Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1323,2,Mod(656,1323)]
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, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1323.656");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1323 = 3^{3} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1323.s (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: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 63) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 656.1 | ||
Root | \(0.500000 - 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1323.656 |
Dual form | 1323.2.s.a.962.1 |
$q$-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 \(\left(\mathbb{Z}/1323\mathbb{Z}\right)^\times\).
\(n\) | \(785\) | \(1081\) |
\(\chi(n)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{5}{6}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.50000 | − | 0.866025i | 1.06066 | − | 0.612372i | 0.135045 | − | 0.990839i | \(-0.456882\pi\) |
0.925615 | + | 0.378467i | \(0.123549\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0.500000 | − | 0.866025i | 0.250000 | − | 0.433013i | ||||
\(5\) | −3.00000 | −1.34164 | −0.670820 | − | 0.741620i | \(-0.734058\pi\) | ||||
−0.670820 | + | 0.741620i | \(0.734058\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 1.73205i | 0.612372i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −4.50000 | + | 2.59808i | −1.42302 | + | 0.821584i | ||||
\(11\) | − | 1.73205i | − | 0.522233i | −0.965307 | − | 0.261116i | \(-0.915909\pi\) | ||
0.965307 | − | 0.261116i | \(-0.0840907\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.50000 | − | 0.866025i | 0.416025 | − | 0.240192i | −0.277350 | − | 0.960769i | \(-0.589456\pi\) |
0.693375 | + | 0.720577i | \(0.256123\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 2.50000 | + | 4.33013i | 0.625000 | + | 1.08253i | ||||
\(17\) | 1.50000 | + | 2.59808i | 0.363803 | + | 0.630126i | 0.988583 | − | 0.150675i | \(-0.0481447\pi\) |
−0.624780 | + | 0.780801i | \(0.714811\pi\) | |||||||
\(18\) | 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 | ||||
\(23\) | 5.19615i | 1.08347i | 0.840548 | + | 0.541736i | \(0.182233\pi\) | ||||
−0.840548 | + | 0.541736i | \(0.817767\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 4.00000 | 0.800000 | ||||||||
\(26\) | 1.50000 | − | 2.59808i | 0.294174 | − | 0.509525i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 4.50000 | + | 2.59808i | 0.835629 | + | 0.482451i | 0.855776 | − | 0.517346i | \(-0.173080\pi\) |
−0.0201471 | + | 0.999797i | \(0.506413\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.00000 | + | 1.73205i | 0.538816 | + | 0.311086i | 0.744599 | − | 0.667512i | \(-0.232641\pi\) |
−0.205783 | + | 0.978598i | \(0.565974\pi\) | |||||||
\(32\) | 4.50000 | + | 2.59808i | 0.795495 | + | 0.459279i | ||||
\(33\) | 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 | \(0.971514\pi\) | |||||||
\(38\) | 9.00000 | 1.45999 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | − | 5.19615i | − | 0.821584i | ||||||
\(41\) | 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 | −0.901629 | − | 0.432511i | \(-0.857628\pi\) |
0.825380 | + | 0.564578i | \(0.190961\pi\) | |||||||
\(44\) | −1.50000 | − | 0.866025i | −0.226134 | − | 0.130558i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 4.50000 | + | 7.79423i | 0.663489 | + | 1.14920i | ||||
\(47\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 6.00000 | − | 3.46410i | 0.848528 | − | 0.489898i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | − | 1.73205i | − | 0.240192i | ||||||
\(53\) | 7.50000 | − | 4.33013i | 1.03020 | − | 0.594789i | 0.113161 | − | 0.993577i | \(-0.463902\pi\) |
0.917043 | + | 0.398788i | \(0.130569\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 5.19615i | 0.700649i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 9.00000 | 1.18176 | ||||||||
\(59\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −12.0000 | + | 6.92820i | −1.53644 | + | 0.887066i | −0.537400 | + | 0.843328i | \(0.680593\pi\) |
−0.999043 | + | 0.0437377i | \(0.986073\pi\) | |||||||
\(62\) | 6.00000 | 0.762001 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | −4.50000 | + | 2.59808i | −0.558156 | + | 0.322252i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2.00000 | − | 3.46410i | 0.244339 | − | 0.423207i | −0.717607 | − | 0.696449i | \(-0.754762\pi\) |
0.961946 | + | 0.273241i | \(0.0880957\pi\) | |||||||
\(68\) | 3.00000 | 0.363803 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 3.46410i | − | 0.411113i | −0.978645 | − | 0.205557i | \(-0.934100\pi\) | ||
0.978645 | − | 0.205557i | \(-0.0659005\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 4.50000 | − | 2.59808i | 0.526685 | − | 0.304082i | −0.212980 | − | 0.977056i | \(-0.568317\pi\) |
0.739666 | + | 0.672975i | \(0.234984\pi\) | |||||||
\(74\) | 12.1244i | 1.40943i | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 4.50000 | − | 2.59808i | 0.516185 | − | 0.298020i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −4.00000 | − | 6.92820i | −0.450035 | − | 0.779484i | 0.548352 | − | 0.836247i | \(-0.315255\pi\) |
−0.998388 | + | 0.0567635i | \(0.981922\pi\) | |||||||
\(80\) | −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 | 0.0800311 | + | 0.996792i | \(0.474498\pi\) |
−0.903263 | + | 0.429087i | \(0.858835\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −4.50000 | − | 7.79423i | −0.488094 | − | 0.845403i | ||||
\(86\) | 1.73205i | 0.186772i | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 3.00000 | 0.319801 | ||||||||
\(89\) | 1.50000 | − | 2.59808i | 0.159000 | − | 0.275396i | −0.775509 | − | 0.631337i | \(-0.782506\pi\) |
0.934508 | + | 0.355942i | \(0.115840\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 4.50000 | + | 2.59808i | 0.469157 | + | 0.270868i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −13.5000 | − | 7.79423i | −1.38507 | − | 0.799671i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1.50000 | + | 0.866025i | 0.152302 | + | 0.0879316i | 0.574214 | − | 0.818705i | \(-0.305308\pi\) |
−0.421912 | + | 0.906637i | \(0.638641\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 2.00000 | − | 3.46410i | 0.200000 | − | 0.346410i | ||||
\(101\) | −3.00000 | −0.298511 | −0.149256 | − | 0.988799i | \(-0.547688\pi\) | ||||
−0.149256 | + | 0.988799i | \(0.547688\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 12.1244i | − | 1.19465i | −0.802000 | − | 0.597324i | \(-0.796231\pi\) | ||
0.802000 | − | 0.597324i | \(-0.203769\pi\) | |||||||
\(104\) | 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 | 0.816609 | − | 0.577191i | \(-0.195851\pi\) |
−0.0915571 | + | 0.995800i | \(0.529184\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −9.50000 | − | 16.4545i | −0.909935 | − | 1.57605i | −0.814152 | − | 0.580651i | \(-0.802798\pi\) |
−0.0957826 | − | 0.995402i | \(-0.530535\pi\) | |||||||
\(110\) | 4.50000 | + | 7.79423i | 0.429058 | + | 0.743151i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −1.50000 | + | 0.866025i | −0.141108 | + | 0.0814688i | −0.568892 | − | 0.822412i | \(-0.692628\pi\) |
0.427784 | + | 0.903881i | \(0.359294\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − | 15.5885i | − | 1.45363i | ||||||
\(116\) | 4.50000 | − | 2.59808i | 0.417815 | − | 0.241225i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 8.00000 | 0.727273 | ||||||||
\(122\) | −12.0000 | + | 20.7846i | −1.08643 | + | 1.88175i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 3.00000 | − | 1.73205i | 0.269408 | − | 0.155543i | ||||
\(125\) | 3.00000 | 0.268328 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 20.0000 | 1.77471 | 0.887357 | − | 0.461084i | \(-0.152539\pi\) | ||||
0.887357 | + | 0.461084i | \(0.152539\pi\) | |||||||
\(128\) | −10.5000 | + | 6.06218i | −0.928078 | + | 0.535826i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −4.50000 | + | 7.79423i | −0.394676 | + | 0.683599i | ||||
\(131\) | −9.00000 | −0.786334 | −0.393167 | − | 0.919467i | \(-0.628621\pi\) | ||||
−0.393167 | + | 0.919467i | \(0.628621\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | − | 6.92820i | − | 0.598506i | ||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −4.50000 | + | 2.59808i | −0.385872 | + | 0.222783i | ||||
\(137\) | 12.1244i | 1.03585i | 0.855425 | + | 0.517927i | \(0.173296\pi\) | ||||
−0.855425 | + | 0.517927i | \(0.826704\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 7.50000 | − | 4.33013i | 0.636142 | − | 0.367277i | −0.146985 | − | 0.989139i | \(-0.546957\pi\) |
0.783127 | + | 0.621862i | \(0.213624\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −3.00000 | − | 5.19615i | −0.251754 | − | 0.436051i | ||||
\(143\) | −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 | ||||
\(149\) | 1.73205i | 0.141895i | 0.997480 | + | 0.0709476i | \(0.0226023\pi\) | ||||
−0.997480 | + | 0.0709476i | \(0.977398\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −17.0000 | −1.38344 | −0.691720 | − | 0.722166i | \(-0.743147\pi\) | ||||
−0.691720 | + | 0.722166i | \(0.743147\pi\) | |||||||
\(152\) | −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 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(158\) | −12.0000 | − | 6.92820i | −0.954669 | − | 0.551178i | ||||
\(159\) | 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 | \(0.308433\pi\) | |||||||
\(164\) | 3.00000 | 0.234261 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 25.9808i | 2.01650i | ||||||||
\(167\) | −4.50000 | − | 7.79423i | −0.348220 | − | 0.603136i | 0.637713 | − | 0.770274i | \(-0.279881\pi\) |
−0.985933 | + | 0.167139i | \(0.946547\pi\) | |||||||
\(168\) | 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 | ||||
\(173\) | −3.00000 | − | 5.19615i | −0.228086 | − | 0.395056i | 0.729155 | − | 0.684349i | \(-0.239913\pi\) |
−0.957241 | + | 0.289292i | \(0.906580\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 7.50000 | − | 4.33013i | 0.565334 | − | 0.326396i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | − | 5.19615i | − | 0.389468i | ||||||
\(179\) | −13.5000 | + | 7.79423i | −1.00904 | + | 0.582568i | −0.910910 | − | 0.412606i | \(-0.864619\pi\) |
−0.0981277 | + | 0.995174i | \(0.531285\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −9.00000 | −0.663489 | ||||||||
\(185\) | 10.5000 | − | 18.1865i | 0.771975 | − | 1.33710i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 4.50000 | − | 2.59808i | 0.329073 | − | 0.189990i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −27.0000 | −1.95879 | ||||||||
\(191\) | 15.0000 | − | 8.66025i | 1.08536 | − | 0.626634i | 0.153024 | − | 0.988222i | \(-0.451099\pi\) |
0.932338 | + | 0.361588i | \(0.117765\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1.00000 | − | 1.73205i | 0.0719816 | − | 0.124676i | −0.827788 | − | 0.561041i | \(-0.810401\pi\) |
0.899770 | + | 0.436365i | \(0.143734\pi\) | |||||||
\(194\) | 3.00000 | 0.215387 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 13.8564i | 0.987228i | 0.869681 | + | 0.493614i | \(0.164324\pi\) | ||||
−0.869681 | + | 0.493614i | \(0.835676\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 7.50000 | − | 4.33013i | 0.531661 | − | 0.306955i | −0.210032 | − | 0.977695i | \(-0.567357\pi\) |
0.741693 | + | 0.670740i | \(0.234023\pi\) | |||||||
\(200\) | 6.92820i | 0.489898i | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −4.50000 | + | 2.59808i | −0.316619 | + | 0.182800i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −4.50000 | − | 7.79423i | −0.314294 | − | 0.544373i | ||||
\(206\) | −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 | 0.939156 | − | 0.343490i | \(-0.111609\pi\) |
−0.767049 | + | 0.641588i | \(0.778276\pi\) | |||||||
\(212\) | − | 8.66025i | − | 0.594789i | ||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 15.0000 | 1.02538 | ||||||||
\(215\) | 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 | ||||||||
\(220\) | 4.50000 | + | 2.59808i | 0.303390 | + | 0.175162i | ||||
\(221\) | 4.50000 | + | 2.59808i | 0.302703 | + | 0.174766i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 4.50000 | + | 2.59808i | 0.301342 | + | 0.173980i | 0.643046 | − | 0.765828i | \(-0.277671\pi\) |
−0.341703 | + | 0.939808i | \(0.611004\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −1.50000 | + | 2.59808i | −0.0997785 | + | 0.172821i | ||||
\(227\) | 21.0000 | 1.39382 | 0.696909 | − | 0.717159i | \(-0.254558\pi\) | ||||
0.696909 | + | 0.717159i | \(0.254558\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 8.66025i | − | 0.572286i | −0.958187 | − | 0.286143i | \(-0.907627\pi\) | ||
0.958187 | − | 0.286143i | \(-0.0923732\pi\) | |||||||
\(230\) | −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 | 0.345302 | − | 0.938492i | \(-0.387777\pi\) |
−0.640107 | + | 0.768286i | \(0.721110\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −1.50000 | + | 0.866025i | −0.0970269 | + | 0.0560185i | −0.547728 | − | 0.836656i | \(-0.684507\pi\) |
0.450701 | + | 0.892675i | \(0.351174\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 22.5167i | 1.45043i | 0.688525 | + | 0.725213i | \(0.258259\pi\) | ||||
−0.688525 | + | 0.725213i | \(0.741741\pi\) | |||||||
\(242\) | 12.0000 | − | 6.92820i | 0.771389 | − | 0.445362i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 13.8564i | 0.887066i | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 9.00000 | 0.572656 | ||||||||
\(248\) | −3.00000 | + | 5.19615i | −0.190500 | + | 0.329956i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 4.50000 | − | 2.59808i | 0.284605 | − | 0.164317i | ||||
\(251\) | 12.0000 | 0.757433 | 0.378717 | − | 0.925513i | \(-0.376365\pi\) | ||||
0.378717 | + | 0.925513i | \(0.376365\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 9.00000 | 0.565825 | ||||||||
\(254\) | 30.0000 | − | 17.3205i | 1.88237 | − | 1.08679i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −9.50000 | + | 16.4545i | −0.593750 | + | 1.02841i | ||||
\(257\) | −3.00000 | −0.187135 | −0.0935674 | − | 0.995613i | \(-0.529827\pi\) | ||||
−0.0935674 | + | 0.995613i | \(0.529827\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 5.19615i | 0.322252i | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −13.5000 | + | 7.79423i | −0.834033 | + | 0.481529i | ||||
\(263\) | − | 22.5167i | − | 1.38844i | −0.719764 | − | 0.694218i | \(-0.755750\pi\) | ||
0.719764 | − | 0.694218i | \(-0.244250\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −22.5000 | + | 12.9904i | −1.38216 | + | 0.797993i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −2.00000 | − | 3.46410i | −0.122169 | − | 0.211604i | ||||
\(269\) | 7.50000 | + | 12.9904i | 0.457283 | + | 0.792038i | 0.998816 | − | 0.0486418i | \(-0.0154893\pi\) |
−0.541533 | + | 0.840679i | \(0.682156\pi\) | |||||||
\(270\) | 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 | ||||
\(275\) | − | 6.92820i | − | 0.417786i | ||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −1.00000 | −0.0600842 | −0.0300421 | − | 0.999549i | \(-0.509564\pi\) | ||||
−0.0300421 | + | 0.999549i | \(0.509564\pi\) | |||||||
\(278\) | 7.50000 | − | 12.9904i | 0.449820 | − | 0.779111i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 16.5000 | + | 9.52628i | 0.984307 | + | 0.568290i | 0.903568 | − | 0.428445i | \(-0.140938\pi\) |
0.0807396 | + | 0.996735i | \(0.474272\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −3.00000 | − | 1.73205i | −0.178331 | − | 0.102960i | 0.408177 | − | 0.912903i | \(-0.366165\pi\) |
−0.586509 | + | 0.809943i | \(0.699498\pi\) | |||||||
\(284\) | −3.00000 | − | 1.73205i | −0.178017 | − | 0.102778i | ||||
\(285\) | 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 | ||||
\(290\) | −27.0000 | −1.58549 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | − | 5.19615i | − | 0.304082i | ||||||
\(293\) | −4.50000 | − | 7.79423i | −0.262893 | − | 0.455344i | 0.704117 | − | 0.710084i | \(-0.251343\pi\) |
−0.967009 | + | 0.254741i | \(0.918010\pi\) | |||||||
\(294\) | 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 | ||||
\(299\) | 4.50000 | + | 7.79423i | 0.260242 | + | 0.450752i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −25.5000 | + | 14.7224i | −1.46736 | + | 0.847181i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 25.9808i | 1.49010i | ||||||||
\(305\) | 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 | ||||||||
\(310\) | −18.0000 | −1.02233 | ||||||||
\(311\) | −12.0000 | + | 20.7846i | −0.680458 | + | 1.17859i | 0.294384 | + | 0.955687i | \(0.404886\pi\) |
−0.974841 | + | 0.222900i | \(0.928448\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 18.0000 | − | 10.3923i | 1.01742 | − | 0.587408i | 0.104065 | − | 0.994571i | \(-0.466815\pi\) |
0.913356 | + | 0.407163i | \(0.133482\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −8.00000 | −0.450035 | ||||||||
\(317\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 4.50000 | − | 7.79423i | 0.251952 | − | 0.436393i | ||||
\(320\) | 3.00000 | 0.167705 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 15.5885i | 0.867365i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 6.00000 | − | 3.46410i | 0.332820 | − | 0.192154i | ||||
\(326\) | 19.0526i | 1.05522i | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −4.50000 | + | 2.59808i | −0.248471 | + | 0.143455i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 4.00000 | + | 6.92820i | 0.219860 | + | 0.380808i | 0.954765 | − | 0.297361i | \(-0.0961066\pi\) |
−0.734905 | + | 0.678170i | \(0.762773\pi\) | |||||||
\(332\) | 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 | −0.999793 | − | 0.0203242i | \(-0.993530\pi\) |
0.482295 | − | 0.876009i | \(-0.339803\pi\) | |||||||
\(338\) | 17.3205i | 0.942111i | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −9.00000 | −0.488094 | ||||||||
\(341\) | 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 | ||||||||
\(346\) | −9.00000 | − | 5.19615i | −0.483843 | − | 0.279347i | ||||
\(347\) | 3.00000 | + | 1.73205i | 0.161048 | + | 0.0929814i | 0.578358 | − | 0.815783i | \(-0.303694\pi\) |
−0.417310 | + | 0.908764i | \(0.637027\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −10.5000 | − | 6.06218i | −0.562052 | − | 0.324501i | 0.191917 | − | 0.981411i | \(-0.438530\pi\) |
−0.753969 | + | 0.656910i | \(0.771863\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 4.50000 | − | 7.79423i | 0.239851 | − | 0.415434i | ||||
\(353\) | 21.0000 | 1.11772 | 0.558859 | − | 0.829263i | \(-0.311239\pi\) | ||||
0.558859 | + | 0.829263i | \(0.311239\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 10.3923i | 0.551566i | ||||||||
\(356\) | −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 | 0.916747 | − | 0.399468i | \(-0.130805\pi\) |
0.112424 | + | 0.993660i | \(0.464139\pi\) | |||||||
\(360\) | 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 | ||||||||
\(367\) | − | 5.19615i | − | 0.271237i | −0.990761 | − | 0.135618i | \(-0.956698\pi\) | ||
0.990761 | − | 0.135618i | \(-0.0433021\pi\) | |||||||
\(368\) | −22.5000 | + | 12.9904i | −1.17289 | + | 0.677170i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | − | 36.3731i | − | 1.89095i | ||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −37.0000 | −1.91579 | −0.957894 | − | 0.287123i | \(-0.907301\pi\) | ||||
−0.957894 | + | 0.287123i | \(0.907301\pi\) | |||||||
\(374\) | 4.50000 | − | 7.79423i | 0.232689 | − | 0.403030i | ||||
\(375\) | 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 | \(0.671713\pi\) | |||||||
\(380\) | −13.5000 | + | 7.79423i | −0.692535 | + | 0.399835i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 15.0000 | − | 25.9808i | 0.767467 | − | 1.32929i | ||||
\(383\) | −9.00000 | −0.459879 | −0.229939 | − | 0.973205i | \(-0.573853\pi\) | ||||
−0.229939 | + | 0.973205i | \(0.573853\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | − | 3.46410i | − | 0.176318i | ||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 1.50000 | − | 0.866025i | 0.0761510 | − | 0.0439658i | ||||
\(389\) | − | 36.3731i | − | 1.84419i | −0.386966 | − | 0.922094i | \(-0.626477\pi\) | ||
0.386966 | − | 0.922094i | \(-0.373523\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −13.5000 | + | 7.79423i | −0.682724 | + | 0.394171i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 12.0000 | + | 20.7846i | 0.604551 | + | 1.04711i | ||||
\(395\) | 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 | ||||
\(401\) | − | 32.9090i | − | 1.64340i | −0.569924 | − | 0.821698i | \(-0.693027\pi\) | ||
0.569924 | − | 0.821698i | \(-0.306973\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 6.00000 | 0.298881 | ||||||||
\(404\) | −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 | ||||||||
\(409\) | 6.00000 | + | 3.46410i | 0.296681 | + | 0.171289i | 0.640951 | − | 0.767582i | \(-0.278540\pi\) |
−0.344270 | + | 0.938871i | \(0.611874\pi\) | |||||||
\(410\) | −13.5000 | − | 7.79423i | −0.666717 | − | 0.384930i | ||||
\(411\) | 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 | ||||
\(416\) | 9.00000 | 0.441261 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | − | 15.5885i | − | 0.762456i | ||||||
\(419\) | −16.5000 | − | 28.5788i | −0.806078 | − | 1.39617i | −0.915561 | − | 0.402179i | \(-0.868253\pi\) |
0.109483 | − | 0.993989i | \(-0.465080\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −5.50000 | + | 9.52628i | −0.268054 | + | 0.464282i | −0.968359 | − | 0.249561i | \(-0.919714\pi\) |
0.700306 | + | 0.713843i | \(0.253047\pi\) | |||||||
\(422\) | 7.50000 | + | 4.33013i | 0.365094 | + | 0.210787i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 7.50000 | + | 12.9904i | 0.364232 | + | 0.630869i | ||||
\(425\) | 6.00000 | + | 10.3923i | 0.291043 | + | 0.504101i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 7.50000 | − | 4.33013i | 0.362526 | − | 0.209305i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | − | 5.19615i | − | 0.250581i | ||||||
\(431\) | −13.5000 | + | 7.79423i | −0.650272 | + | 0.375435i | −0.788560 | − | 0.614957i | \(-0.789173\pi\) |
0.138288 | + | 0.990392i | \(0.455840\pi\) | |||||||
\(432\) | 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 | ||||||||
\(436\) | −19.0000 | −0.909935 | ||||||||
\(437\) | −13.5000 | + | 23.3827i | −0.645793 | + | 1.11855i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −27.0000 | + | 15.5885i | −1.28864 | + | 0.743996i | −0.978412 | − | 0.206666i | \(-0.933739\pi\) |
−0.310228 | + | 0.950662i | \(0.600405\pi\) | |||||||
\(440\) | −9.00000 | −0.429058 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 9.00000 | 0.428086 | ||||||||
\(443\) | −27.0000 | + | 15.5885i | −1.28281 | + | 0.740630i | −0.977361 | − | 0.211579i | \(-0.932139\pi\) |
−0.305448 | + | 0.952209i | \(0.598806\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −4.50000 | + | 7.79423i | −0.213320 | + | 0.369482i | ||||
\(446\) | 9.00000 | 0.426162 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 34.6410i | − | 1.63481i | −0.576063 | − | 0.817405i | \(-0.695412\pi\) | ||
0.576063 | − | 0.817405i | \(-0.304588\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 4.50000 | − | 2.59808i | 0.211897 | − | 0.122339i | ||||
\(452\) | 1.73205i | 0.0814688i | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 31.5000 | − | 18.1865i | 1.47837 | − | 0.853536i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 13.0000 | + | 22.5167i | 0.608114 | + | 1.05328i | 0.991551 | + | 0.129718i | \(0.0414071\pi\) |
−0.383437 | + | 0.923567i | \(0.625260\pi\) | |||||||
\(458\) | −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 | \(-0.719749\pi\) |
0.986127 | + | 0.165992i | \(0.0530827\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 0.500000 | + | 0.866025i | 0.0232370 | + | 0.0402476i | 0.877410 | − | 0.479741i | \(-0.159269\pi\) |
−0.854173 | + | 0.519989i | \(0.825936\pi\) | |||||||
\(464\) | 25.9808i | 1.20613i | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −9.00000 | −0.416917 | ||||||||
\(467\) | 1.50000 | − | 2.59808i | 0.0694117 | − | 0.120225i | −0.829231 | − | 0.558906i | \(-0.811221\pi\) |
0.898642 | + | 0.438682i | \(0.144554\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 1.50000 | + | 0.866025i | 0.0689701 | + | 0.0398199i | ||||
\(474\) | 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 | ||||
\(479\) | −27.0000 | −1.23366 | −0.616831 | − | 0.787096i | \(-0.711584\pi\) | ||||
−0.616831 | + | 0.787096i | \(0.711584\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 12.1244i | 0.552823i | ||||||||
\(482\) | 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 | \(0.658850\pi\) | |||||||
\(488\) | −12.0000 | − | 20.7846i | −0.543214 | − | 0.940875i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 22.5000 | − | 12.9904i | 1.01541 | − | 0.586248i | 0.102639 | − | 0.994719i | \(-0.467271\pi\) |
0.912771 | + | 0.408471i | \(0.133938\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 15.5885i | 0.702069i | ||||||||
\(494\) | 13.5000 | − | 7.79423i | 0.607394 | − | 0.350679i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 17.3205i | 0.777714i | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 25.0000 | 1.11915 | 0.559577 | − | 0.828778i | \(-0.310964\pi\) | ||||
0.559577 | + | 0.828778i | \(0.310964\pi\) | |||||||
\(500\) | 1.50000 | − | 2.59808i | 0.0670820 | − | 0.116190i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 18.0000 | − | 10.3923i | 0.803379 | − | 0.463831i | ||||
\(503\) | −24.0000 | −1.07011 | −0.535054 | − | 0.844818i | \(-0.679709\pi\) | ||||
−0.535054 | + | 0.844818i | \(0.679709\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 9.00000 | 0.400495 | ||||||||
\(506\) | 13.5000 | − | 7.79423i | 0.600148 | − | 0.346496i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 10.0000 | − | 17.3205i | 0.443678 | − | 0.768473i | ||||
\(509\) | 33.0000 | 1.46270 | 0.731350 | − | 0.682003i | \(-0.238891\pi\) | ||||
0.731350 | + | 0.682003i | \(0.238891\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 8.66025i | 0.382733i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −4.50000 | + | 2.59808i | −0.198486 | + | 0.114596i | ||||
\(515\) | 36.3731i | 1.60279i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −4.50000 | − | 7.79423i | −0.197338 | − | 0.341800i | ||||
\(521\) | −22.5000 | − | 38.9711i | −0.985743 | − | 1.70736i | −0.638588 | − | 0.769549i | \(-0.720481\pi\) |
−0.347155 | − | 0.937808i | \(-0.612852\pi\) | |||||||
\(522\) | 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 | ||||
\(527\) | 10.3923i | 0.452696i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −4.00000 | −0.173913 | ||||||||
\(530\) | −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 | ||||||||
\(535\) | −22.5000 | − | 12.9904i | −0.972760 | − | 0.561623i | ||||
\(536\) | 6.00000 | + | 3.46410i | 0.259161 | + | 0.149626i | ||||
\(537\) | 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 | \(0.0765123\pi\) | |||||||
\(542\) | 21.0000 | 0.902027 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 15.5885i | 0.668350i | ||||||||
\(545\) | 28.5000 | + | 49.3634i | 1.22081 | + | 2.11450i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 9.50000 | − | 16.4545i | 0.406191 | − | 0.703543i | −0.588269 | − | 0.808666i | \(-0.700190\pi\) |
0.994459 | + | 0.105123i | \(0.0335235\pi\) | |||||||
\(548\) | 10.5000 | + | 6.06218i | 0.448538 | + | 0.258963i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −6.00000 | − | 10.3923i | −0.255841 | − | 0.443129i | ||||
\(551\) | 13.5000 | + | 23.3827i | 0.575119 | + | 0.996136i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −1.50000 | + | 0.866025i | −0.0637289 | + | 0.0367939i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | − | 8.66025i | − | 0.367277i | ||||||
\(557\) | −10.5000 | + | 6.06218i | −0.444899 | + | 0.256863i | −0.705674 | − | 0.708537i | \(-0.749355\pi\) |
0.260774 | + | 0.965400i | \(0.416022\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1.73205i | 0.0732579i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 33.0000 | 1.39202 | ||||||||
\(563\) | 18.0000 | − | 31.1769i | 0.758610 | − | 1.31395i | −0.184950 | − | 0.982748i | \(-0.559212\pi\) |
0.943560 | − | 0.331202i | \(-0.107454\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 4.50000 | − | 2.59808i | 0.189316 | − | 0.109302i | ||||
\(566\) | −6.00000 | −0.252199 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 6.00000 | 0.251754 | ||||||||
\(569\) | −6.00000 | + | 3.46410i | −0.251533 | + | 0.145223i | −0.620466 | − | 0.784233i | \(-0.713057\pi\) |
0.368933 | + | 0.929456i | \(0.379723\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −16.0000 | + | 27.7128i | −0.669579 | + | 1.15975i | 0.308443 | + | 0.951243i | \(0.400192\pi\) |
−0.978022 | + | 0.208502i | \(0.933141\pi\) | |||||||
\(572\) | −3.00000 | −0.125436 | ||||||||
\(573\) | 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 | \(0.0221175\pi\) | |||||||
\(578\) | − | 13.8564i | − | 0.576351i | ||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −13.5000 | + | 7.79423i | −0.560557 | + | 0.323638i | ||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −7.50000 | − | 12.9904i | −0.310618 | − | 0.538007i | ||||
\(584\) | 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 | \(-0.690654\pi\) |
0.997162 | + | 0.0752860i | \(0.0239870\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 9.00000 | + | 15.5885i | 0.370839 | + | 0.642311i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −35.0000 | −1.43849 | ||||||||
\(593\) | 19.5000 | − | 33.7750i | 0.800769 | − | 1.38697i | −0.118342 | − | 0.992973i | \(-0.537758\pi\) |
0.919111 | − | 0.394000i | \(-0.128909\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 1.50000 | + | 0.866025i | 0.0614424 | + | 0.0354738i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 13.5000 | + | 7.79423i | 0.552056 | + | 0.318730i | ||||
\(599\) | 21.0000 | + | 12.1244i | 0.858037 | + | 0.495388i | 0.863354 | − | 0.504598i | \(-0.168359\pi\) |
−0.00531761 | + | 0.999986i | \(0.501693\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 25.5000 | + | 14.7224i | 1.04017 | + | 0.600541i | 0.919881 | − | 0.392199i | \(-0.128285\pi\) |
0.120286 | + | 0.992739i | \(0.461619\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −8.50000 | + | 14.7224i | −0.345860 | + | 0.599047i | ||||
\(605\) | −24.0000 | −0.975739 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 15.5885i | 0.632716i | 0.948640 | + | 0.316358i | \(0.102460\pi\) | ||||
−0.948640 | + | 0.316358i | \(0.897540\pi\) | |||||||
\(608\) | 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 | \(-0.564727\pi\) | |||||||
\(614\) | −21.0000 | − | 36.3731i | −0.847491 | − | 1.46790i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 4.50000 | − | 2.59808i | 0.181163 | − | 0.104595i | −0.406676 | − | 0.913573i | \(-0.633312\pi\) |
0.587839 | + | 0.808978i | \(0.299979\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 19.0526i | − | 0.765787i | −0.923792 | − | 0.382893i | \(-0.874928\pi\) | ||
0.923792 | − | 0.382893i | \(-0.125072\pi\) | |||||||
\(620\) | −9.00000 | + | 5.19615i | −0.361449 | + | 0.208683i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 41.5692i | 1.66677i | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −29.0000 | −1.16000 | ||||||||
\(626\) | 18.0000 | − | 31.1769i | 0.719425 | − | 1.24608i | ||||
\(627\) | 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 | \(0.449096\pi\) | |||||||
\(632\) | 12.0000 | − | 6.92820i | 0.477334 | − | 0.275589i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −60.0000 | −2.38103 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | − | 15.5885i | − | 0.617153i | ||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 31.5000 | − | 18.1865i | 1.24515 | − | 0.718886i | ||||
\(641\) | 12.1244i | 0.478883i | 0.970911 | + | 0.239442i | \(0.0769644\pi\) | ||||
−0.970911 | + | 0.239442i | \(0.923036\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −10.5000 | + | 6.06218i | −0.414080 | + | 0.239069i | −0.692541 | − | 0.721378i | \(-0.743509\pi\) |
0.278462 | + | 0.960447i | \(0.410176\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 13.5000 | + | 23.3827i | 0.531150 | + | 0.919979i | ||||
\(647\) | −1.50000 | − | 2.59808i | −0.0589711 | − | 0.102141i | 0.835033 | − | 0.550200i | \(-0.185449\pi\) |
−0.894004 | + | 0.448059i | \(0.852115\pi\) | |||||||
\(648\) | 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 | ||||
\(653\) | − | 39.8372i | − | 1.55895i | −0.626434 | − | 0.779474i | \(-0.715486\pi\) | ||
0.626434 | − | 0.779474i | \(-0.284514\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 27.0000 | 1.05498 | ||||||||
\(656\) | −7.50000 | + | 12.9904i | −0.292826 | + | 0.507189i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −10.5000 | − | 6.06218i | −0.409022 | − | 0.236149i | 0.281347 | − | 0.959606i | \(-0.409219\pi\) |
−0.690369 | + | 0.723457i | \(0.742552\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −36.0000 | − | 20.7846i | −1.40024 | − | 0.808428i | −0.405821 | − | 0.913953i | \(-0.633014\pi\) |
−0.994417 | + | 0.105525i | \(0.966348\pi\) | |||||||
\(662\) | 12.0000 | + | 6.92820i | 0.466393 | + | 0.269272i | ||||
\(663\) | 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 | ||||
\(668\) | −9.00000 | −0.348220 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 20.7846i | 0.802980i | ||||||||
\(671\) | 12.0000 | + | 20.7846i | 0.463255 | + | 0.802381i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 14.5000 | − | 25.1147i | 0.558934 | − | 0.968102i | −0.438652 | − | 0.898657i | \(-0.644544\pi\) |
0.997586 | − | 0.0694449i | \(-0.0221228\pi\) | |||||||
\(674\) | −28.5000 | − | 16.4545i | −1.09778 | − | 0.633803i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 5.00000 | + | 8.66025i | 0.192308 | + | 0.333087i | ||||
\(677\) | 9.00000 | + | 15.5885i | 0.345898 | + | 0.599113i | 0.985517 | − | 0.169580i | \(-0.0542410\pi\) |
−0.639618 | + | 0.768693i | \(0.720908\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 13.5000 | − | 7.79423i | 0.517701 | − | 0.298895i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | − | 10.3923i | − | 0.397942i | ||||||
\(683\) | −7.50000 | + | 4.33013i | −0.286980 | + | 0.165688i | −0.636579 | − | 0.771212i | \(-0.719651\pi\) |
0.349599 | + | 0.936899i | \(0.386318\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 36.3731i | − | 1.38974i | ||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −5.00000 | −0.190623 | ||||||||
\(689\) | 7.50000 | − | 12.9904i | 0.285727 | − | 0.494894i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 3.00000 | − | 1.73205i | 0.114125 | − | 0.0658903i | −0.441851 | − | 0.897089i | \(-0.645678\pi\) |
0.555976 | + | 0.831198i | \(0.312345\pi\) | |||||||
\(692\) | −6.00000 | −0.228086 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 6.00000 | 0.227757 | ||||||||
\(695\) | −22.5000 | + | 12.9904i | −0.853474 | + | 0.492753i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −4.50000 | + | 7.79423i | −0.170450 | + | 0.295227i | ||||
\(698\) | −21.0000 | −0.794862 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 34.6410i | − | 1.30837i | −0.756333 | − | 0.654187i | \(-0.773011\pi\) | ||
0.756333 | − | 0.654187i | \(-0.226989\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −31.5000 | + | 18.1865i | −1.18805 | + | 0.685918i | ||||
\(704\) | 1.73205i | 0.0652791i | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 31.5000 | − | 18.1865i | 1.18552 | − | 0.684459i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −5.00000 | − | 8.66025i | −0.187779 | − | 0.325243i | 0.756730 | − | 0.653727i | \(-0.226796\pi\) |
−0.944509 | + | 0.328484i | \(0.893462\pi\) | |||||||
\(710\) | 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 | ||||
\(716\) | 15.5885i | 0.582568i | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 39.0000 | 1.45547 | ||||||||
\(719\) | −4.50000 | + | 7.79423i | −0.167822 | + | 0.290676i | −0.937654 | − | 0.347571i | \(-0.887007\pi\) |
0.769832 | + | 0.638247i | \(0.220340\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 12.0000 | + | 6.92820i | 0.446594 | + | 0.257841i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 18.0000 | + | 10.3923i | 0.668503 | + | 0.385961i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 10.5000 | + | 6.06218i | 0.389423 | + | 0.224834i | 0.681910 | − | 0.731436i | \(-0.261149\pi\) |
−0.292487 | + | 0.956270i | \(0.594483\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −13.5000 | + | 23.3827i | −0.499657 | + | 0.865432i | ||||
\(731\) | −3.00000 | −0.110959 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 43.3013i | − | 1.59937i | −0.600420 | − | 0.799684i | \(-0.705000\pi\) | ||
0.600420 | − | 0.799684i | \(-0.295000\pi\) | |||||||
\(734\) | −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 | \(0.792237\pi\) | |||||||
\(740\) | −10.5000 | − | 18.1865i | −0.385988 | − | 0.668550i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 10.5000 | − | 6.06218i | 0.385208 | − | 0.222400i | −0.294874 | − | 0.955536i | \(-0.595278\pi\) |
0.680082 | + | 0.733136i | \(0.261944\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | − | 5.19615i | − | 0.190372i | ||||||
\(746\) | −55.5000 | + | 32.0429i | −2.03200 | + | 1.17318i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | − | 5.19615i | − | 0.189990i | ||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 37.0000 | 1.35015 | 0.675075 | − | 0.737749i | \(-0.264111\pi\) | ||||
0.675075 | + | 0.737749i | \(0.264111\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 13.5000 | − | 7.79423i | 0.491641 | − | 0.283849i | ||||
\(755\) | 51.0000 | 1.85608 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 10.0000 | 0.363456 | 0.181728 | − | 0.983349i | \(-0.441831\pi\) | ||||
0.181728 | + | 0.983349i | \(0.441831\pi\) | |||||||
\(758\) | −30.0000 | + | 17.3205i | −1.08965 | + | 0.629109i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 13.5000 | − | 23.3827i | 0.489696 | − | 0.848179i | ||||
\(761\) | 45.0000 | 1.63125 | 0.815624 | − | 0.578582i | \(-0.196394\pi\) | ||||
0.815624 | + | 0.578582i | \(0.196394\pi\) | |||||||
\(762\) | 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 | \(-0.575978\pi\) |
0.723255 | + | 0.690581i | \(0.242645\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −1.00000 | − | 1.73205i | −0.0359908 | − | 0.0623379i | ||||
\(773\) | 25.5000 | + | 44.1673i | 0.917171 | + | 1.58859i | 0.803691 | + | 0.595047i | \(0.202867\pi\) |
0.113480 | + | 0.993540i | \(0.463800\pi\) | |||||||
\(774\) | 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 | ||||
\(779\) | 15.5885i | 0.558514i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −6.00000 | −0.214697 | ||||||||
\(782\) | −13.5000 | + | 23.3827i | −0.482759 | + | 0.836163i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 33.0000 | + | 19.0526i | 1.17632 | + | 0.679150i | 0.955161 | − | 0.296087i | \(-0.0956817\pi\) |
0.221162 | + | 0.975237i | \(0.429015\pi\) | |||||||
\(788\) | 12.0000 | + | 6.92820i | 0.427482 | + | 0.246807i | ||||
\(789\) | 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 | ||||
\(794\) | −15.0000 | −0.532330 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | − | 8.66025i | − | 0.306955i | ||||||
\(797\) | −22.5000 | − | 38.9711i | −0.796991 | − | 1.38043i | −0.921567 | − | 0.388219i | \(-0.873091\pi\) |
0.124576 | − | 0.992210i | \(-0.460243\pi\) | |||||||
\(798\) | 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 | ||||
\(803\) | −4.50000 | − | 7.79423i | −0.158802 | − | 0.275052i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 9.00000 | − | 5.19615i | 0.317011 | − | 0.183027i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | − | 5.19615i | − | 0.182800i | ||||||
\(809\) | 1.50000 | − | 0.866025i | 0.0527372 | − | 0.0304478i | −0.473400 | − | 0.880848i | \(-0.656973\pi\) |
0.526137 | + | 0.850400i | \(0.323640\pi\) | |||||||
\(810\) | 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 | ||||||||
\(814\) | 21.0000 | 0.736050 | ||||||||
\(815\) | 16.5000 | − | 28.5788i | 0.577970 | − | 1.00107i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −4.50000 | + | 2.59808i | −0.157435 | + | 0.0908952i | ||||
\(818\) | 12.0000 | 0.419570 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −9.00000 | −0.314294 | ||||||||
\(821\) | −6.00000 | + | 3.46410i | −0.209401 | + | 0.120898i | −0.601033 | − | 0.799224i | \(-0.705244\pi\) |
0.391632 | + | 0.920122i | \(0.371911\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 8.00000 | − | 13.8564i | 0.278862 | − | 0.483004i | −0.692240 | − | 0.721668i | \(-0.743376\pi\) |
0.971102 | + | 0.238664i | \(0.0767093\pi\) | |||||||
\(824\) | 21.0000 | 0.731570 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 24.2487i | 0.843210i | 0.906780 | + | 0.421605i | \(0.138533\pi\) | ||||
−0.906780 | + | 0.421605i | \(0.861467\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −31.5000 | + | 18.1865i | −1.09404 | + | 0.631644i | −0.934649 | − | 0.355571i | \(-0.884286\pi\) |
−0.159391 | + | 0.987216i | \(0.550953\pi\) | |||||||
\(830\) | − | 77.9423i | − | 2.70542i | ||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −1.50000 | + | 0.866025i | −0.0520031 | + | 0.0300240i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 13.5000 | + | 23.3827i | 0.467187 | + | 0.809191i | ||||
\(836\) | −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 | 0.303773 | + | 0.952745i | \(0.401754\pi\) |
−0.976987 | + | 0.213298i | \(0.931580\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.00000 | − | 1.73205i | −0.0344828 | − | 0.0597259i | ||||
\(842\) | 19.0526i | 0.656595i | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 5.00000 | 0.172107 | ||||||||
\(845\) | 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 | ||||||||
\(850\) | 18.0000 | + | 10.3923i | 0.617395 | + | 0.356453i | ||||
\(851\) | −31.5000 | − | 18.1865i | −1.07981 | − | 0.623426i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −22.5000 | − | 12.9904i | −0.770385 | − | 0.444782i | 0.0626267 | − | 0.998037i | \(-0.480052\pi\) |
−0.833012 | + | 0.553255i | \(0.813386\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −7.50000 | + | 12.9904i | −0.256345 | + | 0.444002i | ||||
\(857\) | −27.0000 | −0.922302 | −0.461151 | − | 0.887322i | \(-0.652563\pi\) | ||||
−0.461151 | + | 0.887322i | \(0.652563\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 50.2295i | 1.71381i | 0.515476 | + | 0.856904i | \(0.327615\pi\) | ||||
−0.515476 | + | 0.856904i | \(0.672385\pi\) | |||||||
\(860\) | −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 | 0.976206 | − | 0.216846i | \(-0.0695769\pi\) |
0.300309 | + | 0.953842i | \(0.402910\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 9.00000 | + | 15.5885i | 0.306009 | + | 0.530023i | ||||
\(866\) | 12.0000 | + | 20.7846i | 0.407777 | + | 0.706290i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −12.0000 | + | 6.92820i | −0.407072 | + | 0.235023i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 6.92820i | − | 0.234753i | ||||||
\(872\) | 28.5000 | − | 16.4545i | 0.965132 | − | 0.557219i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 46.7654i | 1.58186i | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 23.0000 | 0.776655 | 0.388327 | − | 0.921521i | \(-0.373053\pi\) | ||||
0.388327 | + | 0.921521i | \(0.373053\pi\) | |||||||
\(878\) | −27.0000 | + | 46.7654i | −0.911206 | + | 1.57825i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −22.5000 | + | 12.9904i | −0.758475 | + | 0.437906i | ||||
\(881\) | −54.0000 | −1.81931 | −0.909653 | − | 0.415369i | \(-0.863653\pi\) | ||||
−0.909653 | + | 0.415369i | \(0.863653\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 4.00000 | 0.134611 | 0.0673054 | − | 0.997732i | \(-0.478560\pi\) | ||||
0.0673054 | + | 0.997732i | \(0.478560\pi\) | |||||||
\(884\) | 4.50000 | − | 2.59808i | 0.151351 | − | 0.0873828i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −27.0000 | + | 46.7654i | −0.907083 | + | 1.57111i | ||||
\(887\) | 15.0000 | 0.503651 | 0.251825 | − | 0.967773i | \(-0.418969\pi\) | ||||
0.251825 | + | 0.967773i | \(0.418969\pi\) | |||||||
\(888\) | 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 | ||||||||
\(898\) | −30.0000 | − | 51.9615i | −1.00111 | − | 1.73398i | ||||
\(899\) | 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 | ||||||||
\(907\) | 19.0000 | 0.630885 | 0.315442 | − | 0.948945i | \(-0.397847\pi\) | ||||
0.315442 | + | 0.948945i | \(0.397847\pi\) | |||||||
\(908\) | 10.5000 | − | 18.1865i | 0.348455 | − | 0.603541i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −4.50000 | − | 2.59808i | −0.149092 | − | 0.0860781i | 0.423598 | − | 0.905850i | \(-0.360767\pi\) |
−0.572690 | + | 0.819772i | \(0.694100\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 22.5000 | + | 12.9904i | 0.744641 | + | 0.429919i | ||||
\(914\) | 39.0000 | + | 22.5167i | 1.29001 | + | 0.744785i | ||||
\(915\) | 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 | \(0.00791589\pi\) | |||||||
\(920\) | 27.0000 | 0.890164 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | − | 25.9808i | − | 0.855631i | ||||||
\(923\) | −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 | ||||
\(929\) | −15.0000 | − | 25.9808i | −0.492134 | − | 0.852401i | 0.507825 | − | 0.861460i | \(-0.330450\pi\) |
−0.999959 | + | 0.00905914i | \(0.997116\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −4.50000 | + | 2.59808i | −0.147402 | + | 0.0851028i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | − | 5.19615i | − | 0.170023i | ||||||
\(935\) | −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 | ||||||||
\(941\) | 9.00000 | − | 15.5885i | 0.293392 | − | 0.508169i | −0.681218 | − | 0.732081i | \(-0.738549\pi\) |
0.974609 | + | 0.223912i | \(0.0718827\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −13.5000 | + | 7.79423i | −0.439620 | + | 0.253815i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 3.00000 | 0.0975384 | ||||||||
\(947\) | 45.0000 | − | 25.9808i | 1.46230 | − | 0.844261i | 0.463186 | − | 0.886261i | \(-0.346706\pi\) |
0.999118 | + | 0.0419998i | \(0.0133729\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 4.50000 | − | 7.79423i | 0.146076 | − | 0.253011i | ||||
\(950\) | 36.0000 | 1.16799 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 20.7846i | − | 0.673280i | −0.941634 | − | 0.336640i | \(-0.890710\pi\) | ||
0.941634 | − | 0.336640i | \(-0.109290\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −45.0000 | + | 25.9808i | −1.45617 | + | 0.840718i | ||||
\(956\) | 1.73205i | 0.0560185i | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −40.5000 | + | 23.3827i | −1.30850 | + | 0.755460i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −9.50000 | − | 16.4545i | −0.306452 | − | 0.530790i | ||||
\(962\) | 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 | 0.993964 | − | 0.109707i | \(-0.0349913\pi\) |
−0.591991 | + | 0.805945i | \(0.701658\pi\) | |||||||
\(968\) | 13.8564i | 0.445362i | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −9.00000 | −0.288973 | ||||||||
\(971\) | −28.5000 | + | 49.3634i | −0.914609 | + | 1.58415i | −0.107135 | + | 0.994244i | \(0.534168\pi\) |
−0.807473 | + | 0.589904i | \(0.799166\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 34.5000 | + | 19.9186i | 1.10545 | + | 0.638233i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −60.0000 | − | 34.6410i | −1.92055 | − | 1.10883i | ||||
\(977\) | 36.0000 | + | 20.7846i | 1.15174 | + | 0.664959i | 0.949311 | − | 0.314338i | \(-0.101783\pi\) |
0.202431 | + | 0.979297i | \(0.435116\pi\) | |||||||
\(978\) | 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 | ||||
\(983\) | −39.0000 | −1.24391 | −0.621953 | − | 0.783054i | \(-0.713661\pi\) | ||||
−0.621953 | + | 0.783054i | \(0.713661\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | − | 41.5692i | − | 1.32451i | ||||||
\(986\) | 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 | \(0.565065\pi\) | |||||||
\(992\) | 9.00000 | + | 15.5885i | 0.285750 | + | 0.494934i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −22.5000 | + | 12.9904i | −0.713298 | + | 0.411823i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 8.66025i | 0.274273i | 0.990552 | + | 0.137136i | \(0.0437899\pi\) | ||||
−0.990552 | + | 0.137136i | \(0.956210\pi\) | |||||||
\(998\) | 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 \(a_p\))