −0.682777 | − | 0.730627i | \(-0.739228\pi\) |
−0.291353 | − | 0.956616i | \(-0.594105\pi\) | |||||||
\(608\) | 4.00000 | 0.162221 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −12.0000 | −0.485866 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 21.0000 | − | 36.3731i | 0.848182 | − | 1.46909i | −0.0346469 | − | 0.999400i | \(-0.511031\pi\) |
0.882829 | − | 0.469695i | \(-0.155636\pi\) | |||||||
\(614\) | 14.0000 | + | 24.2487i | 0.564994 | + | 0.978598i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 22.0000 | 0.885687 | 0.442843 | − | 0.896599i | \(-0.353970\pi\) | ||||
0.442843 | + | 0.896599i | \(0.353970\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 22.0000 | − | 38.1051i | 0.884255 | − | 1.53157i | 0.0376891 | − | 0.999290i | \(-0.488000\pi\) |
0.846566 | − | 0.532284i | \(-0.178666\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −8.00000 | −0.320771 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 9.50000 | + | 16.4545i | 0.380000 | + | 0.658179i | ||||
\(626\) | 5.00000 | − | 8.66025i | 0.199840 | − | 0.346133i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 5.00000 | + | 8.66025i | 0.199522 | + | 0.345582i | ||||
\(629\) | 20.0000 | 0.797452 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 8.00000 | 0.318475 | 0.159237 | − | 0.987240i | \(-0.449096\pi\) | ||||
0.159237 | + | 0.987240i | \(0.449096\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 9.00000 | − | 15.5885i | 0.357436 | − | 0.619097i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −8.00000 | −0.316723 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 1.00000 | − | 1.73205i | 0.0395285 | − | 0.0684653i | ||||
\(641\) | 1.00000 | − | 1.73205i | 0.0394976 | − | 0.0684119i | −0.845601 | − | 0.533816i | \(-0.820758\pi\) |
0.885098 | + | 0.465404i | \(0.154091\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −4.00000 | −0.157745 | −0.0788723 | − | 0.996885i | \(-0.525132\pi\) | ||||
−0.0788723 | + | 0.996885i | \(0.525132\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 4.00000 | + | 6.92820i | 0.157378 | + | 0.272587i | ||||
\(647\) | 12.0000 | − | 20.7846i | 0.471769 | − | 0.817127i | −0.527710 | − | 0.849425i | \(-0.676949\pi\) |
0.999478 | + | 0.0322975i | \(0.0102824\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 8.00000 | + | 13.8564i | 0.314027 | + | 0.543912i | ||||
\(650\) | 6.00000 | 0.235339 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 20.0000 | 0.783260 | ||||||||
\(653\) | −9.00000 | − | 15.5885i | −0.352197 | − | 0.610023i | 0.634437 | − | 0.772975i | \(-0.281232\pi\) |
−0.986634 | + | 0.162951i | \(0.947899\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −20.0000 | + | 34.6410i | −0.781465 | + | 1.35354i | ||||
\(656\) | −3.00000 | − | 5.19615i | −0.117130 | − | 0.202876i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 28.0000 | 1.09073 | 0.545363 | − | 0.838200i | \(-0.316392\pi\) | ||||
0.545363 | + | 0.838200i | \(0.316392\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1.00000 | − | 1.73205i | 0.0388955 | − | 0.0673690i | −0.845922 | − | 0.533306i | \(-0.820949\pi\) |
0.884818 | + | 0.465937i | \(0.154283\pi\) | |||||||
\(662\) | −2.00000 | + | 3.46410i | −0.0777322 | + | 0.134636i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −4.00000 | −0.155230 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 8.00000 | + | 13.8564i | 0.309761 | + | 0.536522i | ||||
\(668\) | −4.00000 | + | 6.92820i | −0.154765 | + | 0.268060i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 4.00000 | + | 6.92820i | 0.154533 | + | 0.267660i | ||||
\(671\) | 24.0000 | 0.926510 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 2.00000 | 0.0770943 | 0.0385472 | − | 0.999257i | \(-0.487727\pi\) | ||||
0.0385472 | + | 0.999257i | \(0.487727\pi\) | |||||||
\(674\) | 9.00000 | + | 15.5885i | 0.346667 | + | 0.600445i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −11.5000 | + | 19.9186i | −0.442308 | + | 0.766099i | ||||
\(677\) | −9.00000 | − | 15.5885i | −0.345898 | − | 0.599113i | 0.639618 | − | 0.768693i | \(-0.279092\pi\) |
−0.985517 | + | 0.169580i | \(0.945759\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 4.00000 | 0.153393 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 6.00000 | − | 10.3923i | 0.229584 | − | 0.397650i | −0.728101 | − | 0.685470i | \(-0.759597\pi\) |
0.957685 | + | 0.287819i | \(0.0929302\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −20.0000 | −0.764161 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 2.00000 | + | 3.46410i | 0.0762493 | + | 0.132068i | ||||
\(689\) | 18.0000 | − | 31.1769i | 0.685745 | − | 1.18775i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 2.00000 | + | 3.46410i | 0.0760836 | + | 0.131781i | 0.901557 | − | 0.432660i | \(-0.142425\pi\) |
−0.825473 | + | 0.564441i | \(0.809092\pi\) | |||||||
\(692\) | −22.0000 | −0.836315 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 12.0000 | 0.455514 | ||||||||
\(695\) | −4.00000 | − | 6.92820i | −0.151729 | − | 0.262802i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 6.00000 | − | 10.3923i | 0.227266 | − | 0.393637i | ||||
\(698\) | 11.0000 | + | 19.0526i | 0.416356 | + | 0.721150i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 2.00000 | 0.0755390 | 0.0377695 | − | 0.999286i | \(-0.487975\pi\) | ||||
0.0377695 | + | 0.999286i | \(0.487975\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −20.0000 | + | 34.6410i | −0.754314 | + | 1.30651i | ||||
\(704\) | −2.00000 | + | 3.46410i | −0.0753778 | + | 0.130558i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −30.0000 | −1.12906 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 5.00000 | + | 8.66025i | 0.187779 | + | 0.325243i | 0.944509 | − | 0.328484i | \(-0.106538\pi\) |
−0.756730 | + | 0.653727i | \(0.773204\pi\) | |||||||
\(710\) | −8.00000 | + | 13.8564i | −0.300235 | + | 0.520022i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 3.00000 | + | 5.19615i | 0.112430 | + | 0.194734i | ||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 48.0000 | 1.79510 | ||||||||
\(716\) | −6.00000 | − | 10.3923i | −0.224231 | − | 0.388379i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 4.00000 | − | 6.92820i | 0.149279 | − | 0.258558i | ||||
\(719\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 3.00000 | 0.111648 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 9.00000 | − | 15.5885i | 0.334482 | − | 0.579340i | ||||
\(725\) | 1.00000 | − | 1.73205i | 0.0371391 | − | 0.0643268i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −8.00000 | −0.296704 | −0.148352 | − | 0.988935i | \(-0.547397\pi\) | ||||
−0.148352 | + | 0.988935i | \(0.547397\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 10.0000 | + | 17.3205i | 0.370117 | + | 0.641061i | ||||
\(731\) | −4.00000 | + | 6.92820i | −0.147945 | + | 0.256249i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −3.00000 | − | 5.19615i | −0.110808 | − | 0.191924i | 0.805289 | − | 0.592883i | \(-0.202010\pi\) |
−0.916096 | + | 0.400959i | \(0.868677\pi\) | |||||||
\(734\) | −32.0000 | −1.18114 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 8.00000 | 0.294884 | ||||||||
\(737\) | −8.00000 | − | 13.8564i | −0.294684 | − | 0.510407i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 6.00000 | − | 10.3923i | 0.220714 | − | 0.382287i | −0.734311 | − | 0.678813i | \(-0.762495\pi\) |
0.955025 | + | 0.296526i | \(0.0958281\pi\) | |||||||
\(740\) | 10.0000 | + | 17.3205i | 0.367607 | + | 0.636715i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −24.0000 | −0.880475 | −0.440237 | − | 0.897881i | \(-0.645106\pi\) | ||||
−0.440237 | + | 0.897881i | \(0.645106\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 6.00000 | − | 10.3923i | 0.219823 | − | 0.380745i | ||||
\(746\) | 11.0000 | − | 19.0526i | 0.402739 | − | 0.697564i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −8.00000 | −0.292509 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −24.0000 | − | 41.5692i | −0.875772 | − | 1.51688i | −0.855938 | − | 0.517079i | \(-0.827019\pi\) |
−0.0198348 | − | 0.999803i | \(-0.506314\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 6.00000 | + | 10.3923i | 0.218507 | + | 0.378465i | ||||
\(755\) | −16.0000 | −0.582300 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 6.00000 | 0.218074 | 0.109037 | − | 0.994038i | \(-0.465223\pi\) | ||||
0.109037 | + | 0.994038i | \(0.465223\pi\) | |||||||
\(758\) | −10.0000 | − | 17.3205i | −0.363216 | − | 0.629109i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −4.00000 | + | 6.92820i | −0.145095 | + | 0.251312i | ||||
\(761\) | −11.0000 | − | 19.0526i | −0.398750 | − | 0.690655i | 0.594822 | − | 0.803857i | \(-0.297222\pi\) |
−0.993572 | + | 0.113203i | \(0.963889\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 8.00000 | − | 13.8564i | 0.289052 | − | 0.500652i | ||||
\(767\) | 12.0000 | − | 20.7846i | 0.433295 | − | 0.750489i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −14.0000 | −0.504853 | −0.252426 | − | 0.967616i | \(-0.581229\pi\) | ||||
−0.252426 | + | 0.967616i | \(0.581229\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −1.00000 | − | 1.73205i | −0.0359908 | − | 0.0623379i | ||||
\(773\) | −1.00000 | + | 1.73205i | −0.0359675 | + | 0.0622975i | −0.883449 | − | 0.468528i | \(-0.844785\pi\) |
0.847481 | + | 0.530825i | \(0.178118\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 14.0000 | 0.502571 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −26.0000 | −0.932145 | ||||||||
\(779\) | 12.0000 | + | 20.7846i | 0.429945 | + | 0.744686i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 16.0000 | − | 27.7128i | 0.572525 | − | 0.991642i | ||||
\(782\) | 8.00000 | + | 13.8564i | 0.286079 | + | 0.495504i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −20.0000 | −0.713831 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 18.0000 | − | 31.1769i | 0.641631 | − | 1.11134i | −0.343438 | − | 0.939175i | \(-0.611592\pi\) |
0.985069 | − | 0.172162i | \(-0.0550751\pi\) | |||||||
\(788\) | −5.00000 | + | 8.66025i | −0.178118 | + | 0.308509i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −18.0000 | − | 31.1769i | −0.639199 | − | 1.10712i | ||||
\(794\) | 3.00000 | − | 5.19615i | 0.106466 | − | 0.184405i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −4.00000 | − | 6.92820i | −0.141776 | − | 0.245564i | ||||
\(797\) | −6.00000 | −0.212531 | −0.106265 | − | 0.994338i | \(-0.533889\pi\) | ||||
−0.106265 | + | 0.994338i | \(0.533889\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | −0.500000 | − | 0.866025i | −0.0176777 | − | 0.0306186i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −9.00000 | + | 15.5885i | −0.317801 | + | 0.550448i | ||||
\(803\) | −20.0000 | − | 34.6410i | −0.705785 | − | 1.22245i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 1.00000 | − | 1.73205i | 0.0351799 | − | 0.0609333i | ||||
\(809\) | 5.00000 | − | 8.66025i | 0.175791 | − | 0.304478i | −0.764644 | − | 0.644453i | \(-0.777085\pi\) |
0.940435 | + | 0.339975i | \(0.110418\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −44.0000 | −1.54505 | −0.772524 | − | 0.634985i | \(-0.781006\pi\) | ||||
−0.772524 | + | 0.634985i | \(0.781006\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −20.0000 | − | 34.6410i | −0.701000 | − | 1.21417i | ||||
\(815\) | −20.0000 | + | 34.6410i | −0.700569 | + | 1.21342i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −8.00000 | − | 13.8564i | −0.279885 | − | 0.484774i | ||||
\(818\) | 22.0000 | 0.769212 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 12.0000 | 0.419058 | ||||||||
\(821\) | 19.0000 | + | 32.9090i | 0.663105 | + | 1.14853i | 0.979795 | + | 0.200002i | \(0.0640949\pi\) |
−0.316691 | + | 0.948529i | \(0.602572\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 28.0000 | − | 48.4974i | 0.976019 | − | 1.69051i | 0.299487 | − | 0.954100i | \(-0.403185\pi\) |
0.676532 | − | 0.736413i | \(-0.263482\pi\) | |||||||
\(824\) | 4.00000 | + | 6.92820i | 0.139347 | + | 0.241355i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 36.0000 | 1.25184 | 0.625921 | − | 0.779886i | \(-0.284723\pi\) | ||||
0.625921 | + | 0.779886i | \(0.284723\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 13.0000 | − | 22.5167i | 0.451509 | − | 0.782036i | −0.546971 | − | 0.837151i | \(-0.684219\pi\) |
0.998480 | + | 0.0551154i | \(0.0175527\pi\) | |||||||
\(830\) | 4.00000 | − | 6.92820i | 0.138842 | − | 0.240481i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 6.00000 | 0.208013 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −8.00000 | − | 13.8564i | −0.276851 | − | 0.479521i | ||||
\(836\) | 8.00000 | − | 13.8564i | 0.276686 | − | 0.479234i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 18.0000 | + | 31.1769i | 0.621800 | + | 1.07699i | ||||
\(839\) | −56.0000 | −1.93333 | −0.966667 | − | 0.256036i | \(-0.917584\pi\) | ||||
−0.966667 | + | 0.256036i | \(0.917584\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −25.0000 | −0.862069 | ||||||||
\(842\) | 3.00000 | + | 5.19615i | 0.103387 | + | 0.179071i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −10.0000 | + | 17.3205i | −0.344214 | + | 0.596196i | ||||
\(845\) | −23.0000 | − | 39.8372i | −0.791224 | − | 1.37044i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −6.00000 | −0.206041 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 1.00000 | − | 1.73205i | 0.0342997 | − | 0.0594089i | ||||
\(851\) | −40.0000 | + | 69.2820i | −1.37118 | + | 2.37496i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 14.0000 | 0.479351 | 0.239675 | − | 0.970853i | \(-0.422959\pi\) | ||||
0.239675 | + | 0.970853i | \(0.422959\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −6.00000 | − | 10.3923i | −0.205076 | − | 0.355202i | ||||
\(857\) | 21.0000 | − | 36.3731i | 0.717346 | − | 1.24248i | −0.244701 | − | 0.969599i | \(-0.578690\pi\) |
0.962048 | − | 0.272882i | \(-0.0879768\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −10.0000 | − | 17.3205i | −0.341196 | − | 0.590968i | 0.643459 | − | 0.765480i | \(-0.277499\pi\) |
−0.984655 | + | 0.174512i | \(0.944165\pi\) | |||||||
\(860\) | −8.00000 | −0.272798 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −16.0000 | − | 27.7128i | −0.544646 | − | 0.943355i | −0.998629 | − | 0.0523446i | \(-0.983331\pi\) |
0.453983 | − | 0.891010i | \(-0.350003\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 22.0000 | − | 38.1051i | 0.748022 | − | 1.29561i | ||||
\(866\) | 1.00000 | + | 1.73205i | 0.0339814 | + | 0.0588575i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −12.0000 | + | 20.7846i | −0.406604 | + | 0.704260i | ||||
\(872\) | −1.00000 | + | 1.73205i | −0.0338643 | + | 0.0586546i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −32.0000 | −1.08242 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 1.00000 | + | 1.73205i | 0.0337676 | + | 0.0584872i | 0.882415 | − | 0.470471i | \(-0.155916\pi\) |
−0.848648 | + | 0.528958i | \(0.822583\pi\) | |||||||
\(878\) | −12.0000 | + | 20.7846i | −0.404980 | + | 0.701447i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −4.00000 | − | 6.92820i | −0.134840 | − | 0.233550i | ||||
\(881\) | −18.0000 | −0.606435 | −0.303218 | − | 0.952921i | \(-0.598061\pi\) | ||||
−0.303218 | + | 0.952921i | \(0.598061\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 20.0000 | 0.673054 | 0.336527 | − | 0.941674i | \(-0.390748\pi\) | ||||
0.336527 | + | 0.941674i | \(0.390748\pi\) | |||||||
\(884\) | 6.00000 | + | 10.3923i | 0.201802 | + | 0.349531i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 2.00000 | − | 3.46410i | 0.0671913 | − | 0.116379i | ||||
\(887\) | −12.0000 | − | 20.7846i | −0.402921 | − | 0.697879i | 0.591156 | − | 0.806557i | \(-0.298672\pi\) |
−0.994077 | + | 0.108678i | \(0.965338\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −12.0000 | −0.402241 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 8.00000 | − | 13.8564i | 0.267860 | − | 0.463947i | ||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 24.0000 | 0.802232 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −17.0000 | − | 29.4449i | −0.567297 | − | 0.982588i | ||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −6.00000 | − | 10.3923i | −0.199889 | − | 0.346218i | ||||
\(902\) | −24.0000 | −0.799113 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −14.0000 | −0.465633 | ||||||||
\(905\) | 18.0000 | + | 31.1769i | 0.598340 | + | 1.03636i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −6.00000 | + | 10.3923i | −0.199227 | + | 0.345071i | −0.948278 | − | 0.317441i | \(-0.897176\pi\) |
0.749051 | + | 0.662512i | \(0.230510\pi\) | |||||||
\(908\) | 6.00000 | + | 10.3923i | 0.199117 | + | 0.344881i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −8.00000 | + | 13.8564i | −0.264761 | + | 0.458580i | ||||
\(914\) | 5.00000 | − | 8.66025i | 0.165385 | − | 0.286456i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −2.00000 | −0.0660819 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −20.0000 | − | 34.6410i | −0.659739 | − | 1.14270i | −0.980683 | − | 0.195603i | \(-0.937333\pi\) |
0.320944 | − | 0.947098i | \(-0.396000\pi\) | |||||||
\(920\) | −8.00000 | + | 13.8564i | −0.263752 | + | 0.456832i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −11.0000 | − | 19.0526i | −0.362266 | − | 0.627463i | ||||
\(923\) | −48.0000 | −1.57994 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 10.0000 | 0.328798 | ||||||||
\(926\) | −16.0000 | − | 27.7128i | −0.525793 | − | 0.910700i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 1.00000 | − | 1.73205i | 0.0328266 | − | 0.0568574i | ||||
\(929\) | 9.00000 | + | 15.5885i | 0.295280 | + | 0.511441i | 0.975050 | − | 0.221985i | \(-0.0712536\pi\) |
−0.679770 | + | 0.733426i | \(0.737920\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 22.0000 | 0.720634 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −14.0000 | + | 24.2487i | −0.458094 | + | 0.793442i | ||||
\(935\) | 8.00000 | − | 13.8564i | 0.261628 | − | 0.453153i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −22.0000 | −0.718709 | −0.359354 | − | 0.933201i | \(-0.617003\pi\) | ||||
−0.359354 | + | 0.933201i | \(0.617003\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −13.0000 | + | 22.5167i | −0.423788 | + | 0.734022i | −0.996306 | − | 0.0858697i | \(-0.972633\pi\) |
0.572518 | + | 0.819892i | \(0.305966\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 24.0000 | + | 41.5692i | 0.781548 | + | 1.35368i | ||||
\(944\) | −4.00000 | −0.130189 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 16.0000 | 0.520205 | ||||||||
\(947\) | 2.00000 | + | 3.46410i | 0.0649913 | + | 0.112568i | 0.896690 | − | 0.442659i | \(-0.145965\pi\) |
−0.831699 | + | 0.555227i | \(0.812631\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −30.0000 | + | 51.9615i | −0.973841 | + | 1.68674i | ||||
\(950\) | 2.00000 | + | 3.46410i | 0.0648886 | + | 0.112390i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −26.0000 | −0.842223 | −0.421111 | − | 0.907009i | \(-0.638360\pi\) | ||||
−0.421111 | + | 0.907009i | \(0.638360\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −16.0000 | −0.516937 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 15.5000 | + | 26.8468i | 0.500000 | + | 0.866025i | ||||
\(962\) | −30.0000 | + | 51.9615i | −0.967239 | + | 1.67531i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −1.00000 | − | 1.73205i | −0.0322078 | − | 0.0557856i | ||||
\(965\) | 4.00000 | 0.128765 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 8.00000 | 0.257263 | 0.128631 | − | 0.991692i | \(-0.458942\pi\) | ||||
0.128631 | + | 0.991692i | \(0.458942\pi\) | |||||||
\(968\) | 2.50000 | + | 4.33013i | 0.0803530 | + | 0.139176i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −14.0000 | + | 24.2487i | −0.449513 | + | 0.778579i | ||||
\(971\) | −6.00000 | − | 10.3923i | −0.192549 | − | 0.333505i | 0.753545 | − | 0.657396i | \(-0.228342\pi\) |
−0.946094 | + | 0.323891i | \(0.895009\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −8.00000 | −0.256337 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −3.00000 | + | 5.19615i | −0.0960277 | + | 0.166325i | ||||
\(977\) | 9.00000 | − | 15.5885i | 0.287936 | − | 0.498719i | −0.685381 | − | 0.728184i | \(-0.740364\pi\) |
0.973317 | + | 0.229465i | \(0.0736978\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 24.0000 | 0.767043 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −6.00000 | − | 10.3923i | −0.191468 | − | 0.331632i | ||||
\(983\) | −12.0000 | + | 20.7846i | −0.382741 | + | 0.662926i | −0.991453 | − | 0.130465i | \(-0.958353\pi\) |
0.608712 | + | 0.793391i | \(0.291686\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −10.0000 | − | 17.3205i | −0.318626 | − | 0.551877i | ||||
\(986\) | 4.00000 | 0.127386 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −24.0000 | −0.763542 | ||||||||
\(989\) | −16.0000 | − | 27.7128i | −0.508770 | − | 0.881216i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 8.00000 | − | 13.8564i | 0.254128 | − | 0.440163i | −0.710530 | − | 0.703667i | \(-0.751545\pi\) |
0.964658 | + | 0.263504i | \(0.0848781\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 16.0000 | 0.507234 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −7.00000 | + | 12.1244i | −0.221692 | + | 0.383982i | −0.955322 | − | 0.295567i | \(-0.904491\pi\) |
0.733630 | + | 0.679549i | \(0.237825\pi\) | |||||||
\(998\) | −22.0000 | + | 38.1051i | −0.696398 | + | 1.20620i | ||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))