Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [63,2,Mod(47,63)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(63, 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("63.47");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 63 = 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 63.s (of order \(6\), degree \(2\), 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: | \(0.503057532734\) |
Analytic rank: | \(1\) |
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: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 47.1 | ||
Root | \(0.500000 - 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 63.47 |
Dual form | 63.2.s.a.59.1 |
$q$-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 \(\left(\mathbb{Z}/63\mathbb{Z}\right)^\times\).
\(n\) | \(10\) | \(29\) |
\(\chi(n)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{1}{6}\right)\) |
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 | −0.925615 | − | 0.378467i | \(-0.876451\pi\) |
−0.135045 | + | 0.990839i | \(0.543118\pi\) | |||||||
\(3\) | −1.50000 | − | 0.866025i | −0.866025 | − | 0.500000i | ||||
\(4\) | 0.500000 | − | 0.866025i | 0.250000 | − | 0.433013i | ||||
\(5\) | −3.00000 | −1.34164 | −0.670820 | − | 0.741620i | \(-0.734058\pi\) | ||||
−0.670820 | + | 0.741620i | \(0.734058\pi\) | |||||||
\(6\) | 3.00000 | 1.22474 | ||||||||
\(7\) | −2.50000 | − | 0.866025i | −0.944911 | − | 0.327327i | ||||
\(8\) | − | 1.73205i | − | 0.612372i | ||||||
\(9\) | 1.50000 | + | 2.59808i | 0.500000 | + | 0.866025i | ||||
\(10\) | 4.50000 | − | 2.59808i | 1.42302 | − | 0.821584i | ||||
\(11\) | 1.73205i | 0.522233i | 0.965307 | + | 0.261116i | \(0.0840907\pi\) | ||||
−0.965307 | + | 0.261116i | \(0.915909\pi\) | |||||||
\(12\) | −1.50000 | + | 0.866025i | −0.433013 | + | 0.250000i | ||||
\(13\) | −1.50000 | + | 0.866025i | −0.416025 | + | 0.240192i | −0.693375 | − | 0.720577i | \(-0.743877\pi\) |
0.277350 | + | 0.960769i | \(0.410544\pi\) | |||||||
\(14\) | 4.50000 | − | 0.866025i | 1.20268 | − | 0.231455i | ||||
\(15\) | 4.50000 | + | 2.59808i | 1.16190 | + | 0.670820i | ||||
\(16\) | 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 | \(0.714811\pi\) | |||||||
\(18\) | −4.50000 | − | 2.59808i | −1.06066 | − | 0.612372i | ||||
\(19\) | −4.50000 | − | 2.59808i | −1.03237 | − | 0.596040i | −0.114708 | − | 0.993399i | \(-0.536593\pi\) |
−0.917663 | + | 0.397360i | \(0.869927\pi\) | |||||||
\(20\) | −1.50000 | + | 2.59808i | −0.335410 | + | 0.580948i | ||||
\(21\) | 3.00000 | + | 3.46410i | 0.654654 | + | 0.755929i | ||||
\(22\) | −1.50000 | − | 2.59808i | −0.319801 | − | 0.553912i | ||||
\(23\) | − | 5.19615i | − | 1.08347i | −0.840548 | − | 0.541736i | \(-0.817767\pi\) | ||
0.840548 | − | 0.541736i | \(-0.182233\pi\) | |||||||
\(24\) | −1.50000 | + | 2.59808i | −0.306186 | + | 0.530330i | ||||
\(25\) | 4.00000 | 0.800000 | ||||||||
\(26\) | 1.50000 | − | 2.59808i | 0.294174 | − | 0.509525i | ||||
\(27\) | − | 5.19615i | − | 1.00000i | ||||||
\(28\) | −2.00000 | + | 1.73205i | −0.377964 | + | 0.327327i | ||||
\(29\) | −4.50000 | − | 2.59808i | −0.835629 | − | 0.482451i | 0.0201471 | − | 0.999797i | \(-0.493587\pi\) |
−0.855776 | + | 0.517346i | \(0.826920\pi\) | |||||||
\(30\) | −9.00000 | −1.64317 | ||||||||
\(31\) | −3.00000 | − | 1.73205i | −0.538816 | − | 0.311086i | 0.205783 | − | 0.978598i | \(-0.434026\pi\) |
−0.744599 | + | 0.667512i | \(0.767359\pi\) | |||||||
\(32\) | −4.50000 | − | 2.59808i | −0.795495 | − | 0.459279i | ||||
\(33\) | 1.50000 | − | 2.59808i | 0.261116 | − | 0.452267i | ||||
\(34\) | −4.50000 | − | 2.59808i | −0.771744 | − | 0.445566i | ||||
\(35\) | 7.50000 | + | 2.59808i | 1.26773 | + | 0.439155i | ||||
\(36\) | 3.00000 | 0.500000 | ||||||||
\(37\) | −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 | ||||||||
\(39\) | 3.00000 | 0.480384 | ||||||||
\(40\) | 5.19615i | 0.821584i | ||||||||
\(41\) | 1.50000 | + | 2.59808i | 0.234261 | + | 0.405751i | 0.959058 | − | 0.283211i | \(-0.0913998\pi\) |
−0.724797 | + | 0.688963i | \(0.758066\pi\) | |||||||
\(42\) | −7.50000 | − | 2.59808i | −1.15728 | − | 0.400892i | ||||
\(43\) | −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 | ||||
\(45\) | −4.50000 | − | 7.79423i | −0.670820 | − | 1.16190i | ||||
\(46\) | 4.50000 | + | 7.79423i | 0.663489 | + | 1.14920i | ||||
\(47\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(48\) | − | 8.66025i | − | 1.25000i | ||||||
\(49\) | 5.50000 | + | 4.33013i | 0.785714 | + | 0.618590i | ||||
\(50\) | −6.00000 | + | 3.46410i | −0.848528 | + | 0.489898i | ||||
\(51\) | − | 5.19615i | − | 0.727607i | ||||||
\(52\) | 1.73205i | 0.240192i | ||||||||
\(53\) | −7.50000 | + | 4.33013i | −1.03020 | + | 0.594789i | −0.917043 | − | 0.398788i | \(-0.869431\pi\) |
−0.113161 | + | 0.993577i | \(0.536098\pi\) | |||||||
\(54\) | 4.50000 | + | 7.79423i | 0.612372 | + | 1.06066i | ||||
\(55\) | − | 5.19615i | − | 0.700649i | ||||||
\(56\) | −1.50000 | + | 4.33013i | −0.200446 | + | 0.578638i | ||||
\(57\) | 4.50000 | + | 7.79423i | 0.596040 | + | 1.03237i | ||||
\(58\) | 9.00000 | 1.18176 | ||||||||
\(59\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(60\) | 4.50000 | − | 2.59808i | 0.580948 | − | 0.335410i | ||||
\(61\) | 12.0000 | − | 6.92820i | 1.53644 | − | 0.887066i | 0.537400 | − | 0.843328i | \(-0.319407\pi\) |
0.999043 | − | 0.0437377i | \(-0.0139266\pi\) | |||||||
\(62\) | 6.00000 | 0.762001 | ||||||||
\(63\) | −1.50000 | − | 7.79423i | −0.188982 | − | 0.981981i | ||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 4.50000 | − | 2.59808i | 0.558156 | − | 0.322252i | ||||
\(66\) | 5.19615i | 0.639602i | ||||||||
\(67\) | 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 | ||||||||
\(69\) | −4.50000 | + | 7.79423i | −0.541736 | + | 0.938315i | ||||
\(70\) | −13.5000 | + | 2.59808i | −1.61356 | + | 0.310530i | ||||
\(71\) | 3.46410i | 0.411113i | 0.978645 | + | 0.205557i | \(0.0659005\pi\) | ||||
−0.978645 | + | 0.205557i | \(0.934100\pi\) | |||||||
\(72\) | 4.50000 | − | 2.59808i | 0.530330 | − | 0.306186i | ||||
\(73\) | −4.50000 | + | 2.59808i | −0.526685 | + | 0.304082i | −0.739666 | − | 0.672975i | \(-0.765016\pi\) |
0.212980 | + | 0.977056i | \(0.431683\pi\) | |||||||
\(74\) | − | 12.1244i | − | 1.40943i | ||||||
\(75\) | −6.00000 | − | 3.46410i | −0.692820 | − | 0.400000i | ||||
\(76\) | −4.50000 | + | 2.59808i | −0.516185 | + | 0.298020i | ||||
\(77\) | 1.50000 | − | 4.33013i | 0.170941 | − | 0.493464i | ||||
\(78\) | −4.50000 | + | 2.59808i | −0.509525 | + | 0.294174i | ||||
\(79\) | −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 | ||||
\(81\) | −4.50000 | + | 7.79423i | −0.500000 | + | 0.866025i | ||||
\(82\) | −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 | \(0.858835\pi\) | |||||||
\(84\) | 4.50000 | − | 0.866025i | 0.490990 | − | 0.0944911i | ||||
\(85\) | −4.50000 | − | 7.79423i | −0.488094 | − | 0.845403i | ||||
\(86\) | − | 1.73205i | − | 0.186772i | ||||||
\(87\) | 4.50000 | + | 7.79423i | 0.482451 | + | 0.835629i | ||||
\(88\) | 3.00000 | 0.319801 | ||||||||
\(89\) | 1.50000 | − | 2.59808i | 0.159000 | − | 0.275396i | −0.775509 | − | 0.631337i | \(-0.782506\pi\) |
0.934508 | + | 0.355942i | \(0.115840\pi\) | |||||||
\(90\) | 13.5000 | + | 7.79423i | 1.42302 | + | 0.821584i | ||||
\(91\) | 4.50000 | − | 0.866025i | 0.471728 | − | 0.0907841i | ||||
\(92\) | −4.50000 | − | 2.59808i | −0.469157 | − | 0.270868i | ||||
\(93\) | 3.00000 | + | 5.19615i | 0.311086 | + | 0.538816i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 13.5000 | + | 7.79423i | 1.38507 | + | 0.799671i | ||||
\(96\) | 4.50000 | + | 7.79423i | 0.459279 | + | 0.795495i | ||||
\(97\) | −1.50000 | − | 0.866025i | −0.152302 | − | 0.0879316i | 0.421912 | − | 0.906637i | \(-0.361359\pi\) |
−0.574214 | + | 0.818705i | \(0.694692\pi\) | |||||||
\(98\) | −12.0000 | − | 1.73205i | −1.21218 | − | 0.174964i | ||||
\(99\) | −4.50000 | + | 2.59808i | −0.452267 | + | 0.261116i | ||||
\(100\) | 2.00000 | − | 3.46410i | 0.200000 | − | 0.346410i | ||||
\(101\) | −3.00000 | −0.298511 | −0.149256 | − | 0.988799i | \(-0.547688\pi\) | ||||
−0.149256 | + | 0.988799i | \(0.547688\pi\) | |||||||
\(102\) | 4.50000 | + | 7.79423i | 0.445566 | + | 0.771744i | ||||
\(103\) | 12.1244i | 1.19465i | 0.802000 | + | 0.597324i | \(0.203769\pi\) | ||||
−0.802000 | + | 0.597324i | \(0.796231\pi\) | |||||||
\(104\) | 1.50000 | + | 2.59808i | 0.147087 | + | 0.254762i | ||||
\(105\) | −9.00000 | − | 10.3923i | −0.878310 | − | 1.01419i | ||||
\(106\) | 7.50000 | − | 12.9904i | 0.728464 | − | 1.26174i | ||||
\(107\) | −7.50000 | − | 4.33013i | −0.725052 | − | 0.418609i | 0.0915571 | − | 0.995800i | \(-0.470816\pi\) |
−0.816609 | + | 0.577191i | \(0.804149\pi\) | |||||||
\(108\) | −4.50000 | − | 2.59808i | −0.433013 | − | 0.250000i | ||||
\(109\) | −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 | ||||
\(111\) | 10.5000 | − | 6.06218i | 0.996616 | − | 0.575396i | ||||
\(112\) | −2.50000 | − | 12.9904i | −0.236228 | − | 1.22748i | ||||
\(113\) | 1.50000 | − | 0.866025i | 0.141108 | − | 0.0814688i | −0.427784 | − | 0.903881i | \(-0.640706\pi\) |
0.568892 | + | 0.822412i | \(0.307372\pi\) | |||||||
\(114\) | −13.5000 | − | 7.79423i | −1.26439 | − | 0.729996i | ||||
\(115\) | 15.5885i | 1.45363i | ||||||||
\(116\) | −4.50000 | + | 2.59808i | −0.417815 | + | 0.241225i | ||||
\(117\) | −4.50000 | − | 2.59808i | −0.416025 | − | 0.240192i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −1.50000 | − | 7.79423i | −0.137505 | − | 0.714496i | ||||
\(120\) | 4.50000 | − | 7.79423i | 0.410792 | − | 0.711512i | ||||
\(121\) | 8.00000 | 0.727273 | ||||||||
\(122\) | −12.0000 | + | 20.7846i | −1.08643 | + | 1.88175i | ||||
\(123\) | − | 5.19615i | − | 0.468521i | ||||||
\(124\) | −3.00000 | + | 1.73205i | −0.269408 | + | 0.155543i | ||||
\(125\) | 3.00000 | 0.268328 | ||||||||
\(126\) | 9.00000 | + | 10.3923i | 0.801784 | + | 0.925820i | ||||
\(127\) | 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 | ||||
\(129\) | 1.50000 | − | 0.866025i | 0.132068 | − | 0.0762493i | ||||
\(130\) | −4.50000 | + | 7.79423i | −0.394676 | + | 0.683599i | ||||
\(131\) | −9.00000 | −0.786334 | −0.393167 | − | 0.919467i | \(-0.628621\pi\) | ||||
−0.393167 | + | 0.919467i | \(0.628621\pi\) | |||||||
\(132\) | −1.50000 | − | 2.59808i | −0.130558 | − | 0.226134i | ||||
\(133\) | 9.00000 | + | 10.3923i | 0.780399 | + | 0.901127i | ||||
\(134\) | 6.92820i | 0.598506i | ||||||||
\(135\) | 15.5885i | 1.34164i | ||||||||
\(136\) | 4.50000 | − | 2.59808i | 0.385872 | − | 0.222783i | ||||
\(137\) | − | 12.1244i | − | 1.03585i | −0.855425 | − | 0.517927i | \(-0.826704\pi\) | ||
0.855425 | − | 0.517927i | \(-0.173296\pi\) | |||||||
\(138\) | − | 15.5885i | − | 1.32698i | ||||||
\(139\) | −7.50000 | + | 4.33013i | −0.636142 | + | 0.367277i | −0.783127 | − | 0.621862i | \(-0.786376\pi\) |
0.146985 | + | 0.989139i | \(0.453043\pi\) | |||||||
\(140\) | 6.00000 | − | 5.19615i | 0.507093 | − | 0.439155i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −3.00000 | − | 5.19615i | −0.251754 | − | 0.436051i | ||||
\(143\) | −1.50000 | − | 2.59808i | −0.125436 | − | 0.217262i | ||||
\(144\) | −7.50000 | + | 12.9904i | −0.625000 | + | 1.08253i | ||||
\(145\) | 13.5000 | + | 7.79423i | 1.12111 | + | 0.647275i | ||||
\(146\) | 4.50000 | − | 7.79423i | 0.372423 | − | 0.645055i | ||||
\(147\) | −4.50000 | − | 11.2583i | −0.371154 | − | 0.928571i | ||||
\(148\) | 3.50000 | + | 6.06218i | 0.287698 | + | 0.498308i | ||||
\(149\) | − | 1.73205i | − | 0.141895i | −0.997480 | − | 0.0709476i | \(-0.977398\pi\) | ||
0.997480 | − | 0.0709476i | \(-0.0226023\pi\) | |||||||
\(150\) | 12.0000 | 0.979796 | ||||||||
\(151\) | −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 | ||||
\(153\) | −4.50000 | + | 7.79423i | −0.363803 | + | 0.630126i | ||||
\(154\) | 1.50000 | + | 7.79423i | 0.120873 | + | 0.628077i | ||||
\(155\) | 9.00000 | + | 5.19615i | 0.722897 | + | 0.417365i | ||||
\(156\) | 1.50000 | − | 2.59808i | 0.120096 | − | 0.208013i | ||||
\(157\) | 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 | ||||
\(159\) | 15.0000 | 1.18958 | ||||||||
\(160\) | 13.5000 | + | 7.79423i | 1.06727 | + | 0.616188i | ||||
\(161\) | −4.50000 | + | 12.9904i | −0.354650 | + | 1.02379i | ||||
\(162\) | − | 15.5885i | − | 1.22474i | ||||||
\(163\) | −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 | ||||||||
\(165\) | −4.50000 | + | 7.79423i | −0.350325 | + | 0.606780i | ||||
\(166\) | − | 25.9808i | − | 2.01650i | ||||||
\(167\) | −4.50000 | − | 7.79423i | −0.348220 | − | 0.603136i | 0.637713 | − | 0.770274i | \(-0.279881\pi\) |
−0.985933 | + | 0.167139i | \(0.946547\pi\) | |||||||
\(168\) | 6.00000 | − | 5.19615i | 0.462910 | − | 0.400892i | ||||
\(169\) | −5.00000 | + | 8.66025i | −0.384615 | + | 0.666173i | ||||
\(170\) | 13.5000 | + | 7.79423i | 1.03540 | + | 0.597790i | ||||
\(171\) | − | 15.5885i | − | 1.19208i | ||||||
\(172\) | 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 | \(0.906580\pi\) | |||||||
\(174\) | −13.5000 | − | 7.79423i | −1.02343 | − | 0.590879i | ||||
\(175\) | −10.0000 | − | 3.46410i | −0.755929 | − | 0.261861i | ||||
\(176\) | −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 | 0.0981277 | − | 0.995174i | \(-0.468715\pi\) |
0.910910 | + | 0.412606i | \(0.135381\pi\) | |||||||
\(180\) | −9.00000 | −0.670820 | ||||||||
\(181\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(182\) | −6.00000 | + | 5.19615i | −0.444750 | + | 0.385164i | ||||
\(183\) | −24.0000 | −1.77413 | ||||||||
\(184\) | −9.00000 | −0.663489 | ||||||||
\(185\) | 10.5000 | − | 18.1865i | 0.771975 | − | 1.33710i | ||||
\(186\) | −9.00000 | − | 5.19615i | −0.659912 | − | 0.381000i | ||||
\(187\) | −4.50000 | + | 2.59808i | −0.329073 | + | 0.189990i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −4.50000 | + | 12.9904i | −0.327327 | + | 0.944911i | ||||
\(190\) | −27.0000 | −1.95879 | ||||||||
\(191\) | −15.0000 | + | 8.66025i | −1.08536 | + | 0.626634i | −0.932338 | − | 0.361588i | \(-0.882235\pi\) |
−0.153024 | + | 0.988222i | \(0.548901\pi\) | |||||||
\(192\) | 1.50000 | + | 0.866025i | 0.108253 | + | 0.0625000i | ||||
\(193\) | 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 | ||||||||
\(195\) | −9.00000 | −0.644503 | ||||||||
\(196\) | 6.50000 | − | 2.59808i | 0.464286 | − | 0.185577i | ||||
\(197\) | − | 13.8564i | − | 0.987228i | −0.869681 | − | 0.493614i | \(-0.835676\pi\) | ||
0.869681 | − | 0.493614i | \(-0.164324\pi\) | |||||||
\(198\) | 4.50000 | − | 7.79423i | 0.319801 | − | 0.553912i | ||||
\(199\) | −7.50000 | + | 4.33013i | −0.531661 | + | 0.306955i | −0.741693 | − | 0.670740i | \(-0.765977\pi\) |
0.210032 | + | 0.977695i | \(0.432643\pi\) | |||||||
\(200\) | − | 6.92820i | − | 0.489898i | ||||||
\(201\) | −6.00000 | + | 3.46410i | −0.423207 | + | 0.244339i | ||||
\(202\) | 4.50000 | − | 2.59808i | 0.316619 | − | 0.182800i | ||||
\(203\) | 9.00000 | + | 10.3923i | 0.631676 | + | 0.729397i | ||||
\(204\) | −4.50000 | − | 2.59808i | −0.315063 | − | 0.181902i | ||||
\(205\) | −4.50000 | − | 7.79423i | −0.314294 | − | 0.544373i | ||||
\(206\) | −10.5000 | − | 18.1865i | −0.731570 | − | 1.26712i | ||||
\(207\) | 13.5000 | − | 7.79423i | 0.938315 | − | 0.541736i | ||||
\(208\) | −7.50000 | − | 4.33013i | −0.520031 | − | 0.300240i | ||||
\(209\) | 4.50000 | − | 7.79423i | 0.311272 | − | 0.539138i | ||||
\(210\) | 22.5000 | + | 7.79423i | 1.55265 | + | 0.537853i | ||||
\(211\) | 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 | ||||||||
\(213\) | 3.00000 | − | 5.19615i | 0.205557 | − | 0.356034i | ||||
\(214\) | 15.0000 | 1.02538 | ||||||||
\(215\) | 1.50000 | − | 2.59808i | 0.102299 | − | 0.177187i | ||||
\(216\) | −9.00000 | −0.612372 | ||||||||
\(217\) | 6.00000 | + | 6.92820i | 0.407307 | + | 0.470317i | ||||
\(218\) | 28.5000 | + | 16.4545i | 1.93026 | + | 1.11444i | ||||
\(219\) | 9.00000 | 0.608164 | ||||||||
\(220\) | −4.50000 | − | 2.59808i | −0.303390 | − | 0.175162i | ||||
\(221\) | −4.50000 | − | 2.59808i | −0.302703 | − | 0.174766i | ||||
\(222\) | −10.5000 | + | 18.1865i | −0.704714 | + | 1.22060i | ||||
\(223\) | −4.50000 | − | 2.59808i | −0.301342 | − | 0.173980i | 0.341703 | − | 0.939808i | \(-0.388996\pi\) |
−0.643046 | + | 0.765828i | \(0.722329\pi\) | |||||||
\(224\) | 9.00000 | + | 10.3923i | 0.601338 | + | 0.694365i | ||||
\(225\) | 6.00000 | + | 10.3923i | 0.400000 | + | 0.692820i | ||||
\(226\) | −1.50000 | + | 2.59808i | −0.0997785 | + | 0.172821i | ||||
\(227\) | 21.0000 | 1.39382 | 0.696909 | − | 0.717159i | \(-0.254558\pi\) | ||||
0.696909 | + | 0.717159i | \(0.254558\pi\) | |||||||
\(228\) | 9.00000 | 0.596040 | ||||||||
\(229\) | 8.66025i | 0.572286i | 0.958187 | + | 0.286143i | \(0.0923732\pi\) | ||||
−0.958187 | + | 0.286143i | \(0.907627\pi\) | |||||||
\(230\) | −13.5000 | − | 23.3827i | −0.890164 | − | 1.54181i | ||||
\(231\) | −6.00000 | + | 5.19615i | −0.394771 | + | 0.341882i | ||||
\(232\) | −4.50000 | + | 7.79423i | −0.295439 | + | 0.511716i | ||||
\(233\) | 4.50000 | + | 2.59808i | 0.294805 | + | 0.170206i | 0.640107 | − | 0.768286i | \(-0.278890\pi\) |
−0.345302 | + | 0.938492i | \(0.612223\pi\) | |||||||
\(234\) | 9.00000 | 0.588348 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 13.8564i | 0.900070i | ||||||||
\(238\) | 9.00000 | + | 10.3923i | 0.583383 | + | 0.673633i | ||||
\(239\) | 1.50000 | − | 0.866025i | 0.0970269 | − | 0.0560185i | −0.450701 | − | 0.892675i | \(-0.648826\pi\) |
0.547728 | + | 0.836656i | \(0.315493\pi\) | |||||||
\(240\) | 25.9808i | 1.67705i | ||||||||
\(241\) | − | 22.5167i | − | 1.45043i | −0.688525 | − | 0.725213i | \(-0.741741\pi\) | ||
0.688525 | − | 0.725213i | \(-0.258259\pi\) | |||||||
\(242\) | −12.0000 | + | 6.92820i | −0.771389 | + | 0.445362i | ||||
\(243\) | 13.5000 | − | 7.79423i | 0.866025 | − | 0.500000i | ||||
\(244\) | − | 13.8564i | − | 0.887066i | ||||||
\(245\) | −16.5000 | − | 12.9904i | −1.05415 | − | 0.829925i | ||||
\(246\) | 4.50000 | + | 7.79423i | 0.286910 | + | 0.496942i | ||||
\(247\) | 9.00000 | 0.572656 | ||||||||
\(248\) | −3.00000 | + | 5.19615i | −0.190500 | + | 0.329956i | ||||
\(249\) | 22.5000 | − | 12.9904i | 1.42588 | − | 0.823232i | ||||
\(250\) | −4.50000 | + | 2.59808i | −0.284605 | + | 0.164317i | ||||
\(251\) | 12.0000 | 0.757433 | 0.378717 | − | 0.925513i | \(-0.376365\pi\) | ||||
0.378717 | + | 0.925513i | \(0.376365\pi\) | |||||||
\(252\) | −7.50000 | − | 2.59808i | −0.472456 | − | 0.163663i | ||||
\(253\) | 9.00000 | 0.565825 | ||||||||
\(254\) | −30.0000 | + | 17.3205i | −1.88237 | + | 1.08679i | ||||
\(255\) | 15.5885i | 0.976187i | ||||||||
\(256\) | −9.50000 | + | 16.4545i | −0.593750 | + | 1.02841i | ||||
\(257\) | −3.00000 | −0.187135 | −0.0935674 | − | 0.995613i | \(-0.529827\pi\) | ||||
−0.0935674 | + | 0.995613i | \(0.529827\pi\) | |||||||
\(258\) | −1.50000 | + | 2.59808i | −0.0933859 | + | 0.161749i | ||||
\(259\) | 14.0000 | − | 12.1244i | 0.869918 | − | 0.753371i | ||||
\(260\) | − | 5.19615i | − | 0.322252i | ||||||
\(261\) | − | 15.5885i | − | 0.964901i | ||||||
\(262\) | 13.5000 | − | 7.79423i | 0.834033 | − | 0.481529i | ||||
\(263\) | 22.5167i | 1.38844i | 0.719764 | + | 0.694218i | \(0.244250\pi\) | ||||
−0.719764 | + | 0.694218i | \(0.755750\pi\) | |||||||
\(264\) | −4.50000 | − | 2.59808i | −0.276956 | − | 0.159901i | ||||
\(265\) | 22.5000 | − | 12.9904i | 1.38216 | − | 0.797993i | ||||
\(266\) | −22.5000 | − | 7.79423i | −1.37956 | − | 0.477895i | ||||
\(267\) | −4.50000 | + | 2.59808i | −0.275396 | + | 0.159000i | ||||
\(268\) | −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 | \(0.682156\pi\) | |||||||
\(270\) | −13.5000 | − | 23.3827i | −0.821584 | − | 1.42302i | ||||
\(271\) | −10.5000 | − | 6.06218i | −0.637830 | − | 0.368251i | 0.145948 | − | 0.989292i | \(-0.453377\pi\) |
−0.783778 | + | 0.621041i | \(0.786710\pi\) | |||||||
\(272\) | −7.50000 | + | 12.9904i | −0.454754 | + | 0.787658i | ||||
\(273\) | −7.50000 | − | 2.59808i | −0.453921 | − | 0.157243i | ||||
\(274\) | 10.5000 | + | 18.1865i | 0.634328 | + | 1.09869i | ||||
\(275\) | 6.92820i | 0.417786i | ||||||||
\(276\) | 4.50000 | + | 7.79423i | 0.270868 | + | 0.469157i | ||||
\(277\) | −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 | ||||
\(279\) | − | 10.3923i | − | 0.622171i | ||||||
\(280\) | 4.50000 | − | 12.9904i | 0.268926 | − | 0.776324i | ||||
\(281\) | −16.5000 | − | 9.52628i | −0.984307 | − | 0.568290i | −0.0807396 | − | 0.996735i | \(-0.525728\pi\) |
−0.903568 | + | 0.428445i | \(0.859062\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 3.00000 | + | 1.73205i | 0.178331 | + | 0.102960i | 0.586509 | − | 0.809943i | \(-0.300502\pi\) |
−0.408177 | + | 0.912903i | \(0.633835\pi\) | |||||||
\(284\) | 3.00000 | + | 1.73205i | 0.178017 | + | 0.102778i | ||||
\(285\) | −13.5000 | − | 23.3827i | −0.799671 | − | 1.38507i | ||||
\(286\) | 4.50000 | + | 2.59808i | 0.266091 | + | 0.153627i | ||||
\(287\) | −1.50000 | − | 7.79423i | −0.0885422 | − | 0.460079i | ||||
\(288\) | − | 15.5885i | − | 0.918559i | ||||||
\(289\) | 4.00000 | − | 6.92820i | 0.235294 | − | 0.407541i | ||||
\(290\) | −27.0000 | −1.58549 | ||||||||
\(291\) | 1.50000 | + | 2.59808i | 0.0879316 | + | 0.152302i | ||||
\(292\) | 5.19615i | 0.304082i | ||||||||
\(293\) | −4.50000 | − | 7.79423i | −0.262893 | − | 0.455344i | 0.704117 | − | 0.710084i | \(-0.251343\pi\) |
−0.967009 | + | 0.254741i | \(0.918010\pi\) | |||||||
\(294\) | 16.5000 | + | 12.9904i | 0.962300 | + | 0.757614i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 10.5000 | + | 6.06218i | 0.610300 | + | 0.352357i | ||||
\(297\) | 9.00000 | 0.522233 | ||||||||
\(298\) | 1.50000 | + | 2.59808i | 0.0868927 | + | 0.150503i | ||||
\(299\) | 4.50000 | + | 7.79423i | 0.260242 | + | 0.450752i | ||||
\(300\) | −6.00000 | + | 3.46410i | −0.346410 | + | 0.200000i | ||||
\(301\) | 2.00000 | − | 1.73205i | 0.115278 | − | 0.0998337i | ||||
\(302\) | 25.5000 | − | 14.7224i | 1.46736 | − | 0.847181i | ||||
\(303\) | 4.50000 | + | 2.59808i | 0.258518 | + | 0.149256i | ||||
\(304\) | − | 25.9808i | − | 1.49010i | ||||||
\(305\) | −36.0000 | + | 20.7846i | −2.06135 | + | 1.19012i | ||||
\(306\) | − | 15.5885i | − | 0.891133i | ||||||
\(307\) | 24.2487i | 1.38395i | 0.721923 | + | 0.691974i | \(0.243259\pi\) | ||||
−0.721923 | + | 0.691974i | \(0.756741\pi\) | |||||||
\(308\) | −3.00000 | − | 3.46410i | −0.170941 | − | 0.197386i | ||||
\(309\) | 10.5000 | − | 18.1865i | 0.597324 | − | 1.03460i | ||||
\(310\) | −18.0000 | −1.02233 | ||||||||
\(311\) | −12.0000 | + | 20.7846i | −0.680458 | + | 1.17859i | 0.294384 | + | 0.955687i | \(0.404886\pi\) |
−0.974841 | + | 0.222900i | \(0.928448\pi\) | |||||||
\(312\) | − | 5.19615i | − | 0.294174i | ||||||
\(313\) | −18.0000 | + | 10.3923i | −1.01742 | + | 0.587408i | −0.913356 | − | 0.407163i | \(-0.866518\pi\) |
−0.104065 | + | 0.994571i | \(0.533185\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 4.50000 | + | 23.3827i | 0.253546 | + | 1.31747i | ||||
\(316\) | −8.00000 | −0.450035 | ||||||||
\(317\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(318\) | −22.5000 | + | 12.9904i | −1.26174 | + | 0.728464i | ||||
\(319\) | 4.50000 | − | 7.79423i | 0.251952 | − | 0.436393i | ||||
\(320\) | 3.00000 | 0.167705 | ||||||||
\(321\) | 7.50000 | + | 12.9904i | 0.418609 | + | 0.725052i | ||||
\(322\) | −4.50000 | − | 23.3827i | −0.250775 | − | 1.30307i | ||||
\(323\) | − | 15.5885i | − | 0.867365i | ||||||
\(324\) | 4.50000 | + | 7.79423i | 0.250000 | + | 0.433013i | ||||
\(325\) | −6.00000 | + | 3.46410i | −0.332820 | + | 0.192154i | ||||
\(326\) | − | 19.0526i | − | 1.05522i | ||||||
\(327\) | 32.9090i | 1.81987i | ||||||||
\(328\) | 4.50000 | − | 2.59808i | 0.248471 | − | 0.143455i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | − | 15.5885i | − | 0.858116i | ||||||
\(331\) | 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 | ||||
\(333\) | −21.0000 | −1.15079 | ||||||||
\(334\) | 13.5000 | + | 7.79423i | 0.738687 | + | 0.426481i | ||||
\(335\) | −6.00000 | + | 10.3923i | −0.327815 | + | 0.567792i | ||||
\(336\) | −7.50000 | + | 21.6506i | −0.409159 | + | 1.18114i | ||||
\(337\) | −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 | ||||||
\(339\) | −3.00000 | −0.162938 | ||||||||
\(340\) | −9.00000 | −0.488094 | ||||||||
\(341\) | 3.00000 | − | 5.19615i | 0.162459 | − | 0.281387i | ||||
\(342\) | 13.5000 | + | 23.3827i | 0.729996 | + | 1.26439i | ||||
\(343\) | −10.0000 | − | 15.5885i | −0.539949 | − | 0.841698i | ||||
\(344\) | 1.50000 | + | 0.866025i | 0.0808746 | + | 0.0466930i | ||||
\(345\) | 13.5000 | − | 23.3827i | 0.726816 | − | 1.25888i | ||||
\(346\) | 9.00000 | + | 5.19615i | 0.483843 | + | 0.279347i | ||||
\(347\) | −3.00000 | − | 1.73205i | −0.161048 | − | 0.0929814i | 0.417310 | − | 0.908764i | \(-0.362973\pi\) |
−0.578358 | + | 0.815783i | \(0.696306\pi\) | |||||||
\(348\) | 9.00000 | 0.482451 | ||||||||
\(349\) | 10.5000 | + | 6.06218i | 0.562052 | + | 0.324501i | 0.753969 | − | 0.656910i | \(-0.228137\pi\) |
−0.191917 | + | 0.981411i | \(0.561470\pi\) | |||||||
\(350\) | 18.0000 | − | 3.46410i | 0.962140 | − | 0.185164i | ||||
\(351\) | 4.50000 | + | 7.79423i | 0.240192 | + | 0.416025i | ||||
\(352\) | 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 | ||||
\(357\) | −4.50000 | + | 12.9904i | −0.238165 | + | 0.687524i | ||||
\(358\) | −13.5000 | + | 23.3827i | −0.713497 | + | 1.23581i | ||||
\(359\) | −19.5000 | − | 11.2583i | −1.02917 | − | 0.594192i | −0.112424 | − | 0.993660i | \(-0.535861\pi\) |
−0.916747 | + | 0.399468i | \(0.869195\pi\) | |||||||
\(360\) | −13.5000 | + | 7.79423i | −0.711512 | + | 0.410792i | ||||
\(361\) | 4.00000 | + | 6.92820i | 0.210526 | + | 0.364642i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −12.0000 | − | 6.92820i | −0.629837 | − | 0.363636i | ||||
\(364\) | 1.50000 | − | 4.33013i | 0.0786214 | − | 0.226960i | ||||
\(365\) | 13.5000 | − | 7.79423i | 0.706622 | − | 0.407969i | ||||
\(366\) | 36.0000 | − | 20.7846i | 1.88175 | − | 1.08643i | ||||
\(367\) | 5.19615i | 0.271237i | 0.990761 | + | 0.135618i | \(0.0433021\pi\) | ||||
−0.990761 | + | 0.135618i | \(0.956698\pi\) | |||||||
\(368\) | 22.5000 | − | 12.9904i | 1.17289 | − | 0.677170i | ||||
\(369\) | −4.50000 | + | 7.79423i | −0.234261 | + | 0.405751i | ||||
\(370\) | 36.3731i | 1.89095i | ||||||||
\(371\) | 22.5000 | − | 4.33013i | 1.16814 | − | 0.224809i | ||||
\(372\) | 6.00000 | 0.311086 | ||||||||
\(373\) | −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 | ||||
\(375\) | −4.50000 | − | 2.59808i | −0.232379 | − | 0.134164i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 9.00000 | 0.463524 | ||||||||
\(378\) | −4.50000 | − | 23.3827i | −0.231455 | − | 1.20268i | ||||
\(379\) | −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 | ||||
\(381\) | −30.0000 | − | 17.3205i | −1.53695 | − | 0.887357i | ||||
\(382\) | 15.0000 | − | 25.9808i | 0.767467 | − | 1.32929i | ||||
\(383\) | −9.00000 | −0.459879 | −0.229939 | − | 0.973205i | \(-0.573853\pi\) | ||||
−0.229939 | + | 0.973205i | \(0.573853\pi\) | |||||||
\(384\) | −21.0000 | −1.07165 | ||||||||
\(385\) | −4.50000 | + | 12.9904i | −0.229341 | + | 0.662051i | ||||
\(386\) | 3.46410i | 0.176318i | ||||||||
\(387\) | −3.00000 | −0.152499 | ||||||||
\(388\) | −1.50000 | + | 0.866025i | −0.0761510 | + | 0.0439658i | ||||
\(389\) | 36.3731i | 1.84419i | 0.386966 | + | 0.922094i | \(0.373523\pi\) | ||||
−0.386966 | + | 0.922094i | \(0.626477\pi\) | |||||||
\(390\) | 13.5000 | − | 7.79423i | 0.683599 | − | 0.394676i | ||||
\(391\) | 13.5000 | − | 7.79423i | 0.682724 | − | 0.394171i | ||||
\(392\) | 7.50000 | − | 9.52628i | 0.378807 | − | 0.481150i | ||||
\(393\) | 13.5000 | + | 7.79423i | 0.680985 | + | 0.393167i | ||||
\(394\) | 12.0000 | + | 20.7846i | 0.604551 | + | 1.04711i | ||||
\(395\) | 12.0000 | + | 20.7846i | 0.603786 | + | 1.04579i | ||||
\(396\) | 5.19615i | 0.261116i | ||||||||
\(397\) | 7.50000 | + | 4.33013i | 0.376414 | + | 0.217323i | 0.676257 | − | 0.736666i | \(-0.263601\pi\) |
−0.299843 | + | 0.953989i | \(0.596934\pi\) | |||||||
\(398\) | 7.50000 | − | 12.9904i | 0.375941 | − | 0.651149i | ||||
\(399\) | −4.50000 | − | 23.3827i | −0.225282 | − | 1.17060i | ||||
\(400\) | 10.0000 | + | 17.3205i | 0.500000 | + | 0.866025i | ||||
\(401\) | 32.9090i | 1.64340i | 0.569924 | + | 0.821698i | \(0.306973\pi\) | ||||
−0.569924 | + | 0.821698i | \(0.693027\pi\) | |||||||
\(402\) | 6.00000 | − | 10.3923i | 0.299253 | − | 0.518321i | ||||
\(403\) | 6.00000 | 0.298881 | ||||||||
\(404\) | −1.50000 | + | 2.59808i | −0.0746278 | + | 0.129259i | ||||
\(405\) | 13.5000 | − | 23.3827i | 0.670820 | − | 1.16190i | ||||
\(406\) | −22.5000 | − | 7.79423i | −1.11666 | − | 0.386821i | ||||
\(407\) | −10.5000 | − | 6.06218i | −0.520466 | − | 0.300491i | ||||
\(408\) | −9.00000 | −0.445566 | ||||||||
\(409\) | −6.00000 | − | 3.46410i | −0.296681 | − | 0.171289i | 0.344270 | − | 0.938871i | \(-0.388126\pi\) |
−0.640951 | + | 0.767582i | \(0.721460\pi\) | |||||||
\(410\) | 13.5000 | + | 7.79423i | 0.666717 | + | 0.384930i | ||||
\(411\) | −10.5000 | + | 18.1865i | −0.517927 | + | 0.897076i | ||||
\(412\) | 10.5000 | + | 6.06218i | 0.517298 | + | 0.298662i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −13.5000 | + | 23.3827i | −0.663489 | + | 1.14920i | ||||
\(415\) | 22.5000 | − | 38.9711i | 1.10448 | − | 1.91302i | ||||
\(416\) | 9.00000 | 0.441261 | ||||||||
\(417\) | 15.0000 | 0.734553 | ||||||||
\(418\) | 15.5885i | 0.762456i | ||||||||
\(419\) | −16.5000 | − | 28.5788i | −0.806078 | − | 1.39617i | −0.915561 | − | 0.402179i | \(-0.868253\pi\) |
0.109483 | − | 0.993989i | \(-0.465080\pi\) | |||||||
\(420\) | −13.5000 | + | 2.59808i | −0.658733 | + | 0.126773i | ||||
\(421\) | −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 | ||||
\(426\) | 10.3923i | 0.503509i | ||||||||
\(427\) | −36.0000 | + | 6.92820i | −1.74216 | + | 0.335279i | ||||
\(428\) | −7.50000 | + | 4.33013i | −0.362526 | + | 0.209305i | ||||
\(429\) | 5.19615i | 0.250873i | ||||||||
\(430\) | 5.19615i | 0.250581i | ||||||||
\(431\) | 13.5000 | − | 7.79423i | 0.650272 | − | 0.375435i | −0.138288 | − | 0.990392i | \(-0.544160\pi\) |
0.788560 | + | 0.614957i | \(0.210827\pi\) | |||||||
\(432\) | 22.5000 | − | 12.9904i | 1.08253 | − | 0.625000i | ||||
\(433\) | − | 13.8564i | − | 0.665896i | −0.942945 | − | 0.332948i | \(-0.891957\pi\) | ||
0.942945 | − | 0.332948i | \(-0.108043\pi\) | |||||||
\(434\) | −15.0000 | − | 5.19615i | −0.720023 | − | 0.249423i | ||||
\(435\) | −13.5000 | − | 23.3827i | −0.647275 | − | 1.12111i | ||||
\(436\) | −19.0000 | −0.909935 | ||||||||
\(437\) | −13.5000 | + | 23.3827i | −0.645793 | + | 1.11855i | ||||
\(438\) | −13.5000 | + | 7.79423i | −0.645055 | + | 0.372423i | ||||
\(439\) | 27.0000 | − | 15.5885i | 1.28864 | − | 0.743996i | 0.310228 | − | 0.950662i | \(-0.399595\pi\) |
0.978412 | + | 0.206666i | \(0.0662612\pi\) | |||||||
\(440\) | −9.00000 | −0.429058 | ||||||||
\(441\) | −3.00000 | + | 20.7846i | −0.142857 | + | 0.989743i | ||||
\(442\) | 9.00000 | 0.428086 | ||||||||
\(443\) | 27.0000 | − | 15.5885i | 1.28281 | − | 0.740630i | 0.305448 | − | 0.952209i | \(-0.401194\pi\) |
0.977361 | + | 0.211579i | \(0.0678605\pi\) | |||||||
\(444\) | − | 12.1244i | − | 0.575396i | ||||||
\(445\) | −4.50000 | + | 7.79423i | −0.213320 | + | 0.369482i | ||||
\(446\) | 9.00000 | 0.426162 | ||||||||
\(447\) | −1.50000 | + | 2.59808i | −0.0709476 | + | 0.122885i | ||||
\(448\) | 2.50000 | + | 0.866025i | 0.118114 | + | 0.0409159i | ||||
\(449\) | 34.6410i | 1.63481i | 0.576063 | + | 0.817405i | \(0.304588\pi\) | ||||
−0.576063 | + | 0.817405i | \(0.695412\pi\) | |||||||
\(450\) | −18.0000 | − | 10.3923i | −0.848528 | − | 0.489898i | ||||
\(451\) | −4.50000 | + | 2.59808i | −0.211897 | + | 0.122339i | ||||
\(452\) | − | 1.73205i | − | 0.0814688i | ||||||
\(453\) | 25.5000 | + | 14.7224i | 1.19809 | + | 0.691720i | ||||
\(454\) | −31.5000 | + | 18.1865i | −1.47837 | + | 0.853536i | ||||
\(455\) | −13.5000 | + | 2.59808i | −0.632890 | + | 0.121800i | ||||
\(456\) | 13.5000 | − | 7.79423i | 0.632195 | − | 0.364998i | ||||
\(457\) | 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 | ||||
\(459\) | 13.5000 | − | 7.79423i | 0.630126 | − | 0.363803i | ||||
\(460\) | 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 | \(0.0530827\pi\) | |||||||
\(462\) | 4.50000 | − | 12.9904i | 0.209359 | − | 0.604367i | ||||
\(463\) | 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 | ||||||
\(465\) | −9.00000 | − | 15.5885i | −0.417365 | − | 0.722897i | ||||
\(466\) | −9.00000 | −0.416917 | ||||||||
\(467\) | 1.50000 | − | 2.59808i | 0.0694117 | − | 0.120225i | −0.829231 | − | 0.558906i | \(-0.811221\pi\) |
0.898642 | + | 0.438682i | \(0.144554\pi\) | |||||||
\(468\) | −4.50000 | + | 2.59808i | −0.208013 | + | 0.120096i | ||||
\(469\) | −8.00000 | + | 6.92820i | −0.369406 | + | 0.319915i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −1.50000 | − | 0.866025i | −0.0689701 | − | 0.0398199i | ||||
\(474\) | −12.0000 | − | 20.7846i | −0.551178 | − | 0.954669i | ||||
\(475\) | −18.0000 | − | 10.3923i | −0.825897 | − | 0.476832i | ||||
\(476\) | −7.50000 | − | 2.59808i | −0.343762 | − | 0.119083i | ||||
\(477\) | −22.5000 | − | 12.9904i | −1.03020 | − | 0.594789i | ||||
\(478\) | −1.50000 | + | 2.59808i | −0.0686084 | + | 0.118833i | ||||
\(479\) | −27.0000 | −1.23366 | −0.616831 | − | 0.787096i | \(-0.711584\pi\) | ||||
−0.616831 | + | 0.787096i | \(0.711584\pi\) | |||||||
\(480\) | −13.5000 | − | 23.3827i | −0.616188 | − | 1.06727i | ||||
\(481\) | − | 12.1244i | − | 0.552823i | ||||||
\(482\) | 19.5000 | + | 33.7750i | 0.888201 | + | 1.53841i | ||||
\(483\) | 18.0000 | − | 15.5885i | 0.819028 | − | 0.709299i | ||||
\(484\) | 4.00000 | − | 6.92820i | 0.181818 | − | 0.314918i | ||||
\(485\) | 4.50000 | + | 2.59808i | 0.204334 | + | 0.117973i | ||||
\(486\) | −13.5000 | + | 23.3827i | −0.612372 | + | 1.06066i | ||||
\(487\) | 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 | ||||
\(489\) | 16.5000 | − | 9.52628i | 0.746156 | − | 0.430793i | ||||
\(490\) | 36.0000 | + | 5.19615i | 1.62631 | + | 0.234738i | ||||
\(491\) | −22.5000 | + | 12.9904i | −1.01541 | + | 0.586248i | −0.912771 | − | 0.408471i | \(-0.866062\pi\) |
−0.102639 | + | 0.994719i | \(0.532729\pi\) | |||||||
\(492\) | −4.50000 | − | 2.59808i | −0.202876 | − | 0.117130i | ||||
\(493\) | − | 15.5885i | − | 0.702069i | ||||||
\(494\) | −13.5000 | + | 7.79423i | −0.607394 | + | 0.350679i | ||||
\(495\) | 13.5000 | − | 7.79423i | 0.606780 | − | 0.350325i | ||||
\(496\) | − | 17.3205i | − | 0.777714i | ||||||
\(497\) | 3.00000 | − | 8.66025i | 0.134568 | − | 0.388465i | ||||
\(498\) | −22.5000 | + | 38.9711i | −1.00825 | + | 1.74634i | ||||
\(499\) | 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 | ||||
\(501\) | 15.5885i | 0.696441i | ||||||||
\(502\) | −18.0000 | + | 10.3923i | −0.803379 | + | 0.463831i | ||||
\(503\) | −24.0000 | −1.07011 | −0.535054 | − | 0.844818i | \(-0.679709\pi\) | ||||
−0.535054 | + | 0.844818i | \(0.679709\pi\) | |||||||
\(504\) | −13.5000 | + | 2.59808i | −0.601338 | + | 0.115728i | ||||
\(505\) | 9.00000 | 0.400495 | ||||||||
\(506\) | −13.5000 | + | 7.79423i | −0.600148 | + | 0.346496i | ||||
\(507\) | 15.0000 | − | 8.66025i | 0.666173 | − | 0.384615i | ||||
\(508\) | 10.0000 | − | 17.3205i | 0.443678 | − | 0.768473i | ||||
\(509\) | 33.0000 | 1.46270 | 0.731350 | − | 0.682003i | \(-0.238891\pi\) | ||||
0.731350 | + | 0.682003i | \(0.238891\pi\) | |||||||
\(510\) | −13.5000 | − | 23.3827i | −0.597790 | − | 1.03540i | ||||
\(511\) | 13.5000 | − | 2.59808i | 0.597205 | − | 0.114932i | ||||
\(512\) | − | 8.66025i | − | 0.382733i | ||||||
\(513\) | −13.5000 | + | 23.3827i | −0.596040 | + | 1.03237i | ||||
\(514\) | 4.50000 | − | 2.59808i | 0.198486 | − | 0.114596i | ||||
\(515\) | − | 36.3731i | − | 1.60279i | ||||||
\(516\) | − | 1.73205i | − | 0.0762493i | ||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | −10.5000 | + | 30.3109i | −0.461344 | + | 1.33178i | ||||
\(519\) | 10.3923i | 0.456172i | ||||||||
\(520\) | −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 | \(-0.612852\pi\) | |||||||
\(522\) | 13.5000 | + | 23.3827i | 0.590879 | + | 1.02343i | ||||
\(523\) | −16.5000 | − | 9.52628i | −0.721495 | − | 0.416555i | 0.0938079 | − | 0.995590i | \(-0.470096\pi\) |
−0.815303 | + | 0.579035i | \(0.803429\pi\) | |||||||
\(524\) | −4.50000 | + | 7.79423i | −0.196583 | + | 0.340492i | ||||
\(525\) | 12.0000 | + | 13.8564i | 0.523723 | + | 0.604743i | ||||
\(526\) | −19.5000 | − | 33.7750i | −0.850240 | − | 1.47266i | ||||
\(527\) | − | 10.3923i | − | 0.452696i | ||||||
\(528\) | 15.0000 | 0.652791 | ||||||||
\(529\) | −4.00000 | −0.173913 | ||||||||
\(530\) | −22.5000 | + | 38.9711i | −0.977338 | + | 1.69280i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 13.5000 | − | 2.59808i | 0.585299 | − | 0.112641i | ||||
\(533\) | −4.50000 | − | 2.59808i | −0.194917 | − | 0.112535i | ||||
\(534\) | 4.50000 | − | 7.79423i | 0.194734 | − | 0.337289i | ||||
\(535\) | 22.5000 | + | 12.9904i | 0.972760 | + | 0.561623i | ||||
\(536\) | −6.00000 | − | 3.46410i | −0.259161 | − | 0.149626i | ||||
\(537\) | −27.0000 | −1.16514 | ||||||||
\(538\) | −22.5000 | − | 12.9904i | −0.970044 | − | 0.560055i | ||||
\(539\) | −7.50000 | + | 9.52628i | −0.323048 | + | 0.410326i | ||||
\(540\) | 13.5000 | + | 7.79423i | 0.580948 | + | 0.335410i | ||||
\(541\) | 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 | ||||
\(546\) | 13.5000 | − | 2.59808i | 0.577747 | − | 0.111187i | ||||
\(547\) | 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 | ||||
\(549\) | 36.0000 | + | 20.7846i | 1.53644 | + | 0.887066i | ||||
\(550\) | −6.00000 | − | 10.3923i | −0.255841 | − | 0.443129i | ||||
\(551\) | 13.5000 | + | 23.3827i | 0.575119 | + | 0.996136i | ||||
\(552\) | 13.5000 | + | 7.79423i | 0.574598 | + | 0.331744i | ||||
\(553\) | 4.00000 | + | 20.7846i | 0.170097 | + | 0.883852i | ||||
\(554\) | 1.50000 | − | 0.866025i | 0.0637289 | − | 0.0367939i | ||||
\(555\) | −31.5000 | + | 18.1865i | −1.33710 | + | 0.771975i | ||||
\(556\) | 8.66025i | 0.367277i | ||||||||
\(557\) | 10.5000 | − | 6.06218i | 0.444899 | − | 0.256863i | −0.260774 | − | 0.965400i | \(-0.583978\pi\) |
0.705674 | + | 0.708537i | \(0.250645\pi\) | |||||||
\(558\) | 9.00000 | + | 15.5885i | 0.381000 | + | 0.659912i | ||||
\(559\) | − | 1.73205i | − | 0.0732579i | ||||||
\(560\) | 7.50000 | + | 38.9711i | 0.316933 | + | 1.64683i | ||||
\(561\) | 9.00000 | 0.379980 | ||||||||
\(562\) | 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 | ||||||||
\(567\) | 18.0000 | − | 15.5885i | 0.755929 | − | 0.654654i | ||||
\(568\) | 6.00000 | 0.251754 | ||||||||
\(569\) | 6.00000 | − | 3.46410i | 0.251533 | − | 0.145223i | −0.368933 | − | 0.929456i | \(-0.620277\pi\) |
0.620466 | + | 0.784233i | \(0.286943\pi\) | |||||||
\(570\) | 40.5000 | + | 23.3827i | 1.69636 | + | 0.979393i | ||||
\(571\) | −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 | ||||||||
\(573\) | 30.0000 | 1.25327 | ||||||||
\(574\) | 9.00000 | + | 10.3923i | 0.375653 | + | 0.433766i | ||||
\(575\) | − | 20.7846i | − | 0.866778i | ||||||
\(576\) | −1.50000 | − | 2.59808i | −0.0625000 | − | 0.108253i | ||||
\(577\) | −34.5000 | + | 19.9186i | −1.43625 | + | 0.829222i | −0.997587 | − | 0.0694283i | \(-0.977883\pi\) |
−0.438667 | + | 0.898650i | \(0.644549\pi\) | |||||||
\(578\) | 13.8564i | 0.576351i | ||||||||
\(579\) | −3.00000 | + | 1.73205i | −0.124676 | + | 0.0719816i | ||||
\(580\) | 13.5000 | − | 7.79423i | 0.560557 | − | 0.323638i | ||||
\(581\) | 30.0000 | − | 25.9808i | 1.24461 | − | 1.07786i | ||||
\(582\) | −4.50000 | − | 2.59808i | −0.186531 | − | 0.107694i | ||||
\(583\) | −7.50000 | − | 12.9904i | −0.310618 | − | 0.538007i | ||||
\(584\) | 4.50000 | + | 7.79423i | 0.186211 | + | 0.322527i | ||||
\(585\) | 13.5000 | + | 7.79423i | 0.558156 | + | 0.322252i | ||||
\(586\) | 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 | \(0.0239870\pi\) | |||||||
\(588\) | −12.0000 | − | 1.73205i | −0.494872 | − | 0.0714286i | ||||
\(589\) | 9.00000 | + | 15.5885i | 0.370839 | + | 0.642311i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −12.0000 | + | 20.7846i | −0.493614 | + | 0.854965i | ||||
\(592\) | −35.0000 | −1.43849 | ||||||||
\(593\) | 19.5000 | − | 33.7750i | 0.800769 | − | 1.38697i | −0.118342 | − | 0.992973i | \(-0.537758\pi\) |
0.919111 | − | 0.394000i | \(-0.128909\pi\) | |||||||
\(594\) | −13.5000 | + | 7.79423i | −0.553912 | + | 0.319801i | ||||
\(595\) | 4.50000 | + | 23.3827i | 0.184482 | + | 0.958597i | ||||
\(596\) | −1.50000 | − | 0.866025i | −0.0614424 | − | 0.0354738i | ||||
\(597\) | 15.0000 | 0.613909 | ||||||||
\(598\) | −13.5000 | − | 7.79423i | −0.552056 | − | 0.318730i | ||||
\(599\) | −21.0000 | − | 12.1244i | −0.858037 | − | 0.495388i | 0.00531761 | − | 0.999986i | \(-0.498307\pi\) |
−0.863354 | + | 0.504598i | \(0.831641\pi\) | |||||||
\(600\) | −6.00000 | + | 10.3923i | −0.244949 | + | 0.424264i | ||||
\(601\) | −25.5000 | − | 14.7224i | −1.04017 | − | 0.600541i | −0.120286 | − | 0.992739i | \(-0.538381\pi\) |
−0.919881 | + | 0.392199i | \(0.871715\pi\) | |||||||
\(602\) | −1.50000 | + | 4.33013i | −0.0611354 | + | 0.176483i | ||||
\(603\) | 12.0000 | 0.488678 | ||||||||
\(604\) | −8.50000 | + | 14.7224i | −0.345860 | + | 0.599047i | ||||
\(605\) | −24.0000 | −0.975739 | ||||||||
\(606\) | −9.00000 | −0.365600 | ||||||||
\(607\) | − | 15.5885i | − | 0.632716i | −0.948640 | − | 0.316358i | \(-0.897540\pi\) | ||
0.948640 | − | 0.316358i | \(-0.102460\pi\) | |||||||
\(608\) | 13.5000 | + | 23.3827i | 0.547497 | + | 0.948293i | ||||
\(609\) | −4.50000 | − | 23.3827i | −0.182349 | − | 0.947514i | ||||
\(610\) | 36.0000 | − | 62.3538i | 1.45760 | − | 2.52463i | ||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 4.50000 | + | 7.79423i | 0.181902 | + | 0.315063i | ||||
\(613\) | −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 | ||||
\(615\) | 15.5885i | 0.628587i | ||||||||
\(616\) | −7.50000 | − | 2.59808i | −0.302184 | − | 0.104679i | ||||
\(617\) | −4.50000 | + | 2.59808i | −0.181163 | + | 0.104595i | −0.587839 | − | 0.808978i | \(-0.700021\pi\) |
0.406676 | + | 0.913573i | \(0.366688\pi\) | |||||||
\(618\) | 36.3731i | 1.46314i | ||||||||
\(619\) | 19.0526i | 0.765787i | 0.923792 | + | 0.382893i | \(0.125072\pi\) | ||||
−0.923792 | + | 0.382893i | \(0.874928\pi\) | |||||||
\(620\) | 9.00000 | − | 5.19615i | 0.361449 | − | 0.208683i | ||||
\(621\) | −27.0000 | −1.08347 | ||||||||
\(622\) | − | 41.5692i | − | 1.66677i | ||||||
\(623\) | −6.00000 | + | 5.19615i | −0.240385 | + | 0.208179i | ||||
\(624\) | 7.50000 | + | 12.9904i | 0.300240 | + | 0.520031i | ||||
\(625\) | −29.0000 | −1.16000 | ||||||||
\(626\) | 18.0000 | − | 31.1769i | 0.719425 | − | 1.24608i | ||||
\(627\) | −13.5000 | + | 7.79423i | −0.539138 | + | 0.311272i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −21.0000 | −0.837325 | ||||||||
\(630\) | −27.0000 | − | 31.1769i | −1.07571 | − | 1.24212i | ||||
\(631\) | 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 | ||||
\(633\) | − | 8.66025i | − | 0.344214i | ||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −60.0000 | −2.38103 | ||||||||
\(636\) | 7.50000 | − | 12.9904i | 0.297394 | − | 0.515102i | ||||
\(637\) | −12.0000 | − | 1.73205i | −0.475457 | − | 0.0686264i | ||||
\(638\) | 15.5885i | 0.617153i | ||||||||
\(639\) | −9.00000 | + | 5.19615i | −0.356034 | + | 0.205557i | ||||
\(640\) | −31.5000 | + | 18.1865i | −1.24515 | + | 0.718886i | ||||
\(641\) | − | 12.1244i | − | 0.478883i | −0.970911 | − | 0.239442i | \(-0.923036\pi\) | ||
0.970911 | − | 0.239442i | \(-0.0769644\pi\) | |||||||
\(642\) | −22.5000 | − | 12.9904i | −0.888004 | − | 0.512689i | ||||
\(643\) | 10.5000 | − | 6.06218i | 0.414080 | − | 0.239069i | −0.278462 | − | 0.960447i | \(-0.589824\pi\) |
0.692541 | + | 0.721378i | \(0.256491\pi\) | |||||||
\(644\) | 9.00000 | + | 10.3923i | 0.354650 | + | 0.409514i | ||||
\(645\) | −4.50000 | + | 2.59808i | −0.177187 | + | 0.102299i | ||||
\(646\) | 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 | \(0.852115\pi\) | |||||||
\(648\) | 13.5000 | + | 7.79423i | 0.530330 | + | 0.306186i | ||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 6.00000 | − | 10.3923i | 0.235339 | − | 0.407620i | ||||
\(651\) | −3.00000 | − | 15.5885i | −0.117579 | − | 0.610960i | ||||
\(652\) | 5.50000 | + | 9.52628i | 0.215397 | + | 0.373078i | ||||
\(653\) | 39.8372i | 1.55895i | 0.626434 | + | 0.779474i | \(0.284514\pi\) | ||||
−0.626434 | + | 0.779474i | \(0.715486\pi\) | |||||||
\(654\) | −28.5000 | − | 49.3634i | −1.11444 | − | 1.93026i | ||||
\(655\) | 27.0000 | 1.05498 | ||||||||
\(656\) | −7.50000 | + | 12.9904i | −0.292826 | + | 0.507189i | ||||
\(657\) | −13.5000 | − | 7.79423i | −0.526685 | − | 0.304082i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 10.5000 | + | 6.06218i | 0.409022 | + | 0.236149i | 0.690369 | − | 0.723457i | \(-0.257448\pi\) |
−0.281347 | + | 0.959606i | \(0.590781\pi\) | |||||||
\(660\) | 4.50000 | + | 7.79423i | 0.175162 | + | 0.303390i | ||||
\(661\) | 36.0000 | + | 20.7846i | 1.40024 | + | 0.808428i | 0.994417 | − | 0.105525i | \(-0.0336523\pi\) |
0.405821 | + | 0.913953i | \(0.366986\pi\) | |||||||
\(662\) | −12.0000 | − | 6.92820i | −0.466393 | − | 0.269272i | ||||
\(663\) | 4.50000 | + | 7.79423i | 0.174766 | + | 0.302703i | ||||
\(664\) | 22.5000 | + | 12.9904i | 0.873169 | + | 0.504125i | ||||
\(665\) | −27.0000 | − | 31.1769i | −1.04702 | − | 1.20899i | ||||
\(666\) | 31.5000 | − | 18.1865i | 1.22060 | − | 0.704714i | ||||
\(667\) | −13.5000 | + | 23.3827i | −0.522722 | + | 0.905381i | ||||
\(668\) | −9.00000 | −0.348220 | ||||||||
\(669\) | 4.50000 | + | 7.79423i | 0.173980 | + | 0.301342i | ||||
\(670\) | − | 20.7846i | − | 0.802980i | ||||||
\(671\) | 12.0000 | + | 20.7846i | 0.463255 | + | 0.802381i | ||||
\(672\) | −4.50000 | − | 23.3827i | −0.173591 | − | 0.902007i | ||||
\(673\) | 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 | ||||
\(675\) | − | 20.7846i | − | 0.800000i | ||||||
\(676\) | 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 | \(0.720908\pi\) | |||||||
\(678\) | 4.50000 | − | 2.59808i | 0.172821 | − | 0.0997785i | ||||
\(679\) | 3.00000 | + | 3.46410i | 0.115129 | + | 0.132940i | ||||
\(680\) | −13.5000 | + | 7.79423i | −0.517701 | + | 0.298895i | ||||
\(681\) | −31.5000 | − | 18.1865i | −1.20708 | − | 0.696909i | ||||
\(682\) | 10.3923i | 0.397942i | ||||||||
\(683\) | 7.50000 | − | 4.33013i | 0.286980 | − | 0.165688i | −0.349599 | − | 0.936899i | \(-0.613682\pi\) |
0.636579 | + | 0.771212i | \(0.280349\pi\) | |||||||
\(684\) | −13.5000 | − | 7.79423i | −0.516185 | − | 0.298020i | ||||
\(685\) | 36.3731i | 1.38974i | ||||||||
\(686\) | 28.5000 | + | 14.7224i | 1.08814 | + | 0.562105i | ||||
\(687\) | 7.50000 | − | 12.9904i | 0.286143 | − | 0.495614i | ||||
\(688\) | −5.00000 | −0.190623 | ||||||||
\(689\) | 7.50000 | − | 12.9904i | 0.285727 | − | 0.494894i | ||||
\(690\) | 46.7654i | 1.78033i | ||||||||
\(691\) | −3.00000 | + | 1.73205i | −0.114125 | + | 0.0658903i | −0.555976 | − | 0.831198i | \(-0.687655\pi\) |
0.441851 | + | 0.897089i | \(0.354322\pi\) | |||||||
\(692\) | −6.00000 | −0.228086 | ||||||||
\(693\) | 13.5000 | − | 2.59808i | 0.512823 | − | 0.0986928i | ||||
\(694\) | 6.00000 | 0.227757 | ||||||||
\(695\) | 22.5000 | − | 12.9904i | 0.853474 | − | 0.492753i | ||||
\(696\) | 13.5000 | − | 7.79423i | 0.511716 | − | 0.295439i | ||||
\(697\) | −4.50000 | + | 7.79423i | −0.170450 | + | 0.295227i | ||||
\(698\) | −21.0000 | −0.794862 | ||||||||
\(699\) | −4.50000 | − | 7.79423i | −0.170206 | − | 0.294805i | ||||
\(700\) | −8.00000 | + | 6.92820i | −0.302372 | + | 0.261861i | ||||
\(701\) | 34.6410i | 1.30837i | 0.756333 | + | 0.654187i | \(0.226989\pi\) | ||||
−0.756333 | + | 0.654187i | \(0.773011\pi\) | |||||||
\(702\) | −13.5000 | − | 7.79423i | −0.509525 | − | 0.294174i | ||||
\(703\) | 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 | ||||
\(707\) | 7.50000 | + | 2.59808i | 0.282067 | + | 0.0977107i | ||||
\(708\) | 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 | ||||
\(711\) | 12.0000 | − | 20.7846i | 0.450035 | − | 0.779484i | ||||
\(712\) | −4.50000 | − | 2.59808i | −0.168645 | − | 0.0973670i | ||||
\(713\) | −9.00000 | + | 15.5885i | −0.337053 | + | 0.583792i | ||||
\(714\) | −4.50000 | − | 23.3827i | −0.168408 | − | 0.875075i | ||||
\(715\) | 4.50000 | + | 7.79423i | 0.168290 | + | 0.291488i | ||||
\(716\) | − | 15.5885i | − | 0.582568i | ||||||
\(717\) | −3.00000 | −0.112037 | ||||||||
\(718\) | 39.0000 | 1.45547 | ||||||||
\(719\) | −4.50000 | + | 7.79423i | −0.167822 | + | 0.290676i | −0.937654 | − | 0.347571i | \(-0.887007\pi\) |
0.769832 | + | 0.638247i | \(0.220340\pi\) | |||||||
\(720\) | 22.5000 | − | 38.9711i | 0.838525 | − | 1.45237i | ||||
\(721\) | 10.5000 | − | 30.3109i | 0.391040 | − | 1.12884i | ||||
\(722\) | −12.0000 | − | 6.92820i | −0.446594 | − | 0.257841i | ||||
\(723\) | −19.5000 | + | 33.7750i | −0.725213 | + | 1.25611i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −18.0000 | − | 10.3923i | −0.668503 | − | 0.385961i | ||||
\(726\) | 24.0000 | 0.890724 | ||||||||
\(727\) | −10.5000 | − | 6.06218i | −0.389423 | − | 0.224834i | 0.292487 | − | 0.956270i | \(-0.405517\pi\) |
−0.681910 | + | 0.731436i | \(0.738851\pi\) | |||||||
\(728\) | −1.50000 | − | 7.79423i | −0.0555937 | − | 0.288873i | ||||
\(729\) | −27.0000 | −1.00000 | ||||||||
\(730\) | −13.5000 | + | 23.3827i | −0.499657 | + | 0.865432i | ||||
\(731\) | −3.00000 | −0.110959 | ||||||||
\(732\) | −12.0000 | + | 20.7846i | −0.443533 | + | 0.768221i | ||||
\(733\) | 43.3013i | 1.59937i | 0.600420 | + | 0.799684i | \(0.295000\pi\) | ||||
−0.600420 | + | 0.799684i | \(0.705000\pi\) | |||||||
\(734\) | −4.50000 | − | 7.79423i | −0.166098 | − | 0.287690i | ||||
\(735\) | 13.5000 | + | 33.7750i | 0.497955 | + | 1.24581i | ||||
\(736\) | −13.5000 | + | 23.3827i | −0.497617 | + | 0.861897i | ||||
\(737\) | 6.00000 | + | 3.46410i | 0.221013 | + | 0.127602i | ||||
\(738\) | − | 15.5885i | − | 0.573819i | ||||||
\(739\) | 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 | ||||
\(741\) | −13.5000 | − | 7.79423i | −0.495935 | − | 0.286328i | ||||
\(742\) | −30.0000 | + | 25.9808i | −1.10133 | + | 0.953784i | ||||
\(743\) | −10.5000 | + | 6.06218i | −0.385208 | + | 0.222400i | −0.680082 | − | 0.733136i | \(-0.738056\pi\) |
0.294874 | + | 0.955536i | \(0.404722\pi\) | |||||||
\(744\) | 9.00000 | − | 5.19615i | 0.329956 | − | 0.190500i | ||||
\(745\) | 5.19615i | 0.190372i | ||||||||
\(746\) | 55.5000 | − | 32.0429i | 2.03200 | − | 1.17318i | ||||
\(747\) | −45.0000 | −1.64646 | ||||||||
\(748\) | 5.19615i | 0.189990i | ||||||||
\(749\) | 15.0000 | + | 17.3205i | 0.548088 | + | 0.632878i | ||||
\(750\) | 9.00000 | 0.328634 | ||||||||
\(751\) | 37.0000 | 1.35015 | 0.675075 | − | 0.737749i | \(-0.264111\pi\) | ||||
0.675075 | + | 0.737749i | \(0.264111\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −18.0000 | − | 10.3923i | −0.655956 | − | 0.378717i | ||||
\(754\) | −13.5000 | + | 7.79423i | −0.491641 | + | 0.283849i | ||||
\(755\) | 51.0000 | 1.85608 | ||||||||
\(756\) | 9.00000 | + | 10.3923i | 0.327327 | + | 0.377964i | ||||
\(757\) | 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 | ||||
\(759\) | −13.5000 | − | 7.79423i | −0.490019 | − | 0.282913i | ||||
\(760\) | 13.5000 | − | 23.3827i | 0.489696 | − | 0.848179i | ||||
\(761\) | 45.0000 | 1.63125 | 0.815624 | − | 0.578582i | \(-0.196394\pi\) | ||||
0.815624 | + | 0.578582i | \(0.196394\pi\) | |||||||
\(762\) | 60.0000 | 2.17357 | ||||||||
\(763\) | 9.50000 | + | 49.3634i | 0.343923 | + | 1.78708i | ||||
\(764\) | 17.3205i | 0.626634i | ||||||||
\(765\) | 13.5000 | − | 23.3827i | 0.488094 | − | 0.845403i | ||||
\(766\) | 13.5000 | − | 7.79423i | 0.487775 | − | 0.281617i | ||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 28.5000 | − | 16.4545i | 1.02841 | − | 0.593750i | ||||
\(769\) | −13.5000 | + | 7.79423i | −0.486822 | + | 0.281067i | −0.723255 | − | 0.690581i | \(-0.757355\pi\) |
0.236433 | + | 0.971648i | \(0.424022\pi\) | |||||||
\(770\) | −4.50000 | − | 23.3827i | −0.162169 | − | 0.842654i | ||||
\(771\) | 4.50000 | + | 2.59808i | 0.162064 | + | 0.0935674i | ||||
\(772\) | −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 | \(0.463800\pi\) | |||||||
\(774\) | 4.50000 | − | 2.59808i | 0.161749 | − | 0.0933859i | ||||
\(775\) | −12.0000 | − | 6.92820i | −0.431053 | − | 0.248868i | ||||
\(776\) | −1.50000 | + | 2.59808i | −0.0538469 | + | 0.0932655i | ||||
\(777\) | −31.5000 | + | 6.06218i | −1.13006 | + | 0.217479i | ||||
\(778\) | −31.5000 | − | 54.5596i | −1.12933 | − | 1.95606i | ||||
\(779\) | − | 15.5885i | − | 0.558514i | ||||||
\(780\) | −4.50000 | + | 7.79423i | −0.161126 | + | 0.279078i | ||||
\(781\) | −6.00000 | −0.214697 | ||||||||
\(782\) | −13.5000 | + | 23.3827i | −0.482759 | + | 0.836163i | ||||
\(783\) | −13.5000 | + | 23.3827i | −0.482451 | + | 0.835629i | ||||
\(784\) | −5.00000 | + | 34.6410i | −0.178571 | + | 1.23718i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −27.0000 | −0.963058 | ||||||||
\(787\) | −33.0000 | − | 19.0526i | −1.17632 | − | 0.679150i | −0.221162 | − | 0.975237i | \(-0.570985\pi\) |
−0.955161 | + | 0.296087i | \(0.904318\pi\) | |||||||
\(788\) | −12.0000 | − | 6.92820i | −0.427482 | − | 0.246807i | ||||
\(789\) | 19.5000 | − | 33.7750i | 0.694218 | − | 1.20242i | ||||
\(790\) | −36.0000 | − | 20.7846i | −1.28082 | − | 0.739483i | ||||
\(791\) | −4.50000 | + | 0.866025i | −0.160002 | + | 0.0307923i | ||||
\(792\) | 4.50000 | + | 7.79423i | 0.159901 | + | 0.276956i | ||||
\(793\) | −12.0000 | + | 20.7846i | −0.426132 | + | 0.738083i | ||||
\(794\) | −15.0000 | −0.532330 | ||||||||
\(795\) | −45.0000 | −1.59599 | ||||||||
\(796\) | 8.66025i | 0.306955i | ||||||||
\(797\) | −22.5000 | − | 38.9711i | −0.796991 | − | 1.38043i | −0.921567 | − | 0.388219i | \(-0.873091\pi\) |
0.124576 | − | 0.992210i | \(-0.460243\pi\) | |||||||
\(798\) | 27.0000 | + | 31.1769i | 0.955790 | + | 1.10365i | ||||
\(799\) | 0 | 0 | ||||||||
\(800\) | −18.0000 | − | 10.3923i | −0.636396 | − | 0.367423i | ||||
\(801\) | 9.00000 | 0.317999 | ||||||||
\(802\) | −28.5000 | − | 49.3634i | −1.00637 | − | 1.74308i | ||||
\(803\) | −4.50000 | − | 7.79423i | −0.158802 | − | 0.275052i | ||||
\(804\) | 6.92820i | 0.244339i | ||||||||
\(805\) | 13.5000 | − | 38.9711i | 0.475812 | − | 1.37355i | ||||
\(806\) | −9.00000 | + | 5.19615i | −0.317011 | + | 0.183027i | ||||
\(807\) | − | 25.9808i | − | 0.914566i | ||||||
\(808\) | 5.19615i | 0.182800i | ||||||||
\(809\) | −1.50000 | + | 0.866025i | −0.0527372 | + | 0.0304478i | −0.526137 | − | 0.850400i | \(-0.676360\pi\) |
0.473400 | + | 0.880848i | \(0.343027\pi\) | |||||||
\(810\) | 46.7654i | 1.64317i | ||||||||
\(811\) | 10.3923i | 0.364923i | 0.983213 | + | 0.182462i | \(0.0584065\pi\) | ||||
−0.983213 | + | 0.182462i | \(0.941593\pi\) | |||||||
\(812\) | 13.5000 | − | 2.59808i | 0.473757 | − | 0.0911746i | ||||
\(813\) | 10.5000 | + | 18.1865i | 0.368251 | + | 0.637830i | ||||
\(814\) | 21.0000 | 0.736050 | ||||||||
\(815\) | 16.5000 | − | 28.5788i | 0.577970 | − | 1.00107i | ||||
\(816\) | 22.5000 | − | 12.9904i | 0.787658 | − | 0.454754i | ||||
\(817\) | 4.50000 | − | 2.59808i | 0.157435 | − | 0.0908952i | ||||
\(818\) | 12.0000 | 0.419570 | ||||||||
\(819\) | 9.00000 | + | 10.3923i | 0.314485 | + | 0.363137i | ||||
\(820\) | −9.00000 | −0.314294 | ||||||||
\(821\) | 6.00000 | − | 3.46410i | 0.209401 | − | 0.120898i | −0.391632 | − | 0.920122i | \(-0.628089\pi\) |
0.601033 | + | 0.799224i | \(0.294756\pi\) | |||||||
\(822\) | − | 36.3731i | − | 1.26866i | ||||||
\(823\) | 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 | ||||||||
\(825\) | 6.00000 | − | 10.3923i | 0.208893 | − | 0.361814i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 24.2487i | − | 0.843210i | −0.906780 | − | 0.421605i | \(-0.861467\pi\) | ||
0.906780 | − | 0.421605i | \(-0.138533\pi\) | |||||||
\(828\) | − | 15.5885i | − | 0.541736i | ||||||
\(829\) | 31.5000 | − | 18.1865i | 1.09404 | − | 0.631644i | 0.159391 | − | 0.987216i | \(-0.449047\pi\) |
0.934649 | + | 0.355571i | \(0.115714\pi\) | |||||||
\(830\) | 77.9423i | 2.70542i | ||||||||
\(831\) | 1.50000 | + | 0.866025i | 0.0520344 | + | 0.0300421i | ||||
\(832\) | 1.50000 | − | 0.866025i | 0.0520031 | − | 0.0300240i | ||||
\(833\) | −3.00000 | + | 20.7846i | −0.103944 | + | 0.720144i | ||||
\(834\) | −22.5000 | + | 12.9904i | −0.779111 | + | 0.449820i | ||||
\(835\) | 13.5000 | + | 23.3827i | 0.467187 | + | 0.809191i | ||||
\(836\) | −4.50000 | − | 7.79423i | −0.155636 | − | 0.269569i | ||||
\(837\) | −9.00000 | + | 15.5885i | −0.311086 | + | 0.538816i | ||||
\(838\) | 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 | \(0.931580\pi\) | |||||||
\(840\) | −18.0000 | + | 15.5885i | −0.621059 | + | 0.537853i | ||||
\(841\) | −1.00000 | − | 1.73205i | −0.0344828 | − | 0.0597259i | ||||
\(842\) | − | 19.0526i | − | 0.656595i | ||||||
\(843\) | 16.5000 | + | 28.5788i | 0.568290 | + | 0.984307i | ||||
\(844\) | 5.00000 | 0.172107 | ||||||||
\(845\) | 15.0000 | − | 25.9808i | 0.516016 | − | 0.893765i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −20.0000 | − | 6.92820i | −0.687208 | − | 0.238056i | ||||
\(848\) | −37.5000 | − | 21.6506i | −1.28776 | − | 0.743486i | ||||
\(849\) | −3.00000 | − | 5.19615i | −0.102960 | − | 0.178331i | ||||
\(850\) | −18.0000 | − | 10.3923i | −0.617395 | − | 0.356453i | ||||
\(851\) | 31.5000 | + | 18.1865i | 1.07981 | + | 0.623426i | ||||
\(852\) | −3.00000 | − | 5.19615i | −0.102778 | − | 0.178017i | ||||
\(853\) | 22.5000 | + | 12.9904i | 0.770385 | + | 0.444782i | 0.833012 | − | 0.553255i | \(-0.186614\pi\) |
−0.0626267 | + | 0.998037i | \(0.519948\pi\) | |||||||
\(854\) | 48.0000 | − | 41.5692i | 1.64253 | − | 1.42247i | ||||
\(855\) | 46.7654i | 1.59934i | ||||||||
\(856\) | −7.50000 | + | 12.9904i | −0.256345 | + | 0.444002i | ||||
\(857\) | −27.0000 | −0.922302 | −0.461151 | − | 0.887322i | \(-0.652563\pi\) | ||||
−0.461151 | + | 0.887322i | \(0.652563\pi\) | |||||||
\(858\) | −4.50000 | − | 7.79423i | −0.153627 | − | 0.266091i | ||||
\(859\) | − | 50.2295i | − | 1.71381i | −0.515476 | − | 0.856904i | \(-0.672385\pi\) | ||
0.515476 | − | 0.856904i | \(-0.327615\pi\) | |||||||
\(860\) | −1.50000 | − | 2.59808i | −0.0511496 | − | 0.0885937i | ||||
\(861\) | −4.50000 | + | 12.9904i | −0.153360 | + | 0.442711i | ||||
\(862\) | −13.5000 | + | 23.3827i | −0.459812 | + | 0.796417i | ||||
\(863\) | −37.5000 | − | 21.6506i | −1.27651 | − | 0.736996i | −0.300309 | − | 0.953842i | \(-0.597090\pi\) |
−0.976206 | + | 0.216846i | \(0.930423\pi\) | |||||||
\(864\) | −13.5000 | + | 23.3827i | −0.459279 | + | 0.795495i | ||||
\(865\) | 9.00000 | + | 15.5885i | 0.306009 | + | 0.530023i | ||||
\(866\) | 12.0000 | + | 20.7846i | 0.407777 | + | 0.706290i | ||||
\(867\) | −12.0000 | + | 6.92820i | −0.407541 | + | 0.235294i | ||||
\(868\) | 9.00000 | − | 1.73205i | 0.305480 | − | 0.0587896i | ||||
\(869\) | 12.0000 | − | 6.92820i | 0.407072 | − | 0.235023i | ||||
\(870\) | 40.5000 | + | 23.3827i | 1.37308 | + | 0.792747i | ||||
\(871\) | 6.92820i | 0.234753i | ||||||||
\(872\) | −28.5000 | + | 16.4545i | −0.965132 | + | 0.557219i | ||||
\(873\) | − | 5.19615i | − | 0.175863i | ||||||
\(874\) | − | 46.7654i | − | 1.58186i | ||||||
\(875\) | −7.50000 | − | 2.59808i | −0.253546 | − | 0.0878310i | ||||
\(876\) | 4.50000 | − | 7.79423i | 0.152041 | − | 0.263343i | ||||
\(877\) | 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 | ||||
\(879\) | 15.5885i | 0.525786i | ||||||||
\(880\) | 22.5000 | − | 12.9904i | 0.758475 | − | 0.437906i | ||||
\(881\) | −54.0000 | −1.81931 | −0.909653 | − | 0.415369i | \(-0.863653\pi\) | ||||
−0.909653 | + | 0.415369i | \(0.863653\pi\) | |||||||
\(882\) | −13.5000 | − | 33.7750i | −0.454569 | − | 1.13726i | ||||
\(883\) | 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 | \(0.418969\pi\) | |||||||
\(888\) | −10.5000 | − | 18.1865i | −0.352357 | − | 0.610300i | ||||
\(889\) | −50.0000 | − | 17.3205i | −1.67695 | − | 0.580911i | ||||
\(890\) | − | 15.5885i | − | 0.522526i | ||||||
\(891\) | −13.5000 | − | 7.79423i | −0.452267 | − | 0.261116i | ||||
\(892\) | −4.50000 | + | 2.59808i | −0.150671 | + | 0.0869900i | ||||
\(893\) | 0 | 0 | ||||||||
\(894\) | − | 5.19615i | − | 0.173785i | ||||||
\(895\) | −40.5000 | + | 23.3827i | −1.35377 | + | 0.781597i | ||||
\(896\) | −31.5000 | + | 6.06218i | −1.05234 | + | 0.202523i | ||||
\(897\) | − | 15.5885i | − | 0.520483i | ||||||
\(898\) | −30.0000 | − | 51.9615i | −1.00111 | − | 1.73398i | ||||
\(899\) | 9.00000 | + | 15.5885i | 0.300167 | + | 0.519904i | ||||
\(900\) | 12.0000 | 0.400000 | ||||||||
\(901\) | −22.5000 | − | 12.9904i | −0.749584 | − | 0.432772i | ||||
\(902\) | 4.50000 | − | 7.79423i | 0.149834 | − | 0.259519i | ||||
\(903\) | −4.50000 | + | 0.866025i | −0.149751 | + | 0.0288195i | ||||
\(904\) | −1.50000 | − | 2.59808i | −0.0498893 | − | 0.0864107i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −51.0000 | −1.69436 | ||||||||
\(907\) | 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 | ||||
\(909\) | −4.50000 | − | 7.79423i | −0.149256 | − | 0.258518i | ||||
\(910\) | 18.0000 | − | 15.5885i | 0.596694 | − | 0.516752i | ||||
\(911\) | 4.50000 | + | 2.59808i | 0.149092 | + | 0.0860781i | 0.572690 | − | 0.819772i | \(-0.305900\pi\) |
−0.423598 | + | 0.905850i | \(0.639233\pi\) | |||||||
\(912\) | −22.5000 | + | 38.9711i | −0.745049 | + | 1.29046i | ||||
\(913\) | −22.5000 | − | 12.9904i | −0.744641 | − | 0.429919i | ||||
\(914\) | −39.0000 | − | 22.5167i | −1.29001 | − | 0.744785i | ||||
\(915\) | 72.0000 | 2.38025 | ||||||||
\(916\) | 7.50000 | + | 4.33013i | 0.247807 | + | 0.143071i | ||||
\(917\) | 22.5000 | + | 7.79423i | 0.743015 | + | 0.257388i | ||||
\(918\) | −13.5000 | + | 23.3827i | −0.445566 | + | 0.771744i | ||||
\(919\) | 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 | ||||||||
\(921\) | 21.0000 | − | 36.3731i | 0.691974 | − | 1.19853i | ||||
\(922\) | 25.9808i | 0.855631i | ||||||||
\(923\) | −3.00000 | − | 5.19615i | −0.0987462 | − | 0.171033i | ||||
\(924\) | 1.50000 | + | 7.79423i | 0.0493464 | + | 0.256411i | ||||
\(925\) | −14.0000 | + | 24.2487i | −0.460317 | + | 0.797293i | ||||
\(926\) | −1.50000 | − | 0.866025i | −0.0492931 | − | 0.0284594i | ||||
\(927\) | −31.5000 | + | 18.1865i | −1.03460 | + | 0.597324i | ||||
\(928\) | 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 | \(0.997116\pi\) | |||||||
\(930\) | 27.0000 | + | 15.5885i | 0.885365 | + | 0.511166i | ||||
\(931\) | −13.5000 | − | 33.7750i | −0.442445 | − | 1.10693i | ||||
\(932\) | 4.50000 | − | 2.59808i | 0.147402 | − | 0.0851028i | ||||
\(933\) | 36.0000 | − | 20.7846i | 1.17859 | − | 0.680458i | ||||
\(934\) | 5.19615i | 0.170023i | ||||||||
\(935\) | 13.5000 | − | 7.79423i | 0.441497 | − | 0.254899i | ||||
\(936\) | −4.50000 | + | 7.79423i | −0.147087 | + | 0.254762i | ||||
\(937\) | − | 13.8564i | − | 0.452669i | −0.974050 | − | 0.226335i | \(-0.927326\pi\) | ||
0.974050 | − | 0.226335i | \(-0.0726743\pi\) | |||||||
\(938\) | 6.00000 | − | 17.3205i | 0.195907 | − | 0.565535i | ||||
\(939\) | 36.0000 | 1.17482 | ||||||||
\(940\) | 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 | ||||||||
\(945\) | 13.5000 | − | 38.9711i | 0.439155 | − | 1.26773i | ||||
\(946\) | 3.00000 | 0.0975384 | ||||||||
\(947\) | −45.0000 | + | 25.9808i | −1.46230 | + | 0.844261i | −0.999118 | − | 0.0419998i | \(-0.986627\pi\) |
−0.463186 | + | 0.886261i | \(0.653294\pi\) | |||||||
\(948\) | 12.0000 | + | 6.92820i | 0.389742 | + | 0.225018i | ||||
\(949\) | 4.50000 | − | 7.79423i | 0.146076 | − | 0.253011i | ||||
\(950\) | 36.0000 | 1.16799 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −13.5000 | + | 2.59808i | −0.437538 | + | 0.0842041i | ||||
\(953\) | 20.7846i | 0.673280i | 0.941634 | + | 0.336640i | \(0.109290\pi\) | ||||
−0.941634 | + | 0.336640i | \(0.890710\pi\) | |||||||
\(954\) | 45.0000 | 1.45693 | ||||||||
\(955\) | 45.0000 | − | 25.9808i | 1.45617 | − | 0.840718i | ||||
\(956\) | − | 1.73205i | − | 0.0560185i | ||||||
\(957\) | −13.5000 | + | 7.79423i | −0.436393 | + | 0.251952i | ||||
\(958\) | 40.5000 | − | 23.3827i | 1.30850 | − | 0.755460i | ||||
\(959\) | −10.5000 | + | 30.3109i | −0.339063 | + | 0.978790i | ||||
\(960\) | −4.50000 | − | 2.59808i | −0.145237 | − | 0.0838525i | ||||
\(961\) | −9.50000 | − | 16.4545i | −0.306452 | − | 0.530790i | ||||
\(962\) | 10.5000 | + | 18.1865i | 0.338534 | + | 0.586357i | ||||
\(963\) | − | 25.9808i | − | 0.837218i | ||||||
\(964\) | −19.5000 | − | 11.2583i | −0.628053 | − | 0.362606i | ||||
\(965\) | −3.00000 | + | 5.19615i | −0.0965734 | + | 0.167270i | ||||
\(966\) | −13.5000 | + | 38.9711i | −0.434355 | + | 1.25388i | ||||
\(967\) | 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 | ||||||
\(969\) | −13.5000 | + | 23.3827i | −0.433682 | + | 0.751160i | ||||
\(970\) | −9.00000 | −0.288973 | ||||||||
\(971\) | −28.5000 | + | 49.3634i | −0.914609 | + | 1.58415i | −0.107135 | + | 0.994244i | \(0.534168\pi\) |
−0.807473 | + | 0.589904i | \(0.799166\pi\) | |||||||
\(972\) | − | 15.5885i | − | 0.500000i | ||||||
\(973\) | 22.5000 | − | 4.33013i | 0.721317 | − | 0.138817i | ||||
\(974\) | −34.5000 | − | 19.9186i | −1.10545 | − | 0.638233i | ||||
\(975\) | 12.0000 | 0.384308 | ||||||||
\(976\) | 60.0000 | + | 34.6410i | 1.92055 | + | 1.10883i | ||||
\(977\) | −36.0000 | − | 20.7846i | −1.15174 | − | 0.664959i | −0.202431 | − | 0.979297i | \(-0.564884\pi\) |
−0.949311 | + | 0.314338i | \(0.898217\pi\) | |||||||
\(978\) | −16.5000 | + | 28.5788i | −0.527612 | + | 0.913850i | ||||
\(979\) | 4.50000 | + | 2.59808i | 0.143821 | + | 0.0830349i | ||||
\(980\) | −19.5000 | + | 7.79423i | −0.622905 | + | 0.248978i | ||||
\(981\) | 28.5000 | − | 49.3634i | 0.909935 | − | 1.57605i | ||||
\(982\) | 22.5000 | − | 38.9711i | 0.718004 | − | 1.24362i | ||||
\(983\) | −39.0000 | −1.24391 | −0.621953 | − | 0.783054i | \(-0.713661\pi\) | ||||
−0.621953 | + | 0.783054i | \(0.713661\pi\) | |||||||
\(984\) | −9.00000 | −0.286910 | ||||||||
\(985\) | 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 | ||||
\(990\) | −13.5000 | + | 23.3827i | −0.429058 | + | 0.743151i | ||||
\(991\) | 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 | ||||
\(993\) | − | 13.8564i | − | 0.439720i | ||||||
\(994\) | 3.00000 | + | 15.5885i | 0.0951542 | + | 0.494436i | ||||
\(995\) | 22.5000 | − | 12.9904i | 0.713298 | − | 0.411823i | ||||
\(996\) | − | 25.9808i | − | 0.823232i | ||||||
\(997\) | − | 8.66025i | − | 0.274273i | −0.990552 | − | 0.137136i | \(-0.956210\pi\) | ||
0.990552 | − | 0.137136i | \(-0.0437899\pi\) | |||||||
\(998\) | −37.5000 | + | 21.6506i | −1.18704 | + | 0.685339i | ||||
\(999\) | 31.5000 | + | 18.1865i | 0.996616 | + | 0.575396i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))