Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1323,2,Mod(521,1323)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1323, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1323.521");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1323 = 3^{3} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1323.i (of order \(6\), 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: | \(10.5642081874\) |
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: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 63) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 1097.1 | ||
Root | \(0.500000 - 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1323.1097 |
Dual form | 1323.2.i.a.521.1 |
$q$-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 \(\left(\mathbb{Z}/1323\mathbb{Z}\right)^\times\).
\(n\) | \(785\) | \(1081\) |
\(\chi(n)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{5}{6}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 1.73205i | − | 1.22474i | −0.790569 | − | 0.612372i | \(-0.790215\pi\) | ||
0.790569 | − | 0.612372i | \(-0.209785\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | −1.50000 | − | 2.59808i | −0.670820 | − | 1.16190i | −0.977672 | − | 0.210138i | \(-0.932609\pi\) |
0.306851 | − | 0.951757i | \(-0.400725\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | − | 1.73205i | − | 0.612372i | ||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −4.50000 | + | 2.59808i | −1.42302 | + | 0.821584i | ||||
\(11\) | −1.50000 | − | 0.866025i | −0.452267 | − | 0.261116i | 0.256520 | − | 0.966539i | \(-0.417424\pi\) |
−0.708787 | + | 0.705422i | \(0.750757\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.50000 | − | 0.866025i | −0.416025 | − | 0.240192i | 0.277350 | − | 0.960769i | \(-0.410544\pi\) |
−0.693375 | + | 0.720577i | \(0.743877\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −5.00000 | −1.25000 | ||||||||
\(17\) | −1.50000 | − | 2.59808i | −0.363803 | − | 0.630126i | 0.624780 | − | 0.780801i | \(-0.285189\pi\) |
−0.988583 | + | 0.150675i | \(0.951855\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.50000 | + | 2.59808i | 1.03237 | + | 0.596040i | 0.917663 | − | 0.397360i | \(-0.130073\pi\) |
0.114708 | + | 0.993399i | \(0.463407\pi\) | |||||||
\(20\) | 1.50000 | + | 2.59808i | 0.335410 | + | 0.580948i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −1.50000 | + | 2.59808i | −0.319801 | + | 0.553912i | ||||
\(23\) | −4.50000 | + | 2.59808i | −0.938315 | + | 0.541736i | −0.889432 | − | 0.457068i | \(-0.848900\pi\) |
−0.0488832 | + | 0.998805i | \(0.515566\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.00000 | + | 3.46410i | −0.400000 | + | 0.692820i | ||||
\(26\) | −1.50000 | + | 2.59808i | −0.294174 | + | 0.509525i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 4.50000 | − | 2.59808i | 0.835629 | − | 0.482451i | −0.0201471 | − | 0.999797i | \(-0.506413\pi\) |
0.855776 | + | 0.517346i | \(0.173080\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 3.46410i | − | 0.622171i | −0.950382 | − | 0.311086i | \(-0.899307\pi\) | ||
0.950382 | − | 0.311086i | \(-0.100693\pi\) | |||||||
\(32\) | 5.19615i | 0.918559i | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −4.50000 | + | 2.59808i | −0.771744 | + | 0.445566i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −3.50000 | + | 6.06218i | −0.575396 | + | 0.996616i | 0.420602 | + | 0.907245i | \(0.361819\pi\) |
−0.995998 | + | 0.0893706i | \(0.971514\pi\) | |||||||
\(38\) | 4.50000 | − | 7.79423i | 0.729996 | − | 1.26439i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −4.50000 | + | 2.59808i | −0.711512 | + | 0.410792i | ||||
\(41\) | −1.50000 | + | 2.59808i | −0.234261 | + | 0.405751i | −0.959058 | − | 0.283211i | \(-0.908600\pi\) |
0.724797 | + | 0.688963i | \(0.241934\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −0.500000 | − | 0.866025i | −0.0762493 | − | 0.132068i | 0.825380 | − | 0.564578i | \(-0.190961\pi\) |
−0.901629 | + | 0.432511i | \(0.857628\pi\) | |||||||
\(44\) | 1.50000 | + | 0.866025i | 0.226134 | + | 0.130558i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 4.50000 | + | 7.79423i | 0.663489 | + | 1.14920i | ||||
\(47\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 6.00000 | + | 3.46410i | 0.848528 | + | 0.489898i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 1.50000 | + | 0.866025i | 0.208013 | + | 0.120096i | ||||
\(53\) | −7.50000 | + | 4.33013i | −1.03020 | + | 0.594789i | −0.917043 | − | 0.398788i | \(-0.869431\pi\) |
−0.113161 | + | 0.993577i | \(0.536098\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 5.19615i | 0.700649i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −4.50000 | − | 7.79423i | −0.590879 | − | 1.02343i | ||||
\(59\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 13.8564i | − | 1.77413i | −0.461644 | − | 0.887066i | \(-0.652740\pi\) | ||
0.461644 | − | 0.887066i | \(-0.347260\pi\) | |||||||
\(62\) | −6.00000 | −0.762001 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 5.19615i | 0.644503i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −4.00000 | −0.488678 | −0.244339 | − | 0.969690i | \(-0.578571\pi\) | ||||
−0.244339 | + | 0.969690i | \(0.578571\pi\) | |||||||
\(68\) | 1.50000 | + | 2.59808i | 0.181902 | + | 0.315063i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 3.46410i | 0.411113i | 0.978645 | + | 0.205557i | \(0.0659005\pi\) | ||||
−0.978645 | + | 0.205557i | \(0.934100\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 4.50000 | − | 2.59808i | 0.526685 | − | 0.304082i | −0.212980 | − | 0.977056i | \(-0.568317\pi\) |
0.739666 | + | 0.672975i | \(0.234984\pi\) | |||||||
\(74\) | 10.5000 | + | 6.06218i | 1.22060 | + | 0.704714i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −4.50000 | − | 2.59808i | −0.516185 | − | 0.298020i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 8.00000 | 0.900070 | 0.450035 | − | 0.893011i | \(-0.351411\pi\) | ||||
0.450035 | + | 0.893011i | \(0.351411\pi\) | |||||||
\(80\) | 7.50000 | + | 12.9904i | 0.838525 | + | 1.45237i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 4.50000 | + | 2.59808i | 0.496942 | + | 0.286910i | ||||
\(83\) | 7.50000 | + | 12.9904i | 0.823232 | + | 1.42588i | 0.903263 | + | 0.429087i | \(0.141165\pi\) |
−0.0800311 | + | 0.996792i | \(0.525502\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −4.50000 | + | 7.79423i | −0.488094 | + | 0.845403i | ||||
\(86\) | −1.50000 | + | 0.866025i | −0.161749 | + | 0.0933859i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −1.50000 | + | 2.59808i | −0.159901 | + | 0.276956i | ||||
\(89\) | −1.50000 | + | 2.59808i | −0.159000 | + | 0.275396i | −0.934508 | − | 0.355942i | \(-0.884160\pi\) |
0.775509 | + | 0.631337i | \(0.217494\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 4.50000 | − | 2.59808i | 0.469157 | − | 0.270868i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | − | 15.5885i | − | 1.59934i | ||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1.50000 | + | 0.866025i | −0.152302 | + | 0.0879316i | −0.574214 | − | 0.818705i | \(-0.694692\pi\) |
0.421912 | + | 0.906637i | \(0.361359\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 2.00000 | − | 3.46410i | 0.200000 | − | 0.346410i | ||||
\(101\) | −1.50000 | + | 2.59808i | −0.149256 | + | 0.258518i | −0.930953 | − | 0.365140i | \(-0.881021\pi\) |
0.781697 | + | 0.623658i | \(0.214354\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −10.5000 | + | 6.06218i | −1.03460 | + | 0.597324i | −0.918298 | − | 0.395890i | \(-0.870436\pi\) |
−0.116298 | + | 0.993214i | \(0.537103\pi\) | |||||||
\(104\) | −1.50000 | + | 2.59808i | −0.147087 | + | 0.254762i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 7.50000 | + | 12.9904i | 0.728464 | + | 1.26174i | ||||
\(107\) | −7.50000 | − | 4.33013i | −0.725052 | − | 0.418609i | 0.0915571 | − | 0.995800i | \(-0.470816\pi\) |
−0.816609 | + | 0.577191i | \(0.804149\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −9.50000 | − | 16.4545i | −0.909935 | − | 1.57605i | −0.814152 | − | 0.580651i | \(-0.802798\pi\) |
−0.0957826 | − | 0.995402i | \(-0.530535\pi\) | |||||||
\(110\) | 9.00000 | 0.858116 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −1.50000 | − | 0.866025i | −0.141108 | − | 0.0814688i | 0.427784 | − | 0.903881i | \(-0.359294\pi\) |
−0.568892 | + | 0.822412i | \(0.692628\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 13.5000 | + | 7.79423i | 1.25888 | + | 0.726816i | ||||
\(116\) | −4.50000 | + | 2.59808i | −0.417815 | + | 0.241225i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −4.00000 | − | 6.92820i | −0.363636 | − | 0.629837i | ||||
\(122\) | −24.0000 | −2.17286 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 3.46410i | 0.311086i | ||||||||
\(125\) | −3.00000 | −0.268328 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 20.0000 | 1.77471 | 0.887357 | − | 0.461084i | \(-0.152539\pi\) | ||||
0.887357 | + | 0.461084i | \(0.152539\pi\) | |||||||
\(128\) | 12.1244i | 1.07165i | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 9.00000 | 0.789352 | ||||||||
\(131\) | −4.50000 | − | 7.79423i | −0.393167 | − | 0.680985i | 0.599699 | − | 0.800226i | \(-0.295287\pi\) |
−0.992865 | + | 0.119241i | \(0.961954\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 6.92820i | 0.598506i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −4.50000 | + | 2.59808i | −0.385872 | + | 0.222783i | ||||
\(137\) | 10.5000 | + | 6.06218i | 0.897076 | + | 0.517927i | 0.876250 | − | 0.481856i | \(-0.160037\pi\) |
0.0208253 | + | 0.999783i | \(0.493371\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −7.50000 | − | 4.33013i | −0.636142 | − | 0.367277i | 0.146985 | − | 0.989139i | \(-0.453043\pi\) |
−0.783127 | + | 0.621862i | \(0.786376\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 6.00000 | 0.503509 | ||||||||
\(143\) | 1.50000 | + | 2.59808i | 0.125436 | + | 0.217262i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −13.5000 | − | 7.79423i | −1.12111 | − | 0.647275i | ||||
\(146\) | −4.50000 | − | 7.79423i | −0.372423 | − | 0.645055i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 3.50000 | − | 6.06218i | 0.287698 | − | 0.498308i | ||||
\(149\) | −1.50000 | + | 0.866025i | −0.122885 | + | 0.0709476i | −0.560182 | − | 0.828369i | \(-0.689269\pi\) |
0.437298 | + | 0.899317i | \(0.355936\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 8.50000 | − | 14.7224i | 0.691720 | − | 1.19809i | −0.279554 | − | 0.960130i | \(-0.590186\pi\) |
0.971274 | − | 0.237964i | \(-0.0764802\pi\) | |||||||
\(152\) | 4.50000 | − | 7.79423i | 0.364998 | − | 0.632195i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −9.00000 | + | 5.19615i | −0.722897 | + | 0.417365i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(158\) | − | 13.8564i | − | 1.10236i | ||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 13.5000 | − | 7.79423i | 1.06727 | − | 0.616188i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −5.50000 | + | 9.52628i | −0.430793 | + | 0.746156i | −0.996942 | − | 0.0781474i | \(-0.975100\pi\) |
0.566149 | + | 0.824303i | \(0.308433\pi\) | |||||||
\(164\) | 1.50000 | − | 2.59808i | 0.117130 | − | 0.202876i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 22.5000 | − | 12.9904i | 1.74634 | − | 1.00825i | ||||
\(167\) | 4.50000 | − | 7.79423i | 0.348220 | − | 0.603136i | −0.637713 | − | 0.770274i | \(-0.720119\pi\) |
0.985933 | + | 0.167139i | \(0.0534527\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −5.00000 | − | 8.66025i | −0.384615 | − | 0.666173i | ||||
\(170\) | 13.5000 | + | 7.79423i | 1.03540 | + | 0.597790i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0.500000 | + | 0.866025i | 0.0381246 | + | 0.0660338i | ||||
\(173\) | −6.00000 | −0.456172 | −0.228086 | − | 0.973641i | \(-0.573247\pi\) | ||||
−0.228086 | + | 0.973641i | \(0.573247\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 7.50000 | + | 4.33013i | 0.565334 | + | 0.326396i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 4.50000 | + | 2.59808i | 0.337289 | + | 0.194734i | ||||
\(179\) | 13.5000 | − | 7.79423i | 1.00904 | − | 0.582568i | 0.0981277 | − | 0.995174i | \(-0.468715\pi\) |
0.910910 | + | 0.412606i | \(0.135381\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 4.50000 | + | 7.79423i | 0.331744 | + | 0.574598i | ||||
\(185\) | 21.0000 | 1.54395 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 5.19615i | 0.379980i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −27.0000 | −1.95879 | ||||||||
\(191\) | − | 17.3205i | − | 1.25327i | −0.779314 | − | 0.626634i | \(-0.784432\pi\) | ||
0.779314 | − | 0.626634i | \(-0.215568\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −2.00000 | −0.143963 | −0.0719816 | − | 0.997406i | \(-0.522932\pi\) | ||||
−0.0719816 | + | 0.997406i | \(0.522932\pi\) | |||||||
\(194\) | 1.50000 | + | 2.59808i | 0.107694 | + | 0.186531i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 13.8564i | − | 0.987228i | −0.869681 | − | 0.493614i | \(-0.835676\pi\) | ||
0.869681 | − | 0.493614i | \(-0.164324\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 7.50000 | − | 4.33013i | 0.531661 | − | 0.306955i | −0.210032 | − | 0.977695i | \(-0.567357\pi\) |
0.741693 | + | 0.670740i | \(0.234023\pi\) | |||||||
\(200\) | 6.00000 | + | 3.46410i | 0.424264 | + | 0.244949i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 4.50000 | + | 2.59808i | 0.316619 | + | 0.182800i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 9.00000 | 0.628587 | ||||||||
\(206\) | 10.5000 | + | 18.1865i | 0.731570 | + | 1.26712i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 7.50000 | + | 4.33013i | 0.520031 | + | 0.300240i | ||||
\(209\) | −4.50000 | − | 7.79423i | −0.311272 | − | 0.539138i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2.50000 | − | 4.33013i | 0.172107 | − | 0.298098i | −0.767049 | − | 0.641588i | \(-0.778276\pi\) |
0.939156 | + | 0.343490i | \(0.111609\pi\) | |||||||
\(212\) | 7.50000 | − | 4.33013i | 0.515102 | − | 0.297394i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −7.50000 | + | 12.9904i | −0.512689 | + | 0.888004i | ||||
\(215\) | −1.50000 | + | 2.59808i | −0.102299 | + | 0.177187i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −28.5000 | + | 16.4545i | −1.93026 | + | 1.11444i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | − | 5.19615i | − | 0.350325i | ||||||
\(221\) | 5.19615i | 0.349531i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −4.50000 | + | 2.59808i | −0.301342 | + | 0.173980i | −0.643046 | − | 0.765828i | \(-0.722329\pi\) |
0.341703 | + | 0.939808i | \(0.388996\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −1.50000 | + | 2.59808i | −0.0997785 | + | 0.172821i | ||||
\(227\) | 10.5000 | − | 18.1865i | 0.696909 | − | 1.20708i | −0.272623 | − | 0.962121i | \(-0.587891\pi\) |
0.969533 | − | 0.244962i | \(-0.0787754\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −7.50000 | + | 4.33013i | −0.495614 | + | 0.286143i | −0.726900 | − | 0.686743i | \(-0.759040\pi\) |
0.231287 | + | 0.972886i | \(0.425707\pi\) | |||||||
\(230\) | 13.5000 | − | 23.3827i | 0.890164 | − | 1.54181i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −4.50000 | − | 7.79423i | −0.295439 | − | 0.511716i | ||||
\(233\) | 4.50000 | + | 2.59808i | 0.294805 | + | 0.170206i | 0.640107 | − | 0.768286i | \(-0.278890\pi\) |
−0.345302 | + | 0.938492i | \(0.612223\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −1.50000 | − | 0.866025i | −0.0970269 | − | 0.0560185i | 0.450701 | − | 0.892675i | \(-0.351174\pi\) |
−0.547728 | + | 0.836656i | \(0.684507\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −19.5000 | − | 11.2583i | −1.25611 | − | 0.725213i | −0.283790 | − | 0.958886i | \(-0.591592\pi\) |
−0.972315 | + | 0.233674i | \(0.924925\pi\) | |||||||
\(242\) | −12.0000 | + | 6.92820i | −0.771389 | + | 0.445362i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 13.8564i | 0.887066i | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −4.50000 | − | 7.79423i | −0.286328 | − | 0.495935i | ||||
\(248\) | −6.00000 | −0.381000 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 5.19615i | 0.328634i | ||||||||
\(251\) | −12.0000 | −0.757433 | −0.378717 | − | 0.925513i | \(-0.623635\pi\) | ||||
−0.378717 | + | 0.925513i | \(0.623635\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 9.00000 | 0.565825 | ||||||||
\(254\) | − | 34.6410i | − | 2.17357i | ||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 19.0000 | 1.18750 | ||||||||
\(257\) | −1.50000 | − | 2.59808i | −0.0935674 | − | 0.162064i | 0.815442 | − | 0.578838i | \(-0.196494\pi\) |
−0.909010 | + | 0.416775i | \(0.863160\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | − | 5.19615i | − | 0.322252i | ||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −13.5000 | + | 7.79423i | −0.834033 | + | 0.481529i | ||||
\(263\) | −19.5000 | − | 11.2583i | −1.20242 | − | 0.694218i | −0.241329 | − | 0.970443i | \(-0.577583\pi\) |
−0.961093 | + | 0.276225i | \(0.910916\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 22.5000 | + | 12.9904i | 1.38216 | + | 0.797993i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 4.00000 | 0.244339 | ||||||||
\(269\) | −7.50000 | − | 12.9904i | −0.457283 | − | 0.792038i | 0.541533 | − | 0.840679i | \(-0.317844\pi\) |
−0.998816 | + | 0.0486418i | \(0.984511\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 10.5000 | + | 6.06218i | 0.637830 | + | 0.368251i | 0.783778 | − | 0.621041i | \(-0.213290\pi\) |
−0.145948 | + | 0.989292i | \(0.546623\pi\) | |||||||
\(272\) | 7.50000 | + | 12.9904i | 0.454754 | + | 0.787658i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 10.5000 | − | 18.1865i | 0.634328 | − | 1.09869i | ||||
\(275\) | 6.00000 | − | 3.46410i | 0.361814 | − | 0.208893i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 0.500000 | − | 0.866025i | 0.0300421 | − | 0.0520344i | −0.850613 | − | 0.525792i | \(-0.823769\pi\) |
0.880656 | + | 0.473757i | \(0.157103\pi\) | |||||||
\(278\) | −7.50000 | + | 12.9904i | −0.449820 | + | 0.779111i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 16.5000 | − | 9.52628i | 0.984307 | − | 0.568290i | 0.0807396 | − | 0.996735i | \(-0.474272\pi\) |
0.903568 | + | 0.428445i | \(0.140938\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 3.46410i | 0.205919i | 0.994686 | + | 0.102960i | \(0.0328313\pi\) | ||||
−0.994686 | + | 0.102960i | \(0.967169\pi\) | |||||||
\(284\) | − | 3.46410i | − | 0.205557i | ||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 4.50000 | − | 2.59808i | 0.266091 | − | 0.153627i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 4.00000 | − | 6.92820i | 0.235294 | − | 0.407541i | ||||
\(290\) | −13.5000 | + | 23.3827i | −0.792747 | + | 1.37308i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −4.50000 | + | 2.59808i | −0.263343 | + | 0.152041i | ||||
\(293\) | 4.50000 | − | 7.79423i | 0.262893 | − | 0.455344i | −0.704117 | − | 0.710084i | \(-0.748657\pi\) |
0.967009 | + | 0.254741i | \(0.0819901\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 10.5000 | + | 6.06218i | 0.610300 | + | 0.352357i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 1.50000 | + | 2.59808i | 0.0868927 | + | 0.150503i | ||||
\(299\) | 9.00000 | 0.520483 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −25.5000 | − | 14.7224i | −1.46736 | − | 0.847181i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −22.5000 | − | 12.9904i | −1.29046 | − | 0.745049i | ||||
\(305\) | −36.0000 | + | 20.7846i | −2.06135 | + | 1.19012i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 24.2487i | − | 1.38395i | −0.721923 | − | 0.691974i | \(-0.756741\pi\) | ||
0.721923 | − | 0.691974i | \(-0.243259\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 9.00000 | + | 15.5885i | 0.511166 | + | 0.885365i | ||||
\(311\) | −24.0000 | −1.36092 | −0.680458 | − | 0.732787i | \(-0.738219\pi\) | ||||
−0.680458 | + | 0.732787i | \(0.738219\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 20.7846i | 1.17482i | 0.809291 | + | 0.587408i | \(0.199852\pi\) | ||||
−0.809291 | + | 0.587408i | \(0.800148\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −8.00000 | −0.450035 | ||||||||
\(317\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −9.00000 | −0.503903 | ||||||||
\(320\) | 1.50000 | + | 2.59808i | 0.0838525 | + | 0.145237i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 15.5885i | − | 0.867365i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 6.00000 | − | 3.46410i | 0.332820 | − | 0.192154i | ||||
\(326\) | 16.5000 | + | 9.52628i | 0.913850 | + | 0.527612i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 4.50000 | + | 2.59808i | 0.248471 | + | 0.143455i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −8.00000 | −0.439720 | −0.219860 | − | 0.975531i | \(-0.570560\pi\) | ||||
−0.219860 | + | 0.975531i | \(0.570560\pi\) | |||||||
\(332\) | −7.50000 | − | 12.9904i | −0.411616 | − | 0.712940i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −13.5000 | − | 7.79423i | −0.738687 | − | 0.426481i | ||||
\(335\) | 6.00000 | + | 10.3923i | 0.327815 | + | 0.567792i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −9.50000 | + | 16.4545i | −0.517498 | + | 0.896333i | 0.482295 | + | 0.876009i | \(0.339803\pi\) |
−0.999793 | + | 0.0203242i | \(0.993530\pi\) | |||||||
\(338\) | −15.0000 | + | 8.66025i | −0.815892 | + | 0.471056i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 4.50000 | − | 7.79423i | 0.244047 | − | 0.422701i | ||||
\(341\) | −3.00000 | + | 5.19615i | −0.162459 | + | 0.281387i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −1.50000 | + | 0.866025i | −0.0808746 | + | 0.0466930i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 10.3923i | 0.558694i | ||||||||
\(347\) | 3.46410i | 0.185963i | 0.995668 | + | 0.0929814i | \(0.0296397\pi\) | ||||
−0.995668 | + | 0.0929814i | \(0.970360\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 10.5000 | − | 6.06218i | 0.562052 | − | 0.324501i | −0.191917 | − | 0.981411i | \(-0.561470\pi\) |
0.753969 | + | 0.656910i | \(0.228137\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 4.50000 | − | 7.79423i | 0.239851 | − | 0.415434i | ||||
\(353\) | 10.5000 | − | 18.1865i | 0.558859 | − | 0.967972i | −0.438733 | − | 0.898617i | \(-0.644573\pi\) |
0.997592 | − | 0.0693543i | \(-0.0220939\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 9.00000 | − | 5.19615i | 0.477670 | − | 0.275783i | ||||
\(356\) | 1.50000 | − | 2.59808i | 0.0794998 | − | 0.137698i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −13.5000 | − | 23.3827i | −0.713497 | − | 1.23581i | ||||
\(359\) | −19.5000 | − | 11.2583i | −1.02917 | − | 0.594192i | −0.112424 | − | 0.993660i | \(-0.535861\pi\) |
−0.916747 | + | 0.399468i | \(0.869195\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 4.00000 | + | 6.92820i | 0.210526 | + | 0.364642i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −13.5000 | − | 7.79423i | −0.706622 | − | 0.407969i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 4.50000 | + | 2.59808i | 0.234898 | + | 0.135618i | 0.612830 | − | 0.790215i | \(-0.290031\pi\) |
−0.377932 | + | 0.925834i | \(0.623365\pi\) | |||||||
\(368\) | 22.5000 | − | 12.9904i | 1.17289 | − | 0.677170i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | − | 36.3731i | − | 1.89095i | ||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 18.5000 | + | 32.0429i | 0.957894 | + | 1.65912i | 0.727603 | + | 0.685999i | \(0.240634\pi\) |
0.230291 | + | 0.973122i | \(0.426032\pi\) | |||||||
\(374\) | 9.00000 | 0.465379 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −9.00000 | −0.463524 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −20.0000 | −1.02733 | −0.513665 | − | 0.857991i | \(-0.671713\pi\) | ||||
−0.513665 | + | 0.857991i | \(0.671713\pi\) | |||||||
\(380\) | 15.5885i | 0.799671i | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −30.0000 | −1.53493 | ||||||||
\(383\) | −4.50000 | − | 7.79423i | −0.229939 | − | 0.398266i | 0.727851 | − | 0.685736i | \(-0.240519\pi\) |
−0.957790 | + | 0.287469i | \(0.907186\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 3.46410i | 0.176318i | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 1.50000 | − | 0.866025i | 0.0761510 | − | 0.0439658i | ||||
\(389\) | −31.5000 | − | 18.1865i | −1.59711 | − | 0.922094i | −0.992040 | − | 0.125924i | \(-0.959810\pi\) |
−0.605074 | − | 0.796170i | \(-0.706856\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 13.5000 | + | 7.79423i | 0.682724 | + | 0.394171i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −24.0000 | −1.20910 | ||||||||
\(395\) | −12.0000 | − | 20.7846i | −0.603786 | − | 1.04579i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −7.50000 | − | 4.33013i | −0.376414 | − | 0.217323i | 0.299843 | − | 0.953989i | \(-0.403066\pi\) |
−0.676257 | + | 0.736666i | \(0.736399\pi\) | |||||||
\(398\) | −7.50000 | − | 12.9904i | −0.375941 | − | 0.651149i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 10.0000 | − | 17.3205i | 0.500000 | − | 0.866025i | ||||
\(401\) | 28.5000 | − | 16.4545i | 1.42322 | − | 0.821698i | 0.426649 | − | 0.904417i | \(-0.359694\pi\) |
0.996573 | + | 0.0827195i | \(0.0263606\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −3.00000 | + | 5.19615i | −0.149441 | + | 0.258839i | ||||
\(404\) | 1.50000 | − | 2.59808i | 0.0746278 | − | 0.129259i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 10.5000 | − | 6.06218i | 0.520466 | − | 0.300491i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 6.92820i | − | 0.342578i | −0.985221 | − | 0.171289i | \(-0.945207\pi\) | ||
0.985221 | − | 0.171289i | \(-0.0547931\pi\) | |||||||
\(410\) | − | 15.5885i | − | 0.769859i | ||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 10.5000 | − | 6.06218i | 0.517298 | − | 0.298662i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 22.5000 | − | 38.9711i | 1.10448 | − | 1.91302i | ||||
\(416\) | 4.50000 | − | 7.79423i | 0.220631 | − | 0.382143i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −13.5000 | + | 7.79423i | −0.660307 | + | 0.381228i | ||||
\(419\) | 16.5000 | − | 28.5788i | 0.806078 | − | 1.39617i | −0.109483 | − | 0.993989i | \(-0.534920\pi\) |
0.915561 | − | 0.402179i | \(-0.131747\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −5.50000 | − | 9.52628i | −0.268054 | − | 0.464282i | 0.700306 | − | 0.713843i | \(-0.253047\pi\) |
−0.968359 | + | 0.249561i | \(0.919714\pi\) | |||||||
\(422\) | −7.50000 | − | 4.33013i | −0.365094 | − | 0.210787i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 7.50000 | + | 12.9904i | 0.364232 | + | 0.630869i | ||||
\(425\) | 12.0000 | 0.582086 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 7.50000 | + | 4.33013i | 0.362526 | + | 0.209305i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 4.50000 | + | 2.59808i | 0.217009 | + | 0.125290i | ||||
\(431\) | 13.5000 | − | 7.79423i | 0.650272 | − | 0.375435i | −0.138288 | − | 0.990392i | \(-0.544160\pi\) |
0.788560 | + | 0.614957i | \(0.210827\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 13.8564i | 0.665896i | 0.942945 | + | 0.332948i | \(0.108043\pi\) | ||||
−0.942945 | + | 0.332948i | \(0.891957\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 9.50000 | + | 16.4545i | 0.454967 | + | 0.788027i | ||||
\(437\) | −27.0000 | −1.29159 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 31.1769i | − | 1.48799i | −0.668184 | − | 0.743996i | \(-0.732928\pi\) | ||
0.668184 | − | 0.743996i | \(-0.267072\pi\) | |||||||
\(440\) | 9.00000 | 0.429058 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 9.00000 | 0.428086 | ||||||||
\(443\) | 31.1769i | 1.48126i | 0.671913 | + | 0.740630i | \(0.265473\pi\) | ||||
−0.671913 | + | 0.740630i | \(0.734527\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 9.00000 | 0.426641 | ||||||||
\(446\) | 4.50000 | + | 7.79423i | 0.213081 | + | 0.369067i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 34.6410i | 1.63481i | 0.576063 | + | 0.817405i | \(0.304588\pi\) | ||||
−0.576063 | + | 0.817405i | \(0.695412\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 4.50000 | − | 2.59808i | 0.211897 | − | 0.122339i | ||||
\(452\) | 1.50000 | + | 0.866025i | 0.0705541 | + | 0.0407344i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −31.5000 | − | 18.1865i | −1.47837 | − | 0.853536i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −26.0000 | −1.21623 | −0.608114 | − | 0.793849i | \(-0.708074\pi\) | ||||
−0.608114 | + | 0.793849i | \(0.708074\pi\) | |||||||
\(458\) | 7.50000 | + | 12.9904i | 0.350452 | + | 0.607001i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −13.5000 | − | 7.79423i | −0.629441 | − | 0.363408i | ||||
\(461\) | −7.50000 | − | 12.9904i | −0.349310 | − | 0.605022i | 0.636817 | − | 0.771015i | \(-0.280251\pi\) |
−0.986127 | + | 0.165992i | \(0.946917\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 0.500000 | − | 0.866025i | 0.0232370 | − | 0.0402476i | −0.854173 | − | 0.519989i | \(-0.825936\pi\) |
0.877410 | + | 0.479741i | \(0.159269\pi\) | |||||||
\(464\) | −22.5000 | + | 12.9904i | −1.04454 | + | 0.603063i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 4.50000 | − | 7.79423i | 0.208458 | − | 0.361061i | ||||
\(467\) | −1.50000 | + | 2.59808i | −0.0694117 | + | 0.120225i | −0.898642 | − | 0.438682i | \(-0.855446\pi\) |
0.829231 | + | 0.558906i | \(0.188779\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 1.73205i | 0.0796398i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −18.0000 | + | 10.3923i | −0.825897 | + | 0.476832i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −1.50000 | + | 2.59808i | −0.0686084 | + | 0.118833i | ||||
\(479\) | −13.5000 | + | 23.3827i | −0.616831 | + | 1.06838i | 0.373230 | + | 0.927739i | \(0.378250\pi\) |
−0.990060 | + | 0.140643i | \(0.955083\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 10.5000 | − | 6.06218i | 0.478759 | − | 0.276412i | ||||
\(482\) | −19.5000 | + | 33.7750i | −0.888201 | + | 1.53841i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 4.00000 | + | 6.92820i | 0.181818 | + | 0.314918i | ||||
\(485\) | 4.50000 | + | 2.59808i | 0.204334 | + | 0.117973i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 11.5000 | + | 19.9186i | 0.521115 | + | 0.902597i | 0.999698 | + | 0.0245553i | \(0.00781698\pi\) |
−0.478584 | + | 0.878042i | \(0.658850\pi\) | |||||||
\(488\) | −24.0000 | −1.08643 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 22.5000 | + | 12.9904i | 1.01541 | + | 0.586248i | 0.912771 | − | 0.408471i | \(-0.133938\pi\) |
0.102639 | + | 0.994719i | \(0.467271\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −13.5000 | − | 7.79423i | −0.608009 | − | 0.351034i | ||||
\(494\) | −13.5000 | + | 7.79423i | −0.607394 | + | 0.350679i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 17.3205i | 0.777714i | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −12.5000 | − | 21.6506i | −0.559577 | − | 0.969216i | −0.997532 | − | 0.0702185i | \(-0.977630\pi\) |
0.437955 | − | 0.898997i | \(-0.355703\pi\) | |||||||
\(500\) | 3.00000 | 0.134164 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 20.7846i | 0.927663i | ||||||||
\(503\) | 24.0000 | 1.07011 | 0.535054 | − | 0.844818i | \(-0.320291\pi\) | ||||
0.535054 | + | 0.844818i | \(0.320291\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 9.00000 | 0.400495 | ||||||||
\(506\) | − | 15.5885i | − | 0.692991i | ||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −20.0000 | −0.887357 | ||||||||
\(509\) | 16.5000 | + | 28.5788i | 0.731350 | + | 1.26673i | 0.956306 | + | 0.292366i | \(0.0944425\pi\) |
−0.224957 | + | 0.974369i | \(0.572224\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | − | 8.66025i | − | 0.382733i | ||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −4.50000 | + | 2.59808i | −0.198486 | + | 0.114596i | ||||
\(515\) | 31.5000 | + | 18.1865i | 1.38806 | + | 0.801394i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 9.00000 | 0.394676 | ||||||||
\(521\) | 22.5000 | + | 38.9711i | 0.985743 | + | 1.70736i | 0.638588 | + | 0.769549i | \(0.279519\pi\) |
0.347155 | + | 0.937808i | \(0.387148\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 16.5000 | + | 9.52628i | 0.721495 | + | 0.416555i | 0.815303 | − | 0.579035i | \(-0.196571\pi\) |
−0.0938079 | + | 0.995590i | \(0.529904\pi\) | |||||||
\(524\) | 4.50000 | + | 7.79423i | 0.196583 | + | 0.340492i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −19.5000 | + | 33.7750i | −0.850240 | + | 1.47266i | ||||
\(527\) | −9.00000 | + | 5.19615i | −0.392046 | + | 0.226348i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 2.00000 | − | 3.46410i | 0.0869565 | − | 0.150613i | ||||
\(530\) | 22.5000 | − | 38.9711i | 0.977338 | − | 1.69280i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 4.50000 | − | 2.59808i | 0.194917 | − | 0.112535i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 25.9808i | 1.12325i | ||||||||
\(536\) | 6.92820i | 0.299253i | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −22.5000 | + | 12.9904i | −0.970044 | + | 0.560055i | ||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 6.50000 | − | 11.2583i | 0.279457 | − | 0.484033i | −0.691793 | − | 0.722096i | \(-0.743179\pi\) |
0.971250 | + | 0.238062i | \(0.0765123\pi\) | |||||||
\(542\) | 10.5000 | − | 18.1865i | 0.451014 | − | 0.781179i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 13.5000 | − | 7.79423i | 0.578808 | − | 0.334175i | ||||
\(545\) | −28.5000 | + | 49.3634i | −1.22081 | + | 2.11450i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 9.50000 | + | 16.4545i | 0.406191 | + | 0.703543i | 0.994459 | − | 0.105123i | \(-0.0335235\pi\) |
−0.588269 | + | 0.808666i | \(0.700190\pi\) | |||||||
\(548\) | −10.5000 | − | 6.06218i | −0.448538 | − | 0.258963i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −6.00000 | − | 10.3923i | −0.255841 | − | 0.443129i | ||||
\(551\) | 27.0000 | 1.15024 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −1.50000 | − | 0.866025i | −0.0637289 | − | 0.0367939i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 7.50000 | + | 4.33013i | 0.318071 | + | 0.183638i | ||||
\(557\) | 10.5000 | − | 6.06218i | 0.444899 | − | 0.256863i | −0.260774 | − | 0.965400i | \(-0.583978\pi\) |
0.705674 | + | 0.708537i | \(0.250645\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1.73205i | 0.0732579i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −16.5000 | − | 28.5788i | −0.696010 | − | 1.20553i | ||||
\(563\) | 36.0000 | 1.51722 | 0.758610 | − | 0.651546i | \(-0.225879\pi\) | ||||
0.758610 | + | 0.651546i | \(0.225879\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 5.19615i | 0.218604i | ||||||||
\(566\) | 6.00000 | 0.252199 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 6.00000 | 0.251754 | ||||||||
\(569\) | 6.92820i | 0.290445i | 0.989399 | + | 0.145223i | \(0.0463899\pi\) | ||||
−0.989399 | + | 0.145223i | \(0.953610\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 32.0000 | 1.33916 | 0.669579 | − | 0.742741i | \(-0.266474\pi\) | ||||
0.669579 | + | 0.742741i | \(0.266474\pi\) | |||||||
\(572\) | −1.50000 | − | 2.59808i | −0.0627182 | − | 0.108631i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 20.7846i | − | 0.866778i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 34.5000 | − | 19.9186i | 1.43625 | − | 0.829222i | 0.438667 | − | 0.898650i | \(-0.355451\pi\) |
0.997587 | + | 0.0694283i | \(0.0221175\pi\) | |||||||
\(578\) | −12.0000 | − | 6.92820i | −0.499134 | − | 0.288175i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 13.5000 | + | 7.79423i | 0.560557 | + | 0.323638i | ||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 15.0000 | 0.621237 | ||||||||
\(584\) | −4.50000 | − | 7.79423i | −0.186211 | − | 0.322527i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −13.5000 | − | 7.79423i | −0.557680 | − | 0.321977i | ||||
\(587\) | −10.5000 | − | 18.1865i | −0.433381 | − | 0.750639i | 0.563781 | − | 0.825925i | \(-0.309346\pi\) |
−0.997162 | + | 0.0752860i | \(0.976013\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 9.00000 | − | 15.5885i | 0.370839 | − | 0.642311i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 17.5000 | − | 30.3109i | 0.719246 | − | 1.24577i | ||||
\(593\) | −19.5000 | + | 33.7750i | −0.800769 | + | 1.38697i | 0.118342 | + | 0.992973i | \(0.462242\pi\) |
−0.919111 | + | 0.394000i | \(0.871091\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 1.50000 | − | 0.866025i | 0.0614424 | − | 0.0354738i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | − | 15.5885i | − | 0.637459i | ||||||
\(599\) | 24.2487i | 0.990775i | 0.868672 | + | 0.495388i | \(0.164974\pi\) | ||||
−0.868672 | + | 0.495388i | \(0.835026\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −25.5000 | + | 14.7224i | −1.04017 | + | 0.600541i | −0.919881 | − | 0.392199i | \(-0.871715\pi\) |
−0.120286 | + | 0.992739i | \(0.538381\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −8.50000 | + | 14.7224i | −0.345860 | + | 0.599047i | ||||
\(605\) | −12.0000 | + | 20.7846i | −0.487869 | + | 0.845015i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 13.5000 | − | 7.79423i | 0.547948 | − | 0.316358i | −0.200346 | − | 0.979725i | \(-0.564207\pi\) |
0.748294 | + | 0.663367i | \(0.230873\pi\) | |||||||
\(608\) | −13.5000 | + | 23.3827i | −0.547497 | + | 0.948293i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 36.0000 | + | 62.3538i | 1.45760 | + | 2.52463i | ||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −23.5000 | − | 40.7032i | −0.949156 | − | 1.64399i | −0.747208 | − | 0.664590i | \(-0.768606\pi\) |
−0.201948 | − | 0.979396i | \(-0.564727\pi\) | |||||||
\(614\) | −42.0000 | −1.69498 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 4.50000 | + | 2.59808i | 0.181163 | + | 0.104595i | 0.587839 | − | 0.808978i | \(-0.299979\pi\) |
−0.406676 | + | 0.913573i | \(0.633312\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 16.5000 | + | 9.52628i | 0.663191 | + | 0.382893i | 0.793492 | − | 0.608581i | \(-0.208261\pi\) |
−0.130301 | + | 0.991475i | \(0.541594\pi\) | |||||||
\(620\) | 9.00000 | − | 5.19615i | 0.361449 | − | 0.208683i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 41.5692i | 1.66677i | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 14.5000 | + | 25.1147i | 0.580000 | + | 1.00459i | ||||
\(626\) | 36.0000 | 1.43885 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 21.0000 | 0.837325 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 8.00000 | 0.318475 | 0.159237 | − | 0.987240i | \(-0.449096\pi\) | ||||
0.159237 | + | 0.987240i | \(0.449096\pi\) | |||||||
\(632\) | − | 13.8564i | − | 0.551178i | ||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −30.0000 | − | 51.9615i | −1.19051 | − | 2.06203i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 15.5885i | 0.617153i | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 31.5000 | − | 18.1865i | 1.24515 | − | 0.718886i | ||||
\(641\) | 10.5000 | + | 6.06218i | 0.414725 | + | 0.239442i | 0.692818 | − | 0.721113i | \(-0.256369\pi\) |
−0.278093 | + | 0.960554i | \(0.589702\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 10.5000 | + | 6.06218i | 0.414080 | + | 0.239069i | 0.692541 | − | 0.721378i | \(-0.256491\pi\) |
−0.278462 | + | 0.960447i | \(0.589824\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −27.0000 | −1.06230 | ||||||||
\(647\) | 1.50000 | + | 2.59808i | 0.0589711 | + | 0.102141i | 0.894004 | − | 0.448059i | \(-0.147885\pi\) |
−0.835033 | + | 0.550200i | \(0.814551\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | −6.00000 | − | 10.3923i | −0.235339 | − | 0.407620i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 5.50000 | − | 9.52628i | 0.215397 | − | 0.373078i | ||||
\(653\) | 34.5000 | − | 19.9186i | 1.35009 | − | 0.779474i | 0.361828 | − | 0.932245i | \(-0.382153\pi\) |
0.988262 | + | 0.152771i | \(0.0488196\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −13.5000 | + | 23.3827i | −0.527489 | + | 0.913637i | ||||
\(656\) | 7.50000 | − | 12.9904i | 0.292826 | − | 0.507189i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −10.5000 | + | 6.06218i | −0.409022 | + | 0.236149i | −0.690369 | − | 0.723457i | \(-0.742552\pi\) |
0.281347 | + | 0.959606i | \(0.409219\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 41.5692i | 1.61686i | 0.588596 | + | 0.808428i | \(0.299681\pi\) | ||||
−0.588596 | + | 0.808428i | \(0.700319\pi\) | |||||||
\(662\) | 13.8564i | 0.538545i | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 22.5000 | − | 12.9904i | 0.873169 | − | 0.504125i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −13.5000 | + | 23.3827i | −0.522722 | + | 0.905381i | ||||
\(668\) | −4.50000 | + | 7.79423i | −0.174110 | + | 0.301568i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 18.0000 | − | 10.3923i | 0.695401 | − | 0.401490i | ||||
\(671\) | −12.0000 | + | 20.7846i | −0.463255 | + | 0.802381i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 14.5000 | + | 25.1147i | 0.558934 | + | 0.968102i | 0.997586 | + | 0.0694449i | \(0.0221228\pi\) |
−0.438652 | + | 0.898657i | \(0.644544\pi\) | |||||||
\(674\) | 28.5000 | + | 16.4545i | 1.09778 | + | 0.633803i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 5.00000 | + | 8.66025i | 0.192308 | + | 0.333087i | ||||
\(677\) | 18.0000 | 0.691796 | 0.345898 | − | 0.938272i | \(-0.387574\pi\) | ||||
0.345898 | + | 0.938272i | \(0.387574\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 13.5000 | + | 7.79423i | 0.517701 | + | 0.298895i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 9.00000 | + | 5.19615i | 0.344628 | + | 0.198971i | ||||
\(683\) | 7.50000 | − | 4.33013i | 0.286980 | − | 0.165688i | −0.349599 | − | 0.936899i | \(-0.613682\pi\) |
0.636579 | + | 0.771212i | \(0.280349\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 36.3731i | − | 1.38974i | ||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 2.50000 | + | 4.33013i | 0.0953116 | + | 0.165085i | ||||
\(689\) | 15.0000 | 0.571454 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 3.46410i | 0.131781i | 0.997827 | + | 0.0658903i | \(0.0209887\pi\) | ||||
−0.997827 | + | 0.0658903i | \(0.979011\pi\) | |||||||
\(692\) | 6.00000 | 0.228086 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 6.00000 | 0.227757 | ||||||||
\(695\) | 25.9808i | 0.985506i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 9.00000 | 0.340899 | ||||||||
\(698\) | −10.5000 | − | 18.1865i | −0.397431 | − | 0.688370i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 34.6410i | 1.30837i | 0.756333 | + | 0.654187i | \(0.226989\pi\) | ||||
−0.756333 | + | 0.654187i | \(0.773011\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −31.5000 | + | 18.1865i | −1.18805 | + | 0.685918i | ||||
\(704\) | 1.50000 | + | 0.866025i | 0.0565334 | + | 0.0326396i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −31.5000 | − | 18.1865i | −1.18552 | − | 0.684459i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 10.0000 | 0.375558 | 0.187779 | − | 0.982211i | \(-0.439871\pi\) | ||||
0.187779 | + | 0.982211i | \(0.439871\pi\) | |||||||
\(710\) | −9.00000 | − | 15.5885i | −0.337764 | − | 0.585024i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 4.50000 | + | 2.59808i | 0.168645 | + | 0.0973670i | ||||
\(713\) | 9.00000 | + | 15.5885i | 0.337053 | + | 0.583792i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 4.50000 | − | 7.79423i | 0.168290 | − | 0.291488i | ||||
\(716\) | −13.5000 | + | 7.79423i | −0.504519 | + | 0.291284i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −19.5000 | + | 33.7750i | −0.727734 | + | 1.26047i | ||||
\(719\) | 4.50000 | − | 7.79423i | 0.167822 | − | 0.290676i | −0.769832 | − | 0.638247i | \(-0.779660\pi\) |
0.937654 | + | 0.347571i | \(0.112993\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 12.0000 | − | 6.92820i | 0.446594 | − | 0.257841i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 20.7846i | 0.771921i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −10.5000 | + | 6.06218i | −0.389423 | + | 0.224834i | −0.681910 | − | 0.731436i | \(-0.738851\pi\) |
0.292487 | + | 0.956270i | \(0.405517\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −13.5000 | + | 23.3827i | −0.499657 | + | 0.865432i | ||||
\(731\) | −1.50000 | + | 2.59808i | −0.0554795 | + | 0.0960933i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −37.5000 | + | 21.6506i | −1.38509 | + | 0.799684i | −0.992757 | − | 0.120137i | \(-0.961667\pi\) |
−0.392337 | + | 0.919822i | \(0.628333\pi\) | |||||||
\(734\) | 4.50000 | − | 7.79423i | 0.166098 | − | 0.287690i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −13.5000 | − | 23.3827i | −0.497617 | − | 0.861897i | ||||
\(737\) | 6.00000 | + | 3.46410i | 0.221013 | + | 0.127602i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 3.50000 | + | 6.06218i | 0.128750 | + | 0.223001i | 0.923192 | − | 0.384338i | \(-0.125570\pi\) |
−0.794443 | + | 0.607339i | \(0.792237\pi\) | |||||||
\(740\) | −21.0000 | −0.771975 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 10.5000 | + | 6.06218i | 0.385208 | + | 0.222400i | 0.680082 | − | 0.733136i | \(-0.261944\pi\) |
−0.294874 | + | 0.955536i | \(0.595278\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 4.50000 | + | 2.59808i | 0.164867 | + | 0.0951861i | ||||
\(746\) | 55.5000 | − | 32.0429i | 2.03200 | − | 1.17318i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | − | 5.19615i | − | 0.189990i | ||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −18.5000 | − | 32.0429i | −0.675075 | − | 1.16926i | −0.976447 | − | 0.215757i | \(-0.930778\pi\) |
0.301373 | − | 0.953506i | \(-0.402555\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 15.5885i | 0.567698i | ||||||||
\(755\) | −51.0000 | −1.85608 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 10.0000 | 0.363456 | 0.181728 | − | 0.983349i | \(-0.441831\pi\) | ||||
0.181728 | + | 0.983349i | \(0.441831\pi\) | |||||||
\(758\) | 34.6410i | 1.25822i | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −27.0000 | −0.979393 | ||||||||
\(761\) | 22.5000 | + | 38.9711i | 0.815624 | + | 1.41270i | 0.908879 | + | 0.417061i | \(0.136940\pi\) |
−0.0932544 | + | 0.995642i | \(0.529727\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 17.3205i | 0.626634i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −13.5000 | + | 7.79423i | −0.487775 | + | 0.281617i | ||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −13.5000 | − | 7.79423i | −0.486822 | − | 0.281067i | 0.236433 | − | 0.971648i | \(-0.424022\pi\) |
−0.723255 | + | 0.690581i | \(0.757355\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 2.00000 | 0.0719816 | ||||||||
\(773\) | −25.5000 | − | 44.1673i | −0.917171 | − | 1.58859i | −0.803691 | − | 0.595047i | \(-0.797133\pi\) |
−0.113480 | − | 0.993540i | \(-0.536200\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 12.0000 | + | 6.92820i | 0.431053 | + | 0.248868i | ||||
\(776\) | 1.50000 | + | 2.59808i | 0.0538469 | + | 0.0932655i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −31.5000 | + | 54.5596i | −1.12933 | + | 1.95606i | ||||
\(779\) | −13.5000 | + | 7.79423i | −0.483688 | + | 0.279257i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 3.00000 | − | 5.19615i | 0.107348 | − | 0.185933i | ||||
\(782\) | 13.5000 | − | 23.3827i | 0.482759 | − | 0.836163i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 38.1051i | − | 1.35830i | −0.733999 | − | 0.679150i | \(-0.762348\pi\) | ||
0.733999 | − | 0.679150i | \(-0.237652\pi\) | |||||||
\(788\) | 13.8564i | 0.493614i | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −36.0000 | + | 20.7846i | −1.28082 | + | 0.739483i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −12.0000 | + | 20.7846i | −0.426132 | + | 0.738083i | ||||
\(794\) | −7.50000 | + | 12.9904i | −0.266165 | + | 0.461011i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −7.50000 | + | 4.33013i | −0.265830 | + | 0.153477i | ||||
\(797\) | 22.5000 | − | 38.9711i | 0.796991 | − | 1.38043i | −0.124576 | − | 0.992210i | \(-0.539757\pi\) |
0.921567 | − | 0.388219i | \(-0.126909\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | −18.0000 | − | 10.3923i | −0.636396 | − | 0.367423i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −28.5000 | − | 49.3634i | −1.00637 | − | 1.74308i | ||||
\(803\) | −9.00000 | −0.317603 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 9.00000 | + | 5.19615i | 0.317011 | + | 0.183027i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 4.50000 | + | 2.59808i | 0.158309 | + | 0.0914000i | ||||
\(809\) | −1.50000 | + | 0.866025i | −0.0527372 | + | 0.0304478i | −0.526137 | − | 0.850400i | \(-0.676360\pi\) |
0.473400 | + | 0.880848i | \(0.343027\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 10.3923i | − | 0.364923i | −0.983213 | − | 0.182462i | \(-0.941593\pi\) | ||
0.983213 | − | 0.182462i | \(-0.0584065\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −10.5000 | − | 18.1865i | −0.368025 | − | 0.637438i | ||||
\(815\) | 33.0000 | 1.15594 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 5.19615i | − | 0.181790i | ||||||
\(818\) | −12.0000 | −0.419570 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −9.00000 | −0.314294 | ||||||||
\(821\) | 6.92820i | 0.241796i | 0.992665 | + | 0.120898i | \(0.0385774\pi\) | ||||
−0.992665 | + | 0.120898i | \(0.961423\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −16.0000 | −0.557725 | −0.278862 | − | 0.960331i | \(-0.589957\pi\) | ||||
−0.278862 | + | 0.960331i | \(0.589957\pi\) | |||||||
\(824\) | 10.5000 | + | 18.1865i | 0.365785 | + | 0.633558i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 24.2487i | − | 0.843210i | −0.906780 | − | 0.421605i | \(-0.861467\pi\) | ||
0.906780 | − | 0.421605i | \(-0.138533\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −31.5000 | + | 18.1865i | −1.09404 | + | 0.631644i | −0.934649 | − | 0.355571i | \(-0.884286\pi\) |
−0.159391 | + | 0.987216i | \(0.550953\pi\) | |||||||
\(830\) | −67.5000 | − | 38.9711i | −2.34296 | − | 1.35271i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 1.50000 | + | 0.866025i | 0.0520031 | + | 0.0300240i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −27.0000 | −0.934374 | ||||||||
\(836\) | 4.50000 | + | 7.79423i | 0.155636 | + | 0.269569i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −49.5000 | − | 28.5788i | −1.70995 | − | 0.987240i | ||||
\(839\) | 19.5000 | + | 33.7750i | 0.673215 | + | 1.16604i | 0.976987 | + | 0.213298i | \(0.0684204\pi\) |
−0.303773 | + | 0.952745i | \(0.598246\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.00000 | + | 1.73205i | −0.0344828 | + | 0.0597259i | ||||
\(842\) | −16.5000 | + | 9.52628i | −0.568628 | + | 0.328297i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −2.50000 | + | 4.33013i | −0.0860535 | + | 0.149049i | ||||
\(845\) | −15.0000 | + | 25.9808i | −0.516016 | + | 0.893765i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 37.5000 | − | 21.6506i | 1.28776 | − | 0.743486i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | − | 20.7846i | − | 0.712906i | ||||||
\(851\) | − | 36.3731i | − | 1.24685i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 22.5000 | − | 12.9904i | 0.770385 | − | 0.444782i | −0.0626267 | − | 0.998037i | \(-0.519948\pi\) |
0.833012 | + | 0.553255i | \(0.186614\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −7.50000 | + | 12.9904i | −0.256345 | + | 0.444002i | ||||
\(857\) | −13.5000 | + | 23.3827i | −0.461151 | + | 0.798737i | −0.999019 | − | 0.0442921i | \(-0.985897\pi\) |
0.537867 | + | 0.843029i | \(0.319230\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 43.5000 | − | 25.1147i | 1.48420 | − | 0.856904i | 0.484362 | − | 0.874868i | \(-0.339052\pi\) |
0.999839 | + | 0.0179638i | \(0.00571836\pi\) | |||||||
\(860\) | 1.50000 | − | 2.59808i | 0.0511496 | − | 0.0885937i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −13.5000 | − | 23.3827i | −0.459812 | − | 0.796417i | ||||
\(863\) | −37.5000 | − | 21.6506i | −1.27651 | − | 0.736996i | −0.300309 | − | 0.953842i | \(-0.597090\pi\) |
−0.976206 | + | 0.216846i | \(0.930423\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 9.00000 | + | 15.5885i | 0.306009 | + | 0.530023i | ||||
\(866\) | 24.0000 | 0.815553 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −12.0000 | − | 6.92820i | −0.407072 | − | 0.235023i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 6.00000 | + | 3.46410i | 0.203302 | + | 0.117377i | ||||
\(872\) | −28.5000 | + | 16.4545i | −0.965132 | + | 0.557219i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 46.7654i | 1.58186i | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −11.5000 | − | 19.9186i | −0.388327 | − | 0.672603i | 0.603897 | − | 0.797062i | \(-0.293614\pi\) |
−0.992225 | + | 0.124459i | \(0.960280\pi\) | |||||||
\(878\) | −54.0000 | −1.82241 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | − | 25.9808i | − | 0.875811i | ||||||
\(881\) | 54.0000 | 1.81931 | 0.909653 | − | 0.415369i | \(-0.136347\pi\) | ||||
0.909653 | + | 0.415369i | \(0.136347\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 4.00000 | 0.134611 | 0.0673054 | − | 0.997732i | \(-0.478560\pi\) | ||||
0.0673054 | + | 0.997732i | \(0.478560\pi\) | |||||||
\(884\) | − | 5.19615i | − | 0.174766i | ||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 54.0000 | 1.81417 | ||||||||
\(887\) | 7.50000 | + | 12.9904i | 0.251825 | + | 0.436174i | 0.964028 | − | 0.265799i | \(-0.0856358\pi\) |
−0.712203 | + | 0.701974i | \(0.752302\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | − | 15.5885i | − | 0.522526i | ||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 4.50000 | − | 2.59808i | 0.150671 | − | 0.0869900i | ||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −40.5000 | − | 23.3827i | −1.35377 | − | 0.781597i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 60.0000 | 2.00223 | ||||||||
\(899\) | −9.00000 | − | 15.5885i | −0.300167 | − | 0.519904i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 22.5000 | + | 12.9904i | 0.749584 | + | 0.432772i | ||||
\(902\) | −4.50000 | − | 7.79423i | −0.149834 | − | 0.259519i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −1.50000 | + | 2.59808i | −0.0498893 | + | 0.0864107i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −9.50000 | + | 16.4545i | −0.315442 | + | 0.546362i | −0.979531 | − | 0.201291i | \(-0.935486\pi\) |
0.664089 | + | 0.747653i | \(0.268820\pi\) | |||||||
\(908\) | −10.5000 | + | 18.1865i | −0.348455 | + | 0.603541i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −4.50000 | + | 2.59808i | −0.149092 | + | 0.0860781i | −0.572690 | − | 0.819772i | \(-0.694100\pi\) |
0.423598 | + | 0.905850i | \(0.360767\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 25.9808i | − | 0.859838i | ||||||
\(914\) | 45.0333i | 1.48957i | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 7.50000 | − | 4.33013i | 0.247807 | − | 0.143071i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 14.5000 | − | 25.1147i | 0.478311 | − | 0.828459i | −0.521380 | − | 0.853325i | \(-0.674583\pi\) |
0.999691 | + | 0.0248659i | \(0.00791589\pi\) | |||||||
\(920\) | 13.5000 | − | 23.3827i | 0.445082 | − | 0.770904i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −22.5000 | + | 12.9904i | −0.740998 | + | 0.427815i | ||||
\(923\) | 3.00000 | − | 5.19615i | 0.0987462 | − | 0.171033i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −14.0000 | − | 24.2487i | −0.460317 | − | 0.797293i | ||||
\(926\) | −1.50000 | − | 0.866025i | −0.0492931 | − | 0.0284594i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 13.5000 | + | 23.3827i | 0.443159 | + | 0.767574i | ||||
\(929\) | −30.0000 | −0.984268 | −0.492134 | − | 0.870519i | \(-0.663783\pi\) | ||||
−0.492134 | + | 0.870519i | \(0.663783\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −4.50000 | − | 2.59808i | −0.147402 | − | 0.0851028i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 4.50000 | + | 2.59808i | 0.147244 | + | 0.0850117i | ||||
\(935\) | 13.5000 | − | 7.79423i | 0.441497 | − | 0.254899i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 13.8564i | 0.452669i | 0.974050 | + | 0.226335i | \(0.0726743\pi\) | ||||
−0.974050 | + | 0.226335i | \(0.927326\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 18.0000 | 0.586783 | 0.293392 | − | 0.955992i | \(-0.405216\pi\) | ||||
0.293392 | + | 0.955992i | \(0.405216\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 15.5885i | − | 0.507630i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 3.00000 | 0.0975384 | ||||||||
\(947\) | − | 51.9615i | − | 1.68852i | −0.535932 | − | 0.844261i | \(-0.680040\pi\) | ||
0.535932 | − | 0.844261i | \(-0.319960\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −9.00000 | −0.292152 | ||||||||
\(950\) | 18.0000 | + | 31.1769i | 0.583997 | + | 1.01151i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 20.7846i | 0.673280i | 0.941634 | + | 0.336640i | \(0.109290\pi\) | ||||
−0.941634 | + | 0.336640i | \(0.890710\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −45.0000 | + | 25.9808i | −1.45617 | + | 0.840718i | ||||
\(956\) | 1.50000 | + | 0.866025i | 0.0485135 | + | 0.0280093i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 40.5000 | + | 23.3827i | 1.30850 | + | 0.755460i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 19.0000 | 0.612903 | ||||||||
\(962\) | −10.5000 | − | 18.1865i | −0.338534 | − | 0.586357i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 19.5000 | + | 11.2583i | 0.628053 | + | 0.362606i | ||||
\(965\) | 3.00000 | + | 5.19615i | 0.0965734 | + | 0.167270i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 12.5000 | − | 21.6506i | 0.401973 | − | 0.696237i | −0.591991 | − | 0.805945i | \(-0.701658\pi\) |
0.993964 | + | 0.109707i | \(0.0349913\pi\) | |||||||
\(968\) | −12.0000 | + | 6.92820i | −0.385695 | + | 0.222681i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 4.50000 | − | 7.79423i | 0.144486 | − | 0.250258i | ||||
\(971\) | 28.5000 | − | 49.3634i | 0.914609 | − | 1.58415i | 0.107135 | − | 0.994244i | \(-0.465832\pi\) |
0.807473 | − | 0.589904i | \(-0.200834\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 34.5000 | − | 19.9186i | 1.10545 | − | 0.638233i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 69.2820i | 2.21766i | ||||||||
\(977\) | 41.5692i | 1.32992i | 0.746880 | + | 0.664959i | \(0.231551\pi\) | ||||
−0.746880 | + | 0.664959i | \(0.768449\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 4.50000 | − | 2.59808i | 0.143821 | − | 0.0830349i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 22.5000 | − | 38.9711i | 0.718004 | − | 1.24362i | ||||
\(983\) | −19.5000 | + | 33.7750i | −0.621953 | + | 1.07725i | 0.367168 | + | 0.930155i | \(0.380327\pi\) |
−0.989122 | + | 0.147100i | \(0.953006\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −36.0000 | + | 20.7846i | −1.14706 | + | 0.662253i | ||||
\(986\) | −13.5000 | + | 23.3827i | −0.429928 | + | 0.744656i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 4.50000 | + | 7.79423i | 0.143164 | + | 0.247967i | ||||
\(989\) | 4.50000 | + | 2.59808i | 0.143092 | + | 0.0826140i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 23.5000 | + | 40.7032i | 0.746502 | + | 1.29298i | 0.949490 | + | 0.313798i | \(0.101602\pi\) |
−0.202988 | + | 0.979181i | \(0.565065\pi\) | |||||||
\(992\) | 18.0000 | 0.571501 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −22.5000 | − | 12.9904i | −0.713298 | − | 0.411823i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −7.50000 | − | 4.33013i | −0.237527 | − | 0.137136i | 0.376512 | − | 0.926412i | \(-0.377123\pi\) |
−0.614040 | + | 0.789275i | \(0.710457\pi\) | |||||||
\(998\) | −37.5000 | + | 21.6506i | −1.18704 | + | 0.685339i | ||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))