Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2646,2,Mod(361,2646)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2646, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([2, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2646.361");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2646 = 2 \cdot 3^{3} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2646.h (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: | \(21.1284163748\) |
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 126) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 667.1 | ||
Root | \(0.500000 - 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2646.667 |
Dual form | 2646.2.h.b.361.1 |
$q$-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 \(\left(\mathbb{Z}/2646\mathbb{Z}\right)^\times\).
\(n\) | \(785\) | \(1081\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{1}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.500000 | − | 0.866025i | −0.353553 | − | 0.612372i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −0.500000 | + | 0.866025i | −0.250000 | + | 0.433013i | ||||
\(5\) | −2.00000 | −0.894427 | −0.447214 | − | 0.894427i | \(-0.647584\pi\) | ||||
−0.447214 | + | 0.894427i | \(0.647584\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 1.00000 | + | 1.73205i | 0.316228 | + | 0.547723i | ||||
\(11\) | −1.00000 | −0.301511 | −0.150756 | − | 0.988571i | \(-0.548171\pi\) | ||||
−0.150756 | + | 0.988571i | \(0.548171\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.00000 | + | 5.19615i | 0.832050 | + | 1.44115i | 0.896410 | + | 0.443227i | \(0.146166\pi\) |
−0.0643593 | + | 0.997927i | \(0.520500\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.500000 | − | 0.866025i | −0.125000 | − | 0.216506i | ||||
\(17\) | −2.50000 | − | 4.33013i | −0.606339 | − | 1.05021i | −0.991838 | − | 0.127502i | \(-0.959304\pi\) |
0.385499 | − | 0.922708i | \(-0.374029\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.50000 | − | 6.06218i | 0.802955 | − | 1.39076i | −0.114708 | − | 0.993399i | \(-0.536593\pi\) |
0.917663 | − | 0.397360i | \(-0.130073\pi\) | |||||||
\(20\) | 1.00000 | − | 1.73205i | 0.223607 | − | 0.387298i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0.500000 | + | 0.866025i | 0.106600 | + | 0.184637i | ||||
\(23\) | −4.00000 | −0.834058 | −0.417029 | − | 0.908893i | \(-0.636929\pi\) | ||||
−0.417029 | + | 0.908893i | \(0.636929\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.00000 | −0.200000 | ||||||||
\(26\) | 3.00000 | − | 5.19615i | 0.588348 | − | 1.01905i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −2.00000 | + | 3.46410i | −0.371391 | + | 0.643268i | −0.989780 | − | 0.142605i | \(-0.954452\pi\) |
0.618389 | + | 0.785872i | \(0.287786\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.00000 | − | 5.19615i | 0.538816 | − | 0.933257i | −0.460152 | − | 0.887840i | \(-0.652205\pi\) |
0.998968 | − | 0.0454165i | \(-0.0144615\pi\) | |||||||
\(32\) | −0.500000 | + | 0.866025i | −0.0883883 | + | 0.153093i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −2.50000 | + | 4.33013i | −0.428746 | + | 0.742611i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −1.00000 | + | 1.73205i | −0.164399 | + | 0.284747i | −0.936442 | − | 0.350823i | \(-0.885902\pi\) |
0.772043 | + | 0.635571i | \(0.219235\pi\) | |||||||
\(38\) | −7.00000 | −1.13555 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −2.00000 | −0.316228 | ||||||||
\(41\) | 1.50000 | + | 2.59808i | 0.234261 | + | 0.405751i | 0.959058 | − | 0.283211i | \(-0.0913998\pi\) |
−0.724797 | + | 0.688963i | \(0.758066\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0.500000 | − | 0.866025i | 0.0762493 | − | 0.132068i | −0.825380 | − | 0.564578i | \(-0.809039\pi\) |
0.901629 | + | 0.432511i | \(0.142372\pi\) | |||||||
\(44\) | 0.500000 | − | 0.866025i | 0.0753778 | − | 0.130558i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 2.00000 | + | 3.46410i | 0.294884 | + | 0.510754i | ||||
\(47\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0.500000 | + | 0.866025i | 0.0707107 | + | 0.122474i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −6.00000 | −0.832050 | ||||||||
\(53\) | 6.00000 | + | 10.3923i | 0.824163 | + | 1.42749i | 0.902557 | + | 0.430570i | \(0.141688\pi\) |
−0.0783936 | + | 0.996922i | \(0.524979\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 2.00000 | 0.269680 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 4.00000 | 0.525226 | ||||||||
\(59\) | −3.50000 | + | 6.06218i | −0.455661 | + | 0.789228i | −0.998726 | − | 0.0504625i | \(-0.983930\pi\) |
0.543065 | + | 0.839691i | \(0.317264\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 6.00000 | + | 10.3923i | 0.768221 | + | 1.33060i | 0.938527 | + | 0.345207i | \(0.112191\pi\) |
−0.170305 | + | 0.985391i | \(0.554475\pi\) | |||||||
\(62\) | −6.00000 | −0.762001 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −6.00000 | − | 10.3923i | −0.744208 | − | 1.28901i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −6.50000 | + | 11.2583i | −0.794101 | + | 1.37542i | 0.129307 | + | 0.991605i | \(0.458725\pi\) |
−0.923408 | + | 0.383819i | \(0.874609\pi\) | |||||||
\(68\) | 5.00000 | 0.606339 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 8.00000 | 0.949425 | 0.474713 | − | 0.880141i | \(-0.342552\pi\) | ||||
0.474713 | + | 0.880141i | \(0.342552\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −0.500000 | − | 0.866025i | −0.0585206 | − | 0.101361i | 0.835281 | − | 0.549823i | \(-0.185305\pi\) |
−0.893801 | + | 0.448463i | \(0.851972\pi\) | |||||||
\(74\) | 2.00000 | 0.232495 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 3.50000 | + | 6.06218i | 0.401478 | + | 0.695379i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 3.00000 | + | 5.19615i | 0.337526 | + | 0.584613i | 0.983967 | − | 0.178352i | \(-0.0570765\pi\) |
−0.646440 | + | 0.762964i | \(0.723743\pi\) | |||||||
\(80\) | 1.00000 | + | 1.73205i | 0.111803 | + | 0.193649i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 1.50000 | − | 2.59808i | 0.165647 | − | 0.286910i | ||||
\(83\) | 8.00000 | − | 13.8564i | 0.878114 | − | 1.52094i | 0.0247060 | − | 0.999695i | \(-0.492135\pi\) |
0.853408 | − | 0.521243i | \(-0.174532\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 5.00000 | + | 8.66025i | 0.542326 | + | 0.939336i | ||||
\(86\) | −1.00000 | −0.107833 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −1.00000 | −0.106600 | ||||||||
\(89\) | −3.00000 | + | 5.19615i | −0.317999 | + | 0.550791i | −0.980071 | − | 0.198650i | \(-0.936344\pi\) |
0.662071 | + | 0.749441i | \(0.269678\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 2.00000 | − | 3.46410i | 0.208514 | − | 0.361158i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −7.00000 | + | 12.1244i | −0.718185 | + | 1.24393i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 2.50000 | − | 4.33013i | 0.253837 | − | 0.439658i | −0.710742 | − | 0.703452i | \(-0.751641\pi\) |
0.964579 | + | 0.263795i | \(0.0849741\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0.500000 | − | 0.866025i | 0.0500000 | − | 0.0866025i | ||||
\(101\) | 4.00000 | 0.398015 | 0.199007 | − | 0.979998i | \(-0.436228\pi\) | ||||
0.199007 | + | 0.979998i | \(0.436228\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 14.0000 | 1.37946 | 0.689730 | − | 0.724066i | \(-0.257729\pi\) | ||||
0.689730 | + | 0.724066i | \(0.257729\pi\) | |||||||
\(104\) | 3.00000 | + | 5.19615i | 0.294174 | + | 0.509525i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 6.00000 | − | 10.3923i | 0.582772 | − | 1.00939i | ||||
\(107\) | 1.50000 | − | 2.59808i | 0.145010 | − | 0.251166i | −0.784366 | − | 0.620298i | \(-0.787012\pi\) |
0.929377 | + | 0.369132i | \(0.120345\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1.00000 | + | 1.73205i | 0.0957826 | + | 0.165900i | 0.909935 | − | 0.414751i | \(-0.136131\pi\) |
−0.814152 | + | 0.580651i | \(0.802798\pi\) | |||||||
\(110\) | −1.00000 | − | 1.73205i | −0.0953463 | − | 0.165145i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −5.00000 | − | 8.66025i | −0.470360 | − | 0.814688i | 0.529065 | − | 0.848581i | \(-0.322543\pi\) |
−0.999425 | + | 0.0338931i | \(0.989209\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 8.00000 | 0.746004 | ||||||||
\(116\) | −2.00000 | − | 3.46410i | −0.185695 | − | 0.321634i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 7.00000 | 0.644402 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.0000 | −0.909091 | ||||||||
\(122\) | 6.00000 | − | 10.3923i | 0.543214 | − | 0.940875i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 3.00000 | + | 5.19615i | 0.269408 | + | 0.466628i | ||||
\(125\) | 12.0000 | 1.07331 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −12.0000 | −1.06483 | −0.532414 | − | 0.846484i | \(-0.678715\pi\) | ||||
−0.532414 | + | 0.846484i | \(0.678715\pi\) | |||||||
\(128\) | −0.500000 | − | 0.866025i | −0.0441942 | − | 0.0765466i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −6.00000 | + | 10.3923i | −0.526235 | + | 0.911465i | ||||
\(131\) | 4.00000 | 0.349482 | 0.174741 | − | 0.984614i | \(-0.444091\pi\) | ||||
0.174741 | + | 0.984614i | \(0.444091\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 13.0000 | 1.12303 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −2.50000 | − | 4.33013i | −0.214373 | − | 0.371305i | ||||
\(137\) | 19.0000 | 1.62328 | 0.811640 | − | 0.584158i | \(-0.198575\pi\) | ||||
0.811640 | + | 0.584158i | \(0.198575\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2.50000 | + | 4.33013i | 0.212047 | + | 0.367277i | 0.952355 | − | 0.304991i | \(-0.0986536\pi\) |
−0.740308 | + | 0.672268i | \(0.765320\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −4.00000 | − | 6.92820i | −0.335673 | − | 0.581402i | ||||
\(143\) | −3.00000 | − | 5.19615i | −0.250873 | − | 0.434524i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 4.00000 | − | 6.92820i | 0.332182 | − | 0.575356i | ||||
\(146\) | −0.500000 | + | 0.866025i | −0.0413803 | + | 0.0716728i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −1.00000 | − | 1.73205i | −0.0821995 | − | 0.142374i | ||||
\(149\) | 24.0000 | 1.96616 | 0.983078 | − | 0.183186i | \(-0.0586410\pi\) | ||||
0.983078 | + | 0.183186i | \(0.0586410\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 10.0000 | 0.813788 | 0.406894 | − | 0.913475i | \(-0.366612\pi\) | ||||
0.406894 | + | 0.913475i | \(0.366612\pi\) | |||||||
\(152\) | 3.50000 | − | 6.06218i | 0.283887 | − | 0.491708i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −6.00000 | + | 10.3923i | −0.481932 | + | 0.834730i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1.00000 | + | 1.73205i | −0.0798087 | + | 0.138233i | −0.903167 | − | 0.429289i | \(-0.858764\pi\) |
0.823359 | + | 0.567521i | \(0.192098\pi\) | |||||||
\(158\) | 3.00000 | − | 5.19615i | 0.238667 | − | 0.413384i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 1.00000 | − | 1.73205i | 0.0790569 | − | 0.136931i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 2.00000 | − | 3.46410i | 0.156652 | − | 0.271329i | −0.777007 | − | 0.629492i | \(-0.783263\pi\) |
0.933659 | + | 0.358162i | \(0.116597\pi\) | |||||||
\(164\) | −3.00000 | −0.234261 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −16.0000 | −1.24184 | ||||||||
\(167\) | 10.0000 | + | 17.3205i | 0.773823 | + | 1.34030i | 0.935454 | + | 0.353450i | \(0.114991\pi\) |
−0.161630 | + | 0.986851i | \(0.551675\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −11.5000 | + | 19.9186i | −0.884615 | + | 1.53220i | ||||
\(170\) | 5.00000 | − | 8.66025i | 0.383482 | − | 0.664211i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0.500000 | + | 0.866025i | 0.0381246 | + | 0.0660338i | ||||
\(173\) | 1.00000 | + | 1.73205i | 0.0760286 | + | 0.131685i | 0.901533 | − | 0.432710i | \(-0.142443\pi\) |
−0.825505 | + | 0.564396i | \(0.809109\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0.500000 | + | 0.866025i | 0.0376889 | + | 0.0652791i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 6.00000 | 0.449719 | ||||||||
\(179\) | 12.0000 | + | 20.7846i | 0.896922 | + | 1.55351i | 0.831408 | + | 0.555663i | \(0.187536\pi\) |
0.0655145 | + | 0.997852i | \(0.479131\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −4.00000 | −0.294884 | ||||||||
\(185\) | 2.00000 | − | 3.46410i | 0.147043 | − | 0.254686i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 2.50000 | + | 4.33013i | 0.182818 | + | 0.316650i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 14.0000 | 1.01567 | ||||||||
\(191\) | 6.00000 | + | 10.3923i | 0.434145 | + | 0.751961i | 0.997225 | − | 0.0744412i | \(-0.0237173\pi\) |
−0.563081 | + | 0.826402i | \(0.690384\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −8.50000 | + | 14.7224i | −0.611843 | + | 1.05974i | 0.379086 | + | 0.925361i | \(0.376238\pi\) |
−0.990930 | + | 0.134382i | \(0.957095\pi\) | |||||||
\(194\) | −5.00000 | −0.358979 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −10.0000 | −0.712470 | −0.356235 | − | 0.934396i | \(-0.615940\pi\) | ||||
−0.356235 | + | 0.934396i | \(0.615940\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −7.00000 | − | 12.1244i | −0.496217 | − | 0.859473i | 0.503774 | − | 0.863836i | \(-0.331945\pi\) |
−0.999990 | + | 0.00436292i | \(0.998611\pi\) | |||||||
\(200\) | −1.00000 | −0.0707107 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −2.00000 | − | 3.46410i | −0.140720 | − | 0.243733i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −3.00000 | − | 5.19615i | −0.209529 | − | 0.362915i | ||||
\(206\) | −7.00000 | − | 12.1244i | −0.487713 | − | 0.844744i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 3.00000 | − | 5.19615i | 0.208013 | − | 0.360288i | ||||
\(209\) | −3.50000 | + | 6.06218i | −0.242100 | + | 0.419330i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 8.00000 | + | 13.8564i | 0.550743 | + | 0.953914i | 0.998221 | + | 0.0596196i | \(0.0189888\pi\) |
−0.447478 | + | 0.894295i | \(0.647678\pi\) | |||||||
\(212\) | −12.0000 | −0.824163 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −3.00000 | −0.205076 | ||||||||
\(215\) | −1.00000 | + | 1.73205i | −0.0681994 | + | 0.118125i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 1.00000 | − | 1.73205i | 0.0677285 | − | 0.117309i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −1.00000 | + | 1.73205i | −0.0674200 | + | 0.116775i | ||||
\(221\) | 15.0000 | − | 25.9808i | 1.00901 | − | 1.74766i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 2.00000 | − | 3.46410i | 0.133930 | − | 0.231973i | −0.791258 | − | 0.611482i | \(-0.790574\pi\) |
0.925188 | + | 0.379509i | \(0.123907\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −5.00000 | + | 8.66025i | −0.332595 | + | 0.576072i | ||||
\(227\) | −3.00000 | −0.199117 | −0.0995585 | − | 0.995032i | \(-0.531743\pi\) | ||||
−0.0995585 | + | 0.995032i | \(0.531743\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −26.0000 | −1.71813 | −0.859064 | − | 0.511868i | \(-0.828954\pi\) | ||||
−0.859064 | + | 0.511868i | \(0.828954\pi\) | |||||||
\(230\) | −4.00000 | − | 6.92820i | −0.263752 | − | 0.456832i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −2.00000 | + | 3.46410i | −0.131306 | + | 0.227429i | ||||
\(233\) | −14.5000 | + | 25.1147i | −0.949927 | + | 1.64532i | −0.204354 | + | 0.978897i | \(0.565509\pi\) |
−0.745573 | + | 0.666424i | \(0.767824\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −3.50000 | − | 6.06218i | −0.227831 | − | 0.394614i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 3.00000 | + | 5.19615i | 0.194054 | + | 0.336111i | 0.946590 | − | 0.322440i | \(-0.104503\pi\) |
−0.752536 | + | 0.658551i | \(0.771170\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 23.0000 | 1.48156 | 0.740780 | − | 0.671748i | \(-0.234456\pi\) | ||||
0.740780 | + | 0.671748i | \(0.234456\pi\) | |||||||
\(242\) | 5.00000 | + | 8.66025i | 0.321412 | + | 0.556702i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −12.0000 | −0.768221 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 42.0000 | 2.67240 | ||||||||
\(248\) | 3.00000 | − | 5.19615i | 0.190500 | − | 0.329956i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −6.00000 | − | 10.3923i | −0.379473 | − | 0.657267i | ||||
\(251\) | −3.00000 | −0.189358 | −0.0946792 | − | 0.995508i | \(-0.530183\pi\) | ||||
−0.0946792 | + | 0.995508i | \(0.530183\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 4.00000 | 0.251478 | ||||||||
\(254\) | 6.00000 | + | 10.3923i | 0.376473 | + | 0.652071i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.500000 | + | 0.866025i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | 15.0000 | 0.935674 | 0.467837 | − | 0.883815i | \(-0.345033\pi\) | ||||
0.467837 | + | 0.883815i | \(0.345033\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 12.0000 | 0.744208 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −2.00000 | − | 3.46410i | −0.123560 | − | 0.214013i | ||||
\(263\) | −18.0000 | −1.10993 | −0.554964 | − | 0.831875i | \(-0.687268\pi\) | ||||
−0.554964 | + | 0.831875i | \(0.687268\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −12.0000 | − | 20.7846i | −0.737154 | − | 1.27679i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −6.50000 | − | 11.2583i | −0.397051 | − | 0.687712i | ||||
\(269\) | 10.0000 | + | 17.3205i | 0.609711 | + | 1.05605i | 0.991288 | + | 0.131713i | \(0.0420477\pi\) |
−0.381577 | + | 0.924337i | \(0.624619\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 3.00000 | − | 5.19615i | 0.182237 | − | 0.315644i | −0.760405 | − | 0.649449i | \(-0.775000\pi\) |
0.942642 | + | 0.333805i | \(0.108333\pi\) | |||||||
\(272\) | −2.50000 | + | 4.33013i | −0.151585 | + | 0.262553i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −9.50000 | − | 16.4545i | −0.573916 | − | 0.994052i | ||||
\(275\) | 1.00000 | 0.0603023 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 2.00000 | 0.120168 | 0.0600842 | − | 0.998193i | \(-0.480863\pi\) | ||||
0.0600842 | + | 0.998193i | \(0.480863\pi\) | |||||||
\(278\) | 2.50000 | − | 4.33013i | 0.149940 | − | 0.259704i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 11.0000 | − | 19.0526i | 0.656205 | − | 1.13658i | −0.325385 | − | 0.945582i | \(-0.605494\pi\) |
0.981590 | − | 0.190999i | \(-0.0611727\pi\) | |||||||
\(282\) | 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 | ||||||||
\(286\) | −3.00000 | + | 5.19615i | −0.177394 | + | 0.307255i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −4.00000 | + | 6.92820i | −0.235294 | + | 0.407541i | ||||
\(290\) | −8.00000 | −0.469776 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 1.00000 | 0.0585206 | ||||||||
\(293\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 7.00000 | − | 12.1244i | 0.407556 | − | 0.705907i | ||||
\(296\) | −1.00000 | + | 1.73205i | −0.0581238 | + | 0.100673i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −12.0000 | − | 20.7846i | −0.695141 | − | 1.20402i | ||||
\(299\) | −12.0000 | − | 20.7846i | −0.693978 | − | 1.20201i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −5.00000 | − | 8.66025i | −0.287718 | − | 0.498342i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −7.00000 | −0.401478 | ||||||||
\(305\) | −12.0000 | − | 20.7846i | −0.687118 | − | 1.19012i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 7.00000 | 0.399511 | 0.199756 | − | 0.979846i | \(-0.435985\pi\) | ||||
0.199756 | + | 0.979846i | \(0.435985\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 12.0000 | 0.681554 | ||||||||
\(311\) | 1.00000 | − | 1.73205i | 0.0567048 | − | 0.0982156i | −0.836280 | − | 0.548303i | \(-0.815274\pi\) |
0.892984 | + | 0.450088i | \(0.148607\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 8.50000 | + | 14.7224i | 0.480448 | + | 0.832161i | 0.999748 | − | 0.0224310i | \(-0.00714060\pi\) |
−0.519300 | + | 0.854592i | \(0.673807\pi\) | |||||||
\(314\) | 2.00000 | 0.112867 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −6.00000 | −0.337526 | ||||||||
\(317\) | −3.00000 | − | 5.19615i | −0.168497 | − | 0.291845i | 0.769395 | − | 0.638774i | \(-0.220558\pi\) |
−0.937892 | + | 0.346929i | \(0.887225\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 2.00000 | − | 3.46410i | 0.111979 | − | 0.193952i | ||||
\(320\) | −2.00000 | −0.111803 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −35.0000 | −1.94745 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −3.00000 | − | 5.19615i | −0.166410 | − | 0.288231i | ||||
\(326\) | −4.00000 | −0.221540 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 1.50000 | + | 2.59808i | 0.0828236 | + | 0.143455i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −4.00000 | − | 6.92820i | −0.219860 | − | 0.380808i | 0.734905 | − | 0.678170i | \(-0.237227\pi\) |
−0.954765 | + | 0.297361i | \(0.903893\pi\) | |||||||
\(332\) | 8.00000 | + | 13.8564i | 0.439057 | + | 0.760469i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 10.0000 | − | 17.3205i | 0.547176 | − | 0.947736i | ||||
\(335\) | 13.0000 | − | 22.5167i | 0.710266 | − | 1.23022i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 4.50000 | + | 7.79423i | 0.245131 | + | 0.424579i | 0.962168 | − | 0.272456i | \(-0.0878358\pi\) |
−0.717038 | + | 0.697034i | \(0.754502\pi\) | |||||||
\(338\) | 23.0000 | 1.25104 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −10.0000 | −0.542326 | ||||||||
\(341\) | −3.00000 | + | 5.19615i | −0.162459 | + | 0.281387i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0.500000 | − | 0.866025i | 0.0269582 | − | 0.0466930i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 1.00000 | − | 1.73205i | 0.0537603 | − | 0.0931156i | ||||
\(347\) | −1.50000 | + | 2.59808i | −0.0805242 | + | 0.139472i | −0.903475 | − | 0.428640i | \(-0.858993\pi\) |
0.822951 | + | 0.568112i | \(0.192326\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 7.00000 | − | 12.1244i | 0.374701 | − | 0.649002i | −0.615581 | − | 0.788074i | \(-0.711079\pi\) |
0.990282 | + | 0.139072i | \(0.0444119\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0.500000 | − | 0.866025i | 0.0266501 | − | 0.0461593i | ||||
\(353\) | 15.0000 | 0.798369 | 0.399185 | − | 0.916871i | \(-0.369293\pi\) | ||||
0.399185 | + | 0.916871i | \(0.369293\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −16.0000 | −0.849192 | ||||||||
\(356\) | −3.00000 | − | 5.19615i | −0.159000 | − | 0.275396i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 12.0000 | − | 20.7846i | 0.634220 | − | 1.09850i | ||||
\(359\) | 1.00000 | − | 1.73205i | 0.0527780 | − | 0.0914141i | −0.838429 | − | 0.545010i | \(-0.816526\pi\) |
0.891207 | + | 0.453596i | \(0.149859\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −15.0000 | − | 25.9808i | −0.789474 | − | 1.36741i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 1.00000 | + | 1.73205i | 0.0523424 | + | 0.0906597i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −22.0000 | −1.14839 | −0.574195 | − | 0.818718i | \(-0.694685\pi\) | ||||
−0.574195 | + | 0.818718i | \(0.694685\pi\) | |||||||
\(368\) | 2.00000 | + | 3.46410i | 0.104257 | + | 0.180579i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −4.00000 | −0.207950 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 22.0000 | 1.13912 | 0.569558 | − | 0.821951i | \(-0.307114\pi\) | ||||
0.569558 | + | 0.821951i | \(0.307114\pi\) | |||||||
\(374\) | 2.50000 | − | 4.33013i | 0.129272 | − | 0.223906i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −24.0000 | −1.23606 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −17.0000 | −0.873231 | −0.436616 | − | 0.899648i | \(-0.643823\pi\) | ||||
−0.436616 | + | 0.899648i | \(0.643823\pi\) | |||||||
\(380\) | −7.00000 | − | 12.1244i | −0.359092 | − | 0.621966i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 6.00000 | − | 10.3923i | 0.306987 | − | 0.531717i | ||||
\(383\) | −4.00000 | −0.204390 | −0.102195 | − | 0.994764i | \(-0.532587\pi\) | ||||
−0.102195 | + | 0.994764i | \(0.532587\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 17.0000 | 0.865277 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 2.50000 | + | 4.33013i | 0.126918 | + | 0.219829i | ||||
\(389\) | −8.00000 | −0.405616 | −0.202808 | − | 0.979219i | \(-0.565007\pi\) | ||||
−0.202808 | + | 0.979219i | \(0.565007\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 10.0000 | + | 17.3205i | 0.505722 | + | 0.875936i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 5.00000 | + | 8.66025i | 0.251896 | + | 0.436297i | ||||
\(395\) | −6.00000 | − | 10.3923i | −0.301893 | − | 0.522894i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −9.00000 | + | 15.5885i | −0.451697 | + | 0.782362i | −0.998492 | − | 0.0549046i | \(-0.982515\pi\) |
0.546795 | + | 0.837267i | \(0.315848\pi\) | |||||||
\(398\) | −7.00000 | + | 12.1244i | −0.350878 | + | 0.607739i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0.500000 | + | 0.866025i | 0.0250000 | + | 0.0433013i | ||||
\(401\) | −9.00000 | −0.449439 | −0.224719 | − | 0.974424i | \(-0.572147\pi\) | ||||
−0.224719 | + | 0.974424i | \(0.572147\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 36.0000 | 1.79329 | ||||||||
\(404\) | −2.00000 | + | 3.46410i | −0.0995037 | + | 0.172345i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 1.00000 | − | 1.73205i | 0.0495682 | − | 0.0858546i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −5.50000 | + | 9.52628i | −0.271957 | + | 0.471044i | −0.969363 | − | 0.245633i | \(-0.921004\pi\) |
0.697406 | + | 0.716677i | \(0.254338\pi\) | |||||||
\(410\) | −3.00000 | + | 5.19615i | −0.148159 | + | 0.256620i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −7.00000 | + | 12.1244i | −0.344865 | + | 0.597324i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −16.0000 | + | 27.7128i | −0.785409 | + | 1.36037i | ||||
\(416\) | −6.00000 | −0.294174 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 7.00000 | 0.342381 | ||||||||
\(419\) | −6.00000 | − | 10.3923i | −0.293119 | − | 0.507697i | 0.681426 | − | 0.731887i | \(-0.261360\pi\) |
−0.974546 | + | 0.224189i | \(0.928027\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 6.00000 | − | 10.3923i | 0.292422 | − | 0.506490i | −0.681960 | − | 0.731390i | \(-0.738872\pi\) |
0.974382 | + | 0.224900i | \(0.0722054\pi\) | |||||||
\(422\) | 8.00000 | − | 13.8564i | 0.389434 | − | 0.674519i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 6.00000 | + | 10.3923i | 0.291386 | + | 0.504695i | ||||
\(425\) | 2.50000 | + | 4.33013i | 0.121268 | + | 0.210042i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 1.50000 | + | 2.59808i | 0.0725052 | + | 0.125583i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 2.00000 | 0.0964486 | ||||||||
\(431\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −25.0000 | −1.20142 | −0.600712 | − | 0.799466i | \(-0.705116\pi\) | ||||
−0.600712 | + | 0.799466i | \(0.705116\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −2.00000 | −0.0957826 | ||||||||
\(437\) | −14.0000 | + | 24.2487i | −0.669711 | + | 1.15997i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 12.0000 | + | 20.7846i | 0.572729 | + | 0.991995i | 0.996284 | + | 0.0861252i | \(0.0274485\pi\) |
−0.423556 | + | 0.905870i | \(0.639218\pi\) | |||||||
\(440\) | 2.00000 | 0.0953463 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −30.0000 | −1.42695 | ||||||||
\(443\) | 3.50000 | + | 6.06218i | 0.166290 | + | 0.288023i | 0.937113 | − | 0.349027i | \(-0.113488\pi\) |
−0.770823 | + | 0.637050i | \(0.780155\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 6.00000 | − | 10.3923i | 0.284427 | − | 0.492642i | ||||
\(446\) | −4.00000 | −0.189405 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −17.0000 | −0.802280 | −0.401140 | − | 0.916017i | \(-0.631386\pi\) | ||||
−0.401140 | + | 0.916017i | \(0.631386\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.50000 | − | 2.59808i | −0.0706322 | − | 0.122339i | ||||
\(452\) | 10.0000 | 0.470360 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 1.50000 | + | 2.59808i | 0.0703985 | + | 0.121934i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −0.500000 | − | 0.866025i | −0.0233890 | − | 0.0405110i | 0.854094 | − | 0.520119i | \(-0.174112\pi\) |
−0.877483 | + | 0.479608i | \(0.840779\pi\) | |||||||
\(458\) | 13.0000 | + | 22.5167i | 0.607450 | + | 1.05213i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −4.00000 | + | 6.92820i | −0.186501 | + | 0.323029i | ||||
\(461\) | 7.00000 | − | 12.1244i | 0.326023 | − | 0.564688i | −0.655696 | − | 0.755025i | \(-0.727625\pi\) |
0.981719 | + | 0.190337i | \(0.0609581\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 4.00000 | + | 6.92820i | 0.185896 | + | 0.321981i | 0.943878 | − | 0.330294i | \(-0.107148\pi\) |
−0.757982 | + | 0.652275i | \(0.773815\pi\) | |||||||
\(464\) | 4.00000 | 0.185695 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 29.0000 | 1.34340 | ||||||||
\(467\) | −6.50000 | + | 11.2583i | −0.300784 | + | 0.520973i | −0.976314 | − | 0.216359i | \(-0.930582\pi\) |
0.675530 | + | 0.737333i | \(0.263915\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −3.50000 | + | 6.06218i | −0.161101 | + | 0.279034i | ||||
\(473\) | −0.500000 | + | 0.866025i | −0.0229900 | + | 0.0398199i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −3.50000 | + | 6.06218i | −0.160591 | + | 0.278152i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 3.00000 | − | 5.19615i | 0.137217 | − | 0.237666i | ||||
\(479\) | 20.0000 | 0.913823 | 0.456912 | − | 0.889512i | \(-0.348956\pi\) | ||||
0.456912 | + | 0.889512i | \(0.348956\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −12.0000 | −0.547153 | ||||||||
\(482\) | −11.5000 | − | 19.9186i | −0.523811 | − | 0.907267i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 5.00000 | − | 8.66025i | 0.227273 | − | 0.393648i | ||||
\(485\) | −5.00000 | + | 8.66025i | −0.227038 | + | 0.393242i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 5.00000 | + | 8.66025i | 0.226572 | + | 0.392434i | 0.956790 | − | 0.290780i | \(-0.0939149\pi\) |
−0.730218 | + | 0.683214i | \(0.760582\pi\) | |||||||
\(488\) | 6.00000 | + | 10.3923i | 0.271607 | + | 0.470438i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 16.5000 | + | 28.5788i | 0.744635 | + | 1.28974i | 0.950365 | + | 0.311136i | \(0.100710\pi\) |
−0.205731 | + | 0.978609i | \(0.565957\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 20.0000 | 0.900755 | ||||||||
\(494\) | −21.0000 | − | 36.3731i | −0.944835 | − | 1.63650i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −6.00000 | −0.269408 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −29.0000 | −1.29822 | −0.649109 | − | 0.760695i | \(-0.724858\pi\) | ||||
−0.649109 | + | 0.760695i | \(0.724858\pi\) | |||||||
\(500\) | −6.00000 | + | 10.3923i | −0.268328 | + | 0.464758i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 1.50000 | + | 2.59808i | 0.0669483 | + | 0.115958i | ||||
\(503\) | −6.00000 | −0.267527 | −0.133763 | − | 0.991013i | \(-0.542706\pi\) | ||||
−0.133763 | + | 0.991013i | \(0.542706\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −8.00000 | −0.355995 | ||||||||
\(506\) | −2.00000 | − | 3.46410i | −0.0889108 | − | 0.153998i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 6.00000 | − | 10.3923i | 0.266207 | − | 0.461084i | ||||
\(509\) | −30.0000 | −1.32973 | −0.664863 | − | 0.746965i | \(-0.731510\pi\) | ||||
−0.664863 | + | 0.746965i | \(0.731510\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −7.50000 | − | 12.9904i | −0.330811 | − | 0.572981i | ||||
\(515\) | −28.0000 | −1.23383 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −6.00000 | − | 10.3923i | −0.263117 | − | 0.455733i | ||||
\(521\) | −4.50000 | − | 7.79423i | −0.197149 | − | 0.341471i | 0.750454 | − | 0.660922i | \(-0.229835\pi\) |
−0.947603 | + | 0.319451i | \(0.896501\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 14.0000 | − | 24.2487i | 0.612177 | − | 1.06032i | −0.378695 | − | 0.925521i | \(-0.623627\pi\) |
0.990873 | − | 0.134801i | \(-0.0430394\pi\) | |||||||
\(524\) | −2.00000 | + | 3.46410i | −0.0873704 | + | 0.151330i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 9.00000 | + | 15.5885i | 0.392419 | + | 0.679689i | ||||
\(527\) | −30.0000 | −1.30682 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −7.00000 | −0.304348 | ||||||||
\(530\) | −12.0000 | + | 20.7846i | −0.521247 | + | 0.902826i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −9.00000 | + | 15.5885i | −0.389833 | + | 0.675211i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −3.00000 | + | 5.19615i | −0.129701 | + | 0.224649i | ||||
\(536\) | −6.50000 | + | 11.2583i | −0.280757 | + | 0.486286i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 10.0000 | − | 17.3205i | 0.431131 | − | 0.746740i | ||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 12.0000 | − | 20.7846i | 0.515920 | − | 0.893600i | −0.483909 | − | 0.875118i | \(-0.660783\pi\) |
0.999829 | − | 0.0184818i | \(-0.00588327\pi\) | |||||||
\(542\) | −6.00000 | −0.257722 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 5.00000 | 0.214373 | ||||||||
\(545\) | −2.00000 | − | 3.46410i | −0.0856706 | − | 0.148386i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 10.5000 | − | 18.1865i | 0.448948 | − | 0.777600i | −0.549370 | − | 0.835579i | \(-0.685132\pi\) |
0.998318 | + | 0.0579790i | \(0.0184657\pi\) | |||||||
\(548\) | −9.50000 | + | 16.4545i | −0.405820 | + | 0.702901i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −0.500000 | − | 0.866025i | −0.0213201 | − | 0.0369274i | ||||
\(551\) | 14.0000 | + | 24.2487i | 0.596420 | + | 1.03303i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −1.00000 | − | 1.73205i | −0.0424859 | − | 0.0735878i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −5.00000 | −0.212047 | ||||||||
\(557\) | −14.0000 | − | 24.2487i | −0.593199 | − | 1.02745i | −0.993798 | − | 0.111198i | \(-0.964531\pi\) |
0.400599 | − | 0.916253i | \(-0.368802\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 6.00000 | 0.253773 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −22.0000 | −0.928014 | ||||||||
\(563\) | 15.5000 | − | 26.8468i | 0.653247 | − | 1.13146i | −0.329083 | − | 0.944301i | \(-0.606740\pi\) |
0.982330 | − | 0.187156i | \(-0.0599271\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 10.0000 | + | 17.3205i | 0.420703 | + | 0.728679i | ||||
\(566\) | 4.00000 | 0.168133 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 8.00000 | 0.335673 | ||||||||
\(569\) | −7.50000 | − | 12.9904i | −0.314416 | − | 0.544585i | 0.664897 | − | 0.746935i | \(-0.268475\pi\) |
−0.979313 | + | 0.202350i | \(0.935142\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 16.5000 | − | 28.5788i | 0.690504 | − | 1.19599i | −0.281170 | − | 0.959658i | \(-0.590722\pi\) |
0.971673 | − | 0.236329i | \(-0.0759443\pi\) | |||||||
\(572\) | 6.00000 | 0.250873 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 4.00000 | 0.166812 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 17.5000 | + | 30.3109i | 0.728535 | + | 1.26186i | 0.957503 | + | 0.288425i | \(0.0931316\pi\) |
−0.228968 | + | 0.973434i | \(0.573535\pi\) | |||||||
\(578\) | 8.00000 | 0.332756 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 4.00000 | + | 6.92820i | 0.166091 | + | 0.287678i | ||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −6.00000 | − | 10.3923i | −0.248495 | − | 0.430405i | ||||
\(584\) | −0.500000 | − | 0.866025i | −0.0206901 | − | 0.0358364i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −23.5000 | + | 40.7032i | −0.969949 | + | 1.68000i | −0.274263 | + | 0.961655i | \(0.588434\pi\) |
−0.695686 | + | 0.718346i | \(0.744900\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −21.0000 | − | 36.3731i | −0.865290 | − | 1.49873i | ||||
\(590\) | −14.0000 | −0.576371 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 2.00000 | 0.0821995 | ||||||||
\(593\) | −3.00000 | + | 5.19615i | −0.123195 | + | 0.213380i | −0.921026 | − | 0.389501i | \(-0.872647\pi\) |
0.797831 | + | 0.602881i | \(0.205981\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −12.0000 | + | 20.7846i | −0.491539 | + | 0.851371i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −12.0000 | + | 20.7846i | −0.490716 | + | 0.849946i | ||||
\(599\) | 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 | ||||||||
\(601\) | 9.50000 | − | 16.4545i | 0.387513 | − | 0.671192i | −0.604601 | − | 0.796528i | \(-0.706668\pi\) |
0.992114 | + | 0.125336i | \(0.0400009\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −5.00000 | + | 8.66025i | −0.203447 | + | 0.352381i | ||||
\(605\) | 20.0000 | 0.813116 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −24.0000 | −0.974130 | −0.487065 | − | 0.873366i | \(-0.661933\pi\) | ||||
−0.487065 | + | 0.873366i | \(0.661933\pi\) | |||||||
\(608\) | 3.50000 | + | 6.06218i | 0.141944 | + | 0.245854i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −12.0000 | + | 20.7846i | −0.485866 | + | 0.841544i | ||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −21.0000 | − | 36.3731i | −0.848182 | − | 1.46909i | −0.882829 | − | 0.469695i | \(-0.844364\pi\) |
0.0346469 | − | 0.999400i | \(-0.488969\pi\) | |||||||
\(614\) | −3.50000 | − | 6.06218i | −0.141249 | − | 0.244650i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −8.50000 | − | 14.7224i | −0.342197 | − | 0.592703i | 0.642643 | − | 0.766165i | \(-0.277838\pi\) |
−0.984840 | + | 0.173463i | \(0.944504\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 37.0000 | 1.48716 | 0.743578 | − | 0.668649i | \(-0.233127\pi\) | ||||
0.743578 | + | 0.668649i | \(0.233127\pi\) | |||||||
\(620\) | −6.00000 | − | 10.3923i | −0.240966 | − | 0.417365i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −2.00000 | −0.0801927 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −19.0000 | −0.760000 | ||||||||
\(626\) | 8.50000 | − | 14.7224i | 0.339728 | − | 0.588427i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −1.00000 | − | 1.73205i | −0.0399043 | − | 0.0691164i | ||||
\(629\) | 10.0000 | 0.398726 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 8.00000 | 0.318475 | 0.159237 | − | 0.987240i | \(-0.449096\pi\) | ||||
0.159237 | + | 0.987240i | \(0.449096\pi\) | |||||||
\(632\) | 3.00000 | + | 5.19615i | 0.119334 | + | 0.206692i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −3.00000 | + | 5.19615i | −0.119145 | + | 0.206366i | ||||
\(635\) | 24.0000 | 0.952411 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −4.00000 | −0.158362 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 1.00000 | + | 1.73205i | 0.0395285 | + | 0.0684653i | ||||
\(641\) | −1.00000 | −0.0394976 | −0.0197488 | − | 0.999805i | \(-0.506287\pi\) | ||||
−0.0197488 | + | 0.999805i | \(0.506287\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 3.50000 | + | 6.06218i | 0.138027 | + | 0.239069i | 0.926750 | − | 0.375680i | \(-0.122591\pi\) |
−0.788723 | + | 0.614749i | \(0.789257\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 17.5000 | + | 30.3109i | 0.688528 | + | 1.19257i | ||||
\(647\) | 6.00000 | + | 10.3923i | 0.235884 | + | 0.408564i | 0.959529 | − | 0.281609i | \(-0.0908680\pi\) |
−0.723645 | + | 0.690172i | \(0.757535\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 3.50000 | − | 6.06218i | 0.137387 | − | 0.237961i | ||||
\(650\) | −3.00000 | + | 5.19615i | −0.117670 | + | 0.203810i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 2.00000 | + | 3.46410i | 0.0783260 | + | 0.135665i | ||||
\(653\) | 6.00000 | 0.234798 | 0.117399 | − | 0.993085i | \(-0.462544\pi\) | ||||
0.117399 | + | 0.993085i | \(0.462544\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −8.00000 | −0.312586 | ||||||||
\(656\) | 1.50000 | − | 2.59808i | 0.0585652 | − | 0.101438i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 8.00000 | − | 13.8564i | 0.311636 | − | 0.539769i | −0.667081 | − | 0.744985i | \(-0.732456\pi\) |
0.978717 | + | 0.205216i | \(0.0657898\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −14.0000 | + | 24.2487i | −0.544537 | + | 0.943166i | 0.454099 | + | 0.890951i | \(0.349961\pi\) |
−0.998636 | + | 0.0522143i | \(0.983372\pi\) | |||||||
\(662\) | −4.00000 | + | 6.92820i | −0.155464 | + | 0.269272i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 8.00000 | − | 13.8564i | 0.310460 | − | 0.537733i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 8.00000 | − | 13.8564i | 0.309761 | − | 0.536522i | ||||
\(668\) | −20.0000 | −0.773823 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −26.0000 | −1.00447 | ||||||||
\(671\) | −6.00000 | − | 10.3923i | −0.231627 | − | 0.401190i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −7.00000 | + | 12.1244i | −0.269830 | + | 0.467360i | −0.968818 | − | 0.247774i | \(-0.920301\pi\) |
0.698988 | + | 0.715134i | \(0.253634\pi\) | |||||||
\(674\) | 4.50000 | − | 7.79423i | 0.173334 | − | 0.300222i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −11.5000 | − | 19.9186i | −0.442308 | − | 0.766099i | ||||
\(677\) | 15.0000 | + | 25.9808i | 0.576497 | + | 0.998522i | 0.995877 | + | 0.0907112i | \(0.0289140\pi\) |
−0.419380 | + | 0.907811i | \(0.637753\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 5.00000 | + | 8.66025i | 0.191741 | + | 0.332106i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 6.00000 | 0.229752 | ||||||||
\(683\) | 19.5000 | + | 33.7750i | 0.746147 | + | 1.29236i | 0.949657 | + | 0.313291i | \(0.101432\pi\) |
−0.203510 | + | 0.979073i | \(0.565235\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −38.0000 | −1.45191 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −1.00000 | −0.0381246 | ||||||||
\(689\) | −36.0000 | + | 62.3538i | −1.37149 | + | 2.37549i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −16.0000 | − | 27.7128i | −0.608669 | − | 1.05425i | −0.991460 | − | 0.130410i | \(-0.958371\pi\) |
0.382791 | − | 0.923835i | \(-0.374963\pi\) | |||||||
\(692\) | −2.00000 | −0.0760286 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 3.00000 | 0.113878 | ||||||||
\(695\) | −5.00000 | − | 8.66025i | −0.189661 | − | 0.328502i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 7.50000 | − | 12.9904i | 0.284083 | − | 0.492046i | ||||
\(698\) | −14.0000 | −0.529908 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −8.00000 | −0.302156 | −0.151078 | − | 0.988522i | \(-0.548274\pi\) | ||||
−0.151078 | + | 0.988522i | \(0.548274\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 7.00000 | + | 12.1244i | 0.264010 | + | 0.457279i | ||||
\(704\) | −1.00000 | −0.0376889 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −7.50000 | − | 12.9904i | −0.282266 | − | 0.488899i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 2.00000 | + | 3.46410i | 0.0751116 | + | 0.130097i | 0.901135 | − | 0.433539i | \(-0.142735\pi\) |
−0.826023 | + | 0.563636i | \(0.809402\pi\) | |||||||
\(710\) | 8.00000 | + | 13.8564i | 0.300235 | + | 0.520022i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −3.00000 | + | 5.19615i | −0.112430 | + | 0.194734i | ||||
\(713\) | −12.0000 | + | 20.7846i | −0.449404 | + | 0.778390i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 6.00000 | + | 10.3923i | 0.224387 | + | 0.388650i | ||||
\(716\) | −24.0000 | −0.896922 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −2.00000 | −0.0746393 | ||||||||
\(719\) | 3.00000 | − | 5.19615i | 0.111881 | − | 0.193784i | −0.804648 | − | 0.593753i | \(-0.797646\pi\) |
0.916529 | + | 0.399969i | \(0.130979\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −15.0000 | + | 25.9808i | −0.558242 | + | 0.966904i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 2.00000 | − | 3.46410i | 0.0742781 | − | 0.128654i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 7.00000 | − | 12.1244i | 0.259616 | − | 0.449667i | −0.706523 | − | 0.707690i | \(-0.749737\pi\) |
0.966139 | + | 0.258022i | \(0.0830708\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 1.00000 | − | 1.73205i | 0.0370117 | − | 0.0641061i | ||||
\(731\) | −5.00000 | −0.184932 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −18.0000 | −0.664845 | −0.332423 | − | 0.943131i | \(-0.607866\pi\) | ||||
−0.332423 | + | 0.943131i | \(0.607866\pi\) | |||||||
\(734\) | 11.0000 | + | 19.0526i | 0.406017 | + | 0.703243i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 2.00000 | − | 3.46410i | 0.0737210 | − | 0.127688i | ||||
\(737\) | 6.50000 | − | 11.2583i | 0.239431 | − | 0.414706i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 16.5000 | + | 28.5788i | 0.606962 | + | 1.05129i | 0.991738 | + | 0.128279i | \(0.0409454\pi\) |
−0.384776 | + | 0.923010i | \(0.625721\pi\) | |||||||
\(740\) | 2.00000 | + | 3.46410i | 0.0735215 | + | 0.127343i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −3.00000 | − | 5.19615i | −0.110059 | − | 0.190628i | 0.805735 | − | 0.592277i | \(-0.201771\pi\) |
−0.915794 | + | 0.401648i | \(0.868437\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −48.0000 | −1.75858 | ||||||||
\(746\) | −11.0000 | − | 19.0526i | −0.402739 | − | 0.697564i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −5.00000 | −0.182818 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −18.0000 | −0.656829 | −0.328415 | − | 0.944534i | \(-0.606514\pi\) | ||||
−0.328415 | + | 0.944534i | \(0.606514\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 12.0000 | + | 20.7846i | 0.437014 | + | 0.756931i | ||||
\(755\) | −20.0000 | −0.727875 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −48.0000 | −1.74459 | −0.872295 | − | 0.488980i | \(-0.837369\pi\) | ||||
−0.872295 | + | 0.488980i | \(0.837369\pi\) | |||||||
\(758\) | 8.50000 | + | 14.7224i | 0.308734 | + | 0.534743i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −7.00000 | + | 12.1244i | −0.253917 | + | 0.439797i | ||||
\(761\) | −10.0000 | −0.362500 | −0.181250 | − | 0.983437i | \(-0.558014\pi\) | ||||
−0.181250 | + | 0.983437i | \(0.558014\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −12.0000 | −0.434145 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 2.00000 | + | 3.46410i | 0.0722629 | + | 0.125163i | ||||
\(767\) | −42.0000 | −1.51653 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −11.0000 | − | 19.0526i | −0.396670 | − | 0.687053i | 0.596643 | − | 0.802507i | \(-0.296501\pi\) |
−0.993313 | + | 0.115454i | \(0.963168\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −8.50000 | − | 14.7224i | −0.305922 | − | 0.529872i | ||||
\(773\) | −26.0000 | − | 45.0333i | −0.935155 | − | 1.61974i | −0.774357 | − | 0.632749i | \(-0.781927\pi\) |
−0.160798 | − | 0.986987i | \(-0.551407\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −3.00000 | + | 5.19615i | −0.107763 | + | 0.186651i | ||||
\(776\) | 2.50000 | − | 4.33013i | 0.0897448 | − | 0.155443i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 4.00000 | + | 6.92820i | 0.143407 | + | 0.248388i | ||||
\(779\) | 21.0000 | 0.752403 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −8.00000 | −0.286263 | ||||||||
\(782\) | 10.0000 | − | 17.3205i | 0.357599 | − | 0.619380i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 2.00000 | − | 3.46410i | 0.0713831 | − | 0.123639i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 6.00000 | − | 10.3923i | 0.213877 | − | 0.370446i | −0.739048 | − | 0.673653i | \(-0.764724\pi\) |
0.952925 | + | 0.303207i | \(0.0980575\pi\) | |||||||
\(788\) | 5.00000 | − | 8.66025i | 0.178118 | − | 0.308509i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −6.00000 | + | 10.3923i | −0.213470 | + | 0.369742i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −36.0000 | + | 62.3538i | −1.27840 | + | 2.21425i | ||||
\(794\) | 18.0000 | 0.638796 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 14.0000 | 0.496217 | ||||||||
\(797\) | −6.00000 | − | 10.3923i | −0.212531 | − | 0.368114i | 0.739975 | − | 0.672634i | \(-0.234837\pi\) |
−0.952506 | + | 0.304520i | \(0.901504\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 0.500000 | − | 0.866025i | 0.0176777 | − | 0.0306186i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 4.50000 | + | 7.79423i | 0.158901 | + | 0.275224i | ||||
\(803\) | 0.500000 | + | 0.866025i | 0.0176446 | + | 0.0305614i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −18.0000 | − | 31.1769i | −0.634023 | − | 1.09816i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 4.00000 | 0.140720 | ||||||||
\(809\) | −21.5000 | − | 37.2391i | −0.755900 | − | 1.30926i | −0.944926 | − | 0.327285i | \(-0.893866\pi\) |
0.189026 | − | 0.981972i | \(-0.439467\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 31.0000 | 1.08856 | 0.544279 | − | 0.838905i | \(-0.316803\pi\) | ||||
0.544279 | + | 0.838905i | \(0.316803\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −2.00000 | −0.0701000 | ||||||||
\(815\) | −4.00000 | + | 6.92820i | −0.140114 | + | 0.242684i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −3.50000 | − | 6.06218i | −0.122449 | − | 0.212089i | ||||
\(818\) | 11.0000 | 0.384606 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 6.00000 | 0.209529 | ||||||||
\(821\) | 23.0000 | + | 39.8372i | 0.802706 | + | 1.39033i | 0.917829 | + | 0.396976i | \(0.129940\pi\) |
−0.115124 | + | 0.993351i | \(0.536726\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −17.0000 | + | 29.4449i | −0.592583 | + | 1.02638i | 0.401300 | + | 0.915947i | \(0.368558\pi\) |
−0.993883 | + | 0.110437i | \(0.964775\pi\) | |||||||
\(824\) | 14.0000 | 0.487713 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −12.0000 | −0.417281 | −0.208640 | − | 0.977992i | \(-0.566904\pi\) | ||||
−0.208640 | + | 0.977992i | \(0.566904\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −2.00000 | − | 3.46410i | −0.0694629 | − | 0.120313i | 0.829202 | − | 0.558949i | \(-0.188795\pi\) |
−0.898665 | + | 0.438636i | \(0.855462\pi\) | |||||||
\(830\) | 32.0000 | 1.11074 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 3.00000 | + | 5.19615i | 0.104006 | + | 0.180144i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −20.0000 | − | 34.6410i | −0.692129 | − | 1.19880i | ||||
\(836\) | −3.50000 | − | 6.06218i | −0.121050 | − | 0.209665i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −6.00000 | + | 10.3923i | −0.207267 | + | 0.358996i | ||||
\(839\) | −10.0000 | + | 17.3205i | −0.345238 | + | 0.597970i | −0.985397 | − | 0.170272i | \(-0.945535\pi\) |
0.640159 | + | 0.768243i | \(0.278869\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 6.50000 | + | 11.2583i | 0.224138 | + | 0.388218i | ||||
\(842\) | −12.0000 | −0.413547 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −16.0000 | −0.550743 | ||||||||
\(845\) | 23.0000 | − | 39.8372i | 0.791224 | − | 1.37044i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 6.00000 | − | 10.3923i | 0.206041 | − | 0.356873i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 2.50000 | − | 4.33013i | 0.0857493 | − | 0.148522i | ||||
\(851\) | 4.00000 | − | 6.92820i | 0.137118 | − | 0.237496i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −22.0000 | + | 38.1051i | −0.753266 | + | 1.30469i | 0.192966 | + | 0.981205i | \(0.438189\pi\) |
−0.946232 | + | 0.323489i | \(0.895144\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 1.50000 | − | 2.59808i | 0.0512689 | − | 0.0888004i | ||||
\(857\) | −30.0000 | −1.02478 | −0.512390 | − | 0.858753i | \(-0.671240\pi\) | ||||
−0.512390 | + | 0.858753i | \(0.671240\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 29.0000 | 0.989467 | 0.494734 | − | 0.869045i | \(-0.335266\pi\) | ||||
0.494734 | + | 0.869045i | \(0.335266\pi\) | |||||||
\(860\) | −1.00000 | − | 1.73205i | −0.0340997 | − | 0.0590624i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 19.0000 | − | 32.9090i | 0.646768 | − | 1.12023i | −0.337123 | − | 0.941461i | \(-0.609454\pi\) |
0.983890 | − | 0.178774i | \(-0.0572129\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −2.00000 | − | 3.46410i | −0.0680020 | − | 0.117783i | ||||
\(866\) | 12.5000 | + | 21.6506i | 0.424767 | + | 0.735719i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −3.00000 | − | 5.19615i | −0.101768 | − | 0.176267i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −78.0000 | −2.64293 | ||||||||
\(872\) | 1.00000 | + | 1.73205i | 0.0338643 | + | 0.0586546i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 28.0000 | 0.947114 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 16.0000 | 0.540282 | 0.270141 | − | 0.962821i | \(-0.412930\pi\) | ||||
0.270141 | + | 0.962821i | \(0.412930\pi\) | |||||||
\(878\) | 12.0000 | − | 20.7846i | 0.404980 | − | 0.701447i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −1.00000 | − | 1.73205i | −0.0337100 | − | 0.0583874i | ||||
\(881\) | −42.0000 | −1.41502 | −0.707508 | − | 0.706705i | \(-0.750181\pi\) | ||||
−0.707508 | + | 0.706705i | \(0.750181\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 53.0000 | 1.78359 | 0.891796 | − | 0.452438i | \(-0.149446\pi\) | ||||
0.891796 | + | 0.452438i | \(0.149446\pi\) | |||||||
\(884\) | 15.0000 | + | 25.9808i | 0.504505 | + | 0.873828i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 3.50000 | − | 6.06218i | 0.117585 | − | 0.203663i | ||||
\(887\) | 6.00000 | 0.201460 | 0.100730 | − | 0.994914i | \(-0.467882\pi\) | ||||
0.100730 | + | 0.994914i | \(0.467882\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −12.0000 | −0.402241 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 2.00000 | + | 3.46410i | 0.0669650 | + | 0.115987i | ||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −24.0000 | − | 41.5692i | −0.802232 | − | 1.38951i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 8.50000 | + | 14.7224i | 0.283649 | + | 0.491294i | ||||
\(899\) | 12.0000 | + | 20.7846i | 0.400222 | + | 0.693206i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 30.0000 | − | 51.9615i | 0.999445 | − | 1.73109i | ||||
\(902\) | −1.50000 | + | 2.59808i | −0.0499445 | + | 0.0865065i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −5.00000 | − | 8.66025i | −0.166298 | − | 0.288036i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −27.0000 | −0.896520 | −0.448260 | − | 0.893903i | \(-0.647956\pi\) | ||||
−0.448260 | + | 0.893903i | \(0.647956\pi\) | |||||||
\(908\) | 1.50000 | − | 2.59808i | 0.0497792 | − | 0.0862202i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −8.00000 | + | 13.8564i | −0.264761 | + | 0.458580i | ||||
\(914\) | −0.500000 | + | 0.866025i | −0.0165385 | + | 0.0286456i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 13.0000 | − | 22.5167i | 0.429532 | − | 0.743971i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −8.00000 | + | 13.8564i | −0.263896 | + | 0.457081i | −0.967274 | − | 0.253735i | \(-0.918341\pi\) |
0.703378 | + | 0.710816i | \(0.251674\pi\) | |||||||
\(920\) | 8.00000 | 0.263752 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −14.0000 | −0.461065 | ||||||||
\(923\) | 24.0000 | + | 41.5692i | 0.789970 | + | 1.36827i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1.00000 | − | 1.73205i | 0.0328798 | − | 0.0569495i | ||||
\(926\) | 4.00000 | − | 6.92820i | 0.131448 | − | 0.227675i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −2.00000 | − | 3.46410i | −0.0656532 | − | 0.113715i | ||||
\(929\) | −9.00000 | − | 15.5885i | −0.295280 | − | 0.511441i | 0.679770 | − | 0.733426i | \(-0.262080\pi\) |
−0.975050 | + | 0.221985i | \(0.928746\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −14.5000 | − | 25.1147i | −0.474963 | − | 0.822661i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 13.0000 | 0.425373 | ||||||||
\(935\) | −5.00000 | − | 8.66025i | −0.163517 | − | 0.283221i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 2.00000 | 0.0653372 | 0.0326686 | − | 0.999466i | \(-0.489599\pi\) | ||||
0.0326686 | + | 0.999466i | \(0.489599\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 10.0000 | − | 17.3205i | 0.325991 | − | 0.564632i | −0.655722 | − | 0.755003i | \(-0.727636\pi\) |
0.981712 | + | 0.190370i | \(0.0609689\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −6.00000 | − | 10.3923i | −0.195387 | − | 0.338420i | ||||
\(944\) | 7.00000 | 0.227831 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 1.00000 | 0.0325128 | ||||||||
\(947\) | −18.5000 | − | 32.0429i | −0.601169 | − | 1.04126i | −0.992644 | − | 0.121067i | \(-0.961368\pi\) |
0.391475 | − | 0.920189i | \(-0.371965\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 3.00000 | − | 5.19615i | 0.0973841 | − | 0.168674i | ||||
\(950\) | 7.00000 | 0.227110 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 35.0000 | 1.13376 | 0.566881 | − | 0.823800i | \(-0.308150\pi\) | ||||
0.566881 | + | 0.823800i | \(0.308150\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −12.0000 | − | 20.7846i | −0.388311 | − | 0.672574i | ||||
\(956\) | −6.00000 | −0.194054 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −10.0000 | − | 17.3205i | −0.323085 | − | 0.559600i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2.50000 | − | 4.33013i | −0.0806452 | − | 0.139682i | ||||
\(962\) | 6.00000 | + | 10.3923i | 0.193448 | + | 0.335061i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −11.5000 | + | 19.9186i | −0.370390 | + | 0.641534i | ||||
\(965\) | 17.0000 | − | 29.4449i | 0.547249 | − | 0.947864i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −7.00000 | − | 12.1244i | −0.225105 | − | 0.389893i | 0.731246 | − | 0.682114i | \(-0.238939\pi\) |
−0.956351 | + | 0.292221i | \(0.905606\pi\) | |||||||
\(968\) | −10.0000 | −0.321412 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 10.0000 | 0.321081 | ||||||||
\(971\) | −6.00000 | + | 10.3923i | −0.192549 | + | 0.333505i | −0.946094 | − | 0.323891i | \(-0.895009\pi\) |
0.753545 | + | 0.657396i | \(0.228342\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 5.00000 | − | 8.66025i | 0.160210 | − | 0.277492i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 6.00000 | − | 10.3923i | 0.192055 | − | 0.332650i | ||||
\(977\) | −7.50000 | + | 12.9904i | −0.239946 | + | 0.415599i | −0.960699 | − | 0.277594i | \(-0.910463\pi\) |
0.720752 | + | 0.693193i | \(0.243796\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 3.00000 | − | 5.19615i | 0.0958804 | − | 0.166070i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 16.5000 | − | 28.5788i | 0.526536 | − | 0.911987i | ||||
\(983\) | 60.0000 | 1.91370 | 0.956851 | − | 0.290578i | \(-0.0938475\pi\) | ||||
0.956851 | + | 0.290578i | \(0.0938475\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 20.0000 | 0.637253 | ||||||||
\(986\) | −10.0000 | − | 17.3205i | −0.318465 | − | 0.551597i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −21.0000 | + | 36.3731i | −0.668099 | + | 1.15718i | ||||
\(989\) | −2.00000 | + | 3.46410i | −0.0635963 | + | 0.110152i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 14.0000 | + | 24.2487i | 0.444725 | + | 0.770286i | 0.998033 | − | 0.0626908i | \(-0.0199682\pi\) |
−0.553308 | + | 0.832977i | \(0.686635\pi\) | |||||||
\(992\) | 3.00000 | + | 5.19615i | 0.0952501 | + | 0.164978i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 14.0000 | + | 24.2487i | 0.443830 | + | 0.768736i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 2.00000 | 0.0633406 | 0.0316703 | − | 0.999498i | \(-0.489917\pi\) | ||||
0.0316703 | + | 0.999498i | \(0.489917\pi\) | |||||||
\(998\) | 14.5000 | + | 25.1147i | 0.458989 | + | 0.794993i | ||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))